%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ALG131+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 16:36:34 EDT 2023

% Result   : Unsatisfiable 24.69s 4.04s
% Output   : Proof 245.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : ALG131+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.07  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.07/0.26  % Computer : n025.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Mon Aug 28 04:39:39 EDT 2023
% 0.07/0.26  % CPUTime  : 
% 0.10/0.52  ________       _____
% 0.10/0.52  ___  __ \_________(_)________________________________
% 0.10/0.52  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.10/0.52  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.10/0.52  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.10/0.52  
% 0.10/0.52  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.10/0.52  (2023-06-19)
% 0.10/0.52  
% 0.10/0.52  (c) Philipp Rümmer, 2009-2023
% 0.10/0.52  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.10/0.52                Amanda Stjerna.
% 0.10/0.52  Free software under BSD-3-Clause.
% 0.10/0.52  
% 0.10/0.52  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.10/0.52  
% 0.10/0.52  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.10/0.53  Running up to 7 provers in parallel.
% 0.10/0.54  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.10/0.54  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.10/0.54  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.10/0.54  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.10/0.54  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.10/0.54  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.10/0.54  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 4.50/1.29  Prover 4: Preprocessing ...
% 4.50/1.29  Prover 1: Preprocessing ...
% 4.50/1.33  Prover 0: Preprocessing ...
% 4.50/1.33  Prover 6: Preprocessing ...
% 4.50/1.34  Prover 3: Preprocessing ...
% 4.50/1.34  Prover 2: Preprocessing ...
% 4.50/1.34  Prover 5: Preprocessing ...
% 7.80/1.73  Prover 3: Constructing countermodel ...
% 7.80/1.73  Prover 2: Constructing countermodel ...
% 8.08/1.75  Prover 1: Constructing countermodel ...
% 8.08/1.76  Prover 4: Constructing countermodel ...
% 8.08/1.76  Prover 6: Constructing countermodel ...
% 8.08/1.77  Prover 0: Constructing countermodel ...
% 9.14/2.04  Prover 5: Constructing countermodel ...
% 24.69/4.04  Prover 3: proved (3497ms)
% 24.69/4.04  
% 24.69/4.04  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.69/4.04  
% 24.69/4.04  Prover 2: stopped
% 24.69/4.04  Prover 6: stopped
% 24.69/4.05  Prover 0: stopped
% 24.69/4.06  Prover 5: stopped
% 24.69/4.06  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 24.69/4.07  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 24.69/4.07  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 24.69/4.07  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 24.69/4.07  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.92/4.33  Prover 8: Preprocessing ...
% 26.92/4.34  Prover 10: Preprocessing ...
% 27.54/4.36  Prover 11: Preprocessing ...
% 27.54/4.36  Prover 7: Preprocessing ...
% 27.54/4.36  Prover 13: Preprocessing ...
% 28.18/4.44  Prover 8: Constructing countermodel ...
% 28.79/4.53  Prover 11: Constructing countermodel ...
% 28.79/4.55  Prover 7: Constructing countermodel ...
% 28.79/4.55  Prover 13: Constructing countermodel ...
% 29.35/4.59  Prover 10: Constructing countermodel ...
% 66.05/9.45  Prover 13: stopped
% 66.05/9.45  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 67.47/9.55  Prover 16: Preprocessing ...
% 68.58/9.71  Prover 16: Constructing countermodel ...
% 111.31/15.29  Prover 16: stopped
% 111.31/15.29  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 111.99/15.37  Prover 19: Preprocessing ...
% 112.83/15.50  Prover 19: Constructing countermodel ...
% 115.92/15.89  Prover 1: stopped
% 137.13/19.04  Prover 19: stopped
% 178.00/26.70  Prover 7: stopped
% 183.38/27.87  Prover 4: stopped
% 220.66/39.34  Prover 11: Found proof (size 25309248)
% 220.66/39.34  Prover 11: proved (35270ms)
% 220.66/39.35  Prover 10: stopped
% 220.66/39.35  Prover 8: stopped
% 220.66/39.35  
% 220.66/39.35  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 220.66/39.35  
% 225.12/41.12  % SZS output start Proof for theBenchmark
% 225.59/41.52  Assumptions after simplification:
% 225.59/41.52  ---------------------------------
% 225.59/41.52  
% 225.59/41.53    (ax1)
% 226.29/41.65    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 226.29/41.65    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 226.29/41.65      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 226.29/41.65      $i] :  ? [v14: $i] :  ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 226.29/41.65      op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 226.29/41.65      op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 226.29/41.65      op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 226.29/41.65      op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 226.29/41.65      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 226.29/41.65      $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 226.29/41.65        e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 226.29/41.65        v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 226.29/41.65        = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 226.29/41.65        v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 226.29/41.65        v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 226.29/41.65        v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 226.29/41.65      (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 226.29/41.65        = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 226.29/41.65        = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 226.29/41.65  
% 226.29/41.65    (ax10)
% 226.29/41.66    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.29/41.66    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 226.29/41.66          op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 &
% 226.29/41.66          $i(v1))))
% 226.29/41.66  
% 226.29/41.66    (ax11)
% 226.29/41.66    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.29/41.66    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 226.29/41.66          op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 &
% 226.29/41.66          $i(v1))))
% 226.29/41.66  
% 226.29/41.66    (ax12)
% 226.29/41.66    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.29/41.66    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 226.29/41.66          op(e3, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 &
% 226.29/41.67          $i(v1))))
% 226.29/41.67  
% 226.29/41.67    (ax13)
% 226.29/41.67    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.29/41.67    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 226.29/41.67          op(e2, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 &
% 226.29/41.67          $i(v1))))
% 226.29/41.67  
% 226.29/41.67    (ax14)
% 226.29/41.67    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.29/41.67    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 226.29/41.67          op(e3, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 &
% 226.29/41.67          $i(v1))))
% 226.29/41.67  
% 226.29/41.67    (ax15)
% 226.29/41.67    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.29/41.67    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 226.29/41.67          op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 &
% 226.29/41.67          $i(v1))))
% 226.29/41.67  
% 226.29/41.67    (ax16)
% 226.29/41.67    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.29/41.67    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 226.29/41.67          op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 &
% 226.29/41.67          $i(v1))))
% 226.29/41.67  
% 226.29/41.67    (ax17)
% 226.29/41.68    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.29/41.68    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 226.29/41.68          op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 &
% 226.29/41.68          $i(v1))))
% 226.29/41.68  
% 226.29/41.68    (ax18)
% 226.29/41.68    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.29/41.68    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 226.29/41.68          op(e3, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 &
% 226.29/41.68          $i(v1))))
% 226.29/41.68  
% 226.29/41.68    (ax19)
% 226.29/41.68    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.29/41.68    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 226.29/41.68          op(e1, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 &
% 226.29/41.68          $i(v1))))
% 226.29/41.68  
% 226.29/41.68    (ax2)
% 226.29/41.72    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 226.29/41.72    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 226.29/41.72      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 226.29/41.72      $i] :  ? [v14: $i] :  ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 =
% 226.29/41.72          e3 & op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3,
% 226.29/41.72            e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 226.29/41.72          e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v15
% 226.29/41.72          = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 = e2 &
% 226.29/41.72          op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = e2 & op(e3,
% 226.29/41.72            e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2)
% 226.29/41.72        | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1
% 226.29/41.72          & op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & op(e3,
% 226.29/41.72            e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) =
% 226.29/41.72          e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15
% 226.29/41.72          = e0 & op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 226.29/41.72          op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & op(e3,
% 226.29/41.72            e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0)
% 226.29/41.72        | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3
% 226.29/41.72          & op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & op(e0, e2)
% 226.29/41.72          = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 226.29/41.72        (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 226.29/41.72          op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & op(e1, e2)
% 226.29/41.72          = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) |
% 226.29/41.72        (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 &
% 226.29/41.72          op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & op(e2,
% 226.29/41.72            e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) =
% 226.29/41.72          e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 226.29/41.72        (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 226.29/41.72          op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & op(e2, e1)
% 226.29/41.72          = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) |
% 226.29/41.72        (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 &
% 226.29/41.72          op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & op(e2,
% 226.29/41.72            e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3))
% 226.29/41.72      & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 226.29/41.72          op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & op(e3,
% 226.29/41.72            e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1)
% 226.29/41.72        | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0
% 226.29/41.72          & op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1)
% 226.29/41.72          = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) |
% 226.29/41.72        (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 226.29/41.72          op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) =
% 226.29/41.72          e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8
% 226.29/41.72          = e1 & op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 &
% 226.29/41.72          op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & op(e1, e2)
% 226.29/41.72          = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) &
% 226.29/41.72      ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 226.29/41.72          op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0)
% 226.29/41.72          = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0
% 226.29/41.72          = e2 & op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 &
% 226.29/41.72          op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) =
% 226.29/41.72          e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1
% 226.29/41.72          = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 226.29/41.72          op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) =
% 226.29/41.72          e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2
% 226.29/41.72          = e1 & op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 &
% 226.29/41.72          op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & op(e3,
% 226.29/41.72                e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) =
% 226.29/41.72              e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) |
% 226.29/41.72            (v1 = e0 & op(e0, e1) = e0)))))
% 226.29/41.72  
% 226.29/41.72    (ax20)
% 226.29/41.72    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.29/41.72    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 226.29/41.72          op(e3, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 &
% 226.29/41.72          $i(v1))))
% 226.73/41.72  
% 226.73/41.72    (ax21)
% 226.73/41.73    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.73/41.73    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 226.73/41.73          op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 &
% 226.73/41.73          $i(v1))))
% 226.73/41.73  
% 226.73/41.73    (ax22)
% 226.73/41.73    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.73/41.73    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 226.73/41.73          op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 &
% 226.73/41.73          $i(v1))))
% 226.73/41.73  
% 226.73/41.73    (ax23)
% 226.73/41.73    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.73/41.73    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 226.73/41.73          op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 &
% 226.73/41.73          $i(v1))))
% 226.73/41.73  
% 226.73/41.73    (ax24)
% 226.73/41.73    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.73/41.73    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 226.73/41.73          op(e2, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 &
% 226.73/41.73          $i(v1))))
% 226.73/41.73  
% 226.73/41.73    (ax25)
% 226.73/41.74    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.73/41.74    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 226.73/41.74          op(e1, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 &
% 226.73/41.74          $i(v1))))
% 226.73/41.74  
% 226.73/41.74    (ax26)
% 226.73/41.74    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.73/41.74    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 226.73/41.74          op(e2, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 &
% 226.73/41.74          $i(v1))))
% 226.73/41.74  
% 226.73/41.74    (ax27)
% 226.73/41.74    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.73/41.74    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 226.73/41.74          op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 &
% 226.73/41.74          $i(v1))))
% 226.73/41.74  
% 226.73/41.74    (ax28)
% 226.73/41.74    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.73/41.74    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 226.73/41.74          op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 &
% 226.73/41.74          $i(v1))))
% 226.73/41.74  
% 226.73/41.74    (ax29)
% 226.73/41.75    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 226.73/41.75    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 226.73/41.75          op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 &
% 226.73/41.75          $i(v1))))
% 226.73/41.75  
% 226.73/41.75    (ax3)
% 226.73/41.76    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 226.73/41.76    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 226.73/41.76      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 226.73/41.76      $i] :  ? [v14: $i] :  ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~
% 226.73/41.76      (v15 = v12) &  ~ (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 =
% 226.73/41.76        v13) &  ~ (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) & 
% 226.73/41.76      ~ (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12 =
% 226.73/41.76        v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 = v9) &  ~
% 226.73/41.76      (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9) &  ~ (v10 = v8) &
% 226.73/41.76       ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~ (v9 = v5) &  ~ (v9 = v1) &
% 226.73/41.76       ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6) &  ~ (v7 = v5) &  ~ (v7 = v4) & 
% 226.73/41.76      ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6 = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~
% 226.73/41.76      (v5 = v1) &  ~ (v4 = v0) &  ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~
% 226.73/41.76      (v2 = v1) &  ~ (v2 = v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 226.73/41.76      v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 226.73/41.76      v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 226.73/41.76      & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 226.73/41.76      op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 226.73/41.76      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 226.73/41.76      $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 226.73/41.76  
% 226.73/41.76    (ax4)
% 226.73/41.76     ~ (e3 = e2) &  ~ (e3 = e1) &  ~ (e3 = e0) &  ~ (e2 = e1) &  ~ (e2 = e0) &  ~
% 226.73/41.76    (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 226.73/41.76  
% 226.73/41.76    (ax5)
% 226.73/41.78    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 226.73/41.78    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 226.73/41.78      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 226.73/41.78      $i] :  ? [v14: $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18:
% 226.73/41.78      $i] :  ? [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23:
% 226.73/41.78      $i] :  ? [v24: $i] :  ? [v25: $i] :  ? [v26: $i] :  ? [v27: $i] :  ? [v28:
% 226.73/41.78      $i] :  ? [v29: $i] :  ? [v30: $i] :  ? [v31: $i] : (op(e3, e3) = v30 &
% 226.73/41.78      op(e2, e2) = v20 & op(e1, e1) = v10 & op(e0, e0) = v0 & $i(v30) & $i(v20) &
% 226.73/41.78      $i(v10) & $i(v0) & ((v31 = e3 & op(e3, v30) = e3) | (v29 = e2 & op(e2, v28)
% 226.73/41.78          = e2 & op(e2, e3) = v28 & $i(v28)) | (v27 = e1 & op(e1, v26) = e1 &
% 226.73/41.78          op(e1, e3) = v26 & $i(v26)) | (v25 = e0 & op(e0, v24) = e0 & op(e0, e3)
% 226.73/41.78          = v24 & $i(v24))) & ((v28 = e3 & v22 = e3 &  ~ (v30 = e2) &  ~ (v20 =
% 226.73/41.78            e2) &  ~ (v10 = e2) &  ~ (v0 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 226.73/41.78          e3) | (v28 = e2 & v22 = e2 &  ~ (v30 = e3) &  ~ (v20 = e3) &  ~ (v10 =
% 226.73/41.78            e3) &  ~ (v0 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (v26 = e3 &
% 226.73/41.78          v14 = e3 &  ~ (v30 = e1) &  ~ (v20 = e1) &  ~ (v10 = e1) &  ~ (v0 = e1)
% 226.73/41.78          & op(e3, e1) = e3 & op(e1, e3) = e3) | (v26 = e1 & v14 = e1 &  ~ (v30 =
% 226.73/41.78            e3) &  ~ (v20 = e3) &  ~ (v10 = e3) &  ~ (v0 = e3) & op(e3, e1) = e1 &
% 226.73/41.78          op(e1, e3) = e1) | (v24 = e3 & v6 = e3 &  ~ (v30 = e0) &  ~ (v20 = e0) &
% 226.73/41.78           ~ (v10 = e0) &  ~ (v0 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (v24
% 226.73/41.78          = e0 & v6 = e0 &  ~ (v30 = e3) &  ~ (v20 = e3) &  ~ (v10 = e3) &  ~ (v0
% 226.73/41.78            = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (v18 = e2 & v12 = e2 &  ~
% 226.73/41.78          (v30 = e1) &  ~ (v20 = e1) &  ~ (v10 = e1) &  ~ (v0 = e1) & op(e2, e1) =
% 226.73/41.78          e2 & op(e1, e2) = e2) | (v18 = e1 & v12 = e1 &  ~ (v30 = e2) &  ~ (v20 =
% 226.73/41.78            e2) &  ~ (v10 = e2) &  ~ (v0 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 226.73/41.78          e1) | (v16 = e2 & v4 = e2 &  ~ (v30 = e0) &  ~ (v20 = e0) &  ~ (v10 =
% 226.73/41.78            e0) &  ~ (v0 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (v16 = e0 &
% 226.73/41.78          v4 = e0 &  ~ (v30 = e2) &  ~ (v20 = e2) &  ~ (v10 = e2) &  ~ (v0 = e2) &
% 226.73/41.78          op(e2, e0) = e0 & op(e0, e2) = e0) | (v8 = e1 & v2 = e1 &  ~ (v30 = e0)
% 226.73/41.78          &  ~ (v20 = e0) &  ~ (v10 = e0) &  ~ (v0 = e0) & op(e1, e0) = e1 &
% 226.73/41.78          op(e0, e1) = e1) | (v8 = e0 & v2 = e0 &  ~ (v30 = e1) &  ~ (v20 = e1) & 
% 226.73/41.78          ~ (v10 = e1) &  ~ (v0 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)) &
% 226.73/41.78      ((v23 = e3 & op(e3, v22) = e3 & op(e3, e2) = v22 & $i(v22)) | (v21 = e2 &
% 226.73/41.78          op(e2, v20) = e2) | (v19 = e1 & op(e1, v18) = e1 & op(e1, e2) = v18 &
% 226.73/41.78          $i(v18)) | (v17 = e0 & op(e0, v16) = e0 & op(e0, e2) = v16 & $i(v16))) &
% 226.73/41.78      ((v15 = e3 & op(e3, v14) = e3 & op(e3, e1) = v14 & $i(v14)) | (v13 = e2 &
% 226.73/41.78          op(e2, v12) = e2 & op(e2, e1) = v12 & $i(v12)) | (v11 = e1 & op(e1, v10)
% 226.73/41.78          = e1) | (v9 = e0 & op(e0, v8) = e0 & op(e0, e1) = v8 & $i(v8))) & ((v7 =
% 226.73/41.78          e3 & op(e3, v6) = e3 & op(e3, e0) = v6 & $i(v6)) | (v5 = e2 & op(e2, v4)
% 226.73/41.78          = e2 & op(e2, e0) = v4 & $i(v4)) | (v3 = e1 & op(e1, v2) = e1 & op(e1,
% 226.73/41.78            e0) = v2 & $i(v2)) | (v1 = e0 & op(e0, v0) = e0)))
% 226.73/41.78  
% 226.73/41.78    (ax6)
% 227.03/41.79    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 227.03/41.79    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 227.03/41.79          op(e3, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 &
% 227.03/41.79          $i(v1))))
% 227.03/41.79  
% 227.03/41.79    (ax7)
% 227.03/41.79    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 227.03/41.79    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 227.03/41.79          op(e2, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 &
% 227.03/41.79          $i(v1))))
% 227.03/41.79  
% 227.03/41.79    (ax8)
% 227.03/41.79    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 227.03/41.79    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 227.03/41.79          op(e3, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 &
% 227.03/41.79          $i(v1))))
% 227.03/41.79  
% 227.03/41.79    (ax9)
% 227.03/41.79    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 227.03/41.79    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 227.03/41.79          op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 &
% 227.03/41.79          $i(v1))))
% 227.03/41.79  
% 227.03/41.79    (function-axioms)
% 227.03/41.79     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (op(v3,
% 227.03/41.79          v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.03/41.79  
% 227.03/41.79  Those formulas are unsatisfiable:
% 227.03/41.79  ---------------------------------
% 227.03/41.79  
% 227.03/41.79  Begin of proof
% 227.03/41.80  | 
% 227.03/41.80  | ALPHA: (ax1) implies:
% 227.03/41.81  |   (1)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 227.03/41.81  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 227.03/41.81  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 227.03/41.81  |         ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 227.03/41.81  |          & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 227.03/41.81  |          = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 227.03/41.81  |            e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 227.03/41.81  |          op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 227.03/41.81  |          $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 227.03/41.81  |          $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 227.03/41.81  |            = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 227.03/41.81  |            = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 227.03/41.81  |            v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 227.03/41.81  |            v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 227.03/41.81  |            | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 227.03/41.81  |            = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 227.03/41.81  |            e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 227.03/41.81  |          (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 227.03/41.81  |            e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 227.03/41.81  |            | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 227.03/41.81  |            = e0))
% 227.03/41.81  | 
% 227.03/41.81  | ALPHA: (ax2) implies:
% 227.03/41.83  |   (2)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 227.03/41.83  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 227.03/41.83  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 227.03/41.83  |         ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = e3 & op(e3, e2)
% 227.03/41.83  |              = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, e0) =
% 227.03/41.83  |              e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 227.03/41.83  |              e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3))
% 227.03/41.83  |          & ((v15 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11
% 227.03/41.83  |              = e2 & op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 =
% 227.03/41.83  |              e2 & op(e3, e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 &
% 227.03/41.83  |              op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 &
% 227.03/41.83  |              op(e3, e3) = e1) | (v14 = e1 & op(e3, e2) = e1) | (v11 = e1 &
% 227.03/41.83  |              op(e3, e1) = e1) | (v6 = e1 & op(e3, e0) = e1)) & ((v15 = e1 &
% 227.03/41.83  |              op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = e1) | (v9 = e1 &
% 227.03/41.84  |              op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 = e0 &
% 227.03/41.84  |              op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 227.03/41.84  |              op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 &
% 227.03/41.84  |              op(e3, e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 &
% 227.03/41.84  |              op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 &
% 227.03/41.84  |              op(e3, e2) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v8 = e3 &
% 227.03/41.84  |              op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v14 = e2 &
% 227.03/41.84  |              op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v8 = e2 &
% 227.03/41.84  |              op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 227.03/41.84  |              op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 &
% 227.03/41.84  |              op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 &
% 227.03/41.84  |              op(e3, e2) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 &
% 227.03/41.84  |              op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v13 = e3 &
% 227.03/41.84  |              op(e2, e3) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v10 = e3 &
% 227.03/41.84  |              op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = e3)) & ((v13 = e2 &
% 227.03/41.84  |              op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v10 = e2 &
% 227.03/41.84  |              op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 227.03/41.84  |              op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 &
% 227.03/41.84  |              op(e2, e1) = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 &
% 227.03/41.84  |              op(e2, e3) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 &
% 227.03/41.84  |              op(e2, e1) = e0) | (v5 = e0 & op(e2, e0) = e0)) & ((v11 = e3 &
% 227.03/41.84  |              op(e3, e1) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v7 = e3 &
% 227.03/41.84  |              op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v11 = e2 &
% 227.03/41.84  |              op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 227.03/41.84  |              op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 &
% 227.03/41.84  |              op(e3, e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 &
% 227.03/41.84  |              op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 &
% 227.03/41.84  |              op(e3, e1) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v7 = e0 &
% 227.03/41.84  |              op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v9 = e3 &
% 227.03/41.84  |              op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v7 = e3 &
% 227.03/41.84  |              op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 227.03/41.84  |              op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 &
% 227.03/41.84  |              op(e1, e1) = e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 &
% 227.03/41.84  |              op(e1, e3) = e1) | (v8 = e1 & op(e1, e2) = e1) | (v7 = e1 &
% 227.03/41.84  |              op(e1, e1) = e1) | (v4 = e1 & op(e1, e0) = e1)) & ((v9 = e0 &
% 227.03/41.84  |              op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v7 = e0 &
% 227.03/41.84  |              op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v6 = e3 &
% 227.03/41.84  |              op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 227.03/41.84  |              op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 &
% 227.03/41.84  |              op(e3, e0) = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 &
% 227.03/41.84  |              op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v6 = e1 &
% 227.03/41.84  |              op(e3, e0) = e1) | (v5 = e1 & op(e2, e0) = e1) | (v4 = e1 &
% 227.03/41.84  |              op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v3 = e3 &
% 227.03/41.84  |              op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 &
% 227.03/41.84  |              op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 227.03/41.84  |              op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 &
% 227.03/41.84  |              op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 &
% 227.03/41.84  |              op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 &
% 227.03/41.84  |              op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 &
% 227.03/41.84  |              op(e0, e0) = e0) | (((v6 = e0 & op(e3, e0) = e0) | (v5 = e0 &
% 227.03/41.84  |                  op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v3 = e0 &
% 227.03/41.84  |                  op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 &
% 227.03/41.84  |                  op(e0, e1) = e0)))))
% 227.03/41.84  | 
% 227.03/41.84  | ALPHA: (ax3) implies:
% 227.03/41.85  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 227.03/41.85  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 227.03/41.85  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 227.03/41.85  |         ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~ (v15 = v12) &  ~
% 227.03/41.85  |          (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 = v13) &  ~
% 227.03/41.85  |          (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) &  ~
% 227.03/41.85  |          (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12
% 227.03/41.85  |            = v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 =
% 227.03/41.85  |            v9) &  ~ (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9)
% 227.03/41.85  |          &  ~ (v10 = v8) &  ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~
% 227.03/41.85  |          (v9 = v5) &  ~ (v9 = v1) &  ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6)
% 227.03/41.85  |          &  ~ (v7 = v5) &  ~ (v7 = v4) &  ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6
% 227.03/41.85  |            = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~ (v5 = v1) &  ~ (v4 = v0) &
% 227.03/41.85  |           ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~ (v2 = v1) &  ~ (v2 =
% 227.03/41.85  |            v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 227.03/41.85  |            e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 227.03/41.85  |          op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 227.03/41.85  |          v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 227.03/41.85  |            e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 227.03/41.85  |          $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 227.03/41.85  |          $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 227.03/41.85  | 
% 227.03/41.85  | ALPHA: (ax4) implies:
% 227.03/41.85  |   (4)   ~ (e1 = e0)
% 227.03/41.85  |   (5)   ~ (e2 = e0)
% 227.03/41.85  |   (6)   ~ (e2 = e1)
% 227.03/41.85  |   (7)   ~ (e3 = e0)
% 227.03/41.85  |   (8)   ~ (e3 = e1)
% 227.03/41.85  |   (9)   ~ (e3 = e2)
% 227.03/41.85  | 
% 227.03/41.85  | ALPHA: (ax5) implies:
% 227.34/41.87  |   (10)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 227.34/41.87  |         ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] : 
% 227.34/41.87  |         ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14:
% 227.34/41.87  |           $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ?
% 227.34/41.87  |         [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23: $i]
% 227.34/41.87  |         :  ? [v24: $i] :  ? [v25: $i] :  ? [v26: $i] :  ? [v27: $i] :  ? [v28:
% 227.34/41.87  |           $i] :  ? [v29: $i] :  ? [v30: $i] :  ? [v31: $i] : (op(e3, e3) = v30
% 227.34/41.87  |           & op(e2, e2) = v20 & op(e1, e1) = v10 & op(e0, e0) = v0 & $i(v30) &
% 227.34/41.87  |           $i(v20) & $i(v10) & $i(v0) & ((v31 = e3 & op(e3, v30) = e3) | (v29 =
% 227.34/41.87  |               e2 & op(e2, v28) = e2 & op(e2, e3) = v28 & $i(v28)) | (v27 = e1
% 227.34/41.87  |               & op(e1, v26) = e1 & op(e1, e3) = v26 & $i(v26)) | (v25 = e0 &
% 227.34/41.87  |               op(e0, v24) = e0 & op(e0, e3) = v24 & $i(v24))) & ((v28 = e3 &
% 227.34/41.87  |               v22 = e3 &  ~ (v30 = e2) &  ~ (v20 = e2) &  ~ (v10 = e2) &  ~
% 227.34/41.87  |               (v0 = e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (v28 = e2 & v22
% 227.34/41.87  |               = e2 &  ~ (v30 = e3) &  ~ (v20 = e3) &  ~ (v10 = e3) &  ~ (v0 =
% 227.34/41.87  |                 e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (v26 = e3 & v14 =
% 227.34/41.87  |               e3 &  ~ (v30 = e1) &  ~ (v20 = e1) &  ~ (v10 = e1) &  ~ (v0 =
% 227.34/41.87  |                 e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (v26 = e1 & v14 =
% 227.34/41.87  |               e1 &  ~ (v30 = e3) &  ~ (v20 = e3) &  ~ (v10 = e3) &  ~ (v0 =
% 227.34/41.87  |                 e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (v24 = e3 & v6 = e3
% 227.34/41.87  |               &  ~ (v30 = e0) &  ~ (v20 = e0) &  ~ (v10 = e0) &  ~ (v0 = e0) &
% 227.34/41.87  |               op(e3, e0) = e3 & op(e0, e3) = e3) | (v24 = e0 & v6 = e0 &  ~
% 227.34/41.87  |               (v30 = e3) &  ~ (v20 = e3) &  ~ (v10 = e3) &  ~ (v0 = e3) &
% 227.34/41.87  |               op(e3, e0) = e0 & op(e0, e3) = e0) | (v18 = e2 & v12 = e2 &  ~
% 227.34/41.87  |               (v30 = e1) &  ~ (v20 = e1) &  ~ (v10 = e1) &  ~ (v0 = e1) &
% 227.34/41.87  |               op(e2, e1) = e2 & op(e1, e2) = e2) | (v18 = e1 & v12 = e1 &  ~
% 227.34/41.87  |               (v30 = e2) &  ~ (v20 = e2) &  ~ (v10 = e2) &  ~ (v0 = e2) &
% 227.34/41.87  |               op(e2, e1) = e1 & op(e1, e2) = e1) | (v16 = e2 & v4 = e2 &  ~
% 227.34/41.87  |               (v30 = e0) &  ~ (v20 = e0) &  ~ (v10 = e0) &  ~ (v0 = e0) &
% 227.34/41.87  |               op(e2, e0) = e2 & op(e0, e2) = e2) | (v16 = e0 & v4 = e0 &  ~
% 227.34/41.87  |               (v30 = e2) &  ~ (v20 = e2) &  ~ (v10 = e2) &  ~ (v0 = e2) &
% 227.34/41.87  |               op(e2, e0) = e0 & op(e0, e2) = e0) | (v8 = e1 & v2 = e1 &  ~
% 227.34/41.87  |               (v30 = e0) &  ~ (v20 = e0) &  ~ (v10 = e0) &  ~ (v0 = e0) &
% 227.34/41.87  |               op(e1, e0) = e1 & op(e0, e1) = e1) | (v8 = e0 & v2 = e0 &  ~
% 227.34/41.87  |               (v30 = e1) &  ~ (v20 = e1) &  ~ (v10 = e1) &  ~ (v0 = e1) &
% 227.34/41.87  |               op(e1, e0) = e0 & op(e0, e1) = e0)) & ((v23 = e3 & op(e3, v22) =
% 227.34/41.87  |               e3 & op(e3, e2) = v22 & $i(v22)) | (v21 = e2 & op(e2, v20) = e2)
% 227.34/41.87  |             | (v19 = e1 & op(e1, v18) = e1 & op(e1, e2) = v18 & $i(v18)) |
% 227.34/41.87  |             (v17 = e0 & op(e0, v16) = e0 & op(e0, e2) = v16 & $i(v16))) &
% 227.34/41.87  |           ((v15 = e3 & op(e3, v14) = e3 & op(e3, e1) = v14 & $i(v14)) | (v13 =
% 227.34/41.87  |               e2 & op(e2, v12) = e2 & op(e2, e1) = v12 & $i(v12)) | (v11 = e1
% 227.34/41.87  |               & op(e1, v10) = e1) | (v9 = e0 & op(e0, v8) = e0 & op(e0, e1) =
% 227.34/41.87  |               v8 & $i(v8))) & ((v7 = e3 & op(e3, v6) = e3 & op(e3, e0) = v6 &
% 227.34/41.87  |               $i(v6)) | (v5 = e2 & op(e2, v4) = e2 & op(e2, e0) = v4 & $i(v4))
% 227.34/41.87  |             | (v3 = e1 & op(e1, v2) = e1 & op(e1, e0) = v2 & $i(v2)) | (v1 =
% 227.34/41.87  |               e0 & op(e0, v0) = e0)))
% 227.34/41.87  | 
% 227.34/41.87  | ALPHA: (ax6) implies:
% 227.34/41.87  |   (11)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 227.34/41.87  |           ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e3, e1) = v1 &
% 227.34/41.87  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 & $i(v1))))
% 227.34/41.87  | 
% 227.34/41.87  | ALPHA: (ax7) implies:
% 227.34/41.87  |   (12)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 227.34/41.87  |           ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e2, e1) = v1 &
% 227.34/41.87  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 & $i(v1))))
% 227.34/41.87  | 
% 227.34/41.87  | ALPHA: (ax8) implies:
% 227.34/41.87  |   (13)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 227.34/41.87  |           ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e3, e2) = v1 &
% 227.34/41.87  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 & $i(v1))))
% 227.34/41.87  | 
% 227.34/41.87  | ALPHA: (ax9) implies:
% 227.34/41.87  |   (14)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 227.34/41.87  |           ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e1, e2) = v1 &
% 227.34/41.87  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 & $i(v1))))
% 227.34/41.87  | 
% 227.34/41.87  | ALPHA: (ax10) implies:
% 227.34/41.88  |   (15)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 227.34/41.88  |           ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e2, e3) = v1 &
% 227.34/41.88  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 & $i(v1))))
% 227.34/41.88  | 
% 227.34/41.88  | ALPHA: (ax11) implies:
% 227.34/41.88  |   (16)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 227.34/41.88  |           ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e1, e3) = v1 &
% 227.34/41.88  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 & $i(v1))))
% 227.34/41.88  | 
% 227.34/41.88  | ALPHA: (ax12) implies:
% 227.34/41.88  |   (17)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 227.34/41.88  |           ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e3, e0) = v1 &
% 227.34/41.88  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 & $i(v1))))
% 227.34/41.88  | 
% 227.34/41.88  | ALPHA: (ax13) implies:
% 227.34/41.88  |   (18)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 227.34/41.88  |           ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e2, e0) = v1 &
% 227.34/41.88  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 & $i(v1))))
% 227.34/41.88  | 
% 227.34/41.88  | ALPHA: (ax14) implies:
% 227.34/41.88  |   (19)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 227.34/41.88  |           ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e3, e2) = v1 &
% 227.34/41.88  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 & $i(v1))))
% 227.34/41.88  | 
% 227.34/41.88  | ALPHA: (ax15) implies:
% 227.34/41.88  |   (20)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 227.34/41.88  |           ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e0, e2) = v1 &
% 227.34/41.88  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 & $i(v1))))
% 227.34/41.88  | 
% 227.34/41.88  | ALPHA: (ax16) implies:
% 227.34/41.89  |   (21)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 227.34/41.89  |           ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e2, e3) = v1 &
% 227.34/41.89  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 & $i(v1))))
% 227.34/41.89  | 
% 227.34/41.89  | ALPHA: (ax17) implies:
% 227.34/41.89  |   (22)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 227.34/41.89  |           ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e0, e3) = v1 &
% 227.34/41.89  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 & $i(v1))))
% 227.34/41.89  | 
% 227.34/41.89  | ALPHA: (ax18) implies:
% 227.34/41.89  |   (23)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 227.34/41.89  |           ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e3, e0) = v1 &
% 227.34/41.89  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 & $i(v1))))
% 227.34/41.89  | 
% 227.34/41.89  | ALPHA: (ax19) implies:
% 227.34/41.89  |   (24)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 227.34/41.89  |           ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e1, e0) = v1 &
% 227.34/41.89  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 & $i(v1))))
% 227.34/41.89  | 
% 227.34/41.89  | ALPHA: (ax20) implies:
% 227.34/41.89  |   (25)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 227.34/41.89  |           ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e3, e1) = v1 &
% 227.34/41.89  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 & $i(v1))))
% 227.34/41.89  | 
% 227.34/41.89  | ALPHA: (ax21) implies:
% 227.34/41.89  |   (26)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 227.34/41.89  |           ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e0, e1) = v1 &
% 227.34/41.89  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 & $i(v1))))
% 227.34/41.89  | 
% 227.34/41.89  | ALPHA: (ax22) implies:
% 227.34/41.90  |   (27)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 227.34/41.90  |           ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e1, e3) = v1 &
% 227.34/41.90  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 & $i(v1))))
% 227.34/41.90  | 
% 227.34/41.90  | ALPHA: (ax23) implies:
% 227.34/41.90  |   (28)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 227.34/41.90  |           ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e0, e3) = v1 &
% 227.34/41.90  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 & $i(v1))))
% 227.34/41.90  | 
% 227.34/41.90  | ALPHA: (ax24) implies:
% 227.34/41.90  |   (29)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 227.34/41.90  |           ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e2, e0) = v1 &
% 227.34/41.90  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 & $i(v1))))
% 227.34/41.90  | 
% 227.34/41.90  | ALPHA: (ax25) implies:
% 227.34/41.90  |   (30)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 227.34/41.90  |           ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e1, e0) = v1 &
% 227.34/41.90  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 & $i(v1))))
% 227.34/41.90  | 
% 227.34/41.90  | ALPHA: (ax26) implies:
% 227.34/41.90  |   (31)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 227.34/41.90  |           ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e2, e1) = v1 &
% 227.34/41.90  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 & $i(v1))))
% 227.34/41.90  | 
% 227.34/41.90  | ALPHA: (ax27) implies:
% 227.34/41.90  |   (32)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 227.34/41.90  |           ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e0, e1) = v1 &
% 227.34/41.90  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 & $i(v1))))
% 227.34/41.90  | 
% 227.34/41.90  | ALPHA: (ax28) implies:
% 227.34/41.90  |   (33)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 227.34/41.90  |           ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e1, e2) = v1 &
% 227.34/41.90  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 & $i(v1))))
% 227.34/41.90  | 
% 227.34/41.90  | ALPHA: (ax29) implies:
% 227.34/41.91  |   (34)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 227.34/41.91  |           ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e0, e2) = v1 &
% 227.34/41.91  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 & $i(v1))))
% 227.34/41.91  | 
% 227.34/41.91  | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 227.34/41.91  |   (35)  op(e0, e0) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e2) | ( ~ (all_4_0
% 227.34/41.91  |               = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 227.34/41.91  |             $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e0, e2) =
% 227.34/41.91  |             all_4_1 & $i(all_4_1)))
% 227.34/41.91  | 
% 227.34/41.91  | ALPHA: (35) implies:
% 227.34/41.91  |   (36)  op(e0, e0) = all_4_2
% 227.34/41.91  |   (37)   ~ (all_4_2 = e2) | ( ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 227.34/41.91  |           op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 =
% 227.34/41.91  |             e3) & op(e0, e2) = all_4_1 & $i(all_4_1))
% 227.34/41.91  | 
% 227.34/41.91  | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 227.34/41.91  |   (38)  op(e1, e1) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e3) | ( ~ (all_6_0
% 227.34/41.91  |               = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 227.34/41.91  |             $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e1, e3) =
% 227.34/41.91  |             all_6_1 & $i(all_6_1)))
% 227.34/41.91  | 
% 227.34/41.91  | ALPHA: (38) implies:
% 227.34/41.91  |   (39)  op(e1, e1) = all_6_2
% 227.34/41.91  |   (40)   ~ (all_6_2 = e3) | ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 &
% 227.34/41.91  |           op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 =
% 227.34/41.91  |             e0) & op(e1, e3) = all_6_1 & $i(all_6_1))
% 227.34/41.91  | 
% 227.34/41.91  | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 227.34/41.91  |   (41)  op(e2, e2) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e3) | ( ~ (all_8_0
% 227.34/41.91  |               = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 227.34/41.91  |             $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) =
% 227.34/41.91  |             all_8_1 & $i(all_8_1)))
% 227.34/41.91  | 
% 227.34/41.91  | ALPHA: (41) implies:
% 227.34/41.91  |   (42)  op(e2, e2) = all_8_2
% 227.34/41.91  |   (43)   ~ (all_8_2 = e3) | ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 227.34/41.91  |           op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 =
% 227.34/41.91  |             e0) & op(e2, e3) = all_8_1 & $i(all_8_1))
% 227.34/41.91  | 
% 227.34/41.91  | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 227.34/41.91  |        gives:
% 227.34/41.91  |   (44)  op(e3, e3) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e1) | ( ~
% 227.34/41.91  |             (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 227.34/41.91  |             all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) &
% 227.34/41.91  |             op(e3, e1) = all_10_1 & $i(all_10_1)))
% 227.34/41.91  | 
% 227.34/41.91  | ALPHA: (44) implies:
% 227.34/41.91  |   (45)  op(e3, e3) = all_10_2
% 227.34/41.91  |   (46)   ~ (all_10_2 = e1) | ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0
% 227.34/41.91  |           & op(e3, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 227.34/41.91  |           (all_10_1 = e2) & op(e3, e1) = all_10_1 & $i(all_10_1))
% 227.34/41.91  | 
% 227.34/41.91  | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 227.34/41.91  |        gives:
% 227.34/41.92  |   (47)  op(e0, e0) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e3) | ( ~
% 227.34/41.92  |             (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.34/41.92  |             all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) &
% 227.34/41.92  |             op(e0, e3) = all_12_1 & $i(all_12_1)))
% 227.34/41.92  | 
% 227.34/41.92  | ALPHA: (47) implies:
% 227.34/41.92  |   (48)  op(e0, e0) = all_12_2
% 227.34/41.92  |   (49)   ~ (all_12_2 = e3) | ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0
% 227.34/41.92  |           & op(e0, e3) = all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 227.34/41.92  |           (all_12_1 = e2) & op(e0, e3) = all_12_1 & $i(all_12_1))
% 227.34/41.92  | 
% 227.34/41.92  | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 227.34/41.92  |        gives:
% 227.34/41.92  |   (50)  op(e2, e2) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e0) | ( ~
% 227.34/41.92  |             (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 227.34/41.92  |             all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) &
% 227.34/41.92  |             op(e2, e0) = all_14_1 & $i(all_14_1)))
% 227.34/41.92  | 
% 227.34/41.92  | ALPHA: (50) implies:
% 227.34/41.92  |   (51)  op(e2, e2) = all_14_2
% 227.34/41.92  |   (52)   ~ (all_14_2 = e0) | ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0
% 227.34/41.92  |           & op(e2, e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 227.34/41.92  |           (all_14_1 = e1) & op(e2, e0) = all_14_1 & $i(all_14_1))
% 227.34/41.92  | 
% 227.34/41.92  | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1, all_16_2
% 227.34/41.92  |        gives:
% 227.34/41.92  |   (53)  op(e3, e3) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e0) | ( ~
% 227.34/41.92  |             (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 227.34/41.92  |             all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) &
% 227.34/41.92  |             op(e3, e0) = all_16_1 & $i(all_16_1)))
% 227.34/41.92  | 
% 227.34/41.92  | ALPHA: (53) implies:
% 227.34/41.92  |   (54)  op(e3, e3) = all_16_2
% 227.34/41.92  |   (55)   ~ (all_16_2 = e0) | ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0
% 227.34/41.92  |           & op(e3, e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~
% 227.34/41.92  |           (all_16_1 = e1) & op(e3, e0) = all_16_1 & $i(all_16_1))
% 227.34/41.92  | 
% 227.34/41.92  | DELTA: instantiating (24) with fresh symbols all_18_0, all_18_1, all_18_2
% 227.34/41.92  |        gives:
% 227.34/41.92  |   (56)  op(e1, e1) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e0) | ( ~
% 227.34/41.92  |             (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 & op(e1, e0) =
% 227.34/41.92  |             all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) &
% 227.34/41.92  |             op(e1, e0) = all_18_1 & $i(all_18_1)))
% 227.34/41.92  | 
% 227.34/41.92  | ALPHA: (56) implies:
% 227.34/41.92  |   (57)  op(e1, e1) = all_18_2
% 227.34/41.92  |   (58)   ~ (all_18_2 = e0) | ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0
% 227.34/41.92  |           & op(e1, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~
% 227.34/41.92  |           (all_18_1 = e3) & op(e1, e0) = all_18_1 & $i(all_18_1))
% 227.34/41.92  | 
% 227.34/41.92  | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1, all_20_2
% 227.34/41.92  |        gives:
% 227.34/41.92  |   (59)  op(e0, e0) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e1) | ( ~
% 227.34/41.92  |             (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 227.34/41.92  |             all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) &
% 227.34/41.92  |             op(e0, e1) = all_20_1 & $i(all_20_1)))
% 227.34/41.92  | 
% 227.34/41.92  | ALPHA: (59) implies:
% 227.34/41.92  |   (60)  op(e0, e0) = all_20_2
% 227.34/41.92  |   (61)   ~ (all_20_2 = e1) | ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 227.34/41.92  |           & op(e0, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~
% 227.34/41.92  |           (all_20_1 = e3) & op(e0, e1) = all_20_1 & $i(all_20_1))
% 227.34/41.92  | 
% 227.34/41.92  | DELTA: instantiating (31) with fresh symbols all_22_0, all_22_1, all_22_2
% 227.34/41.92  |        gives:
% 227.34/41.93  |   (62)  op(e2, e2) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e1) | ( ~
% 227.34/41.93  |             (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) =
% 227.34/41.93  |             all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) &
% 227.34/41.93  |             op(e2, e1) = all_22_1 & $i(all_22_1)))
% 227.34/41.93  | 
% 227.34/41.93  | ALPHA: (62) implies:
% 227.34/41.93  |   (63)  op(e2, e2) = all_22_2
% 227.34/41.93  |   (64)   ~ (all_22_2 = e1) | ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 227.34/41.93  |           & op(e2, e1) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 227.34/41.93  |           (all_22_1 = e0) & op(e2, e1) = all_22_1 & $i(all_22_1))
% 227.34/41.93  | 
% 227.34/41.93  | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1, all_24_2
% 227.34/41.93  |        gives:
% 227.34/41.93  |   (65)  op(e3, e3) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e2) | ( ~
% 227.34/41.93  |             (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) =
% 227.34/41.93  |             all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) &
% 227.34/41.93  |             op(e3, e2) = all_24_1 & $i(all_24_1)))
% 227.34/41.93  | 
% 227.34/41.93  | ALPHA: (65) implies:
% 227.34/41.93  |   (66)  op(e3, e3) = all_24_2
% 227.34/41.93  |   (67)   ~ (all_24_2 = e2) | ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 227.34/41.93  |           & op(e3, e2) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 227.34/41.93  |           (all_24_1 = e1) & op(e3, e2) = all_24_1 & $i(all_24_1))
% 227.34/41.93  | 
% 227.34/41.93  | DELTA: instantiating (28) with fresh symbols all_26_0, all_26_1, all_26_2
% 227.34/41.93  |        gives:
% 227.34/41.93  |   (68)  op(e0, e0) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e3) | ( ~
% 227.34/41.93  |             (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 227.34/41.93  |             all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) &
% 227.34/41.93  |             op(e0, e3) = all_26_1 & $i(all_26_1)))
% 227.34/41.93  | 
% 227.34/41.93  | ALPHA: (68) implies:
% 227.34/41.93  |   (69)  op(e0, e0) = all_26_2
% 227.34/41.93  |   (70)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 227.34/41.93  |           & op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 227.34/41.93  |           (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 227.34/41.93  | 
% 227.34/41.93  | DELTA: instantiating (30) with fresh symbols all_28_0, all_28_1, all_28_2
% 227.34/41.93  |        gives:
% 227.34/41.93  |   (71)  op(e1, e1) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e0) | ( ~
% 227.34/41.93  |             (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 & op(e1, e0) =
% 227.34/41.93  |             all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e2) &
% 227.34/41.93  |             op(e1, e0) = all_28_1 & $i(all_28_1)))
% 227.34/41.93  | 
% 227.34/41.93  | ALPHA: (71) implies:
% 227.34/41.93  |   (72)  op(e1, e1) = all_28_2
% 227.34/41.93  |   (73)   ~ (all_28_2 = e0) | ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0
% 227.34/41.93  |           & op(e1, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~
% 227.34/41.93  |           (all_28_1 = e2) & op(e1, e0) = all_28_1 & $i(all_28_1))
% 227.34/41.93  | 
% 227.34/41.93  | DELTA: instantiating (12) with fresh symbols all_30_0, all_30_1, all_30_2
% 227.34/41.93  |        gives:
% 227.34/41.93  |   (74)  op(e2, e2) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e1) | ( ~
% 227.34/41.93  |             (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) =
% 227.34/41.93  |             all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) &
% 227.34/41.93  |             op(e2, e1) = all_30_1 & $i(all_30_1)))
% 227.34/41.93  | 
% 227.34/41.93  | ALPHA: (74) implies:
% 227.34/41.93  |   (75)  op(e2, e2) = all_30_2
% 227.34/41.93  |   (76)   ~ (all_30_2 = e1) | ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 227.34/41.93  |           & op(e2, e1) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~
% 227.34/41.93  |           (all_30_1 = e3) & op(e2, e1) = all_30_1 & $i(all_30_1))
% 227.34/41.93  | 
% 227.34/41.93  | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2
% 227.34/41.93  |        gives:
% 227.34/41.94  |   (77)  op(e3, e3) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e2) | ( ~
% 227.34/41.94  |             (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 227.34/41.94  |             all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) &
% 227.34/41.94  |             op(e3, e2) = all_32_1 & $i(all_32_1)))
% 227.34/41.94  | 
% 227.34/41.94  | ALPHA: (77) implies:
% 227.34/41.94  |   (78)  op(e3, e3) = all_32_2
% 227.34/41.94  |   (79)   ~ (all_32_2 = e2) | ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 227.34/41.94  |           & op(e3, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~
% 227.34/41.94  |           (all_32_1 = e0) & op(e3, e2) = all_32_1 & $i(all_32_1))
% 227.34/41.94  | 
% 227.34/41.94  | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1, all_34_2
% 227.34/41.94  |        gives:
% 227.34/41.94  |   (80)  op(e0, e0) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e1) | ( ~
% 227.34/41.94  |             (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 227.34/41.94  |             all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) &
% 227.34/41.94  |             op(e0, e1) = all_34_1 & $i(all_34_1)))
% 227.34/41.94  | 
% 227.34/41.94  | ALPHA: (80) implies:
% 227.34/41.94  |   (81)  op(e0, e0) = all_34_2
% 227.34/41.94  |   (82)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 227.34/41.94  |           & op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~
% 227.34/41.94  |           (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 227.34/41.94  | 
% 227.34/41.94  | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1, all_36_2
% 227.34/41.94  |        gives:
% 227.34/41.94  |   (83)  op(e1, e1) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e2) | ( ~
% 227.34/41.94  |             (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 227.34/41.94  |             all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) &
% 227.34/41.94  |             op(e1, e2) = all_36_1 & $i(all_36_1)))
% 227.34/41.94  | 
% 227.34/41.94  | ALPHA: (83) implies:
% 227.34/41.94  |   (84)  op(e1, e1) = all_36_2
% 227.34/41.94  |   (85)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 227.34/41.94  |           & op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~
% 227.34/41.94  |           (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 227.34/41.94  | 
% 227.34/41.94  | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2
% 227.34/41.94  |        gives:
% 227.34/41.94  |   (86)  op(e3, e3) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e1) | ( ~
% 227.34/41.94  |             (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 227.34/41.94  |             all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) &
% 227.34/41.94  |             op(e3, e1) = all_38_1 & $i(all_38_1)))
% 227.34/41.94  | 
% 227.34/41.94  | ALPHA: (86) implies:
% 227.34/41.94  |   (87)  op(e3, e3) = all_38_2
% 227.34/41.94  |   (88)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 227.34/41.94  |           & op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 227.34/41.94  |           (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 227.34/41.94  | 
% 227.34/41.94  | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2
% 227.34/41.94  |        gives:
% 227.34/41.94  |   (89)  op(e1, e1) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e2) | ( ~
% 227.34/41.94  |             (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 227.34/41.94  |             all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) &
% 227.34/41.94  |             op(e1, e2) = all_40_1 & $i(all_40_1)))
% 227.34/41.94  | 
% 227.34/41.94  | ALPHA: (89) implies:
% 227.34/41.94  |   (90)  op(e1, e1) = all_40_2
% 227.34/41.94  |   (91)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 227.34/41.94  |           & op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 227.34/41.94  |           (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 227.34/41.94  | 
% 227.34/41.94  | DELTA: instantiating (15) with fresh symbols all_42_0, all_42_1, all_42_2
% 227.34/41.94  |        gives:
% 227.34/41.94  |   (92)  op(e2, e2) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e3) | ( ~
% 227.34/41.94  |             (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 227.34/41.94  |             all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) &
% 227.34/41.94  |             op(e2, e3) = all_42_1 & $i(all_42_1)))
% 227.34/41.94  | 
% 227.34/41.94  | ALPHA: (92) implies:
% 227.34/41.95  |   (93)  op(e2, e2) = all_42_2
% 227.34/41.95  |   (94)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 227.34/41.95  |           & op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 227.34/41.95  |           (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 227.34/41.95  | 
% 227.34/41.95  | DELTA: instantiating (34) with fresh symbols all_44_0, all_44_1, all_44_2
% 227.34/41.95  |        gives:
% 227.34/41.95  |   (95)  op(e0, e0) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e2) | ( ~
% 227.34/41.95  |             (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 227.34/41.95  |             all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) &
% 227.34/41.95  |             op(e0, e2) = all_44_1 & $i(all_44_1)))
% 227.34/41.95  | 
% 227.34/41.95  | ALPHA: (95) implies:
% 227.34/41.95  |   (96)  op(e0, e0) = all_44_2
% 227.34/41.95  |   (97)   ~ (all_44_2 = e2) | ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 227.34/41.95  |           & op(e0, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~
% 227.34/41.95  |           (all_44_1 = e1) & op(e0, e2) = all_44_1 & $i(all_44_1))
% 227.34/41.95  | 
% 227.34/41.95  | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 227.34/41.95  |        gives:
% 227.34/41.95  |   (98)  op(e1, e1) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e3) | ( ~
% 227.34/41.95  |             (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 227.34/41.95  |             all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) &
% 227.34/41.95  |             op(e1, e3) = all_46_1 & $i(all_46_1)))
% 227.34/41.95  | 
% 227.34/41.95  | ALPHA: (98) implies:
% 227.34/41.95  |   (99)  op(e1, e1) = all_46_2
% 227.34/41.95  |   (100)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e0) & op(all_46_1, e1) =
% 227.34/41.95  |            all_46_0 & op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | (
% 227.34/41.95  |            ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 227.34/41.95  | 
% 227.34/41.95  | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1, all_48_2
% 227.34/41.95  |        gives:
% 227.34/41.95  |   (101)  op(e2, e2) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e0) | ( ~
% 227.34/41.95  |              (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 227.34/41.95  |              all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) &
% 227.34/41.95  |              op(e2, e0) = all_48_1 & $i(all_48_1)))
% 227.34/41.95  | 
% 227.34/41.95  | ALPHA: (101) implies:
% 227.34/41.95  |   (102)  op(e2, e2) = all_48_2
% 227.34/41.95  |   (103)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e1) & op(all_48_1, e2) =
% 227.34/41.95  |            all_48_0 & op(e2, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | (
% 227.34/41.95  |            ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 & $i(all_48_1))
% 227.34/41.95  | 
% 227.34/41.95  | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2
% 227.34/41.95  |        gives:
% 227.34/41.95  |   (104)  op(e3, e3) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e0) | ( ~
% 227.34/41.95  |              (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 227.34/41.95  |              all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) &
% 227.34/41.95  |              op(e3, e0) = all_50_1 & $i(all_50_1)))
% 227.34/41.95  | 
% 227.34/41.95  | ALPHA: (104) implies:
% 227.34/41.95  |   (105)  op(e3, e3) = all_50_2
% 227.34/41.95  |   (106)   ~ (all_50_2 = e0) | ( ~ (all_50_0 = e1) & op(all_50_1, e3) =
% 227.34/41.95  |            all_50_0 & op(e3, e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | (
% 227.34/41.95  |            ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 & $i(all_50_1))
% 227.34/41.95  | 
% 227.34/41.95  | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2,
% 227.34/41.95  |        all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 227.34/41.95  |        all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives:
% 227.34/41.96  |   (107)   ~ (all_52_0 = all_52_1) &  ~ (all_52_0 = all_52_2) &  ~ (all_52_0 =
% 227.34/41.96  |            all_52_3) &  ~ (all_52_0 = all_52_4) &  ~ (all_52_0 = all_52_8) & 
% 227.34/41.96  |          ~ (all_52_0 = all_52_12) &  ~ (all_52_1 = all_52_2) &  ~ (all_52_1 =
% 227.34/41.96  |            all_52_3) &  ~ (all_52_1 = all_52_5) &  ~ (all_52_1 = all_52_9) & 
% 227.34/41.96  |          ~ (all_52_1 = all_52_13) &  ~ (all_52_2 = all_52_3) &  ~ (all_52_2 =
% 227.34/41.96  |            all_52_6) &  ~ (all_52_2 = all_52_10) &  ~ (all_52_2 = all_52_14) &
% 227.34/41.96  |           ~ (all_52_3 = all_52_7) &  ~ (all_52_3 = all_52_11) &  ~ (all_52_3 =
% 227.34/41.96  |            all_52_15) &  ~ (all_52_4 = all_52_5) &  ~ (all_52_4 = all_52_6) & 
% 227.34/41.96  |          ~ (all_52_4 = all_52_7) &  ~ (all_52_4 = all_52_8) &  ~ (all_52_4 =
% 227.34/41.96  |            all_52_12) &  ~ (all_52_5 = all_52_6) &  ~ (all_52_5 = all_52_7) & 
% 227.34/41.96  |          ~ (all_52_5 = all_52_9) &  ~ (all_52_5 = all_52_13) &  ~ (all_52_6 =
% 227.34/41.96  |            all_52_7) &  ~ (all_52_6 = all_52_10) &  ~ (all_52_6 = all_52_14) &
% 227.34/41.96  |           ~ (all_52_7 = all_52_11) &  ~ (all_52_7 = all_52_15) &  ~ (all_52_8
% 227.34/41.96  |            = all_52_9) &  ~ (all_52_8 = all_52_10) &  ~ (all_52_8 = all_52_11)
% 227.34/41.96  |          &  ~ (all_52_8 = all_52_12) &  ~ (all_52_9 = all_52_10) &  ~
% 227.34/41.96  |          (all_52_9 = all_52_11) &  ~ (all_52_9 = all_52_13) &  ~ (all_52_10 =
% 227.34/41.96  |            all_52_11) &  ~ (all_52_10 = all_52_14) &  ~ (all_52_11 =
% 227.34/41.96  |            all_52_15) &  ~ (all_52_12 = all_52_13) &  ~ (all_52_12 =
% 227.34/41.96  |            all_52_14) &  ~ (all_52_12 = all_52_15) &  ~ (all_52_13 =
% 227.34/41.96  |            all_52_14) &  ~ (all_52_13 = all_52_15) &  ~ (all_52_14 =
% 227.34/41.96  |            all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) = all_52_4 & op(e3,
% 227.34/41.96  |            e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3) = all_52_1 &
% 227.34/41.96  |          op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2, e0) =
% 227.34/41.96  |          all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 & op(e1,
% 227.34/41.96  |            e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) = all_52_3 &
% 227.34/41.96  |          op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0) =
% 227.34/41.96  |          all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3)
% 227.34/41.96  |          & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) &
% 227.34/41.96  |          $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) &
% 227.34/41.96  |          $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15)
% 227.34/41.96  | 
% 227.34/41.96  | ALPHA: (107) implies:
% 227.34/41.96  |   (108)   ~ (all_52_14 = all_52_15)
% 227.34/41.96  |   (109)   ~ (all_52_13 = all_52_15)
% 227.34/41.96  |   (110)   ~ (all_52_13 = all_52_14)
% 227.34/41.96  |   (111)   ~ (all_52_12 = all_52_15)
% 227.34/41.96  |   (112)   ~ (all_52_12 = all_52_14)
% 227.34/41.96  |   (113)   ~ (all_52_12 = all_52_13)
% 227.34/41.96  |   (114)   ~ (all_52_11 = all_52_15)
% 227.34/41.96  |   (115)   ~ (all_52_10 = all_52_14)
% 227.34/41.96  |   (116)   ~ (all_52_10 = all_52_11)
% 227.34/41.96  |   (117)   ~ (all_52_9 = all_52_13)
% 227.34/41.96  |   (118)   ~ (all_52_9 = all_52_11)
% 227.34/41.96  |   (119)   ~ (all_52_9 = all_52_10)
% 227.34/41.96  |   (120)   ~ (all_52_8 = all_52_12)
% 227.34/41.96  |   (121)   ~ (all_52_8 = all_52_11)
% 227.34/41.96  |   (122)   ~ (all_52_8 = all_52_10)
% 227.34/41.96  |   (123)   ~ (all_52_8 = all_52_9)
% 227.34/41.96  |   (124)   ~ (all_52_7 = all_52_15)
% 227.34/41.96  |   (125)   ~ (all_52_7 = all_52_11)
% 227.34/41.96  |   (126)   ~ (all_52_6 = all_52_14)
% 227.34/41.96  |   (127)   ~ (all_52_6 = all_52_10)
% 227.34/41.96  |   (128)   ~ (all_52_6 = all_52_7)
% 227.34/41.96  |   (129)   ~ (all_52_5 = all_52_13)
% 227.34/41.96  |   (130)   ~ (all_52_5 = all_52_9)
% 227.34/41.96  |   (131)   ~ (all_52_5 = all_52_7)
% 227.34/41.96  |   (132)   ~ (all_52_5 = all_52_6)
% 227.34/41.96  |   (133)   ~ (all_52_4 = all_52_12)
% 227.34/41.96  |   (134)   ~ (all_52_4 = all_52_8)
% 227.34/41.96  |   (135)   ~ (all_52_4 = all_52_7)
% 227.34/41.96  |   (136)   ~ (all_52_4 = all_52_6)
% 227.34/41.96  |   (137)   ~ (all_52_4 = all_52_5)
% 227.34/41.96  |   (138)   ~ (all_52_3 = all_52_15)
% 227.34/41.96  |   (139)   ~ (all_52_3 = all_52_11)
% 227.34/41.96  |   (140)   ~ (all_52_3 = all_52_7)
% 227.34/41.96  |   (141)   ~ (all_52_2 = all_52_14)
% 227.34/41.96  |   (142)   ~ (all_52_2 = all_52_10)
% 227.34/41.96  |   (143)   ~ (all_52_2 = all_52_6)
% 227.34/41.96  |   (144)   ~ (all_52_2 = all_52_3)
% 227.34/41.96  |   (145)   ~ (all_52_1 = all_52_13)
% 227.34/41.96  |   (146)   ~ (all_52_1 = all_52_9)
% 227.34/41.96  |   (147)   ~ (all_52_1 = all_52_5)
% 227.34/41.96  |   (148)   ~ (all_52_1 = all_52_3)
% 227.34/41.96  |   (149)   ~ (all_52_1 = all_52_2)
% 227.34/41.96  |   (150)   ~ (all_52_0 = all_52_12)
% 227.34/41.96  |   (151)   ~ (all_52_0 = all_52_8)
% 227.34/41.96  |   (152)   ~ (all_52_0 = all_52_4)
% 227.34/41.97  |   (153)   ~ (all_52_0 = all_52_3)
% 227.34/41.97  |   (154)   ~ (all_52_0 = all_52_2)
% 227.34/41.97  |   (155)   ~ (all_52_0 = all_52_1)
% 227.34/41.97  |   (156)  op(e0, e0) = all_52_15
% 227.34/41.97  |   (157)  op(e0, e1) = all_52_11
% 227.34/41.97  |   (158)  op(e0, e2) = all_52_7
% 227.34/41.97  |   (159)  op(e0, e3) = all_52_3
% 227.34/41.97  |   (160)  op(e1, e0) = all_52_14
% 227.34/41.97  |   (161)  op(e1, e1) = all_52_10
% 227.34/41.97  |   (162)  op(e1, e2) = all_52_6
% 227.34/41.97  |   (163)  op(e1, e3) = all_52_2
% 227.34/41.97  |   (164)  op(e2, e0) = all_52_13
% 227.34/41.97  |   (165)  op(e2, e1) = all_52_9
% 227.34/41.97  |   (166)  op(e2, e2) = all_52_5
% 227.34/41.97  |   (167)  op(e2, e3) = all_52_1
% 227.34/41.97  |   (168)  op(e3, e0) = all_52_12
% 227.34/41.97  |   (169)  op(e3, e1) = all_52_8
% 227.34/41.97  |   (170)  op(e3, e2) = all_52_4
% 227.34/41.97  |   (171)  op(e3, e3) = all_52_0
% 227.34/41.97  | 
% 227.34/41.97  | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2,
% 227.34/41.97  |        all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 227.34/41.97  |        all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 227.34/41.97  |   (172)  op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2
% 227.34/41.97  |          & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) =
% 227.34/41.97  |          all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3)
% 227.34/41.97  |          = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1,
% 227.34/41.97  |            e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 &
% 227.34/41.97  |          op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) &
% 227.34/41.97  |          $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) &
% 227.34/41.97  |          $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) &
% 227.34/41.97  |          $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) &
% 227.34/41.97  |          $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 |
% 227.34/41.97  |            all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 |
% 227.34/41.97  |            all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 |
% 227.34/41.97  |            all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 |
% 227.34/41.97  |            all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 |
% 227.34/41.97  |            all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 |
% 227.34/41.97  |            all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 |
% 227.34/41.97  |            all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 |
% 227.34/41.97  |            all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 |
% 227.34/41.97  |            all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 |
% 227.34/41.97  |            all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 |
% 227.34/41.97  |            all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3
% 227.34/41.97  |            | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 =
% 227.34/41.97  |            e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13
% 227.34/41.97  |            = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) &
% 227.34/41.97  |          (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) &
% 227.34/41.97  |          (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0)
% 227.34/41.97  | 
% 227.34/41.97  | ALPHA: (172) implies:
% 227.34/41.97  |   (173)  op(e0, e0) = all_54_15
% 227.34/41.97  |   (174)  op(e0, e1) = all_54_14
% 227.34/41.97  |   (175)  op(e0, e2) = all_54_13
% 227.34/41.98  |   (176)  op(e0, e3) = all_54_12
% 227.34/41.98  |   (177)  op(e1, e0) = all_54_11
% 227.34/41.98  |   (178)  op(e1, e1) = all_54_10
% 227.34/41.98  |   (179)  op(e1, e2) = all_54_9
% 227.34/41.98  |   (180)  op(e1, e3) = all_54_8
% 227.34/41.98  |   (181)  op(e2, e0) = all_54_7
% 227.34/41.98  |   (182)  op(e2, e1) = all_54_6
% 227.34/41.98  |   (183)  op(e2, e2) = all_54_5
% 227.34/41.98  |   (184)  op(e2, e3) = all_54_4
% 227.34/41.98  |   (185)  op(e3, e0) = all_54_3
% 227.34/41.98  |   (186)  op(e3, e1) = all_54_2
% 227.34/41.98  |   (187)  op(e3, e2) = all_54_1
% 227.34/41.98  |   (188)  op(e3, e3) = all_54_0
% 227.34/41.98  |   (189)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 227.34/41.98  |   (190)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 227.34/41.98  |   (191)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 227.34/41.98  |   (192)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 227.34/41.98  |   (193)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 227.34/41.98  |   (194)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 227.34/41.98  |   (195)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 227.34/41.98  |   (196)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 227.34/41.98  |   (197)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 227.34/41.98  |   (198)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 227.34/41.98  |   (199)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 227.34/41.98  |   (200)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 227.34/41.98  |   (201)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 227.34/41.98  |   (202)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 227.34/41.98  |   (203)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 227.34/41.98  |   (204)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 227.34/41.98  | 
% 227.34/41.98  | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1, all_56_2,
% 227.34/41.98  |        all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 227.34/41.98  |        all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15,
% 227.34/41.98  |        all_56_16, all_56_17, all_56_18, all_56_19, all_56_20, all_56_21,
% 227.34/41.98  |        all_56_22, all_56_23, all_56_24, all_56_25, all_56_26, all_56_27,
% 227.34/41.98  |        all_56_28, all_56_29, all_56_30, all_56_31 gives:
% 227.34/41.99  |   (205)  op(e3, e3) = all_56_1 & op(e2, e2) = all_56_11 & op(e1, e1) =
% 227.34/41.99  |          all_56_21 & op(e0, e0) = all_56_31 & $i(all_56_1) & $i(all_56_11) &
% 227.34/41.99  |          $i(all_56_21) & $i(all_56_31) & ((all_56_0 = e3 & op(e3, all_56_1) =
% 227.34/41.99  |              e3) | (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 227.34/41.99  |              all_56_3 & $i(all_56_3)) | (all_56_4 = e1 & op(e1, all_56_5) = e1
% 227.34/41.99  |              & op(e1, e3) = all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 227.34/41.99  |                all_56_7) = e0 & op(e0, e3) = all_56_7 & $i(all_56_7))) &
% 227.34/41.99  |          ((all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 227.34/41.99  |                = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2)
% 227.34/41.99  |              = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 227.34/41.99  |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 227.34/41.99  |              (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 227.34/41.99  |              = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1)
% 227.34/41.99  |              &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 227.34/41.99  |              op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 227.34/41.99  |                = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 227.34/41.99  |              (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 227.34/41.99  |              = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0)
% 227.34/41.99  |              &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 227.34/41.99  |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 227.34/41.99  |                = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 227.34/41.99  |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) |
% 227.34/41.99  |            (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 227.34/41.99  |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 227.34/41.99  |              op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 227.34/41.99  |              = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 227.34/41.99  |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1)
% 227.34/41.99  |            | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 227.34/41.99  |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 227.34/41.99  |              op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27
% 227.34/41.99  |              = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 227.34/41.99  |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0)
% 227.34/41.99  |            | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 227.34/41.99  |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 227.34/41.99  |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29
% 227.34/41.99  |              = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 227.34/41.99  |                e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0))
% 227.34/41.99  |          & ((all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 227.34/41.99  |              $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) |
% 227.34/41.99  |            (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 227.34/41.99  |              $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 &
% 227.34/41.99  |              op(e0, e2) = all_56_15 & $i(all_56_15))) & ((all_56_16 = e3 &
% 227.34/41.99  |              op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 & $i(all_56_17))
% 227.34/41.99  |            | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19
% 227.34/41.99  |              & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 227.34/41.99  |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 227.34/41.99  |              $i(all_56_23))) & ((all_56_24 = e3 & op(e3, all_56_25) = e3 &
% 227.34/41.99  |              op(e3, e0) = all_56_25 & $i(all_56_25)) | (all_56_26 = e2 &
% 227.34/41.99  |              op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 & $i(all_56_27))
% 227.34/41.99  |            | (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29
% 227.34/41.99  |              & $i(all_56_29)) | (all_56_30 = e0 & op(e0, all_56_31) = e0))
% 227.34/41.99  | 
% 227.34/41.99  | ALPHA: (205) implies:
% 227.34/41.99  |   (206)  op(e0, e0) = all_56_31
% 227.34/41.99  |   (207)  op(e1, e1) = all_56_21
% 227.34/41.99  |   (208)  op(e2, e2) = all_56_11
% 227.34/41.99  |   (209)  op(e3, e3) = all_56_1
% 227.34/41.99  |   (210)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 227.34/41.99  |            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 227.34/41.99  |              e0) = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1,
% 227.34/41.99  |              all_56_29) = e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) |
% 227.34/41.99  |          (all_56_30 = e0 & op(e0, all_56_31) = e0)
% 227.34/42.00  |   (211)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 227.34/42.00  |            $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 227.34/42.00  |              e1) = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1,
% 227.34/42.00  |              all_56_21) = e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 &
% 227.34/42.00  |            op(e0, e1) = all_56_23 & $i(all_56_23))
% 227.34/42.00  |   (212)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 227.34/42.00  |            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) |
% 227.34/42.00  |          (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 227.34/42.00  |            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 227.34/42.00  |              e2) = all_56_15 & $i(all_56_15))
% 227.34/42.00  |   (213)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 227.34/42.00  |              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3
% 227.34/42.00  |            & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 227.34/42.00  |              = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 227.34/42.00  |              = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 227.34/42.00  |            all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 227.34/42.00  |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 227.34/42.00  |              e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3)
% 227.34/42.00  |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 227.34/42.00  |            op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 227.34/42.00  |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 227.34/42.00  |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 227.34/42.00  |          (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 227.34/42.00  |              = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) =
% 227.34/42.00  |            e0 & op(e0, e3) = e0) | (all_56_13 = e2 & all_56_19 = e2 &  ~
% 227.34/42.00  |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 227.34/42.00  |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13
% 227.34/42.00  |            = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 227.34/42.00  |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 227.34/42.00  |              e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0)
% 227.34/42.00  |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 227.34/42.00  |            op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 227.34/42.00  |            e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 227.34/42.00  |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 227.34/42.00  |          (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 227.34/42.00  |              = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) =
% 227.34/42.00  |            e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 227.34/42.00  |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 227.34/42.00  |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 227.34/42.00  |   (214)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 227.34/42.00  |              all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) |
% 227.34/42.00  |          (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 227.34/42.00  |            $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 227.34/42.00  |            = all_56_7 & $i(all_56_7))
% 227.34/42.00  | 
% 227.34/42.00  | DELTA: instantiating (2) with fresh symbols all_58_0, all_58_1, all_58_2,
% 227.34/42.00  |        all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9,
% 227.34/42.00  |        all_58_10, all_58_11, all_58_12, all_58_13, all_58_14, all_58_15 gives:
% 227.34/42.02  |   (215)  ((all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 227.34/42.02  |              e3) | (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 227.34/42.02  |                e0) = e3)) & ((all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 =
% 227.34/42.02  |              e3 & op(e2, e3) = e3) | (all_58_6 = e3 & op(e1, e3) = e3) |
% 227.34/42.02  |            (all_58_12 = e3 & op(e0, e3) = e3)) & ((all_58_0 = e2 & op(e3, e3)
% 227.34/42.02  |              = e2) | (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_4 = e2 &
% 227.34/42.02  |              op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)) &
% 227.34/42.02  |          ((all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 227.34/42.02  |              e2) | (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 &
% 227.34/42.02  |              op(e0, e3) = e2)) & ((all_58_0 = e1 & op(e3, e3) = e1) |
% 227.34/42.02  |            (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_4 = e1 & op(e3, e1) =
% 227.34/42.02  |              e1) | (all_58_9 = e1 & op(e3, e0) = e1)) & ((all_58_0 = e1 &
% 227.34/42.02  |              op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_6
% 227.34/42.02  |              = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)) &
% 227.34/42.02  |          ((all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 227.34/42.02  |              e0) | (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 227.34/42.02  |                e0) = e0)) & ((all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 =
% 227.34/42.02  |              e0 & op(e2, e3) = e0) | (all_58_6 = e0 & op(e1, e3) = e0) |
% 227.34/42.02  |            (all_58_12 = e0 & op(e0, e3) = e0)) & ((all_58_1 = e3 & op(e3, e2)
% 227.34/42.02  |              = e3) | (all_58_3 = e3 & op(e2, e2) = e3) | (all_58_7 = e3 &
% 227.34/42.02  |              op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)) &
% 227.34/42.02  |          ((all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 227.34/42.02  |              e2) | (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 &
% 227.34/42.02  |              op(e0, e2) = e2)) & ((all_58_1 = e1 & op(e3, e2) = e1) |
% 227.34/42.02  |            (all_58_3 = e1 & op(e2, e2) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 227.34/42.02  |              e1) | (all_58_13 = e1 & op(e0, e2) = e1)) & ((all_58_1 = e0 &
% 227.34/42.02  |              op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) | (all_58_7
% 227.34/42.02  |              = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)) &
% 227.34/42.02  |          ((all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 227.34/42.02  |              e3) | (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 &
% 227.34/42.02  |              op(e2, e0) = e3)) & ((all_58_2 = e2 & op(e2, e3) = e2) |
% 227.34/42.02  |            (all_58_3 = e2 & op(e2, e2) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 227.34/42.02  |              e2) | (all_58_10 = e2 & op(e2, e0) = e2)) & ((all_58_2 = e1 &
% 227.34/42.02  |              op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) | (all_58_5
% 227.34/42.02  |              = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)) &
% 227.34/42.02  |          ((all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 227.34/42.02  |              e0) | (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 227.34/42.02  |              op(e2, e0) = e0)) & ((all_58_4 = e3 & op(e3, e1) = e3) |
% 227.34/42.02  |            (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_8 = e3 & op(e1, e1) =
% 227.34/42.02  |              e3) | (all_58_14 = e3 & op(e0, e1) = e3)) & ((all_58_4 = e2 &
% 227.34/42.02  |              op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_8
% 227.34/42.02  |              = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)) &
% 227.34/42.02  |          ((all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 227.34/42.02  |              e1) | (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 227.34/42.02  |              op(e0, e1) = e1)) & ((all_58_4 = e0 & op(e3, e1) = e0) |
% 227.34/42.02  |            (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_8 = e0 & op(e1, e1) =
% 227.34/42.02  |              e0) | (all_58_14 = e0 & op(e0, e1) = e0)) & ((all_58_6 = e3 &
% 227.34/42.02  |              op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_8
% 227.34/42.02  |              = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)) &
% 227.34/42.02  |          ((all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 227.34/42.02  |              e2) | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 227.34/42.02  |              op(e1, e0) = e2)) & ((all_58_6 = e1 & op(e1, e3) = e1) |
% 227.34/42.02  |            (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_8 = e1 & op(e1, e1) =
% 227.34/42.02  |              e1) | (all_58_11 = e1 & op(e1, e0) = e1)) & ((all_58_6 = e0 &
% 227.34/42.02  |              op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_8
% 227.34/42.02  |              = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 227.34/42.02  |          ((all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 227.34/42.02  |              e3) | (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 227.34/42.02  |              op(e0, e0) = e3)) & ((all_58_9 = e2 & op(e3, e0) = e2) |
% 227.34/42.02  |            (all_58_10 = e2 & op(e2, e0) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 227.34/42.02  |              e2) | (all_58_15 = e2 & op(e0, e0) = e2)) & ((all_58_9 = e1 &
% 227.34/42.02  |              op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 227.34/42.02  |            (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 227.34/42.02  |              e1)) & ((all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 227.34/42.02  |              op(e0, e2) = e3) | (all_58_14 = e3 & op(e0, e1) = e3) |
% 227.34/42.02  |            (all_58_15 = e3 & op(e0, e0) = e3)) & ((all_58_12 = e2 & op(e0, e3)
% 227.34/42.02  |              = e2) | (all_58_13 = e2 & op(e0, e2) = e2) | (all_58_14 = e2 &
% 227.34/42.02  |              op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)) &
% 227.34/42.02  |          ((all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 227.34/42.02  |              e1) | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 227.34/42.02  |              op(e0, e0) = e1)) & ((all_58_15 = e0 & op(e0, e0) = e0) |
% 227.34/42.02  |            (((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 227.34/42.02  |                  = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 =
% 227.34/42.02  |                  e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 227.34/42.02  |                (all_58_14 = e0 & op(e0, e1) = e0))))
% 227.74/42.02  | 
% 227.74/42.02  | ALPHA: (215) implies:
% 227.74/42.02  |   (216)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 227.74/42.02  |                e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 227.74/42.02  |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 227.74/42.02  |              (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 227.74/42.02  |                = e0)))
% 227.74/42.02  |   (217)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 227.74/42.02  |            e1) | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 227.74/42.02  |              e0) = e1)
% 227.74/42.02  |   (218)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 227.74/42.02  |            e2) | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 227.74/42.02  |              e0) = e2)
% 227.74/42.02  |   (219)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 227.74/42.02  |            e3) | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 227.74/42.02  |              e0) = e3)
% 227.74/42.02  |   (220)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 227.74/42.02  |            e1) | (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 227.74/42.02  |              e0) = e1)
% 227.74/42.02  |   (221)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 227.74/42.02  |            e2) | (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 227.74/42.02  |              e0) = e2)
% 227.74/42.02  |   (222)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 227.74/42.02  |            e3) | (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 227.74/42.02  |              e0) = e3)
% 227.74/42.02  |   (223)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 227.74/42.02  |          | (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 227.74/42.02  |            e0)
% 227.74/42.03  |   (224)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 227.74/42.03  |          | (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 227.74/42.03  |            e1)
% 227.74/42.03  |   (225)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 227.74/42.03  |          | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 227.74/42.03  |            e2)
% 227.74/42.03  |   (226)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 227.74/42.03  |          | (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 227.74/42.03  |            e3)
% 227.74/42.03  |   (227)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 227.74/42.03  |          | (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 227.74/42.03  |            e0)
% 227.74/42.03  |   (228)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 227.74/42.03  |          | (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 227.74/42.03  |            e1)
% 227.74/42.03  |   (229)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2)
% 227.74/42.03  |          | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 227.74/42.03  |            e2)
% 227.74/42.03  |   (230)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 227.74/42.03  |          | (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 227.74/42.03  |            e3)
% 227.74/42.03  |   (231)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 227.74/42.03  |          | (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 227.74/42.03  |            e0)
% 227.74/42.03  |   (232)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 227.74/42.03  |          | (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 227.74/42.03  |            e1)
% 227.74/42.03  |   (233)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 227.74/42.03  |          | (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 227.74/42.03  |            e2)
% 227.74/42.03  |   (234)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 227.74/42.03  |          | (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 227.74/42.03  |            e3)
% 227.74/42.03  |   (235)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 227.74/42.03  |          | (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 227.74/42.03  |            e0)
% 227.74/42.03  |   (236)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 227.74/42.03  |          | (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 227.74/42.03  |            e1)
% 227.74/42.03  |   (237)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 227.74/42.03  |          | (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 227.74/42.03  |            e2)
% 227.74/42.03  |   (238)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 227.74/42.03  |          | (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 227.74/42.03  |            e3)
% 227.74/42.04  |   (239)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 227.74/42.04  |          | (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 227.74/42.04  |            e0)
% 227.74/42.04  |   (240)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 227.74/42.04  |          | (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 227.74/42.04  |            e0)
% 227.74/42.04  |   (241)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 227.74/42.04  |          | (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 227.74/42.04  |            e1)
% 227.74/42.04  |   (242)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 227.74/42.04  |          | (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 227.74/42.04  |            e1)
% 227.74/42.04  |   (243)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 227.74/42.04  |          | (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 227.74/42.04  |            e2)
% 227.74/42.04  |   (244)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 227.74/42.04  |          | (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 227.74/42.04  |            e2)
% 227.74/42.04  |   (245)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 227.74/42.04  |          | (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 227.74/42.04  |            e3)
% 227.74/42.04  |   (246)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 227.74/42.04  |          | (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 227.74/42.04  |            e3)
% 227.74/42.04  | 
% 227.74/42.04  | GROUND_INST: instantiating (function-axioms) with all_12_2, all_20_2, e0, e0,
% 227.74/42.04  |              simplifying with (48), (60) gives:
% 227.74/42.04  |   (247)  all_20_2 = all_12_2
% 227.74/42.04  | 
% 227.74/42.04  | GROUND_INST: instantiating (function-axioms) with all_26_2, all_34_2, e0, e0,
% 227.74/42.04  |              simplifying with (69), (81) gives:
% 227.74/42.04  |   (248)  all_34_2 = all_26_2
% 227.74/42.04  | 
% 227.74/42.04  | GROUND_INST: instantiating (function-axioms) with all_20_2, all_34_2, e0, e0,
% 227.74/42.04  |              simplifying with (60), (81) gives:
% 227.74/42.04  |   (249)  all_34_2 = all_20_2
% 227.74/42.04  | 
% 227.74/42.04  | GROUND_INST: instantiating (function-axioms) with all_34_2, all_44_2, e0, e0,
% 227.74/42.04  |              simplifying with (81), (96) gives:
% 227.74/42.04  |   (250)  all_44_2 = all_34_2
% 227.74/42.04  | 
% 227.74/42.04  | GROUND_INST: instantiating (function-axioms) with all_44_2, all_52_15, e0, e0,
% 227.74/42.04  |              simplifying with (96), (156) gives:
% 227.74/42.04  |   (251)  all_52_15 = all_44_2
% 227.74/42.04  | 
% 227.74/42.04  | GROUND_INST: instantiating (function-axioms) with all_52_15, all_54_15, e0,
% 227.74/42.04  |              e0, simplifying with (156), (173) gives:
% 227.74/42.04  |   (252)  all_54_15 = all_52_15
% 227.74/42.04  | 
% 227.74/42.04  | GROUND_INST: instantiating (function-axioms) with all_54_15, all_56_31, e0,
% 227.74/42.04  |              e0, simplifying with (173), (206) gives:
% 227.74/42.04  |   (253)  all_56_31 = all_54_15
% 227.74/42.04  | 
% 227.74/42.04  | GROUND_INST: instantiating (function-axioms) with all_4_2, all_56_31, e0, e0,
% 227.74/42.04  |              simplifying with (36), (206) gives:
% 227.74/42.04  |   (254)  all_56_31 = all_4_2
% 227.74/42.04  | 
% 227.74/42.04  | GROUND_INST: instantiating (function-axioms) with all_52_11, all_54_14, e1,
% 227.74/42.04  |              e0, simplifying with (157), (174) gives:
% 227.74/42.04  |   (255)  all_54_14 = all_52_11
% 227.74/42.04  | 
% 227.74/42.04  | GROUND_INST: instantiating (function-axioms) with all_52_7, all_54_13, e2, e0,
% 227.74/42.04  |              simplifying with (158), (175) gives:
% 227.74/42.04  |   (256)  all_54_13 = all_52_7
% 227.74/42.04  | 
% 227.74/42.04  | GROUND_INST: instantiating (function-axioms) with all_52_3, all_54_12, e3, e0,
% 227.74/42.04  |              simplifying with (159), (176) gives:
% 227.74/42.05  |   (257)  all_54_12 = all_52_3
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_52_14, all_54_11, e0,
% 227.74/42.05  |              e1, simplifying with (160), (177) gives:
% 227.74/42.05  |   (258)  all_54_11 = all_52_14
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_18_2, all_28_2, e1, e1,
% 227.74/42.05  |              simplifying with (57), (72) gives:
% 227.74/42.05  |   (259)  all_28_2 = all_18_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_28_2, all_36_2, e1, e1,
% 227.74/42.05  |              simplifying with (72), (84) gives:
% 227.74/42.05  |   (260)  all_36_2 = all_28_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_46_2, all_52_10, e1, e1,
% 227.74/42.05  |              simplifying with (99), (161) gives:
% 227.74/42.05  |   (261)  all_52_10 = all_46_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_40_2, all_52_10, e1, e1,
% 227.74/42.05  |              simplifying with (90), (161) gives:
% 227.74/42.05  |   (262)  all_52_10 = all_40_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_36_2, all_52_10, e1, e1,
% 227.74/42.05  |              simplifying with (84), (161) gives:
% 227.74/42.05  |   (263)  all_52_10 = all_36_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_46_2, all_54_10, e1, e1,
% 227.74/42.05  |              simplifying with (99), (178) gives:
% 227.74/42.05  |   (264)  all_54_10 = all_46_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_54_10, all_56_21, e1,
% 227.74/42.05  |              e1, simplifying with (178), (207) gives:
% 227.74/42.05  |   (265)  all_56_21 = all_54_10
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_6_2, all_56_21, e1, e1,
% 227.74/42.05  |              simplifying with (39), (207) gives:
% 227.74/42.05  |   (266)  all_56_21 = all_6_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_52_6, all_54_9, e2, e1,
% 227.74/42.05  |              simplifying with (162), (179) gives:
% 227.74/42.05  |   (267)  all_54_9 = all_52_6
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_52_2, all_54_8, e3, e1,
% 227.74/42.05  |              simplifying with (163), (180) gives:
% 227.74/42.05  |   (268)  all_54_8 = all_52_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_52_13, all_54_7, e0, e2,
% 227.74/42.05  |              simplifying with (164), (181) gives:
% 227.74/42.05  |   (269)  all_54_7 = all_52_13
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_52_9, all_54_6, e1, e2,
% 227.74/42.05  |              simplifying with (165), (182) gives:
% 227.74/42.05  |   (270)  all_54_6 = all_52_9
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_22_2, all_30_2, e2, e2,
% 227.74/42.05  |              simplifying with (63), (75) gives:
% 227.74/42.05  |   (271)  all_30_2 = all_22_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_14_2, all_30_2, e2, e2,
% 227.74/42.05  |              simplifying with (51), (75) gives:
% 227.74/42.05  |   (272)  all_30_2 = all_14_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_22_2, all_42_2, e2, e2,
% 227.74/42.05  |              simplifying with (63), (93) gives:
% 227.74/42.05  |   (273)  all_42_2 = all_22_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_52_5, all_54_5, e2, e2,
% 227.74/42.05  |              simplifying with (166), (183) gives:
% 227.74/42.05  |   (274)  all_54_5 = all_52_5
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_8_2, all_54_5, e2, e2,
% 227.74/42.05  |              simplifying with (42), (183) gives:
% 227.74/42.05  |   (275)  all_54_5 = all_8_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_52_5, all_56_11, e2, e2,
% 227.74/42.05  |              simplifying with (166), (208) gives:
% 227.74/42.05  |   (276)  all_56_11 = all_52_5
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_48_2, all_56_11, e2, e2,
% 227.74/42.05  |              simplifying with (102), (208) gives:
% 227.74/42.05  |   (277)  all_56_11 = all_48_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_42_2, all_56_11, e2, e2,
% 227.74/42.05  |              simplifying with (93), (208) gives:
% 227.74/42.05  |   (278)  all_56_11 = all_42_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_52_1, all_54_4, e3, e2,
% 227.74/42.05  |              simplifying with (167), (184) gives:
% 227.74/42.05  |   (279)  all_54_4 = all_52_1
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_52_12, all_54_3, e0, e3,
% 227.74/42.05  |              simplifying with (168), (185) gives:
% 227.74/42.05  |   (280)  all_54_3 = all_52_12
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_52_8, all_54_2, e1, e3,
% 227.74/42.05  |              simplifying with (169), (186) gives:
% 227.74/42.05  |   (281)  all_54_2 = all_52_8
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_52_4, all_54_1, e2, e3,
% 227.74/42.05  |              simplifying with (170), (187) gives:
% 227.74/42.05  |   (282)  all_54_1 = all_52_4
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_24_2, all_32_2, e3, e3,
% 227.74/42.05  |              simplifying with (66), (78) gives:
% 227.74/42.05  |   (283)  all_32_2 = all_24_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_32_2, all_38_2, e3, e3,
% 227.74/42.05  |              simplifying with (78), (87) gives:
% 227.74/42.05  |   (284)  all_38_2 = all_32_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_38_2, all_50_2, e3, e3,
% 227.74/42.05  |              simplifying with (87), (105) gives:
% 227.74/42.05  |   (285)  all_50_2 = all_38_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_50_2, all_52_0, e3, e3,
% 227.74/42.05  |              simplifying with (105), (171) gives:
% 227.74/42.05  |   (286)  all_52_0 = all_50_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_16_2, all_52_0, e3, e3,
% 227.74/42.05  |              simplifying with (54), (171) gives:
% 227.74/42.05  |   (287)  all_52_0 = all_16_2
% 227.74/42.05  | 
% 227.74/42.05  | GROUND_INST: instantiating (function-axioms) with all_24_2, all_54_0, e3, e3,
% 227.74/42.06  |              simplifying with (66), (188) gives:
% 227.74/42.06  |   (288)  all_54_0 = all_24_2
% 227.74/42.06  | 
% 227.74/42.06  | GROUND_INST: instantiating (function-axioms) with all_54_0, all_56_1, e3, e3,
% 227.74/42.06  |              simplifying with (188), (209) gives:
% 227.74/42.06  |   (289)  all_56_1 = all_54_0
% 227.74/42.06  | 
% 227.74/42.06  | GROUND_INST: instantiating (function-axioms) with all_10_2, all_56_1, e3, e3,
% 227.74/42.06  |              simplifying with (45), (209) gives:
% 227.74/42.06  |   (290)  all_56_1 = all_10_2
% 227.74/42.06  | 
% 227.74/42.06  | COMBINE_EQS: (289), (290) imply:
% 227.74/42.06  |   (291)  all_54_0 = all_10_2
% 227.74/42.06  | 
% 227.74/42.06  | SIMP: (291) implies:
% 227.74/42.06  |   (292)  all_54_0 = all_10_2
% 227.74/42.06  | 
% 227.74/42.06  | COMBINE_EQS: (276), (277) imply:
% 227.74/42.06  |   (293)  all_52_5 = all_48_2
% 227.74/42.06  | 
% 227.74/42.06  | SIMP: (293) implies:
% 227.74/42.06  |   (294)  all_52_5 = all_48_2
% 227.74/42.06  | 
% 227.74/42.06  | COMBINE_EQS: (277), (278) imply:
% 227.74/42.06  |   (295)  all_48_2 = all_42_2
% 227.74/42.06  | 
% 227.74/42.06  | COMBINE_EQS: (265), (266) imply:
% 227.74/42.06  |   (296)  all_54_10 = all_6_2
% 227.74/42.06  | 
% 227.74/42.06  | SIMP: (296) implies:
% 227.74/42.06  |   (297)  all_54_10 = all_6_2
% 227.74/42.06  | 
% 227.74/42.06  | COMBINE_EQS: (253), (254) imply:
% 227.74/42.06  |   (298)  all_54_15 = all_4_2
% 227.74/42.06  | 
% 227.74/42.06  | SIMP: (298) implies:
% 227.74/42.06  |   (299)  all_54_15 = all_4_2
% 227.74/42.06  | 
% 227.74/42.06  | COMBINE_EQS: (288), (292) imply:
% 227.74/42.06  |   (300)  all_24_2 = all_10_2
% 227.74/42.06  | 
% 227.74/42.06  | SIMP: (300) implies:
% 227.74/42.06  |   (301)  all_24_2 = all_10_2
% 227.74/42.06  | 
% 227.74/42.06  | COMBINE_EQS: (274), (275) imply:
% 227.74/42.06  |   (302)  all_52_5 = all_8_2
% 227.74/42.06  | 
% 227.74/42.06  | SIMP: (302) implies:
% 227.74/42.06  |   (303)  all_52_5 = all_8_2
% 227.74/42.06  | 
% 227.74/42.06  | COMBINE_EQS: (264), (297) imply:
% 227.74/42.06  |   (304)  all_46_2 = all_6_2
% 227.74/42.06  | 
% 227.74/42.06  | SIMP: (304) implies:
% 227.74/42.06  |   (305)  all_46_2 = all_6_2
% 227.74/42.06  | 
% 227.74/42.06  | COMBINE_EQS: (252), (299) imply:
% 227.74/42.06  |   (306)  all_52_15 = all_4_2
% 227.74/42.06  | 
% 227.74/42.06  | SIMP: (306) implies:
% 227.74/42.06  |   (307)  all_52_15 = all_4_2
% 227.74/42.06  | 
% 227.74/42.06  | COMBINE_EQS: (286), (287) imply:
% 227.74/42.06  |   (308)  all_50_2 = all_16_2
% 227.74/42.06  | 
% 228.18/42.06  | SIMP: (308) implies:
% 228.18/42.06  |   (309)  all_50_2 = all_16_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (294), (303) imply:
% 228.18/42.06  |   (310)  all_48_2 = all_8_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (310) implies:
% 228.18/42.06  |   (311)  all_48_2 = all_8_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (261), (262) imply:
% 228.18/42.06  |   (312)  all_46_2 = all_40_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (312) implies:
% 228.18/42.06  |   (313)  all_46_2 = all_40_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (262), (263) imply:
% 228.18/42.06  |   (314)  all_40_2 = all_36_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (251), (307) imply:
% 228.18/42.06  |   (315)  all_44_2 = all_4_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (315) implies:
% 228.18/42.06  |   (316)  all_44_2 = all_4_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (285), (309) imply:
% 228.18/42.06  |   (317)  all_38_2 = all_16_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (317) implies:
% 228.18/42.06  |   (318)  all_38_2 = all_16_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (295), (311) imply:
% 228.18/42.06  |   (319)  all_42_2 = all_8_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (319) implies:
% 228.18/42.06  |   (320)  all_42_2 = all_8_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (305), (313) imply:
% 228.18/42.06  |   (321)  all_40_2 = all_6_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (321) implies:
% 228.18/42.06  |   (322)  all_40_2 = all_6_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (250), (316) imply:
% 228.18/42.06  |   (323)  all_34_2 = all_4_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (323) implies:
% 228.18/42.06  |   (324)  all_34_2 = all_4_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (273), (320) imply:
% 228.18/42.06  |   (325)  all_22_2 = all_8_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (325) implies:
% 228.18/42.06  |   (326)  all_22_2 = all_8_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (314), (322) imply:
% 228.18/42.06  |   (327)  all_36_2 = all_6_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (327) implies:
% 228.18/42.06  |   (328)  all_36_2 = all_6_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (284), (318) imply:
% 228.18/42.06  |   (329)  all_32_2 = all_16_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (329) implies:
% 228.18/42.06  |   (330)  all_32_2 = all_16_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (260), (328) imply:
% 228.18/42.06  |   (331)  all_28_2 = all_6_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (331) implies:
% 228.18/42.06  |   (332)  all_28_2 = all_6_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (248), (249) imply:
% 228.18/42.06  |   (333)  all_26_2 = all_20_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (248), (324) imply:
% 228.18/42.06  |   (334)  all_26_2 = all_4_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (283), (330) imply:
% 228.18/42.06  |   (335)  all_24_2 = all_16_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (335) implies:
% 228.18/42.06  |   (336)  all_24_2 = all_16_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (271), (272) imply:
% 228.18/42.06  |   (337)  all_22_2 = all_14_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (337) implies:
% 228.18/42.06  |   (338)  all_22_2 = all_14_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (259), (332) imply:
% 228.18/42.06  |   (339)  all_18_2 = all_6_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (333), (334) imply:
% 228.18/42.06  |   (340)  all_20_2 = all_4_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (340) implies:
% 228.18/42.06  |   (341)  all_20_2 = all_4_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (301), (336) imply:
% 228.18/42.06  |   (342)  all_16_2 = all_10_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (326), (338) imply:
% 228.18/42.06  |   (343)  all_14_2 = all_8_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (343) implies:
% 228.18/42.06  |   (344)  all_14_2 = all_8_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (247), (341) imply:
% 228.18/42.06  |   (345)  all_12_2 = all_4_2
% 228.18/42.06  | 
% 228.18/42.06  | SIMP: (345) implies:
% 228.18/42.06  |   (346)  all_12_2 = all_4_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (272), (344) imply:
% 228.18/42.06  |   (347)  all_30_2 = all_8_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (330), (342) imply:
% 228.18/42.06  |   (348)  all_32_2 = all_10_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (318), (342) imply:
% 228.18/42.06  |   (349)  all_38_2 = all_10_2
% 228.18/42.06  | 
% 228.18/42.06  | COMBINE_EQS: (309), (342) imply:
% 228.18/42.07  |   (350)  all_50_2 = all_10_2
% 228.18/42.07  | 
% 228.18/42.07  | COMBINE_EQS: (262), (322) imply:
% 228.18/42.07  |   (351)  all_52_10 = all_6_2
% 228.18/42.07  | 
% 228.18/42.07  | COMBINE_EQS: (287), (342) imply:
% 228.18/42.07  |   (352)  all_52_0 = all_10_2
% 228.18/42.07  | 
% 228.18/42.07  | COMBINE_EQS: (277), (311) imply:
% 228.18/42.07  |   (353)  all_56_11 = all_8_2
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (155), (352) imply:
% 228.18/42.07  |   (354)   ~ (all_52_1 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (354) implies:
% 228.18/42.07  |   (355)   ~ (all_52_1 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (154), (352) imply:
% 228.18/42.07  |   (356)   ~ (all_52_2 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (356) implies:
% 228.18/42.07  |   (357)   ~ (all_52_2 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (153), (352) imply:
% 228.18/42.07  |   (358)   ~ (all_52_3 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (358) implies:
% 228.18/42.07  |   (359)   ~ (all_52_3 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (152), (352) imply:
% 228.18/42.07  |   (360)   ~ (all_52_4 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (360) implies:
% 228.18/42.07  |   (361)   ~ (all_52_4 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (151), (352) imply:
% 228.18/42.07  |   (362)   ~ (all_52_8 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (362) implies:
% 228.18/42.07  |   (363)   ~ (all_52_8 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (150), (352) imply:
% 228.18/42.07  |   (364)   ~ (all_52_12 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (364) implies:
% 228.18/42.07  |   (365)   ~ (all_52_12 = all_10_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (147), (303) imply:
% 228.18/42.07  |   (366)   ~ (all_52_1 = all_8_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (142), (351) imply:
% 228.18/42.07  |   (367)   ~ (all_52_2 = all_6_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (138), (307) imply:
% 228.18/42.07  |   (368)   ~ (all_52_3 = all_4_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (137), (303) imply:
% 228.18/42.07  |   (369)   ~ (all_52_4 = all_8_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (132), (303) imply:
% 228.18/42.07  |   (370)   ~ (all_52_6 = all_8_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (370) implies:
% 228.18/42.07  |   (371)   ~ (all_52_6 = all_8_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (131), (303) imply:
% 228.18/42.07  |   (372)   ~ (all_52_7 = all_8_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (372) implies:
% 228.18/42.07  |   (373)   ~ (all_52_7 = all_8_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (130), (303) imply:
% 228.18/42.07  |   (374)   ~ (all_52_9 = all_8_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (374) implies:
% 228.18/42.07  |   (375)   ~ (all_52_9 = all_8_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (129), (303) imply:
% 228.18/42.07  |   (376)   ~ (all_52_13 = all_8_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (376) implies:
% 228.18/42.07  |   (377)   ~ (all_52_13 = all_8_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (127), (351) imply:
% 228.18/42.07  |   (378)   ~ (all_52_6 = all_6_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (124), (307) imply:
% 228.18/42.07  |   (379)   ~ (all_52_7 = all_4_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (122), (351) imply:
% 228.18/42.07  |   (380)   ~ (all_52_8 = all_6_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (119), (351) imply:
% 228.18/42.07  |   (381)   ~ (all_52_9 = all_6_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (116), (351) imply:
% 228.18/42.07  |   (382)   ~ (all_52_11 = all_6_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (382) implies:
% 228.18/42.07  |   (383)   ~ (all_52_11 = all_6_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (115), (351) imply:
% 228.18/42.07  |   (384)   ~ (all_52_14 = all_6_2)
% 228.18/42.07  | 
% 228.18/42.07  | SIMP: (384) implies:
% 228.18/42.07  |   (385)   ~ (all_52_14 = all_6_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (114), (307) imply:
% 228.18/42.07  |   (386)   ~ (all_52_11 = all_4_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (111), (307) imply:
% 228.18/42.07  |   (387)   ~ (all_52_12 = all_4_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (109), (307) imply:
% 228.18/42.07  |   (388)   ~ (all_52_13 = all_4_2)
% 228.18/42.07  | 
% 228.18/42.07  | REDUCE: (108), (307) imply:
% 228.18/42.07  |   (389)   ~ (all_52_14 = all_4_2)
% 228.18/42.07  | 
% 228.18/42.07  | BETA: splitting (37) gives:
% 228.18/42.07  | 
% 228.18/42.07  | Case 1:
% 228.18/42.07  | | 
% 228.18/42.07  | |   (390)   ~ (all_4_2 = e2)
% 228.18/42.07  | | 
% 228.18/42.07  | | BETA: splitting (40) gives:
% 228.18/42.07  | | 
% 228.18/42.07  | | Case 1:
% 228.18/42.07  | | | 
% 228.18/42.07  | | |   (391)   ~ (all_6_2 = e3)
% 228.18/42.07  | | | 
% 228.18/42.07  | | | BETA: splitting (43) gives:
% 228.18/42.07  | | | 
% 228.18/42.07  | | | Case 1:
% 228.18/42.07  | | | | 
% 228.18/42.07  | | | |   (392)   ~ (all_8_2 = e3)
% 228.18/42.07  | | | | 
% 228.18/42.07  | | | | BETA: splitting (46) gives:
% 228.18/42.07  | | | | 
% 228.18/42.07  | | | | Case 1:
% 228.18/42.07  | | | | | 
% 228.18/42.07  | | | | |   (393)   ~ (all_10_2 = e1)
% 228.18/42.07  | | | | | 
% 228.18/42.07  | | | | | BETA: splitting (49) gives:
% 228.18/42.07  | | | | | 
% 228.18/42.07  | | | | | Case 1:
% 228.18/42.07  | | | | | | 
% 228.18/42.07  | | | | | |   (394)   ~ (all_12_2 = e3)
% 228.18/42.07  | | | | | | 
% 228.18/42.07  | | | | | | REDUCE: (346), (394) imply:
% 228.18/42.07  | | | | | |   (395)   ~ (all_4_2 = e3)
% 228.18/42.07  | | | | | | 
% 228.18/42.07  | | | | | | BETA: splitting (52) gives:
% 228.18/42.07  | | | | | | 
% 228.18/42.07  | | | | | | Case 1:
% 228.18/42.07  | | | | | | | 
% 228.18/42.07  | | | | | | |   (396)   ~ (all_14_2 = e0)
% 228.18/42.07  | | | | | | | 
% 228.18/42.07  | | | | | | | REDUCE: (344), (396) imply:
% 228.18/42.07  | | | | | | |   (397)   ~ (all_8_2 = e0)
% 228.18/42.07  | | | | | | | 
% 228.18/42.07  | | | | | | | BETA: splitting (55) gives:
% 228.18/42.07  | | | | | | | 
% 228.18/42.07  | | | | | | | Case 1:
% 228.18/42.07  | | | | | | | | 
% 228.18/42.07  | | | | | | | |   (398)   ~ (all_16_2 = e0)
% 228.18/42.07  | | | | | | | | 
% 228.18/42.07  | | | | | | | | REDUCE: (342), (398) imply:
% 228.18/42.07  | | | | | | | |   (399)   ~ (all_10_2 = e0)
% 228.18/42.07  | | | | | | | | 
% 228.18/42.07  | | | | | | | | BETA: splitting (58) gives:
% 228.18/42.07  | | | | | | | | 
% 228.18/42.07  | | | | | | | | Case 1:
% 228.18/42.07  | | | | | | | | | 
% 228.18/42.07  | | | | | | | | |   (400)   ~ (all_18_2 = e0)
% 228.18/42.07  | | | | | | | | | 
% 228.18/42.07  | | | | | | | | | REDUCE: (339), (400) imply:
% 228.18/42.07  | | | | | | | | |   (401)   ~ (all_6_2 = e0)
% 228.18/42.07  | | | | | | | | | 
% 228.18/42.08  | | | | | | | | | BETA: splitting (61) gives:
% 228.18/42.08  | | | | | | | | | 
% 228.18/42.08  | | | | | | | | | Case 1:
% 228.18/42.08  | | | | | | | | | | 
% 228.18/42.08  | | | | | | | | | |   (402)   ~ (all_20_2 = e1)
% 228.18/42.08  | | | | | | | | | | 
% 228.18/42.08  | | | | | | | | | | REDUCE: (341), (402) imply:
% 228.18/42.08  | | | | | | | | | |   (403)   ~ (all_4_2 = e1)
% 228.18/42.08  | | | | | | | | | | 
% 228.18/42.08  | | | | | | | | | | BETA: splitting (189) gives:
% 228.18/42.08  | | | | | | | | | | 
% 228.18/42.08  | | | | | | | | | | Case 1:
% 228.18/42.08  | | | | | | | | | | | 
% 228.18/42.08  | | | | | | | | | | |   (404)  all_54_15 = e3
% 228.29/42.09  | | | | | | | | | | | 
% 228.29/42.09  | | | | | | | | | | | REF_CLOSE: (299), (395), (404) are inconsistent by sub-proof
% 228.29/42.09  | | | | | | | | | | |            #2340.
% 228.29/42.09  | | | | | | | | | | | 
% 228.29/42.09  | | | | | | | | | | Case 2:
% 228.29/42.09  | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | |   (405)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 228.29/42.10  | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | BETA: splitting (405) gives:
% 228.29/42.10  | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | Case 1:
% 228.29/42.10  | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | |   (406)  all_54_15 = e2
% 228.29/42.10  | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | REF_CLOSE: (299), (390), (406) are inconsistent by sub-proof
% 228.29/42.10  | | | | | | | | | | | |            #2339.
% 228.29/42.10  | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | Case 2:
% 228.29/42.10  | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | |   (407)  all_54_15 = e1 | all_54_15 = e0
% 228.29/42.10  | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | BETA: splitting (407) gives:
% 228.29/42.10  | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | Case 1:
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | |   (408)  all_54_15 = e1
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | REF_CLOSE: (299), (403), (408) are inconsistent by sub-proof
% 228.29/42.10  | | | | | | | | | | | | |            #2338.
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | Case 2:
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | |   (409)  all_54_15 = e0
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | COMBINE_EQS: (299), (409) imply:
% 228.29/42.10  | | | | | | | | | | | | |   (410)  all_4_2 = e0
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | SIMP: (410) implies:
% 228.29/42.10  | | | | | | | | | | | | |   (411)  all_4_2 = e0
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | COMBINE_EQS: (254), (411) imply:
% 228.29/42.10  | | | | | | | | | | | | |   (412)  all_56_31 = e0
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | REDUCE: (368), (411) imply:
% 228.29/42.10  | | | | | | | | | | | | |   (413)   ~ (all_52_3 = e0)
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | REDUCE: (387), (411) imply:
% 228.29/42.10  | | | | | | | | | | | | |   (414)   ~ (all_52_12 = e0)
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | REDUCE: (388), (411) imply:
% 228.29/42.10  | | | | | | | | | | | | |   (415)   ~ (all_52_13 = e0)
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | REDUCE: (389), (411) imply:
% 228.29/42.10  | | | | | | | | | | | | |   (416)   ~ (all_52_14 = e0)
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | REDUCE: (36), (411) imply:
% 228.29/42.10  | | | | | | | | | | | | |   (417)  op(e0, e0) = e0
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 228.29/42.10  | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | Case 1:
% 228.29/42.10  | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | |   (418)   ~ (all_22_2 = e1)
% 228.29/42.10  | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | REDUCE: (326), (418) imply:
% 228.29/42.10  | | | | | | | | | | | | | |   (419)   ~ (all_8_2 = e1)
% 228.29/42.10  | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 228.29/42.10  | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | Case 1:
% 228.29/42.10  | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | |   (420)  all_54_5 = e3
% 228.29/42.10  | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | COMBINE_EQS: (275), (420) imply:
% 228.29/42.10  | | | | | | | | | | | | | | |   (421)  all_8_2 = e3
% 228.29/42.10  | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | REDUCE: (392), (421) imply:
% 228.29/42.10  | | | | | | | | | | | | | | |   (422)  $false
% 228.29/42.10  | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | CLOSE: (422) is inconsistent.
% 228.29/42.10  | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | Case 2:
% 228.29/42.10  | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | |   (423)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 228.29/42.10  | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | BETA: splitting (423) gives:
% 228.29/42.10  | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | Case 1:
% 228.29/42.10  | | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | |   (424)  all_54_5 = e2
% 228.29/42.10  | | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (424) imply:
% 228.29/42.10  | | | | | | | | | | | | | | | |   (425)  all_8_2 = e2
% 228.29/42.10  | | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (425) imply:
% 228.29/42.10  | | | | | | | | | | | | | | | |   (426)  all_56_11 = e2
% 228.29/42.10  | | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | | REDUCE: (366), (425) imply:
% 228.29/42.10  | | | | | | | | | | | | | | | |   (427)   ~ (all_52_1 = e2)
% 228.29/42.10  | | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | | REDUCE: (373), (425) imply:
% 228.29/42.10  | | | | | | | | | | | | | | | |   (428)   ~ (all_52_7 = e2)
% 228.29/42.10  | | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | | REDUCE: (375), (425) imply:
% 228.29/42.10  | | | | | | | | | | | | | | | |   (429)   ~ (all_52_9 = e2)
% 228.29/42.10  | | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | | REDUCE: (377), (425) imply:
% 228.29/42.10  | | | | | | | | | | | | | | | |   (430)   ~ (all_52_13 = e2)
% 228.29/42.10  | | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 228.29/42.10  | | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | | Case 1:
% 228.29/42.10  | | | | | | | | | | | | | | | | | 
% 228.29/42.10  | | | | | | | | | | | | | | | | |   (431)   ~ (all_24_2 = e2)
% 228.29/42.10  | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | REDUCE: (301), (431) imply:
% 228.29/42.11  | | | | | | | | | | | | | | | | |   (432)   ~ (all_10_2 = e2)
% 228.29/42.11  | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 228.29/42.11  | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | Case 1:
% 228.29/42.11  | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | |   (433)  all_54_0 = e3
% 228.29/42.11  | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (433) imply:
% 228.29/42.11  | | | | | | | | | | | | | | | | | |   (434)  all_10_2 = e3
% 228.29/42.11  | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | SIMP: (434) implies:
% 228.29/42.11  | | | | | | | | | | | | | | | | | |   (435)  all_10_2 = e3
% 228.29/42.11  | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (435) imply:
% 228.29/42.11  | | | | | | | | | | | | | | | | | |   (436)  all_56_1 = e3
% 228.29/42.11  | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | REDUCE: (355), (435) imply:
% 228.29/42.11  | | | | | | | | | | | | | | | | | |   (437)   ~ (all_52_1 = e3)
% 228.29/42.11  | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | REDUCE: (357), (435) imply:
% 228.29/42.11  | | | | | | | | | | | | | | | | | |   (438)   ~ (all_52_2 = e3)
% 228.29/42.11  | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | REDUCE: (359), (435) imply:
% 228.29/42.11  | | | | | | | | | | | | | | | | | |   (439)   ~ (all_52_3 = e3)
% 228.29/42.11  | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 228.29/42.11  | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | Case 1:
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |   (440)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (440) gives:
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |   (441)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            = e3)
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (427), (437), (438), (441),
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            #2333.
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |   (442)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            = e0)
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (413), (436), (439), (442),
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | |            #2329.
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | End of split
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | Case 2:
% 228.29/42.11  | | | | | | | | | | | | | | | | | | | 
% 228.29/42.11  | | | | | | | | | | | | | | | | | | |   (443)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 228.29/42.12  | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (443) gives:
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |   (444)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            = e2)
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (426), (428), (429), (444),
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            #2325.
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |   (445)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            = e0)
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (412), (415), (416), (445),
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | |            #2321.
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | End of split
% 228.29/42.12  | | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | End of split
% 228.29/42.12  | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | Case 2:
% 228.29/42.12  | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | |   (446)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 228.29/42.12  | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (399), (432), (446) are inconsistent
% 228.29/42.12  | | | | | | | | | | | | | | | | | |            by sub-proof #2319.
% 228.29/42.12  | | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | End of split
% 228.29/42.12  | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | Case 2:
% 228.29/42.12  | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | |   (447)  all_24_2 = e2
% 228.29/42.12  | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (447) imply:
% 228.29/42.12  | | | | | | | | | | | | | | | | |   (448)  all_10_2 = e2
% 228.29/42.12  | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | SIMP: (448) implies:
% 228.29/42.12  | | | | | | | | | | | | | | | | |   (449)  all_10_2 = e2
% 228.29/42.12  | | | | | | | | | | | | | | | | | 
% 228.29/42.12  | | | | | | | | | | | | | | | | | REDUCE: (359), (449) imply:
% 228.29/42.12  | | | | | | | | | | | | | | | | |   (450)   ~ (all_52_3 = e2)
% 228.29/42.12  | | | | | | | | | | | | | | | | | 
% 228.29/42.13  | | | | | | | | | | | | | | | | | REDUCE: (365), (449) imply:
% 228.29/42.13  | | | | | | | | | | | | | | | | |   (451)   ~ (all_52_12 = e2)
% 228.29/42.13  | | | | | | | | | | | | | | | | | 
% 228.29/42.13  | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 228.29/42.13  | | | | | | | | | | | | | | | | | 
% 228.29/42.13  | | | | | | | | | | | | | | | | | Case 1:
% 228.29/42.13  | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | |   (452)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 228.45/42.13  | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 228.45/42.13  | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (430), (451), (452),
% 228.45/42.13  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.45/42.13  | | | | | | | | | | | | | | | | | |            #2316.
% 228.45/42.13  | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | Case 2:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | |   (453)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 228.45/42.13  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 228.45/42.13  | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | BETA: splitting (453) gives:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | Case 1:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | |   (454)  all_58_11 = e2 & op(e1, e0) = e2
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | ALPHA: (454) implies:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | |   (455)  op(e1, e0) = e2
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | Case 1:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | |   (456)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (159), (428), (450), (456),
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | |            #2314.
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | Case 2:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | |   (457)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | BETA: splitting (457) gives:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | |   (458)  all_58_14 = e2 & op(e0, e1) = e2
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (458) implies:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | |   (459)  op(e0, e1) = e2
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | |              e2, e1, e0, simplifying with (157), (459) gives:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | |   (460)  all_52_11 = e2
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (160), (455) gives:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | |   (461)  all_52_14 = e2
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (461) imply:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | |   (462)   ~ (all_6_2 = e2)
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | SIMP: (462) implies:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | |   (463)   ~ (all_6_2 = e2)
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | |   (464)  all_54_10 = e3
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (464) are inconsistent by sub-proof
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | |            #2313.
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | |   (465)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (465) gives:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | |   (466)  all_54_10 = e2
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (463), (466) are inconsistent by sub-proof
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | |            #2312.
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | |   (467)  all_54_10 = e1 | all_54_10 = e0
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (467) gives:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | |   (468)  all_54_10 = e1
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (468) imply:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | |   (469)  all_6_2 = e1
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (469) implies:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | |   (470)  all_6_2 = e1
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (470) imply:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | |   (471)  all_56_21 = e1
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (470) imply:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | |   (472)   ~ (all_52_8 = e1)
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (470) imply:
% 228.45/42.13  | | | | | | | | | | | | | | | | | | | | | | | |   (473)   ~ (all_52_9 = e1)
% 228.45/42.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 228.45/42.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.45/42.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.45/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (474)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (474) gives:
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (475)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (426), (427), (471), (475),
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2310.
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (476)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (412), (413), (472), (476),
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2307.
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (477)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (477) gives:
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (478)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (478) gives:
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (479)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (479) implies:
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (480)  op(e2, e1) = e2
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (429), (480), (function-axioms) are
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (481)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (428), (473), (481),
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2305.
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (482)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (482) gives:
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (483)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (483) implies:
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (484)  op(e2, e0) = e0
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (415), (484), (function-axioms) are
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2324.
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (485)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (485) gives:
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (486)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e1
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (486) implies:
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  op(e1, e0) = e1
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (297), (385), (401), (467), (487),
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2302.
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (488)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e0
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (488) implies:
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  op(e1, e0) = e0
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (416), (489), (function-axioms) are
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2323.
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | |   (490)  all_54_10 = e0
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.16  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (401), (490) are inconsistent by sub-proof
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | | | |            #2303.
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | |   (491)  all_58_15 = e2 & op(e0, e0) = e2
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | ALPHA: (491) implies:
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | |   (492)  op(e0, e0) = e2
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (417), (492), (function-axioms) are
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | |   (493)  all_58_15 = e2 & op(e0, e0) = e2
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | ALPHA: (493) implies:
% 228.49/42.17  | | | | | | | | | | | | | | | | | | |   (494)  op(e0, e0) = e2
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (417), (494), (function-axioms) are
% 228.49/42.17  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 228.49/42.17  | | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | | End of split
% 228.49/42.17  | | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | | End of split
% 228.49/42.17  | | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | End of split
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | Case 2:
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | |   (495)  all_54_5 = e1 | all_54_5 = e0
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | REF_CLOSE: (275), (397), (419), (495) are inconsistent by
% 228.49/42.17  | | | | | | | | | | | | | | | |            sub-proof #2300.
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | End of split
% 228.49/42.17  | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | End of split
% 228.49/42.17  | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | Case 2:
% 228.49/42.17  | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | |   (496)  all_22_2 = e1
% 228.49/42.17  | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | COMBINE_EQS: (326), (496) imply:
% 228.49/42.17  | | | | | | | | | | | | | |   (497)  all_8_2 = e1
% 228.49/42.17  | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | SIMP: (497) implies:
% 228.49/42.17  | | | | | | | | | | | | | |   (498)  all_8_2 = e1
% 228.49/42.17  | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | COMBINE_EQS: (353), (498) imply:
% 228.49/42.17  | | | | | | | | | | | | | |   (499)  all_56_11 = e1
% 228.49/42.17  | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | REDUCE: (373), (498) imply:
% 228.49/42.17  | | | | | | | | | | | | | |   (500)   ~ (all_52_7 = e1)
% 228.49/42.17  | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | REDUCE: (375), (498) imply:
% 228.49/42.17  | | | | | | | | | | | | | |   (501)   ~ (all_52_9 = e1)
% 228.49/42.17  | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | REDUCE: (377), (498) imply:
% 228.49/42.17  | | | | | | | | | | | | | |   (502)   ~ (all_52_13 = e1)
% 228.49/42.17  | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 228.49/42.17  | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | Case 1:
% 228.49/42.17  | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | |   (503)   ~ (all_24_2 = e2)
% 228.49/42.17  | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | REDUCE: (301), (503) imply:
% 228.49/42.17  | | | | | | | | | | | | | | |   (504)   ~ (all_10_2 = e2)
% 228.49/42.17  | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 228.49/42.17  | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | Case 1:
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | |   (505)  all_54_0 = e3
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (505) imply:
% 228.49/42.17  | | | | | | | | | | | | | | | |   (506)  all_10_2 = e3
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | SIMP: (506) implies:
% 228.49/42.17  | | | | | | | | | | | | | | | |   (507)  all_10_2 = e3
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (507) imply:
% 228.49/42.17  | | | | | | | | | | | | | | | |   (508)  all_56_1 = e3
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | REDUCE: (355), (507) imply:
% 228.49/42.17  | | | | | | | | | | | | | | | |   (509)   ~ (all_52_1 = e3)
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | REDUCE: (357), (507) imply:
% 228.49/42.17  | | | | | | | | | | | | | | | |   (510)   ~ (all_52_2 = e3)
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | REDUCE: (359), (507) imply:
% 228.49/42.17  | | | | | | | | | | | | | | | |   (511)   ~ (all_52_3 = e3)
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 228.49/42.17  | | | | | | | | | | | | | | | | 
% 228.49/42.17  | | | | | | | | | | | | | | | | Case 1:
% 228.49/42.17  | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | |   (512)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 228.49/42.18  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.49/42.18  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 228.49/42.18  | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 228.49/42.18  | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.49/42.18  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.49/42.18  | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 228.49/42.18  | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 228.49/42.18  | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.49/42.18  | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 228.49/42.18  | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 228.49/42.18  | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.49/42.18  | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 228.49/42.18  | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | | BETA: splitting (512) gives:
% 228.49/42.18  | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | | Case 1:
% 228.49/42.18  | | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | | |   (513)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 228.49/42.18  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.49/42.18  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            = e3)
% 228.49/42.18  | | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (508), (509), (510), (513),
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            #2299.
% 228.49/42.18  | | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.18  | | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | | |   (514)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 228.49/42.18  | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 228.49/42.18  | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            = e0)
% 228.49/42.18  | | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (413), (508), (511), (514),
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.49/42.18  | | | | | | | | | | | | | | | | | |            #2329.
% 228.49/42.18  | | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | | End of split
% 228.49/42.18  | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.18  | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | |   (515)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.49/42.18  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 228.49/42.18  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 228.49/42.18  | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 228.49/42.18  | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 228.49/42.18  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 228.49/42.18  | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 228.49/42.18  | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 228.49/42.18  | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 228.49/42.18  | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 228.49/42.18  | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 228.49/42.18  | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 228.49/42.18  | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 228.49/42.18  | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (112), (113), (118), (121), (133), (145),
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (157), (159), (160), (164), (165), (167), (169),
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (170), (194), (197), (201), (213), (266), (269),
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (280), (297), (381), (385), (391), (401), (412),
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (413), (414), (415), (416), (499), (501), (515),
% 228.49/42.18  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.49/42.18  | | | | | | | | | | | | | | | | |            #2280.
% 228.49/42.18  | | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | | End of split
% 228.49/42.18  | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | Case 2:
% 228.49/42.18  | | | | | | | | | | | | | | | | 
% 228.49/42.18  | | | | | | | | | | | | | | | |   (516)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 228.49/42.18  | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (399), (504), (516) are inconsistent
% 228.49/42.19  | | | | | | | | | | | | | | | |            by sub-proof #2319.
% 228.49/42.19  | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | End of split
% 228.49/42.19  | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | Case 2:
% 228.49/42.19  | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | |   (517)  all_24_2 = e2
% 228.49/42.19  | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | COMBINE_EQS: (301), (517) imply:
% 228.49/42.19  | | | | | | | | | | | | | | |   (518)  all_10_2 = e2
% 228.49/42.19  | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | COMBINE_EQS: (290), (518) imply:
% 228.49/42.19  | | | | | | | | | | | | | | |   (519)  all_56_1 = e2
% 228.49/42.19  | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | REDUCE: (355), (518) imply:
% 228.49/42.19  | | | | | | | | | | | | | | |   (520)   ~ (all_52_1 = e2)
% 228.49/42.19  | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 228.49/42.19  | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | Case 1:
% 228.49/42.19  | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | |   (521)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 228.49/42.19  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.49/42.19  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 228.49/42.19  | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 228.49/42.19  | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.49/42.19  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.49/42.19  | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 228.49/42.19  | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 228.49/42.19  | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.49/42.19  | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 228.49/42.19  | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 228.49/42.19  | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.49/42.19  | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 228.49/42.19  | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | BETA: splitting (521) gives:
% 228.49/42.19  | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | Case 1:
% 228.49/42.19  | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | |   (522)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 228.49/42.19  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.49/42.19  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 228.49/42.19  | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 228.49/42.19  | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.49/42.19  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.49/42.19  | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 228.49/42.19  | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 228.49/42.19  | | | | | | | | | | | | | | | | |            = e3)
% 228.49/42.19  | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (499), (519), (520), (522),
% 228.49/42.19  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.49/42.19  | | | | | | | | | | | | | | | | |            #2279.
% 228.49/42.19  | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.19  | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | |   (523)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 228.49/42.19  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 228.49/42.19  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 228.49/42.19  | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 228.49/42.19  | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 228.49/42.19  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 228.49/42.19  | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 228.49/42.19  | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 228.49/42.19  | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 228.49/42.19  | | | | | | | | | | | | | | | | |            = e0)
% 228.49/42.19  | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | | BETA: splitting (523) gives:
% 228.49/42.19  | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | | Case 1:
% 228.49/42.19  | | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | | |   (524)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 228.49/42.19  | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 228.49/42.19  | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 228.49/42.19  | | | | | | | | | | | | | | | | | |            e3) = e1
% 228.49/42.19  | | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | | | ALPHA: (524) implies:
% 228.49/42.19  | | | | | | | | | | | | | | | | | |   (525)   ~ (all_56_21 = e3)
% 228.49/42.19  | | | | | | | | | | | | | | | | | |   (526)  op(e1, e3) = e1
% 228.49/42.19  | | | | | | | | | | | | | | | | | |   (527)  op(e3, e1) = e1
% 228.49/42.19  | | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 228.49/42.19  | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (526) gives:
% 228.49/42.19  | | | | | | | | | | | | | | | | | |   (528)  all_52_2 = e1
% 228.49/42.19  | | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 228.49/42.19  | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (527) gives:
% 228.49/42.19  | | | | | | | | | | | | | | | | | |   (529)  all_52_8 = e1
% 228.49/42.19  | | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | | | REDUCE: (144), (528) imply:
% 228.49/42.19  | | | | | | | | | | | | | | | | | |   (530)   ~ (all_52_3 = e1)
% 228.49/42.19  | | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | | | SIMP: (530) implies:
% 228.49/42.19  | | | | | | | | | | | | | | | | | |   (531)   ~ (all_52_3 = e1)
% 228.49/42.19  | | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | | | REDUCE: (120), (529) imply:
% 228.49/42.19  | | | | | | | | | | | | | | | | | |   (532)   ~ (all_52_12 = e1)
% 228.49/42.19  | | | | | | | | | | | | | | | | | | 
% 228.49/42.19  | | | | | | | | | | | | | | | | | | SIMP: (532) implies:
% 228.49/42.20  | | | | | | | | | | | | | | | | | |   (533)   ~ (all_52_12 = e1)
% 228.49/42.20  | | | | | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (110), (112), (113), (118), (121), (133),
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            (145), (157), (158), (159), (160), (164), (165),
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (194), (197), (201),
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            (213), (217), (220), (266), (269), (280), (297),
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            (381), (385), (391), (401), (412), (413), (414),
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            (415), (416), (417), (499), (500), (502), (531),
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            (533), (function-axioms) are inconsistent by
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            sub-proof #2273.
% 228.49/42.20  | | | | | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | | | | | Case 2:
% 228.49/42.20  | | | | | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | | | | | |   (534)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 228.49/42.20  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 228.49/42.20  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 228.49/42.20  | | | | | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (412), (413), (534), (function-axioms) are
% 228.49/42.20  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2308.
% 228.49/42.20  | | | | | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | | | | | End of split
% 228.49/42.20  | | | | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | | | | End of split
% 228.49/42.20  | | | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | | | Case 2:
% 228.49/42.20  | | | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | | | |   (535)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.49/42.20  | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 228.49/42.20  | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 228.49/42.20  | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 228.49/42.20  | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 228.49/42.20  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 228.49/42.20  | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 228.49/42.20  | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 228.49/42.20  | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.49/42.20  | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 228.49/42.20  | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 228.49/42.20  | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 228.49/42.20  | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 228.49/42.20  | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 228.49/42.20  | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 228.49/42.20  | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.49/42.20  | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 228.49/42.20  | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 228.49/42.20  | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 228.49/42.20  | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 228.49/42.20  | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 228.49/42.20  | | | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | | | | REF_CLOSE: (110), (112), (113), (118), (121), (133), (145),
% 228.49/42.20  | | | | | | | | | | | | | | | |            (157), (159), (160), (164), (165), (167), (169),
% 228.49/42.20  | | | | | | | | | | | | | | | |            (170), (194), (197), (201), (213), (266), (269),
% 228.49/42.20  | | | | | | | | | | | | | | | |            (280), (297), (381), (385), (391), (401), (412),
% 228.49/42.20  | | | | | | | | | | | | | | | |            (413), (414), (415), (416), (499), (501), (535),
% 228.49/42.20  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.49/42.20  | | | | | | | | | | | | | | | |            #2280.
% 228.49/42.20  | | | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | | | End of split
% 228.49/42.20  | | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | | End of split
% 228.49/42.20  | | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | | End of split
% 228.49/42.20  | | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | | End of split
% 228.49/42.20  | | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | | End of split
% 228.49/42.20  | | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | End of split
% 228.49/42.20  | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | Case 2:
% 228.49/42.20  | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | |   (536)  all_20_2 = e1
% 228.49/42.20  | | | | | | | | | |   (537)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 228.49/42.20  | | | | | | | | | |            op(e0, e1) = all_20_1 & $i(all_20_0) &
% 228.49/42.20  | | | | | | | | | |            $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 228.49/42.20  | | | | | | | | | |            = all_20_1 & $i(all_20_1))
% 228.49/42.20  | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | COMBINE_EQS: (341), (536) imply:
% 228.49/42.20  | | | | | | | | | |   (538)  all_4_2 = e1
% 228.49/42.20  | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | SIMP: (538) implies:
% 228.49/42.20  | | | | | | | | | |   (539)  all_4_2 = e1
% 228.49/42.20  | | | | | | | | | | 
% 228.49/42.20  | | | | | | | | | | COMBINE_EQS: (324), (539) imply:
% 228.49/42.21  | | | | | | | | | |   (540)  all_34_2 = e1
% 228.49/42.21  | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | COMBINE_EQS: (254), (539) imply:
% 228.49/42.21  | | | | | | | | | |   (541)  all_56_31 = e1
% 228.49/42.21  | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | REDUCE: (368), (539) imply:
% 228.49/42.21  | | | | | | | | | |   (542)   ~ (all_52_3 = e1)
% 228.49/42.21  | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | REDUCE: (379), (539) imply:
% 228.49/42.21  | | | | | | | | | |   (543)   ~ (all_52_7 = e1)
% 228.49/42.21  | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | REDUCE: (386), (539) imply:
% 228.49/42.21  | | | | | | | | | |   (544)   ~ (all_52_11 = e1)
% 228.49/42.21  | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | REDUCE: (387), (539) imply:
% 228.49/42.21  | | | | | | | | | |   (545)   ~ (all_52_12 = e1)
% 228.49/42.21  | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | REDUCE: (388), (539) imply:
% 228.49/42.21  | | | | | | | | | |   (546)   ~ (all_52_13 = e1)
% 228.49/42.21  | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | REDUCE: (389), (539) imply:
% 228.49/42.21  | | | | | | | | | |   (547)   ~ (all_52_14 = e1)
% 228.49/42.21  | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | BETA: splitting (217) gives:
% 228.49/42.21  | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | Case 1:
% 228.49/42.21  | | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | |   (548)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 228.49/42.21  | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 228.49/42.21  | | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | | BETA: splitting (548) gives:
% 228.49/42.21  | | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | | Case 1:
% 228.49/42.21  | | | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | | |   (549)  all_58_12 = e1 & op(e0, e3) = e1
% 228.49/42.21  | | | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | | | REF_CLOSE: (159), (542), (549), (function-axioms) are
% 228.49/42.21  | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 228.49/42.21  | | | | | | | | | | | | 
% 228.49/42.21  | | | | | | | | | | | Case 2:
% 228.49/42.21  | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | |   (550)  all_58_13 = e1 & op(e0, e2) = e1
% 228.78/42.21  | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | REF_CLOSE: (158), (543), (550), (function-axioms) are
% 228.78/42.21  | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 228.78/42.21  | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | End of split
% 228.78/42.21  | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | Case 2:
% 228.78/42.21  | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | |   (551)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 228.78/42.21  | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 228.78/42.21  | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | BETA: splitting (551) gives:
% 228.78/42.21  | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | Case 1:
% 228.78/42.21  | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | |   (552)  all_58_14 = e1 & op(e0, e1) = e1
% 228.78/42.21  | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | ALPHA: (552) implies:
% 228.78/42.21  | | | | | | | | | | | |   (553)  op(e0, e1) = e1
% 228.78/42.21  | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | REF_CLOSE: (157), (544), (553), (function-axioms) are
% 228.78/42.21  | | | | | | | | | | | |            inconsistent by sub-proof #2272.
% 228.78/42.21  | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | Case 2:
% 228.78/42.21  | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | |   (554)  all_58_15 = e1 & op(e0, e0) = e1
% 228.78/42.21  | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | ALPHA: (554) implies:
% 228.78/42.21  | | | | | | | | | | | |   (555)  all_58_15 = e1
% 228.78/42.21  | | | | | | | | | | | |   (556)  op(e0, e0) = e1
% 228.78/42.21  | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | BETA: splitting (64) gives:
% 228.78/42.21  | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | Case 1:
% 228.78/42.21  | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | |   (557)   ~ (all_22_2 = e1)
% 228.78/42.21  | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | REDUCE: (326), (557) imply:
% 228.78/42.21  | | | | | | | | | | | | |   (558)   ~ (all_8_2 = e1)
% 228.78/42.21  | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | BETA: splitting (199) gives:
% 228.78/42.21  | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | Case 1:
% 228.78/42.21  | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | |   (559)  all_54_5 = e3
% 228.78/42.21  | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | COMBINE_EQS: (275), (559) imply:
% 228.78/42.21  | | | | | | | | | | | | | |   (560)  all_8_2 = e3
% 228.78/42.21  | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | REDUCE: (392), (560) imply:
% 228.78/42.21  | | | | | | | | | | | | | |   (561)  $false
% 228.78/42.21  | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | CLOSE: (561) is inconsistent.
% 228.78/42.21  | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | Case 2:
% 228.78/42.21  | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | |   (562)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 228.78/42.21  | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | BETA: splitting (562) gives:
% 228.78/42.21  | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | Case 1:
% 228.78/42.21  | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | |   (563)  all_54_5 = e2
% 228.78/42.21  | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | COMBINE_EQS: (275), (563) imply:
% 228.78/42.21  | | | | | | | | | | | | | | |   (564)  all_8_2 = e2
% 228.78/42.21  | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | COMBINE_EQS: (353), (564) imply:
% 228.78/42.21  | | | | | | | | | | | | | | |   (565)  all_56_11 = e2
% 228.78/42.21  | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | REDUCE: (366), (564) imply:
% 228.78/42.21  | | | | | | | | | | | | | | |   (566)   ~ (all_52_1 = e2)
% 228.78/42.21  | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | REDUCE: (373), (564) imply:
% 228.78/42.21  | | | | | | | | | | | | | | |   (567)   ~ (all_52_7 = e2)
% 228.78/42.21  | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | REDUCE: (375), (564) imply:
% 228.78/42.21  | | | | | | | | | | | | | | |   (568)   ~ (all_52_9 = e2)
% 228.78/42.21  | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | REDUCE: (377), (564) imply:
% 228.78/42.21  | | | | | | | | | | | | | | |   (569)   ~ (all_52_13 = e2)
% 228.78/42.21  | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | REDUCE: (42), (564) imply:
% 228.78/42.21  | | | | | | | | | | | | | | |   (570)  op(e2, e2) = e2
% 228.78/42.21  | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 228.78/42.21  | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | Case 1:
% 228.78/42.21  | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | |   (571)   ~ (all_24_2 = e2)
% 228.78/42.21  | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | REDUCE: (301), (571) imply:
% 228.78/42.21  | | | | | | | | | | | | | | | |   (572)   ~ (all_10_2 = e2)
% 228.78/42.21  | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 228.78/42.21  | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.21  | | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | |   (573)  all_54_0 = e3
% 228.78/42.21  | | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (573) imply:
% 228.78/42.21  | | | | | | | | | | | | | | | | |   (574)  all_10_2 = e3
% 228.78/42.21  | | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | | SIMP: (574) implies:
% 228.78/42.21  | | | | | | | | | | | | | | | | |   (575)  all_10_2 = e3
% 228.78/42.21  | | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (575) imply:
% 228.78/42.21  | | | | | | | | | | | | | | | | |   (576)  all_56_1 = e3
% 228.78/42.21  | | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | | REDUCE: (355), (575) imply:
% 228.78/42.21  | | | | | | | | | | | | | | | | |   (577)   ~ (all_52_1 = e3)
% 228.78/42.21  | | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | | REDUCE: (357), (575) imply:
% 228.78/42.21  | | | | | | | | | | | | | | | | |   (578)   ~ (all_52_2 = e3)
% 228.78/42.21  | | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | | REDUCE: (359), (575) imply:
% 228.78/42.21  | | | | | | | | | | | | | | | | |   (579)   ~ (all_52_3 = e3)
% 228.78/42.21  | | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 228.78/42.21  | | | | | | | | | | | | | | | | | 
% 228.78/42.21  | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.21  | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | |   (580)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.78/42.22  | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.78/42.22  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 228.78/42.22  | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | BETA: splitting (580) gives:
% 228.78/42.22  | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |   (581)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            = e3)
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (566), (577), (578), (581),
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            #2333.
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |   (582)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            = e0)
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (576), (579), (582), (function-axioms) are
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2270.
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | End of split
% 228.78/42.22  | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.22  | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | |   (583)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 228.78/42.22  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 228.78/42.22  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 228.78/42.22  | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | BETA: splitting (583) gives:
% 228.78/42.22  | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |   (584)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            = e2)
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (565), (567), (568), (584),
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.78/42.22  | | | | | | | | | | | | | | | | | | |            #2325.
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.22  | | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.22  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |   (585)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            = e0)
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (541), (547), (565), (585),
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            #2268.
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | End of split
% 228.78/42.23  | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | End of split
% 228.78/42.23  | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.23  | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | |   (586)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 228.78/42.23  | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (399), (572), (586) are inconsistent
% 228.78/42.23  | | | | | | | | | | | | | | | | |            by sub-proof #2319.
% 228.78/42.23  | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | End of split
% 228.78/42.23  | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | Case 2:
% 228.78/42.23  | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | |   (587)  all_24_2 = e2
% 228.78/42.23  | | | | | | | | | | | | | | | |   (588)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 228.78/42.23  | | | | | | | | | | | | | | | |            & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 228.78/42.23  | | | | | | | | | | | | | | | |            $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 228.78/42.23  | | | | | | | | | | | | | | | |            = all_24_1 & $i(all_24_1))
% 228.78/42.23  | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (587) imply:
% 228.78/42.23  | | | | | | | | | | | | | | | |   (589)  all_10_2 = e2
% 228.78/42.23  | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (589) imply:
% 228.78/42.23  | | | | | | | | | | | | | | | |   (590)  all_32_2 = e2
% 228.78/42.23  | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (589) imply:
% 228.78/42.23  | | | | | | | | | | | | | | | |   (591)  all_56_1 = e2
% 228.78/42.23  | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | REDUCE: (359), (589) imply:
% 228.78/42.23  | | | | | | | | | | | | | | | |   (592)   ~ (all_52_3 = e2)
% 228.78/42.23  | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | REDUCE: (361), (589) imply:
% 228.78/42.23  | | | | | | | | | | | | | | | |   (593)   ~ (all_52_4 = e2)
% 228.78/42.23  | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | REDUCE: (365), (589) imply:
% 228.78/42.23  | | | | | | | | | | | | | | | |   (594)   ~ (all_52_12 = e2)
% 228.78/42.23  | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | REDUCE: (45), (589) imply:
% 228.78/42.23  | | | | | | | | | | | | | | | |   (595)  op(e3, e3) = e2
% 228.78/42.23  | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 228.78/42.23  | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.23  | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | |   (596)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 228.78/42.23  | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 228.78/42.23  | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (569), (594), (596),
% 228.78/42.23  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.78/42.23  | | | | | | | | | | | | | | | | |            #2316.
% 228.78/42.23  | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.23  | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | |   (597)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 228.78/42.23  | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 228.78/42.23  | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | BETA: splitting (597) gives:
% 228.78/42.23  | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | |   (598)  all_58_11 = e2 & op(e1, e0) = e2
% 228.78/42.23  | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | ALPHA: (598) implies:
% 228.78/42.23  | | | | | | | | | | | | | | | | | |   (599)  op(e1, e0) = e2
% 228.78/42.23  | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |   (600)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (159), (567), (592), (600),
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            #2314.
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |   (601)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 228.78/42.23  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | BETA: splitting (601) gives:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | |   (602)  all_58_14 = e2 & op(e0, e1) = e2
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | ALPHA: (602) implies:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | |   (603)  op(e0, e1) = e2
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | |              e2, e1, e0, simplifying with (157), (603) gives:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | |   (604)  all_52_11 = e2
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (160), (599) gives:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | |   (605)  all_52_14 = e2
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (605) imply:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | |   (606)   ~ (all_52_2 = e2)
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (605) imply:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | |   (607)   ~ (all_6_2 = e2)
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | SIMP: (607) implies:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | |   (608)   ~ (all_6_2 = e2)
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | |   (609)   ~ (all_34_2 = e1)
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | REDUCE: (540), (609) imply:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | |   (610)  $false
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | CLOSE: (610) is inconsistent.
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | |   (611)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | |            $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | |            = all_34_1 & $i(all_34_1))
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | |   (612)  all_54_10 = e3
% 228.78/42.23  | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (612) are inconsistent by sub-proof
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | |            #2313.
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | |   (613)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (537) gives:
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |   (614)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |          op(e0, e1) = all_20_1 & $i(all_20_0) &
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |          $i(all_20_1)
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (614) implies:
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |   (615)  op(e0, e1) = all_20_1
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (79), (113), (117), (120), (133), (134), (140),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (144), (145), (146), (148), (149), (158), (159),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (160), (163), (164), (165), (167), (168), (169),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (170), (192), (196), (197), (198), (201), (213),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (214), (219), (232), (242), (257), (268), (269),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (270), (280), (297), (380), (381), (401), (537),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (541), (545), (546), (547), (555), (556), (568),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (569), (570), (588), (590), (591), (592), (593),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (594), (595), (603), (606), (608), (611), (613),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (615), (function-axioms) are inconsistent by
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2232.
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |   (616)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |          $i(all_20_1)
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (616) implies:
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |   (617)  op(e0, e1) = all_20_1
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (79), (113), (117), (120), (133), (134), (140),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (144), (145), (146), (148), (149), (158), (159),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (160), (163), (164), (165), (167), (168), (169),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (170), (192), (196), (197), (198), (201), (213),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (214), (219), (232), (242), (257), (268), (269),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (270), (280), (297), (380), (381), (401), (537),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (541), (545), (546), (547), (555), (556), (568),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (569), (570), (588), (590), (591), (592), (593),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (594), (595), (603), (606), (608), (611), (613),
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            (617), (function-axioms) are inconsistent by
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2232.
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | End of split
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | End of split
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | |   (618)  all_58_15 = e2 & op(e0, e0) = e2
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | ALPHA: (618) implies:
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | |   (619)  all_58_15 = e2
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (555), (619) are inconsistent by sub-proof
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | |            #2231.
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | End of split
% 228.78/42.24  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | End of split
% 228.78/42.24  | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.24  | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | |   (620)  all_58_15 = e2 & op(e0, e0) = e2
% 228.78/42.24  | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | ALPHA: (620) implies:
% 228.78/42.24  | | | | | | | | | | | | | | | | | |   (621)  all_58_15 = e2
% 228.78/42.24  | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (555), (621) are inconsistent by sub-proof
% 228.78/42.24  | | | | | | | | | | | | | | | | | |            #2231.
% 228.78/42.24  | | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | | End of split
% 228.78/42.24  | | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | | End of split
% 228.78/42.24  | | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | End of split
% 228.78/42.24  | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | Case 2:
% 228.78/42.24  | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | |   (622)  all_54_5 = e1 | all_54_5 = e0
% 228.78/42.24  | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | | REF_CLOSE: (275), (397), (558), (622) are inconsistent by
% 228.78/42.24  | | | | | | | | | | | | | | |            sub-proof #2300.
% 228.78/42.24  | | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | | End of split
% 228.78/42.24  | | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | End of split
% 228.78/42.24  | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | Case 2:
% 228.78/42.24  | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | |   (623)  all_22_2 = e1
% 228.78/42.24  | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | COMBINE_EQS: (326), (623) imply:
% 228.78/42.24  | | | | | | | | | | | | |   (624)  all_8_2 = e1
% 228.78/42.24  | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | SIMP: (624) implies:
% 228.78/42.24  | | | | | | | | | | | | |   (625)  all_8_2 = e1
% 228.78/42.24  | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | COMBINE_EQS: (353), (625) imply:
% 228.78/42.24  | | | | | | | | | | | | |   (626)  all_56_11 = e1
% 228.78/42.24  | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | REDUCE: (366), (625) imply:
% 228.78/42.24  | | | | | | | | | | | | |   (627)   ~ (all_52_1 = e1)
% 228.78/42.24  | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | REDUCE: (369), (625) imply:
% 228.78/42.24  | | | | | | | | | | | | |   (628)   ~ (all_52_4 = e1)
% 228.78/42.24  | | | | | | | | | | | | | 
% 228.78/42.24  | | | | | | | | | | | | | REDUCE: (392), (625) imply:
% 228.78/42.25  | | | | | | | | | | | | |   (629)   ~ (e3 = e1)
% 228.78/42.25  | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | BETA: splitting (241) gives:
% 228.78/42.25  | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | Case 1:
% 228.78/42.25  | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | |   (630)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 228.78/42.25  | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 228.78/42.25  | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | BETA: splitting (630) gives:
% 228.78/42.25  | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | Case 1:
% 228.78/42.25  | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | |   (631)  all_58_0 = e1 & op(e3, e3) = e1
% 228.78/42.25  | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | REF_CLOSE: (45), (393), (631), (function-axioms) are
% 228.78/42.25  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2230.
% 228.78/42.25  | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | Case 2:
% 228.78/42.25  | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | |   (632)  all_58_2 = e1 & op(e2, e3) = e1
% 228.78/42.25  | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | REF_CLOSE: (167), (627), (632), (function-axioms) are
% 228.78/42.25  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 228.78/42.25  | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | End of split
% 228.78/42.25  | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | Case 2:
% 228.78/42.25  | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | |   (633)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 228.78/42.25  | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 228.78/42.25  | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | BETA: splitting (633) gives:
% 228.78/42.25  | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | Case 1:
% 228.78/42.25  | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | |   (634)  all_58_6 = e1 & op(e1, e3) = e1
% 228.78/42.25  | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | ALPHA: (634) implies:
% 228.78/42.25  | | | | | | | | | | | | | | |   (635)  all_58_6 = e1
% 228.78/42.25  | | | | | | | | | | | | | | |   (636)  op(e1, e3) = e1
% 228.78/42.25  | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 228.78/42.25  | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | Case 1:
% 228.78/42.25  | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | |   (637)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 228.78/42.25  | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (170), (393), (628), (637),
% 228.78/42.25  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.78/42.25  | | | | | | | | | | | | | | | |            #2227.
% 228.78/42.25  | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | Case 2:
% 228.78/42.25  | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | |   (638)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 228.78/42.25  | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | BETA: splitting (638) gives:
% 228.78/42.25  | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (639)  all_58_4 = e1 & op(e3, e1) = e1
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | ALPHA: (639) implies:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (640)  op(e3, e1) = e1
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 228.78/42.25  | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (636) gives:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (641)  all_52_2 = e1
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 228.78/42.25  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (640) gives:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (642)  all_52_8 = e1
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | REDUCE: (144), (641) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (643)   ~ (all_52_3 = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | REDUCE: (143), (641) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (644)   ~ (all_52_6 = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | SIMP: (644) implies:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (645)   ~ (all_52_6 = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | REDUCE: (141), (641) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (646)   ~ (all_52_14 = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | REDUCE: (123), (642) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (647)   ~ (all_52_9 = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | SIMP: (647) implies:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (648)   ~ (all_52_9 = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | REDUCE: (121), (642) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (649)   ~ (all_52_11 = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | REDUCE: (120), (642) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (650)   ~ (all_52_12 = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | REDUCE: (363), (642) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (651)   ~ (all_10_2 = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | REDUCE: (380), (642) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (652)   ~ (all_6_2 = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | SIMP: (652) implies:
% 228.78/42.25  | | | | | | | | | | | | | | | | |   (653)   ~ (all_6_2 = e1)
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 228.78/42.25  | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | |   (654)  all_54_10 = e3
% 228.78/42.25  | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (654) are inconsistent by sub-proof
% 228.78/42.25  | | | | | | | | | | | | | | | | | |            #2313.
% 228.78/42.25  | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | |   (655)   ~ (all_54_10 = e3)
% 228.78/42.25  | | | | | | | | | | | | | | | | | |   (656)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 228.78/42.25  | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | BETA: splitting (656) gives:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (657)  all_54_10 = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (657) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (658)  all_6_2 = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | SIMP: (658) implies:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (659)  all_6_2 = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (659) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (660)  all_36_2 = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (659) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (661)  all_40_2 = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (659) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (662)  all_56_21 = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | REDUCE: (378), (659) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (663)   ~ (all_52_6 = e2)
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | REDUCE: (381), (659) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (664)   ~ (all_52_9 = e2)
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | REDUCE: (383), (659) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (665)   ~ (all_52_11 = e2)
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | REDUCE: (385), (659) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (666)   ~ (all_52_14 = e2)
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | REDUCE: (391), (659) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (667)   ~ (e3 = e2)
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (659) imply:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | |   (668)  op(e1, e1) = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | |   (669)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (669) gives:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | |   (670)  all_58_6 = e2 & op(e1, e3) = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (670) implies:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | |   (671)  op(e1, e3) = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (636), (671), (function-axioms) are
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | |   (672)  all_58_7 = e2 & op(e1, e2) = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (672) implies:
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | |   (673)  all_58_7 = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | |   (674)  op(e1, e2) = e2
% 228.78/42.25  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (224),
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | |            (225), (226), (635), (668), (673), (674),
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | |            #2200.
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | End of split
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | |   (675)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (675) gives:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | |   (676)  all_58_8 = e2 & op(e1, e1) = e2
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | ALPHA: (676) implies:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | |   (677)  all_58_8 = e2
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | |   (678)   ~ (all_24_2 = e2)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (678) imply:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | |   (679)   ~ (all_10_2 = e2)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | |   (680)  all_54_0 = e3
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (680) imply:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | |   (681)  all_10_2 = e3
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (681) imply:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | |   (682)  all_56_1 = e3
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (355), (681) imply:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | |   (683)   ~ (all_52_1 = e3)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (681) imply:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | |   (684)   ~ (all_52_3 = e3)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (681) imply:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | |   (685)   ~ (all_52_12 = e3)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (681) imply:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | |   (686)  op(e3, e3) = e3
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |   (687)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (167), (636), (682), (683), (684),
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (687), (function-axioms) are inconsistent by
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2199.
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |   (688)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (688) gives:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (689)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (689) gives:
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (690)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (690) implies:
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (691)  op(e2, e1) = e2
% 228.78/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (297), (381), (401), (653), (656), (691),
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2198.
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (692)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (692) gives:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (693)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (693) implies:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (694)  op(e2, e1) = e1
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (648), (694), (function-axioms) are
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (695)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (695) implies:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (696)   ~ (all_56_31 = e0)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (697)   ~ (all_56_21 = e0)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (698)   ~ (all_56_1 = e0)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (699)  op(e0, e2) = e2
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (700)  op(e2, e0) = e2
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (699) gives:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (701)  all_52_7 = e2
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (700) gives:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (702)  all_52_13 = e2
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (701) imply:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (703)   ~ (all_52_3 = e2)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (702) imply:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (704)   ~ (all_52_12 = e2)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (702) imply:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (705)   ~ (all_52_14 = e2)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (706)  all_54_3 = e3
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (706) imply:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (707)  all_52_12 = e3
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (685), (707) imply:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (708)  $false
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (708) is inconsistent.
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (709)   ~ (all_54_3 = e3)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (710)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (710) gives:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (711)  all_54_3 = e2
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (711) imply:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (712)  all_52_12 = e2
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (704), (712) imply:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (713)  $false
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (713) is inconsistent.
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (714)   ~ (all_54_3 = e2)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (715)  all_54_3 = e1 | all_54_3 = e0
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (716)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (546), (627),
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (648), (683), (716), (function-axioms) are
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2195.
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (717)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (717) gives:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (718)  all_58_5 = e3 & op(e2, e1) = e3
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (718) implies:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (719)  all_58_5 = e3
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (720)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (720) gives:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (721)  all_58_0 = e2 & op(e3, e3) = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (721) implies:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (722)  op(e3, e3) = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (686), (722), (function-axioms) are
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (723)  all_58_1 = e2 & op(e3, e2) = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (723) implies:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (724)  all_58_1 = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (725)  op(e3, e2) = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (726)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (726) gives:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (727)  all_58_1 = e3 & op(e3, e2) = e3
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (727) implies:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (728)  op(e3, e2) = e3
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (725), (728), (function-axioms) are
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2193.
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (729)  all_58_3 = e3 & op(e2, e2) = e3
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (546), (627),
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (648), (729), (function-axioms) are inconsistent
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2196.
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (730)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (730) gives:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (731)  all_58_7 = e3 & op(e1, e2) = e3
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (731) implies:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (732)  op(e1, e2) = e3
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (733)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (733) gives:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (734)  all_58_0 = e2 & op(e3, e3) = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (734) implies:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (735)  op(e3, e3) = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (136), (162), (168),
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (195), (240), (242), (246), (267), (685),
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (724), (732), (735), (function-axioms) are
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2178.
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (736)  all_58_2 = e2 & op(e2, e3) = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (736) implies:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (737)  op(e2, e3) = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (112), (113), (145), (167), (193), (197),
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (269), (280), (545), (546), (547), (666),
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (715), (737), (function-axioms) are inconsistent
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2172.
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (738)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (636), (703), (738), (function-axioms)
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2171.
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (739)  all_58_13 = e3 & op(e0, e2) = e3
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (739) implies:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (740)  op(e0, e2) = e3
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (699), (740), (function-axioms) are
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (741)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (741) gives:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (742)  all_58_4 = e2 & op(e3, e1) = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (742) implies:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (743)  all_58_4 = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (227), (228),
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (668), (719), (743), (function-axioms) are
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2155.
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (744)  all_58_9 = e2 & op(e3, e0) = e2
% 229.03/42.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (744) implies:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (745)  op(e3, e0) = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (280), (545), (704), (715), (745),
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2153.
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (746)  all_58_10 = e3 & op(e2, e0) = e3
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (746) implies:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (747)  op(e2, e0) = e3
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (700), (747), (function-axioms) are
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (748)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (541), (547), (662), (748),
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |            #2151.
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | |   (749)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (399), (679), (749) are inconsistent
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2319.
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |   (750)  all_24_2 = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |   (751)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |            = all_24_1 & $i(all_24_1))
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (750) imply:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |   (752)  all_10_2 = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | SIMP: (752) implies:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |   (753)  all_10_2 = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (753) imply:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |   (754)  all_32_2 = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (753) imply:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |   (755)  all_56_1 = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (355), (753) imply:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |   (756)   ~ (all_52_1 = e2)
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (753) imply:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |   (757)   ~ (all_52_3 = e2)
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (753) imply:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |   (758)   ~ (all_52_4 = e2)
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (753) imply:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |   (759)   ~ (all_52_12 = e2)
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (753) imply:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | |   (760)  op(e3, e3) = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | |   (761)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (761) gives:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | |   (762)  all_58_9 = e2 & op(e3, e0) = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (759), (762), (function-axioms) are
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2318.
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | |   (763)  all_58_10 = e2 & op(e2, e0) = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (763) implies:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | |   (764)  op(e2, e0) = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (765)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (766)  all_58_12 = e2 & op(e0, e3) = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (757), (766), (function-axioms) are
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2315.
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (767)  all_58_13 = e2 & op(e0, e2) = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (767) implies:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (768)  op(e0, e2) = e2
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (769)   ~ (all_32_2 = e2)
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (754), (769) imply:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (770)  $false
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (770) is inconsistent.
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (771)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_32_1 & $i(all_32_1))
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (772)   ~ (all_34_2 = e1)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (540), (772) imply:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (773)  $false
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (773) is inconsistent.
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (774)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_34_1 & $i(all_34_1))
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (775)   ~ (all_36_2 = e2)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (660), (775) imply:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (776)  $false
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (776) is inconsistent.
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (777)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_36_1 & $i(all_36_1))
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (778)   ~ (all_40_2 = e2)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (661), (778) imply:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (779)  $false
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (779) is inconsistent.
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (780)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_40_1 & $i(all_40_1))
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (781)  all_54_9 = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (781) imply:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (782)  all_52_6 = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (782) implies:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (783)  all_52_6 = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (783) imply:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (784)   ~ (all_52_14 = e3)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (784) implies:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (785)   ~ (all_52_14 = e3)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (786)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (786) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (787)  all_58_6 = e3 & op(e1, e3) = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (787) implies:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (788)  op(e1, e3) = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (636), (788), (function-axioms) are
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (789)  all_58_7 = e3 & op(e1, e2) = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (789) implies:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (790)  all_58_7 = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (791)  op(e1, e2) = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (792)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (792) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (793)  all_58_9 = e3 & op(e3, e0) = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (793) implies:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (794)  all_58_9 = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (795)  op(e3, e0) = e3
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (796)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (796) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (797)  all_58_0 = e0 & op(e3, e3) = e0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (797) implies:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (798)  op(e3, e3) = e0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (760), (798), (function-axioms) are
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (799)  all_58_1 = e0 & op(e3, e2) = e0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (799) implies:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (800)  op(e3, e2) = e0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (801)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (801) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (802)  all_58_6 = e0 & op(e1, e3) = e0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (635), (802) are inconsistent by sub-proof
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2205.
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (803)  all_58_7 = e0 & op(e1, e2) = e0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (803) implies:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (804)  all_58_7 = e0
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (160), (226), (636), (668), (785),
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (804), (function-axioms) are inconsistent by
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2147.
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (805)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (805) gives:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (806)  all_58_8 = e0 & op(e1, e1) = e0
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (806) implies:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (807)  op(e1, e1) = e0
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (668), (807), (function-axioms) are
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (808)  all_58_11 = e0 & op(e1, e0) = e0
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (808) implies:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (809)  all_58_11 = e0
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (810)  op(e1, e0) = e0
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (811)  all_58_15 = e0 & op(e0, e0) = e0
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (811) implies:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (812)  op(e0, e0) = e0
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (556), (812), (function-axioms) are
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (813)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (813) implies:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (814)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (815)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0)
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (777) gives:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (816)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e2) = all_36_1 & $i(all_36_0) &
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_36_1)
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (816) implies:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (817)  op(e1, e2) = all_36_1
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (818)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_24_1 & $i(all_24_0) &
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_24_1)
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (818) implies:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (819)   ~ (all_24_0 = e0)
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (820)  op(e3, e2) = all_24_1
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (821)  op(all_24_1, e3) = all_24_0
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (822)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (123), (126),
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (158), (159), (160), (162), (164), (165),
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (194), (213), (218),
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (227), (230), (231), (232),
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (238), (266), (297),
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (381), (391), (401), (541), (543), (546), (555),
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (627), (628), (664), (760), (764), (777), (780),
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (791), (795), (822), (function-axioms) are
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2104.
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (823)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (823) gives:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (824)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_29 & $i(all_56_29)
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (824) implies:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (825)  op(e1, e0) = all_56_29
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (826)  op(e1, all_56_29) = e1
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_29, e0, e1, simplifying with (810), (825)
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (827)  all_56_29 = e0
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (826), (827) imply:
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (828)  op(e1, e0) = e1
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (764), (794), (815), (828),
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2101.
% 229.03/42.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (829)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (829) implies:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (830)  op(e0, all_56_31) = e0
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (830) imply:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (831)  op(e0, e1) = e0
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (118), (139), (146), (157), (159),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (192), (198), (200), (211),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (217), (218), (219), (226), (227), (232),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (257), (270), (279), (391), (537), (542),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (544), (546), (627), (636), (640), (648), (662),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (664), (665), (668), (755), (756), (757), (760),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (764), (771), (774), (777), (780), (791), (800),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (809), (814), (817), (819), (820), (821), (831),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2064.
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (832)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_24_1)
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (832) implies:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (833)   ~ (all_24_1 = e1)
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (834)  op(e3, e2) = all_24_1
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (835)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (123), (126),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (158), (159), (160), (162), (164), (165),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (194), (213), (218),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (227), (230), (231), (232),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (238), (266), (297),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (381), (391), (401), (541), (543), (546), (555),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (627), (628), (664), (760), (764), (777), (780),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (791), (795), (835), (function-axioms) are
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2104.
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (836)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (836) gives:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (837)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_29 & $i(all_56_29)
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (837) implies:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (838)  op(e1, e0) = all_56_29
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (839)  op(e1, all_56_29) = e1
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (771) gives:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (840)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_32_1 & $i(all_32_0) &
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_32_1)
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (840) implies:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (841)  op(e3, e2) = all_32_1
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (780) gives:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_29, e0, e1, simplifying with (810), (838)
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (842)  all_56_29 = e0
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e3, simplifying with (834), (841)
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (843)  all_32_1 = all_24_1
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_32_1,
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (800), (841) gives:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (844)  all_32_1 = e0
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (843), (844) imply:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (845)  all_24_1 = e0
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (833), (845) imply:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (846)   ~ (e1 = e0)
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (839), (842) imply:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (847)  op(e1, e0) = e1
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (764), (794), (815), (847),
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2101.
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (848)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 229.03/42.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_40_1)
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (777), (791), (848), (function-axioms) are
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2144.
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (849)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_32_1)
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (849) implies:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (850)   ~ (all_32_1 = e0)
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (851)  op(e3, e2) = all_32_1
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (800), (834), (850), (851), (function-axioms) are
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2065.
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (852)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (852) implies:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (853)  op(e0, all_56_31) = e0
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (853) imply:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (854)  op(e0, e1) = e0
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (118), (139), (146), (157), (159),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (192), (198), (200), (211),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (217), (218), (219), (226), (227), (232),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (257), (270), (279), (391), (537), (542),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (546), (627), (636), (640), (648), (662), (664),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (665), (668), (755), (756), (757), (760), (764),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (771), (774), (777), (780), (791), (800), (809),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (814), (817), (833), (834), (854),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2061.
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (855)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_36_1)
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (855) implies:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (856)   ~ (all_36_1 = e0)
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (857)  op(e1, e2) = all_36_1
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (858)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_24_1 & $i(all_24_0) &
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_24_1)
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (858) implies:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (859)   ~ (all_24_0 = e0)
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (860)  op(e3, e2) = all_24_1
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (861)  op(all_24_1, e3) = all_24_0
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (862)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (123), (126),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (158), (159), (160), (162), (164), (165),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (194), (213), (218),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (227), (230), (231), (232),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (238), (266), (297),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (381), (391), (401), (541), (543), (546), (555),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (627), (628), (664), (760), (764), (777), (780),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (791), (795), (856), (857), (862),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2060.
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (863)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (863) gives:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (864)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_29 & $i(all_56_29)
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (764), (777), (780), (791), (794),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (810), (815), (856), (857), (864),
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2059.
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (865)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (865) implies:
% 229.03/42.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (866)  op(e0, all_56_31) = e0
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (866) imply:
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (867)  op(e0, e1) = e0
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (118), (139), (146), (157), (159),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (192), (198), (200), (211),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (217), (218), (219), (226), (227), (232),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (257), (270), (279), (391), (537), (542),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (544), (546), (627), (636), (640), (648), (662),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (664), (665), (668), (755), (756), (757), (760),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (764), (771), (774), (777), (780), (791), (800),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (809), (814), (857), (859), (860), (861), (867),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2064.
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (868)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_24_1)
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (868) implies:
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (869)   ~ (all_24_1 = e1)
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (870)  op(e3, e2) = all_24_1
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (871)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (123), (126),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (158), (159), (160), (162), (164), (165),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (194), (213), (218),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (227), (230), (231), (232),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (238), (266), (297),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (381), (391), (401), (541), (543), (546), (555),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (627), (628), (664), (760), (764), (777), (780),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (791), (795), (856), (857), (871),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2060.
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (872)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (872) gives:
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (873)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_29 & $i(all_56_29)
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (764), (777), (780), (791), (794),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (810), (815), (856), (857), (873),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2059.
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (874)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (874) implies:
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (875)  op(e0, all_56_31) = e0
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (541), (875) imply:
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (876)  op(e0, e1) = e0
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (118), (139), (146), (157), (159),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (192), (198), (200), (211),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (217), (218), (219), (226), (227), (232),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (257), (270), (279), (391), (537), (542),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (546), (627), (636), (640), (648), (662), (664),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (665), (668), (755), (756), (757), (760), (764),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (771), (774), (777), (780), (791), (800), (809),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (814), (857), (869), (870), (876),
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2061.
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (877)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (877) gives:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (878)  all_58_4 = e0 & op(e3, e1) = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (878) implies:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (879)  op(e3, e1) = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (640), (879), (function-axioms) are
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2089.
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (880)  all_58_9 = e0 & op(e3, e0) = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (880) implies:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (881)  all_58_9 = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (794), (881) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (882)  e3 = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (882) implies:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (883)  e3 = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (790), (883) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (884)  all_58_7 = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (160), (226), (636), (668), (785),
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (884), (function-axioms) are inconsistent by
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2147.
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (885)  all_58_10 = e3 & op(e2, e0) = e3
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (885) implies:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (886)  op(e2, e0) = e3
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (764), (886), (function-axioms) are
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (887)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (555), (785), (887), (function-axioms)
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2058.
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (888)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (668), (785), (888), (function-axioms)
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2148.
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (889)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (889) gives:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (890)  all_54_9 = e2
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (890) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (891)  all_52_6 = e2
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (663), (891) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (892)  $false
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (892) is inconsistent.
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (893)  all_54_9 = e1 | all_54_9 = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (893) gives:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (894)  all_54_9 = e1
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (894) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (895)  all_52_6 = e1
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (645), (895) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (896)  $false
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (896) is inconsistent.
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (897)  all_54_9 = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (897) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (898)  all_52_6 = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (898) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (899)   ~ (all_52_4 = e0)
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (898) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (900)   ~ (all_52_14 = e0)
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (900) implies:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (901)   ~ (all_52_14 = e0)
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (902)  all_54_11 = e3
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (902) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (903)  all_52_14 = e3
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (903) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (904)   ~ (all_52_12 = e3)
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (905)  all_54_3 = e3
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (904), (905) are inconsistent by sub-proof
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2057.
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (906)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (907)  all_54_1 = e3
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (907) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (908)  all_52_4 = e3
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (908) implies:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (909)  all_52_4 = e3
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (909) imply:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (910)  op(e3, e2) = e3
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (906) gives:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (911)  all_54_3 = e2
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (759), (911) are inconsistent by sub-proof
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2290.
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (912)   ~ (all_54_3 = e2)
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (913)  all_54_3 = e1 | all_54_3 = e0
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (771) gives:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (914)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 229.03/42.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_32_1 & $i(all_32_0) &
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_32_1)
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (914) implies:
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (915)  op(e3, e2) = all_32_1
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (162), (165), (212), (267), (280),
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (297), (381), (401), (545), (547), (626), (645),
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (653), (656), (759), (760), (768), (893), (910),
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (913), (915), (function-axioms) are inconsistent
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2052.
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (916)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_32_1)
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (916) implies:
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (917)  op(e3, e2) = all_32_1
% 229.03/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (162), (165), (212), (267), (280),
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (297), (381), (401), (545), (547), (626), (645),
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (653), (656), (759), (760), (768), (893), (910),
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (913), (917), (function-axioms) are inconsistent
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2052.
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (918)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (628), (758), (899), (918) are inconsistent
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2048.
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (919)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (547), (666), (901), (919) are inconsistent
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2173.
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (920)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (920) gives:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (921)  all_58_14 = e2 & op(e0, e1) = e2
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (921) implies:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (922)  all_58_14 = e2
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (923)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (923) gives:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (924)  all_58_4 = e0 & op(e3, e1) = e0
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (924) implies:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (925)  all_58_4 = e0
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (926)  op(e3, e1) = e0
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (228), (230), (668),
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (677), (922), (925), (926), (function-axioms) are
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2043.
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (927)  all_58_5 = e0 & op(e2, e1) = e0
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (927) implies:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (928)  all_58_5 = e0
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (929)  op(e2, e1) = e0
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (165), (228), (230),
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (668), (677), (922), (928), (929),
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2037.
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (930)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (668), (922), (930), (function-axioms) are
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2035.
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (931)  all_58_15 = e2 & op(e0, e0) = e2
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (931) implies:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (932)  all_58_15 = e2
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (555), (932) are inconsistent by sub-proof
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2231.
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | |   (933)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (226), (555),
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | |            (635), (636), (668), (933), (function-axioms) are
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2027.
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | |   (934)  all_58_11 = e2 & op(e1, e0) = e2
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.36  | | | | | | | | | | | | | | | | | | | | | ALPHA: (934) implies:
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | | |   (935)  all_58_11 = e2
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (223), (226), (635),
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | | |            (636), (668), (935), (function-axioms) are
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2028.
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | | | |   (936)  all_54_10 = e1 | all_54_10 = e0
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (401), (653), (936) are inconsistent by
% 229.40/42.37  | | | | | | | | | | | | | | | | | | |            sub-proof #2282.
% 229.40/42.37  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.37  | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | |   (937)  all_58_9 = e1 & op(e3, e0) = e1
% 229.40/42.37  | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (545), (937), (function-axioms) are
% 229.40/42.37  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 229.40/42.37  | | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | Case 2:
% 229.40/42.37  | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | |   (938)  all_58_12 = e1 & op(e0, e3) = e1
% 229.40/42.37  | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | | REF_CLOSE: (159), (542), (938), (function-axioms) are
% 229.40/42.37  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 229.40/42.37  | | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | End of split
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | Case 2:
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | |   (939)  all_18_2 = e0
% 229.40/42.37  | | | | | | | | |   (940)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 &
% 229.40/42.37  | | | | | | | | |            op(e1, e0) = all_18_1 & $i(all_18_0) &
% 229.40/42.37  | | | | | | | | |            $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1, e0) =
% 229.40/42.37  | | | | | | | | |            all_18_1 & $i(all_18_1))
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | COMBINE_EQS: (339), (939) imply:
% 229.40/42.37  | | | | | | | | |   (941)  all_6_2 = e0
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | COMBINE_EQS: (332), (941) imply:
% 229.40/42.37  | | | | | | | | |   (942)  all_28_2 = e0
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | COMBINE_EQS: (266), (941) imply:
% 229.40/42.37  | | | | | | | | |   (943)  all_56_21 = e0
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | REDUCE: (367), (941) imply:
% 229.40/42.37  | | | | | | | | |   (944)   ~ (all_52_2 = e0)
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | REDUCE: (378), (941) imply:
% 229.40/42.37  | | | | | | | | |   (945)   ~ (all_52_6 = e0)
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | REDUCE: (380), (941) imply:
% 229.40/42.37  | | | | | | | | |   (946)   ~ (all_52_8 = e0)
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | REDUCE: (381), (941) imply:
% 229.40/42.37  | | | | | | | | |   (947)   ~ (all_52_9 = e0)
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | REDUCE: (383), (941) imply:
% 229.40/42.37  | | | | | | | | |   (948)   ~ (all_52_11 = e0)
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | REDUCE: (385), (941) imply:
% 229.40/42.37  | | | | | | | | |   (949)   ~ (all_52_14 = e0)
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | REDUCE: (391), (941) imply:
% 229.40/42.37  | | | | | | | | |   (950)   ~ (e3 = e0)
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | REDUCE: (39), (941) imply:
% 229.40/42.37  | | | | | | | | |   (951)  op(e1, e1) = e0
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | BETA: splitting (61) gives:
% 229.40/42.37  | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | Case 1:
% 229.40/42.37  | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | |   (952)   ~ (all_20_2 = e1)
% 229.40/42.37  | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | REDUCE: (341), (952) imply:
% 229.40/42.37  | | | | | | | | | |   (953)   ~ (all_4_2 = e1)
% 229.40/42.37  | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | BETA: splitting (189) gives:
% 229.40/42.37  | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | Case 1:
% 229.40/42.37  | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | |   (954)  all_54_15 = e3
% 229.40/42.37  | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | COMBINE_EQS: (299), (954) imply:
% 229.40/42.37  | | | | | | | | | | |   (955)  all_4_2 = e3
% 229.40/42.37  | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | REDUCE: (395), (955) imply:
% 229.40/42.37  | | | | | | | | | | |   (956)  $false
% 229.40/42.37  | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | CLOSE: (956) is inconsistent.
% 229.40/42.37  | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | Case 2:
% 229.40/42.37  | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | |   (957)   ~ (all_54_15 = e3)
% 229.40/42.37  | | | | | | | | | | |   (958)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 229.40/42.37  | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | BETA: splitting (958) gives:
% 229.40/42.37  | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | Case 1:
% 229.40/42.37  | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | |   (959)  all_54_15 = e2
% 229.40/42.37  | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | COMBINE_EQS: (299), (959) imply:
% 229.40/42.37  | | | | | | | | | | | |   (960)  all_4_2 = e2
% 229.40/42.37  | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | REDUCE: (390), (960) imply:
% 229.40/42.37  | | | | | | | | | | | |   (961)  $false
% 229.40/42.37  | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | CLOSE: (961) is inconsistent.
% 229.40/42.37  | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | Case 2:
% 229.40/42.37  | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | |   (962)   ~ (all_54_15 = e2)
% 229.40/42.37  | | | | | | | | | | | |   (963)  all_54_15 = e1 | all_54_15 = e0
% 229.40/42.37  | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | BETA: splitting (963) gives:
% 229.40/42.37  | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | Case 1:
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | |   (964)  all_54_15 = e1
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | COMBINE_EQS: (299), (964) imply:
% 229.40/42.37  | | | | | | | | | | | | |   (965)  all_4_2 = e1
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | REDUCE: (953), (965) imply:
% 229.40/42.37  | | | | | | | | | | | | |   (966)  $false
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | CLOSE: (966) is inconsistent.
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | Case 2:
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | |   (967)  all_54_15 = e0
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | COMBINE_EQS: (299), (967) imply:
% 229.40/42.37  | | | | | | | | | | | | |   (968)  all_4_2 = e0
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | COMBINE_EQS: (254), (968) imply:
% 229.40/42.37  | | | | | | | | | | | | |   (969)  all_56_31 = e0
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | REDUCE: (379), (968) imply:
% 229.40/42.37  | | | | | | | | | | | | |   (970)   ~ (all_52_7 = e0)
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | REDUCE: (388), (968) imply:
% 229.40/42.37  | | | | | | | | | | | | |   (971)   ~ (all_52_13 = e0)
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | REDUCE: (390), (968) imply:
% 229.40/42.37  | | | | | | | | | | | | |   (972)   ~ (e2 = e0)
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | REDUCE: (953), (968) imply:
% 229.40/42.37  | | | | | | | | | | | | |   (973)   ~ (e1 = e0)
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | REDUCE: (36), (968) imply:
% 229.40/42.37  | | | | | | | | | | | | |   (974)  op(e0, e0) = e0
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | BETA: splitting (235) gives:
% 229.40/42.37  | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | Case 1:
% 229.40/42.37  | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | |   (975)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 229.40/42.37  | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.40/42.37  | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | BETA: splitting (975) gives:
% 229.40/42.37  | | | | | | | | | | | | | | 
% 229.40/42.37  | | | | | | | | | | | | | | Case 1:
% 229.40/42.37  | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | |   (976)  all_58_1 = e0 & op(e3, e2) = e0
% 229.40/42.38  | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | ALPHA: (976) implies:
% 229.40/42.38  | | | | | | | | | | | | | | |   (977)  all_58_1 = e0
% 229.40/42.38  | | | | | | | | | | | | | | |   (978)  op(e3, e2) = e0
% 229.40/42.38  | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | Case 1:
% 229.40/42.38  | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | |   (979)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 229.40/42.38  | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.40/42.38  | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | BETA: splitting (979) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (980)  all_58_2 = e0 & op(e2, e3) = e0
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | ALPHA: (980) implies:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (981)  all_58_2 = e0
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (982)  op(e2, e3) = e0
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 229.40/42.38  | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (982) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (983)  all_52_1 = e0
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 229.40/42.38  | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (978) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (984)  all_52_4 = e0
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | REDUCE: (149), (983) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (985)   ~ (all_52_2 = e0)
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | REDUCE: (148), (983) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (986)   ~ (all_52_3 = e0)
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | SIMP: (986) implies:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (987)   ~ (all_52_3 = e0)
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | REDUCE: (145), (983) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (988)   ~ (all_52_13 = e0)
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | REDUCE: (136), (984) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (989)   ~ (all_52_6 = e0)
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | REDUCE: (135), (984) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (990)   ~ (all_52_7 = e0)
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | REDUCE: (133), (984) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (991)   ~ (all_52_12 = e0)
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | SIMP: (991) implies:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (992)   ~ (all_52_12 = e0)
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | REDUCE: (361), (984) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (993)   ~ (all_10_2 = e0)
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | REDUCE: (369), (984) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | |   (994)   ~ (all_8_2 = e0)
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | |   (995)   ~ (all_22_2 = e1)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | REDUCE: (326), (995) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | |   (996)   ~ (all_8_2 = e1)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | |   (997)  all_54_5 = e3
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (997) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | |   (998)  all_8_2 = e3
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | REDUCE: (392), (998) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | |   (999)  $false
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | CLOSE: (999) is inconsistent.
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | |   (1000)   ~ (all_54_5 = e3)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | |   (1001)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (1001) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | |   (1002)  all_54_5 = e2
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1002) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | |   (1003)  all_8_2 = e2
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (1003) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | |   (1004)  all_56_11 = e2
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (1003) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | |   (1005)   ~ (all_52_7 = e2)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (1003) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | |   (1006)   ~ (all_52_9 = e2)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (377), (1003) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | |   (1007)   ~ (all_52_13 = e2)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (1003) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | |   (1008)   ~ (e3 = e2)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (1003) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | |   (1009)  op(e2, e2) = e2
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | |   (1010)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1010) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | |   (1011)  all_58_1 = e2 & op(e3, e2) = e2
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1011) implies:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | |   (1012)  op(e3, e2) = e2
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (978), (1012), (function-axioms) are
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2026.
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | |   (1013)  all_58_3 = e2 & op(e2, e2) = e2
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1013) implies:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | |   (1014)  all_58_3 = e2
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | |   (1015)   ~ (all_24_2 = e2)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (1015) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | |   (1016)   ~ (all_10_2 = e2)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1017)  all_54_0 = e3
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (1017) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1018)  all_10_2 = e3
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (1018) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1019)  all_56_1 = e3
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (357), (1018) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1020)   ~ (all_52_2 = e3)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (1018) imply:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | |   (1021)   ~ (all_52_3 = e3)
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.40/42.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.40/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (1022)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.40/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1022) gives:
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1023)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1023) gives:
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1024)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1024) implies:
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1025)  op(e3, e2) = e3
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (978), (1025), (function-axioms) are
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2099.
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1026)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (978), (1020), (1026),
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2025.
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1027)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (987), (1019), (1021), (1027),
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2329.
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (1028)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1028) gives:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1029)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (1004), (1005), (1006), (1029),
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2325.
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1030)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (949), (969), (971), (1030),
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2321.
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | |   (1031)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (399), (1016), (1031) are
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | |   (1032)  all_24_2 = e2
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | |   (1033)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | |             = all_24_1 & $i(all_24_1))
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (1032) imply:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | |   (1034)  all_10_2 = e2
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (1034) imply:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | |   (1035)  all_32_2 = e2
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (1034) imply:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | |   (1036)  all_56_1 = e2
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (1034) imply:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | |   (1037)   ~ (all_52_3 = e2)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (1034) imply:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | |   (1038)   ~ (all_52_12 = e2)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | |   (1039)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1039) gives:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (1040)  all_58_6 = e2 & op(e1, e3) = e2
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1040) implies:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (1041)  all_58_6 = e2
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (1042)  op(e1, e3) = e2
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1043)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (1007), (1038), (1043),
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2316.
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1044)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1044) gives:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1045)  all_58_11 = e2 & op(e1, e0) = e2
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1045) implies:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1046)  all_58_11 = e2
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1047)  op(e1, e0) = e2
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1048)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1048) gives:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1049)  all_58_6 = e3 & op(e1, e3) = e3
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1049) implies:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1050)  all_58_6 = e3
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1041), (1050) are inconsistent by sub-proof
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2024.
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1051)  all_58_7 = e3 & op(e1, e2) = e3
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1051) implies:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1052)  op(e1, e2) = e3
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1053)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1053) gives:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1054)  all_58_6 = e1 & op(e1, e3) = e1
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1054) implies:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1055)  op(e1, e3) = e1
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1042), (1055), (function-axioms) are
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1056)  all_58_7 = e1 & op(e1, e2) = e1
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1056) implies:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1057)  op(e1, e2) = e1
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1052), (1057), (function-axioms) are
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2094.
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1058)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1058) gives:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1059)  all_58_8 = e1 & op(e1, e1) = e1
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1059) implies:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1060)  op(e1, e1) = e1
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (944), (945),
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (949), (1060), (function-axioms) are inconsistent
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2020.
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1061)  all_58_11 = e1 & op(e1, e0) = e1
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1061) implies:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1062)  op(e1, e0) = e1
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1047), (1062), (function-axioms) are
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2019.
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1063)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (951), (1046), (1063), (function-axioms)
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2017.
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1064)  all_58_15 = e2 & op(e0, e0) = e2
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1064) implies:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1065)  op(e0, e0) = e2
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (974), (1065), (function-axioms) are
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (1066)  all_58_7 = e2 & op(e1, e2) = e2
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1066) implies:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (1067)  all_58_7 = e2
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (1068)  op(e1, e2) = e2
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (236),
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (977), (978), (1009), (1014),
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (1067), (1068), (function-axioms) are inconsistent
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2012.
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | |   (1069)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1069) gives:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (1070)  all_58_8 = e2 & op(e1, e1) = e2
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1070) implies:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (1071)  op(e1, e1) = e2
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (951), (1071), (function-axioms) are
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (1072)  all_58_11 = e2 & op(e1, e0) = e2
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1072) implies:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (1073)  op(e1, e0) = e2
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1074)   ~ (all_32_2 = e2)
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1035), (1074) imply:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1075)  $false
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1075) is inconsistent.
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1076)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_32_1 & $i(all_32_1))
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1076) gives:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1077)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_32_1 & $i(all_32_0) &
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_32_1)
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1077) implies:
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1078)   ~ (all_32_0 = e1)
% 229.53/42.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1079)  op(e3, e2) = all_32_1
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1080)  op(all_32_1, e3) = all_32_0
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1081)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (159), (1005), (1037), (1081),
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2314.
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1082)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1082) gives:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1083)  all_58_14 = e2 & op(e0, e1) = e2
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1083) implies:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1084)  op(e0, e1) = e2
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, e0, simplifying with (157), (1084) gives:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1085)  all_52_11 = e2
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (160), (1073) gives:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1086)  all_52_14 = e2
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_32_1,
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (978), (1079) gives:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1087)  all_32_1 = e0
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (1086) imply:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1088)   ~ (all_52_2 = e2)
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1080), (1087) imply:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1089)  op(e0, e3) = all_32_0
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1033) gives:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1090)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_24_1 & $i(all_24_0) &
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_24_1)
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1090) implies:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1091)  op(e3, e2) = all_24_1
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (144), (159), (163), (164), (191), (192),
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (214), (256), (257), (268), (944), (951),
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (970), (978), (982), (987), (1005), (1007),
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1036), (1037), (1078), (1088), (1089), (1091),
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2003.
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1092)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_24_1)
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1092) implies:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1093)  op(e3, e2) = all_24_1
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (144), (159), (163), (164), (191), (192),
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (214), (256), (257), (268), (944), (951),
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (970), (978), (982), (987), (1005), (1007),
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1036), (1037), (1078), (1088), (1089), (1093),
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2003.
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1094)  all_58_15 = e2 & op(e0, e0) = e2
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1094) implies:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1095)  op(e0, e0) = e2
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (974), (1095), (function-axioms) are
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1096)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_32_1)
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (978), (1033), (1096), (function-axioms) are
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2002.
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | |   (1097)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1097) gives:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | |   (1098)  all_58_7 = e2 & op(e1, e2) = e2
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1098) implies:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | |   (1099)  all_58_7 = e2
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | |   (1100)  op(e1, e2) = e2
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (236), (238), (977),
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | |            (978), (1009), (1099), (1100), (function-axioms)
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2001.
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | |   (1101)  all_58_13 = e2 & op(e0, e2) = e2
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1101) implies:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | |   (1102)  op(e0, e2) = e2
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1005), (1102), (function-axioms) are
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | |   (1103)  all_54_5 = e1 | all_54_5 = e0
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (397), (996), (1103) are inconsistent by
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | |            sub-proof #2300.
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | End of split
% 229.53/42.42  | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | Case 2:
% 229.53/42.42  | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | |   (1104)  all_22_2 = e1
% 229.53/42.42  | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (1104) imply:
% 229.53/42.42  | | | | | | | | | | | | | | | | | |   (1105)  all_8_2 = e1
% 229.53/42.42  | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (1105) imply:
% 229.53/42.42  | | | | | | | | | | | | | | | | | |   (1106)  all_56_11 = e1
% 229.53/42.42  | | | | | | | | | | | | | | | | | | 
% 229.53/42.42  | | | | | | | | | | | | | | | | | | REDUCE: (373), (1105) imply:
% 229.53/42.43  | | | | | | | | | | | | | | | | | |   (1107)   ~ (all_52_7 = e1)
% 229.53/42.43  | | | | | | | | | | | | | | | | | | 
% 229.53/42.43  | | | | | | | | | | | | | | | | | | REDUCE: (375), (1105) imply:
% 229.53/42.43  | | | | | | | | | | | | | | | | | |   (1108)   ~ (all_52_9 = e1)
% 229.53/42.43  | | | | | | | | | | | | | | | | | | 
% 229.53/42.43  | | | | | | | | | | | | | | | | | | REDUCE: (377), (1105) imply:
% 229.53/42.43  | | | | | | | | | | | | | | | | | |   (1109)   ~ (all_52_13 = e1)
% 229.53/42.43  | | | | | | | | | | | | | | | | | | 
% 229.53/42.43  | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 229.53/42.43  | | | | | | | | | | | | | | | | | | 
% 229.53/42.43  | | | | | | | | | | | | | | | | | | Case 1:
% 229.53/42.43  | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |   (1110)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.69/42.43  | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | BETA: splitting (1110) gives:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |   (1111)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             = e3)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (978), (1106), (1111), (function-axioms)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2000.
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |   (1112)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | |             = e0)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1112) gives:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | |   (1113)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1113) implies:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | |   (1114)   ~ (all_56_31 = e3)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | |   (1115)   ~ (all_56_11 = e3)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | |   (1116)   ~ (all_56_1 = e3)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | |   (1117)  op(e1, e3) = e1
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | |   (1118)  op(e3, e1) = e1
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | REDUCE: (290), (1116) imply:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | |   (1119)   ~ (all_10_2 = e3)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | REDUCE: (1106), (1115) imply:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | |   (1120)   ~ (e3 = e1)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | |   (1121)  all_54_0 = e3
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (1121) imply:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | |   (1122)  all_10_2 = e3
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1119), (1122) imply:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | |   (1123)  $false
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1123) is inconsistent.
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | |   (1124)   ~ (all_54_0 = e3)
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | |   (1125)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1125) gives:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | |   (1126)  all_54_0 = e2
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (1126) imply:
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | |   (1127)  all_10_2 = e2
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.43  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (1127) imply:
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | |   (1128)  all_24_2 = e2
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (1127) imply:
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | |   (1129)  all_32_2 = e2
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (1127) imply:
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | |   (1130)   ~ (all_52_8 = e2)
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (1127) imply:
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | |   (1131)   ~ (all_52_12 = e2)
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1119), (1127) imply:
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | |   (1132)   ~ (e3 = e2)
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | |   (1133)   ~ (all_24_2 = e2)
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1128), (1133) imply:
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | |   (1134)  $false
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1134) is inconsistent.
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.69/42.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | |   (1135)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | |             = all_24_1 & $i(all_24_1))
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (1136)   ~ (all_32_2 = e2)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1129), (1136) imply:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (1137)  $false
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1137) is inconsistent.
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (1138)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_32_1 & $i(all_32_1))
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1139)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1139) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1140)  all_58_1 = e1 & op(e3, e2) = e1
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (977), (1140) are inconsistent by sub-proof
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2015.
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1141)  all_58_3 = e1 & op(e2, e2) = e1
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1141) implies:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1142)  all_58_3 = e1
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1143)  op(e2, e2) = e1
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1138) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (1117) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1144)  all_52_2 = e1
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (1118) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1145)  all_52_8 = e1
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (1144) imply:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1146)   ~ (all_52_14 = e1)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1146) implies:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1147)   ~ (all_52_14 = e1)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (1145) imply:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1148)   ~ (all_52_12 = e1)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1148) implies:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1149)   ~ (all_52_12 = e1)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1130), (1145) imply:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1150)   ~ (e2 = e1)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1151)  all_54_3 = e3
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (1151) imply:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1152)  all_52_12 = e3
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (1152) imply:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1153)   ~ (all_52_13 = e3)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1153) implies:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1154)   ~ (all_52_13 = e3)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (1152) imply:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1155)   ~ (all_52_14 = e3)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1155) implies:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1156)   ~ (all_52_14 = e3)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1157)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1157) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1158)  all_58_2 = e3 & op(e2, e3) = e3
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1158) implies:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1159)  all_58_2 = e3
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (981), (1159) imply:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1160)  e3 = e0
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1160) imply:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1161)  $false
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1161) is inconsistent.
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1162)  all_58_3 = e3 & op(e2, e2) = e3
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1162) implies:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1163)  all_58_3 = e3
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1142), (1163) are inconsistent by sub-proof
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1999.
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1164)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1164) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1165)  all_58_5 = e3 & op(e2, e1) = e3
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1165) implies:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1166)  op(e2, e1) = e3
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1167)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1167) gives:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1168)  all_58_2 = e2 & op(e2, e3) = e2
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1168) implies:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1169)  op(e2, e3) = e2
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (197), (269), (971), (1109), (1154),
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1169), (function-axioms) are inconsistent by
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2291.
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1170)  all_58_3 = e2 & op(e2, e2) = e2
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1170) implies:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1171)  op(e2, e2) = e2
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1143), (1171), (function-axioms) are
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1172)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1172) gives:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1173)  all_58_5 = e2 & op(e2, e1) = e2
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1173) implies:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1174)  op(e2, e1) = e2
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1166), (1174), (function-axioms) are
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1175)  all_58_10 = e2 & op(e2, e0) = e2
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1175) implies:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1176)  op(e2, e0) = e2
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1177)  all_54_7 = e3
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1154), (1177) are inconsistent by
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1178)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1179)  all_54_11 = e3
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1156), (1179) are inconsistent by
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1180)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1180) gives:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1181)  all_54_11 = e2
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1181) imply:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1182)  all_52_14 = e2
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1182) implies:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1183)  all_52_14 = e2
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (1183) imply:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1184)   ~ (all_52_13 = e2)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (269), (1109), (1176), (1178), (1184),
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1995.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1185)  all_54_11 = e1 | all_54_11 = e0
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (949), (1147), (1185) are inconsistent by
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2174.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1186)  all_58_10 = e3 & op(e2, e0) = e3
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1186) implies:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1187)  op(e2, e0) = e3
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1154), (1187), (function-axioms) are
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1188)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (992), (1131), (1149), (1188) are
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1189)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_32_1)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (978), (1135), (1189), (function-axioms) are
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2002.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1190)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1190) gives:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1191)  all_58_7 = e1 & op(e1, e2) = e1
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1191) implies:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1192)  all_58_7 = e1
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1193)  op(e1, e2) = e1
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (225), (226), (951),
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1117), (1192), (1193), (function-axioms) are
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1993.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1194)  all_58_13 = e1 & op(e0, e2) = e1
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1107), (1194), (function-axioms) are
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | |   (1195)  all_54_0 = e1 | all_54_0 = e0
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (399), (1195) are inconsistent by
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2320.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | |   (1196)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (969), (987), (1196), (function-axioms) are
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2308.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |   (1197)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 229.74/42.45  | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | BETA: splitting (1197) gives:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |   (1198)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             = e2)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (969), (1106), (1108), (1198),
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |            #2297.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |   (1199)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |             = e0)
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (949), (969), (971), (1199),
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | |            #2321.
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | |   (1200)  all_58_3 = e0 & op(e2, e2) = e0
% 229.74/42.45  | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (397), (1200), (function-axioms) are
% 229.74/42.45  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 229.74/42.45  | | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | End of split
% 229.74/42.45  | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | Case 2:
% 229.74/42.45  | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | |   (1201)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 229.74/42.45  | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 229.74/42.45  | | | | | | | | | | | | | | | | 
% 229.74/42.45  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (947), (971), (1201),
% 229.74/42.45  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.46  | | | | | | | | | | | | | | | |            #1991.
% 229.74/42.46  | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | End of split
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | Case 2:
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | |   (1202)  all_58_3 = e0 & op(e2, e2) = e0
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | REF_CLOSE: (42), (397), (1202), (function-axioms) are
% 229.74/42.46  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | End of split
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | Case 2:
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | |   (1203)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 229.74/42.46  | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (945), (970), (1203),
% 229.74/42.46  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.46  | | | | | | | | | | | | | |            #1990.
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | End of split
% 229.74/42.46  | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | End of split
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | End of split
% 229.74/42.46  | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | End of split
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | Case 2:
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | |   (1204)  all_20_2 = e1
% 229.74/42.46  | | | | | | | | | |   (1205)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 229.74/42.46  | | | | | | | | | |             & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 229.74/42.46  | | | | | | | | | |             $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 229.74/42.46  | | | | | | | | | |             = all_20_1 & $i(all_20_1))
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | COMBINE_EQS: (341), (1204) imply:
% 229.74/42.46  | | | | | | | | | |   (1206)  all_4_2 = e1
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | SIMP: (1206) implies:
% 229.74/42.46  | | | | | | | | | |   (1207)  all_4_2 = e1
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | COMBINE_EQS: (324), (1207) imply:
% 229.74/42.46  | | | | | | | | | |   (1208)  all_34_2 = e1
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | COMBINE_EQS: (254), (1207) imply:
% 229.74/42.46  | | | | | | | | | |   (1209)  all_56_31 = e1
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | REDUCE: (368), (1207) imply:
% 229.74/42.46  | | | | | | | | | |   (1210)   ~ (all_52_3 = e1)
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | REDUCE: (379), (1207) imply:
% 229.74/42.46  | | | | | | | | | |   (1211)   ~ (all_52_7 = e1)
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | REDUCE: (387), (1207) imply:
% 229.74/42.46  | | | | | | | | | |   (1212)   ~ (all_52_12 = e1)
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | REDUCE: (388), (1207) imply:
% 229.74/42.46  | | | | | | | | | |   (1213)   ~ (all_52_13 = e1)
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | REDUCE: (389), (1207) imply:
% 229.74/42.46  | | | | | | | | | |   (1214)   ~ (all_52_14 = e1)
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | REDUCE: (390), (1207) imply:
% 229.74/42.46  | | | | | | | | | |   (1215)   ~ (e2 = e1)
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | BETA: splitting (220) gives:
% 229.74/42.46  | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | Case 1:
% 229.74/42.46  | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | |   (1216)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 229.74/42.46  | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 229.74/42.46  | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | BETA: splitting (1216) gives:
% 229.74/42.46  | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | Case 1:
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | |   (1217)  all_58_9 = e1 & op(e3, e0) = e1
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | REF_CLOSE: (168), (1212), (1217), (function-axioms) are
% 229.74/42.46  | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | Case 2:
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | |   (1218)  all_58_10 = e1 & op(e2, e0) = e1
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | REF_CLOSE: (164), (1213), (1218), (function-axioms) are
% 229.74/42.46  | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | End of split
% 229.74/42.46  | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | Case 2:
% 229.74/42.46  | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | |   (1219)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 229.74/42.46  | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 229.74/42.46  | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | BETA: splitting (1219) gives:
% 229.74/42.46  | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | Case 1:
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | |   (1220)  all_58_11 = e1 & op(e1, e0) = e1
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | ALPHA: (1220) implies:
% 229.74/42.46  | | | | | | | | | | | |   (1221)  op(e1, e0) = e1
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | REF_CLOSE: (160), (1214), (1221), (function-axioms) are
% 229.74/42.46  | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | Case 2:
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | |   (1222)  all_58_15 = e1 & op(e0, e0) = e1
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | ALPHA: (1222) implies:
% 229.74/42.46  | | | | | | | | | | | |   (1223)  all_58_15 = e1
% 229.74/42.46  | | | | | | | | | | | |   (1224)  op(e0, e0) = e1
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | BETA: splitting (64) gives:
% 229.74/42.46  | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | Case 1:
% 229.74/42.46  | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | |   (1225)   ~ (all_22_2 = e1)
% 229.74/42.46  | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | REDUCE: (326), (1225) imply:
% 229.74/42.46  | | | | | | | | | | | | |   (1226)   ~ (all_8_2 = e1)
% 229.74/42.46  | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | BETA: splitting (199) gives:
% 229.74/42.46  | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | Case 1:
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | |   (1227)  all_54_5 = e3
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | COMBINE_EQS: (275), (1227) imply:
% 229.74/42.46  | | | | | | | | | | | | | |   (1228)  all_8_2 = e3
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | REDUCE: (392), (1228) imply:
% 229.74/42.46  | | | | | | | | | | | | | |   (1229)  $false
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | CLOSE: (1229) is inconsistent.
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | Case 2:
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | |   (1230)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | BETA: splitting (1230) gives:
% 229.74/42.46  | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | Case 1:
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | |   (1231)  all_54_5 = e2
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1231) imply:
% 229.74/42.46  | | | | | | | | | | | | | | |   (1232)  all_8_2 = e2
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | COMBINE_EQS: (353), (1232) imply:
% 229.74/42.46  | | | | | | | | | | | | | | |   (1233)  all_56_11 = e2
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | REDUCE: (366), (1232) imply:
% 229.74/42.46  | | | | | | | | | | | | | | |   (1234)   ~ (all_52_1 = e2)
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | REDUCE: (373), (1232) imply:
% 229.74/42.46  | | | | | | | | | | | | | | |   (1235)   ~ (all_52_7 = e2)
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | REDUCE: (375), (1232) imply:
% 229.74/42.46  | | | | | | | | | | | | | | |   (1236)   ~ (all_52_9 = e2)
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | REDUCE: (377), (1232) imply:
% 229.74/42.46  | | | | | | | | | | | | | | |   (1237)   ~ (all_52_13 = e2)
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | REDUCE: (42), (1232) imply:
% 229.74/42.46  | | | | | | | | | | | | | | |   (1238)  op(e2, e2) = e2
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 229.74/42.46  | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | Case 1:
% 229.74/42.46  | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | |   (1239)   ~ (all_24_2 = e2)
% 229.74/42.46  | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | REDUCE: (301), (1239) imply:
% 229.74/42.46  | | | | | | | | | | | | | | | |   (1240)   ~ (all_10_2 = e2)
% 229.74/42.46  | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 229.74/42.46  | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.46  | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | |   (1241)  all_54_0 = e3
% 229.74/42.46  | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (1241) imply:
% 229.74/42.46  | | | | | | | | | | | | | | | | |   (1242)  all_10_2 = e3
% 229.74/42.46  | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (1242) imply:
% 229.74/42.46  | | | | | | | | | | | | | | | | |   (1243)  all_56_1 = e3
% 229.74/42.46  | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | | REDUCE: (355), (1242) imply:
% 229.74/42.46  | | | | | | | | | | | | | | | | |   (1244)   ~ (all_52_1 = e3)
% 229.74/42.46  | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | | REDUCE: (357), (1242) imply:
% 229.74/42.46  | | | | | | | | | | | | | | | | |   (1245)   ~ (all_52_2 = e3)
% 229.74/42.46  | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | | REDUCE: (359), (1242) imply:
% 229.74/42.46  | | | | | | | | | | | | | | | | |   (1246)   ~ (all_52_3 = e3)
% 229.74/42.46  | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 229.74/42.46  | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.46  | | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | | |   (1247)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.74/42.46  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.46  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.74/42.46  | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.74/42.46  | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.74/42.46  | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 229.74/42.46  | | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | | | BETA: splitting (1247) gives:
% 229.74/42.46  | | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.46  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.46  | | | | | | | | | | | | | | | | | | |   (1248)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.74/42.46  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.46  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.74/42.46  | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.74/42.46  | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.46  | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             = e3)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (1234), (1244), (1245), (1248),
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |            #2333.
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |   (1249)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             = e0)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1243), (1246), (1249), (function-axioms)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2270.
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.47  | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | |   (1250)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 229.74/42.47  | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 229.74/42.47  | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | BETA: splitting (1250) gives:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |   (1251)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             = e2)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (1233), (1235), (1236), (1251),
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |            #2325.
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |   (1252)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             = e0)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (949), (1214), (1233), (1252),
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |            #1988.
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.47  | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | End of split
% 229.74/42.47  | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.47  | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | |   (1253)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 229.74/42.47  | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (399), (1240), (1253) are
% 229.74/42.47  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 229.74/42.47  | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | End of split
% 229.74/42.47  | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | Case 2:
% 229.74/42.47  | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | |   (1254)  all_24_2 = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (1254) imply:
% 229.74/42.47  | | | | | | | | | | | | | | | |   (1255)  all_10_2 = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | SIMP: (1255) implies:
% 229.74/42.47  | | | | | | | | | | | | | | | |   (1256)  all_10_2 = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (1256) imply:
% 229.74/42.47  | | | | | | | | | | | | | | | |   (1257)  all_56_1 = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | REDUCE: (359), (1256) imply:
% 229.74/42.47  | | | | | | | | | | | | | | | |   (1258)   ~ (all_52_3 = e2)
% 229.74/42.47  | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | REDUCE: (361), (1256) imply:
% 229.74/42.47  | | | | | | | | | | | | | | | |   (1259)   ~ (all_52_4 = e2)
% 229.74/42.47  | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | REDUCE: (365), (1256) imply:
% 229.74/42.47  | | | | | | | | | | | | | | | |   (1260)   ~ (all_52_12 = e2)
% 229.74/42.47  | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | REDUCE: (45), (1256) imply:
% 229.74/42.47  | | | | | | | | | | | | | | | |   (1261)  op(e3, e3) = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 229.74/42.47  | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.47  | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | |   (1262)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 229.74/42.47  | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 229.74/42.47  | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (159), (1235), (1258), (1262),
% 229.74/42.47  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.47  | | | | | | | | | | | | | | | | |            #2314.
% 229.74/42.47  | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.47  | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | |   (1263)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 229.74/42.47  | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 229.74/42.47  | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | BETA: splitting (1263) gives:
% 229.74/42.47  | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | |   (1264)  all_58_14 = e2 & op(e0, e1) = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | ALPHA: (1264) implies:
% 229.74/42.47  | | | | | | | | | | | | | | | | | |   (1265)  op(e0, e1) = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |   (1266)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (1237), (1260), (1266),
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |            #2316.
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |   (1267)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 229.74/42.47  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (1267) gives:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | |   (1268)  all_58_11 = e2 & op(e1, e0) = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | | ALPHA: (1268) implies:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | |   (1269)  all_58_11 = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | |   (1270)  op(e1, e0) = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | |              e2, e1, e0, simplifying with (157), (1265) gives:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | |   (1271)  all_52_11 = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (160), (1270) gives:
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | |   (1272)  all_52_14 = e2
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.47  | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (1272) imply:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | |   (1273)   ~ (all_52_2 = e2)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (1272) imply:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | |   (1274)   ~ (all_52_6 = e2)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1271) imply:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | |   (1275)   ~ (all_52_8 = e2)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | |   (1276)   ~ (all_28_2 = e0)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | REDUCE: (942), (1276) imply:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | |   (1277)  $false
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | CLOSE: (1277) is inconsistent.
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | |   (1278)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_28_1 & $i(all_28_0) &
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | |             $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | |             = all_28_1 & $i(all_28_1))
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (940) gives:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | |   (1279)   ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 &
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_18_1 & $i(all_18_0) &
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1279) implies:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | |   (1280)  op(e1, e0) = all_18_1
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | |   (1281)  op(all_18_1, e1) = all_18_0
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | |   (1282)   ~ (all_34_2 = e1)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1208), (1282) imply:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | |   (1283)  $false
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1283) is inconsistent.
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | |   (1284)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1284) gives:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | |   (1285)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_34_1 & $i(all_34_0) &
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1285) implies:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | |   (1286)   ~ (all_34_0 = e3)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | |   (1287)  op(e0, e1) = all_34_1
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | |   (1288)  op(all_34_1, e0) = all_34_0
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1205) gives:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (1289)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_20_1 & $i(all_20_0) &
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1289) implies:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (1290)  op(e0, e1) = all_20_1
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (120), (123), (133), (134), (135), (140),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (143), (144), (145), (146), (148), (149), (158),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (191), (195), (196), (197),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (198), (200), (201), (202), (203), (213), (214),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (224), (225), (226), (235), (239), (240),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (243), (246), (256), (267), (268), (269),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (279), (280), (281), (282), (944), (945),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (946), (947), (949), (951), (1211), (1212),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (1213), (1223), (1224), (1234), (1236), (1237),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (1238), (1257), (1259), (1260), (1261), (1265),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (1269), (1270), (1273), (1274), (1275), (1278),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (1280), (1281), (1286), (1287), (1288), (1290),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            #1943.
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (1291)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1291) implies:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (1292)  op(e0, e1) = all_20_1
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (120), (123), (133), (134), (135), (140),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (143), (144), (145), (146), (148), (149), (158),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (191), (195), (196), (197),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (198), (200), (201), (202), (203), (213), (214),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (224), (225), (226), (235), (239), (240),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (243), (246), (256), (267), (268), (269),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (279), (280), (281), (282), (944), (945),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (946), (947), (949), (951), (1211), (1212),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (1213), (1223), (1224), (1234), (1236), (1237),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (1238), (1257), (1259), (1260), (1261), (1265),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (1269), (1270), (1273), (1274), (1275), (1278),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (1280), (1281), (1286), (1287), (1288), (1292),
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | |            #1943.
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | |   (1293)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 &
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1293) implies:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | |   (1294)   ~ (all_34_1 = e2)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | |   (1295)  op(e0, e1) = all_34_1
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1205), (1265), (1294), (1295), (function-axioms)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2236.
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | |   (1296)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 &
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1296) implies:
% 229.74/42.48  | | | | | | | | | | | | | | | | | | | | | |   (1297)  op(e1, e0) = all_18_1
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | |   (1298)   ~ (all_34_2 = e1)
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1208), (1298) imply:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | |   (1299)  $false
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1299) is inconsistent.
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | |   (1300)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1300) gives:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | |   (1301)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_34_1 & $i(all_34_0) &
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1301) implies:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | |   (1302)   ~ (all_34_0 = e3)
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | |   (1303)  op(e0, e1) = all_34_1
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | |   (1304)  op(all_34_1, e0) = all_34_0
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1205) gives:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (1305)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_20_1 & $i(all_20_0) &
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1305) implies:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (1306)  op(e0, e1) = all_20_1
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (117), (120), (123), (133), (134), (135),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (143), (144), (145), (146), (148), (149),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (159), (160), (162), (163), (164), (165),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (191), (195), (196),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (198), (200), (201), (202), (203), (213),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (219), (224), (225), (226), (235), (239),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (241), (243), (246), (256), (267), (268),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (279), (280), (281), (282), (944),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (945), (946), (949), (951), (1211), (1212),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (1213), (1223), (1224), (1234), (1236), (1237),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (1238), (1257), (1259), (1260), (1261), (1265),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (1269), (1270), (1273), (1274), (1275), (1278),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (1297), (1302), (1303), (1304), (1306),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            #1942.
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (1307)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1307) implies:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (1308)  op(e0, e1) = all_20_1
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (117), (120), (123), (133), (134), (135),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (143), (144), (145), (146), (148), (149),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (159), (160), (162), (163), (164), (165),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (191), (195), (196),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (198), (200), (201), (202), (203), (213),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (219), (224), (225), (226), (235), (239),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (241), (243), (246), (256), (267), (268),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (279), (280), (281), (282), (944),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (945), (946), (949), (951), (1211), (1212),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (1213), (1223), (1224), (1234), (1236), (1237),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (1238), (1257), (1259), (1260), (1261), (1265),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (1269), (1270), (1273), (1274), (1275), (1278),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (1297), (1302), (1303), (1304), (1308),
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | |            #1942.
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | |   (1309)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 &
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1309) implies:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | |   (1310)   ~ (all_34_1 = e2)
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | |   (1311)  op(e0, e1) = all_34_1
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1205), (1265), (1310), (1311), (function-axioms)
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2236.
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | |   (1312)  all_58_15 = e2 & op(e0, e0) = e2
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | ALPHA: (1312) implies:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | |   (1313)  all_58_15 = e2
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1223), (1313) are inconsistent by sub-proof
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | |            #2231.
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.49  | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | |   (1314)  all_58_15 = e2 & op(e0, e0) = e2
% 229.74/42.49  | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | ALPHA: (1314) implies:
% 229.74/42.49  | | | | | | | | | | | | | | | | | |   (1315)  all_58_15 = e2
% 229.74/42.49  | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1223), (1315) are inconsistent by sub-proof
% 229.74/42.49  | | | | | | | | | | | | | | | | | |            #2231.
% 229.74/42.49  | | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | Case 2:
% 229.74/42.49  | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | |   (1316)  all_54_5 = e1 | all_54_5 = e0
% 229.74/42.49  | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | REF_CLOSE: (275), (397), (1226), (1316) are inconsistent by
% 229.74/42.49  | | | | | | | | | | | | | | |            sub-proof #2300.
% 229.74/42.49  | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | End of split
% 229.74/42.49  | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | Case 2:
% 229.74/42.49  | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | |   (1317)  all_22_2 = e1
% 229.74/42.49  | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | COMBINE_EQS: (326), (1317) imply:
% 229.74/42.49  | | | | | | | | | | | | |   (1318)  all_8_2 = e1
% 229.74/42.49  | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | SIMP: (1318) implies:
% 229.74/42.49  | | | | | | | | | | | | |   (1319)  all_8_2 = e1
% 229.74/42.49  | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | COMBINE_EQS: (353), (1319) imply:
% 229.74/42.49  | | | | | | | | | | | | |   (1320)  all_56_11 = e1
% 229.74/42.49  | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | REDUCE: (366), (1319) imply:
% 229.74/42.49  | | | | | | | | | | | | |   (1321)   ~ (all_52_1 = e1)
% 229.74/42.49  | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | REDUCE: (369), (1319) imply:
% 229.74/42.49  | | | | | | | | | | | | |   (1322)   ~ (all_52_4 = e1)
% 229.74/42.49  | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | REDUCE: (392), (1319) imply:
% 229.74/42.49  | | | | | | | | | | | | |   (1323)   ~ (e3 = e1)
% 229.74/42.49  | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | REDUCE: (42), (1319) imply:
% 229.74/42.49  | | | | | | | | | | | | |   (1324)  op(e2, e2) = e1
% 229.74/42.49  | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | BETA: splitting (224) gives:
% 229.74/42.49  | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | Case 1:
% 229.74/42.49  | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | |   (1325)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 229.74/42.49  | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 229.74/42.49  | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | BETA: splitting (1325) gives:
% 229.74/42.49  | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | Case 1:
% 229.74/42.49  | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | |   (1326)  all_58_6 = e1 & op(e1, e3) = e1
% 229.74/42.49  | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | ALPHA: (1326) implies:
% 229.74/42.49  | | | | | | | | | | | | | | |   (1327)  op(e1, e3) = e1
% 229.74/42.49  | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 229.74/42.49  | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | Case 1:
% 229.74/42.49  | | | | | | | | | | | | | | | | 
% 229.74/42.49  | | | | | | | | | | | | | | | |   (1328)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 229.74/42.49  | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 229.74/42.49  | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (170), (393), (1322), (1328),
% 229.74/42.50  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.50  | | | | | | | | | | | | | | | |            #2227.
% 229.74/42.50  | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | Case 2:
% 229.74/42.50  | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | |   (1329)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 229.74/42.50  | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | BETA: splitting (1329) gives:
% 229.74/42.50  | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1330)  all_58_4 = e1 & op(e3, e1) = e1
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | ALPHA: (1330) implies:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1331)  op(e3, e1) = e1
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 229.74/42.50  | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (1327) gives:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1332)  all_52_2 = e1
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 229.74/42.50  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (1331) gives:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1333)  all_52_8 = e1
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | REDUCE: (144), (1332) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1334)   ~ (all_52_3 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | REDUCE: (143), (1332) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1335)   ~ (all_52_6 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | SIMP: (1335) implies:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1336)   ~ (all_52_6 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | REDUCE: (141), (1332) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1337)   ~ (all_52_14 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | REDUCE: (123), (1333) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1338)   ~ (all_52_9 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | SIMP: (1338) implies:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1339)   ~ (all_52_9 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | REDUCE: (121), (1333) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1340)   ~ (all_52_11 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | SIMP: (1340) implies:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1341)   ~ (all_52_11 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | REDUCE: (120), (1333) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1342)   ~ (all_52_12 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | REDUCE: (363), (1333) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | |   (1343)   ~ (all_10_2 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 229.74/42.50  | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | |   (1344)   ~ (all_24_2 = e2)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | REDUCE: (301), (1344) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | | |   (1345)   ~ (all_10_2 = e2)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | |   (1346)  all_54_0 = e3
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (1346) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | |   (1347)  all_10_2 = e3
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (1347) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | |   (1348)  all_56_1 = e3
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | REDUCE: (355), (1347) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | |   (1349)   ~ (all_52_1 = e3)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | REDUCE: (359), (1347) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | |   (1350)   ~ (all_52_3 = e3)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | REDUCE: (45), (1347) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | |   (1351)  op(e3, e3) = e3
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |   (1352)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (167), (1327), (1348), (1349), (1350),
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |            (1352), (function-axioms) are inconsistent by
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |            sub-proof #2199.
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |   (1353)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1353) gives:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |   (1354)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             = e2)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1354) gives:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |   (1355)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1355) implies:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |   (1356)   ~ (all_56_31 = e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1209), (1356) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |   (1357)  $false
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1357) is inconsistent.
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |   (1358)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (943), (1339), (1358), (function-axioms)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1941.
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |   (1359)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | |             = e0)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1359) gives:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |   (1360)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |             e2) = e0
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1360) implies:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |   (1361)  op(e0, e2) = e0
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |   (1362)  op(e2, e0) = e0
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (1361) gives:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |   (1363)  all_52_7 = e0
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (1362) gives:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |   (1364)  all_52_13 = e0
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (1364) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |   (1365)   ~ (all_52_1 = e0)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1363) imply:
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | |   (1366)   ~ (all_52_3 = e0)
% 229.74/42.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (944), (1351),
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |            (1365), (1366), (function-axioms) are inconsistent
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1938.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |   (1367)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (949), (1214), (1367), (function-axioms)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1989.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | |   (1368)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (399), (1345), (1368) are
% 229.74/42.51  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.51  | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | |   (1369)  all_24_2 = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (1369) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | |   (1370)  all_10_2 = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (1370) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | |   (1371)  all_56_1 = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | REDUCE: (355), (1370) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | |   (1372)   ~ (all_52_1 = e2)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | REDUCE: (359), (1370) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | |   (1373)   ~ (all_52_3 = e2)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | REDUCE: (361), (1370) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | |   (1374)   ~ (all_52_4 = e2)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | REDUCE: (365), (1370) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | |   (1375)   ~ (all_52_12 = e2)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | REDUCE: (45), (1370) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | |   (1376)  op(e3, e3) = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | |   (1377)  all_54_11 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1377) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | |   (1378)  all_52_14 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | SIMP: (1378) implies:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | |   (1379)  all_52_14 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | REDUCE: (126), (1379) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | |   (1380)   ~ (all_52_6 = e3)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | REDUCE: (112), (1379) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | |   (1381)   ~ (all_52_12 = e3)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | REDUCE: (110), (1379) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | |   (1382)   ~ (all_52_13 = e3)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | |   (1383)  all_54_3 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (1381), (1383) are inconsistent by
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | |   (1384)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | |   (1385)  all_54_9 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (1385) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | |   (1386)  all_52_6 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | REDUCE: (1380), (1386) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | |   (1387)  $false
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | CLOSE: (1387) is inconsistent.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | |   (1388)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1388) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |   (1389)  all_54_9 = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (1389) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |   (1390)  all_52_6 = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (1390) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |   (1391)   ~ (all_52_7 = e2)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | SIMP: (1391) implies:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |   (1392)   ~ (all_52_7 = e2)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (1390) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | |   (1393)  op(e1, e2) = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1384) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | |   (1394)  all_54_3 = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (1375), (1394) are inconsistent by
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2290.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | |   (1395)  all_54_3 = e1 | all_54_3 = e0
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1395) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | |   (1396)  all_54_3 = e1
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (1212), (1396) are inconsistent by
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2289.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | |   (1397)  all_54_3 = e0
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (1397) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | |   (1398)  all_52_12 = e0
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1398) implies:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | |   (1399)  all_52_12 = e0
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (1399) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | |   (1400)   ~ (all_52_4 = e0)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (1399) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | |   (1401)   ~ (all_52_13 = e0)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1401) implies:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | |   (1402)   ~ (all_52_13 = e0)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (1403)  all_54_7 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1382), (1403) are inconsistent by
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (1404)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1404) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1405)  all_54_7 = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1405) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1406)  all_52_13 = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1406) implies:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1407)  all_52_13 = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (1407) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1408)   ~ (all_52_9 = e2)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1409)  all_54_1 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (1409) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1410)  all_52_4 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1410) implies:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1411)  all_52_4 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1411) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1412)   ~ (all_52_7 = e3)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1412) implies:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1413)   ~ (all_52_7 = e3)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (1411) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1414)  op(e3, e2) = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1415)  all_54_13 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (1413), (1415) are inconsistent by
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1416)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1417)  all_54_6 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (1417) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1418)  all_52_9 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1418) implies:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1419)  all_52_9 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1419) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1420)   ~ (all_52_11 = e3)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1420) implies:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1421)   ~ (all_52_11 = e3)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (1419) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1422)  op(e2, e1) = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1423)  all_54_14 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (1423) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1424)  all_52_11 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1421), (1424) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1425)  $false
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1425) is inconsistent.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1426)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1427)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1427) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1428)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_9 & $i(all_56_9)
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1428) implies:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1429)  op(e3, e2) = all_56_9
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1430)  op(e3, all_56_9) = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1416) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1431)  all_54_13 = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1431) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1432)  all_52_7 = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1392), (1432) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1433)  $false
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1433) is inconsistent.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1434)  all_54_13 = e1 | all_54_13 = e0
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1434) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1435)  all_54_13 = e1
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1435) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1436)  all_52_7 = e1
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1211), (1436) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1437)  $false
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1437) is inconsistent.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_9,
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (1414), (1429) gives:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1438)  all_56_9 = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1430), (1438) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1439)  op(e3, e3) = e3
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1376), (1439), (function-axioms) are
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1440)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1440) implies:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1441)  op(e2, all_56_11) = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1320), (1441) imply:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1442)  op(e2, e1) = e2
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1422), (1442), (function-axioms) are
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1443)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1443) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1444)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1444) implies:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1445)  op(e1, e2) = all_56_13
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1446)  op(e1, all_56_13) = e1
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1416) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1447)  all_54_13 = e2
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1447) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1448)  all_52_7 = e2
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1392), (1448) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1449)  $false
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1449) is inconsistent.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1450)  all_54_13 = e1 | all_54_13 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1450) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1451)  all_54_13 = e1
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1451) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1452)  all_52_7 = e1
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1211), (1452) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1453)  $false
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1453) is inconsistent.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1454)  all_54_13 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1454) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1455)  all_52_7 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1211), (1455) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1456)   ~ (e1 = e0)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (1393), (1445)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1457)  all_56_13 = e2
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1446), (1457) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1458)  op(e1, e2) = e1
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (255), (948), (951), (1341), (1426), (1445),
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1446), (1458), (function-axioms) are inconsistent
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1934.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1459)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (256), (1211), (1224), (1392), (1416),
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1459), (function-axioms) are inconsistent by
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1932.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1460)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (947), (1339), (1408), (1460) are
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2244.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1461)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (1322), (1374), (1400), (1461) are
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2048.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1462)  all_54_7 = e1 | all_54_7 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1213), (1402), (1462) are inconsistent by
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2293.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | |   (1463)  all_54_9 = e1 | all_54_9 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (163), (267), (945), (1327), (1463),
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | |            #1931.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | |   (1464)   ~ (all_54_11 = e3)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | |   (1465)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | REDUCE: (258), (1464) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | |   (1466)   ~ (all_52_14 = e3)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (1465) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | |   (1467)  all_54_11 = e2
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1467) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | |   (1468)  all_52_14 = e2
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | SIMP: (1468) implies:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | |   (1469)  all_52_14 = e2
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (1469) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | |   (1470)   ~ (all_52_13 = e2)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (1469) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | |   (1471)  op(e1, e0) = e2
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | |   (1472)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1472) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | |   (1473)  all_58_6 = e3 & op(e1, e3) = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1473) implies:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | |   (1474)  op(e1, e3) = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1327), (1474), (function-axioms) are
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | |   (1475)  all_58_7 = e3 & op(e1, e2) = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1475) implies:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | |   (1476)  op(e1, e2) = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | |   (1477)  all_54_9 = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (1477) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | |   (1478)  all_52_6 = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (1478) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | |   (1479)   ~ (all_52_4 = e3)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (1478) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | |   (1480)   ~ (all_52_7 = e3)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1480) implies:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | |   (1481)   ~ (all_52_7 = e3)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | |   (1482)  all_54_1 = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (1479), (1482) are inconsistent by
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | |   (1483)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (1484)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (1324), (1372), (1484),
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |            #1929.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (1485)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1485) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1486)  all_58_5 = e2 & op(e2, e1) = e2
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1486) implies:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1487)  op(e2, e1) = e2
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1483) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1488)  all_54_1 = e2
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (1374), (1488) are inconsistent by
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1928.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1489)   ~ (all_54_1 = e2)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1490)  all_54_1 = e1 | all_54_1 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1490) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1491)  all_54_1 = e1
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (1322), (1491) are inconsistent by
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2051.
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1492)  all_54_1 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (1492) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1493)  all_52_4 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1493) implies:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1494)  all_52_4 = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (1494) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1495)   ~ (all_52_12 = e0)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1495) implies:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1496)   ~ (all_52_12 = e0)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1374), (1494) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1497)   ~ (e2 = e0)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1322), (1494) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1498)   ~ (e1 = e0)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (1494) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1499)  op(e3, e2) = e0
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1500)  all_54_3 = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (1500) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1501)  all_52_12 = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1501) implies:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1502)  all_52_12 = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (1502) imply:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1503)   ~ (all_52_13 = e3)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1503) implies:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1504)   ~ (all_52_13 = e3)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1505)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_27 & $i(all_56_27))
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1505) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1506)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) = all_56_25 & $i(all_56_25)
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1506) implies:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1507)  op(e3, e0) = all_56_25
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1508)  op(e3, all_56_25) = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1509)  all_54_7 = e3
% 229.74/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1504), (1509) are inconsistent by
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1510)   ~ (all_54_7 = e3)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1511)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1512)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1512) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1513)  all_58_2 = e3 & op(e2, e3) = e3
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1513) implies:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1514)  all_58_2 = e3
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1515)  all_58_15 = e0 & op(e0, e0) = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1515) implies:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1516)  op(e0, e0) = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1224), (1516), (function-axioms) are
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1517)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1517) implies:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1518)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1519)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (1376), (1514), (1519),
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1927.
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1520)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1520) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1521)  all_58_6 = e0 & op(e1, e3) = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1521) implies:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1522)  op(e1, e3) = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (944), (1522), (function-axioms) are
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1523)  all_58_12 = e0 & op(e0, e3) = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1523) implies:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1524)  all_58_12 = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1518) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1525)  all_58_9 = e0 & op(e3, e0) = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1525) implies:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1526)  op(e3, e0) = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1507), (1508), (1526), (function-axioms) are
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1926.
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1527)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1527) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1528)  all_58_10 = e0 & op(e2, e0) = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1528) implies:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1529)  op(e2, e0) = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1530)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1530) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1531)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (1327), (1499), (1531),
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1925.
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1532)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1532) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1533)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1533) implies:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1534)  all_56_5 = e1
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1511) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1535)  all_54_7 = e2
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1470), (1535) are inconsistent by
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1997.
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1536)  all_54_7 = e1 | all_54_7 = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1536) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1537)  all_54_7 = e1
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1213), (1537) are inconsistent by
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1538)  all_54_7 = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1538) imply:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1539)  all_52_13 = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1539) implies:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1540)  all_52_13 = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (1540) imply:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1541)   ~ (all_52_1 = e0)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1542)  all_54_4 = e3
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (1542) imply:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1543)  all_52_1 = e3
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1543) implies:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1544)  all_52_1 = e3
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (1544) imply:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1545)   ~ (all_52_3 = e3)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1545) implies:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1546)   ~ (all_52_3 = e3)
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (1544) imply:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1547)  op(e2, e3) = e3
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1548)  all_54_12 = e3
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (1548) imply:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1549)  all_52_3 = e3
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1546), (1549) imply:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1550)  $false
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1550) is inconsistent.
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1551)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1552)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (1371), (1499), (1547), (1552),
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1924.
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1553)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1553) gives:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1554)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_5 & $i(all_56_5)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1554) implies:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1555)  op(e1, all_56_5) = e1
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1534), (1555) imply:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1556)  op(e1, e1) = e1
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (944), (945),
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (949), (1556), (function-axioms) are inconsistent
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2020.
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1557)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_7 & $i(all_56_7)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (257), (1210), (1224), (1373), (1551),
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1557), (function-axioms) are inconsistent by
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2242.
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1558)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (1321), (1372), (1541), (1558) are
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1921.
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1559)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1559) gives:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1560)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1560) implies:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1561)   ~ (all_56_21 = e0)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (943), (1561) imply:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1562)  $false
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1562) is inconsistent.
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1563)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e0
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1563) implies:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1564)  op(e3, e0) = e0
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1507), (1508), (1564), (function-axioms) are
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1926.
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1565)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1565) gives:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1566)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1566) gives:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1567)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1567) implies:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1568)  op(e1, e2) = e2
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1476), (1568), (function-axioms) are
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2207.
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1569)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (165), (1339), (1529), (1569),
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1920.
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1570)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1570) gives:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1571)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e0
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1571) implies:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1572)  op(e0, e2) = e0
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (158), (218), (219),
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1223), (1481), (1524), (1572), (function-axioms)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1914.
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1573)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (949), (1471), (1573),
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1960.
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1574)  all_58_11 = e0 & op(e1, e0) = e0
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1574) implies:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1575)  op(e1, e0) = e0
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (949), (1575), (function-axioms) are
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2323.
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1576)  all_58_3 = e3 & op(e2, e2) = e3
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (1213), (1321),
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1339), (1576), (function-axioms) are inconsistent
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2196.
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1577)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (1487), (1504), (1577),
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1913.
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1578)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) = all_56_27 & $i(all_56_27)
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1578) implies:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1579)  op(e2, e0) = all_56_27
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1580)  op(e2, all_56_27) = e2
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1581)  all_58_15 = e0 & op(e0, e0) = e0
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1581) implies:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1582)  op(e0, e0) = e0
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1224), (1582), (function-axioms) are
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1583)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1583) implies:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1584)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1584) gives:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1585)  all_58_9 = e0 & op(e3, e0) = e0
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1585) implies:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1586)  op(e3, e0) = e0
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1496), (1586), (function-axioms) are
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2258.
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1587)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1587) gives:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1588)  all_58_10 = e0 & op(e2, e0) = e0
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1588) implies:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1589)  op(e2, e0) = e0
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (949), (1214), (1465), (1579), (1580),
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1589), (function-axioms) are inconsistent by
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1912.
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1590)  all_58_11 = e0 & op(e1, e0) = e0
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1590) implies:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1591)  op(e1, e0) = e0
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (949), (1591), (function-axioms) are
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2323.
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1592)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_31) = e0)
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (162), (948), (1209), (1336), (1471),
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1592), (function-axioms) are inconsistent by
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1910.
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1593)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (1212), (1375), (1496), (1593) are
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1594)  all_58_10 = e2 & op(e2, e0) = e2
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1594) implies:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1595)  op(e2, e0) = e2
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1470), (1595), (function-axioms) are
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | |   (1596)   ~ (all_54_9 = e3)
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (1596) imply:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | |   (1597)   ~ (all_52_6 = e3)
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1476), (1597), (function-axioms) are
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | |   (1598)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (951), (1466), (1598),
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | |            #1909.
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | |   (1599)  all_54_11 = e1 | all_54_11 = e0
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (949), (1214), (1599) are inconsistent by
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | |            sub-proof #2174.
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | |   (1600)  all_58_9 = e1 & op(e3, e0) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1212), (1600), (function-axioms) are
% 229.74/42.55  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | |   (1601)  all_58_7 = e1 & op(e1, e2) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | ALPHA: (1601) implies:
% 229.74/42.55  | | | | | | | | | | | | | | |   (1602)  all_58_7 = e1
% 229.74/42.55  | | | | | | | | | | | | | | |   (1603)  op(e1, e2) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | Case 1:
% 229.74/42.55  | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | |   (1604)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 229.74/42.55  | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 229.74/42.55  | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | BETA: splitting (1604) gives:
% 229.74/42.55  | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | |   (1605)  all_58_0 = e1 & op(e3, e3) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (393), (1605), (function-axioms) are
% 229.74/42.55  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2230.
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | |   (1606)  all_58_2 = e1 & op(e2, e3) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1321), (1606), (function-axioms) are
% 229.74/42.55  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | |   (1607)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 229.74/42.55  | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 229.74/42.55  | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | BETA: splitting (1607) gives:
% 229.74/42.55  | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | |   (1608)  all_58_6 = e1 & op(e1, e3) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | ALPHA: (1608) implies:
% 229.74/42.55  | | | | | | | | | | | | | | | | |   (1609)  op(e1, e3) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (225), (226), (951),
% 229.74/42.55  | | | | | | | | | | | | | | | | |            (1602), (1603), (1609), (function-axioms) are
% 229.74/42.55  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1993.
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | |   (1610)  all_58_12 = e1 & op(e0, e3) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1210), (1610), (function-axioms) are
% 229.74/42.55  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 229.74/42.55  | | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | |   (1611)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 229.74/42.55  | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 229.74/42.55  | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | BETA: splitting (1611) gives:
% 229.74/42.55  | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | Case 1:
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | |   (1612)  all_58_8 = e1 & op(e1, e1) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | ALPHA: (1612) implies:
% 229.74/42.55  | | | | | | | | | | | | | | |   (1613)  op(e1, e1) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (944), (945),
% 229.74/42.55  | | | | | | | | | | | | | | |            (949), (1613), (function-axioms) are inconsistent
% 229.74/42.55  | | | | | | | | | | | | | | |            by sub-proof #2020.
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | |   (1614)  all_58_11 = e1 & op(e1, e0) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | ALPHA: (1614) implies:
% 229.74/42.55  | | | | | | | | | | | | | | |   (1615)  op(e1, e0) = e1
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | | REF_CLOSE: (160), (1214), (1615), (function-axioms) are
% 229.74/42.55  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 229.74/42.55  | | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | | 
% 229.74/42.55  | | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | | 
% 229.74/42.55  | | | | | | | | End of split
% 229.74/42.55  | | | | | | | | 
% 229.74/42.55  | | | | | | | Case 2:
% 229.74/42.55  | | | | | | | | 
% 229.74/42.55  | | | | | | | |   (1616)  all_16_2 = e0
% 229.74/42.55  | | | | | | | |   (1617)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 229.74/42.55  | | | | | | | |             op(e3, e0) = all_16_1 & $i(all_16_0) & $i(all_16_1))
% 229.74/42.55  | | | | | | | |           | ( ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 229.74/42.55  | | | | | | | |             $i(all_16_1))
% 229.74/42.55  | | | | | | | | 
% 229.74/42.55  | | | | | | | | COMBINE_EQS: (342), (1616) imply:
% 229.74/42.55  | | | | | | | |   (1618)  all_10_2 = e0
% 229.74/42.55  | | | | | | | | 
% 229.74/42.55  | | | | | | | | SIMP: (1618) implies:
% 229.74/42.55  | | | | | | | |   (1619)  all_10_2 = e0
% 229.74/42.55  | | | | | | | | 
% 229.74/42.56  | | | | | | | | COMBINE_EQS: (350), (1619) imply:
% 229.74/42.56  | | | | | | | |   (1620)  all_50_2 = e0
% 229.74/42.56  | | | | | | | | 
% 229.74/42.56  | | | | | | | | COMBINE_EQS: (290), (1619) imply:
% 229.74/42.56  | | | | | | | |   (1621)  all_56_1 = e0
% 229.74/42.56  | | | | | | | | 
% 229.74/42.56  | | | | | | | | REDUCE: (355), (1619) imply:
% 229.74/42.56  | | | | | | | |   (1622)   ~ (all_52_1 = e0)
% 229.74/42.56  | | | | | | | | 
% 229.74/42.56  | | | | | | | | REDUCE: (357), (1619) imply:
% 229.74/42.56  | | | | | | | |   (1623)   ~ (all_52_2 = e0)
% 229.74/42.56  | | | | | | | | 
% 229.74/42.56  | | | | | | | | REDUCE: (359), (1619) imply:
% 229.74/42.56  | | | | | | | |   (1624)   ~ (all_52_3 = e0)
% 229.74/42.56  | | | | | | | | 
% 229.74/42.56  | | | | | | | | REDUCE: (361), (1619) imply:
% 229.74/42.56  | | | | | | | |   (1625)   ~ (all_52_4 = e0)
% 229.74/42.56  | | | | | | | | 
% 229.74/42.56  | | | | | | | | REDUCE: (363), (1619) imply:
% 229.74/42.56  | | | | | | | |   (1626)   ~ (all_52_8 = e0)
% 229.74/42.56  | | | | | | | | 
% 229.74/42.56  | | | | | | | | REDUCE: (365), (1619) imply:
% 229.74/42.56  | | | | | | | |   (1627)   ~ (all_52_12 = e0)
% 229.74/42.56  | | | | | | | | 
% 229.74/42.56  | | | | | | | | REDUCE: (45), (1619) imply:
% 229.74/42.56  | | | | | | | |   (1628)  op(e3, e3) = e0
% 229.74/42.56  | | | | | | | | 
% 229.74/42.56  | | | | | | | | BETA: splitting (58) gives:
% 229.74/42.56  | | | | | | | | 
% 229.74/42.56  | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | 
% 229.74/42.56  | | | | | | | | |   (1629)   ~ (all_18_2 = e0)
% 229.74/42.56  | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | REDUCE: (339), (1629) imply:
% 229.74/42.56  | | | | | | | | |   (1630)   ~ (all_6_2 = e0)
% 229.74/42.56  | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | BETA: splitting (61) gives:
% 229.74/42.56  | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | |   (1631)   ~ (all_20_2 = e1)
% 229.74/42.56  | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | REDUCE: (341), (1631) imply:
% 229.74/42.56  | | | | | | | | | |   (1632)   ~ (all_4_2 = e1)
% 229.74/42.56  | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | BETA: splitting (189) gives:
% 229.74/42.56  | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | |   (1633)  all_54_15 = e3
% 229.74/42.56  | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | COMBINE_EQS: (299), (1633) imply:
% 229.74/42.56  | | | | | | | | | | |   (1634)  all_4_2 = e3
% 229.74/42.56  | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | REDUCE: (395), (1634) imply:
% 229.74/42.56  | | | | | | | | | | |   (1635)  $false
% 229.74/42.56  | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | CLOSE: (1635) is inconsistent.
% 229.74/42.56  | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | Case 2:
% 229.74/42.56  | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | |   (1636)   ~ (all_54_15 = e3)
% 229.74/42.56  | | | | | | | | | | |   (1637)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 229.74/42.56  | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | BETA: splitting (1637) gives:
% 229.74/42.56  | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | |   (1638)  all_54_15 = e2
% 229.74/42.56  | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | COMBINE_EQS: (299), (1638) imply:
% 229.74/42.56  | | | | | | | | | | | |   (1639)  all_4_2 = e2
% 229.74/42.56  | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | REDUCE: (390), (1639) imply:
% 229.74/42.56  | | | | | | | | | | | |   (1640)  $false
% 229.74/42.56  | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | CLOSE: (1640) is inconsistent.
% 229.74/42.56  | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | Case 2:
% 229.74/42.56  | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | |   (1641)  all_54_15 = e1 | all_54_15 = e0
% 229.74/42.56  | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | BETA: splitting (1641) gives:
% 229.74/42.56  | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | |   (1642)  all_54_15 = e1
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | COMBINE_EQS: (299), (1642) imply:
% 229.74/42.56  | | | | | | | | | | | | |   (1643)  all_4_2 = e1
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | REDUCE: (1632), (1643) imply:
% 229.74/42.56  | | | | | | | | | | | | |   (1644)  $false
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | CLOSE: (1644) is inconsistent.
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | Case 2:
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | |   (1645)  all_54_15 = e0
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | COMBINE_EQS: (299), (1645) imply:
% 229.74/42.56  | | | | | | | | | | | | |   (1646)  all_4_2 = e0
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | COMBINE_EQS: (254), (1646) imply:
% 229.74/42.56  | | | | | | | | | | | | |   (1647)  all_56_31 = e0
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | REDUCE: (379), (1646) imply:
% 229.74/42.56  | | | | | | | | | | | | |   (1648)   ~ (all_52_7 = e0)
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | REDUCE: (386), (1646) imply:
% 229.74/42.56  | | | | | | | | | | | | |   (1649)   ~ (all_52_11 = e0)
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | REDUCE: (395), (1646) imply:
% 229.74/42.56  | | | | | | | | | | | | |   (1650)   ~ (e3 = e0)
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | REDUCE: (1632), (1646) imply:
% 229.74/42.56  | | | | | | | | | | | | |   (1651)   ~ (e1 = e0)
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | REDUCE: (36), (1646) imply:
% 229.74/42.56  | | | | | | | | | | | | |   (1652)  op(e0, e0) = e0
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | BETA: splitting (235) gives:
% 229.74/42.56  | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | |   (1653)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 229.74/42.56  | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 229.74/42.56  | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | BETA: splitting (1653) gives:
% 229.74/42.56  | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | |   (1654)  all_58_1 = e0 & op(e3, e2) = e0
% 229.74/42.56  | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | REF_CLOSE: (170), (1625), (1654), (function-axioms) are
% 229.74/42.56  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 229.74/42.56  | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | Case 2:
% 229.74/42.56  | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | |   (1655)  all_58_3 = e0 & op(e2, e2) = e0
% 229.74/42.56  | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | REF_CLOSE: (42), (397), (1655), (function-axioms) are
% 229.74/42.56  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 229.74/42.56  | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | End of split
% 229.74/42.56  | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | Case 2:
% 229.74/42.56  | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | |   (1656)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 229.74/42.56  | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 229.74/42.56  | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | BETA: splitting (1656) gives:
% 229.74/42.56  | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | |   (1657)  all_58_7 = e0 & op(e1, e2) = e0
% 229.74/42.56  | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | ALPHA: (1657) implies:
% 229.74/42.56  | | | | | | | | | | | | | | |   (1658)  all_58_7 = e0
% 229.74/42.56  | | | | | | | | | | | | | | |   (1659)  op(e1, e2) = e0
% 229.74/42.56  | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | |   (1660)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 229.74/42.56  | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 229.74/42.56  | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | BETA: splitting (1660) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1661)  all_58_4 = e0 & op(e3, e1) = e0
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1626), (1661), (function-axioms) are
% 229.74/42.56  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1662)  all_58_5 = e0 & op(e2, e1) = e0
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | ALPHA: (1662) implies:
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1663)  all_58_5 = e0
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1664)  op(e2, e1) = e0
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0,
% 229.74/42.56  | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (1659) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1665)  all_52_6 = e0
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 229.74/42.56  | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (1664) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1666)  all_52_9 = e0
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | REDUCE: (128), (1665) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1667)   ~ (all_52_7 = e0)
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | REDUCE: (126), (1665) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1668)   ~ (all_52_14 = e0)
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | SIMP: (1668) implies:
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1669)   ~ (all_52_14 = e0)
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | REDUCE: (118), (1666) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1670)   ~ (all_52_11 = e0)
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | REDUCE: (117), (1666) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1671)   ~ (all_52_13 = e0)
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | SIMP: (1671) implies:
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1672)   ~ (all_52_13 = e0)
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | REDUCE: (375), (1666) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1673)   ~ (all_8_2 = e0)
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | REDUCE: (381), (1666) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | |   (1674)   ~ (all_6_2 = e0)
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | |   (1675)   ~ (all_22_2 = e1)
% 229.74/42.56  | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | REDUCE: (326), (1675) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | | |   (1676)   ~ (all_8_2 = e1)
% 229.74/42.56  | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | |   (1677)  all_54_5 = e3
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (392), (1677) are inconsistent by sub-proof
% 229.74/42.56  | | | | | | | | | | | | | | | | | | |            #1907.
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | |   (1678)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (1678) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | |   (1679)  all_54_5 = e2
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1679) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | |   (1680)  all_8_2 = e2
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | SIMP: (1680) implies:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | |   (1681)  all_8_2 = e2
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (1681) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | |   (1682)  all_56_11 = e2
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (1681) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | |   (1683)   ~ (all_52_1 = e2)
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (1681) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | |   (1684)   ~ (all_52_7 = e2)
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (377), (1681) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | |   (1685)   ~ (all_52_13 = e2)
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | |   (1686)   ~ (all_36_2 = e2)
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | REDUCE: (328), (1686) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | |   (1687)   ~ (all_6_2 = e2)
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | |   (1688)  all_54_10 = e3
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (1688) are inconsistent by sub-proof
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | |            #2313.
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | |   (1689)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1689) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | |   (1690)  all_54_10 = e2
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (1687), (1690) are inconsistent by
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | |   (1691)  all_54_10 = e1 | all_54_10 = e0
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1691) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | |   (1692)  all_54_10 = e1
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (1692) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | |   (1693)  all_6_2 = e1
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1693) implies:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | |   (1694)  all_6_2 = e1
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (1694) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | |   (1695)  all_56_21 = e1
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (1694) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | |   (1696)   ~ (all_52_8 = e1)
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (1694) imply:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | |   (1697)   ~ (all_52_14 = e1)
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (1698)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.56  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1698) gives:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1699)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1682), (1683), (1695), (1699),
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2310.
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1700)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (1624), (1647), (1696), (1700),
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2307.
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (1701)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1701) gives:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1702)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1702) gives:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1703)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1703) implies:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1704)  op(e2, e1) = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1664), (1704), (function-axioms) are
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1705)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (297), (381), (1630), (1684),
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1691), (1705), (function-axioms) are inconsistent
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1904.
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1706)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (1669), (1672), (1697), (1706),
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1903.
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | |   (1707)  all_54_10 = e0
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (1630), (1707) are inconsistent by
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | |   (1708)  all_36_2 = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | |   (1709)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (1708) imply:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | |   (1710)  all_6_2 = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (1710) imply:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | |   (1711)  all_40_2 = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (1710) imply:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | |   (1712)  all_56_21 = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (1710) imply:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | |   (1713)   ~ (e3 = e2)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (1710) imply:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | |   (1714)  op(e1, e1) = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | |   (1715)   ~ (all_40_2 = e2)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1711), (1715) imply:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | |   (1716)  $false
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1716) is inconsistent.
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | |   (1717)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | |             $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | |             = all_40_1 & $i(all_40_1))
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | |   (1718)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1718) gives:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | |   (1719)  all_58_4 = e2 & op(e3, e1) = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1719) implies:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | |   (1720)  all_58_4 = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (227), (228),
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | |            (230), (1714), (1720), (function-axioms) are
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1899.
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | |   (1721)  all_58_5 = e2 & op(e2, e1) = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1721) implies:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | |   (1722)  op(e2, e1) = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1664), (1722), (function-axioms) are
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | |   (1723)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1723) gives:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | |   (1724)  all_58_8 = e2 & op(e1, e1) = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1724) implies:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | |   (1725)  all_58_8 = e2
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (1726)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1726) gives:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1727)  all_58_9 = e2 & op(e3, e0) = e2
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1727) implies:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1728)  op(e3, e0) = e2
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1717) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1729)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e2) = all_40_1 & $i(all_40_0) &
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_40_1)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1729) implies:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1730)  op(e1, e2) = all_40_1
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1731)  op(all_40_1, e1) = all_40_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1732)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1732) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1733)  all_58_12 = e2 & op(e0, e3) = e2
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1733) implies:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1734)  op(e0, e3) = e2
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (1734) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1735)  all_52_3 = e2
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_40_1,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (1659), (1730) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1736)  all_40_1 = e0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (168), (1728) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1737)  all_52_12 = e2
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1735) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1738)   ~ (all_52_7 = e2)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (1735) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1739)   ~ (all_52_11 = e2)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1739) implies:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1740)   ~ (all_52_11 = e2)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1731), (1736) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1741)  op(e0, e1) = all_40_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1742)   ~ (all_50_2 = e0)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1620), (1742) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1743)  $false
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1743) is inconsistent.
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1744)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1709) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1745)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e2) = all_36_1 & $i(all_36_0) &
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1745) implies:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1746)   ~ (all_36_0 = e3)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1747)  op(e1, e2) = all_36_1
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1748)  op(all_36_1, e1) = all_36_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1744) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1749)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_50_1 & $i(all_50_0) &
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1749) implies:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1750)   ~ (all_50_0 = e1)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1751)  op(e3, e0) = all_50_1
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1752)  op(all_50_1, e3) = all_50_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1617) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1753)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_16_1 & $i(all_16_0) &
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1753) implies:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1754)  op(e3, e0) = all_16_1
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1755)  op(all_16_1, e3) = all_16_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_0, e1, e0, simplifying with (157), (1741)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1756)  all_52_11 = all_40_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_36_1,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (1659), (1747) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1757)  all_36_1 = e0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (1728), (1751) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1758)  all_50_1 = e2
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (1751), (1754)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1759)  all_50_1 = all_16_1
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1758), (1759) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1760)  all_16_1 = e2
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1760) implies:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1761)  all_16_1 = e2
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (1756) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1762)  all_54_14 = all_40_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1756) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1763)   ~ (all_52_8 = all_40_0)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1740), (1756) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1764)   ~ (all_40_0 = e2)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1649), (1756) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1765)   ~ (all_40_0 = e0)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1752), (1758) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1766)  op(e2, e3) = all_50_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1748), (1757) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1767)  op(e0, e1) = all_36_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1755), (1761) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1768)  op(e2, e3) = all_16_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_0,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_36_0, e1, e0, simplifying with (1741), (1767)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1769)  all_40_0 = all_36_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_16_0, e3, e2, simplifying with (167), (1768)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1770)  all_52_1 = all_16_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_0, e3, e2, simplifying with (167), (1766)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1771)  all_52_1 = all_50_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1770), (1771) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1772)  all_50_0 = all_16_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1762), (1769) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1773)  all_54_14 = all_36_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (1770) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1774)  all_54_4 = all_16_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1770) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1775)   ~ (all_52_2 = all_16_0)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1775) implies:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1776)   ~ (all_52_2 = all_16_0)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1683), (1770) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1777)   ~ (all_16_0 = e2)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1622), (1770) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1778)   ~ (all_16_0 = e0)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1763), (1769) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1779)   ~ (all_52_8 = all_36_0)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1750), (1772) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1780)   ~ (all_16_0 = e1)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1764), (1769) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1781)   ~ (all_36_0 = e2)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1765), (1769) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1782)   ~ (all_36_0 = e0)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1783)  all_54_4 = e3
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1774), (1783) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1784)  all_16_0 = e3
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1776), (1784) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1785)   ~ (all_52_2 = e3)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1768), (1784) imply:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1786)  op(e2, e3) = e3
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (160), (163),
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (190), (213), (214), (226),
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1621), (1658), (1664), (1669), (1672), (1684),
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1712), (1714), (1728), (1734), (1746), (1773),
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1779), (1781), (1782), (1785), (1786),
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1887.
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1787)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1774), (1777), (1778), (1780), (1787) are
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1886.
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1788)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1788) implies:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1789)   ~ (all_16_1 = e1)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1790)  op(e3, e0) = all_16_1
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_0, e1, e0, simplifying with (157), (1741)
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1791)  all_52_11 = all_40_0
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_36_1,
% 229.74/42.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (1659), (1747) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1792)  all_36_1 = e0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (1728), (1751) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1793)  all_50_1 = e2
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (1751), (1790)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1794)  all_50_1 = all_16_1
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1793), (1794) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1795)  all_16_1 = e2
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1795) implies:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1796)  all_16_1 = e2
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (1791) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1797)  all_54_14 = all_40_0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1791) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1798)   ~ (all_52_8 = all_40_0)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1740), (1791) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1799)   ~ (all_40_0 = e2)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1649), (1791) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1800)   ~ (all_40_0 = e0)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1752), (1793) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1801)  op(e2, e3) = all_50_0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1748), (1792) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1802)  op(e0, e1) = all_36_0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_0,
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_36_0, e1, e0, simplifying with (1741), (1802)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1803)  all_40_0 = all_36_0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_0, e3, e2, simplifying with (167), (1801)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1804)  all_52_1 = all_50_0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1797), (1803) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1805)  all_54_14 = all_36_0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (1804) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1806)  all_54_4 = all_50_0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1804) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1807)   ~ (all_52_2 = all_50_0)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1807) implies:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1808)   ~ (all_52_2 = all_50_0)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1683), (1804) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1809)   ~ (all_50_0 = e2)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1622), (1804) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1810)   ~ (all_50_0 = e0)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1798), (1803) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1811)   ~ (all_52_8 = all_36_0)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1799), (1803) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1812)   ~ (all_36_0 = e2)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1800), (1803) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1813)   ~ (all_36_0 = e0)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1814)  all_54_4 = e3
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1806), (1814) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1815)  all_50_0 = e3
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1808), (1815) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1816)   ~ (all_52_2 = e3)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1801), (1815) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1817)  op(e2, e3) = e3
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (160), (163),
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (190), (213), (214), (226),
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1621), (1658), (1664), (1669), (1672), (1684),
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1712), (1714), (1728), (1734), (1746), (1805),
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1811), (1812), (1813), (1816), (1817),
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1887.
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1818)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1750), (1806), (1809), (1810), (1818) are
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1885.
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1819)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1819) implies:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1820)   ~ (all_50_1 = e2)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1821)  op(e3, e0) = all_50_1
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1728), (1820), (1821), (function-axioms) are
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1884.
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1822)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1822) implies:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1823)   ~ (all_36_1 = e0)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1824)  op(e1, e2) = all_36_1
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1659), (1730), (1823), (1824), (function-axioms)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1883.
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1825)  all_58_13 = e2 & op(e0, e2) = e2
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1825) implies:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1826)  op(e0, e2) = e2
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1684), (1826), (function-axioms) are
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1827)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (230),
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1652), (1663), (1664), (1714), (1725), (1827),
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1882.
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1828)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_40_1)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1828) implies:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1829)   ~ (all_40_1 = e3)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1830)  op(e1, e2) = all_40_1
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1831)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1831) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1832)  all_58_12 = e2 & op(e0, e3) = e2
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1832) implies:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1833)  op(e0, e3) = e2
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (1833) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1834)  all_52_3 = e2
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_40_1,
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (1659), (1830) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1835)  all_40_1 = e0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (168), (1728) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1836)  all_52_12 = e2
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1834) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1837)   ~ (all_52_7 = e2)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (1834) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1838)   ~ (all_52_11 = e2)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1838) implies:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1839)   ~ (all_52_11 = e2)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1840)   ~ (all_50_2 = e0)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1620), (1840) imply:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1841)  $false
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1841) is inconsistent.
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1842)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1709) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1843)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e2) = all_36_1 & $i(all_36_0) &
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1843) implies:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1844)   ~ (all_36_0 = e3)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1845)  op(e1, e2) = all_36_1
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1846)  op(all_36_1, e1) = all_36_0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1842) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1847)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_50_1 & $i(all_50_0) &
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1847) implies:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1848)   ~ (all_50_0 = e1)
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1849)  op(e3, e0) = all_50_1
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1850)  op(all_50_1, e3) = all_50_0
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1617) gives:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1851)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_16_1 & $i(all_16_0) &
% 229.74/42.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1851) implies:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1852)  op(e3, e0) = all_16_1
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1853)  op(all_16_1, e3) = all_16_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_36_1,
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (1659), (1845) gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1854)  all_36_1 = e0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (1728), (1849) gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1855)  all_50_1 = e2
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (1849), (1852)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1856)  all_50_1 = all_16_1
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1855), (1856) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1857)  all_16_1 = e2
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1857) implies:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1858)  all_16_1 = e2
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1850), (1855) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1859)  op(e2, e3) = all_50_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1846), (1854) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1860)  op(e0, e1) = all_36_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1853), (1858) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1861)  op(e2, e3) = all_16_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_36_0, e1, e0, simplifying with (157), (1860)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1862)  all_52_11 = all_36_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_16_0, e3, e2, simplifying with (167), (1861)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1863)  all_52_1 = all_16_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_0, e3, e2, simplifying with (167), (1859)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1864)  all_52_1 = all_50_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1863), (1864) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1865)  all_50_0 = all_16_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (1862) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1866)  all_54_14 = all_36_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (1863) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1867)  all_54_4 = all_16_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1863) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1868)   ~ (all_52_2 = all_16_0)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1868) implies:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1869)   ~ (all_52_2 = all_16_0)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1683), (1863) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1870)   ~ (all_16_0 = e2)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1622), (1863) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1871)   ~ (all_16_0 = e0)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1862) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1872)   ~ (all_52_8 = all_36_0)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1839), (1862) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1873)   ~ (all_36_0 = e2)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1649), (1862) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1874)   ~ (all_36_0 = e0)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1848), (1865) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1875)   ~ (all_16_0 = e1)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1876)  all_54_4 = e3
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1867), (1876) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1877)  all_16_0 = e3
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1869), (1877) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1878)   ~ (all_52_2 = e3)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1861), (1877) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1879)  op(e2, e3) = e3
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (160), (163),
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (190), (213), (214), (226),
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1621), (1664), (1669), (1672), (1684), (1712),
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1714), (1728), (1829), (1830), (1833), (1844),
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1845), (1866), (1872), (1873), (1874), (1878),
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1879), (function-axioms) are inconsistent by
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1881.
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1880)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1867), (1870), (1871), (1875), (1880) are
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1886.
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1881)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1881) implies:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1882)   ~ (all_16_1 = e1)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1883)  op(e3, e0) = all_16_1
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_36_1,
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (1659), (1845) gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1884)  all_36_1 = e0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (1728), (1849) gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1885)  all_50_1 = e2
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (1849), (1883)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1886)  all_50_1 = all_16_1
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1885), (1886) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1887)  all_16_1 = e2
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1887) implies:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1888)  all_16_1 = e2
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1850), (1885) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1889)  op(e2, e3) = all_50_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1846), (1884) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1890)  op(e0, e1) = all_36_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_36_0, e1, e0, simplifying with (157), (1890)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1891)  all_52_11 = all_36_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_0, e3, e2, simplifying with (167), (1889)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1892)  all_52_1 = all_50_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (1891) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1893)  all_54_14 = all_36_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (1892) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1894)  all_54_4 = all_50_0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1892) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1895)   ~ (all_52_2 = all_50_0)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1895) implies:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1896)   ~ (all_52_2 = all_50_0)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1683), (1892) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1897)   ~ (all_50_0 = e2)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1622), (1892) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1898)   ~ (all_50_0 = e0)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1891) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1899)   ~ (all_52_8 = all_36_0)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1839), (1891) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1900)   ~ (all_36_0 = e2)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1649), (1891) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1901)   ~ (all_36_0 = e0)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1902)  all_54_4 = e3
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1894), (1902) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1903)  all_50_0 = e3
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1896), (1903) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1904)   ~ (all_52_2 = e3)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1889), (1903) imply:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1905)  op(e2, e3) = e3
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (160), (163),
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (190), (213), (214), (226),
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1621), (1664), (1669), (1672), (1684), (1712),
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1714), (1728), (1829), (1830), (1833), (1844),
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1845), (1893), (1899), (1900), (1901), (1904),
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1905), (function-axioms) are inconsistent by
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1881.
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1906)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1848), (1894), (1897), (1898), (1906) are
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1885.
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1907)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1907) implies:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1908)   ~ (all_50_1 = e2)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1909)  op(e3, e0) = all_50_1
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1728), (1908), (1909), (function-axioms) are
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1884.
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1910)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1910) implies:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1911)   ~ (all_36_1 = e0)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1912)  op(e1, e2) = all_36_1
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1659), (1830), (1911), (1912), (function-axioms)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1883.
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1913)  all_58_13 = e2 & op(e0, e2) = e2
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1913) implies:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1914)  op(e0, e2) = e2
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1684), (1914), (function-axioms) are
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1915)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 229.74/42.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (230),
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1652), (1663), (1664), (1714), (1725), (1915),
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1882.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1916)  all_58_10 = e2 & op(e2, e0) = e2
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1916) implies:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1917)  op(e2, e0) = e2
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1685), (1917), (function-axioms) are
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (1918)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1918) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1919)  all_58_11 = e2 & op(e1, e0) = e2
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1919) implies:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1920)  all_58_11 = e2
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1921)  op(e1, e0) = e2
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1922)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1922) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1923)  all_58_6 = e1 & op(e1, e3) = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1923) implies:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1924)  all_58_6 = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1925)  op(e1, e3) = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (223), (226), (1714),
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1920), (1924), (1925), (function-axioms) are
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2028.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1926)  all_58_7 = e1 & op(e1, e2) = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1926) implies:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1927)  all_58_7 = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1928)  op(e1, e2) = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (162), (223), (226),
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1714), (1920), (1927), (1928), (function-axioms)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2106.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1929)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1714), (1921), (1929), (function-axioms) are
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1880.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1930)  all_58_15 = e2 & op(e0, e0) = e2
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1930) implies:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1931)  op(e0, e0) = e2
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1652), (1931), (function-axioms) are
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1932)  all_58_14 = e2 & op(e0, e1) = e2
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1932) implies:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1933)  all_58_14 = e2
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (1934)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (165), (228), (1663), (1664),
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | |            (1714), (1933), (1934), (function-axioms) are
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1878.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (1935)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1714), (1933), (1935), (function-axioms) are
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2116.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | |   (1936)  all_54_5 = e1 | all_54_5 = e0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (397), (1676), (1936) are inconsistent by
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | |            sub-proof #2300.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.61  | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | |   (1937)  all_22_2 = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | |   (1938)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 229.74/42.61  | | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_22_1 & $i(all_22_0) &
% 229.74/42.61  | | | | | | | | | | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 229.74/42.61  | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (1937) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | |   (1939)  all_8_2 = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (1939) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | |   (1940)  all_30_2 = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (1939) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | |   (1941)  all_56_11 = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | REDUCE: (369), (1939) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | |   (1942)   ~ (all_52_4 = e1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | REDUCE: (373), (1939) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | |   (1943)   ~ (all_52_7 = e1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | |   (1944)   ~ (all_30_2 = e1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | REDUCE: (1940), (1944) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | |   (1945)  $false
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | CLOSE: (1945) is inconsistent.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | |   (1946)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_30_1 & $i(all_30_0) &
% 229.74/42.61  | | | | | | | | | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | BETA: splitting (1946) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | |   (1947)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_30_1 & $i(all_30_0) &
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | ALPHA: (1947) implies:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | |   (1948)  op(e2, e1) = all_30_1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | |   (1949)  op(all_30_1, e2) = all_30_0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | |   (1950)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1950) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | |   (1951)  all_58_1 = e1 & op(e3, e2) = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1951) implies:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | |   (1952)  op(e3, e2) = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (1942), (1952), (function-axioms) are
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2228.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | |   (1953)  all_58_3 = e1 & op(e2, e2) = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1953) implies:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | |   (1954)  all_58_3 = e1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_30_1,
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (1664), (1948) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | |   (1955)  all_30_1 = e0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1949), (1955) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | |   (1956)  op(e0, e2) = all_30_0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1938) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1957)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_22_1 & $i(all_22_0) &
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1957) implies:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1958)   ~ (all_22_0 = e3)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1959)  op(e2, e1) = all_22_1
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1960)  op(all_22_1, e2) = all_22_0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |              all_30_0, e2, e0, simplifying with (158), (1956)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1961)  all_52_7 = all_30_0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_22_1,
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (1664), (1959) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1962)  all_22_1 = e0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1961) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1963)  all_54_13 = all_30_0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1961) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1964)   ~ (all_52_3 = all_30_0)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1961) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1965)   ~ (all_52_4 = all_30_0)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1943), (1961) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1966)   ~ (all_30_0 = e1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1648), (1961) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1967)   ~ (all_30_0 = e0)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1960), (1962) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1968)  op(e0, e2) = all_22_0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_0,
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |              all_22_0, e2, e0, simplifying with (1956), (1968)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1969)  all_30_0 = all_22_0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1963), (1969) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1970)  all_54_13 = all_22_0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1964), (1969) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1971)   ~ (all_52_3 = all_22_0)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1965), (1969) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1972)   ~ (all_52_4 = all_22_0)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1966), (1969) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1973)   ~ (all_22_0 = e1)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1967), (1969) imply:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | |   (1974)   ~ (all_22_0 = e0)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1975)  all_54_13 = e3
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1958), (1970), (1975) are inconsistent by
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1877.
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1976)   ~ (all_54_13 = e3)
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | |   (1977)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1977) gives:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (1978)  all_54_13 = e2
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.61  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1970), (1978) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (1979)  all_22_0 = e2
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1979) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (1980)  all_22_0 = e2
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1971), (1980) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (1981)   ~ (all_52_3 = e2)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1972), (1980) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (1982)   ~ (all_52_4 = e2)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1968), (1980) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (1983)  op(e0, e2) = e2
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1984)  all_54_1 = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (1984) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1985)  all_52_4 = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1985) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1986)  all_52_4 = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1986) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1987)   ~ (all_52_8 = e3)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1987) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1988)   ~ (all_52_8 = e3)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (1986) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1989)  op(e3, e2) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1990)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1990) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1991)  all_58_4 = e3 & op(e3, e1) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1991) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1992)  op(e3, e1) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1988), (1992), (function-axioms) are
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1993)  all_58_5 = e3 & op(e2, e1) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1993) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1994)  op(e2, e1) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1948), (1949), (1958), (1959), (1960), (1989),
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1994), (function-axioms) are inconsistent by
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1875.
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1995)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1995) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1996)  all_58_8 = e3 & op(e1, e1) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (391), (1996), (function-axioms) are
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1997)  all_58_14 = e3 & op(e0, e1) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1997) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1998)  all_58_14 = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1999)  op(e0, e1) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2000)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2000) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2001)  all_58_12 = e1 & op(e0, e3) = e1
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2001) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2002)  op(e0, e3) = e1
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2003)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2003) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2004)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_9 & $i(all_56_9)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2004) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2005)  op(e3, e2) = all_56_9
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2006)  op(e3, all_56_9) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (159), (163),
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (216), (217), (218), (219), (239), (1622),
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1623), (1624), (1649), (1652), (1664), (1946),
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1958), (1959), (1960), (1989), (1998), (2005),
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2006), (function-axioms) are inconsistent by
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1859.
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2007)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2007) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2008)  op(e2, all_56_11) = e2
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1941), (2008) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2009)  op(e2, e1) = e2
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1664), (2009), (function-axioms) are
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2010)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2010) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2011)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2011) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2012)  op(e1, e2) = all_56_13
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2013)  op(e1, all_56_13) = e1
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (1999) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2014)  all_52_11 = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (2002) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2015)  all_52_3 = e1
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (1659), (2012)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2016)  all_56_13 = e0
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (2015) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2017)   ~ (all_52_1 = e1)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (2015) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2018)   ~ (all_52_2 = e1)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1981), (2015) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2019)   ~ (e2 = e1)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (383), (2014) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2020)   ~ (all_6_2 = e3)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2013), (2016) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2021)  op(e1, e0) = e1
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2022)   ~ (all_36_2 = e2)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (328), (2022) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2023)   ~ (all_6_2 = e2)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (194), (297), (385), (391), (1630), (2021),
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2023), (function-axioms) are inconsistent by
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1858.
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2024)  all_36_2 = e2
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (2024) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2025)  all_6_2 = e2
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (2025) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2026)   ~ (all_52_2 = e2)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (2025) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2027)  op(e1, e1) = e2
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2028)  all_54_8 = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (2028) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2029)  all_52_2 = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2029) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2030)  all_52_2 = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (2030) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2031)   ~ (all_52_1 = e3)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2032)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2032) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2033)  all_58_2 = e3 & op(e2, e3) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2033) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2034)  op(e2, e3) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2031), (2034), (function-axioms) are
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2035)  all_58_3 = e3 & op(e2, e2) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2035) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2036)  all_58_3 = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1954), (2036) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2037)  e3 = e1
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (2037) imply:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2038)  $false
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2038) is inconsistent.
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2039)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2039) gives:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2040)  all_58_5 = e3 & op(e2, e1) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2040) implies:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2041)  op(e2, e1) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1948), (1949), (1958), (1959), (1960), (1989),
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2041), (function-axioms) are inconsistent by
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1875.
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2042)  all_58_10 = e3 & op(e2, e0) = e3
% 229.74/42.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (110), (112), (113), (118),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (121), (125), (133), (139), (140), (141), (144),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (145), (149), (157), (158), (159), (160), (163),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (169), (170), (190), (192),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (194), (196), (197), (200), (201), (213), (214),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (227), (244), (255), (257),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (266), (268), (269), (279), (280), (297), (381),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (385), (391), (1621), (1622), (1623), (1624),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1627), (1628), (1630), (1647), (1649), (1652),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1664), (1669), (1672), (1941), (1983), (1989),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1999), (2017), (2018), (2021), (2026), (2027),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2042), (function-axioms) are inconsistent by
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1845.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2043)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (1623), (2018), (2026), (2043) are
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1949.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2044)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2044) implies:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2045)  op(e0, e2) = all_56_15
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2046)  op(e0, all_56_15) = e0
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1983), (2045), (2046), (function-axioms) are
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2053.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2047)  all_58_13 = e1 & op(e0, e2) = e1
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1943), (2047), (function-axioms) are
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2048)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (1652), (1998), (2048),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1843.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2049)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (1625), (1942), (1982), (2049) are
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2048.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (2050)  all_54_13 = e1 | all_54_13 = e0
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1970), (1973), (1974), (2050) are inconsistent by
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1842.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2051)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2051) implies:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2052)   ~ (all_22_1 = e0)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2053)  op(e2, e1) = all_22_1
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1664), (1948), (2052), (2053), (function-axioms)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1841.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | |   (2054)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (158), (162), (1659), (1943), (2054),
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | |            #1840.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | |   (2055)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | ALPHA: (2055) implies:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | |   (2056)   ~ (all_30_1 = e3)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | |   (2057)  op(e2, e1) = all_30_1
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | |   (2058)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2058) gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | |   (2059)  all_58_1 = e1 & op(e3, e2) = e1
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2059) implies:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | |   (2060)  op(e3, e2) = e1
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (1942), (2060), (function-axioms) are
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2228.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | |   (2061)  all_58_3 = e1 & op(e2, e2) = e1
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2061) implies:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | |   (2062)  all_58_3 = e1
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_30_1,
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (1664), (2057) gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | |   (2063)  all_30_1 = e0
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1938) gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2064)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_22_1 & $i(all_22_0) &
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2064) implies:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2065)   ~ (all_22_0 = e3)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2066)  op(e2, e1) = all_22_1
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2067)  op(all_22_1, e2) = all_22_0
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_22_1,
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (1664), (2066) gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2068)  all_22_1 = e0
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2067), (2068) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2069)  op(e0, e2) = all_22_0
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |              all_22_0, e2, e0, simplifying with (158), (2069)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2070)  all_52_7 = all_22_0
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2070) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2071)  all_54_13 = all_22_0
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (2070) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2072)   ~ (all_52_3 = all_22_0)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (2070) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2073)   ~ (all_52_4 = all_22_0)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1943), (2070) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2074)   ~ (all_22_0 = e1)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1648), (2070) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | |   (2075)   ~ (all_22_0 = e0)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | |   (2076)  all_54_13 = e3
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2065), (2071), (2076) are inconsistent by
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1877.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | |   (2077)   ~ (all_54_13 = e3)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | |   (2078)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2078) gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (2079)  all_54_13 = e2
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2071), (2079) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (2080)  all_22_0 = e2
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2080) implies:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (2081)  all_22_0 = e2
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2072), (2081) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (2082)   ~ (all_52_3 = e2)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2073), (2081) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (2083)   ~ (all_52_4 = e2)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2069), (2081) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (2084)  op(e0, e2) = e2
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2085)  all_54_1 = e3
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (2085) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2086)  all_52_4 = e3
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2086) implies:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2087)  all_52_4 = e3
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (2087) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2088)   ~ (all_52_8 = e3)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2088) implies:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2089)   ~ (all_52_8 = e3)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (2087) imply:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2090)  op(e3, e2) = e3
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2091)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2091) gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2092)  all_58_4 = e3 & op(e3, e1) = e3
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2092) implies:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2093)  op(e3, e1) = e3
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2089), (2093), (function-axioms) are
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2094)  all_58_5 = e3 & op(e2, e1) = e3
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2094) implies:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2095)  op(e2, e1) = e3
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2056), (2057), (2095), (function-axioms) are
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1839.
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2096)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2096) gives:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2097)  all_58_8 = e3 & op(e1, e1) = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (391), (2097), (function-axioms) are
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2098)  all_58_14 = e3 & op(e0, e1) = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2098) implies:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2099)  all_58_14 = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2100)  op(e0, e1) = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2101)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2101) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2102)  all_58_12 = e1 & op(e0, e3) = e1
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2102) implies:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2103)  op(e0, e3) = e1
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2104)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2104) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2105)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_9 & $i(all_56_9)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2105) implies:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2106)  op(e3, e2) = all_56_9
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2107)  op(e3, all_56_9) = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (159), (163),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (216), (217), (218), (219), (239), (1622),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1623), (1624), (1649), (1652), (1664), (1946),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2065), (2066), (2067), (2090), (2099), (2106),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2107), (function-axioms) are inconsistent by
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1859.
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2108)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2108) implies:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2109)  op(e2, all_56_11) = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1941), (2109) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2110)  op(e2, e1) = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1664), (2110), (function-axioms) are
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2111)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2111) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2112)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2112) implies:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2113)  op(e1, e2) = all_56_13
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2114)  op(e1, all_56_13) = e1
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (2100) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2115)  all_52_11 = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (2103) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2116)  all_52_3 = e1
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (1659), (2113)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2117)  all_56_13 = e0
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (2116) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2118)   ~ (all_52_1 = e1)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (2116) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2119)   ~ (all_52_2 = e1)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2115), (2116) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2120)   ~ (e3 = e1)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2082), (2116) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2121)   ~ (e2 = e1)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (383), (2115) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2122)   ~ (all_6_2 = e3)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2114), (2117) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2123)  op(e1, e0) = e1
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2124)   ~ (all_36_2 = e2)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (328), (2124) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2125)   ~ (all_6_2 = e2)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (194), (297), (385), (391), (1630), (2123),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2125), (function-axioms) are inconsistent by
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1858.
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2126)  all_36_2 = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (2126) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2127)  all_6_2 = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2127) implies:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2128)  all_6_2 = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (2128) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2129)   ~ (all_52_2 = e2)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (2128) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2130)   ~ (e3 = e2)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (2128) imply:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2131)  op(e1, e1) = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2132)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2132) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2133)  all_58_0 = e2 & op(e3, e3) = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2133) implies:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2134)  op(e3, e3) = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1628), (2134), (function-axioms) are
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2135)  all_58_2 = e2 & op(e2, e3) = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2135) implies:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2136)  op(e2, e3) = e2
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2137)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2137) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2138)  all_58_2 = e3 & op(e2, e3) = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2138) implies:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2139)  op(e2, e3) = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2136), (2139), (function-axioms) are
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2140)  all_58_3 = e3 & op(e2, e2) = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2140) implies:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2141)  all_58_3 = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2062), (2141) are inconsistent by sub-proof
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1999.
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2142)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2142) gives:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2143)  all_58_5 = e3 & op(e2, e1) = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2143) implies:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2144)  op(e2, e1) = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2056), (2057), (2144), (function-axioms) are
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1839.
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2145)  all_58_10 = e3 & op(e2, e0) = e3
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (110), (112), (113), (118),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (121), (125), (133), (139), (140), (141), (144),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (145), (149), (157), (158), (159), (160), (163),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (169), (170), (190), (192),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (194), (196), (197), (200), (201), (213), (214),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (227), (244), (255), (257),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (266), (268), (269), (279), (280), (297), (381),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (385), (391), (1621), (1622), (1623), (1624),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1627), (1628), (1630), (1647), (1649), (1652),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1664), (1669), (1672), (1941), (2084), (2090),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2100), (2118), (2119), (2123), (2129), (2131),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2145), (function-axioms) are inconsistent by
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1845.
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2146)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (159), (223), (226),
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2082), (2123), (2131), (2146), (function-axioms)
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1834.
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2147)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2147) implies:
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2148)  op(e0, e2) = all_56_15
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2149)  op(e0, all_56_15) = e0
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2084), (2148), (2149), (function-axioms) are
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2053.
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2150)  all_58_13 = e1 & op(e0, e2) = e1
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1943), (2150), (function-axioms) are
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2151)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (1652), (2099), (2151),
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1843.
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2152)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (1625), (1942), (2083), (2152) are
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2048.
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (2153)  all_54_13 = e1 | all_54_13 = e0
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2071), (2074), (2075), (2153) are inconsistent by
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1842.
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | |   (2154)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2154) implies:
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | |   (2155)   ~ (all_22_1 = e0)
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | |   (2156)  op(e2, e1) = all_22_1
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1664), (2057), (2155), (2156), (function-axioms)
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1841.
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | |   (2157)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (158), (162), (1659), (1943), (2157),
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | |            #1840.
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | |   (2158)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 229.74/42.65  | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 229.74/42.65  | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (1630), (1649), (2158),
% 229.74/42.65  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.65  | | | | | | | | | | | | | | | |            #1832.
% 229.74/42.65  | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | |   (2159)  all_58_13 = e0 & op(e0, e2) = e0
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | ALPHA: (2159) implies:
% 229.74/42.65  | | | | | | | | | | | | | | |   (2160)  op(e0, e2) = e0
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | REF_CLOSE: (158), (1648), (2160), (function-axioms) are
% 229.74/42.65  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2252.
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | |   (2161)  all_20_2 = e1
% 229.74/42.65  | | | | | | | | | |   (2162)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 229.74/42.65  | | | | | | | | | |             & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 229.74/42.65  | | | | | | | | | |             $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 229.74/42.65  | | | | | | | | | |             = all_20_1 & $i(all_20_1))
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | COMBINE_EQS: (341), (2161) imply:
% 229.74/42.65  | | | | | | | | | |   (2163)  all_4_2 = e1
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | SIMP: (2163) implies:
% 229.74/42.65  | | | | | | | | | |   (2164)  all_4_2 = e1
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | COMBINE_EQS: (324), (2164) imply:
% 229.74/42.65  | | | | | | | | | |   (2165)  all_34_2 = e1
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | COMBINE_EQS: (254), (2164) imply:
% 229.74/42.65  | | | | | | | | | |   (2166)  all_56_31 = e1
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | REDUCE: (368), (2164) imply:
% 229.74/42.65  | | | | | | | | | |   (2167)   ~ (all_52_3 = e1)
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | REDUCE: (379), (2164) imply:
% 229.74/42.65  | | | | | | | | | |   (2168)   ~ (all_52_7 = e1)
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | REDUCE: (387), (2164) imply:
% 229.74/42.65  | | | | | | | | | |   (2169)   ~ (all_52_12 = e1)
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | REDUCE: (388), (2164) imply:
% 229.74/42.65  | | | | | | | | | |   (2170)   ~ (all_52_13 = e1)
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | REDUCE: (389), (2164) imply:
% 229.74/42.65  | | | | | | | | | |   (2171)   ~ (all_52_14 = e1)
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | BETA: splitting (220) gives:
% 229.74/42.65  | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | Case 1:
% 229.74/42.65  | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | |   (2172)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 229.74/42.65  | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 229.74/42.65  | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | BETA: splitting (2172) gives:
% 229.74/42.65  | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | Case 1:
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | |   (2173)  all_58_9 = e1 & op(e3, e0) = e1
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | REF_CLOSE: (168), (2169), (2173), (function-axioms) are
% 229.74/42.65  | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | |   (2174)  all_58_10 = e1 & op(e2, e0) = e1
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | REF_CLOSE: (164), (2170), (2174), (function-axioms) are
% 229.74/42.65  | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | End of split
% 229.74/42.65  | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | |   (2175)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 229.74/42.65  | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 229.74/42.65  | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | BETA: splitting (2175) gives:
% 229.74/42.65  | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | Case 1:
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | |   (2176)  all_58_11 = e1 & op(e1, e0) = e1
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | ALPHA: (2176) implies:
% 229.74/42.65  | | | | | | | | | | | |   (2177)  op(e1, e0) = e1
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | REF_CLOSE: (160), (2171), (2177), (function-axioms) are
% 229.74/42.65  | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | |   (2178)  all_58_15 = e1 & op(e0, e0) = e1
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | ALPHA: (2178) implies:
% 229.74/42.65  | | | | | | | | | | | |   (2179)  all_58_15 = e1
% 229.74/42.65  | | | | | | | | | | | |   (2180)  op(e0, e0) = e1
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | BETA: splitting (64) gives:
% 229.74/42.65  | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | Case 1:
% 229.74/42.65  | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | |   (2181)   ~ (all_22_2 = e1)
% 229.74/42.65  | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | REDUCE: (326), (2181) imply:
% 229.74/42.65  | | | | | | | | | | | | |   (2182)   ~ (all_8_2 = e1)
% 229.74/42.65  | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | BETA: splitting (199) gives:
% 229.74/42.65  | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | Case 1:
% 229.74/42.65  | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | |   (2183)  all_54_5 = e3
% 229.74/42.65  | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | COMBINE_EQS: (275), (2183) imply:
% 229.74/42.65  | | | | | | | | | | | | | |   (2184)  all_8_2 = e3
% 229.74/42.65  | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | REDUCE: (392), (2184) imply:
% 229.74/42.65  | | | | | | | | | | | | | |   (2185)  $false
% 229.74/42.65  | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | CLOSE: (2185) is inconsistent.
% 229.74/42.65  | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | |   (2186)   ~ (all_54_5 = e3)
% 229.74/42.65  | | | | | | | | | | | | | |   (2187)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 229.74/42.65  | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | BETA: splitting (2187) gives:
% 229.74/42.65  | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | Case 1:
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | |   (2188)  all_54_5 = e2
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | COMBINE_EQS: (275), (2188) imply:
% 229.74/42.65  | | | | | | | | | | | | | | |   (2189)  all_8_2 = e2
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | COMBINE_EQS: (353), (2189) imply:
% 229.74/42.65  | | | | | | | | | | | | | | |   (2190)  all_56_11 = e2
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | REDUCE: (366), (2189) imply:
% 229.74/42.65  | | | | | | | | | | | | | | |   (2191)   ~ (all_52_1 = e2)
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | REDUCE: (373), (2189) imply:
% 229.74/42.65  | | | | | | | | | | | | | | |   (2192)   ~ (all_52_7 = e2)
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | REDUCE: (375), (2189) imply:
% 229.74/42.65  | | | | | | | | | | | | | | |   (2193)   ~ (all_52_9 = e2)
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 229.74/42.65  | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | Case 1:
% 229.74/42.65  | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | |   (2194)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.74/42.65  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.65  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.74/42.65  | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.74/42.65  | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.65  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.65  | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.74/42.65  | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.65  | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.65  | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.74/42.65  | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 229.74/42.65  | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.74/42.65  | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.74/42.65  | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 229.74/42.65  | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.65  | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.65  | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 229.74/42.65  | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 229.74/42.65  | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 229.74/42.65  | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 229.74/42.65  | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 229.74/42.65  | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | BETA: splitting (2194) gives:
% 229.74/42.65  | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.65  | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | |   (2195)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 229.74/42.65  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.65  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 229.74/42.65  | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 229.74/42.65  | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.65  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.65  | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 229.74/42.65  | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.65  | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.65  | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 229.74/42.65  | | | | | | | | | | | | | | | | |             = e3)
% 229.74/42.65  | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2166), (2190), (2191), (2195),
% 229.74/42.65  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.65  | | | | | | | | | | | | | | | | |            #1831.
% 229.74/42.65  | | | | | | | | | | | | | | | | | 
% 229.74/42.65  | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.65  | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | |   (2196)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 229.74/42.66  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 229.74/42.66  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 229.74/42.66  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 229.74/42.66  | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.66  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.66  | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 229.74/42.66  | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 229.74/42.66  | | | | | | | | | | | | | | | | |             = e0)
% 229.74/42.66  | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | BETA: splitting (2196) gives:
% 229.74/42.66  | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2197)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 229.74/42.66  | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 229.74/42.66  | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 229.74/42.66  | | | | | | | | | | | | | | | | | |             e3) = e1
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | | ALPHA: (2197) implies:
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2198)   ~ (all_56_31 = e3)
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2199)   ~ (all_56_21 = e3)
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2200)   ~ (all_56_1 = e3)
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2201)  op(e1, e3) = e1
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2202)  op(e3, e1) = e1
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | | REDUCE: (1621), (2200) imply:
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2203)   ~ (e3 = e0)
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | | REDUCE: (2166), (2198) imply:
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2204)   ~ (e3 = e1)
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 229.74/42.66  | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (2201) gives:
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2205)  all_52_2 = e1
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 229.74/42.66  | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (2202) gives:
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2206)  all_52_8 = e1
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | | REDUCE: (149), (2205) imply:
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2207)   ~ (all_52_1 = e1)
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | | REDUCE: (134), (2206) imply:
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2208)   ~ (all_52_4 = e1)
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (39), (42), (123), (126), (148),
% 229.74/42.66  | | | | | | | | | | | | | | | | | |            (158), (159), (160), (162), (164), (165), (167),
% 229.74/42.66  | | | | | | | | | | | | | | | | | |            (168), (169), (170), (194), (199), (213), (218),
% 229.74/42.66  | | | | | | | | | | | | | | | | | |            (221), (223), (226), (227), (230), (231), (232),
% 229.74/42.66  | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (238), (266), (275),
% 229.74/42.66  | | | | | | | | | | | | | | | | | |            (297), (375), (381), (391), (392), (397), (1630),
% 229.74/42.66  | | | | | | | | | | | | | | | | | |            (2166), (2168), (2170), (2179), (2182), (2207),
% 229.74/42.66  | | | | | | | | | | | | | | | | | |            (2208), (function-axioms) are inconsistent by
% 229.74/42.66  | | | | | | | | | | | | | | | | | |            sub-proof #1830.
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | |   (2209)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 229.74/42.66  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 229.74/42.66  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 229.74/42.66  | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 229.74/42.66  | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 229.74/42.66  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 229.74/42.66  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1621), (1624), (2209), (function-axioms)
% 229.74/42.66  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1829.
% 229.74/42.66  | | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | End of split
% 229.74/42.66  | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | End of split
% 229.74/42.66  | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | Case 2:
% 229.74/42.66  | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | |   (2210)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.66  | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.66  | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.66  | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.66  | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.66  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.66  | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.66  | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.66  | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 229.74/42.66  | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 229.74/42.66  | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 229.74/42.66  | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 229.74/42.66  | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 229.74/42.66  | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | BETA: splitting (2210) gives:
% 229.74/42.66  | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | Case 1:
% 229.74/42.66  | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | |   (2211)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 229.74/42.66  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 229.74/42.66  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 229.74/42.66  | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 229.74/42.66  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 229.74/42.66  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 229.74/42.66  | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 229.74/42.66  | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 229.74/42.66  | | | | | | | | | | | | | | | | |             = e2)
% 229.74/42.66  | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (2190), (2192), (2193), (2211),
% 229.74/42.66  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.66  | | | | | | | | | | | | | | | | |            #2325.
% 229.74/42.66  | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | Case 2:
% 229.74/42.66  | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | |   (2212)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 229.74/42.66  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 229.74/42.66  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 229.74/42.66  | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 229.74/42.66  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 229.74/42.66  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 229.74/42.66  | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 229.74/42.66  | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 229.74/42.66  | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 229.74/42.66  | | | | | | | | | | | | | | | | |             = e0)
% 229.74/42.66  | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2166), (2171), (2190), (2212),
% 229.74/42.66  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.66  | | | | | | | | | | | | | | | | |            #2268.
% 229.74/42.66  | | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | | End of split
% 229.74/42.66  | | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | End of split
% 229.74/42.66  | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | Case 2:
% 229.74/42.66  | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | |   (2213)  all_54_5 = e1 | all_54_5 = e0
% 229.74/42.66  | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | | REF_CLOSE: (275), (397), (2182), (2213) are inconsistent by
% 229.74/42.66  | | | | | | | | | | | | | | |            sub-proof #2300.
% 229.74/42.66  | | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | End of split
% 229.74/42.66  | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | End of split
% 229.74/42.66  | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | Case 2:
% 229.74/42.66  | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | |   (2214)  all_22_2 = e1
% 229.74/42.66  | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | COMBINE_EQS: (326), (2214) imply:
% 229.74/42.66  | | | | | | | | | | | | |   (2215)  all_8_2 = e1
% 229.74/42.66  | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | SIMP: (2215) implies:
% 229.74/42.66  | | | | | | | | | | | | |   (2216)  all_8_2 = e1
% 229.74/42.66  | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | COMBINE_EQS: (347), (2216) imply:
% 229.74/42.66  | | | | | | | | | | | | |   (2217)  all_30_2 = e1
% 229.74/42.66  | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | REDUCE: (366), (2216) imply:
% 229.74/42.66  | | | | | | | | | | | | |   (2218)   ~ (all_52_1 = e1)
% 229.74/42.66  | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | REDUCE: (369), (2216) imply:
% 229.74/42.66  | | | | | | | | | | | | |   (2219)   ~ (all_52_4 = e1)
% 229.74/42.66  | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | REDUCE: (392), (2216) imply:
% 229.74/42.66  | | | | | | | | | | | | |   (2220)   ~ (e3 = e1)
% 229.74/42.66  | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | REDUCE: (42), (2216) imply:
% 229.74/42.66  | | | | | | | | | | | | |   (2221)  op(e2, e2) = e1
% 229.74/42.66  | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | BETA: splitting (241) gives:
% 229.74/42.66  | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | Case 1:
% 229.74/42.66  | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | |   (2222)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 229.74/42.66  | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 229.74/42.66  | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (1628), (2218), (2222),
% 229.74/42.66  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 229.74/42.66  | | | | | | | | | | | | | |            #1827.
% 229.74/42.66  | | | | | | | | | | | | | | 
% 229.74/42.66  | | | | | | | | | | | | | Case 2:
% 229.74/42.66  | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | |   (2223)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 230.38/42.66  | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 230.38/42.66  | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | BETA: splitting (2223) gives:
% 230.38/42.66  | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | Case 1:
% 230.38/42.66  | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | |   (2224)  all_58_6 = e1 & op(e1, e3) = e1
% 230.38/42.66  | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | ALPHA: (2224) implies:
% 230.38/42.66  | | | | | | | | | | | | | | |   (2225)  all_58_6 = e1
% 230.38/42.66  | | | | | | | | | | | | | | |   (2226)  op(e1, e3) = e1
% 230.38/42.66  | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 230.38/42.66  | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | Case 1:
% 230.38/42.66  | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | |   (2227)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 230.38/42.66  | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 230.38/42.66  | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (1628), (2219), (2227),
% 230.38/42.66  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.66  | | | | | | | | | | | | | | | |            #1826.
% 230.38/42.66  | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | Case 2:
% 230.38/42.66  | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | |   (2228)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 230.38/42.66  | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 230.38/42.66  | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | BETA: splitting (2228) gives:
% 230.38/42.66  | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.66  | | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | |   (2229)  all_58_4 = e1 & op(e3, e1) = e1
% 230.38/42.66  | | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | | ALPHA: (2229) implies:
% 230.38/42.66  | | | | | | | | | | | | | | | | |   (2230)  op(e3, e1) = e1
% 230.38/42.66  | | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 230.38/42.66  | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (2226) gives:
% 230.38/42.66  | | | | | | | | | | | | | | | | |   (2231)  all_52_2 = e1
% 230.38/42.66  | | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 230.38/42.66  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (2230) gives:
% 230.38/42.66  | | | | | | | | | | | | | | | | |   (2232)  all_52_8 = e1
% 230.38/42.66  | | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | | REDUCE: (144), (2231) imply:
% 230.38/42.66  | | | | | | | | | | | | | | | | |   (2233)   ~ (all_52_3 = e1)
% 230.38/42.66  | | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | | REDUCE: (143), (2231) imply:
% 230.38/42.66  | | | | | | | | | | | | | | | | |   (2234)   ~ (all_52_6 = e1)
% 230.38/42.66  | | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | | SIMP: (2234) implies:
% 230.38/42.66  | | | | | | | | | | | | | | | | |   (2235)   ~ (all_52_6 = e1)
% 230.38/42.66  | | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | | REDUCE: (123), (2232) imply:
% 230.38/42.66  | | | | | | | | | | | | | | | | |   (2236)   ~ (all_52_9 = e1)
% 230.38/42.66  | | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | | SIMP: (2236) implies:
% 230.38/42.66  | | | | | | | | | | | | | | | | |   (2237)   ~ (all_52_9 = e1)
% 230.38/42.66  | | | | | | | | | | | | | | | | | 
% 230.38/42.66  | | | | | | | | | | | | | | | | | REDUCE: (121), (2232) imply:
% 230.38/42.66  | | | | | | | | | | | | | | | | |   (2238)   ~ (all_52_11 = e1)
% 230.38/42.67  | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | SIMP: (2238) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | |   (2239)   ~ (all_52_11 = e1)
% 230.38/42.67  | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | REDUCE: (120), (2232) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | |   (2240)   ~ (all_52_12 = e1)
% 230.38/42.67  | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | REDUCE: (380), (2232) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | |   (2241)   ~ (all_6_2 = e1)
% 230.38/42.67  | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | SIMP: (2241) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | |   (2242)   ~ (all_6_2 = e1)
% 230.38/42.67  | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | |   (2243)  all_54_10 = e3
% 230.38/42.67  | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (2243) are inconsistent by sub-proof
% 230.38/42.67  | | | | | | | | | | | | | | | | | |            #2313.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | |   (2244)   ~ (all_54_10 = e3)
% 230.38/42.67  | | | | | | | | | | | | | | | | | |   (2245)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 230.38/42.67  | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | BETA: splitting (2245) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | |   (2246)  all_54_10 = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (2246) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | |   (2247)  all_6_2 = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | SIMP: (2247) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | |   (2248)  all_6_2 = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (2248) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | |   (2249)  all_56_21 = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | REDUCE: (381), (2248) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | |   (2250)   ~ (all_52_9 = e2)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | REDUCE: (383), (2248) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | |   (2251)   ~ (all_52_11 = e2)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | REDUCE: (391), (2248) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | |   (2252)   ~ (e3 = e2)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (2248) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | |   (2253)  op(e1, e1) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | |   (2254)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2254) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | |   (2255)  all_58_6 = e2 & op(e1, e3) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2255) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | |   (2256)  op(e1, e3) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2226), (2256), (function-axioms) are
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | |   (2257)  all_58_7 = e2 & op(e1, e2) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2257) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | |   (2258)  all_58_7 = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | |   (2259)  op(e1, e2) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (224),
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | |            (225), (226), (2225), (2253), (2258), (2259),
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | |            #2200.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | |   (2260)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2260) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | |   (2261)  all_58_8 = e2 & op(e1, e1) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2261) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | |   (2262)  all_58_8 = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | |   (2263)   ~ (all_30_2 = e1)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2217), (2263) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | |   (2264)  $false
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2264) is inconsistent.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | |   (2265)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_30_1 & $i(all_30_0) &
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | |   (2266)   ~ (all_34_2 = e1)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2165), (2266) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | |   (2267)  $false
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2267) is inconsistent.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | |   (2268)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | |   (2269)   ~ (all_50_2 = e0)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1620), (2269) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | |   (2270)  $false
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2270) is inconsistent.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | |   (2271)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (2272)  all_54_4 = e3
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (2272) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (2273)  all_52_1 = e3
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2273) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (2274)  all_52_1 = e3
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (2274) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (2275)   ~ (all_52_3 = e3)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2275) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (2276)   ~ (all_52_3 = e3)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (2274) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (2277)   ~ (all_52_9 = e3)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2277) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (2278)   ~ (all_52_9 = e3)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (2274) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (2279)   ~ (all_52_13 = e3)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2279) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (2280)   ~ (all_52_13 = e3)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (2274) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (2281)  op(e2, e3) = e3
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2282)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2282) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2283)  all_58_2 = e2 & op(e2, e3) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2283) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2284)  op(e2, e3) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2281), (2284), (function-axioms) are
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2285)  all_58_3 = e2 & op(e2, e2) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2285) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2286)  op(e2, e2) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (123), (126),
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (158), (159), (160), (162), (164), (165),
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (194), (213), (218),
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (227), (230), (231), (232),
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (238), (266), (297),
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (381), (391), (1630), (2166), (2168), (2170),
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2179), (2218), (2219), (2250), (2286),
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2105.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2287)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2287) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2288)  all_58_5 = e2 & op(e2, e1) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2288) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2289)  op(e2, e1) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (297), (381), (1630), (2242), (2245),
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2289), (function-axioms) are inconsistent by
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2198.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2290)  all_58_10 = e2 & op(e2, e0) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2290) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2291)  op(e2, e0) = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2292)  all_54_6 = e3
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2278), (2292) are inconsistent by
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2293)   ~ (all_54_6 = e3)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2294)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2295)  all_54_12 = e3
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (2295) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2296)  all_52_3 = e3
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2276), (2296) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2297)  $false
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2297) is inconsistent.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2298)   ~ (all_54_12 = e3)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2299)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2299) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2300)  all_54_12 = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (2300) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2301)  all_52_3 = e2
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (2301) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2302)   ~ (all_52_7 = e2)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2302) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2303)   ~ (all_52_7 = e2)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2301) imply:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2304)   ~ (all_52_11 = e2)
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2305)  all_58_15 = e0 & op(e0, e0) = e0
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2305) implies:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2306)  op(e0, e0) = e0
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2180), (2306), (function-axioms) are
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2307)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2307) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2308)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2308) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2309)  all_58_9 = e0 & op(e3, e0) = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2309) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2310)  op(e3, e0) = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1627), (2310), (function-axioms) are
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2258.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2311)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2311) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2312)  all_58_10 = e0 & op(e2, e0) = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2312) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2313)  op(e2, e0) = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2291), (2313), (function-axioms) are
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2314)  all_58_11 = e0 & op(e1, e0) = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2314) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2315)  all_58_11 = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2316)  op(e1, e0) = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2317)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2317) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2318)  all_58_6 = e3 & op(e1, e3) = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2318) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2319)  op(e1, e3) = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2226), (2319), (function-axioms) are
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2320)  all_58_7 = e3 & op(e1, e2) = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2320) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2321)  op(e1, e2) = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2322)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (1628), (2281), (2322),
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1824.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2323)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2323) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2324)  all_58_6 = e2 & op(e1, e3) = e2
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2324) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2325)  op(e1, e3) = e2
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2226), (2325), (function-axioms) are
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2326)  all_58_12 = e2 & op(e0, e3) = e2
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2326) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2327)  all_58_12 = e2
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2328)  op(e0, e3) = e2
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2294) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2329)  all_54_6 = e2
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2250), (2329) are inconsistent by
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2330)   ~ (all_54_6 = e2)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2331)  all_54_6 = e1 | all_54_6 = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2332)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (2230), (2278), (2332),
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1821.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2333)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2333) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2334)  all_58_8 = e3 & op(e1, e1) = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2334) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2335)  op(e1, e1) = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2253), (2335), (function-axioms) are
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2336)  all_58_14 = e3 & op(e0, e1) = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2336) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2337)  all_58_14 = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2331) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2338)  all_54_6 = e1
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2237), (2338) are inconsistent by
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2246.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2339)  all_54_6 = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (2339) imply:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2340)  all_52_9 = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2340) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2341)  all_52_9 = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2341) imply:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2342)   ~ (all_52_11 = e0)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2342) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2343)   ~ (all_52_11 = e0)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (2341) imply:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2344)   ~ (all_52_13 = e0)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2344) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2345)   ~ (all_52_13 = e0)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2250), (2341) imply:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2346)   ~ (e2 = e0)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2237), (2341) imply:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2347)   ~ (e1 = e0)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (2341) imply:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2348)  op(e2, e1) = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2349)  all_54_14 = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (2349) imply:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2350)  all_52_11 = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2350) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2351)  all_52_11 = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (2351) imply:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2352)   ~ (all_52_7 = e3)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (2351) imply:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2353)  op(e0, e1) = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2162) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2354)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_20_1 & $i(all_20_0) &
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2354) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2355)  op(e0, e1) = all_20_1
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2356)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2356) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2357)  all_58_1 = e2 & op(e3, e2) = e2
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2357) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2358)  all_58_1 = e2
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2359)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_19 & $i(all_56_19))
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2359) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2360)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_17 & $i(all_56_17)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2360) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2361)  op(e3, e1) = all_56_17
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2362)  op(e3, all_56_17) = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2363)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2363) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2364)  all_58_9 = e3 & op(e3, e0) = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2364) implies:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2365)  all_58_9 = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2366)  all_54_13 = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2352), (2366) are inconsistent by
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2367)   ~ (all_54_13 = e3)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2368)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2368) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2369)  all_54_13 = e2
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2303), (2369) are inconsistent by
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2370)   ~ (all_54_13 = e2)
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2371)  all_54_13 = e1 | all_54_13 = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2372)  all_54_7 = e3
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (2280), (2372) are inconsistent by
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2373)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2371) gives:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2374)  all_54_13 = e1
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2168), (2374) are inconsistent by
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1966.
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2375)  all_54_13 = e0
% 230.38/42.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2375) imply:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2376)  all_52_7 = e0
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2376) implies:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2377)  all_52_7 = e0
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (2377) imply:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2378)   ~ (all_52_6 = e0)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2373) gives:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2379)  all_54_7 = e2
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (2379) imply:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2380)  all_52_13 = e2
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2380) implies:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2381)  all_52_13 = e2
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (2381) imply:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2382)   ~ (all_52_12 = e2)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2383)  all_54_9 = e3
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (2383) imply:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2384)  all_52_6 = e3
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2384) implies:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2385)  all_52_6 = e3
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (2385) imply:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2386)   ~ (all_52_4 = e3)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2387)  all_54_1 = e3
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (2386), (2387) are inconsistent by
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2388)   ~ (all_54_1 = e3)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2389)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2390)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2390) gives:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2391)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2391) gives:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2392)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2392) implies:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2393)  op(e3, e2) = e3
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (2386), (2393), (function-axioms) are
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2394)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2394) gives:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2395)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2395) implies:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2396)  op(e2, e3) = e2
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (145), (167), (197), (201), (269), (280),
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1627), (2169), (2170), (2345), (2382), (2396),
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2285.
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2397)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2397) implies:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2398)  op(e1, e3) = e3
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2226), (2398), (function-axioms) are
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2399)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2399) gives:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2400)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2400) implies:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2401)  all_56_17 = e1
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2402)   ~ (all_56_1 = e3)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1621), (2402) imply:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2403)   ~ (e3 = e0)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2362), (2401) imply:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2404)  op(e3, e1) = e3
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (191), (256), (1628), (2303), (2352), (2361),
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2362), (2404), (function-axioms) are inconsistent
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1820.
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2405)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (2276), (2328), (2405),
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1819.
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2406)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2406) gives:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2407)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2407) gives:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2408)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2408) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2409)  op(e2, e1) = e2
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2348), (2409), (function-axioms) are
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2410)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2410) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2411)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e1
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2411) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2412)  op(e2, e1) = e1
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (165), (2348), (2412), (function-axioms) are
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2165.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2413)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2413) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2414)  op(e0, e2) = e2
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (135), (158), (191), (256), (282), (1625), (2168),
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2219), (2352), (2389), (2414), (function-axioms)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1815.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2415)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2415) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2416)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e0
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2416) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2417)  op(e2, e0) = e0
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2345), (2417), (function-axioms) are
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2324.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2418)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2418) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2419)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = e1
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2419) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2420)  op(e1, e0) = e1
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (2291), (2308), (2365), (2420),
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2101.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2421)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = e0
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2421) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2422)  op(e0, e1) = e0
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (2343), (2422), (function-axioms) are
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1911.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2423)   ~ (all_54_9 = e3)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (2423) imply:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2424)   ~ (all_52_6 = e3)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2321), (2424), (function-axioms) are
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2425)  all_54_7 = e1 | all_54_7 = e0
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (2170), (2345), (2425) are inconsistent by
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2293.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2426)  all_58_10 = e3 & op(e2, e0) = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2426) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2427)  op(e2, e0) = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2291), (2427), (function-axioms) are
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2428)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2428) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2429)  all_58_11 = e3 & op(e1, e0) = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2315), (2429) are inconsistent by sub-proof
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2091.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2430)  all_58_15 = e3 & op(e0, e0) = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (158), (219), (2179), (2327), (2337),
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2352), (2430), (function-axioms) are inconsistent
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1813.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2431)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_19 & $i(all_56_19)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2431) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2432)  op(e2, e1) = all_56_19
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2433)  op(e2, all_56_19) = e2
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2434)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2434) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2435)  all_58_9 = e3 & op(e3, e0) = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2435) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2436)  all_58_9 = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2437)  op(e3, e0) = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2438)  all_54_13 = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2352), (2438) are inconsistent by
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2439)   ~ (all_54_13 = e3)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2440)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2440) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2441)  all_54_13 = e2
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2303), (2441) are inconsistent by
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2442)  all_54_13 = e1 | all_54_13 = e0
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2442) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2443)  all_54_13 = e1
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2168), (2443) are inconsistent by
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1966.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2444)  all_54_13 = e0
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2444) imply:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2445)  all_52_7 = e0
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2445) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2446)  all_52_7 = e0
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (2446) imply:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2447)   ~ (all_52_6 = e0)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2448)  all_54_9 = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (2448) imply:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2449)  all_52_6 = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2449) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2450)  all_52_6 = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (2450) imply:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2451)   ~ (all_52_4 = e3)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2452)  all_54_1 = e3
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (2451), (2452) are inconsistent by
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2453)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2265) gives:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2454)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_30_1 & $i(all_30_0) &
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2454) implies:
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2455)  op(e2, e1) = all_30_1
% 230.38/42.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (157), (158), (159), (162), (163),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (210), (235), (236), (238), (239),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (1622), (1623), (1624), (1625), (2166),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2219), (2268), (2271), (2291), (2308), (2316),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2343), (2348), (2352), (2353), (2355), (2358),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2432), (2433), (2436), (2437), (2453), (2455),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1808.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2456)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2456) implies:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2457)  op(e2, e1) = all_30_1
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (157), (158), (159), (162), (163),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (210), (235), (236), (238), (239),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (1622), (1623), (1624), (1625), (2166),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2219), (2268), (2271), (2291), (2308), (2316),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2343), (2348), (2352), (2353), (2355), (2358),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2432), (2433), (2436), (2437), (2453), (2457),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1808.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2458)   ~ (all_54_9 = e3)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (2458) imply:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2459)   ~ (all_52_6 = e3)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2321), (2459), (function-axioms) are
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2460)  all_58_10 = e3 & op(e2, e0) = e3
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2460) implies:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2461)  op(e2, e0) = e3
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2291), (2461), (function-axioms) are
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2462)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2462) gives:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2463)  all_58_11 = e3 & op(e1, e0) = e3
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2315), (2463) are inconsistent by sub-proof
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2091.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2464)  all_58_15 = e3 & op(e0, e0) = e3
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (158), (219), (2179), (2327), (2337),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2352), (2464), (function-axioms) are inconsistent
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1813.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2465)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_23 & $i(all_56_23))
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2465) gives:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2466)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2466) implies:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2467)  op(e1, all_56_21) = e1
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2249), (2467) imply:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2468)  op(e1, e2) = e1
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2321), (2468), (function-axioms) are
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2094.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2469)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_23 & $i(all_56_23)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (257), (1624), (2162), (2167), (2268),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2299), (2353), (2469), (function-axioms) are
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1804.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2470)  all_58_3 = e2 & op(e2, e2) = e2
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2470) implies:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2471)  op(e2, e2) = e2
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (123), (126),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (158), (159), (160), (162), (164), (165),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (194), (213), (218),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (227), (230), (231), (232),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (238), (266), (297),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (381), (391), (1630), (2166), (2168), (2170),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2179), (2218), (2219), (2250), (2471),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2105.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2472)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2472) gives:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2473)  all_58_7 = e2 & op(e1, e2) = e2
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2473) implies:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2474)  all_58_7 = e2
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (226),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2225), (2253), (2262), (2474), (function-axioms)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1799.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2475)  all_58_13 = e2 & op(e0, e2) = e2
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2475) implies:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2476)  op(e0, e2) = e2
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (191), (256), (2168), (2303), (2352),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2476), (function-axioms) are inconsistent by
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1816.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2477)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2268), (2353), (2477), (function-axioms) are
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1805.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2478)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (2239), (2251), (2343), (2478) are
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1798.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2479)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (2253), (2315), (2479),
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1797.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2480)  all_54_12 = e1 | all_54_12 = e0
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1624), (2167), (2480) are inconsistent by
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2067.
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (2481)   ~ (all_54_4 = e3)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (2482)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (2481) imply:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (2483)   ~ (all_52_1 = e3)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2482) gives:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2484)  all_54_4 = e2
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (2484) imply:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2485)  all_52_1 = e2
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2485) implies:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2486)  all_52_1 = e2
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (2486) imply:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2487)   ~ (all_52_3 = e2)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2487) implies:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2488)   ~ (all_52_3 = e2)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (2486) imply:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2489)   ~ (all_52_9 = e2)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (2486) imply:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2490)   ~ (all_52_13 = e2)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2490) implies:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2491)   ~ (all_52_13 = e2)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (2486) imply:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2492)  op(e2, e3) = e2
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2493)  all_54_12 = e3
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (2493) imply:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2494)  all_52_3 = e3
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (2494) imply:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2495)   ~ (all_52_7 = e3)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2495) implies:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2496)   ~ (all_52_7 = e3)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2494) imply:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2497)   ~ (all_52_11 = e3)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2497) implies:
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2498)   ~ (all_52_11 = e3)
% 230.38/42.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (2494) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2499)  op(e0, e3) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2500)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2500) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2501)  all_58_9 = e2 & op(e3, e0) = e2
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2501) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2502)  op(e3, e0) = e2
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2503)  all_54_14 = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (2498), (2503) are inconsistent by
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1796.
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2504)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2505)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (1621), (2221), (2271), (2492), (2502),
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2505), (function-axioms) are inconsistent by
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1795.
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2506)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2506) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2507)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_5 & $i(all_56_5)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2507) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2508)  op(e1, e3) = all_56_5
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2509)  op(e1, all_56_5) = e1
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2510)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2510) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2511)  all_58_0 = e3 & op(e3, e3) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2511) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2512)  op(e3, e3) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (1622), (1623),
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1624), (2512), (function-axioms) are inconsistent
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1938.
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2513)  all_58_1 = e3 & op(e3, e2) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2513) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2514)  op(e3, e2) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2504) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2515)  all_54_14 = e2
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (2251), (2515) are inconsistent by
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1856.
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2516)  all_54_14 = e1 | all_54_14 = e0
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2517)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2517) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2518)  all_58_6 = e3 & op(e1, e3) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2518) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2519)  op(e1, e3) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2508), (2509), (2519), (function-axioms) are
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2243.
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2520)  all_58_7 = e3 & op(e1, e2) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2520) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2521)  op(e1, e2) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (162), (170), (195), (267), (2514), (2521),
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2190.
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2522)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2522) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2523)  all_58_8 = e3 & op(e1, e1) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2523) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2524)  op(e1, e1) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2253), (2524), (function-axioms) are
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2525)  all_58_11 = e3 & op(e1, e0) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2525) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2526)  op(e1, e0) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2516) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2527)  all_54_14 = e1
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (2239), (2527) are inconsistent by
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1937.
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2528)  all_54_14 = e0
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (2528) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2529)  all_52_11 = e0
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2529) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2530)  all_52_11 = e0
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (2530) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2531)   ~ (all_52_7 = e0)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2530) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2532)   ~ (all_52_9 = e0)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2533)  all_54_13 = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2496), (2533) are inconsistent by
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2534)   ~ (all_54_13 = e3)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2535)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2536)  all_54_6 = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (2536) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2537)  all_52_9 = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2537) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2538)  all_52_9 = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (2538) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2539)   ~ (all_52_13 = e3)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2539) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2540)   ~ (all_52_13 = e3)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (2538) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2541)  op(e2, e1) = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2542)  all_54_7 = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (2540), (2542) are inconsistent by
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2543)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2535) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2544)  all_54_13 = e2
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2544) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2545)  all_52_7 = e2
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2545) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2546)  all_52_7 = e2
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (2546) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2547)   ~ (all_52_4 = e2)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (2546) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2548)  op(e0, e2) = e2
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2549)  all_54_1 = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (2549) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2550)  all_52_4 = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2550) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2551)  all_52_4 = e3
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (2551) imply:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2552)   ~ (all_52_12 = e3)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2552) implies:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2553)   ~ (all_52_12 = e3)
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2554)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2554) gives:
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2555)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2555) gives:
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2556)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2556) implies:
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2557)  op(e2, e3) = e3
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2483), (2557), (function-axioms) are
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2558)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 230.90/42.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2558) gives:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2559)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2559) implies:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2560)  op(e3, e2) = e2
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2514), (2560), (function-axioms) are
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2193.
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2561)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2561) implies:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2562)  op(e1, e3) = e3
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2508), (2509), (2562), (function-axioms) are
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2243.
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2563)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2563) gives:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2564)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2564) implies:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2565)  all_56_5 = e1
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2509), (2565) imply:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2566)  op(e1, e1) = e1
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2253), (2566), (function-axioms) are
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2567)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (168), (1624), (2553), (2567),
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1794.
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2568)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2568) gives:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2569)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2569) gives:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2570)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2570) implies:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2571)  op(e2, e1) = e2
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2541), (2571), (function-axioms) are
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2572)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2572) gives:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2573)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e1
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2573) implies:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2574)  op(e2, e1) = e1
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2541), (2574), (function-axioms) are
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2255.
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2575)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2575) implies:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2576)  op(e2, e0) = e2
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (269), (2170), (2491), (2543), (2576),
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1995.
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2577)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2577) gives:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2578)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e0
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2578) implies:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2579)  op(e0, e2) = e0
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (135), (158), (191), (203), (256), (282), (1625),
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2168), (2219), (2531), (2547), (2579),
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1963.
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2580)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2580) gives:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2581)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = e1
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2581) implies:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2582)  op(e1, e0) = e1
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2526), (2582), (function-axioms) are
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2583)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = e0
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2583) implies:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2584)   ~ (all_56_31 = e1)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2166), (2584) imply:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2585)  $false
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2585) is inconsistent.
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2586)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (135), (158), (191), (256), (282), (1625), (2168),
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2219), (2496), (2548), (2586), (function-axioms)
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1815.
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2587)  all_54_13 = e1 | all_54_13 = e0
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2168), (2531), (2587) are inconsistent by
% 230.90/42.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1793.
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2588)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2237), (2250), (2532), (2588) are
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2244.
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2589)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (2230), (2502), (2589),
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1792.
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2590)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_7 & $i(all_56_7)
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2590) implies:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2591)  op(e0, e3) = all_56_7
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2592)  op(e0, all_56_7) = e0
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2499), (2591), (2592), (function-axioms) are
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2070.
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2593)  all_58_10 = e2 & op(e2, e0) = e2
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2593) implies:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2594)  op(e2, e0) = e2
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2491), (2594), (function-axioms) are
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2595)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (226),
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2179), (2225), (2226), (2253), (2595),
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2027.
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2596)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1624), (2167), (2488), (2596) are
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2066.
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2597)  all_54_4 = e1 | all_54_4 = e0
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (1622), (2218), (2597) are inconsistent by
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1922.
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | |   (2598)  all_58_11 = e2 & op(e1, e0) = e2
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2598) implies:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | |   (2599)  all_58_11 = e2
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (223), (226), (2225),
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | |            (2226), (2253), (2599), (function-axioms) are
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2028.
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | |   (2600)  all_54_10 = e1 | all_54_10 = e0
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (1630), (2242), (2600) are inconsistent by
% 230.90/42.74  | | | | | | | | | | | | | | | | | | |            sub-proof #2282.
% 230.90/42.74  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | |   (2601)  all_58_9 = e1 & op(e3, e0) = e1
% 230.90/42.74  | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2169), (2601), (function-axioms) are
% 230.90/42.74  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 230.90/42.74  | | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | |   (2602)  all_58_12 = e1 & op(e0, e3) = e1
% 230.90/42.74  | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | REF_CLOSE: (159), (2167), (2602), (function-axioms) are
% 230.90/42.74  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 230.90/42.74  | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | 
% 230.90/42.74  | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | 
% 230.90/42.74  | | | | | | | | |   (2603)  all_18_2 = e0
% 230.90/42.74  | | | | | | | | |   (2604)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 &
% 230.90/42.74  | | | | | | | | |             op(e1, e0) = all_18_1 & $i(all_18_0) &
% 230.90/42.74  | | | | | | | | |             $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1, e0) =
% 230.90/42.74  | | | | | | | | |             all_18_1 & $i(all_18_1))
% 230.90/42.74  | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | COMBINE_EQS: (339), (2603) imply:
% 230.90/42.74  | | | | | | | | |   (2605)  all_6_2 = e0
% 230.90/42.74  | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | COMBINE_EQS: (332), (2605) imply:
% 230.90/42.74  | | | | | | | | |   (2606)  all_28_2 = e0
% 230.90/42.74  | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | COMBINE_EQS: (266), (2605) imply:
% 230.90/42.74  | | | | | | | | |   (2607)  all_56_21 = e0
% 230.90/42.74  | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | REDUCE: (378), (2605) imply:
% 230.90/42.74  | | | | | | | | |   (2608)   ~ (all_52_6 = e0)
% 230.90/42.74  | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | REDUCE: (381), (2605) imply:
% 230.90/42.74  | | | | | | | | |   (2609)   ~ (all_52_9 = e0)
% 230.90/42.74  | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | REDUCE: (391), (2605) imply:
% 230.90/42.74  | | | | | | | | |   (2610)   ~ (e3 = e0)
% 230.90/42.74  | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | REDUCE: (39), (2605) imply:
% 230.90/42.74  | | | | | | | | |   (2611)  op(e1, e1) = e0
% 230.90/42.74  | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | BETA: splitting (235) gives:
% 230.90/42.74  | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | Case 1:
% 230.90/42.74  | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | |   (2612)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 230.90/42.74  | | | | | | | | | |             & op(e2, e2) = e0)
% 230.90/42.74  | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | BETA: splitting (2612) gives:
% 230.90/42.74  | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | Case 1:
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | |   (2613)  all_58_1 = e0 & op(e3, e2) = e0
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | REF_CLOSE: (170), (1625), (2613), (function-axioms) are
% 230.90/42.74  | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | |   (2614)  all_58_3 = e0 & op(e2, e2) = e0
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | REF_CLOSE: (42), (397), (2614), (function-axioms) are
% 230.90/42.74  | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | |   (2615)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 230.90/42.74  | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 230.90/42.74  | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | BETA: splitting (2615) gives:
% 230.90/42.74  | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | Case 1:
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | |   (2616)  all_58_7 = e0 & op(e1, e2) = e0
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | REF_CLOSE: (162), (2608), (2616), (function-axioms) are
% 230.90/42.74  | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | |   (2617)  all_58_13 = e0 & op(e0, e2) = e0
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | ALPHA: (2617) implies:
% 230.90/42.74  | | | | | | | | | | |   (2618)  op(e0, e2) = e0
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | BETA: splitting (231) gives:
% 230.90/42.74  | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | Case 1:
% 230.90/42.74  | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | |   (2619)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 230.90/42.74  | | | | | | | | | | | |             & op(e2, e2) = e0)
% 230.90/42.74  | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | BETA: splitting (2619) gives:
% 230.90/42.74  | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | Case 1:
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | |   (2620)  all_58_2 = e0 & op(e2, e3) = e0
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | REF_CLOSE: (167), (1622), (2620), (function-axioms) are
% 230.90/42.74  | | | | | | | | | | | | |            inconsistent by sub-proof #1985.
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | |   (2621)  all_58_3 = e0 & op(e2, e2) = e0
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | REF_CLOSE: (42), (397), (2621), (function-axioms) are
% 230.90/42.74  | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | End of split
% 230.90/42.74  | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | |   (2622)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 230.90/42.74  | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 230.90/42.74  | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | BETA: splitting (2622) gives:
% 230.90/42.74  | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | Case 1:
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | |   (2623)  all_58_5 = e0 & op(e2, e1) = e0
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | REF_CLOSE: (165), (2609), (2623), (function-axioms) are
% 230.90/42.74  | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | |   (2624)  all_58_10 = e0 & op(e2, e0) = e0
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | ALPHA: (2624) implies:
% 230.90/42.74  | | | | | | | | | | | | |   (2625)  op(e2, e0) = e0
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 230.90/42.74  | | | | | | | | | | | | |              e2, e0, simplifying with (158), (2618) gives:
% 230.90/42.74  | | | | | | | | | | | | |   (2626)  all_52_7 = e0
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 230.90/42.74  | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (2625) gives:
% 230.90/42.74  | | | | | | | | | | | | |   (2627)  all_52_13 = e0
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | REDUCE: (125), (2626) imply:
% 230.90/42.74  | | | | | | | | | | | | |   (2628)   ~ (all_52_11 = e0)
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | SIMP: (2628) implies:
% 230.90/42.74  | | | | | | | | | | | | |   (2629)   ~ (all_52_11 = e0)
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | REDUCE: (110), (2627) imply:
% 230.90/42.74  | | | | | | | | | | | | |   (2630)   ~ (all_52_14 = e0)
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | SIMP: (2630) implies:
% 230.90/42.74  | | | | | | | | | | | | |   (2631)   ~ (all_52_14 = e0)
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | REDUCE: (377), (2627) imply:
% 230.90/42.74  | | | | | | | | | | | | |   (2632)   ~ (all_8_2 = e0)
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | REDUCE: (388), (2627) imply:
% 230.90/42.74  | | | | | | | | | | | | |   (2633)   ~ (all_4_2 = e0)
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | SIMP: (2633) implies:
% 230.90/42.74  | | | | | | | | | | | | |   (2634)   ~ (all_4_2 = e0)
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | BETA: splitting (189) gives:
% 230.90/42.74  | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | Case 1:
% 230.90/42.74  | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | |   (2635)  all_54_15 = e3
% 230.90/42.74  | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | REF_CLOSE: (299), (395), (2635) are inconsistent by sub-proof
% 230.90/42.74  | | | | | | | | | | | | | |            #2340.
% 230.90/42.74  | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | |   (2636)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 230.90/42.74  | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | BETA: splitting (2636) gives:
% 230.90/42.74  | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | Case 1:
% 230.90/42.74  | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | |   (2637)  all_54_15 = e2
% 230.90/42.74  | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | REF_CLOSE: (299), (390), (2637) are inconsistent by sub-proof
% 230.90/42.74  | | | | | | | | | | | | | | |            #2339.
% 230.90/42.74  | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | Case 2:
% 230.90/42.74  | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | |   (2638)   ~ (all_54_15 = e2)
% 230.90/42.74  | | | | | | | | | | | | | | |   (2639)  all_54_15 = e1 | all_54_15 = e0
% 230.90/42.74  | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | BETA: splitting (2639) gives:
% 230.90/42.74  | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | Case 1:
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | |   (2640)  all_54_15 = e1
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (2640) imply:
% 230.90/42.74  | | | | | | | | | | | | | | | |   (2641)  all_4_2 = e1
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | SIMP: (2641) implies:
% 230.90/42.74  | | | | | | | | | | | | | | | |   (2642)  all_4_2 = e1
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (2642) imply:
% 230.90/42.74  | | | | | | | | | | | | | | | |   (2643)  all_20_2 = e1
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (2642) imply:
% 230.90/42.74  | | | | | | | | | | | | | | | |   (2644)  all_34_2 = e1
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (2642) imply:
% 230.90/42.74  | | | | | | | | | | | | | | | |   (2645)  all_56_31 = e1
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | REDUCE: (368), (2642) imply:
% 230.90/42.74  | | | | | | | | | | | | | | | |   (2646)   ~ (all_52_3 = e1)
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | REDUCE: (386), (2642) imply:
% 230.90/42.74  | | | | | | | | | | | | | | | |   (2647)   ~ (all_52_11 = e1)
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | REDUCE: (387), (2642) imply:
% 230.90/42.74  | | | | | | | | | | | | | | | |   (2648)   ~ (all_52_12 = e1)
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | REDUCE: (389), (2642) imply:
% 230.90/42.74  | | | | | | | | | | | | | | | |   (2649)   ~ (all_52_14 = e1)
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | REDUCE: (390), (2642) imply:
% 230.90/42.74  | | | | | | | | | | | | | | | |   (2650)   ~ (e2 = e1)
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 230.90/42.74  | | | | | | | | | | | | | | | | 
% 230.90/42.74  | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.74  | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | |   (2651)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 230.90/42.75  | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 230.90/42.75  | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (2618), (2646), (2651),
% 230.90/42.75  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.75  | | | | | | | | | | | | | | | | |            #1791.
% 230.90/42.75  | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.75  | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | |   (2652)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 230.90/42.75  | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 230.90/42.75  | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | BETA: splitting (2652) gives:
% 230.90/42.75  | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | |   (2653)  all_58_14 = e1 & op(e0, e1) = e1
% 230.90/42.75  | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | ALPHA: (2653) implies:
% 230.90/42.75  | | | | | | | | | | | | | | | | | |   (2654)  op(e0, e1) = e1
% 230.90/42.75  | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (2647), (2654), (function-axioms) are
% 230.90/42.75  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2272.
% 230.90/42.75  | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | |   (2655)  all_58_15 = e1 & op(e0, e0) = e1
% 230.90/42.75  | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | ALPHA: (2655) implies:
% 230.90/42.75  | | | | | | | | | | | | | | | | | |   (2656)  all_58_15 = e1
% 230.90/42.75  | | | | | | | | | | | | | | | | | |   (2657)  op(e0, e0) = e1
% 230.90/42.75  | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | |   (2658)   ~ (all_20_2 = e1)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | REDUCE: (2643), (2658) imply:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | |   (2659)  $false
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | CLOSE: (2659) is inconsistent.
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | |   (2660)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 230.90/42.75  | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | |             $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | |             = all_20_1 & $i(all_20_1))
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | |   (2661)   ~ (all_22_2 = e1)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (326), (2661) imply:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | |   (2662)   ~ (all_8_2 = e1)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | |   (2663)  all_54_5 = e3
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (392), (2663) are inconsistent by sub-proof
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | |            #1907.
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | |   (2664)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2664) gives:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | |   (2665)  all_54_5 = e2
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (2665) imply:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | |   (2666)  all_8_2 = e2
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | SIMP: (2666) implies:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | |   (2667)  all_8_2 = e2
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (2667) imply:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | |   (2668)  all_56_11 = e2
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (2667) imply:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | |   (2669)   ~ (all_52_1 = e2)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (2667) imply:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | |   (2670)   ~ (all_52_9 = e2)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |   (2671)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2671) gives:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |   (2672)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2645), (2668), (2669), (2672),
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |            #1831.
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |   (2673)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2673) gives:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (2674)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2674) implies:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (2675)  op(e1, e3) = e1
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (2676)  op(e3, e1) = e1
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (146), (149), (163), (169), (198), (200),
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (279), (1622), (2609), (2669), (2670),
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |            (2675), (2676), (function-axioms) are inconsistent
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1789.
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (2677)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1624), (2607), (2677), (function-axioms)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1788.
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |   (2678)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2678) gives:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |   (2679)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2679) gives:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (2680)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2680) implies:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (2681)  op(e2, e1) = e2
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2670), (2681), (function-axioms) are
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (2682)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2682) gives:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2683)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e1
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2683) implies:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2684)   ~ (all_56_11 = e2)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2668), (2684) imply:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2685)  $false
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2685) is inconsistent.
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2686)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2686) implies:
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2687)  op(e0, e2) = e2
% 230.90/42.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2618), (2687), (function-axioms) are
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2688)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2631), (2649), (2668), (2688),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |            #1988.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | |   (2689)  all_54_5 = e1 | all_54_5 = e0
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (397), (2662), (2689) are inconsistent by
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2300.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |   (2690)  all_22_2 = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |   (2691)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_22_1 & $i(all_22_0) &
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (2690) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |   (2692)  all_8_2 = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (2692) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |   (2693)  all_30_2 = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (2692) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |   (2694)  all_56_11 = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (2692) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |   (2695)   ~ (all_52_1 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (2692) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |   (2696)   ~ (all_52_4 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (2692) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |   (2697)   ~ (e3 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (2692) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | |   (2698)  op(e2, e2) = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | |   (2699)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (1628), (2695), (2699),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | |            #1827.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | |   (2700)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2700) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | |   (2701)  all_58_6 = e1 & op(e1, e3) = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2701) implies:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | |   (2702)  op(e1, e3) = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | |   (2703)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (1628), (2696), (2703),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | |            #1826.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | |   (2704)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2704) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2705)  all_58_4 = e1 & op(e3, e1) = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2705) implies:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2706)  all_58_4 = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2707)  op(e3, e1) = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (2702) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2708)  all_52_2 = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (2707) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2709)  all_52_8 = e1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (2708) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2710)   ~ (all_52_3 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (2708) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2711)   ~ (all_52_6 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2711) implies:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2712)   ~ (all_52_6 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (2708) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2713)   ~ (all_52_14 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (2709) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2714)   ~ (all_52_9 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2714) implies:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2715)   ~ (all_52_9 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (2709) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | |   (2716)   ~ (all_52_11 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (2717)   ~ (all_28_2 = e0)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2606), (2717) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (2718)  $false
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2718) is inconsistent.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (2719)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_28_1 & $i(all_28_0) &
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_28_1 & $i(all_28_1))
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2720)   ~ (all_30_2 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2693), (2720) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2721)  $false
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2721) is inconsistent.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2722)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_30_1 & $i(all_30_0) &
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2723)   ~ (all_34_2 = e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2644), (2723) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2724)  $false
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2724) is inconsistent.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2725)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2726)   ~ (all_50_2 = e0)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1620), (2726) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2727)  $false
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2727) is inconsistent.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2728)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2729)  all_54_3 = e3
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (2729) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2730)  all_52_12 = e3
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2730) implies:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2731)  all_52_12 = e3
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (2731) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2732)   ~ (all_52_4 = e3)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (2731) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2733)   ~ (all_52_14 = e3)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2733) implies:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2734)   ~ (all_52_14 = e3)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (2731) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2735)  op(e3, e0) = e3
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2728) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2736)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_50_1 & $i(all_50_0) &
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2736) implies:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2737)  op(e3, e0) = all_50_1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (159), (160), (162), (163), (167),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (203), (210), (239), (258), (282), (1622),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1623), (1624), (1625), (2625), (2629), (2631),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2645), (2649), (2696), (2712), (2732), (2734),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2735), (2737), (function-axioms) are inconsistent
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1787.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2738)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2738) implies:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2739)  op(e3, e0) = all_50_1
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (159), (160), (162), (163), (167),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (203), (210), (239), (258), (282), (1622),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1623), (1624), (1625), (2625), (2629), (2631),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2645), (2649), (2696), (2712), (2732), (2734),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2735), (2739), (function-axioms) are inconsistent
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1787.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2740)   ~ (all_54_3 = e3)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (280), (2740) imply:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2741)   ~ (all_52_12 = e3)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2742)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2742) gives:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2743)  all_58_0 = e3 & op(e3, e3) = e3
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2743) implies:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2744)  op(e3, e3) = e3
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (1622), (1623),
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1624), (2744), (function-axioms) are inconsistent
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1938.
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2745)  all_58_1 = e3 & op(e3, e2) = e3
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2745) implies:
% 230.90/42.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2746)  all_58_1 = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2747)  op(e3, e2) = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2748)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (1628), (2747), (2748),
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1857.
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2749)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2749) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2750)  all_58_4 = e2 & op(e3, e1) = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2750) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2751)  all_58_4 = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2706), (2751) are inconsistent by sub-proof
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1786.
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2752)  all_58_9 = e2 & op(e3, e0) = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2752) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2753)  all_58_9 = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2754)  op(e3, e0) = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2755)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (2698), (2747), (2755),
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1785.
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2756)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2756) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2757)  all_58_7 = e2 & op(e1, e2) = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2757) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2758)  all_58_7 = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2759)  op(e1, e2) = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2760)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2760) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2761)  all_58_6 = e3 & op(e1, e3) = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2761) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2762)  op(e1, e3) = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2702), (2762), (function-axioms) are
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2763)  all_58_7 = e3 & op(e1, e2) = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2763) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2764)  op(e1, e2) = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2759), (2764), (function-axioms) are
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2207.
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2765)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2765) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2766)  all_58_8 = e3 & op(e1, e1) = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2611), (2766), (function-axioms) are
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2767)  all_58_11 = e3 & op(e1, e0) = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2767) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2768)  all_58_11 = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2769)  op(e1, e0) = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2719) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2770)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_28_1 & $i(all_28_0) &
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2770) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2771)   ~ (all_28_0 = e3)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2772)  op(e1, e0) = all_28_1
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2773)  op(all_28_1, e1) = all_28_0
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2604) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2774)   ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 &
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_18_1 & $i(all_18_0) &
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2774) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2775)   ~ (all_18_0 = e2)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2776)  op(e1, e0) = all_18_1
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2777)  op(all_18_1, e1) = all_18_0
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2778)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2778) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2779)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_9 & $i(all_56_9)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (1622), (1623),
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1624), (2747), (2779), (function-axioms) are
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1784.
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2780)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2780) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2781)  op(e2, all_56_11) = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2694), (2781) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2782)  op(e2, e1) = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_1, e0, e1, simplifying with (2772), (2776)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2783)  all_28_1 = all_18_1
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (2769), (2772) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2784)  all_28_1 = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (2782) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2785)  all_52_9 = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2783), (2784) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2786)  all_18_1 = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2785) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2787)   ~ (all_52_11 = e2)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2787) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2788)   ~ (all_52_11 = e2)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2773), (2784) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2789)  op(e3, e1) = all_28_0
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2777), (2786) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2790)  op(e3, e1) = all_18_0
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2791)  all_54_14 = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (2791) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2792)  all_52_11 = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2792) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2793)  all_52_11 = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2793) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2794)   ~ (all_52_3 = e3)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (2793) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2795)  op(e0, e1) = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2796)  all_54_12 = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (2794), (2796) are inconsistent by
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2797)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2798)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_19 & $i(all_56_19))
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2798) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2799)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_17 & $i(all_56_17)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2799) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2800)  op(e3, e1) = all_56_17
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2801)  op(e3, all_56_17) = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2797) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_28_0,
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (2707), (2789) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2802)  all_28_0 = e1
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_0,
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_17, e1, e3, simplifying with (2789), (2800)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2803)  all_56_17 = all_28_0
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_0,
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_17, e1, e3, simplifying with (2790), (2800)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2804)  all_56_17 = all_18_0
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2803), (2804) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2805)  all_28_0 = all_18_0
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2805) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2806)  all_28_0 = all_18_0
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2802), (2806) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2807)  all_18_0 = e1
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2807) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2808)  all_18_0 = e1
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2804), (2808) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2809)  all_56_17 = e1
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2801), (2809) imply:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2810)  op(e3, e1) = e3
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2771), (2789), (2810), (function-axioms) are
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1783.
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2811)  all_54_12 = e1 | all_54_12 = e0
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1624), (2646), (2811) are inconsistent by
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2067.
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2812)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_19 & $i(all_56_19)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2812) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2813)  op(e2, e1) = all_56_19
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2814)  op(e2, all_56_19) = e2
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2691) gives:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2815)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_22_1 & $i(all_22_0) &
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2815) implies:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2816)  op(e2, e1) = all_22_1
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1624), (2646), (2698), (2707), (2722),
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2775), (2782), (2789), (2790), (2797), (2813),
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2814), (2816), (function-axioms) are inconsistent
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1780.
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2817)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 230.90/42.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2817) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2818)  op(e2, e1) = all_22_1
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1624), (2646), (2698), (2707), (2722),
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2775), (2782), (2789), (2790), (2797), (2813),
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2814), (2818), (function-axioms) are inconsistent
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1780.
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2819)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_23 & $i(all_56_23))
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (257), (1624), (2607), (2646), (2660),
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2725), (2769), (2795), (2797), (2819),
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1779.
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2820)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (2629), (2647), (2788), (2820) are
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1798.
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2821)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2821) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2822)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2822) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2823)  op(e1, e2) = all_56_13
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2824)  op(e1, all_56_13) = e1
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (2759), (2823)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2825)  all_56_13 = e2
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (165), (167),
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (237), (238), (2618), (2625), (2695),
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2698), (2715), (2758), (2823), (2824), (2825),
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1774.
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2826)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2826) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2827)  op(e0, e2) = all_56_15
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2828)  op(e0, all_56_15) = e0
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (2618), (2827)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2829)  all_56_15 = e0
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (217), (218),
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (2646), (2827), (2828), (2829),
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1769.
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2830)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 &
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2719), (2769), (2830), (function-axioms) are
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1767.
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2831)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2831) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2832)   ~ (all_28_1 = e2)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2833)  op(e1, e0) = all_28_1
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2728) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2834)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_50_1 & $i(all_50_0) &
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2834) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2835)   ~ (all_50_0 = e1)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2836)  op(e3, e0) = all_50_1
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2837)  op(all_50_1, e3) = all_50_0
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1617) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2838)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_16_1 & $i(all_16_0) &
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2838) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2839)  op(e3, e0) = all_16_1
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2840)  op(all_16_1, e3) = all_16_0
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2604) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2841)   ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 &
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_18_1 & $i(all_18_0) &
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2841) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2842)   ~ (all_18_0 = e2)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2843)  op(e1, e0) = all_18_1
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2844)  op(all_18_1, e1) = all_18_0
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2845)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2845) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2846)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_9 & $i(all_56_9)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (1622), (1623),
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1624), (2747), (2846), (function-axioms) are
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1784.
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2847)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2847) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2848)  op(e2, all_56_11) = e2
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2694), (2848) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2849)  op(e2, e1) = e2
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_1, e0, e1, simplifying with (2833), (2843)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2850)  all_28_1 = all_18_1
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (2769), (2833) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2851)  all_28_1 = e3
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (2849) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2852)  all_52_9 = e2
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (2836), (2839)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2853)  all_50_1 = all_16_1
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (2754), (2836) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2854)  all_50_1 = e2
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2853), (2854) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2855)  all_16_1 = e2
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2855) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2856)  all_16_1 = e2
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2850), (2851) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2857)  all_18_1 = e3
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (2852) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2858)   ~ (all_52_1 = e2)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2852) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2859)   ~ (all_52_11 = e2)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2859) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2860)   ~ (all_52_11 = e2)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2837), (2854) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2861)  op(e2, e3) = all_50_0
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2844), (2857) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2862)  op(e3, e1) = all_18_0
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2840), (2856) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2863)  op(e2, e3) = all_16_0
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2864)  all_54_4 = e3
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (2864) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2865)  all_52_1 = e3
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2865) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2866)  all_52_1 = e3
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (2866) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2867)  op(e2, e3) = e3
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2868)  all_54_14 = e3
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (2868) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2869)  all_52_11 = e3
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2869) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2870)  all_52_11 = e3
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2870) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2871)   ~ (all_52_3 = e3)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (2870) imply:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2872)  op(e0, e1) = e3
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2873)  all_54_12 = e3
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (2871), (2873) are inconsistent by
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2874)   ~ (all_54_12 = e3)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2875)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2876)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_19 & $i(all_56_19))
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2876) gives:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2877)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_17 & $i(all_56_17)
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2877) implies:
% 230.90/42.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2878)  op(e3, e1) = all_56_17
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2879)  op(e3, all_56_17) = e3
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2875) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_0,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_0, e3, e2, simplifying with (2861), (2863)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2880)  all_50_0 = all_16_0
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_0,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (2861), (2867) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2881)  all_50_0 = e3
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_17, e1, e3, simplifying with (2707), (2878)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2882)  all_56_17 = e1
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_0,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_17, e1, e3, simplifying with (2862), (2878)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2883)  all_56_17 = all_18_0
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2882), (2883) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2884)  all_18_0 = e1
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2880), (2881) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2885)  all_16_0 = e3
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2835), (2862), (2879), (2881), (2883), (2884),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1766.
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2886)  all_54_12 = e1 | all_54_12 = e0
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1624), (2646), (2886) are inconsistent by
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2067.
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2887)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_19 & $i(all_56_19)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2887) implies:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2888)  op(e2, e1) = all_56_19
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2889)  op(e2, all_56_19) = e2
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (167), (216),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (221), (235), (236), (239), (241),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (245), (1622), (2618), (2656), (2657),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2698), (2702), (2707), (2746), (2747), (2753),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2758), (2768), (2842), (2849), (2862), (2867),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2871), (2888), (2889), (function-axioms) are
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1738.
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2890)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_23 & $i(all_56_23))
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (257), (1624), (2607), (2646), (2660),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2725), (2769), (2872), (2875), (2890),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1779.
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2891)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (2629), (2647), (2860), (2891) are
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1798.
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2892)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (1622), (2695), (2858), (2892) are
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1921.
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2893)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2893) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2894)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2894) implies:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2895)  op(e1, e2) = all_56_13
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2896)  op(e1, all_56_13) = e1
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_1, e0, e1, simplifying with (2833), (2843)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2897)  all_28_1 = all_18_1
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (2769), (2833) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2898)  all_28_1 = e3
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (2759), (2895)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2899)  all_56_13 = e2
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2897), (2898) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2900)  all_18_1 = e3
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (165), (167),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (237), (238), (2618), (2625), (2695),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2698), (2715), (2758), (2895), (2896), (2899),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1774.
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2901)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2901) implies:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2902)  op(e0, e2) = all_56_15
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2903)  op(e0, all_56_15) = e0
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (2618), (2902)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2904)  all_56_15 = e0
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_1, e0, e1, simplifying with (2833), (2843)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2905)  all_28_1 = all_18_1
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (2769), (2833) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2906)  all_28_1 = e3
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2905), (2906) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2907)  all_18_1 = e3
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (217), (218),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (2646), (2902), (2903), (2904),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1769.
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2908)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 &
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2719), (2769), (2908), (function-axioms) are
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1767.
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2909)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2909) implies:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2910)   ~ (all_16_1 = e1)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2911)  op(e3, e0) = all_16_1
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2604) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2912)   ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 &
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_18_1 & $i(all_18_0) &
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2912) implies:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2913)   ~ (all_18_0 = e2)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2914)  op(e1, e0) = all_18_1
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2915)  op(all_18_1, e1) = all_18_0
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2916)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2916) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2917)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_9 & $i(all_56_9)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (1622), (1623),
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1624), (2747), (2917), (function-axioms) are
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1784.
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2918)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2918) implies:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2919)  op(e2, all_56_11) = e2
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2694), (2919) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2920)  op(e2, e1) = e2
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_1, e0, e1, simplifying with (2833), (2914)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2921)  all_28_1 = all_18_1
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (2769), (2833) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2922)  all_28_1 = e3
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (2920) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2923)  all_52_9 = e2
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (2836), (2911)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2924)  all_50_1 = all_16_1
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (2754), (2836) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2925)  all_50_1 = e2
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2924), (2925) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2926)  all_16_1 = e2
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2926) implies:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2927)  all_16_1 = e2
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2921), (2922) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2928)  all_18_1 = e3
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (2923) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2929)   ~ (all_52_1 = e2)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2923) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2930)   ~ (all_52_11 = e2)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2930) implies:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2931)   ~ (all_52_11 = e2)
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2837), (2925) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2932)  op(e2, e3) = all_50_0
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2915), (2928) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2933)  op(e3, e1) = all_18_0
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2934)  all_54_4 = e3
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (2934) imply:
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2935)  all_52_1 = e3
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2935) implies:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2936)  all_52_1 = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (2936) imply:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2937)  op(e2, e3) = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2938)  all_54_14 = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (2938) imply:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2939)  all_52_11 = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2939) implies:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2940)  all_52_11 = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2940) imply:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2941)   ~ (all_52_3 = e3)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (2940) imply:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2942)  op(e0, e1) = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2943)  all_54_12 = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (2941), (2943) are inconsistent by
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2944)   ~ (all_54_12 = e3)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2945)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2946)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_19 & $i(all_56_19))
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2946) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2947)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_17 & $i(all_56_17)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2947) implies:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2948)  op(e3, e1) = all_56_17
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2949)  op(e3, all_56_17) = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2950)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2950) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2951)  all_58_12 = e2 & op(e0, e3) = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2951) implies:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2952)  all_58_12 = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2953)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (167), (239),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (245), (1622), (2937), (2941), (2952),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2953), (function-axioms) are inconsistent by
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1754.
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2954)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2954) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2955)  all_58_6 = e2 & op(e1, e3) = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2955) implies:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2956)  op(e1, e3) = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2702), (2956), (function-axioms) are
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_0,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (2932), (2937) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2957)  all_50_0 = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_17, e1, e3, simplifying with (2707), (2948)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2958)  all_56_17 = e1
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_0,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_17, e1, e3, simplifying with (2933), (2948)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2959)  all_56_17 = all_18_0
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2958), (2959) imply:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2960)  all_18_0 = e1
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2835), (2933), (2949), (2957), (2959), (2960),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1766.
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2961)  all_58_13 = e2 & op(e0, e2) = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2961) implies:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2962)  all_58_13 = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2963)  op(e0, e2) = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (235), (236), (2746),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2747), (2758), (2962), (2963), (function-axioms)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1748.
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2964)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (216), (219),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (2618), (2656), (2657), (2753), (2768),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2941), (2964), (function-axioms) are inconsistent
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1739.
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2965)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_19 & $i(all_56_19)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2965) implies:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2966)  op(e2, e1) = all_56_19
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2967)  op(e2, all_56_19) = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (167), (216),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (221), (235), (236), (239), (241),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (245), (1622), (2618), (2656), (2657),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2698), (2702), (2707), (2746), (2747), (2753),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2758), (2768), (2913), (2920), (2933), (2937),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2941), (2966), (2967), (function-axioms) are
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1738.
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2968)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_23 & $i(all_56_23))
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (257), (1624), (2607), (2646), (2660),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2725), (2769), (2942), (2945), (2968),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1779.
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2969)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (2629), (2647), (2931), (2969) are
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1798.
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2970)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (1622), (2695), (2929), (2970) are
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1921.
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2971)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2971) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2972)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2972) implies:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2973)  op(e1, e2) = all_56_13
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2974)  op(e1, all_56_13) = e1
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_1, e0, e1, simplifying with (2833), (2914)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2975)  all_28_1 = all_18_1
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (2769), (2833) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2976)  all_28_1 = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (2759), (2973)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2977)  all_56_13 = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (2836), (2911)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2978)  all_50_1 = all_16_1
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (2754), (2836) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2979)  all_50_1 = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2978), (2979) imply:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2980)  all_16_1 = e2
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2975), (2976) imply:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2981)  all_18_1 = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (165), (167),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (237), (238), (2618), (2625), (2695),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2698), (2715), (2758), (2973), (2974), (2977),
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1774.
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2982)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2982) implies:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2983)  op(e0, e2) = all_56_15
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2984)  op(e0, all_56_15) = e0
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (2618), (2983)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2985)  all_56_15 = e0
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_1, e0, e1, simplifying with (2833), (2914)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2986)  all_28_1 = all_18_1
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (2769), (2833) gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2987)  all_28_1 = e3
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (2836), (2911)
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2988)  all_50_1 = all_16_1
% 230.90/42.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (2754), (2836) gives:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2989)  all_50_1 = e2
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2988), (2989) imply:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2990)  all_16_1 = e2
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2986), (2987) imply:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2991)  all_18_1 = e3
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (217), (218),
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (2646), (2983), (2984), (2985),
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1769.
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2992)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 &
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2719), (2769), (2992), (function-axioms) are
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1767.
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2993)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2993) implies:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2994)   ~ (all_50_1 = e2)
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2995)  op(e3, e0) = all_50_1
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2754), (2994), (2995), (function-axioms) are
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1884.
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2996)  all_58_13 = e2 & op(e0, e2) = e2
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2996) implies:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2997)  op(e0, e2) = e2
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2618), (2997), (function-axioms) are
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2998)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2998) gives:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2999)  all_58_4 = e3 & op(e3, e1) = e3
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2999) implies:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3000)  op(e3, e1) = e3
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2707), (3000), (function-axioms) are
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1823.
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3001)  all_58_9 = e3 & op(e3, e0) = e3
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3001) implies:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3002)  op(e3, e0) = e3
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2741), (3002), (function-axioms) are
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | |   (3003)  all_58_9 = e1 & op(e3, e0) = e1
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2648), (3003), (function-axioms) are
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | |   (3004)  all_58_12 = e1 & op(e0, e3) = e1
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2646), (3004), (function-axioms) are
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | Case 2:
% 230.90/42.81  | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | |   (3005)  all_54_15 = e0
% 230.90/42.81  | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | | REF_CLOSE: (299), (2634), (3005) are inconsistent by
% 230.90/42.81  | | | | | | | | | | | | | | | |            sub-proof #1737.
% 230.90/42.81  | | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | | 
% 230.90/42.81  | | | | | | | | End of split
% 230.90/42.81  | | | | | | | | 
% 230.90/42.81  | | | | | | | End of split
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | Case 2:
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | |   (3006)  all_14_2 = e0
% 230.90/42.81  | | | | | | |   (3007)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 230.90/42.81  | | | | | | |             op(e2, e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)) |
% 230.90/42.81  | | | | | | |           ( ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 230.90/42.81  | | | | | | |             $i(all_14_1))
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | COMBINE_EQS: (344), (3006) imply:
% 230.90/42.81  | | | | | | |   (3008)  all_8_2 = e0
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | SIMP: (3008) implies:
% 230.90/42.81  | | | | | | |   (3009)  all_8_2 = e0
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | COMBINE_EQS: (311), (3009) imply:
% 230.90/42.81  | | | | | | |   (3010)  all_48_2 = e0
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | COMBINE_EQS: (353), (3009) imply:
% 230.90/42.81  | | | | | | |   (3011)  all_56_11 = e0
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | REDUCE: (366), (3009) imply:
% 230.90/42.81  | | | | | | |   (3012)   ~ (all_52_1 = e0)
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | REDUCE: (369), (3009) imply:
% 230.90/42.81  | | | | | | |   (3013)   ~ (all_52_4 = e0)
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | REDUCE: (371), (3009) imply:
% 230.90/42.81  | | | | | | |   (3014)   ~ (all_52_6 = e0)
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | REDUCE: (373), (3009) imply:
% 230.90/42.81  | | | | | | |   (3015)   ~ (all_52_7 = e0)
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | REDUCE: (375), (3009) imply:
% 230.90/42.81  | | | | | | |   (3016)   ~ (all_52_9 = e0)
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | REDUCE: (377), (3009) imply:
% 230.90/42.81  | | | | | | |   (3017)   ~ (all_52_13 = e0)
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | REDUCE: (392), (3009) imply:
% 230.90/42.81  | | | | | | |   (3018)   ~ (e3 = e0)
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | BETA: splitting (235) gives:
% 230.90/42.81  | | | | | | | 
% 230.90/42.81  | | | | | | | Case 1:
% 230.90/42.81  | | | | | | | | 
% 230.90/42.81  | | | | | | | |   (3019)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 230.90/42.81  | | | | | | | |             op(e2, e2) = e0)
% 230.90/42.81  | | | | | | | | 
% 230.90/42.81  | | | | | | | | BETA: splitting (3019) gives:
% 230.90/42.81  | | | | | | | | 
% 230.90/42.81  | | | | | | | | Case 1:
% 230.90/42.81  | | | | | | | | | 
% 230.90/42.81  | | | | | | | | |   (3020)  all_58_1 = e0 & op(e3, e2) = e0
% 230.90/42.81  | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | REF_CLOSE: (170), (3013), (3020), (function-axioms) are
% 230.90/42.81  | | | | | | | | |            inconsistent by sub-proof #1968.
% 230.90/42.81  | | | | | | | | | 
% 230.90/42.81  | | | | | | | | Case 2:
% 230.90/42.81  | | | | | | | | | 
% 230.90/42.81  | | | | | | | | |   (3021)  all_58_3 = e0 & op(e2, e2) = e0
% 230.90/42.81  | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | ALPHA: (3021) implies:
% 230.90/42.81  | | | | | | | | |   (3022)  all_58_3 = e0
% 230.90/42.81  | | | | | | | | |   (3023)  op(e2, e2) = e0
% 230.90/42.81  | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | BETA: splitting (55) gives:
% 230.90/42.81  | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | Case 1:
% 230.90/42.81  | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | |   (3024)   ~ (all_16_2 = e0)
% 230.90/42.81  | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | REDUCE: (342), (3024) imply:
% 230.90/42.81  | | | | | | | | | |   (3025)   ~ (all_10_2 = e0)
% 230.90/42.81  | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | BETA: splitting (58) gives:
% 230.90/42.81  | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | Case 1:
% 230.90/42.81  | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | |   (3026)   ~ (all_18_2 = e0)
% 230.90/42.81  | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | REDUCE: (339), (3026) imply:
% 230.90/42.81  | | | | | | | | | | |   (3027)   ~ (all_6_2 = e0)
% 230.90/42.81  | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | BETA: splitting (61) gives:
% 230.90/42.81  | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | Case 1:
% 230.90/42.81  | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | |   (3028)   ~ (all_20_2 = e1)
% 230.90/42.81  | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | REDUCE: (341), (3028) imply:
% 230.90/42.81  | | | | | | | | | | | |   (3029)   ~ (all_4_2 = e1)
% 230.90/42.81  | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | BETA: splitting (189) gives:
% 230.90/42.81  | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | Case 1:
% 230.90/42.81  | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | |   (3030)  all_54_15 = e3
% 230.90/42.81  | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | COMBINE_EQS: (299), (3030) imply:
% 230.90/42.81  | | | | | | | | | | | | |   (3031)  all_4_2 = e3
% 230.90/42.81  | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | REDUCE: (395), (3031) imply:
% 230.90/42.81  | | | | | | | | | | | | |   (3032)  $false
% 230.90/42.81  | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | | CLOSE: (3032) is inconsistent.
% 230.90/42.81  | | | | | | | | | | | | | 
% 230.90/42.81  | | | | | | | | | | | | Case 2:
% 230.90/42.81  | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | |   (3033)   ~ (all_54_15 = e3)
% 231.25/42.81  | | | | | | | | | | | | |   (3034)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 231.25/42.81  | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | BETA: splitting (3034) gives:
% 231.25/42.81  | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | Case 1:
% 231.25/42.81  | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | |   (3035)  all_54_15 = e2
% 231.25/42.81  | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | COMBINE_EQS: (299), (3035) imply:
% 231.25/42.81  | | | | | | | | | | | | | |   (3036)  all_4_2 = e2
% 231.25/42.81  | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | REDUCE: (390), (3036) imply:
% 231.25/42.81  | | | | | | | | | | | | | |   (3037)  $false
% 231.25/42.81  | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | CLOSE: (3037) is inconsistent.
% 231.25/42.81  | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | Case 2:
% 231.25/42.81  | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | |   (3038)  all_54_15 = e1 | all_54_15 = e0
% 231.25/42.81  | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | BETA: splitting (3038) gives:
% 231.25/42.81  | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | Case 1:
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | |   (3039)  all_54_15 = e1
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | COMBINE_EQS: (299), (3039) imply:
% 231.25/42.81  | | | | | | | | | | | | | | |   (3040)  all_4_2 = e1
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | REDUCE: (3029), (3040) imply:
% 231.25/42.81  | | | | | | | | | | | | | | |   (3041)  $false
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | CLOSE: (3041) is inconsistent.
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | Case 2:
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | |   (3042)  all_54_15 = e0
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | COMBINE_EQS: (299), (3042) imply:
% 231.25/42.81  | | | | | | | | | | | | | | |   (3043)  all_4_2 = e0
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | COMBINE_EQS: (254), (3043) imply:
% 231.25/42.81  | | | | | | | | | | | | | | |   (3044)  all_56_31 = e0
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | REDUCE: (368), (3043) imply:
% 231.25/42.81  | | | | | | | | | | | | | | |   (3045)   ~ (all_52_3 = e0)
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | REDUCE: (387), (3043) imply:
% 231.25/42.81  | | | | | | | | | | | | | | |   (3046)   ~ (all_52_12 = e0)
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | REDUCE: (3029), (3043) imply:
% 231.25/42.81  | | | | | | | | | | | | | | |   (3047)   ~ (e1 = e0)
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 231.25/42.81  | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | Case 1:
% 231.25/42.81  | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | |   (3048)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 231.25/42.81  | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 231.25/42.81  | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | BETA: splitting (3048) gives:
% 231.25/42.81  | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.81  | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | |   (3049)  all_58_0 = e0 & op(e3, e3) = e0
% 231.25/42.81  | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3025), (3049), (function-axioms) are
% 231.25/42.81  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1736.
% 231.25/42.81  | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.81  | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | |   (3050)  all_58_2 = e0 & op(e2, e3) = e0
% 231.25/42.81  | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (3012), (3050), (function-axioms) are
% 231.25/42.81  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1985.
% 231.25/42.81  | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | End of split
% 231.25/42.81  | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | Case 2:
% 231.25/42.81  | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | |   (3051)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 231.25/42.81  | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 231.25/42.81  | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | BETA: splitting (3051) gives:
% 231.25/42.81  | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.81  | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | |   (3052)  all_58_6 = e0 & op(e1, e3) = e0
% 231.25/42.81  | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | ALPHA: (3052) implies:
% 231.25/42.81  | | | | | | | | | | | | | | | | |   (3053)  op(e1, e3) = e0
% 231.25/42.81  | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 231.25/42.81  | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.81  | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | |   (3054)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 231.25/42.81  | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 231.25/42.81  | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | BETA: splitting (3054) gives:
% 231.25/42.81  | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.81  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | |   (3055)  all_58_0 = e0 & op(e3, e3) = e0
% 231.25/42.81  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3025), (3055), (function-axioms) are
% 231.25/42.81  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1736.
% 231.25/42.81  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.81  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | |   (3056)  all_58_1 = e0 & op(e3, e2) = e0
% 231.25/42.81  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (3013), (3056), (function-axioms) are
% 231.25/42.81  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 231.25/42.81  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.81  | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.81  | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | |   (3057)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 231.25/42.81  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 231.25/42.81  | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | BETA: splitting (3057) gives:
% 231.25/42.81  | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.81  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | |   (3058)  all_58_4 = e0 & op(e3, e1) = e0
% 231.25/42.81  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.81  | | | | | | | | | | | | | | | | | | | ALPHA: (3058) implies:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | |   (3059)  op(e3, e1) = e0
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 231.25/42.82  | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (3053) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | |   (3060)  all_52_2 = e0
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 231.25/42.82  | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (3059) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | |   (3061)  all_52_8 = e0
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | REDUCE: (144), (3060) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | |   (3062)   ~ (all_52_3 = e0)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | REDUCE: (141), (3060) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | |   (3063)   ~ (all_52_14 = e0)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | SIMP: (3063) implies:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | |   (3064)   ~ (all_52_14 = e0)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | REDUCE: (363), (3061) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | |   (3065)   ~ (all_10_2 = e0)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | REDUCE: (380), (3061) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | |   (3066)   ~ (all_6_2 = e0)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | |   (3067)   ~ (all_24_2 = e2)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (3067) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | |   (3068)   ~ (all_10_2 = e2)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | |   (3069)  all_54_0 = e3
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (3069) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | |   (3070)  all_10_2 = e3
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (3070) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | |   (3071)  all_56_1 = e3
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (355), (3070) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | |   (3072)   ~ (all_52_1 = e3)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (3070) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | |   (3073)   ~ (all_52_3 = e3)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | |   (3074)   ~ (all_36_2 = e2)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (328), (3074) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | |   (3075)   ~ (all_6_2 = e2)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |   (3076)  all_54_10 = e3
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (3076) are inconsistent by sub-proof
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |            #2313.
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |   (3077)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3077) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |   (3078)  all_54_10 = e2
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (3075), (3078) are inconsistent by
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |   (3079)  all_54_10 = e1 | all_54_10 = e0
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3079) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (3080)  all_54_10 = e1
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (3080) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (3081)  all_6_2 = e1
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3081) implies:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (3082)  all_6_2 = e1
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (3082) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (3083)  all_56_21 = e1
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (3082) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (3084)   ~ (all_52_9 = e1)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (3082) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (3085)   ~ (all_52_14 = e1)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3086)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (159), (167), (3045), (3059), (3071),
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3072), (3073), (3086), (function-axioms) are
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1734.
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3087)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3087) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3088)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3044), (3083), (3084), (3088),
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1733.
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3089)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (3017), (3064), (3085), (3089),
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1903.
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (3090)  all_54_10 = e0
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (3027), (3090) are inconsistent by
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | |   (3091)  all_36_2 = e2
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (3091) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | |   (3092)  all_6_2 = e2
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (3092) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | |   (3093)  all_56_21 = e2
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (3092) imply:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | |   (3094)   ~ (all_52_9 = e2)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |   (3095)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (159), (167), (3045), (3059), (3071),
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |            (3072), (3073), (3095), (function-axioms) are
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1734.
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |   (3096)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3096) gives:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |   (3097)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.25/42.82  | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3044), (3093), (3094), (3097),
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |            #1732.
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |   (3098)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (3017), (3044), (3064), (3098),
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |            #2321.
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |   (3099)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (3025), (3068), (3099) are
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | |   (3100)  all_24_2 = e2
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (3100) imply:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | |   (3101)  all_10_2 = e2
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (3101) imply:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | |   (3102)  all_56_1 = e2
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | REDUCE: (355), (3101) imply:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | |   (3103)   ~ (all_52_1 = e2)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |   (3104)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3104) gives:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |   (3105)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3105) gives:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3106)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |           e3
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3106) implies:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3107)   ~ (all_56_1 = e2)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3102), (3107) imply:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3108)  $false
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3108) is inconsistent.
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3109)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3109) gives:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |   (3110)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |           e2
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3110) implies:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |   (3111)  op(e2, e3) = e2
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (3103), (3111), (function-axioms) are
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |   (3112)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3112) implies:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |   (3113)  op(e3, e1) = e3
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3059), (3113), (function-axioms) are
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2118.
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |   (3114)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3114) gives:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3115)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3115) implies:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3116)  op(e3, e1) = e1
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e1, e1,
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (3059), (3116) gives:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3117)  e1 = e0
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (3117) imply:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3118)  $false
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3118) is inconsistent.
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3119)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3044), (3045), (3119), (function-axioms)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2308.
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |   (3120)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3120) gives:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |   (3121)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3121) gives:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3122)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3122) implies:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3123)   ~ (all_56_21 = e1)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3124)  op(e2, e1) = e2
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (266), (3123) imply:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3125)   ~ (all_6_2 = e1)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |   (3126)  all_54_10 = e3
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (3126) are inconsistent by sub-proof
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |            #2313.
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |   (3127)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (297), (381), (3027), (3124), (3125),
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |            (3127), (function-axioms) are inconsistent by
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2198.
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |   (3128)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3044), (3102), (3128) are inconsistent by
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1731.
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.83  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |   (3129)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (3017), (3044), (3064), (3129),
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | |            #2321.
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |   (3130)  all_58_9 = e0 & op(e3, e0) = e0
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | ALPHA: (3130) implies:
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |   (3131)  op(e3, e0) = e0
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3046), (3131), (function-axioms) are
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2258.
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | |   (3132)  all_58_12 = e0 & op(e0, e3) = e0
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | ALPHA: (3132) implies:
% 231.25/42.84  | | | | | | | | | | | | | | | | |   (3133)  op(e0, e3) = e0
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3045), (3133), (function-axioms) are
% 231.25/42.84  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | Case 2:
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | |   (3134)  all_20_2 = e1
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | COMBINE_EQS: (341), (3134) imply:
% 231.25/42.84  | | | | | | | | | | | |   (3135)  all_4_2 = e1
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | SIMP: (3135) implies:
% 231.25/42.84  | | | | | | | | | | | |   (3136)  all_4_2 = e1
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | COMBINE_EQS: (254), (3136) imply:
% 231.25/42.84  | | | | | | | | | | | |   (3137)  all_56_31 = e1
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | REDUCE: (368), (3136) imply:
% 231.25/42.84  | | | | | | | | | | | |   (3138)   ~ (all_52_3 = e1)
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | REDUCE: (379), (3136) imply:
% 231.25/42.84  | | | | | | | | | | | |   (3139)   ~ (all_52_7 = e1)
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | REDUCE: (386), (3136) imply:
% 231.25/42.84  | | | | | | | | | | | |   (3140)   ~ (all_52_11 = e1)
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | REDUCE: (387), (3136) imply:
% 231.25/42.84  | | | | | | | | | | | |   (3141)   ~ (all_52_12 = e1)
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | REDUCE: (388), (3136) imply:
% 231.25/42.84  | | | | | | | | | | | |   (3142)   ~ (all_52_13 = e1)
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | REDUCE: (389), (3136) imply:
% 231.25/42.84  | | | | | | | | | | | |   (3143)   ~ (all_52_14 = e1)
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | REDUCE: (395), (3136) imply:
% 231.25/42.84  | | | | | | | | | | | |   (3144)   ~ (e3 = e1)
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | BETA: splitting (217) gives:
% 231.25/42.84  | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | Case 1:
% 231.25/42.84  | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | |   (3145)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 231.25/42.84  | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 231.25/42.84  | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | BETA: splitting (3145) gives:
% 231.25/42.84  | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | Case 1:
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | |   (3146)  all_58_12 = e1 & op(e0, e3) = e1
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | REF_CLOSE: (159), (3138), (3146), (function-axioms) are
% 231.25/42.84  | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | Case 2:
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | |   (3147)  all_58_13 = e1 & op(e0, e2) = e1
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | REF_CLOSE: (158), (3139), (3147), (function-axioms) are
% 231.25/42.84  | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | Case 2:
% 231.25/42.84  | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | |   (3148)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 231.25/42.84  | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 231.25/42.84  | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | BETA: splitting (3148) gives:
% 231.25/42.84  | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | Case 1:
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | |   (3149)  all_58_14 = e1 & op(e0, e1) = e1
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | ALPHA: (3149) implies:
% 231.25/42.84  | | | | | | | | | | | | | |   (3150)  op(e0, e1) = e1
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | REF_CLOSE: (157), (3140), (3150), (function-axioms) are
% 231.25/42.84  | | | | | | | | | | | | | |            inconsistent by sub-proof #2272.
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | Case 2:
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | |   (3151)  all_58_15 = e1 & op(e0, e0) = e1
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | ALPHA: (3151) implies:
% 231.25/42.84  | | | | | | | | | | | | | |   (3152)  all_58_15 = e1
% 231.25/42.84  | | | | | | | | | | | | | |   (3153)  op(e0, e0) = e1
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 231.25/42.84  | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | Case 1:
% 231.25/42.84  | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | |   (3154)   ~ (all_24_2 = e2)
% 231.25/42.84  | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | REDUCE: (301), (3154) imply:
% 231.25/42.84  | | | | | | | | | | | | | | |   (3155)   ~ (all_10_2 = e2)
% 231.25/42.84  | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 231.25/42.84  | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | Case 1:
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | |   (3156)  all_54_0 = e3
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (3156) imply:
% 231.25/42.84  | | | | | | | | | | | | | | | |   (3157)  all_10_2 = e3
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | SIMP: (3157) implies:
% 231.25/42.84  | | | | | | | | | | | | | | | |   (3158)  all_10_2 = e3
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (3158) imply:
% 231.25/42.84  | | | | | | | | | | | | | | | |   (3159)  all_56_1 = e3
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | REDUCE: (355), (3158) imply:
% 231.25/42.84  | | | | | | | | | | | | | | | |   (3160)   ~ (all_52_1 = e3)
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | REDUCE: (357), (3158) imply:
% 231.25/42.84  | | | | | | | | | | | | | | | |   (3161)   ~ (all_52_2 = e3)
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | REDUCE: (359), (3158) imply:
% 231.25/42.84  | | | | | | | | | | | | | | | |   (3162)   ~ (all_52_3 = e3)
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | |   (3163)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.25/42.84  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.84  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.25/42.84  | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.25/42.84  | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.25/42.84  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.25/42.84  | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.25/42.84  | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.25/42.84  | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.25/42.84  | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 231.25/42.84  | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 231.25/42.84  | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.25/42.84  | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | BETA: splitting (3163) gives:
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | |   (3164)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             = e3)
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (3159), (3160), (3161), (3164),
% 231.25/42.84  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.84  | | | | | | | | | | | | | | | | | |            #2299.
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | |   (3165)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             = e0)
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3159), (3162), (3165), (function-axioms)
% 231.25/42.84  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2270.
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | |   (3166)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.84  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.25/42.84  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.25/42.84  | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.25/42.84  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.25/42.84  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.25/42.84  | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.25/42.84  | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.25/42.84  | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 231.25/42.84  | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 231.25/42.84  | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 231.25/42.84  | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 231.25/42.84  | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | BETA: splitting (3166) gives:
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | |   (3167)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             = e2)
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | BETA: splitting (3167) gives:
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |   (3168)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |             e2) = e2
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | ALPHA: (3168) implies:
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |   (3169)   ~ (all_56_31 = e1)
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | REDUCE: (3137), (3169) imply:
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |   (3170)  $false
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | CLOSE: (3170) is inconsistent.
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |   (3171)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (194), (266), (297), (381), (391), (3011),
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |            (3027), (3171), (function-axioms) are inconsistent
% 231.25/42.84  | | | | | | | | | | | | | | | | | | |            by sub-proof #1728.
% 231.25/42.84  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | |   (3172)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 231.25/42.84  | | | | | | | | | | | | | | | | | |             = e0)
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (3017), (3137), (3143), (3172),
% 231.25/42.84  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.84  | | | | | | | | | | | | | | | | | |            #1727.
% 231.25/42.84  | | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | | End of split
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.84  | | | | | | | | | | | | | | | Case 2:
% 231.25/42.84  | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | |   (3173)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 231.25/42.85  | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (3025), (3155), (3173) are
% 231.25/42.85  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 231.25/42.85  | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | End of split
% 231.25/42.85  | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | Case 2:
% 231.25/42.85  | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | |   (3174)  all_24_2 = e2
% 231.25/42.85  | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | COMBINE_EQS: (301), (3174) imply:
% 231.25/42.85  | | | | | | | | | | | | | | |   (3175)  all_10_2 = e2
% 231.25/42.85  | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | SIMP: (3175) implies:
% 231.25/42.85  | | | | | | | | | | | | | | |   (3176)  all_10_2 = e2
% 231.25/42.85  | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | COMBINE_EQS: (290), (3176) imply:
% 231.25/42.85  | | | | | | | | | | | | | | |   (3177)  all_56_1 = e2
% 231.25/42.85  | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | REDUCE: (359), (3176) imply:
% 231.25/42.85  | | | | | | | | | | | | | | |   (3178)   ~ (all_52_3 = e2)
% 231.25/42.85  | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | REDUCE: (365), (3176) imply:
% 231.25/42.85  | | | | | | | | | | | | | | |   (3179)   ~ (all_52_12 = e2)
% 231.25/42.85  | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | REDUCE: (45), (3176) imply:
% 231.25/42.85  | | | | | | | | | | | | | | |   (3180)  op(e3, e3) = e2
% 231.25/42.85  | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | |   (3181)   ~ (all_36_2 = e2)
% 231.25/42.85  | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | REDUCE: (328), (3181) imply:
% 231.25/42.85  | | | | | | | | | | | | | | | |   (3182)   ~ (all_6_2 = e2)
% 231.25/42.85  | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | |   (3183)  all_54_10 = e3
% 231.25/42.85  | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (3183) are inconsistent by sub-proof
% 231.25/42.85  | | | | | | | | | | | | | | | | |            #2313.
% 231.25/42.85  | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.85  | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | |   (3184)   ~ (all_54_10 = e3)
% 231.25/42.85  | | | | | | | | | | | | | | | | |   (3185)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 231.25/42.85  | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | BETA: splitting (3185) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | |   (3186)  all_54_10 = e2
% 231.25/42.85  | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (3182), (3186) are inconsistent by
% 231.25/42.85  | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 231.25/42.85  | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | |   (3187)   ~ (all_54_10 = e2)
% 231.25/42.85  | | | | | | | | | | | | | | | | | |   (3188)  all_54_10 = e1 | all_54_10 = e0
% 231.25/42.85  | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | BETA: splitting (3188) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | |   (3189)  all_54_10 = e1
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (3189) imply:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | |   (3190)  all_6_2 = e1
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | SIMP: (3190) implies:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | |   (3191)  all_6_2 = e1
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | REDUCE: (380), (3191) imply:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | |   (3192)   ~ (all_52_8 = e1)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | REDUCE: (381), (3191) imply:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | |   (3193)   ~ (all_52_9 = e1)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | REDUCE: (3182), (3191) imply:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | |   (3194)   ~ (e2 = e1)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (3191) imply:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | |   (3195)  op(e1, e1) = e1
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | |   (3196)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3196) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | |   (3197)  all_58_1 = e1 & op(e3, e2) = e1
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3197) implies:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | |   (3198)  op(e3, e2) = e1
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |   (3199)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3199) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |   (3200)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (3137), (3198), (3200),
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |            #1725.
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |   (3201)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3201) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |   (3202)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3202) implies:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |   (3203)  op(e3, e1) = e1
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3192), (3203), (function-axioms) are
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |   (3204)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3204) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3205)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3205) implies:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3206)   ~ (all_56_11 = e0)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3011), (3206) imply:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3207)  $false
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3207) is inconsistent.
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3208)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e0
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3208) implies:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3209)  op(e0, e3) = e0
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3210)  op(e3, e0) = e0
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (3209) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3211)  all_52_3 = e0
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (168), (3210) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3212)  all_52_12 = e0
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (3211) imply:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3213)   ~ (all_52_2 = e0)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (3212) imply:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3214)   ~ (all_52_14 = e0)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3214) implies:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3215)   ~ (all_52_14 = e0)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3141), (3212) imply:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (3216)   ~ (e1 = e0)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (3014), (3195),
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |            (3213), (3215), (function-axioms) are inconsistent
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2020.
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |   (3217)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3217) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |   (3218)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3218) gives:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |   (3219)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3219) implies:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |   (3220)   ~ (all_56_31 = e1)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3137), (3220) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |   (3221)  $false
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3221) is inconsistent.
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |   (3222)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3011), (3193), (3222), (function-axioms)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1724.
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |   (3223)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (3017), (3137), (3143), (3223),
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |            #1727.
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |   (3224)  all_58_3 = e1 & op(e2, e2) = e1
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3022), (3224) are inconsistent by sub-proof
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |            #1752.
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3225)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3225) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |   (3226)  all_58_7 = e1 & op(e1, e2) = e1
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3226) implies:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |   (3227)  all_58_7 = e1
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |   (3228)  op(e1, e2) = e1
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (168), (169),
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |            (235), (237), (238), (242), (3023), (3141),
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |            (3180), (3192), (3227), (3228), (function-axioms)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1712.
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |   (3229)  all_58_13 = e1 & op(e0, e2) = e1
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3139), (3229), (function-axioms) are
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | |   (3230)  all_54_10 = e0
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (3027), (3230) are inconsistent by
% 231.25/42.86  | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.86  | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | End of split
% 231.25/42.86  | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | End of split
% 231.25/42.86  | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | Case 2:
% 231.25/42.86  | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | |   (3231)  all_36_2 = e2
% 231.25/42.86  | | | | | | | | | | | | | | | |   (3232)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 231.25/42.86  | | | | | | | | | | | | | | | |             & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 231.25/42.86  | | | | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 231.25/42.86  | | | | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 231.25/42.86  | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (3231) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | |   (3233)  all_6_2 = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (3233) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | |   (3234)  all_40_2 = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (3233) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | |   (3235)  all_56_21 = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | REDUCE: (367), (3233) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | |   (3236)   ~ (all_52_2 = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | REDUCE: (391), (3233) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | |   (3237)   ~ (e3 = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | REDUCE: (39), (3233) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | |   (3238)  op(e1, e1) = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.86  | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | |   (3239)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 231.25/42.86  | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | BETA: splitting (3239) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | |   (3240)  all_58_9 = e2 & op(e3, e0) = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3179), (3240), (function-axioms) are
% 231.25/42.86  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2318.
% 231.25/42.86  | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | |   (3241)  all_58_10 = e2 & op(e2, e0) = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | ALPHA: (3241) implies:
% 231.25/42.86  | | | | | | | | | | | | | | | | | |   (3242)  op(e2, e0) = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | |   (3243)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 231.25/42.86  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | BETA: splitting (3243) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3244)  all_58_12 = e2 & op(e0, e3) = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3178), (3244), (function-axioms) are
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2315.
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3245)  all_58_13 = e2 & op(e0, e2) = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | ALPHA: (3245) implies:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3246)  op(e0, e2) = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (3246) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3247)  all_52_7 = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (3242) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3248)  all_52_13 = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (3248) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3249)   ~ (all_52_1 = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (3247) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3250)   ~ (all_52_4 = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (3247) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3251)   ~ (all_52_6 = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (3248) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3252)   ~ (all_52_9 = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (3248) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3253)   ~ (all_52_14 = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | SIMP: (3253) implies:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | |   (3254)   ~ (all_52_14 = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |   (3255)   ~ (all_48_2 = e0)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | REDUCE: (3010), (3255) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |   (3256)  $false
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | CLOSE: (3256) is inconsistent.
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |   (3257)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |             $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | |             = all_48_1 & $i(all_48_1))
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3007) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | |   (3258)   ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_14_1 & $i(all_14_0) &
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3258) implies:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | |   (3259)   ~ (all_14_0 = e3)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | |   (3260)  op(e2, e0) = all_14_1
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | |   (3261)  op(all_14_1, e2) = all_14_0
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_14_1,
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (3242), (3260) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | |   (3262)  all_14_1 = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3261), (3262) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | |   (3263)  op(e2, e2) = all_14_0
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3257) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |   (3264)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_48_1 & $i(all_48_0) &
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3264) implies:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |   (3265)   ~ (all_48_0 = e1)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |   (3266)  op(e2, e0) = all_48_1
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |   (3267)  op(all_48_1, e2) = all_48_0
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_1,
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (3242), (3266) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |   (3268)  all_48_1 = e2
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (3023), (3263) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |   (3269)  all_14_0 = e0
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3267), (3268) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |   (3270)  op(e2, e2) = all_48_0
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_48_0,
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (3023), (3270) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |   (3271)  all_48_0 = e0
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3265), (3271) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | |   (3272)   ~ (e1 = e0)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |   (3273)   ~ (all_40_2 = e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3234), (3273) imply:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |   (3274)  $false
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3274) is inconsistent.
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |   (3275)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | |             = all_40_1 & $i(all_40_1))
% 231.25/42.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (112), (120), (126),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (133), (134), (136), (141), (143), (144), (148),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (149), (158), (159), (160), (162), (163), (165),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (192), (193), (195),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (196), (200), (201), (203), (213), (214), (219),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (226), (234), (235), (236),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (239), (240), (241), (242), (244),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (245), (246), (257), (258), (267), (268), (279),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (280), (282), (3011), (3012), (3013), (3014),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (3022), (3023), (3138), (3139), (3141), (3143),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (3152), (3153), (3177), (3178), (3179), (3180),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (3232), (3235), (3236), (3238), (3242), (3246),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (3249), (3250), (3251), (3252), (3254), (3275),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | |            #1681.
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3276)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3276) implies:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3277)   ~ (all_48_1 = e3)
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3278)  op(e2, e0) = all_48_1
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_1,
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (3242), (3278) gives:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3279)  all_48_1 = e2
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (3023), (3263) gives:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3280)  all_14_0 = e0
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (91), (112), (120),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (126), (133), (134), (136), (141), (143), (144),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (148), (149), (158), (159), (160), (162), (163),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (169), (170), (192), (193),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (195), (196), (200), (201), (203), (213), (214),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (219), (222), (223), (224), (226), (234), (235),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (238), (239), (240), (241), (242),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (257), (258), (267), (268),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (279), (280), (282), (3011), (3012), (3013),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (3014), (3022), (3023), (3138), (3139), (3141),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (3143), (3152), (3153), (3177), (3178), (3179),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (3180), (3232), (3234), (3235), (3236), (3238),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (3242), (3246), (3249), (3250), (3251), (3252),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (3254), (function-axioms) are inconsistent by
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1680.
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | |   (3281)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3281) implies:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | |   (3282)   ~ (all_14_1 = e1)
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | |   (3283)  op(e2, e0) = all_14_1
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_14_1,
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (3242), (3283) gives:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | |   (3284)  all_14_1 = e2
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3257) gives:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3285)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_48_1 & $i(all_48_0) &
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3285) implies:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3286)   ~ (all_48_0 = e1)
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3287)  op(e2, e0) = all_48_1
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3288)  op(all_48_1, e2) = all_48_0
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_1,
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (3242), (3287) gives:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3289)  all_48_1 = e2
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3288), (3289) imply:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3290)  op(e2, e2) = all_48_0
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_48_0,
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (3023), (3290) gives:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3291)  all_48_0 = e0
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3286), (3291) imply:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3292)   ~ (e1 = e0)
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (91), (112), (120),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (126), (133), (134), (136), (141), (143), (144),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (148), (149), (158), (159), (160), (162), (163),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (169), (170), (192), (193),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (195), (196), (200), (201), (203), (213), (214),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (219), (222), (223), (224), (226), (234), (235),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (238), (239), (240), (241), (242),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (257), (258), (267), (268),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (279), (280), (282), (3011), (3012), (3013),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (3014), (3022), (3023), (3138), (3139), (3141),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (3143), (3152), (3153), (3177), (3178), (3179),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (3180), (3232), (3234), (3235), (3236), (3238),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (3242), (3246), (3249), (3250), (3251), (3252),
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            (3254), (function-axioms) are inconsistent by
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1680.
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3293)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3293) implies:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3294)   ~ (all_48_1 = e3)
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3295)  op(e2, e0) = all_48_1
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_1,
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (3242), (3295) gives:
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | |   (3296)  all_48_1 = e2
% 231.25/42.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (91), (112), (120),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (126), (133), (134), (136), (141), (143), (144),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (148), (149), (158), (159), (160), (162), (163),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (169), (170), (192), (193),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (195), (196), (200), (201), (203), (213), (214),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (219), (222), (223), (224), (226), (234), (235),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (238), (239), (240), (241), (242),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (257), (258), (267), (268),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (279), (280), (282), (3011), (3012), (3013),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (3014), (3022), (3023), (3138), (3139), (3141),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (3143), (3152), (3153), (3177), (3178), (3179),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (3180), (3232), (3234), (3235), (3236), (3238),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (3242), (3246), (3249), (3250), (3251), (3252),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (3254), (function-axioms) are inconsistent by
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1680.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | |   (3297)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 231.25/42.88  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | BETA: splitting (3297) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | |   (3298)  all_58_14 = e2 & op(e0, e1) = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | ALPHA: (3298) implies:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | |   (3299)  all_58_14 = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | |   (3300)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3300) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | |   (3301)  all_58_6 = e2 & op(e1, e3) = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3301) implies:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | |   (3302)  all_58_6 = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | |   (3303)  op(e1, e3) = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |   (3304)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3304) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |   (3305)  all_58_6 = e1 & op(e1, e3) = e1
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3305) implies:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |   (3306)  op(e1, e3) = e1
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3303), (3306), (function-axioms) are
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |   (3307)  all_58_7 = e1 & op(e1, e2) = e1
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3307) implies:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |   (3308)  all_58_7 = e1
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (162), (223), (226), (3014),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |            (3238), (3302), (3308), (function-axioms) are
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1676.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |   (3309)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (3143), (3238), (3309),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            #1692.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | |   (3310)  all_58_7 = e2 & op(e1, e2) = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3310) implies:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | |   (3311)  all_58_7 = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | |   (3312)  op(e1, e2) = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |   (3313)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3313) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |   (3314)  all_58_6 = e1 & op(e1, e3) = e1
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3314) implies:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |   (3315)  all_58_6 = e1
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | |   (3316)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3316) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3317)  all_58_6 = e0 & op(e1, e3) = e0
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3315), (3317) are inconsistent by sub-proof
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2205.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3318)  all_58_7 = e0 & op(e1, e2) = e0
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3014), (3318), (function-axioms) are
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | |   (3319)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (224),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (3238), (3311), (3312), (3319),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | |            #1673.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |   (3320)  all_58_7 = e1 & op(e1, e2) = e1
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3311), (3320) are inconsistent by sub-proof
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |            #2224.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |   (3321)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (3143), (3238), (3321),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            #1692.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | |   (3322)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3322) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | |   (3323)  all_58_8 = e2 & op(e1, e1) = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3323) implies:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | |   (3324)  all_58_8 = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |   (3325)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3325) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |   (3326)  all_58_4 = e0 & op(e3, e1) = e0
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3326) implies:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |   (3327)  all_58_4 = e0
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |   (3328)  op(e3, e1) = e0
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (228), (230), (3238),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |            (3299), (3324), (3327), (3328), (function-axioms)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2043.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |   (3329)  all_58_5 = e0 & op(e2, e1) = e0
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3016), (3329), (function-axioms) are
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |   (3330)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3238), (3299), (3330), (function-axioms) are
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2035.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | |   (3331)  all_58_11 = e2 & op(e1, e0) = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (224),
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | |            (226), (3014), (3238), (3331), (function-axioms)
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1670.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | |   (3332)  all_58_15 = e2 & op(e0, e0) = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | ALPHA: (3332) implies:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | |   (3333)  all_58_15 = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3152), (3333) are inconsistent by sub-proof
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | |            #2231.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | |   (3334)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 231.25/42.88  | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 231.25/42.88  | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | BETA: splitting (3334) gives:
% 231.25/42.88  | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | |   (3335)  all_58_11 = e2 & op(e1, e0) = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (224),
% 231.25/42.88  | | | | | | | | | | | | | | | | | |            (226), (3014), (3238), (3335), (function-axioms)
% 231.25/42.88  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1670.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | |   (3336)  all_58_15 = e2 & op(e0, e0) = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | ALPHA: (3336) implies:
% 231.25/42.88  | | | | | | | | | | | | | | | | | |   (3337)  all_58_15 = e2
% 231.25/42.88  | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3152), (3337) are inconsistent by sub-proof
% 231.25/42.88  | | | | | | | | | | | | | | | | | |            #2231.
% 231.25/42.88  | | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | |   (3338)  all_18_2 = e0
% 231.25/42.88  | | | | | | | | | | |   (3339)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0
% 231.25/42.88  | | | | | | | | | | |             & op(e1, e0) = all_18_1 & $i(all_18_0) &
% 231.25/42.88  | | | | | | | | | | |             $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1, e0)
% 231.25/42.88  | | | | | | | | | | |             = all_18_1 & $i(all_18_1))
% 231.25/42.88  | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | COMBINE_EQS: (339), (3338) imply:
% 231.25/42.88  | | | | | | | | | | |   (3340)  all_6_2 = e0
% 231.25/42.88  | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | COMBINE_EQS: (332), (3340) imply:
% 231.25/42.88  | | | | | | | | | | |   (3341)  all_28_2 = e0
% 231.25/42.88  | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | COMBINE_EQS: (266), (3340) imply:
% 231.25/42.88  | | | | | | | | | | |   (3342)  all_56_21 = e0
% 231.25/42.88  | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | REDUCE: (367), (3340) imply:
% 231.25/42.88  | | | | | | | | | | |   (3343)   ~ (all_52_2 = e0)
% 231.25/42.88  | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | REDUCE: (380), (3340) imply:
% 231.25/42.88  | | | | | | | | | | |   (3344)   ~ (all_52_8 = e0)
% 231.25/42.88  | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | REDUCE: (39), (3340) imply:
% 231.25/42.88  | | | | | | | | | | |   (3345)  op(e1, e1) = e0
% 231.25/42.88  | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | BETA: splitting (239) gives:
% 231.25/42.88  | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | |   (3346)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 231.25/42.88  | | | | | | | | | | | |             & op(e2, e3) = e0)
% 231.25/42.88  | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | BETA: splitting (3346) gives:
% 231.25/42.88  | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | |   (3347)  all_58_0 = e0 & op(e3, e3) = e0
% 231.25/42.88  | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | REF_CLOSE: (45), (3025), (3347), (function-axioms) are
% 231.25/42.88  | | | | | | | | | | | | |            inconsistent by sub-proof #1736.
% 231.25/42.88  | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | |   (3348)  all_58_2 = e0 & op(e2, e3) = e0
% 231.25/42.88  | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | | REF_CLOSE: (167), (3012), (3348), (function-axioms) are
% 231.25/42.88  | | | | | | | | | | | | |            inconsistent by sub-proof #1985.
% 231.25/42.88  | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | End of split
% 231.25/42.88  | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | Case 2:
% 231.25/42.88  | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | |   (3349)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 231.25/42.88  | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 231.25/42.88  | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | BETA: splitting (3349) gives:
% 231.25/42.88  | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | Case 1:
% 231.25/42.88  | | | | | | | | | | | | | 
% 231.25/42.88  | | | | | | | | | | | | |   (3350)  all_58_6 = e0 & op(e1, e3) = e0
% 231.25/42.89  | | | | | | | | | | | | | 
% 231.25/42.89  | | | | | | | | | | | | | ALPHA: (3350) implies:
% 231.25/42.89  | | | | | | | | | | | | |   (3351)  op(e1, e3) = e0
% 231.25/42.89  | | | | | | | | | | | | | 
% 231.25/42.89  | | | | | | | | | | | | | REF_CLOSE: (163), (3343), (3351), (function-axioms) are
% 231.25/42.89  | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 231.25/42.89  | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | |   (3352)  all_58_12 = e0 & op(e0, e3) = e0
% 231.54/42.89  | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | ALPHA: (3352) implies:
% 231.54/42.89  | | | | | | | | | | | | |   (3353)  all_58_12 = e0
% 231.54/42.89  | | | | | | | | | | | | |   (3354)  op(e0, e3) = e0
% 231.54/42.89  | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | BETA: splitting (240) gives:
% 231.54/42.89  | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | |   (3355)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 231.54/42.89  | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 231.54/42.89  | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | BETA: splitting (3355) gives:
% 231.54/42.89  | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | |   (3356)  all_58_0 = e0 & op(e3, e3) = e0
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | REF_CLOSE: (45), (3025), (3356), (function-axioms) are
% 231.54/42.89  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1736.
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | |   (3357)  all_58_1 = e0 & op(e3, e2) = e0
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | REF_CLOSE: (170), (3013), (3357), (function-axioms) are
% 231.54/42.89  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | End of split
% 231.54/42.89  | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | |   (3358)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 231.54/42.89  | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 231.54/42.89  | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | BETA: splitting (3358) gives:
% 231.54/42.89  | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | |   (3359)  all_58_4 = e0 & op(e3, e1) = e0
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | REF_CLOSE: (169), (3344), (3359), (function-axioms) are
% 231.54/42.89  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | |   (3360)  all_58_9 = e0 & op(e3, e0) = e0
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | ALPHA: (3360) implies:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3361)  all_58_9 = e0
% 231.54/42.89  | | | | | | | | | | | | | | |   (3362)  op(e3, e0) = e0
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 231.54/42.89  | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (3354) gives:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3363)  all_52_3 = e0
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 231.54/42.89  | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (168), (3362) gives:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3364)  all_52_12 = e0
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | REDUCE: (140), (3363) imply:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3365)   ~ (all_52_7 = e0)
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | REDUCE: (139), (3363) imply:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3366)   ~ (all_52_11 = e0)
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | SIMP: (3366) implies:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3367)   ~ (all_52_11 = e0)
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | REDUCE: (113), (3364) imply:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3368)   ~ (all_52_13 = e0)
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | REDUCE: (112), (3364) imply:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3369)   ~ (all_52_14 = e0)
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | SIMP: (3369) implies:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3370)   ~ (all_52_14 = e0)
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | REDUCE: (365), (3364) imply:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3371)   ~ (all_10_2 = e0)
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | REDUCE: (387), (3364) imply:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3372)   ~ (all_4_2 = e0)
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | SIMP: (3372) implies:
% 231.54/42.89  | | | | | | | | | | | | | | |   (3373)   ~ (all_4_2 = e0)
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 231.54/42.89  | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | |   (3374)  all_54_15 = e3
% 231.54/42.89  | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | REF_CLOSE: (299), (395), (3374) are inconsistent by sub-proof
% 231.54/42.89  | | | | | | | | | | | | | | | |            #2340.
% 231.54/42.89  | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | |   (3375)   ~ (all_54_15 = e3)
% 231.54/42.89  | | | | | | | | | | | | | | | |   (3376)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 231.54/42.89  | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | BETA: splitting (3376) gives:
% 231.54/42.89  | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | |   (3377)  all_54_15 = e2
% 231.54/42.89  | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (390), (3377) are inconsistent by sub-proof
% 231.54/42.89  | | | | | | | | | | | | | | | | |            #2339.
% 231.54/42.89  | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | |   (3378)  all_54_15 = e1 | all_54_15 = e0
% 231.54/42.89  | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | BETA: splitting (3378) gives:
% 231.54/42.89  | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | |   (3379)  all_54_15 = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (3379) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | |   (3380)  all_4_2 = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | SIMP: (3380) implies:
% 231.54/42.89  | | | | | | | | | | | | | | | | | |   (3381)  all_4_2 = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (3381) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | |   (3382)  all_56_31 = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | REDUCE: (379), (3381) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | |   (3383)   ~ (all_52_7 = e1)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | REDUCE: (386), (3381) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | |   (3384)   ~ (all_52_11 = e1)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | REDUCE: (388), (3381) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | |   (3385)   ~ (all_52_13 = e1)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | REDUCE: (389), (3381) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | |   (3386)   ~ (all_52_14 = e1)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | REDUCE: (395), (3381) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | |   (3387)   ~ (e3 = e1)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | |   (3388)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (3388) gives:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | |   (3389)  all_58_9 = e1 & op(e3, e0) = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3361), (3389) are inconsistent by sub-proof
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | |            #2183.
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | |   (3390)  all_58_10 = e1 & op(e2, e0) = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3385), (3390), (function-axioms) are
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | |   (3391)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (3391) gives:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | |   (3392)  all_58_11 = e1 & op(e1, e0) = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | ALPHA: (3392) implies:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | |   (3393)  op(e1, e0) = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (3386), (3393), (function-axioms) are
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | |   (3394)  all_58_15 = e1 & op(e0, e0) = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | ALPHA: (3394) implies:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | |   (3395)  all_58_15 = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | |   (3396)  op(e0, e0) = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | |   (3397)   ~ (all_24_2 = e2)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (3397) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | |   (3398)   ~ (all_10_2 = e2)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | |   (3399)  all_54_0 = e3
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (3399) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | |   (3400)  all_10_2 = e3
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (3400) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | |   (3401)  all_56_1 = e3
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (355), (3400) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | |   (3402)   ~ (all_52_1 = e3)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (357), (3400) imply:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | |   (3403)   ~ (all_52_2 = e3)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |   (3404)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (168), (204), (292), (365), (393),
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |            (3025), (3398), (3401), (3402), (3403), (3404),
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |            #1668.
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |   (3405)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3405) gives:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | |   (3406)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.89  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3406) gives:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (3407)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3407) implies:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (3408)   ~ (all_56_31 = e1)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3382), (3408) imply:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (3409)  $false
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3409) is inconsistent.
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (3410)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3410) gives:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3411)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3411) implies:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3412)  op(e1, e2) = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3413)  op(e2, e1) = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (3412) gives:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3414)  all_52_6 = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (3413) gives:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3415)  all_52_9 = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (3415) imply:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3416)   ~ (all_52_1 = e1)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (3414) imply:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3417)   ~ (all_52_2 = e1)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3418)  all_54_8 = e3
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (3403), (3418) are inconsistent by
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3419)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3420)  all_54_4 = e3
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (3402), (3420) are inconsistent by
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3421)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3421) gives:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3422)  all_54_4 = e2
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (3422) imply:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3423)  all_52_1 = e2
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3423) implies:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3424)  all_52_1 = e2
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (3424) imply:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3425)   ~ (all_52_2 = e2)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3425) implies:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3426)   ~ (all_52_2 = e2)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3419) gives:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3427)  all_54_8 = e2
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (3426), (3427) are inconsistent by
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2007.
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3428)  all_54_8 = e1 | all_54_8 = e0
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (3343), (3417), (3428) are inconsistent by
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1950.
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3429)  all_54_4 = e1 | all_54_4 = e0
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (3012), (3416), (3429) are inconsistent by
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1922.
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3430)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3430) implies:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3431)   ~ (all_56_21 = e0)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3342), (3431) imply:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3432)  $false
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3432) is inconsistent.
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |   (3433)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (3017), (3370), (3386), (3433),
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | |            #1903.
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | |   (3434)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (3025), (3398), (3434) are
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | |   (3435)  all_24_2 = e2
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (3435) imply:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | |   (3436)  all_10_2 = e2
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (3436) imply:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | |   (3437)  all_56_1 = e2
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | REDUCE: (357), (3436) imply:
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | |   (3438)   ~ (all_52_2 = e2)
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (3436) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | |   (3439)   ~ (all_52_4 = e2)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (3436) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | |   (3440)   ~ (all_52_8 = e2)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (3436) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | |   (3441)  op(e3, e3) = e2
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | |   (3442)   ~ (all_28_2 = e0)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3341), (3442) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | |   (3443)  $false
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3443) is inconsistent.
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | |   (3444)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_28_1 & $i(all_28_0) &
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | |             $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | |             = all_28_1 & $i(all_28_1))
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | |   (3445)   ~ (all_48_2 = e0)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3010), (3445) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | |   (3446)  $false
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3446) is inconsistent.
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | |   (3447)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | |             = all_48_1 & $i(all_48_1))
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | |   (3448)  all_54_2 = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (3448) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | |   (3449)  all_52_8 = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3449) implies:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | |   (3450)  all_52_8 = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (3450) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | |   (3451)   ~ (all_52_4 = e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (3450) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | |   (3452)   ~ (all_52_9 = e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3452) implies:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | |   (3453)   ~ (all_52_9 = e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (3450) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | |   (3454)   ~ (all_52_11 = e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3454) implies:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | |   (3455)   ~ (all_52_11 = e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (3450) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | |   (3456)  op(e3, e1) = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (3457)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3457) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3458)  all_58_0 = e1 & op(e3, e3) = e1
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3458) implies:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3459)  op(e3, e3) = e1
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3441), (3459), (function-axioms) are
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3460)  all_58_1 = e1 & op(e3, e2) = e1
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3460) implies:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3461)  all_58_1 = e1
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3462)  op(e3, e2) = e1
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3463)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3463) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3464)  all_58_0 = e3 & op(e3, e3) = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3464) implies:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3465)  op(e3, e3) = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3441), (3465), (function-axioms) are
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3466)  all_58_1 = e3 & op(e3, e2) = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3466) implies:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3467)  op(e3, e2) = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3462), (3467), (function-axioms) are
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3468)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3468) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3469)  all_58_4 = e3 & op(e3, e1) = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3469) implies:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3470)  all_58_4 = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3471)  all_54_1 = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (3451), (3471) are inconsistent by
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3472)   ~ (all_54_1 = e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3473)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3474)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3474) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3475)  all_58_12 = e3 & op(e0, e3) = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3475) implies:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3476)  all_58_12 = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3353), (3476) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3477)  e3 = e0
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3470), (3477) imply:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3478)  all_58_4 = e0
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (229),
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (3345), (3453), (3478), (function-axioms)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1662.
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3479)  all_58_13 = e3 & op(e0, e2) = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3479) implies:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3480)  op(e0, e2) = e3
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3481)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3481) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3482)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (3382), (3462), (3482),
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1725.
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3483)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3483) gives:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3484)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3484) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3485)  op(e3, e1) = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3456), (3485), (function-axioms) are
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1823.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3486)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3486) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3487)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3487) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3488)   ~ (all_56_21 = e0)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3342), (3488) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3489)  $false
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3489) is inconsistent.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3490)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3490) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3491)  all_56_7 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3492)  all_54_14 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (3492) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3493)  all_52_11 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3455), (3493) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3494)  $false
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3494) is inconsistent.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3495)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3473) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3496)  all_54_1 = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (3439), (3496) are inconsistent by
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1928.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3497)  all_54_1 = e1 | all_54_1 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3497) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3498)  all_54_1 = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (3498) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3499)  all_52_4 = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3499) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3500)  all_52_4 = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (3500) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3501)   ~ (all_52_6 = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3501) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3502)   ~ (all_52_6 = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (3500) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3503)   ~ (all_52_7 = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3495) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3504)  all_54_14 = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (3504) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3505)  all_52_11 = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3505) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3506)  all_52_11 = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (3506) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3507)   ~ (all_52_7 = e2)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3508)  all_54_13 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (3508) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3509)  all_52_7 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (3509) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3510)   ~ (all_52_6 = e3)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3511)  all_54_9 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (3510), (3511) are inconsistent by
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3512)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3512) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3513)  all_54_9 = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (3513) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3514)  all_52_6 = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3514) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3515)  all_52_6 = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (3515) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3516)   ~ (all_52_14 = e2)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3516) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3517)   ~ (all_52_14 = e2)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3518)  all_54_11 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (3518) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3519)  all_52_14 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3519) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3520)  all_52_14 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (3520) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3521)   ~ (all_52_2 = e3)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (3520) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3522)   ~ (all_52_13 = e3)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3523)  all_54_8 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (3521), (3523) are inconsistent by
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3524)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3525)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3525) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3526)  all_58_2 = e3 & op(e2, e3) = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3526) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3527)  op(e2, e3) = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3524) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3528)  all_54_8 = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (3438), (3528) are inconsistent by
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2007.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3529)  all_54_8 = e1 | all_54_8 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3530)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (3437), (3462), (3527), (3530),
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1703.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3531)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3531) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3532)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_5 & $i(all_56_5)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3532) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3533)  op(e1, e3) = all_56_5
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3534)  op(e1, all_56_5) = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (268), (3343), (3345), (3529), (3533),
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3534), (function-axioms) are inconsistent by
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2005.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3535)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_7 & $i(all_56_7)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3535) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3536)  op(e0, all_56_7) = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3491), (3536) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3537)  op(e0, e0) = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (220), (221),
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (3361), (3522), (3537), (function-axioms)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1650.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3538)  all_58_3 = e3 & op(e2, e2) = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3538) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3539)  all_58_3 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3022), (3539) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3540)  e3 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3470), (3540) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3541)  all_58_4 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (229),
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (3345), (3453), (3541), (function-axioms)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1662.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3542)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (3453), (3522), (3542),
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1649.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3543)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (3370), (3386), (3517), (3543) are
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2173.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3544)  all_54_9 = e1 | all_54_9 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3544) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3545)  all_54_9 = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (3502), (3545) are inconsistent by
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2055.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3546)  all_54_9 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (3014), (3546) are inconsistent by
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1953.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3547)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (3015), (3383), (3507), (3547) are
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1648.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3548)  all_54_14 = e1 | all_54_14 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (3367), (3384), (3548) are inconsistent by
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1935.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3549)  all_54_1 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (3013), (3549) are inconsistent by
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2050.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3550)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3550) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3551)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3551) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3552)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3552) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3553)   ~ (all_56_31 = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3382), (3553) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3554)  $false
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3554) is inconsistent.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3555)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3555) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3556)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3556) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3557)   ~ (all_56_1 = e2)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3437), (3557) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3558)  $false
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3558) is inconsistent.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3559)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3559) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3560)  op(e0, e2) = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3480), (3560), (function-axioms) are
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3561)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (3017), (3370), (3386), (3561),
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1903.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3562)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3562) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3563)  all_58_14 = e3 & op(e0, e1) = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3455), (3563), (function-axioms) are
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3564)  all_58_15 = e3 & op(e0, e0) = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3564) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3565)  all_58_15 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (170), (240), (246),
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3395), (3441), (3451), (3461), (3470), (3565),
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1644.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3566)  all_58_9 = e3 & op(e3, e0) = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3566) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3567)  all_58_9 = e3
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3361), (3567) are inconsistent by sub-proof
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1958.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (3568)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3568) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3569)  all_58_4 = e1 & op(e3, e1) = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3569) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3570)  op(e3, e1) = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3456), (3570), (function-axioms) are
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1823.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3571)  all_58_9 = e1 & op(e3, e0) = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3571) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3572)  all_58_9 = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3361), (3572) are inconsistent by sub-proof
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1744.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | |   (3573)   ~ (all_54_2 = e3)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | |   (3574)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (281), (3573) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | |   (3575)   ~ (all_52_8 = e3)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3574) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (3576)  all_54_2 = e2
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (3440), (3576) are inconsistent by
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1986.
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (3577)   ~ (all_54_2 = e2)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (3578)  all_54_2 = e1 | all_54_2 = e0
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3578) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3579)  all_54_2 = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (3579) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3580)  all_52_8 = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3580) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3581)  all_52_8 = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (3581) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3582)   ~ (all_52_4 = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (3581) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3583)   ~ (all_52_9 = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3583) implies:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3584)   ~ (all_52_9 = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (3581) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3585)   ~ (all_52_11 = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3440), (3581) imply:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3586)   ~ (e2 = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3587)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3587) gives:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3588)  all_58_1 = e1 & op(e3, e2) = e1
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3588) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3589)  op(e3, e2) = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (170), (281), (3344), (3578), (3589),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1642.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3590)  all_58_3 = e1 & op(e2, e2) = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3022), (3590) are inconsistent by sub-proof
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1752.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3591)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3591) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3592)  all_58_7 = e1 & op(e1, e2) = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3592) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3593)  all_58_7 = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3594)  op(e1, e2) = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3595)  all_54_1 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (3595) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3596)  all_52_4 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3596) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3597)  all_52_4 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (3597) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3598)   ~ (all_52_6 = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3598) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3599)   ~ (all_52_6 = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (3597) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3600)   ~ (all_52_7 = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3600) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3601)   ~ (all_52_7 = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (3597) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3602)  op(e3, e2) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3603)  all_54_13 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (3603) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3604)  all_52_7 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3601), (3604) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3605)  $false
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3605) is inconsistent.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3606)   ~ (all_54_13 = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3607)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3608)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3608) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3609)  all_58_1 = e2 & op(e3, e2) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3609) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3610)  op(e3, e2) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3602), (3610), (function-axioms) are
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2193.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3611)  all_58_3 = e2 & op(e2, e2) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3611) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3612)  op(e2, e2) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (133), (135), (140), (158), (159), (162),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (170), (191), (203), (235), (256), (282),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3014), (3354), (3362), (3383), (3439), (3582),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3612), (function-axioms) are inconsistent by
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1962.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3613)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3613) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3614)  all_58_7 = e2 & op(e1, e2) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3614) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3615)  all_58_7 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3593), (3615) are inconsistent by sub-proof
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2134.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3616)  all_58_13 = e2 & op(e0, e2) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3616) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3617)  all_58_13 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3618)  op(e0, e2) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3619)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3619) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3620)  all_58_12 = e3 & op(e0, e3) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3620) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3621)  all_58_12 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3353), (3621) are inconsistent by sub-proof
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1971.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3622)  all_58_13 = e3 & op(e0, e2) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3622) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3623)  op(e0, e2) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3618), (3623), (function-axioms) are
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3624)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3624) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3625)  all_58_14 = e3 & op(e0, e1) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3625) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3626)  all_58_14 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3627)  op(e0, e1) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3628)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (3023), (3441), (3593), (3594), (3628),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1713.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3629)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3629) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3630)  all_58_4 = e1 & op(e3, e1) = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3630) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3631)  all_58_4 = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3632)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3632) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3633)  all_58_0 = e3 & op(e3, e3) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3633) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3634)  op(e3, e3) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3441), (3634), (function-axioms) are
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3635)  all_58_1 = e3 & op(e3, e2) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3635) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3636)  all_58_1 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3637)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3637) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3638)  all_58_2 = e1 & op(e2, e3) = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3638) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3639)  all_58_2 = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3640)  op(e2, e3) = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3641)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3641) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3642)  all_58_6 = e2 & op(e1, e3) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3642) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3643)  all_58_6 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3644)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3644) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3645)  all_58_0 = e3 & op(e3, e3) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3645) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3646)  op(e3, e3) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3441), (3646), (function-axioms) are
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3647)  all_58_2 = e3 & op(e2, e3) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3647) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3648)  all_58_2 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3639), (3648) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3649)  e3 = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3636), (3649) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3650)  all_58_1 = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (3023), (3593), (3594), (3650),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1714.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3651)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3651) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3652)  all_58_6 = e3 & op(e1, e3) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3652) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3653)  all_58_6 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3643), (3653) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3654)  e3 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3626), (3654) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3655)  all_58_14 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (158), (216), (219),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3395), (3396), (3601), (3618), (3655),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1636.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3656)  all_58_12 = e3 & op(e0, e3) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3656) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3657)  all_58_12 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (216), (3396), (3618), (3627),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3657), (function-axioms) are inconsistent by
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1634.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3658)  all_58_7 = e2 & op(e1, e2) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3658) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3659)  all_58_7 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (235), (236), (3602),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3617), (3618), (3636), (3659), (function-axioms)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1748.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3660)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3660) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3661)  all_58_8 = e2 & op(e1, e1) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3661) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3662)  op(e1, e1) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3345), (3662), (function-axioms) are
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3663)  all_58_11 = e2 & op(e1, e0) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3663) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3664)  all_58_11 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3665)  op(e1, e0) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3666)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3666) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3667)  all_58_9 = e3 & op(e3, e0) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3667) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3668)  all_58_9 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3361), (3668) are inconsistent by sub-proof
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1958.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3669)  all_58_10 = e3 & op(e2, e0) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3669) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3670)  op(e2, e0) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3671)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3671) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3672)  all_58_6 = e3 & op(e1, e3) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3672) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3673)  all_58_6 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3607) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3674)  all_54_13 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (3674) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3675)  all_52_7 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3675) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3676)  all_52_7 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (3676) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3677)   ~ (all_52_6 = e2)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (3676) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3678)   ~ (all_52_11 = e2)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3678) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3679)   ~ (all_52_11 = e2)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3680)  all_54_9 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (3599), (3680) are inconsistent by
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3681)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3681) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3682)  all_54_9 = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (3677), (3682) are inconsistent by
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1954.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3683)   ~ (all_54_9 = e2)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3684)  all_54_9 = e1 | all_54_9 = e0
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3685)  all_54_14 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (3685) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3686)  all_52_11 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3686) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3687)  all_52_11 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (3687) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3688)   ~ (all_52_9 = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3684) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3689)  all_54_9 = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (3689) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3690)  all_52_6 = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3690) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3691)  all_52_6 = e1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (3691) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3692)   ~ (all_52_2 = e1)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (3691) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3693)   ~ (all_52_14 = e1)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3694)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3694) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3695)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_9 & $i(all_56_9)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3695) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3696)  op(e3, e2) = all_56_9
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3697)  op(e3, all_56_9) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3698)  all_54_8 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3698) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3699)  all_52_2 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3699) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3700)  all_52_2 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (3700) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3701)   ~ (all_52_14 = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3701) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3702)   ~ (all_52_14 = e3)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3703)  all_54_11 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (3703) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3704)  all_52_14 = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3702), (3704) imply:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3705)  $false
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3705) is inconsistent.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3706)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3707)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_27 & $i(all_56_27))
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3707) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3708)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) = all_56_25 & $i(all_56_25)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3708) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3709)  op(e3, e0) = all_56_25
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3710)  op(e3, all_56_25) = e3
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3362), (3709), (3710), (function-axioms) are
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1926.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3711)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) = all_56_27 & $i(all_56_27)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3711) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3712)  op(e2, e0) = all_56_27
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3713)  op(e2, all_56_27) = e2
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3007) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3714)   ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_14_1 & $i(all_14_0) &
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3714) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3715)  op(e2, e0) = all_14_1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (3370), (3386), (3447), (3640), (3670),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3706), (3712), (3713), (3715), (function-axioms)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1631.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3716)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3716) implies:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3717)  op(e2, e0) = all_14_1
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (3370), (3386), (3447), (3640), (3670),
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3706), (3712), (3713), (3717), (function-axioms)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1631.
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3718)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_31) = e0)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3718) gives:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3719)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) = all_56_29 & $i(all_56_29)
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3719) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3720)  op(e1, e0) = all_56_29
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3444) gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3721)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_28_1 & $i(all_28_0) &
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3721) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3722)  op(e1, e0) = all_28_1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3339) gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_9,
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (3602), (3696) gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3723)  all_56_9 = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3697), (3723) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3724)  op(e3, e3) = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (243), (3353), (3639), (3673),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3724), (function-axioms) are inconsistent by
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1629.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3725)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 &
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3725) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3726)   ~ (all_18_1 = e3)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3727)  op(e1, e0) = all_18_1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_1, e0, e1, simplifying with (3722), (3727)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3728)  all_28_1 = all_18_1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_1,
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_29, e0, e1, simplifying with (3720), (3722)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3729)  all_56_29 = all_28_1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_29, e0, e1, simplifying with (3665), (3720)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3730)  all_56_29 = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_9,
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (3602), (3696) gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3731)  all_56_9 = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3729), (3730) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3732)  all_28_1 = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3732) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3733)  all_28_1 = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3728), (3733) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3734)  all_18_1 = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3734) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3735)  all_18_1 = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3726), (3735) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3736)   ~ (e3 = e2)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3697), (3731) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3737)  op(e3, e3) = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (243), (3353), (3639), (3673),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3737), (function-axioms) are inconsistent by
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1629.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3738)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3738) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3739)   ~ (all_28_1 = e2)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3740)  op(e1, e0) = all_28_1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3665), (3739), (3740), (function-axioms) are
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1944.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3741)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3741) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3742)  op(e0, all_56_31) = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3382), (3742) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3743)  op(e0, e1) = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (165), (169), (230), (391), (3575),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3688), (3743), (function-axioms) are inconsistent
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1626.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3744)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (3343), (3438), (3692), (3744) are
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1949.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3745)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3745) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3746)  op(e2, all_56_11) = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3011), (3746) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3747)  op(e2, e0) = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3670), (3747), (function-axioms) are
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3748)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3748) gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3749)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3749) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3750)  op(e1, e2) = all_56_13
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3751)  op(e1, all_56_13) = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3444) gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (3594), (3750)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3752)  all_56_13 = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3751), (3752) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3753)  op(e1, e1) = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (3014), (3343),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3370), (3753), (function-axioms) are inconsistent
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2020.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3754)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3754) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3755)   ~ (all_28_1 = e2)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3756)  op(e1, e0) = all_28_1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3665), (3755), (3756), (function-axioms) are
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1944.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3757)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3757) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3758)  op(e0, e2) = all_56_15
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3759)  op(e0, all_56_15) = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (256), (3015), (3383), (3607), (3618),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3758), (3759), (function-axioms) are inconsistent
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1625.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3760)   ~ (all_54_7 = e3)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (3760) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3761)   ~ (all_52_13 = e3)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3670), (3761), (function-axioms) are
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3762)  all_54_9 = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (3014), (3762) are inconsistent by
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1953.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3763)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (3367), (3384), (3679), (3763) are
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1798.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3764)  all_54_13 = e1 | all_54_13 = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (3015), (3383), (3764) are inconsistent by
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1793.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3765)  all_58_7 = e3 & op(e1, e2) = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3765) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3766)  op(e1, e2) = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (162), (170), (195), (267), (3602), (3766),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2190.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3767)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3767) gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3768)  all_58_8 = e3 & op(e1, e1) = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3345), (3768), (function-axioms) are
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3769)  all_58_11 = e3 & op(e1, e0) = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3769) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3770)  all_58_11 = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3664), (3770) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3771)  e3 = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3626), (3771) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3772)  all_58_14 = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (158), (216), (219),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3395), (3396), (3601), (3618), (3772),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1636.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3773)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3773) gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3774)  all_58_11 = e3 & op(e1, e0) = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3774) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3775)  all_58_11 = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3664), (3775) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3776)  e3 = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3776) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3777)  e3 = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3626), (3777) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3778)  all_58_14 = e2
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (158), (216), (219),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3395), (3396), (3601), (3618), (3778),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1636.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3779)  all_58_15 = e3 & op(e0, e0) = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3779) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3780)  all_58_15 = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3395), (3780) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3781)  e3 = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (3023), (3593), (3594), (3636), (3781),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1624.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3782)  all_58_3 = e1 & op(e2, e2) = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3782) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3783)  all_58_3 = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3022), (3783) imply:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3784)  e1 = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (228), (229), (3345),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3626), (3631), (3784), (function-axioms) are
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1623.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3785)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3785) gives:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3786)  all_58_5 = e1 & op(e2, e1) = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3786) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3787)  op(e2, e1) = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3584), (3787), (function-axioms) are
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3788)  all_58_10 = e1 & op(e2, e0) = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3788) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3789)  all_58_10 = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (221), (222), (3361),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3395), (3789) are inconsistent by sub-proof
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1618.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3790)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (3361), (3575), (3790),
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1957.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3791)  all_58_9 = e1 & op(e3, e0) = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3791) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3792)  all_58_9 = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3361), (3792) are inconsistent by sub-proof
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1744.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3793)  all_58_15 = e3 & op(e0, e0) = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3793) implies:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3794)  all_58_15 = e3
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3395), (3794) are inconsistent by sub-proof
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2249.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3795)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (3013), (3439), (3582), (3795) are
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2048.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3796)  all_58_13 = e1 & op(e0, e2) = e1
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3383), (3796), (function-axioms) are
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3797)  all_54_2 = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (3344), (3797) are inconsistent by
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1643.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | |   (3798)  all_54_15 = e0
% 231.54/42.94  | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (3373), (3798) are inconsistent by
% 231.54/42.94  | | | | | | | | | | | | | | | | | |            sub-proof #1737.
% 231.54/42.94  | | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | End of split
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | |   (3799)  all_16_2 = e0
% 231.54/42.94  | | | | | | | | | |   (3800)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0
% 231.54/42.94  | | | | | | | | | |             & op(e3, e0) = all_16_1 & $i(all_16_0) &
% 231.54/42.94  | | | | | | | | | |             $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0)
% 231.54/42.94  | | | | | | | | | |             = all_16_1 & $i(all_16_1))
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | COMBINE_EQS: (342), (3799) imply:
% 231.54/42.94  | | | | | | | | | |   (3801)  all_10_2 = e0
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | SIMP: (3801) implies:
% 231.54/42.94  | | | | | | | | | |   (3802)  all_10_2 = e0
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | COMBINE_EQS: (350), (3802) imply:
% 231.54/42.94  | | | | | | | | | |   (3803)  all_50_2 = e0
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | COMBINE_EQS: (290), (3802) imply:
% 231.54/42.94  | | | | | | | | | |   (3804)  all_56_1 = e0
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | REDUCE: (357), (3802) imply:
% 231.54/42.94  | | | | | | | | | |   (3805)   ~ (all_52_2 = e0)
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | REDUCE: (359), (3802) imply:
% 231.54/42.94  | | | | | | | | | |   (3806)   ~ (all_52_3 = e0)
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | REDUCE: (363), (3802) imply:
% 231.54/42.94  | | | | | | | | | |   (3807)   ~ (all_52_8 = e0)
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | REDUCE: (393), (3802) imply:
% 231.54/42.94  | | | | | | | | | |   (3808)   ~ (e1 = e0)
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | REDUCE: (45), (3802) imply:
% 231.54/42.94  | | | | | | | | | |   (3809)  op(e3, e3) = e0
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | BETA: splitting (58) gives:
% 231.54/42.94  | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | |   (3810)   ~ (all_18_2 = e0)
% 231.54/42.94  | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | REDUCE: (339), (3810) imply:
% 231.54/42.94  | | | | | | | | | | |   (3811)   ~ (all_6_2 = e0)
% 231.54/42.94  | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | BETA: splitting (223) gives:
% 231.54/42.94  | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | |   (3812)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 231.54/42.94  | | | | | | | | | | | |             & op(e1, e2) = e0)
% 231.54/42.94  | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | REF_CLOSE: (162), (163), (3014), (3805), (3812),
% 231.54/42.94  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.94  | | | | | | | | | | | |            #2021.
% 231.54/42.94  | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | |   (3813)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 231.54/42.94  | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 231.54/42.94  | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | BETA: splitting (3813) gives:
% 231.54/42.94  | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | |   (3814)  all_58_8 = e0 & op(e1, e1) = e0
% 231.54/42.94  | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | REF_CLOSE: (39), (3811), (3814), (function-axioms) are
% 231.54/42.94  | | | | | | | | | | | | |            inconsistent by sub-proof #1833.
% 231.54/42.94  | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | |   (3815)  all_58_11 = e0 & op(e1, e0) = e0
% 231.54/42.94  | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | ALPHA: (3815) implies:
% 231.54/42.94  | | | | | | | | | | | | |   (3816)  all_58_11 = e0
% 231.54/42.94  | | | | | | | | | | | | |   (3817)  op(e1, e0) = e0
% 231.54/42.94  | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | BETA: splitting (227) gives:
% 231.54/42.94  | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | |   (3818)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 231.54/42.94  | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 231.54/42.94  | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | BETA: splitting (3818) gives:
% 231.54/42.94  | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | Case 1:
% 231.54/42.94  | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | |   (3819)  all_58_4 = e0 & op(e3, e1) = e0
% 231.54/42.94  | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | REF_CLOSE: (169), (3807), (3819), (function-axioms) are
% 231.54/42.94  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 231.54/42.94  | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | Case 2:
% 231.54/42.94  | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | |   (3820)  all_58_5 = e0 & op(e2, e1) = e0
% 231.54/42.94  | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | | REF_CLOSE: (165), (3016), (3820), (function-axioms) are
% 231.54/42.94  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 231.54/42.94  | | | | | | | | | | | | | | | 
% 231.54/42.94  | | | | | | | | | | | | | | End of split
% 231.54/42.95  | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | |   (3821)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 231.54/42.95  | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 231.54/42.95  | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | BETA: splitting (3821) gives:
% 231.54/42.95  | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | |   (3822)  all_58_8 = e0 & op(e1, e1) = e0
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | REF_CLOSE: (39), (3811), (3822), (function-axioms) are
% 231.54/42.95  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1833.
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | |   (3823)  all_58_14 = e0 & op(e0, e1) = e0
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | ALPHA: (3823) implies:
% 231.54/42.95  | | | | | | | | | | | | | | |   (3824)  op(e0, e1) = e0
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 231.54/42.95  | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (157), (3824) gives:
% 231.54/42.95  | | | | | | | | | | | | | | |   (3825)  all_52_11 = e0
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 231.54/42.95  | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (3817) gives:
% 231.54/42.95  | | | | | | | | | | | | | | |   (3826)  all_52_14 = e0
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | REDUCE: (112), (3826) imply:
% 231.54/42.95  | | | | | | | | | | | | | | |   (3827)   ~ (all_52_12 = e0)
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | REDUCE: (385), (3826) imply:
% 231.54/42.95  | | | | | | | | | | | | | | |   (3828)   ~ (all_6_2 = e0)
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | REDUCE: (389), (3826) imply:
% 231.54/42.95  | | | | | | | | | | | | | | |   (3829)   ~ (all_4_2 = e0)
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | SIMP: (3829) implies:
% 231.54/42.95  | | | | | | | | | | | | | | |   (3830)   ~ (all_4_2 = e0)
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | |   (3831)  all_54_15 = e3
% 231.54/42.95  | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | REF_CLOSE: (299), (395), (3831) are inconsistent by sub-proof
% 231.54/42.95  | | | | | | | | | | | | | | | |            #2340.
% 231.54/42.95  | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | |   (3832)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 231.54/42.95  | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | BETA: splitting (3832) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | |   (3833)  all_54_15 = e2
% 231.54/42.95  | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (390), (3833) are inconsistent by sub-proof
% 231.54/42.95  | | | | | | | | | | | | | | | | |            #2339.
% 231.54/42.95  | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | |   (3834)   ~ (all_54_15 = e2)
% 231.54/42.95  | | | | | | | | | | | | | | | | |   (3835)  all_54_15 = e1 | all_54_15 = e0
% 231.54/42.95  | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | BETA: splitting (3835) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | |   (3836)  all_54_15 = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (3836) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | |   (3837)  all_4_2 = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | SIMP: (3837) implies:
% 231.54/42.95  | | | | | | | | | | | | | | | | | |   (3838)  all_4_2 = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (3838) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | |   (3839)  all_20_2 = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (3838) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | |   (3840)  all_34_2 = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (3838) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | |   (3841)  all_56_31 = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | REDUCE: (368), (3838) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | |   (3842)   ~ (all_52_3 = e1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | REDUCE: (379), (3838) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | |   (3843)   ~ (all_52_7 = e1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | REDUCE: (387), (3838) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | |   (3844)   ~ (all_52_12 = e1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | REDUCE: (388), (3838) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | |   (3845)   ~ (all_52_13 = e1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | REDUCE: (390), (3838) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | |   (3846)   ~ (e2 = e1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | |   (3847)   ~ (all_20_2 = e1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | REDUCE: (3839), (3847) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | |   (3848)  $false
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | CLOSE: (3848) is inconsistent.
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | |   (3849)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 231.54/42.95  | | | | | | | | | | | | | | | | | | |             $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | |             = all_20_1 & $i(all_20_1))
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | |   (3850)   ~ (all_34_2 = e1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (3840), (3850) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | |   (3851)  $false
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | CLOSE: (3851) is inconsistent.
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | |   (3852)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | |   (3853)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3853) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | |   (3854)  all_58_12 = e1 & op(e0, e3) = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3842), (3854), (function-axioms) are
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | |   (3855)  all_58_13 = e1 & op(e0, e2) = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3843), (3855), (function-axioms) are
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | |   (3856)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3856) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | |   (3857)  all_58_14 = e1 & op(e0, e1) = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3857) implies:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | |   (3858)  op(e0, e1) = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3824), (3858), (function-axioms) are
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2158.
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | |   (3859)  all_58_15 = e1 & op(e0, e0) = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3859) implies:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | |   (3860)  all_58_15 = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | |   (3861)  op(e0, e0) = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3849) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |   (3862)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_20_1 & $i(all_20_0) &
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3862) implies:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |   (3863)   ~ (all_20_0 = e2)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |   (3864)  op(e0, e1) = all_20_1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |   (3865)  op(all_20_1, e0) = all_20_0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_20_1,
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (3824), (3864) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |   (3866)  all_20_1 = e0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3865), (3866) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |   (3867)  op(e0, e0) = all_20_0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3852) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3868)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_34_1 & $i(all_34_0) &
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3868) implies:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3869)  op(e0, e1) = all_34_1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3870)  op(all_34_1, e0) = all_34_0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_20_0,
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (3861), (3867) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3871)  all_20_0 = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_34_1,
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (3824), (3869) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3872)  all_34_1 = e0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3870), (3872) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3873)  op(e0, e0) = all_34_0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_34_0,
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (3861), (3873) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3874)  all_34_0 = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (39), (85), (113), (117),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (120), (123), (133), (134), (145), (158), (159),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (165), (167), (168), (169),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (170), (194), (197), (198), (201), (213), (216),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (226), (227), (228), (230),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (232), (235), (236), (237), (238), (239), (242),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (266), (269), (270), (280),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (297), (328), (380), (381), (391), (3011), (3012),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3013), (3014), (3016), (3017), (3022), (3023),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3805), (3806), (3809), (3811), (3816), (3817),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3824), (3827), (3841), (3843), (3844), (3845),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3860), (3861), (function-axioms) are inconsistent
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1593.
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3875)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 &
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3875) implies:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3876)   ~ (all_34_1 = e2)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3877)  op(e0, e1) = all_34_1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_20_0,
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (3861), (3867) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3878)  all_20_0 = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_34_1,
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (3824), (3877) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3879)  all_34_1 = e0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3876), (3879) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3880)   ~ (e2 = e0)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (3881)   ~ (all_36_2 = e2)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (328), (3881) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (3882)   ~ (all_6_2 = e2)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (134), (158), (159), (162), (164),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (168), (169), (170), (194), (213), (235),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (238), (242), (297), (380), (381),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (3011), (3013), (3017), (3022), (3023),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (3806), (3809), (3811), (3817), (3841), (3843),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (3844), (3882), (function-axioms) are inconsistent
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1611.
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (3883)  all_36_2 = e2
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (39), (113), (117), (120), (123), (133),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (145), (158), (159), (162), (163), (164), (165),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (197), (198), (201),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (216), (221), (222), (223), (226), (227),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (230), (232), (235), (236), (237), (238),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (242), (243), (244), (245), (266), (269),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (280), (328), (381), (391), (3011), (3012),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (3014), (3016), (3017), (3022), (3023), (3805),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (3806), (3809), (3816), (3817), (3824), (3827),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (3841), (3843), (3844), (3845), (3860), (3861),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (3883), (function-axioms) are inconsistent by
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1594.
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |   (3884)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3884) implies:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |   (3885)   ~ (all_20_1 = e3)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |   (3886)  op(e0, e1) = all_20_1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_20_1,
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (3824), (3886) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | |   (3887)  all_20_1 = e0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3852) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3888)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_34_1 & $i(all_34_0) &
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3888) implies:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3889)  op(e0, e1) = all_34_1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3890)  op(all_34_1, e0) = all_34_0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_34_1,
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (3824), (3889) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3891)  all_34_1 = e0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3890), (3891) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3892)  op(e0, e0) = all_34_0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_34_0,
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (3861), (3892) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3893)  all_34_0 = e1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (39), (85), (113), (117),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (120), (123), (133), (134), (145), (158), (159),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (165), (167), (168), (169),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (170), (194), (197), (198), (201), (213), (216),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (226), (227), (228), (230),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (232), (235), (236), (237), (238), (239), (242),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (266), (269), (270), (280),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (297), (328), (380), (381), (391), (3011), (3012),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3013), (3014), (3016), (3017), (3022), (3023),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3805), (3806), (3809), (3811), (3816), (3817),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3824), (3827), (3841), (3843), (3844), (3845),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3860), (3861), (function-axioms) are inconsistent
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1593.
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3894)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 &
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3894) implies:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3895)   ~ (all_34_1 = e2)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3896)  op(e0, e1) = all_34_1
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_34_1,
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (3824), (3896) gives:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3897)  all_34_1 = e0
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3895), (3897) imply:
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |   (3898)   ~ (e2 = e0)
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (39), (85), (113), (117),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (120), (123), (133), (134), (145), (158), (159),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (165), (167), (168), (169),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (170), (194), (197), (198), (201), (213), (216),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (226), (227), (228), (230),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (232), (235), (236), (237), (238), (239), (242),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (266), (269), (270), (280),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (297), (328), (380), (381), (391), (3011), (3012),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3013), (3014), (3016), (3017), (3022), (3023),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3805), (3806), (3809), (3811), (3816), (3817),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3824), (3827), (3841), (3843), (3844), (3845),
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            (3860), (3861), (function-axioms) are inconsistent
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1593.
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.95  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | |   (3899)  all_54_15 = e0
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (3830), (3899) are inconsistent by
% 231.54/42.96  | | | | | | | | | | | | | | | | | |            sub-proof #1737.
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | |   (3900)  all_18_2 = e0
% 231.54/42.96  | | | | | | | | | | |   (3901)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0
% 231.54/42.96  | | | | | | | | | | |             & op(e1, e0) = all_18_1 & $i(all_18_0) &
% 231.54/42.96  | | | | | | | | | | |             $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1, e0)
% 231.54/42.96  | | | | | | | | | | |             = all_18_1 & $i(all_18_1))
% 231.54/42.96  | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | COMBINE_EQS: (339), (3900) imply:
% 231.54/42.96  | | | | | | | | | | |   (3902)  all_6_2 = e0
% 231.54/42.96  | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | SIMP: (3902) implies:
% 231.54/42.96  | | | | | | | | | | |   (3903)  all_6_2 = e0
% 231.54/42.96  | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | COMBINE_EQS: (332), (3903) imply:
% 231.54/42.96  | | | | | | | | | | |   (3904)  all_28_2 = e0
% 231.54/42.96  | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | COMBINE_EQS: (266), (3903) imply:
% 231.54/42.96  | | | | | | | | | | |   (3905)  all_56_21 = e0
% 231.54/42.96  | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | REDUCE: (383), (3903) imply:
% 231.54/42.96  | | | | | | | | | | |   (3906)   ~ (all_52_11 = e0)
% 231.54/42.96  | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | REDUCE: (39), (3903) imply:
% 231.54/42.96  | | | | | | | | | | |   (3907)  op(e1, e1) = e0
% 231.54/42.96  | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | BETA: splitting (216) gives:
% 231.54/42.96  | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | |   (3908)  all_58_15 = e0 & op(e0, e0) = e0
% 231.54/42.96  | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | ALPHA: (3908) implies:
% 231.54/42.96  | | | | | | | | | | | |   (3909)  all_58_15 = e0
% 231.54/42.96  | | | | | | | | | | | |   (3910)  op(e0, e0) = e0
% 231.54/42.96  | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0,
% 231.54/42.96  | | | | | | | | | | | |              e0, e0, simplifying with (36), (3910) gives:
% 231.54/42.96  | | | | | | | | | | | |   (3911)  all_4_2 = e0
% 231.54/42.96  | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | COMBINE_EQS: (254), (3911) imply:
% 231.54/42.96  | | | | | | | | | | | |   (3912)  all_56_31 = e0
% 231.54/42.96  | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | REDUCE: (387), (3911) imply:
% 231.54/42.96  | | | | | | | | | | | |   (3913)   ~ (all_52_12 = e0)
% 231.54/42.96  | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | REDUCE: (389), (3911) imply:
% 231.54/42.96  | | | | | | | | | | | |   (3914)   ~ (all_52_14 = e0)
% 231.54/42.96  | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | REDUCE: (390), (3911) imply:
% 231.54/42.96  | | | | | | | | | | | |   (3915)   ~ (e2 = e0)
% 231.54/42.96  | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | BETA: splitting (73) gives:
% 231.54/42.96  | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | |   (3916)   ~ (all_28_2 = e0)
% 231.54/42.96  | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | REDUCE: (3904), (3916) imply:
% 231.54/42.96  | | | | | | | | | | | | |   (3917)  $false
% 231.54/42.96  | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | CLOSE: (3917) is inconsistent.
% 231.54/42.96  | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | |   (3918)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0
% 231.54/42.96  | | | | | | | | | | | | |             & op(e1, e0) = all_28_1 & $i(all_28_0) &
% 231.54/42.96  | | | | | | | | | | | | |             $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0)
% 231.54/42.96  | | | | | | | | | | | | |             = all_28_1 & $i(all_28_1))
% 231.54/42.96  | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | BETA: splitting (103) gives:
% 231.54/42.96  | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | |   (3919)   ~ (all_48_2 = e0)
% 231.54/42.96  | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | REDUCE: (3010), (3919) imply:
% 231.54/42.96  | | | | | | | | | | | | | |   (3920)  $false
% 231.54/42.96  | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | CLOSE: (3920) is inconsistent.
% 231.54/42.96  | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | |   (3921)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 231.54/42.96  | | | | | | | | | | | | | |             & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 231.54/42.96  | | | | | | | | | | | | | |             $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 231.54/42.96  | | | | | | | | | | | | | |             = all_48_1 & $i(all_48_1))
% 231.54/42.96  | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 231.54/42.96  | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | |   (3922)   ~ (all_50_2 = e0)
% 231.54/42.96  | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | REDUCE: (3803), (3922) imply:
% 231.54/42.96  | | | | | | | | | | | | | | |   (3923)  $false
% 231.54/42.96  | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | CLOSE: (3923) is inconsistent.
% 231.54/42.96  | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | |   (3924)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 231.54/42.96  | | | | | | | | | | | | | | |             & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 231.54/42.96  | | | | | | | | | | | | | | |             $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 231.54/42.96  | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 231.54/42.96  | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | |   (3925)  all_54_1 = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (3925) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | |   (3926)  all_52_4 = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | REDUCE: (136), (3926) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | |   (3927)   ~ (all_52_6 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | SIMP: (3927) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | |   (3928)   ~ (all_52_6 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | REDUCE: (135), (3926) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | |   (3929)   ~ (all_52_7 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | SIMP: (3929) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | |   (3930)   ~ (all_52_7 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | REDUCE: (134), (3926) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | |   (3931)   ~ (all_52_8 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | SIMP: (3931) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | |   (3932)   ~ (all_52_8 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | REDUCE: (133), (3926) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | |   (3933)   ~ (all_52_12 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | SIMP: (3933) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | |   (3934)   ~ (all_52_12 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | |   (3935)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | BETA: splitting (3935) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | |   (3936)  all_58_0 = e3 & op(e3, e3) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | ALPHA: (3936) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | |   (3937)  op(e3, e3) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (3012), (3805),
% 231.54/42.96  | | | | | | | | | | | | | | | | | |            (3806), (3937), (function-axioms) are inconsistent
% 231.54/42.96  | | | | | | | | | | | | | | | | | |            by sub-proof #1938.
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | |   (3938)  all_58_1 = e3 & op(e3, e2) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | ALPHA: (3938) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | |   (3939)  all_58_1 = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | |   (3940)  op(e3, e2) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | |   (3941)  all_54_2 = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (3932), (3941) are inconsistent by
% 231.54/42.96  | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | |   (3942)   ~ (all_54_2 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | |   (3943)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | |   (3944)  all_54_6 = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3944) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | |   (3945)  all_52_9 = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | SIMP: (3945) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | |   (3946)  all_52_9 = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (3946) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | |   (3947)   ~ (all_52_1 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (3946) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | |   (3948)   ~ (all_52_11 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | SIMP: (3948) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | |   (3949)   ~ (all_52_11 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (3946) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | |   (3950)   ~ (all_52_13 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | SIMP: (3950) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | |   (3951)   ~ (all_52_13 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (3946) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | |   (3952)  op(e2, e1) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | |   (3953)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3953) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | |   (3954)  all_58_12 = e3 & op(e0, e3) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3954) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | |   (3955)  all_58_12 = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | |   (3956)  op(e0, e3) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | |   (3957)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (3934), (3951), (3957),
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | |            #1592.
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | |   (3958)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3958) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | |   (3959)  all_58_11 = e3 & op(e1, e0) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3959) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | |   (3960)  op(e1, e0) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (3961)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3961) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3962)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3962) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3963)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3963) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3964)  op(e2, e3) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (3947), (3964), (function-axioms) are
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3965)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3965) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3966)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3966) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3967)  op(e3, e2) = e2
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e2, e2,
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (3940), (3967) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3968)  e3 = e2
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (3968) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3969)  $false
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3969) is inconsistent.
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3970)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3970) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3971)  op(e3, e1) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3932), (3971), (function-axioms) are
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3972)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3972) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3973)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3973) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3974)  all_56_5 = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3975)  op(e1, e3) = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3976)  op(e3, e1) = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (3956) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3977)  all_52_3 = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (160), (3960) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3978)  all_52_14 = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (3975) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3979)  all_52_2 = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (3976) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3980)  all_52_8 = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (3980) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3981)   ~ (all_52_11 = e1)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3981) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3982)   ~ (all_52_11 = e1)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (3980) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3983)   ~ (all_52_12 = e1)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3983) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3984)   ~ (all_52_12 = e1)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3932), (3980) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3985)   ~ (e3 = e1)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3986)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3986) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3987)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3987) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3988)  op(e3, all_56_1) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3804), (3988) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3989)  op(e3, e0) = e3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3934), (3989), (function-axioms) are
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3990)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_3 & $i(all_56_3)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3990) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3991)  op(e2, e3) = all_56_3
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3992)  op(e2, all_56_3) = e2
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3993)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3993) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3994)  all_58_1 = e1 & op(e3, e2) = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3994) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3995)  op(e3, e2) = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3940), (3995), (function-axioms) are
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3996)  all_58_3 = e1 & op(e2, e2) = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3022), (3996) are inconsistent by sub-proof
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1591.
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3997)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3997) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3998)  all_58_7 = e1 & op(e1, e2) = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3998) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3999)  all_58_7 = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4000)  op(e1, e2) = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4001)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4001) gives:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4002)  all_58_12 = e1 & op(e0, e3) = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4002) implies:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4003)  all_58_12 = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3955), (4003) imply:
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4004)  e3 = e1
% 231.54/42.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (3023), (3939), (3999), (4000), (4004),
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1624.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4005)  all_58_13 = e1 & op(e0, e2) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4005) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4006)  all_58_13 = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (237), (3023), (3939), (3999),
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4006), (function-axioms) are inconsistent by
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1588.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4007)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4007) gives:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4008)  all_58_14 = e1 & op(e0, e1) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4008) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4009)  op(e0, e1) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3982), (4009), (function-axioms) are
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2272.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4010)  all_58_15 = e1 & op(e0, e0) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4010) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4011)  op(e0, e0) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3910), (4011), (function-axioms) are
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4012)  all_58_13 = e1 & op(e0, e2) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4012) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4013)  all_58_13 = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4014)  op(e0, e2) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4015)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4015) gives:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4016)  all_58_0 = e2 & op(e3, e3) = e2
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4016) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4017)  op(e3, e3) = e2
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3809), (4017), (function-axioms) are
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4018)  all_58_2 = e2 & op(e2, e3) = e2
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4018) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4019)  op(e2, e3) = e2
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4020)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3023), (3939), (4020),
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1589.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4021)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4021) gives:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4022)  all_58_7 = e2 & op(e1, e2) = e2
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4022) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4023)  all_58_7 = e2
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4024)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4024) gives:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4025)  all_58_9 = e1 & op(e3, e0) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3984), (4025), (function-axioms) are
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4026)  all_58_10 = e1 & op(e2, e0) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4026) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4027)  op(e2, e0) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3007) gives:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_3,
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (3991), (4019) gives:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4028)  all_56_3 = e2
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3992), (4028) imply:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4029)  op(e2, e2) = e2
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (170), (235), (3013), (4014), (4023),
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4029), (function-axioms) are inconsistent by
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1586.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4030)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4030) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4031)   ~ (all_14_1 = e1)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4032)  op(e2, e0) = all_14_1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3921), (4027), (4031), (4032), (function-axioms)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1584.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4033)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (3910), (3960), (4033),
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1583.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4034)  all_58_13 = e2 & op(e0, e2) = e2
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4013), (4034) are inconsistent by sub-proof
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2078.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4035)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (3955), (3975), (4035),
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1582.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4036)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4036) gives:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4037)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_5 & $i(all_56_5)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4037) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4038)  op(e1, all_56_5) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3974), (4038) imply:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4039)  op(e1, e1) = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3907), (4039), (function-axioms) are
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4040)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_7 & $i(all_56_7)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4040) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4041)  op(e0, e3) = all_56_7
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4042)  op(e0, all_56_7) = e0
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3956), (4041), (4042), (function-axioms) are
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2070.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4043)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (168), (3806), (3934), (4043),
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1794.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (4044)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4044) gives:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4045)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (3912), (3952), (4045),
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1581.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4046)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (164), (3017), (3914), (3960), (4046),
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1892.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | |   (4047)  all_58_15 = e3 & op(e0, e0) = e3
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4047) implies:
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | |   (4048)  op(e0, e0) = e3
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3910), (4048), (function-axioms) are
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.97  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | |   (4049)  all_58_13 = e3 & op(e0, e2) = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3930), (4049), (function-axioms) are
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | |   (4050)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (3910), (3949), (4050),
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | |            #1580.
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | End of split
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | |   (4051)   ~ (all_54_6 = e3)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (4051) imply:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | |   (4052)   ~ (all_52_9 = e3)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | |   (4053)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (3932), (4052), (4053),
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | |            #1628.
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | |   (4054)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4054) gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | |   (4055)  all_58_8 = e3 & op(e1, e1) = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3907), (4055), (function-axioms) are
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | |   (4056)  all_58_14 = e3 & op(e0, e1) = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4056) implies:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | |   (4057)  all_58_14 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | |   (4058)  op(e0, e1) = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (4058) gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | |   (4059)  all_52_11 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | |   (4060)  all_54_7 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4060) imply:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | |   (4061)  all_52_13 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (4061) imply:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | |   (4062)   ~ (all_52_1 = e3)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (4061) imply:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | |   (4063)   ~ (all_52_14 = e3)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4063) implies:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | |   (4064)   ~ (all_52_14 = e3)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (4061) imply:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | |   (4065)  op(e2, e0) = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | |   (4066)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (3012), (3805),
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | |            (3806), (4062), (4066), (function-axioms) are
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1579.
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | |   (4067)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4067) gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (4068)  all_58_6 = e3 & op(e1, e3) = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4068) implies:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (4069)  all_58_6 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (4070)  op(e1, e3) = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3007) gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4071)   ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_14_1 & $i(all_14_0) &
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4071) implies:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4072)   ~ (all_14_0 = e3)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4073)  op(e2, e0) = all_14_1
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4074)  op(all_14_1, e2) = all_14_0
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3921) gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4075)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_48_1 & $i(all_48_0) &
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4075) implies:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4076)  op(e2, e0) = all_48_1
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4077)  op(all_48_1, e2) = all_48_0
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_1, e0, e2, simplifying with (4073), (4076)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4078)  all_48_1 = all_14_1
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1,
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (4065), (4076) gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4079)  all_48_1 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4078), (4079) imply:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4080)  all_14_1 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4080) implies:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4081)  all_14_1 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4077), (4079) imply:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4082)  op(e3, e2) = all_48_0
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4074), (4081) imply:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4083)  op(e3, e2) = all_14_0
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_0,
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (3940), (4082) gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4084)  all_48_0 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_0,
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_0, e2, e3, simplifying with (4082), (4083)
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4085)  all_48_0 = all_14_0
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4084), (4085) imply:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4086)  all_14_0 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4086) implies:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4087)  all_14_0 = e3
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4072), (4087) imply:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4088)  $false
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4088) is inconsistent.
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4089)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4089) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4090)   ~ (all_48_1 = e3)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4091)  op(e2, e0) = all_48_1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4065), (4073), (4090), (4091), (function-axioms)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1632.
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4092)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4092) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4093)   ~ (all_14_1 = e1)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4094)  op(e2, e0) = all_14_1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4095)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4095) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4096)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_9 & $i(all_56_9)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4096) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4097)  op(e3, e2) = all_56_9
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4098)  op(e3, all_56_9) = e3
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_9,
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (3940), (4097) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4099)  all_56_9 = e3
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4098), (4099) imply:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4100)  op(e3, e3) = e3
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (239), (241),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (3806), (4069), (4100), (function-axioms)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1572.
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4101)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4101) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4102)  op(e2, all_56_11) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3011), (4102) imply:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4103)  op(e2, e0) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4065), (4103), (function-axioms) are
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4104)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4104) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4105)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4105) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4106)  op(e1, e2) = all_56_13
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4107)  op(e1, all_56_13) = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (162), (4106)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4108)  all_56_13 = all_52_6
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4107), (4108) imply:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4109)  op(e1, all_52_6) = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4110)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4110) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4111)  all_58_4 = e2 & op(e3, e1) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4111) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4112)  all_58_4 = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (221), (224), (242),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3800), (3809), (3907), (3910), (3924), (3940),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4065), (4070), (4106), (4107), (4112),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1565.
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4113)  all_58_5 = e2 & op(e2, e1) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4113) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4114)  all_58_5 = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4115)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4115) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4116)  all_58_4 = e1 & op(e3, e1) = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4116) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4117)  all_58_4 = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4118)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3809), (3940), (4118),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1857.
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4119)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4119) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4120)  all_58_4 = e2 & op(e3, e1) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4120) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4121)  all_58_4 = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (221), (224), (242),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3800), (3809), (3907), (3910), (3924), (3940),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4065), (4070), (4106), (4107), (4121),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1565.
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4122)  all_58_9 = e2 & op(e3, e0) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4122) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4123)  all_58_9 = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4124)  op(e3, e0) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4125)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4125) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4126)  all_58_9 = e1 & op(e3, e0) = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (221), (224), (3800),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3907), (3910), (3924), (4065), (4070), (4106),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4107), (4126), (function-axioms) are inconsistent
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1566.
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4127)  all_58_10 = e1 & op(e2, e0) = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4127) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4128)  op(e2, e0) = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3921), (4093), (4094), (4128), (function-axioms)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1584.
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4129)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4129) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4130)  all_58_11 = e1 & op(e1, e0) = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4130) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4131)  all_58_11 = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4132)  op(e1, e0) = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4133)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4133) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4134)  all_58_6 = e2 & op(e1, e3) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4069), (4134) are inconsistent by sub-proof
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2219.
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4135)  all_58_7 = e2 & op(e1, e2) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4135) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4136)  all_58_7 = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4137)  op(e1, e2) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4138)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4138) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4139)  all_58_2 = e1 & op(e2, e3) = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4139) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4140)  op(e2, e3) = e1
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4141)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4141) gives:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4142)  all_58_0 = e2 & op(e3, e3) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4142) implies:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4143)  op(e3, e3) = e2
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (242),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (3013), (4123), (4124), (4143),
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1559.
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.88/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4144)  all_58_2 = e2 & op(e2, e3) = e2
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4144) implies:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4145)  op(e2, e3) = e2
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4140), (4145), (function-axioms) are
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1633.
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4146)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4146) gives:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4147)  all_58_6 = e2 & op(e1, e3) = e2
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4069), (4147) are inconsistent by sub-proof
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2219.
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4148)  all_58_12 = e2 & op(e0, e3) = e2
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4148) implies:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4149)  all_58_12 = e2
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4150)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4150) gives:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4151)  all_58_12 = e1 & op(e0, e3) = e1
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4151) implies:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4152)  all_58_12 = e1
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4149), (4152) imply:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4153)  e2 = e1
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4136), (4153) imply:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4154)  all_58_7 = e1
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (223), (225), (4069),
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4131), (4132), (4154), (function-axioms) are
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1553.
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4155)  all_58_13 = e1 & op(e0, e2) = e1
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4156)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4156) gives:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4155) implies:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4157)  all_58_13 = e1
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (4132) gives:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4158)  all_52_14 = e1
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (4137) gives:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4159)  all_52_6 = e2
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (168), (4124) gives:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4160)  all_52_12 = e2
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3934), (4160) imply:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4161)   ~ (e3 = e2)
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4109), (4159) imply:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4162)  op(e1, e2) = e1
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3924) gives:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e1, e2,
% 231.95/42.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (4137), (4162) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4163)  e2 = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4136), (4163) imply:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4164)  all_58_7 = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (237), (3023), (3939), (4157),
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4164), (function-axioms) are inconsistent by
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1588.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4165)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4165) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4166)   ~ (all_50_1 = e2)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4167)  op(e3, e0) = all_50_1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4124), (4166), (4167), (function-axioms) are
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1884.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4168)  all_58_13 = e2 & op(e0, e2) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4168) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4169)  all_58_13 = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (236), (3022), (3939), (4136),
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4169) are inconsistent by sub-proof #1750.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4170)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4170) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4171)  all_58_14 = e2 & op(e0, e1) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4171) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4172)  all_58_14 = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4057), (4172) are inconsistent by sub-proof
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2117.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4173)  all_58_15 = e2 & op(e0, e0) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4173) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4174)  op(e0, e0) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3910), (4174), (function-axioms) are
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4175)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (158), (219), (3910), (3930),
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4149), (4175), (function-axioms) are inconsistent
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1549.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4176)  all_58_3 = e1 & op(e2, e2) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4176) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4177)  all_58_3 = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3022), (4177) imply:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4178)  e1 = e0
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (228), (229), (3907),
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4057), (4117), (4178), (function-axioms) are
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1623.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4179)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4179) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4180)  all_58_5 = e1 & op(e2, e1) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4180) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4181)  all_58_5 = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4114), (4181) imply:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4182)  e2 = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4136), (4182) imply:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4183)  all_58_7 = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (223), (225), (4069),
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4131), (4132), (4183), (function-axioms) are
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1553.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4184)  all_58_10 = e1 & op(e2, e0) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4184) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4185)  op(e2, e0) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3921), (4093), (4094), (4185), (function-axioms)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1584.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4186)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4186) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4187)  all_58_8 = e2 & op(e1, e1) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4187) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4188)  op(e1, e1) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3907), (4188), (function-axioms) are
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4189)  all_58_11 = e2 & op(e1, e0) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4189) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4190)  op(e1, e0) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4132), (4190), (function-axioms) are
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2019.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4191)  all_58_15 = e1 & op(e0, e0) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4191) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4192)  op(e0, e0) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3910), (4192), (function-axioms) are
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4193)  all_58_5 = e1 & op(e2, e1) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4114), (4193) are inconsistent by sub-proof
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1548.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4194)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4194) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4195)  all_58_8 = e1 & op(e1, e1) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4195) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4196)  op(e1, e1) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3907), (4196), (function-axioms) are
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4197)  all_58_14 = e1 & op(e0, e1) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4057), (4197) are inconsistent by sub-proof
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1900.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4198)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3907), (4057), (4198),
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1547.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4199)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4199) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4200)  op(e0, e2) = all_56_15
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4201)  op(e0, all_56_15) = e0
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (158), (4200)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4202)  all_56_15 = all_52_7
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4201), (4202) imply:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4203)  op(e0, all_52_7) = e0
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4204)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4204) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4205)  all_58_4 = e2 & op(e3, e1) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4205) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4206)  all_58_4 = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4207)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (3809), (3940), (4207),
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1571.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4208)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4208) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4209)  all_58_4 = e1 & op(e3, e1) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4206), (4209) are inconsistent by sub-proof
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2168.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4210)  all_58_9 = e1 & op(e3, e0) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4210) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4211)  all_58_9 = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4212)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4212) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4213)  all_58_9 = e2 & op(e3, e0) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4211), (4213) are inconsistent by sub-proof
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1745.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4214)  all_58_10 = e2 & op(e2, e0) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4214) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4215)  op(e2, e0) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4065), (4215), (function-axioms) are
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4216)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4216) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4217)  all_58_11 = e2 & op(e1, e0) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4217) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4218)  op(e1, e0) = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4219)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4219) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4220)  all_58_6 = e1 & op(e1, e3) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4220) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4221)  op(e1, e3) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4070), (4221), (function-axioms) are
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4222)  all_58_7 = e1 & op(e1, e2) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4222) implies:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4223)  all_58_7 = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4224)  op(e1, e2) = e1
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4225)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 231.95/42.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3023), (3940), (4225),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1546.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4226)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4226) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4227)  all_58_7 = e2 & op(e1, e2) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4227) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4228)  all_58_7 = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4223), (4228) are inconsistent by sub-proof
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2134.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4229)  all_58_13 = e2 & op(e0, e2) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4229) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4230)  op(e0, e2) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4231)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4231) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4232)  all_58_12 = e1 & op(e0, e3) = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4232) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4233)  all_58_12 = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4234)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4234) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4235)  all_58_12 = e2 & op(e0, e3) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (160), (217),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (223), (224), (225), (226), (237), (3023),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3907), (3910), (3930), (3939), (3940), (4058),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4064), (4069), (4070), (4203), (4235),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1543.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (4230) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4236)  all_52_7 = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (160), (4218) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4237)  all_52_14 = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4203), (4236) imply:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4238)  op(e0, e2) = e0
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4230), (4238), (function-axioms) are
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4239)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4239) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4240)  all_58_14 = e2 & op(e0, e1) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4240) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4241)  all_58_14 = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (158), (216), (219),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3930), (4230), (4233), (4241), (function-axioms)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1536.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4242)  all_58_15 = e2 & op(e0, e0) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4242) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4243)  op(e0, e0) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3910), (4243), (function-axioms) are
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4244)  all_58_13 = e1 & op(e0, e2) = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4244) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4245)  all_58_13 = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (237), (3023), (3939), (4223),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4245), (function-axioms) are inconsistent by
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1588.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4246)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4246) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4247)  all_58_14 = e1 & op(e0, e1) = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4247) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4248)  all_58_14 = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4057), (4248) imply:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4249)  e3 = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3939), (4249) imply:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4250)  all_58_1 = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (3023), (4223), (4224), (4250),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1714.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4251)  all_58_15 = e1 & op(e0, e0) = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4251) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4252)  op(e0, e0) = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3910), (4252), (function-axioms) are
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4253)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (3907), (4218), (4253),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1567.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4254)  all_58_15 = e2 & op(e0, e0) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4254) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4255)  op(e0, e0) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3910), (4255), (function-axioms) are
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4256)  all_58_5 = e2 & op(e2, e1) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4256) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4257)  all_58_5 = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4258)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4258) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4259)  all_58_2 = e1 & op(e2, e3) = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4259) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4260)  op(e2, e3) = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4261)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4261) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4262)  all_58_0 = e2 & op(e3, e3) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4262) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4263)  op(e3, e3) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3809), (4263), (function-axioms) are
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4264)  all_58_2 = e2 & op(e2, e3) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4264) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4265)  op(e2, e3) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4260), (4265), (function-axioms) are
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1633.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4266)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4266) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4267)  all_58_6 = e2 & op(e1, e3) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4069), (4267) are inconsistent by sub-proof
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2219.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4268)  all_58_12 = e2 & op(e0, e3) = e2
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (160), (217),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (223), (224), (225), (226), (237), (3023),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3907), (3910), (3930), (3939), (3940), (4058),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4064), (4069), (4070), (4203), (4268),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1543.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4269)  all_58_3 = e1 & op(e2, e2) = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3022), (4269) are inconsistent by sub-proof
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1752.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4270)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4270) gives:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4271)  all_58_5 = e1 & op(e2, e1) = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4257), (4271) are inconsistent by sub-proof
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1548.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4272)  all_58_10 = e1 & op(e2, e0) = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4272) implies:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4273)  op(e2, e0) = e1
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3921), (4093), (4094), (4273), (function-axioms)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1584.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4274)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3907), (4057), (4274),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1547.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (4275)  all_58_12 = e3 & op(e0, e3) = e3
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (162),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (239), (241), (243), (391), (3928), (4064),
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (4275), (function-axioms) are inconsistent by
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1528.
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | |   (4276)   ~ (all_54_7 = e3)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (4276) imply:
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | |   (4277)   ~ (all_52_13 = e3)
% 231.95/43.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | |   (4278)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4278) gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (4279)  all_58_2 = e3 & op(e2, e3) = e3
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4279) implies:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (4280)  all_58_2 = e3
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4281)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (3934), (4277), (4281),
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1592.
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4282)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4282) gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4283)  all_58_11 = e3 & op(e1, e0) = e3
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4283) implies:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4284)  op(e1, e0) = e3
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (160), (4284) gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4285)  all_52_14 = e3
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3901) gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4286)   ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 &
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_18_1 & $i(all_18_0) &
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4286) implies:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4287)   ~ (all_18_0 = e2)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4288)  op(e1, e0) = all_18_1
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4289)  op(all_18_1, e1) = all_18_0
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3918) gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4290)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_28_1 & $i(all_28_0) &
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4290) implies:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4291)  op(e1, e0) = all_28_1
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4292)  op(all_28_1, e1) = all_28_0
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (4284), (4291) gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4293)  all_28_1 = e3
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_1, e0, e1, simplifying with (4288), (4291)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4294)  all_28_1 = all_18_1
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4293), (4294) imply:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4295)  all_18_1 = e3
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4295) implies:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4296)  all_18_1 = e3
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4292), (4293) imply:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4297)  op(e3, e1) = all_28_0
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4289), (4296) imply:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4298)  op(e3, e1) = all_18_0
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_18_0, e1, e3, simplifying with (169), (4298)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4299)  all_52_8 = all_18_0
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_0, e1, e3, simplifying with (169), (4297)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4300)  all_52_8 = all_28_0
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4299), (4300) imply:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4301)  all_28_0 = all_18_0
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (4299) imply:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4302)  all_54_2 = all_18_0
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (4299) imply:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4303)   ~ (all_52_12 = all_18_0)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4303) implies:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4304)   ~ (all_52_12 = all_18_0)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3807), (4299) imply:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4305)   ~ (all_18_0 = e0)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4306)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3809), (3940), (4306),
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1857.
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4307)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4307) gives:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4308)  all_58_4 = e2 & op(e3, e1) = e2
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (168), (170), (242), (281), (3807), (3809),
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3943), (4287), (4302), (4304), (4305), (4308),
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1525.
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4309)  all_58_9 = e2 & op(e3, e0) = e2
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4309) implies:
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4310)  all_58_9 = e2
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4311)  op(e3, e0) = e2
% 231.95/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (134), (159), (168),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (211), (228), (229), (232), (240),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (242), (281), (3007), (3022), (3023), (3806),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3807), (3809), (3905), (3907), (3921), (3932),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3940), (3943), (4057), (4058), (4280), (4284),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4287), (4302), (4304), (4305), (4310), (4311),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1517.
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4312)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4312) implies:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4313)   ~ (all_28_1 = e2)
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4314)  op(e1, e0) = all_28_1
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (4284), (4314) gives:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4315)  all_28_1 = e3
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_1, e0, e1, simplifying with (4288), (4314)
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4316)  all_28_1 = all_18_1
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4315), (4316) imply:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4317)  all_18_1 = e3
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4317) implies:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4318)  all_18_1 = e3
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4289), (4318) imply:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4319)  op(e3, e1) = all_18_0
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_18_0, e1, e3, simplifying with (169), (4319)
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4320)  all_52_8 = all_18_0
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (4320) imply:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4321)  all_54_2 = all_18_0
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (4320) imply:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4322)   ~ (all_52_12 = all_18_0)
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4322) implies:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4323)   ~ (all_52_12 = all_18_0)
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3807), (4320) imply:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4324)   ~ (all_18_0 = e0)
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4325)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3809), (3940), (4325),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1857.
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4326)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4326) gives:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4327)  all_58_4 = e2 & op(e3, e1) = e2
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (168), (170), (242), (281), (3807), (3809),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3943), (4287), (4321), (4323), (4324), (4327),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1525.
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4328)  all_58_9 = e2 & op(e3, e0) = e2
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4328) implies:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4329)  all_58_9 = e2
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4330)  op(e3, e0) = e2
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (134), (159), (168),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (211), (228), (229), (232), (240),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (242), (281), (3007), (3022), (3023), (3806),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3807), (3809), (3905), (3907), (3921), (3932),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3940), (3943), (4057), (4058), (4280), (4284),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4287), (4321), (4323), (4324), (4329), (4330),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1517.
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4331)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 &
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3918), (4284), (4331), (function-axioms) are
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1767.
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4332)  all_58_15 = e3 & op(e0, e0) = e3
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4332) implies:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4333)  op(e0, e0) = e3
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3910), (4333), (function-axioms) are
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (4334)  all_58_3 = e3 & op(e2, e2) = e3
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3022), (4334) are inconsistent by sub-proof
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | |            #1516.
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | |   (4335)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (4052), (4277), (4335),
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | |            #1649.
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.01  | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | |   (4336)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 232.04/43.01  | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 232.04/43.01  | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (3932), (3934), (4336),
% 232.04/43.01  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.04/43.01  | | | | | | | | | | | | | | | | |            #1515.
% 232.04/43.01  | | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | | End of split
% 232.04/43.01  | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | Case 2:
% 232.04/43.01  | | | | | | | | | | | | | | | | 
% 232.04/43.01  | | | | | | | | | | | | | | | |   (4337)   ~ (all_54_1 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | |   (4338)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 232.04/43.02  | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | REDUCE: (282), (4337) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | |   (4339)   ~ (all_52_4 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | |   (4340)  all_54_11 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (4340) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | |   (4341)  all_52_14 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | SIMP: (4341) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | |   (4342)  all_52_14 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | REDUCE: (141), (4342) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | |   (4343)   ~ (all_52_2 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | REDUCE: (126), (4342) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | |   (4344)   ~ (all_52_6 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | REDUCE: (112), (4342) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | |   (4345)   ~ (all_52_12 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | REDUCE: (110), (4342) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | |   (4346)   ~ (all_52_13 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | REDUCE: (160), (4342) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | |   (4347)  op(e1, e0) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | BETA: splitting (3918) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | |   (4348)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 232.04/43.02  | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_28_1 & $i(all_28_0) &
% 232.04/43.02  | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | ALPHA: (4348) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | |   (4349)   ~ (all_28_0 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | |   (4350)  op(e1, e0) = all_28_1
% 232.04/43.02  | | | | | | | | | | | | | | | | | |   (4351)  op(all_28_1, e1) = all_28_0
% 232.04/43.02  | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |   (4352)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (170), (239), (3012),
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |            (3805), (3806), (4339), (4352), (function-axioms)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1514.
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |   (4353)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | BETA: splitting (4353) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | |   (4354)  all_58_4 = e3 & op(e3, e1) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | ALPHA: (4354) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | |   (4355)  op(e3, e1) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | |   (4356)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (4345), (4346), (4356),
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | |            #1592.
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | |   (4357)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4357) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |   (4358)  all_58_11 = e3 & op(e1, e0) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (4347), (4350) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |   (4359)  all_28_1 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (4355) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |   (4360)  all_52_8 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4351), (4359) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |   (4361)  op(e3, e1) = all_28_0
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4349), (4355), (4361), (function-axioms) are
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1783.
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |   (4362)  all_58_15 = e3 & op(e0, e0) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4362) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |   (4363)  op(e0, e0) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3910), (4363), (function-axioms) are
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | |   (4364)  all_58_9 = e3 & op(e3, e0) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | ALPHA: (4364) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | |   (4365)  op(e3, e0) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4345), (4365), (function-axioms) are
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.02  | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | |   (4366)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 232.04/43.02  | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | ALPHA: (4366) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | |   (4367)   ~ (all_28_1 = e2)
% 232.04/43.02  | | | | | | | | | | | | | | | | | |   (4368)  op(e1, e0) = all_28_1
% 232.04/43.02  | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |   (4369)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (170), (239), (3012),
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |            (3805), (3806), (4339), (4369), (function-axioms)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1514.
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |   (4370)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | BETA: splitting (4370) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | |   (4371)  all_58_4 = e3 & op(e3, e1) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | ALPHA: (4371) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | |   (4372)  all_58_4 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | |   (4373)  op(e3, e1) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3901) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | |   (4374)   ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 &
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_18_1 & $i(all_18_0) &
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4374) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | |   (4375)  op(e1, e0) = all_18_1
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |   (4376)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4376) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4377)  all_58_1 = e3 & op(e3, e2) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4377) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4378)  op(e3, e2) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (4339), (4378), (function-axioms) are
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4379)  all_58_3 = e3 & op(e2, e2) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4379) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4380)  all_58_3 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3022), (4380) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4381)  e3 = e0
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4381) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4382)  e3 = e0
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4372), (4382) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4383)  all_58_4 = e0
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (242), (244),
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |            (246), (3809), (4339), (4383), (function-axioms)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1512.
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |   (4384)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4384) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4385)  all_58_7 = e3 & op(e1, e2) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4385) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4386)  op(e1, e2) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4344), (4386), (function-axioms) are
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4387)  all_58_13 = e3 & op(e0, e2) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4387) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4388)  all_58_13 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | |   (4389)  op(e0, e2) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | |   (4390)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (4345), (4346), (4390),
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | |            #1592.
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | |   (4391)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4391) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4392)  all_58_11 = e3 & op(e1, e0) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4392) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4393)  all_58_11 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (4389) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4394)  all_52_7 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |              all_28_1, e0, e1, simplifying with (4368), (4375)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4395)  all_28_1 = all_18_1
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (4347), (4368) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4396)  all_28_1 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (4373) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4397)  all_52_8 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4395), (4396) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4398)  all_18_1 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4398) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4399)  all_18_1 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (4394) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4400)   ~ (all_52_3 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (4397) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4401)   ~ (all_52_9 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4401) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4402)   ~ (all_52_9 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (4397) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4403)   ~ (all_52_11 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4403) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4404)   ~ (all_52_11 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (4397) imply:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (4405)   ~ (all_52_12 = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4406)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4406) gives:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4407)  all_58_0 = e3 & op(e3, e3) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4407) implies:
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4408)  op(e3, e3) = e3
% 232.04/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (3012), (3805),
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3806), (4408), (function-axioms) are inconsistent
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1938.
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4409)  all_58_2 = e3 & op(e2, e3) = e3
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4409) implies:
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4410)  all_58_2 = e3
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4411)  op(e2, e3) = e3
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4412)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (3804), (4345), (4411), (4412),
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1511.
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4413)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4413) gives:
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4414)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_5 & $i(all_56_5)
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4414) implies:
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4415)  op(e1, e3) = all_56_5
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4416)  op(e1, all_56_5) = e1
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (4415)
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4417)  all_56_5 = all_52_2
% 232.10/43.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4418)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_19 & $i(all_56_19))
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4418) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4419)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_17 & $i(all_56_17)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (3012), (3805),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3806), (4373), (4419), (function-axioms) are
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1510.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4420)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_19 & $i(all_56_19)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4420) implies:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4421)  op(e2, e1) = all_56_19
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4422)  op(e2, all_56_19) = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (165), (4421)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4423)  all_56_19 = all_52_9
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4422), (4423) imply:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4424)  op(e2, all_52_9) = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4425)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3023), (4411), (4425),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1509.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4426)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4426) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4427)  all_58_5 = e2 & op(e2, e1) = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4427) implies:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4428)  all_58_5 = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4429)  op(e2, e1) = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4430)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4430) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4431)  all_58_2 = e1 & op(e2, e3) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4410), (4431) are inconsistent by sub-proof
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1765.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4432)  all_58_3 = e1 & op(e2, e2) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3022), (4432) are inconsistent by sub-proof
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1752.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4433)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4433) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4434)  all_58_5 = e1 & op(e2, e1) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4428), (4434) are inconsistent by sub-proof
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1548.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4435)  all_58_10 = e1 & op(e2, e0) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4435) implies:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4436)  all_58_10 = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4437)  op(e2, e0) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4438)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4438) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4439)  all_58_9 = e2 & op(e3, e0) = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4439) implies:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4440)  all_58_9 = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4441)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (221), (3909), (4373), (4393),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4428), (4436), (4440), (4441), (function-axioms)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1505.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4442)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4442) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4443)  all_58_8 = e1 & op(e1, e1) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4443) implies:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4444)  op(e1, e1) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3907), (4444), (function-axioms) are
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4445)  all_58_14 = e1 & op(e0, e1) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4445) implies:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4446)  op(e0, e1) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (224), (227),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (242), (3007), (3023), (3809), (3907),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3909), (3921), (4372), (4373), (4389), (4393),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4415), (4416), (4429), (4436), (4437), (4446),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1501.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4447)  all_58_10 = e2 & op(e2, e0) = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4447) implies:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4448)  all_58_10 = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4449)  op(e2, e0) = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (113), (157), (162),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (168), (220), (221), (222), (230),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (234), (235), (236), (237), (238),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (3017), (3022), (3023), (3800), (3809),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3907), (3909), (3910), (3913), (3924), (4345),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4346), (4388), (4389), (4393), (4402), (4404),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4410), (4424), (4448), (4449), (function-axioms)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1491.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4450)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (216),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (3017), (3910), (3914),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4346), (4367), (4368), (4450), (function-axioms)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1487.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4451)  all_58_10 = e2 & op(e2, e0) = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4451) implies:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4452)  all_58_10 = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4453)  op(e2, e0) = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (113), (157), (162),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (168), (220), (221), (222), (230),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (234), (235), (236), (237), (238),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (3017), (3022), (3023), (3800), (3809),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3907), (3909), (3910), (3913), (3924), (4345),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4346), (4388), (4389), (4393), (4402), (4404),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4410), (4424), (4452), (4453), (function-axioms)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1491.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4454)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_23 & $i(all_56_23))
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4454) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4455)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4455) implies:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4456)  op(e1, all_56_21) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3905), (4456) imply:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4457)  op(e1, e0) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e1, e0,
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (4347), (4457) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4458)  e3 = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4458) imply:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4459)  $false
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4459) is inconsistent.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4460)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_23 & $i(all_56_23)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4460) implies:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4461)  op(e0, e1) = all_56_23
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4462)  op(e0, all_56_23) = e0
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_23, e1, e0, simplifying with (157), (4461)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4463)  all_56_23 = all_52_11
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4462), (4463) imply:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4464)  op(e0, all_52_11) = e0
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4465)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3023), (4411), (4465),
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1509.
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4466)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4466) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4467)  all_58_5 = e2 & op(e2, e1) = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4467) implies:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4468)  all_58_5 = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4469)  op(e2, e1) = e2
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4470)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4470) gives:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4471)  all_58_4 = e1 & op(e3, e1) = e1
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4471) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4472)  op(e3, e1) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4373), (4472), (function-axioms) are
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1823.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4473)  all_58_5 = e1 & op(e2, e1) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4468), (4473) are inconsistent by sub-proof
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1548.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4474)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4474) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4475)  all_58_8 = e1 & op(e1, e1) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4475) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4476)  op(e1, e1) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3907), (4476), (function-axioms) are
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4477)  all_58_14 = e1 & op(e0, e1) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4477) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4478)  all_58_14 = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4479)  op(e0, e1) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4480)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4480) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4481)  all_58_12 = e2 & op(e0, e3) = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4481) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4482)  all_58_12 = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4483)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (3809), (4410), (4483),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1486.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4484)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4484) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4485)  all_58_6 = e1 & op(e1, e3) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4485) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4486)  all_58_6 = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4487)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4487) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4488)  all_58_2 = e1 & op(e2, e3) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4410), (4488) are inconsistent by sub-proof
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1765.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4489)  all_58_3 = e1 & op(e2, e2) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4489) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4490)  all_58_3 = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3022), (4490) imply:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4491)  e1 = e0
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4491) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4492)  e1 = e0
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4486), (4492) imply:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4493)  all_58_6 = e0
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (224), (225), (3907),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4393), (4493), (function-axioms) are inconsistent
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1978.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4494)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4494) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4495)  all_58_5 = e1 & op(e2, e1) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4495) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4496)  all_58_5 = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (4372),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4478), (4496) are inconsistent by sub-proof
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1481.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4497)  all_58_10 = e1 & op(e2, e0) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4497) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4498)  all_58_10 = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4499)  op(e2, e0) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (224), (227),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (242), (3007), (3023), (3809), (3907),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3909), (3921), (4372), (4373), (4389), (4393),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4415), (4416), (4469), (4479), (4498), (4499),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1501.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4500)  all_58_12 = e1 & op(e0, e3) = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4500) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4501)  all_58_12 = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4482), (4501) imply:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4502)  e2 = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4468), (4502) imply:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4503)  all_58_5 = e1
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (4372),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4478), (4503) are inconsistent by sub-proof
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1481.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4504)  all_58_13 = e2 & op(e0, e2) = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4504) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4505)  op(e0, e2) = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4389), (4505), (function-axioms) are
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4506)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (216),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (227), (229), (3017), (3910),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3914), (4346), (4372), (4468), (4478), (4506),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1479.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4507)  all_58_10 = e2 & op(e2, e0) = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4507) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4508)  all_58_10 = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4509)  op(e2, e0) = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (160), (162),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (170), (216), (218), (220), (221),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (225), (230), (235), (236), (237), (238),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (241), (244), (246), (3017), (3022),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3023), (3809), (3907), (3909), (3910), (3914),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4339), (4346), (4347), (4367), (4368), (4372),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4388), (4389), (4393), (4402), (4404), (4410),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4464), (4508), (4509), (function-axioms) are
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1462.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4510)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_7 & $i(all_56_7)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4510) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4511)  op(e0, e3) = all_56_7
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4512)  op(e0, all_56_7) = e0
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (159), (4511)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4513)  all_56_7 = all_52_3
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4512), (4513) imply:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4514)  op(e0, all_52_3) = e0
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4515)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_19 & $i(all_56_19))
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4515) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4516)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_17 & $i(all_56_17)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (3012), (3805),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3806), (4373), (4516), (function-axioms) are
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1510.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4517)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_19 & $i(all_56_19)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4517) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4518)  op(e2, e1) = all_56_19
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4519)  op(e2, all_56_19) = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (165), (4518)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4520)  all_56_19 = all_52_9
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4519), (4520) imply:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4521)  op(e2, all_52_9) = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4522)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3023), (4411), (4522),
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1509.
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4523)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4523) gives:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4524)  all_58_5 = e2 & op(e2, e1) = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4524) implies:
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4525)  all_58_5 = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4526)  op(e2, e1) = e2
% 232.10/43.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (160), (164),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (216), (218), (219), (220), (221), (222),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (227), (228), (229), (232), (235), (236),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (242), (3017), (3022), (3023),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3809), (3907), (3909), (3910), (3914), (4345),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4346), (4347), (4367), (4368), (4372), (4373),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4389), (4393), (4410), (4514), (4525), (4526),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1452.
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4527)  all_58_10 = e2 & op(e2, e0) = e2
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4527) implies:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4528)  all_58_10 = e2
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4529)  op(e2, e0) = e2
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (113), (157), (162),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (168), (220), (221), (222), (230),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (234), (235), (236), (237), (238),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (3017), (3022), (3023), (3800), (3809),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3907), (3909), (3910), (3913), (3924), (4345),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4346), (4388), (4389), (4393), (4402), (4404),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4410), (4521), (4528), (4529), (function-axioms)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1491.
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4530)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_23 & $i(all_56_23))
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4530) gives:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4531)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4531) implies:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4532)  op(e1, all_56_21) = e1
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3905), (4532) imply:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4533)  op(e1, e0) = e1
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4347), (4533), (function-axioms) are
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4534)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_23 & $i(all_56_23)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4534) implies:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4535)  op(e0, e1) = all_56_23
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4536)  op(e0, all_56_23) = e0
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_23, e1, e0, simplifying with (157), (4535)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4537)  all_56_23 = all_52_11
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4536), (4537) imply:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4538)  op(e0, all_52_11) = e0
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4539)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3023), (4411), (4539),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1509.
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4540)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4540) gives:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4541)  all_58_5 = e2 & op(e2, e1) = e2
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4541) implies:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4542)  all_58_5 = e2
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4543)  op(e2, e1) = e2
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (160), (164),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (216), (218), (219), (220), (221), (222),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (227), (228), (229), (232), (235), (236),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (242), (3017), (3022), (3023),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3809), (3907), (3909), (3910), (3914), (4345),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4346), (4347), (4367), (4368), (4372), (4373),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4389), (4393), (4410), (4514), (4542), (4543),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1452.
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4544)  all_58_10 = e2 & op(e2, e0) = e2
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4544) implies:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4545)  all_58_10 = e2
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4546)  op(e2, e0) = e2
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (160), (162),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (170), (216), (218), (220), (221),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (225), (230), (235), (236), (237), (238),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (241), (244), (246), (3017), (3022),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3023), (3809), (3907), (3909), (3910), (3914),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4339), (4346), (4347), (4367), (4368), (4372),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4388), (4389), (4393), (4402), (4404), (4410),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4538), (4545), (4546), (function-axioms) are
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1462.
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4547)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (4343), (4400), (4547),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1451.
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (4548)  all_58_15 = e3 & op(e0, e0) = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4548) implies:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (4549)  op(e0, e0) = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3910), (4549), (function-axioms) are
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | |   (4550)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 &
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3918), (4347), (4550), (function-axioms) are
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1767.
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | |   (4551)  all_58_9 = e3 & op(e3, e0) = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | ALPHA: (4551) implies:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | |   (4552)  op(e3, e0) = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4345), (4552), (function-axioms) are
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | End of split
% 232.10/43.05  | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.05  | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | |   (4553)   ~ (all_54_11 = e3)
% 232.10/43.05  | | | | | | | | | | | | | | | | |   (4554)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 232.10/43.05  | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | REDUCE: (258), (4553) imply:
% 232.10/43.05  | | | | | | | | | | | | | | | | |   (4555)   ~ (all_52_14 = e3)
% 232.10/43.05  | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 232.10/43.05  | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | |   (4556)  all_54_13 = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4556) imply:
% 232.10/43.05  | | | | | | | | | | | | | | | | | |   (4557)  all_52_7 = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | SIMP: (4557) implies:
% 232.10/43.05  | | | | | | | | | | | | | | | | | |   (4558)  all_52_7 = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | REDUCE: (128), (4558) imply:
% 232.10/43.05  | | | | | | | | | | | | | | | | | |   (4559)   ~ (all_52_6 = e3)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | REDUCE: (125), (4558) imply:
% 232.10/43.05  | | | | | | | | | | | | | | | | | |   (4560)   ~ (all_52_11 = e3)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | SIMP: (4560) implies:
% 232.10/43.05  | | | | | | | | | | | | | | | | | |   (4561)   ~ (all_52_11 = e3)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | |   (4562)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 232.10/43.05  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | BETA: splitting (4562) gives:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | |   (4563)  all_58_12 = e3 & op(e0, e3) = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (162),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | |            (226), (239), (241), (243), (391), (4555), (4559),
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | |            (4563), (function-axioms) are inconsistent by
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | |            sub-proof #1528.
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | |   (4564)  all_58_13 = e3 & op(e0, e2) = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | ALPHA: (4564) implies:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | |   (4565)  all_58_13 = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | |   (4566)  op(e0, e2) = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | |   (4567)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4567) gives:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | |   (4568)  all_58_6 = e3 & op(e1, e3) = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4568) implies:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | |   (4569)  all_58_6 = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | |   (4570)  op(e1, e3) = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (4570) gives:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | |   (4571)  all_52_2 = e3
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (4571) imply:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | |   (4572)   ~ (all_52_1 = e3)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (4571) imply:
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | |   (4573)   ~ (all_52_3 = e3)
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.05  | | | | | | | | | | | | | | | | | | | | | | SIMP: (4573) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | |   (4574)   ~ (all_52_3 = e3)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (4571) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | |   (4575)   ~ (all_52_6 = e3)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (4571) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | |   (4576)   ~ (all_52_14 = e3)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | |   (4577)  all_54_12 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (4574), (4577) are inconsistent by
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | |   (4578)   ~ (all_54_12 = e3)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | |   (4579)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | |   (4580)  all_54_9 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (4559), (4580) are inconsistent by
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | |   (4581)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (4582)  all_54_14 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (4561), (4582) are inconsistent by
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1796.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (4583)   ~ (all_54_14 = e3)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (4584)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4585)  all_54_7 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4585) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4586)  all_52_13 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4586) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4587)  all_52_13 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (4587) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4588)   ~ (all_52_9 = e3)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (4587) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4589)  op(e2, e0) = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3007) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4590)   ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_14_1 & $i(all_14_0) &
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4590) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4591)  op(e2, e0) = all_14_1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4592)  op(all_14_1, e2) = all_14_0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4593)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4593) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4594)  all_58_4 = e3 & op(e3, e1) = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4594) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4595)  all_58_4 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4596)  op(e3, e1) = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3921) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4597)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_48_1 & $i(all_48_0) &
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4597) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4598)   ~ (all_48_0 = e1)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4599)  op(e2, e0) = all_48_1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4600)  op(all_48_1, e2) = all_48_0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_1, e0, e2, simplifying with (4591), (4599)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4601)  all_48_1 = all_14_1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1,
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (4589), (4599) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4602)  all_48_1 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (4596) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4603)  all_52_8 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4601), (4602) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4604)  all_14_1 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4600), (4602) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4605)  op(e3, e2) = all_48_0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4592), (4604) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4606)  op(e3, e2) = all_14_0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_14_0, e2, e3, simplifying with (170), (4606)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4607)  all_52_4 = all_14_0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_0, e2, e3, simplifying with (170), (4605)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4608)  all_52_4 = all_48_0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4607), (4608) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4609)  all_48_0 = all_14_0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4609) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4610)  all_48_0 = all_14_0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (4607) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4611)  all_54_1 = all_14_0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (4607) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4612)   ~ (all_52_6 = all_14_0)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4612) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4613)   ~ (all_52_6 = all_14_0)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4339), (4607) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4614)   ~ (all_14_0 = e3)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3013), (4607) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4615)   ~ (all_14_0 = e0)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4598), (4610) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4616)   ~ (all_14_0 = e1)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4617)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4617) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4618)  all_58_1 = e1 & op(e3, e2) = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4618) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4619)  op(e3, e2) = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4338), (4606), (4611), (4615), (4616), (4619),
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1449.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4620)  all_58_3 = e1 & op(e2, e2) = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3022), (4620) are inconsistent by sub-proof
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1752.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4621)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4621) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4622)  all_58_7 = e1 & op(e1, e2) = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4622) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4623)  all_58_7 = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4624)  op(e1, e2) = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4625)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (3023), (3809), (4623), (4624), (4625),
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1609.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4626)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4626) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4627)  all_58_4 = e1 & op(e3, e1) = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4595), (4627) are inconsistent by sub-proof
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2042.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4628)  all_58_9 = e1 & op(e3, e0) = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4628) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4629)  op(e3, e0) = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4338) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4630)  all_54_1 = e2
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4611), (4630) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4631)  all_14_0 = e2
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4631) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4632)  all_14_0 = e2
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4613), (4632) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4633)   ~ (all_52_6 = e2)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4614), (4632) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4634)   ~ (e3 = e2)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4606), (4632) imply:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4635)  op(e3, e2) = e2
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (126), (159), (170), (212), (258),
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (3011), (3014), (3800), (3806), (3907),
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3914), (3924), (4339), (4554), (4566), (4581),
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4589), (4624), (4629), (4633), (4635),
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1448.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4636)  all_54_1 = e1 | all_54_1 = e0
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4611), (4615), (4616), (4636) are inconsistent by
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1450.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4637)  all_58_13 = e1 & op(e0, e2) = e1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4565), (4637) are inconsistent by sub-proof
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2013.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4638)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4638) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4639)   ~ (all_48_1 = e3)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4640)  op(e2, e0) = all_48_1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4589), (4591), (4639), (4640), (function-axioms)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1632.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4641)  all_58_5 = e3 & op(e2, e1) = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4588), (4641), (function-axioms) are
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4642)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4642) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4643)  all_58_8 = e3 & op(e1, e1) = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3907), (4643), (function-axioms) are
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4644)  all_58_14 = e3 & op(e0, e1) = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4561), (4644), (function-axioms) are
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4645)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4645) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4646)   ~ (all_14_1 = e1)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4647)  op(e2, e0) = all_14_1
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4648)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4648) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4649)  all_58_4 = e3 & op(e3, e1) = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4649) implies:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4650)  all_58_4 = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4651)  op(e3, e1) = e3
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3921) gives:
% 232.10/43.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4652)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_48_1 & $i(all_48_0) &
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4652) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4653)   ~ (all_48_0 = e1)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4654)  op(e2, e0) = all_48_1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4655)  op(all_48_1, e2) = all_48_0
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_1, e0, e2, simplifying with (4647), (4654)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4656)  all_48_1 = all_14_1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1,
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (4589), (4654) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4657)  all_48_1 = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (4651) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4658)  all_52_8 = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4656), (4657) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4659)  all_14_1 = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4655), (4657) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4660)  op(e3, e2) = all_48_0
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_0, e2, e3, simplifying with (170), (4660)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4661)  all_52_4 = all_48_0
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (4661) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4662)  all_54_1 = all_48_0
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (4661) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4663)   ~ (all_52_6 = all_48_0)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4663) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4664)   ~ (all_52_6 = all_48_0)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4339), (4661) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4665)   ~ (all_48_0 = e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3013), (4661) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4666)   ~ (all_48_0 = e0)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4667)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4667) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4668)  all_58_1 = e1 & op(e3, e2) = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4668) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4669)  op(e3, e2) = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4338), (4653), (4660), (4662), (4666), (4669),
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1446.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4670)  all_58_3 = e1 & op(e2, e2) = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3022), (4670) are inconsistent by sub-proof
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1752.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4671)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4671) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4672)  all_58_7 = e1 & op(e1, e2) = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4672) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4673)  all_58_7 = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4674)  op(e1, e2) = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4675)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (3023), (3809), (4673), (4674), (4675),
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1609.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4676)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4676) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4677)  all_58_4 = e1 & op(e3, e1) = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4650), (4677) are inconsistent by sub-proof
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2042.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4678)  all_58_9 = e1 & op(e3, e0) = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4678) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4679)  op(e3, e0) = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4338) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4680)  all_54_1 = e2
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4662), (4680) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4681)  all_48_0 = e2
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4681) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4682)  all_48_0 = e2
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4664), (4682) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4683)   ~ (all_52_6 = e2)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4665), (4682) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4684)   ~ (e3 = e2)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4660), (4682) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4685)  op(e3, e2) = e2
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (126), (159), (170), (212), (258),
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (3011), (3014), (3800), (3806), (3907),
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3914), (3924), (4339), (4554), (4566), (4581),
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4589), (4674), (4679), (4683), (4685),
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1448.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4686)  all_54_1 = e1 | all_54_1 = e0
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4653), (4662), (4666), (4686) are inconsistent by
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1447.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4687)  all_58_13 = e1 & op(e0, e2) = e1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4565), (4687) are inconsistent by sub-proof
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2013.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4688)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4688) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4689)   ~ (all_48_1 = e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4690)  op(e2, e0) = all_48_1
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4589), (4647), (4689), (4690), (function-axioms)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1632.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4691)  all_58_5 = e3 & op(e2, e1) = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4588), (4691), (function-axioms) are
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4692)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4692) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4693)  all_58_8 = e3 & op(e1, e1) = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3907), (4693), (function-axioms) are
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4694)  all_58_14 = e3 & op(e0, e1) = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4561), (4694), (function-axioms) are
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4695)   ~ (all_54_7 = e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4696)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (4695) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4697)   ~ (all_52_13 = e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4698)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4698) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4699)  all_58_9 = e3 & op(e3, e0) = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4699) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4700)  op(e3, e0) = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4701)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4701) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4702)  all_58_2 = e3 & op(e2, e3) = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4702) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4703)  op(e2, e3) = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4572), (4703), (function-axioms) are
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4704)  all_58_3 = e3 & op(e2, e2) = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4704) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4705)  all_58_3 = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3022), (4705) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4706)  e3 = e0
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4706) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4707)  e3 = e0
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4569), (4707) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4708)  all_58_6 = e0
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (241), (243),
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (3809), (4572), (4708), (function-axioms)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1441.
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4709)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4709) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4710)  all_58_5 = e3 & op(e2, e1) = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4710) implies:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4711)  op(e2, e1) = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (4711) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4712)  all_52_9 = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (168), (4700) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4713)  all_52_12 = e3
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (4713) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4714)   ~ (all_52_8 = e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (4713) imply:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4715)   ~ (all_52_13 = e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4716)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4716) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4717)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4717) gives:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4718)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4718) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4719)  op(e2, e3) = e3
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4572), (4719), (function-axioms) are
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4720)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4720) gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4721)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4721) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4722)  all_56_9 = e2
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4723)   ~ (all_56_31 = e3)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4724)  op(e2, e3) = e2
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4725)  op(e3, e2) = e2
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3924) gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4726)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_50_1 & $i(all_50_0) &
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4726) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4727)  op(e3, e0) = all_50_1
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3800) gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4728)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_16_1 & $i(all_16_0) &
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4728) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4729)  op(e3, e0) = all_16_1
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (110), (121), (134), (145),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (159), (160), (164), (167), (169), (170),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (211), (212), (216), (218), (220), (221),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (228), (236), (240), (242), (244), (246),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (255), (257), (269), (281), (3011), (3013),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3017), (3022), (3806), (3807), (3809), (3905),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3906), (3907), (3910), (3914), (4339), (4565),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4566), (4579), (4584), (4696), (4697), (4700),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4711), (4714), (4722), (4724), (4725), (4727),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4729), (function-axioms) are inconsistent by
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1432.
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4730)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4730) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4731)  op(e3, e0) = all_16_1
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (110), (121), (134), (145),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (159), (160), (164), (167), (169), (170),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (211), (212), (216), (218), (220), (221),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (228), (236), (240), (242), (244), (246),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (255), (257), (269), (281), (3011), (3013),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3017), (3022), (3806), (3807), (3809), (3905),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3906), (3907), (3910), (3914), (4339), (4565),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4566), (4579), (4584), (4696), (4697), (4700),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4711), (4714), (4722), (4724), (4725), (4727),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4731), (function-axioms) are inconsistent by
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1432.
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4732)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4732) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4733)   ~ (all_50_1 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4734)  op(e3, e0) = all_50_1
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3800) gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4735)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_16_1 & $i(all_16_0) &
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4735) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4736)  op(e3, e0) = all_16_1
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (4724) gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4737)  all_52_1 = e2
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (4700), (4734) gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4738)  all_50_1 = e3
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (4734), (4736)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4739)  all_50_1 = all_16_1
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (4725) gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4740)  all_52_4 = e2
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4738), (4739) imply:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4741)  all_16_1 = e3
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4741) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4742)  all_16_1 = e3
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (4737) imply:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4743)   ~ (all_52_3 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4743) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4744)   ~ (all_52_3 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (4737) imply:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4745)   ~ (all_52_13 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4745) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4746)   ~ (all_52_13 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (4740) imply:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4747)   ~ (all_52_8 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4747) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4748)   ~ (all_52_8 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (121), (159),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (164), (169), (170), (202), (211), (212),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (220), (221), (222), (228), (236),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (244), (246), (255), (257), (269),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (281), (3011), (3017), (3022), (3806), (3807),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3809), (3905), (3906), (3907), (3910), (3914),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4339), (4565), (4566), (4579), (4584), (4696),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4697), (4711), (4714), (4722), (4736), (4742),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4744), (4746), (4748), (function-axioms) are
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1433.
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4749)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4749) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4750)   ~ (all_16_1 = e1)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4751)  op(e3, e0) = all_16_1
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (4724) gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4752)  all_52_1 = e2
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (4700), (4734) gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4753)  all_50_1 = e3
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (4734), (4751)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4754)  all_50_1 = all_16_1
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (4725) gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4755)  all_52_4 = e2
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4753), (4754) imply:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4756)  all_16_1 = e3
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4756) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4757)  all_16_1 = e3
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (4752) imply:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4758)   ~ (all_52_3 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4758) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4759)   ~ (all_52_3 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (4752) imply:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4760)   ~ (all_52_13 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4760) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4761)   ~ (all_52_13 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (4755) imply:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4762)   ~ (all_52_8 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4762) implies:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4763)   ~ (all_52_8 = e2)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4764)  all_54_2 = e3
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (4714), (4764) are inconsistent by
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4765)   ~ (all_54_2 = e3)
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4766)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (121), (159),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (164), (169), (170), (211), (212), (216),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (221), (222), (228), (236), (240),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (242), (244), (246), (255), (257), (269), (281),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3011), (3017), (3022), (3806), (3807), (3809),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3905), (3906), (3907), (3910), (3914), (4339),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4565), (4566), (4579), (4584), (4696), (4697),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4700), (4711), (4714), (4722), (4759), (4761),
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4763), (4766), (function-axioms) are inconsistent
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1434.
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4767)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4767) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4768)  op(e3, e1) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4714), (4768), (function-axioms) are
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4769)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4769) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4770)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4770) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4771)  op(e1, e3) = e1
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4570), (4771), (function-axioms) are
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4772)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3806), (4574), (4772), (function-axioms)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2330.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4773)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4773) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4774)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (4566), (4711), (4774),
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2253.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4775)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (3017), (3912), (3914), (4775),
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2321.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4776)  all_58_10 = e3 & op(e2, e0) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4776) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4777)  op(e2, e0) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4697), (4777), (function-axioms) are
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4778)  all_58_10 = e3 & op(e2, e0) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4778) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4779)  op(e2, e0) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4697), (4779), (function-axioms) are
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4780)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (3910), (4555), (4780),
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1431.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | |   (4781)  all_58_7 = e3 & op(e1, e2) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4781) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | |   (4782)  op(e1, e2) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4559), (4782), (function-axioms) are
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | |   (4783)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (3907), (4555), (4783),
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | |            #1909.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | |   (4784)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (3910), (4561), (4784),
% 232.10/43.09  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.09  | | | | | | | | | | | | | | | | | | |            #1580.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.09  | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | |   (4785)   ~ (all_54_13 = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | REDUCE: (256), (4785) imply:
% 232.10/43.09  | | | | | | | | | | | | | | | | | |   (4786)   ~ (all_52_7 = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | |   (4787)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (3022), (4339), (4787),
% 232.10/43.09  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.09  | | | | | | | | | | | | | | | | | | |            #1430.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | |   (4788)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (4788) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | |   (4789)  all_58_7 = e3 & op(e1, e2) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | ALPHA: (4789) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | |   (4790)  all_58_7 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | |   (4791)  op(e1, e2) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (4791) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | |   (4792)  all_52_6 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (4792) imply:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | |   (4793)   ~ (all_52_2 = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (4792) imply:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | |   (4794)   ~ (all_52_7 = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (4792) imply:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | |   (4795)   ~ (all_52_14 = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | |   (4796)  all_54_8 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (4793), (4796) are inconsistent by
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | |   (4797)   ~ (all_54_8 = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | |   (4798)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | |   (4799)  all_54_14 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (4799) imply:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | |   (4800)  all_52_11 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | SIMP: (4800) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | |   (4801)  all_52_11 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (4801) imply:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | |   (4802)   ~ (all_52_8 = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (4801) imply:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | |   (4803)   ~ (all_52_9 = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | |   (4804)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (4802), (4803), (4804),
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | |            #1628.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | |   (4805)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4805) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | |   (4806)  all_58_8 = e3 & op(e1, e1) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3907), (4806), (function-axioms) are
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | |   (4807)  all_58_14 = e3 & op(e0, e1) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4807) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | |   (4808)  all_58_14 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (4809)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (170), (239), (3012),
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | |            (3805), (3806), (4339), (4809), (function-axioms)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1514.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (4810)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4810) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4811)  all_58_4 = e3 & op(e3, e1) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4811) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4812)  op(e3, e1) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4802), (4812), (function-axioms) are
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4813)  all_58_9 = e3 & op(e3, e0) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4813) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4814)  all_58_9 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4815)  op(e3, e0) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4816)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4816) gives:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4817)  all_58_0 = e3 & op(e3, e3) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4817) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4818)  op(e3, e3) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (3012), (3805),
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3806), (4818), (function-axioms) are inconsistent
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1938.
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4819)  all_58_2 = e3 & op(e2, e3) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4819) implies:
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4820)  op(e2, e3) = e3
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (4820) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4821)  all_52_1 = e3
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (168), (4815) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4822)  all_52_12 = e3
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (4821) imply:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4823)   ~ (all_52_2 = e3)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (4821) imply:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4824)   ~ (all_52_3 = e3)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4824) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4825)   ~ (all_52_3 = e3)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4826)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4826) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4827)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (163), (170), (4339), (4793), (4820), (4827),
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1429.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4828)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4828) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4829)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4829) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4830)  op(e1, e3) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4831)  op(e3, e1) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (4830) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4832)  all_52_2 = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (4831) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4833)  all_52_8 = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (4832) imply:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4834)   ~ (all_52_14 = e1)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4834) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4835)   ~ (all_52_14 = e1)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4802), (4833) imply:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4836)   ~ (e3 = e1)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4554) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4837)  all_54_11 = e2
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (4837) imply:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4838)  all_52_14 = e2
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4838) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4839)  all_52_14 = e2
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (4839) imply:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4840)  op(e1, e0) = e2
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4841)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4841) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4842)  all_58_9 = e1 & op(e3, e0) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4842) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4843)  all_58_9 = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4814), (4843) are inconsistent by sub-proof
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1709.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4844)  all_58_10 = e1 & op(e2, e0) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4844) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4845)  op(e2, e0) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3007), (3921), (4791), (4845), (function-axioms)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1427.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4846)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4846) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4847)  all_58_11 = e1 & op(e1, e0) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4847) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4848)  op(e1, e0) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4840), (4848), (function-axioms) are
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2019.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4849)  all_58_15 = e1 & op(e0, e0) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4849) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4850)  op(e0, e0) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3910), (4850), (function-axioms) are
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4851)  all_54_11 = e1 | all_54_11 = e0
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (3914), (4835), (4851) are inconsistent by
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2174.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4852)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3806), (4825), (4852), (function-axioms)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2330.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4853)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4853) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4854)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4854) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4855)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4855) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4856)  op(e1, e2) = e2
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4791), (4856), (function-axioms) are
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2207.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4857)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4857) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4858)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4858) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4859)  op(e1, e2) = e1
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4791), (4859), (function-axioms) are
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2094.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4860)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4860) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4861)   ~ (all_56_31 = e0)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3912), (4861) imply:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4862)  $false
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4862) is inconsistent.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4863)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (3017), (3912), (3914), (4863),
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2321.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4864)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4864) gives:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4865)  all_58_6 = e3 & op(e1, e3) = e3
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4865) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4866)  op(e1, e3) = e3
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4793), (4866), (function-axioms) are
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4867)  all_58_12 = e3 & op(e0, e3) = e3
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4867) implies:
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4868)  all_58_12 = e3
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (217), (218),
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4808), (4868), (function-axioms) are inconsistent
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1862.
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | |   (4869)   ~ (all_54_14 = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (255), (4869) imply:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | |   (4870)   ~ (all_52_11 = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | |   (4871)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4871) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | |   (4872)  all_58_12 = e3 & op(e0, e3) = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4872) implies:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | |   (4873)  all_58_12 = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | |   (4874)  op(e0, e3) = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (4874) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | |   (4875)  all_52_3 = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (4875) imply:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | |   (4876)   ~ (all_52_1 = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (4877)  all_54_7 = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4877) imply:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (4878)  all_52_13 = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4878) implies:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (4879)  all_52_13 = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (4879) imply:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (4880)   ~ (all_52_12 = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (4879) imply:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (4881)  op(e2, e0) = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4882)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (170), (239), (3012),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3805), (3806), (4339), (4882), (function-axioms)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1514.
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4883)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4883) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4884)  all_58_4 = e3 & op(e3, e1) = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4884) implies:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4885)  all_58_4 = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4886)  op(e3, e1) = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3007) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4887)   ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_14_1 & $i(all_14_0) &
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4887) implies:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4888)  op(e2, e0) = all_14_1
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (120), (121), (123), (149), (157),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (163), (164), (165), (167), (168),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (213), (214), (230), (268), (3017), (3023),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3804), (3805), (3806), (3807), (3907), (3912),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3914), (3921), (4791), (4793), (4798), (4874),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4876), (4881), (4885), (4886), (4888),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1425.
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4889)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4889) implies:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4890)  op(e2, e0) = all_14_1
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (120), (121), (123), (149), (157),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (163), (164), (165), (167), (168),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (213), (214), (230), (268), (3017), (3023),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3804), (3805), (3806), (3807), (3907), (3912),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3914), (3921), (4791), (4793), (4798), (4874),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4876), (4881), (4885), (4886), (4890),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1425.
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4891)  all_58_9 = e3 & op(e3, e0) = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4891) implies:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4892)  op(e3, e0) = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4880), (4892), (function-axioms) are
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (4893)   ~ (all_54_7 = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (4893) imply:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (4894)   ~ (all_52_13 = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4895)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (3022), (4876), (4895),
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1424.
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4896)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4896) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4897)  all_58_5 = e3 & op(e2, e1) = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4897) implies:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4898)  op(e2, e1) = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4899)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4899) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4900)  all_58_9 = e3 & op(e3, e0) = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4900) implies:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4901)  op(e3, e0) = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (4898) gives:
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4902)  all_52_9 = e3
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 232.10/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (168), (4901) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4903)  all_52_12 = e3
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (4903) imply:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4904)   ~ (all_52_8 = e3)
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (4903) imply:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4905)   ~ (all_52_13 = e3)
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4906)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4906) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4907)  all_58_6 = e2 & op(e1, e3) = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4907) implies:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4908)  all_58_6 = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4909)  op(e1, e3) = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4910)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4910) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4911)  all_58_6 = e1 & op(e1, e3) = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4908), (4911) are inconsistent by sub-proof
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1423.
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4912)  all_58_7 = e1 & op(e1, e2) = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4790), (4912) are inconsistent by sub-proof
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1422.
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4913)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4913) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4914)  all_58_8 = e1 & op(e1, e1) = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4914) implies:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4915)  op(e1, e1) = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3907), (4915), (function-axioms) are
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4916)  all_58_11 = e1 & op(e1, e0) = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4916) implies:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4917)  all_58_11 = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4918)  op(e1, e0) = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4919)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4919) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4920)  all_58_0 = e1 & op(e3, e3) = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4920) implies:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4921)  op(e3, e3) = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3809), (4921), (function-axioms) are
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4922)  all_58_2 = e1 & op(e2, e3) = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4922) implies:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4923)  all_58_2 = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4924)  op(e2, e3) = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4925)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4925) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4926)  all_58_2 = e2 & op(e2, e3) = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4923), (4926) are inconsistent by sub-proof
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1976.
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4927)  all_58_3 = e2 & op(e2, e2) = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4927) implies:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4928)  op(e2, e2) = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3023), (4928), (function-axioms) are
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2137.
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4929)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4929) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4930)  all_58_5 = e2 & op(e2, e1) = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4930) implies:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4931)  op(e2, e1) = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4898), (4931), (function-axioms) are
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4932)  all_58_10 = e2 & op(e2, e0) = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4932) implies:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4933)  op(e2, e0) = e2
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (4918) gives:
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4934)  all_52_14 = e1
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 232.47/43.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (4909) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4935)  all_52_2 = e2
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (4933) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4936)  all_52_13 = e2
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1,
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (4924) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4937)  all_52_1 = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4894), (4936) imply:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4938)   ~ (e3 = e2)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4555), (4934) imply:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4939)   ~ (e3 = e1)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4940)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4940) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4941)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4941) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4942)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4942) implies:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4943)  op(e2, e3) = e3
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4876), (4943), (function-axioms) are
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4944)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4944) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4945)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4945) implies:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4946)  op(e2, e3) = e2
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4924), (4946), (function-axioms) are
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1633.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4947)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4947) implies:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4948)  op(e3, e1) = e3
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4904), (4948), (function-axioms) are
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4949)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4949) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4950)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4950) implies:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4951)  op(e1, e3) = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4909), (4951), (function-axioms) are
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4952)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3806), (3912), (4952), (function-axioms)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2308.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4953)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4953) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4954)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (3912), (4898), (4954),
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1581.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4955)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4955) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4956)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e0
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4956) implies:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4957)  op(e2, e0) = e0
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4933), (4957), (function-axioms) are
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4958)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3912), (4918), (4958), (function-axioms) are
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2283.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4959)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4959) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4960)  all_58_6 = e1 & op(e1, e3) = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4908), (4960) are inconsistent by sub-proof
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1423.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4961)  all_58_12 = e1 & op(e0, e3) = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4961) implies:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4962)  all_58_12 = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4873), (4962) imply:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4963)  e3 = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4790), (4963) imply:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4964)  all_58_7 = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (225),
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (4555), (4917), (4918), (4964),
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1417.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4965)  all_58_7 = e2 & op(e1, e2) = e2
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4790), (4965) are inconsistent by sub-proof
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1416.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4966)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4966) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4967)  all_58_8 = e2 & op(e1, e1) = e2
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4967) implies:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4968)  op(e1, e1) = e2
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3907), (4968), (function-axioms) are
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4969)  all_58_11 = e2 & op(e1, e0) = e2
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4969) implies:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4970)  op(e1, e0) = e2
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4971)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4971) gives:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4972)  all_58_6 = e1 & op(e1, e3) = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4972) implies:
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4973)  all_58_6 = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4974)  op(e1, e3) = e1
% 232.47/43.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (232), (241), (243),
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3007), (3022), (3809), (3921), (4791), (4873),
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4898), (4973), (4974), (function-axioms) are
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1415.
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4975)  all_58_7 = e1 & op(e1, e2) = e1
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4790), (4975) are inconsistent by sub-proof
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1422.
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4976)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (3907), (4970), (4976),
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1567.
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4977)  all_58_10 = e3 & op(e2, e0) = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4977) implies:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4978)  op(e2, e0) = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4894), (4978), (function-axioms) are
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4979)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (3910), (4555), (4979),
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1431.
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4980)  all_58_10 = e3 & op(e2, e0) = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4980) implies:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4981)  op(e2, e0) = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4894), (4981), (function-axioms) are
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | |   (4982)  all_58_13 = e3 & op(e0, e2) = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4786), (4982), (function-axioms) are
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | |   (4983)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (3910), (4870), (4983),
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | |            #1580.
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | |   (4984)  all_58_13 = e3 & op(e0, e2) = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4786), (4984), (function-axioms) are
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | |   (4985)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 232.47/43.13  | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 232.47/43.13  | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 232.47/43.13  | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 232.47/43.13  | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 232.47/43.13  | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | ALPHA: (4985) implies:
% 232.47/43.13  | | | | | | | | | | | |   (4986)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 232.47/43.13  | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 232.47/43.13  | | | | | | | | | | | |               e1) = e0)
% 232.47/43.13  | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | BETA: splitting (4986) gives:
% 232.47/43.13  | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | |   (4987)  all_58_12 = e0 & op(e0, e3) = e0
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | ALPHA: (4987) implies:
% 232.47/43.13  | | | | | | | | | | | | |   (4988)  op(e0, e3) = e0
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | REF_CLOSE: (159), (3806), (4988), (function-axioms) are
% 232.47/43.13  | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | |   (4989)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 232.47/43.13  | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | REF_CLOSE: (157), (158), (3015), (3906), (4989),
% 232.47/43.13  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.13  | | | | | | | | | | | | |            #1414.
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | | 
% 232.47/43.13  | | | | | | | | End of split
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | |   (4990)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 232.47/43.13  | | | | | | | |             op(e0, e2) = e0)
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | | REF_CLOSE: (158), (162), (3014), (3015), (4990),
% 232.47/43.13  | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.13  | | | | | | | |            #1990.
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | End of split
% 232.47/43.13  | | | | | | | 
% 232.47/43.13  | | | | | | End of split
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | Case 2:
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | |   (4991)  all_12_2 = e3
% 232.47/43.13  | | | | | |   (4992)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0,
% 232.47/43.13  | | | | | |               e3) = all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 232.47/43.13  | | | | | |             (all_12_1 = e2) & op(e0, e3) = all_12_1 & $i(all_12_1))
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | | COMBINE_EQS: (346), (4991) imply:
% 232.47/43.13  | | | | | |   (4993)  all_4_2 = e3
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | | COMBINE_EQS: (334), (4993) imply:
% 232.47/43.13  | | | | | |   (4994)  all_26_2 = e3
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | | COMBINE_EQS: (254), (4993) imply:
% 232.47/43.13  | | | | | |   (4995)  all_56_31 = e3
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | | REDUCE: (368), (4993) imply:
% 232.47/43.13  | | | | | |   (4996)   ~ (all_52_3 = e3)
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | | REDUCE: (379), (4993) imply:
% 232.47/43.13  | | | | | |   (4997)   ~ (all_52_7 = e3)
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | | REDUCE: (386), (4993) imply:
% 232.47/43.13  | | | | | |   (4998)   ~ (all_52_11 = e3)
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | | REDUCE: (387), (4993) imply:
% 232.47/43.13  | | | | | |   (4999)   ~ (all_52_12 = e3)
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | | REDUCE: (388), (4993) imply:
% 232.47/43.13  | | | | | |   (5000)   ~ (all_52_13 = e3)
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | | REDUCE: (389), (4993) imply:
% 232.47/43.13  | | | | | |   (5001)   ~ (all_52_14 = e3)
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | | BETA: splitting (222) gives:
% 232.47/43.13  | | | | | | 
% 232.47/43.13  | | | | | | Case 1:
% 232.47/43.13  | | | | | | | 
% 232.47/43.13  | | | | | | |   (5002)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 232.47/43.13  | | | | | | |             op(e2, e0) = e3)
% 232.47/43.13  | | | | | | | 
% 232.47/43.13  | | | | | | | REF_CLOSE: (164), (168), (4999), (5000), (5002), (function-axioms)
% 232.47/43.13  | | | | | | |            are inconsistent by sub-proof #1592.
% 232.47/43.13  | | | | | | | 
% 232.47/43.13  | | | | | | Case 2:
% 232.47/43.13  | | | | | | | 
% 232.47/43.13  | | | | | | |   (5003)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 232.47/43.13  | | | | | | |             op(e0, e0) = e3)
% 232.47/43.13  | | | | | | | 
% 232.47/43.13  | | | | | | | BETA: splitting (5003) gives:
% 232.47/43.13  | | | | | | | 
% 232.47/43.13  | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | |   (5004)  all_58_11 = e3 & op(e1, e0) = e3
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | | ALPHA: (5004) implies:
% 232.47/43.13  | | | | | | | |   (5005)  op(e1, e0) = e3
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | | REF_CLOSE: (160), (5001), (5005), (function-axioms) are
% 232.47/43.13  | | | | | | | |            inconsistent by sub-proof #2149.
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | |   (5006)  all_58_15 = e3 & op(e0, e0) = e3
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | | ALPHA: (5006) implies:
% 232.47/43.13  | | | | | | | |   (5007)  all_58_15 = e3
% 232.47/43.13  | | | | | | | |   (5008)  op(e0, e0) = e3
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | | BETA: splitting (52) gives:
% 232.47/43.13  | | | | | | | | 
% 232.47/43.13  | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | 
% 232.47/43.13  | | | | | | | | |   (5009)   ~ (all_14_2 = e0)
% 232.47/43.13  | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | REDUCE: (344), (5009) imply:
% 232.47/43.13  | | | | | | | | |   (5010)   ~ (all_8_2 = e0)
% 232.47/43.13  | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | BETA: splitting (55) gives:
% 232.47/43.13  | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | |   (5011)   ~ (all_16_2 = e0)
% 232.47/43.13  | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | REDUCE: (342), (5011) imply:
% 232.47/43.13  | | | | | | | | | |   (5012)   ~ (all_10_2 = e0)
% 232.47/43.13  | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | BETA: splitting (58) gives:
% 232.47/43.13  | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | |   (5013)   ~ (all_18_2 = e0)
% 232.47/43.13  | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | REDUCE: (339), (5013) imply:
% 232.47/43.13  | | | | | | | | | | |   (5014)   ~ (all_6_2 = e0)
% 232.47/43.13  | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | BETA: splitting (64) gives:
% 232.47/43.13  | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | |   (5015)   ~ (all_22_2 = e1)
% 232.47/43.13  | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | REDUCE: (326), (5015) imply:
% 232.47/43.13  | | | | | | | | | | | |   (5016)   ~ (all_8_2 = e1)
% 232.47/43.13  | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | BETA: splitting (199) gives:
% 232.47/43.13  | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | |   (5017)  all_54_5 = e3
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | COMBINE_EQS: (275), (5017) imply:
% 232.47/43.13  | | | | | | | | | | | | |   (5018)  all_8_2 = e3
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | REDUCE: (392), (5018) imply:
% 232.47/43.13  | | | | | | | | | | | | |   (5019)  $false
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | CLOSE: (5019) is inconsistent.
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | |   (5020)   ~ (all_54_5 = e3)
% 232.47/43.13  | | | | | | | | | | | | |   (5021)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | BETA: splitting (5021) gives:
% 232.47/43.13  | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | |   (5022)  all_54_5 = e2
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | COMBINE_EQS: (275), (5022) imply:
% 232.47/43.13  | | | | | | | | | | | | | |   (5023)  all_8_2 = e2
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | COMBINE_EQS: (353), (5023) imply:
% 232.47/43.13  | | | | | | | | | | | | | |   (5024)  all_56_11 = e2
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | REDUCE: (366), (5023) imply:
% 232.47/43.13  | | | | | | | | | | | | | |   (5025)   ~ (all_52_1 = e2)
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | REDUCE: (373), (5023) imply:
% 232.47/43.13  | | | | | | | | | | | | | |   (5026)   ~ (all_52_7 = e2)
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | REDUCE: (375), (5023) imply:
% 232.47/43.13  | | | | | | | | | | | | | |   (5027)   ~ (all_52_9 = e2)
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | REDUCE: (377), (5023) imply:
% 232.47/43.13  | | | | | | | | | | | | | |   (5028)   ~ (all_52_13 = e2)
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | REDUCE: (392), (5023) imply:
% 232.47/43.13  | | | | | | | | | | | | | |   (5029)   ~ (e3 = e2)
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | REDUCE: (42), (5023) imply:
% 232.47/43.13  | | | | | | | | | | | | | |   (5030)  op(e2, e2) = e2
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 232.47/43.13  | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | |   (5031)   ~ (all_24_2 = e2)
% 232.47/43.13  | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | REDUCE: (301), (5031) imply:
% 232.47/43.13  | | | | | | | | | | | | | | |   (5032)   ~ (all_10_2 = e2)
% 232.47/43.13  | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 232.47/43.13  | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | |   (5033)  all_54_0 = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (5033) imply:
% 232.47/43.13  | | | | | | | | | | | | | | | |   (5034)  all_10_2 = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | SIMP: (5034) implies:
% 232.47/43.13  | | | | | | | | | | | | | | | |   (5035)  all_10_2 = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | REDUCE: (355), (5035) imply:
% 232.47/43.13  | | | | | | | | | | | | | | | |   (5036)   ~ (all_52_1 = e3)
% 232.47/43.13  | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | REDUCE: (361), (5035) imply:
% 232.47/43.13  | | | | | | | | | | | | | | | |   (5037)   ~ (all_52_4 = e3)
% 232.47/43.13  | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | REDUCE: (45), (5035) imply:
% 232.47/43.13  | | | | | | | | | | | | | | | |   (5038)  op(e3, e3) = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 232.47/43.13  | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | |   (5039)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.47/43.13  | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (5030), (5036), (5039),
% 232.47/43.13  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.13  | | | | | | | | | | | | | | | | |            #1413.
% 232.47/43.13  | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.13  | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | |   (5040)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 232.47/43.13  | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 232.47/43.13  | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | BETA: splitting (5040) gives:
% 232.47/43.13  | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | |   (5041)  all_58_5 = e3 & op(e2, e1) = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | ALPHA: (5041) implies:
% 232.47/43.13  | | | | | | | | | | | | | | | | | |   (5042)  all_58_5 = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | | |   (5043)  op(e2, e1) = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | |   (5044)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | BETA: splitting (5044) gives:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | |   (5045)  all_58_1 = e3 & op(e3, e2) = e3
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.13  | | | | | | | | | | | | | | | | | | | | ALPHA: (5045) implies:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5046)  op(e3, e2) = e3
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5037), (5046), (function-axioms) are
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5047)  all_58_3 = e3 & op(e2, e2) = e3
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | ALPHA: (5047) implies:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5048)  op(e2, e2) = e3
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5030), (5048), (function-axioms) are
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | |   (5049)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (5049) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5050)  all_58_7 = e3 & op(e1, e2) = e3
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | ALPHA: (5050) implies:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5051)  all_58_7 = e3
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5052)  op(e1, e2) = e3
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (5052) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5053)  all_52_6 = e3
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (5043) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5054)  all_52_9 = e3
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (5053) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5055)   ~ (all_52_14 = e3)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (5054) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5056)   ~ (all_52_8 = e3)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (5054) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5057)   ~ (all_52_11 = e3)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (5054) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | |   (5058)   ~ (all_6_2 = e3)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |   (5059)   ~ (all_36_2 = e2)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | REDUCE: (328), (5059) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |   (5060)   ~ (all_6_2 = e2)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | |   (5061)  all_54_10 = e3
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (5061) are inconsistent by sub-proof
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | |            #2313.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | |   (5062)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5062) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | |   (5063)  all_54_10 = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (5060), (5063) are inconsistent by
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | |   (5064)  all_54_10 = e1 | all_54_10 = e0
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5064) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |   (5065)  all_54_10 = e1
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (5065) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |   (5066)  all_6_2 = e1
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5066) implies:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |   (5067)  all_6_2 = e1
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (5067) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |   (5068)  all_56_21 = e1
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (5067) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |   (5069)   ~ (all_52_8 = e1)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (5067) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |   (5070)   ~ (all_52_14 = e1)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (5071)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5071) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5072)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5072) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5073)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5073) implies:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5074)  op(e2, e3) = e3
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5036), (5074), (function-axioms) are
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5075)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (169), (5025), (5056), (5075),
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1608.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5076)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (4995), (4996), (5069), (5076),
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1411.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (5077)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (160), (165), (297), (381), (5014), (5024),
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (5026), (5027), (5064), (5068), (5070), (5077),
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |            #1408.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |   (5078)  all_54_10 = e0
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (5014), (5078) are inconsistent by
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |   (5079)  all_36_2 = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |   (5080)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (5079) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |   (5081)  all_6_2 = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | SIMP: (5081) implies:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |   (5082)  all_6_2 = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (5082) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |   (5083)  all_40_2 = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (5082) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |   (5084)  all_56_21 = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5082) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | |   (5085)  op(e1, e1) = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | |   (5086)   ~ (all_40_2 = e2)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5083), (5086) imply:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | |   (5087)  $false
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5087) is inconsistent.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | |   (5088)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | |             $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | |             = all_40_1 & $i(all_40_1))
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5088) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | |   (5089)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e2) = all_40_1 & $i(all_40_0) &
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_40_1)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5089) implies:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | |   (5090)   ~ (all_40_0 = e0)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | |   (5091)  op(e1, e2) = all_40_1
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | |   (5092)  op(all_40_1, e1) = all_40_0
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |   (5093)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (5025), (5038), (5093),
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |            #1407.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |   (5094)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5094) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (5095)  all_58_6 = e2 & op(e1, e3) = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5095) implies:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (5096)  all_58_6 = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (224),
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (5001), (5052), (5080), (5085), (5091),
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (5096), (function-axioms) are inconsistent by
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1405.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (5097)  all_58_12 = e2 & op(e0, e3) = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5097) implies:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (5098)  all_58_12 = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (5099)  op(e0, e3) = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5100)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5100) gives:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5101)  all_58_0 = e2 & op(e3, e3) = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5101) implies:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5102)  op(e3, e3) = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (241),
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (5036), (5098), (5102), (function-axioms)
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1403.
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5103)  all_58_1 = e2 & op(e3, e2) = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5103) implies:
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5104)  all_58_1 = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5105)  op(e3, e2) = e2
% 232.47/43.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (236),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (5030), (5051), (5104), (5105),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1810.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5106)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5106) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5107)  all_58_4 = e2 & op(e3, e1) = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5107) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5108)  all_58_4 = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (227), (228),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (5042), (5085), (5108), (function-axioms)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2155.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5109)  all_58_9 = e2 & op(e3, e0) = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5109) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5110)  all_58_9 = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5111)  op(e3, e0) = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5112)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5112) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5113)  all_58_4 = e2 & op(e3, e1) = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5113) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5114)  all_58_4 = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (240), (242), (5038),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5110), (5111), (5114), (function-axioms) are
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1402.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5115)  all_58_5 = e2 & op(e2, e1) = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5115) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5116)  op(e2, e1) = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5027), (5116), (function-axioms) are
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5117)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5117) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5118)  all_58_8 = e2 & op(e1, e1) = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (5099) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5119)  all_52_3 = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_40_1,
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (5052), (5091) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5120)  all_40_1 = e3
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (168), (5111) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5121)  all_52_12 = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (5119) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5122)   ~ (all_52_11 = e2)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5122) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5123)   ~ (all_52_11 = e2)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (5121) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5124)   ~ (all_52_8 = e2)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5092), (5120) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5125)  op(e3, e1) = all_40_0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5080) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5126)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e2) = all_36_1 & $i(all_36_0) &
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5126) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5127)  op(e1, e2) = all_36_1
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_36_1,
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (5052), (5127) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5128)  all_36_1 = e3
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_0, e1, e3, simplifying with (169), (5125)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5129)  all_52_8 = all_40_0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (5129) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5130)  all_54_2 = all_40_0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (5129) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5131)   ~ (all_52_4 = all_40_0)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (5129) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5132)   ~ (all_52_11 = all_40_0)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5132) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5133)   ~ (all_52_11 = all_40_0)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5056), (5129) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5134)   ~ (all_40_0 = e3)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5124), (5129) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5135)   ~ (all_40_0 = e2)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5136)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5136) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5137)  all_58_4 = e0 & op(e3, e1) = e0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5137) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5138)  all_58_4 = e0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (170), (202), (242),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (5037), (5090), (5110), (5111), (5130),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5131), (5134), (5135), (5138), (function-axioms)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1399.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5139)  all_58_5 = e0 & op(e2, e1) = e0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5139) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5140)  all_58_5 = e0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5042), (5140) are inconsistent by sub-proof
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2038.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5141)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (167), (169), (190), (202), (211),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (255), (4998), (5008), (5025), (5043), (5052),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5056), (5084), (5085), (5090), (5091), (5123),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5125), (5127), (5130), (5133), (5134), (5135),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5141), (function-axioms) are inconsistent by
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1394.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5142)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5142) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5143)   ~ (all_36_1 = e0)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5144)  op(e1, e2) = all_36_1
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_36_1,
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (5052), (5144) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5145)  all_36_1 = e3
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_0, e1, e3, simplifying with (169), (5125)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5146)  all_52_8 = all_40_0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (5146) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5147)  all_54_2 = all_40_0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (5146) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5148)   ~ (all_52_4 = all_40_0)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (5146) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5149)   ~ (all_52_11 = all_40_0)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5149) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5150)   ~ (all_52_11 = all_40_0)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5056), (5146) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5151)   ~ (all_40_0 = e3)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5124), (5146) imply:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5152)   ~ (all_40_0 = e2)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5153)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5153) gives:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5154)  all_58_4 = e0 & op(e3, e1) = e0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5154) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5155)  all_58_4 = e0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (170), (202), (242),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (5037), (5090), (5110), (5111), (5147),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5148), (5151), (5152), (5155), (function-axioms)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1399.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5156)  all_58_5 = e0 & op(e2, e1) = e0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5156) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5157)  all_58_5 = e0
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5042), (5157) are inconsistent by sub-proof
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2038.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5158)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (167), (169), (190), (202), (211),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (255), (4998), (5008), (5025), (5043), (5052),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5056), (5084), (5085), (5090), (5091), (5123),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5125), (5144), (5147), (5150), (5151), (5152),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5158), (function-axioms) are inconsistent by
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1394.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5159)  all_58_14 = e2 & op(e0, e1) = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5159) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5160)  all_58_14 = e2
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (216), (217), (5007),
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5008), (5098), (5160), (function-axioms) are
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1391.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | |   (5161)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_40_1)
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5052), (5080), (5161), (function-axioms) are
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2144.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | |   (5162)  all_58_13 = e3 & op(e0, e2) = e3
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4997), (5162), (function-axioms) are
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | |   (5163)  all_58_10 = e3 & op(e2, e0) = e3
% 232.47/43.15  | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | ALPHA: (5163) implies:
% 232.47/43.15  | | | | | | | | | | | | | | | | | |   (5164)  op(e2, e0) = e3
% 232.47/43.15  | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5000), (5164), (function-axioms) are
% 232.47/43.15  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 232.47/43.15  | | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | | End of split
% 232.47/43.15  | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | Case 2:
% 232.47/43.15  | | | | | | | | | | | | | | | | 
% 232.47/43.15  | | | | | | | | | | | | | | | |   (5165)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 232.47/43.15  | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (5012), (5032), (5165) are
% 232.47/43.16  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 232.47/43.16  | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | End of split
% 232.47/43.16  | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | Case 2:
% 232.47/43.16  | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | |   (5166)  all_24_2 = e2
% 232.47/43.16  | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | COMBINE_EQS: (301), (5166) imply:
% 232.47/43.16  | | | | | | | | | | | | | | |   (5167)  all_10_2 = e2
% 232.47/43.16  | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | SIMP: (5167) implies:
% 232.47/43.16  | | | | | | | | | | | | | | |   (5168)  all_10_2 = e2
% 232.47/43.16  | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | REDUCE: (359), (5168) imply:
% 232.47/43.16  | | | | | | | | | | | | | | |   (5169)   ~ (all_52_3 = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | REDUCE: (365), (5168) imply:
% 232.47/43.16  | | | | | | | | | | | | | | |   (5170)   ~ (all_52_12 = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | |   (5171)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 232.47/43.16  | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (5028), (5170), (5171),
% 232.47/43.16  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.16  | | | | | | | | | | | | | | | |            #2316.
% 232.47/43.16  | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | Case 2:
% 232.47/43.16  | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | |   (5172)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 232.47/43.16  | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | BETA: splitting (5172) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | |   (5173)  all_58_11 = e2 & op(e1, e0) = e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | ALPHA: (5173) implies:
% 232.47/43.16  | | | | | | | | | | | | | | | | |   (5174)  op(e1, e0) = e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | |   (5175)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (159), (5026), (5169), (5175),
% 232.47/43.16  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.16  | | | | | | | | | | | | | | | | | |            #2314.
% 232.47/43.16  | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | |   (5176)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | BETA: splitting (5176) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | |   (5177)  all_58_14 = e2 & op(e0, e1) = e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | ALPHA: (5177) implies:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | |   (5178)  op(e0, e1) = e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 232.47/43.16  | | | | | | | | | | | | | | | | | | |              e2, e1, e0, simplifying with (157), (5178) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | |   (5179)  all_52_11 = e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 232.47/43.16  | | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (160), (5174) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | |   (5180)  all_52_14 = e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | REDUCE: (385), (5180) imply:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | |   (5181)   ~ (all_6_2 = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | SIMP: (5181) implies:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | |   (5182)   ~ (all_6_2 = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |   (5183)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5183) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |   (5184)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             = e3)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5184) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |   (5185)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |           e3
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5185) implies:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |   (5186)   ~ (all_56_11 = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5024), (5186) imply:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |   (5187)  $false
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5187) is inconsistent.
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |   (5188)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5188) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |   (5189)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |           e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5189) implies:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |   (5190)  op(e2, e3) = e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5025), (5190), (function-axioms) are
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |   (5191)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5191) implies:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |   (5192)   ~ (all_56_21 = e1)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (266), (5192) imply:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |   (5193)   ~ (all_6_2 = e1)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (297), (391), (5014), (5182), (5193) are
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1390.
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |   (5194)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             = e0)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4995), (4996), (5194), (function-axioms)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1389.
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |   (5195)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5195) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |   (5196)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5196) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |   (5197)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5197) implies:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |   (5198)  op(e2, e1) = e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5027), (5198), (function-axioms) are
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |   (5199)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5199) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |   (5200)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |             e2) = e1
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5200) implies:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |   (5201)  op(e2, e1) = e1
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (194), (297), (381), (391), (5014), (5182),
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |            (5201), (function-axioms) are inconsistent by
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1729.
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |   (5202)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5202) implies:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |   (5203)  op(e0, e2) = e2
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5026), (5203), (function-axioms) are
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |   (5204)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | |             = e0)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5204) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |   (5205)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             e2) = e0
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5205) implies:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |   (5206)   ~ (all_56_11 = e2)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5024), (5206) imply:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |   (5207)  $false
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5207) is inconsistent.
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |   (5208)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5208) gives:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |   (5209)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 232.47/43.16  | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |             e1) = e1
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5209) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |   (5210)  op(e1, e0) = e1
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5174), (5210), (function-axioms) are
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2019.
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |   (5211)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |             e1) = e0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5211) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |   (5212)   ~ (all_56_21 = e1)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (266), (5212) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |   (5213)   ~ (all_6_2 = e1)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (297), (391), (5014), (5182), (5213) are
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1390.
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | |   (5214)  all_58_15 = e2 & op(e0, e0) = e2
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | ALPHA: (5214) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | |   (5215)  op(e0, e0) = e2
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (5215), (function-axioms) are
% 232.47/43.17  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.17  | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | End of split
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | |   (5216)  all_58_15 = e2 & op(e0, e0) = e2
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | ALPHA: (5216) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | |   (5217)  op(e0, e0) = e2
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (5217), (function-axioms) are
% 232.47/43.17  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | End of split
% 232.47/43.17  | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | End of split
% 232.47/43.17  | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | End of split
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | Case 2:
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | |   (5218)  all_54_5 = e1 | all_54_5 = e0
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | REF_CLOSE: (275), (5010), (5016), (5218) are inconsistent by
% 232.47/43.17  | | | | | | | | | | | | | |            sub-proof #2300.
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | End of split
% 232.47/43.17  | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | End of split
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | Case 2:
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | |   (5219)  all_22_2 = e1
% 232.47/43.17  | | | | | | | | | | | |   (5220)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 232.47/43.17  | | | | | | | | | | | |             & op(e2, e1) = all_22_1 & $i(all_22_0) &
% 232.47/43.17  | | | | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1)
% 232.47/43.17  | | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | COMBINE_EQS: (326), (5219) imply:
% 232.47/43.17  | | | | | | | | | | | |   (5221)  all_8_2 = e1
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | SIMP: (5221) implies:
% 232.47/43.17  | | | | | | | | | | | |   (5222)  all_8_2 = e1
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | COMBINE_EQS: (347), (5222) imply:
% 232.47/43.17  | | | | | | | | | | | |   (5223)  all_30_2 = e1
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | COMBINE_EQS: (353), (5222) imply:
% 232.47/43.17  | | | | | | | | | | | |   (5224)  all_56_11 = e1
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | REDUCE: (366), (5222) imply:
% 232.47/43.17  | | | | | | | | | | | |   (5225)   ~ (all_52_1 = e1)
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | REDUCE: (369), (5222) imply:
% 232.47/43.17  | | | | | | | | | | | |   (5226)   ~ (all_52_4 = e1)
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | REDUCE: (371), (5222) imply:
% 232.47/43.17  | | | | | | | | | | | |   (5227)   ~ (all_52_6 = e1)
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | REDUCE: (373), (5222) imply:
% 232.47/43.17  | | | | | | | | | | | |   (5228)   ~ (all_52_7 = e1)
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | REDUCE: (375), (5222) imply:
% 232.47/43.17  | | | | | | | | | | | |   (5229)   ~ (all_52_9 = e1)
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | REDUCE: (377), (5222) imply:
% 232.47/43.17  | | | | | | | | | | | |   (5230)   ~ (all_52_13 = e1)
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | REDUCE: (392), (5222) imply:
% 232.47/43.17  | | | | | | | | | | | |   (5231)   ~ (e3 = e1)
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | REDUCE: (42), (5222) imply:
% 232.47/43.17  | | | | | | | | | | | |   (5232)  op(e2, e2) = e1
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | BETA: splitting (236) gives:
% 232.47/43.17  | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | |   (5233)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 232.47/43.17  | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 232.47/43.17  | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | BETA: splitting (5233) gives:
% 232.47/43.17  | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | |   (5234)  all_58_1 = e1 & op(e3, e2) = e1
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | ALPHA: (5234) implies:
% 232.47/43.17  | | | | | | | | | | | | | |   (5235)  op(e3, e2) = e1
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | REF_CLOSE: (170), (5226), (5235), (function-axioms) are
% 232.47/43.17  | | | | | | | | | | | | | |            inconsistent by sub-proof #2228.
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | Case 2:
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | |   (5236)  all_58_3 = e1 & op(e2, e2) = e1
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | ALPHA: (5236) implies:
% 232.47/43.17  | | | | | | | | | | | | | |   (5237)  all_58_3 = e1
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 232.47/43.17  | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | |   (5238)   ~ (all_26_2 = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | REDUCE: (4994), (5238) imply:
% 232.47/43.17  | | | | | | | | | | | | | | |   (5239)  $false
% 232.47/43.17  | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | CLOSE: (5239) is inconsistent.
% 232.47/43.17  | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | Case 2:
% 232.47/43.17  | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | |   (5240)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 232.47/43.17  | | | | | | | | | | | | | | |             & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 232.47/43.17  | | | | | | | | | | | | | | |             $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 232.47/43.17  | | | | | | | | | | | | | | |             = all_26_1 & $i(all_26_1))
% 232.47/43.17  | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | |   (5241)   ~ (all_24_2 = e2)
% 232.47/43.17  | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | REDUCE: (301), (5241) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | |   (5242)   ~ (all_10_2 = e2)
% 232.47/43.17  | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | |   (5243)  all_54_0 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (5243) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | |   (5244)  all_10_2 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | SIMP: (5244) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | |   (5245)  all_10_2 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | REDUCE: (355), (5245) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | |   (5246)   ~ (all_52_1 = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | REDUCE: (45), (5245) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | |   (5247)  op(e3, e3) = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | |   (5248)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (5225), (5229),
% 232.47/43.17  | | | | | | | | | | | | | | | | | |            (5230), (5246), (5248), (function-axioms) are
% 232.47/43.17  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2195.
% 232.47/43.17  | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | |   (5249)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 232.47/43.17  | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | BETA: splitting (5249) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | |   (5250)  all_58_5 = e3 & op(e2, e1) = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | ALPHA: (5250) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | |   (5251)  all_58_5 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | |   (5252)  op(e2, e1) = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | |   (5253)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5253) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5254)  all_58_6 = e3 & op(e1, e3) = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5254) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5255)  all_58_6 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5256)  op(e1, e3) = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (243),
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |            (4992), (5240), (5247), (5255), (5256),
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |            #1383.
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5257)  all_58_7 = e3 & op(e1, e2) = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5257) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5258)  all_58_7 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5259)  op(e1, e2) = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (5259) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5260)  all_52_6 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (5252) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5261)  all_52_9 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (5260) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5262)   ~ (all_52_4 = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (5260) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5263)   ~ (all_52_7 = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (5260) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5264)   ~ (all_52_14 = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (5261) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5265)   ~ (all_52_8 = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (5261) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5266)   ~ (all_52_13 = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (5261) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | |   (5267)   ~ (all_6_2 = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | |   (5268)   ~ (all_30_2 = e1)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5223), (5268) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | |   (5269)  $false
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5269) is inconsistent.
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | |   (5270)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_30_1 & $i(all_30_0) &
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5270) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |   (5271)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_30_1 & $i(all_30_0) &
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5271) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |   (5272)   ~ (all_30_0 = e0)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |   (5273)  op(e2, e1) = all_30_1
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | |   (5274)  op(all_30_1, e2) = all_30_0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5220) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5275)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_22_1 & $i(all_22_0) &
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5275) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5276)  op(e2, e1) = all_22_1
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5277)  op(all_22_1, e2) = all_22_0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (5252), (5273) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5278)  all_30_1 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (5273), (5276)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5279)  all_30_1 = all_22_1
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5278), (5279) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5280)  all_22_1 = e3
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5274), (5278) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5281)  op(e3, e2) = all_30_0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5277), (5280) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5282)  op(e3, e2) = all_22_0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |              all_22_0, e2, e3, simplifying with (170), (5282)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5283)  all_52_4 = all_22_0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |              all_30_0, e2, e3, simplifying with (170), (5281)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5284)  all_52_4 = all_30_0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5283), (5284) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5285)  all_30_0 = all_22_0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5285) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5286)  all_30_0 = all_22_0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (5283) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5287)  all_54_1 = all_22_0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (5283) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5288)   ~ (all_52_7 = all_22_0)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5288) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5289)   ~ (all_52_7 = all_22_0)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (5283) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5290)   ~ (all_52_12 = all_22_0)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5290) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5291)   ~ (all_52_12 = all_22_0)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5262), (5283) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5292)   ~ (all_22_0 = e3)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5226), (5283) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5293)   ~ (all_22_0 = e1)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5272), (5286) imply:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | |   (5294)   ~ (all_22_0 = e0)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (5295)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5295) gives:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5296)  all_58_1 = e0 & op(e3, e2) = e0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5296) implies:
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5297)  op(e3, e2) = e0
% 232.47/43.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5298)  all_54_1 = e3
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5287), (5292), (5298) are inconsistent by
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1382.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5299)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5299) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5300)  all_54_1 = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5287), (5300) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5301)  all_22_0 = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5301) implies:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5302)  all_22_0 = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5282), (5302) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5303)  op(e3, e2) = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5297), (5303), (function-axioms) are
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2026.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5304)  all_54_1 = e1 | all_54_1 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5287), (5293), (5294), (5304) are inconsistent by
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1381.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5305)  all_58_3 = e0 & op(e2, e2) = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (5010), (5305), (function-axioms) are
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (5306)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5306) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5307)  all_58_7 = e0 & op(e1, e2) = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5258), (5307) are inconsistent by sub-proof
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2034.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5308)  all_58_13 = e0 & op(e0, e2) = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5308) implies:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5309)  all_58_13 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5310)  all_54_1 = e3
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5287), (5292), (5310) are inconsistent by
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1382.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5311)   ~ (all_54_1 = e3)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5312)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5312) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5313)  all_54_1 = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5287), (5313) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5314)  all_22_0 = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5314) implies:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5315)  all_22_0 = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5289), (5315) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5316)   ~ (all_52_7 = e2)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5291), (5315) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5317)   ~ (all_52_12 = e2)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5292), (5315) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5318)   ~ (e3 = e2)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5282), (5315) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5319)  op(e3, e2) = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5320)  all_54_13 = e3
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (4997), (5320) are inconsistent by
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5321)   ~ (all_54_13 = e3)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5322)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5322) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5323)  all_54_13 = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (5316), (5323) are inconsistent by
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5324)   ~ (all_54_13 = e2)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5325)  all_54_13 = e1 | all_54_13 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5325) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5326)  all_54_13 = e1
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (5228), (5326) are inconsistent by
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1966.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5327)  all_54_13 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (5327) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5328)  all_52_7 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5328) implies:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5329)  all_52_7 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (5329) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5330)   ~ (all_52_3 = e0)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (5329) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5331)   ~ (all_52_11 = e0)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5331) implies:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5332)   ~ (all_52_11 = e0)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4997), (5329) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5333)   ~ (e3 = e0)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5316), (5329) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5334)   ~ (e2 = e0)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5228), (5329) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5335)   ~ (e1 = e0)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (5329) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5336)  op(e0, e2) = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5337)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5337) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5338)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_9 & $i(all_56_9)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5338) implies:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5339)  op(e3, e2) = all_56_9
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5340)  op(e3, all_56_9) = e3
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5341)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5341) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_9,
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (5319), (5339) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5342)  all_56_9 = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5340), (5342) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5343)  op(e3, e2) = e3
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5252), (5273), (5274), (5276), (5277), (5292),
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5343), (function-axioms) are inconsistent by
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1875.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5344)  all_58_5 = e0 & op(e2, e1) = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5251), (5344) are inconsistent by sub-proof
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2169.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5345)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (5014), (5332), (5345),
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1832.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5346)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5346) implies:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5347)  op(e2, all_56_11) = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5224), (5347) imply:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5348)  op(e2, e1) = e2
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5252), (5348), (function-axioms) are
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5349)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5349) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5350)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5350) implies:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5351)  op(e1, e2) = all_56_13
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5352)  op(e1, all_56_13) = e1
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5353)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5353) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5354)  all_58_4 = e0 & op(e3, e1) = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5354) implies:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5355)  all_58_4 = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5356)  op(e3, e1) = e0
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5357)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5357) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5358)  all_58_0 = e1 & op(e3, e3) = e1
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5358) implies:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5359)  op(e3, e3) = e1
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (168), (246), (4999), (5252), (5270),
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5276), (5277), (5292), (5356), (5359),
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1378.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5360)  all_58_1 = e1 & op(e3, e2) = e1
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5360) implies:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5361)  op(e3, e2) = e1
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5226), (5361), (function-axioms) are
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2228.
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5362)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5362) gives:
% 232.47/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5363)  all_58_4 = e1 & op(e3, e1) = e1
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (236), (237),
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (5226), (5237), (5309), (5336), (5355),
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5363), (function-axioms) are inconsistent by
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1373.
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5364)  all_58_9 = e1 & op(e3, e0) = e1
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5364) implies:
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5365)  all_58_9 = e1
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5366)  op(e3, e0) = e1
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (5259), (5351)
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5367)  all_56_13 = e3
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (168), (5366) gives:
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5368)  all_52_12 = e1
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (5356) gives:
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5369)  all_52_8 = e0
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (5369) imply:
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5370)   ~ (all_6_2 = e0)
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5368) imply:
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5371)   ~ (all_52_14 = e1)
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5371) implies:
% 232.80/43.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5372)   ~ (all_52_14 = e1)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5317), (5368) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5373)   ~ (e2 = e1)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5352), (5367) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5374)  op(e1, e3) = e1
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5375)   ~ (all_40_2 = e2)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (322), (5375) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5376)   ~ (all_6_2 = e2)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (194), (297), (367), (391), (5014), (5374),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5376), (function-axioms) are inconsistent by
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1371.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5377)  all_40_2 = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5378)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_40_1 & $i(all_40_1))
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (5377) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5379)  all_6_2 = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (5379) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5380)  all_36_2 = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5379) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5381)  op(e1, e1) = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5382)   ~ (all_36_2 = e2)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5380), (5382) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5383)  $false
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5383) is inconsistent.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5384)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5385)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (159), (160),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (213), (216), (217),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (241), (256), (4995), (4996),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5000), (5008), (5225), (5228), (5229), (5246),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5247), (5252), (5258), (5316), (5317), (5322),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5330), (5336), (5365), (5372), (5381), (5385),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1366.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5386)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5386) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5387)  all_58_14 = e2 & op(e0, e1) = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5387) implies:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5388)  all_58_14 = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5389)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5389) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5390)  all_58_0 = e2 & op(e3, e3) = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5390) implies:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5391)  op(e3, e3) = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5247), (5391), (function-axioms) are
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5392)  all_58_2 = e2 & op(e2, e3) = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5392) implies:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5393)  all_58_2 = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5394)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (236), (237),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (5226), (5309), (5336), (5393), (5394),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1365.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5395)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5395) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5396)  all_58_5 = e0 & op(e2, e1) = e0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5251), (5396) are inconsistent by sub-proof
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2169.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5397)  all_58_10 = e0 & op(e2, e0) = e0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (168), (221),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (226), (5008), (5258), (5317),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5381), (5397), (function-axioms) are inconsistent
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1363.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5398)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5398) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5399)  all_58_6 = e2 & op(e1, e3) = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5399) implies:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5400)  all_58_6 = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (224),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (5001), (5259), (5378), (5381), (5384),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5400), (function-axioms) are inconsistent by
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1362.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5401)  all_58_12 = e2 & op(e0, e3) = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5401) implies:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5402)  all_58_12 = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (216), (217), (5007),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5008), (5388), (5402), (function-axioms) are
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1391.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5403)  all_58_15 = e2 & op(e0, e0) = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5403) implies:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5404)  op(e0, e0) = e2
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (5404), (function-axioms) are
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5405)  all_58_5 = e0 & op(e2, e1) = e0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5251), (5405) are inconsistent by sub-proof
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2169.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5406)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (5014), (5332), (5406),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1832.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5407)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5407) implies:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5408)  op(e0, e2) = all_56_15
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5409)  op(e0, all_56_15) = e0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5410)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5410) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5411)  all_58_4 = e0 & op(e3, e1) = e0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5008), (5265), (5336), (5408), (5409),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5411), (function-axioms) are inconsistent by
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1361.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5412)  all_58_5 = e0 & op(e2, e1) = e0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5251), (5412) are inconsistent by sub-proof
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2169.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5413)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (5014), (5332), (5413),
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1832.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5414)  all_54_1 = e1 | all_54_1 = e0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5287), (5293), (5294), (5414) are inconsistent by
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1381.
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5415)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5415) implies:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5416)   ~ (all_22_1 = e0)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5417)  op(e2, e1) = all_22_1
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (5252), (5273) gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5418)  all_30_1 = e3
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (5273), (5417)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5419)  all_30_1 = all_22_1
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5418), (5419) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5420)  all_22_1 = e3
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5274), (5418) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5421)  op(e3, e2) = all_30_0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |              all_30_0, e2, e3, simplifying with (170), (5421)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5422)  all_52_4 = all_30_0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (5422) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5423)  all_54_1 = all_30_0
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (5422) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5424)   ~ (all_52_7 = all_30_0)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5424) implies:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5425)   ~ (all_52_7 = all_30_0)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (5422) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5426)   ~ (all_52_12 = all_30_0)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5426) implies:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5427)   ~ (all_52_12 = all_30_0)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5262), (5422) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5428)   ~ (all_30_0 = e3)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5226), (5422) imply:
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | |   (5429)   ~ (all_30_0 = e1)
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.19  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (5430)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5430) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5431)  all_58_1 = e0 & op(e3, e2) = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5431) implies:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5432)  op(e3, e2) = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5433)  all_54_1 = e3
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5423), (5428), (5433) are inconsistent by
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1360.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5434)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5434) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5435)  all_54_1 = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5423), (5435) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5436)  all_30_0 = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5436) implies:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5437)  all_30_0 = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5421), (5437) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5438)  op(e3, e2) = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5432), (5438), (function-axioms) are
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2026.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5439)  all_54_1 = e1 | all_54_1 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5272), (5423), (5429), (5439) are inconsistent by
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1359.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5440)  all_58_3 = e0 & op(e2, e2) = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (5010), (5440), (function-axioms) are
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (5441)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5441) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5442)  all_58_7 = e0 & op(e1, e2) = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5258), (5442) are inconsistent by sub-proof
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2034.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5443)  all_58_13 = e0 & op(e0, e2) = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5443) implies:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5444)  all_58_13 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5445)  all_54_1 = e3
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5423), (5428), (5445) are inconsistent by
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1360.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5446)   ~ (all_54_1 = e3)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5447)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5447) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5448)  all_54_1 = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5423), (5448) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5449)  all_30_0 = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5449) implies:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5450)  all_30_0 = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5425), (5450) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5451)   ~ (all_52_7 = e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5427), (5450) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5452)   ~ (all_52_12 = e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5428), (5450) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5453)   ~ (e3 = e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5421), (5450) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5454)  op(e3, e2) = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5455)  all_54_13 = e3
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (4997), (5455) are inconsistent by
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5456)   ~ (all_54_13 = e3)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5457)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5457) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5458)  all_54_13 = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (5451), (5458) are inconsistent by
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5459)   ~ (all_54_13 = e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5460)  all_54_13 = e1 | all_54_13 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5460) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5461)  all_54_13 = e1
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (5228), (5461) are inconsistent by
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1966.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5462)  all_54_13 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (5462) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5463)  all_52_7 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5463) implies:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5464)  all_52_7 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (5464) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5465)   ~ (all_52_3 = e0)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (5464) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5466)   ~ (all_52_11 = e0)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5466) implies:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5467)   ~ (all_52_11 = e0)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4997), (5464) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5468)   ~ (e3 = e0)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5451), (5464) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5469)   ~ (e2 = e0)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5228), (5464) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5470)   ~ (e1 = e0)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (5464) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5471)  op(e0, e2) = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5472)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5472) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5473)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_9 & $i(all_56_9)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5262), (5454), (5473), (function-axioms)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1358.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5474)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5474) implies:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5475)  op(e2, all_56_11) = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5224), (5475) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5476)  op(e2, e1) = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5252), (5476), (function-axioms) are
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5477)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5477) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5478)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5478) implies:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5479)  op(e1, e2) = all_56_13
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5480)  op(e1, all_56_13) = e1
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5481)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5481) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5482)  all_58_4 = e0 & op(e3, e1) = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5482) implies:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5483)  all_58_4 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5484)  op(e3, e1) = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5485)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (5226), (5247), (5485),
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1357.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5486)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5486) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5487)  all_58_4 = e1 & op(e3, e1) = e1
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (236), (237),
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (5226), (5237), (5444), (5471), (5483),
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5487), (function-axioms) are inconsistent by
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1373.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5488)  all_58_9 = e1 & op(e3, e0) = e1
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5488) implies:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5489)  all_58_9 = e1
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5490)  op(e3, e0) = e1
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (5259), (5479)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5491)  all_56_13 = e3
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (168), (5490) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5492)  all_52_12 = e1
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (5484) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5493)  all_52_8 = e0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (5493) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5494)   ~ (all_6_2 = e0)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5492) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5495)   ~ (all_52_14 = e1)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5495) implies:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5496)   ~ (all_52_14 = e1)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5452), (5492) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5497)   ~ (e2 = e1)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5480), (5491) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5498)  op(e1, e3) = e1
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5499)   ~ (all_40_2 = e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (322), (5499) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5500)   ~ (all_6_2 = e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (194), (297), (367), (391), (5014), (5498),
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5500), (function-axioms) are inconsistent by
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1371.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5501)  all_40_2 = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5502)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_40_1 & $i(all_40_1))
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (5501) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5503)  all_6_2 = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (5503) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5504)  all_36_2 = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5503) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5505)  op(e1, e1) = e2
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5506)   ~ (all_36_2 = e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5504), (5506) imply:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5507)  $false
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5507) is inconsistent.
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5508)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5509)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 232.80/43.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (159), (160),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (213), (216), (217),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (241), (256), (4995), (4996),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5000), (5008), (5225), (5228), (5229), (5246),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5247), (5252), (5258), (5451), (5452), (5457),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5465), (5471), (5489), (5496), (5505), (5509),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1366.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5510)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5510) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5511)  all_58_14 = e2 & op(e0, e1) = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5511) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5512)  all_58_14 = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5513)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5513) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5514)  all_58_0 = e2 & op(e3, e3) = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5514) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5515)  op(e3, e3) = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5247), (5515), (function-axioms) are
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5516)  all_58_2 = e2 & op(e2, e3) = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5516) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5517)  all_58_2 = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5518)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (236), (237),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (5226), (5444), (5471), (5517), (5518),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1365.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5519)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5519) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5520)  all_58_5 = e0 & op(e2, e1) = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5520) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5521)  op(e2, e1) = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5270), (5416), (5417), (5521), (function-axioms)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1356.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5522)  all_58_10 = e0 & op(e2, e0) = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (168), (221),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (226), (5008), (5258), (5452),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5505), (5522), (function-axioms) are inconsistent
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1363.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5523)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5523) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5524)  all_58_6 = e2 & op(e1, e3) = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5524) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5525)  all_58_6 = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (224),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (5001), (5259), (5502), (5505), (5508),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5525), (function-axioms) are inconsistent by
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1362.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5526)  all_58_12 = e2 & op(e0, e3) = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5526) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5527)  all_58_12 = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (216), (217), (5007),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5008), (5512), (5527), (function-axioms) are
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1391.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5528)  all_58_15 = e2 & op(e0, e0) = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5528) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5529)  op(e0, e0) = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (5529), (function-axioms) are
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5530)  all_58_5 = e0 & op(e2, e1) = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5530) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5531)  op(e2, e1) = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5270), (5416), (5417), (5531), (function-axioms)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1356.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5532)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (5014), (5467), (5532),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1832.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5533)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5533) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5534)  op(e0, e2) = all_56_15
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5535)  op(e0, all_56_15) = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5536)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5536) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5537)  all_58_4 = e0 & op(e3, e1) = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5008), (5265), (5471), (5534), (5535),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5537), (function-axioms) are inconsistent by
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1361.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5538)  all_58_5 = e0 & op(e2, e1) = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5538) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5539)  op(e2, e1) = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5270), (5416), (5417), (5539), (function-axioms)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1356.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5540)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (5014), (5467), (5540),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1832.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5541)  all_54_1 = e1 | all_54_1 = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5272), (5423), (5429), (5541) are inconsistent by
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1359.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | |   (5542)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5542) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | |   (5543)   ~ (all_30_1 = e3)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | |   (5544)  op(e2, e1) = all_30_1
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5252), (5543), (5544), (function-axioms) are
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1839.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |   (5545)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (391), (5001), (5545),
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |            #1529.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | |   (5546)  all_58_10 = e3 & op(e2, e0) = e3
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | ALPHA: (5546) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | |   (5547)  op(e2, e0) = e3
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5000), (5547), (function-axioms) are
% 232.80/43.21  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | |   (5548)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (5012), (5242), (5548) are
% 232.80/43.21  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 232.80/43.21  | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | End of split
% 232.80/43.21  | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | |   (5549)  all_24_2 = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (5549) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | |   (5550)  all_10_2 = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (5550) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | |   (5551)  all_56_1 = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | REDUCE: (355), (5550) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | |   (5552)   ~ (all_52_1 = e2)
% 232.80/43.21  | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | REDUCE: (45), (5550) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | |   (5553)  op(e3, e3) = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | |   (5554)   ~ (all_36_2 = e2)
% 232.80/43.21  | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | REDUCE: (328), (5554) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | | |   (5555)   ~ (all_6_2 = e2)
% 232.80/43.21  | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | |   (5556)  all_54_10 = e3
% 232.80/43.21  | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (5556) are inconsistent by sub-proof
% 232.80/43.21  | | | | | | | | | | | | | | | | | |            #2313.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | |   (5557)   ~ (all_54_10 = e3)
% 232.80/43.21  | | | | | | | | | | | | | | | | | |   (5558)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | BETA: splitting (5558) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | |   (5559)  all_54_10 = e2
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (5555), (5559) are inconsistent by
% 232.80/43.21  | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | |   (5560)   ~ (all_54_10 = e2)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | |   (5561)  all_54_10 = e1 | all_54_10 = e0
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | BETA: splitting (5561) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |   (5562)  all_54_10 = e1
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (5562) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |   (5563)  all_6_2 = e1
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | SIMP: (5563) implies:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |   (5564)  all_6_2 = e1
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (5564) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |   (5565)  all_56_21 = e1
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (5564) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |   (5566)   ~ (all_52_2 = e1)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (5564) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |   (5567)   ~ (all_52_8 = e1)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (5564) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |   (5568)   ~ (all_52_14 = e1)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (5555), (5564) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |   (5569)   ~ (e2 = e1)
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5564) imply:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | |   (5570)  op(e1, e1) = e1
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | |   (5571)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 232.80/43.21  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (167), (169), (4995), (4996), (5551),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |            (5552), (5565), (5567), (5571), (function-axioms)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1355.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |   (5572)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5572) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | |   (5573)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5573) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |   (5574)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5574) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |   (5575)   ~ (all_56_21 = e1)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5565), (5575) imply:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |   (5576)  $false
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5576) is inconsistent.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |   (5577)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5577) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |   (5578)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e1
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5578) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |   (5579)  op(e2, e1) = e1
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (297), (381), (5014), (5561), (5579),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |            #1905.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |   (5580)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5580) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |   (5581)   ~ (all_56_31 = e0)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |   (5582)   ~ (all_56_21 = e0)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |   (5583)   ~ (all_56_1 = e0)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |   (5584)  op(e0, e2) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | |   (5585)  op(e2, e0) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (5586)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (5225), (5553), (5586),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | |            #1354.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (5587)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5587) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5588)  all_58_6 = e1 & op(e1, e3) = e1
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5588) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5589)  op(e1, e3) = e1
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5566), (5589), (function-axioms) are
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5590)  all_58_12 = e1 & op(e0, e3) = e1
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5590) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5591)  all_58_12 = e1
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5592)  op(e0, e3) = e1
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5593)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5593) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5594)  all_58_1 = e2 & op(e3, e2) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5594) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5595)  all_58_1 = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5596)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5596) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5597)  all_58_1 = e3 & op(e3, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5595), (5597) are inconsistent by sub-proof
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2141.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5598)  all_58_3 = e3 & op(e2, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5598) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5599)  all_58_3 = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (158), (235), (236),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5228), (5584), (5595), (5599), (function-axioms)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1352.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5600)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5600) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5601)  all_58_7 = e3 & op(e1, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5601) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5602)  op(e1, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (136), (162), (168),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (195), (240), (242), (246), (267), (4999),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5553), (5595), (5602), (function-axioms) are
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2178.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5603)  all_58_13 = e3 & op(e0, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5603) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5604)  op(e0, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5584), (5604), (function-axioms) are
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5605)  all_58_3 = e2 & op(e2, e2) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5605) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5606)  op(e2, e2) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5232), (5606), (function-axioms) are
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5607)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5607) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5608)  all_58_7 = e2 & op(e1, e2) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5608) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5609)  all_58_7 = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5610)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5610) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5611)  all_58_1 = e3 & op(e3, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5611) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5612)  all_58_1 = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5613)  op(e3, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5614)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5614) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5615)  all_58_6 = e3 & op(e1, e3) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5615) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5616)  all_58_6 = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5617)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5617) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5618)  all_58_12 = e2 & op(e0, e3) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5618) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5619)  all_58_12 = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (239), (241), (5553),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5616), (5619), (function-axioms) are inconsistent
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1756.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5620)  all_58_13 = e2 & op(e0, e2) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5620) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5621)  all_58_13 = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (235), (236), (5584),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5609), (5612), (5613), (5621), (function-axioms)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1748.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5622)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5622) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5623)  all_58_14 = e2 & op(e0, e1) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5623) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5624)  all_58_14 = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (216), (5007), (5584), (5591),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5624), (function-axioms) are inconsistent by
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1537.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5625)  all_58_15 = e2 & op(e0, e0) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5625) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5626)  op(e0, e0) = e2
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (5626), (function-axioms) are
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5627)  all_58_7 = e3 & op(e1, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5627) implies:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5628)  op(e1, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (162), (170), (195), (267), (5613), (5628),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2190.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5629)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (391), (5001), (5629),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1529.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5630)  all_58_3 = e3 & op(e2, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (5225), (5229),
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5230), (5630), (function-axioms) are inconsistent
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2196.
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5631)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5631) gives:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5632)  all_58_7 = e3 & op(e1, e2) = e3
% 232.80/43.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5609), (5632) are inconsistent by sub-proof
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1800.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5633)  all_58_13 = e3 & op(e0, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5633) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5634)  op(e0, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5584), (5634), (function-axioms) are
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5635)  all_58_13 = e2 & op(e0, e2) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5635) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5636)  all_58_13 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5637)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5637) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5638)  all_58_6 = e2 & op(e1, e3) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5638) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5639)  all_58_6 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (159), (239), (245), (4992),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4996), (5240), (5553), (5592), (5639),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1348.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5640)  all_58_7 = e2 & op(e1, e2) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5640) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5641)  all_58_7 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (235), (236), (237),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (5584), (5636), (5641), (function-axioms)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1453.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5642)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5642) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5643)  all_58_8 = e2 & op(e1, e1) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5643) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5644)  op(e1, e1) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5570), (5644), (function-axioms) are
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5645)  all_58_11 = e2 & op(e1, e0) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5645) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5646)  all_58_11 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (216), (220), (5007),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5008), (5585), (5646), (function-axioms) are
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1344.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |   (5647)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (5551), (5565), (5568), (5647),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |            #1343.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | |   (5648)  all_54_10 = e0
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (5014), (5648) are inconsistent by
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | |   (5649)  all_36_2 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | |   (5650)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 232.80/43.23  | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 232.80/43.23  | | | | | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 232.80/43.23  | | | | | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (5649) imply:
% 232.80/43.23  | | | | | | | | | | | | | | | | |   (5651)  all_6_2 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | SIMP: (5651) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | |   (5652)  all_6_2 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (5652) imply:
% 232.80/43.23  | | | | | | | | | | | | | | | | |   (5653)  all_40_2 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (5652) imply:
% 232.80/43.23  | | | | | | | | | | | | | | | | |   (5654)  all_56_21 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | REDUCE: (367), (5652) imply:
% 232.80/43.23  | | | | | | | | | | | | | | | | |   (5655)   ~ (all_52_2 = e2)
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | REDUCE: (380), (5652) imply:
% 232.80/43.23  | | | | | | | | | | | | | | | | |   (5656)   ~ (all_52_8 = e2)
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | REDUCE: (381), (5652) imply:
% 232.80/43.23  | | | | | | | | | | | | | | | | |   (5657)   ~ (all_52_9 = e2)
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | REDUCE: (391), (5652) imply:
% 232.80/43.23  | | | | | | | | | | | | | | | | |   (5658)   ~ (e3 = e2)
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | REDUCE: (39), (5652) imply:
% 232.80/43.23  | | | | | | | | | | | | | | | | |   (5659)  op(e1, e1) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | |   (5660)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (5232), (5552), (5660),
% 232.80/43.23  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.23  | | | | | | | | | | | | | | | | | |            #1929.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | |   (5661)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 232.80/43.23  | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | BETA: splitting (5661) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | |   (5662)  all_58_5 = e2 & op(e2, e1) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | ALPHA: (5662) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | |   (5663)  op(e2, e1) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5657), (5663), (function-axioms) are
% 232.80/43.23  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | |   (5664)  all_58_10 = e2 & op(e2, e0) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | ALPHA: (5664) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | |   (5665)  op(e2, e0) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | |   (5666)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5666) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | |   (5667)  all_58_1 = e2 & op(e3, e2) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5667) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | |   (5668)  all_58_1 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |   (5669)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5669) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |   (5670)  all_58_1 = e3 & op(e3, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5668), (5670) are inconsistent by sub-proof
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |            #2141.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |   (5671)  all_58_3 = e3 & op(e2, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (5225), (5229),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |            (5230), (5671), (function-axioms) are inconsistent
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2196.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |   (5672)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5672) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |   (5673)  all_58_7 = e3 & op(e1, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5673) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |   (5674)  op(e1, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (136), (162), (168),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |            (170), (195), (240), (242), (246), (267), (4999),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |            (5553), (5668), (5674), (function-axioms) are
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2178.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |   (5675)  all_58_13 = e3 & op(e0, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4997), (5675), (function-axioms) are
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | |   (5676)  all_58_3 = e2 & op(e2, e2) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5676) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | |   (5677)  op(e2, e2) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5232), (5677), (function-axioms) are
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | |   (5678)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5678) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | |   (5679)  all_58_7 = e2 & op(e1, e2) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5679) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | |   (5680)  all_58_7 = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | |   (5681)  op(e1, e2) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |   (5682)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5682) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |   (5683)  all_58_1 = e3 & op(e3, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5683) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |   (5684)  op(e3, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | |   (5685)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5685) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (5686)  all_58_6 = e3 & op(e1, e3) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (224),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (5659), (5680), (5681), (5686),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | |            #2208.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (5687)  all_58_7 = e3 & op(e1, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5687) implies:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (5688)  op(e1, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (162), (170), (195), (267), (5684), (5688),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | |            #2190.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | |   (5689)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (5001), (5659), (5689),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | |            #2148.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |   (5690)  all_58_3 = e3 & op(e2, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (5225), (5229),
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |            (5230), (5690), (function-axioms) are inconsistent
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2196.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |   (5691)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5691) gives:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |   (5692)  all_58_7 = e3 & op(e1, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5680), (5692) are inconsistent by sub-proof
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |            #1675.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |   (5693)  all_58_13 = e3 & op(e0, e2) = e3
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4997), (5693), (function-axioms) are
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | |   (5694)  all_58_13 = e2 & op(e0, e2) = e2
% 232.80/43.23  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5694) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | |   (5695)  all_58_13 = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | |   (5696)  op(e0, e2) = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | |   (5697)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5697) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5698)  all_58_6 = e2 & op(e1, e3) = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5698) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5699)  all_58_6 = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |   (5700)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (159), (245), (4996), (5553),
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |            (5699), (5700), (function-axioms) are inconsistent
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1341.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |   (5701)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5701) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (5702)  all_58_6 = e1 & op(e1, e3) = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5699), (5702) are inconsistent by sub-proof
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |            #1423.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (5703)  all_58_12 = e1 & op(e0, e3) = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5703) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (5704)  op(e0, e3) = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (159), (239), (245), (4992),
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |            (4996), (5240), (5553), (5699), (5704),
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |            #1348.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5705)  all_58_7 = e2 & op(e1, e2) = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5705) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5706)  all_58_7 = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (235), (236), (237),
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |            (238), (5695), (5696), (5706), (function-axioms)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1453.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | |   (5707)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5707) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5708)  all_58_8 = e2 & op(e1, e1) = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5708) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5709)  all_58_8 = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (5696) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5710)  all_52_7 = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (5665) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5711)  all_52_13 = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (5710) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5712)   ~ (all_52_3 = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (5710) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5713)   ~ (all_52_4 = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (5710) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5714)   ~ (all_52_6 = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (5710) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5715)   ~ (all_52_11 = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5715) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5716)   ~ (all_52_11 = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (5711) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5717)   ~ (all_52_12 = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (5711) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5718)   ~ (all_52_14 = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5718) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | |   (5719)   ~ (all_52_14 = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |   (5720)   ~ (all_40_2 = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5653), (5720) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |   (5721)  $false
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5721) is inconsistent.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |   (5722)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | |             = all_40_1 & $i(all_40_1))
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (5723)  all_54_9 = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (5723) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (5724)  all_52_6 = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5724) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (5725)  all_52_6 = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (5725) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (5726)   ~ (all_52_4 = e3)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (5725) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (5727)  op(e1, e2) = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5728)  all_54_1 = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (5726), (5728) are inconsistent by
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5729)   ~ (all_54_1 = e3)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5730)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5730) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5731)  all_54_1 = e2
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (5713), (5731) are inconsistent by
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1928.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5732)   ~ (all_54_1 = e2)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5733)  all_54_1 = e1 | all_54_1 = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5733) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5734)  all_54_1 = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (5226), (5734) are inconsistent by
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2051.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5735)  all_54_1 = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (5735) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5736)  all_52_4 = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5736) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5737)  all_52_4 = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (5737) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5738)   ~ (all_52_8 = e0)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5738) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5739)   ~ (all_52_8 = e0)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (5737) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5740)   ~ (all_52_12 = e0)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5740) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5741)   ~ (all_52_12 = e0)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5726), (5737) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5742)   ~ (e3 = e0)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5713), (5737) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5743)   ~ (e2 = e0)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5226), (5737) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5744)   ~ (e1 = e0)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (5737) imply:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5745)  op(e3, e2) = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5746)  all_54_3 = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (4999), (5746) are inconsistent by
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5747)   ~ (all_54_3 = e3)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5748)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5749)  all_58_15 = e0 & op(e0, e0) = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5749) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5750)  op(e0, e0) = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5008), (5750), (function-axioms) are
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5751)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5751) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5752)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5753)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5753) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5754)  all_58_0 = e3 & op(e3, e3) = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5754) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5755)  op(e3, e3) = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5553), (5755), (function-axioms) are
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5756)  all_58_1 = e3 & op(e3, e2) = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5756) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5757)  op(e3, e2) = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5745), (5757), (function-axioms) are
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2099.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5758)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5758) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5759)  all_58_4 = e3 & op(e3, e1) = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5759) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5760)  all_58_4 = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5761)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5761) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5762)  all_58_0 = e3 & op(e3, e3) = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5762) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5763)  op(e3, e3) = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5553), (5763), (function-axioms) are
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5764)  all_58_2 = e3 & op(e2, e3) = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5764) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5765)  op(e2, e3) = e3
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5766)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (5226), (5553), (5766),
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1340.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5767)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5767) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5768)  all_58_4 = e1 & op(e3, e1) = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5760), (5768) are inconsistent by sub-proof
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2042.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5769)  all_58_9 = e1 & op(e3, e0) = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5769) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5770)  all_58_9 = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5771)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (5229), (5760), (5771),
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1339.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5772)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5772) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5773)  all_58_8 = e1 & op(e1, e1) = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5773) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5774)  op(e1, e1) = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5659), (5774), (function-axioms) are
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5775)  all_58_14 = e1 & op(e0, e1) = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5775) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5776)  op(e0, e1) = e1
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5752) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5777)  all_58_12 = e0 & op(e0, e3) = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5777) implies:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5778)  op(e0, e3) = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5779)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5779) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5780)  all_58_0 = e0 & op(e3, e3) = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5780) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5781)  op(e3, e3) = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5553), (5781), (function-axioms) are
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5782)  all_58_1 = e0 & op(e3, e2) = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5782) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5783)  all_58_1 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5784)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5784) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5785)  all_58_0 = e1 & op(e3, e3) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5785) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5786)  op(e3, e3) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (244), (5760), (5770), (5783),
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5786), (function-axioms) are inconsistent by
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1338.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5787)  all_58_2 = e1 & op(e2, e3) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5225), (5787), (function-axioms) are
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5788)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5788) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5789)  all_58_6 = e1 & op(e1, e3) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5789) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5790)  op(e1, e3) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5748) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5791)  all_54_3 = e2
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (5717), (5791) are inconsistent by
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2290.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5792)  all_54_3 = e1 | all_54_3 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5792) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5793)  all_54_3 = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (5793) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5794)  all_52_12 = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5794) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5795)  all_52_12 = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (5795) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5796)   ~ (all_52_8 = e1)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5797)  all_54_2 = e3
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (5797) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5798)  all_52_8 = e3
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5798) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5799)  all_52_8 = e3
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (5799) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5800)   ~ (all_52_9 = e3)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5800) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5801)   ~ (all_52_9 = e3)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (5799) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5802)   ~ (all_52_11 = e3)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5803)  all_54_6 = e3
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (5801), (5803) are inconsistent by
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5804)   ~ (all_54_6 = e3)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5805)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5805) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5806)  all_54_6 = e2
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (5657), (5806) are inconsistent by
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5807)  all_54_6 = e1 | all_54_6 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5807) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5808)  all_54_6 = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (5229), (5808) are inconsistent by
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2246.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5809)  all_54_6 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (5809) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5810)  all_52_9 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5810) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5811)  all_52_9 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (5811) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5812)   ~ (all_52_11 = e0)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5812) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5813)   ~ (all_52_11 = e0)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5814)  all_54_14 = e3
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (5814) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5815)  all_52_11 = e3
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4998), (5815) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5816)  $false
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5816) is inconsistent.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5817)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5817) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5818)  all_54_14 = e2
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (5716), (5818) are inconsistent by
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1856.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5819)   ~ (all_54_14 = e2)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5820)  all_54_14 = e1 | all_54_14 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5820) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5821)  all_54_14 = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (5821) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5822)  all_52_11 = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5822) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5823)  all_52_11 = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (5823) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5824)   ~ (all_52_3 = e1)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5716), (5823) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5825)   ~ (e2 = e1)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5826)  all_54_12 = e3
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (4996), (5826) are inconsistent by
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5827)   ~ (all_54_12 = e3)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5828)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5829)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (5551), (5745), (5765), (5829),
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1924.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5830)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5830) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5831)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_5 & $i(all_56_5)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (257), (5659), (5712), (5790), (5824),
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5828), (5831), (function-axioms) are inconsistent
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1702.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5832)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_7 & $i(all_56_7)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5832) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5833)  op(e0, e3) = all_56_7
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5834)  op(e0, all_56_7) = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5828) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5835)  all_54_12 = e2
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (5835) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5836)  all_52_3 = e2
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5712), (5836) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5837)  $false
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5837) is inconsistent.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5838)  all_54_12 = e1 | all_54_12 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5838) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5839)  all_54_12 = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (5839) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5840)  all_52_3 = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5824), (5840) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5841)  $false
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5841) is inconsistent.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5842)  all_54_12 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (5842) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5843)  all_52_3 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_7,
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (5778), (5833) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5844)  all_56_7 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5834), (5844) imply:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5845)  op(e0, e0) = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5008), (5845), (function-axioms) are
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5846)  all_54_14 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (5813), (5846) are inconsistent by
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1936.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5847)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (5656), (5739), (5796), (5847) are
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1335.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5848)  all_54_3 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (5741), (5848) are inconsistent by
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2288.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5849)  all_58_12 = e1 & op(e0, e3) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5849) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5850)  op(e0, e3) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4992), (5240), (5778), (5850),
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1384.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5851)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (5739), (5741), (5851),
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1334.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5852)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (5696), (5776), (5852),
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1333.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5853)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5853) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5854)  all_58_6 = e3 & op(e1, e3) = e3
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5854) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5855)  op(e1, e3) = e3
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5856)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5856) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5857)  all_58_6 = e1 & op(e1, e3) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5857) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5858)  op(e1, e3) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5855), (5858), (function-axioms) are
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5859)  all_58_7 = e1 & op(e1, e2) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5859) implies:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5860)  op(e1, e2) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5650), (5722), (5727), (5860),
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1332.
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5861)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5861) gives:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5862)  all_58_8 = e1 & op(e1, e1) = e1
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5862) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5863)  op(e1, e1) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5659), (5863), (function-axioms) are
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5864)  all_58_11 = e1 & op(e1, e0) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5864) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5865)  op(e1, e0) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (160), (280), (5717), (5741), (5748),
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5865), (function-axioms) are inconsistent by
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1330.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5866)  all_58_12 = e3 & op(e0, e3) = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5866) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5867)  op(e0, e3) = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4996), (5867), (function-axioms) are
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5868)  all_58_9 = e3 & op(e3, e0) = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5868) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5869)  op(e3, e0) = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4999), (5869), (function-axioms) are
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (5870)   ~ (all_54_9 = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (5871)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (5870) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (5872)   ~ (all_52_6 = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5871) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5873)  all_54_9 = e2
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (5714), (5873) are inconsistent by
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1954.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5874)   ~ (all_54_9 = e2)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5875)  all_54_9 = e1 | all_54_9 = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5875) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5876)  all_54_9 = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (5227), (5876) are inconsistent by
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2055.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5877)  all_54_9 = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (5877) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5878)  all_52_6 = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5878) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5879)  all_52_6 = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (5879) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5880)   ~ (all_52_2 = e0)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (5879) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5881)   ~ (all_52_4 = e0)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (5879) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5882)   ~ (all_52_14 = e0)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5882) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5883)   ~ (all_52_14 = e0)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5714), (5879) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5884)   ~ (e2 = e0)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5227), (5879) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5885)   ~ (e1 = e0)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5886)  all_54_11 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (5886) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5887)  all_52_14 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5001), (5887) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5888)  $false
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5888) is inconsistent.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5889)   ~ (all_54_11 = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5890)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5891)  all_54_1 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (5891) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5892)  all_52_4 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5892) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5893)  all_52_4 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (5893) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5894)   ~ (all_52_8 = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5894) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5895)   ~ (all_52_8 = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (5893) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5896)   ~ (all_52_12 = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5897)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5897) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5898)  all_58_6 = e3 & op(e1, e3) = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5898) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5899)  all_58_6 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5900)  op(e1, e3) = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5901)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (5225), (5553), (5901),
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1354.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5902)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5902) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5903)  all_58_6 = e1 & op(e1, e3) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5903) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5904)  op(e1, e3) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5900), (5904), (function-axioms) are
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5905)  all_58_12 = e1 & op(e0, e3) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5905) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5906)  all_58_12 = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5907)  op(e0, e3) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5908)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5908) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5909)  all_58_0 = e0 & op(e3, e3) = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5909) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5910)  op(e3, e3) = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5553), (5910), (function-axioms) are
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5911)  all_58_2 = e0 & op(e2, e3) = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5911) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5912)  all_58_2 = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5913)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5913) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5914)  all_58_2 = e3 & op(e2, e3) = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5914) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5915)  all_58_2 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5912), (5915) are inconsistent by sub-proof
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2124.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5916)  all_58_3 = e3 & op(e2, e2) = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (5225), (5229),
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5230), (5916), (function-axioms) are inconsistent
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2196.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5917)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5917) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5918)  all_58_5 = e3 & op(e2, e1) = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5918) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5919)  all_58_5 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5920)  op(e2, e1) = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5890) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5921)  all_54_11 = e2
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (5719), (5921) are inconsistent by
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2177.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5922)   ~ (all_54_11 = e2)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5923)  all_54_11 = e1 | all_54_11 = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5923) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5924)  all_54_11 = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (5924) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5925)  all_52_14 = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5925) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5926)  all_52_14 = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (5926) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5927)   ~ (all_52_2 = e1)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5926) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5928)   ~ (all_52_12 = e1)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5719), (5926) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5929)   ~ (e2 = e1)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (5926) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5930)  op(e1, e0) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5931)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5931) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5932)  all_58_0 = e1 & op(e3, e3) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5932) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5933)  op(e3, e3) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (243), (5899), (5906), (5912),
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5933), (function-axioms) are inconsistent by
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1328.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5934)  all_58_1 = e1 & op(e3, e2) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5934) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5935)  all_58_1 = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (168), (169), (246), (4999), (5553),
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5895), (5935), (function-axioms) are inconsistent
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1327.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5936)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5936) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5937)  all_58_4 = e1 & op(e3, e1) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5937) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5938)  all_58_4 = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5939)  op(e3, e1) = e1
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5940)  all_54_8 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (5940) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5941)  all_52_2 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5941) implies:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5942)  all_52_2 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (5942) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5943)   ~ (all_52_1 = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (5942) imply:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5944)   ~ (all_52_3 = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5945)  all_54_4 = e3
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (5943), (5945) are inconsistent by
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5946)   ~ (all_54_4 = e3)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5947)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5947) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5948)  all_54_4 = e2
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (5552), (5948) are inconsistent by
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2096.
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5949)   ~ (all_54_4 = e2)
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5950)  all_54_4 = e1 | all_54_4 = e0
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5951)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5951) gives:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5952)  all_58_1 = e0 & op(e3, e2) = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5881), (5952), (function-axioms) are
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5953)  all_58_3 = e0 & op(e2, e2) = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (5010), (5953), (function-axioms) are
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5954)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5954) gives:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5955)  all_58_7 = e0 & op(e1, e2) = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5955) implies:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5956)  all_58_7 = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5957)  op(e1, e2) = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5958)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5958) gives:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5959)  all_58_6 = e1 & op(e1, e3) = e1
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5959) implies:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5960)  op(e1, e3) = e1
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5927), (5960), (function-axioms) are
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5961)  all_58_7 = e1 & op(e1, e2) = e1
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5961) implies:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5962)  all_58_7 = e1
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (223), (5709), (5899), (5930),
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5962), (function-axioms) are inconsistent by
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1555.
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5963)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5963) gives:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5964)  all_58_8 = e1 & op(e1, e1) = e1
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5964) implies:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5965)  op(e1, e1) = e1
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5659), (5965), (function-axioms) are
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5966)  all_58_11 = e1 & op(e1, e0) = e1
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5966) implies:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5967)  all_58_11 = e1
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5968)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5968) gives:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5969)  all_58_4 = e0 & op(e3, e1) = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5969) implies:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5970)  all_58_4 = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5938), (5970) are inconsistent by sub-proof
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1710.
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5971)  all_58_5 = e0 & op(e2, e1) = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5971) implies:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5972)  all_58_5 = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5919), (5972) are inconsistent by sub-proof
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2038.
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5973)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5973) gives:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5974)  all_58_8 = e0 & op(e1, e1) = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5974) implies:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5975)  op(e1, e1) = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (5899), (5956), (5967),
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5975), (function-axioms) are inconsistent by
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1325.
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5976)  all_58_14 = e0 & op(e0, e1) = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5976) implies:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5977)  op(e0, e1) = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5950) gives:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5978)  all_54_4 = e1
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (5225), (5978) are inconsistent by
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2086.
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5979)  all_54_4 = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (5979) imply:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5980)  all_52_1 = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5980) implies:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5981)  all_52_1 = e0
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (5981) imply:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5982)   ~ (all_52_3 = e0)
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5982) implies:
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5983)   ~ (all_52_3 = e0)
% 232.80/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5943), (5981) imply:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5984)   ~ (e3 = e0)
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5985)  all_54_12 = e3
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (4996), (5985) are inconsistent by
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5986)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5986) gives:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5987)  all_54_12 = e2
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (5712), (5987) are inconsistent by
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2264.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5988)  all_54_12 = e1 | all_54_12 = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5988) gives:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5989)  all_54_12 = e1
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (5989) imply:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5990)  all_52_3 = e1
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5990) implies:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5991)  all_52_3 = e1
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (5991) imply:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5992)   ~ (all_52_11 = e1)
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5992) implies:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5993)   ~ (all_52_11 = e1)
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5994)  all_54_14 = e3
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (4998), (5994) are inconsistent by
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1796.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5995)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5996)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_19 & $i(all_56_19))
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5996) gives:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5997)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_17 & $i(all_56_17)
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (255), (5716), (5895), (5939), (5993),
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5995), (5997), (function-axioms) are inconsistent
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1397.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5998)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_19 & $i(all_56_19)
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (255), (5552), (5716), (5920), (5993),
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5995), (5998), (function-axioms) are inconsistent
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1396.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5999)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_23 & $i(all_56_23))
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (162), (5008), (5654), (5957), (5977),
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5999), (function-axioms) are inconsistent by
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1324.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6000)  all_54_12 = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (5983), (6000) are inconsistent by
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2068.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6001)  all_58_13 = e0 & op(e0, e2) = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6001) implies:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6002)  op(e0, e2) = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5696), (6002), (function-axioms) are
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6003)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (5655), (5880), (5927), (6003) are
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1949.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6004)  all_58_9 = e1 & op(e3, e0) = e1
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5928), (6004), (function-axioms) are
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6005)  all_54_11 = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (5883), (6005) are inconsistent by
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2175.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6006)  all_58_10 = e3 & op(e2, e0) = e3
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6006) implies:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6007)  op(e2, e0) = e3
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5665), (6007), (function-axioms) are
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6008)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6008) gives:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6009)  all_58_6 = e0 & op(e1, e3) = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6009) implies:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6010)  op(e1, e3) = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5880), (6010), (function-axioms) are
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6011)  all_58_12 = e0 & op(e0, e3) = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6011) implies:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6012)  op(e0, e3) = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4992), (5240), (5907), (6012),
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1384.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6013)  all_58_7 = e3 & op(e1, e2) = e3
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6013) implies:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6014)  op(e1, e2) = e3
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5872), (6014), (function-axioms) are
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6015)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (5001), (5659), (6015),
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2148.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6016)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (5226), (5713), (5881), (6016) are
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2048.
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | |   (6017)  all_58_11 = e2 & op(e1, e0) = e2
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6017) implies:
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | |   (6018)  all_58_11 = e2
% 233.15/43.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (216), (220), (5007),
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |            (5008), (5665), (6018), (function-axioms) are
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1344.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | |   (6019)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 233.15/43.28  | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | BETA: splitting (6019) gives:
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | |   (6020)  all_58_7 = e1 & op(e1, e2) = e1
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | ALPHA: (6020) implies:
% 233.15/43.28  | | | | | | | | | | | | | |   (6021)  all_58_7 = e1
% 233.15/43.28  | | | | | | | | | | | | | |   (6022)  op(e1, e2) = e1
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | |   (6023)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 233.15/43.28  | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 233.15/43.28  | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | BETA: splitting (6023) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | |   (6024)  all_58_1 = e3 & op(e3, e2) = e3
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | ALPHA: (6024) implies:
% 233.15/43.28  | | | | | | | | | | | | | | | |   (6025)  all_58_1 = e3
% 233.15/43.28  | | | | | | | | | | | | | | | |   (6026)  op(e3, e2) = e3
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | |   (6027)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 233.15/43.28  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 233.15/43.28  | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (5010), (6026), (6027),
% 233.15/43.28  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.28  | | | | | | | | | | | | | | | | |            #1323.
% 233.15/43.28  | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | |   (6028)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 233.15/43.28  | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 233.15/43.28  | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | BETA: splitting (6028) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | |   (6029)  all_58_7 = e0 & op(e1, e2) = e0
% 233.15/43.28  | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | ALPHA: (6029) implies:
% 233.15/43.28  | | | | | | | | | | | | | | | | | |   (6030)  op(e1, e2) = e0
% 233.15/43.28  | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (6022), (6030), (function-axioms) are
% 233.15/43.28  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2136.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | |   (6031)  all_58_13 = e0 & op(e0, e2) = e0
% 233.15/43.28  | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | ALPHA: (6031) implies:
% 233.15/43.28  | | | | | | | | | | | | | | | | | |   (6032)  op(e0, e2) = e0
% 233.15/43.28  | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | |   (6033)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 233.15/43.28  | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | BETA: splitting (6033) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | |   (6034)  all_58_6 = e3 & op(e1, e3) = e3
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | ALPHA: (6034) implies:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | |   (6035)  all_58_6 = e3
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (6036)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (162), (6022), (6035), (6036),
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | |            #2111.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (6037)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6037) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | |   (6038)  all_58_8 = e0 & op(e1, e1) = e0
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (5014), (6038), (function-axioms) are
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1833.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | |   (6039)  all_58_11 = e0 & op(e1, e0) = e0
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6039) implies:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | |   (6040)  all_58_11 = e0
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (6041)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6041) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | |   (6042)  all_58_6 = e2 & op(e1, e3) = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6035), (6042) are inconsistent by sub-proof
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | |            #2219.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | |   (6043)  all_58_7 = e2 & op(e1, e2) = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6021), (6043) are inconsistent by sub-proof
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | |            #2218.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (6044)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6044) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | |   (6045)  all_58_8 = e2 & op(e1, e1) = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6045) implies:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | |   (6046)  all_58_8 = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | |   (6047)  op(e1, e1) = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (6048)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (5232), (6025), (6048),
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | |            #1322.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (6049)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6049) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6050)  all_58_7 = e2 & op(e1, e2) = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6050) implies:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6051)  all_58_7 = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (224),
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (5001), (6046), (6047), (6051),
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1545.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6052)  all_58_13 = e2 & op(e0, e2) = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6052) implies:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6053)  op(e0, e2) = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6032), (6053), (function-axioms) are
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | |   (6054)  all_58_11 = e2 & op(e1, e0) = e2
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6040), (6054) are inconsistent by sub-proof
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | |            #2216.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | |   (6055)  all_58_7 = e3 & op(e1, e2) = e3
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | ALPHA: (6055) implies:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | |   (6056)  op(e1, e2) = e3
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (162), (170), (195), (267), (6026), (6056),
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | |            #2190.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | |   (6057)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 233.15/43.28  | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (391), (5001), (6057),
% 233.15/43.28  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.28  | | | | | | | | | | | | | | | | | | |            #1529.
% 233.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | |   (6058)  all_58_3 = e3 & op(e2, e2) = e3
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (5225), (5229),
% 233.15/43.28  | | | | | | | | | | | | | | | |            (5230), (6058), (function-axioms) are inconsistent
% 233.15/43.28  | | | | | | | | | | | | | | | |            by sub-proof #2196.
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | |   (6059)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 233.15/43.28  | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 233.15/43.28  | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | BETA: splitting (6059) gives:
% 233.15/43.28  | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | |   (6060)  all_58_7 = e3 & op(e1, e2) = e3
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6021), (6060) are inconsistent by sub-proof
% 233.15/43.28  | | | | | | | | | | | | | | | |            #2138.
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | |   (6061)  all_58_13 = e3 & op(e0, e2) = e3
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4997), (6061), (function-axioms) are
% 233.15/43.28  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 233.15/43.28  | | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | |   (6062)  all_58_13 = e1 & op(e0, e2) = e1
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | REF_CLOSE: (158), (5228), (6062), (function-axioms) are
% 233.15/43.28  | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | |   (6063)  all_18_2 = e0
% 233.15/43.28  | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | COMBINE_EQS: (339), (6063) imply:
% 233.15/43.28  | | | | | | | | | | |   (6064)  all_6_2 = e0
% 233.15/43.28  | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | COMBINE_EQS: (266), (6064) imply:
% 233.15/43.28  | | | | | | | | | | |   (6065)  all_56_21 = e0
% 233.15/43.28  | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | REDUCE: (367), (6064) imply:
% 233.15/43.28  | | | | | | | | | | |   (6066)   ~ (all_52_2 = e0)
% 233.15/43.28  | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | REDUCE: (385), (6064) imply:
% 233.15/43.28  | | | | | | | | | | |   (6067)   ~ (all_52_14 = e0)
% 233.15/43.28  | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | BETA: splitting (64) gives:
% 233.15/43.28  | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | |   (6068)   ~ (all_22_2 = e1)
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | REDUCE: (326), (6068) imply:
% 233.15/43.28  | | | | | | | | | | | |   (6069)   ~ (all_8_2 = e1)
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | REF_CLOSE: (42), (123), (149), (158), (159), (160), (163),
% 233.15/43.28  | | | | | | | | | | | |            (164), (165), (167), (169), (199), (213), (234),
% 233.15/43.28  | | | | | | | | | | | |            (275), (353), (366), (373), (375), (392), (4995),
% 233.15/43.28  | | | | | | | | | | | |            (4996), (5000), (5010), (6065), (6067), (6069),
% 233.15/43.28  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.28  | | | | | | | | | | | |            #1318.
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | |   (6070)  all_22_2 = e1
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | COMBINE_EQS: (326), (6070) imply:
% 233.15/43.28  | | | | | | | | | | | |   (6071)  all_8_2 = e1
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | SIMP: (6071) implies:
% 233.15/43.28  | | | | | | | | | | | |   (6072)  all_8_2 = e1
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | COMBINE_EQS: (353), (6072) imply:
% 233.15/43.28  | | | | | | | | | | | |   (6073)  all_56_11 = e1
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | REDUCE: (366), (6072) imply:
% 233.15/43.28  | | | | | | | | | | | |   (6074)   ~ (all_52_1 = e1)
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | REDUCE: (375), (6072) imply:
% 233.15/43.28  | | | | | | | | | | | |   (6075)   ~ (all_52_9 = e1)
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | BETA: splitting (67) gives:
% 233.15/43.28  | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | |   (6076)   ~ (all_24_2 = e2)
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | REDUCE: (301), (6076) imply:
% 233.15/43.28  | | | | | | | | | | | | |   (6077)   ~ (all_10_2 = e2)
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | BETA: splitting (204) gives:
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | |   (6078)  all_54_0 = e3
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | COMBINE_EQS: (292), (6078) imply:
% 233.15/43.28  | | | | | | | | | | | | | |   (6079)  all_10_2 = e3
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | REDUCE: (355), (6079) imply:
% 233.15/43.28  | | | | | | | | | | | | | |   (6080)   ~ (all_52_1 = e3)
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | REDUCE: (363), (6079) imply:
% 233.15/43.28  | | | | | | | | | | | | | |   (6081)   ~ (all_52_8 = e3)
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | REDUCE: (45), (6079) imply:
% 233.15/43.28  | | | | | | | | | | | | | |   (6082)  op(e3, e3) = e3
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (140), (145), (158), (159), (160),
% 233.15/43.28  | | | | | | | | | | | | | |            (163), (164), (165), (167), (169), (213), (232),
% 233.15/43.28  | | | | | | | | | | | | | |            (234), (239), (4995), (4996), (5000), (6065),
% 233.15/43.28  | | | | | | | | | | | | | |            (6066), (6067), (6073), (6074), (6075), (6080),
% 233.15/43.28  | | | | | | | | | | | | | |            (6081), (6082), (function-axioms) are inconsistent
% 233.15/43.28  | | | | | | | | | | | | | |            by sub-proof #1314.
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | |   (6083)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (5012), (6077), (6083) are
% 233.15/43.28  | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | End of split
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | Case 2:
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | |   (6084)  all_24_2 = e2
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | COMBINE_EQS: (301), (6084) imply:
% 233.15/43.28  | | | | | | | | | | | | |   (6085)  all_10_2 = e2
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | SIMP: (6085) implies:
% 233.15/43.28  | | | | | | | | | | | | |   (6086)  all_10_2 = e2
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | COMBINE_EQS: (290), (6086) imply:
% 233.15/43.28  | | | | | | | | | | | | |   (6087)  all_56_1 = e2
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | REDUCE: (355), (6086) imply:
% 233.15/43.28  | | | | | | | | | | | | |   (6088)   ~ (all_52_1 = e2)
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | BETA: splitting (213) gives:
% 233.15/43.28  | | | | | | | | | | | | | 
% 233.15/43.28  | | | | | | | | | | | | | Case 1:
% 233.15/43.28  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | |   (6089)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.15/43.29  | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.29  | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.15/43.29  | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.15/43.29  | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.15/43.29  | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.15/43.29  | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.15/43.29  | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.15/43.29  | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.15/43.29  | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 233.15/43.29  | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 233.15/43.29  | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.15/43.29  | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | BETA: splitting (6089) gives:
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | |   (6090)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.15/43.29  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.29  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.15/43.29  | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.15/43.29  | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.15/43.29  | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.15/43.29  | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.15/43.29  | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.15/43.29  | | | | | | | | | | | | | | |             = e3)
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | REF_CLOSE: (167), (6073), (6087), (6088), (6090),
% 233.15/43.29  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.29  | | | | | | | | | | | | | | |            #2279.
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | Case 2:
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | |   (6091)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.15/43.29  | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.15/43.29  | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 233.15/43.29  | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 233.15/43.29  | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.15/43.29  | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.15/43.29  | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 233.15/43.29  | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 233.15/43.29  | | | | | | | | | | | | | | |             = e0)
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | REF_CLOSE: (159), (4995), (4996), (6091), (function-axioms)
% 233.15/43.29  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1389.
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | End of split
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | Case 2:
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | |   (6092)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.15/43.29  | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.15/43.29  | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.15/43.29  | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.15/43.29  | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.15/43.29  | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.15/43.29  | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.15/43.29  | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.15/43.29  | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 233.15/43.29  | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 233.15/43.29  | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 233.15/43.29  | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 233.15/43.29  | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 233.15/43.29  | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | BETA: splitting (6092) gives:
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | |   (6093)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.15/43.29  | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.15/43.29  | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.15/43.29  | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.15/43.29  | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.15/43.29  | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.15/43.29  | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.15/43.29  | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.15/43.29  | | | | | | | | | | | | | | |             = e2)
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | REF_CLOSE: (165), (6065), (6073), (6075), (6093),
% 233.15/43.29  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.29  | | | | | | | | | | | | | | |            #1315.
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | Case 2:
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | |   (6094)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 233.15/43.29  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.29  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 233.15/43.29  | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 233.15/43.29  | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.15/43.29  | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.15/43.29  | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 233.15/43.29  | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 233.15/43.29  | | | | | | | | | | | | | | |             = e0)
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | BETA: splitting (6094) gives:
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | |   (6095)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 233.15/43.29  | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 233.15/43.29  | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 233.15/43.29  | | | | | | | | | | | | | | | |             e2) = e0
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | ALPHA: (6095) implies:
% 233.15/43.29  | | | | | | | | | | | | | | | |   (6096)   ~ (all_56_1 = e2)
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | REDUCE: (6087), (6096) imply:
% 233.15/43.29  | | | | | | | | | | | | | | | |   (6097)  $false
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | CLOSE: (6097) is inconsistent.
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | Case 2:
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | |   (6098)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 233.15/43.29  | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 233.15/43.29  | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 233.15/43.29  | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 233.15/43.29  | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 233.15/43.29  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 233.15/43.29  | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6065), (6067), (6098), (function-axioms)
% 233.15/43.29  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1320.
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | End of split
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | End of split
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | End of split
% 233.15/43.29  | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | End of split
% 233.15/43.29  | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | End of split
% 233.15/43.29  | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | End of split
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | Case 2:
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | |   (6099)  all_16_2 = e0
% 233.15/43.29  | | | | | | | | | |   (6100)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0
% 233.15/43.29  | | | | | | | | | |             & op(e3, e0) = all_16_1 & $i(all_16_0) &
% 233.15/43.29  | | | | | | | | | |             $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0)
% 233.15/43.29  | | | | | | | | | |             = all_16_1 & $i(all_16_1))
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | COMBINE_EQS: (342), (6099) imply:
% 233.15/43.29  | | | | | | | | | |   (6101)  all_10_2 = e0
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | SIMP: (6101) implies:
% 233.15/43.29  | | | | | | | | | |   (6102)  all_10_2 = e0
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | COMBINE_EQS: (350), (6102) imply:
% 233.15/43.29  | | | | | | | | | |   (6103)  all_50_2 = e0
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | COMBINE_EQS: (290), (6102) imply:
% 233.15/43.29  | | | | | | | | | |   (6104)  all_56_1 = e0
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | REDUCE: (355), (6102) imply:
% 233.15/43.29  | | | | | | | | | |   (6105)   ~ (all_52_1 = e0)
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | REDUCE: (357), (6102) imply:
% 233.15/43.29  | | | | | | | | | |   (6106)   ~ (all_52_2 = e0)
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | REDUCE: (359), (6102) imply:
% 233.15/43.29  | | | | | | | | | |   (6107)   ~ (all_52_3 = e0)
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | REDUCE: (361), (6102) imply:
% 233.15/43.29  | | | | | | | | | |   (6108)   ~ (all_52_4 = e0)
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | REDUCE: (363), (6102) imply:
% 233.15/43.29  | | | | | | | | | |   (6109)   ~ (all_52_8 = e0)
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | REDUCE: (365), (6102) imply:
% 233.15/43.29  | | | | | | | | | |   (6110)   ~ (all_52_12 = e0)
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | REDUCE: (393), (6102) imply:
% 233.15/43.29  | | | | | | | | | |   (6111)   ~ (e1 = e0)
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | REDUCE: (45), (6102) imply:
% 233.15/43.29  | | | | | | | | | |   (6112)  op(e3, e3) = e0
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | BETA: splitting (58) gives:
% 233.15/43.29  | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | |   (6113)   ~ (all_18_2 = e0)
% 233.15/43.29  | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | REDUCE: (339), (6113) imply:
% 233.15/43.29  | | | | | | | | | | |   (6114)   ~ (all_6_2 = e0)
% 233.15/43.29  | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | BETA: splitting (64) gives:
% 233.15/43.29  | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | |   (6115)   ~ (all_22_2 = e1)
% 233.15/43.29  | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | REDUCE: (326), (6115) imply:
% 233.15/43.29  | | | | | | | | | | | |   (6116)   ~ (all_8_2 = e1)
% 233.15/43.29  | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | BETA: splitting (199) gives:
% 233.15/43.29  | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | |   (6117)  all_54_5 = e3
% 233.15/43.29  | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | COMBINE_EQS: (275), (6117) imply:
% 233.15/43.29  | | | | | | | | | | | | |   (6118)  all_8_2 = e3
% 233.15/43.29  | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | REDUCE: (392), (6118) imply:
% 233.15/43.29  | | | | | | | | | | | | |   (6119)  $false
% 233.15/43.29  | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | CLOSE: (6119) is inconsistent.
% 233.15/43.29  | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | Case 2:
% 233.15/43.29  | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | |   (6120)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 233.15/43.29  | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | BETA: splitting (6120) gives:
% 233.15/43.29  | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | |   (6121)  all_54_5 = e2
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | COMBINE_EQS: (275), (6121) imply:
% 233.15/43.29  | | | | | | | | | | | | | |   (6122)  all_8_2 = e2
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | COMBINE_EQS: (353), (6122) imply:
% 233.15/43.29  | | | | | | | | | | | | | |   (6123)  all_56_11 = e2
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | REDUCE: (366), (6122) imply:
% 233.15/43.29  | | | | | | | | | | | | | |   (6124)   ~ (all_52_1 = e2)
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | REDUCE: (373), (6122) imply:
% 233.15/43.29  | | | | | | | | | | | | | |   (6125)   ~ (all_52_7 = e2)
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | REDUCE: (375), (6122) imply:
% 233.15/43.29  | | | | | | | | | | | | | |   (6126)   ~ (all_52_9 = e2)
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | REDUCE: (377), (6122) imply:
% 233.15/43.29  | | | | | | | | | | | | | |   (6127)   ~ (all_52_13 = e2)
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | REDUCE: (42), (6122) imply:
% 233.15/43.29  | | | | | | | | | | | | | |   (6128)  op(e2, e2) = e2
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 233.15/43.29  | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | |   (6129)   ~ (all_26_2 = e3)
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | REDUCE: (4994), (6129) imply:
% 233.15/43.29  | | | | | | | | | | | | | | |   (6130)  $false
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | CLOSE: (6130) is inconsistent.
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | Case 2:
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | |   (6131)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 233.15/43.29  | | | | | | | | | | | | | | |             & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 233.15/43.29  | | | | | | | | | | | | | | |             $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 233.15/43.29  | | | | | | | | | | | | | | |             = all_26_1 & $i(all_26_1))
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 233.15/43.29  | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | |   (6132)   ~ (all_36_2 = e2)
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | REDUCE: (328), (6132) imply:
% 233.15/43.29  | | | | | | | | | | | | | | | |   (6133)   ~ (all_6_2 = e2)
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 233.15/43.29  | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | |   (6134)  all_54_10 = e3
% 233.15/43.29  | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (6134) are inconsistent by sub-proof
% 233.15/43.29  | | | | | | | | | | | | | | | | |            #2313.
% 233.15/43.29  | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.29  | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | |   (6135)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 233.15/43.29  | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | BETA: splitting (6135) gives:
% 233.15/43.29  | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | |   (6136)  all_54_10 = e2
% 233.15/43.29  | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (6133), (6136) are inconsistent by
% 233.15/43.29  | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 233.15/43.29  | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | |   (6137)  all_54_10 = e1 | all_54_10 = e0
% 233.15/43.29  | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | BETA: splitting (6137) gives:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | |   (6138)  all_54_10 = e1
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (6138) imply:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | |   (6139)  all_6_2 = e1
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | SIMP: (6139) implies:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | |   (6140)  all_6_2 = e1
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (6140) imply:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | |   (6141)  all_56_21 = e1
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | REDUCE: (380), (6140) imply:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | |   (6142)   ~ (all_52_8 = e1)
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | REDUCE: (385), (6140) imply:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | |   (6143)   ~ (all_52_14 = e1)
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |   (6144)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6144) gives:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |   (6145)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             = e3)
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (6123), (6124), (6141), (6145),
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |            #2310.
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |   (6146)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |             = e0)
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (4996), (6107), (6142), (6146),
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | |            #1313.
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.29  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |   (6147)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (160), (165), (297), (381), (6114), (6123),
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |            (6125), (6126), (6137), (6141), (6143), (6147),
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |            #1408.
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | |   (6148)  all_54_10 = e0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (6114), (6148) are inconsistent by
% 233.15/43.30  | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.30  | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | End of split
% 233.15/43.30  | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | End of split
% 233.15/43.30  | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | Case 2:
% 233.15/43.30  | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | |   (6149)  all_36_2 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (6149) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | |   (6150)  all_6_2 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | REDUCE: (391), (6150) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | |   (6151)   ~ (e3 = e2)
% 233.15/43.30  | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | REDUCE: (39), (6150) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | |   (6152)  op(e1, e1) = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.30  | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | |   (6153)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 233.15/43.30  | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.15/43.30  | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | BETA: splitting (6153) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | |   (6154)  all_58_12 = e2 & op(e0, e3) = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | ALPHA: (6154) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | |   (6155)  all_58_12 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | |   (6156)  op(e0, e3) = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | |   (6157)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 233.15/43.30  | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | BETA: splitting (6157) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |   (6158)  all_58_9 = e2 & op(e3, e0) = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | ALPHA: (6158) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |   (6159)  op(e3, e0) = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (6156) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |   (6160)  all_52_3 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (168), (6159) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |   (6161)  all_52_12 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (6161) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | |   (6162)   ~ (all_52_13 = e2)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | |   (6163)   ~ (all_50_2 = e0)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (6103), (6163) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | |   (6164)  $false
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | CLOSE: (6164) is inconsistent.
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | |   (6165)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | |             $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6131) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | |   (6166)   ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = all_26_1 & $i(all_26_0) &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | |           $i(all_26_1)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6166) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | |   (6167)   ~ (all_26_0 = e2)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | |   (6168)  op(e0, e3) = all_26_1
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | |   (6169)  op(all_26_1, e0) = all_26_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6165) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | |   (6170)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_50_1 & $i(all_50_0) &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6170) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | |   (6171)   ~ (all_50_0 = e1)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | |   (6172)  op(e3, e0) = all_50_1
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | |   (6173)  op(all_50_1, e3) = all_50_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4992) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | |   (6174)   ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = all_12_1 & $i(all_12_0) &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_12_1)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6174) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | |   (6175)   ~ (all_12_0 = e1)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | |   (6176)  op(e0, e3) = all_12_1
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | |   (6177)  op(all_12_1, e0) = all_12_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6100) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6178)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_16_1 & $i(all_16_0) &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6178) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6179)  op(e3, e0) = all_16_1
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6180)  op(all_16_1, e3) = all_16_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_26_1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (6156), (6168) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6181)  all_26_1 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              all_26_1, e3, e0, simplifying with (6168), (6176)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6182)  all_26_1 = all_12_1
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (6159), (6172) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6183)  all_50_1 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (6172), (6179)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6184)  all_50_1 = all_16_1
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6183), (6184) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6185)  all_16_1 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6181), (6182) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6186)  all_12_1 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6186) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6187)  all_12_1 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6173), (6183) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6188)  op(e2, e3) = all_50_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6169), (6181) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6189)  op(e2, e0) = all_26_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6180), (6185) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6190)  op(e2, e3) = all_16_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6177), (6187) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6191)  op(e2, e0) = all_12_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              all_12_0, e0, e2, simplifying with (164), (6191)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6192)  all_52_13 = all_12_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              all_26_0, e0, e2, simplifying with (164), (6189)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6193)  all_52_13 = all_26_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              all_16_0, e3, e2, simplifying with (167), (6190)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6194)  all_52_1 = all_16_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_0, e3, e2, simplifying with (167), (6188)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6195)  all_52_1 = all_50_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6194), (6195) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6196)  all_50_0 = all_16_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6192), (6193) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6197)  all_26_0 = all_12_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6197) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6198)  all_26_0 = all_12_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (6192) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6199)  all_54_7 = all_12_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (6194) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6200)  all_54_4 = all_16_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (6194) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6201)   ~ (all_52_9 = all_16_0)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6201) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6202)   ~ (all_52_9 = all_16_0)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (6192), (6194) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6203)   ~ (all_16_0 = all_12_0)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6124), (6194) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6204)   ~ (all_16_0 = e2)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (6192) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6205)   ~ (all_52_14 = all_12_0)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6205) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6206)   ~ (all_52_14 = all_12_0)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5000), (6192) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6207)   ~ (all_12_0 = e3)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6171), (6196) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6208)   ~ (all_16_0 = e1)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6167), (6198) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6209)   ~ (all_12_0 = e2)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6210)  all_54_7 = e3
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6199), (6210) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6211)  all_12_0 = e3
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6207), (6211) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6212)  $false
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6212) is inconsistent.
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6213)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (163), (164), (165), (200), (223),
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (234), (241), (5000), (5001), (6106),
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6112), (6128), (6152), (6155), (6175), (6199),
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6200), (6202), (6203), (6204), (6206), (6208),
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6209), (6213), (function-axioms) are inconsistent
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1310.
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6214)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6214) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6215)   ~ (all_16_1 = e1)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6216)  op(e3, e0) = all_16_1
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_26_1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (6156), (6168) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6217)  all_26_1 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              all_26_1, e3, e0, simplifying with (6168), (6176)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6218)  all_26_1 = all_12_1
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (6159), (6172) gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6219)  all_50_1 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (6172), (6216)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6220)  all_50_1 = all_16_1
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6219), (6220) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6221)  all_16_1 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6217), (6218) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6222)  all_12_1 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6222) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6223)  all_12_1 = e2
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6173), (6219) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6224)  op(e2, e3) = all_50_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6169), (6217) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6225)  op(e2, e0) = all_26_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6177), (6223) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6226)  op(e2, e0) = all_12_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              all_12_0, e0, e2, simplifying with (164), (6226)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6227)  all_52_13 = all_12_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              all_26_0, e0, e2, simplifying with (164), (6225)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6228)  all_52_13 = all_26_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_0, e3, e2, simplifying with (167), (6224)
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6229)  all_52_1 = all_50_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6227), (6228) imply:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6230)  all_26_0 = all_12_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6230) implies:
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (6231)  all_26_0 = all_12_0
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (6227) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6232)  all_54_7 = all_12_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (6229) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6233)  all_54_4 = all_50_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (6229) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6234)   ~ (all_52_9 = all_50_0)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6234) implies:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6235)   ~ (all_52_9 = all_50_0)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (6227), (6229) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6236)   ~ (all_50_0 = all_12_0)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6124), (6229) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6237)   ~ (all_50_0 = e2)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (6227) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6238)   ~ (all_52_14 = all_12_0)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6238) implies:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6239)   ~ (all_52_14 = all_12_0)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5000), (6227) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6240)   ~ (all_12_0 = e3)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6167), (6231) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6241)   ~ (all_12_0 = e2)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6242)  all_54_7 = e3
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6232), (6242) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6243)  all_12_0 = e3
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6240), (6243) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6244)  $false
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6244) is inconsistent.
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6245)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (163), (164), (165), (200), (223),
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (234), (241), (5000), (5001), (6106),
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6112), (6128), (6152), (6155), (6171), (6175),
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6232), (6233), (6235), (6236), (6237), (6239),
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6241), (6245), (function-axioms) are inconsistent
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1309.
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | |   (6246)   ~ (all_12_1 = e2) & op(e0, e3) = all_12_1 &
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_12_1)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6246) implies:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | |   (6247)   ~ (all_12_1 = e2)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | |   (6248)  op(e0, e3) = all_12_1
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6156), (6168), (6247), (6248), (function-axioms)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1308.
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | |   (6249)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6249) implies:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | |   (6250)   ~ (all_50_1 = e2)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | |   (6251)  op(e3, e0) = all_50_1
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6159), (6250), (6251), (function-axioms) are
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1884.
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | |   (6252)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 &
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | |           $i(all_26_1)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6252) implies:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | |   (6253)   ~ (all_26_1 = e1)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | |   (6254)  op(e0, e3) = all_26_1
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6165) gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | |   (6255)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_50_1 & $i(all_50_0) &
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6255) implies:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | |   (6256)   ~ (all_50_0 = e1)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | |   (6257)  op(e3, e0) = all_50_1
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | |   (6258)  op(all_50_1, e3) = all_50_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4992) gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | |   (6259)   ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 &
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = all_12_1 & $i(all_12_0) &
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_12_1)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6259) implies:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | |   (6260)   ~ (all_12_0 = e1)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | |   (6261)  op(e0, e3) = all_12_1
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | |   (6262)  op(all_12_1, e0) = all_12_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6100) gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6263)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_16_1 & $i(all_16_0) &
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6263) implies:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6264)  op(e3, e0) = all_16_1
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6265)  op(all_16_1, e3) = all_16_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_26_1,
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (6156), (6254) gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6266)  all_26_1 = e2
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1,
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              all_26_1, e3, e0, simplifying with (6254), (6261)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6267)  all_26_1 = all_12_1
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (6159), (6257) gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6268)  all_50_1 = e2
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (6257), (6264)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6269)  all_50_1 = all_16_1
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6268), (6269) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6270)  all_16_1 = e2
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6266), (6267) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6271)  all_12_1 = e2
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6271) implies:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6272)  all_12_1 = e2
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6258), (6268) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6273)  op(e2, e3) = all_50_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6265), (6270) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6274)  op(e2, e3) = all_16_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6262), (6272) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6275)  op(e2, e0) = all_12_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              all_12_0, e0, e2, simplifying with (164), (6275)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6276)  all_52_13 = all_12_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              all_16_0, e3, e2, simplifying with (167), (6274)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6277)  all_52_1 = all_16_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_0, e3, e2, simplifying with (167), (6273)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6278)  all_52_1 = all_50_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6277), (6278) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6279)  all_50_0 = all_16_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (6276) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6280)  all_54_7 = all_12_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (6277) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6281)  all_54_4 = all_16_0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (6277) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6282)   ~ (all_52_9 = all_16_0)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6282) implies:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6283)   ~ (all_52_9 = all_16_0)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (6276), (6277) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6284)   ~ (all_16_0 = all_12_0)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6124), (6277) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6285)   ~ (all_16_0 = e2)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (6276) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6286)   ~ (all_52_14 = all_12_0)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6286) implies:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6287)   ~ (all_52_14 = all_12_0)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5000), (6276) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6288)   ~ (all_12_0 = e3)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6127), (6276) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6289)   ~ (all_12_0 = e2)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6256), (6279) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (6290)   ~ (all_16_0 = e1)
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6291)  all_54_7 = e3
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6280), (6291) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6292)  all_12_0 = e3
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6288), (6292) imply:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6293)  $false
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6293) is inconsistent.
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6294)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 233.15/43.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (163), (164), (165), (200), (223),
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (234), (241), (5000), (5001), (6106),
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6112), (6128), (6152), (6155), (6260), (6280),
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6281), (6283), (6284), (6285), (6287), (6289),
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6290), (6294), (function-axioms) are inconsistent
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1310.
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6295)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_16_1)
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6295) implies:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6296)   ~ (all_16_1 = e1)
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6297)  op(e3, e0) = all_16_1
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_26_1,
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (6156), (6254) gives:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6298)  all_26_1 = e2
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1,
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |              all_26_1, e3, e0, simplifying with (6254), (6261)
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6299)  all_26_1 = all_12_1
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_50_1,
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (6159), (6257) gives:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6300)  all_50_1 = e2
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1,
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e3, simplifying with (6257), (6297)
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6301)  all_50_1 = all_16_1
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6300), (6301) imply:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6302)  all_16_1 = e2
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6298), (6299) imply:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6303)  all_12_1 = e2
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6303) implies:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6304)  all_12_1 = e2
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6258), (6300) imply:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6305)  op(e2, e3) = all_50_0
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6262), (6304) imply:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6306)  op(e2, e0) = all_12_0
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |              all_12_0, e0, e2, simplifying with (164), (6306)
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (6307)  all_52_13 = all_12_0
% 233.15/43.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_0, e3, e2, simplifying with (167), (6305)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6308)  all_52_1 = all_50_0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (6307) imply:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6309)  all_54_7 = all_12_0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (6308) imply:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6310)  all_54_4 = all_50_0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (6308) imply:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6311)   ~ (all_52_9 = all_50_0)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6311) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6312)   ~ (all_52_9 = all_50_0)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (6307), (6308) imply:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6313)   ~ (all_50_0 = all_12_0)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6124), (6308) imply:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6314)   ~ (all_50_0 = e2)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (6307) imply:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6315)   ~ (all_52_14 = all_12_0)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6315) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6316)   ~ (all_52_14 = all_12_0)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5000), (6307) imply:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6317)   ~ (all_12_0 = e3)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6127), (6307) imply:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6318)   ~ (all_12_0 = e2)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6319)  all_54_7 = e3
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6309), (6319) imply:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6320)  all_12_0 = e3
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6317), (6320) imply:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6321)  $false
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6321) is inconsistent.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6322)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (163), (164), (165), (200), (223),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (234), (241), (5000), (5001), (6106),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6112), (6128), (6152), (6155), (6256), (6260),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6309), (6310), (6312), (6313), (6314), (6316),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6318), (6322), (function-axioms) are inconsistent
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1309.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | |   (6323)   ~ (all_12_1 = e2) & op(e0, e3) = all_12_1 &
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_12_1)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6323) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | |   (6324)   ~ (all_12_1 = e2)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | |   (6325)  op(e0, e3) = all_12_1
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6156), (6254), (6324), (6325), (function-axioms)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1308.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6326)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6326) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6327)   ~ (all_50_1 = e2)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6328)  op(e3, e0) = all_50_1
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6159), (6327), (6328), (function-axioms) are
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1884.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |   (6329)  all_58_10 = e2 & op(e2, e0) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | ALPHA: (6329) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |   (6330)  op(e2, e0) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6127), (6330), (function-axioms) are
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | |   (6331)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 233.15/43.35  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | BETA: splitting (6331) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |   (6332)  all_58_11 = e2 & op(e1, e0) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | ALPHA: (6332) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |   (6333)  all_58_11 = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |   (6334)  op(e1, e0) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |   (6335)  all_58_15 = e0 & op(e0, e0) = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6335) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |   (6336)  op(e0, e0) = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5008), (6336), (function-axioms) are
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |   (6337)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6337) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |   (6338)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | |   (6339)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6339) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6340)  all_58_0 = e2 & op(e3, e3) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6340) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6341)  op(e3, e3) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (167), (239),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |            (241), (245), (4996), (6105), (6155), (6341),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |            #1755.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6342)  all_58_1 = e2 & op(e3, e2) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6342) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6343)  all_58_1 = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6344)  op(e3, e2) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (235),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |            (236), (238), (4997), (6128), (6343), (6344),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |            #1809.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | |   (6345)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6345) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6346)  all_58_4 = e2 & op(e3, e1) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6346) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6347)  all_58_4 = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (165), (227),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |            (228), (230), (4998), (6152), (6347),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |            #1306.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6348)  all_58_9 = e2 & op(e3, e0) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6348) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6349)  all_58_9 = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | |   (6350)  op(e3, e0) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6338) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | |   (6351)  all_58_9 = e0 & op(e3, e0) = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6351) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | |   (6352)  op(e3, e0) = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6350), (6352), (function-axioms) are
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | |   (6353)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6353) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6354)  all_58_10 = e0 & op(e2, e0) = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6354) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6355)  op(e2, e0) = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (164), (220), (5007), (6334),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (6349), (6355), (function-axioms) are inconsistent
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1305.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (6356)  all_58_11 = e0 & op(e1, e0) = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6333), (6356) are inconsistent by sub-proof
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | |            #2033.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |   (6357)  all_58_15 = e2 & op(e0, e0) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | ALPHA: (6357) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |   (6358)  op(e0, e0) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (6358), (function-axioms) are
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | |   (6359)  all_58_13 = e2 & op(e0, e2) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | ALPHA: (6359) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | |   (6360)  op(e0, e2) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (6125), (6360), (function-axioms) are
% 233.15/43.35  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | |   (6361)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 233.15/43.35  | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.15/43.35  | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | BETA: splitting (6361) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | |   (6362)  all_58_14 = e2 & op(e0, e1) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | ALPHA: (6362) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | |   (6363)  all_58_14 = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | |   (6364)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | BETA: splitting (6364) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |   (6365)  all_58_4 = e0 & op(e3, e1) = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6109), (6365), (function-axioms) are
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |   (6366)  all_58_5 = e0 & op(e2, e1) = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | ALPHA: (6366) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |   (6367)  all_58_5 = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | |   (6368)  op(e2, e1) = e0
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |   (6369)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (165), (228), (6152), (6363),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |            (6367), (6368), (6369), (function-axioms) are
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1878.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |   (6370)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (4998), (6152), (6370),
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | |            #1307.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | |   (6371)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 233.15/43.35  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6152), (6363), (6371), (function-axioms) are
% 233.15/43.35  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2035.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | |   (6372)  all_58_15 = e2 & op(e0, e0) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | ALPHA: (6372) implies:
% 233.15/43.35  | | | | | | | | | | | | | | | | | |   (6373)  op(e0, e0) = e2
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (6373), (function-axioms) are
% 233.15/43.35  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 233.15/43.35  | | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | |   (6374)  all_54_5 = e1 | all_54_5 = e0
% 233.15/43.35  | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | | REF_CLOSE: (275), (5010), (6116), (6374) are inconsistent by
% 233.15/43.35  | | | | | | | | | | | | | |            sub-proof #2300.
% 233.15/43.35  | | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | End of split
% 233.15/43.35  | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | Case 2:
% 233.15/43.35  | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | |   (6375)  all_22_2 = e1
% 233.15/43.35  | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | COMBINE_EQS: (326), (6375) imply:
% 233.15/43.35  | | | | | | | | | | | |   (6376)  all_8_2 = e1
% 233.15/43.35  | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | SIMP: (6376) implies:
% 233.15/43.35  | | | | | | | | | | | |   (6377)  all_8_2 = e1
% 233.15/43.35  | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | COMBINE_EQS: (353), (6377) imply:
% 233.15/43.35  | | | | | | | | | | | |   (6378)  all_56_11 = e1
% 233.15/43.35  | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | REDUCE: (373), (6377) imply:
% 233.15/43.35  | | | | | | | | | | | |   (6379)   ~ (all_52_7 = e1)
% 233.15/43.35  | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | REDUCE: (375), (6377) imply:
% 233.15/43.35  | | | | | | | | | | | |   (6380)   ~ (all_52_9 = e1)
% 233.15/43.35  | | | | | | | | | | | | 
% 233.15/43.35  | | | | | | | | | | | | REDUCE: (377), (6377) imply:
% 233.15/43.35  | | | | | | | | | | | |   (6381)   ~ (all_52_13 = e1)
% 233.15/43.36  | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | BETA: splitting (70) gives:
% 233.15/43.36  | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | |   (6382)   ~ (all_26_2 = e3)
% 233.15/43.36  | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | REDUCE: (4994), (6382) imply:
% 233.15/43.36  | | | | | | | | | | | | |   (6383)  $false
% 233.15/43.36  | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | CLOSE: (6383) is inconsistent.
% 233.15/43.36  | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | |   (6384)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 233.15/43.36  | | | | | | | | | | | | |             & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 233.15/43.36  | | | | | | | | | | | | |             $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 233.15/43.36  | | | | | | | | | | | | |             = all_26_1 & $i(all_26_1))
% 233.15/43.36  | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | BETA: splitting (85) gives:
% 233.15/43.36  | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | |   (6385)   ~ (all_36_2 = e2)
% 233.15/43.36  | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | REDUCE: (328), (6385) imply:
% 233.15/43.36  | | | | | | | | | | | | | |   (6386)   ~ (all_6_2 = e2)
% 233.15/43.36  | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 233.15/43.36  | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | |   (6387)  all_54_10 = e3
% 233.15/43.36  | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (6387) are inconsistent by sub-proof
% 233.15/43.36  | | | | | | | | | | | | | | |            #2313.
% 233.15/43.36  | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | |   (6388)   ~ (all_54_10 = e3)
% 233.15/43.36  | | | | | | | | | | | | | | |   (6389)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 233.15/43.36  | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | BETA: splitting (6389) gives:
% 233.15/43.36  | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | |   (6390)  all_54_10 = e2
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | REF_CLOSE: (297), (6386), (6390) are inconsistent by
% 233.15/43.36  | | | | | | | | | | | | | | | |            sub-proof #2312.
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | |   (6391)   ~ (all_54_10 = e2)
% 233.15/43.36  | | | | | | | | | | | | | | | |   (6392)  all_54_10 = e1 | all_54_10 = e0
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | BETA: splitting (6392) gives:
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6393)  all_54_10 = e1
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (6393) imply:
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6394)  all_6_2 = e1
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | SIMP: (6394) implies:
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6395)  all_6_2 = e1
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | REDUCE: (383), (6395) imply:
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6396)   ~ (all_52_11 = e1)
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | REDUCE: (385), (6395) imply:
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6397)   ~ (all_52_14 = e1)
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | REDUCE: (391), (6395) imply:
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6398)   ~ (e3 = e1)
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | REDUCE: (6386), (6395) imply:
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6399)   ~ (e2 = e1)
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | |   (6400)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 233.15/43.36  | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | BETA: splitting (6400) gives:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | |   (6401)  all_58_12 = e1 & op(e0, e3) = e1
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | ALPHA: (6401) implies:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | |   (6402)  all_58_12 = e1
% 233.15/43.36  | | | | | | | | | | | | | | | | | | |   (6403)  op(e0, e3) = e1
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | |   (6404)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6404) gives:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | |   (6405)  all_58_9 = e1 & op(e3, e0) = e1
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6405) implies:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | |   (6406)  op(e3, e0) = e1
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (39), (106), (110), (112), (113),
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | |            (143), (144), (145), (159), (160), (162), (163),
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | |            (167), (168), (193), (196), (197), (226), (243),
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | |            (258), (268), (269), (391), (4992), (5000),
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | |            (5001), (6100), (6103), (6106), (6112), (6384),
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | |            (6402), (6403), (6406), (function-axioms) are
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1298.
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | |   (6407)  all_58_10 = e1 & op(e2, e0) = e1
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6381), (6407), (function-axioms) are
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | |   (6408)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (5007), (6397), (6408),
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | |            #1297.
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | |   (6409)  all_58_13 = e1 & op(e0, e2) = e1
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (6379), (6409), (function-axioms) are
% 233.15/43.36  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 233.15/43.36  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | |   (6410)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 233.15/43.36  | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (5007), (6396), (6410),
% 233.15/43.36  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.36  | | | | | | | | | | | | | | | | | |            #1296.
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | End of split
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6411)  all_54_10 = e0
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (6114), (6411) are inconsistent by
% 233.15/43.36  | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | End of split
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | End of split
% 233.15/43.36  | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | End of split
% 233.15/43.36  | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | |   (6412)  all_36_2 = e2
% 233.15/43.36  | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | COMBINE_EQS: (328), (6412) imply:
% 233.15/43.36  | | | | | | | | | | | | | |   (6413)  all_6_2 = e2
% 233.15/43.36  | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | COMBINE_EQS: (266), (6413) imply:
% 233.15/43.36  | | | | | | | | | | | | | |   (6414)  all_56_21 = e2
% 233.15/43.36  | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | REDUCE: (381), (6413) imply:
% 233.15/43.36  | | | | | | | | | | | | | |   (6415)   ~ (all_52_9 = e2)
% 233.15/43.36  | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 233.15/43.36  | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | |   (6416)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.15/43.36  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.36  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.15/43.36  | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.15/43.36  | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.15/43.36  | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.15/43.36  | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.15/43.36  | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.15/43.36  | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 233.15/43.36  | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.15/43.36  | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 233.15/43.36  | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 233.15/43.36  | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 233.15/43.36  | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.15/43.36  | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 233.15/43.36  | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | BETA: splitting (6416) gives:
% 233.15/43.36  | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | |   (6417)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.15/43.36  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.36  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.15/43.36  | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.15/43.36  | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.15/43.36  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.15/43.36  | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.15/43.36  | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.15/43.36  | | | | | | | | | | | | | | | |             = e3)
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | BETA: splitting (6417) gives:
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6418)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 233.15/43.36  | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 233.15/43.36  | | | | | | | | | | | | | | | | |           e3
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | ALPHA: (6418) implies:
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6419)   ~ (all_56_21 = e2)
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | REDUCE: (6414), (6419) imply:
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6420)  $false
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | CLOSE: (6420) is inconsistent.
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | |   (6421)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 233.15/43.36  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.15/43.36  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 233.15/43.36  | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 233.15/43.36  | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 233.15/43.36  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 233.15/43.36  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | BETA: splitting (6421) gives:
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | |   (6422)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 233.15/43.36  | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 233.15/43.36  | | | | | | | | | | | | | | | | | |           e2
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | ALPHA: (6422) implies:
% 233.15/43.36  | | | | | | | | | | | | | | | | | |   (6423)   ~ (all_56_31 = e3)
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | REDUCE: (4995), (6423) imply:
% 233.15/43.36  | | | | | | | | | | | | | | | | | |   (6424)  $false
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | CLOSE: (6424) is inconsistent.
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | |   (6425)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 233.15/43.36  | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 233.15/43.36  | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 233.15/43.36  | | | | | | | | | | | | | | | | | |             e3) = e3
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | ALPHA: (6425) implies:
% 233.15/43.36  | | | | | | | | | | | | | | | | | |   (6426)   ~ (all_56_11 = e1)
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | REDUCE: (6378), (6426) imply:
% 233.15/43.36  | | | | | | | | | | | | | | | | | |   (6427)  $false
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | | CLOSE: (6427) is inconsistent.
% 233.15/43.36  | | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | | End of split
% 233.15/43.36  | | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | | End of split
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | Case 2:
% 233.15/43.36  | | | | | | | | | | | | | | | | 
% 233.15/43.36  | | | | | | | | | | | | | | | |   (6428)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.15/43.36  | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.15/43.36  | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 233.15/43.36  | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 233.15/43.36  | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.15/43.36  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.15/43.36  | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 233.15/43.36  | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.15/43.36  | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 233.15/43.36  | | | | | | | | | | | | | | | |             = e0)
% 233.15/43.37  | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4995), (4996), (6107), (6428),
% 233.15/43.37  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.37  | | | | | | | | | | | | | | | |            #1368.
% 233.15/43.37  | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | End of split
% 233.15/43.37  | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | Case 2:
% 233.15/43.37  | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | |   (6429)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.15/43.37  | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.15/43.37  | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.15/43.37  | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.15/43.37  | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.15/43.37  | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.15/43.37  | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.15/43.37  | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.37  | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.37  | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.15/43.37  | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 233.15/43.37  | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 233.15/43.37  | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 233.15/43.37  | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 233.15/43.37  | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.37  | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.37  | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 233.15/43.37  | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 233.15/43.37  | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 233.15/43.37  | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 233.15/43.37  | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 233.15/43.37  | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | BETA: splitting (6429) gives:
% 233.15/43.37  | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | Case 1:
% 233.15/43.37  | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | |   (6430)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.15/43.37  | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.15/43.37  | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.15/43.37  | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.15/43.37  | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.15/43.37  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.15/43.37  | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.15/43.37  | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.37  | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.37  | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.15/43.37  | | | | | | | | | | | | | | | |             = e2)
% 233.15/43.37  | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | BETA: splitting (6430) gives:
% 233.15/43.37  | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | |   (6431)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.15/43.37  | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 233.15/43.37  | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 233.15/43.37  | | | | | | | | | | | | | | | | |             e2) = e2
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | | ALPHA: (6431) implies:
% 233.15/43.37  | | | | | | | | | | | | | | | | |   (6432)  op(e2, e1) = e2
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6415), (6432), (function-axioms) are
% 233.15/43.37  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | |   (6433)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 233.15/43.37  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.37  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 233.15/43.37  | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 233.15/43.37  | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.15/43.37  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.15/43.37  | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6104), (6380), (6433), (function-axioms)
% 233.15/43.37  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1295.
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | End of split
% 233.15/43.37  | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | Case 2:
% 233.15/43.37  | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | |   (6434)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 233.15/43.37  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.37  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 233.15/43.37  | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 233.15/43.37  | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.15/43.37  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.15/43.37  | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 233.15/43.37  | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 233.15/43.37  | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.15/43.37  | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 233.15/43.37  | | | | | | | | | | | | | | | |             = e0)
% 233.15/43.37  | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | BETA: splitting (6434) gives:
% 233.15/43.37  | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | |   (6435)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 233.15/43.37  | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 233.15/43.37  | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 233.15/43.37  | | | | | | | | | | | | | | | | |             e2) = e0
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | | ALPHA: (6435) implies:
% 233.15/43.37  | | | | | | | | | | | | | | | | |   (6436)   ~ (all_56_21 = e2)
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | | REDUCE: (6414), (6436) imply:
% 233.15/43.37  | | | | | | | | | | | | | | | | |   (6437)  $false
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | | CLOSE: (6437) is inconsistent.
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | |   (6438)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 233.15/43.37  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 233.15/43.37  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 233.15/43.37  | | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 233.15/43.37  | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 233.15/43.37  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 233.15/43.37  | | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (6104), (6378), (6438) are inconsistent by
% 233.15/43.37  | | | | | | | | | | | | | | | | |            sub-proof #1294.
% 233.15/43.37  | | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | | End of split
% 233.15/43.37  | | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | | End of split
% 233.15/43.37  | | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | | End of split
% 233.15/43.37  | | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | End of split
% 233.15/43.37  | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | End of split
% 233.15/43.37  | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | End of split
% 233.15/43.37  | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | Case 2:
% 233.15/43.37  | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | |   (6439)  all_18_2 = e0
% 233.15/43.37  | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | COMBINE_EQS: (339), (6439) imply:
% 233.15/43.37  | | | | | | | | | | |   (6440)  all_6_2 = e0
% 233.15/43.37  | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | SIMP: (6440) implies:
% 233.15/43.37  | | | | | | | | | | |   (6441)  all_6_2 = e0
% 233.15/43.37  | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | COMBINE_EQS: (266), (6441) imply:
% 233.15/43.37  | | | | | | | | | | |   (6442)  all_56_21 = e0
% 233.15/43.37  | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | REDUCE: (378), (6441) imply:
% 233.15/43.37  | | | | | | | | | | |   (6443)   ~ (all_52_6 = e0)
% 233.15/43.37  | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | REDUCE: (385), (6441) imply:
% 233.15/43.37  | | | | | | | | | | |   (6444)   ~ (all_52_14 = e0)
% 233.15/43.37  | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | REDUCE: (391), (6441) imply:
% 233.15/43.37  | | | | | | | | | | |   (6445)   ~ (e3 = e0)
% 233.15/43.37  | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | REDUCE: (39), (6441) imply:
% 233.15/43.37  | | | | | | | | | | |   (6446)  op(e1, e1) = e0
% 233.15/43.37  | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | BETA: splitting (235) gives:
% 233.15/43.37  | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | Case 1:
% 233.15/43.37  | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | |   (6447)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 233.15/43.37  | | | | | | | | | | | |             & op(e2, e2) = e0)
% 233.15/43.37  | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | BETA: splitting (6447) gives:
% 233.15/43.37  | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | Case 1:
% 233.15/43.37  | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | |   (6448)  all_58_1 = e0 & op(e3, e2) = e0
% 233.15/43.37  | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | REF_CLOSE: (170), (6108), (6448), (function-axioms) are
% 233.15/43.37  | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 233.15/43.37  | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | Case 2:
% 233.15/43.37  | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | |   (6449)  all_58_3 = e0 & op(e2, e2) = e0
% 233.15/43.37  | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | | REF_CLOSE: (42), (5010), (6449), (function-axioms) are
% 233.15/43.37  | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 233.15/43.37  | | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | | End of split
% 233.15/43.37  | | | | | | | | | | | | 
% 233.15/43.37  | | | | | | | | | | | Case 2:
% 233.15/43.37  | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | |   (6450)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 233.15/43.38  | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 233.15/43.38  | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | BETA: splitting (6450) gives:
% 233.15/43.38  | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | Case 1:
% 233.15/43.38  | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | |   (6451)  all_58_7 = e0 & op(e1, e2) = e0
% 233.15/43.38  | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | REF_CLOSE: (162), (6443), (6451), (function-axioms) are
% 233.15/43.38  | | | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 233.15/43.38  | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | Case 2:
% 233.15/43.38  | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | |   (6452)  all_58_13 = e0 & op(e0, e2) = e0
% 233.15/43.38  | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | ALPHA: (6452) implies:
% 233.15/43.38  | | | | | | | | | | | | |   (6453)  op(e0, e2) = e0
% 233.15/43.38  | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | BETA: splitting (216) gives:
% 233.15/43.38  | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | Case 1:
% 233.15/43.38  | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | |   (6454)  all_58_15 = e0 & op(e0, e0) = e0
% 233.15/43.38  | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | ALPHA: (6454) implies:
% 233.15/43.38  | | | | | | | | | | | | | |   (6455)  op(e0, e0) = e0
% 233.15/43.38  | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | REF_CLOSE: (7), (5008), (6455), (function-axioms) are
% 233.15/43.38  | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 233.15/43.38  | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | Case 2:
% 233.15/43.38  | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | |   (6456)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.15/43.38  | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 233.15/43.38  | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 233.15/43.38  | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 233.15/43.38  | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 233.15/43.38  | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | ALPHA: (6456) implies:
% 233.15/43.38  | | | | | | | | | | | | | |   (6457)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 233.15/43.38  | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 233.15/43.38  | | | | | | | | | | | | | |               e1) = e0)
% 233.15/43.38  | | | | | | | | | | | | | |   (6458)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.15/43.38  | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 233.15/43.38  | | | | | | | | | | | | | |               e0) = e0)
% 233.15/43.38  | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | BETA: splitting (6458) gives:
% 233.15/43.38  | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | Case 1:
% 233.15/43.38  | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | |   (6459)  all_58_9 = e0 & op(e3, e0) = e0
% 233.15/43.38  | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | ALPHA: (6459) implies:
% 233.15/43.38  | | | | | | | | | | | | | | |   (6460)  op(e3, e0) = e0
% 233.15/43.38  | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | REF_CLOSE: (168), (6110), (6460), (function-axioms) are
% 233.15/43.38  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2258.
% 233.15/43.38  | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | Case 2:
% 233.15/43.38  | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | |   (6461)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 233.15/43.38  | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 233.15/43.38  | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | BETA: splitting (6461) gives:
% 233.15/43.38  | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | Case 1:
% 233.15/43.38  | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | |   (6462)  all_58_10 = e0 & op(e2, e0) = e0
% 233.15/43.38  | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | ALPHA: (6462) implies:
% 233.15/43.38  | | | | | | | | | | | | | | | |   (6463)  op(e2, e0) = e0
% 233.15/43.38  | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 233.15/43.38  | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (6453) gives:
% 233.15/43.38  | | | | | | | | | | | | | | | |   (6464)  all_52_7 = e0
% 233.15/43.38  | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.15/43.38  | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (6463) gives:
% 233.15/43.38  | | | | | | | | | | | | | | | |   (6465)  all_52_13 = e0
% 233.15/43.38  | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | REDUCE: (125), (6464) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | |   (6466)   ~ (all_52_11 = e0)
% 233.15/43.38  | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | SIMP: (6466) implies:
% 233.15/43.38  | | | | | | | | | | | | | | | |   (6467)   ~ (all_52_11 = e0)
% 233.15/43.38  | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | REDUCE: (117), (6465) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | |   (6468)   ~ (all_52_9 = e0)
% 233.15/43.38  | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | REDUCE: (110), (6465) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | |   (6469)   ~ (all_52_14 = e0)
% 233.15/43.38  | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | REDUCE: (377), (6465) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | |   (6470)   ~ (all_8_2 = e0)
% 233.15/43.38  | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 233.15/43.38  | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | |   (6471)   ~ (all_22_2 = e1)
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | REDUCE: (326), (6471) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | | |   (6472)   ~ (all_8_2 = e1)
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (123), (149), (158), (159), (160), (163),
% 233.15/43.38  | | | | | | | | | | | | | | | | |            (164), (165), (167), (169), (199), (213), (234),
% 233.15/43.38  | | | | | | | | | | | | | | | | |            (275), (353), (366), (373), (375), (392), (4995),
% 233.15/43.38  | | | | | | | | | | | | | | | | |            (4996), (5000), (5010), (6442), (6444), (6472),
% 233.15/43.38  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.38  | | | | | | | | | | | | | | | | |            #1318.
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | |   (6473)  all_22_2 = e1
% 233.15/43.38  | | | | | | | | | | | | | | | | |   (6474)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 233.15/43.38  | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_22_1 & $i(all_22_0) &
% 233.15/43.38  | | | | | | | | | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1)
% 233.15/43.38  | | | | | | | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (6473) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | | |   (6475)  all_8_2 = e1
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (6475) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | | |   (6476)  all_30_2 = e1
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (6475) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | | |   (6477)  all_56_11 = e1
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | REDUCE: (366), (6475) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | | |   (6478)   ~ (all_52_1 = e1)
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | REDUCE: (369), (6475) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | | |   (6479)   ~ (all_52_4 = e1)
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | REDUCE: (375), (6475) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | | |   (6480)   ~ (all_52_9 = e1)
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | REDUCE: (42), (6475) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | | |   (6481)  op(e2, e2) = e1
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 233.15/43.38  | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.38  | | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | |   (6482)   ~ (all_26_2 = e3)
% 233.15/43.38  | | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | | REDUCE: (4994), (6482) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | | | |   (6483)  $false
% 233.15/43.38  | | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | | CLOSE: (6483) is inconsistent.
% 233.15/43.38  | | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.38  | | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | |   (6484)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 233.15/43.38  | | | | | | | | | | | | | | | | | |             & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 233.15/43.38  | | | | | | | | | | | | | | | | | |             $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 233.15/43.38  | | | | | | | | | | | | | | | | | |             = all_26_1 & $i(all_26_1))
% 233.15/43.38  | | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 233.15/43.38  | | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.38  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | | |   (6485)   ~ (all_30_2 = e1)
% 233.15/43.38  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | | | REDUCE: (6476), (6485) imply:
% 233.15/43.38  | | | | | | | | | | | | | | | | | | |   (6486)  $false
% 233.15/43.38  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | | | CLOSE: (6486) is inconsistent.
% 233.15/43.38  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.38  | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | |   (6487)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 233.15/43.39  | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_30_1 & $i(all_30_0) &
% 233.15/43.39  | | | | | | | | | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | |   (6488)   ~ (all_50_2 = e0)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | REDUCE: (6103), (6488) imply:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | |   (6489)  $false
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | CLOSE: (6489) is inconsistent.
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | |   (6490)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | |             $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | |   (6491)  all_54_4 = e3
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (6491) imply:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | |   (6492)  all_52_1 = e3
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | SIMP: (6492) implies:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | |   (6493)  all_52_1 = e3
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (6493) imply:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | |   (6494)   ~ (all_52_2 = e3)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | SIMP: (6494) implies:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | |   (6495)   ~ (all_52_2 = e3)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (6493) imply:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | |   (6496)   ~ (all_52_3 = e3)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (6493) imply:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | |   (6497)   ~ (all_52_9 = e3)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | SIMP: (6497) implies:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | |   (6498)   ~ (all_52_9 = e3)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (6493) imply:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | |   (6499)  op(e2, e3) = e3
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | |   (6500)  all_54_6 = e3
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (6498), (6500) are inconsistent by
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | |   (6501)   ~ (all_54_6 = e3)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | |   (6502)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6502) gives:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | |   (6503)  all_54_6 = e2
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (6503) imply:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | |   (6504)  all_52_9 = e2
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6504) implies:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | |   (6505)  all_52_9 = e2
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (6505) imply:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | |   (6506)   ~ (all_52_8 = e2)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (6505) imply:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | |   (6507)   ~ (all_52_11 = e2)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6507) implies:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | |   (6508)   ~ (all_52_11 = e2)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6498), (6505) imply:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | |   (6509)   ~ (e3 = e2)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (6505) imply:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | |   (6510)  op(e2, e1) = e2
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | |   (6511)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6511) gives:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (6512)  all_58_4 = e3 & op(e3, e1) = e3
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6512) implies:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (6513)  all_58_4 = e3
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6514)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6514) gives:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6515)  all_58_12 = e2 & op(e0, e3) = e2
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6515) implies:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6516)  all_58_12 = e2
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6487) gives:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6517)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_30_1 & $i(all_30_0) &
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6517) implies:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6518)  op(e2, e1) = all_30_1
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (106), (110),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (120), (121), (134), (139), (140),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (141), (143), (144), (145), (149), (157), (159),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (168),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (190), (191), (192), (193), (196),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (200), (201), (202), (203), (211), (214),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (220), (221), (223), (226), (227), (228),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (235), (236), (238), (239), (240),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (242), (243), (244), (245), (255), (256),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (258), (268), (269), (279), (280), (281),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (391), (4992), (4996), (4997), (4998),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5000), (5001), (5007), (5008), (6100), (6103),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6104), (6105), (6106), (6107), (6108), (6109),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6110), (6112), (6442), (6444), (6446), (6457),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6463), (6467), (6474), (6478), (6479), (6480),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6484), (6495), (6498), (6499), (6506), (6508),
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6513), (6516), (6518), (function-axioms) are
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1287.
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6519)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6519) implies:
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6520)  op(e2, e1) = all_30_1
% 233.15/43.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (106), (110),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (120), (121), (134), (139), (140),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (141), (143), (144), (145), (149), (157), (159),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (168),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (190), (191), (192), (193), (196),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (200), (201), (202), (203), (211), (214),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (220), (221), (223), (226), (227), (228),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (235), (236), (238), (239), (240),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (242), (243), (244), (245), (255), (256),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (258), (268), (269), (279), (280), (281),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (391), (4992), (4996), (4997), (4998),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5000), (5001), (5007), (5008), (6100), (6103),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6104), (6105), (6106), (6107), (6108), (6109),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6110), (6112), (6442), (6444), (6446), (6457),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6463), (6467), (6474), (6478), (6479), (6480),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6484), (6495), (6498), (6499), (6506), (6508),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6513), (6516), (6520), (function-axioms) are
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1287.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6521)  all_58_13 = e2 & op(e0, e2) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6521) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6522)  op(e0, e2) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6453), (6522), (function-axioms) are
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6523)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6523) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6524)  all_58_14 = e2 & op(e0, e1) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (165), (227), (228),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6480), (6510), (6513), (6524), (function-axioms)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1284.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6525)  all_58_15 = e2 & op(e0, e0) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6525) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6526)  op(e0, e0) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (6526), (function-axioms) are
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (6527)  all_58_5 = e3 & op(e2, e1) = e3
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6498), (6527), (function-axioms) are
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | |   (6528)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6528) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (6529)  all_58_8 = e3 & op(e1, e1) = e3
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6446), (6529), (function-axioms) are
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (6530)  all_58_14 = e3 & op(e0, e1) = e3
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4998), (6530), (function-axioms) are
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | |   (6531)   ~ (all_54_6 = e2)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (6531) imply:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | |   (6532)   ~ (all_52_9 = e2)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | |   (6533)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6533) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (6534)  all_58_4 = e3 & op(e3, e1) = e3
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6534) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (6535)  all_58_4 = e3
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6536)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (6480), (6535), (6536),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1339.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6537)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6537) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6538)  all_58_8 = e1 & op(e1, e1) = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6538) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6539)  op(e1, e1) = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6446), (6539), (function-axioms) are
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6540)  all_58_14 = e1 & op(e0, e1) = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6540) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6541)  all_58_14 = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6542)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6542) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6543)  all_58_12 = e2 & op(e0, e3) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6543) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6544)  all_58_12 = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6545)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (6112), (6479), (6545),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1826.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6546)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6546) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6547)  all_58_4 = e1 & op(e3, e1) = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6547) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6548)  all_58_4 = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6535), (6548) imply:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6549)  e3 = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5007), (6549) imply:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6550)  all_58_15 = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (158), (219), (4997), (6541), (6544),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6550), (function-axioms) are inconsistent by
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1814.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6551)  all_58_9 = e1 & op(e3, e0) = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6551) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6552)  all_58_9 = e1
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6553)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6553) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6554)  all_58_0 = e2 & op(e3, e3) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6554) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6555)  op(e3, e3) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (167), (239),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (245), (4996), (6105), (6544), (6555),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1755.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6556)  all_58_1 = e2 & op(e3, e2) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6556) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6557)  all_58_1 = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6558)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6558) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6559)  all_58_9 = e2 & op(e3, e0) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6559) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6560)  all_58_9 = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6552), (6560) are inconsistent by sub-proof
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1605.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6561)  all_58_10 = e2 & op(e2, e0) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6561) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6562)  op(e2, e0) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6463), (6562), (function-axioms) are
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6563)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6563) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6564)  all_58_11 = e2 & op(e1, e0) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6564) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6565)  all_58_11 = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6566)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6566) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6567)  all_58_2 = e2 & op(e2, e3) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6567) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6568)  op(e2, e3) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6499), (6568), (function-axioms) are
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6569)  all_58_3 = e2 & op(e2, e2) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6569) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6570)  op(e2, e2) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (236),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (6453), (6557), (6570), (function-axioms)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1811.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6571)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6571) gives:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6572)  all_58_5 = e2 & op(e2, e1) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6572) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6573)  op(e2, e1) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6532), (6573), (function-axioms) are
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6574)  all_58_10 = e2 & op(e2, e0) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6574) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6575)  op(e2, e0) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (216), (220), (5007),
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5008), (6565), (6575), (function-axioms) are
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1344.
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6576)  all_58_15 = e2 & op(e0, e0) = e2
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6576) implies:
% 233.15/43.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6577)  op(e0, e0) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (6577), (function-axioms) are
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6578)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6578) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6579)  all_58_4 = e2 & op(e3, e1) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6579) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6580)  all_58_4 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (157), (165), (230), (4998), (6446),
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6498), (6580), (function-axioms) are inconsistent
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1493.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6581)  all_58_9 = e2 & op(e3, e0) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6581) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6582)  all_58_9 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6552), (6582) are inconsistent by sub-proof
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1605.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6583)  all_58_13 = e2 & op(e0, e2) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6583) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6584)  op(e0, e2) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6453), (6584), (function-axioms) are
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6585)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (5008), (6541), (6585),
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1283.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (6586)  all_58_5 = e3 & op(e2, e1) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6498), (6586), (function-axioms) are
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | |   (6587)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6587) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (6588)  all_58_8 = e3 & op(e1, e1) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6446), (6588), (function-axioms) are
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (6589)  all_58_14 = e3 & op(e0, e1) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4998), (6589), (function-axioms) are
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | |   (6590)   ~ (all_54_4 = e3)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | |   (6591)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (6590) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | |   (6592)   ~ (all_52_1 = e3)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6591) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | |   (6593)  all_54_4 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (6593) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | |   (6594)  all_52_1 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | SIMP: (6594) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | |   (6595)  all_52_1 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (6595) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | |   (6596)   ~ (all_52_3 = e2)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | SIMP: (6596) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | |   (6597)   ~ (all_52_3 = e2)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (6595) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | |   (6598)   ~ (all_52_9 = e2)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | SIMP: (6598) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | |   (6599)   ~ (all_52_9 = e2)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (6595) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | |   (6600)  op(e2, e3) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | |   (6601)  all_54_12 = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (6601) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | |   (6602)  all_52_3 = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4996), (6602) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | |   (6603)  $false
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6603) is inconsistent.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | |   (6604)   ~ (all_54_12 = e3)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | |   (6605)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | |   (6606)  all_54_6 = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (6606) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | |   (6607)  all_52_9 = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6607) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | |   (6608)  all_52_9 = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (6608) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | |   (6609)   ~ (all_52_8 = e3)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (6608) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | |   (6610)   ~ (all_52_11 = e3)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (6611)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6611) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6612)  all_58_0 = e3 & op(e3, e3) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6612) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6613)  op(e3, e3) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (140), (145), (158), (159), (160),
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (169), (213), (232),
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (239), (4995), (4996), (5000), (6106),
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6442), (6444), (6477), (6478), (6480), (6592),
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6609), (6613), (function-axioms) are inconsistent
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1314.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6614)  all_58_2 = e3 & op(e2, e3) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6614) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6615)  op(e2, e3) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6600), (6615), (function-axioms) are
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (6616)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6616) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6617)  all_58_6 = e3 & op(e1, e3) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6617) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6618)  all_58_6 = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6619)  op(e1, e3) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6620)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6620) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6621)  all_58_12 = e2 & op(e0, e3) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (6597), (6621), (function-axioms) are
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2315.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6622)  all_58_13 = e2 & op(e0, e2) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6622) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6623)  op(e0, e2) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6453), (6623), (function-axioms) are
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6624)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6624) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6625)  all_58_14 = e2 & op(e0, e1) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6625) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6626)  all_58_14 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6627)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6627) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6628)  all_58_0 = e3 & op(e3, e3) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6628) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6629)  op(e3, e3) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (243),
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4992), (6484), (6618), (6619), (6629),
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1383.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6630)  all_58_1 = e3 & op(e3, e2) = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6630) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6631)  all_58_1 = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6632)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6632) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6633)  all_58_12 = e1 & op(e0, e3) = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6633) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6634)  all_58_12 = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6635)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (6481), (6631), (6635),
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1322.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6636)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6636) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6637)  all_58_7 = e2 & op(e1, e2) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6637) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6638)  all_58_7 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6639)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (6619), (6638), (6639),
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2223.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6640)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6640) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6641)  all_58_8 = e1 & op(e1, e1) = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6641) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6642)  op(e1, e1) = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6446), (6642), (function-axioms) are
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6643)  all_58_11 = e1 & op(e1, e0) = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6643) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6644)  all_58_11 = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6645)  op(e1, e0) = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6646)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6646) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6647)  all_58_9 = e2 & op(e3, e0) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6647) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6648)  op(e3, e0) = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6605) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6649)  all_54_12 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (6597), (6649) are inconsistent by
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2264.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6650)  all_54_12 = e1 | all_54_12 = e0
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6650) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6651)  all_54_12 = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (6651) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6652)  all_52_3 = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6652) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6653)  all_52_3 = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (6653) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6654)   ~ (all_52_11 = e1)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6654) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6655)   ~ (all_52_11 = e1)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4996), (6653) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6656)   ~ (e3 = e1)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (6653) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6657)  op(e0, e3) = e1
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6658)  all_54_14 = e3
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (4998), (6658) are inconsistent by
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1796.
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6659)   ~ (all_54_14 = e3)
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6660)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6660) gives:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6661)  all_54_14 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (6661) imply:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6662)  all_52_11 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6662) implies:
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6663)  all_52_11 = e2
% 233.15/43.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (6663) imply:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6664)   ~ (all_52_8 = e2)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4998), (6663) imply:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6665)   ~ (e3 = e2)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (6663) imply:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6666)  op(e0, e1) = e2
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6667)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (6104), (6481), (6490), (6600), (6648),
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6667), (function-axioms) are inconsistent by
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1795.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6668)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6668) gives:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6669)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_5 & $i(all_56_5)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6669) implies:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6670)  op(e1, e3) = all_56_5
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6671)  op(e1, all_56_5) = e1
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6619), (6670), (6671), (function-axioms) are
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2243.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6672)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_7 & $i(all_56_7)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6672) implies:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6673)  op(e0, e3) = all_56_7
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6674)  op(e0, all_56_7) = e0
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4992) gives:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6675)   ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 &
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = all_12_1 & $i(all_12_0) &
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_12_1)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6675) implies:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6676)  op(e0, e3) = all_12_1
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (201), (202), (225), (280), (281), (4999),
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6109), (6110), (6446), (6484), (6609), (6618),
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6638), (6644), (6657), (6664), (6666), (6673),
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6674), (6676), (function-axioms) are inconsistent
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1282.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6677)   ~ (all_12_1 = e2) & op(e0, e3) = all_12_1 &
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_12_1)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6677) implies:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6678)  op(e0, e3) = all_12_1
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (201), (202), (225), (280), (281), (4999),
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6109), (6110), (6446), (6484), (6609), (6618),
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6638), (6644), (6657), (6664), (6666), (6673),
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6674), (6678), (function-axioms) are inconsistent
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1282.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6679)  all_54_14 = e1 | all_54_14 = e0
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (6467), (6655), (6679) are inconsistent by
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1935.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6680)  all_54_12 = e0
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (6107), (6680) are inconsistent by
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2068.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6681)  all_58_10 = e2 & op(e2, e0) = e2
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6681) implies:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6682)  op(e2, e0) = e2
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6463), (6682), (function-axioms) are
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6683)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (5008), (6645), (6683),
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1281.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6684)  all_58_13 = e2 & op(e0, e2) = e2
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6684) implies:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6685)  op(e0, e2) = e2
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (158), (216), (219),
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4997), (6626), (6634), (6685), (function-axioms)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1536.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6686)  all_58_13 = e1 & op(e0, e2) = e1
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6686) implies:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6687)  op(e0, e2) = e1
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6453), (6687), (function-axioms) are
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6688)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6688) gives:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6689)  all_58_14 = e1 & op(e0, e1) = e1
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6626), (6689) are inconsistent by sub-proof
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2040.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6690)  all_58_15 = e1 & op(e0, e0) = e1
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5007), (6690) are inconsistent by sub-proof
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1393.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6691)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (4999), (6609), (6691),
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1515.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6692)  all_58_15 = e2 & op(e0, e0) = e2
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6692) implies:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6693)  op(e0, e0) = e2
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (6693), (function-axioms) are
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6694)  all_58_12 = e3 & op(e0, e3) = e3
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6694) implies:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6695)  op(e0, e3) = e3
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4996), (6695), (function-axioms) are
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | |   (6696)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (6468), (6480), (6599), (6696) are
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2244.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | |   (6697)  all_54_4 = e1 | all_54_4 = e0
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (6105), (6478), (6697) are inconsistent by
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1922.
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | |   (6698)  all_58_11 = e0 & op(e1, e0) = e0
% 233.15/43.42  | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | ALPHA: (6698) implies:
% 233.15/43.42  | | | | | | | | | | | | | | | |   (6699)  op(e1, e0) = e0
% 233.15/43.42  | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6444), (6699), (function-axioms) are
% 233.15/43.42  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2323.
% 233.15/43.42  | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | End of split
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | |   (6700)  all_14_2 = e0
% 233.15/43.42  | | | | | | | | |   (6701)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 233.15/43.42  | | | | | | | | |             op(e2, e0) = all_14_1 & $i(all_14_0) &
% 233.15/43.42  | | | | | | | | |             $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0) =
% 233.15/43.42  | | | | | | | | |             all_14_1 & $i(all_14_1))
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | COMBINE_EQS: (344), (6700) imply:
% 233.15/43.42  | | | | | | | | |   (6702)  all_8_2 = e0
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | COMBINE_EQS: (311), (6702) imply:
% 233.15/43.42  | | | | | | | | |   (6703)  all_48_2 = e0
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | COMBINE_EQS: (353), (6702) imply:
% 233.15/43.42  | | | | | | | | |   (6704)  all_56_11 = e0
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | REDUCE: (366), (6702) imply:
% 233.15/43.42  | | | | | | | | |   (6705)   ~ (all_52_1 = e0)
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | REDUCE: (369), (6702) imply:
% 233.15/43.42  | | | | | | | | |   (6706)   ~ (all_52_4 = e0)
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | REDUCE: (371), (6702) imply:
% 233.15/43.42  | | | | | | | | |   (6707)   ~ (all_52_6 = e0)
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | REDUCE: (373), (6702) imply:
% 233.15/43.42  | | | | | | | | |   (6708)   ~ (all_52_7 = e0)
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | REDUCE: (375), (6702) imply:
% 233.15/43.42  | | | | | | | | |   (6709)   ~ (all_52_9 = e0)
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | REDUCE: (377), (6702) imply:
% 233.15/43.42  | | | | | | | | |   (6710)   ~ (all_52_13 = e0)
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | REDUCE: (392), (6702) imply:
% 233.15/43.42  | | | | | | | | |   (6711)   ~ (e3 = e0)
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | BETA: splitting (235) gives:
% 233.15/43.42  | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | |   (6712)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 233.15/43.42  | | | | | | | | | |             & op(e2, e2) = e0)
% 233.15/43.42  | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | BETA: splitting (6712) gives:
% 233.15/43.42  | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | |   (6713)  all_58_1 = e0 & op(e3, e2) = e0
% 233.15/43.42  | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | REF_CLOSE: (170), (6706), (6713), (function-axioms) are
% 233.15/43.42  | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 233.15/43.42  | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | |   (6714)  all_58_3 = e0 & op(e2, e2) = e0
% 233.15/43.42  | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | ALPHA: (6714) implies:
% 233.15/43.42  | | | | | | | | | | |   (6715)  all_58_3 = e0
% 233.15/43.42  | | | | | | | | | | |   (6716)  op(e2, e2) = e0
% 233.15/43.42  | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | BETA: splitting (55) gives:
% 233.15/43.42  | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | |   (6717)   ~ (all_16_2 = e0)
% 233.15/43.42  | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | REDUCE: (342), (6717) imply:
% 233.15/43.42  | | | | | | | | | | | |   (6718)   ~ (all_10_2 = e0)
% 233.15/43.42  | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | BETA: splitting (58) gives:
% 233.15/43.42  | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | |   (6719)   ~ (all_18_2 = e0)
% 233.15/43.42  | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | REDUCE: (339), (6719) imply:
% 233.15/43.42  | | | | | | | | | | | | |   (6720)   ~ (all_6_2 = e0)
% 233.15/43.42  | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | BETA: splitting (67) gives:
% 233.15/43.42  | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | |   (6721)   ~ (all_24_2 = e2)
% 233.15/43.42  | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | REDUCE: (301), (6721) imply:
% 233.15/43.42  | | | | | | | | | | | | | |   (6722)   ~ (all_10_2 = e2)
% 233.15/43.42  | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 233.15/43.42  | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | |   (6723)  all_54_0 = e3
% 233.15/43.42  | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | COMBINE_EQS: (292), (6723) imply:
% 233.15/43.42  | | | | | | | | | | | | | | |   (6724)  all_10_2 = e3
% 233.15/43.42  | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | SIMP: (6724) implies:
% 233.15/43.42  | | | | | | | | | | | | | | |   (6725)  all_10_2 = e3
% 233.15/43.42  | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | REDUCE: (355), (6725) imply:
% 233.15/43.42  | | | | | | | | | | | | | | |   (6726)   ~ (all_52_1 = e3)
% 233.15/43.42  | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | REDUCE: (361), (6725) imply:
% 233.15/43.42  | | | | | | | | | | | | | | |   (6727)   ~ (all_52_4 = e3)
% 233.15/43.42  | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 233.15/43.42  | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | |   (6728)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 233.15/43.42  | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 233.15/43.42  | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (6715), (6726), (6728),
% 233.15/43.42  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.42  | | | | | | | | | | | | | | | |            #1424.
% 233.15/43.42  | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | Case 2:
% 233.15/43.42  | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | |   (6729)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 233.15/43.42  | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 233.15/43.42  | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | BETA: splitting (6729) gives:
% 233.15/43.42  | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.42  | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | |   (6730)  all_58_5 = e3 & op(e2, e1) = e3
% 233.15/43.42  | | | | | | | | | | | | | | | | | 
% 233.15/43.42  | | | | | | | | | | | | | | | | | ALPHA: (6730) implies:
% 233.15/43.42  | | | | | | | | | | | | | | | | |   (6731)  op(e2, e1) = e3
% 233.15/43.42  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (39), (70), (85), (91), (110), (112),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (113), (117), (118), (120), (121), (123), (125),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (126), (128), (133), (134), (135), (136), (139),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (140), (141), (144), (146), (149), (157), (158),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (168), (169), (170), (191), (192), (194), (195),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (196), (198), (200), (201), (202), (203), (211),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (212), (213), (216), (217), (218), (220), (221),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (229),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (230), (232), (233), (234), (236), (237), (238),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (239), (241), (242), (243), (244), (245), (246),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (256), (257), (266), (267), (268), (270), (279),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (280), (281), (282), (297), (322), (328), (367),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (378), (380), (381), (385), (4994), (4995),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (4996), (4997), (4999), (5007), (5008), (6704),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (6705), (6706), (6710), (6715), (6716), (6720),
% 233.15/43.43  | | | | | | | | | | | | | | | | |            (6727), (6731), (function-axioms) are inconsistent
% 233.15/43.43  | | | | | | | | | | | | | | | | |            by sub-proof #1251.
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | |   (6732)  all_58_10 = e3 & op(e2, e0) = e3
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | ALPHA: (6732) implies:
% 233.15/43.43  | | | | | | | | | | | | | | | | |   (6733)  op(e2, e0) = e3
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5000), (6733), (function-axioms) are
% 233.15/43.43  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | End of split
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | End of split
% 233.15/43.43  | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | |   (6734)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 233.15/43.43  | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | REF_CLOSE: (292), (393), (6718), (6722), (6734) are
% 233.15/43.43  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 233.15/43.43  | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | End of split
% 233.15/43.43  | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | |   (6735)  all_24_2 = e2
% 233.15/43.43  | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | COMBINE_EQS: (301), (6735) imply:
% 233.15/43.43  | | | | | | | | | | | | | |   (6736)  all_10_2 = e2
% 233.15/43.43  | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | SIMP: (6736) implies:
% 233.15/43.43  | | | | | | | | | | | | | |   (6737)  all_10_2 = e2
% 233.15/43.43  | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | COMBINE_EQS: (290), (6737) imply:
% 233.15/43.43  | | | | | | | | | | | | | |   (6738)  all_56_1 = e2
% 233.15/43.43  | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | REDUCE: (355), (6737) imply:
% 233.15/43.43  | | | | | | | | | | | | | |   (6739)   ~ (all_52_1 = e2)
% 233.15/43.43  | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | REDUCE: (45), (6737) imply:
% 233.15/43.43  | | | | | | | | | | | | | |   (6740)  op(e3, e3) = e2
% 233.15/43.43  | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 233.15/43.43  | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | |   (6741)   ~ (all_26_2 = e3)
% 233.15/43.43  | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | REDUCE: (4994), (6741) imply:
% 233.15/43.43  | | | | | | | | | | | | | | |   (6742)  $false
% 233.15/43.43  | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | CLOSE: (6742) is inconsistent.
% 233.15/43.43  | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | |   (6743)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 233.15/43.43  | | | | | | | | | | | | | | |             & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 233.15/43.43  | | | | | | | | | | | | | | |             $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 233.15/43.43  | | | | | | | | | | | | | | |             = all_26_1 & $i(all_26_1))
% 233.15/43.43  | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | |   (6744)   ~ (all_36_2 = e2)
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | REDUCE: (328), (6744) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | |   (6745)   ~ (all_6_2 = e2)
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | |   (6746)  all_54_10 = e3
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (6746) are inconsistent by sub-proof
% 233.15/43.43  | | | | | | | | | | | | | | | | |            #2313.
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | |   (6747)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | BETA: splitting (6747) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | |   (6748)  all_54_10 = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (6745), (6748) are inconsistent by
% 233.15/43.43  | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | |   (6749)  all_54_10 = e1 | all_54_10 = e0
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | BETA: splitting (6749) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | |   (6750)  all_54_10 = e1
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (6750) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | |   (6751)  all_6_2 = e1
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | SIMP: (6751) implies:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | |   (6752)  all_6_2 = e1
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (6752) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | |   (6753)  all_56_21 = e1
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | REDUCE: (380), (6752) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | |   (6754)   ~ (all_52_8 = e1)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | REDUCE: (381), (6752) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | |   (6755)   ~ (all_52_9 = e1)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | REDUCE: (385), (6752) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | |   (6756)   ~ (all_52_14 = e1)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |   (6757)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (167), (169), (4995), (4996), (6738),
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |            (6739), (6753), (6754), (6757), (function-axioms)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1355.
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |   (6758)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6758) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |   (6759)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             = e2)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6759) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |   (6760)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6760) implies:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |   (6761)   ~ (all_56_21 = e1)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6753), (6761) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |   (6762)  $false
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6762) is inconsistent.
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |   (6763)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6704), (6755), (6763), (function-axioms)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1724.
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |   (6764)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             = e0)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (6710), (6753), (6756), (6764),
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |            #1250.
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | |   (6765)  all_54_10 = e0
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (6720), (6765) are inconsistent by
% 233.15/43.43  | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | End of split
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | End of split
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | |   (6766)  all_36_2 = e2
% 233.15/43.43  | | | | | | | | | | | | | | | |   (6767)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 233.15/43.43  | | | | | | | | | | | | | | | |             & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 233.15/43.43  | | | | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 233.15/43.43  | | | | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (6766) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | |   (6768)  all_6_2 = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (6768) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | |   (6769)  all_40_2 = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (6768) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | |   (6770)  all_56_21 = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | REDUCE: (381), (6768) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | |   (6771)   ~ (all_52_9 = e2)
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | REDUCE: (391), (6768) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | |   (6772)   ~ (e3 = e2)
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | REDUCE: (39), (6768) imply:
% 233.15/43.43  | | | | | | | | | | | | | | | |   (6773)  op(e1, e1) = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | |   (6774)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 233.15/43.43  | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | BETA: splitting (6774) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | |   (6775)  all_58_12 = e2 & op(e0, e3) = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | ALPHA: (6775) implies:
% 233.15/43.43  | | | | | | | | | | | | | | | | | |   (6776)  all_58_12 = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (167), (239),
% 233.15/43.43  | | | | | | | | | | | | | | | | | |            (241), (245), (4996), (6705), (6740), (6776),
% 233.15/43.43  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.43  | | | | | | | | | | | | | | | | | |            #1755.
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | |   (6777)  all_58_13 = e2 & op(e0, e2) = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | ALPHA: (6777) implies:
% 233.15/43.43  | | | | | | | | | | | | | | | | | |   (6778)  all_58_13 = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | |   (6779)  op(e0, e2) = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | |   (6780)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 233.15/43.43  | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | BETA: splitting (6780) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |   (6781)  all_58_9 = e2 & op(e3, e0) = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | ALPHA: (6781) implies:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |   (6782)  all_58_9 = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |   (6783)  op(e3, e0) = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (242),
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |            (246), (6706), (6740), (6782), (6783),
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |            #1559.
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |   (6784)  all_58_10 = e2 & op(e2, e0) = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | ALPHA: (6784) implies:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | |   (6785)  op(e2, e0) = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |   (6786)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6786) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |   (6787)  all_58_6 = e2 & op(e1, e3) = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6787) implies:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | |   (6788)  all_58_6 = e2
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | |   (6789)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6789) gives:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | |   (6790)  all_58_6 = e3 & op(e1, e3) = e3
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6790) implies:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | |   (6791)  all_58_6 = e3
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6788), (6791) are inconsistent by sub-proof
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | |            #2024.
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | |   (6792)  all_58_7 = e3 & op(e1, e2) = e3
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6792) implies:
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | |   (6793)  all_58_7 = e3
% 233.15/43.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (162),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (217), (223), (226), (227), (229),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (239), (245), (4992), (4996),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |            (5007), (6705), (6707), (6715), (6720), (6740),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |            (6743), (6773), (6778), (6785), (6788), (6793),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |            #1246.
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |   (6794)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (162), (223), (6707), (6773),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |            (6788), (6794), (function-axioms) are inconsistent
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1677.
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | |   (6795)  all_58_7 = e2 & op(e1, e2) = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6795) implies:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | |   (6796)  all_58_7 = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |   (6797)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6797) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |   (6798)  all_58_6 = e3 & op(e1, e3) = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6798) implies:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |   (6799)  all_58_6 = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6800)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6800) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6801)  all_58_1 = e3 & op(e3, e2) = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6801) implies:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6802)  all_58_1 = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (236), (6715), (6778), (6796),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6802) are inconsistent by sub-proof #1750.
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6803)  all_58_3 = e3 & op(e2, e2) = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6803) implies:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6804)  all_58_3 = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (235), (236), (237),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6778), (6779), (6796), (6804), (function-axioms)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1454.
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6805)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6805) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6806)  all_58_7 = e3 & op(e1, e2) = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6806) implies:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6807)  all_58_7 = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6796), (6807) imply:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6808)  e3 = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6808) implies:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6809)  e3 = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6799), (6809) imply:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6810)  all_58_6 = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (162),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (217), (223), (226), (227), (229),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (239), (245), (4992), (4996),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5007), (6705), (6707), (6715), (6720), (6740),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6743), (6773), (6778), (6785), (6807), (6810),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1246.
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6811)  all_58_13 = e3 & op(e0, e2) = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6811) implies:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6812)  op(e0, e2) = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6779), (6812), (function-axioms) are
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |   (6813)  all_58_7 = e3 & op(e1, e2) = e3
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6796), (6813) are inconsistent by sub-proof
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |            #1675.
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |   (6814)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (5001), (6773), (6814),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |            #2148.
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | |   (6815)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6815) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | |   (6816)  all_58_8 = e2 & op(e1, e1) = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6816) implies:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | |   (6817)  all_58_8 = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (6779) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | |   (6818)  all_52_7 = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (6785) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | |   (6819)  all_52_13 = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (6818) imply:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | |   (6820)   ~ (all_52_4 = e2)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |   (6821)   ~ (all_48_2 = e0)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6703), (6821) imply:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |   (6822)  $false
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6822) is inconsistent.
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |   (6823)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | |             = all_48_1 & $i(all_48_1))
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6701) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |   (6824)   ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_14_1 & $i(all_14_0) &
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6824) implies:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |   (6825)   ~ (all_14_0 = e3)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |   (6826)  op(e2, e0) = all_14_1
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |   (6827)  op(all_14_1, e2) = all_14_0
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_14_1,
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (6785), (6826) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |   (6828)  all_14_1 = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6827), (6828) imply:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | |   (6829)  op(e2, e2) = all_14_0
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6823) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6830)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_48_1 & $i(all_48_0) &
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6830) implies:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6831)   ~ (all_48_0 = e1)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6832)  op(e2, e0) = all_48_1
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6833)  op(all_48_1, e2) = all_48_0
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_1,
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (6785), (6832) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6834)  all_48_1 = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (6716), (6829) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6835)  all_14_0 = e0
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6833), (6834) imply:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6836)  op(e2, e2) = all_48_0
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_48_0,
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (6716), (6836) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6837)  all_48_0 = e0
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6831), (6837) imply:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6838)   ~ (e1 = e0)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6839)   ~ (all_40_2 = e2)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6769), (6839) imply:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6840)  $false
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6840) is inconsistent.
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6841)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_40_1 & $i(all_40_1))
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (85),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (110), (112), (113), (117), (118), (120),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (121), (123), (125), (126), (128), (133), (134),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (136), (139), (140), (141), (144), (146),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (157), (158), (159), (160), (162), (163),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (191),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (198), (200), (201),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (203), (211), (212), (213), (216), (217),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (221), (222), (223), (224), (225),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (232), (233),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (236), (237), (238), (239), (240), (241),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (242), (243), (244), (245), (246), (256), (257),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (266), (267), (268), (270), (279), (280), (281),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (297), (322), (328), (367), (378), (380),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (381), (385), (391), (4994), (4995), (4996),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4997), (4998), (4999), (5000), (5001), (5007),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5008), (6704), (6705), (6706), (6707), (6709),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6710), (6715), (6716), (6720), (6738), (6739),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6740), (6743), (6766), (6767), (6770), (6771),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6773), (6778), (6779), (6785), (6817), (6820),
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6841), (function-axioms) are inconsistent by
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1236.
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6842)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6842) implies:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6843)   ~ (all_48_1 = e3)
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6844)  op(e2, e0) = all_48_1
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_1,
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (6785), (6844) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6845)  all_48_1 = e2
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (6716), (6829) gives:
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (6846)  all_14_0 = e0
% 233.15/43.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (85),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (110), (112), (113), (117), (118), (120),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (121), (123), (125), (126), (128), (133), (134),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (136), (139), (140), (141), (144), (146),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (157), (158), (159), (160), (162), (163),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (191),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (198), (200), (201),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (203), (211), (212), (213), (216), (217),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (221), (222), (223), (224), (225),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (232), (233),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (236), (237), (238), (239), (240), (241),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (242), (243), (244), (245), (246), (256), (257),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (266), (267), (268), (270), (279), (280), (281),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (297), (322), (328), (367), (378), (380),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (381), (385), (391), (4994), (4995), (4996),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (4997), (4998), (4999), (5000), (5001), (5007),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (5008), (6704), (6705), (6706), (6707), (6709),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6710), (6715), (6716), (6720), (6738), (6739),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6740), (6743), (6766), (6767), (6769), (6770),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6771), (6773), (6778), (6779), (6785), (6817),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6820), (function-axioms) are inconsistent by
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1235.
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | |   (6847)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6847) implies:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | |   (6848)   ~ (all_14_1 = e1)
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | |   (6849)  op(e2, e0) = all_14_1
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_14_1,
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (6785), (6849) gives:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | |   (6850)  all_14_1 = e2
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6823) gives:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6851)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_48_1 & $i(all_48_0) &
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6851) implies:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6852)   ~ (all_48_0 = e1)
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6853)  op(e2, e0) = all_48_1
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6854)  op(all_48_1, e2) = all_48_0
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_1,
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (6785), (6853) gives:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6855)  all_48_1 = e2
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6854), (6855) imply:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6856)  op(e2, e2) = all_48_0
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_48_0,
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (6716), (6856) gives:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6857)  all_48_0 = e0
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6852), (6857) imply:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6858)   ~ (e1 = e0)
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (85),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (110), (112), (113), (117), (118), (120),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (121), (123), (125), (126), (128), (133), (134),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (136), (139), (140), (141), (144), (146),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (157), (158), (159), (160), (162), (163),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (191),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (198), (200), (201),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (203), (211), (212), (213), (216), (217),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (221), (222), (223), (224), (225),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (232), (233),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (236), (237), (238), (239), (240), (241),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (242), (243), (244), (245), (246), (256), (257),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (266), (267), (268), (270), (279), (280), (281),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (297), (322), (328), (367), (378), (380),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (381), (385), (391), (4994), (4995), (4996),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (4997), (4998), (4999), (5000), (5001), (5007),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (5008), (6704), (6705), (6706), (6707), (6709),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6710), (6715), (6716), (6720), (6738), (6739),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6740), (6743), (6766), (6767), (6769), (6770),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6771), (6773), (6778), (6779), (6785), (6817),
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6820), (function-axioms) are inconsistent by
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1235.
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6859)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6859) implies:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6860)   ~ (all_48_1 = e3)
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6861)  op(e2, e0) = all_48_1
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_1,
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (6785), (6861) gives:
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (6862)  all_48_1 = e2
% 233.15/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (85),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (110), (112), (113), (117), (118), (120),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (121), (123), (125), (126), (128), (133), (134),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (136), (139), (140), (141), (144), (146),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (157), (158), (159), (160), (162), (163),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (191),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (198), (200), (201),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (203), (211), (212), (213), (216), (217),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (221), (222), (223), (224), (225),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (232), (233),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (236), (237), (238), (239), (240), (241),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (242), (243), (244), (245), (246), (256), (257),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (266), (267), (268), (270), (279), (280), (281),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (297), (322), (328), (367), (378), (380),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (381), (385), (391), (4994), (4995), (4996),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (4997), (4998), (4999), (5000), (5001), (5007),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (5008), (6704), (6705), (6706), (6707), (6709),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6710), (6715), (6716), (6720), (6738), (6739),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6740), (6743), (6766), (6767), (6769), (6770),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6771), (6773), (6778), (6779), (6785), (6817),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (6820), (function-axioms) are inconsistent by
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1235.
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | |   (6863)  all_58_11 = e2 & op(e1, e0) = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6863) implies:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | |   (6864)  all_58_11 = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (216), (220), (5007),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | |            (5008), (6785), (6864), (function-axioms) are
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1344.
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | |   (6865)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 233.57/43.45  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | BETA: splitting (6865) gives:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |   (6866)  all_58_11 = e2 & op(e1, e0) = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | ALPHA: (6866) implies:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |   (6867)  all_58_11 = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (165), (167), (216),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |            (220), (233), (5007), (5008), (6716), (6739),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |            (6771), (6867), (function-axioms) are inconsistent
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |            by sub-proof #1233.
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |   (6868)  all_58_15 = e2 & op(e0, e0) = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | ALPHA: (6868) implies:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |   (6869)  op(e0, e0) = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (6869), (function-axioms) are
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.45  | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | End of split
% 233.57/43.45  | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.45  | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | |   (6870)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 233.57/43.45  | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.57/43.45  | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | BETA: splitting (6870) gives:
% 233.57/43.45  | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | |   (6871)  all_58_14 = e2 & op(e0, e1) = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | ALPHA: (6871) implies:
% 233.57/43.45  | | | | | | | | | | | | | | | | | |   (6872)  all_58_14 = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | |   (6873)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 233.57/43.45  | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | BETA: splitting (6873) gives:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |   (6874)  all_58_9 = e2 & op(e3, e0) = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | ALPHA: (6874) implies:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |   (6875)  all_58_9 = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |   (6876)  op(e3, e0) = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (242),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |            (246), (6706), (6740), (6875), (6876),
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |            #1559.
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |   (6877)  all_58_10 = e2 & op(e2, e0) = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | ALPHA: (6877) implies:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | |   (6878)  op(e2, e0) = e2
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | |   (6879)  all_58_15 = e0 & op(e0, e0) = e0
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.45  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6879) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | |   (6880)  op(e0, e0) = e0
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5008), (6880), (function-axioms) are
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | |   (6881)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6881) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | |   (6882)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | |   (6883)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6883) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | |   (6884)  all_58_4 = e0 & op(e3, e1) = e0
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6884) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | |   (6885)  all_58_4 = e0
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | |   (6886)  op(e3, e1) = e0
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | |   (6887)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6887) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (6888)  all_58_4 = e3 & op(e3, e1) = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6888) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (6889)  op(e3, e1) = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6886), (6889), (function-axioms) are
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2118.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (6890)  all_58_5 = e3 & op(e2, e1) = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6890) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (6891)  all_58_5 = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6892)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6892) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6893)  all_58_2 = e1 & op(e2, e3) = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6893) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6894)  all_58_2 = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6882) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6895)  all_58_12 = e0 & op(e0, e3) = e0
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6895) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6896)  all_58_12 = e0
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6897)  op(e0, e3) = e0
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6898)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6898) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6899)  all_58_6 = e2 & op(e1, e3) = e2
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6899) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6900)  all_58_6 = e2
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6901)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (230), (6740), (6773), (6872),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6886), (6891), (6894), (6901), (function-axioms)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1232.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6902)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6902) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6903)  all_58_6 = e3 & op(e1, e3) = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6900), (6903) are inconsistent by sub-proof
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1838.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6904)  all_58_12 = e3 & op(e0, e3) = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6904) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6905)  op(e0, e3) = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4996), (6905), (function-axioms) are
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6906)  all_58_7 = e2 & op(e1, e2) = e2
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6906) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6907)  all_58_7 = e2
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6908)  op(e1, e2) = e2
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6909)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (230), (6740), (6773), (6872),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6886), (6891), (6894), (6909), (function-axioms)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1232.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6910)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6910) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6911)  all_58_6 = e3 & op(e1, e3) = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6911) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6912)  all_58_6 = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6913)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6913) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6914)  all_58_12 = e1 & op(e0, e3) = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6914) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6915)  op(e0, e3) = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4992), (6743), (6897), (6915),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1384.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6916)  all_58_13 = e1 & op(e0, e2) = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6916) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6917)  all_58_13 = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6918)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (230), (6773), (6872), (6885),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6886), (6918), (function-axioms) are inconsistent
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2046.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6919)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6919) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6920)  all_58_8 = e1 & op(e1, e1) = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (223), (225),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6773), (6907), (6908), (6912), (6920),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2214.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6921)  all_58_14 = e1 & op(e0, e1) = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6921) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6922)  all_58_14 = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (218), (5007), (6896), (6917),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6922) are inconsistent by sub-proof #1230.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6923)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6923) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6924)  all_58_14 = e1 & op(e0, e1) = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6924) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6925)  all_58_14 = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6872), (6925) are inconsistent by sub-proof
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2044.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6926)  all_58_15 = e1 & op(e0, e0) = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6926) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6927)  all_58_15 = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5007), (6927) imply:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6928)  e3 = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6928) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6929)  e3 = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6891), (6929) imply:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6930)  all_58_5 = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (230), (6773), (6872), (6886),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6930), (function-axioms) are inconsistent by
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2115.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6931)  all_58_12 = e3 & op(e0, e3) = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6931) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6932)  op(e0, e3) = e3
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4996), (6932), (function-axioms) are
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6933)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6933) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6934)  all_58_8 = e2 & op(e1, e1) = e2
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6934) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6935)  all_58_8 = e2
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (228), (230), (6773),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6872), (6885), (6886), (6935), (function-axioms)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2043.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6936)  all_58_11 = e2 & op(e1, e0) = e2
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6936) implies:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6937)  all_58_11 = e2
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (39), (70), (85), (91), (110),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (117), (118), (120), (121), (123),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (126), (128), (133), (134), (135), (136),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (139), (140), (141), (144), (146), (149), (157),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (159), (160), (162), (163), (164), (165),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (191), (192), (194),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (195), (196), (198), (200), (201), (202), (203),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (213), (216), (217), (218), (220),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (232), (233), (234), (236), (237),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (239), (241), (242), (243), (244), (245),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (256), (257), (266), (267), (268), (270),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (279), (280), (281), (282), (297), (322), (328),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (367), (378), (380), (381), (385), (4994), (4995),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4996), (4998), (4999), (5001), (5007), (5008),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6704), (6705), (6706), (6707), (6710), (6715),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6716), (6720), (6773), (6886), (6937),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1229.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6938)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (6708), (6872), (6938),
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1228.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6939)  all_58_3 = e1 & op(e2, e2) = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6715), (6939) are inconsistent by sub-proof
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1752.
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6940)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6940) gives:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6941)  all_58_5 = e1 & op(e2, e1) = e1
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6941) implies:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6942)  all_58_5 = e1
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (230), (6773), (6872), (6886),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6942), (function-axioms) are inconsistent by
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2115.
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6943)  all_58_10 = e1 & op(e2, e0) = e1
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6943) implies:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6944)  op(e2, e0) = e1
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6878), (6944), (function-axioms) are
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1659.
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | |   (6945)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (4998), (6773), (6945),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | |            #1307.
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | |   (6946)  all_58_5 = e0 & op(e2, e1) = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6709), (6946), (function-axioms) are
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |   (6947)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6773), (6872), (6947), (function-axioms) are
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2035.
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | |   (6948)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 233.57/43.47  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (6948) gives:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | |   (6949)  all_58_11 = e2 & op(e1, e0) = e2
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | ALPHA: (6949) implies:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | |   (6950)  all_58_11 = e2
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | |   (6951)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6951) gives:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |   (6952)  all_58_4 = e0 & op(e3, e1) = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6952) implies:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |   (6953)  op(e3, e1) = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (39), (70), (85), (91), (110),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (117), (118), (120), (121), (123),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (125), (126), (128), (133), (134), (135), (136),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (139), (140), (141), (144), (146), (149), (157),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (158), (159), (160), (162), (163), (164), (165),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (191), (192), (194),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (195), (196), (198), (200), (201), (202), (203),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (213), (216), (217), (218), (220),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (232), (233), (234), (236), (237),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (238), (239), (241), (242), (243), (244), (245),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (246), (256), (257), (266), (267), (268), (270),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (279), (280), (281), (282), (297), (322), (328),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (367), (378), (380), (381), (385), (4994), (4995),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (4996), (4998), (4999), (5001), (5007), (5008),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (6704), (6705), (6706), (6707), (6710), (6715),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (6716), (6720), (6773), (6950), (6953),
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            #1229.
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |   (6954)  all_58_5 = e0 & op(e2, e1) = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6709), (6954), (function-axioms) are
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | |   (6955)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6773), (6872), (6955), (function-axioms) are
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2035.
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | |   (6956)  all_58_15 = e2 & op(e0, e0) = e2
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | ALPHA: (6956) implies:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | |   (6957)  op(e0, e0) = e2
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (6957), (function-axioms) are
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | |   (6958)  all_58_15 = e2 & op(e0, e0) = e2
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | ALPHA: (6958) implies:
% 233.57/43.47  | | | | | | | | | | | | | | | | | |   (6959)  op(e0, e0) = e2
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5008), (6959), (function-axioms) are
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | |   (6960)  all_18_2 = e0
% 233.57/43.47  | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | COMBINE_EQS: (339), (6960) imply:
% 233.57/43.47  | | | | | | | | | | | | |   (6961)  all_6_2 = e0
% 233.57/43.47  | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | SIMP: (6961) implies:
% 233.57/43.47  | | | | | | | | | | | | |   (6962)  all_6_2 = e0
% 233.57/43.47  | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | COMBINE_EQS: (266), (6962) imply:
% 233.57/43.47  | | | | | | | | | | | | |   (6963)  all_56_21 = e0
% 233.57/43.47  | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | REDUCE: (380), (6962) imply:
% 233.57/43.47  | | | | | | | | | | | | |   (6964)   ~ (all_52_8 = e0)
% 233.57/43.47  | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | REDUCE: (383), (6962) imply:
% 233.57/43.47  | | | | | | | | | | | | |   (6965)   ~ (all_52_11 = e0)
% 233.57/43.47  | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | REDUCE: (39), (6962) imply:
% 233.57/43.47  | | | | | | | | | | | | |   (6966)  op(e1, e1) = e0
% 233.57/43.47  | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | BETA: splitting (216) gives:
% 233.57/43.47  | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | Case 1:
% 233.57/43.47  | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | |   (6967)  all_58_15 = e0 & op(e0, e0) = e0
% 233.57/43.47  | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | ALPHA: (6967) implies:
% 233.57/43.47  | | | | | | | | | | | | | |   (6968)  op(e0, e0) = e0
% 233.57/43.47  | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | REF_CLOSE: (7), (5008), (6968), (function-axioms) are
% 233.57/43.47  | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 233.57/43.47  | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | |   (6969)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.57/43.47  | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 233.57/43.47  | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 233.57/43.47  | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 233.57/43.47  | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 233.57/43.47  | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | ALPHA: (6969) implies:
% 233.57/43.47  | | | | | | | | | | | | | |   (6970)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 233.57/43.47  | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 233.57/43.47  | | | | | | | | | | | | | |               e1) = e0)
% 233.57/43.47  | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 233.57/43.47  | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | Case 1:
% 233.57/43.47  | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | |   (6971)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 233.57/43.47  | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 233.57/43.47  | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | BETA: splitting (6971) gives:
% 233.57/43.47  | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | Case 1:
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | |   (6972)  all_58_0 = e0 & op(e3, e3) = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (6718), (6972), (function-axioms) are
% 233.57/43.47  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1736.
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | |   (6973)  all_58_1 = e0 & op(e3, e2) = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | REF_CLOSE: (170), (6706), (6973), (function-axioms) are
% 233.57/43.47  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | End of split
% 233.57/43.47  | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | |   (6974)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 233.57/43.47  | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 233.57/43.47  | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | BETA: splitting (6974) gives:
% 233.57/43.47  | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | Case 1:
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | |   (6975)  all_58_4 = e0 & op(e3, e1) = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6964), (6975), (function-axioms) are
% 233.57/43.47  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | |   (6976)  all_58_9 = e0 & op(e3, e0) = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | ALPHA: (6976) implies:
% 233.57/43.47  | | | | | | | | | | | | | | | |   (6977)  all_58_9 = e0
% 233.57/43.47  | | | | | | | | | | | | | | | |   (6978)  op(e3, e0) = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | BETA: splitting (6970) gives:
% 233.57/43.47  | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | |   (6979)  all_58_12 = e0 & op(e0, e3) = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | ALPHA: (6979) implies:
% 233.57/43.47  | | | | | | | | | | | | | | | | |   (6980)  op(e0, e3) = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 233.57/43.47  | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (6980) gives:
% 233.57/43.47  | | | | | | | | | | | | | | | | |   (6981)  all_52_3 = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 233.57/43.47  | | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (168), (6978) gives:
% 233.57/43.47  | | | | | | | | | | | | | | | | |   (6982)  all_52_12 = e0
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | REDUCE: (144), (6981) imply:
% 233.57/43.47  | | | | | | | | | | | | | | | | |   (6983)   ~ (all_52_2 = e0)
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | REDUCE: (113), (6982) imply:
% 233.57/43.47  | | | | | | | | | | | | | | | | |   (6984)   ~ (all_52_13 = e0)
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | REDUCE: (112), (6982) imply:
% 233.57/43.47  | | | | | | | | | | | | | | | | |   (6985)   ~ (all_52_14 = e0)
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | SIMP: (6985) implies:
% 233.57/43.47  | | | | | | | | | | | | | | | | |   (6986)   ~ (all_52_14 = e0)
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | REDUCE: (365), (6982) imply:
% 233.57/43.47  | | | | | | | | | | | | | | | | |   (6987)   ~ (all_10_2 = e0)
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | BETA: splitting (4992) gives:
% 233.57/43.47  | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | Case 1:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | |   (6988)   ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 &
% 233.57/43.47  | | | | | | | | | | | | | | | | | |           op(e0, e3) = all_12_1 & $i(all_12_0) &
% 233.57/43.47  | | | | | | | | | | | | | | | | | |           $i(all_12_1)
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | ALPHA: (6988) implies:
% 233.57/43.47  | | | | | | | | | | | | | | | | | |   (6989)  op(e0, e3) = all_12_1
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (45), (67), (70), (123),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (136), (141), (145), (146), (149), (157), (159),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (169),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (170), (195), (196), (198), (200), (204), (213),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (216), (220), (225), (226), (230), (233), (234),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (239), (240), (241), (242), (243), (245), (267),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (268), (270), (279), (290), (292), (301), (355),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (357), (393), (4994), (4995), (4996), (4998),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (5000), (5001), (5007), (5008), (6705), (6710),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (6715), (6716), (6718), (6963), (6966), (6977),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (6980), (6983), (6986), (6989), (function-axioms)
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1214.
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | |   (6990)   ~ (all_12_1 = e2) & op(e0, e3) = all_12_1 &
% 233.57/43.47  | | | | | | | | | | | | | | | | | |           $i(all_12_1)
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | ALPHA: (6990) implies:
% 233.57/43.47  | | | | | | | | | | | | | | | | | |   (6991)  op(e0, e3) = all_12_1
% 233.57/43.47  | | | | | | | | | | | | | | | | | | 
% 233.57/43.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (45), (67), (70), (123),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (136), (141), (145), (146), (149), (157), (159),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (169),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (170), (195), (196), (198), (200), (204), (213),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (216), (220), (225), (226), (230), (233), (234),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (239), (240), (241), (242), (243), (245), (267),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (268), (270), (279), (290), (292), (301), (355),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (357), (393), (4994), (4995), (4996), (4998),
% 233.57/43.47  | | | | | | | | | | | | | | | | | |            (5000), (5001), (5007), (5008), (6705), (6710),
% 233.57/43.48  | | | | | | | | | | | | | | | | | |            (6715), (6716), (6718), (6963), (6966), (6977),
% 233.57/43.48  | | | | | | | | | | | | | | | | | |            (6980), (6983), (6986), (6991), (function-axioms)
% 233.57/43.48  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1214.
% 233.57/43.48  | | | | | | | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | | | | | | End of split
% 233.57/43.48  | | | | | | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | | | | | Case 2:
% 233.57/43.48  | | | | | | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | | | | | |   (6992)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 233.57/43.48  | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.57/43.48  | | | | | | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (6708), (6965), (6992),
% 233.57/43.48  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.57/43.48  | | | | | | | | | | | | | | | | |            #1414.
% 233.57/43.48  | | | | | | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | | | | | End of split
% 233.57/43.48  | | | | | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | | | | End of split
% 233.57/43.48  | | | | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | | | End of split
% 233.57/43.48  | | | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | | End of split
% 233.57/43.48  | | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | End of split
% 233.57/43.48  | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | Case 2:
% 233.57/43.48  | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | |   (6993)  all_16_2 = e0
% 233.57/43.48  | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | COMBINE_EQS: (342), (6993) imply:
% 233.57/43.48  | | | | | | | | | | | |   (6994)  all_10_2 = e0
% 233.57/43.48  | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | REDUCE: (359), (6994) imply:
% 233.57/43.48  | | | | | | | | | | | |   (6995)   ~ (all_52_3 = e0)
% 233.57/43.48  | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | REDUCE: (365), (6994) imply:
% 233.57/43.48  | | | | | | | | | | | |   (6996)   ~ (all_52_12 = e0)
% 233.57/43.48  | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | REDUCE: (393), (6994) imply:
% 233.57/43.48  | | | | | | | | | | | |   (6997)   ~ (e1 = e0)
% 233.57/43.48  | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | REDUCE: (45), (6994) imply:
% 233.57/43.48  | | | | | | | | | | | |   (6998)  op(e3, e3) = e0
% 233.57/43.48  | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (39), (70), (85), (91), (110),
% 233.57/43.48  | | | | | | | | | | | |            (112), (113), (118), (120), (121), (123), (125),
% 233.57/43.48  | | | | | | | | | | | |            (126), (128), (133), (134), (135), (136), (139),
% 233.57/43.48  | | | | | | | | | | | |            (140), (141), (144), (146), (149), (157), (158),
% 233.57/43.48  | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 233.57/43.48  | | | | | | | | | | | |            (169), (170), (191), (192), (194), (195), (196),
% 233.57/43.48  | | | | | | | | | | | |            (198), (200), (201), (202), (203), (211), (212),
% 233.57/43.48  | | | | | | | | | | | |            (213), (216), (217), (218), (220), (221), (222),
% 233.57/43.48  | | | | | | | | | | | |            (223), (224), (225), (226), (227), (229), (230),
% 233.57/43.48  | | | | | | | | | | | |            (232), (233), (234), (236), (237), (238), (239),
% 233.57/43.48  | | | | | | | | | | | |            (241), (242), (243), (244), (245), (246), (256),
% 233.57/43.48  | | | | | | | | | | | |            (257), (266), (267), (268), (270), (279), (280),
% 233.57/43.48  | | | | | | | | | | | |            (281), (282), (297), (322), (328), (367), (378),
% 233.57/43.48  | | | | | | | | | | | |            (380), (381), (385), (391), (4994), (4995),
% 233.57/43.48  | | | | | | | | | | | |            (4996), (4997), (4999), (5000), (5001), (5007),
% 233.57/43.48  | | | | | | | | | | | |            (5008), (6704), (6705), (6706), (6708), (6710),
% 233.57/43.48  | | | | | | | | | | | |            (6715), (6716), (6995), (6996), (6998),
% 233.57/43.48  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.57/43.48  | | | | | | | | | | | |            #1254.
% 233.57/43.48  | | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | | End of split
% 233.57/43.48  | | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | End of split
% 233.57/43.48  | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | Case 2:
% 233.57/43.48  | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | |   (6999)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 233.57/43.48  | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 233.57/43.48  | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | | REF_CLOSE: (158), (162), (6707), (6708), (6999),
% 233.57/43.48  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.57/43.48  | | | | | | | | | |            #1990.
% 233.57/43.48  | | | | | | | | | | 
% 233.57/43.48  | | | | | | | | | End of split
% 233.57/43.48  | | | | | | | | | 
% 233.57/43.48  | | | | | | | | End of split
% 233.57/43.48  | | | | | | | | 
% 233.57/43.48  | | | | | | | End of split
% 233.57/43.48  | | | | | | | 
% 233.57/43.48  | | | | | | End of split
% 233.57/43.48  | | | | | | 
% 233.57/43.48  | | | | | End of split
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | Case 2:
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | |   (7000)  all_10_2 = e1
% 233.57/43.48  | | | | |   (7001)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3,
% 233.57/43.48  | | | | |               e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 233.57/43.48  | | | | |             (all_10_1 = e2) & op(e3, e1) = all_10_1 & $i(all_10_1))
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | | COMBINE_EQS: (349), (7000) imply:
% 233.57/43.48  | | | | |   (7002)  all_38_2 = e1
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | | COMBINE_EQS: (290), (7000) imply:
% 233.57/43.48  | | | | |   (7003)  all_56_1 = e1
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | | REDUCE: (355), (7000) imply:
% 233.57/43.48  | | | | |   (7004)   ~ (all_52_1 = e1)
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | | REDUCE: (357), (7000) imply:
% 233.57/43.48  | | | | |   (7005)   ~ (all_52_2 = e1)
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | | REDUCE: (359), (7000) imply:
% 233.57/43.48  | | | | |   (7006)   ~ (all_52_3 = e1)
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | | REDUCE: (361), (7000) imply:
% 233.57/43.48  | | | | |   (7007)   ~ (all_52_4 = e1)
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | | REDUCE: (363), (7000) imply:
% 233.57/43.48  | | | | |   (7008)   ~ (all_52_8 = e1)
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | | REDUCE: (365), (7000) imply:
% 233.57/43.48  | | | | |   (7009)   ~ (all_52_12 = e1)
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | | REDUCE: (45), (7000) imply:
% 233.57/43.48  | | | | |   (7010)  op(e3, e3) = e1
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | | BETA: splitting (49) gives:
% 233.57/43.48  | | | | | 
% 233.57/43.48  | | | | | Case 1:
% 233.57/43.48  | | | | | | 
% 233.57/43.48  | | | | | |   (7011)   ~ (all_12_2 = e3)
% 233.57/43.48  | | | | | | 
% 233.75/43.48  | | | | | | REDUCE: (346), (7011) imply:
% 233.75/43.48  | | | | | |   (7012)   ~ (all_4_2 = e3)
% 233.75/43.48  | | | | | | 
% 233.75/43.48  | | | | | | BETA: splitting (52) gives:
% 233.75/43.48  | | | | | | 
% 233.75/43.48  | | | | | | Case 1:
% 233.75/43.48  | | | | | | | 
% 233.75/43.48  | | | | | | |   (7013)   ~ (all_14_2 = e0)
% 233.75/43.48  | | | | | | | 
% 233.75/43.48  | | | | | | | REDUCE: (344), (7013) imply:
% 233.75/43.48  | | | | | | |   (7014)   ~ (all_8_2 = e0)
% 233.75/43.48  | | | | | | | 
% 233.75/43.48  | | | | | | | BETA: splitting (58) gives:
% 233.75/43.48  | | | | | | | 
% 233.75/43.48  | | | | | | | Case 1:
% 233.75/43.48  | | | | | | | | 
% 233.75/43.48  | | | | | | | |   (7015)   ~ (all_18_2 = e0)
% 233.75/43.48  | | | | | | | | 
% 233.75/43.48  | | | | | | | | REDUCE: (339), (7015) imply:
% 233.75/43.48  | | | | | | | |   (7016)   ~ (all_6_2 = e0)
% 233.75/43.48  | | | | | | | | 
% 233.75/43.48  | | | | | | | | BETA: splitting (61) gives:
% 233.75/43.48  | | | | | | | | 
% 233.75/43.48  | | | | | | | | Case 1:
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | |   (7017)   ~ (all_20_2 = e1)
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | REDUCE: (341), (7017) imply:
% 233.75/43.48  | | | | | | | | |   (7018)   ~ (all_4_2 = e1)
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | BETA: splitting (189) gives:
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | Case 1:
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | |   (7019)  all_54_15 = e3
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | COMBINE_EQS: (299), (7019) imply:
% 233.75/43.48  | | | | | | | | | |   (7020)  all_4_2 = e3
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | REDUCE: (7012), (7020) imply:
% 233.75/43.48  | | | | | | | | | |   (7021)  $false
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | CLOSE: (7021) is inconsistent.
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | Case 2:
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | |   (7022)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | BETA: splitting (7022) gives:
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | Case 1:
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | |   (7023)  all_54_15 = e2
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | COMBINE_EQS: (299), (7023) imply:
% 233.75/43.48  | | | | | | | | | | |   (7024)  all_4_2 = e2
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | REDUCE: (390), (7024) imply:
% 233.75/43.48  | | | | | | | | | | |   (7025)  $false
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | CLOSE: (7025) is inconsistent.
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | Case 2:
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | |   (7026)  all_54_15 = e1 | all_54_15 = e0
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | BETA: splitting (7026) gives:
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | Case 1:
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | |   (7027)  all_54_15 = e1
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | COMBINE_EQS: (299), (7027) imply:
% 233.75/43.48  | | | | | | | | | | | |   (7028)  all_4_2 = e1
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | REDUCE: (7018), (7028) imply:
% 233.75/43.48  | | | | | | | | | | | |   (7029)  $false
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | CLOSE: (7029) is inconsistent.
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | Case 2:
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | |   (7030)  all_54_15 = e0
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | COMBINE_EQS: (299), (7030) imply:
% 233.75/43.48  | | | | | | | | | | | |   (7031)  all_4_2 = e0
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | COMBINE_EQS: (254), (7031) imply:
% 233.75/43.48  | | | | | | | | | | | |   (7032)  all_56_31 = e0
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | REDUCE: (368), (7031) imply:
% 233.75/43.48  | | | | | | | | | | | |   (7033)   ~ (all_52_3 = e0)
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | REDUCE: (387), (7031) imply:
% 233.75/43.48  | | | | | | | | | | | |   (7034)   ~ (all_52_12 = e0)
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | REDUCE: (388), (7031) imply:
% 233.75/43.48  | | | | | | | | | | | |   (7035)   ~ (all_52_13 = e0)
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | REDUCE: (389), (7031) imply:
% 233.75/43.48  | | | | | | | | | | | |   (7036)   ~ (all_52_14 = e0)
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | REDUCE: (36), (7031) imply:
% 233.75/43.48  | | | | | | | | | | | |   (7037)  op(e0, e0) = e0
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | BETA: splitting (64) gives:
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | Case 1:
% 233.75/43.48  | | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | |   (7038)   ~ (all_22_2 = e1)
% 233.75/43.48  | | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | | REDUCE: (326), (7038) imply:
% 233.75/43.48  | | | | | | | | | | | | |   (7039)   ~ (all_8_2 = e1)
% 233.75/43.48  | | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | | REF_CLOSE: (159), (160), (164), (165), (167), (169), (199),
% 233.75/43.48  | | | | | | | | | | | | |            (213), (275), (353), (366), (375), (392), (7003),
% 233.75/43.48  | | | | | | | | | | | | |            (7008), (7014), (7032), (7033), (7035), (7036),
% 233.75/43.48  | | | | | | | | | | | | |            (7039), (function-axioms) are inconsistent by
% 233.75/43.48  | | | | | | | | | | | | |            sub-proof #1212.
% 233.75/43.48  | | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | Case 2:
% 233.75/43.48  | | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | |   (7040)  all_22_2 = e1
% 233.75/43.48  | | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | | COMBINE_EQS: (326), (7040) imply:
% 233.75/43.48  | | | | | | | | | | | | |   (7041)  all_8_2 = e1
% 233.75/43.48  | | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | | COMBINE_EQS: (353), (7041) imply:
% 233.75/43.48  | | | | | | | | | | | | |   (7042)  all_56_11 = e1
% 233.75/43.48  | | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | | REDUCE: (373), (7041) imply:
% 233.75/43.48  | | | | | | | | | | | | |   (7043)   ~ (all_52_7 = e1)
% 233.75/43.48  | | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | | REDUCE: (377), (7041) imply:
% 233.75/43.48  | | | | | | | | | | | | |   (7044)   ~ (all_52_13 = e1)
% 233.75/43.48  | | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | | REF_CLOSE: (4), (110), (112), (113), (118), (121), (133),
% 233.75/43.48  | | | | | | | | | | | | |            (145), (157), (158), (159), (160), (164), (165),
% 233.75/43.48  | | | | | | | | | | | | |            (167), (168), (169), (170), (194), (197), (201),
% 233.75/43.48  | | | | | | | | | | | | |            (213), (217), (220), (266), (269), (280), (297),
% 233.75/43.48  | | | | | | | | | | | | |            (381), (385), (391), (7006), (7009), (7016),
% 233.75/43.48  | | | | | | | | | | | | |            (7032), (7033), (7034), (7035), (7036), (7037),
% 233.75/43.48  | | | | | | | | | | | | |            (7042), (7043), (7044), (function-axioms) are
% 233.75/43.48  | | | | | | | | | | | | |            inconsistent by sub-proof #2273.
% 233.75/43.48  | | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | End of split
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | End of split
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | End of split
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | End of split
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | Case 2:
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | |   (7045)  all_20_2 = e1
% 233.75/43.48  | | | | | | | | |   (7046)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 233.75/43.48  | | | | | | | | |             op(e0, e1) = all_20_1 & $i(all_20_0) &
% 233.75/43.48  | | | | | | | | |             $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1) =
% 233.75/43.48  | | | | | | | | |             all_20_1 & $i(all_20_1))
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | COMBINE_EQS: (341), (7045) imply:
% 233.75/43.48  | | | | | | | | |   (7047)  all_4_2 = e1
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | SIMP: (7047) implies:
% 233.75/43.48  | | | | | | | | |   (7048)  all_4_2 = e1
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | COMBINE_EQS: (324), (7048) imply:
% 233.75/43.48  | | | | | | | | |   (7049)  all_34_2 = e1
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | COMBINE_EQS: (254), (7048) imply:
% 233.75/43.48  | | | | | | | | |   (7050)  all_56_31 = e1
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | REDUCE: (379), (7048) imply:
% 233.75/43.48  | | | | | | | | |   (7051)   ~ (all_52_7 = e1)
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | REDUCE: (386), (7048) imply:
% 233.75/43.48  | | | | | | | | |   (7052)   ~ (all_52_11 = e1)
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | REDUCE: (388), (7048) imply:
% 233.75/43.48  | | | | | | | | |   (7053)   ~ (all_52_13 = e1)
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | REDUCE: (389), (7048) imply:
% 233.75/43.48  | | | | | | | | |   (7054)   ~ (all_52_14 = e1)
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | REDUCE: (7012), (7048) imply:
% 233.75/43.48  | | | | | | | | |   (7055)   ~ (e3 = e1)
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | REDUCE: (390), (7048) imply:
% 233.75/43.48  | | | | | | | | |   (7056)   ~ (e2 = e1)
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | BETA: splitting (220) gives:
% 233.75/43.48  | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | Case 1:
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | |   (7057)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 233.75/43.48  | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | BETA: splitting (7057) gives:
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | Case 1:
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | |   (7058)  all_58_9 = e1 & op(e3, e0) = e1
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | REF_CLOSE: (168), (7009), (7058), (function-axioms) are
% 233.75/43.48  | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | Case 2:
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | |   (7059)  all_58_10 = e1 & op(e2, e0) = e1
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | REF_CLOSE: (164), (7053), (7059), (function-axioms) are
% 233.75/43.48  | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | End of split
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | Case 2:
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | |   (7060)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 233.75/43.48  | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | BETA: splitting (7060) gives:
% 233.75/43.48  | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | Case 1:
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | |   (7061)  all_58_11 = e1 & op(e1, e0) = e1
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | ALPHA: (7061) implies:
% 233.75/43.48  | | | | | | | | | | |   (7062)  op(e1, e0) = e1
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | REF_CLOSE: (160), (7054), (7062), (function-axioms) are
% 233.75/43.48  | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | Case 2:
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | |   (7063)  all_58_15 = e1 & op(e0, e0) = e1
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | ALPHA: (7063) implies:
% 233.75/43.48  | | | | | | | | | | |   (7064)  all_58_15 = e1
% 233.75/43.48  | | | | | | | | | | |   (7065)  op(e0, e0) = e1
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | BETA: splitting (64) gives:
% 233.75/43.48  | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | Case 1:
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | |   (7066)   ~ (all_22_2 = e1)
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.48  | | | | | | | | | | | | REDUCE: (326), (7066) imply:
% 233.75/43.48  | | | | | | | | | | | |   (7067)   ~ (all_8_2 = e1)
% 233.75/43.48  | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (39), (42), (123), (126), (148),
% 233.75/43.49  | | | | | | | | | | | |            (158), (159), (160), (162), (164), (165), (167),
% 233.75/43.49  | | | | | | | | | | | |            (168), (169), (170), (194), (199), (213), (218),
% 233.75/43.49  | | | | | | | | | | | |            (221), (223), (226), (227), (230), (231), (232),
% 233.75/43.49  | | | | | | | | | | | |            (234), (235), (236), (237), (238), (266), (275),
% 233.75/43.49  | | | | | | | | | | | |            (297), (375), (381), (391), (392), (7004), (7007),
% 233.75/43.49  | | | | | | | | | | | |            (7014), (7016), (7050), (7051), (7053), (7064),
% 233.75/43.49  | | | | | | | | | | | |            (7067), (function-axioms) are inconsistent by
% 233.75/43.49  | | | | | | | | | | | |            sub-proof #1830.
% 233.75/43.49  | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | |   (7068)  all_22_2 = e1
% 233.75/43.49  | | | | | | | | | | | |   (7069)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 233.75/43.49  | | | | | | | | | | | |             & op(e2, e1) = all_22_1 & $i(all_22_0) &
% 233.75/43.49  | | | | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1)
% 233.75/43.49  | | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 233.75/43.49  | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | COMBINE_EQS: (326), (7068) imply:
% 233.75/43.49  | | | | | | | | | | | |   (7070)  all_8_2 = e1
% 233.75/43.49  | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | SIMP: (7070) implies:
% 233.75/43.49  | | | | | | | | | | | |   (7071)  all_8_2 = e1
% 233.75/43.49  | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | COMBINE_EQS: (347), (7071) imply:
% 233.75/43.49  | | | | | | | | | | | |   (7072)  all_30_2 = e1
% 233.75/43.49  | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | COMBINE_EQS: (353), (7071) imply:
% 233.75/43.49  | | | | | | | | | | | |   (7073)  all_56_11 = e1
% 233.75/43.49  | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | REDUCE: (375), (7071) imply:
% 233.75/43.49  | | | | | | | | | | | |   (7074)   ~ (all_52_9 = e1)
% 233.75/43.49  | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | BETA: splitting (232) gives:
% 233.75/43.49  | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | |   (7075)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 233.75/43.49  | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 233.75/43.49  | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | BETA: splitting (7075) gives:
% 233.75/43.49  | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | |   (7076)  all_58_2 = e1 & op(e2, e3) = e1
% 233.75/43.49  | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | REF_CLOSE: (167), (7004), (7076), (function-axioms) are
% 233.75/43.49  | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 233.75/43.49  | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | |   (7077)  all_58_3 = e1 & op(e2, e2) = e1
% 233.75/43.49  | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | ALPHA: (7077) implies:
% 233.75/43.49  | | | | | | | | | | | | | |   (7078)  all_58_3 = e1
% 233.75/43.49  | | | | | | | | | | | | | |   (7079)  op(e2, e2) = e1
% 233.75/43.49  | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 233.75/43.49  | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | |   (7080)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 233.75/43.49  | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 233.75/43.49  | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (7008), (7074), (7080),
% 233.75/43.49  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.75/43.49  | | | | | | | | | | | | | | |            #1211.
% 233.75/43.49  | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | |   (7081)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 233.75/43.49  | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 233.75/43.49  | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | BETA: splitting (7081) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | |   (7082)  all_58_8 = e1 & op(e1, e1) = e1
% 233.75/43.49  | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | ALPHA: (7082) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | |   (7083)  all_58_8 = e1
% 233.75/43.49  | | | | | | | | | | | | | | | |   (7084)  op(e1, e1) = e1
% 233.75/43.49  | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1,
% 233.75/43.49  | | | | | | | | | | | | | | | |              e1, e1, simplifying with (39), (7084) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | |   (7085)  all_6_2 = e1
% 233.75/43.49  | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | REDUCE: (378), (7085) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | |   (7086)   ~ (all_52_6 = e1)
% 233.75/43.49  | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | |   (7087)   ~ (all_30_2 = e1)
% 233.75/43.49  | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | REDUCE: (7072), (7087) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | | |   (7088)  $false
% 233.75/43.49  | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | CLOSE: (7088) is inconsistent.
% 233.75/43.49  | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | |   (7089)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 233.75/43.49  | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_30_1 & $i(all_30_0) &
% 233.75/43.49  | | | | | | | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1)
% 233.75/43.49  | | | | | | | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 233.75/43.49  | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | |   (7090)   ~ (all_34_2 = e1)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | REDUCE: (7049), (7090) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | | | |   (7091)  $false
% 233.75/43.49  | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | CLOSE: (7091) is inconsistent.
% 233.75/43.49  | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | |   (7092)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 233.75/43.49  | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 233.75/43.49  | | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 233.75/43.49  | | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 233.75/43.49  | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | |   (7093)   ~ (all_38_2 = e1)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | REDUCE: (7002), (7093) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | |   (7094)  $false
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | CLOSE: (7094) is inconsistent.
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | |   (7095)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 233.75/43.49  | | | | | | | | | | | | | | | | | | |             & op(e3, e1) = all_38_1 & $i(all_38_0) &
% 233.75/43.49  | | | | | | | | | | | | | | | | | | |             $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | |             = all_38_1 & $i(all_38_1))
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | |   (7096)  all_54_3 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (7096) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | |   (7097)  all_52_12 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | SIMP: (7097) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | |   (7098)  all_52_12 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (7098) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | |   (7099)   ~ (all_52_4 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (7098) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | |   (7100)   ~ (all_52_8 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (7098) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | |   (7101)   ~ (all_52_13 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | SIMP: (7101) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | |   (7102)   ~ (all_52_13 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (7098) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | |   (7103)   ~ (all_52_14 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | SIMP: (7103) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | |   (7104)   ~ (all_52_14 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | |   (7105)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7105) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | |   (7106)  all_58_9 = e3 & op(e3, e0) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7106) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | |   (7107)  all_58_9 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | |   (7108)  op(e3, e0) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | |   (7109)  all_54_1 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (7099), (7109) are inconsistent by
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | |   (7110)   ~ (all_54_1 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | |   (7111)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | |   (7112)  all_54_7 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (7102), (7112) are inconsistent by
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | |   (7113)   ~ (all_54_7 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | |   (7114)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (7115)  all_54_2 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (7100), (7115) are inconsistent by
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (7116)   ~ (all_54_2 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (7117)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7118)  all_54_11 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (7104), (7118) are inconsistent by
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7119)   ~ (all_54_11 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7120)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7121)  all_54_4 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (7121) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7122)  all_52_1 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7122) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7123)  all_52_1 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (7123) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7124)   ~ (all_52_9 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7124) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7125)   ~ (all_52_9 = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7126)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7126) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7127)  all_58_2 = e3 & op(e2, e3) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7127) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7128)  all_58_2 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7129)  op(e2, e3) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7130)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7130) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7131)  all_58_6 = e3 & op(e1, e3) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7131) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7132)  all_58_6 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (239), (243), (7010),
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7128), (7132), (function-axioms) are inconsistent
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1221.
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7133)  all_58_7 = e3 & op(e1, e2) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7133) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7134)  all_58_7 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7135)  op(e1, e2) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7136)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (7100), (7125), (7136),
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1628.
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7137)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7137) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7138)  all_58_8 = e3 & op(e1, e1) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (391), (7138), (function-axioms) are
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7139)  all_58_14 = e3 & op(e0, e1) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7139) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7140)  all_58_14 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7141)  op(e0, e1) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (7141) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7142)  all_52_11 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (7135) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7143)  all_52_6 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7144)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_27 & $i(all_56_27))
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7144) gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7145)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) = all_56_25 & $i(all_56_25)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7145) implies:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7146)  op(e3, e0) = all_56_25
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7147)  op(e3, all_56_25) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25, e0, e3, simplifying with (7108), (7146)
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7148)  all_56_25 = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7147), (7148) imply:
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7149)  op(e3, e3) = e3
% 233.75/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7010), (7149), (function-axioms) are
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1578.
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7150)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) = all_56_27 & $i(all_56_27)
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7150) implies:
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7151)  op(e2, e0) = all_56_27
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7152)  op(e2, all_56_27) = e2
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27, e0, e2, simplifying with (164), (7151)
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7153)  all_56_27 = all_52_13
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7152), (7153) imply:
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7154)  op(e2, all_52_13) = e2
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7155)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (7003), (7100), (7129), (7155),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1210.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7156)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7156) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7157)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_5 & $i(all_56_5)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7157) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7158)  op(e1, e3) = all_56_5
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7159)  op(e1, all_56_5) = e1
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (7158)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7160)  all_56_5 = all_52_2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7159), (7160) imply:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7161)  op(e1, all_52_2) = e1
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7162)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7162) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7163)  all_58_9 = e2 & op(e3, e0) = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7163) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7164)  op(e3, e0) = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7108), (7164), (function-axioms) are
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2125.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7165)  all_58_10 = e2 & op(e2, e0) = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7165) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7166)  op(e2, e0) = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7167)  all_58_15 = e0 & op(e0, e0) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7167) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7168)  op(e0, e0) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7065), (7168), (function-axioms) are
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (7166) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7169)  all_52_13 = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7154), (7169) imply:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7170)  op(e2, e2) = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7079), (7170), (function-axioms) are
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7171)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (88), (110),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (144), (148), (149), (159), (160), (163), (164),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (169), (170), (192), (200), (214),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (223), (227), (228), (229),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (233), (234), (235), (237), (239),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (246), (257), (279), (391),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7001), (7002), (7003), (7004), (7006), (7008),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7054), (7064), (7065), (7079), (7084),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7099), (7107), (7125), (7128), (7134), (7141),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7161), (7171), (function-axioms) are inconsistent
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1184.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7172)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_7 & $i(all_56_7)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7172) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7173)  op(e0, e3) = all_56_7
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7174)  op(e0, all_56_7) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (159), (7173)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7175)  all_56_7 = all_52_3
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7174), (7175) imply:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7176)  op(e0, all_52_3) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7177)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7177) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7178)  all_58_6 = e2 & op(e1, e3) = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7178) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7179)  all_58_6 = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (159), (160), (216), (223), (239),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7054), (7065), (7084), (7128), (7134),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7176), (7179), (function-axioms) are inconsistent
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1183.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7180)  all_58_7 = e2 & op(e1, e2) = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7134), (7180) are inconsistent by sub-proof
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1416.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7181)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7181) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7182)  all_58_8 = e2 & op(e1, e1) = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7182) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7183)  all_58_8 = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7083), (7183) are inconsistent by sub-proof
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1802.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7184)  all_58_11 = e2 & op(e1, e0) = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7184) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7185)  all_58_11 = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7186)  all_58_15 = e0 & op(e0, e0) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7186) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7187)  op(e0, e0) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7065), (7187), (function-axioms) are
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7188)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7188) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7189)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7190)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7191)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (7010), (7128), (7191),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1223.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7192)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7192) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7193)  all_58_6 = e2 & op(e1, e3) = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7193) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7194)  all_58_6 = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (159), (160), (216), (223), (239),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7054), (7065), (7084), (7128), (7134),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7176), (7194), (function-axioms) are inconsistent
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1183.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7195)  all_58_12 = e2 & op(e0, e3) = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7195) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7196)  all_58_12 = e2
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7189) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7197)  all_58_12 = e0 & op(e0, e3) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7196), (7197) are inconsistent by sub-proof
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1760.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7198)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7198) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7199)  all_58_13 = e0 & op(e0, e2) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7199) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7200)  op(e0, e2) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7190) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7201)  all_58_9 = e0 & op(e3, e0) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7107), (7201) are inconsistent by sub-proof
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2103.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7202)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7202) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7203)  all_58_10 = e0 & op(e2, e0) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7203) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7204)  op(e2, e0) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (110), (160), (164), (221), (7064),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7108), (7154), (7203), (7204), (function-axioms)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1181.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7205)  all_58_11 = e0 & op(e1, e0) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7205) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7206)  all_58_11 = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7185), (7206) imply:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7207)  e2 = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7196), (7207) imply:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7208)  all_58_12 = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (218), (7064), (7140), (7200),
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7208), (function-axioms) are inconsistent by
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1916.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7209)  all_58_14 = e0 & op(e0, e1) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7209) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7210)  op(e0, e1) = e0
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7141), (7210), (function-axioms) are
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2164.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7211)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_31) = e0)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7211) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7212)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) = all_56_29 & $i(all_56_29)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7212) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7213)  op(e1, e0) = all_56_29
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7214)  op(e1, all_56_29) = e1
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_29, e0, e1, simplifying with (160), (7213)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7215)  all_56_29 = all_52_14
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7214), (7215) imply:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7216)  op(e1, all_52_14) = e1
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7217)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7217) gives:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7218)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7218) implies:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7219)  op(e3, all_56_1) = e3
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7003), (7219) imply:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7220)  op(e3, e1) = e3
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7100), (7220), (function-axioms) are
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7221)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_3 & $i(all_56_3)
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7221) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7222)  op(e2, e3) = all_56_3
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7223)  op(e2, all_56_3) = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7129), (7222), (7223), (function-axioms) are
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2262.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7224)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7224) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7225)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_5 & $i(all_56_5)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7225) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7226)  op(e1, e3) = all_56_5
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7227)  op(e1, all_56_5) = e1
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (7226)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7228)  all_56_5 = all_52_2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7227), (7228) imply:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7229)  op(e1, all_52_2) = e1
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7230)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7230) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7231)  all_58_6 = e2 & op(e1, e3) = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7231) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7232)  all_58_6 = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7233)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7233) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7234)  all_58_6 = e0 & op(e1, e3) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7232), (7234) are inconsistent by sub-proof
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1678.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7235)  all_58_7 = e0 & op(e1, e2) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7134), (7235) are inconsistent by sub-proof
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2034.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7236)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7236) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7237)  all_58_8 = e0 & op(e1, e1) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7237) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7238)  op(e1, e1) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7084), (7238), (function-axioms) are
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7239)  all_58_11 = e0 & op(e1, e0) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7239) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7240)  op(e1, e0) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7241)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7241) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7242)  all_58_9 = e2 & op(e3, e0) = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7242) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7243)  op(e3, e0) = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7108), (7243), (function-axioms) are
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2125.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7244)  all_58_10 = e2 & op(e2, e0) = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7244) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7245)  op(e2, e0) = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (110), (160), (164),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (231), (233), (7054), (7065), (7078),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7079), (7104), (7107), (7128), (7216), (7240),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7245), (function-axioms) are inconsistent by
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1179.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7246)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (88), (110),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (144), (148), (149), (159), (160), (163), (164),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (169), (170), (192), (200), (214),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (223), (227), (228), (229),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (233), (234), (235), (237), (239),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (246), (257), (279), (391),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7001), (7002), (7003), (7004), (7006), (7008),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7054), (7064), (7065), (7079), (7084),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7099), (7107), (7125), (7128), (7134), (7141),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7229), (7246), (function-axioms) are inconsistent
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1184.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7247)  all_58_7 = e2 & op(e1, e2) = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7134), (7247) are inconsistent by sub-proof
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1416.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7248)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7248) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7249)  all_58_8 = e2 & op(e1, e1) = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7249) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7250)  all_58_8 = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7083), (7250) are inconsistent by sub-proof
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1802.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7251)  all_58_11 = e2 & op(e1, e0) = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7251) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7252)  all_58_11 = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (88), (110),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (144), (148), (149), (159), (160), (163), (164),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (169), (170), (192), (200), (214),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (223), (227), (228), (229),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (233), (234), (235), (237), (239),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (246), (257), (279), (391),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7001), (7002), (7003), (7004), (7006), (7008),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7054), (7065), (7079), (7084), (7099),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7107), (7125), (7128), (7134), (7141), (7229),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7252), (function-axioms) are inconsistent by
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1185.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7253)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_7 & $i(all_56_7)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7253) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7254)  op(e0, e3) = all_56_7
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (159), (7254)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7255)  all_56_7 = all_52_3
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7256)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7256) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7257)  all_58_6 = e2 & op(e1, e3) = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7257) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7258)  all_58_6 = e2
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7259)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7259) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7260)  all_58_6 = e0 & op(e1, e3) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7258), (7260) are inconsistent by sub-proof
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1678.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7261)  all_58_7 = e0 & op(e1, e2) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7134), (7261) are inconsistent by sub-proof
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2034.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7262)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7262) gives:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7263)  all_58_8 = e0 & op(e1, e1) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7263) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7264)  op(e1, e1) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7084), (7264), (function-axioms) are
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7265)  all_58_11 = e0 & op(e1, e0) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7265) implies:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7266)  all_58_11 = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7267)  op(e1, e0) = e0
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (110), (160), (164),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (221), (231), (233), (7054), (7064),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7065), (7078), (7079), (7104), (7107), (7108),
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7128), (7216), (7266), (7267), (function-axioms)
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1177.
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.77/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7268)  all_58_7 = e2 & op(e1, e2) = e2
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7134), (7268) are inconsistent by sub-proof
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1416.
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7269)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7269) gives:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7270)  all_58_8 = e2 & op(e1, e1) = e2
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7270) implies:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7271)  all_58_8 = e2
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7083), (7271) are inconsistent by sub-proof
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1802.
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7272)  all_58_11 = e2 & op(e1, e0) = e2
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7272) implies:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7273)  op(e1, e0) = e2
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7274)  all_58_15 = e0 & op(e0, e0) = e0
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7274) implies:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7275)  op(e0, e0) = e0
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7065), (7275), (function-axioms) are
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7276)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7276) implies:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7277)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7278)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7278) gives:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7279)  all_58_9 = e0 & op(e3, e0) = e0
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7107), (7279) are inconsistent by sub-proof
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2103.
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7280)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7280) gives:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7281)  all_58_10 = e0 & op(e2, e0) = e0
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7281) implies:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7282)  op(e2, e0) = e0
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.78/43.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7283)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (7079), (7128), (7283),
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1209.
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7284)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7284) gives:
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7285)  all_58_5 = e2 & op(e2, e1) = e2
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7285) implies:
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7286)  op(e2, e1) = e2
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.78/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7287)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7287) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7288)  all_58_4 = e0 & op(e3, e1) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7288) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7289)  all_58_4 = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7290)  op(e3, e1) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7291)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7291) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7292)  all_58_6 = e0 & op(e1, e3) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7292) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7293)  all_58_6 = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7294)  op(e1, e3) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7295)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7295) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7296)  all_58_0 = e2 & op(e3, e3) = e2
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7296) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7297)  op(e3, e3) = e2
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7010), (7297), (function-axioms) are
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7298)  all_58_1 = e2 & op(e3, e2) = e2
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7298) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7299)  all_58_1 = e2
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7300)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (88), (110), (144), (148), (149),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (163), (164), (167), (169), (192),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (200), (214), (216), (217), (218), (230), (232),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (239), (243), (245), (257), (279), (391),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7001), (7002), (7003), (7004), (7006), (7008),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7289), (7290), (7293), (7294), (7299),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7300), (function-axioms) are inconsistent by
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1192.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7301)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7301) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7302)  all_58_7 = e0 & op(e1, e2) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (246), (7010), (7107), (7134),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7289), (7299), (7302), (function-axioms) are
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1176.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7303)  all_58_13 = e0 & op(e0, e2) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7303) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7304)  op(e0, e2) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7277) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7305)  all_58_12 = e0 & op(e0, e3) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7305) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7306)  all_58_12 = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (218), (7064), (7140), (7304),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7306), (function-axioms) are inconsistent by
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1916.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7307)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7307) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (160), (7273) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7308)  all_52_14 = e2
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (7282) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7309)  all_52_13 = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (7290) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7310)  all_52_8 = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (7308), (7309) imply:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7311)   ~ (e2 = e0)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7102), (7309) imply:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7312)   ~ (e3 = e0)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7053), (7309) imply:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7313)   ~ (e1 = e0)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7104), (7308) imply:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7314)   ~ (e3 = e2)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7216), (7308) imply:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7315)  op(e1, e2) = e1
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7001) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7316)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_10_1 & $i(all_10_0) &
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7316) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7317)  op(e3, e1) = all_10_1
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (7064), (7065), (7095), (7102), (7107),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7135), (7290), (7315), (7317), (function-axioms)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1175.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7318)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7318) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7319)  op(e3, e1) = all_10_1
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (7064), (7065), (7095), (7102), (7107),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7135), (7290), (7315), (7319), (function-axioms)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1175.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7320)  all_58_14 = e0 & op(e0, e1) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7320) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7321)  all_58_14 = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7322)  op(e0, e1) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (228),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (391), (7008), (7289), (7321),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7322), (function-axioms) are inconsistent by
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1242.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7323)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (170), (246), (7010), (7099),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7289), (7323), (function-axioms) are inconsistent
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1187.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7324)  all_58_7 = e0 & op(e1, e2) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (7010),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7107), (7134), (7289), (7324), (function-axioms)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1189.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7325)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7325) gives:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7326)  all_58_8 = e0 & op(e1, e1) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7326) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7327)  op(e1, e1) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (229),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (7125), (7289), (7327), (function-axioms)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1662.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7328)  all_58_11 = e0 & op(e1, e0) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7328) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7329)  all_58_11 = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7330)  op(e1, e0) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (110), (160), (164),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (221), (231), (233), (7054), (7064),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7065), (7078), (7079), (7104), (7107), (7108),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7128), (7216), (7329), (7330), (function-axioms)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1177.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7331)  all_58_5 = e0 & op(e2, e1) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7331) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7332)  op(e2, e1) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7286), (7332), (function-axioms) are
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7333)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (7084), (7141), (7333),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1186.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7334)  all_58_10 = e2 & op(e2, e0) = e2
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7334) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7335)  op(e2, e0) = e2
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7282), (7335), (function-axioms) are
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7336)  all_58_11 = e0 & op(e1, e0) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7336) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7337)  all_58_11 = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7338)  op(e1, e0) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (110), (160), (164),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (221), (231), (233), (7054), (7064),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7065), (7078), (7079), (7104), (7107), (7108),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7128), (7216), (7337), (7338), (function-axioms)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1177.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7339)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7339) implies:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7340)  op(e0, all_56_31) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7050), (7340) imply:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7341)  op(e0, e1) = e0
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7141), (7341), (function-axioms) are
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2164.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7342)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (391), (7104), (7342),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1529.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7343)  all_58_3 = e3 & op(e2, e2) = e3
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (7064), (7065), (7078), (7102), (7107),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7343), (function-axioms) are inconsistent by
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1174.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7344)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (7102), (7125), (7344),
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1649.
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7345)   ~ (all_54_4 = e3)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7346)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (7345) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7347)   ~ (all_52_1 = e3)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7348)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7348) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7349)  all_58_2 = e3 & op(e2, e3) = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7349) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7350)  op(e2, e3) = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7347), (7350), (function-axioms) are
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7351)  all_58_3 = e3 & op(e2, e2) = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (7064), (7065), (7078), (7102), (7107),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7351), (function-axioms) are inconsistent by
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1174.
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7352)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7352) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7353)  all_58_5 = e3 & op(e2, e1) = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7353) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7354)  all_58_5 = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7355)  op(e2, e1) = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (7355) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7356)  all_52_9 = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (7356) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7357)   ~ (all_52_11 = e3)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7357) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7358)   ~ (all_52_11 = e3)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7089) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7359)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_30_1 & $i(all_30_0) &
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7359) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7360)   ~ (all_30_0 = e0)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7361)  op(e2, e1) = all_30_1
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7362)  op(all_30_1, e2) = all_30_0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7069) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7363)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_22_1 & $i(all_22_0) &
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7363) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7364)  op(e2, e1) = all_22_1
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7365)  op(all_22_1, e2) = all_22_0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (7355), (7361) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7366)  all_30_1 = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (7361), (7364)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7367)  all_30_1 = all_22_1
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7366), (7367) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7368)  all_22_1 = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7368) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7369)  all_22_1 = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7362), (7366) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7370)  op(e3, e2) = all_30_0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7365), (7369) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7371)  op(e3, e2) = all_22_0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_22_0, e2, e3, simplifying with (170), (7371)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7372)  all_52_4 = all_22_0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_0, e2, e3, simplifying with (170), (7370)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7373)  all_52_4 = all_30_0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7372), (7373) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7374)  all_30_0 = all_22_0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7374) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7375)  all_30_0 = all_22_0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (7372) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7376)  all_54_1 = all_22_0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (7372) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7377)   ~ (all_52_6 = all_22_0)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7377) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7378)   ~ (all_52_6 = all_22_0)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (7372) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7379)   ~ (all_52_7 = all_22_0)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7379) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7380)   ~ (all_52_7 = all_22_0)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (7372) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7381)   ~ (all_52_8 = all_22_0)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7381) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7382)   ~ (all_52_8 = all_22_0)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7099), (7372) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7383)   ~ (all_22_0 = e3)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7007), (7372) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7384)   ~ (all_22_0 = e1)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7360), (7375) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7385)   ~ (all_22_0 = e0)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7386)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7386) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7387)  all_58_0 = e0 & op(e3, e3) = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7387) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7388)  op(e3, e3) = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7010), (7388), (function-axioms) are
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7389)  all_58_1 = e0 & op(e3, e2) = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7389) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7390)  all_58_1 = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7111) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7391)  all_54_1 = e2
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7376), (7391) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7392)  all_22_0 = e2
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7378), (7392) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7393)   ~ (all_52_6 = e2)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7380), (7392) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7394)   ~ (all_52_7 = e2)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7382), (7392) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7395)   ~ (all_52_8 = e2)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7383), (7392) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7396)   ~ (e3 = e2)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (39), (110), (121), (125), (126),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (128), (139), (140), (143), (148), (157), (158),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (190), (191), (192), (195), (210),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (218), (219), (221),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (226), (227), (229), (231), (232), (235),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (238), (239), (240), (241), (242),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (246), (255), (256), (257),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (267), (269), (279), (281), (391), (7001),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7003), (7004), (7005), (7006), (7007), (7008),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7046), (7050), (7051), (7052), (7053),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7054), (7064), (7065), (7073), (7074), (7078),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7079), (7083), (7084), (7086), (7092), (7095),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7099), (7100), (7104), (7107), (7108), (7114),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7117), (7120), (7346), (7347), (7354), (7355),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7358), (7390), (7393), (7394), (7395),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1140.
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7397)  all_54_1 = e1 | all_54_1 = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7376), (7384), (7385), (7397) are inconsistent by
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1381.
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7398)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7398) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7399)  all_58_4 = e0 & op(e3, e1) = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7399) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7400)  all_58_4 = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7111) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7401)  all_54_1 = e2
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7376), (7401) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7402)  all_22_0 = e2
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7378), (7402) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7403)   ~ (all_52_6 = e2)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7380), (7402) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7404)   ~ (all_52_7 = e2)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7382), (7402) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7405)   ~ (all_52_8 = e2)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7383), (7402) imply:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7406)   ~ (e3 = e2)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (39), (110), (121), (125), (126),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (128), (139), (140), (143), (148), (157), (158),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (190), (191), (192), (195), (210),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (218), (219), (221),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (226), (229), (231), (232), (235), (236),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (239), (240), (241), (242), (243),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (255), (256), (257), (258),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (269), (279), (281), (391), (7001), (7003),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7004), (7005), (7006), (7007), (7008), (7010),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7046), (7050), (7051), (7052), (7053), (7054),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7065), (7073), (7074), (7078), (7079),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7083), (7086), (7092), (7095), (7099), (7100),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7104), (7107), (7108), (7114), (7117), (7120),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7346), (7347), (7354), (7355), (7358), (7400),
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7403), (7404), (7405), (function-axioms) are
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1139.
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7407)  all_54_1 = e1 | all_54_1 = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7376), (7384), (7385), (7407) are inconsistent by
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1381.
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7408)  all_58_9 = e0 & op(e3, e0) = e0
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7107), (7408) are inconsistent by sub-proof
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2103.
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7409)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7409) implies:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7410)   ~ (all_22_1 = e0)
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7411)  op(e2, e1) = all_22_1
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (7355), (7361) gives:
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7412)  all_30_1 = e3
% 233.79/43.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (7361), (7411)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7413)  all_30_1 = all_22_1
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7412), (7413) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7414)  all_22_1 = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7414) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7415)  all_22_1 = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7362), (7412) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7416)  op(e3, e2) = all_30_0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_0, e2, e3, simplifying with (170), (7416)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7417)  all_52_4 = all_30_0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (7417) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7418)  all_54_1 = all_30_0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (7417) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7419)   ~ (all_52_6 = all_30_0)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7419) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7420)   ~ (all_52_6 = all_30_0)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (7417) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7421)   ~ (all_52_7 = all_30_0)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7421) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7422)   ~ (all_52_7 = all_30_0)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (7417) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7423)   ~ (all_52_8 = all_30_0)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7423) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7424)   ~ (all_52_8 = all_30_0)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7099), (7417) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7425)   ~ (all_30_0 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7007), (7417) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7426)   ~ (all_30_0 = e1)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7427)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7427) gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7428)  all_58_0 = e0 & op(e3, e3) = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7428) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7429)  op(e3, e3) = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7010), (7429), (function-axioms) are
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7430)  all_58_1 = e0 & op(e3, e2) = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7430) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7431)  all_58_1 = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7111) gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7432)  all_54_1 = e2
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7418), (7432) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7433)  all_30_0 = e2
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7420), (7433) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7434)   ~ (all_52_6 = e2)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7422), (7433) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7435)   ~ (all_52_7 = e2)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7424), (7433) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7436)   ~ (all_52_8 = e2)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7425), (7433) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7437)   ~ (e3 = e2)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (39), (110), (121), (125), (126),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (128), (139), (140), (143), (148), (157), (158),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (190), (191), (192), (195), (210),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (218), (219), (221),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (226), (227), (229), (231), (232), (235),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (238), (239), (240), (241), (242),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (246), (255), (256), (257),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (267), (269), (279), (281), (391), (7001),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7003), (7004), (7005), (7006), (7007), (7008),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7046), (7050), (7051), (7052), (7053),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7054), (7064), (7065), (7073), (7074), (7078),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7079), (7083), (7084), (7086), (7092), (7095),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7099), (7100), (7104), (7107), (7108), (7114),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7117), (7120), (7346), (7347), (7354), (7355),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7358), (7431), (7434), (7435), (7436),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1140.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7438)  all_54_1 = e1 | all_54_1 = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7360), (7418), (7426), (7438) are inconsistent by
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1359.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7439)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7439) gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7440)  all_58_4 = e0 & op(e3, e1) = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7440) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7441)  all_58_4 = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7111) gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7442)  all_54_1 = e2
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7418), (7442) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7443)  all_30_0 = e2
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7420), (7443) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7444)   ~ (all_52_6 = e2)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7422), (7443) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7445)   ~ (all_52_7 = e2)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7424), (7443) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7446)   ~ (all_52_8 = e2)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7425), (7443) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7447)   ~ (e3 = e2)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (39), (110), (121), (125), (126),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (128), (139), (140), (143), (148), (157), (158),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (190), (191), (192), (195), (210),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (218), (219), (221),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (226), (229), (231), (232), (235), (236),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (239), (240), (241), (242), (243),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (255), (256), (257), (258),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (269), (279), (281), (391), (7001), (7003),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7004), (7005), (7006), (7007), (7008), (7010),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7046), (7050), (7051), (7052), (7053), (7054),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7065), (7073), (7074), (7078), (7079),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7083), (7086), (7092), (7095), (7099), (7100),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7104), (7107), (7108), (7114), (7117), (7120),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7346), (7347), (7354), (7355), (7358), (7441),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7444), (7445), (7446), (function-axioms) are
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1139.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7448)  all_54_1 = e1 | all_54_1 = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7360), (7418), (7426), (7448) are inconsistent by
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1359.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7449)  all_58_9 = e0 & op(e3, e0) = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7107), (7449) are inconsistent by sub-proof
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2103.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7450)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7450) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7451)   ~ (all_30_1 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7452)  op(e2, e1) = all_30_1
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7355), (7451), (7452), (function-axioms) are
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1839.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7453)  all_58_10 = e3 & op(e2, e0) = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7453) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7454)  op(e2, e0) = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7102), (7454), (function-axioms) are
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | |   (7455)  all_58_10 = e3 & op(e2, e0) = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7455) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | |   (7456)  op(e2, e0) = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7102), (7456), (function-axioms) are
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |   (7457)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (7064), (7104), (7457),
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |            #2058.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | |   (7458)   ~ (all_54_3 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | |   (7459)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | REDUCE: (280), (7458) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | |   (7460)   ~ (all_52_12 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |   (7461)  all_54_1 = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (7461) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |   (7462)  all_52_4 = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (7462) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |   (7463)   ~ (all_52_6 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | SIMP: (7463) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |   (7464)   ~ (all_52_6 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (7462) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |   (7465)   ~ (all_52_7 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | SIMP: (7465) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |   (7466)   ~ (all_52_7 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (7462) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |   (7467)   ~ (all_52_8 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | SIMP: (7467) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |   (7468)   ~ (all_52_8 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (7462) imply:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | |   (7469)   ~ (all_52_12 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | |   (7470)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7470) gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | |   (7471)  all_58_0 = e3 & op(e3, e3) = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7471) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | |   (7472)  op(e3, e3) = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7010), (7472), (function-axioms) are
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1578.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | |   (7473)  all_58_1 = e3 & op(e3, e2) = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7473) implies:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | |   (7474)  all_58_1 = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | |   (7475)  op(e3, e2) = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | |   (7476)  all_54_2 = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (7468), (7476) are inconsistent by
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | |   (7477)   ~ (all_54_2 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | |   (7478)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (7479)  all_54_9 = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (7464), (7479) are inconsistent by
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (7480)   ~ (all_54_9 = e3)
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (7481)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7482)  all_54_13 = e3
% 233.79/43.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (7466), (7482) are inconsistent by
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7483)   ~ (all_54_13 = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7484)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7485)  all_54_12 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (7485) imply:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7486)  all_52_3 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7486) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7487)  all_52_3 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (7487) imply:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7488)   ~ (all_52_1 = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (7487) imply:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7489)   ~ (all_52_11 = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7489) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7490)   ~ (all_52_11 = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7491)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7491) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7492)  all_58_4 = e3 & op(e3, e1) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7492) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7493)  op(e3, e1) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7468), (7493), (function-axioms) are
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7494)  all_58_5 = e3 & op(e2, e1) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7494) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7495)  all_58_5 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7496)  op(e2, e1) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7497)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (7010), (7488), (7497),
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1208.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7498)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7498) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7499)  all_58_6 = e3 & op(e1, e3) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7499) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7500)  all_58_6 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7501)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (239), (241),
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (7466), (7500), (7501), (function-axioms)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1138.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7502)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7502) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7503)  all_58_14 = e3 & op(e0, e1) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7490), (7503), (function-axioms) are
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7504)  all_58_15 = e3 & op(e0, e0) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (7010), (7064), (7488), (7500), (7504),
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1137.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7505)  all_58_12 = e3 & op(e0, e3) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7505) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7506)  all_58_12 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7507)  op(e0, e3) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7508)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (239), (243),
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7464), (7506), (7508), (function-axioms)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1136.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7509)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7509) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7510)  all_58_8 = e3 & op(e1, e1) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (391), (7510), (function-axioms) are
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7511)  all_58_11 = e3 & op(e1, e0) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7511) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7512)  all_58_11 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7513)  op(e1, e0) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (160), (7513) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7514)  all_52_14 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (7496) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7515)  all_52_9 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7069) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7516)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_22_1 & $i(all_22_0) &
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7516) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7517)   ~ (all_22_0 = e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7518)  op(e2, e1) = all_22_1
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7519)  op(all_22_1, e2) = all_22_0
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7089), (7475), (7496), (7517), (7518), (7519),
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1380.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7520)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7520) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7521)   ~ (all_22_1 = e0)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7522)  op(e2, e1) = all_22_1
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7089) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7523)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_30_1 & $i(all_30_0) &
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7523) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7524)   ~ (all_30_0 = e0)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7525)  op(e2, e1) = all_30_1
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7526)  op(all_30_1, e2) = all_30_0
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (7496), (7525) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7527)  all_30_1 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (7522), (7525)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7528)  all_30_1 = all_22_1
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7527), (7528) imply:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7529)  all_22_1 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7526), (7527) imply:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7530)  op(e3, e2) = all_30_0
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_0,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (7475), (7530) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7531)  all_30_0 = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7532)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7532) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7533)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7533) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7534)  op(e3, all_56_1) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7003), (7534) imply:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7535)  op(e3, e1) = e3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7468), (7535), (function-axioms) are
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7536)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_3 & $i(all_56_3)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7536) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7537)  op(e2, e3) = all_56_3
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7538)  op(e2, all_56_3) = e2
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_3, e3, e2, simplifying with (167), (7537)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7539)  all_56_3 = all_52_1
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7538), (7539) imply:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7540)  op(e2, all_52_1) = e2
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7541)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7010), (7073), (7475), (7496), (7541),
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1134.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7542)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7542) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7543)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7543) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7544)  op(e1, e2) = all_56_13
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7545)  op(e1, all_56_13) = e1
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (162), (7544)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7546)  all_56_13 = all_52_6
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7545), (7546) imply:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7547)  op(e1, all_52_6) = e1
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7548)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7548) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7549)  all_58_12 = e2 & op(e0, e3) = e2
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7549) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7550)  all_58_12 = e2
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7506), (7550) are inconsistent by sub-proof
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1552.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7551)  all_58_13 = e2 & op(e0, e2) = e2
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7551) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7552)  op(e0, e2) = e2
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (162),
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (216), (225), (228), (229), (230), (235),
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (243), (391), (7008), (7010), (7054),
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7065), (7078), (7083), (7474), (7496), (7506),
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7512), (7547), (7552), (function-axioms) are
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1133.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7553)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7553) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7554)  all_58_14 = e2 & op(e0, e1) = e2
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7554) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7555)  all_58_14 = e2
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7556)  all_58_15 = e0 & op(e0, e0) = e0
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7556) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7557)  op(e0, e0) = e0
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7065), (7557), (function-axioms) are
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7558)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7558) implies:
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7559)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 233.79/43.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7560)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7559) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7561)  all_58_12 = e0 & op(e0, e3) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7561) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7562)  all_58_12 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7506), (7562) are inconsistent by sub-proof
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1971.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7563)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7563) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7564)  all_58_13 = e0 & op(e0, e2) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7564) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7565)  op(e0, e2) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7566)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7566) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7567)  all_58_4 = e0 & op(e3, e1) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7567) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7568)  all_58_4 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7569)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (7010), (7474), (7569),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1132.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7570)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7570) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7571)  all_58_4 = e2 & op(e3, e1) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (229), (7083), (7495), (7555),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7568), (7571) are inconsistent by sub-proof
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1156.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7572)  all_58_9 = e2 & op(e3, e0) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7572) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7573)  all_58_9 = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7574)  op(e3, e0) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7560) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7575)  all_58_9 = e0 & op(e3, e0) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7575) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7576)  all_58_9 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (7010),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7568), (7576), (function-axioms) are inconsistent
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1190.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7577)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7577) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7578)  all_58_10 = e0 & op(e2, e0) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7578) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7579)  op(e2, e0) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7580)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7580) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7581)  all_58_2 = e2 & op(e2, e3) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7581) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7582)  all_58_2 = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7583)  op(e2, e3) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7584)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (244), (246),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7568), (7573), (7582), (7584),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1130.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7585)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7585) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7586)  all_58_6 = e0 & op(e1, e3) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7586) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7587)  all_58_6 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7588)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7588) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7589)  all_58_0 = e0 & op(e3, e3) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7589) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7590)  op(e3, e3) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (241), (243),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (7488), (7587), (7590), (function-axioms)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1441.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7591)  all_58_1 = e0 & op(e3, e2) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7591) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7592)  all_58_1 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7474), (7592) imply:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7593)  e3 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7506), (7593) imply:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7594)  all_58_12 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (158), (218), (219),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7466), (7565), (7594), (function-axioms)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1914.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7595)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7595) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (7583) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7596)  all_52_1 = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (168), (7574) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7597)  all_52_12 = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7540), (7596) imply:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7598)  op(e2, e2) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7079), (7598), (function-axioms) are
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7599)  all_58_9 = e0 & op(e3, e0) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7599) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7600)  all_58_9 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (7010),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7568), (7600), (function-axioms) are inconsistent
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1190.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7601)  all_58_12 = e0 & op(e0, e3) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7601) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7602)  all_58_12 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (158), (218), (219),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7466), (7565), (7602), (function-axioms)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1914.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7603)  all_58_3 = e2 & op(e2, e2) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7603) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7604)  op(e2, e2) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7079), (7604), (function-axioms) are
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7605)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (7496), (7579), (7605),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1129.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7606)  all_58_11 = e0 & op(e1, e0) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (158), (218), (219),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7466), (7506), (7512), (7565), (7606),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1128.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7607)  all_58_5 = e0 & op(e2, e1) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7607) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7608)  op(e2, e1) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7521), (7522), (7525), (7608), (function-axioms)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1841.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7609)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7084), (7555), (7609),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1127.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7610)  all_58_14 = e0 & op(e0, e1) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7555), (7610) are inconsistent by sub-proof
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2036.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7611)  all_58_15 = e2 & op(e0, e0) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7611) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7612)  all_58_15 = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7064), (7612) are inconsistent by sub-proof
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2231.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7613)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7613) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7614)  op(e0, e2) = all_56_15
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7615)  op(e0, all_56_15) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (158), (7614)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7616)  all_56_15 = all_52_7
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7615), (7616) imply:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7617)  op(e0, all_52_7) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7618)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7618) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7619)  all_58_12 = e2 & op(e0, e3) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7619) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7620)  all_58_12 = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7506), (7620) are inconsistent by sub-proof
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1552.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7621)  all_58_13 = e2 & op(e0, e2) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7621) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7622)  op(e0, e2) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (113), (158), (164),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (216), (219), (223), (225),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (233), (235), (239), (240), (243),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (7008), (7010), (7064),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7065), (7078), (7079), (7083), (7084), (7466),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7474), (7488), (7495), (7496), (7506), (7512),
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7617), (7622), (function-axioms) are inconsistent
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1126.
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7623)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7623) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7624)  all_58_14 = e2 & op(e0, e1) = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7624) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7625)  all_58_14 = e2
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7626)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7626) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7627)  all_58_4 = e0 & op(e3, e1) = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7627) implies:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7628)  all_58_4 = e0
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7629)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (7010), (7474), (7629),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1132.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7630)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7630) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7631)  all_58_4 = e2 & op(e3, e1) = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (229), (7083), (7495), (7625),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7628), (7631) are inconsistent by sub-proof
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1156.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7632)  all_58_9 = e2 & op(e3, e0) = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7632) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7633)  all_58_9 = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7634)  all_58_15 = e0 & op(e0, e0) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7634) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7635)  op(e0, e0) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7065), (7635), (function-axioms) are
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7636)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7636) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7637)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7637) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7638)  all_58_12 = e0 & op(e0, e3) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7506), (7638) are inconsistent by sub-proof
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1641.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7639)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7639) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7640)  all_58_13 = e0 & op(e0, e2) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7640) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7641)  all_58_13 = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7642)  op(e0, e2) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7643)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (7079), (7474), (7643),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1322.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7644)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7644) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7645)  all_58_7 = e2 & op(e1, e2) = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7645) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7646)  all_58_7 = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7647)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7647) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7648)  all_58_6 = e0 & op(e1, e3) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7648) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7649)  all_58_6 = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7650)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7650) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7651)  all_58_0 = e2 & op(e3, e3) = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7651) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7652)  op(e3, e3) = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7010), (7652), (function-axioms) are
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7653)  all_58_2 = e2 & op(e2, e3) = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7653) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7654)  all_58_2 = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7655)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7655) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7656)  all_58_2 = e0 & op(e2, e3) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (7010),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7628), (7633), (7654), (7656), (function-axioms)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1131.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7657)  all_58_3 = e0 & op(e2, e2) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7657) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7658)  all_58_3 = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (236), (237),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (7007), (7641), (7642), (7658),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1374.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7659)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7659) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7660)  all_58_5 = e0 & op(e2, e1) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7660) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7661)  op(e2, e1) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7521), (7522), (7525), (7661), (function-axioms)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1841.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7662)  all_58_10 = e0 & op(e2, e0) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7662) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7663)  op(e2, e0) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (7642) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7664)  all_52_7 = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (7663) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7665)  all_52_13 = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7053), (7665) imply:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7666)   ~ (e1 = e0)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7617), (7664) imply:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7667)  op(e0, e0) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7065), (7667), (function-axioms) are
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7668)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7668) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7669)  all_58_6 = e2 & op(e1, e3) = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7669) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7670)  all_58_6 = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7649), (7670) imply:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7671)  e2 = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7671) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7672)  e2 = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7633), (7672) imply:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7673)  all_58_9 = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (7010),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7628), (7673), (function-axioms) are inconsistent
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1190.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7674)  all_58_12 = e2 & op(e0, e3) = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7506), (7674) are inconsistent by sub-proof
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1974.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7675)  all_58_7 = e0 & op(e1, e2) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (7010),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7628), (7633), (7646), (7675), (function-axioms)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1125.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7676)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7676) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7677)  all_58_8 = e0 & op(e1, e1) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7677) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7678)  op(e1, e1) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7084), (7678), (function-axioms) are
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7679)  all_58_11 = e0 & op(e1, e0) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (158), (218), (219),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7466), (7506), (7512), (7642), (7679),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1128.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7680)  all_58_13 = e2 & op(e0, e2) = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7680) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7681)  op(e0, e2) = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7642), (7681), (function-axioms) are
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7682)  all_58_14 = e0 & op(e0, e1) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7682) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7683)  all_58_14 = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (229), (7083), (7495), (7628),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7683) are inconsistent by sub-proof #1265.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7684)  all_58_5 = e0 & op(e2, e1) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7684) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7685)  op(e2, e1) = e0
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7521), (7522), (7525), (7685), (function-axioms)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1841.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7686)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7084), (7625), (7686),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1127.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7687)  all_58_15 = e2 & op(e0, e0) = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7687) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7688)  all_58_15 = e2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7064), (7688) are inconsistent by sub-proof
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2231.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7689)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7689) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7690)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_5 & $i(all_56_5)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7690) implies:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7691)  op(e1, e3) = all_56_5
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7692)  op(e1, all_56_5) = e1
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (7691)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7693)  all_56_5 = all_52_2
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7692), (7693) imply:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7694)  op(e1, all_52_2) = e1
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7695)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7010), (7073), (7475), (7496), (7695),
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1134.
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7696)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7696) gives:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7697)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 233.79/43.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7697) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7698)  op(e1, e2) = all_56_13
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7699)  op(e1, all_56_13) = e1
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (162), (7698)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7700)  all_56_13 = all_52_6
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7699), (7700) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7701)  op(e1, all_52_6) = e1
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7702)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7702) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7703)  all_58_12 = e2 & op(e0, e3) = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7703) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7704)  all_58_12 = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7506), (7704) are inconsistent by sub-proof
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1552.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7705)  all_58_13 = e2 & op(e0, e2) = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7705) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7706)  op(e0, e2) = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (162),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (216), (225), (228), (229), (230), (235),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (243), (391), (7008), (7010), (7054),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7065), (7078), (7083), (7474), (7496), (7506),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7512), (7701), (7706), (function-axioms) are
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1133.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7707)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7707) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7708)  all_58_14 = e2 & op(e0, e1) = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7708) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7709)  all_58_14 = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (160), (163),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (219), (223), (224), (227), (229),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (237), (239), (244), (246), (7010), (7054),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7065), (7079), (7083), (7084), (7466),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7474), (7495), (7496), (7506), (7512), (7521),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7522), (7525), (7694), (7709), (function-axioms)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1124.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7710)  all_58_15 = e2 & op(e0, e0) = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7710) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7711)  all_58_15 = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7064), (7711) are inconsistent by sub-proof
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2231.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7712)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7712) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7713)  op(e0, e2) = all_56_15
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7714)  op(e0, all_56_15) = e0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (158), (7713)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7715)  all_56_15 = all_52_7
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7714), (7715) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7716)  op(e0, all_52_7) = e0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7717)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7717) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7718)  all_58_12 = e2 & op(e0, e3) = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7718) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7719)  all_58_12 = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7506), (7719) are inconsistent by sub-proof
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1552.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7720)  all_58_13 = e2 & op(e0, e2) = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7720) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7721)  op(e0, e2) = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (113), (158), (164),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (216), (219), (223), (225),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (233), (235), (239), (240), (243),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (7008), (7010), (7064),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7065), (7078), (7079), (7083), (7084), (7466),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7474), (7488), (7495), (7496), (7506), (7512),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7716), (7721), (function-axioms) are inconsistent
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1126.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7722)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7722) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7723)  all_58_14 = e2 & op(e0, e1) = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7723) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7724)  all_58_14 = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (160), (163),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (219), (223), (224), (227), (229),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (237), (239), (244), (246), (7010), (7054),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7065), (7079), (7083), (7084), (7466),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7474), (7495), (7496), (7506), (7512), (7521),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7522), (7525), (7694), (7724), (function-axioms)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1124.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7725)  all_58_15 = e2 & op(e0, e0) = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7725) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7726)  all_58_15 = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7064), (7726) are inconsistent by sub-proof
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2231.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7727)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_7 & $i(all_56_7)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7727) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7728)  op(e0, e3) = all_56_7
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7729)  op(e0, all_56_7) = e0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7507), (7728), (7729), (function-axioms) are
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2070.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7730)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7730) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7731)   ~ (all_30_1 = e3)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7732)  op(e2, e1) = all_30_1
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7496), (7731), (7732), (function-axioms) are
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1839.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7733)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7733) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7734)  all_58_8 = e3 & op(e1, e1) = e3
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (391), (7734), (function-axioms) are
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7735)  all_58_14 = e3 & op(e0, e1) = e3
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7490), (7735), (function-axioms) are
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7736)   ~ (all_54_12 = e3)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7737)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (257), (7736) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7738)   ~ (all_52_3 = e3)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7739)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (159), (7466), (7738), (7739),
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1123.
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7740)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7740) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7741)  all_58_14 = e3 & op(e0, e1) = e3
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7741) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7742)  all_58_14 = e3
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7743)  op(e0, e1) = e3
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (7743) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7744)  all_52_11 = e3
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (7744) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7745)   ~ (all_52_9 = e3)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7046) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7746)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_20_1 & $i(all_20_0) &
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7746) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7747)   ~ (all_20_0 = e2)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7748)  op(e0, e1) = all_20_1
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7749)  op(all_20_1, e0) = all_20_0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7092) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7750)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_34_1 & $i(all_34_0) &
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7750) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7751)   ~ (all_34_0 = e3)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7752)  op(e0, e1) = all_34_1
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7753)  op(all_34_1, e0) = all_34_0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_34_1,
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (7743), (7752) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7754)  all_34_1 = e3
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_1,
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_34_1, e1, e0, simplifying with (7748), (7752)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7755)  all_34_1 = all_20_1
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7754), (7755) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7756)  all_20_1 = e3
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7756) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7757)  all_20_1 = e3
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7753), (7754) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7758)  op(e3, e0) = all_34_0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7749), (7757) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7759)  op(e3, e0) = all_20_0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_20_0, e0, e3, simplifying with (168), (7759)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7760)  all_52_12 = all_20_0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_34_0, e0, e3, simplifying with (168), (7758)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7761)  all_52_12 = all_34_0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7760), (7761) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7762)  all_34_0 = all_20_0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (7760) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7763)  all_54_3 = all_20_0
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (7760) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7764)   ~ (all_52_8 = all_20_0)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (7760) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7765)   ~ (all_52_13 = all_20_0)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7765) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7766)   ~ (all_52_13 = all_20_0)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (7760) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7767)   ~ (all_52_14 = all_20_0)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7767) implies:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7768)   ~ (all_52_14 = all_20_0)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7009), (7760) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7769)   ~ (all_20_0 = e1)
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7459) gives:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7770)  all_54_3 = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7763), (7770) imply:
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7771)  all_20_0 = e2
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7747), (7771) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7772)  $false
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7772) is inconsistent.
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7773)   ~ (all_54_3 = e2)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7774)  all_54_3 = e1 | all_54_3 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7774) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7775)  all_54_3 = e1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7763), (7775) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7776)  all_20_0 = e1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7769), (7776) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7777)  $false
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7777) is inconsistent.
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7778)  all_54_3 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7763), (7778) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7779)  all_20_0 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7764), (7779) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7780)   ~ (all_52_8 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7768), (7779) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7781)   ~ (all_52_14 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7478) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7782)  all_54_2 = e2
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (7782) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7783)  all_52_8 = e2
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (7783) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7784)   ~ (all_52_9 = e2)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7784) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7785)   ~ (all_52_9 = e2)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7468), (7783) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7786)   ~ (e3 = e2)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (7783) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7787)  op(e3, e1) = e2
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7788)  all_54_6 = e3
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7745), (7788) are inconsistent by
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7789)   ~ (all_54_6 = e3)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7790)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7001) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7791)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_10_1 & $i(all_10_0) &
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7791) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7792)  op(e3, e1) = all_10_1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7793)  op(all_10_1, e3) = all_10_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7095) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7794)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_38_1 & $i(all_38_0) &
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_38_1)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7794) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7795)   ~ (all_38_0 = e2)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7796)  op(e3, e1) = all_38_1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7797)  op(all_38_1, e3) = all_38_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7790) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7798)  all_54_6 = e2
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7785), (7798) are inconsistent by
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7799)   ~ (all_54_6 = e2)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7800)  all_54_6 = e1 | all_54_6 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7800) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7801)  all_54_6 = e1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7074), (7801) are inconsistent by
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2246.
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7802)  all_54_6 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (7802) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7803)  all_52_9 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7803) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7804)  all_52_9 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (7804) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7805)   ~ (all_52_1 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7785), (7804) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7806)   ~ (e2 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7074), (7804) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7807)   ~ (e1 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (7792), (7796)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7808)  all_38_1 = all_10_1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_38_1,
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (7787), (7796) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7809)  all_38_1 = e2
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7808), (7809) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7810)  all_10_1 = e2
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7810) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7811)  all_10_1 = e2
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7797), (7809) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7812)  op(e2, e3) = all_38_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7793), (7811) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7813)  op(e2, e3) = all_10_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e3, e2, simplifying with (167), (7813)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7814)  all_52_1 = all_10_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_0, e3, e2, simplifying with (167), (7812)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7815)  all_52_1 = all_38_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7814), (7815) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7816)  all_38_0 = all_10_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (7814) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7817)  all_54_4 = all_10_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7814) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7818)   ~ (all_52_13 = all_10_0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7818) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7819)   ~ (all_52_13 = all_10_0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7004), (7814) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7820)   ~ (all_10_0 = e1)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7805), (7814) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7821)   ~ (all_10_0 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7795), (7816) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7822)   ~ (all_10_0 = e2)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7823)  all_54_4 = e3
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7817), (7823) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7824)  all_10_0 = e3
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7819), (7824) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7825)   ~ (all_52_13 = e3)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (163), (164),
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (210), (216), (221), (222), (7005), (7050),
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7065), (7079), (7459), (7460), (7743),
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7747), (7748), (7751), (7752), (7753), (7763),
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7766), (7769), (7781), (7825), (function-axioms)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1119.
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7826)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (7004), (7805), (7817), (7822), (7826) are
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1118.
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7827)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_38_1)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7827) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7828)   ~ (all_38_1 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7829)  op(e3, e1) = all_38_1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7790) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7830)  all_54_6 = e2
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7785), (7830) are inconsistent by
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7831)  all_54_6 = e1 | all_54_6 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7831) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7832)  all_54_6 = e1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7074), (7832) are inconsistent by
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2246.
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7833)  all_54_6 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (7833) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7834)  all_52_9 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7834) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7835)  all_52_9 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (7835) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7836)   ~ (all_52_1 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (7835) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7837)   ~ (all_52_13 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7837) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7838)   ~ (all_52_13 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7745), (7835) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7839)   ~ (e3 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7074), (7835) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7840)   ~ (e1 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (7835) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7841)  op(e2, e1) = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7089) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7842)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_30_1 & $i(all_30_0) &
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7842) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7843)   ~ (all_30_0 = e0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7844)  op(e2, e1) = all_30_1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7845)  op(all_30_1, e2) = all_30_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (128), (140), (158), (160), (162),
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (216), (218), (256), (257), (267), (7006),
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7051), (7054), (7064), (7065), (7069),
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7073), (7086), (7089), (7466), (7475), (7481),
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7484), (7737), (7742), (7743), (7841), (7843),
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7844), (7845), (function-axioms) are inconsistent
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1117.
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7846)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7846) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7847)   ~ (all_30_1 = e3)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7848)  op(e2, e1) = all_30_1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7069) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7849)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_22_1 & $i(all_22_0) &
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7849) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7850)  op(e2, e1) = all_22_1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (7848), (7850)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7851)  all_30_1 = all_22_1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_30_1,
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (7841), (7848) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7852)  all_30_1 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (7792), (7829)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7853)  all_38_1 = all_10_1
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_38_1,
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (7787), (7829) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7854)  all_38_1 = e2
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7853), (7854) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7855)  all_10_1 = e2
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7855) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7856)  all_10_1 = e2
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7851), (7852) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7857)  all_22_1 = e0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7793), (7856) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7858)  op(e2, e3) = all_10_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e3, e2, simplifying with (167), (7858)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7859)  all_52_1 = all_10_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (7859) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7860)  all_54_4 = all_10_0
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7859) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7861)   ~ (all_52_13 = all_10_0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7861) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7862)   ~ (all_52_13 = all_10_0)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7863)  all_54_7 = e3
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (7863) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7864)  all_52_13 = e3
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7864) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7865)  all_52_13 = e3
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (7865) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7866)   ~ (all_52_14 = e3)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7866) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7867)   ~ (all_52_14 = e3)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7862), (7865) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7868)   ~ (all_10_0 = e3)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7868) implies:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7869)   ~ (all_10_0 = e3)
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (7865) imply:
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7870)  op(e2, e0) = e3
% 233.79/43.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (126), (160),
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (167), (169), (193), (200), (214), (226),
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (239), (258), (267), (279), (391), (7003),
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7004), (7010), (7054), (7065), (7079), (7086),
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7464), (7468), (7481), (7781), (7836), (7841),
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7860), (7867), (7869), (7870), (function-axioms)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1115.
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7871)   ~ (all_54_7 = e3)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (7871) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7872)   ~ (all_52_13 = e3)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (163), (164),
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (210), (216), (221), (222), (7005), (7050),
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7065), (7079), (7459), (7460), (7743),
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7747), (7748), (7751), (7752), (7753), (7763),
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7766), (7769), (7781), (7872), (function-axioms)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1119.
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7873)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7873) implies:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7874)   ~ (all_22_1 = e0)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7875)  op(e2, e1) = all_22_1
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7089), (7841), (7874), (7875), (function-axioms)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1356.
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7876)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7095), (7787), (7876), (function-axioms) are
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1113.
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7877)  all_54_2 = e1 | all_54_2 = e0
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (7008), (7780), (7877) are inconsistent by
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1336.
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7878)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 &
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7878) implies:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7879)  op(e0, e1) = all_34_1
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_34_1,
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (7743), (7879) gives:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7880)  all_34_1 = e3
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_1,
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_34_1, e1, e0, simplifying with (7748), (7879)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7881)  all_34_1 = all_20_1
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7880), (7881) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7882)  all_20_1 = e3
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7882) implies:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7883)  all_20_1 = e3
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7749), (7883) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7884)  op(e3, e0) = all_20_0
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_20_0, e0, e3, simplifying with (168), (7884)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7885)  all_52_12 = all_20_0
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (7885) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7886)  all_54_3 = all_20_0
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (7885) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7887)   ~ (all_52_8 = all_20_0)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (7885) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7888)   ~ (all_52_13 = all_20_0)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7888) implies:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7889)   ~ (all_52_13 = all_20_0)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (7885) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7890)   ~ (all_52_14 = all_20_0)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7890) implies:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7891)   ~ (all_52_14 = all_20_0)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7009), (7885) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7892)   ~ (all_20_0 = e1)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7459) gives:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7893)  all_54_3 = e2
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7886), (7893) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7894)  all_20_0 = e2
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7747), (7894) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7895)  $false
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7895) is inconsistent.
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7896)   ~ (all_54_3 = e2)
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7897)  all_54_3 = e1 | all_54_3 = e0
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7897) gives:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7898)  all_54_3 = e1
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7886), (7898) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7899)  all_20_0 = e1
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7892), (7899) imply:
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7900)  $false
% 233.79/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7900) is inconsistent.
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7901)  all_54_3 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7886), (7901) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7902)  all_20_0 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7887), (7902) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7903)   ~ (all_52_8 = e0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7891), (7902) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7904)   ~ (all_52_14 = e0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7478) gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7905)  all_54_2 = e2
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (7905) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7906)  all_52_8 = e2
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (7906) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7907)   ~ (all_52_9 = e2)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7907) implies:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7908)   ~ (all_52_9 = e2)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7468), (7906) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7909)   ~ (e3 = e2)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (7906) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7910)  op(e3, e1) = e2
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7911)  all_54_6 = e3
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7745), (7911) are inconsistent by
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7912)   ~ (all_54_6 = e3)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7913)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7001) gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7914)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_10_1 & $i(all_10_0) &
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7914) implies:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7915)  op(e3, e1) = all_10_1
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7916)  op(all_10_1, e3) = all_10_0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7095) gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7917)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_38_1 & $i(all_38_0) &
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_38_1)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7917) implies:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7918)   ~ (all_38_0 = e2)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7919)  op(e3, e1) = all_38_1
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7920)  op(all_38_1, e3) = all_38_0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7913) gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7921)  all_54_6 = e2
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7908), (7921) are inconsistent by
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7922)   ~ (all_54_6 = e2)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7923)  all_54_6 = e1 | all_54_6 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7923) gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7924)  all_54_6 = e1
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7074), (7924) are inconsistent by
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2246.
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7925)  all_54_6 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (7925) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7926)  all_52_9 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7926) implies:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7927)  all_52_9 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (7927) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7928)   ~ (all_52_1 = e0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7908), (7927) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7929)   ~ (e2 = e0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7074), (7927) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7930)   ~ (e1 = e0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (7915), (7919)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7931)  all_38_1 = all_10_1
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_38_1,
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (7910), (7919) gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7932)  all_38_1 = e2
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7931), (7932) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7933)  all_10_1 = e2
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7933) implies:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7934)  all_10_1 = e2
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7920), (7932) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7935)  op(e2, e3) = all_38_0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7916), (7934) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7936)  op(e2, e3) = all_10_0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e3, e2, simplifying with (167), (7936)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7937)  all_52_1 = all_10_0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_0, e3, e2, simplifying with (167), (7935)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7938)  all_52_1 = all_38_0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7937), (7938) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7939)  all_38_0 = all_10_0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (7937) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7940)  all_54_4 = all_10_0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7937) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7941)   ~ (all_52_13 = all_10_0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7941) implies:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7942)   ~ (all_52_13 = all_10_0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7004), (7937) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7943)   ~ (all_10_0 = e1)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7928), (7937) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7944)   ~ (all_10_0 = e0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7918), (7939) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7945)   ~ (all_10_0 = e2)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7946)  all_54_4 = e3
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7940), (7946) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7947)  all_10_0 = e3
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7942), (7947) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7948)   ~ (all_52_13 = e3)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (163), (164),
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (210), (216), (221), (222), (7005), (7050),
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7065), (7079), (7459), (7460), (7743),
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7747), (7886), (7889), (7892), (7904), (7948),
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1112.
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7949)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (7004), (7928), (7940), (7945), (7949) are
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1118.
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7950)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_38_1)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7950) implies:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7951)   ~ (all_38_1 = e0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7952)  op(e3, e1) = all_38_1
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7913) gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7953)  all_54_6 = e2
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7908), (7953) are inconsistent by
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7954)  all_54_6 = e1 | all_54_6 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7954) gives:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7955)  all_54_6 = e1
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7074), (7955) are inconsistent by
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2246.
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7956)  all_54_6 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (7956) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7957)  all_52_9 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7957) implies:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7958)  all_52_9 = e0
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (7958) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7959)   ~ (all_52_1 = e0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (7958) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7960)   ~ (all_52_13 = e0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7960) implies:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7961)   ~ (all_52_13 = e0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7745), (7958) imply:
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7962)   ~ (e3 = e0)
% 233.94/43.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7074), (7958) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7963)   ~ (e1 = e0)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (7958) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7964)  op(e2, e1) = e0
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7089) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7965)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_30_1 & $i(all_30_0) &
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7965) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7966)   ~ (all_30_0 = e0)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7967)  op(e2, e1) = all_30_1
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7968)  op(all_30_1, e2) = all_30_0
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (128), (140), (158), (160), (162),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (216), (218), (256), (257), (267), (7006),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (7051), (7054), (7064), (7065), (7069),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7073), (7086), (7089), (7466), (7475), (7481),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7484), (7737), (7742), (7743), (7964), (7966),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7967), (7968), (function-axioms) are inconsistent
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1117.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7969)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7969) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7970)   ~ (all_30_1 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7971)  op(e2, e1) = all_30_1
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7069) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7972)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_22_1 & $i(all_22_0) &
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7972) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7973)  op(e2, e1) = all_22_1
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (7971), (7973)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7974)  all_30_1 = all_22_1
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_30_1,
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (7964), (7971) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7975)  all_30_1 = e0
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (7915), (7952)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7976)  all_38_1 = all_10_1
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_38_1,
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (7910), (7952) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7977)  all_38_1 = e2
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7976), (7977) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7978)  all_10_1 = e2
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7978) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7979)  all_10_1 = e2
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7974), (7975) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7980)  all_22_1 = e0
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7916), (7979) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7981)  op(e2, e3) = all_10_0
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e3, e2, simplifying with (167), (7981)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7982)  all_52_1 = all_10_0
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (7982) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7983)  all_54_4 = all_10_0
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7982) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7984)   ~ (all_52_13 = all_10_0)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7984) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7985)   ~ (all_52_13 = all_10_0)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7986)  all_54_7 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (7986) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7987)  all_52_13 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7987) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7988)  all_52_13 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (7988) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7989)   ~ (all_52_14 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7989) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7990)   ~ (all_52_14 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7985), (7988) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7991)   ~ (all_10_0 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7991) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7992)   ~ (all_10_0 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (7988) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7993)  op(e2, e0) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (126), (160),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (167), (169), (193), (200), (214), (226),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (239), (258), (267), (279), (391), (7003),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7004), (7010), (7054), (7065), (7079), (7086),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7464), (7468), (7481), (7904), (7959), (7964),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7983), (7990), (7992), (7993), (function-axioms)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1115.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7994)   ~ (all_54_7 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (7994) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7995)   ~ (all_52_13 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (163), (164),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (210), (216), (221), (222), (7005), (7050),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (7065), (7079), (7459), (7460), (7743),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7747), (7886), (7889), (7892), (7904), (7995),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1112.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7996)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7996) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7997)   ~ (all_22_1 = e0)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7998)  op(e2, e1) = all_22_1
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7089), (7964), (7997), (7998), (function-axioms)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1356.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7999)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7095), (7910), (7999), (function-axioms) are
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1113.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8000)  all_54_2 = e1 | all_54_2 = e0
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (7008), (7903), (8000) are inconsistent by
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1336.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8001)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7092), (7743), (8001), (function-axioms) are
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1805.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8002)  all_58_15 = e3 & op(e0, e0) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8002) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8003)  all_58_15 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7064), (8003) are inconsistent by sub-proof
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2249.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | |   (8004)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (7460), (7468), (8004),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | |            #1515.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | |   (8005)   ~ (all_54_1 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | REDUCE: (282), (8005) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | |   (8006)   ~ (all_52_4 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | |   (8007)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (7010), (8006), (8007),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | |            #1401.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | |   (8008)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8008) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | |   (8009)  all_58_4 = e3 & op(e3, e1) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8009) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | |   (8010)  all_58_4 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | |   (8011)  op(e3, e1) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (8011) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | |   (8012)  all_52_8 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (8012) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | |   (8013)   ~ (all_52_9 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8013) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | |   (8014)   ~ (all_52_9 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (8012) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | |   (8015)   ~ (all_52_12 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | |   (8016)  all_54_11 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (8016) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | |   (8017)  all_52_14 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8017) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | |   (8018)  all_52_14 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (8018) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | |   (8019)   ~ (all_52_6 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (8018) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | |   (8020)   ~ (all_52_13 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (8021)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8021) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8022)  all_58_2 = e3 & op(e2, e3) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8022) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8023)  op(e2, e3) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8024)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8024) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8025)  all_58_1 = e3 & op(e3, e2) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8025) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8026)  op(e3, e2) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (8006), (8026), (function-axioms) are
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8027)  all_58_3 = e3 & op(e2, e2) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8027) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8028)  all_58_3 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (7010), (7078), (8006), (8010), (8028),
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1111.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8029)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8029) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8030)  all_58_7 = e3 & op(e1, e2) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8030) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8031)  op(e1, e2) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (8019), (8031), (function-axioms) are
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8032)  all_58_13 = e3 & op(e0, e2) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8032) implies:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8033)  op(e0, e2) = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (8033) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8034)  all_52_7 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (8023) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8035)  all_52_1 = e3
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (8034) imply:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8036)   ~ (all_52_3 = e3)
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8037)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8037) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8038)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8038) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8039)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8039) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8040)  op(e3, e2) = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (8006), (8040), (function-axioms) are
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8041)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8041) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8042)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8042) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8043)  op(e2, e3) = e2
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8023), (8043), (function-axioms) are
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8044)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8044) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8045)   ~ (all_56_31 = e1)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7050), (8045) imply:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8046)  $false
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8046) is inconsistent.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8047)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8047) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8048)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8048) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8049)  op(e3, e1) = e1
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7008), (8049), (function-axioms) are
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8050)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8050) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8051)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8051) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8052)  op(e0, e3) = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8036), (8052), (function-axioms) are
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8053)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e0
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8053) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8054)  op(e0, e3) = e0
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8055)  op(e3, e0) = e0
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (8054) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8056)  all_52_3 = e0
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (168), (8055) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8057)  all_52_12 = e0
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (8056) imply:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8058)   ~ (all_52_11 = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8058) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8059)   ~ (all_52_11 = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7460), (8057) imply:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8060)   ~ (e3 = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7009), (8057) imply:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8061)   ~ (e1 = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8062)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7069), (7089), (8011), (8033), (8062),
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1109.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8063)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (157), (7084), (8059), (8063),
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1141.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8064)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (160), (165), (7050), (7054), (7074),
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8033), (8064), (function-axioms) are inconsistent
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1107.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8065)  all_58_3 = e3 & op(e2, e2) = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8065) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8066)  all_58_3 = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (7010), (7078), (8006), (8010), (8066),
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1111.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (8067)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (8014), (8020), (8067),
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | |            #1649.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | |   (8068)   ~ (all_54_11 = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (8068) imply:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | |   (8069)   ~ (all_52_14 = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (8070)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8070) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8071)  all_58_9 = e3 & op(e3, e0) = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8071) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8072)  op(e3, e0) = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7460), (8072), (function-axioms) are
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8073)  all_58_10 = e3 & op(e2, e0) = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8073) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8074)  all_58_10 = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8075)  op(e2, e0) = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (164), (8075) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8076)  all_52_13 = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (8076) imply:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8077)   ~ (all_52_1 = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (8076) imply:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8078)   ~ (all_52_14 = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8079)  all_54_12 = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (8079) imply:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8080)  all_52_3 = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8080) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8081)  all_52_3 = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (8081) imply:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8082)   ~ (all_52_7 = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8082) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8083)   ~ (all_52_7 = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8084)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8084) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8085)  all_58_6 = e3 & op(e1, e3) = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8085) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8086)  all_58_6 = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8087)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (170), (231),
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (7004), (8006), (8074), (8087),
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1098.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8088)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8088) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8089)  all_58_7 = e3 & op(e1, e2) = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8089) implies:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8090)  all_58_7 = e3
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8091)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8091) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8092)  all_58_6 = e0 & op(e1, e3) = e0
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8086), (8092) are inconsistent by sub-proof
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2213.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8093)  all_58_7 = e0 & op(e1, e2) = e0
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8090), (8093) are inconsistent by sub-proof
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2034.
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8094)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8094) gives:
% 233.94/43.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8095)  all_58_8 = e0 & op(e1, e1) = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8095) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8096)  op(e1, e1) = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7084), (8096), (function-axioms) are
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8097)  all_58_11 = e0 & op(e1, e0) = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8097) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8098)  all_58_11 = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8099)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8099) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8100)  all_58_9 = e2 & op(e3, e0) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8100) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8101)  all_58_9 = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8102)  op(e3, e0) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8103)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8103) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8104)  all_58_0 = e0 & op(e3, e3) = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8104) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8105)  op(e3, e3) = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7010), (8105), (function-axioms) are
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8106)  all_58_1 = e0 & op(e3, e2) = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8106) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8107)  all_58_1 = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8108)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8108) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8109)  all_58_6 = e2 & op(e1, e3) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8086), (8109) are inconsistent by sub-proof
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2219.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8110)  all_58_7 = e2 & op(e1, e2) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8090), (8110) are inconsistent by sub-proof
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1416.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8111)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8111) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8112)  all_58_8 = e2 & op(e1, e1) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8112) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8113)  all_58_8 = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7083), (8113) imply:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8114)  e2 = e1
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8101), (8114) imply:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8115)  all_58_9 = e1
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (244), (7010), (8010), (8107),
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8115), (function-axioms) are inconsistent by
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1338.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8116)  all_58_11 = e2 & op(e1, e0) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8116) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8117)  all_58_11 = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8098), (8117) imply:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8118)  e2 = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8118) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8119)  e2 = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8101), (8119) imply:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8120)  all_58_9 = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (244), (7010), (8010), (8107),
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8120), (function-axioms) are inconsistent by
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1097.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8121)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (170), (246), (7010), (8006),
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8102), (8121), (function-axioms) are inconsistent
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1096.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8122)  all_58_10 = e2 & op(e2, e0) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8122) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8123)  op(e2, e0) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8075), (8123), (function-axioms) are
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8124)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7064), (8098), (8124) are inconsistent
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1178.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8125)  all_58_13 = e3 & op(e0, e2) = e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8083), (8125), (function-axioms) are
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8126)  all_58_7 = e3 & op(e1, e2) = e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8126) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8127)  op(e1, e2) = e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8128)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8128) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8129)  all_58_12 = e3 & op(e0, e3) = e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8129) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8130)  all_58_12 = e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8131)  op(e0, e3) = e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8132)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8132) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8133)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8133) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8134)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8134) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8135)  op(e2, e3) = e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8077), (8135), (function-axioms) are
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8136)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8136) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8137)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8137) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8138)  all_56_9 = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8139)  op(e2, e3) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8140)  op(e3, e2) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (8127) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8141)  all_52_6 = e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (8139) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8142)  all_52_1 = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (8140) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8143)  all_52_4 = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (8142) imply:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8144)   ~ (all_52_9 = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8144) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8145)   ~ (all_52_9 = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (8143) imply:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8146)   ~ (all_52_7 = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8146) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8147)   ~ (all_52_7 = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8006), (8143) imply:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8148)   ~ (e3 = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8149)  all_54_13 = e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (8083), (8149) are inconsistent by
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8150)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8151)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8151) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8152)  all_58_4 = e2 & op(e3, e1) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8010), (8152) are inconsistent by sub-proof
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1476.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8153)  all_58_5 = e2 & op(e2, e1) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8153) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8154)  op(e2, e1) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8145), (8154), (function-axioms) are
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8155)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8155) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8156)  all_58_8 = e2 & op(e1, e1) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8156) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8157)  all_58_8 = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7083), (8157) are inconsistent by sub-proof
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1802.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8158)  all_58_14 = e2 & op(e0, e1) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8158) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8159)  op(e0, e1) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8160)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8160) gives:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8161)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_9 & $i(all_56_9)
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8161) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8162)  op(e3, all_56_9) = e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8138), (8162) imply:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8163)  op(e3, e2) = e3
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (8006), (8163), (function-axioms) are
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8164)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8164) implies:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8165)  op(e2, all_56_11) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7073), (8165) imply:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8166)  op(e2, e1) = e2
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8145), (8166), (function-axioms) are
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8167)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8167) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8168)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8168) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8169)  op(e1, e2) = all_56_13
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8170)  op(e1, all_56_13) = e1
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7046) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8171)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_20_1 & $i(all_20_0) &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8171) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8172)  op(e0, e1) = all_20_1
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7005), (7092), (8127), (8159), (8169),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8170), (8172), (function-axioms) are inconsistent
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1095.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8173)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8173) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8174)  op(e0, e1) = all_20_1
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7005), (7092), (8127), (8159), (8169),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8170), (8174), (function-axioms) are inconsistent
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1095.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8175)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (256), (7051), (7065), (8147), (8150),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8175), (function-axioms) are inconsistent by
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1932.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8176)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8176) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8177)   ~ (all_56_31 = e1)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7050), (8177) imply:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8178)  $false
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8178) is inconsistent.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8179)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8179) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8180)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8180) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8181)  op(e3, e1) = e1
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7008), (8181), (function-axioms) are
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8182)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8182) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8183)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8183) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8184)  op(e3, e0) = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7460), (8184), (function-axioms) are
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8185)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e0
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8185) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8186)   ~ (all_56_31 = e3)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8187)  op(e0, e3) = e0
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e3,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, simplifying with (8131), (8187) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8188)  e3 = e0
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8130), (8188) imply:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8189)  all_58_12 = e0
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (8083), (8128), (8189),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1918.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8190)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8190) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8191)  all_58_14 = e3 & op(e0, e1) = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8191) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8192)  all_58_14 = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8193)  op(e0, e1) = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (165), (227),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (7016), (8010), (8192), (8193),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1094.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8194)  all_58_15 = e3 & op(e0, e0) = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8194) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8195)  all_58_15 = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (7010), (7064), (8006), (8010), (8195),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1093.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8196)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8196) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8197)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7050), (7074), (8075), (8197),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1092.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8198)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8198) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8199)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e0
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8199) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8200)   ~ (all_56_31 = e2)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8201)  op(e0, e2) = e0
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8202)  op(e2, e0) = e0
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e0, e0,
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (8075), (8202) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8203)  e3 = e0
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8130), (8203) imply:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8204)  all_58_12 = e0
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (158), (218), (219),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7064), (8083), (8201), (8204), (function-axioms)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1914.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8205)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7050), (7054), (8205), (function-axioms)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2269.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8206)  all_58_13 = e3 & op(e0, e2) = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8083), (8206), (function-axioms) are
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8207)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (165), (170),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (240), (244), (246), (7010),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7016), (7064), (8006), (8010), (8207),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1090.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8208)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (391), (8069), (8208),
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1529.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8209)   ~ (all_54_12 = e3)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (257), (8209) imply:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8210)   ~ (all_52_3 = e3)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8211)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8211) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8212)  all_58_12 = e3 & op(e0, e3) = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8212) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8213)  op(e0, e3) = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8210), (8213), (function-axioms) are
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8214)  all_58_13 = e3 & op(e0, e2) = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8214) implies:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8215)  all_58_13 = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8216)  op(e0, e2) = e3
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8217)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8217) gives:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8218)  all_58_4 = e2 & op(e3, e1) = e2
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8218) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8219)  all_58_4 = e2
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8010), (8219) are inconsistent by sub-proof
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1902.
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8220)  all_58_5 = e2 & op(e2, e1) = e2
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8220) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8221)  op(e2, e1) = e2
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8222)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7069), (7089), (8011), (8216), (8222),
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1109.
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8223)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8223) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8224)  all_58_8 = e0 & op(e1, e1) = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8224) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8225)  op(e1, e1) = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7084), (8225), (function-axioms) are
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8226)  all_58_14 = e0 & op(e0, e1) = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8226) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8227)  all_58_14 = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8228)  op(e0, e1) = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8229)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8229) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8230)  all_58_12 = e2 & op(e0, e3) = e2
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8230) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8231)  all_58_12 = e2
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8232)  op(e0, e3) = e2
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8233)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8233) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8234)  all_58_2 = e0 & op(e2, e3) = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8234) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8235)  all_58_2 = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8236)  op(e2, e3) = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8237)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8237) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8238)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8238) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8239)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8239) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8240)  op(e2, e3) = e3
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8077), (8240), (function-axioms) are
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8241)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8241) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8242)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8242) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8243)   ~ (all_56_31 = e3)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8244)  op(e2, e3) = e2
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e3,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (8236), (8244) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8245)  e2 = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8231), (8245) imply:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8246)  all_58_12 = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (167), (243), (245),
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (8077), (8235), (8246), (function-axioms)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1149.
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8247)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8247) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8248)   ~ (all_56_31 = e1)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7050), (8248) imply:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8249)  $false
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8249) is inconsistent.
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8250)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8250) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8251)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8251) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8252)  op(e3, e1) = e1
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7008), (8252), (function-axioms) are
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8253)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8253) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8254)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8254) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8255)  op(e0, e3) = e3
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8210), (8255), (function-axioms) are
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8256)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8256) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8257)   ~ (all_56_31 = e3)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8258)  op(e0, e3) = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e0, e3,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, simplifying with (8232), (8258) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8259)  e2 = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8231), (8259) imply:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8260)  all_58_12 = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (167), (243), (245),
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (8077), (8235), (8260), (function-axioms)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1149.
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8261)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8261) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8262)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7050), (7074), (8075), (8262),
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1092.
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8263)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8263) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8264)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8264) implies:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8265)   ~ (all_56_31 = e2)
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8266)  op(e2, e0) = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e0, e0,
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (8075), (8266) gives:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8267)  e3 = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8010), (8267) imply:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8268)  all_58_4 = e0
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (228),
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (391), (7008), (8227), (8228),
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8268), (function-axioms) are inconsistent by
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1242.
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8269)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7050), (7054), (8269), (function-axioms)
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2269.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8270)  all_58_3 = e0 & op(e2, e2) = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7078), (8270) are inconsistent by sub-proof
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1180.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8271)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8271) gives:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8272)  all_58_5 = e0 & op(e2, e1) = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8272) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8273)  op(e2, e1) = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8221), (8273), (function-axioms) are
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8274)  all_58_10 = e0 & op(e2, e0) = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8274) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8275)  all_58_10 = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8074), (8275) imply:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8276)  e3 = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8276) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8277)  e3 = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8010), (8277) imply:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8278)  all_58_4 = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (228),
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (391), (7008), (8227), (8228),
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8278), (function-axioms) are inconsistent by
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1242.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8279)  all_58_13 = e2 & op(e0, e2) = e2
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8279) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8280)  all_58_13 = e2
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8215), (8280) imply:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8281)  e3 = e2
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (8281) imply:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8282)  $false
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8282) is inconsistent.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8283)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8283) gives:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8284)  all_58_14 = e2 & op(e0, e1) = e2
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8284) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8285)  all_58_14 = e2
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (227), (7084), (8010), (8221),
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8285), (function-axioms) are inconsistent by
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1285.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8286)  all_58_15 = e2 & op(e0, e0) = e2
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8286) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8287)  all_58_15 = e2
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7064), (8287) are inconsistent by sub-proof
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2231.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8288)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8288) gives:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8289)  all_58_8 = e2 & op(e1, e1) = e2
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8289) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8290)  all_58_8 = e2
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7083), (8290) are inconsistent by sub-proof
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1802.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8291)  all_58_14 = e2 & op(e0, e1) = e2
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8291) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8292)  all_58_14 = e2
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8293)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7069), (7089), (8011), (8216), (8293),
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1109.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8294)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7084), (8292), (8294),
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1127.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8295)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (165), (170),
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (240), (244), (246), (7010),
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7016), (7064), (8006), (8010), (8295),
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1090.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (8296)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8296) gives:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8297)  all_58_11 = e3 & op(e1, e0) = e3
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8297) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8298)  op(e1, e0) = e3
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8069), (8298), (function-axioms) are
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2149.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8299)  all_58_15 = e3 & op(e0, e0) = e3
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8299) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8300)  all_58_15 = e3
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (7010), (7064), (8006), (8010), (8300),
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1093.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | |   (8301)  all_58_9 = e3 & op(e3, e0) = e3
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8301) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | |   (8302)  op(e3, e0) = e3
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7460), (8302), (function-axioms) are
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | |   (8303)  all_58_14 = e1 & op(e0, e1) = e1
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | ALPHA: (8303) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | |   (8304)  op(e0, e1) = e1
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7052), (8304), (function-axioms) are
% 233.94/43.66  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2272.
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | |   (8305)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 233.94/43.66  | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 233.94/43.66  | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | REF_CLOSE: (164), (165), (7053), (7074), (8305),
% 233.94/43.66  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.66  | | | | | | | | | | | | |            #2234.
% 233.94/43.66  | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | | 
% 233.94/43.66  | | | | | | | | End of split
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | |   (8306)  all_18_2 = e0
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | | COMBINE_EQS: (339), (8306) imply:
% 233.94/43.66  | | | | | | | |   (8307)  all_6_2 = e0
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | | COMBINE_EQS: (266), (8307) imply:
% 233.94/43.66  | | | | | | | |   (8308)  all_56_21 = e0
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | | REDUCE: (378), (8307) imply:
% 233.94/43.66  | | | | | | | |   (8309)   ~ (all_52_6 = e0)
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | | REDUCE: (380), (8307) imply:
% 233.94/43.66  | | | | | | | |   (8310)   ~ (all_52_8 = e0)
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | | REDUCE: (381), (8307) imply:
% 233.94/43.66  | | | | | | | |   (8311)   ~ (all_52_9 = e0)
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | | REDUCE: (385), (8307) imply:
% 233.94/43.66  | | | | | | | |   (8312)   ~ (all_52_14 = e0)
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | | REDUCE: (391), (8307) imply:
% 233.94/43.66  | | | | | | | |   (8313)   ~ (e3 = e0)
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | | REDUCE: (39), (8307) imply:
% 233.94/43.66  | | | | | | | |   (8314)  op(e1, e1) = e0
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | | BETA: splitting (61) gives:
% 233.94/43.66  | | | | | | | | 
% 233.94/43.66  | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | 
% 233.94/43.66  | | | | | | | | |   (8315)   ~ (all_20_2 = e1)
% 233.94/43.66  | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | REDUCE: (341), (8315) imply:
% 233.94/43.66  | | | | | | | | |   (8316)   ~ (all_4_2 = e1)
% 233.94/43.66  | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | BETA: splitting (189) gives:
% 233.94/43.66  | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | |   (8317)  all_54_15 = e3
% 233.94/43.66  | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | REF_CLOSE: (299), (7012), (8317) are inconsistent by
% 233.94/43.66  | | | | | | | | | |            sub-proof #2340.
% 233.94/43.66  | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | |   (8318)   ~ (all_54_15 = e3)
% 233.94/43.66  | | | | | | | | | |   (8319)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 233.94/43.66  | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | BETA: splitting (8319) gives:
% 233.94/43.66  | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | |   (8320)  all_54_15 = e2
% 233.94/43.66  | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | REF_CLOSE: (299), (390), (8320) are inconsistent by sub-proof
% 233.94/43.66  | | | | | | | | | | |            #2339.
% 233.94/43.66  | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | |   (8321)   ~ (all_54_15 = e2)
% 233.94/43.66  | | | | | | | | | | |   (8322)  all_54_15 = e1 | all_54_15 = e0
% 233.94/43.66  | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | BETA: splitting (8322) gives:
% 233.94/43.66  | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | |   (8323)  all_54_15 = e1
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | REF_CLOSE: (299), (8316), (8323) are inconsistent by
% 233.94/43.66  | | | | | | | | | | | |            sub-proof #2338.
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | |   (8324)  all_54_15 = e0
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | COMBINE_EQS: (299), (8324) imply:
% 233.94/43.66  | | | | | | | | | | | |   (8325)  all_4_2 = e0
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | SIMP: (8325) implies:
% 233.94/43.66  | | | | | | | | | | | |   (8326)  all_4_2 = e0
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | COMBINE_EQS: (254), (8326) imply:
% 233.94/43.66  | | | | | | | | | | | |   (8327)  all_56_31 = e0
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | REDUCE: (388), (8326) imply:
% 233.94/43.66  | | | | | | | | | | | |   (8328)   ~ (all_52_13 = e0)
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | REDUCE: (390), (8326) imply:
% 233.94/43.66  | | | | | | | | | | | |   (8329)   ~ (e2 = e0)
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | REDUCE: (8316), (8326) imply:
% 233.94/43.66  | | | | | | | | | | | |   (8330)   ~ (e1 = e0)
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | REDUCE: (36), (8326) imply:
% 233.94/43.66  | | | | | | | | | | | |   (8331)  op(e0, e0) = e0
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | BETA: splitting (240) gives:
% 233.94/43.66  | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | |   (8332)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 233.94/43.66  | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 233.94/43.66  | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | BETA: splitting (8332) gives:
% 233.94/43.66  | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | |   (8333)  all_58_0 = e0 & op(e3, e3) = e0
% 233.94/43.66  | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | ALPHA: (8333) implies:
% 233.94/43.66  | | | | | | | | | | | | | |   (8334)  op(e3, e3) = e0
% 233.94/43.66  | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | REF_CLOSE: (4), (7010), (8334), (function-axioms) are
% 233.94/43.66  | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 233.94/43.66  | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | Case 2:
% 233.94/43.66  | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | |   (8335)  all_58_1 = e0 & op(e3, e2) = e0
% 233.94/43.66  | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | ALPHA: (8335) implies:
% 233.94/43.66  | | | | | | | | | | | | | |   (8336)  op(e3, e2) = e0
% 233.94/43.66  | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 233.94/43.66  | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | |   (8337)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 233.94/43.66  | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 233.94/43.66  | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | BETA: splitting (8337) gives:
% 233.94/43.66  | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | |   (8338)  all_58_2 = e0 & op(e2, e3) = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | ALPHA: (8338) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | |   (8339)  op(e2, e3) = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 233.94/43.66  | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (8339) gives:
% 233.94/43.66  | | | | | | | | | | | | | | | |   (8340)  all_52_1 = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 233.94/43.66  | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (8336) gives:
% 233.94/43.66  | | | | | | | | | | | | | | | |   (8341)  all_52_4 = e0
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | REDUCE: (148), (8340) imply:
% 233.94/43.66  | | | | | | | | | | | | | | | |   (8342)   ~ (all_52_3 = e0)
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | SIMP: (8342) implies:
% 233.94/43.66  | | | | | | | | | | | | | | | |   (8343)   ~ (all_52_3 = e0)
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | REDUCE: (145), (8340) imply:
% 233.94/43.66  | | | | | | | | | | | | | | | |   (8344)   ~ (all_52_13 = e0)
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | REDUCE: (369), (8341) imply:
% 233.94/43.66  | | | | | | | | | | | | | | | |   (8345)   ~ (all_8_2 = e0)
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 233.94/43.66  | | | | | | | | | | | | | | | | 
% 233.94/43.66  | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.66  | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | |   (8346)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.67  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.94/43.67  | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.94/43.67  | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.67  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.67  | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.94/43.67  | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.94/43.67  | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.94/43.67  | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 233.94/43.67  | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 233.94/43.67  | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.94/43.67  | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 233.94/43.67  | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | BETA: splitting (8346) gives:
% 233.94/43.67  | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | |   (8347)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             = e3)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | BETA: splitting (8347) gives:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |   (8348)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |           e3
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | ALPHA: (8348) implies:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |   (8349)  op(e3, e2) = e3
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8336), (8349), (function-axioms) are
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2099.
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |   (8350)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (8350) gives:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8351)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |           e2
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | ALPHA: (8351) implies:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8352)  op(e3, e2) = e2
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e2,
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (8336), (8352) gives:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8353)  e2 = e0
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (8353) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8354)  $false
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | CLOSE: (8354) is inconsistent.
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8355)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | ALPHA: (8355) implies:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8356)   ~ (all_56_1 = e1)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (7003), (8356) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8357)  $false
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | CLOSE: (8357) is inconsistent.
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | |   (8358)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             = e0)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (7008), (8327), (8343), (8358),
% 233.94/43.67  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.67  | | | | | | | | | | | | | | | | | |            #2307.
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | |   (8359)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.94/43.67  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.94/43.67  | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.94/43.67  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.94/43.67  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.94/43.67  | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.94/43.67  | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.94/43.67  | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 233.94/43.67  | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 233.94/43.67  | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 233.94/43.67  | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 233.94/43.67  | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 233.94/43.67  | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | BETA: splitting (8359) gives:
% 233.94/43.67  | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | |   (8360)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             = e2)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | BETA: splitting (8360) gives:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |   (8361)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |             e2) = e2
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | ALPHA: (8361) implies:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |   (8362)   ~ (all_56_1 = e1)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | REDUCE: (7003), (8362) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |   (8363)  $false
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | CLOSE: (8363) is inconsistent.
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |   (8364)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.94/43.67  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (8364) gives:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8365)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |             e2) = e1
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | ALPHA: (8365) implies:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8366)   ~ (all_56_11 = e2)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8367)  op(e2, e1) = e1
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (353), (8366) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8368)   ~ (all_8_2 = e2)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | |   (8369)  all_54_5 = e3
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (8369) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | |   (8370)  all_8_2 = e3
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (392), (8370) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | |   (8371)  $false
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | CLOSE: (8371) is inconsistent.
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | |   (8372)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8372) gives:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | |   (8373)  all_54_5 = e2
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (8373) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | |   (8374)  all_8_2 = e2
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8368), (8374) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | |   (8375)  $false
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8375) is inconsistent.
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | |   (8376)  all_54_5 = e1 | all_54_5 = e0
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8376) gives:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | |   (8377)  all_54_5 = e1
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (8377) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | |   (8378)  all_8_2 = e1
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (8378) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | |   (8379)   ~ (all_52_9 = e1)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8367), (8379), (function-axioms) are
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | |   (8380)  all_54_5 = e0
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (8380) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | |   (8381)  all_8_2 = e0
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7014), (8381) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | |   (8382)  $false
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8382) is inconsistent.
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8383)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |             e2) = e2
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | ALPHA: (8383) implies:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8384)   ~ (all_56_31 = e0)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (8327), (8384) imply:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | |   (8385)  $false
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | CLOSE: (8385) is inconsistent.
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | |   (8386)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 233.94/43.67  | | | | | | | | | | | | | | | | | |             = e0)
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (8312), (8327), (8328), (8386),
% 233.94/43.67  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.67  | | | | | | | | | | | | | | | | | |            #2321.
% 233.94/43.67  | | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | |   (8387)  all_58_3 = e0 & op(e2, e2) = e0
% 233.94/43.67  | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | | REF_CLOSE: (42), (7014), (8387), (function-axioms) are
% 233.94/43.67  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 233.94/43.67  | | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | |   (8388)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 233.94/43.67  | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 233.94/43.67  | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (8311), (8328), (8388),
% 233.94/43.67  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.67  | | | | | | | | | | | | | | |            #1991.
% 233.94/43.67  | | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | |   (8389)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 233.94/43.67  | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 233.94/43.67  | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | BETA: splitting (8389) gives:
% 233.94/43.67  | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | |   (8390)  all_58_4 = e0 & op(e3, e1) = e0
% 233.94/43.67  | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | REF_CLOSE: (169), (8310), (8390), (function-axioms) are
% 233.94/43.67  | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 233.94/43.67  | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | |   (8391)  all_58_9 = e0 & op(e3, e0) = e0
% 233.94/43.67  | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | ALPHA: (8391) implies:
% 233.94/43.67  | | | | | | | | | | | | | |   (8392)  all_58_9 = e0
% 233.94/43.67  | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (159), (162),
% 233.94/43.67  | | | | | | | | | | | | | |            (217), (218), (219), (235), (244), (246), (7006),
% 233.94/43.67  | | | | | | | | | | | | | |            (7010), (7014), (8309), (8331), (8392),
% 233.94/43.67  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.67  | | | | | | | | | | | | | |            #1087.
% 233.94/43.67  | | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | End of split
% 233.94/43.67  | | | | | | | | | 
% 233.94/43.67  | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | 
% 233.94/43.67  | | | | | | | | |   (8393)  all_20_2 = e1
% 233.94/43.67  | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | COMBINE_EQS: (341), (8393) imply:
% 233.94/43.67  | | | | | | | | |   (8394)  all_4_2 = e1
% 233.94/43.67  | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | SIMP: (8394) implies:
% 233.94/43.67  | | | | | | | | |   (8395)  all_4_2 = e1
% 233.94/43.67  | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | COMBINE_EQS: (254), (8395) imply:
% 233.94/43.67  | | | | | | | | |   (8396)  all_56_31 = e1
% 233.94/43.67  | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | REDUCE: (386), (8395) imply:
% 233.94/43.67  | | | | | | | | |   (8397)   ~ (all_52_11 = e1)
% 233.94/43.67  | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | REDUCE: (389), (8395) imply:
% 233.94/43.67  | | | | | | | | |   (8398)   ~ (all_52_14 = e1)
% 233.94/43.67  | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | REDUCE: (7012), (8395) imply:
% 233.94/43.67  | | | | | | | | |   (8399)   ~ (e3 = e1)
% 233.94/43.67  | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | BETA: splitting (224) gives:
% 233.94/43.67  | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | |   (8400)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 233.94/43.67  | | | | | | | | | |             & op(e1, e2) = e1)
% 233.94/43.67  | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | BETA: splitting (8400) gives:
% 233.94/43.67  | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | |   (8401)  all_58_6 = e1 & op(e1, e3) = e1
% 233.94/43.67  | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | ALPHA: (8401) implies:
% 233.94/43.67  | | | | | | | | | | |   (8402)  op(e1, e3) = e1
% 233.94/43.67  | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | REF_CLOSE: (163), (7005), (8402), (function-axioms) are
% 233.94/43.67  | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 233.94/43.67  | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | Case 2:
% 233.94/43.67  | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | |   (8403)  all_58_7 = e1 & op(e1, e2) = e1
% 233.94/43.67  | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | ALPHA: (8403) implies:
% 233.94/43.67  | | | | | | | | | | |   (8404)  op(e1, e2) = e1
% 233.94/43.67  | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | BETA: splitting (228) gives:
% 233.94/43.67  | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | |   (8405)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 233.94/43.67  | | | | | | | | | | | |             & op(e2, e1) = e1)
% 233.94/43.67  | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | BETA: splitting (8405) gives:
% 233.94/43.67  | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | Case 1:
% 233.94/43.67  | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | |   (8406)  all_58_4 = e1 & op(e3, e1) = e1
% 233.94/43.67  | | | | | | | | | | | | | 
% 233.94/43.67  | | | | | | | | | | | | | ALPHA: (8406) implies:
% 233.94/43.67  | | | | | | | | | | | | |   (8407)  op(e3, e1) = e1
% 233.94/43.67  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | REF_CLOSE: (169), (7008), (8407), (function-axioms) are
% 233.94/43.68  | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | Case 2:
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | |   (8408)  all_58_5 = e1 & op(e2, e1) = e1
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | ALPHA: (8408) implies:
% 233.94/43.68  | | | | | | | | | | | | |   (8409)  all_58_5 = e1
% 233.94/43.68  | | | | | | | | | | | | |   (8410)  op(e2, e1) = e1
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 233.94/43.68  | | | | | | | | | | | | |              e2, e1, simplifying with (162), (8404) gives:
% 233.94/43.68  | | | | | | | | | | | | |   (8411)  all_52_6 = e1
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 233.94/43.68  | | | | | | | | | | | | |              e1, e2, simplifying with (165), (8410) gives:
% 233.94/43.68  | | | | | | | | | | | | |   (8412)  all_52_9 = e1
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | REDUCE: (128), (8411) imply:
% 233.94/43.68  | | | | | | | | | | | | |   (8413)   ~ (all_52_7 = e1)
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | SIMP: (8413) implies:
% 233.94/43.68  | | | | | | | | | | | | |   (8414)   ~ (all_52_7 = e1)
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | REDUCE: (126), (8411) imply:
% 233.94/43.68  | | | | | | | | | | | | |   (8415)   ~ (all_52_14 = e1)
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | REDUCE: (375), (8412) imply:
% 233.94/43.68  | | | | | | | | | | | | |   (8416)   ~ (all_8_2 = e1)
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | SIMP: (8416) implies:
% 233.94/43.68  | | | | | | | | | | | | |   (8417)   ~ (all_8_2 = e1)
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | BETA: splitting (199) gives:
% 233.94/43.68  | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | Case 1:
% 233.94/43.68  | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | |   (8418)  all_54_5 = e3
% 233.94/43.68  | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | REF_CLOSE: (275), (392), (8418) are inconsistent by sub-proof
% 233.94/43.68  | | | | | | | | | | | | | |            #1907.
% 233.94/43.68  | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | Case 2:
% 233.94/43.68  | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | |   (8419)   ~ (all_54_5 = e3)
% 233.94/43.68  | | | | | | | | | | | | | |   (8420)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 233.94/43.68  | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | BETA: splitting (8420) gives:
% 233.94/43.68  | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | Case 1:
% 233.94/43.68  | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | |   (8421)  all_54_5 = e2
% 233.94/43.68  | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | COMBINE_EQS: (275), (8421) imply:
% 233.94/43.68  | | | | | | | | | | | | | | |   (8422)  all_8_2 = e2
% 233.94/43.68  | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | SIMP: (8422) implies:
% 233.94/43.68  | | | | | | | | | | | | | | |   (8423)  all_8_2 = e2
% 233.94/43.68  | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | COMBINE_EQS: (353), (8423) imply:
% 233.94/43.68  | | | | | | | | | | | | | | |   (8424)  all_56_11 = e2
% 233.94/43.68  | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | REDUCE: (366), (8423) imply:
% 233.94/43.68  | | | | | | | | | | | | | | |   (8425)   ~ (all_52_1 = e2)
% 233.94/43.68  | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | REDUCE: (369), (8423) imply:
% 233.94/43.68  | | | | | | | | | | | | | | |   (8426)   ~ (all_52_4 = e2)
% 233.94/43.68  | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | REDUCE: (392), (8423) imply:
% 233.94/43.68  | | | | | | | | | | | | | | |   (8427)   ~ (e3 = e2)
% 233.94/43.68  | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | REDUCE: (42), (8423) imply:
% 233.94/43.68  | | | | | | | | | | | | | | |   (8428)  op(e2, e2) = e2
% 233.94/43.68  | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 233.94/43.68  | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | Case 1:
% 233.94/43.68  | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | |   (8429)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.94/43.68  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.68  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.94/43.68  | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.94/43.68  | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.68  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.68  | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.94/43.68  | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.94/43.68  | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.94/43.68  | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 233.94/43.68  | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 233.94/43.68  | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 233.94/43.68  | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 233.94/43.68  | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | BETA: splitting (8429) gives:
% 233.94/43.68  | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.68  | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | |   (8430)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 233.94/43.68  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 233.94/43.68  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 233.94/43.68  | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 233.94/43.68  | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.68  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.68  | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 233.94/43.68  | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 233.94/43.68  | | | | | | | | | | | | | | | | |             = e3)
% 233.94/43.68  | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8396), (8424), (8425), (8430),
% 233.94/43.68  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 233.94/43.68  | | | | | | | | | | | | | | | | |            #1831.
% 233.94/43.68  | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.68  | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | |   (8431)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.94/43.68  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 233.94/43.68  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 233.94/43.68  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 233.94/43.68  | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 233.94/43.68  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 233.94/43.68  | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 233.94/43.68  | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 233.94/43.68  | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 233.94/43.68  | | | | | | | | | | | | | | | | |             = e0)
% 233.94/43.68  | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | BETA: splitting (8431) gives:
% 233.94/43.68  | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.68  | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | |   (8432)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 233.94/43.68  | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 233.94/43.68  | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 233.94/43.68  | | | | | | | | | | | | | | | | | |             e3) = e1
% 233.94/43.68  | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | | ALPHA: (8432) implies:
% 233.94/43.68  | | | | | | | | | | | | | | | | | |   (8433)  op(e3, e1) = e1
% 233.94/43.68  | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7008), (8433), (function-axioms) are
% 233.94/43.68  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 233.94/43.68  | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.68  | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | |   (8434)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 233.94/43.68  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 233.94/43.68  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 233.94/43.68  | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 233.94/43.68  | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 233.94/43.68  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 233.94/43.68  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 233.94/43.68  | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | | BETA: splitting (8434) gives:
% 233.94/43.68  | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | | Case 1:
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |   (8435)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |             e3) = e3
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | ALPHA: (8435) implies:
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |   (8436)   ~ (all_56_21 = e0)
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | REDUCE: (8308), (8436) imply:
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |   (8437)  $false
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | CLOSE: (8437) is inconsistent.
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | | Case 2:
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |   (8438)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |             e3) = e0
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | 
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | ALPHA: (8438) implies:
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |   (8439)  op(e0, e3) = e0
% 233.94/43.68  | | | | | | | | | | | | | | | | | | |   (8440)  op(e3, e0) = e0
% 233.94/43.68  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (133), (135), (140), (158), (159), (162),
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |            (168), (170), (191), (203), (235), (256), (282),
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |            (7007), (8309), (8414), (8426), (8428), (8439),
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |            (8440), (function-axioms) are inconsistent by
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |            sub-proof #1962.
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | Case 2:
% 234.07/43.68  | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | |   (8441)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.07/43.68  | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.07/43.68  | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.07/43.68  | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.07/43.68  | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.07/43.68  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.07/43.68  | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.07/43.68  | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.07/43.68  | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 234.07/43.68  | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 234.07/43.68  | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 234.07/43.68  | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 234.07/43.68  | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 234.07/43.68  | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | BETA: splitting (8441) gives:
% 234.07/43.68  | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.68  | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | |   (8442)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.07/43.68  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.07/43.68  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.07/43.68  | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.07/43.68  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.07/43.68  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.07/43.68  | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.07/43.68  | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.07/43.68  | | | | | | | | | | | | | | | | |             = e2)
% 234.07/43.68  | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | BETA: splitting (8442) gives:
% 234.07/43.68  | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.68  | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | |   (8443)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.07/43.68  | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 234.07/43.68  | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 234.07/43.68  | | | | | | | | | | | | | | | | | |             e2) = e2
% 234.07/43.68  | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | ALPHA: (8443) implies:
% 234.07/43.68  | | | | | | | | | | | | | | | | | |   (8444)   ~ (all_56_31 = e1)
% 234.07/43.68  | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | REDUCE: (8396), (8444) imply:
% 234.07/43.68  | | | | | | | | | | | | | | | | | |   (8445)  $false
% 234.07/43.68  | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | CLOSE: (8445) is inconsistent.
% 234.07/43.68  | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.68  | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | |   (8446)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.07/43.68  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.07/43.68  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 234.07/43.68  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 234.07/43.68  | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.07/43.68  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.07/43.68  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 234.07/43.68  | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | BETA: splitting (8446) gives:
% 234.07/43.68  | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |   (8447)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |             e2) = e1
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | ALPHA: (8447) implies:
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |   (8448)   ~ (all_56_11 = e2)
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | REDUCE: (8424), (8448) imply:
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |   (8449)  $false
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | CLOSE: (8449) is inconsistent.
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |   (8450)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |             e2) = e2
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | ALPHA: (8450) implies:
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |   (8451)  op(e2, e0) = e2
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (165), (231), (234),
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |            (8409), (8410), (8428), (8451), (function-axioms)
% 234.07/43.68  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2119.
% 234.07/43.68  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.68  | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | |   (8452)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.07/43.68  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.07/43.68  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 234.07/43.68  | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 234.07/43.68  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.07/43.68  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.07/43.68  | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 234.07/43.68  | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.07/43.68  | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 234.07/43.68  | | | | | | | | | | | | | | | | |             = e0)
% 234.07/43.68  | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8312), (8398), (8424), (8452),
% 234.07/43.68  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.68  | | | | | | | | | | | | | | | | |            #1988.
% 234.07/43.68  | | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | Case 2:
% 234.07/43.68  | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | |   (8453)  all_54_5 = e1 | all_54_5 = e0
% 234.07/43.68  | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | | REF_CLOSE: (275), (7014), (8417), (8453) are inconsistent by
% 234.07/43.68  | | | | | | | | | | | | | | |            sub-proof #2300.
% 234.07/43.68  | | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | Case 2:
% 234.07/43.68  | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | |   (8454)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 234.07/43.68  | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 234.07/43.68  | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | BETA: splitting (8454) gives:
% 234.07/43.68  | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | Case 1:
% 234.07/43.68  | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | |   (8455)  all_58_8 = e1 & op(e1, e1) = e1
% 234.07/43.68  | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | ALPHA: (8455) implies:
% 234.07/43.68  | | | | | | | | | | | | |   (8456)  op(e1, e1) = e1
% 234.07/43.68  | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | REF_CLOSE: (4), (8314), (8456), (function-axioms) are
% 234.07/43.68  | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 234.07/43.68  | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | Case 2:
% 234.07/43.68  | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | |   (8457)  all_58_14 = e1 & op(e0, e1) = e1
% 234.07/43.68  | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | ALPHA: (8457) implies:
% 234.07/43.68  | | | | | | | | | | | | |   (8458)  op(e0, e1) = e1
% 234.07/43.68  | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | | REF_CLOSE: (157), (8397), (8458), (function-axioms) are
% 234.07/43.68  | | | | | | | | | | | | |            inconsistent by sub-proof #2272.
% 234.07/43.68  | | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | Case 2:
% 234.07/43.68  | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | |   (8459)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 234.07/43.68  | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 234.07/43.68  | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | | REF_CLOSE: (4), (160), (8314), (8398), (8459),
% 234.07/43.68  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.68  | | | | | | | | | |            #1086.
% 234.07/43.68  | | | | | | | | | | 
% 234.07/43.68  | | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | | 
% 234.07/43.68  | | | | | | | | End of split
% 234.07/43.68  | | | | | | | | 
% 234.07/43.68  | | | | | | | End of split
% 234.07/43.68  | | | | | | | 
% 234.07/43.68  | | | | | | Case 2:
% 234.07/43.68  | | | | | | | 
% 234.07/43.68  | | | | | | |   (8460)  all_14_2 = e0
% 234.07/43.68  | | | | | | |   (8461)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 234.07/43.68  | | | | | | |             op(e2, e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)) |
% 234.07/43.68  | | | | | | |           ( ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 234.07/43.68  | | | | | | |             $i(all_14_1))
% 234.07/43.68  | | | | | | | 
% 234.07/43.68  | | | | | | | COMBINE_EQS: (344), (8460) imply:
% 234.07/43.68  | | | | | | |   (8462)  all_8_2 = e0
% 234.07/43.68  | | | | | | | 
% 234.07/43.69  | | | | | | | SIMP: (8462) implies:
% 234.07/43.69  | | | | | | |   (8463)  all_8_2 = e0
% 234.07/43.69  | | | | | | | 
% 234.07/43.69  | | | | | | | COMBINE_EQS: (311), (8463) imply:
% 234.07/43.69  | | | | | | |   (8464)  all_48_2 = e0
% 234.07/43.69  | | | | | | | 
% 234.07/43.69  | | | | | | | COMBINE_EQS: (353), (8463) imply:
% 234.07/43.69  | | | | | | |   (8465)  all_56_11 = e0
% 234.07/43.69  | | | | | | | 
% 234.07/43.69  | | | | | | | REDUCE: (366), (8463) imply:
% 234.07/43.69  | | | | | | |   (8466)   ~ (all_52_1 = e0)
% 234.07/43.69  | | | | | | | 
% 234.07/43.69  | | | | | | | REDUCE: (369), (8463) imply:
% 234.07/43.69  | | | | | | |   (8467)   ~ (all_52_4 = e0)
% 234.07/43.69  | | | | | | | 
% 234.07/43.69  | | | | | | | REDUCE: (371), (8463) imply:
% 234.07/43.69  | | | | | | |   (8468)   ~ (all_52_6 = e0)
% 234.07/43.69  | | | | | | | 
% 234.07/43.69  | | | | | | | REDUCE: (373), (8463) imply:
% 234.07/43.69  | | | | | | |   (8469)   ~ (all_52_7 = e0)
% 234.07/43.69  | | | | | | | 
% 234.07/43.69  | | | | | | | REDUCE: (375), (8463) imply:
% 234.07/43.69  | | | | | | |   (8470)   ~ (all_52_9 = e0)
% 234.07/43.69  | | | | | | | 
% 234.07/43.69  | | | | | | | REDUCE: (377), (8463) imply:
% 234.07/43.69  | | | | | | |   (8471)   ~ (all_52_13 = e0)
% 234.07/43.69  | | | | | | | 
% 234.07/43.69  | | | | | | | REDUCE: (392), (8463) imply:
% 234.07/43.69  | | | | | | |   (8472)   ~ (e3 = e0)
% 234.07/43.69  | | | | | | | 
% 234.07/43.69  | | | | | | | BETA: splitting (231) gives:
% 234.07/43.69  | | | | | | | 
% 234.07/43.69  | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | 
% 234.07/43.69  | | | | | | | |   (8473)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 234.07/43.69  | | | | | | | |             op(e2, e2) = e0)
% 234.07/43.69  | | | | | | | | 
% 234.07/43.69  | | | | | | | | BETA: splitting (8473) gives:
% 234.07/43.69  | | | | | | | | 
% 234.07/43.69  | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | 
% 234.07/43.69  | | | | | | | | |   (8474)  all_58_2 = e0 & op(e2, e3) = e0
% 234.07/43.69  | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | REF_CLOSE: (167), (8466), (8474), (function-axioms) are
% 234.07/43.69  | | | | | | | | |            inconsistent by sub-proof #1985.
% 234.07/43.69  | | | | | | | | | 
% 234.07/43.69  | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | 
% 234.07/43.69  | | | | | | | | |   (8475)  all_58_3 = e0 & op(e2, e2) = e0
% 234.07/43.69  | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | ALPHA: (8475) implies:
% 234.07/43.69  | | | | | | | | |   (8476)  all_58_3 = e0
% 234.07/43.69  | | | | | | | | |   (8477)  op(e2, e2) = e0
% 234.07/43.69  | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | BETA: splitting (58) gives:
% 234.07/43.69  | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | |   (8478)   ~ (all_18_2 = e0)
% 234.07/43.69  | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | REDUCE: (339), (8478) imply:
% 234.07/43.69  | | | | | | | | | |   (8479)   ~ (all_6_2 = e0)
% 234.07/43.69  | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | BETA: splitting (61) gives:
% 234.07/43.69  | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | |   (8480)   ~ (all_20_2 = e1)
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | REDUCE: (341), (8480) imply:
% 234.07/43.69  | | | | | | | | | | |   (8481)   ~ (all_4_2 = e1)
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | BETA: splitting (189) gives:
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | |   (8482)  all_54_15 = e3
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | REF_CLOSE: (299), (7012), (8482) are inconsistent by
% 234.07/43.69  | | | | | | | | | | | |            sub-proof #2340.
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | |   (8483)   ~ (all_54_15 = e3)
% 234.07/43.69  | | | | | | | | | | | |   (8484)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | BETA: splitting (8484) gives:
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | |   (8485)  all_54_15 = e2
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | REF_CLOSE: (299), (390), (8485) are inconsistent by sub-proof
% 234.07/43.69  | | | | | | | | | | | | |            #2339.
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | |   (8486)   ~ (all_54_15 = e2)
% 234.07/43.69  | | | | | | | | | | | | |   (8487)  all_54_15 = e1 | all_54_15 = e0
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | BETA: splitting (8487) gives:
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | |   (8488)  all_54_15 = e1
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | REF_CLOSE: (299), (8481), (8488) are inconsistent by
% 234.07/43.69  | | | | | | | | | | | | | |            sub-proof #2338.
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | |   (8489)  all_54_15 = e0
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | COMBINE_EQS: (299), (8489) imply:
% 234.07/43.69  | | | | | | | | | | | | | |   (8490)  all_4_2 = e0
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | SIMP: (8490) implies:
% 234.07/43.69  | | | | | | | | | | | | | |   (8491)  all_4_2 = e0
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | REDUCE: (389), (8491) imply:
% 234.07/43.69  | | | | | | | | | | | | | |   (8492)   ~ (all_52_14 = e0)
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | REDUCE: (390), (8491) imply:
% 234.07/43.69  | | | | | | | | | | | | | |   (8493)   ~ (e2 = e0)
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | REDUCE: (8481), (8491) imply:
% 234.07/43.69  | | | | | | | | | | | | | |   (8494)   ~ (e1 = e0)
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | REDUCE: (36), (8491) imply:
% 234.07/43.69  | | | | | | | | | | | | | |   (8495)  op(e0, e0) = e0
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | |   (8496)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 234.07/43.69  | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 234.07/43.69  | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | BETA: splitting (8496) gives:
% 234.07/43.69  | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | |   (8497)  all_58_6 = e0 & op(e1, e3) = e0
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | ALPHA: (8497) implies:
% 234.07/43.69  | | | | | | | | | | | | | | | |   (8498)  all_58_6 = e0
% 234.07/43.69  | | | | | | | | | | | | | | | |   (8499)  op(e1, e3) = e0
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (88), (110),
% 234.07/43.69  | | | | | | | | | | | | | | | |            (144), (148), (149), (159), (160), (163), (164),
% 234.07/43.69  | | | | | | | | | | | | | | | |            (165), (167), (169), (192), (200), (214), (216),
% 234.07/43.69  | | | | | | | | | | | | | | | |            (217), (218), (219), (227), (230), (232), (234),
% 234.07/43.69  | | | | | | | | | | | | | | | |            (239), (243), (245), (257), (279), (391), (7001),
% 234.07/43.69  | | | | | | | | | | | | | | | |            (7002), (7003), (7004), (7006), (7008), (7010),
% 234.07/43.69  | | | | | | | | | | | | | | | |            (8470), (8476), (8477), (8479), (8495), (8498),
% 234.07/43.69  | | | | | | | | | | | | | | | |            (8499), (function-axioms) are inconsistent by
% 234.07/43.69  | | | | | | | | | | | | | | | |            sub-proof #1084.
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | |   (8500)  all_58_7 = e0 & op(e1, e2) = e0
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | REF_CLOSE: (162), (8468), (8500), (function-axioms) are
% 234.07/43.69  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | End of split
% 234.07/43.69  | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | |   (8501)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 234.07/43.69  | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 234.07/43.69  | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (8479), (8492), (8501),
% 234.07/43.69  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.69  | | | | | | | | | | | | | | |            #1083.
% 234.07/43.69  | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | End of split
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | End of split
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | End of split
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | End of split
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | |   (8502)  all_20_2 = e1
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | COMBINE_EQS: (341), (8502) imply:
% 234.07/43.69  | | | | | | | | | | |   (8503)  all_4_2 = e1
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | SIMP: (8503) implies:
% 234.07/43.69  | | | | | | | | | | |   (8504)  all_4_2 = e1
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | COMBINE_EQS: (254), (8504) imply:
% 234.07/43.69  | | | | | | | | | | |   (8505)  all_56_31 = e1
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | REDUCE: (379), (8504) imply:
% 234.07/43.69  | | | | | | | | | | |   (8506)   ~ (all_52_7 = e1)
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | REDUCE: (388), (8504) imply:
% 234.07/43.69  | | | | | | | | | | |   (8507)   ~ (all_52_13 = e1)
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | REDUCE: (7012), (8504) imply:
% 234.07/43.69  | | | | | | | | | | |   (8508)   ~ (e3 = e1)
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | REDUCE: (390), (8504) imply:
% 234.07/43.69  | | | | | | | | | | |   (8509)   ~ (e2 = e1)
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | BETA: splitting (232) gives:
% 234.07/43.69  | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | |   (8510)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 234.07/43.69  | | | | | | | | | | | |             & op(e2, e2) = e1)
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | BETA: splitting (8510) gives:
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | |   (8511)  all_58_2 = e1 & op(e2, e3) = e1
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | REF_CLOSE: (167), (7004), (8511), (function-axioms) are
% 234.07/43.69  | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | |   (8512)  all_58_3 = e1 & op(e2, e2) = e1
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | REF_CLOSE: (4), (8476), (8512) are inconsistent by sub-proof
% 234.07/43.69  | | | | | | | | | | | | |            #1752.
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | End of split
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | |   (8513)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 234.07/43.69  | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | BETA: splitting (8513) gives:
% 234.07/43.69  | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | |   (8514)  all_58_5 = e1 & op(e2, e1) = e1
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | ALPHA: (8514) implies:
% 234.07/43.69  | | | | | | | | | | | | |   (8515)  all_58_5 = e1
% 234.07/43.69  | | | | | | | | | | | | |   (8516)  op(e2, e1) = e1
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | BETA: splitting (236) gives:
% 234.07/43.69  | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | |   (8517)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 234.07/43.69  | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (7007), (8476), (8517),
% 234.07/43.69  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.69  | | | | | | | | | | | | | |            #1377.
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | |   (8518)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 234.07/43.69  | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | BETA: splitting (8518) gives:
% 234.07/43.69  | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | |   (8519)  all_58_7 = e1 & op(e1, e2) = e1
% 234.07/43.69  | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | ALPHA: (8519) implies:
% 234.07/43.69  | | | | | | | | | | | | | | |   (8520)  all_58_7 = e1
% 234.07/43.69  | | | | | | | | | | | | | | |   (8521)  op(e1, e2) = e1
% 234.07/43.69  | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 234.07/43.69  | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | |   (8522)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 234.07/43.69  | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | BETA: splitting (8522) gives:
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8523)  all_58_12 = e1 & op(e0, e3) = e1
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7006), (8523), (function-axioms) are
% 234.07/43.69  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8524)  all_58_13 = e1 & op(e0, e2) = e1
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8506), (8524), (function-axioms) are
% 234.07/43.69  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | End of split
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | |   (8525)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 234.07/43.69  | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | BETA: splitting (8525) gives:
% 234.07/43.69  | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8526)  all_58_14 = e1 & op(e0, e1) = e1
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | ALPHA: (8526) implies:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8527)  all_58_14 = e1
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8528)  op(e0, e1) = e1
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (165), (227),
% 234.07/43.69  | | | | | | | | | | | | | | | | |            (229), (230), (8479), (8515), (8516), (8527),
% 234.07/43.69  | | | | | | | | | | | | | | | | |            (8528), (function-axioms) are inconsistent by
% 234.07/43.69  | | | | | | | | | | | | | | | | |            sub-proof #1247.
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8529)  all_58_15 = e1 & op(e0, e0) = e1
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | ALPHA: (8529) implies:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8530)  all_58_15 = e1
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8531)  op(e0, e0) = e1
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 234.07/43.69  | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (8521) gives:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8532)  all_52_6 = e1
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 234.07/43.69  | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (8516) gives:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8533)  all_52_9 = e1
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | REDUCE: (128), (8532) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8534)   ~ (all_52_7 = e1)
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | REDUCE: (126), (8532) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8535)   ~ (all_52_14 = e1)
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | SIMP: (8535) implies:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8536)   ~ (all_52_14 = e1)
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | REDUCE: (118), (8533) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8537)   ~ (all_52_11 = e1)
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | SIMP: (8537) implies:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8538)   ~ (all_52_11 = e1)
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | REDUCE: (117), (8533) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8539)   ~ (all_52_13 = e1)
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | REDUCE: (381), (8533) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8540)   ~ (all_6_2 = e1)
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | SIMP: (8540) implies:
% 234.07/43.69  | | | | | | | | | | | | | | | | |   (8541)   ~ (all_6_2 = e1)
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 234.07/43.69  | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | |   (8542)  all_54_10 = e3
% 234.07/43.69  | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (8542) are inconsistent by sub-proof
% 234.07/43.69  | | | | | | | | | | | | | | | | | |            #2313.
% 234.07/43.69  | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | |   (8543)   ~ (all_54_10 = e3)
% 234.07/43.69  | | | | | | | | | | | | | | | | | |   (8544)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 234.07/43.69  | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | BETA: splitting (8544) gives:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | |   (8545)  all_54_10 = e2
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (8545) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | |   (8546)  all_6_2 = e2
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | SIMP: (8546) implies:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | |   (8547)  all_6_2 = e2
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (8547) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | |   (8548)  all_56_21 = e2
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | REDUCE: (380), (8547) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | |   (8549)   ~ (all_52_8 = e2)
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | REDUCE: (383), (8547) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | |   (8550)   ~ (all_52_11 = e2)
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | REDUCE: (385), (8547) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | |   (8551)   ~ (all_52_14 = e2)
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | REDUCE: (391), (8547) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | |   (8552)   ~ (e3 = e2)
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (8547) imply:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | |   (8553)  op(e1, e1) = e2
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | |   (8554)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8554) gives:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | |   (8555)  all_58_6 = e2 & op(e1, e3) = e2
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8555) implies:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | |   (8556)  all_58_6 = e2
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (162), (223), (226), (8468),
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | |            (8520), (8553), (8556), (function-axioms) are
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1676.
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | |   (8557)  all_58_7 = e2 & op(e1, e2) = e2
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8557) implies:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | |   (8558)  all_58_7 = e2
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8520), (8558) are inconsistent by sub-proof
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | |            #2134.
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | |   (8559)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8559) gives:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.69  | | | | | | | | | | | | | | | | | | | | |   (8560)  all_58_8 = e2 & op(e1, e1) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8560) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | |   (8561)  all_58_8 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | |   (8562)  all_54_1 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (8562) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | |   (8563)  all_52_4 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | SIMP: (8563) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | |   (8564)  all_52_4 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (8564) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | |   (8565)   ~ (all_52_7 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | SIMP: (8565) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | |   (8566)   ~ (all_52_7 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (8564) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | |   (8567)   ~ (all_52_8 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | SIMP: (8567) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | |   (8568)   ~ (all_52_8 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (8564) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | |   (8569)   ~ (all_52_12 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | SIMP: (8569) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | |   (8570)   ~ (all_52_12 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | |   (8571)  all_54_2 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (8568), (8571) are inconsistent by
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | |   (8572)   ~ (all_54_2 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | |   (8573)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8573) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | |   (8574)  all_54_2 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (8549), (8574) are inconsistent by
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1986.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | |   (8575)   ~ (all_54_2 = e2)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | |   (8576)  all_54_2 = e1 | all_54_2 = e0
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8576) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (8577)  all_54_2 = e1
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (7008), (8577) are inconsistent by
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1337.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (8578)  all_54_2 = e0
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (8578) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (8579)  all_52_8 = e0
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8579) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (8580)  all_52_8 = e0
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (8580) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (8581)   ~ (all_52_11 = e0)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8581) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (8582)   ~ (all_52_11 = e0)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (8580) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (8583)   ~ (all_52_12 = e0)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8583) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (8584)   ~ (all_52_12 = e0)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8549), (8580) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (8585)   ~ (e2 = e0)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7008), (8580) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (8586)   ~ (e1 = e0)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8587)  all_54_3 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (8570), (8587) are inconsistent by
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8588)   ~ (all_54_3 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8589)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8590)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8590) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8591)  all_58_4 = e3 & op(e3, e1) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8591) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8592)  op(e3, e1) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8568), (8592), (function-axioms) are
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8593)  all_58_5 = e3 & op(e2, e1) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8593) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8594)  all_58_5 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8515), (8594) are inconsistent by sub-proof
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2123.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8595)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8595) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8596)  all_58_8 = e3 & op(e1, e1) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8596) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8597)  op(e1, e1) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8553), (8597), (function-axioms) are
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8598)  all_58_14 = e3 & op(e0, e1) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8598) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8599)  all_58_14 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8600)  op(e0, e1) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8601)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8601) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8602)  all_58_0 = e3 & op(e3, e3) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8602) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8603)  op(e3, e3) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7010), (8603), (function-axioms) are
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1578.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8604)  all_58_1 = e3 & op(e3, e2) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8604) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8605)  all_58_1 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8606)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (7010), (8605), (8606),
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1132.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8607)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8607) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8608)  all_58_4 = e2 & op(e3, e1) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8608) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8609)  all_58_4 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (165), (227), (8516), (8553),
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8600), (8609), (function-axioms) are inconsistent
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2162.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8610)  all_58_9 = e2 & op(e3, e0) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8610) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8611)  all_58_9 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8612)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8612) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8613)  all_58_1 = e2 & op(e3, e2) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8605), (8613) are inconsistent by sub-proof
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1590.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8614)  all_58_3 = e2 & op(e2, e2) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8476), (8614) are inconsistent by sub-proof
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1082.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8615)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8615) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8616)  all_58_7 = e2 & op(e1, e2) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8616) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8617)  all_58_7 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8520), (8617) are inconsistent by sub-proof
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2134.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8618)  all_58_13 = e2 & op(e0, e2) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8618) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8619)  op(e0, e2) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8620)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8620) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8621)  all_58_0 = e2 & op(e3, e3) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8621) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8622)  op(e3, e3) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7010), (8622), (function-axioms) are
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8623)  all_58_2 = e2 & op(e2, e3) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8623) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8624)  all_58_2 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8625)  op(e2, e3) = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8626)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8626) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8627)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8627) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8628)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8628) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8629)   ~ (all_56_21 = e2)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8548), (8629) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8630)  $false
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8630) is inconsistent.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8631)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8631) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8632)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8632) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8633)  all_56_3 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8634)   ~ (all_56_31 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8635)   ~ (all_56_21 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8636)   ~ (all_56_11 = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8637)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (158), (216), (219),
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (8530), (8531), (8566), (8599), (8619),
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8624), (8637), (function-axioms) are inconsistent
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1081.
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8638)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8638) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8639)  all_58_6 = e3 & op(e1, e3) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8639) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8640)  op(e1, e3) = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8589) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8641)  all_54_3 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (8641) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8642)  all_52_12 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8642) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8643)  all_52_12 = e2
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (8643) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8644)   ~ (all_52_13 = e2)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8644) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8645)   ~ (all_52_13 = e2)
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8646)  all_54_7 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8646) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8647)  all_52_13 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8647) implies:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8648)  all_52_13 = e3
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (8648) imply:
% 234.07/43.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8649)   ~ (all_52_1 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8650)  all_54_4 = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (8649), (8650) are inconsistent by
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8651)   ~ (all_54_4 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8652)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (169), (214),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (239), (243), (245), (279),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7003), (7004), (7010), (8466), (8477), (8531),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8568), (8599), (8624), (8633), (8640), (8649),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8652), (function-axioms) are inconsistent by
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1079.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8653)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (269), (8471), (8507), (8625),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8653), (function-axioms) are inconsistent by
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2292.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8654)  all_54_3 = e1 | all_54_3 = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (7009), (8584), (8654) are inconsistent by
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2287.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8655)  all_58_12 = e3 & op(e0, e3) = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8655) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8656)  all_58_12 = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (157), (190), (216), (255), (8531),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8538), (8550), (8582), (8619), (8656),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1078.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8657)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8657) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8658)  op(e3, e1) = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8568), (8658), (function-axioms) are
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8659)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8659) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8660)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e1
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8660) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8661)  op(e3, e1) = e1
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7008), (8661), (function-axioms) are
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8662)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e0 & op(e0, e3) = e0)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8662) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8663)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8663) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8664)  op(e3, e0) = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8570), (8664), (function-axioms) are
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8665)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8665) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8666)   ~ (all_56_31 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8667)   ~ (all_56_21 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8668)   ~ (all_56_11 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8669)  op(e0, e3) = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8670)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (158), (216), (219),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (8530), (8531), (8566), (8599), (8619),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8624), (8670), (function-axioms) are inconsistent
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1081.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8671)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8671) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8672)  all_58_6 = e3 & op(e1, e3) = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8672) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8673)  op(e1, e3) = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8589) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8674)  all_54_3 = e2
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (8674) imply:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8675)  all_52_12 = e2
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8675) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8676)  all_52_12 = e2
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (8676) imply:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8677)   ~ (all_52_13 = e2)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8677) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8678)   ~ (all_52_13 = e2)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (8676) imply:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8679)   ~ (all_52_14 = e2)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8680)  all_54_7 = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8680) imply:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8681)  all_52_13 = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8681) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8682)  all_52_13 = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (8682) imply:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8683)   ~ (all_52_1 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (8682) imply:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8684)   ~ (all_52_14 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8684) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8685)   ~ (all_52_14 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8686)  all_54_11 = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (8685), (8686) are inconsistent by
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8687)   ~ (all_54_11 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8688)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8689)  all_54_4 = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (8683), (8689) are inconsistent by
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8690)   ~ (all_54_4 = e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8691)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8692)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8692) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8693)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8693) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8694)  op(e3, all_56_1) = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7003), (8694) imply:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8695)  op(e3, e1) = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8568), (8695), (function-axioms) are
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8696)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_3 & $i(all_56_3)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8696) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8697)  op(e2, e3) = all_56_3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8688) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8698)  all_54_11 = e2
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (8551), (8698) are inconsistent by
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2177.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8699)   ~ (all_54_11 = e2)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8700)  all_54_11 = e1 | all_54_11 = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8700) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8701)  all_54_11 = e1
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (8536), (8701) are inconsistent by
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2176.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8702)  all_54_11 = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (8702) imply:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8703)  all_52_14 = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8703) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8704)  all_52_14 = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_3,
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (8625), (8697) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8705)  all_56_3 = e2
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (169), (214),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (239), (243), (245), (279),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7003), (7004), (7010), (8466), (8477), (8531),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8568), (8599), (8624), (8673), (8683), (8691),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8705), (function-axioms) are inconsistent by
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1079.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8706)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (279), (7004), (8466), (8531), (8669),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8673), (8691), (8706), (function-axioms) are
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1152.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8707)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (269), (8471), (8507), (8625),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8707), (function-axioms) are inconsistent by
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2292.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8708)  all_54_3 = e1 | all_54_3 = e0
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (7009), (8584), (8708) are inconsistent by
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2287.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8709)  all_58_12 = e3 & op(e0, e3) = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8709) implies:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8710)  all_58_12 = e3
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (157), (190), (216), (255), (8531),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8538), (8550), (8582), (8619), (8710),
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1078.
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8711)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8711) gives:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8712)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8465), (8505), (8548), (8712) are inconsistent by
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1077.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8713)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8713) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8714)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8714) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8715)  op(e2, e0) = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8471), (8715), (function-axioms) are
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2324.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8716)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (8536), (8600), (8716),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1699.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8717)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8717) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8718)  all_58_6 = e2 & op(e1, e3) = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8718) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8719)  all_58_6 = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (162), (223), (226), (8468),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8520), (8553), (8719), (function-axioms) are
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1676.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8720)  all_58_12 = e2 & op(e0, e3) = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8720) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8721)  all_58_12 = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8722)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (7010), (8466), (8722),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1272.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8723)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8723) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8724)  all_58_6 = e0 & op(e1, e3) = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8724) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8725)  all_58_6 = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8589) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8726)  all_54_3 = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (8726) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8727)  all_52_12 = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8727) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8728)  all_52_12 = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (8728) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8729)   ~ (all_52_13 = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8729) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8730)   ~ (all_52_13 = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8731)  all_54_7 = e3
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8731) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8732)  all_52_13 = e3
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8732) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8733)  all_52_13 = e3
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (8733) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8734)   ~ (all_52_1 = e3)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (216), (217),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (239), (243), (245), (7010), (8599),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8725), (8734), (function-axioms) are inconsistent
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1199.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8735)   ~ (all_54_7 = e3)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (8735) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8736)   ~ (all_52_13 = e3)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8737)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8737) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8738)  all_58_2 = e2 & op(e2, e3) = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8738) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8739)  op(e2, e3) = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (197), (269), (8471), (8507),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8736), (8739), (function-axioms) are inconsistent
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2291.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8740)  all_58_3 = e2 & op(e2, e2) = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8476), (8740) are inconsistent by sub-proof
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1082.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8741)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8741) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8742)  all_58_5 = e2 & op(e2, e1) = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8742) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8743)  all_58_5 = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8515), (8743) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8744)  e2 = e1
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8611), (8744) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8745)  all_58_9 = e1
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (8531), (8736), (8745), (function-axioms)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1600.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8746)  all_58_10 = e2 & op(e2, e0) = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8746) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8747)  op(e2, e0) = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8748)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (8570), (8736), (8748),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1592.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8749)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8749) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8750)  all_58_11 = e3 & op(e1, e0) = e3
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8750) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8751)  all_58_11 = e3
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8752)  all_58_15 = e0 & op(e0, e0) = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8752) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8753)  op(e0, e0) = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8531), (8753), (function-axioms) are
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8754)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8754) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8755)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8755) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8756)  all_58_9 = e0 & op(e3, e0) = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8611), (8756) are inconsistent by sub-proof
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1563.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8757)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8747), (8751), (8757),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1743.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8758)  all_58_15 = e3 & op(e0, e0) = e3
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (158), (219), (8530), (8566), (8599),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8721), (8758), (function-axioms) are inconsistent
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1813.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8759)  all_54_3 = e1 | all_54_3 = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (7009), (8584), (8759) are inconsistent by
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2287.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8760)  all_58_12 = e0 & op(e0, e3) = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8760) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8761)  all_58_12 = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8721), (8761) are inconsistent by sub-proof
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2083.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8762)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8762) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8763)  all_58_4 = e3 & op(e3, e1) = e3
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8763) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8764)  all_58_4 = e3
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (165), (227),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (8479), (8599), (8600), (8764),
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1094.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8765)  all_58_9 = e3 & op(e3, e0) = e3
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8765) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8766)  op(e3, e0) = e3
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8570), (8766), (function-axioms) are
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | |   (8767)   ~ (all_54_1 = e3)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | |   (8768)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (282), (8767) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | |   (8769)   ~ (all_52_4 = e3)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8768) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | |   (8770)  all_54_1 = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (8770) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | |   (8771)  all_52_4 = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8771) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | |   (8772)  all_52_4 = e2
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (8772) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | |   (8773)   ~ (all_52_7 = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8773) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | |   (8774)   ~ (all_52_7 = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (8772) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | |   (8775)   ~ (all_52_8 = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (8772) imply:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | |   (8776)   ~ (all_52_12 = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8776) implies:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | |   (8777)   ~ (all_52_12 = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | |   (8778)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 234.07/43.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8778) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (8779)  all_58_9 = e2 & op(e3, e0) = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8779) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (8780)  all_58_9 = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (8781)  op(e3, e0) = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8782)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8782) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8783)  all_58_12 = e2 & op(e0, e3) = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (112), (113),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (120), (121), (125), (139), (145), (159), (160),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (190), (191), (193),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (201), (202), (213), (233), (239), (240),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (255), (256), (258), (269),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (280), (281), (7008), (7009), (7010), (8465),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8466), (8469), (8476), (8505), (8506), (8507),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8515), (8536), (8538), (8548), (8549), (8550),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8551), (8769), (8774), (8777), (8780), (8781),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8783), (function-axioms) are inconsistent by
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1072.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8784)  all_58_13 = e2 & op(e0, e2) = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8784) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8785)  all_58_13 = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8786)  op(e0, e2) = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8787)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (7010), (8769), (8787),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1401.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8788)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8788) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8789)  all_58_4 = e3 & op(e3, e1) = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8789) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8790)  all_58_4 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8791)  all_54_13 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (8791) imply:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8792)  all_52_7 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (8792) imply:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8793)   ~ (all_52_11 = e3)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8793) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8794)   ~ (all_52_11 = e3)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8795)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8795) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8796)  all_58_12 = e3 & op(e0, e3) = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8796) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8797)  all_58_12 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8798)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (7010), (8466), (8798),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1272.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8799)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8799) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8800)  all_58_6 = e0 & op(e1, e3) = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8800) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8801)  all_58_6 = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8802)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8802) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8803)  all_58_1 = e3 & op(e3, e2) = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8803) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8804)  op(e3, e2) = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (8769), (8804), (function-axioms) are
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8805)  all_58_3 = e3 & op(e2, e2) = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8805) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8806)  all_58_3 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8476), (8806) imply:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8807)  e3 = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8807) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8808)  e3 = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8790), (8808) imply:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8809)  all_58_4 = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (170), (246), (7010), (8769),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8781), (8809), (function-axioms) are inconsistent
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1400.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8810)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8810) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8811)  all_58_7 = e3 & op(e1, e2) = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (7010), (8520), (8769), (8790), (8811),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1071.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8812)  all_58_13 = e3 & op(e0, e2) = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8812) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8813)  all_58_13 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8785), (8813) imply:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8814)  e3 = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8814) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8815)  e3 = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8797), (8815) imply:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8816)  all_58_12 = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (112), (113),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (120), (121), (125), (139), (145), (159), (160),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (190), (191), (193),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (201), (202), (213), (233), (240), (244),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (246), (255), (256), (258), (269), (280),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (281), (7008), (7009), (7010), (8465), (8469),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8476), (8505), (8506), (8507), (8515), (8536),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8538), (8548), (8549), (8550), (8551), (8769),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8774), (8777), (8780), (8781), (8801), (8816),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1073.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8817)  all_58_12 = e0 & op(e0, e3) = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8817) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8818)  all_58_12 = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8797), (8818) imply:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8819)  e3 = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8790), (8819) imply:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8820)  all_58_4 = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (170), (246), (7010), (8769),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8781), (8820), (function-axioms) are inconsistent
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1400.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8821)  all_58_13 = e3 & op(e0, e2) = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8821) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8822)  all_58_13 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8785), (8822) are inconsistent by sub-proof
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2129.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8823)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (170), (240),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (246), (7010), (8530), (8769), (8790),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8794), (8823), (function-axioms) are inconsistent
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1070.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8824)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (256), (8506), (8774), (8786), (8824),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1817.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8825)  all_58_9 = e3 & op(e3, e0) = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8825) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8826)  op(e3, e0) = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8781), (8826), (function-axioms) are
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2125.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8827)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8827) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8828)  all_58_14 = e2 & op(e0, e1) = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8828) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8829)  all_58_14 = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8830)  all_58_15 = e0 & op(e0, e0) = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8830) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8831)  op(e0, e0) = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8531), (8831), (function-axioms) are
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8832)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8832) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8833)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8834)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8835)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8835) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8836)  all_58_4 = e3 & op(e3, e1) = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8836) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8837)  all_58_4 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8838)  all_54_13 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (8838) imply:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8839)  all_52_7 = e3
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (8839) imply:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8840)   ~ (all_52_11 = e3)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8840) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8841)   ~ (all_52_11 = e3)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8833) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8842)  all_58_12 = e0 & op(e0, e3) = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8842) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8843)  all_58_12 = e0
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8844)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8844) gives:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8845)  all_58_0 = e2 & op(e3, e3) = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8845) implies:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8846)  op(e3, e3) = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (242),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (8769), (8780), (8781), (8846),
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1069.
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8847)  all_58_2 = e2 & op(e2, e3) = e2
% 234.07/43.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8847) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8848)  all_58_2 = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8834) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8849)  all_58_9 = e0 & op(e3, e0) = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8780), (8849) are inconsistent by sub-proof
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1563.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8850)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8850) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8851)  all_58_10 = e0 & op(e2, e0) = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8851) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8852)  op(e2, e0) = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8471), (8852), (function-axioms) are
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2324.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8853)  all_58_11 = e0 & op(e1, e0) = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8853) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8854)  all_58_11 = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8855)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8855) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8856)  all_58_12 = e3 & op(e0, e3) = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8856) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8857)  all_58_12 = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (237), (238), (8476),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8520), (8829), (8833), (8857), (function-axioms)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1067.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8858)  all_58_13 = e3 & op(e0, e2) = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8858) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8859)  all_58_13 = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8860)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8860) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8861)  all_58_6 = e3 & op(e1, e3) = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8861) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8862)  all_58_6 = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8863)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8863) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8864)  all_58_1 = e2 & op(e3, e2) = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8864) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8865)  all_58_1 = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8866)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (7010), (8467), (8866),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1066.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8867)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8867) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8868)  all_58_4 = e0 & op(e3, e1) = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8868) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8869)  all_58_4 = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (170), (246), (7010), (8769),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8781), (8869), (function-axioms) are inconsistent
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1400.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8870)  all_58_9 = e0 & op(e3, e0) = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8870) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8871)  all_58_9 = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (244), (7010), (8780), (8837),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8865), (8871), (function-axioms) are inconsistent
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1065.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8872)  all_58_3 = e2 & op(e2, e2) = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8872) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8873)  all_58_3 = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8476), (8873) imply:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8874)  e2 = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8848), (8874) imply:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8875)  all_58_2 = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (243), (7010), (8843), (8862),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8875), (function-axioms) are inconsistent by
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1150.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8876)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8876) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8877)  all_58_7 = e2 & op(e1, e2) = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8877) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8878)  all_58_7 = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (223), (224), (8553),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8561), (8862), (8878), (function-axioms) are
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1801.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8879)  all_58_13 = e2 & op(e0, e2) = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8879) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8880)  all_58_13 = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8859), (8880) are inconsistent by sub-proof
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2129.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8881)  all_58_7 = e3 & op(e1, e2) = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (7010), (8520), (8769), (8837), (8881),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1071.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8882)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8882) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8883)  all_58_8 = e3 & op(e1, e1) = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8883) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8884)  op(e1, e1) = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8553), (8884), (function-axioms) are
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8885)  all_58_11 = e3 & op(e1, e0) = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (170), (246), (7010), (8769),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8781), (8837), (8854), (8885), (function-axioms)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1064.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8886)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (170), (240),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (246), (7010), (8530), (8769), (8837),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8841), (8886), (function-axioms) are inconsistent
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1070.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8887)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8887) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8888)  all_58_6 = e2 & op(e1, e3) = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8888) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8889)  all_58_6 = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (162), (223), (226), (8468),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8520), (8553), (8889), (function-axioms) are
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1676.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8890)  all_58_12 = e2 & op(e0, e3) = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (112), (113),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (120), (121), (125), (139), (145), (159), (160),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (190), (191), (193),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (201), (202), (213), (233), (239), (240),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (255), (256), (258), (269),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (280), (281), (7008), (7009), (7010), (8465),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8466), (8469), (8476), (8505), (8506), (8507),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8515), (8536), (8538), (8548), (8549), (8550),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8551), (8769), (8774), (8777), (8780), (8781),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8890), (function-axioms) are inconsistent by
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1072.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8891)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (237), (238), (8476),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8520), (8829), (8891), (function-axioms) are
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1068.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8892)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (8469), (8506), (8774), (8892) are
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1648.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8893)  all_58_5 = e3 & op(e2, e1) = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8893) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8894)  all_58_5 = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8515), (8894) are inconsistent by sub-proof
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2123.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8895)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8895) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8896)  all_58_8 = e3 & op(e1, e1) = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8896) implies:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8897)  op(e1, e1) = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8553), (8897), (function-axioms) are
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8898)  all_58_14 = e3 & op(e0, e1) = e3
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8829), (8898) are inconsistent by sub-proof
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1747.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8899)  all_58_15 = e2 & op(e0, e0) = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8530), (8899) are inconsistent by sub-proof
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1917.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (8900)  all_58_10 = e2 & op(e2, e0) = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (112), (113), (120), (121), (125), (139),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |            (145), (159), (160), (167), (168), (169), (170),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (201), (202), (213),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |            (255), (256), (258), (269), (280), (281), (7008),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |            (7009), (8465), (8469), (8505), (8506), (8507),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |            (8536), (8538), (8548), (8549), (8550), (8551),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |            (8769), (8774), (8777), (8900), (function-axioms)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1075.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | |   (8901)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8901) gives:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (8902)  all_58_11 = e2 & op(e1, e0) = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (162), (223), (226), (8468),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |            (8520), (8553), (8902), (function-axioms) are
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1063.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (8903)  all_58_15 = e2 & op(e0, e0) = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8530), (8903) are inconsistent by sub-proof
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | |            #1917.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | |   (8904)  all_54_1 = e1 | all_54_1 = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (7007), (8467), (8904) are inconsistent by
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2049.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | |   (8905)  all_58_11 = e2 & op(e1, e0) = e2
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (162), (223), (226), (8468),
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | |            (8520), (8553), (8905), (function-axioms) are
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1063.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | |   (8906)  all_54_10 = e1 | all_54_10 = e0
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (8479), (8541), (8906) are inconsistent by
% 234.07/43.74  | | | | | | | | | | | | | | | | | | |            sub-proof #2282.
% 234.07/43.74  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | | 
% 234.07/43.74  | | | | | | | | | | | | | | | | | End of split
% 234.07/43.74  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | End of split
% 234.07/43.75  | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | End of split
% 234.07/43.75  | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | |   (8907)  all_58_13 = e1 & op(e0, e2) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | REF_CLOSE: (158), (8506), (8907), (function-axioms) are
% 234.07/43.75  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 234.07/43.75  | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | End of split
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | End of split
% 234.07/43.75  | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | |   (8908)  all_58_10 = e1 & op(e2, e0) = e1
% 234.07/43.75  | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | REF_CLOSE: (164), (8507), (8908), (function-axioms) are
% 234.07/43.75  | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 234.07/43.75  | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | End of split
% 234.07/43.75  | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | End of split
% 234.07/43.75  | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | End of split
% 234.07/43.75  | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | |   (8909)  all_18_2 = e0
% 234.07/43.75  | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | COMBINE_EQS: (339), (8909) imply:
% 234.07/43.75  | | | | | | | | | |   (8910)  all_6_2 = e0
% 234.07/43.75  | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | SIMP: (8910) implies:
% 234.07/43.75  | | | | | | | | | |   (8911)  all_6_2 = e0
% 234.07/43.75  | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | COMBINE_EQS: (332), (8911) imply:
% 234.07/43.75  | | | | | | | | | |   (8912)  all_28_2 = e0
% 234.07/43.75  | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | COMBINE_EQS: (266), (8911) imply:
% 234.07/43.75  | | | | | | | | | |   (8913)  all_56_21 = e0
% 234.07/43.75  | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | REDUCE: (367), (8911) imply:
% 234.07/43.75  | | | | | | | | | |   (8914)   ~ (all_52_2 = e0)
% 234.07/43.75  | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | REDUCE: (380), (8911) imply:
% 234.07/43.75  | | | | | | | | | |   (8915)   ~ (all_52_8 = e0)
% 234.07/43.75  | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | REDUCE: (39), (8911) imply:
% 234.07/43.75  | | | | | | | | | |   (8916)  op(e1, e1) = e0
% 234.07/43.75  | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | BETA: splitting (240) gives:
% 234.07/43.75  | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | |   (8917)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 234.07/43.75  | | | | | | | | | | |             & op(e3, e2) = e0)
% 234.07/43.75  | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | REF_CLOSE: (4), (170), (7010), (8467), (8917),
% 234.07/43.75  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.75  | | | | | | | | | | |            #1066.
% 234.07/43.75  | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | |   (8918)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 234.07/43.75  | | | | | | | | | | |             & op(e3, e0) = e0)
% 234.07/43.75  | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | BETA: splitting (8918) gives:
% 234.07/43.75  | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | |   (8919)  all_58_4 = e0 & op(e3, e1) = e0
% 234.07/43.75  | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | REF_CLOSE: (169), (8915), (8919), (function-axioms) are
% 234.07/43.75  | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 234.07/43.75  | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | |   (8920)  all_58_9 = e0 & op(e3, e0) = e0
% 234.07/43.75  | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | ALPHA: (8920) implies:
% 234.07/43.75  | | | | | | | | | | | |   (8921)  all_58_9 = e0
% 234.07/43.75  | | | | | | | | | | | |   (8922)  op(e3, e0) = e0
% 234.07/43.75  | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | BETA: splitting (239) gives:
% 234.07/43.75  | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | |   (8923)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 234.07/43.75  | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 234.07/43.75  | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | REF_CLOSE: (4), (167), (7010), (8466), (8923),
% 234.07/43.75  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.75  | | | | | | | | | | | | |            #1272.
% 234.07/43.75  | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | |   (8924)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 234.07/43.75  | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 234.07/43.75  | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | BETA: splitting (8924) gives:
% 234.07/43.75  | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | |   (8925)  all_58_6 = e0 & op(e1, e3) = e0
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | ALPHA: (8925) implies:
% 234.07/43.75  | | | | | | | | | | | | | |   (8926)  op(e1, e3) = e0
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 234.07/43.75  | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (8926) gives:
% 234.07/43.75  | | | | | | | | | | | | | |   (8927)  all_52_2 = e0
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | REDUCE: (8914), (8927) imply:
% 234.07/43.75  | | | | | | | | | | | | | |   (8928)  $false
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | CLOSE: (8928) is inconsistent.
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | |   (8929)  all_58_12 = e0 & op(e0, e3) = e0
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | ALPHA: (8929) implies:
% 234.07/43.75  | | | | | | | | | | | | | |   (8930)  all_58_12 = e0
% 234.07/43.75  | | | | | | | | | | | | | |   (8931)  op(e0, e3) = e0
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 234.07/43.75  | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (8931) gives:
% 234.07/43.75  | | | | | | | | | | | | | |   (8932)  all_52_3 = e0
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 234.07/43.75  | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (168), (8922) gives:
% 234.07/43.75  | | | | | | | | | | | | | |   (8933)  all_52_12 = e0
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | REDUCE: (139), (8932) imply:
% 234.07/43.75  | | | | | | | | | | | | | |   (8934)   ~ (all_52_11 = e0)
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | SIMP: (8934) implies:
% 234.07/43.75  | | | | | | | | | | | | | |   (8935)   ~ (all_52_11 = e0)
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | REDUCE: (387), (8933) imply:
% 234.07/43.75  | | | | | | | | | | | | | |   (8936)   ~ (all_4_2 = e0)
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | SIMP: (8936) implies:
% 234.07/43.75  | | | | | | | | | | | | | |   (8937)   ~ (all_4_2 = e0)
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 234.07/43.75  | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | |   (8938)  all_54_15 = e3
% 234.07/43.75  | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | REF_CLOSE: (299), (7012), (8938) are inconsistent by
% 234.07/43.75  | | | | | | | | | | | | | | |            sub-proof #2340.
% 234.07/43.75  | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | |   (8939)   ~ (all_54_15 = e3)
% 234.07/43.75  | | | | | | | | | | | | | | |   (8940)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 234.07/43.75  | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | BETA: splitting (8940) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | |   (8941)  all_54_15 = e2
% 234.07/43.75  | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | REF_CLOSE: (299), (390), (8941) are inconsistent by sub-proof
% 234.07/43.75  | | | | | | | | | | | | | | | |            #2339.
% 234.07/43.75  | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | |   (8942)   ~ (all_54_15 = e2)
% 234.07/43.75  | | | | | | | | | | | | | | | |   (8943)  all_54_15 = e1 | all_54_15 = e0
% 234.07/43.75  | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | BETA: splitting (8943) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | |   (8944)  all_54_15 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (8944) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | |   (8945)  all_4_2 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | SIMP: (8945) implies:
% 234.07/43.75  | | | | | | | | | | | | | | | | |   (8946)  all_4_2 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (8946) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | |   (8947)  all_20_2 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (8946) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | |   (8948)  all_34_2 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (8946) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | |   (8949)  all_56_31 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | REDUCE: (379), (8946) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | |   (8950)   ~ (all_52_7 = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | REDUCE: (388), (8946) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | |   (8951)   ~ (all_52_13 = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | REDUCE: (389), (8946) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | |   (8952)   ~ (all_52_14 = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | REDUCE: (7012), (8946) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | |   (8953)   ~ (e3 = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | REDUCE: (390), (8946) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | |   (8954)   ~ (e2 = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | |   (8955)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (7007), (8476), (8955),
% 234.07/43.75  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.75  | | | | | | | | | | | | | | | | | |            #1377.
% 234.07/43.75  | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | |   (8956)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 234.07/43.75  | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | BETA: splitting (8956) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | |   (8957)  all_58_7 = e1 & op(e1, e2) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | ALPHA: (8957) implies:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | |   (8958)  all_58_7 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | |   (8959)  op(e1, e2) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | |   (8960)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8960) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | |   (8961)  all_58_9 = e1 & op(e3, e0) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8961) implies:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | |   (8962)  all_58_9 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8921), (8962) are inconsistent by sub-proof
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | |            #1744.
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | |   (8963)  all_58_10 = e1 & op(e2, e0) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8951), (8963), (function-axioms) are
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | |   (8964)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8964) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | |   (8965)  all_58_11 = e1 & op(e1, e0) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8965) implies:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | |   (8966)  op(e1, e0) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8952), (8966), (function-axioms) are
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | |   (8967)  all_58_15 = e1 & op(e0, e0) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8967) implies:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | |   (8968)  all_58_15 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | |   (8969)  op(e0, e0) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | |   (8970)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8970) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |   (8971)  all_58_2 = e1 & op(e2, e3) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7004), (8971), (function-axioms) are
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |   (8972)  all_58_3 = e1 & op(e2, e2) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8476), (8972) are inconsistent by sub-proof
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |            #1752.
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | |   (8973)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8973) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |   (8974)  all_58_5 = e1 & op(e2, e1) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8974) implies:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |   (8975)  all_58_5 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |   (8976)  op(e2, e1) = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (8959) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |   (8977)  all_52_6 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (8976) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |   (8978)  all_52_9 = e1
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (8977) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | |   (8979)   ~ (all_52_14 = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | |   (8980)   ~ (all_20_2 = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8947), (8980) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | |   (8981)  $false
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8981) is inconsistent.
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | |   (8982)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | |             = all_20_1 & $i(all_20_1))
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (8983)   ~ (all_28_2 = e0)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8912), (8983) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (8984)  $false
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8984) is inconsistent.
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (8985)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_28_1 & $i(all_28_0) &
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_28_1 & $i(all_28_1))
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8986)   ~ (all_34_2 = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8948), (8986) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8987)  $false
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8987) is inconsistent.
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8988)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8989)   ~ (all_38_2 = e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7002), (8989) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8990)  $false
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8990) is inconsistent.
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8991)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e1) = all_38_1 & $i(all_38_0) &
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_38_1 & $i(all_38_1))
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8992)   ~ (all_48_2 = e0)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8464), (8992) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8993)  $false
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8993) is inconsistent.
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8994)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_48_1 & $i(all_48_1))
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8995)  all_54_4 = e3
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (8995) imply:
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8996)  all_52_1 = e3
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (8996) imply:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8997)   ~ (all_52_13 = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8997) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8998)   ~ (all_52_13 = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8999)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (164), (8921), (8998), (8999),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1062.
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9000)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (163), (210),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (224), (225), (7005), (8477), (8916),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8921), (8922), (8935), (8949), (8958), (8968),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8994), (9000), (function-axioms) are inconsistent
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1055.
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9001)   ~ (all_54_4 = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9002)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (9001) imply:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9003)   ~ (all_52_1 = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9004)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9004) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9005)  all_58_9 = e3 & op(e3, e0) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9005) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9006)  all_58_9 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8921), (9006) are inconsistent by sub-proof
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1958.
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9007)  all_58_10 = e3 & op(e2, e0) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9007) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9008)  all_58_10 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9009)  op(e2, e0) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9010)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9010) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9011)  all_58_9 = e2 & op(e3, e0) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9011) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9012)  all_58_9 = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8921), (9012) are inconsistent by sub-proof
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1660.
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9013)  all_58_10 = e2 & op(e2, e0) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9008), (9013) are inconsistent by sub-proof
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1105.
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9014)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9014) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9015)  all_58_11 = e2 & op(e1, e0) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9015) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9016)  all_58_11 = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9017)  op(e1, e0) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8461) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9018)   ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_14_1 & $i(all_14_0) &
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9018) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9019)   ~ (all_14_0 = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9020)  op(e2, e0) = all_14_1
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9021)  op(all_14_1, e2) = all_14_0
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9022)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9022) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9023)  all_58_6 = e3 & op(e1, e3) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9023) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9024)  all_58_6 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9025)  op(e1, e3) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8994) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9026)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_48_1 & $i(all_48_0) &
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9026) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9027)   ~ (all_48_0 = e1)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9028)  op(e2, e0) = all_48_1
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9029)  op(all_48_1, e2) = all_48_0
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9030)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9030) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9031)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9031) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9032)  op(e3, all_56_1) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7003), (9032) imply:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9033)  op(e3, e1) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8985) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9034)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_28_1 & $i(all_28_0) &
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9034) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9035)   ~ (all_28_0 = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9036)  op(e1, e0) = all_28_1
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9037)  op(all_28_1, e1) = all_28_0
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9038)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9038) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9039)  all_58_0 = e2 & op(e3, e3) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9039) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9040)  op(e3, e3) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7010), (9040), (function-axioms) are
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9041)  all_58_2 = e2 & op(e2, e3) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9041) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9042)  all_58_2 = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_28_1,
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (9017), (9036) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9043)  all_28_1 = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_1, e0, e2, simplifying with (9020), (9028)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9044)  all_48_1 = all_14_1
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1,
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (9009), (9028) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9045)  all_48_1 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (9033) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9046)  all_52_8 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9044), (9045) imply:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9047)  all_14_1 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (9046) imply:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9048)   ~ (all_52_4 = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (9046) imply:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9049)   ~ (all_52_11 = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9049) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9050)   ~ (all_52_11 = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9029), (9045) imply:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9051)  op(e3, e2) = all_48_0
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9037), (9043) imply:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9052)  op(e2, e1) = all_28_0
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9021), (9047) imply:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9053)  op(e3, e2) = all_14_0
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9054)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9054) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9055)  all_58_12 = e3 & op(e0, e3) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9055) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9056)  all_58_12 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (243),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9024), (9056), (function-axioms) are inconsistent
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1531.
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9057)  all_58_13 = e3 & op(e0, e2) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9057) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9058)  all_58_13 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9059)  op(e0, e2) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9060)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_19 & $i(all_56_19))
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9060) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9061)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_17 & $i(all_56_17)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9061) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9062)  op(e3, e1) = all_56_17
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9063)  op(e3, all_56_17) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (170), (218), (243),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (246), (7001), (7010), (8921), (8930),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8968), (8976), (8982), (8988), (8991), (9024),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9033), (9035), (9042), (9048), (9052), (9058),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9062), (9063), (function-axioms) are inconsistent
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1047.
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9064)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_19 & $i(all_56_19)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9064) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9065)  op(e2, e1) = all_56_19
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9066)  op(e2, all_56_19) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9067)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9067) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9068)  all_58_0 = e2 & op(e3, e3) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9068) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9069)  op(e3, e3) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7010), (9069), (function-axioms) are
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9070)  all_58_1 = e2 & op(e3, e2) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9070) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9071)  all_58_1 = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9072)  op(e3, e2) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9073)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (7010), (9048), (9073),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1401.
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9074)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9074) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9075)  all_58_4 = e3 & op(e3, e1) = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9075) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9076)  all_58_4 = e3
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9077)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (170), (244), (246),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (8921), (8930), (9048), (9058), (9071),
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9076), (9077), (function-axioms) are inconsistent
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1053.
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9078)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9078) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9079)  all_58_14 = e2 & op(e0, e1) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9079) implies:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9080)  all_58_14 = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9081)  op(e0, e1) = e2
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9082)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (8465), (9009), (9048), (9072),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9082), (function-axioms) are inconsistent by
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1046.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9083)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9083) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9084)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9084) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9085)  op(e1, e2) = all_56_13
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9086)  op(e1, all_56_13) = e1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8982) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9087)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_20_1 & $i(all_20_0) &
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9087) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9088)  op(e0, e1) = all_20_1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8916), (8959), (8988), (9081), (9085),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9086), (9088), (function-axioms) are inconsistent
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1045.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9089)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9089) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9090)  op(e0, e1) = all_20_1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8916), (8959), (8988), (9081), (9085),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9086), (9090), (function-axioms) are inconsistent
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1045.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (8976), (9065)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9091)  all_56_19 = e1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_0,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (9052), (9065)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9092)  all_56_19 = all_28_0
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_0,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_0, e2, e3, simplifying with (9051), (9053)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9093)  all_48_0 = all_14_0
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_0,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (9051), (9072) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9094)  all_48_0 = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9091), (9092) imply:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9095)  all_28_0 = e1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9095) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9096)  all_28_0 = e1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9093), (9094) imply:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9097)  all_14_0 = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9097) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9098)  all_14_0 = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9019), (9098) imply:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9099)   ~ (e3 = e2)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (227), (229),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (7010), (8921), (8975), (9048), (9052),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9066), (9080), (9091), (9096), (function-axioms)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1043.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9100)  all_58_15 = e2 & op(e0, e0) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8968), (9100) are inconsistent by sub-proof
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1917.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9101)  all_58_9 = e3 & op(e3, e0) = e3
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9101) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9102)  all_58_9 = e3
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8921), (9102) are inconsistent by sub-proof
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1958.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9103)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (170), (243), (246),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (8921), (8930), (9024), (9042), (9048),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9103), (function-axioms) are inconsistent by
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1048.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9104)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_23 & $i(all_56_23))
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9104) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9105)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9105) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9106)  op(e1, all_56_21) = e1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8913), (9106) imply:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9107)  op(e1, e0) = e1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8952), (9107), (function-axioms) are
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9108)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_23 & $i(all_56_23)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9108) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9109)  op(e0, e1) = all_56_23
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9110)  op(e0, all_56_23) = e0
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9111)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9111) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9112)  all_58_0 = e2 & op(e3, e3) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9112) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9113)  op(e3, e3) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7010), (9113), (function-axioms) are
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9114)  all_58_1 = e2 & op(e3, e2) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9114) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9115)  all_58_1 = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9116)  op(e3, e2) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9117)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (7010), (9048), (9117),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1401.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9118)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9118) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9119)  all_58_4 = e3 & op(e3, e1) = e3
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9119) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9120)  all_58_4 = e3
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9121)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9121) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9122)  all_58_12 = e2 & op(e0, e3) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (244), (7010), (8921), (8930),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9115), (9120), (9122), (function-axioms) are
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1054.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9123)  all_58_13 = e2 & op(e0, e2) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9123) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9124)  all_58_13 = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9058), (9124) are inconsistent by sub-proof
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2129.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9125)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9125) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9126)  all_58_14 = e2 & op(e0, e1) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9126) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9127)  op(e0, e1) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9128)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, all_56_11) = e2)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (8465), (9009), (9048), (9116),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9128), (function-axioms) are inconsistent by
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1046.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9129)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_15 & $i(all_56_15))
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9129) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9130)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_13 & $i(all_56_13)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9130) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9131)  op(e1, e2) = all_56_13
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9132)  op(e1, all_56_13) = e1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (8959), (9131)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9133)  all_56_13 = e1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9132), (9133) imply:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9134)  op(e1, e1) = e1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8916), (9134), (function-axioms) are
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9135)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) = all_56_15 & $i(all_56_15)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9135) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9136)  op(e0, e2) = all_56_15
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8982) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9137)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_20_1 & $i(all_20_0) &
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9137) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9138)  op(e0, e1) = all_20_1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (246), (7010), (8921), (8976), (8988),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9019), (9035), (9051), (9052), (9053), (9059),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9109), (9110), (9115), (9116), (9120), (9127),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9136), (9138), (function-axioms) are inconsistent
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1041.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9139)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9139) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9140)  op(e0, e1) = all_20_1
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (246), (7010), (8921), (8976), (8988),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9019), (9035), (9051), (9052), (9053), (9059),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9109), (9110), (9115), (9116), (9120), (9127),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9136), (9140), (function-axioms) are inconsistent
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1041.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9141)  all_58_15 = e2 & op(e0, e0) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8968), (9141) are inconsistent by sub-proof
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1917.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9142)  all_58_9 = e3 & op(e3, e0) = e3
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9142) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9143)  all_58_9 = e3
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8921), (9143) are inconsistent by sub-proof
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1958.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9144)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9144) gives:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9145)  all_58_4 = e2 & op(e3, e1) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9145) implies:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9146)  all_58_4 = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (170), (246), (7010), (8921),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9048), (9146), (function-axioms) are inconsistent
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1143.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9147)  all_58_9 = e2 & op(e3, e0) = e2
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (243), (7010), (8921), (8930),
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9024), (9042), (9147), (function-axioms) are
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1049.
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9148)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9148) gives:
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9149)  all_58_14 = e3 & op(e0, e1) = e3
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9050), (9149), (function-axioms) are
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9150)  all_58_15 = e3 & op(e0, e0) = e3
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (7010), (8968), (9003), (9024), (9150),
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1137.
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9151)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (8930), (9024), (9151) are inconsistent
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1151.
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9152)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9152) implies:
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9153)   ~ (all_28_1 = e2)
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9154)  op(e1, e0) = all_28_1
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9017), (9153), (9154), (function-axioms) are
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1944.
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9155)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_3 & $i(all_56_3)
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (167), (243), (245),
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (279), (7004), (7010), (8466), (8477), (8930),
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9002), (9003), (9024), (9155), (function-axioms)
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1040.
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9156)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (279), (7004), (8466), (8931), (8969),
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9002), (9025), (9156), (function-axioms) are
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1152.
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9157)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9157) implies:
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9158)   ~ (all_48_1 = e3)
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9159)  op(e2, e0) = all_48_1
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9009), (9020), (9158), (9159), (function-axioms)
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1632.
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.07/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9160)  all_58_7 = e3 & op(e1, e2) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (222), (8921), (8958), (8968),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9008), (9016), (9160) are inconsistent by
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1039.
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9161)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9161) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9162)  all_58_8 = e3 & op(e1, e1) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8916), (9162), (function-axioms) are
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9163)  all_58_11 = e3 & op(e1, e0) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (163), (210),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (224), (225), (7005), (8477), (8916),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8921), (8922), (8935), (8949), (8958), (8968),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8994), (9163), (function-axioms) are inconsistent
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1056.
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9164)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9164) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9165)   ~ (all_14_1 = e1)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9166)  op(e2, e0) = all_14_1
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9167)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9167) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9168)  all_58_6 = e3 & op(e1, e3) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9168) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9169)  all_58_6 = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9170)  op(e1, e3) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8994) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9171)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_48_1 & $i(all_48_0) &
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9171) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9172)   ~ (all_48_0 = e1)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9173)  op(e2, e0) = all_48_1
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9174)  op(all_48_1, e2) = all_48_0
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9175)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9175) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9176)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9176) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9177)  op(e3, all_56_1) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7003), (9177) imply:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9178)  op(e3, e1) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8985) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9179)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_28_1 & $i(all_28_0) &
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9179) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9180)   ~ (all_28_0 = e3)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9181)  op(e1, e0) = all_28_1
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9182)  op(all_28_1, e1) = all_28_0
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9183)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9183) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9184)  all_58_0 = e2 & op(e3, e3) = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9184) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9185)  op(e3, e3) = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7010), (9185), (function-axioms) are
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9186)  all_58_2 = e2 & op(e2, e3) = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9186) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9187)  all_58_2 = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_28_1,
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (9017), (9181) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9188)  all_28_1 = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_1, e0, e2, simplifying with (9166), (9173)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9189)  all_48_1 = all_14_1
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1,
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (9009), (9173) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9190)  all_48_1 = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (9178) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9191)  all_52_8 = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9189), (9190) imply:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9192)  all_14_1 = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (9191) imply:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9193)   ~ (all_52_4 = e3)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (9191) imply:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9194)   ~ (all_52_11 = e3)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9194) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9195)   ~ (all_52_11 = e3)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9174), (9190) imply:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9196)  op(e3, e2) = all_48_0
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9182), (9188) imply:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9197)  op(e2, e1) = all_28_0
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9198)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9198) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9199)  all_58_12 = e3 & op(e0, e3) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9199) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9200)  all_58_12 = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (243),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9169), (9200), (function-axioms) are inconsistent
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1531.
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9201)  all_58_13 = e3 & op(e0, e2) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9201) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9202)  all_58_13 = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9203)  op(e0, e2) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9204)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_19 & $i(all_56_19))
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9204) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9205)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_17 & $i(all_56_17)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9205) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9206)  op(e3, e1) = all_56_17
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9207)  op(e3, all_56_17) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (170), (218), (243),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (246), (7001), (7010), (8921), (8930),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8968), (8976), (8982), (8988), (8991), (9169),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9178), (9180), (9187), (9193), (9197), (9202),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9206), (9207), (function-axioms) are inconsistent
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1047.
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9208)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_19 & $i(all_56_19)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9208) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9209)  op(e2, e1) = all_56_19
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9210)  op(e2, all_56_19) = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9211)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9211) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9212)  all_58_0 = e2 & op(e3, e3) = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9212) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9213)  op(e3, e3) = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7010), (9213), (function-axioms) are
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9214)  all_58_1 = e2 & op(e3, e2) = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9214) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9215)  all_58_1 = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9216)  op(e3, e2) = e2
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9217)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (7010), (9193), (9217),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1401.
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9218)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9218) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9219)  all_58_4 = e3 & op(e3, e1) = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9219) implies:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9220)  all_58_4 = e3
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9221)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (170), (244), (246),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (8921), (8930), (9193), (9202), (9215),
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9220), (9221), (function-axioms) are inconsistent
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1053.
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9222)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9222) gives:
% 234.26/43.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9223)  all_58_14 = e2 & op(e0, e1) = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9223) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9224)  all_58_14 = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9225)  op(e0, e1) = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8982) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9226)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_20_1 & $i(all_20_0) &
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9226) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9227)  op(e0, e1) = all_20_1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8988) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (8976), (9209)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9228)  all_56_19 = e1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_0,
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (9197), (9209)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9229)  all_56_19 = all_28_0
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_0,
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (9196), (9216) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9230)  all_48_0 = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9228), (9229) imply:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9231)  all_28_0 = e1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (227), (229),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (7010), (8921), (8975), (9193), (9197),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9210), (9224), (9228), (9231), (function-axioms)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1043.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9232)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 &
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9232) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9233)   ~ (all_34_1 = e2)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9234)  op(e0, e1) = all_34_1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9225), (9227), (9233), (9234), (function-axioms)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2237.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9235)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9235) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9236)   ~ (all_20_1 = e3)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9237)  op(e0, e1) = all_20_1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8988) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9238)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_34_1 & $i(all_34_0) &
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9238) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9239)  op(e0, e1) = all_34_1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_1,
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_34_1, e1, e0, simplifying with (9237), (9239)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9240)  all_34_1 = all_20_1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_34_1,
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (9225), (9239) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9241)  all_34_1 = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (8976), (9209)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9242)  all_56_19 = e1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_0,
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (9197), (9209)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9243)  all_56_19 = all_28_0
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_0,
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (9196), (9216) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9244)  all_48_0 = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9242), (9243) imply:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9245)  all_28_0 = e1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9240), (9241) imply:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9246)  all_20_1 = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9236), (9246) imply:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9247)   ~ (e3 = e2)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (227), (229),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (7010), (8921), (8975), (9193), (9197),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9210), (9224), (9242), (9245), (function-axioms)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1043.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9248)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 &
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9248) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9249)   ~ (all_34_1 = e2)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9250)  op(e0, e1) = all_34_1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9225), (9237), (9249), (9250), (function-axioms)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2237.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9251)  all_58_15 = e2 & op(e0, e0) = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8968), (9251) are inconsistent by sub-proof
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1917.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9252)  all_58_9 = e3 & op(e3, e0) = e3
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9252) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9253)  all_58_9 = e3
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8921), (9253) are inconsistent by sub-proof
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1958.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9254)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (170), (243), (246),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (8921), (8930), (9169), (9187), (9193),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9254), (function-axioms) are inconsistent by
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1048.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9255)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_56_23 & $i(all_56_23))
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9255) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9256)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9256) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9257)  op(e1, all_56_21) = e1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8913), (9257) imply:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9258)  op(e1, e0) = e1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8952), (9258), (function-axioms) are
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9259)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_56_23 & $i(all_56_23)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9259) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9260)  op(e0, e1) = all_56_23
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9261)  op(e0, all_56_23) = e0
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9262)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9262) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9263)  all_58_0 = e2 & op(e3, e3) = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9263) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9264)  op(e3, e3) = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7010), (9264), (function-axioms) are
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9265)  all_58_1 = e2 & op(e3, e2) = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9265) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9266)  all_58_1 = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9267)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (7010), (9193), (9267),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1401.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9268)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9268) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9269)  all_58_4 = e3 & op(e3, e1) = e3
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9269) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9270)  all_58_4 = e3
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9271)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (170), (244), (246),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (8921), (8930), (9193), (9202), (9266),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9270), (9271), (function-axioms) are inconsistent
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1053.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9272)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9272) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9273)  all_58_14 = e2 & op(e0, e1) = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9273) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9274)  op(e0, e1) = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8982) gives:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9275)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_20_1 & $i(all_20_0) &
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9275) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9276)  op(e0, e1) = all_20_1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (246), (7010), (8921), (8976), (8988),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9180), (9197), (9203), (9260), (9261), (9266),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9270), (9274), (9276), (function-axioms) are
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9277)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_20_1)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9277) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9278)  op(e0, e1) = all_20_1
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (246), (7010), (8921), (8976), (8988),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9180), (9197), (9203), (9260), (9261), (9266),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9270), (9274), (9278), (function-axioms) are
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9279)  all_58_15 = e2 & op(e0, e0) = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8968), (9279) are inconsistent by sub-proof
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1917.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9280)  all_58_9 = e3 & op(e3, e0) = e3
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9280) implies:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9281)  all_58_9 = e3
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8921), (9281) are inconsistent by sub-proof
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1958.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9282)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (170), (243), (246),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (8921), (8930), (9169), (9187), (9193),
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9282), (function-axioms) are inconsistent by
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1048.
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.26/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9283)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9283) gives:
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9284)  all_58_14 = e3 & op(e0, e1) = e3
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9195), (9284), (function-axioms) are
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9285)  all_58_15 = e3 & op(e0, e0) = e3
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (7010), (8968), (9003), (9169), (9285),
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1137.
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9286)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (8930), (9169), (9286) are inconsistent
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1151.
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9287)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9287) implies:
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9288)   ~ (all_28_1 = e2)
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9289)  op(e1, e0) = all_28_1
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9017), (9288), (9289), (function-axioms) are
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1944.
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9290)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_3 & $i(all_56_3)
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (167), (243), (245),
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (279), (7004), (7010), (8466), (8477), (8930),
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9002), (9003), (9169), (9290), (function-axioms)
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1040.
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9291)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (279), (7004), (8466), (8931), (8969),
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9002), (9170), (9291), (function-axioms) are
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1152.
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9292)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9292) implies:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9293)   ~ (all_48_1 = e3)
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9294)  op(e2, e0) = all_48_1
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9009), (9166), (9293), (9294), (function-axioms)
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1632.
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9295)  all_58_7 = e3 & op(e1, e2) = e3
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (222), (8921), (8958), (8968),
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9008), (9016), (9295) are inconsistent by
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1039.
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9296)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9296) gives:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9297)  all_58_8 = e3 & op(e1, e1) = e3
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8916), (9297), (function-axioms) are
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9298)  all_58_11 = e3 & op(e1, e0) = e3
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (163), (210),
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (224), (225), (7005), (8477), (8916),
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8921), (8922), (8935), (8949), (8958), (8968),
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8994), (9298), (function-axioms) are inconsistent
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1056.
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9299)  all_58_15 = e2 & op(e0, e0) = e2
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9299) implies:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9300)  all_58_15 = e2
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8968), (9300) are inconsistent by sub-proof
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2231.
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9301)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (163), (210),
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (224), (225), (7005), (8477), (8916),
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8921), (8922), (8935), (8949), (8958), (8968),
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8994), (9301), (function-axioms) are inconsistent
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1055.
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | |   (9302)  all_58_10 = e1 & op(e2, e0) = e1
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9302) implies:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | |   (9303)  all_58_10 = e1
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (221), (222), (8921),
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | |            (8968), (9303) are inconsistent by sub-proof
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | |            #1618.
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | |   (9304)  all_58_13 = e1 & op(e0, e2) = e1
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8950), (9304), (function-axioms) are
% 234.33/43.80  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 234.33/43.80  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | |   (9305)  all_54_15 = e0
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (8937), (9305) are inconsistent by
% 234.33/43.80  | | | | | | | | | | | | | | | | |            sub-proof #1737.
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | 
% 234.33/43.80  | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | |   (9306)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 234.33/43.80  | | | | | | | |             op(e2, e0) = e0)
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | | REF_CLOSE: (164), (165), (8470), (8471), (9306),
% 234.33/43.80  | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.33/43.80  | | | | | | | |            #1991.
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | End of split
% 234.33/43.80  | | | | | | | 
% 234.33/43.80  | | | | | | End of split
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | Case 2:
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | |   (9307)  all_12_2 = e3
% 234.33/43.80  | | | | | |   (9308)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0,
% 234.33/43.80  | | | | | |               e3) = all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 234.33/43.80  | | | | | |             (all_12_1 = e2) & op(e0, e3) = all_12_1 & $i(all_12_1))
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | | COMBINE_EQS: (346), (9307) imply:
% 234.33/43.80  | | | | | |   (9309)  all_4_2 = e3
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | | COMBINE_EQS: (334), (9309) imply:
% 234.33/43.80  | | | | | |   (9310)  all_26_2 = e3
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | | COMBINE_EQS: (254), (9309) imply:
% 234.33/43.80  | | | | | |   (9311)  all_56_31 = e3
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | | REDUCE: (368), (9309) imply:
% 234.33/43.80  | | | | | |   (9312)   ~ (all_52_3 = e3)
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | | REDUCE: (379), (9309) imply:
% 234.33/43.80  | | | | | |   (9313)   ~ (all_52_7 = e3)
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | | REDUCE: (386), (9309) imply:
% 234.33/43.80  | | | | | |   (9314)   ~ (all_52_11 = e3)
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | | REDUCE: (387), (9309) imply:
% 234.33/43.80  | | | | | |   (9315)   ~ (all_52_12 = e3)
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | | REDUCE: (388), (9309) imply:
% 234.33/43.80  | | | | | |   (9316)   ~ (all_52_13 = e3)
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | | REDUCE: (389), (9309) imply:
% 234.33/43.80  | | | | | |   (9317)   ~ (all_52_14 = e3)
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | | BETA: splitting (222) gives:
% 234.33/43.80  | | | | | | 
% 234.33/43.80  | | | | | | Case 1:
% 234.33/43.80  | | | | | | | 
% 234.33/43.80  | | | | | | |   (9318)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 234.33/43.80  | | | | | | |             op(e2, e0) = e3)
% 234.33/43.80  | | | | | | | 
% 234.33/43.80  | | | | | | | REF_CLOSE: (164), (168), (9315), (9316), (9318), (function-axioms)
% 234.33/43.80  | | | | | | |            are inconsistent by sub-proof #1592.
% 234.33/43.80  | | | | | | | 
% 234.33/43.80  | | | | | | Case 2:
% 234.33/43.80  | | | | | | | 
% 234.33/43.80  | | | | | | |   (9319)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 234.33/43.80  | | | | | | |             op(e0, e0) = e3)
% 234.33/43.80  | | | | | | | 
% 234.33/43.80  | | | | | | | BETA: splitting (9319) gives:
% 234.33/43.80  | | | | | | | 
% 234.33/43.80  | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | |   (9320)  all_58_11 = e3 & op(e1, e0) = e3
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | | ALPHA: (9320) implies:
% 234.33/43.80  | | | | | | | |   (9321)  op(e1, e0) = e3
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | | REF_CLOSE: (160), (9317), (9321), (function-axioms) are
% 234.33/43.80  | | | | | | | |            inconsistent by sub-proof #2149.
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | |   (9322)  all_58_15 = e3 & op(e0, e0) = e3
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | | ALPHA: (9322) implies:
% 234.33/43.80  | | | | | | | |   (9323)  all_58_15 = e3
% 234.33/43.80  | | | | | | | |   (9324)  op(e0, e0) = e3
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | | BETA: splitting (52) gives:
% 234.33/43.80  | | | | | | | | 
% 234.33/43.80  | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | 
% 234.33/43.80  | | | | | | | | |   (9325)   ~ (all_14_2 = e0)
% 234.33/43.80  | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | REDUCE: (344), (9325) imply:
% 234.33/43.80  | | | | | | | | |   (9326)   ~ (all_8_2 = e0)
% 234.33/43.80  | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | BETA: splitting (58) gives:
% 234.33/43.80  | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | |   (9327)   ~ (all_18_2 = e0)
% 234.33/43.80  | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | REDUCE: (339), (9327) imply:
% 234.33/43.80  | | | | | | | | | |   (9328)   ~ (all_6_2 = e0)
% 234.33/43.80  | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | BETA: splitting (64) gives:
% 234.33/43.80  | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | |   (9329)   ~ (all_22_2 = e1)
% 234.33/43.80  | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | REDUCE: (326), (9329) imply:
% 234.33/43.80  | | | | | | | | | | |   (9330)   ~ (all_8_2 = e1)
% 234.33/43.80  | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | BETA: splitting (199) gives:
% 234.33/43.80  | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | |   (9331)  all_54_5 = e3
% 234.33/43.80  | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | COMBINE_EQS: (275), (9331) imply:
% 234.33/43.80  | | | | | | | | | | | |   (9332)  all_8_2 = e3
% 234.33/43.80  | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | REDUCE: (392), (9332) imply:
% 234.33/43.80  | | | | | | | | | | | |   (9333)  $false
% 234.33/43.80  | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | CLOSE: (9333) is inconsistent.
% 234.33/43.80  | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | |   (9334)   ~ (all_54_5 = e3)
% 234.33/43.80  | | | | | | | | | | | |   (9335)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 234.33/43.80  | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | BETA: splitting (9335) gives:
% 234.33/43.80  | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | |   (9336)  all_54_5 = e2
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | COMBINE_EQS: (275), (9336) imply:
% 234.33/43.80  | | | | | | | | | | | | |   (9337)  all_8_2 = e2
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | COMBINE_EQS: (353), (9337) imply:
% 234.33/43.80  | | | | | | | | | | | | |   (9338)  all_56_11 = e2
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | REDUCE: (366), (9337) imply:
% 234.33/43.80  | | | | | | | | | | | | |   (9339)   ~ (all_52_1 = e2)
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | REDUCE: (373), (9337) imply:
% 234.33/43.80  | | | | | | | | | | | | |   (9340)   ~ (all_52_7 = e2)
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | REDUCE: (375), (9337) imply:
% 234.33/43.80  | | | | | | | | | | | | |   (9341)   ~ (all_52_9 = e2)
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | REDUCE: (377), (9337) imply:
% 234.33/43.80  | | | | | | | | | | | | |   (9342)   ~ (all_52_13 = e2)
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | REDUCE: (392), (9337) imply:
% 234.33/43.80  | | | | | | | | | | | | |   (9343)   ~ (e3 = e2)
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | REDUCE: (42), (9337) imply:
% 234.33/43.80  | | | | | | | | | | | | |   (9344)  op(e2, e2) = e2
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | BETA: splitting (213) gives:
% 234.33/43.80  | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | |   (9345)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.33/43.80  | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.33/43.80  | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.33/43.80  | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.33/43.80  | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.33/43.80  | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.33/43.80  | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.33/43.80  | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.33/43.80  | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.33/43.80  | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 234.33/43.80  | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 234.33/43.80  | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.33/43.80  | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 234.33/43.80  | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | BETA: splitting (9345) gives:
% 234.33/43.80  | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | |   (9346)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.33/43.80  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.33/43.80  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.33/43.80  | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.33/43.80  | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.33/43.80  | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.33/43.80  | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.33/43.80  | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.33/43.80  | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.33/43.80  | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.33/43.80  | | | | | | | | | | | | | | |             = e3)
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | REF_CLOSE: (167), (7003), (9338), (9339), (9346),
% 234.33/43.80  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.33/43.80  | | | | | | | | | | | | | | |            #1213.
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | |   (9347)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.33/43.80  | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.33/43.80  | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 234.33/43.80  | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 234.33/43.80  | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.33/43.80  | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.33/43.80  | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 234.33/43.80  | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 234.33/43.80  | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.33/43.80  | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 234.33/43.80  | | | | | | | | | | | | | | |             = e0)
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (7008), (9311), (9312), (9347),
% 234.33/43.80  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.33/43.80  | | | | | | | | | | | | | | |            #1411.
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | |   (9348)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.33/43.80  | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.33/43.80  | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.33/43.80  | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.33/43.80  | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.33/43.80  | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.33/43.80  | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.33/43.80  | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.33/43.80  | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 234.33/43.80  | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 234.33/43.80  | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 234.33/43.80  | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 234.33/43.80  | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 234.33/43.80  | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 234.33/43.80  | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | BETA: splitting (9348) gives:
% 234.33/43.80  | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | |   (9349)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.33/43.80  | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.33/43.80  | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.33/43.80  | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.33/43.80  | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.33/43.80  | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.33/43.80  | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.33/43.80  | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.33/43.80  | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.33/43.80  | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.33/43.80  | | | | | | | | | | | | | | |             = e2)
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | BETA: splitting (9349) gives:
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | |   (9350)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.33/43.80  | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 234.33/43.80  | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 234.33/43.80  | | | | | | | | | | | | | | | |             e2) = e2
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | ALPHA: (9350) implies:
% 234.33/43.80  | | | | | | | | | | | | | | | |   (9351)  op(e2, e1) = e2
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9341), (9351), (function-axioms) are
% 234.33/43.80  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | |   (9352)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.33/43.80  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.33/43.80  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 234.33/43.80  | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 234.33/43.80  | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.33/43.80  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.33/43.80  | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | BETA: splitting (9352) gives:
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | |   (9353)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.33/43.80  | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 234.33/43.80  | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 234.33/43.80  | | | | | | | | | | | | | | | | |             e2) = e1
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | ALPHA: (9353) implies:
% 234.33/43.80  | | | | | | | | | | | | | | | | |   (9354)   ~ (all_56_11 = e2)
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | REDUCE: (9338), (9354) imply:
% 234.33/43.80  | | | | | | | | | | | | | | | | |   (9355)  $false
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | CLOSE: (9355) is inconsistent.
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | |   (9356)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 234.33/43.80  | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 234.33/43.80  | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 234.33/43.80  | | | | | | | | | | | | | | | | |             e2) = e2
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | ALPHA: (9356) implies:
% 234.33/43.80  | | | | | | | | | | | | | | | | |   (9357)  op(e2, e0) = e2
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 234.33/43.80  | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (9357) gives:
% 234.33/43.80  | | | | | | | | | | | | | | | | |   (9358)  all_52_13 = e2
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | REDUCE: (9342), (9358) imply:
% 234.33/43.80  | | | | | | | | | | | | | | | | |   (9359)  $false
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | | CLOSE: (9359) is inconsistent.
% 234.33/43.80  | | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | End of split
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | Case 2:
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | |   (9360)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.33/43.80  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.33/43.80  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 234.33/43.80  | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 234.33/43.80  | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.33/43.80  | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.33/43.80  | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 234.33/43.80  | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 234.33/43.80  | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.33/43.80  | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 234.33/43.80  | | | | | | | | | | | | | | |             = e0)
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | BETA: splitting (9360) gives:
% 234.33/43.80  | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | Case 1:
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | |   (9361)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.33/43.80  | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 234.33/43.80  | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 234.33/43.80  | | | | | | | | | | | | | | | |             e2) = e0
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.80  | | | | | | | | | | | | | | | | ALPHA: (9361) implies:
% 234.33/43.80  | | | | | | | | | | | | | | | |   (9362)   ~ (all_56_11 = e2)
% 234.33/43.80  | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | REDUCE: (9338), (9362) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | |   (9363)  $false
% 234.33/43.81  | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | CLOSE: (9363) is inconsistent.
% 234.33/43.81  | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | |   (9364)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 234.33/43.81  | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 234.33/43.81  | | | | | | | | | | | | | | | |               e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 234.33/43.81  | | | | | | | | | | | | | | | |             op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 234.33/43.81  | | | | | | | | | | | | | | | |             e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 234.33/43.81  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 234.33/43.81  | | | | | | | | | | | | | | | |             op(e1, e0) = e0 & op(e0, e1) = e0)
% 234.33/43.81  | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | BETA: splitting (9364) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9365)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 234.33/43.81  | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 234.33/43.81  | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 234.33/43.81  | | | | | | | | | | | | | | | | |             e1) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | ALPHA: (9365) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9366)   ~ (all_56_31 = e0)
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9367)   ~ (all_56_21 = e0)
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9368)   ~ (all_56_11 = e0)
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9369)   ~ (all_56_1 = e0)
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9370)  op(e0, e1) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9371)  op(e1, e0) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 234.33/43.81  | | | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (157), (9370) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9372)  all_52_11 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 234.33/43.81  | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (9371) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9373)  all_52_14 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | REDUCE: (125), (9372) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9374)   ~ (all_52_7 = e1)
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | REDUCE: (110), (9373) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9375)   ~ (all_52_13 = e1)
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | REDUCE: (9317), (9373) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9376)   ~ (e3 = e1)
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | |   (9377)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 234.33/43.81  | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | BETA: splitting (9377) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |   (9378)  all_58_9 = e1 & op(e3, e0) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7009), (9378), (function-axioms) are
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |   (9379)  all_58_10 = e1 & op(e2, e0) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9375), (9379), (function-axioms) are
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | |   (9380)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 234.33/43.81  | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | BETA: splitting (9380) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |   (9381)  all_58_11 = e1 & op(e1, e0) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | ALPHA: (9381) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |   (9382)  all_58_11 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | |   (9383)  all_54_13 = e3
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (9313), (9383) are inconsistent by
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | |   (9384)   ~ (all_54_13 = e3)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | |   (9385)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | |   (9386)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9386) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |   (9387)  all_58_12 = e1 & op(e0, e3) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7006), (9387), (function-axioms) are
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |   (9388)  all_58_13 = e1 & op(e0, e2) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9374), (9388), (function-axioms) are
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | |   (9389)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9389) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |   (9390)  all_58_14 = e1 & op(e0, e1) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9390) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |   (9391)  all_58_14 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | |   (9392)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9392) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | |   (9393)  all_58_12 = e2 & op(e0, e3) = e2
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9393) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | |   (9394)  all_58_12 = e2
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (9395)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (7007), (9344), (9395),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | |            #2142.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (9396)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9396) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9397)  all_58_7 = e1 & op(e1, e2) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9397) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9398)  all_58_7 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9399)  all_54_7 = e3
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (9316), (9399) are inconsistent by
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9400)   ~ (all_54_7 = e3)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9401)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9402)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9402) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9403)  all_58_6 = e3 & op(e1, e3) = e3
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9403) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9404)  all_58_6 = e3
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9401) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9405)  all_54_7 = e2
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (9342), (9405) are inconsistent by
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1997.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9406)   ~ (all_54_7 = e2)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9407)  all_54_7 = e1 | all_54_7 = e0
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9407) gives:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9408)  all_54_7 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (9375), (9408) are inconsistent by
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9409)  all_54_7 = e0
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (9409) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9410)  all_52_13 = e0
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9410) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9411)  all_52_13 = e0
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (9411) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9412)   ~ (all_52_1 = e0)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9316), (9411) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9413)   ~ (e3 = e0)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9342), (9411) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9414)   ~ (e2 = e0)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9375), (9411) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9415)   ~ (e1 = e0)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (167), (239), (7010), (9394),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9404), (9412), (function-axioms) are inconsistent
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1271.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9416)  all_58_7 = e3 & op(e1, e2) = e3
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9416) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9417)  all_58_7 = e3
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9398), (9417) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9418)  e3 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9323), (9418) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9419)  all_58_15 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (158), (219), (9313), (9391), (9394),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9419), (function-axioms) are inconsistent by
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1814.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9420)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (160), (223), (225),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9317), (9371), (9382), (9398), (9420),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1418.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9421)  all_58_13 = e1 & op(e0, e2) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9374), (9421), (function-axioms) are
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | |   (9422)  all_58_13 = e2 & op(e0, e2) = e2
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9422) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | |   (9423)  op(e0, e2) = e2
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (256), (9340), (9374), (9385), (9423),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | |            #1817.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | |   (9424)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (9324), (9391), (9424),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | |            #1037.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |   (9425)  all_58_15 = e1 & op(e0, e0) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9425) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |   (9426)  all_58_15 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9323), (9426) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |   (9427)  e3 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9311), (9427) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |   (9428)  all_56_31 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (39), (42), (123), (126), (148),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |            (158), (159), (160), (162), (164), (165), (167),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (194), (199), (213), (218),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (227), (230), (231), (232),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (238), (266), (275),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |            (297), (375), (381), (391), (392), (7004), (7007),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |            (9326), (9328), (9330), (9374), (9375), (9426),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |            (9428), (function-axioms) are inconsistent by
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1830.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |   (9429)  all_58_15 = e1 & op(e0, e0) = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | ALPHA: (9429) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |   (9430)  all_58_15 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9323), (9430) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |   (9431)  e3 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | SIMP: (9431) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |   (9432)  e3 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9311), (9432) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |   (9433)  all_56_31 = e1
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (39), (42), (123), (126), (148),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |            (158), (159), (160), (162), (164), (165), (167),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (194), (199), (213), (218),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (227), (230), (231), (232),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (238), (266), (275),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |            (297), (375), (381), (391), (392), (7004), (7007),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |            (9326), (9328), (9330), (9374), (9375), (9430),
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |            (9433), (function-axioms) are inconsistent by
% 234.33/43.81  | | | | | | | | | | | | | | | | | | |            sub-proof #1830.
% 234.33/43.81  | | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9434)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 234.33/43.81  | | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 234.33/43.81  | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 234.33/43.81  | | | | | | | | | | | | | | | | |             e1) = e0
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | ALPHA: (9434) implies:
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9435)   ~ (all_56_1 = e1)
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | REDUCE: (7003), (9435) imply:
% 234.33/43.81  | | | | | | | | | | | | | | | | |   (9436)  $false
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | | CLOSE: (9436) is inconsistent.
% 234.33/43.81  | | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | |   (9437)  all_54_5 = e1 | all_54_5 = e0
% 234.33/43.81  | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | | REF_CLOSE: (275), (9326), (9330), (9437) are inconsistent by
% 234.33/43.81  | | | | | | | | | | | | |            sub-proof #2300.
% 234.33/43.81  | | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | End of split
% 234.33/43.81  | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | Case 2:
% 234.33/43.81  | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | |   (9438)  all_22_2 = e1
% 234.33/43.81  | | | | | | | | | | |   (9439)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 234.33/43.81  | | | | | | | | | | |             & op(e2, e1) = all_22_1 & $i(all_22_0) &
% 234.33/43.81  | | | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1)
% 234.33/43.81  | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 234.33/43.81  | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | COMBINE_EQS: (326), (9438) imply:
% 234.33/43.81  | | | | | | | | | | |   (9440)  all_8_2 = e1
% 234.33/43.81  | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | SIMP: (9440) implies:
% 234.33/43.81  | | | | | | | | | | |   (9441)  all_8_2 = e1
% 234.33/43.81  | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | COMBINE_EQS: (347), (9441) imply:
% 234.33/43.81  | | | | | | | | | | |   (9442)  all_30_2 = e1
% 234.33/43.81  | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | COMBINE_EQS: (353), (9441) imply:
% 234.33/43.81  | | | | | | | | | | |   (9443)  all_56_11 = e1
% 234.33/43.81  | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | REDUCE: (373), (9441) imply:
% 234.33/43.81  | | | | | | | | | | |   (9444)   ~ (all_52_7 = e1)
% 234.33/43.81  | | | | | | | | | | | 
% 234.33/43.81  | | | | | | | | | | | REDUCE: (377), (9441) imply:
% 234.40/43.81  | | | | | | | | | | |   (9445)   ~ (all_52_13 = e1)
% 234.40/43.81  | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | REDUCE: (392), (9441) imply:
% 234.40/43.81  | | | | | | | | | | |   (9446)   ~ (e3 = e1)
% 234.40/43.81  | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | REDUCE: (42), (9441) imply:
% 234.40/43.81  | | | | | | | | | | |   (9447)  op(e2, e2) = e1
% 234.40/43.81  | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | BETA: splitting (220) gives:
% 234.40/43.81  | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | Case 1:
% 234.40/43.81  | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | |   (9448)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 234.40/43.81  | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 234.40/43.81  | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | BETA: splitting (9448) gives:
% 234.40/43.81  | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | Case 1:
% 234.40/43.81  | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | |   (9449)  all_58_9 = e1 & op(e3, e0) = e1
% 234.40/43.81  | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | REF_CLOSE: (168), (7009), (9449), (function-axioms) are
% 234.40/43.81  | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 234.40/43.81  | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | Case 2:
% 234.40/43.81  | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | |   (9450)  all_58_10 = e1 & op(e2, e0) = e1
% 234.40/43.81  | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | REF_CLOSE: (164), (9445), (9450), (function-axioms) are
% 234.40/43.81  | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 234.40/43.81  | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | End of split
% 234.40/43.81  | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | Case 2:
% 234.40/43.81  | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | |   (9451)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 234.40/43.81  | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 234.40/43.81  | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | BETA: splitting (9451) gives:
% 234.40/43.81  | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | Case 1:
% 234.40/43.81  | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | |   (9452)  all_58_11 = e1 & op(e1, e0) = e1
% 234.40/43.81  | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | ALPHA: (9452) implies:
% 234.40/43.81  | | | | | | | | | | | | |   (9453)  all_58_11 = e1
% 234.40/43.81  | | | | | | | | | | | | |   (9454)  op(e1, e0) = e1
% 234.40/43.81  | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | BETA: splitting (217) gives:
% 234.40/43.81  | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | Case 1:
% 234.40/43.81  | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | |   (9455)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 234.40/43.81  | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 234.40/43.81  | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | BETA: splitting (9455) gives:
% 234.40/43.81  | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | Case 1:
% 234.40/43.81  | | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | |   (9456)  all_58_12 = e1 & op(e0, e3) = e1
% 234.40/43.81  | | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | | REF_CLOSE: (159), (7006), (9456), (function-axioms) are
% 234.40/43.81  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 234.40/43.81  | | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | Case 2:
% 234.40/43.81  | | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | |   (9457)  all_58_13 = e1 & op(e0, e2) = e1
% 234.40/43.81  | | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | | REF_CLOSE: (158), (9444), (9457), (function-axioms) are
% 234.40/43.81  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 234.40/43.81  | | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | End of split
% 234.40/43.81  | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | Case 2:
% 234.40/43.81  | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | |   (9458)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 234.40/43.81  | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 234.40/43.81  | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | BETA: splitting (9458) gives:
% 234.40/43.81  | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | Case 1:
% 234.40/43.81  | | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | |   (9459)  all_58_14 = e1 & op(e0, e1) = e1
% 234.40/43.81  | | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | | ALPHA: (9459) implies:
% 234.40/43.81  | | | | | | | | | | | | | | |   (9460)  all_58_14 = e1
% 234.40/43.81  | | | | | | | | | | | | | | |   (9461)  op(e0, e1) = e1
% 234.40/43.81  | | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 234.40/43.81  | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (157), (9461) gives:
% 234.40/43.81  | | | | | | | | | | | | | | |   (9462)  all_52_11 = e1
% 234.40/43.81  | | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 234.40/43.81  | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (9454) gives:
% 234.40/43.81  | | | | | | | | | | | | | | |   (9463)  all_52_14 = e1
% 234.40/43.81  | | | | | | | | | | | | | | | 
% 234.40/43.81  | | | | | | | | | | | | | | | REDUCE: (126), (9463) imply:
% 234.40/43.82  | | | | | | | | | | | | | | |   (9464)   ~ (all_52_6 = e1)
% 234.40/43.82  | | | | | | | | | | | | | | | 
% 234.40/43.82  | | | | | | | | | | | | | | | REDUCE: (118), (9462) imply:
% 234.40/43.82  | | | | | | | | | | | | | | |   (9465)   ~ (all_52_9 = e1)
% 234.40/43.82  | | | | | | | | | | | | | | | 
% 234.40/43.82  | | | | | | | | | | | | | | | REDUCE: (385), (9463) imply:
% 234.40/43.82  | | | | | | | | | | | | | | |   (9466)   ~ (all_6_2 = e1)
% 234.40/43.82  | | | | | | | | | | | | | | | 
% 234.40/43.82  | | | | | | | | | | | | | | | SIMP: (9466) implies:
% 234.40/43.82  | | | | | | | | | | | | | | |   (9467)   ~ (all_6_2 = e1)
% 234.40/43.82  | | | | | | | | | | | | | | | 
% 234.40/43.82  | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | |   (9468)  all_54_10 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (9468) are inconsistent by sub-proof
% 234.41/43.82  | | | | | | | | | | | | | | | |            #2313.
% 234.41/43.82  | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | |   (9469)   ~ (all_54_10 = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | |   (9470)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | BETA: splitting (9470) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | |   (9471)  all_54_10 = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (9471) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | |   (9472)  all_6_2 = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | SIMP: (9472) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | |   (9473)  all_6_2 = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (9473) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | |   (9474)  all_36_2 = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (9473) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | |   (9475)  all_40_2 = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | REDUCE: (378), (9473) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | |   (9476)   ~ (all_52_6 = e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | REDUCE: (380), (9473) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | |   (9477)   ~ (all_52_8 = e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | REDUCE: (381), (9473) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | |   (9478)   ~ (all_52_9 = e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | REDUCE: (391), (9473) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | |   (9479)   ~ (e3 = e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | REDUCE: (39), (9473) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | |   (9480)  op(e1, e1) = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | |   (9481)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | BETA: splitting (9481) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | |   (9482)  all_58_6 = e2 & op(e1, e3) = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | ALPHA: (9482) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | |   (9483)  all_58_6 = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (160), (223), (226), (9317),
% 234.41/43.82  | | | | | | | | | | | | | | | | | | |            (9454), (9480), (9483), (function-axioms) are
% 234.41/43.82  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1406.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | |   (9484)  all_58_7 = e2 & op(e1, e2) = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | ALPHA: (9484) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | |   (9485)  all_58_7 = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (160), (223), (226), (9317),
% 234.41/43.82  | | | | | | | | | | | | | | | | | | |            (9454), (9480), (9485), (function-axioms) are
% 234.41/43.82  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1263.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.82  | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | |   (9486)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 234.41/43.82  | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | BETA: splitting (9486) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | |   (9487)  all_58_8 = e2 & op(e1, e1) = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | ALPHA: (9487) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | |   (9488)  all_58_8 = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | |   (9489)   ~ (all_26_2 = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | REDUCE: (9310), (9489) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | |   (9490)  $false
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | CLOSE: (9490) is inconsistent.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | |   (9491)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | |             & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | |             $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | |             = all_26_1 & $i(all_26_1))
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | |   (9492)   ~ (all_30_2 = e1)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (9442), (9492) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | |   (9493)  $false
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | CLOSE: (9493) is inconsistent.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | |   (9494)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_30_1 & $i(all_30_0) &
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | |   (9495)   ~ (all_36_2 = e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9474), (9495) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | |   (9496)  $false
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9496) is inconsistent.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | |   (9497)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | |   (9498)   ~ (all_40_2 = e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9475), (9498) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | |   (9499)  $false
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9499) is inconsistent.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | |   (9500)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | |             = all_40_1 & $i(all_40_1))
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | |   (9501)  all_54_3 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (9315), (9501) are inconsistent by
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | |   (9502)   ~ (all_54_3 = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | |   (9503)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (9504)  all_54_7 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (9316), (9504) are inconsistent by
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (9505)   ~ (all_54_7 = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (9506)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9507)  all_54_6 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (9507) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9508)  all_52_9 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (9508) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9509)   ~ (all_52_1 = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (9508) imply:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9510)   ~ (all_52_8 = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9511)  all_54_2 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (9510), (9511) are inconsistent by
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9512)   ~ (all_54_2 = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9513)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9514)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9514) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9515)  all_58_4 = e3 & op(e3, e1) = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9515) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9516)  op(e3, e1) = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9510), (9516), (function-axioms) are
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9517)  all_58_5 = e3 & op(e2, e1) = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9517) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9518)  all_58_5 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9519)  op(e2, e1) = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9439) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9520)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_22_1 & $i(all_22_0) &
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9520) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9521)   ~ (all_22_0 = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9522)  op(e2, e1) = all_22_1
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9523)  op(all_22_1, e2) = all_22_0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9524)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9524) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9525)  all_58_4 = e0 & op(e3, e1) = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9525) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9526)  op(e3, e1) = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (168), (246), (7010), (9315), (9494),
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9519), (9521), (9522), (9523), (9526),
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1378.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9527)  all_58_5 = e0 & op(e2, e1) = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9527) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9528)  all_58_5 = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9518), (9528) are inconsistent by sub-proof
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2038.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9529)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9461), (9480), (9529),
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1036.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9530)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9530) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9531)   ~ (all_22_1 = e0)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9532)  op(e2, e1) = all_22_1
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9533)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9533) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9534)  all_58_4 = e0 & op(e3, e1) = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9534) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9535)  all_58_4 = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9536)  op(e3, e1) = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9537)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (7010), (9509), (9537),
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1208.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9538)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9538) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9539)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9539) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9540)  all_58_6 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9541)  op(e1, e3) = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9542)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9542) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9543)  all_58_0 = e3 & op(e3, e3) = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9543) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9544)  op(e3, e3) = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7010), (9544), (function-axioms) are
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1578.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9545)  all_58_1 = e3 & op(e3, e2) = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9545) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9546)  all_58_1 = e3
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9547)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (9447), (9546), (9547),
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1322.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9548)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9548) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9549)  all_58_7 = e2 & op(e1, e2) = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9549) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9550)  all_58_7 = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (223), (224), (9480),
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9488), (9540), (9550), (function-axioms) are
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1801.
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9551)  all_58_13 = e2 & op(e0, e2) = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9551) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9552)  op(e0, e2) = e2
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9494) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9553)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_30_1 & $i(all_30_0) &
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9553) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9554)  op(e2, e1) = all_30_1
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9555)  all_58_15 = e0 & op(e0, e0) = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9555) implies:
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9556)  op(e0, e0) = e0
% 234.41/43.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9324), (9556), (function-axioms) are
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9557)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9557) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9558)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9513) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9559)  all_54_2 = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (9477), (9559) are inconsistent by
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1986.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9560)  all_54_2 = e1 | all_54_2 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9561)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (7010), (9546), (9561),
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1132.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9562)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9562) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9563)  all_58_4 = e2 & op(e3, e1) = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9563) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9564)  all_58_4 = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9535), (9564) are inconsistent by sub-proof
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1666.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9565)  all_58_9 = e2 & op(e3, e0) = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9565) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9566)  all_58_9 = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9558) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9567)  all_58_12 = e0 & op(e0, e3) = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9567) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9568)  all_58_12 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9569)  op(e0, e3) = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9570)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9570) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9571)  all_58_0 = e2 & op(e3, e3) = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9571) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9572)  op(e3, e3) = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7010), (9572), (function-axioms) are
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9573)  all_58_2 = e2 & op(e2, e3) = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9573) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9574)  op(e2, e3) = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9560) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9575)  all_54_2 = e1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (7008), (9575) are inconsistent by
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1337.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9576)  all_54_2 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (9576) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9577)  all_52_8 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9577) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9578)  all_52_8 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (9578) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9579)   ~ (all_52_4 = e0)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (9578) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9580)   ~ (all_52_12 = e0)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9580) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9581)   ~ (all_52_12 = e0)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7008), (9578) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9582)   ~ (e1 = e0)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9503) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9583)  all_54_3 = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (9583) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9584)  all_52_12 = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9584) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9585)  all_52_12 = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (9585) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9586)   ~ (all_52_4 = e2)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9587)  all_54_1 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (9587) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9588)  all_52_4 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9588) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9589)  all_52_4 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (9589) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9590)   ~ (all_52_6 = e3)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9590) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9591)   ~ (all_52_6 = e3)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (9589) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9592)   ~ (all_52_7 = e3)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9593)  all_54_9 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (9591), (9593) are inconsistent by
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9594)   ~ (all_54_9 = e3)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9595)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9596)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_3 & $i(all_56_3))
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9596) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9597)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9597) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9598)  op(e3, all_56_1) = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7003), (9598) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9599)  op(e3, e1) = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9536), (9599), (function-axioms) are
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2118.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9600)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_3 & $i(all_56_3)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9600) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9601)  op(e2, e3) = all_56_3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9602)  op(e2, all_56_3) = e2
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (267), (9447), (9464), (9476), (9574),
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9595), (9601), (9602), (function-axioms) are
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1116.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9603)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_56_7 & $i(all_56_7))
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9603) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9604)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_5 & $i(all_56_5)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9604) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9605)  op(e1, e3) = all_56_5
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9606)  op(e1, all_56_5) = e1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9541), (9605), (9606), (function-axioms) are
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2243.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9607)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           = all_56_7 & $i(all_56_7)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9607) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9608)  op(e0, e3) = all_56_7
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9609)  op(e0, all_56_7) = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9308) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9610)   ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 &
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = all_12_1 & $i(all_12_0) &
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_12_1)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9610) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9611)  op(e0, e3) = all_12_1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9491) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_7,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (9569), (9608) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9612)  all_56_7 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (9532), (9554)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9613)  all_30_1 = all_22_1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (9519), (9554) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9614)  all_30_1 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9613), (9614) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9615)  all_22_1 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9615) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9616)  all_22_1 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9609), (9612) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9617)  op(e0, e0) = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (157), (158),
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (219), (226), (239), (241), (243),
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (9313), (9314), (9317), (9591), (9617),
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1035.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9618)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 &
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_26_1)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9618) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9619)   ~ (all_26_1 = e1)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9620)  op(e0, e3) = all_26_1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_26_1, e3, e0, simplifying with (9611), (9620)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9621)  all_26_1 = all_12_1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (9608), (9620)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9622)  all_56_7 = all_26_1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_7,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (9569), (9608) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9623)  all_56_7 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (9532), (9554)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9624)  all_30_1 = all_22_1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (9519), (9554) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9625)  all_30_1 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9622), (9623) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9626)  all_26_1 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9626) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9627)  all_26_1 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9624), (9625) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9628)  all_22_1 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9628) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9629)  all_22_1 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9621), (9627) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9630)  all_12_1 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9609), (9623) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9631)  op(e0, e0) = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (157), (158),
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (219), (226), (239), (241), (243),
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (9313), (9314), (9317), (9591), (9631),
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1035.
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9632)   ~ (all_12_1 = e2) & op(e0, e3) = all_12_1 &
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_12_1)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9632) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9633)   ~ (all_12_1 = e2)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9634)  op(e0, e3) = all_12_1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9491) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9635)   ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e3) = all_26_1 & $i(all_26_0) &
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_26_1)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9635) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9636)  op(e0, e3) = all_26_1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_26_1, e3, e0, simplifying with (9634), (9636)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9637)  all_26_1 = all_12_1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (9608), (9636)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9638)  all_56_7 = all_26_1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_7,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (9569), (9608) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9639)  all_56_7 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (9532), (9554)
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9640)  all_30_1 = all_22_1
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (9519), (9554) gives:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9641)  all_30_1 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9638), (9639) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9642)  all_26_1 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9642) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9643)  all_26_1 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9640), (9641) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9644)  all_22_1 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9644) implies:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9645)  all_22_1 = e3
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9637), (9643) imply:
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9646)  all_12_1 = e0
% 234.41/43.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (157), (158), (160),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (219), (226), (239), (241), (243), (391),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9313), (9314), (9317), (9531), (9591), (9609),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9633), (9639), (9645), (9646), (function-axioms)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1034.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9647)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 &
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_26_1)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9647) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9648)   ~ (all_26_1 = e1)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9649)  op(e0, e3) = all_26_1
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1,
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_26_1, e3, e0, simplifying with (9634), (9649)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9650)  all_26_1 = all_12_1
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1,
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (9608), (9649)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9651)  all_56_7 = all_26_1
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_7,
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (9569), (9608) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9652)  all_56_7 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (9532), (9554)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9653)  all_30_1 = all_22_1
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (9519), (9554) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9654)  all_30_1 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9651), (9652) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9655)  all_26_1 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9655) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9656)  all_26_1 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9653), (9654) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9657)  all_22_1 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9657) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9658)  all_22_1 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9650), (9656) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9659)  all_12_1 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (157), (158), (160),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (219), (226), (239), (241), (243), (391),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9313), (9314), (9317), (9531), (9591), (9609),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9633), (9652), (9658), (9659), (function-axioms)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1034.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9660)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (7007), (9579), (9586), (9660) are
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2048.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9661)  all_54_3 = e1 | all_54_3 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (7009), (9581), (9661) are inconsistent by
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2287.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9662)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9662) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9663)  all_58_6 = e2 & op(e1, e3) = e2
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9540), (9663) are inconsistent by sub-proof
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2219.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9664)  all_58_12 = e2 & op(e0, e3) = e2
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9664) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9665)  all_58_12 = e2
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9568), (9665) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9666)  e2 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9666) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9667)  e2 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9566), (9667) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9668)  all_58_9 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (7010),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9535), (9668), (function-axioms) are inconsistent
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1190.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9669)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9669) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9670)  all_58_13 = e0 & op(e0, e2) = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9670) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9671)  op(e0, e2) = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9552), (9671), (function-axioms) are
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9672)  all_58_14 = e0 & op(e0, e1) = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9672) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9673)  all_58_14 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9674)  op(e0, e1) = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (228),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (391), (7008), (9535), (9673),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9674), (function-axioms) are inconsistent by
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1242.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9675)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9675) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9676)   ~ (all_30_1 = e3)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9677)  op(e2, e1) = all_30_1
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9519), (9676), (9677), (function-axioms) are
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1839.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9678)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (9315), (9536), (9678),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1379.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9679)  all_58_12 = e3 & op(e0, e3) = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9679) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9680)  all_58_12 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (218), (9323),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9460), (9680), (function-axioms) are inconsistent
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1031.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9681)  all_58_5 = e0 & op(e2, e1) = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9681) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9682)  op(e2, e1) = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9494), (9531), (9532), (9682), (function-axioms)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1356.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9683)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9461), (9480), (9683),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1036.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9684)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (9314), (9480), (9684),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1307.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9685)   ~ (all_54_6 = e3)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9686)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (9685) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9687)   ~ (all_52_9 = e3)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9686) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9688)  all_54_6 = e2
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (9688) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9689)  all_52_9 = e2
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9478), (9689) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9690)  $false
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9690) is inconsistent.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9691)   ~ (all_54_6 = e2)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9692)  all_54_6 = e1 | all_54_6 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9693)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9693) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9694)  all_58_4 = e3 & op(e3, e1) = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9694) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9695)  all_58_4 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9692) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9696)  all_54_6 = e1
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (9696) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9697)  all_52_9 = e1
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9465), (9697) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9698)  $false
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9698) is inconsistent.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9699)  all_54_6 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (9699) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9700)  all_52_9 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (9700) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9701)   ~ (all_52_8 = e0)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (9700) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9702)   ~ (all_52_13 = e0)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9702) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9703)   ~ (all_52_13 = e0)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9478), (9700) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9704)   ~ (e2 = e0)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9465), (9700) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9705)   ~ (e1 = e0)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (9700) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9706)  op(e2, e1) = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9707)  all_54_2 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (9707) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9708)  all_52_8 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9708) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9709)  all_52_8 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (9709) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9710)   ~ (all_52_4 = e3)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (9709) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9711)   ~ (all_52_12 = e3)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9712)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (167), (170),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (229), (232), (240), (244), (246), (7004),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (9445), (9460), (9695), (9710), (9712),
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1028.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9713)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9713) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9714)  all_58_7 = e3 & op(e1, e2) = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9714) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9715)  all_58_7 = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9716)  op(e1, e2) = e3
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9506) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9717)  all_54_7 = e2
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (9717) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9718)  all_52_13 = e2
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (9718) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9719)   ~ (all_52_12 = e2)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9503) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9720)  all_54_3 = e2
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (9719), (9720) are inconsistent by
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2290.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9721)   ~ (all_54_3 = e2)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9722)  all_54_3 = e1 | all_54_3 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9722) gives:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9723)  all_54_3 = e1
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (7009), (9723) are inconsistent by
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2289.
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9724)  all_54_3 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (9724) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9725)  all_52_12 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9725) implies:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9726)  all_52_12 = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (9726) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9727)   ~ (all_52_4 = e0)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9315), (9726) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9728)   ~ (e3 = e0)
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (9726) imply:
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9729)  op(e3, e0) = e0
% 234.41/43.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9730)  all_54_1 = e3
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (9710), (9730) are inconsistent by
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9731)   ~ (all_54_1 = e3)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9732)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9733)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9733) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9734)  all_58_0 = e2 & op(e3, e3) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9734) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9735)  op(e3, e3) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7010), (9735), (function-axioms) are
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9736)  all_58_1 = e2 & op(e3, e2) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9736) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9737)  all_58_1 = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9738)  op(e3, e2) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9739)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9739) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9740)  all_58_0 = e2 & op(e3, e3) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9740) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9741)  op(e3, e3) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (240), (242), (9695),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9737), (9741), (function-axioms) are inconsistent
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2180.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9742)  all_58_2 = e2 & op(e2, e3) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9742) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9743)  op(e2, e3) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (197), (269), (9316), (9445),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9703), (9743), (function-axioms) are inconsistent
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2291.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9744)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9744) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9745)  all_58_6 = e2 & op(e1, e3) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9745) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9746)  all_58_6 = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9747)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (7010), (9727), (9747),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1066.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9748)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9748) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9749)  all_58_4 = e0 & op(e3, e1) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9701), (9749), (function-axioms) are
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9750)  all_58_9 = e0 & op(e3, e0) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9750) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9751)  all_58_9 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9752)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9752) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9753)  all_58_6 = e0 & op(e1, e3) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9753) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9754)  all_58_6 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9746), (9754) imply:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9755)  e2 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9755) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9756)  e2 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9737), (9756) imply:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9757)  all_58_1 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (244), (7010), (9695), (9751),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9757), (function-axioms) are inconsistent by
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1097.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9758)  all_58_7 = e0 & op(e1, e2) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (7010),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9695), (9715), (9751), (9758), (function-axioms)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1027.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9759)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9759) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9760)  all_58_8 = e0 & op(e1, e1) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9760) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9761)  op(e1, e1) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (165), (228), (229),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9695), (9706), (9761), (function-axioms) are
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1025.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9762)  all_58_11 = e0 & op(e1, e0) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9762) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9763)  op(e1, e0) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9454), (9763), (function-axioms) are
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2284.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9764)  all_58_12 = e2 & op(e0, e3) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9764) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9765)  op(e0, e3) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9766)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (7010), (9727), (9766),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1066.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9767)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9767) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9768)  all_58_4 = e0 & op(e3, e1) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9701), (9768), (function-axioms) are
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9769)  all_58_9 = e0 & op(e3, e0) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9769) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9770)  all_58_9 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9771)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9771) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9772)  all_58_1 = e0 & op(e3, e2) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9772) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9773)  all_58_1 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (244), (7010), (9695), (9770),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9773), (function-axioms) are inconsistent by
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1097.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9774)  all_58_3 = e0 & op(e2, e2) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (9326), (9774), (function-axioms) are
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9775)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9775) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9776)  all_58_7 = e0 & op(e1, e2) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (7010),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9695), (9715), (9770), (9776), (function-axioms)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1027.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9777)  all_58_13 = e0 & op(e0, e2) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9777) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9778)  op(e0, e2) = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9497) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9779)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e2) = all_36_1 & $i(all_36_0) &
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9779) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9780)  op(e1, e2) = all_36_1
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (170), (197), (212), (269),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (7005), (7007), (9308), (9316), (9324),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9443), (9445), (9491), (9500), (9703), (9706),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9710), (9716), (9727), (9732), (9738), (9765),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9778), (9780), (function-axioms) are inconsistent
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1021.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9781)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9781) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9782)  op(e1, e2) = all_36_1
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (170), (197), (212), (269),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (7005), (7007), (9308), (9316), (9324),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9443), (9445), (9491), (9500), (9703), (9706),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9710), (9716), (9727), (9732), (9738), (9765),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9778), (9782), (function-axioms) are inconsistent
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1021.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9783)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9783) gives:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9784)  all_58_4 = e2 & op(e3, e1) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9695), (9784) are inconsistent by sub-proof
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1476.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9785)  all_58_9 = e2 & op(e3, e0) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9785) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9786)  op(e3, e0) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9729), (9786), (function-axioms) are
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9787)  all_54_7 = e1 | all_54_7 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (9445), (9703), (9787) are inconsistent by
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2293.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9788)  all_58_13 = e3 & op(e0, e2) = e3
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9788) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9789)  op(e0, e2) = e3
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9439), (9494), (9706), (9789), (function-axioms)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1110.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9790)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (7008), (9477), (9701), (9790) are
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1335.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9791)  all_58_5 = e3 & op(e2, e1) = e3
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9687), (9791), (function-axioms) are
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9792)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (9314), (9480), (9792),
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1307.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | |   (9793)  all_58_11 = e2 & op(e1, e0) = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | ALPHA: (9793) implies:
% 234.41/43.85  | | | | | | | | | | | | | | | | | | |   (9794)  all_58_11 = e2
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9453), (9794) are inconsistent by sub-proof
% 234.41/43.85  | | | | | | | | | | | | | | | | | | |            #1020.
% 234.41/43.85  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | |   (9795)  all_54_10 = e1 | all_54_10 = e0
% 234.41/43.85  | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (9328), (9467), (9795) are inconsistent by
% 234.41/43.85  | | | | | | | | | | | | | | | | |            sub-proof #2282.
% 234.41/43.85  | | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | End of split
% 234.41/43.85  | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | Case 2:
% 234.41/43.85  | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | |   (9796)  all_58_15 = e1 & op(e0, e0) = e1
% 234.41/43.85  | | | | | | | | | | | | | | | 
% 234.41/43.85  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9323), (9796) are inconsistent by sub-proof
% 234.41/43.86  | | | | | | | | | | | | | | |            #1393.
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | |   (9797)  all_58_15 = e1 & op(e0, e0) = e1
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | REF_CLOSE: (8), (9323), (9797) are inconsistent by sub-proof
% 234.41/43.86  | | | | | | | | | | | | |            #1393.
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | |   (9798)  all_18_2 = e0
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | COMBINE_EQS: (339), (9798) imply:
% 234.41/43.86  | | | | | | | | | |   (9799)  all_6_2 = e0
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | SIMP: (9799) implies:
% 234.41/43.86  | | | | | | | | | |   (9800)  all_6_2 = e0
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | COMBINE_EQS: (266), (9800) imply:
% 234.41/43.86  | | | | | | | | | |   (9801)  all_56_21 = e0
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | REDUCE: (367), (9800) imply:
% 234.41/43.86  | | | | | | | | | |   (9802)   ~ (all_52_2 = e0)
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | REDUCE: (378), (9800) imply:
% 234.41/43.86  | | | | | | | | | |   (9803)   ~ (all_52_6 = e0)
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | REDUCE: (380), (9800) imply:
% 234.41/43.86  | | | | | | | | | |   (9804)   ~ (all_52_8 = e0)
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | REDUCE: (381), (9800) imply:
% 234.41/43.86  | | | | | | | | | |   (9805)   ~ (all_52_9 = e0)
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | REDUCE: (385), (9800) imply:
% 234.41/43.86  | | | | | | | | | |   (9806)   ~ (all_52_14 = e0)
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | REDUCE: (391), (9800) imply:
% 234.41/43.86  | | | | | | | | | |   (9807)   ~ (e3 = e0)
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | REDUCE: (39), (9800) imply:
% 234.41/43.86  | | | | | | | | | |   (9808)  op(e1, e1) = e0
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | BETA: splitting (64) gives:
% 234.41/43.86  | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | |   (9809)   ~ (all_22_2 = e1)
% 234.41/43.86  | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | REDUCE: (326), (9809) imply:
% 234.41/43.86  | | | | | | | | | | |   (9810)   ~ (all_8_2 = e1)
% 234.41/43.86  | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | BETA: splitting (199) gives:
% 234.41/43.86  | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | |   (9811)  all_54_5 = e3
% 234.41/43.86  | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | COMBINE_EQS: (275), (9811) imply:
% 234.41/43.86  | | | | | | | | | | | |   (9812)  all_8_2 = e3
% 234.41/43.86  | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | REDUCE: (392), (9812) imply:
% 234.41/43.86  | | | | | | | | | | | |   (9813)  $false
% 234.41/43.86  | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | CLOSE: (9813) is inconsistent.
% 234.41/43.86  | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | |   (9814)   ~ (all_54_5 = e3)
% 234.41/43.86  | | | | | | | | | | | |   (9815)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 234.41/43.86  | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | BETA: splitting (9815) gives:
% 234.41/43.86  | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | |   (9816)  all_54_5 = e2
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | COMBINE_EQS: (275), (9816) imply:
% 234.41/43.86  | | | | | | | | | | | | |   (9817)  all_8_2 = e2
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | COMBINE_EQS: (353), (9817) imply:
% 234.41/43.86  | | | | | | | | | | | | |   (9818)  all_56_11 = e2
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | REDUCE: (366), (9817) imply:
% 234.41/43.86  | | | | | | | | | | | | |   (9819)   ~ (all_52_1 = e2)
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | REDUCE: (375), (9817) imply:
% 234.41/43.86  | | | | | | | | | | | | |   (9820)   ~ (all_52_9 = e2)
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | REDUCE: (392), (9817) imply:
% 234.41/43.86  | | | | | | | | | | | | |   (9821)   ~ (e3 = e2)
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | REDUCE: (42), (9817) imply:
% 234.41/43.86  | | | | | | | | | | | | |   (9822)  op(e2, e2) = e2
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | BETA: splitting (213) gives:
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | |   (9823)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.86  | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.86  | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.86  | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.86  | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.86  | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.86  | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.86  | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.86  | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.86  | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 234.41/43.86  | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 234.41/43.86  | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.86  | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 234.41/43.86  | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | BETA: splitting (9823) gives:
% 234.41/43.86  | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | |   (9824)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.86  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.86  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.86  | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.86  | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.86  | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.86  | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.86  | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.86  | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.86  | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.86  | | | | | | | | | | | | | | |             = e3)
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | REF_CLOSE: (167), (7003), (9818), (9819), (9824),
% 234.41/43.86  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.86  | | | | | | | | | | | | | | |            #1213.
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | |   (9825)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.41/43.86  | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.86  | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 234.41/43.86  | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 234.41/43.86  | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.86  | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.86  | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 234.41/43.86  | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 234.41/43.86  | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.41/43.86  | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 234.41/43.86  | | | | | | | | | | | | | | |             = e0)
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (7008), (9311), (9312), (9825),
% 234.41/43.86  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.86  | | | | | | | | | | | | | | |            #1411.
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | |   (9826)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.86  | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.86  | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.86  | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.86  | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.86  | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.86  | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.86  | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.86  | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 234.41/43.86  | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 234.41/43.86  | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 234.41/43.86  | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 234.41/43.86  | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 234.41/43.86  | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 234.41/43.86  | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | BETA: splitting (9826) gives:
% 234.41/43.86  | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | |   (9827)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.86  | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.86  | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.86  | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.86  | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.86  | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.86  | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.86  | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.86  | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.86  | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.86  | | | | | | | | | | | | | | |             = e2)
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | BETA: splitting (9827) gives:
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | |   (9828)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.86  | | | | | | | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 234.41/43.86  | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 234.41/43.86  | | | | | | | | | | | | | | | |             e2) = e2
% 234.41/43.86  | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | ALPHA: (9828) implies:
% 234.41/43.86  | | | | | | | | | | | | | | | |   (9829)  op(e2, e1) = e2
% 234.41/43.86  | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9820), (9829), (function-axioms) are
% 234.41/43.86  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 234.41/43.86  | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | |   (9830)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.41/43.86  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.86  | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 234.41/43.86  | | | | | | | | | | | | | | | |             op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 234.41/43.86  | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.86  | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.86  | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & op(e0, e2) = e2)
% 234.41/43.86  | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | BETA: splitting (9830) gives:
% 234.41/43.86  | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | |   (9831)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.41/43.86  | | | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 234.41/43.86  | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 234.41/43.86  | | | | | | | | | | | | | | | | |             e2) = e1
% 234.41/43.86  | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | ALPHA: (9831) implies:
% 234.41/43.86  | | | | | | | | | | | | | | | | |   (9832)   ~ (all_56_11 = e2)
% 234.41/43.86  | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | REDUCE: (9818), (9832) imply:
% 234.41/43.86  | | | | | | | | | | | | | | | | |   (9833)  $false
% 234.41/43.86  | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | CLOSE: (9833) is inconsistent.
% 234.41/43.86  | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | |   (9834)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 234.41/43.86  | | | | | | | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 234.41/43.86  | | | | | | | | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 234.41/43.86  | | | | | | | | | | | | | | | | |             e2) = e2
% 234.41/43.86  | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | ALPHA: (9834) implies:
% 234.41/43.86  | | | | | | | | | | | | | | | | |   (9835)  op(e2, e0) = e2
% 234.41/43.86  | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 234.41/43.86  | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | |   (9836)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 234.41/43.86  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 234.41/43.86  | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | BETA: splitting (9836) gives:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | |   (9837)  all_58_2 = e0 & op(e2, e3) = e0
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | ALPHA: (9837) implies:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | |   (9838)  all_58_2 = e0
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | |   (9839)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9839) gives:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |   (9840)  all_58_2 = e1 & op(e2, e3) = e1
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7004), (9840), (function-axioms) are
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |   (9841)  all_58_3 = e1 & op(e2, e2) = e1
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9841) implies:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |   (9842)  op(e2, e2) = e1
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9822), (9842), (function-axioms) are
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | |   (9843)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9843) gives:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |   (9844)  all_58_5 = e1 & op(e2, e1) = e1
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9844) implies:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |   (9845)  all_58_5 = e1
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (234), (9822), (9835), (9838),
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |            (9845), (function-axioms) are inconsistent by
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2122.
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |   (9846)  all_58_10 = e1 & op(e2, e0) = e1
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9846) implies:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |   (9847)  op(e2, e0) = e1
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9835), (9847), (function-axioms) are
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1659.
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | |   (9848)  all_58_3 = e0 & op(e2, e2) = e0
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | ALPHA: (9848) implies:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | |   (9849)  op(e2, e2) = e0
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9822), (9849), (function-axioms) are
% 234.41/43.86  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2137.
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | |   (9850)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 234.41/43.86  | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 234.41/43.86  | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | BETA: splitting (9850) gives:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | |   (9851)  all_58_5 = e0 & op(e2, e1) = e0
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9805), (9851), (function-axioms) are
% 234.41/43.86  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | |   (9852)  all_58_10 = e0 & op(e2, e0) = e0
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | ALPHA: (9852) implies:
% 234.41/43.86  | | | | | | | | | | | | | | | | | | |   (9853)  op(e2, e0) = e0
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9835), (9853), (function-axioms) are
% 234.41/43.86  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 234.41/43.86  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | |   (9854)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.41/43.86  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.86  | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 234.41/43.86  | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 234.41/43.86  | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.86  | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.86  | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 234.41/43.86  | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.86  | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.86  | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 234.41/43.86  | | | | | | | | | | | | | | |             = e0)
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | | REF_CLOSE: (160), (9801), (9806), (9818), (9854),
% 234.41/43.86  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.86  | | | | | | | | | | | | | | |            #1319.
% 234.41/43.86  | | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | |   (9855)  all_54_5 = e1 | all_54_5 = e0
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | | REF_CLOSE: (275), (9326), (9810), (9855) are inconsistent by
% 234.41/43.86  | | | | | | | | | | | | |            sub-proof #2300.
% 234.41/43.86  | | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | End of split
% 234.41/43.86  | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | Case 2:
% 234.41/43.86  | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | |   (9856)  all_22_2 = e1
% 234.41/43.86  | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | COMBINE_EQS: (326), (9856) imply:
% 234.41/43.86  | | | | | | | | | | |   (9857)  all_8_2 = e1
% 234.41/43.86  | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | COMBINE_EQS: (353), (9857) imply:
% 234.41/43.86  | | | | | | | | | | |   (9858)  all_56_11 = e1
% 234.41/43.86  | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | REDUCE: (375), (9857) imply:
% 234.41/43.86  | | | | | | | | | | |   (9859)   ~ (all_52_9 = e1)
% 234.41/43.86  | | | | | | | | | | | 
% 234.41/43.86  | | | | | | | | | | | REDUCE: (377), (9857) imply:
% 234.41/43.87  | | | | | | | | | | |   (9860)   ~ (all_52_13 = e1)
% 234.41/43.87  | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | REDUCE: (392), (9857) imply:
% 234.41/43.87  | | | | | | | | | | |   (9861)   ~ (e3 = e1)
% 234.41/43.87  | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | REDUCE: (42), (9857) imply:
% 234.41/43.87  | | | | | | | | | | |   (9862)  op(e2, e2) = e1
% 234.41/43.87  | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | BETA: splitting (224) gives:
% 234.41/43.87  | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | |   (9863)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 234.41/43.87  | | | | | | | | | | | |             & op(e1, e2) = e1)
% 234.41/43.87  | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | BETA: splitting (9863) gives:
% 234.41/43.87  | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | |   (9864)  all_58_6 = e1 & op(e1, e3) = e1
% 234.41/43.87  | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | ALPHA: (9864) implies:
% 234.41/43.87  | | | | | | | | | | | | |   (9865)  op(e1, e3) = e1
% 234.41/43.87  | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | REF_CLOSE: (163), (7005), (9865), (function-axioms) are
% 234.41/43.87  | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 234.41/43.87  | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | |   (9866)  all_58_7 = e1 & op(e1, e2) = e1
% 234.41/43.87  | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | ALPHA: (9866) implies:
% 234.41/43.87  | | | | | | | | | | | | |   (9867)  all_58_7 = e1
% 234.41/43.87  | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.41/43.87  | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | |   (9868)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.41/43.87  | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 234.41/43.87  | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | BETA: splitting (9868) gives:
% 234.41/43.87  | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | |   (9869)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/43.87  | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | ALPHA: (9869) implies:
% 234.41/43.87  | | | | | | | | | | | | | | |   (9870)  all_58_6 = e3
% 234.41/43.87  | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | |   (9871)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 234.41/43.87  | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 234.41/43.87  | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (7008), (9859), (9871),
% 234.41/43.87  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.87  | | | | | | | | | | | | | | | |            #1211.
% 234.41/43.87  | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | |   (9872)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 234.41/43.87  | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 234.41/43.87  | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | BETA: splitting (9872) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | |   (9873)  all_58_8 = e1 & op(e1, e1) = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | ALPHA: (9873) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | |   (9874)  all_58_8 = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | |   (9875)  op(e1, e1) = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (223), (225),
% 234.41/43.87  | | | | | | | | | | | | | | | | |            (9803), (9867), (9870), (9874), (9875),
% 234.41/43.87  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.87  | | | | | | | | | | | | | | | | |            #1269.
% 234.41/43.87  | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | |   (9876)  all_58_14 = e1 & op(e0, e1) = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | ALPHA: (9876) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | |   (9877)  all_58_14 = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | |   (9878)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 234.41/43.87  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | BETA: splitting (9878) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | |   (9879)  all_58_1 = e3 & op(e3, e2) = e3
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | ALPHA: (9879) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | |   (9880)  op(e3, e2) = e3
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | |   (9881)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9881) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | |   (9882)  all_58_6 = e2 & op(e1, e3) = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9870), (9882) are inconsistent by sub-proof
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | |            #2219.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | |   (9883)  all_58_7 = e2 & op(e1, e2) = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9867), (9883) are inconsistent by sub-proof
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | |            #2218.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | |   (9884)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9884) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | |   (9885)  all_58_8 = e2 & op(e1, e1) = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9885) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | |   (9886)  op(e1, e1) = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9808), (9886), (function-axioms) are
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | |   (9887)  all_58_11 = e2 & op(e1, e0) = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9887) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | |   (9888)  all_58_11 = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | |   (9889)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (7010), (9880), (9889),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | |            #1524.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | |   (9890)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9890) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | |   (9891)  all_58_4 = e0 & op(e3, e1) = e0
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9804), (9891), (function-axioms) are
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | |   (9892)  all_58_9 = e0 & op(e3, e0) = e0
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9892) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | |   (9893)  all_58_9 = e0
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | |   (9894)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (42), (244), (246),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | |            (7010), (9326), (9893), (9894), (function-axioms)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1088.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | |   (9895)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9895) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (9896)  all_58_7 = e0 & op(e1, e2) = e0
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9896) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (9897)  all_58_7 = e0
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (9898)  op(e1, e2) = e0
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (162), (224), (225),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | |            (9808), (9870), (9897), (9898), (function-axioms)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1018.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (9899)  all_58_13 = e0 & op(e0, e2) = e0
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9899) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (9900)  op(e0, e2) = e0
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9901)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9901) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9902)  all_58_12 = e2 & op(e0, e3) = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9902) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9903)  all_58_12 = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9904)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9904) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9905)  all_58_9 = e1 & op(e3, e0) = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7009), (9905), (function-axioms) are
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9906)  all_58_10 = e1 & op(e2, e0) = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9860), (9906), (function-axioms) are
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9907)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9907) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9908)  all_58_11 = e1 & op(e1, e0) = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9908) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9909)  all_58_11 = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (42), (117), (123),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (145), (146), (157), (158), (159), (160),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (165), (167), (168), (169),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (197), (198), (202), (213), (216), (218),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (227), (228), (229), (230), (232), (235),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (239), (240), (242), (244), (246),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (281), (7004), (7008), (7010),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9311), (9312), (9313), (9314), (9315), (9316),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9323), (9324), (9326), (9801), (9802), (9803),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9804), (9805), (9806), (9808), (9858), (9859),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9860), (9862), (9877), (9909), (function-axioms)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1009.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9910)  all_58_15 = e1 & op(e0, e0) = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9910) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9911)  all_58_15 = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (158), (219), (9313), (9877), (9903),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9911), (function-axioms) are inconsistent by
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1814.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9912)  all_58_13 = e2 & op(e0, e2) = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9912) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9913)  op(e0, e2) = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9900), (9913), (function-axioms) are
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9914)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9914) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9915)  all_58_14 = e2 & op(e0, e1) = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9915) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9916)  all_58_14 = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9877), (9916) imply:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9917)  e2 = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9888), (9917) imply:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9918)  all_58_11 = e1
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (42), (117), (123),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (145), (146), (157), (158), (159), (160),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (165), (167), (168), (169),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (197), (198), (202), (213), (216), (218),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (227), (228), (229), (230), (232), (235),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (239), (240), (242), (244), (246),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (281), (7004), (7008), (7010),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9311), (9312), (9313), (9314), (9315), (9316),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9323), (9324), (9326), (9801), (9802), (9803),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9804), (9805), (9806), (9808), (9858), (9859),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9860), (9862), (9877), (9918), (function-axioms)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1009.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9919)  all_58_15 = e2 & op(e0, e0) = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9919) implies:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9920)  op(e0, e0) = e2
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9324), (9920), (function-axioms) are
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | |   (9921)  all_58_3 = e3 & op(e2, e2) = e3
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (7004), (9859),
% 234.41/43.87  | | | | | | | | | | | | | | | | | | |            (9860), (9921), (function-axioms) are inconsistent
% 234.41/43.87  | | | | | | | | | | | | | | | | | | |            by sub-proof #2196.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | |   (9922)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 234.41/43.87  | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 234.41/43.87  | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | BETA: splitting (9922) gives:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | |   (9923)  all_58_7 = e3 & op(e1, e2) = e3
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9867), (9923) are inconsistent by sub-proof
% 234.41/43.87  | | | | | | | | | | | | | | | | | | |            #2138.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | |   (9924)  all_58_13 = e3 & op(e0, e2) = e3
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9313), (9924), (function-axioms) are
% 234.41/43.87  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 234.41/43.87  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | Case 2:
% 234.41/43.87  | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | |   (9925)  all_58_7 = e3 & op(e1, e2) = e3
% 234.41/43.87  | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9867), (9925) are inconsistent by sub-proof
% 234.41/43.87  | | | | | | | | | | | | | | |            #2138.
% 234.41/43.87  | | | | | | | | | | | | | | | 
% 234.41/43.87  | | | | | | | | | | | | | | End of split
% 234.41/43.87  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | |   (9926)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 234.41/43.88  | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (9317), (9808), (9926),
% 234.41/43.88  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.88  | | | | | | | | | | | | | |            #1909.
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | |   (9927)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 234.41/43.88  | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 234.41/43.88  | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | BETA: splitting (9927) gives:
% 234.41/43.88  | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | |   (9928)  all_58_8 = e1 & op(e1, e1) = e1
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | ALPHA: (9928) implies:
% 234.41/43.88  | | | | | | | | | | | | |   (9929)  op(e1, e1) = e1
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | REF_CLOSE: (4), (9808), (9929), (function-axioms) are
% 234.41/43.88  | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | |   (9930)  all_58_11 = e1 & op(e1, e0) = e1
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | ALPHA: (9930) implies:
% 234.41/43.88  | | | | | | | | | | | | |   (9931)  all_58_11 = e1
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | BETA: splitting (228) gives:
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | |   (9932)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 234.41/43.88  | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (7008), (9859), (9932),
% 234.41/43.88  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.88  | | | | | | | | | | | | | |            #1211.
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | |   (9933)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 234.41/43.88  | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | BETA: splitting (9933) gives:
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | |   (9934)  all_58_8 = e1 & op(e1, e1) = e1
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | ALPHA: (9934) implies:
% 234.41/43.88  | | | | | | | | | | | | | | |   (9935)  op(e1, e1) = e1
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | REF_CLOSE: (4), (9808), (9935), (function-axioms) are
% 234.41/43.88  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | |   (9936)  all_58_14 = e1 & op(e0, e1) = e1
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | ALPHA: (9936) implies:
% 234.41/43.88  | | | | | | | | | | | | | | |   (9937)  all_58_14 = e1
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (42), (117), (123),
% 234.41/43.88  | | | | | | | | | | | | | | |            (134), (145), (146), (157), (158), (159), (160),
% 234.41/43.88  | | | | | | | | | | | | | | |            (162), (163), (164), (165), (167), (168), (169),
% 234.41/43.88  | | | | | | | | | | | | | | |            (170), (197), (198), (202), (213), (216), (218),
% 234.41/43.88  | | | | | | | | | | | | | | |            (221), (227), (228), (229), (230), (232), (235),
% 234.41/43.88  | | | | | | | | | | | | | | |            (237), (238), (239), (240), (242), (244), (246),
% 234.41/43.88  | | | | | | | | | | | | | | |            (269), (270), (281), (7004), (7008), (7010),
% 234.41/43.88  | | | | | | | | | | | | | | |            (9311), (9312), (9313), (9314), (9315), (9316),
% 234.41/43.88  | | | | | | | | | | | | | | |            (9323), (9324), (9326), (9801), (9802), (9803),
% 234.41/43.88  | | | | | | | | | | | | | | |            (9804), (9805), (9806), (9808), (9858), (9859),
% 234.41/43.88  | | | | | | | | | | | | | | |            (9860), (9862), (9931), (9937), (function-axioms)
% 234.41/43.88  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1009.
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | 
% 234.41/43.88  | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | 
% 234.41/43.88  | | | | | | | | |   (9938)  all_14_2 = e0
% 234.41/43.88  | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | COMBINE_EQS: (344), (9938) imply:
% 234.41/43.88  | | | | | | | | |   (9939)  all_8_2 = e0
% 234.41/43.88  | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | COMBINE_EQS: (353), (9939) imply:
% 234.41/43.88  | | | | | | | | |   (9940)  all_56_11 = e0
% 234.41/43.88  | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | REDUCE: (366), (9939) imply:
% 234.41/43.88  | | | | | | | | |   (9941)   ~ (all_52_1 = e0)
% 234.41/43.88  | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | REDUCE: (369), (9939) imply:
% 234.41/43.88  | | | | | | | | |   (9942)   ~ (all_52_4 = e0)
% 234.41/43.88  | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | REDUCE: (373), (9939) imply:
% 234.41/43.88  | | | | | | | | |   (9943)   ~ (all_52_7 = e0)
% 234.41/43.88  | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | REDUCE: (375), (9939) imply:
% 234.41/43.88  | | | | | | | | |   (9944)   ~ (all_52_9 = e0)
% 234.41/43.88  | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | REDUCE: (377), (9939) imply:
% 234.41/43.88  | | | | | | | | |   (9945)   ~ (all_52_13 = e0)
% 234.41/43.88  | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | BETA: splitting (231) gives:
% 234.41/43.88  | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | |   (9946)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 234.41/43.88  | | | | | | | | | |             & op(e2, e2) = e0)
% 234.41/43.88  | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | BETA: splitting (9946) gives:
% 234.41/43.88  | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | |   (9947)  all_58_2 = e0 & op(e2, e3) = e0
% 234.41/43.88  | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | REF_CLOSE: (167), (9941), (9947), (function-axioms) are
% 234.41/43.88  | | | | | | | | | | |            inconsistent by sub-proof #1985.
% 234.41/43.88  | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | |   (9948)  all_58_3 = e0 & op(e2, e2) = e0
% 234.41/43.88  | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | ALPHA: (9948) implies:
% 234.41/43.88  | | | | | | | | | | |   (9949)  all_58_3 = e0
% 234.41/43.88  | | | | | | | | | | |   (9950)  op(e2, e2) = e0
% 234.41/43.88  | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | BETA: splitting (58) gives:
% 234.41/43.88  | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | |   (9951)   ~ (all_18_2 = e0)
% 234.41/43.88  | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | REDUCE: (339), (9951) imply:
% 234.41/43.88  | | | | | | | | | | | |   (9952)   ~ (all_6_2 = e0)
% 234.41/43.88  | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | BETA: splitting (85) gives:
% 234.41/43.88  | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | |   (9953)   ~ (all_36_2 = e2)
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | REDUCE: (328), (9953) imply:
% 234.41/43.88  | | | | | | | | | | | | |   (9954)   ~ (all_6_2 = e2)
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | BETA: splitting (194) gives:
% 234.41/43.88  | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | |   (9955)  all_54_10 = e3
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (9955) are inconsistent by sub-proof
% 234.41/43.88  | | | | | | | | | | | | | |            #2313.
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | |   (9956)   ~ (all_54_10 = e3)
% 234.41/43.88  | | | | | | | | | | | | | |   (9957)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | BETA: splitting (9957) gives:
% 234.41/43.88  | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | |   (9958)  all_54_10 = e2
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | REF_CLOSE: (297), (9954), (9958) are inconsistent by
% 234.41/43.88  | | | | | | | | | | | | | | |            sub-proof #2312.
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | |   (9959)  all_54_10 = e1 | all_54_10 = e0
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | BETA: splitting (9959) gives:
% 234.41/43.88  | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | |   (9960)  all_54_10 = e1
% 234.41/43.88  | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (9960) imply:
% 234.41/43.88  | | | | | | | | | | | | | | | |   (9961)  all_6_2 = e1
% 234.41/43.88  | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | SIMP: (9961) implies:
% 234.41/43.88  | | | | | | | | | | | | | | | |   (9962)  all_6_2 = e1
% 234.41/43.88  | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (9962) imply:
% 234.41/43.88  | | | | | | | | | | | | | | | |   (9963)  all_56_21 = e1
% 234.41/43.88  | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | REDUCE: (383), (9962) imply:
% 234.41/43.88  | | | | | | | | | | | | | | | |   (9964)   ~ (all_52_11 = e1)
% 234.41/43.88  | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | REDUCE: (385), (9962) imply:
% 234.41/43.88  | | | | | | | | | | | | | | | |   (9965)   ~ (all_52_14 = e1)
% 234.41/43.88  | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | REDUCE: (391), (9962) imply:
% 234.41/43.88  | | | | | | | | | | | | | | | |   (9966)   ~ (e3 = e1)
% 234.41/43.88  | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 234.41/43.88  | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | |   (9967)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.88  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.88  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.88  | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.88  | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.88  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.88  | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.88  | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.88  | | | | | | | | | | | | | | | | |             = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.88  | | | | | | | | | | | | | | | | |               e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 234.41/43.88  | | | | | | | | | | | | | | | | |             all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 234.41/43.88  | | | | | | | | | | | | | | | | |             = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | |             (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | |             (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.88  | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e3) = e0)
% 234.41/43.88  | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | BETA: splitting (9967) gives:
% 234.41/43.88  | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | |   (9968)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             = e3)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | BETA: splitting (9968) gives:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |   (9969)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |           e3
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | ALPHA: (9969) implies:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |   (9970)   ~ (all_56_31 = e2)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |   (9971)   ~ (all_56_21 = e2)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |   (9972)   ~ (all_56_11 = e2)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |   (9973)  op(e2, e3) = e3
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |   (9974)  op(e3, e2) = e3
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | REDUCE: (9940), (9972) imply:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |   (9975)   ~ (e2 = e0)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | REDUCE: (9963), (9971) imply:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |   (9976)   ~ (e2 = e1)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | |   (9977)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9977) gives:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | |   (9978)  all_58_9 = e1 & op(e3, e0) = e1
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7009), (9978), (function-axioms) are
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | |   (9979)  all_58_10 = e1 & op(e2, e0) = e1
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9979) implies:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | |   (9980)  op(e2, e0) = e1
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | |   (9981)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9981) gives:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |   (9982)  all_58_12 = e1 & op(e0, e3) = e1
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7006), (9982), (function-axioms) are
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (164), (9980) gives:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |   (9983)  all_52_13 = e1
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (9973) gives:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |   (9984)  all_52_1 = e3
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (9974) gives:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |   (9985)  all_52_4 = e3
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (9984) imply:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |   (9986)   ~ (all_52_9 = e3)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9986) implies:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |   (9987)   ~ (all_52_9 = e3)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (9985) imply:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |   (9988)   ~ (all_52_6 = e3)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9988) implies:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |   (9989)   ~ (all_52_6 = e3)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (162),
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (226), (234), (239), (241), (243),
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |            (245), (391), (7010), (9316), (9317), (9949),
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |            (9987), (9989), (function-axioms) are inconsistent
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1008.
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | |   (9990)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (9323), (9964), (9990),
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | |            #1296.
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | |   (9991)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (9323), (9965), (9991),
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | |            #1297.
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |   (9992)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |             op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e1, e3) = e3)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9311), (9963), (9992) are inconsistent by
% 234.41/43.88  | | | | | | | | | | | | | | | | | | |            sub-proof #1280.
% 234.41/43.88  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.88  | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.88  | | | | | | | | | | | | | | | | | | 
% 234.41/43.88  | | | | | | | | | | | | | | | | | |   (9993)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 234.41/43.88  | | | | | | | | | | | | | | | | | |             = e0)
% 234.41/43.88  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (7008), (9311), (9312), (9993),
% 234.41/43.89  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.89  | | | | | | | | | | | | | | | | | |            #1411.
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | End of split
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | |   (9994)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.89  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.89  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.89  | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.89  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.89  | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.89  | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.89  | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.89  | | | | | | | | | | | | | | | | |             = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | |             (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | |             (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 234.41/43.89  | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 234.41/43.89  | | | | | | | | | | | | | | | | |             & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 234.41/43.89  | | | | | | | | | | | | | | | | |             = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | |             (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | |             (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 234.41/43.89  | | | | | | | | | | | | | | | | |               e0) = e0 & op(e0, e1) = e0)
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | BETA: splitting (9994) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | |   (9995)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.89  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.89  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             = e2)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (297), (381), (9940), (9952), (9959),
% 234.41/43.89  | | | | | | | | | | | | | | | | | |            (9963), (9995), (function-axioms) are inconsistent
% 234.41/43.89  | | | | | | | | | | | | | | | | | |            by sub-proof #1279.
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | |   (9996)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.41/43.89  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.89  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 234.41/43.89  | | | | | | | | | | | | | | | | | |             = e0)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (9945), (9963), (9965), (9996),
% 234.41/43.89  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.89  | | | | | | | | | | | | | | | | | |            #1250.
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | End of split
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | End of split
% 234.41/43.89  | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | |   (9997)  all_54_10 = e0
% 234.41/43.89  | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | REF_CLOSE: (297), (9952), (9997) are inconsistent by
% 234.41/43.89  | | | | | | | | | | | | | | | |            sub-proof #2303.
% 234.41/43.89  | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | End of split
% 234.41/43.89  | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | End of split
% 234.41/43.89  | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | End of split
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | |   (9998)  all_36_2 = e2
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | COMBINE_EQS: (328), (9998) imply:
% 234.41/43.89  | | | | | | | | | | | | |   (9999)  all_6_2 = e2
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | COMBINE_EQS: (266), (9999) imply:
% 234.41/43.89  | | | | | | | | | | | | |   (10000)  all_56_21 = e2
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | REDUCE: (381), (9999) imply:
% 234.41/43.89  | | | | | | | | | | | | |   (10001)   ~ (all_52_9 = e2)
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | REF_CLOSE: (159), (164), (165), (169), (213), (7003), (7008),
% 234.41/43.89  | | | | | | | | | | | | |            (9311), (9312), (9940), (9945), (10000), (10001),
% 234.41/43.89  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.89  | | | | | | | | | | | | |            #1237.
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | End of split
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | |   (10002)  all_18_2 = e0
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | COMBINE_EQS: (339), (10002) imply:
% 234.41/43.89  | | | | | | | | | | | |   (10003)  all_6_2 = e0
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | SIMP: (10003) implies:
% 234.41/43.89  | | | | | | | | | | | |   (10004)  all_6_2 = e0
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | COMBINE_EQS: (266), (10004) imply:
% 234.41/43.89  | | | | | | | | | | | |   (10005)  all_56_21 = e0
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | REDUCE: (367), (10004) imply:
% 234.41/43.89  | | | | | | | | | | | |   (10006)   ~ (all_52_2 = e0)
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | REDUCE: (378), (10004) imply:
% 234.41/43.89  | | | | | | | | | | | |   (10007)   ~ (all_52_6 = e0)
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | REDUCE: (380), (10004) imply:
% 234.41/43.89  | | | | | | | | | | | |   (10008)   ~ (all_52_8 = e0)
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | REDUCE: (383), (10004) imply:
% 234.41/43.89  | | | | | | | | | | | |   (10009)   ~ (all_52_11 = e0)
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | REDUCE: (385), (10004) imply:
% 234.41/43.89  | | | | | | | | | | | |   (10010)   ~ (all_52_14 = e0)
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | REDUCE: (391), (10004) imply:
% 234.41/43.89  | | | | | | | | | | | |   (10011)   ~ (e3 = e0)
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | REDUCE: (39), (10004) imply:
% 234.41/43.89  | | | | | | | | | | | |   (10012)  op(e1, e1) = e0
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | BETA: splitting (239) gives:
% 234.41/43.89  | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | |   (10013)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 234.41/43.89  | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | REF_CLOSE: (4), (167), (7010), (9941), (10013),
% 234.41/43.89  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.89  | | | | | | | | | | | | |            #1272.
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | |   (10014)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 234.41/43.89  | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | BETA: splitting (10014) gives:
% 234.41/43.89  | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | |   (10015)  all_58_6 = e0 & op(e1, e3) = e0
% 234.41/43.89  | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | ALPHA: (10015) implies:
% 234.41/43.89  | | | | | | | | | | | | | |   (10016)  op(e1, e3) = e0
% 234.41/43.89  | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | REF_CLOSE: (163), (10006), (10016), (function-axioms) are
% 234.41/43.89  | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 234.41/43.89  | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | |   (10017)  all_58_12 = e0 & op(e0, e3) = e0
% 234.41/43.89  | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | ALPHA: (10017) implies:
% 234.41/43.89  | | | | | | | | | | | | | |   (10018)  all_58_12 = e0
% 234.41/43.89  | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 234.41/43.89  | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | |   (10019)  all_54_14 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | REF_CLOSE: (255), (9314), (10019) are inconsistent by
% 234.41/43.89  | | | | | | | | | | | | | | |            sub-proof #1796.
% 234.41/43.89  | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | |   (10020)   ~ (all_54_14 = e3)
% 234.41/43.89  | | | | | | | | | | | | | | |   (10021)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 234.41/43.89  | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | |   (10022)  all_54_13 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | REF_CLOSE: (256), (9313), (10022) are inconsistent by
% 234.41/43.89  | | | | | | | | | | | | | | | |            sub-proof #2010.
% 234.41/43.89  | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | |   (10023)   ~ (all_54_13 = e3)
% 234.41/43.89  | | | | | | | | | | | | | | | |   (10024)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 234.41/43.89  | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | |   (10025)  all_54_1 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (10025) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | |   (10026)  all_52_4 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | SIMP: (10026) implies:
% 234.41/43.89  | | | | | | | | | | | | | | | | |   (10027)  all_52_4 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | REDUCE: (136), (10027) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | |   (10028)   ~ (all_52_6 = e3)
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | SIMP: (10028) implies:
% 234.41/43.89  | | | | | | | | | | | | | | | | |   (10029)   ~ (all_52_6 = e3)
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | REDUCE: (134), (10027) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | |   (10030)   ~ (all_52_8 = e3)
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | SIMP: (10030) implies:
% 234.41/43.89  | | | | | | | | | | | | | | | | |   (10031)   ~ (all_52_8 = e3)
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | |   (10032)  all_54_2 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (10031), (10032) are inconsistent by
% 234.41/43.89  | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | |   (10033)   ~ (all_54_2 = e3)
% 234.41/43.89  | | | | | | | | | | | | | | | | | |   (10034)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | |   (10035)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (10035) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | |   (10036)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | ALPHA: (10036) implies:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | |   (10037)  all_58_6 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | |   (10038)  op(e1, e3) = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10034) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | |   (10039)  all_54_2 = e2
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (10039) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | |   (10040)  all_52_8 = e2
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | SIMP: (10040) implies:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | |   (10041)  all_52_8 = e2
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (10041) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | |   (10042)   ~ (all_52_11 = e2)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | SIMP: (10042) implies:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | |   (10043)   ~ (all_52_11 = e2)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10021) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | |   (10044)  all_54_14 = e2
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (10044) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | |   (10045)  all_52_11 = e2
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10043), (10045) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | |   (10046)  $false
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10046) is inconsistent.
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | |   (10047)  all_54_14 = e1 | all_54_14 = e0
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10047) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | |   (10048)  all_54_14 = e1
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (10048) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | |   (10049)  all_52_11 = e1
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (10049) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | |   (10050)   ~ (all_52_9 = e1)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | |   (10051)  all_54_6 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10051) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | |   (10052)  all_52_9 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10052) implies:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | |   (10053)  all_52_9 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (10053) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | |   (10054)   ~ (all_52_1 = e3)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (10053) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | |   (10055)  op(e2, e1) = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (10056)  all_54_4 = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (10054), (10056) are inconsistent by
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (10057)   ~ (all_54_4 = e3)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (10058)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10059)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10059) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10060)  all_58_2 = e1 & op(e2, e3) = e1
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7004), (10060), (function-axioms) are
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10061)  all_58_3 = e1 & op(e2, e2) = e1
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9949), (10061) are inconsistent by sub-proof
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1752.
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10062)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10062) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10063)  all_58_5 = e1 & op(e2, e1) = e1
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10063) implies:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10064)  op(e2, e1) = e1
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10050), (10064), (function-axioms) are
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10065)  all_58_10 = e1 & op(e2, e0) = e1
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10065) implies:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10066)  op(e2, e0) = e1
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10058) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10067)  all_54_4 = e2
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (10067) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10068)  all_52_1 = e2
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10068) implies:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10069)  all_52_1 = e2
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10054), (10069) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10070)   ~ (e3 = e2)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (10069) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10071)  op(e2, e3) = e2
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10072)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10072) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10073)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10073) implies:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10074)  op(e3, all_56_1) = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7003), (10074) imply:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10075)  op(e3, e1) = e3
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10031), (10075), (function-axioms) are
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10076)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (167), (243), (245),
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (279), (7004), (7010), (9941), (9950), (10018),
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10037), (10054), (10058), (10076),
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1040.
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10077)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10077) gives:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10078)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10078) implies:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10079)  op(e1, e3) = all_56_5
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10080)  op(e1, all_56_5) = e1
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10038), (10079), (10080), (function-axioms)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2243.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10081)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10081) implies:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10082)  op(e0, e3) = all_56_7
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10083)  op(e0, all_56_7) = e0
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10084)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10084) gives:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10085)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10085) gives:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10086)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10086) implies:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10087)  op(e2, e3) = e3
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10071), (10087), (function-axioms) are
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10088)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9311), (10031), (10088), (function-axioms)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1317.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10089)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10089) gives:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10090)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10090) implies:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10091)  op(e3, e1) = e1
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7008), (10091), (function-axioms) are
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10092)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10092) gives:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10093)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10093) implies:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10094)  op(e0, e3) = e3
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10082), (10083), (10094), (function-axioms)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2070.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10095)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10095) implies:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10096)   ~ (all_56_31 = e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9311), (10096) imply:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10097)  $false
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10097) is inconsistent.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10098)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10098) gives:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10099)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10099) gives:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10100)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10100) implies:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10101)  op(e2, e1) = e2
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10055), (10101), (function-axioms) are
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10102)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10102) gives:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10103)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10103) implies:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10104)  op(e2, e1) = e1
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10050), (10104), (function-axioms) are
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10105)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10105) implies:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10106)  op(e2, e0) = e2
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10066), (10106), (function-axioms) are
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1659.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10107)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10107) gives:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10108)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10108) implies:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10109)  op(e2, e0) = e0
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (10066), (10109), (function-axioms)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10110)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10005), (10010), (10110),
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1320.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10111)  all_54_4 = e1 | all_54_4 = e0
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (7004), (9941), (10111) are inconsistent by
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1922.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | |   (10112)   ~ (all_54_6 = e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (10112) imply:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | |   (10113)   ~ (all_52_9 = e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (165), (169), (230), (9314), (10012),
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | |            (10031), (10113), (function-axioms) are
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1010.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | |   (10114)  all_54_14 = e0
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (10114) imply:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | |   (10115)  all_52_11 = e0
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10009), (10115) imply:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | |   (10116)  $false
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10116) is inconsistent.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | |   (10117)  all_54_2 = e1 | all_54_2 = e0
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (7008), (10008), (10117) are inconsistent
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1336.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | |   (10118)  all_58_7 = e3 & op(e1, e2) = e3
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | ALPHA: (10118) implies:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | |   (10119)  op(e1, e2) = e3
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10029), (10119), (function-axioms) are
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | |   (10120)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 234.41/43.90  | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (9317), (10012), (10120),
% 234.41/43.90  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.90  | | | | | | | | | | | | | | | | | | |            #1909.
% 234.41/43.90  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | End of split
% 234.41/43.90  | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.90  | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | |   (10121)   ~ (all_54_1 = e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | |   (10122)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 234.41/43.90  | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | REDUCE: (282), (10121) imply:
% 234.41/43.90  | | | | | | | | | | | | | | | | |   (10123)   ~ (all_52_4 = e3)
% 234.41/43.90  | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | BETA: splitting (10122) gives:
% 234.41/43.90  | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.90  | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | |   (10124)  all_54_1 = e2
% 234.41/43.90  | | | | | | | | | | | | | | | | | | 
% 234.41/43.90  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (10124) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | |   (10125)  all_52_4 = e2
% 234.41/43.91  | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | SIMP: (10125) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | |   (10126)  all_52_4 = e2
% 234.41/43.91  | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | REDUCE: (135), (10126) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | |   (10127)   ~ (all_52_7 = e2)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | SIMP: (10127) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | |   (10128)   ~ (all_52_7 = e2)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | |   (10129)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (9949), (10123), (10129),
% 234.41/43.91  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.91  | | | | | | | | | | | | | | | | | | |            #1430.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | |   (10130)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (10130) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | |   (10131)  all_58_7 = e3 & op(e1, e2) = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | ALPHA: (10131) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | |   (10132)  op(e1, e2) = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | |   (10133)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (7010), (10123), (10133),
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | |            #1401.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | |   (10134)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10134) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | |   (10135)  all_58_4 = e3 & op(e3, e1) = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10135) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | |   (10136)  all_58_4 = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |   (10137)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10137) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |   (10138)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10138) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (10139)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10139) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (10140)  op(e3, e2) = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (10123), (10140), (function-axioms) are
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (10141)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7003), (9311), (10141) are inconsistent by
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1239.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |   (10142)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (7008), (9311), (9312), (10142),
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |            #1411.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |   (10143)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10143) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |   (10144)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10144) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (10145)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10145) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (10146)   ~ (all_56_1 = e1)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7003), (10146) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (10147)  $false
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10147) is inconsistent.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (10148)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10148) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10149)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10149) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10150)  op(e1, e2) = e1
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10024) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10151)  all_54_13 = e2
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (10128), (10151) are inconsistent by
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10152)  all_54_13 = e1 | all_54_13 = e0
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10152) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10153)  all_54_13 = e1
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (10153) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10154)  all_52_7 = e1
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10154) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10155)  all_52_7 = e1
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (10155) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10156)   ~ (all_52_6 = e1)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10157)  all_54_9 = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (10157) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10158)  all_52_6 = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10158) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10159)  all_52_6 = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (10159) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10160)   ~ (all_52_2 = e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10161)  all_54_8 = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (10160), (10161) are inconsistent by
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10162)   ~ (all_54_8 = e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10163)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10163) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10164)  all_54_8 = e2
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (10164) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10165)  all_52_2 = e2
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10165) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10166)  all_52_2 = e2
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10160), (10166) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10167)   ~ (e3 = e2)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e2,
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (10132), (10150) gives:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10168)  e3 = e1
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10136), (10168) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10169)  all_58_4 = e1
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (7010), (10123), (10169), (function-axioms)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1468.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10170)  all_54_8 = e1 | all_54_8 = e0
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7005), (10006), (10170) are inconsistent
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1950.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10171)   ~ (all_54_9 = e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (10171) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10172)   ~ (all_52_6 = e3)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10132), (10172), (function-axioms) are
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10173)  all_54_13 = e0
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (9943), (10173) are inconsistent by
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2008.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10174)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10174) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10175)   ~ (all_56_21 = e0)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10005), (10175) imply:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10176)  $false
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10176) is inconsistent.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |   (10177)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (9945), (10005), (10010), (10177),
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | |            #1227.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | |   (10178)  all_58_9 = e3 & op(e3, e0) = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10178) implies:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | |   (10179)  op(e3, e0) = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9315), (10179), (function-axioms) are
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | |   (10180)  all_58_13 = e3 & op(e0, e2) = e3
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9313), (10180), (function-axioms) are
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | |   (10181)  all_54_1 = e1 | all_54_1 = e0
% 234.41/43.91  | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (7007), (9942), (10181) are inconsistent by
% 234.41/43.91  | | | | | | | | | | | | | | | | | |            sub-proof #2049.
% 234.41/43.91  | | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | | End of split
% 234.41/43.91  | | | | | | | | | | 
% 234.41/43.91  | | | | | | | | | Case 2:
% 234.41/43.91  | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | |   (10182)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 234.41/43.92  | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 234.41/43.92  | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | REF_CLOSE: (164), (165), (9944), (9945), (10182),
% 234.41/43.92  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.92  | | | | | | | | | |            #1991.
% 234.41/43.92  | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | End of split
% 234.41/43.92  | | | | | | | | | 
% 234.41/43.92  | | | | | | | | End of split
% 234.41/43.92  | | | | | | | | 
% 234.41/43.92  | | | | | | | End of split
% 234.41/43.92  | | | | | | | 
% 234.41/43.92  | | | | | | End of split
% 234.41/43.92  | | | | | | 
% 234.41/43.92  | | | | | End of split
% 234.41/43.92  | | | | | 
% 234.41/43.92  | | | | End of split
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | Case 2:
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | |   (10183)  all_8_2 = e3
% 234.41/43.92  | | | |   (10184)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) =
% 234.41/43.92  | | | |              all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) &
% 234.41/43.92  | | | |              op(e2, e3) = all_8_1 & $i(all_8_1))
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | | COMBINE_EQS: (320), (10183) imply:
% 234.41/43.92  | | | |   (10185)  all_42_2 = e3
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | | COMBINE_EQS: (353), (10183) imply:
% 234.41/43.92  | | | |   (10186)  all_56_11 = e3
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | | REDUCE: (366), (10183) imply:
% 234.41/43.92  | | | |   (10187)   ~ (all_52_1 = e3)
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | | REDUCE: (369), (10183) imply:
% 234.41/43.92  | | | |   (10188)   ~ (all_52_4 = e3)
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | | REDUCE: (371), (10183) imply:
% 234.41/43.92  | | | |   (10189)   ~ (all_52_6 = e3)
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | | REDUCE: (373), (10183) imply:
% 234.41/43.92  | | | |   (10190)   ~ (all_52_7 = e3)
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | | REDUCE: (375), (10183) imply:
% 234.41/43.92  | | | |   (10191)   ~ (all_52_9 = e3)
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | | REDUCE: (377), (10183) imply:
% 234.41/43.92  | | | |   (10192)   ~ (all_52_13 = e3)
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | | BETA: splitting (234) gives:
% 234.41/43.92  | | | | 
% 234.41/43.92  | | | | Case 1:
% 234.41/43.92  | | | | | 
% 234.41/43.92  | | | | |   (10193)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2,
% 234.41/43.92  | | | | |                e2) = e3)
% 234.41/43.92  | | | | | 
% 234.41/43.92  | | | | | BETA: splitting (10193) gives:
% 234.41/43.92  | | | | | 
% 234.41/43.92  | | | | | Case 1:
% 234.41/43.92  | | | | | | 
% 234.41/43.92  | | | | | |   (10194)  all_58_2 = e3 & op(e2, e3) = e3
% 234.41/43.92  | | | | | | 
% 234.41/43.92  | | | | | | ALPHA: (10194) implies:
% 234.41/43.92  | | | | | |   (10195)  op(e2, e3) = e3
% 234.41/43.92  | | | | | | 
% 234.41/43.92  | | | | | | REF_CLOSE: (167), (10187), (10195), (function-axioms) are
% 234.41/43.92  | | | | | |            inconsistent by sub-proof #2337.
% 234.41/43.92  | | | | | | 
% 234.41/43.92  | | | | | Case 2:
% 234.41/43.92  | | | | | | 
% 234.41/43.92  | | | | | |   (10196)  all_58_3 = e3 & op(e2, e2) = e3
% 234.41/43.92  | | | | | | 
% 234.41/43.92  | | | | | | ALPHA: (10196) implies:
% 234.41/43.92  | | | | | |   (10197)  all_58_3 = e3
% 234.41/43.92  | | | | | |   (10198)  op(e2, e2) = e3
% 234.41/43.92  | | | | | | 
% 234.41/43.92  | | | | | | BETA: splitting (46) gives:
% 234.41/43.92  | | | | | | 
% 234.41/43.92  | | | | | | Case 1:
% 234.41/43.92  | | | | | | | 
% 234.41/43.92  | | | | | | |   (10199)   ~ (all_10_2 = e1)
% 234.41/43.92  | | | | | | | 
% 234.41/43.92  | | | | | | | BETA: splitting (49) gives:
% 234.41/43.92  | | | | | | | 
% 234.41/43.92  | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | 
% 234.41/43.92  | | | | | | | |   (10200)   ~ (all_12_2 = e3)
% 234.41/43.92  | | | | | | | | 
% 234.41/43.92  | | | | | | | | REDUCE: (346), (10200) imply:
% 234.41/43.92  | | | | | | | |   (10201)   ~ (all_4_2 = e3)
% 234.41/43.92  | | | | | | | | 
% 234.41/43.92  | | | | | | | | BETA: splitting (55) gives:
% 234.41/43.92  | | | | | | | | 
% 234.41/43.92  | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | 
% 234.41/43.92  | | | | | | | | |   (10202)   ~ (all_16_2 = e0)
% 234.41/43.92  | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | REDUCE: (342), (10202) imply:
% 234.41/43.92  | | | | | | | | |   (10203)   ~ (all_10_2 = e0)
% 234.41/43.92  | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | BETA: splitting (58) gives:
% 234.41/43.92  | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | |   (10204)   ~ (all_18_2 = e0)
% 234.41/43.92  | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | REDUCE: (339), (10204) imply:
% 234.41/43.92  | | | | | | | | | |   (10205)   ~ (all_6_2 = e0)
% 234.41/43.92  | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | BETA: splitting (61) gives:
% 234.41/43.92  | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | |   (10206)   ~ (all_20_2 = e1)
% 234.41/43.92  | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | REDUCE: (341), (10206) imply:
% 234.41/43.92  | | | | | | | | | | |   (10207)   ~ (all_4_2 = e1)
% 234.41/43.92  | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | BETA: splitting (189) gives:
% 234.41/43.92  | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | |   (10208)  all_54_15 = e3
% 234.41/43.92  | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | COMBINE_EQS: (299), (10208) imply:
% 234.41/43.92  | | | | | | | | | | | |   (10209)  all_4_2 = e3
% 234.41/43.92  | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | REDUCE: (10201), (10209) imply:
% 234.41/43.92  | | | | | | | | | | | |   (10210)  $false
% 234.41/43.92  | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | CLOSE: (10210) is inconsistent.
% 234.41/43.92  | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | Case 2:
% 234.41/43.92  | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | |   (10211)   ~ (all_54_15 = e3)
% 234.41/43.92  | | | | | | | | | | | |   (10212)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 234.41/43.92  | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | BETA: splitting (10212) gives:
% 234.41/43.92  | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | |   (10213)  all_54_15 = e2
% 234.41/43.92  | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | COMBINE_EQS: (299), (10213) imply:
% 234.41/43.92  | | | | | | | | | | | | |   (10214)  all_4_2 = e2
% 234.41/43.92  | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | REDUCE: (390), (10214) imply:
% 234.41/43.92  | | | | | | | | | | | | |   (10215)  $false
% 234.41/43.92  | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | CLOSE: (10215) is inconsistent.
% 234.41/43.92  | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | Case 2:
% 234.41/43.92  | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | |   (10216)   ~ (all_54_15 = e2)
% 234.41/43.92  | | | | | | | | | | | | |   (10217)  all_54_15 = e1 | all_54_15 = e0
% 234.41/43.92  | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | BETA: splitting (10217) gives:
% 234.41/43.92  | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | |   (10218)  all_54_15 = e1
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | COMBINE_EQS: (299), (10218) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10219)  all_4_2 = e1
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | REDUCE: (10207), (10219) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10220)  $false
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | CLOSE: (10220) is inconsistent.
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | Case 2:
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | |   (10221)  all_54_15 = e0
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | COMBINE_EQS: (299), (10221) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10222)  all_4_2 = e0
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | COMBINE_EQS: (254), (10222) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10223)  all_56_31 = e0
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | REDUCE: (368), (10222) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10224)   ~ (all_52_3 = e0)
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | REDUCE: (386), (10222) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10225)   ~ (all_52_11 = e0)
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | REDUCE: (388), (10222) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10226)   ~ (all_52_13 = e0)
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | REDUCE: (389), (10222) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10227)   ~ (all_52_14 = e0)
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | REDUCE: (10201), (10222) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10228)   ~ (e3 = e0)
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | REDUCE: (390), (10222) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10229)   ~ (e2 = e0)
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | REDUCE: (10207), (10222) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10230)   ~ (e1 = e0)
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | REDUCE: (36), (10222) imply:
% 234.41/43.92  | | | | | | | | | | | | | |   (10231)  op(e0, e0) = e0
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 234.41/43.92  | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | |   (10232)  all_58_15 = e0 & op(e0, e0) = e0
% 234.41/43.92  | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | ALPHA: (10232) implies:
% 234.41/43.92  | | | | | | | | | | | | | | |   (10233)  all_58_15 = e0
% 234.41/43.92  | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | |   (10234)   ~ (all_24_2 = e2)
% 234.41/43.92  | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | REDUCE: (301), (10234) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | |   (10235)   ~ (all_10_2 = e2)
% 234.41/43.92  | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | |   (10236)  all_54_0 = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (10236) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | |   (10237)  all_10_2 = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | SIMP: (10237) implies:
% 234.41/43.92  | | | | | | | | | | | | | | | | |   (10238)  all_10_2 = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | REDUCE: (363), (10238) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | |   (10239)   ~ (all_52_8 = e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | REDUCE: (365), (10238) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | |   (10240)   ~ (all_52_12 = e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | |   (10241)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (10191), (10239), (10241),
% 234.41/43.92  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.92  | | | | | | | | | | | | | | | | | |            #1628.
% 234.41/43.92  | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | |   (10242)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | BETA: splitting (10242) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | |   (10243)  all_58_8 = e3 & op(e1, e1) = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (391), (10243), (function-axioms) are
% 234.41/43.92  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | |   (10244)  all_58_14 = e3 & op(e0, e1) = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | ALPHA: (10244) implies:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | |   (10245)  op(e0, e1) = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | |   (10246)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (10192), (10240), (10246),
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | |            #1592.
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | |   (10247)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10247) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | |   (10248)  all_58_11 = e3 & op(e1, e0) = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10248) implies:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | |   (10249)  op(e1, e0) = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (10245) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | |   (10250)  all_52_11 = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (160), (10249) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | |   (10251)  all_52_14 = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (10251) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | |   (10252)   ~ (all_6_2 = e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | |   (10253)   ~ (all_36_2 = e2)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (328), (10253) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | |   (10254)   ~ (all_6_2 = e2)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | |   (10255)  all_54_10 = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (10255) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | |   (10256)  all_6_2 = e3
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (10256) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | |   (10257)  $false
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10257) is inconsistent.
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | |   (10258)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10258) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | |   (10259)  all_54_10 = e2
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (10259) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | |   (10260)  all_6_2 = e2
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10254), (10260) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | |   (10261)  $false
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10261) is inconsistent.
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | |   (10262)  all_54_10 = e1 | all_54_10 = e0
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10262) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (10263)  all_54_10 = e1
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (10263) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (10264)  all_6_2 = e1
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (10264) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (10265)  all_56_21 = e1
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (10264) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (10266)   ~ (all_52_2 = e1)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (10264) imply:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (10267)   ~ (all_52_9 = e1)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10268)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10268) gives:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10269)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (169), (10186), (10187), (10239), (10269),
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1006.
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10270)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (168), (10224), (10240), (10266),
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10270), (function-axioms) are inconsistent by
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1005.
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10271)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10271) gives:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10272)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10223), (10265), (10267), (10272),
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1733.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10273)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (10223), (10226), (10227), (10273),
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2321.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (10274)  all_54_10 = e0
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (10274) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (10275)  all_6_2 = e0
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10205), (10275) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (10276)  $false
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10276) is inconsistent.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |   (10277)  all_36_2 = e2
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (10277) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |   (10278)  all_6_2 = e2
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (10278) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |   (10279)  all_56_21 = e2
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (10278) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |   (10280)   ~ (all_52_9 = e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |   (10281)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10281) gives:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |   (10282)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (169), (10186), (10187), (10239), (10282),
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |            #1006.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |   (10283)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (168), (10186), (10224), (10240), (10283),
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |            #1004.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |   (10284)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10284) gives:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |   (10285)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10223), (10279), (10280), (10285),
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |            #1732.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |   (10286)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10286) gives:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (10287)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10287) implies:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (10288)   ~ (all_56_21 = e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10279), (10288) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (10289)  $false
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10289) is inconsistent.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (10290)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10223), (10227), (10290),
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | |            #2322.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |   (10291)  all_58_15 = e3 & op(e0, e0) = e3
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10291) implies:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |   (10292)  op(e0, e0) = e3
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10231), (10292), (function-axioms) are
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | |   (10293)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 234.41/43.93  | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (10199), (10203), (10235), (10293) are
% 234.41/43.93  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 234.41/43.93  | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | |   (10294)  all_24_2 = e2
% 234.41/43.93  | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (10294) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | |   (10295)  all_10_2 = e2
% 234.41/43.93  | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (10295) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | |   (10296)  all_56_1 = e2
% 234.41/43.93  | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | REDUCE: (355), (10295) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | |   (10297)   ~ (all_52_1 = e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | REDUCE: (45), (10295) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | |   (10298)  op(e3, e3) = e2
% 234.41/43.93  | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 234.41/43.93  | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.93  | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | |   (10299)   ~ (all_36_2 = e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | REDUCE: (328), (10299) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | |   (10300)   ~ (all_6_2 = e2)
% 234.41/43.93  | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 234.41/43.93  | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | |   (10301)  all_54_10 = e3
% 234.41/43.93  | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (10301) are inconsistent by
% 234.41/43.93  | | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | |   (10302)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 234.41/43.93  | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | BETA: splitting (10302) gives:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | |   (10303)  all_54_10 = e2
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (10300), (10303) are inconsistent by
% 234.41/43.93  | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | |   (10304)  all_54_10 = e1 | all_54_10 = e0
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | BETA: splitting (10304) gives:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | |   (10305)  all_54_10 = e1
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (10305) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | |   (10306)  all_6_2 = e1
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | SIMP: (10306) implies:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | |   (10307)  all_6_2 = e1
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (10307) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | |   (10308)  all_56_21 = e1
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (10307) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | |   (10309)   ~ (all_52_2 = e1)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (10307) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | |   (10310)   ~ (all_52_9 = e1)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (10307) imply:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | |   (10311)   ~ (all_52_14 = e1)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |   (10312)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10312) gives:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |   (10313)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10187), (10297), (10308), (10313),
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |            #1003.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |   (10314)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (10223), (10224), (10309), (10314),
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | |            #1002.
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.93  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |   (10315)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10315) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |   (10316)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10223), (10308), (10310), (10316),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |            #1733.
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |   (10317)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10296), (10308), (10311), (10317),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |            #1343.
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |   (10318)  all_54_10 = e0
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (10205), (10318) are inconsistent by
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.94  | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | End of split
% 234.41/43.94  | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.94  | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | |   (10319)  all_36_2 = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (10319) imply:
% 234.41/43.94  | | | | | | | | | | | | | | | | |   (10320)  all_6_2 = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (10320) imply:
% 234.41/43.94  | | | | | | | | | | | | | | | | |   (10321)  all_56_21 = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | REDUCE: (381), (10320) imply:
% 234.41/43.94  | | | | | | | | | | | | | | | | |   (10322)   ~ (all_52_9 = e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | REDUCE: (391), (10320) imply:
% 234.41/43.94  | | | | | | | | | | | | | | | | |   (10323)   ~ (e3 = e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | REDUCE: (39), (10320) imply:
% 234.41/43.94  | | | | | | | | | | | | | | | | |   (10324)  op(e1, e1) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | |   (10325)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | BETA: splitting (10325) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | |   (10326)  all_58_1 = e2 & op(e3, e2) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | ALPHA: (10326) implies:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | |   (10327)  all_58_1 = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |   (10328)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (121), (125), (139),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            (140), (144), (158), (159), (160), (162), (163),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (169), (170), (190), (192),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            (213), (216), (219), (220), (221), (222), (223),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (230), (231),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (239), (240), (241), (242),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            (243), (245), (246), (255), (257), (10186),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            (10187), (10188), (10189), (10190), (10191),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            (10192), (10197), (10198), (10223), (10224),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            (10225), (10227), (10231), (10233), (10297),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            (10298), (10321), (10322), (10324), (10328),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |            #979.
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |   (10329)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10329) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |   (10330)  all_58_14 = e2 & op(e0, e1) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10330) implies:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |   (10331)  all_58_14 = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |   (10332)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (165), (240), (242),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |            (10191), (10298), (10327), (10332),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |            #978.
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |   (10333)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10324), (10331), (10333), (function-axioms)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2116.
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |   (10334)  all_58_15 = e2 & op(e0, e0) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10334) implies:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |   (10335)  all_58_15 = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10233), (10335) are inconsistent by
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1507.
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | |   (10336)  all_58_3 = e2 & op(e2, e2) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | ALPHA: (10336) implies:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | |   (10337)  op(e2, e2) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (10337), (function-axioms) are
% 234.41/43.94  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.94  | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | |   (10338)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | BETA: splitting (10338) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | |   (10339)  all_58_7 = e2 & op(e1, e2) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | ALPHA: (10339) implies:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | |   (10340)  all_58_7 = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |   (10341)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10341) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |   (10342)  all_58_6 = e0 & op(e1, e3) = e0
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10342) implies:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |   (10343)  all_58_6 = e0
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | |   (10344)  op(e1, e3) = e0
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |   (10345)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10345) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | |   (10346)  all_58_9 = e2 & op(e3, e0) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10346) implies:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | |   (10347)  all_58_9 = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | |   (10348)  op(e3, e0) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (242),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | |            (246), (10188), (10298), (10347), (10348),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | |            #1069.
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | |   (10349)  all_58_10 = e2 & op(e2, e0) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10349) implies:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | |   (10350)  all_58_10 = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | |   (10351)  op(e2, e0) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |   (10352)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10352) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (10353)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10353) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10354)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10354) implies:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10355)  op(e2, e3) = e3
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10187), (10355), (function-axioms) are
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10356)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10356) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10357)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10357) implies:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10358)  op(e2, e3) = e2
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10297), (10358), (function-axioms) are
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10359)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10359) implies:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10360)   ~ (all_56_31 = e1)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10361)   ~ (all_56_21 = e1)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10362)   ~ (all_56_11 = e1)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10363)  op(e1, e3) = e3
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10364)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (121), (125), (139),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (144), (158), (159), (160), (162), (163),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (169), (170), (190), (192),
% 234.41/43.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (216), (219), (220), (221), (222), (223),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (230), (231),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (239), (240), (241), (242),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (245), (246), (255), (257), (10186),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10187), (10188), (10189), (10190), (10191),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10192), (10197), (10198), (10223), (10224),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10225), (10227), (10231), (10233), (10297),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10298), (10321), (10322), (10324), (10364),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #979.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10365)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10365) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10366)  all_58_14 = e2 & op(e0, e1) = e2
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10366) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10367)  all_58_14 = e2
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10368)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10368) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10369)  all_58_4 = e3 & op(e3, e1) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10369) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10370)  all_58_4 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10371)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10371) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10372)  all_58_4 = e0 & op(e3, e1) = e0
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10372) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10373)  all_58_4 = e0
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10370), (10373) are inconsistent by
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2186.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10374)  all_58_5 = e0 & op(e2, e1) = e0
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10374) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10375)  op(e2, e1) = e0
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10376)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (10187), (10298), (10376),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1404.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10377)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10377) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10378)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10343), (10378) are inconsistent by
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1690.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10379)  all_58_12 = e3 & op(e0, e3) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10379) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10380)  all_58_12 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10381)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10381) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10382)  all_58_0 = e1 & op(e3, e3) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10382) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10383)  op(e3, e3) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10298), (10383), (function-axioms) are
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10384)  all_58_2 = e1 & op(e2, e3) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10384) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10385)  all_58_2 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10386)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (239), (243),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10189), (10380), (10385), (10386),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #977.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10387)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10387) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10388)  all_58_8 = e3 & op(e1, e1) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10388) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10389)  op(e1, e1) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10324), (10389), (function-axioms) are
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10390)  all_58_11 = e3 & op(e1, e0) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10390) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10391)  all_58_11 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10392)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10392) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10393)  all_58_9 = e1 & op(e3, e0) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10393) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10394)  all_58_9 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10395)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10395) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10396)  all_58_12 = e1 & op(e0, e3) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10396) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10397)  all_58_12 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (167), (232),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (245), (10187), (10197), (10298), (10351),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10375), (10397), (function-axioms) are
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #972.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10398)  all_58_13 = e1 & op(e0, e2) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10398) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10399)  all_58_13 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10400)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10400) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10401)  all_58_6 = e1 & op(e1, e3) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10401) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10402)  all_58_6 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (223), (10324), (10340), (10391),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10402), (function-axioms) are inconsistent by
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2202.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10403)  all_58_7 = e1 & op(e1, e2) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10403) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10404)  all_58_7 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (235), (237), (10197),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10399), (10404) are inconsistent by sub-proof
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1457.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10405)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10405) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (10344) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10406)  all_52_2 = e0
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (10363) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10407)  all_52_2 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10406), (10407) imply:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10408)  e3 = e0
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10370), (10408) imply:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10409)  all_58_4 = e0
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10410)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (10188), (10298), (10410),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1959.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10411)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10411) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10370), (10409) imply:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10412)  e3 = e0
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10391), (10408) imply:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10413)  all_58_11 = e0
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10414)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10414) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10415)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10415) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10416)  all_58_6 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10417)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (10192), (10394), (10417),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1602.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10418)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10418) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (10324), (10343),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10413), (function-axioms) are inconsistent by
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1686.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10419)  all_58_15 = e3 & op(e0, e0) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10419) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10420)  op(e0, e0) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10231), (10420), (function-axioms) are
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10421)  all_58_7 = e3 & op(e1, e2) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10421) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10422)  op(e1, e2) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10189), (10422), (function-axioms) are
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10324), (10387), (10413),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1797.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10423)  all_58_9 = e3 & op(e3, e0) = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10423) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10424)  all_58_9 = e3
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10394), (10424) are inconsistent by
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1709.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10425)  all_58_11 = e1 & op(e1, e0) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10425) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10426)  all_58_11 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10391), (10426) imply:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10427)  e3 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10427) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10428)  e3 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10380), (10428) imply:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10429)  all_58_12 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (167), (232),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (245), (10187), (10197), (10298), (10351),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10375), (10429), (function-axioms) are
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #972.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10430)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10430) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10431)  all_58_14 = e1 & op(e0, e1) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10431) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10432)  all_58_14 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10367), (10432) imply:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10433)  e2 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10433) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10434)  e2 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10350), (10434) imply:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10435)  all_58_10 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (221), (222), (10233),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10394), (10435) are inconsistent by sub-proof
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1495.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10436)  all_58_15 = e1 & op(e0, e0) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10436) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10437)  all_58_15 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10438)  op(e0, e0) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (164), (216), (222), (10192),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10351), (10394), (10437), (10438),
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #971.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10439)  all_58_10 = e1 & op(e2, e0) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10439) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10440)  op(e2, e0) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10351), (10440), (function-axioms) are
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1659.
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10441)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10441) gives:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10442)  all_58_11 = e1 & op(e1, e0) = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10442) implies:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10443)  all_58_11 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10391), (10443) imply:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10444)  e3 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10380), (10444) imply:
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10445)  all_58_12 = e1
% 234.41/43.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (167), (232),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (245), (10187), (10197), (10298), (10351),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10375), (10445), (function-axioms) are
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #972.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10446)  all_58_15 = e1 & op(e0, e0) = e1
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10446) implies:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10447)  op(e0, e0) = e1
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10231), (10447), (function-axioms) are
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10448)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10448) gives:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10449)  all_58_6 = e1 & op(e1, e3) = e1
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10449) implies:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10450)  all_58_6 = e1
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (226),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (241), (243), (10189), (10324), (10340),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10380), (10450), (function-axioms) are
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #970.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10451)  all_58_12 = e1 & op(e0, e3) = e1
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10451) implies:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10452)  all_58_12 = e1
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (167), (232),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (245), (10187), (10197), (10298), (10351),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10375), (10452), (function-axioms) are
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #972.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10453)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10324), (10367), (10453), (function-axioms)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2113.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10454)  all_58_5 = e3 & op(e2, e1) = e3
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10191), (10454), (function-axioms) are
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10455)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10324), (10367), (10455), (function-axioms)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2116.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10456)  all_58_15 = e2 & op(e0, e0) = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10456) implies:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10457)  all_58_15 = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10233), (10457) are inconsistent by
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1507.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (10458)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (10186), (10223), (10224), (10458),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |            #1001.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |   (10459)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10459) gives:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (10460)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10460) gives:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10461)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10461) implies:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10462)  op(e2, e1) = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10322), (10462), (function-axioms) are
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10463)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10463) gives:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10464)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10464) implies:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10465)   ~ (all_56_21 = e2)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10321), (10465) imply:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10466)  $false
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10466) is inconsistent.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10467)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10467) implies:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10468)  op(e0, e2) = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (121), (125), (139), (140), (144), (158),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (163), (165), (167), (169), (190),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (213), (255), (257), (10186), (10187),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10223), (10224), (10225), (10227), (10297),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10321), (10322), (10351), (10468),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #999.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (10469)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (10223), (10227), (10351), (10469),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | |            #1000.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | |   (10470)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10470) gives:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | |   (10471)  all_58_11 = e2 & op(e1, e0) = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10471) implies:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | |   (10472)  all_58_11 = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (10324), (10343),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | |            (10472), (function-axioms) are inconsistent by
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #997.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | |   (10473)  all_58_15 = e2 & op(e0, e0) = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10473) implies:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | |   (10474)  all_58_15 = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10233), (10474) are inconsistent by
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1507.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | |   (10475)  all_58_7 = e0 & op(e1, e2) = e0
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10340), (10475) are inconsistent by
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2212.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | |   (10476)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (10227), (10324), (10476),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | |            #1851.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |   (10477)  all_58_13 = e2 & op(e0, e2) = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | ALPHA: (10477) implies:
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |   (10478)  all_58_13 = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |   (10479)  op(e0, e2) = e2
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (121), (125), (139),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            (140), (144), (158), (159), (160), (162), (163),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (169), (170), (190), (192),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            (213), (216), (219), (220), (221), (222), (223),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (230), (231),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (239), (240), (241), (242),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            (243), (246), (255), (257), (10186), (10187),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            (10188), (10189), (10190), (10191), (10192),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            (10197), (10198), (10223), (10224), (10225),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            (10227), (10231), (10233), (10297), (10298),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            (10321), (10322), (10324), (10478), (10479),
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.96  | | | | | | | | | | | | | | | | | | |            #980.
% 234.41/43.96  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | |   (10480)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.41/43.96  | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 234.41/43.96  | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 234.41/43.96  | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 234.41/43.96  | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 234.41/43.96  | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (220),
% 234.41/43.96  | | | | | | | | | | | | | | |            (221), (222), (10192), (10226), (10227), (10231),
% 234.41/43.96  | | | | | | | | | | | | | | |            (10480), (function-axioms) are inconsistent by
% 234.41/43.96  | | | | | | | | | | | | | | |            sub-proof #1489.
% 234.41/43.96  | | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | End of split
% 234.41/43.96  | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | Case 2:
% 234.41/43.96  | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | |   (10481)  all_20_2 = e1
% 234.41/43.96  | | | | | | | | | | |   (10482)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 234.41/43.96  | | | | | | | | | | |              & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 234.41/43.96  | | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 234.41/43.96  | | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 234.41/43.96  | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | COMBINE_EQS: (341), (10481) imply:
% 234.41/43.96  | | | | | | | | | | |   (10483)  all_4_2 = e1
% 234.41/43.96  | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | SIMP: (10483) implies:
% 234.41/43.96  | | | | | | | | | | |   (10484)  all_4_2 = e1
% 234.41/43.96  | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | COMBINE_EQS: (324), (10484) imply:
% 234.41/43.96  | | | | | | | | | | |   (10485)  all_34_2 = e1
% 234.41/43.96  | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | COMBINE_EQS: (254), (10484) imply:
% 234.41/43.96  | | | | | | | | | | |   (10486)  all_56_31 = e1
% 234.41/43.96  | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | REDUCE: (368), (10484) imply:
% 234.41/43.96  | | | | | | | | | | |   (10487)   ~ (all_52_3 = e1)
% 234.41/43.96  | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | REDUCE: (379), (10484) imply:
% 234.41/43.96  | | | | | | | | | | |   (10488)   ~ (all_52_7 = e1)
% 234.41/43.96  | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | REDUCE: (386), (10484) imply:
% 234.41/43.96  | | | | | | | | | | |   (10489)   ~ (all_52_11 = e1)
% 234.41/43.96  | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | REDUCE: (387), (10484) imply:
% 234.41/43.96  | | | | | | | | | | |   (10490)   ~ (all_52_12 = e1)
% 234.41/43.96  | | | | | | | | | | | 
% 234.41/43.96  | | | | | | | | | | | REDUCE: (388), (10484) imply:
% 234.41/43.97  | | | | | | | | | | |   (10491)   ~ (all_52_13 = e1)
% 234.41/43.97  | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | REDUCE: (389), (10484) imply:
% 234.41/43.97  | | | | | | | | | | |   (10492)   ~ (all_52_14 = e1)
% 234.41/43.97  | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | REDUCE: (10201), (10484) imply:
% 234.41/43.97  | | | | | | | | | | |   (10493)   ~ (e3 = e1)
% 234.41/43.97  | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | REDUCE: (390), (10484) imply:
% 234.41/43.97  | | | | | | | | | | |   (10494)   ~ (e2 = e1)
% 234.41/43.97  | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | REDUCE: (36), (10484) imply:
% 234.41/43.97  | | | | | | | | | | |   (10495)  op(e0, e0) = e1
% 234.41/43.97  | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | BETA: splitting (220) gives:
% 234.41/43.97  | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | |   (10496)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 234.41/43.97  | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 234.41/43.97  | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | BETA: splitting (10496) gives:
% 234.41/43.97  | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | |   (10497)  all_58_9 = e1 & op(e3, e0) = e1
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | ALPHA: (10497) implies:
% 234.41/43.97  | | | | | | | | | | | | |   (10498)  all_58_9 = e1
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 234.41/43.97  | | | | | | | | | | | | |            (222), (10192), (10495), (10498),
% 234.41/43.97  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.97  | | | | | | | | | | | | |            #1600.
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | |   (10499)  all_58_10 = e1 & op(e2, e0) = e1
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | REF_CLOSE: (164), (10491), (10499), (function-axioms) are
% 234.41/43.97  | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | End of split
% 234.41/43.97  | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | |   (10500)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 234.41/43.97  | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 234.41/43.97  | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | BETA: splitting (10500) gives:
% 234.41/43.97  | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | |   (10501)  all_58_11 = e1 & op(e1, e0) = e1
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | ALPHA: (10501) implies:
% 234.41/43.97  | | | | | | | | | | | | |   (10502)  op(e1, e0) = e1
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | REF_CLOSE: (160), (10492), (10502), (function-axioms) are
% 234.41/43.97  | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | |   (10503)  all_58_15 = e1 & op(e0, e0) = e1
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | ALPHA: (10503) implies:
% 234.41/43.97  | | | | | | | | | | | | |   (10504)  all_58_15 = e1
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | BETA: splitting (67) gives:
% 234.41/43.97  | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | |   (10505)   ~ (all_24_2 = e2)
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | REDUCE: (301), (10505) imply:
% 234.41/43.97  | | | | | | | | | | | | | |   (10506)   ~ (all_10_2 = e2)
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | |   (10507)  all_54_0 = e3
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | COMBINE_EQS: (292), (10507) imply:
% 234.41/43.97  | | | | | | | | | | | | | | |   (10508)  all_10_2 = e3
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | SIMP: (10508) implies:
% 234.41/43.97  | | | | | | | | | | | | | | |   (10509)  all_10_2 = e3
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | REDUCE: (365), (10509) imply:
% 234.41/43.97  | | | | | | | | | | | | | | |   (10510)   ~ (all_52_12 = e3)
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | REDUCE: (45), (10509) imply:
% 234.41/43.97  | | | | | | | | | | | | | | |   (10511)  op(e3, e3) = e3
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | |   (10512)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.41/43.97  | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | BETA: splitting (10512) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | |   (10513)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | ALPHA: (10513) implies:
% 234.41/43.97  | | | | | | | | | | | | | | | | |   (10514)  all_58_6 = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | |   (10515)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 234.41/43.97  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (239), (241),
% 234.41/43.97  | | | | | | | | | | | | | | | | | |            (243), (10190), (10514), (10515),
% 234.41/43.97  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.97  | | | | | | | | | | | | | | | | | |            #1138.
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | |   (10516)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 234.41/43.97  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | BETA: splitting (10516) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |   (10517)  all_58_14 = e3 & op(e0, e1) = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | ALPHA: (10517) implies:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |   (10518)  all_58_14 = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (162), (164),
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |            (168), (216), (218), (222), (223), (224), (225),
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |            (226), (235), (237), (239), (241), (243), (10189),
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |            (10192), (10197), (10492), (10495), (10504),
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |            (10510), (10511), (10514), (10518),
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |            #959.
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |   (10519)  all_58_15 = e3 & op(e0, e0) = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | ALPHA: (10519) implies:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |   (10520)  all_58_15 = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10504), (10520) are inconsistent by
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |            sub-proof #2249.
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | End of split
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | |   (10521)  all_58_7 = e3 & op(e1, e2) = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | ALPHA: (10521) implies:
% 234.41/43.97  | | | | | | | | | | | | | | | | |   (10522)  op(e1, e2) = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10189), (10522), (function-axioms) are
% 234.41/43.97  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | End of split
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | |   (10523)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 234.41/43.97  | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | BETA: splitting (10523) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | |   (10524)  all_58_8 = e3 & op(e1, e1) = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (391), (10524), (function-axioms) are
% 234.41/43.97  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | |   (10525)  all_58_11 = e3 & op(e1, e0) = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | ALPHA: (10525) implies:
% 234.41/43.97  | | | | | | | | | | | | | | | | |   (10526)  all_58_11 = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | |   (10527)  op(e1, e0) = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (82), (110),
% 234.41/43.97  | | | | | | | | | | | | | | | | |            (112), (113), (149), (157), (158), (160), (163),
% 234.41/43.97  | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (197), (201), (210),
% 234.41/43.97  | | | | | | | | | | | | | | | | |            (216), (218), (219), (221), (222), (227), (230),
% 234.41/43.97  | | | | | | | | | | | | | | | | |            (232), (240), (242), (244), (269), (280), (391),
% 234.41/43.97  | | | | | | | | | | | | | | | | |            (10190), (10191), (10197), (10198), (10205),
% 234.41/43.97  | | | | | | | | | | | | | | | | |            (10482), (10485), (10486), (10490), (10491),
% 234.41/43.97  | | | | | | | | | | | | | | | | |            (10492), (10495), (10504), (10511), (10526),
% 234.41/43.97  | | | | | | | | | | | | | | | | |            (10527), (function-axioms) are inconsistent by
% 234.41/43.97  | | | | | | | | | | | | | | | | |            sub-proof #950.
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | End of split
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | End of split
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | |   (10528)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | REF_CLOSE: (292), (10199), (10203), (10506), (10528) are
% 234.41/43.97  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | End of split
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | |   (10529)  all_24_2 = e2
% 234.41/43.97  | | | | | | | | | | | | | |   (10530)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 234.41/43.97  | | | | | | | | | | | | | |              & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 234.41/43.97  | | | | | | | | | | | | | |              $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 234.41/43.97  | | | | | | | | | | | | | |              = all_24_1 & $i(all_24_1))
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | COMBINE_EQS: (301), (10529) imply:
% 234.41/43.97  | | | | | | | | | | | | | |   (10531)  all_10_2 = e2
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | SIMP: (10531) implies:
% 234.41/43.97  | | | | | | | | | | | | | |   (10532)  all_10_2 = e2
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | COMBINE_EQS: (348), (10532) imply:
% 234.41/43.97  | | | | | | | | | | | | | |   (10533)  all_32_2 = e2
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | COMBINE_EQS: (290), (10532) imply:
% 234.41/43.97  | | | | | | | | | | | | | |   (10534)  all_56_1 = e2
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | REDUCE: (355), (10532) imply:
% 234.41/43.97  | | | | | | | | | | | | | |   (10535)   ~ (all_52_1 = e2)
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | REDUCE: (357), (10532) imply:
% 234.41/43.97  | | | | | | | | | | | | | |   (10536)   ~ (all_52_2 = e2)
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | REDUCE: (361), (10532) imply:
% 234.41/43.97  | | | | | | | | | | | | | |   (10537)   ~ (all_52_4 = e2)
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | REDUCE: (45), (10532) imply:
% 234.41/43.97  | | | | | | | | | | | | | |   (10538)  op(e3, e3) = e2
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 234.41/43.97  | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | |   (10539)   ~ (all_32_2 = e2)
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | REDUCE: (10533), (10539) imply:
% 234.41/43.97  | | | | | | | | | | | | | | |   (10540)  $false
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | CLOSE: (10540) is inconsistent.
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | |   (10541)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 234.41/43.97  | | | | | | | | | | | | | | |              & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 234.41/43.97  | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 234.41/43.97  | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | |   (10542)   ~ (all_36_2 = e2)
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | REDUCE: (328), (10542) imply:
% 234.41/43.97  | | | | | | | | | | | | | | | |   (10543)   ~ (all_6_2 = e2)
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | |   (10544)  all_54_10 = e3
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (10544) are inconsistent by
% 234.41/43.97  | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | |   (10545)   ~ (all_54_10 = e3)
% 234.41/43.97  | | | | | | | | | | | | | | | | |   (10546)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | BETA: splitting (10546) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | |   (10547)  all_54_10 = e2
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (10543), (10547) are inconsistent by
% 234.41/43.97  | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | |   (10548)   ~ (all_54_10 = e2)
% 234.41/43.97  | | | | | | | | | | | | | | | | | |   (10549)  all_54_10 = e1 | all_54_10 = e0
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | BETA: splitting (10549) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |   (10550)  all_54_10 = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (10550) imply:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |   (10551)  all_6_2 = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | SIMP: (10551) implies:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |   (10552)  all_6_2 = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | REDUCE: (367), (10552) imply:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |   (10553)   ~ (all_52_2 = e1)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | REDUCE: (381), (10552) imply:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |   (10554)   ~ (all_52_9 = e1)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (10552) imply:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | |   (10555)  op(e1, e1) = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | |   (10556)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10556) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | |   (10557)  all_58_1 = e1 & op(e3, e2) = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10557) implies:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | |   (10558)  all_58_1 = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | |   (10559)  op(e3, e2) = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | |   (10560)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10560) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | |   (10561)  all_58_2 = e1 & op(e2, e3) = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10561) implies:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | |   (10562)  all_58_2 = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | |   (10563)  op(e2, e3) = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | |   (10564)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (163), (235),
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | |            (237), (10197), (10198), (10553), (10558),
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | |            (10564), (function-axioms) are inconsistent by
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #949.
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | |   (10565)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10565) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (10566)  all_58_8 = e1 & op(e1, e1) = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10566) implies:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (10567)  all_58_8 = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1,
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (10563) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (10568)  all_52_1 = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e1,
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (10559) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (10569)  all_52_4 = e1
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (10568) imply:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (10570)   ~ (all_52_2 = e1)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (10569) imply:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (10571)   ~ (all_52_6 = e1)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10571) implies:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (10572)   ~ (all_52_6 = e1)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (10569) imply:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (10573)   ~ (all_52_7 = e1)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10574)   ~ (all_42_2 = e3)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10185), (10574) imply:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10575)  $false
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10575) is inconsistent.
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10576)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10576) gives:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10577)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_42_1 & $i(all_42_0) &
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_42_1)
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10577) implies:
% 234.41/43.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10578)   ~ (all_42_0 = e0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10579)  op(e2, e3) = all_42_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10580)  op(all_42_1, e2) = all_42_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10541) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10581)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_32_1 & $i(all_32_0) &
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10581) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10582)   ~ (all_32_0 = e1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10583)  op(e3, e2) = all_32_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10584)  op(all_32_1, e3) = all_32_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10530) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10585)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_24_1 & $i(all_24_0) &
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10585) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10586)   ~ (all_24_0 = e0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10587)  op(e3, e2) = all_24_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10588)  op(all_24_1, e3) = all_24_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10184) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10589)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10589) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10590)  op(e2, e3) = all_8_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10591)  op(all_8_1, e2) = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_42_1,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (10563), (10579) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10592)  all_42_1 = e1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_42_1, e3, e2, simplifying with (10579),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (10590) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10593)  all_42_1 = all_8_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_32_1,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (10559), (10583) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10594)  all_32_1 = e1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e3, simplifying with (10583),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (10587) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10595)  all_32_1 = all_24_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10592), (10593) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10596)  all_8_1 = e1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10594), (10595) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10597)  all_24_1 = e1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10597) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10598)  all_24_1 = e1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10580), (10592) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10599)  op(e1, e2) = all_42_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10584), (10594) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10600)  op(e1, e3) = all_32_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10588), (10598) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10601)  op(e1, e3) = all_24_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10591), (10596) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10602)  op(e1, e2) = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_8_0, e2, e1, simplifying with (162), (10602)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10603)  all_52_6 = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_42_0, e2, e1, simplifying with (162), (10599)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10604)  all_52_6 = all_42_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_24_0, e3, e1, simplifying with (163), (10601)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10605)  all_52_2 = all_24_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_0, e3, e1, simplifying with (163), (10600)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10606)  all_52_2 = all_32_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10605), (10606) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10607)  all_32_0 = all_24_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10603), (10604) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10608)  all_42_0 = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10608) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10609)  all_42_0 = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (10603) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10610)  all_54_9 = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (10605) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10611)  all_54_8 = all_24_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (10603), (10605) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10612)   ~ (all_24_0 = all_8_0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (10605) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10613)   ~ (all_52_14 = all_24_0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10613) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10614)   ~ (all_52_14 = all_24_0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10536), (10605) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10615)   ~ (all_24_0 = e2)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (10603) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10616)   ~ (all_52_7 = all_8_0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10616) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10617)   ~ (all_52_7 = all_8_0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10189), (10603) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10618)   ~ (all_8_0 = e3)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10572), (10603) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10619)   ~ (all_8_0 = e1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10578), (10609) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10620)   ~ (all_8_0 = e0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10582), (10607) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10621)   ~ (all_24_0 = e1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10622)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10622) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10623)  all_58_6 = e0 & op(e1, e3) = e0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (160), (162), (196), (226), (391),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10189), (10586), (10611), (10614), (10615),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10621), (10623), (function-axioms) are
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #947.
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10624)  all_58_7 = e0 & op(e1, e2) = e0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10624) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10625)  all_58_7 = e0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (158), (191), (195), (237), (256),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10198), (10488), (10558), (10610),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10617), (10618), (10619), (10620), (10625),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #943.
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10626)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10626) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10627)  all_58_8 = e0 & op(e1, e1) = e0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (297), (10205), (10549), (10627),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #942.
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10628)  all_58_11 = e0 & op(e1, e0) = e0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10628) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10629)  all_58_11 = e0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (39), (158), (160), (162),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (195), (196), (218), (219), (225), (226),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (241), (243), (256), (391), (10189),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10488), (10504), (10538), (10562),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10567), (10586), (10610), (10611), (10612),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10614), (10615), (10617), (10619), (10620),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10621), (10629), (function-axioms) are
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #939.
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10630)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_8_1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10630) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10631)   ~ (all_8_1 = e0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10632)  op(e2, e3) = all_8_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (39), (128), (141), (143),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (160), (162), (163), (191), (195), (196),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (223), (225), (226), (237), (239),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (243), (256), (267), (268), (297), (391),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10189), (10190), (10198), (10205), (10488),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10504), (10536), (10538), (10549), (10553),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10558), (10559), (10562), (10563), (10567),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10572), (10578), (10579), (10580), (10583),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10586), (10587), (10588), (10631), (10632),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #936.
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10633)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10633) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10634)   ~ (all_24_1 = e1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10635)  op(e3, e2) = all_24_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10559), (10583), (10634), (10635),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2239.
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10636)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10636) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10637)   ~ (all_32_1 = e0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10638)  op(e3, e2) = all_32_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10530) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10639)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_24_1 & $i(all_24_0) &
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10639) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10640)   ~ (all_24_0 = e0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10641)  op(e3, e2) = all_24_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10642)  op(all_24_1, e3) = all_24_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10184) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10643)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10643) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10644)  op(e2, e3) = all_8_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10645)  op(all_8_1, e2) = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_42_1,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (10563), (10579) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10646)  all_42_1 = e1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_42_1, e3, e2, simplifying with (10579),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (10644) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10647)  all_42_1 = all_8_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_32_1,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (10559), (10638) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10648)  all_32_1 = e1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e3, simplifying with (10638),
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (10641) gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10649)  all_32_1 = all_24_1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10646), (10647) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10650)  all_8_1 = e1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10648), (10649) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10651)  all_24_1 = e1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10651) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10652)  all_24_1 = e1
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10580), (10646) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10653)  op(e1, e2) = all_42_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10642), (10652) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10654)  op(e1, e3) = all_24_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10645), (10650) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10655)  op(e1, e2) = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_8_0, e2, e1, simplifying with (162), (10655)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10656)  all_52_6 = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_42_0, e2, e1, simplifying with (162), (10653)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10657)  all_52_6 = all_42_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_24_0, e3, e1, simplifying with (163), (10654)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10658)  all_52_2 = all_24_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10656), (10657) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10659)  all_42_0 = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10659) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10660)  all_42_0 = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (10656) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10661)  all_54_9 = all_8_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (10658) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10662)  all_54_8 = all_24_0
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (10656), (10658) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10663)   ~ (all_24_0 = all_8_0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (10658) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10664)   ~ (all_52_14 = all_24_0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10664) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10665)   ~ (all_52_14 = all_24_0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10536), (10658) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10666)   ~ (all_24_0 = e2)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10553), (10658) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10667)   ~ (all_24_0 = e1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (10656) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10668)   ~ (all_52_7 = all_8_0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10668) implies:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10669)   ~ (all_52_7 = all_8_0)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10189), (10656) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10670)   ~ (all_8_0 = e3)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10572), (10656) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10671)   ~ (all_8_0 = e1)
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10578), (10660) imply:
% 234.41/43.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10672)   ~ (all_8_0 = e0)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10673)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10673) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10674)  all_58_6 = e0 & op(e1, e3) = e0
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (160), (162), (196), (226), (391),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10189), (10640), (10662), (10665), (10666),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10667), (10674), (function-axioms) are
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #947.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10675)  all_58_7 = e0 & op(e1, e2) = e0
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10675) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10676)  all_58_7 = e0
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (158), (191), (195), (237), (256),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10198), (10488), (10558), (10661),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10669), (10670), (10671), (10672), (10676),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #943.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10677)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10677) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10678)  all_58_8 = e0 & op(e1, e1) = e0
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (297), (10205), (10549), (10678),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #942.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10679)  all_58_11 = e0 & op(e1, e0) = e0
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10679) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10680)  all_58_11 = e0
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (39), (158), (160), (162),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (195), (196), (218), (219), (225), (226),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (241), (243), (256), (391), (10189),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10488), (10504), (10538), (10562),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10567), (10640), (10661), (10662), (10663),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10665), (10666), (10667), (10669), (10671),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10672), (10680), (function-axioms) are
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #939.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10681)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_8_1)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10681) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10682)   ~ (all_8_1 = e0)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10683)  op(e2, e3) = all_8_1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (39), (128), (141), (143),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (160), (162), (163), (191), (195), (196),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (223), (225), (226), (237), (239),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (243), (256), (267), (268), (297), (391),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10189), (10190), (10198), (10205), (10488),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10504), (10536), (10538), (10549), (10553),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10558), (10559), (10562), (10563), (10567),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10572), (10578), (10579), (10580), (10638),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10640), (10641), (10642), (10682), (10683),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #936.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10684)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10684) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10685)   ~ (all_24_1 = e1)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10686)  op(e3, e2) = all_24_1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10559), (10638), (10685), (10686),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2239.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10687)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_42_1)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10687) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10688)   ~ (all_42_1 = e1)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10689)  op(e2, e3) = all_42_1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10184), (10563), (10688), (10689),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #934.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (10690)  all_58_11 = e1 & op(e1, e0) = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10690) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (10691)  op(e1, e0) = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10492), (10691), (function-axioms) are
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | |   (10692)  all_58_3 = e1 & op(e2, e2) = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (10692) are inconsistent by
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | |   (10693)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (10491), (10554), (10693),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | |            #2234.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | |   (10694)  all_58_3 = e1 & op(e2, e2) = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (10694) are inconsistent by
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | |   (10695)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10695) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | |   (10696)  all_58_7 = e1 & op(e1, e2) = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10696) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | |   (10697)  all_58_7 = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | |   (10698)  op(e1, e2) = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | |   (10699)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10699) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | |   (10700)  all_58_2 = e1 & op(e2, e3) = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10700) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | |   (10701)  all_58_2 = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | |   (10702)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10702) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (10703)  all_58_6 = e2 & op(e1, e3) = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10703) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (10704)  all_58_6 = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10705)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (162), (10189), (10704), (10705),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            #933.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10706)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10706) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10707)  all_58_8 = e3 & op(e1, e1) = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (391), (10707), (function-axioms) are
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10708)  all_58_11 = e3 & op(e1, e0) = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10708) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10709)  all_58_11 = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (162), (223), (297), (10205),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10549), (10698), (10704), (10709),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #932.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (10710)  all_58_7 = e2 & op(e1, e2) = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10710) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (10711)  all_58_7 = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10697), (10711) are inconsistent by
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2134.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | |   (10712)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10712) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (10713)  all_58_8 = e2 & op(e1, e1) = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10713) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (10714)  op(e1, e1) = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10715)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (165), (167),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (219), (230), (235), (236), (239),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (241), (242), (245), (10187), (10190),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (10191), (10197), (10198), (10488), (10504),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (10538), (10714), (10715), (function-axioms) are
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #929.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10716)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10716) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10717)  all_58_7 = e2 & op(e1, e2) = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10717) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10718)  all_58_7 = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10697), (10718) are inconsistent by
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2134.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10719)  all_58_13 = e2 & op(e0, e2) = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10719) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10720)  all_58_13 = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10721)  op(e0, e2) = e2
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10722)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (162), (235), (10197),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10538), (10698), (10721), (10722),
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #928.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10723)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10723) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10724)  all_58_4 = e1 & op(e3, e1) = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10724) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10725)  all_58_4 = e1
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10726)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10726) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10727)  all_58_4 = e3 & op(e3, e1) = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10727) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10728)  all_58_4 = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10725), (10728) are inconsistent by
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2184.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10729)  all_58_5 = e3 & op(e2, e1) = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10191), (10729), (function-axioms) are
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10730)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10730) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10731)  all_58_8 = e3 & op(e1, e1) = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10731) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10732)  op(e1, e1) = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10714), (10732), (function-axioms) are
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10733)  all_58_14 = e3 & op(e0, e1) = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10733) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10734)  op(e0, e1) = e3
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10735)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10735) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10736)  all_58_4 = e0 & op(e3, e1) = e0
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10725), (10736) are inconsistent by
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1473.
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10737)  all_58_5 = e0 & op(e2, e1) = e0
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10737) implies:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10738)  op(e2, e1) = e0
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/43.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10739)  all_58_15 = e0 & op(e0, e0) = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10739) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10740)  op(e0, e0) = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10495), (10740), (function-axioms) are
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10741)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10741) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10742)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10743)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (10187), (10538), (10743),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1404.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10744)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10744) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10745)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10745) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10746)  all_58_6 = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (216),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (223), (225), (226), (229), (235), (237),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10189), (10190), (10197), (10495), (10504),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10555), (10697), (10698), (10720), (10721),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10725), (10738), (10746), (function-axioms) are
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #927.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10747)  all_58_12 = e3 & op(e0, e3) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10747) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10748)  all_58_12 = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10742) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10749)  all_58_12 = e0 & op(e0, e3) = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10748), (10749) are inconsistent by
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1641.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10750)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (10721), (10734), (10750),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1635.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10751)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (297), (10205), (10549), (10734),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10751), (function-axioms) are inconsistent by
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #926.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10752)  all_58_9 = e1 & op(e3, e0) = e1
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10752) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10753)  all_58_9 = e1
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (10192), (10495), (10504), (10753),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1601.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (10754)  all_58_11 = e2 & op(e1, e0) = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10754) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (10755)  all_58_11 = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10756)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10756) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10757)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10757) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10758)  all_58_6 = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10759)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10759) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10760)  all_58_1 = e2 & op(e3, e2) = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10760) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10761)  all_58_1 = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10762)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10538), (10701), (10762),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1761.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10763)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10763) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10764)  all_58_6 = e0 & op(e1, e3) = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10758), (10764) are inconsistent by
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2213.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10765)  all_58_12 = e0 & op(e0, e3) = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10765) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10766)  all_58_12 = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (218),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (235), (10190), (10197), (10504), (10698),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10761), (10766), (function-axioms) are
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10767)  all_58_3 = e2 & op(e2, e2) = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10767) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10768)  op(e2, e2) = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (10768), (function-axioms) are
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10769)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10769) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10770)  all_58_7 = e2 & op(e1, e2) = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10770) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10771)  all_58_7 = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10697), (10771) are inconsistent by
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2134.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10772)  all_58_13 = e2 & op(e0, e2) = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10772) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10773)  all_58_13 = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10774)  op(e0, e2) = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10775)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10775) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10776)  all_58_9 = e3 & op(e3, e0) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10776) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10777)  all_58_9 = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10778)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (162), (235), (10197),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10538), (10698), (10774), (10778),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #928.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10779)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10779) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10780)  all_58_4 = e1 & op(e3, e1) = e1
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10780) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10781)  all_58_4 = e1
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10782)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10782) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10783)  all_58_4 = e3 & op(e3, e1) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10781), (10783) are inconsistent by
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1474.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10784)  all_58_5 = e3 & op(e2, e1) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10191), (10784), (function-axioms) are
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10785)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10785) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10786)  all_58_8 = e3 & op(e1, e1) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (391), (10786), (function-axioms) are
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10787)  all_58_14 = e3 & op(e0, e1) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10787) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10788)  op(e0, e1) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10789)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10789) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10790)  all_58_4 = e0 & op(e3, e1) = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10790) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10791)  all_58_4 = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10781), (10791) are inconsistent by
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1710.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10792)  all_58_5 = e0 & op(e2, e1) = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10792) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10793)  op(e2, e1) = e0
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (216),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (223), (225), (226), (229), (235), (237),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10189), (10190), (10197), (10495), (10504),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10555), (10697), (10698), (10758), (10773),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10774), (10781), (10793), (function-axioms) are
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #927.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10794)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (297), (10205), (10549), (10788),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10794), (function-axioms) are inconsistent by
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #926.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10795)  all_58_9 = e1 & op(e3, e0) = e1
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10795) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10796)  all_58_9 = e1
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10777), (10796) are inconsistent by
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1709.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10797)  all_58_10 = e3 & op(e2, e0) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10797) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10798)  op(e2, e0) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (10192), (10798), (function-axioms) are
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10799)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10799) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10800)  all_58_11 = e3 & op(e1, e0) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10800) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10801)  all_58_11 = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10755), (10801) imply:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10802)  e3 = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10802) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10803)  e3 = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10758), (10803) imply:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10804)  all_58_6 = e2
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (162), (223), (297), (10205),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10549), (10698), (10801), (10804),
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #932.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10805)  all_58_15 = e3 & op(e0, e0) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10805) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10806)  all_58_15 = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10504), (10806) are inconsistent by
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2249.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10807)  all_58_7 = e3 & op(e1, e2) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10807) implies:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10808)  op(e1, e2) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10189), (10808), (function-axioms) are
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10809)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10809) gives:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10810)  all_58_8 = e3 & op(e1, e1) = e3
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (391), (10810), (function-axioms) are
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 234.41/44.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10811)  all_58_11 = e3 & op(e1, e0) = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10811) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10812)  all_58_11 = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10755), (10812) are inconsistent by
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2030.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | |   (10813)  all_58_3 = e1 & op(e2, e2) = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (10813) are inconsistent by
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | |   (10814)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (10491), (10554), (10814),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | |            #2234.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |   (10815)  all_58_13 = e1 & op(e0, e2) = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10488), (10815), (function-axioms) are
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | |   (10816)  all_54_10 = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (10205), (10816) are inconsistent by
% 234.41/44.01  | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | |   (10817)  all_36_2 = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (10817) imply:
% 234.41/44.01  | | | | | | | | | | | | | | | |   (10818)  all_6_2 = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (10818) imply:
% 234.41/44.01  | | | | | | | | | | | | | | | |   (10819)  all_40_2 = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (10818) imply:
% 234.41/44.01  | | | | | | | | | | | | | | | |   (10820)  all_56_21 = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | REDUCE: (380), (10818) imply:
% 234.41/44.01  | | | | | | | | | | | | | | | |   (10821)   ~ (all_52_8 = e2)
% 234.41/44.01  | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | REDUCE: (391), (10818) imply:
% 234.41/44.01  | | | | | | | | | | | | | | | |   (10822)   ~ (e3 = e2)
% 234.41/44.01  | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | REDUCE: (39), (10818) imply:
% 234.41/44.01  | | | | | | | | | | | | | | | |   (10823)  op(e1, e1) = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | |   (10824)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 234.41/44.01  | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 234.41/44.01  | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | BETA: splitting (10824) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | |   (10825)  all_58_9 = e2 & op(e3, e0) = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | ALPHA: (10825) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | |   (10826)  all_58_9 = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | | |   (10827)  op(e3, e0) = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | |   (10828)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 234.41/44.01  | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | BETA: splitting (10828) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | |   (10829)  all_58_9 = e3 & op(e3, e0) = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | ALPHA: (10829) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | |   (10830)  op(e3, e0) = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10827), (10830), (function-axioms) are
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2125.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | |   (10831)  all_58_10 = e3 & op(e2, e0) = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | ALPHA: (10831) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | |   (10832)  op(e2, e0) = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (10192), (10832), (function-axioms) are
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | |   (10833)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 234.41/44.01  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | BETA: splitting (10833) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | |   (10834)  all_58_11 = e3 & op(e1, e0) = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | ALPHA: (10834) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | |   (10835)  all_58_11 = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | |   (10836)  op(e1, e0) = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |   (10837)  all_58_15 = e0 & op(e0, e0) = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10837) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |   (10838)  op(e0, e0) = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10495), (10838), (function-axioms) are
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |   (10839)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10839) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |   (10840)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | |   (10841)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10841) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | |   (10842)  all_58_6 = e2 & op(e1, e3) = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10842) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | |   (10843)  all_58_6 = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |   (10844)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (82), (110),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (149), (157), (158), (160), (163),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (197), (201), (210),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (219), (221), (222), (227), (230),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |            (232), (240), (242), (244), (269), (280), (391),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |            (10187), (10190), (10191), (10197), (10198),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |            (10205), (10482), (10485), (10486), (10490),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |            (10491), (10492), (10495), (10504), (10835),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |            (10836), (10844), (function-axioms) are
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #924.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |   (10845)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10845) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10846)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10843), (10846) are inconsistent by
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1838.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10847)  all_58_12 = e3 & op(e0, e3) = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (216), (218),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (240), (242), (10191), (10504), (10538),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (10823), (10826), (10847), (function-axioms) are
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #922.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | |   (10848)  all_58_7 = e2 & op(e1, e2) = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10848) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | |   (10849)  all_58_7 = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |   (10850)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10850) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10851)  all_58_6 = e1 & op(e1, e3) = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10851) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10852)  all_58_6 = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (223), (10823), (10835), (10849),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (10852), (function-axioms) are inconsistent by
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2202.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10853)  all_58_7 = e1 & op(e1, e2) = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10853) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10854)  all_58_7 = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10849), (10854) imply:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10855)  e2 = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10826), (10855) imply:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10856)  all_58_9 = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (221), (10495),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (10504), (10835), (10856), (function-axioms) are
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1740.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |   (10857)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10857) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10858)  all_58_8 = e1 & op(e1, e1) = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10858) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10859)  op(e1, e1) = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10860)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10860) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10861)  all_58_6 = e0 & op(e1, e3) = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10861) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10862)  all_58_6 = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10863)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (82), (110),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (149), (157), (158), (160), (163),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (197), (201), (210),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (219), (221), (222), (227), (230),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (240), (242), (244), (269), (280), (391),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10187), (10190), (10191), (10197), (10198),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10205), (10482), (10485), (10486), (10490),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10491), (10492), (10495), (10504), (10835),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10836), (10863), (function-axioms) are
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #924.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10864)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10864) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10865)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10865) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10866)  all_58_6 = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10862), (10866) imply:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10867)  e3 = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10835), (10867) imply:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10868)  all_58_11 = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (10823), (10862),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10868), (function-axioms) are inconsistent by
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1686.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10869)  all_58_12 = e3 & op(e0, e3) = e3
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (216), (218),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (240), (242), (10191), (10504), (10538),
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10823), (10826), (10869), (function-axioms) are
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #922.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10870)  all_58_7 = e0 & op(e1, e2) = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10849), (10870) are inconsistent by
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2212.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10871)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10871) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10872)  all_58_8 = e0 & op(e1, e1) = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10872) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10873)  op(e1, e1) = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10859), (10873), (function-axioms) are
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10874)  all_58_11 = e0 & op(e1, e0) = e0
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10835), (10874) are inconsistent by
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2204.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10875)  all_58_11 = e1 & op(e1, e0) = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10875) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (10876)  op(e1, e0) = e1
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10492), (10876), (function-axioms) are
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | |   (10877)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10877) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | |   (10878)  all_58_8 = e2 & op(e1, e1) = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10878) implies:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | |   (10879)  all_58_8 = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |   (10880)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 234.41/44.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (10198), (10535), (10880),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            #998.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10881)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10881) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (10882)  all_58_5 = e2 & op(e2, e1) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10882) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (10883)  all_58_5 = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (10884)  op(e2, e1) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10885)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10885) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10886)  all_58_4 = e1 & op(e3, e1) = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10886) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10887)  all_58_4 = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10888)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10888) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10889)  all_58_4 = e0 & op(e3, e1) = e0
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10887), (10889) are inconsistent by
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1473.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10890)  all_58_5 = e0 & op(e2, e1) = e0
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10890) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10891)  op(e2, e1) = e0
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10884), (10891), (function-axioms) are
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10892)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10892) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10893)  all_58_8 = e0 & op(e1, e1) = e0
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10893) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10894)  op(e1, e1) = e0
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10823), (10894), (function-axioms) are
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10895)  all_58_14 = e0 & op(e0, e1) = e0
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10895) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10896)  op(e0, e1) = e0
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10897)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (165), (240), (242),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10191), (10538), (10826), (10897),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #923.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10898)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10823), (10896), (10898),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1595.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10899)  all_58_5 = e1 & op(e2, e1) = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10899) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10900)  all_58_5 = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10883), (10900) imply:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10901)  e2 = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10826), (10901) imply:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10902)  all_58_9 = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (221), (10495),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10504), (10835), (10902), (function-axioms) are
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1740.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10903)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10903) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10904)  all_58_8 = e1 & op(e1, e1) = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10904) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10905)  all_58_8 = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10879), (10905) imply:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10906)  e2 = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10826), (10906) imply:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10907)  all_58_9 = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (221), (10495),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10504), (10835), (10907), (function-axioms) are
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1740.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10908)  all_58_14 = e1 & op(e0, e1) = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10908) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10909)  all_58_14 = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10910)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (165), (240), (242),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10191), (10538), (10826), (10910),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #923.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10911)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (10823), (10909), (10911),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1249.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (10912)  all_58_10 = e2 & op(e2, e0) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10912) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (10913)  op(e2, e0) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10840) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10914)  all_58_9 = e0 & op(e3, e0) = e0
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10826), (10914) are inconsistent by
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1563.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10915)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (10835), (10913), (10915),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1743.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | |   (10916)  all_58_11 = e2 & op(e1, e0) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10835), (10916) are inconsistent by
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1741.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | |   (10917)  all_58_15 = e3 & op(e0, e0) = e3
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | ALPHA: (10917) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | |   (10918)  all_58_15 = e3
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10504), (10918) are inconsistent by
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | |            sub-proof #2249.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | |   (10919)  all_58_10 = e2 & op(e2, e0) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | ALPHA: (10919) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | |   (10920)  all_58_10 = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | |   (10921)  op(e2, e0) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | |   (10922)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (165), (167),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | |            (216), (218), (219), (230), (235), (236), (239),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | |            (240), (241), (242), (245), (10187), (10190),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | |            (10191), (10197), (10198), (10488), (10504),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | |            (10538), (10823), (10922), (function-axioms) are
% 234.41/44.02  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #929.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | |   (10923)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | BETA: splitting (10923) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | |   (10924)  all_58_7 = e2 & op(e1, e2) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | ALPHA: (10924) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | |   (10925)  all_58_7 = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | |   (10926)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10926) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | |   (10927)  all_58_6 = e1 & op(e1, e3) = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10927) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | |   (10928)  all_58_6 = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | |   (10929)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10929) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10930)  all_58_12 = e2 & op(e0, e3) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (167), (216),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (239), (241), (245), (10187),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10504), (10538), (10930),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            #931.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10931)  all_58_13 = e2 & op(e0, e2) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10931) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10932)  all_58_13 = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10933)  op(e0, e2) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (235), (236),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            (237), (10197), (10488), (10925), (10932),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            (10933), (function-axioms) are inconsistent by
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #921.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | |   (10934)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10934) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10935)  all_58_14 = e2 & op(e0, e1) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10935) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10936)  all_58_14 = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (10937)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10937) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10938)  all_58_12 = e3 & op(e0, e3) = e3
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10938) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10939)  all_58_12 = e3
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (226),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (241), (243), (10189), (10823), (10925),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            (10928), (10939), (function-axioms) are
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #970.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10940)  all_58_13 = e3 & op(e0, e2) = e3
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10190), (10940), (function-axioms) are
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (10941)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (10504), (10936), (10941) are
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1638.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10942)  all_58_15 = e2 & op(e0, e0) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10942) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10943)  all_58_15 = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10504), (10943) are inconsistent by
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2231.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | |   (10944)  all_58_7 = e1 & op(e1, e2) = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10925), (10944) are inconsistent by
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2224.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | |   (10945)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10945) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | |   (10946)  all_58_8 = e1 & op(e1, e1) = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10946) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | |   (10947)  op(e1, e1) = e1
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | |   (10948)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10948) gives:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10949)  all_58_12 = e2 & op(e0, e3) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (167), (216),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (239), (241), (245), (10187),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10504), (10538), (10949),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            #931.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10950)  all_58_13 = e2 & op(e0, e2) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10950) implies:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10951)  all_58_13 = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |   (10952)  op(e0, e2) = e2
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (235), (236),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            (237), (10197), (10488), (10925), (10951),
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            (10952), (function-axioms) are inconsistent by
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #921.
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | |   (10953)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10953) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10954)  all_58_14 = e2 & op(e0, e1) = e2
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10954) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10955)  all_58_14 = e2
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (10956)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10956) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10957)  all_58_1 = e1 & op(e3, e2) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10957) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10958)  all_58_1 = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10959)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10959) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10960)  all_58_12 = e3 & op(e0, e3) = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10960) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10961)  all_58_12 = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10962)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10962) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10963)  all_58_4 = e3 & op(e3, e1) = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10963) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10964)  all_58_4 = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10965)  all_58_15 = e0 & op(e0, e0) = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10965) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10966)  op(e0, e0) = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10495), (10966), (function-axioms) are
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10967)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10967) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10968)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10969)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10969) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10970)  all_58_4 = e0 & op(e3, e1) = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10964), (10970) are inconsistent by
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1697.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10971)  all_58_5 = e0 & op(e2, e1) = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10971) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10972)  op(e2, e1) = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (226), (232), (239), (240), (243),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10189), (10192), (10197), (10504), (10538),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10823), (10920), (10921), (10947), (10958),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10961), (10964), (10968), (10972),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #918.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10973)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10947), (10955), (10973),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1286.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10974)  all_58_5 = e3 & op(e2, e1) = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10191), (10974), (function-axioms) are
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10975)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (218), (10504),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10823), (10961), (10975), (function-axioms) are
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #930.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10976)  all_58_13 = e3 & op(e0, e2) = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10190), (10976), (function-axioms) are
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10977)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (10504), (10955), (10977) are
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1638.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10978)  all_58_3 = e1 & op(e2, e2) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (10978) are inconsistent by
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (10979)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10979) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10980)  all_58_7 = e1 & op(e1, e2) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10925), (10980) are inconsistent by
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2224.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10981)  all_58_13 = e1 & op(e0, e2) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10488), (10981), (function-axioms) are
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10982)  all_58_15 = e2 & op(e0, e0) = e2
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10982) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10983)  all_58_15 = e2
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10504), (10983) are inconsistent by
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2231.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | |   (10984)  all_58_11 = e1 & op(e1, e0) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10984) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | |   (10985)  op(e1, e0) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10492), (10985), (function-axioms) are
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | |   (10986)  all_58_13 = e2 & op(e0, e2) = e2
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | ALPHA: (10986) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | |   (10987)  all_58_13 = e2
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | |   (10988)  op(e0, e2) = e2
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | |   (10989)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10989) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | |   (10990)  all_58_6 = e2 & op(e1, e3) = e2
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10990) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | |   (10991)  all_58_6 = e2
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | |   (10992)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (162), (10189), (10991), (10992),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | |            #933.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | |   (10993)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10993) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10994)  all_58_8 = e3 & op(e1, e1) = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10994) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10995)  op(e1, e1) = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10823), (10995), (function-axioms) are
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10996)  all_58_11 = e3 & op(e1, e0) = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10996) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10997)  all_58_11 = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10998)  op(e1, e0) = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (10999)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10999) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11000)  all_58_6 = e1 & op(e1, e3) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10991), (11000) are inconsistent by
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1423.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11001)  all_58_7 = e1 & op(e1, e2) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11001) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11002)  op(e1, e2) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (162), (223), (226), (10189),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            (10823), (10991), (11002), (function-axioms) are
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #917.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (11003)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11003) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11004)  all_58_8 = e1 & op(e1, e1) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11004) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11005)  op(e1, e1) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11006)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11006) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11007)  all_58_6 = e0 & op(e1, e3) = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10991), (11007) are inconsistent by
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1678.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11008)  all_58_7 = e0 & op(e1, e2) = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11008) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11009)  op(e1, e2) = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11010)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11010) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11011)  all_58_1 = e1 & op(e3, e2) = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11011) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11012)  all_58_1 = e1
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11013)  all_58_15 = e0 & op(e0, e0) = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11013) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11014)  op(e0, e0) = e0
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10495), (11014), (function-axioms) are
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11015)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11015) implies:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11016)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11017)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (82), (110),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (149), (157), (158), (160), (163),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (197), (201), (210),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (219), (221), (222), (227), (230),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (240), (242), (244), (269), (280), (391),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10187), (10190), (10191), (10197), (10198),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10205), (10482), (10485), (10486), (10490),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10491), (10492), (10495), (10504), (10997),
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10998), (11017), (function-axioms) are
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #924.
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11018)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11018) gives:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11019)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11019) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11020)  all_58_6 = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10991), (11020) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11021)  e3 = e2
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10997), (11021) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11022)  all_58_11 = e2
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (160), (162),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (216), (221), (222), (223),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (230), (231), (232),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (236), (240), (10189), (10191), (10192),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (10198), (10488), (10491), (10492),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10495), (10504), (10535), (10538), (10823),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11020), (11022), (function-axioms) are
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #911.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11023)  all_58_12 = e3 & op(e0, e3) = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11023) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11024)  all_58_12 = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11025)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11025) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11026)  all_58_0 = e1 & op(e3, e3) = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11026) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11027)  op(e3, e3) = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10538), (11027), (function-axioms) are
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11028)  all_58_2 = e1 & op(e2, e3) = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11028) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11029)  all_58_2 = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11030)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11030) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11031)  all_58_2 = e0 & op(e2, e3) = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11031) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11032)  all_58_2 = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11029), (11032) are inconsistent by
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1268.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11033)  all_58_3 = e0 & op(e2, e2) = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11033) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11034)  all_58_3 = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10197), (11034) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11035)  e3 = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10997), (11035) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11036)  all_58_11 = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (10823), (10991),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11036), (function-axioms) are inconsistent by
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #967.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11037)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11037) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11038)  all_58_5 = e0 & op(e2, e1) = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11038) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11039)  op(e2, e1) = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11040)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11040) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11041)  all_58_0 = e3 & op(e3, e3) = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11041) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11042)  op(e3, e3) = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (82), (110),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (149), (157), (158), (160), (163),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (197), (201), (210),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (219), (221), (222), (227), (230),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (240), (242), (244), (269), (280), (391),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10197), (10198), (10205),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10482), (10485), (10486), (10490), (10491),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10492), (10495), (10504), (10997), (10998),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11042), (function-axioms) are inconsistent by
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #950.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11043)  all_58_1 = e3 & op(e3, e2) = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11043) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11044)  op(e3, e2) = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (10188), (11044), (function-axioms) are
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11045)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11045) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11046)  all_58_4 = e3 & op(e3, e1) = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11046) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11047)  all_58_4 = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (226), (232), (239), (240), (243),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10189), (10192), (10197), (10504), (10538),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10823), (10920), (10921), (11005), (11012),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11016), (11024), (11039), (11047),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #918.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11048)  all_58_9 = e3 & op(e3, e0) = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (10921), (10997), (11016), (11048),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #920.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11049)  all_58_10 = e0 & op(e2, e0) = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11049) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11050)  op(e2, e0) = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10921), (11050), (function-axioms) are
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11051)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11051) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11052)  all_58_6 = e1 & op(e1, e3) = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11052) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11053)  all_58_6 = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10991), (11053) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11054)  e2 = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11054) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11055)  e2 = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10920), (11055) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11056)  all_58_10 = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (222),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10504), (11016), (11056), (function-axioms) are
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #910.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11057)  all_58_12 = e1 & op(e0, e3) = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11057) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11058)  all_58_12 = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11024), (11058) are inconsistent by
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1542.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11059)  all_58_3 = e1 & op(e2, e2) = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (11059) are inconsistent by
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11060)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (158), (162), (10488), (11009), (11060),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1840.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11061)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11061) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11062)  all_58_8 = e0 & op(e1, e1) = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11062) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11063)  op(e1, e1) = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11005), (11063), (function-axioms) are
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11064)  all_58_11 = e0 & op(e1, e0) = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11064) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11065)  all_58_11 = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (10823), (10991),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11065), (function-axioms) are inconsistent by
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #967.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11066)  all_58_11 = e1 & op(e1, e0) = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11066) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11067)  op(e1, e0) = e1
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10492), (11067), (function-axioms) are
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11068)  all_58_7 = e2 & op(e1, e2) = e2
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11068) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11069)  all_58_7 = e2
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (235), (236),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |            (237), (10197), (10488), (10987), (10988),
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |            (11069), (function-axioms) are inconsistent by
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #921.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | |   (11070)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11070) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11071)  all_58_8 = e2 & op(e1, e1) = e2
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11071) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11072)  all_58_8 = e2
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (10988) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11073)  all_52_7 = e2
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (10921) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11074)  all_52_13 = e2
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (11073) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11075)   ~ (all_52_3 = e2)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (11073) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11076)   ~ (all_52_6 = e2)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (11073) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11077)   ~ (all_52_11 = e2)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | SIMP: (11077) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11078)   ~ (all_52_11 = e2)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (11074) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11079)   ~ (all_52_9 = e2)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (11074) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11080)   ~ (all_52_14 = e2)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | SIMP: (11080) implies:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | |   (11081)   ~ (all_52_14 = e2)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | |   (11082)   ~ (all_40_2 = e2)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10819), (11082) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | |   (11083)  $false
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11083) is inconsistent.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | |   (11084)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | |              = all_40_1 & $i(all_40_1))
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | |   (11085)   ~ (all_42_2 = e3)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10185), (11085) imply:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | |   (11086)  $false
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11086) is inconsistent.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | |   (11087)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (11088)  all_54_1 = e3
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (10188), (11088) are inconsistent by
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (11089)   ~ (all_54_1 = e3)
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (11090)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11091)  all_54_12 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11091) imply:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11092)  all_52_3 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11092) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11093)  all_52_3 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (11093) imply:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11094)   ~ (all_52_2 = e3)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (11093) imply:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11095)   ~ (all_52_11 = e3)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11095) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11096)   ~ (all_52_11 = e3)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11097)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11097) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11098)  all_58_4 = e3 & op(e3, e1) = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11098) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11099)  all_58_4 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11100)  all_54_14 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (11100) imply:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11101)  all_52_11 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11096), (11101) imply:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11102)  $false
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11102) is inconsistent.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11103)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11104)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (10187), (10538), (11104),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1404.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11105)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11105) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11106)  all_58_6 = e3 & op(e1, e3) = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11106) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11107)  all_58_6 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11108)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11108) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11109)  all_58_0 = e1 & op(e3, e3) = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11109) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11110)  op(e3, e3) = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10538), (11110), (function-axioms) are
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11111)  all_58_1 = e1 & op(e3, e2) = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11111) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11112)  all_58_1 = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11113)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10538), (11112), (11113),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1698.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11114)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11114) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11115)  all_58_4 = e0 & op(e3, e1) = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11099), (11115) are inconsistent by
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1697.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11116)  all_58_9 = e0 & op(e3, e0) = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11116) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11117)  all_58_9 = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11118)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11118) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11119)  all_58_0 = e1 & op(e3, e3) = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11119) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11120)  op(e3, e3) = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10538), (11120), (function-axioms) are
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11121)  all_58_2 = e1 & op(e2, e3) = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11121) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11122)  all_58_2 = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11123)  all_58_15 = e0 & op(e0, e0) = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11123) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11124)  op(e0, e0) = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10495), (11124), (function-axioms) are
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11125)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11125) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11126)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (82), (110),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (149), (157), (158), (160), (163),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (197), (201), (210),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (219), (221), (222), (223), (224),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (232), (239), (240), (242), (243), (244),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (269), (280), (10187), (10190), (10192),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (10198), (10205), (10482), (10485),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10486), (10490), (10491), (10492), (10495),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10504), (10538), (10823), (10920), (10921),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11072), (11099), (11107), (11122), (11126),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #906.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11127)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11127) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11128)  all_58_6 = e1 & op(e1, e3) = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11107), (11128) are inconsistent by
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1803.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11129)  all_58_12 = e1 & op(e0, e3) = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11129) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11130)  all_58_12 = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11131)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (164), (10192), (11117), (11131),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1062.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11132)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11132) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11133)  all_58_11 = e3 & op(e1, e0) = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11133) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11134)  all_58_11 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11135)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11135) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11136)  all_58_1 = e0 & op(e3, e2) = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11112), (11136) are inconsistent by
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1720.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11137)  all_58_3 = e0 & op(e2, e2) = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11137) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11138)  all_58_3 = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10197), (11138) imply:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11139)  e3 = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11134), (11139) imply:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11140)  all_58_11 = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11107), (11139) imply:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11141)  all_58_6 = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (10823), (11140),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11141), (function-axioms) are inconsistent by
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1686.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11142)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11142) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11143)  all_58_7 = e0 & op(e1, e2) = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11143) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11144)  all_58_7 = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11145)  op(e1, e2) = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11146)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (239), (241),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (10190), (11107), (11146),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1138.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11147)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11147) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11148)  all_58_14 = e3 & op(e0, e1) = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11148) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11149)  all_58_14 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (162), (216),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (235), (237), (10189),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (10492), (10495), (10987), (10988),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11107), (11130), (11134), (11144), (11145),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11149), (function-axioms) are inconsistent by
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #962.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11150)  all_58_15 = e3 & op(e0, e0) = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11150) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11151)  all_58_15 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10504), (11151) are inconsistent by
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2249.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11152)  all_58_13 = e0 & op(e0, e2) = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11152) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11153)  op(e0, e2) = e0
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (158), (191), (255), (256), (10190),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10488), (10489), (11078), (11103), (11153),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #904.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11154)  all_58_15 = e3 & op(e0, e0) = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11154) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11155)  all_58_15 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10504), (11155) are inconsistent by
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2249.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11156)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (164), (216), (222), (10192),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10495), (10504), (10921), (11099), (11156),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #907.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11157)  all_58_12 = e3 & op(e0, e3) = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11157) implies:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11158)  all_58_12 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11159)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (239), (241),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (10189), (11158), (11159),
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1530.
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 234.41/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11160)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11160) gives:
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11161)  all_58_8 = e3 & op(e1, e1) = e3
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11161) implies:
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11162)  op(e1, e1) = e3
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10823), (11162), (function-axioms) are
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11163)  all_58_11 = e3 & op(e1, e0) = e3
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11163) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11164)  all_58_11 = e3
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11165)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11165) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11166)  all_58_0 = e1 & op(e3, e3) = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11166) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11167)  op(e3, e3) = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10538), (11167), (function-axioms) are
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11168)  all_58_1 = e1 & op(e3, e2) = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11168) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11169)  all_58_1 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11170)  op(e3, e2) = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11171)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10538), (11169), (11171),
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1698.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11172)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11172) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11173)  all_58_4 = e0 & op(e3, e1) = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11099), (11173) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1697.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11174)  all_58_9 = e0 & op(e3, e0) = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11174) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11175)  all_58_9 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11176)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11176) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11177)  all_58_1 = e0 & op(e3, e2) = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11169), (11177) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1720.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11178)  all_58_3 = e0 & op(e2, e2) = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10197), (11178) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1719.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11179)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11179) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11180)  all_58_7 = e0 & op(e1, e2) = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11180) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11181)  op(e1, e2) = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11103) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11182)  all_54_14 = e2
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (11182) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11183)  all_52_11 = e2
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11078), (11183) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11184)  $false
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11184) is inconsistent.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11185)  all_54_14 = e1 | all_54_14 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11185) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11186)  all_54_14 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (11186) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11187)  all_52_11 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10489), (11187) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11188)  $false
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11188) is inconsistent.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11189)  all_54_14 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (11189) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11190)  all_52_11 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (11190) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11191)   ~ (all_52_8 = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (11190) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11192)   ~ (all_52_9 = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (11190) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11193)  op(e0, e1) = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11194)  all_54_6 = e3
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (10191), (11194) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11195)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11195) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11196)  all_54_6 = e2
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (11079), (11196) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11197)  all_54_6 = e1 | all_54_6 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11197) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11198)  all_54_6 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (11198) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11199)  all_52_9 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11199) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11200)  all_52_9 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (11200) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11201)   ~ (all_52_1 = e1)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (11200) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11202)   ~ (all_52_8 = e1)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (11200) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11203)  op(e2, e1) = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11204)  all_54_4 = e3
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (10187), (11204) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11205)   ~ (all_54_4 = e3)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11206)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11206) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11207)  all_54_4 = e2
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (10535), (11207) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2096.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11208)   ~ (all_54_4 = e2)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11209)  all_54_4 = e1 | all_54_4 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11209) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11210)  all_54_4 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (11201), (11210) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2086.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11211)  all_54_4 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (11211) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11212)  all_52_1 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11212) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11213)  all_52_1 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (11213) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11214)   ~ (all_52_2 = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11214) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11215)   ~ (all_52_2 = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10535), (11213) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11216)   ~ (e2 = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11201), (11213) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11217)   ~ (e1 = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (11213) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11218)  op(e2, e3) = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11219)  all_54_8 = e3
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (11094), (11219) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11220)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11221)  all_54_2 = e3
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (11221) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11222)  all_52_8 = e3
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11222) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11223)  all_52_8 = e3
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (11223) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11224)   ~ (all_52_12 = e3)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11224) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11225)   ~ (all_52_12 = e3)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (11223) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11226)  op(e3, e1) = e3
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11227)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11227) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11228)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11228) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11229)  op(e3, e1) = all_56_17
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11230)  op(e3, all_56_17) = e3
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10538), (11226), (11229), (11230),
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2098.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11231)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11231) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11232)  op(e2, e1) = all_56_19
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11233)  op(e2, all_56_19) = e2
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11220) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11234)  all_54_8 = e2
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (10536), (11234) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2007.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11235)  all_54_8 = e1 | all_54_8 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11235) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11236)  all_54_8 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (11236) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11237)  all_52_2 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11237) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11238)  all_52_2 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (11238) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11239)   ~ (all_52_6 = e1)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11239) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11240)   ~ (all_52_6 = e1)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11241)  all_54_9 = e3
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10189), (11241) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11242)   ~ (all_54_9 = e3)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11243)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11243) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11244)  all_54_9 = e2
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (11076), (11244) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1954.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11245)   ~ (all_54_9 = e2)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11246)  all_54_9 = e1 | all_54_9 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11246) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11247)  all_54_9 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (11240), (11247) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2055.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11248)  all_54_9 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (11248) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11249)  all_52_6 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11249) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11250)  all_52_6 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (11250) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11251)   ~ (all_52_4 = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10189), (11250) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11252)   ~ (e3 = e0)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11090) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11253)  all_54_1 = e2
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (10537), (11253) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1928.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11254)   ~ (all_54_1 = e2)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11255)  all_54_1 = e1 | all_54_1 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11255) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11256)  all_54_1 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (11256) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11257)  all_52_4 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11257) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11258)  all_52_4 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (11203),
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (11232) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11259)  all_56_19 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11233), (11259) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11260)  op(e2, e1) = e2
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e1,
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (11203), (11260) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11261)  e2 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10920), (11261) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11262)  all_58_10 = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (221), (222), (10504),
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11175), (11262) are inconsistent by sub-proof
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1618.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11263)  all_54_1 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (11251), (11263) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2050.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11264)  all_54_8 = e0
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (11215), (11264) are inconsistent by
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2006.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11265)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11265) gives:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11266)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11266) implies:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11267)  op(e1, all_56_21) = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10820), (11267) imply:
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11268)  op(e1, e2) = e1
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (11181), (11268), (function-axioms)
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 235.04/44.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11269)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11269) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11270)  op(e0, e1) = all_56_23
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11271)  op(e0, all_56_23) = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10184) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11272)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11272) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11273)  op(e2, e3) = all_8_1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11087) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11274)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_42_1 & $i(all_42_0) &
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_42_1)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11274) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11275)  op(e2, e3) = all_42_1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (125), (158), (160), (162), (167),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (191), (212), (213), (255), (256), (10186),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10187), (10190), (10486), (10488), (10489),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10492), (10495), (10530), (10541), (10820),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10921), (11084), (11170), (11181), (11185),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11193), (11218), (11225), (11270), (11271),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11273), (11275), (function-axioms) are
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #899.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11276)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_42_1)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11276) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11277)  op(e2, e3) = all_42_1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (125), (158), (160), (162), (167),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (191), (212), (213), (255), (256), (10186),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10187), (10190), (10486), (10488), (10489),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10492), (10495), (10530), (10541), (10820),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10921), (11084), (11170), (11181), (11185),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11193), (11218), (11225), (11270), (11271),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11273), (11277), (function-axioms) are
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #899.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11278)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_8_1)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11278) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11279)   ~ (all_8_1 = e0)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11280)  op(e2, e3) = all_8_1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11087), (11218), (11279), (11280),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #897.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11281)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (10821), (11191), (11202), (11281) are
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1335.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11282)  all_54_6 = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (11192), (11282) are inconsistent by
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2245.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11283)  all_58_13 = e0 & op(e0, e2) = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11283) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11284)  op(e0, e2) = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (158), (191), (255), (256), (10190),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10488), (10489), (11078), (11103), (11284),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #904.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11285)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11285) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11286)  all_58_4 = e1 & op(e3, e1) = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11099), (11286) are inconsistent by
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2042.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11287)  all_58_9 = e1 & op(e3, e0) = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11287) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11288)  all_58_9 = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (221), (10495),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10504), (11164), (11288), (function-axioms) are
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1740.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11289)  all_58_5 = e3 & op(e2, e1) = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10191), (11289), (function-axioms) are
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11290)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (10823), (11096), (11290),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1307.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11291)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11291) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11292)  all_54_12 = e2
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (11075), (11292) are inconsistent by
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2264.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11293)   ~ (all_54_12 = e2)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11294)  all_54_12 = e1 | all_54_12 = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11295)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (10187), (10538), (11295),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1404.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11296)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11296) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11297)  all_58_6 = e3 & op(e1, e3) = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11297) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11298)  all_58_6 = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11299)  op(e1, e3) = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11294) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11300)  all_54_12 = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11300) imply:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11301)  all_52_3 = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10487), (11301) imply:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11302)  $false
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11302) is inconsistent.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11303)  all_54_12 = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11303) imply:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11304)  all_52_3 = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (11304) imply:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11305)   ~ (all_52_1 = e0)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (11304) imply:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11306)   ~ (all_52_2 = e0)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (11304) imply:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11307)   ~ (all_52_11 = e0)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11307) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11308)   ~ (all_52_11 = e0)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11075), (11304) imply:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11309)   ~ (e2 = e0)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10487), (11304) imply:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11310)   ~ (e1 = e0)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (11304) imply:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11311)  op(e0, e3) = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11312)  all_54_14 = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (11312) imply:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11313)  all_52_11 = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (11313) imply:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11314)  op(e0, e1) = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11315)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (10188), (10538), (11315),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1959.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11316)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11316) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11317)  all_58_4 = e3 & op(e3, e1) = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11317) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11318)  all_58_4 = e3
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11319)  all_58_15 = e0 & op(e0, e0) = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11319) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11320)  op(e0, e0) = e0
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10495), (11320), (function-axioms) are
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11321)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11321) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11322)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11323)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11324)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11324) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11325)  all_58_0 = e1 & op(e3, e3) = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11325) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11326)  op(e3, e3) = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10538), (11326), (function-axioms) are
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11327)  all_58_2 = e1 & op(e2, e3) = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11327) implies:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11328)  all_58_2 = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (82), (110),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (149), (157), (158), (160), (163),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (197), (201), (210),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (219), (221), (222), (223), (224),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (232), (239), (240), (242), (243), (244),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (269), (280), (10187), (10190), (10192),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (10198), (10205), (10482), (10485),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10486), (10490), (10491), (10492), (10495),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10504), (10538), (10823), (10920), (10921),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11072), (11298), (11318), (11323), (11328),
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #906.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11329)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11329) gives:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11330)  all_58_6 = e1 & op(e1, e3) = e1
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11298), (11330) are inconsistent by
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1803.
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11331)  all_58_12 = e1 & op(e0, e3) = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11331) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11332)  all_58_12 = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (10988), (11314), (11322), (11332),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #896.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11333)  all_58_9 = e3 & op(e3, e0) = e3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11333) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11334)  all_58_9 = e3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11335)  all_54_4 = e3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (10187), (11335) are inconsistent by
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11336)   ~ (all_54_4 = e3)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11337)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11338)  all_58_15 = e0 & op(e0, e0) = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11338) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11339)  op(e0, e0) = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10495), (11339), (function-axioms) are
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11340)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11340) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11341)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11342)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11343)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11343) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11344)  all_58_0 = e1 & op(e3, e3) = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11344) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11345)  op(e3, e3) = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10538), (11345), (function-axioms) are
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11346)  all_58_2 = e1 & op(e2, e3) = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11346) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11347)  all_58_2 = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11348)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11348) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11349)  all_58_2 = e0 & op(e2, e3) = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11347), (11349) are inconsistent by
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1972.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11350)  all_58_3 = e0 & op(e2, e2) = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11350) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11351)  all_58_3 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10197), (11351) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11352)  e3 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11334), (11352) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11353)  all_58_9 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (82), (110),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (149), (157), (158), (160), (163),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (197), (201), (210),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (219), (221), (222), (223), (224),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (232), (239), (242), (243), (244), (245),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (280), (10187), (10190), (10192), (10197),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10198), (10205), (10482), (10485), (10486),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10490), (10491), (10492), (10495), (10504),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10823), (10920), (10921), (11072), (11298),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11342), (11347), (11353), (function-axioms) are
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #908.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11354)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11354) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11355)  all_58_5 = e0 & op(e2, e1) = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11355) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11356)  op(e2, e1) = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11337) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11357)  all_54_4 = e2
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (10535), (11357) are inconsistent by
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2096.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11358)  all_54_4 = e1 | all_54_4 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11358) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11359)  all_54_4 = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (11359) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11360)  all_52_1 = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11360) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11361)  all_52_1 = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (11361) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11362)   ~ (all_52_2 = e1)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11362) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11363)   ~ (all_52_2 = e1)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (11361) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11364)  op(e2, e3) = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11365)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11365) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11366)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11366) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11367)  op(e3, all_56_1) = e3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10534), (11367) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11368)  op(e3, e2) = e3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (10188), (11368), (function-axioms) are
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11369)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11369) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11370)  op(e2, e3) = all_56_3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11371)  op(e2, all_56_3) = e2
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10184) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11372)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11372) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11373)  op(e2, e3) = all_8_1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (141), (143), (193), (195), (196), (258),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (268), (10492), (10536), (11076), (11081),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11087), (11306), (11356), (11363), (11364),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11370), (11371), (11373), (function-axioms) are
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #895.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11374)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_8_1)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11374) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11375)  op(e2, e3) = all_8_1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (141), (143), (193), (195), (196), (258),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (268), (10492), (10536), (11076), (11081),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11087), (11306), (11356), (11363), (11364),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11370), (11371), (11375), (function-axioms) are
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #895.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11376)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11376) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11377)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11377) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11378)  op(e1, e3) = all_56_5
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11379)  op(e1, all_56_5) = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11299), (11378), (11379), (function-axioms)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2243.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11380)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11380) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11381)  op(e0, e3) = all_56_7
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11382)  op(e0, all_56_7) = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11383)  all_54_8 = e3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (11383) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11384)  all_52_2 = e3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11384) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11385)  all_52_2 = e3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (11385) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11386)   ~ (all_52_6 = e3)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (11385) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11387)   ~ (all_52_14 = e3)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11387) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11388)   ~ (all_52_14 = e3)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11389)  all_54_11 = e3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11389) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11390)  all_52_14 = e3
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11388), (11390) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11391)  $false
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11391) is inconsistent.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11392)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11392) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11393)  all_54_11 = e2
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (11081), (11393) are inconsistent by
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2177.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11394)  all_54_11 = e1 | all_54_11 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11394) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11395)  all_54_11 = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11395) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11396)  all_52_14 = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10492), (11396) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11397)  $false
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11397) is inconsistent.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11398)  all_54_11 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11398) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11399)  all_52_14 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (11399) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11400)   ~ (all_52_6 = e0)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (195), (267), (10189), (10495), (11076), (11311),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11381), (11382), (11400), (function-axioms) are
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1952.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11401)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (10536), (11306), (11363), (11401) are
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1949.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11402)  all_54_4 = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (11305), (11402) are inconsistent by
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1923.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11403)  all_58_10 = e0 & op(e2, e0) = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11403) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11404)  op(e2, e0) = e0
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10921), (11404), (function-axioms) are
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11405)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11405) gives:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11406)  all_58_6 = e1 & op(e1, e3) = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11406) implies:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11407)  all_58_6 = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11298), (11407) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11408)  e3 = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11334), (11408) imply:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11409)  all_58_9 = e1
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (164), (216), (222), (10192),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10495), (10504), (10921), (11409),
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #971.
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11410)  all_58_12 = e1 & op(e0, e3) = e1
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11410) implies:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11411)  all_58_12 = e1
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (10988), (11314), (11341), (11411),
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #896.
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11412)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (10489), (11078), (11308), (11412) are
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1798.
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11413)  all_58_12 = e3 & op(e0, e3) = e3
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11413) implies:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11414)  all_58_12 = e3
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11294) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11415)  all_54_12 = e1
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11415) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11416)  all_52_3 = e1
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10487), (11416) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11417)  $false
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11417) is inconsistent.
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11418)  all_54_12 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11418) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11419)  all_52_3 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (11419) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11420)   ~ (all_52_11 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11420) implies:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11421)   ~ (all_52_11 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11075), (11419) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11422)   ~ (e2 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10487), (11419) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11423)   ~ (e1 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (157), (190), (216), (255), (10489),
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10495), (10988), (11078), (11414), (11421),
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1078.
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11424)  all_58_11 = e2 & op(e1, e0) = e2
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (160), (162),
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (216), (221), (222), (223),
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (230), (231), (232),
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |            (233), (236), (240), (10189), (10191), (10192),
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |            (10197), (10198), (10488), (10491), (10492),
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |            (10495), (10504), (10535), (10538), (10823),
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |            (11424), (function-axioms) are inconsistent by
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #894.
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | |   (11425)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 235.04/44.09  | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | BETA: splitting (11425) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | |   (11426)  all_58_11 = e2 & op(e1, e0) = e2
% 235.04/44.09  | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (160), (162),
% 235.04/44.09  | | | | | | | | | | | | | | | | | |            (164), (165), (167), (216), (221), (222), (223),
% 235.04/44.09  | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (230), (231), (232),
% 235.04/44.09  | | | | | | | | | | | | | | | | | |            (233), (236), (240), (10189), (10191), (10192),
% 235.04/44.09  | | | | | | | | | | | | | | | | | |            (10197), (10198), (10488), (10491), (10492),
% 235.04/44.09  | | | | | | | | | | | | | | | | | |            (10495), (10504), (10535), (10538), (10823),
% 235.04/44.09  | | | | | | | | | | | | | | | | | |            (11426), (function-axioms) are inconsistent by
% 235.04/44.09  | | | | | | | | | | | | | | | | | |            sub-proof #894.
% 235.04/44.09  | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | |   (11427)  all_58_15 = e2 & op(e0, e0) = e2
% 235.04/44.09  | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | ALPHA: (11427) implies:
% 235.04/44.09  | | | | | | | | | | | | | | | | | |   (11428)  all_58_15 = e2
% 235.04/44.09  | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10504), (11428) are inconsistent by
% 235.04/44.09  | | | | | | | | | | | | | | | | | |            sub-proof #2231.
% 235.04/44.09  | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | End of split
% 235.04/44.09  | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | |   (11429)  all_18_2 = e0
% 235.04/44.09  | | | | | | | | | |   (11430)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0
% 235.04/44.09  | | | | | | | | | |              & op(e1, e0) = all_18_1 & $i(all_18_0) &
% 235.04/44.09  | | | | | | | | | |              $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1, e0)
% 235.04/44.09  | | | | | | | | | |              = all_18_1 & $i(all_18_1))
% 235.04/44.09  | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | COMBINE_EQS: (339), (11429) imply:
% 235.04/44.09  | | | | | | | | | |   (11431)  all_6_2 = e0
% 235.04/44.09  | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | COMBINE_EQS: (332), (11431) imply:
% 235.04/44.09  | | | | | | | | | |   (11432)  all_28_2 = e0
% 235.04/44.09  | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | COMBINE_EQS: (266), (11431) imply:
% 235.04/44.09  | | | | | | | | | |   (11433)  all_56_21 = e0
% 235.04/44.09  | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | REDUCE: (380), (11431) imply:
% 235.04/44.09  | | | | | | | | | |   (11434)   ~ (all_52_8 = e0)
% 235.04/44.09  | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | REDUCE: (385), (11431) imply:
% 235.04/44.09  | | | | | | | | | |   (11435)   ~ (all_52_14 = e0)
% 235.04/44.09  | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | REDUCE: (391), (11431) imply:
% 235.04/44.09  | | | | | | | | | |   (11436)   ~ (e3 = e0)
% 235.04/44.09  | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | REDUCE: (39), (11431) imply:
% 235.04/44.09  | | | | | | | | | |   (11437)  op(e1, e1) = e0
% 235.04/44.09  | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | BETA: splitting (61) gives:
% 235.04/44.09  | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | |   (11438)   ~ (all_20_2 = e1)
% 235.04/44.09  | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | REDUCE: (341), (11438) imply:
% 235.04/44.09  | | | | | | | | | | |   (11439)   ~ (all_4_2 = e1)
% 235.04/44.09  | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | BETA: splitting (189) gives:
% 235.04/44.09  | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | |   (11440)  all_54_15 = e3
% 235.04/44.09  | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | REF_CLOSE: (299), (10201), (11440) are inconsistent by
% 235.04/44.09  | | | | | | | | | | | |            sub-proof #2340.
% 235.04/44.09  | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | |   (11441)   ~ (all_54_15 = e3)
% 235.04/44.09  | | | | | | | | | | | |   (11442)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 235.04/44.09  | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | BETA: splitting (11442) gives:
% 235.04/44.09  | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | |   (11443)  all_54_15 = e2
% 235.04/44.09  | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | REF_CLOSE: (299), (390), (11443) are inconsistent by
% 235.04/44.09  | | | | | | | | | | | | |            sub-proof #2339.
% 235.04/44.09  | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | |   (11444)   ~ (all_54_15 = e2)
% 235.04/44.09  | | | | | | | | | | | | |   (11445)  all_54_15 = e1 | all_54_15 = e0
% 235.04/44.09  | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | BETA: splitting (11445) gives:
% 235.04/44.09  | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | |   (11446)  all_54_15 = e1
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | REF_CLOSE: (299), (11439), (11446) are inconsistent by
% 235.04/44.09  | | | | | | | | | | | | | |            sub-proof #2338.
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | |   (11447)  all_54_15 = e0
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | COMBINE_EQS: (299), (11447) imply:
% 235.04/44.09  | | | | | | | | | | | | | |   (11448)  all_4_2 = e0
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | SIMP: (11448) implies:
% 235.04/44.09  | | | | | | | | | | | | | |   (11449)  all_4_2 = e0
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | COMBINE_EQS: (254), (11449) imply:
% 235.04/44.09  | | | | | | | | | | | | | |   (11450)  all_56_31 = e0
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | REDUCE: (368), (11449) imply:
% 235.04/44.09  | | | | | | | | | | | | | |   (11451)   ~ (all_52_3 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | REDUCE: (386), (11449) imply:
% 235.04/44.09  | | | | | | | | | | | | | |   (11452)   ~ (all_52_11 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | REDUCE: (388), (11449) imply:
% 235.04/44.09  | | | | | | | | | | | | | |   (11453)   ~ (all_52_13 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | REDUCE: (390), (11449) imply:
% 235.04/44.09  | | | | | | | | | | | | | |   (11454)   ~ (e2 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | REDUCE: (11439), (11449) imply:
% 235.04/44.09  | | | | | | | | | | | | | |   (11455)   ~ (e1 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | REDUCE: (36), (11449) imply:
% 235.04/44.09  | | | | | | | | | | | | | |   (11456)  op(e0, e0) = e0
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 235.04/44.09  | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | |   (11457)  all_58_15 = e0 & op(e0, e0) = e0
% 235.04/44.09  | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | ALPHA: (11457) implies:
% 235.04/44.09  | | | | | | | | | | | | | | |   (11458)  all_58_15 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | |   (11459)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | BETA: splitting (11459) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | |   (11460)  all_58_0 = e0 & op(e3, e3) = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (10203), (11460), (function-axioms) are
% 235.04/44.09  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1736.
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | |   (11461)  all_58_1 = e0 & op(e3, e2) = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | ALPHA: (11461) implies:
% 235.04/44.09  | | | | | | | | | | | | | | | | |   (11462)  all_58_1 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | |   (11463)  op(e3, e2) = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | |   (11464)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | BETA: splitting (11464) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11465)  all_58_0 = e0 & op(e3, e3) = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (10203), (11465), (function-axioms) are
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1736.
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11466)  all_58_2 = e0 & op(e2, e3) = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | ALPHA: (11466) implies:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11467)  all_58_2 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11468)  op(e2, e3) = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (11468) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11469)  all_52_1 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (11463) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11470)  all_52_4 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | REDUCE: (148), (11469) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11471)   ~ (all_52_3 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | REDUCE: (145), (11469) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11472)   ~ (all_52_13 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | REDUCE: (136), (11470) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11473)   ~ (all_52_6 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | SIMP: (11473) implies:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11474)   ~ (all_52_6 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | REDUCE: (135), (11470) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11475)   ~ (all_52_7 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | SIMP: (11475) implies:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11476)   ~ (all_52_7 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | REDUCE: (134), (11470) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11477)   ~ (all_52_8 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | REDUCE: (361), (11470) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | |   (11478)   ~ (all_10_2 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (10184) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | |   (11479)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | ALPHA: (11479) implies:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | |   (11480)   ~ (all_8_0 = e1)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | |   (11481)  op(e2, e3) = all_8_1
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | |   (11482)  op(all_8_1, e2) = all_8_0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | |   (11483)   ~ (all_42_2 = e3)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (10185), (11483) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | |   (11484)  $false
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | CLOSE: (11484) is inconsistent.
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | |   (11485)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_8_1,
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (11468), (11481) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | |   (11486)  all_8_1 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (11482), (11486) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | |   (11487)  op(e0, e2) = all_8_0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11485) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11488)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_42_1 & $i(all_42_0) &
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |            $i(all_42_1)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11488) implies:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11489)   ~ (all_42_0 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11490)  op(e2, e3) = all_42_1
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11491)  op(all_42_1, e2) = all_42_0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |              all_8_0, e2, e0, simplifying with (158), (11487)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11492)  all_52_7 = all_8_0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_42_1,
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (11468), (11490) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11493)  all_42_1 = e0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (11492) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11494)  all_54_13 = all_8_0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (11492) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11495)   ~ (all_52_3 = all_8_0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (11492) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11496)   ~ (all_52_6 = all_8_0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (11492) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11497)   ~ (all_52_11 = all_8_0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | SIMP: (11497) implies:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11498)   ~ (all_52_11 = all_8_0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10190), (11492) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11499)   ~ (all_8_0 = e3)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11476), (11492) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11500)   ~ (all_8_0 = e0)
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11491), (11493) imply:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | |   (11501)  op(e0, e2) = all_42_0
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | |   (11502)  all_54_13 = e3
% 235.04/44.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11494), (11499), (11502) are inconsistent by
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #893.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | |   (11503)   ~ (all_54_13 = e3)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | |   (11504)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11504) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | |   (11505)  all_54_13 = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11494), (11505) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | |   (11506)  all_8_0 = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11506) implies:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | |   (11507)  all_8_0 = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11495), (11507) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | |   (11508)   ~ (all_52_3 = e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11496), (11507) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | |   (11509)   ~ (all_52_6 = e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11498), (11507) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | |   (11510)   ~ (all_52_11 = e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11499), (11507) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | |   (11511)   ~ (e3 = e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11487), (11507) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | |   (11512)  op(e0, e2) = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (11513)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (10197), (11462), (11513) are
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #892.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (11514)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11514) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11515)  all_58_7 = e1 & op(e1, e2) = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11515) implies:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11516)  all_58_7 = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11517)  all_54_9 = e3
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10189), (11517) are inconsistent by
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11518)   ~ (all_54_9 = e3)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11519)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11520)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (235), (10197), (10198),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11512), (11516), (11520), (function-axioms) are
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #891.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11521)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11521) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11522)  all_58_7 = e2 & op(e1, e2) = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11522) implies:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11523)  all_58_7 = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11516), (11523) are inconsistent by
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2134.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11524)  all_58_13 = e2 & op(e0, e2) = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11524) implies:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11525)  all_58_13 = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11519) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11526)  all_54_9 = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (11509), (11526) are inconsistent by
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1954.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11527)  all_54_9 = e1 | all_54_9 = e0
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11527) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11528)  all_54_9 = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (11528) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11529)  all_52_6 = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11529) implies:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11530)  all_52_6 = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (11530) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11531)   ~ (all_52_2 = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (11530) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11532)   ~ (all_52_14 = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11532) implies:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11533)   ~ (all_52_14 = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10189), (11530) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11534)   ~ (e3 = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (11530) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11535)  op(e1, e2) = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11536)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, all_56_11) = e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11536) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11537)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_9 & $i(all_56_9)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11537) implies:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11538)  op(e3, e2) = all_56_9
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11539)  op(e3, all_56_9) = e3
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11540)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (45), (10199), (11467), (11540),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #890.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11541)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11541) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11542)  all_58_6 = e1 & op(e1, e3) = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11542) implies:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11543)  op(e1, e3) = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (11531), (11543), (function-axioms) are
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11544)  all_58_12 = e1 & op(e0, e3) = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11544) implies:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11545)  all_58_12 = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11546)  op(e0, e3) = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11547)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11547) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11548)  all_58_12 = e3 & op(e0, e3) = e3
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11545), (11548) are inconsistent by
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1205.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11549)  all_58_13 = e3 & op(e0, e2) = e3
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10190), (11549), (function-axioms) are
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11550)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11550) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11551)  all_58_14 = e3 & op(e0, e1) = e3
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11551) implies:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11552)  all_58_14 = e3
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11553)  op(e0, e1) = e3
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (11553) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11554)  all_52_11 = e3
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_42_0,
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (11501), (11512) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11555)  all_42_0 = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (11546) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11556)  all_52_3 = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_9,
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (11463), (11538) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11557)  all_56_9 = e0
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (11556) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11558)   ~ (all_10_2 = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (11554) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11559)   ~ (all_52_8 = e3)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11539), (11557) imply:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11560)  op(e3, e0) = e3
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11561)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (121), (125), (139), (140), (144), (158),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (163), (167), (169), (190), (192), (255),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (10184), (10187), (11450), (11451),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11452), (11468), (11490), (11512), (11531),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11561), (function-axioms) are inconsistent by
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #888.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11562)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11562) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11563)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11563) gives:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11564)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11564) implies:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11565)   ~ (all_56_31 = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11566)   ~ (all_56_11 = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11567)   ~ (all_56_1 = e1)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11568)  op(e1, e2) = e2
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (45), (73), (79), (123),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (160), (162), (163), (164), (165), (167),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (202), (204), (216), (217), (218), (219),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (224), (225), (229), (231),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (236), (237), (242), (243),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (281), (292), (348), (363), (365), (10187),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10192), (10197), (10199), (10203),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11432), (11434), (11437), (11456), (11458),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11467), (11512), (11525), (11531), (11533),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11535), (11545), (11552), (11559), (11560),
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11568), (function-axioms) are inconsistent by
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #886.
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11569)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 235.04/44.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (204), (290), (292), (365), (10199),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10203), (11450), (11560), (11569),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #885.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11570)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (11435), (11453), (11533), (11570),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1903.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11571)  all_58_15 = e3 & op(e0, e0) = e3
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11571) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11572)  op(e0, e0) = e3
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11456), (11572), (function-axioms) are
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11573)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10184), (10186), (11468), (11490), (11573),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #884.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11574)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15 & $i(all_56_15))
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11574) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11575)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11575) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11576)  op(e1, e2) = all_56_13
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11577)  op(e1, all_56_13) = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (45), (159), (163), (241), (10199), (11437),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11451), (11467), (11531), (11535), (11576),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11577), (function-axioms) are inconsistent by
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #883.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11578)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_15 & $i(all_56_15)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11578) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11579)  op(e0, e2) = all_56_15
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11580)  op(e0, all_56_15) = e0
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11581)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (45), (10199), (11467), (11581),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #890.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11582)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11582) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11583)  all_58_6 = e1 & op(e1, e3) = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11583) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11584)  op(e1, e3) = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (11531), (11584), (function-axioms) are
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11585)  all_58_12 = e1 & op(e0, e3) = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11585) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11586)  all_58_12 = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11587)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11587) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11588)  all_58_12 = e3 & op(e0, e3) = e3
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11586), (11588) are inconsistent by
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1205.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11589)  all_58_13 = e3 & op(e0, e2) = e3
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10190), (11589), (function-axioms) are
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11590)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11590) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11591)  all_58_14 = e3 & op(e0, e1) = e3
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11591) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11592)  op(e0, e1) = e3
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11585) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11593)  op(e0, e3) = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (11592) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11594)  all_52_11 = e3
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_42_0,
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (11501),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (11579) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11595)  all_56_15 = all_42_0
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (11512),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (11579) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11596)  all_56_15 = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (11593) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11597)  all_52_3 = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11595), (11596) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11598)  all_42_0 = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11508), (11597) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11599)   ~ (e2 = e1)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11580), (11596) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11600)  op(e0, e2) = e0
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (237), (10198), (11462), (11516),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11600), (function-axioms) are inconsistent by
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #882.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11601)  all_58_15 = e3 & op(e0, e0) = e3
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11601) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11602)  op(e0, e0) = e3
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11456), (11602), (function-axioms) are
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11603)  all_54_9 = e0
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (11474), (11603) are inconsistent by
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1953.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11604)  all_58_13 = e1 & op(e0, e2) = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11604) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11605)  all_58_13 = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (126), (143), (160), (163), (195),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (235), (237), (267), (10189), (10197),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (11437), (11474), (11509), (11605),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            #881.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | |   (11606)  all_54_13 = e1 | all_54_13 = e0
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11480), (11494), (11500), (11606) are
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #880.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11607)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |            $i(all_42_1)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11607) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11608)   ~ (all_42_1 = e1)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11609)  op(e2, e3) = all_42_1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |              all_8_0, e2, e0, simplifying with (158), (11487)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11610)  all_52_7 = all_8_0
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_42_1,
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (11468), (11609) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11611)  all_42_1 = e0
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (11610) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11612)  all_54_13 = all_8_0
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (11610) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11613)   ~ (all_52_3 = all_8_0)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (11610) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11614)   ~ (all_52_6 = all_8_0)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (11610) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11615)   ~ (all_52_11 = all_8_0)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | SIMP: (11615) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11616)   ~ (all_52_11 = all_8_0)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10190), (11610) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11617)   ~ (all_8_0 = e3)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11476), (11610) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | |   (11618)   ~ (all_8_0 = e0)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | |   (11619)  all_54_13 = e3
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11612), (11617), (11619) are inconsistent by
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #893.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | |   (11620)   ~ (all_54_13 = e3)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | |   (11621)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11621) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | |   (11622)  all_54_13 = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11612), (11622) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | |   (11623)  all_8_0 = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11623) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | |   (11624)  all_8_0 = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11613), (11624) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | |   (11625)   ~ (all_52_3 = e2)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11614), (11624) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | |   (11626)   ~ (all_52_6 = e2)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11616), (11624) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | |   (11627)   ~ (all_52_11 = e2)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11617), (11624) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | |   (11628)   ~ (e3 = e2)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11487), (11624) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | |   (11629)  op(e0, e2) = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (11630)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (10197), (11462), (11630) are
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #892.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (11631)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11631) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11632)  all_58_7 = e1 & op(e1, e2) = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11632) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11633)  all_58_7 = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11634)  all_54_9 = e3
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10189), (11634) are inconsistent by
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11635)   ~ (all_54_9 = e3)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11636)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11637)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (235), (10197), (10198),
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11629), (11633), (11637), (function-axioms) are
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #891.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11638)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11638) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11639)  all_58_7 = e2 & op(e1, e2) = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11639) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11640)  all_58_7 = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11633), (11640) are inconsistent by
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2134.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11641)  all_58_13 = e2 & op(e0, e2) = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11641) implies:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11642)  all_58_13 = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11636) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11643)  all_54_9 = e2
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (11626), (11643) are inconsistent by
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1954.
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11644)   ~ (all_54_9 = e2)
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11645)  all_54_9 = e1 | all_54_9 = e0
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11645) gives:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11646)  all_54_9 = e1
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (11646) imply:
% 235.04/44.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11647)  all_52_6 = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11647) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11648)  all_52_6 = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (11648) imply:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11649)   ~ (all_52_2 = e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (11648) imply:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11650)   ~ (all_52_14 = e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11650) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11651)   ~ (all_52_14 = e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10189), (11648) imply:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11652)   ~ (e3 = e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11626), (11648) imply:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11653)   ~ (e2 = e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (11648) imply:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11654)  op(e1, e2) = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11655)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, all_56_11) = e2)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11655) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11656)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_9 & $i(all_56_9)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11656) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11657)  op(e3, e2) = all_56_9
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11658)  op(e3, all_56_9) = e3
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11659)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (10184), (10199), (11608), (11609), (11659),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #879.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11660)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11660) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11661)  all_58_6 = e1 & op(e1, e3) = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11661) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11662)  op(e1, e3) = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (11649), (11662), (function-axioms) are
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11663)  all_58_12 = e1 & op(e0, e3) = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11663) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11664)  all_58_12 = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11665)  op(e0, e3) = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11666)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11666) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11667)  all_58_12 = e3 & op(e0, e3) = e3
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11664), (11667) are inconsistent by
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1205.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11668)  all_58_13 = e3 & op(e0, e2) = e3
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10190), (11668), (function-axioms) are
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11669)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11669) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11670)  all_58_14 = e3 & op(e0, e1) = e3
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11670) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11671)  all_58_14 = e3
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11672)  op(e0, e1) = e3
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (11672) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11673)  all_52_11 = e3
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (11665) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11674)  all_52_3 = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_9,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (11463), (11657) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11675)  all_56_9 = e0
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (11674) imply:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11676)   ~ (all_10_2 = e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (11673) imply:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11677)   ~ (all_52_8 = e3)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11658), (11675) imply:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11678)  op(e3, e0) = e3
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11679)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (121), (125), (139), (140), (144), (158),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (163), (167), (169), (190), (192), (255),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (10184), (10187), (11450), (11451),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11452), (11468), (11609), (11629), (11649),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11679), (function-axioms) are inconsistent by
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #888.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11680)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11680) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11681)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11681) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11682)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11682) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11683)  op(e1, e2) = e2
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (45), (73), (79), (123),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (160), (162), (163), (164), (165), (167),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (202), (204), (216), (217), (218), (219),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (224), (225), (229), (231),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (236), (237), (242), (243),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (281), (292), (348), (363), (365), (10187),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10192), (10197), (10199), (10203),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11432), (11434), (11437), (11456), (11458),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11467), (11629), (11642), (11649), (11651),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11654), (11664), (11671), (11677), (11678),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11683), (function-axioms) are inconsistent by
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #886.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11684)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (204), (290), (292), (365), (10199),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10203), (11450), (11678), (11684),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #885.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11685)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (11435), (11453), (11651), (11685),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1903.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11686)  all_58_15 = e3 & op(e0, e0) = e3
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11686) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11687)  op(e0, e0) = e3
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11456), (11687), (function-axioms) are
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11688)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10184), (10186), (11468), (11609), (11688),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #884.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11689)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15 & $i(all_56_15))
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11689) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11690)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11690) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11691)  op(e1, e2) = all_56_13
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11692)  op(e1, all_56_13) = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (45), (159), (163), (241), (10199), (11437),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11451), (11467), (11649), (11654), (11691),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11692), (function-axioms) are inconsistent by
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #883.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11693)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_15 & $i(all_56_15)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11693) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11694)  op(e0, e2) = all_56_15
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11695)  op(e0, all_56_15) = e0
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11696)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (10184), (10199), (11608), (11609), (11696),
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #879.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11697)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11697) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11698)  all_58_6 = e1 & op(e1, e3) = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11698) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11699)  op(e1, e3) = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (11649), (11699), (function-axioms) are
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11700)  all_58_12 = e1 & op(e0, e3) = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11700) implies:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11701)  all_58_12 = e1
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11702)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11702) gives:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11703)  all_58_12 = e3 & op(e0, e3) = e3
% 235.04/44.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11701), (11703) are inconsistent by
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1205.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11704)  all_58_13 = e3 & op(e0, e2) = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10190), (11704), (function-axioms) are
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11705)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11705) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11706)  all_58_14 = e3 & op(e0, e1) = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11706) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11707)  all_58_14 = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11708)  op(e0, e1) = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11709)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11709) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11700) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11710)  op(e0, e3) = e1
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (11708) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11711)  all_52_11 = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (11629),
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (11694) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11712)  all_56_15 = e2
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (11710) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11713)  all_52_3 = e1
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11695), (11712) imply:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11714)  op(e0, e2) = e0
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (237), (10198), (11462), (11633),
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11714), (function-axioms) are inconsistent by
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #882.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11715)  all_58_13 = e1 & op(e0, e2) = e1
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11715) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11716)  all_58_13 = e1
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (160), (163), (224),
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (237), (10197), (11437), (11649), (11651),
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11716), (function-axioms) are inconsistent by
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #887.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11717)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11717) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11718)  all_58_14 = e1 & op(e0, e1) = e1
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11707), (11718) are inconsistent by
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1900.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11719)  all_58_15 = e1 & op(e0, e0) = e1
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11719) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11720)  op(e0, e0) = e1
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11456), (11720), (function-axioms) are
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11721)  all_58_15 = e3 & op(e0, e0) = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11721) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11722)  op(e0, e0) = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11456), (11722), (function-axioms) are
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11723)  all_54_9 = e0
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (11474), (11723) are inconsistent by
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1953.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11724)  all_58_13 = e1 & op(e0, e2) = e1
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11724) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11725)  all_58_13 = e1
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (126), (143), (160), (163), (195),
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (235), (237), (267), (10189), (10197),
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            (11437), (11474), (11626), (11725),
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            #881.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | |   (11726)  all_54_13 = e1 | all_54_13 = e0
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11480), (11612), (11618), (11726) are
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #880.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | |   (11727)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | |            $i(all_8_1)
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | ALPHA: (11727) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | |   (11728)   ~ (all_8_1 = e0)
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | |   (11729)  op(e2, e3) = all_8_1
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | |   (11730)   ~ (all_42_2 = e3)
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | REDUCE: (10185), (11730) imply:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | |   (11731)  $false
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | CLOSE: (11731) is inconsistent.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | |   (11732)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11468), (11728), (11729), (11732),
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | |            #897.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | |   (11733)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 235.04/44.13  | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 235.04/44.13  | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | BETA: splitting (11733) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | |   (11734)  all_58_6 = e0 & op(e1, e3) = e0
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | ALPHA: (11734) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | |   (11735)  all_58_6 = e0
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (224), (225),
% 235.04/44.13  | | | | | | | | | | | | | | | | | | |            (226), (10189), (11437), (11735),
% 235.04/44.13  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.13  | | | | | | | | | | | | | | | | | | |            #1977.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | |   (11736)  all_58_12 = e0 & op(e0, e3) = e0
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | ALPHA: (11736) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | |   (11737)  op(e0, e3) = e0
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11451), (11737), (function-axioms) are
% 235.04/44.13  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | |   (11738)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 235.04/44.13  | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 235.04/44.13  | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | BETA: splitting (11738) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | |   (11739)  all_58_4 = e0 & op(e3, e1) = e0
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | ALPHA: (11739) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | |   (11740)  all_58_4 = e0
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (229),
% 235.04/44.13  | | | | | | | | | | | | | | | | |            (230), (10191), (11437), (11740),
% 235.04/44.13  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.13  | | | | | | | | | | | | | | | | |            #1662.
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | |   (11741)  all_58_9 = e0 & op(e3, e0) = e0
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | ALPHA: (11741) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | |   (11742)  all_58_9 = e0
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (220), (221),
% 235.04/44.13  | | | | | | | | | | | | | | | | |            (222), (10192), (11456), (11458), (11742),
% 235.04/44.13  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.13  | | | | | | | | | | | | | | | | |            #1652.
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | |   (11743)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 235.04/44.13  | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 235.04/44.13  | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 235.04/44.13  | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 235.04/44.13  | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 235.04/44.13  | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (220),
% 235.04/44.13  | | | | | | | | | | | | | | |            (221), (222), (10192), (11435), (11453), (11456),
% 235.04/44.13  | | | | | | | | | | | | | | |            (11743), (function-axioms) are inconsistent by
% 235.04/44.13  | | | | | | | | | | | | | | |            sub-proof #1489.
% 235.04/44.13  | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | End of split
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | |   (11744)  all_20_2 = e1
% 235.04/44.13  | | | | | | | | | | |   (11745)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 235.04/44.13  | | | | | | | | | | |              & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 235.04/44.13  | | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 235.04/44.13  | | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | COMBINE_EQS: (341), (11744) imply:
% 235.04/44.13  | | | | | | | | | | |   (11746)  all_4_2 = e1
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | SIMP: (11746) implies:
% 235.04/44.13  | | | | | | | | | | |   (11747)  all_4_2 = e1
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | COMBINE_EQS: (324), (11747) imply:
% 235.04/44.13  | | | | | | | | | | |   (11748)  all_34_2 = e1
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | COMBINE_EQS: (254), (11747) imply:
% 235.04/44.13  | | | | | | | | | | |   (11749)  all_56_31 = e1
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | REDUCE: (379), (11747) imply:
% 235.04/44.13  | | | | | | | | | | |   (11750)   ~ (all_52_7 = e1)
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | REDUCE: (387), (11747) imply:
% 235.04/44.13  | | | | | | | | | | |   (11751)   ~ (all_52_12 = e1)
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | REDUCE: (388), (11747) imply:
% 235.04/44.13  | | | | | | | | | | |   (11752)   ~ (all_52_13 = e1)
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | REDUCE: (389), (11747) imply:
% 235.04/44.13  | | | | | | | | | | |   (11753)   ~ (all_52_14 = e1)
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | REDUCE: (10201), (11747) imply:
% 235.04/44.13  | | | | | | | | | | |   (11754)   ~ (e3 = e1)
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | REDUCE: (390), (11747) imply:
% 235.04/44.13  | | | | | | | | | | |   (11755)   ~ (e2 = e1)
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | REDUCE: (36), (11747) imply:
% 235.04/44.13  | | | | | | | | | | |   (11756)  op(e0, e0) = e1
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | BETA: splitting (220) gives:
% 235.04/44.13  | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | |   (11757)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 235.04/44.13  | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 235.04/44.13  | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 235.04/44.13  | | | | | | | | | | | |            (222), (10192), (11752), (11756), (11757),
% 235.04/44.13  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.13  | | | | | | | | | | | |            #878.
% 235.04/44.13  | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | |   (11758)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 235.04/44.13  | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 235.04/44.13  | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | BETA: splitting (11758) gives:
% 235.04/44.13  | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | |   (11759)  all_58_11 = e1 & op(e1, e0) = e1
% 235.04/44.13  | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | ALPHA: (11759) implies:
% 235.04/44.13  | | | | | | | | | | | | |   (11760)  op(e1, e0) = e1
% 235.04/44.13  | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | REF_CLOSE: (160), (11753), (11760), (function-axioms) are
% 235.04/44.13  | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 235.04/44.13  | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | |   (11761)  all_58_15 = e1 & op(e0, e0) = e1
% 235.04/44.13  | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | ALPHA: (11761) implies:
% 235.04/44.13  | | | | | | | | | | | | |   (11762)  all_58_15 = e1
% 235.04/44.13  | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | BETA: splitting (67) gives:
% 235.04/44.13  | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | |   (11763)   ~ (all_24_2 = e2)
% 235.04/44.13  | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | REDUCE: (301), (11763) imply:
% 235.04/44.13  | | | | | | | | | | | | | |   (11764)   ~ (all_10_2 = e2)
% 235.04/44.13  | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 235.04/44.13  | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | |   (11765)  all_54_0 = e3
% 235.04/44.13  | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | COMBINE_EQS: (292), (11765) imply:
% 235.04/44.13  | | | | | | | | | | | | | | |   (11766)  all_10_2 = e3
% 235.04/44.13  | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | REDUCE: (363), (11766) imply:
% 235.04/44.13  | | | | | | | | | | | | | | |   (11767)   ~ (all_52_8 = e3)
% 235.04/44.13  | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | REDUCE: (365), (11766) imply:
% 235.04/44.13  | | | | | | | | | | | | | | |   (11768)   ~ (all_52_12 = e3)
% 235.04/44.13  | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | REDUCE: (45), (11766) imply:
% 235.04/44.13  | | | | | | | | | | | | | | |   (11769)  op(e3, e3) = e3
% 235.04/44.13  | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | |   (11770)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 235.04/44.13  | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 235.04/44.13  | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (10191), (11767), (11770),
% 235.04/44.13  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.13  | | | | | | | | | | | | | | | |            #1628.
% 235.04/44.13  | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | |   (11771)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 235.04/44.13  | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 235.04/44.13  | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | BETA: splitting (11771) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | |   (11772)  all_58_8 = e3 & op(e1, e1) = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11437), (11772), (function-axioms) are
% 235.04/44.13  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | |   (11773)  all_58_14 = e3 & op(e0, e1) = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | ALPHA: (11773) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | |   (11774)  all_58_14 = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | |   (11775)  op(e0, e1) = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | |   (11776)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 235.04/44.13  | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | BETA: splitting (11776) gives:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | |   (11777)  all_58_6 = e3 & op(e1, e3) = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | ALPHA: (11777) implies:
% 235.04/44.13  | | | | | | | | | | | | | | | | | | |   (11778)  all_58_6 = e3
% 235.04/44.13  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.14  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (162), (164),
% 235.04/44.14  | | | | | | | | | | | | | | | | | | |            (168), (216), (218), (222), (223), (224), (225),
% 235.04/44.14  | | | | | | | | | | | | | | | | | | |            (226), (235), (237), (239), (241), (243), (10189),
% 235.04/44.14  | | | | | | | | | | | | | | | | | | |            (10192), (10197), (11753), (11756), (11762),
% 235.04/44.14  | | | | | | | | | | | | | | | | | | |            (11768), (11769), (11774), (11778),
% 235.04/44.14  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.04/44.14  | | | | | | | | | | | | | | | | | | |            #959.
% 235.04/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.14  | | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.14  | | | | | | | | | | | | | | | | | | |   (11779)  all_58_7 = e3 & op(e1, e2) = e3
% 235.04/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.14  | | | | | | | | | | | | | | | | | | | ALPHA: (11779) implies:
% 235.04/44.14  | | | | | | | | | | | | | | | | | | |   (11780)  op(e1, e2) = e3
% 235.04/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.14  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10189), (11780), (function-axioms) are
% 235.04/44.14  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 235.04/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.14  | | | | | | | | | | | | | | | | | | End of split
% 235.04/44.14  | | | | | | | | | | | | | | | | | | 
% 235.04/44.14  | | | | | | | | | | | | | | | | | Case 2:
% 235.04/44.14  | | | | | | | | | | | | | | | | | | 
% 235.04/44.14  | | | | | | | | | | | | | | | | | |   (11781)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 235.04/44.14  | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 235.04/44.14  | | | | | | | | | | | | | | | | | | 
% 235.04/44.14  | | | | | | | | | | | | | | | | | | BETA: splitting (11781) gives:
% 235.04/44.14  | | | | | | | | | | | | | | | | | | 
% 235.04/44.14  | | | | | | | | | | | | | | | | | | Case 1:
% 235.04/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.04/44.14  | | | | | | | | | | | | | | | | | | |   (11782)  all_58_8 = e3 & op(e1, e1) = e3
% 235.04/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11437), (11782), (function-axioms) are
% 235.58/44.14  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | |   (11783)  all_58_11 = e3 & op(e1, e0) = e3
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | ALPHA: (11783) implies:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | |   (11784)  all_58_11 = e3
% 235.58/44.14  | | | | | | | | | | | | | | | | | | |   (11785)  op(e1, e0) = e3
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 235.58/44.14  | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (11775) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | |   (11786)  all_52_11 = e3
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 235.58/44.14  | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (160), (11785) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | |   (11787)  all_52_14 = e3
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | |   (11788)   ~ (all_28_2 = e0)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | REDUCE: (11432), (11788) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | |   (11789)  $false
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | CLOSE: (11789) is inconsistent.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | |   (11790)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = all_28_1 & $i(all_28_0) &
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | |              $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | |              = all_28_1 & $i(all_28_1))
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | |   (11791)   ~ (all_34_2 = e1)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | REDUCE: (11748), (11791) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | |   (11792)  $false
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | CLOSE: (11792) is inconsistent.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | |   (11793)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | |              $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | |              = all_34_1 & $i(all_34_1))
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11430) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | |   (11794)   ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 &
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_18_1 & $i(all_18_0) &
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | |            $i(all_18_1)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11794) implies:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | |   (11795)   ~ (all_18_0 = e2)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | |   (11796)  op(e1, e0) = all_18_1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | |   (11797)  op(all_18_1, e1) = all_18_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11793) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | |   (11798)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = all_34_1 & $i(all_34_0) &
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_34_1)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11798) implies:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | |   (11799)   ~ (all_34_0 = e3)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | |   (11800)  op(e0, e1) = all_34_1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | |   (11801)  op(all_34_1, e0) = all_34_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11745) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11802)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = all_20_1 & $i(all_20_0) &
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_20_1)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11802) implies:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11803)   ~ (all_20_0 = e2)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11804)  op(e0, e1) = all_20_1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11805)  op(all_20_1, e0) = all_20_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_34_1,
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (11775), (11800) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11806)  all_34_1 = e3
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_1,
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |              all_34_1, e1, e0, simplifying with (11800),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |              (11804) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11807)  all_34_1 = all_20_1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_18_1,
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (11785), (11796) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11808)  all_18_1 = e3
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11806), (11807) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11809)  all_20_1 = e3
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11801), (11806) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11810)  op(e3, e0) = all_34_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11805), (11809) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11811)  op(e3, e0) = all_20_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11797), (11808) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11812)  op(e3, e1) = all_18_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11790) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11813)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_28_1 & $i(all_28_0) &
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_28_1)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11813) implies:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11814)  op(e1, e0) = all_28_1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (11785), (11814) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11815)  all_28_1 = e3
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |              all_20_0, e0, e3, simplifying with (168), (11811)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11816)  all_52_12 = all_20_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |              all_34_0, e0, e3, simplifying with (168), (11810)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11817)  all_52_12 = all_34_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |              all_18_0, e1, e3, simplifying with (169), (11812)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11818)  all_52_8 = all_18_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11816), (11817) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11819)  all_34_0 = all_20_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (11816) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11820)  all_54_3 = all_20_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (11818) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11821)  all_54_2 = all_18_0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11767), (11818) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11822)   ~ (all_18_0 = e3)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (11816) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11823)   ~ (all_52_13 = all_20_0)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11823) implies:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11824)   ~ (all_52_13 = all_20_0)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11751), (11816) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11825)   ~ (all_20_0 = e1)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11799), (11819) imply:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11826)   ~ (all_20_0 = e3)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11827)  all_54_2 = e3
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11821), (11822), (11827) are inconsistent by
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #877.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11828)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11829)  all_54_3 = e3
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11820), (11826), (11829) are inconsistent by
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #957.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11830)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11831)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11831) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11832)  all_58_0 = e2 & op(e3, e3) = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11832) implies:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11833)  op(e3, e3) = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11769), (11833), (function-axioms) are
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11834)  all_58_1 = e2 & op(e3, e2) = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11834) implies:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11835)  all_58_1 = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11828) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11836)  all_54_2 = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11795), (11821), (11836) are inconsistent by
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1527.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11837)  all_54_2 = e1 | all_54_2 = e0
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11838)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11838) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11839)  all_58_9 = e2 & op(e3, e0) = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (160), (164), (216), (11435), (11756),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11803), (11820), (11824), (11825), (11830),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11839), (function-axioms) are inconsistent by
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1122.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11840)  all_58_10 = e2 & op(e2, e0) = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11840) implies:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11841)  op(e2, e0) = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11842)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (134), (170), (281), (10197), (11434),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11837), (11842), (function-axioms) are
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #876.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11843)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11843) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11844)  all_58_7 = e1 & op(e1, e2) = e1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11844) implies:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11845)  all_58_7 = e1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11846)  op(e1, e2) = e1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11847)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (149), (163), (167),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (210), (216), (10198), (11749), (11756),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11768), (11769), (11775), (11784), (11785),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11841), (11847), (function-axioms) are
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11848)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11848) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11849)  all_58_6 = e1 & op(e1, e3) = e1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11849) implies:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11850)  all_58_6 = e1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11851)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (235), (237),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (10198), (11835), (11845), (11846),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11850), (11851), (function-axioms) are
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #873.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11852)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (11437), (11784), (11852),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1057.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11853)  all_58_12 = e1 & op(e0, e3) = e1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (218), (235),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (10197), (10198), (11762), (11774),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11835), (11845), (11846), (11853),
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #870.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11854)  all_58_13 = e1 & op(e0, e2) = e1
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11750), (11854), (function-axioms) are
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11855)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11855) gives:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11856)  all_58_11 = e2 & op(e1, e0) = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11784), (11856) are inconsistent by
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1741.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11857)  all_58_15 = e2 & op(e0, e0) = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11762), (11857) are inconsistent by
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1917.
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11858)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 235.58/44.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (134), (160), (164),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (216), (221), (242), (281), (11434),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11435), (11756), (11762), (11769), (11784),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11795), (11803), (11820), (11821), (11824),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11825), (11828), (11830), (11858),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #867.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11859)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_28_1)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11859) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11860)   ~ (all_28_1 = e2)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11861)  op(e1, e0) = all_28_1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (11785), (11861) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11862)  all_28_1 = e3
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              all_20_0, e0, e3, simplifying with (168), (11811)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11863)  all_52_12 = all_20_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              all_34_0, e0, e3, simplifying with (168), (11810)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11864)  all_52_12 = all_34_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              all_18_0, e1, e3, simplifying with (169), (11812)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11865)  all_52_8 = all_18_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11863), (11864) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11866)  all_34_0 = all_20_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (11863) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11867)  all_54_3 = all_20_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (11865) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11868)  all_54_2 = all_18_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11767), (11865) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11869)   ~ (all_18_0 = e3)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (11863) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11870)   ~ (all_52_13 = all_20_0)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11870) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11871)   ~ (all_52_13 = all_20_0)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11751), (11863) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11872)   ~ (all_20_0 = e1)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11799), (11866) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11873)   ~ (all_20_0 = e3)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11874)  all_54_2 = e3
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11868), (11869), (11874) are inconsistent by
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #877.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11875)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11876)  all_54_3 = e3
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11867), (11873), (11876) are inconsistent by
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #957.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11877)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11878)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11878) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11879)  all_58_0 = e2 & op(e3, e3) = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11879) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11880)  op(e3, e3) = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11769), (11880), (function-axioms) are
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11881)  all_58_1 = e2 & op(e3, e2) = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11881) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11882)  all_58_1 = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11875) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11883)  all_54_2 = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11795), (11868), (11883) are inconsistent by
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1527.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11884)  all_54_2 = e1 | all_54_2 = e0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11885)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11885) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11886)  all_58_9 = e2 & op(e3, e0) = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (160), (164), (216), (11435), (11756),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11803), (11867), (11871), (11872), (11877),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11886), (function-axioms) are inconsistent by
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1122.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11887)  all_58_10 = e2 & op(e2, e0) = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11887) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11888)  op(e2, e0) = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11889)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (134), (170), (281), (10197), (11434),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11884), (11889), (function-axioms) are
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #876.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11890)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11890) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11891)  all_58_7 = e1 & op(e1, e2) = e1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11891) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11892)  all_58_7 = e1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11893)  op(e1, e2) = e1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11894)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (149), (163), (167),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (210), (216), (10198), (11749), (11756),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11768), (11769), (11775), (11784), (11785),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11888), (11894), (function-axioms) are
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11895)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11895) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11896)  all_58_6 = e1 & op(e1, e3) = e1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11896) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11897)  all_58_6 = e1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11898)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (235), (237),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (10198), (11882), (11892), (11893),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11897), (11898), (function-axioms) are
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #873.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11899)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11437), (11860), (11861), (11899),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1463.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11900)  all_58_12 = e1 & op(e0, e3) = e1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (218), (235),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (10197), (10198), (11762), (11774),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11882), (11892), (11893), (11900),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #870.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11901)  all_58_13 = e1 & op(e0, e2) = e1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11750), (11901), (function-axioms) are
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11902)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11762), (11860), (11861), (11902),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #866.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11903)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (134), (160), (164),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (216), (221), (242), (281), (11434),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11435), (11756), (11762), (11769), (11784),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11795), (11803), (11867), (11868), (11871),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11872), (11875), (11877), (11903),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #867.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11904)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_20_1)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11904) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11905)   ~ (all_20_1 = e3)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11906)  op(e0, e1) = all_20_1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11775), (11800), (11905), (11906),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |            #1806.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | |   (11907)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 &
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_34_1)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11907) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | |   (11908)   ~ (all_34_1 = e2)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | |   (11909)  op(e0, e1) = all_34_1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11745) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11910)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = all_20_1 & $i(all_20_0) &
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_20_1)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11910) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11911)   ~ (all_20_0 = e2)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11912)  op(e0, e1) = all_20_1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11913)  op(all_20_1, e0) = all_20_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_34_1,
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (11775), (11909) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11914)  all_34_1 = e3
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_1,
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |              all_34_1, e1, e0, simplifying with (11909),
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |              (11912) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11915)  all_34_1 = all_20_1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_18_1,
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (11785), (11796) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11916)  all_18_1 = e3
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11914), (11915) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11917)  all_20_1 = e3
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11913), (11917) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11918)  op(e3, e0) = all_20_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11797), (11916) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11919)  op(e3, e1) = all_18_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11790) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11920)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_28_1 & $i(all_28_0) &
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_28_1)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11920) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11921)  op(e1, e0) = all_28_1
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (11785), (11921) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11922)  all_28_1 = e3
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              all_20_0, e0, e3, simplifying with (168), (11918)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11923)  all_52_12 = all_20_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              all_18_0, e1, e3, simplifying with (169), (11919)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11924)  all_52_8 = all_18_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (11923) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11925)  all_54_3 = all_20_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (11924) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11926)  all_54_2 = all_18_0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11767), (11924) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11927)   ~ (all_18_0 = e3)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (11923) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11928)   ~ (all_52_13 = all_20_0)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11928) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11929)   ~ (all_52_13 = all_20_0)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11768), (11923) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11930)   ~ (all_20_0 = e3)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11751), (11923) imply:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (11931)   ~ (all_20_0 = e1)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11932)  all_54_2 = e3
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11926), (11927), (11932) are inconsistent by
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #877.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11933)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11934)  all_54_3 = e3
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11925), (11930), (11934) are inconsistent by
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #957.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11935)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11936)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11936) gives:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11937)  all_58_0 = e2 & op(e3, e3) = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11937) implies:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11938)  op(e3, e3) = e2
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11769), (11938), (function-axioms) are
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11939)  all_58_1 = e2 & op(e3, e2) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11939) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11940)  all_58_1 = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11933) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11941)  all_54_2 = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11795), (11926), (11941) are inconsistent by
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1527.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11942)  all_54_2 = e1 | all_54_2 = e0
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11943)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11943) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11944)  all_58_9 = e2 & op(e3, e0) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (160), (164), (216), (11435), (11756),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11911), (11925), (11929), (11931), (11935),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11944), (function-axioms) are inconsistent by
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1122.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11945)  all_58_10 = e2 & op(e2, e0) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11945) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11946)  op(e2, e0) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11947)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (134), (170), (281), (10197), (11434),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11942), (11947), (function-axioms) are
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #876.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11948)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11948) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11949)  all_58_7 = e1 & op(e1, e2) = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11949) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11950)  all_58_7 = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11951)  op(e1, e2) = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11952)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (149), (163), (167),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (210), (216), (10198), (11749), (11756),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11768), (11769), (11775), (11784), (11785),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11946), (11952), (function-axioms) are
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11953)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11953) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11954)  all_58_6 = e1 & op(e1, e3) = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11954) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11955)  all_58_6 = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11956)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (235), (237),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (10198), (11940), (11950), (11951),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11955), (11956), (function-axioms) are
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #873.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11957)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (11437), (11784), (11957),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1057.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11958)  all_58_12 = e1 & op(e0, e3) = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (218), (235),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (10197), (10198), (11762), (11908),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11909), (11912), (11940), (11950), (11951),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11958), (function-axioms) are inconsistent by
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #865.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11959)  all_58_13 = e1 & op(e0, e2) = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11750), (11959), (function-axioms) are
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11960)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (11762), (11784), (11960) are
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11961)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (134), (160), (164),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (216), (221), (242), (281), (11434),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11435), (11756), (11762), (11769), (11784),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11795), (11911), (11925), (11926), (11929),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11931), (11933), (11935), (11961),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #867.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11962)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_28_1)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11962) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11963)   ~ (all_28_1 = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11964)  op(e1, e0) = all_28_1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_28_1,
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (11785), (11964) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11965)  all_28_1 = e3
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |              all_20_0, e0, e3, simplifying with (168), (11918)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11966)  all_52_12 = all_20_0
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |              all_18_0, e1, e3, simplifying with (169), (11919)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11967)  all_52_8 = all_18_0
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (11966) imply:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11968)  all_54_3 = all_20_0
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (11967) imply:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11969)  all_54_2 = all_18_0
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11767), (11967) imply:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11970)   ~ (all_18_0 = e3)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (11966) imply:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11971)   ~ (all_52_13 = all_20_0)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11971) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11972)   ~ (all_52_13 = all_20_0)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11768), (11966) imply:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11973)   ~ (all_20_0 = e3)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11751), (11966) imply:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (11974)   ~ (all_20_0 = e1)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11975)  all_54_2 = e3
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11969), (11970), (11975) are inconsistent by
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #877.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11976)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11977)  all_54_3 = e3
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11968), (11973), (11977) are inconsistent by
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #957.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11978)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11979)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11979) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11980)  all_58_0 = e2 & op(e3, e3) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11980) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11981)  op(e3, e3) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11769), (11981), (function-axioms) are
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11982)  all_58_1 = e2 & op(e3, e2) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11982) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11983)  all_58_1 = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11976) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11984)  all_54_2 = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11795), (11969), (11984) are inconsistent by
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1527.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11985)  all_54_2 = e1 | all_54_2 = e0
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11986)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11986) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11987)  all_58_9 = e2 & op(e3, e0) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (160), (164), (216), (11435), (11756),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11911), (11968), (11972), (11974), (11978),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11987), (function-axioms) are inconsistent by
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1122.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11988)  all_58_10 = e2 & op(e2, e0) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11988) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11989)  op(e2, e0) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11990)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (134), (170), (281), (10197), (11434),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11985), (11990), (function-axioms) are
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #876.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11991)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11991) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11992)  all_58_7 = e1 & op(e1, e2) = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11992) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11993)  all_58_7 = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11994)  op(e1, e2) = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11995)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (149), (163), (167),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (210), (216), (10198), (11749), (11756),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11768), (11769), (11775), (11784), (11785),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11989), (11995), (function-axioms) are
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11996)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11996) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11997)  all_58_6 = e1 & op(e1, e3) = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11997) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11998)  all_58_6 = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11999)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (235), (237),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (10198), (11983), (11993), (11994),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11998), (11999), (function-axioms) are
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #873.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12000)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11437), (11963), (11964), (12000),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1463.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12001)  all_58_12 = e1 & op(e0, e3) = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (218), (235),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (10197), (10198), (11762), (11908),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11909), (11912), (11983), (11993), (11994),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12001), (function-axioms) are inconsistent by
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #865.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12002)  all_58_13 = e1 & op(e0, e2) = e1
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11750), (12002), (function-axioms) are
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12003)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11762), (11963), (11964), (12003),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #866.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12004)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12004) gives:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12005)  all_58_4 = e2 & op(e3, e1) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12005) implies:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12006)  all_58_4 = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (134), (170), (216),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (242), (281), (11434), (11756), (11762),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11769), (11784), (11795), (11969), (11976),
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12006), (function-axioms) are inconsistent by
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #868.
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12007)  all_58_9 = e2 & op(e3, e0) = e2
% 235.58/44.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (160), (164), (216), (11435), (11756),
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11911), (11968), (11972), (11974), (11978),
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12007), (function-axioms) are inconsistent by
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1122.
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | |   (12008)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_20_1)
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12008) implies:
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | |   (12009)   ~ (all_20_1 = e3)
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | |   (12010)  op(e0, e1) = all_20_1
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11775), (11909), (12009), (12010),
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | |            #1806.
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | |   (12011)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 &
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | |            $i(all_18_1)
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11785), (11790), (12011), (function-axioms) are
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1767.
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | |   (12012)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | REF_CLOSE: (292), (10199), (10203), (11764), (12012) are
% 235.58/44.17  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | |   (12013)  all_24_2 = e2
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | COMBINE_EQS: (301), (12013) imply:
% 235.58/44.17  | | | | | | | | | | | | | |   (12014)  all_10_2 = e2
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | COMBINE_EQS: (290), (12014) imply:
% 235.58/44.17  | | | | | | | | | | | | | |   (12015)  all_56_1 = e2
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | REDUCE: (355), (12014) imply:
% 235.58/44.17  | | | | | | | | | | | | | |   (12016)   ~ (all_52_1 = e2)
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | |   (12017)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.17  | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.58/44.17  | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.58/44.17  | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.58/44.17  | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.58/44.17  | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.58/44.17  | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.58/44.17  | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.58/44.17  | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 235.58/44.17  | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 235.58/44.17  | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.58/44.17  | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | BETA: splitting (12017) gives:
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | |   (12018)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.17  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.58/44.17  | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.58/44.17  | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.58/44.17  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.58/44.17  | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.58/44.17  | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.58/44.17  | | | | | | | | | | | | | | | |              = e3)
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | BETA: splitting (12018) gives:
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | |   (12019)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 235.58/44.17  | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 235.58/44.17  | | | | | | | | | | | | | | | | |            e3
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | ALPHA: (12019) implies:
% 235.58/44.17  | | | | | | | | | | | | | | | | |   (12020)  op(e2, e3) = e3
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10187), (12020), (function-axioms) are
% 235.58/44.17  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | |   (12021)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 235.58/44.17  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 235.58/44.17  | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 235.58/44.17  | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 235.58/44.17  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 235.58/44.17  | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (11749), (12016), (12021),
% 235.58/44.17  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.17  | | | | | | | | | | | | | | | | |            #2126.
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | |   (12022)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 235.58/44.17  | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 235.58/44.17  | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 235.58/44.17  | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.58/44.17  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.58/44.17  | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 235.58/44.17  | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 235.58/44.17  | | | | | | | | | | | | | | | |              = e0)
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | REF_CLOSE: (10186), (11433), (12022) are inconsistent by
% 235.58/44.17  | | | | | | | | | | | | | | | |            sub-proof #863.
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | |   (12023)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.58/44.17  | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.58/44.17  | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.58/44.17  | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.58/44.17  | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.58/44.17  | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.58/44.17  | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.58/44.17  | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 235.58/44.17  | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 235.58/44.17  | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 235.58/44.17  | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 235.58/44.17  | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | BETA: splitting (12023) gives:
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | |   (12024)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.58/44.17  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.58/44.17  | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.58/44.17  | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.58/44.17  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.58/44.17  | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.58/44.17  | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.58/44.17  | | | | | | | | | | | | | | | |              = e2)
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | BETA: splitting (12024) gives:
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | |   (12025)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 235.58/44.17  | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 235.58/44.17  | | | | | | | | | | | | | | | | |              e2) = e2
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | ALPHA: (12025) implies:
% 235.58/44.17  | | | | | | | | | | | | | | | | |   (12026)   ~ (all_56_31 = e1)
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | REDUCE: (11749), (12026) imply:
% 235.58/44.17  | | | | | | | | | | | | | | | | |   (12027)  $false
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | CLOSE: (12027) is inconsistent.
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | |   (12028)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.17  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 235.58/44.17  | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 235.58/44.17  | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.58/44.17  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.58/44.17  | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | BETA: splitting (12028) gives:
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | |   (12029)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 235.58/44.17  | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 235.58/44.17  | | | | | | | | | | | | | | | | | |              e2) = e1
% 235.58/44.17  | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | ALPHA: (12029) implies:
% 235.58/44.17  | | | | | | | | | | | | | | | | | |   (12030)   ~ (all_56_1 = e2)
% 235.58/44.17  | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | REDUCE: (12015), (12030) imply:
% 235.58/44.17  | | | | | | | | | | | | | | | | | |   (12031)  $false
% 235.58/44.17  | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | CLOSE: (12031) is inconsistent.
% 235.58/44.17  | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | |   (12032)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 235.58/44.17  | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 235.58/44.17  | | | | | | | | | | | | | | | | | |              e2) = e2
% 235.58/44.17  | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | ALPHA: (12032) implies:
% 235.58/44.17  | | | | | | | | | | | | | | | | | |   (12033)   ~ (all_56_21 = e0)
% 235.58/44.17  | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | REDUCE: (11433), (12033) imply:
% 235.58/44.17  | | | | | | | | | | | | | | | | | |   (12034)  $false
% 235.58/44.17  | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | | CLOSE: (12034) is inconsistent.
% 235.58/44.17  | | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | |   (12035)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.17  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 235.58/44.17  | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 235.58/44.17  | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.58/44.17  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.58/44.17  | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 235.58/44.17  | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.17  | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 235.58/44.17  | | | | | | | | | | | | | | | |              = e0)
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | BETA: splitting (12035) gives:
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | |   (12036)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 235.58/44.17  | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 235.58/44.17  | | | | | | | | | | | | | | | | |              e2) = e0
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | ALPHA: (12036) implies:
% 235.58/44.17  | | | | | | | | | | | | | | | | |   (12037)   ~ (all_56_1 = e2)
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | REDUCE: (12015), (12037) imply:
% 235.58/44.17  | | | | | | | | | | | | | | | | |   (12038)  $false
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | CLOSE: (12038) is inconsistent.
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | |   (12039)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 235.58/44.17  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 235.58/44.17  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 235.58/44.17  | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 235.58/44.17  | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 235.58/44.17  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 235.58/44.17  | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (11435), (11753), (12039),
% 235.58/44.17  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.17  | | | | | | | | | | | | | | | | |            #1989.
% 235.58/44.17  | | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | End of split
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | |   (12040)  all_16_2 = e0
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | COMBINE_EQS: (342), (12040) imply:
% 235.58/44.17  | | | | | | | | |   (12041)  all_10_2 = e0
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | SIMP: (12041) implies:
% 235.58/44.17  | | | | | | | | |   (12042)  all_10_2 = e0
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | COMBINE_EQS: (290), (12042) imply:
% 235.58/44.17  | | | | | | | | |   (12043)  all_56_1 = e0
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | REDUCE: (355), (12042) imply:
% 235.58/44.17  | | | | | | | | |   (12044)   ~ (all_52_1 = e0)
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | REDUCE: (359), (12042) imply:
% 235.58/44.17  | | | | | | | | |   (12045)   ~ (all_52_3 = e0)
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | REDUCE: (361), (12042) imply:
% 235.58/44.17  | | | | | | | | |   (12046)   ~ (all_52_4 = e0)
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | REDUCE: (363), (12042) imply:
% 235.58/44.17  | | | | | | | | |   (12047)   ~ (all_52_8 = e0)
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | REDUCE: (10199), (12042) imply:
% 235.58/44.17  | | | | | | | | |   (12048)   ~ (e1 = e0)
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | REDUCE: (45), (12042) imply:
% 235.58/44.17  | | | | | | | | |   (12049)  op(e3, e3) = e0
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | BETA: splitting (58) gives:
% 235.58/44.17  | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | |   (12050)   ~ (all_18_2 = e0)
% 235.58/44.17  | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | REDUCE: (339), (12050) imply:
% 235.58/44.17  | | | | | | | | | |   (12051)   ~ (all_6_2 = e0)
% 235.58/44.17  | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | BETA: splitting (61) gives:
% 235.58/44.17  | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | |   (12052)   ~ (all_20_2 = e1)
% 235.58/44.17  | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | REDUCE: (341), (12052) imply:
% 235.58/44.17  | | | | | | | | | | |   (12053)   ~ (all_4_2 = e1)
% 235.58/44.17  | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | BETA: splitting (189) gives:
% 235.58/44.17  | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | |   (12054)  all_54_15 = e3
% 235.58/44.17  | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | REF_CLOSE: (299), (10201), (12054) are inconsistent by
% 235.58/44.17  | | | | | | | | | | | |            sub-proof #2340.
% 235.58/44.17  | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | |   (12055)   ~ (all_54_15 = e3)
% 235.58/44.17  | | | | | | | | | | | |   (12056)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 235.58/44.17  | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | BETA: splitting (12056) gives:
% 235.58/44.17  | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | |   (12057)  all_54_15 = e2
% 235.58/44.17  | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | REF_CLOSE: (299), (390), (12057) are inconsistent by
% 235.58/44.17  | | | | | | | | | | | | |            sub-proof #2339.
% 235.58/44.17  | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | |   (12058)   ~ (all_54_15 = e2)
% 235.58/44.17  | | | | | | | | | | | | |   (12059)  all_54_15 = e1 | all_54_15 = e0
% 235.58/44.17  | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | BETA: splitting (12059) gives:
% 235.58/44.17  | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | |   (12060)  all_54_15 = e1
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | REF_CLOSE: (299), (12053), (12060) are inconsistent by
% 235.58/44.17  | | | | | | | | | | | | | |            sub-proof #2338.
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | Case 2:
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | |   (12061)  all_54_15 = e0
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | COMBINE_EQS: (299), (12061) imply:
% 235.58/44.17  | | | | | | | | | | | | | |   (12062)  all_4_2 = e0
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | SIMP: (12062) implies:
% 235.58/44.17  | | | | | | | | | | | | | |   (12063)  all_4_2 = e0
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | COMBINE_EQS: (254), (12063) imply:
% 235.58/44.17  | | | | | | | | | | | | | |   (12064)  all_56_31 = e0
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | REDUCE: (388), (12063) imply:
% 235.58/44.17  | | | | | | | | | | | | | |   (12065)   ~ (all_52_13 = e0)
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | REDUCE: (389), (12063) imply:
% 235.58/44.17  | | | | | | | | | | | | | |   (12066)   ~ (all_52_14 = e0)
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | REDUCE: (10201), (12063) imply:
% 235.58/44.17  | | | | | | | | | | | | | |   (12067)   ~ (e3 = e0)
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | REDUCE: (390), (12063) imply:
% 235.58/44.17  | | | | | | | | | | | | | |   (12068)   ~ (e2 = e0)
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | REDUCE: (36), (12063) imply:
% 235.58/44.17  | | | | | | | | | | | | | |   (12069)  op(e0, e0) = e0
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 235.58/44.17  | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | |   (12070)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 235.58/44.17  | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | BETA: splitting (12070) gives:
% 235.58/44.17  | | | | | | | | | | | | | | | 
% 235.58/44.17  | | | | | | | | | | | | | | | Case 1:
% 235.58/44.17  | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | |   (12071)  all_58_6 = e0 & op(e1, e3) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | ALPHA: (12071) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | |   (12072)  all_58_6 = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (241), (243),
% 235.58/44.18  | | | | | | | | | | | | | | | |            (245), (10187), (12049), (12072),
% 235.58/44.18  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.18  | | | | | | | | | | | | | | | |            #1441.
% 235.58/44.18  | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | |   (12073)  all_58_7 = e0 & op(e1, e2) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | ALPHA: (12073) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | |   (12074)  op(e1, e2) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | |   (12075)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 235.58/44.18  | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | BETA: splitting (12075) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | |   (12076)  all_58_2 = e0 & op(e2, e3) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | ALPHA: (12076) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | |   (12077)  all_58_2 = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |   (12078)  all_58_15 = e0 & op(e0, e0) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | ALPHA: (12078) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |   (12079)  all_58_15 = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |   (12080)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12080) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |   (12081)  all_58_4 = e0 & op(e3, e1) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12081) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |   (12082)  all_58_4 = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (242), (244),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |            (246), (10188), (12049), (12082),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |            #1512.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |   (12083)  all_58_5 = e0 & op(e2, e1) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12083) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |   (12084)  op(e2, e1) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (165), (232), (233),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |            (10197), (10198), (12077), (12084),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |            #861.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |   (12085)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12085) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |   (12086)  all_58_8 = e0 & op(e1, e1) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (12051), (12086), (function-axioms) are
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1833.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |   (12087)  all_58_14 = e0 & op(e0, e1) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12087) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |   (12088)  all_58_14 = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |   (12089)  op(e0, e1) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12090)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12090) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | |   (12091)  all_58_4 = e3 & op(e3, e1) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12091) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | |   (12092)  all_58_4 = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | |   (12093)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12093) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12094)  all_58_12 = e3 & op(e0, e3) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12094) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12095)  all_58_12 = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (217), (218),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (10190), (12069), (12079), (12088),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (12089), (12095), (function-axioms) are
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #859.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12096)  all_58_13 = e3 & op(e0, e2) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10190), (12096), (function-axioms) are
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | |   (12097)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12097) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12098)  all_58_14 = e3 & op(e0, e1) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12098) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12099)  all_58_14 = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12100)  op(e0, e1) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (165), (227),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (12051), (12092), (12099), (12100),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            #1094.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12101)  all_58_15 = e3 & op(e0, e0) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12101) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12102)  op(e0, e0) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12069), (12102), (function-axioms) are
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | |   (12103)  all_58_5 = e3 & op(e2, e1) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10191), (12103), (function-axioms) are
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12104)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (391), (12089), (12104),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |            #1627.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |   (12105)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (220),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |            (221), (222), (10192), (12065), (12066), (12069),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |            (12105), (function-axioms) are inconsistent by
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |            sub-proof #1489.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | |   (12106)  all_58_3 = e0 & op(e2, e2) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10197), (12106) are inconsistent by
% 235.58/44.18  | | | | | | | | | | | | | | | | | |            sub-proof #1719.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | |   (12107)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 235.58/44.18  | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 235.58/44.18  | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | BETA: splitting (12107) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | |   (12108)  all_58_5 = e0 & op(e2, e1) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | ALPHA: (12108) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | |   (12109)  op(e2, e1) = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0,
% 235.58/44.18  | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (12074) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | |   (12110)  all_52_6 = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 235.58/44.18  | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (12109) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | |   (12111)  all_52_9 = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | REDUCE: (126), (12110) imply:
% 235.58/44.18  | | | | | | | | | | | | | | | | | |   (12112)   ~ (all_52_14 = e0)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | REDUCE: (117), (12111) imply:
% 235.58/44.18  | | | | | | | | | | | | | | | | | |   (12113)   ~ (all_52_13 = e0)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | REDUCE: (381), (12111) imply:
% 235.58/44.18  | | | | | | | | | | | | | | | | | |   (12114)   ~ (all_6_2 = e0)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |   (12115)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.58/44.18  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | BETA: splitting (12115) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |   (12116)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | |              = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12116) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |   (12117)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |            e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12117) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |   (12118)  op(e2, e3) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10187), (12118), (function-axioms) are
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |   (12119)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12119) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12120)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |            e2
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12120) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12121)   ~ (all_56_11 = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10186), (12121) imply:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12122)  $false
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12122) is inconsistent.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12123)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12123) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12124)   ~ (all_56_31 = e1)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12125)   ~ (all_56_21 = e1)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12126)   ~ (all_56_11 = e1)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12127)  op(e1, e3) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12128)  op(e3, e1) = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (266), (12125) imply:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | |   (12129)   ~ (all_6_2 = e1)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | |   (12130)  all_54_10 = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (12130) are inconsistent by
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | |   (12131)   ~ (all_54_10 = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | |   (12132)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12132) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | |   (12133)  all_54_10 = e2
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (12133) imply:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | |   (12134)  all_6_2 = e2
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12134) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | |   (12135)  all_6_2 = e2
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (12135) imply:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | |   (12136)  all_36_2 = e2
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (12135) imply:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | |   (12137)   ~ (all_52_8 = e2)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12138)   ~ (all_36_2 = e2)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12136), (12138) imply:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12139)  $false
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12139) is inconsistent.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (12127) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12140)  all_52_2 = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (12128) gives:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12141)  all_52_8 = e3
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (12140) imply:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12142)   ~ (all_52_14 = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12142) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12143)   ~ (all_52_14 = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (12141) imply:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12144)   ~ (all_52_11 = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12144) implies:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (12145)   ~ (all_52_11 = e3)
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (157), (158),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (219), (226), (239), (241), (243),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (10189), (10190), (12069), (12143),
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (12145), (function-axioms) are inconsistent by
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1035.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | |   (12146)  all_54_10 = e1 | all_54_10 = e0
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (12051), (12129), (12146) are inconsistent
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2282.
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.18  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |   (12147)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              = e0)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (10186), (12045), (12064), (12147),
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |            #1001.
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |   (12148)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (160), (164), (165), (12064), (12065),
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |            (12066), (12109), (12148), (function-axioms) are
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.19  | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | |   (12149)  all_58_10 = e0 & op(e2, e0) = e0
% 235.58/44.19  | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | ALPHA: (12149) implies:
% 235.58/44.19  | | | | | | | | | | | | | | | | | |   (12150)  op(e2, e0) = e0
% 235.58/44.19  | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (12065), (12150), (function-axioms) are
% 235.58/44.19  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2324.
% 235.58/44.19  | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | End of split
% 235.58/44.19  | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | End of split
% 235.58/44.19  | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | End of split
% 235.58/44.19  | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | |   (12151)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 235.58/44.19  | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 235.58/44.19  | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (12051), (12066), (12151),
% 235.58/44.19  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.19  | | | | | | | | | | | | | | |            #1083.
% 235.58/44.19  | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | End of split
% 235.58/44.19  | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | End of split
% 235.58/44.19  | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | End of split
% 235.58/44.19  | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | End of split
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | |   (12152)  all_20_2 = e1
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | COMBINE_EQS: (341), (12152) imply:
% 235.58/44.19  | | | | | | | | | | |   (12153)  all_4_2 = e1
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | SIMP: (12153) implies:
% 235.58/44.19  | | | | | | | | | | |   (12154)  all_4_2 = e1
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | COMBINE_EQS: (254), (12154) imply:
% 235.58/44.19  | | | | | | | | | | |   (12155)  all_56_31 = e1
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | REDUCE: (379), (12154) imply:
% 235.58/44.19  | | | | | | | | | | |   (12156)   ~ (all_52_7 = e1)
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | REDUCE: (388), (12154) imply:
% 235.58/44.19  | | | | | | | | | | |   (12157)   ~ (all_52_13 = e1)
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | REDUCE: (389), (12154) imply:
% 235.58/44.19  | | | | | | | | | | |   (12158)   ~ (all_52_14 = e1)
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | REDUCE: (10201), (12154) imply:
% 235.58/44.19  | | | | | | | | | | |   (12159)   ~ (e3 = e1)
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | REDUCE: (390), (12154) imply:
% 235.58/44.19  | | | | | | | | | | |   (12160)   ~ (e2 = e1)
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | REDUCE: (36), (12154) imply:
% 235.58/44.19  | | | | | | | | | | |   (12161)  op(e0, e0) = e1
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | BETA: splitting (220) gives:
% 235.58/44.19  | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | |   (12162)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 235.58/44.19  | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 235.58/44.19  | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 235.58/44.19  | | | | | | | | | | | |            (222), (10192), (12157), (12161), (12162),
% 235.58/44.19  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.19  | | | | | | | | | | | |            #878.
% 235.58/44.19  | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | |   (12163)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 235.58/44.19  | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 235.58/44.19  | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | BETA: splitting (12163) gives:
% 235.58/44.19  | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | |   (12164)  all_58_11 = e1 & op(e1, e0) = e1
% 235.58/44.19  | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | ALPHA: (12164) implies:
% 235.58/44.19  | | | | | | | | | | | | |   (12165)  op(e1, e0) = e1
% 235.58/44.19  | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | REF_CLOSE: (160), (12158), (12165), (function-axioms) are
% 235.58/44.19  | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 235.58/44.19  | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | |   (12166)  all_58_15 = e1 & op(e0, e0) = e1
% 235.58/44.19  | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | ALPHA: (12166) implies:
% 235.58/44.19  | | | | | | | | | | | | |   (12167)  all_58_15 = e1
% 235.58/44.19  | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | BETA: splitting (85) gives:
% 235.58/44.19  | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | |   (12168)   ~ (all_36_2 = e2)
% 235.58/44.19  | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | REDUCE: (328), (12168) imply:
% 235.58/44.19  | | | | | | | | | | | | | |   (12169)   ~ (all_6_2 = e2)
% 235.58/44.19  | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 235.58/44.19  | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | |   (12170)  all_54_10 = e3
% 235.58/44.19  | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (12170) are inconsistent by
% 235.58/44.19  | | | | | | | | | | | | | | |            sub-proof #2313.
% 235.58/44.19  | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | |   (12171)   ~ (all_54_10 = e3)
% 235.58/44.19  | | | | | | | | | | | | | | |   (12172)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 235.58/44.19  | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | BETA: splitting (12172) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | |   (12173)  all_54_10 = e2
% 235.58/44.19  | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | REF_CLOSE: (297), (12169), (12173) are inconsistent by
% 235.58/44.19  | | | | | | | | | | | | | | | |            sub-proof #2312.
% 235.58/44.19  | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | |   (12174)   ~ (all_54_10 = e2)
% 235.58/44.19  | | | | | | | | | | | | | | | |   (12175)  all_54_10 = e1 | all_54_10 = e0
% 235.58/44.19  | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | BETA: splitting (12175) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | |   (12176)  all_54_10 = e1
% 235.58/44.19  | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (12176) imply:
% 235.58/44.19  | | | | | | | | | | | | | | | | |   (12177)  all_6_2 = e1
% 235.58/44.19  | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | SIMP: (12177) implies:
% 235.58/44.19  | | | | | | | | | | | | | | | | |   (12178)  all_6_2 = e1
% 235.58/44.19  | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | REDUCE: (367), (12178) imply:
% 235.58/44.19  | | | | | | | | | | | | | | | | |   (12179)   ~ (all_52_2 = e1)
% 235.58/44.19  | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | REDUCE: (380), (12178) imply:
% 235.58/44.19  | | | | | | | | | | | | | | | | |   (12180)   ~ (all_52_8 = e1)
% 235.58/44.19  | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | REDUCE: (381), (12178) imply:
% 235.58/44.19  | | | | | | | | | | | | | | | | |   (12181)   ~ (all_52_9 = e1)
% 235.58/44.19  | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | REDUCE: (383), (12178) imply:
% 235.58/44.19  | | | | | | | | | | | | | | | | |   (12182)   ~ (all_52_11 = e1)
% 235.58/44.19  | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | |   (12183)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.58/44.19  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | BETA: splitting (12183) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |   (12184)  all_58_0 = e1 & op(e3, e3) = e1
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | ALPHA: (12184) implies:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |   (12185)  op(e3, e3) = e1
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12049), (12185), (function-axioms) are
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |   (12186)  all_58_2 = e1 & op(e2, e3) = e1
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | ALPHA: (12186) implies:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | |   (12187)  all_58_2 = e1
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |   (12188)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (167), (10186), (10187), (12043),
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |            (12045), (12155), (12179), (12188),
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |            #856.
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |   (12189)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12189) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |   (12190)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              = e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (12043), (12155), (12181), (12190),
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |            #855.
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |   (12191)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | |              = e0)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12191) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | |   (12192)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12192) implies:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | |   (12193)   ~ (all_56_31 = e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | |   (12194)   ~ (all_56_11 = e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | |   (12195)   ~ (all_56_1 = e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | |   (12196)  op(e0, e2) = e0
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | |   (12197)  op(e2, e0) = e0
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12043), (12195) imply:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | |   (12198)   ~ (e2 = e0)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | |   (12199)  all_54_6 = e3
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (10191), (12199) are inconsistent by
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | |   (12200)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | |   (12201)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12201) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (12202)  all_58_2 = e2 & op(e2, e3) = e2
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12187), (12202) are inconsistent by
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1630.
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (12203)  all_58_3 = e2 & op(e2, e2) = e2
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12203) implies:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (12204)  op(e2, e2) = e2
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (12204), (function-axioms) are
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | |   (12205)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12205) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (12206)  all_58_5 = e2 & op(e2, e1) = e2
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12206) implies:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (12207)  op(e2, e1) = e2
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12200) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12208)  all_54_6 = e2
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (12208) imply:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12209)  all_52_9 = e2
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12209) implies:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12210)  all_52_9 = e2
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (12210) imply:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12211)   ~ (all_52_8 = e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (12210) imply:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12212)   ~ (all_52_11 = e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12212) implies:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12213)   ~ (all_52_11 = e2)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12214)  all_54_2 = e3
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (12214) imply:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12215)  all_52_8 = e3
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (12215) imply:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12216)   ~ (all_52_11 = e3)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12216) implies:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12217)   ~ (all_52_11 = e3)
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12218)  all_54_14 = e3
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (12217), (12218) are inconsistent by
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1796.
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12219)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (158), (191), (255), (256), (10190),
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12156), (12182), (12196), (12213), (12219),
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #904.
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12220)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (12047), (12180), (12211), (12220) are
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1335.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12221)   ~ (all_54_6 = e2)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (12221) imply:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12222)   ~ (all_52_9 = e2)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (12207), (12222), (function-axioms) are
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (12223)  all_58_10 = e2 & op(e2, e0) = e2
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12223) implies:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (12224)  op(e2, e0) = e2
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12197), (12224), (function-axioms) are
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |   (12225)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (12155), (12158), (12225),
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |            #2269.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | |   (12226)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | BETA: splitting (12226) gives:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | |   (12227)  all_58_6 = e1 & op(e1, e3) = e1
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | ALPHA: (12227) implies:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | |   (12228)  op(e1, e3) = e1
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (12179), (12228), (function-axioms) are
% 235.58/44.20  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | |   (12229)  all_58_12 = e1 & op(e0, e3) = e1
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | ALPHA: (12229) implies:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | |   (12230)  all_58_12 = e1
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | |   (12231)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (158), (10190), (12230), (12231),
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | |            #1541.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | |   (12232)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12232) gives:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | |   (12233)  all_58_14 = e3 & op(e0, e1) = e3
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12233) implies:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | |   (12234)  all_58_14 = e3
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | |   (12235)  op(e0, e1) = e3
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |   (12236)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12236) gives:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | |   (12237)  all_58_12 = e2 & op(e0, e3) = e2
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12237) implies:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | |   (12238)  all_58_12 = e2
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12230), (12238) are inconsistent by
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1757.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | |   (12239)  all_58_13 = e2 & op(e0, e2) = e2
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12239) implies:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | |   (12240)  op(e0, e2) = e2
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |   (12241)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (167), (10186), (10187), (12043),
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |            (12045), (12155), (12179), (12241),
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |            #856.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |   (12242)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12242) gives:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (12243)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (12043), (12155), (12181), (12243),
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |            #855.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (12244)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12244) gives:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12245)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12245) implies:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12246)  op(e0, e2) = e0
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12240), (12246), (function-axioms) are
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12247)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (12158), (12235), (12247),
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1699.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |   (12248)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12248) gives:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | |   (12249)  all_58_14 = e2 & op(e0, e1) = e2
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12234), (12249) are inconsistent by
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1864.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | |   (12250)  all_58_15 = e2 & op(e0, e0) = e2
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12250) implies:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | |   (12251)  all_58_15 = e2
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12167), (12251) are inconsistent by
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2231.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | |   (12252)  all_58_15 = e3 & op(e0, e0) = e3
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12252) implies:
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | |   (12253)  all_58_15 = e3
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12167), (12253) are inconsistent by
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2249.
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | |   (12254)  all_54_10 = e0
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (12051), (12254) are inconsistent by
% 235.58/44.20  | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | |   (12255)  all_36_2 = e2
% 235.58/44.20  | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | COMBINE_EQS: (328), (12255) imply:
% 235.58/44.20  | | | | | | | | | | | | | |   (12256)  all_6_2 = e2
% 235.58/44.20  | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | SIMP: (12256) implies:
% 235.58/44.20  | | | | | | | | | | | | | |   (12257)  all_6_2 = e2
% 235.58/44.20  | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | COMBINE_EQS: (266), (12257) imply:
% 235.58/44.20  | | | | | | | | | | | | | |   (12258)  all_56_21 = e2
% 235.58/44.20  | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | REDUCE: (381), (12257) imply:
% 235.58/44.20  | | | | | | | | | | | | | |   (12259)   ~ (all_52_9 = e2)
% 235.58/44.20  | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 235.58/44.20  | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | |   (12260)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.20  | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.58/44.20  | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.58/44.20  | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.58/44.20  | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.58/44.20  | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.58/44.20  | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.58/44.20  | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 235.58/44.20  | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.58/44.20  | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 235.58/44.20  | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 235.58/44.20  | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 235.58/44.20  | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.58/44.20  | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 235.58/44.20  | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | BETA: splitting (12260) gives:
% 235.58/44.20  | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | |   (12261)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.20  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.58/44.20  | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.58/44.20  | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.58/44.20  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.58/44.20  | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.58/44.20  | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.58/44.20  | | | | | | | | | | | | | | | |              = e3)
% 235.58/44.20  | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10186), (10187), (12155), (12261),
% 235.58/44.20  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.20  | | | | | | | | | | | | | | | |            #857.
% 235.58/44.20  | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | |   (12262)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 235.58/44.20  | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 235.58/44.20  | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 235.58/44.20  | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.58/44.20  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.58/44.20  | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 235.58/44.20  | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 235.58/44.20  | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 235.58/44.20  | | | | | | | | | | | | | | | |              = e0)
% 235.58/44.20  | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | BETA: splitting (12262) gives:
% 235.58/44.20  | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | |   (12263)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 235.58/44.20  | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 235.58/44.20  | | | | | | | | | | | | | | | | |              e3) = e1
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | ALPHA: (12263) implies:
% 235.58/44.20  | | | | | | | | | | | | | | | | |   (12264)   ~ (all_56_11 = e3)
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | REDUCE: (10186), (12264) imply:
% 235.58/44.20  | | | | | | | | | | | | | | | | |   (12265)  $false
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | CLOSE: (12265) is inconsistent.
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | |   (12266)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 235.58/44.20  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 235.58/44.20  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 235.58/44.20  | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 235.58/44.20  | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.58/44.20  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.58/44.20  | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (12043), (12045), (12266),
% 235.58/44.20  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.20  | | | | | | | | | | | | | | | | |            #1829.
% 235.58/44.20  | | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | | End of split
% 235.58/44.20  | | | | | | | | | | | | | | | 
% 235.58/44.20  | | | | | | | | | | | | | | Case 2:
% 235.58/44.20  | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | |   (12267)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.58/44.21  | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.58/44.21  | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.58/44.21  | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.58/44.21  | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.58/44.21  | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.58/44.21  | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.58/44.21  | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.21  | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.21  | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.58/44.21  | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 235.58/44.21  | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 235.58/44.21  | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 235.58/44.21  | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 235.58/44.21  | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.21  | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.21  | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 235.58/44.21  | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 235.58/44.21  | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 235.58/44.21  | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 235.58/44.21  | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 235.58/44.21  | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | BETA: splitting (12267) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | |   (12268)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.58/44.21  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.58/44.21  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.58/44.21  | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.58/44.21  | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.58/44.21  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.58/44.21  | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.58/44.21  | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.58/44.21  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.58/44.21  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.58/44.21  | | | | | | | | | | | | | | | |              = e2)
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | BETA: splitting (12268) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12269)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.58/44.21  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 235.58/44.21  | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 235.58/44.21  | | | | | | | | | | | | | | | | |              e2) = e2
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | ALPHA: (12269) implies:
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12270)  op(e2, e1) = e2
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (12259), (12270), (function-axioms) are
% 235.58/44.21  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12271)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 235.58/44.21  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.21  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 235.58/44.21  | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 235.58/44.21  | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.58/44.21  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.58/44.21  | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | BETA: splitting (12271) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | |   (12272)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 235.58/44.21  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 235.58/44.21  | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 235.58/44.21  | | | | | | | | | | | | | | | | | |              e2) = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | ALPHA: (12272) implies:
% 235.58/44.21  | | | | | | | | | | | | | | | | | |   (12273)   ~ (all_56_21 = e2)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | REDUCE: (12258), (12273) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | | |   (12274)  $false
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | CLOSE: (12274) is inconsistent.
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | |   (12275)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 235.58/44.21  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 235.58/44.21  | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 235.58/44.21  | | | | | | | | | | | | | | | | | |              e2) = e2
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | ALPHA: (12275) implies:
% 235.58/44.21  | | | | | | | | | | | | | | | | | |   (12276)   ~ (all_56_1 = e0)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | REDUCE: (12043), (12276) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | | |   (12277)  $false
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | CLOSE: (12277) is inconsistent.
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | End of split
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | End of split
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | |   (12278)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.58/44.21  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.58/44.21  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 235.58/44.21  | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 235.58/44.21  | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.58/44.21  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.58/44.21  | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 235.58/44.21  | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 235.58/44.21  | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.58/44.21  | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 235.58/44.21  | | | | | | | | | | | | | | | |              = e0)
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | REF_CLOSE: (160), (12155), (12158), (12258), (12278),
% 235.58/44.21  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.21  | | | | | | | | | | | | | | | |            #2151.
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | End of split
% 235.58/44.21  | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | End of split
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | End of split
% 235.58/44.21  | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | End of split
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | End of split
% 235.58/44.21  | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | End of split
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | |   (12279)  all_18_2 = e0
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | COMBINE_EQS: (339), (12279) imply:
% 235.58/44.21  | | | | | | | | | |   (12280)  all_6_2 = e0
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | SIMP: (12280) implies:
% 235.58/44.21  | | | | | | | | | |   (12281)  all_6_2 = e0
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | COMBINE_EQS: (266), (12281) imply:
% 235.58/44.21  | | | | | | | | | |   (12282)  all_56_21 = e0
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | REDUCE: (367), (12281) imply:
% 235.58/44.21  | | | | | | | | | |   (12283)   ~ (all_52_2 = e0)
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | REDUCE: (378), (12281) imply:
% 235.58/44.21  | | | | | | | | | |   (12284)   ~ (all_52_6 = e0)
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | REDUCE: (381), (12281) imply:
% 235.58/44.21  | | | | | | | | | |   (12285)   ~ (all_52_9 = e0)
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | REDUCE: (391), (12281) imply:
% 235.58/44.21  | | | | | | | | | |   (12286)   ~ (e3 = e0)
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | REDUCE: (39), (12281) imply:
% 235.58/44.21  | | | | | | | | | |   (12287)  op(e1, e1) = e0
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | BETA: splitting (235) gives:
% 235.58/44.21  | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | |   (12288)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 235.58/44.21  | | | | | | | | | | |              & op(e2, e2) = e0)
% 235.58/44.21  | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | BETA: splitting (12288) gives:
% 235.58/44.21  | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | |   (12289)  all_58_1 = e0 & op(e3, e2) = e0
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | REF_CLOSE: (170), (12046), (12289), (function-axioms) are
% 235.58/44.21  | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | |   (12290)  all_58_3 = e0 & op(e2, e2) = e0
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | REF_CLOSE: (7), (10197), (12290) are inconsistent by
% 235.58/44.21  | | | | | | | | | | | |            sub-proof #1719.
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | End of split
% 235.58/44.21  | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | |   (12291)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 235.58/44.21  | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 235.58/44.21  | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | BETA: splitting (12291) gives:
% 235.58/44.21  | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | |   (12292)  all_58_7 = e0 & op(e1, e2) = e0
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | REF_CLOSE: (162), (12284), (12292), (function-axioms) are
% 235.58/44.21  | | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | |   (12293)  all_58_13 = e0 & op(e0, e2) = e0
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | ALPHA: (12293) implies:
% 235.58/44.21  | | | | | | | | | | | |   (12294)  op(e0, e2) = e0
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | BETA: splitting (231) gives:
% 235.58/44.21  | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | |   (12295)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 235.58/44.21  | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 235.58/44.21  | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | BETA: splitting (12295) gives:
% 235.58/44.21  | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | |   (12296)  all_58_2 = e0 & op(e2, e3) = e0
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | ALPHA: (12296) implies:
% 235.58/44.21  | | | | | | | | | | | | | |   (12297)  op(e2, e3) = e0
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 235.58/44.21  | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (12297) gives:
% 235.58/44.21  | | | | | | | | | | | | | |   (12298)  all_52_1 = e0
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | REDUCE: (12044), (12298) imply:
% 235.58/44.21  | | | | | | | | | | | | | |   (12299)  $false
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | CLOSE: (12299) is inconsistent.
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | |   (12300)  all_58_3 = e0 & op(e2, e2) = e0
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | REF_CLOSE: (7), (10197), (12300) are inconsistent by
% 235.58/44.21  | | | | | | | | | | | | | |            sub-proof #1719.
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | End of split
% 235.58/44.21  | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | |   (12301)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 235.58/44.21  | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 235.58/44.21  | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | BETA: splitting (12301) gives:
% 235.58/44.21  | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | |   (12302)  all_58_5 = e0 & op(e2, e1) = e0
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | REF_CLOSE: (165), (12285), (12302), (function-axioms) are
% 235.58/44.21  | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | |   (12303)  all_58_10 = e0 & op(e2, e0) = e0
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | ALPHA: (12303) implies:
% 235.58/44.21  | | | | | | | | | | | | | |   (12304)  op(e2, e0) = e0
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 235.58/44.21  | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (12294) gives:
% 235.58/44.21  | | | | | | | | | | | | | |   (12305)  all_52_7 = e0
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 235.58/44.21  | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (12304) gives:
% 235.58/44.21  | | | | | | | | | | | | | |   (12306)  all_52_13 = e0
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | REDUCE: (125), (12305) imply:
% 235.58/44.21  | | | | | | | | | | | | | |   (12307)   ~ (all_52_11 = e0)
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | SIMP: (12307) implies:
% 235.58/44.21  | | | | | | | | | | | | | |   (12308)   ~ (all_52_11 = e0)
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | REDUCE: (110), (12306) imply:
% 235.58/44.21  | | | | | | | | | | | | | |   (12309)   ~ (all_52_14 = e0)
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | SIMP: (12309) implies:
% 235.58/44.21  | | | | | | | | | | | | | |   (12310)   ~ (all_52_14 = e0)
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | REDUCE: (388), (12306) imply:
% 235.58/44.21  | | | | | | | | | | | | | |   (12311)   ~ (all_4_2 = e0)
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | SIMP: (12311) implies:
% 235.58/44.21  | | | | | | | | | | | | | |   (12312)   ~ (all_4_2 = e0)
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 235.58/44.21  | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | |   (12313)  all_54_15 = e3
% 235.58/44.21  | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | REF_CLOSE: (299), (10201), (12313) are inconsistent by
% 235.58/44.21  | | | | | | | | | | | | | | |            sub-proof #2340.
% 235.58/44.21  | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | |   (12314)   ~ (all_54_15 = e3)
% 235.58/44.21  | | | | | | | | | | | | | | |   (12315)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 235.58/44.21  | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | BETA: splitting (12315) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | |   (12316)  all_54_15 = e2
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | REF_CLOSE: (299), (390), (12316) are inconsistent by
% 235.58/44.21  | | | | | | | | | | | | | | | |            sub-proof #2339.
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | |   (12317)   ~ (all_54_15 = e2)
% 235.58/44.21  | | | | | | | | | | | | | | | |   (12318)  all_54_15 = e1 | all_54_15 = e0
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | BETA: splitting (12318) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12319)  all_54_15 = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (12319) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12320)  all_4_2 = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | SIMP: (12320) implies:
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12321)  all_4_2 = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (12321) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12322)  all_56_31 = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | REDUCE: (368), (12321) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12323)   ~ (all_52_3 = e1)
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | REDUCE: (386), (12321) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12324)   ~ (all_52_11 = e1)
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | REDUCE: (389), (12321) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12325)   ~ (all_52_14 = e1)
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | REDUCE: (10201), (12321) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12326)   ~ (e3 = e1)
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | REDUCE: (390), (12321) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12327)   ~ (e2 = e1)
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | REDUCE: (36), (12321) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | |   (12328)  op(e0, e0) = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | |   (12329)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 235.58/44.21  | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | BETA: splitting (12329) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |   (12330)  all_58_9 = e1 & op(e3, e0) = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | ALPHA: (12330) implies:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |   (12331)  all_58_9 = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |            (222), (10192), (12328), (12331),
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |            #1600.
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |   (12332)  all_58_10 = e1 & op(e2, e0) = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | ALPHA: (12332) implies:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |   (12333)  op(e2, e0) = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (12304), (12333), (function-axioms)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | |   (12334)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 235.58/44.21  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | BETA: splitting (12334) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |   (12335)  all_58_11 = e1 & op(e1, e0) = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | ALPHA: (12335) implies:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |   (12336)  op(e1, e0) = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (12325), (12336), (function-axioms) are
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |   (12337)  all_58_15 = e1 & op(e0, e0) = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | ALPHA: (12337) implies:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | |   (12338)  all_58_15 = e1
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | |   (12339)   ~ (all_42_2 = e3)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (10185), (12339) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | |   (12340)  $false
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | CLOSE: (12340) is inconsistent.
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | |   (12341)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | |   (12342)  all_54_14 = e3
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (12342) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | |   (12343)  all_52_11 = e3
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | SIMP: (12343) implies:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | |   (12344)  all_52_11 = e3
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (12344) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | |   (12345)   ~ (all_52_3 = e3)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (12344) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | |   (12346)   ~ (all_52_8 = e3)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (12344) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | |   (12347)  op(e0, e1) = e3
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | |   (12348)  all_54_12 = e3
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12345), (12348) are inconsistent by
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | |   (12349)   ~ (all_54_12 = e3)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | |   (12350)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12350) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | |   (12351)  all_54_12 = e2
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (12351) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | |   (12352)  all_52_3 = e2
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12352) implies:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | |   (12353)  all_52_3 = e2
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (12353) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | |   (12354)   ~ (all_52_1 = e2)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (12353) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | |   (12355)   ~ (all_52_2 = e2)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12345), (12353) imply:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | |   (12356)   ~ (e3 = e2)
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | |   (12357)  all_54_4 = e3
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (10187), (12357) are inconsistent by
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | |   (12358)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12358) gives:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (12359)  all_54_4 = e2
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (12354), (12359) are inconsistent by
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2096.
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (12360)   ~ (all_54_4 = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (12361)  all_54_4 = e1 | all_54_4 = e0
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12362)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (10198), (12354), (12362),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            #998.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12363)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12363) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12364)  all_58_5 = e2 & op(e2, e1) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12364) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12365)  op(e2, e1) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12361) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12366)  all_54_4 = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (12366) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12367)  all_52_1 = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12367) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12368)  all_52_1 = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (12368) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12369)   ~ (all_52_2 = e1)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12369) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12370)   ~ (all_52_2 = e1)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (12368) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12371)  op(e2, e3) = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12372)  all_54_8 = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (12372) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12373)  all_52_2 = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12373) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12374)  all_52_2 = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (12374) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12375)   ~ (all_52_6 = e3)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (12374) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12376)   ~ (all_52_14 = e3)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12376) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12377)   ~ (all_52_14 = e3)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12378)  all_54_11 = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (12377), (12378) are inconsistent by
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12379)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10184) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12380)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12380) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12381)  op(e2, e3) = all_8_1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (134), (136), (159), (160), (169), (195),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (203), (211), (258), (267), (281), (282),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10189), (10198), (12045), (12046),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12047), (12282), (12284), (12310), (12325),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12341), (12346), (12347), (12365), (12371),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12379), (12381), (function-axioms) are
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12382)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_8_1)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12382) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12383)  op(e2, e3) = all_8_1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (134), (136), (159), (160), (169), (195),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (203), (211), (258), (267), (281), (282),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10189), (10198), (12045), (12046),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12047), (12282), (12284), (12310), (12325),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12341), (12346), (12347), (12365), (12371),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12379), (12383), (function-axioms) are
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12384)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (12283), (12355), (12370), (12384) are
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1949.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12385)  all_54_4 = e0
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (12044), (12385) are inconsistent by
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1923.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12386)  all_58_10 = e2 & op(e2, e0) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12386) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12387)  op(e2, e0) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12304), (12387), (function-axioms) are
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | |   (12388)  all_54_12 = e1 | all_54_12 = e0
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12045), (12323), (12388) are inconsistent
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2067.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | |   (12389)   ~ (all_54_14 = e3)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | |   (12390)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | REDUCE: (255), (12389) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | |   (12391)   ~ (all_52_11 = e3)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12390) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | |   (12392)  all_54_14 = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (12392) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | |   (12393)  all_52_11 = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | SIMP: (12393) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | |   (12394)  all_52_11 = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (12394) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | |   (12395)   ~ (all_52_3 = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (12394) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | |   (12396)   ~ (all_52_8 = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (12394) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | |   (12397)   ~ (all_52_9 = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12391), (12394) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | |   (12398)   ~ (e3 = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | |   (12399)  all_54_6 = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (10191), (12399) are inconsistent by
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | |   (12400)   ~ (all_54_6 = e3)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | |   (12401)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | |   (12402)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12402) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (12403)  all_58_4 = e2 & op(e3, e1) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12403) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (12404)  all_58_4 = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12405)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12405) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12406)  all_58_2 = e2 & op(e2, e3) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12406) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12407)  all_58_2 = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12408)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (12049), (12407), (12408),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #851.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12409)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12409) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12410)  all_58_6 = e1 & op(e1, e3) = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12410) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12411)  all_58_6 = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12412)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12412) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12413)  all_58_12 = e2 & op(e0, e3) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12413) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12414)  all_58_12 = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12415)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (10189), (12411), (12415),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #850.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12416)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12416) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12417)  all_58_8 = e3 & op(e1, e1) = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12287), (12417), (function-axioms) are
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12418)  all_58_11 = e3 & op(e1, e0) = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12418) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12419)  all_58_11 = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12420)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12420) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12421)  all_58_9 = e2 & op(e3, e0) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12421) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12422)  op(e3, e0) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12423)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (10188), (12049), (12423),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1513.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12424)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12424) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12425)  all_58_4 = e3 & op(e3, e1) = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12404), (12425) are inconsistent by
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2167.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12426)  all_58_9 = e3 & op(e3, e0) = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12426) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12427)  op(e3, e0) = e3
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12422), (12427), (function-axioms) are
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2125.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12428)  all_58_10 = e2 & op(e2, e0) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12428) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12429)  op(e2, e0) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12304), (12429), (function-axioms) are
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12430)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12430) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12431)  all_58_11 = e2 & op(e1, e0) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12419), (12431) are inconsistent by
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1741.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12432)  all_58_15 = e2 & op(e0, e0) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12432) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12433)  all_58_15 = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12338), (12433) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12434)  e2 = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12434) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12435)  e2 = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12414), (12435) imply:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12436)  all_58_12 = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (164), (165),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (227), (230), (232), (10191), (10197),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12294), (12304), (12338), (12391), (12404),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12407), (12436), (function-axioms) are
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #846.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12437)  all_58_13 = e2 & op(e0, e2) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12437) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12438)  op(e0, e2) = e2
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12294), (12438), (function-axioms) are
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12439)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (164), (165),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (230), (232), (10191), (10197), (12304),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12338), (12391), (12404), (12407), (12439),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #847.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12440)  all_58_12 = e1 & op(e0, e3) = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12440) implies:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12441)  all_58_12 = e1
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12442)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (12294), (12441), (12442),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #849.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12443)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (164), (165),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (230), (232), (10191), (10197), (12304),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12338), (12391), (12404), (12407), (12443),
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #847.
% 235.58/44.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12444)  all_58_3 = e2 & op(e2, e2) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12444) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12445)  op(e2, e2) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (12445), (function-axioms) are
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12446)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (165), (12304), (12397), (12446),
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            #845.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12447)  all_58_5 = e2 & op(e2, e1) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12447) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12448)  op(e2, e1) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (12397), (12448), (function-axioms) are
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | |   (12449)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12449) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12450)  all_58_8 = e2 & op(e1, e1) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12450) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12451)  op(e1, e1) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12287), (12451), (function-axioms) are
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12452)  all_58_14 = e2 & op(e0, e1) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12452) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12453)  all_58_14 = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12454)  all_54_12 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (12454) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12455)  all_52_3 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (12455) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12456)   ~ (all_52_2 = e3)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12457)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12457) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12458)  all_58_2 = e2 & op(e2, e3) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12458) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12459)  all_58_2 = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12460)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (12049), (12459), (12460),
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #851.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12461)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12461) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12462)  all_58_6 = e1 & op(e1, e3) = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12462) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12463)  all_58_6 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12464)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12464) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12465)  all_58_2 = e1 & op(e2, e3) = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12459), (12465) are inconsistent by
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #852.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12466)  all_58_3 = e1 & op(e2, e2) = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (12466) are inconsistent by
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12467)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12467) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12468)  all_58_5 = e1 & op(e2, e1) = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12468) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12469)  all_58_5 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12470)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (10189), (12463), (12470),
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #850.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12471)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12471) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12472)  all_58_8 = e3 & op(e1, e1) = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12287), (12472), (function-axioms) are
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12473)  all_58_11 = e3 & op(e1, e0) = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12473) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12474)  all_58_11 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12475)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12475) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12476)  all_58_9 = e2 & op(e3, e0) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12476) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12477)  all_58_9 = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12478)  op(e3, e0) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12479)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (10188), (12049), (12479),
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1513.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12480)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12480) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12481)  all_58_4 = e3 & op(e3, e1) = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12481) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12482)  all_58_4 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12483)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12483) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12484)  all_58_12 = e3 & op(e0, e3) = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12484) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12485)  all_58_12 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12486)  op(e0, e3) = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12487)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12487) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12488)  all_58_6 = e2 & op(e1, e3) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12488) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12489)  all_58_6 = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12463), (12489) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12490)  e2 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12490) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12491)  e2 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12477), (12491) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12492)  all_58_9 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (221), (12328),
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12474), (12492), (function-axioms) are
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1604.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12493)  all_58_7 = e2 & op(e1, e2) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12493) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12494)  all_58_7 = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12495)  op(e1, e2) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12496)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12496) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12497)  all_58_0 = e1 & op(e3, e3) = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12497) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12498)  op(e3, e3) = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (239), (12459), (12463), (12485),
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12498), (function-axioms) are inconsistent by
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1164.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12499)  all_58_1 = e1 & op(e3, e2) = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12499) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12500)  all_58_1 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12401) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12501)  all_54_6 = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (12397), (12501) are inconsistent by
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12502)   ~ (all_54_6 = e2)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12503)  all_54_6 = e1 | all_54_6 = e0
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12503) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12504)  all_54_6 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (12504) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12505)  all_52_9 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12505) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12506)  all_52_9 = e1
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (12506) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12507)   ~ (all_52_1 = e1)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (12506) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12508)   ~ (all_52_8 = e1)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12509)  all_54_2 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (12509) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12510)  all_52_8 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12510) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12511)  all_52_8 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (12511) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12512)   ~ (all_52_12 = e3)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12512) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12513)   ~ (all_52_12 = e3)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12514)  all_54_4 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (10187), (12514) are inconsistent by
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12515)   ~ (all_54_4 = e3)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12516)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12516) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12517)  all_54_4 = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (12517) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12518)  all_52_1 = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12518) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12519)  all_52_1 = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (12519) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12520)   ~ (all_52_2 = e2)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12520) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12521)   ~ (all_52_2 = e2)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (12519) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12522)  op(e2, e3) = e2
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12523)  all_54_8 = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (12456), (12523) are inconsistent by
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12524)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12525)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12525) gives:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12526)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12526) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12527)  op(e3, all_56_1) = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12043), (12527) imply:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12528)  op(e3, e0) = e3
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (12513), (12528), (function-axioms) are
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12529)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12529) implies:
% 235.58/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12530)  op(e2, e3) = all_56_3
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12531)  op(e2, all_56_3) = e2
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12524) gives:
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12532)  all_54_8 = e2
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (12521), (12532) are inconsistent by
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2007.
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12533)   ~ (all_54_8 = e2)
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12534)  all_54_8 = e1 | all_54_8 = e0
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12535)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12535) gives:
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12536)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10186), (10187), (12322), (12536),
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #857.
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12537)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (168), (10186), (12045), (12513), (12537),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1004.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12538)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12538) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12539)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12539) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12540)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12540) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12541)  op(e2, e1) = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (12397), (12541), (function-axioms) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12542)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12542) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12543)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12543) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12544)   ~ (all_56_21 = e2)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12545)   ~ (all_56_11 = e2)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12546)  op(e1, e2) = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12282), (12544) imply:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12547)   ~ (e2 = e0)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12534) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12548)  all_54_8 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (12548) imply:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12549)  all_52_2 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12549) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12550)  all_52_2 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e2,
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (12495), (12546) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12551)  e2 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12494), (12551) imply:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12552)  all_58_7 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (235), (237),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (10198), (12500), (12546), (12552),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1717.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12553)  all_54_8 = e0
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (12283), (12553) are inconsistent by
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2006.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12554)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12554) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12555)  op(e0, e2) = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (235), (10197), (12494), (12500),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12555), (function-axioms) are inconsistent by
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1461.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12556)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12556) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12557)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12557) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12558)   ~ (all_56_11 = e2)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_3,
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (12522), (12530) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12559)  all_56_3 = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12531), (12559) imply:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12560)  op(e2, e2) = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (12560), (function-axioms) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12561)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (12310), (12325), (12561),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1989.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12562)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12562) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12563)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12563) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12564)  op(e1, e3) = all_56_5
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12565)  op(e1, all_56_5) = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (268), (12283), (12287), (12521), (12524),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12564), (12565), (function-axioms) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2004.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12566)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12566) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12567)  op(e0, e3) = all_56_7
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12568)  op(e0, all_56_7) = e0
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12524) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12569)  all_54_8 = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (12521), (12569) are inconsistent by
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2007.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12570)  all_54_8 = e1 | all_54_8 = e0
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12570) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12571)  all_54_8 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (12571) imply:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12572)  all_52_2 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12572) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12573)  all_52_2 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_7,
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (12486), (12567) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12574)  all_56_7 = e3
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12568), (12574) imply:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12575)  op(e0, e3) = e0
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (279), (12044), (12328), (12507), (12516),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12567), (12568), (12575), (function-axioms) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1153.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12576)  all_54_8 = e0
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (12283), (12576) are inconsistent by
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2006.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12577)  all_54_4 = e1 | all_54_4 = e0
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (12044), (12507), (12577) are inconsistent
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1922.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12578)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (12047), (12396), (12508), (12578) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1335.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12579)  all_54_6 = e0
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (12285), (12579) are inconsistent by
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2245.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12580)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12580) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12581)  all_58_4 = e1 & op(e3, e1) = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12581) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12582)  all_58_4 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12482), (12582) imply:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12583)  e3 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12474), (12583) imply:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12584)  all_58_11 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (222), (231), (233),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (12338), (12469), (12478), (12584),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #914.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12585)  all_58_9 = e1 & op(e3, e0) = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12585) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12586)  all_58_9 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (221), (12328),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12474), (12586), (function-axioms) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1604.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12587)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12587) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12588)  all_58_8 = e2 & op(e1, e1) = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12588) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12589)  op(e1, e1) = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12287), (12589), (function-axioms) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12590)  all_58_11 = e2 & op(e1, e0) = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (165), (216), (218),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (10191), (12287), (12338), (12474),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12482), (12485), (12590), (function-axioms) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #842.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12591)  all_58_13 = e3 & op(e0, e2) = e3
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10190), (12591), (function-axioms) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12592)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (222), (231),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (10197), (12338), (12391), (12469),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12474), (12478), (12592), (function-axioms) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #841.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12593)  all_58_9 = e3 & op(e3, e0) = e3
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12593) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12594)  op(e3, e0) = e3
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12478), (12594), (function-axioms) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2125.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12595)  all_58_10 = e2 & op(e2, e0) = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12595) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12596)  op(e2, e0) = e2
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (10197), (12459), (12469),
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12596), (function-axioms) are inconsistent by
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #840.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12597)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (12338), (12474), (12597) are
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1058.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12598)  all_58_10 = e1 & op(e2, e0) = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12598) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12599)  op(e2, e0) = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (12304), (12599), (function-axioms)
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12600)  all_58_12 = e1 & op(e0, e3) = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12600) implies:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12601)  all_58_12 = e1
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12602)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12602) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12603)  all_58_2 = e1 & op(e2, e3) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12459), (12603) are inconsistent by
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #852.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12604)  all_58_3 = e1 & op(e2, e2) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (12604) are inconsistent by
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12605)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12605) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12606)  all_58_5 = e1 & op(e2, e1) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12606) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12607)  all_58_5 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12608)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12608) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12609)  all_58_4 = e3 & op(e3, e1) = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12609) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12610)  all_58_4 = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12611)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12611) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12612)  all_58_0 = e1 & op(e3, e3) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12612) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12613)  op(e3, e3) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12049), (12613), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12614)  all_58_1 = e1 & op(e3, e2) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12614) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12615)  all_58_1 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12616)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12616) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12617)  all_58_6 = e3 & op(e1, e3) = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12617) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12618)  all_58_6 = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12619)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12619) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12620)  all_58_0 = e2 & op(e3, e3) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12620) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12621)  op(e3, e3) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12049), (12621), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12622)  all_58_1 = e2 & op(e3, e2) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12622) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12623)  all_58_1 = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12615), (12623) imply:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12624)  e2 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (12453),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12607), (12610), (12624) are inconsistent by
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #839.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12625)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12625) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12626)  all_58_4 = e2 & op(e3, e1) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12626) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12627)  all_58_4 = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (164), (165),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (227), (230), (232), (10191), (10197),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12294), (12304), (12338), (12391), (12459),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12601), (12627), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #846.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12628)  all_58_9 = e2 & op(e3, e0) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12628) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12629)  op(e3, e0) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12630)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12630) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12631)  all_58_6 = e1 & op(e1, e3) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12631) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12632)  all_58_6 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12618), (12632) are inconsistent by
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1758.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12633)  all_58_7 = e1 & op(e1, e2) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12633) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12634)  all_58_7 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12635)  op(e1, e2) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (235), (237),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (10198), (12615), (12634), (12635),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1717.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12636)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12636) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12637)  all_58_8 = e1 & op(e1, e1) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12637) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12638)  op(e1, e1) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12287), (12638), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12639)  all_58_11 = e1 & op(e1, e0) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12639) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12640)  all_58_11 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (222), (231), (233),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (12338), (12607), (12629), (12640),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #914.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12641)  all_58_7 = e3 & op(e1, e2) = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12641) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12642)  op(e1, e2) = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10189), (12642), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12643)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12643) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12644)  all_58_8 = e3 & op(e1, e1) = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12287), (12644), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12645)  all_58_11 = e3 & op(e1, e0) = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12645) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12646)  all_58_11 = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12647)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12647) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12648)  all_58_9 = e2 & op(e3, e0) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12648) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12649)  op(e3, e0) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12650)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12650) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12651)  all_58_12 = e3 & op(e0, e3) = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12651) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12652)  all_58_12 = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12601), (12652) imply:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12653)  e3 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12646), (12653) imply:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12654)  all_58_11 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (222), (231), (233),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (12338), (12607), (12649), (12654),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #914.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12655)  all_58_13 = e3 & op(e0, e2) = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10190), (12655), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12656)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (222), (231),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (10197), (12338), (12391), (12607),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12646), (12649), (12656), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #841.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12657)  all_58_10 = e2 & op(e2, e0) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12657) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12658)  op(e2, e0) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (10197), (12459), (12607),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12658), (function-axioms) are inconsistent by
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #840.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12659)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12659) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12660)  all_58_11 = e2 & op(e1, e0) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12660) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12661)  all_58_11 = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12646), (12661) imply:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12662)  e3 = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12610), (12662) imply:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12663)  all_58_4 = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (164), (165),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (227), (230), (232), (10191), (10197),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12294), (12304), (12338), (12391), (12459),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12601), (12663), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #846.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12664)  all_58_15 = e2 & op(e0, e0) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12664) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12665)  all_58_15 = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12338), (12665) imply:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12666)  e2 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (12453),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12607), (12610), (12666) are inconsistent by
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #839.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12667)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12667) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12668)  all_58_4 = e1 & op(e3, e1) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12610), (12668) are inconsistent by
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2042.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12669)  all_58_9 = e1 & op(e3, e0) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12669) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12670)  all_58_9 = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (10192), (12328), (12670),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1600.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12671)  all_58_5 = e3 & op(e2, e1) = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10191), (12671), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12672)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12672) gives:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12673)  all_58_8 = e3 & op(e1, e1) = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12287), (12673), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12674)  all_58_14 = e3 & op(e0, e1) = e3
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (12391), (12674), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12675)  all_58_10 = e1 & op(e2, e0) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12675) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12676)  op(e2, e0) = e1
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (12304), (12676), (function-axioms)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12677)  all_58_3 = e2 & op(e2, e2) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12677) implies:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12678)  op(e2, e2) = e2
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (12678), (function-axioms) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12679)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (165), (12304), (12397), (12679),
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #845.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12680)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12045), (12323), (12395), (12680) are
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2066.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | |   (12681)  all_54_14 = e1 | all_54_14 = e0
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (12308), (12324), (12681) are inconsistent
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1935.
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | |   (12682)  all_54_15 = e0
% 235.87/44.25  | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (12312), (12682) are inconsistent by
% 235.87/44.25  | | | | | | | | | | | | | | | | |            sub-proof #1737.
% 235.87/44.25  | | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | | 
% 235.87/44.25  | | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | | 
% 235.87/44.25  | | | | | | | | End of split
% 235.87/44.25  | | | | | | | | 
% 235.87/44.25  | | | | | | | Case 2:
% 235.87/44.25  | | | | | | | | 
% 235.87/44.25  | | | | | | | |   (12683)  all_12_2 = e3
% 235.87/44.26  | | | | | | | |   (12684)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 &
% 235.87/44.26  | | | | | | | |              op(e0, e3) = all_12_1 & $i(all_12_0) &
% 235.87/44.26  | | | | | | | |              $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 235.87/44.26  | | | | | | | |              all_12_1 & $i(all_12_1))
% 235.87/44.26  | | | | | | | | 
% 235.87/44.26  | | | | | | | | COMBINE_EQS: (346), (12683) imply:
% 235.87/44.26  | | | | | | | |   (12685)  all_4_2 = e3
% 235.87/44.26  | | | | | | | | 
% 235.87/44.26  | | | | | | | | COMBINE_EQS: (334), (12685) imply:
% 235.87/44.26  | | | | | | | |   (12686)  all_26_2 = e3
% 235.87/44.26  | | | | | | | | 
% 235.87/44.26  | | | | | | | | COMBINE_EQS: (254), (12685) imply:
% 235.87/44.26  | | | | | | | |   (12687)  all_56_31 = e3
% 235.87/44.26  | | | | | | | | 
% 235.87/44.26  | | | | | | | | REDUCE: (386), (12685) imply:
% 235.87/44.26  | | | | | | | |   (12688)   ~ (all_52_11 = e3)
% 235.87/44.26  | | | | | | | | 
% 235.87/44.26  | | | | | | | | REDUCE: (387), (12685) imply:
% 235.87/44.26  | | | | | | | |   (12689)   ~ (all_52_12 = e3)
% 235.87/44.26  | | | | | | | | 
% 235.87/44.26  | | | | | | | | REDUCE: (389), (12685) imply:
% 235.87/44.26  | | | | | | | |   (12690)   ~ (all_52_14 = e3)
% 235.87/44.26  | | | | | | | | 
% 235.87/44.26  | | | | | | | | BETA: splitting (230) gives:
% 235.87/44.26  | | | | | | | | 
% 235.87/44.26  | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | 
% 235.87/44.26  | | | | | | | | |   (12691)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 235.87/44.26  | | | | | | | | |              & op(e2, e1) = e3)
% 235.87/44.26  | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | BETA: splitting (12691) gives:
% 235.87/44.26  | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | |   (12692)  all_58_4 = e3 & op(e3, e1) = e3
% 235.87/44.26  | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | ALPHA: (12692) implies:
% 235.87/44.26  | | | | | | | | | |   (12693)  all_58_4 = e3
% 235.87/44.26  | | | | | | | | | |   (12694)  op(e3, e1) = e3
% 235.87/44.26  | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | BETA: splitting (226) gives:
% 235.87/44.26  | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | |   (12695)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 235.87/44.26  | | | | | | | | | | |              & op(e1, e2) = e3)
% 235.87/44.26  | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | BETA: splitting (12695) gives:
% 235.87/44.26  | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | |   (12696)  all_58_6 = e3 & op(e1, e3) = e3
% 235.87/44.26  | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | ALPHA: (12696) implies:
% 235.87/44.26  | | | | | | | | | | | |   (12697)  all_58_6 = e3
% 235.87/44.26  | | | | | | | | | | | |   (12698)  op(e1, e3) = e3
% 235.87/44.26  | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | BETA: splitting (222) gives:
% 235.87/44.26  | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | |   (12699)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 235.87/44.26  | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 235.87/44.26  | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | BETA: splitting (12699) gives:
% 235.87/44.26  | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | |   (12700)  all_58_9 = e3 & op(e3, e0) = e3
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | ALPHA: (12700) implies:
% 235.87/44.26  | | | | | | | | | | | | | |   (12701)  op(e3, e0) = e3
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | REF_CLOSE: (168), (12689), (12701), (function-axioms) are
% 235.87/44.26  | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | Case 2:
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | |   (12702)  all_58_10 = e3 & op(e2, e0) = e3
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | ALPHA: (12702) implies:
% 235.87/44.26  | | | | | | | | | | | | | |   (12703)  op(e2, e0) = e3
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 235.87/44.26  | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (164), (12703) gives:
% 235.87/44.26  | | | | | | | | | | | | | |   (12704)  all_52_13 = e3
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | REDUCE: (10192), (12704) imply:
% 235.87/44.26  | | | | | | | | | | | | | |   (12705)  $false
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | CLOSE: (12705) is inconsistent.
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | End of split
% 235.87/44.26  | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | Case 2:
% 235.87/44.26  | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | |   (12706)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 235.87/44.26  | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 235.87/44.26  | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | BETA: splitting (12706) gives:
% 235.87/44.26  | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | |   (12707)  all_58_11 = e3 & op(e1, e0) = e3
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | ALPHA: (12707) implies:
% 235.87/44.26  | | | | | | | | | | | | | |   (12708)  op(e1, e0) = e3
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | REF_CLOSE: (160), (12690), (12708), (function-axioms) are
% 235.87/44.26  | | | | | | | | | | | | | |            inconsistent by sub-proof #2149.
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | Case 2:
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | |   (12709)  all_58_15 = e3 & op(e0, e0) = e3
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | ALPHA: (12709) implies:
% 235.87/44.26  | | | | | | | | | | | | | |   (12710)  all_58_15 = e3
% 235.87/44.26  | | | | | | | | | | | | | |   (12711)  op(e0, e0) = e3
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 235.87/44.26  | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (12698) gives:
% 235.87/44.26  | | | | | | | | | | | | | |   (12712)  all_52_2 = e3
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 235.87/44.26  | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (12694) gives:
% 235.87/44.26  | | | | | | | | | | | | | |   (12713)  all_52_8 = e3
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | REDUCE: (144), (12712) imply:
% 235.87/44.26  | | | | | | | | | | | | | |   (12714)   ~ (all_52_3 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | SIMP: (12714) implies:
% 235.87/44.26  | | | | | | | | | | | | | |   (12715)   ~ (all_52_3 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | REDUCE: (143), (12712) imply:
% 235.87/44.26  | | | | | | | | | | | | | |   (12716)   ~ (all_52_6 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | REDUCE: (141), (12712) imply:
% 235.87/44.26  | | | | | | | | | | | | | |   (12717)   ~ (all_52_14 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | REDUCE: (123), (12713) imply:
% 235.87/44.26  | | | | | | | | | | | | | |   (12718)   ~ (all_52_9 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | REDUCE: (121), (12713) imply:
% 235.87/44.26  | | | | | | | | | | | | | |   (12719)   ~ (all_52_11 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | REDUCE: (120), (12713) imply:
% 235.87/44.26  | | | | | | | | | | | | | |   (12720)   ~ (all_52_12 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | REDUCE: (363), (12713) imply:
% 235.87/44.26  | | | | | | | | | | | | | |   (12721)   ~ (all_10_2 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | SIMP: (12721) implies:
% 235.87/44.26  | | | | | | | | | | | | | |   (12722)   ~ (all_10_2 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | REDUCE: (380), (12713) imply:
% 235.87/44.26  | | | | | | | | | | | | | |   (12723)   ~ (all_6_2 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 235.87/44.26  | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | |   (12724)   ~ (all_16_2 = e0)
% 235.87/44.26  | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | REDUCE: (342), (12724) imply:
% 235.87/44.26  | | | | | | | | | | | | | | |   (12725)   ~ (all_10_2 = e0)
% 235.87/44.26  | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | |   (12726)  all_54_0 = e3
% 235.87/44.26  | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (12726) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | |   (12727)  all_10_2 = e3
% 235.87/44.26  | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | REDUCE: (12722), (12727) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | |   (12728)  $false
% 235.87/44.26  | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | CLOSE: (12728) is inconsistent.
% 235.87/44.26  | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | Case 2:
% 235.87/44.26  | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | |   (12729)   ~ (all_54_0 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | | |   (12730)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 235.87/44.26  | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | BETA: splitting (12730) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | |   (12731)  all_54_0 = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (12731) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | |   (12732)  all_10_2 = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (12732) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | |   (12733)  all_24_2 = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (12732) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | |   (12734)  all_32_2 = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (12732) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | |   (12735)  all_56_1 = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | REDUCE: (355), (12732) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | |   (12736)   ~ (all_52_1 = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | REDUCE: (361), (12732) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | |   (12737)   ~ (all_52_4 = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | REDUCE: (365), (12732) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | |   (12738)   ~ (all_52_12 = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | REDUCE: (12722), (12732) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | |   (12739)   ~ (e3 = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | REDUCE: (45), (12732) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | |   (12740)  op(e3, e3) = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | |   (12741)   ~ (all_18_2 = e0)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | REDUCE: (339), (12741) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | | |   (12742)   ~ (all_6_2 = e0)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | |   (12743)   ~ (all_26_2 = e3)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | REDUCE: (12686), (12743) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | |   (12744)  $false
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | CLOSE: (12744) is inconsistent.
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | |   (12745)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 235.87/44.26  | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | |              $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | |              = all_26_1 & $i(all_26_1))
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | |   (12746)   ~ (all_36_2 = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (328), (12746) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | |   (12747)   ~ (all_6_2 = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | |   (12748)  all_54_10 = e3
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (12748) are inconsistent by
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | |   (12749)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12749) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | |   (12750)  all_54_10 = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (12747), (12750) are inconsistent by
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | |   (12751)  all_54_10 = e1 | all_54_10 = e0
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12751) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | |   (12752)  all_54_10 = e1
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (12752) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | |   (12753)  all_6_2 = e1
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12753) implies:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | |   (12754)  all_6_2 = e1
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (12754) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | |   (12755)  all_56_21 = e1
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (12754) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | |   (12756)   ~ (all_52_6 = e1)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (12754) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | |   (12757)   ~ (all_52_9 = e1)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (12754) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | |   (12758)   ~ (all_52_14 = e1)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |   (12759)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12759) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12760)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10187), (12736), (12755), (12760),
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |            #1003.
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12761)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (12687), (12689), (12761),
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |            #838.
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |   (12762)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12762) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12763)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12763) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12764)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12764) implies:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12765)   ~ (all_56_21 = e1)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12755), (12765) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12766)  $false
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12766) is inconsistent.
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12767)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12767) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12768)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12768) implies:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12769)  op(e2, e1) = e1
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (12757), (12769), (function-axioms) are
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12770)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12770) implies:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12771)  op(e0, e2) = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12772)  op(e2, e0) = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (12771) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12773)  all_52_7 = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (12772) gives:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12774)  all_52_13 = e2
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (12773) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12775)   ~ (all_52_6 = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (12774) imply:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12776)   ~ (all_52_14 = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12776) implies:
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12777)   ~ (all_52_14 = e2)
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (193), (195), (258), (267), (10189),
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12690), (12756), (12758), (12775), (12777) are
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #837.
% 235.87/44.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (12778)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (12735), (12755), (12758), (12778),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |            #1343.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | |   (12779)  all_54_10 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (12742), (12779) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | |   (12780)  all_36_2 = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (12780) imply:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | |   (12781)  all_6_2 = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (12781) imply:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | |   (12782)  all_56_21 = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (12781) imply:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | |   (12783)   ~ (all_52_6 = e2)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (12781) imply:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | |   (12784)   ~ (all_52_9 = e2)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | REDUCE: (383), (12781) imply:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | |   (12785)   ~ (all_52_11 = e2)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (12781) imply:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | |   (12786)  op(e1, e1) = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | |   (12787)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12787) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |   (12788)  all_58_1 = e2 & op(e3, e2) = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12788) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |   (12789)  all_58_1 = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (240), (242), (12693),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (12740), (12789), (function-axioms) are
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2180.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |   (12790)  all_58_3 = e2 & op(e2, e2) = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10197), (12790) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1458.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | |   (12791)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12791) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |   (12792)  all_58_7 = e2 & op(e1, e2) = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12792) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |   (12793)  all_58_7 = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | |   (12794)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12794) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |   (12795)  all_58_12 = e2 & op(e0, e3) = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12795) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |   (12796)  all_58_12 = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (12797)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12797) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12798)  all_58_6 = e0 & op(e1, e3) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12697), (12798) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2213.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12799)  all_58_7 = e0 & op(e1, e2) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12793), (12799) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2212.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (12800)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12800) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12801)  all_58_8 = e0 & op(e1, e1) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12801) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12802)  op(e1, e1) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12786), (12802), (function-axioms) are
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12803)  all_58_11 = e0 & op(e1, e0) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12803) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12804)  all_58_11 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12805)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12805) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12806)  all_58_0 = e1 & op(e3, e3) = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12806) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12807)  op(e3, e3) = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12740), (12807), (function-axioms) are
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12808)  all_58_2 = e1 & op(e2, e3) = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12808) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12809)  all_58_2 = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12810)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (12740), (12809), (12810),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1761.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12811)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12811) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12812)  all_58_6 = e0 & op(e1, e3) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12812) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12813)  all_58_6 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (12786), (12804),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12813), (function-axioms) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1686.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12814)  all_58_12 = e0 & op(e0, e3) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12796), (12814) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1760.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12815)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12815) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12816)  all_58_6 = e1 & op(e1, e3) = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12697), (12816) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1803.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12817)  all_58_12 = e1 & op(e0, e3) = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12796), (12817) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1763.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |   (12818)  all_58_13 = e2 & op(e0, e2) = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (94), (118), (126),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (136), (157), (159), (160), (162), (165), (167),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (168), (170), (203), (211), (212), (214), (216),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (217), (221), (222), (223), (224), (225), (226),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (239), (240), (241), (242),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (246), (282), (10184),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (10191), (10197), (12684), (12688), (12689),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (12693), (12694), (12697), (12698), (12710),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (12711), (12735), (12736), (12737), (12740),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (12745), (12782), (12783), (12784), (12785),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            (12786), (12818), (function-axioms) are
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #807.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | |   (12819)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12819) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |   (12820)  all_58_14 = e2 & op(e0, e1) = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12820) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |   (12821)  all_58_14 = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (12822)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12822) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12823)  all_58_4 = e0 & op(e3, e1) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12693), (12823) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1697.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12824)  all_58_5 = e0 & op(e2, e1) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12824) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12825)  op(e2, e1) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12826)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12826) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12827)  all_58_6 = e0 & op(e1, e3) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12697), (12827) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2213.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12828)  all_58_7 = e0 & op(e1, e2) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12793), (12828) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2212.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12829)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12829) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12830)  all_58_8 = e0 & op(e1, e1) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12830) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12831)  op(e1, e1) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12786), (12831), (function-axioms) are
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12832)  all_58_11 = e0 & op(e1, e0) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12832) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12833)  all_58_11 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12834)  op(e1, e0) = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12835)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12835) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12836)  all_58_6 = e1 & op(e1, e3) = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12697), (12836) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1803.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12837)  all_58_7 = e1 & op(e1, e2) = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12793), (12837) are inconsistent by
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2224.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12838)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12838) gives:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12839)  all_58_8 = e1 & op(e1, e1) = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12839) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12840)  all_58_8 = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12841)  op(e1, e1) = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (165), (220),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (225), (226), (232), (235), (236),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (239), (240), (241), (242), (244), (10189),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (12693), (12697), (12710), (12711),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12740), (12786), (12793), (12825), (12833),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12839), (12840), (12841), (function-axioms) are
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #803.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12842)  all_58_11 = e1 & op(e1, e0) = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12842) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12843)  op(e1, e0) = e1
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12834), (12843), (function-axioms) are
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2284.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (12844)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12786), (12821), (12844), (function-axioms)
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2035.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |   (12845)  all_58_15 = e2 & op(e0, e0) = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12845) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |   (12846)  op(e0, e0) = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12711), (12846), (function-axioms) are
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |   (12847)  all_58_13 = e2 & op(e0, e2) = e2
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (94), (118), (126),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (136), (157), (159), (160), (162), (165), (167),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (168), (170), (203), (211), (212), (214), (216),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (217), (221), (222), (223), (224), (225), (226),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (239), (240), (241), (242),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (246), (282), (10184),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (10191), (10197), (12684), (12688), (12689),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (12693), (12694), (12697), (12698), (12710),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (12711), (12735), (12736), (12737), (12740),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (12745), (12782), (12783), (12784), (12785),
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            (12786), (12847), (function-axioms) are
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #807.
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.27  | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.27  | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | |   (12848)  all_18_2 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | |   (12849)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0
% 235.87/44.27  | | | | | | | | | | | | | | | | | |              & op(e1, e0) = all_18_1 & $i(all_18_0) &
% 235.87/44.27  | | | | | | | | | | | | | | | | | |              $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1, e0)
% 235.87/44.27  | | | | | | | | | | | | | | | | | |              = all_18_1 & $i(all_18_1))
% 235.87/44.27  | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (12848) imply:
% 235.87/44.27  | | | | | | | | | | | | | | | | | |   (12850)  all_6_2 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | SIMP: (12850) implies:
% 235.87/44.27  | | | | | | | | | | | | | | | | | |   (12851)  all_6_2 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (12851) imply:
% 235.87/44.27  | | | | | | | | | | | | | | | | | |   (12852)  all_28_2 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (12851) imply:
% 235.87/44.27  | | | | | | | | | | | | | | | | | |   (12853)  all_56_21 = e0
% 235.87/44.27  | | | | | | | | | | | | | | | | | | 
% 235.87/44.27  | | | | | | | | | | | | | | | | | | REDUCE: (385), (12851) imply:
% 235.87/44.28  | | | | | | | | | | | | | | | | | |   (12854)   ~ (all_52_14 = e0)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | REDUCE: (391), (12851) imply:
% 235.87/44.28  | | | | | | | | | | | | | | | | | |   (12855)   ~ (e3 = e0)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | REDUCE: (39), (12851) imply:
% 235.87/44.28  | | | | | | | | | | | | | | | | | |   (12856)  op(e1, e1) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | |   (12857)   ~ (all_24_2 = e2)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | REDUCE: (12733), (12857) imply:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | |   (12858)  $false
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | CLOSE: (12858) is inconsistent.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | |   (12859)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 235.87/44.28  | | | | | | | | | | | | | | | | | | |              $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | |              = all_24_1 & $i(all_24_1))
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | |   (12860)   ~ (all_26_2 = e3)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | REDUCE: (12686), (12860) imply:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | |   (12861)  $false
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | CLOSE: (12861) is inconsistent.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | |   (12862)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | |              $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | |              = all_26_1 & $i(all_26_1))
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | |   (12863)   ~ (all_28_2 = e0)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (12852), (12863) imply:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | |   (12864)  $false
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | CLOSE: (12864) is inconsistent.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | |   (12865)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = all_28_1 & $i(all_28_0) &
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | |              $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | |              = all_28_1 & $i(all_28_1))
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | |   (12866)   ~ (all_32_2 = e2)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12734), (12866) imply:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | |   (12867)  $false
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12867) is inconsistent.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | |   (12868)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | |   (12869)   ~ (all_42_2 = e3)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10185), (12869) imply:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | |   (12870)  $false
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12870) is inconsistent.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | |   (12871)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | |   (12872)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12872) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (12873)  all_58_12 = e2 & op(e0, e3) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12873) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (12874)  all_58_12 = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (239), (241), (12697),
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | |            (12740), (12874), (function-axioms) are
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1756.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (12875)  all_58_13 = e2 & op(e0, e2) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12875) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (12876)  all_58_13 = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (12877)  op(e0, e2) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12878)  all_58_15 = e0 & op(e0, e0) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12878) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12879)  op(e0, e0) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12711), (12879), (function-axioms) are
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12880)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12880) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12881)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12882)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12882) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12883)  all_58_1 = e0 & op(e3, e2) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12883) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12884)  all_58_1 = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12885)  op(e3, e2) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12886)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (12740), (12884), (12886),
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1564.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12887)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12887) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12888)  all_58_4 = e1 & op(e3, e1) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12693), (12888) are inconsistent by
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2042.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12889)  all_58_9 = e1 & op(e3, e0) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12889) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12890)  all_58_9 = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12891)  op(e3, e0) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12892)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12892) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12893)  all_58_1 = e1 & op(e3, e2) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12884), (12893) are inconsistent by
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2015.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12894)  all_58_3 = e1 & op(e2, e2) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (12894) are inconsistent by
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12895)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12895) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12896)  all_58_7 = e1 & op(e1, e2) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12896) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12897)  all_58_7 = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12898)  op(e1, e2) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12899)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12899) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12900)  all_58_6 = e2 & op(e1, e3) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12697), (12900) are inconsistent by
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2219.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12901)  all_58_7 = e2 & op(e1, e2) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (235), (237), (10197),
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12876), (12897), (12901) are inconsistent by
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #802.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12902)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12902) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12903)  all_58_8 = e2 & op(e1, e1) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12903) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12904)  op(e1, e1) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12856), (12904), (function-axioms) are
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12905)  all_58_11 = e2 & op(e1, e0) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12905) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12906)  op(e1, e0) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12881) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12907)  all_58_12 = e0 & op(e0, e3) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12907) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12908)  all_58_12 = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12909)  op(e0, e3) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12910)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12910) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12911)  all_58_12 = e1 & op(e0, e3) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12911) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12912)  op(e0, e3) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12684), (12862), (12909), (12912),
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1384.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12913)  all_58_13 = e1 & op(e0, e2) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12913) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12914)  all_58_13 = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (235), (237), (10197),
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12897), (12914) are inconsistent by sub-proof
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1457.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12915)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12915) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12916)  all_58_14 = e1 & op(e0, e1) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12916) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12917)  all_58_14 = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12918)  op(e0, e1) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12919)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12919) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12920)  all_58_0 = e1 & op(e3, e3) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12920) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12921)  op(e3, e3) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (240), (244), (12693),
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12890), (12921), (function-axioms) are
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1292.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12922)  all_58_2 = e1 & op(e2, e3) = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12922) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12923)  all_58_2 = e1
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12924)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12924) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12925)  all_58_4 = e2 & op(e3, e1) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12693), (12925) are inconsistent by
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1476.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12926)  all_58_5 = e2 & op(e2, e1) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12926) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12927)  all_58_5 = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12928)  op(e2, e1) = e2
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12929)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12929) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12930)  all_58_2 = e0 & op(e2, e3) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12923), (12930) are inconsistent by
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1972.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12931)  all_58_3 = e0 & op(e2, e2) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10197), (12931) are inconsistent by
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1719.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12932)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12932) gives:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12933)  all_58_5 = e0 & op(e2, e1) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12933) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12934)  op(e2, e1) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12928), (12934), (function-axioms) are
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12935)  all_58_10 = e0 & op(e2, e0) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12935) implies:
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12936)  op(e2, e0) = e0
% 235.87/44.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (157), (12918) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12937)  all_52_11 = e1
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (12877) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12938)  all_52_7 = e2
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (160), (12906) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12939)  all_52_14 = e2
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (12898) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12940)  all_52_6 = e1
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (12936) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12941)  all_52_13 = e0
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (12928) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12942)  all_52_9 = e2
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (168), (12891) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12943)  all_52_12 = e1
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (12885) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12944)  all_52_4 = e0
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12738), (12943) imply:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12945)   ~ (e2 = e1)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12946)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12946) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12947)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12947) implies:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12948)  op(e3, e1) = all_56_17
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12949)  op(e3, all_56_17) = e3
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12694), (12740), (12948), (12949),
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2098.
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12950)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12950) implies:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12951)  op(e2, e1) = all_56_19
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12952)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, all_56_11) = e2)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12952) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12953)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_9 & $i(all_56_9)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12953) implies:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12954)  op(e3, e2) = all_56_9
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12955)  op(e3, all_56_9) = e3
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12859) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12956)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_24_1 & $i(all_24_0) &
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12956) implies:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12957)  op(e3, e2) = all_24_1
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (12689), (12868), (12885), (12954),
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12955), (12957), (function-axioms) are
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #801.
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12958)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12958) implies:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12959)  op(e3, e2) = all_24_1
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (12689), (12868), (12885), (12954),
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12955), (12959), (function-axioms) are
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #801.
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12960)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12960) implies:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12961)  op(e2, all_56_11) = e2
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10186), (12961) imply:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12962)  op(e2, e3) = e2
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (12736), (12962), (function-axioms) are
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12963)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15 & $i(all_56_15))
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12963) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12964)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12964) implies:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12965)  op(e1, e2) = all_56_13
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12966)  op(e1, all_56_13) = e1
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12859) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12967)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_24_1 & $i(all_24_0) &
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12967) implies:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12968)  op(e3, e2) = all_24_1
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12868) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (12898),
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (12965) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12969)  all_56_13 = e1
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (12928),
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (12951) gives:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12970)  all_56_19 = e2
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12966), (12969) imply:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12971)  op(e1, e1) = e1
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (227), (12693), (12918), (12928),
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12971), (function-axioms) are inconsistent by
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1503.
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12972)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12972) implies:
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12973)   ~ (all_32_1 = e0)
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12974)  op(e3, e2) = all_32_1
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12885), (12968), (12973), (12974),
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2065.
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 235.87/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12975)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12975) implies:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12976)   ~ (all_24_1 = e1)
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12977)  op(e3, e2) = all_24_1
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12868) gives:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12978)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_32_1 & $i(all_32_0) &
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12978) implies:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12979)  op(e3, e2) = all_32_1
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (12898),
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (12965) gives:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12980)  all_56_13 = e1
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (12928),
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (12951) gives:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12981)  all_56_19 = e2
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_32_1,
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (12885), (12979) gives:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12982)  all_32_1 = e0
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e3, simplifying with (12977),
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (12979) gives:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12983)  all_32_1 = all_24_1
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12982), (12983) imply:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12984)  all_24_1 = e0
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12976), (12984) imply:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12985)   ~ (e1 = e0)
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12966), (12980) imply:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12986)  op(e1, e1) = e1
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (227), (12693), (12918), (12928),
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12986), (function-axioms) are inconsistent by
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1503.
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12987)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12987) implies:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12988)   ~ (all_32_1 = e0)
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12989)  op(e3, e2) = all_32_1
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12885), (12977), (12988), (12989),
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2065.
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12990)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_15 & $i(all_56_15)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12990) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12991)  op(e0, e2) = all_56_15
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12992)  op(e0, all_56_15) = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12859) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12993)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_24_1 & $i(all_24_0) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12993) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12994)  op(e3, e2) = all_24_1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (218), (12710), (12868), (12877),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12885), (12908), (12917), (12991), (12992),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12994), (function-axioms) are inconsistent by
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #800.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12995)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12995) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12996)  op(e3, e2) = all_24_1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (218), (12710), (12868), (12877),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12885), (12908), (12917), (12991), (12992),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12996), (function-axioms) are inconsistent by
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #800.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12997)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12997) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12998)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12998) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12999)  op(e1, all_56_21) = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12853), (12999) imply:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13000)  op(e1, e0) = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12865) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13001)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_28_1 & $i(all_28_0) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_28_1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13001) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13002)  op(e1, e0) = all_28_1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12859) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13003)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_24_1 & $i(all_24_0) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13003) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13004)  op(e3, e2) = all_24_1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (12693),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12849), (12868), (12885), (12906), (12917),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12927), (13000), (13002), (13004),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #798.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13005)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13005) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13006)  op(e3, e2) = all_24_1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (12693),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12849), (12868), (12885), (12906), (12917),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12927), (13000), (13002), (13006),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #798.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13007)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_28_1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13007) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13008)   ~ (all_28_1 = e2)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13009)  op(e1, e0) = all_28_1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12906), (13008), (13009), (function-axioms) are
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1944.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13010)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13010) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13011)  op(e0, e1) = all_56_23
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13012)  op(e0, all_56_23) = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12859) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13013)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_24_1 & $i(all_24_0) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13013) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13014)  op(e3, e2) = all_24_1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12711), (12868), (12885), (12918), (13011),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13012), (13014), (function-axioms) are
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #797.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13015)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13015) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13016)  op(e3, e2) = all_24_1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12711), (12868), (12885), (12918), (13011),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13012), (13016), (function-axioms) are
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #797.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13017)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13017) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13018)  all_58_8 = e2 & op(e1, e1) = e2
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13018) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13019)  op(e1, e1) = e2
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12856), (13019), (function-axioms) are
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13020)  all_58_14 = e2 & op(e0, e1) = e2
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13020) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13021)  all_58_14 = e2
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (165), (167),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (210), (216), (217), (218), (220), (224),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (231), (232), (233),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (237), (239), (241), (242), (10197),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10198), (12684), (12687), (12689), (12693),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12697), (12710), (12711), (12736), (12740),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12856), (12862), (12871), (13021),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #792.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13022)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13022) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13023)  all_58_6 = e1 & op(e1, e3) = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12697), (13023) are inconsistent by
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1803.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13024)  all_58_12 = e1 & op(e0, e3) = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13024) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13025)  op(e0, e3) = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12684), (12862), (12909), (13025),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1384.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13026)  all_58_15 = e1 & op(e0, e0) = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12710), (13026) are inconsistent by
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1393.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13027)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (228), (229), (12693),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12856), (12877), (13027), (function-axioms) are
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1011.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13028)  all_58_13 = e1 & op(e0, e2) = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12876), (13028) are inconsistent by
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1751.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13029)  all_58_3 = e0 & op(e2, e2) = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10197), (13029) are inconsistent by
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1719.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13030)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13030) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13031)  all_58_7 = e0 & op(e1, e2) = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13031) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13032)  all_58_7 = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13033)  op(e1, e2) = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (162), (224), (225),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12697), (12856), (13032), (13033),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1018.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13034)  all_58_13 = e0 & op(e0, e2) = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13034) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13035)  op(e0, e2) = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12877), (13035), (function-axioms) are
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13036)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13036) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13037)  all_58_14 = e2 & op(e0, e1) = e2
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13037) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13038)  all_58_14 = e2
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (165), (167),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (210), (216), (217), (218), (220), (224),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (231), (232), (233),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (237), (239), (241), (242), (10197),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (10198), (12684), (12687), (12689), (12693),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (12697), (12710), (12711), (12736), (12740),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (12856), (12862), (12871), (13038),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |            #792.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13039)  all_58_15 = e2 & op(e0, e0) = e2
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13039) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13040)  op(e0, e0) = e2
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12711), (13040), (function-axioms) are
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | |   (13041)  all_54_0 = e1 | all_54_0 = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (10199), (12725), (13041) are inconsistent
% 236.09/44.30  | | | | | | | | | | | | | | | | |            by sub-proof #2320.
% 236.09/44.30  | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | |   (13042)  all_16_2 = e0
% 236.09/44.30  | | | | | | | | | | | | | | |   (13043)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0
% 236.09/44.30  | | | | | | | | | | | | | | |              & op(e3, e0) = all_16_1 & $i(all_16_0) &
% 236.09/44.30  | | | | | | | | | | | | | | |              $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0)
% 236.09/44.30  | | | | | | | | | | | | | | |              = all_16_1 & $i(all_16_1))
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | COMBINE_EQS: (342), (13042) imply:
% 236.09/44.30  | | | | | | | | | | | | | | |   (13044)  all_10_2 = e0
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | COMBINE_EQS: (350), (13044) imply:
% 236.09/44.30  | | | | | | | | | | | | | | |   (13045)  all_50_2 = e0
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | COMBINE_EQS: (290), (13044) imply:
% 236.09/44.30  | | | | | | | | | | | | | | |   (13046)  all_56_1 = e0
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | REDUCE: (359), (13044) imply:
% 236.09/44.30  | | | | | | | | | | | | | | |   (13047)   ~ (all_52_3 = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | REDUCE: (365), (13044) imply:
% 236.09/44.30  | | | | | | | | | | | | | | |   (13048)   ~ (all_52_12 = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | REDUCE: (12722), (13044) imply:
% 236.09/44.30  | | | | | | | | | | | | | | |   (13049)   ~ (e3 = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | REDUCE: (10199), (13044) imply:
% 236.09/44.30  | | | | | | | | | | | | | | |   (13050)   ~ (e1 = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | REDUCE: (45), (13044) imply:
% 236.09/44.30  | | | | | | | | | | | | | | |   (13051)  op(e3, e3) = e0
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | |   (13052)   ~ (all_18_2 = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | REDUCE: (339), (13052) imply:
% 236.09/44.30  | | | | | | | | | | | | | | | |   (13053)   ~ (all_6_2 = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | |   (13054)   ~ (all_26_2 = e3)
% 236.09/44.30  | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | REDUCE: (12686), (13054) imply:
% 236.09/44.30  | | | | | | | | | | | | | | | | |   (13055)  $false
% 236.09/44.30  | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | CLOSE: (13055) is inconsistent.
% 236.09/44.30  | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | |   (13056)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 236.09/44.30  | | | | | | | | | | | | | | | | |              & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 236.09/44.30  | | | | | | | | | | | | | | | | |              $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 236.09/44.30  | | | | | | | | | | | | | | | | |              = all_26_1 & $i(all_26_1))
% 236.09/44.30  | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | |   (13057)   ~ (all_36_2 = e2)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | REDUCE: (328), (13057) imply:
% 236.09/44.30  | | | | | | | | | | | | | | | | | |   (13058)   ~ (all_6_2 = e2)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | |   (13059)  all_54_10 = e3
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (391), (13059) are inconsistent by
% 236.09/44.30  | | | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | |   (13060)   ~ (all_54_10 = e3)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | |   (13061)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | BETA: splitting (13061) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | |   (13062)  all_54_10 = e2
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (13058), (13062) are inconsistent by
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | |   (13063)   ~ (all_54_10 = e2)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | |   (13064)  all_54_10 = e1 | all_54_10 = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | BETA: splitting (13064) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | |   (13065)  all_54_10 = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (13065) imply:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | |   (13066)  all_6_2 = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | SIMP: (13066) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | |   (13067)  all_6_2 = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (13067) imply:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | |   (13068)  all_56_21 = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (13067) imply:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | |   (13069)   ~ (all_52_9 = e1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (383), (13067) imply:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | |   (13070)   ~ (all_52_11 = e1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (13067) imply:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | |   (13071)   ~ (all_52_14 = e1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |   (13072)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13072) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |   (13073)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10187), (12687), (13068), (13073),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |            #791.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |   (13074)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13074) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13075)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13075) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13076)   ~ (all_56_31 = e3)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12687), (13076) imply:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13077)  $false
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13077) is inconsistent.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13078)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (168), (12689), (13047), (13078),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |            #1794.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |   (13079)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13079) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |   (13080)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13080) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13081)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13081) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13082)   ~ (all_56_21 = e1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13068), (13082) imply:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13083)  $false
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13083) is inconsistent.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13084)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (13046), (13069), (13084),
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |            #1295.
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |   (13085)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13085) gives:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13086)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13086) implies:
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13087)  op(e0, e2) = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13088)  op(e2, e0) = e0
% 236.09/44.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (13087) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13089)  all_52_7 = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (13088) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13090)  all_52_13 = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (13089) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13091)   ~ (all_52_11 = e0)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13091) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13092)   ~ (all_52_11 = e0)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13093)  all_54_14 = e3
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (12688), (13093) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1796.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13094)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13094) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13095)  all_54_14 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (13095) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13096)  all_52_11 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13096) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13097)  all_52_11 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (13097) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13098)   ~ (all_52_3 = e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13099)  all_54_12 = e3
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12715), (13099) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13100)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13100) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13101)  all_54_12 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (13098), (13101) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2264.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13102)  all_54_12 = e1 | all_54_12 = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13102) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13103)  all_54_12 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (13103) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13104)  all_52_3 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13104) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13105)  all_52_3 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (13105) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13106)   ~ (all_52_1 = e1)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (167), (232), (297), (381), (391),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (13053), (13058), (13061), (13088),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13106), (function-axioms) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #790.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13107)  all_54_12 = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (13047), (13107) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2068.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13108)  all_54_14 = e1 | all_54_14 = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (13070), (13092), (13108) are inconsistent
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1935.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13109)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (13068), (13071), (13109),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |            #1409.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |   (13110)  all_54_10 = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (13053), (13110) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | |   (13111)  all_36_2 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | |   (13112)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 236.09/44.31  | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 236.09/44.31  | | | | | | | | | | | | | | | | | |              $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | |              = all_36_1 & $i(all_36_1))
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (13111) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | |   (13113)  all_6_2 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | SIMP: (13113) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | |   (13114)  all_6_2 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (13114) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | |   (13115)  all_40_2 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (13114) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | |   (13116)  all_56_21 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | REDUCE: (381), (13114) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | |   (13117)   ~ (all_52_9 = e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | REDUCE: (385), (13114) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | |   (13118)   ~ (all_52_14 = e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | REDUCE: (391), (13114) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | |   (13119)   ~ (e3 = e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | REDUCE: (39), (13114) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | |   (13120)  op(e1, e1) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | |   (13121)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (13121) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | |   (13122)  all_58_4 = e2 & op(e3, e1) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12693), (13122) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | |            sub-proof #1476.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | |   (13123)  all_58_5 = e2 & op(e2, e1) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (13123) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | |   (13124)  all_58_5 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | |   (13125)  op(e2, e1) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |   (13126)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (241), (243),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |            (10197), (12697), (13051), (13126),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |            #789.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |   (13127)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13127) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | |   (13128)  all_58_5 = e0 & op(e2, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13128) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | |   (13129)  op(e2, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13125), (13129), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | |   (13130)  all_58_10 = e0 & op(e2, e0) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13130) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | |   (13131)  op(e2, e0) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | |   (13132)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13132) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13133)  all_58_9 = e2 & op(e3, e0) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13133) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13134)  all_58_9 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13135)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (12693), (13125), (13135),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |            #1504.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13136)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13136) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13137)  all_58_8 = e0 & op(e1, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13137) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13138)  op(e1, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13120), (13138), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13139)  all_58_14 = e0 & op(e0, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13139) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13140)  op(e0, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13141)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13141) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13142)  all_58_4 = e1 & op(e3, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12693), (13142) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2042.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13143)  all_58_5 = e1 & op(e2, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13143) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13144)  all_58_5 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13124), (13144) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1665.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13145)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13145) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13146)  all_58_8 = e1 & op(e1, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13146) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13147)  all_58_8 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13148)  op(e1, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13149)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13149) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13150)  all_58_9 = e1 & op(e3, e0) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13134), (13150) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1518.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13151)  all_58_10 = e1 & op(e2, e0) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13151) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13152)  op(e2, e0) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (13131), (13152), (function-axioms)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13153)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13153) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13154)  all_58_11 = e1 & op(e1, e0) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13154) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13155)  all_58_11 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13156)  op(e1, e0) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (225),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (10189), (13147), (13148), (13155),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13156), (function-axioms) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #787.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13157)  all_58_15 = e1 & op(e0, e0) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13157) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13158)  all_58_15 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12710), (13158) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2249.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13159)  all_58_14 = e1 & op(e0, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13159) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13160)  op(e0, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13140), (13160), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2158.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13161)  all_58_10 = e2 & op(e2, e0) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13161) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13162)  op(e2, e0) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13131), (13162), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | |   (13163)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13163) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13164)  all_58_11 = e2 & op(e1, e0) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13164) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13165)  all_58_11 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13166)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13166) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13167)  all_58_4 = e0 & op(e3, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (12693), (12697),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13165), (13167), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13168)  all_58_5 = e0 & op(e2, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13168) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13169)  op(e2, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13125), (13169), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13170)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13170) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13171)  all_58_8 = e0 & op(e1, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13171) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13172)  op(e1, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13120), (13172), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13173)  all_58_14 = e0 & op(e0, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13173) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13174)  op(e0, e1) = e0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13175)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13175) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13176)  all_58_4 = e1 & op(e3, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12693), (13176) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2042.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13177)  all_58_5 = e1 & op(e2, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13124), (13177) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1548.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13178)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13178) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13179)  all_58_8 = e1 & op(e1, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13179) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13180)  all_58_8 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13181)  op(e1, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (216), (223),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (10189), (12697), (12711), (13120),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13165), (13180), (13181), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #985.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13182)  all_58_14 = e1 & op(e0, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13182) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13183)  op(e0, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13174), (13183), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2158.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13184)  all_58_15 = e2 & op(e0, e0) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13184) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13185)  op(e0, e0) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12711), (13185), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | |   (13186)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (13186) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | |   (13187)  all_58_8 = e2 & op(e1, e1) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (13187) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | |   (13188)  all_58_8 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |   (13189)   ~ (all_40_2 = e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | REDUCE: (13115), (13189) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |   (13190)  $false
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | CLOSE: (13190) is inconsistent.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |   (13191)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |              $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | |              = all_40_1 & $i(all_40_1))
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | |   (13192)   ~ (all_42_2 = e3)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10185), (13192) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | |   (13193)  $false
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13193) is inconsistent.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | |   (13194)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | |   (13195)   ~ (all_50_2 = e0)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13045), (13195) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | |   (13196)  $false
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13196) is inconsistent.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | |   (13197)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | |              = all_50_1 & $i(all_50_1))
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |   (13198)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13198) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13199)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13199) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13200)  op(e3, all_56_1) = e3
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13046), (13200) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13201)  op(e3, e0) = e3
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (12689), (13201), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13202)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13202) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13203)  op(e2, e3) = all_56_3
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13204)  op(e2, all_56_3) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_3, e3, e2, simplifying with (167), (13203)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13205)  all_56_3 = all_52_1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13204), (13205) imply:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13206)  op(e2, all_52_1) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13207)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13207) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13208)  all_58_0 = e1 & op(e3, e3) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13208) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13209)  op(e3, e3) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13051), (13209), (function-axioms) are
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13210)  all_58_1 = e1 & op(e3, e2) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13210) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13211)  all_58_1 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (228), (231), (235), (237), (240),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (242), (243), (244), (10184), (10187), (10188),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10192), (10197), (10198), (12684), (12687),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12689), (12693), (12697), (12710), (12711),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13043), (13046), (13047), (13048), (13051),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13056), (13112), (13116), (13118), (13120),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13188), (13191), (13194), (13197), (13211),
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #776.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13212)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13212) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13213)  all_58_4 = e1 & op(e3, e1) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13213) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13214)  all_58_4 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12693), (13214) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2184.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13215)  all_58_9 = e1 & op(e3, e0) = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13215) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13216)  all_58_9 = e1
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13217)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13217) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13218)  all_58_9 = e2 & op(e3, e0) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13216), (13218) are inconsistent by
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1745.
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13219)  all_58_10 = e2 & op(e2, e0) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13219) implies:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13220)  op(e2, e0) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13221)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13221) gives:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13222)  all_58_0 = e2 & op(e3, e3) = e2
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13222) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13223)  op(e3, e3) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13051), (13223), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13224)  all_58_1 = e2 & op(e3, e2) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13224) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13225)  all_58_1 = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13226)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (241), (243),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (12697), (13051), (13226),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #789.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13227)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13227) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13228)  all_58_5 = e0 & op(e2, e1) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13228) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13229)  op(e2, e1) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13230)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (165), (12693), (13229), (13230),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2041.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13231)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13231) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13232)  all_58_8 = e1 & op(e1, e1) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13232) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13233)  all_58_8 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13188), (13233) imply:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13234)  e2 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13234) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13235)  e2 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13225), (13235) imply:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13236)  all_58_1 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (228), (231), (235), (237), (240),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (242), (243), (244), (10184), (10187), (10188),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10192), (10197), (10198), (12684), (12687),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12689), (12693), (12697), (12710), (12711),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13043), (13046), (13047), (13048), (13051),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13056), (13112), (13116), (13118), (13120),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13188), (13191), (13194), (13197), (13236),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #776.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13237)  all_58_14 = e1 & op(e0, e1) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13237) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13238)  all_58_14 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13239)  op(e0, e1) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13240)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13240) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13241)  all_58_2 = e1 & op(e2, e3) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13241) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13242)  op(e2, e3) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (165), (167), (216), (227),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12693), (12711), (13117), (13120), (13206),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13239), (13242), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13243)  all_58_3 = e1 & op(e2, e2) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (13243) are inconsistent by
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13244)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (227), (12693), (13188),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13220), (13238), (13244), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #775.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13245)  all_58_10 = e0 & op(e2, e0) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13245) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13246)  op(e2, e0) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13220), (13246), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13247)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (12693), (13216), (13247) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1475.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13248)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13248) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13249)  all_58_11 = e2 & op(e1, e0) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13249) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13250)  all_58_11 = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (216), (223),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (10189), (12697), (12711),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13250), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #984.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13251)  all_58_15 = e2 & op(e0, e0) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13251) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13252)  op(e0, e0) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12711), (13252), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | |   (13253)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13253) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (13254)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13254) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (13255)  op(e1, e3) = all_56_5
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (13256)  op(e1, all_56_5) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12698), (13255), (13256), (function-axioms)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2243.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (13257)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13257) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (13258)  op(e0, e3) = all_56_7
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (13259)  op(e0, all_56_7) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (159), (13258)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (13260)  all_56_7 = all_52_3
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13259), (13260) imply:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (13261)  op(e0, all_52_3) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13262)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13262) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13263)  all_58_0 = e1 & op(e3, e3) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13263) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13264)  op(e3, e3) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13051), (13264), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13265)  all_58_1 = e1 & op(e3, e2) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13265) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13266)  all_58_1 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13266), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #774.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13267)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13267) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13268)  all_58_4 = e1 & op(e3, e1) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13268) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13269)  all_58_4 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12693), (13269) are inconsistent by
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2184.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13270)  all_58_9 = e1 & op(e3, e0) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13270) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13271)  all_58_9 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13272)  op(e3, e0) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13273)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13273) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13274)  all_58_9 = e2 & op(e3, e0) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13271), (13274) are inconsistent by
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1745.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13275)  all_58_10 = e2 & op(e2, e0) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13275) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13276)  op(e2, e0) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13277)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13277) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13278)  all_58_0 = e2 & op(e3, e3) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13278) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13279)  op(e3, e3) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13051), (13279), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13280)  all_58_1 = e2 & op(e3, e2) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13280) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13281)  all_58_1 = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13282)  op(e3, e2) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13283)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (241), (243),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (12697), (13051), (13283),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #789.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13284)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13284) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13285)  all_58_5 = e0 & op(e2, e1) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13285) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13286)  op(e2, e1) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13287)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (165), (12693), (13286), (13287),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2041.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13288)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13288) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13289)  all_58_8 = e1 & op(e1, e1) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13289) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13290)  all_58_8 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13188), (13290) imply:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13291)  e2 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13281), (13291), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #773.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13292)  all_58_14 = e1 & op(e0, e1) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13292) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13293)  all_58_14 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13294)  op(e0, e1) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13295)  all_58_15 = e0 & op(e0, e0) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13295) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13296)  op(e0, e0) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12711), (13296), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13297)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13297) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13298)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13299)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13300)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13300) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13301)  all_58_2 = e1 & op(e2, e3) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13301) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13302)  all_58_2 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13303)  op(e2, e3) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13304)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13304) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13305)  all_58_0 = e2 & op(e3, e3) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13305) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13306)  op(e3, e3) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (240), (242), (12693),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13281), (13306), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2180.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13307)  all_58_2 = e2 & op(e2, e3) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13307) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13308)  all_58_2 = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13302), (13308) imply:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13309)  e2 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13281), (13309), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #773.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13310)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13310) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13311)  all_58_6 = e2 & op(e1, e3) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12697), (13311) are inconsistent by
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2219.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13312)  all_58_12 = e2 & op(e0, e3) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13312) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13313)  all_58_12 = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13314)  op(e0, e3) = e2
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13298) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13315)  all_58_12 = e0 & op(e0, e3) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13315) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13316)  op(e0, e3) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (159), (165), (216), (227),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10191), (12693), (12710), (12711), (13120),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13294), (13316), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #812.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13317)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13317) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13318)  all_58_13 = e0 & op(e0, e2) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13318) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13319)  op(e0, e2) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13320)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13320) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13321)  all_58_1 = e1 & op(e3, e2) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13321) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13322)  all_58_1 = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13322), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #774.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13323)  all_58_3 = e1 & op(e2, e2) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (158), (219), (10190), (10197), (12710),
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13293), (13313), (13323), (function-axioms) are
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #772.
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13324)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13324) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13325)  all_58_7 = e1 & op(e1, e2) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13325) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13326)  op(e1, e2) = e1
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13299) gives:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13327)  all_58_9 = e0 & op(e3, e0) = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13327) implies:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13328)  all_58_9 = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13271), (13328) imply:
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13329)  e1 = e0
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13302), (13329) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13330)  all_58_2 = e0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (165), (232), (10197), (13276),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13286), (13330), (function-axioms) are
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13331)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13331) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13332)  all_58_10 = e0 & op(e2, e0) = e0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13332) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13333)  op(e2, e0) = e0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13276), (13333), (function-axioms) are
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13334)  all_58_11 = e0 & op(e1, e0) = e0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13334) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13335)  op(e1, e0) = e0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (157), (13294) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13336)  all_52_11 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (13319) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13337)  all_52_7 = e0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (13314) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13338)  all_52_3 = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (13335) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13339)  all_52_14 = e0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (13326) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13340)  all_52_6 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (164), (13276) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13341)  all_52_13 = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (13303) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13342)  all_52_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (168), (13272) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13343)  all_52_12 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (13282) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13344)  all_52_4 = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (13341), (13343) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13345)   ~ (e2 = e1)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12689), (13343) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13346)   ~ (e3 = e1)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13118), (13339) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13347)   ~ (e2 = e0)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13348)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13348) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13349)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13349) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13350)  op(e3, e0) = all_56_25
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13351)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, all_56_11) = e2)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13351) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13352)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_9 & $i(all_56_9)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (10188), (12684), (13056), (13282),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13314), (13352), (function-axioms) are
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #771.
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13353)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13353) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13354)  op(e2, all_56_11) = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10186), (13354) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13355)  op(e2, e3) = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13281), (13303), (13355),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #769.
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13356)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15 & $i(all_56_15))
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13356) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13357)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13357) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13358)  op(e1, e2) = all_56_13
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13359)  op(e1, all_56_13) = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13112) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13360)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_36_1 & $i(all_36_0) &
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_36_1)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13360) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13361)  op(e1, e2) = all_36_1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13362)  op(all_36_1, e1) = all_36_0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13191) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13363)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_40_1 & $i(all_40_0) &
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_40_1)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13363) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13364)  op(e1, e2) = all_40_1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13365)  op(all_40_1, e1) = all_40_0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13197) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_1, e2, e1, simplifying with (13361),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13364) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13366)  all_40_1 = all_36_1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (13326),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13358) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13367)  all_56_13 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (13358),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13364) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13368)  all_56_13 = all_40_1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13367), (13368) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13369)  all_40_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13369) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13370)  all_40_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13366), (13370) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13371)  all_36_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13371) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13372)  all_36_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13365), (13370) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13373)  op(e1, e1) = all_40_0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13362), (13372) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13374)  op(e1, e1) = all_36_0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13359), (13367) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13375)  op(e1, e1) = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_40_0,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (13120), (13373) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13376)  all_40_0 = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_0,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_0, e1, e1, simplifying with (13373),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13374) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13377)  all_40_0 = all_36_0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_40_0,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (13373), (13375) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13378)  all_40_0 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13377), (13378) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13379)  all_36_0 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13376), (13377) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13380)  all_36_0 = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13281), (13379), (13380),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #768.
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13381)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13381) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13382)   ~ (all_50_1 = e2)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13383)  op(e3, e0) = all_50_1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_1, e2, e1, simplifying with (13361),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13364) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13384)  all_40_1 = all_36_1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (13326),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13358) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13385)  all_56_13 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (13358),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13364) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13386)  all_56_13 = all_40_1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25, e0, e3, simplifying with (13272),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13350) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13387)  all_56_25 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_50_1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25, e0, e3, simplifying with (13350),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13383) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13388)  all_56_25 = all_50_1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13385), (13386) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13389)  all_40_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13389) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13390)  all_40_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13387), (13388) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13391)  all_50_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13384), (13390) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13392)  all_36_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13392) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13393)  all_36_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13365), (13390) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13394)  op(e1, e1) = all_40_0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13362), (13393) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13395)  op(e1, e1) = all_36_0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13359), (13385) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13396)  op(e1, e1) = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_36_0,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (13395), (13396) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13397)  all_36_0 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_40_0,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (13120), (13394) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13398)  all_40_0 = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_0,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_0, e1, e1, simplifying with (13394),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13395) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13399)  all_40_0 = all_36_0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13398), (13399) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13400)  all_36_0 = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13400) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13401)  all_36_0 = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13281), (13397), (13401),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #768.
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13402)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_40_1)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13402) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13403)   ~ (all_40_1 = e3)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13404)  op(e1, e2) = all_40_1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_1, e2, e1, simplifying with (13361),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13404) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13405)  all_40_1 = all_36_1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (13326),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13358) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13406)  all_56_13 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_1,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (13358),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13404) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13407)  all_56_13 = all_40_1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13406), (13407) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13408)  all_40_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13408) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13409)  all_40_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13405), (13409) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13410)  all_36_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13410) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13411)  all_36_1 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13362), (13411) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13412)  op(e1, e1) = all_36_0
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13359), (13406) imply:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13413)  op(e1, e1) = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_36_0,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (13120), (13412) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13414)  all_36_0 = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_36_0,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (13412), (13413) gives:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13415)  all_36_0 = e1
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13281), (13414), (13415),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #768.
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13416)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_36_1)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13281), (13326), (13358), (13359),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13416), (function-axioms) are inconsistent by
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #767.
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13417)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_15 & $i(all_56_15)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12684), (12711), (13056), (13314), (13319),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13417), (function-axioms) are inconsistent by
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1022.
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13418)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13418) implies:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13419)  op(e2, e0) = all_56_27
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13420)  op(e2, all_56_27) = e2
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (13276), (13419), (13420),
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #954.
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13421)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13421) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13422)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13422) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13423)  op(e1, e0) = all_56_29
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13424)  op(e1, all_56_29) = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13425)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, all_56_11) = e2)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13425) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13426)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_9 & $i(all_56_9)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (10188), (12684), (13056), (13282),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13314), (13426), (function-axioms) are
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #771.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13427)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13427) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13428)  op(e2, all_56_11) = e2
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10186), (13428) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13429)  op(e2, e3) = e2
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13281), (13303), (13429),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #769.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13430)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15 & $i(all_56_15))
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13430) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13431)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13431) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13432)  op(e1, e2) = all_56_13
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13433)  op(e1, all_56_13) = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13112) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13434)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_36_1 & $i(all_36_0) &
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_36_1)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13434) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13435)  op(e1, e2) = all_36_1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13436)  op(all_36_1, e1) = all_36_0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13056) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13335), (13423), (13424), (function-axioms)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #766.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13437)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 &
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_26_1)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13437) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13438)   ~ (all_26_1 = e1)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13439)  op(e0, e3) = all_26_1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13191) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13440)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_40_1 & $i(all_40_0) &
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_40_1)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13440) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13441)  op(e1, e2) = all_40_1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13442)  op(all_40_1, e1) = all_40_0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_26_1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (13314), (13439) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13443)  all_26_1 = e2
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_1, e2, e1, simplifying with (13435),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13441) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13444)  all_40_1 = all_36_1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (13326),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13432) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13445)  all_56_13 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (13432),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13441) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13446)  all_56_13 = all_40_1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13445), (13446) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13447)  all_40_1 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13447) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13448)  all_40_1 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13444), (13448) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13449)  all_36_1 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13449) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13450)  all_36_1 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13442), (13448) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13451)  op(e1, e1) = all_40_0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13436), (13450) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13452)  op(e1, e1) = all_36_0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13433), (13445) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13453)  op(e1, e1) = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_40_0,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (13120), (13451) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13454)  all_40_0 = e2
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_0,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_0, e1, e1, simplifying with (13451),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13452) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13455)  all_40_0 = all_36_0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_40_0,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (13451), (13453) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13456)  all_40_0 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13454), (13455) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13457)  all_36_0 = e2
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13455), (13456) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13458)  all_36_0 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13457), (13458) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13459)  e2 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13281), (13459), (function-axioms) are
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #773.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13460)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_40_1)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13460) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13461)   ~ (all_40_1 = e3)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13462)  op(e1, e2) = all_40_1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_26_1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (13314), (13439) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13463)  all_26_1 = e2
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_1, e2, e1, simplifying with (13435),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13462) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13464)  all_40_1 = all_36_1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (13326),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13432) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13465)  all_56_13 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_1,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (13432),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13462) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13466)  all_56_13 = all_40_1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13465), (13466) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13467)  all_40_1 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13467) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13468)  all_40_1 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13464), (13468) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13469)  all_36_1 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13469) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13470)  all_36_1 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13436), (13470) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13471)  op(e1, e1) = all_36_0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13433), (13465) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13472)  op(e1, e1) = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_36_0,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (13120), (13471) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13473)  all_36_0 = e2
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_36_0,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (13471), (13472) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13474)  all_36_0 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13473), (13474) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13475)  e2 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13281), (13475), (function-axioms) are
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #773.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13476)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_36_1)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (110), (157), (158),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (164), (165), (167), (168),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (211), (213), (216), (217), (223),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (231), (235), (237),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (242), (243), (244), (10184), (10187),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10191), (10192), (10197), (10198),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12684), (12687), (12689), (12693), (12697),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12710), (12711), (13043), (13046), (13048),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13056), (13112), (13116), (13118),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13188), (13191), (13194), (13197),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13281), (13326), (13432), (13433),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13476), (function-axioms) are inconsistent by
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #767.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13477)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_15 & $i(all_56_15)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12684), (12711), (13056), (13314), (13319),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13477), (function-axioms) are inconsistent by
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1022.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13478)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13478) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13479)  op(e0, all_56_31) = e0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12687), (13479) imply:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13480)  op(e0, e3) = e0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (159), (165), (216), (227),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10191), (12693), (12710), (12711), (13120),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13261), (13294), (13480), (function-axioms) are
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #812.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13481)  all_58_13 = e1 & op(e0, e2) = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13481) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13482)  all_58_13 = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13483)  op(e0, e2) = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (218), (12710), (13293),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13294), (13298), (13482), (13483),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #765.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13484)  all_58_14 = e0 & op(e0, e1) = e0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13484) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13485)  op(e0, e1) = e0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13294), (13485), (function-axioms) are
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2158.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13486)  all_58_3 = e1 & op(e2, e2) = e1
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (13486) are inconsistent by
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13487)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (227), (12693), (13188),
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13276), (13293), (13487), (function-axioms) are
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #775.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13488)  all_58_10 = e0 & op(e2, e0) = e0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13488) implies:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13489)  op(e2, e0) = e0
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13276), (13489), (function-axioms) are
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13490)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (12693), (13271), (13490) are
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1475.
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13491)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13491) gives:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13492)  all_58_11 = e2 & op(e1, e0) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13492) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13493)  all_58_11 = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (216), (223),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (10189), (12697), (12711),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13493), (function-axioms) are
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #984.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13494)  all_58_15 = e2 & op(e0, e0) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13494) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13495)  op(e0, e0) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12711), (13495), (function-axioms) are
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | |   (13496)  all_58_14 = e2 & op(e0, e1) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | ALPHA: (13496) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | |   (13497)  all_58_14 = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | |   (13498)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13498) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | |   (13499)  all_58_4 = e0 & op(e3, e1) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12693), (13499) are inconsistent by
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1697.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | |   (13500)  all_58_5 = e0 & op(e2, e1) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13500) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | |   (13501)  op(e2, e1) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | |   (13502)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13502) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13503)  all_58_6 = e2 & op(e1, e3) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12697), (13503) are inconsistent by
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2219.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13504)  all_58_7 = e2 & op(e1, e2) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13504) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13505)  all_58_7 = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13506)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13506) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13507)  all_58_6 = e0 & op(e1, e3) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12697), (13507) are inconsistent by
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2213.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13508)  all_58_7 = e0 & op(e1, e2) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13505), (13508) are inconsistent by
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2212.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13509)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13509) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13510)  all_58_8 = e0 & op(e1, e1) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13510) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13511)  op(e1, e1) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (165), (228), (12693), (13497),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            (13501), (13511), (function-axioms) are
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1026.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13512)  all_58_11 = e0 & op(e1, e0) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13512) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13513)  all_58_11 = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13514)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (165), (12693), (13501), (13514),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2041.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13515)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13515) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13516)  all_58_8 = e1 & op(e1, e1) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13516) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13517)  all_58_8 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13518)  op(e1, e1) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13519)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13519) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13520)  all_58_1 = e0 & op(e3, e2) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13520) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13521)  all_58_1 = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (242), (244), (12693),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13521), (function-axioms) are
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #764.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13522)  all_58_3 = e0 & op(e2, e2) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (10197), (12697),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13513), (13522), (function-axioms) are
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #763.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13523)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13523) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13524)  all_58_7 = e0 & op(e1, e2) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13505), (13524) are inconsistent by
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2212.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13525)  all_58_13 = e0 & op(e0, e2) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13525) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13526)  op(e0, e2) = e0
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13527)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13527) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13528)  all_58_12 = e1 & op(e0, e3) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13528) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13529)  all_58_12 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13530)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13530) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13531)  all_58_0 = e2 & op(e3, e3) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13531) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13532)  op(e3, e3) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (165), (220),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (225), (226), (232), (235), (236),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (239), (240), (241), (242), (244), (10189),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (12693), (12697), (12710), (12711),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13501), (13505), (13513), (13516),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13517), (13518), (13532), (function-axioms) are
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #803.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13533)  all_58_2 = e2 & op(e2, e3) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13533) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13534)  all_58_2 = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13535)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13535) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13536)  all_58_2 = e1 & op(e2, e3) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13536) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13537)  all_58_2 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13534), (13537) imply:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13538)  e2 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13505), (13538) imply:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13539)  all_58_7 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (12697), (13513), (13517),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13539) are inconsistent by sub-proof #2215.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13540)  all_58_3 = e1 & op(e2, e2) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13540) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13541)  all_58_3 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (13541) are inconsistent by
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1999.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13542)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13542) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13543)  all_58_5 = e1 & op(e2, e1) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13543) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13544)  op(e2, e1) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (165), (13501), (13544), (function-axioms)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2165.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13545)  all_58_10 = e1 & op(e2, e0) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13545) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13546)  op(e2, e0) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13547)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13547) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e1,
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (13120), (13518) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13548)  e2 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13505), (13548) imply:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13549)  all_58_7 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (12697), (13513), (13517),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13549) are inconsistent by sub-proof #2215.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13550)  all_58_10 = e2 & op(e2, e0) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13550) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13551)  op(e2, e0) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13546), (13551), (function-axioms) are
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1659.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13552)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13552) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13553)  all_58_11 = e2 & op(e1, e0) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13553) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13554)  all_58_11 = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (216), (223),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (10189), (12697), (12711), (13120),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13517), (13518), (13554), (function-axioms) are
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #985.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13555)  all_58_15 = e2 & op(e0, e0) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13555) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13556)  op(e0, e0) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12711), (13556), (function-axioms) are
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13557)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13557) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13558)  all_58_6 = e2 & op(e1, e3) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13558) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13559)  all_58_6 = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (13120), (13513),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13559), (function-axioms) are inconsistent by
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #967.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13560)  all_58_12 = e2 & op(e0, e3) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13560) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13561)  all_58_12 = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13529), (13561) imply:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13562)  e2 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13505), (13562) imply:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13563)  all_58_7 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (12697), (13513), (13517),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13563) are inconsistent by sub-proof #2215.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13564)  all_58_13 = e1 & op(e0, e2) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13564) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13565)  op(e0, e2) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13526), (13565), (function-axioms) are
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13566)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13566) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13567)  all_58_14 = e1 & op(e0, e1) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13567) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13568)  all_58_14 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13497), (13568) imply:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13569)  e2 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13569) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13570)  e2 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13505), (13570) imply:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13571)  all_58_7 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (12697), (13513), (13517),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13571) are inconsistent by sub-proof #2215.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13572)  all_58_15 = e1 & op(e0, e0) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13572) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13573)  all_58_15 = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12710), (13573) are inconsistent by
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2249.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13574)  all_58_14 = e1 & op(e0, e1) = e1
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13497), (13574) are inconsistent by
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2040.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | |   (13575)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13575) gives:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13576)  all_58_8 = e2 & op(e1, e1) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13576) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13577)  all_58_8 = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (165), (228), (12693), (13497),
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | |            (13501), (13577), (function-axioms) are
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2039.
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13578)  all_58_11 = e2 & op(e1, e0) = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13578) implies:
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13579)  all_58_11 = e2
% 236.09/44.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (216), (223),
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (10189), (12697), (12711),
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | | | |            (13120), (13579), (function-axioms) are
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #984.
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | |   (13580)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13120), (13497), (13580), (function-axioms)
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2035.
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | End of split
% 236.09/44.36  | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | End of split
% 236.09/44.36  | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | End of split
% 236.09/44.36  | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | Case 2:
% 236.09/44.36  | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | |   (13581)  all_18_2 = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (13581) imply:
% 236.09/44.36  | | | | | | | | | | | | | | | |   (13582)  all_6_2 = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | SIMP: (13582) implies:
% 236.09/44.36  | | | | | | | | | | | | | | | |   (13583)  all_6_2 = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (13583) imply:
% 236.09/44.36  | | | | | | | | | | | | | | | |   (13584)  all_56_21 = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | REDUCE: (39), (13583) imply:
% 236.09/44.36  | | | | | | | | | | | | | | | |   (13585)  op(e1, e1) = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 236.09/44.36  | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.36  | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | |   (13586)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.09/44.36  | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (241), (243),
% 236.09/44.36  | | | | | | | | | | | | | | | | |            (10197), (12697), (13051), (13586),
% 236.09/44.36  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.09/44.36  | | | | | | | | | | | | | | | | |            #789.
% 236.09/44.36  | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.36  | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | |   (13587)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 236.09/44.36  | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 236.09/44.36  | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | BETA: splitting (13587) gives:
% 236.09/44.36  | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.36  | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | |   (13588)  all_58_5 = e0 & op(e2, e1) = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | ALPHA: (13588) implies:
% 236.09/44.36  | | | | | | | | | | | | | | | | | |   (13589)  op(e2, e1) = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (165), (228), (229),
% 236.09/44.36  | | | | | | | | | | | | | | | | | |            (12693), (13585), (13589), (function-axioms) are
% 236.09/44.36  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1025.
% 236.09/44.36  | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.36  | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | |   (13590)  all_58_10 = e0 & op(e2, e0) = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | ALPHA: (13590) implies:
% 236.09/44.36  | | | | | | | | | | | | | | | | | |   (13591)  op(e2, e0) = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 236.09/44.36  | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | |   (13592)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (13592) gives:
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | |   (13593)  all_58_1 = e0 & op(e3, e2) = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | ALPHA: (13593) implies:
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | |   (13594)  all_58_1 = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (242), (244), (12693),
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | |            (13051), (13594), (function-axioms) are
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #764.
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | |   (13595)  all_58_3 = e0 & op(e2, e2) = e0
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10197), (13595) are inconsistent by
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | |            sub-proof #1719.
% 236.09/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | End of split
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | Case 2:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | |   (13596)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 236.22/44.36  | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (13596) gives:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |   (13597)  all_58_7 = e0 & op(e1, e2) = e0
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | ALPHA: (13597) implies:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |   (13598)  all_58_7 = e0
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |   (13599)  op(e1, e2) = e0
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (162), (224), (225),
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |            (12697), (13585), (13598), (13599),
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |            #1018.
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |   (13600)  all_58_13 = e0 & op(e0, e2) = e0
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | ALPHA: (13600) implies:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |   (13601)  op(e0, e2) = e0
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (13601) gives:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |   (13602)  all_52_7 = e0
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (13591) gives:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |   (13603)  all_52_13 = e0
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (13602) imply:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |   (13604)   ~ (all_52_11 = e0)
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | SIMP: (13604) implies:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |   (13605)   ~ (all_52_11 = e0)
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (13603) imply:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |   (13606)   ~ (all_52_14 = e0)
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | SIMP: (13606) implies:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | |   (13607)   ~ (all_52_14 = e0)
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | |   (13608)   ~ (all_26_2 = e3)
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (12686), (13608) imply:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | |   (13609)  $false
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | CLOSE: (13609) is inconsistent.
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | |   (13610)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | |              $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | |              = all_26_1 & $i(all_26_1))
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | |   (13611)   ~ (all_42_2 = e3)
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10185), (13611) imply:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | |   (13612)  $false
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13612) is inconsistent.
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | |   (13613)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | |   (13614)  all_54_3 = e3
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (12689), (13614) are inconsistent by
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | |   (13615)   ~ (all_54_3 = e3)
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | |   (13616)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.22/44.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | |   (13617)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13617) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (13618)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13618) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (13619)  op(e3, all_56_1) = e3
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13046), (13619) imply:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (13620)  op(e3, e0) = e3
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (12689), (13620), (function-axioms) are
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (13621)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13621) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (13622)  op(e2, e3) = all_56_3
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (13623)  op(e2, all_56_3) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_3, e3, e2, simplifying with (167), (13622)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (13624)  all_56_3 = all_52_1
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13623), (13624) imply:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (13625)  op(e2, all_52_1) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13626)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13626) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13627)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13627) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13628)  op(e3, e0) = all_56_25
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13629)  op(e3, all_56_25) = e3
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25, e0, e3, simplifying with (168), (13628)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13630)  all_56_25 = all_52_12
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13629), (13630) imply:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13631)  op(e3, all_52_12) = e3
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13632)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13632) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13633)  all_58_2 = e2 & op(e2, e3) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13633) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13634)  all_58_2 = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (157), (164), (167),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (232), (10197), (10198), (12688), (12693),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13585), (13591), (13625), (13633), (13634),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #761.
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13635)  all_58_3 = e2 & op(e2, e2) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13635) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13636)  op(e2, e2) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (13636), (function-axioms) are
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13637)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13637) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13638)  all_58_5 = e2 & op(e2, e1) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13638) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13639)  all_58_5 = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13640)  op(e2, e1) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (112), (158), (160),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (170), (211), (218), (219), (228), (232),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (280), (10184), (10188), (10190), (10197),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10198), (12693), (12694), (12710), (12711),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13048), (13051), (13584), (13585), (13591),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13601), (13613), (13616), (13631), (13639),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13640), (function-axioms) are inconsistent by
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #753.
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13641)  all_58_10 = e2 & op(e2, e0) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13641) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13642)  op(e2, e0) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13591), (13642), (function-axioms) are
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13643)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (13591), (13643), (function-axioms)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #752.
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13644)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13644) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13645)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13645) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13646)  op(e1, e0) = all_56_29
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13647)  op(e1, all_56_29) = e1
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_29, e0, e1, simplifying with (160), (13646)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13648)  all_56_29 = all_52_14
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13647), (13648) imply:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13649)  op(e1, all_52_14) = e1
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13650)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13650) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13651)  all_58_2 = e2 & op(e2, e3) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13651) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13652)  all_58_2 = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (157), (164), (167),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (232), (10197), (10198), (12688), (12693),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13585), (13591), (13625), (13651), (13652),
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #761.
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13653)  all_58_3 = e2 & op(e2, e2) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13653) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13654)  op(e2, e2) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (13654), (function-axioms) are
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13655)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13655) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13656)  all_58_5 = e2 & op(e2, e1) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13656) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13657)  all_58_5 = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13658)  op(e2, e1) = e2
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13659)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13659) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13660)  all_58_2 = e1 & op(e2, e3) = e1
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13660) implies:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13661)  op(e2, e3) = e1
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13662)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13662) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13663)  all_58_4 = e1 & op(e3, e1) = e1
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12693), (13663) are inconsistent by
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2042.
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13664)  all_58_5 = e1 & op(e2, e1) = e1
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13657), (13664) are inconsistent by
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1548.
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13665)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13665) gives:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13666)  all_58_8 = e1 & op(e1, e1) = e1
% 236.23/44.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13666) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13667)  op(e1, e1) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13585), (13667), (function-axioms) are
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13668)  all_58_14 = e1 & op(e0, e1) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13668) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13669)  all_58_14 = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13670)  op(e0, e1) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13671)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13671) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13672)  all_58_0 = e2 & op(e3, e3) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13672) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13673)  op(e3, e3) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13051), (13673), (function-axioms) are
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13674)  all_58_2 = e2 & op(e2, e3) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13674) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13675)  all_58_2 = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (157), (164), (167),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (232), (10197), (10198), (12688), (12693),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13585), (13591), (13625), (13674), (13675),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #761.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13676)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (158), (160), (211),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (227), (10184), (10190), (10198),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12693), (12694), (12697), (12710), (12711),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13584), (13601), (13607), (13610),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13613), (13649), (13658), (13661), (13669),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13670), (13676), (function-axioms) are
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #749.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13677)  all_58_3 = e1 & op(e2, e2) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (13677) are inconsistent by
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13678)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (164), (13591), (13657), (13678),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #754.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13679)  all_58_10 = e2 & op(e2, e0) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13679) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13680)  op(e2, e0) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13591), (13680), (function-axioms) are
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13681)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13681) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13682)  op(e0, all_56_31) = e0
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12687), (13682) imply:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13683)  op(e0, e3) = e0
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (13683) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13684)  all_52_3 = e0
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13047), (13684) imply:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13685)  $false
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13685) is inconsistent.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | |   (13686)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13686) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (13687)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13687) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (13688)  op(e1, e3) = all_56_5
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (13689)  op(e1, all_56_5) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12698), (13688), (13689), (function-axioms)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2243.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (13690)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13690) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (13691)  op(e0, e3) = all_56_7
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (13692)  op(e0, all_56_7) = e0
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (159), (13691)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (13693)  all_56_7 = all_52_3
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13692), (13693) imply:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (13694)  op(e0, all_52_3) = e0
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13695)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13695) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13696)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13696) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13697)  op(e3, e0) = all_56_25
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13698)  op(e3, all_56_25) = e3
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25, e0, e3, simplifying with (168), (13697)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13699)  all_56_25 = all_52_12
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13698), (13699) imply:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13700)  op(e3, all_52_12) = e3
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13701)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13701) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13702)  all_58_2 = e2 & op(e2, e3) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13702) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13703)  all_58_2 = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13704)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13704) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13705)  all_58_2 = e1 & op(e2, e3) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13703), (13705) are inconsistent by
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #852.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13706)  all_58_3 = e1 & op(e2, e2) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (13706) are inconsistent by
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13707)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13707) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13708)  all_58_5 = e1 & op(e2, e1) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13708) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13709)  all_58_5 = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13710)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13710) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13711)  all_58_4 = e2 & op(e3, e1) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12693), (13711) are inconsistent by
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1476.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13712)  all_58_5 = e2 & op(e2, e1) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13712) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13713)  all_58_5 = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13714)  op(e2, e1) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (112), (158), (160),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (170), (211), (218), (219), (228), (232),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (280), (10184), (10188), (10190), (10197),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10198), (12693), (12694), (12710), (12711),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13048), (13051), (13584), (13585), (13591),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13601), (13613), (13616), (13700), (13713),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13714), (function-axioms) are inconsistent by
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #753.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13715)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13715) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13716)  all_58_8 = e2 & op(e1, e1) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13716) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13717)  op(e1, e1) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13585), (13717), (function-axioms) are
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13718)  all_58_14 = e2 & op(e0, e1) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (118), (157), (159),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (217), (227), (229), (243), (12688),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12693), (12697), (12710), (13051), (13601),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13605), (13610), (13694), (13702), (13708),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13709), (13718), (function-axioms) are
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #748.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13719)  all_58_10 = e1 & op(e2, e0) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13719) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13720)  op(e2, e0) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (13591), (13720), (function-axioms)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13721)  all_58_3 = e2 & op(e2, e2) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13721) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13722)  op(e2, e2) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (13722), (function-axioms) are
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13723)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13723) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13724)  all_58_5 = e2 & op(e2, e1) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13724) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13725)  all_58_5 = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13726)  op(e2, e1) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (112), (158), (160),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (170), (211), (218), (219), (228), (232),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (280), (10184), (10188), (10190), (10197),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10198), (12693), (12694), (12710), (12711),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13048), (13051), (13584), (13585), (13591),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13601), (13613), (13616), (13700), (13725),
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13726), (function-axioms) are inconsistent by
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #753.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13727)  all_58_10 = e2 & op(e2, e0) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13727) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13728)  op(e2, e0) = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13591), (13728), (function-axioms) are
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13729)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (13591), (13729), (function-axioms)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #752.
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13730)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13730) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13731)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13731) implies:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13732)  op(e1, e0) = all_56_29
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13733)  op(e1, all_56_29) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_29, e0, e1, simplifying with (160), (13732)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13734)  all_56_29 = all_52_14
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13733), (13734) imply:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13735)  op(e1, all_52_14) = e1
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13736)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13736) gives:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13737)  all_58_2 = e2 & op(e2, e3) = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13737) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13738)  all_58_2 = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (118), (157), (159),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (217), (227), (229), (232), (243),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (12688), (12693), (12697), (12710),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13585), (13591), (13601), (13605),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13610), (13694), (13737), (13738),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #747.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13739)  all_58_3 = e2 & op(e2, e2) = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13739) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13740)  op(e2, e2) = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10198), (13740), (function-axioms) are
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13741)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13741) gives:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13742)  all_58_5 = e2 & op(e2, e1) = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13742) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13743)  all_58_5 = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13744)  op(e2, e1) = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13745)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13745) gives:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13746)  all_58_2 = e1 & op(e2, e3) = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13746) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13747)  all_58_2 = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13748)  op(e2, e3) = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13749)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13749) gives:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13750)  all_58_4 = e1 & op(e3, e1) = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12693), (13750) are inconsistent by
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2042.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13751)  all_58_5 = e1 & op(e2, e1) = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13743), (13751) are inconsistent by
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1548.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13752)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13752) gives:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13753)  all_58_8 = e1 & op(e1, e1) = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13753) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13754)  op(e1, e1) = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13585), (13754), (function-axioms) are
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13755)  all_58_14 = e1 & op(e0, e1) = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13755) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13756)  all_58_14 = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13757)  op(e0, e1) = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13758)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13758) gives:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13759)  all_58_0 = e2 & op(e3, e3) = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13759) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13760)  op(e3, e3) = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13761)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (13747), (13760), (13761),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #806.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13762)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13762) gives:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13763)  all_58_6 = e0 & op(e1, e3) = e0
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13763) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13764)  all_58_6 = e0
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12697), (13764) are inconsistent by
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2222.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13765)  all_58_12 = e0 & op(e0, e3) = e0
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13765) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13766)  op(e0, e3) = e0
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (13766) gives:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13767)  all_52_3 = e0
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13694), (13767) imply:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13768)  op(e0, e0) = e0
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12711), (13768), (function-axioms) are
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13769)  all_58_2 = e2 & op(e2, e3) = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13769) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13770)  all_58_2 = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (118), (157), (159),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (217), (227), (229), (232), (243),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (12688), (12693), (12697), (12710),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13585), (13591), (13601), (13605),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13610), (13694), (13769), (13770),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #747.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13771)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (158), (160), (211),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (227), (10184), (10190), (10198),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12693), (12694), (12697), (12710), (12711),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13051), (13584), (13601), (13607), (13610),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13613), (13735), (13744), (13748), (13756),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13757), (13771), (function-axioms) are
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #749.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13772)  all_58_3 = e1 & op(e2, e2) = e1
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10197), (13772) are inconsistent by
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13773)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (164), (13591), (13743), (13773),
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #754.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13774)  all_58_10 = e2 & op(e2, e0) = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13774) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13775)  op(e2, e0) = e2
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13591), (13775), (function-axioms) are
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13776)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13776) implies:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13777)  op(e0, all_56_31) = e0
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12687), (13777) imply:
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13778)  op(e0, e3) = e0
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (13047), (13778), (function-axioms) are
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | |   (13779)  all_58_7 = e3 & op(e1, e2) = e3
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | ALPHA: (13779) implies:
% 236.23/44.38  | | | | | | | | | | | |   (13780)  op(e1, e2) = e3
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | REF_CLOSE: (162), (10189), (13780), (function-axioms) are
% 236.23/44.38  | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | |   (13781)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 236.23/44.38  | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 236.23/44.38  | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | REF_CLOSE: (39), (160), (391), (12690), (13781),
% 236.23/44.38  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.38  | | | | | | | | | | |            #1529.
% 236.23/44.38  | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | |   (13782)  all_58_5 = e3 & op(e2, e1) = e3
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | REF_CLOSE: (165), (10191), (13782), (function-axioms) are
% 236.23/44.38  | | | | | | | | | |            inconsistent by sub-proof #1822.
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | 
% 236.23/44.38  | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | 
% 236.23/44.38  | | | | | | | | |   (13783)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3
% 236.23/44.38  | | | | | | | | |              & op(e0, e1) = e3)
% 236.23/44.38  | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | BETA: splitting (13783) gives:
% 236.23/44.38  | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | |   (13784)  all_58_8 = e3 & op(e1, e1) = e3
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | REF_CLOSE: (39), (391), (13784), (function-axioms) are
% 236.23/44.38  | | | | | | | | | |            inconsistent by sub-proof #2092.
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | |   (13785)  all_58_14 = e3 & op(e0, e1) = e3
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | REF_CLOSE: (157), (12688), (13785), (function-axioms) are
% 236.23/44.38  | | | | | | | | | |            inconsistent by sub-proof #1647.
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | 
% 236.23/44.38  | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | 
% 236.23/44.38  | | | | | | | End of split
% 236.23/44.38  | | | | | | | 
% 236.23/44.38  | | | | | | Case 2:
% 236.23/44.38  | | | | | | | 
% 236.23/44.38  | | | | | | |   (13786)  all_10_2 = e1
% 236.23/44.38  | | | | | | |   (13787)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 236.23/44.38  | | | | | | |              op(e3, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1))
% 236.23/44.38  | | | | | | |            | ( ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 236.23/44.38  | | | | | | |              $i(all_10_1))
% 236.23/44.38  | | | | | | | 
% 236.23/44.38  | | | | | | | COMBINE_EQS: (349), (13786) imply:
% 236.23/44.38  | | | | | | |   (13788)  all_38_2 = e1
% 236.23/44.38  | | | | | | | 
% 236.23/44.38  | | | | | | | COMBINE_EQS: (290), (13786) imply:
% 236.23/44.38  | | | | | | |   (13789)  all_56_1 = e1
% 236.23/44.38  | | | | | | | 
% 236.23/44.38  | | | | | | | REDUCE: (355), (13786) imply:
% 236.23/44.38  | | | | | | |   (13790)   ~ (all_52_1 = e1)
% 236.23/44.38  | | | | | | | 
% 236.23/44.38  | | | | | | | REDUCE: (361), (13786) imply:
% 236.23/44.38  | | | | | | |   (13791)   ~ (all_52_4 = e1)
% 236.23/44.38  | | | | | | | 
% 236.23/44.38  | | | | | | | REDUCE: (363), (13786) imply:
% 236.23/44.38  | | | | | | |   (13792)   ~ (all_52_8 = e1)
% 236.23/44.38  | | | | | | | 
% 236.23/44.38  | | | | | | | REDUCE: (365), (13786) imply:
% 236.23/44.38  | | | | | | |   (13793)   ~ (all_52_12 = e1)
% 236.23/44.38  | | | | | | | 
% 236.23/44.38  | | | | | | | REDUCE: (45), (13786) imply:
% 236.23/44.38  | | | | | | |   (13794)  op(e3, e3) = e1
% 236.23/44.38  | | | | | | | 
% 236.23/44.38  | | | | | | | BETA: splitting (49) gives:
% 236.23/44.38  | | | | | | | 
% 236.23/44.38  | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | 
% 236.23/44.38  | | | | | | | |   (13795)   ~ (all_12_2 = e3)
% 236.23/44.38  | | | | | | | | 
% 236.23/44.38  | | | | | | | | REDUCE: (346), (13795) imply:
% 236.23/44.38  | | | | | | | |   (13796)   ~ (all_4_2 = e3)
% 236.23/44.38  | | | | | | | | 
% 236.23/44.38  | | | | | | | | BETA: splitting (58) gives:
% 236.23/44.38  | | | | | | | | 
% 236.23/44.38  | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | 
% 236.23/44.38  | | | | | | | | |   (13797)   ~ (all_18_2 = e0)
% 236.23/44.38  | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | REDUCE: (339), (13797) imply:
% 236.23/44.38  | | | | | | | | |   (13798)   ~ (all_6_2 = e0)
% 236.23/44.38  | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | BETA: splitting (61) gives:
% 236.23/44.38  | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | |   (13799)   ~ (all_20_2 = e1)
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | REDUCE: (341), (13799) imply:
% 236.23/44.38  | | | | | | | | | |   (13800)   ~ (all_4_2 = e1)
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | BETA: splitting (189) gives:
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | |   (13801)  all_54_15 = e3
% 236.23/44.38  | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | REF_CLOSE: (299), (13796), (13801) are inconsistent by
% 236.23/44.38  | | | | | | | | | | |            sub-proof #2340.
% 236.23/44.38  | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | |   (13802)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 236.23/44.38  | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | BETA: splitting (13802) gives:
% 236.23/44.38  | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | |   (13803)  all_54_15 = e2
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | REF_CLOSE: (299), (390), (13803) are inconsistent by
% 236.23/44.38  | | | | | | | | | | | |            sub-proof #2339.
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | |   (13804)  all_54_15 = e1 | all_54_15 = e0
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | BETA: splitting (13804) gives:
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | Case 1:
% 236.23/44.38  | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | |   (13805)  all_54_15 = e1
% 236.23/44.38  | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | REF_CLOSE: (299), (13800), (13805) are inconsistent by
% 236.23/44.38  | | | | | | | | | | | | |            sub-proof #2338.
% 236.23/44.38  | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | |   (13806)  all_54_15 = e0
% 236.23/44.38  | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | COMBINE_EQS: (299), (13806) imply:
% 236.23/44.38  | | | | | | | | | | | | |   (13807)  all_4_2 = e0
% 236.23/44.38  | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | SIMP: (13807) implies:
% 236.23/44.38  | | | | | | | | | | | | |   (13808)  all_4_2 = e0
% 236.23/44.38  | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | COMBINE_EQS: (254), (13808) imply:
% 236.23/44.38  | | | | | | | | | | | | |   (13809)  all_56_31 = e0
% 236.23/44.38  | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | | REF_CLOSE: (164), (165), (167), (194), (213), (232), (266),
% 236.23/44.38  | | | | | | | | | | | | |            (297), (381), (391), (10186), (10187), (10197),
% 236.23/44.38  | | | | | | | | | | | | |            (13789), (13790), (13798), (13809),
% 236.23/44.38  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.38  | | | | | | | | | | | | |            #742.
% 236.23/44.38  | | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | End of split
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | Case 2:
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | |   (13810)  all_20_2 = e1
% 236.23/44.38  | | | | | | | | | |   (13811)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 236.23/44.38  | | | | | | | | | |              & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 236.23/44.38  | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 236.23/44.38  | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | COMBINE_EQS: (341), (13810) imply:
% 236.23/44.38  | | | | | | | | | |   (13812)  all_4_2 = e1
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | SIMP: (13812) implies:
% 236.23/44.38  | | | | | | | | | |   (13813)  all_4_2 = e1
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | COMBINE_EQS: (324), (13813) imply:
% 236.23/44.38  | | | | | | | | | |   (13814)  all_34_2 = e1
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | COMBINE_EQS: (254), (13813) imply:
% 236.23/44.38  | | | | | | | | | |   (13815)  all_56_31 = e1
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | REDUCE: (368), (13813) imply:
% 236.23/44.38  | | | | | | | | | |   (13816)   ~ (all_52_3 = e1)
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | REDUCE: (379), (13813) imply:
% 236.23/44.38  | | | | | | | | | |   (13817)   ~ (all_52_7 = e1)
% 236.23/44.38  | | | | | | | | | | 
% 236.23/44.38  | | | | | | | | | | REDUCE: (388), (13813) imply:
% 236.23/44.39  | | | | | | | | | |   (13818)   ~ (all_52_13 = e1)
% 236.23/44.39  | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | REDUCE: (13796), (13813) imply:
% 236.23/44.39  | | | | | | | | | |   (13819)   ~ (e3 = e1)
% 236.23/44.39  | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | REDUCE: (390), (13813) imply:
% 236.23/44.39  | | | | | | | | | |   (13820)   ~ (e2 = e1)
% 236.23/44.39  | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | BETA: splitting (236) gives:
% 236.23/44.39  | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | |   (13821)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 236.23/44.39  | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.23/44.39  | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | REF_CLOSE: (8), (170), (10197), (13791), (13821),
% 236.23/44.39  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.39  | | | | | | | | | | |            #741.
% 236.23/44.39  | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | |   (13822)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 236.23/44.39  | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 236.23/44.39  | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | BETA: splitting (13822) gives:
% 236.23/44.39  | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | |   (13823)  all_58_7 = e1 & op(e1, e2) = e1
% 236.23/44.39  | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | ALPHA: (13823) implies:
% 236.23/44.39  | | | | | | | | | | | |   (13824)  all_58_7 = e1
% 236.23/44.39  | | | | | | | | | | | |   (13825)  op(e1, e2) = e1
% 236.23/44.39  | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | BETA: splitting (217) gives:
% 236.23/44.39  | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | |   (13826)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 236.23/44.39  | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 236.23/44.39  | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (235), (237),
% 236.23/44.39  | | | | | | | | | | | | |            (239), (243), (245), (10187), (10197), (13794),
% 236.23/44.39  | | | | | | | | | | | | |            (13824), (13826), (function-axioms) are
% 236.23/44.39  | | | | | | | | | | | | |            inconsistent by sub-proof #740.
% 236.23/44.39  | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | |   (13827)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 236.23/44.39  | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.23/44.39  | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | BETA: splitting (13827) gives:
% 236.23/44.39  | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | |   (13828)  all_58_14 = e1 & op(e0, e1) = e1
% 236.23/44.39  | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | ALPHA: (13828) implies:
% 236.23/44.39  | | | | | | | | | | | | | |   (13829)  all_58_14 = e1
% 236.23/44.39  | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 236.23/44.39  | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | |   (13830)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 236.23/44.39  | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 236.23/44.39  | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (165), (167),
% 236.23/44.39  | | | | | | | | | | | | | | |            (170), (227), (229), (232), (240), (244), (246),
% 236.23/44.39  | | | | | | | | | | | | | | |            (10188), (10191), (10197), (13790), (13794),
% 236.23/44.39  | | | | | | | | | | | | | | |            (13818), (13829), (13830), (function-axioms) are
% 236.23/44.39  | | | | | | | | | | | | | | |            inconsistent by sub-proof #739.
% 236.23/44.39  | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | |   (13831)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 236.23/44.39  | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 236.23/44.39  | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | BETA: splitting (13831) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | |   (13832)  all_58_8 = e3 & op(e1, e1) = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | ALPHA: (13832) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | |   (13833)  all_58_8 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | |   (13834)  op(e1, e1) = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | |   (13835)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 236.23/44.39  | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 236.23/44.39  | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | BETA: splitting (13835) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | |   (13836)  all_58_12 = e3 & op(e0, e3) = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | ALPHA: (13836) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | |   (13837)  all_58_12 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | |   (13838)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (13838) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |   (13839)  all_58_2 = e1 & op(e2, e3) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (13790), (13839), (function-axioms) are
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |   (13840)  all_58_3 = e1 & op(e2, e2) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |            (245), (10187), (10197), (13794), (13837),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |            (13840), (function-axioms) are inconsistent by
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |            sub-proof #738.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | |   (13841)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.23/44.39  | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (13841) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |   (13842)  all_58_5 = e1 & op(e2, e1) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | ALPHA: (13842) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |   (13843)  all_58_5 = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |   (13844)  op(e2, e1) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |   (13845)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (10188), (13794), (13845),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |            #1401.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |   (13846)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13846) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |   (13847)  all_58_4 = e3 & op(e3, e1) = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13847) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |   (13848)  all_58_4 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (13829),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (13843), (13848) are inconsistent by sub-proof
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            #1481.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |   (13849)  all_58_9 = e3 & op(e3, e0) = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13849) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |   (13850)  all_58_9 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | |   (13851)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13851) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |   (13852)  all_58_9 = e1 & op(e3, e0) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (245), (10187), (13794), (13837), (13850),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (13852), (function-axioms) are inconsistent by
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #737.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |   (13853)  all_58_10 = e1 & op(e2, e0) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (13818), (13853), (function-axioms) are
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | |   (13854)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13854) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |   (13855)  all_58_11 = e1 & op(e1, e0) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13855) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |   (13856)  all_58_11 = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |   (13857)  op(e1, e0) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (223), (225), (13824),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (13833), (13834), (13856), (13857),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            #1419.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |   (13858)  all_58_15 = e1 & op(e0, e0) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13858) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |   (13859)  all_58_15 = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (39), (82), (85), (91), (94), (118),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (121), (123), (125), (128), (134), (135), (136),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (139), (140), (143), (144), (146), (148), (149),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (157), (158), (159), (162), (165), (167), (170),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (192), (194), (196), (200), (202),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (203), (213), (216), (218), (219), (221), (222),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (223), (225), (226), (227), (229), (230), (231),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (237), (239), (240), (243), (244),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (245), (246), (255), (256), (257), (266), (268),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (279), (281), (282), (297), (322), (328), (367),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (380), (381), (383), (391), (10184), (10185),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (10186), (10187), (10188), (10189), (10190),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (10191), (10197), (13794), (13798), (13811),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (13814), (13815), (13816), (13824), (13825),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            (13843), (13844), (13859), (function-axioms) are
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #680.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |   (13860)  all_58_10 = e1 & op(e2, e0) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (13818), (13860), (function-axioms) are
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | |   (13861)  all_58_13 = e3 & op(e0, e2) = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10190), (13861), (function-axioms) are
% 236.23/44.39  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | |   (13862)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 236.23/44.39  | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 236.23/44.39  | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | BETA: splitting (13862) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | |   (13863)  all_58_14 = e3 & op(e0, e1) = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | ALPHA: (13863) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | |   (13864)  all_58_14 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13829), (13864) are inconsistent by
% 236.23/44.39  | | | | | | | | | | | | | | | | | |            sub-proof #1844.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | |   (13865)  all_58_15 = e3 & op(e0, e0) = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | ALPHA: (13865) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | |   (13866)  all_58_15 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | |   (13867)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 236.23/44.39  | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (13867) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |   (13868)  all_58_9 = e1 & op(e3, e0) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | ALPHA: (13868) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |   (13869)  all_58_9 = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |   (13870)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (10188), (13794), (13870),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |            #1401.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |   (13871)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13871) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |   (13872)  all_58_4 = e3 & op(e3, e1) = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13872) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |   (13873)  all_58_4 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (167), (170),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (227), (229), (232), (240), (244), (246), (10188),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (10197), (13790), (13794), (13818), (13829),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (13873), (function-axioms) are inconsistent by
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1029.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |   (13874)  all_58_9 = e3 & op(e3, e0) = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13874) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |   (13875)  all_58_9 = e3
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13869), (13875) imply:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |   (13876)  e3 = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13866), (13876) imply:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |   (13877)  all_58_15 = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (39), (82), (85), (91), (94),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (118), (121), (123), (125), (128), (134), (135),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (136), (139), (140), (143), (144), (146), (148),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (149), (157), (158), (159), (162), (164), (165),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (190), (191), (192), (194), (196),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (200), (202), (203), (213), (216), (218), (219),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (225), (226), (227), (229),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (235), (237), (239),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (240), (243), (244), (245), (246), (255), (256),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (257), (266), (268), (279), (281), (282), (297),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (322), (328), (367), (380), (381), (383), (391),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (10184), (10185), (10186), (10187), (10188),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (10189), (10190), (10191), (10197), (13790),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (13794), (13798), (13811), (13814), (13815),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (13816), (13818), (13824), (13825), (13877),
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | |            #679.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |   (13878)  all_58_10 = e1 & op(e2, e0) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (13818), (13878), (function-axioms) are
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | |   (13879)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 236.23/44.39  | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (13879) gives:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |   (13880)  all_58_11 = e1 & op(e1, e0) = e1
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | | ALPHA: (13880) implies:
% 236.23/44.39  | | | | | | | | | | | | | | | | | | | |   (13881)  all_58_11 = e1
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |   (13882)  op(e1, e0) = e1
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (223), (225), (13824),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (13833), (13834), (13881), (13882),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            #1419.
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |   (13883)  all_58_15 = e1 & op(e0, e0) = e1
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | | ALPHA: (13883) implies:
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |   (13884)  all_58_15 = e1
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (39), (82), (85), (91), (94),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (118), (121), (123), (125), (128), (134), (135),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (136), (139), (140), (143), (144), (146), (148),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (149), (157), (158), (159), (162), (164), (165),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (167), (170), (190), (191), (192), (194), (196),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (200), (202), (203), (213), (216), (218), (219),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (225), (226), (227), (229),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (235), (237), (239),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (240), (243), (244), (245), (246), (255), (256),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (257), (266), (268), (279), (281), (282), (297),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (322), (328), (367), (380), (381), (383), (391),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (10184), (10185), (10186), (10187), (10188),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (10189), (10190), (10191), (10197), (13790),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (13794), (13798), (13811), (13814), (13815),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (13816), (13818), (13824), (13825), (13884),
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | |            #679.
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.40  | | | | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | | | | End of split
% 236.23/44.40  | | | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | | | End of split
% 236.23/44.40  | | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | | End of split
% 236.23/44.40  | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | Case 2:
% 236.23/44.40  | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | |   (13885)  all_58_14 = e3 & op(e0, e1) = e3
% 236.23/44.40  | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | | ALPHA: (13885) implies:
% 236.23/44.40  | | | | | | | | | | | | | | | |   (13886)  all_58_14 = e3
% 236.23/44.40  | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13829), (13886) are inconsistent by
% 236.23/44.40  | | | | | | | | | | | | | | | |            sub-proof #1844.
% 236.23/44.40  | | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | | End of split
% 236.23/44.40  | | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | End of split
% 236.23/44.40  | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | Case 2:
% 236.23/44.40  | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | |   (13887)  all_58_15 = e1 & op(e0, e0) = e1
% 236.23/44.40  | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | ALPHA: (13887) implies:
% 236.23/44.40  | | | | | | | | | | | | | |   (13888)  all_58_15 = e1
% 236.23/44.40  | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (39), (82), (85), (91), (94),
% 236.23/44.40  | | | | | | | | | | | | | |            (118), (121), (123), (125), (128), (134), (135),
% 236.23/44.40  | | | | | | | | | | | | | |            (136), (139), (140), (143), (144), (146), (148),
% 236.23/44.40  | | | | | | | | | | | | | |            (149), (157), (158), (159), (162), (164), (165),
% 236.23/44.40  | | | | | | | | | | | | | |            (167), (170), (190), (191), (192), (194), (196),
% 236.23/44.40  | | | | | | | | | | | | | |            (200), (202), (203), (213), (216), (218), (219),
% 236.23/44.40  | | | | | | | | | | | | | |            (221), (222), (223), (225), (226), (227), (229),
% 236.23/44.40  | | | | | | | | | | | | | |            (230), (231), (232), (233), (235), (237), (239),
% 236.23/44.40  | | | | | | | | | | | | | |            (240), (243), (244), (245), (246), (255), (256),
% 236.23/44.40  | | | | | | | | | | | | | |            (257), (266), (268), (279), (281), (282), (297),
% 236.23/44.40  | | | | | | | | | | | | | |            (322), (328), (367), (380), (381), (383), (391),
% 236.23/44.40  | | | | | | | | | | | | | |            (10184), (10185), (10186), (10187), (10188),
% 236.23/44.40  | | | | | | | | | | | | | |            (10189), (10190), (10191), (10197), (13790),
% 236.23/44.40  | | | | | | | | | | | | | |            (13794), (13798), (13811), (13814), (13815),
% 236.23/44.40  | | | | | | | | | | | | | |            (13816), (13818), (13824), (13825), (13888),
% 236.23/44.40  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.23/44.40  | | | | | | | | | | | | | |            #679.
% 236.23/44.40  | | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | | End of split
% 236.23/44.40  | | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | End of split
% 236.23/44.40  | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | Case 2:
% 236.23/44.40  | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | |   (13889)  all_58_13 = e1 & op(e0, e2) = e1
% 236.23/44.40  | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | | REF_CLOSE: (158), (13817), (13889), (function-axioms) are
% 236.23/44.40  | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 236.23/44.40  | | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | | End of split
% 236.23/44.40  | | | | | | | | | | | 
% 236.23/44.40  | | | | | | | | | | End of split
% 236.23/44.40  | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | End of split
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | Case 2:
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | |   (13890)  all_18_2 = e0
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | COMBINE_EQS: (339), (13890) imply:
% 236.29/44.40  | | | | | | | | |   (13891)  all_6_2 = e0
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | SIMP: (13891) implies:
% 236.29/44.40  | | | | | | | | |   (13892)  all_6_2 = e0
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | COMBINE_EQS: (266), (13892) imply:
% 236.29/44.40  | | | | | | | | |   (13893)  all_56_21 = e0
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | REDUCE: (380), (13892) imply:
% 236.29/44.40  | | | | | | | | |   (13894)   ~ (all_52_8 = e0)
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | REDUCE: (381), (13892) imply:
% 236.29/44.40  | | | | | | | | |   (13895)   ~ (all_52_9 = e0)
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | REDUCE: (383), (13892) imply:
% 236.29/44.40  | | | | | | | | |   (13896)   ~ (all_52_11 = e0)
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | REDUCE: (385), (13892) imply:
% 236.29/44.40  | | | | | | | | |   (13897)   ~ (all_52_14 = e0)
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | REDUCE: (391), (13892) imply:
% 236.29/44.40  | | | | | | | | |   (13898)   ~ (e3 = e0)
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | REDUCE: (39), (13892) imply:
% 236.29/44.40  | | | | | | | | |   (13899)  op(e1, e1) = e0
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | BETA: splitting (223) gives:
% 236.29/44.40  | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | |   (13900)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 236.29/44.40  | | | | | | | | | |              & op(e1, e2) = e0)
% 236.29/44.40  | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | BETA: splitting (13900) gives:
% 236.29/44.40  | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | |   (13901)  all_58_6 = e0 & op(e1, e3) = e0
% 236.29/44.40  | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | ALPHA: (13901) implies:
% 236.29/44.40  | | | | | | | | | | |   (13902)  all_58_6 = e0
% 236.29/44.40  | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 236.29/44.40  | | | | | | | | | | |            (167), (170), (216), (217), (218), (220), (221),
% 236.29/44.40  | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.29/44.40  | | | | | | | | | | |            (229), (230), (231), (232), (233), (235), (237),
% 236.29/44.40  | | | | | | | | | | |            (239), (240), (243), (244), (245), (246), (10187),
% 236.29/44.40  | | | | | | | | | | |            (10188), (10189), (10191), (10197), (13790),
% 236.29/44.40  | | | | | | | | | | |            (13794), (13899), (13902), (function-axioms) are
% 236.29/44.40  | | | | | | | | | | |            inconsistent by sub-proof #664.
% 236.29/44.40  | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | Case 2:
% 236.29/44.40  | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | |   (13903)  all_58_7 = e0 & op(e1, e2) = e0
% 236.29/44.40  | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | ALPHA: (13903) implies:
% 236.29/44.40  | | | | | | | | | | |   (13904)  all_58_7 = e0
% 236.29/44.40  | | | | | | | | | | |   (13905)  op(e1, e2) = e0
% 236.29/44.40  | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | BETA: splitting (224) gives:
% 236.29/44.40  | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | |   (13906)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 236.29/44.40  | | | | | | | | | | | |              & op(e1, e2) = e1)
% 236.29/44.40  | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | BETA: splitting (13906) gives:
% 236.29/44.40  | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | |   (13907)  all_58_6 = e1 & op(e1, e3) = e1
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | ALPHA: (13907) implies:
% 236.29/44.40  | | | | | | | | | | | | |   (13908)  all_58_6 = e1
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 236.29/44.40  | | | | | | | | | | | | |            (245), (10187), (13794), (13908),
% 236.29/44.40  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.40  | | | | | | | | | | | | |            #1161.
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | Case 2:
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | |   (13909)  all_58_7 = e1 & op(e1, e2) = e1
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | ALPHA: (13909) implies:
% 236.29/44.40  | | | | | | | | | | | | |   (13910)  op(e1, e2) = e1
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | REF_CLOSE: (4), (162), (13905), (13910), (function-axioms)
% 236.29/44.40  | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | End of split
% 236.29/44.40  | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | Case 2:
% 236.29/44.40  | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | |   (13911)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 236.29/44.40  | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 236.29/44.40  | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | BETA: splitting (13911) gives:
% 236.29/44.40  | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | |   (13912)  all_58_8 = e1 & op(e1, e1) = e1
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | ALPHA: (13912) implies:
% 236.29/44.40  | | | | | | | | | | | | |   (13913)  op(e1, e1) = e1
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | REF_CLOSE: (4), (13899), (13913), (function-axioms) are
% 236.29/44.40  | | | | | | | | | | | | |            inconsistent by sub-proof #2220.
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | Case 2:
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | |   (13914)  all_58_11 = e1 & op(e1, e0) = e1
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | ALPHA: (13914) implies:
% 236.29/44.40  | | | | | | | | | | | | |   (13915)  all_58_11 = e1
% 236.29/44.40  | | | | | | | | | | | | |   (13916)  op(e1, e0) = e1
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.29/44.40  | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | |   (13917)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.29/44.40  | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.29/44.40  | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | BETA: splitting (13917) gives:
% 236.29/44.40  | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | |   (13918)  all_58_6 = e2 & op(e1, e3) = e2
% 236.29/44.40  | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | ALPHA: (13918) implies:
% 236.29/44.40  | | | | | | | | | | | | | | |   (13919)  all_58_6 = e2
% 236.29/44.40  | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (167), (226),
% 236.29/44.40  | | | | | | | | | | | | | | |            (239), (243), (245), (10187), (10189), (13794),
% 236.29/44.40  | | | | | | | | | | | | | | |            (13899), (13915), (13919), (function-axioms) are
% 236.29/44.40  | | | | | | | | | | | | | | |            inconsistent by sub-proof #661.
% 236.29/44.40  | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | Case 2:
% 236.29/44.40  | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | |   (13920)  all_58_7 = e2 & op(e1, e2) = e2
% 236.29/44.40  | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | REF_CLOSE: (5), (13904), (13920) are inconsistent by
% 236.29/44.40  | | | | | | | | | | | | | | |            sub-proof #1326.
% 236.29/44.40  | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | End of split
% 236.29/44.40  | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | Case 2:
% 236.29/44.40  | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | |   (13921)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 236.29/44.40  | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 236.29/44.40  | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | BETA: splitting (13921) gives:
% 236.29/44.40  | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | |   (13922)  all_58_8 = e2 & op(e1, e1) = e2
% 236.29/44.40  | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | ALPHA: (13922) implies:
% 236.29/44.40  | | | | | | | | | | | | | | |   (13923)  all_58_8 = e2
% 236.29/44.40  | | | | | | | | | | | | | | |   (13924)  op(e1, e1) = e2
% 236.29/44.40  | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 236.29/44.40  | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | |   (13925)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 236.29/44.40  | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 236.29/44.40  | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | BETA: splitting (13925) gives:
% 236.29/44.40  | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | |   (13926)  all_58_6 = e3 & op(e1, e3) = e3
% 236.29/44.40  | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | ALPHA: (13926) implies:
% 236.29/44.40  | | | | | | | | | | | | | | | | |   (13927)  all_58_6 = e3
% 236.29/44.40  | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 236.29/44.40  | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | |   (13928)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 236.29/44.40  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.29/44.40  | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (170), (239),
% 236.29/44.40  | | | | | | | | | | | | | | | | | |            (243), (245), (10187), (10197), (13791), (13794),
% 236.29/44.40  | | | | | | | | | | | | | | | | | |            (13927), (13928), (function-axioms) are
% 236.29/44.40  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #659.
% 236.29/44.40  | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | |   (13929)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 236.29/44.40  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 236.29/44.40  | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | BETA: splitting (13929) gives:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | |   (13930)  all_58_7 = e1 & op(e1, e2) = e1
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | ALPHA: (13930) implies:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | |   (13931)  all_58_7 = e1
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (223), (13916), (13923), (13927),
% 236.29/44.40  | | | | | | | | | | | | | | | | | | |            (13931), (function-axioms) are inconsistent by
% 236.29/44.40  | | | | | | | | | | | | | | | | | | |            sub-proof #1555.
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | |   (13932)  all_58_13 = e1 & op(e0, e2) = e1
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | ALPHA: (13932) implies:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | |   (13933)  all_58_13 = e1
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | |   (13934)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | BETA: splitting (13934) gives:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | |   (13935)  all_58_9 = e3 & op(e3, e0) = e3
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | | ALPHA: (13935) implies:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | |   (13936)  all_58_9 = e3
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | | |   (13937)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 236.29/44.40  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (13904),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (13915), (13923), (13927), (13933), (13937),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            #557.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |   (13938)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13938) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |   (13939)  all_58_4 = e0 & op(e3, e1) = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13939) implies:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |   (13940)  all_58_4 = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | |   (13941)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13941) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (13942)  all_58_1 = e2 & op(e3, e2) = e2
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13942) implies:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (13943)  all_58_1 = e2
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13944)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13944) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13945)  all_58_4 = e1 & op(e3, e1) = e1
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13945) implies:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13946)  all_58_4 = e1
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (240), (13794), (13936), (13943),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13946), (function-axioms) are inconsistent by
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1472.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e1,
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (13899), (13924) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13947)  e2 = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13943), (13947) imply:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13948)  all_58_1 = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (13904),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13915), (13923), (13927), (13933), (13948),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #558.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13949)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13949) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13950)  all_58_8 = e1 & op(e1, e1) = e1
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13950) implies:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13951)  all_58_8 = e1
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (13904), (13915), (13927),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13951) are inconsistent by sub-proof #988.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13952)  all_58_14 = e1 & op(e0, e1) = e1
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13952) implies:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13953)  all_58_14 = e1
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (216), (217), (218), (220), (221),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (235), (237),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (240), (243), (244), (245), (246), (10187),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10189), (10191), (10197), (13790),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13794), (13899), (13927), (13940), (13953),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #582.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (13954)  all_58_3 = e2 & op(e2, e2) = e2
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (167), (226),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (243), (245), (10187), (10189), (10197),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (13794), (13899), (13915), (13927), (13954),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            #556.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | |   (13955)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13955) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (13956)  all_58_7 = e2 & op(e1, e2) = e2
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (13904),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (13923), (13956), (function-axioms) are
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #560.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (13957)  all_58_13 = e2 & op(e0, e2) = e2
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (13904), (13915), (13923),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (13927), (13933), (13957) are inconsistent by
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #555.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |   (13958)  all_58_9 = e0 & op(e3, e0) = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13958) implies:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |   (13959)  all_58_9 = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13936), (13959) imply:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |   (13960)  e3 = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (216), (217), (218), (220), (221),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (235), (237),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |            (239), (240), (243), (244), (245), (246), (10187),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10189), (10191), (10197), (13790),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |            (13794), (13899), (13927), (13960),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |            #642.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |   (13961)  all_58_10 = e3 & op(e2, e0) = e3
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (13961) implies:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |   (13962)  all_58_10 = e3
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (231), (232),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |            (233), (10197), (13790), (13962),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |            #1099.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | |   (13963)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | BETA: splitting (13963) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |   (13964)  all_58_11 = e3 & op(e1, e0) = e3
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (13964) implies:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |   (13965)  all_58_11 = e3
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13915), (13965) imply:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |   (13966)  e3 = e1
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13927), (13966) imply:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |   (13967)  all_58_6 = e1
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |            (245), (10187), (13794), (13967),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |            #1161.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |   (13968)  all_58_15 = e3 & op(e0, e0) = e3
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (13968) implies:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | |   (13969)  all_58_15 = e3
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |   (13970)  all_58_15 = e0 & op(e0, e0) = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13970) implies:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |   (13971)  all_58_15 = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13969), (13971) imply:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |   (13972)  e3 = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13927), (13972) imply:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |   (13973)  all_58_6 = e0
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (216), (217), (218), (220), (221),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (235), (237),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (239), (240), (243), (244), (245), (246), (10187),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (10188), (10189), (10191), (10197), (13790),
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            (13794), (13899), (13973), (function-axioms) are
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #664.
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |   (13974)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13974) implies:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |   (13975)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |   (13976)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |   (13977)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13977) gives:
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.41  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | |   (13978)  all_58_1 = e2 & op(e3, e2) = e2
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13978) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | |   (13979)  all_58_1 = e2
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (13980)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (13904),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (13915), (13923), (13927), (13933), (13980),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |            #557.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (13981)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13981) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13982)  all_58_4 = e0 & op(e3, e1) = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13982) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13983)  all_58_4 = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13984)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (216), (217), (218), (220), (221),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (235), (237),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (240), (243), (244), (245), (246), (10187),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10189), (10191), (10197), (13790),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13794), (13899), (13927), (13983), (13984),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #621.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13985)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13985) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13986)  all_58_8 = e3 & op(e1, e1) = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13986) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13987)  op(e1, e1) = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (13924), (13987), (function-axioms) are
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13988)  all_58_14 = e3 & op(e0, e1) = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13988) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13989)  all_58_14 = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (13904),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13915), (13923), (13927), (13933), (13969),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13975), (13979), (13989), (function-axioms) are
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #554.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13990)  all_58_9 = e0 & op(e3, e0) = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13990) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13991)  all_58_9 = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13975) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13992)  all_58_12 = e0 & op(e0, e3) = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13992) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13993)  all_58_12 = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13994)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (10188), (13794), (13994),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1401.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13995)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13995) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13996)  all_58_4 = e3 & op(e3, e1) = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13996) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13997)  all_58_4 = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (221), (231),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (243), (244), (10197), (13790), (13794),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13915), (13927), (13969), (13979), (13991),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13993), (13997), (function-axioms) are
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #614.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13998)  all_58_9 = e3 & op(e3, e0) = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13998) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13999)  all_58_9 = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13991), (13999) imply:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14000)  e3 = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (216), (217), (218), (220), (221),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (235), (237),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (240), (243), (244), (245), (246), (10187),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10189), (10191), (10197), (13790),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13794), (13899), (13927), (14000),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #642.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14001)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14001) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14002)  all_58_13 = e0 & op(e0, e2) = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13933), (14002) are inconsistent by
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #609.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14003)  all_58_14 = e0 & op(e0, e1) = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14003) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14004)  all_58_14 = e0
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14005)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14005) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14006)  all_58_4 = e1 & op(e3, e1) = e1
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14006) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14007)  all_58_4 = e1
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (10188), (13794), (14007),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1468.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14008)  all_58_5 = e1 & op(e2, e1) = e1
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14008) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14009)  all_58_5 = e1
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14010)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14010) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14011)  all_58_12 = e2 & op(e0, e3) = e2
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14011) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14012)  all_58_12 = e2
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14013)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14013) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14014)  all_58_4 = e3 & op(e3, e1) = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14014) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14015)  all_58_4 = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (167), (221),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (231), (239), (243), (244), (245),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10187), (10189), (10197), (13794), (13899),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13904), (13915), (13923), (13924), (13927),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13969), (13979), (13991), (14009), (14015),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #553.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14016)  all_58_5 = e3 & op(e2, e1) = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10191), (14016), (function-axioms) are
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14017)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14017) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14018)  all_58_8 = e3 & op(e1, e1) = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14018) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14019)  op(e1, e1) = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14020)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (10188), (13794), (14020),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1401.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14021)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14021) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14022)  all_58_4 = e3 & op(e3, e1) = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14022) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14023)  all_58_4 = e3
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14024)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14024) gives:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14025)  all_58_9 = e2 & op(e3, e0) = e2
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14025) implies:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14026)  all_58_9 = e2
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (244), (13794), (13979), (13991),
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14023), (14026), (function-axioms) are
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1065.
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14027)  all_58_10 = e2 & op(e2, e0) = e2
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14027) implies:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14028)  all_58_10 = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14029)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (244), (13794), (13904), (13927),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13979), (13991), (14023), (14029),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #552.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13921) gives:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (13924), (14019), (function-axioms) are
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14030)  all_58_11 = e2 & op(e1, e0) = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14030) implies:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14031)  all_58_11 = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13915), (14031) imply:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14032)  e2 = e1
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14028), (14032) imply:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14033)  all_58_10 = e1
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (221), (239), (243),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13794), (13915), (13927), (13969), (13991),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14012), (14033), (function-axioms) are
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #550.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14034)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (239), (243), (13794),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13915), (13927), (13969), (14012), (14034),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #551.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14035)  all_58_9 = e3 & op(e3, e0) = e3
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14035) implies:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14036)  all_58_9 = e3
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14037)  op(e3, e0) = e3
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14038)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14038) gives:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14039)  all_58_9 = e2 & op(e3, e0) = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14039) implies:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14040)  op(e3, e0) = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14037), (14040), (function-axioms) are
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2125.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14041)  all_58_10 = e2 & op(e2, e0) = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14041) implies:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14042)  op(e2, e0) = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (13916), (13976), (14036), (14042),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2101.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14043)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (239), (243), (13794),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13915), (13927), (13969), (14012), (14043),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #551.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14044)  all_58_14 = e3 & op(e0, e1) = e3
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14044) implies:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14045)  all_58_14 = e3
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (13904),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13915), (13923), (13927), (13933), (13969),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13975), (13979), (14045), (function-axioms) are
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #554.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14046)  all_58_13 = e2 & op(e0, e2) = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (13904), (13915), (13923),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13927), (13933), (14046) are inconsistent by
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #555.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14047)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14047) gives:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14048)  all_58_14 = e2 & op(e0, e1) = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14048) implies:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14049)  all_58_14 = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14004), (14049) imply:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14050)  e2 = e0
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13979), (14050) imply:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14051)  all_58_1 = e0
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (13904),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13915), (13923), (13927), (13933), (14051),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #558.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14052)  all_58_15 = e2 & op(e0, e0) = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14052) implies:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14053)  all_58_15 = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13969), (14053) imply:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14054)  e3 = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (167), (226),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (243), (245), (10187), (10189), (13794),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13899), (13915), (13927), (14054),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #561.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14055)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (225), (13904), (13915),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13927), (14004), (14055) are inconsistent by
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #549.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |   (14056)  all_58_3 = e2 & op(e2, e2) = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (167), (226),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (239), (243), (245), (10187), (10189), (10197),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (13794), (13899), (13915), (13927), (14056),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            #556.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | |   (14057)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14057) gives:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |   (14058)  all_58_7 = e2 & op(e1, e2) = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14058) implies:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |   (14059)  all_58_7 = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13904), (14059) imply:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |   (14060)  e2 = e0
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (13923),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (14060), (function-axioms) are inconsistent by
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #562.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |   (14061)  all_58_13 = e2 & op(e0, e2) = e2
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (13904), (13915), (13923),
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            (13927), (13933), (14061) are inconsistent by
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #559.
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | |   (14062)  all_58_7 = e3 & op(e1, e2) = e3
% 236.29/44.43  | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | ALPHA: (14062) implies:
% 236.29/44.43  | | | | | | | | | | | | | | | | |   (14063)  op(e1, e2) = e3
% 236.29/44.43  | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10189), (14063), (function-axioms) are
% 236.29/44.43  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 236.29/44.43  | | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | | End of split
% 236.29/44.43  | | | | | | | | | | | | | | | | 
% 236.29/44.43  | | | | | | | | | | | | | | | Case 2:
% 236.29/44.43  | | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | |   (14064)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 236.29/44.44  | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 236.29/44.44  | | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | | BETA: splitting (14064) gives:
% 236.29/44.44  | | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | | Case 1:
% 236.29/44.44  | | | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | | |   (14065)  all_58_8 = e3 & op(e1, e1) = e3
% 236.29/44.44  | | | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | | | ALPHA: (14065) implies:
% 236.29/44.44  | | | | | | | | | | | | | | | | |   (14066)  op(e1, e1) = e3
% 236.29/44.44  | | | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (13924), (14066), (function-axioms) are
% 236.29/44.44  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 236.29/44.44  | | | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | | Case 2:
% 236.29/44.44  | | | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | | |   (14067)  all_58_11 = e3 & op(e1, e0) = e3
% 236.29/44.44  | | | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13915), (14067) are inconsistent by
% 236.29/44.44  | | | | | | | | | | | | | | | | |            sub-proof #788.
% 236.29/44.44  | | | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | | End of split
% 236.29/44.44  | | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | End of split
% 236.29/44.44  | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | Case 2:
% 236.29/44.44  | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | |   (14068)  all_58_11 = e2 & op(e1, e0) = e2
% 236.29/44.44  | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | ALPHA: (14068) implies:
% 236.29/44.44  | | | | | | | | | | | | | | |   (14069)  all_58_11 = e2
% 236.29/44.44  | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | | REF_CLOSE: (6), (13915), (14069) are inconsistent by
% 236.29/44.44  | | | | | | | | | | | | | | |            sub-proof #1020.
% 236.29/44.44  | | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | | End of split
% 236.29/44.44  | | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | | End of split
% 236.29/44.44  | | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | | End of split
% 236.29/44.44  | | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | | End of split
% 236.29/44.44  | | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | | End of split
% 236.29/44.44  | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | Case 2:
% 236.29/44.44  | | | | | | | | | | 
% 236.29/44.44  | | | | | | | | | |   (14070)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 236.29/44.44  | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.29/44.44  | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | BETA: splitting (14070) gives:
% 236.33/44.44  | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | |   (14071)  all_58_8 = e0 & op(e1, e1) = e0
% 236.33/44.44  | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | ALPHA: (14071) implies:
% 236.33/44.44  | | | | | | | | | | |   (14072)  all_58_8 = e0
% 236.33/44.44  | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.33/44.44  | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.33/44.44  | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.33/44.44  | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.33/44.44  | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.33/44.44  | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.33/44.44  | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.33/44.44  | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.33/44.44  | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.33/44.44  | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.33/44.44  | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.33/44.44  | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.33/44.44  | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.33/44.44  | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.33/44.44  | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.33/44.44  | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.33/44.44  | | | | | | | | | | |            (13895), (13896), (13897), (13899), (14072),
% 236.33/44.44  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.44  | | | | | | | | | | |            #563.
% 236.33/44.44  | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | Case 2:
% 236.33/44.44  | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | |   (14073)  all_58_11 = e0 & op(e1, e0) = e0
% 236.33/44.44  | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | ALPHA: (14073) implies:
% 236.33/44.44  | | | | | | | | | | |   (14074)  all_58_11 = e0
% 236.33/44.44  | | | | | | | | | | |   (14075)  op(e1, e0) = e0
% 236.33/44.44  | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | BETA: splitting (224) gives:
% 236.33/44.44  | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | |   (14076)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 236.33/44.44  | | | | | | | | | | | |              & op(e1, e2) = e1)
% 236.33/44.44  | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | BETA: splitting (14076) gives:
% 236.33/44.44  | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | |   (14077)  all_58_6 = e1 & op(e1, e3) = e1
% 236.33/44.44  | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | ALPHA: (14077) implies:
% 236.33/44.44  | | | | | | | | | | | | |   (14078)  all_58_6 = e1
% 236.33/44.44  | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 236.33/44.44  | | | | | | | | | | | | |            (245), (10187), (13794), (14078),
% 236.33/44.44  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.44  | | | | | | | | | | | | |            #1161.
% 236.33/44.44  | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | Case 2:
% 236.33/44.44  | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | |   (14079)  all_58_7 = e1 & op(e1, e2) = e1
% 236.33/44.44  | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | ALPHA: (14079) implies:
% 236.33/44.44  | | | | | | | | | | | | |   (14080)  all_58_7 = e1
% 236.33/44.44  | | | | | | | | | | | | |   (14081)  op(e1, e2) = e1
% 236.33/44.44  | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.33/44.44  | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | |   (14082)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.33/44.44  | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.33/44.44  | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | BETA: splitting (14082) gives:
% 236.33/44.44  | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | |   (14083)  all_58_6 = e2 & op(e1, e3) = e2
% 236.33/44.44  | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | ALPHA: (14083) implies:
% 236.33/44.44  | | | | | | | | | | | | | | |   (14084)  all_58_6 = e2
% 236.33/44.44  | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 236.33/44.44  | | | | | | | | | | | | | | |            (167), (170), (216), (217), (218), (220), (221),
% 236.33/44.44  | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.33/44.44  | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (235), (237),
% 236.33/44.44  | | | | | | | | | | | | | | |            (239), (240), (243), (244), (245), (246), (10187),
% 236.33/44.44  | | | | | | | | | | | | | | |            (10188), (10189), (10191), (10197), (13790),
% 236.33/44.44  | | | | | | | | | | | | | | |            (13794), (13899), (14074), (14084),
% 236.33/44.44  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.44  | | | | | | | | | | | | | | |            #548.
% 236.33/44.44  | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | Case 2:
% 236.33/44.44  | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | |   (14085)  all_58_7 = e2 & op(e1, e2) = e2
% 236.33/44.44  | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | REF_CLOSE: (6), (14080), (14085) are inconsistent by
% 236.33/44.44  | | | | | | | | | | | | | | |            sub-proof #2218.
% 236.33/44.44  | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | End of split
% 236.33/44.44  | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | Case 2:
% 236.33/44.44  | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | |   (14086)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 236.33/44.44  | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 236.33/44.44  | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | BETA: splitting (14086) gives:
% 236.33/44.44  | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | |   (14087)  all_58_8 = e2 & op(e1, e1) = e2
% 236.33/44.44  | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | ALPHA: (14087) implies:
% 236.33/44.44  | | | | | | | | | | | | | | |   (14088)  all_58_8 = e2
% 236.33/44.44  | | | | | | | | | | | | | | |   (14089)  op(e1, e1) = e2
% 236.33/44.44  | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 236.33/44.44  | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | |   (14090)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 236.33/44.44  | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 236.33/44.44  | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | BETA: splitting (14090) gives:
% 236.33/44.44  | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | |   (14091)  all_58_6 = e3 & op(e1, e3) = e3
% 236.33/44.44  | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | ALPHA: (14091) implies:
% 236.33/44.44  | | | | | | | | | | | | | | | | |   (14092)  all_58_6 = e3
% 236.33/44.44  | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 236.33/44.44  | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | |   (14093)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 236.33/44.44  | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 236.33/44.44  | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | BETA: splitting (14093) gives:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | |   (14094)  all_58_9 = e3 & op(e3, e0) = e3
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | ALPHA: (14094) implies:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | |   (14095)  all_58_9 = e3
% 236.33/44.44  | | | | | | | | | | | | | | | | | | |   (14096)  op(e3, e0) = e3
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | |   (14097)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | BETA: splitting (14097) gives:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | |   (14098)  all_58_0 = e2 & op(e3, e3) = e2
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14098) implies:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | |   (14099)  op(e3, e3) = e2
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13794), (14099), (function-axioms) are
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | |   (14100)  all_58_1 = e2 & op(e3, e2) = e2
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | |   (14101)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14101) gives:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |   (14102)  all_58_1 = e0 & op(e3, e2) = e0
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14102) implies:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |   (14103)  all_58_1 = e0
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (14074),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (14080), (14088), (14089), (14092), (14095),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (14096), (14103), (function-axioms) are
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #543.
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |   (14104)  all_58_3 = e0 & op(e2, e2) = e0
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (10197), (14074),
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            (14089), (14092), (14104), (function-axioms) are
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #763.
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | |   (14105)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14105) gives:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |   (14106)  all_58_7 = e0 & op(e1, e2) = e0
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14106) implies:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |   (14107)  op(e1, e2) = e0
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (14081), (14107), (function-axioms)
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14100) implies:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |   (14108)  all_58_1 = e2
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e1,
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (13899), (14089) gives:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |   (14109)  e2 = e0
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14108), (14109) imply:
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | |   (14110)  all_58_1 = e0
% 236.33/44.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (14074),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (14080), (14088), (14089), (14092), (14095),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            (14096), (14110), (function-axioms) are
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #543.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | |   (14111)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | BETA: splitting (14111) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |   (14112)  all_58_4 = e2 & op(e3, e1) = e2
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14112) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |   (14113)  all_58_4 = e2
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (167), (170), (216), (217), (218), (220), (221),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (235), (237),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (239), (240), (243), (244), (245), (246), (10187),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (10188), (10189), (10191), (10197), (13790),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (13794), (13899), (14074), (14080), (14088),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (14089), (14092), (14095), (14096), (14113),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            #544.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |   (14114)  all_58_9 = e2 & op(e3, e0) = e2
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14114) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |   (14115)  op(e3, e0) = e2
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14096), (14115), (function-axioms) are
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2125.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | |   (14116)  all_58_10 = e3 & op(e2, e0) = e3
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | ALPHA: (14116) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | |   (14117)  all_58_10 = e3
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (231), (232),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | |            (233), (10197), (13790), (14117),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.45  | | | | | | | | | | | | | | | | | | |            #1099.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.45  | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | |   (14118)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 236.33/44.45  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | BETA: splitting (14118) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | |   (14119)  all_58_11 = e3 & op(e1, e0) = e3
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | ALPHA: (14119) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | |   (14120)  all_58_11 = e3
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (223), (14080), (14088), (14092),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | |            (14120) are inconsistent by sub-proof #909.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | |   (14121)  all_58_15 = e3 & op(e0, e0) = e3
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | ALPHA: (14121) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | |   (14122)  all_58_15 = e3
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | |   (14123)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | BETA: splitting (14123) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |   (14124)  all_58_9 = e1 & op(e3, e0) = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14124) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |   (14125)  all_58_9 = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (167), (170), (216), (217), (218), (220), (221),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (235), (237),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (239), (240), (243), (244), (245), (246), (10187),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (10188), (10189), (10191), (10197), (13790),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (13794), (13899), (14092), (14125),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |            #640.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |   (14126)  all_58_10 = e1 & op(e2, e0) = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14126) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | |   (14127)  all_58_10 = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | |   (14128)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14128) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |   (14129)  all_58_4 = e0 & op(e3, e1) = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14129) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |   (14130)  all_58_4 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |   (14131)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (231), (233),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |            (240), (244), (246), (10188), (10197), (13794),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |            (14127), (14131), (function-axioms) are
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |   (14132)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14132) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (14133)  all_58_8 = e1 & op(e1, e1) = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14133) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (14134)  all_58_8 = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (14074), (14080), (14092),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (14134) are inconsistent by sub-proof #2215.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (14135)  all_58_14 = e1 & op(e0, e1) = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14135) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (14136)  all_58_14 = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (164), (165),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (216), (217), (218), (220), (221),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (235), (237),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (240), (243), (244), (245), (246), (10187),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (10188), (10189), (10191), (10197), (13790),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (13794), (13899), (14092), (14130), (14136),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            #582.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |   (14137)  all_58_5 = e0 & op(e2, e1) = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14137) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | |   (14138)  all_58_5 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |   (14139)  all_58_15 = e0 & op(e0, e0) = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14139) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |   (14140)  all_58_15 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14122), (14140) imply:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |   (14141)  e3 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14092), (14141) imply:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |   (14142)  all_58_6 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (14074), (14089),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |            (14142), (function-axioms) are inconsistent by
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1686.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |   (14143)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14143) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |   (14144)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (14145)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (231), (233),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (244), (246), (10188), (10197), (13794),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (14127), (14145), (function-axioms) are
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (14146)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14146) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14147)  all_58_8 = e1 & op(e1, e1) = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14147) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14148)  all_58_8 = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (14074), (14080), (14092),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            (14148) are inconsistent by sub-proof #2215.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14149)  all_58_14 = e1 & op(e0, e1) = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14149) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14150)  all_58_14 = e1
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14151)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14151) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14152)  all_58_2 = e2 & op(e2, e3) = e2
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14152) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14153)  all_58_2 = e2
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14154)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14154) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14155)  all_58_0 = e0 & op(e3, e3) = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14155) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14156)  op(e3, e3) = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13794), (14156), (function-axioms) are
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14157)  all_58_2 = e0 & op(e2, e3) = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14157) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14158)  all_58_2 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14153), (14158) imply:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14159)  e2 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14088), (14159) imply:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14160)  all_58_8 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (14160),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #563.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14161)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14161) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14162)  all_58_6 = e0 & op(e1, e3) = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14162) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14163)  all_58_6 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (216), (218),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (10187), (13794), (14122), (14150),
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14163), (function-axioms) are inconsistent by
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #542.
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14164)  all_58_12 = e0 & op(e0, e3) = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14164) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14165)  all_58_12 = e0
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14166)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14166) gives:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14167)  all_58_4 = e3 & op(e3, e1) = e3
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14167) implies:
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14168)  all_58_4 = e3
% 236.33/44.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (165), (167),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (221), (225), (226), (228), (230), (231),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (237), (239), (240), (243), (244),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (246), (10187), (10188), (10189), (10191),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10197), (13790), (13794), (13899), (14074),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14079), (14080), (14088), (14089), (14092),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14122), (14127), (14144), (14150), (14153),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14165), (14168), (function-axioms) are
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #539.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14169)  all_58_5 = e3 & op(e2, e1) = e3
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10191), (14169), (function-axioms) are
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14170)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14170) gives:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14171)  all_58_8 = e3 & op(e1, e1) = e3
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14171) implies:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14172)  op(e1, e1) = e3
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14173)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (10187), (13794), (14173),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1208.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14174)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14174) gives:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (14074), (14080), (14092),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14172), (function-axioms) are inconsistent by
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #546.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14175)  all_58_12 = e3 & op(e0, e3) = e3
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14175) implies:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14176)  all_58_12 = e3
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (218), (14122),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14150), (14176), (function-axioms) are
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1031.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14177)  all_58_14 = e3 & op(e0, e1) = e3
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (10187), (13794), (14092), (14150),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14177), (function-axioms) are inconsistent by
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #646.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14178)  all_58_3 = e2 & op(e2, e2) = e2
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (10189), (10197), (14074),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14089), (14092), (14178), (function-axioms) are
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #966.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14179)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14179) gives:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14180)  all_58_5 = e2 & op(e2, e1) = e2
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14180) implies:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14181)  all_58_5 = e2
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14138), (14181) imply:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14182)  e2 = e0
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14088), (14182) imply:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14183)  all_58_8 = e0
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (14183),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #563.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14184)  all_58_10 = e2 & op(e2, e0) = e2
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14184) implies:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14185)  all_58_10 = e2
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14127), (14185) imply:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14186)  e2 = e1
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14088), (14186) imply:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14187)  all_58_8 = e1
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (225), (14074), (14080), (14092),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14187) are inconsistent by sub-proof #2215.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | |   (14188)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14188) gives:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |   (14189)  all_58_8 = e0 & op(e1, e1) = e0
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14189) implies:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |   (14190)  all_58_8 = e0
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (61), (88),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (94), (110), (112), (113), (117), (120), (121),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (125), (128), (133), (134), (135), (145), (158),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (189),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (190), (191), (193), (197), (200), (201), (202),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (203), (212), (213), (214), (216), (217), (218),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (237), (239), (240), (243),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (254), (255), (256), (258),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (280), (281), (282), (299), (341),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (379), (386), (387), (388), (389), (390), (10184),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (10185), (10186), (10187), (10188), (10189),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (10190), (10191), (10192), (10197), (10198),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (13787), (13788), (13789), (13790), (13791),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (13792), (13794), (13796), (13893), (13894),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (13895), (13896), (13897), (13899), (14190),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            #563.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |   (14191)  all_58_14 = e0 & op(e0, e1) = e0
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14191) implies:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |   (14192)  all_58_14 = e0
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (225), (228),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (240), (244), (246), (10188),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (10197), (13794), (14074), (14080), (14092),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            (14127), (14192), (function-axioms) are
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #540.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | |   (14193)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | BETA: splitting (14193) gives:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | |   (14194)  all_58_11 = e1 & op(e1, e0) = e1
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14194) implies:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | |   (14195)  op(e1, e0) = e1
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (223), (14080), (14088), (14092),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | |            (14195), (function-axioms) are inconsistent by
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1555.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | |   (14196)  all_58_15 = e1 & op(e0, e0) = e1
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14196) implies:
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | |   (14197)  all_58_15 = e1
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | |            (245), (10187), (13794), (14092), (14122),
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | |            (14197), (function-axioms) are inconsistent by
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1160.
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | |   (14198)  all_58_7 = e3 & op(e1, e2) = e3
% 236.33/44.46  | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | ALPHA: (14198) implies:
% 236.33/44.46  | | | | | | | | | | | | | | | | |   (14199)  op(e1, e2) = e3
% 236.33/44.46  | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10189), (14199), (function-axioms) are
% 236.33/44.46  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 236.33/44.46  | | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | |   (14200)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 236.33/44.46  | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 236.33/44.46  | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (14074), (14089), (14200),
% 236.33/44.46  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.46  | | | | | | | | | | | | | | | |            #1797.
% 236.33/44.46  | | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | |   (14201)  all_58_11 = e2 & op(e1, e0) = e2
% 236.33/44.46  | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | ALPHA: (14201) implies:
% 236.33/44.46  | | | | | | | | | | | | | | |   (14202)  all_58_11 = e2
% 236.33/44.46  | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | | REF_CLOSE: (5), (14074), (14202) are inconsistent by
% 236.33/44.46  | | | | | | | | | | | | | | |            sub-proof #2110.
% 236.33/44.46  | | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | |   (14203)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 236.33/44.46  | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | REF_CLOSE: (4), (13899), (14075), (14203), (function-axioms)
% 236.33/44.46  | | | | | | | | | | | |            are inconsistent by sub-proof #795.
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | 
% 236.33/44.46  | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | 
% 236.33/44.46  | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | 
% 236.33/44.46  | | | | | | | |   (14204)  all_12_2 = e3
% 236.33/44.46  | | | | | | | | 
% 236.33/44.46  | | | | | | | | COMBINE_EQS: (346), (14204) imply:
% 236.33/44.46  | | | | | | | |   (14205)  all_4_2 = e3
% 236.33/44.46  | | | | | | | | 
% 236.33/44.46  | | | | | | | | COMBINE_EQS: (254), (14205) imply:
% 236.33/44.46  | | | | | | | |   (14206)  all_56_31 = e3
% 236.33/44.46  | | | | | | | | 
% 236.33/44.46  | | | | | | | | REDUCE: (387), (14205) imply:
% 236.33/44.46  | | | | | | | |   (14207)   ~ (all_52_12 = e3)
% 236.33/44.46  | | | | | | | | 
% 236.33/44.46  | | | | | | | | REDUCE: (36), (14205) imply:
% 236.33/44.46  | | | | | | | |   (14208)  op(e0, e0) = e3
% 236.33/44.46  | | | | | | | | 
% 236.33/44.46  | | | | | | | | BETA: splitting (245) gives:
% 236.33/44.46  | | | | | | | | 
% 236.33/44.46  | | | | | | | | Case 1:
% 236.33/44.46  | | | | | | | | | 
% 236.33/44.46  | | | | | | | | |   (14209)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 236.33/44.46  | | | | | | | | |              & op(e2, e3) = e3)
% 236.33/44.46  | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | REF_CLOSE: (8), (167), (10187), (13794), (14209),
% 236.33/44.46  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.46  | | | | | | | | |            #1208.
% 236.33/44.46  | | | | | | | | | 
% 236.33/44.46  | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | 
% 236.33/44.46  | | | | | | | | |   (14210)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3
% 236.33/44.46  | | | | | | | | |              & op(e0, e3) = e3)
% 236.33/44.46  | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | BETA: splitting (14210) gives:
% 236.33/44.46  | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | Case 1:
% 236.33/44.46  | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | |   (14211)  all_58_6 = e3 & op(e1, e3) = e3
% 236.33/44.46  | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | ALPHA: (14211) implies:
% 236.33/44.46  | | | | | | | | | |   (14212)  all_58_6 = e3
% 236.33/44.46  | | | | | | | | | |   (14213)  op(e1, e3) = e3
% 236.33/44.46  | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | BETA: splitting (222) gives:
% 236.33/44.46  | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | Case 1:
% 236.33/44.46  | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | |   (14214)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 236.33/44.46  | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 236.33/44.46  | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | BETA: splitting (14214) gives:
% 236.33/44.46  | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | Case 1:
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | |   (14215)  all_58_9 = e3 & op(e3, e0) = e3
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | ALPHA: (14215) implies:
% 236.33/44.46  | | | | | | | | | | | |   (14216)  op(e3, e0) = e3
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | REF_CLOSE: (168), (14207), (14216), (function-axioms) are
% 236.33/44.46  | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | |   (14217)  all_58_10 = e3 & op(e2, e0) = e3
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | ALPHA: (14217) implies:
% 236.33/44.46  | | | | | | | | | | | |   (14218)  all_58_10 = e3
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (231), (232),
% 236.33/44.46  | | | | | | | | | | | |            (233), (10197), (13790), (14218),
% 236.33/44.46  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.46  | | | | | | | | | | | |            #1099.
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | End of split
% 236.33/44.46  | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | Case 2:
% 236.33/44.46  | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | |   (14219)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 236.33/44.46  | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 236.33/44.46  | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | BETA: splitting (14219) gives:
% 236.33/44.46  | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | Case 1:
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.46  | | | | | | | | | | | |   (14220)  all_58_11 = e3 & op(e1, e0) = e3
% 236.33/44.46  | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | ALPHA: (14220) implies:
% 236.33/44.47  | | | | | | | | | | | |   (14221)  all_58_11 = e3
% 236.33/44.47  | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | BETA: splitting (246) gives:
% 236.33/44.47  | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | Case 1:
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | |   (14222)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 236.33/44.47  | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | REF_CLOSE: (8), (170), (10188), (13794), (14222),
% 236.33/44.47  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.47  | | | | | | | | | | | | |            #1401.
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | Case 2:
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | |   (14223)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 236.33/44.47  | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | BETA: splitting (14223) gives:
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | Case 1:
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | |   (14224)  all_58_4 = e3 & op(e3, e1) = e3
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | ALPHA: (14224) implies:
% 236.33/44.47  | | | | | | | | | | | | | |   (14225)  all_58_4 = e3
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (164), (167),
% 236.33/44.47  | | | | | | | | | | | | | |            (170), (216), (217), (219), (220), (221), (222),
% 236.33/44.47  | | | | | | | | | | | | | |            (223), (224), (229), (231), (232), (233), (235),
% 236.33/44.47  | | | | | | | | | | | | | |            (237), (239), (240), (243), (244), (245), (246),
% 236.33/44.47  | | | | | | | | | | | | | |            (10187), (10188), (10190), (10197), (13790),
% 236.33/44.47  | | | | | | | | | | | | | |            (13794), (14208), (14212), (14221), (14224),
% 236.33/44.47  | | | | | | | | | | | | | |            (14225), (function-axioms) are inconsistent by
% 236.33/44.47  | | | | | | | | | | | | | |            sub-proof #529.
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | Case 2:
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | |   (14226)  all_58_9 = e3 & op(e3, e0) = e3
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | ALPHA: (14226) implies:
% 236.33/44.47  | | | | | | | | | | | | | |   (14227)  op(e3, e0) = e3
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | REF_CLOSE: (168), (14207), (14227), (function-axioms) are
% 236.33/44.47  | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | End of split
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | End of split
% 236.33/44.47  | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | Case 2:
% 236.33/44.47  | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | |   (14228)  all_58_15 = e3 & op(e0, e0) = e3
% 236.33/44.47  | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | ALPHA: (14228) implies:
% 236.33/44.47  | | | | | | | | | | | |   (14229)  all_58_15 = e3
% 236.33/44.47  | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | BETA: splitting (246) gives:
% 236.33/44.47  | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | Case 1:
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | |   (14230)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 236.33/44.47  | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | REF_CLOSE: (8), (170), (10188), (13794), (14230),
% 236.33/44.47  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.47  | | | | | | | | | | | | |            #1401.
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | Case 2:
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | |   (14231)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 236.33/44.47  | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | BETA: splitting (14231) gives:
% 236.33/44.47  | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | Case 1:
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | |   (14232)  all_58_4 = e3 & op(e3, e1) = e3
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | ALPHA: (14232) implies:
% 236.33/44.47  | | | | | | | | | | | | | |   (14233)  all_58_4 = e3
% 236.33/44.47  | | | | | | | | | | | | | |   (14234)  op(e3, e1) = e3
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 236.33/44.47  | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (14213) gives:
% 236.33/44.47  | | | | | | | | | | | | | |   (14235)  all_52_2 = e3
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 236.33/44.47  | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (14234) gives:
% 236.33/44.47  | | | | | | | | | | | | | |   (14236)  all_52_8 = e3
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | REDUCE: (143), (14235) imply:
% 236.33/44.47  | | | | | | | | | | | | | |   (14237)   ~ (all_52_6 = e3)
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | REDUCE: (141), (14235) imply:
% 236.33/44.47  | | | | | | | | | | | | | |   (14238)   ~ (all_52_14 = e3)
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | SIMP: (14238) implies:
% 236.33/44.47  | | | | | | | | | | | | | |   (14239)   ~ (all_52_14 = e3)
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | REDUCE: (123), (14236) imply:
% 236.33/44.47  | | | | | | | | | | | | | |   (14240)   ~ (all_52_9 = e3)
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | REDUCE: (120), (14236) imply:
% 236.33/44.47  | | | | | | | | | | | | | |   (14241)   ~ (all_52_12 = e3)
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | REDUCE: (380), (14236) imply:
% 236.33/44.47  | | | | | | | | | | | | | |   (14242)   ~ (all_6_2 = e3)
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 236.33/44.47  | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | Case 1:
% 236.33/44.47  | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | |   (14243)   ~ (all_38_2 = e1)
% 236.33/44.47  | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | REDUCE: (13788), (14243) imply:
% 236.33/44.47  | | | | | | | | | | | | | | |   (14244)  $false
% 236.33/44.47  | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | CLOSE: (14244) is inconsistent.
% 236.33/44.47  | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | Case 2:
% 236.33/44.47  | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | |   (14245)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 236.33/44.47  | | | | | | | | | | | | | | |              & op(e3, e1) = all_38_1 & $i(all_38_0) &
% 236.33/44.47  | | | | | | | | | | | | | | |              $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1)
% 236.33/44.47  | | | | | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 236.33/44.47  | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | BETA: splitting (14245) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | Case 1:
% 236.33/44.47  | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | |   (14246)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 236.33/44.47  | | | | | | | | | | | | | | | |            op(e3, e1) = all_38_1 & $i(all_38_0) &
% 236.33/44.47  | | | | | | | | | | | | | | | |            $i(all_38_1)
% 236.33/44.47  | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | ALPHA: (14246) implies:
% 236.33/44.47  | | | | | | | | | | | | | | | |   (14247)   ~ (all_38_0 = e2)
% 236.33/44.47  | | | | | | | | | | | | | | | |   (14248)  op(e3, e1) = all_38_1
% 236.33/44.47  | | | | | | | | | | | | | | | |   (14249)  op(all_38_1, e3) = all_38_0
% 236.33/44.47  | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | BETA: splitting (13787) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14250)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 236.33/44.47  | | | | | | | | | | | | | | | | |            op(e3, e1) = all_10_1 & $i(all_10_0) &
% 236.33/44.47  | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | ALPHA: (14250) implies:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14251)   ~ (all_10_0 = e0)
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14252)  op(e3, e1) = all_10_1
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14253)  op(all_10_1, e3) = all_10_0
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_38_1,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (14234), (14248) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14254)  all_38_1 = e3
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (14248),
% 236.33/44.47  | | | | | | | | | | | | | | | | |              (14252) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14255)  all_38_1 = all_10_1
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (14254), (14255) imply:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14256)  all_10_1 = e3
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | REDUCE: (14249), (14254) imply:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14257)  op(e3, e3) = all_38_0
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | REDUCE: (14253), (14256) imply:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14258)  op(e3, e3) = all_10_0
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_38_0,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (13794), (14257) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14259)  all_38_0 = e1
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_0,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              all_38_0, e3, e3, simplifying with (14257),
% 236.33/44.47  | | | | | | | | | | | | | | | | |              (14258) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14260)  all_38_0 = all_10_0
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (14259), (14260) imply:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14261)  all_10_0 = e1
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | REDUCE: (14247), (14259) imply:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14262)   ~ (e2 = e1)
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (58), (85),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (94), (110), (113), (117), (145), (157), (158),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (160), (162), (164), (165), (167), (168), (170),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (194), (213), (216), (217), (218), (219), (220),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (235),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (236), (237), (239), (240), (243), (244), (245),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (246), (266), (297), (328), (339), (381), (385),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (391), (10184), (10185), (10186), (10187),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (10188), (10189), (10190), (10191), (10192),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (10197), (13789), (13790), (13791), (13793),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (13794), (14206), (14207), (14212), (14229),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (14233), (14239), (function-axioms) are
% 236.33/44.47  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #488.
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14263)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 236.33/44.47  | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | ALPHA: (14263) implies:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14264)   ~ (all_10_1 = e2)
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14265)  op(e3, e1) = all_10_1
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_38_1,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (14234), (14248) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14266)  all_38_1 = e3
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (14248),
% 236.33/44.47  | | | | | | | | | | | | | | | | |              (14265) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14267)  all_38_1 = all_10_1
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (14266), (14267) imply:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14268)  all_10_1 = e3
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | REDUCE: (14249), (14266) imply:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14269)  op(e3, e3) = all_38_0
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_38_0,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (13794), (14269) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14270)  all_38_0 = e1
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | REDUCE: (14247), (14270) imply:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14271)   ~ (e2 = e1)
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (58), (85),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (94), (110), (113), (117), (145), (157), (158),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (160), (162), (164), (165), (167), (168), (170),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (194), (213), (216), (217), (218), (219), (220),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (235),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (236), (237), (239), (240), (243), (244), (245),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (246), (266), (297), (328), (339), (381), (385),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (391), (10184), (10185), (10186), (10187),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (10188), (10189), (10190), (10191), (10192),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (10197), (13789), (13790), (13791), (13793),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (13794), (14206), (14207), (14212), (14229),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (14233), (14239), (function-axioms) are
% 236.33/44.47  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #488.
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | End of split
% 236.33/44.47  | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | Case 2:
% 236.33/44.47  | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | |   (14272)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 236.33/44.47  | | | | | | | | | | | | | | | |            $i(all_38_1)
% 236.33/44.47  | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | ALPHA: (14272) implies:
% 236.33/44.47  | | | | | | | | | | | | | | | |   (14273)   ~ (all_38_1 = e0)
% 236.33/44.47  | | | | | | | | | | | | | | | |   (14274)  op(e3, e1) = all_38_1
% 236.33/44.47  | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | BETA: splitting (13787) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14275)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 236.33/44.47  | | | | | | | | | | | | | | | | |            op(e3, e1) = all_10_1 & $i(all_10_0) &
% 236.33/44.47  | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | ALPHA: (14275) implies:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14276)   ~ (all_10_0 = e0)
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14277)  op(e3, e1) = all_10_1
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14278)  op(all_10_1, e3) = all_10_0
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_38_1,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (14234), (14274) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14279)  all_38_1 = e3
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (14274),
% 236.33/44.47  | | | | | | | | | | | | | | | | |              (14277) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14280)  all_38_1 = all_10_1
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (14279), (14280) imply:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14281)  all_10_1 = e3
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | REDUCE: (14278), (14281) imply:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14282)  op(e3, e3) = all_10_0
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_10_0,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (13794), (14282) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14283)  all_10_0 = e1
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (58), (85),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (94), (110), (113), (117), (145), (157), (158),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (160), (162), (164), (165), (167), (168), (170),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (194), (213), (216), (217), (218), (219), (220),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (235),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (236), (237), (239), (240), (243), (244), (245),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (246), (266), (297), (328), (339), (381), (385),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (391), (10184), (10185), (10186), (10187),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (10188), (10189), (10190), (10191), (10192),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (10197), (13789), (13790), (13791), (13793),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (13794), (14206), (14207), (14212), (14229),
% 236.33/44.47  | | | | | | | | | | | | | | | | |            (14233), (14239), (function-axioms) are
% 236.33/44.47  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #488.
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14284)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 236.33/44.47  | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | ALPHA: (14284) implies:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14285)   ~ (all_10_1 = e2)
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14286)  op(e3, e1) = all_10_1
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_38_1,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (14234), (14274) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14287)  all_38_1 = e3
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 236.33/44.47  | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (14274),
% 236.33/44.47  | | | | | | | | | | | | | | | | |              (14286) gives:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14288)  all_38_1 = all_10_1
% 236.33/44.47  | | | | | | | | | | | | | | | | | 
% 236.33/44.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (14287), (14288) imply:
% 236.33/44.47  | | | | | | | | | | | | | | | | |   (14289)  all_10_1 = e3
% 236.33/44.48  | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 236.33/44.48  | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | |   (14290)   ~ (all_18_2 = e0)
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (85), (94),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (110), (113), (117), (145), (157), (158), (160),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (168), (170), (194),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (213), (216), (217), (218), (219), (220), (221),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (235), (236),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (237), (239), (240), (243), (244), (245), (246),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (266), (297), (328), (339), (381), (385), (391),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (10184), (10185), (10186), (10187), (10188),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (10189), (10190), (10191), (10192), (10197),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (13789), (13790), (13791), (13793), (13794),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (14206), (14207), (14212), (14229), (14233),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (14239), (14290), (function-axioms) are
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #489.
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | |   (14291)  all_18_2 = e0
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (14291) imply:
% 236.33/44.48  | | | | | | | | | | | | | | | | | |   (14292)  all_6_2 = e0
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | SIMP: (14292) implies:
% 236.33/44.48  | | | | | | | | | | | | | | | | | |   (14293)  all_6_2 = e0
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (14293) imply:
% 236.33/44.48  | | | | | | | | | | | | | | | | | |   (14294)  all_56_21 = e0
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | REDUCE: (391), (14293) imply:
% 236.33/44.48  | | | | | | | | | | | | | | | | | |   (14295)   ~ (e3 = e0)
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | REDUCE: (39), (14293) imply:
% 236.33/44.48  | | | | | | | | | | | | | | | | | |   (14296)  op(e1, e1) = e0
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (94), (158), (162),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (164), (165), (167), (170), (213), (216), (217),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (218), (219), (220), (221), (222), (223), (224),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (232), (233), (235), (236), (237), (239), (240),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (243), (244), (245), (246), (10184), (10185),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (10187), (10188), (10189), (10190), (10191),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (10197), (13789), (13790), (13791), (13794),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (14206), (14212), (14229), (14233), (14294),
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            (14296), (function-axioms) are inconsistent by
% 236.33/44.48  | | | | | | | | | | | | | | | | | |            sub-proof #497.
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | Case 2:
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | |   (14297)  all_58_9 = e3 & op(e3, e0) = e3
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | ALPHA: (14297) implies:
% 236.33/44.48  | | | | | | | | | | | | | |   (14298)  op(e3, e0) = e3
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | REF_CLOSE: (168), (14207), (14298), (function-axioms) are
% 236.33/44.48  | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | Case 2:
% 236.33/44.48  | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | |   (14299)  all_58_12 = e3 & op(e0, e3) = e3
% 236.33/44.48  | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | ALPHA: (14299) implies:
% 236.33/44.48  | | | | | | | | | |   (14300)  all_58_12 = e3
% 236.33/44.48  | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | BETA: splitting (230) gives:
% 236.33/44.48  | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | |   (14301)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 236.33/44.48  | | | | | | | | | | |              & op(e2, e1) = e3)
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | BETA: splitting (14301) gives:
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | |   (14302)  all_58_4 = e3 & op(e3, e1) = e3
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | ALPHA: (14302) implies:
% 236.33/44.48  | | | | | | | | | | | |   (14303)  all_58_4 = e3
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (162),
% 236.33/44.48  | | | | | | | | | | | |            (164), (167), (170), (216), (217), (219), (220),
% 236.33/44.48  | | | | | | | | | | | |            (221), (222), (223), (224), (226), (229), (231),
% 236.33/44.48  | | | | | | | | | | | |            (232), (233), (235), (237), (239), (240), (243),
% 236.33/44.48  | | | | | | | | | | | |            (244), (245), (246), (391), (10187), (10188),
% 236.33/44.48  | | | | | | | | | | | |            (10189), (10190), (10197), (13790), (13794),
% 236.33/44.48  | | | | | | | | | | | |            (14208), (14300), (14302), (14303),
% 236.33/44.48  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.48  | | | | | | | | | | | |            #487.
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | Case 2:
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | |   (14304)  all_58_5 = e3 & op(e2, e1) = e3
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | REF_CLOSE: (165), (10191), (14304), (function-axioms) are
% 236.33/44.48  | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | Case 2:
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | |   (14305)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 236.33/44.48  | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | BETA: splitting (14305) gives:
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | |   (14306)  all_58_8 = e3 & op(e1, e1) = e3
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | REF_CLOSE: (39), (391), (14306), (function-axioms) are
% 236.33/44.48  | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | Case 2:
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | |   (14307)  all_58_14 = e3 & op(e0, e1) = e3
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | ALPHA: (14307) implies:
% 236.33/44.48  | | | | | | | | | | | |   (14308)  all_58_14 = e3
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (216), (217),
% 236.33/44.48  | | | | | | | | | | | |            (218), (239), (243), (245), (10187), (13794),
% 236.33/44.48  | | | | | | | | | | | |            (14300), (14308), (function-axioms) are
% 236.33/44.48  | | | | | | | | | | | |            inconsistent by sub-proof #1200.
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | | 
% 236.33/44.48  | | | | | | | | End of split
% 236.33/44.48  | | | | | | | | 
% 236.33/44.48  | | | | | | | End of split
% 236.33/44.48  | | | | | | | 
% 236.33/44.48  | | | | | | End of split
% 236.33/44.48  | | | | | | 
% 236.33/44.48  | | | | | End of split
% 236.33/44.48  | | | | | 
% 236.33/44.48  | | | | Case 2:
% 236.33/44.48  | | | | | 
% 236.33/44.48  | | | | |   (14309)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 &
% 236.33/44.48  | | | | |              op(e2, e0) = e3)
% 236.33/44.48  | | | | | 
% 236.33/44.48  | | | | | REF_CLOSE: (164), (165), (10191), (10192), (14309), (function-axioms)
% 236.33/44.48  | | | | |            are inconsistent by sub-proof #1649.
% 236.33/44.48  | | | | | 
% 236.33/44.48  | | | | End of split
% 236.33/44.48  | | | | 
% 236.33/44.48  | | | End of split
% 236.33/44.48  | | | 
% 236.33/44.48  | | Case 2:
% 236.33/44.48  | | | 
% 236.33/44.48  | | |   (14310)  all_6_2 = e3
% 236.33/44.48  | | |   (14311)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) =
% 236.33/44.48  | | |              all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) &
% 236.33/44.48  | | |              op(e1, e3) = all_6_1 & $i(all_6_1))
% 236.33/44.48  | | | 
% 236.33/44.48  | | | COMBINE_EQS: (305), (14310) imply:
% 236.33/44.48  | | |   (14312)  all_46_2 = e3
% 236.33/44.48  | | | 
% 236.33/44.48  | | | COMBINE_EQS: (266), (14310) imply:
% 236.33/44.48  | | |   (14313)  all_56_21 = e3
% 236.33/44.48  | | | 
% 236.33/44.48  | | | REDUCE: (367), (14310) imply:
% 236.33/44.48  | | |   (14314)   ~ (all_52_2 = e3)
% 236.33/44.48  | | | 
% 236.33/44.48  | | | REDUCE: (378), (14310) imply:
% 236.33/44.48  | | |   (14315)   ~ (all_52_6 = e3)
% 236.33/44.48  | | | 
% 236.33/44.48  | | | REDUCE: (380), (14310) imply:
% 236.33/44.48  | | |   (14316)   ~ (all_52_8 = e3)
% 236.33/44.48  | | | 
% 236.33/44.48  | | | REDUCE: (381), (14310) imply:
% 236.33/44.48  | | |   (14317)   ~ (all_52_9 = e3)
% 236.33/44.48  | | | 
% 236.33/44.48  | | | REDUCE: (383), (14310) imply:
% 236.33/44.48  | | |   (14318)   ~ (all_52_11 = e3)
% 236.33/44.48  | | | 
% 236.33/44.48  | | | REDUCE: (385), (14310) imply:
% 236.33/44.48  | | |   (14319)   ~ (all_52_14 = e3)
% 236.33/44.48  | | | 
% 236.33/44.48  | | | BETA: splitting (230) gives:
% 236.33/44.48  | | | 
% 236.33/44.48  | | | Case 1:
% 236.33/44.48  | | | | 
% 236.33/44.48  | | | |   (14320)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2,
% 236.33/44.48  | | | |                e1) = e3)
% 236.33/44.48  | | | | 
% 236.33/44.48  | | | | REF_CLOSE: (165), (169), (14316), (14317), (14320), (function-axioms)
% 236.33/44.48  | | | |            are inconsistent by sub-proof #1628.
% 236.33/44.48  | | | | 
% 236.33/44.48  | | | Case 2:
% 236.33/44.48  | | | | 
% 236.33/44.48  | | | |   (14321)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0,
% 236.33/44.48  | | | |                e1) = e3)
% 236.33/44.48  | | | | 
% 236.33/44.48  | | | | BETA: splitting (14321) gives:
% 236.33/44.48  | | | | 
% 236.33/44.48  | | | | Case 1:
% 236.33/44.48  | | | | | 
% 236.33/44.48  | | | | |   (14322)  all_58_8 = e3 & op(e1, e1) = e3
% 236.33/44.48  | | | | | 
% 236.33/44.48  | | | | | ALPHA: (14322) implies:
% 236.33/44.48  | | | | |   (14323)  all_58_8 = e3
% 236.33/44.48  | | | | |   (14324)  op(e1, e1) = e3
% 236.33/44.48  | | | | | 
% 236.33/44.48  | | | | | BETA: splitting (43) gives:
% 236.33/44.48  | | | | | 
% 236.33/44.48  | | | | | Case 1:
% 236.33/44.48  | | | | | | 
% 236.33/44.48  | | | | | |   (14325)   ~ (all_8_2 = e3)
% 236.33/44.48  | | | | | | 
% 236.33/44.48  | | | | | | BETA: splitting (46) gives:
% 236.33/44.48  | | | | | | 
% 236.33/44.48  | | | | | | Case 1:
% 236.33/44.48  | | | | | | | 
% 236.33/44.48  | | | | | | |   (14326)   ~ (all_10_2 = e1)
% 236.33/44.48  | | | | | | | 
% 236.33/44.48  | | | | | | | BETA: splitting (49) gives:
% 236.33/44.48  | | | | | | | 
% 236.33/44.48  | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | 
% 236.33/44.48  | | | | | | | |   (14327)   ~ (all_12_2 = e3)
% 236.33/44.48  | | | | | | | | 
% 236.33/44.48  | | | | | | | | REDUCE: (346), (14327) imply:
% 236.33/44.48  | | | | | | | |   (14328)   ~ (all_4_2 = e3)
% 236.33/44.48  | | | | | | | | 
% 236.33/44.48  | | | | | | | | BETA: splitting (52) gives:
% 236.33/44.48  | | | | | | | | 
% 236.33/44.48  | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | 
% 236.33/44.48  | | | | | | | | |   (14329)   ~ (all_14_2 = e0)
% 236.33/44.48  | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | REDUCE: (344), (14329) imply:
% 236.33/44.48  | | | | | | | | |   (14330)   ~ (all_8_2 = e0)
% 236.33/44.48  | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | BETA: splitting (55) gives:
% 236.33/44.48  | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | |   (14331)   ~ (all_16_2 = e0)
% 236.33/44.48  | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | REDUCE: (342), (14331) imply:
% 236.33/44.48  | | | | | | | | | |   (14332)   ~ (all_10_2 = e0)
% 236.33/44.48  | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | BETA: splitting (61) gives:
% 236.33/44.48  | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | |   (14333)   ~ (all_20_2 = e1)
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | REDUCE: (341), (14333) imply:
% 236.33/44.48  | | | | | | | | | | |   (14334)   ~ (all_4_2 = e1)
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | BETA: splitting (189) gives:
% 236.33/44.48  | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | |   (14335)  all_54_15 = e3
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | COMBINE_EQS: (299), (14335) imply:
% 236.33/44.48  | | | | | | | | | | | |   (14336)  all_4_2 = e3
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | REDUCE: (14328), (14336) imply:
% 236.33/44.48  | | | | | | | | | | | |   (14337)  $false
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | CLOSE: (14337) is inconsistent.
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | Case 2:
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | |   (14338)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | BETA: splitting (14338) gives:
% 236.33/44.48  | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | |   (14339)  all_54_15 = e2
% 236.33/44.48  | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | COMBINE_EQS: (299), (14339) imply:
% 236.33/44.48  | | | | | | | | | | | | |   (14340)  all_4_2 = e2
% 236.33/44.48  | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | REDUCE: (390), (14340) imply:
% 236.33/44.48  | | | | | | | | | | | | |   (14341)  $false
% 236.33/44.48  | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | CLOSE: (14341) is inconsistent.
% 236.33/44.48  | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | Case 2:
% 236.33/44.48  | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | |   (14342)  all_54_15 = e1 | all_54_15 = e0
% 236.33/44.48  | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | BETA: splitting (14342) gives:
% 236.33/44.48  | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | |   (14343)  all_54_15 = e1
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | COMBINE_EQS: (299), (14343) imply:
% 236.33/44.48  | | | | | | | | | | | | | |   (14344)  all_4_2 = e1
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | REDUCE: (14334), (14344) imply:
% 236.33/44.48  | | | | | | | | | | | | | |   (14345)  $false
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | CLOSE: (14345) is inconsistent.
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | Case 2:
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | |   (14346)  all_54_15 = e0
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | COMBINE_EQS: (299), (14346) imply:
% 236.33/44.48  | | | | | | | | | | | | | |   (14347)  all_4_2 = e0
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | COMBINE_EQS: (254), (14347) imply:
% 236.33/44.48  | | | | | | | | | | | | | |   (14348)  all_56_31 = e0
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | REDUCE: (368), (14347) imply:
% 236.33/44.48  | | | | | | | | | | | | | |   (14349)   ~ (all_52_3 = e0)
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | REDUCE: (388), (14347) imply:
% 236.33/44.48  | | | | | | | | | | | | | |   (14350)   ~ (all_52_13 = e0)
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | REDUCE: (389), (14347) imply:
% 236.33/44.48  | | | | | | | | | | | | | |   (14351)   ~ (all_52_14 = e0)
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 236.33/44.48  | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | |   (14352)   ~ (all_22_2 = e1)
% 236.33/44.48  | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | REDUCE: (326), (14352) imply:
% 236.33/44.48  | | | | | | | | | | | | | | |   (14353)   ~ (all_8_2 = e1)
% 236.33/44.48  | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 236.33/44.48  | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | |   (14354)  all_54_5 = e3
% 236.33/44.48  | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (14354) imply:
% 236.33/44.48  | | | | | | | | | | | | | | | |   (14355)  all_8_2 = e3
% 236.33/44.48  | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | REDUCE: (14325), (14355) imply:
% 236.33/44.48  | | | | | | | | | | | | | | | |   (14356)  $false
% 236.33/44.48  | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | CLOSE: (14356) is inconsistent.
% 236.33/44.48  | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | Case 2:
% 236.33/44.48  | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | |   (14357)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 236.33/44.48  | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | BETA: splitting (14357) gives:
% 236.33/44.48  | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | |   (14358)  all_54_5 = e2
% 236.33/44.48  | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (14358) imply:
% 236.33/44.48  | | | | | | | | | | | | | | | | |   (14359)  all_8_2 = e2
% 236.33/44.48  | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (14359) imply:
% 236.33/44.48  | | | | | | | | | | | | | | | | |   (14360)  all_56_11 = e2
% 236.33/44.48  | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | REDUCE: (366), (14359) imply:
% 236.33/44.48  | | | | | | | | | | | | | | | | |   (14361)   ~ (all_52_1 = e2)
% 236.33/44.48  | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | REDUCE: (373), (14359) imply:
% 236.33/44.48  | | | | | | | | | | | | | | | | |   (14362)   ~ (all_52_7 = e2)
% 236.33/44.48  | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | REDUCE: (375), (14359) imply:
% 236.33/44.48  | | | | | | | | | | | | | | | | |   (14363)   ~ (all_52_9 = e2)
% 236.33/44.48  | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.33/44.48  | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | |   (14364)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.48  | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.48  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | BETA: splitting (14364) gives:
% 236.33/44.48  | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.48  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |   (14365)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              = e3)
% 236.33/44.48  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (14314), (14360), (14361), (14365),
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |            #486.
% 236.33/44.48  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.48  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |   (14366)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.33/44.48  | | | | | | | | | | | | | | | | | | |              = e0)
% 236.33/44.48  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14313), (14348), (14349), (14366),
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |            #485.
% 236.33/44.49  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | |   (14367)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.33/44.49  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.33/44.49  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | BETA: splitting (14367) gives:
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |   (14368)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              = e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (14360), (14362), (14363), (14368),
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |            #2325.
% 236.33/44.49  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |   (14369)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |              = e0)
% 236.33/44.49  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (14348), (14350), (14351), (14369),
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.49  | | | | | | | | | | | | | | | | | | |            #2321.
% 236.33/44.49  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | |   (14370)  all_54_5 = e1 | all_54_5 = e0
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (14330), (14353), (14370) are inconsistent
% 236.33/44.49  | | | | | | | | | | | | | | | | |            by sub-proof #2300.
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | |   (14371)  all_22_2 = e1
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | COMBINE_EQS: (326), (14371) imply:
% 236.33/44.49  | | | | | | | | | | | | | | |   (14372)  all_8_2 = e1
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | COMBINE_EQS: (353), (14372) imply:
% 236.33/44.49  | | | | | | | | | | | | | | |   (14373)  all_56_11 = e1
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | REDUCE: (375), (14372) imply:
% 236.33/44.49  | | | | | | | | | | | | | | |   (14374)   ~ (all_52_9 = e1)
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | |   (14375)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.49  | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.49  | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.49  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.49  | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.49  | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.49  | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.49  | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.33/44.49  | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.33/44.49  | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.49  | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | BETA: splitting (14375) gives:
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | |   (14376)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.49  | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.49  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.49  | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.49  | | | | | | | | | | | | | | | | |              = e3)
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | BETA: splitting (14376) gives:
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | |   (14377)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 236.33/44.49  | | | | | | | | | | | | | | | | | |            e3
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | ALPHA: (14377) implies:
% 236.33/44.49  | | | | | | | | | | | | | | | | | |   (14378)   ~ (all_56_1 = e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | | |   (14379)  op(e3, e2) = e3
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | REDUCE: (290), (14378) imply:
% 236.33/44.49  | | | | | | | | | | | | | | | | | |   (14380)   ~ (all_10_2 = e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (204), (292), (361), (14326), (14332),
% 236.33/44.49  | | | | | | | | | | | | | | | | | |            (14379), (14380), (function-axioms) are
% 236.33/44.49  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #484.
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | |   (14381)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (14313), (14314), (14381),
% 236.33/44.49  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.49  | | | | | | | | | | | | | | | | | |            #483.
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | |   (14382)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.33/44.49  | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.49  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.49  | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.33/44.49  | | | | | | | | | | | | | | | | |              = e0)
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14313), (14348), (14349), (14382),
% 236.33/44.49  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.49  | | | | | | | | | | | | | | | | |            #485.
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | |   (14383)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.33/44.49  | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.33/44.49  | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.33/44.49  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.33/44.49  | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.33/44.49  | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.33/44.49  | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.33/44.49  | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.33/44.49  | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.33/44.49  | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.33/44.49  | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | BETA: splitting (14383) gives:
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | |   (14384)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.33/44.49  | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.33/44.49  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.33/44.49  | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.33/44.49  | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | |              = e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14348), (14373), (14374), (14384),
% 236.33/44.49  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.49  | | | | | | | | | | | | | | | | |            #2297.
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | |   (14385)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.33/44.49  | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.49  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.49  | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.33/44.49  | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.33/44.49  | | | | | | | | | | | | | | | | |              = e0)
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (14348), (14350), (14351), (14385),
% 236.33/44.49  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.49  | | | | | | | | | | | | | | | | |            #2321.
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | |   (14386)  all_20_2 = e1
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | COMBINE_EQS: (341), (14386) imply:
% 236.33/44.49  | | | | | | | | | | |   (14387)  all_4_2 = e1
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | SIMP: (14387) implies:
% 236.33/44.49  | | | | | | | | | | |   (14388)  all_4_2 = e1
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | COMBINE_EQS: (254), (14388) imply:
% 236.33/44.49  | | | | | | | | | | |   (14389)  all_56_31 = e1
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | REDUCE: (368), (14388) imply:
% 236.33/44.49  | | | | | | | | | | |   (14390)   ~ (all_52_3 = e1)
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | REDUCE: (386), (14388) imply:
% 236.33/44.49  | | | | | | | | | | |   (14391)   ~ (all_52_11 = e1)
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | REDUCE: (387), (14388) imply:
% 236.33/44.49  | | | | | | | | | | |   (14392)   ~ (all_52_12 = e1)
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | REDUCE: (388), (14388) imply:
% 236.33/44.49  | | | | | | | | | | |   (14393)   ~ (all_52_13 = e1)
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | REDUCE: (389), (14388) imply:
% 236.33/44.49  | | | | | | | | | | |   (14394)   ~ (all_52_14 = e1)
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | REDUCE: (390), (14388) imply:
% 236.33/44.49  | | | | | | | | | | |   (14395)   ~ (e2 = e1)
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | BETA: splitting (220) gives:
% 236.33/44.49  | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | |   (14396)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 236.33/44.49  | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.33/44.49  | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | BETA: splitting (14396) gives:
% 236.33/44.49  | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | |   (14397)  all_58_9 = e1 & op(e3, e0) = e1
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | REF_CLOSE: (168), (14392), (14397), (function-axioms) are
% 236.33/44.49  | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | |   (14398)  all_58_10 = e1 & op(e2, e0) = e1
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | REF_CLOSE: (164), (14393), (14398), (function-axioms) are
% 236.33/44.49  | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | End of split
% 236.33/44.49  | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | |   (14399)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 236.33/44.49  | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.33/44.49  | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | BETA: splitting (14399) gives:
% 236.33/44.49  | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | |   (14400)  all_58_11 = e1 & op(e1, e0) = e1
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | ALPHA: (14400) implies:
% 236.33/44.49  | | | | | | | | | | | | |   (14401)  op(e1, e0) = e1
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | REF_CLOSE: (160), (14394), (14401), (function-axioms) are
% 236.33/44.49  | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | |   (14402)  all_58_15 = e1 & op(e0, e0) = e1
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | ALPHA: (14402) implies:
% 236.33/44.49  | | | | | | | | | | | | |   (14403)  all_58_15 = e1
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 236.33/44.49  | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | |   (14404)   ~ (all_22_2 = e1)
% 236.33/44.49  | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | REDUCE: (326), (14404) imply:
% 236.33/44.49  | | | | | | | | | | | | | |   (14405)   ~ (all_8_2 = e1)
% 236.33/44.49  | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 236.33/44.49  | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | |   (14406)  all_54_5 = e3
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | COMBINE_EQS: (275), (14406) imply:
% 236.33/44.49  | | | | | | | | | | | | | | |   (14407)  all_8_2 = e3
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | REDUCE: (14325), (14407) imply:
% 236.33/44.49  | | | | | | | | | | | | | | |   (14408)  $false
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | CLOSE: (14408) is inconsistent.
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | |   (14409)   ~ (all_54_5 = e3)
% 236.33/44.49  | | | | | | | | | | | | | | |   (14410)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | BETA: splitting (14410) gives:
% 236.33/44.49  | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | |   (14411)  all_54_5 = e2
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (14411) imply:
% 236.33/44.49  | | | | | | | | | | | | | | | |   (14412)  all_8_2 = e2
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (14412) imply:
% 236.33/44.49  | | | | | | | | | | | | | | | |   (14413)  all_56_11 = e2
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | REDUCE: (366), (14412) imply:
% 236.33/44.49  | | | | | | | | | | | | | | | |   (14414)   ~ (all_52_1 = e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | REDUCE: (373), (14412) imply:
% 236.33/44.49  | | | | | | | | | | | | | | | |   (14415)   ~ (all_52_7 = e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | REDUCE: (375), (14412) imply:
% 236.33/44.49  | | | | | | | | | | | | | | | |   (14416)   ~ (all_52_9 = e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | REDUCE: (14325), (14412) imply:
% 236.33/44.49  | | | | | | | | | | | | | | | |   (14417)   ~ (e3 = e2)
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | REDUCE: (42), (14412) imply:
% 236.33/44.49  | | | | | | | | | | | | | | | |   (14418)  op(e2, e2) = e2
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.33/44.49  | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | |   (14419)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.49  | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.49  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.49  | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.49  | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.49  | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.33/44.49  | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.33/44.49  | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.49  | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | BETA: splitting (14419) gives:
% 236.33/44.49  | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | |   (14420)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.49  | | | | | | | | | | | | | | | | | |              = e3)
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (14314), (14413), (14414), (14420),
% 236.33/44.49  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.49  | | | | | | | | | | | | | | | | | |            #486.
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.49  | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.49  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | |   (14421)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              = e0)
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | BETA: splitting (14421) gives:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |   (14422)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |              e3) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | ALPHA: (14422) implies:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |   (14423)  op(e1, e3) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |   (14424)  op(e3, e1) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (67), (100), (113),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            (117), (123), (140), (141), (144), (145), (146),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            (148), (149), (157), (158), (159), (160), (162),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (168), (169), (170),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            (192), (197), (198), (200), (204), (213), (219),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            (221), (231), (232), (233), (234), (238), (257),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            (269), (270), (279), (290), (292), (301), (355),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            (359), (361), (363), (365), (14311), (14312),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            (14313), (14315), (14316), (14317), (14318),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            (14324), (14332), (14389), (14393), (14403),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            (14423), (14424), (function-axioms) are
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #470.
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |   (14425)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.50  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | BETA: splitting (14425) gives:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |   (14426)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | ALPHA: (14426) implies:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |   (14427)  op(e0, e3) = e3
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |   (14428)  op(e3, e0) = e3
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (113), (148), (159), (164), (165), (167),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |            (168), (234), (14317), (14418), (14427), (14428),
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |            #469.
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |   (14429)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |              e3) = e0
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | ALPHA: (14429) implies:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |   (14430)   ~ (all_56_21 = e3)
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | REDUCE: (14313), (14430) imply:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | |   (14431)  $false
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | CLOSE: (14431) is inconsistent.
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | |   (14432)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.50  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.33/44.50  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.33/44.50  | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.33/44.50  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.33/44.50  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.33/44.50  | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.33/44.50  | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.33/44.50  | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.33/44.50  | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.33/44.50  | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.33/44.50  | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | BETA: splitting (14432) gives:
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | |   (14433)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              = e2)
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (14413), (14415), (14416), (14433),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            #2325.
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | |   (14434)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.33/44.50  | | | | | | | | | | | | | | | | | |              = e0)
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14389), (14394), (14413), (14434),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            #2268.
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | |   (14435)  all_54_5 = e1 | all_54_5 = e0
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | REF_CLOSE: (275), (14330), (14405), (14435) are inconsistent
% 236.33/44.50  | | | | | | | | | | | | | | | |            by sub-proof #2300.
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | |   (14436)  all_22_2 = e1
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | COMBINE_EQS: (326), (14436) imply:
% 236.33/44.50  | | | | | | | | | | | | | |   (14437)  all_8_2 = e1
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | SIMP: (14437) implies:
% 236.33/44.50  | | | | | | | | | | | | | |   (14438)  all_8_2 = e1
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | REDUCE: (366), (14438) imply:
% 236.33/44.50  | | | | | | | | | | | | | |   (14439)   ~ (all_52_1 = e1)
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | REDUCE: (375), (14438) imply:
% 236.33/44.50  | | | | | | | | | | | | | |   (14440)   ~ (all_52_9 = e1)
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | REDUCE: (14325), (14438) imply:
% 236.33/44.50  | | | | | | | | | | | | | |   (14441)   ~ (e3 = e1)
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | |   (14442)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 236.33/44.50  | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | BETA: splitting (14442) gives:
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | |   (14443)  all_58_0 = e1 & op(e3, e3) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (14326), (14443), (function-axioms) are
% 236.33/44.50  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2230.
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | |   (14444)  all_58_2 = e1 & op(e2, e3) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | REF_CLOSE: (167), (14439), (14444), (function-axioms) are
% 236.33/44.50  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | |   (14445)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 236.33/44.50  | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | BETA: splitting (14445) gives:
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | |   (14446)  all_58_6 = e1 & op(e1, e3) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | ALPHA: (14446) implies:
% 236.33/44.50  | | | | | | | | | | | | | | | |   (14447)  op(e1, e3) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | |   (14448)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | BETA: splitting (14448) gives:
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | |   (14449)  all_58_4 = e1 & op(e3, e1) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | ALPHA: (14449) implies:
% 236.33/44.50  | | | | | | | | | | | | | | | | | |   (14450)  op(e3, e1) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (67), (100), (113),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (117), (123), (140), (141), (144), (145), (146),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (148), (149), (157), (158), (159), (160), (162),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (168), (169), (170),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (192), (197), (198), (200), (204), (213), (219),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (221), (231), (232), (233), (234), (238), (257),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (269), (270), (279), (290), (292), (301), (355),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (359), (361), (363), (365), (14311), (14312),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (14313), (14315), (14316), (14317), (14318),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (14324), (14332), (14389), (14393), (14403),
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            (14447), (14450), (function-axioms) are
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #470.
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | |   (14451)  all_58_5 = e1 & op(e2, e1) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | ALPHA: (14451) implies:
% 236.33/44.50  | | | | | | | | | | | | | | | | | |   (14452)  op(e2, e1) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14440), (14452), (function-axioms) are
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | |   (14453)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.33/44.50  | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (14324), (14391), (14453),
% 236.33/44.50  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.50  | | | | | | | | | | | | | | | | |            #467.
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | |   (14454)  all_58_12 = e1 & op(e0, e3) = e1
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14390), (14454), (function-axioms) are
% 236.33/44.50  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | |   (14455)  all_16_2 = e0
% 236.33/44.50  | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | COMBINE_EQS: (342), (14455) imply:
% 236.33/44.50  | | | | | | | | | |   (14456)  all_10_2 = e0
% 236.33/44.50  | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | COMBINE_EQS: (290), (14456) imply:
% 236.33/44.50  | | | | | | | | | |   (14457)  all_56_1 = e0
% 236.33/44.50  | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | REDUCE: (355), (14456) imply:
% 236.33/44.50  | | | | | | | | | |   (14458)   ~ (all_52_1 = e0)
% 236.33/44.50  | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | REDUCE: (357), (14456) imply:
% 236.33/44.50  | | | | | | | | | |   (14459)   ~ (all_52_2 = e0)
% 236.33/44.50  | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | REDUCE: (359), (14456) imply:
% 236.33/44.50  | | | | | | | | | |   (14460)   ~ (all_52_3 = e0)
% 236.33/44.50  | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | REDUCE: (361), (14456) imply:
% 236.33/44.50  | | | | | | | | | |   (14461)   ~ (all_52_4 = e0)
% 236.33/44.50  | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | REDUCE: (45), (14456) imply:
% 236.33/44.50  | | | | | | | | | |   (14462)  op(e3, e3) = e0
% 236.33/44.50  | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | BETA: splitting (61) gives:
% 236.33/44.50  | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | |   (14463)   ~ (all_20_2 = e1)
% 236.33/44.50  | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | REDUCE: (341), (14463) imply:
% 236.33/44.50  | | | | | | | | | | |   (14464)   ~ (all_4_2 = e1)
% 236.33/44.50  | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | BETA: splitting (189) gives:
% 236.33/44.50  | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | |   (14465)  all_54_15 = e3
% 236.33/44.50  | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | REF_CLOSE: (299), (14328), (14465) are inconsistent by
% 236.33/44.50  | | | | | | | | | | | |            sub-proof #2340.
% 236.33/44.50  | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | |   (14466)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 236.33/44.50  | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | BETA: splitting (14466) gives:
% 236.33/44.50  | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | |   (14467)  all_54_15 = e2
% 236.33/44.50  | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | REF_CLOSE: (299), (390), (14467) are inconsistent by
% 236.33/44.50  | | | | | | | | | | | | |            sub-proof #2339.
% 236.33/44.50  | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | |   (14468)   ~ (all_54_15 = e2)
% 236.33/44.50  | | | | | | | | | | | | |   (14469)  all_54_15 = e1 | all_54_15 = e0
% 236.33/44.50  | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | BETA: splitting (14469) gives:
% 236.33/44.50  | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | |   (14470)  all_54_15 = e1
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | REF_CLOSE: (299), (14464), (14470) are inconsistent by
% 236.33/44.50  | | | | | | | | | | | | | |            sub-proof #2338.
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | |   (14471)  all_54_15 = e0
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | COMBINE_EQS: (299), (14471) imply:
% 236.33/44.50  | | | | | | | | | | | | | |   (14472)  all_4_2 = e0
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | SIMP: (14472) implies:
% 236.33/44.50  | | | | | | | | | | | | | |   (14473)  all_4_2 = e0
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | COMBINE_EQS: (254), (14473) imply:
% 236.33/44.50  | | | | | | | | | | | | | |   (14474)  all_56_31 = e0
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | REDUCE: (379), (14473) imply:
% 236.33/44.50  | | | | | | | | | | | | | |   (14475)   ~ (all_52_7 = e0)
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | REDUCE: (388), (14473) imply:
% 236.33/44.50  | | | | | | | | | | | | | |   (14476)   ~ (all_52_13 = e0)
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | REDUCE: (390), (14473) imply:
% 236.33/44.50  | | | | | | | | | | | | | |   (14477)   ~ (e2 = e0)
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | REDUCE: (14464), (14473) imply:
% 236.33/44.50  | | | | | | | | | | | | | |   (14478)   ~ (e1 = e0)
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | REDUCE: (36), (14473) imply:
% 236.33/44.50  | | | | | | | | | | | | | |   (14479)  op(e0, e0) = e0
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 236.33/44.50  | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | |   (14480)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 236.33/44.50  | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | BETA: splitting (14480) gives:
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | |   (14481)  all_58_2 = e0 & op(e2, e3) = e0
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | REF_CLOSE: (167), (14458), (14481), (function-axioms) are
% 236.33/44.50  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1985.
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | |   (14482)  all_58_3 = e0 & op(e2, e2) = e0
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | REF_CLOSE: (42), (14330), (14482), (function-axioms) are
% 236.33/44.50  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | |   (14483)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 236.33/44.50  | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | BETA: splitting (14483) gives:
% 236.33/44.50  | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | |   (14484)  all_58_5 = e0 & op(e2, e1) = e0
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | ALPHA: (14484) implies:
% 236.33/44.50  | | | | | | | | | | | | | | | |   (14485)  op(e2, e1) = e0
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 236.33/44.50  | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | |   (14486)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 236.33/44.50  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | BETA: splitting (14486) gives:
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | |   (14487)  all_58_1 = e0 & op(e3, e2) = e0
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (14461), (14487), (function-axioms) are
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | |   (14488)  all_58_3 = e0 & op(e2, e2) = e0
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (14330), (14488), (function-axioms) are
% 236.33/44.50  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 236.33/44.50  | | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | | End of split
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.50  | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.50  | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | |   (14489)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 236.33/44.51  | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 236.33/44.51  | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | BETA: splitting (14489) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | |   (14490)  all_58_7 = e0 & op(e1, e2) = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | ALPHA: (14490) implies:
% 236.33/44.51  | | | | | | | | | | | | | | | | | |   (14491)  op(e1, e2) = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0,
% 236.33/44.51  | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (14491) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | |   (14492)  all_52_6 = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 236.33/44.51  | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (14485) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | |   (14493)  all_52_9 = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | REDUCE: (126), (14492) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | |   (14494)   ~ (all_52_14 = e0)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | SIMP: (14494) implies:
% 236.33/44.51  | | | | | | | | | | | | | | | | | |   (14495)   ~ (all_52_14 = e0)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | REDUCE: (117), (14493) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | |   (14496)   ~ (all_52_13 = e0)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | REDUCE: (375), (14493) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | |   (14497)   ~ (all_8_2 = e0)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |   (14498)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | BETA: splitting (14498) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |   (14499)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | BETA: splitting (14499) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |   (14500)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |            e3
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14500) implies:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |   (14501)   ~ (all_56_11 = e2)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |   (14502)  op(e2, e3) = e3
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |   (14503)  op(e3, e2) = e3
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | REDUCE: (353), (14501) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |   (14504)   ~ (all_8_2 = e2)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | |   (14505)  all_54_5 = e3
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (14505) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | |   (14506)  all_8_2 = e3
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14325), (14506) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | |   (14507)  $false
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (14507) is inconsistent.
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | |   (14508)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14508) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | |   (14509)  all_54_5 = e2
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (14509) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | |   (14510)  all_8_2 = e2
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14504), (14510) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | |   (14511)  $false
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (14511) is inconsistent.
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | |   (14512)  all_54_5 = e1 | all_54_5 = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14512) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | |   (14513)  all_54_5 = e1
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (14513) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | |   (14514)  all_8_2 = e1
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (14514) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | |   (14515)  all_22_2 = e1
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (14514) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | |   (14516)  all_30_2 = e1
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (14517)   ~ (all_22_2 = e1)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14515), (14517) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (14518)  $false
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (14518) is inconsistent.
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (14519)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = all_22_1 & $i(all_22_0) &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_22_1 & $i(all_22_1))
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14520)   ~ (all_30_2 = e1)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14516), (14520) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14521)  $false
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (14521) is inconsistent.
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14522)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = all_30_1 & $i(all_30_0) &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_30_1 & $i(all_30_1))
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14522) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14523)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_30_1 & $i(all_30_0) &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14523) implies:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14524)  op(e2, e1) = all_30_1
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_30_1,
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (14485), (14524) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14525)  all_30_1 = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (14502) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14526)  all_52_1 = e3
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (14503) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14527)  all_52_4 = e3
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (14526) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14528)   ~ (all_52_3 = e3)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14528) implies:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14529)   ~ (all_52_3 = e3)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (159), (219), (14318), (14479),
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14519), (14522), (14524), (14525), (14529),
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #466.
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14530)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14530) implies:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14531)   ~ (all_30_1 = e3)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14532)  op(e2, e1) = all_30_1
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_30_1,
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (14485), (14532) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14533)  all_30_1 = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (14502) gives:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14534)  all_52_1 = e3
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (14534) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14535)   ~ (all_52_3 = e3)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14535) implies:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14536)   ~ (all_52_3 = e3)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14531), (14533) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14537)   ~ (e3 = e0)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (159), (219), (14318), (14479),
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14519), (14522), (14532), (14533), (14536),
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #466.
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | |   (14538)  all_54_5 = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (14538) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | |   (14539)  all_8_2 = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14330), (14539) imply:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | |   (14540)  $false
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (14540) is inconsistent.
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |   (14541)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (14313), (14314), (14541),
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | |            #483.
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |   (14542)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14313), (14460), (14474), (14542),
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | |            #485.
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |   (14543)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (160), (164), (165), (14474), (14476),
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |            (14485), (14495), (14543), (function-axioms) are
% 236.33/44.51  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 236.33/44.51  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | |   (14544)  all_58_13 = e0 & op(e0, e2) = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | ALPHA: (14544) implies:
% 236.33/44.51  | | | | | | | | | | | | | | | | | |   (14545)  op(e0, e2) = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (14475), (14545), (function-axioms) are
% 236.33/44.51  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2252.
% 236.33/44.51  | | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | |   (14546)  all_58_10 = e0 & op(e2, e0) = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | ALPHA: (14546) implies:
% 236.33/44.51  | | | | | | | | | | | | | | | |   (14547)  op(e2, e0) = e0
% 236.33/44.51  | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (14476), (14547), (function-axioms) are
% 236.33/44.51  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2324.
% 236.33/44.51  | | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | |   (14548)  all_20_2 = e1
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | COMBINE_EQS: (341), (14548) imply:
% 236.33/44.51  | | | | | | | | | | |   (14549)  all_4_2 = e1
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | SIMP: (14549) implies:
% 236.33/44.51  | | | | | | | | | | |   (14550)  all_4_2 = e1
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | COMBINE_EQS: (254), (14550) imply:
% 236.33/44.51  | | | | | | | | | | |   (14551)  all_56_31 = e1
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | REDUCE: (368), (14550) imply:
% 236.33/44.51  | | | | | | | | | | |   (14552)   ~ (all_52_3 = e1)
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | REDUCE: (379), (14550) imply:
% 236.33/44.51  | | | | | | | | | | |   (14553)   ~ (all_52_7 = e1)
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | REDUCE: (386), (14550) imply:
% 236.33/44.51  | | | | | | | | | | |   (14554)   ~ (all_52_11 = e1)
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | REDUCE: (387), (14550) imply:
% 236.33/44.51  | | | | | | | | | | |   (14555)   ~ (all_52_12 = e1)
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | REDUCE: (389), (14550) imply:
% 236.33/44.51  | | | | | | | | | | |   (14556)   ~ (all_52_14 = e1)
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | REDUCE: (390), (14550) imply:
% 236.33/44.51  | | | | | | | | | | |   (14557)   ~ (e2 = e1)
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | BETA: splitting (217) gives:
% 236.33/44.51  | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | |   (14558)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 236.33/44.51  | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 236.33/44.51  | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | BETA: splitting (14558) gives:
% 236.33/44.51  | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | |   (14559)  all_58_12 = e1 & op(e0, e3) = e1
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | REF_CLOSE: (159), (14552), (14559), (function-axioms) are
% 236.33/44.51  | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | |   (14560)  all_58_13 = e1 & op(e0, e2) = e1
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | REF_CLOSE: (158), (14553), (14560), (function-axioms) are
% 236.33/44.51  | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | End of split
% 236.33/44.51  | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | |   (14561)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 236.33/44.51  | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.33/44.51  | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | BETA: splitting (14561) gives:
% 236.33/44.51  | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | |   (14562)  all_58_14 = e1 & op(e0, e1) = e1
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | ALPHA: (14562) implies:
% 236.33/44.51  | | | | | | | | | | | | |   (14563)  op(e0, e1) = e1
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | REF_CLOSE: (157), (14554), (14563), (function-axioms) are
% 236.33/44.51  | | | | | | | | | | | | |            inconsistent by sub-proof #2272.
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | Case 2:
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | |   (14564)  all_58_15 = e1 & op(e0, e0) = e1
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | ALPHA: (14564) implies:
% 236.33/44.51  | | | | | | | | | | | | |   (14565)  all_58_15 = e1
% 236.33/44.51  | | | | | | | | | | | | |   (14566)  op(e0, e0) = e1
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 236.33/44.51  | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | |   (14567)   ~ (all_22_2 = e1)
% 236.33/44.51  | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | REDUCE: (326), (14567) imply:
% 236.33/44.51  | | | | | | | | | | | | | |   (14568)   ~ (all_8_2 = e1)
% 236.33/44.51  | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 236.33/44.51  | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | Case 1:
% 236.33/44.51  | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | |   (14569)  all_54_5 = e3
% 236.33/44.51  | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | COMBINE_EQS: (275), (14569) imply:
% 236.33/44.51  | | | | | | | | | | | | | | |   (14570)  all_8_2 = e3
% 236.33/44.51  | | | | | | | | | | | | | | | 
% 236.33/44.51  | | | | | | | | | | | | | | | REDUCE: (14325), (14570) imply:
% 236.33/44.51  | | | | | | | | | | | | | | |   (14571)  $false
% 236.33/44.52  | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | CLOSE: (14571) is inconsistent.
% 236.33/44.52  | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | |   (14572)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 236.33/44.52  | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | BETA: splitting (14572) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | |   (14573)  all_54_5 = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (14573) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | |   (14574)  all_8_2 = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (14574) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | |   (14575)  all_56_11 = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | REDUCE: (366), (14574) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | |   (14576)   ~ (all_52_1 = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | REDUCE: (373), (14574) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | |   (14577)   ~ (all_52_7 = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | REDUCE: (375), (14574) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | |   (14578)   ~ (all_52_9 = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | |   (14579)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.52  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.52  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.52  | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.52  | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.52  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.52  | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.52  | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.52  | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.33/44.52  | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.52  | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | BETA: splitting (14579) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | |   (14580)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              = e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (14314), (14575), (14576), (14580),
% 236.33/44.52  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.52  | | | | | | | | | | | | | | | | | |            #486.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | |   (14581)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              = e0)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14313), (14457), (14460), (14581),
% 236.33/44.52  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.52  | | | | | | | | | | | | | | | | | |            #465.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | End of split
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | |   (14582)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.52  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.33/44.52  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.33/44.52  | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.33/44.52  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.33/44.52  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.33/44.52  | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.33/44.52  | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.33/44.52  | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.33/44.52  | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.33/44.52  | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.33/44.52  | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | BETA: splitting (14582) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | |   (14583)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (14575), (14577), (14578), (14583),
% 236.33/44.52  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.52  | | | | | | | | | | | | | | | | | |            #2325.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | |   (14584)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.33/44.52  | | | | | | | | | | | | | | | | | |              = e0)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14551), (14556), (14575), (14584),
% 236.33/44.52  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.52  | | | | | | | | | | | | | | | | | |            #2268.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | End of split
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | End of split
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | |   (14585)  all_54_5 = e1 | all_54_5 = e0
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | REF_CLOSE: (275), (14330), (14568), (14585) are inconsistent
% 236.33/44.52  | | | | | | | | | | | | | | | |            by sub-proof #2300.
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | End of split
% 236.33/44.52  | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | End of split
% 236.33/44.52  | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | |   (14586)  all_22_2 = e1
% 236.33/44.52  | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | COMBINE_EQS: (326), (14586) imply:
% 236.33/44.52  | | | | | | | | | | | | | |   (14587)  all_8_2 = e1
% 236.33/44.52  | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | REDUCE: (366), (14587) imply:
% 236.33/44.52  | | | | | | | | | | | | | |   (14588)   ~ (all_52_1 = e1)
% 236.33/44.52  | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | REDUCE: (369), (14587) imply:
% 236.33/44.52  | | | | | | | | | | | | | |   (14589)   ~ (all_52_4 = e1)
% 236.33/44.52  | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | REDUCE: (375), (14587) imply:
% 236.33/44.52  | | | | | | | | | | | | | |   (14590)   ~ (all_52_9 = e1)
% 236.33/44.52  | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | REDUCE: (377), (14587) imply:
% 236.33/44.52  | | | | | | | | | | | | | |   (14591)   ~ (all_52_13 = e1)
% 236.33/44.52  | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | REDUCE: (14325), (14587) imply:
% 236.33/44.52  | | | | | | | | | | | | | |   (14592)   ~ (e3 = e1)
% 236.33/44.52  | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | REDUCE: (42), (14587) imply:
% 236.33/44.52  | | | | | | | | | | | | | |   (14593)  op(e2, e2) = e1
% 236.33/44.52  | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 236.33/44.52  | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | |   (14594)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 236.33/44.52  | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 236.33/44.52  | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | BETA: splitting (14594) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | |   (14595)  all_58_6 = e1 & op(e1, e3) = e1
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | ALPHA: (14595) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | |   (14596)  op(e1, e3) = e1
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | |   (14597)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 236.33/44.52  | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (14462), (14589), (14597),
% 236.33/44.52  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.52  | | | | | | | | | | | | | | | | |            #1826.
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | |   (14598)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 236.33/44.52  | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | BETA: splitting (14598) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | |   (14599)  all_58_4 = e1 & op(e3, e1) = e1
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | ALPHA: (14599) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | |   (14600)  all_58_4 = e1
% 236.33/44.52  | | | | | | | | | | | | | | | | | |   (14601)  op(e3, e1) = e1
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | |   (14602)  all_54_12 = e3
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (14602) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | |   (14603)  all_52_3 = e3
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | SIMP: (14603) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | |   (14604)  all_52_3 = e3
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | REDUCE: (148), (14604) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | |   (14605)   ~ (all_52_1 = e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | REDUCE: (140), (14604) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | |   (14606)   ~ (all_52_7 = e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | SIMP: (14606) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | |   (14607)   ~ (all_52_7 = e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | |   (14608)  all_54_4 = e3
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (14605), (14608) are inconsistent by
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | |   (14609)   ~ (all_54_4 = e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | |   (14610)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | |   (14611)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14611) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | |   (14612)  all_58_1 = e3 & op(e3, e2) = e3
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14612) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | |   (14613)  op(e3, e2) = e3
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14610) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | |   (14614)  all_54_4 = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (14614) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | |   (14615)  all_52_1 = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14615) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | |   (14616)  all_52_1 = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (14616) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | |   (14617)   ~ (all_52_9 = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14617) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | |   (14618)   ~ (all_52_9 = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14605), (14616) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | |   (14619)   ~ (e3 = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (14616) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | |   (14620)  op(e2, e3) = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | |   (14621)  all_54_6 = e3
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (14621) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | |   (14622)  all_52_9 = e3
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14317), (14622) imply:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | |   (14623)  $false
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (14623) is inconsistent.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | |   (14624)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (14625)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (165), (14600), (14618), (14625),
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | |            #464.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (14626)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14626) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14627)  all_58_8 = e2 & op(e1, e1) = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14627) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14628)  op(e1, e1) = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14324), (14628), (function-axioms) are
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14629)  all_58_14 = e2 & op(e0, e1) = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14629) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14630)  all_58_14 = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14631)  op(e0, e1) = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14632)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (14462), (14613), (14632),
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1857.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14633)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14633) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14634)  all_58_4 = e2 & op(e3, e1) = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14634) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14635)  all_58_4 = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14600), (14635) are inconsistent by
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1786.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14636)  all_58_9 = e2 & op(e3, e0) = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14636) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14637)  op(e3, e0) = e2
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14638)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14638) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14639)  all_58_4 = e0 & op(e3, e1) = e0
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14639) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14640)  op(e3, e1) = e0
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14601), (14640), (function-axioms) are
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2089.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14641)  all_58_5 = e0 & op(e2, e1) = e0
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14641) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14642)  op(e2, e1) = e0
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14643)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14643) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14644)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14644) gives:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14645)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14645) implies:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14646)  op(e2, e3) = e3
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14620), (14646), (function-axioms) are
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14647)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14647) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14648)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14648) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14649)  op(e3, e2) = e2
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (159), (163), (167), (239), (246),
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14458), (14459), (14460), (14601), (14637),
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14649), (function-axioms) are inconsistent by
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #462.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14650)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14650) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14651)  op(e1, e3) = e3
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14596), (14651), (function-axioms) are
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14652)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (159), (14313), (14460), (14637), (14652),
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #461.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14653)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14653) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14654)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14654) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14655)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14655) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14656)  op(e2, e1) = e2
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14642), (14656), (function-axioms) are
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14657)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14657) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14658)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14658) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14659)  op(e2, e1) = e1
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14590), (14659), (function-axioms) are
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14660)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14660) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14661)  op(e0, e2) = e2
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (158), (216), (219),
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14565), (14566), (14607), (14630), (14661),
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1636.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14662)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14662) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14663)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14663) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14664)  op(e2, e0) = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (164), (270), (14590), (14618), (14624),
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14664), (function-axioms) are inconsistent by
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #459.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14665)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14665) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14666)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14666) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14667)  op(e1, e0) = e1
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14556), (14667), (function-axioms) are
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14668)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14668) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14669)  op(e0, e1) = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14631), (14669), (function-axioms) are
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #458.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14670)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14670) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14671)  all_58_8 = e0 & op(e1, e1) = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14671) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14672)  op(e1, e1) = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (160), (162), (226), (14315), (14319),
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14596), (14672), (function-axioms) are
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #457.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14673)  all_58_14 = e0 & op(e0, e1) = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14673) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14674)  op(e0, e1) = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14631), (14674), (function-axioms) are
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #458.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | |   (14675)  all_54_4 = e1 | all_54_4 = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (14458), (14588), (14675) are inconsistent
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1922.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | |   (14676)  all_58_3 = e3 & op(e2, e2) = e3
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (14588), (14590),
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | |            (14591), (14676), (function-axioms) are
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2196.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | |   (14677)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (14315), (14607), (14677),
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | |            #475.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | End of split
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | |   (14678)   ~ (all_54_12 = e3)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | |   (14679)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | REDUCE: (257), (14678) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | |   (14680)   ~ (all_52_3 = e3)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (14679) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | |   (14681)  all_54_12 = e2
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (14681) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | |   (14682)  all_52_3 = e2
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | SIMP: (14682) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | |   (14683)  all_52_3 = e2
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (14683) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | |   (14684)   ~ (all_52_1 = e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (14683) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | |   (14685)   ~ (all_52_7 = e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | SIMP: (14685) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | |   (14686)   ~ (all_52_7 = e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (14683) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | |   (14687)   ~ (all_52_11 = e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | SIMP: (14687) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | |   (14688)   ~ (all_52_11 = e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (14683) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | |   (14689)  op(e0, e3) = e2
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | |   (14690)  all_54_4 = e3
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (14690) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | |   (14691)  all_52_1 = e3
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | SIMP: (14691) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | |   (14692)  all_52_1 = e3
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (14692) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | |   (14693)  op(e2, e3) = e3
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | |   (14694)  all_54_14 = e3
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (14694) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | |   (14695)  all_52_11 = e3
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14318), (14695) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | |   (14696)  $false
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (14696) is inconsistent.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | |   (14697)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14697) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | |   (14698)  all_54_14 = e2
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (14688), (14698) are inconsistent by
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1856.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | |   (14699)   ~ (all_54_14 = e2)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | |   (14700)  all_54_14 = e1 | all_54_14 = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14700) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | |   (14701)  all_54_14 = e1
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (14554), (14701) are inconsistent by
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1937.
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | |   (14702)  all_54_14 = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (14702) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | |   (14703)  all_52_11 = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14703) implies:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | |   (14704)  all_52_11 = e0
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (14704) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | |   (14705)   ~ (all_52_7 = e0)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14688), (14704) imply:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | |   (14706)   ~ (e2 = e0)
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.33/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (14707)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14707) gives:
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14708)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14708) gives:
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14709)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14709) implies:
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14710)  op(e3, e2) = e3
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (135), (170), (191), (256), (14553), (14686),
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14705), (14710), (function-axioms) are
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #456.
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14711)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (14596), (14693), (14711),
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1218.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14712)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14712) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14713)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14713) implies:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14714)   ~ (all_56_21 = e3)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14313), (14714) imply:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14715)  $false
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (14715) is inconsistent.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14716)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (14680), (14689), (14716),
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1819.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (14717)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14717) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14718)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14718) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14719)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14719) implies:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14720)   ~ (all_56_31 = e1)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14551), (14720) imply:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14721)  $false
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (14721) is inconsistent.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14722)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (14590), (14686), (14722),
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2305.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14723)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (160), (14551), (14556), (14705), (14723),
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2251.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | |   (14724)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (14458), (14588), (14684), (14724) are
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1921.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | |   (14725)  all_54_12 = e1 | all_54_12 = e0
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (14460), (14552), (14725) are inconsistent
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | |            by sub-proof #2067.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | |   (14726)  all_58_9 = e1 & op(e3, e0) = e1
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (14555), (14726), (function-axioms) are
% 236.59/44.54  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | |   (14727)  all_58_7 = e1 & op(e1, e2) = e1
% 236.59/44.54  | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | ALPHA: (14727) implies:
% 236.59/44.54  | | | | | | | | | | | | | | | |   (14728)  all_58_7 = e1
% 236.59/44.54  | | | | | | | | | | | | | | | |   (14729)  op(e1, e2) = e1
% 236.59/44.54  | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | |   (14730)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.59/44.54  | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.59/44.54  | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | BETA: splitting (14730) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | |   (14731)  all_58_4 = e1 & op(e3, e1) = e1
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | ALPHA: (14731) implies:
% 236.59/44.54  | | | | | | | | | | | | | | | | | |   (14732)  all_58_4 = e1
% 236.59/44.54  | | | | | | | | | | | | | | | | | |   (14733)  op(e3, e1) = e1
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | |   (14734)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 236.59/44.54  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (14734) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | |   (14735)  all_58_1 = e0 & op(e3, e2) = e0
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (14461), (14735), (function-axioms) are
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | |   (14736)  all_58_3 = e0 & op(e2, e2) = e0
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (14330), (14736), (function-axioms) are
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | |   (14737)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (14737) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | |   (14738)  all_58_7 = e0 & op(e1, e2) = e0
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | ALPHA: (14738) implies:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | |   (14739)  op(e1, e2) = e0
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (14729), (14739), (function-axioms)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | |   (14740)  all_58_13 = e0 & op(e0, e2) = e0
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | ALPHA: (14740) implies:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | |   (14741)  op(e0, e2) = e0
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | |   (14742)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14742) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | |   (14743)  all_58_1 = e3 & op(e3, e2) = e3
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14743) implies:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | |   (14744)  op(e3, e2) = e3
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | |   (14745)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (14462), (14744), (14745),
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | |            #1857.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | |   (14746)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14746) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | |   (14747)  all_58_4 = e2 & op(e3, e1) = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14747) implies:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | |   (14748)  all_58_4 = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14732), (14748) are inconsistent by
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1786.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | |   (14749)  all_58_9 = e2 & op(e3, e0) = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14749) implies:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | |   (14750)  op(e3, e0) = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (14751)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14751) gives:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14752)  all_58_1 = e2 & op(e3, e2) = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14752) implies:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14753)  op(e3, e2) = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (159), (163), (167), (239), (246),
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (14458), (14459), (14460), (14733), (14750),
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (14753), (function-axioms) are inconsistent by
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #462.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14754)  all_58_3 = e2 & op(e2, e2) = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14754) implies:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14755)  op(e2, e2) = e2
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14593), (14755), (function-axioms) are
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (14756)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14728), (14741), (14756),
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | |            #1376.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | |   (14757)  all_58_3 = e3 & op(e2, e2) = e3
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (14588), (14590),
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | |            (14591), (14757), (function-axioms) are
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2196.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | |   (14758)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (14729), (14741), (14758),
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | |            #1775.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | |   (14759)  all_58_5 = e1 & op(e2, e1) = e1
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (123), (126), (148), (158), (159), (160),
% 236.59/44.54  | | | | | | | | | | | | | | | | | |            (162), (163), (164), (165), (167), (168), (169),
% 236.59/44.54  | | | | | | | | | | | | | | | | | |            (199), (213), (233), (234), (275), (353), (366),
% 236.59/44.54  | | | | | | | | | | | | | | | | | |            (373), (375), (377), (14313), (14314), (14317),
% 236.59/44.54  | | | | | | | | | | | | | | | | | |            (14325), (14330), (14551), (14729), (14759),
% 236.59/44.54  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.54  | | | | | | | | | | | | | | | | | |            #454.
% 236.59/44.54  | | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | |   (14760)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.59/44.54  | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.59/44.54  | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (14324), (14554), (14760),
% 236.59/44.54  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.54  | | | | | | | | | | | | | | | | |            #467.
% 236.59/44.54  | | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | |   (14761)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 236.59/44.54  | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 236.59/44.54  | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (14324), (14556), (14761),
% 236.59/44.54  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.54  | | | | | | | | | | | | | | |            #453.
% 236.59/44.54  | | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | End of split
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | |   (14762)  all_14_2 = e0
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | COMBINE_EQS: (344), (14762) imply:
% 236.59/44.54  | | | | | | | | |   (14763)  all_8_2 = e0
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | SIMP: (14763) implies:
% 236.59/44.54  | | | | | | | | |   (14764)  all_8_2 = e0
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | COMBINE_EQS: (353), (14764) imply:
% 236.59/44.54  | | | | | | | | |   (14765)  all_56_11 = e0
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | REDUCE: (369), (14764) imply:
% 236.59/44.54  | | | | | | | | |   (14766)   ~ (all_52_4 = e0)
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | REDUCE: (371), (14764) imply:
% 236.59/44.54  | | | | | | | | |   (14767)   ~ (all_52_6 = e0)
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | REDUCE: (373), (14764) imply:
% 236.59/44.54  | | | | | | | | |   (14768)   ~ (all_52_7 = e0)
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | REDUCE: (375), (14764) imply:
% 236.59/44.54  | | | | | | | | |   (14769)   ~ (all_52_9 = e0)
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | REDUCE: (377), (14764) imply:
% 236.59/44.54  | | | | | | | | |   (14770)   ~ (all_52_13 = e0)
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | REDUCE: (14325), (14764) imply:
% 236.59/44.54  | | | | | | | | |   (14771)   ~ (e3 = e0)
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | BETA: splitting (235) gives:
% 236.59/44.54  | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | |   (14772)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 236.59/44.54  | | | | | | | | | |              & op(e2, e2) = e0)
% 236.59/44.54  | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | BETA: splitting (14772) gives:
% 236.59/44.54  | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | |   (14773)  all_58_1 = e0 & op(e3, e2) = e0
% 236.59/44.54  | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | REF_CLOSE: (170), (14766), (14773), (function-axioms) are
% 236.59/44.54  | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 236.59/44.54  | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | |   (14774)  all_58_3 = e0 & op(e2, e2) = e0
% 236.59/44.54  | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | ALPHA: (14774) implies:
% 236.59/44.54  | | | | | | | | | | |   (14775)  all_58_3 = e0
% 236.59/44.54  | | | | | | | | | | |   (14776)  op(e2, e2) = e0
% 236.59/44.54  | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | BETA: splitting (55) gives:
% 236.59/44.54  | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | |   (14777)   ~ (all_16_2 = e0)
% 236.59/44.54  | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | REDUCE: (342), (14777) imply:
% 236.59/44.54  | | | | | | | | | | | |   (14778)   ~ (all_10_2 = e0)
% 236.59/44.54  | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | BETA: splitting (61) gives:
% 236.59/44.54  | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | |   (14779)   ~ (all_20_2 = e1)
% 236.59/44.54  | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | REDUCE: (341), (14779) imply:
% 236.59/44.54  | | | | | | | | | | | | |   (14780)   ~ (all_4_2 = e1)
% 236.59/44.54  | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | BETA: splitting (189) gives:
% 236.59/44.54  | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | Case 1:
% 236.59/44.54  | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | |   (14781)  all_54_15 = e3
% 236.59/44.54  | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | | REF_CLOSE: (299), (14328), (14781) are inconsistent by
% 236.59/44.54  | | | | | | | | | | | | | |            sub-proof #2340.
% 236.59/44.54  | | | | | | | | | | | | | | 
% 236.59/44.54  | | | | | | | | | | | | | Case 2:
% 236.59/44.54  | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | |   (14782)   ~ (all_54_15 = e3)
% 236.59/44.55  | | | | | | | | | | | | | |   (14783)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 236.59/44.55  | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | BETA: splitting (14783) gives:
% 236.59/44.55  | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | |   (14784)  all_54_15 = e2
% 236.59/44.55  | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | REF_CLOSE: (299), (390), (14784) are inconsistent by
% 236.59/44.55  | | | | | | | | | | | | | | |            sub-proof #2339.
% 236.59/44.55  | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | |   (14785)   ~ (all_54_15 = e2)
% 236.59/44.55  | | | | | | | | | | | | | | |   (14786)  all_54_15 = e1 | all_54_15 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | BETA: splitting (14786) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | |   (14787)  all_54_15 = e1
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | REF_CLOSE: (299), (14780), (14787) are inconsistent by
% 236.59/44.55  | | | | | | | | | | | | | | | |            sub-proof #2338.
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | |   (14788)  all_54_15 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (14788) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | |   (14789)  all_4_2 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | SIMP: (14789) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | |   (14790)  all_4_2 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | REDUCE: (387), (14790) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | |   (14791)   ~ (all_52_12 = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | REDUCE: (389), (14790) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | |   (14792)   ~ (all_52_14 = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | REDUCE: (390), (14790) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | |   (14793)   ~ (e2 = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | REDUCE: (14780), (14790) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | |   (14794)   ~ (e1 = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | |   (14795)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | BETA: splitting (14795) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | |   (14796)  all_58_6 = e0 & op(e1, e3) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | ALPHA: (14796) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | |   (14797)  op(e1, e3) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | |   (14798)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (14798) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14799)  all_58_0 = e0 & op(e3, e3) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (14778), (14799), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1736.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14800)  all_58_1 = e0 & op(e3, e2) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (14766), (14800), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | |   (14801)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (14801) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14802)  all_58_4 = e0 & op(e3, e1) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (14802) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14803)  all_58_4 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14804)  op(e3, e1) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (14797) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14805)  all_52_2 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (14804) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14806)  all_52_8 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (14805) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14807)   ~ (all_52_1 = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (14806) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14808)   ~ (all_52_11 = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | SIMP: (14808) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14809)   ~ (all_52_11 = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | |   (14810)   ~ (all_46_2 = e3)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | REDUCE: (14312), (14810) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | |   (14811)  $false
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | CLOSE: (14811) is inconsistent.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | |   (14812)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14812) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | |   (14813)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_46_1 & $i(all_46_0) &
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14813) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | |   (14814)   ~ (all_46_0 = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | |   (14815)  op(e1, e3) = all_46_1
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | |   (14816)  op(all_46_1, e1) = all_46_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14311) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14817)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 &
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14817) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14818)   ~ (all_6_0 = e2)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14819)  op(e1, e3) = all_6_1
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14820)  op(all_6_1, e1) = all_6_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_46_1,
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (14797), (14815) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14821)  all_46_1 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              all_46_1, e3, e1, simplifying with (14815),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              (14819) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14822)  all_46_1 = all_6_1
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14821), (14822) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14823)  all_6_1 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14816), (14821) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14824)  op(e0, e1) = all_46_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14820), (14823) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14825)  op(e0, e1) = all_6_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              all_6_0, e1, e0, simplifying with (157), (14825)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14826)  all_52_11 = all_6_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              all_46_0, e1, e0, simplifying with (157), (14824)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14827)  all_52_11 = all_46_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14826), (14827) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14828)  all_46_0 = all_6_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14828) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14829)  all_46_0 = all_6_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (14826) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14830)  all_54_14 = all_6_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (14826) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14831)   ~ (all_52_3 = all_6_0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (14826) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14832)   ~ (all_52_9 = all_6_0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14318), (14826) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14833)   ~ (all_6_0 = e3)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14814), (14829) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14834)   ~ (all_6_0 = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |   (14835)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (42), (45), (113), (159), (164), (167),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            (168), (190), (211), (234), (241), (14313),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            (14325), (14326), (14776), (14797), (14803),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            (14804), (14807), (14818), (14825), (14830),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            (14831), (14833), (14834), (14835),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            #447.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |   (14836)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14836) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (14837)  all_58_8 = e2 & op(e1, e1) = e2
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14837) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (14838)  op(e1, e1) = e2
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14324), (14838), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (14839)  all_58_14 = e2 & op(e0, e1) = e2
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14839) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (14840)  all_58_14 = e2
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (165), (190), (228), (14324),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (14804), (14818), (14830), (14832), (14833),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (14834), (14840), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #445.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14841)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 &
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_6_1)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14797), (14812), (14841), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #443.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | |   (14842)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 &
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14842) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | |   (14843)   ~ (all_46_1 = e2)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | |   (14844)  op(e1, e3) = all_46_1
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14311) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14845)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 &
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14845) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14846)   ~ (all_6_0 = e2)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14847)  op(e1, e3) = all_6_1
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14848)  op(all_6_1, e1) = all_6_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_46_1,
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (14797), (14844) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14849)  all_46_1 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1,
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              all_46_1, e3, e1, simplifying with (14844),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              (14847) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14850)  all_46_1 = all_6_1
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14849), (14850) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14851)  all_6_1 = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14848), (14851) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14852)  op(e0, e1) = all_6_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              all_6_0, e1, e0, simplifying with (157), (14852)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14853)  all_52_11 = all_6_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (14853) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14854)  all_54_14 = all_6_0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (14853) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14855)   ~ (all_52_3 = all_6_0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (14853) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14856)   ~ (all_52_9 = all_6_0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14318), (14853) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14857)   ~ (all_6_0 = e3)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14809), (14853) imply:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14858)   ~ (all_6_0 = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |   (14859)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (42), (45), (113), (159), (164), (167),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            (168), (190), (211), (234), (241), (14313),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            (14325), (14326), (14776), (14797), (14803),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            (14804), (14807), (14846), (14852), (14854),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            (14855), (14857), (14858), (14859),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |            #447.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |   (14860)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14860) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (14861)  all_58_8 = e2 & op(e1, e1) = e2
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14861) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (14862)  op(e1, e1) = e2
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14324), (14862), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (14863)  all_58_14 = e2 & op(e0, e1) = e2
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14863) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (14864)  all_58_14 = e2
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (165), (190), (228), (14324),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (14804), (14846), (14854), (14856), (14857),
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (14858), (14864), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #445.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |   (14865)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 &
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_6_1)
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14797), (14812), (14865), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #443.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14866)  all_58_9 = e0 & op(e3, e0) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (14866) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |   (14867)  op(e3, e0) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (14791), (14867), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2258.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | |   (14868)  all_58_7 = e0 & op(e1, e2) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (14767), (14868), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | |   (14869)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 236.59/44.55  | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.59/44.55  | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | BETA: splitting (14869) gives:
% 236.59/44.55  | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | |   (14870)  all_58_8 = e0 & op(e1, e1) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | ALPHA: (14870) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | |   (14871)  op(e1, e1) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (165), (169), (230), (14316), (14317),
% 236.59/44.55  | | | | | | | | | | | | | | | | | |            (14318), (14871), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1010.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | |   (14872)  all_58_11 = e0 & op(e1, e0) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | ALPHA: (14872) implies:
% 236.59/44.55  | | | | | | | | | | | | | | | | | |   (14873)  op(e1, e0) = e0
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14792), (14873), (function-axioms) are
% 236.59/44.55  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2323.
% 236.59/44.55  | | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | End of split
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | Case 2:
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | |   (14874)  all_20_2 = e1
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | COMBINE_EQS: (341), (14874) imply:
% 236.59/44.55  | | | | | | | | | | | | |   (14875)  all_4_2 = e1
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | SIMP: (14875) implies:
% 236.59/44.55  | | | | | | | | | | | | |   (14876)  all_4_2 = e1
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | COMBINE_EQS: (254), (14876) imply:
% 236.59/44.55  | | | | | | | | | | | | |   (14877)  all_56_31 = e1
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | REDUCE: (368), (14876) imply:
% 236.59/44.55  | | | | | | | | | | | | |   (14878)   ~ (all_52_3 = e1)
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | REDUCE: (379), (14876) imply:
% 236.59/44.55  | | | | | | | | | | | | |   (14879)   ~ (all_52_7 = e1)
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | REDUCE: (386), (14876) imply:
% 236.59/44.55  | | | | | | | | | | | | |   (14880)   ~ (all_52_11 = e1)
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | REDUCE: (388), (14876) imply:
% 236.59/44.55  | | | | | | | | | | | | |   (14881)   ~ (all_52_13 = e1)
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | REDUCE: (389), (14876) imply:
% 236.59/44.55  | | | | | | | | | | | | |   (14882)   ~ (all_52_14 = e1)
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | REDUCE: (390), (14876) imply:
% 236.59/44.55  | | | | | | | | | | | | |   (14883)   ~ (e2 = e1)
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | BETA: splitting (217) gives:
% 236.59/44.55  | | | | | | | | | | | | | 
% 236.59/44.55  | | | | | | | | | | | | | Case 1:
% 236.59/44.55  | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | |   (14884)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 236.59/44.56  | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 236.59/44.56  | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | BETA: splitting (14884) gives:
% 236.59/44.56  | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | |   (14885)  all_58_12 = e1 & op(e0, e3) = e1
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | REF_CLOSE: (159), (14878), (14885), (function-axioms) are
% 236.59/44.56  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | |   (14886)  all_58_13 = e1 & op(e0, e2) = e1
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | REF_CLOSE: (158), (14879), (14886), (function-axioms) are
% 236.59/44.56  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | |   (14887)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 236.59/44.56  | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.59/44.56  | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | BETA: splitting (14887) gives:
% 236.59/44.56  | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | |   (14888)  all_58_14 = e1 & op(e0, e1) = e1
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | ALPHA: (14888) implies:
% 236.59/44.56  | | | | | | | | | | | | | | |   (14889)  op(e0, e1) = e1
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | REF_CLOSE: (157), (14880), (14889), (function-axioms) are
% 236.59/44.56  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2272.
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | |   (14890)  all_58_15 = e1 & op(e0, e0) = e1
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | ALPHA: (14890) implies:
% 236.59/44.56  | | | | | | | | | | | | | | |   (14891)  all_58_15 = e1
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | |   (14892)   ~ (all_24_2 = e2)
% 236.59/44.56  | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | REDUCE: (301), (14892) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | |   (14893)   ~ (all_10_2 = e2)
% 236.59/44.56  | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | |   (14894)  all_54_0 = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (14894) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | | |   (14895)  all_10_2 = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | REDUCE: (355), (14895) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | | |   (14896)   ~ (all_52_1 = e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | REDUCE: (359), (14895) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | | |   (14897)   ~ (all_52_3 = e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | REDUCE: (361), (14895) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | | |   (14898)   ~ (all_52_4 = e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | REDUCE: (365), (14895) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | | |   (14899)   ~ (all_52_12 = e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | REDUCE: (45), (14895) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | | |   (14900)  op(e3, e3) = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | |   (14901)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | BETA: splitting (14901) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | |   (14902)  all_58_9 = e3 & op(e3, e0) = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | ALPHA: (14902) implies:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | |   (14903)  op(e3, e0) = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (14899), (14903), (function-axioms) are
% 236.59/44.56  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | |   (14904)  all_58_10 = e3 & op(e2, e0) = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | ALPHA: (14904) implies:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | |   (14905)  op(e2, e0) = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | |   (14906)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (170), (14325), (14898), (14906),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | |            #442.
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | |   (14907)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | BETA: splitting (14907) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | |   (14908)  all_58_7 = e3 & op(e1, e2) = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14908) implies:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | |   (14909)  op(e1, e2) = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (14315), (14909), (function-axioms) are
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | |   (14910)  all_58_13 = e3 & op(e0, e2) = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14910) implies:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | |   (14911)  op(e0, e2) = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |   (14912)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14912) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |   (14913)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (14313), (14314), (14896), (14913),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |            #441.
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |   (14914)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14914) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |   (14915)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14915) implies:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |   (14916)  op(e1, e3) = e1
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |   (14917)  op(e3, e1) = e1
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (67), (100), (113),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            (117), (123), (140), (141), (144), (145), (146),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            (148), (149), (157), (158), (159), (160), (162),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (168), (169), (170),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            (192), (197), (198), (200), (204), (213), (219),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            (221), (231), (232), (233), (234), (238), (257),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (279), (290), (292), (301), (355),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            (359), (361), (363), (365), (14311), (14312),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            (14313), (14315), (14316), (14317), (14318),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            (14324), (14778), (14877), (14881), (14891),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            (14916), (14917), (function-axioms) are
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #470.
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |   (14918)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14313), (14897), (14918),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            #482.
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |   (14919)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14919) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |   (14920)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14920) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |   (14921)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14921) implies:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |   (14922)   ~ (all_56_31 = e1)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14877), (14922) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |   (14923)  $false
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (14923) is inconsistent.
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |   (14924)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14924) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (14925)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14925) implies:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (14926)  op(e1, e2) = e1
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (14927)  op(e2, e1) = e1
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (14926) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (14928)  all_52_6 = e1
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (164), (14905) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (14929)  all_52_13 = e3
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (14927) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (14930)  all_52_9 = e1
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (14930) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (14931)   ~ (all_52_1 = e1)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (14928) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (14932)   ~ (all_52_2 = e1)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (14878), (14900),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |            (14931), (14932), (function-axioms) are
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (14933)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14933) implies:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (14934)  op(e0, e2) = e2
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14911), (14934), (function-axioms) are
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |   (14935)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (14770), (14877), (14882), (14935),
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | |            #1727.
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | |   (14936)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 236.59/44.56  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 236.59/44.56  | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (14319), (14891), (14936),
% 236.59/44.56  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.56  | | | | | | | | | | | | | | | | | |            #2058.
% 236.59/44.56  | | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | |   (14937)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (14326), (14778), (14893), (14937) are
% 236.59/44.56  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | End of split
% 236.59/44.56  | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | Case 2:
% 236.59/44.56  | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | |   (14938)  all_24_2 = e2
% 236.59/44.56  | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (14938) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | |   (14939)  all_10_2 = e2
% 236.59/44.56  | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (14939) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | |   (14940)  all_56_1 = e2
% 236.59/44.56  | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | REDUCE: (355), (14939) imply:
% 236.59/44.56  | | | | | | | | | | | | | | | |   (14941)   ~ (all_52_1 = e2)
% 236.59/44.56  | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.59/44.56  | | | | | | | | | | | | | | | | 
% 236.59/44.56  | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.56  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | |   (14942)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.59/44.57  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.57  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.59/44.57  | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.59/44.57  | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.57  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.57  | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.59/44.57  | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.59/44.57  | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.59/44.57  | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.59/44.57  | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.59/44.57  | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.59/44.57  | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | BETA: splitting (14942) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | |   (14943)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              = e3)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | BETA: splitting (14943) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14944)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            e3
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | ALPHA: (14944) implies:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14945)   ~ (all_56_1 = e2)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | REDUCE: (14940), (14945) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14946)  $false
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | CLOSE: (14946) is inconsistent.
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14947)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (14314), (14941), (14947),
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            #2334.
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | |   (14948)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              = e0)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | BETA: splitting (14948) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14949)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              e3) = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | ALPHA: (14949) implies:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14950)  op(e1, e3) = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14951)  op(e3, e1) = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (67), (100), (113),
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (117), (123), (140), (141), (144), (145), (146),
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (148), (149), (157), (158), (159), (160), (162),
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (168), (169), (170),
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (192), (197), (198), (200), (204), (213), (219),
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (221), (231), (232), (233), (234), (238), (257),
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (269), (270), (279), (290), (292), (301), (355),
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (359), (361), (363), (365), (14311), (14312),
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (14313), (14315), (14316), (14317), (14318),
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (14324), (14778), (14877), (14881), (14891),
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            (14950), (14951), (function-axioms) are
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #470.
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14952)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14313), (14765), (14952) are inconsistent by
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            sub-proof #439.
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | |   (14953)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.57  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.59/44.57  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.59/44.57  | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.59/44.57  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.59/44.57  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.59/44.57  | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.59/44.57  | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.59/44.57  | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.59/44.57  | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.59/44.57  | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.59/44.57  | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | BETA: splitting (14953) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | |   (14954)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              = e2)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | BETA: splitting (14954) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14955)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | ALPHA: (14955) implies:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14956)   ~ (all_56_31 = e1)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | REDUCE: (14877), (14956) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14957)  $false
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | CLOSE: (14957) is inconsistent.
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14958)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14765), (14940), (14958) are inconsistent by
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |            sub-proof #438.
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | |   (14959)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.59/44.57  | | | | | | | | | | | | | | | | | |              = e0)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (14770), (14877), (14882), (14959),
% 236.59/44.57  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.57  | | | | | | | | | | | | | | | | | |            #1727.
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | |   (14960)  all_16_2 = e0
% 236.59/44.57  | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | COMBINE_EQS: (342), (14960) imply:
% 236.59/44.57  | | | | | | | | | | | |   (14961)  all_10_2 = e0
% 236.59/44.57  | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | SIMP: (14961) implies:
% 236.59/44.57  | | | | | | | | | | | |   (14962)  all_10_2 = e0
% 236.59/44.57  | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | REDUCE: (355), (14962) imply:
% 236.59/44.57  | | | | | | | | | | | |   (14963)   ~ (all_52_1 = e0)
% 236.59/44.57  | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | REDUCE: (357), (14962) imply:
% 236.59/44.57  | | | | | | | | | | | |   (14964)   ~ (all_52_2 = e0)
% 236.59/44.57  | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | REDUCE: (363), (14962) imply:
% 236.59/44.57  | | | | | | | | | | | |   (14965)   ~ (all_52_8 = e0)
% 236.59/44.57  | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | REDUCE: (14326), (14962) imply:
% 236.59/44.57  | | | | | | | | | | | |   (14966)   ~ (e1 = e0)
% 236.59/44.57  | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | REDUCE: (45), (14962) imply:
% 236.59/44.57  | | | | | | | | | | | |   (14967)  op(e3, e3) = e0
% 236.59/44.57  | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | BETA: splitting (227) gives:
% 236.59/44.57  | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | |   (14968)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 236.59/44.57  | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 236.59/44.57  | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | BETA: splitting (14968) gives:
% 236.59/44.57  | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | |   (14969)  all_58_4 = e0 & op(e3, e1) = e0
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | REF_CLOSE: (169), (14965), (14969), (function-axioms) are
% 236.59/44.57  | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | |   (14970)  all_58_5 = e0 & op(e2, e1) = e0
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | REF_CLOSE: (165), (14769), (14970), (function-axioms) are
% 236.59/44.57  | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | |   (14971)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 236.59/44.57  | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.59/44.57  | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | BETA: splitting (14971) gives:
% 236.59/44.57  | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | |   (14972)  all_58_8 = e0 & op(e1, e1) = e0
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | ALPHA: (14972) implies:
% 236.59/44.57  | | | | | | | | | | | | | |   (14973)  op(e1, e1) = e0
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (165), (169), (230), (14316), (14317),
% 236.59/44.57  | | | | | | | | | | | | | |            (14318), (14973), (function-axioms) are
% 236.59/44.57  | | | | | | | | | | | | | |            inconsistent by sub-proof #1010.
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | |   (14974)  all_58_14 = e0 & op(e0, e1) = e0
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | ALPHA: (14974) implies:
% 236.59/44.57  | | | | | | | | | | | | | |   (14975)  all_58_14 = e0
% 236.59/44.57  | | | | | | | | | | | | | |   (14976)  op(e0, e1) = e0
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 236.59/44.57  | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | |   (14977)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 236.59/44.57  | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 236.59/44.57  | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (14767), (14964), (14977),
% 236.59/44.57  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.57  | | | | | | | | | | | | | | |            #2021.
% 236.59/44.57  | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | |   (14978)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 236.59/44.57  | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.59/44.57  | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | BETA: splitting (14978) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | |   (14979)  all_58_8 = e0 & op(e1, e1) = e0
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | ALPHA: (14979) implies:
% 236.59/44.57  | | | | | | | | | | | | | | | |   (14980)  op(e1, e1) = e0
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (229),
% 236.59/44.57  | | | | | | | | | | | | | | | |            (230), (14317), (14975), (14976), (14980),
% 236.59/44.57  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.57  | | | | | | | | | | | | | | | |            #437.
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | |   (14981)  all_58_11 = e0 & op(e1, e0) = e0
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | ALPHA: (14981) implies:
% 236.59/44.57  | | | | | | | | | | | | | | | |   (14982)  all_58_11 = e0
% 236.59/44.57  | | | | | | | | | | | | | | | |   (14983)  op(e1, e0) = e0
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.59/44.57  | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (157), (14976) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | |   (14984)  all_52_11 = e0
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 236.59/44.57  | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (14983) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | |   (14985)  all_52_14 = e0
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | REDUCE: (139), (14984) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | |   (14986)   ~ (all_52_3 = e0)
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | REDUCE: (112), (14985) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | |   (14987)   ~ (all_52_12 = e0)
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | REDUCE: (389), (14985) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | |   (14988)   ~ (all_4_2 = e0)
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | SIMP: (14988) implies:
% 236.59/44.57  | | | | | | | | | | | | | | | |   (14989)   ~ (all_4_2 = e0)
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | |   (14990)  all_54_15 = e3
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (14328), (14990) are inconsistent by
% 236.59/44.57  | | | | | | | | | | | | | | | | |            sub-proof #2340.
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | |   (14991)   ~ (all_54_15 = e3)
% 236.59/44.57  | | | | | | | | | | | | | | | | |   (14992)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | BETA: splitting (14992) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | |   (14993)  all_54_15 = e2
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (390), (14993) are inconsistent by
% 236.59/44.57  | | | | | | | | | | | | | | | | | |            sub-proof #2339.
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | |   (14994)  all_54_15 = e1 | all_54_15 = e0
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | BETA: splitting (14994) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14995)  all_54_15 = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (14995) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14996)  all_4_2 = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | SIMP: (14996) implies:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14997)  all_4_2 = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (14997) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14998)  all_56_31 = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | REDUCE: (368), (14997) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (14999)   ~ (all_52_3 = e1)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | REDUCE: (379), (14997) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (15000)   ~ (all_52_7 = e1)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | REDUCE: (387), (14997) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (15001)   ~ (all_52_12 = e1)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | REDUCE: (388), (14997) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (15002)   ~ (all_52_13 = e1)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | REDUCE: (14328), (14997) imply:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | |   (15003)   ~ (e3 = e1)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | |   (15004)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | BETA: splitting (15004) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | |   (15005)  all_58_9 = e1 & op(e3, e0) = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (15001), (15005), (function-axioms) are
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | |   (15006)  all_58_10 = e1 & op(e2, e0) = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (15002), (15006), (function-axioms) are
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | |   (15007)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | BETA: splitting (15007) gives:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | |   (15008)  all_58_11 = e1 & op(e1, e0) = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | ALPHA: (15008) implies:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | |   (15009)  op(e1, e0) = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14983), (15009), (function-axioms) are
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2284.
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | |   (15010)  all_58_15 = e1 & op(e0, e0) = e1
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | | ALPHA: (15010) implies:
% 236.59/44.57  | | | | | | | | | | | | | | | | | | | | |   (15011)  all_58_15 = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | |   (15012)  op(e0, e0) = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | |   (15013)  all_54_9 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (14315), (15013) are inconsistent by
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | |   (15014)   ~ (all_54_9 = e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | |   (15015)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | |   (15016)  all_54_8 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14314), (15016) are inconsistent by
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | |   (15017)   ~ (all_54_8 = e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | |   (15018)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | |   (15019)  all_54_2 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (14316), (15019) are inconsistent by
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | |   (15020)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (15021)  all_54_7 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (15021) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (15022)  all_52_13 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15022) implies:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (15023)  all_52_13 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (15023) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (15024)   ~ (all_52_1 = e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (15023) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (15025)   ~ (all_52_12 = e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (15023) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (15026)  op(e2, e0) = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15027)  all_54_3 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (15027) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15028)  all_52_12 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15025), (15028) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15029)  $false
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15029) is inconsistent.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15030)   ~ (all_54_3 = e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15031)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15031) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15032)  all_54_3 = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (15032) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15033)  all_52_12 = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (15033) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15034)   ~ (all_52_8 = e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15025), (15033) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15035)   ~ (e3 = e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (15033) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15036)  op(e3, e0) = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15037)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15037) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15038)  all_58_4 = e2 & op(e3, e1) = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15038) implies:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15039)  all_58_4 = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15020) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15040)  all_54_2 = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (15034), (15040) are inconsistent by
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1986.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15041)  all_54_2 = e1 | all_54_2 = e0
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (134), (168), (170), (242), (281),
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14965), (14967), (15001), (15039), (15041),
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1526.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15042)  all_58_5 = e2 & op(e2, e1) = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15042) implies:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15043)  all_58_5 = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15044)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15044) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15045)  all_58_2 = e1 & op(e2, e3) = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15045) implies:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15046)  op(e2, e3) = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15047)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15047) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15048)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (167), (14314), (15024), (15046),
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15048), (function-axioms) are inconsistent by
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #436.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15049)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (159), (14313), (14986), (15036), (15049),
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #461.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15050)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15050) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15051)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15051) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15052)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15052) implies:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15053)   ~ (all_56_31 = e1)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14998), (15053) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15054)  $false
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15054) is inconsistent.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15055)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15055) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15056)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15056) implies:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15057)  op(e2, e1) = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (165), (281), (14965), (15020), (15034),
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15057), (function-axioms) are inconsistent by
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #434.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15058)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15058) implies:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15059)  op(e2, e0) = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (15026), (15059), (function-axioms) are
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15060)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (14770), (14983), (14998), (15060),
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1613.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15061)  all_58_3 = e1 & op(e2, e2) = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14775), (15061) are inconsistent by
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1752.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15062)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15062) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15063)  all_58_5 = e1 & op(e2, e1) = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15043), (15063) are inconsistent by
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1548.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15064)  all_58_10 = e1 & op(e2, e0) = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15064) implies:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15065)  all_58_10 = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (222), (14982), (15011), (15036),
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15065), (function-axioms) are inconsistent by
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1599.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15066)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (14324), (14976), (15066),
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #433.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15067)  all_54_3 = e1 | all_54_3 = e0
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (14987), (15001), (15067) are inconsistent
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2287.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (15068)   ~ (all_54_7 = e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (15069)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (15068) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (15070)   ~ (all_52_13 = e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15071)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15071) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15072)  all_58_9 = e3 & op(e3, e0) = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15072) implies:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15073)  all_58_9 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15069) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15074)  all_54_7 = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (15074) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15075)  all_52_13 = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (15075) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15076)   ~ (all_52_1 = e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (15075) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15077)   ~ (all_52_9 = e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (15075) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15078)   ~ (all_52_12 = e2)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (15075) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15079)  op(e2, e0) = e2
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15080)  all_54_3 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (15080) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15081)  all_52_12 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (15081) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15082)   ~ (all_52_4 = e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (15081) imply:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15083)  op(e3, e0) = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15084)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15084) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15085)  all_58_2 = e3 & op(e2, e3) = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15085) implies:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15086)  all_58_2 = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15087)  op(e2, e3) = e3
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15088)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15088) gives:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15089)  all_58_2 = e1 & op(e2, e3) = e1
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (164), (216), (222), (15011),
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15012), (15070), (15073), (15079), (15086),
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15089), (function-axioms) are inconsistent by
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #432.
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15090)  all_58_3 = e1 & op(e2, e2) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14775), (15090) are inconsistent by
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1752.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15091)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15091) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15092)  all_58_5 = e1 & op(e2, e1) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15092) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15093)  all_58_5 = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15094)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15094) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15095)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (163), (170), (14314), (15082), (15087),
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15095), (function-axioms) are inconsistent by
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1429.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15096)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15096) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15097)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15097) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15098)  op(e1, e3) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15099)  op(e3, e1) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (146), (149), (163), (169), (198), (200),
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (279), (14769), (14963), (15076), (15077),
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15098), (15099), (function-axioms) are
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1789.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15100)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14765), (14986), (15100),
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1617.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15101)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15101) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15102)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15102) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15103)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15103) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15104)  op(e2, e1) = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (15077), (15104), (function-axioms) are
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15105)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15105) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15106)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15106) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15107)   ~ (all_56_31 = e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15108)   ~ (all_56_21 = e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15109)   ~ (all_56_11 = e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15110)  op(e1, e2) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15111)  op(e2, e1) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14765), (15109) imply:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15112)   ~ (e2 = e0)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14998), (15107) imply:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15113)   ~ (e2 = e1)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15114)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15114) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15115)  all_58_4 = e2 & op(e3, e1) = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15115) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15116)  all_58_4 = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15117)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15117) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15118)  all_58_0 = e1 & op(e3, e3) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15118) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15119)  op(e3, e3) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14967), (15119), (function-axioms) are
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15120)  all_58_2 = e1 & op(e2, e3) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (164), (216), (222), (15011),
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15012), (15070), (15073), (15079), (15086),
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15120), (function-axioms) are inconsistent by
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #432.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15121)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15121) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15122)  all_58_6 = e1 & op(e1, e3) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15122) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15123)  op(e1, e3) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15124)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15124) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15125)  all_58_6 = e2 & op(e1, e3) = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15125) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15126)  op(e1, e3) = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15123), (15126), (function-axioms) are
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15127)  all_58_7 = e2 & op(e1, e2) = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15127) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15128)  all_58_7 = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15129)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (170), (14325), (15082), (15129),
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #442.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15130)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15130) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15131)  all_58_7 = e3 & op(e1, e2) = e3
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15131) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15132)  op(e1, e2) = e3
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15110), (15132), (function-axioms) are
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2094.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15133)  all_58_13 = e3 & op(e0, e2) = e3
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15133) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15134)  op(e0, e2) = e3
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15135)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15135) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15136)  all_58_1 = e1 & op(e3, e2) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15136) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15137)  all_58_1 = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15015) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15138)  all_54_9 = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (15138) imply:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15139)  all_52_6 = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (15139) imply:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15140)   ~ (all_52_2 = e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14315), (15139) imply:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15141)   ~ (e3 = e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (15139) imply:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15142)  op(e1, e2) = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15018) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15143)  all_54_8 = e2
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (15140), (15143) are inconsistent by
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2007.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15144)   ~ (all_54_8 = e2)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15145)  all_54_8 = e1 | all_54_8 = e0
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15145) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15146)  all_54_8 = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (15146) imply:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15147)  all_52_2 = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15147) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15148)  all_52_2 = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e2,
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (15110), (15142) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15149)  e2 = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15116), (15149) imply:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15150)  all_58_4 = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (15082), (15083), (15137), (15150),
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1437.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15151)  all_54_8 = e0
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14964), (15151) are inconsistent by
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2006.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15152)  all_54_9 = e1 | all_54_9 = e0
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (163), (267), (14767), (15123), (15152),
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1931.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15153)  all_58_3 = e1 & op(e2, e2) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14775), (15153) are inconsistent by
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1591.
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15154)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15154) gives:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15155)  all_58_7 = e1 & op(e1, e2) = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15155) implies:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15156)  all_58_7 = e1
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15128), (15156) imply:
% 236.59/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15157)  e2 = e1
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15157) implies:
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15158)  e2 = e1
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15116), (15158) imply:
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15159)  all_58_4 = e1
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15160)  all_58_15 = e0 & op(e0, e0) = e0
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15160) implies:
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15161)  op(e0, e0) = e0
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15012), (15161), (function-axioms) are
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15162)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15162) implies:
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15163)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 236.72/44.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (159), (165), (229), (14324),
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14986), (15077), (15134), (15159), (15163),
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #431.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15164)  all_58_13 = e1 & op(e0, e2) = e1
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (15000), (15164), (function-axioms) are
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15165)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15165) gives:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15166)  all_58_8 = e2 & op(e1, e1) = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15166) implies:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15167)  op(e1, e1) = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (165), (227), (230),
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15093), (15111), (15116), (15167),
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2161.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15168)  all_58_11 = e2 & op(e1, e0) = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15168) implies:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15169)  op(e1, e0) = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14983), (15169), (function-axioms) are
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #478.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15170)  all_58_12 = e1 & op(e0, e3) = e1
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14999), (15170), (function-axioms) are
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15171)  all_58_5 = e2 & op(e2, e1) = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15171) implies:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15172)  op(e2, e1) = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (15077), (15172), (function-axioms) are
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15173)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (14324), (14976), (15173),
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #433.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15174)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15174) implies:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15175)   ~ (all_56_11 = e0)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14765), (15175) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15176)  $false
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15176) is inconsistent.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15177)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (14983), (14998), (15079), (15177),
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1596.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15178)  all_58_10 = e1 & op(e2, e0) = e1
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15178) implies:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15179)  all_58_10 = e1
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (221), (222), (14982),
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15011), (15179), (function-axioms) are
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1597.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15180)  all_58_3 = e3 & op(e2, e2) = e3
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (14325), (15180), (function-axioms) are
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #450.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15181)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15181) gives:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15182)  all_58_5 = e3 & op(e2, e1) = e3
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14317), (15182), (function-axioms) are
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15183)  all_58_10 = e3 & op(e2, e0) = e3
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15183) implies:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15184)  op(e2, e0) = e3
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (15079), (15184), (function-axioms) are
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15185)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (14987), (15001), (15078), (15185) are
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15186)  all_54_7 = e1 | all_54_7 = e0
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (14770), (15002), (15186) are inconsistent
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2293.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15187)  all_58_10 = e3 & op(e2, e0) = e3
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15187) implies:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15188)  op(e2, e0) = e3
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (15070), (15188), (function-axioms) are
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15189)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15189) gives:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15190)  all_58_11 = e3 & op(e1, e0) = e3
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15190) implies:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15191)  op(e1, e0) = e3
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14319), (15191), (function-axioms) are
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2149.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15192)  all_58_15 = e3 & op(e0, e0) = e3
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15011), (15192) are inconsistent by
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1915.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | |   (15193)  all_54_15 = e0
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (14989), (15193) are inconsistent by
% 236.72/44.60  | | | | | | | | | | | | | | | | | | |            sub-proof #1737.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | |   (15194)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 236.72/44.60  | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | REF_CLOSE: (158), (162), (14767), (14768), (15194),
% 236.72/44.60  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.60  | | | | | | | | | |            #1990.
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | | 
% 236.72/44.60  | | | | | | | | End of split
% 236.72/44.60  | | | | | | | | 
% 236.72/44.60  | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | 
% 236.72/44.60  | | | | | | | |   (15195)  all_12_2 = e3
% 236.72/44.60  | | | | | | | |   (15196)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 &
% 236.72/44.60  | | | | | | | |              op(e0, e3) = all_12_1 & $i(all_12_0) &
% 236.72/44.60  | | | | | | | |              $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 236.72/44.60  | | | | | | | |              all_12_1 & $i(all_12_1))
% 236.72/44.60  | | | | | | | | 
% 236.72/44.60  | | | | | | | | COMBINE_EQS: (346), (15195) imply:
% 236.72/44.60  | | | | | | | |   (15197)  all_4_2 = e3
% 236.72/44.60  | | | | | | | | 
% 236.72/44.60  | | | | | | | | COMBINE_EQS: (334), (15197) imply:
% 236.72/44.60  | | | | | | | |   (15198)  all_26_2 = e3
% 236.72/44.60  | | | | | | | | 
% 236.72/44.60  | | | | | | | | COMBINE_EQS: (254), (15197) imply:
% 236.72/44.60  | | | | | | | |   (15199)  all_56_31 = e3
% 236.72/44.60  | | | | | | | | 
% 236.72/44.60  | | | | | | | | REDUCE: (379), (15197) imply:
% 236.72/44.60  | | | | | | | |   (15200)   ~ (all_52_7 = e3)
% 236.72/44.60  | | | | | | | | 
% 236.72/44.60  | | | | | | | | REDUCE: (387), (15197) imply:
% 236.72/44.60  | | | | | | | |   (15201)   ~ (all_52_12 = e3)
% 236.72/44.60  | | | | | | | | 
% 236.72/44.60  | | | | | | | | REDUCE: (388), (15197) imply:
% 236.72/44.60  | | | | | | | |   (15202)   ~ (all_52_13 = e3)
% 236.72/44.60  | | | | | | | | 
% 236.72/44.60  | | | | | | | | BETA: splitting (222) gives:
% 236.72/44.60  | | | | | | | | 
% 236.72/44.60  | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | 
% 236.72/44.60  | | | | | | | | |   (15203)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3
% 236.72/44.60  | | | | | | | | |              & op(e2, e0) = e3)
% 236.72/44.60  | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | REF_CLOSE: (164), (168), (15201), (15202), (15203),
% 236.72/44.60  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.60  | | | | | | | | |            #1592.
% 236.72/44.60  | | | | | | | | | 
% 236.72/44.60  | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | 
% 236.72/44.60  | | | | | | | | |   (15204)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 236.72/44.60  | | | | | | | | |              e3 & op(e0, e0) = e3)
% 236.72/44.60  | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | BETA: splitting (15204) gives:
% 236.72/44.60  | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | |   (15205)  all_58_11 = e3 & op(e1, e0) = e3
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | ALPHA: (15205) implies:
% 236.72/44.60  | | | | | | | | | |   (15206)  op(e1, e0) = e3
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | REF_CLOSE: (160), (14319), (15206), (function-axioms) are
% 236.72/44.60  | | | | | | | | | |            inconsistent by sub-proof #2149.
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | |   (15207)  all_58_15 = e3 & op(e0, e0) = e3
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | ALPHA: (15207) implies:
% 236.72/44.60  | | | | | | | | | |   (15208)  all_58_15 = e3
% 236.72/44.60  | | | | | | | | | |   (15209)  op(e0, e0) = e3
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | BETA: splitting (234) gives:
% 236.72/44.60  | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | |   (15210)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 236.72/44.60  | | | | | | | | | | |              & op(e2, e2) = e3)
% 236.72/44.60  | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | BETA: splitting (15210) gives:
% 236.72/44.60  | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | |   (15211)  all_58_2 = e3 & op(e2, e3) = e3
% 236.72/44.60  | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | ALPHA: (15211) implies:
% 236.72/44.60  | | | | | | | | | | | |   (15212)  all_58_2 = e3
% 236.72/44.60  | | | | | | | | | | | |   (15213)  op(e2, e3) = e3
% 236.72/44.60  | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | BETA: splitting (238) gives:
% 236.72/44.60  | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | |   (15214)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 236.72/44.60  | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 236.72/44.60  | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | BETA: splitting (15214) gives:
% 236.72/44.60  | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | |   (15215)  all_58_1 = e3 & op(e3, e2) = e3
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | ALPHA: (15215) implies:
% 236.72/44.60  | | | | | | | | | | | | | |   (15216)  all_58_1 = e3
% 236.72/44.60  | | | | | | | | | | | | | |   (15217)  op(e3, e2) = e3
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 236.72/44.60  | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (15213) gives:
% 236.72/44.60  | | | | | | | | | | | | | |   (15218)  all_52_1 = e3
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 236.72/44.60  | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (15217) gives:
% 236.72/44.60  | | | | | | | | | | | | | |   (15219)  all_52_4 = e3
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | REDUCE: (149), (15218) imply:
% 236.72/44.60  | | | | | | | | | | | | | |   (15220)   ~ (all_52_2 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | REDUCE: (148), (15218) imply:
% 236.72/44.60  | | | | | | | | | | | | | |   (15221)   ~ (all_52_3 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | SIMP: (15221) implies:
% 236.72/44.60  | | | | | | | | | | | | | |   (15222)   ~ (all_52_3 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | REDUCE: (146), (15218) imply:
% 236.72/44.60  | | | | | | | | | | | | | |   (15223)   ~ (all_52_9 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | REDUCE: (145), (15218) imply:
% 236.72/44.60  | | | | | | | | | | | | | |   (15224)   ~ (all_52_13 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | REDUCE: (136), (15219) imply:
% 236.72/44.60  | | | | | | | | | | | | | |   (15225)   ~ (all_52_6 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | REDUCE: (135), (15219) imply:
% 236.72/44.60  | | | | | | | | | | | | | |   (15226)   ~ (all_52_7 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | REDUCE: (134), (15219) imply:
% 236.72/44.60  | | | | | | | | | | | | | |   (15227)   ~ (all_52_8 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | REDUCE: (133), (15219) imply:
% 236.72/44.60  | | | | | | | | | | | | | |   (15228)   ~ (all_52_12 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | REDUCE: (361), (15219) imply:
% 236.72/44.60  | | | | | | | | | | | | | |   (15229)   ~ (all_10_2 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | SIMP: (15229) implies:
% 236.72/44.60  | | | | | | | | | | | | | |   (15230)   ~ (all_10_2 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | REDUCE: (369), (15219) imply:
% 236.72/44.60  | | | | | | | | | | | | | |   (15231)   ~ (all_8_2 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 236.72/44.60  | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | |   (15232)   ~ (all_14_2 = e0)
% 236.72/44.60  | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | REDUCE: (344), (15232) imply:
% 236.72/44.60  | | | | | | | | | | | | | | |   (15233)   ~ (all_8_2 = e0)
% 236.72/44.60  | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 236.72/44.60  | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | |   (15234)   ~ (all_16_2 = e0)
% 236.72/44.60  | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | REDUCE: (342), (15234) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | |   (15235)   ~ (all_10_2 = e0)
% 236.72/44.60  | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 236.72/44.60  | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | |   (15236)  all_54_0 = e3
% 236.72/44.60  | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (15236) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | |   (15237)  all_10_2 = e3
% 236.72/44.60  | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | REDUCE: (15230), (15237) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | |   (15238)  $false
% 236.72/44.60  | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | CLOSE: (15238) is inconsistent.
% 236.72/44.60  | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | |   (15239)   ~ (all_54_0 = e3)
% 236.72/44.60  | | | | | | | | | | | | | | | | |   (15240)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 236.72/44.60  | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | BETA: splitting (15240) gives:
% 236.72/44.60  | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | |   (15241)  all_54_0 = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (15241) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | | |   (15242)  all_10_2 = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (15242) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | | |   (15243)  all_24_2 = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (15242) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | | |   (15244)  all_32_2 = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (15242) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | | |   (15245)  all_56_1 = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | REDUCE: (359), (15242) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | | |   (15246)   ~ (all_52_3 = e2)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | REDUCE: (365), (15242) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | | |   (15247)   ~ (all_52_12 = e2)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | REDUCE: (15230), (15242) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | | |   (15248)   ~ (e3 = e2)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | REDUCE: (45), (15242) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | | |   (15249)  op(e3, e3) = e2
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | |   (15250)   ~ (all_24_2 = e2)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | REDUCE: (15243), (15250) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | |   (15251)  $false
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | CLOSE: (15251) is inconsistent.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | |   (15252)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 236.72/44.60  | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 236.72/44.60  | | | | | | | | | | | | | | | | | | |              $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | |              = all_24_1 & $i(all_24_1))
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | BETA: splitting (15252) gives:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | |   (15253)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_24_1 & $i(all_24_0) &
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | ALPHA: (15253) implies:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | |   (15254)   ~ (all_24_0 = e0)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | |   (15255)  op(e3, e2) = all_24_1
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | |   (15256)  op(all_24_1, e3) = all_24_0
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | |   (15257)   ~ (all_32_2 = e2)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | REDUCE: (15244), (15257) imply:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | |   (15258)  $false
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | CLOSE: (15258) is inconsistent.
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | |   (15259)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 236.72/44.60  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_24_1,
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15255) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | |   (15260)  all_24_1 = e3
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | REDUCE: (15256), (15260) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | |   (15261)  op(e3, e3) = all_24_0
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15259) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15262)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_32_1 & $i(all_32_0) &
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15262) implies:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15263)   ~ (all_32_0 = e1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15264)  op(e3, e2) = all_32_1
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15265)  op(all_32_1, e3) = all_32_0
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15264) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15266)  all_32_1 = e3
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_24_0,
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (15249), (15261) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15267)  all_24_0 = e2
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15265), (15266) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15268)  op(e3, e3) = all_32_0
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_32_0,
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (15249), (15268) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15269)  all_32_0 = e2
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |   (15270)   ~ (all_22_2 = e1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (326), (15270) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |   (15271)   ~ (all_8_2 = e1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (125), (157), (158), (159), (160), (163),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (168), (199), (213), (218), (221),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (275), (353), (373), (377), (14314), (14319),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (14325), (15199), (15209), (15217), (15222),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (15233), (15246), (15247), (15271),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            #429.
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |   (15272)  all_22_2 = e1
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |   (15273)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = all_22_1 & $i(all_22_0) &
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |              = all_22_1 & $i(all_22_1))
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (42), (70), (76), (100),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (110), (158), (159), (160), (162), (163), (164),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (165), (168), (169), (210), (213), (216), (217),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (221), (222), (223), (224), (225),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (231), (233), (235),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (239), (240), (241), (242), (245), (246), (326),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (347), (353), (373), (375), (377), (14312),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (14315), (14316), (14319), (14323), (14324),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (14325), (15196), (15198), (15199), (15201),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (15202), (15208), (15209), (15212), (15213),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (15216), (15217), (15222), (15233), (15245),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (15246), (15247), (15249), (15272), (15273),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | |            #411.
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15274)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15274) implies:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15275)   ~ (all_32_1 = e0)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15276)  op(e3, e2) = all_32_1
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15276) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15277)  all_32_1 = e3
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_24_0,
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (15249), (15261) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15278)  all_24_0 = e2
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (42), (64), (70), (76), (100),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (110), (118), (125), (157), (158), (159), (160),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (165), (168), (169), (199),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (210), (213), (216), (217), (218), (220), (221),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (229), (231), (233), (235), (239), (240), (241),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (242), (245), (246), (275), (326), (347), (353),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (373), (375), (377), (14312), (14314), (14315),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (14316), (14319), (14323), (14324), (14325),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15196), (15198), (15199), (15201), (15202),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15208), (15209), (15212), (15213), (15216),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15217), (15222), (15233), (15245), (15246),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15247), (15249), (function-axioms) are
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #410.
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | |   (15279)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | ALPHA: (15279) implies:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | |   (15280)  op(e3, e2) = all_24_1
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | |   (15281)   ~ (all_32_2 = e2)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | REDUCE: (15244), (15281) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | |   (15282)  $false
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | CLOSE: (15282) is inconsistent.
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | |   (15283)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_24_1,
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15280) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | |   (15284)  all_24_1 = e3
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15283) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15285)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_32_1 & $i(all_32_0) &
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15285) implies:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15286)   ~ (all_32_0 = e1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15287)  op(e3, e2) = all_32_1
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15288)  op(all_32_1, e3) = all_32_0
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15287) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15289)  all_32_1 = e3
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15288), (15289) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15290)  op(e3, e3) = all_32_0
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_32_0,
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (15249), (15290) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15291)  all_32_0 = e2
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (42), (64), (70), (76), (100),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (110), (118), (125), (157), (158), (159), (160),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (165), (168), (169), (199),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (210), (213), (216), (217), (218), (220), (221),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (229), (231), (233), (235), (239), (240), (241),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (242), (245), (246), (275), (326), (347), (353),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (373), (375), (377), (14312), (14314), (14315),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (14316), (14319), (14323), (14324), (14325),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15196), (15198), (15199), (15201), (15202),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15208), (15209), (15212), (15213), (15216),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15217), (15222), (15233), (15245), (15246),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15247), (15249), (function-axioms) are
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #410.
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15292)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15292) implies:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15293)   ~ (all_32_1 = e0)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15294)  op(e3, e2) = all_32_1
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15294) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |   (15295)  all_32_1 = e3
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (42), (64), (70), (76), (100),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (110), (118), (125), (157), (158), (159), (160),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (165), (168), (169), (199),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (210), (213), (216), (217), (218), (220), (221),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (229), (231), (233), (235), (239), (240), (241),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (242), (245), (246), (275), (326), (347), (353),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (373), (375), (377), (14312), (14314), (14315),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (14316), (14319), (14323), (14324), (14325),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15196), (15198), (15199), (15201), (15202),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15208), (15209), (15212), (15213), (15216),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15217), (15222), (15233), (15245), (15246),
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            (15247), (15249), (function-axioms) are
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #410.
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | |   (15296)  all_54_0 = e1 | all_54_0 = e0
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (14326), (15235), (15296) are inconsistent
% 236.72/44.61  | | | | | | | | | | | | | | | | | |            by sub-proof #2320.
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | End of split
% 236.72/44.61  | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | End of split
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | Case 2:
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15297)  all_16_2 = e0
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15298)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0
% 236.72/44.61  | | | | | | | | | | | | | | | |              & op(e3, e0) = all_16_1 & $i(all_16_0) &
% 236.72/44.61  | | | | | | | | | | | | | | | |              $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0)
% 236.72/44.61  | | | | | | | | | | | | | | | |              = all_16_1 & $i(all_16_1))
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | COMBINE_EQS: (342), (15297) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15299)  all_10_2 = e0
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | SIMP: (15299) implies:
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15300)  all_10_2 = e0
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (15300) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15301)  all_50_2 = e0
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (15300) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15302)  all_56_1 = e0
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | REDUCE: (357), (15300) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15303)   ~ (all_52_2 = e0)
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | REDUCE: (359), (15300) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15304)   ~ (all_52_3 = e0)
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | REDUCE: (363), (15300) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15305)   ~ (all_52_8 = e0)
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | REDUCE: (365), (15300) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15306)   ~ (all_52_12 = e0)
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | REDUCE: (15230), (15300) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15307)   ~ (e3 = e0)
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | REDUCE: (45), (15300) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | |   (15308)  op(e3, e3) = e0
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.61  | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | |   (15309)   ~ (all_22_2 = e1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | REDUCE: (326), (15309) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | |   (15310)   ~ (all_8_2 = e1)
% 236.72/44.61  | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | |   (15311)  all_54_5 = e3
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (15311) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | |   (15312)  all_8_2 = e3
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | REDUCE: (14325), (15312) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | |   (15313)  $false
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | CLOSE: (15313) is inconsistent.
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | |   (15314)   ~ (all_54_5 = e3)
% 236.72/44.61  | | | | | | | | | | | | | | | | | |   (15315)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | BETA: splitting (15315) gives:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | |   (15316)  all_54_5 = e2
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (15316) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | |   (15317)  all_8_2 = e2
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (15317) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | |   (15318)  all_56_11 = e2
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (15317) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | |   (15319)   ~ (all_52_7 = e2)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | REDUCE: (375), (15317) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | |   (15320)   ~ (all_52_9 = e2)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | REDUCE: (14325), (15317) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | |   (15321)   ~ (e3 = e2)
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | REDUCE: (42), (15317) imply:
% 236.72/44.61  | | | | | | | | | | | | | | | | | | |   (15322)  op(e2, e2) = e2
% 236.72/44.61  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |   (15323)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (15323) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |   (15324)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (163), (14314), (15217), (15318), (15324),
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |            #430.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |   (15325)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (15199), (15222), (15304), (15325),
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |            #1368.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |   (15326)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (15326) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |   (15327)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              = e2)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (15318), (15319), (15320), (15327),
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |            #2325.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |   (15328)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15328) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |   (15329)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15329) implies:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |   (15330)   ~ (all_56_11 = e2)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15318), (15330) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |   (15331)  $false
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15331) is inconsistent.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |   (15332)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15332) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15333)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15333) implies:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15334)   ~ (all_56_1 = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15302), (15334) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15335)  $false
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15335) is inconsistent.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15336)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15336) implies:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15337)  op(e0, e1) = e0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15338)  op(e1, e0) = e0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (157), (15337) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15339)  all_52_11 = e0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (15338) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15340)  all_52_14 = e0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (15340) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15341)   ~ (all_52_6 = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (15339) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15342)   ~ (all_52_7 = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (158), (162), (235), (15217), (15322),
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |            (15341), (15342), (function-axioms) are
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #408.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | |   (15343)  all_54_5 = e1 | all_54_5 = e0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (15233), (15310), (15343) are inconsistent
% 236.72/44.62  | | | | | | | | | | | | | | | | | | |            by sub-proof #2300.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.62  | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | End of split
% 236.72/44.62  | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | |   (15344)  all_22_2 = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | |   (15345)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 236.72/44.62  | | | | | | | | | | | | | | | | |              & op(e2, e1) = all_22_1 & $i(all_22_0) &
% 236.72/44.62  | | | | | | | | | | | | | | | | |              $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | |              = all_22_1 & $i(all_22_1))
% 236.72/44.62  | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (15344) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | |   (15346)  all_8_2 = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (15346) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | |   (15347)  all_30_2 = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | REDUCE: (371), (15346) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | |   (15348)   ~ (all_52_6 = e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | REDUCE: (375), (15346) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | |   (15349)   ~ (all_52_9 = e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | REDUCE: (377), (15346) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | |   (15350)   ~ (all_52_13 = e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | REDUCE: (14325), (15346) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | |   (15351)   ~ (e3 = e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | REDUCE: (42), (15346) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | |   (15352)  op(e2, e2) = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | |   (15353)   ~ (all_26_2 = e3)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | REDUCE: (15198), (15353) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | | |   (15354)  $false
% 236.72/44.62  | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | CLOSE: (15354) is inconsistent.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | |   (15355)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 236.72/44.62  | | | | | | | | | | | | | | | | | |              & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 236.72/44.62  | | | | | | | | | | | | | | | | | |              $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 236.72/44.62  | | | | | | | | | | | | | | | | | |              = all_26_1 & $i(all_26_1))
% 236.72/44.62  | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | |   (15356)   ~ (all_30_2 = e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | REDUCE: (15347), (15356) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | |   (15357)  $false
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | CLOSE: (15357) is inconsistent.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | |   (15358)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = all_30_1 & $i(all_30_0) &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | |              $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | |              = all_30_1 & $i(all_30_1))
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |   (15359)   ~ (all_46_2 = e3)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | REDUCE: (14312), (15359) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |   (15360)  $false
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | CLOSE: (15360) is inconsistent.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |   (15361)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |   (15362)   ~ (all_50_2 = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | REDUCE: (15301), (15362) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |   (15363)  $false
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | CLOSE: (15363) is inconsistent.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |   (15364)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | |              = all_50_1 & $i(all_50_1))
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |   (15365)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (15201), (15213), (15302), (15365),
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |            #1511.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |   (15366)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15366) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15367)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15367) implies:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15368)  op(e1, e3) = all_56_5
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15369)  op(e1, all_56_5) = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (15368)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15370)  all_56_5 = all_52_2
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15369), (15370) imply:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | |   (15371)  op(e1, all_52_2) = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | |   (15372)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15372) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (15373)  all_58_9 = e1 & op(e3, e0) = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15373) implies:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (15374)  all_58_9 = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (15375)  op(e3, e0) = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15376)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (15217), (15308), (15376),
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1857.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15377)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15377) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15378)  all_58_4 = e2 & op(e3, e1) = e2
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15378) implies:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15379)  all_58_4 = e2
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15380)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (165), (15349), (15379), (15380),
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #407.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15381)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15381) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15382)  all_58_8 = e1 & op(e1, e1) = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14323), (15382) are inconsistent by
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #406.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15383)  all_58_14 = e1 & op(e0, e1) = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15383) implies:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15384)  op(e0, e1) = e1
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15385)  all_58_15 = e0 & op(e0, e0) = e0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15385) implies:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15386)  op(e0, e0) = e0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15209), (15386), (function-axioms) are
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15387)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15387) implies:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15388)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15389)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15389) gives:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15390)  all_58_4 = e0 & op(e3, e1) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (15305), (15390), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15391)  all_58_5 = e0 & op(e2, e1) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15391) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15392)  op(e2, e1) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15393)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (15213), (15352), (15393),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #428.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15394)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15394) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15395)  all_58_5 = e2 & op(e2, e1) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15395) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15396)  op(e2, e1) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15392), (15396), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15397)  all_58_10 = e2 & op(e2, e0) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15397) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15398)  op(e2, e0) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15388) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15399)  all_58_9 = e0 & op(e3, e0) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15399) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15400)  op(e3, e0) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (15306), (15400), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2258.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15401)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15401) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15402)  all_58_10 = e0 & op(e2, e0) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15402) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15403)  op(e2, e0) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15398), (15403), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15404)  all_58_11 = e0 & op(e1, e0) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15404) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15405)  op(e1, e0) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15406)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (14316), (15298), (15345), (15352),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15358), (15364), (15375), (15392), (15398),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15406), (function-axioms) are inconsistent by
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #404.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15407)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15407) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15408)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15298), (15364), (15375), (15405), (15408),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #402.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15409)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15409) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15410)  op(e0, all_56_31) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15199), (15410) imply:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15411)  op(e0, e3) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (15304), (15411), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15412)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (157), (165), (230), (14317),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14318), (15379), (15384), (15412),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #401.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15413)  all_58_9 = e2 & op(e3, e0) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15374), (15413) are inconsistent by
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1745.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (15414)  all_58_10 = e1 & op(e2, e0) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (15350), (15414), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | |   (15415)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15415) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (15416)  all_58_11 = e1 & op(e1, e0) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15416) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (15417)  op(e1, e0) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15418)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15418) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15419)  all_58_6 = e0 & op(e1, e3) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15419) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15420)  op(e1, e3) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (15303), (15420), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15421)  all_58_7 = e0 & op(e1, e2) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15421) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15422)  all_58_7 = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15423)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15423) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15424)  all_58_6 = e2 & op(e1, e3) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15424) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15425)  all_58_6 = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15426)  op(e1, e3) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (42), (157), (162),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (165), (169), (223), (230), (235), (237),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14316), (14317), (14318), (15217), (15233),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15348), (15352), (15371), (15417), (15425),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15426), (function-axioms) are inconsistent by
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #399.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15427)  all_58_7 = e2 & op(e1, e2) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15427) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15428)  all_58_7 = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15422), (15428) are inconsistent by
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1587.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15429)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (14324), (15417), (15429),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #398.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15430)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (157), (165), (169), (230), (14316),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (14317), (14318), (15417), (15430),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            #400.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (15431)  all_58_15 = e1 & op(e0, e0) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15208), (15431) are inconsistent by
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1393.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | |   (15432)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15432) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | |   (15433)  op(e0, e3) = all_56_7
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | |   (15434)  op(e0, all_56_7) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (159), (15433)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | |   (15435)  all_56_7 = all_52_3
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15434), (15435) imply:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | |   (15436)  op(e0, all_52_3) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | |   (15437)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (15217), (15308), (15437),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | |            #1571.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | |   (15438)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15438) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (15439)  all_58_4 = e1 & op(e3, e1) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15439) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (15440)  all_58_4 = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (15441)  op(e3, e1) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15442)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (15217), (15308), (15442),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1857.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15443)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15443) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15444)  all_58_4 = e2 & op(e3, e1) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15444) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15445)  all_58_4 = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15440), (15445) are inconsistent by
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1786.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15446)  all_58_9 = e2 & op(e3, e0) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15446) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15447)  op(e3, e0) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15448)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15448) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15449)  all_58_9 = e1 & op(e3, e0) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15449) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15450)  all_58_9 = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15451)  op(e3, e0) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (159), (165),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (210), (216), (227), (228), (230),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (244), (14316), (14317), (14318), (14323),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15199), (15208), (15209), (15213), (15217),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15298), (15305), (15306), (15308), (15345),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15349), (15352), (15358), (15364), (15436),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15450), (15451), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #397.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15452)  all_58_10 = e1 & op(e2, e0) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (15350), (15452), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15453)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15453) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15454)  all_58_11 = e1 & op(e1, e0) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15454) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15455)  op(e1, e0) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15456)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15456) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15457)  all_58_6 = e0 & op(e1, e3) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15457) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15458)  op(e1, e3) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (15303), (15458), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15459)  all_58_7 = e0 & op(e1, e2) = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15459) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15460)  all_58_7 = e0
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15461)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15461) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15462)  all_58_6 = e2 & op(e1, e3) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15462) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15463)  all_58_6 = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15464)  op(e1, e3) = e2
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15465)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15465) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15466)  all_58_0 = e1 & op(e3, e3) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15466) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15467)  op(e3, e3) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (157), (159), (162), (165), (169),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (230), (239), (14315), (14316), (14317),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14318), (15209), (15212), (15436), (15455),
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15463), (15467), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #396.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15468)  all_58_2 = e1 & op(e2, e3) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15212), (15468) are inconsistent by
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1765.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15469)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15469) gives:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15470)  all_58_6 = e1 & op(e1, e3) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15470) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15471)  op(e1, e3) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15464), (15471), (function-axioms) are
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15472)  all_58_12 = e1 & op(e0, e3) = e1
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15472) implies:
% 236.72/44.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15473)  all_58_12 = e1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15474)  op(e0, e3) = e1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15475)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (15217), (15352), (15475),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1785.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15476)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15476) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15477)  all_58_7 = e2 & op(e1, e2) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15477) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15478)  all_58_7 = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15460), (15478) are inconsistent by
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1587.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15479)  all_58_13 = e2 & op(e0, e2) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15479) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15480)  op(e0, e2) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15481)  all_58_15 = e0 & op(e0, e0) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15481) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15482)  op(e0, e0) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15209), (15482), (function-axioms) are
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15483)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15483) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15484)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15484) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15485)  all_58_12 = e0 & op(e0, e3) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15485) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15486)  op(e0, e3) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15196), (15355), (15474), (15486),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1384.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15487)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15487) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15488)  all_58_13 = e0 & op(e0, e2) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15488) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15489)  op(e0, e2) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15480), (15489), (function-axioms) are
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15490)  all_58_14 = e0 & op(e0, e1) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15490) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15491)  op(e0, e1) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15492)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15492) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15493)  all_58_4 = e2 & op(e3, e1) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15493) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15494)  all_58_4 = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15440), (15494) are inconsistent by
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1786.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15495)  all_58_5 = e2 & op(e2, e1) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15495) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15496)  op(e2, e1) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15497)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15497) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15498)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14316), (15361), (15441), (15464),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15498), (function-axioms) are inconsistent by
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #394.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15499)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15499) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15500)  op(e2, e1) = all_56_19
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15501)  op(e2, all_56_19) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15358) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15502)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_30_1 & $i(all_30_0) &
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15502) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15503)  op(e2, e1) = all_30_1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15345), (15352), (15364), (15447), (15496),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15500), (15501), (15503), (function-axioms) are
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #392.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15504)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15504) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15505)  op(e2, e1) = all_30_1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15345), (15352), (15364), (15447), (15496),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15500), (15501), (15505), (function-axioms) are
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #392.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15506)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15506) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15507)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15507) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15508)  op(e1, all_56_21) = e1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14313), (15508) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15509)  op(e1, e3) = e1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15464), (15509), (function-axioms) are
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15510)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15510) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15511)  op(e0, e1) = all_56_23
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15512)  op(e0, all_56_23) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15209), (15491), (15511), (15512),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1395.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15513)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15513) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15514)  all_58_8 = e2 & op(e1, e1) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15514) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15515)  op(e1, e1) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (223), (226), (15455),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15463), (15515), (function-axioms) are
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1835.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15516)  all_58_14 = e2 & op(e0, e1) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15516) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15517)  all_58_14 = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (158), (216), (219),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15200), (15473), (15480), (15517),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1536.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15518)  all_58_7 = e2 & op(e1, e2) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15518) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15519)  all_58_7 = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15460), (15519) are inconsistent by
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1587.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15520)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (14324), (15455), (15520),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #398.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15521)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (157), (165), (169), (230), (14316),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14317), (14318), (15455), (15521),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #400.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15522)  all_58_15 = e1 & op(e0, e0) = e1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15208), (15522) are inconsistent by
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1393.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (15523)  all_58_9 = e1 & op(e3, e0) = e1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15523) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (15524)  all_58_9 = e1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (15525)  op(e3, e0) = e1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (159), (165),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (210), (216), (227), (228), (230),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (244), (14316), (14317), (14318), (14323),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | |            (15199), (15208), (15209), (15213), (15217),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | |            (15298), (15305), (15306), (15308), (15345),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | |            (15349), (15352), (15358), (15364), (15436),
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | |            (15524), (15525), (function-axioms) are
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #397.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | End of split
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | |   (15526)  all_14_2 = e0
% 236.72/44.64  | | | | | | | | | | | | | | |   (15527)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0
% 236.72/44.64  | | | | | | | | | | | | | | |              & op(e2, e0) = all_14_1 & $i(all_14_0) &
% 236.72/44.64  | | | | | | | | | | | | | | |              $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0)
% 236.72/44.64  | | | | | | | | | | | | | | |              = all_14_1 & $i(all_14_1))
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | COMBINE_EQS: (344), (15526) imply:
% 236.72/44.64  | | | | | | | | | | | | | | |   (15528)  all_8_2 = e0
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | COMBINE_EQS: (311), (15528) imply:
% 236.72/44.64  | | | | | | | | | | | | | | |   (15529)  all_48_2 = e0
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | COMBINE_EQS: (353), (15528) imply:
% 236.72/44.64  | | | | | | | | | | | | | | |   (15530)  all_56_11 = e0
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | REDUCE: (371), (15528) imply:
% 236.72/44.64  | | | | | | | | | | | | | | |   (15531)   ~ (all_52_6 = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | REDUCE: (373), (15528) imply:
% 236.72/44.64  | | | | | | | | | | | | | | |   (15532)   ~ (all_52_7 = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | REDUCE: (375), (15528) imply:
% 236.72/44.64  | | | | | | | | | | | | | | |   (15533)   ~ (all_52_9 = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | REDUCE: (377), (15528) imply:
% 236.72/44.64  | | | | | | | | | | | | | | |   (15534)   ~ (all_52_13 = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | REDUCE: (14325), (15528) imply:
% 236.72/44.64  | | | | | | | | | | | | | | |   (15535)   ~ (e3 = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | |   (15536)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 236.72/44.64  | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | BETA: splitting (15536) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | |   (15537)  all_58_2 = e0 & op(e2, e3) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15212), (15537) are inconsistent by
% 236.72/44.64  | | | | | | | | | | | | | | | | |            sub-proof #1351.
% 236.72/44.64  | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | |   (15538)  all_58_3 = e0 & op(e2, e2) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | ALPHA: (15538) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | |   (15539)  all_58_3 = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | |   (15540)  op(e2, e2) = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | |   (15541)   ~ (all_16_2 = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | REDUCE: (342), (15541) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | |   (15542)   ~ (all_10_2 = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | |   (15543)  all_54_0 = e3
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (15543) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | |   (15544)  all_10_2 = e3
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | REDUCE: (15230), (15544) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | |   (15545)  $false
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | CLOSE: (15545) is inconsistent.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | |   (15546)   ~ (all_54_0 = e3)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | |   (15547)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | BETA: splitting (15547) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | |   (15548)  all_54_0 = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (15548) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | |   (15549)  all_10_2 = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (15549) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | |   (15550)  all_24_2 = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (15549) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | |   (15551)  all_32_2 = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (15549) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | |   (15552)  all_56_1 = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (15549) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | |   (15553)   ~ (all_52_12 = e2)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | REDUCE: (15230), (15549) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | |   (15554)   ~ (e3 = e2)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (15549) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | |   (15555)  op(e3, e3) = e2
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | |   (15556)   ~ (all_24_2 = e2)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | REDUCE: (15550), (15556) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | |   (15557)  $false
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | CLOSE: (15557) is inconsistent.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | |   (15558)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | |              $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | |              = all_24_1 & $i(all_24_1))
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15558) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | |   (15559)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_24_1 & $i(all_24_0) &
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15559) implies:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | |   (15560)   ~ (all_24_0 = e0)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | |   (15561)  op(e3, e2) = all_24_1
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | |   (15562)  op(all_24_1, e3) = all_24_0
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | |   (15563)   ~ (all_32_2 = e2)
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15551), (15563) imply:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | |   (15564)  $false
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15564) is inconsistent.
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |   (15565)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_24_1,
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15561) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |   (15566)  all_24_1 = e3
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15562), (15566) imply:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |   (15567)  op(e3, e3) = all_24_0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15565) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15568)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_32_1 & $i(all_32_0) &
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15568) implies:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15569)   ~ (all_32_0 = e1)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15570)  op(e3, e2) = all_32_1
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15571)  op(all_32_1, e3) = all_32_0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15570) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15572)  all_32_1 = e3
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_24_0,
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (15555), (15567) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15573)  all_24_0 = e2
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15571), (15572) imply:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15574)  op(e3, e3) = all_32_0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_32_0,
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (15555), (15574) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15575)  all_32_0 = e2
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (15576)   ~ (all_26_2 = e3)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15198), (15576) imply:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (15577)  $false
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15577) is inconsistent.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (15578)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_26_1 & $i(all_26_1))
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (100), (103), (157),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (159), (160), (162), (163), (164), (165),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (213), (216), (217), (218), (219),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (240), (241), (242), (246), (14311),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (14312), (14314), (14315), (14316), (14317),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (14318), (14319), (14324), (15196), (15199),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (15200), (15201), (15202), (15208), (15209),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (15212), (15213), (15216), (15217), (15222),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (15527), (15529), (15530), (15531), (15532),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (15539), (15540), (15552), (15553), (15555),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (15578), (function-axioms) are inconsistent by
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #382.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15579)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15579) implies:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15580)   ~ (all_32_1 = e0)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15581)  op(e3, e2) = all_32_1
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15581) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15582)  all_32_1 = e3
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_24_0,
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (15555), (15567) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15583)  all_24_0 = e2
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (70), (100), (103),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (157), (158), (159), (160), (162), (163), (164),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (165), (168), (169), (213), (216), (217), (218),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (219), (221), (222), (223), (224), (225), (226),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (227), (229), (230), (231), (232), (233), (234),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (235), (237), (238), (240), (241), (242), (246),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (14311), (14312), (14314), (14315), (14316),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (14317), (14318), (14319), (14324), (15196),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15198), (15199), (15200), (15201), (15202),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15208), (15209), (15212), (15213), (15216),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15217), (15222), (15527), (15529), (15530),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15531), (15532), (15539), (15540), (15552),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15553), (15555), (function-axioms) are
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #381.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | |   (15584)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15584) implies:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | |   (15585)   ~ (all_24_1 = e1)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | |   (15586)  op(e3, e2) = all_24_1
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |   (15587)   ~ (all_32_2 = e2)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15551), (15587) imply:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |   (15588)  $false
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15588) is inconsistent.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |   (15589)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_24_1,
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15586) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | |   (15590)  all_24_1 = e3
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15589) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15591)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_32_1 & $i(all_32_0) &
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15591) implies:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15592)   ~ (all_32_0 = e1)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15593)  op(e3, e2) = all_32_1
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15594)  op(all_32_1, e3) = all_32_0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15593) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15595)  all_32_1 = e3
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15594), (15595) imply:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15596)  op(e3, e3) = all_32_0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_32_0,
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (15555), (15596) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15597)  all_32_0 = e2
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (70), (100), (103),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (157), (158), (159), (160), (162), (163), (164),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (165), (168), (169), (213), (216), (217), (218),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (219), (221), (222), (223), (224), (225), (226),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (227), (229), (230), (231), (232), (233), (234),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (235), (237), (238), (240), (241), (242), (246),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (14311), (14312), (14314), (14315), (14316),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (14317), (14318), (14319), (14324), (15196),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15198), (15199), (15200), (15201), (15202),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15208), (15209), (15212), (15213), (15216),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15217), (15222), (15527), (15529), (15530),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15531), (15532), (15539), (15540), (15552),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15553), (15555), (function-axioms) are
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #381.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15598)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15598) implies:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15599)   ~ (all_32_1 = e0)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15600)  op(e3, e2) = all_32_1
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (15217), (15600) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |   (15601)  all_32_1 = e3
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (70), (100), (103),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (157), (158), (159), (160), (162), (163), (164),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (165), (168), (169), (213), (216), (217), (218),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (219), (221), (222), (223), (224), (225), (226),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (227), (229), (230), (231), (232), (233), (234),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (235), (237), (238), (240), (241), (242), (246),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (14311), (14312), (14314), (14315), (14316),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (14317), (14318), (14319), (14324), (15196),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15198), (15199), (15200), (15201), (15202),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15208), (15209), (15212), (15213), (15216),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15217), (15222), (15527), (15529), (15530),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15531), (15532), (15539), (15540), (15552),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            (15553), (15555), (function-axioms) are
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #381.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |   (15602)  all_54_0 = e1 | all_54_0 = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (14326), (15542), (15602) are inconsistent
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |            by sub-proof #2320.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.65  | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | |   (15603)  all_16_2 = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (342), (15603) imply:
% 236.72/44.65  | | | | | | | | | | | | | | | | | |   (15604)  all_10_2 = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | SIMP: (15604) implies:
% 236.72/44.65  | | | | | | | | | | | | | | | | | |   (15605)  all_10_2 = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (15605) imply:
% 236.72/44.65  | | | | | | | | | | | | | | | | | |   (15606)  all_56_1 = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | REDUCE: (357), (15605) imply:
% 236.72/44.65  | | | | | | | | | | | | | | | | | |   (15607)   ~ (all_52_2 = e0)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | REDUCE: (363), (15605) imply:
% 236.72/44.65  | | | | | | | | | | | | | | | | | |   (15608)   ~ (all_52_8 = e0)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | REDUCE: (14326), (15605) imply:
% 236.72/44.65  | | | | | | | | | | | | | | | | | |   (15609)   ~ (e1 = e0)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | REDUCE: (45), (15605) imply:
% 236.72/44.65  | | | | | | | | | | | | | | | | | |   (15610)  op(e3, e3) = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | |   (15611)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | BETA: splitting (15611) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |   (15612)  all_58_4 = e0 & op(e3, e1) = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (15608), (15612), (function-axioms) are
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |   (15613)  all_58_5 = e0 & op(e2, e1) = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (15533), (15613), (function-axioms) are
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | End of split
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | |   (15614)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 236.72/44.65  | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | BETA: splitting (15614) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |   (15615)  all_58_8 = e0 & op(e1, e1) = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | ALPHA: (15615) implies:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |   (15616)  op(e1, e1) = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (165), (169), (230), (14316), (14317),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |            (14318), (15616), (function-axioms) are
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1010.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |   (15617)  all_58_14 = e0 & op(e0, e1) = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | ALPHA: (15617) implies:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |   (15618)  all_58_14 = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | |   (15619)  op(e0, e1) = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | |   (15620)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (15531), (15607), (15620),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | |            #2021.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | |   (15621)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15621) gives:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | |   (15622)  all_58_8 = e0 & op(e1, e1) = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15622) implies:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | |   (15623)  op(e1, e1) = e0
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (229),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | |            (230), (14317), (15618), (15619), (15623),
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | |            #437.
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.65  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | |   (15624)  all_58_11 = e0 & op(e1, e0) = e0
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15624) implies:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | |   (15625)  op(e1, e0) = e0
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |   (15626)  all_58_15 = e0 & op(e0, e0) = e0
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15626) implies:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |   (15627)  op(e0, e0) = e0
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15209), (15627), (function-axioms) are
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |   (15628)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15628) implies:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |   (15629)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (157), (15619) gives:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |   (15630)  all_52_11 = e0
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (15625) gives:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |   (15631)  all_52_14 = e0
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (15630) imply:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |   (15632)   ~ (all_52_3 = e0)
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (15631) imply:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | |   (15633)   ~ (all_52_12 = e0)
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | |   (15634)   ~ (all_26_2 = e3)
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15198), (15634) imply:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | |   (15635)  $false
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15635) is inconsistent.
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | |   (15636)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | |              = all_26_1 & $i(all_26_1))
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (15637)   ~ (all_46_2 = e3)
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14312), (15637) imply:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (15638)  $false
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15638) is inconsistent.
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (15639)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15640)   ~ (all_48_2 = e0)
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15529), (15640) imply:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15641)  $false
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15641) is inconsistent.
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15642)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_48_1 & $i(all_48_1))
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.72/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15643)  all_54_3 = e3
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (15201), (15643) are inconsistent by
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15644)   ~ (all_54_3 = e3)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15645)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15646)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (15201), (15213), (15606), (15646),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1511.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15647)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15647) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15648)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15648) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15649)  op(e1, e3) = all_56_5
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15650)  op(e1, all_56_5) = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (15649)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15651)  all_56_5 = all_52_2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15650), (15651) imply:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15652)  op(e1, all_52_2) = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15653)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15653) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15654)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15654) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15655)  op(e3, e0) = all_56_25
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15656)  op(e3, all_56_25) = e3
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25, e0, e3, simplifying with (168), (15655)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15657)  all_56_25 = all_52_12
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15656), (15657) imply:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15658)  op(e3, all_52_12) = e3
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15659)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (15213), (15610), (15659),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1824.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15660)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15660) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15661)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15661) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15662)  op(e1, e3) = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15663)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (15212), (15610), (15663),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1486.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15664)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15664) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15665)  all_58_6 = e1 & op(e1, e3) = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15665) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15666)  op(e1, e3) = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15662), (15666), (function-axioms) are
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15667)  all_58_12 = e1 & op(e0, e3) = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15667) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15668)  op(e0, e3) = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15669)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15669) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15670)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15670) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15671)  all_58_12 = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (158), (163), (217),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (225), (236), (237), (241), (14324),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15200), (15208), (15212), (15216), (15217),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15539), (15540), (15610), (15625), (15629),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15652), (15671), (function-axioms) are
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #378.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15672)  all_58_13 = e2 & op(e0, e2) = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (113), (128), (158), (159),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (169), (212), (235), (236),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (280), (14315), (14316), (14324),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15200), (15216), (15217), (15530), (15531),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15532), (15539), (15540), (15610), (15633),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15636), (15639), (15645), (15658), (15662),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15668), (15672), (function-axioms) are
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #375.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15673)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (15209), (15618), (15673),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #374.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15674)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15674) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15675)  all_58_12 = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (158), (163), (217),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (225), (236), (237), (241), (14324),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15200), (15208), (15212), (15216), (15217),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15539), (15540), (15610), (15625), (15629),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15652), (15675), (function-axioms) are
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #378.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15676)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15676) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15677)  op(e2, e0) = all_56_27
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15678)  op(e2, all_56_27) = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15679)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (15213), (15610), (15679),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1824.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15680)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15680) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15681)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15681) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15682)  op(e1, e3) = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15683)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (15212), (15610), (15683),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1486.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15684)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15684) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15685)  all_58_6 = e1 & op(e1, e3) = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15685) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15686)  op(e1, e3) = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15682), (15686), (function-axioms) are
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15687)  all_58_12 = e1 & op(e0, e3) = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15687) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15688)  all_58_12 = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15689)  op(e0, e3) = e1
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15690)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15690) gives:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15691)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15691) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15692)  all_58_12 = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15688), (15692) are inconsistent by
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1757.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15693)  all_58_13 = e2 & op(e0, e2) = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (128), (158), (159), (162),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (212), (235), (236), (237), (238), (14315),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14324), (15200), (15216), (15217), (15530),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15531), (15532), (15539), (15540), (15610),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15636), (15639), (15642), (15677), (15678),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15682), (15689), (15693), (function-axioms) are
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #373.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15694)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (15209), (15618), (15694),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #374.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15695)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15695) implies:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15696)  all_58_12 = e2
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (158), (163), (217),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (225), (236), (237), (241), (14324),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15200), (15208), (15212), (15216), (15217),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15539), (15540), (15610), (15625), (15629),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15652), (15696), (function-axioms) are
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #378.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15697)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (15199), (15625), (15632), (15697),
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #371.
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15698)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15698) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15699)  op(e0, e3) = all_56_7
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15700)  op(e0, all_56_7) = e0
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (159), (15699)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15701)  all_56_7 = all_52_3
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15700), (15701) imply:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15702)  op(e0, all_52_3) = e0
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15703)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15703) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15704)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15704) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15705)  op(e3, e0) = all_56_25
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15706)  op(e3, all_56_25) = e3
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25, e0, e3, simplifying with (168), (15705)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15707)  all_56_25 = all_52_12
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15706), (15707) imply:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15708)  op(e3, all_52_12) = e3
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15709)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (15213), (15610), (15709),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1824.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15710)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15710) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15711)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15711) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15712)  op(e1, e3) = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15713)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (15212), (15610), (15713),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1486.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15714)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15714) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15715)  all_58_6 = e1 & op(e1, e3) = e1
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15715) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15716)  op(e1, e3) = e1
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15712), (15716), (function-axioms) are
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15717)  all_58_12 = e1 & op(e0, e3) = e1
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15717) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15718)  op(e0, e3) = e1
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15719)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15719) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15720)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15720) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15721)  all_58_12 = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (158), (159), (225),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (241), (14324), (15212), (15217), (15532),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15539), (15610), (15625), (15702), (15720),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15721), (function-axioms) are inconsistent by
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #370.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15722)  all_58_13 = e2 & op(e0, e2) = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (113), (128), (158), (159),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (169), (212), (235), (236),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (280), (14315), (14316), (14324),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15200), (15216), (15217), (15530), (15531),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15532), (15539), (15540), (15610), (15633),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15636), (15639), (15645), (15708), (15712),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15718), (15722), (function-axioms) are
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #375.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15723)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (15209), (15618), (15723),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #374.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15724)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15724) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15725)  all_58_12 = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (158), (159), (225),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (241), (14324), (15212), (15217), (15532),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15539), (15610), (15625), (15702), (15724),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15725), (function-axioms) are inconsistent by
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #370.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15726)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15726) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15727)  op(e2, e0) = all_56_27
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15728)  op(e2, all_56_27) = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15729)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (15213), (15610), (15729),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1824.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15730)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15730) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15731)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15731) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15732)  op(e1, e3) = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15733)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (15212), (15610), (15733),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1486.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15734)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15734) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15735)  all_58_6 = e1 & op(e1, e3) = e1
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15735) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15736)  op(e1, e3) = e1
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15732), (15736), (function-axioms) are
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15737)  all_58_12 = e1 & op(e0, e3) = e1
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15737) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15738)  op(e0, e3) = e1
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15739)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15739) gives:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15740)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15740) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15741)  all_58_12 = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (158), (159), (225),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (241), (14324), (15212), (15217), (15532),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15539), (15610), (15625), (15702), (15740),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15741), (function-axioms) are inconsistent by
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #370.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15742)  all_58_13 = e2 & op(e0, e2) = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (128), (158), (159), (162),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (212), (235), (236), (237), (238), (14315),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14324), (15200), (15216), (15217), (15530),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15531), (15532), (15539), (15540), (15610),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15636), (15639), (15642), (15727), (15728),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15732), (15738), (15742), (function-axioms) are
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #373.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15743)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (15209), (15618), (15743),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #374.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15744)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15744) implies:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15745)  all_58_12 = e2
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (158), (159), (225),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (241), (14324), (15212), (15217), (15532),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15539), (15610), (15625), (15702), (15744),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15745), (function-axioms) are inconsistent by
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #370.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15746)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (15199), (15625), (15632), (15746),
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #371.
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | |   (15747)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 236.84/44.67  | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 236.84/44.67  | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (15533), (15534), (15747),
% 236.84/44.67  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.67  | | | | | | | | | | | | | | | |            #1991.
% 236.84/44.67  | | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | |   (15748)  all_58_3 = e3 & op(e2, e2) = e3
% 236.84/44.67  | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | ALPHA: (15748) implies:
% 236.84/44.67  | | | | | | | | | | | | | |   (15749)  op(e2, e2) = e3
% 236.84/44.67  | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e3,
% 236.84/44.67  | | | | | | | | | | | | | |              e2, e2, simplifying with (42), (15749) gives:
% 236.84/44.67  | | | | | | | | | | | | | |   (15750)  all_8_2 = e3
% 236.84/44.67  | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | REDUCE: (14325), (15750) imply:
% 236.84/44.67  | | | | | | | | | | | | | |   (15751)  $false
% 236.84/44.67  | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | | CLOSE: (15751) is inconsistent.
% 236.84/44.67  | | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | |   (15752)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 236.84/44.67  | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 236.84/44.67  | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | | REF_CLOSE: (158), (162), (14315), (15200), (15752),
% 236.84/44.67  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.67  | | | | | | | | | | | | |            #475.
% 236.84/44.67  | | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | |   (15753)  all_58_3 = e3 & op(e2, e2) = e3
% 236.84/44.67  | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | | REF_CLOSE: (42), (14325), (15753), (function-axioms) are
% 236.84/44.67  | | | | | | | | | | | |            inconsistent by sub-proof #450.
% 236.84/44.67  | | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | |   (15754)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 236.84/44.67  | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 236.84/44.67  | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | REF_CLOSE: (164), (165), (14317), (15202), (15754),
% 236.84/44.67  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.67  | | | | | | | | | | |            #1649.
% 236.84/44.67  | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | | 
% 236.84/44.67  | | | | | | | | End of split
% 236.84/44.67  | | | | | | | | 
% 236.84/44.67  | | | | | | | End of split
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | Case 2:
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | |   (15755)  all_10_2 = e1
% 236.84/44.67  | | | | | | |   (15756)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 236.84/44.67  | | | | | | |              op(e3, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1))
% 236.84/44.67  | | | | | | |            | ( ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 236.84/44.67  | | | | | | |              $i(all_10_1))
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | | COMBINE_EQS: (349), (15755) imply:
% 236.84/44.67  | | | | | | |   (15757)  all_38_2 = e1
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | | COMBINE_EQS: (290), (15755) imply:
% 236.84/44.67  | | | | | | |   (15758)  all_56_1 = e1
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | | REDUCE: (355), (15755) imply:
% 236.84/44.67  | | | | | | |   (15759)   ~ (all_52_1 = e1)
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | | REDUCE: (357), (15755) imply:
% 236.84/44.67  | | | | | | |   (15760)   ~ (all_52_2 = e1)
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | | REDUCE: (359), (15755) imply:
% 236.84/44.67  | | | | | | |   (15761)   ~ (all_52_3 = e1)
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | | REDUCE: (361), (15755) imply:
% 236.84/44.67  | | | | | | |   (15762)   ~ (all_52_4 = e1)
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | | REDUCE: (363), (15755) imply:
% 236.84/44.67  | | | | | | |   (15763)   ~ (all_52_8 = e1)
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | | REDUCE: (365), (15755) imply:
% 236.84/44.67  | | | | | | |   (15764)   ~ (all_52_12 = e1)
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | | REDUCE: (45), (15755) imply:
% 236.84/44.67  | | | | | | |   (15765)  op(e3, e3) = e1
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | | BETA: splitting (49) gives:
% 236.84/44.67  | | | | | | | 
% 236.84/44.67  | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | 
% 236.84/44.67  | | | | | | | |   (15766)   ~ (all_12_2 = e3)
% 236.84/44.67  | | | | | | | | 
% 236.84/44.67  | | | | | | | | REDUCE: (346), (15766) imply:
% 236.84/44.67  | | | | | | | |   (15767)   ~ (all_4_2 = e3)
% 236.84/44.67  | | | | | | | | 
% 236.84/44.67  | | | | | | | | BETA: splitting (52) gives:
% 236.84/44.67  | | | | | | | | 
% 236.84/44.67  | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | 
% 236.84/44.67  | | | | | | | | |   (15768)   ~ (all_14_2 = e0)
% 236.84/44.67  | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | REDUCE: (344), (15768) imply:
% 236.84/44.67  | | | | | | | | |   (15769)   ~ (all_8_2 = e0)
% 236.84/44.67  | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | BETA: splitting (61) gives:
% 236.84/44.67  | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | |   (15770)   ~ (all_20_2 = e1)
% 236.84/44.67  | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | REDUCE: (341), (15770) imply:
% 236.84/44.67  | | | | | | | | | |   (15771)   ~ (all_4_2 = e1)
% 236.84/44.67  | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | BETA: splitting (189) gives:
% 236.84/44.67  | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | Case 1:
% 236.84/44.67  | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | |   (15772)  all_54_15 = e3
% 236.84/44.67  | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | REF_CLOSE: (299), (15767), (15772) are inconsistent by
% 236.84/44.67  | | | | | | | | | | |            sub-proof #2340.
% 236.84/44.67  | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | Case 2:
% 236.84/44.67  | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | |   (15773)   ~ (all_54_15 = e3)
% 236.84/44.67  | | | | | | | | | | |   (15774)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 236.84/44.67  | | | | | | | | | | | 
% 236.84/44.67  | | | | | | | | | | | BETA: splitting (15774) gives:
% 236.84/44.68  | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | |   (15775)  all_54_15 = e2
% 236.84/44.68  | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | REF_CLOSE: (299), (390), (15775) are inconsistent by
% 236.84/44.68  | | | | | | | | | | | |            sub-proof #2339.
% 236.84/44.68  | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | |   (15776)   ~ (all_54_15 = e2)
% 236.84/44.68  | | | | | | | | | | | |   (15777)  all_54_15 = e1 | all_54_15 = e0
% 236.84/44.68  | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | BETA: splitting (15777) gives:
% 236.84/44.68  | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | |   (15778)  all_54_15 = e1
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | REF_CLOSE: (299), (15771), (15778) are inconsistent by
% 236.84/44.68  | | | | | | | | | | | | |            sub-proof #2338.
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | |   (15779)  all_54_15 = e0
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | COMBINE_EQS: (299), (15779) imply:
% 236.84/44.68  | | | | | | | | | | | | |   (15780)  all_4_2 = e0
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | SIMP: (15780) implies:
% 236.84/44.68  | | | | | | | | | | | | |   (15781)  all_4_2 = e0
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | COMBINE_EQS: (254), (15781) imply:
% 236.84/44.68  | | | | | | | | | | | | |   (15782)  all_56_31 = e0
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | REDUCE: (368), (15781) imply:
% 236.84/44.68  | | | | | | | | | | | | |   (15783)   ~ (all_52_3 = e0)
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | REDUCE: (379), (15781) imply:
% 236.84/44.68  | | | | | | | | | | | | |   (15784)   ~ (all_52_7 = e0)
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | REDUCE: (388), (15781) imply:
% 236.84/44.68  | | | | | | | | | | | | |   (15785)   ~ (all_52_13 = e0)
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | REDUCE: (389), (15781) imply:
% 236.84/44.68  | | | | | | | | | | | | |   (15786)   ~ (all_52_14 = e0)
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | REDUCE: (15767), (15781) imply:
% 236.84/44.68  | | | | | | | | | | | | |   (15787)   ~ (e3 = e0)
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | REDUCE: (390), (15781) imply:
% 236.84/44.68  | | | | | | | | | | | | |   (15788)   ~ (e2 = e0)
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | REDUCE: (36), (15781) imply:
% 236.84/44.68  | | | | | | | | | | | | |   (15789)  op(e0, e0) = e0
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 236.84/44.68  | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | |   (15790)   ~ (all_22_2 = e1)
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | REDUCE: (326), (15790) imply:
% 236.84/44.68  | | | | | | | | | | | | | |   (15791)   ~ (all_8_2 = e1)
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | REF_CLOSE: (159), (160), (164), (165), (167), (169), (199),
% 236.84/44.68  | | | | | | | | | | | | | |            (213), (275), (353), (366), (375), (14325),
% 236.84/44.68  | | | | | | | | | | | | | |            (15758), (15763), (15769), (15782), (15783),
% 236.84/44.68  | | | | | | | | | | | | | |            (15785), (15786), (15791), (function-axioms) are
% 236.84/44.68  | | | | | | | | | | | | | |            inconsistent by sub-proof #1212.
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | |   (15792)  all_22_2 = e1
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | COMBINE_EQS: (326), (15792) imply:
% 236.84/44.68  | | | | | | | | | | | | | |   (15793)  all_8_2 = e1
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | SIMP: (15793) implies:
% 236.84/44.68  | | | | | | | | | | | | | |   (15794)  all_8_2 = e1
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | COMBINE_EQS: (353), (15794) imply:
% 236.84/44.68  | | | | | | | | | | | | | |   (15795)  all_56_11 = e1
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | REDUCE: (375), (15794) imply:
% 236.84/44.68  | | | | | | | | | | | | | |   (15796)   ~ (all_52_9 = e1)
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | REDUCE: (377), (15794) imply:
% 236.84/44.68  | | | | | | | | | | | | | |   (15797)   ~ (all_52_13 = e1)
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | REDUCE: (14325), (15794) imply:
% 236.84/44.68  | | | | | | | | | | | | | |   (15798)   ~ (e3 = e1)
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | REDUCE: (42), (15794) imply:
% 236.84/44.68  | | | | | | | | | | | | | |   (15799)  op(e2, e2) = e1
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 236.84/44.68  | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | |   (15800)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 236.84/44.68  | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 236.84/44.68  | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | BETA: splitting (15800) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | |   (15801)  all_58_6 = e1 & op(e1, e3) = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | ALPHA: (15801) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | |   (15802)  op(e1, e3) = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (15760), (15802), (function-axioms) are
% 236.84/44.68  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | |   (15803)  all_58_7 = e1 & op(e1, e2) = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | ALPHA: (15803) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | |   (15804)  all_58_7 = e1
% 236.84/44.68  | | | | | | | | | | | | | | | |   (15805)  op(e1, e2) = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | |   (15806)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 236.84/44.68  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | BETA: splitting (15806) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15807)  all_58_1 = e0 & op(e3, e2) = e0
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | ALPHA: (15807) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15808)  op(e3, e2) = e0
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |   (15809)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | BETA: splitting (15809) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |   (15810)  all_58_1 = e3 & op(e3, e2) = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | ALPHA: (15810) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |   (15811)  op(e3, e2) = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15808), (15811), (function-axioms) are
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2099.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |   (15812)  all_58_3 = e3 & op(e2, e2) = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (232), (15759), (15796),
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |            (15797), (15812), (function-axioms) are
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2196.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |   (15813)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | BETA: splitting (15813) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |   (15814)  all_58_7 = e3 & op(e1, e2) = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | ALPHA: (15814) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |   (15815)  op(e1, e2) = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15805), (15815), (function-axioms) are
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2094.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |   (15816)  all_58_13 = e3 & op(e0, e2) = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | ALPHA: (15816) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |   (15817)  op(e0, e2) = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (237), (15799), (15804), (15808),
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |            (15817), (function-axioms) are inconsistent by
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |            sub-proof #368.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15818)  all_58_3 = e0 & op(e2, e2) = e0
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (15769), (15818), (function-axioms) are
% 236.84/44.68  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | End of split
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | |   (15819)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 236.84/44.68  | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | BETA: splitting (15819) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15820)  all_58_7 = e0 & op(e1, e2) = e0
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | ALPHA: (15820) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15821)  op(e1, e2) = e0
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (15805), (15821), (function-axioms)
% 236.84/44.68  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15822)  all_58_13 = e0 & op(e0, e2) = e0
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | ALPHA: (15822) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15823)  op(e0, e2) = e0
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (15784), (15823), (function-axioms) are
% 236.84/44.68  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2252.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | End of split
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | End of split
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | End of split
% 236.84/44.68  | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | |   (15824)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 236.84/44.68  | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 236.84/44.68  | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | BETA: splitting (15824) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | |   (15825)  all_58_8 = e1 & op(e1, e1) = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14323), (15825) are inconsistent by
% 236.84/44.68  | | | | | | | | | | | | | | | |            sub-proof #406.
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | |   (15826)  all_58_11 = e1 & op(e1, e0) = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | ALPHA: (15826) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | |   (15827)  all_58_11 = e1
% 236.84/44.68  | | | | | | | | | | | | | | | |   (15828)  op(e1, e0) = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | |   (15829)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (15763), (15796), (15829),
% 236.84/44.68  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.68  | | | | | | | | | | | | | | | | |            #1211.
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | |   (15830)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.84/44.68  | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | BETA: splitting (15830) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15831)  all_58_8 = e1 & op(e1, e1) = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | ALPHA: (15831) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15832)  all_58_8 = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15833)  op(e1, e1) = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (225),
% 236.84/44.68  | | | | | | | | | | | | | | | | | |            (226), (14315), (15827), (15828), (15832),
% 236.84/44.68  | | | | | | | | | | | | | | | | | |            (15833), (function-axioms) are inconsistent by
% 236.84/44.68  | | | | | | | | | | | | | | | | | |            sub-proof #787.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15834)  all_58_14 = e1 & op(e0, e1) = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | ALPHA: (15834) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15835)  all_58_14 = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | | |   (15836)  op(e0, e1) = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |   (15837)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.84/44.68  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | BETA: splitting (15837) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |   (15838)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | BETA: splitting (15838) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15839)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |            e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | ALPHA: (15839) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15840)  op(e2, e3) = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15841)  op(e3, e2) = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (157), (15836) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15842)  all_52_11 = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (15828) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15843)  all_52_14 = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (15840) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15844)  all_52_1 = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (15841) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15845)  all_52_4 = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (15844) imply:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15846)   ~ (all_52_3 = e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | SIMP: (15846) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15847)   ~ (all_52_3 = e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (15844) imply:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15848)   ~ (all_52_13 = e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | SIMP: (15848) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15849)   ~ (all_52_13 = e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (15845) imply:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15850)   ~ (all_52_7 = e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | SIMP: (15850) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | |   (15851)   ~ (all_52_7 = e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | |   (15852)  all_54_12 = e3
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (15847), (15852) are inconsistent by
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | |   (15853)   ~ (all_54_12 = e3)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | |   (15854)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15854) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | |   (15855)  all_54_12 = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (15855) imply:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | |   (15856)  all_52_3 = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15856) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | |   (15857)  all_52_3 = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (15857) imply:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | |   (15858)   ~ (all_52_7 = e2)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15858) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | |   (15859)   ~ (all_52_7 = e2)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15847), (15857) imply:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | |   (15860)   ~ (e3 = e2)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | |   (15861)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (15799), (15841), (15861),
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | |            #1785.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | |   (15862)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15862) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (15863)  all_58_7 = e2 & op(e1, e2) = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15863) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (15864)  all_58_7 = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15865)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15865) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15866)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15866) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15867)  all_58_12 = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (158), (219), (15789), (15835),
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15851), (15867), (function-axioms) are
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1550.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15868)  all_58_13 = e2 & op(e0, e2) = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15868) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15869)  all_58_13 = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15870)  op(e0, e2) = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (235), (236), (237),
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (15864), (15869), (15870),
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1453.
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15871)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15871) gives:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15872)  all_58_14 = e2 & op(e0, e1) = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15872) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15873)  all_58_14 = e2
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15835), (15873) imply:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15874)  e2 = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15874) implies:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15875)  e2 = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15864), (15875) imply:
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15876)  all_58_7 = e1
% 236.84/44.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (225),
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (14319), (15827), (15828), (15876),
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1417.
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15877)  all_58_15 = e2 & op(e0, e0) = e2
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (216),
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (15785), (15786), (15789),
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15849), (15877), (function-axioms) are
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1488.
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (15878)  all_58_13 = e2 & op(e0, e2) = e2
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15878) implies:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (15879)  op(e0, e2) = e2
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (15859), (15879), (function-axioms) are
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | |   (15880)  all_54_12 = e1 | all_54_12 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (15761), (15783), (15880) are inconsistent
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2067.
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | |   (15881)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (14313), (14314), (15881),
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | |            #483.
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |   (15882)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (15763), (15782), (15783), (15882),
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |            #2307.
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |   (15883)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | BETA: splitting (15883) gives:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |   (15884)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              = e2)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (15782), (15795), (15796), (15884),
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |            #2297.
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |   (15885)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (15782), (15785), (15786), (15885),
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |            #2321.
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | |   (15886)  all_20_2 = e1
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | COMBINE_EQS: (341), (15886) imply:
% 236.84/44.69  | | | | | | | | | |   (15887)  all_4_2 = e1
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | SIMP: (15887) implies:
% 236.84/44.69  | | | | | | | | | |   (15888)  all_4_2 = e1
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | COMBINE_EQS: (254), (15888) imply:
% 236.84/44.69  | | | | | | | | | |   (15889)  all_56_31 = e1
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | REDUCE: (386), (15888) imply:
% 236.84/44.69  | | | | | | | | | |   (15890)   ~ (all_52_11 = e1)
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | REDUCE: (389), (15888) imply:
% 236.84/44.69  | | | | | | | | | |   (15891)   ~ (all_52_14 = e1)
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | REDUCE: (15767), (15888) imply:
% 236.84/44.69  | | | | | | | | | |   (15892)   ~ (e3 = e1)
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | BETA: splitting (224) gives:
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | |   (15893)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 236.84/44.69  | | | | | | | | | | |              & op(e1, e2) = e1)
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | BETA: splitting (15893) gives:
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | |   (15894)  all_58_6 = e1 & op(e1, e3) = e1
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | ALPHA: (15894) implies:
% 236.84/44.69  | | | | | | | | | | | |   (15895)  op(e1, e3) = e1
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | REF_CLOSE: (163), (15760), (15895), (function-axioms) are
% 236.84/44.69  | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | |   (15896)  all_58_7 = e1 & op(e1, e2) = e1
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | ALPHA: (15896) implies:
% 236.84/44.69  | | | | | | | | | | | |   (15897)  op(e1, e2) = e1
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | |   (15898)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.84/44.69  | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | BETA: splitting (15898) gives:
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | |   (15899)  all_58_4 = e1 & op(e3, e1) = e1
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | ALPHA: (15899) implies:
% 236.84/44.69  | | | | | | | | | | | | | |   (15900)  op(e3, e1) = e1
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | REF_CLOSE: (169), (15763), (15900), (function-axioms) are
% 236.84/44.69  | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | |   (15901)  all_58_5 = e1 & op(e2, e1) = e1
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | REF_CLOSE: (113), (123), (126), (148), (158), (159), (160),
% 236.84/44.69  | | | | | | | | | | | | | |            (162), (163), (164), (165), (167), (168), (169),
% 236.84/44.69  | | | | | | | | | | | | | |            (199), (213), (233), (234), (275), (353), (366),
% 236.84/44.69  | | | | | | | | | | | | | |            (373), (375), (377), (14313), (14314), (14317),
% 236.84/44.69  | | | | | | | | | | | | | |            (14325), (15769), (15889), (15897), (15901),
% 236.84/44.69  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.69  | | | | | | | | | | | | | |            #454.
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | |   (15902)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.84/44.69  | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | BETA: splitting (15902) gives:
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | |   (15903)  all_58_8 = e1 & op(e1, e1) = e1
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | REF_CLOSE: (8), (14323), (15903) are inconsistent by
% 236.84/44.69  | | | | | | | | | | | | | |            sub-proof #406.
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | |   (15904)  all_58_14 = e1 & op(e0, e1) = e1
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | ALPHA: (15904) implies:
% 236.84/44.69  | | | | | | | | | | | | | |   (15905)  op(e0, e1) = e1
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | REF_CLOSE: (157), (15890), (15905), (function-axioms) are
% 236.84/44.69  | | | | | | | | | | | | | |            inconsistent by sub-proof #2272.
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | |   (15906)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 236.84/44.69  | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | REF_CLOSE: (8), (160), (14323), (15891), (15906),
% 236.84/44.69  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.69  | | | | | | | | | | |            #367.
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | End of split
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | |   (15907)  all_14_2 = e0
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | COMBINE_EQS: (344), (15907) imply:
% 236.84/44.69  | | | | | | | | |   (15908)  all_8_2 = e0
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | SIMP: (15908) implies:
% 236.84/44.69  | | | | | | | | |   (15909)  all_8_2 = e0
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | COMBINE_EQS: (311), (15909) imply:
% 236.84/44.69  | | | | | | | | |   (15910)  all_48_2 = e0
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | REDUCE: (366), (15909) imply:
% 236.84/44.69  | | | | | | | | |   (15911)   ~ (all_52_1 = e0)
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | REDUCE: (369), (15909) imply:
% 236.84/44.69  | | | | | | | | |   (15912)   ~ (all_52_4 = e0)
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | REDUCE: (371), (15909) imply:
% 236.84/44.69  | | | | | | | | |   (15913)   ~ (all_52_6 = e0)
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | REDUCE: (373), (15909) imply:
% 236.84/44.69  | | | | | | | | |   (15914)   ~ (all_52_7 = e0)
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | REDUCE: (375), (15909) imply:
% 236.84/44.69  | | | | | | | | |   (15915)   ~ (all_52_9 = e0)
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | REDUCE: (377), (15909) imply:
% 236.84/44.69  | | | | | | | | |   (15916)   ~ (all_52_13 = e0)
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | REDUCE: (14325), (15909) imply:
% 236.84/44.69  | | | | | | | | |   (15917)   ~ (e3 = e0)
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | BETA: splitting (235) gives:
% 236.84/44.69  | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | |   (15918)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 236.84/44.69  | | | | | | | | | |              & op(e2, e2) = e0)
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | BETA: splitting (15918) gives:
% 236.84/44.69  | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | |   (15919)  all_58_1 = e0 & op(e3, e2) = e0
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | REF_CLOSE: (170), (15912), (15919), (function-axioms) are
% 236.84/44.69  | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | |   (15920)  all_58_3 = e0 & op(e2, e2) = e0
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | ALPHA: (15920) implies:
% 236.84/44.69  | | | | | | | | | | |   (15921)  all_58_3 = e0
% 236.84/44.69  | | | | | | | | | | |   (15922)  op(e2, e2) = e0
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | BETA: splitting (61) gives:
% 236.84/44.69  | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | |   (15923)   ~ (all_20_2 = e1)
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | REDUCE: (341), (15923) imply:
% 236.84/44.69  | | | | | | | | | | | |   (15924)   ~ (all_4_2 = e1)
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | BETA: splitting (189) gives:
% 236.84/44.69  | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | |   (15925)  all_54_15 = e3
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | REF_CLOSE: (299), (15767), (15925) are inconsistent by
% 236.84/44.69  | | | | | | | | | | | | |            sub-proof #2340.
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | |   (15926)   ~ (all_54_15 = e3)
% 236.84/44.69  | | | | | | | | | | | | |   (15927)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | BETA: splitting (15927) gives:
% 236.84/44.69  | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | |   (15928)  all_54_15 = e2
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | REF_CLOSE: (299), (390), (15928) are inconsistent by
% 236.84/44.69  | | | | | | | | | | | | | |            sub-proof #2339.
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | |   (15929)   ~ (all_54_15 = e2)
% 236.84/44.69  | | | | | | | | | | | | | |   (15930)  all_54_15 = e1 | all_54_15 = e0
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | BETA: splitting (15930) gives:
% 236.84/44.69  | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | |   (15931)  all_54_15 = e1
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | REF_CLOSE: (299), (15924), (15931) are inconsistent by
% 236.84/44.69  | | | | | | | | | | | | | | |            sub-proof #2338.
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | Case 2:
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | |   (15932)  all_54_15 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | COMBINE_EQS: (299), (15932) imply:
% 236.84/44.69  | | | | | | | | | | | | | | |   (15933)  all_4_2 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | SIMP: (15933) implies:
% 236.84/44.69  | | | | | | | | | | | | | | |   (15934)  all_4_2 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | COMBINE_EQS: (254), (15934) imply:
% 236.84/44.69  | | | | | | | | | | | | | | |   (15935)  all_56_31 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | REDUCE: (368), (15934) imply:
% 236.84/44.69  | | | | | | | | | | | | | | |   (15936)   ~ (all_52_3 = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | REDUCE: (386), (15934) imply:
% 236.84/44.69  | | | | | | | | | | | | | | |   (15937)   ~ (all_52_11 = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | REDUCE: (389), (15934) imply:
% 236.84/44.69  | | | | | | | | | | | | | | |   (15938)   ~ (all_52_14 = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | REDUCE: (390), (15934) imply:
% 236.84/44.69  | | | | | | | | | | | | | | |   (15939)   ~ (e2 = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | REDUCE: (15924), (15934) imply:
% 236.84/44.69  | | | | | | | | | | | | | | |   (15940)   ~ (e1 = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | REDUCE: (36), (15934) imply:
% 236.84/44.69  | | | | | | | | | | | | | | |   (15941)  op(e0, e0) = e0
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 236.84/44.69  | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | |   (15942)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | BETA: splitting (15942) gives:
% 236.84/44.69  | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | |   (15943)  all_58_4 = e0 & op(e3, e1) = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | ALPHA: (15943) implies:
% 236.84/44.69  | | | | | | | | | | | | | | | | |   (15944)  all_58_4 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | |   (15945)  op(e3, e1) = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 236.84/44.69  | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | |   (15946)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | BETA: splitting (15946) gives:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |   (15947)  all_58_6 = e0 & op(e1, e3) = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | ALPHA: (15947) implies:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |   (15948)  all_58_6 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | | | |   (15949)  op(e1, e3) = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |   (15950)  all_58_15 = e0 & op(e0, e0) = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | ALPHA: (15950) implies:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |   (15951)  all_58_15 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (15949) gives:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |   (15952)  all_52_2 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (15945) gives:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |   (15953)  all_52_8 = e0
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (15952) imply:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |   (15954)   ~ (all_52_3 = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (15952) imply:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |   (15955)   ~ (all_52_14 = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (15953) imply:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |   (15956)   ~ (all_52_9 = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (15953) imply:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | |   (15957)   ~ (all_52_11 = e0)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | |   (15958)   ~ (all_38_2 = e1)
% 236.84/44.69  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | REDUCE: (15757), (15958) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | |   (15959)  $false
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | CLOSE: (15959) is inconsistent.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | |   (15960)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e1) = all_38_1 & $i(all_38_0) &
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | |              $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15756) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | |   (15961)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_10_1 & $i(all_10_0) &
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15961) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | |   (15962)  op(e3, e1) = all_10_1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | |   (15963)  op(all_10_1, e3) = all_10_0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | |   (15964)   ~ (all_46_2 = e3)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14312), (15964) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | |   (15965)  $false
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15965) is inconsistent.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | |   (15966)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14311) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | |   (15967)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 &
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15967) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | |   (15968)   ~ (all_6_0 = e2)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | |   (15969)  op(e1, e3) = all_6_1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | |   (15970)  op(all_6_1, e1) = all_6_0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (15949), (15969) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | |   (15971)  all_6_1 = e0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_10_1,
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (15945), (15962) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | |   (15972)  all_10_1 = e0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15963), (15972) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | |   (15973)  op(e0, e3) = all_10_0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15970), (15971) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | |   (15974)  op(e0, e1) = all_6_0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15960) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15975)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_38_1 & $i(all_38_0) &
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15975) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15976)  op(e3, e1) = all_38_1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |              all_6_0, e1, e0, simplifying with (157), (15974)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15977)  all_52_11 = all_6_0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e3, e0, simplifying with (159), (15973)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15978)  all_52_3 = all_10_0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_1,
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (15945), (15976) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15979)  all_38_1 = e0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (15977) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15980)  all_54_14 = all_6_0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (15978) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15981)  all_54_12 = all_10_0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (15978) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15982)   ~ (all_52_1 = all_10_0)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (15978) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15983)   ~ (all_52_7 = all_10_0)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15983) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15984)   ~ (all_52_7 = all_10_0)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (15977), (15978) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15985)   ~ (all_10_0 = all_6_0)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15936), (15978) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15986)   ~ (all_10_0 = e0)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (15977) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15987)   ~ (all_52_7 = all_6_0)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (15977) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15988)   ~ (all_52_9 = all_6_0)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14318), (15977) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15989)   ~ (all_6_0 = e3)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15937), (15977) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (15990)   ~ (all_6_0 = e0)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15991)  all_54_14 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15980), (15989), (15991) are inconsistent by
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #452.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15992)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15993)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (165), (15945), (15968), (15980), (15988),
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15990), (15992), (15993), (function-axioms) are
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #366.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15994)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15994) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15995)  all_58_8 = e1 & op(e1, e1) = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14323), (15995) are inconsistent by
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #365.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15996)  all_58_14 = e1 & op(e0, e1) = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15996) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15997)  all_58_14 = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15992) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15998)  all_54_14 = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15968), (15980), (15998) are inconsistent by
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #451.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15999)  all_54_14 = e1 | all_54_14 = e0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16000)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16000) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16001)  all_58_2 = e1 & op(e2, e3) = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (15759), (16001), (function-axioms) are
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16002)  all_58_3 = e1 & op(e2, e2) = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15921), (16002) are inconsistent by
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1752.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16003)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16003) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16004)  all_58_5 = e1 & op(e2, e1) = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16004) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16005)  all_58_5 = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (229), (230),
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15944), (15997), (16005), (function-axioms) are
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1248.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16006)  all_58_10 = e1 & op(e2, e0) = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16006) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16007)  all_58_10 = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16008)  op(e2, e0) = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16009)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16009) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16010)  all_58_9 = e3 & op(e3, e0) = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16010) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16011)  all_58_9 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15999) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16012)  all_54_14 = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15980), (16012) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16013)  all_6_0 = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16013) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16014)  all_6_0 = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15987), (16014) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16015)   ~ (all_52_7 = e1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15988), (16014) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16016)   ~ (all_52_9 = e1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15985), (16014) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16017)   ~ (all_10_0 = e1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16018)  all_54_6 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (16018) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16019)  all_52_9 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14317), (16019) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16020)  $false
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16020) is inconsistent.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16021)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16021) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16022)  all_54_6 = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (16022) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16023)  all_52_9 = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (16023) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16024)   ~ (all_52_1 = e2)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (16023) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16025)   ~ (all_52_13 = e2)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16025) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16026)   ~ (all_52_13 = e2)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (16023) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16027)  op(e2, e1) = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16028)  all_54_4 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (16028) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16029)  all_52_1 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (16029) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16030)   ~ (all_52_13 = e3)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16030) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16031)   ~ (all_52_13 = e3)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15982), (16029) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16032)   ~ (all_10_0 = e3)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16032) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16033)   ~ (all_10_0 = e3)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16034)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (15762), (15921), (16034),
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1377.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16035)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16035) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16036)  all_58_7 = e1 & op(e1, e2) = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16036) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16037)  all_58_7 = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16038)  op(e1, e2) = e1
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16039)  all_54_12 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15981), (16039) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16040)  all_10_0 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16040) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16041)  all_10_0 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16033), (16041) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16042)  $false
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16042) is inconsistent.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16043)   ~ (all_54_12 = e3)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16044)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16044) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16045)  all_54_12 = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15981), (16045) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16046)  all_10_0 = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16046) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16047)  all_10_0 = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15984), (16047) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16048)   ~ (all_52_7 = e2)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16033), (16047) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16049)   ~ (e3 = e2)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16050)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16050) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16051)  all_58_0 = e2 & op(e3, e3) = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16051) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16052)  op(e3, e3) = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (168), (169),
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (237), (238), (242), (15763), (15764),
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15922), (16037), (16038), (16052),
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1712.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16053)  all_58_2 = e2 & op(e2, e3) = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16053) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16054)  op(e2, e3) = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (16024), (16054), (function-axioms) are
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16055)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16055) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16056)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16056) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16057)  all_58_6 = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15948), (16057) are inconsistent by
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1982.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16058)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16058) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16059)  all_58_12 = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16060)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16060) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16061)  all_58_2 = e3 & op(e2, e3) = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16061) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16062)  all_58_2 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16063)  all_54_13 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (16063) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16064)  all_52_7 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16064) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16065)  all_52_7 = e3
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (16065) imply:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16066)   ~ (all_52_4 = e3)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16067)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16067) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16068)  all_58_9 = e2 & op(e3, e0) = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16068) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16069)  op(e3, e0) = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (170), (246), (15765), (15944),
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16066), (16069), (function-axioms) are
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1400.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16070)  all_58_10 = e2 & op(e2, e0) = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16070) implies:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16071)  op(e2, e0) = e2
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (16026), (16071), (function-axioms) are
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16072)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16072) gives:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16073)  all_58_11 = e2 & op(e1, e0) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16073) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16074)  all_58_11 = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16075)  op(e1, e0) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16076)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16076) gives:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16077)  all_58_0 = e2 & op(e3, e3) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16077) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16078)  op(e3, e3) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (241), (15948), (16059), (16062),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16078), (function-axioms) are inconsistent by
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1762.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16079)  all_58_1 = e2 & op(e3, e2) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16079) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16080)  all_58_1 = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16081)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16081) gives:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16082)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16082) gives:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16083)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16083) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16084)  op(e3, e2) = e3
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (16066), (16084), (function-axioms) are
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16085)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (14314), (16024), (16085),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2334.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16086)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (15935), (15936), (15945), (16086),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #364.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16087)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16087) gives:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16088)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16088) gives:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16089)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16089) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16090)   ~ (all_56_1 = e1)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15758), (16090) imply:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16091)  $false
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16091) is inconsistent.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16092)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16092) gives:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16093)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16093) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16094)  op(e2, e1) = e1
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15960) gives:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (15922), (16027), (16037), (16038),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16080), (16094), (function-axioms) are
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1498.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16095)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16095) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16096)   ~ (all_38_1 = e0)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15756), (15945), (15976), (16096),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1194.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16097)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16097) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16098)  op(e0, e2) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (16048), (16098), (function-axioms) are
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16099)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (160), (164), (15938), (16008), (16075),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16099), (function-axioms) are inconsistent by
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #363.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16100)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16100) gives:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16101)  all_58_4 = e2 & op(e3, e1) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16101) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16102)  all_58_4 = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15944), (16102) imply:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16103)  e2 = e0
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16103) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16104)  e2 = e0
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16074), (16104) imply:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16105)  all_58_11 = e0
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (162), (225), (226), (14315),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15948), (16037), (16105), (function-axioms) are
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16106)  all_58_9 = e2 & op(e3, e0) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16106) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16107)  op(e3, e0) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (170), (246), (15765), (15944),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16066), (16107), (function-axioms) are
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1400.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16108)  all_58_15 = e2 & op(e0, e0) = e2
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (216),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (15916), (15938), (15941),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16031), (16108), (function-axioms) are
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1488.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16109)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (15914), (16015), (16048), (16109) are
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1648.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16110)  all_58_3 = e3 & op(e2, e2) = e3
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16110) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16111)  all_58_3 = e3
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15921), (16111) imply:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16112)  e3 = e0
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16112) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16113)  e3 = e0
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16011), (16113) imply:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16114)  all_58_9 = e0
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (220), (221),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (15941), (16031), (16114),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1650.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16115)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (16027), (16031), (16115),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1913.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16116)  all_54_12 = e1 | all_54_12 = e0
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15981), (15986), (16017), (16116) are
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16117)  all_58_13 = e1 & op(e0, e2) = e1
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (16015), (16117), (function-axioms) are
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16118)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (15759), (15911), (16024), (16118) are
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1921.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16119)  all_54_6 = e1 | all_54_6 = e0
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (15915), (16016), (16119) are inconsistent
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #476.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16120)  all_54_14 = e0
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15980), (15990), (16120) are inconsistent by
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #448.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16121)  all_58_10 = e3 & op(e2, e0) = e3
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16007), (16121) are inconsistent by
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1620.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16122)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (14319), (15941), (16122),
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1431.
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (16123)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16123) implies:
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (16124)   ~ (all_38_1 = e0)
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (16125)  op(e3, e1) = all_38_1
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.71  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15756), (15945), (16124), (16125),
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |            #1194.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |   (16126)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_6_1)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15949), (15966), (16126), (function-axioms) are
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #443.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | |   (16127)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16127) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | |   (16128)   ~ (all_10_1 = e2)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | |   (16129)  op(e3, e1) = all_10_1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | |   (16130)   ~ (all_46_2 = e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14312), (16130) imply:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | |   (16131)  $false
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16131) is inconsistent.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | |   (16132)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14311) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |   (16133)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16133) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |   (16134)   ~ (all_6_0 = e2)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |   (16135)  op(e1, e3) = all_6_1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |   (16136)  op(all_6_1, e1) = all_6_0
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (15949), (16135) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |   (16137)  all_6_1 = e0
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_10_1,
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (15945), (16129) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |   (16138)  all_10_1 = e0
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16136), (16137) imply:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | |   (16139)  op(e0, e1) = all_6_0
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15960) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (16140)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_38_1 & $i(all_38_0) &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16140) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (16141)  op(e3, e1) = all_38_1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |              all_6_0, e1, e0, simplifying with (157), (16139)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (16142)  all_52_11 = all_6_0
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_1,
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (15945), (16141) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (16143)  all_38_1 = e0
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (16142) imply:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (16144)  all_54_14 = all_6_0
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (16142) imply:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (16145)   ~ (all_52_9 = all_6_0)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14318), (16142) imply:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (16146)   ~ (all_6_0 = e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15937), (16142) imply:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (16147)   ~ (all_6_0 = e0)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16148)  all_54_14 = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16144), (16146), (16148) are inconsistent by
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #452.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16149)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16150)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16150) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16151)  all_58_4 = e2 & op(e3, e1) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16151) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16152)  op(e3, e1) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16128), (16129), (16141), (16152),
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1114.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16153)  all_58_5 = e2 & op(e2, e1) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16153) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16154)  op(e2, e1) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16155)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16155) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16156)  all_58_2 = e1 & op(e2, e3) = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (15759), (16156), (function-axioms) are
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16157)  all_58_3 = e1 & op(e2, e2) = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15921), (16157) are inconsistent by
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1752.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16158)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16158) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16159)  all_58_5 = e1 & op(e2, e1) = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16159) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16160)  op(e2, e1) = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (16134), (16144), (16145), (16147),
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16149), (16160), (function-axioms) are
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #446.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16161)  all_58_10 = e1 & op(e2, e0) = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16161) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16162)  all_58_10 = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16163)  op(e2, e0) = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16164)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16164) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16165)  all_58_9 = e3 & op(e3, e0) = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16165) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16166)  all_58_9 = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16167)  op(e3, e0) = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16168)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16168) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16169)  all_58_2 = e3 & op(e2, e3) = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16169) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16170)  op(e2, e3) = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16171)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16171) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16172)  all_58_9 = e2 & op(e3, e0) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16172) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16173)  op(e3, e0) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16167), (16173), (function-axioms) are
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2125.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16174)  all_58_10 = e2 & op(e2, e0) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16174) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16175)  op(e2, e0) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16163), (16175), (function-axioms) are
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1659.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16176)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16176) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16177)  all_58_11 = e2 & op(e1, e0) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16177) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16178)  op(e1, e0) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16179)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16179) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16180)  all_58_0 = e2 & op(e3, e3) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16180) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16181)  op(e3, e3) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15765), (16181), (function-axioms) are
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16182)  all_58_1 = e2 & op(e3, e2) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16182) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16183)  op(e3, e2) = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16184)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16184) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16185)  all_58_1 = e3 & op(e3, e2) = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16185) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16186)  op(e3, e2) = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16183), (16186), (function-axioms) are
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2193.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16187)  all_58_3 = e3 & op(e2, e2) = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (15765),
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15921), (15944), (16166), (16187),
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #362.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16188)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16188) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16189)  all_58_7 = e3 & op(e1, e2) = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16189) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16190)  op(e1, e2) = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (14315), (16190), (function-axioms) are
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16191)  all_58_13 = e3 & op(e0, e2) = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16191) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16192)  op(e0, e2) = e3
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16149) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16193)  all_54_14 = e2
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16134), (16144), (16193) are inconsistent by
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #451.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16194)   ~ (all_54_14 = e2)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16195)  all_54_14 = e1 | all_54_14 = e0
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16195) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16196)  all_54_14 = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16144), (16196) imply:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16197)  all_6_0 = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16197) implies:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16198)  all_6_0 = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16145), (16198) imply:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16199)   ~ (all_52_9 = e1)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16134), (16198) imply:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16200)   ~ (e2 = e1)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16201)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16201) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16202)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (163), (14314), (16170), (16183), (16202),
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #361.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16203)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (15935), (15936), (15945), (16203),
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #364.
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16204)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16204) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16205)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16205) gives:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16206)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16206) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16207)   ~ (all_56_1 = e1)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15758), (16207) imply:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16208)  $false
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16208) is inconsistent.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16209)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (16192), (16199), (16209),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1108.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16210)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (160), (164), (15938), (16163), (16178),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16210), (function-axioms) are inconsistent by
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #363.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16211)  all_54_14 = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16144), (16147), (16211) are inconsistent by
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #448.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16212)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16212) gives:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16213)  all_58_4 = e2 & op(e3, e1) = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16213) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16214)  op(e3, e1) = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16128), (16129), (16141), (16214),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1114.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16215)  all_58_9 = e2 & op(e3, e0) = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16215) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16216)  op(e3, e0) = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16167), (16216), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2125.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16217)  all_58_15 = e2 & op(e0, e0) = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16217) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16218)  op(e0, e0) = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15941), (16218), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16219)  all_58_3 = e3 & op(e2, e2) = e3
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (15765),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15921), (15944), (16166), (16219),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #362.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16220)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16220) gives:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16221)  all_58_5 = e3 & op(e2, e1) = e3
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16221) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16222)  op(e2, e1) = e3
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16154), (16222), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16223)  all_58_10 = e3 & op(e2, e0) = e3
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16223) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16224)  all_58_10 = e3
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16162), (16224) imply:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16225)  e3 = e1
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16225) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16226)  e3 = e1
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16166), (16226) imply:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16227)  all_58_9 = e1
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (221), (222), (15951),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16162), (16227) are inconsistent by sub-proof
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1495.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16228)  all_58_10 = e3 & op(e2, e0) = e3
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16162), (16228) are inconsistent by
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1620.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16229)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (14319), (15941), (16229),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1431.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16230)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16230) gives:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16231)  all_58_8 = e2 & op(e1, e1) = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16231) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16232)  op(e1, e1) = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14324), (16232), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16233)  all_58_14 = e2 & op(e0, e1) = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16233) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16234)  all_58_14 = e2
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16235)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (165), (15945), (16134), (16144), (16145),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16147), (16149), (16235), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #366.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16236)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16236) gives:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16237)  all_58_8 = e1 & op(e1, e1) = e1
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14323), (16237) are inconsistent by
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #365.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16238)  all_58_14 = e1 & op(e0, e1) = e1
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16238) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16239)  all_58_14 = e1
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16234), (16239) are inconsistent by
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2044.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (16240)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16240) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (16241)   ~ (all_38_1 = e0)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (16242)  op(e3, e1) = all_38_1
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15756), (15945), (16241), (16242),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | |            #1194.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | |   (16243)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 &
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_6_1)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15949), (16132), (16243), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #443.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | |   (16244)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | ALPHA: (16244) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | |   (16245)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | BETA: splitting (16245) gives:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | |   (16246)  all_58_12 = e0 & op(e0, e3) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | ALPHA: (16246) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | |   (16247)  op(e0, e3) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (15936), (16247), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | |   (16248)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16248) gives:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | |   (16249)  all_58_13 = e0 & op(e0, e2) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16249) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | |   (16250)  op(e0, e2) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (217), (218),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | |            (219), (15761), (15941), (16250),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | |            #1770.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | |   (16251)  all_58_14 = e0 & op(e0, e1) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16251) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | |   (16252)  all_58_14 = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | |   (16253)  op(e0, e1) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (217), (218),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | |            (219), (15761), (15941), (16245), (16252),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | |            (16253), (function-axioms) are inconsistent by
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2073.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | |   (16254)  all_58_7 = e0 & op(e1, e2) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (15913), (16254), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | |   (16255)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 236.84/44.73  | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.84/44.73  | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | BETA: splitting (16255) gives:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | |   (16256)  all_58_8 = e0 & op(e1, e1) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | ALPHA: (16256) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | |   (16257)  op(e1, e1) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (229),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | |            (230), (14317), (15944), (16257),
% 236.84/44.73  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.73  | | | | | | | | | | | | | | | | | | |            #1662.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | |   (16258)  all_58_11 = e0 & op(e1, e0) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | ALPHA: (16258) implies:
% 236.84/44.73  | | | | | | | | | | | | | | | | | | |   (16259)  op(e1, e0) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (15938), (16259), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2323.
% 236.84/44.73  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | |   (16260)  all_58_5 = e0 & op(e2, e1) = e0
% 236.84/44.73  | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (15915), (16260), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 236.84/44.73  | | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | |   (16261)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 236.84/44.73  | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.84/44.73  | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (165), (169), (230), (14316), (14317),
% 236.84/44.73  | | | | | | | | | | | | | | | |            (14318), (15937), (16261), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #360.
% 236.84/44.73  | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | |   (16262)  all_20_2 = e1
% 236.84/44.73  | | | | | | | | | | | |   (16263)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 236.84/44.73  | | | | | | | | | | | |              & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 236.84/44.73  | | | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 236.84/44.73  | | | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 236.84/44.73  | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | COMBINE_EQS: (341), (16262) imply:
% 236.84/44.73  | | | | | | | | | | | |   (16264)  all_4_2 = e1
% 236.84/44.73  | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | COMBINE_EQS: (324), (16264) imply:
% 236.84/44.73  | | | | | | | | | | | |   (16265)  all_34_2 = e1
% 236.84/44.73  | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | COMBINE_EQS: (254), (16264) imply:
% 236.84/44.73  | | | | | | | | | | | |   (16266)  all_56_31 = e1
% 236.84/44.73  | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | REDUCE: (388), (16264) imply:
% 236.84/44.73  | | | | | | | | | | | |   (16267)   ~ (all_52_13 = e1)
% 236.84/44.73  | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | REDUCE: (389), (16264) imply:
% 236.84/44.73  | | | | | | | | | | | |   (16268)   ~ (all_52_14 = e1)
% 236.84/44.73  | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | REDUCE: (15767), (16264) imply:
% 236.84/44.73  | | | | | | | | | | | |   (16269)   ~ (e3 = e1)
% 236.84/44.73  | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | REDUCE: (390), (16264) imply:
% 236.84/44.73  | | | | | | | | | | | |   (16270)   ~ (e2 = e1)
% 236.84/44.73  | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | BETA: splitting (224) gives:
% 236.84/44.73  | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | |   (16271)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 236.84/44.73  | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 236.84/44.73  | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | BETA: splitting (16271) gives:
% 236.84/44.73  | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | |   (16272)  all_58_6 = e1 & op(e1, e3) = e1
% 236.84/44.73  | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | ALPHA: (16272) implies:
% 236.84/44.73  | | | | | | | | | | | | | |   (16273)  op(e1, e3) = e1
% 236.84/44.73  | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | REF_CLOSE: (163), (15760), (16273), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 236.84/44.73  | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | |   (16274)  all_58_7 = e1 & op(e1, e2) = e1
% 236.84/44.73  | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | ALPHA: (16274) implies:
% 236.84/44.73  | | | | | | | | | | | | | |   (16275)  all_58_7 = e1
% 236.84/44.73  | | | | | | | | | | | | | |   (16276)  op(e1, e2) = e1
% 236.84/44.73  | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 236.84/44.73  | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | |   (16277)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 236.84/44.73  | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.84/44.73  | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | BETA: splitting (16277) gives:
% 236.84/44.73  | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | |   (16278)  all_58_2 = e1 & op(e2, e3) = e1
% 236.84/44.73  | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | REF_CLOSE: (167), (15759), (16278), (function-axioms) are
% 236.84/44.73  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 236.84/44.73  | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | |   (16279)  all_58_3 = e1 & op(e2, e2) = e1
% 236.84/44.73  | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15921), (16279) are inconsistent by
% 236.84/44.73  | | | | | | | | | | | | | | | |            sub-proof #1752.
% 236.84/44.73  | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | End of split
% 236.84/44.73  | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | Case 2:
% 236.84/44.73  | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | |   (16280)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 236.84/44.73  | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.84/44.73  | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | BETA: splitting (16280) gives:
% 236.84/44.73  | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | Case 1:
% 236.84/44.73  | | | | | | | | | | | | | | | | 
% 236.84/44.73  | | | | | | | | | | | | | | | |   (16281)  all_58_5 = e1 & op(e2, e1) = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | ALPHA: (16281) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | |   (16282)  all_58_5 = e1
% 236.84/44.74  | | | | | | | | | | | | | | | |   (16283)  op(e2, e1) = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | |   (16284)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 236.84/44.74  | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 236.84/44.74  | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | BETA: splitting (16284) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16285)  all_58_9 = e1 & op(e3, e0) = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (15764), (16285), (function-axioms) are
% 236.84/44.74  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16286)  all_58_10 = e1 & op(e2, e0) = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (16267), (16286), (function-axioms) are
% 236.84/44.74  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | End of split
% 236.84/44.74  | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | |   (16287)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 236.84/44.74  | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 236.84/44.74  | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | BETA: splitting (16287) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16288)  all_58_11 = e1 & op(e1, e0) = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | ALPHA: (16288) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16289)  all_58_11 = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16290)  op(e1, e0) = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (223), (225), (14323),
% 236.84/44.74  | | | | | | | | | | | | | | | | | |            (14324), (16275), (16289), (16290),
% 236.84/44.74  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.74  | | | | | | | | | | | | | | | | | |            #1419.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16291)  all_58_15 = e1 & op(e0, e0) = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | ALPHA: (16291) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16292)  all_58_15 = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16293)  op(e0, e0) = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 236.84/44.74  | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (16276) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16294)  all_52_6 = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 236.84/44.74  | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (16283) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16295)  all_52_9 = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | REDUCE: (126), (16294) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16296)   ~ (all_52_14 = e1)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | REDUCE: (118), (16295) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16297)   ~ (all_52_11 = e1)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | SIMP: (16297) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16298)   ~ (all_52_11 = e1)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | REDUCE: (117), (16295) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | |   (16299)   ~ (all_52_13 = e1)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | |   (16300)   ~ (all_34_2 = e1)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | REDUCE: (16265), (16300) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | |   (16301)  $false
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | CLOSE: (16301) is inconsistent.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | |   (16302)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 236.84/44.74  | | | | | | | | | | | | | | | | | | |              $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | |              = all_34_1 & $i(all_34_1))
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | |   (16303)   ~ (all_46_2 = e3)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | REDUCE: (14312), (16303) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | |   (16304)  $false
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | CLOSE: (16304) is inconsistent.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | |   (16305)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | |   (16306)   ~ (all_48_2 = e0)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | REDUCE: (15910), (16306) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | |   (16307)  $false
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | CLOSE: (16307) is inconsistent.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | |   (16308)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | |              $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | |              = all_48_1 & $i(all_48_1))
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | |   (16309)  all_54_8 = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14314), (16309) are inconsistent by
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | |   (16310)   ~ (all_54_8 = e3)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | |   (16311)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | |   (16312)  all_54_4 = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (16312) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | |   (16313)  all_52_1 = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16313) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | |   (16314)  all_52_1 = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (16314) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | |   (16315)   ~ (all_52_3 = e3)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16315) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | |   (16316)   ~ (all_52_3 = e3)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (16314) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | |   (16317)   ~ (all_52_13 = e3)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16317) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | |   (16318)   ~ (all_52_13 = e3)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | |   (16319)  all_54_7 = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (16318), (16319) are inconsistent by
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | |   (16320)   ~ (all_54_7 = e3)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | |   (16321)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16321) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (16322)  all_54_7 = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (16322) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (16323)  all_52_13 = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16323) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (16324)  all_52_13 = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (16324) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (16325)   ~ (all_52_12 = e2)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (16324) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (16326)   ~ (all_52_14 = e2)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16326) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (16327)   ~ (all_52_14 = e2)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16318), (16324) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (16328)   ~ (e3 = e2)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16329)  all_54_11 = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (16329) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16330)  all_52_14 = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14319), (16330) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16331)  $false
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16331) is inconsistent.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16332)   ~ (all_54_11 = e3)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16333)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16333) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16334)  all_54_11 = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (16334) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16335)  all_52_14 = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16327), (16335) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16336)  $false
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16336) is inconsistent.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16337)   ~ (all_54_11 = e2)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16338)  all_54_11 = e1 | all_54_11 = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16339)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16339) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16340)  all_58_12 = e3 & op(e0, e3) = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16340) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16341)  op(e0, e3) = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (16316), (16341), (function-axioms) are
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16342)  all_58_13 = e3 & op(e0, e2) = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16342) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16343)  op(e0, e2) = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16344)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16344) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16345)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16345) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16346)  all_58_6 = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16347)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16347) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16348)  all_58_6 = e0 & op(e1, e3) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16346), (16348) are inconsistent by
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1678.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16349)  all_58_7 = e0 & op(e1, e2) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (15913), (16349), (function-axioms) are
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16350)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16350) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16351)  all_58_8 = e0 & op(e1, e1) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16351) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16352)  op(e1, e1) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (165), (169), (230), (14316), (14317),
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14318), (16352), (function-axioms) are
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1010.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16353)  all_58_11 = e0 & op(e1, e0) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16353) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16354)  all_58_11 = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16355)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16355) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16356)  all_58_9 = e2 & op(e3, e0) = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (16325), (16356), (function-axioms) are
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2318.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16357)  all_58_10 = e2 & op(e2, e0) = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16357) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16358)  all_58_10 = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16359)  op(e2, e0) = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16360)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16360) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16361)  all_58_1 = e2 & op(e3, e2) = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16361) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16362)  all_58_1 = e2
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16363)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16363) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16364)  all_58_0 = e0 & op(e3, e3) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16364) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16365)  op(e3, e3) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (168), (169),
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (237), (238), (242), (15763), (15764),
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15922), (16275), (16276), (16365),
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1612.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16366)  all_58_2 = e0 & op(e2, e3) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (15911), (16366), (function-axioms) are
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1985.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16367)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16367) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16368)  all_58_6 = e0 & op(e1, e3) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16368) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16369)  all_58_6 = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (162), (225), (226), (14315),
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16275), (16354), (16369), (function-axioms) are
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16370)  all_58_12 = e0 & op(e0, e3) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16370) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16371)  op(e0, e3) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16338) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16372)  all_54_11 = e1
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (16268), (16372) are inconsistent by
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2176.
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16373)  all_54_11 = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (16373) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16374)  all_52_14 = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16374) implies:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16375)  all_52_14 = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (16375) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16376)   ~ (all_52_2 = e0)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (16375) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16377)   ~ (all_52_12 = e0)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16327), (16375) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16378)   ~ (e2 = e0)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16268), (16375) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16379)   ~ (e1 = e0)
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (16375) imply:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16380)  op(e1, e0) = e0
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16381)  all_54_3 = e3
% 236.84/44.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (16381) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16382)  all_52_12 = e3
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16382) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16383)  all_52_12 = e3
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (16383) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16384)   ~ (all_52_4 = e3)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (16383) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16385)  op(e3, e0) = e3
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16386)  all_54_1 = e3
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (16384), (16386) are inconsistent by
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16387)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16388)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16388) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16389)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16389) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16390)  op(e0, e3) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16371), (16390), (function-axioms) are
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1896.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16391)  all_58_13 = e2 & op(e0, e2) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16391) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16392)  op(e0, e2) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16343), (16392), (function-axioms) are
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16393)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16393) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16394)  all_58_14 = e2 & op(e0, e1) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16394) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16395)  op(e0, e1) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16311) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16396)  all_54_8 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (16396) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16397)  all_52_2 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16397) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16398)  all_52_2 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (16398) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16399)   ~ (all_52_3 = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16399) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16400)   ~ (all_52_3 = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16401)  all_54_12 = e3
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (16316), (16401) are inconsistent by
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16402)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16402) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16403)  all_54_12 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (16400), (16403) are inconsistent by
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2264.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16404)   ~ (all_54_12 = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16405)  all_54_12 = e1 | all_54_12 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16405) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16406)  all_54_12 = e1
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (15761), (16406) are inconsistent by
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2263.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16407)  all_54_12 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (16407) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16408)  all_52_3 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16408) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16409)  all_52_3 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (16409) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16410)   ~ (all_52_11 = e0)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16410) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16411)   ~ (all_52_11 = e0)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16412)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16412) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16413)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16413) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16414)  op(e3, e0) = all_56_25
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16415)  op(e3, all_56_25) = e3
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16302) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25, e0, e3, simplifying with (16385),
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (16414) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16416)  all_56_25 = e3
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16415), (16416) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16417)  op(e3, e3) = e3
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15765), (16417), (function-axioms) are
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1578.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16418)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 &
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_34_1)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16418) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16419)   ~ (all_34_1 = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16420)  op(e0, e1) = all_34_1
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16263), (16395), (16419), (16420),
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2236.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16421)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16421) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16422)  op(e2, e0) = all_56_27
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16423)  op(e2, all_56_27) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15922), (16308), (16359), (16422), (16423),
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1059.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16424)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16424) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16425)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16425) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16426)  op(e1, e0) = all_56_29
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16427)  op(e1, all_56_29) = e1
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16387) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16428)  all_54_1 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (16428) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16429)  all_52_4 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16429) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16430)  all_52_4 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (16430) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16431)   ~ (all_52_8 = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16431) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16432)   ~ (all_52_8 = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16433)  all_54_2 = e3
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (16433) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16434)  all_52_8 = e3
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14316), (16434) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16435)  $false
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16435) is inconsistent.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16436)   ~ (all_54_2 = e3)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16437)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16437) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16438)  all_54_2 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (16432), (16438) are inconsistent by
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1986.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16439)   ~ (all_54_2 = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16440)  all_54_2 = e1 | all_54_2 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16440) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16441)  all_54_2 = e1
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (15763), (16441) are inconsistent by
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1337.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16442)  all_54_2 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (16442) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16443)  all_52_8 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16443) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16444)  all_52_8 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_29, e0, e1, simplifying with (16380),
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (16426) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16445)  all_56_29 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16427), (16445) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16446)  op(e1, e0) = e1
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (223), (14323), (16275), (16346),
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16446), (function-axioms) are inconsistent by
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1420.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16447)  all_54_1 = e1 | all_54_1 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (15762), (15912), (16447) are inconsistent
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2049.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16448)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16448) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16449)  op(e0, all_56_31) = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16266), (16449) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16450)  op(e0, e1) = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (16411), (16450), (function-axioms) are
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1911.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16451)  all_54_8 = e1 | all_54_8 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (15760), (16376), (16451) are inconsistent
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1950.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16452)  all_58_15 = e2 & op(e0, e0) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16452) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16453)  all_58_15 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (15922), (16275), (16276), (16292),
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16362), (16453), (function-axioms) are
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #359.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16454)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (15764), (16325), (16377), (16454) are
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16455)  all_58_3 = e2 & op(e2, e2) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16455) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16456)  op(e2, e2) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (165), (231), (234),
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16282), (16283), (16359), (16456),
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2119.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16457)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16457) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16458)  all_58_7 = e2 & op(e1, e2) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16458) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16459)  all_58_7 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16275), (16459) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16460)  e2 = e1
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16460) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16461)  e2 = e1
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16358), (16461) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16462)  all_58_10 = e1
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (221), (222), (16292),
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16354), (16462), (function-axioms) are
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1597.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16463)  all_58_13 = e2 & op(e0, e2) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16463) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16464)  op(e0, e2) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16343), (16464), (function-axioms) are
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16465)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16465) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16466)  all_58_11 = e2 & op(e1, e0) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16466) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16467)  all_58_11 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16354), (16467) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16468)  e2 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16468) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16469)  e2 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16346), (16469) imply:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16470)  all_58_6 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (162), (225), (226), (14315),
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16275), (16354), (16470), (function-axioms) are
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #960.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16471)  all_58_15 = e2 & op(e0, e0) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16471) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16472)  all_58_15 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16292), (16472) are inconsistent by
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2231.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16473)  all_58_7 = e2 & op(e1, e2) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16473) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16474)  all_58_7 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16275), (16474) are inconsistent by
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2134.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16475)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16475) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16476)  all_58_8 = e2 & op(e1, e1) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16476) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16477)  op(e1, e1) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14324), (16477), (function-axioms) are
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16478)  all_58_11 = e2 & op(e1, e0) = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16478) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16479)  all_58_11 = e2
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16480)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16480) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16481)  all_58_6 = e0 & op(e1, e3) = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16481) implies:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16482)  op(e1, e3) = e0
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16338) gives:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16483)  all_54_11 = e1
% 236.84/44.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (16268), (16483) are inconsistent by
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2176.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16484)  all_54_11 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (16484) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16485)  all_52_14 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16485) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16486)  all_52_14 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (16486) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16487)   ~ (all_52_2 = e0)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (16482), (16487), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16488)  all_58_7 = e0 & op(e1, e2) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (15913), (16488), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16489)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16489) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16490)  all_58_8 = e0 & op(e1, e1) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16490) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16491)  op(e1, e1) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (165), (169), (230), (14316), (14317),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14318), (16491), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1010.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16492)  all_58_11 = e0 & op(e1, e0) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16492) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16493)  all_58_11 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16479), (16493) are inconsistent by
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2110.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16494)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16494) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16495)  all_58_14 = e3 & op(e0, e1) = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (14318), (16495), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16496)  all_58_15 = e3 & op(e0, e0) = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16496) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16497)  all_58_15 = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (168),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (223), (225), (226), (14319), (15764),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16267), (16275), (16497), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #358.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (16498)  all_54_7 = e1 | all_54_7 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (15916), (16267), (16498) are inconsistent
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2293.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | |   (16499)   ~ (all_54_4 = e3)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | |   (16500)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (16499) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | |   (16501)   ~ (all_52_1 = e3)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | |   (16502)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (15765), (16501), (16502),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | |            #1208.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | |   (16503)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16503) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (16504)  all_58_6 = e3 & op(e1, e3) = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16504) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (16505)  op(e1, e3) = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (14314), (16505), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (16506)  all_58_12 = e3 & op(e0, e3) = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16506) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (16507)  all_58_12 = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (16508)  op(e0, e3) = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16509)  all_58_15 = e0 & op(e0, e0) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16509) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16510)  op(e0, e0) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16293), (16510), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16511)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16511) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16512)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16512) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16513)  all_58_12 = e0 & op(e0, e3) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16507), (16513) are inconsistent by
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1641.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16514)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16514) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16515)  all_58_13 = e0 & op(e0, e2) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16515) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16516)  all_58_13 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16517)  op(e0, e2) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (237), (238), (15921),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16275), (16516), (16517), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1375.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16518)  all_58_14 = e0 & op(e0, e1) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16518) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16519)  op(e0, e1) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16500) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16520)  all_54_4 = e2
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (16520) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16521)  all_52_1 = e2
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16521) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16522)  all_52_1 = e2
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (16522) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16523)   ~ (all_52_2 = e2)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16523) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16524)   ~ (all_52_2 = e2)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (16522) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16525)   ~ (all_52_3 = e2)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16525) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16526)   ~ (all_52_3 = e2)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (16522) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16527)   ~ (all_52_13 = e2)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16527) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16528)   ~ (all_52_13 = e2)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (16522) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16529)  op(e2, e3) = e2
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16530)  all_54_7 = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (16530) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16531)  all_52_13 = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (16531) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16532)   ~ (all_52_12 = e3)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (16531) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16533)   ~ (all_52_14 = e3)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16534)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16534) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16535)  all_58_0 = e3 & op(e3, e3) = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16535) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16536)  op(e3, e3) = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15765), (16536), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1578.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16537)  all_58_1 = e3 & op(e3, e2) = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16537) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16538)  all_58_1 = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16539)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16539) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16540)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (16526), (16540), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2315.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16541)  all_58_13 = e2 & op(e0, e2) = e2
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16541) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16542)  op(e0, e2) = e2
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16311) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16543)  all_54_8 = e2
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (16524), (16543) are inconsistent by
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2007.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16544)   ~ (all_54_8 = e2)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16545)  all_54_8 = e1 | all_54_8 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16545) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16546)  all_54_8 = e1
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (15760), (16546) are inconsistent by
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1951.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16547)  all_54_8 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (16547) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16548)  all_52_2 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16548) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16549)  all_52_2 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (16549) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16550)   ~ (all_52_14 = e0)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16550) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16551)   ~ (all_52_14 = e0)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16524), (16549) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16552)   ~ (e2 = e0)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15760), (16549) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16553)   ~ (e1 = e0)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (16549) imply:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16554)  op(e1, e3) = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14311) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16555)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 &
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16555) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16556)  op(e1, e3) = all_6_1
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16557)  all_54_11 = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (14319), (16557) are inconsistent by
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16558)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16305) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16559)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_46_1 & $i(all_46_0) &
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16559) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16560)  op(e1, e3) = all_46_1
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (112), (120), (121), (160), (162),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (190), (201), (202), (214), (235), (255),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (280), (281), (14316), (14318), (15758),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15763), (15764), (16263), (16268), (16276),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16298), (16302), (16508), (16519), (16529),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16532), (16538), (16542), (16551), (16554),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16556), (16558), (16560), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #356.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16561)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 &
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16561) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16562)  op(e1, e3) = all_46_1
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (112), (120), (121), (160), (162),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (190), (201), (202), (214), (235), (255),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (280), (281), (14316), (14318), (15758),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15763), (15764), (16263), (16268), (16276),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16298), (16302), (16508), (16519), (16529),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16532), (16538), (16542), (16551), (16554),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16556), (16558), (16562), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #356.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16563)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 &
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_6_1)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16305), (16554), (16563), (function-axioms) are
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #443.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16564)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16564) gives:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16565)  all_58_14 = e2 & op(e0, e1) = e2
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16565) implies:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16566)  all_58_14 = e2
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (237), (238), (15921),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16275), (16507), (16512), (16566),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1067.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16567)  all_58_15 = e2 & op(e0, e0) = e2
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16292), (16567) are inconsistent by
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1917.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16568)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (14316), (16532), (16568),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1515.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16569)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (269), (15916), (16267), (16529),
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16569), (function-axioms) are inconsistent by
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2292.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16570)  all_54_4 = e1 | all_54_4 = e0
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (15759), (15911), (16570) are inconsistent
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1922.
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | |   (16571)  all_58_10 = e1 & op(e2, e0) = e1
% 236.84/44.77  | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (16267), (16571), (function-axioms) are
% 236.84/44.77  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 236.84/44.77  | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | |   (16572)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 236.84/44.77  | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 236.84/44.77  | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | REF_CLOSE: (8), (160), (14323), (16268), (16572),
% 236.84/44.77  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.77  | | | | | | | | | | | | |            #367.
% 236.84/44.77  | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | |   (16573)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 236.84/44.77  | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | REF_CLOSE: (158), (162), (15913), (15914), (16573),
% 236.84/44.77  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.77  | | | | | | | | | |            #1990.
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | 
% 236.84/44.77  | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | 
% 236.84/44.77  | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | 
% 236.84/44.77  | | | | | | | |   (16574)  all_12_2 = e3
% 236.84/44.77  | | | | | | | |   (16575)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 &
% 236.84/44.77  | | | | | | | |              op(e0, e3) = all_12_1 & $i(all_12_0) &
% 236.84/44.77  | | | | | | | |              $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 236.84/44.77  | | | | | | | |              all_12_1 & $i(all_12_1))
% 236.84/44.77  | | | | | | | | 
% 236.84/44.77  | | | | | | | | COMBINE_EQS: (346), (16574) imply:
% 236.84/44.77  | | | | | | | |   (16576)  all_4_2 = e3
% 236.84/44.77  | | | | | | | | 
% 236.84/44.77  | | | | | | | | COMBINE_EQS: (334), (16576) imply:
% 236.84/44.77  | | | | | | | |   (16577)  all_26_2 = e3
% 236.84/44.77  | | | | | | | | 
% 236.84/44.77  | | | | | | | | COMBINE_EQS: (254), (16576) imply:
% 236.84/44.77  | | | | | | | |   (16578)  all_56_31 = e3
% 236.84/44.77  | | | | | | | | 
% 236.84/44.77  | | | | | | | | REDUCE: (368), (16576) imply:
% 236.84/44.77  | | | | | | | |   (16579)   ~ (all_52_3 = e3)
% 236.84/44.77  | | | | | | | | 
% 236.84/44.77  | | | | | | | | REDUCE: (387), (16576) imply:
% 236.84/44.77  | | | | | | | |   (16580)   ~ (all_52_12 = e3)
% 236.84/44.77  | | | | | | | | 
% 236.84/44.77  | | | | | | | | REDUCE: (388), (16576) imply:
% 236.84/44.77  | | | | | | | |   (16581)   ~ (all_52_13 = e3)
% 236.84/44.77  | | | | | | | | 
% 236.84/44.77  | | | | | | | | BETA: splitting (222) gives:
% 236.84/44.77  | | | | | | | | 
% 236.84/44.77  | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | 
% 236.84/44.77  | | | | | | | | |   (16582)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3
% 236.84/44.77  | | | | | | | | |              & op(e2, e0) = e3)
% 236.84/44.77  | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | REF_CLOSE: (164), (168), (16580), (16581), (16582),
% 236.84/44.77  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.77  | | | | | | | | |            #1592.
% 236.84/44.77  | | | | | | | | | 
% 236.84/44.77  | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | 
% 236.84/44.77  | | | | | | | | |   (16583)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 236.84/44.77  | | | | | | | | |              e3 & op(e0, e0) = e3)
% 236.84/44.77  | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | BETA: splitting (16583) gives:
% 236.84/44.77  | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | |   (16584)  all_58_11 = e3 & op(e1, e0) = e3
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | ALPHA: (16584) implies:
% 236.84/44.77  | | | | | | | | | |   (16585)  op(e1, e0) = e3
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | REF_CLOSE: (160), (14319), (16585), (function-axioms) are
% 236.84/44.77  | | | | | | | | | |            inconsistent by sub-proof #2149.
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | |   (16586)  all_58_15 = e3 & op(e0, e0) = e3
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | ALPHA: (16586) implies:
% 236.84/44.77  | | | | | | | | | |   (16587)  all_58_15 = e3
% 236.84/44.77  | | | | | | | | | |   (16588)  op(e0, e0) = e3
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | BETA: splitting (245) gives:
% 236.84/44.77  | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | |   (16589)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 236.84/44.77  | | | | | | | | | | |              & op(e2, e3) = e3)
% 236.84/44.77  | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | BETA: splitting (16589) gives:
% 236.84/44.77  | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | |   (16590)  all_58_0 = e3 & op(e3, e3) = e3
% 236.84/44.77  | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | ALPHA: (16590) implies:
% 236.84/44.77  | | | | | | | | | | | |   (16591)  op(e3, e3) = e3
% 236.84/44.77  | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | REF_CLOSE: (8), (15765), (16591), (function-axioms) are
% 236.84/44.77  | | | | | | | | | | | |            inconsistent by sub-proof #1578.
% 236.84/44.77  | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | |   (16592)  all_58_2 = e3 & op(e2, e3) = e3
% 236.84/44.77  | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | ALPHA: (16592) implies:
% 236.84/44.77  | | | | | | | | | | | |   (16593)  all_58_2 = e3
% 236.84/44.77  | | | | | | | | | | | |   (16594)  op(e2, e3) = e3
% 236.84/44.77  | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | BETA: splitting (246) gives:
% 236.84/44.77  | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | |   (16595)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 236.84/44.77  | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 236.84/44.77  | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | BETA: splitting (16595) gives:
% 236.84/44.77  | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | |   (16596)  all_58_0 = e3 & op(e3, e3) = e3
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | ALPHA: (16596) implies:
% 236.84/44.77  | | | | | | | | | | | | | |   (16597)  op(e3, e3) = e3
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | REF_CLOSE: (8), (15765), (16597), (function-axioms) are
% 236.84/44.77  | | | | | | | | | | | | | |            inconsistent by sub-proof #1578.
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | |   (16598)  all_58_1 = e3 & op(e3, e2) = e3
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | ALPHA: (16598) implies:
% 236.84/44.77  | | | | | | | | | | | | | |   (16599)  op(e3, e2) = e3
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e3,
% 236.84/44.77  | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (16594) gives:
% 236.84/44.77  | | | | | | | | | | | | | |   (16600)  all_52_1 = e3
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 236.84/44.77  | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (16599) gives:
% 236.84/44.77  | | | | | | | | | | | | | |   (16601)  all_52_4 = e3
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | REDUCE: (149), (16600) imply:
% 236.84/44.77  | | | | | | | | | | | | | |   (16602)   ~ (all_52_2 = e3)
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | REDUCE: (148), (16600) imply:
% 236.84/44.77  | | | | | | | | | | | | | |   (16603)   ~ (all_52_3 = e3)
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | REDUCE: (146), (16600) imply:
% 236.84/44.77  | | | | | | | | | | | | | |   (16604)   ~ (all_52_9 = e3)
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | REDUCE: (145), (16600) imply:
% 236.84/44.77  | | | | | | | | | | | | | |   (16605)   ~ (all_52_13 = e3)
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | REDUCE: (136), (16601) imply:
% 236.84/44.77  | | | | | | | | | | | | | |   (16606)   ~ (all_52_6 = e3)
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | REDUCE: (134), (16601) imply:
% 236.84/44.77  | | | | | | | | | | | | | |   (16607)   ~ (all_52_8 = e3)
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | REDUCE: (369), (16601) imply:
% 236.84/44.77  | | | | | | | | | | | | | |   (16608)   ~ (all_8_2 = e3)
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 236.84/44.77  | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | |   (16609)   ~ (all_14_2 = e0)
% 236.84/44.77  | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | REDUCE: (344), (16609) imply:
% 236.84/44.77  | | | | | | | | | | | | | | |   (16610)   ~ (all_8_2 = e0)
% 236.84/44.77  | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 236.84/44.77  | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | |   (16611)   ~ (all_22_2 = e1)
% 236.84/44.77  | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | REDUCE: (326), (16611) imply:
% 236.84/44.77  | | | | | | | | | | | | | | | |   (16612)   ~ (all_8_2 = e1)
% 236.84/44.77  | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 236.84/44.77  | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | |   (16613)  all_54_5 = e3
% 236.84/44.77  | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (16613) imply:
% 236.84/44.77  | | | | | | | | | | | | | | | | |   (16614)  all_8_2 = e3
% 236.84/44.77  | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | REDUCE: (14325), (16614) imply:
% 236.84/44.77  | | | | | | | | | | | | | | | | |   (16615)  $false
% 236.84/44.77  | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | CLOSE: (16615) is inconsistent.
% 236.84/44.77  | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | |   (16616)   ~ (all_54_5 = e3)
% 236.84/44.77  | | | | | | | | | | | | | | | | |   (16617)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 236.84/44.77  | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | BETA: splitting (16617) gives:
% 236.84/44.77  | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | |   (16618)  all_54_5 = e2
% 236.84/44.77  | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (16618) imply:
% 236.84/44.77  | | | | | | | | | | | | | | | | | |   (16619)  all_8_2 = e2
% 236.84/44.77  | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (16619) imply:
% 236.84/44.77  | | | | | | | | | | | | | | | | | |   (16620)  all_56_11 = e2
% 236.84/44.77  | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | REDUCE: (373), (16619) imply:
% 236.84/44.77  | | | | | | | | | | | | | | | | | |   (16621)   ~ (all_52_7 = e2)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | REDUCE: (375), (16619) imply:
% 236.84/44.77  | | | | | | | | | | | | | | | | | |   (16622)   ~ (all_52_9 = e2)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | REDUCE: (14325), (16619) imply:
% 236.84/44.77  | | | | | | | | | | | | | | | | | |   (16623)   ~ (e3 = e2)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | REDUCE: (42), (16619) imply:
% 236.84/44.77  | | | | | | | | | | | | | | | | | |   (16624)  op(e2, e2) = e2
% 236.84/44.77  | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |   (16625)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (16625) gives:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |   (16626)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              = e3)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (163), (14314), (16599), (16620), (16626),
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |            #430.
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |   (16627)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (15763), (16578), (16579), (16627),
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |            #1411.
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |   (16628)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 236.84/44.77  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (16628) gives:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |   (16629)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              = e2)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (16620), (16621), (16622), (16629),
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |            #2325.
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |   (16630)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | |              = e0)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (16630) gives:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |   (16631)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | ALPHA: (16631) implies:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |   (16632)   ~ (all_56_11 = e2)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (16620), (16632) imply:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |   (16633)  $false
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | CLOSE: (16633) is inconsistent.
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |   (16634)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16634) gives:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | |   (16635)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16635) implies:
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | |   (16636)   ~ (all_56_31 = e0)
% 236.84/44.77  | | | | | | | | | | | | | | | | | | | | | |   (16637)   ~ (all_56_11 = e0)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16638)   ~ (all_56_1 = e0)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16639)  op(e0, e1) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16640)  op(e1, e0) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (157), (16639) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16641)  all_52_11 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (16640) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16642)  all_52_14 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (16641) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16643)   ~ (all_52_7 = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (16642) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16644)   ~ (all_52_13 = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14319), (16642) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16645)   ~ (e3 = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | |   (16646)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16646) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |   (16647)  all_58_1 = e1 & op(e3, e2) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16647) implies:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |   (16648)  op(e3, e2) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16599), (16648), (function-axioms) are
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |   (16649)  all_58_3 = e1 & op(e2, e2) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16649) implies:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |   (16650)  op(e2, e2) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16624), (16650), (function-axioms) are
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | |   (16651)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16651) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |   (16652)  all_58_7 = e1 & op(e1, e2) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16652) implies:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |   (16653)  all_58_7 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (168),
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |            (220), (223), (225), (226), (14319), (15764),
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |            (16587), (16644), (16653), (function-axioms) are
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #358.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |   (16654)  all_58_13 = e1 & op(e0, e2) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (16643), (16654), (function-axioms) are
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16655)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16655) implies:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16656)   ~ (all_56_1 = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15758), (16656) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16657)  $false
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16657) is inconsistent.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.78  | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | |   (16658)  all_54_5 = e1 | all_54_5 = e0
% 236.84/44.78  | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (16610), (16612), (16658) are inconsistent
% 236.84/44.78  | | | | | | | | | | | | | | | | | |            by sub-proof #2300.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | End of split
% 236.84/44.78  | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | End of split
% 236.84/44.78  | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | |   (16659)  all_22_2 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (16659) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | |   (16660)  all_8_2 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (16660) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | |   (16661)  all_56_11 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | REDUCE: (375), (16660) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | |   (16662)   ~ (all_52_9 = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | REDUCE: (377), (16660) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | |   (16663)   ~ (all_52_13 = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | REDUCE: (14325), (16660) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | |   (16664)   ~ (e3 = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | REDUCE: (42), (16660) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | |   (16665)  op(e2, e2) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | |   (16666)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (15763), (16662), (16666),
% 236.84/44.78  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.78  | | | | | | | | | | | | | | | | |            #1211.
% 236.84/44.78  | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | |   (16667)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 236.84/44.78  | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | BETA: splitting (16667) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | |   (16668)  all_58_8 = e1 & op(e1, e1) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14323), (16668) are inconsistent by
% 236.84/44.78  | | | | | | | | | | | | | | | | | |            sub-proof #406.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | |   (16669)  all_58_14 = e1 & op(e0, e1) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | ALPHA: (16669) implies:
% 236.84/44.78  | | | | | | | | | | | | | | | | | |   (16670)  op(e0, e1) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | |   (16671)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | BETA: splitting (16671) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |   (16672)  all_58_6 = e1 & op(e1, e3) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | ALPHA: (16672) implies:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |   (16673)  op(e1, e3) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (15760), (16673), (function-axioms) are
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |   (16674)  all_58_7 = e1 & op(e1, e2) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | ALPHA: (16674) implies:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |   (16675)  all_58_7 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (168),
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |            (220), (223), (225), (226), (14319), (15764),
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |            (16587), (16663), (16675), (function-axioms) are
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #358.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | |   (16676)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 236.84/44.78  | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | BETA: splitting (16676) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |   (16677)  all_58_8 = e1 & op(e1, e1) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14323), (16677) are inconsistent by
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |            sub-proof #406.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |   (16678)  all_58_11 = e1 & op(e1, e0) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | ALPHA: (16678) implies:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |   (16679)  all_58_11 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |   (16680)  op(e1, e0) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (157), (16670) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |   (16681)  all_52_11 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (16680) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |   (16682)  all_52_14 = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (16682) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | |   (16683)   ~ (all_52_6 = e1)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | |   (16684)   ~ (all_26_2 = e3)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | REDUCE: (16577), (16684) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | |   (16685)  $false
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | CLOSE: (16685) is inconsistent.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | |   (16686)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | |              $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | |              = all_26_1 & $i(all_26_1))
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16687)   ~ (all_46_2 = e3)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14312), (16687) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16688)  $false
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16688) is inconsistent.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |   (16689)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | |   (16690)  all_54_2 = e3
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (14316), (16690) are inconsistent by
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | |   (16691)   ~ (all_54_2 = e3)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | |   (16692)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |   (16693)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16693) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (16694)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16694) implies:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (16695)  op(e3, e1) = all_56_17
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (16696)  op(e3, all_56_17) = e3
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_17, e1, e3, simplifying with (169), (16695)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (16697)  all_56_17 = all_52_8
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16696), (16697) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (16698)  op(e3, all_52_8) = e3
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16699)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (14316), (15758), (16594), (16699),
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1210.
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16700)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16700) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16701)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16701) implies:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16702)  op(e1, e3) = all_56_5
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16703)  op(e1, all_56_5) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (16702)
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16704)  all_56_5 = all_52_2
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16703), (16704) imply:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16705)  op(e1, all_52_2) = e1
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16706)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (15765), (16594), (16706),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #355.
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16707)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16707) gives:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16708)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16708) implies:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16709)  all_58_6 = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16710)  op(e1, e3) = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (42), (157), (162),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (165), (169), (223), (230), (235), (237),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14316), (14317), (14318), (16599), (16610),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16665), (16680), (16683), (16705), (16709),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16710), (function-axioms) are inconsistent by
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #399.
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16711)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16711) implies:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16712)  op(e0, e3) = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16713)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (15765), (16593), (16713),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1222.
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16714)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16714) gives:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16715)  all_58_6 = e0 & op(e1, e3) = e0
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16715) implies:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16716)  op(e1, e3) = e0
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16717)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16717) gives:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16718)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16718) implies:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16719)  all_58_6 = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16720)  op(e1, e3) = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (42), (157), (162),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (165), (169), (223), (230), (235), (237),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14316), (14317), (14318), (16599), (16610),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16665), (16680), (16683), (16705), (16719),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16720), (function-axioms) are inconsistent by
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #399.
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16721)  all_58_7 = e2 & op(e1, e2) = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (117), (123),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (164), (165), (197), (212), (221), (223),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (235), (269), (281), (14311),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14317), (14319), (15763), (15765), (16575),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16581), (16588), (16599), (16610), (16661),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16662), (16663), (16679), (16680), (16686),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16689), (16692), (16698), (16712), (16716),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16721), (function-axioms) are inconsistent by
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #351.
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16722)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (14324), (16680), (16722),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #398.
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16723)  all_58_12 = e0 & op(e0, e3) = e0
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16723) implies:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16724)  op(e0, e3) = e0
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16712), (16724), (function-axioms) are
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1896.
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16725)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16725) implies:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16726)  op(e0, e3) = all_56_7
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16727)  op(e0, all_56_7) = e0
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (159), (16726)
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16728)  all_56_7 = all_52_3
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16727), (16728) imply:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16729)  op(e0, all_52_3) = e0
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16730)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (15765), (16594), (16730),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #355.
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16731)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16731) gives:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16732)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16732) implies:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16733)  all_58_6 = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (157), (159), (162), (165), (169),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (230), (239), (14315), (14316), (14317),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14318), (15765), (16588), (16593), (16680),
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16729), (16733), (function-axioms) are
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #396.
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16734)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16734) implies:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16735)  op(e0, e3) = e2
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16736)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (15765), (16593), (16736),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1222.
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16737)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16737) gives:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16738)  all_58_6 = e0 & op(e1, e3) = e0
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16738) implies:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16739)  op(e1, e3) = e0
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16740)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16740) gives:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16741)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16741) implies:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16742)  all_58_6 = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (157), (159), (162), (165), (169),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (230), (239), (14315), (14316), (14317),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14318), (15765), (16588), (16593), (16680),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16729), (16742), (function-axioms) are
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #396.
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16743)  all_58_7 = e2 & op(e1, e2) = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (117), (123),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (164), (165), (197), (212), (221), (223),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (235), (269), (281), (14311),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14317), (14319), (15763), (15765), (16575),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16581), (16588), (16599), (16610), (16661),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16662), (16663), (16679), (16680), (16686),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16689), (16692), (16698), (16735), (16739),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16743), (function-axioms) are inconsistent by
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #351.
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16744)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (14324), (16680), (16744),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #398.
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16745)  all_58_12 = e0 & op(e0, e3) = e0
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16745) implies:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16746)  op(e0, e3) = e0
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16735), (16746), (function-axioms) are
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1896.
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (16747)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16747) implies:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (16748)  op(e2, e1) = all_56_19
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (16749)  op(e2, all_56_19) = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (165), (16748)
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (16750)  all_56_19 = all_52_9
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16749), (16750) imply:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (16751)  op(e2, all_52_9) = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16752)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (14316), (15758), (16594), (16752),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1210.
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16753)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16753) gives:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16754)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16754) implies:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16755)  op(e1, e3) = all_56_5
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16756)  op(e1, all_56_5) = e1
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (16755)
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16757)  all_56_5 = all_52_2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16756), (16757) imply:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16758)  op(e1, all_52_2) = e1
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16759)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (15765), (16594), (16759),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #355.
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16760)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16760) gives:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16761)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16761) implies:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16762)  all_58_6 = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16763)  op(e1, e3) = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (42), (157), (162),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (165), (169), (223), (230), (235), (237),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14316), (14317), (14318), (16599), (16610),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16665), (16680), (16683), (16758), (16762),
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16763), (function-axioms) are inconsistent by
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #399.
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16764)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16764) implies:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16765)  op(e0, e3) = e2
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16766)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16766) gives:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16767)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16767) implies:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16768)  all_58_6 = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16769)  op(e1, e3) = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (42), (157), (162),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (165), (169), (223), (230), (235), (237),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14316), (14317), (14318), (16599), (16610),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16665), (16680), (16683), (16758), (16768),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16769), (function-axioms) are inconsistent by
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #399.
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16770)  all_58_7 = e2 & op(e1, e2) = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (160), (165),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (223), (225), (226), (235), (14319),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15765), (16575), (16588), (16599), (16610),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16661), (16662), (16665), (16679), (16680),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16686), (16751), (16765), (16770),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #350.
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16771)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (14324), (16680), (16771),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #398.
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16772)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16772) implies:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16773)  op(e0, e3) = all_56_7
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16774)  op(e0, all_56_7) = e0
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7, e3, e0, simplifying with (159), (16773)
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16775)  all_56_7 = all_52_3
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16774), (16775) imply:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16776)  op(e0, all_52_3) = e0
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16777)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (15765), (16594), (16777),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #355.
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16778)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16778) gives:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16779)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16779) implies:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16780)  all_58_6 = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (157), (159), (162), (165), (169),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (230), (239), (14315), (14316), (14317),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14318), (15765), (16588), (16593), (16680),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16776), (16780), (function-axioms) are
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #396.
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16781)  all_58_12 = e2 & op(e0, e3) = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16781) implies:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16782)  op(e0, e3) = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16783)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (15765), (16593), (16783),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1222.
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16784)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16784) gives:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16785)  all_58_6 = e0 & op(e1, e3) = e0
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16785) implies:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16786)  all_58_6 = e0
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16787)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16787) gives:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16788)  all_58_6 = e2 & op(e1, e3) = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16788) implies:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16789)  all_58_6 = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16786), (16789) are inconsistent by
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1982.
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16790)  all_58_7 = e2 & op(e1, e2) = e2
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (160), (165),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (223), (225), (226), (235), (14319),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15765), (16575), (16588), (16599), (16610),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16661), (16662), (16665), (16679), (16680),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16686), (16751), (16782), (16790),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #350.
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16791)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (14324), (16680), (16791),
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #398.
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16792)  all_58_12 = e0 & op(e0, e3) = e0
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16792) implies:
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16793)  op(e0, e3) = e0
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16782), (16793), (function-axioms) are
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1896.
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 236.84/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.81  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | |   (16794)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16794) gives:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (16795)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16795) implies:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (16796)  op(e1, all_56_21) = e1
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14313), (16796) imply:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (16797)  op(e1, e3) = e1
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (15760), (16797), (function-axioms) are
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (16798)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16588), (16670), (16798), (function-axioms)
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #349.
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.82  | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | End of split
% 237.14/44.82  | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | End of split
% 237.14/44.82  | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | End of split
% 237.14/44.82  | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | Case 2:
% 237.14/44.82  | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | |   (16799)  all_14_2 = e0
% 237.14/44.82  | | | | | | | | | | | | | | |   (16800)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0
% 237.14/44.82  | | | | | | | | | | | | | | |              & op(e2, e0) = all_14_1 & $i(all_14_0) &
% 237.14/44.82  | | | | | | | | | | | | | | |              $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0)
% 237.14/44.82  | | | | | | | | | | | | | | |              = all_14_1 & $i(all_14_1))
% 237.14/44.82  | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | COMBINE_EQS: (344), (16799) imply:
% 237.14/44.82  | | | | | | | | | | | | | | |   (16801)  all_8_2 = e0
% 237.14/44.82  | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | SIMP: (16801) implies:
% 237.14/44.82  | | | | | | | | | | | | | | |   (16802)  all_8_2 = e0
% 237.14/44.82  | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | COMBINE_EQS: (311), (16802) imply:
% 237.14/44.82  | | | | | | | | | | | | | | |   (16803)  all_48_2 = e0
% 237.14/44.82  | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | REDUCE: (371), (16802) imply:
% 237.14/44.82  | | | | | | | | | | | | | | |   (16804)   ~ (all_52_6 = e0)
% 237.14/44.82  | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | REDUCE: (375), (16802) imply:
% 237.14/44.82  | | | | | | | | | | | | | | |   (16805)   ~ (all_52_9 = e0)
% 237.14/44.82  | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | REDUCE: (377), (16802) imply:
% 237.14/44.82  | | | | | | | | | | | | | | |   (16806)   ~ (all_52_13 = e0)
% 237.14/44.82  | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | REDUCE: (14325), (16802) imply:
% 237.14/44.82  | | | | | | | | | | | | | | |   (16807)   ~ (e3 = e0)
% 237.14/44.82  | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 237.14/44.82  | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | Case 1:
% 237.14/44.82  | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | |   (16808)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 237.14/44.82  | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 237.14/44.82  | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | BETA: splitting (16808) gives:
% 237.14/44.82  | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.82  | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | |   (16809)  all_58_2 = e0 & op(e2, e3) = e0
% 237.14/44.82  | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16593), (16809) are inconsistent by
% 237.14/44.82  | | | | | | | | | | | | | | | | |            sub-proof #1351.
% 237.14/44.82  | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.82  | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | |   (16810)  all_58_3 = e0 & op(e2, e2) = e0
% 237.14/44.82  | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | ALPHA: (16810) implies:
% 237.14/44.82  | | | | | | | | | | | | | | | | |   (16811)  all_58_3 = e0
% 237.14/44.82  | | | | | | | | | | | | | | | | |   (16812)  op(e2, e2) = e0
% 237.14/44.82  | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 237.14/44.82  | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | |   (16813)   ~ (all_38_2 = e1)
% 237.14/44.82  | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | REDUCE: (15757), (16813) imply:
% 237.14/44.82  | | | | | | | | | | | | | | | | | |   (16814)  $false
% 237.14/44.82  | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | CLOSE: (16814) is inconsistent.
% 237.14/44.82  | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | |   (16815)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 237.14/44.82  | | | | | | | | | | | | | | | | | |              & op(e3, e1) = all_38_1 & $i(all_38_0) &
% 237.14/44.82  | | | | | | | | | | | | | | | | | |              $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1)
% 237.14/44.82  | | | | | | | | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 237.14/44.82  | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | |   (16816)   ~ (all_46_2 = e3)
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | REDUCE: (14312), (16816) imply:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | |   (16817)  $false
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | CLOSE: (16817) is inconsistent.
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | |   (16818)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 237.14/44.82  | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 237.14/44.82  | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 237.14/44.82  | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | |   (16819)   ~ (all_48_2 = e0)
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | REDUCE: (16803), (16819) imply:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | |   (16820)  $false
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | CLOSE: (16820) is inconsistent.
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | |   (16821)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | |              $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | |              = all_48_1 & $i(all_48_1))
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | |   (16822)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16822) gives:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | |   (16823)  all_58_2 = e1 & op(e2, e3) = e1
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (15759), (16823), (function-axioms) are
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | |   (16824)  all_58_3 = e1 & op(e2, e2) = e1
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16811), (16824) are inconsistent by
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1752.
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | |   (16825)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16825) gives:
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.82  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | |   (16826)  all_58_5 = e1 & op(e2, e1) = e1
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16826) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | |   (16827)  all_58_5 = e1
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | |   (16828)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (16594), (16812), (16828),
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | |            #1509.
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | |   (16829)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16829) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | |   (16830)  all_58_5 = e2 & op(e2, e1) = e2
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16830) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | |   (16831)  all_58_5 = e2
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16827), (16831) are inconsistent by
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1665.
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | |   (16832)  all_58_10 = e2 & op(e2, e0) = e2
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16832) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | |   (16833)  op(e2, e0) = e2
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (16834)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16834) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16835)  all_58_9 = e1 & op(e3, e0) = e1
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (15764), (16835), (function-axioms) are
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16836)  all_58_10 = e1 & op(e2, e0) = e1
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16836) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16837)  all_58_10 = e1
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16838)  op(e2, e0) = e1
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (162), (163),
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (168), (169), (170), (211), (216),
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (224), (227), (228), (230), (233),
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (238), (242), (243), (244),
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (14313), (14316), (14317), (14318),
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            (14323), (15756), (15760), (15762), (15763),
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            (15764), (15765), (16587), (16588), (16594),
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            (16599), (16800), (16805), (16811), (16812),
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            (16815), (16818), (16821), (16837), (16838),
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            #345.
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (16839)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16839) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16840)  all_58_11 = e1 & op(e1, e0) = e1
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16840) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16841)  all_58_11 = e1
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16842)  op(e1, e0) = e1
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16843)  all_58_15 = e0 & op(e0, e0) = e0
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16843) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16844)  op(e0, e0) = e0
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16588), (16844), (function-axioms) are
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2079.
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16845)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16845) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16846)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16847)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16847) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16848)  all_58_6 = e0 & op(e1, e3) = e0
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16848) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16849)  all_58_6 = e0
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16850)  op(e1, e3) = e0
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16851)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (15765), (16594), (16851),
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #355.
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16852)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16852) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16853)  all_58_6 = e2 & op(e1, e3) = e2
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16853) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16854)  all_58_6 = e2
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16849), (16854) are inconsistent by
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1982.
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16855)  all_58_12 = e2 & op(e0, e3) = e2
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16855) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16856)  op(e0, e3) = e2
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16846) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16857)  all_58_9 = e0 & op(e3, e0) = e0
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16857) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16858)  op(e3, e0) = e0
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16859)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16859) gives:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16860)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16860) implies:
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16861)  op(e3, e0) = all_56_25
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16862)  op(e3, all_56_25) = e3
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16858), (16861), (16862), (function-axioms)
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1926.
% 237.14/44.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16863)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16863) implies:
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16864)  op(e2, e0) = all_56_27
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16865)  op(e2, all_56_27) = e2
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16812), (16821), (16833), (16864), (16865),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1059.
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16866)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (225),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (14315), (14323), (14324), (16578),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16818), (16841), (16842), (16850), (16856),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16866), (function-axioms) are inconsistent by
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #344.
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16867)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (16833), (16842), (16867),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2102.
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16868)  all_58_7 = e0 & op(e1, e2) = e0
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (16804), (16868), (function-axioms) are
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16869)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (157), (165), (169), (230), (14316),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14317), (14318), (16842), (16869),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #400.
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16870)  all_58_15 = e1 & op(e0, e0) = e1
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16587), (16870) are inconsistent by
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1393.
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |   (16871)  all_58_10 = e1 & op(e2, e0) = e1
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16871) implies:
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |   (16872)  all_58_10 = e1
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |   (16873)  op(e2, e0) = e1
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (162), (163),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (168), (169), (170), (211), (216),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (224), (227), (228), (230), (233),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (238), (242), (243), (244),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |            (246), (14313), (14316), (14317), (14318),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |            (14323), (15756), (15760), (15762), (15763),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |            (15764), (15765), (16587), (16588), (16594),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |            (16599), (16800), (16805), (16811), (16812),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |            (16815), (16818), (16821), (16872), (16873),
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | |            #345.
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | Case 2:
% 237.14/44.84  | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | |   (16874)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 237.14/44.84  | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 237.14/44.84  | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (16805), (16806), (16874),
% 237.14/44.84  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.14/44.84  | | | | | | | | | | | | | | | |            #1991.
% 237.14/44.84  | | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | Case 2:
% 237.14/44.84  | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | |   (16875)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 237.14/44.84  | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 237.14/44.84  | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | | REF_CLOSE: (168), (169), (14316), (16580), (16875),
% 237.14/44.84  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.14/44.84  | | | | | | | | | | | | |            #1515.
% 237.14/44.84  | | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | Case 2:
% 237.14/44.84  | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | |   (16876)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 237.14/44.84  | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 237.14/44.84  | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | | REF_CLOSE: (159), (163), (14314), (16579), (16876),
% 237.14/44.84  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.14/44.84  | | | | | | | | | | |            #1451.
% 237.14/44.84  | | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | | 
% 237.14/44.84  | | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | | 
% 237.14/44.84  | | | | | | | | End of split
% 237.14/44.84  | | | | | | | | 
% 237.14/44.84  | | | | | | | End of split
% 237.14/44.84  | | | | | | | 
% 237.14/44.84  | | | | | | End of split
% 237.14/44.84  | | | | | | 
% 237.14/44.84  | | | | | Case 2:
% 237.14/44.84  | | | | | | 
% 237.14/44.84  | | | | | |   (16877)  all_8_2 = e3
% 237.14/44.84  | | | | | |   (16878)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2,
% 237.14/44.84  | | | | | |                e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~
% 237.14/44.84  | | | | | |              (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1))
% 237.14/44.84  | | | | | | 
% 237.14/44.84  | | | | | | COMBINE_EQS: (320), (16877) imply:
% 237.14/44.84  | | | | | |   (16879)  all_42_2 = e3
% 237.14/44.84  | | | | | | 
% 237.14/44.84  | | | | | | COMBINE_EQS: (353), (16877) imply:
% 237.14/44.84  | | | | | |   (16880)  all_56_11 = e3
% 237.14/44.84  | | | | | | 
% 237.14/44.84  | | | | | | REDUCE: (366), (16877) imply:
% 237.14/44.84  | | | | | |   (16881)   ~ (all_52_1 = e3)
% 237.14/44.84  | | | | | | 
% 237.14/44.84  | | | | | | REDUCE: (369), (16877) imply:
% 237.14/44.84  | | | | | |   (16882)   ~ (all_52_4 = e3)
% 237.14/44.84  | | | | | | 
% 237.14/44.84  | | | | | | REDUCE: (373), (16877) imply:
% 237.14/44.84  | | | | | |   (16883)   ~ (all_52_7 = e3)
% 237.14/44.84  | | | | | | 
% 237.14/44.84  | | | | | | REDUCE: (377), (16877) imply:
% 237.14/44.84  | | | | | |   (16884)   ~ (all_52_13 = e3)
% 237.14/44.84  | | | | | | 
% 237.14/44.84  | | | | | | BETA: splitting (234) gives:
% 237.14/44.84  | | | | | | 
% 237.14/44.84  | | | | | | Case 1:
% 237.14/44.84  | | | | | | | 
% 237.14/44.84  | | | | | | |   (16885)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 &
% 237.14/44.84  | | | | | | |              op(e2, e2) = e3)
% 237.14/44.84  | | | | | | | 
% 237.14/44.84  | | | | | | | BETA: splitting (16885) gives:
% 237.14/44.84  | | | | | | | 
% 237.14/44.84  | | | | | | | Case 1:
% 237.14/44.84  | | | | | | | | 
% 237.14/44.84  | | | | | | | |   (16886)  all_58_2 = e3 & op(e2, e3) = e3
% 237.14/44.84  | | | | | | | | 
% 237.14/44.84  | | | | | | | | ALPHA: (16886) implies:
% 237.14/44.84  | | | | | | | |   (16887)  op(e2, e3) = e3
% 237.14/44.84  | | | | | | | | 
% 237.14/44.84  | | | | | | | | REF_CLOSE: (167), (16881), (16887), (function-axioms) are
% 237.14/44.84  | | | | | | | |            inconsistent by sub-proof #2337.
% 237.14/44.85  | | | | | | | | 
% 237.14/44.85  | | | | | | | Case 2:
% 237.14/44.85  | | | | | | | | 
% 237.14/44.85  | | | | | | | |   (16888)  all_58_3 = e3 & op(e2, e2) = e3
% 237.14/44.85  | | | | | | | | 
% 237.14/44.85  | | | | | | | | ALPHA: (16888) implies:
% 237.14/44.85  | | | | | | | |   (16889)  all_58_3 = e3
% 237.14/44.85  | | | | | | | |   (16890)  op(e2, e2) = e3
% 237.14/44.85  | | | | | | | | 
% 237.14/44.85  | | | | | | | | BETA: splitting (46) gives:
% 237.14/44.85  | | | | | | | | 
% 237.14/44.85  | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | 
% 237.14/44.85  | | | | | | | | |   (16891)   ~ (all_10_2 = e1)
% 237.14/44.85  | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | BETA: splitting (49) gives:
% 237.14/44.85  | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | |   (16892)   ~ (all_12_2 = e3)
% 237.14/44.85  | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | REDUCE: (346), (16892) imply:
% 237.14/44.85  | | | | | | | | | |   (16893)   ~ (all_4_2 = e3)
% 237.14/44.85  | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | BETA: splitting (222) gives:
% 237.14/44.85  | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | |   (16894)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 237.14/44.85  | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 237.14/44.85  | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | BETA: splitting (16894) gives:
% 237.14/44.85  | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | |   (16895)  all_58_9 = e3 & op(e3, e0) = e3
% 237.14/44.85  | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | ALPHA: (16895) implies:
% 237.14/44.85  | | | | | | | | | | | |   (16896)  all_58_9 = e3
% 237.14/44.85  | | | | | | | | | | | |   (16897)  op(e3, e0) = e3
% 237.14/44.85  | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | BETA: splitting (219) gives:
% 237.14/44.85  | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | |   (16898)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 237.14/44.85  | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 237.14/44.85  | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | BETA: splitting (16898) gives:
% 237.14/44.85  | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | |   (16899)  all_58_12 = e3 & op(e0, e3) = e3
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | ALPHA: (16899) implies:
% 237.14/44.85  | | | | | | | | | | | | | |   (16900)  all_58_12 = e3
% 237.14/44.85  | | | | | | | | | | | | | |   (16901)  op(e0, e3) = e3
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 237.14/44.85  | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (16901) gives:
% 237.14/44.85  | | | | | | | | | | | | | |   (16902)  all_52_3 = e3
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 237.14/44.85  | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (168), (16897) gives:
% 237.14/44.85  | | | | | | | | | | | | | |   (16903)  all_52_12 = e3
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | REDUCE: (140), (16902) imply:
% 237.14/44.85  | | | | | | | | | | | | | |   (16904)   ~ (all_52_7 = e3)
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | REDUCE: (139), (16902) imply:
% 237.14/44.85  | | | | | | | | | | | | | |   (16905)   ~ (all_52_11 = e3)
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | REDUCE: (113), (16903) imply:
% 237.14/44.85  | | | | | | | | | | | | | |   (16906)   ~ (all_52_13 = e3)
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | REDUCE: (112), (16903) imply:
% 237.14/44.85  | | | | | | | | | | | | | |   (16907)   ~ (all_52_14 = e3)
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | REDUCE: (365), (16903) imply:
% 237.14/44.85  | | | | | | | | | | | | | |   (16908)   ~ (all_10_2 = e3)
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | SIMP: (16908) implies:
% 237.14/44.85  | | | | | | | | | | | | | |   (16909)   ~ (all_10_2 = e3)
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | REDUCE: (387), (16903) imply:
% 237.14/44.85  | | | | | | | | | | | | | |   (16910)   ~ (all_4_2 = e3)
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 237.14/44.85  | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | |   (16911)   ~ (all_16_2 = e0)
% 237.14/44.85  | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | REDUCE: (342), (16911) imply:
% 237.14/44.85  | | | | | | | | | | | | | | |   (16912)   ~ (all_10_2 = e0)
% 237.14/44.85  | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 237.14/44.85  | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | |   (16913)  all_54_0 = e3
% 237.14/44.85  | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (16913) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | |   (16914)  all_10_2 = e3
% 237.14/44.85  | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | REDUCE: (16909), (16914) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | |   (16915)  $false
% 237.14/44.85  | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | CLOSE: (16915) is inconsistent.
% 237.14/44.85  | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | Case 2:
% 237.14/44.85  | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | |   (16916)   ~ (all_54_0 = e3)
% 237.14/44.85  | | | | | | | | | | | | | | | |   (16917)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 237.14/44.85  | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | BETA: splitting (16917) gives:
% 237.14/44.85  | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | |   (16918)  all_54_0 = e2
% 237.14/44.85  | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (16918) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | | |   (16919)  all_10_2 = e2
% 237.14/44.85  | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (16919) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | | |   (16920)  all_56_1 = e2
% 237.14/44.85  | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | REDUCE: (355), (16919) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | | |   (16921)   ~ (all_52_1 = e2)
% 237.14/44.85  | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | REDUCE: (16909), (16919) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | | |   (16922)   ~ (e3 = e2)
% 237.14/44.85  | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | REDUCE: (45), (16919) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | | |   (16923)  op(e3, e3) = e2
% 237.14/44.85  | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 237.14/44.85  | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | |   (16924)   ~ (all_20_2 = e1)
% 237.14/44.85  | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | REDUCE: (341), (16924) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | | | |   (16925)   ~ (all_4_2 = e1)
% 237.14/44.85  | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | |   (16926)  all_54_15 = e3
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (16893), (16926) are inconsistent by
% 237.14/44.85  | | | | | | | | | | | | | | | | | | |            sub-proof #2340.
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | |   (16927)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | BETA: splitting (16927) gives:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | |   (16928)  all_54_15 = e2
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (390), (16928) are inconsistent by
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | |            sub-proof #2339.
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | |   (16929)  all_54_15 = e1 | all_54_15 = e0
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | BETA: splitting (16929) gives:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | |   (16930)  all_54_15 = e1
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (16925), (16930) are inconsistent by
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2338.
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | |   (16931)  all_54_15 = e0
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (16931) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | |   (16932)  all_4_2 = e0
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | SIMP: (16932) implies:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | |   (16933)  all_4_2 = e0
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (16933) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | |   (16934)  all_56_31 = e0
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | REDUCE: (388), (16933) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | |   (16935)   ~ (all_52_13 = e0)
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | REDUCE: (389), (16933) imply:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | |   (16936)   ~ (all_52_14 = e0)
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | |   (16937)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.14/44.85  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16937) gives:
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | | 
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.14/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |   (16938)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (14314), (16881), (16921), (16938),
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |            #2333.
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |   (16939)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14313), (16934), (16939) are inconsistent by
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #342.
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |   (16940)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16940) gives:
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |   (16941)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16941) gives:
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |   (16942)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16942) implies:
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |   (16943)  op(e1, e2) = e2
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |   (16944)  op(e2, e1) = e2
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (117), (126), (162), (165), (193), (197),
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |            (258), (269), (14319), (16884), (16935), (16936),
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |            (16943), (16944), (function-axioms) are
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #340.
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |   (16945)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16920), (16934), (16945) are inconsistent by
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1731.
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |   (16946)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (16934), (16935), (16936), (16946),
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | |            #2321.
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.86  | | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16947)  all_20_2 = e1
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16948)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 237.49/44.86  | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 237.49/44.86  | | | | | | | | | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 237.49/44.86  | | | | | | | | | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (16947) imply:
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16949)  all_4_2 = e1
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | SIMP: (16949) implies:
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16950)  all_4_2 = e1
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (16950) imply:
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16951)  all_34_2 = e1
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (16950) imply:
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16952)  all_56_31 = e1
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | REDUCE: (379), (16950) imply:
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16953)   ~ (all_52_7 = e1)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | REDUCE: (386), (16950) imply:
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16954)   ~ (all_52_11 = e1)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | REDUCE: (388), (16950) imply:
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16955)   ~ (all_52_13 = e1)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | REDUCE: (389), (16950) imply:
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16956)   ~ (all_52_14 = e1)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | REDUCE: (16893), (16950) imply:
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16957)   ~ (e3 = e1)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | REDUCE: (390), (16950) imply:
% 237.49/44.86  | | | | | | | | | | | | | | | | | |   (16958)   ~ (e2 = e1)
% 237.49/44.86  | | | | | | | | | | | | | | | | | | 
% 237.49/44.86  | | | | | | | | | | | | | | | | | | REDUCE: (36), (16950) imply:
% 237.49/44.87  | | | | | | | | | | | | | | | | | |   (16959)  op(e0, e0) = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | |   (16960)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 237.49/44.87  | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 237.49/44.87  | | | | | | | | | | | | | | | | | | |            (222), (16884), (16955), (16959), (16960),
% 237.49/44.87  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.87  | | | | | | | | | | | | | | | | | | |            #878.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | |   (16961)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 237.49/44.87  | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | BETA: splitting (16961) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | |   (16962)  all_58_11 = e1 & op(e1, e0) = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | ALPHA: (16962) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | |   (16963)  op(e1, e0) = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (16956), (16963), (function-axioms) are
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | |   (16964)  all_58_15 = e1 & op(e0, e0) = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | ALPHA: (16964) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | |   (16965)  all_58_15 = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | |   (16966)   ~ (all_34_2 = e1)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | REDUCE: (16951), (16966) imply:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | |   (16967)  $false
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | CLOSE: (16967) is inconsistent.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | |   (16968)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_34_1 & $i(all_34_0) &
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | |              $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | |              = all_34_1 & $i(all_34_1))
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | |   (16969)   ~ (all_42_2 = e3)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16879), (16969) imply:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | |   (16970)  $false
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16970) is inconsistent.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | |   (16971)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | |   (16972)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16972) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | |   (16973)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16973) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | |   (16974)  op(e3, all_56_1) = e3
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16920), (16974) imply:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | |   (16975)  op(e3, e2) = e3
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (16882), (16975), (function-axioms) are
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | |   (16976)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16976) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | |   (16977)  op(e2, e3) = all_56_3
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | |   (16978)  op(e2, all_56_3) = e2
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | |              all_56_3, e3, e2, simplifying with (167), (16977)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | |   (16979)  all_56_3 = all_52_1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (16980)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16980) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16981)  all_58_0 = e1 & op(e3, e3) = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16981) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16982)  op(e3, e3) = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16923), (16982), (function-axioms) are
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16983)  all_58_1 = e1 & op(e3, e2) = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16983) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16984)  all_58_1 = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16985)  op(e3, e2) = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16986)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (16923), (16984), (16986),
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1698.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16987)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16987) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16988)  all_58_4 = e0 & op(e3, e1) = e0
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16988) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16989)  all_58_4 = e0
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16990)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16990) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16991)  all_58_4 = e1 & op(e3, e1) = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16991) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16992)  all_58_4 = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (16882), (16897), (16984), (16992),
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1437.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16993)  all_58_5 = e1 & op(e2, e1) = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16993) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16994)  all_58_5 = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16995)  op(e2, e1) = e1
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16996)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (16989), (16994), (16996) are
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #339.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16997)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16997) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16998)  all_58_8 = e2 & op(e1, e1) = e2
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16998) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16999)  op(e1, e1) = e2
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14324), (16999), (function-axioms) are
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17000)  all_58_14 = e2 & op(e0, e1) = e2
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17000) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17001)  all_58_14 = e2
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17002)  op(e0, e1) = e2
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17003)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (16890), (16921), (17003),
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #998.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17004)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17004) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17005)  all_58_5 = e2 & op(e2, e1) = e2
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (229), (230),
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16989), (16994), (17001), (17005),
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #338.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17006)  all_58_10 = e2 & op(e2, e0) = e2
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17006) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17007)  op(e2, e0) = e2
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17008)  all_58_15 = e0 & op(e0, e0) = e0
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17008) implies:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17009)  op(e0, e0) = e0
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16959), (17009), (function-axioms) are
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17010)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.49/44.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17010) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17011)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17012)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17012) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17013)  all_58_2 = e0 & op(e2, e3) = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17013) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17014)  all_58_2 = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17015)  op(e2, e3) = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17016)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (16923), (17014), (17016),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #796.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17017)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17017) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17018)  all_58_6 = e1 & op(e1, e3) = e1
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17018) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17019)  op(e1, e3) = e1
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17011) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17020)  all_58_12 = e0 & op(e0, e3) = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (14316), (16882),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16896), (16900), (16923), (17020),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #337.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17021)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17021) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17022)  all_58_13 = e0 & op(e0, e2) = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17022) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17023)  op(e0, e2) = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17024)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (234), (16985), (16994),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17007), (17014), (17024), (function-axioms) are
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #336.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17025)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17025) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17026)  all_58_7 = e2 & op(e1, e2) = e2
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17026) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17027)  all_58_7 = e2
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17028)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17019), (17027), (17028),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #335.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17029)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17029) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17030)  all_58_8 = e0 & op(e1, e1) = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17030) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17031)  op(e1, e1) = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (160), (162), (226), (14315), (14319),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17019), (17031), (function-axioms) are
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #457.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17032)  all_58_11 = e0 & op(e1, e0) = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17032) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17033)  op(e1, e0) = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17034)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17034) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17035)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17035) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17036)  op(e3, e0) = all_56_25
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17037)  op(e3, all_56_25) = e3
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17038)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17038) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17039)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17039) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17040)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17040) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17041)  op(e2, e3) = e3
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16977), (16978), (17041), (function-axioms)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2262.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17042)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16985), (17019), (17042),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #334.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17043)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17043) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17044)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17044) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17045)  op(e3, e1) = e1
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (67), (100), (113),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (117), (123), (140), (141), (144), (145), (146),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (149), (157), (158), (159), (160), (162),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (168), (169), (170),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (197), (198), (200), (204), (213), (219),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (231), (232), (233), (234), (238), (257),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (279), (290), (292), (301), (355),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (359), (361), (363), (365), (14311), (14312),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14313), (14315), (14316), (14317), (14318),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14324), (16912), (16952), (16955), (16965),
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17019), (17045), (function-axioms) are
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #470.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17046)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17046) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17047)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17047) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17048)  all_56_25 = e3
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17037), (17048) imply:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17049)  op(e3, e3) = e3
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16923), (17049), (function-axioms) are
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17050)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17050) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17051)  op(e3, e0) = e0
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17036), (17037), (17051), (function-axioms)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1926.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17052)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17052) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17053)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17053) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17054)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17054) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17055)   ~ (all_56_31 = e1)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16952), (17055) imply:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17056)  $false
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17056) is inconsistent.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17057)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17057) gives:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17058)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17058) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17059)   ~ (all_56_1 = e2)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16920), (17059) imply:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17060)  $false
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17060) is inconsistent.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17061)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17061) implies:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17062)  op(e0, e2) = e2
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17023), (17062), (function-axioms) are
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17063)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17002), (17007), (17033), (17063),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #389.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17064)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17064) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17065)  op(e2, e0) = all_56_27
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17066)  op(e2, all_56_27) = e2
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16890), (17007), (17065), (17066),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #954.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17067)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17067) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17068)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17068) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17069)  op(e1, e0) = all_56_29
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17070)  op(e1, all_56_29) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16878) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17071)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17071) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17072)  op(e2, e3) = all_8_1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16971) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17033), (17069), (17070), (function-axioms)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #766.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17073)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_42_1)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17073) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17074)   ~ (all_42_1 = e1)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17075)  op(e2, e3) = all_42_1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_29, e0, e1, simplifying with (17033),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (17069) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17076)  all_56_29 = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_42_1,
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (17015), (17075) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17077)  all_42_1 = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1,
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_42_1, e3, e2, simplifying with (17072),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (17075) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17078)  all_42_1 = all_8_1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17077), (17078) imply:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17079)  all_8_1 = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17074), (17077) imply:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17080)   ~ (e1 = e0)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17070), (17076) imply:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17081)  op(e1, e0) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17033), (17081), (function-axioms) are
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2284.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17082)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_8_1)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17082) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17083)   ~ (all_8_1 = e0)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17084)  op(e2, e3) = all_8_1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16971), (17015), (17083), (17084),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #897.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17085)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17085) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17086)  op(e0, all_56_31) = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16952), (17086) imply:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17087)  op(e0, e1) = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17002), (17087), (function-axioms) are
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #458.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17088)  all_58_13 = e2 & op(e0, e2) = e2
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17088) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17089)  op(e0, e2) = e2
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17023), (17089), (function-axioms) are
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17090)  all_58_14 = e0 & op(e0, e1) = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17090) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17091)  op(e0, e1) = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17002), (17091), (function-axioms) are
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #458.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17092)  all_58_12 = e1 & op(e0, e3) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (164), (216), (222), (16884),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16896), (16900), (16959), (16965), (17007),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17092), (function-axioms) are inconsistent by
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #333.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17093)  all_58_3 = e0 & op(e2, e2) = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (14316), (16882),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16889), (16896), (16923), (17093),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #332.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17094)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (165), (16995), (17007), (17094),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2120.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17095)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (14324), (16954), (17095),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #467.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17096)  all_58_9 = e0 & op(e3, e0) = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17096) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17097)  all_58_9 = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (14316), (16882),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16923), (17097), (function-axioms) are
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1956.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (17098)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (158), (162),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (170), (211), (216), (217),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (221), (222), (223), (225), (226), (229),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (235), (236), (237), (238), (239),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (241), (242), (244), (246), (14313),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (14315), (14316), (14317), (14318), (14324),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (16878), (16882), (16883), (16884), (16889),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (16890), (16896), (16897), (16900), (16923),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (16948), (16953), (16959), (16965), (16968),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (16971), (17098), (function-axioms) are
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #321.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | |   (17099)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17099) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | |   (17100)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17100) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | |   (17101)  op(e1, e3) = all_56_5
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | |   (17102)  op(e1, all_56_5) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (17101)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | |   (17103)  all_56_5 = all_52_2
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17102), (17103) imply:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | |   (17104)  op(e1, all_52_2) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (17105)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17105) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17106)  all_58_0 = e1 & op(e3, e3) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17106) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17107)  op(e3, e3) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16923), (17107), (function-axioms) are
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17108)  all_58_1 = e1 & op(e3, e2) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17108) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17109)  all_58_1 = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17110)  op(e3, e2) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17111)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (16923), (17109), (17111),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1698.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17112)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17112) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17113)  all_58_4 = e0 & op(e3, e1) = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17113) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17114)  all_58_4 = e0
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17115)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17115) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17116)  all_58_4 = e1 & op(e3, e1) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17116) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17117)  all_58_4 = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (16882), (16897), (17109), (17117),
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1437.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17118)  all_58_5 = e1 & op(e2, e1) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17118) implies:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17119)  all_58_5 = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17120)  op(e2, e1) = e1
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17121)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (17114), (17119), (17121) are
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #339.
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.49/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17122)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17122) gives:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17123)  all_58_8 = e2 & op(e1, e1) = e2
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17123) implies:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17124)  op(e1, e1) = e2
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14324), (17124), (function-axioms) are
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17125)  all_58_14 = e2 & op(e0, e1) = e2
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17125) implies:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17126)  all_58_14 = e2
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17127)  op(e0, e1) = e2
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17128)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (16890), (16921), (17128),
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #998.
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17129)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17129) gives:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17130)  all_58_5 = e2 & op(e2, e1) = e2
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (229), (230),
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17114), (17119), (17126), (17130),
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #338.
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17131)  all_58_10 = e2 & op(e2, e0) = e2
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17131) implies:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17132)  all_58_10 = e2
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17133)  op(e2, e0) = e2
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17134)  all_58_15 = e0 & op(e0, e0) = e0
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17134) implies:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17135)  op(e0, e0) = e0
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16959), (17135), (function-axioms) are
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2274.
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17136)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 237.61/44.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17136) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17137)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17138)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17139)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17139) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17140)  all_58_2 = e0 & op(e2, e3) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17140) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17141)  all_58_2 = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17142)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (16923), (17141), (17142),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #796.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17143)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17143) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17144)  all_58_6 = e1 & op(e1, e3) = e1
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17144) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17145)  op(e1, e3) = e1
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17137) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17146)  all_58_12 = e0 & op(e0, e3) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (14316), (16882),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16896), (16900), (16923), (17146),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #337.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17147)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17147) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17148)  all_58_13 = e0 & op(e0, e2) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17148) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17149)  op(e0, e2) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17150)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (234), (17110), (17119),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17133), (17141), (17150), (function-axioms) are
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #336.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17151)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17151) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17152)  all_58_7 = e2 & op(e1, e2) = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17152) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17153)  all_58_7 = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17154)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17145), (17153), (17154),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #335.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17155)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17155) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17156)  all_58_8 = e0 & op(e1, e1) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17156) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17157)  op(e1, e1) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (160), (162), (226), (14315), (14319),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17145), (17157), (function-axioms) are
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #457.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17158)  all_58_11 = e0 & op(e1, e0) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17158) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17159)  op(e1, e0) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17160)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17160) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17161)  all_58_9 = e2 & op(e3, e0) = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17161) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17162)  all_58_9 = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17163)  op(e3, e0) = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (240), (242), (246),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16923), (17114), (17162), (17163),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1560.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (17145) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17164)  all_52_2 = e1
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (17120) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17165)  all_52_9 = e1
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17104), (17164) imply:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17166)  op(e1, e1) = e1
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14324), (17166), (function-axioms) are
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #468.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17167)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17167) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17168)  all_58_11 = e2 & op(e1, e0) = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17168) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17169)  op(e1, e0) = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17159), (17169), (function-axioms) are
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #478.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17170)  all_58_15 = e2 & op(e0, e0) = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17170) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17171)  all_58_15 = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16965), (17171) imply:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17172)  e2 = e1
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17132), (17172) imply:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17173)  all_58_10 = e1
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (222), (231),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (16889), (17119), (17138), (17171),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17173), (function-axioms) are inconsistent by
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #831.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17174)  all_58_13 = e2 & op(e0, e2) = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17174) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17175)  op(e0, e2) = e2
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17149), (17175), (function-axioms) are
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17176)  all_58_14 = e0 & op(e0, e1) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17176) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17177)  op(e0, e1) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17127), (17177), (function-axioms) are
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #458.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17178)  all_58_12 = e1 & op(e0, e3) = e1
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (164), (216), (222), (16884),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16896), (16900), (16959), (16965), (17133),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17178), (function-axioms) are inconsistent by
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #333.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17179)  all_58_3 = e0 & op(e2, e2) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (14316), (16882),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16889), (16896), (16923), (17179),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #332.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17180)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (165), (17120), (17133), (17180),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2120.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17181)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (14324), (16954), (17181),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #467.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17182)  all_58_9 = e0 & op(e3, e0) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17182) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17183)  all_58_9 = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (14316), (16882),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16923), (17183), (function-axioms) are
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1956.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (17184)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (158), (162),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (170), (211), (216), (217),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (221), (222), (223), (225), (226), (229),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (235), (236), (237), (238), (239),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (241), (242), (244), (246), (14313),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (14315), (14316), (14317), (14318), (14324),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (16878), (16882), (16883), (16884), (16889),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (16890), (16896), (16897), (16900), (16923),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (16948), (16953), (16959), (16965), (16968),
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |            (16971), (17184), (function-axioms) are
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #321.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | |   (17185)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17185) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | |   (17186)  op(e0, e3) = all_56_7
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | |   (17187)  op(e0, all_56_7) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16901), (17186), (17187), (function-axioms)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2070.
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | |   (17188)  all_54_0 = e1 | all_54_0 = e0
% 237.61/44.90  | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (16891), (16912), (17188) are inconsistent
% 237.61/44.90  | | | | | | | | | | | | | | | | |            by sub-proof #2320.
% 237.61/44.90  | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | End of split
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | |   (17189)  all_16_2 = e0
% 237.61/44.90  | | | | | | | | | | | | | | |   (17190)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0
% 237.61/44.90  | | | | | | | | | | | | | | |              & op(e3, e0) = all_16_1 & $i(all_16_0) &
% 237.61/44.90  | | | | | | | | | | | | | | |              $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0)
% 237.61/44.90  | | | | | | | | | | | | | | |              = all_16_1 & $i(all_16_1))
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | COMBINE_EQS: (342), (17189) imply:
% 237.61/44.90  | | | | | | | | | | | | | | |   (17191)  all_10_2 = e0
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | SIMP: (17191) implies:
% 237.61/44.90  | | | | | | | | | | | | | | |   (17192)  all_10_2 = e0
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | COMBINE_EQS: (350), (17192) imply:
% 237.61/44.90  | | | | | | | | | | | | | | |   (17193)  all_50_2 = e0
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | COMBINE_EQS: (290), (17192) imply:
% 237.61/44.90  | | | | | | | | | | | | | | |   (17194)  all_56_1 = e0
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | REDUCE: (361), (17192) imply:
% 237.61/44.90  | | | | | | | | | | | | | | |   (17195)   ~ (all_52_4 = e0)
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | REDUCE: (16909), (17192) imply:
% 237.61/44.90  | | | | | | | | | | | | | | |   (17196)   ~ (e3 = e0)
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | REDUCE: (16891), (17192) imply:
% 237.61/44.90  | | | | | | | | | | | | | | |   (17197)   ~ (e1 = e0)
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | REDUCE: (45), (17192) imply:
% 237.61/44.90  | | | | | | | | | | | | | | |   (17198)  op(e3, e3) = e0
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | |   (17199)   ~ (all_50_2 = e0)
% 237.61/44.90  | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | REDUCE: (17193), (17199) imply:
% 237.61/44.90  | | | | | | | | | | | | | | | |   (17200)  $false
% 237.61/44.90  | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | CLOSE: (17200) is inconsistent.
% 237.61/44.90  | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | Case 2:
% 237.61/44.90  | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | |   (17201)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 237.61/44.90  | | | | | | | | | | | | | | | |              & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 237.61/44.90  | | | | | | | | | | | | | | | |              $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 237.61/44.90  | | | | | | | | | | | | | | | |              = all_50_1 & $i(all_50_1))
% 237.61/44.90  | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | BETA: splitting (17190) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | |   (17202)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 237.61/44.90  | | | | | | | | | | | | | | | | |            op(e3, e0) = all_16_1 & $i(all_16_0) &
% 237.61/44.90  | | | | | | | | | | | | | | | | |            $i(all_16_1)
% 237.61/44.90  | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | ALPHA: (17202) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | |   (17203)   ~ (all_16_0 = e2)
% 237.61/44.90  | | | | | | | | | | | | | | | | |   (17204)  op(e3, e0) = all_16_1
% 237.61/44.90  | | | | | | | | | | | | | | | | |   (17205)  op(all_16_1, e3) = all_16_0
% 237.61/44.90  | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_16_1,
% 237.61/44.90  | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (16897), (17204) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | |   (17206)  all_16_1 = e3
% 237.61/44.90  | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | REDUCE: (17205), (17206) imply:
% 237.61/44.90  | | | | | | | | | | | | | | | | |   (17207)  op(e3, e3) = all_16_0
% 237.61/44.90  | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | BETA: splitting (17201) gives:
% 237.61/44.90  | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.90  | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | |   (17208)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 237.61/44.90  | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_50_1 & $i(all_50_0) &
% 237.61/44.90  | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 237.61/44.90  | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | ALPHA: (17208) implies:
% 237.61/44.90  | | | | | | | | | | | | | | | | | |   (17209)   ~ (all_50_0 = e1)
% 237.61/44.90  | | | | | | | | | | | | | | | | | |   (17210)  op(e3, e0) = all_50_1
% 237.61/44.90  | | | | | | | | | | | | | | | | | |   (17211)  op(all_50_1, e3) = all_50_0
% 237.61/44.90  | | | | | | | | | | | | | | | | | | 
% 237.61/44.90  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 237.61/44.91  | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (16897), (17210) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17212)  all_50_1 = e3
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_16_0,
% 237.61/44.91  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (17198), (17207) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17213)  all_16_0 = e0
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | REDUCE: (17203), (17213) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17214)   ~ (e2 = e0)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | REDUCE: (17211), (17212) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17215)  op(e3, e3) = all_50_0
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_50_0,
% 237.61/44.91  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (17198), (17215) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17216)  all_50_0 = e0
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17217)   ~ (all_20_2 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (341), (17217) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17218)   ~ (all_4_2 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (117), (126), (157), (158),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (169),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (170), (189), (213), (220), (221), (222), (227),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (230), (235), (242), (244), (246), (254), (299),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (379), (386), (390), (14313), (14314), (14316),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (14317), (14318), (16881), (16882), (16884),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (16889), (16893), (16896), (17195), (17198),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (17218), (function-axioms) are inconsistent by
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            sub-proof #320.
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17219)  all_20_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17220)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (17219) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17221)  all_4_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | SIMP: (17221) implies:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17222)  all_4_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (17222) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17223)  all_34_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (17222) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17224)  all_56_31 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (379), (17222) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17225)   ~ (all_52_7 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (386), (17222) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17226)   ~ (all_52_11 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (388), (17222) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17227)   ~ (all_52_13 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (389), (17222) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17228)   ~ (all_52_14 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (16893), (17222) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17229)   ~ (e3 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (390), (17222) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17230)   ~ (e2 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (17222) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17231)  op(e0, e0) = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (82), (94), (100),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (157), (158), (160), (162), (163), (164), (165),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (167), (169), (170), (210), (211), (213), (216),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (217), (218), (219), (220), (221), (222), (223),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (236), (237), (238),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (239), (240), (241), (242), (243), (244), (246),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (14312), (14313), (14314), (14315), (14316),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (14317), (14318), (14319), (14323), (14324),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (16878), (16879), (16881), (16882), (16883),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (16884), (16889), (16890), (16896), (16897),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (16900), (17194), (17195), (17198), (17220),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (17223), (17224), (17225), (17226), (17227),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (17228), (17231), (function-axioms) are
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #305.
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17232)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 237.61/44.91  | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | ALPHA: (17232) implies:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17233)   ~ (all_50_1 = e2)
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17234)  op(e3, e0) = all_50_1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 237.61/44.91  | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (16897), (17234) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17235)  all_50_1 = e3
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_16_0,
% 237.61/44.91  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (17198), (17207) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17236)  all_16_0 = e0
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | REDUCE: (17203), (17236) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17237)   ~ (e2 = e0)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17238)   ~ (all_20_2 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (341), (17238) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17239)   ~ (all_4_2 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (117), (126), (157), (158),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (169),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (170), (189), (213), (220), (221), (222), (227),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (230), (235), (242), (244), (246), (254), (299),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (379), (386), (390), (14313), (14314), (14316),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (14317), (14318), (16881), (16882), (16884),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (16889), (16893), (16896), (17195), (17198),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (17239), (function-axioms) are inconsistent by
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            sub-proof #320.
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17240)  all_20_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17241)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (17240) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17242)  all_4_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | SIMP: (17242) implies:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17243)  all_4_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (17243) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17244)  all_34_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (17243) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17245)  all_56_31 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (379), (17243) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17246)   ~ (all_52_7 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (386), (17243) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17247)   ~ (all_52_11 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (388), (17243) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17248)   ~ (all_52_13 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (389), (17243) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17249)   ~ (all_52_14 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (16893), (17243) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17250)   ~ (e3 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (390), (17243) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17251)   ~ (e2 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (17243) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17252)  op(e0, e0) = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (82), (94), (100),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (157), (158), (160), (162), (163), (164), (165),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (167), (169), (170), (210), (211), (213), (216),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (217), (218), (219), (220), (221), (222), (223),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (236), (237), (238),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (239), (240), (241), (242), (243), (244), (246),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (14312), (14313), (14314), (14315), (14316),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (14317), (14318), (14319), (14323), (14324),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (16878), (16879), (16881), (16882), (16883),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (16884), (16889), (16890), (16896), (16897),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (16900), (17194), (17195), (17198), (17233),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (17234), (17241), (17244), (17245), (17246),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (17247), (17248), (17249), (17252),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            #304.
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | End of split
% 237.61/44.91  | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.91  | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | |   (17253)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 237.61/44.91  | | | | | | | | | | | | | | | | |            $i(all_16_1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | ALPHA: (17253) implies:
% 237.61/44.91  | | | | | | | | | | | | | | | | |   (17254)   ~ (all_16_1 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | |   (17255)  op(e3, e0) = all_16_1
% 237.61/44.91  | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_16_1,
% 237.61/44.91  | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (16897), (17255) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | |   (17256)  all_16_1 = e3
% 237.61/44.91  | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | BETA: splitting (17201) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17257)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 237.61/44.91  | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_50_1 & $i(all_50_0) &
% 237.61/44.91  | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | ALPHA: (17257) implies:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17258)   ~ (all_50_0 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17259)  op(e3, e0) = all_50_1
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17260)  op(all_50_1, e3) = all_50_0
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 237.61/44.91  | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (16897), (17259) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17261)  all_50_1 = e3
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | REDUCE: (17260), (17261) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17262)  op(e3, e3) = all_50_0
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_50_0,
% 237.61/44.91  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (17198), (17262) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | | |   (17263)  all_50_0 = e0
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17264)   ~ (all_20_2 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (341), (17264) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17265)   ~ (all_4_2 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (117), (126), (157), (158),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (169),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (170), (189), (213), (220), (221), (222), (227),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (230), (235), (242), (244), (246), (254), (299),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (379), (386), (390), (14313), (14314), (14316),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (14317), (14318), (16881), (16882), (16884),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (16889), (16893), (16896), (17195), (17198),
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            (17265), (function-axioms) are inconsistent by
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |            sub-proof #320.
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17266)  all_20_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17267)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (17266) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17268)  all_4_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | SIMP: (17268) implies:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17269)  all_4_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (17269) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17270)  all_34_2 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (17269) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17271)  all_56_31 = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (379), (17269) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17272)   ~ (all_52_7 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (386), (17269) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17273)   ~ (all_52_11 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (388), (17269) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17274)   ~ (all_52_13 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (389), (17269) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17275)   ~ (all_52_14 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (16893), (17269) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17276)   ~ (e3 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (390), (17269) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17277)   ~ (e2 = e1)
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (17269) imply:
% 237.61/44.91  | | | | | | | | | | | | | | | | | | |   (17278)  op(e0, e0) = e1
% 237.61/44.91  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (82), (94), (100),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (157), (158), (160), (162), (163), (164), (165),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (167), (169), (170), (210), (211), (213), (216),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (217), (218), (219), (220), (221), (222), (223),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (236), (237), (238),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (239), (240), (241), (242), (243), (244), (246),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (14312), (14313), (14314), (14315), (14316),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (14317), (14318), (14319), (14323), (14324),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (16878), (16879), (16881), (16882), (16883),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (16884), (16889), (16890), (16896), (16897),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (16900), (17194), (17195), (17198), (17267),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (17270), (17271), (17272), (17273), (17274),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (17275), (17278), (function-axioms) are
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #305.
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | |   (17279)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 237.61/44.92  | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | ALPHA: (17279) implies:
% 237.61/44.92  | | | | | | | | | | | | | | | | | |   (17280)   ~ (all_50_1 = e2)
% 237.61/44.92  | | | | | | | | | | | | | | | | | |   (17281)  op(e3, e0) = all_50_1
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 237.61/44.92  | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (16897), (17281) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | | | |   (17282)  all_50_1 = e3
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17283)   ~ (all_20_2 = e1)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REDUCE: (341), (17283) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17284)   ~ (all_4_2 = e1)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (117), (126), (157), (158),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (169),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (170), (189), (213), (220), (221), (222), (227),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (230), (235), (242), (244), (246), (254), (299),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (379), (386), (390), (14313), (14314), (14316),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (14317), (14318), (16881), (16882), (16884),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (16889), (16893), (16896), (17195), (17198),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (17284), (function-axioms) are inconsistent by
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            sub-proof #320.
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17285)  all_20_2 = e1
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17286)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_20_1 & $i(all_20_0) &
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (17285) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17287)  all_4_2 = e1
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | SIMP: (17287) implies:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17288)  all_4_2 = e1
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (17288) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17289)  all_34_2 = e1
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (17288) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17290)  all_56_31 = e1
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REDUCE: (379), (17288) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17291)   ~ (all_52_7 = e1)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REDUCE: (386), (17288) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17292)   ~ (all_52_11 = e1)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REDUCE: (388), (17288) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17293)   ~ (all_52_13 = e1)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REDUCE: (389), (17288) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17294)   ~ (all_52_14 = e1)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REDUCE: (16893), (17288) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17295)   ~ (e3 = e1)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REDUCE: (390), (17288) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17296)   ~ (e2 = e1)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (17288) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17297)  op(e0, e0) = e1
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (82), (94), (100),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (157), (158), (160), (162), (163), (164), (165),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (167), (169), (170), (210), (211), (213), (216),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (217), (218), (219), (220), (221), (222), (223),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (236), (237), (238),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (239), (240), (241), (242), (243), (244), (246),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (14312), (14313), (14314), (14315), (14316),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (14317), (14318), (14319), (14323), (14324),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (16878), (16879), (16881), (16882), (16883),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (16884), (16889), (16890), (16896), (16897),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (16900), (17194), (17195), (17198), (17280),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (17281), (17286), (17289), (17290), (17291),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (17292), (17293), (17294), (17297),
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            #304.
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | |   (17298)  all_58_13 = e3 & op(e0, e2) = e3
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | REF_CLOSE: (158), (16883), (17298), (function-axioms) are
% 237.61/44.92  | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | |   (17299)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 237.61/44.92  | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 237.61/44.92  | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | BETA: splitting (17299) gives:
% 237.61/44.92  | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | |   (17300)  all_58_14 = e3 & op(e0, e1) = e3
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | REF_CLOSE: (157), (14318), (17300), (function-axioms) are
% 237.61/44.92  | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | |   (17301)  all_58_15 = e3 & op(e0, e0) = e3
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | ALPHA: (17301) implies:
% 237.61/44.92  | | | | | | | | | | | | | |   (17302)  op(e0, e0) = e3
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3,
% 237.61/44.92  | | | | | | | | | | | | | |              e0, e0, simplifying with (36), (17302) gives:
% 237.61/44.92  | | | | | | | | | | | | | |   (17303)  all_4_2 = e3
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | REDUCE: (16893), (17303) imply:
% 237.61/44.92  | | | | | | | | | | | | | |   (17304)  $false
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | CLOSE: (17304) is inconsistent.
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | |   (17305)  all_58_10 = e3 & op(e2, e0) = e3
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | ALPHA: (17305) implies:
% 237.61/44.92  | | | | | | | | | | | |   (17306)  op(e2, e0) = e3
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | REF_CLOSE: (164), (16884), (17306), (function-axioms) are
% 237.61/44.92  | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | |   (17307)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 237.61/44.92  | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 237.61/44.92  | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | BETA: splitting (17307) gives:
% 237.61/44.92  | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | |   (17308)  all_58_11 = e3 & op(e1, e0) = e3
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | ALPHA: (17308) implies:
% 237.61/44.92  | | | | | | | | | | | |   (17309)  op(e1, e0) = e3
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | REF_CLOSE: (160), (14319), (17309), (function-axioms) are
% 237.61/44.92  | | | | | | | | | | | |            inconsistent by sub-proof #2149.
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | |   (17310)  all_58_15 = e3 & op(e0, e0) = e3
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | ALPHA: (17310) implies:
% 237.61/44.92  | | | | | | | | | | | |   (17311)  op(e0, e0) = e3
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3,
% 237.61/44.92  | | | | | | | | | | | |              e0, e0, simplifying with (36), (17311) gives:
% 237.61/44.92  | | | | | | | | | | | |   (17312)  all_4_2 = e3
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | REDUCE: (16893), (17312) imply:
% 237.61/44.92  | | | | | | | | | | | |   (17313)  $false
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | CLOSE: (17313) is inconsistent.
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | End of split
% 237.61/44.92  | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | |   (17314)  all_12_2 = e3
% 237.61/44.92  | | | | | | | | | |   (17315)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0
% 237.61/44.92  | | | | | | | | | |              & op(e0, e3) = all_12_1 & $i(all_12_0) &
% 237.61/44.92  | | | | | | | | | |              $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3)
% 237.61/44.92  | | | | | | | | | |              = all_12_1 & $i(all_12_1))
% 237.61/44.92  | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | COMBINE_EQS: (346), (17314) imply:
% 237.61/44.92  | | | | | | | | | |   (17316)  all_4_2 = e3
% 237.61/44.92  | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | COMBINE_EQS: (334), (17316) imply:
% 237.61/44.92  | | | | | | | | | |   (17317)  all_26_2 = e3
% 237.61/44.92  | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | COMBINE_EQS: (254), (17316) imply:
% 237.61/44.92  | | | | | | | | | |   (17318)  all_56_31 = e3
% 237.61/44.92  | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | REDUCE: (368), (17316) imply:
% 237.61/44.92  | | | | | | | | | |   (17319)   ~ (all_52_3 = e3)
% 237.61/44.92  | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | BETA: splitting (219) gives:
% 237.61/44.92  | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | |   (17320)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 237.61/44.92  | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 237.61/44.92  | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | REF_CLOSE: (158), (159), (16883), (17319), (17320),
% 237.61/44.92  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.92  | | | | | | | | | | |            #1123.
% 237.61/44.92  | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | |   (17321)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 237.61/44.92  | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 237.61/44.92  | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | BETA: splitting (17321) gives:
% 237.61/44.92  | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | |   (17322)  all_58_14 = e3 & op(e0, e1) = e3
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | REF_CLOSE: (157), (14318), (17322), (function-axioms) are
% 237.61/44.92  | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | |   (17323)  all_58_15 = e3 & op(e0, e0) = e3
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | ALPHA: (17323) implies:
% 237.61/44.92  | | | | | | | | | | | |   (17324)  all_58_15 = e3
% 237.61/44.92  | | | | | | | | | | | |   (17325)  op(e0, e0) = e3
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | BETA: splitting (245) gives:
% 237.61/44.92  | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | |   (17326)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 237.61/44.92  | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 237.61/44.92  | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | BETA: splitting (17326) gives:
% 237.61/44.92  | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | |   (17327)  all_58_0 = e3 & op(e3, e3) = e3
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | ALPHA: (17327) implies:
% 237.61/44.92  | | | | | | | | | | | | | |   (17328)  op(e3, e3) = e3
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 237.61/44.92  | | | | | | | | | | | | | |              e3, e3, simplifying with (45), (17328) gives:
% 237.61/44.92  | | | | | | | | | | | | | |   (17329)  all_10_2 = e3
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | REDUCE: (365), (17329) imply:
% 237.61/44.92  | | | | | | | | | | | | | |   (17330)   ~ (all_52_12 = e3)
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 237.61/44.92  | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | |   (17331)   ~ (all_26_2 = e3)
% 237.61/44.92  | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | REDUCE: (17317), (17331) imply:
% 237.61/44.92  | | | | | | | | | | | | | | |   (17332)  $false
% 237.61/44.92  | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | CLOSE: (17332) is inconsistent.
% 237.61/44.92  | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | |   (17333)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0
% 237.61/44.92  | | | | | | | | | | | | | | |              & op(e0, e3) = all_26_1 & $i(all_26_0) &
% 237.61/44.92  | | | | | | | | | | | | | | |              $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3)
% 237.61/44.92  | | | | | | | | | | | | | | |              = all_26_1 & $i(all_26_1))
% 237.61/44.92  | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | |   (17334)   ~ (all_42_2 = e3)
% 237.61/44.92  | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | REDUCE: (16879), (17334) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | |   (17335)  $false
% 237.61/44.92  | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | CLOSE: (17335) is inconsistent.
% 237.61/44.92  | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | |   (17336)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 237.61/44.92  | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 237.61/44.92  | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 237.61/44.92  | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 237.61/44.92  | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | |   (17337)   ~ (all_46_2 = e3)
% 237.61/44.92  | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | REDUCE: (14312), (17337) imply:
% 237.61/44.92  | | | | | | | | | | | | | | | | |   (17338)  $false
% 237.61/44.92  | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | CLOSE: (17338) is inconsistent.
% 237.61/44.92  | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | |   (17339)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 237.61/44.92  | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 237.61/44.92  | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 237.61/44.92  | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 237.61/44.92  | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | |   (17340)  all_54_13 = e3
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (16883), (17340) are inconsistent by
% 237.61/44.92  | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | |   (17341)   ~ (all_54_13 = e3)
% 237.61/44.92  | | | | | | | | | | | | | | | | | |   (17342)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17343)  all_54_11 = e3
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (14319), (17343) are inconsistent by
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17344)   ~ (all_54_11 = e3)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | |   (17345)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | |   (17346)  all_54_4 = e3
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (16881), (17346) are inconsistent by
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | |   (17347)   ~ (all_54_4 = e3)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | |   (17348)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | |   (17349)  all_54_9 = e3
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (14315), (17349) are inconsistent by
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | |   (17350)   ~ (all_54_9 = e3)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | |   (17351)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | |   (17352)  all_54_7 = e3
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (16884), (17352) are inconsistent by
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | |   (17353)   ~ (all_54_7 = e3)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | |   (17354)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | |   (17355)  all_54_12 = e3
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (17319), (17355) are inconsistent by
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | |   (17356)   ~ (all_54_12 = e3)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | |   (17357)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | |   (17358)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17358) gives:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (17359)  all_58_4 = e1 & op(e3, e1) = e1
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17359) implies:
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (17360)  all_58_4 = e1
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (17361)  op(e3, e1) = e1
% 237.61/44.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (117), (118), (121),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (125), (139), (144), (157), (158), (159),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (169), (211), (213),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (227), (229), (230), (239), (14313),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (14314), (14316), (14317), (14318), (14324),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (16878), (16881), (16890), (17318), (17319),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (17324), (17325), (17328), (17336), (17360),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (17361), (function-axioms) are inconsistent by
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #301.
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17362)  all_58_5 = e1 & op(e2, e1) = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17362) implies:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17363)  all_58_5 = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17364)  op(e2, e1) = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (110), (117), (118),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (120), (121), (123), (125), (128), (134), (139),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (144), (145), (148), (149), (157), (158),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (197), (210), (211), (213),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (235), (236), (237), (238), (239),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (242), (243), (244), (246), (257), (258),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (279), (14311), (14313), (14314), (14315),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (14316), (14317), (14318), (14319), (14323),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (14324), (16878), (16881), (16882), (16883),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (16884), (16889), (16890), (17315), (17318),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (17319), (17324), (17325), (17328), (17330),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (17333), (17336), (17339), (17345), (17348),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (17354), (17357), (17363), (17364),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            #288.
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | |   (17365)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17365) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17366)  all_58_8 = e1 & op(e1, e1) = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17366) implies:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17367)  op(e1, e1) = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14324), (17367), (function-axioms) are
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #468.
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17368)  all_58_14 = e1 & op(e0, e1) = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17368) implies:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17369)  all_58_14 = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17370)  op(e0, e1) = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (157), (17370) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17371)  all_52_11 = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (17371) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17372)   ~ (all_52_7 = e1)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (17371) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17373)   ~ (all_52_8 = e1)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (17371) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17374)   ~ (all_52_9 = e1)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14318), (17371) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (17375)   ~ (e3 = e1)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17376)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17376) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17377)  all_58_4 = e2 & op(e3, e1) = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17377) implies:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17378)  all_58_4 = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17379)  op(e3, e1) = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (110), (113), (117),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (120), (121), (123), (125), (128), (134),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (139), (140), (144), (145), (146), (148), (149),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (157), (158), (159), (160), (162), (163), (164),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (169), (170), (191), (197),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (212), (213), (216), (217), (218),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (226),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (238), (239), (240), (241),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (242), (243), (244), (245), (246), (256), (257),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (267), (269), (279), (14311), (14313),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14314), (14315), (14316), (14317), (14318),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14319), (14323), (14324), (16878), (16880),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16881), (16882), (16883), (16884), (16889),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16890), (17315), (17318), (17319), (17324),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17325), (17328), (17330), (17333), (17336),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17339), (17345), (17348), (17351), (17354),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17357), (17369), (17370), (17372), (17373),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17374), (17378), (17379), (function-axioms) are
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #274.
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17380)  all_58_5 = e2 & op(e2, e1) = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17380) implies:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17381)  all_58_5 = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17382)  op(e2, e1) = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17383)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17383) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17384)  all_58_4 = e0 & op(e3, e1) = e0
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17384) implies:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17385)  all_58_4 = e0
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17386)  op(e3, e1) = e0
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (17382) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17387)  all_52_9 = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (17386) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17388)  all_52_8 = e0
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (17387) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17389)   ~ (all_52_1 = e2)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (17388) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17390)   ~ (all_52_4 = e0)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (17387), (17388) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17391)   ~ (e2 = e0)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14316), (17388) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17392)   ~ (e3 = e0)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17373), (17388) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17393)   ~ (e1 = e0)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14317), (17387) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17394)   ~ (e3 = e2)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17395)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17395) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17396)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (17330), (17386), (17396),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #298.
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17397)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16890), (17382), (17397), (function-axioms)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #758.
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17398)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17398) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17399)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17399) implies:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17400)  op(e1, all_56_21) = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14313), (17400) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17401)  op(e1, e3) = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (17401) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17402)  all_52_2 = e1
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (17402) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17403)   ~ (all_52_1 = e1)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (17402) imply:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17404)   ~ (all_52_3 = e1)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17404) implies:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17405)   ~ (all_52_3 = e1)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17406)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (17328), (17389), (17406),
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1407.
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17407)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17407) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17408)  all_58_6 = e2 & op(e1, e3) = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17408) implies:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17409)  op(e1, e3) = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17401), (17409), (function-axioms) are
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17410)  all_58_12 = e2 & op(e0, e3) = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17410) implies:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17411)  all_58_12 = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17412)  op(e0, e3) = e2
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17413)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17413) gives:
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17414)  all_58_1 = e1 & op(e3, e2) = e1
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17414) implies:
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17415)  all_58_1 = e1
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17416)  op(e3, e2) = e1
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17417)  all_58_15 = e0 & op(e0, e0) = e0
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17417) implies:
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17418)  op(e0, e0) = e0
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (158), (219), (16883), (17369),
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17411), (17418), (function-axioms) are
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1550.
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.61/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17419)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17419) implies:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17420)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17421)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17421) gives:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17422)  all_58_0 = e2 & op(e3, e3) = e2
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17422) implies:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17423)  op(e3, e3) = e2
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (168), (169), (246), (14316), (17330),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17415), (17423), (function-axioms) are
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1327.
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17424)  all_58_1 = e2 & op(e3, e2) = e2
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17424) implies:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17425)  op(e3, e2) = e2
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17416), (17425), (function-axioms) are
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2261.
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17426)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17426) gives:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17427)  all_58_4 = e2 & op(e3, e1) = e2
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17427) implies:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17428)  all_58_4 = e2
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17429)  op(e3, e1) = e2
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (110), (113), (117),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (120), (121), (123), (125), (128), (134),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (139), (140), (144), (145), (146), (148), (149),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (157), (158), (159), (160), (162), (163), (164),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (169), (170), (191), (197),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (212), (213), (216), (217), (218),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (226),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (238), (239), (240), (241),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (242), (243), (244), (245), (246), (256), (257),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (267), (269), (279), (14311), (14313),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14314), (14315), (14316), (14317), (14318),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14319), (14323), (14324), (16878), (16880),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16881), (16882), (16883), (16884), (16889),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16890), (17315), (17318), (17319), (17324),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17325), (17328), (17330), (17333), (17336),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17339), (17345), (17348), (17351), (17354),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17357), (17369), (17370), (17372), (17373),
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17374), (17428), (17429), (function-axioms) are
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #274.
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17430)  all_58_9 = e2 & op(e3, e0) = e2
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17430) implies:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17431)  all_58_9 = e2
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17420) gives:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17432)  all_58_12 = e0 & op(e0, e3) = e0
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17432) implies:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17433)  op(e0, e3) = e0
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17412), (17433), (function-axioms) are
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1896.
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17434)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17434) gives:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17435)  all_58_13 = e0 & op(e0, e2) = e0
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.74/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17435) implies:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17436)  op(e0, e2) = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17437)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (16890), (17416), (17437),
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #287.
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17438)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17438) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17439)  all_58_7 = e2 & op(e1, e2) = e2
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17439) implies:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17440)  all_58_7 = e2
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17441)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17441) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17442)  all_58_6 = e0 & op(e1, e3) = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17442) implies:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17443)  op(e1, e3) = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17401), (17443), (function-axioms) are
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #449.
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17444)  all_58_7 = e0 & op(e1, e2) = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17444) implies:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17445)  all_58_7 = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17440), (17445) imply:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17446)  e2 = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17431), (17446) imply:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17447)  all_58_9 = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (244), (17328), (17385), (17415),
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17447), (function-axioms) are inconsistent by
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #956.
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17448)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17448) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17449)  all_58_8 = e0 & op(e1, e1) = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17449) implies:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17450)  op(e1, e1) = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (160), (162), (226), (14315), (14319),
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17401), (17450), (function-axioms) are
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #457.
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17451)  all_58_11 = e0 & op(e1, e0) = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17451) implies:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17452)  op(e1, e0) = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17348) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17453)  all_54_4 = e2
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (17389), (17453) are inconsistent by
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2096.
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17454)   ~ (all_54_4 = e2)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17455)  all_54_4 = e1 | all_54_4 = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17455) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17456)  all_54_4 = e1
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (17403), (17456) are inconsistent by
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2086.
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17457)  all_54_4 = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (17457) imply:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17458)  all_52_1 = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17458) implies:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17459)  all_52_1 = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (17459) imply:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17460)   ~ (all_52_3 = e0)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17460) implies:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17461)   ~ (all_52_3 = e0)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (17459) imply:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17462)  op(e2, e3) = e0
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17463)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17463) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17464)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (167), (16881), (17401), (17416),
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17464), (function-axioms) are inconsistent by
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #273.
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17465)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (17319), (17386), (17461), (17465),
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1735.
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17466)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17466) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17467)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17467) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17468)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17468) implies:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17469)  all_56_13 = e2
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17470)   ~ (all_56_31 = e1)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17336) gives:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17471)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_42_1 & $i(all_42_0) &
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_42_1)
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17471) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17472)  op(e2, e3) = all_42_1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (140), (159), (212), (227), (229),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (256), (257), (16878), (16880), (16883),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17315), (17319), (17325), (17333), (17342),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17357), (17369), (17372), (17381), (17385),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17386), (17405), (17416), (17436), (17461),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17462), (17469), (17472), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #272.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17473)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_42_1)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17473) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17474)  op(e2, e3) = all_42_1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (140), (159), (212), (227), (229),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (256), (257), (16878), (16880), (16883),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17315), (17319), (17325), (17333), (17342),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17357), (17369), (17372), (17381), (17385),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17386), (17405), (17416), (17436), (17461),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17462), (17469), (17474), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #272.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17475)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (165), (17374), (17436), (17475),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #271.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17476)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17476) gives:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17477)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17477) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17478)  op(e2, e0) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (164), (165), (167), (232), (16889),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17374), (17403), (17478), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1777.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17479)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17370), (17452), (17479), (function-axioms)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #496.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17480)  all_58_13 = e2 & op(e0, e2) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17480) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17481)  op(e0, e2) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17436), (17481), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17482)  all_58_14 = e0 & op(e0, e1) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17482) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17483)  op(e0, e1) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17370), (17483), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2158.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17484)  all_58_3 = e1 & op(e2, e2) = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (158), (219), (16883), (16889), (17324),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17369), (17411), (17484), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #772.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17485)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17485) gives:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17486)  all_58_7 = e1 & op(e1, e2) = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17486) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17487)  all_58_7 = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17488)  op(e1, e2) = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17489)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17489) gives:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17490)  all_58_1 = e0 & op(e3, e2) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (17390), (17490), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17491)  all_58_3 = e0 & op(e2, e2) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16889), (17491) are inconsistent by
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1719.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17492)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17492) gives:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17493)  all_58_7 = e0 & op(e1, e2) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17493) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17494)  op(e1, e2) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (17488), (17494), (function-axioms)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17495)  all_58_13 = e0 & op(e0, e2) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17495) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17496)  op(e0, e2) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17497)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (17328), (17403), (17497),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1370.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17498)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17498) gives:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17499)  all_58_6 = e1 & op(e1, e3) = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17499) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17500)  all_58_6 = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17501)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17501) gives:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17502)  all_58_6 = e2 & op(e1, e3) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17502) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17503)  op(e1, e3) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17401), (17503), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17504)  all_58_7 = e2 & op(e1, e2) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17504) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17505)  all_58_7 = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17487), (17505) imply:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17506)  e2 = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17381), (17506) imply:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17507)  all_58_5 = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (229), (230),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17369), (17385), (17507), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1248.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17508)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17508) gives:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17509)  all_58_8 = e2 & op(e1, e1) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17509) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17510)  op(e1, e1) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14324), (17510), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17511)  all_58_11 = e2 & op(e1, e0) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17511) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17512)  op(e1, e0) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (225),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (17401), (17487), (17488), (17500),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17512), (function-axioms) are inconsistent by
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #418.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17513)  all_58_12 = e1 & op(e0, e3) = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17513) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17514)  all_58_12 = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (218), (17325), (17369), (17496),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17514), (function-axioms) are inconsistent by
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #417.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17515)  all_58_13 = e1 & op(e0, e2) = e1
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17372), (17515), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17516)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17325), (17370), (17516), (function-axioms)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #349.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17517)  all_58_5 = e0 & op(e2, e1) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17517) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17518)  op(e2, e1) = e0
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17382), (17518), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17519)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (157), (165), (169), (230), (14316),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14317), (14318), (17370), (17519),
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #346.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17520)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17520) gives:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17521)  all_58_8 = e2 & op(e1, e1) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17521) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17522)  op(e1, e1) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14324), (17522), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17523)  all_58_14 = e2 & op(e0, e1) = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17523) implies:
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17524)  all_58_14 = e2
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17369), (17524) are inconsistent by
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2044.
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | |   (17525)  all_58_2 = e3 & op(e2, e3) = e3
% 237.75/44.95  | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | ALPHA: (17525) implies:
% 237.75/44.95  | | | | | | | | | | | | | |   (17526)  op(e2, e3) = e3
% 237.75/44.95  | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | | REF_CLOSE: (167), (16881), (17526), (function-axioms) are
% 237.75/44.95  | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 237.75/44.95  | | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | |   (17527)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 237.75/44.95  | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 237.75/44.95  | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | | REF_CLOSE: (159), (163), (14314), (17319), (17527),
% 237.75/44.95  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.95  | | | | | | | | | | | | |            #1451.
% 237.75/44.95  | | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | End of split
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | |   (17528)  all_10_2 = e1
% 237.75/44.95  | | | | | | | | |   (17529)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 237.75/44.95  | | | | | | | | |              op(e3, e1) = all_10_1 & $i(all_10_0) &
% 237.75/44.95  | | | | | | | | |              $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3, e1)
% 237.75/44.95  | | | | | | | | |              = all_10_1 & $i(all_10_1))
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | COMBINE_EQS: (349), (17528) imply:
% 237.75/44.95  | | | | | | | | |   (17530)  all_38_2 = e1
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | COMBINE_EQS: (290), (17528) imply:
% 237.75/44.95  | | | | | | | | |   (17531)  all_56_1 = e1
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | REDUCE: (355), (17528) imply:
% 237.75/44.95  | | | | | | | | |   (17532)   ~ (all_52_1 = e1)
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | REDUCE: (357), (17528) imply:
% 237.75/44.95  | | | | | | | | |   (17533)   ~ (all_52_2 = e1)
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | REDUCE: (359), (17528) imply:
% 237.75/44.95  | | | | | | | | |   (17534)   ~ (all_52_3 = e1)
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | REDUCE: (361), (17528) imply:
% 237.75/44.95  | | | | | | | | |   (17535)   ~ (all_52_4 = e1)
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | REDUCE: (363), (17528) imply:
% 237.75/44.95  | | | | | | | | |   (17536)   ~ (all_52_8 = e1)
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | REDUCE: (45), (17528) imply:
% 237.75/44.95  | | | | | | | | |   (17537)  op(e3, e3) = e1
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | BETA: splitting (245) gives:
% 237.75/44.95  | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | Case 1:
% 237.75/44.95  | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | |   (17538)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 237.75/44.95  | | | | | | | | | |              & op(e2, e3) = e3)
% 237.75/44.95  | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (16881), (17532),
% 237.75/44.95  | | | | | | | | | |            (17533), (17534), (17538), (function-axioms) are
% 237.75/44.95  | | | | | | | | | |            inconsistent by sub-proof #270.
% 237.75/44.95  | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | Case 2:
% 237.75/44.95  | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | |   (17539)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 237.75/44.95  | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 237.75/44.95  | | | | | | | | | | 
% 237.75/44.95  | | | | | | | | | | BETA: splitting (17539) gives:
% 237.75/44.96  | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | |   (17540)  all_58_6 = e3 & op(e1, e3) = e3
% 237.75/44.96  | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | ALPHA: (17540) implies:
% 237.75/44.96  | | | | | | | | | | |   (17541)  op(e1, e3) = e3
% 237.75/44.96  | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | REF_CLOSE: (163), (14314), (17541), (function-axioms) are
% 237.75/44.96  | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 237.75/44.96  | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | |   (17542)  all_58_12 = e3 & op(e0, e3) = e3
% 237.75/44.96  | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | ALPHA: (17542) implies:
% 237.75/44.96  | | | | | | | | | | |   (17543)  all_58_12 = e3
% 237.75/44.96  | | | | | | | | | | |   (17544)  op(e0, e3) = e3
% 237.75/44.96  | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | BETA: splitting (246) gives:
% 237.75/44.96  | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | |   (17545)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 237.75/44.96  | | | | | | | | | | | |              & op(e3, e2) = e3)
% 237.75/44.96  | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (170), (241), (16882),
% 237.75/44.96  | | | | | | | | | | | |            (17532), (17533), (17534), (17545),
% 237.75/44.96  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.96  | | | | | | | | | | | |            #269.
% 237.75/44.96  | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | |   (17546)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 237.75/44.96  | | | | | | | | | | | |              & op(e3, e0) = e3)
% 237.75/44.96  | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | BETA: splitting (17546) gives:
% 237.75/44.96  | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | |   (17547)  all_58_4 = e3 & op(e3, e1) = e3
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | ALPHA: (17547) implies:
% 237.75/44.96  | | | | | | | | | | | | |   (17548)  op(e3, e1) = e3
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | REF_CLOSE: (169), (14316), (17548), (function-axioms) are
% 237.75/44.96  | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | |   (17549)  all_58_9 = e3 & op(e3, e0) = e3
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | ALPHA: (17549) implies:
% 237.75/44.96  | | | | | | | | | | | | |   (17550)  all_58_9 = e3
% 237.75/44.96  | | | | | | | | | | | | |   (17551)  op(e3, e0) = e3
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 237.75/44.96  | | | | | | | | | | | | |              e3, e0, simplifying with (159), (17544) gives:
% 237.75/44.96  | | | | | | | | | | | | |   (17552)  all_52_3 = e3
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 237.75/44.96  | | | | | | | | | | | | |              e3, e0, e3, simplifying with (168), (17551) gives:
% 237.75/44.96  | | | | | | | | | | | | |   (17553)  all_52_12 = e3
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | REDUCE: (140), (17552) imply:
% 237.75/44.96  | | | | | | | | | | | | |   (17554)   ~ (all_52_7 = e3)
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | REDUCE: (139), (17552) imply:
% 237.75/44.96  | | | | | | | | | | | | |   (17555)   ~ (all_52_11 = e3)
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | REDUCE: (113), (17553) imply:
% 237.75/44.96  | | | | | | | | | | | | |   (17556)   ~ (all_52_13 = e3)
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | REDUCE: (112), (17553) imply:
% 237.75/44.96  | | | | | | | | | | | | |   (17557)   ~ (all_52_14 = e3)
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | REDUCE: (387), (17553) imply:
% 237.75/44.96  | | | | | | | | | | | | |   (17558)   ~ (all_4_2 = e3)
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | SIMP: (17558) implies:
% 237.75/44.96  | | | | | | | | | | | | |   (17559)   ~ (all_4_2 = e3)
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | BETA: splitting (61) gives:
% 237.75/44.96  | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | |   (17560)   ~ (all_20_2 = e1)
% 237.75/44.96  | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | REDUCE: (341), (17560) imply:
% 237.75/44.96  | | | | | | | | | | | | | |   (17561)   ~ (all_4_2 = e1)
% 237.75/44.96  | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 237.75/44.96  | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | |   (17562)  all_54_15 = e3
% 237.75/44.96  | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | REF_CLOSE: (299), (17559), (17562) are inconsistent by
% 237.75/44.96  | | | | | | | | | | | | | | |            sub-proof #2340.
% 237.75/44.96  | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | |   (17563)   ~ (all_54_15 = e3)
% 237.75/44.96  | | | | | | | | | | | | | | |   (17564)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 237.75/44.96  | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | BETA: splitting (17564) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | |   (17565)  all_54_15 = e2
% 237.75/44.96  | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | REF_CLOSE: (299), (390), (17565) are inconsistent by
% 237.75/44.96  | | | | | | | | | | | | | | | |            sub-proof #2339.
% 237.75/44.96  | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | |   (17566)  all_54_15 = e1 | all_54_15 = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | BETA: splitting (17566) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | |   (17567)  all_54_15 = e1
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | REF_CLOSE: (299), (17561), (17567) are inconsistent by
% 237.75/44.96  | | | | | | | | | | | | | | | | |            sub-proof #2338.
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | |   (17568)  all_54_15 = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (17568) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | |   (17569)  all_4_2 = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | SIMP: (17569) implies:
% 237.75/44.96  | | | | | | | | | | | | | | | | |   (17570)  all_4_2 = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (17570) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | |   (17571)  all_56_31 = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | REDUCE: (388), (17570) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | |   (17572)   ~ (all_52_13 = e0)
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | REDUCE: (389), (17570) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | |   (17573)   ~ (all_52_14 = e0)
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | REDUCE: (17559), (17570) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | |   (17574)   ~ (e3 = e0)
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | REDUCE: (17561), (17570) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | |   (17575)   ~ (e1 = e0)
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | REDUCE: (36), (17570) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | |   (17576)  op(e0, e0) = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | |   (17577)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.75/44.96  | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.75/44.96  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | BETA: splitting (17577) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |   (17578)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              = e3)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (14313), (14314), (16881), (17578),
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |            #441.
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |   (17579)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              = e0)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | BETA: splitting (17579) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |   (17580)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | ALPHA: (17580) implies:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |   (17581)  op(e3, e1) = e1
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (17536), (17581), (function-axioms) are
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |   (17582)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14313), (17571), (17582) are inconsistent by
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |            sub-proof #343.
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.96  | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | |   (17583)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.75/44.96  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.75/44.96  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | BETA: splitting (17583) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |   (17584)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | |              = e2)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | BETA: splitting (17584) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |   (17585)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | ALPHA: (17585) implies:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |   (17586)  op(e1, e2) = e2
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |   (17587)  op(e2, e1) = e2
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (117), (126), (162), (165), (193), (197),
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |            (258), (269), (14319), (16884), (17572), (17573),
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |            (17586), (17587), (function-axioms) are
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #340.
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |   (17588)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17588) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17589)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17589) implies:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17590)   ~ (all_56_31 = e2)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17591)   ~ (all_56_21 = e2)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17592)   ~ (all_56_1 = e2)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17593)  op(e1, e2) = e1
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17594)  op(e2, e1) = e1
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | REDUCE: (17531), (17592) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17595)   ~ (e2 = e1)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | REDUCE: (17571), (17590) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17596)   ~ (e2 = e0)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (17593) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17597)  all_52_6 = e1
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (17594) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17598)  all_52_9 = e1
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (17597) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17599)   ~ (all_52_7 = e1)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | SIMP: (17599) implies:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17600)   ~ (all_52_7 = e1)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (17598) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17601)   ~ (all_52_13 = e1)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | SIMP: (17601) implies:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17602)   ~ (all_52_13 = e1)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | REDUCE: (14317), (17598) imply:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | |   (17603)   ~ (e3 = e1)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | |   (17604)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17604) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | |   (17605)  all_58_6 = e0 & op(e1, e3) = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17605) implies:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | |   (17606)  all_58_6 = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | |   (17607)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17607) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (17608)  all_58_0 = e2 & op(e3, e3) = e2
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17608) implies:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (17609)  op(e3, e3) = e2
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17537), (17609), (function-axioms) are
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (17610)  all_58_2 = e2 & op(e2, e3) = e2
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17610) implies:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (17611)  op(e2, e3) = e2
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (197), (269), (16884), (17572),
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | |            (17602), (17611), (function-axioms) are
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2291.
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | |   (17612)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (17543), (17606), (17612) are
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #724.
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | |   (17613)  all_58_7 = e0 & op(e1, e2) = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17613) implies:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | |   (17614)  op(e1, e2) = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (17593), (17614), (function-axioms)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | |   (17615)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17615) gives:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | |   (17616)  all_58_8 = e0 & op(e1, e1) = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17616) implies:
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | |   (17617)  op(e1, e1) = e0
% 237.75/44.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (164), (165),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (217), (227), (229), (230), (232),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |            (239), (240), (243), (244), (245), (246), (14317),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |            (16881), (16882), (16889), (17532), (17537),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |            (17576), (17600), (17602), (17617),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |            #656.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |   (17618)  all_58_11 = e0 & op(e1, e0) = e0
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17618) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |   (17619)  op(e1, e0) = e0
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (17573), (17619), (function-axioms) are
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2323.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |   (17620)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17620) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |   (17621)   ~ (all_56_31 = e0)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | REDUCE: (17571), (17621) imply:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |   (17622)  $false
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | CLOSE: (17622) is inconsistent.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |   (17623)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |              = e0)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (17571), (17572), (17573), (17623),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |            #2321.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | |   (17624)  all_20_2 = e1
% 237.75/44.97  | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | COMBINE_EQS: (341), (17624) imply:
% 237.75/44.97  | | | | | | | | | | | | | |   (17625)  all_4_2 = e1
% 237.75/44.97  | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | REDUCE: (379), (17625) imply:
% 237.75/44.97  | | | | | | | | | | | | | |   (17626)   ~ (all_52_7 = e1)
% 237.75/44.97  | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | REDUCE: (386), (17625) imply:
% 237.75/44.97  | | | | | | | | | | | | | |   (17627)   ~ (all_52_11 = e1)
% 237.75/44.97  | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | REDUCE: (388), (17625) imply:
% 237.75/44.97  | | | | | | | | | | | | | |   (17628)   ~ (all_52_13 = e1)
% 237.75/44.97  | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | REDUCE: (17559), (17625) imply:
% 237.75/44.97  | | | | | | | | | | | | | |   (17629)   ~ (e3 = e1)
% 237.75/44.97  | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | REDUCE: (390), (17625) imply:
% 237.75/44.97  | | | | | | | | | | | | | |   (17630)   ~ (e2 = e1)
% 237.75/44.97  | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | REDUCE: (36), (17625) imply:
% 237.75/44.97  | | | | | | | | | | | | | |   (17631)  op(e0, e0) = e1
% 237.75/44.97  | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 237.75/44.97  | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | |   (17632)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 237.75/44.97  | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 237.75/44.97  | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | BETA: splitting (17632) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | |   (17633)  all_58_2 = e1 & op(e2, e3) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | REF_CLOSE: (167), (17532), (17633), (function-axioms) are
% 237.75/44.97  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 237.75/44.97  | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | |   (17634)  all_58_3 = e1 & op(e2, e2) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 237.75/44.97  | | | | | | | | | | | | | | | |            (222), (16884), (16889), (17550), (17631),
% 237.75/44.97  | | | | | | | | | | | | | | | |            (17634), (function-axioms) are inconsistent by
% 237.75/44.97  | | | | | | | | | | | | | | | |            sub-proof #331.
% 237.75/44.97  | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | |   (17635)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 237.75/44.97  | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 237.75/44.97  | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | BETA: splitting (17635) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | |   (17636)  all_58_5 = e1 & op(e2, e1) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | ALPHA: (17636) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | |   (17637)  all_58_5 = e1
% 237.75/44.97  | | | | | | | | | | | | | | | |   (17638)  op(e2, e1) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | |   (17639)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 237.75/44.97  | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | BETA: splitting (17639) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | |   (17640)  all_58_1 = e1 & op(e3, e2) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | ALPHA: (17640) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | |   (17641)  op(e3, e2) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (17535), (17641), (function-axioms) are
% 237.75/44.97  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2228.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | |   (17642)  all_58_3 = e1 & op(e2, e2) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 237.75/44.97  | | | | | | | | | | | | | | | | | |            (222), (16884), (16889), (17550), (17631),
% 237.75/44.97  | | | | | | | | | | | | | | | | | |            (17642), (function-axioms) are inconsistent by
% 237.75/44.97  | | | | | | | | | | | | | | | | | |            sub-proof #331.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | |   (17643)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 237.75/44.97  | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.75/44.97  | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | BETA: splitting (17643) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | |   (17644)  all_58_7 = e1 & op(e1, e2) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | ALPHA: (17644) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | |   (17645)  all_58_7 = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | |   (17646)  op(e1, e2) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |   (17647)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | BETA: splitting (17647) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |   (17648)  all_58_9 = e1 & op(e3, e0) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | ALPHA: (17648) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |   (17649)  all_58_9 = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (216), (221),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |            (222), (16884), (17631), (17649),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |            #1600.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |   (17650)  all_58_10 = e1 & op(e2, e0) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | ALPHA: (17650) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |   (17651)  all_58_10 = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (231), (233), (16889),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |            (17637), (17651) are inconsistent by sub-proof
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |            #992.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |   (17652)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 237.75/44.97  | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | BETA: splitting (17652) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |   (17653)  all_58_11 = e1 & op(e1, e0) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | ALPHA: (17653) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |   (17654)  all_58_11 = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |   (17655)  op(e1, e0) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (225),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |            (226), (14319), (17645), (17654), (17655),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |            #1417.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |   (17656)  all_58_15 = e1 & op(e0, e0) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | ALPHA: (17656) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | |   (17657)  all_58_15 = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |   (17658)   ~ (all_38_2 = e1)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | REDUCE: (17530), (17658) imply:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |   (17659)  $false
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | CLOSE: (17659) is inconsistent.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |   (17660)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e1) = all_38_1 & $i(all_38_0) &
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |              $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | |   (17661)  all_54_8 = e3
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14314), (17661) are inconsistent by
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | |   (17662)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |   (17663)  all_54_7 = e3
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (16884), (17663) are inconsistent by
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | |   (17664)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | |   (17665)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17665) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (17666)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17666) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (17667)  op(e3, e1) = all_56_17
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (17668)  op(e3, all_56_17) = e3
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_17, e1, e3, simplifying with (169), (17667)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (17669)  all_56_17 = all_52_8
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17668), (17669) imply:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (17670)  op(e3, all_52_8) = e3
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17671)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17671) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17672)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17672) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17673)  op(e3, all_56_1) = e3
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17531), (17673) imply:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17674)  op(e3, e1) = e3
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14316), (17674), (function-axioms) are
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17675)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17675) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17676)  op(e2, e3) = all_56_3
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17677)  op(e2, all_56_3) = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_3, e3, e2, simplifying with (167), (17676)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17678)  all_56_3 = all_52_1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17677), (17678) imply:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17679)  op(e2, all_52_1) = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17680)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17680) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17681)  all_58_1 = e2 & op(e3, e2) = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17681) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17682)  all_58_1 = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17683)  op(e3, e2) = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (159), (162),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (212), (217), (218), (219), (235),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (238), (240), (14324), (16880),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16881), (16882), (16883), (16889), (16890),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17529), (17532), (17534), (17537), (17543),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17550), (17645), (17646), (17657), (17660),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17679), (17682), (17683), (function-axioms) are
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #264.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17684)  all_58_3 = e2 & op(e2, e2) = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17684) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17685)  op(e2, e2) = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16890), (17685), (function-axioms) are
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17686)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17686) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17687)  all_58_7 = e2 & op(e1, e2) = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17687) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17688)  all_58_7 = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17645), (17688) are inconsistent by
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2134.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17689)  all_58_13 = e2 & op(e0, e2) = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17689) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17690)  op(e0, e2) = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (158), (162),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (169), (170), (227), (230), (235), (236),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (14317), (14318), (16889), (17537),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17550), (17551), (17626), (17638), (17645),
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17646), (17670), (17690), (function-axioms) are
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #261.
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17691)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17691) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17692)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17692) implies:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17693)  op(e1, e3) = all_56_5
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17694)  op(e1, all_56_5) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (17693)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17695)  all_56_5 = all_52_2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17694), (17695) imply:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17696)  op(e1, all_52_2) = e1
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17697)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17697) gives:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17698)  all_58_1 = e2 & op(e3, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17698) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17699)  all_58_1 = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17700)  op(e3, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (145), (149), (158),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (162), (164), (167), (170), (212), (217),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (221), (235), (236), (237), (238),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (246), (268), (269), (14324), (16880),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16881), (16882), (16883), (16889), (16890),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17529), (17532), (17533), (17534), (17537),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17543), (17550), (17628), (17645), (17646),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17657), (17660), (17662), (17664), (17696),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17699), (17700), (function-axioms) are
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #260.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17701)  all_58_3 = e2 & op(e2, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17701) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17702)  op(e2, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16890), (17702), (function-axioms) are
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17703)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17703) gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17704)  all_58_7 = e2 & op(e1, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17704) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17705)  all_58_7 = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17645), (17705) are inconsistent by
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2134.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17706)  all_58_13 = e2 & op(e0, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17706) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17707)  op(e0, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (158), (162),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (169), (170), (227), (230), (235), (236),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (14317), (14318), (16889), (17537),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17550), (17551), (17626), (17638), (17645),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17646), (17670), (17707), (function-axioms) are
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #261.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17708)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17708) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17709)  op(e0, e3) = all_56_7
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17710)  op(e0, all_56_7) = e0
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17544), (17709), (17710), (function-axioms)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2070.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (17711)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17711) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (17712)  op(e2, e1) = all_56_19
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (17713)  op(e2, all_56_19) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17638), (17712), (17713), (function-axioms)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #299.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | |   (17714)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17714) gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (17715)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17715) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (17716)  op(e1, all_56_21) = e1
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14313), (17716) imply:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (17717)  op(e1, e3) = e1
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (17533), (17717), (function-axioms) are
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (17718)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17718) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (17719)  op(e0, e1) = all_56_23
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (17720)  op(e0, all_56_23) = e0
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_23, e1, e0, simplifying with (157), (17719)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (17721)  all_56_23 = all_52_11
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17720), (17721) imply:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (17722)  op(e0, all_52_11) = e0
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17723)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17723) gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17724)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17724) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17725)  op(e3, all_56_1) = e3
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17531), (17725) imply:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17726)  op(e3, e1) = e3
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14316), (17726), (function-axioms) are
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17727)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17727) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17728)  op(e2, e3) = all_56_3
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17729)  op(e2, all_56_3) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_3, e3, e2, simplifying with (167), (17728)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17730)  all_56_3 = all_52_1
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17729), (17730) imply:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17731)  op(e2, all_52_1) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17732)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17732) gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17733)  all_58_1 = e2 & op(e3, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17733) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17734)  all_58_1 = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17735)  op(e3, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (159), (162),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (212), (217), (218), (219), (235),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (238), (240), (14324), (16880),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16881), (16882), (16883), (16889), (16890),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17529), (17532), (17534), (17537), (17543),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17550), (17645), (17646), (17657), (17660),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17731), (17734), (17735), (function-axioms) are
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #264.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17736)  all_58_3 = e2 & op(e2, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17736) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17737)  op(e2, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16890), (17737), (function-axioms) are
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17738)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (121), (157), (158),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (165), (169), (216), (217), (218), (219),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (230), (235), (236), (244), (14316),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14317), (14318), (16883), (16889), (17534),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17536), (17537), (17543), (17550), (17551),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17626), (17627), (17638), (17645), (17722),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17738), (function-axioms) are inconsistent by
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #259.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17739)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17739) gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17740)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17740) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17741)  op(e1, e3) = all_56_5
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17742)  op(e1, all_56_5) = e1
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (17741)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17743)  all_56_5 = all_52_2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17742), (17743) imply:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17744)  op(e1, all_52_2) = e1
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17745)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17745) gives:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17746)  all_58_1 = e2 & op(e3, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17746) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17747)  all_58_1 = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17748)  op(e3, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (145), (149), (158),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (162), (164), (167), (170), (212), (217),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (221), (235), (236), (237), (238),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (246), (268), (269), (14324), (16880),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16881), (16882), (16883), (16889), (16890),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17529), (17532), (17533), (17534), (17537),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17543), (17550), (17628), (17645), (17646),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17657), (17660), (17662), (17664), (17744),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17747), (17748), (function-axioms) are
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #260.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17749)  all_58_3 = e2 & op(e2, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17749) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17750)  op(e2, e2) = e2
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16890), (17750), (function-axioms) are
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17751)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (121), (157), (158),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (165), (169), (216), (217), (218), (219),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (230), (235), (236), (244), (14316),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14317), (14318), (16883), (16889), (17534),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17536), (17537), (17543), (17550), (17551),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17626), (17627), (17638), (17645), (17722),
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17751), (function-axioms) are inconsistent by
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #259.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17752)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17752) implies:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17753)  op(e0, e3) = all_56_7
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17754)  op(e0, all_56_7) = e0
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17544), (17753), (17754), (function-axioms)
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2070.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | |   (17755)  all_58_13 = e1 & op(e0, e2) = e1
% 237.75/44.98  | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17626), (17755), (function-axioms) are
% 237.75/44.98  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 237.75/44.98  | | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | Case 2:
% 237.75/44.98  | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | |   (17756)  all_58_10 = e1 & op(e2, e0) = e1
% 237.75/44.98  | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17628), (17756), (function-axioms) are
% 237.75/44.98  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 237.75/44.98  | | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | | 
% 237.75/44.98  | | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | | 
% 237.75/44.98  | | | | | | | | End of split
% 237.75/44.98  | | | | | | | | 
% 237.75/44.98  | | | | | | | End of split
% 237.75/44.98  | | | | | | | 
% 237.75/44.98  | | | | | | Case 2:
% 237.75/44.98  | | | | | | | 
% 237.75/44.98  | | | | | | |   (17757)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 &
% 237.75/44.98  | | | | | | |              op(e2, e0) = e3)
% 237.75/44.98  | | | | | | | 
% 237.75/44.98  | | | | | | | REF_CLOSE: (164), (165), (14317), (16884), (17757),
% 237.75/44.98  | | | | | | |            (function-axioms) are inconsistent by sub-proof #1649.
% 237.75/44.98  | | | | | | | 
% 237.75/44.98  | | | | | | End of split
% 237.75/44.98  | | | | | | 
% 237.75/44.98  | | | | | End of split
% 237.75/44.98  | | | | | 
% 237.75/44.98  | | | | Case 2:
% 237.75/44.98  | | | | | 
% 237.75/44.98  | | | | |   (17758)  all_58_14 = e3 & op(e0, e1) = e3
% 237.75/44.98  | | | | | 
% 237.75/44.98  | | | | | REF_CLOSE: (157), (14318), (17758), (function-axioms) are inconsistent
% 237.75/44.98  | | | | |            by sub-proof #1647.
% 237.75/44.98  | | | | | 
% 237.75/44.98  | | | | End of split
% 237.75/44.98  | | | | 
% 237.75/44.98  | | | End of split
% 237.75/44.98  | | | 
% 237.75/44.98  | | End of split
% 237.75/44.98  | | 
% 237.75/44.98  | Case 2:
% 237.75/44.98  | | 
% 237.75/44.98  | |   (17759)  all_4_2 = e2
% 237.75/44.99  | |   (17760)  ( ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) =
% 237.75/44.99  | |              all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) &
% 237.75/44.99  | |              op(e0, e2) = all_4_1 & $i(all_4_1))
% 237.75/44.99  | | 
% 237.75/44.99  | | COMBINE_EQS: (316), (17759) imply:
% 237.75/44.99  | |   (17761)  all_44_2 = e2
% 237.75/44.99  | | 
% 237.75/44.99  | | COMBINE_EQS: (254), (17759) imply:
% 237.75/44.99  | |   (17762)  all_56_31 = e2
% 237.75/44.99  | | 
% 237.75/44.99  | | REDUCE: (368), (17759) imply:
% 237.75/44.99  | |   (17763)   ~ (all_52_3 = e2)
% 237.75/44.99  | | 
% 237.75/44.99  | | REDUCE: (379), (17759) imply:
% 237.75/44.99  | |   (17764)   ~ (all_52_7 = e2)
% 237.75/44.99  | | 
% 237.75/44.99  | | REDUCE: (386), (17759) imply:
% 237.75/44.99  | |   (17765)   ~ (all_52_11 = e2)
% 237.75/44.99  | | 
% 237.75/44.99  | | REDUCE: (387), (17759) imply:
% 237.75/44.99  | |   (17766)   ~ (all_52_12 = e2)
% 237.75/44.99  | | 
% 237.75/44.99  | | REDUCE: (388), (17759) imply:
% 237.75/44.99  | |   (17767)   ~ (all_52_13 = e2)
% 237.75/44.99  | | 
% 237.75/44.99  | | REDUCE: (389), (17759) imply:
% 237.75/44.99  | |   (17768)   ~ (all_52_14 = e2)
% 237.75/44.99  | | 
% 237.75/44.99  | | BETA: splitting (221) gives:
% 237.75/44.99  | | 
% 237.75/44.99  | | Case 1:
% 237.75/44.99  | | | 
% 237.75/44.99  | | |   (17769)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 237.75/44.99  | | |                e0) = e2)
% 237.75/44.99  | | | 
% 237.75/44.99  | | | REF_CLOSE: (164), (168), (17766), (17767), (17769), (function-axioms) are
% 237.75/44.99  | | |            inconsistent by sub-proof #2316.
% 237.75/44.99  | | | 
% 237.75/44.99  | | Case 2:
% 237.75/44.99  | | | 
% 237.75/44.99  | | |   (17770)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 237.75/44.99  | | |                e0) = e2)
% 237.75/44.99  | | | 
% 237.75/44.99  | | | BETA: splitting (17770) gives:
% 237.75/44.99  | | | 
% 237.75/44.99  | | | Case 1:
% 237.75/44.99  | | | | 
% 237.75/44.99  | | | |   (17771)  all_58_11 = e2 & op(e1, e0) = e2
% 237.75/44.99  | | | | 
% 237.75/44.99  | | | | REF_CLOSE: (160), (17768), (17771), (function-axioms) are inconsistent
% 237.75/44.99  | | | |            by sub-proof #258.
% 237.75/44.99  | | | | 
% 237.75/44.99  | | | Case 2:
% 237.75/44.99  | | | | 
% 237.75/44.99  | | | |   (17772)  all_58_15 = e2 & op(e0, e0) = e2
% 237.75/44.99  | | | | 
% 237.75/44.99  | | | | ALPHA: (17772) implies:
% 237.75/44.99  | | | |   (17773)  all_58_15 = e2
% 237.75/44.99  | | | |   (17774)  op(e0, e0) = e2
% 237.75/44.99  | | | | 
% 237.75/44.99  | | | | BETA: splitting (40) gives:
% 237.75/44.99  | | | | 
% 237.75/44.99  | | | | Case 1:
% 237.75/44.99  | | | | | 
% 237.75/44.99  | | | | |   (17775)   ~ (all_6_2 = e3)
% 237.75/44.99  | | | | | 
% 237.75/44.99  | | | | | BETA: splitting (43) gives:
% 237.75/44.99  | | | | | 
% 237.75/44.99  | | | | | Case 1:
% 237.75/44.99  | | | | | | 
% 237.75/44.99  | | | | | |   (17776)   ~ (all_8_2 = e3)
% 237.75/44.99  | | | | | | 
% 237.75/44.99  | | | | | | BETA: splitting (46) gives:
% 237.75/44.99  | | | | | | 
% 237.75/44.99  | | | | | | Case 1:
% 237.75/44.99  | | | | | | | 
% 237.75/44.99  | | | | | | |   (17777)   ~ (all_10_2 = e1)
% 237.75/44.99  | | | | | | | 
% 237.75/44.99  | | | | | | | BETA: splitting (52) gives:
% 237.75/44.99  | | | | | | | 
% 237.75/44.99  | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | 
% 237.75/44.99  | | | | | | | |   (17778)   ~ (all_14_2 = e0)
% 237.75/44.99  | | | | | | | | 
% 237.75/44.99  | | | | | | | | REDUCE: (344), (17778) imply:
% 237.75/44.99  | | | | | | | |   (17779)   ~ (all_8_2 = e0)
% 237.75/44.99  | | | | | | | | 
% 237.75/44.99  | | | | | | | | BETA: splitting (55) gives:
% 237.75/44.99  | | | | | | | | 
% 237.75/44.99  | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | 
% 237.75/44.99  | | | | | | | | |   (17780)   ~ (all_16_2 = e0)
% 237.75/44.99  | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | REDUCE: (342), (17780) imply:
% 237.75/44.99  | | | | | | | | |   (17781)   ~ (all_10_2 = e0)
% 237.75/44.99  | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | BETA: splitting (58) gives:
% 237.75/44.99  | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | |   (17782)   ~ (all_18_2 = e0)
% 237.75/44.99  | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | REDUCE: (339), (17782) imply:
% 237.75/44.99  | | | | | | | | | |   (17783)   ~ (all_6_2 = e0)
% 237.75/44.99  | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | BETA: splitting (64) gives:
% 237.75/44.99  | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | |   (17784)   ~ (all_22_2 = e1)
% 237.75/44.99  | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | REDUCE: (326), (17784) imply:
% 237.75/44.99  | | | | | | | | | | |   (17785)   ~ (all_8_2 = e1)
% 237.75/44.99  | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | BETA: splitting (199) gives:
% 237.75/44.99  | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | |   (17786)  all_54_5 = e3
% 237.75/44.99  | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | COMBINE_EQS: (275), (17786) imply:
% 237.75/44.99  | | | | | | | | | | | |   (17787)  all_8_2 = e3
% 237.75/44.99  | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | REDUCE: (17776), (17787) imply:
% 237.75/44.99  | | | | | | | | | | | |   (17788)  $false
% 237.75/44.99  | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | CLOSE: (17788) is inconsistent.
% 237.75/44.99  | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | |   (17789)   ~ (all_54_5 = e3)
% 237.75/44.99  | | | | | | | | | | | |   (17790)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 237.75/44.99  | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | BETA: splitting (17790) gives:
% 237.75/44.99  | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | |   (17791)  all_54_5 = e2
% 237.75/44.99  | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | COMBINE_EQS: (275), (17791) imply:
% 237.75/44.99  | | | | | | | | | | | | |   (17792)  all_8_2 = e2
% 237.75/44.99  | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | REDUCE: (366), (17792) imply:
% 237.75/44.99  | | | | | | | | | | | | |   (17793)   ~ (all_52_1 = e2)
% 237.75/44.99  | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | REDUCE: (369), (17792) imply:
% 237.75/44.99  | | | | | | | | | | | | |   (17794)   ~ (all_52_4 = e2)
% 237.75/44.99  | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | REDUCE: (371), (17792) imply:
% 237.75/44.99  | | | | | | | | | | | | |   (17795)   ~ (all_52_6 = e2)
% 237.75/44.99  | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | REDUCE: (375), (17792) imply:
% 237.75/44.99  | | | | | | | | | | | | |   (17796)   ~ (all_52_9 = e2)
% 237.75/44.99  | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | REDUCE: (17776), (17792) imply:
% 237.75/44.99  | | | | | | | | | | | | |   (17797)   ~ (e3 = e2)
% 237.75/44.99  | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | BETA: splitting (233) gives:
% 237.75/44.99  | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | |   (17798)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 237.75/44.99  | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.75/44.99  | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | BETA: splitting (17798) gives:
% 237.75/44.99  | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | |   (17799)  all_58_2 = e2 & op(e2, e3) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | ALPHA: (17799) implies:
% 237.75/44.99  | | | | | | | | | | | | | | |   (17800)  op(e2, e3) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | REF_CLOSE: (167), (17793), (17800), (function-axioms) are
% 237.75/44.99  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 237.75/44.99  | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | |   (17801)  all_58_3 = e2 & op(e2, e2) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | ALPHA: (17801) implies:
% 237.75/44.99  | | | | | | | | | | | | | | |   (17802)  all_58_3 = e2
% 237.75/44.99  | | | | | | | | | | | | | | |   (17803)  op(e2, e2) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | |   (17804)   ~ (all_24_2 = e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | REDUCE: (301), (17804) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | |   (17805)   ~ (all_10_2 = e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | |   (17806)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | BETA: splitting (17806) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | |   (17807)  all_58_0 = e2 & op(e3, e3) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | ALPHA: (17807) implies:
% 237.75/44.99  | | | | | | | | | | | | | | | | | |   (17808)  op(e3, e3) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |   (17809)  all_54_0 = e3
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (17809) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |   (17810)  all_10_2 = e3
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | REDUCE: (45), (17810) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |   (17811)  op(e3, e3) = e3
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17808), (17811), (function-axioms) are
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |   (17812)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (17777), (17781), (17805), (17812) are
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | |   (17813)  all_58_2 = e2 & op(e2, e3) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | ALPHA: (17813) implies:
% 237.75/44.99  | | | | | | | | | | | | | | | | | |   (17814)  op(e2, e3) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (17793), (17814), (function-axioms) are
% 237.75/44.99  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | End of split
% 237.75/44.99  | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | |   (17815)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 237.75/44.99  | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | BETA: splitting (17815) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | |   (17816)  all_58_6 = e2 & op(e1, e3) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | ALPHA: (17816) implies:
% 237.75/44.99  | | | | | | | | | | | | | | | | | |   (17817)  all_58_6 = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | |   (17818)  op(e1, e3) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |   (17819)  all_54_0 = e3
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (17819) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |   (17820)  all_10_2 = e3
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (17820) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |   (17821)  all_56_1 = e3
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | REDUCE: (355), (17820) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |   (17822)   ~ (all_52_1 = e3)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | REDUCE: (357), (17820) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |   (17823)   ~ (all_52_2 = e3)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | REDUCE: (359), (17820) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | |   (17824)   ~ (all_52_3 = e3)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | |   (17825)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17825) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |   (17826)  all_58_0 = e2 & op(e3, e3) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17826) implies:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |   (17827)  op(e3, e3) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (241),
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |            (245), (17817), (17818), (17822), (17827),
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |            #255.
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |   (17828)  all_58_1 = e2 & op(e3, e2) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17828) implies:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |   (17829)  op(e3, e2) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (17794), (17829), (function-axioms) are
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #254.
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | |   (17830)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17830) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |   (17831)  all_58_4 = e2 & op(e3, e1) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17831) implies:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |   (17832)  op(e3, e1) = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (17832) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |   (17833)  all_52_8 = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (17833) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |   (17834)   ~ (all_52_9 = e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (17833) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |   (17835)   ~ (all_6_2 = e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | SIMP: (17835) implies:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | |   (17836)   ~ (all_6_2 = e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | |   (17837)  all_54_10 = e3
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (17837) are inconsistent by
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | |   (17838)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17838) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | |   (17839)  all_54_10 = e2
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (17836), (17839) are inconsistent by
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | |   (17840)  all_54_10 = e1 | all_54_10 = e0
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17840) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | |   (17841)  all_54_10 = e1
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (17841) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | |   (17842)  all_6_2 = e1
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17842) implies:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | |   (17843)  all_6_2 = e1
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (17843) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | |   (17844)  all_56_21 = e1
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (17843) imply:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | |   (17845)   ~ (all_52_14 = e1)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (17846)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17846) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17847)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (170), (17794), (17822), (17823),
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17847), (function-axioms) are inconsistent by
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #252.
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17848)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17848) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17849)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17849) implies:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17850)  op(e1, e3) = e1
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (297), (367), (17783), (17840), (17850),
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1372.
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17851)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (17821), (17824), (17851),
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2271.
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (17852)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17852) gives:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17853)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 237.75/44.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (297), (381), (17764), (17783),
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17796), (17840), (17853), (function-axioms) are
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1410.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17854)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (17762), (17844), (17845), (17854),
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            #251.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | |   (17855)  all_54_10 = e0
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (17783), (17855) are inconsistent by
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | |   (17856)  all_58_9 = e2 & op(e3, e0) = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (17766), (17856), (function-axioms) are
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2318.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | End of split
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | End of split
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | |   (17857)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (17777), (17781), (17805), (17857) are
% 237.75/45.00  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | End of split
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17858)  all_58_12 = e2 & op(e0, e3) = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (17763), (17858), (function-axioms) are
% 237.75/45.00  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2315.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | End of split
% 237.75/45.00  | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | End of split
% 237.75/45.00  | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | |   (17859)  all_24_2 = e2
% 237.75/45.00  | | | | | | | | | | | | | | | |   (17860)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 237.75/45.00  | | | | | | | | | | | | | | | |              & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 237.75/45.00  | | | | | | | | | | | | | | | |              $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 237.75/45.00  | | | | | | | | | | | | | | | |              = all_24_1 & $i(all_24_1))
% 237.75/45.00  | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (17859) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | |   (17861)  all_10_2 = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (17861) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | |   (17862)  all_32_2 = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (17861) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | |   (17863)  all_56_1 = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | REDUCE: (357), (17861) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | |   (17864)   ~ (all_52_2 = e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | REDUCE: (45), (17861) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | |   (17865)  op(e3, e3) = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 237.75/45.00  | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | Case 1:
% 237.75/45.00  | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | |   (17866)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | BETA: splitting (17866) gives:
% 237.75/45.00  | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | Case 1:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17867)  all_58_4 = e2 & op(e3, e1) = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | ALPHA: (17867) implies:
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17868)  all_58_4 = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (162), (163),
% 237.75/45.00  | | | | | | | | | | | | | | | | | |            (165), (225), (227), (228), (230), (17768),
% 237.75/45.00  | | | | | | | | | | | | | | | | | |            (17795), (17864), (17868), (function-axioms) are
% 237.75/45.00  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #247.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17869)  all_58_5 = e2 & op(e2, e1) = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | ALPHA: (17869) implies:
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17870)  op(e2, e1) = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (17796), (17870), (function-axioms) are
% 237.75/45.00  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | End of split
% 237.75/45.00  | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | |   (17871)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 237.75/45.00  | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | BETA: splitting (17871) gives:
% 237.75/45.00  | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | Case 1:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17872)  all_58_8 = e2 & op(e1, e1) = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | ALPHA: (17872) implies:
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17873)  op(e1, e1) = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e2,
% 237.75/45.00  | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (39), (17873) gives:
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17874)  all_6_2 = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (17874) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17875)  all_36_2 = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (17874) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17876)  all_40_2 = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (17874) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17877)  all_56_21 = e2
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | REDUCE: (380), (17874) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | |   (17878)   ~ (all_52_8 = e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | |   (17879)   ~ (all_32_2 = e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | REDUCE: (17862), (17879) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | |   (17880)  $false
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | CLOSE: (17880) is inconsistent.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | |   (17881)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 237.75/45.00  | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 237.75/45.00  | | | | | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | |   (17882)   ~ (all_36_2 = e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (17875), (17882) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | |   (17883)  $false
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | CLOSE: (17883) is inconsistent.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | |   (17884)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | |              $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | |              = all_36_1 & $i(all_36_1))
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | |   (17885)   ~ (all_40_2 = e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | REDUCE: (17876), (17885) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | |   (17886)  $false
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | CLOSE: (17886) is inconsistent.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | |   (17887)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | |              $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | |              = all_40_1 & $i(all_40_1))
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | |   (17888)   ~ (all_44_2 = e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17761), (17888) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | |   (17889)  $false
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17889) is inconsistent.
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | |   (17890)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | |   (17891)  all_54_9 = e3
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (17891) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | |   (17892)  all_52_6 = e3
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17892) implies:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | |   (17893)  all_52_6 = e3
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (17893) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | |   (17894)   ~ (all_52_2 = e3)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (17893) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | |   (17895)   ~ (all_52_4 = e3)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (17893) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | |   (17896)   ~ (all_52_7 = e3)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17896) implies:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | |   (17897)   ~ (all_52_7 = e3)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (17893) imply:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | |   (17898)   ~ (all_52_14 = e3)
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17898) implies:
% 237.75/45.00  | | | | | | | | | | | | | | | | | | | | | | |   (17899)   ~ (all_52_14 = e3)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (17893) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | |   (17900)  op(e1, e2) = e3
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17887) gives:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | |   (17901)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_40_1 & $i(all_40_0) &
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_40_1)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17901) implies:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | |   (17902)   ~ (all_40_0 = e0)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | |   (17903)  op(e1, e2) = all_40_1
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | |   (17904)  op(all_40_1, e1) = all_40_0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17884) gives:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17905)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_36_1 & $i(all_36_0) &
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_36_1)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17905) implies:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17906)   ~ (all_36_0 = e3)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17907)  op(e1, e2) = all_36_1
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17908)  op(all_36_1, e1) = all_36_0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_1,
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_1, e2, e1, simplifying with (17903),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |              (17907) gives:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17909)  all_40_1 = all_36_1
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_40_1,
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (17900), (17903) gives:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17910)  all_40_1 = e3
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17909), (17910) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17911)  all_36_1 = e3
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17904), (17910) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17912)  op(e3, e1) = all_40_0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17908), (17911) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17913)  op(e3, e1) = all_36_0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |              all_36_0, e1, e3, simplifying with (169), (17913)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17914)  all_52_8 = all_36_0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_0, e1, e3, simplifying with (169), (17912)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17915)  all_52_8 = all_40_0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17914), (17915) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17916)  all_40_0 = all_36_0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (17914) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17917)  all_54_2 = all_36_0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (17914) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17918)   ~ (all_52_4 = all_36_0)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (17914) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17919)   ~ (all_52_9 = all_36_0)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17919) implies:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17920)   ~ (all_52_9 = all_36_0)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (17914) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17921)   ~ (all_52_12 = all_36_0)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17921) implies:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17922)   ~ (all_52_12 = all_36_0)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17878), (17914) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17923)   ~ (all_36_0 = e2)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17902), (17916) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17924)   ~ (all_36_0 = e0)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17925)  all_54_2 = e3
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17917), (17925) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17926)  all_36_0 = e3
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17906), (17926) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17927)  $false
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17927) is inconsistent.
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17928)   ~ (all_54_2 = e3)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17929)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17929) gives:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17930)  all_54_2 = e2
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17917), (17930) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17931)  all_36_0 = e2
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17923), (17931) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17932)  $false
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17932) is inconsistent.
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17933)   ~ (all_54_2 = e2)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17934)  all_54_2 = e1 | all_54_2 = e0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17934) gives:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17935)  all_54_2 = e1
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17917), (17935) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17936)  all_36_0 = e1
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17918), (17936) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17937)   ~ (all_52_4 = e1)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17920), (17936) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17938)   ~ (all_52_9 = e1)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17922), (17936) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17939)   ~ (all_52_12 = e1)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17906), (17936) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17940)   ~ (e3 = e1)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17923), (17936) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17941)   ~ (e2 = e1)
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (110), (112),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (113), (117), (118), (120), (125), (128), (133),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (136), (139), (140), (157), (158), (159),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (168),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (190), (191), (192), (193), (194),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (195), (197), (198), (201), (203), (210), (211),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (214), (216), (217), (218), (219), (223),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (230), (233), (235), (236), (237),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (240), (241), (242), (243), (244), (245),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (255), (256), (257), (258), (266), (267),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (280), (282), (297), (380), (381),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17760), (17762), (17763), (17764), (17765),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17766), (17767), (17768), (17773), (17774),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17775), (17783), (17793), (17794), (17796),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17803), (17860), (17863), (17865), (17873),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17877), (17881), (17884), (17887), (17890),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17894), (17895), (17897), (17900), (17903),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17907), (17937), (17938), (17939),
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #219.
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17942)  all_54_2 = e0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17917), (17942) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17943)  all_36_0 = e0
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17924), (17943) imply:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17944)  $false
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17944) is inconsistent.
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (17945)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_36_1)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17945) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17946)   ~ (all_36_1 = e0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17947)  op(e1, e2) = all_36_1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_1,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_1, e2, e1, simplifying with (17903),
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |              (17947) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17948)  all_40_1 = all_36_1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_40_1,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (17900), (17903) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17949)  all_40_1 = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17948), (17949) imply:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17950)  all_36_1 = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17904), (17949) imply:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17951)  op(e3, e1) = all_40_0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |              all_40_0, e1, e3, simplifying with (169), (17951)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17952)  all_52_8 = all_40_0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (17952) imply:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17953)  all_54_2 = all_40_0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (17952) imply:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17954)   ~ (all_52_4 = all_40_0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (17952) imply:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17955)   ~ (all_52_9 = all_40_0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17955) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17956)   ~ (all_52_9 = all_40_0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (17952) imply:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17957)   ~ (all_52_12 = all_40_0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17957) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17958)   ~ (all_52_12 = all_40_0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17878), (17952) imply:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (17959)   ~ (all_40_0 = e2)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17960)  all_54_2 = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17953), (17960) imply:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17961)  all_40_0 = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17961) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17962)  all_40_0 = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17958), (17962) imply:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17963)   ~ (all_52_12 = e3)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17964)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (136), (162), (170), (195), (267), (17865),
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17900), (17964), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2189.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17965)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17965) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17966)  all_58_4 = e3 & op(e3, e1) = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17966) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17967)  all_58_4 = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17968)  op(e3, e1) = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17969)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17969) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17970)  all_58_9 = e3 & op(e3, e0) = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17970) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17971)  op(e3, e0) = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (17963), (17971), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17972)  all_58_10 = e3 & op(e2, e0) = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17972) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17973)  op(e2, e0) = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17974)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17974) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17975)  all_58_12 = e3 & op(e0, e3) = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17975) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17976)  all_58_12 = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17977)  op(e0, e3) = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (17977) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17978)  all_52_3 = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (164), (17973) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17979)  all_52_13 = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17980)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17980) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17981)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17981) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17982)  op(e3, e1) = all_56_17
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17983)  op(e3, all_56_17) = e3
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17865), (17968), (17982), (17983),
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2098.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17984)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17984) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17985)  op(e2, e1) = all_56_19
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17986)  op(e2, all_56_19) = e2
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (165), (17985)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17987)  all_56_19 = all_52_9
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17986), (17987) imply:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17988)  op(e2, all_52_9) = e2
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17989)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17989) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17990)  all_58_12 = e1 & op(e0, e3) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17990) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17991)  all_58_12 = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17976), (17991) are inconsistent by
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1542.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17992)  all_58_13 = e1 & op(e0, e2) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17992) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17993)  op(e0, e2) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17994)  all_58_15 = e0 & op(e0, e0) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17994) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17995)  op(e0, e0) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (17995), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17996)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17996) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17997)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17997) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17998)  all_58_12 = e0 & op(e0, e3) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17998) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17999)  op(e0, e3) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17977), (17999), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #221.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18000)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18000) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18001)  all_58_13 = e0 & op(e0, e2) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18001) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18002)  op(e0, e2) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17993), (18002), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18003)  all_58_14 = e0 & op(e0, e1) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18003) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18004)  op(e0, e1) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18005)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18005) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18006)  all_58_4 = e1 & op(e3, e1) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18006) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18007)  op(e3, e1) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17968), (18007), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1823.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18008)  all_58_5 = e1 & op(e2, e1) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18008) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18009)  op(e2, e1) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (191), (256), (17764), (17796), (17897),
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17985), (17986), (18009), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1256.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18010)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (17873), (18004), (18010),
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2157.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18011)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18011) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18012)  all_58_14 = e1 & op(e0, e1) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18012) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18013)  op(e0, e1) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18014)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18014) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18015)  all_58_4 = e0 & op(e3, e1) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18015) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18016)  op(e3, e1) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17968), (18016), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2118.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18017)  all_58_5 = e0 & op(e2, e1) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18017) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18018)  op(e2, e1) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18019)  all_58_15 = e0 & op(e0, e0) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18019) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18020)  op(e0, e0) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (18020), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18021)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18021) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18022)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18022) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18023)  all_58_12 = e0 & op(e0, e3) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18023) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18024)  op(e0, e3) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17977), (18024), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #221.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18025)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18025) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18026)  all_58_13 = e0 & op(e0, e2) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18026) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18027)  op(e0, e2) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18028)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18028) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18029)  all_58_1 = e1 & op(e3, e2) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18029) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18030)  all_58_1 = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18031)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18031) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18032)  all_58_1 = e0 & op(e3, e2) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18030), (18032) are inconsistent by
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1720.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18033)  all_58_3 = e0 & op(e2, e2) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18033) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18034)  op(e2, e2) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17803), (18034), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2137.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18035)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18035) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18036)  all_58_7 = e0 & op(e1, e2) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18036) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18037)  op(e1, e2) = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17887), (17946), (17947), (18037),
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #782.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (18018) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18038)  all_52_9 = e0
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17988), (18038) imply:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18039)  op(e2, e0) = e2
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (18039), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18040)  all_58_3 = e1 & op(e2, e2) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18040) implies:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18041)  op(e2, e2) = e1
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17803), (18041), (function-axioms) are
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18042)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18042) gives:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18043)  all_58_7 = e1 & op(e1, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18043) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18044)  op(e1, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17900), (17903), (17947), (18044),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1701.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18045)  all_58_13 = e1 & op(e0, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18045) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18046)  op(e0, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18027), (18046), (function-axioms) are
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18047)  all_58_14 = e0 & op(e0, e1) = e0
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18047) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18048)  op(e0, e1) = e0
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18013), (18048), (function-axioms) are
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2158.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18049)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17873), (18013), (18049),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1036.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18050)  all_58_15 = e1 & op(e0, e0) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (18050) are inconsistent by
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #218.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18051)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18051) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18052)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18052) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18053)  op(e1, all_56_21) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17877), (18053) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18054)  op(e1, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17900), (17903), (17947), (18054),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1701.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18055)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18055) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18056)  op(e0, e1) = all_56_23
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18057)  op(e0, all_56_23) = e0
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18058)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18058) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18059)  all_58_12 = e1 & op(e0, e3) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18059) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18060)  all_58_12 = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17976), (18060) are inconsistent by
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1542.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18061)  all_58_13 = e1 & op(e0, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18061) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18062)  all_58_13 = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18063)  op(e0, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (218), (219),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (17890), (17977), (18056), (18057),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18062), (18063), (function-axioms) are
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #217.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18064)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18064) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18065)  all_58_14 = e1 & op(e0, e1) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18065) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18066)  op(e0, e1) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18067)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18067) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18068)  all_58_1 = e1 & op(e3, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18068) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18069)  op(e3, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17860), (17881), (18056), (18057), (18066),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18069), (function-axioms) are inconsistent by
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #215.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18070)  all_58_3 = e1 & op(e2, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18070) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18071)  op(e2, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17803), (18071), (function-axioms) are
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18072)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18072) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18073)  all_58_7 = e1 & op(e1, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18073) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18074)  op(e1, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17900), (17903), (17947), (18074),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1701.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18075)  all_58_13 = e1 & op(e0, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18075) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18076)  all_58_13 = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18077)  op(e0, e2) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (218), (219),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (17890), (17977), (18056), (18057),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18076), (18077), (function-axioms) are
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #217.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18078)  all_58_15 = e1 & op(e0, e0) = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (18078) are inconsistent by
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #218.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18079)  all_58_13 = e3 & op(e0, e2) = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17897), (18079), (function-axioms) are
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18080)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18080) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18081)  all_58_14 = e3 & op(e0, e1) = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18081) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18082)  all_58_14 = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18083)  op(e0, e1) = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (165), (227),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (17783), (17967), (18082), (18083),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1094.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18084)  all_58_15 = e3 & op(e0, e0) = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18084) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18085)  op(e0, e0) = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17774), (18085), (function-axioms) are
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18086)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (17774), (17899), (18086),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #214.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18087)  all_58_9 = e3 & op(e3, e0) = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18087) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18088)  op(e3, e0) = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (17963), (18088), (function-axioms) are
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18089)   ~ (all_54_2 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18090)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17953), (18089) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18091)   ~ (all_40_0 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18090) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18092)  all_54_2 = e2
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17953), (18092) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18093)  all_40_0 = e2
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18093) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18094)  all_40_0 = e2
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17959), (18094) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18095)  $false
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18095) is inconsistent.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18096)   ~ (all_54_2 = e2)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18097)  all_54_2 = e1 | all_54_2 = e0
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18097) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18098)  all_54_2 = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17953), (18098) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18099)  all_40_0 = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18099) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18100)  all_40_0 = e1
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17954), (18100) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18101)   ~ (all_52_4 = e1)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17956), (18100) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18102)   ~ (all_52_9 = e1)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17958), (18100) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18103)   ~ (all_52_12 = e1)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18091), (18100) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18104)   ~ (e3 = e1)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17959), (18100) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18105)   ~ (e2 = e1)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (110), (112),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (113), (117), (118), (120), (125), (128), (133),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (136), (139), (140), (157), (158), (159),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (168),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (190), (191), (192), (193), (194),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (195), (197), (198), (201), (203), (210), (211),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (214), (216), (217), (218), (219), (223),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (230), (233), (235), (236), (237),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (240), (241), (242), (243), (244), (245),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (255), (256), (257), (258), (266), (267),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (280), (282), (297), (380), (381),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17760), (17762), (17763), (17764), (17765),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17766), (17767), (17768), (17773), (17774),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17775), (17783), (17793), (17794), (17796),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17803), (17860), (17863), (17865), (17873),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17877), (17881), (17884), (17887), (17890),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17894), (17895), (17897), (17900), (17903),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17947), (18101), (18102), (18103),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #219.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18106)  all_54_2 = e0
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17953), (18106) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18107)  all_40_0 = e0
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18107) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18108)  all_40_0 = e0
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17902), (18108) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18109)  $false
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18109) is inconsistent.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18110)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_40_1)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17884), (17900), (18110), (function-axioms) are
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2144.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | |   (18111)   ~ (all_54_9 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (18111) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | |   (18112)   ~ (all_52_6 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18113)  all_54_4 = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (18113) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18114)  all_52_1 = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18114) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18115)  all_52_1 = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (18115) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18116)   ~ (all_52_2 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18116) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18117)   ~ (all_52_2 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (18115) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18118)   ~ (all_52_3 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18118) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18119)   ~ (all_52_3 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (18115) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18120)   ~ (all_52_9 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18120) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18121)   ~ (all_52_9 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (18115) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18122)   ~ (all_52_13 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18122) implies:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18123)   ~ (all_52_13 = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (18115) imply:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | |   (18124)  op(e2, e3) = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (18125)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (18112), (18117), (18125),
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | |            #213.
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (18126)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18126) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18127)  all_58_8 = e3 & op(e1, e1) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18127) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18128)  op(e1, e1) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17873), (18128), (function-axioms) are
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18129)  all_58_11 = e3 & op(e1, e0) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18129) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18130)  op(e1, e0) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18131)  all_54_8 = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (18117), (18131) are inconsistent by
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18132)   ~ (all_54_8 = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18133)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18134)  all_54_13 = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (18134) imply:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18135)  all_52_7 = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18135) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18136)  all_52_7 = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (18136) imply:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18137)   ~ (all_52_11 = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18137) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18138)   ~ (all_52_11 = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (18136) imply:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18139)  op(e0, e2) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18140)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18140) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18141)  all_58_4 = e3 & op(e3, e1) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18141) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18142)  op(e3, e1) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18143)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18143) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18144)  op(e0, e2) = all_4_1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17890) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18145)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_44_1 & $i(all_44_0) &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18145) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18146)  op(e0, e2) = all_44_1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (134), (144), (159), (163), (165),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (213), (214), (268), (17762),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (17794), (17796), (17863), (17864),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17873), (17878), (18117), (18119), (18124),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18130), (18133), (18139), (18142), (18144),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18146), (function-axioms) are inconsistent by
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #212.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18147)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18147) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18148)  op(e0, e2) = all_44_1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (134), (144), (159), (163), (165),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (213), (214), (268), (17762),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (17794), (17796), (17863), (17864),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17873), (17878), (18117), (18119), (18124),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18130), (18133), (18139), (18142), (18144),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18148), (function-axioms) are inconsistent by
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #212.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18149)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18149) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18150)   ~ (all_4_1 = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18151)  op(e0, e2) = all_4_1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17890), (18139), (18150), (18151),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #211.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18152)  all_58_5 = e3 & op(e2, e1) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (18121), (18152), (function-axioms) are
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18153)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17873), (18138), (18153),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1307.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18154)   ~ (all_54_13 = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (256), (18154) imply:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18155)   ~ (all_52_7 = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18156)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18156) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18157)  all_58_1 = e3 & op(e3, e2) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18157) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18158)  op(e3, e2) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18159)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (159), (18119), (18155), (18159),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1123.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18160)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18160) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18161)  all_58_14 = e3 & op(e0, e1) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18161) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18162)  op(e0, e1) = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (18162) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18163)  all_52_11 = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (18158) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18164)  all_52_4 = e3
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18165)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18165) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18166)  all_58_6 = e1 & op(e1, e3) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18166) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18167)  op(e1, e3) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18168)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18168) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18169)  all_58_6 = e0 & op(e1, e3) = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18169) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18170)  op(e1, e3) = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18167), (18170), (function-axioms) are
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #449.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18171)  all_58_7 = e0 & op(e1, e2) = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17884), (17887), (18162), (18171),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #224.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18172)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (17873), (18130), (18172),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #209.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18173)  all_58_7 = e1 & op(e1, e2) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18173) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18174)  op(e1, e2) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18175)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18175) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18176)  all_58_6 = e0 & op(e1, e3) = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18176) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18177)  op(e1, e3) = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18178)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18178) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18179)  all_58_0 = e1 & op(e3, e3) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18179) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18180)  op(e3, e3) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17865), (18180), (function-axioms) are
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18181)  all_58_2 = e1 & op(e2, e3) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (164), (165), (234), (17803), (18121),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18123), (18181), (function-axioms) are
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1312.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18182)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18182) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18183)  all_58_6 = e1 & op(e1, e3) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18183) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18184)  op(e1, e3) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18177), (18184), (function-axioms) are
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #449.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18185)  all_58_12 = e1 & op(e0, e3) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18185) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18186)  op(e0, e3) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18187)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (17803), (18158), (18187),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #409.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18188)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18188) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18189)  all_58_7 = e0 & op(e1, e2) = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18189) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18190)  op(e1, e2) = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (18174), (18190), (function-axioms)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18191)  all_58_13 = e0 & op(e0, e2) = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18191) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18192)  op(e0, e2) = e0
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18193)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18193) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18194)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (163), (17762), (18117), (18158), (18194),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #208.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18195)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18195) gives:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18196)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18196) implies:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18197)  op(e1, e3) = e1
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18177), (18197), (function-axioms) are
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #449.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18198)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (18119), (18186), (18198),
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #206.
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18199)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18199) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18200)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (165), (17762), (17796), (18192), (18200),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #205.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18201)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (17762), (18130), (18201),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #204.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18202)  all_58_7 = e0 & op(e1, e2) = e0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18202) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18203)  op(e1, e2) = e0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (18174), (18203), (function-axioms)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18204)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (17873), (18130), (18204),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #209.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18205)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18205) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18206)  all_58_8 = e1 & op(e1, e1) = e1
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18206) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18207)  op(e1, e1) = e1
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17873), (18207), (function-axioms) are
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18208)  all_58_11 = e1 & op(e1, e0) = e1
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18208) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18209)  op(e1, e0) = e1
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18130), (18209), (function-axioms) are
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18210)  all_58_15 = e3 & op(e0, e0) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18210) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18211)  op(e0, e0) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17774), (18211), (function-axioms) are
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18212)  all_58_3 = e3 & op(e2, e2) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18212) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18213)  op(e2, e2) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17803), (18213), (function-axioms) are
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18214)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (18112), (18155), (18214),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #475.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | |   (18215)   ~ (all_54_4 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | |   (18216)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (18215) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | |   (18217)   ~ (all_52_1 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (18218)  all_54_13 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (18218) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (18219)  all_52_7 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18219) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (18220)  all_52_7 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (18220) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (18221)   ~ (all_52_3 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (18220) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (18222)   ~ (all_52_11 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18222) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (18223)   ~ (all_52_11 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (18220) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (18224)  op(e0, e2) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18225)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (17865), (18217), (18225),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1404.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18226)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18226) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18227)  all_58_6 = e3 & op(e1, e3) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18227) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18228)  all_58_6 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18229)  op(e1, e3) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18230)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18230) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18231)   ~ (all_4_0 = e1)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18232)  op(e0, e2) = all_4_1
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18233)  op(all_4_1, e0) = all_4_0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17890) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18234)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_44_1 & $i(all_44_0) &
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18234) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18235)   ~ (all_44_0 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18236)  op(e0, e2) = all_44_1
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18237)  op(all_44_1, e0) = all_44_0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_44_1, e2, e0, simplifying with (18232),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (18236) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18238)  all_44_1 = all_4_1
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1,
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (18224), (18236) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18239)  all_44_1 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (18229) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18240)  all_52_2 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18238), (18239) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18241)  all_4_1 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (18240) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18242)   ~ (all_52_14 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18242) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18243)   ~ (all_52_14 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18237), (18239) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18244)  op(e3, e0) = all_44_0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18233), (18241) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18245)  op(e3, e0) = all_4_0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_4_0, e0, e3, simplifying with (168), (18245)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18246)  all_52_12 = all_4_0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_44_0, e0, e3, simplifying with (168), (18244)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18247)  all_52_12 = all_44_0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18246), (18247) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18248)  all_44_0 = all_4_0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (18246) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18249)  all_54_3 = all_4_0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (18246) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18250)   ~ (all_52_13 = all_4_0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18250) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18251)   ~ (all_52_13 = all_4_0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (18246) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18252)   ~ (all_52_14 = all_4_0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18252) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18253)   ~ (all_52_14 = all_4_0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17766), (18246) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18254)   ~ (all_4_0 = e2)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18235), (18248) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18255)   ~ (all_4_0 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18256)  all_54_3 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18249), (18256) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18257)  all_4_0 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18255), (18257) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18258)  $false
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18258) is inconsistent.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18259)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (110), (160), (162), (164), (167),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (210), (223), (224), (226), (258),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (17762), (17767), (17768), (17793),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17873), (17884), (17887), (18224), (18228),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18231), (18243), (18245), (18249), (18251),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18253), (18254), (18255), (18259),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #200.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18260)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 &
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18260) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18261)   ~ (all_44_1 = e1)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18262)  op(e0, e2) = all_44_1
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_44_1, e2, e0, simplifying with (18232),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (18262) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18263)  all_44_1 = all_4_1
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1,
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (18224), (18262) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18264)  all_44_1 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (18229) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18265)  all_52_2 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18263), (18264) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18266)  all_4_1 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (18265) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18267)   ~ (all_52_6 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (18265) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18268)   ~ (all_52_14 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18268) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18269)   ~ (all_52_14 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18233), (18266) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18270)  op(e3, e0) = all_4_0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_4_0, e0, e3, simplifying with (168), (18270)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18271)  all_52_12 = all_4_0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (18271) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18272)  all_54_3 = all_4_0
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (18271) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18273)   ~ (all_52_4 = all_4_0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (18271) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18274)   ~ (all_52_8 = all_4_0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (18271) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18275)   ~ (all_52_13 = all_4_0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18275) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18276)   ~ (all_52_13 = all_4_0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (18271) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18277)   ~ (all_52_14 = all_4_0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18277) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18278)   ~ (all_52_14 = all_4_0)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17766), (18271) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18279)   ~ (all_4_0 = e2)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18280)  all_54_3 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18272), (18280) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18281)  all_4_0 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18281) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18282)  all_4_0 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18273), (18282) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18283)   ~ (all_52_4 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18274), (18282) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18284)   ~ (all_52_8 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18276), (18282) imply:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18285)   ~ (all_52_13 = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18286)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (17803), (18217), (18286),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1413.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18287)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18287) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18288)  all_58_5 = e3 & op(e2, e1) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18288) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18289)  all_58_5 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18290)  op(e2, e1) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18291)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (17865), (18283), (18291),
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1959.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18292)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18292) gives:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18293)  all_58_4 = e3 & op(e3, e1) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18293) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18294)  op(e3, e1) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (18284), (18294), (function-axioms) are
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18295)  all_58_9 = e3 & op(e3, e0) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18295) implies:
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18296)  all_58_9 = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18297)  op(e3, e0) = e3
% 237.87/45.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18298)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18298) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18299)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18299) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18300)  op(e3, e0) = all_56_25
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18301)  op(e3, all_56_25) = e3
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25, e0, e3, simplifying with (18297),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (18300) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18302)  all_56_25 = e3
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18301), (18302) imply:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18303)  op(e3, e3) = e3
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17865), (18303), (function-axioms) are
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18304)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18304) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18305)  op(e2, e0) = all_56_27
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18306)  op(e2, all_56_27) = e2
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27, e0, e2, simplifying with (164), (18305)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18307)  all_56_27 = all_52_13
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18306), (18307) imply:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18308)  op(e2, all_52_13) = e2
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18309)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18309) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18310)  all_58_0 = e1 & op(e3, e3) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18310) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18311)  op(e3, e3) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17865), (18311), (function-axioms) are
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18312)  all_58_1 = e1 & op(e3, e2) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18312) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18313)  all_58_1 = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18314)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (18283), (18290), (18297), (18313),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18314), (function-axioms) are inconsistent by
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #199.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18315)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18315) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18316)  all_58_8 = e1 & op(e1, e1) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18316) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18317)  op(e1, e1) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17873), (18317), (function-axioms) are
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18318)  all_58_14 = e1 & op(e0, e1) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18318) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18319)  op(e0, e1) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18320)  all_58_15 = e0 & op(e0, e0) = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18320) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18321)  op(e0, e0) = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (18321), (function-axioms) are
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18322)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18322) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18323)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18324)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18323) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18325)  all_58_12 = e0 & op(e0, e3) = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18325) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18326)  op(e0, e3) = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18327)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18327) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18328)  all_58_0 = e1 & op(e3, e3) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18328) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18329)  op(e3, e3) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17865), (18329), (function-axioms) are
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18330)  all_58_2 = e1 & op(e2, e3) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18330) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18331)  all_58_2 = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18332)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17803), (18331), (18332),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #198.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18333)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18333) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18334)  all_58_5 = e0 & op(e2, e1) = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (17865), (18283),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18284), (18289), (18296), (18334),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #197.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18335)  all_58_10 = e0 & op(e2, e0) = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18335) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18336)  op(e2, e0) = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18337)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (164), (170), (240),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (17865), (18283), (18313), (18336),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18337), (function-axioms) are inconsistent by
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #196.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18338)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18338) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18339)  all_58_11 = e1 & op(e1, e0) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18339) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18340)  op(e1, e0) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18341)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18341) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18342)  all_58_6 = e0 & op(e1, e3) = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (17865), (18228),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18283), (18284), (18296), (18342),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #195.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (18340) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18343)  all_52_14 = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (18336) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18344)  all_52_13 = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (18343), (18344) imply:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18345)   ~ (e1 = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18285), (18344) imply:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18346)   ~ (e3 = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17767), (18344) imply:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18347)   ~ (e2 = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18308), (18344) imply:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18348)  op(e2, e0) = e2
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (18296), (18324), (18340), (18348),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2101.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18349)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17873), (18340), (18349),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2210.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18350)  all_58_15 = e1 & op(e0, e0) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18350) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18351)  all_58_15 = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (110), (160), (164), (221),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18297), (18308), (18335), (18336), (18351),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1181.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18352)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (18229), (18326), (18352),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #194.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18353)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (18224), (18319), (18353),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #193.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18354)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18354) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18355)  all_58_4 = e1 & op(e3, e1) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18355) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18356)  all_58_4 = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18357)  op(e3, e1) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18358)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (167), (170),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (240), (246), (17767), (17793), (17865),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18283), (18290), (18356), (18358),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #191.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18359)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18359) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18360)  all_58_7 = e1 & op(e1, e2) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18360) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18361)  all_58_7 = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18362)  op(e1, e2) = e1
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18363)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18363) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18364)  all_58_4 = e0 & op(e3, e1) = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18364) implies:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18365)  op(e3, e1) = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18357), (18365), (function-axioms) are
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2089.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18366)  all_58_5 = e0 & op(e2, e1) = e0
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (17865), (18283),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18284), (18289), (18296), (18366),
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #197.
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18367)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18367) gives:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18368)  all_58_8 = e0 & op(e1, e1) = e0
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18368) implies:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18369)  op(e1, e1) = e0
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17873), (18369), (function-axioms) are
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18370)  all_58_14 = e0 & op(e0, e1) = e0
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18370) implies:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18371)  op(e0, e1) = e0
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18372)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18372) gives:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18373)  all_58_12 = e1 & op(e0, e3) = e1
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18373) implies:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18374)  all_58_12 = e1
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18375)  op(e0, e3) = e1
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18376)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18376) gives:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18377)  all_58_0 = e0 & op(e3, e3) = e0
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18377) implies:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18378)  op(e3, e3) = e0
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17865), (18378), (function-axioms) are
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18379)  all_58_2 = e0 & op(e2, e3) = e0
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18379) implies:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18380)  all_58_2 = e0
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18381)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18381) gives:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18382)  all_58_2 = e1 & op(e2, e3) = e1
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18382) implies:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18383)  all_58_2 = e1
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18380), (18383) are inconsistent by
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1268.
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18384)  all_58_3 = e1 & op(e2, e2) = e1
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18384) implies:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18385)  all_58_3 = e1
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (17803), (18361), (18362), (18385),
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2127.
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18386)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18386) gives:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18387)  all_58_5 = e1 & op(e2, e1) = e1
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18387) implies:
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18388)  op(e2, e1) = e1
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18290), (18388), (function-axioms) are
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2255.
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.87/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18389)  all_58_10 = e1 & op(e2, e0) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18389) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18390)  op(e2, e0) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18391)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18391) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (164), (18390) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18392)  all_52_13 = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18308), (18392) imply:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18393)  op(e2, e1) = e2
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18290), (18393), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18394)  all_58_3 = e0 & op(e2, e2) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18394) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18395)  op(e2, e2) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17803), (18395), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2137.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18396)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18396) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18397)  all_58_7 = e0 & op(e1, e2) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18397) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18398)  op(e1, e2) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (18362), (18398), (function-axioms)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18399)  all_58_13 = e0 & op(e0, e2) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18399) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18400)  op(e0, e2) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (157), (219), (17774), (18223),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18374), (18400), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #190.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18401)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18401) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18402)  all_58_6 = e0 & op(e1, e3) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (17865), (18228),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18283), (18284), (18296), (18402),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #195.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18403)  all_58_12 = e0 & op(e0, e3) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18403) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18404)  op(e0, e3) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18375), (18404), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #207.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18405)  all_58_13 = e1 & op(e0, e2) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18405) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18406)  op(e0, e2) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18261), (18262), (18406), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #230.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18407)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18407) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18408)  all_58_14 = e1 & op(e0, e1) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18408) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18409)  op(e0, e1) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18371), (18409), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2158.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18410)  all_58_15 = e1 & op(e0, e0) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18410) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18411)  all_58_15 = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (17773), (17802), (17803), (18361),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18362), (18411), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2112.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18412)  all_58_13 = e1 & op(e0, e2) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18412) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18413)  op(e0, e2) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18261), (18262), (18413), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #230.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18414)  all_58_9 = e1 & op(e3, e0) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18414) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18415)  op(e3, e0) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18297), (18415), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18416)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18416) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18417)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18417) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18418)  op(e1, e0) = all_56_29
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18419)  op(e1, all_56_29) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_29, e0, e1, simplifying with (160), (18418)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18420)  all_56_29 = all_52_14
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18419), (18420) imply:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18421)  op(e1, all_52_14) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18422)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18422) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18423)  all_58_0 = e1 & op(e3, e3) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18423) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18424)  op(e3, e3) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17865), (18424), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18425)  all_58_1 = e1 & op(e3, e2) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18425) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18426)  all_58_1 = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18427)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (18283), (18290), (18297), (18426),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18427), (function-axioms) are inconsistent by
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #199.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18428)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18428) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18429)  all_58_8 = e1 & op(e1, e1) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18429) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18430)  op(e1, e1) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17873), (18430), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18431)  all_58_14 = e1 & op(e0, e1) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18431) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18432)  op(e0, e1) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18433)  all_58_15 = e0 & op(e0, e0) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18433) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18434)  op(e0, e0) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (18434), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18435)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18435) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18436)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18436) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18437)  all_58_12 = e0 & op(e0, e3) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18437) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18438)  op(e0, e3) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18439)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18439) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18440)  all_58_0 = e1 & op(e3, e3) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18440) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18441)  op(e3, e3) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17865), (18441), (function-axioms) are
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18442)  all_58_2 = e1 & op(e2, e3) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18442) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18443)  all_58_2 = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18444)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17803), (18443), (18444),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #198.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18445)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18445) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18446)  all_58_5 = e0 & op(e2, e1) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (17865), (18283),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18284), (18289), (18296), (18446),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #197.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18447)  all_58_10 = e0 & op(e2, e0) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18447) implies:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18448)  op(e2, e0) = e0
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18449)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (164), (170), (240),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (17865), (18283), (18426), (18448),
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18449), (function-axioms) are inconsistent by
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #196.
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18450)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18450) gives:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18451)  all_58_11 = e1 & op(e1, e0) = e1
% 237.95/45.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (160), (164), (167),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (225), (233), (236), (17767), (17768),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17793), (17873), (18228), (18261), (18262),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18290), (18421), (18451), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #189.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18452)  all_58_15 = e1 & op(e0, e0) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18452) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18453)  all_58_15 = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (18453) are inconsistent by
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2231.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18454)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (18229), (18438), (18454),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #194.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18455)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (18224), (18432), (18455),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #193.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18456)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18456) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18457)  all_58_4 = e1 & op(e3, e1) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18457) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18458)  all_58_4 = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18459)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (167), (170),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (240), (246), (17767), (17793), (17865),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18283), (18290), (18458), (18459),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #191.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18460)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18460) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18461)  all_58_7 = e1 & op(e1, e2) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18461) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18462)  all_58_7 = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18463)  op(e1, e2) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18464)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18464) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18465)  all_58_6 = e0 & op(e1, e3) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (170), (246), (17865), (18228),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18283), (18284), (18296), (18465),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #195.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18466)  all_58_7 = e0 & op(e1, e2) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18466) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18467)  op(e1, e2) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (18463), (18467), (function-axioms)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18468)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18468) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18469)  all_58_8 = e0 & op(e1, e1) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18469) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18470)  op(e1, e1) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17873), (18470), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18471)  all_58_11 = e0 & op(e1, e0) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18471) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18472)  all_58_11 = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18473)  op(e1, e0) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18474)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18474) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18475)  all_58_9 = e1 & op(e3, e0) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18475) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18476)  op(e3, e0) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18297), (18476), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18477)  all_58_10 = e1 & op(e2, e0) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18477) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18478)  op(e2, e0) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18479)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18479) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (18473) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18480)  all_52_14 = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (164), (18478) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18481)  all_52_13 = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18421), (18480) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18482)  op(e1, e0) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18473), (18482), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2284.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18483)  all_58_3 = e0 & op(e2, e2) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18483) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18484)  op(e2, e2) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17803), (18484), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2137.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18485)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18485) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18486)  all_58_5 = e0 & op(e2, e1) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18486) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18487)  all_58_5 = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18289), (18487) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18488)  e3 = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18228), (18488) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18489)  all_58_6 = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (226), (17873), (18112), (18472),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18489), (function-axioms) are inconsistent by
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1686.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18490)  all_58_10 = e0 & op(e2, e0) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18490) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18491)  op(e2, e0) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (18478), (18491), (function-axioms)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18492)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18492) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18493)  all_58_11 = e1 & op(e1, e0) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (160), (164), (167),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (225), (233), (236), (17767), (17768),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17793), (17873), (18228), (18261), (18262),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18290), (18421), (18493), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #189.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18494)  all_58_15 = e1 & op(e0, e0) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18494) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18495)  all_58_15 = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (17773), (17802), (17803), (18462),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18463), (18495), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2112.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18496)  all_58_13 = e1 & op(e0, e2) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18496) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18497)  op(e0, e2) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18261), (18262), (18497), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #230.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18498)  all_58_9 = e1 & op(e3, e0) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18498) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18499)  op(e3, e0) = e1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18297), (18499), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18500)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18500) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18501)  op(e0, all_56_31) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (18501) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18502)  op(e0, e2) = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18224), (18502), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1961.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18503)  all_58_10 = e3 & op(e2, e0) = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18503) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18504)  op(e2, e0) = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (18285), (18504), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18505)   ~ (all_54_3 = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18506)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18272), (18505) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18507)   ~ (all_4_0 = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (110), (160), (162), (164), (167),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (210), (223), (224), (226), (258),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (17762), (17767), (17768), (17793),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17873), (17884), (17887), (18224), (18228),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18231), (18269), (18270), (18272), (18276),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18278), (18279), (18506), (18507),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #200.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18508)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18508) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18509)   ~ (all_4_1 = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18510)  op(e0, e2) = all_4_1
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17890), (18224), (18509), (18510),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #211.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18511)  all_58_12 = e3 & op(e0, e3) = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18511) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18512)  op(e0, e3) = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (18221), (18512), (function-axioms) are
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (18513)   ~ (all_54_13 = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (256), (18513) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (18514)   ~ (all_52_7 = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18515)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18515) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18516)  all_58_1 = e3 & op(e3, e2) = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18516) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18517)  all_58_1 = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18518)  op(e3, e2) = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (18518) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18519)  all_52_4 = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (18519) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18520)   ~ (all_52_6 = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (18519) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18521)   ~ (all_52_7 = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (18519) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18522)   ~ (all_52_12 = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18522) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18523)   ~ (all_52_12 = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18524)  all_54_11 = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (18524) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18525)  all_52_14 = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18525) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18526)  all_52_14 = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (18526) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18527)   ~ (all_52_2 = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (18526) imply:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18528)   ~ (all_52_13 = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18529)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (17803), (18217), (18529),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1413.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18530)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18530) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18531)  all_58_5 = e3 & op(e2, e1) = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18531) implies:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18532)  all_58_5 = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18533)  op(e2, e1) = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18534)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (17865), (18217), (18534),
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1404.
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18535)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18535) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18536)  all_58_6 = e3 & op(e1, e3) = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18536) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18537)  op(e1, e3) = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (18527), (18537), (function-axioms) are
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18538)  all_58_12 = e3 & op(e0, e3) = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18538) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18539)  all_58_12 = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18540)  op(e0, e3) = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18541)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (239), (241),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (18112), (18539), (18541),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1530.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18542)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18542) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18543)  all_58_8 = e3 & op(e1, e1) = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18543) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18544)  op(e1, e1) = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17873), (18544), (function-axioms) are
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18545)  all_58_11 = e3 & op(e1, e0) = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18545) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18546)  all_58_11 = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18547)  op(e1, e0) = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (18540) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18548)  all_52_3 = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (18533) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18549)  all_52_9 = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (18549) imply:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18550)   ~ (all_52_8 = e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (18549) imply:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18551)   ~ (all_52_11 = e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18551) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18552)   ~ (all_52_11 = e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18553)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18553) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18554)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (163), (167), (18217), (18518), (18527),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18554), (function-axioms) are inconsistent by
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #188.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18555)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18555) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18556)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18556) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18557)   ~ (all_56_31 = e3)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18558)  op(e1, e3) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18559)  op(e3, e1) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (18558) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18560)  all_52_2 = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (18559) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18561)  all_52_8 = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (18561) imply:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18562)   ~ (all_52_11 = e1)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18562) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18563)   ~ (all_52_11 = e1)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18550), (18561) imply:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18564)   ~ (e3 = e1)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17878), (18561) imply:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18565)   ~ (e2 = e1)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18566)  all_54_14 = e3
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (18552), (18566) are inconsistent by
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1796.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18567)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18568)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18568) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18569)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (255), (17765), (18550), (18559), (18563),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18567), (18569), (function-axioms) are
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1397.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18570)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (279), (17793), (18216), (18533), (18570),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2095.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18571)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18571) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18572)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18572) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18573)  op(e1, all_56_21) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17877), (18573) imply:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18574)  op(e1, e2) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18575)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (164), (167), (168), (169), (233),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (17767), (17793), (17865), (18523),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18533), (18550), (18575), (function-axioms) are
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #187.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18576)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18576) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18577)  all_58_7 = e1 & op(e1, e2) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (162), (223),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (17775), (18558), (18577),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #186.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18578)  all_58_13 = e1 & op(e0, e2) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18578) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18579)  op(e0, e2) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18580)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (17803), (18518), (18580),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #409.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18581)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18581) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18582)  all_58_7 = e0 & op(e1, e2) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18582) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18583)  op(e1, e2) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (18574), (18583), (function-axioms)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18584)  all_58_13 = e0 & op(e0, e2) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18584) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18585)  op(e0, e2) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18579), (18585), (function-axioms) are
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18586)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18586) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18587)  op(e0, e1) = all_56_23
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18588)  op(e0, all_56_23) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18589)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (164), (167), (168), (169), (233),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (17767), (17793), (17865), (18523),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18533), (18550), (18589), (function-axioms) are
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #187.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18590)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18590) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18591)  all_58_7 = e1 & op(e1, e2) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (162), (223),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (17775), (18558), (18591),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #186.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18592)  all_58_13 = e1 & op(e0, e2) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18592) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18593)  all_58_13 = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18594)  op(e0, e2) = e1
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18595)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (17865), (18518), (18595),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #423.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18596)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18596) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18597)  all_58_4 = e0 & op(e3, e1) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18597) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18598)  op(e3, e1) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18559), (18598), (function-axioms) are
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2089.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18599)  all_58_9 = e0 & op(e3, e0) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18599) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18600)  all_58_9 = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18601)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18601) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18602)  all_58_4 = e0 & op(e3, e1) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18602) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18603)  op(e3, e1) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18559), (18603), (function-axioms) are
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2089.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18604)  all_58_5 = e0 & op(e2, e1) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18604) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18605)  all_58_5 = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18532), (18605) are inconsistent by
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2038.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18606)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18606) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18607)  all_58_8 = e0 & op(e1, e1) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18607) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18608)  op(e1, e1) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17873), (18608), (function-axioms) are
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18609)  all_58_14 = e0 & op(e0, e1) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18609) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18610)  all_58_14 = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18611)  op(e0, e1) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18612)  all_58_15 = e0 & op(e0, e0) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18612) implies:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18613)  all_58_15 = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18614)  op(e0, e0) = e0
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (220), (221), (18546),
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18600), (18613), (18614), (function-axioms) are
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1653.
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18615)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18615) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18616)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (218), (219),
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17890), (18587), (18588), (18593), (18594),
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18610), (18611), (18616), (function-axioms) are
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #228.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18617)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18617) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18618)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18618) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18619)  op(e3, e0) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (18523), (18619), (function-axioms) are
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18620)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18620) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18621)  op(e0, e3) = e0
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e0, e3,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, simplifying with (18540), (18621) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18622)  e3 = e0
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (18622) imply:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18623)  $false
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18623) is inconsistent.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18624)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18624) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18625)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18625) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18626)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18626) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18627)  op(e2, e1) = e2
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18533), (18627), (function-axioms) are
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18628)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18628) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18629)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18629) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18630)  op(e2, e1) = e1
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18533), (18630), (function-axioms) are
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2255.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18631)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18631) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18632)  op(e0, e2) = e2
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (18632), (function-axioms) are
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18633)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (17762), (18547), (18633),
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #204.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18634)  all_58_10 = e3 & op(e2, e0) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18634) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18635)  op(e2, e0) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (18528), (18635), (function-axioms) are
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18636)   ~ (all_54_11 = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (18636) imply:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18637)   ~ (all_52_14 = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18638)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18638) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18639)  all_58_6 = e3 & op(e1, e3) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18639) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18640)  all_58_6 = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18641)  op(e1, e3) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18642)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18642) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18643)  all_58_9 = e3 & op(e3, e0) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18643) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18644)  op(e3, e0) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (18523), (18644), (function-axioms) are
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18645)  all_58_10 = e3 & op(e2, e0) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18645) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18646)  op(e2, e0) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (18641) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18647)  all_52_2 = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (164), (18646) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18648)  all_52_13 = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18649)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (239), (241),
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (18514), (18640), (18649),
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1138.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18650)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18650) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18651)  all_58_14 = e3 & op(e0, e1) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18651) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18652)  all_58_14 = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18653)  op(e0, e1) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (18653) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18654)  all_52_11 = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (18654) imply:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18655)   ~ (all_52_3 = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (18654) imply:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18656)   ~ (all_52_8 = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (18654) imply:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18657)   ~ (all_52_9 = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18658)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18658) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18659)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18659) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18660)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18660) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18661)  op(e2, e3) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (18217), (18661), (function-axioms) are
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18662)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18662) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18663)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18663) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18664)  op(e3, e2) = e2
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18518), (18664), (function-axioms) are
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2193.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18665)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18665) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18666)  op(e3, e1) = e3
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (18656), (18666), (function-axioms) are
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18667)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18667) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18668)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18668) implies:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18669)  op(e1, e3) = e1
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18641), (18669), (function-axioms) are
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18670)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18670) gives:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18671)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18671) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18672)  op(e0, e3) = e3
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (18655), (18672), (function-axioms) are
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18673)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18673) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18674)   ~ (all_56_31 = e3)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18675)  op(e0, e3) = e0
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18676)  op(e3, e0) = e0
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (18675) gives:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18677)  all_52_3 = e0
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (168), (18676) gives:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18678)  all_52_12 = e0
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18523), (18678) imply:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18679)   ~ (e3 = e0)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17766), (18678) imply:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18680)   ~ (e2 = e0)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18681)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18681) gives:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18682)  all_58_12 = e1 & op(e0, e3) = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18682) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18683)  op(e0, e3) = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18675), (18683), (function-axioms) are
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #207.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18684)  all_58_13 = e1 & op(e0, e2) = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18684) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18685)  op(e0, e2) = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (235), (17803), (17884), (17887),
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18518), (18653), (18685), (function-axioms) are
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #223.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18686)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18686) gives:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18687)  all_58_14 = e1 & op(e0, e1) = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18687) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18688)  all_58_14 = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18652), (18688) imply:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18689)  e3 = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (168), (169), (246), (17865), (18517),
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18523), (18656), (18689), (function-axioms) are
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #419.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18690)  all_58_15 = e1 & op(e0, e0) = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18690) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18691)  all_58_15 = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (18691) are inconsistent by
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2231.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18692)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18692) gives:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18693)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (17762), (17764), (17796), (18693),
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #184.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18694)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18694) gives:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18695)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18695) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18696)   ~ (all_56_31 = e2)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (18696) imply:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18697)  $false
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18697) is inconsistent.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18698)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18698) gives:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18699)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18699) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18700)  op(e0, e1) = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e1, e1,
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, simplifying with (18653), (18700) gives:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18701)  e3 = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18517), (18701) imply:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18702)  all_58_1 = e1
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (168), (169), (246), (17865), (18523),
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18656), (18702), (function-axioms) are
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1327.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18703)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18703) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18704)  op(e0, e1) = e0
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (165), (169), (230), (17775), (18656),
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18657), (18704), (function-axioms) are
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1626.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18705)  all_58_15 = e3 & op(e0, e0) = e3
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18705) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18706)  op(e0, e0) = e3
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17774), (18706), (function-axioms) are
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18707)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (17774), (18637), (18707),
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #214.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18708)  all_58_7 = e3 & op(e1, e2) = e3
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18708) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18709)  op(e1, e2) = e3
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (18112), (18709), (function-axioms) are
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18710)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (17873), (18637), (18710),
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2148.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18711)  all_58_3 = e3 & op(e2, e2) = e3
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18711) implies:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18712)  op(e2, e2) = e3
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17803), (18712), (function-axioms) are
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18713)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (18112), (18514), (18713),
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            #475.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | |   (18714)  all_58_14 = e2 & op(e0, e1) = e2
% 237.95/45.10  | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (17765), (18714), (function-axioms) are
% 237.95/45.10  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #183.
% 237.95/45.10  | | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | |   (18715)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 237.95/45.10  | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 237.95/45.10  | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (17767), (17796), (18715),
% 237.95/45.10  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.10  | | | | | | | | | | | | | |            #182.
% 237.95/45.10  | | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | |   (18716)  all_54_5 = e1 | all_54_5 = e0
% 237.95/45.10  | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | | REF_CLOSE: (275), (17779), (17785), (18716) are inconsistent
% 237.95/45.10  | | | | | | | | | | | | |            by sub-proof #2300.
% 237.95/45.10  | | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | |   (18717)  all_22_2 = e1
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | COMBINE_EQS: (326), (18717) imply:
% 237.95/45.10  | | | | | | | | | | |   (18718)  all_8_2 = e1
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | SIMP: (18718) implies:
% 237.95/45.10  | | | | | | | | | | |   (18719)  all_8_2 = e1
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | COMBINE_EQS: (353), (18719) imply:
% 237.95/45.10  | | | | | | | | | | |   (18720)  all_56_11 = e1
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | REDUCE: (366), (18719) imply:
% 237.95/45.10  | | | | | | | | | | |   (18721)   ~ (all_52_1 = e1)
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | REDUCE: (369), (18719) imply:
% 237.95/45.10  | | | | | | | | | | |   (18722)   ~ (all_52_4 = e1)
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | REDUCE: (375), (18719) imply:
% 237.95/45.10  | | | | | | | | | | |   (18723)   ~ (all_52_9 = e1)
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | REDUCE: (17776), (18719) imply:
% 237.95/45.10  | | | | | | | | | | |   (18724)   ~ (e3 = e1)
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | REDUCE: (42), (18719) imply:
% 237.95/45.10  | | | | | | | | | | |   (18725)  op(e2, e2) = e1
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | BETA: splitting (67) gives:
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | Case 1:
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | |   (18726)   ~ (all_24_2 = e2)
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | REDUCE: (301), (18726) imply:
% 237.95/45.10  | | | | | | | | | | | |   (18727)   ~ (all_10_2 = e2)
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | REF_CLOSE: (45), (139), (141), (157), (158), (159), (160),
% 237.95/45.10  | | | | | | | | | | | |            (163), (165), (167), (204), (213), (241), (290),
% 237.95/45.10  | | | | | | | | | | | |            (292), (355), (357), (359), (17762), (17764),
% 237.95/45.10  | | | | | | | | | | | |            (17777), (17781), (18720), (18721), (18723),
% 237.95/45.10  | | | | | | | | | | | |            (18727), (function-axioms) are inconsistent by
% 237.95/45.10  | | | | | | | | | | | |            sub-proof #180.
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | |   (18728)  all_24_2 = e2
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | COMBINE_EQS: (301), (18728) imply:
% 237.95/45.10  | | | | | | | | | | | |   (18729)  all_10_2 = e2
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | SIMP: (18729) implies:
% 237.95/45.10  | | | | | | | | | | | |   (18730)  all_10_2 = e2
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | REDUCE: (355), (18730) imply:
% 237.95/45.10  | | | | | | | | | | | |   (18731)   ~ (all_52_1 = e2)
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | REDUCE: (361), (18730) imply:
% 237.95/45.10  | | | | | | | | | | | |   (18732)   ~ (all_52_4 = e2)
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | REDUCE: (45), (18730) imply:
% 237.95/45.10  | | | | | | | | | | | |   (18733)  op(e3, e3) = e2
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (112), (120),
% 237.95/45.10  | | | | | | | | | | | |            (128), (136), (158), (159), (160), (162), (164),
% 237.95/45.10  | | | | | | | | | | | |            (165), (167), (168), (169), (170), (194), (213),
% 237.95/45.10  | | | | | | | | | | | |            (223), (226), (233), (237), (239), (241), (242),
% 237.95/45.10  | | | | | | | | | | | |            (243), (245), (266), (297), (380), (381), (17762),
% 237.95/45.10  | | | | | | | | | | | |            (17763), (17764), (17767), (17775), (17783),
% 237.95/45.10  | | | | | | | | | | | |            (18722), (18725), (18731), (18732), (18733),
% 237.95/45.10  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.10  | | | | | | | | | | | |            #236.
% 237.95/45.10  | | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | End of split
% 237.95/45.10  | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | Case 2:
% 237.95/45.10  | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | |   (18734)  all_18_2 = e0
% 237.95/45.10  | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | COMBINE_EQS: (339), (18734) imply:
% 237.95/45.10  | | | | | | | | | |   (18735)  all_6_2 = e0
% 237.95/45.10  | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | COMBINE_EQS: (266), (18735) imply:
% 237.95/45.10  | | | | | | | | | |   (18736)  all_56_21 = e0
% 237.95/45.10  | | | | | | | | | | 
% 237.95/45.10  | | | | | | | | | | REDUCE: (367), (18735) imply:
% 237.95/45.10  | | | | | | | | | |   (18737)   ~ (all_52_2 = e0)
% 237.95/45.10  | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | REDUCE: (378), (18735) imply:
% 237.95/45.11  | | | | | | | | | |   (18738)   ~ (all_52_6 = e0)
% 237.95/45.11  | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | REDUCE: (380), (18735) imply:
% 237.95/45.11  | | | | | | | | | |   (18739)   ~ (all_52_8 = e0)
% 237.95/45.11  | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | REDUCE: (385), (18735) imply:
% 237.95/45.11  | | | | | | | | | |   (18740)   ~ (all_52_14 = e0)
% 237.95/45.11  | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | REDUCE: (17775), (18735) imply:
% 237.95/45.11  | | | | | | | | | |   (18741)   ~ (e3 = e0)
% 237.95/45.11  | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | REDUCE: (39), (18735) imply:
% 237.95/45.11  | | | | | | | | | |   (18742)  op(e1, e1) = e0
% 237.95/45.11  | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | BETA: splitting (64) gives:
% 237.95/45.11  | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | |   (18743)   ~ (all_22_2 = e1)
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | REDUCE: (326), (18743) imply:
% 237.95/45.11  | | | | | | | | | | |   (18744)   ~ (all_8_2 = e1)
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | BETA: splitting (199) gives:
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | |   (18745)  all_54_5 = e3
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | COMBINE_EQS: (275), (18745) imply:
% 237.95/45.11  | | | | | | | | | | | |   (18746)  all_8_2 = e3
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | REDUCE: (17776), (18746) imply:
% 237.95/45.11  | | | | | | | | | | | |   (18747)  $false
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | CLOSE: (18747) is inconsistent.
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | |   (18748)   ~ (all_54_5 = e3)
% 237.95/45.11  | | | | | | | | | | | |   (18749)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | BETA: splitting (18749) gives:
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | |   (18750)  all_54_5 = e2
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | COMBINE_EQS: (275), (18750) imply:
% 237.95/45.11  | | | | | | | | | | | | |   (18751)  all_8_2 = e2
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | REDUCE: (371), (18751) imply:
% 237.95/45.11  | | | | | | | | | | | | |   (18752)   ~ (all_52_6 = e2)
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | REDUCE: (375), (18751) imply:
% 237.95/45.11  | | | | | | | | | | | | |   (18753)   ~ (all_52_9 = e2)
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | REDUCE: (17776), (18751) imply:
% 237.95/45.11  | | | | | | | | | | | | |   (18754)   ~ (e3 = e2)
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | BETA: splitting (229) gives:
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | |   (18755)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 237.95/45.11  | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 237.95/45.11  | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | BETA: splitting (18755) gives:
% 237.95/45.11  | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | |   (18756)  all_58_4 = e2 & op(e3, e1) = e2
% 237.95/45.11  | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | ALPHA: (18756) implies:
% 237.95/45.11  | | | | | | | | | | | | | | |   (18757)  all_58_4 = e2
% 237.95/45.11  | | | | | | | | | | | | | | |   (18758)  op(e3, e1) = e2
% 237.95/45.11  | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | |   (18759)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 237.95/45.11  | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 237.95/45.11  | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | BETA: splitting (18759) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | |   (18760)  all_58_6 = e2 & op(e1, e3) = e2
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | ALPHA: (18760) implies:
% 237.95/45.11  | | | | | | | | | | | | | | | | |   (18761)  op(e1, e3) = e2
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 237.95/45.11  | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (18761) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | | |   (18762)  all_52_2 = e2
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 237.95/45.11  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (18758) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | | |   (18763)  all_52_8 = e2
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | REDUCE: (134), (18763) imply:
% 237.95/45.11  | | | | | | | | | | | | | | | | |   (18764)   ~ (all_52_4 = e2)
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | REDUCE: (123), (18763) imply:
% 237.95/45.11  | | | | | | | | | | | | | | | | |   (18765)   ~ (all_52_9 = e2)
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | REDUCE: (363), (18763) imply:
% 237.95/45.11  | | | | | | | | | | | | | | | | |   (18766)   ~ (all_10_2 = e2)
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | SIMP: (18766) implies:
% 237.95/45.11  | | | | | | | | | | | | | | | | |   (18767)   ~ (all_10_2 = e2)
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | |   (18768)  all_54_0 = e3
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (18768) imply:
% 237.95/45.11  | | | | | | | | | | | | | | | | | |   (18769)  all_10_2 = e3
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | SIMP: (18769) implies:
% 237.95/45.11  | | | | | | | | | | | | | | | | | |   (18770)  all_10_2 = e3
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (18770) imply:
% 237.95/45.11  | | | | | | | | | | | | | | | | | |   (18771)  all_56_1 = e3
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | REDUCE: (355), (18770) imply:
% 237.95/45.11  | | | | | | | | | | | | | | | | | |   (18772)   ~ (all_52_1 = e3)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | REDUCE: (359), (18770) imply:
% 237.95/45.11  | | | | | | | | | | | | | | | | | |   (18773)   ~ (all_52_3 = e3)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |   (18774)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (18774) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |   (18775)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              = e3)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (18775) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |   (18776)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |            e3
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (18776) implies:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |   (18777)  op(e2, e3) = e3
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (18772), (18777), (function-axioms) are
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |   (18778)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18778) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |   (18779)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |            e2
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18779) implies:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |   (18780)  op(e3, e2) = e2
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (18764), (18780), (function-axioms) are
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #254.
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |   (18781)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18781) implies:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |   (18782)  op(e3, e1) = e3
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3, e1,
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (18758), (18782) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |   (18783)  e3 = e2
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (18783) imply:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | |   (18784)  $false
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18784) is inconsistent.
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |   (18785)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (18785) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |   (18786)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (18786) implies:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |   (18787)  op(e1, e3) = e1
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18761), (18787), (function-axioms) are
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |   (18788)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (18771), (18773), (18788),
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | |            #2271.
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |   (18789)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.95/45.11  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (18789) gives:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |   (18790)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              = e2)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (17762), (17764), (18753), (18790),
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |            #184.
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |   (18791)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (17762), (18736), (18740), (18791),
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | |            #179.
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | |   (18792)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (17777), (17781), (18767), (18792) are
% 237.95/45.11  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 237.95/45.11  | | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | |   (18793)  all_58_7 = e2 & op(e1, e2) = e2
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | ALPHA: (18793) implies:
% 237.95/45.11  | | | | | | | | | | | | | | | | |   (18794)  op(e1, e2) = e2
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (18752), (18794), (function-axioms) are
% 237.95/45.11  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #249.
% 237.95/45.11  | | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | |   (18795)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 237.95/45.11  | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 237.95/45.11  | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (165), (227),
% 237.95/45.11  | | | | | | | | | | | | | | | |            (228), (230), (17768), (18757), (18795),
% 237.95/45.11  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.11  | | | | | | | | | | | | | | | |            #248.
% 237.95/45.11  | | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | |   (18796)  all_58_5 = e2 & op(e2, e1) = e2
% 237.95/45.11  | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | ALPHA: (18796) implies:
% 237.95/45.11  | | | | | | | | | | | | | | |   (18797)  op(e2, e1) = e2
% 237.95/45.11  | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | | REF_CLOSE: (165), (18753), (18797), (function-axioms) are
% 237.95/45.11  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 237.95/45.11  | | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | |   (18798)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 237.95/45.11  | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 237.95/45.11  | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (17765), (18742), (18798),
% 237.95/45.11  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.11  | | | | | | | | | | | | | |            #178.
% 237.95/45.11  | | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | |   (18799)  all_54_5 = e1 | all_54_5 = e0
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | REF_CLOSE: (275), (17779), (18744), (18799) are inconsistent
% 237.95/45.11  | | | | | | | | | | | | |            by sub-proof #2300.
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | End of split
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | Case 2:
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | |   (18800)  all_22_2 = e1
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | COMBINE_EQS: (326), (18800) imply:
% 237.95/45.11  | | | | | | | | | | |   (18801)  all_8_2 = e1
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | SIMP: (18801) implies:
% 237.95/45.11  | | | | | | | | | | |   (18802)  all_8_2 = e1
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | COMBINE_EQS: (353), (18802) imply:
% 237.95/45.11  | | | | | | | | | | |   (18803)  all_56_11 = e1
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | REDUCE: (366), (18802) imply:
% 237.95/45.11  | | | | | | | | | | |   (18804)   ~ (all_52_1 = e1)
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | REDUCE: (369), (18802) imply:
% 237.95/45.11  | | | | | | | | | | |   (18805)   ~ (all_52_4 = e1)
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | REDUCE: (375), (18802) imply:
% 237.95/45.11  | | | | | | | | | | |   (18806)   ~ (all_52_9 = e1)
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | REDUCE: (377), (18802) imply:
% 237.95/45.11  | | | | | | | | | | |   (18807)   ~ (all_52_13 = e1)
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | REDUCE: (17776), (18802) imply:
% 237.95/45.11  | | | | | | | | | | |   (18808)   ~ (e3 = e1)
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | REDUCE: (42), (18802) imply:
% 237.95/45.11  | | | | | | | | | | |   (18809)  op(e2, e2) = e1
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | BETA: splitting (67) gives:
% 237.95/45.11  | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | |   (18810)   ~ (all_24_2 = e2)
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | REDUCE: (301), (18810) imply:
% 237.95/45.11  | | | | | | | | | | | |   (18811)   ~ (all_10_2 = e2)
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | BETA: splitting (204) gives:
% 237.95/45.11  | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | |   (18812)  all_54_0 = e3
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | COMBINE_EQS: (292), (18812) imply:
% 237.95/45.11  | | | | | | | | | | | | |   (18813)  all_10_2 = e3
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | COMBINE_EQS: (290), (18813) imply:
% 237.95/45.11  | | | | | | | | | | | | |   (18814)  all_56_1 = e3
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | REDUCE: (355), (18813) imply:
% 237.95/45.11  | | | | | | | | | | | | |   (18815)   ~ (all_52_1 = e3)
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | REDUCE: (357), (18813) imply:
% 237.95/45.11  | | | | | | | | | | | | |   (18816)   ~ (all_52_2 = e3)
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | REDUCE: (359), (18813) imply:
% 237.95/45.11  | | | | | | | | | | | | |   (18817)   ~ (all_52_3 = e3)
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.95/45.11  | | | | | | | | | | | | | 
% 237.95/45.11  | | | | | | | | | | | | | Case 1:
% 237.95/45.11  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | |   (18818)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.12  | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.12  | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.12  | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.12  | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.12  | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.12  | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.12  | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.12  | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.12  | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.95/45.12  | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.95/45.12  | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.12  | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | BETA: splitting (18818) gives:
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | |   (18819)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.12  | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.12  | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.12  | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.12  | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.12  | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.12  | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.12  | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.12  | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.12  | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.12  | | | | | | | | | | | | | | |              = e3)
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (18814), (18815), (18816), (18819),
% 237.95/45.12  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.12  | | | | | | | | | | | | | | |            #2299.
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | |   (18820)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.95/45.12  | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.95/45.12  | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.95/45.12  | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.95/45.12  | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.12  | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.12  | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.95/45.12  | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.95/45.12  | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.95/45.12  | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.95/45.12  | | | | | | | | | | | | | | |              = e0)
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | REF_CLOSE: (159), (18814), (18817), (18820),
% 237.95/45.12  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.12  | | | | | | | | | | | | | | |            #2270.
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | |   (18821)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.12  | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.12  | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.12  | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.12  | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.12  | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.12  | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.12  | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.12  | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.95/45.12  | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.95/45.12  | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.95/45.12  | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.95/45.12  | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.95/45.12  | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | BETA: splitting (18821) gives:
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | |   (18822)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.12  | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.12  | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.12  | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.12  | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.12  | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.12  | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.12  | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.12  | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.12  | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.12  | | | | | | | | | | | | | | |              = e2)
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (17764), (18803), (18806), (18822),
% 237.95/45.12  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.12  | | | | | | | | | | | | | | |            #181.
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | |   (18823)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.95/45.12  | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.12  | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.95/45.12  | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.95/45.12  | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.12  | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.12  | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.95/45.12  | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.12  | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.12  | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.95/45.12  | | | | | | | | | | | | | | |              = e0)
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | REF_CLOSE: (160), (17762), (18736), (18740), (18823),
% 237.95/45.12  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.12  | | | | | | | | | | | | | | |            #179.
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | |   (18824)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 237.95/45.12  | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | REF_CLOSE: (292), (17777), (17781), (18811), (18824) are
% 237.95/45.12  | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 237.95/45.12  | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | |   (18825)  all_24_2 = e2
% 237.95/45.12  | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | COMBINE_EQS: (301), (18825) imply:
% 237.95/45.12  | | | | | | | | | | | |   (18826)  all_10_2 = e2
% 237.95/45.12  | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | COMBINE_EQS: (290), (18826) imply:
% 237.95/45.12  | | | | | | | | | | | |   (18827)  all_56_1 = e2
% 237.95/45.12  | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | REDUCE: (355), (18826) imply:
% 237.95/45.12  | | | | | | | | | | | |   (18828)   ~ (all_52_1 = e2)
% 237.95/45.12  | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | REDUCE: (357), (18826) imply:
% 237.95/45.12  | | | | | | | | | | | |   (18829)   ~ (all_52_2 = e2)
% 237.95/45.12  | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | REDUCE: (361), (18826) imply:
% 237.95/45.12  | | | | | | | | | | | |   (18830)   ~ (all_52_4 = e2)
% 237.95/45.12  | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | REDUCE: (363), (18826) imply:
% 237.95/45.12  | | | | | | | | | | | |   (18831)   ~ (all_52_8 = e2)
% 237.95/45.12  | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | REDUCE: (45), (18826) imply:
% 237.95/45.12  | | | | | | | | | | | |   (18832)  op(e3, e3) = e2
% 237.95/45.12  | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | BETA: splitting (229) gives:
% 237.95/45.12  | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | |   (18833)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 237.95/45.12  | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 237.95/45.12  | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | BETA: splitting (18833) gives:
% 237.95/45.12  | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | |   (18834)  all_58_4 = e2 & op(e3, e1) = e2
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | ALPHA: (18834) implies:
% 237.95/45.12  | | | | | | | | | | | | | |   (18835)  all_58_4 = e2
% 237.95/45.12  | | | | | | | | | | | | | |   (18836)  op(e3, e1) = e2
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | |   (18837)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 237.95/45.12  | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | REF_CLOSE: (6), (165), (18806), (18835), (18837),
% 237.95/45.12  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.12  | | | | | | | | | | | | | | |            #407.
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | |   (18838)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 237.95/45.12  | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | BETA: splitting (18838) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | |   (18839)  all_58_8 = e1 & op(e1, e1) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | ALPHA: (18839) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | |   (18840)  op(e1, e1) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (18737), (18738),
% 237.95/45.12  | | | | | | | | | | | | | | | |            (18740), (18840), (function-axioms) are
% 237.95/45.12  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2020.
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | |   (18841)  all_58_14 = e1 & op(e0, e1) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | ALPHA: (18841) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | |   (18842)  all_58_14 = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (164), (167), (230), (233),
% 237.95/45.12  | | | | | | | | | | | | | | | |            (17767), (18742), (18809), (18828), (18836),
% 237.95/45.12  | | | | | | | | | | | | | | | |            (18842), (function-axioms) are inconsistent by
% 237.95/45.12  | | | | | | | | | | | | | | | |            sub-proof #176.
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | |   (18843)  all_58_5 = e2 & op(e2, e1) = e2
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | ALPHA: (18843) implies:
% 237.95/45.12  | | | | | | | | | | | | | |   (18844)  op(e2, e1) = e2
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 237.95/45.12  | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | |   (18845)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 237.95/45.12  | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | BETA: splitting (18845) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | |   (18846)  all_58_6 = e2 & op(e1, e3) = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | ALPHA: (18846) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | |   (18847)  all_58_6 = e2
% 237.95/45.12  | | | | | | | | | | | | | | | |   (18848)  op(e1, e3) = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | |   (18849)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (18809), (18830), (18849),
% 237.95/45.12  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.12  | | | | | | | | | | | | | | | | |            #246.
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | |   (18850)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 237.95/45.12  | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | BETA: splitting (18850) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | |   (18851)  all_58_7 = e2 & op(e1, e2) = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | ALPHA: (18851) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | | | |   (18852)  all_58_7 = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | | |   (18853)  op(e1, e2) = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | |   (18854)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (18854) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |   (18855)  all_58_6 = e1 & op(e1, e3) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | ALPHA: (18855) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |   (18856)  op(e1, e3) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18848), (18856), (function-axioms) are
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |   (18857)  all_58_7 = e1 & op(e1, e2) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18852), (18857) are inconsistent by
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |            sub-proof #2224.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | |   (18858)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 237.95/45.12  | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (18858) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |   (18859)  all_58_8 = e1 & op(e1, e1) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | ALPHA: (18859) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |   (18860)  op(e1, e1) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (18737), (18738),
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |            (18740), (18860), (function-axioms) are
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2020.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |   (18861)  all_58_11 = e1 & op(e1, e0) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | ALPHA: (18861) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |   (18862)  op(e1, e0) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | |   (18863)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18847), (18853), (18863), (function-axioms)
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #239.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | |   (18864)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (18742), (18862), (18864),
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | |            #175.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | |   (18865)  all_58_13 = e2 & op(e0, e2) = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | ALPHA: (18865) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | | | |   (18866)  op(e0, e2) = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (18866), (function-axioms) are
% 237.95/45.12  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | End of split
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | |   (18867)  all_58_7 = e2 & op(e1, e2) = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | ALPHA: (18867) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | |   (18868)  all_58_7 = e2
% 237.95/45.12  | | | | | | | | | | | | | | | |   (18869)  op(e1, e2) = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | |   (18870)  all_54_11 = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (18870) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | |   (18871)  all_52_14 = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | SIMP: (18871) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | | |   (18872)  all_52_14 = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | REDUCE: (141), (18872) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | |   (18873)   ~ (all_52_2 = e3)
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | REDUCE: (112), (18872) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | |   (18874)   ~ (all_52_12 = e3)
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | REDUCE: (110), (18872) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | |   (18875)   ~ (all_52_13 = e3)
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | REDUCE: (160), (18872) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | |   (18876)  op(e1, e0) = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | |   (18877)  all_54_7 = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (18875), (18877) are inconsistent by
% 237.95/45.12  | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | |   (18878)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | BETA: splitting (18878) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | |   (18879)  all_54_7 = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (17767), (18879) are inconsistent by
% 237.95/45.12  | | | | | | | | | | | | | | | | | | |            sub-proof #1997.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | |   (18880)   ~ (all_54_7 = e2)
% 237.95/45.12  | | | | | | | | | | | | | | | | | | |   (18881)  all_54_7 = e1 | all_54_7 = e0
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |   (18882)  all_54_8 = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (18882) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |   (18883)  all_52_2 = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | REDUCE: (18873), (18883) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |   (18884)  $false
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | CLOSE: (18884) is inconsistent.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | |   (18885)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | |   (18886)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18886) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | |   (18887)  all_58_6 = e1 & op(e1, e3) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18887) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | |   (18888)  op(e1, e3) = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18881) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | |   (18889)  all_54_7 = e1
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (18807), (18889) are inconsistent by
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | |   (18890)  all_54_7 = e0
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (18890) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | |   (18891)  all_52_13 = e0
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18891) implies:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | |   (18892)  all_52_13 = e0
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (18892) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | |   (18893)   ~ (all_52_1 = e0)
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (18892) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | |   (18894)   ~ (all_52_12 = e0)
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17767), (18892) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | |   (18895)   ~ (e2 = e0)
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18807), (18892) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | |   (18896)   ~ (e1 = e0)
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (18892) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | |   (18897)  op(e2, e0) = e0
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | |   (18898)  all_54_4 = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (18898) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | |   (18899)  all_52_1 = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (18899) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | |   (18900)  op(e2, e3) = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (18901)  all_54_3 = e3
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (18874), (18901) are inconsistent by
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (18902)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18902) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18903)  all_54_3 = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (17766), (18903) are inconsistent by
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2290.
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18904)  all_54_3 = e1 | all_54_3 = e0
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18885) gives:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18905)  all_54_8 = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (18905) imply:
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18906)  all_52_2 = e2
% 237.95/45.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18829), (18906) imply:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18907)  $false
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18907) is inconsistent.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18908)  all_54_8 = e1 | all_54_8 = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18909)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18909) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18910)  all_58_0 = e0 & op(e3, e3) = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18910) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18911)  op(e3, e3) = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (18832), (18911), (function-axioms) are
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18912)  all_58_1 = e0 & op(e3, e2) = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18912) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18913)  op(e3, e2) = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18914)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18914) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18915)  all_58_1 = e3 & op(e3, e2) = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18915) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18916)  op(e3, e2) = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18913), (18916), (function-axioms) are
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2099.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18917)  all_58_3 = e3 & op(e2, e2) = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18917) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18918)  all_58_3 = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (164), (165), (167), (232), (18804),
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18806), (18897), (18918), (function-axioms) are
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1777.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18919)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18919) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18920)  all_58_7 = e3 & op(e1, e2) = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18920) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18921)  op(e1, e2) = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18869), (18921), (function-axioms) are
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2207.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18922)  all_58_13 = e3 & op(e0, e2) = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18922) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18923)  op(e0, e2) = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18904) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18924)  all_54_3 = e1
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (18924) imply:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18925)  all_52_12 = e1
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18925) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18926)  all_52_12 = e1
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (18926) imply:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18927)   ~ (all_52_8 = e1)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18928)  all_54_2 = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (18928) imply:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18929)  all_52_8 = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18929) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18930)  all_52_8 = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (18930) imply:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18931)   ~ (all_52_4 = e3)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18932)  all_54_1 = e3
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (18931), (18932) are inconsistent by
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18933)   ~ (all_54_1 = e3)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18934)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18934) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18935)  all_54_1 = e2
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (18830), (18935) are inconsistent by
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1928.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18936)   ~ (all_54_1 = e2)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18937)  all_54_1 = e1 | all_54_1 = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18937) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18938)  all_54_1 = e1
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (18805), (18938) are inconsistent by
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2051.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18939)  all_54_1 = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (18939) imply:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18940)  all_52_4 = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18940) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18941)  all_52_4 = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (18941) imply:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18942)   ~ (all_52_7 = e0)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18942) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18943)   ~ (all_52_7 = e0)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18944)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (18827), (18900), (18913), (18944),
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1924.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18945)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18945) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18946)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18946) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18947)  op(e1, e3) = all_56_5
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18948)  op(e1, all_56_5) = e1
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (268), (18737), (18742), (18908), (18947),
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18948), (function-axioms) are inconsistent by
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2005.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18949)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18949) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18950)  op(e0, e3) = all_56_7
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18951)  op(e0, all_56_7) = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18952)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18952) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18953)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (18888), (18913), (18953),
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1925.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18954)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (169), (18894), (18927), (18950),
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18951), (18954), (function-axioms) are
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #174.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18955)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18955) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18956)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18956) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18957)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18957) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18958)   ~ (all_56_11 = e1)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18803), (18958) imply:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18959)  $false
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18959) is inconsistent.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18960)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (18806), (18923), (18960),
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1108.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18961)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18961) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18962)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18962) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18963)  op(e0, e2) = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (18943), (18963), (function-axioms) are
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2252.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18964)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18964) gives:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18965)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18965) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18966)  op(e1, e0) = e1
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (160), (280), (18894), (18904), (18966),
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1331.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18967)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18967) implies:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18968)  op(e1, e0) = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (18740), (18968), (function-axioms) are
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2323.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18969)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (18739), (18831), (18927), (18969) are
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1335.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18970)  all_54_3 = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (18894), (18970) are inconsistent by
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2288.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18971)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (18739), (18894), (18971),
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1334.
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | |   (18972)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (165), (279), (18804), (18844), (18893),
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | |            (18972), (function-axioms) are inconsistent by
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #173.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | |   (18973)  all_58_7 = e1 & op(e1, e2) = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18868), (18973) are inconsistent by
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2224.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | |   (18974)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (160), (162), (163), (223), (18737),
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | |            (18738), (18740), (18876), (18974),
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | |            #172.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | |   (18975)   ~ (all_54_11 = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | |   (18976)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 237.95/45.14  | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | REDUCE: (258), (18975) imply:
% 237.95/45.14  | | | | | | | | | | | | | | | | |   (18977)   ~ (all_52_14 = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | BETA: splitting (18976) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | |   (18978)  all_54_11 = e2
% 237.95/45.14  | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (17768), (18978) are inconsistent by
% 237.95/45.14  | | | | | | | | | | | | | | | | | |            sub-proof #2177.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | |   (18979)   ~ (all_54_11 = e2)
% 237.95/45.14  | | | | | | | | | | | | | | | | | |   (18980)  all_54_11 = e1 | all_54_11 = e0
% 237.95/45.14  | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | BETA: splitting (18980) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | |   (18981)  all_54_11 = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (18981) imply:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | |   (18982)  all_52_14 = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | REDUCE: (141), (18982) imply:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | |   (18983)   ~ (all_52_2 = e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | REDUCE: (112), (18982) imply:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | |   (18984)   ~ (all_52_12 = e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | REDUCE: (17768), (18982) imply:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | |   (18985)   ~ (e2 = e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | REDUCE: (160), (18982) imply:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | |   (18986)  op(e1, e0) = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | |   (18987)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (18805), (18832), (18987),
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | |            #1340.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | |   (18988)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | BETA: splitting (18988) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | |   (18989)  all_58_4 = e1 & op(e3, e1) = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | ALPHA: (18989) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | |   (18990)  op(e3, e1) = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | |   (18991)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (18804), (18832), (18991),
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | |            #1354.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | |   (18992)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18992) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | |   (18993)  all_58_6 = e1 & op(e1, e3) = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18993) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | |   (18994)  op(e1, e3) = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (18983), (18994), (function-axioms) are
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | |   (18995)  all_58_12 = e1 & op(e0, e3) = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18995) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | |   (18996)  all_58_12 = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | |   (18997)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (18844), (18990), (18997),
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | |            #171.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | |   (18998)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18998) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (18999)  all_58_8 = e3 & op(e1, e1) = e3
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18742), (18999), (function-axioms) are
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (19000)  all_58_14 = e3 & op(e0, e1) = e3
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19000) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (19001)  op(e0, e1) = e3
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19002)  all_54_8 = e3
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (19002) imply:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19003)  all_52_2 = e3
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (19003) imply:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19004)   ~ (all_52_1 = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (19003) imply:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19005)   ~ (all_52_3 = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19005) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19006)   ~ (all_52_3 = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19007)  all_54_4 = e3
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (19004), (19007) are inconsistent by
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19008)   ~ (all_54_4 = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19009)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19010)  all_58_15 = e0 & op(e0, e0) = e0
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19010) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19011)  op(e0, e0) = e0
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (19011), (function-axioms) are
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19012)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19012) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19013)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19014)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19014) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19015)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19015) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19016)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19016) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19017)  op(e2, e3) = e3
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (19004), (19017), (function-axioms) are
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19018)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19018) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19019)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19019) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19020)  op(e3, e2) = e2
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (18830), (19020), (function-axioms) are
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #254.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19021)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19021) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19022)  op(e3, e1) = e3
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18990), (19022), (function-axioms) are
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1823.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19023)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19023) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19024)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19024) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19025)  op(e1, e3) = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (18983), (19025), (function-axioms) are
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1948.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19026)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (148), (159), (279), (18804), (18828), (19006),
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19009), (19026), (function-axioms) are
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #169.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19027)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19027) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19028)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19028) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19029)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19029) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19030)   ~ (all_56_11 = e1)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18803), (19030) imply:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19031)  $false
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19031) is inconsistent.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19032)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19032) gives:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19033)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19033) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19034)  op(e2, e1) = e1
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (18806), (19034), (function-axioms) are
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19035)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19035) implies:
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19036)  op(e0, e2) = e2
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (18996), (19001), (19013), (19036),
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #896.
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19037)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17762), (18736), (18986), (19037),
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #168.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19038)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (18737), (18829), (18983), (19038) are
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1949.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | |   (19039)  all_58_9 = e1 & op(e3, e0) = e1
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (18984), (19039), (function-axioms) are
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | |   (19040)  all_54_11 = e0
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (19040) imply:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | |   (19041)  all_52_14 = e0
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | REDUCE: (18740), (19041) imply:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | |   (19042)  $false
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | CLOSE: (19042) is inconsistent.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | |   (19043)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 237.95/45.15  | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 237.95/45.15  | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (17768), (18742), (19043),
% 237.95/45.15  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.15  | | | | | | | | | | | | | | |            #167.
% 237.95/45.15  | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | |   (19044)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 237.95/45.15  | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 237.95/45.15  | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | REF_CLOSE: (5), (157), (17765), (18742), (19044),
% 237.95/45.15  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.15  | | | | | | | | | | | | |            #178.
% 237.95/45.15  | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | |   (19045)  all_16_2 = e0
% 237.95/45.15  | | | | | | | | |   (19046)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 237.95/45.15  | | | | | | | | |              op(e3, e0) = all_16_1 & $i(all_16_0) &
% 237.95/45.15  | | | | | | | | |              $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0)
% 237.95/45.15  | | | | | | | | |              = all_16_1 & $i(all_16_1))
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | COMBINE_EQS: (342), (19045) imply:
% 237.95/45.15  | | | | | | | | |   (19047)  all_10_2 = e0
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | SIMP: (19047) implies:
% 237.95/45.15  | | | | | | | | |   (19048)  all_10_2 = e0
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | COMBINE_EQS: (350), (19048) imply:
% 237.95/45.15  | | | | | | | | |   (19049)  all_50_2 = e0
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | COMBINE_EQS: (290), (19048) imply:
% 237.95/45.15  | | | | | | | | |   (19050)  all_56_1 = e0
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | REDUCE: (355), (19048) imply:
% 237.95/45.15  | | | | | | | | |   (19051)   ~ (all_52_1 = e0)
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | REDUCE: (357), (19048) imply:
% 237.95/45.15  | | | | | | | | |   (19052)   ~ (all_52_2 = e0)
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | REDUCE: (359), (19048) imply:
% 237.95/45.15  | | | | | | | | |   (19053)   ~ (all_52_3 = e0)
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | REDUCE: (361), (19048) imply:
% 237.95/45.15  | | | | | | | | |   (19054)   ~ (all_52_4 = e0)
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | REDUCE: (363), (19048) imply:
% 237.95/45.15  | | | | | | | | |   (19055)   ~ (all_52_8 = e0)
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | REDUCE: (365), (19048) imply:
% 237.95/45.15  | | | | | | | | |   (19056)   ~ (all_52_12 = e0)
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | REDUCE: (17777), (19048) imply:
% 237.95/45.15  | | | | | | | | |   (19057)   ~ (e1 = e0)
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | REDUCE: (45), (19048) imply:
% 237.95/45.15  | | | | | | | | |   (19058)  op(e3, e3) = e0
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | BETA: splitting (58) gives:
% 237.95/45.15  | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | |   (19059)   ~ (all_18_2 = e0)
% 237.95/45.15  | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | REDUCE: (339), (19059) imply:
% 237.95/45.15  | | | | | | | | | |   (19060)   ~ (all_6_2 = e0)
% 237.95/45.15  | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | BETA: splitting (64) gives:
% 237.95/45.15  | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | |   (19061)   ~ (all_22_2 = e1)
% 237.95/45.15  | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | REDUCE: (326), (19061) imply:
% 237.95/45.15  | | | | | | | | | | |   (19062)   ~ (all_8_2 = e1)
% 237.95/45.15  | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | BETA: splitting (199) gives:
% 237.95/45.15  | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | |   (19063)  all_54_5 = e3
% 237.95/45.15  | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | COMBINE_EQS: (275), (19063) imply:
% 237.95/45.15  | | | | | | | | | | | |   (19064)  all_8_2 = e3
% 237.95/45.15  | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | REDUCE: (17776), (19064) imply:
% 237.95/45.15  | | | | | | | | | | | |   (19065)  $false
% 237.95/45.15  | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | CLOSE: (19065) is inconsistent.
% 237.95/45.15  | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | |   (19066)   ~ (all_54_5 = e3)
% 237.95/45.15  | | | | | | | | | | | |   (19067)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 237.95/45.15  | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | BETA: splitting (19067) gives:
% 237.95/45.15  | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | |   (19068)  all_54_5 = e2
% 237.95/45.15  | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | COMBINE_EQS: (275), (19068) imply:
% 237.95/45.15  | | | | | | | | | | | | |   (19069)  all_8_2 = e2
% 237.95/45.15  | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | REDUCE: (366), (19069) imply:
% 237.95/45.15  | | | | | | | | | | | | |   (19070)   ~ (all_52_1 = e2)
% 237.95/45.15  | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | REDUCE: (369), (19069) imply:
% 237.95/45.15  | | | | | | | | | | | | |   (19071)   ~ (all_52_4 = e2)
% 237.95/45.15  | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | REDUCE: (17776), (19069) imply:
% 237.95/45.15  | | | | | | | | | | | | |   (19072)   ~ (e3 = e2)
% 237.95/45.15  | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | BETA: splitting (243) gives:
% 237.95/45.15  | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | |   (19073)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 237.95/45.15  | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 237.95/45.15  | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (19058), (19070), (19073),
% 237.95/45.15  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.15  | | | | | | | | | | | | | |            #1607.
% 237.95/45.15  | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | |   (19074)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 237.95/45.15  | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 237.95/45.15  | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | BETA: splitting (19074) gives:
% 237.95/45.15  | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | |   (19075)  all_58_6 = e2 & op(e1, e3) = e2
% 237.95/45.15  | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | ALPHA: (19075) implies:
% 237.95/45.15  | | | | | | | | | | | | | | |   (19076)  all_58_6 = e2
% 237.95/45.15  | | | | | | | | | | | | | | |   (19077)  op(e1, e3) = e2
% 237.95/45.15  | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | |   (19078)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 237.95/45.15  | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 237.95/45.15  | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | BETA: splitting (19078) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | |   (19079)  all_58_0 = e2 & op(e3, e3) = e2
% 237.95/45.15  | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | ALPHA: (19079) implies:
% 237.95/45.15  | | | | | | | | | | | | | | | | |   (19080)  op(e3, e3) = e2
% 237.95/45.15  | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | |   (19081)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 237.95/45.15  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 237.95/45.15  | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | BETA: splitting (19081) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | |   (19082)  all_58_0 = e0 & op(e3, e3) = e0
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19058), (19080), (function-axioms) are
% 237.95/45.15  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | |   (19083)  all_58_2 = e0 & op(e2, e3) = e0
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | ALPHA: (19083) implies:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | |   (19084)  all_58_2 = e0
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | |   (19085)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (19080), (19084), (19085),
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | |            #796.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | |   (19086)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | BETA: splitting (19086) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | |   (19087)  all_58_6 = e1 & op(e1, e3) = e1
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19087) implies:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | |   (19088)  op(e1, e3) = e1
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (19077), (19088), (function-axioms) are
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | |   (19089)  all_58_12 = e1 & op(e0, e3) = e1
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19089) implies:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | |   (19090)  all_58_12 = e1
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | |   (19091)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19091) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | |   (19092)  all_58_0 = e3 & op(e3, e3) = e3
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19092) implies:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | |   (19093)  op(e3, e3) = e3
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19080), (19093), (function-axioms) are
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | |   (19094)  all_58_2 = e3 & op(e2, e3) = e3
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19094) implies:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | |   (19095)  all_58_2 = e3
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (19080), (19081), (19095),
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | |            #1927.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | |   (19096)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19096) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (19097)  all_58_6 = e0 & op(e1, e3) = e0
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19097) implies:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (19098)  all_58_6 = e0
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19076), (19098) are inconsistent by
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1982.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (19099)  all_58_12 = e0 & op(e0, e3) = e0
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19099) implies:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (19100)  op(e0, e3) = e0
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (19053), (19100), (function-axioms) are
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | |   (19101)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19101) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | |   (19102)  all_58_6 = e3 & op(e1, e3) = e3
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19076), (19102) are inconsistent by
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1838.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | |   (19103)  all_58_12 = e3 & op(e0, e3) = e3
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19103) implies:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | |   (19104)  all_58_12 = e3
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19090), (19104) are inconsistent by
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1542.
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | End of split
% 237.95/45.15  | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | Case 2:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | |   (19105)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 237.95/45.15  | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 237.95/45.15  | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | BETA: splitting (19105) gives:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | 
% 237.95/45.15  | | | | | | | | | | | | | | | | | | Case 1:
% 237.95/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | |   (19106)  all_58_6 = e0 & op(e1, e3) = e0
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19076), (19106) are inconsistent by
% 238.15/45.15  | | | | | | | | | | | | | | | | | | |            sub-proof #1678.
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | |   (19107)  all_58_12 = e0 & op(e0, e3) = e0
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | ALPHA: (19107) implies:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | |   (19108)  op(e0, e3) = e0
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (19053), (19108), (function-axioms) are
% 238.15/45.15  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.15  | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | End of split
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | |   (19109)  all_58_1 = e2 & op(e3, e2) = e2
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | ALPHA: (19109) implies:
% 238.15/45.15  | | | | | | | | | | | | | | | | |   (19110)  op(e3, e2) = e2
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (19071), (19110), (function-axioms) are
% 238.15/45.15  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #254.
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | End of split
% 238.15/45.15  | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | Case 2:
% 238.15/45.15  | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | |   (19111)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 238.15/45.15  | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 238.15/45.15  | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | BETA: splitting (19111) gives:
% 238.15/45.15  | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | |   (19112)  all_58_4 = e2 & op(e3, e1) = e2
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | ALPHA: (19112) implies:
% 238.15/45.15  | | | | | | | | | | | | | | | | |   (19113)  op(e3, e1) = e2
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 238.15/45.15  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (19113) gives:
% 238.15/45.15  | | | | | | | | | | | | | | | | |   (19114)  all_52_8 = e2
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | REDUCE: (123), (19114) imply:
% 238.15/45.15  | | | | | | | | | | | | | | | | |   (19115)   ~ (all_52_9 = e2)
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | SIMP: (19115) implies:
% 238.15/45.15  | | | | | | | | | | | | | | | | |   (19116)   ~ (all_52_9 = e2)
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | REDUCE: (380), (19114) imply:
% 238.15/45.15  | | | | | | | | | | | | | | | | |   (19117)   ~ (all_6_2 = e2)
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | SIMP: (19117) implies:
% 238.15/45.15  | | | | | | | | | | | | | | | | |   (19118)   ~ (all_6_2 = e2)
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 238.15/45.15  | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | |   (19119)  all_54_10 = e3
% 238.15/45.15  | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (19119) are inconsistent by
% 238.15/45.15  | | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 238.15/45.15  | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | |   (19120)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.15/45.15  | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | BETA: splitting (19120) gives:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | |   (19121)  all_54_10 = e2
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (19118), (19121) are inconsistent by
% 238.15/45.15  | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | |   (19122)  all_54_10 = e1 | all_54_10 = e0
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | BETA: splitting (19122) gives:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | |   (19123)  all_54_10 = e1
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (19123) imply:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | |   (19124)  all_6_2 = e1
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | SIMP: (19124) implies:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | |   (19125)  all_6_2 = e1
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (19125) imply:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | |   (19126)  all_56_21 = e1
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (19125) imply:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | |   (19127)   ~ (all_52_14 = e1)
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |   (19128)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.15  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19128) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |   (19129)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (17762), (19071), (19113), (19129),
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |            #165.
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |   (19130)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19130) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19131)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19131) implies:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19132)  op(e1, e3) = e1
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (297), (367), (19060), (19122), (19132),
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |            #1372.
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19133)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (19050), (19053), (19133),
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |            #1829.
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |   (19134)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19134) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |   (19135)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (297), (381), (17764), (19060),
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |            (19116), (19122), (19135), (function-axioms) are
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1410.
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |   (19136)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (17762), (19126), (19127), (19136),
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |            #251.
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |   (19137)  all_54_10 = e0
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (19060), (19137) are inconsistent by
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | |   (19138)  all_58_9 = e2 & op(e3, e0) = e2
% 238.15/45.16  | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (17766), (19138), (function-axioms) are
% 238.15/45.16  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2318.
% 238.15/45.16  | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | |   (19139)  all_58_12 = e2 & op(e0, e3) = e2
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | REF_CLOSE: (159), (17763), (19139), (function-axioms) are
% 238.15/45.16  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2315.
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | |   (19140)  all_54_5 = e1 | all_54_5 = e0
% 238.15/45.16  | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | REF_CLOSE: (275), (17779), (19062), (19140) are inconsistent
% 238.15/45.16  | | | | | | | | | | | | |            by sub-proof #2300.
% 238.15/45.16  | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | |   (19141)  all_22_2 = e1
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | COMBINE_EQS: (326), (19141) imply:
% 238.15/45.16  | | | | | | | | | | |   (19142)  all_8_2 = e1
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | SIMP: (19142) implies:
% 238.15/45.16  | | | | | | | | | | |   (19143)  all_8_2 = e1
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | COMBINE_EQS: (353), (19143) imply:
% 238.15/45.16  | | | | | | | | | | |   (19144)  all_56_11 = e1
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | REDUCE: (366), (19143) imply:
% 238.15/45.16  | | | | | | | | | | |   (19145)   ~ (all_52_1 = e1)
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | REDUCE: (369), (19143) imply:
% 238.15/45.16  | | | | | | | | | | |   (19146)   ~ (all_52_4 = e1)
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | REDUCE: (373), (19143) imply:
% 238.15/45.16  | | | | | | | | | | |   (19147)   ~ (all_52_7 = e1)
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | REDUCE: (375), (19143) imply:
% 238.15/45.16  | | | | | | | | | | |   (19148)   ~ (all_52_9 = e1)
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | REDUCE: (377), (19143) imply:
% 238.15/45.16  | | | | | | | | | | |   (19149)   ~ (all_52_13 = e1)
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | REDUCE: (17776), (19143) imply:
% 238.15/45.16  | | | | | | | | | | |   (19150)   ~ (e3 = e1)
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | REDUCE: (42), (19143) imply:
% 238.15/45.16  | | | | | | | | | | |   (19151)  op(e2, e2) = e1
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | BETA: splitting (85) gives:
% 238.15/45.16  | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | |   (19152)   ~ (all_36_2 = e2)
% 238.15/45.16  | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | REDUCE: (328), (19152) imply:
% 238.15/45.16  | | | | | | | | | | | |   (19153)   ~ (all_6_2 = e2)
% 238.15/45.16  | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | BETA: splitting (194) gives:
% 238.15/45.16  | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | |   (19154)  all_54_10 = e3
% 238.15/45.16  | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (19154) are inconsistent by
% 238.15/45.16  | | | | | | | | | | | | |            sub-proof #2313.
% 238.15/45.16  | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | |   (19155)   ~ (all_54_10 = e3)
% 238.15/45.16  | | | | | | | | | | | | |   (19156)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.15/45.16  | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | BETA: splitting (19156) gives:
% 238.15/45.16  | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | |   (19157)  all_54_10 = e2
% 238.15/45.16  | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | REF_CLOSE: (297), (19153), (19157) are inconsistent by
% 238.15/45.16  | | | | | | | | | | | | | |            sub-proof #2312.
% 238.15/45.16  | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | |   (19158)   ~ (all_54_10 = e2)
% 238.15/45.16  | | | | | | | | | | | | | |   (19159)  all_54_10 = e1 | all_54_10 = e0
% 238.15/45.16  | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | BETA: splitting (19159) gives:
% 238.15/45.16  | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | |   (19160)  all_54_10 = e1
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | COMBINE_EQS: (297), (19160) imply:
% 238.15/45.16  | | | | | | | | | | | | | | |   (19161)  all_6_2 = e1
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | SIMP: (19161) implies:
% 238.15/45.16  | | | | | | | | | | | | | | |   (19162)  all_6_2 = e1
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | COMBINE_EQS: (266), (19162) imply:
% 238.15/45.16  | | | | | | | | | | | | | | |   (19163)  all_56_21 = e1
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | REDUCE: (378), (19162) imply:
% 238.15/45.16  | | | | | | | | | | | | | | |   (19164)   ~ (all_52_6 = e1)
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | REDUCE: (380), (19162) imply:
% 238.15/45.16  | | | | | | | | | | | | | | |   (19165)   ~ (all_52_8 = e1)
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | REDUCE: (383), (19162) imply:
% 238.15/45.16  | | | | | | | | | | | | | | |   (19166)   ~ (all_52_11 = e1)
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | REDUCE: (385), (19162) imply:
% 238.15/45.16  | | | | | | | | | | | | | | |   (19167)   ~ (all_52_14 = e1)
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | REDUCE: (19153), (19162) imply:
% 238.15/45.16  | | | | | | | | | | | | | | |   (19168)   ~ (e2 = e1)
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | |   (19169)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.15/45.16  | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.15/45.16  | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | BETA: splitting (19169) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | |   (19170)  all_58_9 = e1 & op(e3, e0) = e1
% 238.15/45.16  | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | ALPHA: (19170) implies:
% 238.15/45.16  | | | | | | | | | | | | | | | | |   (19171)  op(e3, e0) = e1
% 238.15/45.16  | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | |   (19172)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | BETA: splitting (19172) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | |   (19173)  all_58_12 = e1 & op(e0, e3) = e1
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | ALPHA: (19173) implies:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | |   (19174)  op(e0, e3) = e1
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |   (19175)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (19175) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |   (19176)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19176) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |   (19177)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |            e3
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19177) implies:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |   (19178)   ~ (all_56_31 = e2)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (19178) imply:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |   (19179)  $false
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19179) is inconsistent.
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |   (19180)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19180) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19181)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |            e2
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19181) implies:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19182)  op(e2, e3) = e2
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19183)  op(e3, e2) = e2
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (19174) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19184)  all_52_3 = e1
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (19182) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19185)  all_52_1 = e2
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (168), (19171) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19186)  all_52_12 = e1
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (19183) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19187)  all_52_4 = e2
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (19185) imply:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19188)   ~ (all_52_2 = e2)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19188) implies:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19189)   ~ (all_52_2 = e2)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (19184) imply:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19190)   ~ (all_52_2 = e1)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (19187) imply:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19191)   ~ (all_52_6 = e2)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19191) implies:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19192)   ~ (all_52_6 = e2)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (19186) imply:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19193)   ~ (all_52_14 = e1)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | |   (19194)  all_54_8 = e3
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (19194) imply:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | |   (19195)  all_52_2 = e3
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19195) implies:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | |   (19196)  all_52_2 = e3
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (19196) imply:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | |   (19197)   ~ (all_52_6 = e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19197) implies:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | |   (19198)   ~ (all_52_6 = e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (19196) imply:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | |   (19199)   ~ (all_52_14 = e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19199) implies:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | |   (19200)   ~ (all_52_14 = e3)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (193), (195), (258), (267), (17768),
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | |            (19164), (19167), (19192), (19198), (19200) are
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #837.
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | |   (19201)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (19052), (19189), (19190), (19201) are
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1949.
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19202)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19202) implies:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19203)   ~ (all_56_21 = e1)
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19163), (19203) imply:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | |   (19204)  $false
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19204) is inconsistent.
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |   (19205)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.15/45.16  | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (169), (19053), (19165), (19171),
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |            (19205), (function-axioms) are inconsistent by
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |            sub-proof #164.
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |   (19206)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (160), (165), (297), (381), (17762),
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |            (17764), (19060), (19159), (19163), (19167),
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |            (19206), (function-axioms) are inconsistent by
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |            sub-proof #241.
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | |   (19207)  all_58_13 = e1 & op(e0, e2) = e1
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (19147), (19207), (function-axioms) are
% 238.15/45.17  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.17  | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | |   (19208)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.15/45.17  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (17773), (19166), (19208),
% 238.15/45.17  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.17  | | | | | | | | | | | | | | | | | |            #163.
% 238.15/45.17  | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | End of split
% 238.15/45.17  | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | |   (19209)  all_58_10 = e1 & op(e2, e0) = e1
% 238.15/45.17  | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (19149), (19209), (function-axioms) are
% 238.15/45.17  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 238.15/45.17  | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | End of split
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19210)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.15/45.17  | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (17773), (19167), (19210),
% 238.15/45.17  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.17  | | | | | | | | | | | | | | | |            #162.
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | End of split
% 238.15/45.17  | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | |   (19211)  all_54_10 = e0
% 238.15/45.17  | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | REF_CLOSE: (297), (19060), (19211) are inconsistent by
% 238.15/45.17  | | | | | | | | | | | | | | |            sub-proof #2303.
% 238.15/45.17  | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | End of split
% 238.15/45.17  | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | End of split
% 238.15/45.17  | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | End of split
% 238.15/45.17  | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | |   (19212)  all_36_2 = e2
% 238.15/45.17  | | | | | | | | | | | |   (19213)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 238.15/45.17  | | | | | | | | | | | |              & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 238.15/45.17  | | | | | | | | | | | |              $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 238.15/45.17  | | | | | | | | | | | |              = all_36_1 & $i(all_36_1))
% 238.15/45.17  | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | COMBINE_EQS: (328), (19212) imply:
% 238.15/45.17  | | | | | | | | | | | |   (19214)  all_6_2 = e2
% 238.15/45.17  | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | SIMP: (19214) implies:
% 238.15/45.17  | | | | | | | | | | | |   (19215)  all_6_2 = e2
% 238.15/45.17  | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | COMBINE_EQS: (322), (19215) imply:
% 238.15/45.17  | | | | | | | | | | | |   (19216)  all_40_2 = e2
% 238.15/45.17  | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | REDUCE: (367), (19215) imply:
% 238.15/45.17  | | | | | | | | | | | |   (19217)   ~ (all_52_2 = e2)
% 238.15/45.17  | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | REDUCE: (378), (19215) imply:
% 238.15/45.17  | | | | | | | | | | | |   (19218)   ~ (all_52_6 = e2)
% 238.15/45.17  | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | REDUCE: (39), (19215) imply:
% 238.15/45.17  | | | | | | | | | | | |   (19219)  op(e1, e1) = e2
% 238.15/45.17  | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | BETA: splitting (243) gives:
% 238.15/45.17  | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | |   (19220)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 238.15/45.17  | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 238.15/45.17  | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | BETA: splitting (19220) gives:
% 238.15/45.17  | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | |   (19221)  all_58_0 = e2 & op(e3, e3) = e2
% 238.15/45.17  | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | ALPHA: (19221) implies:
% 238.15/45.17  | | | | | | | | | | | | | |   (19222)  op(e3, e3) = e2
% 238.15/45.17  | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | REF_CLOSE: (5), (19058), (19222), (function-axioms) are
% 238.15/45.17  | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 238.15/45.17  | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | |   (19223)  all_58_2 = e2 & op(e2, e3) = e2
% 238.15/45.17  | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | ALPHA: (19223) implies:
% 238.15/45.17  | | | | | | | | | | | | | |   (19224)  op(e2, e3) = e2
% 238.15/45.17  | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.15/45.17  | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | |   (19225)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.15/45.17  | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.15/45.17  | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | BETA: splitting (19225) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19226)  all_58_1 = e2 & op(e3, e2) = e2
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | ALPHA: (19226) implies:
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19227)  all_58_1 = e2
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19228)  op(e3, e2) = e2
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 238.15/45.17  | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (19224) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19229)  all_52_1 = e2
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 238.15/45.17  | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (19228) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19230)  all_52_4 = e2
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | REDUCE: (149), (19229) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19231)   ~ (all_52_2 = e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | REDUCE: (148), (19229) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19232)   ~ (all_52_3 = e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | REDUCE: (146), (19229) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19233)   ~ (all_52_9 = e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | SIMP: (19233) implies:
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19234)   ~ (all_52_9 = e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | REDUCE: (145), (19229) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19235)   ~ (all_52_13 = e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | REDUCE: (134), (19230) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19236)   ~ (all_52_8 = e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | SIMP: (19236) implies:
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19237)   ~ (all_52_8 = e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | REDUCE: (133), (19230) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | |   (19238)   ~ (all_52_12 = e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | |   (19239)   ~ (all_40_2 = e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | REDUCE: (19216), (19239) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | | |   (19240)  $false
% 238.15/45.17  | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | CLOSE: (19240) is inconsistent.
% 238.15/45.17  | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | |   (19241)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 238.15/45.17  | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 238.15/45.17  | | | | | | | | | | | | | | | | |              $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | |              = all_40_1 & $i(all_40_1))
% 238.15/45.17  | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | |   (19242)   ~ (all_44_2 = e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | REDUCE: (17761), (19242) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | | | |   (19243)  $false
% 238.15/45.17  | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | CLOSE: (19243) is inconsistent.
% 238.15/45.17  | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | |   (19244)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.15/45.17  | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.15/45.17  | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.15/45.17  | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.15/45.17  | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | |   (19245)   ~ (all_50_2 = e0)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | REDUCE: (19049), (19245) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | |   (19246)  $false
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | CLOSE: (19246) is inconsistent.
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | |   (19247)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 238.15/45.17  | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 238.15/45.17  | | | | | | | | | | | | | | | | | | |              $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | |              = all_50_1 & $i(all_50_1))
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |   (19248)  all_54_3 = e3
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (19248) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |   (19249)  all_52_12 = e3
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | SIMP: (19249) implies:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |   (19250)  all_52_12 = e3
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (19250) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |   (19251)   ~ (all_52_13 = e3)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | SIMP: (19251) implies:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |   (19252)   ~ (all_52_13 = e3)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (19250) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |   (19253)   ~ (all_52_14 = e3)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | SIMP: (19253) implies:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |   (19254)   ~ (all_52_14 = e3)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (19250) imply:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | |   (19255)  op(e3, e0) = e3
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |   (19256)  all_54_7 = e3
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (19252), (19256) are inconsistent by
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |   (19257)   ~ (all_54_7 = e3)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | |   (19258)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | |   (19259)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19259) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | |   (19260)  all_58_9 = e1 & op(e3, e0) = e1
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19260) implies:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | |   (19261)  op(e3, e0) = e1
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19255), (19261), (function-axioms) are
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | |   (19262)  all_58_10 = e1 & op(e2, e0) = e1
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (19149), (19262), (function-axioms) are
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | |   (19263)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19263) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | |   (19264)  all_58_11 = e1 & op(e1, e0) = e1
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19264) implies:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | |   (19265)  op(e1, e0) = e1
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | |   (19266)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19266) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (19267)  all_58_9 = e3 & op(e3, e0) = e3
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19267) implies:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (19268)  all_58_9 = e3
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19247) gives:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19269)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_50_1 & $i(all_50_0) &
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19269) implies:
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19270)  op(e3, e0) = all_50_1
% 238.15/45.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (42), (110), (117), (118), (141),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (143), (144), (157), (158), (159), (160), (162),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (192), (193), (196),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (198), (210), (212), (217), (219), (227), (232),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (238), (239), (241), (242), (243), (244),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (257), (258), (268), (269), (270), (17760),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17762), (17763), (17767), (17768), (17773),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (17779), (19046), (19051), (19052),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19053), (19058), (19144), (19145), (19147),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19148), (19149), (19213), (19217), (19219),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19224), (19228), (19234), (19241), (19244),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19254), (19255), (19258), (19268), (19270),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            #149.
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19271)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19271) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19272)  op(e3, e0) = all_50_1
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (42), (110), (117), (118), (141),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (143), (144), (157), (158), (159), (160), (162),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (192), (193), (196),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (198), (210), (212), (217), (219), (227), (232),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (238), (239), (241), (242), (243), (244),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (257), (258), (268), (269), (270), (17760),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17762), (17763), (17767), (17768), (17773),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (17779), (19046), (19051), (19052),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19053), (19058), (19144), (19145), (19147),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19148), (19149), (19213), (19217), (19219),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19224), (19228), (19234), (19241), (19244),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19254), (19255), (19258), (19268), (19272),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            #149.
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (19273)  all_58_10 = e3 & op(e2, e0) = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19273) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (19274)  op(e2, e0) = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (19252), (19274), (function-axioms) are
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | |   (19275)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (17774), (19265), (19275),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | |            #148.
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | |   (19276)  all_58_15 = e1 & op(e0, e0) = e1
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19276) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | |   (19277)  all_58_15 = e1
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (19277) are inconsistent by
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2231.
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | |   (19278)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (19278) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | |   (19279)  all_54_3 = e2
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (17766), (19279) are inconsistent by
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2290.
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | |   (19280)   ~ (all_54_3 = e2)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | |   (19281)  all_54_3 = e1 | all_54_3 = e0
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19281) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | |   (19282)  all_54_3 = e1
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (19282) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | |   (19283)  all_52_12 = e1
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | SIMP: (19283) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | |   (19284)  all_52_12 = e1
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (19284) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | |   (19285)   ~ (all_52_8 = e1)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (19284) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | |   (19286)   ~ (all_52_13 = e1)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17766), (19284) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | |   (19287)   ~ (e2 = e1)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (19284) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | |   (19288)  op(e3, e0) = e1
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | |   (19289)  all_54_2 = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (19289) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | |   (19290)  all_52_8 = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19290) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | |   (19291)  all_52_8 = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (19291) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | |   (19292)   ~ (all_52_9 = e3)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19292) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | |   (19293)   ~ (all_52_9 = e3)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | |   (19294)  all_54_6 = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (19293), (19294) are inconsistent by
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | |   (19295)   ~ (all_54_6 = e3)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | |   (19296)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (19297)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19297) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19298)  all_58_6 = e1 & op(e1, e3) = e1
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19298) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19299)  op(e1, e3) = e1
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19300)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (159), (163), (167), (239), (19051),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19052), (19053), (19224), (19300),
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #160.
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19301)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19301) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19302)  all_58_6 = e3 & op(e1, e3) = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19302) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19303)  op(e1, e3) = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19299), (19303), (function-axioms) are
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19304)  all_58_12 = e3 & op(e0, e3) = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19304) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19305)  all_58_12 = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19306)  op(e0, e3) = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19296) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19307)  all_54_6 = e2
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (19234), (19307) are inconsistent by
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19308)   ~ (all_54_6 = e2)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19309)  all_54_6 = e1 | all_54_6 = e0
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19309) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19310)  all_54_6 = e1
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (19148), (19310) are inconsistent by
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2246.
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19311)  all_54_6 = e0
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (19311) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19312)  all_52_9 = e0
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19312) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19313)  all_52_9 = e0
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (19313) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19314)   ~ (all_52_13 = e0)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19314) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19315)   ~ (all_52_13 = e0)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19234), (19313) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19316)   ~ (e2 = e0)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (19313) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19317)  op(e2, e1) = e0
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19318)  all_54_7 = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (19318) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19319)  all_52_13 = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19319) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19320)  all_52_13 = e3
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (19320) imply:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19321)   ~ (all_52_14 = e3)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19321) implies:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19322)   ~ (all_52_14 = e3)
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19323)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19323) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19324)  all_58_12 = e1 & op(e0, e3) = e1
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19305), (19324) are inconsistent by
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1874.
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19325)  all_58_13 = e1 & op(e0, e2) = e1
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (19147), (19325), (function-axioms) are
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19326)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19326) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19327)  all_58_14 = e1 & op(e0, e1) = e1
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19327) implies:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19328)  all_58_14 = e1
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19329)  op(e0, e1) = e1
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19330)  all_58_15 = e0 & op(e0, e0) = e0
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19330) implies:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19331)  op(e0, e0) = e0
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (19331), (function-axioms) are
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19332)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19332) implies:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19333)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19334)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19334) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19335)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19335) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19336)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19336) implies:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19337)  op(e2, e3) = e3
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19224), (19337), (function-axioms) are
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19338)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19338) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19339)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19339) implies:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19340)  all_56_3 = e2
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19341)   ~ (all_56_31 = e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19342)   ~ (all_56_11 = e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19343)   ~ (all_56_1 = e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19050), (19343) imply:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19344)   ~ (e3 = e0)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (19341) imply:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19345)   ~ (e3 = e2)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19346)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (159), (163), (167), (239), (19051),
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19052), (19053), (19228), (19346),
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #463.
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19347)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19347) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19348)  all_58_4 = e3 & op(e3, e1) = e3
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19348) implies:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19349)  all_58_4 = e3
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19350)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19350) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19351)  all_58_6 = e3 & op(e1, e3) = e3
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19351) implies:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19352)  all_58_6 = e3
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (243),
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19305), (19352), (function-axioms) are
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1531.
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19353)  all_58_7 = e3 & op(e1, e2) = e3
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19353) implies:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19354)  op(e1, e2) = e3
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19355)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (42), (242), (244),
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17779), (19058), (19349), (19355),
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #147.
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19356)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19356) gives:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19357)  all_58_7 = e0 & op(e1, e2) = e0
% 238.15/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19357) implies:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19358)  all_58_7 = e0
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (160), (226), (19219), (19299),
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19322), (19358), (function-axioms) are
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2147.
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19359)  all_58_13 = e0 & op(e0, e2) = e0
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19359) implies:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19360)  op(e0, e2) = e0
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19361)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19361) gives:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19362)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19362) implies:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19363)  op(e3, all_56_1) = e3
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19050), (19363) imply:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19364)  op(e3, e0) = e3
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19288), (19364), (function-axioms) are
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19365)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19365) implies:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19366)  op(e2, all_56_3) = e2
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19340), (19366) imply:
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19367)  op(e2, e2) = e2
% 238.22/45.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (236),
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (19227), (19360), (19367),
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1811.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19368)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (19213), (19219), (19241), (19299),
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19306), (19354), (19368), (function-axioms) are
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #146.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19369)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (19219), (19322), (19369),
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2148.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19370)  all_58_9 = e3 & op(e3, e0) = e3
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19370) implies:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19371)  op(e3, e0) = e3
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19288), (19371), (function-axioms) are
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19372)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19372) implies:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19373)  op(e1, e3) = e3
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19299), (19373), (function-axioms) are
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19374)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (169), (19053), (19285), (19288),
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19374), (function-axioms) are inconsistent by
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #164.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19375)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19375) gives:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19376)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19376) gives:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19377)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19377) implies:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19378)  op(e2, e1) = e2
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19317), (19378), (function-axioms) are
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19379)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19379) gives:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19380)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19380) implies:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19381)  op(e2, e1) = e1
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (19148), (19381), (function-axioms) are
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19382)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19382) implies:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19383)  op(e0, e2) = e2
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (19305), (19328), (19333), (19383),
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1032.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19384)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19384) gives:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19385)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19385) implies:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19386)  op(e2, e0) = e0
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (19315), (19386), (function-axioms) are
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2324.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19387)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19387) gives:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19388)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19388) implies:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19389)  op(e1, e0) = e1
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (160), (280), (19056), (19281), (19389),
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1331.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19390)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19390) implies:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19391)  op(e0, e1) = e0
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19329), (19391), (function-axioms) are
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2158.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19392)  all_58_15 = e1 & op(e0, e0) = e1
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (19392) are inconsistent by
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #218.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19393)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (269), (19149), (19224), (19315),
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19393), (function-axioms) are inconsistent by
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2292.
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19394)  all_58_7 = e1 & op(e1, e2) = e1
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19394) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19395)  op(e1, e2) = e1
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19396)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (164), (165), (167), (232), (19145),
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19148), (19149), (19224), (19396),
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #145.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19397)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19397) gives:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19398)  all_58_5 = e3 & op(e2, e1) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (19293), (19398), (function-axioms) are
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19399)  all_58_10 = e3 & op(e2, e0) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19399) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19400)  all_58_10 = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19401)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19401) gives:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19402)  all_58_1 = e3 & op(e3, e2) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19402) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19403)  op(e3, e2) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19228), (19403), (function-axioms) are
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2193.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19404)  all_58_3 = e3 & op(e2, e2) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19404) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19405)  all_58_3 = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (231), (232),
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (19145), (19400), (19405),
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1099.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19406)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19406) gives:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19407)  all_58_7 = e3 & op(e1, e2) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19407) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19408)  op(e1, e2) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19213), (19241), (19395), (19408),
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1332.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19409)  all_58_13 = e3 & op(e0, e2) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19409) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19410)  op(e0, e2) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19411)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (159), (163), (167), (239), (19051),
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19052), (19053), (19228), (19411),
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #463.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19412)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19412) gives:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19413)  all_58_4 = e3 & op(e3, e1) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19413) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19414)  all_58_4 = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19415)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (42), (242), (244),
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17779), (19058), (19414), (19415),
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #147.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19416)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19416) gives:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19417)  all_58_7 = e0 & op(e1, e2) = e0
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19417) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19418)  op(e1, e2) = e0
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (19395), (19418), (function-axioms)
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19419)  all_58_13 = e0 & op(e0, e2) = e0
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19419) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19420)  op(e0, e2) = e0
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19410), (19420), (function-axioms) are
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1961.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19421)  all_58_9 = e3 & op(e3, e0) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19421) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19422)  op(e3, e0) = e3
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19288), (19422), (function-axioms) are
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (19423)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19423) gives:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19424)  all_58_8 = e1 & op(e1, e1) = e1
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19424) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19425)  op(e1, e1) = e1
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (19219), (19425), (function-axioms) are
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19426)  all_58_11 = e1 & op(e1, e0) = e1
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19426) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19427)  op(e1, e0) = e1
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (160), (280), (19056), (19281), (19427),
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1331.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | |   (19428)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (19055), (19237), (19285), (19428) are
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1335.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | |   (19429)  all_54_3 = e0
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (19056), (19429) are inconsistent by
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2288.
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | |   (19430)  all_58_3 = e2 & op(e2, e2) = e2
% 238.22/45.21  | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | ALPHA: (19430) implies:
% 238.22/45.21  | | | | | | | | | | | | | | | |   (19431)  op(e2, e2) = e2
% 238.22/45.21  | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (19151), (19431), (function-axioms) are
% 238.22/45.21  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 238.22/45.21  | | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | |   (19432)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.22/45.21  | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.22/45.21  | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (17764), (19218), (19432),
% 238.22/45.21  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.21  | | | | | | | | | | | | | | |            #144.
% 238.22/45.21  | | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | |   (19433)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 238.22/45.21  | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 238.22/45.21  | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | BETA: splitting (19433) gives:
% 238.22/45.21  | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | Case 1:
% 238.22/45.21  | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | |   (19434)  all_58_6 = e2 & op(e1, e3) = e2
% 238.22/45.21  | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | REF_CLOSE: (163), (19217), (19434), (function-axioms) are
% 238.22/45.21  | | | | | | | | | | | | | |            inconsistent by sub-proof #250.
% 238.22/45.21  | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | Case 2:
% 238.22/45.21  | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | |   (19435)  all_58_12 = e2 & op(e0, e3) = e2
% 238.22/45.21  | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | | REF_CLOSE: (159), (17763), (19435), (function-axioms) are
% 238.22/45.21  | | | | | | | | | | | | | |            inconsistent by sub-proof #2315.
% 238.22/45.21  | | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | | End of split
% 238.22/45.21  | | | | | | | | | | 
% 238.22/45.21  | | | | | | | | | Case 2:
% 238.22/45.22  | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | |   (19436)  all_18_2 = e0
% 238.22/45.22  | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | COMBINE_EQS: (339), (19436) imply:
% 238.22/45.22  | | | | | | | | | |   (19437)  all_6_2 = e0
% 238.22/45.22  | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | SIMP: (19437) implies:
% 238.22/45.22  | | | | | | | | | |   (19438)  all_6_2 = e0
% 238.22/45.22  | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | COMBINE_EQS: (266), (19438) imply:
% 238.22/45.22  | | | | | | | | | |   (19439)  all_56_21 = e0
% 238.22/45.22  | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | REDUCE: (378), (19438) imply:
% 238.22/45.22  | | | | | | | | | |   (19440)   ~ (all_52_6 = e0)
% 238.22/45.22  | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | REDUCE: (381), (19438) imply:
% 238.22/45.22  | | | | | | | | | |   (19441)   ~ (all_52_9 = e0)
% 238.22/45.22  | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | REDUCE: (39), (19438) imply:
% 238.22/45.22  | | | | | | | | | |   (19442)  op(e1, e1) = e0
% 238.22/45.22  | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | BETA: splitting (216) gives:
% 238.22/45.22  | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | Case 1:
% 238.22/45.22  | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | |   (19443)  all_58_15 = e0 & op(e0, e0) = e0
% 238.22/45.22  | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | ALPHA: (19443) implies:
% 238.22/45.22  | | | | | | | | | | |   (19444)  op(e0, e0) = e0
% 238.22/45.22  | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | REF_CLOSE: (5), (17774), (19444), (function-axioms) are
% 238.22/45.22  | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.22/45.22  | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | Case 2:
% 238.22/45.22  | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | |   (19445)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.22/45.22  | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.22/45.22  | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.22/45.22  | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.22/45.22  | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.22/45.22  | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | ALPHA: (19445) implies:
% 238.22/45.22  | | | | | | | | | | |   (19446)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.22/45.22  | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.22/45.22  | | | | | | | | | | |                e1) = e0)
% 238.22/45.22  | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | BETA: splitting (235) gives:
% 238.22/45.22  | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | Case 1:
% 238.22/45.22  | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | |   (19447)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 238.22/45.22  | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.22/45.22  | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | BETA: splitting (19447) gives:
% 238.22/45.22  | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | Case 1:
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | |   (19448)  all_58_1 = e0 & op(e3, e2) = e0
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | REF_CLOSE: (170), (19054), (19448), (function-axioms) are
% 238.22/45.22  | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | Case 2:
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | |   (19449)  all_58_3 = e0 & op(e2, e2) = e0
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | REF_CLOSE: (42), (17779), (19449), (function-axioms) are
% 238.22/45.22  | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | End of split
% 238.22/45.22  | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | Case 2:
% 238.22/45.22  | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | |   (19450)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 238.22/45.22  | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 238.22/45.22  | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | BETA: splitting (19450) gives:
% 238.22/45.22  | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | Case 1:
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | |   (19451)  all_58_7 = e0 & op(e1, e2) = e0
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | REF_CLOSE: (162), (19440), (19451), (function-axioms) are
% 238.22/45.22  | | | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | Case 2:
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | |   (19452)  all_58_13 = e0 & op(e0, e2) = e0
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | ALPHA: (19452) implies:
% 238.22/45.22  | | | | | | | | | | | | |   (19453)  op(e0, e2) = e0
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | BETA: splitting (231) gives:
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | Case 1:
% 238.22/45.22  | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | |   (19454)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 238.22/45.22  | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.22/45.22  | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | BETA: splitting (19454) gives:
% 238.22/45.22  | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | Case 1:
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | |   (19455)  all_58_2 = e0 & op(e2, e3) = e0
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | REF_CLOSE: (167), (19051), (19455), (function-axioms) are
% 238.22/45.22  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1985.
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | Case 2:
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | |   (19456)  all_58_3 = e0 & op(e2, e2) = e0
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | REF_CLOSE: (42), (17779), (19456), (function-axioms) are
% 238.22/45.22  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | End of split
% 238.22/45.22  | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | Case 2:
% 238.22/45.22  | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | |   (19457)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 238.22/45.22  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 238.22/45.22  | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | BETA: splitting (19457) gives:
% 238.22/45.22  | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | Case 1:
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | |   (19458)  all_58_5 = e0 & op(e2, e1) = e0
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | REF_CLOSE: (165), (19441), (19458), (function-axioms) are
% 238.22/45.22  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | Case 2:
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | |   (19459)  all_58_10 = e0 & op(e2, e0) = e0
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | ALPHA: (19459) implies:
% 238.22/45.22  | | | | | | | | | | | | | | |   (19460)  op(e2, e0) = e0
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 238.22/45.22  | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (19453) gives:
% 238.22/45.22  | | | | | | | | | | | | | | |   (19461)  all_52_7 = e0
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 238.22/45.22  | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (19460) gives:
% 238.22/45.22  | | | | | | | | | | | | | | |   (19462)  all_52_13 = e0
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | REDUCE: (110), (19462) imply:
% 238.22/45.22  | | | | | | | | | | | | | | |   (19463)   ~ (all_52_14 = e0)
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | SIMP: (19463) implies:
% 238.22/45.22  | | | | | | | | | | | | | | |   (19464)   ~ (all_52_14 = e0)
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | REDUCE: (377), (19462) imply:
% 238.22/45.22  | | | | | | | | | | | | | | |   (19465)   ~ (all_8_2 = e0)
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | REDUCE: (17767), (19462) imply:
% 238.22/45.22  | | | | | | | | | | | | | | |   (19466)   ~ (e2 = e0)
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | Case 1:
% 238.22/45.22  | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | |   (19467)   ~ (all_44_2 = e2)
% 238.22/45.22  | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | REDUCE: (17761), (19467) imply:
% 238.22/45.22  | | | | | | | | | | | | | | | |   (19468)  $false
% 238.22/45.22  | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | CLOSE: (19468) is inconsistent.
% 238.22/45.22  | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | Case 2:
% 238.22/45.22  | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | |   (19469)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.22/45.22  | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.22/45.22  | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.22/45.22  | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.22/45.22  | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 238.22/45.22  | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.22  | | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | |   (19470)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 238.22/45.22  | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 238.22/45.22  | | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | | ALPHA: (19470) implies:
% 238.22/45.22  | | | | | | | | | | | | | | | | |   (19471)  op(e0, e2) = all_4_1
% 238.22/45.22  | | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (64), (112), (120), (121), (123), (126),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (133), (134), (136), (141), (143), (148), (149),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (157), (159), (160), (162), (163), (164), (165),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (193), (195), (196),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (199), (200), (201), (202), (203), (213), (225),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (229), (230), (232), (238), (240), (241), (242),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (244), (246), (258), (267), (268), (275), (279),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (280), (281), (282), (326), (353), (366), (369),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (371), (375), (17762), (17765), (17766), (17768),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (17776), (17779), (19051), (19052), (19053),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (19054), (19055), (19056), (19058), (19439),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (19440), (19442), (19446), (19453), (19460),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (19464), (19469), (19471), (function-axioms) are
% 238.22/45.22  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #137.
% 238.22/45.22  | | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.22  | | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | |   (19472)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 238.22/45.22  | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 238.22/45.22  | | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | | ALPHA: (19472) implies:
% 238.22/45.22  | | | | | | | | | | | | | | | | |   (19473)  op(e0, e2) = all_4_1
% 238.22/45.22  | | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (64), (112), (120), (121), (123), (126),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (133), (134), (136), (141), (143), (148), (149),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (157), (159), (160), (162), (163), (164), (165),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (193), (195), (196),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (199), (200), (201), (202), (203), (213), (225),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (229), (230), (232), (238), (240), (241), (242),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (244), (246), (258), (267), (268), (275), (279),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (280), (281), (282), (326), (353), (366), (369),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (371), (375), (17762), (17765), (17766), (17768),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (17776), (17779), (19051), (19052), (19053),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (19054), (19055), (19056), (19058), (19439),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (19440), (19442), (19446), (19453), (19460),
% 238.22/45.22  | | | | | | | | | | | | | | | | |            (19464), (19469), (19473), (function-axioms) are
% 238.22/45.22  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #137.
% 238.22/45.22  | | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | | End of split
% 238.22/45.22  | | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | | End of split
% 238.22/45.22  | | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | | End of split
% 238.22/45.22  | | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | | End of split
% 238.22/45.22  | | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | | End of split
% 238.22/45.22  | | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | | End of split
% 238.22/45.22  | | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | | End of split
% 238.22/45.22  | | | | | | | | | | 
% 238.22/45.22  | | | | | | | | | End of split
% 238.22/45.22  | | | | | | | | | 
% 238.22/45.22  | | | | | | | | End of split
% 238.22/45.22  | | | | | | | | 
% 238.22/45.22  | | | | | | | Case 2:
% 238.22/45.22  | | | | | | | | 
% 238.22/45.22  | | | | | | | |   (19474)  all_14_2 = e0
% 238.22/45.22  | | | | | | | |   (19475)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 238.22/45.22  | | | | | | | |              op(e2, e0) = all_14_1 & $i(all_14_0) &
% 238.22/45.22  | | | | | | | |              $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0) =
% 238.22/45.22  | | | | | | | |              all_14_1 & $i(all_14_1))
% 238.22/45.22  | | | | | | | | 
% 238.22/45.22  | | | | | | | | COMBINE_EQS: (344), (19474) imply:
% 238.22/45.22  | | | | | | | |   (19476)  all_8_2 = e0
% 238.22/45.22  | | | | | | | | 
% 238.22/45.22  | | | | | | | | COMBINE_EQS: (311), (19476) imply:
% 238.22/45.22  | | | | | | | |   (19477)  all_48_2 = e0
% 238.22/45.22  | | | | | | | | 
% 238.22/45.22  | | | | | | | | COMBINE_EQS: (353), (19476) imply:
% 238.22/45.22  | | | | | | | |   (19478)  all_56_11 = e0
% 238.22/45.22  | | | | | | | | 
% 238.22/45.22  | | | | | | | | REDUCE: (366), (19476) imply:
% 238.22/45.22  | | | | | | | |   (19479)   ~ (all_52_1 = e0)
% 238.22/45.22  | | | | | | | | 
% 238.22/45.22  | | | | | | | | REDUCE: (369), (19476) imply:
% 238.22/45.22  | | | | | | | |   (19480)   ~ (all_52_4 = e0)
% 238.22/45.22  | | | | | | | | 
% 238.22/45.22  | | | | | | | | REDUCE: (371), (19476) imply:
% 238.22/45.22  | | | | | | | |   (19481)   ~ (all_52_6 = e0)
% 238.22/45.22  | | | | | | | | 
% 238.22/45.22  | | | | | | | | REDUCE: (373), (19476) imply:
% 238.22/45.22  | | | | | | | |   (19482)   ~ (all_52_7 = e0)
% 238.22/45.22  | | | | | | | | 
% 238.22/45.22  | | | | | | | | REDUCE: (377), (19476) imply:
% 238.22/45.23  | | | | | | | |   (19483)   ~ (all_52_13 = e0)
% 238.22/45.23  | | | | | | | | 
% 238.22/45.23  | | | | | | | | REDUCE: (17776), (19476) imply:
% 238.22/45.23  | | | | | | | |   (19484)   ~ (e3 = e0)
% 238.22/45.23  | | | | | | | | 
% 238.22/45.23  | | | | | | | | BETA: splitting (235) gives:
% 238.22/45.23  | | | | | | | | 
% 238.22/45.23  | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | 
% 238.22/45.23  | | | | | | | | |   (19485)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 238.22/45.23  | | | | | | | | |              & op(e2, e2) = e0)
% 238.22/45.23  | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | BETA: splitting (19485) gives:
% 238.22/45.23  | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | |   (19486)  all_58_1 = e0 & op(e3, e2) = e0
% 238.22/45.23  | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | REF_CLOSE: (170), (19480), (19486), (function-axioms) are
% 238.22/45.23  | | | | | | | | | |            inconsistent by sub-proof #1968.
% 238.22/45.23  | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | Case 2:
% 238.22/45.23  | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | |   (19487)  all_58_3 = e0 & op(e2, e2) = e0
% 238.22/45.23  | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | ALPHA: (19487) implies:
% 238.22/45.23  | | | | | | | | | |   (19488)  all_58_3 = e0
% 238.22/45.23  | | | | | | | | | |   (19489)  op(e2, e2) = e0
% 238.22/45.23  | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | BETA: splitting (55) gives:
% 238.22/45.23  | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | |   (19490)   ~ (all_16_2 = e0)
% 238.22/45.23  | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | REDUCE: (342), (19490) imply:
% 238.22/45.23  | | | | | | | | | | |   (19491)   ~ (all_10_2 = e0)
% 238.22/45.23  | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | BETA: splitting (58) gives:
% 238.22/45.23  | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | |   (19492)   ~ (all_18_2 = e0)
% 238.22/45.23  | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | REDUCE: (339), (19492) imply:
% 238.22/45.23  | | | | | | | | | | | |   (19493)   ~ (all_6_2 = e0)
% 238.22/45.23  | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | BETA: splitting (67) gives:
% 238.22/45.23  | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | |   (19494)   ~ (all_24_2 = e2)
% 238.22/45.23  | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | REDUCE: (301), (19494) imply:
% 238.22/45.23  | | | | | | | | | | | | |   (19495)   ~ (all_10_2 = e2)
% 238.22/45.23  | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | BETA: splitting (204) gives:
% 238.22/45.23  | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | |   (19496)  all_54_0 = e3
% 238.22/45.23  | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | COMBINE_EQS: (292), (19496) imply:
% 238.22/45.23  | | | | | | | | | | | | | |   (19497)  all_10_2 = e3
% 238.22/45.23  | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | SIMP: (19497) implies:
% 238.22/45.23  | | | | | | | | | | | | | |   (19498)  all_10_2 = e3
% 238.22/45.23  | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | COMBINE_EQS: (290), (19498) imply:
% 238.22/45.23  | | | | | | | | | | | | | |   (19499)  all_56_1 = e3
% 238.22/45.23  | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | REDUCE: (355), (19498) imply:
% 238.22/45.23  | | | | | | | | | | | | | |   (19500)   ~ (all_52_1 = e3)
% 238.22/45.23  | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | REDUCE: (357), (19498) imply:
% 238.22/45.23  | | | | | | | | | | | | | |   (19501)   ~ (all_52_2 = e3)
% 238.22/45.23  | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | REDUCE: (359), (19498) imply:
% 238.22/45.23  | | | | | | | | | | | | | |   (19502)   ~ (all_52_3 = e3)
% 238.22/45.23  | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | REDUCE: (45), (19498) imply:
% 238.22/45.23  | | | | | | | | | | | | | |   (19503)  op(e3, e3) = e3
% 238.22/45.23  | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 238.22/45.23  | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | |   (19504)   ~ (all_36_2 = e2)
% 238.22/45.23  | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | REDUCE: (328), (19504) imply:
% 238.22/45.23  | | | | | | | | | | | | | | |   (19505)   ~ (all_6_2 = e2)
% 238.22/45.23  | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 238.22/45.23  | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | |   (19506)  all_54_10 = e3
% 238.22/45.23  | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (19506) are inconsistent by
% 238.22/45.23  | | | | | | | | | | | | | | | |            sub-proof #2313.
% 238.22/45.23  | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | Case 2:
% 238.22/45.23  | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | |   (19507)   ~ (all_54_10 = e3)
% 238.22/45.23  | | | | | | | | | | | | | | | |   (19508)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.22/45.23  | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | BETA: splitting (19508) gives:
% 238.22/45.23  | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | |   (19509)  all_54_10 = e2
% 238.22/45.23  | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (19505), (19509) are inconsistent by
% 238.22/45.23  | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 238.22/45.23  | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.23  | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | |   (19510)  all_54_10 = e1 | all_54_10 = e0
% 238.22/45.23  | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | BETA: splitting (19510) gives:
% 238.22/45.23  | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | |   (19511)  all_54_10 = e1
% 238.22/45.23  | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (19511) imply:
% 238.22/45.23  | | | | | | | | | | | | | | | | | |   (19512)  all_6_2 = e1
% 238.22/45.23  | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | SIMP: (19512) implies:
% 238.22/45.23  | | | | | | | | | | | | | | | | | |   (19513)  all_6_2 = e1
% 238.22/45.23  | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (19513) imply:
% 238.22/45.23  | | | | | | | | | | | | | | | | | |   (19514)  all_56_21 = e1
% 238.22/45.23  | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | REDUCE: (380), (19513) imply:
% 238.22/45.23  | | | | | | | | | | | | | | | | | |   (19515)   ~ (all_52_8 = e1)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | REDUCE: (381), (19513) imply:
% 238.22/45.23  | | | | | | | | | | | | | | | | | |   (19516)   ~ (all_52_9 = e1)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | REDUCE: (385), (19513) imply:
% 238.22/45.23  | | | | | | | | | | | | | | | | | |   (19517)   ~ (all_52_14 = e1)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |   (19518)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | BETA: splitting (19518) gives:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |   (19519)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (19499), (19500), (19501), (19519),
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |            #2299.
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |   (19520)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | BETA: splitting (19520) gives:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |   (19521)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19521) implies:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |   (19522)  op(e3, e1) = e1
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (19515), (19522), (function-axioms) are
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |   (19523)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (19499), (19502), (19523),
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | |            #2271.
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | End of split
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |   (19524)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.22/45.23  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | BETA: splitting (19524) gives:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |   (19525)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (112), (128), (136), (144), (158), (159),
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (168), (169),
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |            (170), (194), (213), (223), (266), (297), (380),
% 238.22/45.23  | | | | | | | | | | | | | | | | | | | |            (381), (385), (17762), (17764), (17775), (19478),
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |            (19481), (19483), (19493), (19516), (19525),
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |            #135.
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | | 
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |   (19526)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.22/45.24  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (19483), (19514), (19517), (19526),
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | |            #1250.
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | |   (19527)  all_54_10 = e0
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (19493), (19527) are inconsistent by
% 238.29/45.24  | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | Case 2:
% 238.29/45.24  | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | |   (19528)  all_36_2 = e2
% 238.29/45.24  | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | COMBINE_EQS: (328), (19528) imply:
% 238.29/45.24  | | | | | | | | | | | | | | |   (19529)  all_6_2 = e2
% 238.29/45.24  | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | SIMP: (19529) implies:
% 238.29/45.24  | | | | | | | | | | | | | | |   (19530)  all_6_2 = e2
% 238.29/45.24  | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | REDUCE: (381), (19530) imply:
% 238.29/45.24  | | | | | | | | | | | | | | |   (19531)   ~ (all_52_9 = e2)
% 238.29/45.24  | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.29/45.24  | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | Case 1:
% 238.29/45.24  | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | |   (19532)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.29/45.24  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.24  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.29/45.24  | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.29/45.24  | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.24  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.24  | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.29/45.24  | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.29/45.24  | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.24  | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.29/45.24  | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.29/45.24  | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.24  | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.29/45.24  | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | BETA: splitting (19532) gives:
% 238.29/45.24  | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | |   (19533)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.29/45.24  | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.24  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.24  | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.29/45.24  | | | | | | | | | | | | | | | | |              = e3)
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (19499), (19500), (19501), (19533),
% 238.29/45.24  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.24  | | | | | | | | | | | | | | | | |            #2299.
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | |   (19534)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.29/45.24  | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.24  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.24  | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.29/45.24  | | | | | | | | | | | | | | | | |              = e0)
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (19499), (19502), (19534),
% 238.29/45.24  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.24  | | | | | | | | | | | | | | | | |            #2270.
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | Case 2:
% 238.29/45.24  | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | |   (19535)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.24  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.29/45.24  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.29/45.24  | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.29/45.24  | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.29/45.24  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.29/45.24  | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.29/45.24  | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.29/45.24  | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.29/45.24  | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.29/45.24  | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.29/45.24  | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.29/45.24  | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.29/45.24  | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | BETA: splitting (19535) gives:
% 238.29/45.24  | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | |   (19536)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.29/45.24  | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.29/45.24  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.29/45.24  | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.29/45.24  | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.29/45.24  | | | | | | | | | | | | | | | | |              = e2)
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (17762), (17764), (19531), (19536),
% 238.29/45.24  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.24  | | | | | | | | | | | | | | | | |            #184.
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | |   (19537)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.29/45.24  | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.29/45.24  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.24  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.24  | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.29/45.24  | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.24  | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.29/45.24  | | | | | | | | | | | | | | | | |              = e0)
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | BETA: splitting (19537) gives:
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | |   (19538)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.29/45.24  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.29/45.24  | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.29/45.24  | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | ALPHA: (19538) implies:
% 238.29/45.24  | | | | | | | | | | | | | | | | | |   (19539)  op(e2, e0) = e0
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (19483), (19539), (function-axioms) are
% 238.29/45.24  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2324.
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | |   (19540)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.29/45.24  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.29/45.24  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.29/45.24  | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.29/45.24  | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.29/45.24  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.29/45.24  | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | BETA: splitting (19540) gives:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |   (19541)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |              e1) = e1
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | ALPHA: (19541) implies:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |   (19542)   ~ (all_56_11 = e0)
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | REDUCE: (19478), (19542) imply:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |   (19543)  $false
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | CLOSE: (19543) is inconsistent.
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |   (19544)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |              e1) = e0
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | ALPHA: (19544) implies:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |   (19545)  op(e0, e1) = e0
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |   (19546)  op(e1, e0) = e0
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (157), (19545) gives:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |   (19547)  all_52_11 = e0
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (19546) gives:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |   (19548)  all_52_14 = e0
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | REDUCE: (141), (19548) imply:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |   (19549)   ~ (all_52_2 = e0)
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | REDUCE: (139), (19547) imply:
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |   (19550)   ~ (all_52_3 = e0)
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (19479), (19503),
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |            (19549), (19550), (function-axioms) are
% 238.29/45.24  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1938.
% 238.29/45.24  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | Case 2:
% 238.29/45.24  | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | |   (19551)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 238.29/45.24  | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | | REF_CLOSE: (292), (17777), (19491), (19495), (19551) are
% 238.29/45.24  | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 238.29/45.24  | | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | End of split
% 238.29/45.24  | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | Case 2:
% 238.29/45.24  | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | |   (19552)  all_24_2 = e2
% 238.29/45.24  | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | COMBINE_EQS: (301), (19552) imply:
% 238.29/45.24  | | | | | | | | | | | | |   (19553)  all_10_2 = e2
% 238.29/45.24  | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | SIMP: (19553) implies:
% 238.29/45.24  | | | | | | | | | | | | |   (19554)  all_10_2 = e2
% 238.29/45.24  | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | REDUCE: (355), (19554) imply:
% 238.29/45.24  | | | | | | | | | | | | |   (19555)   ~ (all_52_1 = e2)
% 238.29/45.24  | | | | | | | | | | | | | 
% 238.29/45.24  | | | | | | | | | | | | | REDUCE: (361), (19554) imply:
% 238.29/45.25  | | | | | | | | | | | | |   (19556)   ~ (all_52_4 = e2)
% 238.29/45.25  | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.29/45.25  | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | |   (19557)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.29/45.25  | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (19489), (19555), (19557),
% 238.29/45.25  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.25  | | | | | | | | | | | | | |            #1234.
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | |   (19558)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.29/45.25  | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | BETA: splitting (19558) gives:
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | |   (19559)  all_58_5 = e2 & op(e2, e1) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | ALPHA: (19559) implies:
% 238.29/45.25  | | | | | | | | | | | | | | |   (19560)  op(e2, e1) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19561)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.29/45.25  | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | BETA: splitting (19561) gives:
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19562)  all_58_1 = e2 & op(e3, e2) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | ALPHA: (19562) implies:
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19563)  op(e3, e2) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (19556), (19563), (function-axioms) are
% 238.29/45.25  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #254.
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19564)  all_58_3 = e2 & op(e2, e2) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | ALPHA: (19564) implies:
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19565)  op(e2, e2) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19489), (19565), (function-axioms) are
% 238.29/45.25  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2137.
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | End of split
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19566)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.29/45.25  | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | BETA: splitting (19566) gives:
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19567)  all_58_7 = e2 & op(e1, e2) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | ALPHA: (19567) implies:
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19568)  op(e1, e2) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (112), (128), (136), (144), (158), (159),
% 238.29/45.25  | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (168), (169),
% 238.29/45.25  | | | | | | | | | | | | | | | | |            (170), (194), (213), (223), (266), (297), (380),
% 238.29/45.25  | | | | | | | | | | | | | | | | |            (381), (385), (17762), (17775), (19478), (19481),
% 238.29/45.25  | | | | | | | | | | | | | | | | |            (19483), (19493), (19560), (19568),
% 238.29/45.25  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.25  | | | | | | | | | | | | | | | | |            #136.
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19569)  all_58_13 = e2 & op(e0, e2) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | ALPHA: (19569) implies:
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19570)  op(e0, e2) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (19570), (function-axioms) are
% 238.29/45.25  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | End of split
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | End of split
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | |   (19571)  all_58_10 = e2 & op(e2, e0) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | ALPHA: (19571) implies:
% 238.29/45.25  | | | | | | | | | | | | | | |   (19572)  op(e2, e0) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (19572), (function-axioms) are
% 238.29/45.25  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | End of split
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | End of split
% 238.29/45.25  | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | End of split
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | |   (19573)  all_18_2 = e0
% 238.29/45.25  | | | | | | | | | | | |   (19574)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0
% 238.29/45.25  | | | | | | | | | | | |              & op(e1, e0) = all_18_1 & $i(all_18_0) &
% 238.29/45.25  | | | | | | | | | | | |              $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1, e0)
% 238.29/45.25  | | | | | | | | | | | |              = all_18_1 & $i(all_18_1))
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | COMBINE_EQS: (339), (19573) imply:
% 238.29/45.25  | | | | | | | | | | | |   (19575)  all_6_2 = e0
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | SIMP: (19575) implies:
% 238.29/45.25  | | | | | | | | | | | |   (19576)  all_6_2 = e0
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | COMBINE_EQS: (332), (19576) imply:
% 238.29/45.25  | | | | | | | | | | | |   (19577)  all_28_2 = e0
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | COMBINE_EQS: (266), (19576) imply:
% 238.29/45.25  | | | | | | | | | | | |   (19578)  all_56_21 = e0
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | REDUCE: (380), (19576) imply:
% 238.29/45.25  | | | | | | | | | | | |   (19579)   ~ (all_52_8 = e0)
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | REDUCE: (381), (19576) imply:
% 238.29/45.25  | | | | | | | | | | | |   (19580)   ~ (all_52_9 = e0)
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | REDUCE: (383), (19576) imply:
% 238.29/45.25  | | | | | | | | | | | |   (19581)   ~ (all_52_11 = e0)
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | REDUCE: (39), (19576) imply:
% 238.29/45.25  | | | | | | | | | | | |   (19582)  op(e1, e1) = e0
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | BETA: splitting (240) gives:
% 238.29/45.25  | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | |   (19583)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 238.29/45.25  | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 238.29/45.25  | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | BETA: splitting (19583) gives:
% 238.29/45.25  | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | |   (19584)  all_58_0 = e0 & op(e3, e3) = e0
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | REF_CLOSE: (45), (19491), (19584), (function-axioms) are
% 238.29/45.25  | | | | | | | | | | | | | |            inconsistent by sub-proof #1736.
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | |   (19585)  all_58_1 = e0 & op(e3, e2) = e0
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | REF_CLOSE: (170), (19480), (19585), (function-axioms) are
% 238.29/45.25  | | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | End of split
% 238.29/45.25  | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | |   (19586)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 238.29/45.25  | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 238.29/45.25  | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | BETA: splitting (19586) gives:
% 238.29/45.25  | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | |   (19587)  all_58_4 = e0 & op(e3, e1) = e0
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | REF_CLOSE: (169), (19579), (19587), (function-axioms) are
% 238.29/45.25  | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | |   (19588)  all_58_9 = e0 & op(e3, e0) = e0
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | ALPHA: (19588) implies:
% 238.29/45.25  | | | | | | | | | | | | | |   (19589)  op(e3, e0) = e0
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.29/45.25  | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | |   (19590)  all_58_15 = e0 & op(e0, e0) = e0
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | ALPHA: (19590) implies:
% 238.29/45.25  | | | | | | | | | | | | | | |   (19591)  op(e0, e0) = e0
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (19591), (function-axioms) are
% 238.29/45.25  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | |   (19592)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.29/45.25  | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.29/45.25  | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.29/45.25  | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.29/45.25  | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | ALPHA: (19592) implies:
% 238.29/45.25  | | | | | | | | | | | | | | |   (19593)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.29/45.25  | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.29/45.25  | | | | | | | | | | | | | | |                e1) = e0)
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | BETA: splitting (19593) gives:
% 238.29/45.25  | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19594)  all_58_12 = e0 & op(e0, e3) = e0
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | ALPHA: (19594) implies:
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19595)  all_58_12 = e0
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19596)  op(e0, e3) = e0
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 238.29/45.25  | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (19596) gives:
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19597)  all_52_3 = e0
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 238.29/45.25  | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (168), (19589) gives:
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19598)  all_52_12 = e0
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | REDUCE: (144), (19597) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19599)   ~ (all_52_2 = e0)
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | REDUCE: (140), (19597) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19600)   ~ (all_52_7 = e0)
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | REDUCE: (139), (19597) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19601)   ~ (all_52_11 = e0)
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | REDUCE: (113), (19598) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19602)   ~ (all_52_13 = e0)
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | REDUCE: (112), (19598) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19603)   ~ (all_52_14 = e0)
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | SIMP: (19603) implies:
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19604)   ~ (all_52_14 = e0)
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | REDUCE: (365), (19598) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | |   (19605)   ~ (all_10_2 = e0)
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 238.29/45.25  | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19606)   ~ (all_24_2 = e2)
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | REDUCE: (301), (19606) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19607)   ~ (all_10_2 = e2)
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | |   (19608)  all_54_0 = e3
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (19608) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | | | |   (19609)  all_10_2 = e3
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (19609) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | | | |   (19610)  all_56_1 = e3
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | REDUCE: (355), (19609) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | | | |   (19611)   ~ (all_52_1 = e3)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | REDUCE: (357), (19609) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | | | |   (19612)   ~ (all_52_2 = e3)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | REDUCE: (361), (19609) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | | | |   (19613)   ~ (all_52_4 = e3)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | REDUCE: (363), (19609) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | | | |   (19614)   ~ (all_52_8 = e3)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |   (19615)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (168), (204), (292), (365), (17777),
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |            (19491), (19607), (19610), (19611), (19612),
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |            (19615), (function-axioms) are inconsistent by
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |            sub-proof #1668.
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |   (19616)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.29/45.25  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (19616) gives:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |   (19617)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (19617) gives:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |   (19618)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19618) implies:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |   (19619)  op(e1, e2) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |   (19620)  op(e2, e1) = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (134), (136), (162), (165), (170), (202),
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |            (203), (281), (282), (19480), (19579), (19613),
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |            (19614), (19619), (19620), (function-axioms) are
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #141.
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |   (19621)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17762), (17764), (19621),
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | |            #185.
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |   (19622)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (19483), (19578), (19604), (19622),
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | |            #1227.
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.25  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | |   (19623)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (17777), (19491), (19607), (19623) are
% 238.29/45.25  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 238.29/45.25  | | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | End of split
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19624)  all_24_2 = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19625)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 238.29/45.25  | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 238.29/45.25  | | | | | | | | | | | | | | | | |              $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 238.29/45.25  | | | | | | | | | | | | | | | | |              = all_24_1 & $i(all_24_1))
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (19624) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19626)  all_10_2 = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (19626) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19627)  all_32_2 = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (19626) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19628)  all_56_1 = e2
% 238.29/45.25  | | | | | | | | | | | | | | | | | 
% 238.29/45.25  | | | | | | | | | | | | | | | | | REDUCE: (355), (19626) imply:
% 238.29/45.25  | | | | | | | | | | | | | | | | |   (19629)   ~ (all_52_1 = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | REDUCE: (45), (19626) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | |   (19630)  op(e3, e3) = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | |   (19631)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | BETA: splitting (19631) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | |   (19632)  all_58_6 = e2 & op(e1, e3) = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | ALPHA: (19632) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | |   (19633)  all_58_6 = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | |   (19634)  op(e1, e3) = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (245),
% 238.29/45.26  | | | | | | | | | | | | | | | | | | |            (19595), (19630), (19633), (19634),
% 238.29/45.26  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.26  | | | | | | | | | | | | | | | | | | |            #237.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | |   (19635)  all_58_7 = e2 & op(e1, e2) = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | ALPHA: (19635) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | |   (19636)  all_58_7 = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | |   (19637)  op(e1, e2) = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | |   (19638)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (19489), (19629), (19638),
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | |            #1234.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | |   (19639)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (19639) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19640)  all_58_5 = e2 & op(e2, e1) = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19640) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19641)  all_58_5 = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19642)  op(e2, e1) = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (19637) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19643)  all_52_6 = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (19642) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19644)  all_52_9 = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (19643) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19645)   ~ (all_52_2 = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (19643) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19646)   ~ (all_52_4 = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (19643) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19647)   ~ (all_52_7 = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (19643) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19648)   ~ (all_52_14 = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (19644) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19649)   ~ (all_52_8 = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (19644) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19650)   ~ (all_52_11 = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (19644) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | |   (19651)   ~ (all_52_13 = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | |   (19652)   ~ (all_28_2 = e0)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19577), (19652) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | |   (19653)  $false
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19653) is inconsistent.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | |   (19654)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = all_28_1 & $i(all_28_0) &
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | |              $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | |              = all_28_1 & $i(all_28_1))
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | |   (19655)   ~ (all_32_2 = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19627), (19655) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | |   (19656)  $false
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19656) is inconsistent.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | |   (19657)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | |   (19658)   ~ (all_44_2 = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17761), (19658) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | |   (19659)  $false
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19659) is inconsistent.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | |   (19660)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (19661)   ~ (all_48_2 = e0)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19477), (19661) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (19662)  $false
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19662) is inconsistent.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (19663)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_48_1 & $i(all_48_1))
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19664)  all_54_14 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (19664) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19665)  all_52_11 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19665) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19666)  all_52_11 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (19666) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19667)   ~ (all_52_7 = e3)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (19666) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19668)   ~ (all_52_8 = e3)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19669)  all_54_2 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (19668), (19669) are inconsistent by
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19670)   ~ (all_54_2 = e3)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19671)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19672)  all_54_13 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (19667), (19672) are inconsistent by
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19673)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19674)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19674) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19675)  all_58_4 = e1 & op(e3, e1) = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19675) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19676)  all_58_4 = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19677)  op(e3, e1) = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19678)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (19642), (19677), (19678),
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #171.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19679)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19679) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19680)  all_58_8 = e3 & op(e1, e1) = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19582), (19680), (function-axioms) are
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19681)  all_58_14 = e3 & op(e0, e1) = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19681) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19682)  all_58_14 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19683)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19683) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19684)  all_58_12 = e1 & op(e0, e3) = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19684) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19685)  all_58_12 = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19595), (19685) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19686)  e1 = e0
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (228), (229), (19582),
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19676), (19682), (19686), (function-axioms) are
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1623.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19687)  all_58_13 = e1 & op(e0, e2) = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19687) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19688)  all_58_13 = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19671) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19689)  all_54_2 = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (19649), (19689) are inconsistent by
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1986.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19690)   ~ (all_54_2 = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19691)  all_54_2 = e1 | all_54_2 = e0
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19691) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19692)  all_54_2 = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (19692) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19693)  all_52_8 = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19693) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19694)  all_52_8 = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (19694) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19695)   ~ (all_52_4 = e1)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19649), (19694) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19696)   ~ (e2 = e1)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19673) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19697)  all_54_13 = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17764), (19697) are inconsistent by
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19698)  all_54_13 = e1 | all_54_13 = e0
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19699)  all_54_1 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (19699) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19700)  all_52_4 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19700) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19701)  all_52_4 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (19701) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19702)   ~ (all_52_7 = e3)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (19701) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19703)  op(e3, e2) = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19704)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, all_56_11) = e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19704) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19705)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_9 & $i(all_56_9)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19705) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19706)  op(e3, e2) = all_56_9
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19707)  op(e3, all_56_9) = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19657) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19708)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_32_1 & $i(all_32_0) &
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19708) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19709)  op(e3, e2) = all_32_1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19625), (19630), (19703), (19706), (19707),
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19709), (function-axioms) are inconsistent by
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #133.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19710)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19710) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19711)  op(e3, e2) = all_32_1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19625), (19630), (19703), (19706), (19707),
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19711), (function-axioms) are inconsistent by
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #133.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19712)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19712) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19713)  op(e2, all_56_11) = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19478), (19713) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19714)  op(e2, e0) = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (19714), (function-axioms) are
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19715)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15 & $i(all_56_15))
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19715) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19716)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19716) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19717)  op(e1, e2) = all_56_13
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19718)  op(e1, all_56_13) = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19719)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19719) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19720)  all_58_1 = e3 & op(e3, e2) = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19720) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19721)  all_58_1 = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (19637),
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19717) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19722)  all_56_13 = e2
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19718), (19722) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19723)  op(e1, e2) = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e1, e2,
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (19637), (19723) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19724)  e2 = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19636), (19724) imply:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19725)  all_58_7 = e1
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (237), (19489), (19688), (19721),
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19725), (function-axioms) are inconsistent by
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1588.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19726)  all_58_3 = e3 & op(e2, e2) = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (17776), (19726), (function-axioms) are
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #450.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19727)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19727) gives:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19728)  all_58_7 = e3 & op(e1, e2) = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19728) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19729)  op(e1, e2) = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (162), (170), (195), (267), (19703),
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19729), (function-axioms) are inconsistent by
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2190.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19730)  all_58_13 = e3 & op(e0, e2) = e3
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (19667), (19730), (function-axioms) are
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19731)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_15 & $i(all_56_15)
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19731) implies:
% 238.29/45.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19732)  op(e0, e2) = all_56_15
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19733)  op(e0, all_56_15) = e0
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19698) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19734)  all_54_13 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (19734) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19735)  all_52_7 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (19735) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19736)  op(e0, e2) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (19732),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19736) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19737)  all_56_15 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19733), (19737) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19738)  op(e0, e1) = e0
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (19581), (19738), (function-axioms) are
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1911.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19739)  all_54_13 = e0
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (19739) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19740)  all_52_7 = e0
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19482), (19740) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19741)  $false
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19741) is inconsistent.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19742)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (19480), (19646), (19695), (19742) are
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2048.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19743)  all_54_2 = e0
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (19579), (19743) are inconsistent by
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1643.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19744)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19744) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19745)  all_58_14 = e1 & op(e0, e1) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19745) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19746)  all_58_14 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19747)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (19642), (19668), (19747),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #132.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (19582), (19679), (19746),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #658.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19748)  all_58_15 = e1 & op(e0, e0) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (19748) are inconsistent by
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #218.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19749)  all_58_5 = e1 & op(e2, e1) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19749) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19750)  op(e2, e1) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (165), (281), (19579), (19649), (19671),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19750), (function-axioms) are inconsistent by
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #434.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19751)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19751) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19752)  all_58_8 = e1 & op(e1, e1) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19752) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19753)  op(e1, e1) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (19481), (19599),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19604), (19753), (function-axioms) are
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2020.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19754)  all_58_14 = e1 & op(e0, e1) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19754) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19755)  all_58_14 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19756)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (19642), (19668), (19756),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #132.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19757)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (19582), (19755), (19757),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #658.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19758)   ~ (all_54_14 = e3)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19759)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (255), (19758) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19760)   ~ (all_52_11 = e3)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19761)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19761) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19762)  all_58_12 = e3 & op(e0, e3) = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19595), (19762) are inconsistent by
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #581.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19763)  all_58_13 = e3 & op(e0, e2) = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19763) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19764)  all_58_13 = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19765)  op(e0, e2) = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19766)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19766) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19767)  all_58_4 = e3 & op(e3, e1) = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19767) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19768)  all_58_4 = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19769)  op(e3, e1) = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19770)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19770) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19771)  all_58_12 = e1 & op(e0, e3) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19771) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19772)  all_58_12 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19595), (19772) are inconsistent by
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1539.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19773)  all_58_13 = e1 & op(e0, e2) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19764), (19773) are inconsistent by
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2013.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19774)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19774) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19775)  all_58_14 = e1 & op(e0, e1) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19775) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19776)  all_58_14 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19777)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19777) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19778)  all_58_1 = e1 & op(e3, e2) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19778) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19779)  op(e3, e2) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19759) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19780)  all_54_14 = e2
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (17765), (19780) are inconsistent by
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1856.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19781)  all_54_14 = e1 | all_54_14 = e0
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19781) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19782)  all_54_14 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (19782) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19783)  all_52_11 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19783) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19784)  all_52_11 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (19784) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19785)   ~ (all_52_7 = e1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (19784) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19786)  op(e0, e1) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19787)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19787) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19788)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19788) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19789)  op(e3, e1) = all_56_17
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19790)  op(e3, all_56_17) = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19630), (19769), (19789), (19790),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2098.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19791)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19791) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19792)  op(e2, e1) = all_56_19
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19793)  op(e2, all_56_19) = e2
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19625) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (19642),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19792) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19794)  all_56_19 = e2
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19793), (19794) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19795)  op(e2, e2) = e2
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19489), (19795), (function-axioms) are
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2137.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19796)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19657), (19779), (19796), (function-axioms) are
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2238.
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19797)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19797) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19798)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19798) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19799)  op(e1, all_56_21) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19578), (19799) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19800)  op(e1, e0) = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19801)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19801) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19802)   ~ (all_4_0 = e1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19803)  op(e0, e2) = all_4_1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19804)  op(all_4_1, e0) = all_4_0
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19660) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19805)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19805) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19806)  op(e0, e2) = all_44_1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19807)  op(all_44_1, e0) = all_44_0
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19625) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19808)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_24_1 & $i(all_24_0) &
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19808) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19809)   ~ (all_24_0 = e0)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19810)  op(e3, e2) = all_24_1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19811)  op(all_24_1, e3) = all_24_0
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19657) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19812)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_32_1 & $i(all_32_0) &
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19812) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19813)  op(e3, e2) = all_32_1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_44_1, e2, e0, simplifying with (19803),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19806) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19814)  all_44_1 = all_4_1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1,
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (19765), (19806) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19815)  all_44_1 = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (19800) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19816)  all_52_14 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e3, simplifying with (19810),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19813) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19817)  all_32_1 = all_24_1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_32_1,
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (19779), (19813) gives:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19818)  all_32_1 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19814), (19815) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19819)  all_4_1 = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19819) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19820)  all_4_1 = e3
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19817), (19818) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19821)  all_24_1 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19821) implies:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19822)  all_24_1 = e1
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (19816) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19823)   ~ (all_52_2 = e1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (19816) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19824)   ~ (all_52_13 = e1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17768), (19816) imply:
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19825)   ~ (e2 = e1)
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (42), (135), (149), (158), (160),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (167), (170), (191), (196), (200),
% 238.29/45.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (214), (227), (229), (232), (234), (256),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (268), (279), (17762), (17764), (17774), (17776),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19475), (19479), (19482), (19488), (19574),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19589), (19596), (19599), (19628), (19629),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19642), (19645), (19654), (19663), (19768),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19776), (19785), (19786), (19802), (19804),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19807), (19809), (19811), (19815), (19816),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19820), (19822), (19823), (19824),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #123.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19826)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19826) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19827)   ~ (all_32_1 = e0)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19828)  op(e3, e2) = all_32_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_44_1, e2, e0, simplifying with (19803),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19806) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19829)  all_44_1 = all_4_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (19765), (19806) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19830)  all_44_1 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (19800) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19831)  all_52_14 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e3, simplifying with (19810),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19828) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19832)  all_32_1 = all_24_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_32_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (19779), (19828) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19833)  all_32_1 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19829), (19830) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19834)  all_4_1 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19834) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19835)  all_4_1 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19832), (19833) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19836)  all_24_1 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19836) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19837)  all_24_1 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (19831) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19838)   ~ (all_52_2 = e1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (19831) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19839)   ~ (all_52_13 = e1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17768), (19831) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19840)   ~ (e2 = e1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (42), (135), (149), (158), (160),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (167), (170), (191), (196), (200),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (214), (227), (229), (232), (234), (256),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (268), (279), (17762), (17764), (17774), (17776),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19475), (19479), (19482), (19488), (19574),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19589), (19596), (19599), (19628), (19629),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19642), (19645), (19654), (19663), (19768),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19776), (19785), (19786), (19802), (19804),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19807), (19809), (19811), (19830), (19831),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19835), (19837), (19838), (19839),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #123.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19841)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19657), (19779), (19841), (function-axioms) are
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2238.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19842)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 &
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19842) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19843)  op(e0, e2) = all_44_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19625) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19844)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_24_1 & $i(all_24_0) &
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19844) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19845)   ~ (all_24_0 = e0)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19846)  op(e3, e2) = all_24_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19847)  op(all_24_1, e3) = all_24_0
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19657) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19848)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_32_1 & $i(all_32_0) &
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19848) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19849)  op(e3, e2) = all_32_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_44_1, e2, e0, simplifying with (19803),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19843) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19850)  all_44_1 = all_4_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (19765), (19843) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19851)  all_44_1 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (19800) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19852)  all_52_14 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e3, simplifying with (19846),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19849) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19853)  all_32_1 = all_24_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_32_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (19779), (19849) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19854)  all_32_1 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19850), (19851) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19855)  all_4_1 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19855) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19856)  all_4_1 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19853), (19854) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19857)  all_24_1 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19857) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19858)  all_24_1 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (19852) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19859)   ~ (all_52_2 = e1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (19852) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19860)   ~ (all_52_13 = e1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17768), (19852) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19861)   ~ (e2 = e1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19847), (19858) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19862)  op(e1, e3) = all_24_0
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19804), (19856) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19863)  op(e3, e0) = all_4_0
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19864)  all_54_7 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (19864) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19865)  all_52_13 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19865) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19866)  all_52_13 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (19866) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19867)  op(e2, e0) = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (135), (149), (158), (163), (164),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (191), (196), (200), (210), (214),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (229), (232), (256), (268), (279), (17762),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17764), (17774), (19475), (19479), (19482),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19488), (19574), (19589), (19596), (19599),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19628), (19629), (19645), (19654), (19663),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19768), (19776), (19785), (19786), (19800),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19802), (19845), (19859), (19860), (19862),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19863), (19867), (function-axioms) are
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #120.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19868)   ~ (all_54_7 = e3)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (19868) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19869)   ~ (all_52_13 = e3)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (42), (135), (163), (164), (170),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (196), (214), (227), (229), (232), (234),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (268), (17764), (17774), (17776), (19482),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19488), (19596), (19599), (19628), (19642),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19645), (19768), (19776), (19785), (19859),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19860), (19869), (function-axioms) are
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #119.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19870)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19870) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19871)   ~ (all_32_1 = e0)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19872)  op(e3, e2) = all_32_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_44_1, e2, e0, simplifying with (19803),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19843) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19873)  all_44_1 = all_4_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (19765), (19843) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19874)  all_44_1 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (19800) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19875)  all_52_14 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e3, simplifying with (19846),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19872) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19876)  all_32_1 = all_24_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_32_1,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (19779), (19872) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19877)  all_32_1 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19873), (19874) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19878)  all_4_1 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19878) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19879)  all_4_1 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19876), (19877) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19880)  all_24_1 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19880) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19881)  all_24_1 = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (19875) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19882)   ~ (all_52_2 = e1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (19875) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19883)   ~ (all_52_13 = e1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17768), (19875) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19884)   ~ (e2 = e1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19847), (19881) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19885)  op(e1, e3) = all_24_0
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19804), (19879) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19886)  op(e3, e0) = all_4_0
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19887)  all_54_7 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (19887) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19888)  all_52_13 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19888) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19889)  all_52_13 = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (19889) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19890)  op(e2, e0) = e3
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (135), (149), (158), (163), (164),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (170), (191), (196), (200), (210), (214),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (229), (232), (256), (268), (279), (17762),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17764), (17774), (19475), (19479), (19482),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19488), (19574), (19589), (19596), (19599),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19628), (19629), (19645), (19654), (19663),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19768), (19776), (19785), (19786), (19800),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19802), (19845), (19882), (19883), (19885),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19886), (19890), (function-axioms) are
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #120.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19891)   ~ (all_54_7 = e3)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (19891) imply:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19892)   ~ (all_52_13 = e3)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (42), (135), (163), (164), (170),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (196), (214), (227), (229), (232), (234),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (268), (17764), (17774), (17776), (19482),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19488), (19596), (19599), (19628), (19642),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19645), (19768), (19776), (19785), (19882),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19883), (19892), (function-axioms) are
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #119.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19893)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_24_1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19657), (19779), (19893), (function-axioms) are
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2238.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19894)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19894) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19895)   ~ (all_4_1 = e3)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19896)  op(e0, e2) = all_4_1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19660), (19765), (19895), (19896),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #211.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19897)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19897) implies:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19898)  op(e0, e1) = all_56_23
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19899)  op(e0, all_56_23) = e0
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19625), (19657), (19779), (19786), (19898),
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19899), (function-axioms) are inconsistent by
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #215.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19900)  all_54_14 = e0
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (19581), (19900) are inconsistent by
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1936.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19901)  all_58_3 = e1 & op(e2, e2) = e1
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19488), (19901) are inconsistent by
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1752.
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19902)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19902) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19903)  all_58_7 = e1 & op(e1, e2) = e1
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19903) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19904)  all_58_7 = e1
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19636), (19904) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19905)  e2 = e1
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19641), (19905) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19906)  all_58_5 = e1
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (19768),
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19776), (19906) are inconsistent by sub-proof
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1481.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19907)  all_58_13 = e1 & op(e0, e2) = e1
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19764), (19907) are inconsistent by
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2013.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19908)  all_58_15 = e1 & op(e0, e0) = e1
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (19908) are inconsistent by
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #218.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19909)  all_58_5 = e3 & op(e2, e1) = e3
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19909) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19910)  op(e2, e1) = e3
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19642), (19910), (function-axioms) are
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19911)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19911) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19912)  all_58_8 = e3 & op(e1, e1) = e3
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19582), (19912), (function-axioms) are
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19913)  all_58_14 = e3 & op(e0, e1) = e3
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (19760), (19913), (function-axioms) are
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19914)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17774), (19760), (19914),
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #226.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |   (19915)  all_58_10 = e2 & op(e2, e0) = e2
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19915) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |   (19916)  op(e2, e0) = e2
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (19916), (function-axioms) are
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | |   (19917)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (17768), (19582), (19917),
% 238.29/45.29  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.29  | | | | | | | | | | | | | | | | | |            #167.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19918)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 238.29/45.29  | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (19482), (19581), (19918),
% 238.29/45.29  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.29  | | | | | | | | | | | | | | | |            #1414.
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | |   (19919)  all_16_2 = e0
% 238.29/45.29  | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | COMBINE_EQS: (342), (19919) imply:
% 238.29/45.29  | | | | | | | | | | |   (19920)  all_10_2 = e0
% 238.29/45.29  | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | COMBINE_EQS: (290), (19920) imply:
% 238.29/45.29  | | | | | | | | | | |   (19921)  all_56_1 = e0
% 238.29/45.29  | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | REDUCE: (359), (19920) imply:
% 238.29/45.29  | | | | | | | | | | |   (19922)   ~ (all_52_3 = e0)
% 238.29/45.29  | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | REDUCE: (365), (19920) imply:
% 238.29/45.29  | | | | | | | | | | |   (19923)   ~ (all_52_12 = e0)
% 238.29/45.29  | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | REDUCE: (17777), (19920) imply:
% 238.29/45.29  | | | | | | | | | | |   (19924)   ~ (e1 = e0)
% 238.29/45.29  | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | REDUCE: (45), (19920) imply:
% 238.29/45.29  | | | | | | | | | | |   (19925)  op(e3, e3) = e0
% 238.29/45.29  | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | BETA: splitting (216) gives:
% 238.29/45.29  | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | |   (19926)  all_58_15 = e0 & op(e0, e0) = e0
% 238.29/45.29  | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | ALPHA: (19926) implies:
% 238.29/45.29  | | | | | | | | | | | |   (19927)  op(e0, e0) = e0
% 238.29/45.29  | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | REF_CLOSE: (5), (17774), (19927), (function-axioms) are
% 238.29/45.29  | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.29/45.29  | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | |   (19928)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.29/45.29  | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.29/45.29  | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.29/45.29  | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.29/45.29  | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.29/45.29  | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | ALPHA: (19928) implies:
% 238.29/45.29  | | | | | | | | | | | |   (19929)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.29/45.29  | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.29/45.29  | | | | | | | | | | | |                e1) = e0)
% 238.29/45.29  | | | | | | | | | | | |   (19930)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.29/45.29  | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 238.29/45.29  | | | | | | | | | | | |                e0) = e0)
% 238.29/45.29  | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | BETA: splitting (19929) gives:
% 238.29/45.29  | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | |   (19931)  all_58_12 = e0 & op(e0, e3) = e0
% 238.29/45.29  | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | ALPHA: (19931) implies:
% 238.29/45.29  | | | | | | | | | | | | |   (19932)  op(e0, e3) = e0
% 238.29/45.29  | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | REF_CLOSE: (159), (19922), (19932), (function-axioms) are
% 238.29/45.29  | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 238.29/45.29  | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | |   (19933)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 238.29/45.29  | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.29/45.29  | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | BETA: splitting (19933) gives:
% 238.29/45.29  | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | |   (19934)  all_58_13 = e0 & op(e0, e2) = e0
% 238.29/45.29  | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | ALPHA: (19934) implies:
% 238.29/45.29  | | | | | | | | | | | | | |   (19935)  op(e0, e2) = e0
% 238.29/45.29  | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | REF_CLOSE: (158), (19482), (19935), (function-axioms) are
% 238.29/45.29  | | | | | | | | | | | | | |            inconsistent by sub-proof #2252.
% 238.29/45.29  | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | |   (19936)  all_58_14 = e0 & op(e0, e1) = e0
% 238.29/45.29  | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | ALPHA: (19936) implies:
% 238.29/45.29  | | | | | | | | | | | | | |   (19937)  op(e0, e1) = e0
% 238.29/45.29  | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | BETA: splitting (19930) gives:
% 238.29/45.29  | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | |   (19938)  all_58_9 = e0 & op(e3, e0) = e0
% 238.29/45.29  | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | ALPHA: (19938) implies:
% 238.29/45.29  | | | | | | | | | | | | | | |   (19939)  op(e3, e0) = e0
% 238.29/45.29  | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | REF_CLOSE: (168), (19923), (19939), (function-axioms) are
% 238.29/45.29  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2258.
% 238.29/45.29  | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | |   (19940)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 238.29/45.29  | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.29/45.29  | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | BETA: splitting (19940) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19941)  all_58_10 = e0 & op(e2, e0) = e0
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | ALPHA: (19941) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19942)  op(e2, e0) = e0
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (19483), (19942), (function-axioms) are
% 238.29/45.29  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2324.
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19943)  all_58_11 = e0 & op(e1, e0) = e0
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | ALPHA: (19943) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19944)  all_58_11 = e0
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19945)  op(e1, e0) = e0
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 238.29/45.29  | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (157), (19937) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19946)  all_52_11 = e0
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.29/45.29  | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (19945) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19947)  all_52_14 = e0
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | REDUCE: (141), (19947) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19948)   ~ (all_52_2 = e0)
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | REDUCE: (121), (19946) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19949)   ~ (all_52_8 = e0)
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | REDUCE: (118), (19946) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19950)   ~ (all_52_9 = e0)
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | REDUCE: (385), (19947) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19951)   ~ (all_6_2 = e0)
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | SIMP: (19951) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | |   (19952)   ~ (all_6_2 = e0)
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | |   (19953)   ~ (all_36_2 = e2)
% 238.29/45.29  | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | REDUCE: (328), (19953) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | |   (19954)   ~ (all_6_2 = e2)
% 238.29/45.29  | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | |   (19955)  all_54_10 = e3
% 238.29/45.29  | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (19955) are inconsistent by
% 238.29/45.29  | | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | |   (19956)   ~ (all_54_10 = e3)
% 238.29/45.29  | | | | | | | | | | | | | | | | | |   (19957)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.29/45.29  | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | BETA: splitting (19957) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | |   (19958)  all_54_10 = e2
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (19954), (19958) are inconsistent by
% 238.29/45.29  | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | |   (19959)  all_54_10 = e1 | all_54_10 = e0
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | BETA: splitting (19959) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | |   (19960)  all_54_10 = e1
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (19960) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | |   (19961)  all_6_2 = e1
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | SIMP: (19961) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | |   (19962)  all_6_2 = e1
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (19962) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | |   (19963)  all_56_21 = e1
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (19962) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | |   (19964)   ~ (all_52_8 = e1)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (19962) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | |   (19965)   ~ (all_52_9 = e1)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |   (19966)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19966) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | |   (19967)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19967) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |   (19968)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |            e3
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19968) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |   (19969)   ~ (all_56_31 = e2)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (19969) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |   (19970)  $false
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19970) is inconsistent.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |   (19971)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19971) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19972)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |            e2
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19972) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19973)  op(e2, e3) = e2
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19974)  op(e3, e2) = e2
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (19973) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19975)  all_52_1 = e2
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (19974) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19976)  all_52_4 = e2
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (19975) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19977)   ~ (all_52_9 = e2)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19977) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19978)   ~ (all_52_9 = e2)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (19976) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19979)   ~ (all_52_8 = e2)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19979) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19980)   ~ (all_52_8 = e2)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (19981)  all_54_2 = e3
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (19981) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (19982)  all_52_8 = e3
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19982) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (19983)  all_52_8 = e3
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (19983) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (19984)   ~ (all_52_9 = e3)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (198), (270), (19950), (19965), (19978), (19984)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1790.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (19985)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (19949), (19964), (19980), (19985) are
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1335.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19986)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19986) implies:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19987)   ~ (all_56_21 = e1)
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19963), (19987) imply:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | |   (19988)  $false
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19988) is inconsistent.
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.29  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |   (19989)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (169), (19478), (19922), (19964), (19989),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |            #1616.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (19990)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19990) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |   (19991)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (112), (128), (136), (144), (158), (159),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (168), (169),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |            (170), (194), (213), (223), (266), (297), (380),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |            (381), (385), (17762), (17764), (17775), (19478),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |            (19481), (19483), (19952), (19965), (19991),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |            #135.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |   (19992)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19992) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |   (19993)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19993) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |   (19994)  op(e2, e0) = e0
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (19483), (19994), (function-axioms) are
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2324.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |   (19995)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19995) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |   (19996)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19996) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |   (19997)  op(e1, e0) = e1
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (297), (385), (19952), (19959), (19997),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |            #2302.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |   (19998)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19998) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |   (19999)   ~ (all_56_21 = e1)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19963), (19999) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |   (20000)  $false
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20000) is inconsistent.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | |   (20001)  all_54_10 = e0
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (19952), (20001) are inconsistent by
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | |   (20002)  all_36_2 = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | |   (20003)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 238.29/45.30  | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 238.29/45.30  | | | | | | | | | | | | | | | | |              $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | |              = all_36_1 & $i(all_36_1))
% 238.29/45.30  | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (20002) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | |   (20004)  all_6_2 = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (20004) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | |   (20005)  all_40_2 = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | REDUCE: (17775), (20004) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | |   (20006)   ~ (e3 = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | REDUCE: (39), (20004) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | |   (20007)  op(e1, e1) = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | |   (20008)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | BETA: splitting (20008) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | |   (20009)  all_58_0 = e2 & op(e3, e3) = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | ALPHA: (20009) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | |   (20010)  op(e3, e3) = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19925), (20010), (function-axioms) are
% 238.29/45.30  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | |   (20011)  all_58_2 = e2 & op(e2, e3) = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | ALPHA: (20011) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | |   (20012)  op(e2, e3) = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | |   (20013)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | BETA: splitting (20013) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20014)  all_58_1 = e2 & op(e3, e2) = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | ALPHA: (20014) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20015)  all_58_1 = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20016)  op(e3, e2) = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (20012) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20017)  all_52_1 = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (20016) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20018)  all_52_4 = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (20017) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20019)   ~ (all_52_2 = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | SIMP: (20019) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20020)   ~ (all_52_2 = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (20017) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20021)   ~ (all_52_3 = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (20017) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20022)   ~ (all_52_13 = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (20018) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20023)   ~ (all_52_6 = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | SIMP: (20023) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20024)   ~ (all_52_6 = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (20018) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | |   (20025)   ~ (all_52_12 = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |   (20026)   ~ (all_40_2 = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20005), (20026) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |   (20027)  $false
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20027) is inconsistent.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |   (20028)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | |              = all_40_1 & $i(all_40_1))
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |   (20029)   ~ (all_44_2 = e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17761), (20029) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |   (20030)  $false
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20030) is inconsistent.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |   (20031)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |   (20032)   ~ (all_48_2 = e0)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19477), (20032) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |   (20033)  $false
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20033) is inconsistent.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |   (20034)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | |              = all_48_1 & $i(all_48_1))
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (20035)  all_54_9 = e3
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (20035) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (20036)  all_52_6 = e3
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20036) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (20037)  all_52_6 = e3
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (20037) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (20038)   ~ (all_52_2 = e3)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (20037) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (20039)   ~ (all_52_7 = e3)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20039) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (20040)   ~ (all_52_7 = e3)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (20037) imply:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (20041)  op(e1, e2) = e3
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20042)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20042) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20043)  all_58_1 = e3 & op(e3, e2) = e3
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20043) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20044)  op(e3, e2) = e3
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (162), (170), (195), (267), (20041),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20044), (function-axioms) are inconsistent by
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2190.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20045)  all_58_3 = e3 & op(e2, e2) = e3
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (17776), (20045), (function-axioms) are
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #450.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20046)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20046) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20047)  all_58_7 = e3 & op(e1, e2) = e3
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20047) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20048)  all_58_7 = e3
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20003) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20049)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_36_1 & $i(all_36_0) &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_36_1)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20049) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20050)  op(e1, e2) = all_36_1
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (113), (159),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (167), (168), (214), (224),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (234), (235), (236), (238), (239), (241),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (245), (17766), (17776), (19475), (19479),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19488), (19921), (19922), (19925), (19945),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19948), (20003), (20007), (20012), (20015),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20016), (20028), (20031), (20034), (20038),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20041), (20048), (20050), (function-axioms) are
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #117.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20051)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_36_1)
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20051) implies:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20052)  op(e1, e2) = all_36_1
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (113), (159),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (167), (168), (214), (224),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (234), (235), (236), (238), (239), (241),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (245), (17766), (17776), (19475), (19479),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19488), (19921), (19922), (19925), (19945),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19948), (20003), (20007), (20012), (20015),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20016), (20028), (20031), (20034), (20038),
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20041), (20048), (20052), (function-axioms) are
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #117.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20053)  all_58_13 = e3 & op(e0, e2) = e3
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (20040), (20053), (function-axioms) are
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (20054)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20054) gives:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20055)  all_54_9 = e2
% 238.29/45.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (20024), (20055) are inconsistent by
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1954.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20056)  all_54_9 = e1 | all_54_9 = e0
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20056) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20057)  all_54_9 = e1
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (20057) imply:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20058)  all_52_6 = e1
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20058) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20059)  all_52_6 = e1
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (20059) imply:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20060)   ~ (all_52_2 = e1)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (20059) imply:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20061)  op(e1, e2) = e1
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20062)  all_54_8 = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (20062) imply:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20063)  all_52_2 = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (20063) imply:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20064)   ~ (all_52_3 = e3)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20064) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20065)   ~ (all_52_3 = e3)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20066)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20066) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20067)  all_58_12 = e3 & op(e0, e3) = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20067) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20068)  op(e0, e3) = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (20065), (20068), (function-axioms) are
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20069)  all_58_13 = e3 & op(e0, e2) = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20069) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20070)  op(e0, e2) = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20071)  all_54_12 = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (20065), (20071) are inconsistent by
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20072)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20073)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, all_56_11) = e2)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20073) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20074)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_9 & $i(all_56_9)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20074) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20075)  op(e3, e2) = all_56_9
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20076)  op(e3, all_56_9) = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20072) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20077)  all_54_12 = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (17763), (20077) are inconsistent by
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2264.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20078)  all_54_12 = e1 | all_54_12 = e0
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (257), (19922), (19925), (20016), (20075),
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20076), (20078), (function-axioms) are
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #158.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20079)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20079) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20080)  op(e2, all_56_11) = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19478), (20080) imply:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20081)  op(e2, e0) = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (20081), (function-axioms) are
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20082)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15 & $i(all_56_15))
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20082) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20083)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20083) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20084)  op(e1, e2) = all_56_13
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20085)  op(e1, all_56_13) = e1
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20003) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20086)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_36_1 & $i(all_36_0) &
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_36_1)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20086) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20087)  op(e1, e2) = all_36_1
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (17763), (19922), (20007), (20028),
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20061), (20072), (20084), (20085), (20087),
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #115.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20088)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_36_1)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20088) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20089)  op(e1, e2) = all_36_1
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (17763), (19922), (20007), (20028),
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20061), (20072), (20084), (20085), (20089),
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #115.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20090)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_15 & $i(all_56_15)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (17760), (19922), (20031), (20070),
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20090), (function-axioms) are inconsistent by
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #156.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20091)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20091) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20092)  all_58_14 = e3 & op(e0, e1) = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20092) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20093)  op(e0, e1) = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19937), (20093), (function-axioms) are
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2164.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20094)  all_58_15 = e3 & op(e0, e0) = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20094) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20095)  op(e0, e0) = e3
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17774), (20095), (function-axioms) are
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20096)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (19948), (20020), (20060), (20096) are
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1949.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20097)  all_54_9 = e0
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (19481), (20097) are inconsistent by
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1953.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |   (20098)  all_58_3 = e2 & op(e2, e2) = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (20098) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |   (20099)  op(e2, e2) = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19489), (20099), (function-axioms) are
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2137.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | |   (20100)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (20100) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |   (20101)  all_58_7 = e2 & op(e1, e2) = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (20101) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |   (20102)  all_58_7 = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |   (20103)  op(e1, e2) = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (224),
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |            (225), (226), (19944), (20007), (20102), (20103),
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |            #1674.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |   (20104)  all_58_13 = e2 & op(e0, e2) = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (20104) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |   (20105)  op(e0, e2) = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (20105), (function-axioms) are
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | |   (20106)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 238.29/45.31  | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | BETA: splitting (20106) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | |   (20107)  all_58_6 = e2 & op(e1, e3) = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | ALPHA: (20107) implies:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | |   (20108)  all_58_6 = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | |   (20109)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (162), (223), (226),
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | |            (19481), (20007), (20108), (20109),
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | |            #1278.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | |   (20110)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (19945), (20007), (20110),
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | |            #118.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | |   (20111)  all_58_12 = e2 & op(e0, e3) = e2
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (17763), (20111), (function-axioms) are
% 238.29/45.31  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2315.
% 238.29/45.31  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | 
% 238.29/45.31  | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | 
% 238.29/45.31  | | | | | | | | |   (20112)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0
% 238.29/45.31  | | | | | | | | |              & op(e0, e2) = e0)
% 238.29/45.31  | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | REF_CLOSE: (158), (162), (19481), (19482), (20112),
% 238.29/45.31  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.31  | | | | | | | | |            #1990.
% 238.29/45.31  | | | | | | | | | 
% 238.29/45.31  | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | 
% 238.29/45.31  | | | | | | | End of split
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | Case 2:
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | |   (20113)  all_10_2 = e1
% 238.29/45.31  | | | | | | |   (20114)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 238.29/45.31  | | | | | | |              op(e3, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1))
% 238.29/45.31  | | | | | | |            | ( ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 238.29/45.31  | | | | | | |              $i(all_10_1))
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | | COMBINE_EQS: (349), (20113) imply:
% 238.29/45.31  | | | | | | |   (20115)  all_38_2 = e1
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | | COMBINE_EQS: (290), (20113) imply:
% 238.29/45.31  | | | | | | |   (20116)  all_56_1 = e1
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | | REDUCE: (355), (20113) imply:
% 238.29/45.31  | | | | | | |   (20117)   ~ (all_52_1 = e1)
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | | REDUCE: (357), (20113) imply:
% 238.29/45.31  | | | | | | |   (20118)   ~ (all_52_2 = e1)
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | | REDUCE: (359), (20113) imply:
% 238.29/45.31  | | | | | | |   (20119)   ~ (all_52_3 = e1)
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | | REDUCE: (361), (20113) imply:
% 238.29/45.31  | | | | | | |   (20120)   ~ (all_52_4 = e1)
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | | REDUCE: (363), (20113) imply:
% 238.29/45.31  | | | | | | |   (20121)   ~ (all_52_8 = e1)
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | | REDUCE: (365), (20113) imply:
% 238.29/45.31  | | | | | | |   (20122)   ~ (all_52_12 = e1)
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | | REDUCE: (45), (20113) imply:
% 238.29/45.31  | | | | | | |   (20123)  op(e3, e3) = e1
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | | BETA: splitting (52) gives:
% 238.29/45.31  | | | | | | | 
% 238.29/45.31  | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | 
% 238.29/45.31  | | | | | | | |   (20124)   ~ (all_14_2 = e0)
% 238.29/45.31  | | | | | | | | 
% 238.29/45.31  | | | | | | | | REDUCE: (344), (20124) imply:
% 238.29/45.31  | | | | | | | |   (20125)   ~ (all_8_2 = e0)
% 238.29/45.31  | | | | | | | | 
% 238.29/45.31  | | | | | | | | BETA: splitting (58) gives:
% 238.29/45.31  | | | | | | | | 
% 238.29/45.31  | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | 
% 238.29/45.31  | | | | | | | | |   (20126)   ~ (all_18_2 = e0)
% 238.29/45.31  | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | REDUCE: (339), (20126) imply:
% 238.29/45.31  | | | | | | | | |   (20127)   ~ (all_6_2 = e0)
% 238.29/45.31  | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | BETA: splitting (64) gives:
% 238.29/45.31  | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | |   (20128)   ~ (all_22_2 = e1)
% 238.29/45.31  | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | REDUCE: (326), (20128) imply:
% 238.29/45.31  | | | | | | | | | |   (20129)   ~ (all_8_2 = e1)
% 238.29/45.31  | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | BETA: splitting (199) gives:
% 238.29/45.31  | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | |   (20130)  all_54_5 = e3
% 238.29/45.31  | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | COMBINE_EQS: (275), (20130) imply:
% 238.29/45.31  | | | | | | | | | | |   (20131)  all_8_2 = e3
% 238.29/45.31  | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | REDUCE: (17776), (20131) imply:
% 238.29/45.31  | | | | | | | | | | |   (20132)  $false
% 238.29/45.31  | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | CLOSE: (20132) is inconsistent.
% 238.29/45.31  | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | |   (20133)   ~ (all_54_5 = e3)
% 238.29/45.31  | | | | | | | | | | |   (20134)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 238.29/45.31  | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | BETA: splitting (20134) gives:
% 238.29/45.31  | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | |   (20135)  all_54_5 = e2
% 238.29/45.31  | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | COMBINE_EQS: (275), (20135) imply:
% 238.29/45.31  | | | | | | | | | | | |   (20136)  all_8_2 = e2
% 238.29/45.31  | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | REDUCE: (366), (20136) imply:
% 238.29/45.31  | | | | | | | | | | | |   (20137)   ~ (all_52_1 = e2)
% 238.29/45.31  | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | REDUCE: (369), (20136) imply:
% 238.29/45.31  | | | | | | | | | | | |   (20138)   ~ (all_52_4 = e2)
% 238.29/45.31  | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | REDUCE: (17776), (20136) imply:
% 238.29/45.31  | | | | | | | | | | | |   (20139)   ~ (e3 = e2)
% 238.29/45.31  | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | REDUCE: (42), (20136) imply:
% 238.29/45.31  | | | | | | | | | | | |   (20140)  op(e2, e2) = e2
% 238.29/45.31  | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | BETA: splitting (243) gives:
% 238.29/45.31  | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | |   (20141)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 238.29/45.31  | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 238.29/45.31  | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | BETA: splitting (20141) gives:
% 238.29/45.31  | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | |   (20142)  all_58_0 = e2 & op(e3, e3) = e2
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | ALPHA: (20142) implies:
% 238.29/45.31  | | | | | | | | | | | | | |   (20143)  op(e3, e3) = e2
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | REF_CLOSE: (6), (20123), (20143), (function-axioms) are
% 238.29/45.31  | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | |   (20144)  all_58_2 = e2 & op(e2, e3) = e2
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | ALPHA: (20144) implies:
% 238.29/45.31  | | | | | | | | | | | | | |   (20145)  op(e2, e3) = e2
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | REF_CLOSE: (167), (20137), (20145), (function-axioms) are
% 238.29/45.31  | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | End of split
% 238.29/45.31  | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | |   (20146)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 238.29/45.31  | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 238.29/45.31  | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | BETA: splitting (20146) gives:
% 238.29/45.31  | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | |   (20147)  all_58_6 = e2 & op(e1, e3) = e2
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | ALPHA: (20147) implies:
% 238.29/45.31  | | | | | | | | | | | | | |   (20148)  all_58_6 = e2
% 238.29/45.31  | | | | | | | | | | | | | |   (20149)  op(e1, e3) = e2
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 238.29/45.31  | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | Case 1:
% 238.29/45.31  | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | |   (20150)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 238.29/45.31  | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 238.29/45.31  | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (20123), (20138), (20150),
% 238.29/45.31  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.31  | | | | | | | | | | | | | | |            #114.
% 238.29/45.31  | | | | | | | | | | | | | | | 
% 238.29/45.31  | | | | | | | | | | | | | | Case 2:
% 238.29/45.31  | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | |   (20151)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 238.29/45.32  | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | BETA: splitting (20151) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | |   (20152)  all_58_4 = e2 & op(e3, e1) = e2
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | ALPHA: (20152) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | |   (20153)  op(e3, e1) = e2
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 238.29/45.32  | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (20149) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | |   (20154)  all_52_2 = e2
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 238.29/45.32  | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (20153) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | |   (20155)  all_52_8 = e2
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | REDUCE: (144), (20154) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | |   (20156)   ~ (all_52_3 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | REDUCE: (123), (20155) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | |   (20157)   ~ (all_52_9 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | SIMP: (20157) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | |   (20158)   ~ (all_52_9 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | REDUCE: (121), (20155) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | |   (20159)   ~ (all_52_11 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | REDUCE: (120), (20155) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | |   (20160)   ~ (all_52_12 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | REDUCE: (380), (20155) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | |   (20161)   ~ (all_6_2 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | SIMP: (20161) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | |   (20162)   ~ (all_6_2 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | |   (20163)   ~ (all_38_2 = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | REDUCE: (20115), (20163) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | |   (20164)  $false
% 238.29/45.32  | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | CLOSE: (20164) is inconsistent.
% 238.29/45.32  | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.32  | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | |   (20165)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 238.29/45.32  | | | | | | | | | | | | | | | | |              & op(e3, e1) = all_38_1 & $i(all_38_0) &
% 238.29/45.32  | | | | | | | | | | | | | | | | |              $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 238.29/45.32  | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | BETA: splitting (20165) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | |   (20166)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 238.29/45.32  | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_38_1 & $i(all_38_0) &
% 238.29/45.32  | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | ALPHA: (20166) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | |   (20167)   ~ (all_38_0 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | | |   (20168)  op(e3, e1) = all_38_1
% 238.29/45.32  | | | | | | | | | | | | | | | | | |   (20169)  op(all_38_1, e3) = all_38_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | |   (20170)  all_54_10 = e3
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (20170) are inconsistent by
% 238.29/45.32  | | | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | |   (20171)   ~ (all_54_10 = e3)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | |   (20172)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | BETA: splitting (20114) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | |   (20173)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_10_1 & $i(all_10_0) &
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | ALPHA: (20173) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | |   (20174)   ~ (all_10_0 = e0)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | |   (20175)  op(e3, e1) = all_10_1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | |   (20176)  op(all_10_1, e3) = all_10_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | BETA: splitting (20172) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | |   (20177)  all_54_10 = e2
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (20162), (20177) are inconsistent by
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | |   (20178)   ~ (all_54_10 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | |   (20179)  all_54_10 = e1 | all_54_10 = e0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20179) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | |   (20180)  all_54_10 = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (20180) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | |   (20181)  all_6_2 = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | SIMP: (20181) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | |   (20182)  all_6_2 = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (20182) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | |   (20183)  all_56_21 = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (383), (20182) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | |   (20184)   ~ (all_52_11 = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (20182) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | |   (20185)   ~ (all_52_14 = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17775), (20182) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | |   (20186)   ~ (e3 = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20162), (20182) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | |   (20187)   ~ (e2 = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (20182) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | |   (20188)  op(e1, e1) = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | |   (20189)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20189) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | |   (20190)  all_58_12 = e1 & op(e0, e3) = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (20119), (20190), (function-axioms) are
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | |   (20191)  all_58_13 = e1 & op(e0, e2) = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20191) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | |   (20192)  all_58_13 = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | |   (20193)  op(e0, e2) = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (20194)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20194) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20195)  all_58_9 = e1 & op(e3, e0) = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (112), (120), (158), (160), (165),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (213), (297), (381), (17762),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17764), (20127), (20138), (20179), (20183),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            (20195), (function-axioms) are inconsistent by
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #240.
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20196)  all_58_10 = e1 & op(e2, e0) = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20196) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20197)  op(e2, e0) = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e1,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (20193) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20198)  all_52_7 = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (164), (20197) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20199)  all_52_13 = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_38_1,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (20153), (20168) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20200)  all_38_1 = e2
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (20168),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |              (20175) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20201)  all_38_1 = all_10_1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20200), (20201) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20202)  all_10_1 = e2
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20202) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20203)  all_10_1 = e2
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (20198) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20204)   ~ (all_52_11 = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (20199) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20205)   ~ (all_52_9 = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (20199) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20206)   ~ (all_52_14 = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20169), (20200) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20207)  op(e2, e3) = all_38_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20176), (20203) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20208)  op(e2, e3) = all_10_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20209)   ~ (all_44_2 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17761), (20209) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20210)  $false
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20210) is inconsistent.
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20211)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20212)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20212) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20213)  op(e0, e2) = all_4_1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_4_1,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (20193), (20213) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20214)  all_4_1 = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e3, e2, simplifying with (167), (20208)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20215)  all_52_1 = all_10_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_0, e3, e2, simplifying with (167), (20207)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20216)  all_52_1 = all_38_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20215), (20216) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20217)  all_38_0 = all_10_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (20215) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20218)  all_54_4 = all_10_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (20215) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20219)   ~ (all_52_3 = all_10_0)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20219) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20220)   ~ (all_52_3 = all_10_0)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (20215) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20221)   ~ (all_52_9 = all_10_0)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20221) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20222)   ~ (all_52_9 = all_10_0)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20117), (20215) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20223)   ~ (all_10_0 = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20167), (20217) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20224)   ~ (all_10_0 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20225)  all_54_4 = e3
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20218), (20225) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20226)  all_10_0 = e3
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20220), (20226) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20227)   ~ (all_52_3 = e3)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20222), (20226) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20228)   ~ (all_52_9 = e3)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20208), (20226) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20229)  op(e2, e3) = e3
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (117), (139),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (159), (160), (162), (163), (164), (165),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (170), (190), (192), (198),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (214), (216), (219), (223), (226), (231),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (245), (255), (257), (270), (297), (17762),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17763), (17764), (17765), (17766), (17774),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20116), (20117), (20118), (20119), (20121),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20122), (20127), (20138), (20140), (20148),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20149), (20153), (20158), (20179), (20184),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20185), (20188), (20192), (20193), (20205),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20211), (20227), (20228), (20229),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #107.
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20230)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20174), (20218), (20223), (20224), (20230) are
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #106.
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20231)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20231) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20232)   ~ (all_4_1 = e3)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20233)  op(e0, e2) = all_4_1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_4_1,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (20193), (20233) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20234)  all_4_1 = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e3, e2, simplifying with (167), (20208)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20235)  all_52_1 = all_10_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_0, e3, e2, simplifying with (167), (20207)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20236)  all_52_1 = all_38_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20235), (20236) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20237)  all_38_0 = all_10_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (20235) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20238)  all_54_4 = all_10_0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (20235) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20239)   ~ (all_52_3 = all_10_0)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20239) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20240)   ~ (all_52_3 = all_10_0)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (20235) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20241)   ~ (all_52_9 = all_10_0)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20241) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20242)   ~ (all_52_9 = all_10_0)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20117), (20235) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20243)   ~ (all_10_0 = e1)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20167), (20237) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20244)   ~ (all_10_0 = e2)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20245)  all_54_4 = e3
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20238), (20245) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20246)  all_10_0 = e3
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20240), (20246) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20247)   ~ (all_52_3 = e3)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20242), (20246) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20248)   ~ (all_52_9 = e3)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20208), (20246) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20249)  op(e2, e3) = e3
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20250)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20116), (20153), (20249), (20250),
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #113.
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20251)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20251) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20252)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20252) implies:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20253)  op(e1, e3) = all_56_5
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20254)  op(e1, all_56_5) = e1
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20255)  all_54_6 = e3
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (20255) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20256)  all_52_9 = e3
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20248), (20256) imply:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20257)  $false
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20257) is inconsistent.
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20258)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20258) gives:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20259)  all_54_6 = e2
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (20259) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20260)  all_52_9 = e2
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20158), (20260) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20261)  $false
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20261) is inconsistent.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20262)  all_54_6 = e1 | all_54_6 = e0
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20263)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20263) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20264)  all_58_0 = e3 & op(e3, e3) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20264) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20265)  op(e3, e3) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (20117), (20118),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20119), (20265), (function-axioms) are
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20266)  all_58_2 = e3 & op(e2, e3) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20266) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20267)  all_58_2 = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20268)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20268) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20269)  all_58_12 = e3 & op(e0, e3) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20269) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20270)  op(e0, e3) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (20247), (20270), (function-axioms) are
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20271)  all_58_13 = e3 & op(e0, e2) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20271) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20272)  op(e0, e2) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20211), (20232), (20233), (20272),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #211.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20273)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20273) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20274)  all_58_14 = e3 & op(e0, e1) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20274) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20275)  op(e0, e1) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (39), (117), (139), (158),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (164), (165), (168), (169), (170),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (192), (213), (216), (223), (226), (231),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (255), (257), (270), (297), (17762), (17763),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17764), (17765), (17766), (17774), (20119),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20121), (20122), (20127), (20138), (20140),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20148), (20149), (20179), (20184), (20185),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20188), (20193), (20205), (20247), (20253),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20254), (20262), (20267), (20275),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #111.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20276)  all_58_15 = e3 & op(e0, e0) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20276) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20277)  op(e0, e0) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17774), (20277), (function-axioms) are
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20278)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (20247), (20253), (20254), (20278),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #110.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20279)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20279) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20280)  op(e0, e3) = all_56_7
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20281)  op(e0, all_56_7) = e0
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20282)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20282) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20283)  all_58_12 = e3 & op(e0, e3) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20283) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20284)  op(e0, e3) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (20280), (20281), (20284), (function-axioms)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2070.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20285)  all_58_13 = e3 & op(e0, e2) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20285) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20286)  op(e0, e2) = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20211), (20232), (20233), (20286),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #211.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20287)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (216), (17774), (20193),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20211), (20280), (20281), (20287),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #108.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20288)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20174), (20238), (20243), (20244), (20288) are
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #106.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (20289)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (39), (160), (164), (168),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (17766), (17767), (17775),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (20127), (20148), (20185), (20289),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | |            #104.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | |   (20290)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (39), (157), (164), (168),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (17766), (17767), (17775),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | |            (20127), (20148), (20184), (20290),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | |            #103.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | |   (20291)  all_54_10 = e0
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (20127), (20291) are inconsistent by
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |   (20292)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | ALPHA: (20292) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |   (20293)   ~ (all_10_1 = e2)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |   (20294)  op(e3, e1) = all_10_1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20153), (20168), (20293), (20294),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |            #1114.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.33  | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | |   (20295)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 238.29/45.33  | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | ALPHA: (20295) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | |   (20296)   ~ (all_38_1 = e0)
% 238.29/45.33  | | | | | | | | | | | | | | | | | |   (20297)  op(e3, e1) = all_38_1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | |   (20298)  all_54_10 = e3
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (20298) are inconsistent by
% 238.29/45.33  | | | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | |   (20299)   ~ (all_54_10 = e3)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | |   (20300)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | BETA: splitting (20114) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |   (20301)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_10_1 & $i(all_10_0) &
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | ALPHA: (20301) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |   (20302)   ~ (all_10_0 = e0)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |   (20303)  op(e3, e1) = all_10_1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | |   (20304)  op(all_10_1, e3) = all_10_0
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | BETA: splitting (20300) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | |   (20305)  all_54_10 = e2
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (20162), (20305) are inconsistent by
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | |   (20306)   ~ (all_54_10 = e2)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | |   (20307)  all_54_10 = e1 | all_54_10 = e0
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20307) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | |   (20308)  all_54_10 = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (20308) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | |   (20309)  all_6_2 = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | SIMP: (20309) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | |   (20310)  all_6_2 = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (20310) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | |   (20311)  all_56_21 = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (383), (20310) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | |   (20312)   ~ (all_52_11 = e1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (20310) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | |   (20313)   ~ (all_52_14 = e1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17775), (20310) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | |   (20314)   ~ (e3 = e1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20162), (20310) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | |   (20315)   ~ (e2 = e1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (20310) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | |   (20316)  op(e1, e1) = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | |   (20317)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20317) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | |   (20318)  all_58_12 = e1 & op(e0, e3) = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (20119), (20318), (function-axioms) are
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | |   (20319)  all_58_13 = e1 & op(e0, e2) = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20319) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | |   (20320)  all_58_13 = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | |   (20321)  op(e0, e2) = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (20322)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20322) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20323)  all_58_9 = e1 & op(e3, e0) = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (112), (120), (158), (160), (165),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (213), (297), (381), (17762),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17764), (20127), (20138), (20307), (20311),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (20323), (function-axioms) are inconsistent by
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #240.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20324)  all_58_10 = e1 & op(e2, e0) = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20324) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20325)  op(e2, e0) = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e1,
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (20321) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20326)  all_52_7 = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (164), (20325) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20327)  all_52_13 = e1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_38_1,
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (20153), (20297) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20328)  all_38_1 = e2
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (20297),
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |              (20303) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20329)  all_38_1 = all_10_1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20328), (20329) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20330)  all_10_1 = e2
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20330) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20331)  all_10_1 = e2
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (20326) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20332)   ~ (all_52_11 = e1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (20327) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20333)   ~ (all_52_9 = e1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (20327) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20334)   ~ (all_52_14 = e1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20304), (20331) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20335)  op(e2, e3) = all_10_0
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20336)   ~ (all_44_2 = e2)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17761), (20336) imply:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20337)  $false
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20337) is inconsistent.
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20338)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20339)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20339) implies:
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20340)  op(e0, e2) = all_4_1
% 238.29/45.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (39), (117), (139), (146), (148), (158),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (190), (192), (198), (200),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (214), (216), (219), (223), (226), (231),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (245), (255), (257), (270), (279), (297),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17762), (17763), (17764), (17765), (17766),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (20116), (20117), (20118), (20119),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20121), (20122), (20127), (20137), (20138),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20140), (20148), (20149), (20153), (20158),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20302), (20307), (20312), (20313), (20316),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20320), (20321), (20333), (20335), (20338),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20340), (function-axioms) are inconsistent by
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #102.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20341)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20341) implies:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20342)  op(e0, e2) = all_4_1
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (39), (117), (139), (146), (148), (158),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (190), (192), (198), (200),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (214), (216), (219), (223), (226), (231),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (245), (255), (257), (270), (279), (297),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17762), (17763), (17764), (17765), (17766),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (20116), (20117), (20118), (20119),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20121), (20122), (20127), (20137), (20138),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20140), (20148), (20149), (20153), (20158),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20302), (20307), (20312), (20313), (20316),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20320), (20321), (20333), (20335), (20338),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20342), (function-axioms) are inconsistent by
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #102.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (20343)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (39), (160), (164), (168),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (17766), (17767), (17775),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (20127), (20148), (20313), (20343),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | |            #104.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |   (20344)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (39), (157), (164), (168),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (226), (17766), (17767), (17775),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |            (20127), (20148), (20312), (20344),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |            #103.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | |   (20345)  all_54_10 = e0
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (20127), (20345) are inconsistent by
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20346)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | ALPHA: (20346) implies:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20347)   ~ (all_10_1 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20348)  op(e3, e1) = all_10_1
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20153), (20297), (20347), (20348),
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |            #1114.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | |   (20349)  all_58_9 = e2 & op(e3, e0) = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | REF_CLOSE: (168), (17766), (20349), (function-axioms) are
% 238.29/45.34  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2318.
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | |   (20350)  all_58_12 = e2 & op(e0, e3) = e2
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | REF_CLOSE: (159), (17763), (20350), (function-axioms) are
% 238.29/45.34  | | | | | | | | | | | | | |            inconsistent by sub-proof #2315.
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | |   (20351)  all_54_5 = e1 | all_54_5 = e0
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | REF_CLOSE: (275), (20125), (20129), (20351) are inconsistent
% 238.29/45.34  | | | | | | | | | | | |            by sub-proof #2300.
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | |   (20352)  all_22_2 = e1
% 238.29/45.34  | | | | | | | | | |   (20353)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 238.29/45.34  | | | | | | | | | |              & op(e2, e1) = all_22_1 & $i(all_22_0) &
% 238.29/45.34  | | | | | | | | | |              $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1)
% 238.29/45.34  | | | | | | | | | |              = all_22_1 & $i(all_22_1))
% 238.29/45.34  | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | COMBINE_EQS: (326), (20352) imply:
% 238.29/45.34  | | | | | | | | | |   (20354)  all_8_2 = e1
% 238.29/45.34  | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | SIMP: (20354) implies:
% 238.29/45.34  | | | | | | | | | |   (20355)  all_8_2 = e1
% 238.29/45.34  | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | COMBINE_EQS: (347), (20355) imply:
% 238.29/45.34  | | | | | | | | | |   (20356)  all_30_2 = e1
% 238.29/45.34  | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | COMBINE_EQS: (353), (20355) imply:
% 238.29/45.34  | | | | | | | | | |   (20357)  all_56_11 = e1
% 238.29/45.34  | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | REDUCE: (373), (20355) imply:
% 238.29/45.34  | | | | | | | | | |   (20358)   ~ (all_52_7 = e1)
% 238.29/45.34  | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | REDUCE: (377), (20355) imply:
% 238.29/45.34  | | | | | | | | | |   (20359)   ~ (all_52_13 = e1)
% 238.29/45.34  | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | REDUCE: (17776), (20355) imply:
% 238.29/45.34  | | | | | | | | | |   (20360)   ~ (e3 = e1)
% 238.29/45.34  | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | BETA: splitting (217) gives:
% 238.29/45.34  | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | |   (20361)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.29/45.34  | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.29/45.34  | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | BETA: splitting (20361) gives:
% 238.29/45.34  | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | |   (20362)  all_58_12 = e1 & op(e0, e3) = e1
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | REF_CLOSE: (159), (20119), (20362), (function-axioms) are
% 238.29/45.34  | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | |   (20363)  all_58_13 = e1 & op(e0, e2) = e1
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | REF_CLOSE: (158), (20358), (20363), (function-axioms) are
% 238.29/45.34  | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | |   (20364)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.29/45.34  | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.29/45.34  | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | BETA: splitting (20364) gives:
% 238.29/45.34  | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | |   (20365)  all_58_14 = e1 & op(e0, e1) = e1
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | ALPHA: (20365) implies:
% 238.29/45.34  | | | | | | | | | | | |   (20366)  op(e0, e1) = e1
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.29/45.34  | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | |   (20367)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.29/45.34  | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.29/45.34  | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | BETA: splitting (20367) gives:
% 238.29/45.34  | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | |   (20368)  all_58_9 = e1 & op(e3, e0) = e1
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | REF_CLOSE: (168), (20122), (20368), (function-axioms) are
% 238.29/45.34  | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | |   (20369)  all_58_10 = e1 & op(e2, e0) = e1
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | REF_CLOSE: (164), (20359), (20369), (function-axioms) are
% 238.29/45.34  | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | End of split
% 238.29/45.34  | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | |   (20370)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.29/45.34  | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.29/45.34  | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | BETA: splitting (20370) gives:
% 238.29/45.34  | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | |   (20371)  all_58_11 = e1 & op(e1, e0) = e1
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | ALPHA: (20371) implies:
% 238.29/45.34  | | | | | | | | | | | | | |   (20372)  op(e1, e0) = e1
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 238.29/45.34  | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (157), (20366) gives:
% 238.29/45.34  | | | | | | | | | | | | | |   (20373)  all_52_11 = e1
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.29/45.34  | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (20372) gives:
% 238.29/45.34  | | | | | | | | | | | | | |   (20374)  all_52_14 = e1
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | REDUCE: (126), (20374) imply:
% 238.29/45.34  | | | | | | | | | | | | | |   (20375)   ~ (all_52_6 = e1)
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | REDUCE: (118), (20373) imply:
% 238.29/45.34  | | | | | | | | | | | | | |   (20376)   ~ (all_52_9 = e1)
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | REDUCE: (385), (20374) imply:
% 238.29/45.34  | | | | | | | | | | | | | |   (20377)   ~ (all_6_2 = e1)
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | SIMP: (20377) implies:
% 238.29/45.34  | | | | | | | | | | | | | |   (20378)   ~ (all_6_2 = e1)
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 238.29/45.34  | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | |   (20379)  all_54_10 = e3
% 238.29/45.34  | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (20379) are inconsistent by
% 238.29/45.34  | | | | | | | | | | | | | | |            sub-proof #2313.
% 238.29/45.34  | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | |   (20380)   ~ (all_54_10 = e3)
% 238.29/45.34  | | | | | | | | | | | | | | |   (20381)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.29/45.34  | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | BETA: splitting (20381) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | |   (20382)  all_54_10 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (20382) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | |   (20383)  all_6_2 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | SIMP: (20383) implies:
% 238.29/45.34  | | | | | | | | | | | | | | | |   (20384)  all_6_2 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (20384) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | |   (20385)  all_36_2 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | COMBINE_EQS: (322), (20384) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | |   (20386)  all_40_2 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (20384) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | |   (20387)  all_56_21 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | REDUCE: (367), (20384) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | |   (20388)   ~ (all_52_2 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | REDUCE: (378), (20384) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | |   (20389)   ~ (all_52_6 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | REDUCE: (17775), (20384) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | |   (20390)   ~ (e3 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | REDUCE: (39), (20384) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | |   (20391)  op(e1, e1) = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | |   (20392)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | BETA: splitting (20392) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | |   (20393)  all_58_0 = e2 & op(e3, e3) = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | ALPHA: (20393) implies:
% 238.29/45.34  | | | | | | | | | | | | | | | | | |   (20394)  op(e3, e3) = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (20123), (20394), (function-axioms) are
% 238.29/45.34  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | |   (20395)  all_58_1 = e2 & op(e3, e2) = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | ALPHA: (20395) implies:
% 238.29/45.34  | | | | | | | | | | | | | | | | | |   (20396)  all_58_1 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | |   (20397)  op(e3, e2) = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | |   (20398)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | BETA: splitting (20398) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20399)  all_58_0 = e2 & op(e3, e3) = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | ALPHA: (20399) implies:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20400)  op(e3, e3) = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (20123), (20400), (function-axioms) are
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20401)  all_58_2 = e2 & op(e2, e3) = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | ALPHA: (20401) implies:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20402)  all_58_2 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20403)  op(e2, e3) = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (20403) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20404)  all_52_1 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (20397) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20405)  all_52_4 = e2
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (20404) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20406)   ~ (all_52_2 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (20404) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20407)   ~ (all_52_9 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | SIMP: (20407) implies:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20408)   ~ (all_52_9 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (20404) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20409)   ~ (all_52_13 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (20405) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20410)   ~ (all_52_6 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (20405) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20411)   ~ (all_52_7 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (20405) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20412)   ~ (all_52_8 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | SIMP: (20412) implies:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20413)   ~ (all_52_8 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (20405) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | |   (20414)   ~ (all_52_12 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | |   (20415)   ~ (all_30_2 = e1)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | REDUCE: (20356), (20415) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | |   (20416)  $false
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | CLOSE: (20416) is inconsistent.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | |   (20417)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = all_30_1 & $i(all_30_0) &
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | |              $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | |              = all_30_1 & $i(all_30_1))
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | |   (20418)   ~ (all_36_2 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20385), (20418) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | |   (20419)  $false
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20419) is inconsistent.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | |   (20420)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_36_1 & $i(all_36_0) &
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | |              $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | |              = all_36_1 & $i(all_36_1))
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |   (20421)   ~ (all_38_2 = e1)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20115), (20421) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |   (20422)  $false
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20422) is inconsistent.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |   (20423)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e1) = all_38_1 & $i(all_38_0) &
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | |   (20424)   ~ (all_40_2 = e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20386), (20424) imply:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | |   (20425)  $false
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20425) is inconsistent.
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | |   (20426)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | |              = all_40_1 & $i(all_40_1))
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (20427)  all_54_7 = e3
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (20427) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (20428)  all_52_13 = e3
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20428) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (20429)  all_52_13 = e3
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (20429) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (20430)   ~ (all_52_9 = e3)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (20429) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (20431)   ~ (all_52_12 = e3)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20432)  all_54_3 = e3
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (20431), (20432) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20433)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20433) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20434)  all_54_3 = e2
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (17766), (20434) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2290.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20435)   ~ (all_54_3 = e2)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20436)  all_54_3 = e1 | all_54_3 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20437)  all_54_6 = e3
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (20430), (20437) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20438)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20439)  all_58_15 = e0 & op(e0, e0) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20439) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20440)  op(e0, e0) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (20440), (function-axioms) are
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20441)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20441) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20442)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20436) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20443)  all_54_3 = e1
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (20122), (20443) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2289.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20444)  all_54_3 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (20444) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20445)  all_52_12 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20445) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20446)  all_52_12 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (20446) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20447)   ~ (all_52_8 = e0)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17766), (20446) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20448)   ~ (e2 = e0)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20122), (20446) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20449)   ~ (e1 = e0)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20450)  all_54_2 = e3
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (20450) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20451)  all_52_8 = e3
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20451) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20452)  all_52_8 = e3
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (20452) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20453)  op(e3, e1) = e3
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20442) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20454)  all_58_9 = e0 & op(e3, e0) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20454) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20455)  all_58_9 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20456)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20456) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20457)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20457) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20458)  op(e3, e1) = all_56_17
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20459)  op(e3, all_56_17) = e3
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20460)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (42), (244), (246),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20123), (20125), (20396), (20402), (20455),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20460), (function-axioms) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #101.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20461)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20461) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20462)  all_58_5 = e0 & op(e2, e1) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20462) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20463)  op(e2, e1) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20423) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20464)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_38_1 & $i(all_38_0) &
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20464) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20465)  op(e3, e1) = all_38_1
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (20117), (20118),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20119), (20353), (20417), (20453), (20458),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20459), (20463), (20465), (function-axioms) are
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #100.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20466)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20466) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20467)  op(e3, e1) = all_38_1
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (20117), (20118),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20119), (20353), (20417), (20453), (20458),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20459), (20463), (20467), (function-axioms) are
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #100.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20468)  all_58_10 = e0 & op(e2, e0) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20468) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20469)  op(e2, e0) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (164), (270), (20376), (20408), (20438),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20469), (function-axioms) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #459.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20470)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20470) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20471)  op(e2, e1) = all_56_19
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20472)  op(e2, all_56_19) = e2
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20438) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20473)  all_54_6 = e2
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (20408), (20473) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20474)  all_54_6 = e1 | all_54_6 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20474) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20475)  all_54_6 = e1
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (20376), (20475) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2246.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20476)  all_54_6 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (20476) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20477)  all_52_9 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20477) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20478)  all_52_9 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (20478) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20479)  op(e2, e1) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19, e1, e2, simplifying with (20471),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (20479) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20480)  all_56_19 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20472), (20480) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20481)  op(e2, e0) = e2
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (20481), (function-axioms) are
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20482)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20482) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20483)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20483) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20484)  op(e1, all_56_21) = e1
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20387), (20484) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20485)  op(e1, e2) = e1
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (20375), (20485), (function-axioms) are
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #99.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20486)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20486) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20487)  op(e0, e1) = all_56_23
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20488)  op(e0, all_56_23) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20489)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (42), (244), (246),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20123), (20125), (20396), (20402), (20455),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20489), (function-axioms) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #101.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20490)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20490) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20491)  all_58_5 = e0 & op(e2, e1) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20491) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20492)  op(e2, e1) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20353) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20366), (20487), (20488), (function-axioms)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #216.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20493)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_22_1)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20493) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20494)   ~ (all_22_1 = e0)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20495)  op(e2, e1) = all_22_1
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20417), (20492), (20494), (20495),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1356.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20496)  all_58_10 = e0 & op(e2, e0) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20496) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20497)  op(e2, e0) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (164), (270), (20376), (20408), (20438),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20497), (function-axioms) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #459.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20498)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20498) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20499)  all_58_10 = e0 & op(e2, e0) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20499) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20500)  op(e2, e0) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (164), (270), (20376), (20408), (20438),
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20500), (function-axioms) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #459.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20501)  all_58_11 = e0 & op(e1, e0) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20501) implies:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20502)  op(e1, e0) = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20372), (20502), (function-axioms) are
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2284.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20503)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (20121), (20413), (20447), (20503) are
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1335.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (20504)   ~ (all_54_7 = e3)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (20505)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (20504) imply:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (20506)   ~ (all_52_13 = e3)
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20505) gives:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20507)  all_54_7 = e2
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (17767), (20507) are inconsistent by
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1997.
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20508)   ~ (all_54_7 = e2)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20509)  all_54_7 = e1 | all_54_7 = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20510)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (164), (165), (167), (232), (20117),
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20359), (20376), (20403), (20510),
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #145.
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20511)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20511) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20512)  all_58_5 = e3 & op(e2, e1) = e3
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20512) implies:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20513)  op(e2, e1) = e3
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20514)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20514) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20515)  all_58_9 = e3 & op(e3, e0) = e3
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20515) implies:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20516)  op(e3, e0) = e3
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20509) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20517)  all_54_7 = e1
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (20517) imply:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20518)  all_52_13 = e1
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20359), (20518) imply:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20519)  $false
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20519) is inconsistent.
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20520)  all_54_7 = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (20520) imply:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20521)  all_52_13 = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (20521) imply:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20522)   ~ (all_52_12 = e0)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20506), (20521) imply:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20523)   ~ (e3 = e0)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17767), (20521) imply:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20524)   ~ (e2 = e0)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20359), (20521) imply:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20525)   ~ (e1 = e0)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (20521) imply:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20526)  op(e2, e0) = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20527)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (20123), (20397), (20527),
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1017.
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20528)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20528) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20529)  all_58_4 = e0 & op(e3, e1) = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20529) implies:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20530)  op(e3, e1) = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20353) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20531)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_22_1 & $i(all_22_0) &
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_22_1)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20531) implies:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20532)  op(e2, e1) = all_22_1
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20533)  op(all_22_1, e2) = all_22_0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20534)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (164), (167), (241), (269),
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17767), (20114), (20117), (20118), (20119),
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20359), (20417), (20423), (20509), (20513),
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20516), (20526), (20530), (20534),
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #96.
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20535)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20535) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20536)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (20372), (20391), (20417), (20513), (20536),
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #95.
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20537)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20537) implies:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20538)  op(e0, all_56_31) = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (20538) imply:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20539)  op(e0, e2) = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20114) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20540)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_10_1 & $i(all_10_0) &
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20540) implies:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20541)  op(e3, e1) = all_10_1
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20417) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20542)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_30_1 & $i(all_30_0) &
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20542) implies:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20543)  op(e2, e1) = all_30_1
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20544)  op(all_30_1, e2) = all_30_0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20423) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20545)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_38_1 & $i(all_38_0) &
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20545) implies:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20546)  op(e3, e1) = all_38_1
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (20539) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20547)  all_52_7 = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (20532),
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (20543) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20548)  all_30_1 = all_22_1
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (20513), (20543) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20549)  all_30_1 = e3
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (20541),
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (20546) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20550)  all_38_1 = all_10_1
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_1,
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (20530), (20546) gives:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20551)  all_38_1 = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20550), (20551) imply:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20552)  all_10_1 = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20552) implies:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20553)  all_10_1 = e0
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20548), (20549) imply:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20554)  all_22_1 = e3
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20554) implies:
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20555)  all_22_1 = e3
% 238.29/45.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (20547) imply:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20556)   ~ (all_52_6 = e0)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (136), (143), (158),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (162), (163), (164), (165), (167), (170),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (195), (196), (212), (217), (218), (219), (232),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (267), (268), (297), (381), (20114),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20117), (20118), (20119), (20127), (20357),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20375), (20376), (20378), (20381), (20388),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20389), (20397), (20420), (20423), (20426),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20526), (20533), (20541), (20544), (20547),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20549), (20553), (20555), (20556),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #92.
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20557)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20557) implies:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20558)   ~ (all_38_1 = e0)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20559)  op(e3, e1) = all_38_1
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20530), (20541), (20558), (20559),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1195.
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20560)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20560) implies:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20561)   ~ (all_30_1 = e3)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20562)  op(e2, e1) = all_30_1
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20513), (20561), (20562), (function-axioms) are
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1839.
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20563)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20563) implies:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20564)   ~ (all_10_1 = e2)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20565)  op(e3, e1) = all_10_1
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20417) gives:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20566)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_30_1 & $i(all_30_0) &
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20566) implies:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20567)  op(e2, e1) = all_30_1
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20568)  op(all_30_1, e2) = all_30_0
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20423) gives:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20569)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_38_1 & $i(all_38_0) &
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20569) implies:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20570)  op(e3, e1) = all_38_1
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (20539) gives:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20571)  all_52_7 = e0
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (20532),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (20567) gives:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20572)  all_30_1 = all_22_1
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (20513), (20567) gives:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20573)  all_30_1 = e3
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (20565),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (20570) gives:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20574)  all_38_1 = all_10_1
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_1,
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (20530), (20570) gives:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20575)  all_38_1 = e0
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20574), (20575) imply:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20576)  all_10_1 = e0
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20576) implies:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20577)  all_10_1 = e0
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20572), (20573) imply:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20578)  all_22_1 = e3
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20578) implies:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20579)  all_22_1 = e3
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (20571) imply:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20580)   ~ (all_52_6 = e0)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (136), (143), (158),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (162), (163), (164), (165), (167), (170),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (195), (196), (212), (217), (218), (219), (232),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (267), (268), (297), (381), (20114),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20117), (20118), (20119), (20127), (20357),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20375), (20376), (20378), (20381), (20388),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20389), (20397), (20420), (20423), (20426),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20526), (20533), (20565), (20568), (20571),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20573), (20577), (20579), (20580),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #92.
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20581)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20581) implies:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20582)   ~ (all_38_1 = e0)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20583)  op(e3, e1) = all_38_1
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20530), (20565), (20582), (20583),
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1195.
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20584)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20584) implies:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20585)   ~ (all_30_1 = e3)
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20586)  op(e2, e1) = all_30_1
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20513), (20585), (20586), (function-axioms) are
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1839.
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20587)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_22_1)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20587) implies:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20588)   ~ (all_22_1 = e0)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20589)  op(e2, e1) = all_22_1
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20590)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (164), (167), (241), (269),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17767), (20114), (20117), (20118), (20119),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20359), (20417), (20423), (20509), (20513),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20516), (20526), (20530), (20590),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #96.
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20591)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20591) gives:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20592)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (20372), (20391), (20417), (20513), (20592),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #95.
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20593)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20593) implies:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20594)  op(e0, all_56_31) = e0
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (20594) imply:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20595)  op(e0, e2) = e0
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20114) gives:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20596)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_10_1 & $i(all_10_0) &
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20596) implies:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20597)  op(e3, e1) = all_10_1
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20417) gives:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20598)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_30_1 & $i(all_30_0) &
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20598) implies:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20599)  op(e2, e1) = all_30_1
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20600)  op(all_30_1, e2) = all_30_0
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20423) gives:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20601)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_38_1 & $i(all_38_0) &
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20601) implies:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20602)  op(e3, e1) = all_38_1
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (20595) gives:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20603)  all_52_7 = e0
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (20589),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (20599) gives:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20604)  all_30_1 = all_22_1
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (20513), (20599) gives:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20605)  all_30_1 = e3
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (20597),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (20602) gives:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20606)  all_38_1 = all_10_1
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_1,
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (20530), (20602) gives:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20607)  all_38_1 = e0
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20606), (20607) imply:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20608)  all_10_1 = e0
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20608) implies:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20609)  all_10_1 = e0
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20604), (20605) imply:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20610)  all_22_1 = e3
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20610) implies:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20611)  all_22_1 = e3
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (20603) imply:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20612)   ~ (all_52_6 = e0)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (136), (143), (158),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (162), (163), (164), (165), (167), (170),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (195), (196), (212), (217), (218), (219), (232),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (267), (268), (297), (381), (20114),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20117), (20118), (20119), (20127), (20357),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20375), (20376), (20378), (20381), (20388),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20389), (20397), (20420), (20423), (20426),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20526), (20597), (20600), (20603), (20605),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20609), (20612), (function-axioms) are
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #90.
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20613)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20613) implies:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20614)   ~ (all_38_1 = e0)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20615)  op(e3, e1) = all_38_1
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20530), (20597), (20614), (20615),
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1195.
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20616)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20616) implies:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20617)   ~ (all_30_1 = e3)
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20618)  op(e2, e1) = all_30_1
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20513), (20617), (20618), (function-axioms) are
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1839.
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20619)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 238.29/45.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20619) implies:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20620)   ~ (all_10_1 = e2)
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20621)  op(e3, e1) = all_10_1
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20417) gives:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20622)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_30_1 & $i(all_30_0) &
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20622) implies:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20623)  op(e2, e1) = all_30_1
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20624)  op(all_30_1, e2) = all_30_0
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20423) gives:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20625)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_38_1 & $i(all_38_0) &
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20625) implies:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20626)  op(e3, e1) = all_38_1
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (20595) gives:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20627)  all_52_7 = e0
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e2, simplifying with (20589),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (20623) gives:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20628)  all_30_1 = all_22_1
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (20513), (20623) gives:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20629)  all_30_1 = e3
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_1, e1, e3, simplifying with (20621),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (20626) gives:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20630)  all_38_1 = all_10_1
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_1,
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (20530), (20626) gives:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20631)  all_38_1 = e0
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20630), (20631) imply:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20632)  all_10_1 = e0
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20632) implies:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20633)  all_10_1 = e0
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20628), (20629) imply:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20634)  all_22_1 = e3
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20634) implies:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20635)  all_22_1 = e3
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (20627) imply:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20636)   ~ (all_52_6 = e0)
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (136), (143), (158),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (162), (163), (164), (165), (167), (170),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (195), (196), (212), (217), (218), (219), (232),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (267), (268), (297), (381), (20114),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20117), (20118), (20119), (20127), (20357),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20375), (20376), (20378), (20381), (20388),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20389), (20397), (20420), (20423), (20426),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20526), (20621), (20624), (20627), (20629),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20633), (20636), (function-axioms) are
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #90.
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20637)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20637) implies:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20638)   ~ (all_38_1 = e0)
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20639)  op(e3, e1) = all_38_1
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20530), (20621), (20638), (20639),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1195.
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20640)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20640) implies:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20641)   ~ (all_30_1 = e3)
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20642)  op(e2, e1) = all_30_1
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20513), (20641), (20642), (function-axioms) are
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1839.
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20643)  all_58_9 = e0 & op(e3, e0) = e0
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20643) implies:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20644)  op(e3, e0) = e0
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (20522), (20644), (function-axioms) are
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2258.
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20645)  all_58_10 = e3 & op(e2, e0) = e3
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20645) implies:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20646)  op(e2, e0) = e3
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (20506), (20646), (function-axioms) are
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20647)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (17774), (20372), (20647),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #148.
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20648)  all_58_10 = e3 & op(e2, e0) = e3
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20648) implies:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20649)  op(e2, e0) = e3
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (20506), (20649), (function-axioms) are
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | |   (20650)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 238.29/45.39  | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.39  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (159), (223), (226),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | |            (17763), (20372), (20391), (20650),
% 238.29/45.39  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.40  | | | | | | | | | | | | | | | | | | |            #1834.
% 238.29/45.40  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.40  | | | | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | | | End of split
% 238.29/45.40  | | | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.40  | | | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | | |   (20651)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 238.29/45.40  | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 238.29/45.40  | | | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (162), (163),
% 238.29/45.40  | | | | | | | | | | | | | | | | |            (165), (168), (225), (227), (228), (230), (17766),
% 238.29/45.40  | | | | | | | | | | | | | | | | |            (17768), (20388), (20389), (20651),
% 238.29/45.40  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.40  | | | | | | | | | | | | | | | | |            #89.
% 238.29/45.40  | | | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | | End of split
% 238.29/45.40  | | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | Case 2:
% 238.29/45.40  | | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | |   (20652)  all_54_10 = e1 | all_54_10 = e0
% 238.29/45.40  | | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | | REF_CLOSE: (297), (20127), (20378), (20652) are inconsistent
% 238.29/45.40  | | | | | | | | | | | | | | | |            by sub-proof #2282.
% 238.29/45.40  | | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | End of split
% 238.29/45.40  | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | End of split
% 238.29/45.40  | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | Case 2:
% 238.29/45.40  | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | |   (20653)  all_58_15 = e1 & op(e0, e0) = e1
% 238.29/45.40  | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (20653) are inconsistent by
% 238.29/45.40  | | | | | | | | | | | | | |            sub-proof #218.
% 238.29/45.40  | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | End of split
% 238.29/45.40  | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | End of split
% 238.29/45.40  | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | Case 2:
% 238.29/45.40  | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | |   (20654)  all_58_15 = e1 & op(e0, e0) = e1
% 238.29/45.40  | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | REF_CLOSE: (6), (17773), (20654) are inconsistent by
% 238.29/45.40  | | | | | | | | | | | |            sub-proof #218.
% 238.29/45.40  | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | End of split
% 238.29/45.40  | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | End of split
% 238.29/45.40  | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | End of split
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | Case 2:
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | |   (20655)  all_18_2 = e0
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | COMBINE_EQS: (339), (20655) imply:
% 238.29/45.40  | | | | | | | | |   (20656)  all_6_2 = e0
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | SIMP: (20656) implies:
% 238.29/45.40  | | | | | | | | |   (20657)  all_6_2 = e0
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | COMBINE_EQS: (266), (20657) imply:
% 238.29/45.40  | | | | | | | | |   (20658)  all_56_21 = e0
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | REDUCE: (367), (20657) imply:
% 238.29/45.40  | | | | | | | | |   (20659)   ~ (all_52_2 = e0)
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | REDUCE: (378), (20657) imply:
% 238.29/45.40  | | | | | | | | |   (20660)   ~ (all_52_6 = e0)
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | REDUCE: (381), (20657) imply:
% 238.29/45.40  | | | | | | | | |   (20661)   ~ (all_52_9 = e0)
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | REDUCE: (385), (20657) imply:
% 238.29/45.40  | | | | | | | | |   (20662)   ~ (all_52_14 = e0)
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | REDUCE: (17775), (20657) imply:
% 238.29/45.40  | | | | | | | | |   (20663)   ~ (e3 = e0)
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | REDUCE: (39), (20657) imply:
% 238.29/45.40  | | | | | | | | |   (20664)  op(e1, e1) = e0
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | BETA: splitting (64) gives:
% 238.29/45.40  | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | Case 1:
% 238.29/45.40  | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | |   (20665)   ~ (all_22_2 = e1)
% 238.29/45.40  | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | REDUCE: (326), (20665) imply:
% 238.29/45.40  | | | | | | | | | |   (20666)   ~ (all_8_2 = e1)
% 238.29/45.40  | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | BETA: splitting (199) gives:
% 238.29/45.40  | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | Case 1:
% 238.29/45.40  | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | |   (20667)  all_54_5 = e3
% 238.29/45.40  | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | COMBINE_EQS: (275), (20667) imply:
% 238.29/45.40  | | | | | | | | | | |   (20668)  all_8_2 = e3
% 238.29/45.40  | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | REDUCE: (17776), (20668) imply:
% 238.29/45.40  | | | | | | | | | | |   (20669)  $false
% 238.29/45.40  | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | CLOSE: (20669) is inconsistent.
% 238.29/45.40  | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | Case 2:
% 238.29/45.40  | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | |   (20670)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 238.29/45.40  | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | BETA: splitting (20670) gives:
% 238.29/45.40  | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | Case 1:
% 238.29/45.40  | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | |   (20671)  all_54_5 = e2
% 238.29/45.40  | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | COMBINE_EQS: (275), (20671) imply:
% 238.29/45.40  | | | | | | | | | | | |   (20672)  all_8_2 = e2
% 238.29/45.40  | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | REDUCE: (369), (20672) imply:
% 238.29/45.40  | | | | | | | | | | | |   (20673)   ~ (all_52_4 = e2)
% 238.29/45.40  | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | REDUCE: (371), (20672) imply:
% 238.29/45.40  | | | | | | | | | | | |   (20674)   ~ (all_52_6 = e2)
% 238.29/45.40  | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | REDUCE: (375), (20672) imply:
% 238.29/45.40  | | | | | | | | | | | |   (20675)   ~ (all_52_9 = e2)
% 238.29/45.40  | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.29/45.40  | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | Case 1:
% 238.29/45.40  | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | |   (20676)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.29/45.40  | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.40  | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.29/45.40  | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.29/45.40  | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.40  | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.40  | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.29/45.40  | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.40  | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.40  | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.29/45.40  | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.29/45.40  | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.40  | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.40  | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.29/45.40  | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.40  | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.40  | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.29/45.40  | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.29/45.40  | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.40  | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.40  | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.29/45.40  | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | BETA: splitting (20676) gives:
% 238.29/45.40  | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | Case 1:
% 238.29/45.40  | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | |   (20677)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.29/45.40  | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.40  | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.29/45.40  | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.29/45.40  | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.40  | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.40  | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.29/45.40  | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.40  | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.40  | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.29/45.40  | | | | | | | | | | | | | |              = e3)
% 238.29/45.40  | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | BETA: splitting (20677) gives:
% 238.29/45.40  | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | Case 1:
% 238.29/45.40  | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | |   (20678)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.29/45.40  | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.29/45.40  | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.29/45.40  | | | | | | | | | | | | | | |            e3
% 238.29/45.40  | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | ALPHA: (20678) implies:
% 238.29/45.40  | | | | | | | | | | | | | | |   (20679)   ~ (all_56_31 = e2)
% 238.29/45.40  | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | REDUCE: (17762), (20679) imply:
% 238.29/45.40  | | | | | | | | | | | | | | |   (20680)  $false
% 238.29/45.40  | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | | CLOSE: (20680) is inconsistent.
% 238.29/45.40  | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | Case 2:
% 238.29/45.40  | | | | | | | | | | | | | | | 
% 238.29/45.40  | | | | | | | | | | | | | | |   (20681)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.29/45.40  | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.29/45.40  | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.29/45.40  | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.29/45.40  | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.29/45.40  | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.29/45.40  | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.29/45.40  | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | BETA: splitting (20681) gives:
% 238.29/45.41  | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | Case 1:
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | |   (20682)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 238.29/45.41  | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.29/45.41  | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 238.29/45.41  | | | | | | | | | | | | | | | |            e2
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | ALPHA: (20682) implies:
% 238.29/45.41  | | | | | | | | | | | | | | | |   (20683)  op(e3, e2) = e2
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | REF_CLOSE: (170), (20673), (20683), (function-axioms) are
% 238.29/45.41  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #254.
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | Case 2:
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | |   (20684)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 238.29/45.41  | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.29/45.41  | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 238.29/45.41  | | | | | | | | | | | | | | | |              e3) = e3
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | ALPHA: (20684) implies:
% 238.29/45.41  | | | | | | | | | | | | | | | |   (20685)   ~ (all_56_1 = e1)
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | REDUCE: (20116), (20685) imply:
% 238.29/45.41  | | | | | | | | | | | | | | | |   (20686)  $false
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | CLOSE: (20686) is inconsistent.
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | End of split
% 238.29/45.41  | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | End of split
% 238.29/45.41  | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | Case 2:
% 238.29/45.41  | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | |   (20687)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.29/45.41  | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.29/45.41  | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.29/45.41  | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.29/45.41  | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.41  | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.41  | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.29/45.41  | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.29/45.41  | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.29/45.41  | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.29/45.41  | | | | | | | | | | | | | |              = e0)
% 238.29/45.41  | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | BETA: splitting (20687) gives:
% 238.29/45.41  | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | Case 1:
% 238.29/45.41  | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | |   (20688)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.29/45.41  | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.29/45.41  | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.29/45.41  | | | | | | | | | | | | | | |              e3) = e1
% 238.29/45.41  | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | ALPHA: (20688) implies:
% 238.29/45.41  | | | | | | | | | | | | | | |   (20689)  op(e3, e1) = e1
% 238.29/45.41  | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | REF_CLOSE: (169), (20121), (20689), (function-axioms) are
% 238.29/45.41  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.29/45.41  | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | Case 2:
% 238.29/45.41  | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | |   (20690)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.29/45.41  | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.29/45.41  | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.29/45.41  | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.29/45.41  | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.41  | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.41  | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.29/45.41  | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | BETA: splitting (20690) gives:
% 238.29/45.41  | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | Case 1:
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | |   (20691)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.29/45.41  | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.29/45.41  | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 238.29/45.41  | | | | | | | | | | | | | | | |              e3) = e3
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | ALPHA: (20691) implies:
% 238.29/45.41  | | | | | | | | | | | | | | | |   (20692)   ~ (all_56_21 = e0)
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | REDUCE: (20658), (20692) imply:
% 238.29/45.41  | | | | | | | | | | | | | | | |   (20693)  $false
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | CLOSE: (20693) is inconsistent.
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | Case 2:
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | |   (20694)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 238.29/45.41  | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.29/45.41  | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 238.29/45.41  | | | | | | | | | | | | | | | |              e3) = e0
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | ALPHA: (20694) implies:
% 238.29/45.41  | | | | | | | | | | | | | | | |   (20695)  op(e0, e3) = e0
% 238.29/45.41  | | | | | | | | | | | | | | | |   (20696)  op(e3, e0) = e0
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 238.29/45.41  | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.41  | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | |   (20697)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 238.29/45.41  | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 238.29/45.41  | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (20123), (20673), (20697),
% 238.29/45.41  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.41  | | | | | | | | | | | | | | | | |            #114.
% 238.29/45.41  | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.41  | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | |   (20698)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 238.29/45.41  | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 238.29/45.41  | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | BETA: splitting (20698) gives:
% 238.29/45.41  | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.41  | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | |   (20699)  all_58_4 = e2 & op(e3, e1) = e2
% 238.29/45.41  | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | ALPHA: (20699) implies:
% 238.29/45.41  | | | | | | | | | | | | | | | | | |   (20700)  op(e3, e1) = e2
% 238.29/45.41  | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.29/45.41  | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | |   (20701)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.29/45.41  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | BETA: splitting (20701) gives:
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | |   (20702)  all_58_1 = e2 & op(e3, e2) = e2
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | ALPHA: (20702) implies:
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | |   (20703)  op(e3, e2) = e2
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (20673), (20703), (function-axioms) are
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #254.
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | |   (20704)  all_58_3 = e2 & op(e2, e2) = e2
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | ALPHA: (20704) implies:
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | |   (20705)  op(e2, e2) = e2
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (20695) gives:
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | |   (20706)  all_52_3 = e0
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (168), (20696) gives:
% 238.29/45.41  | | | | | | | | | | | | | | | | | | | |   (20707)  all_52_12 = e0
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (20700) gives:
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | |   (20708)  all_52_8 = e2
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (20706) imply:
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | |   (20709)   ~ (all_52_7 = e0)
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | SIMP: (20709) implies:
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | |   (20710)   ~ (all_52_7 = e0)
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (20707) imply:
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | |   (20711)   ~ (all_52_4 = e0)
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | REDUCE: (17766), (20707) imply:
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | |   (20712)   ~ (e2 = e0)
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (162), (170), (203), (235), (282),
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | |            (20120), (20660), (20673), (20705), (20710),
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | |            (20711), (function-axioms) are inconsistent by
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | |            sub-proof #88.
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | |   (20713)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.29/45.42  | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (17764), (20674), (20713),
% 238.29/45.42  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.42  | | | | | | | | | | | | | | | | | | |            #144.
% 238.29/45.42  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.42  | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | |   (20714)  all_58_9 = e2 & op(e3, e0) = e2
% 238.29/45.42  | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (17766), (20714), (function-axioms) are
% 238.29/45.42  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2318.
% 238.29/45.42  | | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | Case 2:
% 238.29/45.42  | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | |   (20715)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.42  | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.29/45.42  | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.29/45.42  | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.29/45.42  | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.29/45.42  | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.29/45.42  | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.29/45.42  | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.42  | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.42  | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.29/45.42  | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.29/45.42  | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.29/45.42  | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.29/45.42  | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.29/45.42  | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.42  | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.42  | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.29/45.42  | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.29/45.42  | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.29/45.42  | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.29/45.42  | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.29/45.42  | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | BETA: splitting (20715) gives:
% 238.29/45.42  | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | Case 1:
% 238.29/45.42  | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | |   (20716)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.42  | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.29/45.42  | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.29/45.42  | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.29/45.42  | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.29/45.42  | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.29/45.42  | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.29/45.42  | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.42  | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.42  | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.29/45.42  | | | | | | | | | | | | | |              = e2)
% 238.29/45.42  | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (17762), (17764), (20675), (20716),
% 238.29/45.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.42  | | | | | | | | | | | | | |            #184.
% 238.29/45.42  | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | Case 2:
% 238.29/45.42  | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | |   (20717)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.29/45.42  | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.42  | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.29/45.42  | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.29/45.42  | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.42  | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.42  | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.29/45.42  | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.42  | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.42  | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.29/45.42  | | | | | | | | | | | | | |              = e0)
% 238.29/45.42  | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | | REF_CLOSE: (160), (17762), (20658), (20662), (20717),
% 238.29/45.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.42  | | | | | | | | | | | | | |            #179.
% 238.29/45.42  | | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | Case 2:
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | |   (20718)  all_54_5 = e1 | all_54_5 = e0
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | REF_CLOSE: (275), (20125), (20666), (20718) are inconsistent
% 238.29/45.42  | | | | | | | | | | | |            by sub-proof #2300.
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | Case 2:
% 238.29/45.42  | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | |   (20719)  all_22_2 = e1
% 238.29/45.42  | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | COMBINE_EQS: (326), (20719) imply:
% 238.29/45.42  | | | | | | | | | |   (20720)  all_8_2 = e1
% 238.29/45.42  | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | REDUCE: (371), (20720) imply:
% 238.29/45.42  | | | | | | | | | |   (20721)   ~ (all_52_6 = e1)
% 238.29/45.42  | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | REDUCE: (373), (20720) imply:
% 238.29/45.42  | | | | | | | | | |   (20722)   ~ (all_52_7 = e1)
% 238.29/45.42  | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | REDUCE: (375), (20720) imply:
% 238.29/45.42  | | | | | | | | | |   (20723)   ~ (all_52_9 = e1)
% 238.29/45.42  | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | REDUCE: (377), (20720) imply:
% 238.29/45.42  | | | | | | | | | |   (20724)   ~ (all_52_13 = e1)
% 238.29/45.42  | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | REDUCE: (42), (20720) imply:
% 238.29/45.42  | | | | | | | | | |   (20725)  op(e2, e2) = e1
% 238.29/45.42  | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | BETA: splitting (220) gives:
% 238.29/45.42  | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | Case 1:
% 238.29/45.42  | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | |   (20726)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.29/45.42  | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.29/45.42  | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | BETA: splitting (20726) gives:
% 238.29/45.42  | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | Case 1:
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | |   (20727)  all_58_9 = e1 & op(e3, e0) = e1
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | REF_CLOSE: (168), (20122), (20727), (function-axioms) are
% 238.29/45.42  | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | Case 2:
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | |   (20728)  all_58_10 = e1 & op(e2, e0) = e1
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | REF_CLOSE: (164), (20724), (20728), (function-axioms) are
% 238.29/45.42  | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | End of split
% 238.29/45.42  | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | Case 2:
% 238.29/45.42  | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | |   (20729)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.29/45.42  | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.29/45.42  | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | BETA: splitting (20729) gives:
% 238.29/45.42  | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | Case 1:
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | |   (20730)  all_58_11 = e1 & op(e1, e0) = e1
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | ALPHA: (20730) implies:
% 238.29/45.42  | | | | | | | | | | | |   (20731)  op(e1, e0) = e1
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | BETA: splitting (192) gives:
% 238.29/45.42  | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | Case 1:
% 238.29/45.42  | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | |   (20732)  all_54_12 = e3
% 238.29/45.42  | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | COMBINE_EQS: (257), (20732) imply:
% 238.29/45.42  | | | | | | | | | | | | |   (20733)  all_52_3 = e3
% 238.29/45.42  | | | | | | | | | | | | | 
% 238.29/45.42  | | | | | | | | | | | | | SIMP: (20733) implies:
% 238.29/45.42  | | | | | | | | | | | | |   (20734)  all_52_3 = e3
% 238.29/45.43  | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | REDUCE: (148), (20734) imply:
% 238.29/45.43  | | | | | | | | | | | | |   (20735)   ~ (all_52_1 = e3)
% 238.29/45.43  | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | REDUCE: (144), (20734) imply:
% 238.29/45.43  | | | | | | | | | | | | |   (20736)   ~ (all_52_2 = e3)
% 238.29/45.43  | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | REDUCE: (140), (20734) imply:
% 238.29/45.43  | | | | | | | | | | | | |   (20737)   ~ (all_52_7 = e3)
% 238.29/45.43  | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | SIMP: (20737) implies:
% 238.29/45.43  | | | | | | | | | | | | |   (20738)   ~ (all_52_7 = e3)
% 238.29/45.43  | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | REDUCE: (159), (20734) imply:
% 238.29/45.43  | | | | | | | | | | | | |   (20739)  op(e0, e3) = e3
% 238.29/45.43  | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | BETA: splitting (226) gives:
% 238.29/45.43  | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | Case 1:
% 238.29/45.43  | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | |   (20740)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 238.29/45.43  | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 238.29/45.43  | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | BETA: splitting (20740) gives:
% 238.29/45.43  | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | Case 1:
% 238.29/45.43  | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | |   (20741)  all_58_6 = e3 & op(e1, e3) = e3
% 238.29/45.43  | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | ALPHA: (20741) implies:
% 238.29/45.43  | | | | | | | | | | | | | | |   (20742)  op(e1, e3) = e3
% 238.29/45.43  | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | REF_CLOSE: (163), (20736), (20742), (function-axioms) are
% 238.29/45.43  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 238.29/45.43  | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | Case 2:
% 238.29/45.43  | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | |   (20743)  all_58_7 = e3 & op(e1, e2) = e3
% 238.29/45.43  | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | ALPHA: (20743) implies:
% 238.29/45.43  | | | | | | | | | | | | | | |   (20744)  op(e1, e2) = e3
% 238.29/45.43  | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 238.29/45.43  | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | Case 1:
% 238.29/45.43  | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | |   (20745)  all_54_8 = e3
% 238.29/45.43  | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | REF_CLOSE: (268), (20736), (20745) are inconsistent by
% 238.29/45.43  | | | | | | | | | | | | | | | |            sub-proof #2011.
% 238.29/45.43  | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | Case 2:
% 238.29/45.43  | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | |   (20746)   ~ (all_54_8 = e3)
% 238.29/45.43  | | | | | | | | | | | | | | | |   (20747)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 238.29/45.43  | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 238.29/45.43  | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.43  | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | |   (20748)  all_54_13 = e3
% 238.29/45.43  | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (20738), (20748) are inconsistent by
% 238.29/45.43  | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 238.29/45.43  | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.43  | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | |   (20749)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 238.29/45.43  | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.29/45.43  | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | |   (20750)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.43  | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.43  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.29/45.43  | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | BETA: splitting (20750) gives:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | |   (20751)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.29/45.43  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.43  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.29/45.43  | | | | | | | | | | | | | | | | | | |              = e3)
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | BETA: splitting (20751) gives:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |   (20752)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |            e3
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | ALPHA: (20752) implies:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |   (20753)  op(e2, e3) = e3
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (20735), (20753), (function-axioms) are
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |   (20754)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | BETA: splitting (20754) gives:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | |   (20755)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | |            e2
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | ALPHA: (20755) implies:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | |   (20756)  op(e2, e3) = e2
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20747) gives:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | |   (20757)  all_54_8 = e2
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (20757) imply:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | |   (20758)  all_52_2 = e2
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | SIMP: (20758) implies:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | |   (20759)  all_52_2 = e2
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (20759) imply:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | |   (20760)   ~ (all_52_1 = e2)
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (20756), (20760), (function-axioms) are
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | |   (20761)  all_54_8 = e1 | all_54_8 = e0
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (20118), (20659), (20761) are inconsistent
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1950.
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | |   (20762)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | ALPHA: (20762) implies:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | |   (20763)  op(e1, e3) = e3
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (20736), (20763), (function-axioms) are
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.43  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.43  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |   (20764)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              = e0)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | BETA: splitting (20764) gives:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |   (20765)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | ALPHA: (20765) implies:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |   (20766)  op(e3, e1) = e1
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (20121), (20766), (function-axioms) are
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |   (20767)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | BETA: splitting (20767) gives:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |   (20768)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | ALPHA: (20768) implies:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |   (20769)   ~ (all_56_21 = e0)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | REDUCE: (20658), (20769) imply:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |   (20770)  $false
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | CLOSE: (20770) is inconsistent.
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |   (20771)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |              e3) = e0
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | ALPHA: (20771) implies:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |   (20772)  op(e0, e3) = e0
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (20739), (20772), (function-axioms) are
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #221.
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.44  | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | |   (20773)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.29/45.44  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.29/45.44  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | BETA: splitting (20773) gives:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |   (20774)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              = e2)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | BETA: splitting (20774) gives:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |   (20775)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | ALPHA: (20775) implies:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |   (20776)  op(e1, e2) = e2
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20744), (20776), (function-axioms) are
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2207.
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |   (20777)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (256), (17764), (20722), (20723),
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |            (20749), (20777), (function-axioms) are
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1367.
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |   (20778)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |              = e0)
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17762), (20658), (20731), (20778),
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.44  | | | | | | | | | | | | | | | | | | |            #168.
% 238.29/45.44  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.44  | | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | | End of split
% 238.29/45.44  | | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | | End of split
% 238.29/45.44  | | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | | End of split
% 238.29/45.44  | | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | End of split
% 238.29/45.44  | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | Case 2:
% 238.29/45.44  | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | |   (20779)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 238.29/45.44  | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 238.29/45.44  | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (20664), (20731), (20779),
% 238.29/45.44  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.44  | | | | | | | | | | | | | |            #175.
% 238.29/45.44  | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | End of split
% 238.29/45.44  | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | Case 2:
% 238.29/45.44  | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | |   (20780)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 238.29/45.44  | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | BETA: splitting (20780) gives:
% 238.29/45.44  | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | Case 1:
% 238.29/45.44  | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | |   (20781)  all_54_12 = e2
% 238.29/45.44  | | | | | | | | | | | | | | 
% 238.29/45.44  | | | | | | | | | | | | | | REF_CLOSE: (257), (17763), (20781) are inconsistent by
% 238.29/45.44  | | | | | | | | | | | | | |            sub-proof #2264.
% 238.29/45.45  | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | |   (20782)   ~ (all_54_12 = e2)
% 238.29/45.45  | | | | | | | | | | | | | |   (20783)  all_54_12 = e1 | all_54_12 = e0
% 238.29/45.45  | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | BETA: splitting (20783) gives:
% 238.29/45.45  | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | |   (20784)  all_54_12 = e1
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | COMBINE_EQS: (257), (20784) imply:
% 238.29/45.45  | | | | | | | | | | | | | | |   (20785)  all_52_3 = e1
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | REDUCE: (20119), (20785) imply:
% 238.29/45.45  | | | | | | | | | | | | | | |   (20786)  $false
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | CLOSE: (20786) is inconsistent.
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | |   (20787)  all_54_12 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | COMBINE_EQS: (257), (20787) imply:
% 238.29/45.45  | | | | | | | | | | | | | | |   (20788)  all_52_3 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | REDUCE: (148), (20788) imply:
% 238.29/45.45  | | | | | | | | | | | | | | |   (20789)   ~ (all_52_1 = e0)
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | REDUCE: (140), (20788) imply:
% 238.29/45.45  | | | | | | | | | | | | | | |   (20790)   ~ (all_52_7 = e0)
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | SIMP: (20790) implies:
% 238.29/45.45  | | | | | | | | | | | | | | |   (20791)   ~ (all_52_7 = e0)
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | REDUCE: (17763), (20788) imply:
% 238.29/45.45  | | | | | | | | | | | | | | |   (20792)   ~ (e2 = e0)
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | REDUCE: (20119), (20788) imply:
% 238.29/45.45  | | | | | | | | | | | | | | |   (20793)   ~ (e1 = e0)
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | |   (20794)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.29/45.45  | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | BETA: splitting (20794) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | |   (20795)  all_58_1 = e0 & op(e3, e2) = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | ALPHA: (20795) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | |   (20796)  op(e3, e2) = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | |   (20797)  all_54_13 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (20797) imply:
% 238.29/45.45  | | | | | | | | | | | | | | | | | |   (20798)  all_52_7 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | SIMP: (20798) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | |   (20799)  all_52_7 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | REDUCE: (135), (20799) imply:
% 238.29/45.45  | | | | | | | | | | | | | | | | | |   (20800)   ~ (all_52_4 = e3)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | REDUCE: (128), (20799) imply:
% 238.29/45.45  | | | | | | | | | | | | | | | | | |   (20801)   ~ (all_52_6 = e3)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | REDUCE: (158), (20799) imply:
% 238.29/45.45  | | | | | | | | | | | | | | | | | |   (20802)  op(e0, e2) = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | |   (20803)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (20725), (20796), (20803),
% 238.29/45.45  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.45  | | | | | | | | | | | | | | | | | | |            #369.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | |   (20804)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.29/45.45  | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | BETA: splitting (20804) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | |   (20805)  all_58_7 = e2 & op(e1, e2) = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | ALPHA: (20805) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | |   (20806)  all_58_7 = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | |   (20807)  op(e1, e2) = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | |   (20808)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (20123), (20789), (20808),
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | |            #1272.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | |   (20809)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20809) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | |   (20810)  all_58_6 = e0 & op(e1, e3) = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20810) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | |   (20811)  all_58_6 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (224), (225),
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | |            (226), (20664), (20801), (20811),
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | |            #1977.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | |   (20812)  all_58_12 = e0 & op(e0, e3) = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20812) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | |   (20813)  all_58_12 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | |   (20814)  op(e0, e3) = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | |   (20815)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20815) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | |   (20816)  all_58_6 = e3 & op(e1, e3) = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20816) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | |   (20817)  all_58_6 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (20818)  all_54_9 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (20801), (20818) are inconsistent by
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (20819)   ~ (all_54_9 = e3)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (20820)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20820) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20821)  all_54_9 = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (20821) imply:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20822)  all_52_6 = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20822) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20823)  all_52_6 = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (20823) imply:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20824)   ~ (all_52_2 = e2)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (20823) imply:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20825)   ~ (all_52_4 = e2)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20826)  all_54_1 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (20800), (20826) are inconsistent by
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20827)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20828)  all_54_8 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (20828) imply:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20829)  all_52_2 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (20829) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20830)  all_52_2 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (20830) imply:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20831)   ~ (all_52_1 = e3)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20827) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20832)  all_54_1 = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (20825), (20832) are inconsistent by
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1928.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20833)   ~ (all_54_1 = e2)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20834)  all_54_1 = e1 | all_54_1 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20835)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20835) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20836)  all_58_2 = e0 & op(e2, e3) = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20836) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20837)  all_58_2 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (167), (243), (245),
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20123), (20813), (20831), (20837),
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1149.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20838)  all_58_3 = e0 & op(e2, e2) = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (20125), (20838), (function-axioms) are
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20839)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20839) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20840)  all_58_5 = e0 & op(e2, e1) = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (20661), (20840), (function-axioms) are
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20841)  all_58_10 = e0 & op(e2, e0) = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20841) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20842)  all_58_10 = e0
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20843)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (20123), (20825), (20843),
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #114.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20844)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20844) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20845)  all_58_4 = e2 & op(e3, e1) = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20845) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20846)  op(e3, e1) = e2
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20847)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20847) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20848)  all_58_2 = e3 & op(e2, e3) = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20848) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20849)  all_58_2 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (239), (243), (20123),
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20817), (20849), (function-axioms) are
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1221.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20850)  all_58_3 = e3 & op(e2, e2) = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20850) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20851)  all_58_3 = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20852)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20852) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20853)  all_58_2 = e1 & op(e2, e3) = e1
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (20117), (20853), (function-axioms) are
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20854)  all_58_3 = e1 & op(e2, e2) = e1
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (20123), (20817), (20831), (20851),
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20854), (function-axioms) are inconsistent by
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #660.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20855)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20855) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20856)  all_58_5 = e1 & op(e2, e1) = e1
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20856) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20857)  op(e2, e1) = e1
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (20723), (20857), (function-axioms) are
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20858)  all_58_10 = e1 & op(e2, e0) = e1
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20858) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20859)  all_58_10 = e1
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20842), (20859) are inconsistent by
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1173.
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20860)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20860) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20861)  all_58_5 = e3 & op(e2, e1) = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20861) implies:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20862)  op(e2, e1) = e3
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20863)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20863) gives:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20864)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20864) gives:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20865)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20865) implies:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20866)  op(e2, e3) = e3
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (20831), (20866), (function-axioms) are
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20867)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (20825), (20846), (20867),
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #166.
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20868)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20868) gives:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20869)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20869) implies:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20870)  op(e3, e1) = e1
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (20121), (20870), (function-axioms) are
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20871)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20871) gives:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20872)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20872) implies:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20873)  op(e0, e3) = e3
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (20814), (20873), (function-axioms) are
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #221.
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20874)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20874) implies:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20875)  op(e3, e0) = e0
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (168), (282), (20120), (20834), (20875),
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #87.
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.29/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20876)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20876) gives:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20877)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (20802), (20862), (20877),
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2253.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20878)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20878) gives:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20879)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20879) implies:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20880)  op(e0, e2) = e0
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (20791), (20880), (function-axioms) are
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2252.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20881)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20881) gives:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20882)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20882) implies:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20883)   ~ (all_56_21 = e0)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20658), (20883) imply:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20884)  $false
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (20884) is inconsistent.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20885)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20885) implies:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20886)  op(e1, e0) = e0
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (224), (20664), (20806), (20817),
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20886), (function-axioms) are inconsistent by
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #794.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20887)  all_58_10 = e3 & op(e2, e0) = e3
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20887) implies:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20888)  all_58_10 = e3
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20842), (20888) imply:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20889)  e3 = e0
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20817), (20889) imply:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20890)  all_58_6 = e0
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (224), (225),
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (20664), (20801), (20890),
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1977.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20891)  all_58_9 = e2 & op(e3, e0) = e2
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (17766), (20891), (function-axioms) are
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2318.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20892)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (159), (268), (20118), (20814), (20824),
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20892), (function-axioms) are inconsistent by
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1684.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20893)  all_54_9 = e1 | all_54_9 = e0
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20893) gives:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20894)  all_54_9 = e1
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (20721), (20894) are inconsistent by
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2055.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20895)  all_54_9 = e0
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (20660), (20895) are inconsistent by
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1953.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | |   (20896)  all_58_7 = e3 & op(e1, e2) = e3
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20896) implies:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | |   (20897)  op(e1, e2) = e3
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20807), (20897), (function-axioms) are
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2207.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | |   (20898)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (20664), (20731), (20898),
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | |            #175.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | |   (20899)  all_58_13 = e2 & op(e0, e2) = e2
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | ALPHA: (20899) implies:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | |   (20900)  op(e0, e2) = e2
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20802), (20900), (function-axioms) are
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | |   (20901)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 238.57/45.46  | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17764), (20722), (20791), (20901) are
% 238.57/45.46  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1648.
% 238.57/45.46  | | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | |   (20902)  all_58_3 = e0 & op(e2, e2) = e0
% 238.57/45.46  | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (20125), (20902), (function-axioms) are
% 238.57/45.46  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1992.
% 238.57/45.46  | | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | |   (20903)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 238.57/45.46  | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 238.57/45.46  | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (20660), (20791), (20903),
% 238.57/45.46  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.46  | | | | | | | | | | | | | | | |            #1990.
% 238.57/45.46  | | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | |   (20904)  all_58_15 = e1 & op(e0, e0) = e1
% 238.57/45.46  | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | | REF_CLOSE: (6), (17773), (20904) are inconsistent by
% 238.57/45.46  | | | | | | | | | | | |            sub-proof #218.
% 238.57/45.46  | | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | | 
% 238.57/45.46  | | | | | | | | End of split
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | |   (20905)  all_14_2 = e0
% 238.57/45.46  | | | | | | | |   (20906)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 238.57/45.46  | | | | | | | |              op(e2, e0) = all_14_1 & $i(all_14_0) &
% 238.57/45.46  | | | | | | | |              $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0) =
% 238.57/45.46  | | | | | | | |              all_14_1 & $i(all_14_1))
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | | COMBINE_EQS: (344), (20905) imply:
% 238.57/45.46  | | | | | | | |   (20907)  all_8_2 = e0
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | | COMBINE_EQS: (311), (20907) imply:
% 238.57/45.46  | | | | | | | |   (20908)  all_48_2 = e0
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | | REDUCE: (366), (20907) imply:
% 238.57/45.46  | | | | | | | |   (20909)   ~ (all_52_1 = e0)
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | | REDUCE: (369), (20907) imply:
% 238.57/45.46  | | | | | | | |   (20910)   ~ (all_52_4 = e0)
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | | REDUCE: (371), (20907) imply:
% 238.57/45.46  | | | | | | | |   (20911)   ~ (all_52_6 = e0)
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | | REDUCE: (373), (20907) imply:
% 238.57/45.46  | | | | | | | |   (20912)   ~ (all_52_7 = e0)
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | | REDUCE: (375), (20907) imply:
% 238.57/45.46  | | | | | | | |   (20913)   ~ (all_52_9 = e0)
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | | REDUCE: (377), (20907) imply:
% 238.57/45.46  | | | | | | | |   (20914)   ~ (all_52_13 = e0)
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | | REDUCE: (17776), (20907) imply:
% 238.57/45.46  | | | | | | | |   (20915)   ~ (e3 = e0)
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | | BETA: splitting (231) gives:
% 238.57/45.46  | | | | | | | | 
% 238.57/45.46  | | | | | | | | Case 1:
% 238.57/45.46  | | | | | | | | | 
% 238.57/45.46  | | | | | | | | |   (20916)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 238.57/45.46  | | | | | | | | |              & op(e2, e2) = e0)
% 238.57/45.46  | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | BETA: splitting (20916) gives:
% 238.57/45.46  | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | Case 1:
% 238.57/45.46  | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | |   (20917)  all_58_2 = e0 & op(e2, e3) = e0
% 238.57/45.46  | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | REF_CLOSE: (167), (20909), (20917), (function-axioms) are
% 238.57/45.46  | | | | | | | | | |            inconsistent by sub-proof #1985.
% 238.57/45.46  | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | Case 2:
% 238.57/45.46  | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | |   (20918)  all_58_3 = e0 & op(e2, e2) = e0
% 238.57/45.46  | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | ALPHA: (20918) implies:
% 238.57/45.46  | | | | | | | | | |   (20919)  all_58_3 = e0
% 238.57/45.46  | | | | | | | | | |   (20920)  op(e2, e2) = e0
% 238.57/45.46  | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | BETA: splitting (58) gives:
% 238.57/45.46  | | | | | | | | | | 
% 238.57/45.46  | | | | | | | | | | Case 1:
% 238.57/45.46  | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | |   (20921)   ~ (all_18_2 = e0)
% 238.57/45.47  | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | REDUCE: (339), (20921) imply:
% 238.57/45.47  | | | | | | | | | | |   (20922)   ~ (all_6_2 = e0)
% 238.57/45.47  | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | BETA: splitting (88) gives:
% 238.57/45.47  | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | |   (20923)   ~ (all_38_2 = e1)
% 238.57/45.47  | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | REDUCE: (20115), (20923) imply:
% 238.57/45.47  | | | | | | | | | | | |   (20924)  $false
% 238.57/45.47  | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | CLOSE: (20924) is inconsistent.
% 238.57/45.47  | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | |   (20925)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 238.57/45.47  | | | | | | | | | | | |              & op(e3, e1) = all_38_1 & $i(all_38_0) &
% 238.57/45.47  | | | | | | | | | | | |              $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1)
% 238.57/45.47  | | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 238.57/45.47  | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | BETA: splitting (85) gives:
% 238.57/45.47  | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | |   (20926)   ~ (all_36_2 = e2)
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | REDUCE: (328), (20926) imply:
% 238.57/45.47  | | | | | | | | | | | | |   (20927)   ~ (all_6_2 = e2)
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | BETA: splitting (194) gives:
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | |   (20928)  all_54_10 = e3
% 238.57/45.47  | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (20928) are inconsistent by
% 238.57/45.47  | | | | | | | | | | | | | |            sub-proof #2313.
% 238.57/45.47  | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | |   (20929)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.57/45.47  | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | BETA: splitting (20929) gives:
% 238.57/45.47  | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | |   (20930)  all_54_10 = e2
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | REF_CLOSE: (297), (20927), (20930) are inconsistent by
% 238.57/45.47  | | | | | | | | | | | | | | |            sub-proof #2312.
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | |   (20931)   ~ (all_54_10 = e2)
% 238.57/45.47  | | | | | | | | | | | | | | |   (20932)  all_54_10 = e1 | all_54_10 = e0
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | BETA: splitting (20932) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | |   (20933)  all_54_10 = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (20933) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | |   (20934)  all_6_2 = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | SIMP: (20934) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | |   (20935)  all_6_2 = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | REDUCE: (378), (20935) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | |   (20936)   ~ (all_52_6 = e1)
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | REDUCE: (385), (20935) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | |   (20937)   ~ (all_52_14 = e1)
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | REDUCE: (20927), (20935) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | |   (20938)   ~ (e2 = e1)
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | |   (20939)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (20120), (20919), (20939),
% 238.57/45.47  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.47  | | | | | | | | | | | | | | | | |            #1377.
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | |   (20940)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.57/45.47  | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | BETA: splitting (20940) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | |   (20941)  all_58_7 = e1 & op(e1, e2) = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | ALPHA: (20941) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | |   (20942)  op(e1, e2) = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (20936), (20942), (function-axioms) are
% 238.57/45.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #99.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | |   (20943)  all_58_13 = e1 & op(e0, e2) = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (42), (97), (103), (110), (112), (113),
% 238.57/45.47  | | | | | | | | | | | | | | | | | |            (133), (135), (158), (160), (164), (168), (170),
% 238.57/45.47  | | | | | | | | | | | | | | | | | |            (193), (201), (203), (220), (238), (258), (280),
% 238.57/45.47  | | | | | | | | | | | | | | | | | |            (282), (17760), (17761), (17766), (17768),
% 238.57/45.47  | | | | | | | | | | | | | | | | | |            (17773), (17776), (20122), (20906), (20908),
% 238.57/45.47  | | | | | | | | | | | | | | | | | |            (20910), (20937), (20943), (function-axioms) are
% 238.57/45.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #83.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | End of split
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | End of split
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | |   (20944)  all_54_10 = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | REF_CLOSE: (297), (20922), (20944) are inconsistent by
% 238.57/45.47  | | | | | | | | | | | | | | | |            sub-proof #2303.
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | End of split
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | End of split
% 238.57/45.47  | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | End of split
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | |   (20945)  all_36_2 = e2
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | COMBINE_EQS: (328), (20945) imply:
% 238.57/45.47  | | | | | | | | | | | | |   (20946)  all_6_2 = e2
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | SIMP: (20946) implies:
% 238.57/45.47  | | | | | | | | | | | | |   (20947)  all_6_2 = e2
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | COMBINE_EQS: (266), (20947) imply:
% 238.57/45.47  | | | | | | | | | | | | |   (20948)  all_56_21 = e2
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | REDUCE: (367), (20947) imply:
% 238.57/45.47  | | | | | | | | | | | | |   (20949)   ~ (all_52_2 = e2)
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | REDUCE: (378), (20947) imply:
% 238.57/45.47  | | | | | | | | | | | | |   (20950)   ~ (all_52_6 = e2)
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | REDUCE: (381), (20947) imply:
% 238.57/45.47  | | | | | | | | | | | | |   (20951)   ~ (all_52_9 = e2)
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | REDUCE: (17775), (20947) imply:
% 238.57/45.47  | | | | | | | | | | | | |   (20952)   ~ (e3 = e2)
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | REDUCE: (39), (20947) imply:
% 238.57/45.47  | | | | | | | | | | | | |   (20953)  op(e1, e1) = e2
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | BETA: splitting (244) gives:
% 238.57/45.47  | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | |   (20954)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 238.57/45.47  | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 238.57/45.47  | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | BETA: splitting (20954) gives:
% 238.57/45.47  | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | |   (20955)  all_58_0 = e2 & op(e3, e3) = e2
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | ALPHA: (20955) implies:
% 238.57/45.47  | | | | | | | | | | | | | | |   (20956)  op(e3, e3) = e2
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | REF_CLOSE: (6), (20123), (20956), (function-axioms) are
% 238.57/45.47  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | |   (20957)  all_58_1 = e2 & op(e3, e2) = e2
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | ALPHA: (20957) implies:
% 238.57/45.47  | | | | | | | | | | | | | | |   (20958)  all_58_1 = e2
% 238.57/45.47  | | | | | | | | | | | | | | |   (20959)  op(e3, e2) = e2
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | |   (20960)   ~ (all_44_2 = e2)
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | REDUCE: (17761), (20960) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | |   (20961)  $false
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | CLOSE: (20961) is inconsistent.
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | |   (20962)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.57/45.47  | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.57/45.47  | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.57/45.47  | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | |   (20963)  all_54_8 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (20963) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | |   (20964)  all_52_2 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | REDUCE: (143), (20964) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | |   (20965)   ~ (all_52_6 = e3)
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | SIMP: (20965) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | |   (20966)   ~ (all_52_6 = e3)
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | REDUCE: (141), (20964) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | |   (20967)   ~ (all_52_14 = e3)
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | SIMP: (20967) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | |   (20968)   ~ (all_52_14 = e3)
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | |   (20969)  all_54_9 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (20969) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | |   (20970)  all_52_6 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | REDUCE: (20966), (20970) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | |   (20971)  $false
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | CLOSE: (20971) is inconsistent.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | |   (20972)   ~ (all_54_9 = e3)
% 238.57/45.47  | | | | | | | | | | | | | | | | | |   (20973)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | |   (20974)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (20974) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | |   (20975)  all_58_6 = e3 & op(e1, e3) = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | ALPHA: (20975) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | |   (20976)  all_58_6 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | |   (20977)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (17776), (20959), (20977),
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | |            #86.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | |   (20978)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20978) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | |   (20979)  all_58_7 = e3 & op(e1, e2) = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20979) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | |   (20980)  op(e1, e2) = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (20966), (20980), (function-axioms) are
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | |   (20981)  all_58_13 = e3 & op(e0, e2) = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20981) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | |   (20982)  all_58_13 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | |   (20983)  op(e0, e2) = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | |   (20984)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (20919), (20959), (20984),
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | |            #1610.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | |   (20985)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20985) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | |   (20986)  all_58_7 = e1 & op(e1, e2) = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20986) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | |   (20987)  all_58_7 = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | |   (20988)  op(e1, e2) = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (20989)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20989) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20990)  all_58_12 = e1 & op(e0, e3) = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20990) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20991)  all_58_12 = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (239), (243), (20123),
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            (20976), (20991), (function-axioms) are
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1206.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20992)  all_58_13 = e1 & op(e0, e2) = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (20982), (20992) are inconsistent by
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2013.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (20993)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20993) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20994)  all_58_14 = e1 & op(e0, e1) = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20994) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (20995)  op(e0, e1) = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20996)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20996) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20997)  all_58_4 = e0 & op(e3, e1) = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (20997) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20998)  op(e3, e1) = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20973) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (20999)  all_54_9 = e2
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (20999) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21000)  all_52_6 = e2
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20950), (21000) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21001)  $false
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (21001) is inconsistent.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21002)  all_54_9 = e1 | all_54_9 = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21002) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21003)  all_54_9 = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (21003) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21004)  all_52_6 = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21004) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21005)  all_52_6 = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (21005) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21006)   ~ (all_52_14 = e1)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21006) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21007)   ~ (all_52_14 = e1)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21008)  all_54_11 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (20968), (21008) are inconsistent by
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21009)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21009) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21010)  all_54_11 = e2
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (17768), (21010) are inconsistent by
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2177.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21011)  all_54_11 = e1 | all_54_11 = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21011) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21012)  all_54_11 = e1
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (21007), (21012) are inconsistent by
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2176.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21013)  all_54_11 = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (21013) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21014)  all_52_14 = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21014) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21015)  all_52_14 = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (21015) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21016)   ~ (all_52_12 = e0)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (21015) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21017)  op(e1, e0) = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21018)  all_54_3 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (21018) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21019)  all_52_12 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21019) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21020)  all_52_12 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (21020) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21021)   ~ (all_52_13 = e3)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21021) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21022)   ~ (all_52_13 = e3)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (21020) imply:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21023)  op(e3, e0) = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21024)  all_54_7 = e3
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (21022), (21024) are inconsistent by
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21025)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21026)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21026) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21027)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (20114), (20117),
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20118), (20119), (20925), (20998), (21023),
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21027), (function-axioms) are inconsistent by
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #97.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21028)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (269), (17767), (20914), (20951),
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21025), (21028), (function-axioms) are
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #232.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21029)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21029) gives:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21030)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (17767), (20914), (21017), (21025),
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21030), (function-axioms) are inconsistent by
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #231.
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21031)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21031) implies:
% 238.57/45.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21032)  op(e0, all_56_31) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (21032) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21033)  op(e0, e2) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (20983), (21033), (function-axioms) are
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1961.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21034)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (17766), (20122), (21016), (21034) are
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21035)  all_54_9 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (20911), (21035) are inconsistent by
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1953.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21036)  all_58_5 = e0 & op(e2, e1) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (20913), (21036), (function-axioms) are
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21037)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (20953), (20995), (21037),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1036.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21038)  all_58_15 = e1 & op(e0, e0) = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21038) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21039)  all_58_15 = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (17773), (20920), (20958), (20987),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | |            (20988), (21039), (function-axioms) are
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #359.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |   (21040)  all_58_13 = e1 & op(e0, e2) = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (20982), (21040) are inconsistent by
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2013.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | |   (21041)  all_58_7 = e3 & op(e1, e2) = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | ALPHA: (21041) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | |   (21042)  op(e1, e2) = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (20966), (21042), (function-axioms) are
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21043)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (20953), (20968), (21043),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |            #2148.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | |   (21044)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | BETA: splitting (21044) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | |   (21045)  all_54_8 = e2
% 238.57/45.48  | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (21045) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | |   (21046)  all_52_2 = e2
% 238.57/45.48  | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | REDUCE: (20949), (21046) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | |   (21047)  $false
% 238.57/45.48  | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | CLOSE: (21047) is inconsistent.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | |   (21048)   ~ (all_54_8 = e2)
% 238.57/45.48  | | | | | | | | | | | | | | | | | |   (21049)  all_54_8 = e1 | all_54_8 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | BETA: splitting (21049) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21050)  all_54_8 = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (21050) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21051)  all_52_2 = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | REDUCE: (20118), (21051) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21052)  $false
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | CLOSE: (21052) is inconsistent.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21053)  all_54_8 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (21053) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21054)  all_52_2 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | REDUCE: (144), (21054) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21055)   ~ (all_52_3 = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | SIMP: (21055) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21056)   ~ (all_52_3 = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | REDUCE: (143), (21054) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21057)   ~ (all_52_6 = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | REDUCE: (141), (21054) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21058)   ~ (all_52_14 = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | SIMP: (21058) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21059)   ~ (all_52_14 = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | REDUCE: (20949), (21054) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21060)   ~ (e2 = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | REDUCE: (20118), (21054) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | |   (21061)   ~ (e1 = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | |   (21062)  all_54_12 = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (21062) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | |   (21063)  all_52_3 = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | SIMP: (21063) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | |   (21064)  all_52_3 = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (21064) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | |   (21065)   ~ (all_52_7 = e3)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | SIMP: (21065) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | |   (21066)   ~ (all_52_7 = e3)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | |   (21067)  all_54_13 = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (21066), (21067) are inconsistent by
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | |   (21068)   ~ (all_54_13 = e3)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | |   (21069)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | |   (21070)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21070) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | |   (21071)  all_58_6 = e0 & op(e1, e3) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21071) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | |   (21072)  all_58_6 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | |   (21073)  op(e1, e3) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |   (21074)  all_58_15 = e0 & op(e0, e0) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21074) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |   (21075)  op(e0, e0) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (88), (110),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |            (144), (148), (149), (159), (160), (163), (164),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (169), (192), (200), (214), (216),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (219), (227), (230), (232), (234),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |            (239), (243), (245), (257), (279), (17775),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |            (20114), (20115), (20116), (20117), (20119),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |            (20121), (20123), (20913), (20919), (20920),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |            (20922), (21072), (21073), (21075),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |            #1084.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |   (21076)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21076) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |   (21077)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |   (21078)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (21079)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (17776), (20959), (21079),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | |            #86.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (21080)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21080) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21081)  all_58_7 = e3 & op(e1, e2) = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21081) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21082)  op(e1, e2) = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21083)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (20919), (20959), (21083),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1610.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21084)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21084) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21085)  all_58_7 = e1 & op(e1, e2) = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21085) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21086)  op(e1, e2) = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21082), (21086), (function-axioms) are
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2094.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21087)  all_58_13 = e1 & op(e0, e2) = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21087) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21088)  all_58_13 = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21077) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21089)  all_58_12 = e0 & op(e0, e3) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21089) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21090)  op(e0, e3) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (21056), (21090), (function-axioms) are
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21091)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21091) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21092)  all_58_13 = e0 & op(e0, e2) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21092) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21093)  op(e0, e2) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (20912), (21093), (function-axioms) are
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2252.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21094)  all_58_14 = e0 & op(e0, e1) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21094) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21095)  all_58_14 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21096)  op(e0, e1) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21097)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21097) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21098)  all_58_4 = e1 & op(e3, e1) = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21098) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21099)  op(e3, e1) = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (20121), (21099), (function-axioms) are
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21100)  all_58_5 = e1 & op(e2, e1) = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21100) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21101)  op(e2, e1) = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21078) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21102)  all_58_9 = e0 & op(e3, e0) = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21102) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21103)  all_58_9 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21069) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21104)  all_54_13 = e2
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17764), (21104) are inconsistent by
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21105)   ~ (all_54_13 = e2)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21106)  all_54_13 = e1 | all_54_13 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21107)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21107) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21108)  all_58_0 = e3 & op(e3, e3) = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21108) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21109)  op(e3, e3) = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (20117), (20118),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20119), (21109), (function-axioms) are
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21110)  all_58_1 = e3 & op(e3, e2) = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21110) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21111)  op(e3, e2) = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (162), (170), (195), (267), (21082),
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21111), (function-axioms) are inconsistent by
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2190.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21112)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21112) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21113)  all_58_4 = e3 & op(e3, e1) = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21113) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21114)  op(e3, e1) = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21106) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21115)  all_54_13 = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (21115) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21116)  all_52_7 = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21116) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21117)  all_52_7 = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (21117) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21118)   ~ (all_52_6 = e1)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17764), (21117) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21119)   ~ (e2 = e1)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (21117) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21120)  op(e0, e2) = e1
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21121)  all_54_9 = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (21121) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21122)  all_52_6 = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21122) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21123)  all_52_6 = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (21123) imply:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21124)   ~ (all_52_14 = e3)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21124) implies:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21125)   ~ (all_52_14 = e3)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21126)  all_54_11 = e3
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (21125), (21126) are inconsistent by
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21127)   ~ (all_54_11 = e3)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21128)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21129)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21129) gives:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21130)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21130) implies:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21131)  op(e3, e1) = all_56_17
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21132)  op(e3, all_56_17) = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21128) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21133)  all_54_11 = e2
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (17768), (21133) are inconsistent by
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2177.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21134)  all_54_11 = e1 | all_54_11 = e0
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21134) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21135)  all_54_11 = e1
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (21135) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21136)  all_52_14 = e1
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21136) implies:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21137)  all_52_14 = e1
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21125), (21137) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21138)   ~ (e3 = e1)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_17, e1, e3, simplifying with (21114),
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (21131) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21139)  all_56_17 = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21132), (21139) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21140)  op(e3, e3) = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (20117), (20118),
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20119), (21140), (function-axioms) are
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21141)  all_54_11 = e0
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (21059), (21141) are inconsistent by
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2175.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21142)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21142) implies:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21143)  op(e2, e1) = all_56_19
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21144)  op(e2, all_56_19) = e2
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (21101), (21143), (21144), (function-axioms)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #299.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21145)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21145) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21146)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21146) implies:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21147)  op(e1, all_56_21) = e1
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20948), (21147) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21148)  op(e1, e2) = e1
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21082), (21148), (function-axioms) are
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2094.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21149)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21149) implies:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21150)  op(e0, e1) = all_56_23
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21151)  op(e0, all_56_23) = e0
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (218), (219),
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20962), (21077), (21088), (21095), (21096),
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21120), (21150), (21151), (function-axioms) are
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #228.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21152)   ~ (all_54_9 = e3)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (21152) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21153)   ~ (all_52_6 = e3)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (21082), (21153), (function-axioms) are
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21154)  all_54_13 = e0
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (20912), (21154) are inconsistent by
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2008.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21155)  all_58_9 = e3 & op(e3, e0) = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21103), (21155) are inconsistent by
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1621.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21156)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (20914), (21059), (21156),
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1490.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21157)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (20953), (21096), (21157),
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2157.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21158)  all_58_13 = e3 & op(e0, e2) = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (21066), (21158), (function-axioms) are
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | |   (21159)  all_58_7 = e0 & op(e1, e2) = e0
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (20911), (21159), (function-axioms) are
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2022.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | |   (21160)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (20953), (21059), (21160),
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | |            #1851.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | |   (21161)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (17763), (20119), (21056), (21161) are
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2066.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | |   (21162)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 238.57/45.49  | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 238.57/45.49  | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (162), (163),
% 238.57/45.49  | | | | | | | | | | | | | |            (165), (168), (225), (227), (228), (230), (17766),
% 238.57/45.49  | | | | | | | | | | | | | |            (17768), (20949), (20950), (21162),
% 238.57/45.49  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.49  | | | | | | | | | | | | | |            #89.
% 238.57/45.49  | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | |   (21163)  all_18_2 = e0
% 238.57/45.49  | | | | | | | | | | |   (21164)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0
% 238.57/45.49  | | | | | | | | | | |              & op(e1, e0) = all_18_1 & $i(all_18_0) &
% 238.57/45.49  | | | | | | | | | | |              $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1, e0)
% 238.57/45.49  | | | | | | | | | | |              = all_18_1 & $i(all_18_1))
% 238.57/45.49  | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | COMBINE_EQS: (339), (21163) imply:
% 238.57/45.49  | | | | | | | | | | |   (21165)  all_6_2 = e0
% 238.57/45.49  | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | SIMP: (21165) implies:
% 238.57/45.49  | | | | | | | | | | |   (21166)  all_6_2 = e0
% 238.57/45.49  | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | COMBINE_EQS: (332), (21166) imply:
% 238.57/45.49  | | | | | | | | | | |   (21167)  all_28_2 = e0
% 238.57/45.49  | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | COMBINE_EQS: (266), (21166) imply:
% 238.57/45.49  | | | | | | | | | | |   (21168)  all_56_21 = e0
% 238.57/45.49  | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | REDUCE: (367), (21166) imply:
% 238.57/45.49  | | | | | | | | | | |   (21169)   ~ (all_52_2 = e0)
% 238.57/45.49  | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | REDUCE: (380), (21166) imply:
% 238.57/45.49  | | | | | | | | | | |   (21170)   ~ (all_52_8 = e0)
% 238.57/45.49  | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | REDUCE: (39), (21166) imply:
% 238.57/45.49  | | | | | | | | | | |   (21171)  op(e1, e1) = e0
% 238.57/45.49  | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | BETA: splitting (240) gives:
% 238.57/45.49  | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | |   (21172)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 238.57/45.49  | | | | | | | | | | | |              & op(e3, e2) = e0)
% 238.57/45.49  | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | REF_CLOSE: (4), (170), (20123), (20910), (21172),
% 238.57/45.49  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.49  | | | | | | | | | | | |            #1066.
% 238.57/45.49  | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | |   (21173)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 238.57/45.49  | | | | | | | | | | | |              & op(e3, e0) = e0)
% 238.57/45.49  | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | BETA: splitting (21173) gives:
% 238.57/45.49  | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | |   (21174)  all_58_4 = e0 & op(e3, e1) = e0
% 238.57/45.49  | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | REF_CLOSE: (169), (21170), (21174), (function-axioms) are
% 238.57/45.49  | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 238.57/45.49  | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | |   (21175)  all_58_9 = e0 & op(e3, e0) = e0
% 238.57/45.49  | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | ALPHA: (21175) implies:
% 238.57/45.49  | | | | | | | | | | | | |   (21176)  all_58_9 = e0
% 238.57/45.49  | | | | | | | | | | | | |   (21177)  op(e3, e0) = e0
% 238.57/45.49  | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | BETA: splitting (239) gives:
% 238.57/45.49  | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | |   (21178)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 238.57/45.49  | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 238.57/45.49  | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (20123), (20909), (21178),
% 238.57/45.49  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.49  | | | | | | | | | | | | | |            #1272.
% 238.57/45.49  | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | |   (21179)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 238.57/45.49  | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 238.57/45.49  | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | BETA: splitting (21179) gives:
% 238.57/45.49  | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | |   (21180)  all_58_6 = e0 & op(e1, e3) = e0
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | ALPHA: (21180) implies:
% 238.57/45.49  | | | | | | | | | | | | | | |   (21181)  op(e1, e3) = e0
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | REF_CLOSE: (163), (21169), (21181), (function-axioms) are
% 238.57/45.49  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | |   (21182)  all_58_12 = e0 & op(e0, e3) = e0
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | ALPHA: (21182) implies:
% 238.57/45.49  | | | | | | | | | | | | | | |   (21183)  all_58_12 = e0
% 238.57/45.49  | | | | | | | | | | | | | | |   (21184)  op(e0, e3) = e0
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 238.57/45.49  | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (21184) gives:
% 238.57/45.49  | | | | | | | | | | | | | | |   (21185)  all_52_3 = e0
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 238.57/45.49  | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (168), (21177) gives:
% 238.57/45.49  | | | | | | | | | | | | | | |   (21186)  all_52_12 = e0
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | REDUCE: (140), (21185) imply:
% 238.57/45.49  | | | | | | | | | | | | | | |   (21187)   ~ (all_52_7 = e0)
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | REDUCE: (139), (21185) imply:
% 238.57/45.49  | | | | | | | | | | | | | | |   (21188)   ~ (all_52_11 = e0)
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | SIMP: (21188) implies:
% 238.57/45.49  | | | | | | | | | | | | | | |   (21189)   ~ (all_52_11 = e0)
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | REDUCE: (113), (21186) imply:
% 238.57/45.49  | | | | | | | | | | | | | | |   (21190)   ~ (all_52_13 = e0)
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | REDUCE: (17766), (21186) imply:
% 238.57/45.49  | | | | | | | | | | | | | | |   (21191)   ~ (e2 = e0)
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | REDUCE: (20122), (21186) imply:
% 238.57/45.49  | | | | | | | | | | | | | | |   (21192)   ~ (e1 = e0)
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | |   (21193)   ~ (all_28_2 = e0)
% 238.57/45.49  | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | REDUCE: (21167), (21193) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | |   (21194)  $false
% 238.57/45.49  | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | CLOSE: (21194) is inconsistent.
% 238.57/45.49  | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | |   (21195)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0
% 238.57/45.49  | | | | | | | | | | | | | | | |              & op(e1, e0) = all_28_1 & $i(all_28_0) &
% 238.57/45.49  | | | | | | | | | | | | | | | |              $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0)
% 238.57/45.49  | | | | | | | | | | | | | | | |              = all_28_1 & $i(all_28_1))
% 238.57/45.49  | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | |   (21196)   ~ (all_44_2 = e2)
% 238.57/45.49  | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | REDUCE: (17761), (21196) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | | |   (21197)  $false
% 238.57/45.49  | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | CLOSE: (21197) is inconsistent.
% 238.57/45.49  | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | |   (21198)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.57/45.49  | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.57/45.49  | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.57/45.49  | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.57/45.49  | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | |   (21199)   ~ (all_48_2 = e0)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | REDUCE: (20908), (21199) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | | | |   (21200)  $false
% 238.57/45.49  | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | CLOSE: (21200) is inconsistent.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | |   (21201)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 238.57/45.49  | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 238.57/45.49  | | | | | | | | | | | | | | | | | |              $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 238.57/45.49  | | | | | | | | | | | | | | | | | |              = all_48_1 & $i(all_48_1))
% 238.57/45.49  | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | |   (21202)  all_54_1 = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (21202) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | |   (21203)  all_52_4 = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | SIMP: (21203) implies:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | |   (21204)  all_52_4 = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | REDUCE: (135), (21204) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | |   (21205)   ~ (all_52_7 = e3)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | SIMP: (21205) implies:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | |   (21206)   ~ (all_52_7 = e3)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | REDUCE: (134), (21204) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | |   (21207)   ~ (all_52_8 = e3)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | SIMP: (21207) implies:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | |   (21208)   ~ (all_52_8 = e3)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | REDUCE: (170), (21204) imply:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | |   (21209)  op(e3, e2) = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | |   (21210)  all_54_13 = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (21206), (21210) are inconsistent by
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | |   (21211)   ~ (all_54_13 = e3)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | |   (21212)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | |   (21213)  all_54_2 = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (21208), (21213) are inconsistent by
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | |   (21214)   ~ (all_54_2 = e3)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | |   (21215)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | |   (21216)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21216) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | |   (21217)  all_58_12 = e3 & op(e0, e3) = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21217) implies:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | |   (21218)  op(e0, e3) = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21184), (21218), (function-axioms) are
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #221.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | |   (21219)  all_58_13 = e3 & op(e0, e2) = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (21206), (21219), (function-axioms) are
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | |   (21220)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21220) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | |   (21221)  all_58_14 = e3 & op(e0, e1) = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21221) implies:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | |   (21222)  all_58_14 = e3
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | |   (21223)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (158), (162), (235), (20911),
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | |            (20912), (21209), (21223), (function-axioms) are
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #82.
% 238.57/45.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | |   (21224)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21224) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (21225)  all_58_7 = e2 & op(e1, e2) = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21225) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (21226)  all_58_7 = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21227)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21227) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21228)  all_58_12 = e1 & op(e0, e3) = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21228) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21229)  op(e0, e3) = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21184), (21229), (function-axioms) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #207.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21230)  all_58_13 = e1 & op(e0, e2) = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21230) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21231)  all_58_13 = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21232)  op(e0, e2) = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21215) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21233)  all_54_2 = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (21233) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21234)  all_52_8 = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21234) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21235)  all_52_8 = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (21235) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21236)   ~ (all_52_9 = e2)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21236) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21237)   ~ (all_52_9 = e2)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (21235) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21238)   ~ (all_52_11 = e2)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21208), (21235) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21239)   ~ (e3 = e2)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (21235) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21240)  op(e3, e1) = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21241)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21241) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21242)  all_58_2 = e2 & op(e2, e3) = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21242) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21243)  op(e2, e3) = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21244)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21244) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21245)  all_58_0 = e3 & op(e3, e3) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21245) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21246)  op(e3, e3) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (20117), (20118),
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20119), (21246), (function-axioms) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21247)  all_58_2 = e3 & op(e2, e3) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21247) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21248)  op(e2, e3) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (21243), (21248), (function-axioms) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21249)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21249) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21250)  all_58_6 = e3 & op(e1, e3) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21250) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21251)  all_58_6 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21252)  op(e1, e3) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21212) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21253)  all_54_13 = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17764), (21253) are inconsistent by
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21254)  all_54_13 = e1 | all_54_13 = e0
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21254) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21255)  all_54_13 = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (21255) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21256)  all_52_7 = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21256) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21257)  all_52_7 = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (21257) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21258)   ~ (all_52_11 = e1)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21258) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21259)   ~ (all_52_11 = e1)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21260)  all_54_14 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (21260) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21261)  all_52_11 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21261) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21262)  all_52_11 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (21262) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21263)   ~ (all_52_9 = e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (21262) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21264)  op(e0, e1) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21265)  all_54_6 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (21263), (21265) are inconsistent by
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21266)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21266) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21267)  all_54_6 = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (21237), (21267) are inconsistent by
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21268)   ~ (all_54_6 = e2)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21269)  all_54_6 = e1 | all_54_6 = e0
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21269) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21270)  all_54_6 = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (21270) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21271)  all_52_9 = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21271) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21272)  all_52_9 = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (21272) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21273)   ~ (all_52_13 = e1)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21273) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21274)   ~ (all_52_13 = e1)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21237), (21272) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21275)   ~ (e2 = e1)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21276)  all_54_7 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (21276) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21277)  all_52_13 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21277) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21278)  all_52_13 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (21278) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21279)   ~ (all_52_1 = e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21280)  all_54_4 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (21279), (21280) are inconsistent by
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21281)   ~ (all_54_4 = e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21282)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21283)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21283) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21284)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21284) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21285)  op(e3, all_56_1) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20116), (21285) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21286)  op(e3, e1) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (21240), (21286), (function-axioms) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #177.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21287)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (167), (243), (245),
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (279), (20117), (20123), (20909), (20920),
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21183), (21251), (21279), (21282), (21287),
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1040.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21288)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21288) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21289)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21289) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21290)  op(e1, e3) = all_56_5
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21291)  op(e1, all_56_5) = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21252), (21290), (21291), (function-axioms)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2243.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21292)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21292) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21293)  op(e0, e3) = all_56_7
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21294)  op(e0, all_56_7) = e0
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (216), (17774), (21198), (21232),
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21264), (21293), (21294), (function-axioms) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #109.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21295)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (269), (20914), (21243), (21274),
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21295), (function-axioms) are inconsistent by
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2292.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21296)  all_54_6 = e0
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (20913), (21296) are inconsistent by
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2245.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21297)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (17765), (21189), (21259), (21297) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1798.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21298)  all_54_13 = e0
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (20912), (21298) are inconsistent by
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2008.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21299)  all_58_12 = e3 & op(e0, e3) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21299) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21300)  all_58_12 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (218), (21222),
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21231), (21232), (21300), (function-axioms) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1868.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21301)  all_58_3 = e2 & op(e2, e2) = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21301) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21302)  all_58_3 = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21303)  op(e2, e2) = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21304)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21304) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21305)  all_58_1 = e3 & op(e3, e2) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21305) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21306)  all_58_1 = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (170), (235),
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (238), (20910), (21226), (21302),
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21303), (21306), (function-axioms) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #81.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21307)  all_58_3 = e3 & op(e2, e2) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21307) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21308)  op(e2, e2) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (21303), (21308), (function-axioms) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21309)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21309) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21310)  all_58_7 = e3 & op(e1, e2) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (21226), (21310) are inconsistent by
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1675.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21311)  all_58_13 = e3 & op(e0, e2) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (21206), (21311), (function-axioms) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21312)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (17767), (21237), (21312),
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #182.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21313)  all_54_2 = e1 | all_54_2 = e0
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (20121), (21170), (21313) are inconsistent
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1336.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21314)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21314) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21315)  all_58_14 = e1 & op(e0, e1) = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21222), (21315) are inconsistent by
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1900.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21316)  all_58_15 = e1 & op(e0, e0) = e1
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (21316) are inconsistent by
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #218.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (21317)  all_58_13 = e2 & op(e0, e2) = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21317) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (21318)  op(e0, e2) = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (21318), (function-axioms) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | |   (21319)  all_58_15 = e3 & op(e0, e0) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21319) implies:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | |   (21320)  op(e0, e0) = e3
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17774), (21320), (function-axioms) are
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | |   (21321)   ~ (all_54_1 = e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | |   (21322)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | REDUCE: (282), (21321) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | |   (21323)   ~ (all_52_4 = e3)
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | BETA: splitting (21322) gives:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | |   (21324)  all_54_1 = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (21324) imply:
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | |   (21325)  all_52_4 = e2
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.50  | | | | | | | | | | | | | | | | | | | | SIMP: (21325) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | |   (21326)  all_52_4 = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (21326) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | |   (21327)   ~ (all_52_6 = e2)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | SIMP: (21327) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | |   (21328)   ~ (all_52_6 = e2)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (21326) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | |   (21329)   ~ (all_52_7 = e2)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (21326) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | |   (21330)   ~ (all_52_8 = e2)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | SIMP: (21330) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | |   (21331)   ~ (all_52_8 = e2)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | REDUCE: (21323), (21326) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | |   (21332)   ~ (e3 = e2)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (21326) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | |   (21333)  op(e3, e2) = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | |   (21334)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21334) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | |   (21335)  all_58_0 = e3 & op(e3, e3) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21335) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | |   (21336)  op(e3, e3) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (20117), (20118),
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | |            (20119), (21336), (function-axioms) are
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | |   (21337)  all_58_1 = e3 & op(e3, e2) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21337) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | |   (21338)  op(e3, e2) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (21333), (21338), (function-axioms) are
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2193.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | |   (21339)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21339) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | |   (21340)  all_58_4 = e3 & op(e3, e1) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21340) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | |   (21341)  all_58_4 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | |   (21342)  all_54_2 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (21342) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | |   (21343)  all_52_8 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21343) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | |   (21344)  all_52_8 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (21344) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | |   (21345)   ~ (all_52_9 = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21345) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | |   (21346)   ~ (all_52_9 = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (21344) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | |   (21347)   ~ (all_52_11 = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21347) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | |   (21348)   ~ (all_52_11 = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (21344) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | |   (21349)  op(e3, e1) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | |   (21350)  all_54_14 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (21350) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | |   (21351)  all_52_11 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21348), (21351) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | |   (21352)  $false
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (21352) is inconsistent.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | |   (21353)   ~ (all_54_14 = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | |   (21354)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (21355)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21355) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21356)  all_58_12 = e3 & op(e0, e3) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21356) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21357)  op(e0, e3) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21184), (21357), (function-axioms) are
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #221.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21358)  all_58_13 = e3 & op(e0, e2) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21358) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21359)  all_58_13 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21354) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21360)  all_54_14 = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (21360) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21361)  all_52_11 = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17765), (21361) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21362)  $false
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (21362) is inconsistent.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21363)  all_54_14 = e1 | all_54_14 = e0
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21364)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21364) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21365)  all_58_6 = e2 & op(e1, e3) = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21365) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21366)  all_58_6 = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21367)  op(e1, e3) = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21368)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21368) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21369)  all_58_0 = e2 & op(e3, e3) = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21369) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21370)  op(e3, e3) = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (245),
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21183), (21366), (21367), (21370),
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21371)  all_58_1 = e2 & op(e3, e2) = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21371) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21372)  all_58_1 = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21373)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (20919), (21333), (21373),
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1610.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21374)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21374) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21375)  all_58_7 = e1 & op(e1, e2) = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21375) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21376)  all_58_7 = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21377)  op(e1, e2) = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21378)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21378) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21379)  all_58_0 = e3 & op(e3, e3) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21379) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21380)  op(e3, e3) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (20117), (20118),
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20119), (21380), (function-axioms) are
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21381)  all_58_2 = e3 & op(e2, e3) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21381) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21382)  all_58_2 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21383)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21383) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21384)  all_58_6 = e3 & op(e1, e3) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21384) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21385)  all_58_6 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (239), (243), (20123),
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21382), (21385), (function-axioms) are
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1221.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21386)  all_58_7 = e3 & op(e1, e2) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21386) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21387)  op(e1, e2) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21377), (21387), (function-axioms) are
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2094.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21388)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21388) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21389)  all_58_8 = e3 & op(e1, e1) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21171), (21389), (function-axioms) are
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21390)  all_58_11 = e3 & op(e1, e0) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21390) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21391)  op(e1, e0) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21392)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21392) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21393)  all_58_9 = e1 & op(e3, e0) = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21393) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21394)  all_58_9 = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (240), (244), (20123),
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21341), (21394), (function-axioms) are
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1292.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21395)  all_58_10 = e1 & op(e2, e0) = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21395) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21396)  op(e2, e0) = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21363) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21397)  all_54_14 = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (21397) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21398)  all_52_11 = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21398) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21399)  all_52_11 = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (21399) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21400)   ~ (all_52_7 = e1)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (21399) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21401)   ~ (all_52_9 = e1)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (21399) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21402)  op(e0, e1) = e1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21403)  all_54_13 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (21403) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21404)  all_52_7 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21404) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21405)  all_52_7 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (21405) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21406)   ~ (all_52_6 = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (21405) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21407)  op(e0, e2) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21408)  all_54_6 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (21346), (21408) are inconsistent by
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21409)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21409) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21410)  all_54_6 = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (21410) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21411)  all_52_9 = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21411) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21412)  all_52_9 = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (21412) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21413)   ~ (all_52_1 = e2)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (21412) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21414)   ~ (all_52_13 = e2)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (21412) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21415)  op(e2, e1) = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21416)  all_54_4 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (21416) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21417)  all_52_1 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21417) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21418)  all_52_1 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (21418) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21419)   ~ (all_52_13 = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21419) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21420)   ~ (all_52_13 = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21421)  all_54_7 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (21420), (21421) are inconsistent by
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21422)   ~ (all_54_7 = e3)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21423)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21424)  all_54_9 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (21406), (21424) are inconsistent by
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21425)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21426)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21426) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21427)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21427) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21428)  op(e3, e1) = all_56_17
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21429)  op(e3, all_56_17) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21425) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21430)  all_54_9 = e2
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (21328), (21430) are inconsistent by
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1954.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21431)  all_54_9 = e1 | all_54_9 = e0
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21164) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21432)   ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 &
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_18_1 & $i(all_18_0) &
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_18_1)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21432) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21433)  op(e1, e0) = all_18_1
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21434)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21434) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21435)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21435) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21436)  op(e3, e0) = all_56_25
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21437)  op(e3, all_56_25) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21177), (21436), (21437), (function-axioms)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1926.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21438)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21438) implies:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21439)  op(e2, e0) = all_56_27
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21201) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_17, e1, e3, simplifying with (21349),
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (21428) gives:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21440)  all_56_17 = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21429), (21440) imply:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21441)  op(e3, e3) = e3
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (20117), (20118),
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20119), (21441), (function-axioms) are
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.57/45.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21442)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_48_1)
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21442) implies:
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21443)   ~ (all_48_1 = e3)
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21444)  op(e2, e0) = all_48_1
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_48_1,
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27, e0, e2, simplifying with (21439),
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (21444) gives:
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21445)  all_56_27 = all_48_1
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27, e0, e2, simplifying with (21396),
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (21439) gives:
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21446)  all_56_27 = e1
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_17, e1, e3, simplifying with (21349),
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (21428) gives:
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21447)  all_56_17 = e3
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21445), (21446) imply:
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21448)  all_48_1 = e1
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21443), (21448) imply:
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21449)   ~ (e3 = e1)
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.57/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21429), (21447) imply:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21450)  op(e3, e3) = e3
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (20117), (20118),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (20119), (21450), (function-axioms) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21451)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21451) gives:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21452)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21452) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21453)  op(e1, e0) = all_56_29
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21454)  op(e1, all_56_29) = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21195) gives:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21455)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_28_1 & $i(all_28_0) &
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_28_1)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21455) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21456)  op(e1, e0) = all_28_1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (163), (267), (269), (17767), (20911),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21391), (21423), (21431), (21433), (21453),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21454), (21456), (function-axioms) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #80.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21457)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_28_1)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21457) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21458)  op(e1, e0) = all_28_1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (163), (267), (269), (17767), (20911),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21391), (21423), (21431), (21433), (21453),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21454), (21458), (function-axioms) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #80.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21459)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21459) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21460)  op(e0, all_56_31) = e0
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (21460) imply:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21461)  op(e0, e2) = e0
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21407), (21461), (function-axioms) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1961.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21462)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 &
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_18_1)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21195), (21391), (21462), (function-axioms) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1767.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21463)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (20906), (20920), (21201), (21396), (21415),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21463), (function-axioms) are inconsistent by
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1520.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21464)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21464) gives:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21465)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21465) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21466)  op(e1, all_56_21) = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21168), (21466) imply:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21467)  op(e1, e0) = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21391), (21467), (function-axioms) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21468)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21468) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21469)  op(e0, e1) = all_56_23
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21470)  op(e0, all_56_23) = e0
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (197), (269), (17767), (20914), (21402), (21420),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21469), (21470), (function-axioms) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #79.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21471)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (148), (159), (279), (20117), (21184), (21413),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21471), (function-axioms) are inconsistent by
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21472)  all_54_6 = e1 | all_54_6 = e0
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (20913), (21401), (21472) are inconsistent
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #476.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21473)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17764), (20912), (21400), (21473) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1648.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21474)  all_54_14 = e0
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (21189), (21474) are inconsistent by
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1936.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21475)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21475) gives:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21476)  all_58_11 = e1 & op(e1, e0) = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21476) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21477)  op(e1, e0) = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21391), (21477), (function-axioms) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21478)  all_58_15 = e1 & op(e0, e0) = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21478) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21479)  all_58_15 = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17773), (21479) imply:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21480)  e2 = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (237),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (20920), (21372), (21376), (21377),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21480), (function-axioms) are inconsistent by
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1497.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21481)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21481) gives:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21482)  all_58_6 = e3 & op(e1, e3) = e3
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21482) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21483)  all_58_6 = e3
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21366), (21483) imply:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21484)  e3 = e2
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21484) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21485)  e3 = e2
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21341), (21485) imply:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21486)  all_58_4 = e2
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (157), (165), (230), (21171), (21346),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21348), (21486), (function-axioms) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1493.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21487)  all_58_12 = e3 & op(e0, e3) = e3
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (167), (239), (20123), (20909),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21366), (21487), (function-axioms) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #280.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21488)  all_58_13 = e1 & op(e0, e2) = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21488) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21489)  all_58_13 = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21359), (21489) imply:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21490)  e3 = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21341), (21490) imply:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21491)  all_58_4 = e1
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (240), (244),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (20123), (21323), (21491),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1468.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21492)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (157), (165), (168), (230), (17766),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21171), (21346), (21348), (21492),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #78.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21493)  all_58_7 = e2 & op(e1, e2) = e2
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21493) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21494)  op(e1, e2) = e2
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (21328), (21494), (function-axioms) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #249.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21495)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (17768), (21171), (21495),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #167.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (21496)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17774), (21348), (21496),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | |            #226.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | |   (21497)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (20121), (21170), (21331), (21497) are
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1335.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | |   (21498)  all_58_9 = e3 & op(e3, e0) = e3
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21498) implies:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | |   (21499)  all_58_9 = e3
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21176), (21499) are inconsistent by
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1958.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | |   (21500)  all_54_1 = e1 | all_54_1 = e0
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (168), (282), (20120), (21177), (21500),
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | |            #87.
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | | 
% 238.66/45.52  | | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | | 
% 238.66/45.52  | | | | | | | | |   (21501)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0
% 238.66/45.52  | | | | | | | | |              & op(e2, e0) = e0)
% 238.66/45.52  | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | REF_CLOSE: (164), (165), (20913), (20914), (21501),
% 238.66/45.52  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.52  | | | | | | | | |            #1991.
% 238.66/45.52  | | | | | | | | | 
% 238.66/45.52  | | | | | | | | End of split
% 238.66/45.52  | | | | | | | | 
% 238.66/45.52  | | | | | | | End of split
% 238.66/45.52  | | | | | | | 
% 238.66/45.52  | | | | | | End of split
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | Case 2:
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | |   (21502)  all_8_2 = e3
% 238.66/45.52  | | | | | |   (21503)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2,
% 238.66/45.52  | | | | | |                e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~
% 238.66/45.52  | | | | | |              (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1))
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | | COMBINE_EQS: (320), (21502) imply:
% 238.66/45.52  | | | | | |   (21504)  all_42_2 = e3
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | | COMBINE_EQS: (353), (21502) imply:
% 238.66/45.52  | | | | | |   (21505)  all_56_11 = e3
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | | REDUCE: (366), (21502) imply:
% 238.66/45.52  | | | | | |   (21506)   ~ (all_52_1 = e3)
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | | REDUCE: (369), (21502) imply:
% 238.66/45.52  | | | | | |   (21507)   ~ (all_52_4 = e3)
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | | REDUCE: (371), (21502) imply:
% 238.66/45.52  | | | | | |   (21508)   ~ (all_52_6 = e3)
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | | REDUCE: (373), (21502) imply:
% 238.66/45.52  | | | | | |   (21509)   ~ (all_52_7 = e3)
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | | REDUCE: (375), (21502) imply:
% 238.66/45.52  | | | | | |   (21510)   ~ (all_52_9 = e3)
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | | REDUCE: (377), (21502) imply:
% 238.66/45.52  | | | | | |   (21511)   ~ (all_52_13 = e3)
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | | BETA: splitting (234) gives:
% 238.66/45.52  | | | | | | 
% 238.66/45.52  | | | | | | Case 1:
% 238.66/45.52  | | | | | | | 
% 238.66/45.52  | | | | | | |   (21512)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 &
% 238.66/45.52  | | | | | | |              op(e2, e2) = e3)
% 238.66/45.52  | | | | | | | 
% 238.66/45.52  | | | | | | | BETA: splitting (21512) gives:
% 238.66/45.52  | | | | | | | 
% 238.66/45.52  | | | | | | | Case 1:
% 238.66/45.52  | | | | | | | | 
% 238.66/45.52  | | | | | | | |   (21513)  all_58_2 = e3 & op(e2, e3) = e3
% 238.66/45.52  | | | | | | | | 
% 238.66/45.52  | | | | | | | | ALPHA: (21513) implies:
% 238.66/45.52  | | | | | | | |   (21514)  op(e2, e3) = e3
% 238.66/45.52  | | | | | | | | 
% 238.66/45.52  | | | | | | | | REF_CLOSE: (167), (21506), (21514), (function-axioms) are
% 238.66/45.52  | | | | | | | |            inconsistent by sub-proof #2337.
% 238.66/45.52  | | | | | | | | 
% 238.66/45.52  | | | | | | | Case 2:
% 238.66/45.52  | | | | | | | | 
% 238.66/45.52  | | | | | | | |   (21515)  all_58_3 = e3 & op(e2, e2) = e3
% 238.66/45.52  | | | | | | | | 
% 238.66/45.52  | | | | | | | | ALPHA: (21515) implies:
% 238.66/45.52  | | | | | | | |   (21516)  all_58_3 = e3
% 238.66/45.52  | | | | | | | |   (21517)  op(e2, e2) = e3
% 238.66/45.52  | | | | | | | | 
% 238.66/45.52  | | | | | | | | BETA: splitting (46) gives:
% 238.66/45.52  | | | | | | | | 
% 238.66/45.52  | | | | | | | | Case 1:
% 238.66/45.52  | | | | | | | | | 
% 238.66/45.52  | | | | | | | | |   (21518)   ~ (all_10_2 = e1)
% 238.66/45.52  | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | BETA: splitting (55) gives:
% 238.66/45.52  | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | Case 1:
% 238.66/45.52  | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | |   (21519)   ~ (all_16_2 = e0)
% 238.66/45.52  | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | REDUCE: (342), (21519) imply:
% 238.66/45.52  | | | | | | | | | |   (21520)   ~ (all_10_2 = e0)
% 238.66/45.52  | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | BETA: splitting (58) gives:
% 238.66/45.52  | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | Case 1:
% 238.66/45.52  | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | |   (21521)   ~ (all_18_2 = e0)
% 238.66/45.52  | | | | | | | | | | | 
% 238.66/45.52  | | | | | | | | | | | REDUCE: (339), (21521) imply:
% 238.66/45.52  | | | | | | | | | | |   (21522)   ~ (all_6_2 = e0)
% 238.66/45.52  | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | BETA: splitting (67) gives:
% 238.66/45.53  | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | |   (21523)   ~ (all_24_2 = e2)
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | REDUCE: (301), (21523) imply:
% 238.66/45.53  | | | | | | | | | | | |   (21524)   ~ (all_10_2 = e2)
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | BETA: splitting (204) gives:
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | |   (21525)  all_54_0 = e3
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | COMBINE_EQS: (292), (21525) imply:
% 238.66/45.53  | | | | | | | | | | | | |   (21526)  all_10_2 = e3
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | SIMP: (21526) implies:
% 238.66/45.53  | | | | | | | | | | | | |   (21527)  all_10_2 = e3
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | REDUCE: (357), (21527) imply:
% 238.66/45.53  | | | | | | | | | | | | |   (21528)   ~ (all_52_2 = e3)
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | REDUCE: (363), (21527) imply:
% 238.66/45.53  | | | | | | | | | | | | |   (21529)   ~ (all_52_8 = e3)
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | BETA: splitting (230) gives:
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | |   (21530)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 238.66/45.53  | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (21510), (21529), (21530),
% 238.66/45.53  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.53  | | | | | | | | | | | | | |            #1628.
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | |   (21531)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 238.66/45.53  | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | BETA: splitting (21531) gives:
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | |   (21532)  all_58_8 = e3 & op(e1, e1) = e3
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | REF_CLOSE: (39), (17775), (21532), (function-axioms) are
% 238.66/45.53  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | |   (21533)  all_58_14 = e3 & op(e0, e1) = e3
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | ALPHA: (21533) implies:
% 238.66/45.53  | | | | | | | | | | | | | | |   (21534)  op(e0, e1) = e3
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | |   (21535)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 238.66/45.53  | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (21508), (21528), (21535),
% 238.66/45.53  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.53  | | | | | | | | | | | | | | | |            #213.
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | |   (21536)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 238.66/45.53  | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | BETA: splitting (21536) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | |   (21537)  all_58_8 = e3 & op(e1, e1) = e3
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (17775), (21537), (function-axioms) are
% 238.66/45.53  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2092.
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | |   (21538)  all_58_11 = e3 & op(e1, e0) = e3
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | ALPHA: (21538) implies:
% 238.66/45.53  | | | | | | | | | | | | | | | | |   (21539)  op(e1, e0) = e3
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 238.66/45.53  | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (21534) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | |   (21540)  all_52_11 = e3
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.66/45.53  | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (160), (21539) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | |   (21541)  all_52_14 = e3
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | REDUCE: (139), (21540) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | | |   (21542)   ~ (all_52_3 = e3)
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | REDUCE: (385), (21541) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | | |   (21543)   ~ (all_6_2 = e3)
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | |   (21544)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.53  | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.53  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (167), (21505), (21506), (21528),
% 238.66/45.53  | | | | | | | | | | | | | | | | | |            (21542), (21544), (function-axioms) are
% 238.66/45.53  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #76.
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | |   (21545)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.66/45.53  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.66/45.53  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | BETA: splitting (21545) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |   (21546)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              = e2)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (21546) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |   (21547)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (21547) implies:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |   (21548)   ~ (all_56_21 = e1)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |   (21549)  op(e2, e1) = e2
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | REDUCE: (266), (21548) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |   (21550)   ~ (all_6_2 = e1)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |   (21551)  all_54_10 = e3
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (21551) are inconsistent by
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |   (21552)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (297), (381), (21522), (21549), (21550),
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |            (21552), (function-axioms) are inconsistent by
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2198.
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |   (21553)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17762), (17764), (21553),
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |            #185.
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |   (21554)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |              = e0)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (21554) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |   (21555)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (21555) implies:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |   (21556)   ~ (all_56_31 = e2)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (21556) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |   (21557)  $false
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | CLOSE: (21557) is inconsistent.
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |   (21558)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (21558) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |   (21559)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | ALPHA: (21559) implies:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |   (21560)  op(e1, e0) = e1
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21539), (21560), (function-axioms) are
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |   (21561)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | ALPHA: (21561) implies:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |   (21562)  op(e0, e1) = e0
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21534), (21562), (function-axioms) are
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2164.
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | |   (21563)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | REF_CLOSE: (292), (21518), (21520), (21524), (21563) are
% 238.66/45.53  | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | |   (21564)  all_24_2 = e2
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | COMBINE_EQS: (301), (21564) imply:
% 238.66/45.53  | | | | | | | | | | | |   (21565)  all_10_2 = e2
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | SIMP: (21565) implies:
% 238.66/45.53  | | | | | | | | | | | |   (21566)  all_10_2 = e2
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | REDUCE: (355), (21566) imply:
% 238.66/45.53  | | | | | | | | | | | |   (21567)   ~ (all_52_1 = e2)
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | REDUCE: (361), (21566) imply:
% 238.66/45.53  | | | | | | | | | | | |   (21568)   ~ (all_52_4 = e2)
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.66/45.53  | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | |   (21569)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.66/45.53  | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | BETA: splitting (21569) gives:
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | |   (21570)  all_58_1 = e2 & op(e3, e2) = e2
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | ALPHA: (21570) implies:
% 238.66/45.53  | | | | | | | | | | | | | |   (21571)  op(e3, e2) = e2
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | REF_CLOSE: (170), (21568), (21571), (function-axioms) are
% 238.66/45.53  | | | | | | | | | | | | | |            inconsistent by sub-proof #254.
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | |   (21572)  all_58_3 = e2 & op(e2, e2) = e2
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | ALPHA: (21572) implies:
% 238.66/45.53  | | | | | | | | | | | | | |   (21573)  op(e2, e2) = e2
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | REF_CLOSE: (9), (21517), (21573), (function-axioms) are
% 238.66/45.53  | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | End of split
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | |   (21574)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.66/45.53  | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | BETA: splitting (21574) gives:
% 238.66/45.53  | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | |   (21575)  all_58_7 = e2 & op(e1, e2) = e2
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | ALPHA: (21575) implies:
% 238.66/45.53  | | | | | | | | | | | | | |   (21576)  op(e1, e2) = e2
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.66/45.53  | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | |   (21577)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.66/45.53  | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (21517), (21567), (21577),
% 238.66/45.53  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.53  | | | | | | | | | | | | | | |            #998.
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | |   (21578)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.66/45.53  | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | BETA: splitting (21578) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | |   (21579)  all_58_5 = e2 & op(e2, e1) = e2
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | ALPHA: (21579) implies:
% 238.66/45.53  | | | | | | | | | | | | | | | |   (21580)  op(e2, e1) = e2
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 238.66/45.53  | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (21576) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | |   (21581)  all_52_6 = e2
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 238.66/45.53  | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (21580) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | |   (21582)  all_52_9 = e2
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | REDUCE: (128), (21581) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | |   (21583)   ~ (all_52_7 = e2)
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | REDUCE: (381), (21582) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | |   (21584)   ~ (all_6_2 = e2)
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | SIMP: (21584) implies:
% 238.66/45.53  | | | | | | | | | | | | | | | |   (21585)   ~ (all_6_2 = e2)
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | |   (21586)  all_54_10 = e3
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (21586) are inconsistent by
% 238.66/45.53  | | | | | | | | | | | | | | | | |            sub-proof #2313.
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | |   (21587)   ~ (all_54_10 = e3)
% 238.66/45.53  | | | | | | | | | | | | | | | | |   (21588)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | BETA: splitting (21588) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | |   (21589)  all_54_10 = e2
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (21585), (21589) are inconsistent by
% 238.66/45.53  | | | | | | | | | | | | | | | | | |            sub-proof #2312.
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | |   (21590)   ~ (all_54_10 = e2)
% 238.66/45.53  | | | | | | | | | | | | | | | | | |   (21591)  all_54_10 = e1 | all_54_10 = e0
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | BETA: splitting (21591) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |   (21592)  all_54_10 = e1
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (21592) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |   (21593)  all_6_2 = e1
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | SIMP: (21593) implies:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |   (21594)  all_6_2 = e1
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (21594) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |   (21595)  all_56_21 = e1
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | REDUCE: (380), (21594) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |   (21596)   ~ (all_52_8 = e1)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | REDUCE: (385), (21594) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |   (21597)   ~ (all_52_14 = e1)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | REDUCE: (17775), (21594) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |   (21598)   ~ (e3 = e1)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | REDUCE: (21585), (21594) imply:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | |   (21599)   ~ (e2 = e1)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |   (21600)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (21600) gives:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.53  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |   (21601)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21601) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |   (21602)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |            e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21602) implies:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |   (21603)  op(e2, e3) = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (21506), (21603), (function-axioms) are
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |   (21604)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (21568), (21595), (21604),
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |            #245.
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |   (21605)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21605) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |   (21606)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21606) implies:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |   (21607)  op(e3, e1) = e1
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (21596), (21607), (function-axioms) are
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |   (21608)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21608) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21609)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21609) implies:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21610)   ~ (all_56_31 = e0)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21611)   ~ (all_56_21 = e0)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21612)   ~ (all_56_11 = e0)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21613)  op(e0, e3) = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21614)  op(e3, e0) = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (21613) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21615)  all_52_3 = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (168), (21614) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21616)  all_52_12 = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (21615) imply:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21617)   ~ (all_52_7 = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (21615) imply:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21618)   ~ (all_52_11 = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21618) implies:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21619)   ~ (all_52_11 = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (21616) imply:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21620)   ~ (all_52_14 = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21620) implies:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21621)   ~ (all_52_14 = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (157), (158),
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (219), (226), (239), (241), (243),
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |            (17774), (17775), (21508), (21509), (21619),
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |            (21621), (function-axioms) are inconsistent by
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #75.
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21622)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21622) implies:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21623)   ~ (all_56_11 = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21505), (21623) imply:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | |   (21624)  $false
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (21624) is inconsistent.
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21625)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (160), (165), (297), (381), (17762),
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |            (17764), (21522), (21591), (21595), (21597),
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |            (21625), (function-axioms) are inconsistent by
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |            sub-proof #241.
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |   (21626)  all_54_10 = e0
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (297), (21522), (21626) are inconsistent by
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |            sub-proof #2303.
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | |   (21627)  all_58_10 = e2 & op(e2, e0) = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | ALPHA: (21627) implies:
% 238.66/45.54  | | | | | | | | | | | | | | | |   (21628)  op(e2, e0) = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (21628), (function-axioms) are
% 238.66/45.54  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.66/45.54  | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | |   (21629)  all_58_13 = e2 & op(e0, e2) = e2
% 238.66/45.54  | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | ALPHA: (21629) implies:
% 238.66/45.54  | | | | | | | | | | | | | |   (21630)  op(e0, e2) = e2
% 238.66/45.54  | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (21630), (function-axioms) are
% 238.66/45.54  | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 238.66/45.54  | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | |   (21631)  all_18_2 = e0
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | COMBINE_EQS: (339), (21631) imply:
% 238.66/45.54  | | | | | | | | | | |   (21632)  all_6_2 = e0
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | SIMP: (21632) implies:
% 238.66/45.54  | | | | | | | | | | |   (21633)  all_6_2 = e0
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | COMBINE_EQS: (266), (21633) imply:
% 238.66/45.54  | | | | | | | | | | |   (21634)  all_56_21 = e0
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | REDUCE: (367), (21633) imply:
% 238.66/45.54  | | | | | | | | | | |   (21635)   ~ (all_52_2 = e0)
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | REDUCE: (378), (21633) imply:
% 238.66/45.54  | | | | | | | | | | |   (21636)   ~ (all_52_6 = e0)
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | REDUCE: (380), (21633) imply:
% 238.66/45.54  | | | | | | | | | | |   (21637)   ~ (all_52_8 = e0)
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | REDUCE: (381), (21633) imply:
% 238.66/45.54  | | | | | | | | | | |   (21638)   ~ (all_52_9 = e0)
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | REDUCE: (383), (21633) imply:
% 238.66/45.54  | | | | | | | | | | |   (21639)   ~ (all_52_11 = e0)
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | REDUCE: (385), (21633) imply:
% 238.66/45.54  | | | | | | | | | | |   (21640)   ~ (all_52_14 = e0)
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | REDUCE: (17775), (21633) imply:
% 238.66/45.54  | | | | | | | | | | |   (21641)   ~ (e3 = e0)
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | REDUCE: (39), (21633) imply:
% 238.66/45.54  | | | | | | | | | | |   (21642)  op(e1, e1) = e0
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | BETA: splitting (67) gives:
% 238.66/45.54  | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | |   (21643)   ~ (all_24_2 = e2)
% 238.66/45.54  | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | REDUCE: (301), (21643) imply:
% 238.66/45.54  | | | | | | | | | | | |   (21644)   ~ (all_10_2 = e2)
% 238.66/45.54  | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | BETA: splitting (204) gives:
% 238.66/45.54  | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | |   (21645)  all_54_0 = e3
% 238.66/45.54  | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | COMBINE_EQS: (292), (21645) imply:
% 238.66/45.54  | | | | | | | | | | | | |   (21646)  all_10_2 = e3
% 238.66/45.54  | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | REDUCE: (357), (21646) imply:
% 238.66/45.54  | | | | | | | | | | | | |   (21647)   ~ (all_52_2 = e3)
% 238.66/45.54  | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | REDUCE: (359), (21646) imply:
% 238.66/45.54  | | | | | | | | | | | | |   (21648)   ~ (all_52_3 = e3)
% 238.66/45.54  | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | REDUCE: (363), (21646) imply:
% 238.66/45.54  | | | | | | | | | | | | |   (21649)   ~ (all_52_8 = e3)
% 238.66/45.54  | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | REDUCE: (45), (21646) imply:
% 238.66/45.54  | | | | | | | | | | | | |   (21650)  op(e3, e3) = e3
% 238.66/45.54  | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | BETA: splitting (230) gives:
% 238.66/45.54  | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | |   (21651)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 238.66/45.54  | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 238.66/45.54  | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (21510), (21649), (21651),
% 238.66/45.54  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.54  | | | | | | | | | | | | | |            #1628.
% 238.66/45.54  | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | |   (21652)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 238.66/45.54  | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 238.66/45.54  | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | BETA: splitting (21652) gives:
% 238.66/45.54  | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | |   (21653)  all_58_8 = e3 & op(e1, e1) = e3
% 238.66/45.54  | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | REF_CLOSE: (7), (21642), (21653), (function-axioms) are
% 238.66/45.54  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 238.66/45.54  | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | |   (21654)  all_58_14 = e3 & op(e0, e1) = e3
% 238.66/45.54  | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | ALPHA: (21654) implies:
% 238.66/45.54  | | | | | | | | | | | | | | |   (21655)  op(e0, e1) = e3
% 238.66/45.54  | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | |   (21656)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 238.66/45.54  | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (21508), (21647), (21656),
% 238.66/45.54  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.54  | | | | | | | | | | | | | | | |            #213.
% 238.66/45.54  | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | |   (21657)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 238.66/45.54  | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | BETA: splitting (21657) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | |   (21658)  all_58_8 = e3 & op(e1, e1) = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21642), (21658), (function-axioms) are
% 238.66/45.54  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 238.66/45.54  | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | |   (21659)  all_58_11 = e3 & op(e1, e0) = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | ALPHA: (21659) implies:
% 238.66/45.54  | | | | | | | | | | | | | | | | |   (21660)  all_58_11 = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | |   (21661)  op(e1, e0) = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | |   (21662)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.54  | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.54  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (167), (21505), (21506), (21647),
% 238.66/45.54  | | | | | | | | | | | | | | | | | |            (21648), (21662), (function-axioms) are
% 238.66/45.54  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #76.
% 238.66/45.54  | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | |   (21663)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.66/45.54  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.66/45.54  | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | BETA: splitting (21663) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |   (21664)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | |              = e2)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (21664) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21665)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | ALPHA: (21665) implies:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21666)  op(e1, e2) = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21667)  op(e2, e1) = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (157), (21655) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21668)  all_52_11 = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (160), (21661) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21669)  all_52_14 = e3
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (21666) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21670)  all_52_6 = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (21667) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21671)  all_52_9 = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (21671) imply:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21672)   ~ (all_52_1 = e2)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (21670) imply:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21673)   ~ (all_52_4 = e2)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (21671) imply:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21674)   ~ (all_52_8 = e2)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (21671) imply:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | |   (21675)   ~ (all_52_13 = e2)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |   (21676)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21676) gives:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |   (21677)  all_58_0 = e2 & op(e3, e3) = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21677) implies:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |   (21678)  op(e3, e3) = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (21650), (21678), (function-axioms) are
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2194.
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |   (21679)  all_58_1 = e2 & op(e3, e2) = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21679) implies:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |   (21680)  op(e3, e2) = e2
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (21673), (21680), (function-axioms) are
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #254.
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.54  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | |   (21681)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21681) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | |   (21682)  all_58_4 = e2 & op(e3, e1) = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21682) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | |   (21683)  all_58_4 = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | |   (21684)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (21517), (21672), (21684),
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | |            #998.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | |   (21685)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21685) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | |   (21686)  all_58_5 = e2 & op(e2, e1) = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21686) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | |   (21687)  all_58_5 = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (21688)  all_54_2 = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (21688) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (21689)  all_52_8 = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21649), (21689) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (21690)  $false
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (21690) is inconsistent.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (21691)   ~ (all_54_2 = e3)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (21692)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21692) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21693)  all_54_2 = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (21693) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21694)  all_52_8 = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21674), (21694) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21695)  $false
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (21695) is inconsistent.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21696)   ~ (all_54_2 = e2)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21697)  all_54_2 = e1 | all_54_2 = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21697) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21698)  all_54_2 = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (21698) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21699)  all_52_8 = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (21699) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21700)   ~ (all_52_4 = e1)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (21699) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21701)   ~ (all_52_12 = e1)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21701) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21702)   ~ (all_52_12 = e1)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21649), (21699) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21703)   ~ (e3 = e1)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21674), (21699) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21704)   ~ (e2 = e1)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21705)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21705) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21706)  all_58_9 = e1 & op(e3, e0) = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (21702), (21706), (function-axioms) are
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21707)  all_58_10 = e1 & op(e2, e0) = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21707) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21708)  all_58_10 = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21709)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (21650), (21700), (21709),
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1357.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21710)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21710) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21711)  all_58_4 = e1 & op(e3, e1) = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21711) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21712)  all_58_4 = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21683), (21712) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21713)  e2 = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21713) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21714)  e2 = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21687), (21714) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21715)  all_58_5 = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (231), (233), (21516),
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21708), (21715) are inconsistent by sub-proof
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #992.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21716)  all_58_9 = e1 & op(e3, e0) = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (21702), (21716), (function-axioms) are
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21717)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21717) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21718)  all_58_11 = e1 & op(e1, e0) = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21718) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21719)  op(e1, e0) = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21661), (21719), (function-axioms) are
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21720)  all_58_15 = e1 & op(e0, e0) = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21720) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21721)  all_58_15 = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21722)  op(e0, e0) = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (134), (170), (216),
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (242), (281), (21637), (21650), (21660),
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21683), (21697), (21721), (21722),
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #869.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21723)  all_54_2 = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (21723) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21724)  all_52_8 = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21637), (21724) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21725)  $false
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (21725) is inconsistent.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | |   (21726)  all_58_10 = e2 & op(e2, e0) = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21726) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | |   (21727)  op(e2, e0) = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (21727), (function-axioms) are
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | |   (21728)  all_58_9 = e2 & op(e3, e0) = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (17766), (21728), (function-axioms) are
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2318.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |   (21729)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17762), (17764), (21729),
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |            #185.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |   (21730)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |              = e0)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (21730) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |   (21731)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (21731) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |   (21732)   ~ (all_56_31 = e2)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (21732) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |   (21733)  $false
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | CLOSE: (21733) is inconsistent.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |   (21734)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (21640), (21661), (21734),
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |            #1893.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | |   (21735)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 238.66/45.55  | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | REF_CLOSE: (292), (21518), (21520), (21644), (21735) are
% 238.66/45.55  | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 238.66/45.55  | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | End of split
% 238.66/45.55  | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | |   (21736)  all_24_2 = e2
% 238.66/45.55  | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | COMBINE_EQS: (301), (21736) imply:
% 238.66/45.55  | | | | | | | | | | | |   (21737)  all_10_2 = e2
% 238.66/45.55  | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | REDUCE: (355), (21737) imply:
% 238.66/45.55  | | | | | | | | | | | |   (21738)   ~ (all_52_1 = e2)
% 238.66/45.55  | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | REDUCE: (357), (21737) imply:
% 238.66/45.55  | | | | | | | | | | | |   (21739)   ~ (all_52_2 = e2)
% 238.66/45.55  | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | REDUCE: (361), (21737) imply:
% 238.66/45.55  | | | | | | | | | | | |   (21740)   ~ (all_52_4 = e2)
% 238.66/45.55  | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | REDUCE: (363), (21737) imply:
% 238.66/45.55  | | | | | | | | | | | |   (21741)   ~ (all_52_8 = e2)
% 238.66/45.55  | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | REDUCE: (45), (21737) imply:
% 238.66/45.55  | | | | | | | | | | | |   (21742)  op(e3, e3) = e2
% 238.66/45.55  | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.66/45.55  | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | |   (21743)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.66/45.55  | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.66/45.55  | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | REF_CLOSE: (9), (167), (21517), (21738), (21743),
% 238.66/45.55  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.55  | | | | | | | | | | | | |            #998.
% 238.66/45.55  | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | |   (21744)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.66/45.55  | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.66/45.55  | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | BETA: splitting (21744) gives:
% 238.66/45.55  | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | |   (21745)  all_58_5 = e2 & op(e2, e1) = e2
% 238.66/45.55  | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | ALPHA: (21745) implies:
% 238.66/45.55  | | | | | | | | | | | | | |   (21746)  all_58_5 = e2
% 238.66/45.55  | | | | | | | | | | | | | |   (21747)  op(e2, e1) = e2
% 238.66/45.55  | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 238.66/45.55  | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | |   (21748)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 238.66/45.55  | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 238.66/45.55  | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | BETA: splitting (21748) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | |   (21749)  all_58_6 = e2 & op(e1, e3) = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | ALPHA: (21749) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | |   (21750)  all_58_6 = e2
% 238.66/45.55  | | | | | | | | | | | | | | | |   (21751)  op(e1, e3) = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (241),
% 238.66/45.55  | | | | | | | | | | | | | | | |            (245), (21506), (21742), (21750), (21751),
% 238.66/45.55  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.55  | | | | | | | | | | | | | | | |            #255.
% 238.66/45.55  | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | |   (21752)  all_58_7 = e2 & op(e1, e2) = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | ALPHA: (21752) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | |   (21753)  all_58_7 = e2
% 238.66/45.55  | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | |   (21754)  all_54_2 = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (21754) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | |   (21755)  all_52_8 = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | SIMP: (21755) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | |   (21756)  all_52_8 = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | REDUCE: (121), (21756) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | |   (21757)   ~ (all_52_11 = e3)
% 238.66/45.55  | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | SIMP: (21757) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | |   (21758)   ~ (all_52_11 = e3)
% 238.66/45.55  | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | REDUCE: (120), (21756) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | |   (21759)   ~ (all_52_12 = e3)
% 238.66/45.55  | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | SIMP: (21759) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | |   (21760)   ~ (all_52_12 = e3)
% 238.66/45.55  | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | |   (21761)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | BETA: splitting (21761) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |   (21762)  all_58_12 = e3 & op(e0, e3) = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | ALPHA: (21762) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | |   (21763)  all_58_12 = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |   (21764)  all_58_15 = e0 & op(e0, e0) = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (21764) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |   (21765)  op(e0, e0) = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (21765), (function-axioms) are
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |   (21766)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (21766) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |   (21767)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | |   (21768)  all_54_14 = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (21768) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | |   (21769)  all_52_11 = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | REDUCE: (21758), (21769) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | |   (21770)  $false
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | CLOSE: (21770) is inconsistent.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | |   (21771)   ~ (all_54_14 = e3)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | |   (21772)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | |   (21773)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (21511), (21760), (21773),
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | |            #1592.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | |   (21774)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21774) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | |   (21775)  all_58_11 = e3 & op(e1, e0) = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21775) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | |   (21776)  op(e1, e0) = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | |   (21777)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21777) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (21778)  all_58_6 = e1 & op(e1, e3) = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21778) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (21779)  op(e1, e3) = e1
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21780)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21780) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21781)  all_58_4 = e3 & op(e3, e1) = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21781) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21782)  all_58_4 = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21783)  op(e3, e1) = e3
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21767) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21784)  all_58_12 = e0 & op(e0, e3) = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21784) implies:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21785)  all_58_12 = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21763), (21785) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21786)  e3 = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21782), (21786) imply:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21787)  all_58_4 = e0
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (229),
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (21510), (21642), (21787),
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1662.
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21788)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21788) gives:
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21789)  all_58_13 = e0 & op(e0, e2) = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21789) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21790)  op(e0, e2) = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21791)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21791) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21792)  all_58_1 = e1 & op(e3, e2) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21792) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21793)  all_58_1 = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21794)  op(e3, e2) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21795)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21795) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21796)  all_58_4 = e1 & op(e3, e1) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21796) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21797)  all_58_4 = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (170), (240), (246),
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21507), (21742), (21793), (21797),
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1645.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21798)  all_58_5 = e1 & op(e2, e1) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (21746), (21798) are inconsistent by
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1548.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21799)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21799) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21800)  all_58_8 = e1 & op(e1, e1) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21800) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21801)  op(e1, e1) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (21635), (21636),
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21640), (21801), (function-axioms) are
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2020.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21802)  all_58_14 = e1 & op(e0, e1) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21802) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21803)  all_58_14 = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21804)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21804) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21805)  all_58_9 = e1 & op(e3, e0) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21805) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21806)  all_58_9 = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (170), (240), (246),
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21507), (21742), (21793), (21806),
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1694.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21807)  all_58_10 = e1 & op(e2, e0) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21807) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21808)  op(e2, e0) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21772) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21809)  all_54_14 = e2
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (21809) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21810)  all_52_11 = e2
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17765), (21810) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21811)  $false
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (21811) is inconsistent.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21812)   ~ (all_54_14 = e2)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21813)  all_54_14 = e1 | all_54_14 = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21813) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21814)  all_54_14 = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (21814) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21815)  all_52_11 = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (21815) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21816)   ~ (all_52_3 = e1)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (21815) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21817)   ~ (all_52_7 = e1)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21758), (21815) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21818)   ~ (e3 = e1)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17765), (21815) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21819)   ~ (e2 = e1)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (21815) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21820)  op(e0, e1) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21821)  all_54_13 = e3
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (21509), (21821) are inconsistent by
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21822)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21823)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_19 & $i(all_56_19))
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21823) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21824)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21824) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21825)  op(e3, e1) = all_56_17
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21826)  op(e3, all_56_17) = e3
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (21742), (21783), (21825), (21826),
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2098.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21827)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_19 & $i(all_56_19)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21827) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21828)  op(e2, e1) = all_56_19
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21829)  op(e2, all_56_19) = e2
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21822) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21830)  all_54_13 = e2
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17764), (21830) are inconsistent by
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21831)   ~ (all_54_13 = e2)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21832)  all_54_13 = e1 | all_54_13 = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21832) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21833)  all_54_13 = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (21817), (21833) are inconsistent by
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1966.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21834)  all_54_13 = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (21834) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21835)  all_52_7 = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21835) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21836)  all_52_7 = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (21836) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21837)   ~ (all_52_3 = e0)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21817), (21836) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21838)   ~ (e1 = e0)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21839)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21839) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21840)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (167), (21506), (21779), (21794),
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21840), (function-axioms) are inconsistent by
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #273.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21841)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (168), (21760), (21783), (21837),
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21841), (function-axioms) are inconsistent by
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1426.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21842)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21842) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21843)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21843) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21844)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21844) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21845)  all_56_19 = e2
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21829), (21845) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21846)  op(e2, e2) = e2
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (21517), (21846), (function-axioms) are
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21847)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21847) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21848)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21848) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21849)  op(e2, e1) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (21828), (21829), (21849), (function-axioms)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #299.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21850)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21850) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21851)  op(e0, e2) = e2
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (256), (17764), (21817), (21832), (21851),
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1818.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21852)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21852) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21853)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21853) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21854)  op(e2, e0) = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (21808), (21854), (function-axioms)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21855)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (21640), (21776), (21855),
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1893.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21856)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_56_23 & $i(all_56_23))
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21856) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21857)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21857) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21858)  op(e1, all_56_21) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21634), (21858) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21859)  op(e1, e0) = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21776), (21859), (function-axioms) are
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21860)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21860) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21861)  op(e0, e1) = all_56_23
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21862)  op(e0, all_56_23) = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21822) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21863)  all_54_13 = e2
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17764), (21863) are inconsistent by
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21864)  all_54_13 = e1 | all_54_13 = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21864) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21865)  all_54_13 = e1
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (21817), (21865) are inconsistent by
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1966.
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21866)  all_54_13 = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (21866) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21867)  all_52_7 = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21867) implies:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21868)  all_52_7 = e0
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (21868) imply:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21869)   ~ (all_52_3 = e0)
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21870)  all_54_12 = e3
% 238.66/45.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (21870) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21871)  all_52_3 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21871) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21872)  all_52_3 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (21872) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21873)   ~ (all_52_2 = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21874)  all_54_8 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (21874) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21875)  all_52_2 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21873), (21875) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21876)  $false
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (21876) is inconsistent.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21877)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21877) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21878)  all_54_8 = e2
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (21739), (21878) are inconsistent by
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2007.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21879)  all_54_8 = e1 | all_54_8 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21879) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21880)  all_54_8 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (21880) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21881)  all_52_2 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21881) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21882)  all_52_2 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (21882) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21883)   ~ (all_52_1 = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21884)  all_54_4 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (21506), (21884) are inconsistent by
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21885)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21885) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21886)  all_54_4 = e2
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (21738), (21886) are inconsistent by
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2096.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21887)  all_54_4 = e1 | all_54_4 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21887) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21888)  all_54_4 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (21883), (21888) are inconsistent by
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2086.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21889)  all_54_4 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (21889) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21890)  all_52_1 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21890) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21891)  all_52_1 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (21891) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21892)   ~ (all_52_13 = e0)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21892) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21893)   ~ (all_52_13 = e0)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (197), (269), (17767), (21511), (21820), (21861),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21862), (21893), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #79.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21894)  all_54_8 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (21635), (21894) are inconsistent by
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2006.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21895)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (17763), (21816), (21869), (21895) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2066.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21896)  all_54_14 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (21896) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21897)  all_52_11 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21639), (21897) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21898)  $false
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (21898) is inconsistent.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21899)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21899) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21900)  all_58_11 = e1 & op(e1, e0) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21900) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21901)  op(e1, e0) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21776), (21901), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21902)  all_58_15 = e1 & op(e0, e0) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21902) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21903)  all_58_15 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17773), (21903) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21904)  e2 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (21746),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21782), (21803), (21904) are inconsistent by
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1480.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21905)  all_58_3 = e1 & op(e2, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (157), (219), (17774), (21516),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21758), (21763), (21790), (21905),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #74.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21906)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21906) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21907)  all_58_7 = e1 & op(e1, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21907) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21908)  all_58_7 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21909)  op(e1, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (225), (226), (21642),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21779), (21908), (21909), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1993.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21910)  all_58_13 = e1 & op(e0, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21910) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21911)  op(e0, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21790), (21911), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21912)  all_58_14 = e0 & op(e0, e1) = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21912) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21913)  all_58_14 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21914)  op(e0, e1) = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (229),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (21510), (21642), (21913), (21914),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #437.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21915)  all_58_5 = e3 & op(e2, e1) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21915) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21916)  op(e2, e1) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (21747), (21916), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2256.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21917)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21917) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21918)  all_58_8 = e3 & op(e1, e1) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21642), (21918), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21919)  all_58_14 = e3 & op(e0, e1) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21919) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21920)  all_58_14 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (217), (218),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21763), (21920), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1862.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (21921)  all_58_7 = e1 & op(e1, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (21753), (21921) are inconsistent by
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2224.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | |   (21922)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (160), (162), (163), (223), (21635),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | |            (21636), (21640), (21776), (21922),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | |            #172.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | |   (21923)  all_58_15 = e3 & op(e0, e0) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21923) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | |   (21924)  op(e0, e0) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17774), (21924), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | |   (21925)  all_58_13 = e3 & op(e0, e2) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (21509), (21925), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | |   (21926)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.66/45.57  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17774), (21758), (21926),
% 238.66/45.57  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.57  | | | | | | | | | | | | | | | | | |            #226.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | |   (21927)   ~ (all_54_2 = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | |   (21928)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | REDUCE: (281), (21927) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | |   (21929)   ~ (all_52_8 = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | |   (21930)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (21747), (21929), (21930),
% 238.66/45.57  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.57  | | | | | | | | | | | | | | | | | |            #132.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | |   (21931)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 238.66/45.57  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | BETA: splitting (21931) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | |   (21932)  all_58_8 = e3 & op(e1, e1) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (21642), (21932), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | |   (21933)  all_58_14 = e3 & op(e0, e1) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | ALPHA: (21933) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | |   (21934)  all_58_14 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | |   (21935)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (21507), (21742), (21935),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | |            #1959.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | |   (21936)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | BETA: splitting (21936) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | |   (21937)  all_58_4 = e3 & op(e3, e1) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | ALPHA: (21937) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | |   (21938)  op(e3, e1) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (21929), (21938), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | |   (21939)  all_58_9 = e3 & op(e3, e0) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | ALPHA: (21939) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | |   (21940)  all_58_9 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | |   (21941)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21941) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | |   (21942)  all_58_4 = e1 & op(e3, e1) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21942) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | |   (21943)  all_58_4 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | |   (21944)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21944) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (21945)  all_58_1 = e1 & op(e3, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21945) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (21946)  all_58_1 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (240), (21742), (21940), (21943),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |            (21946), (function-axioms) are inconsistent by
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1646.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (21947)  all_58_3 = e1 & op(e2, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21516), (21947) are inconsistent by
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | |   (21948)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21948) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (21949)  all_58_7 = e1 & op(e1, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (21753), (21949) are inconsistent by
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2224.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (21950)  all_58_13 = e1 & op(e0, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21950) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (21951)  all_58_13 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (21952)  op(e0, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21928) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21953)  all_54_2 = e2
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (21953) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21954)  all_52_8 = e2
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21741), (21954) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21955)  $false
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (21955) is inconsistent.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21956)   ~ (all_54_2 = e2)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (21957)  all_54_2 = e1 | all_54_2 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21957) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21958)  all_54_2 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (21958) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21959)  all_52_8 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (21959) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21960)   ~ (all_52_4 = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (21959) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21961)   ~ (all_52_11 = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21961) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21962)   ~ (all_52_11 = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (21959) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21963)   ~ (all_52_12 = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21963) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21964)   ~ (all_52_12 = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21741), (21959) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21965)   ~ (e2 = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21966)  all_54_14 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (21966) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21967)  all_52_11 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (21967) imply:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21968)   ~ (all_52_3 = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21969)  all_58_15 = e0 & op(e0, e0) = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21969) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21970)  op(e0, e0) = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (21970), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21971)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21971) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21972)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21973)  all_54_1 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (21507), (21973) are inconsistent by
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21974)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21975)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (21506), (21742), (21975),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1404.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21976)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21976) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21977)  all_58_6 = e3 & op(e1, e3) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21977) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21978)  all_58_6 = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21979)  op(e1, e3) = e3
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21980)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21980) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21981)  all_58_6 = e1 & op(e1, e3) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21981) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21982)  op(e1, e3) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21979), (21982), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21983)  all_58_7 = e1 & op(e1, e2) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21983) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21984)  all_58_7 = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (235), (237), (21516),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21951), (21984) are inconsistent by sub-proof
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1457.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21985)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21985) gives:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21986)  all_58_8 = e1 & op(e1, e1) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21986) implies:
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21987)  op(e1, e1) = e1
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (21635), (21636),
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21640), (21987), (function-axioms) are
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2020.
% 238.66/45.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21988)  all_58_11 = e1 & op(e1, e0) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (21988) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21989)  op(e1, e0) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21974) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21990)  all_54_1 = e2
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (21740), (21990) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1928.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21991)   ~ (all_54_1 = e2)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21992)  all_54_1 = e1 | all_54_1 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21992) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21993)  all_54_1 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (21960), (21993) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2051.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21994)  all_54_1 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (21994) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21995)  all_52_4 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21995) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21996)  all_52_4 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (21996) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21997)   ~ (all_52_7 = e0)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21997) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21998)   ~ (all_52_7 = e0)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (21996) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (21999)   ~ (all_52_12 = e0)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (21999) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22000)   ~ (all_52_12 = e0)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21740), (21996) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22001)   ~ (e2 = e0)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22002)  all_54_13 = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (21509), (22002) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22003)   ~ (all_54_13 = e3)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22004)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22004) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22005)  all_54_13 = e2
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17764), (22005) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22006)   ~ (all_54_13 = e2)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22007)  all_54_13 = e1 | all_54_13 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22008)  all_54_3 = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (22008) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22009)  all_52_12 = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22009) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22010)  all_52_12 = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (22010) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22011)   ~ (all_52_13 = e3)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (22010) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22012)   ~ (all_52_14 = e3)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22012) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22013)   ~ (all_52_14 = e3)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (22010) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22014)  op(e3, e0) = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22007) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22015)  all_54_13 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (22015) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22016)  all_52_7 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (22016) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22017)   ~ (all_52_3 = e1)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21509), (22016) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22018)   ~ (e3 = e1)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22019)  all_54_12 = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (21968), (22019) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22020)   ~ (all_54_12 = e3)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22021)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22022)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22022) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22023)  all_58_0 = e1 & op(e3, e3) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22023) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22024)  op(e3, e3) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (240), (244), (21940),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21943), (22024), (function-axioms) are
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1469.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22025)  all_58_2 = e1 & op(e2, e3) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22025) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22026)  all_58_2 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22021) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22027)  all_54_12 = e2
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (17763), (22027) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2264.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22028)   ~ (all_54_12 = e2)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22029)  all_54_12 = e1 | all_54_12 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22029) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22030)  all_54_12 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (22017), (22030) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2263.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22031)  all_54_12 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (22031) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22032)  all_52_3 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22032) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22033)  all_52_3 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (22033) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22034)   ~ (all_52_1 = e0)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22017), (22033) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22035)   ~ (e1 = e0)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22036)  all_54_4 = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (21506), (22036) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22037)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22038)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (21742), (22034), (22038),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1984.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22039)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22039) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22040)  all_58_6 = e0 & op(e1, e3) = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22040) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22041)  all_58_6 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (224), (225),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (21508), (21642), (22041),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1977.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22042)  all_58_12 = e0 & op(e0, e3) = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22042) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22043)  all_58_12 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22037) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22044)  all_54_4 = e2
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (21738), (22044) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2096.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22045)   ~ (all_54_4 = e2)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22046)  all_54_4 = e1 | all_54_4 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22046) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22047)  all_54_4 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (22047) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22048)  all_52_1 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22048) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22049)  all_52_1 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (22049) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22050)   ~ (all_52_13 = e1)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22050) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22051)   ~ (all_52_13 = e1)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22052)  all_54_7 = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (21511), (22052) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2296.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22053)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22053) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22054)  all_54_7 = e2
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (17767), (22054) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1997.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22055)   ~ (all_54_7 = e2)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22056)  all_54_7 = e1 | all_54_7 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22057)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22057) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22058)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22058) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22059)  op(e3, e0) = all_56_25
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22060)  op(e3, all_56_25) = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22056) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22061)  all_54_7 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (22051), (22061) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22062)  all_54_7 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (22062) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22063)  all_52_13 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22063) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22064)  all_52_13 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25, e0, e3, simplifying with (22014),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (22059) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22065)  all_56_25 = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22060), (22065) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22066)  op(e3, e3) = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (243), (21978), (22026), (22043),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22066), (function-axioms) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1629.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22067)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22067) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22068)  op(e2, e0) = all_56_27
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22069)  op(e2, all_56_27) = e2
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22056) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22070)  all_54_7 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (22051), (22070) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22071)  all_54_7 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (22071) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22072)  all_52_13 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22072) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22073)  all_52_13 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (22073) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22074)  op(e2, e0) = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27, e0, e2, simplifying with (22068),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (22074) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22075)  all_56_27 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22069), (22075) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22076)  op(e2, e0) = e2
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (21517), (22068), (22069), (22076),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #954.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22077)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22077) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22078)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22078) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22079)  op(e1, e0) = all_56_29
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22080)  op(e1, all_56_29) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22056) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22081)  all_54_7 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (22051), (22081) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22082)  all_54_7 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (22082) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22083)  all_52_13 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22083) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22084)  all_52_13 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_29, e0, e1, simplifying with (21989),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (22079) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22085)  all_56_29 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22080), (22085) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22086)  op(e1, e1) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (21635), (21636),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21640), (22086), (function-axioms) are
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2020.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22087)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22087) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22088)  op(e0, all_56_31) = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (22088) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22089)  op(e0, e2) = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (21998), (22089), (function-axioms) are
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2252.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22090)  all_54_4 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (22034), (22090) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1923.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22091)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22091) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22092)  all_58_6 = e1 & op(e1, e3) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22092) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22093)  op(e1, e3) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (160), (162), (226), (21508), (21642),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22013), (22093), (function-axioms) are
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #457.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22094)  all_58_12 = e1 & op(e0, e3) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (22017), (22094), (function-axioms) are
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2276.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22095)  all_54_13 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (22095) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22096)  all_52_7 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21998), (22096) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22097)  $false
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22097) is inconsistent.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22098)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (17766), (21964), (22000), (22098) are
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22099)  all_58_12 = e3 & op(e0, e3) = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22099) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22100)  all_58_12 = e3
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (21934), (21952), (21972), (22100),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1870.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22101)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (17765), (21639), (21962), (22101) are
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1798.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22102)  all_54_2 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (22102) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22103)  all_52_8 = e0
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21637), (22103) imply:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22104)  $false
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22104) is inconsistent.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | |   (22105)  all_58_5 = e1 & op(e2, e1) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22105) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | |   (22106)  op(e2, e1) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (165), (281), (21637), (21741), (21928),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | |            (22106), (function-axioms) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #434.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | |   (22107)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22107) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | |   (22108)  all_58_8 = e1 & op(e1, e1) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22108) implies:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | |   (22109)  op(e1, e1) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (21635), (21636),
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | |            (21640), (22109), (function-axioms) are
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2020.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | |   (22110)  all_58_14 = e1 & op(e0, e1) = e1
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21934), (22110) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1900.
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | |   (22111)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 238.66/45.58  | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (17768), (21642), (22111),
% 238.66/45.58  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.58  | | | | | | | | | | | | | | |            #167.
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | |   (22112)  all_58_10 = e2 & op(e2, e0) = e2
% 238.66/45.58  | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | ALPHA: (22112) implies:
% 238.66/45.58  | | | | | | | | | | | | | |   (22113)  op(e2, e0) = e2
% 238.66/45.58  | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (22113), (function-axioms) are
% 238.66/45.58  | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.66/45.58  | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | End of split
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | |   (22114)  all_16_2 = e0
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | COMBINE_EQS: (342), (22114) imply:
% 238.66/45.58  | | | | | | | | | |   (22115)  all_10_2 = e0
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | COMBINE_EQS: (290), (22115) imply:
% 238.66/45.58  | | | | | | | | | |   (22116)  all_56_1 = e0
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | REDUCE: (355), (22115) imply:
% 238.66/45.58  | | | | | | | | | |   (22117)   ~ (all_52_1 = e0)
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | REDUCE: (357), (22115) imply:
% 238.66/45.58  | | | | | | | | | |   (22118)   ~ (all_52_2 = e0)
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | REDUCE: (359), (22115) imply:
% 238.66/45.58  | | | | | | | | | |   (22119)   ~ (all_52_3 = e0)
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | REDUCE: (363), (22115) imply:
% 238.66/45.58  | | | | | | | | | |   (22120)   ~ (all_52_8 = e0)
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | REDUCE: (21518), (22115) imply:
% 238.66/45.58  | | | | | | | | | |   (22121)   ~ (e1 = e0)
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | REDUCE: (45), (22115) imply:
% 238.66/45.58  | | | | | | | | | |   (22122)  op(e3, e3) = e0
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | BETA: splitting (58) gives:
% 238.66/45.58  | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | |   (22123)   ~ (all_18_2 = e0)
% 238.66/45.58  | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | REDUCE: (339), (22123) imply:
% 238.66/45.58  | | | | | | | | | | |   (22124)   ~ (all_6_2 = e0)
% 238.66/45.58  | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | BETA: splitting (85) gives:
% 238.66/45.58  | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | |   (22125)   ~ (all_36_2 = e2)
% 238.66/45.58  | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | REDUCE: (328), (22125) imply:
% 238.66/45.58  | | | | | | | | | | | |   (22126)   ~ (all_6_2 = e2)
% 238.66/45.58  | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | BETA: splitting (194) gives:
% 238.66/45.58  | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | |   (22127)  all_54_10 = e3
% 238.66/45.58  | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | REF_CLOSE: (297), (17775), (22127) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | |            sub-proof #2313.
% 238.66/45.58  | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | |   (22128)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.66/45.58  | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | BETA: splitting (22128) gives:
% 238.66/45.58  | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | |   (22129)  all_54_10 = e2
% 238.66/45.58  | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | REF_CLOSE: (297), (22126), (22129) are inconsistent by
% 238.66/45.58  | | | | | | | | | | | | | |            sub-proof #2312.
% 238.66/45.58  | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | Case 2:
% 238.66/45.58  | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | |   (22130)  all_54_10 = e1 | all_54_10 = e0
% 238.66/45.58  | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | BETA: splitting (22130) gives:
% 238.66/45.58  | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | Case 1:
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | |   (22131)  all_54_10 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | COMBINE_EQS: (297), (22131) imply:
% 238.66/45.58  | | | | | | | | | | | | | | |   (22132)  all_6_2 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | SIMP: (22132) implies:
% 238.66/45.58  | | | | | | | | | | | | | | |   (22133)  all_6_2 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | COMBINE_EQS: (266), (22133) imply:
% 238.66/45.58  | | | | | | | | | | | | | | |   (22134)  all_56_21 = e1
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | REDUCE: (380), (22133) imply:
% 238.66/45.58  | | | | | | | | | | | | | | |   (22135)   ~ (all_52_8 = e1)
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | REDUCE: (381), (22133) imply:
% 238.66/45.58  | | | | | | | | | | | | | | |   (22136)   ~ (all_52_9 = e1)
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | REDUCE: (385), (22133) imply:
% 238.66/45.58  | | | | | | | | | | | | | | |   (22137)   ~ (all_52_14 = e1)
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.58  | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.66/45.58  | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | |   (22138)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.59  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.59  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.59  | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.59  | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.59  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.59  | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.59  | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.59  | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.59  | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.66/45.59  | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.66/45.59  | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.59  | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | BETA: splitting (22138) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | |   (22139)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.59  | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.59  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.59  | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | |              = e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (21505), (21506), (22134), (22139),
% 238.66/45.59  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.59  | | | | | | | | | | | | | | | | |            #73.
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | |   (22140)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.66/45.59  | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.59  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.59  | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | |              = e0)
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | BETA: splitting (22140) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | |   (22141)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.66/45.59  | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | ALPHA: (22141) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | |   (22142)  op(e3, e1) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (22135), (22142), (function-axioms) are
% 238.66/45.59  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | |   (22143)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.66/45.59  | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.59  | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.59  | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (22116), (22119), (22143),
% 238.66/45.59  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.59  | | | | | | | | | | | | | | | | | |            #1829.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | End of split
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | End of split
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | |   (22144)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.59  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.66/45.59  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.66/45.59  | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.66/45.59  | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.66/45.59  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.66/45.59  | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.66/45.59  | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.66/45.59  | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.66/45.59  | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.66/45.59  | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.66/45.59  | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.66/45.59  | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | BETA: splitting (22144) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | |   (22145)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.66/45.59  | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.66/45.59  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.66/45.59  | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.66/45.59  | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.66/45.59  | | | | | | | | | | | | | | | | |              = e2)
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (17764), (22134), (22136), (22145),
% 238.66/45.59  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.59  | | | | | | | | | | | | | | | | |            #72.
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | |   (22146)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.66/45.59  | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.66/45.59  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.59  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.59  | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.66/45.59  | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.66/45.59  | | | | | | | | | | | | | | | | |              = e0)
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (17762), (22134), (22137), (22146),
% 238.66/45.59  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.59  | | | | | | | | | | | | | | | | |            #251.
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | End of split
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | End of split
% 238.66/45.59  | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | |   (22147)  all_54_10 = e0
% 238.66/45.59  | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | REF_CLOSE: (297), (22124), (22147) are inconsistent by
% 238.66/45.59  | | | | | | | | | | | | | | |            sub-proof #2303.
% 238.66/45.59  | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | End of split
% 238.66/45.59  | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | End of split
% 238.66/45.59  | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | End of split
% 238.66/45.59  | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | |   (22148)  all_36_2 = e2
% 238.66/45.59  | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | COMBINE_EQS: (328), (22148) imply:
% 238.66/45.59  | | | | | | | | | | | |   (22149)  all_6_2 = e2
% 238.66/45.59  | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | REDUCE: (367), (22149) imply:
% 238.66/45.59  | | | | | | | | | | | |   (22150)   ~ (all_52_2 = e2)
% 238.66/45.59  | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | REDUCE: (378), (22149) imply:
% 238.66/45.59  | | | | | | | | | | | |   (22151)   ~ (all_52_6 = e2)
% 238.66/45.59  | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | REDUCE: (380), (22149) imply:
% 238.66/45.59  | | | | | | | | | | | |   (22152)   ~ (all_52_8 = e2)
% 238.66/45.59  | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | REDUCE: (381), (22149) imply:
% 238.66/45.59  | | | | | | | | | | | |   (22153)   ~ (all_52_9 = e2)
% 238.66/45.59  | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | REDUCE: (17775), (22149) imply:
% 238.66/45.59  | | | | | | | | | | | |   (22154)   ~ (e3 = e2)
% 238.66/45.59  | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | REDUCE: (39), (22149) imply:
% 238.66/45.59  | | | | | | | | | | | |   (22155)  op(e1, e1) = e2
% 238.66/45.59  | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.66/45.59  | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | |   (22156)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.66/45.59  | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.66/45.59  | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | BETA: splitting (22156) gives:
% 238.66/45.59  | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | |   (22157)  all_58_1 = e2 & op(e3, e2) = e2
% 238.66/45.59  | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | ALPHA: (22157) implies:
% 238.66/45.59  | | | | | | | | | | | | | |   (22158)  all_58_1 = e2
% 238.66/45.59  | | | | | | | | | | | | | |   (22159)  op(e3, e2) = e2
% 238.66/45.59  | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.66/45.59  | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | |   (22160)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.66/45.59  | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.66/45.59  | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | BETA: splitting (22160) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | |   (22161)  all_58_2 = e2 & op(e2, e3) = e2
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | ALPHA: (22161) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | |   (22162)  op(e2, e3) = e2
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | |   (22163)  all_54_12 = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (22163) imply:
% 238.66/45.59  | | | | | | | | | | | | | | | | |   (22164)  all_52_3 = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | SIMP: (22164) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | |   (22165)  all_52_3 = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | REDUCE: (144), (22165) imply:
% 238.66/45.59  | | | | | | | | | | | | | | | | |   (22166)   ~ (all_52_2 = e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | |   (22167)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (159), (163), (167), (239), (22117),
% 238.66/45.59  | | | | | | | | | | | | | | | | | |            (22118), (22119), (22162), (22167),
% 238.66/45.59  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.59  | | | | | | | | | | | | | | | | | |            #160.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | |   (22168)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | BETA: splitting (22168) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | |   (22169)  all_58_6 = e3 & op(e1, e3) = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | ALPHA: (22169) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | |   (22170)  op(e1, e3) = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (22166), (22170), (function-axioms) are
% 238.66/45.59  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | |   (22171)  all_58_12 = e3 & op(e0, e3) = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | ALPHA: (22171) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | |   (22172)  all_58_12 = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | |   (22173)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | BETA: splitting (22173) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | |   (22174)  all_58_0 = e1 & op(e3, e3) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22174) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | |   (22175)  op(e3, e3) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (22122), (22175), (function-axioms) are
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | |   (22176)  all_58_2 = e1 & op(e2, e3) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22176) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | |   (22177)  op(e2, e3) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (22162), (22177), (function-axioms) are
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1633.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | |   (22178)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | BETA: splitting (22178) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | |   (22179)  all_58_6 = e1 & op(e1, e3) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22179) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | |   (22180)  all_58_6 = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | |   (22181)  op(e1, e3) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | |   (22182)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22182) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | |   (22183)  all_58_4 = e3 & op(e3, e1) = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22183) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | |   (22184)  all_58_4 = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | |   (22185)  op(e3, e1) = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | |   (22186)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22186) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (22187)  all_58_0 = e1 & op(e3, e3) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22187) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (22188)  op(e3, e3) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (239), (243), (22172),
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |            (22180), (22188), (function-axioms) are
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1162.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (22189)  all_58_1 = e1 & op(e3, e2) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22189) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (22190)  op(e3, e2) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (22159), (22190), (function-axioms) are
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2261.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | |   (22191)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22191) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (22192)  all_58_4 = e1 & op(e3, e1) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22192) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (22193)  op(e3, e1) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22185), (22193), (function-axioms) are
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1823.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (22194)  all_58_9 = e1 & op(e3, e0) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22194) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (22195)  all_58_9 = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22196)  all_54_8 = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (22166), (22196) are inconsistent by
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22197)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22197) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22198)  all_54_8 = e2
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (22150), (22198) are inconsistent by
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2007.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22199)  all_54_8 = e1 | all_54_8 = e0
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22200)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (21511), (22195), (22200),
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1606.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22201)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22201) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22202)  all_58_11 = e3 & op(e1, e0) = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22202) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22203)  all_58_11 = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22204)  op(e1, e0) = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22205)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22205) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22206)  all_58_6 = e0 & op(e1, e3) = e0
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22206) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22207)  all_58_6 = e0
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (241), (243), (22122),
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22172), (22207), (function-axioms) are
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1442.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22208)  all_58_7 = e0 & op(e1, e2) = e0
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22208) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22209)  op(e1, e2) = e0
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22210)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21516), (22159), (22210),
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #71.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22211)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22211) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22212)  all_58_7 = e1 & op(e1, e2) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22212) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22213)  op(e1, e2) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (22209), (22213), (function-axioms)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22214)  all_58_13 = e1 & op(e0, e2) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22214) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22215)  op(e0, e2) = e1
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22216)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22216) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22217)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22217) gives:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22218)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22218) implies:
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22219)  op(e2, e3) = e3
% 238.66/45.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22162), (22219), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22220)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22220) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22221)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22221) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22222)   ~ (all_56_11 = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21505), (22222) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22223)  $false
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22223) is inconsistent.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22224)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22224) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22225)  op(e1, e3) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22181), (22225), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2225.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22226)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22226) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22227)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22227) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22228)  op(e3, e1) = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22185), (22228), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1823.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22229)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (22116), (22119), (22229),
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1829.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22230)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22230) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22231)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (158), (162), (165), (17764), (22153),
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22209), (22231), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #70.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22232)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22232) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22233)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22233) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22234)  op(e0, e2) = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (22215), (22234), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22235)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22235) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22236)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22236) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22237)  op(e1, e0) = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22204), (22237), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22238)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22238) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22239)  op(e1, e0) = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22199) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22240)  all_54_8 = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (22240) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22241)  all_52_2 = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (22241) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22242)   ~ (all_52_6 = e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22242) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22243)   ~ (all_52_6 = e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22244)  all_54_9 = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (21508), (22244) are inconsistent by
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22245)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22245) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22246)  all_54_9 = e2
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (22151), (22246) are inconsistent by
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1954.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22247)  all_54_9 = e1 | all_54_9 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22247) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22248)  all_54_9 = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (22243), (22248) are inconsistent by
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2055.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22249)  all_54_9 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (22249) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22250)  all_52_6 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22250) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22251)  all_52_6 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (22251) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22252)   ~ (all_52_14 = e0)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22252) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22253)   ~ (all_52_14 = e0)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (22239), (22253), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2323.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22254)  all_54_8 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (22254) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22255)  all_52_2 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22118), (22255) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22256)  $false
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22256) is inconsistent.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22257)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22257) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22258)  all_58_8 = e0 & op(e1, e1) = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22258) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22259)  op(e1, e1) = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22155), (22259), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22260)  all_58_11 = e0 & op(e1, e0) = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22260) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22261)  all_58_11 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22203), (22261) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22262)  e3 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22184), (22262) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22263)  all_58_4 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (242), (244),
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (21507), (22122), (22263),
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1512.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22264)  all_58_15 = e3 & op(e0, e0) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22264) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22265)  op(e0, e0) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17774), (22265), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22266)  all_58_5 = e3 & op(e2, e1) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (21510), (22266), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | |   (22267)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22267) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22268)  all_58_8 = e3 & op(e1, e1) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22268) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22269)  op(e1, e1) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22155), (22269), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22270)  all_58_14 = e3 & op(e0, e1) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22270) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22271)  all_58_14 = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (217), (218),
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |            (22172), (22271), (function-axioms) are
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1862.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | |   (22272)  all_58_12 = e1 & op(e0, e3) = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22272) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | |   (22273)  all_58_12 = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22172), (22273) are inconsistent by
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1542.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | End of split
% 238.66/45.60  | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | |   (22274)   ~ (all_54_12 = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | |   (22275)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | REDUCE: (257), (22274) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | |   (22276)   ~ (all_52_3 = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | |   (22277)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (159), (163), (167), (239), (22117),
% 238.66/45.60  | | | | | | | | | | | | | | | | | |            (22118), (22119), (22162), (22277),
% 238.66/45.60  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.60  | | | | | | | | | | | | | | | | | |            #160.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | |   (22278)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | BETA: splitting (22278) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | |   (22279)  all_58_6 = e3 & op(e1, e3) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | ALPHA: (22279) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | |   (22280)  all_58_6 = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | |   (22281)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (239), (241),
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | |            (243), (21509), (22280), (22281),
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | |            #1138.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | |   (22282)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | BETA: splitting (22282) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | |   (22283)  all_58_14 = e3 & op(e0, e1) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22283) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | |   (22284)  op(e0, e1) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22275) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | |   (22285)  all_54_12 = e2
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (22285) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | |   (22286)  all_52_3 = e2
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17763), (22286) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | |   (22287)  $false
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22287) is inconsistent.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | |   (22288)   ~ (all_54_12 = e2)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | |   (22289)  all_54_12 = e1 | all_54_12 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22289) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22290)  all_54_12 = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (22290) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22291)  all_52_3 = e1
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (22291) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22292)   ~ (all_52_2 = e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (22291) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22293)   ~ (all_52_7 = e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22293) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22294)   ~ (all_52_7 = e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (22291) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22295)   ~ (all_52_11 = e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22295) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22296)   ~ (all_52_11 = e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17763), (22291) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | |   (22297)   ~ (e2 = e1)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | |   (22298)  all_54_8 = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (22298) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | |   (22299)  all_52_2 = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22299) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | |   (22300)  all_52_2 = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (22300) imply:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | |   (22301)   ~ (all_52_14 = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22301) implies:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | |   (22302)   ~ (all_52_14 = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (22303)  all_54_13 = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (21509), (22303) are inconsistent by
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (22304)   ~ (all_54_13 = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (22305)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22305) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22306)  all_54_13 = e2
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17764), (22306) are inconsistent by
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22307)   ~ (all_54_13 = e2)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22308)  all_54_13 = e1 | all_54_13 = e0
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22309)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22309) gives:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22310)  all_58_9 = e3 & op(e3, e0) = e3
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22310) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22311)  all_58_9 = e3
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22312)  op(e3, e0) = e3
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22313)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21516), (22159), (22313),
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #71.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22314)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22314) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22315)  all_58_7 = e1 & op(e1, e2) = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22315) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22316)  op(e1, e2) = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22317)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22317) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22318)  all_58_4 = e0 & op(e3, e1) = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22318) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22319)  all_58_4 = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (242), (244), (22122),
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22311), (22312), (22319), (function-axioms) are
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1706.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22320)  all_58_5 = e0 & op(e2, e1) = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22320) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22321)  op(e2, e1) = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22322)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22322) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22323)  all_58_2 = e1 & op(e2, e3) = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22323) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22324)  op(e2, e3) = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (22162), (22324), (function-axioms) are
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1633.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22325)  all_58_3 = e1 & op(e2, e2) = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21516), (22325) are inconsistent by
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22326)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22326) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22327)  all_58_5 = e1 & op(e2, e1) = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22327) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22328)  op(e2, e1) = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (165), (22321), (22328), (function-axioms)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2165.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22329)  all_58_10 = e1 & op(e2, e0) = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22329) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22330)  op(e2, e0) = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22308) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22331)  all_54_13 = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (22294), (22331) are inconsistent by
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1966.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22332)  all_54_13 = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (22332) imply:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22333)  all_52_7 = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22333) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22334)  all_52_7 = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (22334) imply:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22335)   ~ (all_52_11 = e0)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22335) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22336)   ~ (all_52_11 = e0)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21509), (22334) imply:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22337)   ~ (e3 = e0)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17764), (22334) imply:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22338)   ~ (e2 = e0)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (22334) imply:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22339)  op(e0, e2) = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22340)  all_58_15 = e0 & op(e0, e0) = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22340) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22341)  op(e0, e0) = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (22341), (function-axioms) are
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22342)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22342) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22343)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22343) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22344)  all_58_9 = e0 & op(e3, e0) = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22344) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22345)  all_58_9 = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (242), (244),
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (21507), (22122), (22345),
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #319.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22346)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22346) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22347)  all_58_10 = e0 & op(e2, e0) = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22347) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22348)  op(e2, e0) = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (22330), (22348), (function-axioms)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22349)  all_58_11 = e0 & op(e1, e0) = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22349) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22350)  all_58_11 = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22351)  op(e1, e0) = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22352)  all_54_14 = e3
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (22352) imply:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22353)  all_52_11 = e3
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22353) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22354)  all_52_11 = e3
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (22354) imply:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22355)   ~ (all_52_8 = e3)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22356)  all_54_2 = e3
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (22355), (22356) are inconsistent by
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22357)   ~ (all_54_2 = e3)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22358)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22359)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22359) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22360)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22360) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22361)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22361) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22362)  op(e2, e3) = e3
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22162), (22362), (function-axioms) are
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22363)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (21505), (22355), (22363),
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1007.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22364)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22364) gives:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22365)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22365) implies:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22366)  op(e1, e3) = e1
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (39), (226), (17775), (22316), (22350),
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22366), (function-axioms) are inconsistent by
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2090.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22367)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (22119), (22276), (22367),
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2330.
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.66/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22368)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22368) gives:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22369)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22369) gives:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22370)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22370) implies:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22371)  op(e2, e1) = e2
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22321), (22371), (function-axioms) are
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22372)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22372) gives:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22373)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22373) implies:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22374)  op(e2, e1) = e1
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (165), (281), (22120), (22152), (22358),
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22374), (function-axioms) are inconsistent by
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #434.
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22375)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22375) implies:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22376)  op(e0, e2) = e2
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22339), (22376), (function-axioms) are
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22377)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22377) gives:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22378)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22378) implies:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22379)  op(e2, e0) = e0
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (22330), (22379), (function-axioms)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22380)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22380) gives:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22381)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22381) implies:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22382)  op(e1, e0) = e1
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (22351), (22382), (function-axioms) are
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2284.
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22383)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22383) implies:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22384)  op(e0, e1) = e0
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (165), (169), (230), (17775), (21510),
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22355), (22384), (function-axioms) are
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1626.
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22385)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (255), (257), (17763), (17765), (22119),
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22275), (22336), (22385) are inconsistent by
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1855.
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22386)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (22155), (22284), (22386),
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2163.
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22387)  all_58_13 = e1 & op(e0, e2) = e1
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (22294), (22387), (function-axioms) are
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22388)  all_58_10 = e3 & op(e2, e0) = e3
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22388) implies:
% 238.76/45.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22389)  op(e2, e0) = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (21511), (22389), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22390)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (17774), (22302), (22390),
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #214.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | |   (22391)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (22118), (22150), (22292), (22391) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1949.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | |   (22392)  all_54_12 = e0
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (22392) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | |   (22393)  all_52_3 = e0
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22119), (22393) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | |   (22394)  $false
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22394) is inconsistent.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | |   (22395)  all_58_15 = e3 & op(e0, e0) = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22395) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | |   (22396)  op(e0, e0) = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17774), (22396), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1388.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | |   (22397)  all_58_12 = e3 & op(e0, e3) = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | ALPHA: (22397) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | |   (22398)  op(e0, e3) = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (22276), (22398), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | |   (22399)  all_58_3 = e2 & op(e2, e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | ALPHA: (22399) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | |   (22400)  op(e2, e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (235),
% 238.76/45.62  | | | | | | | | | | | | | | | |            (236), (238), (21509), (22158), (22159), (22400),
% 238.76/45.62  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.62  | | | | | | | | | | | | | | | |            #1809.
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | |   (22401)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.76/45.62  | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (17767), (22153), (22401),
% 238.76/45.62  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.62  | | | | | | | | | | | | | | |            #182.
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | |   (22402)  all_58_3 = e2 & op(e2, e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | ALPHA: (22402) implies:
% 238.76/45.62  | | | | | | | | | | | | | |   (22403)  op(e2, e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | REF_CLOSE: (9), (21517), (22403), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | |            inconsistent by sub-proof #2140.
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | |   (22404)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.76/45.62  | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | BETA: splitting (22404) gives:
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | |   (22405)  all_58_7 = e2 & op(e1, e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | ALPHA: (22405) implies:
% 238.76/45.62  | | | | | | | | | | | | | |   (22406)  all_58_7 = e2
% 238.76/45.62  | | | | | | | | | | | | | |   (22407)  op(e1, e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | |   (22408)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 238.76/45.62  | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | BETA: splitting (22408) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | |   (22409)  all_58_6 = e0 & op(e1, e3) = e0
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | ALPHA: (22409) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | |   (22410)  all_58_6 = e0
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (241), (243),
% 238.76/45.62  | | | | | | | | | | | | | | | |            (245), (21506), (22122), (22410),
% 238.76/45.62  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.62  | | | | | | | | | | | | | | | |            #1441.
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | |   (22411)  all_58_7 = e0 & op(e1, e2) = e0
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22406), (22411) are inconsistent by
% 238.76/45.62  | | | | | | | | | | | | | | | |            sub-proof #2212.
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | |   (22412)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 238.76/45.62  | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (224),
% 238.76/45.62  | | | | | | | | | | | | | | |            (225), (226), (22155), (22406), (22407), (22412),
% 238.76/45.62  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.62  | | | | | | | | | | | | | | |            #1673.
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | |   (22413)  all_58_13 = e2 & op(e0, e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | ALPHA: (22413) implies:
% 238.76/45.62  | | | | | | | | | | | | | |   (22414)  op(e0, e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (22414), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | |   (22415)  all_18_2 = e0
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | COMBINE_EQS: (339), (22415) imply:
% 238.76/45.62  | | | | | | | | | | |   (22416)  all_6_2 = e0
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | SIMP: (22416) implies:
% 238.76/45.62  | | | | | | | | | | |   (22417)  all_6_2 = e0
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | COMBINE_EQS: (266), (22417) imply:
% 238.76/45.62  | | | | | | | | | | |   (22418)  all_56_21 = e0
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | REDUCE: (378), (22417) imply:
% 238.76/45.62  | | | | | | | | | | |   (22419)   ~ (all_52_6 = e0)
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | REDUCE: (383), (22417) imply:
% 238.76/45.62  | | | | | | | | | | |   (22420)   ~ (all_52_11 = e0)
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | REDUCE: (385), (22417) imply:
% 238.76/45.62  | | | | | | | | | | |   (22421)   ~ (all_52_14 = e0)
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | REDUCE: (17775), (22417) imply:
% 238.76/45.62  | | | | | | | | | | |   (22422)   ~ (e3 = e0)
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | REDUCE: (39), (22417) imply:
% 238.76/45.62  | | | | | | | | | | |   (22423)  op(e1, e1) = e0
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | BETA: splitting (216) gives:
% 238.76/45.62  | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | |   (22424)  all_58_15 = e0 & op(e0, e0) = e0
% 238.76/45.62  | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | ALPHA: (22424) implies:
% 238.76/45.62  | | | | | | | | | | | |   (22425)  op(e0, e0) = e0
% 238.76/45.62  | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | REF_CLOSE: (5), (17774), (22425), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.76/45.62  | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | |   (22426)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.76/45.62  | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.76/45.62  | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.76/45.62  | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.76/45.62  | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.76/45.62  | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | ALPHA: (22426) implies:
% 238.76/45.62  | | | | | | | | | | | |   (22427)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.76/45.62  | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.76/45.62  | | | | | | | | | | | |                e1) = e0)
% 238.76/45.62  | | | | | | | | | | | |   (22428)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.76/45.62  | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 238.76/45.62  | | | | | | | | | | | |                e0) = e0)
% 238.76/45.62  | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | BETA: splitting (22427) gives:
% 238.76/45.62  | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | |   (22429)  all_58_12 = e0 & op(e0, e3) = e0
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | ALPHA: (22429) implies:
% 238.76/45.62  | | | | | | | | | | | | |   (22430)  op(e0, e3) = e0
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | REF_CLOSE: (159), (22119), (22430), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | |   (22431)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 238.76/45.62  | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | BETA: splitting (22431) gives:
% 238.76/45.62  | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | |   (22432)  all_58_13 = e0 & op(e0, e2) = e0
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | ALPHA: (22432) implies:
% 238.76/45.62  | | | | | | | | | | | | | |   (22433)  op(e0, e2) = e0
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | BETA: splitting (22428) gives:
% 238.76/45.62  | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | |   (22434)  all_58_9 = e0 & op(e3, e0) = e0
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | ALPHA: (22434) implies:
% 238.76/45.62  | | | | | | | | | | | | | | |   (22435)  all_58_9 = e0
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (242), (244),
% 238.76/45.62  | | | | | | | | | | | | | | |            (246), (21507), (22122), (22435),
% 238.76/45.62  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.62  | | | | | | | | | | | | | | |            #319.
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | |   (22436)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 238.76/45.62  | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | BETA: splitting (22436) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | |   (22437)  all_58_10 = e0 & op(e2, e0) = e0
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | ALPHA: (22437) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | |   (22438)  op(e2, e0) = e0
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | |   (22439)   ~ (all_42_2 = e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | REDUCE: (21504), (22439) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | |   (22440)  $false
% 238.76/45.62  | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | CLOSE: (22440) is inconsistent.
% 238.76/45.62  | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | |   (22441)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 238.76/45.62  | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 238.76/45.62  | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 238.76/45.62  | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | |   (22442)  all_54_12 = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (22442) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | |   (22443)  all_52_3 = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | SIMP: (22443) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | |   (22444)  all_52_3 = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | REDUCE: (144), (22444) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | |   (22445)   ~ (all_52_2 = e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | REDUCE: (139), (22444) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | |   (22446)   ~ (all_52_11 = e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | SIMP: (22446) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | |   (22447)   ~ (all_52_11 = e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | |   (22448)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (22448) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | |   (22449)  all_58_4 = e3 & op(e3, e1) = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (22449) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | |   (22450)  all_58_4 = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | |   (22451)  op(e3, e1) = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | |   (22452)  all_54_14 = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (22452) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | |   (22453)  all_52_11 = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | REDUCE: (22447), (22453) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | |   (22454)  $false
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | CLOSE: (22454) is inconsistent.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | |   (22455)   ~ (all_54_14 = e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | |   (22456)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22456) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | |   (22457)  all_54_14 = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (22457) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | |   (22458)  all_52_11 = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17765), (22458) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | |   (22459)  $false
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22459) is inconsistent.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | |   (22460)   ~ (all_54_14 = e2)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | |   (22461)  all_54_14 = e1 | all_54_14 = e0
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | |   (22462)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22462) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | |   (22463)  all_58_12 = e1 & op(e0, e3) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22463) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | |   (22464)  all_58_12 = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (157), (219), (17774), (22433),
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | |            (22447), (22464), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #190.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | |   (22465)  all_58_13 = e1 & op(e0, e2) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22465) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | |   (22466)  op(e0, e2) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (22433), (22466), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | |   (22467)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22467) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | |   (22468)  all_58_14 = e1 & op(e0, e1) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22468) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | |   (22469)  all_58_14 = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (22470)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22470) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22471)  all_58_12 = e3 & op(e0, e3) = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22471) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22472)  all_58_12 = e3
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22473)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22473) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22474)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (21505), (21506), (22445), (22474),
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #77.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22475)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22475) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22476)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22476) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22477)  op(e3, e1) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22451), (22477), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1823.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22478)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (22119), (22418), (22478),
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1788.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22479)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22479) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22480)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22480) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22481)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22481) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22482)  op(e1, e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22483)  op(e2, e1) = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22484)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22484) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22485)  all_58_0 = e2 & op(e3, e3) = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22485) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22486)  op(e3, e3) = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22122), (22486), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22487)  all_58_1 = e2 & op(e3, e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22487) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22488)  op(e3, e2) = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22461) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22489)  all_54_14 = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (22489) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22490)  all_52_11 = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (22490) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22491)   ~ (all_52_9 = e1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22447), (22490) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22492)   ~ (e3 = e1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17765), (22490) imply:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22493)   ~ (e2 = e1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22494)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22494) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22495)  all_58_4 = e2 & op(e3, e1) = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22495) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22496)  all_58_4 = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (157), (165), (230), (21510), (22423),
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22447), (22496), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1493.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22497)  all_58_5 = e2 & op(e2, e1) = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22497) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22498)  all_58_5 = e2
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22499)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22499) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22500)  all_58_2 = e1 & op(e2, e3) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22500) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22501)  op(e2, e3) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22502)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22502) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22503)  all_58_1 = e1 & op(e3, e2) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22503) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22504)  op(e3, e2) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (22488), (22504), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2261.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22505)  all_58_3 = e1 & op(e2, e2) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (157), (219), (17774), (21516),
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22433), (22447), (22472), (22505),
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #74.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22506)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22506) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22507)  all_58_7 = e1 & op(e1, e2) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22507) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22508)  op(e1, e2) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21503) gives:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22509)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22509) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22510)  op(e2, e3) = all_8_1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (22441),
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22450), (22469), (22482), (22498), (22501),
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22508), (22510), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #69.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22511)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_8_1)
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22511) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22512)  op(e2, e3) = all_8_1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (22441),
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22450), (22469), (22482), (22498), (22501),
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22508), (22512), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #69.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22513)  all_58_13 = e1 & op(e0, e2) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22513) implies:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22514)  op(e0, e2) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (22433), (22514), (function-axioms) are
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22515)  all_58_3 = e1 & op(e2, e2) = e1
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22515) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22516)  all_58_3 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21516), (22516) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22517)  e3 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22517) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22518)  e3 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22472), (22518) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22519)  all_58_12 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (157), (219), (17774), (22433),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22447), (22519), (function-axioms) are
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #190.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22520)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22520) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22521)  all_58_5 = e1 & op(e2, e1) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22521) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22522)  all_58_5 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (227), (229), (22450),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22469), (22522) are inconsistent by sub-proof
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1481.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22523)  all_58_10 = e1 & op(e2, e0) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22523) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22524)  op(e2, e0) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (22438), (22524), (function-axioms)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22525)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22525) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22526)  all_58_8 = e2 & op(e1, e1) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22526) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22527)  op(e1, e1) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22423), (22527), (function-axioms) are
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22528)  all_58_14 = e2 & op(e0, e1) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (165), (227), (228),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22450), (22483), (22491), (22528),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1284.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22529)  all_54_14 = e0
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (22529) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22530)  all_52_11 = e0
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22420), (22530) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22531)  $false
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22531) is inconsistent.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22532)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (157), (165), (168), (230), (17766),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21510), (22423), (22447), (22532),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #78.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22533)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22533) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22534)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22534) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22535)   ~ (all_56_31 = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (22535) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22536)  $false
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22536) is inconsistent.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22537)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22537) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22538)  op(e0, e2) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (22427), (22469), (22472), (22538),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1032.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22539)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (17762), (22418), (22421), (22539),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #179.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22540)  all_58_13 = e3 & op(e0, e2) = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22540) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22541)  op(e0, e2) = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (22433), (22541), (function-axioms) are
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1961.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (22542)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17774), (22447), (22542),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | |            #226.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | |   (22543)  all_58_15 = e1 & op(e0, e0) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22543) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | |   (22544)  all_58_15 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (22544) are inconsistent by
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2231.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |   (22545)  all_58_5 = e3 & op(e2, e1) = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (21510), (22545), (function-axioms) are
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | |   (22546)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | BETA: splitting (22546) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |   (22547)  all_58_8 = e3 & op(e1, e1) = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (22423), (22547), (function-axioms) are
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2018.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |   (22548)  all_58_14 = e3 & op(e0, e1) = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (22447), (22548), (function-axioms) are
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1647.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | |   (22549)   ~ (all_54_12 = e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | |   (22550)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 238.76/45.63  | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | REDUCE: (257), (22549) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | |   (22551)   ~ (all_52_3 = e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | BETA: splitting (22550) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | |   (22552)  all_54_12 = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (17763), (22552) are inconsistent by
% 238.76/45.63  | | | | | | | | | | | | | | | | | | |            sub-proof #2264.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | |   (22553)   ~ (all_54_12 = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | |   (22554)  all_54_12 = e1 | all_54_12 = e0
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |   (22555)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (21506), (22117),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |            (22118), (22119), (22555), (function-axioms) are
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1579.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |   (22556)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | BETA: splitting (22556) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | |   (22557)  all_58_6 = e3 & op(e1, e3) = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22557) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | |   (22558)  all_58_6 = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | |   (22559)  op(e1, e3) = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | |   (22560)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22560) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | |   (22561)  all_58_6 = e2 & op(e1, e3) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22561) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | |   (22562)  all_58_6 = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22558), (22562) are inconsistent by
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2024.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | |   (22563)  all_58_7 = e2 & op(e1, e2) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22563) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | |   (22564)  all_58_7 = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | |   (22565)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (22559), (22564), (22565),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | |            #2223.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | |   (22566)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22566) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (22567)  all_58_8 = e1 & op(e1, e1) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22567) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (22568)  op(e1, e1) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (162), (163), (223), (22118), (22419),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (22421), (22568), (function-axioms) are
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2020.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (22569)  all_58_11 = e1 & op(e1, e0) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22569) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (22570)  all_58_11 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (22571)  op(e1, e0) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22572)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22572) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22573)  all_58_1 = e1 & op(e3, e2) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22573) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22574)  all_58_1 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22575)  op(e3, e2) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22576)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22576) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22577)  all_58_0 = e2 & op(e3, e3) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22577) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22578)  op(e3, e3) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22122), (22578), (function-axioms) are
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22579)  all_58_2 = e2 & op(e2, e3) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22579) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22580)  op(e2, e3) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22554) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22581)  all_54_12 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (22581) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22582)  all_52_3 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22582) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22583)  all_52_3 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (22583) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22584)   ~ (all_52_1 = e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (22583) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22585)   ~ (all_52_2 = e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (22583) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22586)   ~ (all_52_11 = e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22586) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22587)   ~ (all_52_11 = e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17763), (22583) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22588)   ~ (e2 = e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22589)  all_54_14 = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (22589) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22590)  all_52_11 = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22590) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22591)  all_52_11 = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (22591) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22592)   ~ (all_52_8 = e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22593)  all_54_4 = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (22593) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22594)  all_52_1 = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21506), (22594) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22595)  $false
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22595) is inconsistent.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22596)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22597)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22597) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22598)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22598) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22599)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22599) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22600)  op(e2, e3) = e3
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22580), (22600), (function-axioms) are
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22601)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (22575), (22592), (22601),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2259.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22602)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (22119), (22551), (22585), (22602),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #68.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22603)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22603) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22604)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22604) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22605)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22605) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22606)  op(e2, e1) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (165), (279), (22117), (22584), (22596),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22606), (function-axioms) are inconsistent by
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #173.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22607)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22607) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22608)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22608) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22609)   ~ (all_56_31 = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (22609) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22610)  $false
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22610) is inconsistent.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22611)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22611) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22612)  op(e0, e2) = e2
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (235), (21516), (22564), (22574),
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22612), (function-axioms) are inconsistent by
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1461.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22613)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22613) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22614)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22614) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22615)   ~ (all_56_31 = e2)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (22615) imply:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22616)  $false
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22616) is inconsistent.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22617)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22617) gives:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22618)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22618) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22619)  op(e0, e1) = e1
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (22587), (22619), (function-axioms) are
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2272.
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22620)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22620) implies:
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22621)  op(e1, e0) = e0
% 238.76/45.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (224), (22423), (22558), (22564),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22621), (function-axioms) are inconsistent by
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #794.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22622)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (255), (257), (17763), (17765), (22119),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22420), (22550), (22622) are inconsistent by
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1855.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22623)  all_54_12 = e0
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (22119), (22623) are inconsistent by
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2068.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22624)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22624) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22625)  all_58_6 = e2 & op(e1, e3) = e2
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22558), (22625) are inconsistent by
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2219.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22626)  all_58_12 = e2 & op(e0, e3) = e2
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (17763), (22626), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2315.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22627)  all_58_3 = e1 & op(e2, e2) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21516), (22627) are inconsistent by
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2197.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22628)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22628) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22629)  all_58_7 = e1 & op(e1, e2) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22629) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22630)  all_58_7 = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (223), (225), (22558),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22570), (22571), (22630), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1553.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22631)  all_58_13 = e1 & op(e0, e2) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22631) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22632)  op(e0, e2) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (22433), (22632), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |   (22633)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (17768), (22423), (22633),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |            #167.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |   (22634)  all_58_12 = e3 & op(e0, e3) = e3
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22634) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |   (22635)  op(e0, e3) = e3
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (22551), (22635), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22636)  all_58_11 = e0 & op(e1, e0) = e0
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | ALPHA: (22636) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22637)  op(e1, e0) = e0
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | REF_CLOSE: (160), (22421), (22637), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2323.
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | |   (22638)  all_58_14 = e0 & op(e0, e1) = e0
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | ALPHA: (22638) implies:
% 238.76/45.64  | | | | | | | | | | | | | |   (22639)  op(e0, e1) = e0
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | REF_CLOSE: (157), (22420), (22639), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | | |            inconsistent by sub-proof #1911.
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | |   (22640)  all_10_2 = e1
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | COMBINE_EQS: (290), (22640) imply:
% 238.76/45.64  | | | | | | | | |   (22641)  all_56_1 = e1
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | REDUCE: (355), (22640) imply:
% 238.76/45.64  | | | | | | | | |   (22642)   ~ (all_52_1 = e1)
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | REDUCE: (357), (22640) imply:
% 238.76/45.64  | | | | | | | | |   (22643)   ~ (all_52_2 = e1)
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | REDUCE: (359), (22640) imply:
% 238.76/45.64  | | | | | | | | |   (22644)   ~ (all_52_3 = e1)
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | REDUCE: (361), (22640) imply:
% 238.76/45.64  | | | | | | | | |   (22645)   ~ (all_52_4 = e1)
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | REDUCE: (363), (22640) imply:
% 238.76/45.64  | | | | | | | | |   (22646)   ~ (all_52_8 = e1)
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | REDUCE: (365), (22640) imply:
% 238.76/45.64  | | | | | | | | |   (22647)   ~ (all_52_12 = e1)
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | REDUCE: (45), (22640) imply:
% 238.76/45.64  | | | | | | | | |   (22648)  op(e3, e3) = e1
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | BETA: splitting (58) gives:
% 238.76/45.64  | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | |   (22649)   ~ (all_18_2 = e0)
% 238.76/45.64  | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | REDUCE: (339), (22649) imply:
% 238.76/45.64  | | | | | | | | | |   (22650)   ~ (all_6_2 = e0)
% 238.76/45.64  | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | BETA: splitting (85) gives:
% 238.76/45.64  | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | |   (22651)   ~ (all_36_2 = e2)
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | REDUCE: (328), (22651) imply:
% 238.76/45.64  | | | | | | | | | | |   (22652)   ~ (all_6_2 = e2)
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | BETA: splitting (194) gives:
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | |   (22653)  all_54_10 = e3
% 238.76/45.64  | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | REF_CLOSE: (297), (17775), (22653) are inconsistent by
% 238.76/45.64  | | | | | | | | | | | |            sub-proof #2313.
% 238.76/45.64  | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | |   (22654)   ~ (all_54_10 = e3)
% 238.76/45.64  | | | | | | | | | | | |   (22655)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 238.76/45.64  | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | BETA: splitting (22655) gives:
% 238.76/45.64  | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | |   (22656)  all_54_10 = e2
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | REF_CLOSE: (297), (22652), (22656) are inconsistent by
% 238.76/45.64  | | | | | | | | | | | | |            sub-proof #2312.
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | |   (22657)   ~ (all_54_10 = e2)
% 238.76/45.64  | | | | | | | | | | | | |   (22658)  all_54_10 = e1 | all_54_10 = e0
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | BETA: splitting (22658) gives:
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | |   (22659)  all_54_10 = e1
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | COMBINE_EQS: (297), (22659) imply:
% 238.76/45.64  | | | | | | | | | | | | | |   (22660)  all_6_2 = e1
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | SIMP: (22660) implies:
% 238.76/45.64  | | | | | | | | | | | | | |   (22661)  all_6_2 = e1
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | COMBINE_EQS: (266), (22661) imply:
% 238.76/45.64  | | | | | | | | | | | | | |   (22662)  all_56_21 = e1
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | REDUCE: (381), (22661) imply:
% 238.76/45.64  | | | | | | | | | | | | | |   (22663)   ~ (all_52_9 = e1)
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | REDUCE: (383), (22661) imply:
% 238.76/45.64  | | | | | | | | | | | | | |   (22664)   ~ (all_52_11 = e1)
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | REDUCE: (385), (22661) imply:
% 238.76/45.64  | | | | | | | | | | | | | |   (22665)   ~ (all_52_14 = e1)
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | REDUCE: (17775), (22661) imply:
% 238.76/45.64  | | | | | | | | | | | | | |   (22666)   ~ (e3 = e1)
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | REDUCE: (22652), (22661) imply:
% 238.76/45.64  | | | | | | | | | | | | | |   (22667)   ~ (e2 = e1)
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | |   (22668)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.76/45.64  | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | BETA: splitting (22668) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22669)  all_58_9 = e1 & op(e3, e0) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | REF_CLOSE: (168), (22647), (22669), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22670)  all_58_10 = e1 & op(e2, e0) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | ALPHA: (22670) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22671)  op(e2, e0) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | |   (22672)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.76/45.64  | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.76/45.64  | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | BETA: splitting (22672) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | |   (22673)  all_58_12 = e1 & op(e0, e3) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | ALPHA: (22673) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | |   (22674)  all_58_12 = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 238.76/45.64  | | | | | | | | | | | | | | | | | |            (245), (21506), (22648), (22674),
% 238.76/45.64  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.64  | | | | | | | | | | | | | | | | | |            #1204.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | |   (22675)  all_58_13 = e1 & op(e0, e2) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | ALPHA: (22675) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | |   (22676)  all_58_13 = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |   (22677)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | BETA: splitting (22677) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |   (22678)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (21505), (21506), (22662), (22678),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |            #73.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |   (22679)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | BETA: splitting (22679) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |   (22680)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22680) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |   (22681)  op(e3, e1) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (22646), (22681), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |   (22682)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22682) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |   (22683)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22683) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |   (22684)   ~ (all_56_31 = e0)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |   (22685)   ~ (all_56_21 = e0)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |   (22686)   ~ (all_56_11 = e0)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |   (22687)  op(e0, e3) = e3
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |   (22688)  op(e3, e0) = e3
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | |   (22689)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (235), (237),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | |            (239), (243), (245), (21506), (21516), (22648),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | |            (22676), (22689), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #538.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | |   (22690)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22690) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (22687) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |   (22691)  all_52_3 = e3
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (164), (22671) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |   (22692)  all_52_13 = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (168), (22688) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |   (22693)  all_52_12 = e3
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (22691) imply:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |   (22694)   ~ (all_52_11 = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22694) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |   (22695)   ~ (all_52_11 = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (22693) imply:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |   (22696)   ~ (all_52_14 = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22696) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |   (22697)   ~ (all_52_14 = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (157), (158),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (219), (226), (239), (241), (243),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (17775), (21508), (21509), (22695),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |            (22697), (function-axioms) are inconsistent by
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #75.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |   (22698)  all_58_11 = e1 & op(e1, e0) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22698) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |   (22699)  op(e1, e0) = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (22665), (22699), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |   (22700)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |              e3) = e0
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22700) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |   (22701)   ~ (all_56_11 = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21505), (22701) imply:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | |   (22702)  $false
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22702) is inconsistent.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |   (22703)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.76/45.64  | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | BETA: splitting (22703) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |   (22704)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (17764), (22662), (22663), (22704),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |            #72.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |   (22705)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | BETA: splitting (22705) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |   (22706)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22706) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |   (22707)  op(e2, e0) = e0
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (164), (165), (167), (232), (21516),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |            (22642), (22663), (22707), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1777.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |   (22708)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (22662), (22665), (22708),
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | |            #1409.
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | |   (22709)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.76/45.64  | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.76/45.64  | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (17773), (22664), (22709),
% 238.76/45.64  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.64  | | | | | | | | | | | | | | | | |            #163.
% 238.76/45.64  | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | |   (22710)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.76/45.64  | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (17773), (22665), (22710),
% 238.76/45.64  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.64  | | | | | | | | | | | | | | |            #162.
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | |   (22711)  all_54_10 = e0
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | REF_CLOSE: (297), (22650), (22711) are inconsistent by
% 238.76/45.64  | | | | | | | | | | | | | |            sub-proof #2303.
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | End of split
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | |   (22712)  all_36_2 = e2
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | COMBINE_EQS: (328), (22712) imply:
% 238.76/45.64  | | | | | | | | | | |   (22713)  all_6_2 = e2
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | SIMP: (22713) implies:
% 238.76/45.64  | | | | | | | | | | |   (22714)  all_6_2 = e2
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | REDUCE: (380), (22714) imply:
% 238.76/45.64  | | | | | | | | | | |   (22715)   ~ (all_52_8 = e2)
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | REDUCE: (381), (22714) imply:
% 238.76/45.64  | | | | | | | | | | |   (22716)   ~ (all_52_9 = e2)
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | REDUCE: (17775), (22714) imply:
% 238.76/45.64  | | | | | | | | | | |   (22717)   ~ (e3 = e2)
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | REDUCE: (39), (22714) imply:
% 238.76/45.64  | | | | | | | | | | |   (22718)  op(e1, e1) = e2
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | BETA: splitting (244) gives:
% 238.76/45.64  | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | |   (22719)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 238.76/45.64  | | | | | | | | | | | |              & op(e3, e2) = e2)
% 238.76/45.64  | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | BETA: splitting (22719) gives:
% 238.76/45.64  | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | |   (22720)  all_58_0 = e2 & op(e3, e3) = e2
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | ALPHA: (22720) implies:
% 238.76/45.64  | | | | | | | | | | | | |   (22721)  op(e3, e3) = e2
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | REF_CLOSE: (6), (22648), (22721), (function-axioms) are
% 238.76/45.64  | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | Case 2:
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | |   (22722)  all_58_1 = e2 & op(e3, e2) = e2
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | ALPHA: (22722) implies:
% 238.76/45.64  | | | | | | | | | | | | |   (22723)  all_58_1 = e2
% 238.76/45.64  | | | | | | | | | | | | |   (22724)  op(e3, e2) = e2
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.76/45.64  | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | |   (22725)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.76/45.64  | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | BETA: splitting (22725) gives:
% 238.76/45.64  | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | |   (22726)  all_58_2 = e2 & op(e2, e3) = e2
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | ALPHA: (22726) implies:
% 238.76/45.64  | | | | | | | | | | | | | | |   (22727)  all_58_2 = e2
% 238.76/45.64  | | | | | | | | | | | | | | |   (22728)  op(e2, e3) = e2
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22729)  all_54_2 = e3
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (22729) imply:
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22730)  all_52_8 = e3
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | SIMP: (22730) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22731)  all_52_8 = e3
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | REDUCE: (121), (22731) imply:
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22732)   ~ (all_52_11 = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | SIMP: (22732) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22733)   ~ (all_52_11 = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | REDUCE: (120), (22731) imply:
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22734)   ~ (all_52_12 = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | SIMP: (22734) implies:
% 238.76/45.64  | | | | | | | | | | | | | | | |   (22735)   ~ (all_52_12 = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 238.76/45.64  | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.64  | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | |   (22736)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 238.76/45.64  | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 238.76/45.64  | | | | | | | | | | | | | | | | | 
% 238.76/45.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (170), (241), (21507),
% 238.76/45.64  | | | | | | | | | | | | | | | | |            (22642), (22643), (22644), (22736),
% 238.76/45.64  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.65  | | | | | | | | | | | | | | | | |            #269.
% 238.76/45.65  | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | |   (22737)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | BETA: splitting (22737) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | |   (22738)  all_58_4 = e3 & op(e3, e1) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | ALPHA: (22738) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | |   (22739)  all_58_4 = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | |   (22740)  op(e3, e1) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | |   (22741)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | BETA: splitting (22741) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | |   (22742)  all_58_12 = e3 & op(e0, e3) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | ALPHA: (22742) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | |   (22743)  all_58_12 = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | |   (22744)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22744) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |   (22745)  all_58_9 = e3 & op(e3, e0) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22745) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |   (22746)  op(e3, e0) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (22735), (22746), (function-axioms) are
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |   (22747)  all_58_10 = e3 & op(e2, e0) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22747) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |   (22748)  all_58_10 = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (170), (231),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (240), (244), (246), (21507),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |            (21516), (22642), (22648), (22739), (22748),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |            #653.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | |   (22749)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22749) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |   (22750)  all_58_11 = e3 & op(e1, e0) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22750) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |   (22751)  all_58_11 = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | |   (22752)  op(e1, e0) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | |   (22753)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (22648), (22724), (22753),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | |            #1017.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | |   (22754)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22754) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | |   (22755)  all_58_4 = e0 & op(e3, e1) = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22755) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | |   (22756)  op(e3, e1) = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (22740), (22756), (function-axioms) are
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2118.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | |   (22757)  all_58_9 = e0 & op(e3, e0) = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22757) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | |   (22758)  all_58_9 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (22759)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22759) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22760)  all_58_9 = e1 & op(e3, e0) = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22760) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22761)  all_58_9 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22762)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (22648), (22723), (22762),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #709.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22754) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22763)  all_58_4 = e0 & op(e3, e1) = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22763) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22764)  all_58_4 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22739), (22764) imply:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22765)  e3 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22751), (22765) imply:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22766)  all_58_11 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22767)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22767) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22768)  all_58_9 = e3 & op(e3, e0) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22768) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22769)  all_58_9 = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22761), (22769) imply:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22770)  e3 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22770) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22771)  e3 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22743), (22771) imply:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22772)  all_58_12 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (21506), (22648), (22772),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1204.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22773)  all_58_10 = e3 & op(e2, e0) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22773) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22774)  all_58_10 = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22775)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22775) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22776)  all_58_2 = e1 & op(e2, e3) = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (22642), (22776), (function-axioms) are
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22777)  all_58_3 = e1 & op(e2, e2) = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22777) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22778)  all_58_3 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21516), (22778) imply:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22779)  e3 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22774), (22779) imply:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22780)  all_58_10 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (222), (240),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (246), (17773), (21507), (22648), (22761),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22766), (22780), (function-axioms) are
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22781)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22781) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22782)  all_58_5 = e1 & op(e2, e1) = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22782) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22783)  all_58_5 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (231), (233), (21516),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22774), (22783) are inconsistent by sub-proof
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1101.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22784)  all_58_10 = e1 & op(e2, e0) = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22784) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22785)  all_58_10 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (222), (240),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (246), (17773), (21507), (22648), (22761),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22766), (22785), (function-axioms) are
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22749) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (22750), (22766) are inconsistent by
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2091.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22786)  all_58_15 = e3 & op(e0, e0) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22786) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22787)  all_58_15 = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17773), (22787) are inconsistent by
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #615.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (22757), (22761) are inconsistent by
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1696.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22788)  all_58_10 = e1 & op(e2, e0) = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22788) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22789)  all_58_10 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22790)  op(e2, e0) = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22791)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22791) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22792)  all_58_6 = e1 & op(e1, e3) = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22792) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22793)  all_58_6 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22794)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (239), (22648), (22743),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22793), (22794), (function-axioms) are
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1163.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22795)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22795) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22796)  all_58_6 = e2 & op(e1, e3) = e2
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22796) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22797)  all_58_6 = e2
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22793), (22797) imply:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22798)  e2 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17773), (22798) imply:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22799)  all_58_15 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (221), (222), (22758),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22789), (22799) are inconsistent by sub-proof
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1618.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22800)  all_58_12 = e2 & op(e0, e3) = e2
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22743), (22800) are inconsistent by
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1974.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22801)  all_58_7 = e1 & op(e1, e2) = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22801) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22802)  all_58_7 = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22803)  op(e1, e2) = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22804)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22804) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22805)  all_58_1 = e0 & op(e3, e2) = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22805) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22806)  all_58_1 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (22648),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22758), (22806), (function-axioms) are
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1089.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22807)  all_58_3 = e0 & op(e2, e2) = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22807) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22808)  all_58_3 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21516), (22808) imply:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22809)  e3 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22739), (22809) imply:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22810)  all_58_4 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (22648),
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22758), (22810), (function-axioms) are
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1190.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22811)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22811) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22812)  all_58_7 = e0 & op(e1, e2) = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22812) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22813)  op(e1, e2) = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (22803), (22813), (function-axioms)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22814)  all_58_13 = e0 & op(e0, e2) = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22814) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22815)  all_58_13 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22816)  op(e0, e2) = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22817)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22817) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22818)  all_58_6 = e0 & op(e1, e3) = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22818) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22819)  all_58_6 = e0
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22820)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22820) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22821)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22821) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22822)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22822) implies:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22823)  op(e2, e3) = e3
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22728), (22823), (function-axioms) are
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22824)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21505), (22641), (22824) are inconsistent by
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #746.
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22825)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22825) gives:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22826)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22826) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22827)  op(e3, e1) = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22740), (22827), (function-axioms) are
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1823.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22828)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (21505), (22735), (22828),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #902.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22829)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22829) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22830)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22830) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22831)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22831) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22832)  op(e2, e1) = e2
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (22716), (22832), (function-axioms) are
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22833)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & op(e0, e2) = e2)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22833) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22834)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22834) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22835)  op(e2, e1) = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (165), (225),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (231), (21508), (21516), (22727), (22751),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22789), (22802), (22819), (22835),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #668.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22836)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e2
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22836) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22837)  op(e0, e2) = e2
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22816), (22837), (function-axioms) are
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2132.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22838)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22838) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22839)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22839) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22840)  op(e2, e0) = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (22790), (22840), (function-axioms)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22841)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22841) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22842)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22842) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22843)  op(e1, e0) = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22752), (22843), (function-axioms) are
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22844)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22844) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22845)   ~ (all_56_1 = e1)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22641), (22845) imply:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22846)  $false
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22846) is inconsistent.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22847)  all_58_7 = e0 & op(e1, e2) = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22847) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22848)  op(e1, e2) = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (22803), (22848), (function-axioms)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2136.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22849)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22849) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22850)  all_58_8 = e0 & op(e1, e1) = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22850) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22851)  op(e1, e1) = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22718), (22851), (function-axioms) are
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2211.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22852)  all_58_11 = e0 & op(e1, e0) = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22852) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22853)  all_58_11 = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22751), (22853) imply:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22854)  e3 = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21516), (22854) imply:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22855)  all_58_3 = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (236), (237),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (22645), (22815), (22816), (22855),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1374.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22856)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22856) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22857)  all_58_8 = e1 & op(e1, e1) = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22857) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22858)  op(e1, e1) = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (22718), (22858), (function-axioms) are
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22859)  all_58_11 = e1 & op(e1, e0) = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22859) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22860)  all_58_11 = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22861)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22861) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22862)  all_58_9 = e3 & op(e3, e0) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22862) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22863)  all_58_9 = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (22758), (22863) are inconsistent by
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1958.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22864)  all_58_10 = e3 & op(e2, e0) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (21506), (22648), (22743), (22789),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22864), (function-axioms) are inconsistent by
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1202.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22749) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (21506), (22648), (22743), (22750),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22860), (function-axioms) are inconsistent by
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #663.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22865)  all_58_15 = e3 & op(e0, e0) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17773), (22865) are inconsistent by
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1170.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (22866)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22866) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22867)  all_58_11 = e1 & op(e1, e0) = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22867) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22868)  op(e1, e0) = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22752), (22868), (function-axioms) are
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22869)  all_58_15 = e1 & op(e0, e0) = e1
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (22869) are inconsistent by
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #218.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | |   (22870)  all_58_15 = e3 & op(e0, e0) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22870) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | |   (22871)  op(e0, e0) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (162),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | |            (164), (167), (170), (216), (217), (219), (220),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (226), (229), (231),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (237), (239), (240), (243),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (17775), (21506), (21507),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | |            (21508), (21509), (21516), (22642), (22648),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | |            (22738), (22739), (22743), (22871),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | |            #487.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | |   (22872)  all_58_13 = e3 & op(e0, e2) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (21509), (22872), (function-axioms) are
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1919.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | |   (22873)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17774), (22733), (22873),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.66  | | | | | | | | | | | | | | | | | | |            #226.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | |   (22874)  all_58_9 = e3 & op(e3, e0) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | ALPHA: (22874) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | |   (22875)  op(e3, e0) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (22735), (22875), (function-axioms) are
% 238.76/45.66  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | End of split
% 238.76/45.66  | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | |   (22876)   ~ (all_54_2 = e3)
% 238.76/45.66  | | | | | | | | | | | | | | | |   (22877)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | REDUCE: (281), (22876) imply:
% 238.76/45.66  | | | | | | | | | | | | | | | |   (22878)   ~ (all_52_8 = e3)
% 238.76/45.66  | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | BETA: splitting (22877) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | |   (22879)  all_54_2 = e2
% 238.76/45.66  | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (22715), (22879) are inconsistent by
% 238.76/45.66  | | | | | | | | | | | | | | | | |            sub-proof #1986.
% 238.76/45.66  | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | |   (22880)   ~ (all_54_2 = e2)
% 238.76/45.66  | | | | | | | | | | | | | | | | |   (22881)  all_54_2 = e1 | all_54_2 = e0
% 238.76/45.66  | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | |   (22882)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (21510), (22878), (22882),
% 238.76/45.66  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.66  | | | | | | | | | | | | | | | | | |            #1628.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | |   (22883)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 238.76/45.66  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | BETA: splitting (22883) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | |   (22884)  all_58_8 = e3 & op(e1, e1) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | ALPHA: (22884) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | |   (22885)  op(e1, e1) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22718), (22885), (function-axioms) are
% 238.76/45.66  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | |   (22886)  all_58_14 = e3 & op(e0, e1) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | ALPHA: (22886) implies:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | |   (22887)  all_58_14 = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | |   (22888)  op(e0, e1) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | |   (22889)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (170), (241), (21507),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | |            (22642), (22643), (22644), (22889),
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | |            #269.
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | |   (22890)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | BETA: splitting (22890) gives:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | |   (22891)  all_58_4 = e3 & op(e3, e1) = e3
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.66  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22891) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | |   (22892)  all_58_4 = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (165), (227),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | |            (228), (229), (22650), (22887), (22888), (22892),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | |            #1094.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | |   (22893)  all_58_9 = e3 & op(e3, e0) = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | ALPHA: (22893) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | |   (22894)  all_58_9 = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | |   (22895)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22895) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | |   (22896)  all_58_4 = e1 & op(e3, e1) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22896) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | |   (22897)  all_58_4 = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (240), (244), (22648),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | |            (22894), (22897), (function-axioms) are
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1469.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | |   (22898)  all_58_5 = e1 & op(e2, e1) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22898) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | |   (22899)  all_58_5 = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | |   (22900)  op(e2, e1) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | |   (22901)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22901) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (22902)  all_58_4 = e0 & op(e3, e1) = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22902) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (22903)  all_58_4 = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22881) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22904)  all_54_2 = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (22646), (22904) are inconsistent by
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1337.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22905)  all_54_2 = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (22905) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22906)  all_52_8 = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22906) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22907)  all_52_8 = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (22907) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22908)   ~ (all_52_9 = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22908) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22909)   ~ (all_52_9 = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (22907) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22910)   ~ (all_52_11 = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22910) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22911)   ~ (all_52_11 = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (22907) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22912)   ~ (all_52_12 = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22912) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22913)   ~ (all_52_12 = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22715), (22907) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22914)   ~ (e2 = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22646), (22907) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22915)   ~ (e1 = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (22907) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (22916)  op(e3, e1) = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22917)  all_54_3 = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (22917) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22918)  all_52_12 = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22918) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22919)  all_52_12 = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (22919) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22920)   ~ (all_52_13 = e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (22919) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22921)   ~ (all_52_14 = e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22921) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22922)   ~ (all_52_14 = e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22923)  all_54_6 = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (21510), (22923) are inconsistent by
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22924)   ~ (all_54_6 = e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22925)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22926)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22926) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22927)  all_58_6 = e3 & op(e1, e3) = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22927) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22928)  all_58_6 = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22929)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22929) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22930)  all_58_12 = e1 & op(e0, e3) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22930) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22931)  all_58_12 = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (239), (243), (22648),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22928), (22931), (function-axioms) are
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1206.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22932)  all_58_13 = e1 & op(e0, e2) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22932) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22933)  all_58_13 = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22934)  op(e0, e2) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22925) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22935)  all_54_6 = e2
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (22716), (22935) are inconsistent by
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2247.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22936)   ~ (all_54_6 = e2)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22937)  all_54_6 = e1 | all_54_6 = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22937) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22938)  all_54_6 = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (22938) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22939)  all_52_9 = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22939) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22940)  all_52_9 = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (22940) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22941)   ~ (all_52_11 = e1)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22941) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22942)   ~ (all_52_11 = e1)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22716), (22940) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22943)   ~ (e2 = e1)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22944)  all_54_14 = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (22944) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22945)  all_52_11 = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (22945) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22946)  all_52_11 = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (22946) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22947)   ~ (all_52_3 = e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22948)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22948) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22949)  all_58_1 = e0 & op(e3, e2) = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22949) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22950)  op(e3, e2) = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22724), (22950), (function-axioms) are
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2026.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22951)  all_58_3 = e0 & op(e2, e2) = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22951) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22952)  all_58_3 = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (162),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (226), (234), (239), (241), (243),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (17775), (21508), (21510), (21511),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22648), (22922), (22952), (function-axioms) are
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1008.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22953)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22953) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22954)  all_58_7 = e0 & op(e1, e2) = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22954) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22955)  op(e1, e2) = e0
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22956)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (235), (239),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (245), (21506), (21516), (22648), (22723),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22933), (22956), (function-axioms) are
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #530.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22957)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22957) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22958)  all_58_8 = e1 & op(e1, e1) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22958) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22959)  op(e1, e1) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (22718), (22959), (function-axioms) are
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22960)  all_58_11 = e1 & op(e1, e0) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22960) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22961)  op(e1, e0) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22962)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22962) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22963)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22963) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22964)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22964) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22965)  op(e2, e3) = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (22728), (22965), (function-axioms) are
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1897.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22966)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22966) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22967)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22967) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22968)   ~ (all_56_11 = e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21505), (22968) imply:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22969)  $false
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (22969) is inconsistent.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22970)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22970) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22971)  op(e3, e1) = e3
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (22916), (22971), (function-axioms) are
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2118.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22972)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22972) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22973)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22973) implies:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22974)  op(e3, e1) = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (123), (169), (270), (22909), (22937), (22974),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1945.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22975)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (168), (22913), (22947), (22975),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2257.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22976)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22976) gives:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22977)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (158), (162), (165), (17764), (22716),
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22955), (22977), (function-axioms) are
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #70.
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22978)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22978) gives:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22979)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22979) implies:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22980)  op(e0, e2) = e0
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (22934), (22980), (function-axioms) are
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22981)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (157), (22942), (22961), (22981),
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #140.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22982)  all_58_13 = e0 & op(e0, e2) = e0
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22982) implies:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22983)  op(e0, e2) = e0
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (22934), (22983), (function-axioms) are
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22984)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (17765), (22911), (22942), (22984) are
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1798.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22985)  all_54_6 = e0
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (22909), (22985) are inconsistent by
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2245.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22986)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22986) gives:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22987)  all_58_14 = e1 & op(e0, e1) = e1
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22987) implies:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22988)  all_58_14 = e1
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (229), (230),
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22899), (22903), (22988), (function-axioms) are
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1248.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22989)  all_58_15 = e1 & op(e0, e0) = e1
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (22989) are inconsistent by
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #218.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22990)  all_58_7 = e3 & op(e1, e2) = e3
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22990) implies:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22991)  op(e1, e2) = e3
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (21508), (22991), (function-axioms) are
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22992)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (22718), (22922), (22992),
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2148.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (22993)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (17766), (22647), (22913), (22993) are
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (22994)  all_58_5 = e0 & op(e2, e1) = e0
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22994) implies:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (22995)  op(e2, e1) = e0
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (165), (22900), (22995), (function-axioms)
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2165.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | |   (22996)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (22718), (22888), (22996),
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | |            #2163.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | |   (22997)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22997) gives:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | |   (22998)  all_58_8 = e1 & op(e1, e1) = e1
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (22998) implies:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | |   (22999)  op(e1, e1) = e1
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (22718), (22999), (function-axioms) are
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2159.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | |   (23000)  all_58_14 = e1 & op(e0, e1) = e1
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23000) implies:
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | |   (23001)  all_58_14 = e1
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22887), (23001) are inconsistent by
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1844.
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | |   (23002)  all_58_3 = e2 & op(e2, e2) = e2
% 238.76/45.68  | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | ALPHA: (23002) implies:
% 238.76/45.68  | | | | | | | | | | | | | | |   (23003)  op(e2, e2) = e2
% 238.76/45.68  | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (235),
% 238.76/45.68  | | | | | | | | | | | | | | |            (236), (238), (21509), (22723), (22724), (23003),
% 238.76/45.68  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.68  | | | | | | | | | | | | | | |            #1809.
% 238.76/45.68  | | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | |   (23004)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.76/45.68  | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.76/45.68  | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (17767), (22716), (23004),
% 238.76/45.68  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.68  | | | | | | | | | | | | | |            #182.
% 238.76/45.68  | | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | |   (23005)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 238.76/45.68  | | | | | | | | | | | |              & op(e3, e0) = e2)
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | BETA: splitting (23005) gives:
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | Case 1:
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | |   (23006)  all_58_4 = e2 & op(e3, e1) = e2
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | ALPHA: (23006) implies:
% 238.76/45.68  | | | | | | | | | | | | |   (23007)  all_58_4 = e2
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (227), (228),
% 238.76/45.68  | | | | | | | | | | | | |            (230), (22718), (23007), (function-axioms) are
% 238.76/45.68  | | | | | | | | | | | | |            inconsistent by sub-proof #1899.
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | |   (23008)  all_58_9 = e2 & op(e3, e0) = e2
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | REF_CLOSE: (168), (17766), (23008), (function-axioms) are
% 238.76/45.68  | | | | | | | | | | | | |            inconsistent by sub-proof #2318.
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | |   (23009)  all_18_2 = e0
% 238.76/45.68  | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | COMBINE_EQS: (339), (23009) imply:
% 238.76/45.68  | | | | | | | | | |   (23010)  all_6_2 = e0
% 238.76/45.68  | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | SIMP: (23010) implies:
% 238.76/45.68  | | | | | | | | | |   (23011)  all_6_2 = e0
% 238.76/45.68  | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | COMBINE_EQS: (266), (23011) imply:
% 238.76/45.68  | | | | | | | | | |   (23012)  all_56_21 = e0
% 238.76/45.68  | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | REDUCE: (385), (23011) imply:
% 238.76/45.68  | | | | | | | | | |   (23013)   ~ (all_52_14 = e0)
% 238.76/45.68  | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | BETA: splitting (213) gives:
% 238.76/45.68  | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | Case 1:
% 238.76/45.68  | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | |   (23014)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.68  | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.68  | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.68  | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.68  | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.68  | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.68  | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.68  | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.68  | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.68  | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.76/45.68  | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.76/45.68  | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.76/45.68  | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.76/45.68  | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | BETA: splitting (23014) gives:
% 238.76/45.68  | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | Case 1:
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | |   (23015)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.76/45.68  | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.68  | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.76/45.68  | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.76/45.68  | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.68  | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.68  | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.76/45.68  | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.68  | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.68  | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.76/45.68  | | | | | | | | | | | |              = e3)
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | REF_CLOSE: (167), (21505), (21506), (22641), (23015),
% 238.76/45.68  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.68  | | | | | | | | | | | |            #745.
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | |   (23016)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.76/45.68  | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.76/45.68  | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.76/45.68  | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.76/45.68  | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.68  | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.68  | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.76/45.68  | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.76/45.68  | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.76/45.68  | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.76/45.68  | | | | | | | | | | | |              = e0)
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | BETA: splitting (23016) gives:
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | Case 1:
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | |   (23017)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.76/45.68  | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.76/45.68  | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.76/45.68  | | | | | | | | | | | | |              e3) = e1
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | ALPHA: (23017) implies:
% 238.76/45.68  | | | | | | | | | | | | |   (23018)  op(e3, e1) = e1
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | REF_CLOSE: (169), (22646), (23018), (function-axioms) are
% 238.76/45.68  | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | |   (23019)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.76/45.68  | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.76/45.68  | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.76/45.68  | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.76/45.68  | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.76/45.68  | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.76/45.68  | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | | REF_CLOSE: (21505), (23012), (23019) are inconsistent by
% 238.76/45.68  | | | | | | | | | | | | |            sub-proof #864.
% 238.76/45.68  | | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | |   (23020)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.68  | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.68  | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.68  | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.68  | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.68  | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.68  | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.68  | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.68  | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.76/45.68  | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.76/45.68  | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.76/45.68  | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.76/45.68  | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.76/45.68  | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.76/45.68  | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | BETA: splitting (23020) gives:
% 238.76/45.68  | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | Case 1:
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | |   (23021)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.76/45.68  | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.76/45.68  | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.76/45.68  | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.76/45.68  | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.76/45.68  | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.76/45.68  | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.76/45.68  | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.76/45.68  | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.76/45.68  | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.76/45.68  | | | | | | | | | | | |              = e2)
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | REF_CLOSE: (158), (17762), (17764), (22641), (23021),
% 238.76/45.68  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.68  | | | | | | | | | | | |            #67.
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | Case 2:
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | |   (23022)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.76/45.68  | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.76/45.68  | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.76/45.68  | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.76/45.68  | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.76/45.68  | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.76/45.68  | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.76/45.68  | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.76/45.68  | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.76/45.68  | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.76/45.68  | | | | | | | | | | | |              = e0)
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | | REF_CLOSE: (160), (17762), (23012), (23013), (23022),
% 238.76/45.68  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.68  | | | | | | | | | | | |            #179.
% 238.76/45.68  | | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | | 
% 238.76/45.68  | | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | | 
% 238.76/45.68  | | | | | | | | End of split
% 238.76/45.68  | | | | | | | | 
% 238.76/45.68  | | | | | | | End of split
% 238.76/45.68  | | | | | | | 
% 238.76/45.68  | | | | | | Case 2:
% 238.76/45.68  | | | | | | | 
% 238.76/45.68  | | | | | | |   (23023)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 &
% 238.76/45.68  | | | | | | |              op(e2, e0) = e3)
% 238.76/45.68  | | | | | | | 
% 238.76/45.68  | | | | | | | REF_CLOSE: (164), (165), (21510), (21511), (23023),
% 238.76/45.68  | | | | | | |            (function-axioms) are inconsistent by sub-proof #1649.
% 238.76/45.68  | | | | | | | 
% 238.76/45.68  | | | | | | End of split
% 238.76/45.68  | | | | | | 
% 238.76/45.68  | | | | | End of split
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | Case 2:
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | |   (23024)  all_6_2 = e3
% 238.76/45.68  | | | | |   (23025)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3)
% 238.76/45.68  | | | | |              = all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 =
% 238.76/45.68  | | | | |                e0) & op(e1, e3) = all_6_1 & $i(all_6_1))
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | | COMBINE_EQS: (305), (23024) imply:
% 238.76/45.68  | | | | |   (23026)  all_46_2 = e3
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | | COMBINE_EQS: (266), (23024) imply:
% 238.76/45.68  | | | | |   (23027)  all_56_21 = e3
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | | REDUCE: (367), (23024) imply:
% 238.76/45.68  | | | | |   (23028)   ~ (all_52_2 = e3)
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | | REDUCE: (378), (23024) imply:
% 238.76/45.68  | | | | |   (23029)   ~ (all_52_6 = e3)
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | | REDUCE: (380), (23024) imply:
% 238.76/45.68  | | | | |   (23030)   ~ (all_52_8 = e3)
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | | REDUCE: (381), (23024) imply:
% 238.76/45.68  | | | | |   (23031)   ~ (all_52_9 = e3)
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | | REDUCE: (383), (23024) imply:
% 238.76/45.68  | | | | |   (23032)   ~ (all_52_11 = e3)
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | | REDUCE: (385), (23024) imply:
% 238.76/45.68  | | | | |   (23033)   ~ (all_52_14 = e3)
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | | BETA: splitting (226) gives:
% 238.76/45.68  | | | | | 
% 238.76/45.68  | | | | | Case 1:
% 238.76/45.68  | | | | | | 
% 238.76/45.68  | | | | | |   (23034)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 &
% 238.76/45.68  | | | | | |              op(e1, e2) = e3)
% 238.76/45.68  | | | | | | 
% 238.76/45.68  | | | | | | REF_CLOSE: (162), (163), (23028), (23029), (23034),
% 238.76/45.68  | | | | | |            (function-axioms) are inconsistent by sub-proof #213.
% 238.76/45.68  | | | | | | 
% 238.76/45.69  | | | | | Case 2:
% 238.76/45.69  | | | | | | 
% 238.76/45.69  | | | | | |   (23035)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 &
% 238.76/45.69  | | | | | |              op(e1, e0) = e3)
% 238.76/45.69  | | | | | | 
% 238.76/45.69  | | | | | | BETA: splitting (23035) gives:
% 238.76/45.69  | | | | | | 
% 238.76/45.69  | | | | | | Case 1:
% 238.76/45.69  | | | | | | | 
% 238.76/45.69  | | | | | | |   (23036)  all_58_8 = e3 & op(e1, e1) = e3
% 238.76/45.69  | | | | | | | 
% 238.76/45.69  | | | | | | | ALPHA: (23036) implies:
% 238.76/45.69  | | | | | | |   (23037)  all_58_8 = e3
% 238.76/45.69  | | | | | | |   (23038)  op(e1, e1) = e3
% 238.76/45.69  | | | | | | | 
% 238.76/45.69  | | | | | | | BETA: splitting (43) gives:
% 238.76/45.69  | | | | | | | 
% 238.76/45.69  | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | 
% 238.76/45.69  | | | | | | | |   (23039)   ~ (all_8_2 = e3)
% 238.76/45.69  | | | | | | | | 
% 238.76/45.69  | | | | | | | | BETA: splitting (46) gives:
% 238.76/45.69  | | | | | | | | 
% 238.76/45.69  | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | 
% 238.76/45.69  | | | | | | | | |   (23040)   ~ (all_10_2 = e1)
% 238.76/45.69  | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | BETA: splitting (52) gives:
% 238.76/45.69  | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | |   (23041)   ~ (all_14_2 = e0)
% 238.76/45.69  | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | REDUCE: (344), (23041) imply:
% 238.76/45.69  | | | | | | | | | |   (23042)   ~ (all_8_2 = e0)
% 238.76/45.69  | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | BETA: splitting (55) gives:
% 238.76/45.69  | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | |   (23043)   ~ (all_16_2 = e0)
% 238.76/45.69  | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | REDUCE: (342), (23043) imply:
% 238.76/45.69  | | | | | | | | | | |   (23044)   ~ (all_10_2 = e0)
% 238.76/45.69  | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | BETA: splitting (64) gives:
% 238.76/45.69  | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | |   (23045)   ~ (all_22_2 = e1)
% 238.76/45.69  | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | REDUCE: (326), (23045) imply:
% 238.76/45.69  | | | | | | | | | | | |   (23046)   ~ (all_8_2 = e1)
% 238.76/45.69  | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | BETA: splitting (199) gives:
% 238.76/45.69  | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | |   (23047)  all_54_5 = e3
% 238.76/45.69  | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | COMBINE_EQS: (275), (23047) imply:
% 238.76/45.69  | | | | | | | | | | | | |   (23048)  all_8_2 = e3
% 238.76/45.69  | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | REDUCE: (23039), (23048) imply:
% 238.76/45.69  | | | | | | | | | | | | |   (23049)  $false
% 238.76/45.69  | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | CLOSE: (23049) is inconsistent.
% 238.76/45.69  | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | Case 2:
% 238.76/45.69  | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | |   (23050)   ~ (all_54_5 = e3)
% 238.76/45.69  | | | | | | | | | | | | |   (23051)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 238.76/45.69  | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | BETA: splitting (23051) gives:
% 238.76/45.69  | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | |   (23052)  all_54_5 = e2
% 238.76/45.69  | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | COMBINE_EQS: (275), (23052) imply:
% 238.76/45.69  | | | | | | | | | | | | | |   (23053)  all_8_2 = e2
% 238.76/45.69  | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | REDUCE: (371), (23053) imply:
% 238.76/45.69  | | | | | | | | | | | | | |   (23054)   ~ (all_52_6 = e2)
% 238.76/45.69  | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | REDUCE: (375), (23053) imply:
% 238.76/45.69  | | | | | | | | | | | | | |   (23055)   ~ (all_52_9 = e2)
% 238.76/45.69  | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | REDUCE: (23039), (23053) imply:
% 238.76/45.69  | | | | | | | | | | | | | |   (23056)   ~ (e3 = e2)
% 238.76/45.69  | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | REDUCE: (42), (23053) imply:
% 238.76/45.69  | | | | | | | | | | | | | |   (23057)  op(e2, e2) = e2
% 238.76/45.69  | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 238.76/45.69  | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | |   (23058)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 238.76/45.69  | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 238.76/45.69  | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | BETA: splitting (23058) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | |   (23059)  all_58_4 = e2 & op(e3, e1) = e2
% 238.76/45.69  | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | ALPHA: (23059) implies:
% 238.76/45.69  | | | | | | | | | | | | | | | |   (23060)  all_58_4 = e2
% 238.76/45.69  | | | | | | | | | | | | | | | |   (23061)  op(e3, e1) = e2
% 238.76/45.69  | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | |   (23062)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 238.76/45.69  | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 238.76/45.69  | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | BETA: splitting (23062) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23063)  all_58_6 = e2 & op(e1, e3) = e2
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | ALPHA: (23063) implies:
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23064)  all_58_6 = e2
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23065)  op(e1, e3) = e2
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 238.76/45.69  | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (23065) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23066)  all_52_2 = e2
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 238.76/45.69  | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (23061) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23067)  all_52_8 = e2
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | REDUCE: (149), (23066) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23068)   ~ (all_52_1 = e2)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | REDUCE: (134), (23067) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23069)   ~ (all_52_4 = e2)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | REDUCE: (123), (23067) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23070)   ~ (all_52_9 = e2)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | REDUCE: (121), (23067) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23071)   ~ (all_52_11 = e2)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | REDUCE: (120), (23067) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23072)   ~ (all_52_12 = e2)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | REDUCE: (363), (23067) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23073)   ~ (all_10_2 = e2)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | SIMP: (23073) implies:
% 238.76/45.69  | | | | | | | | | | | | | | | | | |   (23074)   ~ (all_10_2 = e2)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | BETA: splitting (23025) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | |   (23075)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 &
% 238.76/45.69  | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | ALPHA: (23075) implies:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | |   (23076)  op(e1, e3) = all_6_1
% 238.76/45.69  | | | | | | | | | | | | | | | | | | |   (23077)  op(all_6_1, e1) = all_6_0
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | |   (23078)  all_54_0 = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (23078) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | |   (23079)  all_10_2 = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | SIMP: (23079) implies:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | |   (23080)  all_10_2 = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | REDUCE: (355), (23080) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | |   (23081)   ~ (all_52_1 = e3)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (23080) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | |   (23082)   ~ (all_52_3 = e3)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | |   (23083)   ~ (all_46_2 = e3)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | REDUCE: (23026), (23083) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | |   (23084)  $false
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | CLOSE: (23084) is inconsistent.
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | |   (23085)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | |   (23086)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23086) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | |   (23087)  all_58_12 = e3 & op(e0, e3) = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23087) implies:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | |   (23088)  op(e0, e3) = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (23082), (23088), (function-axioms) are
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | |   (23089)  all_58_13 = e3 & op(e0, e2) = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23089) implies:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | |   (23090)  all_58_13 = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | |   (23091)  op(e0, e2) = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | |   (23092)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (23057), (23081), (23092),
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | |            #1413.
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | |   (23093)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23093) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (23094)  all_58_5 = e3 & op(e2, e1) = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (23031), (23094), (function-axioms) are
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (23095)  all_58_10 = e3 & op(e2, e0) = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23095) implies:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (23096)  all_58_10 = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (23097)  op(e2, e0) = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (23091) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (23098)  all_52_7 = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_6_1,
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (23065), (23076) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (23099)  all_6_1 = e2
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (164), (23097) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (23100)  all_52_13 = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (23098) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (23101)   ~ (all_52_11 = e3)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (23100) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (23102)   ~ (all_52_12 = e3)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23077), (23099) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (23103)  op(e2, e1) = all_6_0
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23104)   ~ (all_44_2 = e2)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17761), (23104) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23105)  $false
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (23105) is inconsistent.
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23106)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23107)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23107) implies:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23108)   ~ (all_4_0 = e1)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23109)  op(e0, e2) = all_4_1
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23110)  op(all_4_1, e0) = all_4_0
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23085) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23111)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_46_1 & $i(all_46_0) &
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23111) implies:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23112)   ~ (all_46_0 = e0)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23113)  op(e1, e3) = all_46_1
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23114)  op(all_46_1, e1) = all_46_0
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_1,
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (23091), (23109) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23115)  all_4_1 = e3
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_46_1,
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (23065), (23113) gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23116)  all_46_1 = e2
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_6_0, e1, e2, simplifying with (165), (23103)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23117)  all_52_9 = all_6_0
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (23117) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23118)  all_54_6 = all_6_0
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (23117) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23119)   ~ (all_52_1 = all_6_0)
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (23117) imply:
% 238.76/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23120)   ~ (all_52_11 = all_6_0)
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23120) implies:
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23121)   ~ (all_52_11 = all_6_0)
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23031), (23117) imply:
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23122)   ~ (all_6_0 = e3)
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23055), (23117) imply:
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23123)   ~ (all_6_0 = e2)
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23114), (23116) imply:
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23124)  op(e2, e1) = all_46_0
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23110), (23115) imply:
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23125)  op(e3, e0) = all_4_0
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23106) gives:
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23126)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23126) implies:
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23127)  op(e0, e2) = all_44_1
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (148), (157), (159),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (165), (167), (168), (170), (198),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (200), (201), (213), (217), (219), (220), (223),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (279), (280), (17766), (17773), (17774),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23028), (23031), (23032), (23055), (23060),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23064), (23065), (23068), (23069), (23081),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23082), (23090), (23091), (23096), (23102),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23103), (23108), (23112), (23118), (23119),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23121), (23122), (23123), (23124), (23125),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23127), (function-axioms) are inconsistent by
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #62.
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23128)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 &
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23128) implies:
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23129)  op(e0, e2) = all_44_1
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (148), (157), (159),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (165), (167), (168), (170), (198),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (200), (201), (213), (217), (219), (220), (223),
% 238.85/45.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (279), (280), (17766), (17773), (17774),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23028), (23031), (23032), (23055), (23060),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23064), (23065), (23068), (23069), (23081),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23082), (23090), (23091), (23096), (23102),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23103), (23108), (23112), (23118), (23119),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23121), (23122), (23123), (23124), (23125),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23129), (function-axioms) are inconsistent by
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #62.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23130)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 &
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23065), (23130), (function-axioms) are
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #395.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23131)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23131) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23132)   ~ (all_4_1 = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23133)  op(e0, e2) = all_4_1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23091), (23106), (23132), (23133),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #211.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | |   (23134)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17774), (23032), (23134),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | |            #226.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | |   (23135)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (23040), (23044), (23074), (23135) are
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | |   (23136)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 &
% 238.85/45.70  | | | | | | | | | | | | | | | | | | |            $i(all_6_1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | ALPHA: (23136) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | |   (23137)   ~ (all_6_1 = e0)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | |   (23138)  op(e1, e3) = all_6_1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | |   (23139)  all_54_0 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (23139) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | |   (23140)  all_10_2 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | SIMP: (23140) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | |   (23141)  all_10_2 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | REDUCE: (355), (23141) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | |   (23142)   ~ (all_52_1 = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (23141) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | |   (23143)   ~ (all_52_3 = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | |   (23144)   ~ (all_46_2 = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | REDUCE: (23026), (23144) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | |   (23145)  $false
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | CLOSE: (23145) is inconsistent.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | |   (23146)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | |   (23147)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23147) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | |   (23148)  all_58_12 = e3 & op(e0, e3) = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23148) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | |   (23149)  op(e0, e3) = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (23143), (23149), (function-axioms) are
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | |   (23150)  all_58_13 = e3 & op(e0, e2) = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23150) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | |   (23151)  all_58_13 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | |   (23152)  op(e0, e2) = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | |   (23153)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (23057), (23142), (23153),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | |            #1413.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | |   (23154)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23154) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (23155)  all_58_5 = e3 & op(e2, e1) = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (23031), (23155), (function-axioms) are
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (23156)  all_58_10 = e3 & op(e2, e0) = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23156) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (23157)  all_58_10 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (23158)  op(e2, e0) = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (23152) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (23159)  all_52_7 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_6_1,
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (23065), (23138) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (23160)  all_6_1 = e2
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (164), (23158) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (23161)  all_52_13 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (23159) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (23162)   ~ (all_52_11 = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (23161) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (23163)   ~ (all_52_12 = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23164)   ~ (all_44_2 = e2)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17761), (23164) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23165)  $false
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (23165) is inconsistent.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23166)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23167)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23167) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23168)   ~ (all_4_0 = e1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23169)  op(e0, e2) = all_4_1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23170)  op(all_4_1, e0) = all_4_0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23146) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23171)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_46_1 & $i(all_46_0) &
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23171) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23172)   ~ (all_46_0 = e0)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23173)  op(e1, e3) = all_46_1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23174)  op(all_46_1, e1) = all_46_0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_1,
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (23152), (23169) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23175)  all_4_1 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_46_1,
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (23065), (23173) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23176)  all_46_1 = e2
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23174), (23176) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23177)  op(e2, e1) = all_46_0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23170), (23175) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23178)  op(e3, e0) = all_4_0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23166) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23179)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23179) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23180)  op(e0, e2) = all_44_1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1,
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (23152), (23180) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23181)  all_44_1 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_46_0, e1, e2, simplifying with (165), (23177)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23182)  all_52_9 = all_46_0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_4_0, e0, e3, simplifying with (168), (23178)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23183)  all_52_12 = all_4_0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (23182) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23184)  all_54_6 = all_46_0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (23183) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23185)  all_54_3 = all_4_0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (23182) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23186)   ~ (all_52_11 = all_46_0)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23186) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23187)   ~ (all_52_11 = all_46_0)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23031), (23182) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23188)   ~ (all_46_0 = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23055), (23182) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23189)   ~ (all_46_0 = e2)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23163), (23183) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23190)   ~ (all_4_0 = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17766), (23183) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23191)   ~ (all_4_0 = e2)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23192)  all_54_6 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23184), (23192) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23193)  all_46_0 = e3
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23188), (23193) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23194)  $false
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (23194) is inconsistent.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23195)   ~ (all_54_6 = e3)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23196)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23196) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23197)  all_54_6 = e2
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23184), (23197) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23198)  all_46_0 = e2
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23189), (23198) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23199)  $false
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (23199) is inconsistent.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23200)   ~ (all_54_6 = e2)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23201)  all_54_6 = e1 | all_54_6 = e0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23202)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23202) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23203)  all_58_9 = e1 & op(e3, e0) = e1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23203) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23204)  op(e3, e0) = e1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (201), (23168), (23178), (23185), (23190),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23191), (23204), (function-axioms) are
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #61.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23205)  all_58_10 = e1 & op(e2, e0) = e1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23157), (23205) are inconsistent by
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1100.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23206)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23206) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23207)  all_58_11 = e1 & op(e1, e0) = e1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23207) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23208)  op(e1, e0) = e1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23209)  all_58_15 = e0 & op(e0, e0) = e0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23209) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23210)  op(e0, e0) = e0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (23210), (function-axioms) are
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23211)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23211) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23212)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23213)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23213) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23214)  all_58_9 = e0 & op(e3, e0) = e0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23214) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23215)  op(e3, e0) = e0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23201) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23216)  all_54_6 = e1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23184), (23216) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23217)  all_46_0 = e1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23187), (23217) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23218)   ~ (all_52_11 = e1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23188), (23217) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23219)   ~ (e3 = e1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23189), (23217) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23220)   ~ (e2 = e1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23221)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23221) gives:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23222)  all_58_12 = e1 & op(e0, e3) = e1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23222) implies:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23223)  all_58_12 = e1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (139), (157), (159), (162), (163),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (190), (213), (219), (223), (229),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (239), (242), (243), (245), (255), (17765),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (23028), (23031), (23032), (23038),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23055), (23060), (23065), (23137), (23138),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23142), (23143), (23152), (23173), (23208),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23212), (23215), (23218), (23223),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #60.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23224)  all_58_13 = e1 & op(e0, e2) = e1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23151), (23224) are inconsistent by
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2013.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23225)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (17773), (23218), (23225),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #163.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23226)  all_54_6 = e0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23184), (23226) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23227)  all_46_0 = e0
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23172), (23227) imply:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23228)  $false
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (23228) is inconsistent.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23229)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (23157), (23208), (23229),
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #59.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23230)  all_58_15 = e1 & op(e0, e0) = e1
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (23230) are inconsistent by
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #218.
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23231)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 &
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23231) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23232)   ~ (all_44_1 = e1)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23233)  op(e0, e2) = all_44_1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1,
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (23152), (23233) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23234)  all_44_1 = e3
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_46_0, e1, e2, simplifying with (165), (23177)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23235)  all_52_9 = all_46_0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_4_0, e0, e3, simplifying with (168), (23178)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23236)  all_52_12 = all_4_0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (23235) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23237)  all_54_6 = all_46_0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (23236) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23238)  all_54_3 = all_4_0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (23235) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23239)   ~ (all_52_11 = all_46_0)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23239) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23240)   ~ (all_52_11 = all_46_0)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23031), (23235) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23241)   ~ (all_46_0 = e3)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23055), (23235) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23242)   ~ (all_46_0 = e2)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23163), (23236) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23243)   ~ (all_4_0 = e3)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17766), (23236) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23244)   ~ (all_4_0 = e2)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23245)  all_54_6 = e3
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23237), (23245) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23246)  all_46_0 = e3
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23241), (23246) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23247)  $false
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (23247) is inconsistent.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23248)   ~ (all_54_6 = e3)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23249)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23249) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23250)  all_54_6 = e2
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23237), (23250) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23251)  all_46_0 = e2
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23242), (23251) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23252)  $false
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (23252) is inconsistent.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23253)   ~ (all_54_6 = e2)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23254)  all_54_6 = e1 | all_54_6 = e0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23255)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23255) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23256)  all_58_9 = e1 & op(e3, e0) = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23256) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23257)  op(e3, e0) = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (201), (23168), (23178), (23238), (23243),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23244), (23257), (function-axioms) are
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #61.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23258)  all_58_10 = e1 & op(e2, e0) = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23157), (23258) are inconsistent by
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1100.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23259)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23259) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23260)  all_58_11 = e1 & op(e1, e0) = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23260) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23261)  op(e1, e0) = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23262)  all_58_15 = e0 & op(e0, e0) = e0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23262) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23263)  op(e0, e0) = e0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (23263), (function-axioms) are
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23264)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23264) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23265)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23266)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23266) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23267)  all_58_9 = e0 & op(e3, e0) = e0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23267) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23268)  op(e3, e0) = e0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23254) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23269)  all_54_6 = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23237), (23269) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23270)  all_46_0 = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23240), (23270) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23271)   ~ (all_52_11 = e1)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23241), (23270) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23272)   ~ (e3 = e1)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23242), (23270) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23273)   ~ (e2 = e1)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23274)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23274) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23275)  all_58_12 = e1 & op(e0, e3) = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23275) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23276)  all_58_12 = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (139), (157), (159), (162), (163),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (190), (213), (219), (223), (229),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (239), (242), (243), (245), (255), (17765),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (23028), (23031), (23032), (23038),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23055), (23060), (23065), (23137), (23138),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23142), (23143), (23152), (23173), (23261),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23265), (23268), (23271), (23276),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #60.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23277)  all_58_13 = e1 & op(e0, e2) = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23277) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23278)  op(e0, e2) = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23232), (23233), (23278), (function-axioms) are
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #230.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23279)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (17773), (23271), (23279),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #163.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23280)  all_54_6 = e0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23237), (23280) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23281)  all_46_0 = e0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23172), (23281) imply:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23282)  $false
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (23282) is inconsistent.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23283)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (23157), (23261), (23283),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #59.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23284)  all_58_15 = e1 & op(e0, e0) = e1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (23284) are inconsistent by
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #218.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23285)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 &
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23065), (23285), (function-axioms) are
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #395.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23286)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23286) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23287)   ~ (all_4_1 = e3)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23288)  op(e0, e2) = all_4_1
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23152), (23166), (23287), (23288),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #211.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | |   (23289)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17774), (23032), (23289),
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | |            #226.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | |   (23290)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (23040), (23044), (23074), (23290) are
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | |   (23291)  all_58_7 = e2 & op(e1, e2) = e2
% 238.85/45.71  | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | ALPHA: (23291) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | | |   (23292)  op(e1, e2) = e2
% 238.85/45.71  | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (23054), (23292), (function-axioms) are
% 238.85/45.71  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #249.
% 238.85/45.71  | | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | |   (23293)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 238.85/45.71  | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 238.85/45.71  | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (160), (165),
% 238.85/45.71  | | | | | | | | | | | | | | | | |            (227), (228), (230), (17768), (23032), (23060),
% 238.85/45.71  | | | | | | | | | | | | | | | | |            (23293), (function-axioms) are inconsistent by
% 238.85/45.71  | | | | | | | | | | | | | | | | |            sub-proof #58.
% 238.85/45.71  | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | |   (23294)  all_58_5 = e2 & op(e2, e1) = e2
% 238.85/45.71  | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | ALPHA: (23294) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | |   (23295)  op(e2, e1) = e2
% 238.85/45.71  | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (23055), (23295), (function-axioms) are
% 238.85/45.71  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 238.85/45.71  | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | |   (23296)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 238.85/45.71  | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 238.85/45.71  | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17765), (23038), (23296),
% 238.85/45.71  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.71  | | | | | | | | | | | | | | |            #57.
% 238.85/45.71  | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | |   (23297)  all_54_5 = e1 | all_54_5 = e0
% 238.85/45.71  | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | REF_CLOSE: (275), (23042), (23046), (23297) are inconsistent
% 238.85/45.71  | | | | | | | | | | | | | |            by sub-proof #2300.
% 238.85/45.71  | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | End of split
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | |   (23298)  all_22_2 = e1
% 238.85/45.71  | | | | | | | | | | | |   (23299)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0
% 238.85/45.71  | | | | | | | | | | | |              & op(e2, e1) = all_22_1 & $i(all_22_0) &
% 238.85/45.71  | | | | | | | | | | | |              $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1)
% 238.85/45.71  | | | | | | | | | | | |              = all_22_1 & $i(all_22_1))
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | COMBINE_EQS: (326), (23298) imply:
% 238.85/45.71  | | | | | | | | | | | |   (23300)  all_8_2 = e1
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | SIMP: (23300) implies:
% 238.85/45.71  | | | | | | | | | | | |   (23301)  all_8_2 = e1
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | COMBINE_EQS: (347), (23301) imply:
% 238.85/45.71  | | | | | | | | | | | |   (23302)  all_30_2 = e1
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | COMBINE_EQS: (353), (23301) imply:
% 238.85/45.71  | | | | | | | | | | | |   (23303)  all_56_11 = e1
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | REDUCE: (366), (23301) imply:
% 238.85/45.71  | | | | | | | | | | | |   (23304)   ~ (all_52_1 = e1)
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | REDUCE: (369), (23301) imply:
% 238.85/45.71  | | | | | | | | | | | |   (23305)   ~ (all_52_4 = e1)
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | REDUCE: (373), (23301) imply:
% 238.85/45.71  | | | | | | | | | | | |   (23306)   ~ (all_52_7 = e1)
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | REDUCE: (375), (23301) imply:
% 238.85/45.71  | | | | | | | | | | | |   (23307)   ~ (all_52_9 = e1)
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | REDUCE: (377), (23301) imply:
% 238.85/45.71  | | | | | | | | | | | |   (23308)   ~ (all_52_13 = e1)
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | REDUCE: (23039), (23301) imply:
% 238.85/45.71  | | | | | | | | | | | |   (23309)   ~ (e3 = e1)
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | REDUCE: (42), (23301) imply:
% 238.85/45.71  | | | | | | | | | | | |   (23310)  op(e2, e2) = e1
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | BETA: splitting (67) gives:
% 238.85/45.71  | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | |   (23311)   ~ (all_24_2 = e2)
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | REDUCE: (301), (23311) imply:
% 238.85/45.71  | | | | | | | | | | | | |   (23312)   ~ (all_10_2 = e2)
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | REF_CLOSE: (45), (139), (141), (157), (158), (159), (160),
% 238.85/45.71  | | | | | | | | | | | | |            (163), (165), (167), (204), (213), (241), (290),
% 238.85/45.71  | | | | | | | | | | | | |            (292), (355), (357), (359), (17762), (17764),
% 238.85/45.71  | | | | | | | | | | | | |            (23040), (23044), (23303), (23304), (23307),
% 238.85/45.71  | | | | | | | | | | | | |            (23312), (function-axioms) are inconsistent by
% 238.85/45.71  | | | | | | | | | | | | |            sub-proof #180.
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | |   (23313)  all_24_2 = e2
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | COMBINE_EQS: (301), (23313) imply:
% 238.85/45.71  | | | | | | | | | | | | |   (23314)  all_10_2 = e2
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | REDUCE: (355), (23314) imply:
% 238.85/45.71  | | | | | | | | | | | | |   (23315)   ~ (all_52_1 = e2)
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | REDUCE: (361), (23314) imply:
% 238.85/45.71  | | | | | | | | | | | | |   (23316)   ~ (all_52_4 = e2)
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | REDUCE: (45), (23314) imply:
% 238.85/45.71  | | | | | | | | | | | | |   (23317)  op(e3, e3) = e2
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.85/45.71  | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | |   (23318)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.85/45.71  | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.85/45.71  | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (23310), (23316), (23318),
% 238.85/45.71  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.71  | | | | | | | | | | | | | |            #246.
% 238.85/45.71  | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | Case 2:
% 238.85/45.71  | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | |   (23319)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.85/45.71  | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.85/45.71  | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | BETA: splitting (23319) gives:
% 238.85/45.71  | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | |   (23320)  all_58_7 = e2 & op(e1, e2) = e2
% 238.85/45.71  | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | ALPHA: (23320) implies:
% 238.85/45.71  | | | | | | | | | | | | | | |   (23321)  all_58_7 = e2
% 238.85/45.71  | | | | | | | | | | | | | | |   (23322)  op(e1, e2) = e2
% 238.85/45.71  | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | |   (23323)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 238.85/45.71  | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 238.85/45.71  | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | BETA: splitting (23323) gives:
% 238.85/45.71  | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.71  | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | |   (23324)  all_58_4 = e2 & op(e3, e1) = e2
% 238.85/45.71  | | | | | | | | | | | | | | | | | 
% 238.85/45.71  | | | | | | | | | | | | | | | | | ALPHA: (23324) implies:
% 238.85/45.71  | | | | | | | | | | | | | | | | |   (23325)  all_58_4 = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | |   (23326)  op(e3, e1) = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | |   (23327)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (23310), (23315), (23327),
% 238.85/45.72  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.72  | | | | | | | | | | | | | | | | | |            #1929.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | |   (23328)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.85/45.72  | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | BETA: splitting (23328) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23329)  all_58_5 = e2 & op(e2, e1) = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | ALPHA: (23329) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23330)  op(e2, e1) = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23331)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (165), (23307), (23325), (23331),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            #407.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23332)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | BETA: splitting (23332) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | |   (23333)  all_58_8 = e1 & op(e1, e1) = e1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | ALPHA: (23333) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | |   (23334)  op(e1, e1) = e1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23038), (23334), (function-axioms) are
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #468.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | |   (23335)  all_58_14 = e1 & op(e0, e1) = e1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | ALPHA: (23335) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | |   (23336)  all_58_14 = e1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | |   (23337)  op(e0, e1) = e1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |   (23338)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (23325), (23330), (23338), (function-axioms)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #56.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |   (23339)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23339) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |   (23340)  all_58_8 = e0 & op(e1, e1) = e0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23340) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |   (23341)  op(e1, e1) = e0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (164), (167), (230), (233),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |            (17767), (23310), (23315), (23326), (23336),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |            (23341), (function-axioms) are inconsistent by
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #176.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |   (23342)  all_58_14 = e0 & op(e0, e1) = e0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23342) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |   (23343)  op(e0, e1) = e0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23337), (23343), (function-axioms) are
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2158.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23344)  all_58_10 = e2 & op(e2, e0) = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | ALPHA: (23344) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23345)  op(e2, e0) = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (23345), (function-axioms) are
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | End of split
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | |   (23346)  all_58_5 = e2 & op(e2, e1) = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | ALPHA: (23346) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | |   (23347)  op(e2, e1) = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 238.85/45.72  | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (23322) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | |   (23348)  all_52_6 = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 238.85/45.72  | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (23347) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | |   (23349)  all_52_9 = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | REDUCE: (128), (23348) imply:
% 238.85/45.72  | | | | | | | | | | | | | | | | |   (23350)   ~ (all_52_7 = e2)
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | REDUCE: (123), (23349) imply:
% 238.85/45.72  | | | | | | | | | | | | | | | | |   (23351)   ~ (all_52_8 = e2)
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | REDUCE: (118), (23349) imply:
% 238.85/45.72  | | | | | | | | | | | | | | | | |   (23352)   ~ (all_52_11 = e2)
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | REDUCE: (23031), (23349) imply:
% 238.85/45.72  | | | | | | | | | | | | | | | | |   (23353)   ~ (e3 = e2)
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | |   (23354)   ~ (all_30_2 = e1)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | REDUCE: (23302), (23354) imply:
% 238.85/45.72  | | | | | | | | | | | | | | | | | |   (23355)  $false
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | CLOSE: (23355) is inconsistent.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | |   (23356)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0
% 238.85/45.72  | | | | | | | | | | | | | | | | | |              & op(e2, e1) = all_30_1 & $i(all_30_0) &
% 238.85/45.72  | | | | | | | | | | | | | | | | | |              $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1)
% 238.85/45.72  | | | | | | | | | | | | | | | | | |              = all_30_1 & $i(all_30_1))
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | BETA: splitting (23299) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23357)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_22_1 & $i(all_22_0) &
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |            $i(all_22_1)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | ALPHA: (23357) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23358)   ~ (all_22_0 = e3)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23359)  op(e2, e1) = all_22_1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23360)  op(all_22_1, e2) = all_22_0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_22_1,
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (23347), (23359) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23361)  all_22_1 = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | REDUCE: (23360), (23361) imply:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23362)  op(e2, e2) = all_22_0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (23356) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23363)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_30_1 & $i(all_30_0) &
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | ALPHA: (23363) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23364)  op(e2, e1) = all_30_1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23365)  op(all_30_1, e2) = all_30_0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_30_1,
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (23347), (23364) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23366)  all_30_1 = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_22_0,
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (23310), (23362) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23367)  all_22_0 = e1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | REDUCE: (23365), (23366) imply:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23368)  op(e2, e2) = all_30_0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_30_0,
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |              e2, e2, simplifying with (23310), (23368) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23369)  all_30_0 = e1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (121), (123), (125), (133),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (134), (135), (139), (140), (144), (157), (158),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (190), (191), (192), (202),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (203), (213), (217), (219), (223), (224), (226),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (227), (230), (232), (237), (238), (239), (241),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (242), (245), (246), (255), (256), (257), (281),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (282), (17762), (17763), (17764), (17765),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (17773), (17774), (23027), (23028), (23029),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (23030), (23031), (23032), (23033), (23038),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (23303), (23304), (23305), (23306), (23307),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (23308), (23310), (23316), (23317), (23321),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (23322), (23351), (23358), (23359), (23360),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (23364), (function-axioms) are inconsistent by
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            sub-proof #50.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23370)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 &
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | ALPHA: (23370) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23371)  op(e2, e1) = all_30_1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (121), (123), (125), (133),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (134), (135), (139), (140), (144), (157), (158),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (159), (160), (162), (163), (164), (165), (167),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (168), (169), (170), (190), (191), (192), (202),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (203), (213), (217), (219), (223), (224), (226),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (227), (230), (232), (237), (238), (239), (241),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (242), (245), (246), (255), (256), (257), (281),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (282), (17762), (17763), (17764), (17765),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (17773), (17774), (23027), (23028), (23029),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (23030), (23031), (23032), (23033), (23038),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (23303), (23304), (23305), (23306), (23307),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (23308), (23310), (23316), (23317), (23321),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (23322), (23351), (23358), (23359), (23360),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            (23371), (function-axioms) are inconsistent by
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            sub-proof #50.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23372)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |            $i(all_22_1)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | ALPHA: (23372) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23373)   ~ (all_22_1 = e0)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | |   (23374)  op(e2, e1) = all_22_1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23375)  all_54_14 = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (23032), (23375) are inconsistent by
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |            sub-proof #1796.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23376)   ~ (all_54_14 = e3)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | |   (23377)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | |   (23378)  all_54_2 = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (23030), (23378) are inconsistent by
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | |   (23379)   ~ (all_54_2 = e3)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | |   (23380)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |   (23381)  all_54_1 = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (133), (134), (135), (157), (158),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (165), (167), (168), (169),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |            (170), (191), (213), (219), (223), (226), (241),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |            (246), (256), (282), (17762), (17764), (17774),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |            (23027), (23028), (23029), (23032), (23033),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |            (23303), (23304), (23305), (23306), (23307),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |            (23316), (23317), (23321), (23381),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |            #54.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |   (23382)   ~ (all_54_1 = e3)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |   (23383)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (282), (23382) imply:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | |   (23384)   ~ (all_52_4 = e3)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23383) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |   (23385)  all_54_1 = e2
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (23316), (23385) are inconsistent by
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1928.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |   (23386)   ~ (all_54_1 = e2)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | |   (23387)  all_54_1 = e1 | all_54_1 = e0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | |   (23388)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (23317), (23384), (23388),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | |            #1959.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | |   (23389)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23389) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (23390)  all_58_4 = e3 & op(e3, e1) = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23390) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (23391)  op(e3, e1) = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (23030), (23391), (function-axioms) are
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (23392)  all_58_9 = e3 & op(e3, e0) = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23392) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (23393)  all_58_9 = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (23394)  op(e3, e0) = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23395)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (165), (167), (170), (232), (23304),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            (23307), (23308), (23384), (23395),
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            #53.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23396)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23396) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23397)  all_58_7 = e3 & op(e1, e2) = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23397) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23398)  op(e1, e2) = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (23322), (23398), (function-axioms) are
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2207.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23399)  all_58_13 = e3 & op(e0, e2) = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23399) implies:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23400)  op(e0, e2) = e3
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23387) gives:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23401)  all_54_1 = e1
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (23305), (23401) are inconsistent by
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2051.
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23402)  all_54_1 = e0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (23402) imply:
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23403)  all_52_4 = e0
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23403) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23404)  all_52_4 = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (23404) imply:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23405)   ~ (all_52_7 = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23405) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23406)   ~ (all_52_7 = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (23404) imply:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23407)   ~ (all_52_8 = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23407) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23408)   ~ (all_52_8 = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23384), (23404) imply:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23409)   ~ (e3 = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23316), (23404) imply:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23410)   ~ (e2 = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23305), (23404) imply:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23411)   ~ (e1 = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (23404) imply:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23412)  op(e3, e2) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23413)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (23305), (23317), (23413),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1340.
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23414)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23414) gives:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23415)  all_58_4 = e1 & op(e3, e1) = e1
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23415) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23416)  op(e3, e1) = e1
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23417)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23417) gives:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23418)  all_58_4 = e0 & op(e3, e1) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23418) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23419)  op(e3, e1) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23416), (23419), (function-axioms) are
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2089.
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23420)  all_58_5 = e0 & op(e2, e1) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23420) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23421)  op(e2, e1) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23356), (23373), (23374), (23421),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1356.
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23422)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23422) gives:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23423)  all_58_8 = e0 & op(e1, e1) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23423) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23424)  op(e1, e1) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (165), (169), (230), (23030), (23031),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23032), (23424), (function-axioms) are
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1010.
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23425)  all_58_14 = e0 & op(e0, e1) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23425) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23426)  op(e0, e1) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (121), (123), (125),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (139), (140), (144), (157), (158), (159),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (165), (169), (170), (191), (192), (213),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (219), (224), (237), (239), (245), (246),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (255), (256), (257), (281), (17763), (17764),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17765), (17773), (17774), (23028), (23030),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23038), (23303), (23306), (23310), (23317),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23321), (23351), (23377), (23380), (23384),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23393), (23400), (23406), (23408), (23412),
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23426), (function-axioms) are inconsistent by
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #51.
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23427)  all_58_9 = e1 & op(e3, e0) = e1
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23427) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23428)  op(e3, e0) = e1
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23394), (23428), (function-axioms) are
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | |   (23429)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 238.85/45.73  | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (160), (223),
% 238.85/45.73  | | | | | | | | | | | | | | | |            (224), (226), (17765), (23033), (23321), (23429),
% 238.85/45.73  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.73  | | | | | | | | | | | | | | | |            #49.
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | |   (23430)  all_58_13 = e2 & op(e0, e2) = e2
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | ALPHA: (23430) implies:
% 238.85/45.73  | | | | | | | | | | | | | | |   (23431)  op(e0, e2) = e2
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (23431), (function-axioms) are
% 238.85/45.73  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | |   (23432)  all_16_2 = e0
% 238.85/45.73  | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | COMBINE_EQS: (342), (23432) imply:
% 238.85/45.73  | | | | | | | | | | |   (23433)  all_10_2 = e0
% 238.85/45.73  | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | SIMP: (23433) implies:
% 238.85/45.73  | | | | | | | | | | |   (23434)  all_10_2 = e0
% 238.85/45.73  | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | COMBINE_EQS: (290), (23434) imply:
% 238.85/45.73  | | | | | | | | | | |   (23435)  all_56_1 = e0
% 238.85/45.73  | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | REDUCE: (359), (23434) imply:
% 238.85/45.73  | | | | | | | | | | |   (23436)   ~ (all_52_3 = e0)
% 238.85/45.73  | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | REDUCE: (361), (23434) imply:
% 238.85/45.73  | | | | | | | | | | |   (23437)   ~ (all_52_4 = e0)
% 238.85/45.73  | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | REDUCE: (45), (23434) imply:
% 238.85/45.73  | | | | | | | | | | |   (23438)  op(e3, e3) = e0
% 238.85/45.73  | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | BETA: splitting (64) gives:
% 238.85/45.73  | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | |   (23439)   ~ (all_22_2 = e1)
% 238.85/45.73  | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | REDUCE: (326), (23439) imply:
% 238.85/45.73  | | | | | | | | | | | |   (23440)   ~ (all_8_2 = e1)
% 238.85/45.73  | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | BETA: splitting (199) gives:
% 238.85/45.73  | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | |   (23441)  all_54_5 = e3
% 238.85/45.73  | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | COMBINE_EQS: (275), (23441) imply:
% 238.85/45.73  | | | | | | | | | | | | |   (23442)  all_8_2 = e3
% 238.85/45.73  | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | REDUCE: (23039), (23442) imply:
% 238.85/45.73  | | | | | | | | | | | | |   (23443)  $false
% 238.85/45.73  | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | CLOSE: (23443) is inconsistent.
% 238.85/45.73  | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | |   (23444)   ~ (all_54_5 = e3)
% 238.85/45.73  | | | | | | | | | | | | |   (23445)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 238.85/45.73  | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | BETA: splitting (23445) gives:
% 238.85/45.73  | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | |   (23446)  all_54_5 = e2
% 238.85/45.73  | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | COMBINE_EQS: (275), (23446) imply:
% 238.85/45.73  | | | | | | | | | | | | | |   (23447)  all_8_2 = e2
% 238.85/45.73  | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | REDUCE: (366), (23447) imply:
% 238.85/45.73  | | | | | | | | | | | | | |   (23448)   ~ (all_52_1 = e2)
% 238.85/45.73  | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | REDUCE: (369), (23447) imply:
% 238.85/45.73  | | | | | | | | | | | | | |   (23449)   ~ (all_52_4 = e2)
% 238.85/45.73  | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | REDUCE: (375), (23447) imply:
% 238.85/45.73  | | | | | | | | | | | | | |   (23450)   ~ (all_52_9 = e2)
% 238.85/45.73  | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | REDUCE: (23039), (23447) imply:
% 238.85/45.73  | | | | | | | | | | | | | |   (23451)   ~ (e3 = e2)
% 238.85/45.73  | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | REDUCE: (42), (23447) imply:
% 238.85/45.73  | | | | | | | | | | | | | |   (23452)  op(e2, e2) = e2
% 238.85/45.73  | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.85/45.73  | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | |   (23453)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.85/45.73  | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.85/45.73  | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.85/45.73  | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.85/45.73  | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.85/45.73  | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.85/45.73  | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.85/45.73  | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.85/45.73  | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.85/45.73  | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.85/45.73  | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.85/45.73  | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.85/45.73  | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | BETA: splitting (23453) gives:
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | |   (23454)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.85/45.73  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.85/45.73  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.85/45.73  | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.85/45.73  | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.85/45.73  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.85/45.73  | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.85/45.73  | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.85/45.73  | | | | | | | | | | | | | | | |              = e3)
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | BETA: splitting (23454) gives:
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | |   (23455)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.85/45.73  | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.85/45.73  | | | | | | | | | | | | | | | | |            e3
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | ALPHA: (23455) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | |   (23456)   ~ (all_56_31 = e2)
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | REDUCE: (17762), (23456) imply:
% 238.85/45.73  | | | | | | | | | | | | | | | | |   (23457)  $false
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | CLOSE: (23457) is inconsistent.
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | |   (23458)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.85/45.73  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.85/45.73  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.85/45.73  | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.85/45.73  | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.85/45.73  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.85/45.73  | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (170), (23028), (23449), (23458),
% 238.85/45.73  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.73  | | | | | | | | | | | | | | | | |            #253.
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | |   (23459)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.85/45.73  | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.85/45.73  | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.85/45.73  | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.85/45.73  | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.85/45.73  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.85/45.73  | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.85/45.73  | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.85/45.73  | | | | | | | | | | | | | | | |              = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | REF_CLOSE: (159), (23027), (23435), (23436), (23459),
% 238.85/45.73  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.73  | | | | | | | | | | | | | | | |            #465.
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | End of split
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | |   (23460)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.85/45.73  | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.85/45.73  | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.85/45.73  | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.85/45.73  | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.85/45.73  | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.85/45.73  | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.85/45.73  | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.85/45.73  | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.85/45.73  | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.85/45.73  | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.85/45.73  | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.85/45.73  | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | BETA: splitting (23460) gives:
% 238.85/45.73  | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | |   (23461)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.85/45.73  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.85/45.73  | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.85/45.73  | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.85/45.73  | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.85/45.73  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.85/45.73  | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.85/45.73  | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.85/45.73  | | | | | | | | | | | | | | | |              = e2)
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (17762), (17764), (23450), (23461),
% 238.85/45.73  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.73  | | | | | | | | | | | | | | | |            #184.
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | |   (23462)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.85/45.73  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.85/45.73  | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.85/45.73  | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.85/45.73  | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.85/45.73  | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.85/45.73  | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.85/45.73  | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.85/45.73  | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.85/45.73  | | | | | | | | | | | | | | | |              = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | BETA: splitting (23462) gives:
% 238.85/45.73  | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | |   (23463)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.85/45.73  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.85/45.73  | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.85/45.73  | | | | | | | | | | | | | | | | |              e2) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | ALPHA: (23463) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | |   (23464)   ~ (all_56_31 = e2)
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | REDUCE: (17762), (23464) imply:
% 238.85/45.73  | | | | | | | | | | | | | | | | |   (23465)  $false
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | CLOSE: (23465) is inconsistent.
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | |   (23466)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.85/45.73  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.85/45.73  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.85/45.73  | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.85/45.73  | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.85/45.73  | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.85/45.73  | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | BETA: splitting (23466) gives:
% 238.85/45.73  | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | |   (23467)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.85/45.73  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 238.85/45.73  | | | | | | | | | | | | | | | | | |              e1) = e1
% 238.85/45.73  | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | ALPHA: (23467) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | | |   (23468)   ~ (all_56_1 = e0)
% 238.85/45.73  | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | REDUCE: (23435), (23468) imply:
% 238.85/45.73  | | | | | | | | | | | | | | | | | |   (23469)  $false
% 238.85/45.73  | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | CLOSE: (23469) is inconsistent.
% 238.85/45.73  | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | |   (23470)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 238.85/45.73  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.85/45.73  | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 238.85/45.73  | | | | | | | | | | | | | | | | | |              e1) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | ALPHA: (23470) implies:
% 238.85/45.73  | | | | | | | | | | | | | | | | | |   (23471)  op(e0, e1) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | |   (23472)  op(e1, e0) = e0
% 238.85/45.73  | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.73  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.73  | | | | | | | | | | | | | | | | | | |   (23473)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | BETA: splitting (23473) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | |   (23474)  all_58_4 = e2 & op(e3, e1) = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | ALPHA: (23474) implies:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | |   (23475)  op(e3, e1) = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | |   (23476)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (23438), (23448), (23476),
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | |            #1607.
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | |   (23477)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23477) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23478)  all_58_6 = e2 & op(e1, e3) = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23478) implies:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23479)  op(e1, e3) = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (157), (23471) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23480)  all_52_11 = e0
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (23472) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23481)  all_52_14 = e0
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (23479) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23482)  all_52_2 = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (23475) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23483)  all_52_8 = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (23482) imply:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23484)   ~ (all_52_6 = e2)
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | SIMP: (23484) implies:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23485)   ~ (all_52_6 = e2)
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (23481) imply:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23486)   ~ (all_52_6 = e0)
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (23480) imply:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23487)   ~ (all_52_7 = e0)
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17768), (23481) imply:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23488)   ~ (e2 = e0)
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | |   (23489)  all_54_9 = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (23029), (23489) are inconsistent by
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | |   (23490)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23490) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | |   (23491)  all_54_9 = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (23485), (23491) are inconsistent by
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1954.
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | |   (23492)  all_54_9 = e1 | all_54_9 = e0
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23492) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (23493)  all_54_9 = e1
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (23493) imply:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (23494)  all_52_6 = e1
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23494) implies:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (23495)  all_52_6 = e1
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (23495) imply:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (23496)   ~ (all_52_4 = e1)
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (162), (170), (203), (235), (282),
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | |            (23437), (23449), (23452), (23486), (23487),
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | |            (23496), (function-axioms) are inconsistent by
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #88.
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (23497)  all_54_9 = e0
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (23486), (23497) are inconsistent by
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1953.
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |   (23498)  all_58_12 = e2 & op(e0, e3) = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (17763), (23498), (function-axioms) are
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2315.
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | |   (23499)  all_58_5 = e2 & op(e2, e1) = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | ALPHA: (23499) implies:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | |   (23500)  op(e2, e1) = e2
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (23450), (23500), (function-axioms) are
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | |   (23501)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 238.85/45.74  | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (23038), (23471), (23501),
% 238.85/45.74  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.74  | | | | | | | | | | | | | | | | | | |            #433.
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | |   (23502)  all_54_5 = e1 | all_54_5 = e0
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | REF_CLOSE: (275), (23042), (23440), (23502) are inconsistent
% 238.85/45.74  | | | | | | | | | | | | | |            by sub-proof #2300.
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | |   (23503)  all_22_2 = e1
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | COMBINE_EQS: (326), (23503) imply:
% 238.85/45.74  | | | | | | | | | | | |   (23504)  all_8_2 = e1
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | COMBINE_EQS: (353), (23504) imply:
% 238.85/45.74  | | | | | | | | | | | |   (23505)  all_56_11 = e1
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | REDUCE: (375), (23504) imply:
% 238.85/45.74  | | | | | | | | | | | |   (23506)   ~ (all_52_9 = e1)
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | |   (23507)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.85/45.74  | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.85/45.74  | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.85/45.74  | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.85/45.74  | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.85/45.74  | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.85/45.74  | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.85/45.74  | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.85/45.74  | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.85/45.74  | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.85/45.74  | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.85/45.74  | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.85/45.74  | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | BETA: splitting (23507) gives:
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | |   (23508)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.85/45.74  | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.85/45.74  | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.85/45.74  | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.85/45.74  | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.85/45.74  | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.85/45.74  | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.85/45.74  | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.85/45.74  | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.85/45.74  | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.85/45.74  | | | | | | | | | | | | | |              = e3)
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | REF_CLOSE: (163), (17762), (23027), (23028), (23508),
% 238.85/45.74  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.74  | | | | | | | | | | | | | |            #48.
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | |   (23509)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.85/45.74  | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.85/45.74  | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.85/45.74  | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.85/45.74  | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.85/45.74  | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.85/45.74  | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.85/45.74  | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.85/45.74  | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.85/45.74  | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.85/45.74  | | | | | | | | | | | | | |              = e0)
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | REF_CLOSE: (159), (23027), (23435), (23436), (23509),
% 238.85/45.74  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.74  | | | | | | | | | | | | | |            #465.
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | |   (23510)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.85/45.74  | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.85/45.74  | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.85/45.74  | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.85/45.74  | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.85/45.74  | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.85/45.74  | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.85/45.74  | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.85/45.74  | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.85/45.74  | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.85/45.74  | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.85/45.74  | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.85/45.74  | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.85/45.74  | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | BETA: splitting (23510) gives:
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | |   (23511)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.85/45.74  | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.85/45.74  | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.85/45.74  | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.85/45.74  | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.85/45.74  | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.85/45.74  | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.85/45.74  | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.85/45.74  | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.85/45.74  | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.85/45.74  | | | | | | | | | | | | | |              = e2)
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | REF_CLOSE: (158), (165), (17764), (23505), (23506), (23511),
% 238.85/45.74  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.74  | | | | | | | | | | | | | |            #181.
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | |   (23512)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.85/45.74  | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.85/45.74  | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.85/45.74  | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.85/45.74  | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.85/45.74  | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.85/45.74  | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.85/45.74  | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.85/45.74  | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.85/45.74  | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.85/45.74  | | | | | | | | | | | | | |              = e0)
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | BETA: splitting (23512) gives:
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | |   (23513)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.85/45.74  | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.85/45.74  | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.85/45.74  | | | | | | | | | | | | | | |              e2) = e0
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | ALPHA: (23513) implies:
% 238.85/45.74  | | | | | | | | | | | | | | |   (23514)   ~ (all_56_31 = e2)
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | REDUCE: (17762), (23514) imply:
% 238.85/45.74  | | | | | | | | | | | | | | |   (23515)  $false
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | CLOSE: (23515) is inconsistent.
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | |   (23516)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.85/45.74  | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.85/45.74  | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.85/45.74  | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.85/45.74  | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.85/45.74  | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.85/45.74  | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | REF_CLOSE: (23435), (23505), (23516) are inconsistent by
% 238.85/45.74  | | | | | | | | | | | | | | |            sub-proof #1294.
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | |   (23517)  all_14_2 = e0
% 238.85/45.74  | | | | | | | | | |   (23518)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0
% 238.85/45.74  | | | | | | | | | |              & op(e2, e0) = all_14_1 & $i(all_14_0) &
% 238.85/45.74  | | | | | | | | | |              $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0)
% 238.85/45.74  | | | | | | | | | |              = all_14_1 & $i(all_14_1))
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | COMBINE_EQS: (344), (23517) imply:
% 238.85/45.74  | | | | | | | | | |   (23519)  all_8_2 = e0
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | COMBINE_EQS: (311), (23519) imply:
% 238.85/45.74  | | | | | | | | | |   (23520)  all_48_2 = e0
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | COMBINE_EQS: (353), (23519) imply:
% 238.85/45.74  | | | | | | | | | |   (23521)  all_56_11 = e0
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | REDUCE: (366), (23519) imply:
% 238.85/45.74  | | | | | | | | | |   (23522)   ~ (all_52_1 = e0)
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | REDUCE: (369), (23519) imply:
% 238.85/45.74  | | | | | | | | | |   (23523)   ~ (all_52_4 = e0)
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | REDUCE: (371), (23519) imply:
% 238.85/45.74  | | | | | | | | | |   (23524)   ~ (all_52_6 = e0)
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | REDUCE: (373), (23519) imply:
% 238.85/45.74  | | | | | | | | | |   (23525)   ~ (all_52_7 = e0)
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | REDUCE: (375), (23519) imply:
% 238.85/45.74  | | | | | | | | | |   (23526)   ~ (all_52_9 = e0)
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | REDUCE: (377), (23519) imply:
% 238.85/45.74  | | | | | | | | | |   (23527)   ~ (all_52_13 = e0)
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | REDUCE: (23039), (23519) imply:
% 238.85/45.74  | | | | | | | | | |   (23528)   ~ (e3 = e0)
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | BETA: splitting (235) gives:
% 238.85/45.74  | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | |   (23529)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 238.85/45.74  | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.85/45.74  | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | BETA: splitting (23529) gives:
% 238.85/45.74  | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | |   (23530)  all_58_1 = e0 & op(e3, e2) = e0
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | REF_CLOSE: (170), (23523), (23530), (function-axioms) are
% 238.85/45.74  | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | |   (23531)  all_58_3 = e0 & op(e2, e2) = e0
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | ALPHA: (23531) implies:
% 238.85/45.74  | | | | | | | | | | | |   (23532)  all_58_3 = e0
% 238.85/45.74  | | | | | | | | | | | |   (23533)  op(e2, e2) = e0
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | BETA: splitting (55) gives:
% 238.85/45.74  | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | |   (23534)   ~ (all_16_2 = e0)
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | REDUCE: (342), (23534) imply:
% 238.85/45.74  | | | | | | | | | | | | |   (23535)   ~ (all_10_2 = e0)
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | BETA: splitting (67) gives:
% 238.85/45.74  | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | |   (23536)   ~ (all_24_2 = e2)
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | REDUCE: (301), (23536) imply:
% 238.85/45.74  | | | | | | | | | | | | | |   (23537)   ~ (all_10_2 = e2)
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 238.85/45.74  | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | |   (23538)  all_54_0 = e3
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | COMBINE_EQS: (292), (23538) imply:
% 238.85/45.74  | | | | | | | | | | | | | | |   (23539)  all_10_2 = e3
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | REDUCE: (355), (23539) imply:
% 238.85/45.74  | | | | | | | | | | | | | | |   (23540)   ~ (all_52_1 = e3)
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | |   (23541)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 238.85/45.74  | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.85/45.74  | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | BETA: splitting (23541) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | |   (23542)  all_58_1 = e3 & op(e3, e2) = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | ALPHA: (23542) implies:
% 238.85/45.74  | | | | | | | | | | | | | | | | |   (23543)  op(e3, e2) = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (204), (292), (361), (23040), (23535),
% 238.85/45.74  | | | | | | | | | | | | | | | | |            (23537), (23543), (function-axioms) are
% 238.85/45.74  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #484.
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | |   (23544)  all_58_3 = e3 & op(e2, e2) = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (23039), (23544), (function-axioms) are
% 238.85/45.74  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #450.
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | End of split
% 238.85/45.74  | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | |   (23545)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 238.85/45.74  | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.85/45.74  | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | BETA: splitting (23545) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | |   (23546)  all_58_7 = e3 & op(e1, e2) = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | ALPHA: (23546) implies:
% 238.85/45.74  | | | | | | | | | | | | | | | | |   (23547)  op(e1, e2) = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (23029), (23547), (function-axioms) are
% 238.85/45.74  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2191.
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | |   (23548)  all_58_13 = e3 & op(e0, e2) = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | ALPHA: (23548) implies:
% 238.85/45.74  | | | | | | | | | | | | | | | | |   (23549)  all_58_13 = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | |   (23550)  op(e0, e2) = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | |   (23551)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.85/45.74  | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | BETA: splitting (23551) gives:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | |   (23552)  all_58_2 = e3 & op(e2, e3) = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | ALPHA: (23552) implies:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | |   (23553)  op(e2, e3) = e3
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (23540), (23553), (function-axioms) are
% 238.85/45.74  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.74  | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.74  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |   (23554)  all_58_3 = e3 & op(e2, e2) = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (23039), (23554), (function-axioms) are
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #450.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.75  | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | |   (23555)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 238.85/45.75  | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | BETA: splitting (23555) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |   (23556)  all_58_5 = e3 & op(e2, e1) = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (23031), (23556), (function-axioms) are
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1822.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |   (23557)  all_58_10 = e3 & op(e2, e0) = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | ALPHA: (23557) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |   (23558)  all_58_10 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |   (23559)  op(e2, e0) = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (23550) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |   (23560)  all_52_7 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (164), (23559) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |   (23561)  all_52_13 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | REDUCE: (135), (23560) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |   (23562)   ~ (all_52_4 = e3)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | REDUCE: (113), (23561) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |   (23563)   ~ (all_52_12 = e3)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | REDUCE: (110), (23561) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | |   (23564)   ~ (all_52_14 = e3)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | |   (23565)   ~ (all_44_2 = e2)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (17761), (23565) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | |   (23566)  $false
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | CLOSE: (23566) is inconsistent.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | |   (23567)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | |   (23568)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | ALPHA: (23568) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | |   (23569)   ~ (all_4_0 = e1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | |   (23570)  op(e0, e2) = all_4_1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | |   (23571)  op(all_4_1, e0) = all_4_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | |   (23572)   ~ (all_48_2 = e0)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23520), (23572) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | |   (23573)  $false
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (23573) is inconsistent.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | |   (23574)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | |              $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | |              = all_48_1 & $i(all_48_1))
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23574) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | |   (23575)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_48_1 & $i(all_48_0) &
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_48_1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23575) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | |   (23576)   ~ (all_48_0 = e1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | |   (23577)  op(e2, e0) = all_48_1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | |   (23578)  op(all_48_1, e2) = all_48_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23518) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23579)   ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 &
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_14_1 & $i(all_14_0) &
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_14_1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23579) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23580)  op(e2, e0) = all_14_1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23581)  op(all_14_1, e2) = all_14_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_1,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (23550), (23570) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23582)  all_4_1 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (23559), (23577) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23583)  all_48_1 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              all_48_1, e0, e2, simplifying with (23577),
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              (23580) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23584)  all_48_1 = all_14_1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23583), (23584) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23585)  all_14_1 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23578), (23583) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23586)  op(e3, e2) = all_48_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23581), (23585) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23587)  op(e3, e2) = all_14_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23571), (23582) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23588)  op(e3, e0) = all_4_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              all_4_0, e0, e3, simplifying with (168), (23588)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23589)  all_52_12 = all_4_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              all_14_0, e2, e3, simplifying with (170), (23587)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23590)  all_52_4 = all_14_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              all_48_0, e2, e3, simplifying with (170), (23586)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23591)  all_52_4 = all_48_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23590), (23591) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23592)  all_48_0 = all_14_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (23589) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23593)  all_54_3 = all_4_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (23590) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23594)  all_54_1 = all_14_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23562), (23590) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23595)   ~ (all_14_0 = e3)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23523), (23590) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23596)   ~ (all_14_0 = e0)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23563), (23589) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23597)   ~ (all_4_0 = e3)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17766), (23589) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23598)   ~ (all_4_0 = e2)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23576), (23592) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23599)   ~ (all_14_0 = e1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (23600)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23600) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23601)  all_58_1 = e1 & op(e3, e2) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23601) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23602)  op(e3, e2) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23603)  all_54_1 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23594), (23603) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23604)  all_14_0 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23595), (23604) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23605)  $false
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (23605) is inconsistent.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23606)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23587), (23594), (23596), (23599), (23602),
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23606), (function-axioms) are inconsistent by
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1449.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23607)  all_58_3 = e1 & op(e2, e2) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23532), (23607) are inconsistent by
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1752.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (23608)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23608) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23609)  all_58_7 = e1 & op(e1, e2) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23609) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23610)  all_58_7 = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23611)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23611) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23612)  all_58_9 = e1 & op(e3, e0) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23612) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23613)  op(e3, e0) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (201), (23569), (23588), (23593), (23597),
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23598), (23613), (function-axioms) are
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #61.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23614)  all_58_10 = e1 & op(e2, e0) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23558), (23614) are inconsistent by
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #47.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23615)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (225),
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (17773), (23033), (23610), (23615),
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #46.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23616)  all_58_13 = e1 & op(e0, e2) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23616) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23617)  all_58_13 = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23549), (23617) are inconsistent by
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1436.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23618)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_14_1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23618) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23619)   ~ (all_14_1 = e1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23620)  op(e2, e0) = all_14_1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_1,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (23550), (23570) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23621)  all_4_1 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (23559), (23577) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23622)  all_48_1 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              all_48_1, e0, e2, simplifying with (23577),
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              (23620) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23623)  all_48_1 = all_14_1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23622), (23623) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23624)  all_14_1 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23578), (23622) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23625)  op(e3, e2) = all_48_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23571), (23621) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23626)  op(e3, e0) = all_4_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              all_4_0, e0, e3, simplifying with (168), (23626)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23627)  all_52_12 = all_4_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              all_48_0, e2, e3, simplifying with (170), (23625)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23628)  all_52_4 = all_48_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (23627) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23629)  all_54_3 = all_4_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (23628) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23630)  all_54_1 = all_48_0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23562), (23628) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23631)   ~ (all_48_0 = e3)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23523), (23628) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23632)   ~ (all_48_0 = e0)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23563), (23627) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23633)   ~ (all_4_0 = e3)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17766), (23627) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | |   (23634)   ~ (all_4_0 = e2)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (23635)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23635) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23636)  all_58_1 = e1 & op(e3, e2) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23636) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23637)  op(e3, e2) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23638)  all_54_1 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23630), (23638) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23639)  all_48_0 = e3
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23631), (23639) imply:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23640)  $false
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (23640) is inconsistent.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23641)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23576), (23625), (23630), (23632), (23637),
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23641), (function-axioms) are inconsistent by
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1446.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23642)  all_58_3 = e1 & op(e2, e2) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23532), (23642) are inconsistent by
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1752.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (23643)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23643) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23644)  all_58_7 = e1 & op(e1, e2) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23644) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23645)  all_58_7 = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23646)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23646) gives:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23647)  all_58_9 = e1 & op(e3, e0) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23647) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23648)  op(e3, e0) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (201), (23569), (23626), (23629), (23633),
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23634), (23648), (function-axioms) are
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #61.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23649)  all_58_10 = e1 & op(e2, e0) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23649) implies:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23650)  op(e2, e0) = e1
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23577), (23619), (23620), (23650),
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1585.
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23651)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (225),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (17773), (23033), (23645), (23651),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #46.
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23652)  all_58_13 = e1 & op(e0, e2) = e1
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23652) implies:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23653)  all_58_13 = e1
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23549), (23653) are inconsistent by
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1436.
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | |   (23654)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_48_1)
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23518), (23559), (23654), (function-axioms) are
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #129.
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | |   (23655)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | ALPHA: (23655) implies:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | |   (23656)   ~ (all_4_1 = e3)
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | |   (23657)  op(e0, e2) = all_4_1
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23550), (23567), (23656), (23657),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | |            #211.
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | |   (23658)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | REF_CLOSE: (292), (23040), (23535), (23537), (23658) are
% 238.85/45.76  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2319.
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | |   (23659)  all_24_2 = e2
% 238.85/45.76  | | | | | | | | | | | | | |   (23660)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 238.85/45.76  | | | | | | | | | | | | | |              & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 238.85/45.76  | | | | | | | | | | | | | |              $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 238.85/45.76  | | | | | | | | | | | | | |              = all_24_1 & $i(all_24_1))
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | COMBINE_EQS: (301), (23659) imply:
% 238.85/45.76  | | | | | | | | | | | | | |   (23661)  all_10_2 = e2
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | COMBINE_EQS: (348), (23661) imply:
% 238.85/45.76  | | | | | | | | | | | | | |   (23662)  all_32_2 = e2
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | COMBINE_EQS: (290), (23661) imply:
% 238.85/45.76  | | | | | | | | | | | | | |   (23663)  all_56_1 = e2
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | REDUCE: (355), (23661) imply:
% 238.85/45.76  | | | | | | | | | | | | | |   (23664)   ~ (all_52_1 = e2)
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | REDUCE: (357), (23661) imply:
% 238.85/45.76  | | | | | | | | | | | | | |   (23665)   ~ (all_52_2 = e2)
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | REDUCE: (45), (23661) imply:
% 238.85/45.76  | | | | | | | | | | | | | |   (23666)  op(e3, e3) = e2
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | |   (23667)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 238.85/45.76  | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | BETA: splitting (23667) gives:
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | |   (23668)  all_58_4 = e2 & op(e3, e1) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | ALPHA: (23668) implies:
% 238.85/45.76  | | | | | | | | | | | | | | | |   (23669)  all_58_4 = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23670)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | BETA: splitting (23670) gives:
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | |   (23671)  all_58_6 = e2 & op(e1, e3) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (23665), (23671), (function-axioms) are
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #250.
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | |   (23672)  all_58_7 = e2 & op(e1, e2) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | ALPHA: (23672) implies:
% 238.85/45.76  | | | | | | | | | | | | | | | | | |   (23673)  all_58_7 = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | |   (23674)  op(e1, e2) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | |   (23675)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (23533), (23664), (23675),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.76  | | | | | | | | | | | | | | | | | | |            #1234.
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | |   (23676)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.85/45.76  | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (23676) gives:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |   (23677)  all_58_5 = e2 & op(e2, e1) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | ALPHA: (23677) implies:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |   (23678)  all_58_5 = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |   (23679)  op(e2, e1) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (79), (97), (103), (110),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (112), (113), (117), (118), (120), (123), (125),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (126), (128), (133), (134), (135), (136), (139),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (140), (141), (143), (144), (145), (146), (148),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (149), (157), (158), (159), (160), (162), (163),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (190),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (191), (192), (193), (196), (197), (200), (201),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (202), (203), (211), (212), (213), (214), (216),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (218), (219), (220), (222), (223), (224), (226),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (235), (236), (237),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (238), (239), (240), (242), (244), (246), (255),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (256), (257), (258), (268), (269), (279), (280),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (281), (282), (17760), (17761), (17762), (17763),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (17766), (17773), (17774), (23027), (23028),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (23029), (23030), (23032), (23033), (23038),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (23039), (23518), (23520), (23521), (23522),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (23523), (23524), (23525), (23526), (23527),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (23532), (23533), (23660), (23662), (23663),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (23666), (23673), (23674), (23678), (23679),
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            #39.
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |   (23680)  all_58_10 = e2 & op(e2, e0) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | ALPHA: (23680) implies:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |   (23681)  op(e2, e0) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (23681), (function-axioms) are
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23682)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 238.85/45.76  | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (160), (165),
% 238.85/45.76  | | | | | | | | | | | | | | | | |            (227), (228), (230), (17768), (23032), (23669),
% 238.85/45.76  | | | | | | | | | | | | | | | | |            (23682), (function-axioms) are inconsistent by
% 238.85/45.76  | | | | | | | | | | | | | | | | |            sub-proof #58.
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | |   (23683)  all_58_5 = e2 & op(e2, e1) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | ALPHA: (23683) implies:
% 238.85/45.76  | | | | | | | | | | | | | | | |   (23684)  all_58_5 = e2
% 238.85/45.76  | | | | | | | | | | | | | | | |   (23685)  op(e2, e1) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23686)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | BETA: splitting (23686) gives:
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | |   (23687)  all_58_6 = e2 & op(e1, e3) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (23665), (23687), (function-axioms) are
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #250.
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | |   (23688)  all_58_7 = e2 & op(e1, e2) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | ALPHA: (23688) implies:
% 238.85/45.76  | | | | | | | | | | | | | | | | | |   (23689)  all_58_7 = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | |   (23690)  op(e1, e2) = e2
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (42), (79), (97), (103), (110),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (112), (113), (117), (118), (120), (123), (125),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (126), (128), (133), (134), (135), (136), (139),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (140), (141), (143), (144), (145), (146), (148),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (149), (157), (158), (159), (160), (162), (163),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (190),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (191), (192), (193), (196), (197), (200), (201),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (202), (203), (211), (212), (213), (214), (216),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (218), (219), (220), (222), (223), (224), (226),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (235), (236), (237),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (238), (239), (240), (242), (244), (246), (255),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (256), (257), (258), (268), (269), (279), (280),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (281), (282), (17760), (17761), (17762), (17763),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (17766), (17773), (17774), (23027), (23028),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (23029), (23030), (23032), (23033), (23038),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (23039), (23518), (23520), (23521), (23522),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (23523), (23524), (23525), (23526), (23527),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (23532), (23533), (23660), (23662), (23663),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (23666), (23684), (23685), (23689), (23690),
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.76  | | | | | | | | | | | | | | | | | |            #39.
% 238.85/45.76  | | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23691)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 238.85/45.76  | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (17768), (23038), (23691),
% 238.85/45.76  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.76  | | | | | | | | | | | | | | | | |            #38.
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | |   (23692)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 238.85/45.76  | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17765), (23038), (23692),
% 238.85/45.76  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.76  | | | | | | | | | | | | | | |            #57.
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | |   (23693)  all_16_2 = e0
% 238.85/45.76  | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | COMBINE_EQS: (342), (23693) imply:
% 238.85/45.76  | | | | | | | | | | | | |   (23694)  all_10_2 = e0
% 238.85/45.76  | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | SIMP: (23694) implies:
% 238.85/45.76  | | | | | | | | | | | | |   (23695)  all_10_2 = e0
% 238.85/45.76  | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | COMBINE_EQS: (290), (23695) imply:
% 238.85/45.76  | | | | | | | | | | | | |   (23696)  all_56_1 = e0
% 238.85/45.76  | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | REDUCE: (357), (23695) imply:
% 238.85/45.76  | | | | | | | | | | | | |   (23697)   ~ (all_52_2 = e0)
% 238.85/45.76  | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | REDUCE: (363), (23695) imply:
% 238.85/45.76  | | | | | | | | | | | | |   (23698)   ~ (all_52_8 = e0)
% 238.85/45.76  | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | REDUCE: (23040), (23695) imply:
% 238.85/45.76  | | | | | | | | | | | | |   (23699)   ~ (e1 = e0)
% 238.85/45.76  | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | BETA: splitting (227) gives:
% 238.85/45.76  | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | |   (23700)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 238.85/45.76  | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | BETA: splitting (23700) gives:
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | |   (23701)  all_58_4 = e0 & op(e3, e1) = e0
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | REF_CLOSE: (169), (23698), (23701), (function-axioms) are
% 238.85/45.76  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | |   (23702)  all_58_5 = e0 & op(e2, e1) = e0
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | REF_CLOSE: (165), (23526), (23702), (function-axioms) are
% 238.85/45.76  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | End of split
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | |   (23703)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 238.85/45.76  | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | BETA: splitting (23703) gives:
% 238.85/45.76  | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | |   (23704)  all_58_8 = e0 & op(e1, e1) = e0
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | ALPHA: (23704) implies:
% 238.85/45.76  | | | | | | | | | | | | | | |   (23705)  op(e1, e1) = e0
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (165), (169), (230), (23030), (23031),
% 238.85/45.76  | | | | | | | | | | | | | | |            (23032), (23705), (function-axioms) are
% 238.85/45.76  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1010.
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | |   (23706)  all_58_14 = e0 & op(e0, e1) = e0
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | ALPHA: (23706) implies:
% 238.85/45.76  | | | | | | | | | | | | | | |   (23707)  all_58_14 = e0
% 238.85/45.76  | | | | | | | | | | | | | | |   (23708)  op(e0, e1) = e0
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 238.85/45.76  | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | |   (23709)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 238.85/45.76  | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (23524), (23697), (23709),
% 238.85/45.76  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.76  | | | | | | | | | | | | | | | |            #2021.
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | |   (23710)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 238.85/45.76  | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | BETA: splitting (23710) gives:
% 238.85/45.76  | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23711)  all_58_8 = e0 & op(e1, e1) = e0
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | ALPHA: (23711) implies:
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23712)  op(e1, e1) = e0
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (229),
% 238.85/45.76  | | | | | | | | | | | | | | | | |            (230), (23031), (23707), (23708), (23712),
% 238.85/45.76  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.76  | | | | | | | | | | | | | | | | |            #437.
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23713)  all_58_11 = e0 & op(e1, e0) = e0
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | ALPHA: (23713) implies:
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23714)  op(e1, e0) = e0
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 238.85/45.76  | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (157), (23708) gives:
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23715)  all_52_11 = e0
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.85/45.76  | | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (23714) gives:
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23716)  all_52_14 = e0
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | REDUCE: (139), (23715) imply:
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23717)   ~ (all_52_3 = e0)
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.76  | | | | | | | | | | | | | | | | | REDUCE: (112), (23716) imply:
% 238.85/45.76  | | | | | | | | | | | | | | | | |   (23718)   ~ (all_52_12 = e0)
% 238.85/45.76  | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | REDUCE: (17768), (23716) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | |   (23719)   ~ (e2 = e0)
% 238.85/45.77  | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | |   (23720)   ~ (all_44_2 = e2)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | REDUCE: (17761), (23720) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | |   (23721)  $false
% 238.85/45.77  | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | CLOSE: (23721) is inconsistent.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | |   (23722)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.85/45.77  | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.85/45.77  | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.85/45.77  | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.85/45.77  | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | |   (23723)   ~ (all_46_2 = e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | REDUCE: (23026), (23723) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | |   (23724)  $false
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | CLOSE: (23724) is inconsistent.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | |   (23725)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 238.85/45.77  | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 238.85/45.77  | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | |   (23726)   ~ (all_48_2 = e0)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | REDUCE: (23520), (23726) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | |   (23727)  $false
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | CLOSE: (23727) is inconsistent.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | |   (23728)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_48_1 & $i(all_48_0) &
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | |              $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | |              = all_48_1 & $i(all_48_1))
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | |   (23729)  all_54_7 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (23729) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | |   (23730)  all_52_13 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | SIMP: (23730) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | |   (23731)  all_52_13 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (23731) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | |   (23732)   ~ (all_52_1 = e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (23731) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | |   (23733)   ~ (all_52_12 = e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | |   (23734)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23734) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | |   (23735)  all_58_9 = e3 & op(e3, e0) = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23735) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | |   (23736)  op(e3, e0) = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (23733), (23736), (function-axioms) are
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2179.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | |   (23737)  all_58_10 = e3 & op(e2, e0) = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23737) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | |   (23738)  all_58_10 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | |   (23739)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23739) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (23740)  all_58_9 = e1 & op(e3, e0) = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23740) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (23741)  op(e3, e0) = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23742)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (23522), (23697),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (23717), (23732), (23742), (function-axioms) are
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1579.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23743)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23743) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23744)  all_58_6 = e3 & op(e1, e3) = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23744) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23745)  op(e1, e3) = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (23028), (23745), (function-axioms) are
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23746)  all_58_12 = e3 & op(e0, e3) = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23746) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23747)  all_58_12 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23748)  op(e0, e3) = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23749)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23749) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23750)  all_58_12 = e1 & op(e0, e3) = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23750) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23751)  all_58_12 = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23747), (23751) are inconsistent by
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1542.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23752)  all_58_13 = e1 & op(e0, e2) = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23752) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23753)  all_58_13 = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23754)  op(e0, e2) = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23755)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23755) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23756)  all_58_0 = e3 & op(e3, e3) = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23756) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23757)  op(e3, e3) = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (23522), (23697),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23717), (23757), (function-axioms) are
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1938.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23758)  all_58_1 = e3 & op(e3, e2) = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23758) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23759)  all_58_1 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23760)  op(e3, e2) = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23761)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (158), (162), (235), (23524),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23525), (23760), (23761), (function-axioms) are
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #82.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23762)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23762) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23763)  all_58_7 = e2 & op(e1, e2) = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23763) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23764)  all_58_7 = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23765)  all_54_3 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (23733), (23765) are inconsistent by
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23766)   ~ (all_54_3 = e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23767)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23767) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23768)  all_54_3 = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (17766), (23768) are inconsistent by
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2290.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23769)   ~ (all_54_3 = e2)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23770)  all_54_3 = e1 | all_54_3 = e0
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23770) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23771)  all_54_3 = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (23771) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23772)  all_52_12 = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23772) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23773)  all_52_12 = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (23773) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23774)   ~ (all_52_4 = e1)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (23773) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23775)   ~ (all_52_8 = e1)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23733), (23773) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23776)   ~ (e3 = e1)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17766), (23773) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23777)   ~ (e2 = e1)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23778)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23778) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23779)  all_58_4 = e1 & op(e3, e1) = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23779) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23780)  op(e3, e1) = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (23775), (23780), (function-axioms) are
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23781)  all_58_5 = e1 & op(e2, e1) = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23781) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23782)  all_58_5 = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23783)  all_54_2 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (23030), (23783) are inconsistent by
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23784)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23785)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23785) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23786)  all_58_6 = e1 & op(e1, e3) = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23786) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23787)  op(e1, e3) = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23788)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23788) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23789)  all_58_2 = e2 & op(e2, e3) = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23789) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23790)  op(e2, e3) = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23784) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23791)  all_54_2 = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (23791) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23792)  all_52_8 = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23792) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23793)  all_52_8 = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (23793) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23794)   ~ (all_52_4 = e2)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (23793) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23795)   ~ (all_52_9 = e2)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23795) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23796)   ~ (all_52_9 = e2)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23797)  all_54_6 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (23031), (23797) are inconsistent by
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23798)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23799)  all_54_1 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (23799) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23800)  all_52_4 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23800) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23801)  all_52_4 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (23801) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23802)   ~ (all_52_7 = e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23802) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23803)   ~ (all_52_7 = e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23804)  all_54_13 = e3
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (23803), (23804) are inconsistent by
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23805)   ~ (all_54_13 = e3)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23806)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23806) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23807)  all_54_13 = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17764), (23807) are inconsistent by
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2009.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23808)  all_54_13 = e1 | all_54_13 = e0
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23809)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23809) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23810)  op(e0, e2) = all_4_1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (170), (214), (235), (256), (270),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23025), (23038), (23523), (23525), (23526),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23696), (23722), (23725), (23741), (23748),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23754), (23764), (23787), (23790), (23796),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23798), (23803), (23808), (23810),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #35.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23811)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23811) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23812)  op(e0, e2) = all_4_1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (170), (214), (235), (256), (270),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23025), (23038), (23523), (23525), (23526),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23696), (23722), (23725), (23741), (23748),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23754), (23764), (23787), (23790), (23796),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23798), (23803), (23808), (23812),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #35.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23813)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (23523), (23774), (23794), (23813) are
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2048.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23814)  all_54_2 = e1 | all_54_2 = e0
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (23698), (23775), (23814) are inconsistent
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1336.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23815)  all_58_3 = e2 & op(e2, e2) = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23815) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23816)  all_58_3 = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23817)  op(e2, e2) = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (170), (235),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (238), (23523), (23759), (23764),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23816), (23817), (function-axioms) are
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #81.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23818)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23818) gives:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23819)  all_58_5 = e2 & op(e2, e1) = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23819) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23820)  all_58_5 = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23782), (23820) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23821)  e2 = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23764), (23821) imply:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23822)  all_58_7 = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (237), (23533), (23753), (23759),
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23822), (function-axioms) are inconsistent by
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1588.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23823)  all_58_10 = e2 & op(e2, e0) = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23823) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23824)  op(e2, e0) = e2
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (23824), (function-axioms) are
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23825)  all_58_7 = e1 & op(e1, e2) = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23825) implies:
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23826)  all_58_7 = e1
% 238.85/45.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (237), (23533), (23753), (23759),
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23826), (function-axioms) are inconsistent by
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1588.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23827)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23827) gives:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23828)  all_58_8 = e1 & op(e1, e1) = e1
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23828) implies:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23829)  op(e1, e1) = e1
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23038), (23829), (function-axioms) are
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #468.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23830)  all_58_11 = e1 & op(e1, e0) = e1
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23830) implies:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23831)  op(e1, e0) = e1
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (160), (280), (23718), (23770), (23831),
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1331.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23832)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (23038), (23708), (23832),
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #45.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23833)  all_54_3 = e0
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (23718), (23833) are inconsistent by
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2288.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23834)  all_58_13 = e2 & op(e0, e2) = e2
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23834) implies:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23835)  op(e0, e2) = e2
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (23835), (function-axioms) are
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23836)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23836) gives:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23837)  all_58_4 = e3 & op(e3, e1) = e3
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23837) implies:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23838)  op(e3, e1) = e3
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (23030), (23838), (function-axioms) are
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23839)  all_58_9 = e3 & op(e3, e0) = e3
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23839) implies:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23840)  op(e3, e0) = e3
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23741), (23840), (function-axioms) are
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23841)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (17773), (23708), (23841),
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #150.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (23842)  all_58_10 = e1 & op(e2, e0) = e1
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23738), (23842) are inconsistent by
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #47.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | |   (23843)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23843) gives:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (23844)  all_58_11 = e1 & op(e1, e0) = e1
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23844) implies:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (23845)  op(e1, e0) = e1
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23714), (23845), (function-axioms) are
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2284.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (23846)  all_58_15 = e1 & op(e0, e0) = e1
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23846) implies:
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (23847)  all_58_15 = e1
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (23847) are inconsistent by
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2231.
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.85/45.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | |   (23848)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (17774), (23033), (23848),
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | |            #214.
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | |   (23849)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23849) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | |   (23850)  all_54_7 = e2
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (17767), (23850) are inconsistent by
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1997.
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | |   (23851)   ~ (all_54_7 = e2)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | |   (23852)  all_54_7 = e1 | all_54_7 = e0
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23852) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | |   (23853)  all_54_7 = e1
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (23853) imply:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | |   (23854)  all_52_13 = e1
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23854) implies:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | |   (23855)  all_52_13 = e1
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (23855) imply:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | |   (23856)   ~ (all_52_1 = e1)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (23855) imply:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | |   (23857)   ~ (all_52_9 = e1)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (23855) imply:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | |   (23858)   ~ (all_52_12 = e1)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17767), (23855) imply:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | |   (23859)   ~ (e2 = e1)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (23855) imply:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | |   (23860)  op(e2, e0) = e1
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | |   (23861)  all_54_6 = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (23031), (23861) are inconsistent by
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | |   (23862)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (23863)  all_54_3 = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (23863) imply:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (23864)  all_52_12 = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (23864) implies:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (23865)  all_52_12 = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (23865) imply:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (23866)   ~ (all_52_4 = e3)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23867)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (170), (23039), (23866), (23867),
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            #442.
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (23868)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23868) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23869)  all_58_7 = e3 & op(e1, e2) = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23869) implies:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23870)  op(e1, e2) = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23518), (23728), (23860), (23870),
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1427.
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23871)  all_58_13 = e3 & op(e0, e2) = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23871) implies:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23872)  op(e0, e2) = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23873)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23873) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23874)  all_58_12 = e1 & op(e0, e3) = e1
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23874) implies:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23875)  all_58_12 = e1
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23876)  op(e0, e3) = e1
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23877)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23877) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23878)  all_58_4 = e1 & op(e3, e1) = e1
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23878) implies:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23879)  op(e3, e1) = e1
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23880)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23880) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23881)  all_58_0 = e3 & op(e3, e3) = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23881) implies:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23882)  op(e3, e3) = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (159), (163), (167), (239), (23522), (23697),
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23717), (23882), (function-axioms) are
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1938.
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23883)  all_58_2 = e3 & op(e2, e3) = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23883) implies:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23884)  all_58_2 = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23885)  op(e2, e3) = e3
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23728) gives:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23886)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_48_1 & $i(all_48_0) &
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_48_1)
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23886) implies:
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23887)  op(e2, e0) = all_48_1
% 238.92/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (123), (134), (136),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (146), (148), (149), (159), (162), (163), (164),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (169), (170), (200), (202), (203),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (213), (223), (224), (239), (243), (270),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (279), (281), (282), (17763), (17774), (23027),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23030), (23037), (23038), (23518), (23522),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23523), (23526), (23533), (23697), (23698),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23714), (23725), (23856), (23860), (23862),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23866), (23872), (23875), (23876), (23879),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23884), (23885), (23887), (function-axioms) are
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #34.
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23888)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_48_1)
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23888) implies:
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23889)  op(e2, e0) = all_48_1
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (123), (134), (136),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (146), (148), (149), (159), (162), (163), (164),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (169), (170), (200), (202), (203),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (213), (223), (224), (239), (243), (270),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (279), (281), (282), (17763), (17774), (23027),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23030), (23037), (23038), (23518), (23522),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23523), (23526), (23533), (23697), (23698),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23714), (23725), (23856), (23860), (23862),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23866), (23872), (23875), (23876), (23879),
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23884), (23885), (23889), (function-axioms) are
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #34.
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23890)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 238.93/45.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23890) gives:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23891)  all_58_6 = e3 & op(e1, e3) = e3
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23891) implies:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23892)  op(e1, e3) = e3
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (23028), (23892), (function-axioms) are
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23893)  all_58_12 = e3 & op(e0, e3) = e3
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23875), (23893) are inconsistent by
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1205.
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23894)  all_58_5 = e1 & op(e2, e1) = e1
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23894) implies:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23895)  op(e2, e1) = e1
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (23857), (23895), (function-axioms) are
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23896)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (23038), (23708), (23896),
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #45.
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23897)  all_58_13 = e1 & op(e0, e2) = e1
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23897) implies:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23898)  all_58_13 = e1
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23899)  op(e0, e2) = e1
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (97), (103), (110), (112), (113), (133),
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (158), (160), (164), (170), (193), (201),
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (238), (258), (280), (282), (17760),
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17761), (17766), (17768), (23039), (23518),
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23520), (23523), (23860), (23898), (23899),
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #84.
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (23900)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (17773), (23708), (23900),
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #150.
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (23901)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (17766), (23718), (23858), (23901) are
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | |   (23902)  all_54_7 = e0
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (23527), (23902) are inconsistent by
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2294.
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | Case 2:
% 238.93/45.79  | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | |   (23903)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 238.93/45.79  | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 238.93/45.79  | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | REF_CLOSE: (158), (162), (23524), (23525), (23903),
% 238.93/45.79  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.93/45.79  | | | | | | | | | | |            #1990.
% 238.93/45.79  | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | End of split
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | Case 2:
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | |   (23904)  all_10_2 = e1
% 238.93/45.79  | | | | | | | | |   (23905)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 238.93/45.79  | | | | | | | | |              op(e3, e1) = all_10_1 & $i(all_10_0) &
% 238.93/45.79  | | | | | | | | |              $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3, e1)
% 238.93/45.79  | | | | | | | | |              = all_10_1 & $i(all_10_1))
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | COMBINE_EQS: (349), (23904) imply:
% 238.93/45.79  | | | | | | | | |   (23906)  all_38_2 = e1
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | COMBINE_EQS: (290), (23904) imply:
% 238.93/45.79  | | | | | | | | |   (23907)  all_56_1 = e1
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | REDUCE: (355), (23904) imply:
% 238.93/45.79  | | | | | | | | |   (23908)   ~ (all_52_1 = e1)
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | REDUCE: (357), (23904) imply:
% 238.93/45.79  | | | | | | | | |   (23909)   ~ (all_52_2 = e1)
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | REDUCE: (359), (23904) imply:
% 238.93/45.79  | | | | | | | | |   (23910)   ~ (all_52_3 = e1)
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | REDUCE: (363), (23904) imply:
% 238.93/45.79  | | | | | | | | |   (23911)   ~ (all_52_8 = e1)
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | REDUCE: (365), (23904) imply:
% 238.93/45.79  | | | | | | | | |   (23912)   ~ (all_52_12 = e1)
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | REDUCE: (45), (23904) imply:
% 238.93/45.79  | | | | | | | | |   (23913)  op(e3, e3) = e1
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | BETA: splitting (52) gives:
% 238.93/45.79  | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | Case 1:
% 238.93/45.79  | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | |   (23914)   ~ (all_14_2 = e0)
% 238.93/45.79  | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | REDUCE: (344), (23914) imply:
% 238.93/45.79  | | | | | | | | | |   (23915)   ~ (all_8_2 = e0)
% 238.93/45.79  | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | BETA: splitting (64) gives:
% 238.93/45.79  | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | Case 1:
% 238.93/45.79  | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | |   (23916)   ~ (all_22_2 = e1)
% 238.93/45.79  | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | REDUCE: (326), (23916) imply:
% 238.93/45.79  | | | | | | | | | | |   (23917)   ~ (all_8_2 = e1)
% 238.93/45.79  | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | BETA: splitting (199) gives:
% 238.93/45.79  | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | Case 1:
% 238.93/45.79  | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | |   (23918)  all_54_5 = e3
% 238.93/45.79  | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | COMBINE_EQS: (275), (23918) imply:
% 238.93/45.79  | | | | | | | | | | | |   (23919)  all_8_2 = e3
% 238.93/45.79  | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | REDUCE: (23039), (23919) imply:
% 238.93/45.79  | | | | | | | | | | | |   (23920)  $false
% 238.93/45.79  | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | CLOSE: (23920) is inconsistent.
% 238.93/45.79  | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | Case 2:
% 238.93/45.79  | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | |   (23921)   ~ (all_54_5 = e3)
% 238.93/45.79  | | | | | | | | | | | |   (23922)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 238.93/45.79  | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | BETA: splitting (23922) gives:
% 238.93/45.79  | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | Case 1:
% 238.93/45.79  | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | |   (23923)  all_54_5 = e2
% 238.93/45.79  | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | COMBINE_EQS: (275), (23923) imply:
% 238.93/45.79  | | | | | | | | | | | | |   (23924)  all_8_2 = e2
% 238.93/45.79  | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | REDUCE: (371), (23924) imply:
% 238.93/45.79  | | | | | | | | | | | | |   (23925)   ~ (all_52_6 = e2)
% 238.93/45.79  | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | REDUCE: (375), (23924) imply:
% 238.93/45.79  | | | | | | | | | | | | |   (23926)   ~ (all_52_9 = e2)
% 238.93/45.79  | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | REDUCE: (23039), (23924) imply:
% 238.93/45.79  | | | | | | | | | | | | |   (23927)   ~ (e3 = e2)
% 238.93/45.79  | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | BETA: splitting (229) gives:
% 238.93/45.79  | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | Case 1:
% 238.93/45.79  | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | |   (23928)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 238.93/45.79  | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 238.93/45.79  | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | BETA: splitting (23928) gives:
% 238.93/45.79  | | | | | | | | | | | | | | 
% 238.93/45.79  | | | | | | | | | | | | | | Case 1:
% 238.93/45.80  | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | |   (23929)  all_58_4 = e2 & op(e3, e1) = e2
% 238.93/45.80  | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | ALPHA: (23929) implies:
% 238.93/45.80  | | | | | | | | | | | | | | |   (23930)  all_58_4 = e2
% 238.93/45.80  | | | | | | | | | | | | | | |   (23931)  op(e3, e1) = e2
% 238.93/45.80  | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 238.93/45.80  | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | Case 1:
% 238.93/45.80  | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | |   (23932)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 238.93/45.80  | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 238.93/45.80  | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | BETA: splitting (23932) gives:
% 238.93/45.80  | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | Case 1:
% 238.93/45.80  | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | |   (23933)  all_58_6 = e2 & op(e1, e3) = e2
% 238.93/45.80  | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | ALPHA: (23933) implies:
% 238.93/45.80  | | | | | | | | | | | | | | | | |   (23934)  op(e1, e3) = e2
% 238.93/45.80  | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 238.93/45.80  | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (23934) gives:
% 238.93/45.80  | | | | | | | | | | | | | | | | |   (23935)  all_52_2 = e2
% 238.93/45.80  | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 238.93/45.80  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (23931) gives:
% 238.93/45.80  | | | | | | | | | | | | | | | | |   (23936)  all_52_8 = e2
% 238.93/45.80  | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | REDUCE: (149), (23935) imply:
% 238.93/45.80  | | | | | | | | | | | | | | | | |   (23937)   ~ (all_52_1 = e2)
% 238.93/45.80  | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | REDUCE: (144), (23935) imply:
% 238.93/45.80  | | | | | | | | | | | | | | | | |   (23938)   ~ (all_52_3 = e2)
% 238.93/45.80  | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | REDUCE: (123), (23936) imply:
% 238.93/45.80  | | | | | | | | | | | | | | | | |   (23939)   ~ (all_52_9 = e2)
% 238.93/45.80  | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | REDUCE: (121), (23936) imply:
% 238.93/45.80  | | | | | | | | | | | | | | | | |   (23940)   ~ (all_52_11 = e2)
% 238.93/45.80  | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 238.93/45.80  | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | Case 1:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | |   (23941)   ~ (all_38_2 = e1)
% 238.93/45.80  | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | REDUCE: (23906), (23941) imply:
% 238.93/45.80  | | | | | | | | | | | | | | | | | |   (23942)  $false
% 238.93/45.80  | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | CLOSE: (23942) is inconsistent.
% 238.93/45.80  | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | |   (23943)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 238.93/45.80  | | | | | | | | | | | | | | | | | |              & op(e3, e1) = all_38_1 & $i(all_38_0) &
% 238.93/45.80  | | | | | | | | | | | | | | | | | |              $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1)
% 238.93/45.80  | | | | | | | | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 238.93/45.80  | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | Case 1:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | |   (23944)   ~ (all_46_2 = e3)
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | REDUCE: (23026), (23944) imply:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | |   (23945)  $false
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | CLOSE: (23945) is inconsistent.
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | |   (23946)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 238.93/45.80  | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 238.93/45.80  | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 238.93/45.80  | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | BETA: splitting (23905) gives:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | |   (23947)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_10_1 & $i(all_10_0) &
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | ALPHA: (23947) implies:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | |   (23948)   ~ (all_10_0 = e0)
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | |   (23949)  op(e3, e1) = all_10_1
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | |   (23950)  op(all_10_1, e3) = all_10_0
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | BETA: splitting (23946) gives:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | |   (23951)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_46_1 & $i(all_46_0) &
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | ALPHA: (23951) implies:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | |   (23952)   ~ (all_46_0 = e0)
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | |   (23953)  op(e1, e3) = all_46_1
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | |   (23954)  op(all_46_1, e1) = all_46_0
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23025) gives:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | |   (23955)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 &
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23955) implies:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | |   (23956)  op(e1, e3) = all_6_1
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (139), (148), (165), (167), (190), (192),
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | |            (198), (200), (255), (257), (270), (279), (17763),
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | |            (17765), (23031), (23032), (23908), (23910),
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | |            (23926), (23931), (23934), (23937), (23948),
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | |            (23949), (23950), (23952), (23953), (23954),
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | |            (23956), (function-axioms) are inconsistent by
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #33.
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | |   (23957)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 &
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | |            $i(all_6_1)
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | | 
% 238.93/45.80  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (23957) implies:
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | |   (23958)  op(e1, e3) = all_6_1
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (139), (148), (165), (167), (190), (192),
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | |            (198), (200), (255), (257), (270), (279), (17763),
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | |            (17765), (23031), (23032), (23908), (23910),
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | |            (23926), (23931), (23934), (23937), (23948),
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | |            (23949), (23950), (23952), (23953), (23954),
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | |            (23958), (function-axioms) are inconsistent by
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #33.
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | |   (23959)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 &
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23934), (23959), (function-axioms) are
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #395.
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | |   (23960)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23931), (23943), (23960), (function-axioms) are
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1113.
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | |   (23961)  all_58_7 = e2 & op(e1, e2) = e2
% 238.94/45.80  | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | ALPHA: (23961) implies:
% 238.94/45.80  | | | | | | | | | | | | | | | | |   (23962)  op(e1, e2) = e2
% 238.94/45.80  | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (23925), (23962), (function-axioms) are
% 238.94/45.80  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #249.
% 238.94/45.80  | | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | |   (23963)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 238.94/45.80  | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 238.94/45.80  | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (160), (165),
% 238.94/45.80  | | | | | | | | | | | | | | | |            (227), (228), (230), (17768), (23032), (23930),
% 238.94/45.80  | | | | | | | | | | | | | | | |            (23963), (function-axioms) are inconsistent by
% 238.94/45.80  | | | | | | | | | | | | | | | |            sub-proof #58.
% 238.94/45.80  | | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | |   (23964)  all_58_5 = e2 & op(e2, e1) = e2
% 238.94/45.80  | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | ALPHA: (23964) implies:
% 238.94/45.80  | | | | | | | | | | | | | | |   (23965)  op(e2, e1) = e2
% 238.94/45.80  | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | REF_CLOSE: (165), (23926), (23965), (function-axioms) are
% 238.94/45.80  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2328.
% 238.94/45.80  | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | |   (23966)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 238.94/45.80  | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 238.94/45.80  | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17765), (23038), (23966),
% 238.94/45.80  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.94/45.80  | | | | | | | | | | | | | |            #57.
% 238.94/45.80  | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | |   (23967)  all_54_5 = e1 | all_54_5 = e0
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | REF_CLOSE: (275), (23915), (23917), (23967) are inconsistent
% 238.94/45.80  | | | | | | | | | | | | |            by sub-proof #2300.
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | |   (23968)  all_22_2 = e1
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | COMBINE_EQS: (326), (23968) imply:
% 238.94/45.80  | | | | | | | | | | |   (23969)  all_8_2 = e1
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | COMBINE_EQS: (353), (23969) imply:
% 238.94/45.80  | | | | | | | | | | |   (23970)  all_56_11 = e1
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | REDUCE: (369), (23969) imply:
% 238.94/45.80  | | | | | | | | | | |   (23971)   ~ (all_52_4 = e1)
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | REDUCE: (371), (23969) imply:
% 238.94/45.80  | | | | | | | | | | |   (23972)   ~ (all_52_6 = e1)
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | REDUCE: (373), (23969) imply:
% 238.94/45.80  | | | | | | | | | | |   (23973)   ~ (all_52_7 = e1)
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | REDUCE: (375), (23969) imply:
% 238.94/45.80  | | | | | | | | | | |   (23974)   ~ (all_52_9 = e1)
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | REDUCE: (377), (23969) imply:
% 238.94/45.80  | | | | | | | | | | |   (23975)   ~ (all_52_13 = e1)
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | REDUCE: (23039), (23969) imply:
% 238.94/45.80  | | | | | | | | | | |   (23976)   ~ (e3 = e1)
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | REDUCE: (42), (23969) imply:
% 238.94/45.80  | | | | | | | | | | |   (23977)  op(e2, e2) = e1
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | BETA: splitting (228) gives:
% 238.94/45.80  | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | Case 1:
% 238.94/45.80  | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | |   (23978)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 238.94/45.80  | | | | | | | | | | | |              & op(e2, e1) = e1)
% 238.94/45.80  | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | REF_CLOSE: (165), (169), (23911), (23974), (23978),
% 238.94/45.80  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.94/45.80  | | | | | | | | | | | |            #1211.
% 238.94/45.80  | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | |   (23979)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 238.94/45.80  | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 238.94/45.80  | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | BETA: splitting (23979) gives:
% 238.94/45.80  | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | Case 1:
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | |   (23980)  all_58_8 = e1 & op(e1, e1) = e1
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | ALPHA: (23980) implies:
% 238.94/45.80  | | | | | | | | | | | | |   (23981)  op(e1, e1) = e1
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | REF_CLOSE: (8), (23038), (23981), (function-axioms) are
% 238.94/45.80  | | | | | | | | | | | | |            inconsistent by sub-proof #468.
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | |   (23982)  all_58_14 = e1 & op(e0, e1) = e1
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | ALPHA: (23982) implies:
% 238.94/45.80  | | | | | | | | | | | | |   (23983)  op(e0, e1) = e1
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.94/45.80  | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | Case 1:
% 238.94/45.80  | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | |   (23984)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.94/45.80  | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.94/45.80  | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | BETA: splitting (23984) gives:
% 238.94/45.80  | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | Case 1:
% 238.94/45.80  | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | |   (23985)  all_58_9 = e1 & op(e3, e0) = e1
% 238.94/45.80  | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | REF_CLOSE: (168), (23912), (23985), (function-axioms) are
% 238.94/45.80  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2278.
% 238.94/45.80  | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | |   (23986)  all_58_10 = e1 & op(e2, e0) = e1
% 238.94/45.80  | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | | REF_CLOSE: (164), (23975), (23986), (function-axioms) are
% 238.94/45.80  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2277.
% 238.94/45.80  | | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | | End of split
% 238.94/45.80  | | | | | | | | | | | | | | 
% 238.94/45.80  | | | | | | | | | | | | | Case 2:
% 238.94/45.80  | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | |   (23987)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.94/45.81  | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.94/45.81  | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | BETA: splitting (23987) gives:
% 238.94/45.81  | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | |   (23988)  all_58_11 = e1 & op(e1, e0) = e1
% 238.94/45.81  | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | ALPHA: (23988) implies:
% 238.94/45.81  | | | | | | | | | | | | | | |   (23989)  all_58_11 = e1
% 238.94/45.81  | | | | | | | | | | | | | | |   (23990)  op(e1, e0) = e1
% 238.94/45.81  | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | |   (23991)   ~ (all_44_2 = e2)
% 238.94/45.81  | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | REDUCE: (17761), (23991) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | |   (23992)  $false
% 238.94/45.81  | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | CLOSE: (23992) is inconsistent.
% 238.94/45.81  | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | |   (23993)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.94/45.81  | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.94/45.81  | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.94/45.81  | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.94/45.81  | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | |   (23994)   ~ (all_46_2 = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | REDUCE: (23026), (23994) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | |   (23995)  $false
% 238.94/45.81  | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | CLOSE: (23995) is inconsistent.
% 238.94/45.81  | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | |   (23996)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 238.94/45.81  | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 238.94/45.81  | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 238.94/45.81  | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | |   (23997)  all_54_9 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (23029), (23997) are inconsistent by
% 238.94/45.81  | | | | | | | | | | | | | | | | | |            sub-proof #1955.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | |   (23998)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | |   (23999)  all_54_3 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (23999) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | |   (24000)  all_52_12 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | SIMP: (24000) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | |   (24001)  all_52_12 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | REDUCE: (113), (24001) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | |   (24002)   ~ (all_52_13 = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | SIMP: (24002) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | |   (24003)   ~ (all_52_13 = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | |   (24004)  all_54_7 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (24004) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | |   (24005)  all_52_13 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | REDUCE: (24003), (24005) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | |   (24006)  $false
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | CLOSE: (24006) is inconsistent.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | |   (24007)   ~ (all_54_7 = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | |   (24008)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | BETA: splitting (24008) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | |   (24009)  all_54_7 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (24009) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | |   (24010)  all_52_13 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | REDUCE: (17767), (24010) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | |   (24011)  $false
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | CLOSE: (24011) is inconsistent.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | |   (24012)  all_54_7 = e1 | all_54_7 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24012) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |   (24013)  all_54_7 = e1
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (23975), (24013) are inconsistent by
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |   (24014)  all_54_7 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (24014) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |   (24015)  all_52_13 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | SIMP: (24015) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |   (24016)  all_52_13 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (24016) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |   (24017)   ~ (all_52_1 = e0)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (24016) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |   (24018)   ~ (all_52_9 = e0)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | |   (24019)  all_54_6 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (24019) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | |   (24020)  all_52_9 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23031), (24020) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | |   (24021)  $false
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24021) is inconsistent.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | |   (24022)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24022) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | |   (24023)  all_54_6 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (24023) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | |   (24024)  all_52_9 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24024) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | |   (24025)  all_52_9 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (24025) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | |   (24026)   ~ (all_52_1 = e2)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (24025) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | |   (24027)   ~ (all_52_8 = e2)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (24025) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | |   (24028)  op(e2, e1) = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (24029)  all_54_4 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (24029) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (24030)  all_52_1 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24030) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (24031)  all_52_1 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (24031) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (24032)   ~ (all_52_2 = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (24031) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (24033)   ~ (all_52_3 = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24033) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (24034)   ~ (all_52_3 = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24035)  all_54_2 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (23030), (24035) are inconsistent by
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24036)   ~ (all_54_2 = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24037)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24038)  all_54_12 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (24034), (24038) are inconsistent by
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2266.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24039)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24037) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24040)  all_54_2 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (24027), (24040) are inconsistent by
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1986.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24041)   ~ (all_54_2 = e2)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24042)  all_54_2 = e1 | all_54_2 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24039) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24043)  all_54_12 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (24043) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24044)  all_52_3 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17763), (24044) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24045)  $false
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24045) is inconsistent.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24046)  all_54_12 = e1 | all_54_12 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24046) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24047)  all_54_12 = e1
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (24047) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24048)  all_52_3 = e1
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23910), (24048) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24049)  $false
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24049) is inconsistent.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24050)  all_54_12 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (24050) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24051)  all_52_3 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (24051) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24052)   ~ (all_52_2 = e0)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (24051) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24053)  op(e0, e3) = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24054)  all_54_8 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (23028), (24054) are inconsistent by
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24055)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24056)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24056) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24057)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24057) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24058)  op(e3, all_56_1) = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23907), (24058) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24059)  op(e3, e1) = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (23030), (24059), (function-axioms) are
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24060)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24060) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24061)  op(e2, e3) = all_56_3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24062)  op(e2, all_56_3) = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24063)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (23039), (24061), (24062), (24063),
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #130.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24064)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (24003), (24028), (24064),
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1913.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24065)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24065) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24066)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24066) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24067)  op(e1, e3) = all_56_5
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24068)  op(e1, all_56_5) = e1
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24055) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24069)  all_54_8 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (24069) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24070)  all_52_2 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24070) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24071)  all_52_2 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (24071) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24072)   ~ (all_52_6 = e2)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24072) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24073)   ~ (all_52_6 = e2)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (24071) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24074)  op(e1, e3) = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23025) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24075)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 &
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24075) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24076)  op(e1, e3) = all_6_1
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (267), (23972), (23996), (23998), (24067),
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24068), (24073), (24074), (24076),
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #32.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24077)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 &
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_6_1)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24077) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24078)  op(e1, e3) = all_6_1
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (267), (23972), (23996), (23998), (24067),
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24068), (24073), (24074), (24078),
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #32.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24079)  all_54_8 = e1 | all_54_8 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (23909), (24052), (24079) are inconsistent
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1950.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24080)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (17774), (23911), (24027), (24042),
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24053), (24080), (function-axioms) are
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #44.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (24081)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (23908), (24017), (24026), (24081) are
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1921.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | |   (24082)  all_54_6 = e1 | all_54_6 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (23974), (24018), (24082) are inconsistent
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #476.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | End of split
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | |   (24083)   ~ (all_54_3 = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | |   (24084)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | REDUCE: (280), (24083) imply:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | |   (24085)   ~ (all_52_12 = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | BETA: splitting (24084) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | |   (24086)  all_54_3 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (17766), (24086) are inconsistent by
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | |            sub-proof #2290.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | |   (24087)   ~ (all_54_3 = e2)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | |   (24088)  all_54_3 = e1 | all_54_3 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | |   (24089)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24089) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |   (24090)  all_58_0 = e3 & op(e3, e3) = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24090) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |   (24091)  op(e3, e3) = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (23908), (23909),
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |            (23910), (24091), (function-axioms) are
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |   (24092)  all_58_1 = e3 & op(e3, e2) = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24092) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | |   (24093)  op(e3, e2) = e3
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | |   (24094)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (23913), (24093), (24094),
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | |            #348.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | |   (24095)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24095) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | |   (24096)  all_58_4 = e2 & op(e3, e1) = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24096) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | |   (24097)  all_58_4 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (24098)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (23977), (24093), (24098),
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |            #1785.
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (24099)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24099) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24100)  all_58_7 = e2 & op(e1, e2) = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24100) implies:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24101)  all_58_7 = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24102)  op(e1, e2) = e2
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24103)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24103) gives:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.94/45.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.94/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24104)  all_58_4 = e0 & op(e3, e1) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (24097), (24104) are inconsistent by
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2170.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24105)  all_58_5 = e0 & op(e2, e1) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24105) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24106)  op(e2, e1) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24107)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24107) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24108)  all_58_2 = e2 & op(e2, e3) = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24108) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24109)  all_58_2 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24110)  op(e2, e3) = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24088) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24111)  all_54_3 = e1
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (23912), (24111) are inconsistent by
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2289.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24112)  all_54_3 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (24112) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24113)  all_52_12 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24113) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24114)  all_52_12 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (24114) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24115)   ~ (all_52_4 = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (24114) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24116)   ~ (all_52_8 = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (24114) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24117)   ~ (all_52_13 = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24117) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24118)   ~ (all_52_13 = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23912), (24114) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24119)   ~ (e1 = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24120)  all_54_7 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (24120) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24121)  all_52_13 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (24121) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24122)   ~ (all_52_1 = e3)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24123)  all_54_2 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (23030), (24123) are inconsistent by
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1987.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24124)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24124) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24125)  all_54_2 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (24125) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24126)  all_52_8 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24126) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24127)  all_52_8 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (24127) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24128)   ~ (all_52_4 = e2)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (24127) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24129)   ~ (all_52_9 = e2)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24129) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24130)   ~ (all_52_9 = e2)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24131)  all_54_6 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (23031), (24131) are inconsistent by
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1825.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24132)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24133)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (23908), (23909),
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23910), (24122), (24133), (function-axioms) are
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24134)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24134) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24135)  all_58_6 = e3 & op(e1, e3) = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24135) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24136)  op(e1, e3) = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (23028), (24136), (function-axioms) are
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24137)  all_58_12 = e3 & op(e0, e3) = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24137) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24138)  op(e0, e3) = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24139)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (23913), (24109), (24139),
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1534.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24140)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24140) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24141)  all_58_6 = e0 & op(e1, e3) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24141) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24142)  all_58_6 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24132) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24143)  all_54_6 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (24143) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24144)  all_52_9 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24130), (24144) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24145)  $false
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24145) is inconsistent.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24146)   ~ (all_54_6 = e2)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24147)  all_54_6 = e1 | all_54_6 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24147) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24148)  all_54_6 = e1
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (24148) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24149)  all_52_9 = e1
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23974), (24149) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24150)  $false
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24150) is inconsistent.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24151)  all_54_6 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (24151) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24152)  all_52_9 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (24152) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24153)   ~ (all_52_1 = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24130), (24152) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24154)   ~ (e2 = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24155)  all_54_4 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (24122), (24155) are inconsistent by
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2100.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24156)   ~ (all_54_4 = e3)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24157)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24158)  all_54_1 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (24158) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24159)  all_52_4 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24159) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24160)  all_52_4 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (24160) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24161)   ~ (all_52_7 = e3)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24161) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24162)   ~ (all_52_7 = e3)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24163)  all_54_13 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (24163) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24164)  all_52_7 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24162), (24164) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24165)  $false
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24165) is inconsistent.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24166)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24167)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24167) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24168)  all_58_0 = e0 & op(e3, e3) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24168) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24169)  op(e3, e3) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (241), (243),
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (24122), (24142), (24169),
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1441.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24170)  all_58_1 = e0 & op(e3, e2) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (24115), (24170), (function-axioms) are
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1968.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24171)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24171) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24172)  all_58_4 = e0 & op(e3, e1) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (24116), (24172), (function-axioms) are
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24173)  all_58_9 = e0 & op(e3, e0) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24173) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24174)  all_58_9 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24157) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24175)  all_54_4 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (24175) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24176)  all_52_1 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24176) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24177)  all_52_1 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (24177) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24178)   ~ (all_52_2 = e2)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24178) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24179)   ~ (all_52_2 = e2)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24122), (24177) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24180)   ~ (e3 = e2)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24181)  all_54_8 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (23028), (24181) are inconsistent by
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2011.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24182)   ~ (all_54_8 = e3)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24183)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24184)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (42), (244), (246),
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23913), (23915), (24174), (24184),
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1088.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24185)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24185) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24186)  all_58_7 = e0 & op(e1, e2) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24186) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24187)  all_58_7 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24101), (24187) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24188)  e2 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24097), (24188) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24189)  all_58_4 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (23913),
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24174), (24189), (function-axioms) are
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1190.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24190)  all_58_13 = e0 & op(e0, e2) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24190) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24191)  op(e0, e2) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24183) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24192)  all_54_8 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (24179), (24192) are inconsistent by
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2007.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24193)   ~ (all_54_8 = e2)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24194)  all_54_8 = e1 | all_54_8 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24194) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24195)  all_54_8 = e1
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (23909), (24195) are inconsistent by
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1951.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24196)  all_54_8 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (24196) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24197)  all_52_2 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24197) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24198)  all_52_2 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (24198) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24199)   ~ (all_52_6 = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24199) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24200)   ~ (all_52_6 = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23028), (24198) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24201)   ~ (e3 = e0)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (24198) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24202)  op(e1, e3) = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24203)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, all_56_11) = e2)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24203) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24204)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_9 & $i(all_56_9)
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24204) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24205)  op(e3, e2) = all_56_9
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24206)  op(e3, all_56_9) = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24166) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24207)  all_54_13 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (24207) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24208)  all_52_7 = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17764), (24208) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24209)  $false
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24209) is inconsistent.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24210)  all_54_13 = e1 | all_54_13 = e0
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24210) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24211)  all_54_13 = e1
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (24211) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24212)  all_52_7 = e1
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23973), (24212) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24213)  $false
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24213) is inconsistent.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_9,
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (24093), (24205) gives:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24214)  all_56_9 = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24206), (24214) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24215)  op(e3, e3) = e3
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (163), (167), (241), (23908), (23909),
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23910), (24215), (function-axioms) are
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #440.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24216)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24216) implies:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24217)  op(e2, all_56_11) = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23970), (24217) imply:
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24218)  op(e2, e1) = e2
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (165), (279), (23908), (24153), (24157),
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24218), (function-axioms) are inconsistent by
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #173.
% 238.95/45.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24219)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15 & $i(all_56_15))
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24219) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24220)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24220) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24221)  op(e1, e2) = all_56_13
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24222)  op(e1, all_56_13) = e1
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23025) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24223)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 &
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24223) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24224)  op(e1, e3) = all_6_1
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (225),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (23033), (23989), (23990), (23996),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24101), (24102), (24202), (24221), (24222),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24224), (function-axioms) are inconsistent by
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #353.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24225)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 &
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_6_1)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23996), (24202), (24225), (function-axioms) are
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #443.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24226)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_15 & $i(all_56_15)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24226) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24227)  op(e0, e2) = all_56_15
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24228)  op(e0, all_56_15) = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (24191),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (24227) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24229)  all_56_15 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24228), (24229) imply:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24230)  op(e0, e0) = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (159), (162),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (219), (235), (244), (246), (23910),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23913), (23915), (24174), (24200), (24230),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1087.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24231)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24231) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24232)   ~ (all_4_1 = e3)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24233)  op(e0, e2) = all_4_1
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23993) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24234)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24234) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24235)  op(e0, e2) = all_44_1
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_44_1, e2, e0, simplifying with (24233),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (24235) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24236)  all_44_1 = all_4_1
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_44_1,
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (24227),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (24235) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24237)  all_56_15 = all_44_1
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (24191),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (24227) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24238)  all_56_15 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24237), (24238) imply:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24239)  all_44_1 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24239) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24240)  all_44_1 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24236), (24240) imply:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24241)  all_4_1 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24241) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24242)  all_4_1 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (42), (159), (162),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (219), (235), (244), (246), (23910),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23913), (23915), (24174), (24200), (24228),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24232), (24238), (24242), (function-axioms) are
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #31.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24243)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 &
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24243) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24244)   ~ (all_44_1 = e1)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24245)  op(e0, e2) = all_44_1
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_44_1, e2, e0, simplifying with (24233),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (24245) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24246)  all_44_1 = all_4_1
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_44_1,
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (24227),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (24245) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24247)  all_56_15 = all_44_1
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (24191),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (24227) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24248)  all_56_15 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24247), (24248) imply:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24249)  all_44_1 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24249) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24250)  all_44_1 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24246), (24250) imply:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24251)  all_4_1 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (24251) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24252)  all_4_1 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (42), (159), (162),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (219), (235), (244), (246), (23910),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23913), (23915), (24174), (24200), (24228),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24232), (24248), (24252), (function-axioms) are
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #31.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24253)  all_54_4 = e1 | all_54_4 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (23908), (24153), (24253) are inconsistent
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1922.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24254)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (23971), (24115), (24128), (24254) are
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2048.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24255)  all_58_12 = e0 & op(e0, e3) = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24255) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24256)  op(e0, e3) = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (24138), (24256), (function-axioms) are
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #221.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24257)  all_54_2 = e1 | all_54_2 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (281), (23911), (24116), (24257) are inconsistent
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1336.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24258)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (269), (23975), (24110), (24118),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24258), (function-axioms) are inconsistent by
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2292.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24259)  all_58_3 = e2 & op(e2, e2) = e2
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24259) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24260)  op(e2, e2) = e2
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (23977), (24260), (function-axioms) are
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2235.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24261)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24261) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24262)  all_58_5 = e2 & op(e2, e1) = e2
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24262) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24263)  op(e2, e1) = e2
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (24106), (24263), (function-axioms) are
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1906.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24264)  all_58_10 = e2 & op(e2, e0) = e2
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24264) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24265)  op(e2, e0) = e2
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (24265), (function-axioms) are
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24266)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (157), (165), (230), (23031),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23032), (23983), (24097), (24266),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #401.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24267)  all_58_13 = e2 & op(e0, e2) = e2
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24267) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24268)  op(e0, e2) = e2
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (24268), (function-axioms) are
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | |   (24269)  all_58_9 = e2 & op(e3, e0) = e2
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24269) implies:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | |   (24270)  op(e3, e0) = e2
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24084) gives:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (24271)  all_54_3 = e2
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (17766), (24271) are inconsistent by
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2290.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (280), (17766), (23912), (24088), (24270),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | |            #2153.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | |   (24272)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (23030), (24085), (24272),
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | |            #1515.
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | |   (24273)  all_58_15 = e1 & op(e0, e0) = e1
% 238.95/45.83  | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | | REF_CLOSE: (6), (17773), (24273) are inconsistent by
% 238.95/45.83  | | | | | | | | | | | | | | |            sub-proof #218.
% 238.95/45.83  | | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | |   (24274)  all_14_2 = e0
% 238.95/45.83  | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | COMBINE_EQS: (344), (24274) imply:
% 238.95/45.83  | | | | | | | | | |   (24275)  all_8_2 = e0
% 238.95/45.83  | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | SIMP: (24275) implies:
% 238.95/45.83  | | | | | | | | | |   (24276)  all_8_2 = e0
% 238.95/45.83  | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | COMBINE_EQS: (353), (24276) imply:
% 238.95/45.83  | | | | | | | | | |   (24277)  all_56_11 = e0
% 238.95/45.83  | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | REDUCE: (377), (24276) imply:
% 238.95/45.83  | | | | | | | | | |   (24278)   ~ (all_52_13 = e0)
% 238.95/45.83  | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | BETA: splitting (213) gives:
% 238.95/45.83  | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | Case 1:
% 238.95/45.83  | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | |   (24279)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.95/45.83  | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.95/45.83  | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.95/45.83  | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.95/45.83  | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.95/45.83  | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.95/45.83  | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.95/45.83  | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.95/45.83  | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.95/45.83  | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.95/45.83  | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.95/45.83  | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.95/45.83  | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.95/45.83  | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.95/45.83  | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.95/45.83  | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.95/45.83  | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.95/45.83  | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.95/45.83  | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.95/45.83  | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.95/45.83  | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.95/45.83  | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | BETA: splitting (24279) gives:
% 238.95/45.83  | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | Case 1:
% 238.95/45.83  | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | |   (24280)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.95/45.83  | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.95/45.83  | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.95/45.83  | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.95/45.83  | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.95/45.83  | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.95/45.83  | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.95/45.83  | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.95/45.83  | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.95/45.83  | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.95/45.83  | | | | | | | | | | | |              = e3)
% 238.95/45.83  | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | REF_CLOSE: (163), (17762), (23027), (23028), (24280),
% 238.95/45.83  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.83  | | | | | | | | | | | |            #48.
% 238.95/45.83  | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | |   (24281)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.95/45.83  | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.95/45.83  | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.95/45.83  | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.95/45.83  | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.95/45.83  | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.95/45.83  | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.95/45.83  | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.95/45.83  | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.95/45.83  | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.95/45.83  | | | | | | | | | | | |              = e0)
% 238.95/45.83  | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | BETA: splitting (24281) gives:
% 238.95/45.83  | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | Case 1:
% 238.95/45.83  | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | |   (24282)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.95/45.83  | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.95/45.83  | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.95/45.83  | | | | | | | | | | | | |              e3) = e1
% 238.95/45.83  | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | ALPHA: (24282) implies:
% 238.95/45.83  | | | | | | | | | | | | |   (24283)  op(e3, e1) = e1
% 238.95/45.83  | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | REF_CLOSE: (169), (23911), (24283), (function-axioms) are
% 238.95/45.83  | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.95/45.83  | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | |   (24284)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.95/45.83  | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.95/45.83  | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.95/45.83  | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.95/45.83  | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.95/45.83  | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.95/45.83  | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.95/45.83  | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | | REF_CLOSE: (23027), (24277), (24284) are inconsistent by
% 238.95/45.83  | | | | | | | | | | | | |            sub-proof #439.
% 238.95/45.83  | | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | | End of split
% 238.95/45.83  | | | | | | | | | | | 
% 238.95/45.83  | | | | | | | | | | Case 2:
% 238.95/45.83  | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | |   (24285)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.95/45.84  | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.95/45.84  | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.95/45.84  | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.95/45.84  | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.95/45.84  | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.95/45.84  | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.95/45.84  | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.95/45.84  | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.95/45.84  | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.95/45.84  | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.95/45.84  | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.95/45.84  | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.95/45.84  | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.95/45.84  | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.95/45.84  | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.95/45.84  | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.95/45.84  | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.95/45.84  | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.95/45.84  | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.95/45.84  | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.95/45.84  | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | BETA: splitting (24285) gives:
% 238.95/45.84  | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | |   (24286)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.95/45.84  | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.95/45.84  | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.95/45.84  | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.95/45.84  | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.95/45.84  | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.95/45.84  | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.95/45.84  | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.95/45.84  | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.95/45.84  | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.95/45.84  | | | | | | | | | | | |              = e2)
% 238.95/45.84  | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | REF_CLOSE: (158), (17762), (17764), (23907), (24286),
% 238.95/45.84  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.84  | | | | | | | | | | | |            #67.
% 238.95/45.84  | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | |   (24287)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.95/45.84  | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.95/45.84  | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.95/45.84  | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.95/45.84  | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.95/45.84  | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.95/45.84  | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.95/45.84  | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.95/45.84  | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.95/45.84  | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.95/45.84  | | | | | | | | | | | |              = e0)
% 238.95/45.84  | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | REF_CLOSE: (164), (23907), (24277), (24278), (24287),
% 238.95/45.84  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.84  | | | | | | | | | | | |            #1238.
% 238.95/45.84  | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | | 
% 238.95/45.84  | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | 
% 238.95/45.84  | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | 
% 238.95/45.84  | | | | | | | |   (24288)  all_8_2 = e3
% 238.95/45.84  | | | | | | | |   (24289)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 238.95/45.84  | | | | | | | |              op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)) |
% 238.95/45.84  | | | | | | | |            ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 238.95/45.84  | | | | | | | |              $i(all_8_1))
% 238.95/45.84  | | | | | | | | 
% 238.95/45.84  | | | | | | | | COMBINE_EQS: (320), (24288) imply:
% 238.95/45.84  | | | | | | | |   (24290)  all_42_2 = e3
% 238.95/45.84  | | | | | | | | 
% 238.95/45.84  | | | | | | | | COMBINE_EQS: (353), (24288) imply:
% 238.95/45.84  | | | | | | | |   (24291)  all_56_11 = e3
% 238.95/45.84  | | | | | | | | 
% 238.95/45.84  | | | | | | | | REDUCE: (369), (24288) imply:
% 238.95/45.84  | | | | | | | |   (24292)   ~ (all_52_4 = e3)
% 238.95/45.84  | | | | | | | | 
% 238.95/45.84  | | | | | | | | REDUCE: (373), (24288) imply:
% 238.95/45.84  | | | | | | | |   (24293)   ~ (all_52_7 = e3)
% 238.95/45.84  | | | | | | | | 
% 238.95/45.84  | | | | | | | | REDUCE: (377), (24288) imply:
% 238.95/45.84  | | | | | | | |   (24294)   ~ (all_52_13 = e3)
% 238.95/45.84  | | | | | | | | 
% 238.95/45.84  | | | | | | | | BETA: splitting (219) gives:
% 238.95/45.84  | | | | | | | | 
% 238.95/45.84  | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | 
% 238.95/45.84  | | | | | | | | |   (24295)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 238.95/45.84  | | | | | | | | |              e3 & op(e0, e2) = e3)
% 238.95/45.84  | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | BETA: splitting (24295) gives:
% 238.95/45.84  | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | |   (24296)  all_58_12 = e3 & op(e0, e3) = e3
% 238.95/45.84  | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | ALPHA: (24296) implies:
% 238.95/45.84  | | | | | | | | | |   (24297)  all_58_12 = e3
% 238.95/45.84  | | | | | | | | | |   (24298)  op(e0, e3) = e3
% 238.95/45.84  | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | BETA: splitting (222) gives:
% 238.95/45.84  | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | |   (24299)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 238.95/45.84  | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 238.95/45.84  | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | BETA: splitting (24299) gives:
% 238.95/45.84  | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | |   (24300)  all_58_9 = e3 & op(e3, e0) = e3
% 238.95/45.84  | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | ALPHA: (24300) implies:
% 238.95/45.84  | | | | | | | | | | | |   (24301)  all_58_9 = e3
% 238.95/45.84  | | | | | | | | | | | |   (24302)  op(e3, e0) = e3
% 238.95/45.84  | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | BETA: splitting (238) gives:
% 238.95/45.84  | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | |   (24303)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 238.95/45.84  | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 238.95/45.84  | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | BETA: splitting (24303) gives:
% 238.95/45.84  | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | |   (24304)  all_58_1 = e3 & op(e3, e2) = e3
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | ALPHA: (24304) implies:
% 238.95/45.84  | | | | | | | | | | | | | |   (24305)  op(e3, e2) = e3
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | REF_CLOSE: (170), (24292), (24305), (function-axioms) are
% 238.95/45.84  | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | |   (24306)  all_58_3 = e3 & op(e2, e2) = e3
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | ALPHA: (24306) implies:
% 238.95/45.84  | | | | | | | | | | | | | |   (24307)  all_58_3 = e3
% 238.95/45.84  | | | | | | | | | | | | | |   (24308)  op(e2, e2) = e3
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 238.95/45.84  | | | | | | | | | | | | | |              e3, e0, simplifying with (159), (24298) gives:
% 238.95/45.84  | | | | | | | | | | | | | |   (24309)  all_52_3 = e3
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 238.95/45.84  | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (168), (24302) gives:
% 238.95/45.84  | | | | | | | | | | | | | |   (24310)  all_52_12 = e3
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | REDUCE: (148), (24309) imply:
% 238.95/45.84  | | | | | | | | | | | | | |   (24311)   ~ (all_52_1 = e3)
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | REDUCE: (140), (24309) imply:
% 238.95/45.84  | | | | | | | | | | | | | |   (24312)   ~ (all_52_7 = e3)
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | REDUCE: (139), (24309) imply:
% 238.95/45.84  | | | | | | | | | | | | | |   (24313)   ~ (all_52_11 = e3)
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | REDUCE: (113), (24310) imply:
% 238.95/45.84  | | | | | | | | | | | | | |   (24314)   ~ (all_52_13 = e3)
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | REDUCE: (112), (24310) imply:
% 238.95/45.84  | | | | | | | | | | | | | |   (24315)   ~ (all_52_14 = e3)
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | REDUCE: (365), (24310) imply:
% 238.95/45.84  | | | | | | | | | | | | | |   (24316)   ~ (all_10_2 = e3)
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | SIMP: (24316) implies:
% 238.95/45.84  | | | | | | | | | | | | | |   (24317)   ~ (all_10_2 = e3)
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 238.95/45.84  | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | |   (24318)   ~ (all_10_2 = e1)
% 238.95/45.84  | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | |   (24319)   ~ (all_16_2 = e0)
% 238.95/45.84  | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | REDUCE: (342), (24319) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | |   (24320)   ~ (all_10_2 = e0)
% 238.95/45.84  | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | |   (24321)  all_54_0 = e3
% 238.95/45.84  | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (24321) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | |   (24322)  all_10_2 = e3
% 238.95/45.84  | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | REDUCE: (24317), (24322) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | |   (24323)  $false
% 238.95/45.84  | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | CLOSE: (24323) is inconsistent.
% 238.95/45.84  | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | |   (24324)   ~ (all_54_0 = e3)
% 238.95/45.84  | | | | | | | | | | | | | | | | |   (24325)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 238.95/45.84  | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | BETA: splitting (24325) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | |   (24326)  all_54_0 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (24326) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | |   (24327)  all_10_2 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (301), (24327) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | |   (24328)  all_24_2 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (24327) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | |   (24329)  all_32_2 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (24327) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | |   (24330)  all_56_1 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | REDUCE: (355), (24327) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | |   (24331)   ~ (all_52_1 = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | REDUCE: (361), (24327) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | |   (24332)   ~ (all_52_4 = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | REDUCE: (24317), (24327) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | |   (24333)   ~ (e3 = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | REDUCE: (45), (24327) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | |   (24334)  op(e3, e3) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | |   (24335)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | BETA: splitting (24335) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | |   (24336)  all_58_1 = e2 & op(e3, e2) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | ALPHA: (24336) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | |   (24337)  op(e3, e2) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (24332), (24337), (function-axioms) are
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #254.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | |   (24338)  all_58_3 = e2 & op(e2, e2) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | ALPHA: (24338) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | |   (24339)  op(e2, e2) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (165), (167), (234), (23031), (24294),
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | |            (24311), (24339), (function-axioms) are
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1321.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | |   (24340)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.95/45.84  | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | BETA: splitting (24340) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | |   (24341)  all_58_7 = e2 & op(e1, e2) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | ALPHA: (24341) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | |   (24342)  all_58_7 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | |   (24343)  op(e1, e2) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | |   (24344)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24344) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |   (24345)  all_58_4 = e2 & op(e3, e1) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24345) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |   (24346)  all_58_4 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | |   (24347)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24347) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24348)  all_58_2 = e2 & op(e2, e3) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24348) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24349)  op(e2, e3) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (24331), (24349), (function-axioms) are
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24350)  all_58_3 = e2 & op(e2, e2) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24350) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24351)  op(e2, e2) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (165), (167), (234), (23031), (24294),
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |            (24311), (24351), (function-axioms) are
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1321.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | |   (24352)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24352) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24353)  all_58_5 = e2 & op(e2, e1) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24353) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24354)  all_58_5 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24355)  op(e2, e1) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (24356)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (24346), (24355), (24356), (function-axioms)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #56.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (24357)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24357) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24358)  all_58_8 = e0 & op(e1, e1) = e0
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24358) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24359)  op(e1, e1) = e0
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (157), (165), (230), (23031), (23032),
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            (24346), (24359), (function-axioms) are
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1493.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24360)  all_58_14 = e0 & op(e0, e1) = e0
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24360) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24361)  op(e0, e1) = e0
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24362)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24362) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24363)  all_58_4 = e1 & op(e3, e1) = e1
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24363) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24364)  all_58_4 = e1
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24346), (24364) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24365)  e2 = e1
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24354), (24365) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24366)  all_58_5 = e1
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (113), (148), (159), (164), (165),
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (233), (234), (17767), (23031),
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24298), (24302), (24331), (24366),
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #455.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24367)  all_58_5 = e1 & op(e2, e1) = e1
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24367) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24368)  all_58_5 = e1
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (113), (148), (159), (164), (165),
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (233), (234), (17767), (23031),
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24298), (24302), (24331), (24368),
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #455.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24369)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (23038), (24361), (24369),
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #45.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24370)  all_58_10 = e2 & op(e2, e0) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24370) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24371)  op(e2, e0) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17767), (24371), (function-axioms) are
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2317.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |   (24372)  all_58_5 = e2 & op(e2, e1) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24372) implies:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |   (24373)  all_58_5 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |   (24374)  op(e2, e1) = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (24343) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |   (24375)  all_52_6 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (24374) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |   (24376)  all_52_9 = e2
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (24375) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |   (24377)   ~ (all_52_7 = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (24375) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |   (24378)   ~ (all_52_14 = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (24376) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | |   (24379)   ~ (all_52_13 = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | |   (24380)   ~ (all_24_2 = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24328), (24380) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | |   (24381)  $false
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24381) is inconsistent.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | |   (24382)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_24_1 & $i(all_24_0) &
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | |              = all_24_1 & $i(all_24_1))
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24383)   ~ (all_32_2 = e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24329), (24383) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24384)  $false
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24384) is inconsistent.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |   (24385)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_32_1 & $i(all_32_0) &
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (24386)   ~ (all_42_2 = e3)
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24290), (24386) imply:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (24387)  $false
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24387) is inconsistent.
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (24388)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24389)   ~ (all_46_2 = e3)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23026), (24389) imply:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24390)  $false
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (24390) is inconsistent.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24391)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24392)  all_54_1 = e3
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (282), (24292), (24392) are inconsistent by
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24393)   ~ (all_54_1 = e3)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24394)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24395)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24395) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24396)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24396) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24397)  op(e3, all_56_1) = e3
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24330), (24397) imply:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24398)  op(e3, e2) = e3
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (24292), (24398), (function-axioms) are
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24399)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24399) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24400)  op(e2, e3) = all_56_3
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24401)  op(e2, all_56_3) = e2
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_3, e3, e2, simplifying with (167), (24400)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24402)  all_56_3 = all_52_1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24401), (24402) imply:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24403)  op(e2, all_52_1) = e2
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24404)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, all_56_11) = e2)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24404) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24405)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_9 & $i(all_56_9)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24405) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24406)  op(e3, e2) = all_56_9
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24407)  op(e3, all_56_9) = e3
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_9, e2, e3, simplifying with (170), (24406)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24408)  all_56_9 = all_52_4
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24407), (24408) imply:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24409)  op(e3, all_52_4) = e3
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24410)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24410) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24411)  all_58_6 = e1 & op(e1, e3) = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24411) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24412)  op(e1, e3) = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (113), (148), (159),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (164), (165), (167), (168), (220),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (226), (233), (234), (239), (17767),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17773), (23029), (23031), (23033), (24298),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24302), (24331), (24334), (24342), (24373),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24403), (24412), (function-axioms) are
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #26.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24413)  all_58_7 = e1 & op(e1, e2) = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (113), (148), (159), (164), (165),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (233), (234), (17767), (23031),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24298), (24302), (24331), (24342), (24373),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24413), (function-axioms) are inconsistent by
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #25.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24414)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (113), (125),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (148), (157), (158), (159), (160), (162),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (168), (169), (170),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (223), (225), (226), (227), (228),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (233), (234), (240), (241), (242),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (282), (17762), (17764), (17767), (17768),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23025), (23027), (23029), (23030), (23031),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23032), (23033), (23037), (23038), (24289),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24292), (24293), (24294), (24297), (24298),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24301), (24302), (24307), (24308), (24331),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24332), (24334), (24342), (24374), (24382),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24385), (24388), (24391), (24394), (24409),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24414), (function-axioms) are inconsistent by
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #19.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24415)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24415) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24416)  op(e2, all_56_11) = e2
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24291), (24416) imply:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24417)  op(e2, e3) = e2
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (24331), (24417), (function-axioms) are
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24418)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15 & $i(all_56_15))
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24418) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24419)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (113), (148), (159), (164), (165),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (233), (234), (17767), (23031),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24298), (24302), (24331), (24343), (24373),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24419), (function-axioms) are inconsistent by
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #18.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24420)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_15 & $i(all_56_15)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24420) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24421)  op(e0, e2) = all_56_15
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24422)  op(e0, all_56_15) = e0
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (158), (24421)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24423)  all_56_15 = all_52_7
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24422), (24423) imply:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24424)  op(e0, all_52_7) = e0
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24425)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24425) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24426)  all_58_6 = e1 & op(e1, e3) = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24426) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24427)  op(e1, e3) = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (113), (148), (159),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (164), (165), (167), (168), (220),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (226), (233), (234), (239), (17767),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17773), (23029), (23031), (23033), (24298),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24302), (24331), (24334), (24342), (24373),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24403), (24427), (function-axioms) are
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #26.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24428)  all_58_7 = e1 & op(e1, e2) = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (113), (148), (159), (164), (165),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (233), (234), (17767), (23031),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24298), (24302), (24331), (24342), (24373),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24428), (function-axioms) are inconsistent by
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #25.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24429)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (169),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (223), (225), (226), (230), (231),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (246), (17762), (17764), (17767), (17768),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (23029), (23030), (23031), (23032),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23033), (23037), (23038), (24289), (24292),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24294), (24297), (24301), (24302), (24307),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24308), (24334), (24342), (24374), (24388),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24391), (24424), (24429), (function-axioms) are
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #17.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24430)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24430) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24431)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24431) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24432)  op(e1, e3) = all_56_5
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24433)  op(e1, all_56_5) = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (24432)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24434)  all_56_5 = all_52_2
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24433), (24434) imply:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24435)  op(e1, all_52_2) = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24436)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, all_56_11) = e2)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24436) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24437)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_9 & $i(all_56_9)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24437) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24438)  op(e3, e2) = all_56_9
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24439)  op(e3, all_56_9) = e3
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_9, e2, e3, simplifying with (170), (24438)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24440)  all_56_9 = all_52_4
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24439), (24440) imply:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24441)  op(e3, all_52_4) = e3
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24442)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24442) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24443)  all_58_6 = e1 & op(e1, e3) = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24443) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24444)  op(e1, e3) = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24445)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24445) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24446)  all_58_0 = e0 & op(e3, e3) = e0
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24446) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24447)  op(e3, e3) = e0
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (24334), (24447), (function-axioms) are
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24448)  all_58_2 = e0 & op(e2, e3) = e0
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24448) implies:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24449)  all_58_2 = e0
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24450)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (164), (165),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (231), (232), (233), (246), (23030),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23038), (24292), (24294), (24301), (24302),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24307), (24308), (24334), (24435), (24444),
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24449), (24450), (function-axioms) are
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #16.
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24451)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24451) gives:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24452)  all_58_11 = e1 & op(e1, e0) = e1
% 238.95/45.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (113), (125),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (148), (157), (158), (159), (160), (162),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (168), (169), (170),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (223), (225), (226), (227), (228),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (233), (234), (240), (241), (242),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (282), (17762), (17764), (17767), (17768),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23025), (23027), (23029), (23030), (23031),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23032), (23033), (23037), (23038), (24289),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24292), (24293), (24294), (24297), (24298),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24301), (24302), (24307), (24308), (24331),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24332), (24334), (24342), (24374), (24382),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24385), (24388), (24391), (24394), (24441),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24452), (function-axioms) are inconsistent by
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #20.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24453)  all_58_15 = e1 & op(e0, e0) = e1
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (113), (148), (159), (164), (165),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (233), (234), (17767), (17773),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23031), (24298), (24302), (24331), (24373),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24453), (function-axioms) are inconsistent by
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #29.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24454)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (24298), (24444), (24454),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #27.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24455)  all_58_7 = e1 & op(e1, e2) = e1
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (113), (148), (159), (164), (165),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (233), (234), (17767), (23031),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24298), (24302), (24331), (24342), (24373),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24455), (function-axioms) are inconsistent by
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #25.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24456)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (113), (125),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (135), (148), (157), (158), (159), (160), (162),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (168), (169), (170),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (223), (225), (226), (227), (228),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (233), (234), (240), (241), (242),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (282), (17762), (17764), (17767), (17768),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23025), (23027), (23029), (23030), (23031),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23032), (23033), (23037), (23038), (24289),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24292), (24293), (24294), (24297), (24298),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24301), (24302), (24307), (24308), (24331),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24332), (24334), (24342), (24374), (24382),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24385), (24388), (24391), (24394), (24441),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24456), (function-axioms) are inconsistent by
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #19.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24457)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24457) implies:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24458)  op(e2, all_56_11) = e2
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24291), (24458) imply:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24459)  op(e2, e3) = e2
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (24331), (24459), (function-axioms) are
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24460)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15 & $i(all_56_15))
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24460) gives:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24461)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (113), (148), (159), (164), (165),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (233), (234), (17767), (23031),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24298), (24302), (24331), (24343), (24373),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24461), (function-axioms) are inconsistent by
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #18.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24462)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_15 & $i(all_56_15)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24462) implies:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24463)  op(e0, e2) = all_56_15
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24464)  op(e0, all_56_15) = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15, e2, e0, simplifying with (158), (24463)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24465)  all_56_15 = all_52_7
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24464), (24465) imply:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24466)  op(e0, all_52_7) = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24467)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24467) gives:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24468)  all_58_6 = e1 & op(e1, e3) = e1
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24468) implies:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24469)  op(e1, e3) = e1
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24470)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24470) gives:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24471)  all_58_0 = e0 & op(e3, e3) = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24471) implies:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24472)  op(e3, e3) = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (24334), (24472), (function-axioms) are
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2188.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24473)  all_58_2 = e0 & op(e2, e3) = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24473) implies:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24474)  all_58_2 = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24475)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (24342), (24469), (24475),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #335.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24476)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24476) gives:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24477)  all_58_8 = e0 & op(e1, e1) = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24477) implies:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24478)  op(e1, e1) = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (160), (162), (226), (23029), (23033),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24469), (24478), (function-axioms) are
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #457.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24479)  all_58_11 = e0 & op(e1, e0) = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24479) implies:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24480)  op(e1, e0) = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24481)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (164), (165),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (231), (232), (233), (246), (23030),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23038), (24292), (24294), (24301), (24302),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24307), (24308), (24334), (24435), (24469),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24474), (24481), (function-axioms) are
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #16.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24482)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (113), (148), (159), (164), (165),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (233), (234), (17767), (17773),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23031), (24298), (24302), (24331), (24373),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24480), (24482), (function-axioms) are
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #28.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24483)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (24298), (24469), (24483),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #27.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24484)  all_58_7 = e1 & op(e1, e2) = e1
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (113), (148), (159), (164), (165),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (233), (234), (17767), (23031),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24298), (24302), (24331), (24342), (24373),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24484), (function-axioms) are inconsistent by
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #25.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24485)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (110), (157), (158),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (162), (163), (164), (165), (167), (169),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (170), (210), (223), (225), (226), (230), (231),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (241), (246), (17762), (17764), (17767), (17768),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17774), (23029), (23030), (23031), (23032),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23033), (23037), (23038), (24289), (24292),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24294), (24297), (24301), (24302), (24307),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24308), (24334), (24342), (24374), (24388),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24391), (24466), (24485), (function-axioms) are
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #17.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24486)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24486) implies:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24487)  op(e0, e3) = all_56_7
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24488)  op(e0, all_56_7) = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (24298), (24487), (24488), (function-axioms)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2070.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | |   (24489)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (160), (223),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | |            (224), (226), (17765), (23033), (24342), (24489),
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | |            #49.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | |   (24490)  all_58_13 = e2 & op(e0, e2) = e2
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | ALPHA: (24490) implies:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | |   (24491)  op(e0, e2) = e2
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (24491), (function-axioms) are
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | |   (24492)  all_54_0 = e1 | all_54_0 = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | REF_CLOSE: (292), (24318), (24320), (24492) are inconsistent
% 238.95/45.86  | | | | | | | | | | | | | | | | | |            by sub-proof #2320.
% 238.95/45.86  | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | End of split
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | |   (24493)  all_16_2 = e0
% 238.95/45.86  | | | | | | | | | | | | | | | |   (24494)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0
% 238.95/45.86  | | | | | | | | | | | | | | | |              & op(e3, e0) = all_16_1 & $i(all_16_0) &
% 238.95/45.86  | | | | | | | | | | | | | | | |              $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0)
% 238.95/45.86  | | | | | | | | | | | | | | | |              = all_16_1 & $i(all_16_1))
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | COMBINE_EQS: (342), (24493) imply:
% 238.95/45.86  | | | | | | | | | | | | | | | |   (24495)  all_10_2 = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | SIMP: (24495) implies:
% 238.95/45.86  | | | | | | | | | | | | | | | |   (24496)  all_10_2 = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (24496) imply:
% 238.95/45.86  | | | | | | | | | | | | | | | |   (24497)  all_50_2 = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (24496) imply:
% 238.95/45.86  | | | | | | | | | | | | | | | |   (24498)  all_56_1 = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | REDUCE: (361), (24496) imply:
% 238.95/45.86  | | | | | | | | | | | | | | | |   (24499)   ~ (all_52_4 = e0)
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | REDUCE: (363), (24496) imply:
% 238.95/45.86  | | | | | | | | | | | | | | | |   (24500)   ~ (all_52_8 = e0)
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | REDUCE: (24317), (24496) imply:
% 238.95/45.86  | | | | | | | | | | | | | | | |   (24501)   ~ (e3 = e0)
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | REDUCE: (24318), (24496) imply:
% 238.95/45.86  | | | | | | | | | | | | | | | |   (24502)   ~ (e1 = e0)
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | REDUCE: (45), (24496) imply:
% 238.95/45.86  | | | | | | | | | | | | | | | |   (24503)  op(e3, e3) = e0
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 238.95/45.86  | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.86  | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | |   (24504)   ~ (all_50_2 = e0)
% 238.95/45.86  | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | REDUCE: (24497), (24504) imply:
% 238.95/45.86  | | | | | | | | | | | | | | | | |   (24505)  $false
% 238.95/45.86  | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | CLOSE: (24505) is inconsistent.
% 238.95/45.86  | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.86  | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | |   (24506)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0
% 238.95/45.86  | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_50_1 & $i(all_50_0) &
% 238.95/45.86  | | | | | | | | | | | | | | | | |              $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0)
% 238.95/45.86  | | | | | | | | | | | | | | | | |              = all_50_1 & $i(all_50_1))
% 238.95/45.86  | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | BETA: splitting (24506) gives:
% 238.95/45.86  | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.86  | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | |   (24507)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 238.95/45.86  | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_50_1 & $i(all_50_0) &
% 238.95/45.86  | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 238.95/45.86  | | | | | | | | | | | | | | | | | | 
% 238.95/45.86  | | | | | | | | | | | | | | | | | | ALPHA: (24507) implies:
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24508)   ~ (all_50_0 = e1)
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24509)  op(e3, e0) = all_50_1
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24510)  op(all_50_1, e3) = all_50_0
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 238.95/45.87  | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (24302), (24509) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24511)  all_50_1 = e3
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | REDUCE: (24510), (24511) imply:
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24512)  op(e3, e3) = all_50_0
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | BETA: splitting (24494) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24513)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_16_1 & $i(all_16_0) &
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            $i(all_16_1)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | ALPHA: (24513) implies:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24514)   ~ (all_16_0 = e2)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24515)  op(e3, e0) = all_16_1
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24516)  op(all_16_1, e3) = all_16_0
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_16_1,
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (24302), (24515) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24517)  all_16_1 = e3
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_50_0,
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (24503), (24512) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24518)  all_50_0 = e0
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | REDUCE: (24516), (24517) imply:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24519)  op(e3, e3) = all_16_0
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_16_0,
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (24503), (24519) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24520)  all_16_0 = e0
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | REDUCE: (24514), (24520) imply:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24521)   ~ (e2 = e0)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |   (24522)   ~ (all_42_2 = e3)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | REDUCE: (24290), (24522) imply:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |   (24523)  $false
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | CLOSE: (24523) is inconsistent.
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |   (24524)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (97), (100), (123),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (134), (136), (157), (158), (159), (160), (162),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (164), (165), (167), (169), (170), (202), (203),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (211), (213), (216), (217), (218), (219), (220),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (227), (228),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (234), (235), (237), (240),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (241), (242), (243), (244), (246), (281), (282),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (17761), (17763), (17764), (17765), (17768),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (17773), (17774), (23026), (23027), (23030),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (23031), (23032), (23038), (24289), (24292),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (24294), (24297), (24298), (24301), (24302),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (24307), (24308), (24311), (24498), (24499),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            (24500), (24503), (24524), (function-axioms) are
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #14.
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24525)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            $i(all_16_1)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | ALPHA: (24525) implies:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24526)   ~ (all_16_1 = e1)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24527)  op(e3, e0) = all_16_1
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_16_1,
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (24302), (24527) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24528)  all_16_1 = e3
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_50_0,
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (24503), (24512) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24529)  all_50_0 = e0
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (94), (97), (100),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (123), (134), (136), (157), (158), (159), (160),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (169), (170), (202),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (203), (211), (213), (216), (217), (218), (219),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (227),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (234), (235), (237),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (240), (241), (242), (243), (244), (246), (281),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (282), (17761), (17763), (17764), (17765),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (17768), (17773), (17774), (23026), (23027),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (23030), (23031), (23032), (23038), (24289),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (24290), (24292), (24294), (24297), (24298),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (24301), (24302), (24307), (24308), (24311),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (24498), (24499), (24500), (24503),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            #13.
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24530)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 238.95/45.87  | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | ALPHA: (24530) implies:
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24531)   ~ (all_50_1 = e2)
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24532)  op(e3, e0) = all_50_1
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 238.95/45.87  | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (24302), (24532) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24533)  all_50_1 = e3
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | BETA: splitting (24494) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24534)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_16_1 & $i(all_16_0) &
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            $i(all_16_1)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | ALPHA: (24534) implies:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24535)   ~ (all_16_0 = e2)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24536)  op(e3, e0) = all_16_1
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24537)  op(all_16_1, e3) = all_16_0
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_16_1,
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (24302), (24536) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24538)  all_16_1 = e3
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | REDUCE: (24537), (24538) imply:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24539)  op(e3, e3) = all_16_0
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_16_0,
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (24503), (24539) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24540)  all_16_0 = e0
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | REDUCE: (24535), (24540) imply:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24541)   ~ (e2 = e0)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (94), (97), (100),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (123), (134), (136), (157), (158), (159), (160),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (169), (170), (202),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (203), (211), (213), (216), (217), (218), (219),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (227),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (234), (235), (237),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (240), (241), (242), (243), (244), (246), (281),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (282), (17761), (17763), (17764), (17765),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (17768), (17773), (17774), (23026), (23027),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (23030), (23031), (23032), (23038), (24289),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (24290), (24292), (24294), (24297), (24298),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (24301), (24302), (24307), (24308), (24311),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (24498), (24499), (24500), (24503),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            #13.
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24542)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            $i(all_16_1)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | ALPHA: (24542) implies:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24543)   ~ (all_16_1 = e1)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24544)  op(e3, e0) = all_16_1
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_16_1,
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (24302), (24544) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24545)  all_16_1 = e3
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (94), (97), (100),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (123), (134), (136), (157), (158), (159), (160),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (162), (164), (165), (167), (169), (170), (202),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (203), (211), (213), (216), (217), (218), (219),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (227),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (234), (235), (237),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (240), (241), (242), (243), (244), (246), (281),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (282), (17761), (17763), (17764), (17765),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (17768), (17773), (17774), (23026), (23027),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (23030), (23031), (23032), (23038), (24289),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (24290), (24292), (24294), (24297), (24298),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (24301), (24302), (24307), (24308), (24311),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (24498), (24499), (24500), (24503),
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            #13.
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | End of split
% 238.95/45.87  | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | End of split
% 238.95/45.87  | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | End of split
% 238.95/45.87  | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | Case 2:
% 238.95/45.87  | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | |   (24546)  all_10_2 = e1
% 238.95/45.87  | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | COMBINE_EQS: (290), (24546) imply:
% 238.95/45.87  | | | | | | | | | | | | | | |   (24547)  all_56_1 = e1
% 238.95/45.87  | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | REDUCE: (355), (24546) imply:
% 238.95/45.87  | | | | | | | | | | | | | | |   (24548)   ~ (all_52_1 = e1)
% 238.95/45.87  | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | REDUCE: (361), (24546) imply:
% 238.95/45.87  | | | | | | | | | | | | | | |   (24549)   ~ (all_52_4 = e1)
% 238.95/45.87  | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | REDUCE: (363), (24546) imply:
% 238.95/45.87  | | | | | | | | | | | | | | |   (24550)   ~ (all_52_8 = e1)
% 238.95/45.87  | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | REDUCE: (24317), (24546) imply:
% 238.95/45.87  | | | | | | | | | | | | | | |   (24551)   ~ (e3 = e1)
% 238.95/45.87  | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | REDUCE: (45), (24546) imply:
% 238.95/45.87  | | | | | | | | | | | | | | |   (24552)  op(e3, e3) = e1
% 238.95/45.87  | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | Case 1:
% 238.95/45.87  | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | |   (24553)   ~ (all_42_2 = e3)
% 238.95/45.87  | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | REDUCE: (24290), (24553) imply:
% 238.95/45.87  | | | | | | | | | | | | | | | |   (24554)  $false
% 238.95/45.87  | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | CLOSE: (24554) is inconsistent.
% 238.95/45.87  | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | Case 2:
% 238.95/45.87  | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | |   (24555)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0
% 238.95/45.87  | | | | | | | | | | | | | | | |              & op(e2, e3) = all_42_1 & $i(all_42_0) &
% 238.95/45.87  | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 238.95/45.87  | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 238.95/45.87  | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.87  | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | |   (24556)   ~ (all_44_2 = e2)
% 238.95/45.87  | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | REDUCE: (17761), (24556) imply:
% 238.95/45.87  | | | | | | | | | | | | | | | | |   (24557)  $false
% 238.95/45.87  | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | CLOSE: (24557) is inconsistent.
% 238.95/45.87  | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.87  | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | |   (24558)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0
% 238.95/45.87  | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_44_1 & $i(all_44_0) &
% 238.95/45.87  | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2)
% 238.95/45.87  | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 238.95/45.87  | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24559)   ~ (all_46_2 = e3)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | REDUCE: (23026), (24559) imply:
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24560)  $false
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | CLOSE: (24560) is inconsistent.
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | |   (24561)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0
% 238.95/45.87  | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 238.95/45.87  | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3)
% 238.95/45.87  | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |   (24562)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |            (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 238.95/45.87  | | | | | | | | | | | | | | | | | | |                e3) = all_56_3 & $i(all_56_3))
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | BETA: splitting (24562) gives:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |   (24563)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | ALPHA: (24563) implies:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |   (24564)  op(e3, all_56_1) = e3
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | REDUCE: (24547), (24564) imply:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |   (24565)  op(e3, e1) = e3
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (23030), (24565), (function-axioms) are
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2260.
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |   (24566)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | |            = all_56_3 & $i(all_56_3)
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.87  | | | | | | | | | | | | | | | | | | | | ALPHA: (24566) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | |   (24567)  op(e2, e3) = all_56_3
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | |   (24568)  op(e2, all_56_3) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | |              all_56_3, e3, e2, simplifying with (167), (24567)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | |              gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | |   (24569)  all_56_3 = all_52_1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | REDUCE: (24568), (24569) imply:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | |   (24570)  op(e2, all_52_1) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | |   (24571)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24571) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |   (24572)  all_58_4 = e2 & op(e3, e1) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24572) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |   (24573)  all_58_4 = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |   (24574)  op(e3, e1) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | |   (24575)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24575) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | |   (24576)  all_58_0 = e0 & op(e3, e3) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24576) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | |   (24577)  op(e3, e3) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24552), (24577), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | |   (24578)  all_58_1 = e0 & op(e3, e2) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24578) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | |   (24579)  all_58_1 = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | |   (24580)  op(e3, e2) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | |   (24581)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (164), (165), (167), (234),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (23031), (24294), (24301), (24311),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | |            (24552), (24573), (24581), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #12.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | |   (24582)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24582) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24583)  all_58_7 = e2 & op(e1, e2) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24583) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24584)  all_58_7 = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24585)  op(e1, e2) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24586)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (240),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (24301), (24311), (24552),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24573), (24584), (24586), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #11.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24587)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24587) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24588)  all_58_8 = e1 & op(e1, e1) = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24588) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24589)  op(e1, e1) = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23038), (24589), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #468.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24590)  all_58_11 = e1 & op(e1, e0) = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24590) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24591)  all_58_11 = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24592)  op(e1, e0) = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24593)  all_58_15 = e0 & op(e0, e0) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24593) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24594)  op(e0, e0) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (24594), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24595)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24595) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24596)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24597)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24597) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24598)  all_58_9 = e0 & op(e3, e0) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24598) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24599)  all_58_9 = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (24552),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24579), (24599), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1089.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24600)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24600) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24601)  all_58_10 = e0 & op(e2, e0) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24601) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24602)  op(e2, e0) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24603)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (170), (239),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (245), (24297), (24307), (24311), (24549),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24552), (24603), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #576.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24604)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24604) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24605)  all_58_7 = e1 & op(e1, e2) = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24605) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24606)  all_58_7 = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (225),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (23033), (24591), (24592), (24606),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1417.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24607)  all_58_13 = e1 & op(e0, e2) = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24607) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24608)  op(e0, e2) = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24609)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24609) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24610)  all_58_2 = e2 & op(e2, e3) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24610) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24611)  op(e2, e3) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24596) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24612)  all_58_12 = e0 & op(e0, e3) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24612) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24613)  op(e0, e3) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (24298), (24613), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #221.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24614)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24614) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24615)  all_58_13 = e0 & op(e0, e2) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24615) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24616)  op(e0, e2) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24608), (24616), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (24592) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24617)  all_52_14 = e1
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (24585) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24618)  all_52_6 = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (24602) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24619)  all_52_13 = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (24611) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24620)  all_52_1 = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (24574) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24621)  all_52_8 = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (24580) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24622)  all_52_4 = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23030), (24621) imply:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24623)   ~ (e3 = e2)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (24617), (24619) imply:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24624)   ~ (e1 = e0)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24294), (24619) imply:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24625)   ~ (e3 = e0)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17768), (24617) imply:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24626)   ~ (e2 = e1)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24570), (24620) imply:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24627)  op(e2, e2) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (236), (238), (24579),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24580), (24584), (24585), (24627),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2001.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24628)  all_58_3 = e2 & op(e2, e2) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24628) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24629)  all_58_3 = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24630)  op(e2, e2) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (236),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (24579), (24580), (24584), (24585),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24629), (24630), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2012.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24631)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24631) gives:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24632)  all_58_5 = e2 & op(e2, e1) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24632) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24633)  all_58_5 = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24634)  op(e2, e1) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (162), (164),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (170), (216), (221), (222), (224),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (228), (230), (231), (232), (233), (234),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (238), (239), (240), (241),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (246), (17763), (17767),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17773), (17774), (23031), (23038), (24289),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24292), (24294), (24297), (24298), (24301),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24307), (24308), (24311), (24548), (24549),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24552), (24555), (24570), (24633), (24634),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #5.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24635)  all_58_10 = e2 & op(e2, e0) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24635) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24636)  op(e2, e0) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (24602), (24636), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2121.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24637)  all_58_11 = e0 & op(e1, e0) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24637) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24638)  op(e1, e0) = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24592), (24638), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2284.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24639)  all_58_13 = e2 & op(e0, e2) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24639) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24640)  op(e0, e2) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (24640), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | |   (24641)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (170), (246), (24292),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | |            (24552), (24573), (24641), (function-axioms) are
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #4.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |   (24642)  all_58_5 = e2 & op(e2, e1) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24642) implies:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |   (24643)  all_58_5 = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |   (24644)  op(e2, e1) = e2
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (162), (164),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (170), (216), (221), (222), (224),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |            (225), (228), (230), (231), (232), (233), (234),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (238), (239), (240), (241),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (246), (17763), (17767),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |            (17773), (17774), (23031), (23038), (24289),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |            (24292), (24294), (24297), (24298), (24301),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |            (24307), (24308), (24311), (24548), (24549),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |            (24552), (24555), (24570), (24643), (24644),
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | |            #5.
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | |   (24645)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 238.95/45.88  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17765), (23038), (24645),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | |            #57.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | |   (24646)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | |                e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | |              e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | |              all_56_7 & $i(all_56_7))
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (24646) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | |   (24647)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | |            = all_56_5 & $i(all_56_5)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | ALPHA: (24647) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | |   (24648)  op(e1, e3) = all_56_5
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | |   (24649)  op(e1, all_56_5) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | |              all_56_5, e3, e1, simplifying with (163), (24648)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | |              gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | |   (24650)  all_56_5 = all_52_2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | |   (24651)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24651) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | |   (24652)  all_58_4 = e2 & op(e3, e1) = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24652) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | |   (24653)  all_58_4 = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | |   (24654)  op(e3, e1) = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | |   (24655)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24655) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | |   (24656)  all_58_0 = e0 & op(e3, e3) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24656) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | |   (24657)  op(e3, e3) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24552), (24657), (function-axioms) are
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | |   (24658)  all_58_1 = e0 & op(e3, e2) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24658) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | |   (24659)  all_58_1 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | |   (24660)  op(e3, e2) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (24661)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (164), (165), (167), (234),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (240), (23031), (24294), (24301), (24311),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (24552), (24653), (24661), (function-axioms) are
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #12.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (24662)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24662) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24663)  all_58_7 = e2 & op(e1, e2) = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24663) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24664)  all_58_7 = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24665)  op(e1, e2) = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24666)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (240),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (245), (24301), (24311), (24552),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24653), (24664), (24666), (function-axioms) are
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #11.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24667)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24667) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24668)  all_58_8 = e1 & op(e1, e1) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24668) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24669)  op(e1, e1) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23038), (24669), (function-axioms) are
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #468.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24670)  all_58_11 = e1 & op(e1, e0) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24670) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24671)  all_58_11 = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24672)  op(e1, e0) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24673)  all_58_15 = e0 & op(e0, e0) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24673) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24674)  op(e0, e0) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (24674), (function-axioms) are
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24675)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24675) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24676)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24676) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24677)  all_58_9 = e0 & op(e3, e0) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24677) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24678)  all_58_9 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (244), (246), (24552),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24659), (24678), (function-axioms) are
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1089.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24679)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24679) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24680)  all_58_10 = e0 & op(e2, e0) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24680) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24681)  op(e2, e0) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24682)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24682) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24683)  all_58_2 = e1 & op(e2, e3) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (24548), (24683), (function-axioms) are
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24684)  all_58_3 = e1 & op(e2, e2) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (24297), (24307), (24311), (24552),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24684), (function-axioms) are inconsistent by
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #738.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24685)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24685) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24686)  all_58_5 = e1 & op(e2, e1) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24686) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24687)  all_58_5 = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24688)  op(e2, e1) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24689)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (170), (239),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (245), (24297), (24307), (24311), (24549),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24552), (24689), (function-axioms) are
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #576.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24690)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24690) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24691)  all_58_7 = e1 & op(e1, e2) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24691) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24692)  all_58_7 = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (223), (225),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (23033), (24671), (24672), (24692),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1417.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24693)  all_58_13 = e1 & op(e0, e2) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24693) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24694)  all_58_13 = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24695)  op(e0, e2) = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24696)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24696) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24697)  all_58_4 = e0 & op(e3, e1) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24697) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24698)  all_58_4 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24653), (24698) imply:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24699)  e2 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17773), (24699) imply:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24700)  all_58_15 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24701)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24701) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24702)  all_58_12 = e2 & op(e0, e3) = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (24297), (24702) are inconsistent by
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1974.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24703)  all_58_13 = e2 & op(e0, e2) = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24703) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24704)  all_58_13 = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24694), (24704) imply:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24705)  e2 = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24653), (24705) imply:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24706)  all_58_4 = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (240), (244), (24301),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24552), (24706), (function-axioms) are
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1469.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24707)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24707) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24708)  all_58_14 = e2 & op(e0, e1) = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24708) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24709)  all_58_14 = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (227), (23037), (24653), (24687),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24709) are inconsistent by sub-proof #848.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17772), (24700) are inconsistent by
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1654.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24710)  all_58_5 = e0 & op(e2, e1) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24710) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24711)  op(e2, e1) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (165), (24688), (24711), (function-axioms)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2165.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24712)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24712) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24713)  all_58_8 = e0 & op(e1, e1) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24713) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24714)  op(e1, e1) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (167), (226),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (239), (243), (245), (23029), (24297), (24311),
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24552), (24671), (24714), (function-axioms) are
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #662.
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24715)  all_58_14 = e0 & op(e0, e1) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24715) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24716)  all_58_14 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24717)  op(e0, e1) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24718)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24718) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24719)  all_58_2 = e2 & op(e2, e3) = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24719) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24720)  all_58_2 = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24721)  op(e2, e3) = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24722)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24722) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24723)  all_58_6 = e0 & op(e1, e3) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24723) implies:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24724)  op(e1, e3) = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (157), (24717) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24725)  all_52_11 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e1,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (24695) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24726)  all_52_7 = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (160), (24672) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24727)  all_52_14 = e1
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (24724) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24728)  all_52_2 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (164), (24681) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24729)  all_52_13 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (24721) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24730)  all_52_1 = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (169), (24654) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24731)  all_52_8 = e2
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (24660) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24732)  all_52_4 = e0
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23030), (24731) imply:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24733)   ~ (e3 = e2)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (24727), (24729) imply:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24734)   ~ (e1 = e0)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24294), (24729) imply:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24735)   ~ (e3 = e0)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17767), (24729) imply:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24736)   ~ (e2 = e0)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17768), (24727) imply:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24737)   ~ (e2 = e1)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24738)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_27 & $i(all_56_27))
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24738) gives:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24739)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24739) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24740)  op(e3, all_56_25) = e3
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24741)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e3) = e0)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24741) gives:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24742)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24742) gives:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24743)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24743) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24744)  op(e2, e3) = e3
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (24311), (24744), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2337.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24745)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e1, e3) = e3)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24745) gives:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24746)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24746) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24747)  op(e3, e2) = e2
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (24660), (24747), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2026.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24748)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24748) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24749)  op(e1, e3) = e3
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (24648), (24649), (24749), (function-axioms)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2243.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24750)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24750) gives:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24751)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e1
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24751) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24752)  op(e3, e1) = e1
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (24550), (24752), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2309.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24753)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e0 & op(e0, e3) = e0)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24753) gives:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24754)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e3
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24754) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24755)  all_56_25 = e3
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24740), (24755) imply:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24756)  op(e3, e3) = e3
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (24552), (24756), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1578.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24757)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24757) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24758)  op(e0, e3) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (24298), (24758), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #221.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24759)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0 & op(e0, e1) = e0)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24759) gives:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24760)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17762), (17764), (24547), (24760),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #67.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24761)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24761) gives:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24762)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24762) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24763)  op(e0, e2) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24695), (24763), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24764)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0 & op(e0, e1) = e0)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24672), (24717), (24764), (function-axioms)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1240.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24765)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_27 & $i(all_56_27)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (24289), (24307), (24555),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24681), (24687), (24720), (24721), (24765),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #778.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24766)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_31) = e0)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24766) gives:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24767)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (223), (225),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (23029), (23037), (23038), (24561),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24671), (24672), (24724), (24767),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #412.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24768)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24768) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24769)  op(e0, all_56_31) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17762), (24769) imply:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24770)  op(e0, e2) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24695), (24770), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1872.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24771)  all_58_7 = e0 & op(e1, e2) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24771) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24772)  all_58_7 = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24664), (24772) imply:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24773)  e2 = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24720), (24773) imply:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24774)  all_58_2 = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (222), (231),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (17773), (24307), (24671), (24681),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24687), (24774), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #626.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24775)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24775) gives:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24776)  all_58_8 = e0 & op(e1, e1) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24776) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24777)  op(e1, e1) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (228), (229),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (23031), (24716), (24717), (24777),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #437.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24778)  all_58_11 = e0 & op(e1, e0) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24778) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24779)  op(e1, e0) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24672), (24779), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2284.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24780)  all_58_3 = e2 & op(e2, e2) = e2
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24780) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24781)  all_58_3 = e2
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24782)  op(e2, e2) = e2
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (235), (236),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (24659), (24660), (24664), (24665),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24781), (24782), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2012.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24783)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (240), (244), (24301),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24552), (24653), (24681), (24687), (24783),
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #695.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24784)  all_58_10 = e1 & op(e2, e0) = e1
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24784) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24785)  op(e2, e0) = e1
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (24681), (24785), (function-axioms)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24786)  all_58_11 = e0 & op(e1, e0) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24786) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24787)  op(e1, e0) = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24672), (24787), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2284.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24788)  all_58_13 = e2 & op(e0, e2) = e2
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24788) implies:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24789)  op(e0, e2) = e2
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (17764), (24789), (function-axioms) are
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2327.
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | |   (24790)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 238.95/45.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (170), (246), (24292),
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | |            (24552), (24653), (24790), (function-axioms) are
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #4.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | |   (24791)  all_58_5 = e2 & op(e2, e1) = e2
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24791) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | |   (24792)  all_58_5 = e2
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | |   (24793)  op(e2, e1) = e2
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | |   (24794)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24794) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |   (24795)  all_58_2 = e1 & op(e2, e3) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (24548), (24795), (function-axioms) are
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |   (24796)  all_58_3 = e1 & op(e2, e2) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |            (245), (24297), (24307), (24311), (24552),
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |            (24796), (function-axioms) are inconsistent by
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #738.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | |   (24797)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24797) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |   (24798)  all_58_5 = e1 & op(e2, e1) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24798) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |   (24799)  all_58_5 = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (24792), (24799) are inconsistent by
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1665.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |   (24800)  all_58_10 = e1 & op(e2, e0) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24800) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |   (24801)  all_58_10 = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | |   (24802)  op(e2, e0) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (24803)  all_58_15 = e0 & op(e0, e0) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24803) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (24804)  op(e0, e0) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17774), (24804), (function-axioms) are
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (24805)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24805) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (24806)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (24807)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24807) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24808)  all_58_9 = e0 & op(e3, e0) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (24301), (24808) are inconsistent by
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2103.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (24809)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24809) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24810)  all_58_10 = e0 & op(e2, e0) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24810) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24811)  op(e2, e0) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (24802), (24811), (function-axioms)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1778.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24812)  all_58_11 = e0 & op(e1, e0) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24812) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24813)  all_58_11 = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24814)  op(e1, e0) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24815)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (222), (231),
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (240), (244), (17773), (24301), (24307),
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24552), (24801), (24807), (24815),
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #10.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24816)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24816) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24817)  all_58_8 = e1 & op(e1, e1) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24817) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24818)  op(e1, e1) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23038), (24818), (function-axioms) are
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #468.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24819)  all_58_14 = e1 & op(e0, e1) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24819) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24820)  all_58_14 = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24821)  op(e0, e1) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24806) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24822)  all_58_12 = e0 & op(e0, e3) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24822) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24823)  op(e0, e3) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (24298), (24823), (function-axioms) are
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #221.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24824)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24824) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24825)  all_58_13 = e0 & op(e0, e2) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24825) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24826)  all_58_13 = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24827)  op(e0, e2) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24828)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24828) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24829)  all_58_6 = e1 & op(e1, e3) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24829) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24830)  all_58_6 = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (239), (243),
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (24311), (24552), (24830),
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1161.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24831)  all_58_7 = e1 & op(e1, e2) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24831) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24832)  all_58_7 = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24833)  op(e1, e2) = e1
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24834)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24834) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24835)  all_58_2 = e0 & op(e2, e3) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24835) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24836)  op(e2, e3) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24837)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24837) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24838)  all_58_1 = e2 & op(e3, e2) = e2
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24838) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24839)  all_58_1 = e2
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24840)  op(e3, e2) = e2
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24841)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24841) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24842)  all_58_6 = e2 & op(e1, e3) = e2
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24842) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24843)  op(e1, e3) = e2
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24844)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24844) gives:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24845)  all_58_0 = e0 & op(e3, e3) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24845) implies:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24846)  op(e3, e3) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24552), (24846), (function-axioms) are
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1828.
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24847)  all_58_1 = e0 & op(e3, e2) = e0
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 238.95/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24847) implies:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24848)  all_58_1 = e0
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (237), (24308), (24827), (24832),
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24848), (function-axioms) are inconsistent by
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #882.
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24849)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24849) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24850)  all_58_4 = e0 & op(e3, e1) = e0
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24850) implies:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24851)  all_58_4 = e0
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (158), (24827) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24852)  all_52_7 = e0
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (160), (24814) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24853)  all_52_14 = e0
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (162), (24833) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24854)  all_52_6 = e1
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (163), (24843) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24855)  all_52_2 = e2
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (164), (24802) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24856)  all_52_13 = e1
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (165), (24793) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24857)  all_52_9 = e2
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (167), (24836) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24858)  all_52_1 = e0
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (170), (24840) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24859)  all_52_4 = e2
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23031), (24857) imply:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24860)   ~ (e3 = e2)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17767), (24856) imply:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24861)   ~ (e2 = e1)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23033), (24853) imply:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24862)   ~ (e3 = e0)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17768), (24853) imply:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24863)   ~ (e2 = e0)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24864)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, all_56_11) = e2)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24864) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24865)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_56_9 & $i(all_56_9)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24865) implies:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24866)  op(e3, e2) = all_56_9
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24867)  op(e3, all_56_9) = e3
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24561) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_9,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (24840), (24866) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24868)  all_56_9 = e2
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24867), (24868) imply:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24869)  op(e3, e2) = e3
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (24292), (24869), (function-axioms) are
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2192.
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24870)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 &
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24843), (24870), (function-axioms) are
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #395.
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24871)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24871) implies:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24872)  op(e2, all_56_11) = e2
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24291), (24872) imply:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24873)  op(e2, e3) = e2
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (24289), (24555), (24836), (24873),
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #733.
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24874)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_15 & $i(all_56_15))
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24874) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24875)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24875) implies:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24876)  op(e1, e2) = all_56_13
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24877)  op(e1, all_56_13) = e1
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24289) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_56_13, e2, e1, simplifying with (24833),
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (24876) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24878)  all_56_13 = e1
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24877), (24878) imply:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24879)  op(e1, e1) = e1
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (23038), (24879), (function-axioms) are
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #468.
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24880)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_8_1)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24880) implies:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24881)   ~ (all_8_1 = e0)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24882)  op(e2, e3) = all_8_1
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24555), (24836), (24881), (24882),
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #897.
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24883)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_15 & $i(all_56_15)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24883) implies:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24884)  op(e0, e2) = all_56_15
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24885)  op(e0, all_56_15) = e0
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17760) gives:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24886)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24886) implies:
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24887)  op(e0, e2) = all_4_1
% 239.05/45.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (165), (170),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (225), (229), (230), (237), (239), (240),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (246), (17773), (17774), (23031),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24292), (24297), (24301), (24307), (24552),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24558), (24561), (24801), (24813), (24820),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24827), (24833), (24839), (24843), (24851),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24884), (24885), (24887), (function-axioms) are
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24888)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24888) implies:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24889)  op(e0, e2) = all_4_1
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (165), (170),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (225), (229), (230), (237), (239), (240),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (243), (244), (246), (17773), (17774), (23031),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24292), (24297), (24301), (24307), (24552),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24558), (24561), (24801), (24813), (24820),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24827), (24833), (24839), (24843), (24851),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24884), (24885), (24889), (function-axioms) are
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24890)  all_58_9 = e0 & op(e3, e0) = e0
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24890) implies:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24891)  all_58_9 = e0
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24301), (24891) imply:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24892)  e3 = e0
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24307), (24892) imply:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24893)  all_58_3 = e0
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (237), (238), (24826),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24827), (24832), (24893), (function-axioms) are
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1375.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24894)  all_58_7 = e2 & op(e1, e2) = e2
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (162), (235), (237),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24307), (24308), (24832), (24833), (24839),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24894), (function-axioms) are inconsistent by
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #290.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24895)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (170), (222),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (240), (244), (246), (17773), (23031),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24292), (24301), (24552), (24801), (24813),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24814), (24820), (24839), (24895),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #8.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24896)  all_58_3 = e2 & op(e2, e2) = e2
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24896) implies:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24897)  op(e2, e2) = e2
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (165), (167), (234), (23031), (24294),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24311), (24897), (function-axioms) are
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1321.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24898)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (222), (231),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (17773), (24307), (24792), (24801),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24807), (24827), (24832), (24898),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #7.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24899)  all_58_3 = e0 & op(e2, e2) = e0
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24899) implies:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24900)  all_58_3 = e0
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (237), (238), (24826),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (24827), (24832), (24900), (function-axioms) are
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1375.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24901)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (164), (24793), (24802), (24901),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #6.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24902)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (23038), (24814), (24902),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #289.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24903)  all_58_14 = e0 & op(e0, e1) = e0
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (24903) implies:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (24904)  op(e0, e1) = e0
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24821), (24904), (function-axioms) are
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2158.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | |   (24905)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (17765), (23038), (24905),
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | |            #57.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | |   (24906)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | |            = all_56_7 & $i(all_56_7)
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | ALPHA: (24906) implies:
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | |   (24907)  op(e0, e3) = all_56_7
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | |   (24908)  op(e0, all_56_7) = e0
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (24298), (24907), (24908), (function-axioms)
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2070.
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | |   (24909)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 239.05/45.92  | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 239.05/45.92  | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | | REF_CLOSE: (158), (162), (23029), (24293), (24909),
% 239.05/45.92  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 239.05/45.92  | | | | | | | | | | | | |            #475.
% 239.05/45.92  | | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | |   (24910)  all_58_10 = e3 & op(e2, e0) = e3
% 239.05/45.92  | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | ALPHA: (24910) implies:
% 239.05/45.92  | | | | | | | | | | | |   (24911)  op(e2, e0) = e3
% 239.05/45.92  | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | | REF_CLOSE: (164), (24294), (24911), (function-axioms) are
% 239.05/45.92  | | | | | | | | | | | |            inconsistent by sub-proof #1994.
% 239.05/45.92  | | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | |   (24912)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 239.05/45.92  | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 239.05/45.92  | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | | REF_CLOSE: (9), (160), (17774), (23033), (24912),
% 239.05/45.92  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 239.05/45.92  | | | | | | | | | | |            #214.
% 239.05/45.92  | | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | |   (24913)  all_58_13 = e3 & op(e0, e2) = e3
% 239.05/45.92  | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | | REF_CLOSE: (158), (24293), (24913), (function-axioms) are
% 239.05/45.92  | | | | | | | | | |            inconsistent by sub-proof #1919.
% 239.05/45.92  | | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | | 
% 239.05/45.92  | | | | | | | | Case 2:
% 239.05/45.92  | | | | | | | | | 
% 239.05/45.92  | | | | | | | | |   (24914)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 239.05/45.92  | | | | | | | | |              e3 & op(e0, e0) = e3)
% 239.05/45.92  | | | | | | | | | 
% 239.05/45.92  | | | | | | | | | REF_CLOSE: (9), (157), (17774), (23032), (24914),
% 239.05/45.92  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 239.05/45.92  | | | | | | | | |            #226.
% 239.05/45.92  | | | | | | | | | 
% 239.05/45.92  | | | | | | | | End of split
% 239.05/45.92  | | | | | | | | 
% 239.05/45.92  | | | | | | | End of split
% 239.05/45.92  | | | | | | | 
% 239.05/45.92  | | | | | | Case 2:
% 239.05/45.92  | | | | | | | 
% 239.05/45.92  | | | | | | |   (24915)  all_58_11 = e3 & op(e1, e0) = e3
% 239.05/45.92  | | | | | | | 
% 239.05/45.92  | | | | | | | ALPHA: (24915) implies:
% 239.05/45.92  | | | | | | |   (24916)  op(e1, e0) = e3
% 239.05/45.92  | | | | | | | 
% 239.05/45.92  | | | | | | | REF_CLOSE: (160), (23033), (24916), (function-axioms) are
% 239.05/45.92  | | | | | | |            inconsistent by sub-proof #2149.
% 239.05/45.92  | | | | | | | 
% 239.05/45.92  | | | | | | End of split
% 239.05/45.92  | | | | | | 
% 239.05/45.92  | | | | | End of split
% 239.05/45.92  | | | | | 
% 239.05/45.92  | | | | End of split
% 239.05/45.92  | | | | 
% 239.05/45.92  | | | End of split
% 239.05/45.92  | | | 
% 239.05/45.92  | | End of split
% 239.05/45.92  | | 
% 239.05/45.92  | End of split
% 239.05/45.92  | 
% 239.05/45.92  End of proof
% 239.05/45.93  
% 239.05/45.93  Sub-proof #1 shows that the following formulas are inconsistent:
% 239.05/45.93  ----------------------------------------------------------------
% 239.05/45.93    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.05/45.93         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.05/45.93    (2)   ~ (e3 = e0)
% 239.05/45.93    (3)  op(e1, e2) = e1
% 239.05/45.93    (4)   ~ (e2 = e0)
% 239.05/45.93    (5)  op(e1, e2) = all_52_6
% 239.05/45.93    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.05/45.93         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.05/45.93    (7)   ~ (e3 = e1)
% 239.05/45.93    (8)  all_58_3 = e3
% 239.05/45.93    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.05/45.93         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.05/45.93    (10)  op(e0, e2) = all_4_1
% 239.05/45.93    (11)  op(e1, e3) = e2
% 239.05/45.93    (12)  op(e3, e3) = e1
% 239.05/45.93    (13)  all_58_15 = e2
% 239.05/45.93    (14)  op(e2, e1) = all_52_9
% 239.05/45.93    (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 239.05/45.93          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 239.05/45.93    (16)   ~ (e3 = e2)
% 239.05/45.93    (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.05/45.93          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.05/45.93    (18)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.05/45.93            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 239.05/45.93              e2) = all_44_1 & $i(all_44_1))
% 239.05/45.93    (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.05/45.93          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.05/45.93    (20)  all_58_9 = e3
% 239.05/45.93    (21)  op(e0, e2) = all_56_15
% 239.05/45.93    (22)  all_58_12 = e3
% 239.05/45.93    (23)  op(e0, e2) = e0
% 239.05/45.93    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.05/45.93          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.05/45.93    (25)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.05/45.93          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.05/45.93    (26)   ~ (all_52_4 = e3)
% 239.05/45.93    (27)  op(e3, e2) = all_52_4
% 239.05/45.93    (28)  all_58_1 = e2
% 239.05/45.93    (29)   ~ (all_52_9 = e3)
% 239.05/45.93    (30)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 239.05/45.93          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.05/45.93    (31)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.05/45.93          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.05/45.93    (32)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.05/45.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.05/45.93    (33)  op(e0, all_56_15) = e0
% 239.05/45.93    (34)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.05/45.93            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 239.05/45.93              e3) = all_46_1 & $i(all_46_1))
% 239.05/45.93    (35)  all_58_11 = e0
% 239.05/45.93    (36)   ~ (e1 = e0)
% 239.05/45.93    (37)  op(e0, e0) = e2
% 239.05/45.93    (38)  all_58_14 = e1
% 239.05/45.93    (39)  all_58_10 = e1
% 239.05/45.93    (40)  all_58_4 = e0
% 239.05/45.93    (41)   ~ (e2 = e1)
% 239.05/45.93  
% 239.05/45.93  Begin of proof
% 239.05/45.93  | 
% 239.05/45.93  | BETA: splitting (18) gives:
% 239.05/45.93  | 
% 239.05/45.93  | Case 1:
% 239.05/45.93  | | 
% 239.05/45.93  | |   (42)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.05/45.93  | |         all_44_1 & $i(all_44_0) & $i(all_44_1)
% 239.05/45.93  | | 
% 239.05/45.93  | | ALPHA: (42) implies:
% 239.05/45.93  | |   (43)  op(e0, e2) = all_44_1
% 239.05/45.93  | | 
% 239.05/45.93  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 239.05/45.93  | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 239.05/45.93  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 239.05/45.93  | |            (36), (37), (38), (39), (40), (41), (43) are inconsistent by
% 239.05/45.93  | |            sub-proof #2.
% 239.05/45.93  | | 
% 239.05/45.93  | Case 2:
% 239.05/45.93  | | 
% 239.05/45.93  | |   (44)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 & $i(all_44_1)
% 239.05/45.93  | | 
% 239.05/45.93  | | ALPHA: (44) implies:
% 239.05/45.93  | |   (45)  op(e0, e2) = all_44_1
% 239.05/45.93  | | 
% 239.05/45.93  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 239.05/45.93  | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 239.05/45.93  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 239.05/45.93  | |            (36), (37), (38), (39), (40), (41), (45) are inconsistent by
% 239.05/45.93  | |            sub-proof #2.
% 239.05/45.93  | | 
% 239.05/45.93  | End of split
% 239.05/45.93  | 
% 239.05/45.93  End of proof
% 239.05/45.93  
% 239.05/45.93  Sub-proof #2 shows that the following formulas are inconsistent:
% 239.05/45.93  ----------------------------------------------------------------
% 239.05/45.93    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.05/45.93         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.05/45.93    (2)   ~ (e3 = e0)
% 239.05/45.93    (3)  op(e1, e2) = e1
% 239.05/45.93    (4)   ~ (e2 = e0)
% 239.05/45.93    (5)  op(e1, e2) = all_52_6
% 239.05/45.93    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.05/45.93         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.05/45.93    (7)   ~ (e3 = e1)
% 239.05/45.93    (8)  all_58_3 = e3
% 239.05/45.93    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.05/45.93         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.05/45.93    (10)  op(e0, e2) = all_4_1
% 239.05/45.93    (11)  op(e1, e3) = e2
% 239.05/45.93    (12)  op(e3, e3) = e1
% 239.05/45.93    (13)  all_58_15 = e2
% 239.05/45.93    (14)  op(e2, e1) = all_52_9
% 239.05/45.93    (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 239.05/45.93          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 239.05/45.93    (16)   ~ (e3 = e2)
% 239.05/45.93    (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.05/45.93          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.05/45.93    (18)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.05/45.93          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.05/45.93    (19)  all_58_9 = e3
% 239.05/45.93    (20)  op(e0, e2) = all_56_15
% 239.05/45.93    (21)  all_58_12 = e3
% 239.05/45.93    (22)  op(e0, e2) = e0
% 239.05/45.93    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.05/45.93          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.05/45.93    (24)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.05/45.93          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.05/45.93    (25)   ~ (all_52_4 = e3)
% 239.05/45.93    (26)  op(e3, e2) = all_52_4
% 239.05/45.93    (27)  all_58_1 = e2
% 239.05/45.93    (28)   ~ (all_52_9 = e3)
% 239.05/45.93    (29)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 239.05/45.93          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.05/45.93    (30)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.05/45.93          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.05/45.93    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.05/45.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.05/45.93    (32)  op(e0, all_56_15) = e0
% 239.05/45.93    (33)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.05/45.93            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 239.05/45.93              e3) = all_46_1 & $i(all_46_1))
% 239.05/45.93    (34)  op(e0, e2) = all_44_1
% 239.05/45.93    (35)  all_58_11 = e0
% 239.05/45.93    (36)   ~ (e1 = e0)
% 239.05/45.93    (37)  op(e0, e0) = e2
% 239.05/45.93    (38)  all_58_14 = e1
% 239.05/45.93    (39)  all_58_10 = e1
% 239.05/45.93    (40)  all_58_4 = e0
% 239.05/45.93    (41)   ~ (e2 = e1)
% 239.05/45.93  
% 239.05/45.93  Begin of proof
% 239.05/45.93  | 
% 239.05/45.93  | BETA: splitting (33) gives:
% 239.05/45.93  | 
% 239.05/45.93  | Case 1:
% 239.05/45.93  | | 
% 239.05/45.93  | | 
% 239.05/45.93  | | GROUND_INST: instantiating (31) with e0, all_44_1, e2, e0, simplifying with
% 239.05/45.93  | |              (22), (34) gives:
% 239.05/45.93  | |   (42)  all_44_1 = e0
% 239.05/45.93  | | 
% 239.05/45.93  | | GROUND_INST: instantiating (31) with all_44_1, all_56_15, e2, e0,
% 239.05/45.93  | |              simplifying with (20), (34) gives:
% 239.05/45.93  | |   (43)  all_56_15 = all_44_1
% 239.05/45.93  | | 
% 239.05/45.93  | | GROUND_INST: instantiating (31) with all_4_1, all_56_15, e2, e0, simplifying
% 239.05/45.93  | |              with (10), (20) gives:
% 239.05/45.93  | |   (44)  all_56_15 = all_4_1
% 239.05/45.93  | | 
% 239.05/45.93  | | COMBINE_EQS: (43), (44) imply:
% 239.05/45.93  | |   (45)  all_44_1 = all_4_1
% 239.05/45.93  | | 
% 239.05/45.93  | | SIMP: (45) implies:
% 239.05/45.93  | |   (46)  all_44_1 = all_4_1
% 239.05/45.93  | | 
% 239.05/45.93  | | COMBINE_EQS: (42), (46) imply:
% 239.05/45.93  | |   (47)  all_4_1 = e0
% 239.05/45.93  | | 
% 239.05/45.93  | | COMBINE_EQS: (44), (47) imply:
% 239.05/45.93  | |   (48)  all_56_15 = e0
% 239.05/45.93  | | 
% 239.05/45.93  | | REDUCE: (32), (48) imply:
% 239.05/45.93  | |   (49)  op(e0, e0) = e0
% 239.05/45.93  | | 
% 239.05/45.93  | | BETA: splitting (30) gives:
% 239.05/45.93  | | 
% 239.05/45.93  | | Case 1:
% 239.05/45.93  | | | 
% 239.05/45.93  | | |   (50)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 239.05/45.93  | | |           e2)
% 239.05/45.93  | | | 
% 239.05/45.93  | | | BETA: splitting (50) gives:
% 239.05/45.93  | | | 
% 239.05/45.93  | | | Case 1:
% 239.05/45.93  | | | | 
% 239.05/45.93  | | | |   (51)  all_58_6 = e2 & op(e1, e3) = e2
% 239.05/45.93  | | | | 
% 239.05/45.93  | | | | ALPHA: (51) implies:
% 239.05/45.93  | | | |   (52)  all_58_6 = e2
% 239.05/45.93  | | | | 
% 239.05/45.93  | | | | BETA: splitting (17) gives:
% 239.05/45.93  | | | | 
% 239.05/45.93  | | | | Case 1:
% 239.05/45.93  | | | | | 
% 239.05/45.93  | | | | |   (53)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 239.05/45.93  | | | | |             e1) = e2)
% 239.05/45.93  | | | | | 
% 239.05/45.93  | | | | | BETA: splitting (53) gives:
% 239.05/45.93  | | | | | 
% 239.05/45.93  | | | | | Case 1:
% 239.05/45.93  | | | | | | 
% 239.05/45.93  | | | | | |   (54)  all_58_4 = e2 & op(e3, e1) = e2
% 239.05/45.93  | | | | | | 
% 239.05/45.93  | | | | | | ALPHA: (54) implies:
% 239.05/45.93  | | | | | |   (55)  all_58_4 = e2
% 239.05/45.93  | | | | | | 
% 239.05/45.93  | | | | | | REF_CLOSE: (2), (4), (12), (19), (23), (27), (31), (36), (55) are
% 239.05/45.93  | | | | | |            inconsistent by sub-proof #708.
% 239.05/45.93  | | | | | | 
% 239.05/45.93  | | | | | Case 2:
% 239.05/45.93  | | | | | | 
% 239.05/45.93  | | | | | | 
% 239.05/45.93  | | | | | | GROUND_INST: instantiating (31) with e0, e2, e0, e0, simplifying
% 239.05/45.93  | | | | | |              with (37), (49) gives:
% 239.05/45.93  | | | | | |   (56)  e2 = e0
% 239.05/45.93  | | | | | | 
% 239.05/45.93  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13),
% 239.05/45.93  | | | | | |            (16), (19), (22), (23), (25), (26), (27), (29), (31),
% 239.05/45.93  | | | | | |            (35), (36), (37), (39), (41), (49), (56) are inconsistent
% 239.05/45.93  | | | | | |            by sub-proof #3.
% 239.05/45.93  | | | | | | 
% 239.05/45.93  | | | | | End of split
% 239.05/45.93  | | | | | 
% 239.05/45.93  | | | | Case 2:
% 239.05/45.93  | | | | | 
% 239.05/45.93  | | | | |   (57)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 239.05/45.93  | | | | |             e1) = e2)
% 239.05/45.94  | | | | | 
% 239.05/45.94  | | | | | BETA: splitting (57) gives:
% 239.05/45.94  | | | | | 
% 239.05/45.94  | | | | | Case 1:
% 239.05/45.94  | | | | | | 
% 239.05/45.94  | | | | | |   (58)  all_58_8 = e2 & op(e1, e1) = e2
% 239.05/45.94  | | | | | | 
% 239.05/45.94  | | | | | | ALPHA: (58) implies:
% 239.05/45.94  | | | | | |   (59)  op(e1, e1) = e2
% 239.05/45.94  | | | | | | 
% 239.05/45.94  | | | | | | REF_CLOSE: (1), (2), (4), (7), (9), (12), (13), (14), (16), (19),
% 239.05/45.94  | | | | | |            (23), (24), (25), (26), (28), (29), (31), (35), (36),
% 239.05/45.94  | | | | | |            (38), (39), (40), (41), (59) are inconsistent by
% 239.05/45.94  | | | | | |            sub-proof #9.
% 239.05/45.94  | | | | | | 
% 239.05/45.94  | | | | | Case 2:
% 239.05/45.94  | | | | | | 
% 239.05/45.94  | | | | | |   (60)  all_58_14 = e2 & op(e0, e1) = e2
% 239.05/45.94  | | | | | | 
% 239.05/45.94  | | | | | | ALPHA: (60) implies:
% 239.05/45.94  | | | | | |   (61)  all_58_14 = e2
% 239.05/45.94  | | | | | | 
% 239.05/45.94  | | | | | | COMBINE_EQS: (38), (61) imply:
% 239.05/45.94  | | | | | |   (62)  e2 = e1
% 239.05/45.94  | | | | | | 
% 239.05/45.94  | | | | | | COMBINE_EQS: (52), (62) imply:
% 239.05/45.94  | | | | | |   (63)  all_58_6 = e1
% 239.05/45.94  | | | | | | 
% 239.05/45.94  | | | | | | REF_CLOSE: (2), (4), (12), (15), (16), (18), (21), (31), (36), (41),
% 239.05/45.94  | | | | | |            (63) are inconsistent by sub-proof #1162.
% 239.05/45.94  | | | | | | 
% 239.05/45.94  | | | | | End of split
% 239.05/45.94  | | | | | 
% 239.05/45.94  | | | | End of split
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | Case 2:
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | |   (64)  all_58_7 = e2 & op(e1, e2) = e2
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | | ALPHA: (64) implies:
% 239.05/45.94  | | | |   (65)  op(e1, e2) = e2
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | | REF_CLOSE: (3), (5), (31), (36), (37), (49), (65) are inconsistent by
% 239.05/45.94  | | | |            sub-proof #627.
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | End of split
% 239.05/45.94  | | | 
% 239.05/45.94  | | Case 2:
% 239.05/45.94  | | | 
% 239.05/45.94  | | |   (66)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 239.05/45.94  | | |           e2)
% 239.05/45.94  | | | 
% 239.05/45.94  | | | BETA: splitting (66) gives:
% 239.05/45.94  | | | 
% 239.05/45.94  | | | Case 1:
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | |   (67)  all_58_8 = e2 & op(e1, e1) = e2
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | | ALPHA: (67) implies:
% 239.05/45.94  | | | |   (68)  op(e1, e1) = e2
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | | REF_CLOSE: (1), (2), (4), (7), (9), (12), (13), (14), (16), (19), (23),
% 239.05/45.94  | | | |            (24), (25), (26), (28), (29), (31), (35), (36), (38), (39),
% 239.05/45.94  | | | |            (40), (41), (68) are inconsistent by sub-proof #9.
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | Case 2:
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | |   (69)  all_58_11 = e2 & op(e1, e0) = e2
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | | ALPHA: (69) implies:
% 239.05/45.94  | | | |   (70)  all_58_11 = e2
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | | COMBINE_EQS: (35), (70) imply:
% 239.05/45.94  | | | |   (71)  e2 = e0
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | | SIMP: (71) implies:
% 239.05/45.94  | | | |   (72)  e2 = e0
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13),
% 239.05/45.94  | | | |            (16), (19), (22), (23), (25), (26), (27), (29), (31), (35),
% 239.05/45.94  | | | |            (36), (37), (39), (41), (49), (72) are inconsistent by
% 239.05/45.94  | | | |            sub-proof #3.
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | End of split
% 239.05/45.94  | | | 
% 239.05/45.94  | | End of split
% 239.05/45.94  | | 
% 239.05/45.94  | Case 2:
% 239.05/45.94  | | 
% 239.05/45.94  | |   (73)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 239.05/45.94  | | 
% 239.05/45.94  | | REF_CLOSE: (11), (31), (73) are inconsistent by sub-proof #395.
% 239.05/45.94  | | 
% 239.05/45.94  | End of split
% 239.05/45.94  | 
% 239.05/45.94  End of proof
% 239.05/45.94  
% 239.05/45.94  Sub-proof #3 shows that the following formulas are inconsistent:
% 239.05/45.94  ----------------------------------------------------------------
% 239.05/45.94    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.05/45.94         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.05/45.94    (2)   ~ (e3 = e0)
% 239.05/45.94    (3)  op(e1, e2) = e1
% 239.05/45.94    (4)   ~ (e2 = e0)
% 239.05/45.94    (5)  e2 = e0
% 239.05/45.94    (6)  op(e1, e2) = all_52_6
% 239.05/45.94    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.05/45.94         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.05/45.94    (8)   ~ (e3 = e1)
% 239.05/45.94    (9)  all_58_3 = e3
% 239.05/45.94    (10)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.05/45.94          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.05/45.94    (11)  op(e3, e3) = e1
% 239.05/45.94    (12)  all_58_15 = e2
% 239.05/45.94    (13)   ~ (e3 = e2)
% 239.05/45.94    (14)  all_58_9 = e3
% 239.05/45.94    (15)  op(e0, e2) = e0
% 239.05/45.94    (16)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.05/45.94          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.05/45.94    (17)   ~ (all_52_4 = e3)
% 239.05/45.94    (18)  op(e3, e2) = all_52_4
% 239.05/45.94    (19)  all_58_1 = e2
% 239.05/45.94    (20)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 239.05/45.94          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.05/45.94    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.05/45.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.05/45.94    (22)  op(e0, e0) = e0
% 239.05/45.94    (23)  all_58_11 = e0
% 239.05/45.94    (24)   ~ (e1 = e0)
% 239.05/45.94    (25)  op(e0, e0) = e2
% 239.05/45.94    (26)  all_58_10 = e1
% 239.05/45.94    (27)   ~ (e2 = e1)
% 239.05/45.94  
% 239.05/45.94  Begin of proof
% 239.05/45.94  | 
% 239.05/45.94  | COMBINE_EQS: (5), (19) imply:
% 239.05/45.94  |   (28)  all_58_1 = e0
% 239.05/45.94  | 
% 239.05/45.94  | BETA: splitting (1) gives:
% 239.05/45.94  | 
% 239.05/45.94  | Case 1:
% 239.05/45.94  | | 
% 239.05/45.94  | |   (29)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 239.05/45.94  | |           e2)
% 239.05/45.94  | | 
% 239.05/45.94  | | REF_CLOSE: (4), (11), (21), (27), (28), (29) are inconsistent by sub-proof
% 239.05/45.94  | |            #1477.
% 239.05/45.94  | | 
% 239.05/45.94  | Case 2:
% 239.05/45.94  | | 
% 239.05/45.94  | |   (30)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 239.05/45.94  | |           e2)
% 239.05/45.94  | | 
% 239.05/45.94  | | BETA: splitting (30) gives:
% 239.05/45.94  | | 
% 239.05/45.94  | | Case 1:
% 239.05/45.94  | | | 
% 239.05/45.94  | | |   (31)  all_58_4 = e2 & op(e3, e1) = e2
% 239.05/45.94  | | | 
% 239.05/45.94  | | | ALPHA: (31) implies:
% 239.05/45.94  | | |   (32)  all_58_4 = e2
% 239.05/45.94  | | | 
% 239.05/45.94  | | | BETA: splitting (7) gives:
% 239.05/45.94  | | | 
% 239.05/45.94  | | | Case 1:
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | |   (33)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2)
% 239.05/45.94  | | | |           = e2)
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | | BETA: splitting (33) gives:
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | | Case 1:
% 239.05/45.94  | | | | | 
% 239.05/45.94  | | | | |   (34)  all_58_1 = e2 & op(e3, e2) = e2
% 239.05/45.94  | | | | | 
% 239.05/45.94  | | | | | REF_CLOSE: (2), (4), (11), (14), (16), (19), (21), (24), (32) are
% 239.05/45.94  | | | | |            inconsistent by sub-proof #708.
% 239.05/45.94  | | | | | 
% 239.05/45.94  | | | | Case 2:
% 239.05/45.94  | | | | | 
% 239.05/45.94  | | | | |   (35)  all_58_3 = e2 & op(e2, e2) = e2
% 239.05/45.94  | | | | | 
% 239.05/45.94  | | | | | REF_CLOSE: (9), (13), (35) are inconsistent by sub-proof #1106.
% 239.05/45.94  | | | | | 
% 239.05/45.94  | | | | End of split
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | Case 2:
% 239.05/45.94  | | | | 
% 239.05/45.94  | | | |   (36)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2)
% 239.05/45.94  | | | |           = e2)
% 239.05/45.95  | | | | 
% 239.05/45.95  | | | | BETA: splitting (36) gives:
% 239.05/45.95  | | | | 
% 239.05/45.95  | | | | Case 1:
% 239.05/45.95  | | | | | 
% 239.05/45.95  | | | | |   (37)  all_58_7 = e2 & op(e1, e2) = e2
% 239.05/45.95  | | | | | 
% 239.05/45.95  | | | | | ALPHA: (37) implies:
% 239.05/45.95  | | | | |   (38)  op(e1, e2) = e2
% 239.05/45.95  | | | | | 
% 239.05/45.95  | | | | | REF_CLOSE: (3), (6), (21), (22), (24), (25), (38) are inconsistent by
% 239.05/45.95  | | | | |            sub-proof #627.
% 239.05/45.95  | | | | | 
% 239.05/45.95  | | | | Case 2:
% 239.05/45.95  | | | | | 
% 239.05/45.95  | | | | |   (39)  all_58_13 = e2 & op(e0, e2) = e2
% 239.05/45.95  | | | | | 
% 239.05/45.95  | | | | | ALPHA: (39) implies:
% 239.05/45.95  | | | | |   (40)  op(e0, e2) = e2
% 239.05/45.95  | | | | | 
% 239.05/45.95  | | | | | REF_CLOSE: (4), (15), (21), (40) are inconsistent by sub-proof #2132.
% 239.05/45.95  | | | | | 
% 239.05/45.95  | | | | End of split
% 239.05/45.95  | | | | 
% 239.05/45.95  | | | End of split
% 239.05/45.95  | | | 
% 239.05/45.95  | | Case 2:
% 239.05/45.95  | | | 
% 239.05/45.95  | | |   (41)  all_58_9 = e2 & op(e3, e0) = e2
% 239.05/45.95  | | | 
% 239.05/45.95  | | | ALPHA: (41) implies:
% 239.05/45.95  | | |   (42)  op(e3, e0) = e2
% 239.05/45.95  | | | 
% 239.05/45.95  | | | REF_CLOSE: (1), (2), (4), (8), (10), (11), (12), (13), (16), (17), (18),
% 239.05/45.95  | | |            (20), (21), (23), (24), (26), (27), (42) are inconsistent by
% 239.05/45.95  | | |            sub-proof #526.
% 239.05/45.95  | | | 
% 239.05/45.95  | | End of split
% 239.05/45.95  | | 
% 239.05/45.95  | End of split
% 239.05/45.95  | 
% 239.05/45.95  End of proof
% 239.05/45.95  
% 239.05/45.95  Sub-proof #4 shows that the following formulas are inconsistent:
% 239.05/45.95  ----------------------------------------------------------------
% 239.05/45.95    (1)   ~ (e3 = e0)
% 239.05/45.95    (2)   ~ (e2 = e0)
% 239.05/45.95    (3)  all_58_4 = e2
% 239.05/45.95    (4)   ~ (e3 = e1)
% 239.05/45.95    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.05/45.95         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.05/45.95    (6)  op(e3, e3) = e1
% 239.05/45.95    (7)   ~ (e3 = e2)
% 239.05/45.95    (8)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.05/45.95    (9)   ~ (all_52_4 = e3)
% 239.05/45.95    (10)  op(e3, e2) = all_52_4
% 239.05/45.95    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.05/45.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.05/45.95  
% 239.05/45.95  Begin of proof
% 239.05/45.95  | 
% 239.05/45.95  | BETA: splitting (8) gives:
% 239.05/45.95  | 
% 239.05/45.95  | Case 1:
% 239.05/45.95  | | 
% 239.05/45.95  | |   (12)  all_58_4 = e0 & op(e3, e1) = e0
% 239.05/45.95  | | 
% 239.05/45.95  | | ALPHA: (12) implies:
% 239.05/45.95  | |   (13)  all_58_4 = e0
% 239.05/45.95  | | 
% 239.05/45.95  | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #1666.
% 239.05/45.95  | | 
% 239.05/45.95  | Case 2:
% 239.05/45.95  | | 
% 239.05/45.95  | |   (14)  all_58_9 = e0 & op(e3, e0) = e0
% 239.05/45.95  | | 
% 239.05/45.95  | | ALPHA: (14) implies:
% 239.05/45.95  | |   (15)  all_58_9 = e0
% 239.05/45.95  | | 
% 239.05/45.95  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (15) are
% 239.05/45.95  | |            inconsistent by sub-proof #1143.
% 239.05/45.95  | | 
% 239.05/45.95  | End of split
% 239.05/45.95  | 
% 239.05/45.95  End of proof
% 239.05/45.95  
% 239.05/45.95  Sub-proof #5 shows that the following formulas are inconsistent:
% 239.05/45.95  ----------------------------------------------------------------
% 239.05/45.95    (1)  op(e2, e2) = e3
% 239.05/45.95    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.05/45.95         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.05/45.95    (3)   ~ (e3 = e0)
% 239.05/45.95    (4)  op(e2, all_52_1) = e2
% 239.05/45.95    (5)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 239.05/45.95         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.05/45.95    (6)   ~ (e2 = e0)
% 239.05/45.95    (7)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.05/45.95         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.05/45.95    (8)  op(e1, e2) = all_52_6
% 239.05/45.95    (9)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.05/45.95         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.05/45.95    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.05/45.95          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.05/45.95    (11)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 239.05/45.95          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 239.05/45.95    (12)  op(e0, e3) = all_52_3
% 239.05/45.95    (13)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.05/45.95          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.05/45.95    (14)   ~ (e3 = e1)
% 239.05/45.95    (15)  all_58_3 = e3
% 239.05/45.95    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.05/45.95          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.05/45.95    (17)  op(e2, e1) = e2
% 239.05/45.95    (18)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 239.05/45.95          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 239.05/45.95    (19)  op(e3, e3) = e1
% 239.05/45.95    (20)  all_58_15 = e2
% 239.05/45.95    (21)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 239.05/45.95              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 239.05/45.95                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 239.05/45.95                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 239.05/45.95    (22)  op(e2, e1) = all_52_9
% 239.05/45.95    (23)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 239.05/45.95          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 239.05/45.95    (24)   ~ (e3 = e2)
% 239.05/45.95    (25)  op(e0, e3) = e3
% 239.05/45.95    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.05/45.95          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.05/45.95    (27)   ~ (all_52_3 = e2)
% 239.05/45.95    (28)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 239.05/45.95            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 239.05/45.95              e3) = all_42_1 & $i(all_42_1))
% 239.05/45.95    (29)  all_58_9 = e3
% 239.05/45.95    (30)  op(e2, e3) = all_52_1
% 239.05/45.95    (31)   ~ (all_52_13 = e2)
% 239.05/45.95    (32)  all_58_12 = e3
% 239.05/45.95    (33)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.05/45.95          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.05/45.95    (34)  op(e1, e1) = e3
% 239.05/45.95    (35)  all_58_5 = e2
% 239.05/45.95    (36)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.05/45.95          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.05/45.95    (37)   ~ (all_52_4 = e3)
% 239.05/45.95    (38)  op(e3, e2) = all_52_4
% 239.05/45.95    (39)   ~ (all_52_9 = e3)
% 239.05/45.95    (40)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.05/45.95          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.05/45.95    (41)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 239.05/45.95          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.05/45.95    (42)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.05/45.95          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.05/45.96    (43)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.05/45.96          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.05/45.96    (44)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.05/45.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.05/45.96    (45)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 239.05/45.96          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 239.05/45.96    (46)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.05/45.96          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.05/45.96    (47)   ~ (all_52_4 = e1)
% 239.05/45.96    (48)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.05/45.96          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.05/45.96    (49)   ~ (e1 = e0)
% 239.05/45.96    (50)   ~ (all_52_13 = e3)
% 239.05/45.96    (51)  op(e0, e0) = e2
% 239.05/45.96    (52)  op(e2, e0) = all_52_13
% 239.05/45.96    (53)   ~ (all_52_1 = e3)
% 239.05/45.96    (54)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 239.05/45.96            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 239.05/45.96            & $i(all_8_1))
% 239.05/45.96    (55)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.05/45.96          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.05/45.96    (56)   ~ (e2 = e1)
% 239.05/45.96    (57)   ~ (all_52_1 = e1)
% 239.05/45.96  
% 239.05/45.96  Begin of proof
% 239.05/45.96  | 
% 239.05/45.96  | BETA: splitting (55) gives:
% 239.05/45.96  | 
% 239.05/45.96  | Case 1:
% 239.05/45.96  | | 
% 239.05/45.96  | |   (58)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 239.05/45.96  | |           e1)
% 239.05/45.96  | | 
% 239.05/45.96  | | BETA: splitting (58) gives:
% 239.05/45.96  | | 
% 239.05/45.96  | | Case 1:
% 239.05/45.96  | | | 
% 239.05/45.96  | | |   (59)  all_58_2 = e1 & op(e2, e3) = e1
% 239.05/45.96  | | | 
% 239.05/45.96  | | | REF_CLOSE: (30), (44), (57), (59) are inconsistent by sub-proof #2229.
% 239.05/45.96  | | | 
% 239.05/45.96  | | Case 2:
% 239.05/45.96  | | | 
% 239.05/45.96  | | |   (60)  all_58_3 = e1 & op(e2, e2) = e1
% 239.05/45.96  | | | 
% 239.05/45.96  | | | REF_CLOSE: (3), (6), (14), (15), (18), (19), (23), (24), (26), (30), (32),
% 239.05/45.96  | | |            (44), (49), (53), (56), (60) are inconsistent by sub-proof
% 239.05/45.96  | | |            #738.
% 239.05/45.96  | | | 
% 239.05/45.96  | | End of split
% 239.05/45.96  | | 
% 239.05/45.96  | Case 2:
% 239.05/45.96  | | 
% 239.05/45.96  | |   (61)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 239.05/45.96  | |           e1)
% 239.05/45.96  | | 
% 239.05/45.96  | | BETA: splitting (61) gives:
% 239.05/45.96  | | 
% 239.05/45.96  | | Case 1:
% 239.05/45.96  | | | 
% 239.05/45.96  | | |   (62)  all_58_5 = e1 & op(e2, e1) = e1
% 239.05/45.96  | | | 
% 239.05/45.96  | | | ALPHA: (62) implies:
% 239.05/45.96  | | |   (63)  all_58_5 = e1
% 239.05/45.96  | | | 
% 239.05/45.96  | | | REF_CLOSE: (35), (56), (63) are inconsistent by sub-proof #1665.
% 239.05/45.96  | | | 
% 239.05/45.96  | | Case 2:
% 239.05/45.96  | | | 
% 239.05/45.96  | | |   (64)  all_58_10 = e1 & op(e2, e0) = e1
% 239.05/45.96  | | | 
% 239.05/45.96  | | | ALPHA: (64) implies:
% 239.05/45.96  | | |   (65)  all_58_10 = e1
% 239.05/45.96  | | |   (66)  op(e2, e0) = e1
% 239.05/45.96  | | | 
% 239.05/45.96  | | | BETA: splitting (21) gives:
% 239.05/45.96  | | | 
% 239.05/45.96  | | | Case 1:
% 239.05/45.96  | | | | 
% 239.05/45.96  | | | |   (67)  all_58_15 = e0 & op(e0, e0) = e0
% 239.05/45.96  | | | | 
% 239.05/45.96  | | | | ALPHA: (67) implies:
% 239.05/45.96  | | | |   (68)  op(e0, e0) = e0
% 239.05/45.96  | | | | 
% 239.05/45.96  | | | | REF_CLOSE: (6), (44), (51), (68) are inconsistent by sub-proof #2301.
% 239.05/45.96  | | | | 
% 239.05/45.96  | | | Case 2:
% 239.05/45.96  | | | | 
% 239.05/45.96  | | | |   (69)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 239.05/45.96  | | | |               e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 239.05/45.96  | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 239.05/45.96  | | | |               e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 239.05/45.96  | | | | 
% 239.05/45.96  | | | | ALPHA: (69) implies:
% 239.05/45.96  | | | |   (70)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 239.05/45.96  | | | |             e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.05/45.96  | | | |   (71)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 239.05/45.96  | | | |           = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.05/45.96  | | | | 
% 239.05/45.96  | | | | BETA: splitting (71) gives:
% 239.05/45.96  | | | | 
% 239.05/45.96  | | | | Case 1:
% 239.05/45.96  | | | | | 
% 239.05/45.96  | | | | |   (72)  all_58_9 = e0 & op(e3, e0) = e0
% 239.05/45.96  | | | | | 
% 239.05/45.96  | | | | | REF_CLOSE: (3), (29), (72) are inconsistent by sub-proof #2103.
% 239.05/45.96  | | | | | 
% 239.05/45.96  | | | | Case 2:
% 239.05/45.96  | | | | | 
% 239.05/45.96  | | | | |   (73)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 239.05/45.96  | | | | |             e0) = e0)
% 239.05/45.96  | | | | | 
% 239.05/45.96  | | | | | BETA: splitting (73) gives:
% 239.05/45.96  | | | | | 
% 239.05/45.96  | | | | | Case 1:
% 239.05/45.96  | | | | | | 
% 239.05/45.96  | | | | | |   (74)  all_58_10 = e0 & op(e2, e0) = e0
% 239.05/45.96  | | | | | | 
% 239.05/45.96  | | | | | | ALPHA: (74) implies:
% 239.05/45.96  | | | | | |   (75)  op(e2, e0) = e0
% 239.05/45.96  | | | | | | 
% 239.05/45.96  | | | | | | REF_CLOSE: (44), (49), (52), (66), (75) are inconsistent by
% 239.05/45.96  | | | | | |            sub-proof #1778.
% 239.05/45.96  | | | | | | 
% 239.05/45.96  | | | | | Case 2:
% 239.05/45.96  | | | | | | 
% 239.05/45.96  | | | | | |   (76)  all_58_11 = e0 & op(e1, e0) = e0
% 239.05/45.96  | | | | | | 
% 239.05/45.96  | | | | | | ALPHA: (76) implies:
% 239.05/45.96  | | | | | |   (77)  all_58_11 = e0
% 239.05/45.96  | | | | | |   (78)  op(e1, e0) = e0
% 239.05/45.96  | | | | | | 
% 239.05/45.96  | | | | | | BETA: splitting (11) gives:
% 239.05/45.96  | | | | | | 
% 239.05/45.96  | | | | | | Case 1:
% 239.05/45.96  | | | | | | | 
% 239.05/45.96  | | | | | | |   (79)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 &
% 239.05/45.96  | | | | | | |           op(e2, e1) = e1)
% 239.05/45.96  | | | | | | | 
% 239.05/45.96  | | | | | | | REF_CLOSE: (2), (3), (6), (13), (14), (15), (19), (20), (24),
% 239.05/45.96  | | | | | | |            (29), (33), (41), (43), (44), (45), (49), (56), (65),
% 239.05/45.96  | | | | | | |            (71), (79) are inconsistent by sub-proof #10.
% 239.05/45.96  | | | | | | | 
% 239.05/45.96  | | | | | | Case 2:
% 239.05/45.96  | | | | | | | 
% 239.05/45.96  | | | | | | |   (80)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 239.05/45.96  | | | | | | |           op(e0, e1) = e1)
% 239.05/45.96  | | | | | | | 
% 239.05/45.96  | | | | | | | BETA: splitting (80) gives:
% 239.05/45.96  | | | | | | | 
% 239.05/45.96  | | | | | | | Case 1:
% 239.05/45.96  | | | | | | | | 
% 239.05/45.96  | | | | | | | |   (81)  all_58_8 = e1 & op(e1, e1) = e1
% 239.05/45.96  | | | | | | | | 
% 239.05/45.96  | | | | | | | | ALPHA: (81) implies:
% 239.05/45.96  | | | | | | | |   (82)  op(e1, e1) = e1
% 239.05/45.96  | | | | | | | | 
% 239.05/45.96  | | | | | | | | REF_CLOSE: (14), (34), (44), (82) are inconsistent by sub-proof
% 239.05/45.96  | | | | | | | |            #468.
% 239.05/45.96  | | | | | | | | 
% 239.05/45.96  | | | | | | | Case 2:
% 239.05/45.96  | | | | | | | | 
% 239.05/45.96  | | | | | | | |   (83)  all_58_14 = e1 & op(e0, e1) = e1
% 239.05/45.96  | | | | | | | | 
% 239.05/45.96  | | | | | | | | ALPHA: (83) implies:
% 239.05/45.96  | | | | | | | |   (84)  all_58_14 = e1
% 239.05/45.96  | | | | | | | |   (85)  op(e0, e1) = e1
% 239.05/45.96  | | | | | | | | 
% 239.05/45.96  | | | | | | | | BETA: splitting (70) gives:
% 239.05/45.96  | | | | | | | | 
% 239.05/45.96  | | | | | | | | Case 1:
% 239.05/45.96  | | | | | | | | | 
% 239.05/45.96  | | | | | | | | |   (86)  all_58_12 = e0 & op(e0, e3) = e0
% 239.05/45.96  | | | | | | | | | 
% 239.05/45.96  | | | | | | | | | ALPHA: (86) implies:
% 239.05/45.96  | | | | | | | | |   (87)  op(e0, e3) = e0
% 239.05/45.96  | | | | | | | | | 
% 239.05/45.96  | | | | | | | | | REF_CLOSE: (3), (25), (44), (87) are inconsistent by sub-proof
% 239.05/45.96  | | | | | | | | |            #221.
% 239.05/45.96  | | | | | | | | | 
% 239.05/45.96  | | | | | | | | Case 2:
% 239.05/45.96  | | | | | | | | | 
% 239.05/45.96  | | | | | | | | |   (88)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 239.05/45.96  | | | | | | | | |           op(e0, e1) = e0)
% 239.05/45.96  | | | | | | | | | 
% 239.05/45.96  | | | | | | | | | BETA: splitting (88) gives:
% 239.05/45.96  | | | | | | | | | 
% 239.05/45.96  | | | | | | | | | Case 1:
% 239.05/45.96  | | | | | | | | | | 
% 239.05/45.96  | | | | | | | | | |   (89)  all_58_13 = e0 & op(e0, e2) = e0
% 239.05/45.96  | | | | | | | | | | 
% 239.05/45.96  | | | | | | | | | | ALPHA: (89) implies:
% 239.05/45.97  | | | | | | | | | |   (90)  all_58_13 = e0
% 239.05/45.97  | | | | | | | | | |   (91)  op(e0, e2) = e0
% 239.05/45.97  | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | BETA: splitting (5) gives:
% 239.05/45.97  | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | Case 1:
% 239.05/45.97  | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | |   (92)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 239.05/45.97  | | | | | | | | | | |           & op(e1, e2) = e1)
% 239.05/45.97  | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | BETA: splitting (92) gives:
% 239.05/45.97  | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | Case 1:
% 239.05/45.97  | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | |   (93)  all_58_6 = e1 & op(e1, e3) = e1
% 239.05/45.97  | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | ALPHA: (93) implies:
% 239.05/45.97  | | | | | | | | | | | |   (94)  all_58_6 = e1
% 239.05/45.97  | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | REF_CLOSE: (3), (6), (14), (18), (19), (23), (24), (26),
% 239.05/45.97  | | | | | | | | | | | |            (30), (44), (49), (53), (56), (94) are
% 239.05/45.97  | | | | | | | | | | | |            inconsistent by sub-proof #1161.
% 239.05/45.97  | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | |   (95)  all_58_7 = e1 & op(e1, e2) = e1
% 239.05/45.97  | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | ALPHA: (95) implies:
% 239.05/45.97  | | | | | | | | | | | |   (96)  all_58_7 = e1
% 239.05/45.97  | | | | | | | | | | | |   (97)  op(e1, e2) = e1
% 239.05/45.97  | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | BETA: splitting (43) gives:
% 239.05/45.97  | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | Case 1:
% 239.05/45.97  | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | |   (98)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 239.05/45.97  | | | | | | | | | | | | |           & op(e2, e2) = e0)
% 239.05/45.97  | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | BETA: splitting (98) gives:
% 239.05/45.97  | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | Case 1:
% 239.05/45.97  | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | |   (99)  all_58_2 = e0 & op(e2, e3) = e0
% 239.05/45.97  | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | ALPHA: (99) implies:
% 239.05/45.97  | | | | | | | | | | | | | |   (100)  all_58_2 = e0
% 239.05/45.97  | | | | | | | | | | | | | |   (101)  op(e2, e3) = e0
% 239.05/45.97  | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 239.05/45.97  | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | Case 1:
% 239.05/45.97  | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | |   (102)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 239.05/45.97  | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 239.05/45.97  | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 239.05/45.97  | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | Case 1:
% 239.05/45.97  | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | |   (103)  all_58_1 = e2 & op(e3, e2) = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 239.05/45.97  | | | | | | | | | | | | | | | |   (104)  all_58_1 = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 239.05/45.97  | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.97  | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | |   (105)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 239.05/45.97  | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 239.05/45.97  | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | |   (106)  all_58_6 = e2 & op(e1, e3) = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 239.05/45.97  | | | | | | | | | | | | | | | | | |   (107)  op(e1, e3) = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | |   (108)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | |   (109)  all_58_0 = e2 & op(e3, e3) = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | |   (110)  op(e3, e3) = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (32), (40), (44), (49), (56), (100), (107),
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | |            (110) are inconsistent by sub-proof #257.
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | |   (111)  all_58_2 = e2 & op(e2, e3) = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | |   (112)  op(e2, e3) = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (28), (44), (54), (101), (112) are
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #733.
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | |   (113)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 239.05/45.97  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | Case 1:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (30), (31), (44), (52), (66), (101) are
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #30.
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | |   (114)  all_58_12 = e2 & op(e0, e3) = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (44), (114) are inconsistent by
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | |            sub-proof #2315.
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.97  | | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | End of split
% 239.05/45.97  | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | |   (115)  all_58_7 = e2 & op(e1, e2) = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (8), (9), (10), (15), (24), (44),
% 239.05/45.97  | | | | | | | | | | | | | | | | | |            (49), (56), (96), (97), (104), (115) are
% 239.05/45.97  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #290.
% 239.05/45.97  | | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | End of split
% 239.05/45.97  | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | |   (116)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 239.05/45.97  | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 239.05/45.97  | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (14), (16), (19), (20), (22), (24),
% 239.05/45.97  | | | | | | | | | | | | | | | | |            (29), (33), (36), (37), (38), (39), (41), (44),
% 239.05/45.97  | | | | | | | | | | | | | | | | |            (49), (56), (65), (77), (78), (84), (104), (116)
% 239.05/45.97  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #8.
% 239.05/45.97  | | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | End of split
% 239.05/45.97  | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | |   (117)  all_58_3 = e2 & op(e2, e2) = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 239.05/45.97  | | | | | | | | | | | | | | | |   (118)  op(e2, e2) = e2
% 239.05/45.97  | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (22), (24), (30), (39), (44), (50), (52),
% 239.05/45.97  | | | | | | | | | | | | | | | |            (53), (118) are inconsistent by sub-proof #1321.
% 239.05/45.97  | | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | End of split
% 239.05/45.97  | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | |   (119)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 239.05/45.97  | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 239.05/45.97  | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (13), (14), (15), (20), (24), (35),
% 239.05/45.97  | | | | | | | | | | | | | | |            (41), (43), (44), (45), (49), (56), (65), (71),
% 239.05/45.97  | | | | | | | | | | | | | | |            (91), (96), (119) are inconsistent by sub-proof
% 239.05/45.97  | | | | | | | | | | | | | | |            #7.
% 239.05/45.97  | | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | End of split
% 239.05/45.97  | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | |   (120)  all_58_3 = e0 & op(e2, e2) = e0
% 239.05/45.97  | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | ALPHA: (120) implies:
% 239.05/45.97  | | | | | | | | | | | | | |   (121)  all_58_3 = e0
% 239.05/45.97  | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (14), (24), (38), (44), (46), (47),
% 239.05/45.97  | | | | | | | | | | | | | |            (48), (49), (56), (90), (91), (121) are
% 239.05/45.97  | | | | | | | | | | | | | |            inconsistent by sub-proof #1374.
% 239.05/45.97  | | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | End of split
% 239.05/45.97  | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | |   (122)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 239.05/45.97  | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 239.05/45.97  | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | | REF_CLOSE: (6), (17), (44), (49), (52), (66), (122) are
% 239.05/45.97  | | | | | | | | | | | | |            inconsistent by sub-proof #6.
% 239.05/45.97  | | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | | End of split
% 239.05/45.97  | | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | End of split
% 239.05/45.97  | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | |   (123)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 239.05/45.97  | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 239.05/45.97  | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | | REF_CLOSE: (14), (34), (44), (49), (78), (123) are
% 239.05/45.97  | | | | | | | | | | |            inconsistent by sub-proof #289.
% 239.05/45.97  | | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | End of split
% 239.05/45.97  | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | Case 2:
% 239.05/45.97  | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | |   (124)  all_58_14 = e0 & op(e0, e1) = e0
% 239.05/45.97  | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | ALPHA: (124) implies:
% 239.05/45.97  | | | | | | | | | |   (125)  op(e0, e1) = e0
% 239.05/45.97  | | | | | | | | | | 
% 239.05/45.97  | | | | | | | | | | REF_CLOSE: (44), (49), (85), (125) are inconsistent by
% 239.05/45.98  | | | | | | | | | |            sub-proof #2158.
% 239.05/45.98  | | | | | | | | | | 
% 239.05/45.98  | | | | | | | | | End of split
% 239.05/45.98  | | | | | | | | | 
% 239.05/45.98  | | | | | | | | End of split
% 239.05/45.98  | | | | | | | | 
% 239.05/45.98  | | | | | | | End of split
% 239.05/45.98  | | | | | | | 
% 239.05/45.98  | | | | | | End of split
% 239.05/45.98  | | | | | | 
% 239.05/45.98  | | | | | End of split
% 239.05/45.98  | | | | | 
% 239.05/45.98  | | | | End of split
% 239.05/45.98  | | | | 
% 239.05/45.98  | | | End of split
% 239.05/45.98  | | | 
% 239.05/45.98  | | End of split
% 239.05/45.98  | | 
% 239.05/45.98  | End of split
% 239.05/45.98  | 
% 239.05/45.98  End of proof
% 239.05/45.98  
% 239.05/45.98  Sub-proof #6 shows that the following formulas are inconsistent:
% 239.05/45.98  ----------------------------------------------------------------
% 239.05/45.98    (1)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.05/45.98    (2)   ~ (e2 = e0)
% 239.05/45.98    (3)  op(e2, e1) = e2
% 239.05/45.98    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.05/45.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.05/45.98    (5)   ~ (e1 = e0)
% 239.05/45.98    (6)  op(e2, e0) = e1
% 239.05/45.98    (7)  op(e2, e0) = all_52_13
% 239.05/45.98  
% 239.05/45.98  Begin of proof
% 239.05/45.98  | 
% 239.05/45.98  | BETA: splitting (1) gives:
% 239.05/45.98  | 
% 239.05/45.98  | Case 1:
% 239.05/45.98  | | 
% 239.05/45.98  | |   (8)  all_58_5 = e0 & op(e2, e1) = e0
% 239.05/45.98  | | 
% 239.05/45.98  | | ALPHA: (8) implies:
% 239.05/45.98  | |   (9)  op(e2, e1) = e0
% 239.05/45.98  | | 
% 239.05/45.98  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1906.
% 239.05/45.98  | | 
% 239.05/45.98  | Case 2:
% 239.05/45.98  | | 
% 239.05/45.98  | |   (10)  all_58_10 = e0 & op(e2, e0) = e0
% 239.05/45.98  | | 
% 239.05/45.98  | | ALPHA: (10) implies:
% 239.05/45.98  | |   (11)  op(e2, e0) = e0
% 239.05/45.98  | | 
% 239.05/45.98  | | REF_CLOSE: (4), (5), (6), (7), (11) are inconsistent by sub-proof #1778.
% 239.05/45.98  | | 
% 239.05/45.98  | End of split
% 239.05/45.98  | 
% 239.05/45.98  End of proof
% 239.05/45.98  
% 239.05/45.98  Sub-proof #7 shows that the following formulas are inconsistent:
% 239.05/45.98  ----------------------------------------------------------------
% 239.05/45.98    (1)   ~ (e3 = e0)
% 239.05/45.98    (2)   ~ (e2 = e0)
% 239.05/45.98    (3)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 239.05/45.98         (all_58_11 = e0 & op(e1, e0) = e0)
% 239.05/45.98    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.05/45.98         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.05/45.98    (5)   ~ (e3 = e1)
% 239.05/45.98    (6)  all_58_3 = e3
% 239.05/45.98    (7)  all_58_15 = e2
% 239.05/45.98    (8)   ~ (e3 = e2)
% 239.05/45.98    (9)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.05/45.98    (10)  op(e0, e2) = e0
% 239.05/45.98    (11)  all_58_5 = e2
% 239.05/45.98    (12)  all_58_7 = e1
% 239.05/45.98    (13)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 239.05/45.98          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.05/45.98    (14)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.05/45.98          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.05/45.98    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.05/45.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.05/45.98    (16)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 239.05/45.98          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 239.05/45.98    (17)   ~ (e1 = e0)
% 239.05/45.98    (18)  all_58_10 = e1
% 239.05/45.98    (19)   ~ (e2 = e1)
% 239.05/45.98  
% 239.05/45.98  Begin of proof
% 239.05/45.98  | 
% 239.05/45.98  | BETA: splitting (9) gives:
% 239.05/45.98  | 
% 239.05/45.98  | Case 1:
% 239.05/45.98  | | 
% 239.05/45.98  | |   (20)  all_58_7 = e2 & op(e1, e2) = e2
% 239.05/45.98  | | 
% 239.05/45.98  | | ALPHA: (20) implies:
% 239.05/45.98  | |   (21)  all_58_7 = e2
% 239.05/45.98  | | 
% 239.05/45.98  | | COMBINE_EQS: (12), (21) imply:
% 239.05/45.98  | |   (22)  e2 = e1
% 239.05/45.98  | | 
% 239.05/45.98  | | SIMP: (22) implies:
% 239.05/45.98  | |   (23)  e2 = e1
% 239.05/45.98  | | 
% 239.05/45.98  | | COMBINE_EQS: (11), (23) imply:
% 239.05/45.98  | |   (24)  all_58_5 = e1
% 239.05/45.98  | | 
% 239.05/45.98  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (13), (14), (15), (16),
% 239.05/45.98  | |            (17), (18), (19), (24) are inconsistent by sub-proof #831.
% 239.05/45.98  | | 
% 239.05/45.98  | Case 2:
% 239.05/45.98  | | 
% 239.05/45.98  | |   (25)  all_58_13 = e2 & op(e0, e2) = e2
% 239.05/45.98  | | 
% 239.05/45.98  | | ALPHA: (25) implies:
% 239.05/45.98  | |   (26)  op(e0, e2) = e2
% 239.05/45.98  | | 
% 239.05/45.98  | | REF_CLOSE: (2), (10), (15), (26) are inconsistent by sub-proof #2132.
% 239.05/45.98  | | 
% 239.05/45.98  | End of split
% 239.05/45.98  | 
% 239.05/45.98  End of proof
% 239.05/45.98  
% 239.05/45.98  Sub-proof #8 shows that the following formulas are inconsistent:
% 239.05/45.98  ----------------------------------------------------------------
% 239.05/45.98    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.05/45.98         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.05/45.98    (2)   ~ (e3 = e0)
% 239.05/45.98    (3)  op(e1, e0) = e0
% 239.05/45.98    (4)   ~ (e2 = e0)
% 239.05/45.98    (5)   ~ (e3 = e1)
% 239.05/45.98    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.05/45.98         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.05/45.98    (7)  op(e3, e3) = e1
% 239.05/45.98    (8)  all_58_15 = e2
% 239.05/45.98    (9)  op(e2, e1) = all_52_9
% 239.05/45.98    (10)   ~ (e3 = e2)
% 239.05/45.98    (11)  all_58_9 = e3
% 239.05/45.98    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.05/45.98          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.05/45.98    (13)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.05/45.98    (14)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.05/45.98          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.05/45.98    (15)   ~ (all_52_4 = e3)
% 239.05/45.98    (16)  op(e3, e2) = all_52_4
% 239.05/45.98    (17)  all_58_1 = e2
% 239.05/45.98    (18)   ~ (all_52_9 = e3)
% 239.05/45.98    (19)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 239.05/45.98          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.05/45.98    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.05/45.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.05/45.98    (21)  all_58_11 = e0
% 239.05/45.98    (22)   ~ (e1 = e0)
% 239.05/45.98    (23)  all_58_14 = e1
% 239.05/45.98    (24)  all_58_10 = e1
% 239.05/45.98    (25)   ~ (e2 = e1)
% 239.05/45.98  
% 239.05/45.98  Begin of proof
% 239.05/45.98  | 
% 239.05/45.98  | BETA: splitting (13) gives:
% 239.05/45.98  | 
% 239.05/45.98  | Case 1:
% 239.05/45.98  | | 
% 239.05/45.98  | |   (26)  all_58_8 = e2 & op(e1, e1) = e2
% 239.05/45.98  | | 
% 239.05/45.98  | | ALPHA: (26) implies:
% 239.05/45.98  | |   (27)  op(e1, e1) = e2
% 239.05/45.98  | | 
% 239.05/45.98  | | BETA: splitting (12) gives:
% 239.05/45.98  | | 
% 239.05/45.98  | | Case 1:
% 239.05/45.98  | | | 
% 239.05/45.99  | | |   (28)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 239.05/45.99  | | |           e0)
% 239.05/45.99  | | | 
% 239.05/45.99  | | | REF_CLOSE: (4), (7), (17), (20), (22), (28) are inconsistent by sub-proof
% 239.05/45.99  | | |            #709.
% 239.05/45.99  | | | 
% 239.05/45.99  | | Case 2:
% 239.05/45.99  | | | 
% 239.05/45.99  | | |   (29)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 239.05/45.99  | | |           e0)
% 239.05/45.99  | | | 
% 239.05/45.99  | | | BETA: splitting (29) gives:
% 239.05/45.99  | | | 
% 239.05/45.99  | | | Case 1:
% 239.05/45.99  | | | | 
% 239.05/45.99  | | | |   (30)  all_58_4 = e0 & op(e3, e1) = e0
% 239.05/45.99  | | | | 
% 239.05/45.99  | | | | ALPHA: (30) implies:
% 239.05/45.99  | | | |   (31)  all_58_4 = e0
% 239.05/45.99  | | | | 
% 239.05/45.99  | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 239.05/45.99  | | | |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 239.05/45.99  | | | |            (25), (27), (31) are inconsistent by sub-proof #9.
% 239.05/45.99  | | | | 
% 239.05/45.99  | | | Case 2:
% 239.05/45.99  | | | | 
% 239.05/45.99  | | | |   (32)  all_58_9 = e0 & op(e3, e0) = e0
% 239.05/45.99  | | | | 
% 239.05/45.99  | | | | ALPHA: (32) implies:
% 239.05/45.99  | | | |   (33)  all_58_9 = e0
% 239.05/45.99  | | | | 
% 239.05/45.99  | | | | REF_CLOSE: (2), (11), (33) are inconsistent by sub-proof #1958.
% 239.05/45.99  | | | | 
% 239.05/45.99  | | | End of split
% 239.05/45.99  | | | 
% 239.05/45.99  | | End of split
% 239.05/45.99  | | 
% 239.05/45.99  | Case 2:
% 239.05/45.99  | | 
% 239.05/45.99  | |   (34)  all_58_11 = e2 & op(e1, e0) = e2
% 239.05/45.99  | | 
% 239.05/45.99  | | ALPHA: (34) implies:
% 239.05/45.99  | |   (35)  op(e1, e0) = e2
% 239.05/45.99  | | 
% 239.05/45.99  | | REF_CLOSE: (3), (4), (20), (35) are inconsistent by sub-proof #478.
% 239.05/45.99  | | 
% 239.05/45.99  | End of split
% 239.05/45.99  | 
% 239.05/45.99  End of proof
% 239.05/45.99  
% 239.05/45.99  Sub-proof #9 shows that the following formulas are inconsistent:
% 239.05/45.99  ----------------------------------------------------------------
% 239.05/45.99    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.05/45.99         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.05/45.99    (2)   ~ (e3 = e0)
% 239.05/45.99    (3)   ~ (e2 = e0)
% 239.05/45.99    (4)   ~ (e3 = e1)
% 239.05/45.99    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.05/45.99         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.05/45.99    (6)  op(e3, e3) = e1
% 239.05/45.99    (7)  all_58_15 = e2
% 239.05/45.99    (8)  op(e2, e1) = all_52_9
% 239.05/45.99    (9)   ~ (e3 = e2)
% 239.05/45.99    (10)  all_58_9 = e3
% 239.05/45.99    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.05/45.99          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.05/45.99    (12)  op(e1, e1) = e2
% 239.05/45.99    (13)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.05/45.99          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.05/45.99    (14)   ~ (all_52_4 = e3)
% 239.05/45.99    (15)  op(e3, e2) = all_52_4
% 239.05/45.99    (16)   ~ (all_52_9 = e3)
% 239.05/45.99    (17)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 239.05/45.99          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.05/45.99    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.05/45.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.05/45.99    (19)  all_58_11 = e0
% 239.05/45.99    (20)   ~ (e1 = e0)
% 239.05/45.99    (21)  all_58_14 = e1
% 239.05/45.99    (22)  all_58_10 = e1
% 239.05/45.99    (23)  all_58_4 = e0
% 239.05/45.99    (24)   ~ (e2 = e1)
% 239.05/45.99  
% 239.05/45.99  Begin of proof
% 239.05/45.99  | 
% 239.05/45.99  | BETA: splitting (13) gives:
% 239.05/45.99  | 
% 239.05/45.99  | Case 1:
% 239.05/45.99  | | 
% 239.05/45.99  | |   (25)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 239.05/45.99  | |           e3)
% 239.05/45.99  | | 
% 239.05/45.99  | | REF_CLOSE: (2), (8), (16), (18), (23), (25) are inconsistent by sub-proof
% 239.05/45.99  | |            #1667.
% 239.05/45.99  | | 
% 239.05/45.99  | Case 2:
% 239.05/45.99  | | 
% 239.05/45.99  | |   (26)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 239.05/45.99  | |           e3)
% 239.05/45.99  | | 
% 239.05/45.99  | | BETA: splitting (26) gives:
% 239.05/45.99  | | 
% 239.05/45.99  | | Case 1:
% 239.05/45.99  | | | 
% 239.05/45.99  | | |   (27)  all_58_8 = e3 & op(e1, e1) = e3
% 239.05/45.99  | | | 
% 239.05/45.99  | | | ALPHA: (27) implies:
% 239.05/45.99  | | |   (28)  op(e1, e1) = e3
% 239.05/45.99  | | | 
% 239.05/45.99  | | | REF_CLOSE: (9), (12), (18), (28) are inconsistent by sub-proof #2206.
% 239.05/45.99  | | | 
% 239.05/45.99  | | Case 2:
% 239.05/45.99  | | | 
% 239.05/45.99  | | |   (29)  all_58_14 = e3 & op(e0, e1) = e3
% 239.05/45.99  | | | 
% 239.05/45.99  | | | ALPHA: (29) implies:
% 239.05/45.99  | | |   (30)  all_58_14 = e3
% 239.05/45.99  | | | 
% 239.05/45.99  | | | COMBINE_EQS: (21), (30) imply:
% 239.05/45.99  | | |   (31)  e3 = e1
% 239.05/45.99  | | | 
% 239.05/45.99  | | | COMBINE_EQS: (10), (31) imply:
% 239.05/45.99  | | |   (32)  all_58_9 = e1
% 239.21/45.99  | | | 
% 239.21/45.99  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (14), (15), (17),
% 239.21/45.99  | | |            (18), (19), (20), (22), (24), (32) are inconsistent by
% 239.21/45.99  | | |            sub-proof #1169.
% 239.21/45.99  | | | 
% 239.21/45.99  | | End of split
% 239.21/45.99  | | 
% 239.21/45.99  | End of split
% 239.21/45.99  | 
% 239.21/45.99  End of proof
% 239.21/45.99  
% 239.21/45.99  Sub-proof #10 shows that the following formulas are inconsistent:
% 239.21/45.99  ----------------------------------------------------------------
% 239.21/45.99    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.21/45.99         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.21/45.99    (2)   ~ (e3 = e0)
% 239.21/45.99    (3)   ~ (e2 = e0)
% 239.21/45.99    (4)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 239.21/45.99         (all_58_11 = e0 & op(e1, e0) = e0)
% 239.21/45.99    (5)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 239.21/45.99    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.21/45.99         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.21/45.99    (7)   ~ (e3 = e1)
% 239.21/45.99    (8)  all_58_3 = e3
% 239.21/45.99    (9)  op(e3, e3) = e1
% 239.21/45.99    (10)  all_58_15 = e2
% 239.21/45.99    (11)   ~ (e3 = e2)
% 239.21/45.99    (12)  all_58_9 = e3
% 239.21/45.99    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.21/45.99          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.21/45.99    (14)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 239.21/45.99          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.21/45.99    (15)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.21/45.99          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.21/45.99    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.21/45.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.21/45.99    (17)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 239.21/45.99          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 239.21/45.99    (18)   ~ (e1 = e0)
% 239.21/45.99    (19)  all_58_10 = e1
% 239.21/45.99    (20)   ~ (e2 = e1)
% 239.21/45.99  
% 239.21/45.99  Begin of proof
% 239.21/45.99  | 
% 239.21/45.99  | BETA: splitting (5) gives:
% 239.21/45.99  | 
% 239.21/45.99  | Case 1:
% 239.21/45.99  | | 
% 239.21/45.99  | |   (21)  all_58_4 = e1 & op(e3, e1) = e1
% 239.21/45.99  | | 
% 239.21/45.99  | | ALPHA: (21) implies:
% 239.21/45.99  | |   (22)  all_58_4 = e1
% 239.21/45.99  | | 
% 239.21/45.99  | | REF_CLOSE: (1), (2), (3), (9), (11), (12), (13), (16), (18), (20), (22) are
% 239.21/46.00  | |            inconsistent by sub-proof #1469.
% 239.21/46.00  | | 
% 239.21/46.00  | Case 2:
% 239.21/46.00  | | 
% 239.21/46.00  | |   (23)  all_58_5 = e1 & op(e2, e1) = e1
% 239.21/46.00  | | 
% 239.21/46.00  | | ALPHA: (23) implies:
% 239.21/46.00  | |   (24)  all_58_5 = e1
% 239.21/46.00  | | 
% 239.21/46.00  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (14), (15), (16), (17),
% 239.21/46.00  | |            (18), (19), (20), (24) are inconsistent by sub-proof #831.
% 239.21/46.00  | | 
% 239.21/46.00  | End of split
% 239.21/46.00  | 
% 239.21/46.00  End of proof
% 239.21/46.00  
% 239.21/46.00  Sub-proof #11 shows that the following formulas are inconsistent:
% 239.21/46.00  ----------------------------------------------------------------
% 239.21/46.00    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.21/46.00         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.21/46.00    (2)   ~ (e3 = e0)
% 239.21/46.00    (3)   ~ (e2 = e0)
% 239.21/46.00    (4)  all_58_4 = e2
% 239.21/46.00    (5)   ~ (e3 = e1)
% 239.21/46.00    (6)  all_58_7 = e2
% 239.21/46.00    (7)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 239.21/46.00    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 239.21/46.00         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 239.21/46.00    (9)  op(e3, e3) = e1
% 239.21/46.00    (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 239.21/46.00          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 239.21/46.00    (11)   ~ (e3 = e2)
% 239.21/46.00    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.21/46.00          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.21/46.00    (13)  all_58_9 = e3
% 239.21/46.00    (14)  op(e2, e3) = all_52_1
% 239.21/46.00    (15)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.21/46.00          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.21/46.00    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.21/46.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.21/46.00    (17)   ~ (e1 = e0)
% 239.21/46.00    (18)   ~ (all_52_1 = e3)
% 239.21/46.00    (19)   ~ (e2 = e1)
% 239.21/46.00  
% 239.21/46.00  Begin of proof
% 239.21/46.00  | 
% 239.21/46.00  | BETA: splitting (7) gives:
% 239.21/46.00  | 
% 239.21/46.00  | Case 1:
% 239.21/46.00  | | 
% 239.21/46.00  | |   (20)  all_58_6 = e1 & op(e1, e3) = e1
% 239.21/46.00  | | 
% 239.21/46.00  | | ALPHA: (20) implies:
% 239.21/46.00  | |   (21)  all_58_6 = e1
% 239.21/46.00  | | 
% 239.21/46.00  | | REF_CLOSE: (2), (3), (5), (8), (9), (10), (11), (12), (14), (16), (17),
% 239.21/46.00  | |            (18), (19), (21) are inconsistent by sub-proof #1161.
% 239.21/46.00  | | 
% 239.21/46.00  | Case 2:
% 239.21/46.00  | | 
% 239.21/46.00  | |   (22)  all_58_7 = e1 & op(e1, e2) = e1
% 239.21/46.00  | | 
% 239.21/46.00  | | ALPHA: (22) implies:
% 239.21/46.00  | |   (23)  all_58_7 = e1
% 239.21/46.00  | | 
% 239.21/46.00  | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (11), (13), (15), (16), (17), (19),
% 239.21/46.00  | |            (23) are inconsistent by sub-proof #571.
% 239.21/46.00  | | 
% 239.21/46.00  | End of split
% 239.21/46.00  | 
% 239.21/46.00  End of proof
% 239.21/46.00  
% 239.21/46.00  Sub-proof #12 shows that the following formulas are inconsistent:
% 239.21/46.00  ----------------------------------------------------------------
% 239.21/46.00    (1)   ~ (e3 = e0)
% 239.21/46.00    (2)   ~ (e2 = e0)
% 239.21/46.00    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.21/46.00         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.21/46.00    (4)  all_58_4 = e2
% 239.21/46.00    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 239.21/46.00    (6)  op(e3, e3) = e1
% 239.21/46.00    (7)  op(e2, e1) = all_52_9
% 239.21/46.00    (8)   ~ (e3 = e2)
% 239.21/46.00    (9)  all_58_9 = e3
% 239.21/46.00    (10)  op(e2, e3) = all_52_1
% 239.21/46.00    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.21/46.00          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.21/46.00    (12)   ~ (all_52_9 = e3)
% 239.21/46.00    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.21/46.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.21/46.00    (14)   ~ (e1 = e0)
% 239.21/46.00    (15)   ~ (all_52_13 = e3)
% 239.21/46.00    (16)  op(e2, e0) = all_52_13
% 239.21/46.00    (17)   ~ (all_52_1 = e3)
% 239.21/46.00  
% 239.21/46.00  Begin of proof
% 239.21/46.00  | 
% 239.21/46.00  | BETA: splitting (5) gives:
% 239.21/46.00  | 
% 239.21/46.00  | Case 1:
% 239.21/46.00  | | 
% 239.21/46.00  | |   (18)  all_58_1 = e2 & op(e3, e2) = e2
% 239.21/46.00  | | 
% 239.21/46.00  | | ALPHA: (18) implies:
% 239.21/46.00  | |   (19)  all_58_1 = e2
% 239.21/46.00  | | 
% 239.21/46.00  | | REF_CLOSE: (1), (2), (4), (6), (9), (11), (13), (14), (19) are inconsistent
% 239.21/46.00  | |            by sub-proof #708.
% 239.21/46.00  | | 
% 239.21/46.00  | Case 2:
% 239.21/46.00  | | 
% 239.21/46.00  | |   (20)  all_58_3 = e2 & op(e2, e2) = e2
% 239.21/46.00  | | 
% 239.21/46.00  | | ALPHA: (20) implies:
% 239.21/46.00  | |   (21)  op(e2, e2) = e2
% 239.21/46.00  | | 
% 239.21/46.00  | | REF_CLOSE: (3), (7), (8), (10), (12), (13), (15), (16), (17), (21) are
% 239.21/46.00  | |            inconsistent by sub-proof #1321.
% 239.21/46.00  | | 
% 239.21/46.00  | End of split
% 239.21/46.00  | 
% 239.21/46.00  End of proof
% 239.21/46.00  
% 239.21/46.00  Sub-proof #13 shows that the following formulas are inconsistent:
% 239.21/46.00  ----------------------------------------------------------------
% 239.21/46.00    (1)  all_44_2 = e2
% 239.21/46.00    (2)  op(e2, e2) = e3
% 239.21/46.00    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.21/46.00         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.21/46.00    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 239.21/46.00           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 239.21/46.00           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 239.21/46.00           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 239.21/46.00           & $i(all_56_23))
% 239.21/46.00    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.21/46.00         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.21/46.00    (6)   ~ (e3 = e0)
% 239.21/46.00    (7)   ~ (all_52_7 = e2)
% 239.21/46.00    (8)  op(e0, e1) = all_52_11
% 239.21/46.00    (9)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 239.21/46.00         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.21/46.00    (10)   ~ (all_52_8 = all_52_9)
% 239.21/46.00    (11)   ~ (all_44_2 = e2) | ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 239.21/46.00            op(e0, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 239.21/46.00              e1) & op(e0, e2) = all_44_1 & $i(all_44_1))
% 239.21/46.00    (12)  all_42_2 = e3
% 239.21/46.00    (13)   ~ (e2 = e0)
% 239.21/46.00    (14)   ~ (all_52_11 = e2)
% 239.21/46.00    (15)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.21/46.00          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.21/46.00    (16)  op(e1, e2) = all_52_6
% 239.21/46.00    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.21/46.00          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.21/46.00    (18)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 239.21/46.00          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 239.21/46.01    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.21/46.01              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.21/46.01            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.21/46.01            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.21/46.01            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 239.21/46.01             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.21/46.01            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.21/46.01            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.21/46.01            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.21/46.01            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.21/46.01            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.21/46.01              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.21/46.01            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.21/46.01            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 239.21/46.01            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.21/46.01            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 239.21/46.01            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.21/46.01            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.21/46.01              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.21/46.01            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.21/46.01            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.21/46.01            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.21/46.01            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 239.21/46.01            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.21/46.01            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.21/46.01              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.21/46.01            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.21/46.01            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.21/46.01    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.21/46.01          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.21/46.01    (21)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 239.21/46.01            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 239.21/46.01              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 239.21/46.01    (22)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 239.21/46.01          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 239.21/46.01    (23)  op(e1, e0) = all_52_14
% 239.21/46.01    (24)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.21/46.01    (25)   ~ (all_52_8 = e0)
% 239.21/46.01    (26)  op(e0, e3) = all_52_3
% 239.21/46.01    (27)   ~ (e3 = e1)
% 239.21/46.01    (28)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 239.21/46.01            op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 239.21/46.01              e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 239.21/46.01    (29)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.21/46.01          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.21/46.01    (30)  all_58_3 = e3
% 239.21/46.01    (31)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.21/46.01          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.21/46.01    (32)  all_54_2 = all_52_8
% 239.21/46.01    (33)  all_58_15 = e2
% 239.21/46.01    (34)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 239.21/46.01              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 239.21/46.01                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 239.21/46.01                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 239.21/46.01    (35)   ~ (all_52_11 = e3)
% 239.21/46.01    (36)   ~ (all_52_14 = e2)
% 239.21/46.01    (37)  op(e3, e1) = all_52_8
% 239.21/46.01    (38)  op(e2, e1) = all_52_9
% 239.21/46.01    (39)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 239.21/46.01          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 239.21/46.01    (40)   ~ (e3 = e2)
% 239.21/46.01    (41)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.21/46.01          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.21/46.01    (42)  op(e0, e3) = e3
% 239.21/46.01    (43)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.21/46.01    (44)   ~ (all_52_3 = e2)
% 239.21/46.01    (45)  all_58_9 = e3
% 239.21/46.01    (46)  all_46_2 = e3
% 239.21/46.01    (47)  op(e3, e0) = e3
% 239.21/46.01    (48)  op(e2, e3) = all_52_1
% 239.21/46.01    (49)  all_58_12 = e3
% 239.21/46.01    (50)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.21/46.01          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.21/46.01    (51)  op(e1, e1) = e3
% 239.21/46.01    (52)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.21/46.01          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.21/46.01    (53)  op(e0, e2) = all_52_7
% 239.21/46.01    (54)  all_54_1 = all_52_4
% 239.21/46.01    (55)   ~ (all_52_4 = e3)
% 239.21/46.01    (56)  op(e3, e2) = all_52_4
% 239.21/46.01    (57)   ~ (all_52_9 = e3)
% 239.21/46.01    (58)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.21/46.01          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.21/46.01    (59)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 239.21/46.01          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.21/46.01    (60)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.21/46.01          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.21/46.01    (61)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.21/46.01          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.21/46.01    (62)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.21/46.01          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.21/46.01    (63)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.21/46.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.21/46.01    (64)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 239.21/46.01          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 239.21/46.01    (65)  all_56_21 = e3
% 239.21/46.01    (66)   ~ (e1 = e0)
% 239.21/46.01    (67)  op(e3, e3) = e0
% 239.21/46.01    (68)   ~ (all_52_13 = e3)
% 239.21/46.01    (69)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.21/46.01          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.21/46.01    (70)  all_56_1 = e0
% 239.21/46.01    (71)  op(e0, e0) = e2
% 239.21/46.01    (72)  op(e2, e0) = all_52_13
% 239.21/46.01    (73)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.21/46.01          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 239.21/46.01            e1)
% 239.21/46.01    (74)   ~ (all_52_1 = e3)
% 239.21/46.01    (75)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.21/46.01          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 239.21/46.01            e2)
% 239.21/46.01    (76)   ~ (all_52_4 = all_52_8)
% 239.21/46.01    (77)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 239.21/46.01            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 239.21/46.01            & $i(all_8_1))
% 239.21/46.01    (78)   ~ (all_52_4 = all_52_6)
% 239.21/46.01    (79)   ~ (all_52_4 = e0)
% 239.21/46.01    (80)   ~ (e2 = e1)
% 239.21/46.01    (81)   ~ (all_52_8 = e3)
% 239.21/46.01  
% 239.21/46.01  Begin of proof
% 239.21/46.01  | 
% 239.21/46.01  | BETA: splitting (21) gives:
% 239.21/46.01  | 
% 239.21/46.01  | Case 1:
% 239.21/46.01  | | 
% 239.21/46.01  | |   (82)   ~ (all_42_2 = e3)
% 239.21/46.01  | | 
% 239.21/46.01  | | REDUCE: (12), (82) imply:
% 239.21/46.01  | |   (83)  $false
% 239.21/46.01  | | 
% 239.21/46.01  | | CLOSE: (83) is inconsistent.
% 239.21/46.01  | | 
% 239.21/46.01  | Case 2:
% 239.21/46.01  | | 
% 239.21/46.01  | |   (84)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 239.21/46.01  | |           all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) &
% 239.21/46.01  | |           op(e2, e3) = all_42_1 & $i(all_42_1))
% 239.21/46.01  | | 
% 239.21/46.01  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 239.21/46.01  | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 239.21/46.01  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 239.21/46.01  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 239.21/46.01  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 239.21/46.01  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 239.21/46.02  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 239.21/46.02  | |            (81), (84) are inconsistent by sub-proof #14.
% 239.21/46.02  | | 
% 239.21/46.02  | End of split
% 239.21/46.02  | 
% 239.21/46.02  End of proof
% 239.21/46.02  
% 239.21/46.02  Sub-proof #14 shows that the following formulas are inconsistent:
% 239.21/46.02  ----------------------------------------------------------------
% 239.21/46.02    (1)  all_44_2 = e2
% 239.21/46.02    (2)  op(e2, e2) = e3
% 239.21/46.02    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.21/46.02         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.21/46.02    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 239.21/46.02           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 239.21/46.02           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 239.21/46.02           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 239.21/46.02           & $i(all_56_23))
% 239.21/46.02    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.21/46.02         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.21/46.02    (6)   ~ (e3 = e0)
% 239.21/46.02    (7)   ~ (all_52_7 = e2)
% 239.21/46.02    (8)  op(e0, e1) = all_52_11
% 239.21/46.02    (9)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 239.21/46.02         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.21/46.02    (10)   ~ (all_52_8 = all_52_9)
% 239.21/46.02    (11)   ~ (all_44_2 = e2) | ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 239.21/46.02            op(e0, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 239.21/46.02              e1) & op(e0, e2) = all_44_1 & $i(all_44_1))
% 239.21/46.02    (12)   ~ (e2 = e0)
% 239.21/46.02    (13)   ~ (all_52_11 = e2)
% 239.21/46.02    (14)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.21/46.02          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.21/46.02    (15)  op(e1, e2) = all_52_6
% 239.21/46.02    (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.21/46.02          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.21/46.02    (17)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 239.21/46.02          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 239.21/46.02    (18)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.21/46.02              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.21/46.02            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.21/46.02            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.21/46.02            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 239.21/46.02             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.21/46.02            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.21/46.02            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.21/46.02            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.21/46.02            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.21/46.02            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.21/46.02              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.21/46.02            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.21/46.02            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 239.21/46.02            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.21/46.02            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 239.21/46.02            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.21/46.02            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.21/46.02              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.21/46.02            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.21/46.02            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.21/46.02            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.21/46.02            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 239.21/46.02            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.21/46.02            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.21/46.02              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.21/46.02            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.21/46.02            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.21/46.02    (19)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.21/46.02          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.21/46.02    (20)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 239.21/46.02          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 239.21/46.02    (21)  op(e1, e0) = all_52_14
% 239.21/46.02    (22)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.21/46.02    (23)   ~ (all_52_8 = e0)
% 239.21/46.02    (24)  op(e0, e3) = all_52_3
% 239.21/46.02    (25)   ~ (e3 = e1)
% 239.21/46.02    (26)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 239.21/46.02            op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 239.21/46.02              e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 239.21/46.02    (27)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.21/46.02          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.21/46.02    (28)  all_58_3 = e3
% 239.21/46.02    (29)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.21/46.02          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.21/46.02    (30)  all_54_2 = all_52_8
% 239.21/46.02    (31)  all_58_15 = e2
% 239.21/46.02    (32)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 239.21/46.02              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 239.21/46.02                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 239.21/46.02                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 239.21/46.02    (33)   ~ (all_52_11 = e3)
% 239.21/46.02    (34)   ~ (all_52_14 = e2)
% 239.21/46.02    (35)  op(e3, e1) = all_52_8
% 239.21/46.02    (36)  op(e2, e1) = all_52_9
% 239.21/46.02    (37)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 239.21/46.02          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 239.21/46.02    (38)   ~ (e3 = e2)
% 239.21/46.02    (39)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.21/46.02          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.21/46.02    (40)  op(e0, e3) = e3
% 239.21/46.02    (41)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.21/46.02    (42)   ~ (all_52_3 = e2)
% 239.21/46.02    (43)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 239.21/46.02            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 239.21/46.02              e3) = all_42_1 & $i(all_42_1))
% 239.21/46.02    (44)  all_58_9 = e3
% 239.21/46.02    (45)  all_46_2 = e3
% 239.21/46.02    (46)  op(e3, e0) = e3
% 239.21/46.02    (47)  op(e2, e3) = all_52_1
% 239.21/46.02    (48)  all_58_12 = e3
% 239.21/46.02    (49)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.21/46.02          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.21/46.02    (50)  op(e1, e1) = e3
% 239.21/46.02    (51)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.21/46.02          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.21/46.02    (52)  op(e0, e2) = all_52_7
% 239.21/46.02    (53)  all_54_1 = all_52_4
% 239.21/46.02    (54)   ~ (all_52_4 = e3)
% 239.21/46.02    (55)  op(e3, e2) = all_52_4
% 239.21/46.02    (56)   ~ (all_52_9 = e3)
% 239.21/46.02    (57)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.21/46.02          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.21/46.02    (58)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 239.21/46.02          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.21/46.02    (59)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.21/46.02          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.21/46.02    (60)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.21/46.02          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.21/46.03    (61)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.21/46.03          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.21/46.03    (62)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.21/46.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.21/46.03    (63)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 239.21/46.03          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 239.21/46.03    (64)  all_56_21 = e3
% 239.21/46.03    (65)   ~ (e1 = e0)
% 239.21/46.03    (66)  op(e3, e3) = e0
% 239.21/46.03    (67)   ~ (all_52_13 = e3)
% 239.21/46.03    (68)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.21/46.03          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.21/46.03    (69)  all_56_1 = e0
% 239.21/46.03    (70)  op(e0, e0) = e2
% 239.21/46.03    (71)  op(e2, e0) = all_52_13
% 239.21/46.03    (72)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.21/46.03          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 239.21/46.03            e1)
% 239.21/46.03    (73)   ~ (all_52_1 = e3)
% 239.21/46.03    (74)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.21/46.03          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 239.21/46.03            e2)
% 239.21/46.03    (75)   ~ (all_52_4 = all_52_8)
% 239.21/46.03    (76)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 239.21/46.03            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 239.21/46.03            & $i(all_8_1))
% 239.21/46.03    (77)   ~ (all_52_4 = all_52_6)
% 239.21/46.03    (78)   ~ (all_52_4 = e0)
% 239.21/46.03    (79)   ~ (e2 = e1)
% 239.21/46.03    (80)   ~ (all_52_8 = e3)
% 239.21/46.03  
% 239.21/46.03  Begin of proof
% 239.21/46.03  | 
% 239.21/46.03  | BETA: splitting (11) gives:
% 239.21/46.03  | 
% 239.21/46.03  | Case 1:
% 239.21/46.03  | | 
% 239.21/46.03  | |   (81)   ~ (all_44_2 = e2)
% 239.21/46.03  | | 
% 239.21/46.03  | | REDUCE: (1), (81) imply:
% 239.21/46.03  | |   (82)  $false
% 239.21/46.03  | | 
% 239.21/46.03  | | CLOSE: (82) is inconsistent.
% 239.21/46.03  | | 
% 239.21/46.03  | Case 2:
% 239.21/46.03  | | 
% 239.21/46.03  | |   (83)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.21/46.03  | |           all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) &
% 239.21/46.03  | |           op(e0, e2) = all_44_1 & $i(all_44_1))
% 239.21/46.03  | | 
% 239.21/46.03  | | BETA: splitting (26) gives:
% 239.21/46.03  | | 
% 239.21/46.03  | | Case 1:
% 239.21/46.03  | | | 
% 239.21/46.03  | | |   (84)   ~ (all_46_2 = e3)
% 239.21/46.03  | | | 
% 239.21/46.03  | | | REDUCE: (45), (84) imply:
% 239.21/46.03  | | |   (85)  $false
% 239.21/46.03  | | | 
% 239.21/46.03  | | | CLOSE: (85) is inconsistent.
% 239.21/46.03  | | | 
% 239.21/46.03  | | Case 2:
% 239.21/46.03  | | | 
% 239.21/46.03  | | |   (86)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.21/46.03  | | |           all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) &
% 239.21/46.03  | | |           op(e1, e3) = all_46_1 & $i(all_46_1))
% 239.21/46.03  | | | 
% 239.21/46.03  | | | BETA: splitting (39) gives:
% 239.21/46.03  | | | 
% 239.21/46.03  | | | Case 1:
% 239.21/46.03  | | | | 
% 239.21/46.03  | | | |   (87)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 239.21/46.03  | | | |           = e2)
% 239.21/46.03  | | | | 
% 239.21/46.03  | | | | BETA: splitting (87) gives:
% 239.21/46.03  | | | | 
% 239.21/46.03  | | | | Case 1:
% 239.21/46.03  | | | | | 
% 239.21/46.03  | | | | |   (88)  all_58_4 = e2 & op(e3, e1) = e2
% 239.21/46.03  | | | | | 
% 239.21/46.03  | | | | | ALPHA: (88) implies:
% 239.21/46.03  | | | | |   (89)  all_58_4 = e2
% 239.21/46.03  | | | | | 
% 239.21/46.03  | | | | | BETA: splitting (59) gives:
% 239.21/46.03  | | | | | 
% 239.21/46.03  | | | | | Case 1:
% 239.21/46.03  | | | | | | 
% 239.21/46.03  | | | | | |   (90)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3,
% 239.21/46.03  | | | | | |             e2) = e1)
% 239.21/46.03  | | | | | | 
% 239.21/46.03  | | | | | | BETA: splitting (90) gives:
% 239.21/46.03  | | | | | | 
% 239.21/46.03  | | | | | | Case 1:
% 239.21/46.03  | | | | | | | 
% 239.21/46.03  | | | | | | |   (91)  all_58_0 = e1 & op(e3, e3) = e1
% 239.21/46.03  | | | | | | | 
% 239.21/46.03  | | | | | | | ALPHA: (91) implies:
% 239.21/46.03  | | | | | | |   (92)  op(e3, e3) = e1
% 239.21/46.03  | | | | | | | 
% 239.21/46.03  | | | | | | | REF_CLOSE: (62), (65), (66), (92) are inconsistent by sub-proof
% 239.21/46.03  | | | | | | |            #1828.
% 239.21/46.03  | | | | | | | 
% 239.21/46.03  | | | | | | Case 2:
% 239.21/46.03  | | | | | | | 
% 239.21/46.03  | | | | | | |   (93)  all_58_1 = e1 & op(e3, e2) = e1
% 239.21/46.03  | | | | | | | 
% 239.21/46.03  | | | | | | | ALPHA: (93) implies:
% 239.21/46.03  | | | | | | |   (94)  all_58_1 = e1
% 239.21/46.03  | | | | | | |   (95)  op(e3, e2) = e1
% 239.21/46.03  | | | | | | | 
% 239.21/46.03  | | | | | | | BETA: splitting (16) gives:
% 239.21/46.03  | | | | | | | 
% 239.21/46.03  | | | | | | | Case 1:
% 239.21/46.03  | | | | | | | | 
% 239.21/46.03  | | | | | | | |   (96)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 &
% 239.21/46.03  | | | | | | | |           op(e2, e2) = e2)
% 239.21/46.03  | | | | | | | | 
% 239.21/46.03  | | | | | | | | BETA: splitting (96) gives:
% 239.21/46.03  | | | | | | | | 
% 239.21/46.03  | | | | | | | | Case 1:
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | |   (97)  all_58_1 = e2 & op(e3, e2) = e2
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | ALPHA: (97) implies:
% 239.21/46.03  | | | | | | | | |   (98)  op(e3, e2) = e2
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | REF_CLOSE: (62), (79), (95), (98) are inconsistent by
% 239.21/46.03  | | | | | | | | |            sub-proof #2261.
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | Case 2:
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | |   (99)  all_58_3 = e2 & op(e2, e2) = e2
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | ALPHA: (99) implies:
% 239.21/46.03  | | | | | | | | |   (100)  op(e2, e2) = e2
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | REF_CLOSE: (14), (36), (38), (47), (56), (62), (67), (71),
% 239.21/46.03  | | | | | | | | |            (73), (100) are inconsistent by sub-proof #1321.
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | End of split
% 239.21/46.03  | | | | | | | | 
% 239.21/46.03  | | | | | | | Case 2:
% 239.21/46.03  | | | | | | | | 
% 239.21/46.03  | | | | | | | |   (101)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 &
% 239.21/46.03  | | | | | | | |            op(e0, e2) = e2)
% 239.21/46.03  | | | | | | | | 
% 239.21/46.03  | | | | | | | | BETA: splitting (101) gives:
% 239.21/46.03  | | | | | | | | 
% 239.21/46.03  | | | | | | | | Case 1:
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | |   (102)  all_58_7 = e2 & op(e1, e2) = e2
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | ALPHA: (102) implies:
% 239.21/46.03  | | | | | | | | |   (103)  all_58_7 = e2
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | BETA: splitting (68) gives:
% 239.21/46.03  | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | Case 1:
% 239.21/46.03  | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | |   (104)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 239.21/46.03  | | | | | | | | | |            & op(e1, e2) = e0)
% 239.21/46.03  | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | BETA: splitting (104) gives:
% 239.21/46.03  | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | Case 1:
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | |   (105)  all_58_6 = e0 & op(e1, e3) = e0
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | | ALPHA: (105) implies:
% 239.21/46.03  | | | | | | | | | | |   (106)  all_58_6 = e0
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | | REF_CLOSE: (12), (25), (37), (38), (48), (57), (62), (65),
% 239.21/46.03  | | | | | | | | | | |            (66), (79), (106) are inconsistent by sub-proof
% 239.21/46.03  | | | | | | | | | | |            #1442.
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | Case 2:
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | |   (107)  all_58_7 = e0 & op(e1, e2) = e0
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | | REF_CLOSE: (3), (6), (12), (25), (29), (38), (54), (55),
% 239.21/46.03  | | | | | | | | | | |            (59), (62), (65), (66), (79), (89), (103), (107)
% 239.21/46.03  | | | | | | | | | | |            are inconsistent by sub-proof #15.
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | End of split
% 239.21/46.03  | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | Case 2:
% 239.21/46.03  | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | |   (108)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0
% 239.21/46.03  | | | | | | | | | |            & op(e1, e0) = e0)
% 239.21/46.03  | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | BETA: splitting (108) gives:
% 239.21/46.03  | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | Case 1:
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | |   (109)  all_58_8 = e0 & op(e1, e1) = e0
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | | ALPHA: (109) implies:
% 239.21/46.03  | | | | | | | | | | |   (110)  op(e1, e1) = e0
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | | REF_CLOSE: (6), (8), (33), (36), (38), (51), (56), (62),
% 239.21/46.03  | | | | | | | | | | |            (89), (110) are inconsistent by sub-proof #1493.
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | Case 2:
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | |   (111)  all_58_11 = e0 & op(e1, e0) = e0
% 239.21/46.03  | | | | | | | | | | | 
% 239.21/46.03  | | | | | | | | | | | ALPHA: (111) implies:
% 239.21/46.03  | | | | | | | | | | |   (112)  op(e1, e0) = e0
% 239.21/46.04  | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | BETA: splitting (17) gives:
% 239.21/46.04  | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | |   (113)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 239.21/46.04  | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 239.21/46.04  | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | BETA: splitting (113) gives:
% 239.21/46.04  | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | |   (114)  all_58_9 = e1 & op(e3, e0) = e1
% 239.21/46.04  | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | ALPHA: (114) implies:
% 239.21/46.04  | | | | | | | | | | | | |   (115)  op(e3, e0) = e1
% 239.21/46.04  | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | REF_CLOSE: (25), (46), (62), (115) are inconsistent by
% 239.21/46.04  | | | | | | | | | | | | |            sub-proof #243.
% 239.21/46.04  | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | Case 2:
% 239.21/46.04  | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | |   (116)  all_58_10 = e1 & op(e2, e0) = e1
% 239.21/46.04  | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | ALPHA: (116) implies:
% 239.21/46.04  | | | | | | | | | | | | |   (117)  all_58_10 = e1
% 239.21/46.04  | | | | | | | | | | | | |   (118)  op(e2, e0) = e1
% 239.21/46.04  | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | BETA: splitting (9) gives:
% 239.21/46.04  | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | |   (119)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 239.21/46.04  | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 239.21/46.04  | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 239.21/46.04  | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | |   (120)  all_58_6 = e1 & op(e1, e3) = e1
% 239.21/46.04  | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 239.21/46.04  | | | | | | | | | | | | | | |   (121)  op(e1, e3) = e1
% 239.21/46.04  | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | |   (122)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 239.21/46.04  | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 239.21/46.04  | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | |   (123)  all_58_0 = e2 & op(e3, e3) = e2
% 239.21/46.04  | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 239.21/46.04  | | | | | | | | | | | | | | | | |   (124)  op(e3, e3) = e2
% 239.21/46.04  | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (62), (66), (124) are inconsistent by
% 239.21/46.04  | | | | | | | | | | | | | | | | |            sub-proof #2188.
% 239.21/46.04  | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.04  | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | |   (125)  all_58_2 = e2 & op(e2, e3) = e2
% 239.21/46.04  | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 239.21/46.04  | | | | | | | | | | | | | | | | |   (126)  op(e2, e3) = e2
% 239.21/46.04  | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | |   (127)  all_58_15 = e0 & op(e0, e0) = e0
% 239.21/46.04  | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 239.21/46.04  | | | | | | | | | | | | | | | | | |   (128)  op(e0, e0) = e0
% 239.21/46.04  | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (62), (70), (128) are inconsistent by
% 239.21/46.04  | | | | | | | | | | | | | | | | | |            sub-proof #2301.
% 239.21/46.04  | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | |   (129)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 239.21/46.04  | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 239.21/46.04  | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 239.21/46.04  | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 239.21/46.04  | | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 239.21/46.04  | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 239.21/46.04  | | | | | | | | | | | | | | | | | |   (130)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 239.21/46.04  | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 239.21/46.04  | | | | | | | | | | | | | | | | | |              e0) = e0)
% 239.21/46.04  | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | |   (131)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 239.21/46.04  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | |   (132)  all_58_1 = e0 & op(e3, e2) = e0
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (62), (78), (132) are inconsistent by
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | |            sub-proof #1968.
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | |   (133)  all_58_3 = e0 & op(e2, e2) = e0
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (12), (25), (28), (29), (38), (44),
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | |            (54), (55), (59), (62), (65), (66), (79), (133)
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #318.
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | |   (134)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 239.21/46.04  | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | |   (135)  all_58_7 = e0 & op(e1, e2) = e0
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (12), (25), (29), (38), (54), (55),
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | |            (59), (62), (65), (66), (79), (89), (103), (135)
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #15.
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | |   (136)  all_58_13 = e0 & op(e0, e2) = e0
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | |   (137)  op(e0, e2) = e0
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | |   (138)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | |   (139)  all_58_12 = e1 & op(e0, e3) = e1
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | |   (140)  all_58_12 = e1
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (25), (33), (38), (62), (70),
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | |            (137), (140) are inconsistent by sub-proof #190.
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | |   (141)  all_58_13 = e1 & op(e0, e2) = e1
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | |   (142)  op(e0, e2) = e1
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (65), (137), (142) are inconsistent by
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1872.
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | |   (143)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | |   (144)  all_58_14 = e1 & op(e0, e1) = e1
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | |   (145)  op(e0, e1) = e1
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | |   (146)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (12), (25), (28), (29), (38), (43),
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | |            (44), (54), (55), (59), (62), (65), (66), (76),
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | |            (79), (126), (146) are inconsistent by sub-proof
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | |            #314.
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | |   (147)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | |   (148)  all_58_5 = e0 & op(e2, e1) = e0
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | |   (149)  op(e2, e1) = e0
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (150)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (151)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (47), (62), (73), (79), (95), (121), (151)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #273.
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (152)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (153)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (154)   ~ (all_56_21 = e3)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (154) imply:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (155)  $false
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (156)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (157)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (158)   ~ (all_56_1 = e0)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (69), (158) imply:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (159)  $false
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (160)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e0
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (161)  op(e0, e3) = e0
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (40), (62), (161) are inconsistent by
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #221.
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (162)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (163)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (36), (62), (65), (137), (149), (163) are
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #310.
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (164)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (65), (71), (112), (118), (145), (164) are
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #495.
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | |   (165)  all_58_10 = e0 & op(e2, e0) = e0
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | |   (166)  op(e2, e0) = e0
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (65), (71), (118), (166) are inconsistent by
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1778.
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | |   (167)  all_58_15 = e1 & op(e0, e0) = e1
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | |   (168)  all_58_15 = e1
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (25), (38), (58), (62), (63), (65),
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | |            (79), (117), (130), (168) are inconsistent by
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #910.
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.05  | | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | |   (169)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 239.21/46.06  | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | REF_CLOSE: (24), (42), (62), (79), (121), (169) are
% 239.21/46.06  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2171.
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | |   (170)  all_58_7 = e1 & op(e1, e2) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 239.21/46.06  | | | | | | | | | | | | | | |   (171)  all_58_7 = e1
% 239.21/46.06  | | | | | | | | | | | | | | |   (172)  op(e1, e2) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (12), (15), (16), (19), (28), (38),
% 239.21/46.06  | | | | | | | | | | | | | | |            (62), (65), (79), (94), (171), (172) are
% 239.21/46.06  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1717.
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | |   (173)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 239.21/46.06  | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | REF_CLOSE: (25), (50), (62), (65), (112), (173) are
% 239.21/46.06  | | | | | | | | | | | | | |            inconsistent by sub-proof #289.
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | |   (174)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 239.21/46.06  | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | BETA: splitting (174) gives:
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | |   (175)  all_58_11 = e1 & op(e1, e0) = e1
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | ALPHA: (175) implies:
% 239.21/46.06  | | | | | | | | | | | | |   (176)  op(e1, e0) = e1
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | REF_CLOSE: (62), (65), (112), (176) are inconsistent by
% 239.21/46.06  | | | | | | | | | | | | |            sub-proof #2284.
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | |   (177)  all_58_15 = e1 & op(e0, e0) = e1
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | ALPHA: (177) implies:
% 239.21/46.06  | | | | | | | | | | | | |   (178)  all_58_15 = e1
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | COMBINE_EQS: (31), (178) imply:
% 239.21/46.06  | | | | | | | | | | | | |   (179)  e2 = e1
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | COMBINE_EQS: (89), (179) imply:
% 239.21/46.06  | | | | | | | | | | | | |   (180)  all_58_4 = e1
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | REF_CLOSE: (3), (6), (12), (25), (29), (38), (46), (49),
% 239.21/46.06  | | | | | | | | | | | | |            (54), (55), (62), (65), (79), (94), (180) are
% 239.21/46.06  | | | | | | | | | | | | |            inconsistent by sub-proof #1437.
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | |   (181)  all_58_13 = e2 & op(e0, e2) = e2
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | ALPHA: (181) implies:
% 239.21/46.06  | | | | | | | | |   (182)  op(e0, e2) = e2
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | REF_CLOSE: (7), (52), (62), (182) are inconsistent by
% 239.21/46.06  | | | | | | | | |            sub-proof #2327.
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | 
% 239.21/46.06  | | | | | | | End of split
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | End of split
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | Case 2:
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | |   (183)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3,
% 239.21/46.06  | | | | | |              e0) = e1)
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | | BETA: splitting (183) gives:
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | | Case 1:
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | |   (184)  all_58_4 = e1 & op(e3, e1) = e1
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | ALPHA: (184) implies:
% 239.21/46.06  | | | | | | |   (185)  all_58_4 = e1
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | REF_CLOSE: (79), (89), (185) are inconsistent by sub-proof #1786.
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | Case 2:
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | |   (186)  all_58_9 = e1 & op(e3, e0) = e1
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | ALPHA: (186) implies:
% 239.21/46.06  | | | | | | |   (187)  op(e3, e0) = e1
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | REF_CLOSE: (25), (46), (62), (187) are inconsistent by sub-proof
% 239.21/46.06  | | | | | | |            #243.
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | End of split
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | End of split
% 239.21/46.06  | | | | | 
% 239.21/46.06  | | | | Case 2:
% 239.21/46.06  | | | | | 
% 239.21/46.06  | | | | |   (188)  all_58_5 = e2 & op(e2, e1) = e2
% 239.21/46.06  | | | | | 
% 239.21/46.06  | | | | | ALPHA: (188) implies:
% 239.21/46.06  | | | | |   (189)  all_58_5 = e2
% 239.21/46.06  | | | | |   (190)  op(e2, e1) = e2
% 239.21/46.06  | | | | | 
% 239.21/46.06  | | | | | BETA: splitting (27) gives:
% 239.21/46.06  | | | | | 
% 239.21/46.06  | | | | | Case 1:
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | |   (191)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 239.21/46.06  | | | | | |              e1) = e0)
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | | BETA: splitting (191) gives:
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | | Case 1:
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | |   (192)  all_58_4 = e0 & op(e3, e1) = e0
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | ALPHA: (192) implies:
% 239.21/46.06  | | | | | | |   (193)  all_58_4 = e0
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | REF_CLOSE: (3), (6), (12), (25), (29), (38), (54), (55), (59),
% 239.21/46.06  | | | | | | |            (62), (65), (66), (79), (193) are inconsistent by
% 239.21/46.06  | | | | | | |            sub-proof #1512.
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | Case 2:
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | |   (194)  all_58_5 = e0 & op(e2, e1) = e0
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | ALPHA: (194) implies:
% 239.21/46.06  | | | | | | |   (195)  op(e2, e1) = e0
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | REF_CLOSE: (12), (62), (190), (195) are inconsistent by sub-proof
% 239.21/46.06  | | | | | | |            #1906.
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | End of split
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | Case 2:
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | |   (196)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 239.21/46.06  | | | | | |            op(e0, e1) = e0)
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | | BETA: splitting (196) gives:
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | | Case 1:
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | |   (197)  all_58_8 = e0 & op(e1, e1) = e0
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | ALPHA: (197) implies:
% 239.21/46.06  | | | | | | |   (198)  op(e1, e1) = e0
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | REF_CLOSE: (6), (8), (33), (35), (36), (51), (56), (62), (80),
% 239.21/46.06  | | | | | | |            (198) are inconsistent by sub-proof #1010.
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | Case 2:
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | |   (199)  all_58_14 = e0 & op(e0, e1) = e0
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | ALPHA: (199) implies:
% 239.21/46.06  | | | | | | |   (200)  op(e0, e1) = e0
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | BETA: splitting (20) gives:
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | 
% 239.21/46.06  | | | | | | | |   (201)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 &
% 239.21/46.06  | | | | | | | |            op(e2, e1) = e1)
% 239.21/46.06  | | | | | | | | 
% 239.21/46.06  | | | | | | | | BETA: splitting (201) gives:
% 239.21/46.06  | | | | | | | | 
% 239.21/46.06  | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | |   (202)  all_58_4 = e1 & op(e3, e1) = e1
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | ALPHA: (202) implies:
% 239.21/46.06  | | | | | | | | |   (203)  all_58_4 = e1
% 239.21/46.06  | | | | | | | | |   (204)  op(e3, e1) = e1
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | BETA: splitting (72) gives:
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | |   (205)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 239.21/46.06  | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 239.21/46.06  | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | BETA: splitting (205) gives:
% 239.21/46.06  | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | |   (206)  all_58_12 = e1 & op(e0, e3) = e1
% 239.21/46.06  | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | ALPHA: (206) implies:
% 239.21/46.06  | | | | | | | | | | |   (207)  all_58_12 = e1
% 239.21/46.06  | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | REF_CLOSE: (25), (48), (207) are inconsistent by sub-proof
% 239.21/46.06  | | | | | | | | | | |            #1542.
% 239.21/46.06  | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | |   (208)  all_58_13 = e1 & op(e0, e2) = e1
% 239.21/46.06  | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | ALPHA: (208) implies:
% 239.21/46.06  | | | | | | | | | | |   (209)  all_58_13 = e1
% 239.21/46.06  | | | | | | | | | | |   (210)  op(e0, e2) = e1
% 239.21/46.06  | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | BETA: splitting (60) gives:
% 239.21/46.06  | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | |   (211)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 239.21/46.06  | | | | | | | | | | | |            & op(e1, e2) = e2)
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | BETA: splitting (211) gives:
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | |   (212)  all_58_6 = e2 & op(e1, e3) = e2
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | ALPHA: (212) implies:
% 239.21/46.06  | | | | | | | | | | | | |   (213)  op(e1, e3) = e2
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | BETA: splitting (57) gives:
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | |   (214)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 239.21/46.06  | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | |   (215)  all_58_0 = e1 & op(e3, e3) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 239.21/46.06  | | | | | | | | | | | | | | |   (216)  op(e3, e3) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (12), (25), (29), (38), (49), (54),
% 239.21/46.06  | | | | | | | | | | | | | | |            (55), (62), (65), (79), (203), (216) are
% 239.21/46.06  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1468.
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | |   (217)  all_58_2 = e1 & op(e2, e3) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 239.21/46.06  | | | | | | | | | | | | | | |   (218)  op(e2, e3) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | |   (219)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 239.21/46.06  | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 239.21/46.06  | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 239.21/46.06  | | | | | | | | | | | | | | | |            all_56_19 & $i(all_56_19))
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | |   (220)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 239.21/46.06  | | | | | | | | | | | | | | | | |            e1) = all_56_17 & $i(all_56_17)
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (62), (80), (86), (204), (213), (220) are
% 239.21/46.06  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #394.
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | |   (221)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 239.21/46.06  | | | | | | | | | | | | | | | | |            e1) = all_56_19 & $i(all_56_19)
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 239.21/46.06  | | | | | | | | | | | | | | | | |   (222)  op(e2, e1) = all_56_19
% 239.21/46.06  | | | | | | | | | | | | | | | | |   (223)  op(e2, all_56_19) = e2
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (38), (43), (62), (76), (190), (218), (222),
% 239.21/46.06  | | | | | | | | | | | | | | | | |            (223) are inconsistent by sub-proof #750.
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | |   (224)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 239.21/46.06  | | | | | | | | | | | | | | | |          (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 239.21/46.06  | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23))
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | |   (225)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 239.21/46.06  | | | | | | | | | | | | | | | | |   (226)  op(e1, all_56_21) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | | REDUCE: (64), (226) imply:
% 239.21/46.06  | | | | | | | | | | | | | | | | |   (227)  op(e1, e3) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (79), (213), (227) are inconsistent by
% 239.21/46.06  | | | | | | | | | | | | | | | | |            sub-proof #2226.
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | |   (228)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 239.21/46.06  | | | | | | | | | | | | | | | | |            e1) = all_56_23 & $i(all_56_23)
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 239.21/46.06  | | | | | | | | | | | | | | | | |   (229)  op(e0, e1) = all_56_23
% 239.21/46.06  | | | | | | | | | | | | | | | | |   (230)  op(e0, all_56_23) = e0
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (12), (25), (32), (38), (40), (62),
% 239.21/46.06  | | | | | | | | | | | | | | | | |            (65), (70), (74), (79), (83), (209), (210), (229),
% 239.21/46.06  | | | | | | | | | | | | | | | | |            (230) are inconsistent by sub-proof #217.
% 239.21/46.06  | | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | |   (231)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 239.21/46.06  | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | Case 1:
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | |   (232)  all_58_6 = e1 & op(e1, e3) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 239.21/46.06  | | | | | | | | | | | | | | |   (233)  op(e1, e3) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | REF_CLOSE: (62), (79), (213), (233) are inconsistent by
% 239.21/46.06  | | | | | | | | | | | | | | |            sub-proof #2226.
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | |   (234)  all_58_12 = e1 & op(e0, e3) = e1
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | | REF_CLOSE: (25), (48), (234) are inconsistent by sub-proof
% 239.21/46.06  | | | | | | | | | | | | | | |            #1874.
% 239.21/46.06  | | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | |   (235)  all_58_7 = e2 & op(e1, e2) = e2
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | ALPHA: (235) implies:
% 239.21/46.06  | | | | | | | | | | | | |   (236)  op(e1, e2) = e2
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | | REF_CLOSE: (10), (15), (22), (23), (30), (36), (41), (53),
% 239.21/46.06  | | | | | | | | | | | | |            (54), (55), (62), (75), (77), (78), (80), (190),
% 239.21/46.06  | | | | | | | | | | | | |            (236) are inconsistent by sub-proof #141.
% 239.21/46.06  | | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | |   (237)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 239.21/46.06  | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | | REF_CLOSE: (21), (34), (38), (50), (62), (237) are
% 239.21/46.06  | | | | | | | | | | | |            inconsistent by sub-proof #38.
% 239.21/46.06  | | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | |   (238)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 239.21/46.06  | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 239.21/46.06  | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | | REF_CLOSE: (31), (62), (65), (79), (200), (238) are
% 239.21/46.06  | | | | | | | | | |            inconsistent by sub-proof #150.
% 239.21/46.06  | | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | |   (239)  all_58_5 = e1 & op(e2, e1) = e1
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | ALPHA: (239) implies:
% 239.21/46.06  | | | | | | | | |   (240)  all_58_5 = e1
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | | REF_CLOSE: (79), (189), (240) are inconsistent by sub-proof
% 239.21/46.06  | | | | | | | | |            #1665.
% 239.21/46.06  | | | | | | | | | 
% 239.21/46.06  | | | | | | | | End of split
% 239.21/46.06  | | | | | | | | 
% 239.21/46.06  | | | | | | | Case 2:
% 239.21/46.06  | | | | | | | | 
% 239.21/46.06  | | | | | | | |   (241)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 239.21/46.06  | | | | | | | |            op(e0, e1) = e1)
% 239.21/46.06  | | | | | | | | 
% 239.21/46.06  | | | | | | | | REF_CLOSE: (25), (50), (62), (65), (200), (241) are inconsistent
% 239.21/46.06  | | | | | | | |            by sub-proof #45.
% 239.21/46.06  | | | | | | | | 
% 239.21/46.06  | | | | | | | End of split
% 239.21/46.06  | | | | | | | 
% 239.21/46.06  | | | | | | End of split
% 239.21/46.06  | | | | | | 
% 239.21/46.06  | | | | | End of split
% 239.21/46.06  | | | | | 
% 239.21/46.06  | | | | End of split
% 239.21/46.06  | | | | 
% 239.21/46.06  | | | Case 2:
% 239.21/46.06  | | | | 
% 239.21/46.06  | | | |   (242)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 239.21/46.06  | | | |              e1) = e2)
% 239.21/46.06  | | | | 
% 239.21/46.06  | | | | REF_CLOSE: (8), (13), (38), (50), (62), (242) are inconsistent by
% 239.21/46.06  | | | |            sub-proof #57.
% 239.21/46.06  | | | | 
% 239.21/46.06  | | | End of split
% 239.21/46.06  | | | 
% 239.21/46.06  | | End of split
% 239.21/46.06  | | 
% 239.21/46.06  | End of split
% 239.21/46.06  | 
% 239.21/46.06  End of proof
% 239.21/46.06  
% 239.21/46.06  Sub-proof #15 shows that the following formulas are inconsistent:
% 239.21/46.06  ----------------------------------------------------------------
% 239.21/46.06    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.21/46.06         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.21/46.06    (2)   ~ (e3 = e0)
% 239.21/46.06    (3)  all_58_7 = e0 & op(e1, e2) = e0
% 239.21/46.06    (4)   ~ (e2 = e0)
% 239.21/46.06    (5)  all_58_4 = e2
% 239.21/46.06    (6)   ~ (e3 = e1)
% 239.21/46.06    (7)  all_58_7 = e2
% 239.21/46.06    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.21/46.06         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.21/46.06    (9)   ~ (e3 = e2)
% 239.21/46.06    (10)   ~ (all_52_4 = e3)
% 239.21/46.06    (11)  op(e3, e2) = all_52_4
% 239.21/46.06    (12)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.21/46.06          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.21/46.06    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.21/46.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.21/46.06    (14)   ~ (e1 = e0)
% 239.21/46.06    (15)  op(e3, e3) = e0
% 239.21/46.07    (16)   ~ (e2 = e1)
% 239.21/46.07  
% 239.21/46.07  Begin of proof
% 239.21/46.07  | 
% 239.21/46.07  | ALPHA: (3) implies:
% 239.21/46.07  |   (17)  all_58_7 = e0
% 239.21/46.07  | 
% 239.21/46.07  | COMBINE_EQS: (7), (17) imply:
% 239.21/46.07  |   (18)  e2 = e0
% 239.21/46.07  | 
% 239.21/46.07  | COMBINE_EQS: (5), (18) imply:
% 239.21/46.07  |   (19)  all_58_4 = e0
% 239.21/46.07  | 
% 239.21/46.07  | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (11), (12), (13), (14), (15),
% 239.21/46.07  |            (16), (19) are inconsistent by sub-proof #1512.
% 239.21/46.07  | 
% 239.21/46.07  End of proof
% 239.21/46.07  
% 239.21/46.07  Sub-proof #16 shows that the following formulas are inconsistent:
% 239.21/46.07  ----------------------------------------------------------------
% 239.21/46.07    (1)  op(e2, e2) = e3
% 239.21/46.07    (2)   ~ (e3 = e0)
% 239.21/46.07    (3)   ~ (e2 = e0)
% 239.21/46.07    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.21/46.07         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.21/46.07    (5)   ~ (e3 = e1)
% 239.21/46.07    (6)  all_58_3 = e3
% 239.21/46.07    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.21/46.07         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.21/46.07    (8)  op(e3, e1) = all_52_8
% 239.21/46.07    (9)  op(e1, all_52_2) = e1
% 239.21/46.07    (10)  op(e2, e1) = all_52_9
% 239.21/46.07    (11)   ~ (e3 = e2)
% 239.21/46.07    (12)  op(e1, e3) = e1
% 239.21/46.07    (13)  all_58_9 = e3
% 239.21/46.07    (14)  op(e3, e0) = e3
% 239.21/46.07    (15)  op(e3, e3) = e2
% 239.21/46.07    (16)  op(e1, e1) = e3
% 239.21/46.07    (17)  all_58_2 = e0
% 239.21/46.07    (18)   ~ (all_52_4 = e3)
% 239.21/46.07    (19)  op(e3, e2) = all_52_4
% 239.21/46.07    (20)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.21/46.07          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.21/46.07    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.21/46.07            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.21/46.07    (22)  op(e1, e3) = all_52_2
% 239.21/46.07    (23)   ~ (e1 = e0)
% 239.21/46.07    (24)   ~ (all_52_13 = e3)
% 239.21/46.07    (25)  op(e2, e0) = all_52_13
% 239.21/46.07    (26)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.21/46.07    (27)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.21/46.07          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.21/46.07    (28)   ~ (e2 = e1)
% 239.21/46.07    (29)   ~ (all_52_8 = e3)
% 239.21/46.07  
% 239.21/46.07  Begin of proof
% 239.21/46.07  | 
% 239.21/46.07  | BETA: splitting (26) gives:
% 239.21/46.07  | 
% 239.21/46.07  | Case 1:
% 239.21/46.07  | | 
% 239.21/46.07  | |   (30)  all_58_9 = e1 & op(e3, e0) = e1
% 239.21/46.07  | | 
% 239.21/46.07  | | ALPHA: (30) implies:
% 239.21/46.07  | |   (31)  op(e3, e0) = e1
% 239.21/46.07  | | 
% 239.21/46.07  | | REF_CLOSE: (5), (14), (21), (31) are inconsistent by sub-proof #243.
% 239.21/46.07  | | 
% 239.21/46.07  | Case 2:
% 239.21/46.07  | | 
% 239.21/46.07  | |   (32)  all_58_10 = e1 & op(e2, e0) = e1
% 239.21/46.07  | | 
% 239.21/46.07  | | ALPHA: (32) implies:
% 239.21/46.07  | |   (33)  op(e2, e0) = e1
% 239.21/46.07  | | 
% 239.21/46.07  | | BETA: splitting (20) gives:
% 239.21/46.07  | | 
% 239.21/46.07  | | Case 1:
% 239.21/46.07  | | | 
% 239.21/46.07  | | |   (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 239.21/46.07  | | |           e0)
% 239.21/46.07  | | | 
% 239.21/46.07  | | | BETA: splitting (34) gives:
% 239.21/46.07  | | | 
% 239.21/46.07  | | | Case 1:
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | | GROUND_INST: instantiating (21) with all_52_2, e1, e3, e1, simplifying
% 239.21/46.07  | | | |              with (12), (22) gives:
% 239.21/46.07  | | | |   (35)  all_52_2 = e1
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | | GROUND_INST: instantiating (21) with all_52_13, e1, e0, e2, simplifying
% 239.21/46.07  | | | |              with (25), (33) gives:
% 239.21/46.07  | | | |   (36)  all_52_13 = e1
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | | REDUCE: (24), (36) imply:
% 239.21/46.07  | | | |   (37)   ~ (e3 = e1)
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | | REDUCE: (9), (35) imply:
% 239.21/46.07  | | | |   (38)  op(e1, e1) = e1
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | | REF_CLOSE: (5), (16), (21), (38) are inconsistent by sub-proof #468.
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | Case 2:
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | |   (39)  all_58_3 = e0 & op(e2, e2) = e0
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | | REF_CLOSE: (2), (6), (7), (8), (11), (13), (15), (18), (19), (21), (29),
% 239.21/46.07  | | | |            (39) are inconsistent by sub-proof #332.
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | End of split
% 239.21/46.07  | | | 
% 239.21/46.07  | | Case 2:
% 239.21/46.07  | | | 
% 239.21/46.07  | | |   (40)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 239.21/46.07  | | |           e0)
% 239.21/46.07  | | | 
% 239.21/46.07  | | | BETA: splitting (40) gives:
% 239.21/46.07  | | | 
% 239.21/46.07  | | | Case 1:
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | |   (41)  all_58_5 = e0 & op(e2, e1) = e0
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | | ALPHA: (41) implies:
% 239.21/46.07  | | | |   (42)  op(e2, e1) = e0
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (10), (11), (17), (21), (23), (27),
% 239.21/46.07  | | | |            (28), (42) are inconsistent by sub-proof #861.
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | Case 2:
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | |   (43)  all_58_10 = e0 & op(e2, e0) = e0
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | | ALPHA: (43) implies:
% 239.21/46.07  | | | |   (44)  op(e2, e0) = e0
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | | REF_CLOSE: (21), (23), (25), (33), (44) are inconsistent by sub-proof
% 239.21/46.07  | | | |            #1778.
% 239.21/46.07  | | | | 
% 239.21/46.07  | | | End of split
% 239.21/46.07  | | | 
% 239.21/46.07  | | End of split
% 239.21/46.07  | | 
% 239.21/46.07  | End of split
% 239.21/46.07  | 
% 239.21/46.07  End of proof
% 239.21/46.07  
% 239.21/46.07  Sub-proof #17 shows that the following formulas are inconsistent:
% 239.21/46.07  ----------------------------------------------------------------
% 239.21/46.07    (1)  op(e2, e2) = e3
% 239.21/46.07    (2)   ~ (e3 = e0)
% 239.21/46.07    (3)   ~ (all_52_7 = e2)
% 239.21/46.07    (4)  op(e0, e1) = all_52_11
% 239.21/46.07    (5)   ~ (e2 = e0)
% 239.21/46.07    (6)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.21/46.07    (7)  op(e1, e2) = all_52_6
% 239.21/46.07    (8)  op(e1, e0) = all_52_14
% 239.21/46.07    (9)   ~ (e3 = e1)
% 239.21/46.07    (10)  all_58_7 = e2
% 239.21/46.07    (11)  all_58_3 = e3
% 239.21/46.07    (12)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.21/46.07          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.21/46.07    (13)  op(e2, e1) = e2
% 239.21/46.07    (14)   ~ (all_52_11 = e3)
% 239.21/46.07    (15)   ~ (all_52_14 = e2)
% 239.21/46.07    (16)  op(e3, e1) = all_52_8
% 239.21/46.07    (17)  op(e2, e1) = all_52_9
% 239.21/46.07    (18)   ~ (e3 = e2)
% 239.21/46.07    (19)  all_56_31 = e2
% 239.21/46.07    (20)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 239.21/46.07            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 239.21/46.07            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 239.21/46.07            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 239.21/46.07            op(e0, all_56_31) = e0)
% 239.21/46.07    (21)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.21/46.07          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.21/46.07    (22)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 239.21/46.07            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 239.21/46.08              e3) = all_42_1 & $i(all_42_1))
% 239.21/46.08    (23)  all_58_9 = e3
% 239.21/46.08    (24)  op(e3, e0) = e3
% 239.21/46.08    (25)  op(e2, e3) = all_52_1
% 239.21/46.08    (26)  op(e3, e3) = e2
% 239.21/46.08    (27)   ~ (all_52_14 = e3)
% 239.21/46.08    (28)   ~ (all_52_13 = e2)
% 239.21/46.08    (29)  all_58_12 = e3
% 239.21/46.08    (30)  op(e1, e1) = e3
% 239.21/46.08    (31)   ~ (all_52_6 = e3)
% 239.21/46.08    (32)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.21/46.08          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.21/46.08    (33)  op(e0, e2) = all_52_7
% 239.21/46.08    (34)   ~ (all_52_13 = all_52_14)
% 239.21/46.08    (35)   ~ (all_52_4 = e3)
% 239.21/46.08    (36)  op(e3, e2) = all_52_4
% 239.21/46.08    (37)   ~ (all_52_9 = e3)
% 239.21/46.08    (38)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.21/46.08          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.21/46.08    (39)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.21/46.08          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.21/46.08    (40)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.21/46.08          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.21/46.08    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.21/46.08            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.21/46.08    (42)  all_58_8 = e3
% 239.21/46.08    (43)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.21/46.08            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 239.21/46.08              e3) = all_46_1 & $i(all_46_1))
% 239.21/46.08    (44)  op(e1, e3) = all_52_2
% 239.21/46.08    (45)   ~ (e1 = e0)
% 239.41/46.08    (46)   ~ (all_52_13 = e3)
% 239.41/46.08    (47)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.41/46.08          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.41/46.08    (48)  op(e0, all_52_7) = e0
% 239.41/46.08    (49)  op(e0, e0) = e2
% 239.41/46.08    (50)  op(e2, e0) = all_52_13
% 239.41/46.08    (51)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 239.41/46.08            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 239.41/46.08            & $i(all_8_1))
% 239.41/46.08    (52)   ~ (e2 = e1)
% 239.41/46.08    (53)   ~ (all_52_8 = e3)
% 239.41/46.08  
% 239.41/46.08  Begin of proof
% 239.41/46.08  | 
% 239.41/46.08  | BETA: splitting (6) gives:
% 239.41/46.08  | 
% 239.41/46.08  | Case 1:
% 239.41/46.08  | | 
% 239.41/46.08  | |   (54)  all_58_8 = e1 & op(e1, e1) = e1
% 239.41/46.08  | | 
% 239.41/46.08  | | ALPHA: (54) implies:
% 239.41/46.08  | |   (55)  op(e1, e1) = e1
% 239.41/46.08  | | 
% 239.41/46.08  | | REF_CLOSE: (9), (30), (41), (55) are inconsistent by sub-proof #468.
% 239.41/46.08  | | 
% 239.41/46.08  | Case 2:
% 239.41/46.08  | | 
% 239.41/46.08  | |   (56)  all_58_11 = e1 & op(e1, e0) = e1
% 239.41/46.08  | | 
% 239.41/46.08  | | ALPHA: (56) implies:
% 239.41/46.08  | |   (57)  all_58_11 = e1
% 239.41/46.08  | |   (58)  op(e1, e0) = e1
% 239.41/46.08  | | 
% 239.41/46.08  | | BETA: splitting (47) gives:
% 239.41/46.08  | | 
% 239.41/46.08  | | Case 1:
% 239.41/46.08  | | | 
% 239.41/46.08  | | |   (59)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 239.41/46.08  | | |           e0)
% 239.41/46.08  | | | 
% 239.41/46.08  | | | BETA: splitting (59) gives:
% 239.41/46.08  | | | 
% 239.41/46.08  | | | Case 1:
% 239.41/46.08  | | | | 
% 239.41/46.08  | | | |   (60)  all_58_6 = e0 & op(e1, e3) = e0
% 239.41/46.08  | | | | 
% 239.41/46.08  | | | | ALPHA: (60) implies:
% 239.41/46.08  | | | |   (61)  op(e1, e3) = e0
% 239.41/46.08  | | | | 
% 239.41/46.08  | | | | BETA: splitting (38) gives:
% 239.41/46.08  | | | | 
% 239.41/46.08  | | | | Case 1:
% 239.41/46.08  | | | | | 
% 239.41/46.08  | | | | |   (62)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 239.41/46.08  | | | | |             e3) = e1)
% 239.41/46.08  | | | | | 
% 239.41/46.08  | | | | | BETA: splitting (62) gives:
% 239.41/46.08  | | | | | 
% 239.41/46.08  | | | | | Case 1:
% 239.41/46.08  | | | | | | 
% 239.41/46.08  | | | | | |   (63)  all_58_0 = e1 & op(e3, e3) = e1
% 239.41/46.08  | | | | | | 
% 239.41/46.08  | | | | | | ALPHA: (63) implies:
% 239.41/46.08  | | | | | |   (64)  op(e3, e3) = e1
% 239.41/46.08  | | | | | | 
% 239.41/46.08  | | | | | | REF_CLOSE: (26), (41), (52), (64) are inconsistent by sub-proof
% 239.41/46.08  | | | | | |            #2267.
% 239.41/46.08  | | | | | | 
% 239.41/46.08  | | | | | Case 2:
% 239.41/46.08  | | | | | | 
% 239.41/46.08  | | | | | |   (65)  all_58_2 = e1 & op(e2, e3) = e1
% 239.41/46.08  | | | | | | 
% 239.41/46.08  | | | | | | ALPHA: (65) implies:
% 239.41/46.08  | | | | | |   (66)  all_58_2 = e1
% 239.41/46.08  | | | | | |   (67)  op(e2, e3) = e1
% 239.41/46.08  | | | | | | 
% 239.41/46.08  | | | | | | BETA: splitting (40) gives:
% 239.41/46.08  | | | | | | 
% 239.41/46.08  | | | | | | Case 1:
% 239.41/46.08  | | | | | | | 
% 239.41/46.08  | | | | | | |   (68)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 239.41/46.08  | | | | | | |           op(e2, e2) = e0)
% 239.41/46.08  | | | | | | | 
% 239.41/46.08  | | | | | | | BETA: splitting (68) gives:
% 239.41/46.08  | | | | | | | 
% 239.41/46.08  | | | | | | | Case 1:
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | |   (69)  all_58_2 = e0 & op(e2, e3) = e0
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | REF_CLOSE: (45), (66), (69) are inconsistent by sub-proof #1972.
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | Case 2:
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | |   (70)  all_58_3 = e0 & op(e2, e2) = e0
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | REF_CLOSE: (2), (11), (12), (16), (18), (23), (26), (35), (36),
% 239.41/46.08  | | | | | | | |            (41), (53), (70) are inconsistent by sub-proof #332.
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | End of split
% 239.41/46.08  | | | | | | | 
% 239.41/46.08  | | | | | | Case 2:
% 239.41/46.08  | | | | | | | 
% 239.41/46.08  | | | | | | |   (71)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 239.41/46.08  | | | | | | |           op(e2, e0) = e0)
% 239.41/46.08  | | | | | | | 
% 239.41/46.08  | | | | | | | BETA: splitting (71) gives:
% 239.41/46.08  | | | | | | | 
% 239.41/46.08  | | | | | | | Case 1:
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | |   (72)  all_58_5 = e0 & op(e2, e1) = e0
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | ALPHA: (72) implies:
% 239.41/46.08  | | | | | | | |   (73)  op(e2, e1) = e0
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | REF_CLOSE: (5), (13), (41), (73) are inconsistent by sub-proof
% 239.41/46.08  | | | | | | | |            #1906.
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | Case 2:
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | |   (74)  all_58_10 = e0 & op(e2, e0) = e0
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | ALPHA: (74) implies:
% 239.41/46.08  | | | | | | | |   (75)  op(e2, e0) = e0
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | GROUND_INST: instantiating (41) with all_52_14, e1, e0, e1,
% 239.41/46.08  | | | | | | | |              simplifying with (8), (58) gives:
% 239.41/46.08  | | | | | | | |   (76)  all_52_14 = e1
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | GROUND_INST: instantiating (41) with all_52_2, e0, e3, e1,
% 239.41/46.08  | | | | | | | |              simplifying with (44), (61) gives:
% 239.41/46.08  | | | | | | | |   (77)  all_52_2 = e0
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | GROUND_INST: instantiating (41) with all_52_13, e0, e0, e2,
% 239.41/46.08  | | | | | | | |              simplifying with (50), (75) gives:
% 239.41/46.08  | | | | | | | |   (78)  all_52_13 = e0
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | GROUND_INST: instantiating (41) with all_52_1, e1, e3, e2,
% 239.41/46.08  | | | | | | | |              simplifying with (25), (67) gives:
% 239.41/46.08  | | | | | | | |   (79)  all_52_1 = e1
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | REDUCE: (34), (76), (78) imply:
% 239.41/46.08  | | | | | | | |   (80)   ~ (e1 = e0)
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | REDUCE: (46), (78) imply:
% 239.41/46.08  | | | | | | | |   (81)   ~ (e3 = e0)
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | REDUCE: (28), (78) imply:
% 239.41/46.08  | | | | | | | |   (82)   ~ (e2 = e0)
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | REDUCE: (27), (76) imply:
% 239.41/46.08  | | | | | | | |   (83)   ~ (e3 = e1)
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | REDUCE: (15), (76) imply:
% 239.41/46.08  | | | | | | | |   (84)   ~ (e2 = e1)
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | BETA: splitting (20) gives:
% 239.41/46.08  | | | | | | | | 
% 239.41/46.08  | | | | | | | | Case 1:
% 239.41/46.08  | | | | | | | | | 
% 239.41/46.09  | | | | | | | | |   (85)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0)
% 239.41/46.09  | | | | | | | | |           = all_56_25 & $i(all_56_25)) | (all_56_26 = e2 &
% 239.41/46.09  | | | | | | | | |           op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 239.41/46.09  | | | | | | | | |           $i(all_56_27))
% 239.41/46.09  | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | BETA: splitting (85) gives:
% 239.41/46.09  | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | Case 1:
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | |   (86)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0)
% 239.41/46.09  | | | | | | | | | |         = all_56_25 & $i(all_56_25)
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | | ALPHA: (86) implies:
% 239.41/46.09  | | | | | | | | | |   (87)  op(e3, e0) = all_56_25
% 239.41/46.09  | | | | | | | | | |   (88)  op(e3, all_56_25) = e3
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | | REF_CLOSE: (18), (22), (24), (26), (41), (51), (67), (87),
% 239.41/46.09  | | | | | | | | | |            (88) are inconsistent by sub-proof #24.
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | Case 2:
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | |   (89)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 239.41/46.09  | | | | | | | | | |         = all_56_27 & $i(all_56_27)
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | | REF_CLOSE: (1), (18), (41), (75), (89) are inconsistent by
% 239.41/46.09  | | | | | | | | | |            sub-proof #752.
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | End of split
% 239.41/46.09  | | | | | | | | | 
% 239.41/46.09  | | | | | | | | Case 2:
% 239.41/46.09  | | | | | | | | | 
% 239.41/46.09  | | | | | | | | |   (90)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0)
% 239.41/46.09  | | | | | | | | |           = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 239.41/46.09  | | | | | | | | |           op(e0, all_56_31) = e0)
% 239.41/46.09  | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | BETA: splitting (90) gives:
% 239.41/46.09  | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | Case 1:
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | |   (91)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0)
% 239.41/46.09  | | | | | | | | | |         = all_56_29 & $i(all_56_29)
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | | REF_CLOSE: (2), (5), (7), (9), (18), (21), (30), (31), (39),
% 239.41/46.09  | | | | | | | | | |            (41), (42), (43), (45), (47), (52), (57), (58),
% 239.41/46.09  | | | | | | | | | |            (61), (91) are inconsistent by sub-proof #412.
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | Case 2:
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | |   (92)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | | ALPHA: (92) implies:
% 239.41/46.09  | | | | | | | | | |   (93)  op(e0, all_56_31) = e0
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | | REDUCE: (19), (93) imply:
% 239.41/46.09  | | | | | | | | | |   (94)  op(e0, e2) = e0
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | | GROUND_INST: instantiating (41) with all_52_7, e0, e2, e0,
% 239.41/46.09  | | | | | | | | | |              simplifying with (33), (94) gives:
% 239.41/46.09  | | | | | | | | | |   (95)  all_52_7 = e0
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | | REDUCE: (48), (95) imply:
% 239.41/46.09  | | | | | | | | | |   (96)  op(e0, e0) = e0
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | | REF_CLOSE: (5), (41), (49), (96) are inconsistent by
% 239.41/46.09  | | | | | | | | | |            sub-proof #2301.
% 239.41/46.09  | | | | | | | | | | 
% 239.41/46.09  | | | | | | | | | End of split
% 239.41/46.09  | | | | | | | | | 
% 239.41/46.09  | | | | | | | | End of split
% 239.41/46.09  | | | | | | | | 
% 239.41/46.09  | | | | | | | End of split
% 239.41/46.09  | | | | | | | 
% 239.41/46.09  | | | | | | End of split
% 239.41/46.09  | | | | | | 
% 239.41/46.09  | | | | | End of split
% 239.41/46.09  | | | | | 
% 239.41/46.09  | | | | Case 2:
% 239.41/46.09  | | | | | 
% 239.41/46.09  | | | | |   (97)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 239.41/46.09  | | | | |             e3) = e1)
% 239.41/46.09  | | | | | 
% 239.41/46.09  | | | | | REF_CLOSE: (9), (29), (41), (45), (61), (97) are inconsistent by
% 239.41/46.09  | | | | |            sub-proof #21.
% 239.41/46.09  | | | | | 
% 239.41/46.09  | | | | End of split
% 239.41/46.09  | | | | 
% 239.41/46.09  | | | Case 2:
% 239.41/46.09  | | | | 
% 239.41/46.09  | | | |   (98)  all_58_7 = e0 & op(e1, e2) = e0
% 239.41/46.09  | | | | 
% 239.41/46.09  | | | | REF_CLOSE: (5), (10), (98) are inconsistent by sub-proof #2212.
% 239.41/46.09  | | | | 
% 239.41/46.09  | | | End of split
% 239.41/46.09  | | | 
% 239.41/46.09  | | Case 2:
% 239.41/46.09  | | | 
% 239.41/46.09  | | |   (99)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 239.41/46.09  | | |           e0)
% 239.41/46.09  | | | 
% 239.41/46.09  | | | REF_CLOSE: (2), (4), (14), (16), (17), (32), (37), (41), (45), (53), (58),
% 239.41/46.09  | | |            (99) are inconsistent by sub-proof #400.
% 239.41/46.09  | | | 
% 239.41/46.09  | | End of split
% 239.41/46.09  | | 
% 239.41/46.09  | End of split
% 239.41/46.09  | 
% 239.41/46.09  End of proof
% 239.41/46.09  
% 239.41/46.09  Sub-proof #18 shows that the following formulas are inconsistent:
% 239.41/46.09  ----------------------------------------------------------------
% 239.41/46.09    (1)   ~ (all_52_1 = all_52_3)
% 239.41/46.09    (2)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.41/46.09         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.41/46.09    (3)  op(e0, e3) = all_52_3
% 239.41/46.09    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.41/46.09         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.41/46.09    (5)   ~ (all_52_12 = all_52_13)
% 239.41/46.09    (6)  op(e2, e1) = all_52_9
% 239.41/46.09    (7)   ~ (e3 = e2)
% 239.41/46.09    (8)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 239.41/46.09         $i(all_56_13)
% 239.41/46.09    (9)  op(e0, e3) = e3
% 239.41/46.09    (10)  op(e3, e0) = all_52_12
% 239.41/46.09    (11)  op(e3, e0) = e3
% 239.41/46.09    (12)  op(e2, e3) = all_52_1
% 239.41/46.09    (13)   ~ (all_52_13 = e2)
% 239.41/46.09    (14)  op(e1, e2) = e2
% 239.41/46.09    (15)  all_58_5 = e2
% 239.41/46.09    (16)   ~ (all_52_9 = e3)
% 239.41/46.09    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.09            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.09    (18)  op(e2, e0) = all_52_13
% 239.41/46.09    (19)   ~ (all_52_1 = e2)
% 239.41/46.09    (20)   ~ (e2 = e1)
% 239.41/46.09  
% 239.41/46.09  Begin of proof
% 239.41/46.09  | 
% 239.41/46.09  | ALPHA: (8) implies:
% 239.41/46.09  |   (21)  op(e1, e2) = all_56_13
% 239.41/46.09  |   (22)  op(e1, all_56_13) = e1
% 239.41/46.09  | 
% 239.41/46.09  | GROUND_INST: instantiating (17) with e2, all_56_13, e2, e1, simplifying with
% 239.41/46.09  |              (14), (21) gives:
% 239.41/46.09  |   (23)  all_56_13 = e2
% 239.41/46.09  | 
% 239.41/46.09  | REDUCE: (22), (23) imply:
% 239.41/46.09  |   (24)  op(e1, e2) = e1
% 239.41/46.09  | 
% 239.41/46.09  | GROUND_INST: instantiating (17) with e2, e1, e2, e1, simplifying with (14),
% 239.41/46.09  |              (24) gives:
% 239.41/46.09  |   (25)  e2 = e1
% 239.41/46.09  | 
% 239.41/46.09  | COMBINE_EQS: (15), (25) imply:
% 239.41/46.09  |   (26)  all_58_5 = e1
% 239.41/46.09  | 
% 239.41/46.09  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 239.41/46.09  |            (16), (17), (18), (19), (20), (26) are inconsistent by sub-proof
% 239.41/46.09  |            #455.
% 239.41/46.09  | 
% 239.41/46.09  End of proof
% 239.41/46.09  
% 239.41/46.09  Sub-proof #19 shows that the following formulas are inconsistent:
% 239.41/46.09  ----------------------------------------------------------------
% 239.41/46.09    (1)   ~ (all_52_1 = all_52_3)
% 239.41/46.09    (2)  op(e2, e2) = e3
% 239.41/46.09    (3)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.41/46.09    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 239.41/46.09           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 239.41/46.09           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 239.41/46.09           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 239.41/46.09           & $i(all_56_23))
% 239.41/46.09    (5)   ~ (e3 = e0)
% 239.41/46.09    (6)   ~ (all_52_7 = e2)
% 239.41/46.09    (7)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 239.41/46.09           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 239.41/46.09           all_24_1 & $i(all_24_1))
% 239.41/46.09    (8)  op(e0, e1) = all_52_11
% 239.41/46.09    (9)   ~ (e2 = e0)
% 239.41/46.09    (10)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.41/46.10    (11)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.41/46.10          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.41/46.10    (12)  op(e1, e2) = all_52_6
% 239.41/46.10    (13)   ~ (all_52_7 = all_52_11)
% 239.41/46.10    (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 239.41/46.10          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 239.41/46.10    (15)  op(e1, e0) = all_52_14
% 239.41/46.10    (16)   ~ (all_52_7 = e3)
% 239.41/46.10    (17)  op(e0, e3) = all_52_3
% 239.41/46.10    (18)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.41/46.10          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.41/46.10    (19)   ~ (e3 = e1)
% 239.41/46.10    (20)  all_58_7 = e2
% 239.41/46.10    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.41/46.10          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.41/46.10    (22)  all_58_3 = e3
% 239.41/46.10    (23)   ~ (all_52_12 = all_52_13)
% 239.41/46.10    (24)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.41/46.10          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.41/46.10    (25)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 239.41/46.10            $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e1, e3) = all_6_1
% 239.41/46.10            & $i(all_6_1))
% 239.41/46.10    (26)  op(e2, e1) = e2
% 239.41/46.10    (27)   ~ (all_52_11 = e3)
% 239.41/46.10    (28)   ~ (all_52_14 = e2)
% 239.41/46.10    (29)  op(e3, e1) = all_52_8
% 239.41/46.10    (30)  op(e2, e1) = all_52_9
% 239.41/46.10    (31)   ~ (e3 = e2)
% 239.41/46.10    (32)  all_56_31 = e2
% 239.41/46.10    (33)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 239.41/46.10            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 239.41/46.10            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 239.41/46.10            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 239.41/46.10            op(e0, all_56_31) = e0)
% 239.41/46.10    (34)  op(e0, e3) = e3
% 239.41/46.10    (35)  op(e3, e0) = all_52_12
% 239.41/46.10    (36)  op(e3, all_52_4) = e3
% 239.41/46.10    (37)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.41/46.10          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.41/46.10    (38)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 239.41/46.10            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 239.41/46.10              e3) = all_42_1 & $i(all_42_1))
% 239.41/46.10    (39)  all_58_9 = e3
% 239.41/46.10    (40)  op(e3, e0) = e3
% 239.41/46.10    (41)  op(e2, e3) = all_52_1
% 239.41/46.10    (42)  op(e3, e3) = e2
% 239.41/46.10    (43)   ~ (all_52_14 = e3)
% 239.41/46.10    (44)   ~ (all_52_13 = e2)
% 239.41/46.10    (45)  all_58_12 = e3
% 239.41/46.10    (46)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.41/46.10          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.41/46.10    (47)  op(e1, e1) = e3
% 239.41/46.10    (48)   ~ (all_52_6 = e3)
% 239.41/46.10    (49)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.41/46.10          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.41/46.10    (50)  op(e0, e2) = all_52_7
% 239.41/46.10    (51)   ~ (all_52_13 = all_52_14)
% 239.41/46.10    (52)  all_54_1 = all_52_4
% 239.41/46.10    (53)   ~ (all_52_4 = e3)
% 239.41/46.10    (54)  op(e3, e2) = all_52_4
% 239.41/46.10    (55)   ~ (all_52_9 = e3)
% 239.41/46.10    (56)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.41/46.10          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.41/46.10    (57)   ~ (all_52_4 = e2)
% 239.41/46.10    (58)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.41/46.10          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.41/46.10    (59)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.41/46.10          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.41/46.10    (60)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.41/46.10          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.41/46.10    (61)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.10            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.10    (62)  all_58_8 = e3
% 239.41/46.10    (63)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.41/46.10            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 239.41/46.10              e3) = all_46_1 & $i(all_46_1))
% 239.41/46.10    (64)  op(e1, e3) = all_52_2
% 239.41/46.10    (65)  all_56_21 = e3
% 239.41/46.10    (66)   ~ (e1 = e0)
% 239.41/46.10    (67)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 239.41/46.10            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3,
% 239.41/46.10              e2) = all_32_1 & $i(all_32_1))
% 239.41/46.10    (68)   ~ (all_52_13 = e3)
% 239.41/46.10    (69)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.41/46.10          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.41/46.10    (70)  op(e2, e0) = all_52_13
% 239.41/46.10    (71)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 239.41/46.10            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 239.41/46.10            & $i(all_8_1))
% 239.41/46.10    (72)   ~ (all_52_1 = e2)
% 239.41/46.10    (73)   ~ (e2 = e1)
% 239.41/46.10    (74)   ~ (all_52_4 = all_52_7)
% 239.41/46.10    (75)   ~ (all_52_8 = e3)
% 239.41/46.10  
% 239.41/46.10  Begin of proof
% 239.41/46.10  | 
% 239.41/46.10  | BETA: splitting (10) gives:
% 239.41/46.10  | 
% 239.41/46.10  | Case 1:
% 239.41/46.10  | | 
% 239.41/46.10  | |   (76)  all_58_8 = e1 & op(e1, e1) = e1
% 239.41/46.10  | | 
% 239.41/46.10  | | ALPHA: (76) implies:
% 239.41/46.10  | |   (77)  op(e1, e1) = e1
% 239.41/46.10  | | 
% 239.41/46.10  | | REF_CLOSE: (19), (47), (61), (77) are inconsistent by sub-proof #468.
% 239.41/46.10  | | 
% 239.41/46.10  | Case 2:
% 239.41/46.10  | | 
% 239.41/46.10  | |   (78)  all_58_11 = e1 & op(e1, e0) = e1
% 239.41/46.10  | | 
% 239.41/46.10  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 239.41/46.10  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 239.41/46.10  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 239.41/46.10  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 239.41/46.10  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 239.41/46.10  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 239.41/46.10  | |            (69), (70), (71), (72), (73), (74), (75), (78) are inconsistent
% 239.41/46.10  | |            by sub-proof #20.
% 239.41/46.10  | | 
% 239.41/46.10  | End of split
% 239.41/46.10  | 
% 239.41/46.10  End of proof
% 239.41/46.10  
% 239.41/46.10  Sub-proof #20 shows that the following formulas are inconsistent:
% 239.41/46.10  ----------------------------------------------------------------
% 239.41/46.10    (1)   ~ (all_52_1 = all_52_3)
% 239.41/46.10    (2)  op(e2, e2) = e3
% 239.41/46.10    (3)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.41/46.10    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 239.41/46.10           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 239.41/46.10           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 239.41/46.10           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 239.41/46.10           & $i(all_56_23))
% 239.41/46.10    (5)   ~ (e3 = e0)
% 239.41/46.10    (6)   ~ (all_52_7 = e2)
% 239.41/46.10    (7)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 239.41/46.10           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 239.41/46.10           all_24_1 & $i(all_24_1))
% 239.41/46.10    (8)  op(e0, e1) = all_52_11
% 239.41/46.10    (9)   ~ (e2 = e0)
% 239.41/46.11    (10)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.41/46.11          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.41/46.11    (11)  op(e1, e2) = all_52_6
% 239.41/46.11    (12)   ~ (all_52_7 = all_52_11)
% 239.41/46.11    (13)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 239.41/46.11          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 239.41/46.11    (14)  op(e1, e0) = all_52_14
% 239.41/46.11    (15)   ~ (all_52_7 = e3)
% 239.41/46.11    (16)  op(e0, e3) = all_52_3
% 239.41/46.11    (17)  all_58_11 = e1 & op(e1, e0) = e1
% 239.41/46.11    (18)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.41/46.11          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.41/46.11    (19)   ~ (e3 = e1)
% 239.41/46.11    (20)  all_58_7 = e2
% 239.41/46.11    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.41/46.11          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.41/46.11    (22)  all_58_3 = e3
% 239.41/46.11    (23)   ~ (all_52_12 = all_52_13)
% 239.41/46.11    (24)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.41/46.11          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.41/46.11    (25)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 239.41/46.11            $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e1, e3) = all_6_1
% 239.41/46.11            & $i(all_6_1))
% 239.41/46.11    (26)  op(e2, e1) = e2
% 239.41/46.11    (27)   ~ (all_52_11 = e3)
% 239.41/46.11    (28)   ~ (all_52_14 = e2)
% 239.41/46.11    (29)  op(e3, e1) = all_52_8
% 239.41/46.11    (30)  op(e2, e1) = all_52_9
% 239.41/46.11    (31)   ~ (e3 = e2)
% 239.41/46.11    (32)  all_56_31 = e2
% 239.41/46.11    (33)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 239.41/46.11            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 239.41/46.11            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 239.41/46.11            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 239.41/46.11            op(e0, all_56_31) = e0)
% 239.41/46.11    (34)  op(e0, e3) = e3
% 239.41/46.11    (35)  op(e3, e0) = all_52_12
% 239.41/46.11    (36)  op(e3, all_52_4) = e3
% 239.41/46.11    (37)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.41/46.11          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.41/46.11    (38)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 239.41/46.11            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 239.41/46.11              e3) = all_42_1 & $i(all_42_1))
% 239.41/46.11    (39)  all_58_9 = e3
% 239.41/46.11    (40)  op(e3, e0) = e3
% 239.41/46.11    (41)  op(e2, e3) = all_52_1
% 239.41/46.11    (42)  op(e3, e3) = e2
% 239.41/46.11    (43)   ~ (all_52_14 = e3)
% 239.41/46.11    (44)   ~ (all_52_13 = e2)
% 239.41/46.11    (45)  all_58_12 = e3
% 239.41/46.11    (46)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.41/46.11          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.41/46.11    (47)  op(e1, e1) = e3
% 239.41/46.11    (48)   ~ (all_52_6 = e3)
% 239.41/46.11    (49)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.41/46.11          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.41/46.11    (50)  op(e0, e2) = all_52_7
% 239.41/46.11    (51)   ~ (all_52_13 = all_52_14)
% 239.41/46.11    (52)  all_54_1 = all_52_4
% 239.41/46.11    (53)   ~ (all_52_4 = e3)
% 239.41/46.11    (54)  op(e3, e2) = all_52_4
% 239.41/46.11    (55)   ~ (all_52_9 = e3)
% 239.41/46.11    (56)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.41/46.11          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.41/46.11    (57)   ~ (all_52_4 = e2)
% 239.41/46.11    (58)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.41/46.11          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.41/46.11    (59)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.41/46.11          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.41/46.11    (60)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.41/46.11          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.41/46.11    (61)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.11    (62)  all_58_8 = e3
% 239.41/46.11    (63)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.41/46.11            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 239.41/46.11              e3) = all_46_1 & $i(all_46_1))
% 239.41/46.11    (64)  op(e1, e3) = all_52_2
% 239.41/46.11    (65)  all_56_21 = e3
% 239.41/46.11    (66)   ~ (e1 = e0)
% 239.41/46.11    (67)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 239.41/46.11            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3,
% 239.41/46.11              e2) = all_32_1 & $i(all_32_1))
% 239.41/46.11    (68)   ~ (all_52_13 = e3)
% 239.41/46.11    (69)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.41/46.11          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.41/46.11    (70)  op(e2, e0) = all_52_13
% 239.41/46.11    (71)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 239.41/46.11            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 239.41/46.11            & $i(all_8_1))
% 239.41/46.11    (72)   ~ (all_52_1 = e2)
% 239.41/46.11    (73)   ~ (e2 = e1)
% 239.41/46.11    (74)   ~ (all_52_4 = all_52_7)
% 239.41/46.11    (75)   ~ (all_52_8 = e3)
% 239.41/46.11  
% 239.41/46.11  Begin of proof
% 239.41/46.11  | 
% 239.41/46.11  | ALPHA: (17) implies:
% 239.41/46.11  |   (76)  all_58_11 = e1
% 239.41/46.11  |   (77)  op(e1, e0) = e1
% 239.41/46.11  | 
% 239.41/46.11  | BETA: splitting (69) gives:
% 239.41/46.11  | 
% 239.41/46.11  | Case 1:
% 239.41/46.11  | | 
% 239.41/46.11  | |   (78)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 239.41/46.11  | |           e0)
% 239.41/46.11  | | 
% 239.41/46.11  | | BETA: splitting (78) gives:
% 239.41/46.11  | | 
% 239.41/46.11  | | Case 1:
% 239.41/46.11  | | | 
% 239.41/46.11  | | |   (79)  all_58_6 = e0 & op(e1, e3) = e0
% 239.41/46.11  | | | 
% 239.41/46.11  | | | ALPHA: (79) implies:
% 239.41/46.11  | | |   (80)  op(e1, e3) = e0
% 239.41/46.11  | | | 
% 239.41/46.11  | | | BETA: splitting (56) gives:
% 239.41/46.11  | | | 
% 239.41/46.11  | | | Case 1:
% 239.41/46.11  | | | | 
% 239.41/46.11  | | | |   (81)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 239.41/46.11  | | | |           = e1)
% 239.41/46.11  | | | | 
% 239.41/46.11  | | | | BETA: splitting (81) gives:
% 239.41/46.11  | | | | 
% 239.41/46.11  | | | | Case 1:
% 239.41/46.11  | | | | | 
% 239.41/46.11  | | | | |   (82)  all_58_0 = e1 & op(e3, e3) = e1
% 239.41/46.11  | | | | | 
% 239.41/46.11  | | | | | ALPHA: (82) implies:
% 239.41/46.11  | | | | |   (83)  op(e3, e3) = e1
% 239.41/46.11  | | | | | 
% 239.41/46.11  | | | | | REF_CLOSE: (42), (61), (73), (83) are inconsistent by sub-proof #2267.
% 239.41/46.11  | | | | | 
% 239.41/46.11  | | | | Case 2:
% 239.41/46.11  | | | | | 
% 239.41/46.11  | | | | |   (84)  all_58_2 = e1 & op(e2, e3) = e1
% 239.41/46.11  | | | | | 
% 239.41/46.11  | | | | | ALPHA: (84) implies:
% 239.41/46.11  | | | | |   (85)  all_58_2 = e1
% 239.41/46.11  | | | | |   (86)  op(e2, e3) = e1
% 239.41/46.11  | | | | | 
% 239.41/46.11  | | | | | BETA: splitting (60) gives:
% 239.41/46.11  | | | | | 
% 239.41/46.11  | | | | | Case 1:
% 239.41/46.11  | | | | | | 
% 239.41/46.11  | | | | | |   (87)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2,
% 239.41/46.11  | | | | | |             e2) = e0)
% 239.41/46.11  | | | | | | 
% 239.41/46.11  | | | | | | BETA: splitting (87) gives:
% 239.41/46.11  | | | | | | 
% 239.41/46.11  | | | | | | Case 1:
% 239.41/46.11  | | | | | | | 
% 239.41/46.11  | | | | | | |   (88)  all_58_2 = e0 & op(e2, e3) = e0
% 239.41/46.11  | | | | | | | 
% 239.41/46.11  | | | | | | | REF_CLOSE: (66), (85), (88) are inconsistent by sub-proof #1972.
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | Case 2:
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | |   (89)  all_58_3 = e0 & op(e2, e2) = e0
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | REF_CLOSE: (5), (22), (24), (29), (31), (39), (42), (53), (54),
% 239.41/46.12  | | | | | | |            (61), (75), (89) are inconsistent by sub-proof #332.
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | End of split
% 239.41/46.12  | | | | | | 
% 239.41/46.12  | | | | | Case 2:
% 239.41/46.12  | | | | | | 
% 239.41/46.12  | | | | | |   (90)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2,
% 239.41/46.12  | | | | | |             e0) = e0)
% 239.41/46.12  | | | | | | 
% 239.41/46.12  | | | | | | BETA: splitting (90) gives:
% 239.41/46.12  | | | | | | 
% 239.41/46.12  | | | | | | Case 1:
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | |   (91)  all_58_5 = e0 & op(e2, e1) = e0
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | ALPHA: (91) implies:
% 239.41/46.12  | | | | | | |   (92)  op(e2, e1) = e0
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | REF_CLOSE: (9), (26), (61), (92) are inconsistent by sub-proof
% 239.41/46.12  | | | | | | |            #1906.
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | Case 2:
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | |   (93)  all_58_10 = e0 & op(e2, e0) = e0
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | ALPHA: (93) implies:
% 239.41/46.12  | | | | | | |   (94)  op(e2, e0) = e0
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | GROUND_INST: instantiating (61) with all_52_14, e1, e0, e1,
% 239.41/46.12  | | | | | | |              simplifying with (14), (77) gives:
% 239.41/46.12  | | | | | | |   (95)  all_52_14 = e1
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | GROUND_INST: instantiating (61) with all_52_2, e0, e3, e1,
% 239.41/46.12  | | | | | | |              simplifying with (64), (80) gives:
% 239.41/46.12  | | | | | | |   (96)  all_52_2 = e0
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | GROUND_INST: instantiating (61) with all_52_13, e0, e0, e2,
% 239.41/46.12  | | | | | | |              simplifying with (70), (94) gives:
% 239.41/46.12  | | | | | | |   (97)  all_52_13 = e0
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | GROUND_INST: instantiating (61) with all_52_1, e1, e3, e2,
% 239.41/46.12  | | | | | | |              simplifying with (41), (86) gives:
% 239.41/46.12  | | | | | | |   (98)  all_52_1 = e1
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | REDUCE: (51), (95), (97) imply:
% 239.41/46.12  | | | | | | |   (99)   ~ (e1 = e0)
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | REDUCE: (68), (97) imply:
% 239.41/46.12  | | | | | | |   (100)   ~ (e3 = e0)
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | REDUCE: (44), (97) imply:
% 239.41/46.12  | | | | | | |   (101)   ~ (e2 = e0)
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | REDUCE: (43), (95) imply:
% 239.41/46.12  | | | | | | |   (102)   ~ (e3 = e1)
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | REDUCE: (28), (95) imply:
% 239.41/46.12  | | | | | | |   (103)   ~ (e2 = e1)
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | BETA: splitting (33) gives:
% 239.41/46.12  | | | | | | | 
% 239.41/46.12  | | | | | | | Case 1:
% 239.41/46.12  | | | | | | | | 
% 239.41/46.12  | | | | | | | |   (104)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 239.41/46.12  | | | | | | | |            all_56_25 & $i(all_56_25)) | (all_56_26 = e2 & op(e2,
% 239.41/46.12  | | | | | | | |              all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 239.41/46.12  | | | | | | | |            $i(all_56_27))
% 239.41/46.12  | | | | | | | | 
% 239.41/46.12  | | | | | | | | BETA: splitting (104) gives:
% 239.41/46.12  | | | | | | | | 
% 239.41/46.12  | | | | | | | | Case 1:
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | |   (105)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0)
% 239.41/46.12  | | | | | | | | |          = all_56_25 & $i(all_56_25)
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | ALPHA: (105) implies:
% 239.41/46.12  | | | | | | | | |   (106)  op(e3, e0) = all_56_25
% 239.41/46.12  | | | | | | | | |   (107)  op(e3, all_56_25) = e3
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | REF_CLOSE: (31), (38), (40), (42), (61), (71), (86), (106),
% 239.41/46.12  | | | | | | | | |            (107) are inconsistent by sub-proof #24.
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | Case 2:
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | |   (108)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 239.41/46.12  | | | | | | | | |          = all_56_27 & $i(all_56_27)
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | REF_CLOSE: (2), (31), (61), (94), (108) are inconsistent by
% 239.41/46.12  | | | | | | | | |            sub-proof #752.
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | End of split
% 239.41/46.12  | | | | | | | | 
% 239.41/46.12  | | | | | | | Case 2:
% 239.41/46.12  | | | | | | | | 
% 239.41/46.12  | | | | | | | |   (109)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 239.41/46.12  | | | | | | | |            all_56_29 & $i(all_56_29)) | (all_56_30 = e0 & op(e0,
% 239.41/46.12  | | | | | | | |              all_56_31) = e0)
% 239.41/46.12  | | | | | | | | 
% 239.41/46.12  | | | | | | | | BETA: splitting (109) gives:
% 239.41/46.12  | | | | | | | | 
% 239.41/46.12  | | | | | | | | Case 1:
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | |   (110)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0)
% 239.41/46.12  | | | | | | | | |          = all_56_29 & $i(all_56_29)
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | REF_CLOSE: (5), (9), (11), (19), (31), (37), (47), (48), (59),
% 239.41/46.12  | | | | | | | | |            (61), (62), (63), (66), (69), (73), (76), (77),
% 239.41/46.12  | | | | | | | | |            (80), (110) are inconsistent by sub-proof #412.
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | Case 2:
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | |   (111)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | ALPHA: (111) implies:
% 239.41/46.12  | | | | | | | | |   (112)  op(e0, all_56_31) = e0
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | REDUCE: (32), (112) imply:
% 239.41/46.12  | | | | | | | | |   (113)  op(e0, e2) = e0
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | BETA: splitting (38) gives:
% 239.41/46.12  | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | Case 1:
% 239.41/46.12  | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | |   (114)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 239.41/46.12  | | | | | | | | | |          op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)
% 239.41/46.12  | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | | ALPHA: (114) implies:
% 239.41/46.12  | | | | | | | | | |   (115)  op(e2, e3) = all_42_1
% 239.41/46.12  | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | | BETA: splitting (71) gives:
% 239.41/46.12  | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | | Case 1:
% 239.41/46.12  | | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | | |   (116)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 239.41/46.12  | | | | | | | | | | |          op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 239.41/46.12  | | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | | | ALPHA: (116) implies:
% 239.41/46.12  | | | | | | | | | | |   (117)  op(e2, e3) = all_8_1
% 239.41/46.12  | | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (12),
% 239.41/46.12  | | | | | | | | | | |            (13), (15), (16), (18), (19), (21), (23), (24),
% 239.41/46.12  | | | | | | | | | | |            (25), (26), (27), (29), (30), (31), (34), (35),
% 239.41/46.12  | | | | | | | | | | |            (36), (38), (40), (41), (42), (44), (46), (47),
% 239.41/46.12  | | | | | | | | | | |            (49), (50), (52), (53), (54), (55), (57), (58),
% 239.41/46.12  | | | | | | | | | | |            (61), (63), (65), (66), (67), (70), (71), (72),
% 239.41/46.12  | | | | | | | | | | |            (73), (74), (75), (80), (86), (113), (115), (117)
% 239.41/46.12  | | | | | | | | | | |            are inconsistent by sub-proof #22.
% 239.41/46.12  | | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | | Case 2:
% 239.41/46.12  | | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | | |   (118)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 239.41/46.12  | | | | | | | | | | |          $i(all_8_1)
% 239.41/46.12  | | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | | | ALPHA: (118) implies:
% 239.41/46.12  | | | | | | | | | | |   (119)  op(e2, e3) = all_8_1
% 239.41/46.12  | | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (12),
% 239.41/46.12  | | | | | | | | | | |            (13), (15), (16), (18), (19), (21), (23), (24),
% 239.41/46.12  | | | | | | | | | | |            (25), (26), (27), (29), (30), (31), (34), (35),
% 239.41/46.12  | | | | | | | | | | |            (36), (38), (40), (41), (42), (44), (46), (47),
% 239.41/46.12  | | | | | | | | | | |            (49), (50), (52), (53), (54), (55), (57), (58),
% 239.41/46.12  | | | | | | | | | | |            (61), (63), (65), (66), (67), (70), (71), (72),
% 239.41/46.12  | | | | | | | | | | |            (73), (74), (75), (80), (86), (113), (115), (119)
% 239.41/46.12  | | | | | | | | | | |            are inconsistent by sub-proof #22.
% 239.41/46.12  | | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | | End of split
% 239.41/46.12  | | | | | | | | | | 
% 239.41/46.12  | | | | | | | | | Case 2:
% 239.41/46.12  | | | | | | | | | | 
% 239.41/46.13  | | | | | | | | | |   (120)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 239.41/46.13  | | | | | | | | | |          $i(all_42_1)
% 239.41/46.13  | | | | | | | | | | 
% 239.41/46.13  | | | | | | | | | | ALPHA: (120) implies:
% 239.41/46.13  | | | | | | | | | |   (121)   ~ (all_42_1 = e1)
% 239.41/46.13  | | | | | | | | | |   (122)  op(e2, e3) = all_42_1
% 239.41/46.13  | | | | | | | | | | 
% 239.41/46.13  | | | | | | | | | | REF_CLOSE: (61), (71), (86), (121), (122) are inconsistent by
% 239.41/46.13  | | | | | | | | | |            sub-proof #934.
% 239.41/46.13  | | | | | | | | | | 
% 239.41/46.13  | | | | | | | | | End of split
% 239.41/46.13  | | | | | | | | | 
% 239.41/46.13  | | | | | | | | End of split
% 239.41/46.13  | | | | | | | | 
% 239.41/46.13  | | | | | | | End of split
% 239.41/46.13  | | | | | | | 
% 239.41/46.13  | | | | | | End of split
% 239.41/46.13  | | | | | | 
% 239.41/46.13  | | | | | End of split
% 239.41/46.13  | | | | | 
% 239.41/46.13  | | | | End of split
% 239.41/46.13  | | | | 
% 239.41/46.13  | | | Case 2:
% 239.41/46.13  | | | | 
% 239.41/46.13  | | | |   (123)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 239.41/46.13  | | | |              e3) = e1)
% 239.41/46.13  | | | | 
% 239.41/46.13  | | | | REF_CLOSE: (19), (45), (61), (66), (80), (123) are inconsistent by
% 239.41/46.13  | | | |            sub-proof #21.
% 239.41/46.13  | | | | 
% 239.41/46.13  | | | End of split
% 239.41/46.13  | | | 
% 239.41/46.13  | | Case 2:
% 239.41/46.13  | | | 
% 239.41/46.13  | | |   (124)  all_58_7 = e0 & op(e1, e2) = e0
% 239.41/46.13  | | | 
% 239.41/46.13  | | | REF_CLOSE: (9), (20), (124) are inconsistent by sub-proof #2212.
% 239.41/46.13  | | | 
% 239.41/46.13  | | End of split
% 239.41/46.13  | | 
% 239.41/46.13  | Case 2:
% 239.41/46.13  | | 
% 239.41/46.13  | |   (125)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 239.41/46.13  | |            e0)
% 239.41/46.13  | | 
% 239.41/46.13  | | REF_CLOSE: (5), (8), (27), (29), (30), (49), (55), (61), (66), (75), (77),
% 239.41/46.13  | |            (125) are inconsistent by sub-proof #400.
% 239.41/46.13  | | 
% 239.41/46.13  | End of split
% 239.41/46.13  | 
% 239.41/46.13  End of proof
% 239.41/46.13  
% 239.41/46.13  Sub-proof #21 shows that the following formulas are inconsistent:
% 239.41/46.13  ----------------------------------------------------------------
% 239.41/46.13    (1)   ~ (e3 = e1)
% 239.41/46.13    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.41/46.13    (3)  op(e1, e3) = e0
% 239.41/46.13    (4)  all_58_12 = e3
% 239.41/46.13    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.13    (6)   ~ (e1 = e0)
% 239.41/46.13  
% 239.41/46.13  Begin of proof
% 239.41/46.13  | 
% 239.41/46.13  | BETA: splitting (2) gives:
% 239.41/46.13  | 
% 239.41/46.13  | Case 1:
% 239.41/46.13  | | 
% 239.41/46.13  | |   (7)  all_58_6 = e1 & op(e1, e3) = e1
% 239.41/46.13  | | 
% 239.41/46.13  | | ALPHA: (7) implies:
% 239.41/46.13  | |   (8)  op(e1, e3) = e1
% 239.41/46.13  | | 
% 239.41/46.13  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #449.
% 239.41/46.13  | | 
% 239.41/46.13  | Case 2:
% 239.41/46.13  | | 
% 239.41/46.13  | |   (9)  all_58_12 = e1 & op(e0, e3) = e1
% 239.41/46.13  | | 
% 239.41/46.13  | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #1874.
% 239.41/46.13  | | 
% 239.41/46.13  | End of split
% 239.41/46.13  | 
% 239.41/46.13  End of proof
% 239.41/46.13  
% 239.41/46.13  Sub-proof #22 shows that the following formulas are inconsistent:
% 239.41/46.13  ----------------------------------------------------------------
% 239.41/46.13    (1)   ~ (all_52_1 = all_52_3)
% 239.41/46.13    (2)  op(e2, e2) = e3
% 239.41/46.13    (3)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.41/46.13    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 239.41/46.13           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 239.41/46.13           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 239.41/46.13           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 239.41/46.13           & $i(all_56_23))
% 239.41/46.13    (5)   ~ (all_52_7 = e2)
% 239.41/46.13    (6)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 239.41/46.13           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 239.41/46.13           all_24_1 & $i(all_24_1))
% 239.41/46.13    (7)  op(e0, e1) = all_52_11
% 239.41/46.13    (8)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.41/46.13         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.41/46.13    (9)   ~ (all_52_7 = all_52_11)
% 239.41/46.13    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 239.41/46.13          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 239.41/46.13    (11)   ~ (all_52_7 = e3)
% 239.41/46.13    (12)  op(e0, e3) = all_52_3
% 239.41/46.13    (13)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.41/46.13          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.41/46.13    (14)   ~ (e3 = e1)
% 239.41/46.13    (15)  op(e2, e3) = all_42_1
% 239.41/46.13    (16)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.41/46.13          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.41/46.13    (17)   ~ (all_52_12 = all_52_13)
% 239.41/46.13    (18)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.41/46.13          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.41/46.13    (19)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 239.41/46.13            $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e1, e3) = all_6_1
% 239.41/46.13            & $i(all_6_1))
% 239.41/46.13    (20)  op(e2, e1) = e2
% 239.41/46.13    (21)   ~ (all_52_11 = e3)
% 239.41/46.13    (22)  op(e3, e1) = all_52_8
% 239.41/46.13    (23)  op(e2, e1) = all_52_9
% 239.41/46.13    (24)   ~ (e3 = e2)
% 239.41/46.13    (25)  op(e2, e3) = e1
% 239.41/46.13    (26)  op(e0, e3) = e3
% 239.41/46.13    (27)  op(e3, e0) = all_52_12
% 239.41/46.13    (28)  op(e3, all_52_4) = e3
% 239.41/46.13    (29)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 239.41/46.13            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 239.41/46.13              e3) = all_42_1 & $i(all_42_1))
% 239.41/46.13    (30)  op(e3, e0) = e3
% 239.41/46.13    (31)  op(e2, e3) = all_52_1
% 239.41/46.13    (32)  op(e3, e3) = e2
% 239.41/46.13    (33)  op(e1, e3) = e0
% 239.41/46.13    (34)   ~ (all_52_13 = e2)
% 239.41/46.13    (35)  op(e0, e2) = e0
% 239.41/46.13    (36)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.41/46.13          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.41/46.13    (37)  op(e1, e1) = e3
% 239.41/46.13    (38)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.41/46.13          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.41/46.13    (39)  op(e0, e2) = all_52_7
% 239.41/46.13    (40)  all_54_1 = all_52_4
% 239.41/46.13    (41)   ~ (all_52_4 = e3)
% 239.41/46.13    (42)  op(e3, e2) = all_52_4
% 239.41/46.13    (43)   ~ (all_52_9 = e3)
% 239.41/46.13    (44)   ~ (all_52_4 = e2)
% 239.41/46.13    (45)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.41/46.13          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.41/46.13    (46)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.13    (47)  op(e2, e3) = all_8_1
% 239.41/46.13    (48)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.41/46.13            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 239.41/46.13              e3) = all_46_1 & $i(all_46_1))
% 239.41/46.13    (49)  all_56_21 = e3
% 239.41/46.13    (50)   ~ (e1 = e0)
% 239.41/46.13    (51)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 239.41/46.13            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3,
% 239.41/46.14              e2) = all_32_1 & $i(all_32_1))
% 239.41/46.14    (52)  op(e2, e0) = all_52_13
% 239.41/46.14    (53)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 239.41/46.14            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 239.41/46.14            & $i(all_8_1))
% 239.41/46.14    (54)   ~ (all_52_1 = e2)
% 239.41/46.14    (55)   ~ (e2 = e1)
% 239.41/46.14    (56)   ~ (all_52_4 = all_52_7)
% 239.41/46.14    (57)   ~ (all_52_8 = e3)
% 239.41/46.14  
% 239.41/46.14  Begin of proof
% 239.41/46.14  | 
% 239.41/46.14  | BETA: splitting (19) gives:
% 239.41/46.14  | 
% 239.41/46.14  | Case 1:
% 239.41/46.14  | | 
% 239.41/46.14  | |   (58)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1
% 239.41/46.14  | |         & $i(all_6_0) & $i(all_6_1)
% 239.41/46.14  | | 
% 239.41/46.14  | | ALPHA: (58) implies:
% 239.41/46.14  | |   (59)  op(e1, e3) = all_6_1
% 239.41/46.14  | | 
% 239.41/46.14  | | BETA: splitting (48) gives:
% 239.41/46.14  | | 
% 239.41/46.14  | | Case 1:
% 239.41/46.14  | | | 
% 239.41/46.14  | | |   (60)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.41/46.14  | | |         all_46_1 & $i(all_46_0) & $i(all_46_1)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | ALPHA: (60) implies:
% 239.41/46.14  | | |   (61)  op(e1, e3) = all_46_1
% 239.41/46.14  | | | 
% 239.41/46.14  | | | GROUND_INST: instantiating (46) with all_52_7, e0, e2, e0, simplifying
% 239.41/46.14  | | |              with (35), (39) gives:
% 239.41/46.14  | | |   (62)  all_52_7 = e0
% 239.41/46.14  | | | 
% 239.41/46.14  | | | GROUND_INST: instantiating (46) with e0, all_46_1, e3, e1, simplifying
% 239.41/46.14  | | |              with (33), (61) gives:
% 239.41/46.14  | | |   (63)  all_46_1 = e0
% 239.41/46.14  | | | 
% 239.41/46.14  | | | GROUND_INST: instantiating (46) with all_6_1, all_46_1, e3, e1,
% 239.41/46.14  | | |              simplifying with (59), (61) gives:
% 239.41/46.14  | | |   (64)  all_46_1 = all_6_1
% 239.41/46.14  | | | 
% 239.41/46.14  | | | GROUND_INST: instantiating (46) with e1, all_42_1, e3, e2, simplifying
% 239.41/46.14  | | |              with (15), (25) gives:
% 239.41/46.14  | | |   (65)  all_42_1 = e1
% 239.41/46.14  | | | 
% 239.41/46.14  | | | GROUND_INST: instantiating (46) with all_8_1, all_42_1, e3, e2,
% 239.41/46.14  | | |              simplifying with (15), (47) gives:
% 239.41/46.14  | | |   (66)  all_42_1 = all_8_1
% 239.41/46.14  | | | 
% 239.41/46.14  | | | COMBINE_EQS: (63), (64) imply:
% 239.41/46.14  | | |   (67)  all_6_1 = e0
% 239.41/46.14  | | | 
% 239.41/46.14  | | | COMBINE_EQS: (65), (66) imply:
% 239.41/46.14  | | |   (68)  all_8_1 = e1
% 239.41/46.14  | | | 
% 239.41/46.14  | | | REDUCE: (56), (62) imply:
% 239.41/46.14  | | |   (69)   ~ (all_52_4 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | REDUCE: (9), (62) imply:
% 239.41/46.14  | | |   (70)   ~ (all_52_11 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | SIMP: (70) implies:
% 239.41/46.14  | | |   (71)   ~ (all_52_11 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | REDUCE: (11), (62) imply:
% 239.41/46.14  | | |   (72)   ~ (e3 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | SIMP: (72) implies:
% 239.41/46.14  | | |   (73)   ~ (e3 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | REDUCE: (5), (62) imply:
% 239.41/46.14  | | |   (74)   ~ (e2 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (12), (13), (14),
% 239.41/46.14  | | |            (16), (17), (18), (20), (21), (22), (23), (24), (26), (27),
% 239.41/46.14  | | |            (28), (29), (30), (31), (32), (34), (36), (37), (38), (40),
% 239.41/46.14  | | |            (41), (42), (43), (44), (45), (46), (47), (49), (50), (51),
% 239.41/46.14  | | |            (52), (53), (54), (55), (57), (59), (67), (68), (69), (71),
% 239.41/46.14  | | |            (73), (74) are inconsistent by sub-proof #23.
% 239.41/46.14  | | | 
% 239.41/46.14  | | Case 2:
% 239.41/46.14  | | | 
% 239.41/46.14  | | |   (75)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | ALPHA: (75) implies:
% 239.41/46.14  | | |   (76)   ~ (all_46_1 = e2)
% 239.41/46.14  | | |   (77)  op(e1, e3) = all_46_1
% 239.41/46.14  | | | 
% 239.41/46.14  | | | GROUND_INST: instantiating (46) with all_52_7, e0, e2, e0, simplifying
% 239.41/46.14  | | |              with (35), (39) gives:
% 239.41/46.14  | | |   (78)  all_52_7 = e0
% 239.41/46.14  | | | 
% 239.41/46.14  | | | GROUND_INST: instantiating (46) with e0, all_46_1, e3, e1, simplifying
% 239.41/46.14  | | |              with (33), (77) gives:
% 239.41/46.14  | | |   (79)  all_46_1 = e0
% 239.41/46.14  | | | 
% 239.41/46.14  | | | GROUND_INST: instantiating (46) with all_6_1, all_46_1, e3, e1,
% 239.41/46.14  | | |              simplifying with (59), (77) gives:
% 239.41/46.14  | | |   (80)  all_46_1 = all_6_1
% 239.41/46.14  | | | 
% 239.41/46.14  | | | GROUND_INST: instantiating (46) with e1, all_42_1, e3, e2, simplifying
% 239.41/46.14  | | |              with (15), (25) gives:
% 239.41/46.14  | | |   (81)  all_42_1 = e1
% 239.41/46.14  | | | 
% 239.41/46.14  | | | GROUND_INST: instantiating (46) with all_8_1, all_42_1, e3, e2,
% 239.41/46.14  | | |              simplifying with (15), (47) gives:
% 239.41/46.14  | | |   (82)  all_42_1 = all_8_1
% 239.41/46.14  | | | 
% 239.41/46.14  | | | COMBINE_EQS: (79), (80) imply:
% 239.41/46.14  | | |   (83)  all_6_1 = e0
% 239.41/46.14  | | | 
% 239.41/46.14  | | | COMBINE_EQS: (81), (82) imply:
% 239.41/46.14  | | |   (84)  all_8_1 = e1
% 239.41/46.14  | | | 
% 239.41/46.14  | | | REDUCE: (56), (78) imply:
% 239.41/46.14  | | |   (85)   ~ (all_52_4 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | REDUCE: (9), (78) imply:
% 239.41/46.14  | | |   (86)   ~ (all_52_11 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | SIMP: (86) implies:
% 239.41/46.14  | | |   (87)   ~ (all_52_11 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | REDUCE: (11), (78) imply:
% 239.41/46.14  | | |   (88)   ~ (e3 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | SIMP: (88) implies:
% 239.41/46.14  | | |   (89)   ~ (e3 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | REDUCE: (76), (79) imply:
% 239.41/46.14  | | |   (90)   ~ (e2 = e0)
% 239.41/46.14  | | | 
% 239.41/46.14  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (12), (13), (14),
% 239.41/46.14  | | |            (16), (17), (18), (20), (21), (22), (23), (24), (26), (27),
% 239.41/46.14  | | |            (28), (29), (30), (31), (32), (34), (36), (37), (38), (40),
% 239.41/46.14  | | |            (41), (42), (43), (44), (45), (46), (47), (49), (50), (51),
% 239.41/46.14  | | |            (52), (53), (54), (55), (57), (59), (83), (84), (85), (87),
% 239.41/46.14  | | |            (89), (90) are inconsistent by sub-proof #23.
% 239.41/46.14  | | | 
% 239.41/46.15  | | End of split
% 239.41/46.15  | | 
% 239.41/46.15  | Case 2:
% 239.41/46.15  | | 
% 239.41/46.15  | |   (91)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 & $i(all_6_1)
% 239.41/46.15  | | 
% 239.41/46.15  | | REF_CLOSE: (33), (46), (48), (91) are inconsistent by sub-proof #443.
% 239.41/46.15  | | 
% 239.41/46.15  | End of split
% 239.41/46.15  | 
% 239.41/46.15  End of proof
% 239.41/46.15  
% 239.41/46.15  Sub-proof #23 shows that the following formulas are inconsistent:
% 239.41/46.15  ----------------------------------------------------------------
% 239.41/46.15    (1)   ~ (all_52_1 = all_52_3)
% 239.41/46.15    (2)  op(e2, e2) = e3
% 239.41/46.15    (3)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.41/46.15    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 239.41/46.15           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 239.41/46.15           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 239.41/46.15           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 239.41/46.15           & $i(all_56_23))
% 239.41/46.15    (5)  all_6_1 = e0
% 239.41/46.15    (6)   ~ (e3 = e0)
% 239.41/46.15    (7)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 239.41/46.15           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 239.41/46.15           all_24_1 & $i(all_24_1))
% 239.41/46.15    (8)  op(e0, e1) = all_52_11
% 239.41/46.15    (9)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.41/46.15         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.41/46.15    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 239.41/46.15          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 239.41/46.15    (11)  op(e1, e3) = all_6_1
% 239.41/46.15    (12)  op(e0, e3) = all_52_3
% 239.41/46.15    (13)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.41/46.15          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.41/46.15    (14)   ~ (e3 = e1)
% 239.41/46.15    (15)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.41/46.15          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.41/46.15    (16)   ~ (all_52_12 = all_52_13)
% 239.41/46.15    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.41/46.15          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.41/46.15    (18)  op(e2, e1) = e2
% 239.41/46.15    (19)   ~ (all_52_11 = e3)
% 239.41/46.15    (20)  op(e3, e1) = all_52_8
% 239.41/46.15    (21)  op(e2, e1) = all_52_9
% 239.41/46.15    (22)   ~ (e3 = e2)
% 239.41/46.15    (23)  op(e0, e3) = e3
% 239.41/46.15    (24)  op(e3, e0) = all_52_12
% 239.41/46.15    (25)  op(e3, all_52_4) = e3
% 239.41/46.15    (26)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 239.41/46.15            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 239.41/46.15              e3) = all_42_1 & $i(all_42_1))
% 239.41/46.15    (27)  op(e3, e0) = e3
% 239.41/46.15    (28)   ~ (e2 = e0)
% 239.41/46.15    (29)  op(e2, e3) = all_52_1
% 239.41/46.15    (30)  op(e3, e3) = e2
% 239.41/46.15    (31)   ~ (all_52_13 = e2)
% 239.41/46.15    (32)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.41/46.15          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.41/46.15    (33)  op(e1, e1) = e3
% 239.41/46.15    (34)   ~ (all_52_11 = e0)
% 239.41/46.15    (35)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.41/46.15          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.41/46.15    (36)  all_54_1 = all_52_4
% 239.41/46.15    (37)   ~ (all_52_4 = e3)
% 239.41/46.15    (38)  op(e3, e2) = all_52_4
% 239.41/46.15    (39)   ~ (all_52_9 = e3)
% 239.41/46.15    (40)   ~ (all_52_4 = e2)
% 239.41/46.15    (41)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.41/46.15          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.41/46.15    (42)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.15    (43)  op(e2, e3) = all_8_1
% 239.41/46.15    (44)  all_56_21 = e3
% 239.41/46.15    (45)   ~ (e1 = e0)
% 239.41/46.15    (46)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 239.41/46.15            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3,
% 239.41/46.15              e2) = all_32_1 & $i(all_32_1))
% 239.41/46.15    (47)  all_8_1 = e1
% 239.41/46.15    (48)  op(e2, e0) = all_52_13
% 239.41/46.15    (49)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 239.41/46.15            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 239.41/46.15            & $i(all_8_1))
% 239.41/46.15    (50)   ~ (all_52_1 = e2)
% 239.41/46.15    (51)   ~ (all_52_4 = e0)
% 239.41/46.15    (52)   ~ (e2 = e1)
% 239.41/46.15    (53)   ~ (all_52_8 = e3)
% 239.41/46.15  
% 239.41/46.15  Begin of proof
% 239.41/46.15  | 
% 239.41/46.15  | SIMP: (28) implies:
% 239.41/46.15  |   (54)   ~ (e2 = e0)
% 239.41/46.15  | 
% 239.41/46.15  | REDUCE: (43), (47) imply:
% 239.41/46.15  |   (55)  op(e2, e3) = e1
% 239.41/46.15  | 
% 239.41/46.15  | REDUCE: (5), (11) imply:
% 239.41/46.15  |   (56)  op(e1, e3) = e0
% 239.41/46.15  | 
% 239.41/46.15  | BETA: splitting (15) gives:
% 239.41/46.15  | 
% 239.41/46.15  | Case 1:
% 239.41/46.15  | | 
% 239.41/46.15  | |   (57)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 239.41/46.15  | |           e0)
% 239.41/46.15  | | 
% 239.41/46.15  | | BETA: splitting (57) gives:
% 239.41/46.15  | | 
% 239.41/46.15  | | Case 1:
% 239.41/46.15  | | | 
% 239.41/46.15  | | |   (58)  all_58_4 = e0 & op(e3, e1) = e0
% 239.41/46.15  | | | 
% 239.41/46.15  | | | ALPHA: (58) implies:
% 239.41/46.15  | | |   (59)  op(e3, e1) = e0
% 239.41/46.15  | | | 
% 239.41/46.15  | | | BETA: splitting (41) gives:
% 239.41/46.15  | | | 
% 239.41/46.15  | | | Case 1:
% 239.41/46.15  | | | | 
% 239.41/46.15  | | | |   (60)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 239.41/46.15  | | | |           = e1)
% 239.41/46.15  | | | | 
% 239.41/46.15  | | | | BETA: splitting (60) gives:
% 239.41/46.15  | | | | 
% 239.41/46.15  | | | | Case 1:
% 239.41/46.15  | | | | | 
% 239.41/46.15  | | | | |   (61)  all_58_0 = e1 & op(e3, e3) = e1
% 239.41/46.15  | | | | | 
% 239.41/46.15  | | | | | ALPHA: (61) implies:
% 239.41/46.15  | | | | |   (62)  op(e3, e3) = e1
% 239.41/46.15  | | | | | 
% 239.41/46.15  | | | | | REF_CLOSE: (30), (42), (52), (62) are inconsistent by sub-proof #2267.
% 239.41/46.15  | | | | | 
% 239.41/46.15  | | | | Case 2:
% 239.41/46.15  | | | | | 
% 239.41/46.15  | | | | |   (63)  all_58_1 = e1 & op(e3, e2) = e1
% 239.41/46.15  | | | | | 
% 239.41/46.15  | | | | | ALPHA: (63) implies:
% 239.41/46.15  | | | | |   (64)  all_58_1 = e1
% 239.41/46.15  | | | | |   (65)  op(e3, e2) = e1
% 239.41/46.15  | | | | | 
% 239.41/46.15  | | | | | BETA: splitting (10) gives:
% 239.41/46.15  | | | | | 
% 239.41/46.15  | | | | | Case 1:
% 239.41/46.15  | | | | | | 
% 239.41/46.15  | | | | | |   (66)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 239.41/46.15  | | | | | |             e1) = e1)
% 239.41/46.15  | | | | | | 
% 239.41/46.15  | | | | | | BETA: splitting (66) gives:
% 239.41/46.15  | | | | | | 
% 239.41/46.15  | | | | | | Case 1:
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | |   (67)  all_58_4 = e1 & op(e3, e1) = e1
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | | ALPHA: (67) implies:
% 239.41/46.15  | | | | | | |   (68)  all_58_4 = e1
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | | REF_CLOSE: (6), (14), (17), (22), (30), (32), (37), (38), (42),
% 239.41/46.15  | | | | | | |            (45), (54), (64), (68) are inconsistent by sub-proof
% 239.41/46.15  | | | | | | |            #1645.
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | Case 2:
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | |   (69)  all_58_5 = e1 & op(e2, e1) = e1
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | | ALPHA: (69) implies:
% 239.41/46.15  | | | | | | |   (70)  all_58_5 = e1
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | | REF_CLOSE: (1), (9), (12), (13), (16), (21), (22), (23), (24),
% 239.41/46.15  | | | | | | |            (27), (29), (31), (39), (42), (48), (50), (52), (70)
% 239.41/46.15  | | | | | | |            are inconsistent by sub-proof #455.
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | End of split
% 239.41/46.15  | | | | | | 
% 239.41/46.15  | | | | | Case 2:
% 239.41/46.15  | | | | | | 
% 239.41/46.15  | | | | | |   (71)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0,
% 239.41/46.15  | | | | | |             e1) = e1)
% 239.41/46.15  | | | | | | 
% 239.41/46.15  | | | | | | BETA: splitting (71) gives:
% 239.41/46.15  | | | | | | 
% 239.41/46.15  | | | | | | Case 1:
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | |   (72)  all_58_8 = e1 & op(e1, e1) = e1
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | | ALPHA: (72) implies:
% 239.41/46.15  | | | | | | |   (73)  op(e1, e1) = e1
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | | REF_CLOSE: (14), (33), (42), (73) are inconsistent by sub-proof
% 239.41/46.15  | | | | | | |            #468.
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | Case 2:
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | |   (74)  all_58_14 = e1 & op(e0, e1) = e1
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | | ALPHA: (74) implies:
% 239.41/46.15  | | | | | | |   (75)  op(e0, e1) = e1
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | | BETA: splitting (4) gives:
% 239.41/46.15  | | | | | | | 
% 239.41/46.15  | | | | | | | Case 1:
% 239.41/46.15  | | | | | | | | 
% 239.41/46.15  | | | | | | | |   (76)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 239.41/46.15  | | | | | | | |           all_56_17 & $i(all_56_17)) | (all_56_18 = e2 & op(e2,
% 239.41/46.15  | | | | | | | |             all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 239.41/46.15  | | | | | | | |           $i(all_56_19))
% 239.41/46.15  | | | | | | | | 
% 239.41/46.15  | | | | | | | | BETA: splitting (76) gives:
% 239.41/46.15  | | | | | | | | 
% 239.41/46.15  | | | | | | | | Case 1:
% 239.41/46.15  | | | | | | | | | 
% 239.41/46.15  | | | | | | | | |   (77)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 239.41/46.15  | | | | | | | | |         all_56_17 & $i(all_56_17)
% 239.41/46.15  | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | ALPHA: (77) implies:
% 239.41/46.15  | | | | | | | | |   (78)  op(e3, e1) = all_56_17
% 239.41/46.15  | | | | | | | | |   (79)  op(e3, all_56_17) = e3
% 239.41/46.15  | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | BETA: splitting (3) gives:
% 239.41/46.15  | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | Case 1:
% 239.41/46.15  | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | |   (80)  all_54_1 = e2
% 239.41/46.15  | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | REF_CLOSE: (36), (40), (80) are inconsistent by sub-proof
% 239.41/46.15  | | | | | | | | | |            #1928.
% 239.41/46.15  | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | Case 2:
% 239.41/46.15  | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | |   (81)  all_54_1 = e1 | all_54_1 = e0
% 239.41/46.15  | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | BETA: splitting (81) gives:
% 239.41/46.15  | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | Case 1:
% 239.41/46.15  | | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | |   (82)  all_54_1 = e1
% 239.41/46.15  | | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | | COMBINE_EQS: (36), (82) imply:
% 239.41/46.15  | | | | | | | | | | |   (83)  all_52_4 = e1
% 239.41/46.15  | | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | | SIMP: (83) implies:
% 239.41/46.15  | | | | | | | | | | |   (84)  all_52_4 = e1
% 239.41/46.15  | | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | | REDUCE: (25), (84) imply:
% 239.41/46.15  | | | | | | | | | | |   (85)  op(e3, e1) = e3
% 239.41/46.15  | | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | | REF_CLOSE: (22), (30), (42), (78), (79), (85) are
% 239.41/46.15  | | | | | | | | | | |            inconsistent by sub-proof #2098.
% 239.41/46.15  | | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | Case 2:
% 239.41/46.15  | | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | |   (86)  all_54_1 = e0
% 239.41/46.15  | | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | | REF_CLOSE: (36), (51), (86) are inconsistent by sub-proof
% 239.41/46.15  | | | | | | | | | | |            #2050.
% 239.41/46.15  | | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | | End of split
% 239.41/46.15  | | | | | | | | | | 
% 239.41/46.15  | | | | | | | | | End of split
% 239.41/46.15  | | | | | | | | | 
% 239.41/46.15  | | | | | | | | Case 2:
% 239.41/46.15  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | |   (87)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 239.41/46.16  | | | | | | | | |         all_56_19 & $i(all_56_19)
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | | ALPHA: (87) implies:
% 239.41/46.16  | | | | | | | | |   (88)  op(e2, e1) = all_56_19
% 239.41/46.16  | | | | | | | | |   (89)  op(e2, all_56_19) = e2
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | | REF_CLOSE: (2), (18), (22), (26), (42), (49), (55), (88), (89)
% 239.41/46.16  | | | | | | | | |            are inconsistent by sub-proof #750.
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | End of split
% 239.41/46.16  | | | | | | | | 
% 239.41/46.16  | | | | | | | Case 2:
% 239.41/46.16  | | | | | | | | 
% 239.41/46.16  | | | | | | | |   (90)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 =
% 239.41/46.16  | | | | | | | |           e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 239.41/46.16  | | | | | | | |           $i(all_56_23))
% 239.41/46.16  | | | | | | | | 
% 239.41/46.16  | | | | | | | | BETA: splitting (90) gives:
% 239.41/46.16  | | | | | | | | 
% 239.41/46.16  | | | | | | | | Case 1:
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | |   (91)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | | ALPHA: (91) implies:
% 239.41/46.16  | | | | | | | | |   (92)  op(e1, all_56_21) = e1
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | | REDUCE: (44), (92) imply:
% 239.41/46.16  | | | | | | | | |   (93)  op(e1, e3) = e1
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | | REF_CLOSE: (42), (45), (56), (93) are inconsistent by
% 239.41/46.16  | | | | | | | | |            sub-proof #449.
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | Case 2:
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | |   (94)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 239.41/46.16  | | | | | | | | |         all_56_23 & $i(all_56_23)
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | | ALPHA: (94) implies:
% 239.41/46.16  | | | | | | | | |   (95)  op(e0, e1) = all_56_23
% 239.41/46.16  | | | | | | | | |   (96)  op(e0, all_56_23) = e0
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | | REF_CLOSE: (7), (42), (45), (46), (65), (75), (95), (96) are
% 239.41/46.16  | | | | | | | | |            inconsistent by sub-proof #215.
% 239.41/46.16  | | | | | | | | | 
% 239.41/46.16  | | | | | | | | End of split
% 239.41/46.16  | | | | | | | | 
% 239.41/46.16  | | | | | | | End of split
% 239.41/46.16  | | | | | | | 
% 239.41/46.16  | | | | | | End of split
% 239.41/46.16  | | | | | | 
% 239.41/46.16  | | | | | End of split
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | End of split
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | Case 2:
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | |   (97)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 239.41/46.16  | | | |           = e1)
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | | BETA: splitting (97) gives:
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | | Case 1:
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | |   (98)  all_58_4 = e1 & op(e3, e1) = e1
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | | ALPHA: (98) implies:
% 239.41/46.16  | | | | |   (99)  op(e3, e1) = e1
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | | REF_CLOSE: (42), (45), (59), (99) are inconsistent by sub-proof #2089.
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | Case 2:
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | |   (100)  all_58_9 = e1 & op(e3, e0) = e1
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | | ALPHA: (100) implies:
% 239.41/46.16  | | | | |   (101)  op(e3, e0) = e1
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | | REF_CLOSE: (14), (27), (42), (101) are inconsistent by sub-proof #243.
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | End of split
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | End of split
% 239.41/46.16  | | | 
% 239.41/46.16  | | Case 2:
% 239.41/46.16  | | | 
% 239.41/46.16  | | |   (102)  all_58_5 = e0 & op(e2, e1) = e0
% 239.41/46.16  | | | 
% 239.41/46.16  | | | ALPHA: (102) implies:
% 239.41/46.16  | | |   (103)  op(e2, e1) = e0
% 239.41/46.16  | | | 
% 239.41/46.16  | | | REF_CLOSE: (18), (42), (54), (103) are inconsistent by sub-proof #1906.
% 239.41/46.16  | | | 
% 239.41/46.16  | | End of split
% 239.41/46.16  | | 
% 239.41/46.16  | Case 2:
% 239.41/46.16  | | 
% 239.41/46.16  | |   (104)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 239.41/46.16  | |            e0)
% 239.41/46.16  | | 
% 239.41/46.16  | | REF_CLOSE: (6), (8), (19), (20), (21), (34), (35), (39), (42), (53), (104)
% 239.41/46.16  | |            are inconsistent by sub-proof #360.
% 239.41/46.16  | | 
% 239.41/46.16  | End of split
% 239.41/46.16  | 
% 239.41/46.16  End of proof
% 239.41/46.16  
% 239.41/46.16  Sub-proof #24 shows that the following formulas are inconsistent:
% 239.41/46.16  ----------------------------------------------------------------
% 239.41/46.16    (1)  op(e3, all_56_25) = e3
% 239.41/46.16    (2)   ~ (e3 = e2)
% 239.41/46.16    (3)  op(e2, e3) = e1
% 239.41/46.16    (4)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 239.41/46.16           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 239.41/46.16           all_42_1 & $i(all_42_1))
% 239.41/46.16    (5)  op(e3, e0) = e3
% 239.41/46.16    (6)  op(e3, e3) = e2
% 239.41/46.16    (7)  op(e3, e0) = all_56_25
% 239.41/46.16    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.16    (9)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 239.41/46.16           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 239.41/46.16           & $i(all_8_1))
% 239.41/46.16  
% 239.41/46.16  Begin of proof
% 239.41/46.16  | 
% 239.41/46.16  | BETA: splitting (4) gives:
% 239.41/46.16  | 
% 239.41/46.16  | Case 1:
% 239.41/46.16  | | 
% 239.41/46.16  | | 
% 239.41/46.16  | | GROUND_INST: instantiating (8) with e3, all_56_25, e0, e3, simplifying with
% 239.41/46.16  | |              (5), (7) gives:
% 239.41/46.16  | |   (10)  all_56_25 = e3
% 239.41/46.16  | | 
% 239.41/46.16  | | REDUCE: (1), (10) imply:
% 239.41/46.16  | |   (11)  op(e3, e3) = e3
% 239.41/46.16  | | 
% 239.41/46.16  | | REF_CLOSE: (2), (6), (8), (11) are inconsistent by sub-proof #2194.
% 239.41/46.16  | | 
% 239.41/46.16  | Case 2:
% 239.41/46.16  | | 
% 239.41/46.16  | |   (12)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 239.41/46.16  | | 
% 239.41/46.16  | | ALPHA: (12) implies:
% 239.41/46.16  | |   (13)   ~ (all_42_1 = e1)
% 239.41/46.16  | |   (14)  op(e2, e3) = all_42_1
% 239.41/46.16  | | 
% 239.41/46.16  | | REF_CLOSE: (3), (8), (9), (13), (14) are inconsistent by sub-proof #934.
% 239.41/46.16  | | 
% 239.41/46.16  | End of split
% 239.41/46.16  | 
% 239.41/46.16  End of proof
% 239.41/46.16  
% 239.41/46.16  Sub-proof #25 shows that the following formulas are inconsistent:
% 239.41/46.16  ----------------------------------------------------------------
% 239.41/46.16    (1)   ~ (all_52_1 = all_52_3)
% 239.41/46.16    (2)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.41/46.16         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.41/46.16    (3)  op(e0, e3) = all_52_3
% 239.41/46.16    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.41/46.16         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.41/46.16    (5)  all_58_7 = e2
% 239.41/46.16    (6)   ~ (all_52_12 = all_52_13)
% 239.41/46.16    (7)  op(e2, e1) = all_52_9
% 239.41/46.16    (8)   ~ (e3 = e2)
% 239.41/46.16    (9)  op(e0, e3) = e3
% 239.41/46.16    (10)  op(e3, e0) = all_52_12
% 239.41/46.16    (11)  op(e3, e0) = e3
% 239.41/46.16    (12)  op(e2, e3) = all_52_1
% 239.41/46.16    (13)   ~ (all_52_13 = e2)
% 239.41/46.16    (14)  all_58_5 = e2
% 239.41/46.16    (15)   ~ (all_52_9 = e3)
% 239.41/46.16    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.16    (17)  all_58_7 = e1 & op(e1, e2) = e1
% 239.41/46.16    (18)  op(e2, e0) = all_52_13
% 239.41/46.16    (19)   ~ (all_52_1 = e2)
% 239.41/46.16    (20)   ~ (e2 = e1)
% 239.41/46.16  
% 239.41/46.16  Begin of proof
% 239.41/46.16  | 
% 239.41/46.16  | ALPHA: (17) implies:
% 239.41/46.16  |   (21)  all_58_7 = e1
% 239.41/46.16  | 
% 239.41/46.16  | COMBINE_EQS: (5), (21) imply:
% 239.41/46.16  |   (22)  e2 = e1
% 239.41/46.16  | 
% 239.41/46.16  | COMBINE_EQS: (14), (22) imply:
% 239.41/46.16  |   (23)  all_58_5 = e1
% 239.41/46.16  | 
% 239.41/46.16  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 239.41/46.16  |            (15), (16), (18), (19), (20), (23) are inconsistent by sub-proof
% 239.41/46.16  |            #455.
% 239.41/46.16  | 
% 239.41/46.16  End of proof
% 239.41/46.16  
% 239.41/46.16  Sub-proof #26 shows that the following formulas are inconsistent:
% 239.41/46.16  ----------------------------------------------------------------
% 239.41/46.16    (1)   ~ (all_52_1 = all_52_3)
% 239.41/46.16    (2)   ~ (e3 = e0)
% 239.41/46.16    (3)  op(e2, all_52_1) = e2
% 239.41/46.16    (4)   ~ (e2 = e0)
% 239.41/46.16    (5)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.41/46.16         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.41/46.16    (6)  op(e1, e2) = all_52_6
% 239.41/46.16    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 239.41/46.16         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 239.41/46.16    (8)  op(e1, e0) = all_52_14
% 239.41/46.16    (9)  op(e0, e3) = all_52_3
% 239.41/46.16    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.41/46.16          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.41/46.16    (11)   ~ (e3 = e1)
% 239.41/46.16    (12)  all_58_7 = e2
% 239.41/46.16    (13)   ~ (all_52_12 = all_52_13)
% 239.41/46.16    (14)  all_58_15 = e2
% 239.41/46.16    (15)  op(e2, e1) = all_52_9
% 239.41/46.16    (16)   ~ (e3 = e2)
% 239.41/46.16    (17)  op(e1, e3) = e1
% 239.41/46.16    (18)  op(e0, e3) = e3
% 239.41/46.16    (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.41/46.16          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.41/46.16    (20)  op(e3, e0) = all_52_12
% 239.41/46.16    (21)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.41/46.16          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.41/46.16    (22)  op(e3, e0) = e3
% 239.41/46.16    (23)  op(e2, e3) = all_52_1
% 239.41/46.16    (24)  op(e3, e3) = e2
% 239.41/46.16    (25)   ~ (all_52_14 = e3)
% 239.41/46.16    (26)   ~ (all_52_13 = e2)
% 239.41/46.16    (27)   ~ (all_52_6 = e3)
% 239.41/46.16    (28)  all_58_5 = e2
% 239.41/46.16    (29)   ~ (all_52_9 = e3)
% 239.41/46.16    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.16    (31)   ~ (e1 = e0)
% 239.41/46.16    (32)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.41/46.16          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.41/46.16    (33)  op(e2, e0) = all_52_13
% 239.41/46.16    (34)   ~ (all_52_1 = e2)
% 239.41/46.16    (35)   ~ (e2 = e1)
% 239.41/46.16  
% 239.41/46.16  Begin of proof
% 239.41/46.16  | 
% 239.41/46.16  | BETA: splitting (19) gives:
% 239.41/46.16  | 
% 239.41/46.16  | Case 1:
% 239.41/46.16  | | 
% 239.41/46.16  | |   (36)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 239.41/46.16  | |           e0)
% 239.41/46.16  | | 
% 239.41/46.16  | | BETA: splitting (36) gives:
% 239.41/46.16  | | 
% 239.41/46.16  | | Case 1:
% 239.41/46.16  | | | 
% 239.41/46.16  | | |   (37)  all_58_0 = e0 & op(e3, e3) = e0
% 239.41/46.16  | | | 
% 239.41/46.16  | | | ALPHA: (37) implies:
% 239.41/46.16  | | |   (38)  op(e3, e3) = e0
% 239.41/46.16  | | | 
% 239.41/46.16  | | | REF_CLOSE: (4), (24), (30), (38) are inconsistent by sub-proof #2188.
% 239.41/46.16  | | | 
% 239.41/46.16  | | Case 2:
% 239.41/46.16  | | | 
% 239.41/46.16  | | |   (39)  all_58_2 = e0 & op(e2, e3) = e0
% 239.41/46.16  | | | 
% 239.41/46.16  | | | BETA: splitting (32) gives:
% 239.41/46.16  | | | 
% 239.41/46.16  | | | Case 1:
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | |   (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2)
% 239.41/46.16  | | | |           = e0)
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | | REF_CLOSE: (4), (12), (17), (30), (31), (40) are inconsistent by
% 239.41/46.16  | | | |            sub-proof #335.
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | Case 2:
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | |   (41)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0)
% 239.41/46.16  | | | |           = e0)
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | | BETA: splitting (41) gives:
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | | Case 1:
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | |   (42)  all_58_8 = e0 & op(e1, e1) = e0
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | | ALPHA: (42) implies:
% 239.41/46.16  | | | | |   (43)  op(e1, e1) = e0
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | | REF_CLOSE: (2), (6), (8), (11), (17), (21), (25), (27), (30), (43) are
% 239.41/46.16  | | | | |            inconsistent by sub-proof #457.
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | Case 2:
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | |   (44)  all_58_11 = e0 & op(e1, e0) = e0
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | | ALPHA: (44) implies:
% 239.41/46.16  | | | | |   (45)  op(e1, e0) = e0
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | | BETA: splitting (7) gives:
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | | Case 1:
% 239.41/46.16  | | | | | | 
% 239.41/46.16  | | | | | |   (46)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 239.41/46.16  | | | | | |             e0) = e1)
% 239.41/46.16  | | | | | | 
% 239.41/46.16  | | | | | | BETA: splitting (46) gives:
% 239.41/46.16  | | | | | | 
% 239.41/46.16  | | | | | | Case 1:
% 239.41/46.16  | | | | | | | 
% 239.41/46.16  | | | | | | |   (47)  all_58_9 = e1 & op(e3, e0) = e1
% 239.41/46.16  | | | | | | | 
% 239.41/46.16  | | | | | | | ALPHA: (47) implies:
% 239.41/46.16  | | | | | | |   (48)  op(e3, e0) = e1
% 239.41/46.16  | | | | | | | 
% 239.41/46.16  | | | | | | | REF_CLOSE: (11), (22), (30), (48) are inconsistent by sub-proof
% 239.41/46.16  | | | | | | |            #243.
% 239.41/46.16  | | | | | | | 
% 239.41/46.16  | | | | | | Case 2:
% 239.41/46.16  | | | | | | | 
% 239.41/46.16  | | | | | | |   (49)  all_58_10 = e1 & op(e2, e0) = e1
% 239.41/46.16  | | | | | | | 
% 239.41/46.16  | | | | | | | ALPHA: (39) implies:
% 239.41/46.16  | | | | | | |   (50)  op(e2, e3) = e0
% 239.41/46.16  | | | | | | | 
% 239.41/46.16  | | | | | | | ALPHA: (49) implies:
% 239.41/46.16  | | | | | | |   (51)  op(e2, e0) = e1
% 239.41/46.16  | | | | | | | 
% 239.41/46.16  | | | | | | | REF_CLOSE: (3), (23), (26), (30), (33), (50), (51) are
% 239.41/46.16  | | | | | | |            inconsistent by sub-proof #30.
% 239.41/46.16  | | | | | | | 
% 239.41/46.16  | | | | | | End of split
% 239.41/46.16  | | | | | | 
% 239.41/46.16  | | | | | Case 2:
% 239.41/46.16  | | | | | | 
% 239.41/46.16  | | | | | |   (52)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 239.41/46.16  | | | | | |           op(e0, e0) = e1)
% 239.41/46.16  | | | | | | 
% 239.41/46.16  | | | | | | REF_CLOSE: (1), (5), (9), (10), (13), (14), (15), (16), (18), (20),
% 239.41/46.16  | | | | | |            (22), (23), (26), (28), (29), (30), (31), (33), (34),
% 239.41/46.16  | | | | | |            (35), (45), (52) are inconsistent by sub-proof #28.
% 239.41/46.16  | | | | | | 
% 239.41/46.16  | | | | | End of split
% 239.41/46.16  | | | | | 
% 239.41/46.16  | | | | End of split
% 239.41/46.16  | | | | 
% 239.41/46.16  | | | End of split
% 239.41/46.16  | | | 
% 239.41/46.16  | | End of split
% 239.41/46.16  | | 
% 239.41/46.16  | Case 2:
% 239.41/46.16  | | 
% 239.41/46.16  | |   (53)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 239.41/46.16  | |           e0)
% 239.41/46.16  | | 
% 239.41/46.16  | | REF_CLOSE: (2), (17), (18), (30), (31), (53) are inconsistent by sub-proof
% 239.41/46.16  | |            #27.
% 239.41/46.16  | | 
% 239.41/46.16  | End of split
% 239.41/46.16  | 
% 239.41/46.16  End of proof
% 239.41/46.16  
% 239.41/46.16  Sub-proof #27 shows that the following formulas are inconsistent:
% 239.41/46.16  ----------------------------------------------------------------
% 239.41/46.16    (1)   ~ (e3 = e0)
% 239.41/46.16    (2)  op(e1, e3) = e1
% 239.41/46.16    (3)  op(e0, e3) = e3
% 239.41/46.16    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.16    (5)   ~ (e1 = e0)
% 239.41/46.16    (6)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.41/46.16  
% 239.41/46.16  Begin of proof
% 239.41/46.16  | 
% 239.41/46.16  | BETA: splitting (6) gives:
% 239.41/46.16  | 
% 239.41/46.16  | Case 1:
% 239.41/46.16  | | 
% 239.41/46.16  | |   (7)  all_58_6 = e0 & op(e1, e3) = e0
% 239.41/46.16  | | 
% 239.41/46.16  | | ALPHA: (7) implies:
% 239.41/46.16  | |   (8)  op(e1, e3) = e0
% 239.41/46.16  | | 
% 239.41/46.16  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #449.
% 239.41/46.16  | | 
% 239.41/46.16  | Case 2:
% 239.41/46.16  | | 
% 239.41/46.16  | |   (9)  all_58_12 = e0 & op(e0, e3) = e0
% 239.41/46.16  | | 
% 239.41/46.16  | | ALPHA: (9) implies:
% 239.41/46.16  | |   (10)  op(e0, e3) = e0
% 239.41/46.16  | | 
% 239.41/46.16  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #221.
% 239.41/46.16  | | 
% 239.41/46.16  | End of split
% 239.41/46.16  | 
% 239.41/46.17  End of proof
% 239.41/46.17  
% 239.41/46.17  Sub-proof #28 shows that the following formulas are inconsistent:
% 239.41/46.17  ----------------------------------------------------------------
% 239.41/46.17    (1)   ~ (all_52_1 = all_52_3)
% 239.41/46.17    (2)  op(e1, e0) = e0
% 239.41/46.17    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.41/46.17         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.41/46.17    (4)  op(e0, e3) = all_52_3
% 239.41/46.17    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.41/46.17         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.41/46.17    (6)   ~ (all_52_12 = all_52_13)
% 239.41/46.17    (7)  all_58_15 = e2
% 239.41/46.17    (8)  op(e2, e1) = all_52_9
% 239.41/46.17    (9)   ~ (e3 = e2)
% 239.41/46.17    (10)  op(e0, e3) = e3
% 239.41/46.17    (11)  op(e3, e0) = all_52_12
% 239.41/46.17    (12)  op(e3, e0) = e3
% 239.41/46.17    (13)  op(e2, e3) = all_52_1
% 239.41/46.17    (14)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 239.41/46.17    (15)   ~ (all_52_13 = e2)
% 239.41/46.17    (16)  all_58_5 = e2
% 239.41/46.17    (17)   ~ (all_52_9 = e3)
% 239.41/46.17    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.17    (19)   ~ (e1 = e0)
% 239.41/46.17    (20)  op(e2, e0) = all_52_13
% 239.41/46.17    (21)   ~ (all_52_1 = e2)
% 239.41/46.17    (22)   ~ (e2 = e1)
% 239.41/46.17  
% 239.41/46.17  Begin of proof
% 239.41/46.17  | 
% 239.41/46.17  | BETA: splitting (14) gives:
% 239.41/46.17  | 
% 239.41/46.17  | Case 1:
% 239.41/46.17  | | 
% 239.41/46.17  | |   (23)  all_58_11 = e1 & op(e1, e0) = e1
% 239.41/46.17  | | 
% 239.41/46.17  | | ALPHA: (23) implies:
% 239.41/46.17  | |   (24)  op(e1, e0) = e1
% 239.41/46.17  | | 
% 239.41/46.17  | | REF_CLOSE: (2), (18), (19), (24) are inconsistent by sub-proof #2284.
% 239.41/46.17  | | 
% 239.41/46.17  | Case 2:
% 239.41/46.17  | | 
% 239.41/46.17  | |   (25)  all_58_15 = e1 & op(e0, e0) = e1
% 239.41/46.17  | | 
% 239.41/46.17  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 239.41/46.17  | |            (15), (16), (17), (18), (20), (21), (22), (25) are inconsistent
% 239.41/46.17  | |            by sub-proof #29.
% 239.41/46.17  | | 
% 239.41/46.17  | End of split
% 239.41/46.17  | 
% 239.41/46.17  End of proof
% 239.41/46.17  
% 239.41/46.17  Sub-proof #29 shows that the following formulas are inconsistent:
% 239.41/46.17  ----------------------------------------------------------------
% 239.41/46.17    (1)   ~ (all_52_1 = all_52_3)
% 239.41/46.17    (2)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.41/46.17         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.41/46.17    (3)  op(e0, e3) = all_52_3
% 239.41/46.17    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.41/46.17         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 239.41/46.17    (5)   ~ (all_52_12 = all_52_13)
% 239.41/46.17    (6)  all_58_15 = e2
% 239.41/46.17    (7)  op(e2, e1) = all_52_9
% 239.41/46.17    (8)   ~ (e3 = e2)
% 239.41/46.17    (9)  op(e0, e3) = e3
% 239.41/46.17    (10)  op(e3, e0) = all_52_12
% 239.41/46.17    (11)  op(e3, e0) = e3
% 239.41/46.17    (12)  op(e2, e3) = all_52_1
% 239.41/46.17    (13)   ~ (all_52_13 = e2)
% 239.41/46.17    (14)  all_58_5 = e2
% 239.41/46.17    (15)   ~ (all_52_9 = e3)
% 239.41/46.17    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.17    (17)  all_58_15 = e1 & op(e0, e0) = e1
% 239.41/46.17    (18)  op(e2, e0) = all_52_13
% 239.41/46.17    (19)   ~ (all_52_1 = e2)
% 239.41/46.17    (20)   ~ (e2 = e1)
% 239.41/46.17  
% 239.41/46.17  Begin of proof
% 239.41/46.17  | 
% 239.41/46.17  | ALPHA: (17) implies:
% 239.41/46.17  |   (21)  all_58_15 = e1
% 239.41/46.17  | 
% 239.41/46.17  | COMBINE_EQS: (6), (21) imply:
% 239.41/46.17  |   (22)  e2 = e1
% 239.41/46.17  | 
% 239.41/46.17  | COMBINE_EQS: (14), (22) imply:
% 239.41/46.17  |   (23)  all_58_5 = e1
% 239.41/46.17  | 
% 239.41/46.17  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 239.41/46.17  |            (15), (16), (18), (19), (20), (23) are inconsistent by sub-proof
% 239.41/46.17  |            #455.
% 239.41/46.17  | 
% 239.41/46.17  End of proof
% 239.41/46.17  
% 239.41/46.17  Sub-proof #30 shows that the following formulas are inconsistent:
% 239.41/46.17  ----------------------------------------------------------------
% 239.41/46.17    (1)  op(e2, all_52_1) = e2
% 239.41/46.17    (2)  op(e2, e3) = e0
% 239.41/46.17    (3)  op(e2, e3) = all_52_1
% 239.41/46.17    (4)   ~ (all_52_13 = e2)
% 239.41/46.17    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.17    (6)  op(e2, e0) = e1
% 239.41/46.17    (7)  op(e2, e0) = all_52_13
% 239.41/46.17  
% 239.41/46.17  Begin of proof
% 239.41/46.17  | 
% 239.41/46.17  | GROUND_INST: instantiating (5) with all_52_13, e1, e0, e2, simplifying with
% 239.41/46.17  |              (6), (7) gives:
% 239.41/46.17  |   (8)  all_52_13 = e1
% 239.41/46.17  | 
% 239.41/46.17  | GROUND_INST: instantiating (5) with all_52_1, e0, e3, e2, simplifying with
% 239.41/46.17  |              (2), (3) gives:
% 239.41/46.17  |   (9)  all_52_1 = e0
% 239.41/46.17  | 
% 239.41/46.17  | REDUCE: (4), (8) imply:
% 239.41/46.17  |   (10)   ~ (e2 = e1)
% 239.41/46.17  | 
% 239.41/46.17  | SIMP: (10) implies:
% 239.41/46.17  |   (11)   ~ (e2 = e1)
% 239.41/46.17  | 
% 239.41/46.17  | REDUCE: (1), (9) imply:
% 239.41/46.17  |   (12)  op(e2, e0) = e2
% 239.41/46.17  | 
% 239.41/46.17  | REF_CLOSE: (5), (6), (11), (12) are inconsistent by sub-proof #1659.
% 239.41/46.17  | 
% 239.41/46.17  End of proof
% 239.41/46.17  
% 239.41/46.17  Sub-proof #31 shows that the following formulas are inconsistent:
% 239.41/46.17  ----------------------------------------------------------------
% 239.41/46.17    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.41/46.17         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.41/46.17    (2)   ~ (all_8_2 = e0)
% 239.41/46.17    (3)   ~ (all_52_3 = e1)
% 239.41/46.17    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.41/46.17         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.41/46.17    (5)   ~ (e2 = e0)
% 239.41/46.17    (6)  op(e1, e2) = all_52_6
% 239.41/46.17    (7)  all_58_9 = e0
% 239.41/46.17    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.41/46.17         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.41/46.17    (9)  op(e0, e3) = all_52_3
% 239.41/46.17    (10)   ~ (all_52_6 = e0)
% 239.41/46.17    (11)   ~ (e3 = e1)
% 239.41/46.17    (12)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.41/46.17          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.41/46.17    (13)  all_4_1 = e0
% 239.41/46.17    (14)  op(e3, e3) = e1
% 239.41/46.17    (15)   ~ (all_4_1 = e3)
% 239.41/46.17    (16)   ~ (e3 = e2)
% 239.41/46.17    (17)  all_56_15 = e0
% 239.41/46.17    (18)  op(e2, e2) = all_8_2
% 239.41/46.17    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.17    (20)  op(e0, all_56_15) = e0
% 239.41/46.17    (21)   ~ (e1 = e0)
% 239.41/46.17    (22)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.41/46.17          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 239.41/46.17            e1)
% 239.41/46.17    (23)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.41/46.17          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 239.41/46.17            e2)
% 239.41/46.17    (24)   ~ (e2 = e1)
% 239.41/46.17  
% 239.41/46.17  Begin of proof
% 239.41/46.17  | 
% 239.41/46.17  | REDUCE: (13), (15) imply:
% 239.41/46.17  |   (25)   ~ (e3 = e0)
% 239.41/46.17  | 
% 239.41/46.17  | SIMP: (25) implies:
% 239.41/46.17  |   (26)   ~ (e3 = e0)
% 239.41/46.17  | 
% 239.41/46.17  | REDUCE: (17), (20) imply:
% 239.41/46.17  |   (27)  op(e0, e0) = e0
% 239.41/46.17  | 
% 239.41/46.17  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 239.41/46.17  |            (14), (16), (18), (19), (21), (22), (23), (24), (26), (27) are
% 239.41/46.17  |            inconsistent by sub-proof #1087.
% 239.41/46.17  | 
% 239.41/46.17  End of proof
% 239.41/46.17  
% 239.41/46.17  Sub-proof #32 shows that the following formulas are inconsistent:
% 239.41/46.17  ----------------------------------------------------------------
% 239.41/46.17    (1)   ~ (all_52_6 = e1)
% 239.41/46.18    (2)  op(e1, e2) = all_52_6
% 239.41/46.18    (3)   ~ (all_52_6 = e2)
% 239.41/46.18    (4)  op(e1, all_56_5) = e1
% 239.41/46.18    (5)  op(e1, e3) = all_56_5
% 239.41/46.18    (6)  op(e1, e3) = all_6_1
% 239.41/46.18    (7)  op(e1, e3) = e2
% 239.41/46.18    (8)  all_54_9 = all_52_6
% 239.41/46.18    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.18    (10)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.41/46.18            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 239.41/46.18              e3) = all_46_1 & $i(all_46_1))
% 239.41/46.18    (11)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 239.41/46.18  
% 239.41/46.18  Begin of proof
% 239.41/46.18  | 
% 239.41/46.18  | BETA: splitting (10) gives:
% 239.41/46.18  | 
% 239.41/46.18  | Case 1:
% 239.41/46.18  | | 
% 239.41/46.18  | |   (12)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.41/46.18  | |         all_46_1 & $i(all_46_0) & $i(all_46_1)
% 239.41/46.18  | | 
% 239.41/46.18  | | ALPHA: (12) implies:
% 239.41/46.18  | |   (13)  op(e1, e3) = all_46_1
% 239.41/46.18  | | 
% 239.41/46.18  | | BETA: splitting (11) gives:
% 239.41/46.18  | | 
% 239.41/46.18  | | Case 1:
% 239.41/46.18  | | | 
% 239.41/46.18  | | |   (14)  all_54_9 = e2
% 239.41/46.18  | | | 
% 239.41/46.18  | | | REF_CLOSE: (3), (8), (14) are inconsistent by sub-proof #1954.
% 239.41/46.18  | | | 
% 239.41/46.18  | | Case 2:
% 239.41/46.18  | | | 
% 239.41/46.18  | | |   (15)  all_54_9 = e1 | all_54_9 = e0
% 239.41/46.18  | | | 
% 239.41/46.18  | | | BETA: splitting (15) gives:
% 239.41/46.18  | | | 
% 239.41/46.18  | | | Case 1:
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | |   (16)  all_54_9 = e1
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | REF_CLOSE: (1), (8), (16) are inconsistent by sub-proof #2055.
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | Case 2:
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | |   (17)  all_54_9 = e0
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | COMBINE_EQS: (8), (17) imply:
% 239.41/46.18  | | | |   (18)  all_52_6 = e0
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | SIMP: (18) implies:
% 239.41/46.18  | | | |   (19)  all_52_6 = e0
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | REDUCE: (1), (19) imply:
% 239.41/46.18  | | | |   (20)   ~ (e1 = e0)
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | SIMP: (20) implies:
% 239.41/46.18  | | | |   (21)   ~ (e1 = e0)
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | REDUCE: (2), (19) imply:
% 239.41/46.18  | | | |   (22)  op(e1, e2) = e0
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | GROUND_INST: instantiating (9) with e2, all_46_1, e3, e1, simplifying
% 239.41/46.18  | | | |              with (7), (13) gives:
% 239.41/46.18  | | | |   (23)  all_46_1 = e2
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | GROUND_INST: instantiating (9) with all_46_1, all_56_5, e3, e1,
% 239.41/46.18  | | | |              simplifying with (5), (13) gives:
% 239.41/46.18  | | | |   (24)  all_56_5 = all_46_1
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | GROUND_INST: instantiating (9) with all_6_1, all_56_5, e3, e1,
% 239.41/46.18  | | | |              simplifying with (5), (6) gives:
% 239.41/46.18  | | | |   (25)  all_56_5 = all_6_1
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | COMBINE_EQS: (24), (25) imply:
% 239.41/46.18  | | | |   (26)  all_46_1 = all_6_1
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | SIMP: (26) implies:
% 239.41/46.18  | | | |   (27)  all_46_1 = all_6_1
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | COMBINE_EQS: (23), (27) imply:
% 239.41/46.18  | | | |   (28)  all_6_1 = e2
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | COMBINE_EQS: (25), (28) imply:
% 239.41/46.18  | | | |   (29)  all_56_5 = e2
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | REDUCE: (4), (29) imply:
% 239.41/46.18  | | | |   (30)  op(e1, e2) = e1
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | | REF_CLOSE: (2), (9), (21), (22), (30) are inconsistent by sub-proof
% 239.41/46.18  | | | |            #2136.
% 239.41/46.18  | | | | 
% 239.41/46.18  | | | End of split
% 239.41/46.18  | | | 
% 239.41/46.18  | | End of split
% 239.41/46.18  | | 
% 239.41/46.18  | Case 2:
% 239.41/46.18  | | 
% 239.41/46.18  | |   (31)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 239.41/46.18  | | 
% 239.41/46.18  | | REF_CLOSE: (7), (9), (31) are inconsistent by sub-proof #395.
% 239.41/46.18  | | 
% 239.41/46.18  | End of split
% 239.41/46.18  | 
% 239.41/46.18  End of proof
% 239.41/46.18  
% 239.41/46.18  Sub-proof #33 shows that the following formulas are inconsistent:
% 239.41/46.18  ----------------------------------------------------------------
% 239.41/46.18    (1)   ~ (all_52_1 = all_52_3)
% 239.41/46.18    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.41/46.18    (3)   ~ (all_52_3 = e1)
% 239.41/46.18    (4)   ~ (all_52_11 = e2)
% 239.41/46.18    (5)  op(e1, e3) = all_6_1
% 239.41/46.18    (6)   ~ (all_46_0 = e0)
% 239.41/46.18    (7)  op(all_10_1, e3) = all_10_0
% 239.41/46.18    (8)  all_54_6 = all_52_9
% 239.41/46.18    (9)  op(e1, e3) = e2
% 239.41/46.18    (10)  all_54_4 = all_52_1
% 239.41/46.18    (11)   ~ (all_52_11 = e3)
% 239.41/46.18    (12)  op(e2, e1) = all_52_9
% 239.41/46.18    (13)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.41/46.18    (14)   ~ (all_52_3 = all_52_11)
% 239.41/46.18    (15)  all_54_12 = all_52_3
% 239.41/46.18    (16)   ~ (all_52_3 = e2)
% 239.41/46.18    (17)  op(all_46_1, e1) = all_46_0
% 239.41/46.18    (18)  op(e1, e3) = all_46_1
% 239.41/46.18    (19)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 239.41/46.18    (20)  op(e2, e3) = all_52_1
% 239.41/46.18    (21)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.41/46.18    (22)  op(e3, e1) = e2
% 239.41/46.18    (23)   ~ (all_52_9 = e3)
% 239.41/46.18    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.18    (25)  op(e3, e1) = all_10_1
% 239.41/46.18    (26)   ~ (all_10_0 = e0)
% 239.41/46.18    (27)  all_54_14 = all_52_11
% 239.41/46.18    (28)   ~ (all_52_9 = all_52_11)
% 239.41/46.18    (29)   ~ (all_52_1 = e2)
% 239.41/46.18    (30)   ~ (all_52_1 = e1)
% 239.41/46.18    (31)   ~ (all_52_9 = e2)
% 239.41/46.18  
% 239.41/46.18  Begin of proof
% 239.41/46.18  | 
% 239.41/46.18  | GROUND_INST: instantiating (24) with e2, all_46_1, e3, e1, simplifying with
% 239.41/46.18  |              (9), (18) gives:
% 239.41/46.18  |   (32)  all_46_1 = e2
% 239.41/46.18  | 
% 239.41/46.18  | GROUND_INST: instantiating (24) with all_6_1, all_46_1, e3, e1, simplifying
% 239.41/46.18  |              with (5), (18) gives:
% 239.41/46.18  |   (33)  all_46_1 = all_6_1
% 239.41/46.18  | 
% 239.41/46.18  | GROUND_INST: instantiating (24) with e2, all_10_1, e1, e3, simplifying with
% 239.41/46.18  |              (22), (25) gives:
% 239.41/46.18  |   (34)  all_10_1 = e2
% 239.41/46.18  | 
% 239.41/46.18  | COMBINE_EQS: (32), (33) imply:
% 239.41/46.18  |   (35)  all_6_1 = e2
% 239.41/46.18  | 
% 239.41/46.18  | REDUCE: (17), (32) imply:
% 239.41/46.18  |   (36)  op(e2, e1) = all_46_0
% 239.41/46.18  | 
% 239.41/46.18  | REDUCE: (7), (34) imply:
% 239.41/46.18  |   (37)  op(e2, e3) = all_10_0
% 239.41/46.18  | 
% 239.41/46.18  | GROUND_INST: instantiating (24) with all_52_9, all_46_0, e1, e2, simplifying
% 239.41/46.18  |              with (12), (36) gives:
% 239.41/46.18  |   (38)  all_52_9 = all_46_0
% 239.41/46.18  | 
% 239.41/46.18  | GROUND_INST: instantiating (24) with all_52_1, all_10_0, e3, e2, simplifying
% 239.41/46.18  |              with (20), (37) gives:
% 239.41/46.18  |   (39)  all_52_1 = all_10_0
% 239.41/46.18  | 
% 239.41/46.18  | COMBINE_EQS: (8), (38) imply:
% 239.41/46.18  |   (40)  all_54_6 = all_46_0
% 239.41/46.18  | 
% 239.41/46.18  | COMBINE_EQS: (10), (39) imply:
% 239.41/46.18  |   (41)  all_54_4 = all_10_0
% 239.41/46.18  | 
% 239.41/46.18  | REDUCE: (1), (39) imply:
% 239.41/46.18  |   (42)   ~ (all_52_3 = all_10_0)
% 239.41/46.18  | 
% 239.41/46.18  | SIMP: (42) implies:
% 239.41/46.18  |   (43)   ~ (all_52_3 = all_10_0)
% 239.41/46.18  | 
% 239.41/46.18  | REDUCE: (29), (39) imply:
% 239.41/46.19  |   (44)   ~ (all_10_0 = e2)
% 239.41/46.19  | 
% 239.41/46.19  | REDUCE: (30), (39) imply:
% 239.41/46.19  |   (45)   ~ (all_10_0 = e1)
% 239.41/46.19  | 
% 239.41/46.19  | REDUCE: (28), (38) imply:
% 239.41/46.19  |   (46)   ~ (all_52_11 = all_46_0)
% 239.41/46.19  | 
% 239.41/46.19  | SIMP: (46) implies:
% 239.41/46.19  |   (47)   ~ (all_52_11 = all_46_0)
% 239.41/46.19  | 
% 239.41/46.19  | REDUCE: (23), (38) imply:
% 239.41/46.19  |   (48)   ~ (all_46_0 = e3)
% 239.41/46.19  | 
% 239.41/46.19  | REDUCE: (31), (38) imply:
% 239.41/46.19  |   (49)   ~ (all_46_0 = e2)
% 239.41/46.19  | 
% 239.41/46.19  | BETA: splitting (19) gives:
% 239.41/46.19  | 
% 239.41/46.19  | Case 1:
% 239.41/46.19  | | 
% 239.41/46.19  | |   (50)  all_54_6 = e3
% 239.41/46.19  | | 
% 239.41/46.19  | | COMBINE_EQS: (40), (50) imply:
% 239.41/46.19  | |   (51)  all_46_0 = e3
% 239.41/46.19  | | 
% 239.41/46.19  | | REDUCE: (48), (51) imply:
% 239.41/46.19  | |   (52)  $false
% 239.41/46.19  | | 
% 239.41/46.19  | | CLOSE: (52) is inconsistent.
% 239.41/46.19  | | 
% 239.41/46.19  | Case 2:
% 239.41/46.19  | | 
% 239.41/46.19  | |   (53)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 239.41/46.19  | | 
% 239.41/46.19  | | BETA: splitting (21) gives:
% 239.41/46.19  | | 
% 239.41/46.19  | | Case 1:
% 239.41/46.19  | | | 
% 239.41/46.19  | | |   (54)  all_54_4 = e3
% 239.41/46.19  | | | 
% 239.41/46.19  | | | COMBINE_EQS: (41), (54) imply:
% 239.41/46.19  | | |   (55)  all_10_0 = e3
% 239.41/46.19  | | | 
% 239.41/46.19  | | | SIMP: (55) implies:
% 239.41/46.19  | | |   (56)  all_10_0 = e3
% 239.41/46.19  | | | 
% 239.41/46.19  | | | REDUCE: (43), (56) imply:
% 239.41/46.19  | | |   (57)   ~ (all_52_3 = e3)
% 239.41/46.19  | | | 
% 239.41/46.19  | | | BETA: splitting (2) gives:
% 239.41/46.19  | | | 
% 239.41/46.19  | | | Case 1:
% 239.41/46.19  | | | | 
% 239.41/46.19  | | | |   (58)  all_54_12 = e3
% 239.41/46.19  | | | | 
% 239.41/46.19  | | | | REF_CLOSE: (15), (57), (58) are inconsistent by sub-proof #2266.
% 239.41/46.19  | | | | 
% 239.41/46.19  | | | Case 2:
% 239.41/46.19  | | | | 
% 239.41/46.19  | | | |   (59)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.41/46.19  | | | | 
% 239.41/46.19  | | | | BETA: splitting (53) gives:
% 239.41/46.19  | | | | 
% 239.41/46.19  | | | | Case 1:
% 239.41/46.19  | | | | | 
% 239.41/46.19  | | | | |   (60)  all_54_6 = e2
% 239.41/46.19  | | | | | 
% 239.41/46.19  | | | | | COMBINE_EQS: (40), (60) imply:
% 239.41/46.19  | | | | |   (61)  all_46_0 = e2
% 239.41/46.19  | | | | | 
% 239.41/46.19  | | | | | REDUCE: (49), (61) imply:
% 239.41/46.19  | | | | |   (62)  $false
% 239.41/46.19  | | | | | 
% 239.41/46.19  | | | | | CLOSE: (62) is inconsistent.
% 239.41/46.19  | | | | | 
% 239.41/46.19  | | | | Case 2:
% 239.41/46.19  | | | | | 
% 239.41/46.19  | | | | |   (63)  all_54_6 = e1 | all_54_6 = e0
% 239.41/46.19  | | | | | 
% 239.41/46.19  | | | | | BETA: splitting (63) gives:
% 239.41/46.19  | | | | | 
% 239.41/46.19  | | | | | Case 1:
% 239.41/46.19  | | | | | | 
% 239.41/46.19  | | | | | |   (64)  all_54_6 = e1
% 239.41/46.19  | | | | | | 
% 239.41/46.19  | | | | | | COMBINE_EQS: (40), (64) imply:
% 239.41/46.19  | | | | | |   (65)  all_46_0 = e1
% 239.41/46.19  | | | | | | 
% 239.41/46.19  | | | | | | REDUCE: (47), (65) imply:
% 239.41/46.19  | | | | | |   (66)   ~ (all_52_11 = e1)
% 239.41/46.19  | | | | | | 
% 239.41/46.19  | | | | | | BETA: splitting (13) gives:
% 239.41/46.19  | | | | | | 
% 239.41/46.19  | | | | | | Case 1:
% 239.41/46.19  | | | | | | | 
% 239.41/46.19  | | | | | | |   (67)  all_54_14 = e3
% 239.41/46.19  | | | | | | | 
% 239.41/46.19  | | | | | | | REF_CLOSE: (11), (27), (67) are inconsistent by sub-proof #1796.
% 239.41/46.19  | | | | | | | 
% 239.41/46.19  | | | | | | Case 2:
% 239.41/46.19  | | | | | | | 
% 239.41/46.19  | | | | | | |   (68)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.41/46.19  | | | | | | | 
% 239.41/46.19  | | | | | | | BETA: splitting (68) gives:
% 239.41/46.19  | | | | | | | 
% 239.41/46.19  | | | | | | | Case 1:
% 239.41/46.19  | | | | | | | | 
% 239.41/46.19  | | | | | | | |   (69)  all_54_14 = e2
% 239.41/46.19  | | | | | | | | 
% 239.41/46.19  | | | | | | | | REF_CLOSE: (4), (27), (69) are inconsistent by sub-proof #1856.
% 239.41/46.19  | | | | | | | | 
% 239.41/46.19  | | | | | | | Case 2:
% 239.41/46.19  | | | | | | | | 
% 239.41/46.19  | | | | | | | |   (70)  all_54_14 = e1 | all_54_14 = e0
% 239.41/46.19  | | | | | | | | 
% 239.41/46.19  | | | | | | | | BETA: splitting (70) gives:
% 239.41/46.19  | | | | | | | | 
% 239.41/46.19  | | | | | | | | Case 1:
% 239.41/46.19  | | | | | | | | | 
% 239.41/46.19  | | | | | | | | |   (71)  all_54_14 = e1
% 239.41/46.19  | | | | | | | | | 
% 239.41/46.19  | | | | | | | | | REF_CLOSE: (27), (66), (71) are inconsistent by sub-proof
% 239.41/46.19  | | | | | | | | |            #1937.
% 239.41/46.19  | | | | | | | | | 
% 239.41/46.19  | | | | | | | | Case 2:
% 239.41/46.19  | | | | | | | | | 
% 239.41/46.19  | | | | | | | | |   (72)  all_54_14 = e0
% 239.41/46.19  | | | | | | | | | 
% 239.41/46.19  | | | | | | | | | COMBINE_EQS: (27), (72) imply:
% 239.41/46.19  | | | | | | | | |   (73)  all_52_11 = e0
% 239.41/46.19  | | | | | | | | | 
% 239.41/46.19  | | | | | | | | | SIMP: (73) implies:
% 239.41/46.19  | | | | | | | | |   (74)  all_52_11 = e0
% 239.41/46.19  | | | | | | | | | 
% 239.41/46.19  | | | | | | | | | REDUCE: (14), (74) imply:
% 239.41/46.19  | | | | | | | | |   (75)   ~ (all_52_3 = e0)
% 239.41/46.19  | | | | | | | | | 
% 239.41/46.19  | | | | | | | | | REF_CLOSE: (3), (15), (16), (59), (75) are inconsistent by
% 239.41/46.19  | | | | | | | | |            sub-proof #2066.
% 239.41/46.19  | | | | | | | | | 
% 239.41/46.19  | | | | | | | | End of split
% 239.41/46.19  | | | | | | | | 
% 239.41/46.19  | | | | | | | End of split
% 239.41/46.19  | | | | | | | 
% 239.41/46.19  | | | | | | End of split
% 239.41/46.19  | | | | | | 
% 239.41/46.19  | | | | | Case 2:
% 239.41/46.19  | | | | | | 
% 239.41/46.19  | | | | | |   (76)  all_54_6 = e0
% 239.41/46.19  | | | | | | 
% 239.41/46.19  | | | | | | COMBINE_EQS: (40), (76) imply:
% 239.41/46.19  | | | | | |   (77)  all_46_0 = e0
% 239.41/46.19  | | | | | | 
% 239.41/46.19  | | | | | | REDUCE: (6), (77) imply:
% 239.41/46.19  | | | | | |   (78)  $false
% 239.41/46.19  | | | | | | 
% 239.41/46.19  | | | | | | CLOSE: (78) is inconsistent.
% 239.41/46.19  | | | | | | 
% 239.41/46.19  | | | | | End of split
% 239.41/46.19  | | | | | 
% 239.41/46.19  | | | | End of split
% 239.41/46.19  | | | | 
% 239.41/46.19  | | | End of split
% 239.41/46.19  | | | 
% 239.41/46.19  | | Case 2:
% 239.41/46.19  | | | 
% 239.41/46.19  | | |   (79)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.41/46.19  | | | 
% 239.41/46.19  | | | REF_CLOSE: (26), (41), (44), (45), (79) are inconsistent by sub-proof
% 239.41/46.19  | | |            #106.
% 239.41/46.19  | | | 
% 239.41/46.19  | | End of split
% 239.41/46.19  | | 
% 239.41/46.19  | End of split
% 239.41/46.19  | 
% 239.41/46.19  End of proof
% 239.41/46.19  
% 239.41/46.19  Sub-proof #34 shows that the following formulas are inconsistent:
% 239.41/46.19  ----------------------------------------------------------------
% 239.41/46.19    (1)   ~ (all_52_1 = all_52_3)
% 239.41/46.19    (2)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 239.41/46.19           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 239.41/46.19           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 239.41/46.19           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 239.41/46.19           & $i(all_56_23))
% 239.41/46.19    (3)   ~ (e3 = e0)
% 239.41/46.19    (4)  op(e1, e0) = e0
% 239.41/46.19    (5)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 239.41/46.19         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.41/46.19    (6)   ~ (all_52_8 = all_52_9)
% 239.41/46.19    (7)   ~ (e2 = e0)
% 239.41/46.19    (8)  op(e1, e2) = all_52_6
% 239.41/46.19    (9)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 239.41/46.19           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 239.41/46.19             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 239.41/46.19           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.41/46.19             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.41/46.19           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.41/46.19           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.41/46.19           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.41/46.19           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 239.41/46.19           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.41/46.19           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.41/46.19             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.41/46.19           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.41/46.19           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 239.41/46.19           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.41/46.19           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 239.41/46.19           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.41/46.19           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.41/46.19             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.41/46.19           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.41/46.19           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 239.41/46.20           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.41/46.20           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 239.41/46.20           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.41/46.20           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.41/46.20             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.41/46.20           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.41/46.20           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.41/46.20    (10)   ~ (all_52_1 = all_52_2)
% 239.41/46.20    (11)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.41/46.20    (12)   ~ (all_52_8 = e0)
% 239.41/46.20    (13)  op(e2, e3) = e3
% 239.41/46.20    (14)  op(e0, e3) = all_52_3
% 239.41/46.20    (15)   ~ (e3 = e1)
% 239.41/46.20    (16)  op(e0, e2) = e3
% 239.41/46.20    (17)  op(e2, e2) = e0
% 239.41/46.20    (18)  all_54_6 = all_52_9
% 239.41/46.20    (19)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 239.41/46.20    (20)  all_54_2 = all_52_8
% 239.41/46.20    (21)  all_58_12 = e1
% 239.41/46.20    (22)   ~ (all_52_9 = e0)
% 239.41/46.20    (23)   ~ (all_52_1 = all_52_9)
% 239.41/46.20    (24)  all_54_4 = all_52_1
% 239.41/46.20    (25)  op(e3, e1) = all_52_8
% 239.41/46.20    (26)  op(e2, e1) = all_52_9
% 239.41/46.20    (27)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 239.41/46.20          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 239.41/46.20    (28)   ~ (e3 = e2)
% 239.41/46.20    (29)  op(e3, e1) = e1
% 239.41/46.20    (30)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 239.41/46.20            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 239.41/46.20              e0) = all_14_1 & $i(all_14_1))
% 239.41/46.20    (31)  op(e0, e3) = e1
% 239.41/46.20    (32)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.41/46.20    (33)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.41/46.20          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.41/46.20    (34)   ~ (all_52_3 = e2)
% 239.41/46.20    (35)   ~ (all_52_1 = e0)
% 239.41/46.20    (36)  op(e2, e3) = all_52_1
% 239.41/46.20    (37)  op(e1, e1) = e3
% 239.41/46.20    (38)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.41/46.20    (39)   ~ (all_52_2 = e0)
% 239.41/46.20    (40)  all_54_1 = all_52_4
% 239.41/46.20    (41)   ~ (all_52_4 = e3)
% 239.41/46.20    (42)  op(e3, e2) = all_52_4
% 239.41/46.20    (43)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.20    (44)  all_58_8 = e3
% 239.41/46.20    (45)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.41/46.20            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 239.41/46.20              e3) = all_46_1 & $i(all_46_1))
% 239.41/46.20    (46)  op(e1, e3) = all_52_2
% 239.41/46.20    (47)  all_56_21 = e3
% 239.41/46.20    (48)   ~ (e1 = e0)
% 239.41/46.20    (49)  op(e2, e0) = e1
% 239.41/46.20    (50)  all_58_2 = e3
% 239.41/46.20    (51)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.41/46.20          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.41/46.20    (52)  op(e0, e0) = e2
% 239.41/46.20    (53)  op(e2, e0) = all_52_13
% 239.41/46.20    (54)  op(e2, e0) = all_48_1
% 239.41/46.20    (55)   ~ (all_52_4 = all_52_8)
% 239.41/46.20    (56)   ~ (all_52_4 = all_52_6)
% 239.41/46.20    (57)   ~ (all_52_4 = e0)
% 239.41/46.20    (58)   ~ (e2 = e1)
% 239.41/46.20    (59)   ~ (all_52_1 = e1)
% 239.41/46.20    (60)   ~ (all_52_8 = e3)
% 239.41/46.20  
% 239.41/46.20  Begin of proof
% 239.41/46.20  | 
% 239.41/46.20  | BETA: splitting (27) gives:
% 239.41/46.20  | 
% 239.41/46.20  | Case 1:
% 239.41/46.20  | | 
% 239.41/46.20  | |   (61)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 239.41/46.20  | |           e2)
% 239.41/46.20  | | 
% 239.41/46.20  | | BETA: splitting (61) gives:
% 239.41/46.20  | | 
% 239.41/46.20  | | Case 1:
% 239.41/46.20  | | | 
% 239.41/46.20  | | |   (62)  all_58_0 = e2 & op(e3, e3) = e2
% 239.41/46.20  | | | 
% 239.41/46.20  | | | ALPHA: (62) implies:
% 239.41/46.20  | | |   (63)  op(e3, e3) = e2
% 239.41/46.20  | | | 
% 239.41/46.20  | | | BETA: splitting (33) gives:
% 239.41/46.20  | | | 
% 239.41/46.20  | | | Case 1:
% 239.41/46.20  | | | | 
% 239.41/46.20  | | | |   (64)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 239.41/46.20  | | | |           = e0)
% 239.41/46.20  | | | | 
% 239.41/46.20  | | | | REF_CLOSE: (3), (7), (43), (50), (63), (64) are inconsistent by
% 239.41/46.20  | | | |            sub-proof #1927.
% 239.41/46.20  | | | | 
% 239.41/46.20  | | | Case 2:
% 239.41/46.20  | | | | 
% 239.41/46.20  | | | |   (65)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 239.41/46.20  | | | |           = e0)
% 239.41/46.20  | | | | 
% 239.41/46.20  | | | | BETA: splitting (65) gives:
% 239.41/46.20  | | | | 
% 239.41/46.20  | | | | Case 1:
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | |   (66)  all_58_6 = e0 & op(e1, e3) = e0
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | | ALPHA: (66) implies:
% 239.41/46.20  | | | | |   (67)  op(e1, e3) = e0
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | | REF_CLOSE: (39), (43), (46), (67) are inconsistent by sub-proof #2023.
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | Case 2:
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | |   (68)  all_58_12 = e0 & op(e0, e3) = e0
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | | ALPHA: (68) implies:
% 239.41/46.20  | | | | |   (69)  all_58_12 = e0
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | | REF_CLOSE: (21), (48), (69) are inconsistent by sub-proof #1539.
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | End of split
% 239.41/46.20  | | | | 
% 239.41/46.20  | | | End of split
% 239.41/46.20  | | | 
% 239.41/46.20  | | Case 2:
% 239.41/46.20  | | | 
% 239.41/46.20  | | |   (70)  all_58_2 = e2 & op(e2, e3) = e2
% 239.41/46.20  | | | 
% 239.41/46.20  | | | ALPHA: (70) implies:
% 239.41/46.20  | | |   (71)  op(e2, e3) = e2
% 239.41/46.20  | | | 
% 239.41/46.20  | | | REF_CLOSE: (13), (28), (43), (71) are inconsistent by sub-proof #1897.
% 239.41/46.20  | | | 
% 239.41/46.20  | | End of split
% 239.41/46.20  | | 
% 239.41/46.20  | Case 2:
% 239.41/46.20  | | 
% 239.41/46.20  | |   (72)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 239.41/46.20  | |           e2)
% 239.41/46.20  | | 
% 239.41/46.20  | | BETA: splitting (72) gives:
% 239.41/46.20  | | 
% 239.41/46.20  | | Case 1:
% 239.41/46.20  | | | 
% 239.41/46.20  | | |   (73)  all_58_6 = e2 & op(e1, e3) = e2
% 239.41/46.20  | | | 
% 239.41/46.20  | | | ALPHA: (73) implies:
% 239.41/46.20  | | |   (74)  all_58_6 = e2
% 239.41/46.20  | | |   (75)  op(e1, e3) = e2
% 239.41/46.20  | | | 
% 239.41/46.20  | | | BETA: splitting (5) gives:
% 239.41/46.20  | | | 
% 239.41/46.20  | | | Case 1:
% 239.41/46.20  | | | | 
% 239.41/46.20  | | | |   (76)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 239.41/46.20  | | | |           = e1)
% 239.41/46.20  | | | | 
% 239.41/46.20  | | | | BETA: splitting (76) gives:
% 239.41/46.20  | | | | 
% 239.41/46.20  | | | | Case 1:
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | |   (77)  all_58_6 = e1 & op(e1, e3) = e1
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | | ALPHA: (77) implies:
% 239.41/46.20  | | | | |   (78)  op(e1, e3) = e1
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | | REF_CLOSE: (43), (58), (75), (78) are inconsistent by sub-proof #2226.
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | Case 2:
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | |   (79)  all_58_7 = e1 & op(e1, e2) = e1
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | | ALPHA: (79) implies:
% 239.41/46.20  | | | | |   (80)  all_58_7 = e1
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | | BETA: splitting (19) gives:
% 239.41/46.20  | | | | | 
% 239.41/46.20  | | | | | Case 1:
% 239.41/46.20  | | | | | | 
% 239.41/46.20  | | | | | |   (81)  all_54_6 = e2
% 239.41/46.20  | | | | | | 
% 239.41/46.20  | | | | | | COMBINE_EQS: (18), (81) imply:
% 239.41/46.20  | | | | | |   (82)  all_52_9 = e2
% 239.41/46.20  | | | | | | 
% 239.41/46.20  | | | | | | SIMP: (82) implies:
% 239.41/46.20  | | | | | |   (83)  all_52_9 = e2
% 239.41/46.20  | | | | | | 
% 239.41/46.20  | | | | | | REDUCE: (6), (83) imply:
% 239.41/46.20  | | | | | |   (84)   ~ (all_52_8 = e2)
% 239.41/46.20  | | | | | | 
% 239.41/46.20  | | | | | | REDUCE: (26), (83) imply:
% 239.41/46.20  | | | | | |   (85)  op(e2, e1) = e2
% 239.41/46.20  | | | | | | 
% 239.41/46.20  | | | | | | BETA: splitting (38) gives:
% 239.41/46.20  | | | | | | 
% 239.41/46.20  | | | | | | Case 1:
% 239.41/46.20  | | | | | | | 
% 239.41/46.20  | | | | | | |   (86)  all_54_4 = e3
% 239.41/46.20  | | | | | | | 
% 239.41/46.20  | | | | | | | COMBINE_EQS: (24), (86) imply:
% 239.41/46.20  | | | | | | |   (87)  all_52_1 = e3
% 239.41/46.20  | | | | | | | 
% 239.41/46.20  | | | | | | | SIMP: (87) implies:
% 239.41/46.20  | | | | | | |   (88)  all_52_1 = e3
% 239.41/46.20  | | | | | | | 
% 239.41/46.20  | | | | | | | REDUCE: (10), (88) imply:
% 239.41/46.20  | | | | | | |   (89)   ~ (all_52_2 = e3)
% 239.41/46.20  | | | | | | | 
% 239.41/46.20  | | | | | | | SIMP: (89) implies:
% 239.41/46.20  | | | | | | |   (90)   ~ (all_52_2 = e3)
% 239.41/46.20  | | | | | | | 
% 239.41/46.20  | | | | | | | REDUCE: (1), (88) imply:
% 239.41/46.20  | | | | | | |   (91)   ~ (all_52_3 = e3)
% 239.41/46.20  | | | | | | | 
% 239.41/46.20  | | | | | | | SIMP: (91) implies:
% 239.41/46.20  | | | | | | |   (92)   ~ (all_52_3 = e3)
% 239.41/46.20  | | | | | | | 
% 239.41/46.20  | | | | | | | BETA: splitting (32) gives:
% 239.41/46.20  | | | | | | | 
% 239.41/46.20  | | | | | | | Case 1:
% 239.41/46.20  | | | | | | | | 
% 239.41/46.20  | | | | | | | |   (93)  all_54_2 = e3
% 239.41/46.20  | | | | | | | | 
% 239.41/46.20  | | | | | | | | REF_CLOSE: (20), (60), (93) are inconsistent by sub-proof #1987.
% 239.41/46.20  | | | | | | | | 
% 239.41/46.20  | | | | | | | Case 2:
% 239.41/46.20  | | | | | | | | 
% 239.41/46.20  | | | | | | | |   (94)   ~ (all_54_2 = e3)
% 239.41/46.20  | | | | | | | |   (95)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.41/46.20  | | | | | | | | 
% 239.41/46.20  | | | | | | | | BETA: splitting (95) gives:
% 239.41/46.20  | | | | | | | | 
% 239.41/46.20  | | | | | | | | Case 1:
% 239.41/46.20  | | | | | | | | | 
% 239.41/46.20  | | | | | | | | |   (96)  all_54_2 = e2
% 239.41/46.20  | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | REF_CLOSE: (20), (84), (96) are inconsistent by sub-proof
% 239.41/46.20  | | | | | | | | |            #1986.
% 239.41/46.20  | | | | | | | | | 
% 239.41/46.20  | | | | | | | | Case 2:
% 239.41/46.20  | | | | | | | | | 
% 239.41/46.20  | | | | | | | | |   (97)  all_54_2 = e1 | all_54_2 = e0
% 239.41/46.20  | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | BETA: splitting (97) gives:
% 239.41/46.20  | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | Case 1:
% 239.41/46.20  | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | |   (98)  all_54_2 = e1
% 239.41/46.20  | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | COMBINE_EQS: (20), (98) imply:
% 239.41/46.20  | | | | | | | | | |   (99)  all_52_8 = e1
% 239.41/46.20  | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | SIMP: (99) implies:
% 239.41/46.20  | | | | | | | | | |   (100)  all_52_8 = e1
% 239.41/46.20  | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | REDUCE: (55), (100) imply:
% 239.41/46.20  | | | | | | | | | |   (101)   ~ (all_52_4 = e1)
% 239.41/46.20  | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | BETA: splitting (11) gives:
% 239.41/46.20  | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | Case 1:
% 239.41/46.20  | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | |   (102)  all_54_1 = e3
% 239.41/46.20  | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | REF_CLOSE: (40), (41), (102) are inconsistent by sub-proof
% 239.41/46.20  | | | | | | | | | | |            #1930.
% 239.41/46.20  | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | Case 2:
% 239.41/46.20  | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | |   (103)   ~ (all_54_1 = e3)
% 239.41/46.20  | | | | | | | | | | |   (104)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.41/46.20  | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | BETA: splitting (104) gives:
% 239.41/46.20  | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | Case 1:
% 239.41/46.20  | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | |   (105)  all_54_1 = e2
% 239.41/46.20  | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | COMBINE_EQS: (40), (105) imply:
% 239.41/46.20  | | | | | | | | | | | |   (106)  all_52_4 = e2
% 239.41/46.20  | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | SIMP: (106) implies:
% 239.41/46.20  | | | | | | | | | | | |   (107)  all_52_4 = e2
% 239.41/46.20  | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | REDUCE: (56), (107) imply:
% 239.41/46.20  | | | | | | | | | | | |   (108)   ~ (all_52_6 = e2)
% 239.41/46.20  | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | SIMP: (108) implies:
% 239.41/46.20  | | | | | | | | | | | |   (109)   ~ (all_52_6 = e2)
% 239.41/46.20  | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | REDUCE: (41), (107) imply:
% 239.41/46.20  | | | | | | | | | | | |   (110)   ~ (e3 = e2)
% 239.41/46.20  | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | REDUCE: (42), (107) imply:
% 239.41/46.20  | | | | | | | | | | | |   (111)  op(e3, e2) = e2
% 239.41/46.20  | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | BETA: splitting (2) gives:
% 239.41/46.20  | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | Case 1:
% 239.41/46.20  | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | |   (112)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 239.41/46.20  | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 239.41/46.20  | | | | | | | | | | | | |            = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 239.41/46.20  | | | | | | | | | | | | |            all_56_19 & $i(all_56_19))
% 239.41/46.20  | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | BETA: splitting (112) gives:
% 239.41/46.20  | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | Case 1:
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | |   (113)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 239.41/46.20  | | | | | | | | | | | | | |            e1) = all_56_17 & $i(all_56_17)
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | REF_CLOSE: (25), (29), (43), (45), (60), (75), (113) are
% 239.41/46.20  | | | | | | | | | | | | | |            inconsistent by sub-proof #394.
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | Case 2:
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | |   (114)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 239.41/46.20  | | | | | | | | | | | | | |            e1) = all_56_19 & $i(all_56_19)
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | ALPHA: (114) implies:
% 239.41/46.20  | | | | | | | | | | | | | |   (115)  op(e2, e1) = all_56_19
% 239.41/46.20  | | | | | | | | | | | | | |   (116)  op(e2, all_56_19) = e2
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (30), (43), (49), (54), (85), (115),
% 239.41/46.20  | | | | | | | | | | | | | |            (116) are inconsistent by sub-proof #1521.
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | End of split
% 239.41/46.20  | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | Case 2:
% 239.41/46.20  | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | |   (117)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 239.41/46.20  | | | | | | | | | | | | |          (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 239.41/46.20  | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23))
% 239.41/46.20  | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | BETA: splitting (117) gives:
% 239.41/46.20  | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | Case 1:
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | |   (118)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | ALPHA: (118) implies:
% 239.41/46.20  | | | | | | | | | | | | | |   (119)  op(e1, all_56_21) = e1
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | REDUCE: (47), (119) imply:
% 239.41/46.20  | | | | | | | | | | | | | |   (120)  op(e1, e3) = e1
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | REF_CLOSE: (43), (58), (75), (120) are inconsistent by
% 239.41/46.20  | | | | | | | | | | | | | |            sub-proof #2226.
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | Case 2:
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | |   (121)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 239.41/46.20  | | | | | | | | | | | | | |            e1) = all_56_23 & $i(all_56_23)
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | ALPHA: (121) implies:
% 239.41/46.20  | | | | | | | | | | | | | |   (122)  op(e0, all_56_23) = e0
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 239.41/46.20  | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | Case 1:
% 239.41/46.20  | | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | |   (123)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.41/46.20  | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.41/46.20  | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.41/46.20  | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.41/46.20  | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.41/46.20  | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.41/46.20  | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.41/46.20  | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.41/46.20  | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.41/46.20  | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.41/46.20  | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 239.41/46.20  | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.41/46.20  | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.41/46.20  | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 239.41/46.20  | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.41/46.20  | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.41/46.20  | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 239.41/46.20  | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.41/46.20  | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.41/46.20  | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.41/46.20  | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 239.41/46.20  | | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 239.41/46.20  | | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | | Case 1:
% 239.41/46.20  | | | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | | |   (124)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.41/46.20  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.41/46.20  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.41/46.20  | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.41/46.20  | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.41/46.20  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.41/46.20  | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.41/46.20  | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.41/46.20  | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.41/46.20  | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.41/46.20  | | | | | | | | | | | | | | | |            = e3)
% 239.41/46.20  | | | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (28), (43), (46), (90), (111), (124) are
% 239.41/46.20  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #361.
% 239.41/46.20  | | | | | | | | | | | | | | | | 
% 239.41/46.20  | | | | | | | | | | | | | | | Case 2:
% 239.41/46.20  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | |   (125)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.41/46.21  | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 239.41/46.21  | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 239.41/46.21  | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.41/46.21  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.41/46.21  | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 239.41/46.21  | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 239.41/46.21  | | | | | | | | | | | | | | | |            = e0)
% 239.41/46.21  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 239.41/46.21  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | Case 1:
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | |   (126)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 239.41/46.21  | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 239.41/46.21  | | | | | | | | | | | | | | | | |            e3) = e1
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 239.41/46.21  | | | | | | | | | | | | | | | | |   (127)  op(e1, e3) = e1
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (58), (75), (127) are inconsistent by
% 239.41/46.21  | | | | | | | | | | | | | | | | |            sub-proof #2226.
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | Case 2:
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | |   (128)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 239.41/46.21  | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.41/46.21  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.41/46.21  | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (31), (43), (48), (92), (128) are
% 239.41/46.21  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #206.
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | Case 2:
% 239.41/46.21  | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | |   (129)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.41/46.21  | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.41/46.21  | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.41/46.21  | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.41/46.21  | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.41/46.21  | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.41/46.21  | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.41/46.21  | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 239.41/46.21  | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.41/46.21  | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 239.41/46.21  | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 239.41/46.21  | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.41/46.21  | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 239.41/46.21  | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 239.41/46.21  | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 239.41/46.21  | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | Case 1:
% 239.41/46.21  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | |   (130)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.41/46.21  | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.41/46.21  | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.41/46.21  | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.41/46.21  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.41/46.21  | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.41/46.21  | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.41/46.21  | | | | | | | | | | | | | | | |            = e2)
% 239.41/46.21  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 239.41/46.21  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | Case 1:
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | |   (131)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 239.41/46.21  | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 239.41/46.21  | | | | | | | | | | | | | | | | |            e2) = e2
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 239.41/46.21  | | | | | | | | | | | | | | | | |   (132)  op(e1, e2) = e2
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (43), (109), (132) are inconsistent by
% 239.41/46.21  | | | | | | | | | | | | | | | | |            sub-proof #249.
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | Case 2:
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | |   (133)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 239.41/46.21  | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.41/46.21  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.41/46.21  | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (16), (20), (26), (28), (43), (97),
% 239.41/46.21  | | | | | | | | | | | | | | | | |            (133) are inconsistent by sub-proof #52.
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | Case 2:
% 239.41/46.21  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | |   (134)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.41/46.21  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 239.41/46.21  | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 239.41/46.21  | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.41/46.21  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.41/46.21  | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 239.41/46.21  | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.41/46.21  | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 239.41/46.21  | | | | | | | | | | | | | | | |            = e0)
% 239.41/46.21  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 239.41/46.21  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | Case 1:
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | |   (135)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 239.41/46.21  | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 239.41/46.21  | | | | | | | | | | | | | | | | |            e2) = e0
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 239.41/46.21  | | | | | | | | | | | | | | | | |   (136)  op(e2, e0) = e0
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (48), (49), (53), (136) are inconsistent by
% 239.41/46.21  | | | | | | | | | | | | | | | | |            sub-proof #1778.
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | Case 2:
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | |   (137)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 239.41/46.21  | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 239.41/46.21  | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 239.41/46.21  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.41/46.21  | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | Case 1:
% 239.41/46.21  | | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | |   (138)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 239.41/46.21  | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 239.41/46.21  | | | | | | | | | | | | | | | | | |            e1) = e1
% 239.41/46.21  | | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 239.41/46.21  | | | | | | | | | | | | | | | | | |   (139)  op(e1, e0) = e1
% 239.41/46.21  | | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (43), (44), (48), (51), (74), (80),
% 239.41/46.21  | | | | | | | | | | | | | | | | | |            (139) are inconsistent by sub-proof #1420.
% 239.41/46.21  | | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | Case 2:
% 239.41/46.21  | | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | |   (140)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 239.41/46.21  | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 239.41/46.21  | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 239.41/46.21  | | | | | | | | | | | | | | | | | |            e1) = e0
% 239.41/46.21  | | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 239.41/46.21  | | | | | | | | | | | | | | | | | |   (141)  all_56_23 = e0
% 239.41/46.21  | | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | | REDUCE: (122), (141) imply:
% 239.41/46.21  | | | | | | | | | | | | | | | | | |   (142)  op(e0, e0) = e0
% 239.41/46.21  | | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (43), (52), (142) are inconsistent by
% 239.41/46.21  | | | | | | | | | | | | | | | | | |            sub-proof #2301.
% 239.41/46.21  | | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | Case 2:
% 239.41/46.21  | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | |   (143)  all_54_1 = e1 | all_54_1 = e0
% 239.41/46.21  | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | | REF_CLOSE: (40), (57), (101), (143) are inconsistent by
% 239.41/46.21  | | | | | | | | | | | |            sub-proof #2049.
% 239.41/46.21  | | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | Case 2:
% 239.41/46.21  | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | |   (144)  all_54_2 = e0
% 239.41/46.21  | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | | REF_CLOSE: (12), (20), (144) are inconsistent by sub-proof
% 239.41/46.21  | | | | | | | | | |            #1643.
% 239.41/46.21  | | | | | | | | | | 
% 239.41/46.21  | | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | | 
% 239.41/46.21  | | | | | | | | End of split
% 239.41/46.21  | | | | | | | | 
% 239.41/46.21  | | | | | | | End of split
% 239.41/46.21  | | | | | | | 
% 239.41/46.21  | | | | | | Case 2:
% 239.41/46.21  | | | | | | | 
% 239.41/46.21  | | | | | | |   (145)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.41/46.21  | | | | | | | 
% 239.41/46.21  | | | | | | | REF_CLOSE: (23), (24), (26), (35), (43), (59), (85), (145) are
% 239.41/46.21  | | | | | | |            inconsistent by sub-proof #173.
% 239.41/46.21  | | | | | | | 
% 239.41/46.21  | | | | | | End of split
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | Case 2:
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | |   (146)  all_54_6 = e1 | all_54_6 = e0
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | | REF_CLOSE: (6), (18), (22), (25), (29), (43), (146) are inconsistent
% 239.41/46.21  | | | | | |            by sub-proof #1945.
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | End of split
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | End of split
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | Case 2:
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | |   (147)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1,
% 239.41/46.21  | | | |              e0) = e1)
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | | REF_CLOSE: (4), (15), (37), (43), (48), (147) are inconsistent by
% 239.41/46.21  | | | |            sub-proof #289.
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | End of split
% 239.41/46.21  | | | 
% 239.41/46.21  | | Case 2:
% 239.41/46.21  | | | 
% 239.41/46.21  | | |   (148)  all_58_12 = e2 & op(e0, e3) = e2
% 239.41/46.21  | | | 
% 239.41/46.21  | | | REF_CLOSE: (14), (34), (43), (148) are inconsistent by sub-proof #2315.
% 239.41/46.21  | | | 
% 239.41/46.21  | | End of split
% 239.41/46.21  | | 
% 239.41/46.21  | End of split
% 239.41/46.21  | 
% 239.41/46.21  End of proof
% 239.41/46.21  
% 239.41/46.21  Sub-proof #35 shows that the following formulas are inconsistent:
% 239.41/46.21  ----------------------------------------------------------------
% 239.41/46.21    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.41/46.21             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 239.41/46.21           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 239.41/46.21         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.41/46.21           $i(all_56_7))
% 239.41/46.21    (2)   ~ (e3 = e0)
% 239.41/46.21    (3)   ~ (e2 = e0)
% 239.41/46.21    (4)  all_54_13 = all_52_7
% 239.41/46.21    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.41/46.21         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.41/46.21    (6)  all_54_13 = e1 | all_54_13 = e0
% 239.41/46.21    (7)  op(e3, e0) = e1
% 239.41/46.21    (8)   ~ (all_52_7 = e3)
% 239.41/46.21    (9)   ~ (e3 = e1)
% 239.41/46.21    (10)  all_58_7 = e2
% 239.41/46.21    (11)  all_54_6 = all_52_9
% 239.41/46.21    (12)  op(e0, e2) = all_4_1
% 239.41/46.21    (13)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 239.41/46.21            $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e1, e3) = all_6_1
% 239.41/46.21            & $i(all_6_1))
% 239.41/46.21    (14)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 239.41/46.21    (15)   ~ (all_52_9 = e0)
% 239.41/46.21    (16)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.41/46.21            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 239.41/46.21              e2) = all_44_1 & $i(all_44_1))
% 239.41/46.21    (17)  op(e2, e3) = e2
% 239.41/46.21    (18)  op(e1, e3) = e1
% 239.41/46.21    (19)  op(e0, e3) = e3
% 239.41/46.21    (20)  op(e1, e1) = e3
% 239.41/46.21    (21)  op(e3, e2) = all_52_4
% 239.41/46.21    (22)   ~ (all_52_7 = e0)
% 239.41/46.21    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.21    (24)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.41/46.21            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 239.41/46.21              e3) = all_46_1 & $i(all_46_1))
% 239.41/46.21    (25)  all_56_1 = e0
% 239.41/46.21    (26)  op(e0, e2) = e1
% 239.41/46.21    (27)   ~ (all_52_4 = e0)
% 239.41/46.21    (28)   ~ (all_52_9 = e2)
% 239.41/46.21  
% 239.41/46.21  Begin of proof
% 239.41/46.21  | 
% 239.41/46.21  | BETA: splitting (16) gives:
% 239.41/46.21  | 
% 239.41/46.21  | Case 1:
% 239.41/46.21  | | 
% 239.41/46.21  | |   (29)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.41/46.21  | |         all_44_1 & $i(all_44_0) & $i(all_44_1)
% 239.41/46.21  | | 
% 239.41/46.21  | | ALPHA: (29) implies:
% 239.41/46.21  | |   (30)  op(e0, e2) = all_44_1
% 239.41/46.21  | | 
% 239.41/46.21  | | BETA: splitting (1) gives:
% 239.41/46.21  | | 
% 239.41/46.21  | | Case 1:
% 239.41/46.21  | | | 
% 239.41/46.21  | | |   (31)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.41/46.21  | | |             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 239.41/46.21  | | | 
% 239.41/46.21  | | | BETA: splitting (31) gives:
% 239.41/46.21  | | | 
% 239.41/46.21  | | | Case 1:
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | |   (32)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | | ALPHA: (32) implies:
% 239.41/46.21  | | | |   (33)  op(e3, all_56_1) = e3
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | | REDUCE: (25), (33) imply:
% 239.41/46.21  | | | |   (34)  op(e3, e0) = e3
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | | REF_CLOSE: (7), (9), (23), (34) are inconsistent by sub-proof #243.
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | Case 2:
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | |   (35)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 239.41/46.21  | | | |         $i(all_56_3)
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | | ALPHA: (35) implies:
% 239.41/46.21  | | | |   (36)  op(e2, e3) = all_56_3
% 239.41/46.21  | | | |   (37)  op(e2, all_56_3) = e2
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | | BETA: splitting (14) gives:
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | | Case 1:
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | |   (38)  all_54_6 = e2
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | | REF_CLOSE: (11), (28), (38) are inconsistent by sub-proof #2247.
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | Case 2:
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | |   (39)  all_54_6 = e1 | all_54_6 = e0
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | | BETA: splitting (39) gives:
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | | Case 1:
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | |   (40)  all_54_6 = e1
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | | COMBINE_EQS: (11), (40) imply:
% 239.41/46.21  | | | | | |   (41)  all_52_9 = e1
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | | SIMP: (41) implies:
% 239.41/46.21  | | | | | |   (42)  all_52_9 = e1
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | | REDUCE: (15), (42) imply:
% 239.41/46.21  | | | | | |   (43)   ~ (e1 = e0)
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | | GROUND_INST: instantiating (23) with all_4_1, all_44_1, e2, e0,
% 239.41/46.21  | | | | | |              simplifying with (12), (30) gives:
% 239.41/46.21  | | | | | |   (44)  all_44_1 = all_4_1
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | | GROUND_INST: instantiating (23) with e1, all_44_1, e2, e0,
% 239.41/46.21  | | | | | |              simplifying with (26), (30) gives:
% 239.41/46.21  | | | | | |   (45)  all_44_1 = e1
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | | GROUND_INST: instantiating (23) with e2, all_56_3, e3, e2,
% 239.41/46.21  | | | | | |              simplifying with (17), (36) gives:
% 239.41/46.21  | | | | | |   (46)  all_56_3 = e2
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | | COMBINE_EQS: (44), (45) imply:
% 239.41/46.21  | | | | | |   (47)  all_4_1 = e1
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | | REDUCE: (37), (46) imply:
% 239.41/46.21  | | | | | |   (48)  op(e2, e2) = e2
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | | REF_CLOSE: (3), (5), (10), (21), (23), (26), (27), (43), (48) are
% 239.41/46.21  | | | | | |            inconsistent by sub-proof #1586.
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | Case 2:
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | |   (49)  all_54_6 = e0
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | | REF_CLOSE: (11), (15), (49) are inconsistent by sub-proof #2245.
% 239.41/46.21  | | | | | | 
% 239.41/46.21  | | | | | End of split
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | End of split
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | End of split
% 239.41/46.21  | | | 
% 239.41/46.21  | | Case 2:
% 239.41/46.21  | | | 
% 239.41/46.21  | | |   (50)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 239.41/46.21  | | |           $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0,
% 239.41/46.21  | | |             e3) = all_56_7 & $i(all_56_7))
% 239.41/46.21  | | | 
% 239.41/46.21  | | | BETA: splitting (50) gives:
% 239.41/46.21  | | | 
% 239.41/46.21  | | | Case 1:
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | |   (51)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 239.41/46.21  | | | |         $i(all_56_5)
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | | ALPHA: (51) implies:
% 239.41/46.21  | | | |   (52)  op(e1, e3) = all_56_5
% 239.41/46.21  | | | |   (53)  op(e1, all_56_5) = e1
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | | BETA: splitting (13) gives:
% 239.41/46.21  | | | | 
% 239.41/46.21  | | | | Case 1:
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | |   (54)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) =
% 239.41/46.21  | | | | |         all_6_1 & $i(all_6_0) & $i(all_6_1)
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | | ALPHA: (54) implies:
% 239.41/46.21  | | | | |   (55)  op(e1, e3) = all_6_1
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | | REF_CLOSE: (4), (6), (8), (18), (20), (22), (23), (24), (52), (53),
% 239.41/46.21  | | | | |            (55) are inconsistent by sub-proof #36.
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | Case 2:
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | |   (56)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 & $i(all_6_1)
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | | ALPHA: (56) implies:
% 239.41/46.21  | | | | |   (57)  op(e1, e3) = all_6_1
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | | REF_CLOSE: (4), (6), (8), (18), (20), (22), (23), (24), (52), (53),
% 239.41/46.21  | | | | |            (57) are inconsistent by sub-proof #36.
% 239.41/46.21  | | | | | 
% 239.41/46.21  | | | | End of split
% 239.41/46.21  | | | | 
% 239.41/46.22  | | | Case 2:
% 239.41/46.22  | | | | 
% 239.41/46.22  | | | |   (58)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.41/46.22  | | | |         $i(all_56_7)
% 239.41/46.22  | | | | 
% 239.41/46.22  | | | | ALPHA: (58) implies:
% 239.41/46.22  | | | |   (59)  op(e0, e3) = all_56_7
% 239.41/46.22  | | | |   (60)  op(e0, all_56_7) = e0
% 239.41/46.22  | | | | 
% 239.41/46.22  | | | | REF_CLOSE: (2), (19), (23), (59), (60) are inconsistent by sub-proof
% 239.41/46.22  | | | |            #2070.
% 239.41/46.22  | | | | 
% 239.41/46.22  | | | End of split
% 239.41/46.22  | | | 
% 239.41/46.22  | | End of split
% 239.41/46.22  | | 
% 239.41/46.22  | Case 2:
% 239.41/46.22  | | 
% 239.41/46.22  | |   (61)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 & $i(all_44_1)
% 239.41/46.22  | | 
% 239.41/46.22  | | ALPHA: (61) implies:
% 239.41/46.22  | |   (62)   ~ (all_44_1 = e1)
% 239.41/46.22  | |   (63)  op(e0, e2) = all_44_1
% 239.41/46.22  | | 
% 239.41/46.22  | | REF_CLOSE: (23), (26), (62), (63) are inconsistent by sub-proof #230.
% 239.41/46.22  | | 
% 239.41/46.22  | End of split
% 239.41/46.22  | 
% 239.41/46.22  End of proof
% 239.41/46.22  
% 239.41/46.22  Sub-proof #36 shows that the following formulas are inconsistent:
% 239.41/46.22  ----------------------------------------------------------------
% 239.41/46.22    (1)  all_54_13 = all_52_7
% 239.41/46.22    (2)  all_54_13 = e1 | all_54_13 = e0
% 239.41/46.22    (3)  op(e1, all_56_5) = e1
% 239.41/46.22    (4)  op(e1, e3) = all_56_5
% 239.41/46.22    (5)  op(e1, e3) = all_6_1
% 239.41/46.22    (6)   ~ (all_52_7 = e3)
% 239.41/46.22    (7)  op(e1, e3) = e1
% 239.41/46.22    (8)  op(e1, e1) = e3
% 239.41/46.22    (9)   ~ (all_52_7 = e0)
% 239.41/46.22    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.22    (11)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.41/46.22            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 239.41/46.22              e3) = all_46_1 & $i(all_46_1))
% 239.41/46.22  
% 239.41/46.22  Begin of proof
% 239.41/46.22  | 
% 239.41/46.22  | BETA: splitting (11) gives:
% 239.41/46.22  | 
% 239.41/46.22  | Case 1:
% 239.41/46.22  | | 
% 239.41/46.22  | |   (12)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 239.41/46.22  | |         all_46_1 & $i(all_46_0) & $i(all_46_1)
% 239.41/46.22  | | 
% 239.41/46.22  | | ALPHA: (12) implies:
% 239.41/46.22  | |   (13)  op(e1, e3) = all_46_1
% 239.41/46.22  | | 
% 239.41/46.22  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13) are
% 239.41/46.22  | |            inconsistent by sub-proof #37.
% 239.41/46.22  | | 
% 239.41/46.22  | Case 2:
% 239.41/46.22  | | 
% 239.41/46.22  | |   (14)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 239.41/46.22  | | 
% 239.41/46.22  | | ALPHA: (14) implies:
% 239.41/46.22  | |   (15)  op(e1, e3) = all_46_1
% 239.41/46.22  | | 
% 239.41/46.22  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (15) are
% 239.41/46.22  | |            inconsistent by sub-proof #37.
% 239.41/46.22  | | 
% 239.41/46.22  | End of split
% 239.41/46.22  | 
% 239.41/46.22  End of proof
% 239.41/46.22  
% 239.41/46.22  Sub-proof #37 shows that the following formulas are inconsistent:
% 239.41/46.22  ----------------------------------------------------------------
% 239.41/46.22    (1)  all_54_13 = all_52_7
% 239.41/46.22    (2)  all_54_13 = e1 | all_54_13 = e0
% 239.41/46.22    (3)  op(e1, all_56_5) = e1
% 239.41/46.22    (4)  op(e1, e3) = all_56_5
% 239.41/46.22    (5)  op(e1, e3) = all_6_1
% 239.41/46.22    (6)   ~ (all_52_7 = e3)
% 239.41/46.22    (7)  op(e1, e3) = e1
% 239.41/46.22    (8)  op(e1, e3) = all_46_1
% 239.41/46.22    (9)  op(e1, e1) = e3
% 239.41/46.22    (10)   ~ (all_52_7 = e0)
% 239.41/46.22    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.22  
% 239.41/46.22  Begin of proof
% 239.41/46.22  | 
% 239.41/46.22  | BETA: splitting (2) gives:
% 239.41/46.22  | 
% 239.41/46.22  | Case 1:
% 239.41/46.22  | | 
% 239.41/46.22  | |   (12)  all_54_13 = e1
% 239.41/46.22  | | 
% 239.41/46.22  | | COMBINE_EQS: (1), (12) imply:
% 239.41/46.22  | |   (13)  all_52_7 = e1
% 239.41/46.22  | | 
% 239.41/46.22  | | SIMP: (13) implies:
% 239.41/46.22  | |   (14)  all_52_7 = e1
% 239.41/46.22  | | 
% 239.41/46.22  | | REDUCE: (6), (14) imply:
% 239.41/46.22  | |   (15)   ~ (e3 = e1)
% 239.41/46.22  | | 
% 239.41/46.22  | | SIMP: (15) implies:
% 239.41/46.22  | |   (16)   ~ (e3 = e1)
% 239.41/46.22  | | 
% 239.41/46.22  | | GROUND_INST: instantiating (11) with e1, all_46_1, e3, e1, simplifying with
% 239.41/46.22  | |              (7), (8) gives:
% 239.41/46.22  | |   (17)  all_46_1 = e1
% 239.41/46.22  | | 
% 239.41/46.22  | | GROUND_INST: instantiating (11) with all_46_1, all_56_5, e3, e1, simplifying
% 239.41/46.22  | |              with (4), (8) gives:
% 239.41/46.22  | |   (18)  all_56_5 = all_46_1
% 239.41/46.22  | | 
% 239.41/46.22  | | GROUND_INST: instantiating (11) with all_6_1, all_56_5, e3, e1, simplifying
% 239.41/46.22  | |              with (4), (5) gives:
% 239.41/46.22  | |   (19)  all_56_5 = all_6_1
% 239.41/46.22  | | 
% 239.41/46.22  | | COMBINE_EQS: (18), (19) imply:
% 239.41/46.22  | |   (20)  all_46_1 = all_6_1
% 239.41/46.22  | | 
% 239.41/46.22  | | SIMP: (20) implies:
% 239.41/46.22  | |   (21)  all_46_1 = all_6_1
% 239.41/46.22  | | 
% 239.41/46.22  | | COMBINE_EQS: (17), (21) imply:
% 239.41/46.22  | |   (22)  all_6_1 = e1
% 239.41/46.22  | | 
% 239.41/46.22  | | COMBINE_EQS: (19), (22) imply:
% 239.41/46.22  | |   (23)  all_56_5 = e1
% 239.41/46.22  | | 
% 239.41/46.22  | | REDUCE: (3), (23) imply:
% 239.41/46.22  | |   (24)  op(e1, e1) = e1
% 239.41/46.22  | | 
% 239.41/46.22  | | REF_CLOSE: (9), (11), (16), (24) are inconsistent by sub-proof #468.
% 239.41/46.22  | | 
% 239.41/46.22  | Case 2:
% 239.41/46.22  | | 
% 239.41/46.22  | |   (25)  all_54_13 = e0
% 239.41/46.22  | | 
% 239.41/46.22  | | REF_CLOSE: (1), (10), (25) are inconsistent by sub-proof #2008.
% 239.41/46.22  | | 
% 239.41/46.22  | End of split
% 239.41/46.22  | 
% 239.41/46.22  End of proof
% 239.41/46.22  
% 239.41/46.22  Sub-proof #38 shows that the following formulas are inconsistent:
% 239.41/46.22  ----------------------------------------------------------------
% 239.41/46.22    (1)  op(e1, e0) = all_52_14
% 239.41/46.22    (2)   ~ (all_52_14 = e2)
% 239.41/46.22    (3)   ~ (e3 = e2)
% 239.41/46.22    (4)  op(e1, e1) = e3
% 239.41/46.22    (5)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.41/46.22    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.22  
% 239.41/46.22  Begin of proof
% 239.41/46.22  | 
% 239.41/46.22  | BETA: splitting (5) gives:
% 239.41/46.22  | 
% 239.41/46.22  | Case 1:
% 239.41/46.22  | | 
% 239.41/46.22  | |   (7)  all_58_8 = e2 & op(e1, e1) = e2
% 239.41/46.22  | | 
% 239.41/46.22  | | ALPHA: (7) implies:
% 239.41/46.22  | |   (8)  op(e1, e1) = e2
% 239.41/46.22  | | 
% 239.41/46.22  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #2206.
% 239.41/46.22  | | 
% 239.41/46.22  | Case 2:
% 239.41/46.22  | | 
% 239.41/46.22  | |   (9)  all_58_11 = e2 & op(e1, e0) = e2
% 239.41/46.22  | | 
% 239.41/46.22  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #258.
% 239.41/46.22  | | 
% 239.41/46.22  | End of split
% 239.41/46.22  | 
% 239.41/46.22  End of proof
% 239.41/46.22  
% 239.41/46.22  Sub-proof #39 shows that the following formulas are inconsistent:
% 239.41/46.22  ----------------------------------------------------------------
% 239.41/46.22    (1)  all_44_2 = e2
% 239.41/46.22    (2)   ~ (all_52_1 = all_52_3)
% 239.41/46.22    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.41/46.22             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 239.41/46.22           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 239.41/46.22         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.41/46.22           $i(all_56_7))
% 239.41/46.22    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.41/46.22    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.41/46.22         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.41/46.22    (6)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 239.41/46.22           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 239.41/46.22           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 239.41/46.22           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 239.41/46.22           & $i(all_56_23))
% 239.41/46.22    (7)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.41/46.22    (8)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.41/46.22         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.41/46.22    (9)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 239.41/46.22           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 239.41/46.22           all_24_1 & $i(all_24_1))
% 239.41/46.22    (10)   ~ (all_32_2 = e2) | ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 239.41/46.22            op(e3, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 239.41/46.22              e0) & op(e3, e2) = all_32_1 & $i(all_32_1))
% 239.41/46.22    (11)  op(e0, e1) = all_52_11
% 239.41/46.22    (12)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 239.41/46.22          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.41/46.22    (13)   ~ (all_52_8 = all_52_9)
% 239.41/46.22    (14)   ~ (all_44_2 = e2) | ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 239.41/46.22            op(e0, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 239.41/46.22              e1) & op(e0, e2) = all_44_1 & $i(all_44_1))
% 239.41/46.22    (15)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 239.41/46.22            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 239.41/46.22            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 239.41/46.22            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 239.41/46.22            = all_56_15 & $i(all_56_15))
% 239.41/46.22    (16)  all_54_13 = all_52_7
% 239.41/46.22    (17)  all_48_2 = e0
% 239.41/46.22    (18)  op(e1, e2) = all_52_6
% 239.41/46.22    (19)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.41/46.22          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.41/46.22    (20)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 239.41/46.22          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 239.41/46.22    (21)  ( ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 239.41/46.22            $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e0, e2) = all_4_1
% 239.41/46.22            & $i(all_4_1))
% 239.41/46.22    (22)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.41/46.22              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.41/46.22            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.41/46.22            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.41/46.22            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 239.41/46.22             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.41/46.22            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.41/46.22            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.41/46.22            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.41/46.22            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.41/46.22            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.41/46.22              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.41/46.22            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.41/46.22            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 239.41/46.22            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.41/46.22            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 239.41/46.22            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.41/46.22            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.41/46.22              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.41/46.22            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.41/46.22            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.41/46.22            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.41/46.22            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 239.41/46.22            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.41/46.22            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.41/46.22              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.41/46.22            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.41/46.22            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.41/46.22    (23)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.41/46.22          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.41/46.22    (24)   ~ (all_52_7 = all_52_11)
% 239.41/46.22    (25)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 239.41/46.22          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 239.41/46.22    (26)   ~ (all_52_1 = all_52_2)
% 239.41/46.22    (27)  op(e1, e0) = all_52_14
% 239.41/46.22    (28)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.41/46.22    (29)  op(e0, e3) = all_52_3
% 239.41/46.22    (30)   ~ (all_52_6 = e0)
% 239.41/46.22    (31)   ~ (e3 = e1)
% 239.41/46.22    (32)  all_54_11 = all_52_14
% 239.41/46.22    (33)  all_58_7 = e2
% 239.41/46.22    (34)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.41/46.22          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.41/46.22    (35)   ~ (all_52_2 = all_52_3)
% 239.41/46.22    (36)  op(e2, e2) = e0
% 239.41/46.22    (37)   ~ (all_52_12 = all_52_14)
% 239.41/46.22    (38)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 239.41/46.22            op(e2, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 239.41/46.22              e3) & op(e2, e0) = all_48_1 & $i(all_48_1))
% 239.41/46.22    (39)   ~ (all_52_12 = all_52_13)
% 239.41/46.22    (40)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.41/46.22          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.41/46.22    (41)  op(e2, e1) = e2
% 239.41/46.22    (42)  all_54_2 = all_52_8
% 239.41/46.22    (43)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 239.41/46.22    (44)   ~ (all_52_2 = all_52_14)
% 239.41/46.22    (45)   ~ (all_52_9 = e0)
% 239.41/46.22    (46)   ~ (all_52_1 = all_52_9)
% 239.41/46.22    (47)   ~ (all_52_3 = all_52_7)
% 239.41/46.22    (48)  all_58_15 = e2
% 239.41/46.22    (49)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.41/46.22    (50)  all_54_4 = all_52_1
% 239.41/46.22    (51)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 239.41/46.22              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 239.41/46.22                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 239.41/46.22                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 239.41/46.22    (52)   ~ (all_52_11 = e3)
% 239.41/46.22    (53)   ~ (all_52_8 = all_52_12)
% 239.41/46.22    (54)  op(e3, e1) = all_52_8
% 239.41/46.22    (55)  op(e2, e1) = all_52_9
% 239.41/46.22    (56)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.41/46.22          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.41/46.23    (57)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 239.41/46.23            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 239.41/46.23              e0) = all_14_1 & $i(all_14_1))
% 239.41/46.23    (58)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.41/46.23    (59)   ~ (all_52_3 = all_52_11)
% 239.41/46.23    (60)  all_56_31 = e2
% 239.41/46.23    (61)  all_54_12 = all_52_3
% 239.41/46.23    (62)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 239.41/46.23    (63)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.41/46.23    (64)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.41/46.23          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.41/46.23    (65)  op(e3, e0) = all_52_12
% 239.41/46.23    (66)   ~ (all_52_3 = e2)
% 239.41/46.23    (67)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.41/46.23          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.41/46.23    (68)   ~ (all_52_9 = all_52_13)
% 239.41/46.23    (69)   ~ (all_52_1 = e0)
% 239.41/46.23    (70)  all_56_11 = e0
% 239.41/46.23    (71)   ~ (all_52_4 = all_52_12)
% 239.41/46.23    (72)   ~ (all_52_6 = all_52_14)
% 239.41/46.23    (73)  op(e2, e2) = all_8_2
% 239.41/46.23    (74)  op(e2, e3) = all_52_1
% 239.41/46.23    (75)  op(e3, e3) = e2
% 239.41/46.23    (76)   ~ (all_52_14 = e3)
% 239.41/46.23    (77)   ~ (all_52_12 = e2)
% 239.41/46.23    (78)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.41/46.23          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.41/46.23    (79)  op(e1, e1) = e3
% 239.41/46.23    (80)   ~ (all_52_2 = e3)
% 239.41/46.23    (81)   ~ (all_52_6 = e3)
% 239.41/46.23    (82)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.41/46.23    (83)  op(e1, e2) = e2
% 239.41/46.23    (84)   ~ (all_52_1 = all_52_13)
% 239.41/46.23    (85)  all_58_5 = e2
% 239.41/46.23    (86)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.41/46.23          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.41/46.23    (87)  all_54_7 = all_52_13
% 239.41/46.23    (88)  op(e0, e2) = all_52_7
% 239.41/46.23    (89)   ~ (all_52_13 = all_52_14)
% 239.41/46.23    (90)  all_56_1 = e2
% 239.41/46.23    (91)  all_54_1 = all_52_4
% 239.41/46.23    (92)  op(e3, e2) = all_52_4
% 239.41/46.23    (93)   ~ (all_52_7 = e0)
% 239.41/46.23    (94)  all_32_2 = e2
% 239.41/46.23    (95)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.41/46.23    (96)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 239.41/46.23          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.41/46.23    (97)  all_54_8 = all_52_2
% 239.41/46.23    (98)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.41/46.23          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.41/46.23    (99)   ~ (all_52_2 = all_52_6)
% 239.41/46.23    (100)  all_54_3 = all_52_12
% 239.41/46.23    (101)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.41/46.23             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.41/46.23    (102)  op(e1, e3) = all_52_2
% 239.41/46.23    (103)  all_56_21 = e3
% 239.41/46.23    (104)   ~ (all_52_6 = all_52_7)
% 239.41/46.23    (105)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.41/46.23           (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.41/46.23    (106)   ~ (all_8_2 = e3)
% 239.41/46.23    (107)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.41/46.23           (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.41/46.23    (108)   ~ (e1 = e0)
% 239.41/46.23    (109)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.41/46.23           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.41/46.23    (110)  op(e0, e0) = e2
% 239.41/46.23    (111)  op(e2, e0) = all_52_13
% 239.41/46.23    (112)  all_58_3 = e0
% 239.41/46.23    (113)  all_54_14 = all_52_11
% 239.41/46.23    (114)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.41/46.23           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 239.41/46.23             e2)
% 239.41/46.23    (115)   ~ (all_52_9 = all_52_11)
% 239.41/46.23    (116)   ~ (all_52_4 = all_52_8)
% 239.41/46.23    (117)   ~ (all_52_13 = e0)
% 239.41/46.23    (118)   ~ (all_52_4 = all_52_6)
% 239.41/46.23    (119)   ~ (all_52_4 = e0)
% 239.41/46.23    (120)   ~ (e2 = e1)
% 239.41/46.23    (121)   ~ (all_52_4 = all_52_7)
% 239.41/46.23    (122)   ~ (all_52_8 = e3)
% 239.41/46.23  
% 239.41/46.23  Begin of proof
% 239.41/46.23  | 
% 239.41/46.23  | GROUND_INST: instantiating (101) with all_52_6, e2, e2, e1, simplifying with
% 239.41/46.23  |              (18), (83) gives:
% 239.41/46.23  |   (123)  all_52_6 = e2
% 239.41/46.23  | 
% 239.41/46.23  | GROUND_INST: instantiating (101) with all_52_9, e2, e1, e2, simplifying with
% 239.41/46.23  |              (41), (55) gives:
% 239.41/46.23  |   (124)  all_52_9 = e2
% 239.41/46.23  | 
% 239.41/46.23  | REDUCE: (46), (124) imply:
% 239.41/46.23  |   (125)   ~ (all_52_1 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | REDUCE: (99), (123) imply:
% 239.41/46.23  |   (126)   ~ (all_52_2 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | REDUCE: (118), (123) imply:
% 239.41/46.23  |   (127)   ~ (all_52_4 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | REDUCE: (104), (123) imply:
% 239.41/46.23  |   (128)   ~ (all_52_7 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | SIMP: (128) implies:
% 239.41/46.23  |   (129)   ~ (all_52_7 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | REDUCE: (72), (123) imply:
% 239.41/46.23  |   (130)   ~ (all_52_14 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | SIMP: (130) implies:
% 239.41/46.23  |   (131)   ~ (all_52_14 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | REDUCE: (13), (124) imply:
% 239.41/46.23  |   (132)   ~ (all_52_8 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | REDUCE: (115), (124) imply:
% 239.41/46.23  |   (133)   ~ (all_52_11 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | SIMP: (133) implies:
% 239.41/46.23  |   (134)   ~ (all_52_11 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | REDUCE: (68), (124) imply:
% 239.41/46.23  |   (135)   ~ (all_52_13 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | SIMP: (135) implies:
% 239.41/46.23  |   (136)   ~ (all_52_13 = e2)
% 239.41/46.23  | 
% 239.41/46.23  | REDUCE: (45), (124) imply:
% 239.41/46.23  |   (137)   ~ (e2 = e0)
% 239.41/46.23  | 
% 239.41/46.23  | BETA: splitting (10) gives:
% 239.41/46.23  | 
% 239.41/46.23  | Case 1:
% 239.41/46.23  | | 
% 239.41/46.23  | |   (138)   ~ (all_32_2 = e2)
% 239.41/46.23  | | 
% 239.41/46.23  | | REDUCE: (94), (138) imply:
% 239.41/46.23  | |   (139)  $false
% 239.41/46.23  | | 
% 239.41/46.23  | | CLOSE: (139) is inconsistent.
% 239.41/46.23  | | 
% 239.41/46.23  | Case 2:
% 239.41/46.23  | | 
% 239.41/46.23  | |   (140)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 239.41/46.23  | |            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) &
% 239.41/46.23  | |            op(e3, e2) = all_32_1 & $i(all_32_1))
% 239.41/46.23  | | 
% 239.41/46.23  | | BETA: splitting (14) gives:
% 239.41/46.23  | | 
% 239.41/46.23  | | Case 1:
% 239.41/46.23  | | | 
% 239.41/46.23  | | |   (141)   ~ (all_44_2 = e2)
% 239.41/46.23  | | | 
% 239.41/46.23  | | | REDUCE: (1), (141) imply:
% 239.41/46.23  | | |   (142)  $false
% 239.41/46.23  | | | 
% 239.41/46.23  | | | CLOSE: (142) is inconsistent.
% 239.41/46.23  | | | 
% 239.41/46.23  | | Case 2:
% 239.41/46.23  | | | 
% 239.41/46.23  | | |   (143)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.41/46.23  | | |            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) &
% 239.41/46.23  | | |            op(e0, e2) = all_44_1 & $i(all_44_1))
% 239.41/46.23  | | | 
% 239.41/46.23  | | | BETA: splitting (7) gives:
% 239.41/46.23  | | | 
% 239.41/46.23  | | | Case 1:
% 239.41/46.23  | | | | 
% 239.41/46.23  | | | |   (144)  all_54_8 = e3
% 239.41/46.23  | | | | 
% 239.41/46.23  | | | | REF_CLOSE: (80), (97), (144) are inconsistent by sub-proof #2011.
% 239.41/46.23  | | | | 
% 239.41/46.23  | | | Case 2:
% 239.41/46.23  | | | | 
% 239.41/46.23  | | | |   (145)   ~ (all_54_8 = e3)
% 239.41/46.23  | | | |   (146)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.41/46.23  | | | | 
% 239.41/46.23  | | | | BETA: splitting (58) gives:
% 239.41/46.23  | | | | 
% 239.41/46.23  | | | | Case 1:
% 239.41/46.23  | | | | | 
% 239.41/46.23  | | | | |   (147)  all_54_14 = e3
% 239.41/46.23  | | | | | 
% 239.41/46.23  | | | | | REF_CLOSE: (52), (113), (147) are inconsistent by sub-proof #1796.
% 239.41/46.23  | | | | | 
% 239.41/46.23  | | | | Case 2:
% 239.41/46.23  | | | | | 
% 239.41/46.23  | | | | |   (148)   ~ (all_54_14 = e3)
% 239.41/46.23  | | | | |   (149)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.41/46.23  | | | | | 
% 239.41/46.23  | | | | | BETA: splitting (43) gives:
% 239.41/46.23  | | | | | 
% 239.41/46.23  | | | | | Case 1:
% 239.41/46.23  | | | | | | 
% 239.41/46.23  | | | | | |   (150)  all_54_11 = e3
% 239.41/46.23  | | | | | | 
% 239.41/46.23  | | | | | | REF_CLOSE: (32), (76), (150) are inconsistent by sub-proof #1998.
% 239.41/46.23  | | | | | | 
% 239.41/46.23  | | | | | Case 2:
% 239.41/46.23  | | | | | | 
% 239.41/46.23  | | | | | |   (151)   ~ (all_54_11 = e3)
% 239.41/46.23  | | | | | |   (152)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 239.41/46.23  | | | | | | 
% 239.41/46.23  | | | | | | BETA: splitting (62) gives:
% 239.41/46.23  | | | | | | 
% 239.41/46.23  | | | | | | Case 1:
% 239.41/46.23  | | | | | | | 
% 239.41/46.23  | | | | | | |   (153)  all_54_7 = e3
% 239.41/46.23  | | | | | | | 
% 239.41/46.23  | | | | | | | COMBINE_EQS: (87), (153) imply:
% 239.41/46.23  | | | | | | |   (154)  all_52_13 = e3
% 239.41/46.23  | | | | | | | 
% 239.41/46.23  | | | | | | | REDUCE: (84), (154) imply:
% 239.41/46.23  | | | | | | |   (155)   ~ (all_52_1 = e3)
% 239.41/46.23  | | | | | | | 
% 239.41/46.23  | | | | | | | REDUCE: (39), (154) imply:
% 239.41/46.23  | | | | | | |   (156)   ~ (all_52_12 = e3)
% 239.41/46.23  | | | | | | | 
% 239.41/46.23  | | | | | | | REDUCE: (136), (154) imply:
% 239.41/46.23  | | | | | | |   (157)   ~ (e3 = e2)
% 239.41/46.23  | | | | | | | 
% 239.41/46.23  | | | | | | | REDUCE: (117), (154) imply:
% 239.41/46.23  | | | | | | |   (158)   ~ (e3 = e0)
% 239.41/46.23  | | | | | | | 
% 239.41/46.23  | | | | | | | BETA: splitting (82) gives:
% 239.41/46.23  | | | | | | | 
% 239.41/46.23  | | | | | | | Case 1:
% 239.41/46.23  | | | | | | | | 
% 239.41/46.23  | | | | | | | |   (159)  all_54_4 = e3
% 239.41/46.23  | | | | | | | | 
% 239.41/46.23  | | | | | | | | REF_CLOSE: (50), (155), (159) are inconsistent by sub-proof
% 239.41/46.23  | | | | | | | |            #2100.
% 239.41/46.23  | | | | | | | | 
% 239.41/46.23  | | | | | | | Case 2:
% 239.41/46.23  | | | | | | | | 
% 239.41/46.23  | | | | | | | |   (160)   ~ (all_54_4 = e3)
% 239.41/46.23  | | | | | | | |   (161)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.41/46.23  | | | | | | | | 
% 239.41/46.23  | | | | | | | | BETA: splitting (161) gives:
% 239.41/46.23  | | | | | | | | 
% 239.41/46.23  | | | | | | | | Case 1:
% 239.41/46.23  | | | | | | | | | 
% 239.41/46.23  | | | | | | | | |   (162)  all_54_4 = e2
% 239.41/46.23  | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | REF_CLOSE: (50), (125), (162) are inconsistent by sub-proof
% 239.41/46.23  | | | | | | | | |            #2096.
% 239.41/46.23  | | | | | | | | | 
% 239.41/46.23  | | | | | | | | Case 2:
% 239.41/46.23  | | | | | | | | | 
% 239.41/46.23  | | | | | | | | |   (163)  all_54_4 = e1 | all_54_4 = e0
% 239.41/46.23  | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | BETA: splitting (40) gives:
% 239.41/46.23  | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | Case 1:
% 239.41/46.23  | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | |   (164)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 239.41/46.23  | | | | | | | | | |            & op(e3, e2) = e3)
% 239.41/46.23  | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | BETA: splitting (164) gives:
% 239.41/46.23  | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | Case 1:
% 239.41/46.23  | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | |   (165)  all_58_0 = e3 & op(e3, e3) = e3
% 239.41/46.23  | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | ALPHA: (165) implies:
% 239.41/46.23  | | | | | | | | | | |   (166)  op(e3, e3) = e3
% 239.41/46.23  | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | REF_CLOSE: (75), (101), (157), (166) are inconsistent by
% 239.41/46.23  | | | | | | | | | | |            sub-proof #2194.
% 239.41/46.23  | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | Case 2:
% 239.41/46.23  | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | |   (167)  all_58_1 = e3 & op(e3, e2) = e3
% 239.41/46.23  | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | ALPHA: (167) implies:
% 239.41/46.23  | | | | | | | | | | |   (168)  all_58_1 = e3
% 239.41/46.23  | | | | | | | | | | |   (169)  op(e3, e2) = e3
% 239.41/46.23  | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | BETA: splitting (105) gives:
% 239.41/46.23  | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | Case 1:
% 239.41/46.23  | | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | |   (170)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 239.41/46.23  | | | | | | | | | | | |            & op(e2, e2) = e1)
% 239.41/46.23  | | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | | BETA: splitting (170) gives:
% 239.41/46.23  | | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | | Case 1:
% 239.41/46.23  | | | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | | |   (171)  all_58_1 = e1 & op(e3, e2) = e1
% 239.41/46.23  | | | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | | | ALPHA: (171) implies:
% 239.41/46.23  | | | | | | | | | | | | |   (172)  all_58_1 = e1
% 239.41/46.23  | | | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | | | REF_CLOSE: (31), (40), (54), (65), (75), (101), (122), (156),
% 239.41/46.23  | | | | | | | | | | | | |            (157), (172) are inconsistent by sub-proof #1327.
% 239.41/46.23  | | | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | | Case 2:
% 239.41/46.23  | | | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | | |   (173)  all_58_3 = e1 & op(e2, e2) = e1
% 239.41/46.23  | | | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | | | REF_CLOSE: (108), (112), (173) are inconsistent by sub-proof
% 239.41/46.23  | | | | | | | | | | | | |            #1752.
% 239.41/46.23  | | | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | | End of split
% 239.41/46.23  | | | | | | | | | | | | 
% 239.41/46.23  | | | | | | | | | | | Case 2:
% 239.41/46.23  | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | |   (174)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 239.51/46.23  | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 239.51/46.23  | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | BETA: splitting (174) gives:
% 239.51/46.23  | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | Case 1:
% 239.51/46.23  | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | |   (175)  all_58_7 = e1 & op(e1, e2) = e1
% 239.51/46.23  | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | REF_CLOSE: (33), (120), (175) are inconsistent by sub-proof
% 239.51/46.23  | | | | | | | | | | | | |            #2224.
% 239.51/46.23  | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | Case 2:
% 239.51/46.23  | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | |   (176)  all_58_13 = e1 & op(e0, e2) = e1
% 239.51/46.23  | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | ALPHA: (176) implies:
% 239.51/46.23  | | | | | | | | | | | | |   (177)  all_58_13 = e1
% 239.51/46.23  | | | | | | | | | | | | |   (178)  op(e0, e2) = e1
% 239.51/46.23  | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | BETA: splitting (8) gives:
% 239.51/46.23  | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | Case 1:
% 239.51/46.23  | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | |   (179)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 239.51/46.23  | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 239.51/46.23  | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 239.51/46.23  | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | Case 1:
% 239.51/46.23  | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | |   (180)  all_58_12 = e3 & op(e0, e3) = e3
% 239.51/46.23  | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 239.51/46.23  | | | | | | | | | | | | | | |   (181)  op(e0, e3) = e3
% 239.51/46.23  | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 239.51/46.23  | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | Case 1:
% 239.51/46.23  | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | |   (182)  all_58_15 = e0 & op(e0, e0) = e0
% 239.51/46.23  | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 239.51/46.23  | | | | | | | | | | | | | | | |   (183)  op(e0, e0) = e0
% 239.51/46.23  | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | REF_CLOSE: (101), (110), (137), (183) are inconsistent by
% 239.51/46.23  | | | | | | | | | | | | | | | |            sub-proof #2301.
% 239.51/46.23  | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | Case 2:
% 239.51/46.23  | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | |   (184)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 239.51/46.23  | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 239.51/46.23  | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 239.51/46.23  | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 239.51/46.23  | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 239.51/46.23  | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 239.51/46.23  | | | | | | | | | | | | | | | |   (185)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 239.51/46.23  | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 239.51/46.23  | | | | | | | | | | | | | | | |              e1) = e0)
% 239.51/46.23  | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 239.51/46.23  | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.23  | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | |   (186)  all_58_12 = e0 & op(e0, e3) = e0
% 239.51/46.23  | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 239.51/46.23  | | | | | | | | | | | | | | | | |   (187)  op(e0, e3) = e0
% 239.51/46.23  | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (158), (181), (187) are inconsistent by
% 239.51/46.23  | | | | | | | | | | | | | | | | |            sub-proof #221.
% 239.51/46.23  | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.23  | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | |   (188)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 239.51/46.23  | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 239.51/46.23  | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 239.51/46.23  | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | |   (189)  all_58_13 = e0 & op(e0, e2) = e0
% 239.51/46.23  | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 239.51/46.23  | | | | | | | | | | | | | | | | | |   (190)  op(e0, e2) = e0
% 239.51/46.23  | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (108), (178), (190) are inconsistent by
% 239.51/46.23  | | | | | | | | | | | | | | | | | |            sub-proof #1872.
% 239.51/46.23  | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | |   (191)  all_58_14 = e0 & op(e0, e1) = e0
% 239.51/46.23  | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 239.51/46.23  | | | | | | | | | | | | | | | | | |   (192)  all_58_14 = e0
% 239.51/46.23  | | | | | | | | | | | | | | | | | |   (193)  op(e0, e1) = e0
% 239.51/46.23  | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | |   (194)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 239.51/46.23  | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | |   (195)  all_58_4 = e1 & op(e3, e1) = e1
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | |   (196)  op(e3, e1) = e1
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | |   (197)  all_54_4 = e1
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (197) imply:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | |   (198)  all_52_1 = e1
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | SIMP: (198) implies:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | |   (199)  all_52_1 = e1
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (199) imply:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | |   (200)   ~ (all_52_2 = e1)
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | SIMP: (200) implies:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | |   (201)   ~ (all_52_2 = e1)
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (199) imply:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | |   (202)   ~ (all_52_3 = e1)
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | SIMP: (202) implies:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | |   (203)   ~ (all_52_3 = e1)
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | |   (204)  all_54_8 = e2
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (204) imply:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | |   (205)  all_52_2 = e2
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (205) imply:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | |   (206)  $false
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (206) is inconsistent.
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | |   (207)   ~ (all_54_8 = e2)
% 239.51/46.23  | | | | | | | | | | | | | | | | | | | | | |   (208)  all_54_8 = e1 | all_54_8 = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_54_8 = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (209) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_52_2 = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (201), (210) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | |   (211)  $false
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | |   (212)  all_54_8 = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (212) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_52_2 = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (213) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | |   (214)   ~ (all_52_3 = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (214) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | |   (215)   ~ (all_52_3 = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (213) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | |   (216)   ~ (all_52_14 = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (216) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | |   (217)   ~ (all_52_14 = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (213) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | |   (218)   ~ (e2 = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (201), (213) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | |   (219)   ~ (e1 = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | |   (220)  all_54_12 = e3
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (220) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_52_3 = e3
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (221) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | |   (222)   ~ (all_52_7 = e3)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (222) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | |   (223)   ~ (all_52_7 = e3)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  all_54_13 = e3
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (223), (224) are inconsistent by sub-proof
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (225)   ~ (all_54_13 = e3)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (80), (101), (102), (155), (157), (169),
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228) are inconsistent by sub-proof #188.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (65), (101), (102), (156), (201), (215),
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229) are inconsistent by sub-proof #1005.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  all_56_19 = e2
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  all_54_13 = e2
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (129), (234) are inconsistent by sub-proof
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2009.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)   ~ (all_54_13 = e2)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  all_54_13 = e1 | all_54_13 = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  all_54_13 = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (237) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (238)  all_52_7 = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (238) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (239)  all_52_7 = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (239) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (240)   ~ (all_52_4 = e1)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (239) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (241)   ~ (all_52_11 = e1)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (241) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (242)   ~ (all_52_11 = e1)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (223), (239) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (243)   ~ (e3 = e1)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (239) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (244)   ~ (e2 = e1)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  all_54_14 = e2
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (113), (134), (245) are inconsistent by sub-proof
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1856.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  all_54_14 = e1 | all_54_14 = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_19 & $i(all_56_19))
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_56_17 & $i(all_56_17)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (249)  op(e3, e1) = all_56_17
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (250)  op(e3, all_56_17) = e3
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (101), (113), (122), (196), (242), (246),
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (249), (250) are inconsistent by sub-proof #1398.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_56_19 & $i(all_56_19)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)  op(e2, all_56_19) = e2
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (233), (252) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)  op(e2, e2) = e2
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (23), (28), (30), (88), (91), (92), (93),
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (101), (119), (127), (137), (240), (253) are
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #88.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23))
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (255)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  op(e1, all_56_21) = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (256) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  op(e1, e3) = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (102), (201), (257) are inconsistent by
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1948.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_56_23 & $i(all_56_23)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  op(e0, e1) = all_56_23
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  op(e0, all_56_23) = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (101), (108), (114), (120), (137),
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (143), (157), (158), (177), (178), (185), (192),
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (259), (260) are inconsistent by sub-proof
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #228.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  all_54_13 = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (93), (261) are inconsistent by sub-proof
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2008.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (88), (101), (129), (262) are inconsistent
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #185.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  op(e2, e0) = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (111), (117), (265) are inconsistent by
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2324.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  op(e0, e1) = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (108), (193), (268) are inconsistent by
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2158.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  op(e1, e0) = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (101), (217), (270) are inconsistent by
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2323.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (66), (203), (215), (271) are inconsistent
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2066.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | |   (272)  all_54_4 = e0
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (69), (272) are inconsistent by sub-proof
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | |            #1923.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | |   (273)  all_58_5 = e1 & op(e2, e1) = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | |   (274)  all_58_5 = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (274) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | |   (275)  e2 = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (275) imply:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | |   (276)  all_58_7 = e1
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (36), (101), (120), (137), (157), (168),
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | |            (177), (276) are inconsistent by sub-proof #1588.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | |   (277)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 239.51/46.24  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (79), (101), (108), (193), (277) are
% 239.51/46.24  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #45.
% 239.51/46.24  | | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | |   (278)  all_58_13 = e3 & op(e0, e2) = e3
% 239.51/46.24  | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 239.51/46.24  | | | | | | | | | | | | | | |   (279)  all_58_13 = e3
% 239.51/46.24  | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | COMBINE_EQS: (177), (279) imply:
% 239.51/46.24  | | | | | | | | | | | | | | |   (280)  e3 = e1
% 239.51/46.24  | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | | REF_CLOSE: (31), (40), (54), (65), (75), (101), (122), (156),
% 239.51/46.24  | | | | | | | | | | | | | | |            (157), (168), (280) are inconsistent by sub-proof
% 239.51/46.24  | | | | | | | | | | | | | | |            #419.
% 239.51/46.24  | | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | | End of split
% 239.51/46.24  | | | | | | | | | | | | | | 
% 239.51/46.24  | | | | | | | | | | | | | Case 2:
% 239.51/46.24  | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | |   (281)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 239.51/46.25  | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 239.51/46.25  | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | REF_CLOSE: (11), (52), (101), (110), (157), (281) are
% 239.51/46.25  | | | | | | | | | | | | | |            inconsistent by sub-proof #226.
% 239.51/46.25  | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | End of split
% 239.51/46.25  | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | End of split
% 239.51/46.25  | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | End of split
% 239.51/46.25  | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | End of split
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | |   (282)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 239.51/46.25  | | | | | | | | | |            & op(e3, e0) = e3)
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | REF_CLOSE: (54), (65), (101), (122), (156), (282) are
% 239.51/46.25  | | | | | | | | | |            inconsistent by sub-proof #1515.
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | End of split
% 239.51/46.25  | | | | | | | | | 
% 239.51/46.25  | | | | | | | | End of split
% 239.51/46.25  | | | | | | | | 
% 239.51/46.25  | | | | | | | End of split
% 239.51/46.25  | | | | | | | 
% 239.51/46.25  | | | | | | Case 2:
% 239.51/46.25  | | | | | | | 
% 239.51/46.25  | | | | | | |   (283)   ~ (all_54_7 = e3)
% 239.51/46.25  | | | | | | |   (284)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 239.51/46.25  | | | | | | | 
% 239.51/46.25  | | | | | | | REDUCE: (87), (283) imply:
% 239.51/46.25  | | | | | | |   (285)   ~ (all_52_13 = e3)
% 239.51/46.25  | | | | | | | 
% 239.51/46.25  | | | | | | | BETA: splitting (284) gives:
% 239.51/46.25  | | | | | | | 
% 239.51/46.25  | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | 
% 239.51/46.25  | | | | | | | |   (286)  all_54_7 = e2
% 239.51/46.25  | | | | | | | | 
% 239.51/46.25  | | | | | | | | COMBINE_EQS: (87), (286) imply:
% 239.51/46.25  | | | | | | | |   (287)  all_52_13 = e2
% 239.51/46.25  | | | | | | | | 
% 239.51/46.25  | | | | | | | | REDUCE: (136), (287) imply:
% 239.51/46.25  | | | | | | | |   (288)  $false
% 239.51/46.25  | | | | | | | | 
% 239.51/46.25  | | | | | | | | CLOSE: (288) is inconsistent.
% 239.51/46.25  | | | | | | | | 
% 239.51/46.25  | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | 
% 239.51/46.25  | | | | | | | |   (289)   ~ (all_54_7 = e2)
% 239.51/46.25  | | | | | | | |   (290)  all_54_7 = e1 | all_54_7 = e0
% 239.51/46.25  | | | | | | | | 
% 239.51/46.25  | | | | | | | | BETA: splitting (290) gives:
% 239.51/46.25  | | | | | | | | 
% 239.51/46.25  | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | 
% 239.51/46.25  | | | | | | | | |   (291)  all_54_7 = e1
% 239.51/46.25  | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | COMBINE_EQS: (87), (291) imply:
% 239.51/46.25  | | | | | | | | |   (292)  all_52_13 = e1
% 239.51/46.25  | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | REDUCE: (84), (292) imply:
% 239.51/46.25  | | | | | | | | |   (293)   ~ (all_52_1 = e1)
% 239.51/46.25  | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | REDUCE: (39), (292) imply:
% 239.51/46.25  | | | | | | | | |   (294)   ~ (all_52_12 = e1)
% 239.51/46.25  | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | REDUCE: (89), (292) imply:
% 239.51/46.25  | | | | | | | | |   (295)   ~ (all_52_14 = e1)
% 239.51/46.25  | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | SIMP: (295) implies:
% 239.51/46.25  | | | | | | | | |   (296)   ~ (all_52_14 = e1)
% 239.51/46.25  | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | REDUCE: (136), (292) imply:
% 239.51/46.25  | | | | | | | | |   (297)   ~ (e2 = e1)
% 239.51/46.25  | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | REDUCE: (111), (292) imply:
% 239.51/46.25  | | | | | | | | |   (298)  op(e2, e0) = e1
% 239.51/46.25  | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | BETA: splitting (82) gives:
% 239.51/46.25  | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | |   (299)  all_54_4 = e3
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | COMBINE_EQS: (50), (299) imply:
% 239.51/46.25  | | | | | | | | | |   (300)  all_52_1 = e3
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | SIMP: (300) implies:
% 239.51/46.25  | | | | | | | | | |   (301)  all_52_1 = e3
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | REDUCE: (26), (301) imply:
% 239.51/46.25  | | | | | | | | | |   (302)   ~ (all_52_2 = e3)
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | REDUCE: (2), (301) imply:
% 239.51/46.25  | | | | | | | | | |   (303)   ~ (all_52_3 = e3)
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | SIMP: (303) implies:
% 239.51/46.25  | | | | | | | | | |   (304)   ~ (all_52_3 = e3)
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | REDUCE: (125), (301) imply:
% 239.51/46.25  | | | | | | | | | |   (305)   ~ (e3 = e2)
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | REDUCE: (69), (301) imply:
% 239.51/46.25  | | | | | | | | | |   (306)   ~ (e3 = e0)
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | REDUCE: (74), (301) imply:
% 239.51/46.25  | | | | | | | | | |   (307)  op(e2, e3) = e3
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | BETA: splitting (152) gives:
% 239.51/46.25  | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | |   (308)  all_54_11 = e2
% 239.51/46.25  | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | COMBINE_EQS: (32), (308) imply:
% 239.51/46.25  | | | | | | | | | | |   (309)  all_52_14 = e2
% 239.51/46.25  | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | REDUCE: (131), (309) imply:
% 239.51/46.25  | | | | | | | | | | |   (310)  $false
% 239.51/46.25  | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | CLOSE: (310) is inconsistent.
% 239.51/46.25  | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | |   (311)   ~ (all_54_11 = e2)
% 239.51/46.25  | | | | | | | | | | |   (312)  all_54_11 = e1 | all_54_11 = e0
% 239.51/46.25  | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | BETA: splitting (96) gives:
% 239.51/46.25  | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | |   (313)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 239.51/46.25  | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 239.51/46.25  | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | BETA: splitting (313) gives:
% 239.51/46.25  | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | |   (314)  all_58_9 = e3 & op(e3, e0) = e3
% 239.51/46.25  | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | ALPHA: (314) implies:
% 239.51/46.25  | | | | | | | | | | | | |   (315)  all_58_9 = e3
% 239.51/46.25  | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | BETA: splitting (8) gives:
% 239.51/46.25  | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | |   (316)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 239.51/46.25  | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 239.51/46.25  | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 239.51/46.25  | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | |   (317)  all_58_12 = e3 & op(e0, e3) = e3
% 239.51/46.25  | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 239.51/46.25  | | | | | | | | | | | | | | |   (318)  op(e0, e3) = e3
% 239.51/46.25  | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | REF_CLOSE: (29), (101), (304), (318) are inconsistent by
% 239.51/46.25  | | | | | | | | | | | | | | |            sub-proof #2332.
% 239.51/46.25  | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | |   (319)  all_58_13 = e3 & op(e0, e2) = e3
% 239.51/46.25  | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | ALPHA: (319) implies:
% 239.51/46.25  | | | | | | | | | | | | | | |   (320)  op(e0, e2) = e3
% 239.51/46.25  | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | |   (321)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 239.51/46.25  | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | |   (322)  all_58_1 = e1 & op(e3, e2) = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | ALPHA: (322) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | |   (323)  all_58_1 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | |   (324)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (92), (101), (119), (137), (324) are
% 239.51/46.25  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1711.
% 239.51/46.25  | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | |   (325)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | |   (326)  all_58_4 = e0 & op(e3, e1) = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | |   (327)  all_58_4 = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | |   (328)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |   (329)  all_58_4 = e1 & op(e3, e1) = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |   (330)  all_58_4 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (78), (101), (108), (137), (306), (315),
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |            (323), (330) are inconsistent by sub-proof #1646.
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |   (331)  all_58_5 = e1 & op(e2, e1) = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (331) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |   (332)  all_58_5 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (332) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |   (333)  e2 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (333) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |   (334)  all_58_7 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (36), (101), (120), (137), (305), (320),
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |            (323), (334) are inconsistent by sub-proof #1715.
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | End of split
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | |   (335)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |   (336)  all_58_8 = e1 & op(e1, e1) = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (336) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |   (337)  op(e1, e1) = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (79), (101), (337) are inconsistent by
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |            sub-proof #468.
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |   (338)  all_58_14 = e1 & op(e0, e1) = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | |   (339)  all_58_14 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | |   (340)  all_54_11 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (296), (340) are inconsistent by sub-proof
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | |            #2176.
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | |   (341)  all_54_11 = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (341) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | |   (342)  all_52_14 = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | SIMP: (342) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | |   (343)  all_52_14 = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (343) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | |   (344)   ~ (all_52_2 = e0)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (343) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | |   (345)   ~ (all_52_12 = e0)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (343) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | |   (346)   ~ (e2 = e0)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (296), (343) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | |   (347)   ~ (e1 = e0)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (343) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | |   (348)  op(e1, e0) = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | |   (349)  all_54_3 = e3
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (349) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | |   (350)  all_52_12 = e3
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (350) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | |   (351)  all_52_12 = e3
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (71), (351) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | |   (352)   ~ (all_52_4 = e3)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | |   (353)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (353) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (354)  all_58_6 = e1 & op(e1, e3) = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (354) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (355)  op(e1, e3) = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (356)  all_54_1 = e3
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (352), (356) are inconsistent by sub-proof
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1930.
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (357)   ~ (all_54_1 = e3)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (358)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (358) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (359)  all_54_1 = e2
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (127), (359) are inconsistent by sub-proof
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1928.
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (360)   ~ (all_54_1 = e2)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (361)  all_54_1 = e1 | all_54_1 = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (362)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (31), (40), (69), (74), (92), (98), (101),
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (120), (137), (305), (306), (327), (352),
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (362) are inconsistent by sub-proof #297.
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (363)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (363) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (364)  all_58_6 = e0 & op(e1, e3) = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (364) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (365)  op(e1, e3) = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (108), (355), (365) are inconsistent by
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #449.
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (366)  all_58_12 = e0 & op(e0, e3) = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (366) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (367)  op(e0, e3) = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (368)  all_54_8 = e2
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (126), (368) are inconsistent by sub-proof
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2007.
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (369)   ~ (all_54_8 = e2)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (370)  all_54_8 = e1 | all_54_8 = e0
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (361) gives:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (371)  all_54_1 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (371) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (372)  all_52_4 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (372) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (373)  all_52_4 = e1
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (373) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (374)   ~ (all_52_7 = e1)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (374) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (375)   ~ (all_52_7 = e1)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (373) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (376)   ~ (all_52_8 = e1)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (376) implies:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (377)   ~ (all_52_8 = e1)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (373) imply:
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (378)   ~ (e3 = e1)
% 239.51/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (373) imply:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (379)  op(e3, e2) = e1
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (380)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, all_56_11) = e2)
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (380) gives:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (381)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_9 & $i(all_56_9)
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (381) implies:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (382)  op(e3, e2) = all_56_9
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (383)  op(e3, all_56_9) = e3
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (384)  all_54_2 = e3
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (122), (384) are inconsistent by sub-proof
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1987.
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (385)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (385) gives:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (386)  all_54_2 = e2
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (132), (386) are inconsistent by sub-proof
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1986.
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (387)   ~ (all_54_2 = e2)
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (388)  all_54_2 = e1 | all_54_2 = e0
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (389)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_32_1 & $i(all_32_0) &
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_32_1)
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (389) implies:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (390)  op(e3, e2) = all_32_1
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (9), (21), (31), (42), (75), (79), (90),
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (101), (110), (132), (143), (305), (307), (320),
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (355), (367), (377), (382), (383), (388), (390)
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #43.
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (391)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_32_1)
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (392)  op(e3, e2) = all_32_1
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (9), (21), (31), (42), (75), (79), (90),
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (101), (110), (132), (143), (305), (307), (320),
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (355), (367), (377), (382), (383), (388), (392)
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #43.
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (393)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (393) implies:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (394)  op(e2, all_56_11) = e2
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (394) imply:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (395)  op(e2, e0) = e2
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (120), (298), (395) are inconsistent by
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1659.
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (396)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_15 & $i(all_56_15))
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (396) gives:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (397)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_13 & $i(all_56_13)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (397) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (398)  op(e1, e2) = all_56_13
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (399)  op(e1, all_56_13) = e1
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (400)  all_54_2 = e3
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (122), (400) are inconsistent by sub-proof
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1987.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (401)   ~ (all_54_2 = e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (402)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (402) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (403)  all_54_2 = e2
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (132), (403) are inconsistent by sub-proof
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1986.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (404)   ~ (all_54_2 = e2)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (405)  all_54_2 = e1 | all_54_2 = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (406)  all_54_8 = e1
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (406) imply:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (407)  all_52_2 = e1
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (407) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (408)  all_52_2 = e1
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (408) imply:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (409)   ~ (all_52_3 = e1)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (409) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (410)   ~ (all_52_3 = e1)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (411)  all_54_12 = e3
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (304), (411) are inconsistent by sub-proof
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2266.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (412)   ~ (all_54_12 = e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (413)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (414)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_3 & $i(all_56_3))
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (90), (92), (93), (95), (101), (121), (129),
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (305), (307), (375), (414) are inconsistent by
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #42.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (415)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_7 & $i(all_56_7))
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (415) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (416)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_5 & $i(all_56_5)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (416) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (417)  op(e1, e3) = all_56_5
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (418)  op(e1, all_56_5) = e1
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (413) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (419)  all_54_12 = e2
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (66), (419) are inconsistent by sub-proof
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2264.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (420)   ~ (all_54_12 = e2)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (421)  all_54_12 = e1 | all_54_12 = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (421) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (422)  all_54_12 = e1
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (410), (422) are inconsistent by sub-proof
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2263.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (423)  all_54_12 = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (423) imply:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (424)  all_52_3 = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (424) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (425)  all_52_3 = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (425) imply:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (426)   ~ (all_52_11 = e0)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (426) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (427)   ~ (all_52_11 = e0)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (304), (425) imply:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (428)   ~ (e3 = e0)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (429)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (429) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (430)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (431)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          e3
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (431) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (432)  op(e3, e2) = e3
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (92), (93), (95), (101), (121), (129),
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (375), (432) are inconsistent by sub-proof #456.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (433)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (433) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (434)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          e2
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (434) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (435)  op(e3, e2) = e2
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (120), (379), (435) are inconsistent by
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2261.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (436)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (437)  op(e1, e3) = e3
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (101), (417), (418), (437) are inconsistent
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2243.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (438)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (438) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (439)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (439) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (440)  op(e3, e1) = e1
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (101), (377), (440) are inconsistent by
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2309.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (441)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (101), (306), (345), (367), (441) are
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #220.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (442)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (27), (31), (33), (34), (42), (56),
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (60), (67), (76), (81), (83), (85), (86), (101),
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (108), (109), (111), (120), (122), (132),
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (298), (305), (306), (320), (327), (339),
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (355), (377), (398), (399), (405), (427), (442)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #40.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (443)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_7 & $i(all_56_7)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (443) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (444)  op(e0, e3) = all_56_7
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (445)  op(e0, all_56_7) = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (413) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (446)  all_54_12 = e2
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (66), (446) are inconsistent by sub-proof
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2264.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (447)   ~ (all_54_12 = e2)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (448)  all_54_12 = e1 | all_54_12 = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (448) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (449)  all_54_12 = e1
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (410), (449) are inconsistent by sub-proof
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2263.
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (450)  all_54_12 = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (450) imply:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (451)  all_52_3 = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (451) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (452)  all_52_3 = e0
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (59), (452) imply:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (453)   ~ (all_52_11 = e0)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (453) implies:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (454)   ~ (all_52_11 = e0)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (304), (452) imply:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (455)   ~ (e3 = e0)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (456)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (456) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (457)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (457) gives:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (458)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          e3
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (458) implies:
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)  op(e3, e2) = e3
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (92), (93), (95), (101), (121), (129),
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (375), (459) are inconsistent by sub-proof #456.
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (460)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (101), (120), (355), (379), (460) are
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #334.
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (461)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (65), (101), (306), (345), (377), (444),
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (445), (461) are inconsistent by sub-proof #174.
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (462)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.66/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (27), (31), (33), (34), (42), (56),
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (60), (67), (76), (81), (83), (85), (86), (101),
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (108), (109), (111), (120), (122), (132),
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (298), (305), (306), (320), (327), (339),
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (355), (377), (398), (399), (405), (454), (462)
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #40.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (463)  all_54_8 = e0
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (344), (463) are inconsistent by sub-proof
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2006.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (464)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_15 & $i(all_56_15)
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (464) implies:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (465)  op(e0, e2) = all_56_15
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (466)  all_54_2 = e3
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (122), (466) are inconsistent by sub-proof
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1987.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (467)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (467) gives:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (468)  all_54_2 = e2
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (132), (468) are inconsistent by sub-proof
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1986.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (469)   ~ (all_54_2 = e2)
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (470)  all_54_2 = e1 | all_54_2 = e0
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (471)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_3 & $i(all_56_3))
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (90), (92), (93), (95), (101), (121), (129),
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (305), (307), (375), (471) are inconsistent by
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #42.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (472)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_7 & $i(all_56_7))
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (472) gives:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (473)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_5 & $i(all_56_5)
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (473) implies:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (474)  op(e1, e3) = all_56_5
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (475)  op(e1, all_56_5) = e1
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (101) with e1, all_56_5, e3, e1,
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (355), (474) gives:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (476)  all_56_5 = e1
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (475), (476) imply:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (477)  op(e1, e1) = e1
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (79), (101), (477) are inconsistent by
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #468.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (478)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 &
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_44_1)
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (478) implies:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (479)   ~ (all_44_1 = e1)
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (480)  op(e0, e2) = all_44_1
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (470) gives:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (481)  all_54_2 = e1
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (377), (481) are inconsistent by sub-proof
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1337.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (101) with all_44_1, all_56_15, e2,
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, simplifying with (465), (480) gives:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (482)  all_56_15 = all_44_1
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (101) with e3, all_56_15, e2, e0,
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (320), (465) gives:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (483)  all_56_15 = e3
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (101) with e1, all_56_5, e3, e1,
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (355), (474) gives:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (484)  all_56_5 = e1
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (482), (483) imply:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (485)  all_44_1 = e3
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (485) implies:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (486)  all_44_1 = e3
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (475), (484) imply:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  op(e1, e1) = e1
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (79), (101), (487) are inconsistent by
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #468.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (488)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_7 & $i(all_56_7)
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (101), (110), (132), (367), (377), (470),
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (488) are inconsistent by sub-proof #44.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  all_54_1 = e0
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (119), (489) are inconsistent by sub-proof
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2050.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (490)  all_58_7 = e1 & op(e1, e2) = e1
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (490) implies:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (491)  all_58_7 = e1
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (36), (101), (120), (137), (305), (320),
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (323), (491) are inconsistent by sub-proof #1715.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | |   (492)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (79), (101), (108), (348), (492) are
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #289.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | |   (493)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (100), (294), (345), (493) are inconsistent
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2286.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | |   (494)  all_58_9 = e0 & op(e3, e0) = e0
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (306), (315), (494) are inconsistent by sub-proof
% 239.68/46.27  | | | | | | | | | | | | | | | | | | |            #2103.
% 239.68/46.27  | | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | |   (495)  all_58_3 = e1 & op(e2, e2) = e1
% 239.68/46.27  | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (112), (495) are inconsistent by sub-proof
% 239.68/46.27  | | | | | | | | | | | | | | | | |            #1752.
% 239.68/46.27  | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | |   (496)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 239.68/46.27  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 239.68/46.27  | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | BETA: splitting (496) gives:
% 239.68/46.27  | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | Case 1:
% 239.68/46.27  | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | |   (497)  all_58_7 = e1 & op(e1, e2) = e1
% 239.68/46.27  | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (120), (497) are inconsistent by sub-proof
% 239.68/46.27  | | | | | | | | | | | | | | | | |            #2224.
% 239.68/46.27  | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | |   (498)  all_58_13 = e1 & op(e0, e2) = e1
% 239.68/46.27  | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (14), (17), (20), (21), (27), (28), (32),
% 239.68/46.27  | | | | | | | | | | | | | | | | |            (37), (38), (39), (43), (48), (49), (57), (65),
% 239.68/46.27  | | | | | | | | | | | | | | | | |            (71), (73), (77), (88), (89), (91), (92), (100),
% 239.68/46.27  | | | | | | | | | | | | | | | | |            (101), (106), (107), (111), (119), (120), (121),
% 239.68/46.27  | | | | | | | | | | | | | | | | |            (131), (294), (296), (498) are inconsistent by
% 239.68/46.27  | | | | | | | | | | | | | | | | |            sub-proof #83.
% 239.68/46.27  | | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | |   (499)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 239.68/46.27  | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 239.68/46.27  | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | | REF_CLOSE: (11), (52), (101), (110), (305), (499) are
% 239.68/46.27  | | | | | | | | | | | | | |            inconsistent by sub-proof #226.
% 239.68/46.27  | | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | |   (500)  all_58_10 = e3 & op(e2, e0) = e3
% 239.68/46.27  | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | ALPHA: (500) implies:
% 239.68/46.27  | | | | | | | | | | | | |   (501)  op(e2, e0) = e3
% 239.68/46.27  | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | | REF_CLOSE: (101), (111), (285), (501) are inconsistent by
% 239.68/46.27  | | | | | | | | | | | | |            sub-proof #1994.
% 239.68/46.27  | | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | |   (502)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 239.68/46.27  | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 239.68/46.27  | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | | REF_CLOSE: (27), (76), (101), (110), (305), (502) are
% 239.68/46.27  | | | | | | | | | | | |            inconsistent by sub-proof #214.
% 239.68/46.27  | | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | |   (503)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.68/46.27  | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | | REF_CLOSE: (41), (46), (50), (55), (69), (101), (293), (503)
% 239.68/46.27  | | | | | | | | | |            are inconsistent by sub-proof #173.
% 239.68/46.27  | | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | | 
% 239.68/46.27  | | | | | | | | Case 2:
% 239.68/46.27  | | | | | | | | | 
% 239.68/46.27  | | | | | | | | |   (504)  all_54_7 = e0
% 239.68/46.27  | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | COMBINE_EQS: (87), (504) imply:
% 239.68/46.27  | | | | | | | | |   (505)  all_52_13 = e0
% 239.68/46.27  | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | REDUCE: (117), (505) imply:
% 239.68/46.27  | | | | | | | | |   (506)  $false
% 239.68/46.27  | | | | | | | | | 
% 239.68/46.27  | | | | | | | | | CLOSE: (506) is inconsistent.
% 239.68/46.27  | | | | | | | | | 
% 239.68/46.27  | | | | | | | | End of split
% 239.68/46.27  | | | | | | | | 
% 239.68/46.27  | | | | | | | End of split
% 239.68/46.27  | | | | | | | 
% 239.68/46.27  | | | | | | End of split
% 239.68/46.27  | | | | | | 
% 239.68/46.27  | | | | | End of split
% 239.68/46.27  | | | | | 
% 239.68/46.27  | | | | End of split
% 239.68/46.27  | | | | 
% 239.68/46.27  | | | End of split
% 239.68/46.27  | | | 
% 239.68/46.27  | | End of split
% 239.68/46.27  | | 
% 239.68/46.27  | End of split
% 239.68/46.27  | 
% 239.68/46.27  End of proof
% 239.68/46.27  
% 239.68/46.27  Sub-proof #40 shows that the following formulas are inconsistent:
% 239.68/46.27  ----------------------------------------------------------------
% 239.68/46.27    (1)  op(e1, e2) = all_56_13
% 239.68/46.27    (2)   ~ (e3 = e0)
% 239.68/46.27    (3)  all_54_2 = e1 | all_54_2 = e0
% 239.68/46.27    (4)  op(e0, e1) = all_52_11
% 239.68/46.27    (5)   ~ (e2 = e0)
% 239.68/46.27    (6)  op(e1, e2) = all_52_6
% 239.68/46.27    (7)  op(e1, e0) = all_52_14
% 239.68/46.27    (8)   ~ (e3 = e1)
% 239.68/46.27    (9)  op(e0, e2) = e3
% 239.68/46.27    (10)  all_58_7 = e2
% 239.68/46.27    (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.68/46.27          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.68/46.27    (12)   ~ (all_52_8 = e1)
% 239.68/46.27    (13)  all_54_2 = all_52_8
% 239.68/46.27    (14)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 239.68/46.27              e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.68/46.27            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 239.68/46.27              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 239.68/46.27              e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 239.68/46.27            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 239.68/46.27            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.68/46.27            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 239.68/46.27            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.68/46.27              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 239.68/46.27            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.68/46.27            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 =
% 239.68/46.27            e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.68/46.27            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 239.68/46.27            = e0)
% 239.68/46.27    (15)   ~ (e3 = e2)
% 239.68/46.27    (16)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.68/46.27          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.68/46.27    (17)  all_56_31 = e2
% 239.68/46.27    (18)  op(e1, e3) = e1
% 239.68/46.27    (19)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.68/46.27          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.68/46.27    (20)   ~ (all_52_14 = e3)
% 239.68/46.27    (21)   ~ (all_52_6 = e3)
% 239.68/46.28    (22)  op(e1, e2) = e2
% 239.68/46.28    (23)  all_58_5 = e2
% 239.68/46.28    (24)   ~ (all_52_11 = e0)
% 239.68/46.28    (25)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.68/46.28          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.68/46.28    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.68/46.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.68/46.28    (27)  all_56_21 = e3
% 239.68/46.28    (28)  op(e1, all_56_13) = e1
% 239.68/46.28    (29)   ~ (e1 = e0)
% 239.68/46.28    (30)  op(e2, e0) = e1
% 239.68/46.28    (31)   ~ (all_52_8 = e2)
% 239.68/46.28    (32)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.68/46.28          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.68/46.28    (33)  op(e2, e0) = all_52_13
% 239.68/46.28    (34)  all_58_14 = e1
% 239.68/46.28    (35)  all_58_4 = e0
% 239.68/46.28    (36)   ~ (e2 = e1)
% 239.68/46.28    (37)   ~ (all_52_8 = e3)
% 239.68/46.28  
% 239.68/46.28  Begin of proof
% 239.68/46.28  | 
% 239.68/46.28  | BETA: splitting (14) gives:
% 239.68/46.28  | 
% 239.68/46.28  | Case 1:
% 239.68/46.28  | | 
% 239.68/46.28  | |   (38)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 239.68/46.28  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.68/46.28  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.68/46.28  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.68/46.28  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 239.68/46.28  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.68/46.28  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.68/46.28  | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.68/46.28  | | 
% 239.68/46.28  | | BETA: splitting (38) gives:
% 239.68/46.28  | | 
% 239.68/46.28  | | Case 1:
% 239.68/46.28  | | | 
% 239.68/46.28  | | |   (39)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 239.68/46.28  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.68/46.28  | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 239.68/46.28  | | | 
% 239.68/46.28  | | | ALPHA: (39) implies:
% 239.68/46.28  | | |   (40)  all_56_13 = e2
% 239.68/46.28  | | |   (41)   ~ (all_56_31 = e1)
% 239.68/46.28  | | |   (42)   ~ (all_56_21 = e1)
% 239.68/46.28  | | | 
% 239.68/46.28  | | | REDUCE: (28), (40) imply:
% 239.68/46.28  | | |   (43)  op(e1, e2) = e1
% 239.68/46.28  | | | 
% 239.68/46.28  | | | REF_CLOSE: (3), (8), (11), (12), (13), (15), (16), (22), (23), (25), (26),
% 239.68/46.28  | | |            (31), (34), (35), (36), (37), (43) are inconsistent by
% 239.68/46.28  | | |            sub-proof #41.
% 239.68/46.28  | | | 
% 239.68/46.28  | | Case 2:
% 239.68/46.28  | | | 
% 239.68/46.28  | | |   (44)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.68/46.28  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.68/46.28  | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27
% 239.68/46.28  | | |           = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 239.68/46.28  | | |             = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 239.68/46.28  | | |           e2)
% 239.68/46.28  | | | 
% 239.68/46.28  | | | BETA: splitting (44) gives:
% 239.68/46.28  | | | 
% 239.68/46.28  | | | Case 1:
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | |   (45)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.68/46.28  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.68/46.28  | | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | | ALPHA: (45) implies:
% 239.68/46.28  | | | |   (46)  op(e1, e2) = e1
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | | REF_CLOSE: (3), (8), (11), (12), (13), (15), (16), (22), (23), (25),
% 239.68/46.28  | | | |            (26), (31), (34), (35), (36), (37), (46) are inconsistent by
% 239.68/46.28  | | | |            sub-proof #41.
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | Case 2:
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | |   (47)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.68/46.28  | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.68/46.28  | | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | | ALPHA: (47) implies:
% 239.68/46.28  | | | |   (48)  op(e0, e2) = e2
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | | REF_CLOSE: (9), (15), (26), (48) are inconsistent by sub-proof #2254.
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | End of split
% 239.68/46.28  | | | 
% 239.68/46.28  | | End of split
% 239.68/46.28  | | 
% 239.68/46.28  | Case 2:
% 239.68/46.28  | | 
% 239.68/46.28  | |   (49)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 239.68/46.28  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.68/46.28  | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 239.68/46.28  | |           e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.68/46.28  | |             e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 239.68/46.28  | |         (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 239.68/46.28  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.68/46.28  | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.68/46.28  | | 
% 239.68/46.28  | | BETA: splitting (49) gives:
% 239.68/46.28  | | 
% 239.68/46.28  | | Case 1:
% 239.68/46.28  | | | 
% 239.68/46.28  | | |   (50)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 239.68/46.28  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.68/46.28  | | |         op(e2, e0) = e0 & op(e0, e2) = e0
% 239.68/46.28  | | | 
% 239.68/46.28  | | | ALPHA: (50) implies:
% 239.68/46.28  | | |   (51)  op(e2, e0) = e0
% 239.68/46.28  | | | 
% 239.68/46.28  | | | REF_CLOSE: (26), (29), (30), (33), (51) are inconsistent by sub-proof
% 239.68/46.28  | | |            #1778.
% 239.68/46.28  | | | 
% 239.68/46.28  | | Case 2:
% 239.68/46.28  | | | 
% 239.68/46.28  | | |   (52)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.68/46.28  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.68/46.28  | | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29
% 239.68/46.28  | | |           = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 239.68/46.28  | | |             = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 239.68/46.28  | | |           e0)
% 239.68/46.28  | | | 
% 239.68/46.28  | | | BETA: splitting (52) gives:
% 239.68/46.28  | | | 
% 239.68/46.28  | | | Case 1:
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | |   (53)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.68/46.28  | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.68/46.28  | | | |         op(e1, e0) = e1 & op(e0, e1) = e1
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | | ALPHA: (53) implies:
% 239.68/46.28  | | | |   (54)  op(e1, e0) = e1
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | | REF_CLOSE: (2), (5), (6), (7), (8), (10), (18), (19), (20), (21), (26),
% 239.68/46.28  | | | |            (29), (32), (54) are inconsistent by sub-proof #55.
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | Case 2:
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | |   (55)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 239.68/46.28  | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.68/46.28  | | | |         op(e1, e0) = e0 & op(e0, e1) = e0
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | | ALPHA: (55) implies:
% 239.68/46.28  | | | |   (56)  op(e0, e1) = e0
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | | REF_CLOSE: (4), (24), (26), (56) are inconsistent by sub-proof #1911.
% 239.68/46.28  | | | | 
% 239.68/46.28  | | | End of split
% 239.68/46.28  | | | 
% 239.68/46.28  | | End of split
% 239.68/46.28  | | 
% 239.68/46.28  | End of split
% 239.68/46.28  | 
% 239.68/46.28  End of proof
% 239.68/46.28  
% 239.68/46.28  Sub-proof #41 shows that the following formulas are inconsistent:
% 239.68/46.28  ----------------------------------------------------------------
% 239.68/46.28    (1)  all_54_2 = e1 | all_54_2 = e0
% 239.68/46.28    (2)  op(e1, e2) = e1
% 239.68/46.28    (3)   ~ (e3 = e1)
% 239.68/46.28    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.68/46.28         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.68/46.28    (5)   ~ (all_52_8 = e1)
% 239.68/46.28    (6)  all_54_2 = all_52_8
% 239.68/46.28    (7)   ~ (e3 = e2)
% 239.68/46.28    (8)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.68/46.28         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.68/46.28    (9)  op(e1, e2) = e2
% 239.68/46.28    (10)  all_58_5 = e2
% 239.68/46.28    (11)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.68/46.28          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.68/46.28    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.68/46.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.68/46.28    (13)   ~ (all_52_8 = e2)
% 239.68/46.28    (14)  all_58_14 = e1
% 239.68/46.28    (15)  all_58_4 = e0
% 239.68/46.28    (16)   ~ (e2 = e1)
% 239.68/46.28    (17)   ~ (all_52_8 = e3)
% 239.68/46.28  
% 239.68/46.28  Begin of proof
% 239.68/46.28  | 
% 239.68/46.28  | BETA: splitting (1) gives:
% 239.68/46.28  | 
% 239.68/46.28  | Case 1:
% 239.68/46.28  | | 
% 239.68/46.28  | |   (18)  all_54_2 = e1
% 239.68/46.28  | | 
% 239.68/46.28  | | REF_CLOSE: (5), (6), (18) are inconsistent by sub-proof #1337.
% 239.68/46.28  | | 
% 239.68/46.28  | Case 2:
% 239.68/46.28  | | 
% 239.68/46.28  | |   (19)  all_54_2 = e0
% 239.68/46.28  | | 
% 239.68/46.28  | | COMBINE_EQS: (6), (19) imply:
% 239.68/46.28  | |   (20)  all_52_8 = e0
% 239.68/46.28  | | 
% 239.68/46.28  | | SIMP: (20) implies:
% 239.68/46.28  | |   (21)  all_52_8 = e0
% 239.68/46.28  | | 
% 239.68/46.28  | | REDUCE: (17), (21) imply:
% 239.68/46.28  | |   (22)   ~ (e3 = e0)
% 239.68/46.28  | | 
% 239.68/46.28  | | SIMP: (22) implies:
% 239.68/46.28  | |   (23)   ~ (e3 = e0)
% 239.68/46.28  | | 
% 239.68/46.28  | | REDUCE: (13), (21) imply:
% 239.68/46.28  | |   (24)   ~ (e2 = e0)
% 239.68/46.28  | | 
% 239.68/46.28  | | SIMP: (24) implies:
% 239.68/46.28  | |   (25)   ~ (e2 = e0)
% 239.68/46.28  | | 
% 239.68/46.28  | | REDUCE: (5), (21) imply:
% 239.68/46.28  | |   (26)   ~ (e1 = e0)
% 239.68/46.28  | | 
% 239.68/46.28  | | SIMP: (26) implies:
% 239.68/46.28  | |   (27)   ~ (e1 = e0)
% 239.68/46.28  | | 
% 239.68/46.28  | | GROUND_INST: instantiating (12) with e2, e1, e2, e1, simplifying with (2),
% 239.68/46.28  | |              (9) gives:
% 239.68/46.28  | |   (28)  e2 = e1
% 239.68/46.28  | | 
% 239.68/46.28  | | COMBINE_EQS: (10), (28) imply:
% 239.68/46.28  | |   (29)  all_58_5 = e1
% 239.68/46.28  | | 
% 239.68/46.28  | | REF_CLOSE: (3), (4), (7), (8), (11), (12), (14), (15), (16), (23), (25),
% 239.68/46.28  | |            (27), (29) are inconsistent by sub-proof #1248.
% 239.68/46.28  | | 
% 239.68/46.28  | End of split
% 239.68/46.28  | 
% 239.68/46.28  End of proof
% 239.68/46.28  
% 239.68/46.28  Sub-proof #42 shows that the following formulas are inconsistent:
% 239.68/46.28  ----------------------------------------------------------------
% 239.68/46.28    (1)   ~ (all_52_7 = e2)
% 239.68/46.28    (2)  all_54_13 = all_52_7
% 239.68/46.28    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.68/46.28             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 239.68/46.28    (4)  op(e2, e3) = e3
% 239.68/46.28    (5)   ~ (e3 = e2)
% 239.68/46.28    (6)   ~ (all_52_7 = e1)
% 239.68/46.28    (7)  all_56_1 = e2
% 239.68/46.28    (8)  op(e3, e2) = all_52_4
% 239.68/46.28    (9)   ~ (all_52_7 = e0)
% 239.68/46.28    (10)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.68/46.28    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.68/46.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.68/46.28    (12)   ~ (all_52_4 = all_52_7)
% 239.68/46.28  
% 239.68/46.28  Begin of proof
% 239.68/46.28  | 
% 239.68/46.28  | BETA: splitting (3) gives:
% 239.68/46.28  | 
% 239.68/46.28  | Case 1:
% 239.68/46.28  | | 
% 239.68/46.28  | |   (13)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 239.68/46.28  | | 
% 239.68/46.28  | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (13) are
% 239.68/46.28  | |            inconsistent by sub-proof #131.
% 239.68/46.28  | | 
% 239.68/46.28  | Case 2:
% 239.68/46.28  | | 
% 239.68/46.28  | |   (14)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 239.68/46.28  | |         $i(all_56_3)
% 239.68/46.28  | | 
% 239.68/46.28  | | ALPHA: (14) implies:
% 239.68/46.28  | |   (15)  op(e2, e3) = all_56_3
% 239.68/46.28  | |   (16)  op(e2, all_56_3) = e2
% 239.68/46.28  | | 
% 239.68/46.28  | | REF_CLOSE: (4), (5), (11), (15), (16) are inconsistent by sub-proof #2262.
% 239.68/46.28  | | 
% 239.68/46.28  | End of split
% 239.68/46.28  | 
% 239.68/46.28  End of proof
% 239.68/46.28  
% 239.68/46.28  Sub-proof #43 shows that the following formulas are inconsistent:
% 239.68/46.28  ----------------------------------------------------------------
% 239.68/46.28    (1)  op(e3, e2) = all_56_9
% 239.68/46.28    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.68/46.28             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 239.68/46.28           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 239.68/46.28         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.68/46.28           $i(all_56_7))
% 239.68/46.28    (3)  op(e3, all_56_9) = e3
% 239.68/46.28    (4)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 239.68/46.28           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 239.68/46.28           all_24_1 & $i(all_24_1))
% 239.68/46.28    (5)  all_54_2 = e1 | all_54_2 = e0
% 239.68/46.28    (6)  op(e3, e2) = all_32_1
% 239.68/46.28    (7)  ( ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 239.68/46.28           $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e0, e2) = all_4_1
% 239.68/46.28           & $i(all_4_1))
% 239.68/46.28    (8)  op(e2, e3) = e3
% 239.68/46.28    (9)   ~ (e3 = e1)
% 239.68/46.28    (10)  op(e0, e2) = e3
% 239.68/46.28    (11)   ~ (all_52_8 = e1)
% 239.68/46.28    (12)  all_54_2 = all_52_8
% 239.68/46.28    (13)   ~ (e3 = e2)
% 239.68/46.28    (14)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.68/46.28            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 239.68/46.28              e2) = all_44_1 & $i(all_44_1))
% 239.68/46.28    (15)  op(e1, e3) = e1
% 239.68/46.28    (16)  op(e0, e3) = e0
% 239.68/46.28    (17)  op(e3, e3) = e2
% 239.68/46.28    (18)  op(e1, e1) = e3
% 239.68/46.28    (19)  all_56_1 = e2
% 239.68/46.28    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.68/46.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.68/46.28    (21)   ~ (all_52_8 = e2)
% 239.68/46.28    (22)  op(e0, e0) = e2
% 239.68/46.28  
% 239.68/46.28  Begin of proof
% 239.68/46.28  | 
% 239.68/46.28  | BETA: splitting (2) gives:
% 239.68/46.28  | 
% 239.68/46.28  | Case 1:
% 239.68/46.28  | | 
% 239.68/46.29  | |   (23)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.68/46.29  | |             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 239.68/46.29  | | 
% 239.68/46.29  | | BETA: splitting (23) gives:
% 239.68/46.29  | | 
% 239.68/46.29  | | Case 1:
% 239.68/46.29  | | | 
% 239.68/46.29  | | |   (24)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 239.68/46.29  | | | 
% 239.68/46.29  | | | ALPHA: (24) implies:
% 239.68/46.29  | | |   (25)  op(e3, all_56_1) = e3
% 239.68/46.29  | | | 
% 239.68/46.29  | | | REDUCE: (19), (25) imply:
% 239.68/46.29  | | |   (26)  op(e3, e2) = e3
% 239.68/46.29  | | | 
% 239.68/46.29  | | | REF_CLOSE: (1), (3), (4), (6), (13), (17), (20), (26) are inconsistent by
% 239.68/46.29  | | |            sub-proof #133.
% 239.68/46.29  | | | 
% 239.68/46.29  | | Case 2:
% 239.68/46.29  | | | 
% 239.68/46.29  | | |   (27)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 239.68/46.29  | | |         $i(all_56_3)
% 239.68/46.29  | | | 
% 239.68/46.29  | | | ALPHA: (27) implies:
% 239.68/46.29  | | |   (28)  op(e2, e3) = all_56_3
% 239.68/46.29  | | |   (29)  op(e2, all_56_3) = e2
% 239.68/46.29  | | | 
% 239.68/46.29  | | | REF_CLOSE: (8), (13), (20), (28), (29) are inconsistent by sub-proof
% 239.68/46.29  | | |            #2262.
% 239.68/46.29  | | | 
% 239.68/46.29  | | End of split
% 239.68/46.29  | | 
% 239.68/46.29  | Case 2:
% 239.68/46.29  | | 
% 239.68/46.29  | |   (30)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 239.68/46.29  | |           $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0,
% 239.68/46.29  | |             e3) = all_56_7 & $i(all_56_7))
% 239.68/46.29  | | 
% 239.68/46.29  | | BETA: splitting (30) gives:
% 239.68/46.29  | | 
% 239.68/46.29  | | Case 1:
% 239.68/46.29  | | | 
% 239.68/46.29  | | |   (31)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 239.68/46.29  | | |         $i(all_56_5)
% 239.68/46.29  | | | 
% 239.68/46.29  | | | ALPHA: (31) implies:
% 239.68/46.29  | | |   (32)  op(e1, e3) = all_56_5
% 239.68/46.29  | | |   (33)  op(e1, all_56_5) = e1
% 239.68/46.29  | | | 
% 239.68/46.29  | | | BETA: splitting (7) gives:
% 239.68/46.29  | | | 
% 239.68/46.29  | | | Case 1:
% 239.68/46.29  | | | | 
% 239.68/46.29  | | | |   (34)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) =
% 239.68/46.29  | | | |         all_4_1 & $i(all_4_0) & $i(all_4_1)
% 239.68/46.29  | | | | 
% 239.68/46.29  | | | | ALPHA: (34) implies:
% 239.68/46.29  | | | |   (35)  op(e0, e2) = all_4_1
% 239.68/46.29  | | | | 
% 239.68/46.29  | | | | BETA: splitting (14) gives:
% 239.68/46.29  | | | | 
% 239.68/46.29  | | | | Case 1:
% 239.68/46.29  | | | | | 
% 239.68/46.29  | | | | | 
% 239.68/46.29  | | | | | GROUND_INST: instantiating (20) with e1, all_56_5, e3, e1, simplifying
% 239.68/46.29  | | | | |              with (15), (32) gives:
% 239.68/46.29  | | | | |   (36)  all_56_5 = e1
% 239.68/46.29  | | | | | 
% 239.68/46.29  | | | | | REDUCE: (33), (36) imply:
% 239.68/46.29  | | | | |   (37)  op(e1, e1) = e1
% 239.68/46.29  | | | | | 
% 239.68/46.29  | | | | | REF_CLOSE: (9), (18), (20), (37) are inconsistent by sub-proof #468.
% 239.68/46.29  | | | | | 
% 239.68/46.29  | | | | Case 2:
% 239.68/46.29  | | | | | 
% 239.68/46.29  | | | | |   (38)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 & $i(all_44_1)
% 239.68/46.29  | | | | | 
% 239.68/46.29  | | | | | ALPHA: (38) implies:
% 239.68/46.29  | | | | |   (39)   ~ (all_44_1 = e1)
% 239.68/46.29  | | | | |   (40)  op(e0, e2) = all_44_1
% 239.68/46.29  | | | | | 
% 239.68/46.29  | | | | | BETA: splitting (5) gives:
% 239.68/46.29  | | | | | 
% 239.68/46.29  | | | | | Case 1:
% 239.68/46.29  | | | | | | 
% 239.68/46.29  | | | | | |   (41)  all_54_2 = e1
% 239.68/46.29  | | | | | | 
% 239.68/46.29  | | | | | | REF_CLOSE: (11), (12), (41) are inconsistent by sub-proof #1337.
% 239.68/46.29  | | | | | | 
% 239.68/46.29  | | | | | Case 2:
% 239.68/46.29  | | | | | | 
% 239.68/46.29  | | | | | | 
% 239.68/46.29  | | | | | | GROUND_INST: instantiating (20) with all_4_1, all_44_1, e2, e0,
% 239.68/46.29  | | | | | |              simplifying with (35), (40) gives:
% 239.68/46.29  | | | | | |   (42)  all_44_1 = all_4_1
% 239.68/46.29  | | | | | | 
% 239.68/46.29  | | | | | | GROUND_INST: instantiating (20) with e3, all_44_1, e2, e0,
% 239.68/46.29  | | | | | |              simplifying with (10), (40) gives:
% 239.68/46.29  | | | | | |   (43)  all_44_1 = e3
% 239.68/46.29  | | | | | | 
% 239.68/46.29  | | | | | | GROUND_INST: instantiating (20) with e1, all_56_5, e3, e1,
% 239.68/46.29  | | | | | |              simplifying with (15), (32) gives:
% 239.68/46.29  | | | | | |   (44)  all_56_5 = e1
% 239.68/46.29  | | | | | | 
% 239.68/46.29  | | | | | | COMBINE_EQS: (42), (43) imply:
% 239.68/46.29  | | | | | |   (45)  all_4_1 = e3
% 239.68/46.29  | | | | | | 
% 239.68/46.29  | | | | | | REDUCE: (33), (44) imply:
% 239.68/46.29  | | | | | |   (46)  op(e1, e1) = e1
% 239.68/46.29  | | | | | | 
% 239.68/46.29  | | | | | | REF_CLOSE: (9), (18), (20), (46) are inconsistent by sub-proof #468.
% 239.68/46.29  | | | | | | 
% 239.68/46.29  | | | | | End of split
% 239.68/46.29  | | | | | 
% 239.68/46.29  | | | | End of split
% 239.68/46.29  | | | | 
% 239.68/46.29  | | | Case 2:
% 239.68/46.29  | | | | 
% 239.68/46.29  | | | |   (47)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 & $i(all_4_1)
% 239.68/46.29  | | | | 
% 239.68/46.29  | | | | ALPHA: (47) implies:
% 239.68/46.29  | | | |   (48)   ~ (all_4_1 = e3)
% 239.68/46.29  | | | |   (49)  op(e0, e2) = all_4_1
% 239.68/46.29  | | | | 
% 239.68/46.29  | | | | REF_CLOSE: (10), (14), (20), (48), (49) are inconsistent by sub-proof
% 239.68/46.29  | | | |            #211.
% 239.68/46.29  | | | | 
% 239.68/46.29  | | | End of split
% 239.68/46.29  | | | 
% 239.68/46.29  | | Case 2:
% 239.68/46.29  | | | 
% 239.68/46.29  | | |   (50)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.68/46.29  | | |         $i(all_56_7)
% 239.68/46.29  | | | 
% 239.68/46.29  | | | REF_CLOSE: (5), (11), (12), (16), (20), (21), (22), (50) are inconsistent
% 239.68/46.29  | | |            by sub-proof #44.
% 239.68/46.29  | | | 
% 239.68/46.29  | | End of split
% 239.68/46.29  | | 
% 239.68/46.29  | End of split
% 239.68/46.29  | 
% 239.68/46.29  End of proof
% 239.68/46.29  
% 239.68/46.29  Sub-proof #44 shows that the following formulas are inconsistent:
% 239.68/46.29  ----------------------------------------------------------------
% 239.68/46.29    (1)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.68/46.29         $i(all_56_7)
% 239.68/46.29    (2)  all_54_2 = e1 | all_54_2 = e0
% 239.68/46.29    (3)   ~ (all_52_8 = e1)
% 239.68/46.29    (4)  all_54_2 = all_52_8
% 239.68/46.29    (5)  op(e0, e3) = e0
% 239.68/46.29    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.68/46.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.68/46.29    (7)   ~ (all_52_8 = e2)
% 239.68/46.29    (8)  op(e0, e0) = e2
% 239.68/46.29  
% 239.68/46.29  Begin of proof
% 239.68/46.29  | 
% 239.68/46.29  | ALPHA: (1) implies:
% 239.68/46.29  |   (9)  op(e0, e3) = all_56_7
% 239.68/46.29  |   (10)  op(e0, all_56_7) = e0
% 239.68/46.29  | 
% 239.68/46.29  | BETA: splitting (2) gives:
% 239.68/46.29  | 
% 239.68/46.29  | Case 1:
% 239.68/46.29  | | 
% 239.68/46.29  | |   (11)  all_54_2 = e1
% 239.68/46.29  | | 
% 239.68/46.29  | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #1337.
% 239.68/46.29  | | 
% 239.68/46.29  | Case 2:
% 239.68/46.29  | | 
% 239.68/46.29  | |   (12)  all_54_2 = e0
% 239.68/46.29  | | 
% 239.68/46.29  | | COMBINE_EQS: (4), (12) imply:
% 239.68/46.29  | |   (13)  all_52_8 = e0
% 239.68/46.29  | | 
% 239.68/46.29  | | SIMP: (13) implies:
% 239.68/46.29  | |   (14)  all_52_8 = e0
% 239.68/46.29  | | 
% 239.68/46.29  | | REDUCE: (7), (14) imply:
% 239.68/46.29  | |   (15)   ~ (e2 = e0)
% 239.68/46.29  | | 
% 239.68/46.29  | | SIMP: (15) implies:
% 239.68/46.29  | |   (16)   ~ (e2 = e0)
% 239.68/46.29  | | 
% 239.68/46.29  | | GROUND_INST: instantiating (6) with e0, all_56_7, e3, e0, simplifying with
% 239.68/46.29  | |              (5), (9) gives:
% 239.68/46.29  | |   (17)  all_56_7 = e0
% 239.68/46.29  | | 
% 239.68/46.29  | | REDUCE: (10), (17) imply:
% 239.68/46.29  | |   (18)  op(e0, e0) = e0
% 239.68/46.29  | | 
% 239.68/46.29  | | REF_CLOSE: (6), (8), (16), (18) are inconsistent by sub-proof #2301.
% 239.68/46.29  | | 
% 239.68/46.29  | End of split
% 239.68/46.29  | 
% 239.68/46.29  End of proof
% 239.68/46.29  
% 239.68/46.29  Sub-proof #45 shows that the following formulas are inconsistent:
% 239.68/46.29  ----------------------------------------------------------------
% 239.68/46.29    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 239.68/46.29    (2)   ~ (e3 = e1)
% 239.68/46.29    (3)  op(e0, e1) = e0
% 239.68/46.29    (4)  op(e1, e1) = e3
% 239.68/46.29    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.68/46.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.68/46.29    (6)   ~ (e1 = e0)
% 239.68/46.29  
% 239.68/46.29  Begin of proof
% 239.68/46.29  | 
% 239.68/46.29  | BETA: splitting (1) gives:
% 239.68/46.29  | 
% 239.68/46.29  | Case 1:
% 239.68/46.29  | | 
% 239.68/46.29  | |   (7)  all_58_8 = e1 & op(e1, e1) = e1
% 239.68/46.29  | | 
% 239.68/46.29  | | ALPHA: (7) implies:
% 239.68/46.29  | |   (8)  op(e1, e1) = e1
% 239.68/46.29  | | 
% 239.68/46.29  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #468.
% 239.68/46.29  | | 
% 239.68/46.29  | Case 2:
% 239.68/46.29  | | 
% 239.68/46.29  | |   (9)  all_58_14 = e1 & op(e0, e1) = e1
% 239.68/46.29  | | 
% 239.68/46.29  | | ALPHA: (9) implies:
% 239.68/46.29  | |   (10)  op(e0, e1) = e1
% 239.68/46.29  | | 
% 239.68/46.29  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #2158.
% 239.68/46.29  | | 
% 239.68/46.29  | End of split
% 239.68/46.29  | 
% 239.68/46.29  End of proof
% 239.68/46.29  
% 239.68/46.29  Sub-proof #46 shows that the following formulas are inconsistent:
% 239.68/46.29  ----------------------------------------------------------------
% 239.68/46.29    (1)   ~ (e3 = e0)
% 239.68/46.29    (2)   ~ (e2 = e0)
% 239.68/46.29    (3)  op(e1, e0) = all_52_14
% 239.68/46.29    (4)   ~ (e3 = e1)
% 239.68/46.29    (5)  all_58_15 = e2
% 239.68/46.29    (6)   ~ (e3 = e2)
% 239.68/46.29    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.68/46.29         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.68/46.29    (8)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 239.68/46.29    (9)   ~ (all_52_14 = e3)
% 239.68/46.29    (10)  all_58_7 = e1
% 239.68/46.29    (11)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.68/46.29          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.68/46.29    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.68/46.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.68/46.29    (13)   ~ (e1 = e0)
% 239.68/46.29    (14)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.68/46.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.68/46.29    (15)   ~ (e2 = e1)
% 239.68/46.29  
% 239.68/46.29  Begin of proof
% 239.68/46.29  | 
% 239.68/46.29  | BETA: splitting (8) gives:
% 239.68/46.29  | 
% 239.68/46.29  | Case 1:
% 239.68/46.29  | | 
% 239.68/46.29  | |   (16)  all_58_11 = e1 & op(e1, e0) = e1
% 239.68/46.29  | | 
% 239.68/46.29  | | ALPHA: (16) implies:
% 239.68/46.29  | |   (17)  all_58_11 = e1
% 239.68/46.29  | |   (18)  op(e1, e0) = e1
% 239.68/46.29  | | 
% 239.68/46.29  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14),
% 239.68/46.29  | |            (15), (17), (18) are inconsistent by sub-proof #1417.
% 239.68/46.29  | | 
% 239.68/46.29  | Case 2:
% 239.68/46.29  | | 
% 239.68/46.29  | |   (19)  all_58_15 = e1 & op(e0, e0) = e1
% 239.68/46.29  | | 
% 239.68/46.29  | | ALPHA: (19) implies:
% 239.68/46.29  | |   (20)  all_58_15 = e1
% 239.68/46.29  | | 
% 239.68/46.29  | | REF_CLOSE: (5), (15), (20) are inconsistent by sub-proof #2231.
% 239.68/46.29  | | 
% 239.68/46.29  | End of split
% 239.68/46.29  | 
% 239.68/46.29  End of proof
% 239.68/46.29  
% 239.68/46.29  Sub-proof #47 shows that the following formulas are inconsistent:
% 239.68/46.29  ----------------------------------------------------------------
% 239.68/46.29    (1)  all_58_10 = e1 & op(e2, e0) = e1
% 239.68/46.29    (2)  all_58_10 = e3
% 239.68/46.29    (3)   ~ (e3 = e1)
% 239.68/46.29  
% 239.68/46.29  Begin of proof
% 239.68/46.29  | 
% 239.68/46.29  | ALPHA: (1) implies:
% 239.68/46.29  |   (4)  all_58_10 = e1
% 239.68/46.29  | 
% 239.68/46.29  | COMBINE_EQS: (2), (4) imply:
% 239.68/46.29  |   (5)  e3 = e1
% 239.68/46.29  | 
% 239.68/46.29  | REDUCE: (3), (5) imply:
% 239.68/46.29  |   (6)  $false
% 239.68/46.29  | 
% 239.68/46.29  | CLOSE: (6) is inconsistent.
% 239.68/46.29  | 
% 239.68/46.29  End of proof
% 239.68/46.29  
% 239.68/46.29  Sub-proof #48 shows that the following formulas are inconsistent:
% 239.68/46.29  ----------------------------------------------------------------
% 239.68/46.29    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 239.68/46.29           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 239.68/46.29             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 239.68/46.29           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.68/46.29             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.68/46.29           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.68/46.29           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.68/46.29    (2)  all_56_31 = e2
% 239.68/46.29    (3)   ~ (all_52_2 = e3)
% 239.68/46.29    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.68/46.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.68/46.29    (5)  op(e1, e3) = all_52_2
% 239.68/46.29    (6)  all_56_21 = e3
% 239.68/46.29  
% 239.68/46.29  Begin of proof
% 239.68/46.29  | 
% 239.68/46.29  | BETA: splitting (1) gives:
% 239.68/46.29  | 
% 239.68/46.29  | Case 1:
% 239.68/46.29  | | 
% 239.68/46.29  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.68/46.29  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.68/46.29  | |        op(e2, e3) = e3
% 239.68/46.29  | | 
% 239.68/46.29  | | ALPHA: (7) implies:
% 239.68/46.29  | |   (8)   ~ (all_56_31 = e2)
% 239.68/46.29  | | 
% 239.68/46.29  | | REDUCE: (2), (8) imply:
% 239.68/46.29  | |   (9)  $false
% 239.68/46.29  | | 
% 239.68/46.29  | | CLOSE: (9) is inconsistent.
% 239.68/46.29  | | 
% 239.68/46.29  | Case 2:
% 239.68/46.29  | | 
% 239.68/46.29  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 239.68/46.29  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 239.68/46.29  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.68/46.29  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.68/46.29  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.68/46.29  | | 
% 239.68/46.29  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #483.
% 239.68/46.29  | | 
% 239.68/46.29  | End of split
% 239.68/46.29  | 
% 239.68/46.29  End of proof
% 239.68/46.29  
% 239.68/46.29  Sub-proof #49 shows that the following formulas are inconsistent:
% 239.68/46.29  ----------------------------------------------------------------
% 239.68/46.29    (1)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.68/46.29    (2)   ~ (e3 = e0)
% 239.68/46.29    (3)  op(e0, e1) = all_52_11
% 239.68/46.29    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 239.68/46.29         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.68/46.29    (5)   ~ (e2 = e0)
% 239.68/46.29    (6)   ~ (all_52_11 = e2)
% 239.68/46.29    (7)  op(e1, e0) = all_52_14
% 239.68/46.29    (8)   ~ (e3 = e1)
% 239.68/46.29    (9)  all_58_7 = e2
% 239.68/46.29    (10)   ~ (e3 = e2)
% 239.68/46.29    (11)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.68/46.29          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.68/46.29    (12)   ~ (all_52_14 = e3)
% 239.68/46.29    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.68/46.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.68/46.29    (14)   ~ (e1 = e0)
% 239.68/46.29    (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.68/46.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.68/46.29    (16)   ~ (e2 = e1)
% 239.68/46.29  
% 239.68/46.29  Begin of proof
% 239.68/46.29  | 
% 239.68/46.29  | BETA: splitting (1) gives:
% 239.68/46.29  | 
% 239.68/46.29  | Case 1:
% 239.68/46.29  | | 
% 239.68/46.29  | |   (17)  all_58_8 = e2 & op(e1, e1) = e2
% 239.68/46.29  | | 
% 239.68/46.29  | | ALPHA: (17) implies:
% 239.68/46.29  | |   (18)  all_58_8 = e2
% 239.68/46.29  | |   (19)  op(e1, e1) = e2
% 239.68/46.29  | | 
% 239.68/46.29  | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 239.68/46.29  | |            (16), (18), (19) are inconsistent by sub-proof #1545.
% 239.68/46.29  | | 
% 239.68/46.29  | Case 2:
% 239.68/46.29  | | 
% 239.68/46.29  | |   (20)  all_58_14 = e2 & op(e0, e1) = e2
% 239.68/46.29  | | 
% 239.68/46.29  | | REF_CLOSE: (3), (6), (13), (20) are inconsistent by sub-proof #183.
% 239.68/46.29  | | 
% 239.68/46.29  | End of split
% 239.68/46.29  | 
% 239.68/46.29  End of proof
% 239.68/46.29  
% 239.68/46.29  Sub-proof #50 shows that the following formulas are inconsistent:
% 239.68/46.29  ----------------------------------------------------------------
% 239.68/46.29    (1)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.68/46.29    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.68/46.29         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.68/46.29    (3)   ~ (e3 = e0)
% 239.68/46.29    (4)   ~ (all_52_7 = e2)
% 239.68/46.29    (5)  all_56_11 = e1
% 239.68/46.29    (6)  op(e0, e1) = all_52_11
% 239.68/46.29    (7)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 239.68/46.29         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.68/46.29    (8)   ~ (all_52_8 = all_52_9)
% 239.68/46.29    (9)   ~ (all_52_11 = e2)
% 239.68/46.29    (10)  all_54_13 = all_52_7
% 239.68/46.29    (11)  op(e1, e2) = all_52_6
% 239.68/46.29    (12)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.68/46.29          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.68/46.30    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.68/46.30              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.68/46.30            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.68/46.30            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.68/46.30            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 239.68/46.30             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.68/46.30            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.68/46.30            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.68/46.30            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.68/46.30            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.68/46.30            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.68/46.30              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.68/46.30            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.68/46.30            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 239.68/46.30            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.68/46.30            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 239.68/46.30            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.68/46.30            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.68/46.30              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.68/46.30            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.68/46.30            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.68/46.30            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.68/46.30            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 239.68/46.30            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.68/46.30            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.68/46.30              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.68/46.30            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.68/46.30            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.68/46.30    (14)   ~ (all_52_7 = all_52_11)
% 239.68/46.30    (15)  op(e1, e0) = all_52_14
% 239.68/46.30    (16)   ~ (all_52_13 = e1)
% 239.68/46.30    (17)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.68/46.30    (18)  op(e0, e3) = all_52_3
% 239.68/46.30    (19)   ~ (e3 = e1)
% 239.68/46.30    (20)  all_58_7 = e2
% 239.68/46.30    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.68/46.30          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.68/46.30    (22)   ~ (all_52_2 = all_52_3)
% 239.68/46.30    (23)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.68/46.30          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.68/46.30    (24)   ~ (all_22_0 = e3)
% 239.68/46.30    (25)  all_54_2 = all_52_8
% 239.68/46.30    (26)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 239.68/46.30          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 239.68/46.30    (27)   ~ (all_52_3 = all_52_7)
% 239.68/46.30    (28)  all_58_15 = e2
% 239.68/46.30    (29)   ~ (all_52_11 = e3)
% 239.68/46.30    (30)  op(e3, e1) = all_52_8
% 239.68/46.30    (31)  op(e2, e1) = all_52_9
% 239.68/46.30    (32)   ~ (e3 = e2)
% 239.68/46.30    (33)   ~ (all_52_7 = e1)
% 239.68/46.30    (34)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.68/46.30    (35)   ~ (all_52_3 = all_52_11)
% 239.68/46.30    (36)  all_56_31 = e2
% 239.68/46.30    (37)  op(e2, e2) = e1
% 239.68/46.30    (38)  all_54_12 = all_52_3
% 239.68/46.30    (39)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.68/46.30    (40)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.68/46.30          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.68/46.30    (41)  op(e3, e0) = all_52_12
% 239.68/46.30    (42)   ~ (all_52_3 = e2)
% 239.68/46.30    (43)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.68/46.30          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.68/46.30    (44)   ~ (all_52_4 = all_52_12)
% 239.68/46.30    (45)  op(e2, e3) = all_52_1
% 239.68/46.30    (46)  op(e3, e3) = e2
% 239.68/46.30    (47)   ~ (all_52_14 = e3)
% 239.68/46.30    (48)  op(all_22_1, e2) = all_22_0
% 239.68/46.30    (49)  op(e1, e1) = e3
% 239.68/46.30    (50)   ~ (all_52_2 = e3)
% 239.68/46.30    (51)   ~ (all_52_6 = e3)
% 239.68/46.30    (52)  op(e1, e2) = e2
% 239.68/46.30    (53)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.68/46.30          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.68/46.30    (54)  op(e0, e2) = all_52_7
% 239.68/46.30    (55)  all_54_1 = all_52_4
% 239.68/46.30    (56)  op(e3, e2) = all_52_4
% 239.68/46.30    (57)   ~ (all_52_8 = all_52_11)
% 239.68/46.30    (58)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.68/46.30    (59)   ~ (all_52_9 = e3)
% 239.68/46.30    (60)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.68/46.30          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.68/46.30    (61)   ~ (all_52_4 = e2)
% 239.68/46.30    (62)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.68/46.30          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.68/46.30    (63)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.68/46.30            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.68/46.30    (64)  op(e1, e3) = all_52_2
% 239.68/46.30    (65)  all_56_21 = e3
% 239.68/46.30    (66)   ~ (all_52_4 = e1)
% 239.68/46.30    (67)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.68/46.30          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.68/46.30    (68)  op(e2, e1) = all_22_1
% 239.68/46.30    (69)   ~ (all_52_8 = e2)
% 239.68/46.30    (70)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.68/46.30          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.68/46.30    (71)  op(e0, e0) = e2
% 239.68/46.30    (72)  op(e2, e0) = all_52_13
% 239.68/46.30    (73)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.68/46.30          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 239.68/46.30            e1)
% 239.68/46.30    (74)   ~ (all_52_9 = e1)
% 239.68/46.30    (75)  all_54_14 = all_52_11
% 239.68/46.30    (76)   ~ (all_52_4 = all_52_8)
% 239.68/46.30    (77)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.68/46.30          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.68/46.30    (78)   ~ (e2 = e1)
% 239.68/46.30    (79)   ~ (all_52_1 = e1)
% 239.68/46.30    (80)   ~ (all_52_4 = all_52_7)
% 239.68/46.30    (81)   ~ (all_52_8 = e3)
% 239.68/46.30    (82)  op(e2, e1) = all_30_1
% 239.68/46.30  
% 239.68/46.30  Begin of proof
% 239.68/46.30  | 
% 239.68/46.30  | BETA: splitting (34) gives:
% 239.68/46.30  | 
% 239.68/46.30  | Case 1:
% 239.68/46.30  | | 
% 239.68/46.30  | |   (83)  all_54_14 = e3
% 239.68/46.30  | | 
% 239.68/46.30  | | REF_CLOSE: (29), (75), (83) are inconsistent by sub-proof #1796.
% 239.68/46.30  | | 
% 239.68/46.30  | Case 2:
% 239.68/46.30  | | 
% 239.68/46.30  | |   (84)   ~ (all_54_14 = e3)
% 239.68/46.30  | |   (85)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.68/46.30  | | 
% 239.68/46.30  | | BETA: splitting (39) gives:
% 239.68/46.30  | | 
% 239.68/46.30  | | Case 1:
% 239.68/46.30  | | | 
% 239.68/46.30  | | |   (86)  all_54_2 = e3
% 239.68/46.30  | | | 
% 239.68/46.30  | | | REF_CLOSE: (25), (81), (86) are inconsistent by sub-proof #1987.
% 239.68/46.30  | | | 
% 239.68/46.30  | | Case 2:
% 239.68/46.30  | | | 
% 239.68/46.30  | | |   (87)   ~ (all_54_2 = e3)
% 239.68/46.30  | | |   (88)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.68/46.30  | | | 
% 239.68/46.30  | | | BETA: splitting (17) gives:
% 239.68/46.30  | | | 
% 239.68/46.30  | | | Case 1:
% 239.68/46.30  | | | | 
% 239.68/46.30  | | | |   (89)  all_54_1 = e3
% 239.68/46.30  | | | | 
% 239.68/46.30  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (10), (11), (13), (15), (20), (23),
% 239.68/46.30  | | | |            (29), (30), (31), (33), (36), (41), (43), (44), (45), (46),
% 239.68/46.30  | | | |            (47), (50), (51), (54), (55), (56), (58), (60), (61), (63),
% 239.68/46.30  | | | |            (64), (65), (66), (70), (71), (74), (76), (78), (79), (80),
% 239.68/46.30  | | | |            (89) are inconsistent by sub-proof #54.
% 239.68/46.30  | | | | 
% 239.68/46.30  | | | Case 2:
% 239.68/46.30  | | | | 
% 239.68/46.30  | | | |   (90)   ~ (all_54_1 = e3)
% 239.68/46.30  | | | |   (91)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.68/46.30  | | | | 
% 239.68/46.30  | | | | REDUCE: (55), (90) imply:
% 239.68/46.30  | | | |   (92)   ~ (all_52_4 = e3)
% 239.68/46.30  | | | | 
% 239.68/46.30  | | | | BETA: splitting (91) gives:
% 239.68/46.30  | | | | 
% 239.68/46.30  | | | | Case 1:
% 239.68/46.30  | | | | | 
% 239.68/46.30  | | | | |   (93)  all_54_1 = e2
% 239.68/46.30  | | | | | 
% 239.68/46.30  | | | | | REF_CLOSE: (55), (61), (93) are inconsistent by sub-proof #1928.
% 239.68/46.30  | | | | | 
% 239.68/46.30  | | | | Case 2:
% 239.68/46.30  | | | | | 
% 239.68/46.30  | | | | |   (94)   ~ (all_54_1 = e2)
% 239.68/46.30  | | | | |   (95)  all_54_1 = e1 | all_54_1 = e0
% 239.68/46.30  | | | | | 
% 239.68/46.30  | | | | | BETA: splitting (23) gives:
% 239.68/46.30  | | | | | 
% 239.68/46.30  | | | | | Case 1:
% 239.68/46.30  | | | | | | 
% 239.68/46.30  | | | | | |   (96)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3,
% 239.68/46.30  | | | | | |             e2) = e3)
% 239.68/46.30  | | | | | | 
% 239.68/46.30  | | | | | | REF_CLOSE: (32), (46), (56), (63), (92), (96) are inconsistent by
% 239.68/46.30  | | | | | |            sub-proof #1959.
% 239.68/46.30  | | | | | | 
% 239.68/46.30  | | | | | Case 2:
% 239.68/46.30  | | | | | | 
% 239.68/46.30  | | | | | |   (97)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 239.68/46.30  | | | | | |             e0) = e3)
% 239.68/46.30  | | | | | | 
% 239.68/46.30  | | | | | | BETA: splitting (97) gives:
% 239.68/46.30  | | | | | | 
% 239.68/46.30  | | | | | | Case 1:
% 239.68/46.30  | | | | | | | 
% 239.68/46.30  | | | | | | |   (98)  all_58_4 = e3 & op(e3, e1) = e3
% 239.68/46.30  | | | | | | | 
% 239.68/46.30  | | | | | | | ALPHA: (98) implies:
% 239.68/46.30  | | | | | | |   (99)  op(e3, e1) = e3
% 239.68/46.30  | | | | | | | 
% 239.68/46.30  | | | | | | | REF_CLOSE: (30), (63), (81), (99) are inconsistent by sub-proof
% 239.68/46.30  | | | | | | |            #2260.
% 239.68/46.30  | | | | | | | 
% 239.68/46.30  | | | | | | Case 2:
% 239.68/46.30  | | | | | | | 
% 239.68/46.30  | | | | | | |   (100)  all_58_9 = e3 & op(e3, e0) = e3
% 239.68/46.30  | | | | | | | 
% 239.68/46.30  | | | | | | | ALPHA: (100) implies:
% 239.68/46.30  | | | | | | |   (101)  all_58_9 = e3
% 239.68/46.30  | | | | | | |   (102)  op(e3, e0) = e3
% 239.68/46.30  | | | | | | | 
% 239.68/46.30  | | | | | | | BETA: splitting (67) gives:
% 239.68/46.30  | | | | | | | 
% 239.68/46.30  | | | | | | | Case 1:
% 239.68/46.30  | | | | | | | | 
% 239.68/46.30  | | | | | | | |   (103)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 &
% 239.68/46.30  | | | | | | | |            op(e2, e2) = e3)
% 239.68/46.30  | | | | | | | | 
% 239.68/46.30  | | | | | | | | REF_CLOSE: (16), (19), (31), (45), (56), (63), (72), (74), (77),
% 239.68/46.30  | | | | | | | |            (79), (92), (103) are inconsistent by sub-proof #53.
% 239.68/46.30  | | | | | | | | 
% 239.68/46.30  | | | | | | | Case 2:
% 239.68/46.30  | | | | | | | | 
% 239.68/46.30  | | | | | | | |   (104)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 &
% 239.68/46.30  | | | | | | | |            op(e0, e2) = e3)
% 239.68/46.30  | | | | | | | | 
% 239.68/46.30  | | | | | | | | BETA: splitting (104) gives:
% 239.68/46.30  | | | | | | | | 
% 239.68/46.30  | | | | | | | | Case 1:
% 239.68/46.30  | | | | | | | | | 
% 239.68/46.30  | | | | | | | | |   (105)  all_58_7 = e3 & op(e1, e2) = e3
% 239.68/46.30  | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | ALPHA: (105) implies:
% 239.68/46.30  | | | | | | | | |   (106)  op(e1, e2) = e3
% 239.68/46.30  | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | REF_CLOSE: (32), (52), (63), (106) are inconsistent by
% 239.68/46.30  | | | | | | | | |            sub-proof #2207.
% 239.68/46.30  | | | | | | | | | 
% 239.68/46.30  | | | | | | | | Case 2:
% 239.68/46.30  | | | | | | | | | 
% 239.68/46.30  | | | | | | | | |   (107)  all_58_13 = e3 & op(e0, e2) = e3
% 239.68/46.30  | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | ALPHA: (107) implies:
% 239.68/46.30  | | | | | | | | |   (108)  op(e0, e2) = e3
% 239.68/46.30  | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | BETA: splitting (95) gives:
% 239.68/46.30  | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | Case 1:
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | |   (109)  all_54_1 = e1
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | REF_CLOSE: (55), (66), (109) are inconsistent by sub-proof
% 239.68/46.30  | | | | | | | | | |            #2051.
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | Case 2:
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | |   (110)  all_54_1 = e0
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | COMBINE_EQS: (55), (110) imply:
% 239.68/46.30  | | | | | | | | | |   (111)  all_52_4 = e0
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | SIMP: (111) implies:
% 239.68/46.30  | | | | | | | | | |   (112)  all_52_4 = e0
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | REDUCE: (80), (112) imply:
% 239.68/46.30  | | | | | | | | | |   (113)   ~ (all_52_7 = e0)
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | SIMP: (113) implies:
% 239.68/46.30  | | | | | | | | | |   (114)   ~ (all_52_7 = e0)
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | REDUCE: (76), (112) imply:
% 239.68/46.30  | | | | | | | | | |   (115)   ~ (all_52_8 = e0)
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | SIMP: (115) implies:
% 239.68/46.30  | | | | | | | | | |   (116)   ~ (all_52_8 = e0)
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | REDUCE: (92), (112) imply:
% 239.68/46.30  | | | | | | | | | |   (117)   ~ (e3 = e0)
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | REDUCE: (61), (112) imply:
% 239.68/46.30  | | | | | | | | | |   (118)   ~ (e2 = e0)
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | SIMP: (118) implies:
% 239.68/46.30  | | | | | | | | | |   (119)   ~ (e2 = e0)
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | REDUCE: (66), (112) imply:
% 239.68/46.30  | | | | | | | | | |   (120)   ~ (e1 = e0)
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | SIMP: (120) implies:
% 239.68/46.30  | | | | | | | | | |   (121)   ~ (e1 = e0)
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | REDUCE: (56), (112) imply:
% 239.68/46.30  | | | | | | | | | |   (122)  op(e3, e2) = e0
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | BETA: splitting (62) gives:
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | Case 1:
% 239.68/46.30  | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | |   (123)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 239.68/46.30  | | | | | | | | | | |            & op(e3, e2) = e1)
% 239.68/46.30  | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | REF_CLOSE: (46), (56), (63), (66), (78), (123) are
% 239.68/46.30  | | | | | | | | | | |            inconsistent by sub-proof #1340.
% 239.68/46.30  | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | Case 2:
% 239.68/46.30  | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | |   (124)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 239.68/46.30  | | | | | | | | | | |            & op(e3, e0) = e1)
% 239.68/46.30  | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | BETA: splitting (124) gives:
% 239.68/46.30  | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | Case 1:
% 239.68/46.30  | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | |   (125)  all_58_4 = e1 & op(e3, e1) = e1
% 239.68/46.30  | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | ALPHA: (125) implies:
% 239.68/46.30  | | | | | | | | | | | |   (126)  op(e3, e1) = e1
% 239.68/46.30  | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | BETA: splitting (21) gives:
% 239.68/46.30  | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | Case 1:
% 239.68/46.30  | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | |   (127)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 239.68/46.30  | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 239.68/46.30  | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | BETA: splitting (127) gives:
% 239.68/46.30  | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | Case 1:
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | |   (128)  all_58_4 = e0 & op(e3, e1) = e0
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | | ALPHA: (128) implies:
% 239.68/46.30  | | | | | | | | | | | | | |   (129)  op(e3, e1) = e0
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | | REF_CLOSE: (63), (121), (126), (129) are inconsistent by
% 239.68/46.30  | | | | | | | | | | | | | |            sub-proof #2089.
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | Case 2:
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | |   (130)  all_58_5 = e0 & op(e2, e1) = e0
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | | ALPHA: (130) implies:
% 239.68/46.30  | | | | | | | | | | | | | |   (131)  op(e2, e1) = e0
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | | REF_CLOSE: (24), (48), (63), (68), (82), (108), (131) are
% 239.68/46.30  | | | | | | | | | | | | | |            inconsistent by sub-proof #1861.
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | End of split
% 239.68/46.30  | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | Case 2:
% 239.68/46.30  | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | |   (132)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 239.68/46.30  | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 239.68/46.30  | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | BETA: splitting (132) gives:
% 239.68/46.30  | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | Case 1:
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | |   (133)  all_58_8 = e0 & op(e1, e1) = e0
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | | ALPHA: (133) implies:
% 239.68/46.30  | | | | | | | | | | | | | |   (134)  op(e1, e1) = e0
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (29), (30), (31), (53), (59), (63),
% 239.68/46.30  | | | | | | | | | | | | | |            (81), (134) are inconsistent by sub-proof #1010.
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | Case 2:
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | |   (135)  all_58_14 = e0 & op(e0, e1) = e0
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | | ALPHA: (135) implies:
% 239.68/46.30  | | | | | | | | | | | | | |   (136)  op(e0, e1) = e0
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 239.68/46.30  | | | | | | | | | | | | | |            (12), (13), (14), (18), (19), (20), (22), (23),
% 239.68/46.30  | | | | | | | | | | | | | |            (25), (26), (27), (28), (30), (31), (32), (33),
% 239.68/46.30  | | | | | | | | | | | | | |            (35), (37), (38), (40), (42), (46), (49), (50),
% 239.68/46.30  | | | | | | | | | | | | | |            (54), (56), (57), (58), (63), (64), (69), (71),
% 239.68/46.30  | | | | | | | | | | | | | |            (73), (75), (78), (80), (81), (85), (88), (92),
% 239.68/46.30  | | | | | | | | | | | | | |            (101), (108), (114), (116), (119), (121), (122),
% 239.68/46.30  | | | | | | | | | | | | | |            (136) are inconsistent by sub-proof #51.
% 239.68/46.30  | | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | | End of split
% 239.68/46.30  | | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | End of split
% 239.68/46.30  | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | Case 2:
% 239.68/46.30  | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | |   (137)  all_58_9 = e1 & op(e3, e0) = e1
% 239.68/46.30  | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | ALPHA: (137) implies:
% 239.68/46.30  | | | | | | | | | | | |   (138)  op(e3, e0) = e1
% 239.68/46.30  | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | | REF_CLOSE: (19), (63), (102), (138) are inconsistent by
% 239.68/46.30  | | | | | | | | | | | |            sub-proof #243.
% 239.68/46.30  | | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | | End of split
% 239.68/46.30  | | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | | End of split
% 239.68/46.30  | | | | | | | | | | 
% 239.68/46.30  | | | | | | | | | End of split
% 239.68/46.30  | | | | | | | | | 
% 239.68/46.30  | | | | | | | | End of split
% 239.68/46.30  | | | | | | | | 
% 239.68/46.30  | | | | | | | End of split
% 239.68/46.30  | | | | | | | 
% 239.68/46.30  | | | | | | End of split
% 239.68/46.30  | | | | | | 
% 239.68/46.30  | | | | | End of split
% 239.68/46.30  | | | | | 
% 239.68/46.30  | | | | End of split
% 239.68/46.30  | | | | 
% 239.68/46.30  | | | End of split
% 239.68/46.30  | | | 
% 239.68/46.30  | | End of split
% 239.68/46.30  | | 
% 239.68/46.30  | End of split
% 239.68/46.30  | 
% 239.68/46.30  End of proof
% 239.68/46.30  
% 239.68/46.30  Sub-proof #51 shows that the following formulas are inconsistent:
% 239.68/46.30  ----------------------------------------------------------------
% 239.68/46.30    (1)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.68/46.30    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.68/46.30         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.68/46.30    (3)   ~ (e3 = e0)
% 239.68/46.30    (4)   ~ (all_52_7 = e2)
% 239.68/46.30    (5)  all_56_11 = e1
% 239.68/46.31    (6)  op(e0, e1) = all_52_11
% 239.68/46.31    (7)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 239.68/46.31         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.68/46.31    (8)   ~ (all_52_8 = all_52_9)
% 239.68/46.31    (9)   ~ (e2 = e0)
% 239.68/46.31    (10)   ~ (all_52_11 = e2)
% 239.68/46.31    (11)  all_54_13 = all_52_7
% 239.68/46.31    (12)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.68/46.31          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.68/46.31    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.68/46.31              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.68/46.31            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.68/46.31            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.68/46.31            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 239.68/46.31             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.68/46.31            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.68/46.31            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.68/46.31            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.68/46.31            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.68/46.31            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.68/46.31              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.68/46.31            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.68/46.31            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 239.68/46.31            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.68/46.31            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 239.68/46.31            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.68/46.31            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.68/46.31              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.68/46.31            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.68/46.31            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.68/46.31            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.68/46.31            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 239.68/46.31            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.68/46.31            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.68/46.31              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.68/46.31            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.68/46.31            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.68/46.31    (14)   ~ (all_52_7 = all_52_11)
% 239.68/46.31    (15)   ~ (all_52_8 = e0)
% 239.68/46.31    (16)  op(e0, e3) = all_52_3
% 239.68/46.31    (17)   ~ (e3 = e1)
% 239.68/46.31    (18)  op(e0, e2) = e3
% 239.68/46.31    (19)  all_58_7 = e2
% 239.68/46.31    (20)   ~ (all_52_2 = all_52_3)
% 239.68/46.31    (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.68/46.31          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.68/46.31    (22)  all_54_2 = all_52_8
% 239.68/46.31    (23)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 239.68/46.31          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 239.68/46.31    (24)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.68/46.31    (25)   ~ (all_52_3 = all_52_7)
% 239.68/46.31    (26)  all_58_15 = e2
% 239.68/46.31    (27)  op(e3, e1) = all_52_8
% 239.68/46.31    (28)  op(e2, e1) = all_52_9
% 239.68/46.31    (29)   ~ (e3 = e2)
% 239.68/46.31    (30)   ~ (all_52_7 = e1)
% 239.68/46.31    (31)   ~ (all_52_3 = all_52_11)
% 239.68/46.31    (32)  op(e2, e2) = e1
% 239.68/46.31    (33)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.68/46.31    (34)  all_54_12 = all_52_3
% 239.68/46.31    (35)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.68/46.31          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.68/46.31    (36)  op(e0, e1) = e0
% 239.68/46.31    (37)   ~ (all_52_3 = e2)
% 239.68/46.31    (38)  all_58_9 = e3
% 239.68/46.31    (39)  op(e3, e2) = e0
% 239.68/46.31    (40)  op(e3, e3) = e2
% 239.68/46.31    (41)  op(e1, e1) = e3
% 239.68/46.31    (42)   ~ (all_52_2 = e3)
% 239.68/46.31    (43)  op(e0, e2) = all_52_7
% 239.68/46.31    (44)   ~ (all_52_4 = e3)
% 239.68/46.31    (45)  op(e3, e2) = all_52_4
% 239.68/46.31    (46)   ~ (all_52_8 = all_52_11)
% 239.68/46.31    (47)   ~ (all_52_7 = e0)
% 239.68/46.31    (48)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.68/46.31    (49)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.68/46.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.68/46.31    (50)  op(e1, e3) = all_52_2
% 239.68/46.31    (51)   ~ (e1 = e0)
% 239.68/46.31    (52)   ~ (all_52_8 = e2)
% 239.68/46.31    (53)  op(e0, e0) = e2
% 239.68/46.31    (54)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.68/46.31          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 239.68/46.31            e1)
% 239.68/46.31    (55)  all_54_14 = all_52_11
% 239.68/46.31    (56)   ~ (e2 = e1)
% 239.68/46.31    (57)   ~ (all_52_4 = all_52_7)
% 239.68/46.31    (58)   ~ (all_52_8 = e3)
% 239.68/46.31  
% 239.68/46.31  Begin of proof
% 239.68/46.31  | 
% 239.68/46.31  | BETA: splitting (54) gives:
% 239.68/46.31  | 
% 239.68/46.31  | Case 1:
% 239.68/46.31  | | 
% 239.68/46.31  | |   (59)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 239.68/46.31  | |           e1)
% 239.68/46.31  | | 
% 239.68/46.31  | | BETA: splitting (59) gives:
% 239.68/46.31  | | 
% 239.68/46.31  | | Case 1:
% 239.68/46.31  | | | 
% 239.68/46.31  | | |   (60)  all_58_12 = e1 & op(e0, e3) = e1
% 239.68/46.31  | | | 
% 239.68/46.31  | | | ALPHA: (60) implies:
% 239.68/46.31  | | |   (61)  all_58_12 = e1
% 239.68/46.31  | | |   (62)  op(e0, e3) = e1
% 239.68/46.31  | | | 
% 239.68/46.31  | | | BETA: splitting (23) gives:
% 239.68/46.31  | | | 
% 239.68/46.31  | | | Case 1:
% 239.68/46.31  | | | | 
% 239.68/46.31  | | | |   (63)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 239.68/46.31  | | | |           = e3)
% 239.68/46.31  | | | | 
% 239.68/46.31  | | | | BETA: splitting (63) gives:
% 239.68/46.31  | | | | 
% 239.68/46.31  | | | | Case 1:
% 239.68/46.31  | | | | | 
% 239.68/46.31  | | | | |   (64)  all_58_0 = e3 & op(e3, e3) = e3
% 239.68/46.31  | | | | | 
% 239.68/46.31  | | | | | ALPHA: (64) implies:
% 239.68/46.31  | | | | |   (65)  op(e3, e3) = e3
% 239.68/46.31  | | | | | 
% 239.68/46.31  | | | | | REF_CLOSE: (29), (40), (49), (65) are inconsistent by sub-proof #2194.
% 239.68/46.31  | | | | | 
% 239.68/46.31  | | | | Case 2:
% 239.68/46.31  | | | | | 
% 239.68/46.31  | | | | |   (66)  all_58_2 = e3 & op(e2, e3) = e3
% 239.68/46.31  | | | | | 
% 239.68/46.31  | | | | | ALPHA: (66) implies:
% 239.68/46.31  | | | | |   (67)  all_58_2 = e3
% 239.68/46.31  | | | | | 
% 239.68/46.31  | | | | | BETA: splitting (35) gives:
% 239.68/46.31  | | | | | 
% 239.68/46.31  | | | | | Case 1:
% 239.68/46.31  | | | | | | 
% 239.68/46.31  | | | | | |   (68)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 239.68/46.31  | | | | | |             e3) = e0)
% 239.68/46.31  | | | | | | 
% 239.68/46.31  | | | | | | BETA: splitting (68) gives:
% 239.68/46.31  | | | | | | 
% 239.68/46.31  | | | | | | Case 1:
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | |   (69)  all_58_0 = e0 & op(e3, e3) = e0
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | | ALPHA: (69) implies:
% 239.68/46.31  | | | | | | |   (70)  op(e3, e3) = e0
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | | REF_CLOSE: (9), (40), (49), (70) are inconsistent by sub-proof
% 239.68/46.31  | | | | | | |            #2188.
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | Case 2:
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | |   (71)  all_58_2 = e0 & op(e2, e3) = e0
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | | ALPHA: (71) implies:
% 239.68/46.31  | | | | | | |   (72)  all_58_2 = e0
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | | COMBINE_EQS: (67), (72) imply:
% 239.68/46.31  | | | | | | |   (73)  e3 = e0
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | | COMBINE_EQS: (38), (73) imply:
% 239.68/46.31  | | | | | | |   (74)  all_58_9 = e0
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | | REF_CLOSE: (3), (21), (27), (29), (40), (44), (45), (49), (58),
% 239.68/46.31  | | | | | | |            (74) are inconsistent by sub-proof #1956.
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | End of split
% 239.68/46.31  | | | | | | 
% 239.68/46.31  | | | | | Case 2:
% 239.68/46.31  | | | | | | 
% 239.68/46.31  | | | | | |   (75)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0,
% 239.68/46.31  | | | | | |             e3) = e0)
% 239.68/46.31  | | | | | | 
% 239.68/46.31  | | | | | | BETA: splitting (75) gives:
% 239.68/46.31  | | | | | | 
% 239.68/46.31  | | | | | | Case 1:
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | |   (76)  all_58_6 = e0 & op(e1, e3) = e0
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | | ALPHA: (76) implies:
% 239.68/46.31  | | | | | | |   (77)  op(e1, e3) = e0
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | | BETA: splitting (7) gives:
% 239.68/46.31  | | | | | | | 
% 239.68/46.31  | | | | | | | Case 1:
% 239.68/46.31  | | | | | | | | 
% 239.68/46.31  | | | | | | | |   (78)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 239.68/46.31  | | | | | | | |           op(e1, e2) = e1)
% 239.68/46.31  | | | | | | | | 
% 239.68/46.31  | | | | | | | | BETA: splitting (78) gives:
% 239.68/46.31  | | | | | | | | 
% 239.68/46.31  | | | | | | | | Case 1:
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | |   (79)  all_58_6 = e1 & op(e1, e3) = e1
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | ALPHA: (79) implies:
% 239.68/46.31  | | | | | | | | |   (80)  op(e1, e3) = e1
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | REF_CLOSE: (49), (51), (77), (80) are inconsistent by
% 239.68/46.31  | | | | | | | | |            sub-proof #449.
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | Case 2:
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | |   (81)  all_58_7 = e1 & op(e1, e2) = e1
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | ALPHA: (81) implies:
% 239.68/46.31  | | | | | | | | |   (82)  all_58_7 = e1
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | REF_CLOSE: (9), (12), (18), (29), (32), (39), (49), (56), (82)
% 239.68/46.31  | | | | | | | | |            are inconsistent by sub-proof #368.
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | End of split
% 239.68/46.31  | | | | | | | | 
% 239.68/46.31  | | | | | | | Case 2:
% 239.68/46.31  | | | | | | | | 
% 239.68/46.31  | | | | | | | |   (83)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 239.68/46.31  | | | | | | | |           op(e1, e0) = e1)
% 239.68/46.31  | | | | | | | | 
% 239.68/46.31  | | | | | | | | BETA: splitting (83) gives:
% 239.68/46.31  | | | | | | | | 
% 239.68/46.31  | | | | | | | | Case 1:
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | |   (84)  all_58_8 = e1 & op(e1, e1) = e1
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | ALPHA: (84) implies:
% 239.68/46.31  | | | | | | | | |   (85)  op(e1, e1) = e1
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | REF_CLOSE: (17), (41), (49), (85) are inconsistent by
% 239.68/46.31  | | | | | | | | |            sub-proof #468.
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | Case 2:
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | |   (86)  all_58_11 = e1 & op(e1, e0) = e1
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | ALPHA: (86) implies:
% 239.68/46.31  | | | | | | | | |   (87)  op(e1, e0) = e1
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | BETA: splitting (48) gives:
% 239.68/46.31  | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | Case 1:
% 239.68/46.31  | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | |   (88)  all_54_13 = e3
% 239.68/46.31  | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | COMBINE_EQS: (11), (88) imply:
% 239.68/46.31  | | | | | | | | | |   (89)  all_52_7 = e3
% 239.68/46.31  | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | SIMP: (89) implies:
% 239.68/46.31  | | | | | | | | | |   (90)  all_52_7 = e3
% 239.68/46.31  | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | REDUCE: (25), (90) imply:
% 239.68/46.31  | | | | | | | | | |   (91)   ~ (all_52_3 = e3)
% 239.68/46.31  | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | REDUCE: (14), (90) imply:
% 239.68/46.31  | | | | | | | | | |   (92)   ~ (all_52_11 = e3)
% 239.68/46.31  | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | SIMP: (92) implies:
% 239.68/46.31  | | | | | | | | | |   (93)   ~ (all_52_11 = e3)
% 239.68/46.31  | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | BETA: splitting (33) gives:
% 239.68/46.31  | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | Case 1:
% 239.68/46.31  | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | |   (94)  all_54_2 = e2
% 239.68/46.31  | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | REF_CLOSE: (22), (52), (94) are inconsistent by sub-proof
% 239.68/46.31  | | | | | | | | | | |            #1986.
% 239.68/46.31  | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | Case 2:
% 239.68/46.31  | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | |   (95)  all_54_2 = e1 | all_54_2 = e0
% 239.68/46.31  | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | BETA: splitting (95) gives:
% 239.68/46.31  | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | Case 1:
% 239.68/46.31  | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | |   (96)  all_54_2 = e1
% 239.68/46.31  | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | COMBINE_EQS: (22), (96) imply:
% 239.68/46.31  | | | | | | | | | | | |   (97)  all_52_8 = e1
% 239.68/46.31  | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | SIMP: (97) implies:
% 239.68/46.31  | | | | | | | | | | | |   (98)  all_52_8 = e1
% 239.68/46.31  | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | REDUCE: (46), (98) imply:
% 239.68/46.31  | | | | | | | | | | | |   (99)   ~ (all_52_11 = e1)
% 239.68/46.31  | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | SIMP: (99) implies:
% 239.68/46.31  | | | | | | | | | | | |   (100)   ~ (all_52_11 = e1)
% 239.68/46.31  | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | BETA: splitting (24) gives:
% 239.68/46.31  | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | Case 1:
% 239.68/46.31  | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | |   (101)  all_54_14 = e2
% 239.68/46.31  | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | REF_CLOSE: (10), (55), (101) are inconsistent by sub-proof
% 239.68/46.31  | | | | | | | | | | | | |            #1856.
% 239.68/46.31  | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | Case 2:
% 239.68/46.31  | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | |   (102)   ~ (all_54_14 = e2)
% 239.68/46.31  | | | | | | | | | | | | |   (103)  all_54_14 = e1 | all_54_14 = e0
% 239.68/46.31  | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | BETA: splitting (103) gives:
% 239.68/46.31  | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | Case 1:
% 239.68/46.31  | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | |   (104)  all_54_14 = e1
% 239.68/46.31  | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | REF_CLOSE: (55), (100), (104) are inconsistent by sub-proof
% 239.68/46.31  | | | | | | | | | | | | | |            #1937.
% 239.68/46.31  | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | Case 2:
% 239.68/46.31  | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | |   (105)  all_54_14 = e0
% 239.68/46.31  | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | COMBINE_EQS: (55), (105) imply:
% 239.68/46.31  | | | | | | | | | | | | | |   (106)  all_52_11 = e0
% 239.68/46.31  | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | SIMP: (106) implies:
% 239.68/46.31  | | | | | | | | | | | | | |   (107)  all_52_11 = e0
% 239.68/46.31  | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | REDUCE: (31), (107) imply:
% 239.68/46.31  | | | | | | | | | | | | | |   (108)   ~ (all_52_3 = e0)
% 239.68/46.31  | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | REDUCE: (93), (107) imply:
% 239.68/46.31  | | | | | | | | | | | | | |   (109)   ~ (e3 = e0)
% 239.68/46.31  | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | REDUCE: (10), (107) imply:
% 239.68/46.31  | | | | | | | | | | | | | |   (110)   ~ (e2 = e0)
% 239.68/46.31  | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 239.68/46.31  | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | Case 1:
% 239.68/46.31  | | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | |   (111)  all_54_12 = e3
% 239.68/46.31  | | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | | REF_CLOSE: (34), (91), (111) are inconsistent by sub-proof
% 239.68/46.31  | | | | | | | | | | | | | | |            #2266.
% 239.68/46.31  | | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | Case 2:
% 239.68/46.31  | | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | |   (112)   ~ (all_54_12 = e3)
% 239.68/46.31  | | | | | | | | | | | | | | |   (113)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.68/46.31  | | | | | | | | | | | | | | | 
% 239.68/46.31  | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 239.74/46.31  | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | Case 1:
% 239.74/46.31  | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | |   (114)  all_54_12 = e2
% 239.74/46.31  | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | REF_CLOSE: (34), (37), (114) are inconsistent by sub-proof
% 239.74/46.31  | | | | | | | | | | | | | | | |            #2264.
% 239.74/46.31  | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | Case 2:
% 239.74/46.31  | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | |   (115)  all_54_12 = e1 | all_54_12 = e0
% 239.74/46.31  | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 239.74/46.31  | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | Case 1:
% 239.74/46.31  | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | |   (116)  all_54_12 = e1
% 239.74/46.31  | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (116) imply:
% 239.74/46.31  | | | | | | | | | | | | | | | | |   (117)  all_52_3 = e1
% 239.74/46.31  | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | SIMP: (117) implies:
% 239.74/46.31  | | | | | | | | | | | | | | | | |   (118)  all_52_3 = e1
% 239.74/46.31  | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | REDUCE: (20), (118) imply:
% 239.74/46.31  | | | | | | | | | | | | | | | | |   (119)   ~ (all_52_2 = e1)
% 239.74/46.31  | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | REDUCE: (91), (118) imply:
% 239.74/46.31  | | | | | | | | | | | | | | | | |   (120)   ~ (e3 = e1)
% 239.74/46.31  | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 239.74/46.31  | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | Case 1:
% 239.74/46.31  | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | |   (121)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.74/46.31  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.74/46.31  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.74/46.31  | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.74/46.31  | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.74/46.31  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 239.74/46.31  | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 239.74/46.31  | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | Case 1:
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | |   (122)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.74/46.31  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.74/46.31  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.74/46.31  | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.74/46.31  | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.74/46.31  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.74/46.31  | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.74/46.31  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.74/46.31  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.74/46.31  | | | | | | | | | | | | | | | | | | |            = e3)
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |   (123)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |          e3
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |   (124)  op(e3, e2) = e3
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11), (30), (45), (47), (48), (49), (57),
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |            (124) are inconsistent by sub-proof #456.
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |   (125)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (42), (49), (50), (125) are
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2025.
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | End of split
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.31  | | | | | | | | | | | | | | | | | | Case 2:
% 239.74/46.31  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |   (126)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            = e0)
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (49), (50), (91), (108), (119), (126) are
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #68.
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | Case 2:
% 239.74/46.32  | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | |   (127)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.74/46.32  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 239.74/46.32  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 239.74/46.32  | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 239.74/46.32  | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | Case 1:
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |   (128)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            = e2)
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | Case 1:
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |   (129)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |   (130)   ~ (all_56_11 = e1)
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (130) imply:
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |   (131)  $false
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | CLOSE: (131) is inconsistent.
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | Case 2:
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |   (132)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15), (18), (22), (28), (29), (49), (95),
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | |            (132) are inconsistent by sub-proof #52.
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | Case 2:
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |   (133)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            = e0)
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (17), (29), (49), (51), (53), (61),
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            (87), (93), (100), (133) are inconsistent by
% 239.74/46.32  | | | | | | | | | | | | | | | | | | |            sub-proof #65.
% 239.74/46.32  | | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | Case 2:
% 239.74/46.32  | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | |   (134)  all_54_12 = e0
% 239.74/46.32  | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (108), (134) are inconsistent by sub-proof
% 239.74/46.32  | | | | | | | | | | | | | | | | |            #2068.
% 239.74/46.32  | | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | Case 2:
% 239.74/46.32  | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | |   (135)  all_54_2 = e0
% 239.74/46.32  | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | | REF_CLOSE: (15), (22), (135) are inconsistent by sub-proof
% 239.74/46.32  | | | | | | | | | | | |            #1643.
% 239.74/46.32  | | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | Case 2:
% 239.74/46.32  | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | |   (136)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.74/46.32  | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | | REF_CLOSE: (4), (11), (30), (47), (136) are inconsistent by
% 239.74/46.32  | | | | | | | | | |            sub-proof #1648.
% 239.74/46.32  | | | | | | | | | | 
% 239.74/46.32  | | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | | 
% 239.74/46.32  | | | | | | | | End of split
% 239.74/46.32  | | | | | | | | 
% 239.74/46.32  | | | | | | | End of split
% 239.74/46.32  | | | | | | | 
% 239.74/46.32  | | | | | | Case 2:
% 239.74/46.32  | | | | | | | 
% 239.74/46.32  | | | | | | |   (137)  all_58_12 = e0 & op(e0, e3) = e0
% 239.74/46.32  | | | | | | | 
% 239.74/46.32  | | | | | | | ALPHA: (137) implies:
% 239.74/46.32  | | | | | | |   (138)  op(e0, e3) = e0
% 239.74/46.32  | | | | | | | 
% 239.74/46.32  | | | | | | | REF_CLOSE: (49), (51), (62), (138) are inconsistent by sub-proof
% 239.74/46.32  | | | | | | |            #207.
% 239.74/46.32  | | | | | | | 
% 239.74/46.32  | | | | | | End of split
% 239.74/46.32  | | | | | | 
% 239.74/46.32  | | | | | End of split
% 239.74/46.32  | | | | | 
% 239.74/46.32  | | | | End of split
% 239.74/46.32  | | | | 
% 239.74/46.32  | | | Case 2:
% 239.74/46.32  | | | | 
% 239.74/46.32  | | | |   (139)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0,
% 239.74/46.32  | | | |              e3) = e3)
% 239.74/46.32  | | | | 
% 239.74/46.32  | | | | BETA: splitting (139) gives:
% 239.74/46.32  | | | | 
% 239.74/46.32  | | | | Case 1:
% 239.74/46.32  | | | | | 
% 239.74/46.32  | | | | |   (140)  all_58_6 = e3 & op(e1, e3) = e3
% 239.74/46.32  | | | | | 
% 239.74/46.32  | | | | | ALPHA: (140) implies:
% 239.74/46.32  | | | | |   (141)  op(e1, e3) = e3
% 239.74/46.32  | | | | | 
% 239.74/46.32  | | | | | REF_CLOSE: (42), (49), (50), (141) are inconsistent by sub-proof
% 239.74/46.32  | | | | |            #2335.
% 239.74/46.32  | | | | | 
% 239.74/46.32  | | | | Case 2:
% 239.74/46.32  | | | | | 
% 239.74/46.32  | | | | |   (142)  all_58_12 = e3 & op(e0, e3) = e3
% 239.74/46.32  | | | | | 
% 239.74/46.32  | | | | | ALPHA: (142) implies:
% 239.74/46.32  | | | | |   (143)  all_58_12 = e3
% 239.74/46.32  | | | | | 
% 239.74/46.32  | | | | | REF_CLOSE: (17), (61), (143) are inconsistent by sub-proof #1542.
% 239.74/46.32  | | | | | 
% 239.74/46.32  | | | | End of split
% 239.74/46.32  | | | | 
% 239.74/46.32  | | | End of split
% 239.74/46.32  | | | 
% 239.74/46.32  | | Case 2:
% 239.74/46.32  | | | 
% 239.74/46.32  | | |   (144)  all_58_13 = e1 & op(e0, e2) = e1
% 239.74/46.32  | | | 
% 239.74/46.32  | | | REF_CLOSE: (30), (43), (49), (144) are inconsistent by sub-proof #2275.
% 239.74/46.32  | | | 
% 239.74/46.32  | | End of split
% 239.74/46.32  | | 
% 239.74/46.32  | Case 2:
% 239.74/46.32  | | 
% 239.74/46.32  | |   (145)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 239.74/46.32  | |            e1)
% 239.74/46.32  | | 
% 239.74/46.32  | | BETA: splitting (145) gives:
% 239.74/46.32  | | 
% 239.74/46.32  | | Case 1:
% 239.74/46.32  | | | 
% 239.74/46.32  | | |   (146)  all_58_14 = e1 & op(e0, e1) = e1
% 239.74/46.32  | | | 
% 239.74/46.32  | | | ALPHA: (146) implies:
% 239.74/46.32  | | |   (147)  op(e0, e1) = e1
% 239.74/46.32  | | | 
% 239.74/46.32  | | | REF_CLOSE: (36), (49), (51), (147) are inconsistent by sub-proof #2158.
% 239.74/46.32  | | | 
% 239.74/46.32  | | Case 2:
% 239.74/46.32  | | | 
% 239.74/46.32  | | |   (148)  all_58_15 = e1 & op(e0, e0) = e1
% 239.74/46.32  | | | 
% 239.74/46.32  | | | ALPHA: (148) implies:
% 239.74/46.32  | | |   (149)  all_58_15 = e1
% 239.74/46.32  | | | 
% 239.74/46.32  | | | COMBINE_EQS: (26), (149) imply:
% 239.74/46.32  | | |   (150)  e2 = e1
% 239.74/46.32  | | | 
% 239.74/46.32  | | | COMBINE_EQS: (19), (150) imply:
% 239.74/46.32  | | |   (151)  all_58_7 = e1
% 239.74/46.32  | | | 
% 239.74/46.32  | | | REF_CLOSE: (9), (12), (18), (29), (32), (39), (49), (56), (151) are
% 239.74/46.32  | | |            inconsistent by sub-proof #368.
% 239.74/46.32  | | | 
% 239.74/46.32  | | End of split
% 239.74/46.32  | | 
% 239.74/46.32  | End of split
% 239.74/46.32  | 
% 239.74/46.32  End of proof
% 239.74/46.32  
% 239.74/46.32  Sub-proof #52 shows that the following formulas are inconsistent:
% 239.74/46.32  ----------------------------------------------------------------
% 239.74/46.32    (1)  all_54_2 = e1 | all_54_2 = e0
% 239.74/46.32    (2)   ~ (all_52_8 = all_52_9)
% 239.74/46.32    (3)   ~ (all_52_8 = e0)
% 239.74/46.32    (4)  op(e0, e2) = e3
% 239.74/46.32    (5)  all_54_2 = all_52_8
% 239.74/46.32    (6)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.74/46.32             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 239.74/46.32           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 239.74/46.32             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 239.74/46.32           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.74/46.32    (7)  op(e2, e1) = all_52_9
% 239.74/46.32    (8)   ~ (e3 = e2)
% 239.74/46.32    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.74/46.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.74/46.32  
% 239.74/46.32  Begin of proof
% 239.74/46.32  | 
% 239.74/46.32  | BETA: splitting (6) gives:
% 239.74/46.32  | 
% 239.74/46.32  | Case 1:
% 239.74/46.32  | | 
% 239.74/46.32  | |   (10)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 239.74/46.32  | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) =
% 239.74/46.32  | |         e1 & op(e1, e2) = e1
% 239.74/46.32  | | 
% 239.74/46.32  | | ALPHA: (10) implies:
% 239.74/46.32  | |   (11)  op(e2, e1) = e1
% 239.74/46.32  | | 
% 239.74/46.32  | | REF_CLOSE: (1), (2), (3), (5), (7), (9), (11) are inconsistent by sub-proof
% 239.74/46.32  | |            #435.
% 239.74/46.32  | | 
% 239.74/46.32  | Case 2:
% 239.74/46.32  | | 
% 239.74/46.32  | |   (12)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 239.74/46.32  | |           = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) =
% 239.74/46.32  | |         e2 & op(e0, e2) = e2
% 239.74/46.32  | | 
% 239.74/46.32  | | ALPHA: (12) implies:
% 239.74/46.32  | |   (13)  op(e0, e2) = e2
% 239.74/46.32  | | 
% 239.74/46.32  | | REF_CLOSE: (4), (8), (9), (13) are inconsistent by sub-proof #2254.
% 239.74/46.32  | | 
% 239.74/46.32  | End of split
% 239.74/46.32  | 
% 239.74/46.32  End of proof
% 239.74/46.32  
% 239.74/46.32  Sub-proof #53 shows that the following formulas are inconsistent:
% 239.74/46.32  ----------------------------------------------------------------
% 239.74/46.32    (1)   ~ (all_52_13 = e1)
% 239.74/46.32    (2)   ~ (e3 = e1)
% 239.74/46.32    (3)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 239.74/46.32    (4)  op(e2, e1) = all_52_9
% 239.74/46.32    (5)  op(e2, e3) = all_52_1
% 239.74/46.32    (6)   ~ (all_52_4 = e3)
% 239.74/46.32    (7)  op(e3, e2) = all_52_4
% 239.74/46.32    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.74/46.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.74/46.32    (9)  op(e2, e0) = all_52_13
% 239.74/46.32    (10)   ~ (all_52_9 = e1)
% 239.74/46.32    (11)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.74/46.32          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.74/46.32    (12)   ~ (all_52_1 = e1)
% 239.74/46.32  
% 239.74/46.32  Begin of proof
% 239.74/46.32  | 
% 239.74/46.32  | BETA: splitting (3) gives:
% 239.74/46.32  | 
% 239.74/46.32  | Case 1:
% 239.74/46.32  | | 
% 239.74/46.32  | |   (13)  all_58_1 = e3 & op(e3, e2) = e3
% 239.74/46.32  | | 
% 239.74/46.32  | | ALPHA: (13) implies:
% 239.74/46.32  | |   (14)  op(e3, e2) = e3
% 239.74/46.32  | | 
% 239.74/46.32  | | REF_CLOSE: (6), (7), (8), (14) are inconsistent by sub-proof #2192.
% 239.74/46.32  | | 
% 239.74/46.32  | Case 2:
% 239.74/46.32  | | 
% 239.74/46.32  | |   (15)  all_58_3 = e3 & op(e2, e2) = e3
% 239.74/46.32  | | 
% 239.74/46.32  | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (11), (12), (15) are
% 239.74/46.32  | |            inconsistent by sub-proof #2196.
% 239.74/46.32  | | 
% 239.74/46.32  | End of split
% 239.74/46.32  | 
% 239.74/46.32  End of proof
% 239.74/46.32  
% 239.74/46.32  Sub-proof #54 shows that the following formulas are inconsistent:
% 239.74/46.32  ----------------------------------------------------------------
% 239.74/46.32    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.74/46.32         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.74/46.32    (2)   ~ (e3 = e0)
% 239.74/46.32    (3)   ~ (all_52_7 = e2)
% 239.74/46.32    (4)  all_56_11 = e1
% 239.74/46.32    (5)  op(e0, e1) = all_52_11
% 239.74/46.32    (6)  all_54_13 = all_52_7
% 239.74/46.32    (7)  op(e1, e2) = all_52_6
% 239.74/46.32    (8)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 239.74/46.32           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 239.74/46.32             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 239.74/46.32           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.74/46.32             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.74/46.32           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.74/46.32           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.74/46.32           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.74/46.32           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 239.74/46.32           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.32           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.74/46.32             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.74/46.32           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.74/46.32           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 239.74/46.32           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.74/46.32           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 239.74/46.32           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.74/46.32           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.74/46.32             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.74/46.32           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.74/46.32           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 239.74/46.32           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.74/46.32           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 239.74/46.32           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.32           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.74/46.32             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.74/46.32           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.74/46.32           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.74/46.32    (9)  op(e1, e0) = all_52_14
% 239.74/46.32    (10)  all_58_7 = e2
% 239.74/46.32    (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.74/46.32          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.74/46.32    (12)   ~ (all_52_11 = e3)
% 239.74/46.32    (13)  op(e3, e1) = all_52_8
% 239.74/46.32    (14)  op(e2, e1) = all_52_9
% 239.74/46.32    (15)   ~ (all_52_7 = e1)
% 239.74/46.32    (16)  all_56_31 = e2
% 239.74/46.32    (17)  op(e3, e0) = all_52_12
% 239.74/46.32    (18)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.74/46.32          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.74/46.32    (19)   ~ (all_52_4 = all_52_12)
% 239.74/46.32    (20)  op(e2, e3) = all_52_1
% 239.74/46.32    (21)  op(e3, e3) = e2
% 239.74/46.32    (22)   ~ (all_52_14 = e3)
% 239.74/46.32    (23)   ~ (all_52_2 = e3)
% 239.74/46.32    (24)   ~ (all_52_6 = e3)
% 239.74/46.32    (25)  op(e0, e2) = all_52_7
% 239.74/46.32    (26)  all_54_1 = all_52_4
% 239.74/46.32    (27)  op(e3, e2) = all_52_4
% 239.74/46.32    (28)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.74/46.32    (29)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.74/46.32          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.74/46.32    (30)   ~ (all_52_4 = e2)
% 239.74/46.32    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.74/46.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.74/46.32    (32)  op(e1, e3) = all_52_2
% 239.74/46.32    (33)  all_56_21 = e3
% 239.74/46.32    (34)   ~ (all_52_4 = e1)
% 239.74/46.32    (35)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.74/46.32          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.74/46.32    (36)  op(e0, e0) = e2
% 239.74/46.32    (37)  all_54_1 = e3
% 239.74/46.32    (38)   ~ (all_52_9 = e1)
% 239.74/46.32    (39)   ~ (all_52_4 = all_52_8)
% 239.74/46.32    (40)   ~ (e2 = e1)
% 239.74/46.32    (41)   ~ (all_52_1 = e1)
% 239.74/46.32    (42)   ~ (all_52_4 = all_52_7)
% 239.74/46.32  
% 239.74/46.32  Begin of proof
% 239.74/46.32  | 
% 239.74/46.32  | COMBINE_EQS: (26), (37) imply:
% 239.74/46.32  |   (43)  all_52_4 = e3
% 239.74/46.32  | 
% 239.74/46.32  | SIMP: (43) implies:
% 239.74/46.32  |   (44)  all_52_4 = e3
% 239.74/46.32  | 
% 239.74/46.32  | REDUCE: (42), (44) imply:
% 239.74/46.32  |   (45)   ~ (all_52_7 = e3)
% 239.74/46.32  | 
% 239.74/46.32  | SIMP: (45) implies:
% 239.74/46.32  |   (46)   ~ (all_52_7 = e3)
% 239.74/46.32  | 
% 239.74/46.32  | REDUCE: (39), (44) imply:
% 239.74/46.32  |   (47)   ~ (all_52_8 = e3)
% 239.74/46.32  | 
% 239.74/46.32  | SIMP: (47) implies:
% 239.74/46.32  |   (48)   ~ (all_52_8 = e3)
% 239.74/46.32  | 
% 239.74/46.32  | REDUCE: (19), (44) imply:
% 239.74/46.32  |   (49)   ~ (all_52_12 = e3)
% 239.74/46.32  | 
% 239.74/46.32  | SIMP: (49) implies:
% 239.74/46.32  |   (50)   ~ (all_52_12 = e3)
% 239.74/46.32  | 
% 239.74/46.32  | REDUCE: (30), (44) imply:
% 239.74/46.33  |   (51)   ~ (e3 = e2)
% 239.74/46.33  | 
% 239.74/46.33  | REDUCE: (34), (44) imply:
% 239.74/46.33  |   (52)   ~ (e3 = e1)
% 239.74/46.33  | 
% 239.74/46.33  | REDUCE: (27), (44) imply:
% 239.74/46.33  |   (53)  op(e3, e2) = e3
% 239.74/46.33  | 
% 239.74/46.33  | BETA: splitting (1) gives:
% 239.74/46.33  | 
% 239.74/46.33  | Case 1:
% 239.74/46.33  | | 
% 239.74/46.33  | |   (54)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 239.74/46.33  | |           e3)
% 239.74/46.33  | | 
% 239.74/46.33  | | BETA: splitting (54) gives:
% 239.74/46.33  | | 
% 239.74/46.33  | | Case 1:
% 239.74/46.33  | | | 
% 239.74/46.33  | | |   (55)  all_58_12 = e3 & op(e0, e3) = e3
% 239.74/46.33  | | | 
% 239.74/46.33  | | | ALPHA: (55) implies:
% 239.74/46.33  | | |   (56)  all_58_12 = e3
% 239.74/46.33  | | |   (57)  op(e0, e3) = e3
% 239.74/46.33  | | | 
% 239.74/46.33  | | | BETA: splitting (8) gives:
% 239.74/46.33  | | | 
% 239.74/46.33  | | | Case 1:
% 239.74/46.33  | | | | 
% 239.74/46.33  | | | |   (58)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 239.74/46.33  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.74/46.33  | | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9
% 239.74/46.33  | | | |           = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.74/46.33  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 239.74/46.33  | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.74/46.33  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 239.74/46.33  | | | |           ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 239.74/46.33  | | | |         (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 239.74/46.33  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.74/46.33  | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 239.74/46.33  | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 239.74/46.33  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 239.74/46.33  | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.74/46.33  | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) & 
% 239.74/46.33  | | | |           ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.74/46.33  | | | | 
% 239.74/46.33  | | | | BETA: splitting (58) gives:
% 239.74/46.33  | | | | 
% 239.74/46.33  | | | | Case 1:
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | |   (59)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 239.74/46.33  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 239.74/46.33  | | | | |           & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 &
% 239.74/46.33  | | | | |           all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.74/46.33  | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 239.74/46.33  | | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.74/46.33  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 239.74/46.33  | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | | REF_CLOSE: (16), (23), (31), (32), (51), (53), (59) are inconsistent
% 239.74/46.33  | | | | |            by sub-proof #208.
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | Case 2:
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | |   (60)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 239.74/46.33  | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 239.74/46.33  | | | | |           & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 239.74/46.33  | | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.74/46.33  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 239.74/46.33  | | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.74/46.33  | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 239.74/46.33  | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | | BETA: splitting (60) gives:
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | | Case 1:
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | |   (61)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 239.74/46.33  | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 239.74/46.33  | | | | | |         & op(e3, e1) = e1 & op(e1, e3) = e1
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | ALPHA: (61) implies:
% 239.74/46.33  | | | | | |   (62)   ~ (all_56_21 = e3)
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | REDUCE: (33), (62) imply:
% 239.74/46.33  | | | | | |   (63)  $false
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | CLOSE: (63) is inconsistent.
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | Case 2:
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | |   (64)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.33  | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 239.74/46.33  | | | | | |             e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 239.74/46.33  | | | | | |           e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 239.74/46.33  | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.74/46.33  | | | | | |             e0) = e0 & op(e0, e3) = e0)
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | BETA: splitting (64) gives:
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | Case 1:
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | |   (65)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.33  | | | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 239.74/46.33  | | | | | | |           e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | ALPHA: (65) implies:
% 239.74/46.33  | | | | | | |   (66)  op(e3, e0) = e3
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | REF_CLOSE: (17), (31), (50), (66) are inconsistent by sub-proof
% 239.74/46.33  | | | | | | |            #2179.
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | Case 2:
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | |   (67)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.74/46.33  | | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 239.74/46.33  | | | | | | |           e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | ALPHA: (67) implies:
% 239.74/46.33  | | | | | | |   (68)  op(e0, e3) = e0
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | REF_CLOSE: (2), (31), (57), (68) are inconsistent by sub-proof
% 239.74/46.33  | | | | | | |            #221.
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | End of split
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | End of split
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | End of split
% 239.74/46.33  | | | | 
% 239.74/46.33  | | | Case 2:
% 239.74/46.33  | | | | 
% 239.74/46.33  | | | |   (69)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 239.74/46.33  | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.74/46.33  | | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 239.74/46.33  | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.74/46.33  | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 239.74/46.33  | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.74/46.33  | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) & 
% 239.74/46.33  | | | |           ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 239.74/46.33  | | | |         (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 239.74/46.33  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.74/46.33  | | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 239.74/46.33  | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 239.74/46.33  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 239.74/46.33  | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.74/46.33  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 239.74/46.33  | | | |           ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.74/46.33  | | | | 
% 239.74/46.33  | | | | BETA: splitting (69) gives:
% 239.74/46.33  | | | | 
% 239.74/46.33  | | | | Case 1:
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | |   (70)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 239.74/46.33  | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 239.74/46.33  | | | | |           & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 239.74/46.33  | | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.74/46.33  | | | | |           ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 239.74/46.33  | | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.74/46.33  | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 239.74/46.33  | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | | BETA: splitting (70) gives:
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | | Case 1:
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | |   (71)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 239.74/46.33  | | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 239.74/46.33  | | | | | |         & op(e2, e1) = e2 & op(e1, e2) = e2
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | ALPHA: (71) implies:
% 239.74/46.33  | | | | | |   (72)   ~ (all_56_11 = e1)
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | REDUCE: (4), (72) imply:
% 239.74/46.33  | | | | | |   (73)  $false
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | CLOSE: (73) is inconsistent.
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | Case 2:
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | |   (74)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.74/46.33  | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 239.74/46.33  | | | | | |             e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 =
% 239.74/46.33  | | | | | |           e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 239.74/46.33  | | | | | |             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2,
% 239.74/46.33  | | | | | |             e0) = e2 & op(e0, e2) = e2)
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | BETA: splitting (74) gives:
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | Case 1:
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | |   (75)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.74/46.33  | | | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 239.74/46.33  | | | | | | |           e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | ALPHA: (75) implies:
% 239.74/46.33  | | | | | | |   (76)  op(e2, e1) = e1
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | REF_CLOSE: (14), (31), (38), (76) are inconsistent by sub-proof
% 239.74/46.33  | | | | | | |            #2306.
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | Case 2:
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | |   (77)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.33  | | | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 239.74/46.33  | | | | | | |           e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | ALPHA: (77) implies:
% 239.74/46.33  | | | | | | |   (78)  op(e0, e2) = e2
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | REF_CLOSE: (3), (6), (15), (25), (28), (31), (46), (78) are
% 239.74/46.33  | | | | | | |            inconsistent by sub-proof #1816.
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | End of split
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | End of split
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | Case 2:
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | |   (79)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 239.74/46.33  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 239.74/46.33  | | | | |           & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 239.74/46.33  | | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.74/46.33  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 239.74/46.33  | | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.74/46.33  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 239.74/46.33  | | | | |           &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | | BETA: splitting (79) gives:
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | | Case 1:
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | |   (80)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 239.74/46.33  | | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 239.74/46.33  | | | | | |         & op(e2, e0) = e0 & op(e0, e2) = e0
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | ALPHA: (80) implies:
% 239.74/46.33  | | | | | |   (81)   ~ (all_56_31 = e2)
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | REDUCE: (16), (81) imply:
% 239.74/46.33  | | | | | |   (82)  $false
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | CLOSE: (82) is inconsistent.
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | Case 2:
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | |   (83)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.33  | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 239.74/46.33  | | | | | |             e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 =
% 239.74/46.33  | | | | | |           e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 239.74/46.33  | | | | | |             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 239.74/46.33  | | | | | |             e0) = e0 & op(e0, e1) = e0)
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | BETA: splitting (83) gives:
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | | Case 1:
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | |   (84)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.33  | | | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 239.74/46.33  | | | | | | |           e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | ALPHA: (84) implies:
% 239.74/46.33  | | | | | | |   (85)   ~ (all_56_31 = e0)
% 239.74/46.33  | | | | | | |   (86)   ~ (all_56_21 = e0)
% 239.74/46.33  | | | | | | |   (87)   ~ (all_56_11 = e0)
% 239.74/46.33  | | | | | | |   (88)  op(e1, e0) = e1
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | REDUCE: (4), (87) imply:
% 239.74/46.33  | | | | | | |   (89)   ~ (e1 = e0)
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | REDUCE: (16), (85) imply:
% 239.74/46.33  | | | | | | |   (90)   ~ (e2 = e0)
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | BETA: splitting (11) gives:
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | Case 1:
% 239.74/46.33  | | | | | | | | 
% 239.74/46.33  | | | | | | | |   (91)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 239.74/46.33  | | | | | | | |           op(e3, e2) = e3)
% 239.74/46.33  | | | | | | | | 
% 239.74/46.33  | | | | | | | | BETA: splitting (91) gives:
% 239.74/46.33  | | | | | | | | 
% 239.74/46.33  | | | | | | | | Case 1:
% 239.74/46.33  | | | | | | | | | 
% 239.74/46.33  | | | | | | | | |   (92)  all_58_0 = e3 & op(e3, e3) = e3
% 239.74/46.33  | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | ALPHA: (92) implies:
% 239.74/46.33  | | | | | | | | |   (93)  op(e3, e3) = e3
% 239.74/46.33  | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | REF_CLOSE: (21), (31), (51), (93) are inconsistent by
% 239.74/46.33  | | | | | | | | |            sub-proof #2194.
% 239.74/46.33  | | | | | | | | | 
% 239.74/46.33  | | | | | | | | Case 2:
% 239.74/46.33  | | | | | | | | | 
% 239.74/46.33  | | | | | | | | |   (94)  all_58_1 = e3 & op(e3, e2) = e3
% 239.74/46.33  | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | ALPHA: (94) implies:
% 239.74/46.33  | | | | | | | | |   (95)  all_58_1 = e3
% 239.74/46.33  | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | BETA: splitting (29) gives:
% 239.74/46.33  | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | Case 1:
% 239.74/46.33  | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | |   (96)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 239.74/46.33  | | | | | | | | | |           op(e2, e3) = e1)
% 239.74/46.33  | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | REF_CLOSE: (20), (21), (31), (40), (41), (96) are
% 239.74/46.33  | | | | | | | | | |            inconsistent by sub-proof #1354.
% 239.74/46.33  | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | Case 2:
% 239.74/46.33  | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | |   (97)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 239.74/46.33  | | | | | | | | | |           & op(e0, e3) = e1)
% 239.74/46.33  | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | BETA: splitting (97) gives:
% 239.74/46.33  | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | Case 1:
% 239.74/46.33  | | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | |   (98)  all_58_6 = e1 & op(e1, e3) = e1
% 239.74/46.33  | | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | | ALPHA: (98) implies:
% 239.74/46.33  | | | | | | | | | | |   (99)  op(e1, e3) = e1
% 239.74/46.33  | | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | | REF_CLOSE: (2), (7), (9), (10), (18), (22), (24), (31), (35),
% 239.74/46.33  | | | | | | | | | | |            (52), (88), (89), (90), (99) are inconsistent by
% 239.74/46.33  | | | | | | | | | | |            sub-proof #55.
% 239.74/46.33  | | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | Case 2:
% 239.74/46.33  | | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | |   (100)  all_58_12 = e1 & op(e0, e3) = e1
% 239.74/46.33  | | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | | ALPHA: (100) implies:
% 239.74/46.33  | | | | | | | | | | |   (101)  all_58_12 = e1
% 239.74/46.33  | | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | | COMBINE_EQS: (56), (101) imply:
% 239.74/46.33  | | | | | | | | | | |   (102)  e3 = e1
% 239.74/46.33  | | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | | COMBINE_EQS: (95), (102) imply:
% 239.74/46.33  | | | | | | | | | | |   (103)  all_58_1 = e1
% 239.74/46.33  | | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | | REF_CLOSE: (11), (13), (17), (21), (31), (48), (50), (51),
% 239.74/46.33  | | | | | | | | | | |            (52), (103) are inconsistent by sub-proof #1327.
% 239.74/46.33  | | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | | End of split
% 239.74/46.33  | | | | | | | | | | 
% 239.74/46.33  | | | | | | | | | End of split
% 239.74/46.33  | | | | | | | | | 
% 239.74/46.33  | | | | | | | | End of split
% 239.74/46.33  | | | | | | | | 
% 239.74/46.33  | | | | | | | Case 2:
% 239.74/46.33  | | | | | | | | 
% 239.74/46.33  | | | | | | | |   (104)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 239.74/46.33  | | | | | | | |            op(e3, e0) = e3)
% 239.74/46.33  | | | | | | | | 
% 239.74/46.33  | | | | | | | | REF_CLOSE: (13), (17), (31), (48), (50), (104) are inconsistent
% 239.74/46.33  | | | | | | | |            by sub-proof #1515.
% 239.74/46.33  | | | | | | | | 
% 239.74/46.33  | | | | | | | End of split
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | Case 2:
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | |   (105)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 239.74/46.33  | | | | | | |          (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 239.74/46.33  | | | | | | |            e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | ALPHA: (105) implies:
% 239.74/46.33  | | | | | | |   (106)   ~ (all_56_11 = e1)
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | REDUCE: (4), (106) imply:
% 239.74/46.33  | | | | | | |   (107)  $false
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | | CLOSE: (107) is inconsistent.
% 239.74/46.33  | | | | | | | 
% 239.74/46.33  | | | | | | End of split
% 239.74/46.33  | | | | | | 
% 239.74/46.33  | | | | | End of split
% 239.74/46.33  | | | | | 
% 239.74/46.33  | | | | End of split
% 239.74/46.33  | | | | 
% 239.74/46.33  | | | End of split
% 239.74/46.33  | | | 
% 239.74/46.33  | | Case 2:
% 239.74/46.33  | | | 
% 239.74/46.33  | | |   (108)  all_58_13 = e3 & op(e0, e2) = e3
% 239.74/46.33  | | | 
% 239.74/46.33  | | | REF_CLOSE: (25), (31), (46), (108) are inconsistent by sub-proof #1919.
% 239.74/46.33  | | | 
% 239.74/46.33  | | End of split
% 239.74/46.33  | | 
% 239.74/46.33  | Case 2:
% 239.74/46.33  | | 
% 239.74/46.33  | |   (109)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 239.74/46.33  | |            e3)
% 239.74/46.33  | | 
% 239.74/46.33  | | REF_CLOSE: (5), (12), (31), (36), (51), (109) are inconsistent by sub-proof
% 239.74/46.33  | |            #226.
% 239.74/46.33  | | 
% 239.74/46.33  | End of split
% 239.74/46.33  | 
% 239.74/46.33  End of proof
% 239.74/46.33  
% 239.74/46.33  Sub-proof #55 shows that the following formulas are inconsistent:
% 239.74/46.33  ----------------------------------------------------------------
% 239.74/46.33    (1)   ~ (e3 = e0)
% 239.74/46.33    (2)   ~ (e2 = e0)
% 239.74/46.33    (3)  op(e1, e2) = all_52_6
% 239.74/46.33    (4)  op(e1, e0) = all_52_14
% 239.74/46.33    (5)   ~ (e3 = e1)
% 239.74/46.33    (6)  all_58_7 = e2
% 239.74/46.33    (7)  op(e1, e0) = e1
% 239.74/46.33    (8)  op(e1, e3) = e1
% 239.74/46.33    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.74/46.33         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.74/46.33    (10)   ~ (all_52_14 = e3)
% 239.74/46.33    (11)   ~ (all_52_6 = e3)
% 239.74/46.33    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.74/46.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.74/46.33    (13)   ~ (e1 = e0)
% 239.74/46.33    (14)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.74/46.33          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.74/46.33  
% 239.74/46.33  Begin of proof
% 239.74/46.33  | 
% 239.74/46.33  | BETA: splitting (14) gives:
% 239.74/46.33  | 
% 239.74/46.33  | Case 1:
% 239.74/46.33  | | 
% 239.74/46.33  | |   (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 239.74/46.33  | |           e0)
% 239.74/46.33  | | 
% 239.74/46.33  | | REF_CLOSE: (2), (6), (8), (12), (13), (15) are inconsistent by sub-proof
% 239.74/46.33  | |            #335.
% 239.74/46.33  | | 
% 239.74/46.33  | Case 2:
% 239.74/46.33  | | 
% 239.74/46.33  | |   (16)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 239.74/46.33  | |           e0)
% 239.74/46.33  | | 
% 239.74/46.33  | | BETA: splitting (16) gives:
% 239.74/46.33  | | 
% 239.74/46.33  | | Case 1:
% 239.74/46.33  | | | 
% 239.74/46.33  | | |   (17)  all_58_8 = e0 & op(e1, e1) = e0
% 239.74/46.33  | | | 
% 239.74/46.33  | | | ALPHA: (17) implies:
% 239.74/46.33  | | |   (18)  op(e1, e1) = e0
% 239.74/46.33  | | | 
% 239.74/46.33  | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (11), (12), (18) are
% 239.74/46.33  | | |            inconsistent by sub-proof #457.
% 239.74/46.33  | | | 
% 239.74/46.33  | | Case 2:
% 239.74/46.33  | | | 
% 239.74/46.33  | | |   (19)  all_58_11 = e0 & op(e1, e0) = e0
% 239.74/46.33  | | | 
% 239.74/46.33  | | | ALPHA: (19) implies:
% 239.74/46.34  | | |   (20)  op(e1, e0) = e0
% 239.74/46.34  | | | 
% 239.74/46.34  | | | REF_CLOSE: (7), (12), (13), (20) are inconsistent by sub-proof #2284.
% 239.74/46.34  | | | 
% 239.74/46.34  | | End of split
% 239.74/46.34  | | 
% 239.74/46.34  | End of split
% 239.74/46.34  | 
% 239.74/46.34  End of proof
% 239.74/46.34  
% 239.74/46.34  Sub-proof #56 shows that the following formulas are inconsistent:
% 239.74/46.34  ----------------------------------------------------------------
% 239.74/46.34    (1)   ~ (e2 = e0)
% 239.74/46.34    (2)  all_58_4 = e2
% 239.74/46.34    (3)  op(e2, e1) = e2
% 239.74/46.34    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 239.74/46.34    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.74/46.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.74/46.34  
% 239.74/46.34  Begin of proof
% 239.74/46.34  | 
% 239.74/46.34  | BETA: splitting (4) gives:
% 239.74/46.34  | 
% 239.74/46.34  | Case 1:
% 239.74/46.34  | | 
% 239.74/46.34  | |   (6)  all_58_4 = e0 & op(e3, e1) = e0
% 239.74/46.34  | | 
% 239.74/46.34  | | ALPHA: (6) implies:
% 239.74/46.34  | |   (7)  all_58_4 = e0
% 239.74/46.34  | | 
% 239.74/46.34  | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #1666.
% 239.74/46.34  | | 
% 239.74/46.34  | Case 2:
% 239.74/46.34  | | 
% 239.74/46.34  | |   (8)  all_58_5 = e0 & op(e2, e1) = e0
% 239.74/46.34  | | 
% 239.74/46.34  | | ALPHA: (8) implies:
% 239.74/46.34  | |   (9)  op(e2, e1) = e0
% 239.74/46.34  | | 
% 239.74/46.34  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1906.
% 239.74/46.34  | | 
% 239.74/46.34  | End of split
% 239.74/46.34  | 
% 239.74/46.34  End of proof
% 239.74/46.34  
% 239.74/46.34  Sub-proof #57 shows that the following formulas are inconsistent:
% 239.74/46.34  ----------------------------------------------------------------
% 239.74/46.34    (1)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.74/46.34    (2)  op(e0, e1) = all_52_11
% 239.74/46.34    (3)   ~ (all_52_11 = e2)
% 239.74/46.34    (4)   ~ (e3 = e2)
% 239.74/46.34    (5)  op(e1, e1) = e3
% 239.74/46.34    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.74/46.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.74/46.34  
% 239.74/46.34  Begin of proof
% 239.74/46.34  | 
% 239.74/46.34  | BETA: splitting (1) gives:
% 239.74/46.34  | 
% 239.74/46.34  | Case 1:
% 239.74/46.34  | | 
% 239.74/46.34  | |   (7)  all_58_8 = e2 & op(e1, e1) = e2
% 239.74/46.34  | | 
% 239.74/46.34  | | ALPHA: (7) implies:
% 239.74/46.34  | |   (8)  op(e1, e1) = e2
% 239.74/46.34  | | 
% 239.74/46.34  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2206.
% 239.74/46.34  | | 
% 239.74/46.34  | Case 2:
% 239.74/46.34  | | 
% 239.74/46.34  | |   (9)  all_58_14 = e2 & op(e0, e1) = e2
% 239.74/46.34  | | 
% 239.74/46.34  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #183.
% 239.74/46.34  | | 
% 239.74/46.34  | End of split
% 239.74/46.34  | 
% 239.74/46.34  End of proof
% 239.74/46.34  
% 239.74/46.34  Sub-proof #58 shows that the following formulas are inconsistent:
% 239.74/46.34  ----------------------------------------------------------------
% 239.74/46.34    (1)   ~ (e3 = e0)
% 239.74/46.34    (2)  op(e0, e1) = all_52_11
% 239.74/46.34    (3)   ~ (e2 = e0)
% 239.74/46.34    (4)  all_58_4 = e2
% 239.74/46.34    (5)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 239.74/46.34         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 239.74/46.34    (6)  op(e1, e0) = all_52_14
% 239.74/46.34    (7)   ~ (e3 = e1)
% 239.74/46.34    (8)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.74/46.34         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.74/46.34    (9)   ~ (all_52_11 = e3)
% 239.74/46.34    (10)   ~ (all_52_14 = e2)
% 239.74/46.34    (11)  op(e2, e1) = all_52_9
% 239.74/46.34    (12)   ~ (e3 = e2)
% 239.74/46.34    (13)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.74/46.34    (14)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.74/46.34          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.74/46.34    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.74/46.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.74/46.34    (16)   ~ (e1 = e0)
% 239.74/46.34    (17)   ~ (e2 = e1)
% 239.74/46.34  
% 239.74/46.34  Begin of proof
% 239.74/46.34  | 
% 239.74/46.34  | BETA: splitting (13) gives:
% 239.74/46.34  | 
% 239.74/46.34  | Case 1:
% 239.74/46.34  | | 
% 239.74/46.34  | |   (18)  all_58_8 = e2 & op(e1, e1) = e2
% 239.74/46.34  | | 
% 239.74/46.34  | | ALPHA: (18) implies:
% 239.74/46.34  | |   (19)  op(e1, e1) = e2
% 239.74/46.34  | | 
% 239.74/46.34  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (14), (15),
% 239.74/46.34  | |            (16), (17), (19) are inconsistent by sub-proof #1306.
% 239.74/46.34  | | 
% 239.74/46.34  | Case 2:
% 239.74/46.34  | | 
% 239.74/46.34  | |   (20)  all_58_11 = e2 & op(e1, e0) = e2
% 239.74/46.34  | | 
% 239.74/46.34  | | REF_CLOSE: (6), (10), (15), (20) are inconsistent by sub-proof #258.
% 239.74/46.34  | | 
% 239.74/46.34  | End of split
% 239.74/46.34  | 
% 239.74/46.34  End of proof
% 239.74/46.34  
% 239.74/46.34  Sub-proof #59 shows that the following formulas are inconsistent:
% 239.74/46.34  ----------------------------------------------------------------
% 239.74/46.34    (1)  all_58_10 = e3
% 239.74/46.34    (2)   ~ (e3 = e0)
% 239.74/46.34    (3)  op(e1, e0) = e1
% 239.74/46.34    (4)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.74/46.34    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.74/46.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.74/46.34    (6)   ~ (e1 = e0)
% 239.74/46.34  
% 239.74/46.34  Begin of proof
% 239.74/46.34  | 
% 239.74/46.34  | BETA: splitting (4) gives:
% 239.74/46.34  | 
% 239.74/46.34  | Case 1:
% 239.74/46.34  | | 
% 239.74/46.34  | |   (7)  all_58_10 = e0 & op(e2, e0) = e0
% 239.74/46.34  | | 
% 239.74/46.34  | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #1102.
% 239.74/46.34  | | 
% 239.74/46.34  | Case 2:
% 239.74/46.34  | | 
% 239.74/46.34  | |   (8)  all_58_11 = e0 & op(e1, e0) = e0
% 239.74/46.34  | | 
% 239.74/46.34  | | ALPHA: (8) implies:
% 239.74/46.34  | |   (9)  op(e1, e0) = e0
% 239.74/46.34  | | 
% 239.74/46.34  | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #2284.
% 239.74/46.34  | | 
% 239.74/46.34  | End of split
% 239.74/46.34  | 
% 239.74/46.34  End of proof
% 239.74/46.34  
% 239.74/46.34  Sub-proof #60 shows that the following formulas are inconsistent:
% 239.74/46.34  ----------------------------------------------------------------
% 239.74/46.34    (1)   ~ (all_6_1 = e0)
% 239.74/46.34    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.74/46.34         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.74/46.34    (3)  op(e0, e1) = all_52_11
% 239.74/46.34    (4)   ~ (all_52_11 = e2)
% 239.74/46.34    (5)  op(e1, e2) = all_52_6
% 239.74/46.34    (6)   ~ (all_52_11 = e1)
% 239.74/46.34    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 239.74/46.34           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 239.74/46.34             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 239.74/46.34           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.74/46.34             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.74/46.34           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.74/46.34           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.74/46.34           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.74/46.34           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 239.74/46.34           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.34           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.74/46.34             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.74/46.34           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.74/46.34           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 239.74/46.34           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.74/46.34           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 239.74/46.34           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.74/46.34           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.74/46.34             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.74/46.34           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.74/46.34           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 239.74/46.34           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.74/46.34           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 239.74/46.34           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.74/46.34           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.74/46.34             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.74/46.34           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.74/46.34           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.74/46.34    (8)  all_58_4 = e2
% 239.74/46.34    (9)  op(e1, e3) = all_6_1
% 239.74/46.34    (10)  op(e0, e3) = all_52_3
% 239.74/46.34    (11)   ~ (e3 = e1)
% 239.74/46.34    (12)  op(e0, e2) = e3
% 239.74/46.34    (13)  op(e1, e0) = e1
% 239.74/46.34    (14)  op(e1, e3) = e2
% 239.74/46.34    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 239.74/46.34          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 239.74/46.34    (16)  all_58_12 = e1
% 239.74/46.34    (17)   ~ (all_52_11 = e3)
% 239.74/46.34    (18)  op(e2, e1) = all_52_9
% 239.74/46.34    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 239.74/46.34          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 239.74/46.34    (20)   ~ (e3 = e2)
% 239.74/46.34    (21)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.74/46.34          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.74/46.34    (22)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.74/46.34    (23)   ~ (all_52_3 = all_52_11)
% 239.74/46.34    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.74/46.34          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.74/46.34    (25)   ~ (all_52_3 = e3)
% 239.74/46.34    (26)  op(e1, e3) = all_46_1
% 239.74/46.34    (27)  op(e2, e3) = all_52_1
% 239.74/46.34    (28)  op(e1, e1) = e3
% 239.74/46.34    (29)   ~ (all_52_2 = e3)
% 239.74/46.34    (30)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.74/46.34          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.74/46.34    (31)   ~ (all_52_9 = e3)
% 239.74/46.34    (32)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.74/46.34          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.74/46.34    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.74/46.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.74/46.34    (34)  op(e3, e0) = e0
% 239.74/46.34    (35)  op(e1, e3) = all_52_2
% 239.74/46.34    (36)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.74/46.34          | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.74/46.34    (37)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.74/46.34          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.74/46.34    (38)  op(e0, e0) = e2
% 239.74/46.34    (39)   ~ (all_52_1 = e3)
% 239.74/46.34    (40)  all_54_14 = all_52_11
% 239.74/46.34    (41)   ~ (e2 = e1)
% 239.74/46.34    (42)   ~ (all_52_9 = e2)
% 239.74/46.34  
% 239.74/46.34  Begin of proof
% 239.74/46.34  | 
% 239.74/46.34  | BETA: splitting (22) gives:
% 239.74/46.34  | 
% 239.74/46.34  | Case 1:
% 239.74/46.34  | | 
% 239.74/46.34  | |   (43)  all_54_14 = e3
% 239.74/46.34  | | 
% 239.74/46.34  | | REF_CLOSE: (17), (40), (43) are inconsistent by sub-proof #1796.
% 239.74/46.34  | | 
% 239.74/46.34  | Case 2:
% 239.74/46.34  | | 
% 239.74/46.34  | |   (44)   ~ (all_54_14 = e3)
% 239.74/46.34  | |   (45)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.74/46.34  | | 
% 239.74/46.34  | | BETA: splitting (45) gives:
% 239.74/46.34  | | 
% 239.74/46.34  | | Case 1:
% 239.74/46.34  | | | 
% 239.76/46.34  | | |   (46)  all_54_14 = e2
% 239.76/46.34  | | | 
% 239.76/46.34  | | | REF_CLOSE: (4), (40), (46) are inconsistent by sub-proof #1856.
% 239.76/46.34  | | | 
% 239.76/46.34  | | Case 2:
% 239.76/46.34  | | | 
% 239.76/46.34  | | |   (47)   ~ (all_54_14 = e2)
% 239.76/46.34  | | |   (48)  all_54_14 = e1 | all_54_14 = e0
% 239.76/46.34  | | | 
% 239.76/46.34  | | | BETA: splitting (48) gives:
% 239.76/46.34  | | | 
% 239.76/46.34  | | | Case 1:
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | |   (49)  all_54_14 = e1
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | REF_CLOSE: (6), (40), (49) are inconsistent by sub-proof #1937.
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | Case 2:
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | |   (50)  all_54_14 = e0
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | COMBINE_EQS: (40), (50) imply:
% 239.76/46.34  | | | |   (51)  all_52_11 = e0
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | SIMP: (51) implies:
% 239.76/46.34  | | | |   (52)  all_52_11 = e0
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | REDUCE: (23), (52) imply:
% 239.76/46.34  | | | |   (53)   ~ (all_52_3 = e0)
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | REDUCE: (17), (52) imply:
% 239.76/46.34  | | | |   (54)   ~ (e3 = e0)
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | SIMP: (54) implies:
% 239.76/46.34  | | | |   (55)   ~ (e3 = e0)
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | REDUCE: (4), (52) imply:
% 239.76/46.34  | | | |   (56)   ~ (e2 = e0)
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | SIMP: (56) implies:
% 239.76/46.34  | | | |   (57)   ~ (e2 = e0)
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | REDUCE: (6), (52) imply:
% 239.76/46.34  | | | |   (58)   ~ (e1 = e0)
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | SIMP: (58) implies:
% 239.76/46.34  | | | |   (59)   ~ (e1 = e0)
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | BETA: splitting (37) gives:
% 239.76/46.34  | | | | 
% 239.76/46.34  | | | | Case 1:
% 239.76/46.34  | | | | | 
% 239.76/46.34  | | | | |   (60)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1,
% 239.76/46.34  | | | | |             e2) = e0)
% 239.76/46.34  | | | | | 
% 239.76/46.34  | | | | | BETA: splitting (60) gives:
% 239.76/46.34  | | | | | 
% 239.76/46.34  | | | | | Case 1:
% 239.76/46.34  | | | | | | 
% 239.76/46.34  | | | | | |   (61)  all_58_6 = e0 & op(e1, e3) = e0
% 239.76/46.34  | | | | | | 
% 239.76/46.34  | | | | | | ALPHA: (61) implies:
% 239.76/46.34  | | | | | |   (62)  op(e1, e3) = e0
% 239.76/46.34  | | | | | | 
% 239.76/46.34  | | | | | | REF_CLOSE: (1), (9), (26), (33), (62) are inconsistent by sub-proof
% 239.76/46.34  | | | | | |            #444.
% 239.76/46.34  | | | | | | 
% 239.76/46.34  | | | | | Case 2:
% 239.76/46.34  | | | | | | 
% 239.76/46.34  | | | | | |   (63)  all_58_7 = e0 & op(e1, e2) = e0
% 239.76/46.34  | | | | | | 
% 239.76/46.34  | | | | | | ALPHA: (63) implies:
% 239.76/46.34  | | | | | |   (64)  op(e1, e2) = e0
% 239.76/46.34  | | | | | | 
% 239.76/46.34  | | | | | | BETA: splitting (32) gives:
% 239.76/46.34  | | | | | | 
% 239.76/46.34  | | | | | | Case 1:
% 239.76/46.34  | | | | | | | 
% 239.76/46.34  | | | | | | |   (65)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 &
% 239.76/46.34  | | | | | | |           op(e3, e2) = e1)
% 239.76/46.34  | | | | | | | 
% 239.76/46.34  | | | | | | | BETA: splitting (65) gives:
% 239.76/46.34  | | | | | | | 
% 239.76/46.34  | | | | | | | Case 1:
% 239.76/46.34  | | | | | | | | 
% 239.76/46.34  | | | | | | | |   (66)  all_58_0 = e1 & op(e3, e3) = e1
% 239.76/46.34  | | | | | | | | 
% 239.76/46.34  | | | | | | | | ALPHA: (66) implies:
% 239.76/46.34  | | | | | | | |   (67)  op(e3, e3) = e1
% 239.76/46.34  | | | | | | | | 
% 239.76/46.34  | | | | | | | | REF_CLOSE: (11), (15), (16), (19), (20), (24), (27), (33), (39),
% 239.76/46.34  | | | | | | | |            (41), (55), (57), (59), (67) are inconsistent by
% 239.76/46.34  | | | | | | | |            sub-proof #1204.
% 239.76/46.34  | | | | | | | | 
% 239.76/46.34  | | | | | | | Case 2:
% 239.76/46.34  | | | | | | | | 
% 239.76/46.34  | | | | | | | |   (68)  all_58_1 = e1 & op(e3, e2) = e1
% 239.76/46.34  | | | | | | | | 
% 239.76/46.34  | | | | | | | | ALPHA: (68) implies:
% 239.76/46.34  | | | | | | | |   (69)  op(e3, e2) = e1
% 239.76/46.34  | | | | | | | | 
% 239.76/46.34  | | | | | | | | BETA: splitting (7) gives:
% 239.76/46.34  | | | | | | | | 
% 239.76/46.34  | | | | | | | | Case 1:
% 239.76/46.34  | | | | | | | | | 
% 239.76/46.34  | | | | | | | | |   (70)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 239.76/46.34  | | | | | | | | |           ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 239.76/46.34  | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 239.76/46.34  | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 239.76/46.34  | | | | | | | | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 239.76/46.34  | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3)
% 239.76/46.34  | | | | | | | | |           = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.76/46.34  | | | | | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.76/46.34  | | | | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 239.76/46.34  | | | | | | | | |           = e3 & op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17
% 239.76/46.34  | | | | | | | | |           = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.76/46.34  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1)
% 239.76/46.34  | | | | | | | | |           = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 239.76/46.34  | | | | | | | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 239.76/46.34  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0)
% 239.76/46.34  | | | | | | | | |           = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 239.76/46.34  | | | | | | | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.76/46.34  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 239.76/46.34  | | | | | | | | |           = e0 & op(e0, e3) = e0)
% 239.76/46.34  | | | | | | | | | 
% 239.76/46.34  | | | | | | | | | BETA: splitting (70) gives:
% 239.76/46.34  | | | | | | | | | 
% 239.76/46.34  | | | | | | | | | Case 1:
% 239.76/46.34  | | | | | | | | | | 
% 239.76/46.34  | | | | | | | | | |   (71)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 239.76/46.34  | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 239.76/46.34  | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 239.76/46.34  | | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 239.76/46.34  | | | | | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.76/46.34  | | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.76/46.34  | | | | | | | | | |             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 239.76/46.34  | | | | | | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.76/46.34  | | | | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.76/46.34  | | | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 239.76/46.34  | | | | | | | | | |           e3)
% 239.76/46.34  | | | | | | | | | | 
% 239.76/46.34  | | | | | | | | | | BETA: splitting (71) gives:
% 239.76/46.34  | | | | | | | | | | 
% 239.76/46.34  | | | | | | | | | | Case 1:
% 239.76/46.34  | | | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | | |   (72)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 239.76/46.35  | | | | | | | | | | |         &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 239.76/46.35  | | | | | | | | | | |         (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 239.76/46.35  | | | | | | | | | | |         e3
% 239.76/46.35  | | | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | | | ALPHA: (72) implies:
% 239.76/46.35  | | | | | | | | | | |   (73)  op(e2, e3) = e3
% 239.76/46.35  | | | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | | | REF_CLOSE: (27), (33), (39), (73) are inconsistent by
% 239.76/46.35  | | | | | | | | | | |            sub-proof #2337.
% 239.76/46.35  | | | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | | Case 2:
% 239.76/46.35  | | | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | | |   (74)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 239.76/46.35  | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.76/46.35  | | | | | | | | | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 239.76/46.35  | | | | | | | | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 239.76/46.35  | | | | | | | | | | |           e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 239.76/46.35  | | | | | | | | | | |           ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.76/46.35  | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.76/46.35  | | | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | | | REF_CLOSE: (29), (33), (35), (41), (69), (74) are
% 239.76/46.35  | | | | | | | | | | |            inconsistent by sub-proof #1704.
% 239.76/46.35  | | | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | | End of split
% 239.76/46.35  | | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | Case 2:
% 239.76/46.35  | | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | |   (75)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3)
% 239.76/46.35  | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.76/46.35  | | | | | | | | | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 239.76/46.35  | | | | | | | | | |           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 239.76/46.35  | | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 239.76/46.35  | | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.76/46.35  | | | | | | | | | |             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 239.76/46.35  | | | | | | | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.76/46.35  | | | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.76/46.35  | | | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 239.76/46.35  | | | | | | | | | |           e0)
% 239.76/46.35  | | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | | REF_CLOSE: (10), (14), (25), (33), (41), (53), (75) are
% 239.76/46.35  | | | | | | | | | |            inconsistent by sub-proof #142.
% 239.76/46.35  | | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | End of split
% 239.76/46.35  | | | | | | | | | 
% 239.76/46.35  | | | | | | | | Case 2:
% 239.76/46.35  | | | | | | | | | 
% 239.76/46.35  | | | | | | | | |   (76)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 239.76/46.35  | | | | | | | | |           &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.76/46.35  | | | | | | | | |           (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 239.76/46.35  | | | | | | | | |           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~
% 239.76/46.35  | | | | | | | | |           (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.76/46.35  | | | | | | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1)
% 239.76/46.35  | | | | | | | | |           = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 239.76/46.35  | | | | | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 239.76/46.35  | | | | | | | | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 239.76/46.35  | | | | | | | | |           & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.76/46.35  | | | | | | | | |           e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 239.76/46.35  | | | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 239.76/46.35  | | | | | | | | |           (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 239.76/46.35  | | | | | | | | |           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 239.76/46.35  | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 239.76/46.35  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0)
% 239.76/46.35  | | | | | | | | |           = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 239.76/46.35  | | | | | | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 239.76/46.35  | | | | | | | | |             = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 239.76/46.35  | | | | | | | | |           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.76/46.35  | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (11), (12), (13), (16), (17),
% 239.76/46.35  | | | | | | | | |            (18), (20), (33), (38), (42), (55), (59), (64),
% 239.76/46.35  | | | | | | | | |            (76) are inconsistent by sub-proof #64.
% 239.76/46.35  | | | | | | | | | 
% 239.76/46.35  | | | | | | | | End of split
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | End of split
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | Case 2:
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | |   (77)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 &
% 239.76/46.35  | | | | | | |           op(e3, e0) = e1)
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | | BETA: splitting (77) gives:
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | | Case 1:
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | |   (78)  all_58_4 = e1 & op(e3, e1) = e1
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | | ALPHA: (78) implies:
% 239.76/46.35  | | | | | | | |   (79)  all_58_4 = e1
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | | REF_CLOSE: (10), (12), (18), (20), (21), (28), (33), (36), (41),
% 239.76/46.35  | | | | | | | |            (42), (53), (55), (57), (79) are inconsistent by
% 239.76/46.35  | | | | | | | |            sub-proof #431.
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | Case 2:
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | |   (80)  all_58_9 = e1 & op(e3, e0) = e1
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | | ALPHA: (80) implies:
% 239.76/46.35  | | | | | | | |   (81)  op(e3, e0) = e1
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | | REF_CLOSE: (33), (34), (59), (81) are inconsistent by sub-proof
% 239.76/46.35  | | | | | | | |            #242.
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | End of split
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | End of split
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | End of split
% 239.76/46.35  | | | | | 
% 239.76/46.35  | | | | Case 2:
% 239.76/46.35  | | | | | 
% 239.76/46.35  | | | | |   (82)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1,
% 239.76/46.35  | | | | |             e0) = e0)
% 239.76/46.35  | | | | | 
% 239.76/46.35  | | | | | REF_CLOSE: (3), (8), (13), (17), (18), (20), (30), (31), (33), (55),
% 239.76/46.35  | | | | |            (59), (82) are inconsistent by sub-proof #63.
% 239.76/46.35  | | | | | 
% 239.76/46.35  | | | | End of split
% 239.76/46.35  | | | | 
% 239.76/46.35  | | | End of split
% 239.76/46.35  | | | 
% 239.76/46.35  | | End of split
% 239.76/46.35  | | 
% 239.76/46.35  | End of split
% 239.76/46.35  | 
% 239.76/46.35  End of proof
% 239.76/46.35  
% 239.76/46.35  Sub-proof #61 shows that the following formulas are inconsistent:
% 239.76/46.35  ----------------------------------------------------------------
% 239.76/46.35    (1)  op(e3, e0) = all_4_0
% 239.76/46.35    (2)  op(e3, e0) = e1
% 239.76/46.35    (3)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.76/46.35    (4)   ~ (all_4_0 = e2)
% 239.76/46.35    (5)   ~ (all_4_0 = e1)
% 239.76/46.35    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.35    (7)  all_54_3 = all_4_0
% 239.76/46.35    (8)   ~ (all_4_0 = e3)
% 239.76/46.35  
% 239.76/46.35  Begin of proof
% 239.76/46.35  | 
% 239.76/46.35  | BETA: splitting (3) gives:
% 239.76/46.35  | 
% 239.76/46.35  | Case 1:
% 239.76/46.35  | | 
% 239.76/46.35  | |   (9)  all_54_3 = e3
% 239.76/46.35  | | 
% 239.76/46.35  | | COMBINE_EQS: (7), (9) imply:
% 239.76/46.35  | |   (10)  all_4_0 = e3
% 239.76/46.35  | | 
% 239.76/46.35  | | REDUCE: (8), (10) imply:
% 239.76/46.35  | |   (11)  $false
% 239.76/46.35  | | 
% 239.76/46.35  | | CLOSE: (11) is inconsistent.
% 239.76/46.35  | | 
% 239.76/46.35  | Case 2:
% 239.76/46.35  | | 
% 239.76/46.35  | |   (12)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.76/46.35  | | 
% 239.76/46.35  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (12) are inconsistent by sub-proof
% 239.76/46.35  | |            #66.
% 239.76/46.35  | | 
% 239.76/46.35  | End of split
% 239.76/46.35  | 
% 239.76/46.35  End of proof
% 239.76/46.35  
% 239.76/46.35  Sub-proof #62 shows that the following formulas are inconsistent:
% 239.76/46.35  ----------------------------------------------------------------
% 239.76/46.35    (1)   ~ (all_52_1 = all_52_3)
% 239.76/46.35    (2)  all_58_10 = e3
% 239.76/46.35    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.76/46.35         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.76/46.35    (4)   ~ (e3 = e0)
% 239.76/46.35    (5)  op(e0, e1) = all_52_11
% 239.76/46.35    (6)   ~ (e2 = e0)
% 239.76/46.35    (7)  op(e1, e2) = all_52_6
% 239.76/46.35    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 239.76/46.35         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 239.76/46.35    (9)  all_58_6 = e2
% 239.76/46.35    (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.76/46.35              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.76/46.35            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.76/46.35            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.76/46.35            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 239.76/46.35             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.76/46.35            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.76/46.35            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.76/46.35            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.76/46.35            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.76/46.35            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.76/46.35              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.76/46.35            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.76/46.35            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 239.76/46.35            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.76/46.35            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 239.76/46.35            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.76/46.35            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.76/46.35              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.76/46.35            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.76/46.35            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.76/46.35            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.76/46.35            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 239.76/46.35            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.76/46.35            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.76/46.35              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.76/46.35            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.76/46.35            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.76/46.35    (11)  op(e3, e0) = all_4_0
% 239.76/46.35    (12)  all_58_4 = e2
% 239.76/46.35    (13)   ~ (all_46_0 = e0)
% 239.76/46.35    (14)  op(e0, e3) = all_52_3
% 239.76/46.35    (15)   ~ (e3 = e1)
% 239.76/46.35    (16)  op(e0, e2) = e3
% 239.76/46.35    (17)   ~ (all_52_1 = all_6_0)
% 239.76/46.35    (18)  op(e2, e1) = all_46_0
% 239.76/46.35    (19)  all_54_6 = all_6_0
% 239.76/46.35    (20)  op(e2, e1) = all_6_0
% 239.76/46.35    (21)  op(e1, e3) = e2
% 239.76/46.35    (22)  all_58_15 = e2
% 239.76/46.35    (23)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.76/46.35    (24)  all_54_4 = all_52_1
% 239.76/46.35    (25)   ~ (all_52_11 = e3)
% 239.76/46.35    (26)  op(e2, e1) = all_52_9
% 239.76/46.35    (27)   ~ (e3 = e2)
% 239.76/46.35    (28)  op(e3, e0) = all_52_12
% 239.76/46.35    (29)   ~ (all_52_3 = e3)
% 239.76/46.35    (30)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 239.76/46.35    (31)  op(e2, e3) = all_52_1
% 239.76/46.35    (32)   ~ (all_52_12 = e2)
% 239.76/46.35    (33)   ~ (all_52_2 = e3)
% 239.76/46.35    (34)   ~ (all_6_0 = e3)
% 239.76/46.35    (35)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.76/46.35    (36)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.76/46.35          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.76/46.35    (37)   ~ (all_4_0 = e1)
% 239.76/46.35    (38)  op(e3, e2) = all_52_4
% 239.76/46.35    (39)   ~ (all_52_9 = e3)
% 239.76/46.35    (40)   ~ (all_52_4 = e2)
% 239.76/46.35    (41)  all_54_3 = all_52_12
% 239.76/46.35    (42)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.35    (43)  op(e1, e3) = all_52_2
% 239.76/46.35    (44)  op(e0, e2) = all_44_1
% 239.76/46.35    (45)   ~ (all_52_12 = e3)
% 239.76/46.35    (46)   ~ (all_52_11 = all_6_0)
% 239.76/46.35    (47)   ~ (all_6_0 = e2)
% 239.76/46.35    (48)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.76/46.35          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.76/46.35    (49)  op(e0, e0) = e2
% 239.76/46.35    (50)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.76/46.35          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 239.76/46.35            e1)
% 239.76/46.35    (51)   ~ (all_52_1 = e3)
% 239.76/46.35    (52)   ~ (all_52_1 = e2)
% 239.76/46.35    (53)  all_58_13 = e3
% 239.76/46.35    (54)   ~ (e2 = e1)
% 239.76/46.35    (55)   ~ (all_52_9 = e2)
% 239.76/46.35  
% 239.76/46.35  Begin of proof
% 239.76/46.35  | 
% 239.76/46.35  | GROUND_INST: instantiating (42) with e3, all_44_1, e2, e0, simplifying with
% 239.76/46.35  |              (16), (44) gives:
% 239.76/46.35  |   (56)  all_44_1 = e3
% 239.76/46.35  | 
% 239.76/46.35  | GROUND_INST: instantiating (42) with all_6_0, all_46_0, e1, e2, simplifying
% 239.76/46.35  |              with (18), (20) gives:
% 239.76/46.35  |   (57)  all_46_0 = all_6_0
% 239.76/46.35  | 
% 239.76/46.35  | GROUND_INST: instantiating (42) with all_52_12, all_4_0, e0, e3, simplifying
% 239.76/46.35  |              with (11), (28) gives:
% 239.76/46.35  |   (58)  all_52_12 = all_4_0
% 239.76/46.35  | 
% 239.76/46.35  | COMBINE_EQS: (41), (58) imply:
% 239.76/46.35  |   (59)  all_54_3 = all_4_0
% 239.76/46.35  | 
% 239.76/46.35  | REDUCE: (45), (58) imply:
% 239.76/46.35  |   (60)   ~ (all_4_0 = e3)
% 239.76/46.35  | 
% 239.76/46.35  | REDUCE: (32), (58) imply:
% 239.76/46.35  |   (61)   ~ (all_4_0 = e2)
% 239.76/46.35  | 
% 239.76/46.35  | REDUCE: (13), (57) imply:
% 239.76/46.35  |   (62)   ~ (all_6_0 = e0)
% 239.76/46.35  | 
% 239.76/46.35  | BETA: splitting (30) gives:
% 239.76/46.35  | 
% 239.76/46.35  | Case 1:
% 239.76/46.35  | | 
% 239.76/46.35  | |   (63)  all_54_6 = e3
% 239.76/46.35  | | 
% 239.76/46.35  | | COMBINE_EQS: (19), (63) imply:
% 239.76/46.35  | |   (64)  all_6_0 = e3
% 239.76/46.35  | | 
% 239.76/46.35  | | REDUCE: (34), (64) imply:
% 239.76/46.35  | |   (65)  $false
% 239.76/46.35  | | 
% 239.76/46.35  | | CLOSE: (65) is inconsistent.
% 239.76/46.35  | | 
% 239.76/46.35  | Case 2:
% 239.76/46.35  | | 
% 239.76/46.35  | |   (66)   ~ (all_54_6 = e3)
% 239.76/46.35  | |   (67)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 239.76/46.35  | | 
% 239.76/46.35  | | BETA: splitting (67) gives:
% 239.76/46.35  | | 
% 239.76/46.35  | | Case 1:
% 239.76/46.35  | | | 
% 239.76/46.35  | | |   (68)  all_54_6 = e2
% 239.76/46.35  | | | 
% 239.76/46.35  | | | COMBINE_EQS: (19), (68) imply:
% 239.76/46.35  | | |   (69)  all_6_0 = e2
% 239.76/46.35  | | | 
% 239.76/46.35  | | | REDUCE: (47), (69) imply:
% 239.76/46.35  | | |   (70)  $false
% 239.76/46.35  | | | 
% 239.76/46.35  | | | CLOSE: (70) is inconsistent.
% 239.76/46.35  | | | 
% 239.76/46.35  | | Case 2:
% 239.76/46.35  | | | 
% 239.76/46.35  | | |   (71)   ~ (all_54_6 = e2)
% 239.76/46.35  | | |   (72)  all_54_6 = e1 | all_54_6 = e0
% 239.76/46.35  | | | 
% 239.76/46.35  | | | BETA: splitting (23) gives:
% 239.76/46.35  | | | 
% 239.76/46.35  | | | Case 1:
% 239.76/46.35  | | | | 
% 239.76/46.35  | | | |   (73)  all_54_3 = e3
% 239.76/46.35  | | | | 
% 239.76/46.35  | | | | COMBINE_EQS: (59), (73) imply:
% 239.76/46.35  | | | |   (74)  all_4_0 = e3
% 239.76/46.35  | | | | 
% 239.76/46.35  | | | | REDUCE: (60), (74) imply:
% 239.76/46.35  | | | |   (75)  $false
% 239.76/46.35  | | | | 
% 239.76/46.35  | | | | CLOSE: (75) is inconsistent.
% 239.76/46.35  | | | | 
% 239.76/46.35  | | | Case 2:
% 239.76/46.35  | | | | 
% 239.76/46.35  | | | |   (76)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.76/46.35  | | | | 
% 239.76/46.35  | | | | BETA: splitting (8) gives:
% 239.76/46.35  | | | | 
% 239.76/46.35  | | | | Case 1:
% 239.76/46.35  | | | | | 
% 239.76/46.35  | | | | |   (77)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 239.76/46.35  | | | | |             e0) = e1)
% 239.76/46.35  | | | | | 
% 239.76/46.35  | | | | | BETA: splitting (77) gives:
% 239.76/46.35  | | | | | 
% 239.76/46.35  | | | | | Case 1:
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | |   (78)  all_58_9 = e1 & op(e3, e0) = e1
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | | ALPHA: (78) implies:
% 239.76/46.35  | | | | | |   (79)  op(e3, e0) = e1
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | | REF_CLOSE: (11), (37), (42), (59), (61), (76), (79) are inconsistent
% 239.76/46.35  | | | | | |            by sub-proof #66.
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | Case 2:
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | |   (80)  all_58_10 = e1 & op(e2, e0) = e1
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | | REF_CLOSE: (2), (15), (80) are inconsistent by sub-proof #1100.
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | End of split
% 239.76/46.35  | | | | | 
% 239.76/46.35  | | | | Case 2:
% 239.76/46.35  | | | | | 
% 239.76/46.35  | | | | |   (81)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 239.76/46.35  | | | | |             e0) = e1)
% 239.76/46.35  | | | | | 
% 239.76/46.35  | | | | | BETA: splitting (81) gives:
% 239.76/46.35  | | | | | 
% 239.76/46.35  | | | | | Case 1:
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | |   (82)  all_58_11 = e1 & op(e1, e0) = e1
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | | ALPHA: (82) implies:
% 239.76/46.35  | | | | | |   (83)  op(e1, e0) = e1
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | | BETA: splitting (72) gives:
% 239.76/46.35  | | | | | | 
% 239.76/46.35  | | | | | | Case 1:
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | |   (84)  all_54_6 = e1
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | | COMBINE_EQS: (19), (84) imply:
% 239.76/46.35  | | | | | | |   (85)  all_6_0 = e1
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | | REDUCE: (17), (85) imply:
% 239.76/46.35  | | | | | | |   (86)   ~ (all_52_1 = e1)
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | | REDUCE: (46), (85) imply:
% 239.76/46.35  | | | | | | |   (87)   ~ (all_52_11 = e1)
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | | REDUCE: (34), (85) imply:
% 239.76/46.35  | | | | | | |   (88)   ~ (e3 = e1)
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | | REDUCE: (47), (85) imply:
% 239.76/46.35  | | | | | | |   (89)   ~ (e2 = e1)
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | | REDUCE: (62), (85) imply:
% 239.76/46.35  | | | | | | |   (90)   ~ (e1 = e0)
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | | BETA: splitting (35) gives:
% 239.76/46.35  | | | | | | | 
% 239.76/46.35  | | | | | | | Case 1:
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | |   (91)  all_54_4 = e3
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | | COMBINE_EQS: (24), (91) imply:
% 239.76/46.35  | | | | | | | |   (92)  all_52_1 = e3
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | | REDUCE: (51), (92) imply:
% 239.76/46.35  | | | | | | | |   (93)  $false
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | | CLOSE: (93) is inconsistent.
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | Case 2:
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | |   (94)   ~ (all_54_4 = e3)
% 239.76/46.35  | | | | | | | |   (95)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | | BETA: splitting (50) gives:
% 239.76/46.35  | | | | | | | | 
% 239.76/46.35  | | | | | | | | Case 1:
% 239.76/46.35  | | | | | | | | | 
% 239.76/46.35  | | | | | | | | |   (96)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 239.76/46.35  | | | | | | | | |           op(e0, e2) = e1)
% 239.76/46.35  | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | BETA: splitting (96) gives:
% 239.76/46.35  | | | | | | | | | 
% 239.76/46.35  | | | | | | | | | Case 1:
% 239.76/46.35  | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | |   (97)  all_58_12 = e1 & op(e0, e3) = e1
% 239.76/46.36  | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | ALPHA: (97) implies:
% 239.76/46.36  | | | | | | | | | |   (98)  all_58_12 = e1
% 239.76/46.36  | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | BETA: splitting (48) gives:
% 239.76/46.36  | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | Case 1:
% 239.76/46.36  | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | |   (99)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 239.76/46.36  | | | | | | | | | | |           & op(e1, e2) = e0)
% 239.76/46.36  | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | BETA: splitting (99) gives:
% 239.76/46.36  | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | Case 1:
% 239.76/46.36  | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | |   (100)  all_58_6 = e0 & op(e1, e3) = e0
% 239.76/46.36  | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | REF_CLOSE: (6), (9), (100) are inconsistent by sub-proof
% 239.76/46.36  | | | | | | | | | | | |            #1678.
% 239.76/46.36  | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | Case 2:
% 239.76/46.36  | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | |   (101)  all_58_7 = e0 & op(e1, e2) = e0
% 239.76/46.36  | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | ALPHA: (101) implies:
% 239.76/46.36  | | | | | | | | | | | |   (102)  op(e1, e2) = e0
% 239.76/46.36  | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | BETA: splitting (10) gives:
% 239.76/46.36  | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | Case 1:
% 239.76/46.36  | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | |   (103)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.76/46.36  | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.76/46.36  | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.76/46.36  | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.76/46.36  | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.76/46.36  | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.76/46.36  | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.76/46.36  | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.76/46.36  | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.76/46.36  | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 239.76/46.36  | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 239.76/46.36  | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.76/46.36  | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 239.76/46.36  | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | BETA: splitting (103) gives:
% 239.76/46.36  | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | Case 1:
% 239.76/46.36  | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | |   (104)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.76/46.36  | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.76/46.36  | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.76/46.36  | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.76/46.36  | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.76/46.36  | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.76/46.36  | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.76/46.36  | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.76/46.36  | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.76/46.36  | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.76/46.36  | | | | | | | | | | | | | |            = e3)
% 239.76/46.36  | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | | REF_CLOSE: (31), (33), (38), (40), (42), (43), (51), (104)
% 239.76/46.36  | | | | | | | | | | | | | |            are inconsistent by sub-proof #252.
% 239.76/46.36  | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | Case 2:
% 239.76/46.36  | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | |   (105)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 239.76/46.36  | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.76/46.36  | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 239.76/46.36  | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 239.76/46.36  | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.76/46.36  | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.76/46.36  | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 239.76/46.36  | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.76/46.36  | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.76/46.36  | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 239.76/46.36  | | | | | | | | | | | | | |            = e0)
% 239.76/46.36  | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 239.76/46.36  | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | | Case 1:
% 239.76/46.36  | | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | | |   (106)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 239.76/46.36  | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 239.76/46.36  | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 239.76/46.36  | | | | | | | | | | | | | | |            e3) = e1
% 239.76/46.36  | | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 239.76/46.36  | | | | | | | | | | | | | | |   (107)  op(e1, e3) = e1
% 239.76/46.36  | | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | | | REF_CLOSE: (21), (42), (54), (107) are inconsistent by
% 239.76/46.36  | | | | | | | | | | | | | | |            sub-proof #2226.
% 239.76/46.36  | | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | | Case 2:
% 239.76/46.36  | | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | | |   (108)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 239.76/46.36  | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.76/46.36  | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 239.76/46.36  | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 239.76/46.36  | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.76/46.36  | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.76/46.36  | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.76/46.36  | | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | | | REF_CLOSE: (1), (14), (24), (29), (42), (52), (86), (95),
% 239.76/46.36  | | | | | | | | | | | | | | |            (108) are inconsistent by sub-proof #169.
% 239.76/46.36  | | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | | End of split
% 239.76/46.36  | | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | End of split
% 239.76/46.36  | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | Case 2:
% 239.76/46.36  | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | |   (109)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 239.76/46.36  | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.76/46.36  | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.76/46.36  | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.76/46.36  | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.76/46.36  | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.76/46.36  | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.76/46.36  | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.76/46.36  | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.76/46.36  | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 239.76/46.36  | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 239.76/46.36  | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.76/46.36  | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 239.76/46.36  | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 239.76/46.36  | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (7), (15), (16), (25), (26), (27),
% 239.76/46.36  | | | | | | | | | | | | |            (42), (49), (55), (83), (87), (90), (98), (102),
% 239.76/46.36  | | | | | | | | | | | | |            (109) are inconsistent by sub-proof #64.
% 239.76/46.36  | | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | | End of split
% 239.76/46.36  | | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | End of split
% 239.76/46.36  | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | Case 2:
% 239.76/46.36  | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | |   (110)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 239.76/46.36  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 239.76/46.36  | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | | REF_CLOSE: (4), (5), (12), (25), (26), (27), (36), (39),
% 239.76/46.36  | | | | | | | | | | |            (42), (83), (90), (110) are inconsistent by
% 239.76/46.36  | | | | | | | | | | |            sub-proof #63.
% 239.76/46.36  | | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | End of split
% 239.76/46.36  | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | Case 2:
% 239.76/46.36  | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | |   (111)  all_58_13 = e1 & op(e0, e2) = e1
% 239.76/46.36  | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | | REF_CLOSE: (15), (53), (111) are inconsistent by sub-proof
% 239.76/46.36  | | | | | | | | | |            #2013.
% 239.76/46.36  | | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | End of split
% 239.76/46.36  | | | | | | | | | 
% 239.76/46.36  | | | | | | | | Case 2:
% 239.76/46.36  | | | | | | | | | 
% 239.76/46.36  | | | | | | | | |   (112)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1
% 239.76/46.36  | | | | | | | | |            & op(e0, e0) = e1)
% 239.76/46.36  | | | | | | | | | 
% 239.76/46.36  | | | | | | | | | REF_CLOSE: (5), (22), (42), (54), (87), (112) are inconsistent
% 239.76/46.36  | | | | | | | | |            by sub-proof #163.
% 239.76/46.36  | | | | | | | | | 
% 239.76/46.36  | | | | | | | | End of split
% 239.76/46.36  | | | | | | | | 
% 239.76/46.36  | | | | | | | End of split
% 239.76/46.36  | | | | | | | 
% 239.76/46.36  | | | | | | Case 2:
% 239.76/46.36  | | | | | | | 
% 239.76/46.36  | | | | | | |   (113)  all_54_6 = e0
% 239.76/46.36  | | | | | | | 
% 239.76/46.36  | | | | | | | COMBINE_EQS: (19), (113) imply:
% 239.76/46.36  | | | | | | |   (114)  all_6_0 = e0
% 239.76/46.36  | | | | | | | 
% 239.76/46.36  | | | | | | | REDUCE: (62), (114) imply:
% 239.76/46.36  | | | | | | |   (115)  $false
% 239.76/46.36  | | | | | | | 
% 239.76/46.36  | | | | | | | CLOSE: (115) is inconsistent.
% 239.76/46.36  | | | | | | | 
% 239.76/46.36  | | | | | | End of split
% 239.76/46.36  | | | | | | 
% 239.76/46.36  | | | | | Case 2:
% 239.76/46.36  | | | | | | 
% 239.76/46.36  | | | | | |   (116)  all_58_15 = e1 & op(e0, e0) = e1
% 239.76/46.36  | | | | | | 
% 239.76/46.36  | | | | | | REF_CLOSE: (22), (54), (116) are inconsistent by sub-proof #218.
% 239.76/46.36  | | | | | | 
% 239.76/46.36  | | | | | End of split
% 239.76/46.36  | | | | | 
% 239.76/46.36  | | | | End of split
% 239.76/46.36  | | | | 
% 239.76/46.36  | | | End of split
% 239.76/46.36  | | | 
% 239.76/46.36  | | End of split
% 239.76/46.36  | | 
% 239.76/46.36  | End of split
% 239.76/46.36  | 
% 239.76/46.36  End of proof
% 239.76/46.36  
% 239.76/46.36  Sub-proof #63 shows that the following formulas are inconsistent:
% 239.76/46.36  ----------------------------------------------------------------
% 239.76/46.36    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.76/46.36    (2)   ~ (e3 = e0)
% 239.76/46.36    (3)  op(e0, e1) = all_52_11
% 239.76/46.36    (4)  all_58_4 = e2
% 239.76/46.36    (5)  op(e1, e0) = e1
% 239.76/46.36    (6)   ~ (all_52_11 = e3)
% 239.76/46.36    (7)  op(e2, e1) = all_52_9
% 239.76/46.36    (8)   ~ (e3 = e2)
% 239.76/46.36    (9)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.76/46.36         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.76/46.36    (10)   ~ (all_52_9 = e3)
% 239.76/46.36    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.36    (12)   ~ (e1 = e0)
% 239.76/46.36  
% 239.76/46.36  Begin of proof
% 239.76/46.36  | 
% 239.76/46.36  | BETA: splitting (1) gives:
% 239.76/46.36  | 
% 239.76/46.36  | Case 1:
% 239.76/46.36  | | 
% 239.76/46.36  | |   (13)  all_58_8 = e0 & op(e1, e1) = e0
% 239.76/46.36  | | 
% 239.76/46.36  | | ALPHA: (13) implies:
% 239.76/46.36  | |   (14)  op(e1, e1) = e0
% 239.76/46.36  | | 
% 239.76/46.36  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (14) are
% 239.76/46.36  | |            inconsistent by sub-proof #1493.
% 239.76/46.36  | | 
% 239.76/46.36  | Case 2:
% 239.76/46.36  | | 
% 239.76/46.36  | |   (15)  all_58_11 = e0 & op(e1, e0) = e0
% 239.76/46.36  | | 
% 239.76/46.36  | | ALPHA: (15) implies:
% 239.76/46.36  | |   (16)  op(e1, e0) = e0
% 239.76/46.36  | | 
% 239.76/46.36  | | REF_CLOSE: (5), (11), (12), (16) are inconsistent by sub-proof #2284.
% 239.76/46.36  | | 
% 239.76/46.36  | End of split
% 239.76/46.36  | 
% 239.76/46.36  End of proof
% 239.76/46.36  
% 239.76/46.36  Sub-proof #64 shows that the following formulas are inconsistent:
% 239.76/46.36  ----------------------------------------------------------------
% 239.76/46.36    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.76/46.36         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.76/46.36    (2)   ~ (e3 = e0)
% 239.76/46.36    (3)  op(e0, e1) = all_52_11
% 239.76/46.36    (4)  op(e1, e2) = all_52_6
% 239.76/46.36    (5)   ~ (all_52_11 = e1)
% 239.76/46.36    (6)   ~ (e3 = e1)
% 239.76/46.36    (7)  op(e0, e2) = e3
% 239.76/46.36    (8)  op(e1, e0) = e1
% 239.76/46.36    (9)  all_58_12 = e1
% 239.76/46.36    (10)   ~ (all_52_11 = e3)
% 239.76/46.36    (11)  op(e2, e1) = all_52_9
% 239.76/46.36    (12)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 239.76/46.36              e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.76/46.36            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 239.76/46.36              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 239.76/46.36              e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 239.76/46.36            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 239.76/46.36            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.76/46.36            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 239.76/46.36            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.76/46.36              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 239.76/46.36            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.76/46.36            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 =
% 239.76/46.36            e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.76/46.36            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 239.76/46.36            = e0)
% 239.76/46.36    (13)  op(e1, e2) = e0
% 239.76/46.36    (14)   ~ (e3 = e2)
% 239.76/46.36    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.36    (16)   ~ (e1 = e0)
% 239.76/46.36    (17)  op(e0, e0) = e2
% 239.76/46.36    (18)   ~ (all_52_9 = e2)
% 239.76/46.36  
% 239.76/46.36  Begin of proof
% 239.76/46.36  | 
% 239.76/46.36  | BETA: splitting (12) gives:
% 239.76/46.36  | 
% 239.76/46.36  | Case 1:
% 239.76/46.36  | | 
% 239.76/46.36  | |   (19)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 239.76/46.36  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.76/46.36  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 239.76/46.36  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.76/46.36  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 239.76/46.36  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.76/46.36  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.76/46.36  | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.76/46.36  | | 
% 239.76/46.36  | | BETA: splitting (19) gives:
% 239.76/46.36  | | 
% 239.76/46.36  | | Case 1:
% 239.76/46.36  | | | 
% 239.76/46.36  | | |   (20)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 239.76/46.36  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.76/46.36  | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 239.76/46.36  | | | 
% 239.76/46.36  | | | ALPHA: (20) implies:
% 239.76/46.36  | | |   (21)  op(e2, e1) = e2
% 239.76/46.36  | | | 
% 239.76/46.36  | | | REF_CLOSE: (11), (15), (18), (21) are inconsistent by sub-proof #2328.
% 239.76/46.36  | | | 
% 239.76/46.36  | | Case 2:
% 239.76/46.36  | | | 
% 239.76/46.36  | | |   (22)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.76/46.36  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.76/46.36  | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27
% 239.76/46.36  | | |           = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 239.76/46.36  | | |             = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 239.76/46.36  | | |           e2)
% 239.76/46.36  | | | 
% 239.76/46.36  | | | BETA: splitting (22) gives:
% 239.76/46.36  | | | 
% 239.76/46.36  | | | Case 1:
% 239.76/46.36  | | | | 
% 239.76/46.36  | | | |   (23)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.76/46.36  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.76/46.36  | | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 239.76/46.36  | | | | 
% 239.76/46.36  | | | | ALPHA: (23) implies:
% 239.76/46.36  | | | |   (24)  op(e1, e2) = e1
% 239.76/46.36  | | | | 
% 239.76/46.36  | | | | REF_CLOSE: (4), (13), (15), (16), (24) are inconsistent by sub-proof
% 239.76/46.36  | | | |            #2136.
% 239.76/46.36  | | | | 
% 239.76/46.36  | | | Case 2:
% 239.76/46.36  | | | | 
% 239.76/46.36  | | | |   (25)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.76/46.36  | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.76/46.36  | | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 239.76/46.36  | | | | 
% 239.76/46.36  | | | | ALPHA: (25) implies:
% 239.76/46.36  | | | |   (26)  op(e0, e2) = e2
% 239.76/46.36  | | | | 
% 239.76/46.36  | | | | REF_CLOSE: (7), (14), (15), (26) are inconsistent by sub-proof #2254.
% 239.76/46.36  | | | | 
% 239.76/46.36  | | | End of split
% 239.76/46.36  | | | 
% 239.76/46.36  | | End of split
% 239.76/46.36  | | 
% 239.76/46.36  | Case 2:
% 239.76/46.36  | | 
% 239.76/46.36  | |   (27)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 239.76/46.36  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.76/46.36  | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 239.76/46.36  | |           e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.76/46.36  | |             e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 239.76/46.36  | |         (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 239.76/46.36  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.76/46.36  | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.76/46.36  | | 
% 239.76/46.36  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (14), (15), (16), (17),
% 239.76/46.36  | |            (27) are inconsistent by sub-proof #65.
% 239.76/46.36  | | 
% 239.76/46.36  | End of split
% 239.76/46.36  | 
% 239.76/46.36  End of proof
% 239.76/46.36  
% 239.76/46.36  Sub-proof #65 shows that the following formulas are inconsistent:
% 239.76/46.36  ----------------------------------------------------------------
% 239.76/46.36    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.76/46.36         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.76/46.36    (2)   ~ (e3 = e0)
% 239.76/46.36    (3)  op(e0, e1) = all_52_11
% 239.76/46.36    (4)   ~ (all_52_11 = e1)
% 239.76/46.36    (5)   ~ (e3 = e1)
% 239.76/46.36    (6)  op(e1, e0) = e1
% 239.76/46.36    (7)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.76/46.36             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 239.76/46.36           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 239.76/46.36             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 239.76/46.36           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 239.76/46.36           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.76/46.36           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.76/46.36    (8)  all_58_12 = e1
% 239.76/46.36    (9)   ~ (all_52_11 = e3)
% 239.76/46.36    (10)   ~ (e3 = e2)
% 239.76/46.36    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.36    (12)   ~ (e1 = e0)
% 239.76/46.36    (13)  op(e0, e0) = e2
% 239.76/46.36  
% 239.76/46.36  Begin of proof
% 239.76/46.36  | 
% 239.76/46.36  | BETA: splitting (7) gives:
% 239.76/46.36  | 
% 239.76/46.36  | Case 1:
% 239.76/46.36  | | 
% 239.76/46.36  | |   (14)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 239.76/46.36  | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) =
% 239.76/46.36  | |         e0 & op(e0, e2) = e0
% 239.76/46.36  | | 
% 239.76/46.36  | | ALPHA: (14) implies:
% 239.76/46.36  | |   (15)  op(e0, e2) = e0
% 239.76/46.36  | | 
% 239.76/46.36  | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (10), (11), (13), (15) are
% 239.76/46.36  | |            inconsistent by sub-proof #190.
% 239.76/46.36  | | 
% 239.76/46.36  | Case 2:
% 239.76/46.36  | | 
% 239.76/46.37  | |   (16)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.76/46.37  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.76/46.37  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 239.76/46.37  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.76/46.37  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (3), (4), (6), (11), (12), (16) are inconsistent by sub-proof
% 239.76/46.37  | |            #140.
% 239.76/46.37  | | 
% 239.76/46.37  | End of split
% 239.76/46.37  | 
% 239.76/46.37  End of proof
% 239.76/46.37  
% 239.76/46.37  Sub-proof #66 shows that the following formulas are inconsistent:
% 239.76/46.37  ----------------------------------------------------------------
% 239.76/46.37    (1)  op(e3, e0) = all_4_0
% 239.76/46.37    (2)  op(e3, e0) = e1
% 239.76/46.37    (3)   ~ (all_4_0 = e2)
% 239.76/46.37    (4)   ~ (all_4_0 = e1)
% 239.76/46.37    (5)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.76/46.37    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.37    (7)  all_54_3 = all_4_0
% 239.76/46.37  
% 239.76/46.37  Begin of proof
% 239.76/46.37  | 
% 239.76/46.37  | BETA: splitting (5) gives:
% 239.76/46.37  | 
% 239.76/46.37  | Case 1:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (8)  all_54_3 = e2
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (3), (7), (8) are inconsistent by sub-proof #203.
% 239.76/46.37  | | 
% 239.76/46.37  | Case 2:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (9)  all_54_3 = e1 | all_54_3 = e0
% 239.76/46.37  | | 
% 239.76/46.37  | | BETA: splitting (9) gives:
% 239.76/46.37  | | 
% 239.76/46.37  | | Case 1:
% 239.76/46.37  | | | 
% 239.76/46.37  | | |   (10)  all_54_3 = e1
% 239.76/46.37  | | | 
% 239.76/46.37  | | | REF_CLOSE: (4), (7), (10) are inconsistent by sub-proof #202.
% 239.76/46.37  | | | 
% 239.76/46.37  | | Case 2:
% 239.76/46.37  | | | 
% 239.76/46.37  | | |   (11)  all_54_3 = e0
% 239.76/46.37  | | | 
% 239.76/46.37  | | | COMBINE_EQS: (7), (11) imply:
% 239.76/46.37  | | |   (12)  all_4_0 = e0
% 239.76/46.37  | | | 
% 239.76/46.37  | | | SIMP: (12) implies:
% 239.76/46.37  | | |   (13)  all_4_0 = e0
% 239.76/46.37  | | | 
% 239.76/46.37  | | | REDUCE: (4), (13) imply:
% 239.76/46.37  | | |   (14)   ~ (e1 = e0)
% 239.76/46.37  | | | 
% 239.76/46.37  | | | SIMP: (14) implies:
% 239.76/46.37  | | |   (15)   ~ (e1 = e0)
% 239.76/46.37  | | | 
% 239.76/46.37  | | | REDUCE: (1), (13) imply:
% 239.76/46.37  | | |   (16)  op(e3, e0) = e0
% 239.76/46.37  | | | 
% 239.76/46.37  | | | REF_CLOSE: (2), (6), (15), (16) are inconsistent by sub-proof #242.
% 239.76/46.37  | | | 
% 239.76/46.37  | | End of split
% 239.76/46.37  | | 
% 239.76/46.37  | End of split
% 239.76/46.37  | 
% 239.76/46.37  End of proof
% 239.76/46.37  
% 239.76/46.37  Sub-proof #67 shows that the following formulas are inconsistent:
% 239.76/46.37  ----------------------------------------------------------------
% 239.76/46.37    (1)   ~ (all_52_7 = e2)
% 239.76/46.37    (2)  all_56_31 = e2
% 239.76/46.37    (3)  op(e0, e2) = all_52_7
% 239.76/46.37    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.37    (5)  all_56_1 = e1
% 239.76/46.37    (6)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 239.76/46.37             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.76/46.37           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 239.76/46.37             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 239.76/46.37           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 239.76/46.37           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.76/46.37           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.76/46.37  
% 239.76/46.37  Begin of proof
% 239.76/46.37  | 
% 239.76/46.37  | BETA: splitting (6) gives:
% 239.76/46.37  | 
% 239.76/46.37  | Case 1:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (7)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 239.76/46.37  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 239.76/46.37  | |        & op(e1, e2) = e2
% 239.76/46.37  | | 
% 239.76/46.37  | | ALPHA: (7) implies:
% 239.76/46.37  | |   (8)   ~ (all_56_1 = e1)
% 239.76/46.37  | | 
% 239.76/46.37  | | REDUCE: (5), (8) imply:
% 239.76/46.37  | |   (9)  $false
% 239.76/46.37  | | 
% 239.76/46.37  | | CLOSE: (9) is inconsistent.
% 239.76/46.37  | | 
% 239.76/46.37  | Case 2:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (10)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.76/46.37  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.76/46.37  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 239.76/46.37  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.76/46.37  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (1), (2), (3), (4), (10) are inconsistent by sub-proof #185.
% 239.76/46.37  | | 
% 239.76/46.37  | End of split
% 239.76/46.37  | 
% 239.76/46.37  End of proof
% 239.76/46.37  
% 239.76/46.37  Sub-proof #68 shows that the following formulas are inconsistent:
% 239.76/46.37  ----------------------------------------------------------------
% 239.76/46.37    (1)   ~ (all_52_3 = e0)
% 239.76/46.37    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 239.76/46.37             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 239.76/46.37           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 239.76/46.37           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.76/46.37           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 239.76/46.37           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.76/46.37           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.76/46.37    (3)  op(e0, e3) = all_52_3
% 239.76/46.37    (4)   ~ (all_52_2 = e1)
% 239.76/46.37    (5)   ~ (all_52_3 = e3)
% 239.76/46.37    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.37    (7)  op(e1, e3) = all_52_2
% 239.76/46.37  
% 239.76/46.37  Begin of proof
% 239.76/46.37  | 
% 239.76/46.37  | BETA: splitting (2) gives:
% 239.76/46.37  | 
% 239.76/46.37  | Case 1:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (8)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 239.76/46.37  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 239.76/46.37  | |        op(e1, e3) = e1
% 239.76/46.37  | | 
% 239.76/46.37  | | ALPHA: (8) implies:
% 239.76/46.37  | |   (9)  op(e1, e3) = e1
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (4), (6), (7), (9) are inconsistent by sub-proof #1948.
% 239.76/46.37  | | 
% 239.76/46.37  | Case 2:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 239.76/46.37  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 239.76/46.37  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.76/46.37  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.76/46.37  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #2330.
% 239.76/46.37  | | 
% 239.76/46.37  | End of split
% 239.76/46.37  | 
% 239.76/46.37  End of proof
% 239.76/46.37  
% 239.76/46.37  Sub-proof #69 shows that the following formulas are inconsistent:
% 239.76/46.37  ----------------------------------------------------------------
% 239.76/46.37    (1)   ~ (e3 = e0)
% 239.76/46.37    (2)  op(e1, e2) = e1
% 239.76/46.37    (3)   ~ (e2 = e0)
% 239.76/46.37    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.76/46.37         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.76/46.37    (5)   ~ (e3 = e2)
% 239.76/46.37    (6)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.76/46.37         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.76/46.37    (7)  op(e2, e3) = e1
% 239.76/46.37    (8)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 239.76/46.37           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 239.76/46.37           all_42_1 & $i(all_42_1))
% 239.76/46.37    (9)  op(e1, e2) = e2
% 239.76/46.37    (10)  all_58_5 = e2
% 239.76/46.37    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.37    (12)  op(e2, e3) = all_8_1
% 239.76/46.37    (13)   ~ (e1 = e0)
% 239.76/46.37    (14)  all_58_4 = e3
% 239.76/46.37    (15)  all_58_14 = e1
% 239.76/46.37    (16)   ~ (e2 = e1)
% 239.76/46.37  
% 239.76/46.37  Begin of proof
% 239.76/46.37  | 
% 239.76/46.37  | BETA: splitting (8) gives:
% 239.76/46.37  | 
% 239.76/46.37  | Case 1:
% 239.76/46.37  | | 
% 239.76/46.37  | | 
% 239.76/46.37  | | GROUND_INST: instantiating (11) with e1, e2, e2, e1, simplifying with (2),
% 239.76/46.37  | |              (9) gives:
% 239.76/46.37  | |   (17)  e2 = e1
% 239.76/46.37  | | 
% 239.76/46.37  | | COMBINE_EQS: (10), (17) imply:
% 239.76/46.37  | |   (18)  all_58_5 = e1
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (1), (3), (4), (5), (6), (13), (14), (15), (16), (18) are
% 239.76/46.37  | |            inconsistent by sub-proof #1481.
% 239.76/46.37  | | 
% 239.76/46.37  | Case 2:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (19)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 239.76/46.37  | | 
% 239.76/46.37  | | ALPHA: (19) implies:
% 239.76/46.37  | |   (20)   ~ (all_42_1 = e1)
% 239.76/46.37  | |   (21)  op(e2, e3) = all_42_1
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (7), (11), (12), (20), (21) are inconsistent by sub-proof #935.
% 239.76/46.37  | | 
% 239.76/46.37  | End of split
% 239.76/46.37  | 
% 239.76/46.37  End of proof
% 239.76/46.37  
% 239.76/46.37  Sub-proof #70 shows that the following formulas are inconsistent:
% 239.76/46.37  ----------------------------------------------------------------
% 239.76/46.37    (1)   ~ (all_52_7 = e2)
% 239.76/46.37    (2)  op(e1, e2) = all_52_6
% 239.76/46.37    (3)  op(e2, e1) = all_52_9
% 239.76/46.37    (4)  op(e1, e2) = e0
% 239.76/46.37    (5)  op(e0, e2) = all_52_7
% 239.76/46.37    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.37    (7)   ~ (e1 = e0)
% 239.76/46.37    (8)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 239.76/46.37             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.76/46.37           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 239.76/46.37             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 239.76/46.37           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 239.76/46.37           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.76/46.37           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.76/46.37    (9)   ~ (all_52_9 = e2)
% 239.76/46.37  
% 239.76/46.37  Begin of proof
% 239.76/46.37  | 
% 239.76/46.37  | BETA: splitting (8) gives:
% 239.76/46.37  | 
% 239.76/46.37  | Case 1:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (10)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 239.76/46.37  | |           = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) =
% 239.76/46.37  | |         e2 & op(e1, e2) = e2
% 239.76/46.37  | | 
% 239.76/46.37  | | ALPHA: (10) implies:
% 239.76/46.37  | |   (11)  op(e2, e1) = e2
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (3), (6), (9), (11) are inconsistent by sub-proof #2328.
% 239.76/46.37  | | 
% 239.76/46.37  | Case 2:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (12)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.76/46.37  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.76/46.37  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 239.76/46.37  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.76/46.37  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (12) are inconsistent by sub-proof
% 239.76/46.37  | |            #296.
% 239.76/46.37  | | 
% 239.76/46.37  | End of split
% 239.76/46.37  | 
% 239.76/46.37  End of proof
% 239.76/46.37  
% 239.76/46.37  Sub-proof #71 shows that the following formulas are inconsistent:
% 239.76/46.37  ----------------------------------------------------------------
% 239.76/46.37    (1)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 239.76/46.37    (2)   ~ (e3 = e1)
% 239.76/46.37    (3)  all_58_3 = e3
% 239.76/46.37    (4)  op(e3, e2) = e2
% 239.76/46.37    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.37    (6)   ~ (e2 = e1)
% 239.76/46.37  
% 239.76/46.37  Begin of proof
% 239.76/46.37  | 
% 239.76/46.37  | BETA: splitting (1) gives:
% 239.76/46.37  | 
% 239.76/46.37  | Case 1:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (7)  all_58_1 = e1 & op(e3, e2) = e1
% 239.76/46.37  | | 
% 239.76/46.37  | | ALPHA: (7) implies:
% 239.76/46.37  | |   (8)  op(e3, e2) = e1
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2261.
% 239.76/46.37  | | 
% 239.76/46.37  | Case 2:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (9)  all_58_3 = e1 & op(e2, e2) = e1
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #2197.
% 239.76/46.37  | | 
% 239.76/46.37  | End of split
% 239.76/46.37  | 
% 239.76/46.37  End of proof
% 239.76/46.37  
% 239.76/46.37  Sub-proof #72 shows that the following formulas are inconsistent:
% 239.76/46.37  ----------------------------------------------------------------
% 239.76/46.37    (1)   ~ (all_52_7 = e2)
% 239.76/46.37    (2)  op(e2, e1) = all_52_9
% 239.76/46.37    (3)  op(e0, e2) = all_52_7
% 239.76/46.37    (4)  all_56_21 = e1
% 239.76/46.37    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.37    (6)   ~ (all_52_9 = e1)
% 239.76/46.37    (7)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 239.76/46.37             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.76/46.37           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 239.76/46.37             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 239.76/46.37           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 239.76/46.37           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.76/46.37           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.76/46.37  
% 239.76/46.37  Begin of proof
% 239.76/46.37  | 
% 239.76/46.37  | BETA: splitting (7) gives:
% 239.76/46.37  | 
% 239.76/46.37  | Case 1:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (8)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 239.76/46.37  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 239.76/46.37  | |        & op(e1, e2) = e2
% 239.76/46.37  | | 
% 239.76/46.37  | | ALPHA: (8) implies:
% 239.76/46.37  | |   (9)   ~ (all_56_21 = e1)
% 239.76/46.37  | | 
% 239.76/46.37  | | REDUCE: (4), (9) imply:
% 239.76/46.37  | |   (10)  $false
% 239.76/46.37  | | 
% 239.76/46.37  | | CLOSE: (10) is inconsistent.
% 239.76/46.37  | | 
% 239.76/46.37  | Case 2:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (11)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.76/46.37  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.76/46.37  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 239.76/46.37  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.76/46.37  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (1), (2), (3), (5), (6), (11) are inconsistent by sub-proof
% 239.76/46.37  | |            #2305.
% 239.76/46.37  | | 
% 239.76/46.37  | End of split
% 239.76/46.37  | 
% 239.76/46.37  End of proof
% 239.76/46.37  
% 239.76/46.37  Sub-proof #73 shows that the following formulas are inconsistent:
% 239.76/46.37  ----------------------------------------------------------------
% 239.76/46.37    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 239.76/46.37           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 239.76/46.37             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 239.76/46.37           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.76/46.37             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.76/46.37           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.76/46.37           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.76/46.37    (2)  op(e2, e3) = all_52_1
% 239.76/46.37    (3)  all_56_21 = e1
% 239.76/46.37    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.37    (5)  all_56_11 = e3
% 239.76/46.37    (6)   ~ (all_52_1 = e3)
% 239.76/46.37  
% 239.76/46.37  Begin of proof
% 239.76/46.37  | 
% 239.76/46.37  | BETA: splitting (1) gives:
% 239.76/46.37  | 
% 239.76/46.37  | Case 1:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.76/46.37  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.76/46.37  | |        op(e2, e3) = e3
% 239.76/46.37  | | 
% 239.76/46.37  | | ALPHA: (7) implies:
% 239.76/46.37  | |   (8)  op(e2, e3) = e3
% 239.76/46.37  | | 
% 239.76/46.37  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2337.
% 239.76/46.37  | | 
% 239.76/46.37  | Case 2:
% 239.76/46.37  | | 
% 239.76/46.37  | |   (9)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 239.76/46.37  | |            e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2
% 239.76/46.37  | |          & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1
% 239.76/46.37  | |            = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 239.76/46.37  | |            = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.76/46.37  | | 
% 239.76/46.37  | | BETA: splitting (9) gives:
% 239.76/46.37  | | 
% 239.76/46.37  | | Case 1:
% 239.76/46.37  | | | 
% 239.76/46.37  | | |   (10)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 239.76/46.37  | | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 239.76/46.37  | | |         e2 & op(e2, e3) = e2
% 239.76/46.37  | | | 
% 239.76/46.37  | | | ALPHA: (10) implies:
% 239.76/46.37  | | |   (11)   ~ (all_56_11 = e3)
% 239.76/46.37  | | | 
% 239.76/46.37  | | | REDUCE: (5), (11) imply:
% 239.76/46.37  | | |   (12)  $false
% 239.76/46.37  | | | 
% 239.76/46.37  | | | CLOSE: (12) is inconsistent.
% 239.76/46.37  | | | 
% 239.76/46.37  | | Case 2:
% 239.76/46.37  | | | 
% 239.76/46.37  | | |   (13)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.76/46.37  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.76/46.37  | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 239.76/46.37  | | | 
% 239.76/46.37  | | | ALPHA: (13) implies:
% 239.76/46.37  | | |   (14)   ~ (all_56_21 = e1)
% 239.76/46.37  | | | 
% 239.76/46.37  | | | REDUCE: (3), (14) imply:
% 239.76/46.37  | | |   (15)  $false
% 239.76/46.37  | | | 
% 239.76/46.37  | | | CLOSE: (15) is inconsistent.
% 239.76/46.37  | | | 
% 239.76/46.37  | | End of split
% 239.76/46.37  | | 
% 239.76/46.37  | End of split
% 239.76/46.37  | 
% 239.76/46.37  End of proof
% 239.76/46.37  
% 239.76/46.37  Sub-proof #74 shows that the following formulas are inconsistent:
% 239.76/46.37  ----------------------------------------------------------------
% 239.76/46.38    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.76/46.38         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.76/46.38    (2)   ~ (e3 = e0)
% 239.76/46.38    (3)  op(e0, e1) = all_52_11
% 239.76/46.38    (4)   ~ (e3 = e1)
% 239.76/46.38    (5)  all_58_3 = e3
% 239.76/46.38    (6)   ~ (all_52_11 = e3)
% 239.76/46.38    (7)   ~ (e3 = e2)
% 239.76/46.38    (8)  all_58_12 = e3
% 239.76/46.38    (9)  op(e0, e2) = e0
% 239.76/46.38    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.38    (11)  all_58_3 = e1 & op(e2, e2) = e1
% 239.76/46.38    (12)  op(e0, e0) = e2
% 239.76/46.38  
% 239.76/46.38  Begin of proof
% 239.76/46.38  | 
% 239.76/46.38  | ALPHA: (11) implies:
% 239.76/46.38  |   (13)  all_58_3 = e1
% 239.76/46.38  | 
% 239.76/46.38  | COMBINE_EQS: (5), (13) imply:
% 239.76/46.38  |   (14)  e3 = e1
% 239.76/46.38  | 
% 239.76/46.38  | COMBINE_EQS: (8), (14) imply:
% 239.76/46.38  |   (15)  all_58_12 = e1
% 239.76/46.38  | 
% 239.76/46.38  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (12), (15) are
% 239.76/46.38  |            inconsistent by sub-proof #190.
% 239.76/46.38  | 
% 239.76/46.38  End of proof
% 239.76/46.38  
% 239.76/46.38  Sub-proof #75 shows that the following formulas are inconsistent:
% 239.76/46.38  ----------------------------------------------------------------
% 239.76/46.38    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.76/46.38         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.76/46.38    (2)   ~ (e3 = e0)
% 239.76/46.38    (3)  op(e0, e1) = all_52_11
% 239.76/46.38    (4)   ~ (e2 = e0)
% 239.76/46.38    (5)  op(e1, e2) = all_52_6
% 239.76/46.38    (6)  op(e1, e1) = all_6_2
% 239.76/46.38    (7)  op(e1, e0) = all_52_14
% 239.76/46.38    (8)   ~ (all_52_7 = e3)
% 239.76/46.38    (9)   ~ (e3 = e1)
% 239.76/46.38    (10)   ~ (all_52_11 = e3)
% 239.76/46.38    (11)   ~ (all_6_2 = e3)
% 239.76/46.38    (12)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 239.76/46.38          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 239.76/46.38    (13)   ~ (e3 = e2)
% 239.76/46.38    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.76/46.38          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.76/46.38    (15)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.76/46.38          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.76/46.38    (16)   ~ (all_52_14 = e3)
% 239.76/46.38    (17)   ~ (all_52_6 = e3)
% 239.76/46.38    (18)  op(e0, e2) = all_52_7
% 239.76/46.38    (19)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.76/46.38          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.76/46.38    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.38    (21)   ~ (e1 = e0)
% 239.76/46.38    (22)  op(e0, e0) = e2
% 239.76/46.38    (23)   ~ (e2 = e1)
% 239.76/46.38  
% 239.76/46.38  Begin of proof
% 239.76/46.38  | 
% 239.76/46.38  | BETA: splitting (1) gives:
% 239.76/46.38  | 
% 239.76/46.38  | Case 1:
% 239.76/46.38  | | 
% 239.76/46.38  | |   (24)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 239.76/46.38  | |           e3)
% 239.76/46.38  | | 
% 239.76/46.38  | | BETA: splitting (24) gives:
% 239.76/46.38  | | 
% 239.76/46.38  | | Case 1:
% 239.76/46.38  | | | 
% 239.76/46.38  | | |   (25)  all_58_12 = e3 & op(e0, e3) = e3
% 239.76/46.38  | | | 
% 239.76/46.38  | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (13), (14), (15),
% 239.76/46.38  | | |            (16), (17), (19), (20), (21), (23), (25) are inconsistent by
% 239.76/46.38  | | |            sub-proof #1528.
% 239.76/46.38  | | | 
% 239.76/46.38  | | Case 2:
% 239.76/46.38  | | | 
% 239.76/46.38  | | |   (26)  all_58_13 = e3 & op(e0, e2) = e3
% 239.76/46.38  | | | 
% 239.76/46.38  | | | REF_CLOSE: (8), (18), (20), (26) are inconsistent by sub-proof #1919.
% 239.76/46.38  | | | 
% 239.76/46.38  | | End of split
% 239.76/46.38  | | 
% 239.76/46.38  | Case 2:
% 239.76/46.38  | | 
% 239.76/46.38  | |   (27)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 239.76/46.38  | |           e3)
% 239.76/46.38  | | 
% 239.76/46.38  | | REF_CLOSE: (3), (10), (13), (20), (22), (27) are inconsistent by sub-proof
% 239.76/46.38  | |            #226.
% 239.76/46.38  | | 
% 239.76/46.38  | End of split
% 239.76/46.38  | 
% 239.76/46.38  End of proof
% 239.76/46.38  
% 239.76/46.38  Sub-proof #76 shows that the following formulas are inconsistent:
% 239.76/46.38  ----------------------------------------------------------------
% 239.76/46.38    (1)  op(e0, e3) = all_52_3
% 239.76/46.38    (2)   ~ (all_52_3 = e3)
% 239.76/46.38    (3)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 239.76/46.38           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 239.76/46.38             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 239.76/46.38           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.76/46.38             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.76/46.38           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.76/46.38           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.76/46.38           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.76/46.38           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 239.76/46.38           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.76/46.38           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.76/46.38             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.76/46.38           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.76/46.38           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.76/46.38    (4)  op(e2, e3) = all_52_1
% 239.76/46.38    (5)   ~ (all_52_2 = e3)
% 239.76/46.38    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.38    (7)  op(e1, e3) = all_52_2
% 239.76/46.38    (8)  all_56_11 = e3
% 239.76/46.38    (9)   ~ (all_52_1 = e3)
% 239.76/46.38  
% 239.76/46.38  Begin of proof
% 239.76/46.38  | 
% 239.76/46.38  | BETA: splitting (3) gives:
% 239.76/46.38  | 
% 239.76/46.38  | Case 1:
% 239.76/46.38  | | 
% 239.76/46.38  | |   (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 239.76/46.38  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 239.76/46.38  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 239.76/46.38  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.76/46.38  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 239.76/46.38  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 239.76/46.38  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 239.76/46.38  | |           op(e1, e3) = e3)
% 239.76/46.38  | | 
% 239.76/46.38  | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10) are inconsistent by sub-proof
% 239.76/46.38  | |            #77.
% 239.76/46.38  | | 
% 239.76/46.38  | Case 2:
% 239.76/46.38  | | 
% 239.76/46.38  | |   (11)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 239.76/46.38  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 239.76/46.38  | |           e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 239.76/46.38  | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.76/46.38  | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7
% 239.76/46.38  | |           = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &
% 239.76/46.38  | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 239.76/46.38  | |           op(e0, e3) = e0)
% 239.76/46.38  | | 
% 239.76/46.38  | | BETA: splitting (11) gives:
% 239.76/46.38  | | 
% 239.76/46.38  | | Case 1:
% 239.76/46.38  | | | 
% 239.76/46.38  | | |   (12)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 239.76/46.38  | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.76/46.38  | | |         op(e3, e1) = e1 & op(e1, e3) = e1
% 239.76/46.38  | | | 
% 239.76/46.38  | | | ALPHA: (12) implies:
% 239.76/46.38  | | |   (13)   ~ (all_56_11 = e3)
% 239.76/46.38  | | | 
% 239.76/46.38  | | | REDUCE: (8), (13) imply:
% 239.76/46.38  | | |   (14)  $false
% 239.76/46.38  | | | 
% 239.76/46.38  | | | CLOSE: (14) is inconsistent.
% 239.76/46.38  | | | 
% 239.76/46.38  | | Case 2:
% 239.76/46.38  | | | 
% 239.76/46.38  | | |   (15)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.76/46.38  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.76/46.38  | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 239.76/46.38  | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 239.76/46.38  | | |             = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 239.76/46.38  | | |           e0)
% 239.76/46.38  | | | 
% 239.76/46.38  | | | BETA: splitting (15) gives:
% 239.76/46.38  | | | 
% 239.76/46.38  | | | Case 1:
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | |   (16)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.76/46.38  | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.76/46.38  | | | |         op(e3, e0) = e3 & op(e0, e3) = e3
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | ALPHA: (16) implies:
% 239.76/46.38  | | | |   (17)  op(e0, e3) = e3
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | REF_CLOSE: (1), (2), (6), (17) are inconsistent by sub-proof #2332.
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | Case 2:
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | |   (18)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.76/46.38  | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.76/46.38  | | | |         op(e3, e0) = e0 & op(e0, e3) = e0
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | ALPHA: (18) implies:
% 239.76/46.38  | | | |   (19)   ~ (all_56_11 = e3)
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | REDUCE: (8), (19) imply:
% 239.76/46.38  | | | |   (20)  $false
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | CLOSE: (20) is inconsistent.
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | End of split
% 239.76/46.38  | | | 
% 239.76/46.38  | | End of split
% 239.76/46.38  | | 
% 239.76/46.38  | End of split
% 239.76/46.38  | 
% 239.76/46.38  End of proof
% 239.76/46.38  
% 239.76/46.38  Sub-proof #77 shows that the following formulas are inconsistent:
% 239.76/46.38  ----------------------------------------------------------------
% 239.76/46.38    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 239.76/46.38           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 239.76/46.38             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 239.76/46.38           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.76/46.38             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.76/46.38           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.76/46.38           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.76/46.38    (2)  op(e2, e3) = all_52_1
% 239.76/46.38    (3)   ~ (all_52_2 = e3)
% 239.76/46.38    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.38    (5)  op(e1, e3) = all_52_2
% 239.76/46.38    (6)  all_56_11 = e3
% 239.76/46.38    (7)   ~ (all_52_1 = e3)
% 239.76/46.38  
% 239.76/46.38  Begin of proof
% 239.76/46.38  | 
% 239.76/46.38  | BETA: splitting (1) gives:
% 239.76/46.38  | 
% 239.76/46.38  | Case 1:
% 239.76/46.38  | | 
% 239.76/46.38  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.76/46.38  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.76/46.38  | |        op(e2, e3) = e3
% 239.76/46.38  | | 
% 239.76/46.38  | | ALPHA: (8) implies:
% 239.76/46.38  | |   (9)  op(e2, e3) = e3
% 239.76/46.38  | | 
% 239.76/46.38  | | REF_CLOSE: (2), (4), (7), (9) are inconsistent by sub-proof #2337.
% 239.76/46.38  | | 
% 239.76/46.38  | Case 2:
% 239.76/46.38  | | 
% 239.76/46.38  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 239.76/46.38  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 239.76/46.38  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.76/46.38  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.76/46.38  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.76/46.38  | | 
% 239.76/46.38  | | BETA: splitting (10) gives:
% 239.76/46.38  | | 
% 239.76/46.38  | | Case 1:
% 239.76/46.38  | | | 
% 239.76/46.38  | | |   (11)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 239.76/46.38  | | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 239.76/46.38  | | |         e2 & op(e2, e3) = e2
% 239.76/46.38  | | | 
% 239.76/46.38  | | | ALPHA: (11) implies:
% 239.76/46.38  | | |   (12)   ~ (all_56_11 = e3)
% 239.76/46.38  | | | 
% 239.76/46.38  | | | REDUCE: (6), (12) imply:
% 239.76/46.38  | | |   (13)  $false
% 239.76/46.38  | | | 
% 239.76/46.38  | | | CLOSE: (13) is inconsistent.
% 239.76/46.38  | | | 
% 239.76/46.38  | | Case 2:
% 239.76/46.38  | | | 
% 239.76/46.38  | | |   (14)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.76/46.38  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.76/46.38  | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 239.76/46.38  | | | 
% 239.76/46.38  | | | ALPHA: (14) implies:
% 239.76/46.38  | | |   (15)  op(e1, e3) = e3
% 239.76/46.38  | | | 
% 239.76/46.38  | | | REF_CLOSE: (3), (4), (5), (15) are inconsistent by sub-proof #2335.
% 239.76/46.38  | | | 
% 239.76/46.38  | | End of split
% 239.76/46.38  | | 
% 239.76/46.38  | End of split
% 239.76/46.38  | 
% 239.76/46.38  End of proof
% 239.76/46.38  
% 239.76/46.38  Sub-proof #78 shows that the following formulas are inconsistent:
% 239.76/46.38  ----------------------------------------------------------------
% 239.76/46.38    (1)   ~ (e3 = e0)
% 239.76/46.38    (2)  op(e0, e1) = all_52_11
% 239.76/46.38    (3)   ~ (all_52_11 = e3)
% 239.76/46.38    (4)  op(e2, e1) = all_52_9
% 239.76/46.38    (5)   ~ (e3 = e2)
% 239.76/46.38    (6)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.76/46.38    (7)  op(e3, e0) = all_52_12
% 239.76/46.38    (8)   ~ (all_52_12 = e2)
% 239.76/46.38    (9)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.76/46.38         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.76/46.38    (10)   ~ (all_52_9 = e3)
% 239.76/46.38    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.38    (12)  op(e1, e1) = e0
% 239.76/46.38  
% 239.76/46.38  Begin of proof
% 239.76/46.38  | 
% 239.76/46.38  | BETA: splitting (6) gives:
% 239.76/46.38  | 
% 239.76/46.38  | Case 1:
% 239.76/46.38  | | 
% 239.76/46.38  | |   (13)  all_58_4 = e2 & op(e3, e1) = e2
% 239.76/46.38  | | 
% 239.76/46.38  | | ALPHA: (13) implies:
% 239.76/46.38  | |   (14)  all_58_4 = e2
% 239.76/46.38  | | 
% 239.76/46.38  | | REF_CLOSE: (1), (2), (3), (4), (5), (9), (10), (11), (12), (14) are
% 239.76/46.38  | |            inconsistent by sub-proof #1493.
% 239.76/46.38  | | 
% 239.76/46.38  | Case 2:
% 239.76/46.38  | | 
% 239.76/46.38  | |   (15)  all_58_9 = e2 & op(e3, e0) = e2
% 239.76/46.38  | | 
% 239.76/46.38  | | REF_CLOSE: (7), (8), (11), (15) are inconsistent by sub-proof #2318.
% 239.76/46.38  | | 
% 239.76/46.38  | End of split
% 239.76/46.38  | 
% 239.76/46.38  End of proof
% 239.76/46.38  
% 239.76/46.38  Sub-proof #79 shows that the following formulas are inconsistent:
% 239.76/46.38  ----------------------------------------------------------------
% 239.76/46.38    (1)  op(e0, e1) = all_56_23
% 239.76/46.38    (2)  op(e0, e1) = e1
% 239.76/46.38    (3)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 239.76/46.38    (4)   ~ (all_52_13 = e2)
% 239.76/46.38    (5)  all_54_7 = all_52_13
% 239.76/46.38    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.38    (7)  op(e0, all_56_23) = e0
% 239.76/46.38    (8)   ~ (all_52_13 = e3)
% 239.76/46.38    (9)   ~ (all_52_13 = e0)
% 239.76/46.38  
% 239.76/46.38  Begin of proof
% 239.76/46.38  | 
% 239.76/46.38  | BETA: splitting (3) gives:
% 239.76/46.38  | 
% 239.76/46.38  | Case 1:
% 239.76/46.38  | | 
% 239.76/46.38  | |   (10)  all_54_7 = e3
% 239.76/46.38  | | 
% 239.76/46.38  | | REF_CLOSE: (5), (8), (10) are inconsistent by sub-proof #2296.
% 239.76/46.38  | | 
% 239.76/46.38  | Case 2:
% 239.76/46.38  | | 
% 239.76/46.38  | |   (11)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 239.76/46.38  | | 
% 239.76/46.38  | | BETA: splitting (11) gives:
% 239.76/46.38  | | 
% 239.76/46.38  | | Case 1:
% 239.76/46.38  | | | 
% 239.76/46.38  | | |   (12)  all_54_7 = e2
% 239.76/46.38  | | | 
% 239.76/46.38  | | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #1997.
% 239.76/46.38  | | | 
% 239.76/46.38  | | Case 2:
% 239.76/46.38  | | | 
% 239.76/46.38  | | |   (13)  all_54_7 = e1 | all_54_7 = e0
% 239.76/46.38  | | | 
% 239.76/46.38  | | | BETA: splitting (13) gives:
% 239.76/46.38  | | | 
% 239.76/46.38  | | | Case 1:
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | |   (14)  all_54_7 = e1
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | COMBINE_EQS: (5), (14) imply:
% 239.76/46.38  | | | |   (15)  all_52_13 = e1
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | SIMP: (15) implies:
% 239.76/46.38  | | | |   (16)  all_52_13 = e1
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | REDUCE: (9), (16) imply:
% 239.76/46.38  | | | |   (17)   ~ (e1 = e0)
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | GROUND_INST: instantiating (6) with e1, all_56_23, e1, e0, simplifying
% 239.76/46.38  | | | |              with (1), (2) gives:
% 239.76/46.38  | | | |   (18)  all_56_23 = e1
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | REDUCE: (7), (18) imply:
% 239.76/46.38  | | | |   (19)  op(e0, e1) = e0
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | REF_CLOSE: (2), (6), (17), (19) are inconsistent by sub-proof #2158.
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | Case 2:
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | |   (20)  all_54_7 = e0
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | | REF_CLOSE: (5), (9), (20) are inconsistent by sub-proof #2294.
% 239.76/46.38  | | | | 
% 239.76/46.38  | | | End of split
% 239.76/46.38  | | | 
% 239.76/46.38  | | End of split
% 239.76/46.38  | | 
% 239.76/46.38  | End of split
% 239.76/46.38  | 
% 239.76/46.38  End of proof
% 239.76/46.38  
% 239.76/46.38  Sub-proof #80 shows that the following formulas are inconsistent:
% 239.76/46.38  ----------------------------------------------------------------
% 239.76/46.38    (1)  op(e1, all_56_29) = e1
% 239.76/46.38    (2)   ~ (all_52_6 = e0)
% 239.76/46.38    (3)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 239.76/46.38    (4)  op(e1, e0) = all_18_1
% 239.76/46.38    (5)  all_54_9 = all_52_6
% 239.76/46.38    (6)  op(e1, e0) = e3
% 239.76/46.38    (7)  op(e1, e0) = all_28_1
% 239.76/46.38    (8)   ~ (all_52_13 = e2)
% 239.76/46.38    (9)  all_54_7 = all_52_13
% 239.76/46.38    (10)   ~ (all_52_2 = all_52_6)
% 239.76/46.38    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.38    (12)  op(e1, e3) = all_52_2
% 239.76/46.38    (13)  all_54_9 = e1 | all_54_9 = e0
% 239.76/46.39    (14)  op(e1, e0) = all_56_29
% 239.76/46.39  
% 239.76/46.39  Begin of proof
% 239.76/46.39  | 
% 239.76/46.39  | BETA: splitting (3) gives:
% 239.76/46.39  | 
% 239.76/46.39  | Case 1:
% 239.76/46.39  | | 
% 239.76/46.39  | |   (15)  all_54_7 = e2
% 239.76/46.39  | | 
% 239.76/46.39  | | REF_CLOSE: (8), (9), (15) are inconsistent by sub-proof #1997.
% 239.76/46.39  | | 
% 239.76/46.39  | Case 2:
% 239.76/46.39  | | 
% 239.76/46.39  | | 
% 239.76/46.39  | | GROUND_INST: instantiating (11) with e3, all_28_1, e0, e1, simplifying with
% 239.76/46.39  | |              (6), (7) gives:
% 239.76/46.39  | |   (16)  all_28_1 = e3
% 239.76/46.39  | | 
% 239.76/46.39  | | GROUND_INST: instantiating (11) with all_28_1, all_56_29, e0, e1,
% 239.76/46.39  | |              simplifying with (7), (14) gives:
% 239.76/46.39  | |   (17)  all_56_29 = all_28_1
% 239.76/46.39  | | 
% 239.76/46.39  | | GROUND_INST: instantiating (11) with all_18_1, all_56_29, e0, e1,
% 239.76/46.39  | |              simplifying with (4), (14) gives:
% 239.76/46.39  | |   (18)  all_56_29 = all_18_1
% 239.76/46.39  | | 
% 239.76/46.39  | | COMBINE_EQS: (17), (18) imply:
% 239.76/46.39  | |   (19)  all_28_1 = all_18_1
% 239.76/46.39  | | 
% 239.76/46.39  | | SIMP: (19) implies:
% 239.76/46.39  | |   (20)  all_28_1 = all_18_1
% 239.76/46.39  | | 
% 239.76/46.39  | | COMBINE_EQS: (16), (20) imply:
% 239.76/46.39  | |   (21)  all_18_1 = e3
% 239.76/46.39  | | 
% 239.76/46.39  | | COMBINE_EQS: (18), (21) imply:
% 239.76/46.39  | |   (22)  all_56_29 = e3
% 239.76/46.39  | | 
% 239.76/46.39  | | REDUCE: (1), (22) imply:
% 239.76/46.39  | |   (23)  op(e1, e3) = e1
% 239.76/46.39  | | 
% 239.76/46.39  | | REF_CLOSE: (2), (5), (10), (11), (12), (13), (23) are inconsistent by
% 239.76/46.39  | |            sub-proof #1931.
% 239.76/46.39  | | 
% 239.76/46.39  | End of split
% 239.76/46.39  | 
% 239.76/46.39  End of proof
% 239.76/46.39  
% 239.76/46.39  Sub-proof #81 shows that the following formulas are inconsistent:
% 239.76/46.39  ----------------------------------------------------------------
% 239.76/46.39    (1)   ~ (e3 = e0)
% 239.76/46.39    (2)  all_58_1 = e3
% 239.76/46.39    (3)   ~ (e2 = e0)
% 239.76/46.39    (4)  op(e1, e2) = all_52_6
% 239.76/46.39    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 239.76/46.39         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.76/46.39    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.76/46.39         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.76/46.39    (7)   ~ (e3 = e1)
% 239.76/46.39    (8)  all_58_7 = e2
% 239.76/46.39    (9)   ~ (e3 = e2)
% 239.76/46.39    (10)  op(e3, e2) = all_52_4
% 239.76/46.39    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.39    (12)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.76/46.39          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.76/46.39    (13)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.76/46.39          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.76/46.39    (14)   ~ (e1 = e0)
% 239.76/46.39    (15)  all_58_3 = e2
% 239.76/46.39    (16)  op(e2, e2) = e2
% 239.76/46.39    (17)   ~ (all_52_4 = e0)
% 239.76/46.39    (18)   ~ (e2 = e1)
% 239.76/46.39  
% 239.76/46.39  Begin of proof
% 239.76/46.39  | 
% 239.76/46.39  | BETA: splitting (12) gives:
% 239.76/46.39  | 
% 239.76/46.39  | Case 1:
% 239.76/46.39  | | 
% 239.76/46.39  | |   (19)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 239.76/46.39  | |           e1)
% 239.76/46.39  | | 
% 239.76/46.39  | | BETA: splitting (19) gives:
% 239.76/46.39  | | 
% 239.76/46.39  | | Case 1:
% 239.76/46.39  | | | 
% 239.76/46.39  | | |   (20)  all_58_1 = e1 & op(e3, e2) = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | REF_CLOSE: (2), (7), (20) are inconsistent by sub-proof #1753.
% 239.76/46.39  | | | 
% 239.76/46.39  | | Case 2:
% 239.76/46.39  | | | 
% 239.76/46.39  | | |   (21)  all_58_3 = e1 & op(e2, e2) = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | ALPHA: (21) implies:
% 239.76/46.39  | | |   (22)  op(e2, e2) = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | REF_CLOSE: (11), (16), (18), (22) are inconsistent by sub-proof #2235.
% 239.76/46.39  | | | 
% 239.76/46.39  | | End of split
% 239.76/46.39  | | 
% 239.76/46.39  | Case 2:
% 239.76/46.39  | | 
% 239.76/46.39  | |   (23)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 239.76/46.39  | |           e1)
% 239.76/46.39  | | 
% 239.76/46.39  | | BETA: splitting (23) gives:
% 239.76/46.39  | | 
% 239.76/46.39  | | Case 1:
% 239.76/46.39  | | | 
% 239.76/46.39  | | |   (24)  all_58_7 = e1 & op(e1, e2) = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | ALPHA: (24) implies:
% 239.76/46.39  | | |   (25)  all_58_7 = e1
% 239.76/46.39  | | |   (26)  op(e1, e2) = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | COMBINE_EQS: (8), (25) imply:
% 239.76/46.39  | | |   (27)  e2 = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | SIMP: (27) implies:
% 239.76/46.39  | | |   (28)  e2 = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | COMBINE_EQS: (15), (28) imply:
% 239.76/46.39  | | |   (29)  all_58_3 = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (11), (13), (14), (16),
% 239.76/46.39  | | |            (18), (25), (26), (29) are inconsistent by sub-proof #2127.
% 239.76/46.39  | | | 
% 239.76/46.39  | | Case 2:
% 239.76/46.39  | | | 
% 239.76/46.39  | | |   (30)  all_58_13 = e1 & op(e0, e2) = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | ALPHA: (30) implies:
% 239.76/46.39  | | |   (31)  op(e0, e2) = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | REF_CLOSE: (3), (6), (8), (10), (11), (14), (16), (17), (31) are
% 239.76/46.39  | | |            inconsistent by sub-proof #1586.
% 239.76/46.39  | | | 
% 239.76/46.39  | | End of split
% 239.76/46.39  | | 
% 239.76/46.39  | End of split
% 239.76/46.39  | 
% 239.76/46.39  End of proof
% 239.76/46.39  
% 239.76/46.39  Sub-proof #82 shows that the following formulas are inconsistent:
% 239.76/46.39  ----------------------------------------------------------------
% 239.76/46.39    (1)   ~ (e3 = e0)
% 239.76/46.39    (2)   ~ (e2 = e0)
% 239.76/46.39    (3)  op(e1, e2) = all_52_6
% 239.76/46.39    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.76/46.39         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.76/46.39    (5)   ~ (all_52_6 = e0)
% 239.76/46.39    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 239.76/46.39    (7)   ~ (e3 = e2)
% 239.76/46.39    (8)  op(e0, e2) = all_52_7
% 239.76/46.39    (9)   ~ (all_52_7 = e0)
% 239.76/46.39    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.39    (11)  op(e3, e2) = e3
% 239.76/46.39  
% 239.76/46.39  Begin of proof
% 239.76/46.39  | 
% 239.76/46.39  | BETA: splitting (6) gives:
% 239.76/46.39  | 
% 239.76/46.39  | Case 1:
% 239.76/46.39  | | 
% 239.76/46.39  | |   (12)  all_58_1 = e2 & op(e3, e2) = e2
% 239.76/46.39  | | 
% 239.76/46.39  | | ALPHA: (12) implies:
% 239.76/46.39  | |   (13)  op(e3, e2) = e2
% 239.76/46.39  | | 
% 239.76/46.39  | | REF_CLOSE: (7), (10), (11), (13) are inconsistent by sub-proof #2193.
% 239.76/46.39  | | 
% 239.76/46.39  | Case 2:
% 239.76/46.39  | | 
% 239.76/46.39  | |   (14)  all_58_3 = e2 & op(e2, e2) = e2
% 239.76/46.39  | | 
% 239.76/46.39  | | ALPHA: (14) implies:
% 239.76/46.39  | |   (15)  op(e2, e2) = e2
% 239.76/46.39  | | 
% 239.76/46.39  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (15) are
% 239.76/46.39  | |            inconsistent by sub-proof #408.
% 239.76/46.39  | | 
% 239.76/46.39  | End of split
% 239.76/46.39  | 
% 239.76/46.39  End of proof
% 239.76/46.39  
% 239.76/46.39  Sub-proof #83 shows that the following formulas are inconsistent:
% 239.76/46.39  ----------------------------------------------------------------
% 239.76/46.39    (1)  all_44_2 = e2
% 239.76/46.39    (2)   ~ (all_44_2 = e2) | ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 239.76/46.39           op(e0, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 239.76/46.39             e1) & op(e0, e2) = all_44_1 & $i(all_44_1))
% 239.76/46.39    (3)  all_48_2 = e0
% 239.76/46.39    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 239.76/46.39         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 239.76/46.39    (5)  ( ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 239.76/46.39           $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e0, e2) = all_4_1
% 239.76/46.39           & $i(all_4_1))
% 239.76/46.39    (6)  op(e1, e0) = all_52_14
% 239.76/46.39    (7)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.76/46.39    (8)  all_54_11 = all_52_14
% 239.76/46.39    (9)   ~ (all_52_12 = e1)
% 239.76/46.39    (10)   ~ (all_52_12 = all_52_14)
% 239.76/46.39    (11)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 239.76/46.39            op(e2, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 239.76/46.39              e3) & op(e2, e0) = all_48_1 & $i(all_48_1))
% 239.76/46.39    (12)   ~ (all_52_12 = all_52_13)
% 239.76/46.39    (13)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 239.76/46.39    (14)  all_58_15 = e2
% 239.76/46.39    (15)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.76/46.39    (16)   ~ (all_52_14 = e2)
% 239.76/46.39    (17)   ~ (all_52_14 = e1)
% 239.76/46.39    (18)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 239.76/46.39            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 239.76/46.39              e0) = all_14_1 & $i(all_14_1))
% 239.76/46.39    (19)  op(e3, e0) = all_52_12
% 239.76/46.39    (20)   ~ (all_52_4 = all_52_12)
% 239.76/46.39    (21)  op(e2, e2) = all_8_2
% 239.76/46.39    (22)   ~ (all_52_12 = e2)
% 239.76/46.39    (23)  op(e0, e2) = all_52_7
% 239.76/46.39    (24)   ~ (all_52_13 = all_52_14)
% 239.76/46.39    (25)  all_54_1 = all_52_4
% 239.76/46.39    (26)  op(e3, e2) = all_52_4
% 239.76/46.39    (27)  all_54_3 = all_52_12
% 239.76/46.39    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.39    (29)   ~ (all_8_2 = e3)
% 239.76/46.39    (30)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.76/46.39          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.76/46.39    (31)  op(e2, e0) = all_52_13
% 239.76/46.39    (32)  all_58_13 = e1 & op(e0, e2) = e1
% 239.76/46.39    (33)   ~ (all_52_4 = e0)
% 239.76/46.39    (34)   ~ (e2 = e1)
% 239.76/46.39    (35)   ~ (all_52_4 = all_52_7)
% 239.76/46.39  
% 239.76/46.39  Begin of proof
% 239.76/46.39  | 
% 239.76/46.39  | ALPHA: (32) implies:
% 239.76/46.39  |   (36)  all_58_13 = e1
% 239.76/46.39  |   (37)  op(e0, e2) = e1
% 239.76/46.39  | 
% 239.76/46.39  | BETA: splitting (4) gives:
% 239.76/46.39  | 
% 239.76/46.39  | Case 1:
% 239.76/46.39  | | 
% 239.76/46.39  | |   (38)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 239.76/46.39  | |           e1)
% 239.76/46.39  | | 
% 239.76/46.39  | | BETA: splitting (38) gives:
% 239.76/46.39  | | 
% 239.76/46.39  | | Case 1:
% 239.76/46.39  | | | 
% 239.76/46.39  | | |   (39)  all_58_9 = e1 & op(e3, e0) = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | REF_CLOSE: (9), (19), (28), (39) are inconsistent by sub-proof #2278.
% 239.76/46.39  | | | 
% 239.76/46.39  | | Case 2:
% 239.76/46.39  | | | 
% 239.76/46.39  | | |   (40)  all_58_10 = e1 & op(e2, e0) = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | ALPHA: (40) implies:
% 239.76/46.39  | | |   (41)  op(e2, e0) = e1
% 239.76/46.39  | | | 
% 239.76/46.39  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13),
% 239.76/46.39  | | |            (15), (16), (18), (20), (21), (22), (23), (24), (25), (26),
% 239.76/46.39  | | |            (27), (28), (29), (30), (31), (33), (35), (36), (37), (41) are
% 239.76/46.39  | | |            inconsistent by sub-proof #84.
% 239.76/46.39  | | | 
% 239.76/46.39  | | End of split
% 239.76/46.39  | | 
% 239.76/46.39  | Case 2:
% 239.76/46.39  | | 
% 239.76/46.39  | |   (42)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 239.76/46.39  | |           e1)
% 239.76/46.39  | | 
% 239.76/46.39  | | REF_CLOSE: (6), (14), (17), (28), (34), (42) are inconsistent by sub-proof
% 239.76/46.39  | |            #162.
% 239.76/46.39  | | 
% 239.76/46.39  | End of split
% 239.76/46.39  | 
% 239.76/46.39  End of proof
% 239.76/46.39  
% 239.76/46.39  Sub-proof #84 shows that the following formulas are inconsistent:
% 239.76/46.39  ----------------------------------------------------------------
% 239.76/46.39    (1)  all_44_2 = e2
% 239.76/46.39    (2)   ~ (all_44_2 = e2) | ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 239.76/46.39           op(e0, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 239.76/46.39             e1) & op(e0, e2) = all_44_1 & $i(all_44_1))
% 239.76/46.39    (3)  all_48_2 = e0
% 239.76/46.39    (4)  ( ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 239.76/46.39           $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e0, e2) = all_4_1
% 239.76/46.39           & $i(all_4_1))
% 239.76/46.39    (5)  op(e1, e0) = all_52_14
% 239.76/46.39    (6)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.76/46.39    (7)  all_54_11 = all_52_14
% 239.76/46.39    (8)   ~ (all_52_12 = all_52_14)
% 239.76/46.39    (9)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 239.76/46.39           op(e2, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 239.76/46.39             e3) & op(e2, e0) = all_48_1 & $i(all_48_1))
% 239.76/46.39    (10)   ~ (all_52_12 = all_52_13)
% 239.76/46.39    (11)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 239.76/46.39    (12)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.76/46.39    (13)   ~ (all_52_14 = e2)
% 239.76/46.39    (14)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 239.76/46.39            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 239.76/46.39              e0) = all_14_1 & $i(all_14_1))
% 239.76/46.39    (15)   ~ (all_52_4 = all_52_12)
% 239.76/46.39    (16)  op(e2, e2) = all_8_2
% 239.76/46.39    (17)   ~ (all_52_12 = e2)
% 239.76/46.39    (18)  op(e0, e2) = all_52_7
% 239.76/46.39    (19)   ~ (all_52_13 = all_52_14)
% 239.76/46.39    (20)  all_54_1 = all_52_4
% 239.76/46.39    (21)  op(e3, e2) = all_52_4
% 239.76/46.39    (22)  all_54_3 = all_52_12
% 239.76/46.39    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.39    (24)   ~ (all_8_2 = e3)
% 239.76/46.39    (25)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.76/46.39          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.76/46.39    (26)  all_58_13 = e1
% 239.76/46.39    (27)  op(e2, e0) = e1
% 239.76/46.39    (28)  op(e2, e0) = all_52_13
% 239.76/46.39    (29)  op(e0, e2) = e1
% 239.76/46.39    (30)   ~ (all_52_4 = e0)
% 239.76/46.39    (31)   ~ (all_52_4 = all_52_7)
% 239.76/46.39  
% 239.76/46.39  Begin of proof
% 239.76/46.39  | 
% 239.76/46.39  | GROUND_INST: instantiating (23) with all_52_7, e1, e2, e0, simplifying with
% 239.76/46.39  |              (18), (29) gives:
% 239.76/46.39  |   (32)  all_52_7 = e1
% 239.76/46.39  | 
% 239.76/46.39  | GROUND_INST: instantiating (23) with all_52_13, e1, e0, e2, simplifying with
% 239.76/46.39  |              (27), (28) gives:
% 239.76/46.39  |   (33)  all_52_13 = e1
% 239.76/46.39  | 
% 239.76/46.39  | REDUCE: (31), (32) imply:
% 239.76/46.39  |   (34)   ~ (all_52_4 = e1)
% 239.76/46.39  | 
% 239.76/46.39  | REDUCE: (10), (33) imply:
% 239.76/46.39  |   (35)   ~ (all_52_12 = e1)
% 239.76/46.39  | 
% 239.76/46.39  | REDUCE: (19), (33) imply:
% 239.76/46.39  |   (36)   ~ (all_52_14 = e1)
% 239.76/46.39  | 
% 239.76/46.39  | SIMP: (36) implies:
% 239.76/46.39  |   (37)   ~ (all_52_14 = e1)
% 239.76/46.39  | 
% 239.76/46.39  | BETA: splitting (2) gives:
% 239.76/46.39  | 
% 239.76/46.39  | Case 1:
% 239.76/46.39  | | 
% 239.76/46.39  | |   (38)   ~ (all_44_2 = e2)
% 239.76/46.39  | | 
% 239.76/46.39  | | REDUCE: (1), (38) imply:
% 239.76/46.39  | |   (39)  $false
% 239.76/46.39  | | 
% 239.76/46.39  | | CLOSE: (39) is inconsistent.
% 239.76/46.39  | | 
% 239.76/46.39  | Case 2:
% 239.76/46.39  | | 
% 239.76/46.39  | |   (40)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.76/46.39  | |           all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) &
% 239.76/46.39  | |           op(e0, e2) = all_44_1 & $i(all_44_1))
% 239.76/46.39  | | 
% 239.76/46.39  | | BETA: splitting (9) gives:
% 239.76/46.39  | | 
% 239.76/46.39  | | Case 1:
% 239.76/46.39  | | | 
% 239.76/46.39  | | |   (41)   ~ (all_48_2 = e0)
% 239.76/46.39  | | | 
% 239.76/46.39  | | | REDUCE: (3), (41) imply:
% 239.76/46.39  | | |   (42)  $false
% 239.76/46.39  | | | 
% 239.76/46.39  | | | CLOSE: (42) is inconsistent.
% 239.76/46.39  | | | 
% 239.76/46.39  | | Case 2:
% 239.76/46.39  | | | 
% 239.76/46.39  | | |   (43)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 239.76/46.39  | | |           all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) &
% 239.76/46.39  | | |           op(e2, e0) = all_48_1 & $i(all_48_1))
% 239.76/46.39  | | | 
% 239.76/46.39  | | | BETA: splitting (43) gives:
% 239.76/46.39  | | | 
% 239.76/46.39  | | | Case 1:
% 239.76/46.39  | | | | 
% 239.76/46.39  | | | |   (44)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 239.76/46.39  | | | |         all_48_1 & $i(all_48_0) & $i(all_48_1)
% 239.76/46.39  | | | | 
% 239.76/46.39  | | | | ALPHA: (44) implies:
% 239.76/46.39  | | | |   (45)  op(e2, e0) = all_48_1
% 239.76/46.39  | | | | 
% 239.76/46.39  | | | | REF_CLOSE: (4), (5), (6), (7), (8), (11), (12), (13), (14), (15), (16),
% 239.76/46.39  | | | |            (17), (20), (21), (22), (23), (24), (25), (26), (27), (29),
% 239.76/46.39  | | | |            (30), (34), (35), (37), (40), (43), (45) are inconsistent by
% 239.76/46.39  | | | |            sub-proof #85.
% 239.76/46.39  | | | | 
% 239.76/46.39  | | | Case 2:
% 239.76/46.39  | | | | 
% 239.76/46.39  | | | |   (46)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 & $i(all_48_1)
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | ALPHA: (46) implies:
% 239.76/46.40  | | | |   (47)  op(e2, e0) = all_48_1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | REF_CLOSE: (4), (5), (6), (7), (8), (11), (12), (13), (14), (15), (16),
% 239.76/46.40  | | | |            (17), (20), (21), (22), (23), (24), (25), (26), (27), (29),
% 239.76/46.40  | | | |            (30), (34), (35), (37), (40), (43), (47) are inconsistent by
% 239.76/46.40  | | | |            sub-proof #85.
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | End of split
% 239.76/46.40  | | | 
% 239.76/46.40  | | End of split
% 239.76/46.40  | | 
% 239.76/46.40  | End of split
% 239.76/46.40  | 
% 239.76/46.40  End of proof
% 239.76/46.40  
% 239.76/46.40  Sub-proof #85 shows that the following formulas are inconsistent:
% 239.76/46.40  ----------------------------------------------------------------
% 239.76/46.40    (1)  ( ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 239.76/46.40           $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e0, e2) = all_4_1
% 239.76/46.40           & $i(all_4_1))
% 239.76/46.40    (2)  op(e1, e0) = all_52_14
% 239.76/46.40    (3)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.76/46.40    (4)  all_54_11 = all_52_14
% 239.76/46.40    (5)   ~ (all_52_12 = e1)
% 239.76/46.40    (6)   ~ (all_52_12 = all_52_14)
% 239.76/46.40    (7)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 239.76/46.40    (8)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.76/46.40    (9)   ~ (all_52_14 = e2)
% 239.76/46.40    (10)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.76/46.40            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 239.76/46.40              e2) = all_44_1 & $i(all_44_1))
% 239.76/46.40    (11)   ~ (all_52_14 = e1)
% 239.76/46.40    (12)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 239.76/46.40            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 239.76/46.40              e0) = all_14_1 & $i(all_14_1))
% 239.76/46.40    (13)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 239.76/46.40            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 239.76/46.40              e0) = all_48_1 & $i(all_48_1))
% 239.76/46.40    (14)   ~ (all_52_4 = all_52_12)
% 239.76/46.40    (15)  op(e2, e2) = all_8_2
% 239.76/46.40    (16)   ~ (all_52_12 = e2)
% 239.76/46.40    (17)  all_54_1 = all_52_4
% 239.76/46.40    (18)  op(e3, e2) = all_52_4
% 239.76/46.40    (19)  all_54_3 = all_52_12
% 239.76/46.40    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.40    (21)   ~ (all_52_4 = e1)
% 239.76/46.40    (22)   ~ (all_8_2 = e3)
% 239.76/46.40    (23)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.76/46.40          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.76/46.40    (24)  all_58_13 = e1
% 239.76/46.40    (25)  op(e2, e0) = e1
% 239.76/46.40    (26)  op(e0, e2) = e1
% 239.76/46.40    (27)  op(e2, e0) = all_48_1
% 239.76/46.40    (28)   ~ (all_52_4 = e0)
% 239.76/46.40  
% 239.76/46.40  Begin of proof
% 239.76/46.40  | 
% 239.76/46.40  | BETA: splitting (10) gives:
% 239.76/46.40  | 
% 239.76/46.40  | Case 1:
% 239.76/46.40  | | 
% 239.76/46.40  | |   (29)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.76/46.40  | |         all_44_1 & $i(all_44_0) & $i(all_44_1)
% 239.76/46.40  | | 
% 239.76/46.40  | | ALPHA: (29) implies:
% 239.76/46.40  | |   (30)   ~ (all_44_0 = e3)
% 239.76/46.40  | |   (31)  op(e0, e2) = all_44_1
% 239.76/46.40  | |   (32)  op(all_44_1, e0) = all_44_0
% 239.76/46.40  | | 
% 239.76/46.40  | | BETA: splitting (12) gives:
% 239.76/46.40  | | 
% 239.76/46.40  | | Case 1:
% 239.76/46.40  | | | 
% 239.76/46.40  | | |   (33)   ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 239.76/46.40  | | |         all_14_1 & $i(all_14_0) & $i(all_14_1)
% 239.76/46.40  | | | 
% 239.76/46.40  | | | ALPHA: (33) implies:
% 239.76/46.40  | | |   (34)   ~ (all_14_0 = e3)
% 239.76/46.40  | | |   (35)  op(e2, e0) = all_14_1
% 239.76/46.40  | | |   (36)  op(all_14_1, e2) = all_14_0
% 239.76/46.40  | | | 
% 239.76/46.40  | | | BETA: splitting (1) gives:
% 239.76/46.40  | | | 
% 239.76/46.40  | | | Case 1:
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | |   (37)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) =
% 239.76/46.40  | | | |         all_4_1 & $i(all_4_0) & $i(all_4_1)
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | ALPHA: (37) implies:
% 239.76/46.40  | | | |   (38)  op(e0, e2) = all_4_1
% 239.76/46.40  | | | |   (39)  op(all_4_1, e0) = all_4_0
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | GROUND_INST: instantiating (20) with e1, all_44_1, e2, e0, simplifying
% 239.76/46.40  | | | |              with (26), (31) gives:
% 239.76/46.40  | | | |   (40)  all_44_1 = e1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | GROUND_INST: instantiating (20) with all_4_1, all_44_1, e2, e0,
% 239.76/46.40  | | | |              simplifying with (31), (38) gives:
% 239.76/46.40  | | | |   (41)  all_44_1 = all_4_1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | GROUND_INST: instantiating (20) with e1, all_48_1, e0, e2, simplifying
% 239.76/46.40  | | | |              with (25), (27) gives:
% 239.76/46.40  | | | |   (42)  all_48_1 = e1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | GROUND_INST: instantiating (20) with all_14_1, all_48_1, e0, e2,
% 239.76/46.40  | | | |              simplifying with (27), (35) gives:
% 239.76/46.40  | | | |   (43)  all_48_1 = all_14_1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | COMBINE_EQS: (42), (43) imply:
% 239.76/46.40  | | | |   (44)  all_14_1 = e1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | COMBINE_EQS: (40), (41) imply:
% 239.76/46.40  | | | |   (45)  all_4_1 = e1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | SIMP: (45) implies:
% 239.76/46.40  | | | |   (46)  all_4_1 = e1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | REDUCE: (32), (40) imply:
% 239.76/46.40  | | | |   (47)  op(e1, e0) = all_44_0
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | REDUCE: (39), (46) imply:
% 239.76/46.40  | | | |   (48)  op(e1, e0) = all_4_0
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | GROUND_INST: instantiating (20) with all_52_14, all_4_0, e0, e1,
% 239.76/46.40  | | | |              simplifying with (2), (48) gives:
% 239.76/46.40  | | | |   (49)  all_52_14 = all_4_0
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | GROUND_INST: instantiating (20) with all_52_14, all_44_0, e0, e1,
% 239.76/46.40  | | | |              simplifying with (2), (47) gives:
% 239.76/46.40  | | | |   (50)  all_52_14 = all_44_0
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | COMBINE_EQS: (49), (50) imply:
% 239.76/46.40  | | | |   (51)  all_44_0 = all_4_0
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | SIMP: (51) implies:
% 239.76/46.40  | | | |   (52)  all_44_0 = all_4_0
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | COMBINE_EQS: (4), (49) imply:
% 239.76/46.40  | | | |   (53)  all_54_11 = all_4_0
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | REDUCE: (6), (49) imply:
% 239.76/46.40  | | | |   (54)   ~ (all_52_12 = all_4_0)
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | REDUCE: (9), (49) imply:
% 239.76/46.40  | | | |   (55)   ~ (all_4_0 = e2)
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | REDUCE: (11), (49) imply:
% 239.76/46.40  | | | |   (56)   ~ (all_4_0 = e1)
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | REDUCE: (30), (52) imply:
% 239.76/46.40  | | | |   (57)   ~ (all_4_0 = e3)
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | BETA: splitting (7) gives:
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | Case 1:
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | |   (58)  all_54_11 = e3
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | | REF_CLOSE: (53), (57), (58) are inconsistent by sub-proof #235.
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | Case 2:
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | |   (59)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | | BETA: splitting (59) gives:
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | | Case 1:
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | |   (60)  all_54_11 = e2
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | | REF_CLOSE: (53), (55), (60) are inconsistent by sub-proof #234.
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | Case 2:
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | |   (61)  all_54_11 = e1 | all_54_11 = e0
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | | BETA: splitting (61) gives:
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | | Case 1:
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | |   (62)  all_54_11 = e1
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | REF_CLOSE: (53), (56), (62) are inconsistent by sub-proof #233.
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | Case 2:
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | |   (63)  all_54_11 = e0
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | COMBINE_EQS: (53), (63) imply:
% 239.76/46.40  | | | | | | |   (64)  all_4_0 = e0
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | SIMP: (64) implies:
% 239.76/46.40  | | | | | | |   (65)  all_4_0 = e0
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | REDUCE: (54), (65) imply:
% 239.76/46.40  | | | | | | |   (66)   ~ (all_52_12 = e0)
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | BETA: splitting (8) gives:
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | Case 1:
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | |   (67)  all_54_3 = e3
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | COMBINE_EQS: (19), (67) imply:
% 239.76/46.40  | | | | | | | |   (68)  all_52_12 = e3
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | SIMP: (68) implies:
% 239.76/46.40  | | | | | | | |   (69)  all_52_12 = e3
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | REDUCE: (14), (69) imply:
% 239.76/46.40  | | | | | | | |   (70)   ~ (all_52_4 = e3)
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | REDUCE: (5), (69) imply:
% 239.76/46.40  | | | | | | | |   (71)   ~ (e3 = e1)
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | BETA: splitting (3) gives:
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | Case 1:
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | |   (72)  all_54_1 = e3
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | REF_CLOSE: (17), (70), (72) are inconsistent by sub-proof
% 239.76/46.40  | | | | | | | | |            #1930.
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | Case 2:
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | |   (73)   ~ (all_54_1 = e3)
% 239.76/46.40  | | | | | | | | |   (74)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | BETA: splitting (74) gives:
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | Case 1:
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | |   (75)  all_54_1 = e2
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | COMBINE_EQS: (17), (75) imply:
% 239.76/46.40  | | | | | | | | | |   (76)  all_52_4 = e2
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | SIMP: (76) implies:
% 239.76/46.40  | | | | | | | | | |   (77)  all_52_4 = e2
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | REDUCE: (70), (77) imply:
% 239.76/46.40  | | | | | | | | | |   (78)   ~ (e3 = e2)
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | SIMP: (78) implies:
% 239.76/46.40  | | | | | | | | | |   (79)   ~ (e3 = e2)
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | REDUCE: (18), (77) imply:
% 239.76/46.40  | | | | | | | | | |   (80)  op(e3, e2) = e2
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | BETA: splitting (23) gives:
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | Case 1:
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | |   (81)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 239.76/46.40  | | | | | | | | | | |           & op(e2, e2) = e3)
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | REF_CLOSE: (15), (20), (22), (79), (80), (81) are
% 239.76/46.40  | | | | | | | | | | |            inconsistent by sub-proof #86.
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | Case 2:
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | |   (82)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 239.76/46.40  | | | | | | | | | | |           e3 & op(e0, e2) = e3)
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | BETA: splitting (82) gives:
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | Case 1:
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | |   (83)  all_58_7 = e3 & op(e1, e2) = e3
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | | ALPHA: (83) implies:
% 239.76/46.40  | | | | | | | | | | | |   (84)  op(e1, e2) = e3
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | | REF_CLOSE: (20), (25), (27), (34), (35), (36), (84) are
% 239.76/46.40  | | | | | | | | | | | |            inconsistent by sub-proof #1428.
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | Case 2:
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | |   (85)  all_58_13 = e3 & op(e0, e2) = e3
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | | REF_CLOSE: (24), (71), (85) are inconsistent by sub-proof
% 239.76/46.40  | | | | | | | | | | | |            #2084.
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | End of split
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | End of split
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | Case 2:
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | |   (86)  all_54_1 = e1 | all_54_1 = e0
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | REF_CLOSE: (17), (21), (28), (86) are inconsistent by
% 239.76/46.40  | | | | | | | | | |            sub-proof #2049.
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | End of split
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | End of split
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | Case 2:
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | |   (87)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | REF_CLOSE: (5), (16), (19), (66), (87) are inconsistent by
% 239.76/46.40  | | | | | | | |            sub-proof #2286.
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | End of split
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | End of split
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | End of split
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | End of split
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | Case 2:
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | |   (88)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 & $i(all_4_1)
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | ALPHA: (88) implies:
% 239.76/46.40  | | | |   (89)   ~ (all_4_1 = e3)
% 239.76/46.40  | | | |   (90)  op(e0, e2) = all_4_1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | GROUND_INST: instantiating (20) with e1, all_44_1, e2, e0, simplifying
% 239.76/46.40  | | | |              with (26), (31) gives:
% 239.76/46.40  | | | |   (91)  all_44_1 = e1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | GROUND_INST: instantiating (20) with e1, all_48_1, e0, e2, simplifying
% 239.76/46.40  | | | |              with (25), (27) gives:
% 239.76/46.40  | | | |   (92)  all_48_1 = e1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | GROUND_INST: instantiating (20) with all_14_1, all_48_1, e0, e2,
% 239.76/46.40  | | | |              simplifying with (27), (35) gives:
% 239.76/46.40  | | | |   (93)  all_48_1 = all_14_1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | COMBINE_EQS: (92), (93) imply:
% 239.76/46.40  | | | |   (94)  all_14_1 = e1
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | REDUCE: (32), (91) imply:
% 239.76/46.40  | | | |   (95)  op(e1, e0) = all_44_0
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | GROUND_INST: instantiating (20) with all_52_14, all_44_0, e0, e1,
% 239.76/46.40  | | | |              simplifying with (2), (95) gives:
% 239.76/46.40  | | | |   (96)  all_52_14 = all_44_0
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | COMBINE_EQS: (4), (96) imply:
% 239.76/46.40  | | | |   (97)  all_54_11 = all_44_0
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | REDUCE: (6), (96) imply:
% 239.76/46.40  | | | |   (98)   ~ (all_52_12 = all_44_0)
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | REDUCE: (9), (96) imply:
% 239.76/46.40  | | | |   (99)   ~ (all_44_0 = e2)
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | REDUCE: (11), (96) imply:
% 239.76/46.40  | | | |   (100)   ~ (all_44_0 = e1)
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | BETA: splitting (7) gives:
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | | Case 1:
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | |   (101)  all_54_11 = e3
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | | COMBINE_EQS: (97), (101) imply:
% 239.76/46.40  | | | | |   (102)  all_44_0 = e3
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | | SIMP: (102) implies:
% 239.76/46.40  | | | | |   (103)  all_44_0 = e3
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | | REDUCE: (30), (103) imply:
% 239.76/46.40  | | | | |   (104)  $false
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | | CLOSE: (104) is inconsistent.
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | Case 2:
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | |   (105)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | | BETA: splitting (105) gives:
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | | Case 1:
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | |   (106)  all_54_11 = e2
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | | COMBINE_EQS: (97), (106) imply:
% 239.76/46.40  | | | | | |   (107)  all_44_0 = e2
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | | SIMP: (107) implies:
% 239.76/46.40  | | | | | |   (108)  all_44_0 = e2
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | | REDUCE: (99), (108) imply:
% 239.76/46.40  | | | | | |   (109)  $false
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | | CLOSE: (109) is inconsistent.
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | Case 2:
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | |   (110)  all_54_11 = e1 | all_54_11 = e0
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | | BETA: splitting (110) gives:
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | | Case 1:
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | |   (111)  all_54_11 = e1
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | COMBINE_EQS: (97), (111) imply:
% 239.76/46.40  | | | | | | |   (112)  all_44_0 = e1
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | SIMP: (112) implies:
% 239.76/46.40  | | | | | | |   (113)  all_44_0 = e1
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | REDUCE: (100), (113) imply:
% 239.76/46.40  | | | | | | |   (114)  $false
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | CLOSE: (114) is inconsistent.
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | Case 2:
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | |   (115)  all_54_11 = e0
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | COMBINE_EQS: (97), (115) imply:
% 239.76/46.40  | | | | | | |   (116)  all_44_0 = e0
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | SIMP: (116) implies:
% 239.76/46.40  | | | | | | |   (117)  all_44_0 = e0
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | REDUCE: (98), (117) imply:
% 239.76/46.40  | | | | | | |   (118)   ~ (all_52_12 = e0)
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | BETA: splitting (8) gives:
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | | Case 1:
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | |   (119)  all_54_3 = e3
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | COMBINE_EQS: (19), (119) imply:
% 239.76/46.40  | | | | | | | |   (120)  all_52_12 = e3
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | SIMP: (120) implies:
% 239.76/46.40  | | | | | | | |   (121)  all_52_12 = e3
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | REDUCE: (14), (121) imply:
% 239.76/46.40  | | | | | | | |   (122)   ~ (all_52_4 = e3)
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | BETA: splitting (3) gives:
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | Case 1:
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | |   (123)  all_54_1 = e3
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | REF_CLOSE: (17), (122), (123) are inconsistent by sub-proof
% 239.76/46.40  | | | | | | | | |            #1930.
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | Case 2:
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | |   (124)   ~ (all_54_1 = e3)
% 239.76/46.40  | | | | | | | | |   (125)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | BETA: splitting (125) gives:
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | Case 1:
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | |   (126)  all_54_1 = e2
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | COMBINE_EQS: (17), (126) imply:
% 239.76/46.40  | | | | | | | | | |   (127)  all_52_4 = e2
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | SIMP: (127) implies:
% 239.76/46.40  | | | | | | | | | |   (128)  all_52_4 = e2
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | REDUCE: (122), (128) imply:
% 239.76/46.40  | | | | | | | | | |   (129)   ~ (e3 = e2)
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | SIMP: (129) implies:
% 239.76/46.40  | | | | | | | | | |   (130)   ~ (e3 = e2)
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | REDUCE: (18), (128) imply:
% 239.76/46.40  | | | | | | | | | |   (131)  op(e3, e2) = e2
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | BETA: splitting (23) gives:
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | Case 1:
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | |   (132)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 239.76/46.40  | | | | | | | | | | |            & op(e2, e2) = e3)
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | REF_CLOSE: (15), (20), (22), (130), (131), (132) are
% 239.76/46.40  | | | | | | | | | | |            inconsistent by sub-proof #86.
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | Case 2:
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | |   (133)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 239.76/46.40  | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | BETA: splitting (133) gives:
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | Case 1:
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | |   (134)  all_58_7 = e3 & op(e1, e2) = e3
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | | ALPHA: (134) implies:
% 239.76/46.40  | | | | | | | | | | | |   (135)  op(e1, e2) = e3
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | | REF_CLOSE: (20), (25), (27), (34), (35), (36), (135) are
% 239.76/46.40  | | | | | | | | | | | |            inconsistent by sub-proof #1428.
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | Case 2:
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | |   (136)  all_58_13 = e3 & op(e0, e2) = e3
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | | ALPHA: (136) implies:
% 239.76/46.40  | | | | | | | | | | | |   (137)  op(e0, e2) = e3
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | | REF_CLOSE: (10), (20), (89), (90), (137) are inconsistent by
% 239.76/46.40  | | | | | | | | | | | |            sub-proof #211.
% 239.76/46.40  | | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | | End of split
% 239.76/46.40  | | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | End of split
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | Case 2:
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | |   (138)  all_54_1 = e1 | all_54_1 = e0
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | | REF_CLOSE: (17), (21), (28), (138) are inconsistent by
% 239.76/46.40  | | | | | | | | | |            sub-proof #2049.
% 239.76/46.40  | | | | | | | | | | 
% 239.76/46.40  | | | | | | | | | End of split
% 239.76/46.40  | | | | | | | | | 
% 239.76/46.40  | | | | | | | | End of split
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | Case 2:
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | |   (139)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | | REF_CLOSE: (5), (16), (19), (118), (139) are inconsistent by
% 239.76/46.40  | | | | | | | |            sub-proof #2286.
% 239.76/46.40  | | | | | | | | 
% 239.76/46.40  | | | | | | | End of split
% 239.76/46.40  | | | | | | | 
% 239.76/46.40  | | | | | | End of split
% 239.76/46.40  | | | | | | 
% 239.76/46.40  | | | | | End of split
% 239.76/46.40  | | | | | 
% 239.76/46.40  | | | | End of split
% 239.76/46.40  | | | | 
% 239.76/46.40  | | | End of split
% 239.76/46.40  | | | 
% 239.76/46.40  | | Case 2:
% 239.76/46.40  | | | 
% 239.76/46.40  | | |   (140)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 239.76/46.40  | | | 
% 239.76/46.40  | | | ALPHA: (140) implies:
% 239.76/46.40  | | |   (141)   ~ (all_14_1 = e1)
% 239.76/46.40  | | |   (142)  op(e2, e0) = all_14_1
% 239.76/46.40  | | | 
% 239.76/46.40  | | | REF_CLOSE: (13), (20), (25), (141), (142) are inconsistent by sub-proof
% 239.76/46.40  | | |            #1584.
% 239.76/46.40  | | | 
% 239.76/46.40  | | End of split
% 239.76/46.40  | | 
% 239.76/46.40  | Case 2:
% 239.76/46.40  | | 
% 239.76/46.40  | |   (143)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 & $i(all_44_1)
% 239.76/46.40  | | 
% 239.76/46.40  | | ALPHA: (143) implies:
% 239.76/46.40  | |   (144)   ~ (all_44_1 = e1)
% 239.76/46.40  | |   (145)  op(e0, e2) = all_44_1
% 239.76/46.40  | | 
% 239.76/46.40  | | REF_CLOSE: (20), (26), (144), (145) are inconsistent by sub-proof #230.
% 239.76/46.40  | | 
% 239.76/46.40  | End of split
% 239.76/46.40  | 
% 239.76/46.40  End of proof
% 239.76/46.40  
% 239.76/46.40  Sub-proof #86 shows that the following formulas are inconsistent:
% 239.76/46.40  ----------------------------------------------------------------
% 239.76/46.40    (1)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 239.76/46.40    (2)  op(e3, e2) = e2
% 239.76/46.40    (3)   ~ (e3 = e2)
% 239.76/46.40    (4)  op(e2, e2) = all_8_2
% 239.76/46.40    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.40    (6)   ~ (all_8_2 = e3)
% 239.76/46.40  
% 239.76/46.40  Begin of proof
% 239.76/46.40  | 
% 239.76/46.40  | BETA: splitting (1) gives:
% 239.76/46.40  | 
% 239.76/46.40  | Case 1:
% 239.76/46.40  | | 
% 239.76/46.40  | |   (7)  all_58_1 = e3 & op(e3, e2) = e3
% 239.76/46.40  | | 
% 239.76/46.40  | | ALPHA: (7) implies:
% 239.76/46.40  | |   (8)  op(e3, e2) = e3
% 239.76/46.40  | | 
% 239.76/46.40  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #2193.
% 239.76/46.40  | | 
% 239.76/46.40  | Case 2:
% 239.76/46.40  | | 
% 239.76/46.40  | |   (9)  all_58_3 = e3 & op(e2, e2) = e3
% 239.76/46.40  | | 
% 239.76/46.40  | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #450.
% 239.76/46.40  | | 
% 239.76/46.40  | End of split
% 239.76/46.40  | 
% 239.76/46.40  End of proof
% 239.76/46.40  
% 239.76/46.40  Sub-proof #87 shows that the following formulas are inconsistent:
% 239.76/46.40  ----------------------------------------------------------------
% 239.76/46.40    (1)  all_54_1 = e1 | all_54_1 = e0
% 239.76/46.40    (2)  op(e3, e0) = all_52_12
% 239.76/46.40    (3)   ~ (all_52_4 = all_52_12)
% 239.76/46.40    (4)  all_54_1 = all_52_4
% 239.76/46.40    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.40    (6)  op(e3, e0) = e0
% 239.76/46.40    (7)   ~ (all_52_4 = e1)
% 239.76/46.40  
% 239.76/46.40  Begin of proof
% 239.76/46.40  | 
% 239.76/46.40  | BETA: splitting (1) gives:
% 239.76/46.40  | 
% 239.76/46.40  | Case 1:
% 239.76/46.40  | | 
% 239.76/46.40  | |   (8)  all_54_1 = e1
% 239.76/46.40  | | 
% 239.76/46.40  | | REF_CLOSE: (4), (7), (8) are inconsistent by sub-proof #2051.
% 239.76/46.40  | | 
% 239.76/46.40  | Case 2:
% 239.76/46.40  | | 
% 239.76/46.40  | |   (9)  all_54_1 = e0
% 239.76/46.40  | | 
% 239.76/46.40  | | COMBINE_EQS: (4), (9) imply:
% 239.76/46.40  | |   (10)  all_52_4 = e0
% 239.76/46.40  | | 
% 239.76/46.40  | | SIMP: (10) implies:
% 239.76/46.40  | |   (11)  all_52_4 = e0
% 239.76/46.40  | | 
% 239.76/46.40  | | REDUCE: (3), (11) imply:
% 239.76/46.40  | |   (12)   ~ (all_52_12 = e0)
% 239.76/46.40  | | 
% 239.76/46.40  | | SIMP: (12) implies:
% 239.76/46.40  | |   (13)   ~ (all_52_12 = e0)
% 239.76/46.40  | | 
% 239.76/46.40  | | REF_CLOSE: (2), (5), (6), (13) are inconsistent by sub-proof #2258.
% 239.76/46.40  | | 
% 239.76/46.40  | End of split
% 239.76/46.40  | 
% 239.76/46.40  End of proof
% 239.76/46.40  
% 239.76/46.40  Sub-proof #88 shows that the following formulas are inconsistent:
% 239.76/46.40  ----------------------------------------------------------------
% 239.76/46.40    (1)   ~ (e2 = e0)
% 239.76/46.40    (2)  op(e1, e2) = all_52_6
% 239.76/46.40    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.76/46.40         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.76/46.40    (4)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.76/46.40    (5)   ~ (all_52_6 = e0)
% 239.76/46.40    (6)  op(e0, e2) = all_52_7
% 239.76/46.40    (7)  all_54_1 = all_52_4
% 239.76/46.41    (8)  op(e3, e2) = all_52_4
% 239.76/46.41    (9)   ~ (all_52_7 = e0)
% 239.76/46.41    (10)   ~ (all_52_4 = e2)
% 239.76/46.41    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.41    (12)   ~ (all_52_4 = e1)
% 239.76/46.41    (13)  op(e2, e2) = e2
% 239.76/46.41    (14)   ~ (all_52_4 = e0)
% 239.76/46.41  
% 239.76/46.41  Begin of proof
% 239.76/46.41  | 
% 239.76/46.41  | BETA: splitting (4) gives:
% 239.76/46.41  | 
% 239.76/46.41  | Case 1:
% 239.76/46.41  | | 
% 239.76/46.41  | |   (15)  all_54_1 = e3
% 239.76/46.41  | | 
% 239.76/46.41  | | COMBINE_EQS: (7), (15) imply:
% 239.76/46.41  | |   (16)  all_52_4 = e3
% 239.76/46.41  | | 
% 239.76/46.41  | | SIMP: (16) implies:
% 239.76/46.41  | |   (17)  all_52_4 = e3
% 239.76/46.41  | | 
% 239.76/46.41  | | REDUCE: (14), (17) imply:
% 239.76/46.41  | |   (18)   ~ (e3 = e0)
% 239.76/46.41  | | 
% 239.76/46.41  | | REDUCE: (8), (17) imply:
% 239.76/46.41  | |   (19)  op(e3, e2) = e3
% 239.76/46.41  | | 
% 239.76/46.41  | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (11), (13), (18), (19) are
% 239.76/46.41  | |            inconsistent by sub-proof #408.
% 239.76/46.41  | | 
% 239.76/46.41  | Case 2:
% 239.76/46.41  | | 
% 239.76/46.41  | |   (20)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.76/46.41  | | 
% 239.76/46.41  | | REF_CLOSE: (7), (10), (12), (14), (20) are inconsistent by sub-proof #2048.
% 239.76/46.41  | | 
% 239.76/46.41  | End of split
% 239.76/46.41  | 
% 239.76/46.41  End of proof
% 239.76/46.41  
% 239.76/46.41  Sub-proof #89 shows that the following formulas are inconsistent:
% 239.76/46.41  ----------------------------------------------------------------
% 239.76/46.41    (1)   ~ (e3 = e0)
% 239.76/46.41    (2)   ~ (e2 = e0)
% 239.76/46.41    (3)  op(e1, e2) = all_52_6
% 239.76/46.41    (4)   ~ (all_52_6 = e2)
% 239.76/46.41    (5)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 239.76/46.41         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 239.76/46.41    (6)  op(e1, e0) = all_52_14
% 239.76/46.41    (7)   ~ (e3 = e1)
% 239.76/46.41    (8)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.76/46.41         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.76/46.41    (9)   ~ (all_52_14 = e2)
% 239.76/46.41    (10)  op(e2, e1) = all_52_9
% 239.76/46.41    (11)   ~ (e3 = e2)
% 239.76/46.41    (12)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.76/46.41    (13)  op(e3, e0) = all_52_12
% 239.76/46.41    (14)   ~ (all_52_12 = e2)
% 239.76/46.41    (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.76/46.41          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.76/46.41    (16)   ~ (all_52_2 = e2)
% 239.76/46.41    (17)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.76/46.41          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.76/46.41    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.41    (19)  op(e1, e3) = all_52_2
% 239.76/46.41    (20)   ~ (e1 = e0)
% 239.76/46.41    (21)   ~ (e2 = e1)
% 239.76/46.41  
% 239.76/46.41  Begin of proof
% 239.76/46.41  | 
% 239.76/46.41  | BETA: splitting (12) gives:
% 239.76/46.41  | 
% 239.76/46.41  | Case 1:
% 239.76/46.41  | | 
% 239.76/46.41  | |   (22)  all_58_4 = e2 & op(e3, e1) = e2
% 239.76/46.41  | | 
% 239.76/46.41  | | ALPHA: (22) implies:
% 239.76/46.41  | |   (23)  all_58_4 = e2
% 239.76/46.41  | | 
% 239.76/46.41  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (15),
% 239.76/46.41  | |            (16), (17), (18), (19), (20), (21), (23) are inconsistent by
% 239.76/46.41  | |            sub-proof #247.
% 239.76/46.41  | | 
% 239.76/46.41  | Case 2:
% 239.76/46.41  | | 
% 239.76/46.41  | |   (24)  all_58_9 = e2 & op(e3, e0) = e2
% 239.76/46.41  | | 
% 239.76/46.41  | | REF_CLOSE: (13), (14), (18), (24) are inconsistent by sub-proof #2318.
% 239.76/46.41  | | 
% 239.76/46.41  | End of split
% 239.76/46.41  | 
% 239.76/46.41  End of proof
% 239.76/46.41  
% 239.76/46.41  Sub-proof #90 shows that the following formulas are inconsistent:
% 239.76/46.41  ----------------------------------------------------------------
% 239.76/46.41    (1)   ~ (all_52_6 = e1)
% 239.76/46.41    (2)   ~ (all_52_3 = e1)
% 239.76/46.41    (3)   ~ (all_52_9 = all_6_2)
% 239.76/46.41    (4)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.76/46.41    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.76/46.41         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.76/46.41    (6)   ~ (e3 = e0)
% 239.76/46.41    (7)  all_56_11 = e1
% 239.76/46.41    (8)   ~ (e2 = e0)
% 239.76/46.41    (9)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 239.76/46.41           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 239.76/46.41           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 239.76/46.41         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 239.76/46.41           $i(all_56_15))
% 239.76/46.41    (10)  op(e1, e2) = all_52_6
% 239.76/46.41    (11)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 239.76/46.41            all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3,
% 239.76/46.41              e1) = all_38_1 & $i(all_38_1))
% 239.76/46.41    (12)   ~ (all_52_6 = e2)
% 239.76/46.41    (13)  op(e0, e3) = all_52_3
% 239.76/46.41    (14)   ~ (all_52_6 = e0)
% 239.76/46.41    (15)   ~ (e3 = e1)
% 239.76/46.41    (16)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 239.76/46.41    (17)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 239.76/46.41            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 239.76/46.41              e1) = all_10_1 & $i(all_10_1))
% 239.76/46.41    (18)   ~ (all_52_2 = e1)
% 239.76/46.41    (19)  op(e3, e2) = e2
% 239.76/46.41    (20)  all_54_10 = all_6_2
% 239.76/46.41    (21)  op(e2, e1) = all_52_9
% 239.76/46.41    (22)  all_54_9 = all_52_6
% 239.76/46.41    (23)   ~ (e3 = e2)
% 239.76/46.41    (24)   ~ (all_6_2 = e0)
% 239.76/46.41    (25)   ~ (all_6_2 = e1)
% 239.76/46.41    (26)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 239.76/46.41    (27)  op(e2, e0) = e0
% 239.76/46.41    (28)  op(e2, e3) = all_52_1
% 239.76/46.41    (29)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 239.76/46.41            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 239.76/46.41              e2) = all_40_1 & $i(all_40_1))
% 239.76/46.41    (30)  op(e0, e2) = all_52_7
% 239.76/46.41    (31)  all_10_1 = e0
% 239.76/46.41    (32)  op(e3, e2) = all_52_4
% 239.76/46.41    (33)  all_52_7 = e0
% 239.76/46.41    (34)   ~ (all_52_2 = e2)
% 239.76/46.41    (35)  op(all_30_1, e2) = all_30_0
% 239.76/46.41    (36)  all_54_8 = all_52_2
% 239.76/46.41    (37)   ~ (all_52_2 = all_52_6)
% 239.76/46.41    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.41    (39)  op(e3, e1) = all_10_1
% 239.76/46.41    (40)  op(e1, e3) = all_52_2
% 239.76/46.41    (41)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 239.76/46.41            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 239.76/46.41              e2) = all_36_1 & $i(all_36_1))
% 239.76/46.41    (42)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.76/46.41          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.76/46.41    (43)   ~ (e1 = e0)
% 239.76/46.41    (44)  op(e2, e0) = all_52_13
% 239.76/46.41    (45)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.76/46.41          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 239.76/46.41            e1)
% 239.76/46.41    (46)   ~ (all_52_9 = e1)
% 239.76/46.41    (47)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.76/46.41          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 239.76/46.41            e2)
% 239.76/46.41    (48)  all_30_1 = e3
% 239.76/46.41    (49)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.76/46.41          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.76/46.41    (50)   ~ (all_52_4 = all_52_6)
% 239.76/46.41    (51)   ~ (e2 = e1)
% 239.76/46.41    (52)   ~ (all_52_1 = e1)
% 239.76/46.41  
% 239.76/46.41  Begin of proof
% 239.76/46.41  | 
% 239.76/46.41  | REDUCE: (35), (48) imply:
% 239.76/46.41  |   (53)  op(e3, e2) = all_30_0
% 239.76/46.41  | 
% 239.76/46.41  | REDUCE: (31), (39) imply:
% 239.76/46.41  |   (54)  op(e3, e1) = e0
% 239.76/46.41  | 
% 239.76/46.41  | REDUCE: (30), (33) imply:
% 239.76/46.41  |   (55)  op(e0, e2) = e0
% 239.76/46.41  | 
% 239.76/46.41  | BETA: splitting (26) gives:
% 239.76/46.41  | 
% 239.76/46.41  | Case 1:
% 239.76/46.41  | | 
% 239.76/46.41  | |   (56)  all_54_9 = e3
% 239.76/46.41  | | 
% 239.76/46.41  | | COMBINE_EQS: (22), (56) imply:
% 239.76/46.41  | |   (57)  all_52_6 = e3
% 239.76/46.41  | | 
% 239.76/46.41  | | SIMP: (57) implies:
% 239.76/46.41  | |   (58)  all_52_6 = e3
% 239.76/46.41  | | 
% 239.76/46.41  | | REDUCE: (37), (58) imply:
% 239.76/46.41  | |   (59)   ~ (all_52_2 = e3)
% 239.76/46.41  | | 
% 239.76/46.41  | | REDUCE: (10), (58) imply:
% 239.76/46.41  | |   (60)  op(e1, e2) = e3
% 239.76/46.41  | | 
% 239.76/46.41  | | BETA: splitting (4) gives:
% 239.76/46.41  | | 
% 239.76/46.41  | | Case 1:
% 239.76/46.41  | | | 
% 239.76/46.41  | | |   (61)  all_54_8 = e3
% 239.76/46.41  | | | 
% 239.76/46.41  | | | REF_CLOSE: (36), (59), (61) are inconsistent by sub-proof #2011.
% 239.76/46.41  | | | 
% 239.76/46.41  | | Case 2:
% 239.76/46.41  | | | 
% 239.76/46.41  | | |   (62)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.76/46.41  | | | 
% 239.76/46.41  | | | BETA: splitting (9) gives:
% 239.76/46.41  | | | 
% 239.76/46.41  | | | Case 1:
% 239.76/46.41  | | | | 
% 239.76/46.41  | | | |   (63)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 239.76/46.41  | | | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 239.76/46.41  | | | | 
% 239.76/46.41  | | | | BETA: splitting (63) gives:
% 239.76/46.41  | | | | 
% 239.76/46.41  | | | | Case 1:
% 239.76/46.41  | | | | | 
% 239.76/46.41  | | | | |   (64)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9
% 239.76/46.41  | | | | |         & $i(all_56_9)
% 239.76/46.41  | | | | | 
% 239.76/46.41  | | | | | ALPHA: (64) implies:
% 239.76/46.41  | | | | |   (65)  op(e3, e2) = all_56_9
% 239.76/46.41  | | | | |   (66)  op(e3, all_56_9) = e3
% 239.76/46.41  | | | | | 
% 239.76/46.41  | | | | | BETA: splitting (41) gives:
% 239.76/46.41  | | | | | 
% 239.76/46.41  | | | | | Case 1:
% 239.76/46.41  | | | | | | 
% 239.76/46.41  | | | | | |   (67)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1,
% 239.76/46.41  | | | | | |           e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)
% 239.76/46.41  | | | | | | 
% 239.76/46.41  | | | | | | ALPHA: (67) implies:
% 239.76/46.41  | | | | | |   (68)  op(e1, e2) = all_36_1
% 239.76/46.41  | | | | | | 
% 239.76/46.41  | | | | | | REF_CLOSE: (10), (19), (22), (26), (29), (32), (38), (41), (50),
% 239.76/46.41  | | | | | |            (53), (60), (65), (66), (68) are inconsistent by
% 239.76/46.41  | | | | | |            sub-proof #91.
% 239.76/46.41  | | | | | | 
% 239.76/46.41  | | | | | Case 2:
% 239.76/46.41  | | | | | | 
% 239.76/46.41  | | | | | |   (69)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1)
% 239.76/46.41  | | | | | | 
% 239.76/46.41  | | | | | | ALPHA: (69) implies:
% 239.76/46.41  | | | | | |   (70)  op(e1, e2) = all_36_1
% 239.76/46.41  | | | | | | 
% 239.76/46.41  | | | | | | REF_CLOSE: (10), (19), (22), (26), (29), (32), (38), (41), (50),
% 239.76/46.41  | | | | | |            (53), (60), (65), (66), (70) are inconsistent by
% 239.76/46.41  | | | | | |            sub-proof #91.
% 239.76/46.41  | | | | | | 
% 239.76/46.41  | | | | | End of split
% 239.76/46.41  | | | | | 
% 239.76/46.41  | | | | Case 2:
% 239.76/46.41  | | | | | 
% 239.76/46.41  | | | | |   (71)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 239.76/46.41  | | | | | 
% 239.76/46.41  | | | | | REF_CLOSE: (3), (7), (16), (20), (21), (24), (25), (38), (71) are
% 239.76/46.41  | | | | |            inconsistent by sub-proof #2056.
% 239.76/46.41  | | | | | 
% 239.76/46.41  | | | | End of split
% 239.76/46.41  | | | | 
% 239.76/46.41  | | | Case 2:
% 239.76/46.41  | | | | 
% 239.76/46.41  | | | |   (72)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 239.76/46.41  | | | |           all_56_13 & $i(all_56_13)) | (all_56_14 = e0 & op(e0,
% 239.76/46.41  | | | |             all_56_15) = e0 & op(e0, e2) = all_56_15 & $i(all_56_15))
% 239.76/46.41  | | | | 
% 239.76/46.41  | | | | REF_CLOSE: (2), (5), (6), (8), (11), (13), (15), (17), (18), (23), (29),
% 239.76/46.41  | | | |            (34), (36), (38), (40), (41), (43), (45), (47), (51), (54),
% 239.76/46.41  | | | |            (55), (60), (62), (72) are inconsistent by sub-proof #93.
% 239.76/46.41  | | | | 
% 239.76/46.41  | | | End of split
% 239.76/46.41  | | | 
% 239.76/46.41  | | End of split
% 239.76/46.41  | | 
% 239.76/46.41  | Case 2:
% 239.76/46.41  | | 
% 239.76/46.41  | |   (73)   ~ (all_54_9 = e3)
% 239.76/46.41  | | 
% 239.76/46.41  | | REDUCE: (22), (73) imply:
% 239.76/46.41  | |   (74)   ~ (all_52_6 = e3)
% 239.76/46.41  | | 
% 239.76/46.41  | | REF_CLOSE: (6), (10), (15), (19), (21), (23), (27), (28), (38), (42), (43),
% 239.76/46.41  | |            (44), (46), (49), (52), (55), (74) are inconsistent by sub-proof
% 239.76/46.41  | |            #139.
% 239.76/46.41  | | 
% 239.76/46.41  | End of split
% 239.76/46.41  | 
% 239.76/46.41  End of proof
% 239.76/46.41  
% 239.76/46.41  Sub-proof #91 shows that the following formulas are inconsistent:
% 239.76/46.41  ----------------------------------------------------------------
% 239.76/46.41    (1)  op(e3, e2) = all_56_9
% 239.76/46.41    (2)  op(e3, all_56_9) = e3
% 239.76/46.41    (3)  op(e1, e2) = all_52_6
% 239.76/46.41    (4)  op(e1, e2) = e3
% 239.76/46.41    (5)  op(e3, e2) = e2
% 239.76/46.41    (6)  all_54_9 = all_52_6
% 239.76/46.41    (7)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 239.76/46.41    (8)  op(e1, e2) = all_36_1
% 239.76/46.41    (9)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) = all_40_1
% 239.76/46.41           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2) =
% 239.76/46.41           all_40_1 & $i(all_40_1))
% 239.76/46.41    (10)  op(e3, e2) = all_30_0
% 239.76/46.41    (11)  op(e3, e2) = all_52_4
% 239.76/46.41    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.41    (13)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 239.76/46.41            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 239.76/46.41              e2) = all_36_1 & $i(all_36_1))
% 239.76/46.41    (14)   ~ (all_52_4 = all_52_6)
% 239.76/46.41  
% 239.76/46.41  Begin of proof
% 239.76/46.41  | 
% 239.76/46.41  | BETA: splitting (9) gives:
% 239.76/46.41  | 
% 239.76/46.41  | Case 1:
% 239.76/46.41  | | 
% 239.76/46.41  | |   (15)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 239.76/46.41  | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 239.76/46.41  | | 
% 239.76/46.41  | | ALPHA: (15) implies:
% 239.76/46.41  | |   (16)  op(e1, e2) = all_40_1
% 239.76/46.41  | | 
% 239.76/46.41  | | GROUND_INST: instantiating (12) with all_36_1, all_40_1, e2, e1, simplifying
% 239.76/46.41  | |              with (8), (16) gives:
% 239.76/46.41  | |   (17)  all_40_1 = all_36_1
% 239.76/46.41  | | 
% 239.76/46.41  | | GROUND_INST: instantiating (12) with e3, all_40_1, e2, e1, simplifying with
% 239.76/46.41  | |              (4), (16) gives:
% 239.76/46.41  | |   (18)  all_40_1 = e3
% 239.76/46.41  | | 
% 239.76/46.41  | | GROUND_INST: instantiating (12) with e2, all_56_9, e2, e3, simplifying with
% 239.76/46.41  | |              (1), (5) gives:
% 239.76/46.41  | |   (19)  all_56_9 = e2
% 239.76/46.41  | | 
% 239.76/46.41  | | GROUND_INST: instantiating (12) with all_30_0, all_56_9, e2, e3, simplifying
% 239.76/46.41  | |              with (1), (10) gives:
% 239.76/46.41  | |   (20)  all_56_9 = all_30_0
% 239.76/46.41  | | 
% 239.76/46.41  | | COMBINE_EQS: (19), (20) imply:
% 239.76/46.41  | |   (21)  all_30_0 = e2
% 239.76/46.41  | | 
% 239.76/46.41  | | COMBINE_EQS: (17), (18) imply:
% 239.76/46.41  | |   (22)  all_36_1 = e3
% 239.76/46.41  | | 
% 239.76/46.41  | | REDUCE: (2), (19) imply:
% 239.76/46.41  | |   (23)  op(e3, e2) = e3
% 239.76/46.41  | | 
% 239.76/46.41  | | REF_CLOSE: (3), (4), (6), (7), (11), (12), (14), (23) are inconsistent by
% 239.76/46.41  | |            sub-proof #2190.
% 239.76/46.41  | | 
% 239.76/46.41  | Case 2:
% 239.76/46.41  | | 
% 239.76/46.41  | |   (24)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 239.76/46.41  | | 
% 239.76/46.41  | | REF_CLOSE: (4), (12), (13), (24) are inconsistent by sub-proof #2144.
% 239.76/46.41  | | 
% 239.76/46.41  | End of split
% 239.76/46.41  | 
% 239.76/46.41  End of proof
% 239.76/46.41  
% 239.76/46.41  Sub-proof #92 shows that the following formulas are inconsistent:
% 239.76/46.41  ----------------------------------------------------------------
% 239.76/46.41    (1)   ~ (all_52_6 = e1)
% 239.76/46.41    (2)   ~ (all_52_3 = e1)
% 239.76/46.41    (3)   ~ (all_52_9 = all_6_2)
% 239.76/46.41    (4)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.76/46.41    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.76/46.41         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.76/46.41    (6)   ~ (e3 = e0)
% 239.76/46.41    (7)  all_56_11 = e1
% 239.76/46.41    (8)   ~ (e2 = e0)
% 239.76/46.41    (9)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 239.76/46.41           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 239.76/46.41           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 239.76/46.41         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 239.76/46.41           $i(all_56_15))
% 239.76/46.41    (10)  op(e1, e2) = all_52_6
% 239.76/46.41    (11)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 239.76/46.41            all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3,
% 239.76/46.41              e1) = all_38_1 & $i(all_38_1))
% 239.76/46.41    (12)   ~ (all_52_6 = e2)
% 239.76/46.41    (13)  op(e0, e3) = all_52_3
% 239.76/46.41    (14)   ~ (all_52_6 = e0)
% 239.76/46.42    (15)   ~ (e3 = e1)
% 239.76/46.42    (16)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 239.76/46.42    (17)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 239.76/46.42            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 239.76/46.42              e1) = all_10_1 & $i(all_10_1))
% 239.76/46.42    (18)   ~ (all_52_2 = e1)
% 239.76/46.42    (19)  op(e3, e2) = e2
% 239.76/46.42    (20)  all_54_10 = all_6_2
% 239.76/46.42    (21)  all_22_1 = e3
% 239.76/46.42    (22)  op(e2, e1) = all_52_9
% 239.76/46.42    (23)  all_54_9 = all_52_6
% 239.76/46.42    (24)   ~ (e3 = e2)
% 239.76/46.42    (25)   ~ (all_6_2 = e0)
% 239.76/46.42    (26)   ~ (all_6_2 = e1)
% 239.76/46.42    (27)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 239.76/46.42    (28)  op(e2, e0) = e0
% 239.76/46.42    (29)  op(e2, e3) = all_52_1
% 239.76/46.42    (30)  op(all_22_1, e2) = all_22_0
% 239.76/46.42    (31)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 239.76/46.42            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 239.76/46.42              e2) = all_40_1 & $i(all_40_1))
% 239.76/46.42    (32)  op(e0, e2) = all_52_7
% 239.76/46.42    (33)  all_10_1 = e0
% 239.76/46.42    (34)  op(e3, e2) = all_52_4
% 239.76/46.42    (35)  all_52_7 = e0
% 239.76/46.42    (36)   ~ (all_52_2 = e2)
% 239.76/46.42    (37)  op(all_30_1, e2) = all_30_0
% 239.76/46.42    (38)  all_54_8 = all_52_2
% 239.76/46.42    (39)   ~ (all_52_2 = all_52_6)
% 239.76/46.42    (40)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.42    (41)  op(e3, e1) = all_10_1
% 239.76/46.42    (42)  op(e1, e3) = all_52_2
% 239.76/46.42    (43)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 239.76/46.42            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 239.76/46.42              e2) = all_36_1 & $i(all_36_1))
% 239.76/46.42    (44)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.76/46.42          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.76/46.42    (45)   ~ (e1 = e0)
% 239.76/46.42    (46)  op(e2, e0) = all_52_13
% 239.76/46.42    (47)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.76/46.42          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 239.76/46.42            e1)
% 239.76/46.42    (48)   ~ (all_52_9 = e1)
% 239.76/46.42    (49)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.76/46.42          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 239.76/46.42            e2)
% 239.76/46.42    (50)  all_30_1 = e3
% 239.76/46.42    (51)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.76/46.42          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.76/46.42    (52)   ~ (all_52_4 = all_52_6)
% 239.76/46.42    (53)   ~ (e2 = e1)
% 239.76/46.42    (54)   ~ (all_52_1 = e1)
% 239.76/46.42  
% 239.76/46.42  Begin of proof
% 239.76/46.42  | 
% 239.76/46.42  | REDUCE: (37), (50) imply:
% 239.76/46.42  |   (55)  op(e3, e2) = all_30_0
% 239.76/46.42  | 
% 239.76/46.42  | REDUCE: (21), (30) imply:
% 239.76/46.42  |   (56)  op(e3, e2) = all_22_0
% 239.76/46.42  | 
% 239.76/46.42  | REDUCE: (33), (41) imply:
% 239.76/46.42  |   (57)  op(e3, e1) = e0
% 239.76/46.42  | 
% 239.76/46.42  | REDUCE: (32), (35) imply:
% 239.76/46.42  |   (58)  op(e0, e2) = e0
% 239.76/46.42  | 
% 239.76/46.42  | BETA: splitting (27) gives:
% 239.76/46.42  | 
% 239.76/46.42  | Case 1:
% 239.76/46.42  | | 
% 239.76/46.42  | |   (59)  all_54_9 = e3
% 239.76/46.42  | | 
% 239.76/46.42  | | COMBINE_EQS: (23), (59) imply:
% 239.76/46.42  | |   (60)  all_52_6 = e3
% 239.76/46.42  | | 
% 239.76/46.42  | | SIMP: (60) implies:
% 239.76/46.42  | |   (61)  all_52_6 = e3
% 239.76/46.42  | | 
% 239.76/46.42  | | REDUCE: (39), (61) imply:
% 239.76/46.42  | |   (62)   ~ (all_52_2 = e3)
% 239.76/46.42  | | 
% 239.76/46.42  | | REDUCE: (10), (61) imply:
% 239.76/46.42  | |   (63)  op(e1, e2) = e3
% 239.76/46.42  | | 
% 239.76/46.42  | | BETA: splitting (4) gives:
% 239.76/46.42  | | 
% 239.76/46.42  | | Case 1:
% 239.76/46.42  | | | 
% 239.76/46.42  | | |   (64)  all_54_8 = e3
% 239.76/46.42  | | | 
% 239.76/46.42  | | | REF_CLOSE: (38), (62), (64) are inconsistent by sub-proof #2011.
% 239.76/46.42  | | | 
% 239.76/46.42  | | Case 2:
% 239.76/46.42  | | | 
% 239.76/46.42  | | |   (65)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.76/46.42  | | | 
% 239.76/46.42  | | | BETA: splitting (9) gives:
% 239.76/46.42  | | | 
% 239.76/46.42  | | | Case 1:
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | |   (66)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 239.76/46.42  | | | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | | BETA: splitting (66) gives:
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | | Case 1:
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | |   (67)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9
% 239.76/46.42  | | | | |         & $i(all_56_9)
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | | ALPHA: (67) implies:
% 239.76/46.42  | | | | |   (68)  op(e3, e2) = all_56_9
% 239.76/46.42  | | | | |   (69)  op(e3, all_56_9) = e3
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | | BETA: splitting (43) gives:
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | | Case 1:
% 239.76/46.42  | | | | | | 
% 239.76/46.42  | | | | | |   (70)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1,
% 239.76/46.42  | | | | | |           e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)
% 239.76/46.42  | | | | | | 
% 239.76/46.42  | | | | | | ALPHA: (70) implies:
% 239.76/46.42  | | | | | |   (71)  op(e1, e2) = all_36_1
% 239.76/46.42  | | | | | | 
% 239.76/46.42  | | | | | | REF_CLOSE: (10), (19), (23), (27), (31), (34), (40), (43), (52),
% 239.76/46.42  | | | | | |            (55), (56), (63), (68), (69), (71) are inconsistent by
% 239.76/46.42  | | | | | |            sub-proof #94.
% 239.76/46.42  | | | | | | 
% 239.76/46.42  | | | | | Case 2:
% 239.76/46.42  | | | | | | 
% 239.76/46.42  | | | | | |   (72)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1)
% 239.76/46.42  | | | | | | 
% 239.76/46.42  | | | | | | ALPHA: (72) implies:
% 239.76/46.42  | | | | | |   (73)  op(e1, e2) = all_36_1
% 239.76/46.42  | | | | | | 
% 239.76/46.42  | | | | | | REF_CLOSE: (10), (19), (23), (27), (31), (34), (40), (43), (52),
% 239.76/46.42  | | | | | |            (55), (56), (63), (68), (69), (73) are inconsistent by
% 239.76/46.42  | | | | | |            sub-proof #94.
% 239.76/46.42  | | | | | | 
% 239.76/46.42  | | | | | End of split
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | Case 2:
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | |   (74)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | | REF_CLOSE: (3), (7), (16), (20), (22), (25), (26), (40), (74) are
% 239.76/46.42  | | | | |            inconsistent by sub-proof #2056.
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | End of split
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | Case 2:
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | |   (75)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 239.76/46.42  | | | |           all_56_13 & $i(all_56_13)) | (all_56_14 = e0 & op(e0,
% 239.76/46.42  | | | |             all_56_15) = e0 & op(e0, e2) = all_56_15 & $i(all_56_15))
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | | REF_CLOSE: (2), (5), (6), (8), (11), (13), (15), (17), (18), (24), (31),
% 239.76/46.42  | | | |            (36), (38), (40), (42), (43), (45), (47), (49), (53), (57),
% 239.76/46.42  | | | |            (58), (63), (65), (75) are inconsistent by sub-proof #93.
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | End of split
% 239.76/46.42  | | | 
% 239.76/46.42  | | End of split
% 239.76/46.42  | | 
% 239.76/46.42  | Case 2:
% 239.76/46.42  | | 
% 239.76/46.42  | |   (76)   ~ (all_54_9 = e3)
% 239.76/46.42  | | 
% 239.76/46.42  | | REDUCE: (23), (76) imply:
% 239.76/46.42  | |   (77)   ~ (all_52_6 = e3)
% 239.76/46.42  | | 
% 239.76/46.42  | | REF_CLOSE: (6), (10), (15), (19), (22), (24), (28), (29), (40), (44), (45),
% 239.76/46.42  | |            (46), (48), (51), (54), (58), (77) are inconsistent by sub-proof
% 239.76/46.42  | |            #139.
% 239.76/46.42  | | 
% 239.76/46.42  | End of split
% 239.76/46.42  | 
% 239.76/46.42  End of proof
% 239.76/46.42  
% 239.76/46.42  Sub-proof #93 shows that the following formulas are inconsistent:
% 239.76/46.42  ----------------------------------------------------------------
% 239.76/46.42    (1)   ~ (all_52_3 = e1)
% 239.76/46.42    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.76/46.42         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.76/46.42    (3)   ~ (e3 = e0)
% 239.76/46.42    (4)   ~ (e2 = e0)
% 239.76/46.42    (5)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) = all_38_1
% 239.76/46.42           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 239.76/46.42           all_38_1 & $i(all_38_1))
% 239.76/46.42    (6)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.76/46.42    (7)  op(e0, e3) = all_52_3
% 239.76/46.42    (8)   ~ (e3 = e1)
% 239.76/46.42    (9)  op(e3, e1) = e0
% 239.76/46.42    (10)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 239.76/46.42            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 239.76/46.42              e1) = all_10_1 & $i(all_10_1))
% 239.76/46.42    (11)  op(e1, e2) = e3
% 239.76/46.42    (12)   ~ (all_52_2 = e1)
% 239.76/46.42    (13)   ~ (e3 = e2)
% 239.76/46.42    (14)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 239.76/46.42            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 239.76/46.42            = all_56_15 & $i(all_56_15))
% 239.76/46.42    (15)  op(e0, e2) = e0
% 239.76/46.42    (16)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 239.76/46.42            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 239.76/46.42              e2) = all_40_1 & $i(all_40_1))
% 239.76/46.42    (17)   ~ (all_52_2 = e2)
% 239.76/46.42    (18)  all_54_8 = all_52_2
% 239.76/46.42    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.42    (20)  op(e1, e3) = all_52_2
% 239.76/46.42    (21)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 239.76/46.42            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 239.76/46.42              e2) = all_36_1 & $i(all_36_1))
% 239.76/46.42    (22)   ~ (e1 = e0)
% 239.76/46.42    (23)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.76/46.42          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 239.76/46.42            e1)
% 239.76/46.42    (24)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 239.76/46.42          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 239.76/46.42            e2)
% 239.76/46.42    (25)   ~ (e2 = e1)
% 239.76/46.42  
% 239.76/46.42  Begin of proof
% 239.76/46.42  | 
% 239.76/46.42  | BETA: splitting (14) gives:
% 239.76/46.42  | 
% 239.76/46.42  | Case 1:
% 239.76/46.42  | | 
% 239.76/46.42  | |   (26)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 239.76/46.42  | |         $i(all_56_13)
% 239.76/46.42  | | 
% 239.76/46.42  | | ALPHA: (26) implies:
% 239.76/46.42  | |   (27)  op(e1, e2) = all_56_13
% 239.76/46.42  | |   (28)  op(e1, all_56_13) = e1
% 239.76/46.42  | | 
% 239.76/46.42  | | BETA: splitting (6) gives:
% 239.76/46.42  | | 
% 239.76/46.42  | | Case 1:
% 239.76/46.42  | | | 
% 239.76/46.42  | | |   (29)  all_54_8 = e2
% 239.76/46.42  | | | 
% 239.76/46.42  | | | REF_CLOSE: (17), (18), (29) are inconsistent by sub-proof #2007.
% 239.76/46.42  | | | 
% 239.76/46.42  | | Case 2:
% 239.76/46.42  | | | 
% 239.76/46.42  | | |   (30)  all_54_8 = e1 | all_54_8 = e0
% 239.76/46.42  | | | 
% 239.76/46.42  | | | BETA: splitting (16) gives:
% 239.76/46.42  | | | 
% 239.76/46.42  | | | Case 1:
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | |   (31)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 239.76/46.42  | | | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | | ALPHA: (31) implies:
% 239.76/46.42  | | | |   (32)  op(e1, e2) = all_40_1
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | | BETA: splitting (30) gives:
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | | Case 1:
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | |   (33)  all_54_8 = e1
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | | REF_CLOSE: (12), (18), (33) are inconsistent by sub-proof #1951.
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | Case 2:
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | | GROUND_INST: instantiating (19) with all_40_1, all_56_13, e2, e1,
% 239.76/46.42  | | | | |              simplifying with (27), (32) gives:
% 239.76/46.42  | | | | |   (34)  all_56_13 = all_40_1
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | | GROUND_INST: instantiating (19) with e3, all_56_13, e2, e1,
% 239.76/46.42  | | | | |              simplifying with (11), (27) gives:
% 239.76/46.42  | | | | |   (35)  all_56_13 = e3
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | | COMBINE_EQS: (34), (35) imply:
% 239.76/46.42  | | | | |   (36)  all_40_1 = e3
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | | REDUCE: (28), (35) imply:
% 239.76/46.42  | | | | |   (37)  op(e1, e3) = e1
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | | REF_CLOSE: (12), (19), (20), (37) are inconsistent by sub-proof #1948.
% 239.76/46.42  | | | | | 
% 239.76/46.42  | | | | End of split
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | Case 2:
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | |   (38)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | | REF_CLOSE: (11), (19), (21), (38) are inconsistent by sub-proof #2144.
% 239.76/46.42  | | | | 
% 239.76/46.42  | | | End of split
% 239.76/46.42  | | | 
% 239.76/46.42  | | End of split
% 239.76/46.42  | | 
% 239.76/46.42  | Case 2:
% 239.76/46.42  | | 
% 239.76/46.42  | |   (39)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 239.76/46.42  | |         $i(all_56_15)
% 239.76/46.42  | | 
% 239.76/46.42  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (13), (15), (19),
% 239.76/46.42  | |            (22), (23), (24), (25), (39) are inconsistent by sub-proof #266.
% 239.76/46.42  | | 
% 239.76/46.42  | End of split
% 239.76/46.42  | 
% 239.76/46.42  End of proof
% 239.76/46.42  
% 239.76/46.42  Sub-proof #94 shows that the following formulas are inconsistent:
% 239.76/46.42  ----------------------------------------------------------------
% 239.76/46.42    (1)  op(e3, e2) = all_56_9
% 239.76/46.42    (2)  op(e3, all_56_9) = e3
% 239.76/46.42    (3)  op(e1, e2) = all_52_6
% 239.76/46.42    (4)  op(e3, e2) = all_22_0
% 239.76/46.42    (5)  op(e1, e2) = e3
% 239.76/46.42    (6)  op(e3, e2) = e2
% 239.76/46.42    (7)  all_54_9 = all_52_6
% 239.76/46.42    (8)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 239.76/46.42    (9)  op(e1, e2) = all_36_1
% 239.76/46.42    (10)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 239.76/46.42            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 239.76/46.42              e2) = all_40_1 & $i(all_40_1))
% 239.76/46.42    (11)  op(e3, e2) = all_30_0
% 239.76/46.42    (12)  op(e3, e2) = all_52_4
% 239.76/46.42    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.42    (14)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 239.76/46.42            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 239.76/46.42              e2) = all_36_1 & $i(all_36_1))
% 239.76/46.42    (15)   ~ (all_52_4 = all_52_6)
% 239.76/46.42  
% 239.76/46.42  Begin of proof
% 239.76/46.42  | 
% 239.76/46.42  | BETA: splitting (10) gives:
% 239.76/46.42  | 
% 239.76/46.42  | Case 1:
% 239.76/46.42  | | 
% 239.76/46.42  | |   (16)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 239.76/46.42  | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 239.76/46.42  | | 
% 239.76/46.42  | | ALPHA: (16) implies:
% 239.76/46.42  | |   (17)  op(e1, e2) = all_40_1
% 239.76/46.42  | | 
% 239.76/46.42  | | GROUND_INST: instantiating (13) with all_36_1, all_40_1, e2, e1, simplifying
% 239.76/46.42  | |              with (9), (17) gives:
% 239.76/46.42  | |   (18)  all_40_1 = all_36_1
% 239.76/46.42  | | 
% 239.76/46.42  | | GROUND_INST: instantiating (13) with e3, all_40_1, e2, e1, simplifying with
% 239.76/46.42  | |              (5), (17) gives:
% 239.76/46.42  | |   (19)  all_40_1 = e3
% 239.76/46.42  | | 
% 239.76/46.42  | | GROUND_INST: instantiating (13) with e2, all_30_0, e2, e3, simplifying with
% 239.76/46.42  | |              (6), (11) gives:
% 239.76/46.42  | |   (20)  all_30_0 = e2
% 239.76/46.42  | | 
% 239.76/46.42  | | GROUND_INST: instantiating (13) with all_30_0, all_56_9, e2, e3, simplifying
% 239.76/46.42  | |              with (1), (11) gives:
% 239.76/46.42  | |   (21)  all_56_9 = all_30_0
% 239.76/46.42  | | 
% 239.76/46.42  | | GROUND_INST: instantiating (13) with all_22_0, all_56_9, e2, e3, simplifying
% 239.76/46.42  | |              with (1), (4) gives:
% 239.76/46.42  | |   (22)  all_56_9 = all_22_0
% 239.76/46.42  | | 
% 239.76/46.42  | | COMBINE_EQS: (21), (22) imply:
% 239.76/46.42  | |   (23)  all_30_0 = all_22_0
% 239.76/46.42  | | 
% 239.76/46.42  | | SIMP: (23) implies:
% 239.76/46.42  | |   (24)  all_30_0 = all_22_0
% 239.76/46.42  | | 
% 239.76/46.42  | | COMBINE_EQS: (18), (19) imply:
% 239.76/46.42  | |   (25)  all_36_1 = e3
% 239.76/46.42  | | 
% 239.76/46.42  | | SIMP: (25) implies:
% 239.76/46.42  | |   (26)  all_36_1 = e3
% 239.76/46.42  | | 
% 239.76/46.42  | | COMBINE_EQS: (20), (24) imply:
% 239.76/46.42  | |   (27)  all_22_0 = e2
% 239.76/46.42  | | 
% 239.76/46.42  | | COMBINE_EQS: (22), (27) imply:
% 239.76/46.43  | |   (28)  all_56_9 = e2
% 239.76/46.43  | | 
% 239.76/46.43  | | REDUCE: (2), (28) imply:
% 239.76/46.43  | |   (29)  op(e3, e2) = e3
% 239.76/46.43  | | 
% 239.76/46.43  | | REF_CLOSE: (3), (5), (7), (8), (12), (13), (15), (29) are inconsistent by
% 239.76/46.43  | |            sub-proof #2190.
% 239.76/46.43  | | 
% 239.76/46.43  | Case 2:
% 239.76/46.43  | | 
% 239.76/46.43  | |   (30)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 239.76/46.43  | | 
% 239.76/46.43  | | REF_CLOSE: (5), (13), (14), (30) are inconsistent by sub-proof #2144.
% 239.76/46.43  | | 
% 239.76/46.43  | End of split
% 239.76/46.43  | 
% 239.76/46.43  End of proof
% 239.76/46.43  
% 239.76/46.43  Sub-proof #95 shows that the following formulas are inconsistent:
% 239.76/46.43  ----------------------------------------------------------------
% 239.76/46.43    (1)  op(e1, e0) = e1
% 239.76/46.43    (2)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 239.76/46.43           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 239.76/46.43           all_30_1 & $i(all_30_1))
% 239.76/46.43    (3)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 239.76/46.43         $i(all_56_29)
% 239.76/46.43    (4)  op(e1, e1) = e2
% 239.76/46.43    (5)  op(e2, e1) = e3
% 239.76/46.43    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.76/46.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.76/46.43    (7)   ~ (e2 = e1)
% 239.76/46.43  
% 239.76/46.43  Begin of proof
% 239.76/46.43  | 
% 239.76/46.43  | ALPHA: (3) implies:
% 239.85/46.43  |   (8)  op(e1, e0) = all_56_29
% 239.85/46.43  |   (9)  op(e1, all_56_29) = e1
% 239.85/46.43  | 
% 239.85/46.43  | BETA: splitting (2) gives:
% 239.85/46.43  | 
% 239.85/46.43  | Case 1:
% 239.85/46.43  | | 
% 239.85/46.43  | | 
% 239.85/46.43  | | GROUND_INST: instantiating (6) with e1, all_56_29, e0, e1, simplifying with
% 239.85/46.43  | |              (1), (8) gives:
% 239.85/46.43  | |   (10)  all_56_29 = e1
% 239.85/46.43  | | 
% 239.85/46.43  | | REDUCE: (9), (10) imply:
% 239.85/46.43  | |   (11)  op(e1, e1) = e1
% 239.85/46.43  | | 
% 239.85/46.43  | | REF_CLOSE: (4), (6), (7), (11) are inconsistent by sub-proof #2159.
% 239.85/46.43  | | 
% 239.85/46.43  | Case 2:
% 239.85/46.43  | | 
% 239.85/46.43  | |   (12)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 & $i(all_30_1)
% 239.85/46.43  | | 
% 239.85/46.43  | | ALPHA: (12) implies:
% 239.85/46.43  | |   (13)   ~ (all_30_1 = e3)
% 239.85/46.43  | |   (14)  op(e2, e1) = all_30_1
% 239.85/46.43  | | 
% 239.85/46.43  | | REF_CLOSE: (5), (6), (13), (14) are inconsistent by sub-proof #1839.
% 239.85/46.43  | | 
% 239.85/46.43  | End of split
% 239.85/46.43  | 
% 239.85/46.43  End of proof
% 239.85/46.43  
% 239.85/46.43  Sub-proof #96 shows that the following formulas are inconsistent:
% 239.85/46.43  ----------------------------------------------------------------
% 239.85/46.43    (1)   ~ (all_52_3 = e1)
% 239.85/46.43    (2)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) = all_38_1
% 239.85/46.43           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 239.85/46.43           all_38_1 & $i(all_38_1))
% 239.85/46.43    (3)   ~ (all_52_13 = e1)
% 239.85/46.43    (4)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 239.85/46.43           $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 239.85/46.43           = all_56_27 & $i(all_56_27))
% 239.85/46.43    (5)  op(e0, e3) = all_52_3
% 239.85/46.43    (6)   ~ (e3 = e1)
% 239.85/46.43    (7)  op(e3, e1) = e0
% 239.85/46.43    (8)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) = all_10_1
% 239.85/46.43           & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3, e1) =
% 239.85/46.43           all_10_1 & $i(all_10_1))
% 239.85/46.43    (9)   ~ (all_52_2 = e1)
% 239.85/46.43    (10)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) =
% 239.85/46.43            all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2,
% 239.85/46.43              e1) = all_30_1 & $i(all_30_1))
% 239.85/46.43    (11)  all_54_7 = e1 | all_54_7 = e0
% 239.85/46.43    (12)  op(e2, e0) = e0
% 239.85/46.43    (13)  op(e3, e0) = e3
% 239.85/46.43    (14)  op(e2, e3) = all_52_1
% 239.85/46.43    (15)   ~ (all_52_13 = e2)
% 239.85/46.43    (16)  all_54_7 = all_52_13
% 239.85/46.43    (17)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.85/46.43          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.85/46.43    (18)  op(e2, e1) = e3
% 239.85/46.43    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.43    (20)  op(e1, e3) = all_52_2
% 239.85/46.43    (21)  op(e2, e0) = all_52_13
% 239.85/46.43    (22)   ~ (all_52_1 = e1)
% 239.85/46.43  
% 239.85/46.43  Begin of proof
% 239.85/46.43  | 
% 239.85/46.43  | BETA: splitting (4) gives:
% 239.85/46.43  | 
% 239.85/46.43  | Case 1:
% 239.85/46.43  | | 
% 239.85/46.43  | |   (23)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 239.85/46.43  | |         $i(all_56_25)
% 239.85/46.43  | | 
% 239.85/46.43  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (13), (14), (17), (19), (20),
% 239.85/46.43  | |            (22), (23) are inconsistent by sub-proof #97.
% 239.85/46.43  | | 
% 239.85/46.43  | Case 2:
% 239.85/46.43  | | 
% 239.85/46.43  | |   (24)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 239.85/46.43  | |         $i(all_56_27)
% 239.85/46.43  | | 
% 239.85/46.43  | | ALPHA: (24) implies:
% 239.85/46.43  | |   (25)  op(e2, e0) = all_56_27
% 239.85/46.43  | |   (26)  op(e2, all_56_27) = e2
% 239.85/46.43  | | 
% 239.85/46.43  | | BETA: splitting (10) gives:
% 239.85/46.43  | | 
% 239.85/46.43  | | Case 1:
% 239.85/46.43  | | | 
% 239.85/46.43  | | | 
% 239.85/46.43  | | | REF_CLOSE: (3), (11), (12), (15), (16), (19), (21), (25), (26) are
% 239.85/46.43  | | |            inconsistent by sub-proof #155.
% 239.85/46.43  | | | 
% 239.85/46.43  | | Case 2:
% 239.85/46.43  | | | 
% 239.85/46.43  | | |   (27)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 & $i(all_30_1)
% 239.85/46.43  | | | 
% 239.85/46.43  | | | ALPHA: (27) implies:
% 239.85/46.43  | | |   (28)   ~ (all_30_1 = e3)
% 239.85/46.43  | | |   (29)  op(e2, e1) = all_30_1
% 239.85/46.43  | | | 
% 239.85/46.43  | | | REF_CLOSE: (18), (19), (28), (29) are inconsistent by sub-proof #1839.
% 239.85/46.43  | | | 
% 239.85/46.43  | | End of split
% 239.85/46.43  | | 
% 239.85/46.43  | End of split
% 239.85/46.43  | 
% 239.85/46.43  End of proof
% 239.85/46.43  
% 239.85/46.43  Sub-proof #97 shows that the following formulas are inconsistent:
% 239.85/46.43  ----------------------------------------------------------------
% 239.85/46.43    (1)   ~ (all_52_3 = e1)
% 239.85/46.43    (2)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 239.85/46.43         $i(all_56_25)
% 239.85/46.43    (3)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) = all_38_1
% 239.85/46.43           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 239.85/46.43           all_38_1 & $i(all_38_1))
% 239.85/46.43    (4)  op(e0, e3) = all_52_3
% 239.85/46.43    (5)   ~ (e3 = e1)
% 239.85/46.43    (6)  op(e3, e1) = e0
% 239.85/46.43    (7)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) = all_10_1
% 239.85/46.43           & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3, e1) =
% 239.85/46.43           all_10_1 & $i(all_10_1))
% 239.85/46.43    (8)   ~ (all_52_2 = e1)
% 239.85/46.43    (9)  op(e3, e0) = e3
% 239.85/46.43    (10)  op(e2, e3) = all_52_1
% 239.85/46.43    (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.85/46.43          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.85/46.43    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.43    (13)  op(e1, e3) = all_52_2
% 239.85/46.43    (14)   ~ (all_52_1 = e1)
% 239.85/46.43  
% 239.85/46.43  Begin of proof
% 239.85/46.43  | 
% 239.85/46.43  | ALPHA: (2) implies:
% 239.85/46.43  |   (15)  op(e3, e0) = all_56_25
% 239.85/46.43  |   (16)  op(e3, all_56_25) = e3
% 239.85/46.43  | 
% 239.85/46.43  | BETA: splitting (7) gives:
% 239.85/46.43  | 
% 239.85/46.43  | Case 1:
% 239.85/46.43  | | 
% 239.85/46.43  | |   (17)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 239.85/46.43  | |         all_10_1 & $i(all_10_0) & $i(all_10_1)
% 239.85/46.43  | | 
% 239.85/46.43  | | ALPHA: (17) implies:
% 239.85/46.43  | |   (18)  op(e3, e1) = all_10_1
% 239.85/46.43  | | 
% 239.85/46.43  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 239.85/46.43  | |            (15), (16), (18) are inconsistent by sub-proof #98.
% 239.85/46.43  | | 
% 239.85/46.43  | Case 2:
% 239.85/46.43  | | 
% 239.85/46.43  | |   (19)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 & $i(all_10_1)
% 239.85/46.43  | | 
% 239.85/46.43  | | ALPHA: (19) implies:
% 239.85/46.43  | |   (20)  op(e3, e1) = all_10_1
% 239.85/46.43  | | 
% 239.85/46.43  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 239.85/46.43  | |            (15), (16), (20) are inconsistent by sub-proof #98.
% 239.85/46.43  | | 
% 239.85/46.43  | End of split
% 239.85/46.43  | 
% 239.85/46.43  End of proof
% 239.85/46.43  
% 239.85/46.43  Sub-proof #98 shows that the following formulas are inconsistent:
% 239.85/46.43  ----------------------------------------------------------------
% 239.85/46.43    (1)   ~ (all_52_3 = e1)
% 239.85/46.43    (2)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) = all_38_1
% 239.85/46.43           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 239.85/46.43           all_38_1 & $i(all_38_1))
% 239.85/46.43    (3)  op(e0, e3) = all_52_3
% 239.85/46.43    (4)   ~ (e3 = e1)
% 239.85/46.43    (5)  op(e3, all_56_25) = e3
% 239.85/46.43    (6)  op(e3, e1) = e0
% 239.85/46.43    (7)   ~ (all_52_2 = e1)
% 239.85/46.43    (8)  op(e3, e0) = e3
% 239.85/46.43    (9)  op(e2, e3) = all_52_1
% 239.85/46.43    (10)  op(e3, e0) = all_56_25
% 239.85/46.43    (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.85/46.43          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.85/46.43    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.43    (13)  op(e3, e1) = all_10_1
% 239.85/46.43    (14)  op(e1, e3) = all_52_2
% 239.85/46.43    (15)   ~ (all_52_1 = e1)
% 239.85/46.43  
% 239.85/46.43  Begin of proof
% 239.85/46.43  | 
% 239.85/46.43  | BETA: splitting (2) gives:
% 239.85/46.43  | 
% 239.85/46.43  | Case 1:
% 239.85/46.43  | | 
% 239.85/46.43  | | 
% 239.85/46.43  | | GROUND_INST: instantiating (12) with e3, all_56_25, e0, e3, simplifying with
% 239.85/46.43  | |              (8), (10) gives:
% 239.85/46.43  | |   (16)  all_56_25 = e3
% 239.85/46.43  | | 
% 239.85/46.43  | | REDUCE: (5), (16) imply:
% 239.85/46.43  | |   (17)  op(e3, e3) = e3
% 239.85/46.43  | | 
% 239.85/46.43  | | REF_CLOSE: (1), (3), (4), (7), (9), (11), (12), (14), (15), (17) are
% 239.85/46.43  | |            inconsistent by sub-proof #440.
% 239.85/46.43  | | 
% 239.85/46.43  | Case 2:
% 239.85/46.43  | | 
% 239.85/46.43  | |   (18)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1)
% 239.85/46.43  | | 
% 239.85/46.43  | | ALPHA: (18) implies:
% 239.85/46.43  | |   (19)   ~ (all_38_1 = e0)
% 239.85/46.43  | |   (20)  op(e3, e1) = all_38_1
% 239.85/46.43  | | 
% 239.85/46.43  | | REF_CLOSE: (6), (12), (13), (19), (20) are inconsistent by sub-proof #1195.
% 239.85/46.43  | | 
% 239.85/46.43  | End of split
% 239.85/46.43  | 
% 239.85/46.43  End of proof
% 239.85/46.43  
% 239.85/46.43  Sub-proof #99 shows that the following formulas are inconsistent:
% 239.85/46.43  ----------------------------------------------------------------
% 239.85/46.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.43    (2)  op(e1, e2) = all_52_6
% 239.85/46.43    (3)  op(e1, e2) = e1
% 239.85/46.43    (4)   ~ (all_52_6 = e1)
% 239.85/46.43  
% 239.85/46.43  Begin of proof
% 239.85/46.43  | 
% 239.85/46.43  | GROUND_INST: instantiating (1) with all_52_6, e1, e2, e1, simplifying with
% 239.85/46.43  |              (2), (3) gives:
% 239.85/46.43  |   (5)  all_52_6 = e1
% 239.85/46.43  | 
% 239.85/46.43  | REDUCE: (4), (5) imply:
% 239.85/46.43  |   (6)  $false
% 239.85/46.43  | 
% 239.85/46.43  | CLOSE: (6) is inconsistent.
% 239.85/46.43  | 
% 239.85/46.43  End of proof
% 239.85/46.43  
% 239.85/46.43  Sub-proof #100 shows that the following formulas are inconsistent:
% 239.85/46.43  ----------------------------------------------------------------
% 239.85/46.43    (1)  op(e3, e1) = all_56_17
% 239.85/46.43    (2)   ~ (all_52_3 = e1)
% 239.85/46.43    (3)  op(e0, e3) = all_52_3
% 239.85/46.43    (4)   ~ (e3 = e1)
% 239.85/46.43    (5)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) = all_22_1
% 239.85/46.43           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1) =
% 239.85/46.43           all_22_1 & $i(all_22_1))
% 239.85/46.43    (6)   ~ (all_52_2 = e1)
% 239.85/46.43    (7)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 239.85/46.43           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 239.85/46.43           all_30_1 & $i(all_30_1))
% 239.85/46.43    (8)  op(e3, e1) = all_38_1
% 239.85/46.43    (9)  op(e2, e3) = all_52_1
% 239.85/46.43    (10)  op(e2, e1) = e0
% 239.85/46.43    (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.85/46.43          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.85/46.43    (12)  op(e3, all_56_17) = e3
% 239.85/46.43    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.43    (14)  op(e1, e3) = all_52_2
% 239.85/46.43    (15)  op(e3, e1) = e3
% 239.85/46.43    (16)   ~ (all_52_1 = e1)
% 239.85/46.43  
% 239.85/46.43  Begin of proof
% 239.85/46.43  | 
% 239.85/46.43  | BETA: splitting (5) gives:
% 239.85/46.43  | 
% 239.85/46.43  | Case 1:
% 239.85/46.43  | | 
% 239.85/46.43  | | 
% 239.85/46.43  | | GROUND_INST: instantiating (13) with all_38_1, all_56_17, e1, e3,
% 239.85/46.43  | |              simplifying with (1), (8) gives:
% 239.85/46.43  | |   (17)  all_56_17 = all_38_1
% 239.85/46.43  | | 
% 239.85/46.43  | | GROUND_INST: instantiating (13) with e3, all_56_17, e1, e3, simplifying with
% 239.85/46.43  | |              (1), (15) gives:
% 239.85/46.43  | |   (18)  all_56_17 = e3
% 239.85/46.43  | | 
% 239.85/46.43  | | COMBINE_EQS: (17), (18) imply:
% 239.85/46.43  | |   (19)  all_38_1 = e3
% 239.85/46.43  | | 
% 239.85/46.43  | | REDUCE: (12), (18) imply:
% 239.85/46.43  | |   (20)  op(e3, e3) = e3
% 239.85/46.43  | | 
% 239.85/46.43  | | REF_CLOSE: (2), (3), (4), (6), (9), (11), (13), (14), (16), (20) are
% 239.85/46.43  | |            inconsistent by sub-proof #440.
% 239.85/46.43  | | 
% 239.85/46.43  | Case 2:
% 239.85/46.43  | | 
% 239.85/46.43  | |   (21)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 & $i(all_22_1)
% 239.85/46.43  | | 
% 239.85/46.43  | | ALPHA: (21) implies:
% 239.85/46.43  | |   (22)   ~ (all_22_1 = e0)
% 239.85/46.43  | |   (23)  op(e2, e1) = all_22_1
% 239.85/46.43  | | 
% 239.85/46.44  | | REF_CLOSE: (7), (10), (13), (22), (23) are inconsistent by sub-proof #1356.
% 239.85/46.44  | | 
% 239.85/46.44  | End of split
% 239.85/46.44  | 
% 239.85/46.44  End of proof
% 239.85/46.44  
% 239.85/46.44  Sub-proof #101 shows that the following formulas are inconsistent:
% 239.85/46.44  ----------------------------------------------------------------
% 239.85/46.44    (1)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 239.85/46.44    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.85/46.44         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.85/46.44    (3)   ~ (all_8_2 = e0)
% 239.85/46.44    (4)   ~ (e3 = e0)
% 239.85/46.44    (5)   ~ (e2 = e0)
% 239.85/46.44    (6)  all_58_9 = e0
% 239.85/46.44    (7)   ~ (e3 = e1)
% 239.85/46.44    (8)  all_58_2 = e2
% 239.85/46.44    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.85/46.44         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.85/46.44    (10)  op(e3, e3) = e1
% 239.85/46.44    (11)   ~ (e3 = e2)
% 239.85/46.44    (12)  op(e2, e2) = all_8_2
% 239.85/46.44    (13)  all_58_1 = e2
% 239.85/46.44    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.44    (15)   ~ (e2 = e1)
% 239.85/46.44  
% 239.85/46.44  Begin of proof
% 239.85/46.44  | 
% 239.85/46.44  | BETA: splitting (1) gives:
% 239.85/46.44  | 
% 239.85/46.44  | Case 1:
% 239.85/46.44  | | 
% 239.85/46.44  | |   (16)  all_58_2 = e0 & op(e2, e3) = e0
% 239.85/46.44  | | 
% 239.85/46.44  | | ALPHA: (16) implies:
% 239.85/46.44  | |   (17)  all_58_2 = e0
% 239.85/46.44  | | 
% 239.85/46.44  | | COMBINE_EQS: (8), (17) imply:
% 239.85/46.44  | |   (18)  e2 = e0
% 239.85/46.44  | | 
% 239.85/46.44  | | COMBINE_EQS: (13), (18) imply:
% 239.85/46.44  | |   (19)  all_58_1 = e0
% 239.85/46.44  | | 
% 239.85/46.44  | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (11), (14), (15), (19) are
% 239.85/46.44  | |            inconsistent by sub-proof #1089.
% 239.85/46.44  | | 
% 239.85/46.44  | Case 2:
% 239.85/46.44  | | 
% 239.85/46.44  | |   (20)  all_58_3 = e0 & op(e2, e2) = e0
% 239.85/46.44  | | 
% 239.85/46.44  | | REF_CLOSE: (3), (12), (14), (20) are inconsistent by sub-proof #1992.
% 239.85/46.44  | | 
% 239.85/46.44  | End of split
% 239.85/46.44  | 
% 239.85/46.44  End of proof
% 239.85/46.44  
% 239.85/46.44  Sub-proof #102 shows that the following formulas are inconsistent:
% 239.85/46.44  ----------------------------------------------------------------
% 239.85/46.44    (1)   ~ (all_52_1 = all_52_3)
% 239.85/46.44    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.85/46.44             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 239.85/46.44           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 239.85/46.44         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.85/46.44           $i(all_56_7))
% 239.85/46.44    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.85/46.44    (4)   ~ (all_52_3 = e1)
% 239.85/46.44    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.85/46.44         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.85/46.44    (6)   ~ (all_52_7 = e2)
% 239.85/46.44    (7)  all_54_10 = e1 | all_54_10 = e0
% 239.85/46.44    (8)  op(e1, e1) = e1
% 239.85/46.44    (9)   ~ (e2 = e0)
% 239.85/46.44    (10)   ~ (all_52_11 = e2)
% 239.85/46.44    (11)  op(e1, e2) = all_52_6
% 239.85/46.44    (12)  all_58_6 = e2
% 239.85/46.44    (13)   ~ (all_52_11 = e1)
% 239.85/46.44    (14)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.85/46.44              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.85/46.44            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.85/46.44            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.85/46.44            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 239.85/46.44             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.85/46.44            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.85/46.44            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.85/46.44            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.85/46.44            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.85/46.44            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.85/46.44              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.85/46.44            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.85/46.44            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 239.85/46.44            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.85/46.44            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 239.85/46.44            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.85/46.44            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.85/46.44              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.85/46.44            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.85/46.44            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.85/46.44            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.85/46.44            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 239.85/46.44            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.85/46.44            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.85/46.44              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.85/46.44            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.85/46.44            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.85/46.44    (15)  op(e1, e1) = all_6_2
% 239.85/46.44    (16)  op(e1, e0) = all_52_14
% 239.85/46.44    (17)  op(e0, e3) = all_52_3
% 239.85/46.44    (18)   ~ (all_52_12 = e1)
% 239.85/46.44    (19)  all_54_6 = all_52_9
% 239.85/46.44    (20)   ~ (all_52_8 = e1)
% 239.85/46.44    (21)   ~ (all_52_2 = e1)
% 239.85/46.44    (22)  op(e0, e2) = all_4_1
% 239.85/46.44    (23)  all_54_10 = all_6_2
% 239.85/46.44    (24)  op(e1, e3) = e2
% 239.85/46.44    (25)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 239.85/46.44          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 239.85/46.44    (26)   ~ (all_52_1 = all_52_9)
% 239.85/46.44    (27)  op(e2, e3) = all_10_0
% 239.85/46.44    (28)  all_54_4 = all_52_1
% 239.85/46.44    (29)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 239.85/46.44              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 239.85/46.44                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 239.85/46.44                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 239.85/46.44    (30)  op(e3, e1) = all_52_8
% 239.85/46.44    (31)  op(e2, e1) = all_52_9
% 239.85/46.44    (32)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.85/46.44            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 239.85/46.44              e2) = all_44_1 & $i(all_44_1))
% 239.85/46.44    (33)   ~ (all_52_14 = e1)
% 239.85/46.44    (34)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.85/46.44    (35)   ~ (all_52_3 = all_52_11)
% 239.85/46.44    (36)   ~ (all_6_2 = e0)
% 239.85/46.44    (37)  all_56_31 = e2
% 239.85/46.44    (38)  all_54_12 = all_52_3
% 239.85/46.44    (39)  op(e3, e0) = all_52_12
% 239.85/46.44    (40)   ~ (all_52_3 = e2)
% 239.85/46.44    (41)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.85/46.44          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.85/46.44    (42)   ~ (all_52_9 = all_52_13)
% 239.85/46.44    (43)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 239.85/46.44    (44)  op(e2, e3) = all_52_1
% 239.85/46.44    (45)   ~ (all_52_12 = e2)
% 239.85/46.44    (46)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.85/46.44    (47)  op(e3, e1) = e2
% 239.85/46.44    (48)  op(e0, e2) = all_52_7
% 239.85/46.44    (49)  op(e3, e2) = all_52_4
% 239.85/46.44    (50)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.85/46.44          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.85/46.44    (51)   ~ (all_52_4 = e2)
% 239.85/46.44    (52)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.85/46.44          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.85/46.44    (53)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.44    (54)  op(e1, e3) = all_52_2
% 239.85/46.44    (55)   ~ (e1 = e0)
% 239.85/46.44    (56)  all_58_13 = e1
% 239.85/46.44    (57)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.85/46.44          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.85/46.44    (58)  op(e0, e0) = e2
% 239.85/46.44    (59)  op(e2, e0) = all_52_13
% 239.85/46.44    (60)   ~ (all_10_0 = e0)
% 239.85/46.44    (61)  op(e0, e2) = e1
% 239.85/46.44    (62)   ~ (all_52_9 = e1)
% 239.85/46.44    (63)  all_54_14 = all_52_11
% 239.85/46.44    (64)  op(e2, e2) = e2
% 239.85/46.44    (65)   ~ (all_52_1 = e2)
% 239.85/46.44    (66)  all_56_1 = e1
% 239.85/46.44    (67)   ~ (all_52_1 = e1)
% 239.85/46.44    (68)   ~ (all_52_9 = e2)
% 239.85/46.44  
% 239.85/46.44  Begin of proof
% 239.85/46.44  | 
% 239.85/46.44  | GROUND_INST: instantiating (53) with e1, all_4_1, e2, e0, simplifying with
% 239.85/46.44  |              (22), (61) gives:
% 239.85/46.44  |   (69)  all_4_1 = e1
% 239.85/46.44  | 
% 239.85/46.44  | GROUND_INST: instantiating (53) with all_52_1, all_10_0, e3, e2, simplifying
% 239.85/46.44  |              with (27), (44) gives:
% 239.85/46.44  |   (70)  all_52_1 = all_10_0
% 239.85/46.44  | 
% 239.85/46.44  | COMBINE_EQS: (28), (70) imply:
% 239.85/46.44  |   (71)  all_54_4 = all_10_0
% 239.85/46.44  | 
% 239.85/46.44  | REDUCE: (1), (70) imply:
% 239.85/46.44  |   (72)   ~ (all_52_3 = all_10_0)
% 239.85/46.44  | 
% 239.85/46.44  | SIMP: (72) implies:
% 239.85/46.44  |   (73)   ~ (all_52_3 = all_10_0)
% 239.85/46.44  | 
% 239.85/46.44  | REDUCE: (26), (70) imply:
% 239.85/46.44  |   (74)   ~ (all_52_9 = all_10_0)
% 239.85/46.44  | 
% 239.85/46.44  | SIMP: (74) implies:
% 239.85/46.44  |   (75)   ~ (all_52_9 = all_10_0)
% 239.85/46.44  | 
% 239.85/46.44  | REDUCE: (65), (70) imply:
% 239.85/46.44  |   (76)   ~ (all_10_0 = e2)
% 239.85/46.44  | 
% 239.85/46.44  | REDUCE: (67), (70) imply:
% 239.85/46.44  |   (77)   ~ (all_10_0 = e1)
% 239.85/46.44  | 
% 239.85/46.44  | BETA: splitting (46) gives:
% 239.85/46.44  | 
% 239.85/46.44  | Case 1:
% 239.85/46.44  | | 
% 239.85/46.44  | |   (78)  all_54_4 = e3
% 239.85/46.44  | | 
% 239.85/46.44  | | COMBINE_EQS: (71), (78) imply:
% 239.85/46.44  | |   (79)  all_10_0 = e3
% 239.85/46.44  | | 
% 239.85/46.44  | | REDUCE: (73), (79) imply:
% 239.85/46.44  | |   (80)   ~ (all_52_3 = e3)
% 239.85/46.44  | | 
% 239.85/46.44  | | REDUCE: (75), (79) imply:
% 239.85/46.44  | |   (81)   ~ (all_52_9 = e3)
% 239.85/46.44  | | 
% 239.85/46.44  | | REDUCE: (76), (79) imply:
% 239.85/46.44  | |   (82)   ~ (e3 = e2)
% 239.85/46.44  | | 
% 239.85/46.44  | | REDUCE: (77), (79) imply:
% 239.85/46.44  | |   (83)   ~ (e3 = e1)
% 239.85/46.44  | | 
% 239.85/46.44  | | REDUCE: (60), (79) imply:
% 239.85/46.44  | |   (84)   ~ (e3 = e0)
% 239.85/46.44  | | 
% 239.85/46.44  | | REDUCE: (27), (79) imply:
% 239.85/46.44  | |   (85)  op(e2, e3) = e3
% 239.85/46.44  | | 
% 239.85/46.44  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 239.85/46.44  | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 239.85/46.44  | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 239.85/46.44  | |            (40), (41), (42), (43), (44), (45), (47), (48), (49), (50), (51),
% 239.85/46.44  | |            (52), (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 239.85/46.44  | |            (64), (66), (67), (68), (80), (81), (82), (83), (84), (85) are
% 239.85/46.44  | |            inconsistent by sub-proof #107.
% 239.85/46.44  | | 
% 239.85/46.44  | Case 2:
% 239.85/46.44  | | 
% 239.85/46.44  | |   (86)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.85/46.44  | | 
% 239.85/46.44  | | REF_CLOSE: (60), (71), (76), (77), (86) are inconsistent by sub-proof #106.
% 239.85/46.44  | | 
% 239.85/46.44  | End of split
% 239.85/46.44  | 
% 239.85/46.44  End of proof
% 239.85/46.44  
% 239.85/46.44  Sub-proof #103 shows that the following formulas are inconsistent:
% 239.85/46.44  ----------------------------------------------------------------
% 239.85/46.44    (1)   ~ (e3 = e0)
% 239.85/46.44    (2)  op(e0, e1) = all_52_11
% 239.85/46.44    (3)   ~ (e2 = e0)
% 239.85/46.44    (4)  all_58_6 = e2
% 239.85/46.44    (5)   ~ (all_52_11 = e1)
% 239.85/46.44    (6)  op(e1, e1) = all_6_2
% 239.85/46.44    (7)   ~ (all_6_2 = e3)
% 239.85/46.44    (8)   ~ (e3 = e2)
% 239.85/46.44    (9)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 239.85/46.44    (10)   ~ (all_6_2 = e0)
% 239.85/46.44    (11)  op(e3, e0) = all_52_12
% 239.85/46.44    (12)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.85/46.44          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.85/46.44    (13)   ~ (all_52_12 = e2)
% 239.85/46.44    (14)   ~ (all_52_13 = e2)
% 239.85/46.44    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.44    (16)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 239.85/46.44          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 239.85/46.44    (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.85/46.44          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.85/46.44    (18)  op(e2, e0) = all_52_13
% 239.85/46.44    (19)   ~ (e2 = e1)
% 239.85/46.44  
% 239.85/46.44  Begin of proof
% 239.85/46.44  | 
% 239.85/46.44  | BETA: splitting (9) gives:
% 239.85/46.44  | 
% 239.85/46.44  | Case 1:
% 239.85/46.44  | | 
% 239.85/46.44  | |   (20)  all_58_14 = e1 & op(e0, e1) = e1
% 239.85/46.44  | | 
% 239.85/46.44  | | ALPHA: (20) implies:
% 239.85/46.44  | |   (21)  op(e0, e1) = e1
% 239.85/46.44  | | 
% 239.85/46.44  | | REF_CLOSE: (2), (5), (15), (21) are inconsistent by sub-proof #2272.
% 239.85/46.44  | | 
% 239.85/46.44  | Case 2:
% 239.85/46.44  | | 
% 239.85/46.44  | |   (22)  all_58_15 = e1 & op(e0, e0) = e1
% 239.85/46.44  | | 
% 239.85/46.44  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 239.85/46.44  | |            (16), (17), (18), (19), (22) are inconsistent by sub-proof #105.
% 239.85/46.44  | | 
% 239.85/46.44  | End of split
% 239.85/46.44  | 
% 239.85/46.44  End of proof
% 239.85/46.44  
% 239.85/46.44  Sub-proof #104 shows that the following formulas are inconsistent:
% 239.85/46.44  ----------------------------------------------------------------
% 239.85/46.44    (1)   ~ (e3 = e0)
% 239.85/46.44    (2)   ~ (e2 = e0)
% 239.85/46.44    (3)  all_58_6 = e2
% 239.85/46.44    (4)  op(e1, e1) = all_6_2
% 239.85/46.44    (5)  op(e1, e0) = all_52_14
% 239.85/46.44    (6)   ~ (all_6_2 = e3)
% 239.85/46.44    (7)   ~ (e3 = e2)
% 239.85/46.44    (8)   ~ (all_52_14 = e1)
% 239.85/46.44    (9)   ~ (all_6_2 = e0)
% 239.85/46.44    (10)  op(e3, e0) = all_52_12
% 239.85/46.44    (11)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.85/46.44          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.85/46.44    (12)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 239.85/46.44    (13)   ~ (all_52_12 = e2)
% 239.85/46.44    (14)   ~ (all_52_13 = e2)
% 239.85/46.45    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.45    (16)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 239.85/46.45          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 239.85/46.45    (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.85/46.45          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.85/46.45    (18)  op(e2, e0) = all_52_13
% 239.85/46.45    (19)   ~ (e2 = e1)
% 239.85/46.45  
% 239.85/46.45  Begin of proof
% 239.85/46.45  | 
% 239.85/46.45  | BETA: splitting (12) gives:
% 239.85/46.45  | 
% 239.85/46.45  | Case 1:
% 239.85/46.45  | | 
% 239.85/46.45  | |   (20)  all_58_11 = e1 & op(e1, e0) = e1
% 239.85/46.45  | | 
% 239.85/46.45  | | ALPHA: (20) implies:
% 239.85/46.45  | |   (21)  op(e1, e0) = e1
% 239.85/46.45  | | 
% 239.85/46.45  | | REF_CLOSE: (5), (8), (15), (21) are inconsistent by sub-proof #2304.
% 239.85/46.45  | | 
% 239.85/46.45  | Case 2:
% 239.85/46.45  | | 
% 239.85/46.45  | |   (22)  all_58_15 = e1 & op(e0, e0) = e1
% 239.85/46.45  | | 
% 239.85/46.45  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (13), (14), (15),
% 239.85/46.45  | |            (16), (17), (18), (19), (22) are inconsistent by sub-proof #105.
% 239.85/46.45  | | 
% 239.85/46.45  | End of split
% 239.85/46.45  | 
% 239.85/46.45  End of proof
% 239.85/46.45  
% 239.85/46.45  Sub-proof #105 shows that the following formulas are inconsistent:
% 239.85/46.45  ----------------------------------------------------------------
% 239.85/46.45    (1)   ~ (e3 = e0)
% 239.85/46.45    (2)   ~ (e2 = e0)
% 239.85/46.45    (3)  all_58_6 = e2
% 239.85/46.45    (4)  op(e1, e1) = all_6_2
% 239.85/46.45    (5)   ~ (all_6_2 = e3)
% 239.85/46.45    (6)   ~ (e3 = e2)
% 239.85/46.45    (7)   ~ (all_6_2 = e0)
% 239.85/46.45    (8)  op(e3, e0) = all_52_12
% 239.85/46.45    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.85/46.45         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.85/46.45    (10)   ~ (all_52_12 = e2)
% 239.85/46.45    (11)   ~ (all_52_13 = e2)
% 239.85/46.45    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.45    (13)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 239.85/46.45          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 239.85/46.45    (14)  all_58_15 = e1 & op(e0, e0) = e1
% 239.85/46.45    (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.85/46.45          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.85/46.45    (16)  op(e2, e0) = all_52_13
% 239.85/46.45    (17)   ~ (e2 = e1)
% 239.85/46.45  
% 239.85/46.45  Begin of proof
% 239.85/46.45  | 
% 239.85/46.45  | ALPHA: (14) implies:
% 239.85/46.45  |   (18)  all_58_15 = e1
% 239.85/46.45  | 
% 239.85/46.45  | BETA: splitting (13) gives:
% 239.85/46.45  | 
% 239.85/46.45  | Case 1:
% 239.85/46.45  | | 
% 239.85/46.45  | |   (19)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 239.85/46.45  | |           e2)
% 239.85/46.45  | | 
% 239.85/46.45  | | REF_CLOSE: (8), (10), (11), (12), (16), (19) are inconsistent by sub-proof
% 239.85/46.45  | |            #2316.
% 239.85/46.45  | | 
% 239.85/46.45  | Case 2:
% 239.85/46.45  | | 
% 239.85/46.45  | |   (20)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 239.85/46.45  | |           e2)
% 239.85/46.45  | | 
% 239.85/46.45  | | BETA: splitting (20) gives:
% 239.85/46.45  | | 
% 239.85/46.45  | | Case 1:
% 239.85/46.45  | | | 
% 239.85/46.45  | | |   (21)  all_58_11 = e2 & op(e1, e0) = e2
% 239.85/46.45  | | | 
% 239.85/46.45  | | | ALPHA: (21) implies:
% 239.85/46.45  | | |   (22)  all_58_11 = e2
% 239.85/46.45  | | | 
% 239.85/46.45  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (12), (15), (22) are
% 239.85/46.45  | | |            inconsistent by sub-proof #238.
% 239.85/46.45  | | | 
% 239.85/46.45  | | Case 2:
% 239.85/46.45  | | | 
% 239.85/46.45  | | |   (23)  all_58_15 = e2 & op(e0, e0) = e2
% 239.85/46.45  | | | 
% 239.85/46.45  | | | ALPHA: (23) implies:
% 239.85/46.45  | | |   (24)  all_58_15 = e2
% 239.85/46.45  | | | 
% 239.85/46.45  | | | REF_CLOSE: (17), (18), (24) are inconsistent by sub-proof #2231.
% 239.85/46.45  | | | 
% 239.85/46.45  | | End of split
% 239.85/46.45  | | 
% 239.85/46.45  | End of split
% 239.85/46.45  | 
% 239.85/46.45  End of proof
% 239.85/46.45  
% 239.85/46.45  Sub-proof #106 shows that the following formulas are inconsistent:
% 239.85/46.45  ----------------------------------------------------------------
% 239.85/46.45    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.85/46.45    (2)   ~ (all_10_0 = e1)
% 239.85/46.45    (3)   ~ (all_10_0 = e2)
% 239.85/46.45    (4)   ~ (all_10_0 = e0)
% 239.85/46.45    (5)  all_54_4 = all_10_0
% 239.85/46.45  
% 239.85/46.45  Begin of proof
% 239.85/46.45  | 
% 239.85/46.45  | BETA: splitting (1) gives:
% 239.85/46.45  | 
% 239.85/46.45  | Case 1:
% 239.85/46.45  | | 
% 239.85/46.45  | |   (6)  all_54_4 = e2
% 239.85/46.45  | | 
% 239.85/46.45  | | COMBINE_EQS: (5), (6) imply:
% 239.85/46.45  | |   (7)  all_10_0 = e2
% 239.85/46.45  | | 
% 239.85/46.45  | | REDUCE: (3), (7) imply:
% 239.85/46.45  | |   (8)  $false
% 239.85/46.45  | | 
% 239.85/46.45  | | CLOSE: (8) is inconsistent.
% 239.85/46.45  | | 
% 239.85/46.45  | Case 2:
% 239.85/46.45  | | 
% 239.85/46.45  | |   (9)  all_54_4 = e1 | all_54_4 = e0
% 239.85/46.45  | | 
% 239.85/46.45  | | BETA: splitting (9) gives:
% 239.85/46.45  | | 
% 239.85/46.45  | | Case 1:
% 239.85/46.45  | | | 
% 239.85/46.45  | | |   (10)  all_54_4 = e1
% 239.85/46.45  | | | 
% 239.85/46.45  | | | COMBINE_EQS: (5), (10) imply:
% 239.85/46.45  | | |   (11)  all_10_0 = e1
% 239.85/46.45  | | | 
% 239.85/46.45  | | | REDUCE: (2), (11) imply:
% 239.85/46.45  | | |   (12)  $false
% 239.85/46.45  | | | 
% 239.85/46.45  | | | CLOSE: (12) is inconsistent.
% 239.85/46.45  | | | 
% 239.85/46.45  | | Case 2:
% 239.85/46.45  | | | 
% 239.85/46.45  | | |   (13)  all_54_4 = e0
% 239.85/46.45  | | | 
% 239.85/46.45  | | | COMBINE_EQS: (5), (13) imply:
% 239.85/46.45  | | |   (14)  all_10_0 = e0
% 239.85/46.45  | | | 
% 239.85/46.45  | | | REDUCE: (4), (14) imply:
% 239.85/46.45  | | |   (15)  $false
% 239.85/46.45  | | | 
% 239.85/46.45  | | | CLOSE: (15) is inconsistent.
% 239.85/46.45  | | | 
% 239.85/46.45  | | End of split
% 239.85/46.45  | | 
% 239.85/46.45  | End of split
% 239.85/46.45  | 
% 239.85/46.45  End of proof
% 239.85/46.45  
% 239.85/46.45  Sub-proof #107 shows that the following formulas are inconsistent:
% 239.85/46.45  ----------------------------------------------------------------
% 239.85/46.45    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.85/46.45             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 239.85/46.45           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 239.85/46.45         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.85/46.45           $i(all_56_7))
% 239.85/46.45    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.85/46.45    (3)   ~ (all_52_3 = e1)
% 239.85/46.45    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 239.85/46.45         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.85/46.45    (5)   ~ (e3 = e0)
% 239.85/46.45    (6)   ~ (all_52_7 = e2)
% 239.85/46.45    (7)  all_54_10 = e1 | all_54_10 = e0
% 239.85/46.45    (8)  op(e1, e1) = e1
% 239.85/46.45    (9)   ~ (e2 = e0)
% 239.85/46.45    (10)   ~ (all_52_11 = e2)
% 239.85/46.45    (11)  op(e1, e2) = all_52_6
% 239.85/46.45    (12)  all_58_6 = e2
% 239.85/46.45    (13)   ~ (all_52_11 = e1)
% 239.85/46.45    (14)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.85/46.45              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.85/46.45            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.85/46.45            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.85/46.45            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 239.85/46.45             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.85/46.45            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.85/46.45            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.85/46.45            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.85/46.45            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.85/46.45            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.85/46.45              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.85/46.45            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.85/46.45            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 239.85/46.45            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.85/46.45            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 239.85/46.45            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.85/46.45            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.85/46.45              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.85/46.45            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.85/46.45            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.85/46.45            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.85/46.45            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 239.85/46.45            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.85/46.45            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.85/46.45              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.85/46.45            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.85/46.45            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.85/46.45    (15)  op(e1, e1) = all_6_2
% 239.85/46.45    (16)  op(e1, e0) = all_52_14
% 239.85/46.45    (17)  op(e2, e3) = e3
% 239.85/46.45    (18)  op(e0, e3) = all_52_3
% 239.85/46.45    (19)   ~ (e3 = e1)
% 239.85/46.45    (20)   ~ (all_52_12 = e1)
% 239.85/46.45    (21)  all_54_6 = all_52_9
% 239.85/46.45    (22)   ~ (all_52_8 = e1)
% 239.85/46.45    (23)   ~ (all_52_2 = e1)
% 239.85/46.45    (24)  all_54_10 = all_6_2
% 239.85/46.45    (25)  op(e1, e3) = e2
% 239.85/46.45    (26)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 239.85/46.45          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 239.85/46.45    (27)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 239.85/46.45              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 239.85/46.45                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 239.85/46.45                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 239.85/46.45    (28)  op(e3, e1) = all_52_8
% 239.85/46.45    (29)  op(e2, e1) = all_52_9
% 239.85/46.45    (30)   ~ (e3 = e2)
% 239.85/46.45    (31)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.85/46.45            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 239.85/46.45              e2) = all_44_1 & $i(all_44_1))
% 239.85/46.45    (32)   ~ (all_52_14 = e1)
% 239.85/46.45    (33)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.85/46.45    (34)   ~ (all_52_3 = all_52_11)
% 239.85/46.45    (35)   ~ (all_6_2 = e0)
% 239.85/46.45    (36)  all_56_31 = e2
% 239.85/46.45    (37)  all_54_12 = all_52_3
% 239.85/46.45    (38)  op(e3, e0) = all_52_12
% 239.85/46.45    (39)   ~ (all_52_3 = e2)
% 239.85/46.45    (40)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.85/46.45          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.85/46.45    (41)   ~ (all_52_9 = all_52_13)
% 239.85/46.45    (42)   ~ (all_52_3 = e3)
% 239.85/46.45    (43)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 239.85/46.45    (44)  op(e2, e3) = all_52_1
% 239.85/46.45    (45)   ~ (all_52_12 = e2)
% 239.85/46.45    (46)  op(e3, e1) = e2
% 239.85/46.45    (47)  op(e0, e2) = all_52_7
% 239.85/46.45    (48)  op(e3, e2) = all_52_4
% 239.85/46.45    (49)   ~ (all_52_9 = e3)
% 239.85/46.45    (50)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.85/46.45          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.85/46.45    (51)   ~ (all_52_4 = e2)
% 239.85/46.45    (52)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.85/46.45          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.85/46.45    (53)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.45    (54)  op(e1, e3) = all_52_2
% 239.85/46.45    (55)   ~ (e1 = e0)
% 239.85/46.45    (56)  all_58_13 = e1
% 239.85/46.45    (57)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.85/46.45          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.85/46.45    (58)  op(e0, e0) = e2
% 239.85/46.45    (59)  op(e2, e0) = all_52_13
% 239.85/46.45    (60)  op(e0, e2) = e1
% 239.85/46.45    (61)   ~ (all_52_9 = e1)
% 239.85/46.45    (62)  all_54_14 = all_52_11
% 239.85/46.45    (63)  op(e2, e2) = e2
% 239.85/46.45    (64)  all_56_1 = e1
% 239.85/46.45    (65)   ~ (all_52_1 = e1)
% 239.85/46.45    (66)   ~ (all_52_9 = e2)
% 239.85/46.45  
% 239.85/46.45  Begin of proof
% 239.85/46.45  | 
% 239.85/46.45  | BETA: splitting (1) gives:
% 239.85/46.45  | 
% 239.85/46.45  | Case 1:
% 239.85/46.45  | | 
% 239.85/46.45  | |   (67)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.85/46.45  | |             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 239.85/46.45  | | 
% 239.85/46.45  | | REF_CLOSE: (17), (30), (46), (53), (64), (67) are inconsistent by sub-proof
% 239.85/46.45  | |            #113.
% 239.85/46.45  | | 
% 239.85/46.45  | Case 2:
% 239.85/46.45  | | 
% 239.85/46.45  | |   (68)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 239.85/46.45  | |           $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0,
% 239.85/46.45  | |             e3) = all_56_7 & $i(all_56_7))
% 239.85/46.45  | | 
% 239.85/46.45  | | BETA: splitting (68) gives:
% 239.85/46.45  | | 
% 239.85/46.45  | | Case 1:
% 239.85/46.45  | | | 
% 239.85/46.45  | | |   (69)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 239.85/46.45  | | |         $i(all_56_5)
% 239.85/46.45  | | | 
% 239.85/46.45  | | | ALPHA: (69) implies:
% 239.85/46.45  | | |   (70)  op(e1, e3) = all_56_5
% 239.85/46.45  | | |   (71)  op(e1, all_56_5) = e1
% 239.85/46.45  | | | 
% 239.85/46.45  | | | BETA: splitting (43) gives:
% 239.85/46.45  | | | 
% 239.85/46.45  | | | Case 1:
% 239.85/46.45  | | | | 
% 239.85/46.45  | | | |   (72)  all_54_6 = e3
% 239.85/46.45  | | | | 
% 239.85/46.45  | | | | COMBINE_EQS: (21), (72) imply:
% 239.85/46.45  | | | |   (73)  all_52_9 = e3
% 239.85/46.45  | | | | 
% 239.85/46.45  | | | | REDUCE: (49), (73) imply:
% 239.85/46.45  | | | |   (74)  $false
% 239.85/46.45  | | | | 
% 239.85/46.45  | | | | CLOSE: (74) is inconsistent.
% 239.85/46.45  | | | | 
% 239.85/46.45  | | | Case 2:
% 239.85/46.45  | | | | 
% 239.85/46.45  | | | |   (75)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 239.85/46.45  | | | | 
% 239.85/46.45  | | | | BETA: splitting (75) gives:
% 239.85/46.45  | | | | 
% 239.85/46.45  | | | | Case 1:
% 239.85/46.45  | | | | | 
% 239.85/46.45  | | | | |   (76)  all_54_6 = e2
% 239.85/46.45  | | | | | 
% 239.85/46.45  | | | | | COMBINE_EQS: (21), (76) imply:
% 239.85/46.45  | | | | |   (77)  all_52_9 = e2
% 239.85/46.45  | | | | | 
% 239.85/46.45  | | | | | REDUCE: (66), (77) imply:
% 239.85/46.45  | | | | |   (78)  $false
% 239.85/46.45  | | | | | 
% 239.85/46.45  | | | | | CLOSE: (78) is inconsistent.
% 239.85/46.45  | | | | | 
% 239.85/46.45  | | | | Case 2:
% 239.85/46.45  | | | | | 
% 239.85/46.45  | | | | |   (79)  all_54_6 = e1 | all_54_6 = e0
% 239.85/46.45  | | | | | 
% 239.85/46.45  | | | | | BETA: splitting (26) gives:
% 239.85/46.45  | | | | | 
% 239.85/46.45  | | | | | Case 1:
% 239.85/46.45  | | | | | | 
% 239.85/46.45  | | | | | |   (80)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2,
% 239.85/46.45  | | | | | |             e3) = e3)
% 239.85/46.45  | | | | | | 
% 239.85/46.45  | | | | | | BETA: splitting (80) gives:
% 239.85/46.45  | | | | | | 
% 239.85/46.45  | | | | | | Case 1:
% 239.85/46.45  | | | | | | | 
% 239.85/46.45  | | | | | | |   (81)  all_58_0 = e3 & op(e3, e3) = e3
% 239.85/46.45  | | | | | | | 
% 239.85/46.45  | | | | | | | ALPHA: (81) implies:
% 239.85/46.45  | | | | | | |   (82)  op(e3, e3) = e3
% 239.85/46.45  | | | | | | | 
% 239.85/46.45  | | | | | | | REF_CLOSE: (3), (18), (19), (23), (44), (50), (53), (54), (65),
% 239.85/46.45  | | | | | | |            (82) are inconsistent by sub-proof #440.
% 239.85/46.45  | | | | | | | 
% 239.85/46.45  | | | | | | Case 2:
% 239.85/46.45  | | | | | | | 
% 239.85/46.45  | | | | | | |   (83)  all_58_2 = e3 & op(e2, e3) = e3
% 239.85/46.45  | | | | | | | 
% 239.85/46.45  | | | | | | | ALPHA: (83) implies:
% 239.85/46.45  | | | | | | |   (84)  all_58_2 = e3
% 239.85/46.45  | | | | | | | 
% 239.85/46.45  | | | | | | | BETA: splitting (4) gives:
% 239.85/46.45  | | | | | | | 
% 239.85/46.45  | | | | | | | Case 1:
% 239.85/46.45  | | | | | | | | 
% 239.85/46.45  | | | | | | | |   (85)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 239.85/46.45  | | | | | | | |           op(e0, e2) = e3)
% 239.85/46.45  | | | | | | | | 
% 239.85/46.45  | | | | | | | | BETA: splitting (85) gives:
% 239.85/46.45  | | | | | | | | 
% 239.85/46.45  | | | | | | | | Case 1:
% 239.85/46.45  | | | | | | | | | 
% 239.85/46.45  | | | | | | | | |   (86)  all_58_12 = e3 & op(e0, e3) = e3
% 239.85/46.45  | | | | | | | | | 
% 239.85/46.45  | | | | | | | | | ALPHA: (86) implies:
% 239.85/46.45  | | | | | | | | |   (87)  op(e0, e3) = e3
% 239.85/46.45  | | | | | | | | | 
% 239.85/46.45  | | | | | | | | | REF_CLOSE: (18), (42), (53), (87) are inconsistent by
% 239.85/46.45  | | | | | | | | |            sub-proof #2332.
% 239.85/46.45  | | | | | | | | | 
% 239.85/46.45  | | | | | | | | Case 2:
% 239.85/46.45  | | | | | | | | | 
% 239.85/46.45  | | | | | | | | |   (88)  all_58_13 = e3 & op(e0, e2) = e3
% 239.85/46.45  | | | | | | | | | 
% 239.85/46.45  | | | | | | | | | ALPHA: (88) implies:
% 239.85/46.45  | | | | | | | | |   (89)  all_58_13 = e3
% 239.85/46.45  | | | | | | | | | 
% 239.85/46.45  | | | | | | | | | REF_CLOSE: (19), (56), (89) are inconsistent by sub-proof
% 239.85/46.45  | | | | | | | | |            #1436.
% 239.85/46.45  | | | | | | | | | 
% 239.85/46.45  | | | | | | | | End of split
% 239.85/46.45  | | | | | | | | 
% 239.85/46.45  | | | | | | | Case 2:
% 239.85/46.45  | | | | | | | | 
% 239.85/46.45  | | | | | | | |   (90)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 239.85/46.45  | | | | | | | |           op(e0, e0) = e3)
% 239.85/46.45  | | | | | | | | 
% 239.85/46.45  | | | | | | | | BETA: splitting (90) gives:
% 239.85/46.45  | | | | | | | | 
% 239.85/46.45  | | | | | | | | Case 1:
% 239.85/46.45  | | | | | | | | | 
% 239.85/46.46  | | | | | | | | |   (91)  all_58_14 = e3 & op(e0, e1) = e3
% 239.85/46.46  | | | | | | | | | 
% 239.85/46.46  | | | | | | | | | ALPHA: (91) implies:
% 239.85/46.46  | | | | | | | | |   (92)  op(e0, e1) = e3
% 239.85/46.46  | | | | | | | | | 
% 239.85/46.46  | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11),
% 239.85/46.46  | | | | | | | | |            (12), (13), (14), (15), (16), (19), (20), (21),
% 239.85/46.46  | | | | | | | | |            (22), (24), (25), (27), (28), (29), (32), (33),
% 239.85/46.46  | | | | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41),
% 239.85/46.46  | | | | | | | | |            (42), (45), (47), (48), (51), (52), (53), (55),
% 239.85/46.46  | | | | | | | | |            (57), (58), (59), (60), (61), (62), (63), (70),
% 239.85/46.46  | | | | | | | | |            (71), (79), (84), (92) are inconsistent by
% 239.85/46.46  | | | | | | | | |            sub-proof #111.
% 239.85/46.46  | | | | | | | | | 
% 239.85/46.46  | | | | | | | | Case 2:
% 239.85/46.46  | | | | | | | | | 
% 239.85/46.46  | | | | | | | | |   (93)  all_58_15 = e3 & op(e0, e0) = e3
% 239.85/46.46  | | | | | | | | | 
% 239.85/46.46  | | | | | | | | | ALPHA: (93) implies:
% 239.85/46.46  | | | | | | | | |   (94)  op(e0, e0) = e3
% 239.85/46.46  | | | | | | | | | 
% 239.85/46.46  | | | | | | | | | REF_CLOSE: (30), (53), (58), (94) are inconsistent by
% 239.85/46.46  | | | | | | | | |            sub-proof #1388.
% 239.85/46.46  | | | | | | | | | 
% 239.85/46.46  | | | | | | | | End of split
% 239.85/46.46  | | | | | | | | 
% 239.85/46.46  | | | | | | | End of split
% 239.85/46.46  | | | | | | | 
% 239.85/46.46  | | | | | | End of split
% 239.85/46.46  | | | | | | 
% 239.85/46.46  | | | | | Case 2:
% 239.85/46.46  | | | | | | 
% 239.85/46.46  | | | | | |   (95)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0,
% 239.85/46.46  | | | | | |             e3) = e3)
% 239.85/46.46  | | | | | | 
% 239.85/46.46  | | | | | | REF_CLOSE: (18), (19), (42), (53), (70), (71), (95) are inconsistent
% 239.85/46.46  | | | | | |            by sub-proof #110.
% 239.85/46.46  | | | | | | 
% 239.85/46.46  | | | | | End of split
% 239.85/46.46  | | | | | 
% 239.85/46.46  | | | | End of split
% 239.85/46.46  | | | | 
% 239.85/46.46  | | | End of split
% 239.85/46.46  | | | 
% 239.85/46.46  | | Case 2:
% 239.85/46.46  | | | 
% 239.85/46.46  | | |   (96)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.85/46.46  | | |         $i(all_56_7)
% 239.85/46.46  | | | 
% 239.85/46.46  | | | ALPHA: (96) implies:
% 239.85/46.46  | | |   (97)  op(e0, e3) = all_56_7
% 239.85/46.46  | | |   (98)  op(e0, all_56_7) = e0
% 239.85/46.46  | | | 
% 239.85/46.46  | | | BETA: splitting (4) gives:
% 239.85/46.46  | | | 
% 239.85/46.46  | | | Case 1:
% 239.85/46.46  | | | | 
% 239.85/46.46  | | | |   (99)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 239.85/46.46  | | | |             e2) = e3)
% 239.85/46.46  | | | | 
% 239.85/46.46  | | | | BETA: splitting (99) gives:
% 239.85/46.46  | | | | 
% 239.85/46.46  | | | | Case 1:
% 239.85/46.46  | | | | | 
% 239.85/46.46  | | | | |   (100)  all_58_12 = e3 & op(e0, e3) = e3
% 239.85/46.46  | | | | | 
% 239.85/46.46  | | | | | ALPHA: (100) implies:
% 239.85/46.46  | | | | |   (101)  op(e0, e3) = e3
% 239.85/46.46  | | | | | 
% 239.85/46.46  | | | | | REF_CLOSE: (5), (53), (97), (98), (101) are inconsistent by sub-proof
% 239.85/46.46  | | | | |            #2070.
% 239.85/46.46  | | | | | 
% 239.85/46.46  | | | | Case 2:
% 239.85/46.46  | | | | | 
% 239.85/46.46  | | | | |   (102)  all_58_13 = e3 & op(e0, e2) = e3
% 239.85/46.46  | | | | | 
% 239.85/46.46  | | | | | ALPHA: (102) implies:
% 239.85/46.46  | | | | |   (103)  all_58_13 = e3
% 239.85/46.46  | | | | | 
% 239.85/46.46  | | | | | REF_CLOSE: (19), (56), (103) are inconsistent by sub-proof #1436.
% 239.85/46.46  | | | | | 
% 239.85/46.46  | | | | End of split
% 239.85/46.46  | | | | 
% 239.85/46.46  | | | Case 2:
% 239.85/46.46  | | | | 
% 239.85/46.46  | | | |   (104)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 239.85/46.46  | | | |              e0) = e3)
% 239.85/46.46  | | | | 
% 239.85/46.46  | | | | REF_CLOSE: (5), (9), (27), (30), (31), (53), (55), (58), (60), (97),
% 239.85/46.46  | | | |            (98), (104) are inconsistent by sub-proof #108.
% 239.85/46.46  | | | | 
% 239.85/46.46  | | | End of split
% 239.85/46.46  | | | 
% 239.85/46.46  | | End of split
% 239.85/46.46  | | 
% 239.85/46.46  | End of split
% 239.85/46.46  | 
% 239.85/46.46  End of proof
% 239.85/46.46  
% 239.85/46.46  Sub-proof #108 shows that the following formulas are inconsistent:
% 239.85/46.46  ----------------------------------------------------------------
% 239.85/46.46    (1)   ~ (e3 = e0)
% 239.85/46.46    (2)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 239.85/46.46    (3)   ~ (e2 = e0)
% 239.85/46.46    (4)  op(e0, e3) = all_56_7
% 239.85/46.46    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 239.85/46.46             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 239.85/46.46               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 239.85/46.46               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 239.85/46.46    (6)   ~ (e3 = e2)
% 239.85/46.46    (7)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) = all_44_1
% 239.85/46.46           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2) =
% 239.85/46.46           all_44_1 & $i(all_44_1))
% 239.85/46.46    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.46    (9)  op(e0, all_56_7) = e0
% 239.85/46.46    (10)   ~ (e1 = e0)
% 239.85/46.46    (11)  op(e0, e0) = e2
% 239.85/46.46    (12)  op(e0, e2) = e1
% 239.85/46.46  
% 239.85/46.46  Begin of proof
% 239.85/46.46  | 
% 239.85/46.46  | BETA: splitting (2) gives:
% 239.85/46.46  | 
% 239.85/46.46  | Case 1:
% 239.85/46.46  | | 
% 239.85/46.46  | |   (13)  all_58_14 = e3 & op(e0, e1) = e3
% 239.85/46.46  | | 
% 239.85/46.46  | | ALPHA: (13) implies:
% 239.85/46.46  | |   (14)  op(e0, e1) = e3
% 239.85/46.46  | | 
% 239.85/46.46  | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14) are
% 239.85/46.46  | |            inconsistent by sub-proof #109.
% 239.85/46.46  | | 
% 239.85/46.46  | Case 2:
% 239.85/46.46  | | 
% 239.85/46.46  | |   (15)  all_58_15 = e3 & op(e0, e0) = e3
% 239.85/46.46  | | 
% 239.85/46.46  | | ALPHA: (15) implies:
% 239.85/46.46  | |   (16)  op(e0, e0) = e3
% 239.85/46.46  | | 
% 239.85/46.46  | | REF_CLOSE: (6), (8), (11), (16) are inconsistent by sub-proof #1388.
% 239.85/46.46  | | 
% 239.85/46.46  | End of split
% 239.85/46.46  | 
% 239.85/46.46  End of proof
% 239.85/46.46  
% 239.85/46.46  Sub-proof #109 shows that the following formulas are inconsistent:
% 239.85/46.46  ----------------------------------------------------------------
% 239.85/46.46    (1)   ~ (e3 = e0)
% 239.85/46.46    (2)   ~ (e2 = e0)
% 239.85/46.46    (3)  op(e0, e1) = e3
% 239.85/46.46    (4)  op(e0, e3) = all_56_7
% 239.85/46.46    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 239.85/46.46             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 239.85/46.46               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 239.85/46.46               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 239.85/46.46    (6)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) = all_44_1
% 239.85/46.46           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2) =
% 239.85/46.46           all_44_1 & $i(all_44_1))
% 239.85/46.46    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.46    (8)  op(e0, all_56_7) = e0
% 239.85/46.46    (9)   ~ (e1 = e0)
% 239.85/46.46    (10)  op(e0, e0) = e2
% 239.85/46.46    (11)  op(e0, e2) = e1
% 239.85/46.46  
% 239.85/46.46  Begin of proof
% 239.85/46.46  | 
% 239.85/46.46  | BETA: splitting (5) gives:
% 239.85/46.46  | 
% 239.85/46.46  | Case 1:
% 239.85/46.46  | | 
% 239.85/46.46  | |   (12)  all_58_15 = e0 & op(e0, e0) = e0
% 239.85/46.46  | | 
% 239.85/46.46  | | ALPHA: (12) implies:
% 239.85/46.46  | |   (13)  op(e0, e0) = e0
% 239.85/46.46  | | 
% 239.85/46.46  | | REF_CLOSE: (2), (7), (10), (13) are inconsistent by sub-proof #2301.
% 239.85/46.46  | | 
% 239.85/46.46  | Case 2:
% 239.85/46.46  | | 
% 239.85/46.46  | |   (14)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 239.85/46.46  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 239.85/46.46  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 239.85/46.46  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 239.85/46.46  | | 
% 239.85/46.46  | | ALPHA: (14) implies:
% 239.85/46.46  | |   (15)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 239.85/46.46  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.85/46.46  | | 
% 239.85/46.46  | | BETA: splitting (15) gives:
% 239.85/46.46  | | 
% 239.85/46.46  | | Case 1:
% 239.85/46.46  | | | 
% 239.85/46.46  | | |   (16)  all_58_12 = e0 & op(e0, e3) = e0
% 239.85/46.46  | | | 
% 239.85/46.46  | | | ALPHA: (16) implies:
% 239.85/46.46  | | |   (17)  op(e0, e3) = e0
% 239.85/46.46  | | | 
% 239.85/46.46  | | | REF_CLOSE: (2), (4), (6), (7), (8), (10), (11), (17) are inconsistent by
% 239.85/46.46  | | |            sub-proof #222.
% 239.85/46.46  | | | 
% 239.85/46.46  | | Case 2:
% 239.85/46.46  | | | 
% 239.85/46.46  | | |   (18)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 239.85/46.46  | | |           = e0)
% 239.85/46.46  | | | 
% 239.85/46.46  | | | REF_CLOSE: (1), (3), (7), (9), (11), (18) are inconsistent by sub-proof
% 239.85/46.46  | | |            #112.
% 239.85/46.46  | | | 
% 239.85/46.46  | | End of split
% 239.85/46.46  | | 
% 239.85/46.46  | End of split
% 239.85/46.46  | 
% 239.85/46.46  End of proof
% 239.85/46.46  
% 239.85/46.46  Sub-proof #110 shows that the following formulas are inconsistent:
% 239.85/46.46  ----------------------------------------------------------------
% 239.85/46.46    (1)  op(e1, all_56_5) = e1
% 239.85/46.46    (2)  op(e1, e3) = all_56_5
% 239.85/46.46    (3)  op(e0, e3) = all_52_3
% 239.85/46.46    (4)   ~ (e3 = e1)
% 239.85/46.46    (5)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 239.85/46.46    (6)   ~ (all_52_3 = e3)
% 239.85/46.46    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.46  
% 239.85/46.46  Begin of proof
% 239.85/46.46  | 
% 239.85/46.46  | BETA: splitting (5) gives:
% 239.85/46.46  | 
% 239.85/46.46  | Case 1:
% 239.85/46.46  | | 
% 239.85/46.46  | |   (8)  all_58_6 = e3 & op(e1, e3) = e3
% 239.85/46.46  | | 
% 239.85/46.46  | | ALPHA: (8) implies:
% 239.85/46.46  | |   (9)  op(e1, e3) = e3
% 239.85/46.46  | | 
% 239.85/46.46  | | REF_CLOSE: (1), (2), (4), (7), (9) are inconsistent by sub-proof #2243.
% 239.85/46.46  | | 
% 239.85/46.46  | Case 2:
% 239.85/46.46  | | 
% 239.85/46.46  | |   (10)  all_58_12 = e3 & op(e0, e3) = e3
% 239.85/46.46  | | 
% 239.85/46.46  | | ALPHA: (10) implies:
% 239.85/46.46  | |   (11)  op(e0, e3) = e3
% 239.85/46.46  | | 
% 239.85/46.46  | | REF_CLOSE: (3), (6), (7), (11) are inconsistent by sub-proof #2332.
% 239.85/46.46  | | 
% 239.85/46.46  | End of split
% 239.85/46.46  | 
% 239.85/46.46  End of proof
% 239.85/46.46  
% 239.85/46.46  Sub-proof #111 shows that the following formulas are inconsistent:
% 239.85/46.46  ----------------------------------------------------------------
% 239.85/46.46    (1)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.85/46.46    (2)   ~ (all_52_3 = e1)
% 239.85/46.46    (3)   ~ (e3 = e0)
% 239.85/46.46    (4)   ~ (all_52_7 = e2)
% 239.85/46.46    (5)  all_54_10 = e1 | all_54_10 = e0
% 239.85/46.46    (6)  op(e1, e1) = e1
% 239.85/46.46    (7)   ~ (e2 = e0)
% 239.85/46.46    (8)   ~ (all_52_11 = e2)
% 239.85/46.46    (9)  op(e0, e1) = e3
% 239.85/46.46    (10)  op(e1, e2) = all_52_6
% 239.85/46.46    (11)  all_58_6 = e2
% 239.85/46.46    (12)   ~ (all_52_11 = e1)
% 239.85/46.46    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.85/46.46              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.85/46.46            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.85/46.46            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.85/46.46            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 239.85/46.46             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.85/46.46            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.85/46.46            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.85/46.46            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.85/46.46            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.85/46.46            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.85/46.46              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.85/46.46            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.85/46.46            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 239.85/46.46            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.85/46.46            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 239.85/46.46            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.85/46.46            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.85/46.46              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.85/46.46            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.85/46.46            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.85/46.46            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.85/46.46            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 239.85/46.46            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.85/46.46            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.85/46.46              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.85/46.46            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.85/46.46            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.85/46.46    (14)  op(e1, e1) = all_6_2
% 239.85/46.46    (15)  op(e1, all_56_5) = e1
% 239.85/46.46    (16)  op(e1, e3) = all_56_5
% 239.85/46.46    (17)  op(e1, e0) = all_52_14
% 239.85/46.46    (18)   ~ (e3 = e1)
% 239.85/46.46    (19)   ~ (all_52_12 = e1)
% 239.85/46.46    (20)  all_54_6 = all_52_9
% 239.85/46.46    (21)   ~ (all_52_8 = e1)
% 239.85/46.46    (22)  all_54_10 = all_6_2
% 239.85/46.46    (23)  op(e1, e3) = e2
% 239.85/46.46    (24)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 239.85/46.46              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 239.85/46.46                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 239.85/46.46                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 239.85/46.46    (25)  op(e3, e1) = all_52_8
% 239.85/46.46    (26)  op(e2, e1) = all_52_9
% 239.85/46.46    (27)   ~ (all_52_14 = e1)
% 239.85/46.46    (28)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.85/46.46    (29)   ~ (all_52_3 = all_52_11)
% 239.85/46.46    (30)   ~ (all_6_2 = e0)
% 239.85/46.46    (31)  all_56_31 = e2
% 239.85/46.46    (32)  all_54_12 = all_52_3
% 239.85/46.46    (33)  op(e3, e0) = all_52_12
% 239.85/46.46    (34)   ~ (all_52_3 = e2)
% 239.85/46.46    (35)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 239.85/46.46          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 239.85/46.46    (36)   ~ (all_52_9 = all_52_13)
% 239.85/46.46    (37)   ~ (all_52_3 = e3)
% 239.85/46.46    (38)   ~ (all_52_12 = e2)
% 239.85/46.46    (39)  op(e0, e2) = all_52_7
% 239.85/46.46    (40)  op(e3, e2) = all_52_4
% 239.85/46.46    (41)   ~ (all_52_4 = e2)
% 239.85/46.46    (42)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.85/46.46          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 239.85/46.46    (43)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.46    (44)   ~ (e1 = e0)
% 239.85/46.46    (45)  all_54_6 = e1 | all_54_6 = e0
% 239.85/46.46    (46)  all_58_2 = e3
% 239.85/46.46    (47)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.85/46.46          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.85/46.46    (48)  op(e0, e0) = e2
% 239.85/46.46    (49)  op(e2, e0) = all_52_13
% 239.85/46.46    (50)  op(e0, e2) = e1
% 239.85/46.46    (51)   ~ (all_52_9 = e1)
% 239.85/46.46    (52)  all_54_14 = all_52_11
% 239.85/46.46    (53)  op(e2, e2) = e2
% 239.85/46.46  
% 239.85/46.46  Begin of proof
% 239.85/46.46  | 
% 239.85/46.46  | BETA: splitting (42) gives:
% 239.85/46.46  | 
% 239.85/46.46  | Case 1:
% 239.85/46.46  | | 
% 239.85/46.46  | |   (54)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 239.85/46.46  | |           e0)
% 239.85/46.46  | | 
% 239.85/46.46  | | BETA: splitting (54) gives:
% 239.85/46.46  | | 
% 239.85/46.46  | | Case 1:
% 239.85/46.46  | | | 
% 239.85/46.46  | | |   (55)  all_58_2 = e0 & op(e2, e3) = e0
% 239.85/46.46  | | | 
% 239.85/46.46  | | | REF_CLOSE: (3), (46), (55) are inconsistent by sub-proof #1351.
% 239.85/46.46  | | | 
% 239.85/46.46  | | Case 2:
% 239.85/46.46  | | | 
% 239.85/46.46  | | |   (56)  all_58_3 = e0 & op(e2, e2) = e0
% 239.85/46.46  | | | 
% 239.85/46.46  | | | ALPHA: (56) implies:
% 239.85/46.46  | | |   (57)  op(e2, e2) = e0
% 239.85/46.46  | | | 
% 239.85/46.47  | | | REF_CLOSE: (7), (43), (53), (57) are inconsistent by sub-proof #2137.
% 239.85/46.47  | | | 
% 239.85/46.47  | | End of split
% 239.85/46.47  | | 
% 239.85/46.47  | Case 2:
% 239.85/46.47  | | 
% 239.85/46.47  | |   (58)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 239.85/46.47  | |           e0)
% 239.85/46.47  | | 
% 239.85/46.47  | | BETA: splitting (58) gives:
% 239.85/46.47  | | 
% 239.85/46.47  | | Case 1:
% 239.85/46.47  | | | 
% 239.85/46.47  | | |   (59)  all_58_5 = e0 & op(e2, e1) = e0
% 239.85/46.47  | | | 
% 239.85/46.47  | | | ALPHA: (59) implies:
% 239.85/46.47  | | |   (60)  op(e2, e1) = e0
% 239.85/46.47  | | | 
% 239.85/46.47  | | | BETA: splitting (24) gives:
% 239.85/46.47  | | | 
% 239.85/46.47  | | | Case 1:
% 239.85/46.47  | | | | 
% 239.85/46.47  | | | |   (61)  all_58_15 = e0 & op(e0, e0) = e0
% 239.85/46.47  | | | | 
% 239.85/46.47  | | | | ALPHA: (61) implies:
% 239.85/46.47  | | | |   (62)  op(e0, e0) = e0
% 239.85/46.47  | | | | 
% 239.85/46.47  | | | | REF_CLOSE: (7), (43), (48), (62) are inconsistent by sub-proof #2301.
% 239.85/46.47  | | | | 
% 239.85/46.47  | | | Case 2:
% 239.85/46.47  | | | | 
% 239.85/46.47  | | | |   (63)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 239.85/46.47  | | | |               e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 239.85/46.47  | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 239.85/46.47  | | | |               e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 239.85/46.47  | | | | 
% 239.85/46.47  | | | | ALPHA: (63) implies:
% 239.85/46.47  | | | |   (64)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 239.85/46.47  | | | |             e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.85/46.47  | | | | 
% 239.85/46.47  | | | | BETA: splitting (64) gives:
% 239.85/46.47  | | | | 
% 239.85/46.47  | | | | Case 1:
% 239.85/46.47  | | | | | 
% 239.85/46.47  | | | | |   (65)  all_58_12 = e0 & op(e0, e3) = e0
% 239.85/46.47  | | | | | 
% 239.85/46.47  | | | | | ALPHA: (65) implies:
% 239.85/46.47  | | | | |   (66)  op(e0, e3) = e0
% 239.85/46.47  | | | | | 
% 239.85/46.47  | | | | | BETA: splitting (13) gives:
% 239.85/46.47  | | | | | 
% 239.85/46.47  | | | | | Case 1:
% 239.85/46.47  | | | | | | 
% 239.85/46.47  | | | | | |   (67)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 239.85/46.47  | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 239.85/46.47  | | | | | |             e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 =
% 239.85/46.47  | | | | | |           e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 239.85/46.47  | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.85/46.47  | | | | | |             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17
% 239.85/46.47  | | | | | |           = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.85/46.47  | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 239.85/46.47  | | | | | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 239.85/46.47  | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 239.85/46.47  | | | | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.85/46.47  | | | | | |           = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 239.85/46.47  | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.85/46.47  | | | | | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 239.85/46.47  | | | | | |         (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.85/46.47  | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 239.85/46.47  | | | | | |             e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.85/46.47  | | | | | | 
% 239.85/46.47  | | | | | | BETA: splitting (67) gives:
% 239.85/46.47  | | | | | | 
% 239.85/46.47  | | | | | | Case 1:
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | |   (68)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 239.85/46.47  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 239.85/46.47  | | | | | | |             e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 =
% 239.85/46.47  | | | | | | |           e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 239.85/46.47  | | | | | | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.85/46.47  | | | | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 239.85/46.47  | | | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 239.85/46.47  | | | | | | |             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 239.85/46.47  | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | | BETA: splitting (68) gives:
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | |   (69)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 239.85/46.47  | | | | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 239.85/46.47  | | | | | | | |           e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | ALPHA: (69) implies:
% 239.85/46.47  | | | | | | | |   (70)   ~ (all_56_31 = e2)
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | REDUCE: (31), (70) imply:
% 239.85/46.47  | | | | | | | |   (71)  $false
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | CLOSE: (71) is inconsistent.
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | |   (72)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 239.85/46.47  | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 239.85/46.47  | | | | | | | |             = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 239.85/46.47  | | | | | | | |         (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) & 
% 239.85/46.47  | | | | | | | |           ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.85/46.47  | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | BETA: splitting (72) gives:
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | |   (73)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) & 
% 239.85/46.47  | | | | | | | | |         ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.85/46.47  | | | | | | | | |         (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | ALPHA: (73) implies:
% 239.85/46.47  | | | | | | | | |   (74)  op(e3, e2) = e2
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | REF_CLOSE: (40), (41), (43), (74) are inconsistent by
% 239.85/46.47  | | | | | | | | |            sub-proof #254.
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | |   (75)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) & 
% 239.85/46.47  | | | | | | | | |         ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.85/46.47  | | | | | | | | |         (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | ALPHA: (75) implies:
% 239.85/46.47  | | | | | | | | |   (76)  op(e1, e3) = e3
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | REF_CLOSE: (15), (16), (18), (43), (76) are inconsistent by
% 239.85/46.47  | | | | | | | | |            sub-proof #2243.
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | End of split
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | End of split
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | Case 2:
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | |   (77)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 239.85/46.47  | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 239.85/46.47  | | | | | | |             e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 =
% 239.85/46.47  | | | | | | |           e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 239.85/46.47  | | | | | | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 239.85/46.47  | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 239.85/46.47  | | | | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 239.85/46.47  | | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.85/46.47  | | | | | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | | BETA: splitting (77) gives:
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | |   (78)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 239.85/46.47  | | | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 239.85/46.47  | | | | | | | |           e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | ALPHA: (78) implies:
% 239.85/46.47  | | | | | | | |   (79)  op(e3, e1) = e1
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | REF_CLOSE: (21), (25), (43), (79) are inconsistent by sub-proof
% 239.85/46.47  | | | | | | | |            #2309.
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | |   (80)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) & 
% 239.85/46.47  | | | | | | | |           ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.85/46.47  | | | | | | | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3)
% 239.85/46.47  | | | | | | | |         | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &
% 239.85/46.47  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.85/46.47  | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | BETA: splitting (80) gives:
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | |   (81)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) & 
% 239.85/46.47  | | | | | | | | |         ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.85/46.47  | | | | | | | | |         (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | ALPHA: (81) implies:
% 239.85/46.47  | | | | | | | | |   (82)  op(e0, e3) = e3
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | REF_CLOSE: (3), (43), (66), (82) are inconsistent by sub-proof
% 239.85/46.47  | | | | | | | | |            #221.
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | |   (83)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) & 
% 239.85/46.47  | | | | | | | | |         ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.85/46.47  | | | | | | | | |         (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | ALPHA: (83) implies:
% 239.85/46.47  | | | | | | | | |   (84)  op(e3, e0) = e0
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | BETA: splitting (1) gives:
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | |   (85)  all_54_12 = e3
% 239.85/46.47  | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | COMBINE_EQS: (32), (85) imply:
% 239.85/46.47  | | | | | | | | | |   (86)  all_52_3 = e3
% 239.85/46.47  | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | REDUCE: (37), (86) imply:
% 239.85/46.47  | | | | | | | | | |   (87)  $false
% 239.85/46.47  | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | CLOSE: (87) is inconsistent.
% 239.85/46.47  | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | |   (88)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.85/46.47  | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | BETA: splitting (88) gives:
% 239.85/46.47  | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | |   (89)  all_54_12 = e2
% 239.85/46.47  | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | COMBINE_EQS: (32), (89) imply:
% 239.85/46.47  | | | | | | | | | | |   (90)  all_52_3 = e2
% 239.85/46.47  | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | REDUCE: (34), (90) imply:
% 239.85/46.47  | | | | | | | | | | |   (91)  $false
% 239.85/46.47  | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | CLOSE: (91) is inconsistent.
% 239.85/46.47  | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | |   (92)  all_54_12 = e1 | all_54_12 = e0
% 239.85/46.47  | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | BETA: splitting (92) gives:
% 239.85/46.47  | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | |   (93)  all_54_12 = e1
% 239.85/46.47  | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | REF_CLOSE: (2), (32), (93) are inconsistent by sub-proof
% 239.85/46.47  | | | | | | | | | | | |            #2263.
% 239.85/46.47  | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | |   (94)  all_54_12 = e0
% 239.85/46.47  | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | COMBINE_EQS: (32), (94) imply:
% 239.85/46.47  | | | | | | | | | | | |   (95)  all_52_3 = e0
% 239.85/46.47  | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | SIMP: (95) implies:
% 239.85/46.47  | | | | | | | | | | | |   (96)  all_52_3 = e0
% 239.85/46.47  | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | REDUCE: (29), (96) imply:
% 239.85/46.47  | | | | | | | | | | | |   (97)   ~ (all_52_11 = e0)
% 239.85/46.47  | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | SIMP: (97) implies:
% 239.85/46.47  | | | | | | | | | | | |   (98)   ~ (all_52_11 = e0)
% 239.85/46.47  | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | BETA: splitting (28) gives:
% 239.85/46.47  | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | |   (99)  all_54_14 = e3
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | COMBINE_EQS: (52), (99) imply:
% 239.85/46.47  | | | | | | | | | | | | |   (100)  all_52_11 = e3
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | SIMP: (100) implies:
% 239.85/46.47  | | | | | | | | | | | | |   (101)  all_52_11 = e3
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | REDUCE: (8), (101) imply:
% 239.85/46.47  | | | | | | | | | | | | |   (102)   ~ (e3 = e2)
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | GROUND_INST: instantiating (43) with e2, all_56_5, e3, e1,
% 239.85/46.47  | | | | | | | | | | | | |              simplifying with (16), (23) gives:
% 239.85/46.47  | | | | | | | | | | | | |   (103)  all_56_5 = e2
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | GROUND_INST: instantiating (43) with all_52_12, e0, e0, e3,
% 239.85/46.47  | | | | | | | | | | | | |              simplifying with (33), (84) gives:
% 239.85/46.47  | | | | | | | | | | | | |   (104)  all_52_12 = e0
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | REDUCE: (38), (104) imply:
% 239.85/46.47  | | | | | | | | | | | | |   (105)   ~ (e2 = e0)
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | REDUCE: (19), (104) imply:
% 239.85/46.47  | | | | | | | | | | | | |   (106)   ~ (e1 = e0)
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | REDUCE: (15), (103) imply:
% 239.85/46.47  | | | | | | | | | | | | |   (107)  op(e1, e2) = e1
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | BETA: splitting (35) gives:
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | |   (108)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 239.85/46.47  | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 239.85/46.47  | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 239.85/46.47  | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | |   (109)  all_58_6 = e3 & op(e1, e3) = e3
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 239.85/46.47  | | | | | | | | | | | | | | |   (110)  all_58_6 = e3
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | | REF_CLOSE: (11), (102), (110) are inconsistent by sub-proof
% 239.85/46.47  | | | | | | | | | | | | | | |            #2024.
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | |   (111)  all_58_7 = e3 & op(e1, e2) = e3
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 239.85/46.47  | | | | | | | | | | | | | | |   (112)  op(e1, e2) = e3
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | | REF_CLOSE: (18), (43), (107), (112) are inconsistent by
% 239.85/46.47  | | | | | | | | | | | | | | |            sub-proof #2094.
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | End of split
% 239.85/46.47  | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | |   (113)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 239.85/46.47  | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 239.85/46.47  | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 239.85/46.47  | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | |   (114)  all_58_8 = e3 & op(e1, e1) = e3
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 239.85/46.47  | | | | | | | | | | | | | | |   (115)  op(e1, e1) = e3
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | | REF_CLOSE: (6), (18), (43), (115) are inconsistent by
% 239.85/46.47  | | | | | | | | | | | | | | |            sub-proof #468.
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | |   (116)  all_58_11 = e3 & op(e1, e0) = e3
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 239.85/46.47  | | | | | | | | | | | | | | |   (117)  all_58_11 = e3
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (10), (11), (14), (22), (30), (43),
% 239.85/46.47  | | | | | | | | | | | | | | |            (44), (47), (107), (117) are inconsistent by
% 239.85/46.47  | | | | | | | | | | | | | | |            sub-proof #932.
% 239.85/46.47  | | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | | End of split
% 239.85/46.47  | | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | End of split
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | |   (118)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | | REF_CLOSE: (8), (12), (52), (98), (118) are inconsistent by
% 239.85/46.47  | | | | | | | | | | | | |            sub-proof #1798.
% 239.85/46.47  | | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | | End of split
% 239.85/46.47  | | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | | End of split
% 239.85/46.47  | | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | | End of split
% 239.85/46.47  | | | | | | | | | | 
% 239.85/46.47  | | | | | | | | | End of split
% 239.85/46.47  | | | | | | | | | 
% 239.85/46.47  | | | | | | | | End of split
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | End of split
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | End of split
% 239.85/46.47  | | | | | | 
% 239.85/46.47  | | | | | Case 2:
% 239.85/46.47  | | | | | | 
% 239.85/46.47  | | | | | |   (119)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 239.85/46.47  | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 239.85/46.47  | | | | | |              e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 =
% 239.85/46.47  | | | | | |            e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 239.85/46.47  | | | | | |              = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.85/46.47  | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 239.85/46.47  | | | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0)
% 239.85/46.47  | | | | | |            &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0)
% 239.85/46.47  | | | | | |            = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 239.85/46.47  | | | | | |            e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.85/46.47  | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 239.85/46.47  | | | | | |            & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 & 
% 239.85/46.47  | | | | | |            ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.85/46.47  | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 239.85/46.47  | | | | | |              e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.85/46.47  | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 239.85/46.47  | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 239.85/46.47  | | | | | |              e1) = e0)
% 239.85/46.47  | | | | | | 
% 239.85/46.47  | | | | | | BETA: splitting (119) gives:
% 239.85/46.47  | | | | | | 
% 239.85/46.47  | | | | | | Case 1:
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | |   (120)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) & 
% 239.85/46.47  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.85/46.47  | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 239.85/46.47  | | | | | | |          (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) & 
% 239.85/46.47  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 239.85/46.47  | | | | | | |            (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 239.85/46.47  | | | | | | |          (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) & 
% 239.85/46.47  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.85/46.47  | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | | REF_CLOSE: (4), (7), (26), (39), (43), (44), (60), (120) are
% 239.85/46.47  | | | | | | |            inconsistent by sub-proof #1895.
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | Case 2:
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | |   (121)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) & 
% 239.85/46.47  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 239.85/46.47  | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 239.85/46.47  | | | | | | |          (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) & 
% 239.85/46.47  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.85/46.47  | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 239.85/46.47  | | | | | | |          (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) & 
% 239.85/46.47  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.85/46.47  | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | | BETA: splitting (121) gives:
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | | Case 1:
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | |   (122)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) & 
% 239.85/46.47  | | | | | | | |          ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 239.85/46.47  | | | | | | | |          (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | ALPHA: (122) implies:
% 239.85/46.47  | | | | | | | |   (123)  op(e2, e0) = e0
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | REF_CLOSE: (20), (36), (43), (45), (49), (51), (123) are
% 239.85/46.47  | | | | | | | |            inconsistent by sub-proof #460.
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | Case 2:
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | |   (124)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &
% 239.85/46.47  | | | | | | | |             ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.85/46.47  | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1)
% 239.85/46.47  | | | | | | | |          | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1)
% 239.85/46.47  | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.85/46.47  | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | | REF_CLOSE: (3), (9), (17), (27), (43), (124) are inconsistent by
% 239.85/46.47  | | | | | | | |            sub-proof #1699.
% 239.85/46.47  | | | | | | | | 
% 239.85/46.47  | | | | | | | End of split
% 239.85/46.47  | | | | | | | 
% 239.85/46.47  | | | | | | End of split
% 239.85/46.47  | | | | | | 
% 239.85/46.47  | | | | | End of split
% 239.85/46.47  | | | | | 
% 239.85/46.47  | | | | Case 2:
% 239.85/46.47  | | | | | 
% 239.85/46.47  | | | | |   (125)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 239.85/46.47  | | | | |              e1) = e0)
% 239.85/46.47  | | | | | 
% 239.85/46.47  | | | | | REF_CLOSE: (3), (9), (43), (44), (50), (125) are inconsistent by
% 239.85/46.47  | | | | |            sub-proof #112.
% 239.85/46.47  | | | | | 
% 239.85/46.47  | | | | End of split
% 239.85/46.47  | | | | 
% 239.85/46.47  | | | End of split
% 239.85/46.47  | | | 
% 239.85/46.47  | | Case 2:
% 239.85/46.47  | | | 
% 239.85/46.47  | | |   (126)  all_58_10 = e0 & op(e2, e0) = e0
% 239.85/46.47  | | | 
% 239.85/46.47  | | | ALPHA: (126) implies:
% 239.85/46.47  | | |   (127)  op(e2, e0) = e0
% 239.85/46.47  | | | 
% 239.85/46.47  | | | REF_CLOSE: (20), (36), (43), (45), (49), (51), (127) are inconsistent by
% 239.85/46.47  | | |            sub-proof #460.
% 239.85/46.47  | | | 
% 239.85/46.47  | | End of split
% 239.85/46.47  | | 
% 239.85/46.47  | End of split
% 239.85/46.47  | 
% 239.85/46.47  End of proof
% 239.85/46.47  
% 239.85/46.47  Sub-proof #112 shows that the following formulas are inconsistent:
% 239.85/46.47  ----------------------------------------------------------------
% 239.85/46.47    (1)   ~ (e3 = e0)
% 239.85/46.48    (2)  op(e0, e1) = e3
% 239.85/46.48    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.48    (4)   ~ (e1 = e0)
% 239.85/46.48    (5)  op(e0, e2) = e1
% 239.85/46.48    (6)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.85/46.48  
% 239.85/46.48  Begin of proof
% 239.85/46.48  | 
% 239.85/46.48  | BETA: splitting (6) gives:
% 239.85/46.48  | 
% 239.85/46.48  | Case 1:
% 239.85/46.48  | | 
% 239.85/46.48  | |   (7)  all_58_13 = e0 & op(e0, e2) = e0
% 239.85/46.48  | | 
% 239.85/46.48  | | ALPHA: (7) implies:
% 239.85/46.48  | |   (8)  op(e0, e2) = e0
% 239.85/46.48  | | 
% 239.85/46.48  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1872.
% 239.85/46.48  | | 
% 239.85/46.48  | Case 2:
% 239.85/46.48  | | 
% 239.85/46.48  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 239.85/46.48  | | 
% 239.85/46.48  | | ALPHA: (9) implies:
% 239.85/46.48  | |   (10)  op(e0, e1) = e0
% 239.85/46.48  | | 
% 239.85/46.48  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #2164.
% 239.85/46.48  | | 
% 239.85/46.48  | End of split
% 239.85/46.48  | 
% 239.85/46.48  End of proof
% 239.85/46.48  
% 239.85/46.48  Sub-proof #113 shows that the following formulas are inconsistent:
% 239.85/46.48  ----------------------------------------------------------------
% 239.85/46.48    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.85/46.48             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 239.85/46.48    (2)  op(e2, e3) = e3
% 239.85/46.48    (3)   ~ (e3 = e2)
% 239.85/46.48    (4)  op(e3, e1) = e2
% 239.85/46.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.48    (6)  all_56_1 = e1
% 239.85/46.48  
% 239.85/46.48  Begin of proof
% 239.85/46.48  | 
% 239.85/46.48  | BETA: splitting (1) gives:
% 239.85/46.48  | 
% 239.85/46.48  | Case 1:
% 239.85/46.48  | | 
% 239.85/46.48  | |   (7)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 239.85/46.48  | | 
% 239.85/46.48  | | ALPHA: (7) implies:
% 239.85/46.48  | |   (8)  op(e3, all_56_1) = e3
% 239.85/46.48  | | 
% 239.85/46.48  | | REDUCE: (6), (8) imply:
% 239.85/46.48  | |   (9)  op(e3, e1) = e3
% 239.85/46.48  | | 
% 239.85/46.48  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #177.
% 239.85/46.48  | | 
% 239.85/46.48  | Case 2:
% 239.85/46.48  | | 
% 239.85/46.48  | |   (10)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 239.85/46.48  | |         $i(all_56_3)
% 239.85/46.48  | | 
% 239.85/46.48  | | ALPHA: (10) implies:
% 239.85/46.48  | |   (11)  op(e2, e3) = all_56_3
% 239.85/46.48  | |   (12)  op(e2, all_56_3) = e2
% 239.85/46.48  | | 
% 239.85/46.48  | | REF_CLOSE: (2), (3), (5), (11), (12) are inconsistent by sub-proof #2262.
% 239.85/46.48  | | 
% 239.85/46.48  | End of split
% 239.85/46.48  | 
% 239.85/46.48  End of proof
% 239.85/46.48  
% 239.85/46.48  Sub-proof #114 shows that the following formulas are inconsistent:
% 239.85/46.48  ----------------------------------------------------------------
% 239.85/46.48    (1)  op(e3, e3) = e1
% 239.85/46.48    (2)  op(e3, e2) = all_52_4
% 239.85/46.48    (3)   ~ (all_52_4 = e2)
% 239.85/46.48    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.48    (5)   ~ (e2 = e1)
% 239.85/46.48    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 239.85/46.48  
% 239.85/46.48  Begin of proof
% 239.85/46.48  | 
% 239.85/46.48  | BETA: splitting (6) gives:
% 239.85/46.48  | 
% 239.85/46.48  | Case 1:
% 239.85/46.48  | | 
% 239.85/46.48  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 239.85/46.48  | | 
% 239.85/46.48  | | ALPHA: (7) implies:
% 239.85/46.48  | |   (8)  op(e3, e3) = e2
% 239.85/46.48  | | 
% 239.85/46.48  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2267.
% 239.85/46.48  | | 
% 239.85/46.48  | Case 2:
% 239.85/46.48  | | 
% 239.85/46.48  | |   (9)  all_58_1 = e2 & op(e3, e2) = e2
% 239.85/46.48  | | 
% 239.85/46.48  | | ALPHA: (9) implies:
% 239.85/46.48  | |   (10)  op(e3, e2) = e2
% 239.85/46.48  | | 
% 239.85/46.48  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #254.
% 239.85/46.48  | | 
% 239.85/46.48  | End of split
% 239.85/46.48  | 
% 239.85/46.48  End of proof
% 239.85/46.48  
% 239.85/46.48  Sub-proof #115 shows that the following formulas are inconsistent:
% 239.85/46.48  ----------------------------------------------------------------
% 239.85/46.48    (1)   ~ (all_52_3 = e0)
% 239.85/46.48    (2)  op(e1, e2) = all_56_13
% 239.85/46.48    (3)  op(e1, e2) = e1
% 239.85/46.48    (4)  all_54_12 = all_52_3
% 239.85/46.48    (5)   ~ (all_52_3 = e2)
% 239.85/46.48    (6)  op(e1, e2) = all_36_1
% 239.85/46.48    (7)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) = all_40_1
% 239.85/46.48           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2) =
% 239.85/46.48           all_40_1 & $i(all_40_1))
% 239.85/46.48    (8)  op(e1, e1) = e2
% 239.85/46.48    (9)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 239.85/46.48    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.48    (11)  op(e1, all_56_13) = e1
% 239.85/46.48  
% 239.85/46.48  Begin of proof
% 239.85/46.48  | 
% 239.85/46.48  | BETA: splitting (9) gives:
% 239.85/46.48  | 
% 239.85/46.48  | Case 1:
% 239.85/46.48  | | 
% 239.85/46.48  | |   (12)  all_54_12 = e2
% 239.85/46.48  | | 
% 239.85/46.48  | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #2264.
% 239.85/46.48  | | 
% 239.85/46.48  | Case 2:
% 239.85/46.48  | | 
% 239.85/46.48  | |   (13)   ~ (all_54_12 = e2)
% 239.85/46.48  | |   (14)  all_54_12 = e1 | all_54_12 = e0
% 239.85/46.48  | | 
% 239.85/46.48  | | BETA: splitting (7) gives:
% 239.85/46.48  | | 
% 239.85/46.48  | | Case 1:
% 239.85/46.48  | | | 
% 239.85/46.48  | | |   (15)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 239.85/46.48  | | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 239.85/46.48  | | | 
% 239.85/46.48  | | | ALPHA: (15) implies:
% 239.85/46.48  | | |   (16)  op(e1, e2) = all_40_1
% 239.85/46.48  | | | 
% 239.85/46.48  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (14), (16) are
% 239.85/46.48  | | |            inconsistent by sub-proof #116.
% 239.85/46.48  | | | 
% 239.85/46.48  | | Case 2:
% 239.85/46.48  | | | 
% 239.85/46.48  | | |   (17)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 239.85/46.48  | | | 
% 239.85/46.48  | | | ALPHA: (17) implies:
% 239.85/46.48  | | |   (18)  op(e1, e2) = all_40_1
% 239.85/46.48  | | | 
% 239.85/46.48  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (14), (18) are
% 239.85/46.48  | | |            inconsistent by sub-proof #116.
% 239.85/46.48  | | | 
% 239.85/46.48  | | End of split
% 239.85/46.48  | | 
% 239.85/46.48  | End of split
% 239.85/46.48  | 
% 239.85/46.48  End of proof
% 239.85/46.48  
% 239.85/46.48  Sub-proof #116 shows that the following formulas are inconsistent:
% 239.85/46.48  ----------------------------------------------------------------
% 239.85/46.48    (1)   ~ (all_52_3 = e0)
% 239.85/46.48    (2)  op(e1, e2) = all_56_13
% 239.85/46.48    (3)  op(e1, e2) = e1
% 239.85/46.48    (4)  all_54_12 = e1 | all_54_12 = e0
% 239.85/46.48    (5)  all_54_12 = all_52_3
% 239.85/46.48    (6)   ~ (all_52_3 = e2)
% 239.85/46.48    (7)  op(e1, e2) = all_36_1
% 239.85/46.48    (8)  op(e1, e1) = e2
% 239.85/46.48    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.85/46.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.85/46.48    (10)  op(e1, e2) = all_40_1
% 239.85/46.48    (11)  op(e1, all_56_13) = e1
% 239.85/46.48  
% 239.85/46.48  Begin of proof
% 239.85/46.48  | 
% 239.85/46.48  | BETA: splitting (4) gives:
% 239.85/46.48  | 
% 239.85/46.48  | Case 1:
% 239.85/46.48  | | 
% 239.85/46.48  | |   (12)  all_54_12 = e1
% 239.85/46.48  | | 
% 239.85/46.48  | | COMBINE_EQS: (5), (12) imply:
% 239.85/46.48  | |   (13)  all_52_3 = e1
% 239.85/46.48  | | 
% 239.85/46.48  | | REDUCE: (6), (13) imply:
% 239.85/46.48  | |   (14)   ~ (e2 = e1)
% 239.85/46.48  | | 
% 239.85/46.48  | | SIMP: (14) implies:
% 239.85/46.48  | |   (15)   ~ (e2 = e1)
% 239.85/46.48  | | 
% 239.85/46.48  | | GROUND_INST: instantiating (9) with all_40_1, all_56_13, e2, e1, simplifying
% 239.85/46.48  | |              with (2), (10) gives:
% 239.85/46.48  | |   (16)  all_56_13 = all_40_1
% 239.85/46.48  | | 
% 239.85/46.48  | | GROUND_INST: instantiating (9) with all_36_1, all_56_13, e2, e1, simplifying
% 239.85/46.48  | |              with (2), (7) gives:
% 239.85/46.48  | |   (17)  all_56_13 = all_36_1
% 239.85/46.48  | | 
% 239.85/46.48  | | GROUND_INST: instantiating (9) with e1, all_56_13, e2, e1, simplifying with
% 239.85/46.48  | |              (2), (3) gives:
% 239.85/46.48  | |   (18)  all_56_13 = e1
% 239.85/46.48  | | 
% 239.85/46.48  | | COMBINE_EQS: (16), (18) imply:
% 239.85/46.48  | |   (19)  all_40_1 = e1
% 239.85/46.48  | | 
% 239.85/46.48  | | COMBINE_EQS: (16), (17) imply:
% 239.85/46.48  | |   (20)  all_40_1 = all_36_1
% 239.85/46.48  | | 
% 239.85/46.48  | | COMBINE_EQS: (19), (20) imply:
% 239.85/46.48  | |   (21)  all_36_1 = e1
% 239.85/46.48  | | 
% 239.85/46.48  | | REDUCE: (11), (18) imply:
% 239.85/46.48  | |   (22)  op(e1, e1) = e1
% 239.85/46.48  | | 
% 239.90/46.48  | | REF_CLOSE: (8), (9), (15), (22) are inconsistent by sub-proof #2159.
% 239.90/46.48  | | 
% 239.90/46.48  | Case 2:
% 239.90/46.48  | | 
% 239.90/46.48  | |   (23)  all_54_12 = e0
% 239.90/46.48  | | 
% 239.90/46.48  | | COMBINE_EQS: (5), (23) imply:
% 239.90/46.48  | |   (24)  all_52_3 = e0
% 239.90/46.48  | | 
% 239.90/46.48  | | REDUCE: (1), (24) imply:
% 239.90/46.48  | |   (25)  $false
% 239.90/46.48  | | 
% 239.90/46.48  | | CLOSE: (25) is inconsistent.
% 239.90/46.48  | | 
% 239.90/46.48  | End of split
% 239.90/46.48  | 
% 239.90/46.48  End of proof
% 239.90/46.48  
% 239.90/46.48  Sub-proof #117 shows that the following formulas are inconsistent:
% 239.90/46.48  ----------------------------------------------------------------
% 239.90/46.48    (1)   ~ (all_52_3 = e0)
% 239.90/46.48    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.90/46.48             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 239.90/46.48           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 239.90/46.48         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.90/46.48           $i(all_56_7))
% 239.90/46.48    (3)   ~ (e3 = e0)
% 239.90/46.48    (4)  op(e1, e0) = e0
% 239.90/46.48    (5)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 239.90/46.48         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.90/46.48    (6)   ~ (e2 = e0)
% 239.90/46.48    (7)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.90/46.48         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.90/46.48    (8)  op(e1, e2) = all_52_6
% 239.90/46.48    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 239.90/46.48         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.90/46.48    (10)  op(e0, e3) = all_52_3
% 239.90/46.48    (11)   ~ (e3 = e1)
% 239.90/46.48    (12)   ~ (all_52_12 = all_52_13)
% 239.90/46.48    (13)  op(e1, e2) = e3
% 239.90/46.48    (14)  op(e3, e2) = e2
% 239.90/46.48    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 239.90/46.48          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 239.90/46.48    (16)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 239.90/46.48          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 239.90/46.48    (17)   ~ (e3 = e2)
% 239.90/46.48    (18)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.90/46.48            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 239.90/46.48              e2) = all_44_1 & $i(all_44_1))
% 239.90/46.48    (19)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 239.90/46.48            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 239.90/46.48              e0) = all_14_1 & $i(all_14_1))
% 239.90/46.48    (20)  op(e2, e3) = e2
% 239.90/46.48    (21)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 239.90/46.48            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 239.90/46.48              e0) = all_48_1 & $i(all_48_1))
% 239.90/46.48    (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 239.90/46.48          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 239.90/46.48    (23)  all_58_7 = e3
% 239.90/46.48    (24)  op(e3, e0) = all_52_12
% 239.90/46.48    (25)   ~ (all_52_1 = e0)
% 239.90/46.48    (26)  op(e2, e2) = all_8_2
% 239.90/46.48    (27)  op(e2, e3) = all_52_1
% 239.90/46.48    (28)   ~ (all_52_12 = e2)
% 239.90/46.48    (29)  op(e1, e2) = all_36_1
% 239.90/46.48    (30)   ~ (all_52_2 = e3)
% 239.90/46.48    (31)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 239.90/46.48            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 239.90/46.48              e2) = all_40_1 & $i(all_40_1))
% 239.90/46.48    (32)  op(e1, e1) = e2
% 239.90/46.48    (33)   ~ (all_52_2 = e0)
% 239.90/46.48    (34)  all_58_1 = e2
% 239.90/46.48    (35)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.90/46.48          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.90/46.48    (36)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.48    (37)  op(e1, e3) = all_52_2
% 239.90/46.48    (38)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.90/46.48          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 239.90/46.48    (39)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 239.90/46.48            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 239.90/46.48              e2) = all_36_1 & $i(all_36_1))
% 239.90/46.48    (40)   ~ (all_8_2 = e3)
% 239.90/46.48    (41)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.90/46.48          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.90/46.48    (42)   ~ (e1 = e0)
% 239.90/46.48    (43)  op(e3, e3) = e0
% 239.90/46.48    (44)  all_56_1 = e0
% 239.90/46.48    (45)  op(e2, e0) = all_52_13
% 239.90/46.48    (46)  all_58_3 = e0
% 239.90/46.48    (47)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.90/46.48          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.90/46.48    (48)   ~ (e2 = e1)
% 239.90/46.48  
% 239.90/46.48  Begin of proof
% 239.90/46.48  | 
% 239.90/46.48  | BETA: splitting (15) gives:
% 239.90/46.48  | 
% 239.90/46.48  | Case 1:
% 239.90/46.48  | | 
% 239.90/46.48  | |   (49)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 239.90/46.48  | |           e3)
% 239.90/46.48  | | 
% 239.90/46.48  | | REF_CLOSE: (1), (3), (10), (17), (20), (22), (25), (27), (33), (36), (37),
% 239.90/46.48  | |            (49) are inconsistent by sub-proof #160.
% 239.90/46.48  | | 
% 239.90/46.48  | Case 2:
% 239.90/46.48  | | 
% 239.90/46.48  | |   (50)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 239.90/46.48  | |           e3)
% 239.90/46.48  | | 
% 239.90/46.48  | | BETA: splitting (50) gives:
% 239.90/46.48  | | 
% 239.90/46.48  | | Case 1:
% 239.90/46.48  | | | 
% 239.90/46.48  | | |   (51)  all_58_6 = e3 & op(e1, e3) = e3
% 239.90/46.48  | | | 
% 239.90/46.48  | | | ALPHA: (51) implies:
% 239.90/46.48  | | |   (52)  op(e1, e3) = e3
% 239.90/46.48  | | | 
% 239.90/46.48  | | | REF_CLOSE: (30), (36), (37), (52) are inconsistent by sub-proof #2335.
% 239.90/46.48  | | | 
% 239.90/46.48  | | Case 2:
% 239.90/46.48  | | | 
% 239.90/46.48  | | |   (53)  all_58_12 = e3 & op(e0, e3) = e3
% 239.90/46.48  | | | 
% 239.90/46.48  | | | ALPHA: (53) implies:
% 239.90/46.48  | | |   (54)  all_58_12 = e3
% 239.90/46.48  | | |   (55)  op(e0, e3) = e3
% 239.90/46.48  | | | 
% 239.90/46.48  | | | BETA: splitting (38) gives:
% 239.90/46.48  | | | 
% 239.90/46.48  | | | Case 1:
% 239.90/46.48  | | | | 
% 239.90/46.48  | | | |   (56)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2)
% 239.90/46.48  | | | |           = e1)
% 239.90/46.48  | | | | 
% 239.90/46.48  | | | | REF_CLOSE: (14), (36), (42), (46), (48), (56) are inconsistent by
% 239.90/46.48  | | | |            sub-proof #1610.
% 239.90/46.48  | | | | 
% 239.90/46.48  | | | Case 2:
% 239.90/46.48  | | | | 
% 239.90/46.48  | | | |   (57)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 239.90/46.48  | | | |           = e1)
% 239.90/46.48  | | | | 
% 239.90/46.48  | | | | BETA: splitting (57) gives:
% 239.90/46.48  | | | | 
% 239.90/46.48  | | | | Case 1:
% 239.90/46.48  | | | | | 
% 239.90/46.48  | | | | |   (58)  all_58_7 = e1 & op(e1, e2) = e1
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | | ALPHA: (58) implies:
% 239.90/46.49  | | | | |   (59)  op(e1, e2) = e1
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | | REF_CLOSE: (11), (13), (36), (59) are inconsistent by sub-proof #2094.
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | Case 2:
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | |   (60)  all_58_13 = e1 & op(e0, e2) = e1
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | | ALPHA: (60) implies:
% 239.90/46.49  | | | | |   (61)  op(e0, e2) = e1
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | | BETA: splitting (5) gives:
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | | Case 1:
% 239.90/46.49  | | | | | | 
% 239.90/46.49  | | | | | |   (62)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1,
% 239.90/46.49  | | | | | |             e2) = e1)
% 239.90/46.49  | | | | | | 
% 239.90/46.49  | | | | | | BETA: splitting (62) gives:
% 239.90/46.49  | | | | | | 
% 239.90/46.49  | | | | | | Case 1:
% 239.90/46.49  | | | | | | | 
% 239.90/46.49  | | | | | | |   (63)  all_58_6 = e1 & op(e1, e3) = e1
% 239.90/46.49  | | | | | | | 
% 239.90/46.49  | | | | | | | ALPHA: (63) implies:
% 239.90/46.49  | | | | | | |   (64)  all_58_6 = e1
% 239.90/46.49  | | | | | | |   (65)  op(e1, e3) = e1
% 239.90/46.49  | | | | | | | 
% 239.90/46.49  | | | | | | | BETA: splitting (2) gives:
% 239.90/46.49  | | | | | | | 
% 239.90/46.49  | | | | | | | Case 1:
% 239.90/46.49  | | | | | | | | 
% 239.90/46.49  | | | | | | | |   (66)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2
% 239.90/46.49  | | | | | | | |           & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 239.90/46.49  | | | | | | | |           $i(all_56_3))
% 239.90/46.49  | | | | | | | | 
% 239.90/46.49  | | | | | | | | BETA: splitting (66) gives:
% 239.90/46.49  | | | | | | | | 
% 239.90/46.49  | | | | | | | | Case 1:
% 239.90/46.49  | | | | | | | | | 
% 239.90/46.49  | | | | | | | | |   (67)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 239.90/46.49  | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | ALPHA: (67) implies:
% 239.90/46.49  | | | | | | | | |   (68)  op(e3, all_56_1) = e3
% 239.90/46.49  | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | REDUCE: (44), (68) imply:
% 239.90/46.49  | | | | | | | | |   (69)  op(e3, e0) = e3
% 239.90/46.49  | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | BETA: splitting (31) gives:
% 239.90/46.49  | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | Case 1:
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | |   (70)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 239.90/46.49  | | | | | | | | | |         op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | ALPHA: (70) implies:
% 239.90/46.49  | | | | | | | | | |   (71)  op(e1, e2) = all_40_1
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | BETA: splitting (18) gives:
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | Case 1:
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | GROUND_INST: instantiating (36) with all_36_1, all_40_1, e2,
% 239.90/46.49  | | | | | | | | | | |              e1, simplifying with (29), (71) gives:
% 239.90/46.49  | | | | | | | | | | |   (72)  all_40_1 = all_36_1
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | GROUND_INST: instantiating (36) with e3, all_40_1, e2, e1,
% 239.90/46.49  | | | | | | | | | | |              simplifying with (13), (71) gives:
% 239.90/46.49  | | | | | | | | | | |   (73)  all_40_1 = e3
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | GROUND_INST: instantiating (36) with all_52_12, e3, e0, e3,
% 239.90/46.49  | | | | | | | | | | |              simplifying with (24), (69) gives:
% 239.90/46.49  | | | | | | | | | | |   (74)  all_52_12 = e3
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | COMBINE_EQS: (72), (73) imply:
% 239.90/46.49  | | | | | | | | | | |   (75)  all_36_1 = e3
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | SIMP: (75) implies:
% 239.90/46.49  | | | | | | | | | | |   (76)  all_36_1 = e3
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | REDUCE: (12), (74) imply:
% 239.90/46.49  | | | | | | | | | | |   (77)   ~ (all_52_13 = e3)
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | SIMP: (77) implies:
% 239.90/46.49  | | | | | | | | | | |   (78)   ~ (all_52_13 = e3)
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | BETA: splitting (7) gives:
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | Case 1:
% 239.90/46.49  | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | |   (79)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 239.90/46.49  | | | | | | | | | | | |           & op(e2, e2) = e3)
% 239.90/46.49  | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | BETA: splitting (79) gives:
% 239.90/46.49  | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | Case 1:
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | |   (80)  all_58_2 = e3 & op(e2, e3) = e3
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | | ALPHA: (80) implies:
% 239.90/46.49  | | | | | | | | | | | | |   (81)  op(e2, e3) = e3
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | | REF_CLOSE: (17), (20), (36), (81) are inconsistent by
% 239.90/46.49  | | | | | | | | | | | | |            sub-proof #1897.
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | Case 2:
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | |   (82)  all_58_3 = e3 & op(e2, e2) = e3
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | | REF_CLOSE: (26), (36), (40), (82) are inconsistent by
% 239.90/46.49  | | | | | | | | | | | | |            sub-proof #450.
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | End of split
% 239.90/46.49  | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | Case 2:
% 239.90/46.49  | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | |   (83)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 239.90/46.49  | | | | | | | | | | | |           e3 & op(e2, e0) = e3)
% 239.90/46.49  | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | BETA: splitting (83) gives:
% 239.90/46.49  | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | Case 1:
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | |   (84)  all_58_5 = e3 & op(e2, e1) = e3
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | | ALPHA: (84) implies:
% 239.90/46.49  | | | | | | | | | | | | |   (85)  op(e2, e1) = e3
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | | REF_CLOSE: (6), (11), (13), (16), (17), (19), (21), (35),
% 239.90/46.49  | | | | | | | | | | | | |            (36), (42), (43), (46), (47), (48), (54), (64),
% 239.90/46.49  | | | | | | | | | | | | |            (65), (85) are inconsistent by sub-proof #1415.
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | Case 2:
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | |   (86)  all_58_10 = e3 & op(e2, e0) = e3
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | | ALPHA: (86) implies:
% 239.90/46.49  | | | | | | | | | | | | |   (87)  op(e2, e0) = e3
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | | REF_CLOSE: (36), (45), (78), (87) are inconsistent by
% 239.90/46.49  | | | | | | | | | | | | |            sub-proof #1994.
% 239.90/46.49  | | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | | End of split
% 239.90/46.49  | | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | End of split
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | Case 2:
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | |   (88)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 &
% 239.90/46.49  | | | | | | | | | | |         $i(all_44_1)
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | ALPHA: (88) implies:
% 239.90/46.49  | | | | | | | | | | |   (89)   ~ (all_44_1 = e1)
% 239.90/46.49  | | | | | | | | | | |   (90)  op(e0, e2) = all_44_1
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | | REF_CLOSE: (36), (61), (89), (90) are inconsistent by
% 239.90/46.49  | | | | | | | | | | |            sub-proof #230.
% 239.90/46.49  | | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | End of split
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | Case 2:
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | |   (91)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 239.90/46.49  | | | | | | | | | |         $i(all_40_1)
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | REF_CLOSE: (13), (36), (39), (91) are inconsistent by
% 239.90/46.49  | | | | | | | | | |            sub-proof #2144.
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | End of split
% 239.90/46.49  | | | | | | | | | 
% 239.90/46.49  | | | | | | | | Case 2:
% 239.90/46.49  | | | | | | | | | 
% 239.90/46.49  | | | | | | | | |   (92)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 239.90/46.49  | | | | | | | | |         all_56_3 & $i(all_56_3)
% 239.90/46.49  | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | ALPHA: (92) implies:
% 239.90/46.49  | | | | | | | | |   (93)  op(e2, e3) = all_56_3
% 239.90/46.49  | | | | | | | | |   (94)  op(e2, all_56_3) = e2
% 239.90/46.49  | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | BETA: splitting (18) gives:
% 239.90/46.49  | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | Case 1:
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | GROUND_INST: instantiating (36) with e2, all_56_3, e3, e2,
% 239.90/46.49  | | | | | | | | | |              simplifying with (20), (93) gives:
% 239.90/46.49  | | | | | | | | | |   (95)  all_56_3 = e2
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | REDUCE: (94), (95) imply:
% 239.90/46.49  | | | | | | | | | |   (96)  op(e2, e2) = e2
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | REF_CLOSE: (3), (6), (8), (9), (11), (14), (17), (23), (34),
% 239.90/46.49  | | | | | | | | | |            (36), (38), (41), (42), (48), (96) are
% 239.90/46.49  | | | | | | | | | |            inconsistent by sub-proof #1810.
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | Case 2:
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | |   (97)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 &
% 239.90/46.49  | | | | | | | | | |         $i(all_44_1)
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | ALPHA: (97) implies:
% 239.90/46.49  | | | | | | | | | |   (98)   ~ (all_44_1 = e1)
% 239.90/46.49  | | | | | | | | | |   (99)  op(e0, e2) = all_44_1
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | | REF_CLOSE: (36), (61), (98), (99) are inconsistent by
% 239.90/46.49  | | | | | | | | | |            sub-proof #230.
% 239.90/46.49  | | | | | | | | | | 
% 239.90/46.49  | | | | | | | | | End of split
% 239.90/46.49  | | | | | | | | | 
% 239.90/46.49  | | | | | | | | End of split
% 239.90/46.49  | | | | | | | | 
% 239.90/46.49  | | | | | | | Case 2:
% 239.90/46.49  | | | | | | | | 
% 239.90/46.49  | | | | | | | |   (100)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 239.90/46.49  | | | | | | | |            all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 239.90/46.49  | | | | | | | |              all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.90/46.49  | | | | | | | |            $i(all_56_7))
% 239.90/46.49  | | | | | | | | 
% 239.90/46.49  | | | | | | | | REF_CLOSE: (3), (13), (31), (32), (36), (39), (48), (55), (65),
% 239.90/46.49  | | | | | | | |            (100) are inconsistent by sub-proof #146.
% 239.90/46.49  | | | | | | | | 
% 239.90/46.49  | | | | | | | End of split
% 239.90/46.49  | | | | | | | 
% 239.90/46.49  | | | | | | Case 2:
% 239.90/46.49  | | | | | | | 
% 239.90/46.49  | | | | | | |   (101)  all_58_7 = e1 & op(e1, e2) = e1
% 239.90/46.49  | | | | | | | 
% 239.90/46.49  | | | | | | | ALPHA: (101) implies:
% 239.90/46.49  | | | | | | |   (102)  op(e1, e2) = e1
% 239.90/46.49  | | | | | | | 
% 239.90/46.49  | | | | | | | REF_CLOSE: (11), (13), (36), (102) are inconsistent by sub-proof
% 239.90/46.49  | | | | | | |            #2094.
% 239.90/46.49  | | | | | | | 
% 239.90/46.49  | | | | | | End of split
% 239.90/46.49  | | | | | | 
% 239.90/46.49  | | | | | Case 2:
% 239.90/46.49  | | | | | | 
% 239.90/46.49  | | | | | |   (103)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 239.90/46.49  | | | | | |            op(e1, e0) = e1)
% 239.90/46.49  | | | | | | 
% 239.90/46.49  | | | | | | REF_CLOSE: (4), (32), (36), (42), (48), (103) are inconsistent by
% 239.90/46.49  | | | | | |            sub-proof #118.
% 239.90/46.49  | | | | | | 
% 239.90/46.49  | | | | | End of split
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | End of split
% 239.90/46.49  | | | | 
% 239.90/46.49  | | | End of split
% 239.90/46.49  | | | 
% 239.90/46.49  | | End of split
% 239.90/46.49  | | 
% 239.90/46.49  | End of split
% 239.90/46.49  | 
% 239.90/46.49  End of proof
% 239.90/46.49  
% 239.90/46.49  Sub-proof #118 shows that the following formulas are inconsistent:
% 239.90/46.49  ----------------------------------------------------------------
% 239.90/46.49    (1)  op(e1, e0) = e0
% 239.90/46.49    (2)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 239.90/46.49    (3)  op(e1, e1) = e2
% 239.90/46.49    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.49    (5)   ~ (e1 = e0)
% 239.90/46.49    (6)   ~ (e2 = e1)
% 239.90/46.49  
% 239.90/46.49  Begin of proof
% 239.90/46.49  | 
% 239.90/46.49  | BETA: splitting (2) gives:
% 239.90/46.49  | 
% 239.90/46.49  | Case 1:
% 239.90/46.49  | | 
% 239.90/46.49  | |   (7)  all_58_8 = e1 & op(e1, e1) = e1
% 239.90/46.49  | | 
% 239.90/46.49  | | ALPHA: (7) implies:
% 239.90/46.49  | |   (8)  op(e1, e1) = e1
% 239.90/46.49  | | 
% 239.90/46.49  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #2159.
% 239.90/46.49  | | 
% 239.90/46.49  | Case 2:
% 239.90/46.49  | | 
% 239.90/46.49  | |   (9)  all_58_11 = e1 & op(e1, e0) = e1
% 239.90/46.49  | | 
% 239.90/46.49  | | ALPHA: (9) implies:
% 239.90/46.49  | |   (10)  op(e1, e0) = e1
% 239.90/46.49  | | 
% 239.90/46.49  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2284.
% 239.90/46.49  | | 
% 239.90/46.49  | End of split
% 239.90/46.49  | 
% 239.90/46.49  End of proof
% 239.90/46.49  
% 239.90/46.49  Sub-proof #119 shows that the following formulas are inconsistent:
% 239.90/46.49  ----------------------------------------------------------------
% 239.90/46.49    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.90/46.49             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 239.90/46.49           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 239.90/46.49         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.90/46.49           $i(all_56_7))
% 239.90/46.49    (2)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.90/46.49    (3)   ~ (all_52_7 = e2)
% 239.90/46.49    (4)   ~ (e2 = e0)
% 239.90/46.49    (5)  all_54_13 = all_52_7
% 239.90/46.49    (6)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.90/46.49         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.90/46.49    (7)   ~ (all_52_13 = e1)
% 239.90/46.49    (8)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.90/46.49         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.90/46.49    (9)   ~ (all_52_2 = e1)
% 239.90/46.49    (10)  op(e2, e1) = e2
% 239.90/46.49    (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.90/46.49          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.90/46.49    (12)   ~ (all_52_7 = e1)
% 239.90/46.49    (13)  op(e0, e3) = e0
% 239.90/46.49    (14)  op(e2, e2) = all_8_2
% 239.90/46.49    (15)   ~ (all_52_2 = e0)
% 239.90/46.49    (16)  all_56_1 = e2
% 239.90/46.49    (17)  op(e3, e2) = all_52_4
% 239.90/46.49    (18)   ~ (all_52_7 = e0)
% 239.90/46.49    (19)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.90/46.49    (20)   ~ (all_52_2 = e2)
% 239.90/46.49    (21)  all_54_8 = all_52_2
% 239.90/46.49    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.49    (23)  op(e1, e3) = all_52_2
% 239.90/46.49    (24)   ~ (all_8_2 = e3)
% 239.90/46.49    (25)   ~ (e1 = e0)
% 239.90/46.49    (26)  all_58_4 = e3
% 239.90/46.49    (27)   ~ (all_52_13 = e3)
% 239.90/46.49    (28)  op(e0, e0) = e2
% 239.90/46.49    (29)  op(e2, e0) = all_52_13
% 239.90/46.49    (30)  all_58_3 = e0
% 239.90/46.49    (31)  all_58_14 = e1
% 239.90/46.49    (32)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.90/46.49          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.90/46.49    (33)   ~ (e2 = e1)
% 239.90/46.49    (34)   ~ (all_52_4 = all_52_7)
% 239.90/46.49  
% 239.90/46.49  Begin of proof
% 239.90/46.49  | 
% 239.90/46.49  | BETA: splitting (2) gives:
% 239.90/46.49  | 
% 239.90/46.49  | Case 1:
% 239.90/46.49  | | 
% 239.90/46.49  | |   (35)  all_54_8 = e3
% 239.90/46.49  | | 
% 239.90/46.49  | | COMBINE_EQS: (21), (35) imply:
% 239.90/46.49  | |   (36)  all_52_2 = e3
% 239.90/46.49  | | 
% 239.90/46.49  | | SIMP: (36) implies:
% 239.90/46.49  | |   (37)  all_52_2 = e3
% 239.90/46.49  | | 
% 239.90/46.49  | | REDUCE: (20), (37) imply:
% 239.90/46.49  | |   (38)   ~ (e3 = e2)
% 239.90/46.49  | | 
% 239.90/46.49  | | REDUCE: (9), (37) imply:
% 239.90/46.49  | |   (39)   ~ (e3 = e1)
% 239.90/46.49  | | 
% 239.90/46.49  | | REDUCE: (15), (37) imply:
% 239.90/46.49  | |   (40)   ~ (e3 = e0)
% 239.90/46.49  | | 
% 239.90/46.49  | | REDUCE: (23), (37) imply:
% 239.90/46.49  | |   (41)  op(e1, e3) = e3
% 239.90/46.49  | | 
% 239.90/46.49  | | BETA: splitting (1) gives:
% 239.90/46.49  | | 
% 239.90/46.49  | | Case 1:
% 239.90/46.49  | | | 
% 239.90/46.49  | | |   (42)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.90/46.49  | | |             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 239.90/46.49  | | | 
% 239.90/46.49  | | | BETA: splitting (42) gives:
% 239.90/46.49  | | | 
% 239.90/46.49  | | | Case 1:
% 239.90/46.49  | | | | 
% 239.90/46.49  | | | |   (43)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 239.90/46.49  | | | | 
% 239.90/46.49  | | | | REF_CLOSE: (3), (5), (12), (16), (17), (18), (19), (22), (34), (43) are
% 239.90/46.49  | | | |            inconsistent by sub-proof #131.
% 239.90/46.49  | | | | 
% 239.90/46.49  | | | Case 2:
% 239.90/46.49  | | | | 
% 239.90/46.49  | | | |   (44)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 239.90/46.49  | | | |         $i(all_56_3)
% 239.90/46.49  | | | | 
% 239.90/46.49  | | | | ALPHA: (44) implies:
% 239.90/46.49  | | | |   (45)  op(e2, e3) = all_56_3
% 239.90/46.49  | | | |   (46)  op(e2, all_56_3) = e2
% 239.90/46.49  | | | | 
% 239.90/46.49  | | | | BETA: splitting (6) gives:
% 239.90/46.49  | | | | 
% 239.90/46.49  | | | | Case 1:
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | |   (47)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2,
% 239.90/46.49  | | | | |             e2) = e3)
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | | REF_CLOSE: (14), (22), (24), (38), (45), (46), (47) are inconsistent
% 239.90/46.49  | | | | |            by sub-proof #130.
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | Case 2:
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | |   (48)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2,
% 239.90/46.49  | | | | |             e0) = e3)
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | | REF_CLOSE: (10), (22), (27), (29), (38), (48) are inconsistent by
% 239.90/46.49  | | | | |            sub-proof #1913.
% 239.90/46.49  | | | | | 
% 239.90/46.49  | | | | End of split
% 239.90/46.49  | | | | 
% 239.90/46.49  | | | End of split
% 239.90/46.49  | | | 
% 239.90/46.49  | | Case 2:
% 239.90/46.49  | | | 
% 239.90/46.49  | | |   (49)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 239.90/46.49  | | |           $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0,
% 239.90/46.49  | | |             e3) = all_56_7 & $i(all_56_7))
% 239.90/46.49  | | | 
% 239.90/46.49  | | | REF_CLOSE: (4), (7), (8), (11), (13), (22), (25), (26), (28), (29), (30),
% 239.90/46.49  | | |            (31), (32), (33), (38), (39), (40), (41), (49) are inconsistent
% 239.90/46.49  | | |            by sub-proof #128.
% 239.90/46.49  | | | 
% 239.90/46.49  | | End of split
% 239.90/46.49  | | 
% 239.90/46.49  | Case 2:
% 239.90/46.49  | | 
% 239.90/46.49  | |   (50)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.90/46.49  | | 
% 239.90/46.49  | | REF_CLOSE: (9), (15), (20), (21), (50) are inconsistent by sub-proof #1949.
% 239.90/46.49  | | 
% 239.90/46.49  | End of split
% 239.90/46.49  | 
% 239.90/46.49  End of proof
% 239.90/46.49  
% 239.90/46.49  Sub-proof #120 shows that the following formulas are inconsistent:
% 239.90/46.49  ----------------------------------------------------------------
% 239.90/46.49    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.90/46.49             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 239.90/46.49           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 239.90/46.49         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.90/46.49           $i(all_56_7))
% 239.90/46.49    (2)  op(e1, e3) = all_24_0
% 239.90/46.49    (3)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.90/46.49    (4)   ~ (all_52_7 = e2)
% 239.90/46.49    (5)   ~ (e2 = e0)
% 239.90/46.49    (6)  all_54_13 = all_52_7
% 239.90/46.49    (7)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 & op(e1, e0) = all_28_1
% 239.90/46.49           & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0) =
% 239.90/46.49           all_28_1 & $i(all_28_1))
% 239.90/46.49    (8)  op(e3, e0) = all_4_0
% 239.90/46.49    (9)   ~ (all_52_1 = all_52_2)
% 239.90/46.49    (10)   ~ (all_52_13 = e1)
% 239.90/46.50    (11)  op(e1, e0) = e1
% 239.90/46.50    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.90/46.50          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.90/46.50    (13)  op(e0, e1) = e1
% 239.90/46.50    (14)   ~ (all_52_2 = e1)
% 239.90/46.50    (15)  op(e2, e0) = e3
% 239.90/46.50    (16)   ~ (all_24_0 = e0)
% 239.90/46.50    (17)  all_54_4 = all_52_1
% 239.90/46.50    (18)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.90/46.50          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.90/46.50    (19)   ~ (all_52_7 = e1)
% 239.90/46.50    (20)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 239.90/46.50            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 239.90/46.50              e0) = all_14_1 & $i(all_14_1))
% 239.90/46.50    (21)  all_56_31 = e2
% 239.90/46.50    (22)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 239.90/46.50            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 239.90/46.50              e0) = all_48_1 & $i(all_48_1))
% 239.90/46.50    (23)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 239.90/46.50            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 239.90/46.50            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 239.90/46.50            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 239.90/46.50            op(e0, all_56_31) = e0)
% 239.90/46.50    (24)  op(e0, e3) = e0
% 239.90/46.50    (25)   ~ (all_52_1 = e0)
% 239.90/46.50    (26)  op(e2, e3) = all_52_1
% 239.90/46.50    (27)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.90/46.50    (28)   ~ (all_52_2 = e0)
% 239.90/46.50    (29)  op(e0, e2) = all_52_7
% 239.90/46.50    (30)  all_56_1 = e2
% 239.90/46.50    (31)   ~ (all_4_0 = e1)
% 239.90/46.50    (32)  op(e3, e2) = all_52_4
% 239.90/46.50    (33)   ~ (all_52_7 = e0)
% 239.90/46.50    (34)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.90/46.50    (35)   ~ (all_52_2 = e2)
% 239.90/46.50    (36)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 & op(e1, e0) =
% 239.90/46.50            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1,
% 239.90/46.50              e0) = all_18_1 & $i(all_18_1))
% 239.90/46.50    (37)  all_54_8 = all_52_2
% 239.90/46.50    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.50    (39)  op(e3, e0) = e0
% 239.90/46.50    (40)  op(e1, e3) = all_52_2
% 239.90/46.50    (41)   ~ (e1 = e0)
% 239.90/46.50    (42)  all_58_4 = e3
% 239.90/46.50    (43)  op(e0, e0) = e2
% 239.90/46.50    (44)  op(e2, e0) = all_52_13
% 239.90/46.50    (45)  all_58_3 = e0
% 239.90/46.50    (46)  all_58_14 = e1
% 239.90/46.50    (47)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.90/46.50          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.90/46.50    (48)   ~ (all_52_1 = e2)
% 239.90/46.50    (49)   ~ (e2 = e1)
% 239.90/46.50    (50)   ~ (all_52_4 = all_52_7)
% 239.90/46.50  
% 239.90/46.50  Begin of proof
% 239.90/46.50  | 
% 239.90/46.50  | BETA: splitting (3) gives:
% 239.90/46.50  | 
% 239.90/46.50  | Case 1:
% 239.90/46.50  | | 
% 239.90/46.50  | |   (51)  all_54_8 = e3
% 239.90/46.50  | | 
% 239.90/46.50  | | COMBINE_EQS: (37), (51) imply:
% 239.90/46.50  | |   (52)  all_52_2 = e3
% 239.90/46.50  | | 
% 239.90/46.50  | | SIMP: (52) implies:
% 239.90/46.50  | |   (53)  all_52_2 = e3
% 239.90/46.50  | | 
% 239.90/46.50  | | REDUCE: (9), (53) imply:
% 239.90/46.50  | |   (54)   ~ (all_52_1 = e3)
% 239.90/46.50  | | 
% 239.90/46.50  | | REDUCE: (35), (53) imply:
% 239.90/46.50  | |   (55)   ~ (e3 = e2)
% 239.90/46.50  | | 
% 239.90/46.50  | | REDUCE: (14), (53) imply:
% 239.90/46.50  | |   (56)   ~ (e3 = e1)
% 239.90/46.50  | | 
% 239.90/46.50  | | REDUCE: (28), (53) imply:
% 239.90/46.50  | |   (57)   ~ (e3 = e0)
% 239.90/46.50  | | 
% 239.90/46.50  | | REDUCE: (40), (53) imply:
% 239.90/46.50  | |   (58)  op(e1, e3) = e3
% 239.90/46.50  | | 
% 239.90/46.50  | | BETA: splitting (27) gives:
% 239.90/46.50  | | 
% 239.90/46.50  | | Case 1:
% 239.90/46.50  | | | 
% 239.90/46.50  | | |   (59)  all_54_4 = e3
% 239.90/46.50  | | | 
% 239.90/46.50  | | | REF_CLOSE: (17), (54), (59) are inconsistent by sub-proof #2100.
% 239.90/46.50  | | | 
% 239.90/46.50  | | Case 2:
% 239.90/46.50  | | | 
% 239.90/46.50  | | |   (60)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.90/46.50  | | | 
% 239.90/46.50  | | | BETA: splitting (23) gives:
% 239.90/46.50  | | | 
% 239.90/46.50  | | | Case 1:
% 239.90/46.50  | | | | 
% 239.90/46.50  | | | |   (61)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 239.90/46.50  | | | |           all_56_25 & $i(all_56_25)) | (all_56_26 = e2 & op(e2,
% 239.90/46.50  | | | |             all_56_27) = e2 & op(e2, e0) = all_56_27 & $i(all_56_27))
% 239.90/46.50  | | | | 
% 239.90/46.50  | | | | BETA: splitting (61) gives:
% 239.90/46.50  | | | | 
% 239.90/46.50  | | | | Case 1:
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | |   (62)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 239.90/46.50  | | | | |         all_56_25 & $i(all_56_25)
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | | ALPHA: (62) implies:
% 239.90/46.50  | | | | |   (63)  op(e3, e0) = all_56_25
% 239.90/46.50  | | | | |   (64)  op(e3, all_56_25) = e3
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | | REF_CLOSE: (38), (39), (57), (63), (64) are inconsistent by sub-proof
% 239.90/46.50  | | | | |            #1926.
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | Case 2:
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | |   (65)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 239.90/46.50  | | | | |         all_56_27 & $i(all_56_27)
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | | ALPHA: (65) implies:
% 239.90/46.50  | | | | |   (66)  op(e2, e0) = all_56_27
% 239.90/46.50  | | | | |   (67)  op(e2, all_56_27) = e2
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | | REF_CLOSE: (1), (4), (5), (6), (10), (12), (15), (17), (18), (19),
% 239.90/46.50  | | | | |            (20), (22), (24), (25), (26), (30), (32), (33), (34), (38),
% 239.90/46.50  | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 239.90/46.50  | | | | |            (55), (56), (57), (58), (60), (66), (67) are inconsistent
% 239.90/46.50  | | | | |            by sub-proof #127.
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | End of split
% 239.90/46.50  | | | | 
% 239.90/46.50  | | | Case 2:
% 239.90/46.50  | | | | 
% 239.90/46.50  | | | |   (68)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 239.90/46.50  | | | |           all_56_29 & $i(all_56_29)) | (all_56_30 = e0 & op(e0,
% 239.90/46.50  | | | |             all_56_31) = e0)
% 239.90/46.50  | | | | 
% 239.90/46.50  | | | | BETA: splitting (68) gives:
% 239.90/46.50  | | | | 
% 239.90/46.50  | | | | Case 1:
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | |   (69)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 239.90/46.50  | | | | |         all_56_29 & $i(all_56_29)
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | | ALPHA: (69) implies:
% 239.90/46.50  | | | | |   (70)  op(e1, e0) = all_56_29
% 239.90/46.50  | | | | |   (71)  op(e1, all_56_29) = e1
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | | BETA: splitting (1) gives:
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | | Case 1:
% 239.90/46.50  | | | | | | 
% 239.90/46.50  | | | | | |   (72)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 239.90/46.50  | | | | | |           op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 239.90/46.50  | | | | | |           $i(all_56_3))
% 239.90/46.50  | | | | | | 
% 239.90/46.50  | | | | | | BETA: splitting (72) gives:
% 239.90/46.50  | | | | | | 
% 239.90/46.50  | | | | | | Case 1:
% 239.90/46.50  | | | | | | | 
% 239.90/46.50  | | | | | | |   (73)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 239.90/46.50  | | | | | | | 
% 239.90/46.50  | | | | | | | REF_CLOSE: (4), (6), (19), (30), (32), (33), (34), (38), (50),
% 239.90/46.50  | | | | | | |            (73) are inconsistent by sub-proof #131.
% 239.90/46.50  | | | | | | | 
% 239.90/46.50  | | | | | | Case 2:
% 239.90/46.50  | | | | | | | 
% 239.90/46.50  | | | | | | |   (74)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 239.90/46.50  | | | | | | |         all_56_3 & $i(all_56_3)
% 239.90/46.50  | | | | | | | 
% 239.90/46.50  | | | | | | | ALPHA: (74) implies:
% 239.90/46.50  | | | | | | |   (75)  op(e2, e3) = all_56_3
% 239.90/46.50  | | | | | | |   (76)  op(e2, all_56_3) = e2
% 239.90/46.50  | | | | | | | 
% 239.90/46.50  | | | | | | | BETA: splitting (7) gives:
% 239.90/46.50  | | | | | | | 
% 239.90/46.50  | | | | | | | Case 1:
% 239.90/46.50  | | | | | | | | 
% 239.90/46.50  | | | | | | | |   (77)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 239.90/46.50  | | | | | | | |         op(e1, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)
% 239.90/46.50  | | | | | | | | 
% 239.90/46.50  | | | | | | | | ALPHA: (77) implies:
% 239.90/46.50  | | | | | | | |   (78)  op(e1, e0) = all_28_1
% 239.90/46.50  | | | | | | | | 
% 239.90/46.50  | | | | | | | | REF_CLOSE: (2), (5), (8), (11), (12), (13), (16), (17), (25),
% 239.90/46.50  | | | | | | | |            (26), (31), (36), (38), (39), (42), (48), (58), (60),
% 239.90/46.50  | | | | | | | |            (70), (71), (75), (76), (78) are inconsistent by
% 239.90/46.50  | | | | | | | |            sub-proof #121.
% 239.90/46.50  | | | | | | | | 
% 239.90/46.50  | | | | | | | Case 2:
% 239.90/46.50  | | | | | | | | 
% 239.90/46.50  | | | | | | | |   (79)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 239.90/46.50  | | | | | | | |         $i(all_28_1)
% 239.90/46.50  | | | | | | | | 
% 239.90/46.50  | | | | | | | | ALPHA: (79) implies:
% 239.90/46.50  | | | | | | | |   (80)  op(e1, e0) = all_28_1
% 239.90/46.50  | | | | | | | | 
% 239.90/46.50  | | | | | | | | REF_CLOSE: (2), (5), (8), (11), (12), (13), (16), (17), (25),
% 239.90/46.50  | | | | | | | |            (26), (31), (36), (38), (39), (42), (48), (58), (60),
% 239.90/46.50  | | | | | | | |            (70), (71), (75), (76), (80) are inconsistent by
% 239.90/46.50  | | | | | | | |            sub-proof #121.
% 239.90/46.50  | | | | | | | | 
% 239.90/46.50  | | | | | | | End of split
% 239.90/46.50  | | | | | | | 
% 239.90/46.50  | | | | | | End of split
% 239.90/46.50  | | | | | | 
% 239.90/46.50  | | | | | Case 2:
% 239.90/46.50  | | | | | | 
% 239.90/46.50  | | | | | |   (81)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 239.90/46.50  | | | | | |           all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 239.90/46.50  | | | | | |             all_56_7) = e0 & op(e0, e3) = all_56_7 & $i(all_56_7))
% 239.90/46.50  | | | | | | 
% 239.90/46.50  | | | | | | REF_CLOSE: (5), (10), (12), (18), (24), (38), (41), (42), (43),
% 239.90/46.50  | | | | | |            (44), (45), (46), (47), (49), (55), (56), (57), (58),
% 239.90/46.50  | | | | | |            (81) are inconsistent by sub-proof #128.
% 239.90/46.50  | | | | | | 
% 239.90/46.50  | | | | | End of split
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | Case 2:
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | |   (82)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | | ALPHA: (82) implies:
% 239.90/46.50  | | | | |   (83)  op(e0, all_56_31) = e0
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | | REDUCE: (21), (83) imply:
% 239.90/46.50  | | | | |   (84)  op(e0, e2) = e0
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | | REF_CLOSE: (29), (33), (38), (84) are inconsistent by sub-proof #2252.
% 239.90/46.50  | | | | | 
% 239.90/46.50  | | | | End of split
% 239.90/46.50  | | | | 
% 239.90/46.50  | | | End of split
% 239.90/46.50  | | | 
% 239.90/46.50  | | End of split
% 239.90/46.50  | | 
% 239.90/46.50  | Case 2:
% 239.90/46.50  | | 
% 239.90/46.50  | |   (85)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.90/46.50  | | 
% 239.90/46.50  | | REF_CLOSE: (14), (28), (35), (37), (85) are inconsistent by sub-proof #1949.
% 239.90/46.50  | | 
% 239.90/46.50  | End of split
% 239.90/46.50  | 
% 239.90/46.50  End of proof
% 239.90/46.50  
% 239.90/46.50  Sub-proof #121 shows that the following formulas are inconsistent:
% 239.90/46.50  ----------------------------------------------------------------
% 239.90/46.50    (1)  op(e2, e3) = all_56_3
% 239.90/46.50    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.90/46.50    (3)  op(e1, e3) = all_24_0
% 239.90/46.50    (4)   ~ (e2 = e0)
% 239.90/46.50    (5)  op(e3, e0) = all_4_0
% 239.90/46.50    (6)  op(e1, e3) = e3
% 239.90/46.50    (7)  op(e1, all_56_29) = e1
% 239.90/46.50    (8)  op(e1, e0) = e1
% 239.90/46.50    (9)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.90/46.50         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.90/46.50    (10)  op(e0, e1) = e1
% 239.90/46.50    (11)   ~ (all_24_0 = e0)
% 239.90/46.50    (12)  all_54_4 = all_52_1
% 239.90/46.50    (13)  op(e1, e0) = all_28_1
% 239.90/46.50    (14)   ~ (all_52_1 = e0)
% 239.90/46.50    (15)  op(e2, e3) = all_52_1
% 239.90/46.50    (16)  op(e2, all_56_3) = e2
% 239.90/46.50    (17)   ~ (all_4_0 = e1)
% 239.90/46.50    (18)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 & op(e1, e0) =
% 239.90/46.50            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1,
% 239.90/46.50              e0) = all_18_1 & $i(all_18_1))
% 239.90/46.50    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.50    (20)  op(e3, e0) = e0
% 239.90/46.50    (21)  all_58_4 = e3
% 239.90/46.50    (22)  op(e1, e0) = all_56_29
% 239.90/46.50    (23)   ~ (all_52_1 = e2)
% 239.90/46.50  
% 239.90/46.50  Begin of proof
% 239.90/46.50  | 
% 239.90/46.50  | BETA: splitting (18) gives:
% 239.90/46.50  | 
% 239.90/46.50  | Case 1:
% 239.90/46.50  | | 
% 239.90/46.50  | |   (24)   ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 & op(e1, e0) =
% 239.90/46.50  | |         all_18_1 & $i(all_18_0) & $i(all_18_1)
% 239.90/46.50  | | 
% 239.90/46.50  | | ALPHA: (24) implies:
% 239.90/46.50  | |   (25)  op(e1, e0) = all_18_1
% 239.90/46.50  | | 
% 239.90/46.50  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 239.90/46.50  | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (25)
% 239.90/46.50  | |            are inconsistent by sub-proof #122.
% 239.90/46.50  | | 
% 239.90/46.50  | Case 2:
% 239.90/46.50  | | 
% 239.90/46.50  | |   (26)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 & $i(all_18_1)
% 239.90/46.50  | | 
% 239.90/46.50  | | ALPHA: (26) implies:
% 239.90/46.50  | |   (27)  op(e1, e0) = all_18_1
% 239.90/46.50  | | 
% 239.90/46.50  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 239.90/46.50  | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (27)
% 239.90/46.50  | |            are inconsistent by sub-proof #122.
% 239.90/46.50  | | 
% 239.90/46.50  | End of split
% 239.90/46.50  | 
% 239.90/46.50  End of proof
% 239.90/46.50  
% 239.90/46.50  Sub-proof #122 shows that the following formulas are inconsistent:
% 239.90/46.50  ----------------------------------------------------------------
% 239.90/46.50    (1)  op(e2, e3) = all_56_3
% 239.90/46.50    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.90/46.50    (3)  op(e1, e3) = all_24_0
% 239.90/46.50    (4)   ~ (e2 = e0)
% 239.90/46.50    (5)  op(e3, e0) = all_4_0
% 239.90/46.50    (6)  op(e1, e3) = e3
% 239.90/46.50    (7)  op(e1, all_56_29) = e1
% 239.90/46.50    (8)  op(e1, e0) = e1
% 239.90/46.50    (9)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.90/46.50         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.90/46.50    (10)  op(e0, e1) = e1
% 239.90/46.50    (11)   ~ (all_24_0 = e0)
% 239.90/46.50    (12)  op(e1, e0) = all_18_1
% 239.90/46.50    (13)  all_54_4 = all_52_1
% 239.90/46.50    (14)  op(e1, e0) = all_28_1
% 239.90/46.50    (15)   ~ (all_52_1 = e0)
% 239.90/46.50    (16)  op(e2, e3) = all_52_1
% 239.90/46.50    (17)  op(e2, all_56_3) = e2
% 239.90/46.50    (18)   ~ (all_4_0 = e1)
% 239.90/46.50    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.50    (20)  op(e3, e0) = e0
% 239.90/46.50    (21)  all_58_4 = e3
% 239.90/46.50    (22)  op(e1, e0) = all_56_29
% 239.90/46.50    (23)   ~ (all_52_1 = e2)
% 239.90/46.50  
% 239.90/46.50  Begin of proof
% 239.90/46.50  | 
% 239.90/46.50  | BETA: splitting (2) gives:
% 239.90/46.50  | 
% 239.90/46.50  | Case 1:
% 239.90/46.50  | | 
% 239.90/46.50  | |   (24)  all_54_4 = e2
% 239.90/46.50  | | 
% 239.90/46.50  | | REF_CLOSE: (13), (23), (24) are inconsistent by sub-proof #2096.
% 239.90/46.50  | | 
% 239.90/46.50  | Case 2:
% 239.90/46.50  | | 
% 239.90/46.50  | |   (25)  all_54_4 = e1 | all_54_4 = e0
% 239.90/46.50  | | 
% 239.90/46.50  | | BETA: splitting (25) gives:
% 239.90/46.50  | | 
% 239.90/46.50  | | Case 1:
% 239.90/46.50  | | | 
% 239.90/46.50  | | |   (26)  all_54_4 = e1
% 239.90/46.50  | | | 
% 239.90/46.50  | | | COMBINE_EQS: (13), (26) imply:
% 239.90/46.50  | | |   (27)  all_52_1 = e1
% 239.90/46.50  | | | 
% 239.90/46.50  | | | SIMP: (27) implies:
% 239.90/46.50  | | |   (28)  all_52_1 = e1
% 239.90/46.50  | | | 
% 239.90/46.50  | | | REDUCE: (16), (28) imply:
% 239.90/46.50  | | |   (29)  op(e2, e3) = e1
% 239.90/46.50  | | | 
% 239.90/46.50  | | | GROUND_INST: instantiating (19) with e1, all_56_29, e0, e1, simplifying
% 239.90/46.50  | | |              with (8), (22) gives:
% 239.90/46.50  | | |   (30)  all_56_29 = e1
% 239.90/46.50  | | | 
% 239.90/46.50  | | | GROUND_INST: instantiating (19) with all_28_1, all_56_29, e0, e1,
% 239.90/46.50  | | |              simplifying with (14), (22) gives:
% 239.90/46.51  | | |   (31)  all_56_29 = all_28_1
% 239.90/46.51  | | | 
% 239.90/46.51  | | | GROUND_INST: instantiating (19) with all_18_1, all_56_29, e0, e1,
% 239.90/46.51  | | |              simplifying with (12), (22) gives:
% 239.90/46.51  | | |   (32)  all_56_29 = all_18_1
% 239.90/46.51  | | | 
% 239.90/46.51  | | | GROUND_INST: instantiating (19) with e3, all_24_0, e3, e1, simplifying
% 239.90/46.51  | | |              with (3), (6) gives:
% 239.90/46.51  | | |   (33)  all_24_0 = e3
% 239.90/46.51  | | | 
% 239.90/46.51  | | | GROUND_INST: instantiating (19) with e1, all_56_3, e3, e2, simplifying
% 239.90/46.51  | | |              with (1), (29) gives:
% 239.90/46.51  | | |   (34)  all_56_3 = e1
% 239.90/46.51  | | | 
% 239.90/46.51  | | | GROUND_INST: instantiating (19) with e0, all_4_0, e0, e3, simplifying with
% 239.90/46.51  | | |              (5), (20) gives:
% 239.90/46.51  | | |   (35)  all_4_0 = e0
% 239.90/46.51  | | | 
% 239.90/46.51  | | | COMBINE_EQS: (30), (31) imply:
% 239.90/46.51  | | |   (36)  all_28_1 = e1
% 239.90/46.51  | | | 
% 239.90/46.51  | | | COMBINE_EQS: (31), (32) imply:
% 239.90/46.51  | | |   (37)  all_28_1 = all_18_1
% 239.90/46.51  | | | 
% 239.90/46.51  | | | COMBINE_EQS: (36), (37) imply:
% 239.90/46.51  | | |   (38)  all_18_1 = e1
% 239.90/46.51  | | | 
% 239.90/46.51  | | | REF_CLOSE: (4), (7), (9), (10), (11), (17), (18), (19), (21), (30), (33),
% 239.90/46.51  | | |            (34), (35) are inconsistent by sub-proof #126.
% 239.90/46.51  | | | 
% 239.90/46.51  | | Case 2:
% 239.90/46.51  | | | 
% 239.90/46.51  | | |   (39)  all_54_4 = e0
% 239.90/46.51  | | | 
% 239.90/46.51  | | | REF_CLOSE: (13), (15), (39) are inconsistent by sub-proof #1923.
% 239.90/46.51  | | | 
% 239.90/46.51  | | End of split
% 239.90/46.51  | | 
% 239.90/46.51  | End of split
% 239.90/46.51  | 
% 239.90/46.51  End of proof
% 239.90/46.51  
% 239.90/46.51  Sub-proof #123 shows that the following formulas are inconsistent:
% 239.90/46.51  ----------------------------------------------------------------
% 239.90/46.51    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.90/46.51             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 239.90/46.51           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 239.90/46.51         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.90/46.51           $i(all_56_7))
% 239.90/46.51    (2)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.90/46.51    (3)   ~ (all_52_7 = e2)
% 239.90/46.51    (4)   ~ (e2 = e0)
% 239.90/46.51    (5)  all_54_13 = all_52_7
% 239.90/46.51    (6)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.90/46.51         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 239.90/46.51    (7)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 & op(e1, e0) = all_28_1
% 239.90/46.51           & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0) =
% 239.90/46.51           all_28_1 & $i(all_28_1))
% 239.90/46.51    (8)   ~ (all_52_1 = all_52_2)
% 239.90/46.51    (9)  op(e1, e0) = all_52_14
% 239.90/46.51    (10)   ~ (all_52_13 = e1)
% 239.90/46.51    (11)  op(all_24_1, e3) = all_24_0
% 239.90/46.51    (12)  op(all_4_1, e0) = all_4_0
% 239.90/46.51    (13)  all_24_1 = e1
% 239.90/46.51    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.90/46.51          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.90/46.51    (15)  op(e0, e1) = e1
% 239.90/46.51    (16)   ~ (all_52_2 = e1)
% 239.90/46.51    (17)   ~ (all_24_0 = e0)
% 239.90/46.51    (18)  op(e2, e1) = e2
% 239.90/46.51    (19)  all_4_1 = e3
% 239.90/46.51    (20)  all_54_4 = all_52_1
% 239.90/46.51    (21)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.90/46.51          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.90/46.51    (22)  all_52_14 = e1
% 239.90/46.51    (23)   ~ (all_52_7 = e1)
% 239.90/46.51    (24)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 239.90/46.51            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 239.90/46.51              e0) = all_14_1 & $i(all_14_1))
% 239.90/46.51    (25)  all_56_31 = e2
% 239.90/46.51    (26)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 239.90/46.51            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 239.90/46.51              e0) = all_48_1 & $i(all_48_1))
% 239.90/46.51    (27)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 239.90/46.51            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 239.90/46.51            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 239.90/46.51            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 239.90/46.51            op(e0, all_56_31) = e0)
% 239.90/46.51    (28)  op(e0, e3) = e0
% 239.90/46.51    (29)  op(all_44_1, e0) = all_44_0
% 239.90/46.51    (30)   ~ (all_52_1 = e0)
% 239.90/46.51    (31)  op(e2, e2) = all_8_2
% 239.90/46.51    (32)  op(e2, e3) = all_52_1
% 239.90/46.51    (33)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.90/46.51    (34)   ~ (all_52_2 = e0)
% 239.90/46.51    (35)  op(e0, e2) = all_52_7
% 239.90/46.51    (36)  all_56_1 = e2
% 239.90/46.51    (37)   ~ (all_4_0 = e1)
% 239.90/46.51    (38)  op(e3, e2) = all_52_4
% 239.90/46.51    (39)   ~ (all_52_7 = e0)
% 239.90/46.51    (40)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.90/46.51    (41)   ~ (all_52_2 = e2)
% 239.90/46.51    (42)  all_44_1 = e3
% 239.90/46.51    (43)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 & op(e1, e0) =
% 239.90/46.51            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1,
% 239.90/46.51              e0) = all_18_1 & $i(all_18_1))
% 239.90/46.51    (44)  all_54_8 = all_52_2
% 239.90/46.51    (45)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.51    (46)  op(e3, e0) = e0
% 239.90/46.51    (47)  op(e1, e3) = all_52_2
% 239.90/46.51    (48)   ~ (all_8_2 = e3)
% 239.90/46.51    (49)   ~ (e1 = e0)
% 239.90/46.51    (50)  all_58_4 = e3
% 239.90/46.51    (51)  op(e0, e0) = e2
% 239.90/46.51    (52)  op(e2, e0) = all_52_13
% 239.90/46.51    (53)  all_58_3 = e0
% 239.90/46.51    (54)  all_58_14 = e1
% 239.90/46.51    (55)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.90/46.51          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.90/46.51    (56)   ~ (all_52_1 = e2)
% 239.90/46.51    (57)   ~ (e2 = e1)
% 239.90/46.51    (58)   ~ (all_52_4 = all_52_7)
% 239.90/46.51  
% 239.90/46.51  Begin of proof
% 239.90/46.51  | 
% 239.90/46.51  | REDUCE: (29), (42) imply:
% 239.90/46.51  |   (59)  op(e3, e0) = all_44_0
% 239.90/46.51  | 
% 239.90/46.51  | REDUCE: (11), (13) imply:
% 239.90/46.51  |   (60)  op(e1, e3) = all_24_0
% 239.90/46.51  | 
% 239.90/46.51  | REDUCE: (12), (19) imply:
% 239.90/46.51  |   (61)  op(e3, e0) = all_4_0
% 239.90/46.51  | 
% 239.90/46.51  | REDUCE: (9), (22) imply:
% 239.90/46.51  |   (62)  op(e1, e0) = e1
% 239.90/46.51  | 
% 239.90/46.51  | BETA: splitting (2) gives:
% 239.90/46.51  | 
% 239.90/46.51  | Case 1:
% 239.90/46.51  | | 
% 239.90/46.51  | |   (63)  all_54_8 = e3
% 239.90/46.51  | | 
% 239.90/46.51  | | COMBINE_EQS: (44), (63) imply:
% 239.90/46.51  | |   (64)  all_52_2 = e3
% 239.90/46.51  | | 
% 239.90/46.51  | | SIMP: (64) implies:
% 239.90/46.51  | |   (65)  all_52_2 = e3
% 239.90/46.51  | | 
% 239.90/46.51  | | REDUCE: (8), (65) imply:
% 239.90/46.51  | |   (66)   ~ (all_52_1 = e3)
% 239.90/46.51  | | 
% 239.90/46.51  | | REDUCE: (41), (65) imply:
% 239.90/46.51  | |   (67)   ~ (e3 = e2)
% 239.90/46.51  | | 
% 239.90/46.51  | | REDUCE: (16), (65) imply:
% 239.90/46.51  | |   (68)   ~ (e3 = e1)
% 239.90/46.51  | | 
% 239.90/46.51  | | REDUCE: (34), (65) imply:
% 239.90/46.51  | |   (69)   ~ (e3 = e0)
% 239.90/46.51  | | 
% 239.90/46.51  | | REDUCE: (47), (65) imply:
% 239.90/46.51  | |   (70)  op(e1, e3) = e3
% 239.90/46.51  | | 
% 239.90/46.51  | | BETA: splitting (33) gives:
% 239.90/46.51  | | 
% 239.90/46.51  | | Case 1:
% 239.90/46.51  | | | 
% 239.90/46.51  | | |   (71)  all_54_4 = e3
% 239.90/46.51  | | | 
% 239.90/46.51  | | | REF_CLOSE: (20), (66), (71) are inconsistent by sub-proof #2100.
% 239.90/46.51  | | | 
% 239.90/46.51  | | Case 2:
% 239.90/46.51  | | | 
% 239.90/46.51  | | |   (72)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.90/46.51  | | | 
% 239.90/46.51  | | | BETA: splitting (27) gives:
% 239.90/46.51  | | | 
% 239.90/46.51  | | | Case 1:
% 239.90/46.51  | | | | 
% 239.90/46.51  | | | |   (73)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 239.90/46.51  | | | |           all_56_25 & $i(all_56_25)) | (all_56_26 = e2 & op(e2,
% 239.90/46.51  | | | |             all_56_27) = e2 & op(e2, e0) = all_56_27 & $i(all_56_27))
% 239.90/46.51  | | | | 
% 239.90/46.51  | | | | BETA: splitting (73) gives:
% 239.90/46.51  | | | | 
% 239.90/46.51  | | | | Case 1:
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | |   (74)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 239.90/46.51  | | | | |         all_56_25 & $i(all_56_25)
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | | ALPHA: (74) implies:
% 239.90/46.51  | | | | |   (75)  op(e3, e0) = all_56_25
% 239.90/46.51  | | | | |   (76)  op(e3, all_56_25) = e3
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | | REF_CLOSE: (45), (46), (69), (75), (76) are inconsistent by sub-proof
% 239.90/46.51  | | | | |            #1926.
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | Case 2:
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | |   (77)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 239.90/46.51  | | | | |         all_56_27 & $i(all_56_27)
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | | ALPHA: (77) implies:
% 239.90/46.51  | | | | |   (78)  op(e2, e0) = all_56_27
% 239.90/46.51  | | | | |   (79)  op(e2, all_56_27) = e2
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | | BETA: splitting (1) gives:
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | | Case 1:
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | |   (80)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 239.90/46.51  | | | | | |           op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 239.90/46.51  | | | | | |           $i(all_56_3))
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | | BETA: splitting (80) gives:
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | | Case 1:
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | |   (81)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | | REF_CLOSE: (3), (5), (23), (36), (38), (39), (40), (45), (58),
% 239.90/46.51  | | | | | | |            (81) are inconsistent by sub-proof #131.
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | Case 2:
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | |   (82)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 239.90/46.51  | | | | | | |         all_56_3 & $i(all_56_3)
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | | ALPHA: (82) implies:
% 239.90/46.51  | | | | | | |   (83)  op(e2, e3) = all_56_3
% 239.90/46.51  | | | | | | |   (84)  op(e2, all_56_3) = e2
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | | BETA: splitting (6) gives:
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | | Case 1:
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | |   (85)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 &
% 239.90/46.51  | | | | | | | |           op(e2, e2) = e3)
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | | REF_CLOSE: (31), (45), (48), (67), (83), (84), (85) are
% 239.90/46.51  | | | | | | | |            inconsistent by sub-proof #130.
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | Case 2:
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | |   (86)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 &
% 239.90/46.51  | | | | | | | |           op(e2, e0) = e3)
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | | BETA: splitting (86) gives:
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | | Case 1:
% 239.90/46.51  | | | | | | | | | 
% 239.90/46.51  | | | | | | | | |   (87)  all_58_5 = e3 & op(e2, e1) = e3
% 239.90/46.51  | | | | | | | | | 
% 239.90/46.51  | | | | | | | | | ALPHA: (87) implies:
% 239.90/46.51  | | | | | | | | |   (88)  op(e2, e1) = e3
% 239.90/46.51  | | | | | | | | | 
% 239.90/46.51  | | | | | | | | | REF_CLOSE: (18), (45), (67), (88) are inconsistent by
% 239.90/46.51  | | | | | | | | |            sub-proof #2256.
% 239.90/46.51  | | | | | | | | | 
% 239.90/46.51  | | | | | | | | Case 2:
% 239.90/46.51  | | | | | | | | | 
% 239.90/46.51  | | | | | | | | |   (89)  all_58_10 = e3 & op(e2, e0) = e3
% 239.90/46.51  | | | | | | | | | 
% 239.90/46.51  | | | | | | | | | ALPHA: (89) implies:
% 239.90/46.51  | | | | | | | | |   (90)  op(e2, e0) = e3
% 239.90/46.51  | | | | | | | | | 
% 239.90/46.51  | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (10), (14), (20), (21), (23),
% 239.90/46.51  | | | | | | | | |            (24), (26), (28), (30), (32), (36), (38), (39),
% 239.90/46.51  | | | | | | | | |            (40), (45), (49), (50), (51), (52), (53), (54),
% 239.90/46.51  | | | | | | | | |            (55), (56), (57), (58), (67), (68), (69), (70),
% 239.90/46.51  | | | | | | | | |            (72), (78), (79), (90) are inconsistent by
% 239.90/46.51  | | | | | | | | |            sub-proof #127.
% 239.90/46.51  | | | | | | | | | 
% 239.90/46.51  | | | | | | | | End of split
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | End of split
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | End of split
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | Case 2:
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | |   (91)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 239.90/46.51  | | | | | |           all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 239.90/46.51  | | | | | |             all_56_7) = e0 & op(e0, e3) = all_56_7 & $i(all_56_7))
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | | REF_CLOSE: (4), (10), (14), (21), (28), (45), (49), (50), (51),
% 239.90/46.51  | | | | | |            (52), (53), (54), (55), (57), (67), (68), (69), (70),
% 239.90/46.51  | | | | | |            (91) are inconsistent by sub-proof #128.
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | End of split
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | End of split
% 239.90/46.51  | | | | 
% 239.90/46.51  | | | Case 2:
% 239.90/46.51  | | | | 
% 239.90/46.51  | | | |   (92)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 239.90/46.51  | | | |           all_56_29 & $i(all_56_29)) | (all_56_30 = e0 & op(e0,
% 239.90/46.51  | | | |             all_56_31) = e0)
% 239.90/46.51  | | | | 
% 239.90/46.51  | | | | BETA: splitting (92) gives:
% 239.90/46.51  | | | | 
% 239.90/46.51  | | | | Case 1:
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | |   (93)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 239.90/46.51  | | | | |         all_56_29 & $i(all_56_29)
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | | ALPHA: (93) implies:
% 239.90/46.51  | | | | |   (94)  op(e1, e0) = all_56_29
% 239.90/46.51  | | | | |   (95)  op(e1, all_56_29) = e1
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | | BETA: splitting (1) gives:
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | | Case 1:
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | |   (96)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 239.90/46.51  | | | | | |           op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 239.90/46.51  | | | | | |           $i(all_56_3))
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | | BETA: splitting (96) gives:
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | | Case 1:
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | |   (97)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | | REF_CLOSE: (3), (5), (23), (36), (38), (39), (40), (45), (58),
% 239.90/46.51  | | | | | | |            (97) are inconsistent by sub-proof #131.
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | Case 2:
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | |   (98)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 239.90/46.51  | | | | | | |         all_56_3 & $i(all_56_3)
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | | ALPHA: (98) implies:
% 239.90/46.51  | | | | | | |   (99)  op(e2, e3) = all_56_3
% 239.90/46.51  | | | | | | |   (100)  op(e2, all_56_3) = e2
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | | BETA: splitting (7) gives:
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | | Case 1:
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | |   (101)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 239.90/46.51  | | | | | | | |          op(e1, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | | ALPHA: (101) implies:
% 239.90/46.51  | | | | | | | |   (102)  op(e1, e0) = all_28_1
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | | REF_CLOSE: (4), (14), (15), (17), (20), (30), (32), (37), (43),
% 239.90/46.51  | | | | | | | |            (45), (46), (50), (56), (59), (60), (61), (62), (70),
% 239.90/46.51  | | | | | | | |            (72), (94), (95), (99), (100), (102) are inconsistent
% 239.90/46.51  | | | | | | | |            by sub-proof #124.
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | Case 2:
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | |   (103)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 239.90/46.51  | | | | | | | |          $i(all_28_1)
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | | ALPHA: (103) implies:
% 239.90/46.51  | | | | | | | |   (104)  op(e1, e0) = all_28_1
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | | REF_CLOSE: (4), (14), (15), (17), (20), (30), (32), (37), (43),
% 239.90/46.51  | | | | | | | |            (45), (46), (50), (56), (59), (60), (61), (62), (70),
% 239.90/46.51  | | | | | | | |            (72), (94), (95), (99), (100), (104) are inconsistent
% 239.90/46.51  | | | | | | | |            by sub-proof #124.
% 239.90/46.51  | | | | | | | | 
% 239.90/46.51  | | | | | | | End of split
% 239.90/46.51  | | | | | | | 
% 239.90/46.51  | | | | | | End of split
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | Case 2:
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | |   (105)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 239.90/46.51  | | | | | |            all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 239.90/46.51  | | | | | |              all_56_7) = e0 & op(e0, e3) = all_56_7 & $i(all_56_7))
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | | REF_CLOSE: (4), (10), (14), (21), (28), (45), (49), (50), (51),
% 239.90/46.51  | | | | | |            (52), (53), (54), (55), (57), (67), (68), (69), (70),
% 239.90/46.51  | | | | | |            (105) are inconsistent by sub-proof #128.
% 239.90/46.51  | | | | | | 
% 239.90/46.51  | | | | | End of split
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | Case 2:
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | |   (106)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | | ALPHA: (106) implies:
% 239.90/46.51  | | | | |   (107)  op(e0, all_56_31) = e0
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | | REDUCE: (25), (107) imply:
% 239.90/46.51  | | | | |   (108)  op(e0, e2) = e0
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | | REF_CLOSE: (35), (39), (45), (108) are inconsistent by sub-proof
% 239.90/46.51  | | | | |            #2252.
% 239.90/46.51  | | | | | 
% 239.90/46.51  | | | | End of split
% 239.90/46.52  | | | | 
% 239.90/46.52  | | | End of split
% 239.90/46.52  | | | 
% 239.90/46.52  | | End of split
% 239.90/46.52  | | 
% 239.90/46.52  | Case 2:
% 239.90/46.52  | | 
% 239.90/46.52  | |   (109)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.90/46.52  | | 
% 239.90/46.52  | | REF_CLOSE: (16), (34), (41), (44), (109) are inconsistent by sub-proof
% 239.90/46.52  | |            #1949.
% 239.90/46.52  | | 
% 239.90/46.52  | End of split
% 239.90/46.52  | 
% 239.90/46.52  End of proof
% 239.90/46.52  
% 239.90/46.52  Sub-proof #124 shows that the following formulas are inconsistent:
% 239.90/46.52  ----------------------------------------------------------------
% 239.90/46.52    (1)  op(e2, e3) = all_56_3
% 239.90/46.52    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.90/46.52    (3)  op(e1, e3) = all_24_0
% 239.90/46.52    (4)   ~ (e2 = e0)
% 239.90/46.52    (5)  op(e3, e0) = all_4_0
% 239.90/46.52    (6)  op(e1, e3) = e3
% 239.90/46.52    (7)  op(e1, all_56_29) = e1
% 239.90/46.52    (8)  op(e1, e0) = e1
% 239.90/46.52    (9)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.90/46.52         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.90/46.52    (10)  op(e0, e1) = e1
% 239.90/46.52    (11)   ~ (all_24_0 = e0)
% 239.90/46.52    (12)  all_54_4 = all_52_1
% 239.90/46.52    (13)  op(e3, e0) = all_44_0
% 239.90/46.52    (14)  op(e1, e0) = all_28_1
% 239.90/46.52    (15)   ~ (all_52_1 = e0)
% 239.90/46.52    (16)  op(e2, e3) = all_52_1
% 239.90/46.52    (17)  op(e2, all_56_3) = e2
% 239.90/46.52    (18)   ~ (all_4_0 = e1)
% 239.90/46.52    (19)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 & op(e1, e0) =
% 239.90/46.52            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1,
% 239.90/46.52              e0) = all_18_1 & $i(all_18_1))
% 239.90/46.52    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.52    (21)  op(e3, e0) = e0
% 239.90/46.52    (22)  all_58_4 = e3
% 239.90/46.52    (23)  op(e1, e0) = all_56_29
% 239.90/46.52    (24)   ~ (all_52_1 = e2)
% 239.90/46.52  
% 239.90/46.52  Begin of proof
% 239.90/46.52  | 
% 239.90/46.52  | BETA: splitting (19) gives:
% 239.90/46.52  | 
% 239.90/46.52  | Case 1:
% 239.90/46.52  | | 
% 239.90/46.52  | |   (25)   ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 & op(e1, e0) =
% 239.90/46.52  | |         all_18_1 & $i(all_18_0) & $i(all_18_1)
% 239.90/46.52  | | 
% 239.90/46.52  | | ALPHA: (25) implies:
% 239.90/46.52  | |   (26)  op(e1, e0) = all_18_1
% 239.90/46.52  | | 
% 239.90/46.52  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 239.90/46.52  | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 239.90/46.52  | |            (26) are inconsistent by sub-proof #125.
% 239.90/46.52  | | 
% 239.90/46.52  | Case 2:
% 239.90/46.52  | | 
% 239.90/46.52  | |   (27)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 & $i(all_18_1)
% 239.90/46.52  | | 
% 239.90/46.52  | | ALPHA: (27) implies:
% 239.90/46.52  | |   (28)  op(e1, e0) = all_18_1
% 239.90/46.52  | | 
% 239.90/46.52  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 239.90/46.52  | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 239.90/46.52  | |            (28) are inconsistent by sub-proof #125.
% 239.90/46.52  | | 
% 239.90/46.52  | End of split
% 239.90/46.52  | 
% 239.90/46.52  End of proof
% 239.90/46.52  
% 239.90/46.52  Sub-proof #125 shows that the following formulas are inconsistent:
% 239.90/46.52  ----------------------------------------------------------------
% 239.90/46.52    (1)  op(e2, e3) = all_56_3
% 239.90/46.52    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.90/46.52    (3)  op(e1, e3) = all_24_0
% 239.90/46.52    (4)   ~ (e2 = e0)
% 239.90/46.52    (5)  op(e3, e0) = all_4_0
% 239.90/46.52    (6)  op(e1, e3) = e3
% 239.90/46.52    (7)  op(e1, all_56_29) = e1
% 239.90/46.52    (8)  op(e1, e0) = e1
% 239.90/46.52    (9)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.90/46.52         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.90/46.52    (10)  op(e0, e1) = e1
% 239.90/46.52    (11)   ~ (all_24_0 = e0)
% 239.90/46.52    (12)  op(e1, e0) = all_18_1
% 239.90/46.52    (13)  all_54_4 = all_52_1
% 239.90/46.52    (14)  op(e3, e0) = all_44_0
% 239.90/46.52    (15)  op(e1, e0) = all_28_1
% 239.90/46.52    (16)   ~ (all_52_1 = e0)
% 239.90/46.52    (17)  op(e2, e3) = all_52_1
% 239.90/46.52    (18)  op(e2, all_56_3) = e2
% 239.90/46.52    (19)   ~ (all_4_0 = e1)
% 239.90/46.52    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.52    (21)  op(e3, e0) = e0
% 239.90/46.52    (22)  all_58_4 = e3
% 239.90/46.52    (23)  op(e1, e0) = all_56_29
% 239.90/46.52    (24)   ~ (all_52_1 = e2)
% 239.90/46.52  
% 239.90/46.52  Begin of proof
% 239.90/46.52  | 
% 239.90/46.52  | BETA: splitting (2) gives:
% 239.90/46.52  | 
% 239.90/46.52  | Case 1:
% 239.90/46.52  | | 
% 239.90/46.52  | |   (25)  all_54_4 = e2
% 239.90/46.52  | | 
% 239.90/46.52  | | REF_CLOSE: (13), (24), (25) are inconsistent by sub-proof #2096.
% 239.90/46.52  | | 
% 239.90/46.52  | Case 2:
% 239.90/46.52  | | 
% 239.90/46.52  | |   (26)  all_54_4 = e1 | all_54_4 = e0
% 239.90/46.52  | | 
% 239.90/46.52  | | BETA: splitting (26) gives:
% 239.90/46.52  | | 
% 239.90/46.52  | | Case 1:
% 239.90/46.52  | | | 
% 239.90/46.52  | | |   (27)  all_54_4 = e1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | COMBINE_EQS: (13), (27) imply:
% 239.90/46.52  | | |   (28)  all_52_1 = e1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | SIMP: (28) implies:
% 239.90/46.52  | | |   (29)  all_52_1 = e1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | REDUCE: (17), (29) imply:
% 239.90/46.52  | | |   (30)  op(e2, e3) = e1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | GROUND_INST: instantiating (20) with e1, all_28_1, e0, e1, simplifying
% 239.90/46.52  | | |              with (8), (15) gives:
% 239.90/46.52  | | |   (31)  all_28_1 = e1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | GROUND_INST: instantiating (20) with all_28_1, all_56_29, e0, e1,
% 239.90/46.52  | | |              simplifying with (15), (23) gives:
% 239.90/46.52  | | |   (32)  all_56_29 = all_28_1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | GROUND_INST: instantiating (20) with all_18_1, all_56_29, e0, e1,
% 239.90/46.52  | | |              simplifying with (12), (23) gives:
% 239.90/46.52  | | |   (33)  all_56_29 = all_18_1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | GROUND_INST: instantiating (20) with e3, all_24_0, e3, e1, simplifying
% 239.90/46.52  | | |              with (3), (6) gives:
% 239.90/46.52  | | |   (34)  all_24_0 = e3
% 239.90/46.52  | | | 
% 239.90/46.52  | | | GROUND_INST: instantiating (20) with e1, all_56_3, e3, e2, simplifying
% 239.90/46.52  | | |              with (1), (30) gives:
% 239.90/46.52  | | |   (35)  all_56_3 = e1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | GROUND_INST: instantiating (20) with e0, all_44_0, e0, e3, simplifying
% 239.90/46.52  | | |              with (14), (21) gives:
% 239.90/46.52  | | |   (36)  all_44_0 = e0
% 239.90/46.52  | | | 
% 239.90/46.52  | | | GROUND_INST: instantiating (20) with all_4_0, all_44_0, e0, e3,
% 239.90/46.52  | | |              simplifying with (5), (14) gives:
% 239.90/46.52  | | |   (37)  all_44_0 = all_4_0
% 239.90/46.52  | | | 
% 239.90/46.52  | | | COMBINE_EQS: (32), (33) imply:
% 239.90/46.52  | | |   (38)  all_28_1 = all_18_1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | SIMP: (38) implies:
% 239.90/46.52  | | |   (39)  all_28_1 = all_18_1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | COMBINE_EQS: (36), (37) imply:
% 239.90/46.52  | | |   (40)  all_4_0 = e0
% 239.90/46.52  | | | 
% 239.90/46.52  | | | COMBINE_EQS: (31), (39) imply:
% 239.90/46.52  | | |   (41)  all_18_1 = e1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | COMBINE_EQS: (33), (41) imply:
% 239.90/46.52  | | |   (42)  all_56_29 = e1
% 239.90/46.52  | | | 
% 239.90/46.52  | | | REF_CLOSE: (4), (7), (9), (10), (11), (18), (19), (20), (22), (34), (35),
% 239.90/46.52  | | |            (40), (42) are inconsistent by sub-proof #126.
% 239.90/46.52  | | | 
% 239.90/46.52  | | Case 2:
% 239.90/46.52  | | | 
% 239.90/46.52  | | |   (43)  all_54_4 = e0
% 239.90/46.52  | | | 
% 239.90/46.52  | | | REF_CLOSE: (13), (16), (43) are inconsistent by sub-proof #1923.
% 239.90/46.52  | | | 
% 239.90/46.52  | | End of split
% 239.90/46.52  | | 
% 239.90/46.52  | End of split
% 239.90/46.52  | 
% 239.90/46.52  End of proof
% 239.90/46.52  
% 239.90/46.52  Sub-proof #126 shows that the following formulas are inconsistent:
% 239.90/46.52  ----------------------------------------------------------------
% 239.90/46.52    (1)  all_56_29 = e1
% 239.90/46.52    (2)  all_56_3 = e1
% 239.90/46.52    (3)   ~ (e2 = e0)
% 239.90/46.52    (4)  op(e1, all_56_29) = e1
% 239.90/46.52    (5)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.90/46.52         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.90/46.52    (6)  op(e0, e1) = e1
% 239.90/46.52    (7)   ~ (all_24_0 = e0)
% 239.90/46.52    (8)  op(e2, all_56_3) = e2
% 239.90/46.52    (9)   ~ (all_4_0 = e1)
% 239.90/46.52    (10)  all_4_0 = e0
% 239.90/46.52    (11)  all_24_0 = e3
% 239.90/46.52    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.52    (13)  all_58_4 = e3
% 239.90/46.52  
% 239.90/46.52  Begin of proof
% 239.90/46.52  | 
% 239.90/46.52  | REDUCE: (7), (11) imply:
% 239.90/46.52  |   (14)   ~ (e3 = e0)
% 239.90/46.52  | 
% 239.90/46.52  | REDUCE: (9), (10) imply:
% 239.90/46.52  |   (15)   ~ (e1 = e0)
% 239.90/46.52  | 
% 239.90/46.52  | SIMP: (15) implies:
% 239.90/46.52  |   (16)   ~ (e1 = e0)
% 239.90/46.52  | 
% 239.90/46.52  | REDUCE: (2), (8) imply:
% 239.90/46.52  |   (17)  op(e2, e1) = e2
% 239.90/46.52  | 
% 239.90/46.52  | REDUCE: (1), (4) imply:
% 239.90/46.52  |   (18)  op(e1, e1) = e1
% 239.90/46.52  | 
% 239.90/46.52  | REF_CLOSE: (3), (5), (6), (12), (13), (14), (16), (17), (18) are inconsistent
% 239.90/46.52  |            by sub-proof #1503.
% 239.90/46.52  | 
% 239.90/46.52  End of proof
% 239.90/46.52  
% 239.90/46.52  Sub-proof #127 shows that the following formulas are inconsistent:
% 239.90/46.52  ----------------------------------------------------------------
% 239.90/46.52    (1)  op(e2, e0) = all_56_27
% 239.90/46.52    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.90/46.52    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.90/46.52             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 239.90/46.52           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 239.90/46.52         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.90/46.52           $i(all_56_7))
% 239.90/46.52    (4)   ~ (e3 = e0)
% 239.90/46.52    (5)   ~ (all_52_7 = e2)
% 239.90/46.52    (6)   ~ (e2 = e0)
% 239.90/46.52    (7)  all_54_13 = all_52_7
% 239.90/46.52    (8)  op(e2, all_56_27) = e2
% 239.90/46.52    (9)  op(e1, e3) = e3
% 239.90/46.52    (10)   ~ (all_52_13 = e1)
% 239.90/46.52    (11)   ~ (e3 = e1)
% 239.90/46.52    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.90/46.52          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.90/46.52    (13)  op(e2, e0) = e3
% 239.90/46.52    (14)  all_54_4 = all_52_1
% 239.90/46.52    (15)   ~ (e3 = e2)
% 239.90/46.52    (16)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.90/46.52          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.90/46.52    (17)   ~ (all_52_7 = e1)
% 239.90/46.52    (18)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 239.90/46.52            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 239.90/46.52              e0) = all_14_1 & $i(all_14_1))
% 239.90/46.52    (19)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 239.90/46.52            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 239.90/46.52              e0) = all_48_1 & $i(all_48_1))
% 239.90/46.52    (20)  op(e0, e3) = e0
% 239.90/46.52    (21)   ~ (all_52_1 = e0)
% 239.90/46.52    (22)  op(e2, e3) = all_52_1
% 239.90/46.52    (23)  all_56_1 = e2
% 239.90/46.52    (24)  op(e3, e2) = all_52_4
% 239.90/46.52    (25)   ~ (all_52_7 = e0)
% 239.90/46.52    (26)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.90/46.52    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.52    (28)   ~ (e1 = e0)
% 239.90/46.52    (29)  all_58_4 = e3
% 239.90/46.52    (30)  op(e0, e0) = e2
% 239.90/46.52    (31)  op(e2, e0) = all_52_13
% 239.90/46.52    (32)  all_58_3 = e0
% 239.90/46.52    (33)  all_58_14 = e1
% 239.90/46.52    (34)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.90/46.52          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.90/46.52    (35)   ~ (all_52_1 = e2)
% 239.90/46.52    (36)   ~ (e2 = e1)
% 239.90/46.52    (37)   ~ (all_52_4 = all_52_7)
% 239.90/46.52  
% 239.90/46.52  Begin of proof
% 239.90/46.52  | 
% 239.90/46.52  | BETA: splitting (3) gives:
% 239.90/46.52  | 
% 239.90/46.52  | Case 1:
% 239.90/46.52  | | 
% 239.90/46.52  | |   (38)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 239.90/46.52  | |             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 239.90/46.52  | | 
% 239.90/46.52  | | BETA: splitting (38) gives:
% 239.90/46.52  | | 
% 239.90/46.52  | | Case 1:
% 239.90/46.52  | | | 
% 239.90/46.52  | | |   (39)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 239.90/46.52  | | | 
% 239.90/46.52  | | | REF_CLOSE: (5), (7), (17), (23), (24), (25), (26), (27), (37), (39) are
% 239.90/46.52  | | |            inconsistent by sub-proof #131.
% 239.90/46.52  | | | 
% 239.90/46.52  | | Case 2:
% 239.90/46.52  | | | 
% 239.90/46.52  | | |   (40)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 239.90/46.52  | | |         $i(all_56_3)
% 239.90/46.52  | | | 
% 239.90/46.52  | | | ALPHA: (40) implies:
% 239.90/46.52  | | |   (41)  op(e2, e3) = all_56_3
% 239.90/46.52  | | | 
% 239.90/46.52  | | | BETA: splitting (19) gives:
% 239.90/46.52  | | | 
% 239.90/46.52  | | | Case 1:
% 239.90/46.52  | | | | 
% 239.90/46.52  | | | |   (42)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 239.90/46.52  | | | |         all_48_1 & $i(all_48_0) & $i(all_48_1)
% 239.90/46.52  | | | | 
% 239.90/46.52  | | | | ALPHA: (42) implies:
% 239.90/46.52  | | | |   (43)  op(e2, e0) = all_48_1
% 239.90/46.52  | | | | 
% 239.90/46.52  | | | | BETA: splitting (2) gives:
% 239.90/46.52  | | | | 
% 239.90/46.52  | | | | Case 1:
% 239.90/46.52  | | | | | 
% 239.90/46.52  | | | | |   (44)  all_54_4 = e2
% 239.90/46.52  | | | | | 
% 239.90/46.52  | | | | | REF_CLOSE: (14), (35), (44) are inconsistent by sub-proof #2096.
% 239.90/46.52  | | | | | 
% 239.90/46.52  | | | | Case 2:
% 239.90/46.52  | | | | | 
% 239.90/46.52  | | | | |   (45)   ~ (all_54_4 = e2)
% 239.90/46.52  | | | | |   (46)  all_54_4 = e1 | all_54_4 = e0
% 239.90/46.52  | | | | | 
% 239.90/46.52  | | | | | BETA: splitting (46) gives:
% 239.90/46.52  | | | | | 
% 239.90/46.52  | | | | | Case 1:
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | |   (47)  all_54_4 = e1
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | | COMBINE_EQS: (14), (47) imply:
% 239.90/46.52  | | | | | |   (48)  all_52_1 = e1
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | | SIMP: (48) implies:
% 239.90/46.52  | | | | | |   (49)  all_52_1 = e1
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | | REDUCE: (35), (49) imply:
% 239.90/46.52  | | | | | |   (50)   ~ (e2 = e1)
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | | REDUCE: (22), (49) imply:
% 239.90/46.52  | | | | | |   (51)  op(e2, e3) = e1
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | | GROUND_INST: instantiating (27) with all_48_1, all_56_27, e0, e2,
% 239.90/46.52  | | | | | |              simplifying with (1), (43) gives:
% 239.90/46.52  | | | | | |   (52)  all_56_27 = all_48_1
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | | GROUND_INST: instantiating (27) with e3, all_56_27, e0, e2,
% 239.90/46.52  | | | | | |              simplifying with (1), (13) gives:
% 239.90/46.52  | | | | | |   (53)  all_56_27 = e3
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | | GROUND_INST: instantiating (27) with e1, all_56_3, e3, e2,
% 239.90/46.52  | | | | | |              simplifying with (41), (51) gives:
% 239.90/46.52  | | | | | |   (54)  all_56_3 = e1
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | | COMBINE_EQS: (52), (53) imply:
% 239.90/46.52  | | | | | |   (55)  all_48_1 = e3
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | | REDUCE: (8), (53) imply:
% 239.90/46.52  | | | | | |   (56)  op(e2, e3) = e2
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | | REF_CLOSE: (27), (36), (51), (56) are inconsistent by sub-proof
% 239.90/46.52  | | | | | |            #1633.
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | Case 2:
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | |   (57)  all_54_4 = e0
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | | REF_CLOSE: (14), (21), (57) are inconsistent by sub-proof #1923.
% 239.90/46.52  | | | | | | 
% 239.90/46.52  | | | | | End of split
% 239.90/46.52  | | | | | 
% 239.90/46.52  | | | | End of split
% 239.90/46.52  | | | | 
% 239.90/46.52  | | | Case 2:
% 239.90/46.52  | | | | 
% 239.90/46.52  | | | |   (58)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 & $i(all_48_1)
% 239.90/46.52  | | | | 
% 239.90/46.52  | | | | REF_CLOSE: (13), (18), (27), (58) are inconsistent by sub-proof #129.
% 239.90/46.52  | | | | 
% 239.90/46.52  | | | End of split
% 239.90/46.52  | | | 
% 239.90/46.52  | | End of split
% 239.90/46.52  | | 
% 239.90/46.52  | Case 2:
% 239.90/46.52  | | 
% 239.90/46.52  | |   (59)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 239.90/46.52  | |           $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0,
% 239.90/46.52  | |             e3) = all_56_7 & $i(all_56_7))
% 239.90/46.53  | | 
% 239.90/46.53  | | REF_CLOSE: (4), (6), (9), (10), (11), (12), (15), (16), (20), (27), (28),
% 239.90/46.53  | |            (29), (30), (31), (32), (33), (34), (36), (59) are inconsistent
% 239.90/46.53  | |            by sub-proof #128.
% 239.90/46.53  | | 
% 239.90/46.53  | End of split
% 239.90/46.53  | 
% 239.90/46.53  End of proof
% 239.90/46.53  
% 239.90/46.53  Sub-proof #128 shows that the following formulas are inconsistent:
% 239.90/46.53  ----------------------------------------------------------------
% 239.90/46.53    (1)   ~ (e3 = e0)
% 239.90/46.53    (2)   ~ (e2 = e0)
% 239.90/46.53    (3)  op(e1, e3) = e3
% 239.90/46.53    (4)   ~ (all_52_13 = e1)
% 239.90/46.53    (5)   ~ (e3 = e1)
% 239.90/46.53    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 239.90/46.53         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.90/46.53    (7)   ~ (e3 = e2)
% 239.90/46.53    (8)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.90/46.53         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.90/46.53    (9)  op(e0, e3) = e0
% 239.90/46.53    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.53            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.53    (11)   ~ (e1 = e0)
% 239.90/46.53    (12)  all_58_4 = e3
% 239.90/46.53    (13)  op(e0, e0) = e2
% 239.90/46.53    (14)  op(e2, e0) = all_52_13
% 239.90/46.53    (15)  all_58_3 = e0
% 239.90/46.53    (16)  all_58_14 = e1
% 239.90/46.53    (17)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 239.90/46.53            $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 239.90/46.53            all_56_7 & $i(all_56_7))
% 239.90/46.53    (18)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.90/46.53          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.90/46.53    (19)   ~ (e2 = e1)
% 239.90/46.53  
% 239.90/46.53  Begin of proof
% 239.90/46.53  | 
% 239.90/46.53  | BETA: splitting (17) gives:
% 239.90/46.53  | 
% 239.90/46.53  | Case 1:
% 239.90/46.53  | | 
% 239.90/46.53  | |   (20)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 239.90/46.53  | |         $i(all_56_5)
% 239.90/46.53  | | 
% 239.90/46.53  | | ALPHA: (20) implies:
% 239.90/46.53  | |   (21)  op(e1, e3) = all_56_5
% 239.90/46.53  | |   (22)  op(e1, all_56_5) = e1
% 239.90/46.53  | | 
% 239.90/46.53  | | REF_CLOSE: (3), (5), (10), (21), (22) are inconsistent by sub-proof #2243.
% 239.90/46.53  | | 
% 239.90/46.53  | Case 2:
% 239.90/46.53  | | 
% 239.90/46.53  | |   (23)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 239.90/46.53  | |         $i(all_56_7)
% 239.90/46.53  | | 
% 239.90/46.53  | | ALPHA: (23) implies:
% 239.90/46.53  | |   (24)  op(e0, e3) = all_56_7
% 239.90/46.53  | |   (25)  op(e0, all_56_7) = e0
% 239.90/46.53  | | 
% 239.90/46.53  | | BETA: splitting (18) gives:
% 239.90/46.53  | | 
% 239.90/46.53  | | Case 1:
% 239.90/46.53  | | | 
% 239.90/46.53  | | |   (26)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 239.90/46.53  | | |           e1)
% 239.90/46.53  | | | 
% 239.90/46.53  | | | BETA: splitting (26) gives:
% 239.90/46.53  | | | 
% 239.90/46.53  | | | Case 1:
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | | GROUND_INST: instantiating (10) with e0, all_56_7, e3, e0, simplifying
% 239.90/46.53  | | | |              with (9), (24) gives:
% 239.90/46.53  | | | |   (27)  all_56_7 = e0
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | | REDUCE: (25), (27) imply:
% 239.90/46.53  | | | |   (28)  op(e0, e0) = e0
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | | REF_CLOSE: (2), (10), (13), (28) are inconsistent by sub-proof #2301.
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | Case 2:
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | |   (29)  all_58_3 = e1 & op(e2, e2) = e1
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | | REF_CLOSE: (11), (15), (29) are inconsistent by sub-proof #1752.
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | End of split
% 239.90/46.53  | | | 
% 239.90/46.53  | | Case 2:
% 239.90/46.53  | | | 
% 239.90/46.53  | | |   (30)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 239.90/46.53  | | |           e1)
% 239.90/46.53  | | | 
% 239.90/46.53  | | | BETA: splitting (30) gives:
% 239.90/46.53  | | | 
% 239.90/46.53  | | | Case 1:
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | |   (31)  all_58_5 = e1 & op(e2, e1) = e1
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | | ALPHA: (31) implies:
% 239.90/46.53  | | | |   (32)  all_58_5 = e1
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | | REF_CLOSE: (1), (2), (6), (7), (8), (11), (12), (16), (19), (32) are
% 239.90/46.53  | | | |            inconsistent by sub-proof #1481.
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | Case 2:
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | |   (33)  all_58_10 = e1 & op(e2, e0) = e1
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | | REF_CLOSE: (4), (10), (14), (33) are inconsistent by sub-proof #2277.
% 239.90/46.53  | | | | 
% 239.90/46.53  | | | End of split
% 239.90/46.53  | | | 
% 239.90/46.53  | | End of split
% 239.90/46.53  | | 
% 239.90/46.53  | End of split
% 239.90/46.53  | 
% 239.90/46.53  End of proof
% 239.90/46.53  
% 239.90/46.53  Sub-proof #129 shows that the following formulas are inconsistent:
% 239.90/46.53  ----------------------------------------------------------------
% 239.90/46.53    (1)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 & $i(all_48_1)
% 239.90/46.53    (2)  op(e2, e0) = e3
% 239.90/46.53    (3)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 239.90/46.53           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0) =
% 239.90/46.53           all_14_1 & $i(all_14_1))
% 239.90/46.53    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.53  
% 239.90/46.53  Begin of proof
% 239.90/46.53  | 
% 239.90/46.53  | ALPHA: (1) implies:
% 239.90/46.53  |   (5)   ~ (all_48_1 = e3)
% 239.90/46.53  |   (6)  op(e2, e0) = all_48_1
% 239.90/46.53  | 
% 239.90/46.53  | BETA: splitting (3) gives:
% 239.90/46.53  | 
% 239.90/46.53  | Case 1:
% 239.90/46.53  | | 
% 239.90/46.53  | |   (7)   ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 239.90/46.53  | |        all_14_1 & $i(all_14_0) & $i(all_14_1)
% 239.90/46.53  | | 
% 239.90/46.53  | | ALPHA: (7) implies:
% 239.90/46.53  | |   (8)  op(e2, e0) = all_14_1
% 239.90/46.53  | | 
% 239.90/46.53  | | REF_CLOSE: (2), (4), (5), (6), (8) are inconsistent by sub-proof #1632.
% 239.90/46.53  | | 
% 239.90/46.53  | Case 2:
% 239.90/46.53  | | 
% 239.90/46.53  | |   (9)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 239.90/46.53  | | 
% 239.90/46.53  | | ALPHA: (9) implies:
% 239.90/46.53  | |   (10)  op(e2, e0) = all_14_1
% 239.90/46.53  | | 
% 239.90/46.53  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #1632.
% 239.90/46.53  | | 
% 239.90/46.53  | End of split
% 239.90/46.53  | 
% 239.90/46.53  End of proof
% 239.90/46.53  
% 239.90/46.53  Sub-proof #130 shows that the following formulas are inconsistent:
% 239.90/46.53  ----------------------------------------------------------------
% 239.90/46.53    (1)  op(e2, e3) = all_56_3
% 239.90/46.53    (2)   ~ (e3 = e2)
% 239.90/46.53    (3)  op(e2, e2) = all_8_2
% 239.90/46.53    (4)  op(e2, all_56_3) = e2
% 239.90/46.53    (5)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 239.90/46.53    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.53    (7)   ~ (all_8_2 = e3)
% 239.90/46.53  
% 239.90/46.53  Begin of proof
% 239.90/46.53  | 
% 239.90/46.53  | BETA: splitting (5) gives:
% 239.90/46.53  | 
% 239.90/46.53  | Case 1:
% 239.90/46.53  | | 
% 239.90/46.53  | |   (8)  all_58_2 = e3 & op(e2, e3) = e3
% 239.90/46.53  | | 
% 239.90/46.53  | | ALPHA: (8) implies:
% 239.90/46.53  | |   (9)  op(e2, e3) = e3
% 239.90/46.53  | | 
% 239.90/46.53  | | REF_CLOSE: (1), (2), (4), (6), (9) are inconsistent by sub-proof #2262.
% 239.90/46.53  | | 
% 239.90/46.53  | Case 2:
% 239.90/46.53  | | 
% 239.90/46.53  | |   (10)  all_58_3 = e3 & op(e2, e2) = e3
% 239.90/46.53  | | 
% 239.90/46.53  | | REF_CLOSE: (3), (6), (7), (10) are inconsistent by sub-proof #450.
% 239.90/46.53  | | 
% 239.90/46.53  | End of split
% 239.90/46.53  | 
% 239.90/46.53  End of proof
% 239.90/46.53  
% 239.90/46.53  Sub-proof #131 shows that the following formulas are inconsistent:
% 239.90/46.53  ----------------------------------------------------------------
% 239.90/46.53    (1)   ~ (all_52_7 = e2)
% 239.90/46.53    (2)  all_54_13 = all_52_7
% 239.90/46.53    (3)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 239.90/46.53    (4)   ~ (all_52_7 = e1)
% 239.90/46.53    (5)  all_56_1 = e2
% 239.90/46.53    (6)  op(e3, e2) = all_52_4
% 239.90/46.53    (7)   ~ (all_52_7 = e0)
% 239.90/46.53    (8)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 239.90/46.53    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.53    (10)   ~ (all_52_4 = all_52_7)
% 239.90/46.53  
% 239.90/46.53  Begin of proof
% 239.90/46.53  | 
% 239.90/46.53  | ALPHA: (3) implies:
% 239.90/46.53  |   (11)  op(e3, all_56_1) = e3
% 239.90/46.53  | 
% 239.90/46.53  | REDUCE: (5), (11) imply:
% 239.90/46.53  |   (12)  op(e3, e2) = e3
% 239.90/46.53  | 
% 239.90/46.53  | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (12) are inconsistent by
% 239.90/46.53  |            sub-proof #456.
% 239.90/46.53  | 
% 239.90/46.53  End of proof
% 239.90/46.53  
% 239.90/46.53  Sub-proof #132 shows that the following formulas are inconsistent:
% 239.90/46.53  ----------------------------------------------------------------
% 239.90/46.53    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 239.90/46.53    (2)  op(e2, e1) = e2
% 239.90/46.53    (3)  op(e3, e1) = all_52_8
% 239.90/46.53    (4)   ~ (e3 = e2)
% 239.90/46.53    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.53    (6)   ~ (all_52_8 = e3)
% 239.90/46.53  
% 239.90/46.53  Begin of proof
% 239.90/46.53  | 
% 239.90/46.53  | BETA: splitting (1) gives:
% 239.90/46.53  | 
% 239.90/46.53  | Case 1:
% 239.90/46.53  | | 
% 239.90/46.53  | |   (7)  all_58_4 = e3 & op(e3, e1) = e3
% 239.90/46.53  | | 
% 239.90/46.53  | | ALPHA: (7) implies:
% 239.90/46.53  | |   (8)  op(e3, e1) = e3
% 239.90/46.53  | | 
% 239.90/46.53  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2260.
% 239.90/46.53  | | 
% 239.90/46.53  | Case 2:
% 239.90/46.53  | | 
% 239.90/46.53  | |   (9)  all_58_5 = e3 & op(e2, e1) = e3
% 239.90/46.53  | | 
% 239.90/46.53  | | ALPHA: (9) implies:
% 239.90/46.53  | |   (10)  op(e2, e1) = e3
% 239.90/46.53  | | 
% 239.90/46.53  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #2256.
% 239.90/46.53  | | 
% 239.90/46.53  | End of split
% 239.90/46.53  | 
% 239.90/46.53  End of proof
% 239.90/46.53  
% 239.90/46.53  Sub-proof #133 shows that the following formulas are inconsistent:
% 239.90/46.53  ----------------------------------------------------------------
% 239.90/46.53    (1)  op(e3, e2) = all_56_9
% 239.90/46.53    (2)  op(e3, all_56_9) = e3
% 239.90/46.53    (3)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 239.90/46.53           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 239.90/46.53           all_24_1 & $i(all_24_1))
% 239.90/46.53    (4)  op(e3, e2) = all_32_1
% 239.90/46.53    (5)   ~ (e3 = e2)
% 239.90/46.53    (6)  op(e3, e3) = e2
% 239.90/46.53    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.53    (8)  op(e3, e2) = e3
% 239.90/46.53  
% 239.90/46.53  Begin of proof
% 239.90/46.53  | 
% 239.90/46.53  | BETA: splitting (3) gives:
% 239.90/46.53  | 
% 239.90/46.53  | Case 1:
% 239.90/46.53  | | 
% 239.90/46.53  | |   (9)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) =
% 239.90/46.53  | |        all_24_1 & $i(all_24_0) & $i(all_24_1)
% 239.90/46.53  | | 
% 239.90/46.53  | | ALPHA: (9) implies:
% 239.90/46.53  | |   (10)  op(e3, e2) = all_24_1
% 239.90/46.53  | | 
% 239.90/46.53  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10) are inconsistent by
% 239.90/46.53  | |            sub-proof #134.
% 239.90/46.53  | | 
% 239.90/46.53  | Case 2:
% 239.90/46.53  | | 
% 239.90/46.53  | |   (11)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 & $i(all_24_1)
% 239.90/46.53  | | 
% 239.90/46.53  | | ALPHA: (11) implies:
% 239.90/46.53  | |   (12)  op(e3, e2) = all_24_1
% 239.90/46.53  | | 
% 239.90/46.53  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (12) are inconsistent by
% 239.90/46.53  | |            sub-proof #134.
% 239.90/46.53  | | 
% 239.90/46.53  | End of split
% 239.90/46.53  | 
% 239.90/46.53  End of proof
% 239.90/46.53  
% 239.90/46.53  Sub-proof #134 shows that the following formulas are inconsistent:
% 239.90/46.53  ----------------------------------------------------------------
% 239.90/46.53    (1)  op(e3, e2) = all_56_9
% 239.90/46.53    (2)  op(e3, all_56_9) = e3
% 239.90/46.53    (3)  op(e3, e2) = all_32_1
% 239.90/46.53    (4)   ~ (e3 = e2)
% 239.90/46.53    (5)  op(e3, e2) = all_24_1
% 239.90/46.53    (6)  op(e3, e3) = e2
% 239.90/46.53    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.53    (8)  op(e3, e2) = e3
% 239.90/46.53  
% 239.90/46.53  Begin of proof
% 239.90/46.53  | 
% 239.90/46.53  | GROUND_INST: instantiating (7) with all_32_1, all_56_9, e2, e3, simplifying
% 239.90/46.53  |              with (1), (3) gives:
% 239.90/46.53  |   (9)  all_56_9 = all_32_1
% 239.90/46.53  | 
% 239.90/46.53  | GROUND_INST: instantiating (7) with all_24_1, all_56_9, e2, e3, simplifying
% 239.90/46.53  |              with (1), (5) gives:
% 239.90/46.53  |   (10)  all_56_9 = all_24_1
% 239.90/46.53  | 
% 239.90/46.53  | GROUND_INST: instantiating (7) with e3, all_56_9, e2, e3, simplifying with
% 239.90/46.53  |              (1), (8) gives:
% 239.90/46.53  |   (11)  all_56_9 = e3
% 239.90/46.53  | 
% 239.90/46.53  | COMBINE_EQS: (9), (10) imply:
% 239.90/46.53  |   (12)  all_32_1 = all_24_1
% 239.90/46.53  | 
% 239.90/46.53  | COMBINE_EQS: (9), (11) imply:
% 239.90/46.53  |   (13)  all_32_1 = e3
% 239.90/46.53  | 
% 239.90/46.53  | COMBINE_EQS: (12), (13) imply:
% 239.90/46.53  |   (14)  all_24_1 = e3
% 239.90/46.53  | 
% 239.90/46.53  | REDUCE: (2), (11) imply:
% 239.90/46.53  |   (15)  op(e3, e3) = e3
% 239.90/46.53  | 
% 239.90/46.53  | REF_CLOSE: (4), (6), (7), (15) are inconsistent by sub-proof #2194.
% 239.90/46.53  | 
% 239.90/46.53  End of proof
% 239.90/46.53  
% 239.90/46.53  Sub-proof #135 shows that the following formulas are inconsistent:
% 239.90/46.53  ----------------------------------------------------------------
% 239.90/46.53    (1)   ~ (all_52_9 = all_6_2)
% 239.90/46.53    (2)   ~ (all_52_7 = e2)
% 239.90/46.53    (3)   ~ (all_52_8 = all_6_2)
% 239.90/46.53    (4)  op(e1, e2) = all_52_6
% 239.90/46.53    (5)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 239.90/46.53           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 239.90/46.53             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 239.90/46.53           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.90/46.53             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.90/46.53           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.90/46.53           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.90/46.53           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.90/46.53           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 239.90/46.53           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.90/46.53           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.90/46.53             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.90/46.53           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.90/46.53           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 239.90/46.53           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.90/46.53           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 239.90/46.53           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.90/46.53           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.90/46.53             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.90/46.53           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.90/46.53           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 239.90/46.53           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.90/46.53           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 239.90/46.53           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.90/46.53           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.90/46.53             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.90/46.53           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.90/46.53           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.90/46.53    (6)  op(e1, e1) = all_6_2
% 239.90/46.53    (7)  op(e1, e0) = all_52_14
% 239.90/46.53    (8)  op(e0, e3) = all_52_3
% 239.90/46.53    (9)   ~ (all_52_6 = e0)
% 239.90/46.53    (10)   ~ (all_52_2 = all_52_3)
% 239.90/46.53    (11)   ~ (all_52_12 = all_52_14)
% 239.90/46.53    (12)  all_54_10 = all_6_2
% 239.90/46.53    (13)   ~ (all_6_2 = e3)
% 239.90/46.53    (14)  op(e3, e1) = all_52_8
% 239.90/46.53    (15)  op(e2, e1) = all_52_9
% 239.90/46.53    (16)   ~ (all_52_14 = all_6_2)
% 239.90/46.53    (17)   ~ (all_6_2 = e0)
% 239.90/46.53    (18)  all_56_31 = e2
% 239.90/46.53    (19)  op(e3, e0) = all_52_12
% 239.90/46.53    (20)  all_56_11 = e0
% 239.90/46.53    (21)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 239.90/46.53    (22)  op(e0, e2) = all_52_7
% 239.90/46.53    (23)  op(e3, e2) = all_52_4
% 239.90/46.53    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.53            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.53    (25)  op(e1, e3) = all_52_2
% 239.90/46.54    (26)   ~ (all_52_6 = all_52_7)
% 239.90/46.54    (27)  all_56_21 = all_6_2
% 239.90/46.54    (28)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.90/46.54          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.90/46.54    (29)  op(e2, e0) = all_52_13
% 239.90/46.54    (30)   ~ (all_52_9 = e1)
% 239.90/46.54    (31)   ~ (all_52_13 = e0)
% 239.90/46.54    (32)   ~ (all_52_4 = all_52_6)
% 239.90/46.54    (33)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 239.90/46.54              e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 239.90/46.54            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 239.90/46.54              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 239.90/46.54              e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 239.90/46.54            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 239.90/46.54            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 239.90/46.54            = e2)
% 239.90/46.54  
% 239.90/46.54  Begin of proof
% 239.90/46.54  | 
% 239.90/46.54  | BETA: splitting (33) gives:
% 239.90/46.54  | 
% 239.90/46.54  | Case 1:
% 239.90/46.54  | | 
% 239.90/46.54  | |   (34)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 239.90/46.54  | |           = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) =
% 239.90/46.54  | |         e2 & op(e1, e2) = e2
% 239.90/46.54  | | 
% 239.90/46.54  | | ALPHA: (34) implies:
% 239.90/46.54  | |   (35)  op(e1, e2) = e2
% 239.90/46.54  | |   (36)  op(e2, e1) = e2
% 239.90/46.54  | | 
% 239.90/46.54  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 239.90/46.54  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 239.90/46.54  | |            (25), (26), (27), (28), (29), (31), (32), (35), (36) are
% 239.90/46.54  | |            inconsistent by sub-proof #136.
% 239.90/46.54  | | 
% 239.90/46.54  | Case 2:
% 239.90/46.54  | | 
% 239.90/46.54  | |   (37)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.90/46.54  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 239.90/46.54  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 239.90/46.54  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 239.90/46.54  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.90/46.54  | | 
% 239.90/46.54  | | REF_CLOSE: (2), (15), (22), (24), (30), (37) are inconsistent by sub-proof
% 239.90/46.54  | |            #2305.
% 239.90/46.54  | | 
% 239.90/46.54  | End of split
% 239.90/46.54  | 
% 239.90/46.54  End of proof
% 239.90/46.54  
% 239.90/46.54  Sub-proof #136 shows that the following formulas are inconsistent:
% 239.90/46.54  ----------------------------------------------------------------
% 239.90/46.54    (1)   ~ (all_52_9 = all_6_2)
% 239.90/46.54    (2)   ~ (all_52_8 = all_6_2)
% 239.90/46.54    (3)  op(e1, e2) = all_52_6
% 239.90/46.54    (4)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 239.90/46.54           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 239.90/46.54             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 239.90/46.54           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.90/46.54             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.90/46.54           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.90/46.54           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.90/46.54           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.90/46.54           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 239.90/46.54           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.90/46.54           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.90/46.54             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.90/46.54           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.90/46.54           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 239.90/46.54           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.90/46.54           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 239.90/46.54           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.90/46.54           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.90/46.54             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.90/46.54           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.90/46.54           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 239.90/46.54           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.90/46.54           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 239.90/46.54           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.90/46.54           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.90/46.54             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.90/46.54           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.90/46.54           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.90/46.54    (5)  op(e1, e1) = all_6_2
% 239.90/46.54    (6)  op(e1, e0) = all_52_14
% 239.90/46.54    (7)  op(e0, e3) = all_52_3
% 239.90/46.54    (8)   ~ (all_52_6 = e0)
% 239.90/46.54    (9)   ~ (all_52_2 = all_52_3)
% 239.90/46.54    (10)   ~ (all_52_12 = all_52_14)
% 239.90/46.54    (11)  all_54_10 = all_6_2
% 239.90/46.54    (12)  op(e2, e1) = e2
% 239.90/46.54    (13)   ~ (all_6_2 = e3)
% 239.90/46.54    (14)  op(e3, e1) = all_52_8
% 239.90/46.54    (15)  op(e2, e1) = all_52_9
% 239.90/46.54    (16)   ~ (all_52_14 = all_6_2)
% 239.90/46.54    (17)   ~ (all_6_2 = e0)
% 239.90/46.54    (18)  all_56_31 = e2
% 239.90/46.54    (19)  op(e3, e0) = all_52_12
% 239.90/46.54    (20)  all_56_11 = e0
% 239.90/46.54    (21)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 239.90/46.54    (22)  op(e1, e2) = e2
% 239.90/46.54    (23)  op(e0, e2) = all_52_7
% 239.90/46.54    (24)  op(e3, e2) = all_52_4
% 239.90/46.54    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.90/46.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.90/46.54    (26)  op(e1, e3) = all_52_2
% 239.90/46.54    (27)   ~ (all_52_6 = all_52_7)
% 239.90/46.54    (28)  all_56_21 = all_6_2
% 239.90/46.54    (29)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 239.90/46.54          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 239.90/46.54    (30)  op(e2, e0) = all_52_13
% 239.90/46.54    (31)   ~ (all_52_13 = e0)
% 239.90/46.54    (32)   ~ (all_52_4 = all_52_6)
% 239.90/46.54  
% 239.90/46.54  Begin of proof
% 239.90/46.54  | 
% 239.90/46.54  | GROUND_INST: instantiating (25) with all_52_6, e2, e2, e1, simplifying with
% 239.90/46.54  |              (3), (22) gives:
% 239.90/46.54  |   (33)  all_52_6 = e2
% 239.90/46.54  | 
% 239.90/46.54  | GROUND_INST: instantiating (25) with all_52_9, e2, e1, e2, simplifying with
% 239.90/46.54  |              (12), (15) gives:
% 239.90/46.54  |   (34)  all_52_9 = e2
% 239.90/46.54  | 
% 239.90/46.54  | REDUCE: (32), (33) imply:
% 239.90/46.54  |   (35)   ~ (all_52_4 = e2)
% 239.90/46.54  | 
% 239.90/46.54  | REDUCE: (27), (33) imply:
% 239.90/46.54  |   (36)   ~ (all_52_7 = e2)
% 239.90/46.54  | 
% 239.90/46.54  | SIMP: (36) implies:
% 239.90/46.54  |   (37)   ~ (all_52_7 = e2)
% 239.90/46.54  | 
% 239.90/46.54  | REDUCE: (1), (34) imply:
% 239.90/46.54  |   (38)   ~ (all_6_2 = e2)
% 239.90/46.54  | 
% 239.90/46.54  | SIMP: (38) implies:
% 239.90/46.54  |   (39)   ~ (all_6_2 = e2)
% 239.90/46.54  | 
% 239.90/46.54  | BETA: splitting (21) gives:
% 239.90/46.54  | 
% 239.90/46.54  | Case 1:
% 239.90/46.54  | | 
% 239.90/46.54  | |   (40)  all_54_10 = e3
% 239.90/46.54  | | 
% 239.90/46.54  | | REF_CLOSE: (11), (13), (40) are inconsistent by sub-proof #2313.
% 239.90/46.54  | | 
% 239.90/46.54  | Case 2:
% 239.90/46.54  | | 
% 239.90/46.54  | |   (41)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 239.90/46.54  | | 
% 239.90/46.54  | | BETA: splitting (41) gives:
% 239.90/46.54  | | 
% 239.90/46.54  | | Case 1:
% 239.90/46.54  | | | 
% 239.90/46.54  | | |   (42)  all_54_10 = e2
% 239.90/46.54  | | | 
% 239.90/46.54  | | | REF_CLOSE: (11), (39), (42) are inconsistent by sub-proof #2312.
% 239.90/46.54  | | | 
% 239.90/46.54  | | Case 2:
% 239.90/46.54  | | | 
% 239.90/46.54  | | |   (43)   ~ (all_54_10 = e2)
% 239.90/46.54  | | |   (44)  all_54_10 = e1 | all_54_10 = e0
% 239.90/46.54  | | | 
% 239.90/46.54  | | | BETA: splitting (44) gives:
% 239.90/46.54  | | | 
% 239.90/46.54  | | | Case 1:
% 239.90/46.54  | | | | 
% 239.90/46.54  | | | |   (45)  all_54_10 = e1
% 239.90/46.54  | | | | 
% 239.90/46.54  | | | | COMBINE_EQS: (11), (45) imply:
% 239.90/46.54  | | | |   (46)  all_6_2 = e1
% 239.90/46.54  | | | | 
% 239.90/46.54  | | | | SIMP: (46) implies:
% 239.90/46.54  | | | |   (47)  all_6_2 = e1
% 239.90/46.54  | | | | 
% 239.90/46.54  | | | | COMBINE_EQS: (28), (47) imply:
% 239.90/46.54  | | | |   (48)  all_56_21 = e1
% 239.90/46.54  | | | | 
% 239.90/46.54  | | | | REDUCE: (2), (47) imply:
% 239.90/46.54  | | | |   (49)   ~ (all_52_8 = e1)
% 239.90/46.54  | | | | 
% 239.90/46.54  | | | | REDUCE: (16), (47) imply:
% 239.90/46.54  | | | |   (50)   ~ (all_52_14 = e1)
% 239.90/46.54  | | | | 
% 239.90/46.54  | | | | REDUCE: (17), (47) imply:
% 239.90/46.54  | | | |   (51)   ~ (e1 = e0)
% 239.90/46.54  | | | | 
% 239.90/46.54  | | | | REDUCE: (5), (47) imply:
% 239.90/46.54  | | | |   (52)  op(e1, e1) = e1
% 239.90/46.54  | | | | 
% 239.90/46.54  | | | | BETA: splitting (4) gives:
% 239.90/46.54  | | | | 
% 239.90/46.54  | | | | Case 1:
% 239.90/46.54  | | | | | 
% 239.90/46.54  | | | | |   (53)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 239.90/46.54  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 239.90/46.54  | | | | |           & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 &
% 239.90/46.54  | | | | |           all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.90/46.54  | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 239.90/46.54  | | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 239.90/46.54  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 239.90/46.54  | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 239.90/46.54  | | | | |         (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 239.90/46.54  | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 239.90/46.54  | | | | |           & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 239.90/46.54  | | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.90/46.54  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 239.90/46.54  | | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.90/46.54  | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 239.90/46.54  | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.90/46.54  | | | | | 
% 239.90/46.54  | | | | | BETA: splitting (53) gives:
% 239.90/46.54  | | | | | 
% 239.90/46.54  | | | | | Case 1:
% 239.90/46.54  | | | | | | 
% 239.90/46.54  | | | | | |   (54)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 239.90/46.54  | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 239.90/46.54  | | | | | |             e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 =
% 239.90/46.54  | | | | | |           e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 239.90/46.54  | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.90/46.54  | | | | | |             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17
% 239.90/46.54  | | | | | |           = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.90/46.54  | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 239.90/46.54  | | | | | |           op(e1, e3) = e3)
% 239.90/46.54  | | | | | | 
% 239.90/46.54  | | | | | | REF_CLOSE: (18), (24), (25), (35), (48), (54) are inconsistent by
% 239.90/46.54  | | | | | |            sub-proof #244.
% 239.90/46.54  | | | | | | 
% 239.90/46.54  | | | | | Case 2:
% 239.90/46.54  | | | | | | 
% 239.90/46.54  | | | | | |   (55)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 239.90/46.54  | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 239.90/46.54  | | | | | |             e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 =
% 239.90/46.54  | | | | | |           e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 239.90/46.54  | | | | | |             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.90/46.54  | | | | | |             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 239.90/46.54  | | | | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.90/46.54  | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 239.90/46.54  | | | | | |           op(e0, e3) = e0)
% 239.90/46.54  | | | | | | 
% 239.90/46.54  | | | | | | BETA: splitting (55) gives:
% 239.90/46.54  | | | | | | 
% 239.90/46.54  | | | | | | Case 1:
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | |   (56)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 239.90/46.54  | | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 239.90/46.54  | | | | | | |           e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | | ALPHA: (56) implies:
% 239.90/46.54  | | | | | | |   (57)  op(e3, e1) = e1
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | | REF_CLOSE: (14), (25), (49), (57) are inconsistent by sub-proof
% 239.90/46.54  | | | | | | |            #2309.
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | Case 2:
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | |   (58)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.90/46.54  | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 239.90/46.54  | | | | | | |             e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 239.90/46.54  | | | | | | |           e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 239.90/46.54  | | | | | | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.90/46.54  | | | | | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | | BETA: splitting (58) gives:
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | | Case 1:
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | |   (59)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.90/46.54  | | | | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 239.90/46.54  | | | | | | | |           e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | | ALPHA: (59) implies:
% 239.90/46.54  | | | | | | | |   (60)   ~ (all_56_11 = e0)
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | | REDUCE: (20), (60) imply:
% 239.90/46.54  | | | | | | | |   (61)  $false
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | | CLOSE: (61) is inconsistent.
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | Case 2:
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | |   (62)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 239.90/46.54  | | | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 239.90/46.54  | | | | | | | |           e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | | ALPHA: (62) implies:
% 239.90/46.54  | | | | | | | |   (63)  op(e0, e3) = e0
% 239.90/46.54  | | | | | | | |   (64)  op(e3, e0) = e0
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | | GROUND_INST: instantiating (25) with all_52_3, e0, e3, e0,
% 239.90/46.54  | | | | | | | |              simplifying with (7), (63) gives:
% 239.90/46.54  | | | | | | | |   (65)  all_52_3 = e0
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | | GROUND_INST: instantiating (25) with all_52_12, e0, e0, e3,
% 239.90/46.54  | | | | | | | |              simplifying with (19), (64) gives:
% 239.90/46.54  | | | | | | | |   (66)  all_52_12 = e0
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | | REDUCE: (9), (65) imply:
% 239.90/46.54  | | | | | | | |   (67)   ~ (all_52_2 = e0)
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | | REDUCE: (10), (66) imply:
% 239.90/46.54  | | | | | | | |   (68)   ~ (all_52_14 = e0)
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | | SIMP: (68) implies:
% 239.90/46.54  | | | | | | | |   (69)   ~ (all_52_14 = e0)
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | | REF_CLOSE: (3), (6), (8), (25), (26), (29), (51), (52), (67),
% 239.90/46.54  | | | | | | | |            (69) are inconsistent by sub-proof #2020.
% 239.90/46.54  | | | | | | | | 
% 239.90/46.54  | | | | | | | End of split
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | End of split
% 239.90/46.54  | | | | | | 
% 239.90/46.54  | | | | | End of split
% 239.90/46.54  | | | | | 
% 239.90/46.54  | | | | Case 2:
% 239.90/46.54  | | | | | 
% 239.90/46.54  | | | | |   (70)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 239.90/46.54  | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 239.90/46.54  | | | | |           & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 239.90/46.54  | | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 239.90/46.54  | | | | |           ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 239.90/46.54  | | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.90/46.54  | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 239.90/46.54  | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 239.90/46.54  | | | | |         (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 239.90/46.54  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 239.90/46.54  | | | | |           & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 239.90/46.54  | | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 239.90/46.54  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 239.90/46.54  | | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.90/46.54  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 239.90/46.54  | | | | |           &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.90/46.54  | | | | | 
% 239.90/46.54  | | | | | BETA: splitting (70) gives:
% 239.90/46.54  | | | | | 
% 239.90/46.54  | | | | | Case 1:
% 239.90/46.54  | | | | | | 
% 239.90/46.54  | | | | | |   (71)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 239.90/46.54  | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 239.90/46.54  | | | | | |             e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 =
% 239.90/46.54  | | | | | |           e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.90/46.54  | | | | | |             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.90/46.54  | | | | | |             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 239.90/46.54  | | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0)
% 239.90/46.54  | | | | | |           &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) =
% 239.90/46.54  | | | | | |           e2 & op(e0, e2) = e2)
% 239.90/46.54  | | | | | | 
% 239.90/46.54  | | | | | | BETA: splitting (71) gives:
% 239.90/46.54  | | | | | | 
% 239.90/46.54  | | | | | | Case 1:
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | |   (72)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 239.90/46.54  | | | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 239.90/46.54  | | | | | | |           e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | | ALPHA: (72) implies:
% 239.90/46.54  | | | | | | |   (73)   ~ (all_56_21 = e1)
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | | REDUCE: (48), (73) imply:
% 239.90/46.54  | | | | | | |   (74)  $false
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | | CLOSE: (74) is inconsistent.
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | Case 2:
% 239.90/46.54  | | | | | | | 
% 239.90/46.54  | | | | | | |   (75)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.90/46.55  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 239.90/46.55  | | | | | | |             e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 239.90/46.55  | | | | | | |           = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 239.90/46.55  | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 239.90/46.55  | | | | | | |             e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 239.90/46.55  | | | | | | | 
% 239.90/46.55  | | | | | | | BETA: splitting (75) gives:
% 239.90/46.55  | | | | | | | 
% 239.90/46.55  | | | | | | | Case 1:
% 239.90/46.55  | | | | | | | | 
% 239.90/46.55  | | | | | | | |   (76)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) & 
% 239.90/46.55  | | | | | | | |         ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 239.90/46.55  | | | | | | | |           = e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 239.90/46.55  | | | | | | | | 
% 239.90/46.55  | | | | | | | | ALPHA: (76) implies:
% 239.90/46.55  | | | | | | | |   (77)  op(e2, e1) = e1
% 239.90/46.55  | | | | | | | | 
% 239.90/46.55  | | | | | | | | REF_CLOSE: (1), (11), (15), (17), (25), (39), (41), (77) are
% 239.90/46.55  | | | | | | | |            inconsistent by sub-proof #1730.
% 239.90/46.55  | | | | | | | | 
% 239.90/46.55  | | | | | | | Case 2:
% 239.90/46.55  | | | | | | | | 
% 239.90/46.55  | | | | | | | |   (78)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) & 
% 239.90/46.55  | | | | | | | |         ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31
% 239.90/46.55  | | | | | | | |           = e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 239.90/46.55  | | | | | | | | 
% 239.90/46.55  | | | | | | | | ALPHA: (78) implies:
% 239.90/46.55  | | | | | | | |   (79)  op(e0, e2) = e2
% 239.90/46.55  | | | | | | | | 
% 239.90/46.55  | | | | | | | | REF_CLOSE: (23), (25), (37), (79) are inconsistent by sub-proof
% 239.90/46.55  | | | | | | | |            #2327.
% 239.90/46.55  | | | | | | | | 
% 239.90/46.55  | | | | | | | End of split
% 239.90/46.55  | | | | | | | 
% 239.90/46.55  | | | | | | End of split
% 239.90/46.55  | | | | | | 
% 239.90/46.55  | | | | | Case 2:
% 239.90/46.55  | | | | | | 
% 239.90/46.55  | | | | | |   (80)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 239.90/46.55  | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 239.90/46.55  | | | | | |             e2) & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 =
% 239.90/46.55  | | | | | |           e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 239.90/46.55  | | | | | |             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.90/46.55  | | | | | |             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 239.90/46.55  | | | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1)
% 239.90/46.55  | | | | | |           &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) =
% 239.90/46.55  | | | | | |           e0 & op(e0, e1) = e0)
% 239.90/46.55  | | | | | | 
% 239.90/46.55  | | | | | | REF_CLOSE: (6), (25), (30), (31), (48), (50), (80) are inconsistent
% 239.90/46.55  | | | | | |            by sub-proof #1250.
% 239.90/46.55  | | | | | | 
% 239.90/46.55  | | | | | End of split
% 239.90/46.55  | | | | | 
% 239.90/46.55  | | | | End of split
% 239.90/46.55  | | | | 
% 239.90/46.55  | | | Case 2:
% 239.90/46.55  | | | | 
% 239.90/46.55  | | | |   (81)  all_54_10 = e0
% 239.90/46.55  | | | | 
% 239.90/46.55  | | | | REF_CLOSE: (11), (17), (81) are inconsistent by sub-proof #2303.
% 239.90/46.55  | | | | 
% 239.90/46.55  | | | End of split
% 239.90/46.55  | | | 
% 239.90/46.55  | | End of split
% 239.90/46.55  | | 
% 239.90/46.55  | End of split
% 239.90/46.55  | 
% 239.90/46.55  End of proof
% 239.90/46.55  
% 239.90/46.55  Sub-proof #137 shows that the following formulas are inconsistent:
% 239.90/46.55  ----------------------------------------------------------------
% 239.90/46.55    (1)   ~ (all_52_3 = e0)
% 239.90/46.55    (2)   ~ (all_52_1 = all_52_3)
% 239.90/46.55    (3)   ~ (all_52_6 = all_8_2)
% 239.90/46.55    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.90/46.55         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.90/46.55    (5)   ~ (all_52_9 = all_8_2)
% 239.90/46.55    (6)   ~ (all_8_2 = e0)
% 239.90/46.55    (7)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.90/46.55    (8)  all_22_2 = all_8_2
% 239.90/46.55    (9)  op(e0, e1) = all_52_11
% 239.90/46.55    (10)   ~ (all_52_8 = all_52_9)
% 239.90/46.55    (11)   ~ (e2 = e0)
% 239.90/46.55    (12)   ~ (all_52_11 = e2)
% 239.90/46.55    (13)  op(e1, e2) = all_52_6
% 239.90/46.55    (14)   ~ (all_52_1 = all_8_2)
% 239.90/46.55    (15)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.90/46.55              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.90/46.55            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.90/46.55            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.90/46.55            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 239.90/46.55             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.90/46.55            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.90/46.55            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.90/46.55            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.90/46.55            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.90/46.55            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.90/46.55              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.90/46.55            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.90/46.55            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 239.90/46.55            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.90/46.55            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 239.90/46.55            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.90/46.55            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.90/46.55              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.90/46.55            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.90/46.55            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.90/46.55            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.90/46.55            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 239.90/46.55            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.90/46.55            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.90/46.55              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.90/46.55            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.90/46.55            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.90/46.55    (16)   ~ (all_52_12 = e0)
% 239.90/46.55    (17)   ~ (all_52_1 = all_52_2)
% 239.90/46.55    (18)  op(e1, e0) = all_52_14
% 239.90/46.55    (19)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.90/46.55    (20)   ~ (all_52_8 = e0)
% 239.90/46.55    (21)  op(e0, e3) = all_52_3
% 239.90/46.55    (22)   ~ (all_52_6 = e0)
% 239.90/46.55    (23)  all_54_11 = all_52_14
% 239.90/46.55    (24)   ~ (all_52_12 = all_52_14)
% 239.90/46.55    (25)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.90/46.55          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.90/46.55    (26)  op(e0, e2) = all_4_1
% 239.90/46.55    (27)  all_54_2 = all_52_8
% 239.90/46.55    (28)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 239.90/46.55    (29)   ~ (all_52_2 = all_52_14)
% 239.90/46.55    (30)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.90/46.55    (31)  all_56_21 = e0
% 239.90/46.55    (32)  all_54_4 = all_52_1
% 239.90/46.55    (33)   ~ (all_52_14 = e2)
% 239.90/46.55    (34)   ~ (all_52_8 = all_52_12)
% 239.90/46.55    (35)  op(e3, e1) = all_52_8
% 239.90/46.55    (36)  op(e2, e1) = all_52_9
% 239.90/46.55    (37)  all_54_9 = all_52_6
% 239.90/46.55    (38)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.90/46.55          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.90/46.55    (39)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.90/46.55            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 239.90/46.55              e2) = all_44_1 & $i(all_44_1))
% 239.90/46.55    (40)   ~ (all_52_4 = all_8_2)
% 239.90/46.55    (41)  all_56_31 = e2
% 239.90/46.55    (42)   ~ (all_52_14 = e0)
% 239.90/46.55    (43)   ~ (all_22_2 = e1) | ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 239.90/46.55            op(e2, e1) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 239.90/46.55              e0) & op(e2, e1) = all_22_1 & $i(all_22_1))
% 239.90/46.55    (44)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 239.90/46.55    (45)  op(e2, e0) = e0
% 239.90/46.55    (46)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.90/46.55    (47)  op(e3, e0) = all_52_12
% 239.90/46.55    (48)   ~ (all_52_1 = e0)
% 239.90/46.55    (49)   ~ (all_52_4 = all_52_12)
% 239.90/46.55    (50)   ~ (all_52_6 = all_52_14)
% 239.90/46.55    (51)  all_54_5 = all_8_2
% 239.90/46.55    (52)  op(e2, e3) = all_52_1
% 239.90/46.55    (53)   ~ (all_52_12 = e2)
% 239.90/46.55    (54)  op(e0, e2) = e0
% 239.90/46.55    (55)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.90/46.55          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.90/46.55    (56)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 239.90/46.55    (57)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.90/46.55    (58)   ~ (all_52_2 = e0)
% 239.90/46.55    (59)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.90/46.55          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.90/46.55    (60)  all_54_1 = all_52_4
% 239.90/46.55    (61)  op(e3, e2) = all_52_4
% 239.90/46.55    (62)   ~ (all_52_8 = all_52_11)
% 239.90/46.55    (63)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.90/46.55          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.90/46.55    (64)  all_54_8 = all_52_2
% 239.90/46.55    (65)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.90/46.55          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.90/46.55    (66)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.90/46.55          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.90/46.55    (67)   ~ (all_52_2 = all_52_6)
% 239.90/46.55    (68)  all_54_3 = all_52_12
% 239.98/46.55    (69)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.98/46.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.98/46.55    (70)  op(e1, e3) = all_52_2
% 239.98/46.55    (71)  op(e1, e1) = e0
% 239.98/46.55    (72)   ~ (all_8_2 = e3)
% 239.98/46.55    (73)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.98/46.55          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.98/46.55    (74)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.98/46.55          | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.98/46.55    (75)  op(e3, e3) = e0
% 239.98/46.55    (76)  all_56_11 = all_8_2
% 239.98/46.55    (77)  op(e2, e0) = all_52_13
% 239.98/46.55    (78)   ~ (all_52_4 = all_52_8)
% 239.98/46.55    (79)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.98/46.55          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.98/46.55    (80)   ~ (all_52_4 = all_52_6)
% 239.98/46.55    (81)   ~ (all_52_4 = e0)
% 239.98/46.55  
% 239.98/46.55  Begin of proof
% 239.98/46.55  | 
% 239.98/46.55  | GROUND_INST: instantiating (69) with e0, all_4_1, e2, e0, simplifying with
% 239.98/46.55  |              (26), (54) gives:
% 239.98/46.55  |   (82)  all_4_1 = e0
% 239.98/46.55  | 
% 239.98/46.55  | BETA: splitting (39) gives:
% 239.98/46.55  | 
% 239.98/46.55  | Case 1:
% 239.98/46.55  | | 
% 239.98/46.55  | |   (83)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 239.98/46.55  | |         all_44_1 & $i(all_44_0) & $i(all_44_1)
% 239.98/46.55  | | 
% 239.98/46.55  | | ALPHA: (83) implies:
% 239.98/46.55  | |   (84)  op(e0, e2) = all_44_1
% 239.98/46.55  | | 
% 239.98/46.55  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 239.98/46.55  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 239.98/46.55  | |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 239.98/46.55  | |            (36), (37), (38), (40), (41), (42), (43), (44), (45), (46), (47),
% 239.98/46.55  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 239.98/46.55  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 239.98/46.55  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 239.98/46.55  | |            (81), (84) are inconsistent by sub-proof #138.
% 239.98/46.55  | | 
% 239.98/46.55  | Case 2:
% 239.98/46.55  | | 
% 239.98/46.55  | |   (85)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 & $i(all_44_1)
% 239.98/46.55  | | 
% 239.98/46.55  | | ALPHA: (85) implies:
% 239.98/46.55  | |   (86)  op(e0, e2) = all_44_1
% 239.98/46.55  | | 
% 239.98/46.55  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 239.98/46.55  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 239.98/46.55  | |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 239.98/46.55  | |            (36), (37), (38), (40), (41), (42), (43), (44), (45), (46), (47),
% 239.98/46.55  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 239.98/46.55  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 239.98/46.55  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 239.98/46.55  | |            (81), (86) are inconsistent by sub-proof #138.
% 239.98/46.55  | | 
% 239.98/46.55  | End of split
% 239.98/46.55  | 
% 239.98/46.55  End of proof
% 239.98/46.55  
% 239.98/46.55  Sub-proof #138 shows that the following formulas are inconsistent:
% 239.98/46.55  ----------------------------------------------------------------
% 239.98/46.55    (1)   ~ (all_52_3 = e0)
% 239.98/46.55    (2)   ~ (all_52_1 = all_52_3)
% 239.98/46.55    (3)   ~ (all_52_6 = all_8_2)
% 239.98/46.55    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 239.98/46.55         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 239.98/46.55    (5)   ~ (all_52_9 = all_8_2)
% 239.98/46.55    (6)   ~ (all_8_2 = e0)
% 239.98/46.55    (7)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.98/46.55    (8)  all_22_2 = all_8_2
% 239.98/46.55    (9)  op(e0, e1) = all_52_11
% 239.98/46.55    (10)   ~ (all_52_8 = all_52_9)
% 239.98/46.55    (11)   ~ (e2 = e0)
% 239.98/46.55    (12)   ~ (all_52_11 = e2)
% 239.98/46.55    (13)  op(e1, e2) = all_52_6
% 239.98/46.55    (14)   ~ (all_52_1 = all_8_2)
% 239.98/46.55    (15)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 239.98/46.55              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.98/46.55            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 239.98/46.55            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.98/46.55            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 239.98/46.55             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.98/46.55            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 239.98/46.55            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.98/46.55            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 239.98/46.55            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.98/46.55            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 239.98/46.55              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.98/46.55            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 239.98/46.55            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 239.98/46.55            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 239.98/46.55            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 239.98/46.55            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 239.98/46.55            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 239.98/46.55              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 239.98/46.55            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.98/46.55            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 239.98/46.55            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 239.98/46.55            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 239.98/46.55            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 239.98/46.55            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 239.98/46.55              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 239.98/46.55            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.98/46.55            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 239.98/46.55    (16)   ~ (all_52_12 = e0)
% 239.98/46.55    (17)   ~ (all_52_1 = all_52_2)
% 239.98/46.55    (18)  op(e1, e0) = all_52_14
% 239.98/46.55    (19)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.98/46.55    (20)   ~ (all_52_8 = e0)
% 239.98/46.55    (21)  op(e0, e3) = all_52_3
% 239.98/46.55    (22)   ~ (all_52_6 = e0)
% 239.98/46.55    (23)  all_54_11 = all_52_14
% 239.98/46.55    (24)   ~ (all_52_12 = all_52_14)
% 239.98/46.55    (25)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 239.98/46.55          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 239.98/46.55    (26)  all_54_2 = all_52_8
% 239.98/46.55    (27)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 239.98/46.55    (28)   ~ (all_52_2 = all_52_14)
% 239.98/46.56    (29)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 239.98/46.56    (30)  all_56_21 = e0
% 239.98/46.56    (31)  all_54_4 = all_52_1
% 239.98/46.56    (32)   ~ (all_52_14 = e2)
% 239.98/46.56    (33)   ~ (all_52_8 = all_52_12)
% 239.98/46.56    (34)  op(e3, e1) = all_52_8
% 239.98/46.56    (35)  op(e2, e1) = all_52_9
% 239.98/46.56    (36)  all_54_9 = all_52_6
% 239.98/46.56    (37)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 239.98/46.56          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 239.98/46.56    (38)   ~ (all_52_4 = all_8_2)
% 239.98/46.56    (39)  all_56_31 = e2
% 239.98/46.56    (40)   ~ (all_52_14 = e0)
% 239.98/46.56    (41)   ~ (all_22_2 = e1) | ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 239.98/46.56            op(e2, e1) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 239.98/46.56              e0) & op(e2, e1) = all_22_1 & $i(all_22_1))
% 239.98/46.56    (42)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 239.98/46.56    (43)  op(e2, e0) = e0
% 239.98/46.56    (44)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.98/46.56    (45)  op(e3, e0) = all_52_12
% 239.98/46.56    (46)   ~ (all_52_1 = e0)
% 239.98/46.56    (47)   ~ (all_52_4 = all_52_12)
% 239.98/46.56    (48)   ~ (all_52_6 = all_52_14)
% 239.98/46.56    (49)  all_54_5 = all_8_2
% 239.98/46.56    (50)  op(e2, e3) = all_52_1
% 239.98/46.56    (51)   ~ (all_52_12 = e2)
% 239.98/46.56    (52)  op(e0, e2) = e0
% 239.98/46.56    (53)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 239.98/46.56          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 239.98/46.56    (54)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 239.98/46.56    (55)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 239.98/46.56    (56)   ~ (all_52_2 = e0)
% 239.98/46.56    (57)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 239.98/46.56          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 239.98/46.56    (58)  all_54_1 = all_52_4
% 239.98/46.56    (59)  op(e3, e2) = all_52_4
% 239.98/46.56    (60)   ~ (all_52_8 = all_52_11)
% 239.98/46.56    (61)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 239.98/46.56          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 239.98/46.56    (62)  all_54_8 = all_52_2
% 239.98/46.56    (63)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 239.98/46.56          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 239.98/46.56    (64)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 239.98/46.56          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 239.98/46.56    (65)   ~ (all_52_2 = all_52_6)
% 239.98/46.56    (66)  all_54_3 = all_52_12
% 239.98/46.56    (67)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 239.98/46.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 239.98/46.56    (68)  op(e1, e3) = all_52_2
% 239.98/46.56    (69)  op(e0, e2) = all_44_1
% 239.98/46.56    (70)  op(e1, e1) = e0
% 239.98/46.56    (71)   ~ (all_8_2 = e3)
% 239.98/46.56    (72)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 239.98/46.56          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 239.98/46.56    (73)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 239.98/46.56          | (all_58_14 = e0 & op(e0, e1) = e0)
% 239.98/46.56    (74)  op(e3, e3) = e0
% 239.98/46.56    (75)  all_56_11 = all_8_2
% 239.98/46.56    (76)  op(e2, e0) = all_52_13
% 239.98/46.56    (77)   ~ (all_52_4 = all_52_8)
% 239.98/46.56    (78)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 239.98/46.56          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 239.98/46.56    (79)   ~ (all_52_4 = all_52_6)
% 239.98/46.56    (80)   ~ (all_52_4 = e0)
% 239.98/46.56  
% 239.98/46.56  Begin of proof
% 239.98/46.56  | 
% 239.98/46.56  | GROUND_INST: instantiating (67) with e0, all_44_1, e2, e0, simplifying with
% 239.98/46.56  |              (52), (69) gives:
% 239.98/46.56  |   (81)  all_44_1 = e0
% 239.98/46.56  | 
% 239.98/46.56  | BETA: splitting (41) gives:
% 239.98/46.56  | 
% 239.98/46.56  | Case 1:
% 239.98/46.56  | | 
% 239.98/46.56  | |   (82)   ~ (all_22_2 = e1)
% 239.98/46.56  | | 
% 239.98/46.56  | | REDUCE: (8), (82) imply:
% 239.98/46.56  | |   (83)   ~ (all_8_2 = e1)
% 239.98/46.56  | | 
% 239.98/46.56  | | BETA: splitting (54) gives:
% 239.98/46.56  | | 
% 239.98/46.56  | | Case 1:
% 239.98/46.56  | | | 
% 239.98/46.56  | | |   (84)  all_54_5 = e3
% 239.98/46.56  | | | 
% 239.98/46.56  | | | REF_CLOSE: (49), (71), (84) are inconsistent by sub-proof #1907.
% 239.98/46.56  | | | 
% 239.98/46.56  | | Case 2:
% 239.98/46.56  | | | 
% 239.98/46.56  | | |   (85)   ~ (all_54_5 = e3)
% 239.98/46.56  | | |   (86)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 239.98/46.56  | | | 
% 239.98/46.56  | | | BETA: splitting (86) gives:
% 239.98/46.56  | | | 
% 239.98/46.56  | | | Case 1:
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | |   (87)  all_54_5 = e2
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | COMBINE_EQS: (49), (87) imply:
% 239.98/46.56  | | | |   (88)  all_8_2 = e2
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | SIMP: (88) implies:
% 239.98/46.56  | | | |   (89)  all_8_2 = e2
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | REDUCE: (3), (89) imply:
% 239.98/46.56  | | | |   (90)   ~ (all_52_6 = e2)
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | REDUCE: (5), (89) imply:
% 239.98/46.56  | | | |   (91)   ~ (all_52_9 = e2)
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | REDUCE: (71), (89) imply:
% 239.98/46.56  | | | |   (92)   ~ (e3 = e2)
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | SIMP: (92) implies:
% 239.98/46.56  | | | |   (93)   ~ (e3 = e2)
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | REDUCE: (83), (89) imply:
% 239.98/46.56  | | | |   (94)   ~ (e2 = e1)
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | BETA: splitting (37) gives:
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | Case 1:
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | |   (95)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 239.98/46.56  | | | | |             e1) = e2)
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | | BETA: splitting (95) gives:
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | | Case 1:
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | |   (96)  all_58_4 = e2 & op(e3, e1) = e2
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | | ALPHA: (96) implies:
% 239.98/46.56  | | | | | |   (97)  op(e3, e1) = e2
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | | BETA: splitting (64) gives:
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | | Case 1:
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | |   (98)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 239.98/46.56  | | | | | | |           op(e1, e2) = e2)
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | | BETA: splitting (98) gives:
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | | Case 1:
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | |   (99)  all_58_6 = e2 & op(e1, e3) = e2
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | | ALPHA: (99) implies:
% 239.98/46.56  | | | | | | | |   (100)  op(e1, e3) = e2
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | | REF_CLOSE: (1), (10), (15), (18), (20), (21), (30), (34), (35),
% 239.98/46.56  | | | | | | | |            (39), (40), (52), (59), (67), (68), (77), (93), (94),
% 239.98/46.56  | | | | | | | |            (97), (100) are inconsistent by sub-proof #143.
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | Case 2:
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | |   (101)  all_58_7 = e2 & op(e1, e2) = e2
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | | ALPHA: (101) implies:
% 239.98/46.56  | | | | | | | |   (102)  op(e1, e2) = e2
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | | REF_CLOSE: (13), (67), (90), (102) are inconsistent by sub-proof
% 239.98/46.56  | | | | | | | |            #249.
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | End of split
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | Case 2:
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | |   (103)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 239.98/46.56  | | | | | | |            op(e1, e0) = e2)
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | | REF_CLOSE: (11), (18), (32), (67), (70), (103) are inconsistent by
% 239.98/46.56  | | | | | | |            sub-proof #167.
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | End of split
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | Case 2:
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | |   (104)  all_58_5 = e2 & op(e2, e1) = e2
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | | ALPHA: (104) implies:
% 239.98/46.56  | | | | | |   (105)  op(e2, e1) = e2
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | | REF_CLOSE: (35), (67), (91), (105) are inconsistent by sub-proof
% 239.98/46.56  | | | | | |            #2328.
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | End of split
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | Case 2:
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | |   (106)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 239.98/46.56  | | | | |              e1) = e2)
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | | REF_CLOSE: (9), (11), (12), (67), (70), (106) are inconsistent by
% 239.98/46.56  | | | | |            sub-proof #178.
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | End of split
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | Case 2:
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | |   (107)  all_54_5 = e1 | all_54_5 = e0
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | REF_CLOSE: (6), (49), (83), (107) are inconsistent by sub-proof #2300.
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | End of split
% 239.98/46.56  | | | 
% 239.98/46.56  | | End of split
% 239.98/46.56  | | 
% 239.98/46.56  | Case 2:
% 239.98/46.56  | | 
% 239.98/46.56  | |   (108)  all_22_2 = e1
% 239.98/46.56  | | 
% 239.98/46.56  | | COMBINE_EQS: (8), (108) imply:
% 239.98/46.56  | |   (109)  all_8_2 = e1
% 239.98/46.56  | | 
% 239.98/46.56  | | SIMP: (109) implies:
% 239.98/46.56  | |   (110)  all_8_2 = e1
% 239.98/46.56  | | 
% 239.98/46.56  | | COMBINE_EQS: (75), (110) imply:
% 239.98/46.56  | |   (111)  all_56_11 = e1
% 239.98/46.56  | | 
% 239.98/46.56  | | REDUCE: (14), (110) imply:
% 239.98/46.56  | |   (112)   ~ (all_52_1 = e1)
% 239.98/46.56  | | 
% 239.98/46.56  | | REDUCE: (38), (110) imply:
% 239.98/46.56  | |   (113)   ~ (all_52_4 = e1)
% 239.98/46.56  | | 
% 239.98/46.56  | | REDUCE: (3), (110) imply:
% 239.98/46.56  | |   (114)   ~ (all_52_6 = e1)
% 239.98/46.56  | | 
% 239.98/46.56  | | REDUCE: (5), (110) imply:
% 239.98/46.56  | |   (115)   ~ (all_52_9 = e1)
% 239.98/46.56  | | 
% 239.98/46.56  | | REDUCE: (71), (110) imply:
% 239.98/46.56  | |   (116)   ~ (e3 = e1)
% 239.98/46.56  | | 
% 239.98/46.56  | | SIMP: (116) implies:
% 239.98/46.56  | |   (117)   ~ (e3 = e1)
% 239.98/46.56  | | 
% 239.98/46.56  | | REDUCE: (6), (110) imply:
% 239.98/46.56  | |   (118)   ~ (e1 = e0)
% 239.98/46.56  | | 
% 239.98/46.56  | | BETA: splitting (29) gives:
% 239.98/46.56  | | 
% 239.98/46.56  | | Case 1:
% 239.98/46.56  | | | 
% 239.98/46.56  | | |   (119)  all_54_3 = e3
% 239.98/46.56  | | | 
% 239.98/46.56  | | | COMBINE_EQS: (66), (119) imply:
% 239.98/46.56  | | |   (120)  all_52_12 = e3
% 239.98/46.56  | | | 
% 239.98/46.56  | | | SIMP: (120) implies:
% 239.98/46.56  | | |   (121)  all_52_12 = e3
% 239.98/46.56  | | | 
% 239.98/46.56  | | | REDUCE: (47), (121) imply:
% 239.98/46.56  | | |   (122)   ~ (all_52_4 = e3)
% 239.98/46.56  | | | 
% 239.98/46.56  | | | REDUCE: (33), (121) imply:
% 239.98/46.56  | | |   (123)   ~ (all_52_8 = e3)
% 239.98/46.56  | | | 
% 239.98/46.56  | | | REDUCE: (24), (121) imply:
% 239.98/46.56  | | |   (124)   ~ (all_52_14 = e3)
% 239.98/46.56  | | | 
% 239.98/46.56  | | | SIMP: (124) implies:
% 239.98/46.56  | | |   (125)   ~ (all_52_14 = e3)
% 239.98/46.56  | | | 
% 239.98/46.56  | | | REDUCE: (16), (121) imply:
% 239.98/46.56  | | |   (126)   ~ (e3 = e0)
% 239.98/46.56  | | | 
% 239.98/46.56  | | | REDUCE: (45), (121) imply:
% 239.98/46.56  | | |   (127)  op(e3, e0) = e3
% 239.98/46.56  | | | 
% 239.98/46.56  | | | BETA: splitting (27) gives:
% 239.98/46.56  | | | 
% 239.98/46.56  | | | Case 1:
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | |   (128)  all_54_11 = e3
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | COMBINE_EQS: (23), (128) imply:
% 239.98/46.56  | | | |   (129)  all_52_14 = e3
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | REDUCE: (125), (129) imply:
% 239.98/46.56  | | | |   (130)  $false
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | CLOSE: (130) is inconsistent.
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | Case 2:
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | |   (131)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | BETA: splitting (63) gives:
% 239.98/46.56  | | | | 
% 239.98/46.56  | | | | Case 1:
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | |   (132)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3,
% 239.98/46.56  | | | | |              e2) = e1)
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | | REF_CLOSE: (59), (67), (74), (113), (118), (132) are inconsistent by
% 239.98/46.56  | | | | |            sub-proof #1826.
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | Case 2:
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | |   (133)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3,
% 239.98/46.56  | | | | |              e0) = e1)
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | | BETA: splitting (133) gives:
% 239.98/46.56  | | | | | 
% 239.98/46.56  | | | | | Case 1:
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | |   (134)  all_58_4 = e1 & op(e3, e1) = e1
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | | ALPHA: (134) implies:
% 239.98/46.56  | | | | | |   (135)  all_58_4 = e1
% 239.98/46.56  | | | | | |   (136)  op(e3, e1) = e1
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | | BETA: splitting (19) gives:
% 239.98/46.56  | | | | | | 
% 239.98/46.56  | | | | | | Case 1:
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | |   (137)  all_54_1 = e3
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | | REF_CLOSE: (58), (122), (137) are inconsistent by sub-proof #1930.
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | Case 2:
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | |   (138)   ~ (all_54_1 = e3)
% 239.98/46.56  | | | | | | |   (139)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | | BETA: splitting (72) gives:
% 239.98/46.56  | | | | | | | 
% 239.98/46.56  | | | | | | | Case 1:
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | |   (140)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 &
% 239.98/46.56  | | | | | | | |            op(e2, e2) = e3)
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | | BETA: splitting (140) gives:
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | | Case 1:
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | |   (141)  all_58_1 = e3 & op(e3, e2) = e3
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | ALPHA: (141) implies:
% 239.98/46.56  | | | | | | | | |   (142)  op(e3, e2) = e3
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | REF_CLOSE: (59), (67), (122), (142) are inconsistent by
% 239.98/46.56  | | | | | | | | |            sub-proof #2192.
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | Case 2:
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | |   (143)  all_58_3 = e3 & op(e2, e2) = e3
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | ALPHA: (143) implies:
% 239.98/46.56  | | | | | | | | |   (144)  all_58_3 = e3
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | REF_CLOSE: (35), (43), (50), (67), (76), (78), (112), (115),
% 239.98/46.56  | | | | | | | | |            (117), (118), (144) are inconsistent by sub-proof
% 239.98/46.56  | | | | | | | | |            #1777.
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | End of split
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | Case 2:
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | |   (145)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 &
% 239.98/46.56  | | | | | | | |            op(e0, e2) = e3)
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | | BETA: splitting (145) gives:
% 239.98/46.56  | | | | | | | | 
% 239.98/46.56  | | | | | | | | Case 1:
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | |   (146)  all_58_7 = e3 & op(e1, e2) = e3
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | ALPHA: (146) implies:
% 239.98/46.56  | | | | | | | | |   (147)  op(e1, e2) = e3
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | BETA: splitting (139) gives:
% 239.98/46.56  | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | Case 1:
% 239.98/46.56  | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | |   (148)  all_54_1 = e2
% 239.98/46.56  | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | COMBINE_EQS: (58), (148) imply:
% 239.98/46.56  | | | | | | | | | |   (149)  all_52_4 = e2
% 239.98/46.56  | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | SIMP: (149) implies:
% 239.98/46.56  | | | | | | | | | |   (150)  all_52_4 = e2
% 239.98/46.56  | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | REDUCE: (79), (150) imply:
% 239.98/46.56  | | | | | | | | | |   (151)   ~ (all_52_6 = e2)
% 239.98/46.56  | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | SIMP: (151) implies:
% 239.98/46.56  | | | | | | | | | |   (152)   ~ (all_52_6 = e2)
% 239.98/46.56  | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | REDUCE: (77), (150) imply:
% 239.98/46.56  | | | | | | | | | |   (153)   ~ (all_52_8 = e2)
% 239.98/46.56  | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | SIMP: (153) implies:
% 239.98/46.56  | | | | | | | | | |   (154)   ~ (all_52_8 = e2)
% 239.98/46.56  | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | REDUCE: (113), (150) imply:
% 239.98/46.56  | | | | | | | | | |   (155)   ~ (e2 = e1)
% 239.98/46.56  | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | BETA: splitting (42) gives:
% 239.98/46.56  | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | Case 1:
% 239.98/46.56  | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | |   (156)  all_54_9 = e3
% 239.98/46.56  | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | COMBINE_EQS: (36), (156) imply:
% 239.98/46.56  | | | | | | | | | | |   (157)  all_52_6 = e3
% 239.98/46.56  | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | SIMP: (157) implies:
% 239.98/46.56  | | | | | | | | | | |   (158)  all_52_6 = e3
% 239.98/46.56  | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | REDUCE: (65), (158) imply:
% 239.98/46.56  | | | | | | | | | | |   (159)   ~ (all_52_2 = e3)
% 239.98/46.56  | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | REDUCE: (152), (158) imply:
% 239.98/46.56  | | | | | | | | | | |   (160)   ~ (e3 = e2)
% 239.98/46.56  | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | BETA: splitting (64) gives:
% 239.98/46.56  | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | Case 1:
% 239.98/46.56  | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | |   (161)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 239.98/46.56  | | | | | | | | | | | |            & op(e1, e2) = e2)
% 239.98/46.56  | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | BETA: splitting (161) gives:
% 239.98/46.56  | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | Case 1:
% 239.98/46.56  | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | |   (162)  all_58_6 = e2 & op(e1, e3) = e2
% 239.98/46.56  | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | ALPHA: (162) implies:
% 239.98/46.56  | | | | | | | | | | | | |   (163)  op(e1, e3) = e2
% 239.98/46.56  | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | BETA: splitting (131) gives:
% 239.98/46.56  | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | Case 1:
% 239.98/46.56  | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | |   (164)  all_54_11 = e2
% 239.98/46.56  | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | COMBINE_EQS: (23), (164) imply:
% 239.98/46.56  | | | | | | | | | | | | | |   (165)  all_52_14 = e2
% 239.98/46.56  | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | REDUCE: (32), (165) imply:
% 239.98/46.56  | | | | | | | | | | | | | |   (166)  $false
% 239.98/46.56  | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | CLOSE: (166) is inconsistent.
% 239.98/46.56  | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | Case 2:
% 239.98/46.56  | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | |   (167)  all_54_11 = e1 | all_54_11 = e0
% 239.98/46.56  | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 239.98/46.56  | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | Case 1:
% 239.98/46.56  | | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | |   (168)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 239.98/46.56  | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 239.98/46.56  | | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 239.98/46.56  | | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | | Case 1:
% 239.98/46.56  | | | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | | |   (169)  all_58_0 = e1 & op(e3, e3) = e1
% 239.98/46.56  | | | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 239.98/46.56  | | | | | | | | | | | | | | | |   (170)  op(e3, e3) = e1
% 239.98/46.56  | | | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11), (25), (53), (59), (67), (117), (118),
% 239.98/46.56  | | | | | | | | | | | | | | | |            (122), (126), (135), (155), (160), (170) are
% 239.98/46.56  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1468.
% 239.98/46.56  | | | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | | Case 2:
% 239.98/46.56  | | | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | | |   (171)  all_58_2 = e1 & op(e2, e3) = e1
% 239.98/46.56  | | | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | | | REF_CLOSE: (50), (67), (112), (171) are inconsistent by
% 239.98/46.56  | | | | | | | | | | | | | | | |            sub-proof #2229.
% 239.98/46.56  | | | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | | End of split
% 239.98/46.56  | | | | | | | | | | | | | | | 
% 239.98/46.56  | | | | | | | | | | | | | | Case 2:
% 239.98/46.56  | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | |   (172)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 239.98/46.57  | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 239.98/46.57  | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | |   (173)  all_58_6 = e1 & op(e1, e3) = e1
% 239.98/46.57  | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 239.98/46.57  | | | | | | | | | | | | | | | |   (174)  op(e1, e3) = e1
% 239.98/46.57  | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | REF_CLOSE: (67), (155), (163), (174) are inconsistent by
% 239.98/46.57  | | | | | | | | | | | | | | | |            sub-proof #2226.
% 239.98/46.57  | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | Case 2:
% 239.98/46.57  | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | |   (175)  all_58_12 = e1 & op(e0, e3) = e1
% 239.98/46.57  | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 239.98/46.57  | | | | | | | | | | | | | | | |   (176)  all_58_12 = e1
% 239.98/46.57  | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | |   (177)  all_54_2 = e3
% 239.98/46.57  | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (123), (177) are inconsistent by sub-proof
% 239.98/46.57  | | | | | | | | | | | | | | | | |            #1987.
% 239.98/46.57  | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | Case 2:
% 239.98/46.57  | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | |   (178)   ~ (all_54_2 = e3)
% 239.98/46.57  | | | | | | | | | | | | | | | | |   (179)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 239.98/46.57  | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | |   (180)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 239.98/46.57  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | |   (181)  all_58_4 = e2 & op(e3, e1) = e2
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | |   (182)  op(e3, e1) = e2
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (10), (15), (18), (20), (21), (30), (34),
% 239.98/46.57  | | | | | | | | | | | | | | | | | | |            (35), (39), (40), (52), (59), (67), (68), (77),
% 239.98/46.57  | | | | | | | | | | | | | | | | | | |            (155), (160), (163), (182) are inconsistent by
% 239.98/46.57  | | | | | | | | | | | | | | | | | | |            sub-proof #143.
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | Case 2:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | |   (183)  all_58_5 = e2 & op(e2, e1) = e2
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | |   (184)  op(e2, e1) = e2
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | |   (185)  all_54_2 = e2
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (154), (185) are inconsistent by sub-proof
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | |            #1986.
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | |   (186)   ~ (all_54_2 = e2)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | |   (187)  all_54_2 = e1 | all_54_2 = e0
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | |   (188)  all_54_11 = e1
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (188) imply:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | |   (189)  all_52_14 = e1
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (189) imply:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | |   (190)   ~ (all_52_2 = e1)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (18), (189) imply:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | |   (191)  op(e1, e0) = e1
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | |   (192)  all_54_8 = e3
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (159), (192) are inconsistent by sub-proof
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | |            #2011.
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | |   (193)   ~ (all_54_8 = e3)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | |   (194)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | |   (195)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (117), (136), (160), (184), (195) are
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #171.
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | |   (196)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | |   (197)  all_58_8 = e3 & op(e1, e1) = e3
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (70), (126), (197) are inconsistent by
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2018.
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | |   (198)  all_58_14 = e3 & op(e0, e1) = e3
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (198) implies:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | |   (199)  op(e0, e1) = e3
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_54_8 = e2
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (200) imply:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_52_2 = e2
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (201) imply:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (202)   ~ (all_52_1 = e2)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_54_4 = e3
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (203) imply:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (204)  all_52_1 = e3
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (204) implies:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_52_1 = e3
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (205) imply:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (206)   ~ (all_52_3 = e3)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (206) implies:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (207)   ~ (all_52_3 = e3)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (205) imply:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (208)  op(e2, e3) = e3
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_54_2 = e1
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (209) imply:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_52_8 = e1
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (210) implies:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  all_52_8 = e1
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (211) imply:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (212)   ~ (all_52_11 = e1)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (212) implies:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)   ~ (all_52_11 = e1)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (154), (211) imply:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)   ~ (e2 = e1)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 239.98/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          e3
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  op(e3, e2) = e3
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (36), (42), (59), (67), (79), (147), (218)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2190.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (68), (159), (160), (208), (219) are
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1889.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (21), (67), (155), (163), (207), (220) are
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #142.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  op(e1, e2) = e2
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (19), (20), (26), (35), (44), (58),
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (59), (67), (77), (79), (80), (122), (123), (184),
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224) are inconsistent by sub-proof #141.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  op(e2, e1) = e1
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (20), (26), (35), (67), (187), (227) are
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #435.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  op(e0, e2) = e2
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (67), (73), (118), (126), (176), (199),
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229) are inconsistent by sub-proof #896.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)   ~ (all_56_31 = e2)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (232) imply:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  $false
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (67), (118), (191), (213), (234) are
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #140.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_54_2 = e0
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (26), (235) are inconsistent by sub-proof
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1643.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (46), (112), (202), (236) are inconsistent
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1921.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  all_54_8 = e1 | all_54_8 = e0
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (62), (190), (237) are inconsistent by
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1950.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | |   (238)  all_54_11 = e0
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (238) imply:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | |   (239)  all_52_14 = e0
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (239) imply:
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | |   (240)  $false
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.57  | | | | | | | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | | | | | | |   (241)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 240.01/46.58  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 240.01/46.58  | | | | | | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (12), (67), (70), (241) are
% 240.01/46.58  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #178.
% 240.01/46.58  | | | | | | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | |   (242)  all_58_7 = e2 & op(e1, e2) = e2
% 240.01/46.58  | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | | ALPHA: (242) implies:
% 240.01/46.58  | | | | | | | | | | | | |   (243)  op(e1, e2) = e2
% 240.01/46.58  | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | | REF_CLOSE: (67), (147), (160), (243) are inconsistent by
% 240.01/46.58  | | | | | | | | | | | | |            sub-proof #2207.
% 240.01/46.58  | | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | |   (244)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 240.01/46.58  | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 240.01/46.58  | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | | REF_CLOSE: (11), (18), (32), (67), (70), (244) are
% 240.01/46.58  | | | | | | | | | | | |            inconsistent by sub-proof #167.
% 240.01/46.58  | | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | |   (245)   ~ (all_54_9 = e3)
% 240.01/46.58  | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | REDUCE: (36), (245) imply:
% 240.01/46.58  | | | | | | | | | | |   (246)   ~ (all_52_6 = e3)
% 240.01/46.58  | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | | REF_CLOSE: (13), (67), (147), (246) are inconsistent by
% 240.01/46.58  | | | | | | | | | | |            sub-proof #2191.
% 240.01/46.58  | | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | |   (247)  all_54_1 = e1 | all_54_1 = e0
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | REF_CLOSE: (58), (80), (113), (247) are inconsistent by
% 240.01/46.58  | | | | | | | | | |            sub-proof #2049.
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | |   (248)  all_58_13 = e3 & op(e0, e2) = e3
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | ALPHA: (248) implies:
% 240.01/46.58  | | | | | | | | |   (249)  op(e0, e2) = e3
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | REF_CLOSE: (52), (67), (126), (249) are inconsistent by
% 240.01/46.58  | | | | | | | | |            sub-proof #1961.
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | End of split
% 240.01/46.58  | | | | | | | 
% 240.01/46.58  | | | | | | End of split
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | Case 2:
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | |   (250)  all_58_9 = e1 & op(e3, e0) = e1
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | | ALPHA: (250) implies:
% 240.01/46.58  | | | | | |   (251)  op(e3, e0) = e1
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | | REF_CLOSE: (67), (117), (127), (251) are inconsistent by sub-proof
% 240.01/46.58  | | | | | |            #243.
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | End of split
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | End of split
% 240.01/46.58  | | | | 
% 240.01/46.58  | | | End of split
% 240.01/46.58  | | | 
% 240.01/46.58  | | Case 2:
% 240.01/46.58  | | | 
% 240.01/46.58  | | |   (252)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 240.01/46.58  | | | 
% 240.01/46.58  | | | BETA: splitting (252) gives:
% 240.01/46.58  | | | 
% 240.01/46.58  | | | Case 1:
% 240.01/46.58  | | | | 
% 240.01/46.58  | | | |   (253)  all_54_3 = e2
% 240.01/46.58  | | | | 
% 240.01/46.58  | | | | REF_CLOSE: (51), (66), (253) are inconsistent by sub-proof #2290.
% 240.01/46.58  | | | | 
% 240.01/46.58  | | | Case 2:
% 240.01/46.58  | | | | 
% 240.01/46.58  | | | |   (254)  all_54_3 = e1 | all_54_3 = e0
% 240.01/46.58  | | | | 
% 240.01/46.58  | | | | BETA: splitting (254) gives:
% 240.01/46.58  | | | | 
% 240.01/46.58  | | | | Case 1:
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | |   (255)  all_54_3 = e1
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | | COMBINE_EQS: (66), (255) imply:
% 240.01/46.58  | | | | |   (256)  all_52_12 = e1
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | | SIMP: (256) implies:
% 240.01/46.58  | | | | |   (257)  all_52_12 = e1
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | | REDUCE: (33), (257) imply:
% 240.01/46.58  | | | | |   (258)   ~ (all_52_8 = e1)
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | | REDUCE: (24), (257) imply:
% 240.01/46.58  | | | | |   (259)   ~ (all_52_14 = e1)
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | | SIMP: (259) implies:
% 240.01/46.58  | | | | |   (260)   ~ (all_52_14 = e1)
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | | REDUCE: (45), (257) imply:
% 240.01/46.58  | | | | |   (261)  op(e3, e0) = e1
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | | BETA: splitting (27) gives:
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | | Case 1:
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | |   (262)  all_54_11 = e3
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | | COMBINE_EQS: (23), (262) imply:
% 240.01/46.58  | | | | | |   (263)  all_52_14 = e3
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | | REDUCE: (28), (263) imply:
% 240.01/46.58  | | | | | |   (264)   ~ (all_52_2 = e3)
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | | REDUCE: (48), (263) imply:
% 240.01/46.58  | | | | | |   (265)   ~ (all_52_6 = e3)
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | | REDUCE: (40), (263) imply:
% 240.01/46.58  | | | | | |   (266)   ~ (e3 = e0)
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | | REDUCE: (18), (263) imply:
% 240.01/46.58  | | | | | |   (267)  op(e1, e0) = e3
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | | BETA: splitting (15) gives:
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | | Case 1:
% 240.01/46.58  | | | | | | | 
% 240.01/46.58  | | | | | | |   (268)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.01/46.58  | | | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 240.01/46.58  | | | | | | |              = e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 240.01/46.58  | | | | | | |          (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.01/46.58  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 240.01/46.58  | | | | | | |              = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 240.01/46.58  | | | | | | |          (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.01/46.58  | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 240.01/46.58  | | | | | | |              = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 240.01/46.58  | | | | | | |          (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.01/46.58  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 240.01/46.58  | | | | | | |              = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 240.01/46.58  | | | | | | |          (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.01/46.58  | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31
% 240.01/46.58  | | | | | | |              = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 240.01/46.58  | | | | | | |          (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.01/46.58  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 240.01/46.58  | | | | | | |              = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.01/46.58  | | | | | | | 
% 240.01/46.58  | | | | | | | BETA: splitting (268) gives:
% 240.01/46.58  | | | | | | | 
% 240.01/46.58  | | | | | | | Case 1:
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | |   (269)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 240.01/46.58  | | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) = e3)
% 240.01/46.58  | | | | | | | |          | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &
% 240.01/46.58  | | | | | | | |             ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 240.01/46.58  | | | | | | | |          | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1)
% 240.01/46.58  | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | | BETA: splitting (269) gives:
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | | Case 1:
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | |   (270)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 240.01/46.58  | | | | | | | | |          ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.01/46.58  | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | ALPHA: (270) implies:
% 240.01/46.58  | | | | | | | | |   (271)   ~ (all_56_31 = e2)
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | REDUCE: (39), (271) imply:
% 240.01/46.58  | | | | | | | | |   (272)  $false
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | CLOSE: (272) is inconsistent.
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | |   (273)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &
% 240.01/46.58  | | | | | | | | |             ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.58  | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 240.01/46.58  | | | | | | | | |            e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.01/46.58  | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.01/46.58  | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 240.01/46.58  | | | | | | | | |            = e3 & op(e1, e3) = e3)
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | BETA: splitting (273) gives:
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | Case 1:
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | |   (274)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.01/46.58  | | | | | | | | | |          &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.58  | | | | | | | | | |          (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 240.01/46.58  | | | | | | | | | |          e2
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | ALPHA: (274) implies:
% 240.01/46.58  | | | | | | | | | |   (275)   ~ (all_56_31 = e3)
% 240.01/46.58  | | | | | | | | | |   (276)   ~ (all_56_21 = e3)
% 240.01/46.58  | | | | | | | | | |   (277)   ~ (all_56_11 = e3)
% 240.01/46.58  | | | | | | | | | |   (278)  op(e3, e2) = e2
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | REDUCE: (30), (276) imply:
% 240.01/46.58  | | | | | | | | | |   (279)   ~ (e3 = e0)
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | REDUCE: (39), (275) imply:
% 240.01/46.58  | | | | | | | | | |   (280)   ~ (e3 = e2)
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | SIMP: (280) implies:
% 240.01/46.58  | | | | | | | | | |   (281)   ~ (e3 = e2)
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | REF_CLOSE: (13), (35), (43), (50), (52), (67), (72), (76),
% 240.01/46.58  | | | | | | | | | |            (78), (112), (115), (117), (118), (265), (266),
% 240.01/46.58  | | | | | | | | | |            (278), (281) are inconsistent by sub-proof #139.
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | |   (282)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1)
% 240.01/46.58  | | | | | | | | | |          &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.01/46.58  | | | | | | | | | |          (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 240.01/46.58  | | | | | | | | | |          e3
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | ALPHA: (282) implies:
% 240.01/46.58  | | | | | | | | | |   (283)  op(e1, e3) = e3
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | REF_CLOSE: (67), (68), (264), (283) are inconsistent by
% 240.01/46.58  | | | | | | | | | |            sub-proof #2335.
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | |   (284)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) & 
% 240.01/46.58  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1)
% 240.01/46.58  | | | | | | | |          | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 240.01/46.58  | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3)
% 240.01/46.58  | | | | | | | |          | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 240.01/46.58  | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | | REF_CLOSE: (1), (21), (34), (67), (117), (258), (261), (284) are
% 240.01/46.58  | | | | | | | |            inconsistent by sub-proof #164.
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | End of split
% 240.01/46.58  | | | | | | | 
% 240.01/46.58  | | | | | | Case 2:
% 240.01/46.58  | | | | | | | 
% 240.01/46.58  | | | | | | |   (285)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) & 
% 240.01/46.58  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.01/46.58  | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 240.01/46.58  | | | | | | |          (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) & 
% 240.01/46.58  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.01/46.58  | | | | | | |            (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 240.01/46.58  | | | | | | |          (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) & 
% 240.01/46.58  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.01/46.58  | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 240.01/46.58  | | | | | | |          (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) & 
% 240.01/46.58  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.01/46.58  | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 240.01/46.58  | | | | | | |          (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) & 
% 240.01/46.58  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.01/46.58  | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 240.01/46.58  | | | | | | |          (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) & 
% 240.01/46.58  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.01/46.58  | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.01/46.58  | | | | | | | 
% 240.01/46.58  | | | | | | | BETA: splitting (285) gives:
% 240.01/46.58  | | | | | | | 
% 240.01/46.58  | | | | | | | Case 1:
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | |   (286)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &
% 240.01/46.58  | | | | | | | |             ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2)
% 240.01/46.58  | | | | | | | |          | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2)
% 240.01/46.58  | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1)
% 240.01/46.58  | | | | | | | |          | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0)
% 240.01/46.58  | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | | BETA: splitting (286) gives:
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | | Case 1:
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | |   (287)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 240.01/46.58  | | | | | | | | |          &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.01/46.58  | | | | | | | | |          (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | ALPHA: (287) implies:
% 240.01/46.58  | | | | | | | | |   (288)   ~ (all_56_11 = e1)
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | REDUCE: (111), (288) imply:
% 240.01/46.58  | | | | | | | | |   (289)  $false
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | CLOSE: (289) is inconsistent.
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | |   (290)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2)
% 240.01/46.58  | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.01/46.58  | | | | | | | | |            (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 240.01/46.58  | | | | | | | | |            e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.01/46.58  | | | | | | | | |            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 240.01/46.58  | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0)
% 240.01/46.58  | | | | | | | | |            = e2 & op(e0, e2) = e2)
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | REF_CLOSE: (11), (35), (52), (67), (115), (290) are
% 240.01/46.58  | | | | | | | | |            inconsistent by sub-proof #271.
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | |   (291)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &
% 240.01/46.58  | | | | | | | |             ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0)
% 240.01/46.58  | | | | | | | |          | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0)
% 240.01/46.58  | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1)
% 240.01/46.58  | | | | | | | |          | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1)
% 240.01/46.58  | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.01/46.58  | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | | BETA: splitting (291) gives:
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | | Case 1:
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | |   (292)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2)
% 240.01/46.58  | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.01/46.58  | | | | | | | | |          (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | ALPHA: (292) implies:
% 240.01/46.58  | | | | | | | | |   (293)   ~ (all_56_31 = e2)
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | REDUCE: (39), (293) imply:
% 240.01/46.58  | | | | | | | | |   (294)  $false
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | CLOSE: (294) is inconsistent.
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | |   (295)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0)
% 240.01/46.58  | | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.01/46.58  | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 240.01/46.58  | | | | | | | | |            e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.01/46.58  | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.01/46.58  | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0)
% 240.01/46.58  | | | | | | | | |            = e0 & op(e0, e1) = e0)
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | BETA: splitting (295) gives:
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | Case 1:
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | |   (296)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.01/46.58  | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &
% 240.01/46.58  | | | | | | | | | |           ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.01/46.58  | | | | | | | | | |          = e1
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | ALPHA: (296) implies:
% 240.01/46.58  | | | | | | | | | |   (297)  op(e1, e0) = e1
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | REF_CLOSE: (18), (67), (260), (297) are inconsistent by
% 240.01/46.58  | | | | | | | | | |            sub-proof #2304.
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | Case 2:
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | |   (298)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 240.01/46.58  | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &
% 240.01/46.58  | | | | | | | | | |           ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.01/46.58  | | | | | | | | | |          = e0
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | ALPHA: (298) implies:
% 240.01/46.58  | | | | | | | | | |   (299)  op(e1, e0) = e0
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | | REF_CLOSE: (67), (266), (267), (299) are inconsistent by
% 240.01/46.58  | | | | | | | | | |            sub-proof #210.
% 240.01/46.58  | | | | | | | | | | 
% 240.01/46.58  | | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | | 
% 240.01/46.58  | | | | | | | | End of split
% 240.01/46.58  | | | | | | | | 
% 240.01/46.58  | | | | | | | End of split
% 240.01/46.58  | | | | | | | 
% 240.01/46.58  | | | | | | End of split
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | Case 2:
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | |   (300)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | | REF_CLOSE: (23), (32), (40), (260), (300) are inconsistent by
% 240.01/46.58  | | | | | |            sub-proof #2173.
% 240.01/46.58  | | | | | | 
% 240.01/46.58  | | | | | End of split
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | Case 2:
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | |   (301)  all_54_3 = e0
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | | REF_CLOSE: (16), (66), (301) are inconsistent by sub-proof #2288.
% 240.01/46.58  | | | | | 
% 240.01/46.58  | | | | End of split
% 240.01/46.58  | | | | 
% 240.01/46.58  | | | End of split
% 240.01/46.58  | | | 
% 240.01/46.58  | | End of split
% 240.01/46.58  | | 
% 240.01/46.58  | End of split
% 240.01/46.58  | 
% 240.01/46.58  End of proof
% 240.01/46.58  
% 240.01/46.58  Sub-proof #139 shows that the following formulas are inconsistent:
% 240.01/46.58  ----------------------------------------------------------------
% 240.01/46.58    (1)   ~ (e3 = e0)
% 240.01/46.58    (2)  op(e1, e2) = all_52_6
% 240.01/46.58    (3)   ~ (e3 = e1)
% 240.01/46.58    (4)  op(e3, e2) = e2
% 240.01/46.58    (5)  op(e2, e1) = all_52_9
% 240.01/46.58    (6)   ~ (e3 = e2)
% 240.01/46.58    (7)  op(e2, e0) = e0
% 240.01/46.58    (8)  op(e2, e3) = all_52_1
% 240.01/46.58    (9)  op(e0, e2) = e0
% 240.01/46.58    (10)   ~ (all_52_6 = e3)
% 240.01/46.58    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.01/46.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.01/46.58    (12)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.01/46.58          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.01/46.58    (13)   ~ (e1 = e0)
% 240.01/46.58    (14)  op(e2, e0) = all_52_13
% 240.01/46.58    (15)   ~ (all_52_9 = e1)
% 240.01/46.58    (16)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.01/46.58          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.01/46.58    (17)   ~ (all_52_1 = e1)
% 240.01/46.58  
% 240.01/46.58  Begin of proof
% 240.01/46.58  | 
% 240.01/46.58  | BETA: splitting (12) gives:
% 240.01/46.58  | 
% 240.01/46.58  | Case 1:
% 240.01/46.58  | | 
% 240.01/46.59  | |   (18)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 240.01/46.59  | |           e3)
% 240.01/46.59  | | 
% 240.01/46.59  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (11), (13), (14), (15), (16), (17),
% 240.01/46.59  | |            (18) are inconsistent by sub-proof #1776.
% 240.01/46.59  | | 
% 240.01/46.59  | Case 2:
% 240.01/46.59  | | 
% 240.01/46.59  | |   (19)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 240.01/46.59  | |           e3)
% 240.01/46.59  | | 
% 240.01/46.59  | | BETA: splitting (19) gives:
% 240.01/46.59  | | 
% 240.01/46.59  | | Case 1:
% 240.01/46.59  | | | 
% 240.01/46.59  | | |   (20)  all_58_7 = e3 & op(e1, e2) = e3
% 240.01/46.59  | | | 
% 240.01/46.59  | | | ALPHA: (20) implies:
% 240.01/46.59  | | |   (21)  op(e1, e2) = e3
% 240.01/46.59  | | | 
% 240.01/46.59  | | | REF_CLOSE: (2), (10), (11), (21) are inconsistent by sub-proof #2191.
% 240.01/46.59  | | | 
% 240.01/46.59  | | Case 2:
% 240.01/46.59  | | | 
% 240.01/46.59  | | |   (22)  all_58_13 = e3 & op(e0, e2) = e3
% 240.01/46.59  | | | 
% 240.01/46.59  | | | ALPHA: (22) implies:
% 240.01/46.59  | | |   (23)  op(e0, e2) = e3
% 240.01/46.59  | | | 
% 240.01/46.59  | | | REF_CLOSE: (1), (9), (11), (23) are inconsistent by sub-proof #1961.
% 240.01/46.59  | | | 
% 240.01/46.59  | | End of split
% 240.01/46.59  | | 
% 240.01/46.59  | End of split
% 240.01/46.59  | 
% 240.01/46.59  End of proof
% 240.01/46.59  
% 240.01/46.59  Sub-proof #140 shows that the following formulas are inconsistent:
% 240.01/46.59  ----------------------------------------------------------------
% 240.01/46.59    (1)  op(e0, e1) = all_52_11
% 240.01/46.59    (2)   ~ (all_52_11 = e1)
% 240.01/46.59    (3)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.01/46.59             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.01/46.59           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 240.01/46.59             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 240.01/46.59           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.01/46.59    (4)  op(e1, e0) = e1
% 240.01/46.59    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.01/46.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.01/46.59    (6)   ~ (e1 = e0)
% 240.01/46.59  
% 240.01/46.59  Begin of proof
% 240.01/46.59  | 
% 240.01/46.59  | BETA: splitting (3) gives:
% 240.01/46.59  | 
% 240.01/46.59  | Case 1:
% 240.01/46.59  | | 
% 240.01/46.59  | |   (7)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.01/46.59  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 240.01/46.59  | |        & op(e0, e1) = e1
% 240.01/46.59  | | 
% 240.01/46.59  | | ALPHA: (7) implies:
% 240.01/46.59  | |   (8)  op(e0, e1) = e1
% 240.01/46.59  | | 
% 240.01/46.59  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #2272.
% 240.01/46.59  | | 
% 240.01/46.59  | Case 2:
% 240.01/46.59  | | 
% 240.01/46.59  | |   (9)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 240.01/46.59  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 240.01/46.59  | |        & op(e0, e1) = e0
% 240.01/46.59  | | 
% 240.01/46.59  | | ALPHA: (9) implies:
% 240.01/46.59  | |   (10)  op(e1, e0) = e0
% 240.01/46.59  | | 
% 240.01/46.59  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #2284.
% 240.01/46.59  | | 
% 240.01/46.59  | End of split
% 240.01/46.59  | 
% 240.01/46.59  End of proof
% 240.01/46.59  
% 240.01/46.59  Sub-proof #141 shows that the following formulas are inconsistent:
% 240.01/46.59  ----------------------------------------------------------------
% 240.01/46.59    (1)   ~ (all_52_8 = all_52_9)
% 240.01/46.59    (2)  op(e1, e2) = all_52_6
% 240.01/46.59    (3)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 240.01/46.59    (4)   ~ (all_52_8 = e0)
% 240.01/46.59    (5)  op(e2, e1) = e2
% 240.01/46.59    (6)  all_54_2 = all_52_8
% 240.01/46.59    (7)  op(e2, e1) = all_52_9
% 240.01/46.59    (8)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 240.01/46.59    (9)  op(e1, e2) = e2
% 240.01/46.59    (10)  all_54_1 = all_52_4
% 240.01/46.59    (11)   ~ (all_52_4 = e3)
% 240.01/46.59    (12)  op(e3, e2) = all_52_4
% 240.01/46.59    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.01/46.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.01/46.59    (14)   ~ (all_52_4 = all_52_8)
% 240.01/46.59    (15)   ~ (all_52_4 = all_52_6)
% 240.01/46.59    (16)   ~ (all_52_4 = e0)
% 240.01/46.59    (17)   ~ (all_52_8 = e3)
% 240.01/46.59  
% 240.01/46.59  Begin of proof
% 240.01/46.59  | 
% 240.01/46.59  | GROUND_INST: instantiating (13) with all_52_6, e2, e2, e1, simplifying with
% 240.01/46.59  |              (2), (9) gives:
% 240.01/46.59  |   (18)  all_52_6 = e2
% 240.01/46.59  | 
% 240.01/46.59  | GROUND_INST: instantiating (13) with all_52_9, e2, e1, e2, simplifying with
% 240.01/46.59  |              (5), (7) gives:
% 240.01/46.59  |   (19)  all_52_9 = e2
% 240.01/46.59  | 
% 240.01/46.59  | REDUCE: (15), (18) imply:
% 240.01/46.59  |   (20)   ~ (all_52_4 = e2)
% 240.01/46.59  | 
% 240.01/46.59  | REDUCE: (1), (19) imply:
% 240.01/46.59  |   (21)   ~ (all_52_8 = e2)
% 240.01/46.59  | 
% 240.01/46.59  | BETA: splitting (3) gives:
% 240.01/46.59  | 
% 240.01/46.59  | Case 1:
% 240.01/46.59  | | 
% 240.01/46.59  | |   (22)  all_54_1 = e3
% 240.01/46.59  | | 
% 240.01/46.59  | | REF_CLOSE: (10), (11), (22) are inconsistent by sub-proof #1930.
% 240.01/46.59  | | 
% 240.01/46.59  | Case 2:
% 240.01/46.59  | | 
% 240.01/46.59  | |   (23)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 240.01/46.59  | | 
% 240.01/46.59  | | BETA: splitting (23) gives:
% 240.01/46.59  | | 
% 240.01/46.59  | | Case 1:
% 240.01/46.59  | | | 
% 240.01/46.59  | | |   (24)  all_54_1 = e2
% 240.01/46.59  | | | 
% 240.01/46.59  | | | COMBINE_EQS: (10), (24) imply:
% 240.01/46.59  | | |   (25)  all_52_4 = e2
% 240.01/46.59  | | | 
% 240.01/46.59  | | | REDUCE: (20), (25) imply:
% 240.01/46.59  | | |   (26)  $false
% 240.01/46.59  | | | 
% 240.01/46.59  | | | CLOSE: (26) is inconsistent.
% 240.01/46.59  | | | 
% 240.01/46.59  | | Case 2:
% 240.01/46.59  | | | 
% 240.01/46.59  | | |   (27)  all_54_1 = e1 | all_54_1 = e0
% 240.01/46.59  | | | 
% 240.01/46.59  | | | BETA: splitting (8) gives:
% 240.01/46.59  | | | 
% 240.01/46.59  | | | Case 1:
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | |   (28)  all_54_2 = e3
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | | REF_CLOSE: (6), (17), (28) are inconsistent by sub-proof #1987.
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | Case 2:
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | |   (29)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | | BETA: splitting (29) gives:
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | | Case 1:
% 240.01/46.59  | | | | | 
% 240.01/46.59  | | | | |   (30)  all_54_2 = e2
% 240.01/46.59  | | | | | 
% 240.01/46.59  | | | | | REF_CLOSE: (6), (21), (30) are inconsistent by sub-proof #1986.
% 240.01/46.59  | | | | | 
% 240.01/46.59  | | | | Case 2:
% 240.01/46.59  | | | | | 
% 240.01/46.59  | | | | |   (31)  all_54_2 = e1 | all_54_2 = e0
% 240.01/46.59  | | | | | 
% 240.01/46.59  | | | | | BETA: splitting (27) gives:
% 240.01/46.59  | | | | | 
% 240.01/46.59  | | | | | Case 1:
% 240.01/46.59  | | | | | | 
% 240.01/46.59  | | | | | |   (32)  all_54_1 = e1
% 240.01/46.59  | | | | | | 
% 240.01/46.59  | | | | | | COMBINE_EQS: (10), (32) imply:
% 240.01/46.59  | | | | | |   (33)  all_52_4 = e1
% 240.01/46.59  | | | | | | 
% 240.01/46.59  | | | | | | REDUCE: (12), (33) imply:
% 240.01/46.59  | | | | | |   (34)  op(e3, e2) = e1
% 240.01/46.59  | | | | | | 
% 240.01/46.59  | | | | | | REF_CLOSE: (4), (6), (12), (13), (14), (31), (34) are inconsistent
% 240.01/46.59  | | | | | |            by sub-proof #1642.
% 240.01/46.59  | | | | | | 
% 240.01/46.59  | | | | | Case 2:
% 240.01/46.59  | | | | | | 
% 240.01/46.59  | | | | | |   (35)  all_54_1 = e0
% 240.01/46.59  | | | | | | 
% 240.01/46.59  | | | | | | COMBINE_EQS: (10), (35) imply:
% 240.01/46.59  | | | | | |   (36)  all_52_4 = e0
% 240.01/46.59  | | | | | | 
% 240.01/46.59  | | | | | | REDUCE: (16), (36) imply:
% 240.01/46.59  | | | | | |   (37)  $false
% 240.01/46.59  | | | | | | 
% 240.01/46.59  | | | | | | CLOSE: (37) is inconsistent.
% 240.01/46.59  | | | | | | 
% 240.01/46.59  | | | | | End of split
% 240.01/46.59  | | | | | 
% 240.01/46.59  | | | | End of split
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | End of split
% 240.01/46.59  | | | 
% 240.01/46.59  | | End of split
% 240.01/46.59  | | 
% 240.01/46.59  | End of split
% 240.01/46.59  | 
% 240.01/46.59  End of proof
% 240.01/46.59  
% 240.01/46.59  Sub-proof #142 shows that the following formulas are inconsistent:
% 240.01/46.59  ----------------------------------------------------------------
% 240.01/46.59    (1)   ~ (all_52_3 = e0)
% 240.01/46.59    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.01/46.59             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.01/46.59           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 240.01/46.59           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.01/46.59           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 240.01/46.59           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.59           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.01/46.59    (3)  op(e0, e3) = all_52_3
% 240.01/46.59    (4)  op(e1, e3) = e2
% 240.01/46.59    (5)   ~ (all_52_3 = e3)
% 240.01/46.59    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.01/46.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.01/46.59    (7)   ~ (e2 = e1)
% 240.01/46.59  
% 240.01/46.59  Begin of proof
% 240.01/46.59  | 
% 240.01/46.59  | BETA: splitting (2) gives:
% 240.01/46.59  | 
% 240.01/46.59  | Case 1:
% 240.01/46.59  | | 
% 240.01/46.59  | |   (8)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.01/46.59  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.01/46.59  | |        op(e1, e3) = e1
% 240.01/46.59  | | 
% 240.01/46.59  | | ALPHA: (8) implies:
% 240.01/46.59  | |   (9)  op(e1, e3) = e1
% 240.01/46.59  | | 
% 240.01/46.59  | | REF_CLOSE: (4), (6), (7), (9) are inconsistent by sub-proof #2226.
% 240.01/46.59  | | 
% 240.01/46.59  | Case 2:
% 240.01/46.59  | | 
% 240.01/46.59  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.01/46.59  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 240.01/46.59  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.01/46.59  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.59  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.01/46.59  | | 
% 240.01/46.59  | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #2330.
% 240.01/46.59  | | 
% 240.01/46.59  | End of split
% 240.01/46.59  | 
% 240.01/46.59  End of proof
% 240.01/46.59  
% 240.01/46.59  Sub-proof #143 shows that the following formulas are inconsistent:
% 240.01/46.59  ----------------------------------------------------------------
% 240.01/46.59    (1)   ~ (all_52_3 = e0)
% 240.01/46.59    (2)   ~ (all_52_8 = all_52_9)
% 240.01/46.59    (3)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.01/46.59           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.01/46.59             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.01/46.59           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.01/46.59             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.01/46.59           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.01/46.59           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.01/46.59           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.01/46.59           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.01/46.59           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.01/46.59           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.01/46.59             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.01/46.59           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.59           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 240.01/46.59           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.01/46.59           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.01/46.59           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.01/46.59           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.01/46.59             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.01/46.59           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.01/46.59           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 240.01/46.59           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.01/46.59           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.01/46.59           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.01/46.59           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.01/46.59             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.01/46.59           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.01/46.59           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.01/46.59    (4)  op(e1, e0) = all_52_14
% 240.01/46.59    (5)   ~ (all_52_8 = e0)
% 240.01/46.59    (6)  op(e0, e3) = all_52_3
% 240.01/46.59    (7)  op(e1, e3) = e2
% 240.01/46.59    (8)  all_56_21 = e0
% 240.01/46.59    (9)  op(e3, e1) = all_52_8
% 240.01/46.59    (10)  op(e2, e1) = all_52_9
% 240.01/46.59    (11)   ~ (e3 = e2)
% 240.01/46.59    (12)  all_56_31 = e2
% 240.01/46.59    (13)   ~ (all_52_14 = e0)
% 240.01/46.59    (14)  op(e0, e2) = e0
% 240.01/46.59    (15)  op(e3, e1) = e2
% 240.01/46.59    (16)  op(e3, e2) = all_52_4
% 240.01/46.59    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.01/46.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.01/46.59    (18)  op(e1, e3) = all_52_2
% 240.01/46.59    (19)   ~ (all_52_4 = all_52_8)
% 240.01/46.59    (20)   ~ (e2 = e1)
% 240.01/46.59  
% 240.01/46.59  Begin of proof
% 240.01/46.59  | 
% 240.01/46.59  | GROUND_INST: instantiating (17) with all_52_2, e2, e3, e1, simplifying with
% 240.01/46.59  |              (7), (18) gives:
% 240.01/46.59  |   (21)  all_52_2 = e2
% 240.01/46.59  | 
% 240.01/46.59  | GROUND_INST: instantiating (17) with all_52_8, e2, e1, e3, simplifying with
% 240.01/46.59  |              (9), (15) gives:
% 240.01/46.59  |   (22)  all_52_8 = e2
% 240.01/46.59  | 
% 240.01/46.59  | REDUCE: (19), (22) imply:
% 240.01/46.59  |   (23)   ~ (all_52_4 = e2)
% 240.01/46.59  | 
% 240.01/46.59  | REDUCE: (2), (22) imply:
% 240.01/46.59  |   (24)   ~ (all_52_9 = e2)
% 240.01/46.59  | 
% 240.01/46.59  | SIMP: (24) implies:
% 240.01/46.59  |   (25)   ~ (all_52_9 = e2)
% 240.01/46.59  | 
% 240.01/46.59  | REDUCE: (5), (22) imply:
% 240.01/46.59  |   (26)   ~ (e2 = e0)
% 240.01/46.59  | 
% 240.01/46.59  | BETA: splitting (3) gives:
% 240.01/46.59  | 
% 240.01/46.59  | Case 1:
% 240.01/46.59  | | 
% 240.01/46.59  | |   (27)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.01/46.59  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 240.01/46.59  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 240.01/46.59  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.59  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 240.01/46.59  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 240.01/46.59  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.01/46.59  | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 240.01/46.59  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.59  | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 240.01/46.59  | |           = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &
% 240.01/46.59  | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.01/46.59  | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 240.01/46.59  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.01/46.59  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.01/46.59  | | 
% 240.01/46.59  | | BETA: splitting (27) gives:
% 240.01/46.59  | | 
% 240.01/46.59  | | Case 1:
% 240.01/46.59  | | | 
% 240.01/46.59  | | |   (28)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.01/46.59  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.01/46.59  | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.01/46.59  | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.01/46.59  | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 240.01/46.59  | | |         | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.01/46.59  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.01/46.59  | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.01/46.59  | | | 
% 240.01/46.59  | | | REF_CLOSE: (11), (12), (15), (16), (17), (23), (28) are inconsistent by
% 240.01/46.59  | | |            sub-proof #165.
% 240.01/46.59  | | | 
% 240.01/46.59  | | Case 2:
% 240.01/46.59  | | | 
% 240.01/46.59  | | |   (29)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.01/46.59  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.01/46.59  | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 240.01/46.59  | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 240.01/46.59  | | |             = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 240.01/46.59  | | |           e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.01/46.59  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.01/46.59  | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.01/46.59  | | | 
% 240.01/46.59  | | | BETA: splitting (29) gives:
% 240.01/46.59  | | | 
% 240.01/46.59  | | | Case 1:
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | |   (30)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.01/46.59  | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.01/46.59  | | | |         op(e3, e1) = e1 & op(e1, e3) = e1
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | | ALPHA: (30) implies:
% 240.01/46.59  | | | |   (31)  op(e1, e3) = e1
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | | REF_CLOSE: (7), (17), (20), (31) are inconsistent by sub-proof #2226.
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | Case 2:
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | |   (32)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.01/46.59  | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.01/46.59  | | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 240.01/46.59  | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.01/46.59  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 240.01/46.59  | | | |           op(e0, e3) = e0)
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | | REF_CLOSE: (1), (6), (8), (17), (32) are inconsistent by sub-proof
% 240.01/46.59  | | | |            #1788.
% 240.01/46.59  | | | | 
% 240.01/46.59  | | | End of split
% 240.01/46.59  | | | 
% 240.01/46.59  | | End of split
% 240.01/46.59  | | 
% 240.01/46.59  | Case 2:
% 240.01/46.59  | | 
% 240.01/46.60  | |   (33)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.01/46.60  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.01/46.60  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.01/46.60  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.01/46.60  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 240.01/46.60  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.01/46.60  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.01/46.60  | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 240.01/46.60  | |           e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.01/46.60  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 240.01/46.60  | |         (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.01/46.60  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.01/46.60  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.01/46.60  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.01/46.60  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.01/46.60  | | 
% 240.01/46.60  | | BETA: splitting (33) gives:
% 240.01/46.60  | | 
% 240.01/46.60  | | Case 1:
% 240.01/46.60  | | | 
% 240.01/46.60  | | |   (34)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.01/46.60  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.01/46.60  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 240.01/46.60  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 240.01/46.60  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 240.01/46.60  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.01/46.60  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.01/46.60  | | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.01/46.60  | | | 
% 240.01/46.60  | | | REF_CLOSE: (10), (12), (14), (17), (25), (26), (34) are inconsistent by
% 240.01/46.60  | | |            sub-proof #205.
% 240.01/46.60  | | | 
% 240.01/46.60  | | Case 2:
% 240.01/46.60  | | | 
% 240.01/46.60  | | |   (35)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.01/46.60  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.01/46.60  | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29
% 240.01/46.60  | | |           = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 240.01/46.60  | | |             = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 240.01/46.60  | | |           e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.01/46.60  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.01/46.60  | | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.01/46.60  | | | 
% 240.01/46.60  | | | REF_CLOSE: (4), (8), (12), (13), (17), (35) are inconsistent by sub-proof
% 240.01/46.60  | | |            #179.
% 240.01/46.60  | | | 
% 240.01/46.60  | | End of split
% 240.01/46.60  | | 
% 240.01/46.60  | End of split
% 240.01/46.60  | 
% 240.01/46.60  End of proof
% 240.01/46.60  
% 240.01/46.60  Sub-proof #144 shows that the following formulas are inconsistent:
% 240.01/46.60  ----------------------------------------------------------------
% 240.01/46.60    (1)   ~ (all_52_7 = e2)
% 240.01/46.60    (2)  op(e1, e2) = all_52_6
% 240.01/46.60    (3)   ~ (all_52_6 = e2)
% 240.01/46.60    (4)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.01/46.60    (5)  op(e0, e2) = all_52_7
% 240.01/46.60    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.01/46.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.01/46.60  
% 240.01/46.60  Begin of proof
% 240.01/46.60  | 
% 240.01/46.60  | BETA: splitting (4) gives:
% 240.01/46.60  | 
% 240.01/46.60  | Case 1:
% 240.01/46.60  | | 
% 240.01/46.60  | |   (7)  all_58_7 = e2 & op(e1, e2) = e2
% 240.01/46.60  | | 
% 240.01/46.60  | | ALPHA: (7) implies:
% 240.01/46.60  | |   (8)  op(e1, e2) = e2
% 240.01/46.60  | | 
% 240.01/46.60  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #249.
% 240.01/46.60  | | 
% 240.01/46.60  | Case 2:
% 240.01/46.60  | | 
% 240.01/46.60  | |   (9)  all_58_13 = e2 & op(e0, e2) = e2
% 240.01/46.60  | | 
% 240.01/46.60  | | ALPHA: (9) implies:
% 240.01/46.60  | |   (10)  op(e0, e2) = e2
% 240.01/46.60  | | 
% 240.01/46.60  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #2327.
% 240.01/46.60  | | 
% 240.01/46.60  | End of split
% 240.01/46.60  | 
% 240.01/46.60  End of proof
% 240.01/46.60  
% 240.01/46.60  Sub-proof #145 shows that the following formulas are inconsistent:
% 240.01/46.60  ----------------------------------------------------------------
% 240.01/46.60    (1)   ~ (all_52_13 = e1)
% 240.01/46.60    (2)   ~ (e3 = e1)
% 240.01/46.60    (3)  op(e2, e1) = all_52_9
% 240.01/46.60    (4)   ~ (e3 = e2)
% 240.01/46.60    (5)  op(e2, e3) = e2
% 240.01/46.60    (6)  op(e2, e3) = all_52_1
% 240.01/46.60    (7)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 240.01/46.60    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.01/46.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.01/46.60    (9)  op(e2, e0) = all_52_13
% 240.01/46.60    (10)   ~ (all_52_9 = e1)
% 240.01/46.60    (11)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.01/46.60          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.01/46.60    (12)   ~ (all_52_1 = e1)
% 240.01/46.60  
% 240.01/46.60  Begin of proof
% 240.01/46.60  | 
% 240.01/46.60  | BETA: splitting (7) gives:
% 240.01/46.60  | 
% 240.01/46.60  | Case 1:
% 240.01/46.60  | | 
% 240.01/46.60  | |   (13)  all_58_2 = e3 & op(e2, e3) = e3
% 240.01/46.60  | | 
% 240.01/46.60  | | ALPHA: (13) implies:
% 240.01/46.60  | |   (14)  op(e2, e3) = e3
% 240.01/46.60  | | 
% 240.01/46.60  | | REF_CLOSE: (4), (5), (8), (14) are inconsistent by sub-proof #1897.
% 240.01/46.60  | | 
% 240.01/46.60  | Case 2:
% 240.01/46.60  | | 
% 240.01/46.60  | |   (15)  all_58_3 = e3 & op(e2, e2) = e3
% 240.01/46.60  | | 
% 240.01/46.60  | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (11), (12), (15) are
% 240.01/46.60  | |            inconsistent by sub-proof #2196.
% 240.01/46.60  | | 
% 240.01/46.60  | End of split
% 240.01/46.60  | 
% 240.01/46.60  End of proof
% 240.01/46.60  
% 240.01/46.60  Sub-proof #146 shows that the following formulas are inconsistent:
% 240.01/46.60  ----------------------------------------------------------------
% 240.01/46.60    (1)   ~ (e3 = e0)
% 240.01/46.60    (2)  op(e1, e2) = e3
% 240.01/46.60    (3)  op(e1, e3) = e1
% 240.01/46.60    (4)  op(e0, e3) = e3
% 240.01/46.60    (5)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) = all_40_1
% 240.01/46.60           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2) =
% 240.01/46.60           all_40_1 & $i(all_40_1))
% 240.01/46.60    (6)  op(e1, e1) = e2
% 240.01/46.60    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.01/46.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.01/46.60    (8)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) = all_36_1
% 240.01/46.60           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2) =
% 240.01/46.60           all_36_1 & $i(all_36_1))
% 240.01/46.60    (9)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 240.01/46.60           $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 240.01/46.60           all_56_7 & $i(all_56_7))
% 240.01/46.60    (10)   ~ (e2 = e1)
% 240.01/46.60  
% 240.01/46.60  Begin of proof
% 240.01/46.60  | 
% 240.01/46.60  | BETA: splitting (9) gives:
% 240.01/46.60  | 
% 240.01/46.60  | Case 1:
% 240.01/46.60  | | 
% 240.01/46.60  | |   (11)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 240.01/46.60  | |         $i(all_56_5)
% 240.01/46.60  | | 
% 240.01/46.60  | | ALPHA: (11) implies:
% 240.01/46.60  | |   (12)  op(e1, e3) = all_56_5
% 240.01/46.60  | |   (13)  op(e1, all_56_5) = e1
% 240.01/46.60  | | 
% 240.01/46.60  | | BETA: splitting (5) gives:
% 240.01/46.60  | | 
% 240.01/46.60  | | Case 1:
% 240.01/46.60  | | | 
% 240.01/46.60  | | | 
% 240.01/46.60  | | | GROUND_INST: instantiating (7) with e1, all_56_5, e3, e1, simplifying with
% 240.01/46.60  | | |              (3), (12) gives:
% 240.01/46.60  | | |   (14)  all_56_5 = e1
% 240.01/46.60  | | | 
% 240.01/46.60  | | | REDUCE: (13), (14) imply:
% 240.01/46.60  | | |   (15)  op(e1, e1) = e1
% 240.01/46.60  | | | 
% 240.01/46.60  | | | REF_CLOSE: (6), (7), (10), (15) are inconsistent by sub-proof #2159.
% 240.01/46.60  | | | 
% 240.01/46.60  | | Case 2:
% 240.01/46.60  | | | 
% 240.01/46.60  | | |   (16)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 240.01/46.60  | | | 
% 240.01/46.60  | | | REF_CLOSE: (2), (7), (8), (16) are inconsistent by sub-proof #2144.
% 240.01/46.60  | | | 
% 240.01/46.60  | | End of split
% 240.01/46.60  | | 
% 240.01/46.60  | Case 2:
% 240.01/46.60  | | 
% 240.01/46.60  | |   (17)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 240.01/46.60  | |         $i(all_56_7)
% 240.01/46.60  | | 
% 240.01/46.60  | | ALPHA: (17) implies:
% 240.01/46.60  | |   (18)  op(e0, e3) = all_56_7
% 240.01/46.60  | |   (19)  op(e0, all_56_7) = e0
% 240.01/46.60  | | 
% 240.01/46.60  | | REF_CLOSE: (1), (4), (7), (18), (19) are inconsistent by sub-proof #2070.
% 240.01/46.60  | | 
% 240.01/46.60  | End of split
% 240.01/46.60  | 
% 240.01/46.60  End of proof
% 240.01/46.60  
% 240.01/46.60  Sub-proof #147 shows that the following formulas are inconsistent:
% 240.01/46.60  ----------------------------------------------------------------
% 240.01/46.60    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.01/46.60         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.01/46.60    (2)   ~ (all_8_2 = e0)
% 240.01/46.60    (3)   ~ (e2 = e0)
% 240.01/46.60    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 240.01/46.60    (5)   ~ (e3 = e1)
% 240.01/46.60    (6)   ~ (e3 = e2)
% 240.01/46.60    (7)  op(e2, e2) = all_8_2
% 240.01/46.60    (8)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.01/46.60         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.01/46.60    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.01/46.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.01/46.60    (10)   ~ (e1 = e0)
% 240.01/46.60    (11)  op(e3, e3) = e0
% 240.01/46.60    (12)  all_58_4 = e3
% 240.01/46.60    (13)   ~ (e2 = e1)
% 240.01/46.60  
% 240.01/46.60  Begin of proof
% 240.01/46.60  | 
% 240.01/46.60  | BETA: splitting (4) gives:
% 240.01/46.60  | 
% 240.01/46.60  | Case 1:
% 240.01/46.60  | | 
% 240.01/46.60  | |   (14)  all_58_1 = e0 & op(e3, e2) = e0
% 240.01/46.60  | | 
% 240.01/46.60  | | ALPHA: (14) implies:
% 240.01/46.60  | |   (15)  all_58_1 = e0
% 240.01/46.60  | | 
% 240.01/46.60  | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (12), (13), (15) are
% 240.01/46.60  | |            inconsistent by sub-proof #764.
% 240.01/46.60  | | 
% 240.01/46.60  | Case 2:
% 240.01/46.60  | | 
% 240.01/46.60  | |   (16)  all_58_3 = e0 & op(e2, e2) = e0
% 240.01/46.60  | | 
% 240.01/46.60  | | REF_CLOSE: (2), (7), (9), (16) are inconsistent by sub-proof #1992.
% 240.01/46.60  | | 
% 240.01/46.60  | End of split
% 240.01/46.60  | 
% 240.01/46.60  End of proof
% 240.01/46.60  
% 240.01/46.60  Sub-proof #148 shows that the following formulas are inconsistent:
% 240.01/46.60  ----------------------------------------------------------------
% 240.01/46.60    (1)   ~ (e3 = e1)
% 240.01/46.60    (2)  op(e1, e0) = e1
% 240.01/46.60    (3)   ~ (e3 = e2)
% 240.01/46.60    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.01/46.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.01/46.60    (5)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.01/46.60    (6)  op(e0, e0) = e2
% 240.01/46.60  
% 240.01/46.60  Begin of proof
% 240.01/46.60  | 
% 240.01/46.60  | BETA: splitting (5) gives:
% 240.01/46.60  | 
% 240.01/46.60  | Case 1:
% 240.01/46.60  | | 
% 240.01/46.60  | |   (7)  all_58_11 = e3 & op(e1, e0) = e3
% 240.01/46.60  | | 
% 240.01/46.60  | | ALPHA: (7) implies:
% 240.01/46.60  | |   (8)  op(e1, e0) = e3
% 240.01/46.60  | | 
% 240.01/46.60  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #1894.
% 240.01/46.60  | | 
% 240.01/46.60  | Case 2:
% 240.01/46.60  | | 
% 240.01/46.60  | |   (9)  all_58_15 = e3 & op(e0, e0) = e3
% 240.01/46.60  | | 
% 240.01/46.60  | | ALPHA: (9) implies:
% 240.01/46.60  | |   (10)  op(e0, e0) = e3
% 240.01/46.60  | | 
% 240.01/46.60  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #1388.
% 240.01/46.60  | | 
% 240.01/46.60  | End of split
% 240.01/46.60  | 
% 240.01/46.60  End of proof
% 240.01/46.60  
% 240.01/46.60  Sub-proof #149 shows that the following formulas are inconsistent:
% 240.01/46.60  ----------------------------------------------------------------
% 240.01/46.60    (1)   ~ (all_52_3 = e0)
% 240.01/46.60    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.01/46.60    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.01/46.60         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.01/46.60    (4)   ~ (all_8_2 = e0)
% 240.01/46.60    (5)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 240.01/46.60    (6)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.01/46.60         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.01/46.60    (7)  all_56_11 = e1
% 240.01/46.60    (8)  op(e0, e1) = all_52_11
% 240.01/46.60    (9)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.01/46.60           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 240.01/46.60           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 240.01/46.60         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.01/46.60           $i(all_56_15))
% 240.01/46.60    (10)  op(e1, e2) = all_52_6
% 240.01/46.60    (11)  ( ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 240.01/46.60            $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e0, e2) = all_4_1
% 240.01/46.60            & $i(all_4_1))
% 240.01/46.60    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.01/46.60          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.01/46.60    (13)  op(e1, e0) = all_52_14
% 240.01/46.60    (14)   ~ (all_52_13 = e1)
% 240.01/46.60    (15)  op(e0, e3) = all_52_3
% 240.01/46.60    (16)   ~ (e3 = e1)
% 240.01/46.60    (17)  all_54_11 = all_52_14
% 240.01/46.60    (18)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.01/46.60          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.01/46.60    (19)   ~ (all_52_2 = all_52_3)
% 240.01/46.60    (20)  all_54_6 = all_52_9
% 240.01/46.60    (21)  op(e3, e2) = e2
% 240.01/46.60    (22)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.01/46.60    (23)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 240.01/46.60          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 240.01/46.60    (24)   ~ (all_52_2 = all_52_14)
% 240.01/46.60    (25)  all_58_15 = e2
% 240.01/46.60    (26)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.01/46.60    (27)   ~ (all_52_14 = e2)
% 240.01/46.60    (28)  op(e2, e1) = all_52_9
% 240.01/46.60    (29)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.01/46.60          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.01/46.60    (30)   ~ (e3 = e2)
% 240.01/46.60    (31)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 240.01/46.60            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 240.01/46.60              e2) = all_44_1 & $i(all_44_1))
% 240.01/46.60    (32)   ~ (all_52_7 = e1)
% 240.01/46.60    (33)  op(e2, e3) = e2
% 240.01/46.60    (34)  all_56_31 = e2
% 240.01/46.60    (35)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.01/46.60            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.01/46.60            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.01/46.60            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.01/46.60            op(e0, all_56_31) = e0)
% 240.01/46.60    (36)  all_54_12 = all_52_3
% 240.01/46.60    (37)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 240.01/46.60            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 240.01/46.60              e0) = all_16_1 & $i(all_16_1))
% 240.01/46.60    (38)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.01/46.60          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.01/46.60    (39)   ~ (all_52_3 = e2)
% 240.01/46.60    (40)   ~ (all_52_9 = all_52_13)
% 240.01/46.60    (41)   ~ (all_52_1 = e0)
% 240.01/46.60    (42)  all_58_9 = e3
% 240.01/46.60    (43)  op(e2, e2) = all_8_2
% 240.01/46.60    (44)  op(e3, e0) = e3
% 240.01/46.60    (45)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 240.01/46.60    (46)  op(e2, e3) = all_52_1
% 240.01/46.60    (47)   ~ (all_52_14 = e3)
% 240.01/46.60    (48)   ~ (all_52_13 = e2)
% 240.01/46.60    (49)  op(e3, e0) = all_50_1
% 240.01/46.60    (50)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 240.01/46.60            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 240.01/46.60              e2) = all_40_1 & $i(all_40_1))
% 240.01/46.60    (51)  op(e1, e1) = e2
% 240.01/46.60    (52)   ~ (all_52_2 = e0)
% 240.01/46.60    (53)  all_54_7 = all_52_13
% 240.01/46.61    (54)  op(e0, e2) = all_52_7
% 240.01/46.61    (55)   ~ (all_52_13 = all_52_14)
% 240.01/46.61    (56)   ~ (all_52_2 = e2)
% 240.01/46.61    (57)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.01/46.61          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.01/46.61    (58)  all_54_8 = all_52_2
% 240.01/46.61    (59)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.01/46.61          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.01/46.61    (60)   ~ (all_52_2 = all_52_6)
% 240.01/46.61    (61)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.01/46.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.01/46.61    (62)  op(e1, e3) = all_52_2
% 240.01/46.61    (63)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 240.01/46.61            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 240.01/46.61              e2) = all_36_1 & $i(all_36_1))
% 240.01/46.61    (64)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.01/46.61          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.01/46.61    (65)  op(e3, e3) = e0
% 240.01/46.61    (66)  op(e0, e0) = e2
% 240.01/46.61    (67)  op(e2, e0) = all_52_13
% 240.01/46.61    (68)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.01/46.61          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.01/46.61            e1)
% 240.01/46.61    (69)   ~ (all_52_9 = e1)
% 240.01/46.61    (70)   ~ (all_52_9 = all_52_11)
% 240.01/46.61    (71)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.01/46.61          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.01/46.61    (72)   ~ (e2 = e1)
% 240.01/46.61    (73)   ~ (all_52_1 = e1)
% 240.01/46.61    (74)   ~ (all_52_9 = e2)
% 240.01/46.61  
% 240.01/46.61  Begin of proof
% 240.01/46.61  | 
% 240.01/46.61  | BETA: splitting (37) gives:
% 240.01/46.61  | 
% 240.01/46.61  | Case 1:
% 240.01/46.61  | | 
% 240.01/46.61  | |   (75)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 240.01/46.61  | |         all_16_1 & $i(all_16_0) & $i(all_16_1)
% 240.01/46.61  | | 
% 240.01/46.61  | | ALPHA: (75) implies:
% 240.01/46.61  | |   (76)  op(e3, e0) = all_16_1
% 240.01/46.61  | | 
% 240.01/46.61  | | BETA: splitting (26) gives:
% 240.01/46.61  | | 
% 240.01/46.61  | | Case 1:
% 240.01/46.61  | | | 
% 240.01/46.61  | | |   (77)  all_54_7 = e2
% 240.01/46.61  | | | 
% 240.01/46.61  | | | REF_CLOSE: (48), (53), (77) are inconsistent by sub-proof #1997.
% 240.01/46.61  | | | 
% 240.01/46.61  | | Case 2:
% 240.01/46.61  | | | 
% 240.01/46.61  | | |   (78)   ~ (all_54_7 = e2)
% 240.01/46.61  | | |   (79)  all_54_7 = e1 | all_54_7 = e0
% 240.01/46.61  | | | 
% 240.01/46.61  | | | BETA: splitting (79) gives:
% 240.01/46.61  | | | 
% 240.01/46.61  | | | Case 1:
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | |   (80)  all_54_7 = e1
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | REF_CLOSE: (14), (53), (80) are inconsistent by sub-proof #2295.
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | Case 2:
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | |   (81)  all_54_7 = e0
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | COMBINE_EQS: (53), (81) imply:
% 240.01/46.61  | | | |   (82)  all_52_13 = e0
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | SIMP: (82) implies:
% 240.01/46.61  | | | |   (83)  all_52_13 = e0
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | REDUCE: (40), (83) imply:
% 240.01/46.61  | | | |   (84)   ~ (all_52_9 = e0)
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | REDUCE: (55), (83) imply:
% 240.01/46.61  | | | |   (85)   ~ (all_52_14 = e0)
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | SIMP: (85) implies:
% 240.01/46.61  | | | |   (86)   ~ (all_52_14 = e0)
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | REDUCE: (48), (83) imply:
% 240.01/46.61  | | | |   (87)   ~ (e2 = e0)
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | SIMP: (87) implies:
% 240.01/46.61  | | | |   (88)   ~ (e2 = e0)
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | REDUCE: (14), (83) imply:
% 240.01/46.61  | | | |   (89)   ~ (e1 = e0)
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | SIMP: (89) implies:
% 240.01/46.61  | | | |   (90)   ~ (e1 = e0)
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | REDUCE: (67), (83) imply:
% 240.01/46.61  | | | |   (91)  op(e2, e0) = e0
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | BETA: splitting (18) gives:
% 240.01/46.61  | | | | 
% 240.01/46.61  | | | | Case 1:
% 240.01/46.61  | | | | | 
% 240.01/46.61  | | | | |   (92)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 240.01/46.61  | | | | |             e1) = e0)
% 240.01/46.61  | | | | | 
% 240.01/46.61  | | | | | REF_CLOSE: (3), (16), (28), (30), (42), (44), (59), (61), (65), (72),
% 240.01/46.61  | | | | |            (84), (88), (90), (92) are inconsistent by sub-proof #161.
% 240.01/46.61  | | | | | 
% 240.01/46.61  | | | | Case 2:
% 240.01/46.61  | | | | | 
% 240.01/46.61  | | | | |   (93)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 240.01/46.61  | | | | |             e1) = e0)
% 240.01/46.61  | | | | | 
% 240.01/46.61  | | | | | BETA: splitting (93) gives:
% 240.01/46.61  | | | | | 
% 240.01/46.61  | | | | | Case 1:
% 240.01/46.61  | | | | | | 
% 240.01/46.61  | | | | | |   (94)  all_58_8 = e0 & op(e1, e1) = e0
% 240.01/46.61  | | | | | | 
% 240.01/46.61  | | | | | | ALPHA: (94) implies:
% 240.01/46.61  | | | | | |   (95)  op(e1, e1) = e0
% 240.01/46.61  | | | | | | 
% 240.01/46.61  | | | | | | REF_CLOSE: (51), (61), (88), (95) are inconsistent by sub-proof
% 240.01/46.61  | | | | | |            #2211.
% 240.01/46.61  | | | | | | 
% 240.01/46.61  | | | | | Case 2:
% 240.01/46.61  | | | | | | 
% 240.01/46.61  | | | | | |   (96)  all_58_14 = e0 & op(e0, e1) = e0
% 240.01/46.61  | | | | | | 
% 240.01/46.61  | | | | | | ALPHA: (96) implies:
% 240.01/46.61  | | | | | |   (97)  op(e0, e1) = e0
% 240.01/46.61  | | | | | | 
% 240.01/46.61  | | | | | | BETA: splitting (22) gives:
% 240.01/46.61  | | | | | | 
% 240.01/46.61  | | | | | | Case 1:
% 240.01/46.61  | | | | | | | 
% 240.01/46.61  | | | | | | |   (98)  all_54_11 = e3
% 240.01/46.61  | | | | | | | 
% 240.01/46.61  | | | | | | | COMBINE_EQS: (17), (98) imply:
% 240.01/46.61  | | | | | | |   (99)  all_52_14 = e3
% 240.01/46.61  | | | | | | | 
% 240.01/46.61  | | | | | | | REDUCE: (47), (99) imply:
% 240.01/46.61  | | | | | | |   (100)  $false
% 240.01/46.61  | | | | | | | 
% 240.01/46.61  | | | | | | | CLOSE: (100) is inconsistent.
% 240.01/46.61  | | | | | | | 
% 240.01/46.61  | | | | | | Case 2:
% 240.01/46.61  | | | | | | | 
% 240.01/46.61  | | | | | | |   (101)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.01/46.61  | | | | | | | 
% 240.01/46.61  | | | | | | | BETA: splitting (45) gives:
% 240.01/46.61  | | | | | | | 
% 240.01/46.61  | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | 
% 240.01/46.61  | | | | | | | |   (102)  all_54_6 = e3
% 240.01/46.61  | | | | | | | | 
% 240.01/46.61  | | | | | | | | COMBINE_EQS: (20), (102) imply:
% 240.01/46.61  | | | | | | | |   (103)  all_52_9 = e3
% 240.01/46.61  | | | | | | | | 
% 240.01/46.61  | | | | | | | | SIMP: (103) implies:
% 240.01/46.61  | | | | | | | |   (104)  all_52_9 = e3
% 240.01/46.61  | | | | | | | | 
% 240.01/46.61  | | | | | | | | REDUCE: (70), (104) imply:
% 240.01/46.61  | | | | | | | |   (105)   ~ (all_52_11 = e3)
% 240.01/46.61  | | | | | | | | 
% 240.01/46.61  | | | | | | | | SIMP: (105) implies:
% 240.01/46.61  | | | | | | | |   (106)   ~ (all_52_11 = e3)
% 240.01/46.61  | | | | | | | | 
% 240.01/46.61  | | | | | | | | REDUCE: (84), (104) imply:
% 240.01/46.61  | | | | | | | |   (107)   ~ (e3 = e0)
% 240.01/46.61  | | | | | | | | 
% 240.01/46.61  | | | | | | | | REDUCE: (28), (104) imply:
% 240.01/46.61  | | | | | | | |   (108)  op(e2, e1) = e3
% 240.01/46.61  | | | | | | | | 
% 240.01/46.61  | | | | | | | | BETA: splitting (68) gives:
% 240.01/46.61  | | | | | | | | 
% 240.01/46.61  | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | 
% 240.01/46.61  | | | | | | | | |   (109)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1
% 240.01/46.61  | | | | | | | | |            & op(e0, e2) = e1)
% 240.01/46.61  | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | BETA: splitting (109) gives:
% 240.01/46.61  | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | |   (110)  all_58_12 = e1 & op(e0, e3) = e1
% 240.01/46.61  | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | ALPHA: (110) implies:
% 240.01/46.61  | | | | | | | | | |   (111)  all_58_12 = e1
% 240.01/46.61  | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | BETA: splitting (23) gives:
% 240.01/46.61  | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | |   (112)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 240.01/46.61  | | | | | | | | | | |            & op(e2, e3) = e3)
% 240.01/46.61  | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | REF_CLOSE: (1), (15), (30), (33), (38), (41), (46), (52),
% 240.01/46.61  | | | | | | | | | | |            (61), (62), (107), (112) are inconsistent by
% 240.01/46.61  | | | | | | | | | | |            sub-proof #160.
% 240.01/46.61  | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | Case 2:
% 240.01/46.61  | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | |   (113)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 240.01/46.61  | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 240.01/46.61  | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | BETA: splitting (113) gives:
% 240.01/46.61  | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | |   (114)  all_58_6 = e3 & op(e1, e3) = e3
% 240.01/46.61  | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | ALPHA: (114) implies:
% 240.01/46.61  | | | | | | | | | | | |   (115)  all_58_6 = e3
% 240.01/46.61  | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | BETA: splitting (101) gives:
% 240.01/46.61  | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | |   (116)  all_54_11 = e2
% 240.01/46.61  | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | REF_CLOSE: (17), (27), (116) are inconsistent by sub-proof
% 240.01/46.61  | | | | | | | | | | | | |            #2177.
% 240.01/46.61  | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | Case 2:
% 240.01/46.61  | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | |   (117)   ~ (all_54_11 = e2)
% 240.01/46.61  | | | | | | | | | | | | |   (118)  all_54_11 = e1 | all_54_11 = e0
% 240.01/46.61  | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | BETA: splitting (118) gives:
% 240.01/46.61  | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | |   (119)  all_54_11 = e1
% 240.01/46.61  | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | COMBINE_EQS: (17), (119) imply:
% 240.01/46.61  | | | | | | | | | | | | | |   (120)  all_52_14 = e1
% 240.01/46.61  | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | SIMP: (120) implies:
% 240.01/46.61  | | | | | | | | | | | | | |   (121)  all_52_14 = e1
% 240.01/46.61  | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | REDUCE: (24), (121) imply:
% 240.01/46.61  | | | | | | | | | | | | | |   (122)   ~ (all_52_2 = e1)
% 240.01/46.61  | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | REDUCE: (27), (121) imply:
% 240.01/46.61  | | | | | | | | | | | | | |   (123)   ~ (e2 = e1)
% 240.01/46.61  | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | REDUCE: (13), (121) imply:
% 240.01/46.61  | | | | | | | | | | | | | |   (124)  op(e1, e0) = e1
% 240.01/46.61  | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 240.01/46.61  | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | |   (125)  all_54_8 = e3
% 240.01/46.61  | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | COMBINE_EQS: (58), (125) imply:
% 240.01/46.61  | | | | | | | | | | | | | | |   (126)  all_52_2 = e3
% 240.01/46.61  | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | SIMP: (126) implies:
% 240.01/46.61  | | | | | | | | | | | | | | |   (127)  all_52_2 = e3
% 240.01/46.61  | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | REDUCE: (19), (127) imply:
% 240.01/46.61  | | | | | | | | | | | | | | |   (128)   ~ (all_52_3 = e3)
% 240.01/46.61  | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | SIMP: (128) implies:
% 240.01/46.61  | | | | | | | | | | | | | | |   (129)   ~ (all_52_3 = e3)
% 240.01/46.61  | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | REDUCE: (60), (127) imply:
% 240.01/46.61  | | | | | | | | | | | | | | |   (130)   ~ (all_52_6 = e3)
% 240.01/46.61  | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | SIMP: (130) implies:
% 240.01/46.61  | | | | | | | | | | | | | | |   (131)   ~ (all_52_6 = e3)
% 240.01/46.61  | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | |   (132)  all_54_12 = e3
% 240.01/46.61  | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (129), (132) are inconsistent by sub-proof
% 240.01/46.61  | | | | | | | | | | | | | | | |            #2266.
% 240.01/46.61  | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | Case 2:
% 240.01/46.61  | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | |   (133)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.01/46.61  | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | |   (134)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 240.01/46.61  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 240.01/46.61  | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (21), (28), (30), (46), (61), (67), (69),
% 240.01/46.61  | | | | | | | | | | | | | | | | |            (71), (73), (90), (91), (134) are inconsistent by
% 240.01/46.61  | | | | | | | | | | | | | | | | |            sub-proof #1776.
% 240.01/46.61  | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.61  | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | |   (135)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 240.01/46.61  | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 240.01/46.61  | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | |   (136)  all_58_7 = e3 & op(e1, e2) = e3
% 240.01/46.61  | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 240.01/46.61  | | | | | | | | | | | | | | | | | |   (137)  op(e1, e2) = e3
% 240.01/46.61  | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (61), (131), (137) are inconsistent by
% 240.01/46.61  | | | | | | | | | | | | | | | | | |            sub-proof #2191.
% 240.01/46.61  | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | |   (138)  all_58_13 = e3 & op(e0, e2) = e3
% 240.01/46.61  | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 240.01/46.61  | | | | | | | | | | | | | | | | | |   (139)  op(e0, e2) = e3
% 240.01/46.61  | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | |   (140)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.01/46.61  | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 240.01/46.61  | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 240.01/46.61  | | | | | | | | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | |   (141)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | |            e0) = all_56_25 & $i(all_56_25)
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | |   (142)  op(e3, e0) = all_56_25
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | |   (143)  op(e3, all_56_25) = e3
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | |   (144)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (43), (61), (88), (144) are
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #159.
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | |   (145)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | |   (146)  all_58_7 = e0 & op(e1, e2) = e0
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | |   (147)  op(e1, e2) = e0
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | |   (148)  all_54_12 = e2
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (148) are inconsistent by sub-proof
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | |            #2264.
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | |   (149)  all_54_12 = e1 | all_54_12 = e0
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | |   (150)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, all_56_11) = e2)
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (21), (30), (36), (61), (65), (107),
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | |            (108), (149), (150) are inconsistent by sub-proof
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | |            #157.
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | |   (151)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | |            all_56_15 & $i(all_56_15))
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (152)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_13 & $i(all_56_13)
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (153)  op(e1, e2) = all_56_13
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (154)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e2) = all_40_1 & $i(all_40_0) &
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_40_1)
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (155)  op(e1, e2) = all_40_1
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e3, all_50_1, e0, e3,
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (44), (49) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (156)  all_50_1 = e3
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_50_1, all_56_25, e0,
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (49), (142) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (157)  all_56_25 = all_50_1
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_16_1, all_56_25, e0,
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (76), (142) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (158)  all_56_25 = all_16_1
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (158) imply:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (159)  all_50_1 = all_16_1
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (159) implies:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (160)  all_50_1 = all_16_1
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (156), (160) imply:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (161)  all_16_1 = e3
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (161) imply:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (162)  all_56_25 = e3
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (162) imply:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (163)  op(e3, e3) = e3
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (15), (16), (29), (30), (38), (57), (61),
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (72), (88), (90), (107), (115), (163) are
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1572.
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (164)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_36_1)
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (165)   ~ (all_36_1 = e0)
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (166)  op(e1, e2) = all_36_1
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (147), (155), (165), (166) are inconsistent
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1883.
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (167)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_40_1)
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (168)   ~ (all_40_1 = e3)
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (169)  op(e1, e2) = all_40_1
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_40_1, all_56_13, e2,
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (153), (169) gives:
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (170)  all_56_13 = all_40_1
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e0, all_56_13, e2, e1,
% 240.01/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (147), (153) gives:
% 240.01/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (171)  all_56_13 = e0
% 240.01/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e3, all_50_1, e0, e3,
% 240.01/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (44), (49) gives:
% 240.01/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (172)  all_50_1 = e3
% 240.01/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.01/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_50_1, all_56_25, e0,
% 240.01/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (49), (142) gives:
% 240.01/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (173)  all_56_25 = all_50_1
% 240.01/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_16_1, all_56_25, e0,
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (76), (142) gives:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (174)  all_56_25 = all_16_1
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (171) imply:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (175)  all_40_1 = e0
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (175) implies:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (176)  all_40_1 = e0
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (173), (174) imply:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (177)  all_50_1 = all_16_1
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (177) implies:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (178)  all_50_1 = all_16_1
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (178) imply:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (179)  all_16_1 = e3
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (179) imply:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (180)  all_56_25 = e3
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (176) imply:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (181)   ~ (e3 = e0)
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (180) imply:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (182)  op(e3, e3) = e3
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (15), (16), (29), (30), (38), (57), (61),
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (72), (88), (90), (107), (115), (182) are
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1572.
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (183)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_36_1)
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (184)   ~ (all_36_1 = e0)
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (185)  op(e1, e2) = all_36_1
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (147), (169), (184), (185) are inconsistent
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1883.
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_15 & $i(all_56_15)
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (11), (15), (31), (61), (139), (186) are
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | |   (187)  all_58_13 = e0 & op(e0, e2) = e0
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | |   (188)  op(e0, e2) = e0
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (30), (61), (66), (106), (107),
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | |            (111), (188) are inconsistent by sub-proof #190.
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |   (189)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |            e0) = all_56_27 & $i(all_56_27)
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |   (190)  op(e2, e0) = all_56_27
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |   (191)  op(e2, all_56_27) = e2
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (12), (14), (16), (21), (30), (43),
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |            (48), (50), (53), (61), (63), (66), (67), (79),
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |            (88), (91), (106), (107), (111), (190), (191) are
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #153.
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | |   (192)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.06/46.62  | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 240.06/46.62  | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |   (193)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |            e0) = all_56_29 & $i(all_56_29)
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |   (194)  op(e1, e0) = all_56_29
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |   (195)  op(e1, all_56_29) = e1
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (12), (16), (21), (30), (43), (50),
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |            (51), (61), (63), (66), (72), (88), (106), (107),
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |            (111), (124), (194), (195) are inconsistent by
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |            sub-proof #152.
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |   (196)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (30), (34), (61), (66), (106),
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |            (107), (111), (196) are inconsistent by sub-proof
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |            #151.
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | |   (197)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | REF_CLOSE: (52), (56), (58), (122), (197) are inconsistent by
% 240.06/46.62  | | | | | | | | | | | | | | |            sub-proof #1949.
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | |   (198)  all_54_11 = e0
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | REF_CLOSE: (17), (86), (198) are inconsistent by sub-proof
% 240.06/46.62  | | | | | | | | | | | | | |            #2175.
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | |   (199)  all_58_12 = e3 & op(e0, e3) = e3
% 240.06/46.62  | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | ALPHA: (199) implies:
% 240.06/46.62  | | | | | | | | | | | |   (200)  all_58_12 = e3
% 240.06/46.62  | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | REF_CLOSE: (16), (111), (200) are inconsistent by sub-proof
% 240.06/46.62  | | | | | | | | | | | |            #1542.
% 240.06/46.62  | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | |   (201)  all_58_13 = e1 & op(e0, e2) = e1
% 240.06/46.62  | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | REF_CLOSE: (32), (54), (61), (201) are inconsistent by
% 240.06/46.62  | | | | | | | | | |            sub-proof #2275.
% 240.06/46.62  | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | | 
% 240.06/46.62  | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | 
% 240.06/46.62  | | | | | | | | |   (202)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1
% 240.06/46.62  | | | | | | | | |            & op(e0, e0) = e1)
% 240.06/46.62  | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | REF_CLOSE: (25), (61), (72), (90), (97), (202) are
% 240.06/46.62  | | | | | | | | |            inconsistent by sub-proof #150.
% 240.06/46.62  | | | | | | | | | 
% 240.06/46.62  | | | | | | | | End of split
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | |   (203)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | | REF_CLOSE: (20), (69), (74), (84), (203) are inconsistent by
% 240.06/46.62  | | | | | | | |            sub-proof #2244.
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | End of split
% 240.06/46.62  | | | | | | | 
% 240.06/46.62  | | | | | | End of split
% 240.06/46.62  | | | | | | 
% 240.06/46.62  | | | | | End of split
% 240.06/46.62  | | | | | 
% 240.06/46.62  | | | | End of split
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | End of split
% 240.06/46.62  | | | 
% 240.06/46.62  | | End of split
% 240.06/46.62  | | 
% 240.06/46.62  | Case 2:
% 240.06/46.62  | | 
% 240.06/46.62  | |   (204)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 & $i(all_16_1)
% 240.06/46.62  | | 
% 240.06/46.62  | | ALPHA: (204) implies:
% 240.06/46.62  | |   (205)   ~ (all_16_1 = e1)
% 240.06/46.62  | |   (206)  op(e3, e0) = all_16_1
% 240.06/46.62  | | 
% 240.06/46.62  | | BETA: splitting (26) gives:
% 240.06/46.62  | | 
% 240.06/46.62  | | Case 1:
% 240.06/46.62  | | | 
% 240.06/46.62  | | |   (207)  all_54_7 = e2
% 240.06/46.62  | | | 
% 240.06/46.62  | | | REF_CLOSE: (48), (53), (207) are inconsistent by sub-proof #1997.
% 240.06/46.62  | | | 
% 240.06/46.62  | | Case 2:
% 240.06/46.62  | | | 
% 240.06/46.62  | | |   (208)   ~ (all_54_7 = e2)
% 240.06/46.62  | | |   (209)  all_54_7 = e1 | all_54_7 = e0
% 240.06/46.62  | | | 
% 240.06/46.62  | | | BETA: splitting (209) gives:
% 240.06/46.62  | | | 
% 240.06/46.62  | | | Case 1:
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | |   (210)  all_54_7 = e1
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | REF_CLOSE: (14), (53), (210) are inconsistent by sub-proof #2295.
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | Case 2:
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | |   (211)  all_54_7 = e0
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | COMBINE_EQS: (53), (211) imply:
% 240.06/46.62  | | | |   (212)  all_52_13 = e0
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | SIMP: (212) implies:
% 240.06/46.62  | | | |   (213)  all_52_13 = e0
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | REDUCE: (40), (213) imply:
% 240.06/46.62  | | | |   (214)   ~ (all_52_9 = e0)
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | REDUCE: (55), (213) imply:
% 240.06/46.62  | | | |   (215)   ~ (all_52_14 = e0)
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | SIMP: (215) implies:
% 240.06/46.62  | | | |   (216)   ~ (all_52_14 = e0)
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | REDUCE: (48), (213) imply:
% 240.06/46.62  | | | |   (217)   ~ (e2 = e0)
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | SIMP: (217) implies:
% 240.06/46.62  | | | |   (218)   ~ (e2 = e0)
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | REDUCE: (14), (213) imply:
% 240.06/46.62  | | | |   (219)   ~ (e1 = e0)
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | SIMP: (219) implies:
% 240.06/46.62  | | | |   (220)   ~ (e1 = e0)
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | REDUCE: (67), (213) imply:
% 240.06/46.62  | | | |   (221)  op(e2, e0) = e0
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | BETA: splitting (18) gives:
% 240.06/46.62  | | | | 
% 240.06/46.62  | | | | Case 1:
% 240.06/46.62  | | | | | 
% 240.06/46.62  | | | | |   (222)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 240.06/46.62  | | | | |              e1) = e0)
% 240.06/46.62  | | | | | 
% 240.06/46.62  | | | | | REF_CLOSE: (3), (16), (28), (30), (42), (44), (59), (61), (65), (72),
% 240.06/46.62  | | | | |            (214), (218), (220), (222) are inconsistent by sub-proof
% 240.06/46.62  | | | | |            #161.
% 240.06/46.62  | | | | | 
% 240.06/46.62  | | | | Case 2:
% 240.06/46.62  | | | | | 
% 240.06/46.62  | | | | |   (223)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 240.06/46.62  | | | | |              e1) = e0)
% 240.06/46.62  | | | | | 
% 240.06/46.62  | | | | | BETA: splitting (223) gives:
% 240.06/46.62  | | | | | 
% 240.06/46.62  | | | | | Case 1:
% 240.06/46.62  | | | | | | 
% 240.06/46.62  | | | | | |   (224)  all_58_8 = e0 & op(e1, e1) = e0
% 240.06/46.62  | | | | | | 
% 240.06/46.62  | | | | | | ALPHA: (224) implies:
% 240.06/46.62  | | | | | |   (225)  op(e1, e1) = e0
% 240.06/46.62  | | | | | | 
% 240.06/46.62  | | | | | | REF_CLOSE: (51), (61), (218), (225) are inconsistent by sub-proof
% 240.06/46.62  | | | | | |            #2211.
% 240.06/46.62  | | | | | | 
% 240.06/46.62  | | | | | Case 2:
% 240.06/46.62  | | | | | | 
% 240.06/46.62  | | | | | |   (226)  all_58_14 = e0 & op(e0, e1) = e0
% 240.06/46.62  | | | | | | 
% 240.06/46.62  | | | | | | ALPHA: (226) implies:
% 240.06/46.62  | | | | | |   (227)  op(e0, e1) = e0
% 240.06/46.62  | | | | | | 
% 240.06/46.62  | | | | | | BETA: splitting (22) gives:
% 240.06/46.62  | | | | | | 
% 240.06/46.62  | | | | | | Case 1:
% 240.06/46.62  | | | | | | | 
% 240.06/46.62  | | | | | | |   (228)  all_54_11 = e3
% 240.06/46.62  | | | | | | | 
% 240.06/46.62  | | | | | | | COMBINE_EQS: (17), (228) imply:
% 240.06/46.62  | | | | | | |   (229)  all_52_14 = e3
% 240.06/46.62  | | | | | | | 
% 240.06/46.62  | | | | | | | REDUCE: (47), (229) imply:
% 240.06/46.62  | | | | | | |   (230)  $false
% 240.06/46.62  | | | | | | | 
% 240.06/46.62  | | | | | | | CLOSE: (230) is inconsistent.
% 240.06/46.62  | | | | | | | 
% 240.06/46.62  | | | | | | Case 2:
% 240.06/46.62  | | | | | | | 
% 240.06/46.62  | | | | | | |   (231)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.06/46.62  | | | | | | | 
% 240.06/46.62  | | | | | | | BETA: splitting (45) gives:
% 240.06/46.62  | | | | | | | 
% 240.06/46.62  | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | |   (232)  all_54_6 = e3
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | | COMBINE_EQS: (20), (232) imply:
% 240.06/46.62  | | | | | | | |   (233)  all_52_9 = e3
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | | SIMP: (233) implies:
% 240.06/46.62  | | | | | | | |   (234)  all_52_9 = e3
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | | REDUCE: (70), (234) imply:
% 240.06/46.62  | | | | | | | |   (235)   ~ (all_52_11 = e3)
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | | SIMP: (235) implies:
% 240.06/46.62  | | | | | | | |   (236)   ~ (all_52_11 = e3)
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | | REDUCE: (214), (234) imply:
% 240.06/46.62  | | | | | | | |   (237)   ~ (e3 = e0)
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | | REDUCE: (28), (234) imply:
% 240.06/46.62  | | | | | | | |   (238)  op(e2, e1) = e3
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | | BETA: splitting (68) gives:
% 240.06/46.62  | | | | | | | | 
% 240.06/46.62  | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | 
% 240.06/46.62  | | | | | | | | |   (239)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1
% 240.06/46.62  | | | | | | | | |            & op(e0, e2) = e1)
% 240.06/46.62  | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | BETA: splitting (239) gives:
% 240.06/46.62  | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | |   (240)  all_58_12 = e1 & op(e0, e3) = e1
% 240.06/46.62  | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | ALPHA: (240) implies:
% 240.06/46.62  | | | | | | | | | |   (241)  all_58_12 = e1
% 240.06/46.62  | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | BETA: splitting (23) gives:
% 240.06/46.62  | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | |   (242)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 240.06/46.62  | | | | | | | | | | |            & op(e2, e3) = e3)
% 240.06/46.62  | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | REF_CLOSE: (1), (15), (30), (33), (38), (41), (46), (52),
% 240.06/46.62  | | | | | | | | | | |            (61), (62), (237), (242) are inconsistent by
% 240.06/46.62  | | | | | | | | | | |            sub-proof #160.
% 240.06/46.62  | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | |   (243)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 240.06/46.62  | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 240.06/46.62  | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | BETA: splitting (243) gives:
% 240.06/46.62  | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | |   (244)  all_58_6 = e3 & op(e1, e3) = e3
% 240.06/46.62  | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | ALPHA: (244) implies:
% 240.06/46.62  | | | | | | | | | | | |   (245)  all_58_6 = e3
% 240.06/46.62  | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | BETA: splitting (231) gives:
% 240.06/46.62  | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | |   (246)  all_54_11 = e2
% 240.06/46.62  | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | REF_CLOSE: (17), (27), (246) are inconsistent by sub-proof
% 240.06/46.62  | | | | | | | | | | | | |            #2177.
% 240.06/46.62  | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | |   (247)   ~ (all_54_11 = e2)
% 240.06/46.62  | | | | | | | | | | | | |   (248)  all_54_11 = e1 | all_54_11 = e0
% 240.06/46.62  | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | BETA: splitting (248) gives:
% 240.06/46.62  | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | |   (249)  all_54_11 = e1
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | COMBINE_EQS: (17), (249) imply:
% 240.06/46.62  | | | | | | | | | | | | | |   (250)  all_52_14 = e1
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | SIMP: (250) implies:
% 240.06/46.62  | | | | | | | | | | | | | |   (251)  all_52_14 = e1
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | REDUCE: (24), (251) imply:
% 240.06/46.62  | | | | | | | | | | | | | |   (252)   ~ (all_52_2 = e1)
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | REDUCE: (27), (251) imply:
% 240.06/46.62  | | | | | | | | | | | | | |   (253)   ~ (e2 = e1)
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | REDUCE: (13), (251) imply:
% 240.06/46.62  | | | | | | | | | | | | | |   (254)  op(e1, e0) = e1
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 240.06/46.62  | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | |   (255)  all_54_8 = e3
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | COMBINE_EQS: (58), (255) imply:
% 240.06/46.62  | | | | | | | | | | | | | | |   (256)  all_52_2 = e3
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | SIMP: (256) implies:
% 240.06/46.62  | | | | | | | | | | | | | | |   (257)  all_52_2 = e3
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | REDUCE: (19), (257) imply:
% 240.06/46.62  | | | | | | | | | | | | | | |   (258)   ~ (all_52_3 = e3)
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | SIMP: (258) implies:
% 240.06/46.62  | | | | | | | | | | | | | | |   (259)   ~ (all_52_3 = e3)
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | REDUCE: (60), (257) imply:
% 240.06/46.62  | | | | | | | | | | | | | | |   (260)   ~ (all_52_6 = e3)
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | SIMP: (260) implies:
% 240.06/46.62  | | | | | | | | | | | | | | |   (261)   ~ (all_52_6 = e3)
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 240.06/46.62  | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | |   (262)  all_54_12 = e3
% 240.06/46.62  | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (259), (262) are inconsistent by sub-proof
% 240.06/46.62  | | | | | | | | | | | | | | | |            #2266.
% 240.06/46.62  | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | |   (263)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.06/46.62  | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 240.06/46.62  | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | |   (264)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 240.06/46.62  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 240.06/46.62  | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (21), (28), (30), (46), (61), (67), (69),
% 240.06/46.62  | | | | | | | | | | | | | | | | |            (71), (73), (220), (221), (264) are inconsistent
% 240.06/46.62  | | | | | | | | | | | | | | | | |            by sub-proof #1776.
% 240.06/46.62  | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | |   (265)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 240.06/46.62  | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 240.06/46.62  | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 240.06/46.62  | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | |   (266)  all_58_7 = e3 & op(e1, e2) = e3
% 240.06/46.62  | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 240.06/46.62  | | | | | | | | | | | | | | | | | |   (267)  op(e1, e2) = e3
% 240.06/46.62  | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (61), (261), (267) are inconsistent by
% 240.06/46.62  | | | | | | | | | | | | | | | | | |            sub-proof #2191.
% 240.06/46.62  | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | |   (268)  all_58_13 = e3 & op(e0, e2) = e3
% 240.06/46.62  | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 240.06/46.62  | | | | | | | | | | | | | | | | | |   (269)  op(e0, e2) = e3
% 240.06/46.62  | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | |   (270)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.06/46.62  | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 240.06/46.62  | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 240.06/46.62  | | | | | | | | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |   (271)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |            e0) = all_56_25 & $i(all_56_25)
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |   (272)  op(e3, e0) = all_56_25
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | |   (273)  op(e3, all_56_25) = e3
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | |   (274)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (43), (61), (218), (274) are
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #159.
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | |   (275)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | |   (276)  all_58_7 = e0 & op(e1, e2) = e0
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | |   (277)  op(e1, e2) = e0
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_54_12 = e2
% 240.06/46.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (278) are inconsistent by sub-proof
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | |            #2264.
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_54_12 = e1 | all_54_12 = e0
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | |   (280)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, all_56_11) = e2)
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (21), (30), (36), (61), (65), (237),
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | |            (238), (279), (280) are inconsistent by sub-proof
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | |            #157.
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | |   (281)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | |            all_56_15 & $i(all_56_15))
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_13 & $i(all_56_13)
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  op(e1, e2) = all_56_13
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e3, all_50_1, e0, e3,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (44), (49) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  all_50_1 = e3
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_50_1, all_56_25, e0,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (49), (272) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (285)  all_56_25 = all_50_1
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_16_1, all_56_25, e0,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (206), (272) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (286)  all_56_25 = all_16_1
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (285), (286) imply:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_50_1 = all_16_1
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (287) implies:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (288)  all_50_1 = all_16_1
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (284), (288) imply:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_16_1 = e3
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (286), (289) imply:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)  all_56_25 = e3
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (290) imply:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)  op(e3, e3) = e3
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (15), (16), (29), (30), (38), (57), (61),
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (72), (218), (220), (237), (245), (291) are
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1572.
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_40_1)
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)   ~ (all_40_1 = e3)
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)  op(e1, e2) = all_40_1
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_40_1, all_56_13, e2,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (283), (294) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)  all_56_13 = all_40_1
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e0, all_56_13, e2, e1,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (277), (283) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_56_13 = e0
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e3, all_50_1, e0, e3,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (44), (49) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  all_50_1 = e3
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_50_1, all_56_25, e0,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (49), (272) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  all_56_25 = all_50_1
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_16_1, all_56_25, e0,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (206), (272) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_56_25 = all_16_1
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (296) imply:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (300)  all_40_1 = e0
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (300) implies:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  all_40_1 = e0
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (299) imply:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_50_1 = all_16_1
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (302) implies:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  all_50_1 = all_16_1
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (303) imply:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_16_1 = e3
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (304) imply:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_56_25 = e3
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (293), (301) imply:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)   ~ (e3 = e0)
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (305) imply:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  op(e3, e3) = e3
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (15), (16), (29), (30), (38), (57), (61),
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (72), (218), (220), (237), (245), (307) are
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1572.
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_15 & $i(all_56_15)
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (11), (15), (31), (61), (269), (308) are
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | |   (309)  all_58_13 = e0 & op(e0, e2) = e0
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | |   (310)  op(e0, e2) = e0
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (30), (61), (66), (236), (237),
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | |            (241), (310) are inconsistent by sub-proof #190.
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |   (311)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |            e0) = all_56_27 & $i(all_56_27)
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |   (312)  op(e2, e0) = all_56_27
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |   (313)  op(e2, all_56_27) = e2
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (12), (14), (16), (21), (30), (43),
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |            (48), (50), (53), (61), (63), (66), (67), (209),
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |            (218), (221), (236), (237), (241), (312), (313)
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #153.
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | |   (314)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 240.06/46.63  | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |   (315)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |            e0) = all_56_29 & $i(all_56_29)
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |   (316)  op(e1, e0) = all_56_29
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |   (317)  op(e1, all_56_29) = e1
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (12), (16), (21), (30), (43), (50),
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |            (51), (61), (63), (66), (72), (218), (236), (237),
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |            (241), (254), (316), (317) are inconsistent by
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |            sub-proof #152.
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |   (318)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (30), (34), (61), (66), (236),
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |            (237), (241), (318) are inconsistent by sub-proof
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | |            #151.
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | |   (319)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 240.06/46.63  | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | | REF_CLOSE: (52), (56), (58), (252), (319) are inconsistent by
% 240.06/46.63  | | | | | | | | | | | | | | |            sub-proof #1949.
% 240.06/46.63  | | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | |   (320)  all_54_11 = e0
% 240.06/46.63  | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | | REF_CLOSE: (17), (216), (320) are inconsistent by sub-proof
% 240.06/46.63  | | | | | | | | | | | | | |            #2175.
% 240.06/46.63  | | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | |   (321)  all_58_12 = e3 & op(e0, e3) = e3
% 240.06/46.63  | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | ALPHA: (321) implies:
% 240.06/46.63  | | | | | | | | | | | |   (322)  all_58_12 = e3
% 240.06/46.63  | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | | REF_CLOSE: (16), (241), (322) are inconsistent by sub-proof
% 240.06/46.63  | | | | | | | | | | | |            #1542.
% 240.06/46.63  | | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | |   (323)  all_58_13 = e1 & op(e0, e2) = e1
% 240.06/46.63  | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | | REF_CLOSE: (32), (54), (61), (323) are inconsistent by
% 240.06/46.63  | | | | | | | | | |            sub-proof #2275.
% 240.06/46.63  | | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | | 
% 240.06/46.63  | | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | | 
% 240.06/46.63  | | | | | | | | |   (324)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1
% 240.06/46.63  | | | | | | | | |            & op(e0, e0) = e1)
% 240.06/46.63  | | | | | | | | | 
% 240.06/46.63  | | | | | | | | | REF_CLOSE: (25), (61), (72), (220), (227), (324) are
% 240.06/46.63  | | | | | | | | |            inconsistent by sub-proof #150.
% 240.06/46.63  | | | | | | | | | 
% 240.06/46.63  | | | | | | | | End of split
% 240.06/46.63  | | | | | | | | 
% 240.06/46.63  | | | | | | | Case 2:
% 240.06/46.63  | | | | | | | | 
% 240.06/46.63  | | | | | | | |   (325)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 240.06/46.63  | | | | | | | | 
% 240.06/46.63  | | | | | | | | REF_CLOSE: (20), (69), (74), (214), (325) are inconsistent by
% 240.06/46.63  | | | | | | | |            sub-proof #2244.
% 240.06/46.63  | | | | | | | | 
% 240.06/46.63  | | | | | | | End of split
% 240.06/46.63  | | | | | | | 
% 240.06/46.63  | | | | | | End of split
% 240.06/46.63  | | | | | | 
% 240.06/46.63  | | | | | End of split
% 240.06/46.63  | | | | | 
% 240.06/46.63  | | | | End of split
% 240.06/46.63  | | | | 
% 240.06/46.63  | | | End of split
% 240.06/46.63  | | | 
% 240.06/46.63  | | End of split
% 240.06/46.63  | | 
% 240.06/46.63  | End of split
% 240.06/46.63  | 
% 240.06/46.63  End of proof
% 240.06/46.63  
% 240.06/46.63  Sub-proof #150 shows that the following formulas are inconsistent:
% 240.06/46.63  ----------------------------------------------------------------
% 240.06/46.63    (1)  all_58_15 = e2
% 240.06/46.63    (2)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.06/46.63    (3)  op(e0, e1) = e0
% 240.06/46.63    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.06/46.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.06/46.63    (5)   ~ (e1 = e0)
% 240.06/46.63    (6)   ~ (e2 = e1)
% 240.06/46.63  
% 240.06/46.63  Begin of proof
% 240.06/46.63  | 
% 240.06/46.63  | BETA: splitting (2) gives:
% 240.06/46.63  | 
% 240.06/46.63  | Case 1:
% 240.06/46.63  | | 
% 240.06/46.63  | |   (7)  all_58_14 = e1 & op(e0, e1) = e1
% 240.06/46.63  | | 
% 240.06/46.63  | | ALPHA: (7) implies:
% 240.06/46.63  | |   (8)  op(e0, e1) = e1
% 240.06/46.63  | | 
% 240.06/46.63  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2158.
% 240.06/46.63  | | 
% 240.06/46.63  | Case 2:
% 240.06/46.63  | | 
% 240.06/46.63  | |   (9)  all_58_15 = e1 & op(e0, e0) = e1
% 240.06/46.63  | | 
% 240.06/46.63  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #218.
% 240.06/46.63  | | 
% 240.06/46.63  | End of split
% 240.06/46.63  | 
% 240.06/46.63  End of proof
% 240.06/46.63  
% 240.06/46.63  Sub-proof #151 shows that the following formulas are inconsistent:
% 240.06/46.63  ----------------------------------------------------------------
% 240.06/46.63    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.06/46.63         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.06/46.63    (2)   ~ (e3 = e0)
% 240.06/46.63    (3)  op(e0, e1) = all_52_11
% 240.06/46.63    (4)   ~ (e3 = e1)
% 240.06/46.63    (5)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.06/46.63    (6)  all_58_12 = e1
% 240.06/46.63    (7)   ~ (all_52_11 = e3)
% 240.06/46.63    (8)   ~ (e3 = e2)
% 240.06/46.63    (9)  all_56_31 = e2
% 240.06/46.63    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.06/46.63            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.06/46.63    (11)  op(e0, e0) = e2
% 240.06/46.63  
% 240.06/46.63  Begin of proof
% 240.06/46.63  | 
% 240.06/46.63  | ALPHA: (5) implies:
% 240.06/46.63  |   (12)  op(e0, all_56_31) = e0
% 240.06/46.63  | 
% 240.06/46.63  | REDUCE: (9), (12) imply:
% 240.06/46.63  |   (13)  op(e0, e2) = e0
% 240.06/46.63  | 
% 240.06/46.63  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (13) are
% 240.06/46.63  |            inconsistent by sub-proof #190.
% 240.06/46.63  | 
% 240.06/46.63  End of proof
% 240.06/46.63  
% 240.06/46.63  Sub-proof #152 shows that the following formulas are inconsistent:
% 240.06/46.63  ----------------------------------------------------------------
% 240.06/46.63    (1)   ~ (all_8_2 = e0)
% 240.06/46.63    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.06/46.63         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.06/46.63    (3)   ~ (e3 = e0)
% 240.06/46.63    (4)  op(e0, e1) = all_52_11
% 240.06/46.63    (5)   ~ (e2 = e0)
% 240.06/46.63    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.06/46.63         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.06/46.63    (7)  op(e1, all_56_29) = e1
% 240.06/46.63    (8)   ~ (e3 = e1)
% 240.06/46.63    (9)  op(e1, e0) = e1
% 240.06/46.63    (10)  op(e3, e2) = e2
% 240.06/46.63    (11)  all_58_12 = e1
% 240.06/46.63    (12)   ~ (all_52_11 = e3)
% 240.06/46.63    (13)   ~ (e3 = e2)
% 240.06/46.63    (14)  op(e2, e2) = all_8_2
% 240.06/46.63    (15)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 240.06/46.63            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 240.06/46.63              e2) = all_40_1 & $i(all_40_1))
% 240.06/46.63    (16)  op(e1, e1) = e2
% 240.06/46.63    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.06/46.63            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.06/46.63    (18)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 240.06/46.63            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 240.06/46.63              e2) = all_36_1 & $i(all_36_1))
% 240.06/46.63    (19)  op(e0, e0) = e2
% 240.06/46.63    (20)  op(e1, e0) = all_56_29
% 240.06/46.63    (21)   ~ (e2 = e1)
% 240.06/46.63  
% 240.06/46.63  Begin of proof
% 240.06/46.63  | 
% 240.06/46.63  | BETA: splitting (6) gives:
% 240.06/46.63  | 
% 240.06/46.63  | Case 1:
% 240.06/46.63  | | 
% 240.06/46.63  | |   (22)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 240.06/46.63  | |           e0)
% 240.06/46.63  | | 
% 240.06/46.63  | | REF_CLOSE: (1), (5), (10), (14), (17), (22) are inconsistent by sub-proof
% 240.06/46.63  | |            #159.
% 240.06/46.63  | | 
% 240.06/46.63  | Case 2:
% 240.06/46.63  | | 
% 240.06/46.63  | |   (23)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.06/46.63  | |           e0)
% 240.06/46.63  | | 
% 240.06/46.63  | | BETA: splitting (23) gives:
% 240.06/46.63  | | 
% 240.06/46.63  | | Case 1:
% 240.06/46.63  | | | 
% 240.06/46.63  | | |   (24)  all_58_7 = e0 & op(e1, e2) = e0
% 240.06/46.63  | | | 
% 240.06/46.63  | | | ALPHA: (24) implies:
% 240.06/46.63  | | |   (25)  op(e1, e2) = e0
% 240.06/46.63  | | | 
% 240.06/46.63  | | | REF_CLOSE: (7), (9), (15), (16), (17), (18), (20), (21), (25) are
% 240.06/46.63  | | |            inconsistent by sub-proof #201.
% 240.06/46.63  | | | 
% 240.06/46.63  | | Case 2:
% 240.06/46.63  | | | 
% 240.06/46.63  | | |   (26)  all_58_13 = e0 & op(e0, e2) = e0
% 240.06/46.63  | | | 
% 240.06/46.63  | | | ALPHA: (26) implies:
% 240.06/46.63  | | |   (27)  op(e0, e2) = e0
% 240.06/46.63  | | | 
% 240.06/46.63  | | | REF_CLOSE: (2), (3), (4), (8), (11), (12), (13), (17), (19), (27) are
% 240.06/46.63  | | |            inconsistent by sub-proof #190.
% 240.06/46.63  | | | 
% 240.06/46.63  | | End of split
% 240.06/46.63  | | 
% 240.06/46.63  | End of split
% 240.06/46.63  | 
% 240.06/46.63  End of proof
% 240.06/46.63  
% 240.06/46.63  Sub-proof #153 shows that the following formulas are inconsistent:
% 240.06/46.63  ----------------------------------------------------------------
% 240.06/46.63    (1)  op(e2, e0) = all_56_27
% 240.06/46.63    (2)   ~ (all_8_2 = e0)
% 240.06/46.63    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.06/46.63         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.06/46.63    (4)   ~ (e3 = e0)
% 240.06/46.63    (5)  op(e0, e1) = all_52_11
% 240.06/46.63    (6)   ~ (e2 = e0)
% 240.06/46.63    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.06/46.63         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.06/46.63    (8)  op(e2, all_56_27) = e2
% 240.06/46.63    (9)   ~ (all_52_13 = e1)
% 240.06/46.63    (10)   ~ (e3 = e1)
% 240.06/46.63    (11)  op(e3, e2) = e2
% 240.06/46.63    (12)  all_58_12 = e1
% 240.06/46.63    (13)   ~ (all_52_11 = e3)
% 240.06/46.63    (14)   ~ (e3 = e2)
% 240.06/46.63    (15)  all_54_7 = e1 | all_54_7 = e0
% 240.06/46.63    (16)  op(e2, e0) = e0
% 240.06/46.64    (17)  op(e2, e2) = all_8_2
% 240.06/46.64    (18)   ~ (all_52_13 = e2)
% 240.06/46.64    (19)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 240.06/46.64            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 240.06/46.64              e2) = all_40_1 & $i(all_40_1))
% 240.06/46.64    (20)  all_54_7 = all_52_13
% 240.06/46.64    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.06/46.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.06/46.64    (22)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 240.06/46.64            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 240.06/46.64              e2) = all_36_1 & $i(all_36_1))
% 240.06/46.64    (23)  op(e0, e0) = e2
% 240.06/46.64    (24)  op(e2, e0) = all_52_13
% 240.06/46.64  
% 240.06/46.64  Begin of proof
% 240.06/46.64  | 
% 240.06/46.64  | BETA: splitting (7) gives:
% 240.06/46.64  | 
% 240.06/46.64  | Case 1:
% 240.06/46.64  | | 
% 240.06/46.64  | |   (25)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 240.06/46.64  | |           e0)
% 240.06/46.64  | | 
% 240.06/46.64  | | REF_CLOSE: (2), (6), (11), (17), (21), (25) are inconsistent by sub-proof
% 240.06/46.64  | |            #159.
% 240.06/46.64  | | 
% 240.06/46.64  | Case 2:
% 240.06/46.64  | | 
% 240.06/46.64  | |   (26)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.06/46.64  | |           e0)
% 240.06/46.64  | | 
% 240.06/46.64  | | BETA: splitting (26) gives:
% 240.06/46.64  | | 
% 240.06/46.64  | | Case 1:
% 240.06/46.64  | | | 
% 240.06/46.64  | | |   (27)  all_58_7 = e0 & op(e1, e2) = e0
% 240.06/46.64  | | | 
% 240.06/46.64  | | | ALPHA: (27) implies:
% 240.06/46.64  | | |   (28)  op(e1, e2) = e0
% 240.06/46.64  | | | 
% 240.06/46.64  | | | BETA: splitting (19) gives:
% 240.06/46.64  | | | 
% 240.06/46.64  | | | Case 1:
% 240.06/46.64  | | | | 
% 240.06/46.64  | | | |   (29)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 240.06/46.64  | | | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 240.06/46.64  | | | | 
% 240.06/46.64  | | | | ALPHA: (29) implies:
% 240.06/46.64  | | | |   (30)  op(e1, e2) = all_40_1
% 240.06/46.64  | | | | 
% 240.06/46.64  | | | | REF_CLOSE: (1), (8), (9), (15), (16), (18), (20), (21), (22), (24),
% 240.06/46.64  | | | |            (28), (30) are inconsistent by sub-proof #154.
% 240.06/46.64  | | | | 
% 240.06/46.64  | | | Case 2:
% 240.06/46.64  | | | | 
% 240.06/46.64  | | | |   (31)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 240.06/46.64  | | | | 
% 240.06/46.64  | | | | ALPHA: (31) implies:
% 240.06/46.64  | | | |   (32)  op(e1, e2) = all_40_1
% 240.06/46.64  | | | | 
% 240.06/46.64  | | | | REF_CLOSE: (1), (8), (9), (15), (16), (18), (20), (21), (22), (24),
% 240.06/46.64  | | | |            (28), (32) are inconsistent by sub-proof #154.
% 240.06/46.64  | | | | 
% 240.06/46.64  | | | End of split
% 240.06/46.64  | | | 
% 240.06/46.64  | | Case 2:
% 240.06/46.64  | | | 
% 240.06/46.64  | | |   (33)  all_58_13 = e0 & op(e0, e2) = e0
% 240.06/46.64  | | | 
% 240.06/46.64  | | | ALPHA: (33) implies:
% 240.06/46.64  | | |   (34)  op(e0, e2) = e0
% 240.06/46.64  | | | 
% 240.06/46.64  | | | REF_CLOSE: (3), (4), (5), (10), (12), (13), (14), (21), (23), (34) are
% 240.06/46.64  | | |            inconsistent by sub-proof #190.
% 240.06/46.64  | | | 
% 240.06/46.64  | | End of split
% 240.06/46.64  | | 
% 240.06/46.64  | End of split
% 240.06/46.64  | 
% 240.06/46.64  End of proof
% 240.06/46.64  
% 240.06/46.64  Sub-proof #154 shows that the following formulas are inconsistent:
% 240.06/46.64  ----------------------------------------------------------------
% 240.06/46.64    (1)  op(e2, e0) = all_56_27
% 240.06/46.64    (2)  op(e2, all_56_27) = e2
% 240.06/46.64    (3)   ~ (all_52_13 = e1)
% 240.06/46.64    (4)  op(e1, e2) = e0
% 240.06/46.64    (5)  all_54_7 = e1 | all_54_7 = e0
% 240.06/46.64    (6)  op(e2, e0) = e0
% 240.06/46.64    (7)   ~ (all_52_13 = e2)
% 240.06/46.64    (8)  all_54_7 = all_52_13
% 240.06/46.64    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.06/46.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.06/46.64    (10)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 240.06/46.64            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 240.06/46.64              e2) = all_36_1 & $i(all_36_1))
% 240.06/46.64    (11)  op(e1, e2) = all_40_1
% 240.06/46.64    (12)  op(e2, e0) = all_52_13
% 240.06/46.64  
% 240.06/46.64  Begin of proof
% 240.06/46.64  | 
% 240.06/46.64  | BETA: splitting (10) gives:
% 240.06/46.64  | 
% 240.06/46.64  | Case 1:
% 240.06/46.64  | | 
% 240.06/46.64  | | 
% 240.06/46.64  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (12) are inconsistent by
% 240.06/46.64  | |            sub-proof #155.
% 240.06/46.64  | | 
% 240.06/46.64  | Case 2:
% 240.06/46.64  | | 
% 240.06/46.64  | |   (13)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1)
% 240.06/46.64  | | 
% 240.06/46.64  | | ALPHA: (13) implies:
% 240.06/46.64  | |   (14)   ~ (all_36_1 = e0)
% 240.06/46.64  | |   (15)  op(e1, e2) = all_36_1
% 240.06/46.64  | | 
% 240.06/46.64  | | REF_CLOSE: (4), (9), (11), (14), (15) are inconsistent by sub-proof #1883.
% 240.06/46.64  | | 
% 240.06/46.64  | End of split
% 240.06/46.64  | 
% 240.06/46.64  End of proof
% 240.06/46.64  
% 240.06/46.64  Sub-proof #155 shows that the following formulas are inconsistent:
% 240.06/46.64  ----------------------------------------------------------------
% 240.06/46.64    (1)  op(e2, e0) = all_56_27
% 240.06/46.64    (2)  op(e2, all_56_27) = e2
% 240.06/46.64    (3)   ~ (all_52_13 = e1)
% 240.06/46.64    (4)  all_54_7 = e1 | all_54_7 = e0
% 240.06/46.64    (5)  op(e2, e0) = e0
% 240.06/46.64    (6)   ~ (all_52_13 = e2)
% 240.06/46.64    (7)  all_54_7 = all_52_13
% 240.06/46.64    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.06/46.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.06/46.64    (9)  op(e2, e0) = all_52_13
% 240.06/46.64  
% 240.06/46.64  Begin of proof
% 240.06/46.64  | 
% 240.06/46.64  | GROUND_INST: instantiating (8) with e0, all_56_27, e0, e2, simplifying with
% 240.06/46.64  |              (1), (5) gives:
% 240.06/46.64  |   (10)  all_56_27 = e0
% 240.06/46.64  | 
% 240.06/46.64  | REDUCE: (2), (10) imply:
% 240.06/46.64  |   (11)  op(e2, e0) = e2
% 240.06/46.64  | 
% 240.06/46.64  | REF_CLOSE: (3), (4), (6), (7), (8), (9), (11) are inconsistent by sub-proof
% 240.06/46.64  |            #1996.
% 240.06/46.64  | 
% 240.06/46.64  End of proof
% 240.06/46.64  
% 240.06/46.64  Sub-proof #156 shows that the following formulas are inconsistent:
% 240.06/46.64  ----------------------------------------------------------------
% 240.06/46.64    (1)   ~ (all_52_3 = e0)
% 240.06/46.64    (2)  ( ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 240.06/46.64           $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e0, e2) = all_4_1
% 240.06/46.64           & $i(all_4_1))
% 240.06/46.64    (3)  op(e0, e3) = all_52_3
% 240.06/46.64    (4)  op(e0, e2) = e3
% 240.06/46.64    (5)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.06/46.64         $i(all_56_15)
% 240.06/46.64    (6)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) = all_44_1
% 240.06/46.64           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2) =
% 240.06/46.64           all_44_1 & $i(all_44_1))
% 240.06/46.64    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.06/46.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.06/46.64  
% 240.06/46.64  Begin of proof
% 240.06/46.64  | 
% 240.06/46.64  | ALPHA: (5) implies:
% 240.06/46.64  |   (8)  op(e0, e2) = all_56_15
% 240.06/46.64  |   (9)  op(e0, all_56_15) = e0
% 240.06/46.64  | 
% 240.06/46.64  | BETA: splitting (2) gives:
% 240.06/46.64  | 
% 240.06/46.64  | Case 1:
% 240.06/46.64  | | 
% 240.06/46.64  | | 
% 240.06/46.64  | | GROUND_INST: instantiating (7) with e3, all_56_15, e2, e0, simplifying with
% 240.06/46.64  | |              (4), (8) gives:
% 240.06/46.64  | |   (10)  all_56_15 = e3
% 240.06/46.64  | | 
% 240.06/46.64  | | REDUCE: (9), (10) imply:
% 240.06/46.64  | |   (11)  op(e0, e3) = e0
% 240.06/46.64  | | 
% 240.06/46.64  | | REF_CLOSE: (1), (3), (7), (11) are inconsistent by sub-proof #2331.
% 240.06/46.64  | | 
% 240.06/46.64  | Case 2:
% 240.06/46.64  | | 
% 240.06/46.64  | |   (12)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 & $i(all_4_1)
% 240.06/46.64  | | 
% 240.06/46.64  | | ALPHA: (12) implies:
% 240.06/46.64  | |   (13)   ~ (all_4_1 = e3)
% 240.06/46.64  | |   (14)  op(e0, e2) = all_4_1
% 240.06/46.64  | | 
% 240.06/46.64  | | REF_CLOSE: (4), (6), (7), (13), (14) are inconsistent by sub-proof #211.
% 240.06/46.64  | | 
% 240.06/46.64  | End of split
% 240.06/46.64  | 
% 240.06/46.64  End of proof
% 240.06/46.64  
% 240.06/46.64  Sub-proof #157 shows that the following formulas are inconsistent:
% 240.06/46.64  ----------------------------------------------------------------
% 240.06/46.64    (1)   ~ (all_52_3 = e0)
% 240.06/46.64    (2)   ~ (e3 = e0)
% 240.06/46.64    (3)  all_56_11 = e1
% 240.06/46.64    (4)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.06/46.64           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 240.06/46.64    (5)  all_54_12 = e1 | all_54_12 = e0
% 240.06/46.64    (6)  op(e3, e2) = e2
% 240.06/46.64    (7)   ~ (e3 = e2)
% 240.06/46.64    (8)  all_54_12 = all_52_3
% 240.06/46.64    (9)  op(e2, e1) = e3
% 240.06/46.64    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.06/46.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.06/46.64    (11)  op(e3, e3) = e0
% 240.06/46.64  
% 240.06/46.64  Begin of proof
% 240.06/46.64  | 
% 240.06/46.64  | BETA: splitting (4) gives:
% 240.06/46.64  | 
% 240.06/46.64  | Case 1:
% 240.06/46.64  | | 
% 240.06/46.64  | |   (12)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.06/46.64  | |         $i(all_56_9)
% 240.06/46.64  | | 
% 240.06/46.64  | | ALPHA: (12) implies:
% 240.06/46.64  | |   (13)  op(e3, e2) = all_56_9
% 240.06/46.64  | |   (14)  op(e3, all_56_9) = e3
% 240.06/46.64  | | 
% 240.06/46.64  | | REF_CLOSE: (1), (2), (5), (6), (8), (10), (11), (13), (14) are inconsistent
% 240.06/46.64  | |            by sub-proof #158.
% 240.06/46.64  | | 
% 240.06/46.64  | Case 2:
% 240.06/46.64  | | 
% 240.06/46.64  | |   (15)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 240.06/46.64  | | 
% 240.06/46.64  | | ALPHA: (15) implies:
% 240.06/46.64  | |   (16)  op(e2, all_56_11) = e2
% 240.06/46.64  | | 
% 240.06/46.64  | | REDUCE: (3), (16) imply:
% 240.06/46.64  | |   (17)  op(e2, e1) = e2
% 240.06/46.64  | | 
% 240.06/46.64  | | REF_CLOSE: (7), (9), (10), (17) are inconsistent by sub-proof #2256.
% 240.06/46.64  | | 
% 240.06/46.64  | End of split
% 240.06/46.64  | 
% 240.06/46.64  End of proof
% 240.06/46.64  
% 240.06/46.64  Sub-proof #158 shows that the following formulas are inconsistent:
% 240.06/46.64  ----------------------------------------------------------------
% 240.06/46.64    (1)   ~ (all_52_3 = e0)
% 240.06/46.64    (2)  op(e3, e2) = all_56_9
% 240.06/46.64    (3)  op(e3, all_56_9) = e3
% 240.06/46.64    (4)   ~ (e3 = e0)
% 240.06/46.64    (5)  all_54_12 = e1 | all_54_12 = e0
% 240.06/46.64    (6)  op(e3, e2) = e2
% 240.06/46.64    (7)  all_54_12 = all_52_3
% 240.06/46.64    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.06/46.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.06/46.64    (9)  op(e3, e3) = e0
% 240.06/46.64  
% 240.06/46.64  Begin of proof
% 240.06/46.64  | 
% 240.06/46.64  | BETA: splitting (5) gives:
% 240.06/46.64  | 
% 240.06/46.64  | Case 1:
% 240.06/46.64  | | 
% 240.06/46.64  | | 
% 240.06/46.64  | | GROUND_INST: instantiating (8) with e2, all_56_9, e2, e3, simplifying with
% 240.06/46.64  | |              (2), (6) gives:
% 240.06/46.64  | |   (10)  all_56_9 = e2
% 240.06/46.64  | | 
% 240.06/46.64  | | REDUCE: (3), (10) imply:
% 240.06/46.64  | |   (11)  op(e3, e2) = e3
% 240.06/46.64  | | 
% 240.06/46.64  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11) are inconsistent by
% 240.06/46.64  | |            sub-proof #1440.
% 240.06/46.64  | | 
% 240.06/46.64  | Case 2:
% 240.06/46.64  | | 
% 240.06/46.64  | |   (12)  all_54_12 = e0
% 240.06/46.64  | | 
% 240.06/46.64  | | COMBINE_EQS: (7), (12) imply:
% 240.06/46.64  | |   (13)  all_52_3 = e0
% 240.06/46.64  | | 
% 240.06/46.64  | | REDUCE: (1), (13) imply:
% 240.06/46.64  | |   (14)  $false
% 240.06/46.64  | | 
% 240.06/46.64  | | CLOSE: (14) is inconsistent.
% 240.06/46.64  | | 
% 240.06/46.64  | End of split
% 240.06/46.64  | 
% 240.06/46.64  End of proof
% 240.06/46.64  
% 240.06/46.64  Sub-proof #159 shows that the following formulas are inconsistent:
% 240.06/46.64  ----------------------------------------------------------------
% 240.06/46.64    (1)   ~ (all_8_2 = e0)
% 240.06/46.64    (2)   ~ (e2 = e0)
% 240.06/46.64    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 240.06/46.64    (4)  op(e3, e2) = e2
% 240.06/46.64    (5)  op(e2, e2) = all_8_2
% 240.06/46.64    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.06/46.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.06/46.64  
% 240.06/46.64  Begin of proof
% 240.06/46.64  | 
% 240.06/46.64  | BETA: splitting (3) gives:
% 240.06/46.64  | 
% 240.06/46.64  | Case 1:
% 240.06/46.64  | | 
% 240.06/46.64  | |   (7)  all_58_1 = e0 & op(e3, e2) = e0
% 240.06/46.64  | | 
% 240.06/46.64  | | ALPHA: (7) implies:
% 240.08/46.64  | |   (8)  op(e3, e2) = e0
% 240.08/46.64  | | 
% 240.08/46.64  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2026.
% 240.08/46.64  | | 
% 240.08/46.64  | Case 2:
% 240.08/46.64  | | 
% 240.08/46.64  | |   (9)  all_58_3 = e0 & op(e2, e2) = e0
% 240.08/46.64  | | 
% 240.08/46.64  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #1992.
% 240.08/46.64  | | 
% 240.08/46.64  | End of split
% 240.08/46.64  | 
% 240.08/46.64  End of proof
% 240.08/46.64  
% 240.08/46.64  Sub-proof #160 shows that the following formulas are inconsistent:
% 240.08/46.64  ----------------------------------------------------------------
% 240.08/46.64    (1)   ~ (all_52_3 = e0)
% 240.08/46.64    (2)   ~ (e3 = e0)
% 240.08/46.64    (3)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 240.08/46.64    (4)  op(e0, e3) = all_52_3
% 240.08/46.64    (5)   ~ (e3 = e2)
% 240.08/46.64    (6)  op(e2, e3) = e2
% 240.08/46.64    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.08/46.64         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.08/46.64    (8)   ~ (all_52_1 = e0)
% 240.08/46.64    (9)  op(e2, e3) = all_52_1
% 240.08/46.64    (10)   ~ (all_52_2 = e0)
% 240.08/46.64    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.64    (12)  op(e1, e3) = all_52_2
% 240.08/46.64  
% 240.08/46.64  Begin of proof
% 240.08/46.64  | 
% 240.08/46.64  | BETA: splitting (3) gives:
% 240.08/46.64  | 
% 240.08/46.64  | Case 1:
% 240.08/46.64  | | 
% 240.08/46.64  | |   (13)  all_58_0 = e3 & op(e3, e3) = e3
% 240.08/46.64  | | 
% 240.08/46.64  | | ALPHA: (13) implies:
% 240.08/46.64  | |   (14)  op(e3, e3) = e3
% 240.08/46.64  | | 
% 240.08/46.64  | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (11), (12), (14) are
% 240.08/46.64  | |            inconsistent by sub-proof #1938.
% 240.08/46.64  | | 
% 240.08/46.64  | Case 2:
% 240.08/46.64  | | 
% 240.08/46.64  | |   (15)  all_58_2 = e3 & op(e2, e3) = e3
% 240.08/46.64  | | 
% 240.08/46.64  | | ALPHA: (15) implies:
% 240.08/46.64  | |   (16)  op(e2, e3) = e3
% 240.08/46.64  | | 
% 240.08/46.64  | | REF_CLOSE: (5), (6), (11), (16) are inconsistent by sub-proof #1897.
% 240.08/46.64  | | 
% 240.08/46.64  | End of split
% 240.08/46.64  | 
% 240.08/46.64  End of proof
% 240.08/46.64  
% 240.08/46.64  Sub-proof #161 shows that the following formulas are inconsistent:
% 240.08/46.64  ----------------------------------------------------------------
% 240.08/46.64    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.08/46.64         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.08/46.64    (2)   ~ (e2 = e0)
% 240.08/46.64    (3)   ~ (e3 = e1)
% 240.08/46.64    (4)   ~ (all_52_9 = e0)
% 240.08/46.64    (5)  op(e2, e1) = all_52_9
% 240.08/46.64    (6)   ~ (e3 = e2)
% 240.08/46.64    (7)  all_58_9 = e3
% 240.08/46.64    (8)  op(e3, e0) = e3
% 240.08/46.64    (9)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 240.08/46.64    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.08/46.64          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.08/46.64    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.64    (12)   ~ (e1 = e0)
% 240.08/46.64    (13)  op(e3, e3) = e0
% 240.08/46.64    (14)   ~ (e2 = e1)
% 240.08/46.64  
% 240.08/46.64  Begin of proof
% 240.08/46.64  | 
% 240.08/46.64  | BETA: splitting (9) gives:
% 240.08/46.64  | 
% 240.08/46.64  | Case 1:
% 240.08/46.64  | | 
% 240.08/46.64  | |   (15)  all_58_4 = e0 & op(e3, e1) = e0
% 240.08/46.64  | | 
% 240.08/46.64  | | ALPHA: (15) implies:
% 240.08/46.64  | |   (16)  all_58_4 = e0
% 240.08/46.64  | | 
% 240.08/46.64  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (11), (12), (13), (14), (16)
% 240.08/46.64  | |            are inconsistent by sub-proof #1706.
% 240.08/46.64  | | 
% 240.08/46.64  | Case 2:
% 240.08/46.64  | | 
% 240.08/46.64  | |   (17)  all_58_5 = e0 & op(e2, e1) = e0
% 240.08/46.64  | | 
% 240.08/46.64  | | REF_CLOSE: (4), (5), (11), (17) are inconsistent by sub-proof #2088.
% 240.08/46.64  | | 
% 240.08/46.64  | End of split
% 240.08/46.64  | 
% 240.08/46.64  End of proof
% 240.08/46.64  
% 240.08/46.64  Sub-proof #162 shows that the following formulas are inconsistent:
% 240.08/46.64  ----------------------------------------------------------------
% 240.08/46.64    (1)  op(e1, e0) = all_52_14
% 240.08/46.64    (2)  all_58_15 = e2
% 240.08/46.64    (3)   ~ (all_52_14 = e1)
% 240.08/46.64    (4)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.08/46.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.65    (6)   ~ (e2 = e1)
% 240.08/46.65  
% 240.08/46.65  Begin of proof
% 240.08/46.65  | 
% 240.08/46.65  | BETA: splitting (4) gives:
% 240.08/46.65  | 
% 240.08/46.65  | Case 1:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (7)  all_58_11 = e1 & op(e1, e0) = e1
% 240.08/46.65  | | 
% 240.08/46.65  | | ALPHA: (7) implies:
% 240.08/46.65  | |   (8)  op(e1, e0) = e1
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #2304.
% 240.08/46.65  | | 
% 240.08/46.65  | Case 2:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (9)  all_58_15 = e1 & op(e0, e0) = e1
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #218.
% 240.08/46.65  | | 
% 240.08/46.65  | End of split
% 240.08/46.65  | 
% 240.08/46.65  End of proof
% 240.08/46.65  
% 240.08/46.65  Sub-proof #163 shows that the following formulas are inconsistent:
% 240.08/46.65  ----------------------------------------------------------------
% 240.08/46.65    (1)  op(e0, e1) = all_52_11
% 240.08/46.65    (2)   ~ (all_52_11 = e1)
% 240.08/46.65    (3)  all_58_15 = e2
% 240.08/46.65    (4)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.08/46.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.65    (6)   ~ (e2 = e1)
% 240.08/46.65  
% 240.08/46.65  Begin of proof
% 240.08/46.65  | 
% 240.08/46.65  | BETA: splitting (4) gives:
% 240.08/46.65  | 
% 240.08/46.65  | Case 1:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (7)  all_58_14 = e1 & op(e0, e1) = e1
% 240.08/46.65  | | 
% 240.08/46.65  | | ALPHA: (7) implies:
% 240.08/46.65  | |   (8)  op(e0, e1) = e1
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #2272.
% 240.08/46.65  | | 
% 240.08/46.65  | Case 2:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (9)  all_58_15 = e1 & op(e0, e0) = e1
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #218.
% 240.08/46.65  | | 
% 240.08/46.65  | End of split
% 240.08/46.65  | 
% 240.08/46.65  End of proof
% 240.08/46.65  
% 240.08/46.65  Sub-proof #164 shows that the following formulas are inconsistent:
% 240.08/46.65  ----------------------------------------------------------------
% 240.08/46.65    (1)   ~ (all_52_3 = e0)
% 240.08/46.65    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.08/46.65             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.08/46.65           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 240.08/46.65           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.65           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 240.08/46.65           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.65           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.65    (3)  op(e3, e0) = e1
% 240.08/46.65    (4)  op(e0, e3) = all_52_3
% 240.08/46.65    (5)   ~ (e3 = e1)
% 240.08/46.65    (6)   ~ (all_52_8 = e1)
% 240.08/46.65    (7)  op(e3, e1) = all_52_8
% 240.08/46.65    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.65  
% 240.08/46.65  Begin of proof
% 240.08/46.65  | 
% 240.08/46.65  | BETA: splitting (2) gives:
% 240.08/46.65  | 
% 240.08/46.65  | Case 1:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (9)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.08/46.65  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.08/46.65  | |        op(e1, e3) = e1
% 240.08/46.65  | | 
% 240.08/46.65  | | ALPHA: (9) implies:
% 240.08/46.65  | |   (10)  op(e3, e1) = e1
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (6), (7), (8), (10) are inconsistent by sub-proof #2309.
% 240.08/46.65  | | 
% 240.08/46.65  | Case 2:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (11)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.08/46.65  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 240.08/46.65  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.08/46.65  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.65  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.65  | | 
% 240.08/46.65  | | BETA: splitting (11) gives:
% 240.08/46.65  | | 
% 240.08/46.65  | | Case 1:
% 240.08/46.65  | | | 
% 240.08/46.65  | | |   (12)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.65  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.65  | | |         op(e3, e0) = e3 & op(e0, e3) = e3
% 240.08/46.65  | | | 
% 240.08/46.65  | | | ALPHA: (12) implies:
% 240.08/46.65  | | |   (13)  op(e3, e0) = e3
% 240.08/46.65  | | | 
% 240.08/46.65  | | | REF_CLOSE: (3), (5), (8), (13) are inconsistent by sub-proof #243.
% 240.08/46.65  | | | 
% 240.08/46.65  | | Case 2:
% 240.08/46.65  | | | 
% 240.08/46.65  | | |   (14)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.65  | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.65  | | |         op(e3, e0) = e0 & op(e0, e3) = e0
% 240.08/46.65  | | | 
% 240.08/46.65  | | | ALPHA: (14) implies:
% 240.08/46.65  | | |   (15)  op(e0, e3) = e0
% 240.08/46.65  | | | 
% 240.08/46.65  | | | REF_CLOSE: (1), (4), (8), (15) are inconsistent by sub-proof #2331.
% 240.08/46.65  | | | 
% 240.08/46.65  | | End of split
% 240.08/46.65  | | 
% 240.08/46.65  | End of split
% 240.08/46.65  | 
% 240.08/46.65  End of proof
% 240.08/46.65  
% 240.08/46.65  Sub-proof #165 shows that the following formulas are inconsistent:
% 240.08/46.65  ----------------------------------------------------------------
% 240.08/46.65    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.08/46.65           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.08/46.65             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.65           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.08/46.65             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.65           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.65           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.65    (2)   ~ (e3 = e2)
% 240.08/46.65    (3)  all_56_31 = e2
% 240.08/46.65    (4)  op(e3, e1) = e2
% 240.08/46.65    (5)  op(e3, e2) = all_52_4
% 240.08/46.65    (6)   ~ (all_52_4 = e2)
% 240.08/46.65    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.65  
% 240.08/46.65  Begin of proof
% 240.08/46.65  | 
% 240.08/46.65  | BETA: splitting (1) gives:
% 240.08/46.65  | 
% 240.08/46.65  | Case 1:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.65  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.08/46.65  | |        op(e2, e3) = e3
% 240.08/46.65  | | 
% 240.08/46.65  | | ALPHA: (8) implies:
% 240.08/46.65  | |   (9)   ~ (all_56_31 = e2)
% 240.08/46.65  | | 
% 240.08/46.65  | | REDUCE: (3), (9) imply:
% 240.08/46.65  | |   (10)  $false
% 240.08/46.65  | | 
% 240.08/46.65  | | CLOSE: (10) is inconsistent.
% 240.08/46.65  | | 
% 240.08/46.65  | Case 2:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (11)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.08/46.65  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.08/46.65  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.65  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.65  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (2), (4), (5), (6), (7), (11) are inconsistent by sub-proof #166.
% 240.08/46.65  | | 
% 240.08/46.65  | End of split
% 240.08/46.65  | 
% 240.08/46.65  End of proof
% 240.08/46.65  
% 240.08/46.65  Sub-proof #166 shows that the following formulas are inconsistent:
% 240.08/46.65  ----------------------------------------------------------------
% 240.08/46.65    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 240.08/46.65           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 240.08/46.65             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.65           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 240.08/46.65             e1) = e3 & op(e1, e3) = e3)
% 240.08/46.65    (2)   ~ (e3 = e2)
% 240.08/46.65    (3)  op(e3, e1) = e2
% 240.08/46.65    (4)  op(e3, e2) = all_52_4
% 240.08/46.65    (5)   ~ (all_52_4 = e2)
% 240.08/46.65    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.65  
% 240.08/46.65  Begin of proof
% 240.08/46.65  | 
% 240.08/46.65  | BETA: splitting (1) gives:
% 240.08/46.65  | 
% 240.08/46.65  | Case 1:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.08/46.65  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.08/46.65  | |        op(e2, e3) = e2
% 240.08/46.65  | | 
% 240.08/46.65  | | ALPHA: (7) implies:
% 240.08/46.65  | |   (8)  op(e3, e2) = e2
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #254.
% 240.08/46.65  | | 
% 240.08/46.65  | Case 2:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.08/46.65  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.08/46.65  | |        op(e1, e3) = e3
% 240.08/46.65  | | 
% 240.08/46.65  | | ALPHA: (9) implies:
% 240.08/46.65  | |   (10)  op(e3, e1) = e3
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #177.
% 240.08/46.65  | | 
% 240.08/46.65  | End of split
% 240.08/46.65  | 
% 240.08/46.65  End of proof
% 240.08/46.65  
% 240.08/46.65  Sub-proof #167 shows that the following formulas are inconsistent:
% 240.08/46.65  ----------------------------------------------------------------
% 240.08/46.65    (1)   ~ (e2 = e0)
% 240.08/46.65    (2)  op(e1, e0) = all_52_14
% 240.08/46.65    (3)   ~ (all_52_14 = e2)
% 240.08/46.65    (4)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.08/46.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.65    (6)  op(e1, e1) = e0
% 240.08/46.65  
% 240.08/46.65  Begin of proof
% 240.08/46.65  | 
% 240.08/46.65  | BETA: splitting (4) gives:
% 240.08/46.65  | 
% 240.08/46.65  | Case 1:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (7)  all_58_8 = e2 & op(e1, e1) = e2
% 240.08/46.65  | | 
% 240.08/46.65  | | ALPHA: (7) implies:
% 240.08/46.65  | |   (8)  op(e1, e1) = e2
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2211.
% 240.08/46.65  | | 
% 240.08/46.65  | Case 2:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (9)  all_58_11 = e2 & op(e1, e0) = e2
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #258.
% 240.08/46.65  | | 
% 240.08/46.65  | End of split
% 240.08/46.65  | 
% 240.08/46.65  End of proof
% 240.08/46.65  
% 240.08/46.65  Sub-proof #168 shows that the following formulas are inconsistent:
% 240.08/46.65  ----------------------------------------------------------------
% 240.08/46.65    (1)  op(e1, e0) = e1
% 240.08/46.65    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.65             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.08/46.65           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.08/46.65             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.08/46.65           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 240.08/46.65           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.65           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.65    (3)  all_56_21 = e0
% 240.08/46.65    (4)  all_56_31 = e2
% 240.08/46.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.65    (6)   ~ (e1 = e0)
% 240.08/46.65  
% 240.08/46.65  Begin of proof
% 240.08/46.65  | 
% 240.08/46.65  | BETA: splitting (2) gives:
% 240.08/46.65  | 
% 240.08/46.65  | Case 1:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (7)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.08/46.65  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 240.08/46.65  | |        & op(e0, e2) = e0
% 240.08/46.65  | | 
% 240.08/46.65  | | ALPHA: (7) implies:
% 240.08/46.65  | |   (8)   ~ (all_56_31 = e2)
% 240.08/46.65  | | 
% 240.08/46.65  | | REDUCE: (4), (8) imply:
% 240.08/46.65  | |   (9)  $false
% 240.08/46.65  | | 
% 240.08/46.65  | | CLOSE: (9) is inconsistent.
% 240.08/46.65  | | 
% 240.08/46.65  | Case 2:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.65  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.65  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.08/46.65  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.08/46.65  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #501.
% 240.08/46.65  | | 
% 240.08/46.65  | End of split
% 240.08/46.65  | 
% 240.08/46.65  End of proof
% 240.08/46.65  
% 240.08/46.65  Sub-proof #169 shows that the following formulas are inconsistent:
% 240.08/46.65  ----------------------------------------------------------------
% 240.08/46.65    (1)   ~ (all_52_1 = all_52_3)
% 240.08/46.65    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 240.08/46.65    (3)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.08/46.65             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.08/46.65           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 240.08/46.65           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.65           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.65    (4)  op(e0, e3) = all_52_3
% 240.08/46.65    (5)  all_54_4 = all_52_1
% 240.08/46.65    (6)   ~ (all_52_3 = e3)
% 240.08/46.65    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.65    (8)   ~ (all_52_1 = e2)
% 240.08/46.65    (9)   ~ (all_52_1 = e1)
% 240.08/46.65  
% 240.08/46.65  Begin of proof
% 240.08/46.65  | 
% 240.08/46.65  | BETA: splitting (3) gives:
% 240.08/46.65  | 
% 240.08/46.65  | Case 1:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (10)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.08/46.65  | |           = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 240.08/46.65  | |         e3 & op(e0, e3) = e3
% 240.08/46.65  | | 
% 240.08/46.65  | | ALPHA: (10) implies:
% 240.08/46.65  | |   (11)  op(e0, e3) = e3
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (4), (6), (7), (11) are inconsistent by sub-proof #2332.
% 240.08/46.65  | | 
% 240.08/46.65  | Case 2:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (12)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.08/46.65  | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) =
% 240.08/46.65  | |         e0 & op(e0, e3) = e0
% 240.08/46.65  | | 
% 240.08/46.65  | | ALPHA: (12) implies:
% 240.08/46.65  | |   (13)  op(e0, e3) = e0
% 240.08/46.65  | | 
% 240.08/46.65  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (13) are inconsistent by
% 240.08/46.65  | |            sub-proof #170.
% 240.08/46.65  | | 
% 240.08/46.65  | End of split
% 240.08/46.65  | 
% 240.08/46.65  End of proof
% 240.08/46.65  
% 240.08/46.65  Sub-proof #170 shows that the following formulas are inconsistent:
% 240.08/46.65  ----------------------------------------------------------------
% 240.08/46.65    (1)   ~ (all_52_1 = all_52_3)
% 240.08/46.65    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 240.08/46.65    (3)  op(e0, e3) = all_52_3
% 240.08/46.65    (4)  all_54_4 = all_52_1
% 240.08/46.65    (5)  op(e0, e3) = e0
% 240.08/46.65    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.65    (7)   ~ (all_52_1 = e2)
% 240.08/46.65    (8)   ~ (all_52_1 = e1)
% 240.08/46.65  
% 240.08/46.65  Begin of proof
% 240.08/46.65  | 
% 240.08/46.65  | BETA: splitting (2) gives:
% 240.08/46.65  | 
% 240.08/46.65  | Case 1:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (9)  all_54_4 = e2
% 240.08/46.65  | | 
% 240.08/46.65  | | COMBINE_EQS: (4), (9) imply:
% 240.08/46.65  | |   (10)  all_52_1 = e2
% 240.08/46.65  | | 
% 240.08/46.65  | | REDUCE: (7), (10) imply:
% 240.08/46.65  | |   (11)  $false
% 240.08/46.65  | | 
% 240.08/46.65  | | CLOSE: (11) is inconsistent.
% 240.08/46.65  | | 
% 240.08/46.65  | Case 2:
% 240.08/46.65  | | 
% 240.08/46.65  | |   (12)  all_54_4 = e1 | all_54_4 = e0
% 240.08/46.65  | | 
% 240.08/46.65  | | BETA: splitting (12) gives:
% 240.08/46.65  | | 
% 240.08/46.65  | | Case 1:
% 240.08/46.65  | | | 
% 240.08/46.65  | | |   (13)  all_54_4 = e1
% 240.08/46.65  | | | 
% 240.08/46.65  | | | REF_CLOSE: (4), (8), (13) are inconsistent by sub-proof #2086.
% 240.08/46.65  | | | 
% 240.08/46.65  | | Case 2:
% 240.08/46.65  | | | 
% 240.08/46.65  | | |   (14)  all_54_4 = e0
% 240.08/46.65  | | | 
% 240.08/46.65  | | | COMBINE_EQS: (4), (14) imply:
% 240.08/46.65  | | |   (15)  all_52_1 = e0
% 240.08/46.65  | | | 
% 240.08/46.65  | | | SIMP: (15) implies:
% 240.08/46.66  | | |   (16)  all_52_1 = e0
% 240.08/46.66  | | | 
% 240.08/46.66  | | | REDUCE: (1), (16) imply:
% 240.08/46.66  | | |   (17)   ~ (all_52_3 = e0)
% 240.08/46.66  | | | 
% 240.08/46.66  | | | SIMP: (17) implies:
% 240.08/46.66  | | |   (18)   ~ (all_52_3 = e0)
% 240.08/46.66  | | | 
% 240.08/46.66  | | | REF_CLOSE: (3), (5), (6), (18) are inconsistent by sub-proof #2331.
% 240.08/46.66  | | | 
% 240.08/46.66  | | End of split
% 240.08/46.66  | | 
% 240.08/46.66  | End of split
% 240.08/46.66  | 
% 240.08/46.66  End of proof
% 240.08/46.66  
% 240.08/46.66  Sub-proof #171 shows that the following formulas are inconsistent:
% 240.08/46.66  ----------------------------------------------------------------
% 240.08/46.66    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 240.08/46.66    (2)   ~ (e3 = e1)
% 240.08/46.66    (3)  op(e2, e1) = e2
% 240.08/46.66    (4)   ~ (e3 = e2)
% 240.08/46.66    (5)  op(e3, e1) = e1
% 240.08/46.66    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.66  
% 240.08/46.66  Begin of proof
% 240.08/46.66  | 
% 240.08/46.66  | BETA: splitting (1) gives:
% 240.08/46.66  | 
% 240.08/46.66  | Case 1:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (7)  all_58_4 = e3 & op(e3, e1) = e3
% 240.08/46.66  | | 
% 240.08/46.66  | | ALPHA: (7) implies:
% 240.08/46.66  | |   (8)  op(e3, e1) = e3
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #1823.
% 240.08/46.66  | | 
% 240.08/46.66  | Case 2:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (9)  all_58_5 = e3 & op(e2, e1) = e3
% 240.08/46.66  | | 
% 240.08/46.66  | | ALPHA: (9) implies:
% 240.08/46.66  | |   (10)  op(e2, e1) = e3
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #2256.
% 240.08/46.66  | | 
% 240.08/46.66  | End of split
% 240.08/46.66  | 
% 240.08/46.66  End of proof
% 240.08/46.66  
% 240.08/46.66  Sub-proof #172 shows that the following formulas are inconsistent:
% 240.08/46.66  ----------------------------------------------------------------
% 240.08/46.66    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.08/46.66    (2)  op(e1, e2) = all_52_6
% 240.08/46.66    (3)  op(e1, e0) = all_52_14
% 240.08/46.66    (4)   ~ (all_52_6 = e0)
% 240.08/46.66    (5)   ~ (e3 = e1)
% 240.08/46.66    (6)  op(e1, e0) = e3
% 240.08/46.66    (7)   ~ (all_52_14 = e0)
% 240.08/46.66    (8)   ~ (all_52_2 = e0)
% 240.08/46.66    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.66    (10)  op(e1, e3) = all_52_2
% 240.08/46.66    (11)   ~ (e1 = e0)
% 240.08/46.66    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.08/46.66          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.08/46.66  
% 240.08/46.66  Begin of proof
% 240.08/46.66  | 
% 240.08/46.66  | BETA: splitting (1) gives:
% 240.08/46.66  | 
% 240.08/46.66  | Case 1:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (13)  all_58_8 = e1 & op(e1, e1) = e1
% 240.08/46.66  | | 
% 240.08/46.66  | | ALPHA: (13) implies:
% 240.08/46.66  | |   (14)  op(e1, e1) = e1
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (12), (14) are
% 240.08/46.66  | |            inconsistent by sub-proof #2020.
% 240.08/46.66  | | 
% 240.08/46.66  | Case 2:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (15)  all_58_11 = e1 & op(e1, e0) = e1
% 240.08/46.66  | | 
% 240.08/46.66  | | ALPHA: (15) implies:
% 240.08/46.66  | |   (16)  op(e1, e0) = e1
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (5), (6), (9), (16) are inconsistent by sub-proof #1894.
% 240.08/46.66  | | 
% 240.08/46.66  | End of split
% 240.08/46.66  | 
% 240.08/46.66  End of proof
% 240.08/46.66  
% 240.08/46.66  Sub-proof #173 shows that the following formulas are inconsistent:
% 240.08/46.66  ----------------------------------------------------------------
% 240.08/46.66    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 240.08/46.66    (2)  op(e2, e1) = e2
% 240.08/46.66    (3)   ~ (all_52_1 = all_52_9)
% 240.08/46.66    (4)  all_54_4 = all_52_1
% 240.08/46.66    (5)  op(e2, e1) = all_52_9
% 240.08/46.66    (6)   ~ (all_52_1 = e0)
% 240.08/46.66    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.66    (8)   ~ (all_52_1 = e1)
% 240.08/46.66  
% 240.08/46.66  Begin of proof
% 240.08/46.66  | 
% 240.08/46.66  | BETA: splitting (1) gives:
% 240.08/46.66  | 
% 240.08/46.66  | Case 1:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (9)  all_54_4 = e2
% 240.08/46.66  | | 
% 240.08/46.66  | | COMBINE_EQS: (4), (9) imply:
% 240.08/46.66  | |   (10)  all_52_1 = e2
% 240.08/46.66  | | 
% 240.08/46.66  | | SIMP: (10) implies:
% 240.08/46.66  | |   (11)  all_52_1 = e2
% 240.08/46.66  | | 
% 240.08/46.66  | | REDUCE: (3), (11) imply:
% 240.08/46.66  | |   (12)   ~ (all_52_9 = e2)
% 240.08/46.66  | | 
% 240.08/46.66  | | SIMP: (12) implies:
% 240.08/46.66  | |   (13)   ~ (all_52_9 = e2)
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (2), (5), (7), (13) are inconsistent by sub-proof #2328.
% 240.08/46.66  | | 
% 240.08/46.66  | Case 2:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (14)  all_54_4 = e1 | all_54_4 = e0
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (4), (6), (8), (14) are inconsistent by sub-proof #1922.
% 240.08/46.66  | | 
% 240.08/46.66  | End of split
% 240.08/46.66  | 
% 240.08/46.66  End of proof
% 240.08/46.66  
% 240.08/46.66  Sub-proof #174 shows that the following formulas are inconsistent:
% 240.08/46.66  ----------------------------------------------------------------
% 240.08/46.66    (1)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.08/46.66             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.08/46.66           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 240.08/46.66           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.66           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 240.08/46.66           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.66           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.66    (2)   ~ (e3 = e0)
% 240.08/46.66    (3)   ~ (all_52_12 = e0)
% 240.08/46.66    (4)  op(e0, e3) = all_56_7
% 240.08/46.66    (5)   ~ (all_52_8 = e1)
% 240.08/46.66    (6)  op(e3, e1) = all_52_8
% 240.08/46.66    (7)  op(e3, e0) = all_52_12
% 240.08/46.66    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.66    (9)  op(e0, all_56_7) = e0
% 240.08/46.66  
% 240.08/46.66  Begin of proof
% 240.08/46.66  | 
% 240.08/46.66  | BETA: splitting (1) gives:
% 240.08/46.66  | 
% 240.08/46.66  | Case 1:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (10)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.08/46.66  | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 240.08/46.66  | |         e1 & op(e1, e3) = e1
% 240.08/46.66  | | 
% 240.08/46.66  | | ALPHA: (10) implies:
% 240.08/46.66  | |   (11)  op(e3, e1) = e1
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (5), (6), (8), (11) are inconsistent by sub-proof #2309.
% 240.08/46.66  | | 
% 240.08/46.66  | Case 2:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (12)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.08/46.66  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 240.08/46.66  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.08/46.66  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.66  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.66  | | 
% 240.08/46.66  | | BETA: splitting (12) gives:
% 240.08/46.66  | | 
% 240.08/46.66  | | Case 1:
% 240.08/46.66  | | | 
% 240.08/46.66  | | |   (13)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.66  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.66  | | |         op(e3, e0) = e3 & op(e0, e3) = e3
% 240.08/46.66  | | | 
% 240.08/46.66  | | | ALPHA: (13) implies:
% 240.08/46.66  | | |   (14)  op(e0, e3) = e3
% 240.08/46.66  | | | 
% 240.08/46.66  | | | REF_CLOSE: (2), (4), (8), (9), (14) are inconsistent by sub-proof #2070.
% 240.08/46.66  | | | 
% 240.08/46.66  | | Case 2:
% 240.08/46.66  | | | 
% 240.08/46.66  | | |   (15)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.66  | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.66  | | |         op(e3, e0) = e0 & op(e0, e3) = e0
% 240.08/46.66  | | | 
% 240.08/46.66  | | | ALPHA: (15) implies:
% 240.08/46.66  | | |   (16)  op(e3, e0) = e0
% 240.08/46.66  | | | 
% 240.08/46.66  | | | REF_CLOSE: (3), (7), (8), (16) are inconsistent by sub-proof #2258.
% 240.08/46.66  | | | 
% 240.08/46.66  | | End of split
% 240.08/46.66  | | 
% 240.08/46.66  | End of split
% 240.08/46.66  | 
% 240.08/46.66  End of proof
% 240.08/46.66  
% 240.08/46.66  Sub-proof #175 shows that the following formulas are inconsistent:
% 240.08/46.66  ----------------------------------------------------------------
% 240.08/46.66    (1)   ~ (e3 = e0)
% 240.08/46.66    (2)   ~ (e3 = e1)
% 240.08/46.66    (3)  op(e1, e0) = e1
% 240.08/46.66    (4)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.08/46.66    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.66    (6)  op(e1, e1) = e0
% 240.08/46.66  
% 240.08/46.66  Begin of proof
% 240.08/46.66  | 
% 240.08/46.66  | BETA: splitting (4) gives:
% 240.08/46.66  | 
% 240.08/46.66  | Case 1:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (1), (5), (6), (7) are inconsistent by sub-proof #2018.
% 240.08/46.66  | | 
% 240.08/46.66  | Case 2:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (8)  all_58_11 = e3 & op(e1, e0) = e3
% 240.08/46.66  | | 
% 240.08/46.66  | | ALPHA: (8) implies:
% 240.08/46.66  | |   (9)  op(e1, e0) = e3
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1894.
% 240.08/46.66  | | 
% 240.08/46.66  | End of split
% 240.08/46.66  | 
% 240.08/46.66  End of proof
% 240.08/46.66  
% 240.08/46.66  Sub-proof #176 shows that the following formulas are inconsistent:
% 240.08/46.66  ----------------------------------------------------------------
% 240.08/46.66    (1)   ~ (e3 = e0)
% 240.08/46.66    (2)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.66         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.08/46.66    (3)   ~ (e3 = e1)
% 240.08/46.66    (4)   ~ (e3 = e2)
% 240.08/46.66    (5)  op(e2, e2) = e1
% 240.08/46.66    (6)  op(e2, e3) = all_52_1
% 240.08/46.66    (7)   ~ (all_52_13 = e2)
% 240.08/46.66    (8)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.08/46.66         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.08/46.66    (9)  op(e3, e1) = e2
% 240.08/46.66    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.66    (11)  op(e1, e1) = e0
% 240.08/46.66    (12)  op(e2, e0) = all_52_13
% 240.08/46.66    (13)  all_58_14 = e1
% 240.08/46.66    (14)   ~ (all_52_1 = e2)
% 240.08/46.66    (15)   ~ (e2 = e1)
% 240.08/46.66  
% 240.08/46.66  Begin of proof
% 240.08/46.66  | 
% 240.08/46.66  | BETA: splitting (8) gives:
% 240.08/46.66  | 
% 240.08/46.66  | Case 1:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (16)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 240.08/46.66  | |           e3)
% 240.08/46.66  | | 
% 240.08/46.66  | | BETA: splitting (16) gives:
% 240.08/46.66  | | 
% 240.08/46.66  | | Case 1:
% 240.08/46.66  | | | 
% 240.08/46.66  | | |   (17)  all_58_4 = e3 & op(e3, e1) = e3
% 240.08/46.66  | | | 
% 240.08/46.66  | | | ALPHA: (17) implies:
% 240.08/46.66  | | |   (18)  op(e3, e1) = e3
% 240.08/46.66  | | | 
% 240.08/46.66  | | | REF_CLOSE: (4), (9), (10), (18) are inconsistent by sub-proof #177.
% 240.08/46.66  | | | 
% 240.08/46.66  | | Case 2:
% 240.08/46.66  | | | 
% 240.08/46.66  | | |   (19)  all_58_5 = e3 & op(e2, e1) = e3
% 240.08/46.66  | | | 
% 240.08/46.66  | | | ALPHA: (19) implies:
% 240.08/46.66  | | |   (20)  op(e2, e1) = e3
% 240.08/46.66  | | | 
% 240.08/46.66  | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (12), (14), (15), (20) are
% 240.08/46.66  | | |            inconsistent by sub-proof #192.
% 240.08/46.66  | | | 
% 240.08/46.66  | | End of split
% 240.08/46.66  | | 
% 240.08/46.66  | Case 2:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (21)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 240.08/46.66  | |           e3)
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (1), (3), (10), (11), (13), (21) are inconsistent by sub-proof
% 240.08/46.66  | |            #658.
% 240.08/46.66  | | 
% 240.08/46.66  | End of split
% 240.08/46.66  | 
% 240.08/46.66  End of proof
% 240.08/46.66  
% 240.08/46.66  Sub-proof #177 shows that the following formulas are inconsistent:
% 240.08/46.66  ----------------------------------------------------------------
% 240.08/46.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.66    (2)  op(e3, e1) = e3
% 240.08/46.66    (3)  op(e3, e1) = e2
% 240.08/46.66    (4)   ~ (e3 = e2)
% 240.08/46.66  
% 240.08/46.66  Begin of proof
% 240.08/46.66  | 
% 240.08/46.66  | GROUND_INST: instantiating (1) with e2, e3, e1, e3, simplifying with (2), (3)
% 240.08/46.66  |              gives:
% 240.08/46.66  |   (5)  e3 = e2
% 240.08/46.66  | 
% 240.08/46.66  | REDUCE: (4), (5) imply:
% 240.08/46.66  |   (6)  $false
% 240.08/46.66  | 
% 240.08/46.66  | CLOSE: (6) is inconsistent.
% 240.08/46.66  | 
% 240.08/46.66  End of proof
% 240.08/46.66  
% 240.08/46.66  Sub-proof #178 shows that the following formulas are inconsistent:
% 240.08/46.66  ----------------------------------------------------------------
% 240.08/46.66    (1)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.08/46.66    (2)  op(e0, e1) = all_52_11
% 240.08/46.66    (3)   ~ (e2 = e0)
% 240.08/46.66    (4)   ~ (all_52_11 = e2)
% 240.08/46.66    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.66    (6)  op(e1, e1) = e0
% 240.08/46.66  
% 240.08/46.66  Begin of proof
% 240.08/46.66  | 
% 240.08/46.66  | BETA: splitting (1) gives:
% 240.08/46.66  | 
% 240.08/46.66  | Case 1:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (7)  all_58_8 = e2 & op(e1, e1) = e2
% 240.08/46.66  | | 
% 240.08/46.66  | | ALPHA: (7) implies:
% 240.08/46.66  | |   (8)  op(e1, e1) = e2
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2211.
% 240.08/46.66  | | 
% 240.08/46.66  | Case 2:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (9)  all_58_14 = e2 & op(e0, e1) = e2
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #183.
% 240.08/46.66  | | 
% 240.08/46.66  | End of split
% 240.08/46.66  | 
% 240.08/46.66  End of proof
% 240.08/46.66  
% 240.08/46.66  Sub-proof #179 shows that the following formulas are inconsistent:
% 240.08/46.66  ----------------------------------------------------------------
% 240.08/46.66    (1)  op(e1, e0) = all_52_14
% 240.08/46.66    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.66             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.08/46.66           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.08/46.66             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.08/46.66           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 240.08/46.66           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.66           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.66    (3)  all_56_21 = e0
% 240.08/46.66    (4)  all_56_31 = e2
% 240.08/46.66    (5)   ~ (all_52_14 = e0)
% 240.08/46.66    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.66  
% 240.08/46.66  Begin of proof
% 240.08/46.66  | 
% 240.08/46.66  | BETA: splitting (2) gives:
% 240.08/46.66  | 
% 240.08/46.66  | Case 1:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (7)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.08/46.66  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 240.08/46.66  | |        & op(e0, e2) = e0
% 240.08/46.66  | | 
% 240.08/46.66  | | ALPHA: (7) implies:
% 240.08/46.66  | |   (8)   ~ (all_56_31 = e2)
% 240.08/46.66  | | 
% 240.08/46.66  | | REDUCE: (4), (8) imply:
% 240.08/46.66  | |   (9)  $false
% 240.08/46.66  | | 
% 240.08/46.66  | | CLOSE: (9) is inconsistent.
% 240.08/46.66  | | 
% 240.08/46.66  | Case 2:
% 240.08/46.66  | | 
% 240.08/46.66  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.66  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.66  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.08/46.66  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.08/46.66  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.66  | | 
% 240.08/46.66  | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #1320.
% 240.08/46.66  | | 
% 240.08/46.66  | End of split
% 240.08/46.66  | 
% 240.08/46.66  End of proof
% 240.08/46.66  
% 240.08/46.66  Sub-proof #180 shows that the following formulas are inconsistent:
% 240.08/46.66  ----------------------------------------------------------------
% 240.08/46.66    (1)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 240.08/46.66    (2)   ~ (all_52_7 = e2)
% 240.08/46.66    (3)  all_56_11 = e1
% 240.08/46.66    (4)  op(e0, e1) = all_52_11
% 240.08/46.66    (5)   ~ (all_10_2 = e2)
% 240.08/46.66    (6)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.08/46.66           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.08/46.66             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.66           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.08/46.66             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.66           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.66           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.08/46.66           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.08/46.66           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.08/46.66           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.66           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.08/46.66             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.08/46.66           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.66           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 240.08/46.66           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.08/46.66           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.08/46.66           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.66           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.08/46.66             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.08/46.66           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.66           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 240.08/46.66           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.08/46.66           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.08/46.66           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.66           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.08/46.66             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.08/46.66           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.66           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.66    (7)   ~ (all_10_2 = e0)
% 240.08/46.66    (8)  op(e1, e0) = all_52_14
% 240.08/46.66    (9)   ~ (all_10_2 = e1)
% 240.08/46.66    (10)  op(e0, e3) = all_52_3
% 240.08/46.66    (11)   ~ (all_52_1 = all_10_2)
% 240.08/46.66    (12)   ~ (all_52_3 = all_10_2)
% 240.08/46.66    (13)   ~ (all_52_2 = all_52_14)
% 240.08/46.66    (14)  op(e2, e1) = all_52_9
% 240.08/46.67    (15)   ~ (all_52_3 = all_52_11)
% 240.08/46.67    (16)  all_56_31 = e2
% 240.08/46.67    (17)   ~ (all_52_2 = all_10_2)
% 240.08/46.67    (18)  op(e2, e3) = all_52_1
% 240.08/46.67    (19)  op(e0, e2) = all_52_7
% 240.08/46.67    (20)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.08/46.67          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.08/46.67    (21)  all_56_1 = all_10_2
% 240.08/46.67    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.67    (23)  op(e1, e3) = all_52_2
% 240.08/46.67    (24)  op(e3, e3) = all_10_2
% 240.08/46.67    (25)  all_54_0 = all_10_2
% 240.08/46.67    (26)   ~ (all_52_9 = e1)
% 240.08/46.67    (27)   ~ (all_52_1 = e1)
% 240.08/46.67  
% 240.08/46.67  Begin of proof
% 240.08/46.67  | 
% 240.08/46.67  | BETA: splitting (1) gives:
% 240.08/46.67  | 
% 240.08/46.67  | Case 1:
% 240.08/46.67  | | 
% 240.08/46.67  | |   (28)  all_54_0 = e3
% 240.08/46.67  | | 
% 240.08/46.67  | | COMBINE_EQS: (25), (28) imply:
% 240.08/46.67  | |   (29)  all_10_2 = e3
% 240.08/46.67  | | 
% 240.08/46.67  | | SIMP: (29) implies:
% 240.08/46.67  | |   (30)  all_10_2 = e3
% 240.08/46.67  | | 
% 240.08/46.67  | | COMBINE_EQS: (21), (30) imply:
% 240.08/46.67  | |   (31)  all_56_1 = e3
% 240.08/46.67  | | 
% 240.08/46.67  | | REDUCE: (11), (30) imply:
% 240.08/46.67  | |   (32)   ~ (all_52_1 = e3)
% 240.08/46.67  | | 
% 240.08/46.67  | | REDUCE: (17), (30) imply:
% 240.08/46.67  | |   (33)   ~ (all_52_2 = e3)
% 240.08/46.67  | | 
% 240.08/46.67  | | REDUCE: (12), (30) imply:
% 240.08/46.67  | |   (34)   ~ (all_52_3 = e3)
% 240.08/46.67  | | 
% 240.08/46.67  | | REDUCE: (9), (30) imply:
% 240.08/46.67  | |   (35)   ~ (e3 = e1)
% 240.08/46.67  | | 
% 240.08/46.67  | | REDUCE: (24), (30) imply:
% 240.08/46.67  | |   (36)  op(e3, e3) = e3
% 240.08/46.67  | | 
% 240.08/46.67  | | BETA: splitting (6) gives:
% 240.08/46.67  | | 
% 240.08/46.67  | | Case 1:
% 240.08/46.67  | | | 
% 240.08/46.67  | | |   (37)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.67  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.67  | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.08/46.67  | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.08/46.67  | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 240.08/46.67  | | |         | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.67  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.67  | | |           op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17
% 240.08/46.67  | | |           = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 240.08/46.67  | | |             = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.08/46.67  | | |           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.67  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.67  | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 240.08/46.67  | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 240.08/46.67  | | |             = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 240.08/46.67  | | |           e0)
% 240.08/46.67  | | | 
% 240.08/46.67  | | | BETA: splitting (37) gives:
% 240.08/46.67  | | | 
% 240.08/46.67  | | | Case 1:
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | |   (38)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.67  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.67  | | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9
% 240.08/46.67  | | | |           = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.08/46.67  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.08/46.67  | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.67  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 240.08/46.67  | | | |           ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | | REF_CLOSE: (18), (22), (23), (31), (32), (33), (38) are inconsistent by
% 240.08/46.67  | | | |            sub-proof #2299.
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | Case 2:
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | |   (39)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.67  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.67  | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.08/46.67  | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 240.08/46.67  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.08/46.67  | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.08/46.67  | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) & 
% 240.08/46.67  | | | |           ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | | REF_CLOSE: (10), (22), (31), (34), (39) are inconsistent by sub-proof
% 240.08/46.67  | | | |            #2270.
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | End of split
% 240.08/46.67  | | | 
% 240.08/46.67  | | Case 2:
% 240.08/46.67  | | | 
% 240.08/46.67  | | |   (40)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.67  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.67  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 240.08/46.67  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 240.08/46.67  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 240.08/46.67  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.67  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.67  | | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27
% 240.08/46.67  | | |           = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 240.08/46.67  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.08/46.67  | | |           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.67  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.67  | | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29
% 240.08/46.67  | | |           = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 240.08/46.67  | | |             = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 240.08/46.67  | | |           e0)
% 240.08/46.67  | | | 
% 240.08/46.67  | | | BETA: splitting (40) gives:
% 240.08/46.67  | | | 
% 240.08/46.67  | | | Case 1:
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | |   (41)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.67  | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.67  | | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 240.08/46.67  | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.08/46.67  | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.08/46.67  | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.08/46.67  | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) & 
% 240.08/46.67  | | | |           ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | | REF_CLOSE: (2), (3), (14), (19), (22), (26), (41) are inconsistent by
% 240.08/46.67  | | | |            sub-proof #181.
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | Case 2:
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | |   (42)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.67  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.67  | | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 240.08/46.67  | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 240.08/46.67  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.08/46.67  | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.08/46.67  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 240.08/46.67  | | | |           ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | | BETA: splitting (42) gives:
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | | Case 1:
% 240.08/46.67  | | | | | 
% 240.08/46.67  | | | | |   (43)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.67  | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.67  | | | | |         op(e2, e0) = e0 & op(e0, e2) = e0
% 240.08/46.67  | | | | | 
% 240.08/46.67  | | | | | ALPHA: (43) implies:
% 240.08/46.67  | | | | |   (44)   ~ (all_56_31 = e2)
% 240.08/46.67  | | | | | 
% 240.08/46.67  | | | | | REDUCE: (16), (44) imply:
% 240.08/46.67  | | | | |   (45)  $false
% 240.08/46.67  | | | | | 
% 240.08/46.67  | | | | | CLOSE: (45) is inconsistent.
% 240.08/46.67  | | | | | 
% 240.08/46.67  | | | | Case 2:
% 240.08/46.67  | | | | | 
% 240.08/46.67  | | | | |   (46)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.67  | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.08/46.67  | | | | |           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 240.08/46.67  | | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.08/46.67  | | | | |           ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 &
% 240.08/46.67  | | | | |           op(e0, e1) = e0)
% 240.08/46.67  | | | | | 
% 240.08/46.67  | | | | | BETA: splitting (46) gives:
% 240.08/46.67  | | | | | 
% 240.08/46.67  | | | | | Case 1:
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | |   (47)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.67  | | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.08/46.67  | | | | | |         & op(e1, e0) = e1 & op(e0, e1) = e1
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | | ALPHA: (47) implies:
% 240.08/46.67  | | | | | |   (48)  op(e0, e1) = e1
% 240.08/46.67  | | | | | |   (49)  op(e1, e0) = e1
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | | GROUND_INST: instantiating (22) with all_52_11, e1, e1, e0,
% 240.08/46.67  | | | | | |              simplifying with (4), (48) gives:
% 240.08/46.67  | | | | | |   (50)  all_52_11 = e1
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | | GROUND_INST: instantiating (22) with all_52_14, e1, e0, e1,
% 240.08/46.67  | | | | | |              simplifying with (8), (49) gives:
% 240.08/46.67  | | | | | |   (51)  all_52_14 = e1
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | | REDUCE: (13), (51) imply:
% 240.08/46.67  | | | | | |   (52)   ~ (all_52_2 = e1)
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | | REDUCE: (15), (50) imply:
% 240.08/46.67  | | | | | |   (53)   ~ (all_52_3 = e1)
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | | REF_CLOSE: (10), (18), (20), (22), (23), (27), (35), (36), (52),
% 240.08/46.67  | | | | | |            (53) are inconsistent by sub-proof #440.
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | Case 2:
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | |   (54)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.67  | | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 240.08/46.67  | | | | | |         & op(e1, e0) = e0 & op(e0, e1) = e0
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | | ALPHA: (54) implies:
% 240.08/46.67  | | | | | |   (55)   ~ (all_56_11 = e1)
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | | REDUCE: (3), (55) imply:
% 240.08/46.67  | | | | | |   (56)  $false
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | | CLOSE: (56) is inconsistent.
% 240.08/46.67  | | | | | | 
% 240.08/46.67  | | | | | End of split
% 240.08/46.67  | | | | | 
% 240.08/46.67  | | | | End of split
% 240.08/46.67  | | | | 
% 240.08/46.67  | | | End of split
% 240.08/46.67  | | | 
% 240.08/46.67  | | End of split
% 240.08/46.67  | | 
% 240.08/46.67  | Case 2:
% 240.08/46.67  | | 
% 240.08/46.67  | |   (57)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 240.08/46.67  | | 
% 240.08/46.67  | | REF_CLOSE: (5), (7), (9), (25), (57) are inconsistent by sub-proof #2319.
% 240.08/46.67  | | 
% 240.08/46.67  | End of split
% 240.08/46.67  | 
% 240.08/46.67  End of proof
% 240.08/46.67  
% 240.08/46.67  Sub-proof #181 shows that the following formulas are inconsistent:
% 240.08/46.67  ----------------------------------------------------------------
% 240.08/46.67    (1)   ~ (all_52_7 = e2)
% 240.08/46.67    (2)  all_56_11 = e1
% 240.08/46.67    (3)  op(e2, e1) = all_52_9
% 240.08/46.67    (4)  op(e0, e2) = all_52_7
% 240.08/46.67    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.67    (6)   ~ (all_52_9 = e1)
% 240.08/46.67    (7)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.08/46.67             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.08/46.67           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.08/46.67             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 240.08/46.67           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 240.08/46.67           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.67           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.67  
% 240.08/46.67  Begin of proof
% 240.08/46.67  | 
% 240.08/46.67  | BETA: splitting (7) gives:
% 240.08/46.67  | 
% 240.08/46.67  | Case 1:
% 240.08/46.67  | | 
% 240.08/46.67  | |   (8)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 240.08/46.67  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 240.08/46.67  | |        & op(e1, e2) = e2
% 240.08/46.67  | | 
% 240.08/46.67  | | ALPHA: (8) implies:
% 240.08/46.67  | |   (9)   ~ (all_56_11 = e1)
% 240.08/46.67  | | 
% 240.08/46.67  | | REDUCE: (2), (9) imply:
% 240.08/46.67  | |   (10)  $false
% 240.08/46.67  | | 
% 240.08/46.67  | | CLOSE: (10) is inconsistent.
% 240.08/46.67  | | 
% 240.08/46.67  | Case 2:
% 240.08/46.67  | | 
% 240.08/46.67  | |   (11)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.67  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.67  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.08/46.67  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.08/46.67  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.67  | | 
% 240.08/46.67  | | REF_CLOSE: (1), (3), (4), (5), (6), (11) are inconsistent by sub-proof
% 240.08/46.67  | |            #2305.
% 240.08/46.67  | | 
% 240.08/46.67  | End of split
% 240.08/46.67  | 
% 240.08/46.67  End of proof
% 240.08/46.67  
% 240.08/46.67  Sub-proof #182 shows that the following formulas are inconsistent:
% 240.08/46.67  ----------------------------------------------------------------
% 240.08/46.67    (1)  op(e2, e1) = all_52_9
% 240.08/46.67    (2)   ~ (all_52_13 = e2)
% 240.08/46.67    (3)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.08/46.67    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.67    (5)  op(e2, e0) = all_52_13
% 240.08/46.67    (6)   ~ (all_52_9 = e2)
% 240.08/46.67  
% 240.08/46.67  Begin of proof
% 240.08/46.67  | 
% 240.08/46.67  | BETA: splitting (3) gives:
% 240.08/46.67  | 
% 240.08/46.67  | Case 1:
% 240.08/46.67  | | 
% 240.08/46.67  | |   (7)  all_58_5 = e2 & op(e2, e1) = e2
% 240.08/46.67  | | 
% 240.08/46.67  | | ALPHA: (7) implies:
% 240.08/46.67  | |   (8)  op(e2, e1) = e2
% 240.08/46.67  | | 
% 240.08/46.67  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #2328.
% 240.08/46.67  | | 
% 240.08/46.67  | Case 2:
% 240.08/46.67  | | 
% 240.08/46.67  | |   (9)  all_58_10 = e2 & op(e2, e0) = e2
% 240.08/46.67  | | 
% 240.08/46.67  | | ALPHA: (9) implies:
% 240.08/46.67  | |   (10)  op(e2, e0) = e2
% 240.08/46.67  | | 
% 240.08/46.67  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #2317.
% 240.08/46.67  | | 
% 240.08/46.67  | End of split
% 240.08/46.67  | 
% 240.08/46.67  End of proof
% 240.08/46.67  
% 240.08/46.67  Sub-proof #183 shows that the following formulas are inconsistent:
% 240.08/46.67  ----------------------------------------------------------------
% 240.08/46.67    (1)  all_58_14 = e2 & op(e0, e1) = e2
% 240.08/46.67    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.67    (3)  op(e0, e1) = all_52_11
% 240.08/46.67    (4)   ~ (all_52_11 = e2)
% 240.08/46.67  
% 240.08/46.67  Begin of proof
% 240.08/46.67  | 
% 240.08/46.67  | ALPHA: (1) implies:
% 240.08/46.67  |   (5)  op(e0, e1) = e2
% 240.08/46.67  | 
% 240.08/46.67  | GROUND_INST: instantiating (2) with all_52_11, e2, e1, e0, simplifying with
% 240.08/46.67  |              (3), (5) gives:
% 240.08/46.67  |   (6)  all_52_11 = e2
% 240.08/46.67  | 
% 240.08/46.67  | REDUCE: (4), (6) imply:
% 240.08/46.67  |   (7)  $false
% 240.08/46.67  | 
% 240.08/46.67  | CLOSE: (7) is inconsistent.
% 240.08/46.67  | 
% 240.08/46.67  End of proof
% 240.08/46.67  
% 240.08/46.67  Sub-proof #184 shows that the following formulas are inconsistent:
% 240.08/46.67  ----------------------------------------------------------------
% 240.08/46.67    (1)   ~ (all_52_7 = e2)
% 240.08/46.67    (2)  op(e2, e1) = all_52_9
% 240.08/46.67    (3)  all_56_31 = e2
% 240.08/46.67    (4)  op(e0, e2) = all_52_7
% 240.08/46.67    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.67    (6)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.08/46.67             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.08/46.67           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.08/46.67             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 240.08/46.67           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 240.08/46.67           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.67           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.67    (7)   ~ (all_52_9 = e2)
% 240.08/46.67  
% 240.08/46.67  Begin of proof
% 240.08/46.67  | 
% 240.08/46.67  | BETA: splitting (6) gives:
% 240.08/46.67  | 
% 240.08/46.67  | Case 1:
% 240.08/46.67  | | 
% 240.08/46.67  | |   (8)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 240.08/46.67  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 240.08/46.67  | |        & op(e1, e2) = e2
% 240.08/46.67  | | 
% 240.08/46.67  | | ALPHA: (8) implies:
% 240.08/46.67  | |   (9)  op(e2, e1) = e2
% 240.08/46.67  | | 
% 240.08/46.67  | | REF_CLOSE: (2), (5), (7), (9) are inconsistent by sub-proof #2328.
% 240.08/46.67  | | 
% 240.08/46.67  | Case 2:
% 240.08/46.67  | | 
% 240.08/46.67  | |   (10)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.67  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.67  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.08/46.67  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.08/46.67  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.67  | | 
% 240.08/46.67  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #185.
% 240.08/46.67  | | 
% 240.08/46.67  | End of split
% 240.08/46.67  | 
% 240.08/46.67  End of proof
% 240.08/46.67  
% 240.08/46.67  Sub-proof #185 shows that the following formulas are inconsistent:
% 240.08/46.67  ----------------------------------------------------------------
% 240.08/46.67    (1)   ~ (all_52_7 = e2)
% 240.08/46.67    (2)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.67             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.08/46.67           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 240.08/46.67             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.08/46.67           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.67    (3)  all_56_31 = e2
% 240.08/46.68    (4)  op(e0, e2) = all_52_7
% 240.08/46.68    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.68  
% 240.08/46.68  Begin of proof
% 240.08/46.68  | 
% 240.08/46.68  | BETA: splitting (2) gives:
% 240.08/46.68  | 
% 240.08/46.68  | Case 1:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (6)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.08/46.68  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 240.08/46.68  | |        & op(e1, e2) = e1
% 240.08/46.68  | | 
% 240.08/46.68  | | ALPHA: (6) implies:
% 240.08/46.68  | |   (7)   ~ (all_56_31 = e2)
% 240.08/46.68  | | 
% 240.08/46.68  | | REDUCE: (3), (7) imply:
% 240.08/46.68  | |   (8)  $false
% 240.08/46.68  | | 
% 240.08/46.68  | | CLOSE: (8) is inconsistent.
% 240.08/46.68  | | 
% 240.08/46.68  | Case 2:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (9)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.08/46.68  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 240.08/46.68  | |        & op(e0, e2) = e2
% 240.08/46.68  | | 
% 240.08/46.68  | | ALPHA: (9) implies:
% 240.08/46.68  | |   (10)  op(e0, e2) = e2
% 240.08/46.68  | | 
% 240.08/46.68  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2327.
% 240.08/46.68  | | 
% 240.08/46.68  | End of split
% 240.08/46.68  | 
% 240.08/46.68  End of proof
% 240.08/46.68  
% 240.08/46.68  Sub-proof #186 shows that the following formulas are inconsistent:
% 240.08/46.68  ----------------------------------------------------------------
% 240.08/46.68    (1)   ~ (e3 = e0)
% 240.08/46.68    (2)   ~ (e2 = e0)
% 240.08/46.68    (3)  op(e1, e2) = all_52_6
% 240.08/46.68    (4)  op(e1, e1) = all_6_2
% 240.08/46.68    (5)   ~ (e3 = e1)
% 240.08/46.68    (6)   ~ (all_6_2 = e3)
% 240.08/46.68    (7)   ~ (e3 = e2)
% 240.08/46.68    (8)  op(e1, e3) = e1
% 240.08/46.68    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.08/46.68         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.08/46.68    (10)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.08/46.68          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.08/46.68    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.68    (12)  all_58_7 = e1 & op(e1, e2) = e1
% 240.08/46.68    (13)   ~ (e1 = e0)
% 240.08/46.68    (14)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.08/46.68          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.08/46.68    (15)   ~ (e2 = e1)
% 240.08/46.68  
% 240.08/46.68  Begin of proof
% 240.08/46.68  | 
% 240.08/46.68  | ALPHA: (12) implies:
% 240.08/46.68  |   (16)  all_58_7 = e1
% 240.08/46.68  |   (17)  op(e1, e2) = e1
% 240.08/46.68  | 
% 240.08/46.68  | BETA: splitting (14) gives:
% 240.08/46.68  | 
% 240.08/46.68  | Case 1:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (18)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 240.08/46.68  | |           e0)
% 240.08/46.68  | | 
% 240.08/46.68  | | BETA: splitting (18) gives:
% 240.08/46.68  | | 
% 240.08/46.68  | | Case 1:
% 240.08/46.68  | | | 
% 240.08/46.68  | | |   (19)  all_58_6 = e0 & op(e1, e3) = e0
% 240.08/46.68  | | | 
% 240.08/46.68  | | | ALPHA: (19) implies:
% 240.08/46.68  | | |   (20)  op(e1, e3) = e0
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REF_CLOSE: (8), (11), (13), (20) are inconsistent by sub-proof #449.
% 240.08/46.68  | | | 
% 240.08/46.68  | | Case 2:
% 240.08/46.68  | | | 
% 240.08/46.68  | | |   (21)  all_58_7 = e0 & op(e1, e2) = e0
% 240.08/46.68  | | | 
% 240.08/46.68  | | | ALPHA: (21) implies:
% 240.08/46.68  | | |   (22)  op(e1, e2) = e0
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REF_CLOSE: (3), (11), (13), (17), (22) are inconsistent by sub-proof
% 240.08/46.68  | | |            #2136.
% 240.08/46.68  | | | 
% 240.08/46.68  | | End of split
% 240.08/46.68  | | 
% 240.08/46.68  | Case 2:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (23)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.08/46.68  | |           e0)
% 240.08/46.68  | | 
% 240.08/46.68  | | BETA: splitting (23) gives:
% 240.08/46.68  | | 
% 240.08/46.68  | | Case 1:
% 240.08/46.68  | | | 
% 240.08/46.68  | | |   (24)  all_58_8 = e0 & op(e1, e1) = e0
% 240.08/46.68  | | | 
% 240.08/46.68  | | | ALPHA: (24) implies:
% 240.08/46.68  | | |   (25)  op(e1, e1) = e0
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (11), (15), (16), (17),
% 240.08/46.68  | | |            (25) are inconsistent by sub-proof #1993.
% 240.08/46.68  | | | 
% 240.08/46.68  | | Case 2:
% 240.08/46.68  | | | 
% 240.08/46.68  | | |   (26)  all_58_11 = e0 & op(e1, e0) = e0
% 240.08/46.68  | | | 
% 240.08/46.68  | | | ALPHA: (26) implies:
% 240.08/46.68  | | |   (27)  all_58_11 = e0
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (11), (17), (27) are inconsistent
% 240.08/46.68  | | |            by sub-proof #2090.
% 240.08/46.68  | | | 
% 240.08/46.68  | | End of split
% 240.08/46.68  | | 
% 240.08/46.68  | End of split
% 240.08/46.68  | 
% 240.08/46.68  End of proof
% 240.08/46.68  
% 240.08/46.68  Sub-proof #187 shows that the following formulas are inconsistent:
% 240.08/46.68  ----------------------------------------------------------------
% 240.08/46.68    (1)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 240.08/46.68    (2)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.68         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.08/46.68    (3)   ~ (e3 = e1)
% 240.08/46.68    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.08/46.68         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.08/46.68    (5)  op(e3, e1) = all_52_8
% 240.08/46.68    (6)   ~ (e3 = e2)
% 240.08/46.68    (7)  op(e3, e0) = all_52_12
% 240.08/46.68    (8)  op(e2, e3) = all_52_1
% 240.08/46.68    (9)  op(e3, e3) = e2
% 240.08/46.68    (10)   ~ (all_52_13 = e2)
% 240.08/46.68    (11)  op(e2, e1) = e3
% 240.08/46.68    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.68    (13)   ~ (all_52_12 = e3)
% 240.08/46.68    (14)  op(e2, e0) = all_52_13
% 240.08/46.68    (15)   ~ (all_52_1 = e2)
% 240.08/46.68    (16)   ~ (e2 = e1)
% 240.08/46.68    (17)   ~ (all_52_8 = e3)
% 240.08/46.68  
% 240.08/46.68  Begin of proof
% 240.08/46.68  | 
% 240.08/46.68  | BETA: splitting (1) gives:
% 240.08/46.68  | 
% 240.08/46.68  | Case 1:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (18)  all_58_1 = e1 & op(e3, e2) = e1
% 240.08/46.68  | | 
% 240.08/46.68  | | ALPHA: (18) implies:
% 240.08/46.68  | |   (19)  all_58_1 = e1
% 240.08/46.68  | | 
% 240.08/46.68  | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (12), (13), (17), (19) are
% 240.08/46.68  | |            inconsistent by sub-proof #1327.
% 240.08/46.68  | | 
% 240.08/46.68  | Case 2:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (20)  all_58_3 = e1 & op(e2, e2) = e1
% 240.08/46.68  | | 
% 240.08/46.68  | | ALPHA: (20) implies:
% 240.08/46.68  | |   (21)  op(e2, e2) = e1
% 240.08/46.68  | | 
% 240.08/46.68  | | REF_CLOSE: (2), (6), (8), (10), (11), (12), (14), (15), (16), (21) are
% 240.08/46.68  | |            inconsistent by sub-proof #192.
% 240.08/46.68  | | 
% 240.08/46.68  | End of split
% 240.08/46.68  | 
% 240.08/46.68  End of proof
% 240.08/46.68  
% 240.08/46.68  Sub-proof #188 shows that the following formulas are inconsistent:
% 240.08/46.68  ----------------------------------------------------------------
% 240.08/46.68    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.08/46.68           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.08/46.68             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.68           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.08/46.68             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.68           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.68           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.68    (2)   ~ (e3 = e2)
% 240.08/46.68    (3)  op(e2, e3) = all_52_1
% 240.08/46.68    (4)   ~ (all_52_2 = e3)
% 240.08/46.68    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.68    (6)  op(e1, e3) = all_52_2
% 240.08/46.68    (7)  op(e3, e2) = e3
% 240.08/46.68    (8)   ~ (all_52_1 = e3)
% 240.08/46.68  
% 240.08/46.68  Begin of proof
% 240.08/46.68  | 
% 240.08/46.68  | BETA: splitting (1) gives:
% 240.08/46.68  | 
% 240.08/46.68  | Case 1:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (9)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.68  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.08/46.68  | |        op(e2, e3) = e3
% 240.08/46.68  | | 
% 240.08/46.68  | | ALPHA: (9) implies:
% 240.08/46.68  | |   (10)  op(e2, e3) = e3
% 240.08/46.68  | | 
% 240.08/46.68  | | REF_CLOSE: (3), (5), (8), (10) are inconsistent by sub-proof #2337.
% 240.08/46.68  | | 
% 240.08/46.68  | Case 2:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (11)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.08/46.68  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.08/46.68  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.68  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.68  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.68  | | 
% 240.08/46.68  | | REF_CLOSE: (2), (4), (5), (6), (7), (11) are inconsistent by sub-proof
% 240.08/46.68  | |            #1685.
% 240.08/46.68  | | 
% 240.08/46.68  | End of split
% 240.08/46.68  | 
% 240.08/46.68  End of proof
% 240.08/46.68  
% 240.08/46.68  Sub-proof #189 shows that the following formulas are inconsistent:
% 240.08/46.68  ----------------------------------------------------------------
% 240.08/46.68    (1)   ~ (e3 = e0)
% 240.08/46.68    (2)  all_58_6 = e3
% 240.08/46.68    (3)   ~ (e2 = e0)
% 240.08/46.68    (4)  op(e1, e0) = all_52_14
% 240.08/46.68    (5)  all_58_11 = e1 & op(e1, e0) = e1
% 240.08/46.68    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.68         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.08/46.68    (7)   ~ (all_52_14 = e2)
% 240.08/46.68    (8)   ~ (e3 = e2)
% 240.08/46.68    (9)  op(e2, e3) = all_52_1
% 240.08/46.68    (10)   ~ (all_52_13 = e2)
% 240.08/46.68    (11)   ~ (all_44_1 = e1)
% 240.08/46.68    (12)  op(e1, e1) = e2
% 240.08/46.68    (13)  op(e2, e1) = e3
% 240.08/46.68    (14)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.08/46.68          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.08/46.68    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.68    (16)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.08/46.68          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.68    (17)  op(e0, e2) = all_44_1
% 240.08/46.68    (18)   ~ (e1 = e0)
% 240.08/46.68    (19)  op(e1, all_52_14) = e1
% 240.08/46.68    (20)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.08/46.68          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.08/46.68    (21)  op(e2, e0) = all_52_13
% 240.08/46.68    (22)   ~ (all_52_1 = e2)
% 240.08/46.68    (23)   ~ (e2 = e1)
% 240.08/46.68  
% 240.08/46.68  Begin of proof
% 240.08/46.68  | 
% 240.08/46.68  | ALPHA: (5) implies:
% 240.08/46.68  |   (24)  all_58_11 = e1
% 240.08/46.68  |   (25)  op(e1, e0) = e1
% 240.08/46.68  | 
% 240.08/46.68  | BETA: splitting (16) gives:
% 240.08/46.68  | 
% 240.08/46.68  | Case 1:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (26)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 240.08/46.68  | |           e1)
% 240.08/46.68  | | 
% 240.08/46.68  | | BETA: splitting (26) gives:
% 240.08/46.68  | | 
% 240.08/46.68  | | Case 1:
% 240.08/46.68  | | | 
% 240.08/46.68  | | | 
% 240.08/46.68  | | | GROUND_INST: instantiating (15) with all_52_14, e1, e0, e1, simplifying
% 240.08/46.68  | | |              with (4), (25) gives:
% 240.08/46.68  | | |   (27)  all_52_14 = e1
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REDUCE: (7), (27) imply:
% 240.08/46.68  | | |   (28)   ~ (e2 = e1)
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REDUCE: (19), (27) imply:
% 240.08/46.68  | | |   (29)  op(e1, e1) = e1
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REF_CLOSE: (12), (15), (23), (29) are inconsistent by sub-proof #2159.
% 240.08/46.68  | | | 
% 240.08/46.68  | | Case 2:
% 240.08/46.68  | | | 
% 240.08/46.68  | | |   (30)  all_58_3 = e1 & op(e2, e2) = e1
% 240.08/46.68  | | | 
% 240.08/46.68  | | | ALPHA: (30) implies:
% 240.08/46.68  | | |   (31)  op(e2, e2) = e1
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REF_CLOSE: (6), (8), (9), (10), (13), (15), (21), (22), (23), (31) are
% 240.08/46.68  | | |            inconsistent by sub-proof #192.
% 240.08/46.68  | | | 
% 240.08/46.68  | | End of split
% 240.08/46.68  | | 
% 240.08/46.68  | Case 2:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (32)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 240.08/46.68  | |           e1)
% 240.08/46.68  | | 
% 240.08/46.68  | | BETA: splitting (32) gives:
% 240.08/46.68  | | 
% 240.08/46.68  | | Case 1:
% 240.08/46.68  | | | 
% 240.08/46.68  | | |   (33)  all_58_7 = e1 & op(e1, e2) = e1
% 240.08/46.68  | | | 
% 240.08/46.68  | | | ALPHA: (33) implies:
% 240.08/46.68  | | |   (34)  all_58_7 = e1
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REF_CLOSE: (1), (2), (3), (8), (14), (15), (18), (20), (23), (24), (25),
% 240.08/46.68  | | |            (34) are inconsistent by sub-proof #1553.
% 240.08/46.68  | | | 
% 240.08/46.68  | | Case 2:
% 240.08/46.68  | | | 
% 240.08/46.68  | | |   (35)  all_58_13 = e1 & op(e0, e2) = e1
% 240.08/46.68  | | | 
% 240.08/46.68  | | | ALPHA: (35) implies:
% 240.08/46.68  | | |   (36)  op(e0, e2) = e1
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REF_CLOSE: (11), (15), (17), (36) are inconsistent by sub-proof #230.
% 240.08/46.68  | | | 
% 240.08/46.68  | | End of split
% 240.08/46.68  | | 
% 240.08/46.68  | End of split
% 240.08/46.68  | 
% 240.08/46.68  End of proof
% 240.08/46.68  
% 240.08/46.68  Sub-proof #190 shows that the following formulas are inconsistent:
% 240.08/46.68  ----------------------------------------------------------------
% 240.08/46.68    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.08/46.68         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.68    (2)   ~ (e3 = e0)
% 240.08/46.68    (3)  op(e0, e1) = all_52_11
% 240.08/46.68    (4)   ~ (e3 = e1)
% 240.08/46.68    (5)  all_58_12 = e1
% 240.08/46.68    (6)   ~ (all_52_11 = e3)
% 240.08/46.68    (7)   ~ (e3 = e2)
% 240.08/46.68    (8)  op(e0, e2) = e0
% 240.08/46.68    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.68    (10)  op(e0, e0) = e2
% 240.08/46.68  
% 240.08/46.68  Begin of proof
% 240.08/46.68  | 
% 240.08/46.68  | BETA: splitting (1) gives:
% 240.08/46.68  | 
% 240.08/46.68  | Case 1:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (11)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 240.08/46.68  | |           e3)
% 240.08/46.68  | | 
% 240.08/46.68  | | BETA: splitting (11) gives:
% 240.08/46.68  | | 
% 240.08/46.68  | | Case 1:
% 240.08/46.68  | | | 
% 240.08/46.68  | | |   (12)  all_58_12 = e3 & op(e0, e3) = e3
% 240.08/46.68  | | | 
% 240.08/46.68  | | | ALPHA: (12) implies:
% 240.08/46.68  | | |   (13)  all_58_12 = e3
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #1542.
% 240.08/46.68  | | | 
% 240.08/46.68  | | Case 2:
% 240.08/46.68  | | | 
% 240.08/46.68  | | |   (14)  all_58_13 = e3 & op(e0, e2) = e3
% 240.08/46.68  | | | 
% 240.08/46.68  | | | ALPHA: (14) implies:
% 240.08/46.68  | | |   (15)  op(e0, e2) = e3
% 240.08/46.68  | | | 
% 240.08/46.68  | | | REF_CLOSE: (2), (8), (9), (15) are inconsistent by sub-proof #1961.
% 240.08/46.68  | | | 
% 240.08/46.68  | | End of split
% 240.08/46.68  | | 
% 240.08/46.68  | Case 2:
% 240.08/46.68  | | 
% 240.08/46.68  | |   (16)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 240.08/46.68  | |           e3)
% 240.08/46.68  | | 
% 240.08/46.68  | | REF_CLOSE: (3), (6), (7), (9), (10), (16) are inconsistent by sub-proof
% 240.08/46.68  | |            #226.
% 240.08/46.68  | | 
% 240.08/46.68  | End of split
% 240.08/46.68  | 
% 240.08/46.68  End of proof
% 240.08/46.68  
% 240.08/46.68  Sub-proof #191 shows that the following formulas are inconsistent:
% 240.08/46.68  ----------------------------------------------------------------
% 240.08/46.68    (1)   ~ (e3 = e0)
% 240.08/46.68    (2)   ~ (e2 = e0)
% 240.08/46.68    (3)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 240.08/46.68    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.68         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.08/46.68    (5)   ~ (e3 = e1)
% 240.08/46.68    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.08/46.68         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.08/46.68    (7)   ~ (e3 = e2)
% 240.08/46.68    (8)  all_58_4 = e1
% 240.08/46.68    (9)  op(e2, e3) = all_52_1
% 240.08/46.68    (10)  op(e3, e3) = e2
% 240.08/46.68    (11)   ~ (all_52_13 = e2)
% 240.08/46.69    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.08/46.69          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.08/46.69    (13)   ~ (all_52_4 = e3)
% 240.08/46.69    (14)  op(e3, e2) = all_52_4
% 240.08/46.69    (15)  op(e2, e1) = e3
% 240.08/46.69    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.69    (17)   ~ (e1 = e0)
% 240.08/46.69    (18)  op(e2, e0) = all_52_13
% 240.08/46.69    (19)   ~ (all_52_1 = e2)
% 240.08/46.69    (20)   ~ (e2 = e1)
% 240.08/46.69  
% 240.08/46.69  Begin of proof
% 240.08/46.69  | 
% 240.08/46.69  | BETA: splitting (3) gives:
% 240.08/46.69  | 
% 240.08/46.69  | Case 1:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (21)  all_58_1 = e1 & op(e3, e2) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | ALPHA: (21) implies:
% 240.08/46.69  | |   (22)  all_58_1 = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (12), (13), (14), (16), (17),
% 240.08/46.69  | |            (22) are inconsistent by sub-proof #1645.
% 240.08/46.69  | | 
% 240.08/46.69  | Case 2:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (23)  all_58_3 = e1 & op(e2, e2) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | ALPHA: (23) implies:
% 240.08/46.69  | |   (24)  op(e2, e2) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (4), (7), (9), (11), (15), (16), (18), (19), (20), (24) are
% 240.08/46.69  | |            inconsistent by sub-proof #192.
% 240.08/46.69  | | 
% 240.08/46.69  | End of split
% 240.08/46.69  | 
% 240.08/46.69  End of proof
% 240.08/46.69  
% 240.08/46.69  Sub-proof #192 shows that the following formulas are inconsistent:
% 240.08/46.69  ----------------------------------------------------------------
% 240.08/46.69    (1)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.69         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.08/46.69    (2)   ~ (e3 = e2)
% 240.08/46.69    (3)  op(e2, e2) = e1
% 240.08/46.69    (4)  op(e2, e3) = all_52_1
% 240.08/46.69    (5)   ~ (all_52_13 = e2)
% 240.08/46.69    (6)  op(e2, e1) = e3
% 240.08/46.69    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.69    (8)  op(e2, e0) = all_52_13
% 240.08/46.69    (9)   ~ (all_52_1 = e2)
% 240.08/46.69    (10)   ~ (e2 = e1)
% 240.08/46.69  
% 240.08/46.69  Begin of proof
% 240.08/46.69  | 
% 240.08/46.69  | BETA: splitting (1) gives:
% 240.08/46.69  | 
% 240.08/46.69  | Case 1:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (11)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 240.08/46.69  | |           e2)
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (3), (4), (7), (9), (10), (11) are inconsistent by sub-proof
% 240.08/46.69  | |            #1929.
% 240.08/46.69  | | 
% 240.08/46.69  | Case 2:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (12)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 240.08/46.69  | |           e2)
% 240.08/46.69  | | 
% 240.08/46.69  | | BETA: splitting (12) gives:
% 240.08/46.69  | | 
% 240.08/46.69  | | Case 1:
% 240.08/46.69  | | | 
% 240.08/46.69  | | |   (13)  all_58_5 = e2 & op(e2, e1) = e2
% 240.08/46.69  | | | 
% 240.08/46.69  | | | ALPHA: (13) implies:
% 240.08/46.69  | | |   (14)  op(e2, e1) = e2
% 240.08/46.69  | | | 
% 240.08/46.69  | | | REF_CLOSE: (2), (6), (7), (14) are inconsistent by sub-proof #2256.
% 240.08/46.69  | | | 
% 240.08/46.69  | | Case 2:
% 240.08/46.69  | | | 
% 240.08/46.69  | | |   (15)  all_58_10 = e2 & op(e2, e0) = e2
% 240.08/46.69  | | | 
% 240.08/46.69  | | | ALPHA: (15) implies:
% 240.08/46.69  | | |   (16)  op(e2, e0) = e2
% 240.08/46.69  | | | 
% 240.08/46.69  | | | REF_CLOSE: (5), (7), (8), (16) are inconsistent by sub-proof #2317.
% 240.08/46.69  | | | 
% 240.08/46.69  | | End of split
% 240.08/46.69  | | 
% 240.08/46.69  | End of split
% 240.08/46.69  | 
% 240.08/46.69  End of proof
% 240.08/46.69  
% 240.08/46.69  Sub-proof #193 shows that the following formulas are inconsistent:
% 240.08/46.69  ----------------------------------------------------------------
% 240.08/46.69    (1)   ~ (e3 = e0)
% 240.08/46.69    (2)  op(e0, e2) = e3
% 240.08/46.69    (3)  op(e0, e1) = e1
% 240.08/46.69    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.69    (5)   ~ (e1 = e0)
% 240.08/46.69    (6)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.69  
% 240.08/46.69  Begin of proof
% 240.08/46.69  | 
% 240.08/46.69  | BETA: splitting (6) gives:
% 240.08/46.69  | 
% 240.08/46.69  | Case 1:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (7)  all_58_13 = e0 & op(e0, e2) = e0
% 240.08/46.69  | | 
% 240.08/46.69  | | ALPHA: (7) implies:
% 240.08/46.69  | |   (8)  op(e0, e2) = e0
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #1961.
% 240.08/46.69  | | 
% 240.08/46.69  | Case 2:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 240.08/46.69  | | 
% 240.08/46.69  | | ALPHA: (9) implies:
% 240.08/46.69  | |   (10)  op(e0, e1) = e0
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #2158.
% 240.08/46.69  | | 
% 240.08/46.69  | End of split
% 240.08/46.69  | 
% 240.08/46.69  End of proof
% 240.08/46.69  
% 240.08/46.69  Sub-proof #194 shows that the following formulas are inconsistent:
% 240.08/46.69  ----------------------------------------------------------------
% 240.08/46.69    (1)  op(e1, e3) = e3
% 240.08/46.69    (2)   ~ (e3 = e1)
% 240.08/46.69    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.08/46.69    (4)  op(e0, e3) = e0
% 240.08/46.69    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.69    (6)   ~ (e1 = e0)
% 240.08/46.69  
% 240.08/46.69  Begin of proof
% 240.08/46.69  | 
% 240.08/46.69  | BETA: splitting (3) gives:
% 240.08/46.69  | 
% 240.08/46.69  | Case 1:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (7)  all_58_6 = e1 & op(e1, e3) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | ALPHA: (7) implies:
% 240.08/46.69  | |   (8)  op(e1, e3) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #2225.
% 240.08/46.69  | | 
% 240.08/46.69  | Case 2:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (9)  all_58_12 = e1 & op(e0, e3) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | ALPHA: (9) implies:
% 240.08/46.69  | |   (10)  op(e0, e3) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #207.
% 240.08/46.69  | | 
% 240.08/46.69  | End of split
% 240.08/46.69  | 
% 240.08/46.69  End of proof
% 240.08/46.69  
% 240.08/46.69  Sub-proof #195 shows that the following formulas are inconsistent:
% 240.08/46.69  ----------------------------------------------------------------
% 240.08/46.69    (1)   ~ (e3 = e0)
% 240.08/46.69    (2)  all_58_6 = e3
% 240.08/46.69    (3)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.08/46.69         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.08/46.69    (4)  op(e3, e1) = all_52_8
% 240.08/46.69    (5)   ~ (e3 = e2)
% 240.08/46.69    (6)  all_58_9 = e3
% 240.08/46.69    (7)  op(e3, e3) = e2
% 240.08/46.69    (8)   ~ (all_52_4 = e3)
% 240.08/46.69    (9)  op(e3, e2) = all_52_4
% 240.08/46.69    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.69    (11)  all_58_6 = e0 & op(e1, e3) = e0
% 240.08/46.69    (12)   ~ (all_52_8 = e3)
% 240.08/46.69  
% 240.08/46.69  Begin of proof
% 240.08/46.69  | 
% 240.08/46.69  | ALPHA: (11) implies:
% 240.08/46.69  |   (13)  all_58_6 = e0
% 240.08/46.69  | 
% 240.08/46.69  | COMBINE_EQS: (2), (13) imply:
% 240.08/46.69  |   (14)  e3 = e0
% 240.08/46.69  | 
% 240.08/46.69  | COMBINE_EQS: (6), (14) imply:
% 240.08/46.69  |   (15)  all_58_9 = e0
% 240.08/46.69  | 
% 240.08/46.69  | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (15) are
% 240.08/46.69  |            inconsistent by sub-proof #1956.
% 240.08/46.69  | 
% 240.08/46.69  End of proof
% 240.08/46.69  
% 240.08/46.69  Sub-proof #196 shows that the following formulas are inconsistent:
% 240.08/46.69  ----------------------------------------------------------------
% 240.08/46.69    (1)  all_58_1 = e1
% 240.08/46.69    (2)   ~ (e3 = e0)
% 240.08/46.69    (3)   ~ (e2 = e0)
% 240.08/46.69    (4)   ~ (e3 = e1)
% 240.08/46.69    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.08/46.69         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.08/46.69    (6)   ~ (e3 = e2)
% 240.08/46.69    (7)  op(e2, e0) = e0
% 240.08/46.69    (8)  op(e3, e3) = e2
% 240.08/46.69    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.08/46.69         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.08/46.69    (10)   ~ (all_52_4 = e3)
% 240.08/46.69    (11)  op(e3, e2) = all_52_4
% 240.08/46.69    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.69    (13)   ~ (e1 = e0)
% 240.08/46.69    (14)  op(e2, e0) = all_52_13
% 240.08/46.69    (15)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.08/46.69  
% 240.08/46.69  Begin of proof
% 240.08/46.69  | 
% 240.08/46.69  | BETA: splitting (15) gives:
% 240.08/46.69  | 
% 240.08/46.69  | Case 1:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (16)  all_58_9 = e1 & op(e3, e0) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | ALPHA: (16) implies:
% 240.08/46.69  | |   (17)  all_58_9 = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 240.08/46.69  | |            (17) are inconsistent by sub-proof #1694.
% 240.08/46.69  | | 
% 240.08/46.69  | Case 2:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (18)  all_58_10 = e1 & op(e2, e0) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | ALPHA: (18) implies:
% 240.08/46.69  | |   (19)  op(e2, e0) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (7), (12), (13), (14), (19) are inconsistent by sub-proof #1778.
% 240.08/46.69  | | 
% 240.08/46.69  | End of split
% 240.08/46.69  | 
% 240.08/46.69  End of proof
% 240.08/46.69  
% 240.08/46.69  Sub-proof #197 shows that the following formulas are inconsistent:
% 240.08/46.69  ----------------------------------------------------------------
% 240.08/46.69    (1)   ~ (e3 = e0)
% 240.08/46.69    (2)  all_58_5 = e3
% 240.08/46.69    (3)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.08/46.69         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.08/46.69    (4)  op(e3, e1) = all_52_8
% 240.08/46.69    (5)   ~ (e3 = e2)
% 240.08/46.69    (6)  all_58_9 = e3
% 240.08/46.69    (7)  op(e3, e3) = e2
% 240.08/46.69    (8)   ~ (all_52_4 = e3)
% 240.08/46.69    (9)  op(e3, e2) = all_52_4
% 240.08/46.69    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.69    (11)  all_58_5 = e0 & op(e2, e1) = e0
% 240.08/46.69    (12)   ~ (all_52_8 = e3)
% 240.08/46.69  
% 240.08/46.69  Begin of proof
% 240.08/46.69  | 
% 240.08/46.69  | ALPHA: (11) implies:
% 240.08/46.69  |   (13)  all_58_5 = e0
% 240.08/46.69  | 
% 240.08/46.69  | COMBINE_EQS: (2), (13) imply:
% 240.08/46.69  |   (14)  e3 = e0
% 240.08/46.69  | 
% 240.08/46.69  | COMBINE_EQS: (6), (14) imply:
% 240.08/46.69  |   (15)  all_58_9 = e0
% 240.08/46.69  | 
% 240.08/46.69  | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (15) are
% 240.08/46.69  |            inconsistent by sub-proof #1956.
% 240.08/46.69  | 
% 240.08/46.69  End of proof
% 240.08/46.69  
% 240.08/46.69  Sub-proof #198 shows that the following formulas are inconsistent:
% 240.08/46.69  ----------------------------------------------------------------
% 240.08/46.69    (1)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 240.08/46.69    (2)   ~ (e2 = e0)
% 240.08/46.69    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.69    (4)   ~ (e1 = e0)
% 240.08/46.69    (5)  op(e2, e2) = e2
% 240.08/46.69    (6)  all_58_2 = e1
% 240.08/46.69  
% 240.08/46.69  Begin of proof
% 240.08/46.69  | 
% 240.08/46.69  | BETA: splitting (1) gives:
% 240.08/46.69  | 
% 240.08/46.69  | Case 1:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (7)  all_58_2 = e0 & op(e2, e3) = e0
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #1972.
% 240.08/46.69  | | 
% 240.08/46.69  | Case 2:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (8)  all_58_3 = e0 & op(e2, e2) = e0
% 240.08/46.69  | | 
% 240.08/46.69  | | ALPHA: (8) implies:
% 240.08/46.69  | |   (9)  op(e2, e2) = e0
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #2137.
% 240.08/46.69  | | 
% 240.08/46.69  | End of split
% 240.08/46.69  | 
% 240.08/46.69  End of proof
% 240.08/46.69  
% 240.08/46.69  Sub-proof #199 shows that the following formulas are inconsistent:
% 240.08/46.69  ----------------------------------------------------------------
% 240.08/46.69    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.08/46.69         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.08/46.69    (2)  all_58_1 = e1
% 240.08/46.69    (3)   ~ (e3 = e0)
% 240.08/46.69    (4)   ~ (e2 = e0)
% 240.08/46.69    (5)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 240.08/46.69    (6)   ~ (e3 = e1)
% 240.08/46.69    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.08/46.69         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.08/46.69    (8)   ~ (e3 = e2)
% 240.08/46.69    (9)  op(e3, e0) = e3
% 240.08/46.69    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.08/46.69          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.08/46.69    (11)   ~ (all_52_4 = e3)
% 240.08/46.69    (12)  op(e3, e2) = all_52_4
% 240.08/46.69    (13)  op(e2, e1) = e3
% 240.08/46.69    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.69    (15)   ~ (e1 = e0)
% 240.08/46.69    (16)   ~ (e2 = e1)
% 240.08/46.69  
% 240.08/46.69  Begin of proof
% 240.08/46.69  | 
% 240.08/46.69  | BETA: splitting (5) gives:
% 240.08/46.69  | 
% 240.08/46.69  | Case 1:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (17)  all_58_4 = e1 & op(e3, e1) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | ALPHA: (17) implies:
% 240.08/46.69  | |   (18)  all_58_4 = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 240.08/46.69  | |            (15), (16), (18) are inconsistent by sub-proof #1437.
% 240.08/46.69  | | 
% 240.08/46.69  | Case 2:
% 240.08/46.69  | | 
% 240.08/46.69  | |   (19)  all_58_5 = e1 & op(e2, e1) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | ALPHA: (19) implies:
% 240.08/46.69  | |   (20)  op(e2, e1) = e1
% 240.08/46.69  | | 
% 240.08/46.69  | | REF_CLOSE: (6), (13), (14), (20) are inconsistent by sub-proof #2255.
% 240.08/46.69  | | 
% 240.08/46.69  | End of split
% 240.08/46.69  | 
% 240.08/46.69  End of proof
% 240.08/46.69  
% 240.08/46.69  Sub-proof #200 shows that the following formulas are inconsistent:
% 240.08/46.69  ----------------------------------------------------------------
% 240.08/46.69    (1)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.08/46.69         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.08/46.69    (2)  all_58_6 = e3
% 240.08/46.69    (3)  op(e1, e2) = all_52_6
% 240.08/46.69    (4)  op(e3, e0) = all_4_0
% 240.08/46.69    (5)  op(e1, e0) = all_52_14
% 240.08/46.69    (6)   ~ (e3 = e1)
% 240.08/46.69    (7)  all_54_11 = all_52_14
% 240.08/46.69    (8)  op(e0, e2) = e3
% 240.08/46.69    (9)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.08/46.69    (10)   ~ (all_52_14 = e2)
% 240.08/46.69    (11)   ~ (e3 = e2)
% 240.08/46.69    (12)  all_56_31 = e2
% 240.08/46.69    (13)   ~ (all_4_0 = e2)
% 240.08/46.69    (14)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.08/46.69            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.08/46.69            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.08/46.69            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.08/46.69            op(e0, all_56_31) = e0)
% 240.08/46.69    (15)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.08/46.69    (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.08/46.69          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.08/46.69    (17)  op(e2, e3) = all_52_1
% 240.08/46.69    (18)   ~ (all_52_14 = e3)
% 240.08/46.69    (19)   ~ (all_52_13 = e2)
% 240.08/46.69    (20)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 240.08/46.69            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 240.08/46.69              e2) = all_40_1 & $i(all_40_1))
% 240.08/46.69    (21)  op(e1, e1) = e2
% 240.08/46.69    (22)  all_54_7 = all_52_13
% 240.08/46.69    (23)   ~ (all_52_13 = all_52_14)
% 240.08/46.69    (24)   ~ (all_4_0 = e1)
% 240.08/46.70    (25)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 240.08/46.70    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.70    (27)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 240.08/46.70            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 240.08/46.70              e2) = all_36_1 & $i(all_36_1))
% 240.08/46.70    (28)   ~ (all_52_13 = all_4_0)
% 240.08/46.70    (29)  all_54_3 = all_4_0
% 240.08/46.70    (30)   ~ (all_52_14 = all_4_0)
% 240.08/46.70    (31)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.08/46.70          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.08/46.70    (32)  op(e2, e0) = all_52_13
% 240.08/46.70    (33)   ~ (all_4_0 = e3)
% 240.08/46.70    (34)   ~ (all_52_1 = e2)
% 240.08/46.70    (35)   ~ (e2 = e1)
% 240.08/46.70  
% 240.08/46.70  Begin of proof
% 240.08/46.70  | 
% 240.08/46.70  | BETA: splitting (25) gives:
% 240.08/46.70  | 
% 240.08/46.70  | Case 1:
% 240.08/46.70  | | 
% 240.08/46.70  | |   (36)  all_54_3 = e2
% 240.08/46.70  | | 
% 240.08/46.70  | | REF_CLOSE: (13), (29), (36) are inconsistent by sub-proof #203.
% 240.08/46.70  | | 
% 240.08/46.70  | Case 2:
% 240.08/46.70  | | 
% 240.08/46.70  | |   (37)   ~ (all_54_3 = e2)
% 240.08/46.70  | |   (38)  all_54_3 = e1 | all_54_3 = e0
% 240.08/46.70  | | 
% 240.08/46.70  | | BETA: splitting (38) gives:
% 240.08/46.70  | | 
% 240.08/46.70  | | Case 1:
% 240.08/46.70  | | | 
% 240.08/46.70  | | |   (39)  all_54_3 = e1
% 240.08/46.70  | | | 
% 240.08/46.70  | | | REF_CLOSE: (24), (29), (39) are inconsistent by sub-proof #202.
% 240.08/46.70  | | | 
% 240.08/46.70  | | Case 2:
% 240.08/46.70  | | | 
% 240.08/46.70  | | |   (40)  all_54_3 = e0
% 240.08/46.70  | | | 
% 240.08/46.70  | | | COMBINE_EQS: (29), (40) imply:
% 240.08/46.70  | | |   (41)  all_4_0 = e0
% 240.08/46.70  | | | 
% 240.08/46.70  | | | SIMP: (41) implies:
% 240.08/46.70  | | |   (42)  all_4_0 = e0
% 240.08/46.70  | | | 
% 240.08/46.70  | | | REDUCE: (28), (42) imply:
% 240.08/46.70  | | |   (43)   ~ (all_52_13 = e0)
% 240.08/46.70  | | | 
% 240.08/46.70  | | | REDUCE: (30), (42) imply:
% 240.08/46.70  | | |   (44)   ~ (all_52_14 = e0)
% 240.08/46.70  | | | 
% 240.08/46.70  | | | REDUCE: (33), (42) imply:
% 240.08/46.70  | | |   (45)   ~ (e3 = e0)
% 240.08/46.70  | | | 
% 240.08/46.70  | | | SIMP: (45) implies:
% 240.08/46.70  | | |   (46)   ~ (e3 = e0)
% 240.08/46.70  | | | 
% 240.08/46.70  | | | REDUCE: (13), (42) imply:
% 240.08/46.70  | | |   (47)   ~ (e2 = e0)
% 240.08/46.70  | | | 
% 240.08/46.70  | | | SIMP: (47) implies:
% 240.08/46.70  | | |   (48)   ~ (e2 = e0)
% 240.08/46.70  | | | 
% 240.08/46.70  | | | REDUCE: (24), (42) imply:
% 240.08/46.70  | | |   (49)   ~ (e1 = e0)
% 240.08/46.70  | | | 
% 240.08/46.70  | | | SIMP: (49) implies:
% 240.08/46.70  | | |   (50)   ~ (e1 = e0)
% 240.08/46.70  | | | 
% 240.08/46.70  | | | REDUCE: (4), (42) imply:
% 240.08/46.70  | | |   (51)  op(e3, e0) = e0
% 240.08/46.70  | | | 
% 240.08/46.70  | | | BETA: splitting (9) gives:
% 240.08/46.70  | | | 
% 240.08/46.70  | | | Case 1:
% 240.08/46.70  | | | | 
% 240.08/46.70  | | | |   (52)  all_54_11 = e3
% 240.08/46.70  | | | | 
% 240.08/46.70  | | | | COMBINE_EQS: (7), (52) imply:
% 240.08/46.70  | | | |   (53)  all_52_14 = e3
% 240.08/46.70  | | | | 
% 240.08/46.70  | | | | REDUCE: (18), (53) imply:
% 240.08/46.70  | | | |   (54)  $false
% 240.08/46.70  | | | | 
% 240.08/46.70  | | | | CLOSE: (54) is inconsistent.
% 240.08/46.70  | | | | 
% 240.08/46.70  | | | Case 2:
% 240.08/46.70  | | | | 
% 240.08/46.70  | | | |   (55)   ~ (all_54_11 = e3)
% 240.08/46.70  | | | |   (56)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.08/46.70  | | | | 
% 240.08/46.70  | | | | BETA: splitting (31) gives:
% 240.08/46.70  | | | | 
% 240.08/46.70  | | | | Case 1:
% 240.08/46.70  | | | | | 
% 240.08/46.70  | | | | |   (57)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1,
% 240.08/46.70  | | | | |             e2) = e0)
% 240.08/46.70  | | | | | 
% 240.08/46.70  | | | | | BETA: splitting (57) gives:
% 240.08/46.70  | | | | | 
% 240.08/46.70  | | | | | Case 1:
% 240.08/46.70  | | | | | | 
% 240.08/46.70  | | | | | |   (58)  all_58_6 = e0 & op(e1, e3) = e0
% 240.08/46.70  | | | | | | 
% 240.08/46.70  | | | | | | ALPHA: (58) implies:
% 240.08/46.70  | | | | | |   (59)  all_58_6 = e0
% 240.08/46.70  | | | | | | 
% 240.08/46.70  | | | | | | REF_CLOSE: (2), (46), (59) are inconsistent by sub-proof #2222.
% 240.08/46.70  | | | | | | 
% 240.08/46.70  | | | | | Case 2:
% 240.08/46.70  | | | | | | 
% 240.08/46.70  | | | | | |   (60)  all_58_7 = e0 & op(e1, e2) = e0
% 240.08/46.70  | | | | | | 
% 240.08/46.70  | | | | | | ALPHA: (60) implies:
% 240.08/46.70  | | | | | |   (61)  all_58_7 = e0
% 240.08/46.70  | | | | | |   (62)  op(e1, e2) = e0
% 240.08/46.70  | | | | | | 
% 240.08/46.70  | | | | | | BETA: splitting (1) gives:
% 240.08/46.70  | | | | | | 
% 240.08/46.70  | | | | | | Case 1:
% 240.08/46.70  | | | | | | | 
% 240.08/46.70  | | | | | | |   (63)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 240.08/46.70  | | | | | | |           op(e1, e2) = e1)
% 240.08/46.70  | | | | | | | 
% 240.08/46.70  | | | | | | | BETA: splitting (63) gives:
% 240.08/46.70  | | | | | | | 
% 240.08/46.70  | | | | | | | Case 1:
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | |   (64)  all_58_6 = e1 & op(e1, e3) = e1
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | | ALPHA: (64) implies:
% 240.08/46.70  | | | | | | | |   (65)  op(e1, e3) = e1
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | | REF_CLOSE: (5), (6), (11), (16), (18), (21), (26), (46), (61),
% 240.08/46.70  | | | | | | | |            (65) are inconsistent by sub-proof #2147.
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | Case 2:
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | |   (66)  all_58_7 = e1 & op(e1, e2) = e1
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | | ALPHA: (66) implies:
% 240.08/46.70  | | | | | | | |   (67)  op(e1, e2) = e1
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | | REF_CLOSE: (3), (26), (50), (62), (67) are inconsistent by
% 240.08/46.70  | | | | | | | |            sub-proof #2136.
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | End of split
% 240.08/46.70  | | | | | | | 
% 240.08/46.70  | | | | | | Case 2:
% 240.08/46.70  | | | | | | | 
% 240.08/46.70  | | | | | | |   (68)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 240.08/46.70  | | | | | | |           op(e1, e0) = e1)
% 240.08/46.70  | | | | | | | 
% 240.08/46.70  | | | | | | | BETA: splitting (68) gives:
% 240.08/46.70  | | | | | | | 
% 240.08/46.70  | | | | | | | Case 1:
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | |   (69)  all_58_8 = e1 & op(e1, e1) = e1
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | | ALPHA: (69) implies:
% 240.08/46.70  | | | | | | | |   (70)  op(e1, e1) = e1
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | | REF_CLOSE: (21), (26), (35), (70) are inconsistent by sub-proof
% 240.08/46.70  | | | | | | | |            #2159.
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | Case 2:
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | |   (71)  all_58_11 = e1 & op(e1, e0) = e1
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | | ALPHA: (71) implies:
% 240.08/46.70  | | | | | | | |   (72)  op(e1, e0) = e1
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | | BETA: splitting (15) gives:
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | | Case 1:
% 240.08/46.70  | | | | | | | | | 
% 240.08/46.70  | | | | | | | | |   (73)  all_54_7 = e3
% 240.08/46.70  | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | COMBINE_EQS: (22), (73) imply:
% 240.08/46.70  | | | | | | | | |   (74)  all_52_13 = e3
% 240.08/46.70  | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | SIMP: (74) implies:
% 240.08/46.70  | | | | | | | | |   (75)  all_52_13 = e3
% 240.08/46.70  | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | REDUCE: (32), (75) imply:
% 240.08/46.70  | | | | | | | | |   (76)  op(e2, e0) = e3
% 240.08/46.70  | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | BETA: splitting (14) gives:
% 240.08/46.70  | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | Case 1:
% 240.08/46.70  | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | |   (77)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.08/46.70  | | | | | | | | | |             e0) = all_56_25 & $i(all_56_25)) | (all_56_26 =
% 240.08/46.70  | | | | | | | | | |           e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 240.08/46.70  | | | | | | | | | |           all_56_27 & $i(all_56_27))
% 240.08/46.70  | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | BETA: splitting (77) gives:
% 240.08/46.70  | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | Case 1:
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | |   (78)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.08/46.70  | | | | | | | | | | |           e0) = all_56_25 & $i(all_56_25)
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | ALPHA: (78) implies:
% 240.08/46.70  | | | | | | | | | | |   (79)  op(e3, e0) = all_56_25
% 240.08/46.70  | | | | | | | | | | |   (80)  op(e3, all_56_25) = e3
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | REF_CLOSE: (26), (46), (51), (79), (80) are inconsistent by
% 240.08/46.70  | | | | | | | | | | |            sub-proof #1926.
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | Case 2:
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | |   (81)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 240.08/46.70  | | | | | | | | | | |           e0) = all_56_27 & $i(all_56_27)
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | ALPHA: (81) implies:
% 240.08/46.70  | | | | | | | | | | |   (82)  op(e2, e0) = all_56_27
% 240.08/46.70  | | | | | | | | | | |   (83)  op(e2, all_56_27) = e2
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | BETA: splitting (27) gives:
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | Case 1:
% 240.08/46.70  | | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | | GROUND_INST: instantiating (26) with e3, all_56_27, e0, e2,
% 240.08/46.70  | | | | | | | | | | | |              simplifying with (76), (82) gives:
% 240.08/46.70  | | | | | | | | | | | |   (84)  all_56_27 = e3
% 240.08/46.70  | | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | | REDUCE: (83), (84) imply:
% 240.08/46.70  | | | | | | | | | | | |   (85)  op(e2, e3) = e2
% 240.08/46.70  | | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | | REF_CLOSE: (17), (26), (34), (85) are inconsistent by
% 240.08/46.70  | | | | | | | | | | | |            sub-proof #2336.
% 240.08/46.70  | | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | Case 2:
% 240.08/46.70  | | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | |   (86)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 240.08/46.70  | | | | | | | | | | | |         $i(all_36_1)
% 240.08/46.70  | | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | | ALPHA: (86) implies:
% 240.08/46.70  | | | | | | | | | | | |   (87)   ~ (all_36_1 = e0)
% 240.08/46.70  | | | | | | | | | | | |   (88)  op(e1, e2) = all_36_1
% 240.08/46.70  | | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | | REF_CLOSE: (20), (26), (62), (87), (88) are inconsistent by
% 240.08/46.70  | | | | | | | | | | | |            sub-proof #782.
% 240.08/46.70  | | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | End of split
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | End of split
% 240.08/46.70  | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | Case 2:
% 240.08/46.70  | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | |   (89)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.08/46.70  | | | | | | | | | |             e0) = all_56_29 & $i(all_56_29)) | (all_56_30 =
% 240.08/46.70  | | | | | | | | | |           e0 & op(e0, all_56_31) = e0)
% 240.08/46.70  | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | BETA: splitting (89) gives:
% 240.08/46.70  | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | Case 1:
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | |   (90)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.08/46.70  | | | | | | | | | | |           e0) = all_56_29 & $i(all_56_29)
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | ALPHA: (90) implies:
% 240.08/46.70  | | | | | | | | | | |   (91)  op(e1, e0) = all_56_29
% 240.08/46.70  | | | | | | | | | | |   (92)  op(e1, all_56_29) = e1
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | REF_CLOSE: (20), (21), (26), (27), (35), (62), (72), (91),
% 240.08/46.70  | | | | | | | | | | |            (92) are inconsistent by sub-proof #201.
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | Case 2:
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | |   (93)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | ALPHA: (93) implies:
% 240.08/46.70  | | | | | | | | | | |   (94)  op(e0, all_56_31) = e0
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | REDUCE: (12), (94) imply:
% 240.08/46.70  | | | | | | | | | | |   (95)  op(e0, e2) = e0
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | | REF_CLOSE: (8), (26), (46), (95) are inconsistent by
% 240.08/46.70  | | | | | | | | | | |            sub-proof #1961.
% 240.08/46.70  | | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | | End of split
% 240.08/46.70  | | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | End of split
% 240.08/46.70  | | | | | | | | | 
% 240.08/46.70  | | | | | | | | Case 2:
% 240.08/46.70  | | | | | | | | | 
% 240.08/46.70  | | | | | | | | |   (96)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.08/46.70  | | | | | | | | | 
% 240.08/46.70  | | | | | | | | | REF_CLOSE: (7), (10), (19), (22), (23), (43), (44), (56), (96)
% 240.08/46.70  | | | | | | | | |            are inconsistent by sub-proof #341.
% 240.08/46.70  | | | | | | | | | 
% 240.08/46.70  | | | | | | | | End of split
% 240.08/46.70  | | | | | | | | 
% 240.08/46.70  | | | | | | | End of split
% 240.08/46.70  | | | | | | | 
% 240.08/46.70  | | | | | | End of split
% 240.08/46.70  | | | | | | 
% 240.08/46.70  | | | | | End of split
% 240.08/46.70  | | | | | 
% 240.08/46.70  | | | | Case 2:
% 240.08/46.70  | | | | | 
% 240.08/46.70  | | | | |   (97)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1,
% 240.08/46.70  | | | | |             e0) = e0)
% 240.08/46.70  | | | | | 
% 240.08/46.70  | | | | | REF_CLOSE: (5), (21), (26), (44), (48), (97) are inconsistent by
% 240.08/46.70  | | | | |            sub-proof #1851.
% 240.08/46.70  | | | | | 
% 240.08/46.70  | | | | End of split
% 240.08/46.70  | | | | 
% 240.08/46.70  | | | End of split
% 240.08/46.70  | | | 
% 240.08/46.70  | | End of split
% 240.08/46.70  | | 
% 240.08/46.70  | End of split
% 240.08/46.70  | 
% 240.08/46.70  End of proof
% 240.08/46.70  
% 240.08/46.70  Sub-proof #201 shows that the following formulas are inconsistent:
% 240.08/46.70  ----------------------------------------------------------------
% 240.08/46.70    (1)  op(e1, all_56_29) = e1
% 240.08/46.70    (2)  op(e1, e0) = e1
% 240.08/46.70    (3)  op(e1, e2) = e0
% 240.08/46.70    (4)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) = all_40_1
% 240.08/46.70           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2) =
% 240.08/46.70           all_40_1 & $i(all_40_1))
% 240.08/46.70    (5)  op(e1, e1) = e2
% 240.08/46.70    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.70    (7)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) = all_36_1
% 240.08/46.70           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2) =
% 240.08/46.70           all_36_1 & $i(all_36_1))
% 240.08/46.70    (8)  op(e1, e0) = all_56_29
% 240.08/46.70    (9)   ~ (e2 = e1)
% 240.08/46.70  
% 240.08/46.70  Begin of proof
% 240.08/46.70  | 
% 240.08/46.70  | BETA: splitting (7) gives:
% 240.08/46.70  | 
% 240.08/46.70  | Case 1:
% 240.08/46.70  | | 
% 240.08/46.70  | | 
% 240.08/46.70  | | GROUND_INST: instantiating (6) with e1, all_56_29, e0, e1, simplifying with
% 240.08/46.70  | |              (2), (8) gives:
% 240.08/46.70  | |   (10)  all_56_29 = e1
% 240.08/46.70  | | 
% 240.08/46.70  | | REDUCE: (1), (10) imply:
% 240.08/46.70  | |   (11)  op(e1, e1) = e1
% 240.08/46.70  | | 
% 240.08/46.70  | | REF_CLOSE: (5), (6), (9), (11) are inconsistent by sub-proof #2159.
% 240.08/46.70  | | 
% 240.08/46.70  | Case 2:
% 240.08/46.70  | | 
% 240.08/46.70  | |   (12)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1)
% 240.08/46.70  | | 
% 240.08/46.70  | | ALPHA: (12) implies:
% 240.08/46.70  | |   (13)   ~ (all_36_1 = e0)
% 240.08/46.70  | |   (14)  op(e1, e2) = all_36_1
% 240.08/46.70  | | 
% 240.08/46.70  | | REF_CLOSE: (3), (4), (6), (13), (14) are inconsistent by sub-proof #782.
% 240.08/46.70  | | 
% 240.08/46.70  | End of split
% 240.08/46.70  | 
% 240.08/46.70  End of proof
% 240.08/46.70  
% 240.08/46.70  Sub-proof #202 shows that the following formulas are inconsistent:
% 240.08/46.70  ----------------------------------------------------------------
% 240.08/46.70    (1)  all_54_3 = all_4_0
% 240.08/46.70    (2)  all_54_3 = e1
% 240.08/46.70    (3)   ~ (all_4_0 = e1)
% 240.08/46.70  
% 240.08/46.70  Begin of proof
% 240.08/46.70  | 
% 240.08/46.70  | COMBINE_EQS: (1), (2) imply:
% 240.08/46.70  |   (4)  all_4_0 = e1
% 240.08/46.70  | 
% 240.08/46.70  | SIMP: (4) implies:
% 240.08/46.70  |   (5)  all_4_0 = e1
% 240.08/46.70  | 
% 240.08/46.70  | REDUCE: (3), (5) imply:
% 240.08/46.70  |   (6)  $false
% 240.08/46.70  | 
% 240.08/46.70  | CLOSE: (6) is inconsistent.
% 240.08/46.70  | 
% 240.08/46.70  End of proof
% 240.08/46.70  
% 240.08/46.70  Sub-proof #203 shows that the following formulas are inconsistent:
% 240.08/46.70  ----------------------------------------------------------------
% 240.08/46.70    (1)  all_54_3 = all_4_0
% 240.08/46.70    (2)  all_54_3 = e2
% 240.08/46.70    (3)   ~ (all_4_0 = e2)
% 240.08/46.70  
% 240.08/46.70  Begin of proof
% 240.08/46.70  | 
% 240.08/46.70  | COMBINE_EQS: (1), (2) imply:
% 240.08/46.70  |   (4)  all_4_0 = e2
% 240.08/46.70  | 
% 240.08/46.70  | SIMP: (4) implies:
% 240.08/46.70  |   (5)  all_4_0 = e2
% 240.08/46.70  | 
% 240.08/46.70  | REDUCE: (3), (5) imply:
% 240.08/46.70  |   (6)  $false
% 240.08/46.70  | 
% 240.08/46.70  | CLOSE: (6) is inconsistent.
% 240.08/46.70  | 
% 240.08/46.70  End of proof
% 240.08/46.70  
% 240.08/46.70  Sub-proof #204 shows that the following formulas are inconsistent:
% 240.08/46.70  ----------------------------------------------------------------
% 240.08/46.70    (1)   ~ (e3 = e0)
% 240.08/46.70    (2)   ~ (e3 = e1)
% 240.08/46.70    (3)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.70             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.08/46.70           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.08/46.70             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.08/46.70           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 240.08/46.70           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.70           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.70    (4)  op(e1, e0) = e3
% 240.08/46.70    (5)  all_56_31 = e2
% 240.08/46.70    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.70  
% 240.08/46.70  Begin of proof
% 240.08/46.70  | 
% 240.08/46.70  | BETA: splitting (3) gives:
% 240.08/46.70  | 
% 240.08/46.70  | Case 1:
% 240.08/46.70  | | 
% 240.08/46.70  | |   (7)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.08/46.70  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 240.08/46.70  | |        & op(e0, e2) = e0
% 240.08/46.70  | | 
% 240.08/46.70  | | ALPHA: (7) implies:
% 240.08/46.70  | |   (8)   ~ (all_56_31 = e2)
% 240.08/46.70  | | 
% 240.08/46.70  | | REDUCE: (5), (8) imply:
% 240.08/46.70  | |   (9)  $false
% 240.08/46.70  | | 
% 240.08/46.70  | | CLOSE: (9) is inconsistent.
% 240.08/46.70  | | 
% 240.08/46.70  | Case 2:
% 240.08/46.70  | | 
% 240.08/46.70  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.70  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.70  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.08/46.70  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.08/46.70  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.70  | | 
% 240.08/46.70  | | BETA: splitting (10) gives:
% 240.08/46.70  | | 
% 240.08/46.70  | | Case 1:
% 240.08/46.70  | | | 
% 240.08/46.70  | | |   (11)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.70  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.70  | | |         op(e1, e0) = e1 & op(e0, e1) = e1
% 240.08/46.70  | | | 
% 240.08/46.70  | | | ALPHA: (11) implies:
% 240.08/46.70  | | |   (12)  op(e1, e0) = e1
% 240.08/46.70  | | | 
% 240.08/46.70  | | | REF_CLOSE: (2), (4), (6), (12) are inconsistent by sub-proof #1894.
% 240.08/46.70  | | | 
% 240.08/46.70  | | Case 2:
% 240.08/46.70  | | | 
% 240.08/46.70  | | |   (13)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.70  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.70  | | |         op(e1, e0) = e0 & op(e0, e1) = e0
% 240.08/46.70  | | | 
% 240.08/46.70  | | | ALPHA: (13) implies:
% 240.08/46.70  | | |   (14)  op(e1, e0) = e0
% 240.08/46.70  | | | 
% 240.08/46.70  | | | REF_CLOSE: (1), (4), (6), (14) are inconsistent by sub-proof #210.
% 240.08/46.70  | | | 
% 240.08/46.70  | | End of split
% 240.08/46.70  | | 
% 240.08/46.70  | End of split
% 240.08/46.70  | 
% 240.08/46.70  End of proof
% 240.08/46.70  
% 240.08/46.70  Sub-proof #205 shows that the following formulas are inconsistent:
% 240.08/46.70  ----------------------------------------------------------------
% 240.08/46.70    (1)   ~ (e2 = e0)
% 240.08/46.70    (2)  op(e2, e1) = all_52_9
% 240.08/46.70    (3)  all_56_31 = e2
% 240.08/46.70    (4)  op(e0, e2) = e0
% 240.08/46.70    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.71    (6)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.08/46.71             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.08/46.71           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.08/46.71             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 240.08/46.71           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 240.08/46.71           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.71           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.71    (7)   ~ (all_52_9 = e2)
% 240.08/46.71  
% 240.08/46.71  Begin of proof
% 240.08/46.71  | 
% 240.08/46.71  | BETA: splitting (6) gives:
% 240.08/46.71  | 
% 240.08/46.71  | Case 1:
% 240.08/46.71  | | 
% 240.08/46.71  | |   (8)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 240.08/46.71  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 240.08/46.71  | |        & op(e1, e2) = e2
% 240.08/46.71  | | 
% 240.08/46.71  | | ALPHA: (8) implies:
% 240.08/46.71  | |   (9)  op(e2, e1) = e2
% 240.08/46.71  | | 
% 240.08/46.71  | | REF_CLOSE: (2), (5), (7), (9) are inconsistent by sub-proof #2328.
% 240.08/46.71  | | 
% 240.08/46.71  | Case 2:
% 240.08/46.71  | | 
% 240.08/46.71  | |   (10)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.71  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.71  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.08/46.71  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.08/46.71  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.71  | | 
% 240.08/46.71  | | BETA: splitting (10) gives:
% 240.08/46.71  | | 
% 240.08/46.71  | | Case 1:
% 240.08/46.71  | | | 
% 240.08/46.71  | | |   (11)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.71  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.71  | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 240.08/46.71  | | | 
% 240.08/46.71  | | | ALPHA: (11) implies:
% 240.08/46.71  | | |   (12)   ~ (all_56_31 = e2)
% 240.08/46.71  | | | 
% 240.08/46.71  | | | REDUCE: (3), (12) imply:
% 240.08/46.71  | | |   (13)  $false
% 240.08/46.71  | | | 
% 240.08/46.71  | | | CLOSE: (13) is inconsistent.
% 240.08/46.71  | | | 
% 240.08/46.71  | | Case 2:
% 240.08/46.71  | | | 
% 240.08/46.71  | | |   (14)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.71  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.71  | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 240.08/46.71  | | | 
% 240.08/46.71  | | | ALPHA: (14) implies:
% 240.08/46.71  | | |   (15)  op(e0, e2) = e2
% 240.08/46.71  | | | 
% 240.08/46.71  | | | REF_CLOSE: (1), (4), (5), (15) are inconsistent by sub-proof #2132.
% 240.08/46.71  | | | 
% 240.08/46.71  | | End of split
% 240.08/46.71  | | 
% 240.08/46.71  | End of split
% 240.08/46.71  | 
% 240.08/46.71  End of proof
% 240.08/46.71  
% 240.08/46.71  Sub-proof #206 shows that the following formulas are inconsistent:
% 240.08/46.71  ----------------------------------------------------------------
% 240.08/46.71    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.08/46.71             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.08/46.71           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 240.08/46.71           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.71           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.71    (2)  op(e0, e3) = all_52_3
% 240.08/46.71    (3)  op(e0, e3) = e1
% 240.08/46.71    (4)   ~ (all_52_3 = e3)
% 240.08/46.71    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.71    (6)   ~ (e1 = e0)
% 240.08/46.71  
% 240.08/46.71  Begin of proof
% 240.08/46.71  | 
% 240.08/46.71  | BETA: splitting (1) gives:
% 240.08/46.71  | 
% 240.08/46.71  | Case 1:
% 240.08/46.71  | | 
% 240.08/46.71  | |   (7)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.08/46.71  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.08/46.71  | |        op(e0, e3) = e3
% 240.08/46.71  | | 
% 240.08/46.71  | | ALPHA: (7) implies:
% 240.08/46.71  | |   (8)  op(e0, e3) = e3
% 240.08/46.71  | | 
% 240.08/46.71  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2332.
% 240.08/46.71  | | 
% 240.08/46.71  | Case 2:
% 240.08/46.71  | | 
% 240.08/46.71  | |   (9)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.08/46.71  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 240.08/46.71  | |        op(e0, e3) = e0
% 240.08/46.71  | | 
% 240.08/46.71  | | ALPHA: (9) implies:
% 240.08/46.71  | |   (10)  op(e0, e3) = e0
% 240.08/46.71  | | 
% 240.08/46.71  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #207.
% 240.08/46.71  | | 
% 240.08/46.71  | End of split
% 240.08/46.71  | 
% 240.08/46.71  End of proof
% 240.08/46.71  
% 240.08/46.71  Sub-proof #207 shows that the following formulas are inconsistent:
% 240.08/46.71  ----------------------------------------------------------------
% 240.08/46.71    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.71    (2)  op(e0, e3) = e1
% 240.08/46.71    (3)  op(e0, e3) = e0
% 240.08/46.71    (4)   ~ (e1 = e0)
% 240.08/46.71  
% 240.08/46.71  Begin of proof
% 240.08/46.71  | 
% 240.08/46.71  | GROUND_INST: instantiating (1) with e1, e0, e3, e0, simplifying with (2), (3)
% 240.08/46.71  |              gives:
% 240.08/46.71  |   (5)  e1 = e0
% 240.08/46.71  | 
% 240.08/46.71  | REDUCE: (4), (5) imply:
% 240.08/46.71  |   (6)  $false
% 240.08/46.71  | 
% 240.08/46.71  | CLOSE: (6) is inconsistent.
% 240.08/46.71  | 
% 240.08/46.71  End of proof
% 240.08/46.71  
% 240.08/46.71  Sub-proof #208 shows that the following formulas are inconsistent:
% 240.08/46.71  ----------------------------------------------------------------
% 240.08/46.71    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.08/46.71           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.08/46.71             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.71           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.08/46.71             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.71           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.71           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.71    (2)   ~ (e3 = e2)
% 240.08/46.71    (3)  all_56_31 = e2
% 240.08/46.71    (4)   ~ (all_52_2 = e3)
% 240.08/46.71    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.71    (6)  op(e1, e3) = all_52_2
% 240.08/46.71    (7)  op(e3, e2) = e3
% 240.08/46.71  
% 240.08/46.71  Begin of proof
% 240.08/46.71  | 
% 240.08/46.71  | BETA: splitting (1) gives:
% 240.08/46.71  | 
% 240.08/46.71  | Case 1:
% 240.08/46.71  | | 
% 240.08/46.71  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.71  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.08/46.71  | |        op(e2, e3) = e3
% 240.08/46.71  | | 
% 240.08/46.71  | | ALPHA: (8) implies:
% 240.08/46.71  | |   (9)   ~ (all_56_31 = e2)
% 240.08/46.71  | | 
% 240.08/46.71  | | REDUCE: (3), (9) imply:
% 240.08/46.71  | |   (10)  $false
% 240.08/46.71  | | 
% 240.08/46.71  | | CLOSE: (10) is inconsistent.
% 240.08/46.71  | | 
% 240.08/46.71  | Case 2:
% 240.08/46.71  | | 
% 240.08/46.71  | |   (11)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.08/46.71  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.08/46.71  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.71  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.71  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.71  | | 
% 240.08/46.71  | | REF_CLOSE: (2), (4), (5), (6), (7), (11) are inconsistent by sub-proof
% 240.08/46.71  | |            #1685.
% 240.08/46.71  | | 
% 240.08/46.71  | End of split
% 240.08/46.71  | 
% 240.08/46.71  End of proof
% 240.08/46.71  
% 240.08/46.71  Sub-proof #209 shows that the following formulas are inconsistent:
% 240.08/46.71  ----------------------------------------------------------------
% 240.08/46.71    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.08/46.71    (2)   ~ (e3 = e0)
% 240.08/46.71    (3)   ~ (e2 = e0)
% 240.08/46.71    (4)  op(e1, e0) = e3
% 240.08/46.71    (5)  op(e1, e1) = e2
% 240.08/46.71    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.71  
% 240.08/46.71  Begin of proof
% 240.08/46.71  | 
% 240.08/46.71  | BETA: splitting (1) gives:
% 240.08/46.71  | 
% 240.08/46.71  | Case 1:
% 240.08/46.71  | | 
% 240.08/46.71  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 240.08/46.71  | | 
% 240.08/46.71  | | ALPHA: (7) implies:
% 240.08/46.71  | |   (8)  op(e1, e1) = e0
% 240.08/46.71  | | 
% 240.08/46.71  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2211.
% 240.08/46.71  | | 
% 240.08/46.71  | Case 2:
% 240.08/46.71  | | 
% 240.08/46.71  | |   (9)  all_58_11 = e0 & op(e1, e0) = e0
% 240.08/46.71  | | 
% 240.08/46.71  | | ALPHA: (9) implies:
% 240.08/46.71  | |   (10)  op(e1, e0) = e0
% 240.08/46.71  | | 
% 240.08/46.71  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #210.
% 240.08/46.71  | | 
% 240.08/46.71  | End of split
% 240.08/46.71  | 
% 240.08/46.71  End of proof
% 240.08/46.71  
% 240.08/46.71  Sub-proof #210 shows that the following formulas are inconsistent:
% 240.08/46.71  ----------------------------------------------------------------
% 240.08/46.71    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.71    (2)  op(e1, e0) = e3
% 240.08/46.71    (3)  op(e1, e0) = e0
% 240.08/46.71    (4)   ~ (e3 = e0)
% 240.08/46.71  
% 240.08/46.71  Begin of proof
% 240.08/46.71  | 
% 240.08/46.71  | GROUND_INST: instantiating (1) with e3, e0, e0, e1, simplifying with (2), (3)
% 240.08/46.71  |              gives:
% 240.08/46.71  |   (5)  e3 = e0
% 240.08/46.71  | 
% 240.08/46.71  | REDUCE: (4), (5) imply:
% 240.08/46.71  |   (6)  $false
% 240.08/46.71  | 
% 240.08/46.71  | CLOSE: (6) is inconsistent.
% 240.08/46.71  | 
% 240.08/46.71  End of proof
% 240.08/46.71  
% 240.08/46.71  Sub-proof #211 shows that the following formulas are inconsistent:
% 240.08/46.71  ----------------------------------------------------------------
% 240.08/46.71    (1)  op(e0, e2) = e3
% 240.08/46.71    (2)  op(e0, e2) = all_4_1
% 240.08/46.71    (3)   ~ (all_4_1 = e3)
% 240.08/46.71    (4)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) = all_44_1
% 240.08/46.71           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2) =
% 240.08/46.71           all_44_1 & $i(all_44_1))
% 240.08/46.71    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.71  
% 240.08/46.71  Begin of proof
% 240.08/46.71  | 
% 240.08/46.71  | BETA: splitting (4) gives:
% 240.08/46.71  | 
% 240.08/46.71  | Case 1:
% 240.08/46.71  | | 
% 240.08/46.71  | |   (6)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 240.08/46.71  | |        all_44_1 & $i(all_44_0) & $i(all_44_1)
% 240.08/46.71  | | 
% 240.08/46.71  | | ALPHA: (6) implies:
% 240.08/46.71  | |   (7)  op(e0, e2) = all_44_1
% 240.08/46.71  | | 
% 240.08/46.71  | | REF_CLOSE: (1), (2), (3), (5), (7) are inconsistent by sub-proof #227.
% 240.08/46.71  | | 
% 240.08/46.71  | Case 2:
% 240.08/46.71  | | 
% 240.08/46.71  | |   (8)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 & $i(all_44_1)
% 240.08/46.71  | | 
% 240.08/46.71  | | ALPHA: (8) implies:
% 240.08/46.71  | |   (9)  op(e0, e2) = all_44_1
% 240.08/46.71  | | 
% 240.08/46.71  | | REF_CLOSE: (1), (2), (3), (5), (9) are inconsistent by sub-proof #227.
% 240.08/46.71  | | 
% 240.08/46.71  | End of split
% 240.08/46.71  | 
% 240.08/46.71  End of proof
% 240.08/46.71  
% 240.08/46.71  Sub-proof #212 shows that the following formulas are inconsistent:
% 240.08/46.71  ----------------------------------------------------------------
% 240.08/46.71    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 240.08/46.71             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 240.08/46.71           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 240.08/46.71         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 240.08/46.71           $i(all_56_7))
% 240.08/46.71    (2)   ~ (e3 = e0)
% 240.08/46.71    (3)   ~ (e2 = e0)
% 240.08/46.71    (4)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.08/46.71           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.08/46.71             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.71           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.08/46.71             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.71           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.71           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.08/46.71           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.08/46.71           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.08/46.71           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.71           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.08/46.71             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.08/46.71           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.71           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 240.08/46.71           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.08/46.71           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.08/46.71           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.71           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.08/46.71             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.08/46.71           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.71           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 240.08/46.71           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.08/46.71           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.08/46.71           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.71           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.08/46.71             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.08/46.71           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.71           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.71    (5)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 240.08/46.71    (6)  op(e2, e3) = e3
% 240.08/46.71    (7)  op(e0, e3) = all_52_3
% 240.08/46.71    (8)   ~ (e3 = e1)
% 240.08/46.71    (9)  op(e0, e2) = e3
% 240.08/46.71    (10)   ~ (all_52_2 = all_52_3)
% 240.08/46.71    (11)  op(e0, e2) = all_4_1
% 240.08/46.71    (12)  op(e3, e1) = all_52_8
% 240.08/46.71    (13)  op(e2, e1) = all_52_9
% 240.08/46.71    (14)  op(e1, e0) = e3
% 240.08/46.71    (15)  all_56_31 = e2
% 240.08/46.71    (16)   ~ (all_52_3 = e3)
% 240.08/46.71    (17)   ~ (all_52_2 = e3)
% 240.08/46.71    (18)  op(e1, e1) = e2
% 240.08/46.71    (19)  all_56_1 = e2
% 240.08/46.71    (20)  op(e3, e2) = all_52_4
% 240.08/46.71    (21)   ~ (all_52_2 = e2)
% 240.08/46.71    (22)   ~ (all_52_4 = e2)
% 240.08/46.71    (23)  all_54_8 = all_52_2
% 240.08/46.71    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.71    (25)  op(e1, e3) = all_52_2
% 240.08/46.71    (26)  op(e3, e1) = e3
% 240.08/46.71    (27)  op(e0, e2) = all_44_1
% 240.08/46.71    (28)   ~ (all_52_8 = e2)
% 240.08/46.71    (29)  op(e0, e0) = e2
% 240.08/46.71    (30)   ~ (all_52_4 = all_52_8)
% 240.08/46.71    (31)   ~ (all_52_9 = e2)
% 240.08/46.71  
% 240.08/46.71  Begin of proof
% 240.08/46.71  | 
% 240.08/46.71  | GROUND_INST: instantiating (24) with all_4_1, all_44_1, e2, e0, simplifying
% 240.08/46.71  |              with (11), (27) gives:
% 240.08/46.71  |   (32)  all_44_1 = all_4_1
% 240.08/46.71  | 
% 240.08/46.71  | GROUND_INST: instantiating (24) with e3, all_44_1, e2, e0, simplifying with
% 240.08/46.71  |              (9), (27) gives:
% 240.08/46.71  |   (33)  all_44_1 = e3
% 240.08/46.71  | 
% 240.08/46.71  | GROUND_INST: instantiating (24) with all_52_8, e3, e1, e3, simplifying with
% 240.08/46.71  |              (12), (26) gives:
% 240.08/46.71  |   (34)  all_52_8 = e3
% 240.08/46.71  | 
% 240.08/46.71  | COMBINE_EQS: (32), (33) imply:
% 240.08/46.71  |   (35)  all_4_1 = e3
% 240.08/46.71  | 
% 240.08/46.71  | REDUCE: (30), (34) imply:
% 240.08/46.71  |   (36)   ~ (all_52_4 = e3)
% 240.08/46.71  | 
% 240.08/46.71  | REDUCE: (28), (34) imply:
% 240.08/46.71  |   (37)   ~ (e3 = e2)
% 240.08/46.71  | 
% 240.08/46.71  | BETA: splitting (4) gives:
% 240.08/46.71  | 
% 240.08/46.71  | Case 1:
% 240.08/46.71  | | 
% 240.08/46.71  | |   (38)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.08/46.71  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 240.08/46.71  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 240.08/46.71  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.71  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 240.08/46.71  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 240.08/46.71  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.08/46.71  | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 240.08/46.71  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.71  | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 240.08/46.71  | |           = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &
% 240.08/46.71  | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.08/46.71  | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 240.08/46.71  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.71  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.71  | | 
% 240.08/46.71  | | BETA: splitting (38) gives:
% 240.08/46.71  | | 
% 240.08/46.71  | | Case 1:
% 240.08/46.71  | | | 
% 240.08/46.72  | | |   (39)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.72  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.72  | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.08/46.72  | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.08/46.72  | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 240.08/46.72  | | |         | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.72  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.72  | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.72  | | | 
% 240.08/46.72  | | | BETA: splitting (39) gives:
% 240.08/46.72  | | | 
% 240.08/46.72  | | | Case 1:
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | |   (40)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.72  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.72  | | | |         op(e3, e2) = e3 & op(e2, e3) = e3
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | ALPHA: (40) implies:
% 240.08/46.72  | | | |   (41)  op(e3, e2) = e3
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | REF_CLOSE: (20), (24), (36), (41) are inconsistent by sub-proof #2192.
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | Case 2:
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | |   (42)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.72  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.72  | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 240.08/46.72  | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.08/46.72  | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.08/46.72  | | | |           op(e1, e3) = e3)
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | REF_CLOSE: (17), (20), (22), (24), (25), (42) are inconsistent by
% 240.08/46.72  | | | |            sub-proof #253.
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | End of split
% 240.08/46.72  | | | 
% 240.08/46.72  | | Case 2:
% 240.08/46.72  | | | 
% 240.08/46.72  | | |   (43)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.72  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.72  | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 240.08/46.72  | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 240.08/46.72  | | |             = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 240.08/46.72  | | |           e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.72  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.72  | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.72  | | | 
% 240.08/46.72  | | | BETA: splitting (43) gives:
% 240.08/46.72  | | | 
% 240.08/46.72  | | | Case 1:
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | |   (44)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.72  | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.72  | | | |         op(e3, e1) = e1 & op(e1, e3) = e1
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | ALPHA: (44) implies:
% 240.08/46.72  | | | |   (45)  op(e3, e1) = e1
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | REF_CLOSE: (8), (24), (26), (45) are inconsistent by sub-proof #1823.
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | Case 2:
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | |   (46)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.72  | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.72  | | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 240.08/46.72  | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.08/46.72  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 240.08/46.72  | | | |           op(e0, e3) = e0)
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | BETA: splitting (46) gives:
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | Case 1:
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | |   (47)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.72  | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.72  | | | | |         op(e3, e0) = e3 & op(e0, e3) = e3
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | | ALPHA: (47) implies:
% 240.08/46.72  | | | | |   (48)  op(e0, e3) = e3
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | | REF_CLOSE: (7), (16), (24), (48) are inconsistent by sub-proof #2332.
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | Case 2:
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | |   (49)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.72  | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.72  | | | | |         op(e3, e0) = e0 & op(e0, e3) = e0
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | | ALPHA: (49) implies:
% 240.08/46.72  | | | | |   (50)  all_56_7 = e0
% 240.08/46.72  | | | | |   (51)   ~ (all_56_31 = e3)
% 240.08/46.72  | | | | |   (52)  op(e0, e3) = e0
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | | REDUCE: (15), (51) imply:
% 240.08/46.72  | | | | |   (53)   ~ (e3 = e2)
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | | BETA: splitting (1) gives:
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | | Case 1:
% 240.08/46.72  | | | | | | 
% 240.08/46.72  | | | | | |   (54)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 240.08/46.72  | | | | | |           op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 240.08/46.72  | | | | | |           $i(all_56_3))
% 240.08/46.72  | | | | | | 
% 240.08/46.72  | | | | | | BETA: splitting (54) gives:
% 240.08/46.72  | | | | | | 
% 240.08/46.72  | | | | | | Case 1:
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | |   (55)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | ALPHA: (55) implies:
% 240.08/46.72  | | | | | | |   (56)  op(e3, all_56_1) = e3
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | REDUCE: (19), (56) imply:
% 240.08/46.72  | | | | | | |   (57)  op(e3, e2) = e3
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | REF_CLOSE: (20), (24), (36), (57) are inconsistent by sub-proof
% 240.08/46.72  | | | | | | |            #2192.
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | Case 2:
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | |   (58)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 240.08/46.72  | | | | | | |         all_56_3 & $i(all_56_3)
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | ALPHA: (58) implies:
% 240.08/46.72  | | | | | | |   (59)  op(e2, e3) = all_56_3
% 240.08/46.72  | | | | | | |   (60)  op(e2, all_56_3) = e2
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | REF_CLOSE: (6), (24), (37), (59), (60) are inconsistent by
% 240.08/46.72  | | | | | | |            sub-proof #2262.
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | End of split
% 240.08/46.72  | | | | | | 
% 240.08/46.72  | | | | | Case 2:
% 240.08/46.72  | | | | | | 
% 240.08/46.72  | | | | | |   (61)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 240.08/46.72  | | | | | |           all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 240.08/46.72  | | | | | |             all_56_7) = e0 & op(e0, e3) = all_56_7 & $i(all_56_7))
% 240.08/46.72  | | | | | | 
% 240.08/46.72  | | | | | | BETA: splitting (61) gives:
% 240.08/46.72  | | | | | | 
% 240.08/46.72  | | | | | | Case 1:
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | |   (62)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 240.08/46.72  | | | | | | |         all_56_5 & $i(all_56_5)
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | ALPHA: (62) implies:
% 240.08/46.72  | | | | | | |   (63)  op(e1, e3) = all_56_5
% 240.08/46.72  | | | | | | |   (64)  op(e1, all_56_5) = e1
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | GROUND_INST: instantiating (24) with all_52_3, e0, e3, e0,
% 240.08/46.72  | | | | | | |              simplifying with (7), (52) gives:
% 240.08/46.72  | | | | | | |   (65)  all_52_3 = e0
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | GROUND_INST: instantiating (24) with all_52_2, all_56_5, e3, e1,
% 240.08/46.72  | | | | | | |              simplifying with (25), (63) gives:
% 240.08/46.72  | | | | | | |   (66)  all_56_5 = all_52_2
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | REDUCE: (10), (65) imply:
% 240.08/46.72  | | | | | | |   (67)   ~ (all_52_2 = e0)
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | REDUCE: (64), (66) imply:
% 240.08/46.72  | | | | | | |   (68)  op(e1, all_52_2) = e1
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | BETA: splitting (5) gives:
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | Case 1:
% 240.08/46.72  | | | | | | | | 
% 240.08/46.72  | | | | | | | |   (69)  all_54_8 = e2
% 240.08/46.72  | | | | | | | | 
% 240.08/46.72  | | | | | | | | REF_CLOSE: (21), (23), (69) are inconsistent by sub-proof #2007.
% 240.08/46.72  | | | | | | | | 
% 240.08/46.72  | | | | | | | Case 2:
% 240.08/46.72  | | | | | | | | 
% 240.08/46.72  | | | | | | | |   (70)   ~ (all_54_8 = e2)
% 240.08/46.72  | | | | | | | |   (71)  all_54_8 = e1 | all_54_8 = e0
% 240.08/46.72  | | | | | | | | 
% 240.08/46.72  | | | | | | | | BETA: splitting (71) gives:
% 240.08/46.72  | | | | | | | | 
% 240.08/46.72  | | | | | | | | Case 1:
% 240.08/46.72  | | | | | | | | | 
% 240.08/46.72  | | | | | | | | |   (72)  all_54_8 = e1
% 240.08/46.72  | | | | | | | | | 
% 240.08/46.72  | | | | | | | | | COMBINE_EQS: (23), (72) imply:
% 240.08/46.72  | | | | | | | | |   (73)  all_52_2 = e1
% 240.08/46.72  | | | | | | | | | 
% 240.08/46.72  | | | | | | | | | SIMP: (73) implies:
% 240.08/46.72  | | | | | | | | |   (74)  all_52_2 = e1
% 240.08/46.72  | | | | | | | | | 
% 240.08/46.72  | | | | | | | | | REDUCE: (21), (74) imply:
% 240.08/46.72  | | | | | | | | |   (75)   ~ (e2 = e1)
% 240.08/46.72  | | | | | | | | | 
% 240.08/46.72  | | | | | | | | | SIMP: (75) implies:
% 240.08/46.72  | | | | | | | | |   (76)   ~ (e2 = e1)
% 240.08/46.72  | | | | | | | | | 
% 240.08/46.72  | | | | | | | | | REDUCE: (68), (74) imply:
% 240.08/46.72  | | | | | | | | |   (77)  op(e1, e1) = e1
% 240.08/46.72  | | | | | | | | | 
% 240.08/46.72  | | | | | | | | | REF_CLOSE: (18), (24), (76), (77) are inconsistent by
% 240.08/46.72  | | | | | | | | |            sub-proof #2159.
% 240.08/46.72  | | | | | | | | | 
% 240.08/46.72  | | | | | | | | Case 2:
% 240.08/46.72  | | | | | | | | | 
% 240.08/46.72  | | | | | | | | |   (78)  all_54_8 = e0
% 240.08/46.72  | | | | | | | | | 
% 240.08/46.72  | | | | | | | | | REF_CLOSE: (23), (67), (78) are inconsistent by sub-proof
% 240.08/46.72  | | | | | | | | |            #2006.
% 240.08/46.72  | | | | | | | | | 
% 240.08/46.72  | | | | | | | | End of split
% 240.08/46.72  | | | | | | | | 
% 240.08/46.72  | | | | | | | End of split
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | Case 2:
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | |   (79)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 240.08/46.72  | | | | | | |         all_56_7 & $i(all_56_7)
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | ALPHA: (79) implies:
% 240.08/46.72  | | | | | | |   (80)  op(e0, all_56_7) = e0
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | REDUCE: (50), (80) imply:
% 240.08/46.72  | | | | | | |   (81)  op(e0, e0) = e0
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | | REF_CLOSE: (3), (24), (29), (81) are inconsistent by sub-proof
% 240.08/46.72  | | | | | | |            #2301.
% 240.08/46.72  | | | | | | | 
% 240.08/46.72  | | | | | | End of split
% 240.08/46.72  | | | | | | 
% 240.08/46.72  | | | | | End of split
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | End of split
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | End of split
% 240.08/46.72  | | | 
% 240.08/46.72  | | End of split
% 240.08/46.72  | | 
% 240.08/46.72  | Case 2:
% 240.08/46.72  | | 
% 240.08/46.72  | |   (82)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.72  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.72  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.08/46.72  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.08/46.72  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 240.08/46.72  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.72  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.72  | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 240.08/46.72  | |           e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.08/46.72  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 240.08/46.72  | |         (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.72  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.72  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.08/46.72  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.08/46.72  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.72  | | 
% 240.08/46.72  | | BETA: splitting (82) gives:
% 240.08/46.72  | | 
% 240.08/46.72  | | Case 1:
% 240.08/46.72  | | | 
% 240.08/46.72  | | |   (83)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.72  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.72  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 240.08/46.72  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 240.08/46.72  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 240.08/46.72  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.72  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.72  | | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.72  | | | 
% 240.08/46.72  | | | BETA: splitting (83) gives:
% 240.08/46.72  | | | 
% 240.08/46.72  | | | Case 1:
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | |   (84)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.72  | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.72  | | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | ALPHA: (84) implies:
% 240.08/46.72  | | | |   (85)  op(e2, e1) = e2
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | REF_CLOSE: (13), (24), (31), (85) are inconsistent by sub-proof #2328.
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | Case 2:
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | |   (86)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.72  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.72  | | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 240.08/46.72  | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 240.08/46.72  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 &
% 240.08/46.72  | | | |           op(e0, e2) = e2)
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | BETA: splitting (86) gives:
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | Case 1:
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | |   (87)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.72  | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.72  | | | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | | ALPHA: (87) implies:
% 240.08/46.72  | | | | |   (88)   ~ (all_56_31 = e2)
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | | REDUCE: (15), (88) imply:
% 240.08/46.72  | | | | |   (89)  $false
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | | CLOSE: (89) is inconsistent.
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | Case 2:
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | |   (90)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.72  | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.72  | | | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | | ALPHA: (90) implies:
% 240.08/46.72  | | | | |   (91)  op(e0, e2) = e2
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | | REF_CLOSE: (9), (24), (37), (91) are inconsistent by sub-proof #2254.
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | End of split
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | End of split
% 240.08/46.72  | | | 
% 240.08/46.72  | | Case 2:
% 240.08/46.72  | | | 
% 240.08/46.72  | | |   (92)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.72  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.72  | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29
% 240.08/46.72  | | |           = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 240.08/46.72  | | |             = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 240.08/46.72  | | |           e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.72  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.72  | | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.72  | | | 
% 240.08/46.72  | | | BETA: splitting (92) gives:
% 240.08/46.72  | | | 
% 240.08/46.72  | | | Case 1:
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | |   (93)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.72  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.72  | | | |         op(e2, e0) = e0 & op(e0, e2) = e0
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | ALPHA: (93) implies:
% 240.08/46.72  | | | |   (94)  op(e0, e2) = e0
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | REF_CLOSE: (2), (9), (24), (94) are inconsistent by sub-proof #1961.
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | Case 2:
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | |   (95)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.72  | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.72  | | | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 240.08/46.72  | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.08/46.72  | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 &
% 240.08/46.72  | | | |           op(e0, e1) = e0)
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | BETA: splitting (95) gives:
% 240.08/46.72  | | | | 
% 240.08/46.72  | | | | Case 1:
% 240.08/46.72  | | | | | 
% 240.08/46.72  | | | | |   (96)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.72  | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.72  | | | | |         op(e1, e0) = e1 & op(e0, e1) = e1
% 240.08/46.73  | | | | | 
% 240.08/46.73  | | | | | ALPHA: (96) implies:
% 240.08/46.73  | | | | |   (97)  op(e1, e0) = e1
% 240.08/46.73  | | | | | 
% 240.08/46.73  | | | | | REF_CLOSE: (8), (14), (24), (97) are inconsistent by sub-proof #1894.
% 240.08/46.73  | | | | | 
% 240.08/46.73  | | | | Case 2:
% 240.08/46.73  | | | | | 
% 240.08/46.73  | | | | |   (98)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.73  | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.73  | | | | |         op(e1, e0) = e0 & op(e0, e1) = e0
% 240.08/46.73  | | | | | 
% 240.08/46.73  | | | | | ALPHA: (98) implies:
% 240.08/46.73  | | | | |   (99)  op(e1, e0) = e0
% 240.08/46.73  | | | | | 
% 240.08/46.73  | | | | | GROUND_INST: instantiating (24) with e3, e0, e0, e1, simplifying with
% 240.08/46.73  | | | | |              (14), (99) gives:
% 240.08/46.73  | | | | |   (100)  e3 = e0
% 240.08/46.73  | | | | | 
% 240.08/46.73  | | | | | REDUCE: (2), (100) imply:
% 240.08/46.73  | | | | |   (101)  $false
% 240.08/46.73  | | | | | 
% 240.08/46.73  | | | | | CLOSE: (101) is inconsistent.
% 240.08/46.73  | | | | | 
% 240.08/46.73  | | | | End of split
% 240.08/46.73  | | | | 
% 240.08/46.73  | | | End of split
% 240.08/46.73  | | | 
% 240.08/46.73  | | End of split
% 240.08/46.73  | | 
% 240.08/46.73  | End of split
% 240.08/46.73  | 
% 240.08/46.73  End of proof
% 240.08/46.73  
% 240.08/46.73  Sub-proof #213 shows that the following formulas are inconsistent:
% 240.08/46.73  ----------------------------------------------------------------
% 240.08/46.73    (1)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 240.08/46.73    (2)  op(e1, e2) = all_52_6
% 240.08/46.73    (3)   ~ (all_52_2 = e3)
% 240.08/46.73    (4)   ~ (all_52_6 = e3)
% 240.08/46.73    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.73    (6)  op(e1, e3) = all_52_2
% 240.08/46.73  
% 240.08/46.73  Begin of proof
% 240.08/46.73  | 
% 240.08/46.73  | BETA: splitting (1) gives:
% 240.08/46.73  | 
% 240.08/46.73  | Case 1:
% 240.08/46.73  | | 
% 240.08/46.73  | |   (7)  all_58_6 = e3 & op(e1, e3) = e3
% 240.08/46.73  | | 
% 240.08/46.73  | | ALPHA: (7) implies:
% 240.08/46.73  | |   (8)  op(e1, e3) = e3
% 240.08/46.73  | | 
% 240.08/46.73  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2335.
% 240.08/46.73  | | 
% 240.08/46.73  | Case 2:
% 240.08/46.73  | | 
% 240.08/46.73  | |   (9)  all_58_7 = e3 & op(e1, e2) = e3
% 240.08/46.73  | | 
% 240.08/46.73  | | ALPHA: (9) implies:
% 240.08/46.73  | |   (10)  op(e1, e2) = e3
% 240.08/46.73  | | 
% 240.08/46.73  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #2191.
% 240.08/46.73  | | 
% 240.08/46.73  | End of split
% 240.08/46.73  | 
% 240.08/46.73  End of proof
% 240.08/46.73  
% 240.08/46.73  Sub-proof #214 shows that the following formulas are inconsistent:
% 240.08/46.73  ----------------------------------------------------------------
% 240.08/46.73    (1)  op(e1, e0) = all_52_14
% 240.08/46.73    (2)   ~ (e3 = e2)
% 240.08/46.73    (3)   ~ (all_52_14 = e3)
% 240.08/46.73    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.73    (5)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.73    (6)  op(e0, e0) = e2
% 240.08/46.73  
% 240.08/46.73  Begin of proof
% 240.08/46.73  | 
% 240.08/46.73  | BETA: splitting (5) gives:
% 240.08/46.73  | 
% 240.08/46.73  | Case 1:
% 240.08/46.73  | | 
% 240.08/46.73  | |   (7)  all_58_11 = e3 & op(e1, e0) = e3
% 240.08/46.73  | | 
% 240.08/46.73  | | ALPHA: (7) implies:
% 240.08/46.73  | |   (8)  op(e1, e0) = e3
% 240.08/46.73  | | 
% 240.08/46.73  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2149.
% 240.08/46.73  | | 
% 240.08/46.73  | Case 2:
% 240.08/46.73  | | 
% 240.08/46.73  | |   (9)  all_58_15 = e3 & op(e0, e0) = e3
% 240.08/46.73  | | 
% 240.08/46.73  | | ALPHA: (9) implies:
% 240.08/46.73  | |   (10)  op(e0, e0) = e3
% 240.08/46.73  | | 
% 240.08/46.73  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #1388.
% 240.08/46.73  | | 
% 240.08/46.73  | End of split
% 240.08/46.73  | 
% 240.08/46.73  End of proof
% 240.08/46.73  
% 240.08/46.73  Sub-proof #215 shows that the following formulas are inconsistent:
% 240.08/46.73  ----------------------------------------------------------------
% 240.08/46.73    (1)  op(e3, e2) = e1
% 240.08/46.73    (2)  op(e0, e1) = all_56_23
% 240.08/46.73    (3)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 240.08/46.73           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 240.08/46.73           all_24_1 & $i(all_24_1))
% 240.08/46.73    (4)  op(e0, e1) = e1
% 240.08/46.73    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.73    (6)  op(e0, all_56_23) = e0
% 240.08/46.73    (7)   ~ (e1 = e0)
% 240.08/46.73    (8)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) = all_32_1
% 240.08/46.73           & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2) =
% 240.08/46.73           all_32_1 & $i(all_32_1))
% 240.08/46.73  
% 240.08/46.73  Begin of proof
% 240.08/46.73  | 
% 240.08/46.73  | BETA: splitting (3) gives:
% 240.08/46.73  | 
% 240.08/46.73  | Case 1:
% 240.08/46.73  | | 
% 240.08/46.73  | |   (9)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) =
% 240.08/46.73  | |        all_24_1 & $i(all_24_0) & $i(all_24_1)
% 240.08/46.73  | | 
% 240.08/46.73  | | ALPHA: (9) implies:
% 240.08/46.73  | |   (10)  op(e3, e2) = all_24_1
% 240.08/46.73  | | 
% 240.08/46.73  | | BETA: splitting (8) gives:
% 240.08/46.73  | | 
% 240.08/46.73  | | Case 1:
% 240.08/46.73  | | | 
% 240.08/46.73  | | | 
% 240.08/46.73  | | | REF_CLOSE: (2), (4), (5), (6), (7) are inconsistent by sub-proof #216.
% 240.08/46.73  | | | 
% 240.08/46.73  | | Case 2:
% 240.08/46.73  | | | 
% 240.08/46.73  | | |   (11)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 & $i(all_32_1)
% 240.08/46.73  | | | 
% 240.08/46.73  | | | ALPHA: (11) implies:
% 240.08/46.73  | | |   (12)   ~ (all_32_1 = e0)
% 240.08/46.73  | | |   (13)  op(e3, e2) = all_32_1
% 240.08/46.73  | | | 
% 240.08/46.73  | | | GROUND_INST: instantiating (5) with e1, all_56_23, e1, e0, simplifying
% 240.08/46.73  | | |              with (2), (4) gives:
% 240.08/46.73  | | |   (14)  all_56_23 = e1
% 240.08/46.73  | | | 
% 240.08/46.73  | | | GROUND_INST: instantiating (5) with all_24_1, all_32_1, e2, e3,
% 240.08/46.73  | | |              simplifying with (10), (13) gives:
% 240.08/46.73  | | |   (15)  all_32_1 = all_24_1
% 240.08/46.73  | | | 
% 240.08/46.73  | | | GROUND_INST: instantiating (5) with e1, all_32_1, e2, e3, simplifying with
% 240.08/46.73  | | |              (1), (13) gives:
% 240.08/46.73  | | |   (16)  all_32_1 = e1
% 240.08/46.73  | | | 
% 240.08/46.73  | | | COMBINE_EQS: (15), (16) imply:
% 240.08/46.73  | | |   (17)  all_24_1 = e1
% 240.08/46.73  | | | 
% 240.08/46.73  | | | REDUCE: (6), (14) imply:
% 240.08/46.73  | | |   (18)  op(e0, e1) = e0
% 240.08/46.73  | | | 
% 240.08/46.73  | | | REF_CLOSE: (4), (5), (7), (18) are inconsistent by sub-proof #2158.
% 240.08/46.73  | | | 
% 240.08/46.73  | | End of split
% 240.08/46.73  | | 
% 240.08/46.73  | Case 2:
% 240.08/46.73  | | 
% 240.08/46.73  | |   (19)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 & $i(all_24_1)
% 240.08/46.73  | | 
% 240.08/46.73  | | REF_CLOSE: (1), (5), (8), (19) are inconsistent by sub-proof #2238.
% 240.08/46.73  | | 
% 240.08/46.73  | End of split
% 240.08/46.73  | 
% 240.08/46.73  End of proof
% 240.08/46.73  
% 240.08/46.73  Sub-proof #216 shows that the following formulas are inconsistent:
% 240.08/46.73  ----------------------------------------------------------------
% 240.08/46.73    (1)  op(e0, e1) = all_56_23
% 240.08/46.73    (2)  op(e0, e1) = e1
% 240.08/46.73    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.73    (4)  op(e0, all_56_23) = e0
% 240.08/46.73    (5)   ~ (e1 = e0)
% 240.08/46.73  
% 240.08/46.73  Begin of proof
% 240.08/46.73  | 
% 240.08/46.73  | GROUND_INST: instantiating (3) with e1, all_56_23, e1, e0, simplifying with
% 240.08/46.73  |              (1), (2) gives:
% 240.08/46.73  |   (6)  all_56_23 = e1
% 240.08/46.73  | 
% 240.08/46.73  | REDUCE: (4), (6) imply:
% 240.08/46.73  |   (7)  op(e0, e1) = e0
% 240.08/46.73  | 
% 240.08/46.73  | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #2158.
% 240.08/46.73  | 
% 240.08/46.73  End of proof
% 240.08/46.73  
% 240.08/46.73  Sub-proof #217 shows that the following formulas are inconsistent:
% 240.08/46.73  ----------------------------------------------------------------
% 240.08/46.73    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.08/46.73         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.73    (2)   ~ (e3 = e0)
% 240.08/46.73    (3)  op(e0, e1) = all_56_23
% 240.08/46.73    (4)   ~ (e2 = e0)
% 240.08/46.73    (5)   ~ (e3 = e1)
% 240.08/46.73    (6)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.08/46.73             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.08/46.73               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.08/46.73               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.08/46.73    (7)   ~ (e3 = e2)
% 240.08/46.73    (8)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) = all_44_1
% 240.08/46.73           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2) =
% 240.08/46.73           all_44_1 & $i(all_44_1))
% 240.08/46.73    (9)  op(e0, e3) = e3
% 240.08/46.73    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.73    (11)  op(e0, all_56_23) = e0
% 240.08/46.73    (12)   ~ (e1 = e0)
% 240.08/46.73    (13)  all_58_13 = e1
% 240.08/46.73    (14)  op(e0, e0) = e2
% 240.08/46.73    (15)  op(e0, e2) = e1
% 240.08/46.73    (16)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.73          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.08/46.73            e2)
% 240.08/46.73    (17)   ~ (e2 = e1)
% 240.08/46.73  
% 240.08/46.73  Begin of proof
% 240.08/46.73  | 
% 240.08/46.73  | BETA: splitting (6) gives:
% 240.08/46.73  | 
% 240.08/46.73  | Case 1:
% 240.08/46.73  | | 
% 240.08/46.73  | |   (18)  all_58_15 = e0 & op(e0, e0) = e0
% 240.08/46.73  | | 
% 240.08/46.73  | | ALPHA: (18) implies:
% 240.08/46.73  | |   (19)  op(e0, e0) = e0
% 240.08/46.73  | | 
% 240.08/46.73  | | REF_CLOSE: (4), (10), (14), (19) are inconsistent by sub-proof #2301.
% 240.08/46.73  | | 
% 240.08/46.73  | Case 2:
% 240.08/46.73  | | 
% 240.08/46.73  | |   (20)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 240.08/46.73  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 240.08/46.73  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 240.08/46.73  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 240.08/46.73  | | 
% 240.08/46.73  | | ALPHA: (20) implies:
% 240.08/46.73  | |   (21)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.08/46.73  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.73  | | 
% 240.08/46.73  | | BETA: splitting (21) gives:
% 240.08/46.73  | | 
% 240.08/46.73  | | Case 1:
% 240.08/46.73  | | | 
% 240.08/46.73  | | |   (22)  all_58_12 = e0 & op(e0, e3) = e0
% 240.08/46.73  | | | 
% 240.08/46.73  | | | ALPHA: (22) implies:
% 240.08/46.73  | | |   (23)  op(e0, e3) = e0
% 240.08/46.73  | | | 
% 240.08/46.73  | | | REF_CLOSE: (2), (9), (10), (23) are inconsistent by sub-proof #221.
% 240.08/46.73  | | | 
% 240.08/46.73  | | Case 2:
% 240.08/46.73  | | | 
% 240.08/46.73  | | |   (24)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 240.08/46.73  | | |           = e0)
% 240.08/46.73  | | | 
% 240.08/46.73  | | | BETA: splitting (24) gives:
% 240.08/46.73  | | | 
% 240.08/46.73  | | | Case 1:
% 240.08/46.73  | | | | 
% 240.08/46.73  | | | |   (25)  all_58_13 = e0 & op(e0, e2) = e0
% 240.08/46.73  | | | | 
% 240.08/46.73  | | | | ALPHA: (25) implies:
% 240.08/46.73  | | | |   (26)  op(e0, e2) = e0
% 240.08/46.73  | | | | 
% 240.08/46.73  | | | | REF_CLOSE: (10), (12), (15), (26) are inconsistent by sub-proof #1872.
% 240.08/46.73  | | | | 
% 240.08/46.73  | | | Case 2:
% 240.08/46.73  | | | | 
% 240.08/46.73  | | | |   (27)  all_58_14 = e0 & op(e0, e1) = e0
% 240.08/46.73  | | | | 
% 240.08/46.73  | | | | ALPHA: (27) implies:
% 240.08/46.73  | | | |   (28)  all_58_14 = e0
% 240.08/46.73  | | | |   (29)  op(e0, e1) = e0
% 240.08/46.73  | | | | 
% 240.08/46.73  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (13),
% 240.08/46.73  | | | |            (15), (16), (17), (21), (28), (29) are inconsistent by
% 240.08/46.73  | | | |            sub-proof #228.
% 240.08/46.73  | | | | 
% 240.08/46.73  | | | End of split
% 240.08/46.73  | | | 
% 240.08/46.73  | | End of split
% 240.08/46.73  | | 
% 240.08/46.73  | End of split
% 240.08/46.73  | 
% 240.08/46.73  End of proof
% 240.08/46.73  
% 240.08/46.73  Sub-proof #218 shows that the following formulas are inconsistent:
% 240.08/46.73  ----------------------------------------------------------------
% 240.08/46.73    (1)  all_58_15 = e1 & op(e0, e0) = e1
% 240.08/46.73    (2)  all_58_15 = e2
% 240.08/46.73    (3)   ~ (e2 = e1)
% 240.08/46.73  
% 240.08/46.73  Begin of proof
% 240.08/46.73  | 
% 240.08/46.73  | ALPHA: (1) implies:
% 240.08/46.73  |   (4)  all_58_15 = e1
% 240.08/46.73  | 
% 240.08/46.73  | COMBINE_EQS: (2), (4) imply:
% 240.08/46.73  |   (5)  e2 = e1
% 240.08/46.73  | 
% 240.08/46.73  | REDUCE: (3), (5) imply:
% 240.08/46.73  |   (6)  $false
% 240.08/46.73  | 
% 240.08/46.73  | CLOSE: (6) is inconsistent.
% 240.08/46.73  | 
% 240.08/46.73  End of proof
% 240.08/46.73  
% 240.08/46.73  Sub-proof #219 shows that the following formulas are inconsistent:
% 240.08/46.73  ----------------------------------------------------------------
% 240.08/46.73    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 240.08/46.73             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 240.08/46.73           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 240.08/46.73         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 240.08/46.73           $i(all_56_7))
% 240.08/46.73    (2)  all_56_21 = e2
% 240.08/46.73    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.08/46.73    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.08/46.73         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.08/46.73    (5)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.08/46.73           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.08/46.73           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.08/46.73           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.08/46.73           & $i(all_56_23))
% 240.08/46.73    (6)   ~ (all_52_9 = all_6_2)
% 240.08/46.73    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.08/46.73         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.73    (8)   ~ (e3 = e0)
% 240.08/46.73    (9)   ~ (all_52_7 = e2)
% 240.08/46.73    (10)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) =
% 240.08/46.73            all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3,
% 240.08/46.73              e2) = all_24_1 & $i(all_24_1))
% 240.08/46.73    (11)  op(e0, e1) = all_52_11
% 240.08/46.73    (12)   ~ (e2 = e0)
% 240.08/46.73    (13)   ~ (all_52_11 = e2)
% 240.08/46.73    (14)  all_54_13 = all_52_7
% 240.08/46.73    (15)   ~ (all_52_8 = all_6_2)
% 240.08/46.73    (16)  op(e1, e2) = all_52_6
% 240.08/46.73    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.73          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.73    (18)  ( ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 240.08/46.74            $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e0, e2) = all_4_1
% 240.08/46.74            & $i(all_4_1))
% 240.08/46.74    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.74              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.08/46.74            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.08/46.74            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.74            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.08/46.74             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.74            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.08/46.74            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.08/46.74            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.08/46.74            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.74            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.08/46.74              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.08/46.74            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.74            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.08/46.74            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.08/46.74            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.08/46.74            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.74            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.08/46.74              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.08/46.74            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.74            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.08/46.74            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.08/46.74            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.08/46.74            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.74            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.08/46.74              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.08/46.74            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.74            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.74    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.08/46.74          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.08/46.74    (21)   ~ (all_52_7 = all_52_11)
% 240.08/46.74    (22)  op(e1, e1) = all_6_2
% 240.08/46.74    (23)  op(e1, e0) = all_52_14
% 240.08/46.74    (24)   ~ (all_52_7 = e3)
% 240.08/46.74    (25)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 240.08/46.74    (26)  op(e0, e3) = all_52_3
% 240.08/46.74    (27)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.74          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.08/46.74    (28)   ~ (e3 = e1)
% 240.08/46.74    (29)  all_54_11 = all_52_14
% 240.08/46.74    (30)   ~ (all_52_12 = e1)
% 240.08/46.74    (31)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.08/46.74          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.74    (32)   ~ (all_52_12 = all_52_14)
% 240.08/46.74    (33)  all_54_6 = all_52_9
% 240.08/46.74    (34)   ~ (all_52_12 = all_52_13)
% 240.08/46.74    (35)  op(e1, e2) = e3
% 240.08/46.74    (36)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.08/46.74          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.08/46.74    (37)  all_54_10 = all_6_2
% 240.08/46.74    (38)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.08/46.74    (39)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 240.08/46.74          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 240.08/46.74    (40)   ~ (all_52_3 = all_52_7)
% 240.08/46.74    (41)  all_58_15 = e2
% 240.08/46.74    (42)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 240.08/46.74    (43)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.08/46.74              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.08/46.74                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.08/46.74                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.08/46.74    (44)   ~ (all_52_14 = e2)
% 240.08/46.74    (45)   ~ (all_6_2 = e3)
% 240.08/46.74    (46)   ~ (all_52_8 = all_52_12)
% 240.08/46.74    (47)  op(e3, e1) = all_52_8
% 240.08/46.74    (48)  op(e2, e1) = all_52_9
% 240.08/46.74    (49)  all_54_9 = all_52_6
% 240.08/46.74    (50)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.08/46.74          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.08/46.74    (51)   ~ (e3 = e2)
% 240.08/46.74    (52)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 240.08/46.74            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 240.08/46.74              e2) = all_44_1 & $i(all_44_1))
% 240.08/46.74    (53)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.08/46.74    (54)   ~ (all_52_3 = all_52_11)
% 240.08/46.74    (55)   ~ (all_6_2 = e0)
% 240.08/46.74    (56)  all_56_31 = e2
% 240.08/46.74    (57)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.08/46.74            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.08/46.74            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.08/46.74            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.08/46.74            op(e0, all_56_31) = e0)
% 240.08/46.74    (58)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 240.08/46.74    (59)  all_54_12 = all_52_3
% 240.08/46.74    (60)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.08/46.74    (61)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.08/46.74          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.08/46.74    (62)  op(e3, e0) = all_52_12
% 240.08/46.74    (63)   ~ (all_52_3 = e2)
% 240.08/46.74    (64)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.08/46.74          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.08/46.74    (65)   ~ (all_52_9 = all_52_13)
% 240.08/46.74    (66)   ~ (all_52_4 = all_52_12)
% 240.08/46.74    (67)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 240.08/46.74    (68)  op(e2, e3) = all_52_1
% 240.08/46.74    (69)  op(e3, e3) = e2
% 240.08/46.74    (70)   ~ (all_52_12 = e2)
% 240.08/46.74    (71)   ~ (all_52_13 = e2)
% 240.08/46.74    (72)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 240.08/46.74    (73)  op(e1, e2) = all_36_1
% 240.08/46.74    (74)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.08/46.74          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.08/46.74    (75)   ~ (all_52_2 = e3)
% 240.08/46.74    (76)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 240.08/46.74            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 240.08/46.74              e2) = all_40_1 & $i(all_40_1))
% 240.08/46.74    (77)  op(e1, e1) = e2
% 240.08/46.74    (78)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.08/46.74          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.08/46.74    (79)  all_54_7 = all_52_13
% 240.08/46.74    (80)  op(e0, e2) = all_52_7
% 240.08/46.74    (81)   ~ (all_52_13 = all_52_14)
% 240.08/46.74    (82)  all_56_1 = e2
% 240.08/46.74    (83)  all_54_1 = all_52_4
% 240.08/46.74    (84)   ~ (all_52_4 = e3)
% 240.08/46.74    (85)  op(e3, e2) = all_52_4
% 240.08/46.74    (86)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 240.08/46.74    (87)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.08/46.74          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.08/46.74    (88)   ~ (all_52_4 = e2)
% 240.08/46.74    (89)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.08/46.74          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.08/46.74    (90)  all_54_3 = all_52_12
% 240.08/46.74    (91)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.74            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.74    (92)  op(e1, e3) = all_52_2
% 240.08/46.74    (93)   ~ (all_52_6 = all_52_7)
% 240.08/46.74    (94)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.08/46.74          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.74    (95)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 240.08/46.74            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 240.08/46.74              e2) = all_36_1 & $i(all_36_1))
% 240.08/46.75    (96)  op(e1, e2) = all_40_1
% 240.08/46.75    (97)   ~ (all_52_4 = e1)
% 240.08/46.75    (98)   ~ (e1 = e0)
% 240.08/46.75    (99)  all_56_21 = all_6_2
% 240.08/46.75    (100)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 240.08/46.75             all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) &
% 240.08/46.75             op(e3, e2) = all_32_1 & $i(all_32_1))
% 240.08/46.75    (101)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.08/46.75           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.08/46.75    (102)  op(e0, e0) = e2
% 240.08/46.75    (103)  op(e2, e0) = all_52_13
% 240.08/46.75    (104)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.75           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.08/46.75             e1)
% 240.08/46.75    (105)   ~ (all_52_9 = e1)
% 240.08/46.75    (106)  all_54_14 = all_52_11
% 240.08/46.75    (107)  op(e2, e2) = e2
% 240.08/46.75    (108)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.75           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.08/46.75             e2)
% 240.08/46.75    (109)   ~ (all_52_9 = all_52_11)
% 240.08/46.75    (110)   ~ (all_52_1 = e2)
% 240.08/46.75    (111)   ~ (all_52_4 = all_52_6)
% 240.08/46.75    (112)   ~ (e2 = e1)
% 240.08/46.75    (113)   ~ (all_52_4 = all_52_7)
% 240.08/46.75    (114)   ~ (all_52_9 = e2)
% 240.08/46.75  
% 240.08/46.75  Begin of proof
% 240.08/46.75  | 
% 240.08/46.75  | BETA: splitting (89) gives:
% 240.08/46.75  | 
% 240.08/46.75  | Case 1:
% 240.08/46.75  | | 
% 240.08/46.75  | |   (115)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 240.08/46.75  | |            e1)
% 240.08/46.75  | | 
% 240.08/46.75  | | REF_CLOSE: (69), (85), (91), (97), (112), (115) are inconsistent by
% 240.08/46.75  | |            sub-proof #1340.
% 240.08/46.75  | | 
% 240.08/46.75  | Case 2:
% 240.08/46.75  | | 
% 240.08/46.75  | |   (116)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 240.08/46.75  | |            e1)
% 240.08/46.75  | | 
% 240.08/46.75  | | BETA: splitting (116) gives:
% 240.08/46.75  | | 
% 240.08/46.75  | | Case 1:
% 240.08/46.75  | | | 
% 240.08/46.75  | | |   (117)  all_58_4 = e1 & op(e3, e1) = e1
% 240.08/46.75  | | | 
% 240.08/46.75  | | | ALPHA: (117) implies:
% 240.08/46.75  | | |   (118)  all_58_4 = e1
% 240.08/46.75  | | |   (119)  op(e3, e1) = e1
% 240.08/46.75  | | | 
% 240.08/46.75  | | | BETA: splitting (25) gives:
% 240.08/46.75  | | | 
% 240.08/46.75  | | | Case 1:
% 240.08/46.75  | | | | 
% 240.08/46.75  | | | |   (120)  all_54_1 = e3
% 240.08/46.75  | | | | 
% 240.08/46.75  | | | | COMBINE_EQS: (83), (120) imply:
% 240.08/46.75  | | | |   (121)  all_52_4 = e3
% 240.08/46.75  | | | | 
% 240.08/46.75  | | | | REDUCE: (84), (121) imply:
% 240.08/46.75  | | | |   (122)  $false
% 240.08/46.75  | | | | 
% 240.08/46.75  | | | | CLOSE: (122) is inconsistent.
% 240.08/46.75  | | | | 
% 240.08/46.75  | | | Case 2:
% 240.08/46.75  | | | | 
% 240.08/46.75  | | | |   (123)   ~ (all_54_1 = e3)
% 240.08/46.75  | | | |   (124)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 240.08/46.75  | | | | 
% 240.08/46.75  | | | | BETA: splitting (124) gives:
% 240.08/46.75  | | | | 
% 240.08/46.75  | | | | Case 1:
% 240.08/46.75  | | | | | 
% 240.08/46.75  | | | | |   (125)  all_54_1 = e2
% 240.08/46.75  | | | | | 
% 240.08/46.75  | | | | | COMBINE_EQS: (83), (125) imply:
% 240.08/46.75  | | | | |   (126)  all_52_4 = e2
% 240.08/46.75  | | | | | 
% 240.08/46.75  | | | | | REDUCE: (88), (126) imply:
% 240.08/46.75  | | | | |   (127)  $false
% 240.08/46.75  | | | | | 
% 240.08/46.75  | | | | | CLOSE: (127) is inconsistent.
% 240.08/46.75  | | | | | 
% 240.08/46.75  | | | | Case 2:
% 240.08/46.75  | | | | | 
% 240.08/46.75  | | | | |   (128)   ~ (all_54_1 = e2)
% 240.08/46.75  | | | | |   (129)  all_54_1 = e1 | all_54_1 = e0
% 240.08/46.75  | | | | | 
% 240.08/46.75  | | | | | BETA: splitting (36) gives:
% 240.08/46.75  | | | | | 
% 240.08/46.75  | | | | | Case 1:
% 240.08/46.75  | | | | | | 
% 240.08/46.75  | | | | | |   (130)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3,
% 240.08/46.75  | | | | | |              e2) = e3)
% 240.08/46.75  | | | | | | 
% 240.08/46.75  | | | | | | REF_CLOSE: (16), (35), (49), (51), (58), (69), (85), (91), (111),
% 240.08/46.75  | | | | | |            (130) are inconsistent by sub-proof #2189.
% 240.08/46.75  | | | | | | 
% 240.08/46.75  | | | | | Case 2:
% 240.08/46.75  | | | | | | 
% 240.08/46.75  | | | | | |   (131)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 240.08/46.75  | | | | | |              e0) = e3)
% 240.08/46.75  | | | | | | 
% 240.08/46.75  | | | | | | BETA: splitting (131) gives:
% 240.08/46.75  | | | | | | 
% 240.08/46.75  | | | | | | Case 1:
% 240.08/46.75  | | | | | | | 
% 240.08/46.75  | | | | | | |   (132)  all_58_4 = e3 & op(e3, e1) = e3
% 240.08/46.75  | | | | | | | 
% 240.08/46.75  | | | | | | | ALPHA: (132) implies:
% 240.08/46.75  | | | | | | |   (133)  op(e3, e1) = e3
% 240.08/46.75  | | | | | | | 
% 240.08/46.75  | | | | | | | REF_CLOSE: (28), (91), (119), (133) are inconsistent by sub-proof
% 240.08/46.75  | | | | | | |            #1823.
% 240.08/46.75  | | | | | | | 
% 240.08/46.75  | | | | | | Case 2:
% 240.08/46.75  | | | | | | | 
% 240.08/46.75  | | | | | | |   (134)  all_58_9 = e3 & op(e3, e0) = e3
% 240.08/46.75  | | | | | | | 
% 240.08/46.75  | | | | | | | ALPHA: (134) implies:
% 240.08/46.75  | | | | | | |   (135)  all_58_9 = e3
% 240.08/46.75  | | | | | | |   (136)  op(e3, e0) = e3
% 240.08/46.75  | | | | | | | 
% 240.08/46.75  | | | | | | | BETA: splitting (94) gives:
% 240.08/46.75  | | | | | | | 
% 240.08/46.75  | | | | | | | Case 1:
% 240.08/46.75  | | | | | | | | 
% 240.08/46.75  | | | | | | | |   (137)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 240.08/46.75  | | | | | | | |            op(e2, e2) = e1)
% 240.08/46.75  | | | | | | | | 
% 240.08/46.75  | | | | | | | | BETA: splitting (137) gives:
% 240.08/46.75  | | | | | | | | 
% 240.08/46.75  | | | | | | | | Case 1:
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | |   (138)  all_58_1 = e1 & op(e3, e2) = e1
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | ALPHA: (138) implies:
% 240.08/46.75  | | | | | | | | |   (139)  all_58_1 = e1
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | REF_CLOSE: (4), (8), (12), (28), (36), (51), (74), (84), (85),
% 240.08/46.75  | | | | | | | | |            (91), (98), (112), (118), (136), (139) are
% 240.08/46.75  | | | | | | | | |            inconsistent by sub-proof #1437.
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | Case 2:
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | |   (140)  all_58_3 = e1 & op(e2, e2) = e1
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | ALPHA: (140) implies:
% 240.08/46.75  | | | | | | | | |   (141)  op(e2, e2) = e1
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | REF_CLOSE: (6), (8), (9), (12), (15), (16), (17), (19), (22),
% 240.08/46.75  | | | | | | | | |            (23), (26), (27), (28), (32), (37), (39), (45),
% 240.08/46.75  | | | | | | | | |            (46), (47), (48), (50), (51), (55), (56), (61),
% 240.08/46.75  | | | | | | | | |            (62), (63), (64), (68), (69), (71), (72), (80),
% 240.08/46.75  | | | | | | | | |            (85), (87), (88), (89), (91), (93), (97), (98),
% 240.08/46.75  | | | | | | | | |            (99), (101), (103), (110), (111), (112), (141) are
% 240.08/46.75  | | | | | | | | |            inconsistent by sub-proof #236.
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | End of split
% 240.08/46.75  | | | | | | | | 
% 240.08/46.75  | | | | | | | Case 2:
% 240.08/46.75  | | | | | | | | 
% 240.08/46.75  | | | | | | | |   (142)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 240.08/46.75  | | | | | | | |            op(e0, e2) = e1)
% 240.08/46.75  | | | | | | | | 
% 240.08/46.75  | | | | | | | | BETA: splitting (142) gives:
% 240.08/46.75  | | | | | | | | 
% 240.08/46.75  | | | | | | | | Case 1:
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | |   (143)  all_58_7 = e1 & op(e1, e2) = e1
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | ALPHA: (143) implies:
% 240.08/46.75  | | | | | | | | |   (144)  op(e1, e2) = e1
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | REF_CLOSE: (28), (35), (73), (91), (96), (144) are
% 240.08/46.75  | | | | | | | | |            inconsistent by sub-proof #1701.
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | Case 2:
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | |   (145)  all_58_13 = e1 & op(e0, e2) = e1
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | ALPHA: (145) implies:
% 240.08/46.75  | | | | | | | | |   (146)  all_58_13 = e1
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | BETA: splitting (129) gives:
% 240.08/46.75  | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | Case 1:
% 240.08/46.75  | | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | |   (147)  all_54_1 = e1
% 240.08/46.75  | | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | | REF_CLOSE: (83), (97), (147) are inconsistent by sub-proof
% 240.08/46.75  | | | | | | | | | |            #2051.
% 240.08/46.75  | | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | Case 2:
% 240.08/46.75  | | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | |   (148)  all_54_1 = e0
% 240.08/46.75  | | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | | COMBINE_EQS: (83), (148) imply:
% 240.08/46.75  | | | | | | | | | |   (149)  all_52_4 = e0
% 240.08/46.75  | | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | | SIMP: (149) implies:
% 240.08/46.75  | | | | | | | | | |   (150)  all_52_4 = e0
% 240.08/46.75  | | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | | REDUCE: (113), (150) imply:
% 240.08/46.75  | | | | | | | | | |   (151)   ~ (all_52_7 = e0)
% 240.08/46.75  | | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | | SIMP: (151) implies:
% 240.08/46.75  | | | | | | | | | |   (152)   ~ (all_52_7 = e0)
% 240.08/46.75  | | | | | | | | | | 
% 240.08/46.75  | | | | | | | | | | REDUCE: (66), (150) imply:
% 240.08/46.76  | | | | | | | | | |   (153)   ~ (all_52_12 = e0)
% 240.08/46.76  | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | SIMP: (153) implies:
% 240.08/46.76  | | | | | | | | | |   (154)   ~ (all_52_12 = e0)
% 240.08/46.76  | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | REDUCE: (88), (150) imply:
% 240.08/46.76  | | | | | | | | | |   (155)   ~ (e2 = e0)
% 240.08/46.76  | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | REDUCE: (85), (150) imply:
% 240.08/46.76  | | | | | | | | | |   (156)  op(e3, e2) = e0
% 240.08/46.76  | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | BETA: splitting (86) gives:
% 240.08/46.76  | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | |   (157)  all_54_13 = e3
% 240.08/46.76  | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | REF_CLOSE: (14), (24), (157) are inconsistent by sub-proof
% 240.08/46.76  | | | | | | | | | | |            #2010.
% 240.08/46.76  | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | Case 2:
% 240.08/46.76  | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | |   (158)   ~ (all_54_13 = e3)
% 240.08/46.76  | | | | | | | | | | |   (159)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 240.08/46.76  | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | BETA: splitting (42) gives:
% 240.08/46.76  | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | |   (160)  all_54_3 = e3
% 240.08/46.76  | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | COMBINE_EQS: (90), (160) imply:
% 240.08/46.76  | | | | | | | | | | | |   (161)  all_52_12 = e3
% 240.08/46.76  | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | SIMP: (161) implies:
% 240.08/46.76  | | | | | | | | | | | |   (162)  all_52_12 = e3
% 240.08/46.76  | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | REDUCE: (34), (162) imply:
% 240.08/46.76  | | | | | | | | | | | |   (163)   ~ (all_52_13 = e3)
% 240.08/46.76  | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | SIMP: (163) implies:
% 240.08/46.76  | | | | | | | | | | | |   (164)   ~ (all_52_13 = e3)
% 240.08/46.76  | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | BETA: splitting (159) gives:
% 240.08/46.76  | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | |   (165)  all_54_13 = e2
% 240.08/46.76  | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | REF_CLOSE: (9), (14), (165) are inconsistent by sub-proof
% 240.08/46.76  | | | | | | | | | | | | |            #2009.
% 240.08/46.76  | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | Case 2:
% 240.08/46.76  | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | |   (166)   ~ (all_54_13 = e2)
% 240.08/46.76  | | | | | | | | | | | | |   (167)  all_54_13 = e1 | all_54_13 = e0
% 240.08/46.76  | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | BETA: splitting (167) gives:
% 240.08/46.76  | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | |   (168)  all_54_13 = e1
% 240.08/46.76  | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | COMBINE_EQS: (14), (168) imply:
% 240.08/46.76  | | | | | | | | | | | | | |   (169)  all_52_7 = e1
% 240.08/46.76  | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | SIMP: (169) implies:
% 240.08/46.76  | | | | | | | | | | | | | |   (170)  all_52_7 = e1
% 240.08/46.76  | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | REDUCE: (40), (170) imply:
% 240.08/46.76  | | | | | | | | | | | | | |   (171)   ~ (all_52_3 = e1)
% 240.08/46.76  | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | REDUCE: (21), (170) imply:
% 240.08/46.76  | | | | | | | | | | | | | |   (172)   ~ (all_52_11 = e1)
% 240.08/46.76  | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | SIMP: (172) implies:
% 240.08/46.76  | | | | | | | | | | | | | |   (173)   ~ (all_52_11 = e1)
% 240.08/46.76  | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | REDUCE: (9), (170) imply:
% 240.08/46.76  | | | | | | | | | | | | | |   (174)   ~ (e2 = e1)
% 240.08/46.76  | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | REDUCE: (80), (170) imply:
% 240.08/46.76  | | | | | | | | | | | | | |   (175)  op(e0, e2) = e1
% 240.08/46.76  | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 240.08/46.76  | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | |   (176)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 240.08/46.76  | | | | | | | | | | | | | | |          op(e3, e2) = all_24_1 & $i(all_24_0) &
% 240.08/46.76  | | | | | | | | | | | | | | |          $i(all_24_1)
% 240.08/46.76  | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 240.08/46.76  | | | | | | | | | | | | | | |   (177)   ~ (all_24_0 = e0)
% 240.08/46.76  | | | | | | | | | | | | | | |   (178)  op(e3, e2) = all_24_1
% 240.08/46.76  | | | | | | | | | | | | | | |   (179)  op(all_24_1, e3) = all_24_0
% 240.08/46.76  | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | |   (180)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 240.08/46.76  | | | | | | | | | | | | | | | |          op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | |   (181)   ~ (all_4_0 = e1)
% 240.08/46.76  | | | | | | | | | | | | | | | |   (182)  op(e0, e2) = all_4_1
% 240.08/46.76  | | | | | | | | | | | | | | | |   (183)  op(all_4_1, e0) = all_4_0
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | REF_CLOSE: (23), (29), (35), (38), (44), (48), (51), (52),
% 240.08/46.76  | | | | | | | | | | | | | | | |            (56), (57), (60), (69), (71), (76), (79), (80),
% 240.08/46.76  | | | | | | | | | | | | | | | |            (81), (91), (95), (103), (114), (136), (152),
% 240.08/46.76  | | | | | | | | | | | | | | | |            (164), (175), (181), (182), (183) are inconsistent
% 240.08/46.76  | | | | | | | | | | | | | | | |            by sub-proof #229.
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | Case 2:
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | |   (184)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 240.08/46.76  | | | | | | | | | | | | | | | |          $i(all_4_1)
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | |   (185)   ~ (all_4_1 = e3)
% 240.08/46.76  | | | | | | | | | | | | | | | |   (186)  op(e0, e2) = all_4_1
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | |   (187)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 240.08/46.76  | | | | | | | | | | | | | | | | |          op(e0, e2) = all_44_1 & $i(all_44_0) &
% 240.08/46.76  | | | | | | | | | | | | | | | | |          $i(all_44_1)
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | |   (188)  op(e0, e2) = all_44_1
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (189)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 240.08/46.76  | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_32_1 & $i(all_32_0) &
% 240.08/46.76  | | | | | | | | | | | | | | | | | |          $i(all_32_1)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (190)   ~ (all_32_0 = e1)
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (191)  op(e3, e2) = all_32_1
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (192)  op(all_32_1, e3) = all_32_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (91) with all_4_1, all_44_1, e2, e0,
% 240.08/46.76  | | | | | | | | | | | | | | | | | |              simplifying with (186), (188) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (193)  all_44_1 = all_4_1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (91) with e1, all_44_1, e2, e0,
% 240.08/46.76  | | | | | | | | | | | | | | | | | |              simplifying with (175), (188) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (194)  all_44_1 = e1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (91) with all_24_1, all_32_1, e2,
% 240.08/46.76  | | | | | | | | | | | | | | | | | |              e3, simplifying with (178), (191) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (195)  all_32_1 = all_24_1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (91) with e0, all_32_1, e2, e3,
% 240.08/46.76  | | | | | | | | | | | | | | | | | |              simplifying with (156), (191) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (196)  all_32_1 = e0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (193), (194) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (197)  all_4_1 = e1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | SIMP: (197) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (198)  all_4_1 = e1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (196) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (199)  all_24_1 = e0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | REDUCE: (192), (196) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (200)  op(e0, e3) = all_32_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | REDUCE: (179), (199) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (201)  op(e0, e3) = all_24_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (91) with all_52_3, all_24_0, e3,
% 240.08/46.76  | | | | | | | | | | | | | | | | | |              e0, simplifying with (26), (201) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (202)  all_52_3 = all_24_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (91) with all_52_3, all_32_0, e3,
% 240.08/46.76  | | | | | | | | | | | | | | | | | |              e0, simplifying with (26), (200) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (203)  all_52_3 = all_32_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (203) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (204)  all_32_0 = all_24_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | SIMP: (204) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (205)  all_32_0 = all_24_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (202) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (206)  all_54_12 = all_24_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | REDUCE: (54), (202) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (207)   ~ (all_52_11 = all_24_0)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | SIMP: (207) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (208)   ~ (all_52_11 = all_24_0)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | REDUCE: (63), (202) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (209)   ~ (all_24_0 = e2)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | REDUCE: (190), (205) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (210)   ~ (all_24_0 = e1)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | |   (211)  all_54_12 = e3
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (211) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | |   (212)  all_24_0 = e3
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | SIMP: (212) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | |   (213)  all_24_0 = e3
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | REDUCE: (208), (213) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | |   (214)   ~ (all_52_11 = e3)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |   (215)  all_54_14 = e3
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (106), (214), (215) are inconsistent by sub-proof
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |            #1796.
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |   (216)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (11), (12), (13), (24), (28),
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |            (31), (35), (41), (43), (51), (52), (68), (69),
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |            (73), (77), (78), (80), (91), (96), (98), (102),
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |            (104), (106), (108), (110), (112), (119), (146),
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |            (173), (175), (185), (186), (188), (214), (216)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #225.
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | |   (217)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |   (218)  all_54_12 = e2
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (218) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |   (219)  all_24_0 = e2
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | SIMP: (219) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |   (220)  all_24_0 = e2
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (209), (220) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |   (221)  $false
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | CLOSE: (221) is inconsistent.
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |   (222)  all_54_12 = e1 | all_54_12 = e0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | |   (223)  all_54_12 = e1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (223) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | |   (224)  all_24_0 = e1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | SIMP: (224) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | |   (225)  all_24_0 = e1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | REDUCE: (210), (225) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | |   (226)  $false
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent.
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | |   (227)  all_54_12 = e0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (227) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | |   (228)  all_24_0 = e0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | |   (229)  all_24_0 = e0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (229) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | |   (230)  $false
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (231)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 240.08/46.76  | | | | | | | | | | | | | | | | | |          $i(all_32_1)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (232)   ~ (all_32_1 = e0)
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (233)  op(e3, e2) = all_32_1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (156), (178), (232), (233) are inconsistent
% 240.08/46.76  | | | | | | | | | | | | | | | | | |            by sub-proof #2065.
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | End of split
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | |   (234)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 &
% 240.08/46.76  | | | | | | | | | | | | | | | | |          $i(all_44_1)
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | |   (235)   ~ (all_44_1 = e1)
% 240.08/46.76  | | | | | | | | | | | | | | | | |   (236)  op(e0, e2) = all_44_1
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (175), (235), (236) are inconsistent by
% 240.08/46.76  | | | | | | | | | | | | | | | | |            sub-proof #230.
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | End of split
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | End of split
% 240.08/46.76  | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | Case 2:
% 240.08/46.76  | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | |   (237)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 240.08/46.76  | | | | | | | | | | | | | | |          $i(all_24_1)
% 240.08/46.76  | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 240.08/46.76  | | | | | | | | | | | | | | |   (238)   ~ (all_24_1 = e1)
% 240.08/46.76  | | | | | | | | | | | | | | |   (239)  op(e3, e2) = all_24_1
% 240.08/46.76  | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | |   (240)   ~ (all_4_0 = e1) & op(all_4_1, e0) = all_4_0 &
% 240.08/46.76  | | | | | | | | | | | | | | | |          op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | |   (241)   ~ (all_4_0 = e1)
% 240.08/46.76  | | | | | | | | | | | | | | | |   (242)  op(e0, e2) = all_4_1
% 240.08/46.76  | | | | | | | | | | | | | | | |   (243)  op(all_4_1, e0) = all_4_0
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | REF_CLOSE: (23), (29), (35), (38), (44), (48), (51), (52),
% 240.08/46.76  | | | | | | | | | | | | | | | |            (56), (57), (60), (69), (71), (76), (79), (80),
% 240.08/46.76  | | | | | | | | | | | | | | | |            (81), (91), (95), (103), (114), (136), (152),
% 240.08/46.76  | | | | | | | | | | | | | | | |            (164), (175), (241), (242), (243) are inconsistent
% 240.08/46.76  | | | | | | | | | | | | | | | |            by sub-proof #229.
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | Case 2:
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | |   (244)   ~ (all_4_1 = e3) & op(e0, e2) = all_4_1 &
% 240.08/46.76  | | | | | | | | | | | | | | | |          $i(all_4_1)
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | |   (245)   ~ (all_4_1 = e3)
% 240.08/46.76  | | | | | | | | | | | | | | | |   (246)  op(e0, e2) = all_4_1
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | |   (247)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 &
% 240.08/46.76  | | | | | | | | | | | | | | | | |          op(e0, e2) = all_44_1 & $i(all_44_0) &
% 240.08/46.76  | | | | | | | | | | | | | | | | |          $i(all_44_1)
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | ALPHA: (247) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | |   (248)  op(e0, e2) = all_44_1
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (249)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 240.08/46.76  | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_32_1 & $i(all_32_0) &
% 240.08/46.76  | | | | | | | | | | | | | | | | | |          $i(all_32_1)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (250)  op(e3, e2) = all_32_1
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (251)  op(all_32_1, e3) = all_32_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (91) with all_4_1, all_44_1, e2, e0,
% 240.08/46.76  | | | | | | | | | | | | | | | | | |              simplifying with (246), (248) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (252)  all_44_1 = all_4_1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (91) with e1, all_44_1, e2, e0,
% 240.08/46.76  | | | | | | | | | | | | | | | | | |              simplifying with (175), (248) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (253)  all_44_1 = e1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (91) with all_24_1, all_32_1, e2,
% 240.08/46.76  | | | | | | | | | | | | | | | | | |              e3, simplifying with (239), (250) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (254)  all_32_1 = all_24_1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (91) with e0, all_32_1, e2, e3,
% 240.08/46.76  | | | | | | | | | | | | | | | | | |              simplifying with (156), (250) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (255)  all_32_1 = e0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (253) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (256)  all_4_1 = e1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | SIMP: (256) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (257)  all_4_1 = e1
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (255) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (258)  all_24_1 = e0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | REDUCE: (238), (258) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (259)   ~ (e1 = e0)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | REDUCE: (245), (257) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (260)   ~ (e3 = e1)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | REDUCE: (251), (255) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (261)  op(e0, e3) = all_32_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (91) with all_52_3, all_32_0, e3,
% 240.08/46.76  | | | | | | | | | | | | | | | | | |              e0, simplifying with (26), (261) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (262)  all_52_3 = all_32_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (262) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (263)  all_54_12 = all_32_0
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | REDUCE: (54), (262) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (264)   ~ (all_52_11 = all_32_0)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | SIMP: (264) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | |   (265)   ~ (all_52_11 = all_32_0)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | |   (266)  all_54_14 = e3
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (106), (266) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | |   (267)  all_52_11 = e3
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | REDUCE: (109), (267) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | |   (268)   ~ (all_52_9 = e3)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | REDUCE: (265), (267) imply:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | |   (269)   ~ (all_32_0 = e3)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | SIMP: (269) implies:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | |   (270)   ~ (all_32_0 = e3)
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |   (271)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 240.08/46.76  | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (48), (91), (119), (268), (271) are
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1821.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | |   (272)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | |   (273)  all_58_8 = e3 & op(e1, e1) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | |   (274)  op(e1, e1) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (77), (91), (274) are inconsistent by
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2206.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | |   (275)  all_58_14 = e3 & op(e0, e1) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | |   (276)  all_58_14 = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | |   (277)  op(e0, e1) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | |   (278)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_58_4 = e0 & op(e3, e1) = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | |   (280)  op(e3, e1) = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (98), (119), (280) are inconsistent by
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2089.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | |   (281)  all_58_5 = e0 & op(e2, e1) = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | |   (282)  op(e2, e1) = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | |   (283)  all_58_15 = e0 & op(e0, e0) = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (283) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | |   (284)  op(e0, e0) = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (91), (102), (284) are inconsistent by
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2301.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | |   (285)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | |   (286)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_54_6 = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (268), (287) are inconsistent by sub-proof
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | |            #1825.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (288)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_54_12 = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (289) imply:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)  all_32_0 = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (290) imply:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)  $false
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)  all_58_12 = e0 & op(e0, e3) = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)  op(e0, e3) = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  op(e3, e2) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (20), (76), (91), (95), (98), (107),
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (175), (277), (298) are inconsistent by sub-proof
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #223.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (300)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          e2
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  op(e3, e2) = e2
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (69), (74), (91), (98), (119), (135),
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (301) are inconsistent by sub-proof #388.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  op(e1, e3) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (91), (92), (303) are inconsistent by
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2335.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)   ~ (all_56_31 = e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  op(e1, e3) = e1
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (306) imply:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)   ~ (e3 = e2)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (309)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  all_58_0 = e3 & op(e3, e3) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  op(e3, e3) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (69), (91), (311) are inconsistent by
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2194.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_58_2 = e3 & op(e2, e3) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (312) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  op(e2, e3) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_3 & $i(all_56_3))
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  op(e3, all_56_1) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (316) imply:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  op(e3, e2) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (20), (76), (91), (95), (98), (107),
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (175), (277), (317) are inconsistent by sub-proof
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #223.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_3 & $i(all_56_3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  op(e2, e3) = all_56_3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)  op(e2, all_56_3) = e2
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (91), (313), (319), (320) are inconsistent
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2262.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_7 & $i(all_56_7))
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (322)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_5 & $i(all_56_5)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (63), (77), (91), (112), (171), (292),
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (307), (322) are inconsistent by sub-proof #1702.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (323)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_7 & $i(all_56_7)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  op(e0, e3) = all_56_7
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  op(e0, all_56_7) = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (52), (91), (102), (175), (294), (324),
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (325) are inconsistent by sub-proof #222.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  all_58_6 = e3 & op(e1, e3) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (327) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  op(e1, e3) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (91), (307), (328) are inconsistent by
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2225.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  all_58_12 = e3 & op(e0, e3) = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_58_12 = e3
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (91), (98), (175), (276), (286), (330) are
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1870.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (62), (91), (154), (294), (331) are
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #220.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (332)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (333)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (334)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (335)  op(e2, e1) = e2
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (91), (282), (335) are inconsistent by
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1906.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (336)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (48), (80), (91), (105), (336) are
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (337)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (338)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (339)  op(e2, e0) = e0
% 240.08/46.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (65), (91), (103), (105), (114), (288),
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (339) are inconsistent by sub-proof #459.
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (340)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e1
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (342)  op(e0, e1) = e1
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (91), (173), (342) are inconsistent by
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2272.
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (343)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e0
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (343) implies:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (344)  op(e0, e1) = e0
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (91), (277), (344) are inconsistent by
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2164.
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (345)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (346)  all_58_13 = e0 & op(e0, e2) = e0
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (346) implies:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (347)  op(e0, e2) = e0
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (91), (152), (347) are inconsistent by
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2252.
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (348)  all_58_14 = e0 & op(e0, e1) = e0
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (348) implies:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (349)  op(e0, e1) = e0
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (91), (277), (349) are inconsistent by
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2164.
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | |   (350)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (77), (91), (277), (350) are
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2163.
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | |   (351)   ~ (all_54_14 = e3)
% 240.08/46.78  | | | | | | | | | | | | | | | | | | |   (352)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | REDUCE: (106), (351) imply:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | |   (353)   ~ (all_52_11 = e3)
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (11), (12), (13), (24), (28),
% 240.08/46.78  | | | | | | | | | | | | | | | | | | |            (31), (35), (41), (43), (51), (52), (68), (69),
% 240.08/46.78  | | | | | | | | | | | | | | | | | | |            (73), (77), (78), (80), (91), (96), (98), (102),
% 240.08/46.78  | | | | | | | | | | | | | | | | | | |            (104), (106), (108), (110), (112), (119), (146),
% 240.08/46.78  | | | | | | | | | | | | | | | | | | |            (173), (175), (245), (246), (248), (352), (353)
% 240.08/46.78  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #225.
% 240.08/46.78  | | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.78  | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | |   (354)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 240.08/46.78  | | | | | | | | | | | | | | | | | |          $i(all_32_1)
% 240.08/46.78  | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | ALPHA: (354) implies:
% 240.08/46.78  | | | | | | | | | | | | | | | | | |   (355)   ~ (all_32_1 = e0)
% 240.08/46.78  | | | | | | | | | | | | | | | | | |   (356)  op(e3, e2) = all_32_1
% 240.08/46.78  | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (156), (239), (355), (356) are inconsistent
% 240.08/46.78  | | | | | | | | | | | | | | | | | |            by sub-proof #2065.
% 240.08/46.78  | | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | Case 2:
% 240.08/46.78  | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | |   (357)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 &
% 240.08/46.78  | | | | | | | | | | | | | | | | |          $i(all_44_1)
% 240.08/46.78  | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | ALPHA: (357) implies:
% 240.08/46.78  | | | | | | | | | | | | | | | | |   (358)   ~ (all_44_1 = e1)
% 240.08/46.78  | | | | | | | | | | | | | | | | |   (359)  op(e0, e2) = all_44_1
% 240.08/46.78  | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (175), (358), (359) are inconsistent by
% 240.08/46.78  | | | | | | | | | | | | | | | | |            sub-proof #230.
% 240.08/46.78  | | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | Case 2:
% 240.08/46.78  | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | |   (360)  all_54_13 = e0
% 240.08/46.78  | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | | REF_CLOSE: (14), (152), (360) are inconsistent by sub-proof
% 240.08/46.78  | | | | | | | | | | | | | |            #2008.
% 240.08/46.78  | | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | Case 2:
% 240.08/46.78  | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | |   (361)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 240.08/46.78  | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | | REF_CLOSE: (30), (70), (90), (154), (361) are inconsistent by
% 240.08/46.78  | | | | | | | | | | | |            sub-proof #2286.
% 240.08/46.78  | | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | | 
% 240.08/46.78  | | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | | 
% 240.08/46.78  | | | | | | | | End of split
% 240.08/46.78  | | | | | | | | 
% 240.08/46.78  | | | | | | | End of split
% 240.08/46.78  | | | | | | | 
% 240.08/46.78  | | | | | | End of split
% 240.08/46.78  | | | | | | 
% 240.08/46.78  | | | | | End of split
% 240.08/46.78  | | | | | 
% 240.08/46.78  | | | | End of split
% 240.08/46.78  | | | | 
% 240.08/46.78  | | | End of split
% 240.08/46.78  | | | 
% 240.08/46.78  | | Case 2:
% 240.08/46.78  | | | 
% 240.08/46.78  | | |   (362)  all_58_9 = e1 & op(e3, e0) = e1
% 240.08/46.78  | | | 
% 240.08/46.78  | | | REF_CLOSE: (30), (62), (91), (362) are inconsistent by sub-proof #2278.
% 240.08/46.78  | | | 
% 240.08/46.78  | | End of split
% 240.08/46.78  | | 
% 240.08/46.78  | End of split
% 240.08/46.78  | 
% 240.08/46.78  End of proof
% 240.08/46.78  
% 240.08/46.78  Sub-proof #220 shows that the following formulas are inconsistent:
% 240.08/46.78  ----------------------------------------------------------------
% 240.08/46.78    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.08/46.78             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.08/46.78           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 240.08/46.78           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.78           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.78    (2)   ~ (e3 = e0)
% 240.08/46.78    (3)   ~ (all_52_12 = e0)
% 240.08/46.78    (4)  op(e0, e3) = e0
% 240.08/46.78    (5)  op(e3, e0) = all_52_12
% 240.08/46.78    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.78  
% 240.08/46.78  Begin of proof
% 240.08/46.78  | 
% 240.08/46.78  | BETA: splitting (1) gives:
% 240.08/46.78  | 
% 240.08/46.78  | Case 1:
% 240.08/46.78  | | 
% 240.08/46.78  | |   (7)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.08/46.78  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.08/46.78  | |        op(e0, e3) = e3
% 240.08/46.78  | | 
% 240.08/46.78  | | ALPHA: (7) implies:
% 240.08/46.78  | |   (8)  op(e0, e3) = e3
% 240.08/46.78  | | 
% 240.08/46.78  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #221.
% 240.08/46.78  | | 
% 240.08/46.78  | Case 2:
% 240.08/46.78  | | 
% 240.08/46.78  | |   (9)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.08/46.78  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 240.08/46.78  | |        op(e0, e3) = e0
% 240.08/46.78  | | 
% 240.08/46.78  | | ALPHA: (9) implies:
% 240.08/46.78  | |   (10)  op(e3, e0) = e0
% 240.08/46.78  | | 
% 240.08/46.78  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #2258.
% 240.08/46.78  | | 
% 240.08/46.78  | End of split
% 240.08/46.78  | 
% 240.08/46.78  End of proof
% 240.08/46.78  
% 240.08/46.78  Sub-proof #221 shows that the following formulas are inconsistent:
% 240.08/46.78  ----------------------------------------------------------------
% 240.08/46.78    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.78    (2)  op(e0, e3) = e3
% 240.08/46.78    (3)  op(e0, e3) = e0
% 240.08/46.78    (4)   ~ (e3 = e0)
% 240.08/46.78  
% 240.08/46.78  Begin of proof
% 240.08/46.78  | 
% 240.08/46.78  | GROUND_INST: instantiating (1) with e3, e0, e3, e0, simplifying with (2), (3)
% 240.08/46.78  |              gives:
% 240.08/46.78  |   (5)  e3 = e0
% 240.08/46.78  | 
% 240.08/46.78  | REDUCE: (4), (5) imply:
% 240.08/46.78  |   (6)  $false
% 240.08/46.78  | 
% 240.08/46.78  | CLOSE: (6) is inconsistent.
% 240.08/46.78  | 
% 240.08/46.78  End of proof
% 240.08/46.78  
% 240.08/46.78  Sub-proof #222 shows that the following formulas are inconsistent:
% 240.08/46.78  ----------------------------------------------------------------
% 240.08/46.78    (1)   ~ (e2 = e0)
% 240.08/46.78    (2)  op(e0, e3) = all_56_7
% 240.08/46.78    (3)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) = all_44_1
% 240.08/46.78           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2) =
% 240.08/46.78           all_44_1 & $i(all_44_1))
% 240.08/46.78    (4)  op(e0, e3) = e0
% 240.08/46.78    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.78    (6)  op(e0, all_56_7) = e0
% 240.08/46.78    (7)  op(e0, e0) = e2
% 240.08/46.78    (8)  op(e0, e2) = e1
% 240.08/46.78  
% 240.08/46.78  Begin of proof
% 240.08/46.78  | 
% 240.08/46.78  | BETA: splitting (3) gives:
% 240.08/46.78  | 
% 240.08/46.78  | Case 1:
% 240.08/46.78  | | 
% 240.08/46.78  | | 
% 240.08/46.78  | | GROUND_INST: instantiating (5) with e0, all_56_7, e3, e0, simplifying with
% 240.08/46.78  | |              (2), (4) gives:
% 240.08/46.78  | |   (9)  all_56_7 = e0
% 240.08/46.78  | | 
% 240.08/46.78  | | REDUCE: (6), (9) imply:
% 240.08/46.78  | |   (10)  op(e0, e0) = e0
% 240.08/46.78  | | 
% 240.08/46.78  | | REF_CLOSE: (1), (5), (7), (10) are inconsistent by sub-proof #2301.
% 240.08/46.78  | | 
% 240.08/46.78  | Case 2:
% 240.08/46.78  | | 
% 240.08/46.78  | |   (11)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 & $i(all_44_1)
% 240.08/46.78  | | 
% 240.08/46.78  | | ALPHA: (11) implies:
% 240.08/46.78  | |   (12)   ~ (all_44_1 = e1)
% 240.08/46.78  | |   (13)  op(e0, e2) = all_44_1
% 240.08/46.78  | | 
% 240.08/46.78  | | REF_CLOSE: (5), (8), (12), (13) are inconsistent by sub-proof #230.
% 240.08/46.78  | | 
% 240.08/46.78  | End of split
% 240.08/46.78  | 
% 240.08/46.78  End of proof
% 240.08/46.78  
% 240.08/46.78  Sub-proof #223 shows that the following formulas are inconsistent:
% 240.08/46.78  ----------------------------------------------------------------
% 240.08/46.78    (1)   ~ (e3 = e0)
% 240.08/46.78    (2)   ~ (e2 = e0)
% 240.08/46.78    (3)  op(e0, e1) = e3
% 240.08/46.78    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.08/46.78         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.08/46.78    (5)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) = all_40_1
% 240.08/46.78           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2) =
% 240.08/46.78           all_40_1 & $i(all_40_1))
% 240.08/46.78    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.78    (7)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) = all_36_1
% 240.08/46.78           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2) =
% 240.08/46.78           all_36_1 & $i(all_36_1))
% 240.08/46.78    (8)   ~ (e1 = e0)
% 240.08/46.78    (9)  op(e3, e2) = e3
% 240.08/46.78    (10)  op(e0, e2) = e1
% 240.08/46.78    (11)  op(e2, e2) = e2
% 240.08/46.78  
% 240.08/46.78  Begin of proof
% 240.08/46.78  | 
% 240.08/46.78  | BETA: splitting (4) gives:
% 240.08/46.78  | 
% 240.08/46.78  | Case 1:
% 240.08/46.78  | | 
% 240.08/46.78  | |   (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 240.08/46.78  | |           e0)
% 240.08/46.78  | | 
% 240.08/46.78  | | REF_CLOSE: (1), (2), (6), (9), (11), (12) are inconsistent by sub-proof
% 240.08/46.78  | |            #409.
% 240.08/46.78  | | 
% 240.08/46.78  | Case 2:
% 240.08/46.78  | | 
% 240.08/46.78  | |   (13)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.08/46.78  | |           e0)
% 240.08/46.78  | | 
% 240.08/46.78  | | BETA: splitting (13) gives:
% 240.08/46.78  | | 
% 240.08/46.78  | | Case 1:
% 240.08/46.78  | | | 
% 240.08/46.78  | | |   (14)  all_58_7 = e0 & op(e1, e2) = e0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | REF_CLOSE: (3), (5), (6), (7), (14) are inconsistent by sub-proof #224.
% 240.08/46.78  | | | 
% 240.08/46.78  | | Case 2:
% 240.08/46.78  | | | 
% 240.08/46.78  | | |   (15)  all_58_13 = e0 & op(e0, e2) = e0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | ALPHA: (15) implies:
% 240.08/46.78  | | |   (16)  op(e0, e2) = e0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | REF_CLOSE: (6), (8), (10), (16) are inconsistent by sub-proof #1872.
% 240.08/46.78  | | | 
% 240.08/46.78  | | End of split
% 240.08/46.78  | | 
% 240.08/46.78  | End of split
% 240.08/46.78  | 
% 240.08/46.78  End of proof
% 240.08/46.78  
% 240.08/46.78  Sub-proof #224 shows that the following formulas are inconsistent:
% 240.08/46.78  ----------------------------------------------------------------
% 240.08/46.78    (1)  all_58_7 = e0 & op(e1, e2) = e0
% 240.08/46.78    (2)  op(e0, e1) = e3
% 240.08/46.78    (3)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) = all_40_1
% 240.08/46.78           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2) =
% 240.08/46.78           all_40_1 & $i(all_40_1))
% 240.08/46.78    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.78    (5)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) = all_36_1
% 240.08/46.78           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2) =
% 240.08/46.78           all_36_1 & $i(all_36_1))
% 240.08/46.78  
% 240.08/46.78  Begin of proof
% 240.08/46.78  | 
% 240.08/46.78  | ALPHA: (1) implies:
% 240.08/46.78  |   (6)  op(e1, e2) = e0
% 240.08/46.78  | 
% 240.08/46.78  | BETA: splitting (3) gives:
% 240.08/46.78  | 
% 240.08/46.78  | Case 1:
% 240.08/46.78  | | 
% 240.08/46.78  | |   (7)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 240.08/46.78  | |        all_40_1 & $i(all_40_0) & $i(all_40_1)
% 240.08/46.78  | | 
% 240.08/46.78  | | ALPHA: (7) implies:
% 240.08/46.78  | |   (8)  op(e1, e2) = all_40_1
% 240.08/46.78  | |   (9)  op(all_40_1, e1) = all_40_0
% 240.08/46.78  | | 
% 240.08/46.78  | | BETA: splitting (5) gives:
% 240.08/46.78  | | 
% 240.08/46.78  | | Case 1:
% 240.08/46.78  | | | 
% 240.08/46.78  | | |   (10)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 240.08/46.78  | | |         all_36_1 & $i(all_36_0) & $i(all_36_1)
% 240.08/46.78  | | | 
% 240.08/46.78  | | | ALPHA: (10) implies:
% 240.08/46.78  | | |   (11)   ~ (all_36_0 = e3)
% 240.08/46.78  | | |   (12)  op(e1, e2) = all_36_1
% 240.08/46.78  | | |   (13)  op(all_36_1, e1) = all_36_0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | GROUND_INST: instantiating (4) with e0, all_40_1, e2, e1, simplifying with
% 240.08/46.78  | | |              (6), (8) gives:
% 240.08/46.78  | | |   (14)  all_40_1 = e0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | GROUND_INST: instantiating (4) with all_36_1, all_40_1, e2, e1,
% 240.08/46.78  | | |              simplifying with (8), (12) gives:
% 240.08/46.78  | | |   (15)  all_40_1 = all_36_1
% 240.08/46.78  | | | 
% 240.08/46.78  | | | COMBINE_EQS: (14), (15) imply:
% 240.08/46.78  | | |   (16)  all_36_1 = e0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | REDUCE: (9), (14) imply:
% 240.08/46.78  | | |   (17)  op(e0, e1) = all_40_0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | REDUCE: (13), (16) imply:
% 240.08/46.78  | | |   (18)  op(e0, e1) = all_36_0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | GROUND_INST: instantiating (4) with e3, all_40_0, e1, e0, simplifying with
% 240.08/46.78  | | |              (2), (17) gives:
% 240.08/46.78  | | |   (19)  all_40_0 = e3
% 240.08/46.78  | | | 
% 240.08/46.78  | | | GROUND_INST: instantiating (4) with all_36_0, all_40_0, e1, e0,
% 240.08/46.78  | | |              simplifying with (17), (18) gives:
% 240.08/46.78  | | |   (20)  all_40_0 = all_36_0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | COMBINE_EQS: (19), (20) imply:
% 240.08/46.78  | | |   (21)  all_36_0 = e3
% 240.08/46.78  | | | 
% 240.08/46.78  | | | REDUCE: (11), (21) imply:
% 240.08/46.78  | | |   (22)  $false
% 240.08/46.78  | | | 
% 240.08/46.78  | | | CLOSE: (22) is inconsistent.
% 240.08/46.78  | | | 
% 240.08/46.78  | | Case 2:
% 240.08/46.78  | | | 
% 240.08/46.78  | | |   (23)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1)
% 240.08/46.78  | | | 
% 240.08/46.78  | | | ALPHA: (23) implies:
% 240.08/46.78  | | |   (24)   ~ (all_36_1 = e0)
% 240.08/46.78  | | |   (25)  op(e1, e2) = all_36_1
% 240.08/46.78  | | | 
% 240.08/46.78  | | | REF_CLOSE: (3), (4), (6), (24), (25) are inconsistent by sub-proof #782.
% 240.08/46.78  | | | 
% 240.08/46.78  | | End of split
% 240.08/46.78  | | 
% 240.08/46.78  | Case 2:
% 240.08/46.78  | | 
% 240.08/46.78  | |   (26)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 240.08/46.78  | | 
% 240.08/46.78  | | ALPHA: (26) implies:
% 240.08/46.78  | |   (27)  op(e1, e2) = all_40_1
% 240.08/46.78  | | 
% 240.08/46.78  | | BETA: splitting (5) gives:
% 240.08/46.78  | | 
% 240.08/46.78  | | Case 1:
% 240.08/46.78  | | | 
% 240.08/46.78  | | |   (28)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 240.08/46.78  | | |         all_36_1 & $i(all_36_0) & $i(all_36_1)
% 240.08/46.78  | | | 
% 240.08/46.78  | | | ALPHA: (28) implies:
% 240.08/46.78  | | |   (29)   ~ (all_36_0 = e3)
% 240.08/46.78  | | |   (30)  op(e1, e2) = all_36_1
% 240.08/46.78  | | |   (31)  op(all_36_1, e1) = all_36_0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | GROUND_INST: instantiating (4) with e0, all_40_1, e2, e1, simplifying with
% 240.08/46.78  | | |              (6), (27) gives:
% 240.08/46.78  | | |   (32)  all_40_1 = e0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | GROUND_INST: instantiating (4) with all_36_1, all_40_1, e2, e1,
% 240.08/46.78  | | |              simplifying with (27), (30) gives:
% 240.08/46.78  | | |   (33)  all_40_1 = all_36_1
% 240.08/46.78  | | | 
% 240.08/46.78  | | | COMBINE_EQS: (32), (33) imply:
% 240.08/46.78  | | |   (34)  all_36_1 = e0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | REDUCE: (31), (34) imply:
% 240.08/46.78  | | |   (35)  op(e0, e1) = all_36_0
% 240.08/46.78  | | | 
% 240.08/46.78  | | | GROUND_INST: instantiating (4) with e3, all_36_0, e1, e0, simplifying with
% 240.08/46.78  | | |              (2), (35) gives:
% 240.08/46.78  | | |   (36)  all_36_0 = e3
% 240.08/46.78  | | | 
% 240.08/46.78  | | | REDUCE: (29), (36) imply:
% 240.08/46.78  | | |   (37)  $false
% 240.08/46.78  | | | 
% 240.08/46.78  | | | CLOSE: (37) is inconsistent.
% 240.08/46.78  | | | 
% 240.08/46.78  | | Case 2:
% 240.08/46.78  | | | 
% 240.08/46.78  | | |   (38)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1)
% 240.08/46.78  | | | 
% 240.08/46.78  | | | ALPHA: (38) implies:
% 240.08/46.79  | | |   (39)   ~ (all_36_1 = e0)
% 240.08/46.79  | | |   (40)  op(e1, e2) = all_36_1
% 240.08/46.79  | | | 
% 240.08/46.79  | | | REF_CLOSE: (3), (4), (6), (39), (40) are inconsistent by sub-proof #782.
% 240.08/46.79  | | | 
% 240.08/46.79  | | End of split
% 240.08/46.79  | | 
% 240.08/46.79  | End of split
% 240.08/46.79  | 
% 240.08/46.79  End of proof
% 240.08/46.79  
% 240.08/46.79  Sub-proof #225 shows that the following formulas are inconsistent:
% 240.08/46.79  ----------------------------------------------------------------
% 240.08/46.79    (1)  all_56_21 = e2
% 240.08/46.79    (2)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.08/46.79           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.08/46.79           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.08/46.79           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.08/46.79           & $i(all_56_23))
% 240.08/46.79    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.08/46.79         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.79    (4)   ~ (e3 = e0)
% 240.08/46.79    (5)  op(e0, e1) = all_52_11
% 240.08/46.79    (6)   ~ (e2 = e0)
% 240.08/46.79    (7)   ~ (all_52_11 = e2)
% 240.08/46.79    (8)   ~ (all_52_11 = e1)
% 240.08/46.79    (9)   ~ (all_52_7 = e3)
% 240.08/46.79    (10)   ~ (e3 = e1)
% 240.08/46.79    (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.08/46.79          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.79    (12)  op(e1, e2) = e3
% 240.08/46.79    (13)  op(e0, e2) = all_4_1
% 240.08/46.79    (14)   ~ (all_4_1 = e3)
% 240.08/46.79    (15)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.08/46.79    (16)  all_58_15 = e2
% 240.08/46.79    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.08/46.79              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.08/46.79                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.08/46.79                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.08/46.79    (18)   ~ (all_52_11 = e3)
% 240.08/46.79    (19)   ~ (e3 = e2)
% 240.08/46.79    (20)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 240.08/46.79            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 240.08/46.79              e2) = all_44_1 & $i(all_44_1))
% 240.08/46.79    (21)  op(e3, e1) = e1
% 240.08/46.79    (22)  op(e2, e3) = all_52_1
% 240.08/46.79    (23)  op(e3, e3) = e2
% 240.08/46.79    (24)  op(e1, e2) = all_36_1
% 240.08/46.79    (25)  op(e1, e1) = e2
% 240.08/46.79    (26)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.08/46.79          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.08/46.79    (27)  op(e0, e2) = all_52_7
% 240.08/46.79    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.79    (29)  op(e0, e2) = all_44_1
% 240.08/46.79    (30)  op(e1, e2) = all_40_1
% 240.08/46.79    (31)   ~ (e1 = e0)
% 240.08/46.79    (32)  all_58_13 = e1
% 240.08/46.79    (33)  op(e0, e0) = e2
% 240.08/46.79    (34)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.79          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.08/46.79            e1)
% 240.08/46.79    (35)  op(e0, e2) = e1
% 240.08/46.79    (36)  all_54_14 = all_52_11
% 240.08/46.79    (37)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.79          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.08/46.79            e2)
% 240.08/46.79    (38)   ~ (all_52_1 = e2)
% 240.08/46.79    (39)   ~ (e2 = e1)
% 240.08/46.79  
% 240.08/46.79  Begin of proof
% 240.08/46.79  | 
% 240.08/46.79  | BETA: splitting (3) gives:
% 240.08/46.79  | 
% 240.08/46.79  | Case 1:
% 240.08/46.79  | | 
% 240.08/46.79  | |   (40)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 240.08/46.79  | |           e3)
% 240.08/46.79  | | 
% 240.08/46.79  | | BETA: splitting (40) gives:
% 240.08/46.79  | | 
% 240.08/46.79  | | Case 1:
% 240.08/46.79  | | | 
% 240.08/46.79  | | |   (41)  all_58_12 = e3 & op(e0, e3) = e3
% 240.08/46.79  | | | 
% 240.08/46.79  | | | ALPHA: (41) implies:
% 240.08/46.79  | | |   (42)  all_58_12 = e3
% 240.08/46.79  | | | 
% 240.08/46.79  | | | BETA: splitting (26) gives:
% 240.08/46.79  | | | 
% 240.08/46.79  | | | Case 1:
% 240.08/46.79  | | | | 
% 240.08/46.79  | | | |   (43)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 240.08/46.79  | | | |           = e3)
% 240.08/46.79  | | | | 
% 240.08/46.79  | | | | BETA: splitting (43) gives:
% 240.08/46.79  | | | | 
% 240.08/46.79  | | | | Case 1:
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | |   (44)  all_58_4 = e3 & op(e3, e1) = e3
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | | ALPHA: (44) implies:
% 240.08/46.79  | | | | |   (45)  op(e3, e1) = e3
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | | REF_CLOSE: (10), (21), (28), (45) are inconsistent by sub-proof #1823.
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | Case 2:
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | |   (46)  all_58_5 = e3 & op(e2, e1) = e3
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | | ALPHA: (46) implies:
% 240.08/46.79  | | | | |   (47)  all_58_5 = e3
% 240.08/46.79  | | | | |   (48)  op(e2, e1) = e3
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | | BETA: splitting (11) gives:
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | | Case 1:
% 240.08/46.79  | | | | | | 
% 240.08/46.79  | | | | | |   (49)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 240.08/46.79  | | | | | |             e1) = e0)
% 240.08/46.79  | | | | | | 
% 240.08/46.79  | | | | | | BETA: splitting (49) gives:
% 240.08/46.79  | | | | | | 
% 240.08/46.79  | | | | | | Case 1:
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | |   (50)  all_58_4 = e0 & op(e3, e1) = e0
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | | ALPHA: (50) implies:
% 240.08/46.79  | | | | | | |   (51)  op(e3, e1) = e0
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | | REF_CLOSE: (21), (28), (31), (51) are inconsistent by sub-proof
% 240.08/46.79  | | | | | | |            #2089.
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | Case 2:
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | |   (52)  all_58_5 = e0 & op(e2, e1) = e0
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | | REF_CLOSE: (4), (47), (52) are inconsistent by sub-proof #2169.
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | End of split
% 240.08/46.79  | | | | | | 
% 240.08/46.79  | | | | | Case 2:
% 240.08/46.79  | | | | | | 
% 240.08/46.79  | | | | | |   (53)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 240.08/46.79  | | | | | |             e1) = e0)
% 240.08/46.79  | | | | | | 
% 240.08/46.79  | | | | | | BETA: splitting (53) gives:
% 240.08/46.79  | | | | | | 
% 240.08/46.79  | | | | | | Case 1:
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | |   (54)  all_58_8 = e0 & op(e1, e1) = e0
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | | ALPHA: (54) implies:
% 240.08/46.79  | | | | | | |   (55)  op(e1, e1) = e0
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | | REF_CLOSE: (6), (25), (28), (55) are inconsistent by sub-proof
% 240.08/46.79  | | | | | | |            #2211.
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | Case 2:
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | |   (56)  all_58_14 = e0 & op(e0, e1) = e0
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | | ALPHA: (56) implies:
% 240.08/46.79  | | | | | | |   (57)  all_58_14 = e0
% 240.08/46.79  | | | | | | |   (58)  op(e0, e1) = e0
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | | BETA: splitting (17) gives:
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | | Case 1:
% 240.08/46.79  | | | | | | | | 
% 240.08/46.79  | | | | | | | |   (59)  all_58_15 = e0 & op(e0, e0) = e0
% 240.08/46.79  | | | | | | | | 
% 240.08/46.79  | | | | | | | | ALPHA: (59) implies:
% 240.08/46.79  | | | | | | | |   (60)  all_58_15 = e0
% 240.08/46.79  | | | | | | | |   (61)  op(e0, e0) = e0
% 240.08/46.79  | | | | | | | | 
% 240.08/46.79  | | | | | | | | REF_CLOSE: (3), (4), (6), (9), (10), (19), (27), (28), (31),
% 240.08/46.79  | | | | | | | |            (34), (37), (39), (42), (57), (58), (60), (61) are
% 240.08/46.79  | | | | | | | |            inconsistent by sub-proof #859.
% 240.08/46.79  | | | | | | | | 
% 240.08/46.79  | | | | | | | Case 2:
% 240.08/46.79  | | | | | | | | 
% 240.08/46.79  | | | | | | | |   (62)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 240.08/46.79  | | | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.08/46.79  | | | | | | | |             e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 240.08/46.79  | | | | | | | |           (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 240.08/46.79  | | | | | | | |             op(e0, e1) = e0))
% 240.08/46.79  | | | | | | | | 
% 240.08/46.79  | | | | | | | | ALPHA: (62) implies:
% 240.08/46.79  | | | | | | | |   (63)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.08/46.79  | | | | | | | |           op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.79  | | | | | | | | 
% 240.08/46.79  | | | | | | | | BETA: splitting (2) gives:
% 240.08/46.79  | | | | | | | | 
% 240.08/46.79  | | | | | | | | Case 1:
% 240.08/46.79  | | | | | | | | | 
% 240.08/46.79  | | | | | | | | |   (64)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1)
% 240.08/46.79  | | | | | | | | |           = all_56_17 & $i(all_56_17)) | (all_56_18 = e2 &
% 240.08/46.79  | | | | | | | | |           op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 240.08/46.79  | | | | | | | | |           $i(all_56_19))
% 240.08/46.79  | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | BETA: splitting (64) gives:
% 240.08/46.79  | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | Case 1:
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | |   (65)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1)
% 240.08/46.79  | | | | | | | | | |         = all_56_17 & $i(all_56_17)
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | | ALPHA: (65) implies:
% 240.08/46.79  | | | | | | | | | |   (66)  op(e3, e1) = all_56_17
% 240.08/46.79  | | | | | | | | | |   (67)  op(e3, all_56_17) = e3
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | | GROUND_INST: instantiating (28) with e1, all_56_17, e1, e3,
% 240.08/46.79  | | | | | | | | | |              simplifying with (21), (66) gives:
% 240.08/46.79  | | | | | | | | | |   (68)  all_56_17 = e1
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | | REDUCE: (67), (68) imply:
% 240.08/46.79  | | | | | | | | | |   (69)  op(e3, e1) = e3
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | | REF_CLOSE: (19), (23), (28), (66), (67), (69) are
% 240.08/46.79  | | | | | | | | | |            inconsistent by sub-proof #2098.
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | Case 2:
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | |   (70)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.08/46.79  | | | | | | | | | |         = all_56_19 & $i(all_56_19)
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | | REF_CLOSE: (7), (8), (15), (22), (28), (36), (38), (48), (70)
% 240.08/46.79  | | | | | | | | | |            are inconsistent by sub-proof #1396.
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | End of split
% 240.08/46.79  | | | | | | | | | 
% 240.08/46.79  | | | | | | | | Case 2:
% 240.08/46.79  | | | | | | | | | 
% 240.08/46.79  | | | | | | | | |   (71)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22
% 240.08/46.79  | | | | | | | | |           = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 240.08/46.79  | | | | | | | | |           all_56_23 & $i(all_56_23))
% 240.08/46.79  | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | BETA: splitting (71) gives:
% 240.08/46.79  | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | Case 1:
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | |   (72)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | | ALPHA: (72) implies:
% 240.08/46.79  | | | | | | | | | |   (73)  op(e1, all_56_21) = e1
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | | REDUCE: (1), (73) imply:
% 240.08/46.79  | | | | | | | | | |   (74)  op(e1, e2) = e1
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | | REF_CLOSE: (10), (12), (24), (28), (30), (74) are
% 240.08/46.79  | | | | | | | | | |            inconsistent by sub-proof #1701.
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | Case 2:
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | |   (75)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1)
% 240.08/46.79  | | | | | | | | | |         = all_56_23 & $i(all_56_23)
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | | ALPHA: (75) implies:
% 240.08/46.79  | | | | | | | | | |   (76)  op(e0, e1) = all_56_23
% 240.08/46.79  | | | | | | | | | |   (77)  op(e0, all_56_23) = e0
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | | REF_CLOSE: (3), (4), (6), (10), (19), (20), (28), (31), (32),
% 240.08/46.79  | | | | | | | | | |            (35), (37), (39), (57), (58), (63), (76), (77) are
% 240.08/46.79  | | | | | | | | | |            inconsistent by sub-proof #228.
% 240.08/46.79  | | | | | | | | | | 
% 240.08/46.79  | | | | | | | | | End of split
% 240.08/46.79  | | | | | | | | | 
% 240.08/46.79  | | | | | | | | End of split
% 240.08/46.79  | | | | | | | | 
% 240.08/46.79  | | | | | | | End of split
% 240.08/46.79  | | | | | | | 
% 240.08/46.79  | | | | | | End of split
% 240.08/46.79  | | | | | | 
% 240.08/46.79  | | | | | End of split
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | End of split
% 240.08/46.79  | | | | 
% 240.08/46.79  | | | Case 2:
% 240.08/46.79  | | | | 
% 240.08/46.79  | | | |   (78)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1)
% 240.08/46.79  | | | |           = e3)
% 240.08/46.79  | | | | 
% 240.08/46.79  | | | | BETA: splitting (78) gives:
% 240.08/46.79  | | | | 
% 240.08/46.79  | | | | Case 1:
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | |   (79)  all_58_8 = e3 & op(e1, e1) = e3
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | | ALPHA: (79) implies:
% 240.08/46.79  | | | | |   (80)  op(e1, e1) = e3
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | | REF_CLOSE: (19), (25), (28), (80) are inconsistent by sub-proof #2206.
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | Case 2:
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | |   (81)  all_58_14 = e3 & op(e0, e1) = e3
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | | ALPHA: (81) implies:
% 240.08/46.79  | | | | |   (82)  all_58_14 = e3
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | | REF_CLOSE: (4), (6), (16), (17), (28), (31), (35), (42), (82) are
% 240.08/46.79  | | | | |            inconsistent by sub-proof #1869.
% 240.08/46.79  | | | | | 
% 240.08/46.79  | | | | End of split
% 240.08/46.79  | | | | 
% 240.08/46.79  | | | End of split
% 240.08/46.79  | | | 
% 240.08/46.79  | | Case 2:
% 240.08/46.79  | | | 
% 240.08/46.79  | | |   (83)  all_58_13 = e3 & op(e0, e2) = e3
% 240.08/46.79  | | | 
% 240.08/46.79  | | | ALPHA: (83) implies:
% 240.08/46.79  | | |   (84)  op(e0, e2) = e3
% 240.08/46.79  | | | 
% 240.08/46.79  | | | REF_CLOSE: (13), (14), (28), (29), (84) are inconsistent by sub-proof
% 240.08/46.79  | | |            #227.
% 240.08/46.79  | | | 
% 240.08/46.79  | | End of split
% 240.08/46.79  | | 
% 240.08/46.79  | Case 2:
% 240.08/46.79  | | 
% 240.08/46.79  | |   (85)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 240.08/46.79  | |           e3)
% 240.08/46.79  | | 
% 240.08/46.79  | | REF_CLOSE: (5), (18), (19), (28), (33), (85) are inconsistent by sub-proof
% 240.08/46.79  | |            #226.
% 240.08/46.79  | | 
% 240.08/46.79  | End of split
% 240.08/46.79  | 
% 240.08/46.79  End of proof
% 240.08/46.79  
% 240.08/46.79  Sub-proof #226 shows that the following formulas are inconsistent:
% 240.08/46.79  ----------------------------------------------------------------
% 240.08/46.79    (1)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.79    (2)  op(e0, e1) = all_52_11
% 240.08/46.79    (3)   ~ (all_52_11 = e3)
% 240.08/46.79    (4)   ~ (e3 = e2)
% 240.08/46.79    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.79    (6)  op(e0, e0) = e2
% 240.08/46.79  
% 240.08/46.79  Begin of proof
% 240.08/46.79  | 
% 240.08/46.79  | BETA: splitting (1) gives:
% 240.08/46.79  | 
% 240.08/46.79  | Case 1:
% 240.08/46.79  | | 
% 240.08/46.79  | |   (7)  all_58_14 = e3 & op(e0, e1) = e3
% 240.08/46.79  | | 
% 240.08/46.79  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #1647.
% 240.08/46.79  | | 
% 240.08/46.79  | Case 2:
% 240.08/46.79  | | 
% 240.08/46.79  | |   (8)  all_58_15 = e3 & op(e0, e0) = e3
% 240.08/46.79  | | 
% 240.08/46.79  | | ALPHA: (8) implies:
% 240.08/46.79  | |   (9)  op(e0, e0) = e3
% 240.08/46.79  | | 
% 240.08/46.79  | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #1388.
% 240.08/46.79  | | 
% 240.08/46.79  | End of split
% 240.08/46.79  | 
% 240.08/46.79  End of proof
% 240.08/46.79  
% 240.08/46.79  Sub-proof #227 shows that the following formulas are inconsistent:
% 240.08/46.79  ----------------------------------------------------------------
% 240.08/46.79    (1)  op(e0, e2) = e3
% 240.08/46.79    (2)  op(e0, e2) = all_4_1
% 240.08/46.79    (3)   ~ (all_4_1 = e3)
% 240.08/46.79    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.79    (5)  op(e0, e2) = all_44_1
% 240.08/46.79  
% 240.08/46.79  Begin of proof
% 240.08/46.79  | 
% 240.08/46.79  | GROUND_INST: instantiating (4) with all_4_1, all_44_1, e2, e0, simplifying
% 240.08/46.79  |              with (2), (5) gives:
% 240.08/46.79  |   (6)  all_44_1 = all_4_1
% 240.08/46.79  | 
% 240.08/46.79  | GROUND_INST: instantiating (4) with e3, all_44_1, e2, e0, simplifying with
% 240.08/46.79  |              (1), (5) gives:
% 240.08/46.79  |   (7)  all_44_1 = e3
% 240.08/46.79  | 
% 240.08/46.79  | COMBINE_EQS: (6), (7) imply:
% 240.08/46.79  |   (8)  all_4_1 = e3
% 240.08/46.79  | 
% 240.08/46.79  | SIMP: (8) implies:
% 240.08/46.79  |   (9)  all_4_1 = e3
% 240.08/46.79  | 
% 240.08/46.79  | REDUCE: (3), (9) imply:
% 240.08/46.79  |   (10)  $false
% 240.08/46.79  | 
% 240.08/46.79  | CLOSE: (10) is inconsistent.
% 240.08/46.79  | 
% 240.08/46.79  End of proof
% 240.08/46.79  
% 240.08/46.79  Sub-proof #228 shows that the following formulas are inconsistent:
% 240.08/46.79  ----------------------------------------------------------------
% 240.08/46.79    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.08/46.79         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.79    (2)   ~ (e3 = e0)
% 240.08/46.79    (3)  op(e0, e1) = all_56_23
% 240.08/46.79    (4)   ~ (e2 = e0)
% 240.08/46.79    (5)   ~ (e3 = e1)
% 240.08/46.79    (6)   ~ (e3 = e2)
% 240.08/46.79    (7)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) = all_44_1
% 240.08/46.79           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0, e2) =
% 240.08/46.79           all_44_1 & $i(all_44_1))
% 240.08/46.79    (8)  op(e0, e1) = e0
% 240.08/46.79    (9)  all_58_14 = e0
% 240.08/46.79    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.79    (11)  op(e0, all_56_23) = e0
% 240.08/46.79    (12)   ~ (e1 = e0)
% 240.08/46.79    (13)  all_58_13 = e1
% 240.08/46.79    (14)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.08/46.79          | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.79    (15)  op(e0, e2) = e1
% 240.08/46.79    (16)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.79          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.08/46.79            e2)
% 240.08/46.79    (17)   ~ (e2 = e1)
% 240.08/46.79  
% 240.08/46.79  Begin of proof
% 240.08/46.79  | 
% 240.08/46.79  | BETA: splitting (7) gives:
% 240.08/46.79  | 
% 240.08/46.79  | Case 1:
% 240.08/46.79  | | 
% 240.08/46.79  | | 
% 240.08/46.79  | | GROUND_INST: instantiating (10) with e0, all_56_23, e1, e0, simplifying with
% 240.08/46.79  | |              (3), (8) gives:
% 240.08/46.79  | |   (18)  all_56_23 = e0
% 240.08/46.79  | | 
% 240.08/46.79  | | REDUCE: (11), (18) imply:
% 240.08/46.79  | |   (19)  op(e0, e0) = e0
% 240.08/46.79  | | 
% 240.08/46.79  | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (10), (12), (13), (14), (16), (17),
% 240.08/46.79  | |            (19) are inconsistent by sub-proof #2075.
% 240.08/46.79  | | 
% 240.08/46.79  | Case 2:
% 240.08/46.79  | | 
% 240.08/46.79  | |   (20)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 & $i(all_44_1)
% 240.08/46.79  | | 
% 240.08/46.79  | | ALPHA: (20) implies:
% 240.08/46.79  | |   (21)   ~ (all_44_1 = e1)
% 240.08/46.79  | |   (22)  op(e0, e2) = all_44_1
% 240.08/46.79  | | 
% 240.08/46.79  | | REF_CLOSE: (10), (15), (21), (22) are inconsistent by sub-proof #230.
% 240.08/46.79  | | 
% 240.08/46.79  | End of split
% 240.08/46.79  | 
% 240.08/46.79  End of proof
% 240.08/46.79  
% 240.08/46.79  Sub-proof #229 shows that the following formulas are inconsistent:
% 240.08/46.79  ----------------------------------------------------------------
% 240.08/46.79    (1)  op(e1, e0) = all_52_14
% 240.08/46.79    (2)  all_54_11 = all_52_14
% 240.08/46.79    (3)  op(all_4_1, e0) = all_4_0
% 240.08/46.79    (4)  op(e1, e2) = e3
% 240.08/46.79    (5)  op(e0, e2) = all_4_1
% 240.08/46.79    (6)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.08/46.79    (7)   ~ (all_52_14 = e2)
% 240.08/46.79    (8)  op(e2, e1) = all_52_9
% 240.08/46.79    (9)   ~ (e3 = e2)
% 240.08/46.80    (10)  ( ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 240.08/46.80            all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e0,
% 240.08/46.80              e2) = all_44_1 & $i(all_44_1))
% 240.08/46.80    (11)  all_56_31 = e2
% 240.08/46.80    (12)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.08/46.80            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.08/46.80            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.08/46.80            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.08/46.80            op(e0, all_56_31) = e0)
% 240.08/46.80    (13)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.08/46.80    (14)  op(e3, e0) = e3
% 240.08/46.80    (15)  op(e3, e3) = e2
% 240.08/46.80    (16)   ~ (all_52_13 = e2)
% 240.08/46.80    (17)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 240.08/46.80            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 240.08/46.80              e2) = all_40_1 & $i(all_40_1))
% 240.08/46.80    (18)  all_54_7 = all_52_13
% 240.08/46.80    (19)  op(e0, e2) = all_52_7
% 240.08/46.80    (20)   ~ (all_52_13 = all_52_14)
% 240.08/46.80    (21)   ~ (all_4_0 = e1)
% 240.08/46.80    (22)   ~ (all_52_7 = e0)
% 240.08/46.80    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.80            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.80    (24)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 240.08/46.80            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 240.08/46.80              e2) = all_36_1 & $i(all_36_1))
% 240.08/46.80    (25)   ~ (all_52_13 = e3)
% 240.08/46.80    (26)  op(e2, e0) = all_52_13
% 240.08/46.80    (27)  op(e0, e2) = e1
% 240.08/46.80    (28)   ~ (all_52_9 = e2)
% 240.08/46.80  
% 240.08/46.80  Begin of proof
% 240.08/46.80  | 
% 240.08/46.80  | BETA: splitting (10) gives:
% 240.08/46.80  | 
% 240.08/46.80  | Case 1:
% 240.08/46.80  | | 
% 240.08/46.80  | |   (29)   ~ (all_44_0 = e3) & op(all_44_1, e0) = all_44_0 & op(e0, e2) =
% 240.08/46.80  | |         all_44_1 & $i(all_44_0) & $i(all_44_1)
% 240.08/46.80  | | 
% 240.08/46.80  | | ALPHA: (29) implies:
% 240.08/46.80  | |   (30)   ~ (all_44_0 = e3)
% 240.08/46.80  | |   (31)  op(e0, e2) = all_44_1
% 240.08/46.80  | |   (32)  op(all_44_1, e0) = all_44_0
% 240.08/46.80  | | 
% 240.08/46.80  | | GROUND_INST: instantiating (23) with all_4_1, all_44_1, e2, e0, simplifying
% 240.08/46.80  | |              with (5), (31) gives:
% 240.08/46.80  | |   (33)  all_44_1 = all_4_1
% 240.08/46.80  | | 
% 240.08/46.80  | | GROUND_INST: instantiating (23) with e1, all_44_1, e2, e0, simplifying with
% 240.08/46.80  | |              (27), (31) gives:
% 240.08/46.80  | |   (34)  all_44_1 = e1
% 240.08/46.80  | | 
% 240.08/46.80  | | COMBINE_EQS: (33), (34) imply:
% 240.08/46.80  | |   (35)  all_4_1 = e1
% 240.08/46.80  | | 
% 240.08/46.80  | | SIMP: (35) implies:
% 240.08/46.80  | |   (36)  all_4_1 = e1
% 240.08/46.80  | | 
% 240.08/46.80  | | REDUCE: (32), (34) imply:
% 240.08/46.80  | |   (37)  op(e1, e0) = all_44_0
% 240.08/46.80  | | 
% 240.08/46.80  | | REDUCE: (3), (36) imply:
% 240.08/46.80  | |   (38)  op(e1, e0) = all_4_0
% 240.08/46.80  | | 
% 240.08/46.80  | | GROUND_INST: instantiating (23) with all_52_14, all_4_0, e0, e1, simplifying
% 240.08/46.80  | |              with (1), (38) gives:
% 240.08/46.80  | |   (39)  all_52_14 = all_4_0
% 240.08/46.80  | | 
% 240.08/46.80  | | GROUND_INST: instantiating (23) with all_52_14, all_44_0, e0, e1,
% 240.08/46.80  | |              simplifying with (1), (37) gives:
% 240.08/46.80  | |   (40)  all_52_14 = all_44_0
% 240.08/46.80  | | 
% 240.08/46.80  | | COMBINE_EQS: (39), (40) imply:
% 240.08/46.80  | |   (41)  all_44_0 = all_4_0
% 240.08/46.80  | | 
% 240.08/46.80  | | COMBINE_EQS: (2), (39) imply:
% 240.08/46.80  | |   (42)  all_54_11 = all_4_0
% 240.08/46.80  | | 
% 240.08/46.80  | | REDUCE: (20), (39) imply:
% 240.08/46.80  | |   (43)   ~ (all_52_13 = all_4_0)
% 240.08/46.80  | | 
% 240.08/46.80  | | REDUCE: (7), (39) imply:
% 240.08/46.80  | |   (44)   ~ (all_4_0 = e2)
% 240.08/46.80  | | 
% 240.08/46.80  | | REDUCE: (30), (41) imply:
% 240.08/46.80  | |   (45)   ~ (all_4_0 = e3)
% 240.08/46.80  | | 
% 240.08/46.80  | | BETA: splitting (6) gives:
% 240.08/46.80  | | 
% 240.08/46.80  | | Case 1:
% 240.08/46.80  | | | 
% 240.08/46.80  | | |   (46)  all_54_11 = e3
% 240.08/46.80  | | | 
% 240.08/46.80  | | | REF_CLOSE: (42), (45), (46) are inconsistent by sub-proof #235.
% 240.08/46.80  | | | 
% 240.08/46.80  | | Case 2:
% 240.08/46.80  | | | 
% 240.08/46.80  | | |   (47)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.08/46.80  | | | 
% 240.08/46.80  | | | BETA: splitting (47) gives:
% 240.08/46.80  | | | 
% 240.08/46.80  | | | Case 1:
% 240.08/46.80  | | | | 
% 240.08/46.80  | | | |   (48)  all_54_11 = e2
% 240.08/46.80  | | | | 
% 240.08/46.80  | | | | REF_CLOSE: (42), (44), (48) are inconsistent by sub-proof #234.
% 240.08/46.80  | | | | 
% 240.08/46.80  | | | Case 2:
% 240.08/46.80  | | | | 
% 240.08/46.80  | | | |   (49)  all_54_11 = e1 | all_54_11 = e0
% 240.08/46.80  | | | | 
% 240.08/46.80  | | | | BETA: splitting (49) gives:
% 240.08/46.80  | | | | 
% 240.08/46.80  | | | | Case 1:
% 240.08/46.80  | | | | | 
% 240.08/46.80  | | | | |   (50)  all_54_11 = e1
% 240.08/46.80  | | | | | 
% 240.08/46.80  | | | | | REF_CLOSE: (21), (42), (50) are inconsistent by sub-proof #233.
% 240.08/46.80  | | | | | 
% 240.08/46.80  | | | | Case 2:
% 240.08/46.80  | | | | | 
% 240.08/46.80  | | | | |   (51)  all_54_11 = e0
% 240.08/46.80  | | | | | 
% 240.08/46.80  | | | | | COMBINE_EQS: (42), (51) imply:
% 240.08/46.80  | | | | |   (52)  all_4_0 = e0
% 240.08/46.80  | | | | | 
% 240.08/46.80  | | | | | SIMP: (52) implies:
% 240.08/46.80  | | | | |   (53)  all_4_0 = e0
% 240.08/46.80  | | | | | 
% 240.08/46.80  | | | | | REDUCE: (43), (53) imply:
% 240.08/46.80  | | | | |   (54)   ~ (all_52_13 = e0)
% 240.08/46.80  | | | | | 
% 240.08/46.80  | | | | | REDUCE: (38), (53) imply:
% 240.08/46.80  | | | | |   (55)  op(e1, e0) = e0
% 240.08/46.80  | | | | | 
% 240.08/46.80  | | | | | BETA: splitting (13) gives:
% 240.08/46.80  | | | | | 
% 240.08/46.80  | | | | | Case 1:
% 240.08/46.80  | | | | | | 
% 240.08/46.80  | | | | | |   (56)  all_54_7 = e3
% 240.08/46.80  | | | | | | 
% 240.08/46.80  | | | | | | COMBINE_EQS: (18), (56) imply:
% 240.08/46.80  | | | | | |   (57)  all_52_13 = e3
% 240.08/46.80  | | | | | | 
% 240.08/46.80  | | | | | | REDUCE: (25), (57) imply:
% 240.08/46.80  | | | | | |   (58)  $false
% 240.08/46.80  | | | | | | 
% 240.08/46.80  | | | | | | CLOSE: (58) is inconsistent.
% 240.08/46.80  | | | | | | 
% 240.08/46.80  | | | | | Case 2:
% 240.08/46.80  | | | | | | 
% 240.08/46.80  | | | | | |   (59)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.08/46.80  | | | | | | 
% 240.08/46.80  | | | | | | BETA: splitting (12) gives:
% 240.08/46.80  | | | | | | 
% 240.08/46.80  | | | | | | Case 1:
% 240.08/46.80  | | | | | | | 
% 240.08/46.80  | | | | | | |   (60)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 240.08/46.80  | | | | | | |           all_56_25 & $i(all_56_25)) | (all_56_26 = e2 & op(e2,
% 240.08/46.80  | | | | | | |             all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 240.08/46.80  | | | | | | |           $i(all_56_27))
% 240.08/46.80  | | | | | | | 
% 240.08/46.80  | | | | | | | BETA: splitting (60) gives:
% 240.08/46.80  | | | | | | | 
% 240.08/46.80  | | | | | | | Case 1:
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | |   (61)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 240.08/46.80  | | | | | | | |         all_56_25 & $i(all_56_25)
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | | REF_CLOSE: (4), (9), (14), (15), (17), (23), (24), (61) are
% 240.08/46.80  | | | | | | | |            inconsistent by sub-proof #2143.
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | Case 2:
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | |   (62)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 240.08/46.80  | | | | | | | |         all_56_27 & $i(all_56_27)
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | | REF_CLOSE: (8), (16), (18), (23), (26), (28), (54), (59), (62)
% 240.08/46.80  | | | | | | | |            are inconsistent by sub-proof #232.
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | End of split
% 240.08/46.80  | | | | | | | 
% 240.08/46.80  | | | | | | Case 2:
% 240.08/46.80  | | | | | | | 
% 240.08/46.80  | | | | | | |   (63)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 240.08/46.80  | | | | | | |           all_56_29 & $i(all_56_29)) | (all_56_30 = e0 & op(e0,
% 240.08/46.80  | | | | | | |             all_56_31) = e0)
% 240.08/46.80  | | | | | | | 
% 240.08/46.80  | | | | | | | BETA: splitting (63) gives:
% 240.08/46.80  | | | | | | | 
% 240.08/46.80  | | | | | | | Case 1:
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | |   (64)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 240.08/46.80  | | | | | | | |         all_56_29 & $i(all_56_29)
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | | REF_CLOSE: (16), (18), (23), (54), (55), (59), (64) are
% 240.08/46.80  | | | | | | | |            inconsistent by sub-proof #231.
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | Case 2:
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | |   (65)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | | ALPHA: (65) implies:
% 240.08/46.80  | | | | | | | |   (66)  op(e0, all_56_31) = e0
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | | REDUCE: (11), (66) imply:
% 240.08/46.80  | | | | | | | |   (67)  op(e0, e2) = e0
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | | REF_CLOSE: (19), (22), (23), (67) are inconsistent by sub-proof
% 240.08/46.80  | | | | | | | |            #2252.
% 240.08/46.80  | | | | | | | | 
% 240.08/46.80  | | | | | | | End of split
% 240.08/46.80  | | | | | | | 
% 240.08/46.80  | | | | | | End of split
% 240.08/46.80  | | | | | | 
% 240.08/46.80  | | | | | End of split
% 240.08/46.80  | | | | | 
% 240.08/46.80  | | | | End of split
% 240.08/46.80  | | | | 
% 240.08/46.80  | | | End of split
% 240.08/46.80  | | | 
% 240.08/46.80  | | End of split
% 240.08/46.80  | | 
% 240.08/46.80  | Case 2:
% 240.08/46.80  | | 
% 240.08/46.80  | |   (68)   ~ (all_44_1 = e1) & op(e0, e2) = all_44_1 & $i(all_44_1)
% 240.08/46.80  | | 
% 240.08/46.80  | | ALPHA: (68) implies:
% 240.08/46.80  | |   (69)   ~ (all_44_1 = e1)
% 240.08/46.80  | |   (70)  op(e0, e2) = all_44_1
% 240.08/46.80  | | 
% 240.08/46.80  | | REF_CLOSE: (23), (27), (69), (70) are inconsistent by sub-proof #230.
% 240.08/46.80  | | 
% 240.08/46.80  | End of split
% 240.08/46.80  | 
% 240.08/46.80  End of proof
% 240.08/46.80  
% 240.08/46.80  Sub-proof #230 shows that the following formulas are inconsistent:
% 240.08/46.80  ----------------------------------------------------------------
% 240.08/46.80    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.80    (2)  op(e0, e2) = all_44_1
% 240.08/46.80    (3)  op(e0, e2) = e1
% 240.08/46.80    (4)   ~ (all_44_1 = e1)
% 240.08/46.80  
% 240.08/46.80  Begin of proof
% 240.08/46.80  | 
% 240.08/46.80  | GROUND_INST: instantiating (1) with e1, all_44_1, e2, e0, simplifying with
% 240.08/46.80  |              (2), (3) gives:
% 240.08/46.80  |   (5)  all_44_1 = e1
% 240.08/46.80  | 
% 240.08/46.80  | REDUCE: (4), (5) imply:
% 240.08/46.80  |   (6)  $false
% 240.08/46.80  | 
% 240.08/46.80  | CLOSE: (6) is inconsistent.
% 240.08/46.80  | 
% 240.08/46.80  End of proof
% 240.08/46.80  
% 240.08/46.80  Sub-proof #231 shows that the following formulas are inconsistent:
% 240.08/46.80  ----------------------------------------------------------------
% 240.08/46.80    (1)  op(e1, e0) = e0
% 240.08/46.80    (2)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.08/46.80    (3)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 240.08/46.80         $i(all_56_29)
% 240.08/46.80    (4)   ~ (all_52_13 = e2)
% 240.08/46.80    (5)  all_54_7 = all_52_13
% 240.08/46.80    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.80    (7)   ~ (all_52_13 = e0)
% 240.08/46.80  
% 240.08/46.80  Begin of proof
% 240.08/46.80  | 
% 240.08/46.80  | ALPHA: (3) implies:
% 240.08/46.80  |   (8)  op(e1, e0) = all_56_29
% 240.08/46.80  |   (9)  op(e1, all_56_29) = e1
% 240.08/46.80  | 
% 240.08/46.80  | BETA: splitting (2) gives:
% 240.08/46.80  | 
% 240.08/46.80  | Case 1:
% 240.08/46.80  | | 
% 240.08/46.80  | |   (10)  all_54_7 = e2
% 240.08/46.80  | | 
% 240.08/46.80  | | COMBINE_EQS: (5), (10) imply:
% 240.08/46.80  | |   (11)  all_52_13 = e2
% 240.08/46.80  | | 
% 240.08/46.80  | | REDUCE: (4), (11) imply:
% 240.08/46.80  | |   (12)  $false
% 240.08/46.80  | | 
% 240.08/46.80  | | CLOSE: (12) is inconsistent.
% 240.08/46.80  | | 
% 240.08/46.80  | Case 2:
% 240.08/46.80  | | 
% 240.08/46.80  | |   (13)  all_54_7 = e1 | all_54_7 = e0
% 240.08/46.80  | | 
% 240.08/46.80  | | BETA: splitting (13) gives:
% 240.08/46.80  | | 
% 240.08/46.80  | | Case 1:
% 240.08/46.80  | | | 
% 240.08/46.80  | | |   (14)  all_54_7 = e1
% 240.08/46.80  | | | 
% 240.08/46.80  | | | COMBINE_EQS: (5), (14) imply:
% 240.08/46.80  | | |   (15)  all_52_13 = e1
% 240.08/46.80  | | | 
% 240.08/46.80  | | | REDUCE: (7), (15) imply:
% 240.08/46.80  | | |   (16)   ~ (e1 = e0)
% 240.08/46.80  | | | 
% 240.08/46.80  | | | REF_CLOSE: (1), (6), (8), (9), (16) are inconsistent by sub-proof #372.
% 240.08/46.80  | | | 
% 240.08/46.80  | | Case 2:
% 240.08/46.80  | | | 
% 240.08/46.80  | | |   (17)  all_54_7 = e0
% 240.08/46.80  | | | 
% 240.08/46.80  | | | COMBINE_EQS: (5), (17) imply:
% 240.08/46.80  | | |   (18)  all_52_13 = e0
% 240.08/46.80  | | | 
% 240.08/46.80  | | | REDUCE: (7), (18) imply:
% 240.08/46.80  | | |   (19)  $false
% 240.08/46.80  | | | 
% 240.08/46.80  | | | CLOSE: (19) is inconsistent.
% 240.08/46.80  | | | 
% 240.08/46.80  | | End of split
% 240.08/46.80  | | 
% 240.08/46.80  | End of split
% 240.08/46.80  | 
% 240.08/46.80  End of proof
% 240.08/46.80  
% 240.08/46.80  Sub-proof #232 shows that the following formulas are inconsistent:
% 240.08/46.80  ----------------------------------------------------------------
% 240.08/46.80    (1)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.08/46.80    (2)  op(e2, e1) = all_52_9
% 240.08/46.80    (3)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 240.08/46.80         $i(all_56_27)
% 240.08/46.80    (4)   ~ (all_52_13 = e2)
% 240.08/46.80    (5)  all_54_7 = all_52_13
% 240.08/46.80    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.80    (7)  op(e2, e0) = all_52_13
% 240.08/46.80    (8)   ~ (all_52_13 = e0)
% 240.08/46.80    (9)   ~ (all_52_9 = e2)
% 240.08/46.80  
% 240.08/46.80  Begin of proof
% 240.08/46.80  | 
% 240.08/46.80  | ALPHA: (3) implies:
% 240.08/46.80  |   (10)  op(e2, e0) = all_56_27
% 240.08/46.80  |   (11)  op(e2, all_56_27) = e2
% 240.08/46.80  | 
% 240.08/46.80  | BETA: splitting (1) gives:
% 240.08/46.80  | 
% 240.08/46.80  | Case 1:
% 240.08/46.80  | | 
% 240.08/46.80  | |   (12)  all_54_7 = e2
% 240.08/46.80  | | 
% 240.08/46.80  | | COMBINE_EQS: (5), (12) imply:
% 240.08/46.80  | |   (13)  all_52_13 = e2
% 240.08/46.80  | | 
% 240.08/46.80  | | REDUCE: (4), (13) imply:
% 240.08/46.80  | |   (14)  $false
% 240.08/46.80  | | 
% 240.08/46.80  | | CLOSE: (14) is inconsistent.
% 240.08/46.80  | | 
% 240.08/46.80  | Case 2:
% 240.08/46.80  | | 
% 240.08/46.80  | |   (15)  all_54_7 = e1 | all_54_7 = e0
% 240.08/46.80  | | 
% 240.08/46.80  | | BETA: splitting (15) gives:
% 240.08/46.80  | | 
% 240.08/46.80  | | Case 1:
% 240.08/46.80  | | | 
% 240.08/46.80  | | |   (16)  all_54_7 = e1
% 240.08/46.80  | | | 
% 240.08/46.80  | | | COMBINE_EQS: (5), (16) imply:
% 240.08/46.80  | | |   (17)  all_52_13 = e1
% 240.08/46.80  | | | 
% 240.08/46.80  | | | REDUCE: (7), (17) imply:
% 240.08/46.80  | | |   (18)  op(e2, e0) = e1
% 240.08/46.80  | | | 
% 240.08/46.80  | | | GROUND_INST: instantiating (6) with e1, all_56_27, e0, e2, simplifying
% 240.08/46.80  | | |              with (10), (18) gives:
% 240.08/46.80  | | |   (19)  all_56_27 = e1
% 240.08/46.80  | | | 
% 240.08/46.80  | | | REDUCE: (11), (19) imply:
% 240.08/46.80  | | |   (20)  op(e2, e1) = e2
% 240.08/46.80  | | | 
% 240.08/46.80  | | | REF_CLOSE: (2), (6), (9), (20) are inconsistent by sub-proof #2328.
% 240.08/46.80  | | | 
% 240.08/46.80  | | Case 2:
% 240.08/46.80  | | | 
% 240.08/46.80  | | |   (21)  all_54_7 = e0
% 240.08/46.80  | | | 
% 240.08/46.80  | | | COMBINE_EQS: (5), (21) imply:
% 240.08/46.80  | | |   (22)  all_52_13 = e0
% 240.08/46.80  | | | 
% 240.08/46.80  | | | REDUCE: (8), (22) imply:
% 240.08/46.80  | | |   (23)  $false
% 240.08/46.80  | | | 
% 240.08/46.80  | | | CLOSE: (23) is inconsistent.
% 240.08/46.80  | | | 
% 240.08/46.80  | | End of split
% 240.08/46.80  | | 
% 240.08/46.80  | End of split
% 240.08/46.80  | 
% 240.08/46.80  End of proof
% 240.08/46.80  
% 240.08/46.80  Sub-proof #233 shows that the following formulas are inconsistent:
% 240.08/46.80  ----------------------------------------------------------------
% 240.08/46.80    (1)  all_54_11 = all_4_0
% 240.08/46.80    (2)  all_54_11 = e1
% 240.08/46.80    (3)   ~ (all_4_0 = e1)
% 240.08/46.80  
% 240.08/46.80  Begin of proof
% 240.08/46.80  | 
% 240.08/46.80  | COMBINE_EQS: (1), (2) imply:
% 240.08/46.80  |   (4)  all_4_0 = e1
% 240.08/46.80  | 
% 240.08/46.80  | SIMP: (4) implies:
% 240.08/46.80  |   (5)  all_4_0 = e1
% 240.08/46.80  | 
% 240.08/46.80  | REDUCE: (3), (5) imply:
% 240.08/46.80  |   (6)  $false
% 240.08/46.80  | 
% 240.08/46.80  | CLOSE: (6) is inconsistent.
% 240.08/46.80  | 
% 240.08/46.80  End of proof
% 240.08/46.80  
% 240.08/46.80  Sub-proof #234 shows that the following formulas are inconsistent:
% 240.08/46.80  ----------------------------------------------------------------
% 240.08/46.80    (1)  all_54_11 = all_4_0
% 240.08/46.80    (2)  all_54_11 = e2
% 240.08/46.80    (3)   ~ (all_4_0 = e2)
% 240.08/46.80  
% 240.08/46.80  Begin of proof
% 240.08/46.80  | 
% 240.08/46.80  | COMBINE_EQS: (1), (2) imply:
% 240.08/46.80  |   (4)  all_4_0 = e2
% 240.08/46.80  | 
% 240.08/46.80  | SIMP: (4) implies:
% 240.08/46.80  |   (5)  all_4_0 = e2
% 240.08/46.80  | 
% 240.08/46.80  | REDUCE: (3), (5) imply:
% 240.08/46.80  |   (6)  $false
% 240.08/46.80  | 
% 240.08/46.80  | CLOSE: (6) is inconsistent.
% 240.08/46.80  | 
% 240.08/46.80  End of proof
% 240.08/46.80  
% 240.08/46.80  Sub-proof #235 shows that the following formulas are inconsistent:
% 240.08/46.80  ----------------------------------------------------------------
% 240.08/46.80    (1)  all_54_11 = all_4_0
% 240.08/46.80    (2)  all_54_11 = e3
% 240.08/46.80    (3)   ~ (all_4_0 = e3)
% 240.08/46.80  
% 240.08/46.80  Begin of proof
% 240.08/46.80  | 
% 240.08/46.80  | COMBINE_EQS: (1), (2) imply:
% 240.08/46.80  |   (4)  all_4_0 = e3
% 240.08/46.80  | 
% 240.08/46.80  | SIMP: (4) implies:
% 240.08/46.80  |   (5)  all_4_0 = e3
% 240.08/46.80  | 
% 240.08/46.80  | REDUCE: (3), (5) imply:
% 240.08/46.80  |   (6)  $false
% 240.08/46.80  | 
% 240.08/46.80  | CLOSE: (6) is inconsistent.
% 240.08/46.80  | 
% 240.08/46.80  End of proof
% 240.08/46.80  
% 240.08/46.80  Sub-proof #236 shows that the following formulas are inconsistent:
% 240.08/46.80  ----------------------------------------------------------------
% 240.08/46.80    (1)   ~ (all_52_9 = all_6_2)
% 240.08/46.80    (2)   ~ (e3 = e0)
% 240.08/46.80    (3)   ~ (all_52_7 = e2)
% 240.08/46.80    (4)   ~ (e2 = e0)
% 240.08/46.80    (5)   ~ (all_52_8 = all_6_2)
% 240.08/46.80    (6)  op(e1, e2) = all_52_6
% 240.08/46.80    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.80         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.80    (8)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.08/46.80           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.08/46.80             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.80           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.08/46.80             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.80           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.80           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.08/46.80           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.08/46.80           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.08/46.80           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.80           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.08/46.80             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.08/46.80           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.80           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 240.08/46.80           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.08/46.80           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.08/46.80           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.80           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.08/46.80             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.08/46.80           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.80           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 240.08/46.80           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.08/46.80           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.08/46.80           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.80           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.08/46.80             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.08/46.80           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.80           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.80    (9)  op(e1, e1) = all_6_2
% 240.08/46.80    (10)  op(e1, e0) = all_52_14
% 240.08/46.80    (11)  op(e0, e3) = all_52_3
% 240.08/46.80    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.80          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.08/46.80    (13)   ~ (e3 = e1)
% 240.08/46.80    (14)   ~ (all_52_12 = all_52_14)
% 240.08/46.80    (15)  all_54_10 = all_6_2
% 240.08/46.80    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 240.08/46.80          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 240.08/46.80    (17)   ~ (all_6_2 = e3)
% 240.08/46.80    (18)   ~ (all_52_8 = all_52_12)
% 240.08/46.80    (19)  op(e3, e1) = all_52_8
% 240.08/46.80    (20)  op(e2, e1) = all_52_9
% 240.08/46.80    (21)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.08/46.80          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.08/46.80    (22)   ~ (e3 = e2)
% 240.08/46.80    (23)   ~ (all_6_2 = e0)
% 240.08/46.80    (24)  all_56_31 = e2
% 240.08/46.80    (25)  op(e2, e2) = e1
% 240.08/46.80    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.08/46.80          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.08/46.80    (27)  op(e3, e0) = all_52_12
% 240.08/46.80    (28)   ~ (all_52_3 = e2)
% 240.08/46.81    (29)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.08/46.81          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.08/46.81    (30)  op(e2, e3) = all_52_1
% 240.08/46.81    (31)  op(e3, e3) = e2
% 240.08/46.81    (32)   ~ (all_52_13 = e2)
% 240.08/46.81    (33)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 240.08/46.81    (34)  op(e0, e2) = all_52_7
% 240.08/46.81    (35)  op(e3, e2) = all_52_4
% 240.08/46.81    (36)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.08/46.81          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.08/46.81    (37)   ~ (all_52_4 = e2)
% 240.08/46.81    (38)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.08/46.81          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.08/46.81    (39)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.81    (40)   ~ (all_52_6 = all_52_7)
% 240.08/46.81    (41)   ~ (all_52_4 = e1)
% 240.08/46.81    (42)   ~ (e1 = e0)
% 240.08/46.81    (43)  all_56_21 = all_6_2
% 240.08/46.81    (44)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.08/46.81          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.08/46.81    (45)  op(e2, e0) = all_52_13
% 240.08/46.81    (46)   ~ (all_52_1 = e2)
% 240.08/46.81    (47)   ~ (all_52_4 = all_52_6)
% 240.08/46.81    (48)   ~ (e2 = e1)
% 240.08/46.81  
% 240.08/46.81  Begin of proof
% 240.08/46.81  | 
% 240.08/46.81  | BETA: splitting (7) gives:
% 240.08/46.81  | 
% 240.08/46.81  | Case 1:
% 240.08/46.81  | | 
% 240.08/46.81  | |   (49)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 240.08/46.81  | |           e2)
% 240.08/46.81  | | 
% 240.08/46.81  | | REF_CLOSE: (25), (35), (37), (39), (48), (49) are inconsistent by sub-proof
% 240.08/46.81  | |            #246.
% 240.08/46.81  | | 
% 240.08/46.81  | Case 2:
% 240.08/46.81  | | 
% 240.08/46.81  | |   (50)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 240.08/46.81  | |           e2)
% 240.08/46.81  | | 
% 240.08/46.81  | | BETA: splitting (50) gives:
% 240.08/46.81  | | 
% 240.08/46.81  | | Case 1:
% 240.08/46.81  | | | 
% 240.08/46.81  | | |   (51)  all_58_7 = e2 & op(e1, e2) = e2
% 240.08/46.81  | | | 
% 240.08/46.81  | | | ALPHA: (51) implies:
% 240.08/46.81  | | |   (52)  op(e1, e2) = e2
% 240.08/46.81  | | | 
% 240.08/46.81  | | | BETA: splitting (12) gives:
% 240.08/46.81  | | | 
% 240.08/46.81  | | | Case 1:
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | |   (53)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2)
% 240.08/46.81  | | | |           = e2)
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | | REF_CLOSE: (25), (30), (39), (46), (48), (53) are inconsistent by
% 240.08/46.81  | | | |            sub-proof #1929.
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | Case 2:
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | |   (54)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0)
% 240.08/46.81  | | | |           = e2)
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | | BETA: splitting (54) gives:
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | | Case 1:
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | |   (55)  all_58_5 = e2 & op(e2, e1) = e2
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | ALPHA: (55) implies:
% 240.08/46.81  | | | | |   (56)  op(e2, e1) = e2
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | BETA: splitting (21) gives:
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | Case 1:
% 240.08/46.81  | | | | | | 
% 240.08/46.81  | | | | | |   (57)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2,
% 240.08/46.81  | | | | | |             e3) = e2)
% 240.08/46.81  | | | | | | 
% 240.08/46.81  | | | | | | BETA: splitting (57) gives:
% 240.08/46.81  | | | | | | 
% 240.08/46.81  | | | | | | Case 1:
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | |   (58)  all_58_0 = e2 & op(e3, e3) = e2
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | GROUND_INST: instantiating (39) with all_52_6, e2, e2, e1,
% 240.08/46.81  | | | | | | |              simplifying with (6), (52) gives:
% 240.08/46.81  | | | | | | |   (59)  all_52_6 = e2
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | GROUND_INST: instantiating (39) with all_52_9, e2, e1, e2,
% 240.08/46.81  | | | | | | |              simplifying with (20), (56) gives:
% 240.08/46.81  | | | | | | |   (60)  all_52_9 = e2
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | REDUCE: (40), (59) imply:
% 240.08/46.81  | | | | | | |   (61)   ~ (all_52_7 = e2)
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | REDUCE: (1), (60) imply:
% 240.08/46.81  | | | | | | |   (62)   ~ (all_6_2 = e2)
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | SIMP: (62) implies:
% 240.08/46.81  | | | | | | |   (63)   ~ (all_6_2 = e2)
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | BETA: splitting (33) gives:
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | |   (64)  all_54_10 = e3
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | | REF_CLOSE: (15), (17), (64) are inconsistent by sub-proof #2313.
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | |   (65)   ~ (all_54_10 = e3)
% 240.08/46.81  | | | | | | | |   (66)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | | BETA: splitting (66) gives:
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | |   (67)  all_54_10 = e2
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | REF_CLOSE: (15), (63), (67) are inconsistent by sub-proof
% 240.08/46.81  | | | | | | | | |            #2312.
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | |   (68)   ~ (all_54_10 = e2)
% 240.08/46.81  | | | | | | | | |   (69)  all_54_10 = e1 | all_54_10 = e0
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | BETA: splitting (69) gives:
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | |   (70)  all_54_10 = e1
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | COMBINE_EQS: (15), (70) imply:
% 240.08/46.81  | | | | | | | | | |   (71)  all_6_2 = e1
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | SIMP: (71) implies:
% 240.08/46.81  | | | | | | | | | |   (72)  all_6_2 = e1
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | COMBINE_EQS: (43), (72) imply:
% 240.08/46.81  | | | | | | | | | |   (73)  all_56_21 = e1
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | REDUCE: (5), (72) imply:
% 240.08/46.81  | | | | | | | | | |   (74)   ~ (all_52_8 = e1)
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | REDUCE: (17), (72) imply:
% 240.08/46.81  | | | | | | | | | |   (75)   ~ (e3 = e1)
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | REDUCE: (63), (72) imply:
% 240.08/46.81  | | | | | | | | | |   (76)   ~ (e2 = e1)
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | BETA: splitting (38) gives:
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | |   (77)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 240.08/46.81  | | | | | | | | | | |           & op(e3, e2) = e1)
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | REF_CLOSE: (31), (35), (39), (41), (48), (77) are
% 240.08/46.81  | | | | | | | | | | |            inconsistent by sub-proof #1340.
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | |   (78)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 240.08/46.81  | | | | | | | | | | |           & op(e3, e0) = e1)
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | BETA: splitting (78) gives:
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | |   (79)  all_58_4 = e1 & op(e3, e1) = e1
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | ALPHA: (79) implies:
% 240.08/46.81  | | | | | | | | | | | |   (80)  op(e3, e1) = e1
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | REF_CLOSE: (19), (39), (74), (80) are inconsistent by
% 240.08/46.81  | | | | | | | | | | | |            sub-proof #2309.
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | |   (81)  all_58_9 = e1 & op(e3, e0) = e1
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | REF_CLOSE: (1), (3), (8), (10), (13), (14), (15), (18), (19),
% 240.08/46.81  | | | | | | | | | | | |            (20), (23), (24), (27), (34), (35), (37), (39),
% 240.08/46.81  | | | | | | | | | | | |            (42), (69), (73), (81) are inconsistent by
% 240.08/46.81  | | | | | | | | | | | |            sub-proof #240.
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | End of split
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | End of split
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | |   (82)  all_54_10 = e0
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | REF_CLOSE: (15), (23), (82) are inconsistent by sub-proof
% 240.08/46.81  | | | | | | | | | |            #2303.
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | End of split
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | End of split
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | End of split
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | Case 2:
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | |   (83)  all_58_2 = e2 & op(e2, e3) = e2
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | ALPHA: (83) implies:
% 240.08/46.81  | | | | | | |   (84)  op(e2, e3) = e2
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | REF_CLOSE: (30), (39), (46), (84) are inconsistent by sub-proof
% 240.08/46.81  | | | | | | |            #2336.
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | End of split
% 240.08/46.81  | | | | | | 
% 240.08/46.81  | | | | | Case 2:
% 240.08/46.81  | | | | | | 
% 240.08/46.81  | | | | | |   (85)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0,
% 240.08/46.81  | | | | | |             e3) = e2)
% 240.08/46.81  | | | | | | 
% 240.08/46.81  | | | | | | BETA: splitting (85) gives:
% 240.08/46.81  | | | | | | 
% 240.08/46.81  | | | | | | Case 1:
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | |   (86)  all_58_6 = e2 & op(e1, e3) = e2
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | ALPHA: (86) implies:
% 240.08/46.81  | | | | | | |   (87)  all_58_6 = e2
% 240.08/46.81  | | | | | | |   (88)  op(e1, e3) = e2
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | BETA: splitting (29) gives:
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | |   (89)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 &
% 240.08/46.81  | | | | | | | |           op(e1, e2) = e3)
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | | REF_CLOSE: (22), (39), (52), (87), (89) are inconsistent by
% 240.08/46.81  | | | | | | | |            sub-proof #239.
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | |   (90)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 &
% 240.08/46.81  | | | | | | | |           op(e1, e0) = e3)
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | | BETA: splitting (90) gives:
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | |   (91)  all_58_8 = e3 & op(e1, e1) = e3
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | REF_CLOSE: (9), (17), (39), (91) are inconsistent by sub-proof
% 240.08/46.81  | | | | | | | | |            #2092.
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | |   (92)  all_58_11 = e3 & op(e1, e0) = e3
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | ALPHA: (92) implies:
% 240.08/46.81  | | | | | | | | |   (93)  all_58_11 = e3
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | BETA: splitting (26) gives:
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | |   (94)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 240.08/46.81  | | | | | | | | | |           op(e2, e3) = e0)
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | BETA: splitting (94) gives:
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | |   (95)  all_58_0 = e0 & op(e3, e3) = e0
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | ALPHA: (95) implies:
% 240.08/46.81  | | | | | | | | | | |   (96)  op(e3, e3) = e0
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | REF_CLOSE: (4), (31), (39), (96) are inconsistent by
% 240.08/46.81  | | | | | | | | | | |            sub-proof #2188.
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | |   (97)  all_58_2 = e0 & op(e2, e3) = e0
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | ALPHA: (97) implies:
% 240.08/46.81  | | | | | | | | | | |   (98)  all_58_2 = e0
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | BETA: splitting (16) gives:
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | |   (99)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 240.08/46.81  | | | | | | | | | | | |           & op(e2, e3) = e3)
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | BETA: splitting (99) gives:
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | |   (100)  all_58_0 = e3 & op(e3, e3) = e3
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | | ALPHA: (100) implies:
% 240.08/46.81  | | | | | | | | | | | | |   (101)  op(e3, e3) = e3
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | | REF_CLOSE: (22), (31), (39), (101) are inconsistent by
% 240.08/46.81  | | | | | | | | | | | | |            sub-proof #2194.
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | |   (102)  all_58_2 = e3 & op(e2, e3) = e3
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | | ALPHA: (102) implies:
% 240.08/46.81  | | | | | | | | | | | | |   (103)  all_58_2 = e3
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | | REF_CLOSE: (2), (98), (103) are inconsistent by sub-proof
% 240.08/46.81  | | | | | | | | | | | | |            #2124.
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | End of split
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | |   (104)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 240.08/46.81  | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | BETA: splitting (104) gives:
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | |   (105)  all_58_6 = e3 & op(e1, e3) = e3
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | | ALPHA: (105) implies:
% 240.08/46.81  | | | | | | | | | | | | |   (106)  all_58_6 = e3
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | | COMBINE_EQS: (87), (106) imply:
% 240.08/46.81  | | | | | | | | | | | | |   (107)  e3 = e2
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | | SIMP: (107) implies:
% 240.08/46.81  | | | | | | | | | | | | |   (108)  e3 = e2
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | | COMBINE_EQS: (93), (108) imply:
% 240.08/46.81  | | | | | | | | | | | | |   (109)  all_58_11 = e2
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | | REF_CLOSE: (2), (4), (9), (17), (22), (23), (29), (39), (44),
% 240.08/46.81  | | | | | | | | | | | | |            (87), (109) are inconsistent by sub-proof #238.
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | |   (110)  all_58_12 = e3 & op(e0, e3) = e3
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | | ALPHA: (110) implies:
% 240.08/46.81  | | | | | | | | | | | | |   (111)  all_58_12 = e3
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | | REF_CLOSE: (13), (31), (36), (39), (42), (48), (88), (98),
% 240.08/46.81  | | | | | | | | | | | | |            (111) are inconsistent by sub-proof #257.
% 240.08/46.81  | | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | | End of split
% 240.08/46.81  | | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | End of split
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | End of split
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | |   (112)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0
% 240.08/46.81  | | | | | | | | | |            & op(e0, e3) = e0)
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | BETA: splitting (112) gives:
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | Case 1:
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | |   (113)  all_58_6 = e0 & op(e1, e3) = e0
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | ALPHA: (113) implies:
% 240.08/46.81  | | | | | | | | | | |   (114)  all_58_6 = e0
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | REF_CLOSE: (4), (87), (114) are inconsistent by sub-proof
% 240.08/46.81  | | | | | | | | | | |            #1982.
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | Case 2:
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | |   (115)  all_58_12 = e0 & op(e0, e3) = e0
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | ALPHA: (115) implies:
% 240.08/46.81  | | | | | | | | | | |   (116)  all_58_12 = e0
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | | REF_CLOSE: (2), (4), (13), (16), (22), (26), (31), (36),
% 240.08/46.81  | | | | | | | | | | |            (39), (42), (48), (87), (88), (116) are
% 240.08/46.81  | | | | | | | | | | |            inconsistent by sub-proof #237.
% 240.08/46.81  | | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | | End of split
% 240.08/46.81  | | | | | | | | | | 
% 240.08/46.81  | | | | | | | | | End of split
% 240.08/46.81  | | | | | | | | | 
% 240.08/46.81  | | | | | | | | End of split
% 240.08/46.81  | | | | | | | | 
% 240.08/46.81  | | | | | | | End of split
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | Case 2:
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | |   (117)  all_58_12 = e2 & op(e0, e3) = e2
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | | REF_CLOSE: (11), (28), (39), (117) are inconsistent by sub-proof
% 240.08/46.81  | | | | | | |            #2315.
% 240.08/46.81  | | | | | | | 
% 240.08/46.81  | | | | | | End of split
% 240.08/46.81  | | | | | | 
% 240.08/46.81  | | | | | End of split
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | Case 2:
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | |   (118)  all_58_10 = e2 & op(e2, e0) = e2
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | ALPHA: (118) implies:
% 240.08/46.81  | | | | |   (119)  op(e2, e0) = e2
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | REF_CLOSE: (32), (39), (45), (119) are inconsistent by sub-proof
% 240.08/46.81  | | | | |            #2317.
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | End of split
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | End of split
% 240.08/46.81  | | | 
% 240.08/46.81  | | Case 2:
% 240.08/46.81  | | | 
% 240.08/46.81  | | |   (120)  all_58_13 = e2 & op(e0, e2) = e2
% 240.08/46.81  | | | 
% 240.08/46.81  | | | ALPHA: (120) implies:
% 240.08/46.81  | | |   (121)  op(e0, e2) = e2
% 240.08/46.81  | | | 
% 240.08/46.81  | | | REF_CLOSE: (3), (34), (39), (121) are inconsistent by sub-proof #2327.
% 240.08/46.81  | | | 
% 240.08/46.81  | | End of split
% 240.08/46.81  | | 
% 240.08/46.81  | End of split
% 240.08/46.81  | 
% 240.08/46.81  End of proof
% 240.08/46.81  
% 240.08/46.81  Sub-proof #237 shows that the following formulas are inconsistent:
% 240.08/46.81  ----------------------------------------------------------------
% 240.08/46.81    (1)   ~ (e3 = e0)
% 240.08/46.81    (2)   ~ (e2 = e0)
% 240.08/46.81    (3)  all_58_6 = e2
% 240.08/46.81    (4)   ~ (e3 = e1)
% 240.08/46.81    (5)  op(e1, e3) = e2
% 240.08/46.81    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 240.08/46.81         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 240.08/46.81    (7)   ~ (e3 = e2)
% 240.08/46.81    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.08/46.81         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.08/46.81    (9)  all_58_12 = e0
% 240.08/46.81    (10)  op(e3, e3) = e2
% 240.08/46.81    (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.08/46.81          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.08/46.81    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.81    (13)   ~ (e1 = e0)
% 240.08/46.81    (14)   ~ (e2 = e1)
% 240.08/46.81  
% 240.08/46.81  Begin of proof
% 240.08/46.81  | 
% 240.08/46.81  | BETA: splitting (6) gives:
% 240.08/46.81  | 
% 240.08/46.81  | Case 1:
% 240.08/46.81  | | 
% 240.08/46.81  | |   (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 240.08/46.81  | |           e3)
% 240.08/46.81  | | 
% 240.08/46.81  | | BETA: splitting (15) gives:
% 240.08/46.81  | | 
% 240.08/46.81  | | Case 1:
% 240.08/46.81  | | | 
% 240.08/46.81  | | |   (16)  all_58_0 = e3 & op(e3, e3) = e3
% 240.08/46.81  | | | 
% 240.08/46.81  | | | ALPHA: (16) implies:
% 240.08/46.81  | | |   (17)  op(e3, e3) = e3
% 240.08/46.81  | | | 
% 240.08/46.81  | | | REF_CLOSE: (7), (10), (12), (17) are inconsistent by sub-proof #2194.
% 240.08/46.81  | | | 
% 240.08/46.81  | | Case 2:
% 240.08/46.81  | | | 
% 240.08/46.81  | | |   (18)  all_58_2 = e3 & op(e2, e3) = e3
% 240.08/46.81  | | | 
% 240.08/46.81  | | | ALPHA: (18) implies:
% 240.08/46.81  | | |   (19)  all_58_2 = e3
% 240.08/46.81  | | | 
% 240.08/46.81  | | | BETA: splitting (11) gives:
% 240.08/46.81  | | | 
% 240.08/46.81  | | | Case 1:
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | |   (20)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 240.08/46.81  | | | |           = e1)
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | | REF_CLOSE: (4), (10), (12), (14), (19), (20) are inconsistent by
% 240.08/46.81  | | | |            sub-proof #1764.
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | Case 2:
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | |   (21)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 240.08/46.81  | | | |           = e1)
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | | BETA: splitting (21) gives:
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | | Case 1:
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | |   (22)  all_58_6 = e1 & op(e1, e3) = e1
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | ALPHA: (22) implies:
% 240.08/46.81  | | | | |   (23)  op(e1, e3) = e1
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | REF_CLOSE: (5), (12), (14), (23) are inconsistent by sub-proof #2226.
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | Case 2:
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | |   (24)  all_58_12 = e1 & op(e0, e3) = e1
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | ALPHA: (24) implies:
% 240.08/46.81  | | | | |   (25)  all_58_12 = e1
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | REF_CLOSE: (9), (13), (25) are inconsistent by sub-proof #1539.
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | End of split
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | End of split
% 240.08/46.81  | | | 
% 240.08/46.81  | | End of split
% 240.08/46.81  | | 
% 240.08/46.81  | Case 2:
% 240.08/46.81  | | 
% 240.08/46.81  | |   (26)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 240.08/46.81  | |           e3)
% 240.08/46.81  | | 
% 240.08/46.81  | | BETA: splitting (26) gives:
% 240.08/46.81  | | 
% 240.08/46.81  | | Case 1:
% 240.08/46.81  | | | 
% 240.08/46.81  | | |   (27)  all_58_6 = e3 & op(e1, e3) = e3
% 240.08/46.81  | | | 
% 240.08/46.81  | | | ALPHA: (27) implies:
% 240.08/46.81  | | |   (28)  all_58_6 = e3
% 240.08/46.81  | | | 
% 240.08/46.81  | | | REF_CLOSE: (3), (7), (28) are inconsistent by sub-proof #2024.
% 240.08/46.81  | | | 
% 240.08/46.81  | | Case 2:
% 240.08/46.81  | | | 
% 240.08/46.81  | | |   (29)  all_58_12 = e3 & op(e0, e3) = e3
% 240.08/46.81  | | | 
% 240.08/46.81  | | | ALPHA: (29) implies:
% 240.08/46.81  | | |   (30)  all_58_12 = e3
% 240.08/46.81  | | | 
% 240.08/46.81  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (11), (12), (13), (14),
% 240.08/46.81  | | |            (30) are inconsistent by sub-proof #256.
% 240.08/46.81  | | | 
% 240.08/46.81  | | End of split
% 240.08/46.81  | | 
% 240.08/46.81  | End of split
% 240.08/46.81  | 
% 240.08/46.81  End of proof
% 240.08/46.81  
% 240.08/46.81  Sub-proof #238 shows that the following formulas are inconsistent:
% 240.08/46.81  ----------------------------------------------------------------
% 240.08/46.81    (1)   ~ (e3 = e0)
% 240.08/46.81    (2)   ~ (e2 = e0)
% 240.08/46.81    (3)  all_58_6 = e2
% 240.08/46.81    (4)  op(e1, e1) = all_6_2
% 240.08/46.81    (5)   ~ (all_6_2 = e3)
% 240.08/46.81    (6)   ~ (e3 = e2)
% 240.08/46.81    (7)   ~ (all_6_2 = e0)
% 240.08/46.81    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.08/46.81         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.08/46.81    (9)  all_58_11 = e2
% 240.08/46.81    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.81    (11)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.08/46.81          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.08/46.81  
% 240.08/46.81  Begin of proof
% 240.08/46.81  | 
% 240.08/46.81  | BETA: splitting (11) gives:
% 240.08/46.81  | 
% 240.08/46.81  | Case 1:
% 240.08/46.81  | | 
% 240.08/46.81  | |   (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 240.08/46.81  | |           e0)
% 240.08/46.81  | | 
% 240.08/46.81  | | BETA: splitting (12) gives:
% 240.08/46.81  | | 
% 240.08/46.81  | | Case 1:
% 240.08/46.81  | | | 
% 240.08/46.81  | | |   (13)  all_58_6 = e0 & op(e1, e3) = e0
% 240.08/46.81  | | | 
% 240.08/46.81  | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #1678.
% 240.08/46.81  | | | 
% 240.08/46.81  | | Case 2:
% 240.08/46.81  | | | 
% 240.08/46.81  | | |   (14)  all_58_7 = e0 & op(e1, e2) = e0
% 240.08/46.81  | | | 
% 240.08/46.81  | | | ALPHA: (14) implies:
% 240.08/46.81  | | |   (15)  all_58_7 = e0
% 240.08/46.81  | | | 
% 240.08/46.81  | | | BETA: splitting (8) gives:
% 240.08/46.81  | | | 
% 240.08/46.81  | | | Case 1:
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | |   (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 240.08/46.81  | | | |           = e3)
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | | BETA: splitting (16) gives:
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | | Case 1:
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | |   (17)  all_58_6 = e3 & op(e1, e3) = e3
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | ALPHA: (17) implies:
% 240.08/46.81  | | | | |   (18)  all_58_6 = e3
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | REF_CLOSE: (3), (6), (18) are inconsistent by sub-proof #2024.
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | Case 2:
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | |   (19)  all_58_7 = e3 & op(e1, e2) = e3
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | REF_CLOSE: (1), (15), (19) are inconsistent by sub-proof #2150.
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | End of split
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | Case 2:
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | |   (20)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 240.08/46.81  | | | |           = e3)
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | | BETA: splitting (20) gives:
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | | Case 1:
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | |   (21)  all_58_8 = e3 & op(e1, e1) = e3
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | REF_CLOSE: (4), (5), (10), (21) are inconsistent by sub-proof #2092.
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | Case 2:
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | |   (22)  all_58_11 = e3 & op(e1, e0) = e3
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | | REF_CLOSE: (6), (9), (22) are inconsistent by sub-proof #2108.
% 240.08/46.81  | | | | | 
% 240.08/46.81  | | | | End of split
% 240.08/46.81  | | | | 
% 240.08/46.81  | | | End of split
% 240.08/46.81  | | | 
% 240.08/46.81  | | End of split
% 240.08/46.81  | | 
% 240.08/46.81  | Case 2:
% 240.08/46.81  | | 
% 240.08/46.81  | |   (23)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.08/46.81  | |           e0)
% 240.08/46.81  | | 
% 240.08/46.81  | | BETA: splitting (23) gives:
% 240.08/46.81  | | 
% 240.08/46.81  | | Case 1:
% 240.08/46.81  | | | 
% 240.08/46.81  | | |   (24)  all_58_8 = e0 & op(e1, e1) = e0
% 240.08/46.81  | | | 
% 240.08/46.81  | | | REF_CLOSE: (4), (7), (10), (24) are inconsistent by sub-proof #1833.
% 240.08/46.81  | | | 
% 240.08/46.81  | | Case 2:
% 240.08/46.81  | | | 
% 240.08/46.81  | | |   (25)  all_58_11 = e0 & op(e1, e0) = e0
% 240.08/46.81  | | | 
% 240.08/46.81  | | | REF_CLOSE: (2), (9), (25) are inconsistent by sub-proof #2033.
% 240.08/46.81  | | | 
% 240.08/46.81  | | End of split
% 240.08/46.81  | | 
% 240.08/46.81  | End of split
% 240.08/46.81  | 
% 240.08/46.81  End of proof
% 240.08/46.81  
% 240.08/46.81  Sub-proof #239 shows that the following formulas are inconsistent:
% 240.08/46.81  ----------------------------------------------------------------
% 240.08/46.81    (1)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 240.08/46.81    (2)  all_58_6 = e2
% 240.08/46.81    (3)   ~ (e3 = e2)
% 240.08/46.81    (4)  op(e1, e2) = e2
% 240.08/46.81    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.81  
% 240.08/46.81  Begin of proof
% 240.08/46.81  | 
% 240.08/46.81  | BETA: splitting (1) gives:
% 240.08/46.81  | 
% 240.08/46.81  | Case 1:
% 240.08/46.81  | | 
% 240.08/46.81  | |   (6)  all_58_6 = e3 & op(e1, e3) = e3
% 240.08/46.81  | | 
% 240.08/46.81  | | ALPHA: (6) implies:
% 240.08/46.81  | |   (7)  all_58_6 = e3
% 240.08/46.81  | | 
% 240.08/46.81  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #2024.
% 240.08/46.81  | | 
% 240.08/46.81  | Case 2:
% 240.08/46.81  | | 
% 240.08/46.82  | |   (8)  all_58_7 = e3 & op(e1, e2) = e3
% 240.08/46.82  | | 
% 240.08/46.82  | | ALPHA: (8) implies:
% 240.08/46.82  | |   (9)  op(e1, e2) = e3
% 240.08/46.82  | | 
% 240.08/46.82  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #2207.
% 240.08/46.82  | | 
% 240.08/46.82  | End of split
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #240 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)   ~ (all_52_9 = all_6_2)
% 240.08/46.82    (2)   ~ (all_52_7 = e2)
% 240.08/46.82    (3)  all_54_10 = e1 | all_54_10 = e0
% 240.08/46.82    (4)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.08/46.82           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.08/46.82             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.82           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.08/46.82             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.82           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.82           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.08/46.82           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.08/46.82           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.08/46.82           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.82           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.08/46.82             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.08/46.82           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.82           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 240.08/46.82           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.08/46.82           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.08/46.82           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.82           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.08/46.82             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.08/46.82           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.82           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 240.08/46.82           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.08/46.82           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.08/46.82           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.82           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.08/46.82             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.08/46.82           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.82           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.82    (5)  op(e1, e0) = all_52_14
% 240.08/46.82    (6)   ~ (e3 = e1)
% 240.08/46.82    (7)   ~ (all_52_12 = all_52_14)
% 240.08/46.82    (8)  all_54_10 = all_6_2
% 240.08/46.82    (9)  all_58_9 = e1 & op(e3, e0) = e1
% 240.08/46.82    (10)   ~ (all_52_8 = all_52_12)
% 240.08/46.82    (11)  op(e3, e1) = all_52_8
% 240.08/46.82    (12)  op(e2, e1) = all_52_9
% 240.08/46.82    (13)   ~ (all_6_2 = e0)
% 240.08/46.82    (14)  all_56_31 = e2
% 240.08/46.82    (15)  op(e3, e0) = all_52_12
% 240.08/46.82    (16)  op(e0, e2) = all_52_7
% 240.08/46.82    (17)  op(e3, e2) = all_52_4
% 240.08/46.82    (18)  all_56_21 = e1
% 240.08/46.82    (19)   ~ (all_52_4 = e2)
% 240.08/46.82    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.82    (21)   ~ (e1 = e0)
% 240.08/46.82  
% 240.08/46.82  Begin of proof
% 240.08/46.82  | 
% 240.08/46.82  | ALPHA: (9) implies:
% 240.08/46.82  |   (22)  op(e3, e0) = e1
% 240.08/46.82  | 
% 240.08/46.82  | GROUND_INST: instantiating (20) with all_52_12, e1, e0, e3, simplifying with
% 240.08/46.82  |              (15), (22) gives:
% 240.08/46.82  |   (23)  all_52_12 = e1
% 240.08/46.82  | 
% 240.08/46.82  | REDUCE: (10), (23) imply:
% 240.08/46.82  |   (24)   ~ (all_52_8 = e1)
% 240.08/46.82  | 
% 240.08/46.82  | REDUCE: (7), (23) imply:
% 240.08/46.82  |   (25)   ~ (all_52_14 = e1)
% 240.08/46.82  | 
% 240.08/46.82  | SIMP: (25) implies:
% 240.08/46.82  |   (26)   ~ (all_52_14 = e1)
% 240.08/46.82  | 
% 240.08/46.82  | BETA: splitting (4) gives:
% 240.08/46.82  | 
% 240.08/46.82  | Case 1:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (27)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.08/46.82  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 240.08/46.82  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 240.08/46.82  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.82  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 240.08/46.82  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 240.08/46.82  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.08/46.82  | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 240.08/46.82  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.82  | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 240.08/46.82  | |           = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &
% 240.08/46.82  | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.08/46.82  | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 240.08/46.82  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.08/46.82  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.82  | | 
% 240.08/46.82  | | BETA: splitting (27) gives:
% 240.08/46.82  | | 
% 240.08/46.82  | | Case 1:
% 240.08/46.82  | | | 
% 240.08/46.82  | | |   (28)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.82  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.82  | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.08/46.82  | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.08/46.82  | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 240.08/46.82  | | |         | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.82  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.82  | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.82  | | | 
% 240.08/46.82  | | | REF_CLOSE: (14), (17), (18), (19), (20), (28) are inconsistent by
% 240.08/46.82  | | |            sub-proof #244.
% 240.08/46.82  | | | 
% 240.08/46.82  | | Case 2:
% 240.08/46.82  | | | 
% 240.08/46.82  | | |   (29)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.82  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.82  | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 240.08/46.82  | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 240.08/46.82  | | |             = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 240.08/46.82  | | |           e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.82  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.82  | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.08/46.82  | | | 
% 240.08/46.82  | | | BETA: splitting (29) gives:
% 240.08/46.82  | | | 
% 240.08/46.82  | | | Case 1:
% 240.08/46.82  | | | | 
% 240.08/46.82  | | | |   (30)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.82  | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.82  | | | |         op(e3, e1) = e1 & op(e1, e3) = e1
% 240.08/46.82  | | | | 
% 240.08/46.82  | | | | ALPHA: (30) implies:
% 240.08/46.82  | | | |   (31)  op(e3, e1) = e1
% 240.08/46.82  | | | | 
% 240.08/46.82  | | | | REF_CLOSE: (11), (20), (24), (31) are inconsistent by sub-proof #2309.
% 240.08/46.82  | | | | 
% 240.08/46.82  | | | Case 2:
% 240.08/46.82  | | | | 
% 240.08/46.82  | | | |   (32)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.82  | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.82  | | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 240.08/46.82  | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.08/46.82  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 240.08/46.82  | | | |           op(e0, e3) = e0)
% 240.08/46.82  | | | | 
% 240.08/46.82  | | | | BETA: splitting (32) gives:
% 240.08/46.82  | | | | 
% 240.08/46.82  | | | | Case 1:
% 240.08/46.82  | | | | | 
% 240.08/46.82  | | | | |   (33)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.82  | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.82  | | | | |         op(e3, e0) = e3 & op(e0, e3) = e3
% 240.08/46.82  | | | | | 
% 240.08/46.82  | | | | | ALPHA: (33) implies:
% 240.08/46.82  | | | | |   (34)  op(e3, e0) = e3
% 240.08/46.82  | | | | | 
% 240.08/46.82  | | | | | REF_CLOSE: (6), (20), (22), (34) are inconsistent by sub-proof #243.
% 240.08/46.82  | | | | | 
% 240.08/46.82  | | | | Case 2:
% 240.08/46.82  | | | | | 
% 240.08/46.82  | | | | |   (35)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.82  | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.08/46.82  | | | | |         op(e3, e0) = e0 & op(e0, e3) = e0
% 240.08/46.82  | | | | | 
% 240.08/46.82  | | | | | ALPHA: (35) implies:
% 240.08/46.82  | | | | |   (36)  op(e3, e0) = e0
% 240.08/46.82  | | | | | 
% 240.08/46.82  | | | | | REF_CLOSE: (20), (21), (22), (36) are inconsistent by sub-proof #242.
% 240.08/46.82  | | | | | 
% 240.08/46.82  | | | | End of split
% 240.08/46.82  | | | | 
% 240.08/46.82  | | | End of split
% 240.08/46.82  | | | 
% 240.08/46.82  | | End of split
% 240.08/46.82  | | 
% 240.08/46.82  | Case 2:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (37)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.82  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.82  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.08/46.82  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.08/46.82  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 240.08/46.82  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.82  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.82  | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 240.08/46.82  | |           e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.08/46.82  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 240.08/46.82  | |         (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.82  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.82  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.08/46.82  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.08/46.82  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.82  | | 
% 240.08/46.82  | | REF_CLOSE: (1), (2), (3), (5), (8), (12), (13), (14), (16), (18), (20),
% 240.08/46.82  | |            (26), (37) are inconsistent by sub-proof #241.
% 240.08/46.82  | | 
% 240.08/46.82  | End of split
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #241 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)   ~ (all_52_9 = all_6_2)
% 240.08/46.82    (2)   ~ (all_52_7 = e2)
% 240.08/46.82    (3)  all_54_10 = e1 | all_54_10 = e0
% 240.08/46.82    (4)  op(e1, e0) = all_52_14
% 240.08/46.82    (5)  all_54_10 = all_6_2
% 240.08/46.82    (6)  op(e2, e1) = all_52_9
% 240.08/46.82    (7)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.08/46.82             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.08/46.82           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.08/46.82             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 240.08/46.82           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 240.08/46.82           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.08/46.82           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 240.08/46.82           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.08/46.82           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.08/46.82           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.82           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.08/46.82             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.08/46.82           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.82           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.82    (8)   ~ (all_52_14 = e1)
% 240.08/46.82    (9)   ~ (all_6_2 = e0)
% 240.08/46.82    (10)  all_56_31 = e2
% 240.08/46.82    (11)  op(e0, e2) = all_52_7
% 240.08/46.82    (12)  all_56_21 = e1
% 240.08/46.82    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.82  
% 240.08/46.82  Begin of proof
% 240.08/46.82  | 
% 240.08/46.82  | BETA: splitting (7) gives:
% 240.08/46.82  | 
% 240.08/46.82  | Case 1:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (14)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.82  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.82  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.08/46.82  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.08/46.82  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 240.08/46.82  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.82  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.82  | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.82  | | 
% 240.08/46.82  | | BETA: splitting (14) gives:
% 240.08/46.82  | | 
% 240.08/46.82  | | Case 1:
% 240.08/46.82  | | | 
% 240.08/46.82  | | |   (15)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.82  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.82  | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 240.08/46.82  | | | 
% 240.08/46.82  | | | ALPHA: (15) implies:
% 240.08/46.82  | | |   (16)   ~ (all_56_21 = e1)
% 240.08/46.82  | | | 
% 240.08/46.82  | | | REDUCE: (12), (16) imply:
% 240.08/46.82  | | |   (17)  $false
% 240.08/46.82  | | | 
% 240.08/46.82  | | | CLOSE: (17) is inconsistent.
% 240.08/46.82  | | | 
% 240.08/46.82  | | Case 2:
% 240.08/46.82  | | | 
% 240.08/46.82  | | |   (18)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.82  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.82  | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27
% 240.08/46.82  | | |           = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 240.08/46.82  | | |             = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 240.08/46.82  | | |           e2)
% 240.08/46.82  | | | 
% 240.08/46.82  | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (11), (13), (18) are inconsistent
% 240.08/46.82  | | |            by sub-proof #1904.
% 240.08/46.82  | | | 
% 240.08/46.82  | | End of split
% 240.08/46.82  | | 
% 240.08/46.82  | Case 2:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (19)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.08/46.82  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.08/46.82  | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.08/46.82  | |           e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.08/46.82  | |             e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 240.08/46.82  | |         (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.82  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.08/46.82  | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.82  | | 
% 240.08/46.82  | | REF_CLOSE: (4), (8), (10), (12), (13), (19) are inconsistent by sub-proof
% 240.08/46.82  | |            #251.
% 240.08/46.82  | | 
% 240.08/46.82  | End of split
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #242 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.82    (2)  op(e3, e0) = e1
% 240.08/46.82    (3)  op(e3, e0) = e0
% 240.08/46.82    (4)   ~ (e1 = e0)
% 240.08/46.82  
% 240.08/46.82  Begin of proof
% 240.08/46.82  | 
% 240.08/46.82  | GROUND_INST: instantiating (1) with e1, e0, e0, e3, simplifying with (2), (3)
% 240.08/46.82  |              gives:
% 240.08/46.82  |   (5)  e1 = e0
% 240.08/46.82  | 
% 240.08/46.82  | REDUCE: (4), (5) imply:
% 240.08/46.82  |   (6)  $false
% 240.08/46.82  | 
% 240.08/46.82  | CLOSE: (6) is inconsistent.
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #243 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.82    (2)  op(e3, e0) = e3
% 240.08/46.82    (3)  op(e3, e0) = e1
% 240.08/46.82    (4)   ~ (e3 = e1)
% 240.08/46.82  
% 240.08/46.82  Begin of proof
% 240.08/46.82  | 
% 240.08/46.82  | GROUND_INST: instantiating (1) with e1, e3, e0, e3, simplifying with (2), (3)
% 240.08/46.82  |              gives:
% 240.08/46.82  |   (5)  e3 = e1
% 240.08/46.82  | 
% 240.08/46.82  | REDUCE: (4), (5) imply:
% 240.08/46.82  |   (6)  $false
% 240.08/46.82  | 
% 240.08/46.82  | CLOSE: (6) is inconsistent.
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #244 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.08/46.82           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.08/46.82             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.82           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.08/46.82             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.82           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.82           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.82    (2)  all_56_31 = e2
% 240.08/46.82    (3)  op(e3, e2) = all_52_4
% 240.08/46.82    (4)  all_56_21 = e1
% 240.08/46.82    (5)   ~ (all_52_4 = e2)
% 240.08/46.82    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.82  
% 240.08/46.82  Begin of proof
% 240.08/46.82  | 
% 240.08/46.82  | BETA: splitting (1) gives:
% 240.08/46.82  | 
% 240.08/46.82  | Case 1:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.82  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.08/46.82  | |        op(e2, e3) = e3
% 240.08/46.82  | | 
% 240.08/46.82  | | ALPHA: (7) implies:
% 240.08/46.82  | |   (8)   ~ (all_56_31 = e2)
% 240.08/46.82  | | 
% 240.08/46.82  | | REDUCE: (2), (8) imply:
% 240.08/46.82  | |   (9)  $false
% 240.08/46.82  | | 
% 240.08/46.82  | | CLOSE: (9) is inconsistent.
% 240.08/46.82  | | 
% 240.08/46.82  | Case 2:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.08/46.82  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.08/46.82  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.82  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.82  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.82  | | 
% 240.08/46.82  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #245.
% 240.08/46.82  | | 
% 240.08/46.82  | End of split
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #245 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 240.08/46.82           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 240.08/46.82             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.82           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 240.08/46.82             e1) = e3 & op(e1, e3) = e3)
% 240.08/46.82    (2)  op(e3, e2) = all_52_4
% 240.08/46.82    (3)  all_56_21 = e1
% 240.08/46.82    (4)   ~ (all_52_4 = e2)
% 240.08/46.82    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.82  
% 240.08/46.82  Begin of proof
% 240.08/46.82  | 
% 240.08/46.82  | BETA: splitting (1) gives:
% 240.08/46.82  | 
% 240.08/46.82  | Case 1:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (6)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.08/46.82  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.08/46.82  | |        op(e2, e3) = e2
% 240.08/46.82  | | 
% 240.08/46.82  | | ALPHA: (6) implies:
% 240.08/46.82  | |   (7)  op(e3, e2) = e2
% 240.08/46.82  | | 
% 240.08/46.82  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #254.
% 240.08/46.82  | | 
% 240.08/46.82  | Case 2:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (8)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.08/46.82  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.08/46.82  | |        op(e1, e3) = e3
% 240.08/46.82  | | 
% 240.08/46.82  | | ALPHA: (8) implies:
% 240.08/46.82  | |   (9)   ~ (all_56_21 = e1)
% 240.08/46.82  | | 
% 240.08/46.82  | | REDUCE: (3), (9) imply:
% 240.08/46.82  | |   (10)  $false
% 240.08/46.82  | | 
% 240.08/46.82  | | CLOSE: (10) is inconsistent.
% 240.08/46.82  | | 
% 240.08/46.82  | End of split
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #246 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 240.08/46.82    (2)  op(e2, e2) = e1
% 240.08/46.82    (3)  op(e3, e2) = all_52_4
% 240.08/46.82    (4)   ~ (all_52_4 = e2)
% 240.08/46.82    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.82    (6)   ~ (e2 = e1)
% 240.08/46.82  
% 240.08/46.82  Begin of proof
% 240.08/46.82  | 
% 240.08/46.82  | BETA: splitting (1) gives:
% 240.08/46.82  | 
% 240.08/46.82  | Case 1:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (7)  all_58_1 = e2 & op(e3, e2) = e2
% 240.08/46.82  | | 
% 240.08/46.82  | | ALPHA: (7) implies:
% 240.08/46.82  | |   (8)  op(e3, e2) = e2
% 240.08/46.82  | | 
% 240.08/46.82  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #254.
% 240.08/46.82  | | 
% 240.08/46.82  | Case 2:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (9)  all_58_3 = e2 & op(e2, e2) = e2
% 240.08/46.82  | | 
% 240.08/46.82  | | ALPHA: (9) implies:
% 240.08/46.82  | |   (10)  op(e2, e2) = e2
% 240.08/46.82  | | 
% 240.08/46.82  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #2235.
% 240.08/46.82  | | 
% 240.08/46.82  | End of split
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #247 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)   ~ (e3 = e0)
% 240.08/46.82    (2)   ~ (e2 = e0)
% 240.08/46.82    (3)  op(e1, e2) = all_52_6
% 240.08/46.82    (4)   ~ (all_52_6 = e2)
% 240.08/46.82    (5)  all_58_4 = e2
% 240.08/46.82    (6)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.08/46.82         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.08/46.82    (7)  op(e1, e0) = all_52_14
% 240.08/46.82    (8)   ~ (e3 = e1)
% 240.08/46.82    (9)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.08/46.82         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.82    (10)   ~ (all_52_14 = e2)
% 240.08/46.82    (11)  op(e2, e1) = all_52_9
% 240.08/46.82    (12)   ~ (e3 = e2)
% 240.08/46.82    (13)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.08/46.82          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.08/46.82    (14)   ~ (all_52_2 = e2)
% 240.08/46.82    (15)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.08/46.82          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.08/46.82    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.82    (17)  op(e1, e3) = all_52_2
% 240.08/46.82    (18)   ~ (e1 = e0)
% 240.08/46.82    (19)   ~ (e2 = e1)
% 240.08/46.82  
% 240.08/46.82  Begin of proof
% 240.08/46.82  | 
% 240.08/46.82  | BETA: splitting (15) gives:
% 240.08/46.82  | 
% 240.08/46.82  | Case 1:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (20)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 240.08/46.82  | |           e2)
% 240.08/46.82  | | 
% 240.08/46.82  | | BETA: splitting (20) gives:
% 240.08/46.82  | | 
% 240.08/46.82  | | Case 1:
% 240.08/46.82  | | | 
% 240.08/46.82  | | |   (21)  all_58_6 = e2 & op(e1, e3) = e2
% 240.08/46.82  | | | 
% 240.08/46.82  | | | REF_CLOSE: (14), (16), (17), (21) are inconsistent by sub-proof #250.
% 240.08/46.82  | | | 
% 240.08/46.82  | | Case 2:
% 240.08/46.82  | | | 
% 240.08/46.82  | | |   (22)  all_58_7 = e2 & op(e1, e2) = e2
% 240.08/46.82  | | | 
% 240.08/46.82  | | | ALPHA: (22) implies:
% 240.08/46.82  | | |   (23)  op(e1, e2) = e2
% 240.08/46.82  | | | 
% 240.08/46.82  | | | REF_CLOSE: (3), (4), (16), (23) are inconsistent by sub-proof #249.
% 240.08/46.82  | | | 
% 240.08/46.82  | | End of split
% 240.08/46.82  | | 
% 240.08/46.82  | Case 2:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (24)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 240.08/46.82  | |           e2)
% 240.08/46.82  | | 
% 240.08/46.82  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (16),
% 240.08/46.82  | |            (18), (19), (24) are inconsistent by sub-proof #248.
% 240.08/46.82  | | 
% 240.08/46.82  | End of split
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #248 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)   ~ (e3 = e0)
% 240.08/46.82    (2)   ~ (e2 = e0)
% 240.08/46.82    (3)  all_58_4 = e2
% 240.08/46.82    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.08/46.82         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.08/46.82    (5)  op(e1, e0) = all_52_14
% 240.08/46.82    (6)   ~ (e3 = e1)
% 240.08/46.82    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.08/46.82         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.82    (8)   ~ (all_52_14 = e2)
% 240.08/46.82    (9)  op(e2, e1) = all_52_9
% 240.08/46.82    (10)   ~ (e3 = e2)
% 240.08/46.82    (11)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.08/46.82    (12)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.08/46.82          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.08/46.82    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.82    (14)   ~ (e1 = e0)
% 240.08/46.82    (15)   ~ (e2 = e1)
% 240.08/46.82  
% 240.08/46.82  Begin of proof
% 240.08/46.82  | 
% 240.08/46.82  | BETA: splitting (11) gives:
% 240.08/46.82  | 
% 240.08/46.82  | Case 1:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (16)  all_58_8 = e2 & op(e1, e1) = e2
% 240.08/46.82  | | 
% 240.08/46.82  | | ALPHA: (16) implies:
% 240.08/46.82  | |   (17)  op(e1, e1) = e2
% 240.08/46.82  | | 
% 240.08/46.82  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (12), (13), (14), (15),
% 240.08/46.82  | |            (17) are inconsistent by sub-proof #1899.
% 240.08/46.82  | | 
% 240.08/46.82  | Case 2:
% 240.08/46.82  | | 
% 240.08/46.82  | |   (18)  all_58_11 = e2 & op(e1, e0) = e2
% 240.08/46.82  | | 
% 240.08/46.82  | | REF_CLOSE: (5), (8), (13), (18) are inconsistent by sub-proof #258.
% 240.08/46.82  | | 
% 240.08/46.82  | End of split
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #249 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.82    (2)  op(e1, e2) = all_52_6
% 240.08/46.82    (3)  op(e1, e2) = e2
% 240.08/46.82    (4)   ~ (all_52_6 = e2)
% 240.08/46.82  
% 240.08/46.82  Begin of proof
% 240.08/46.82  | 
% 240.08/46.82  | GROUND_INST: instantiating (1) with all_52_6, e2, e2, e1, simplifying with
% 240.08/46.82  |              (2), (3) gives:
% 240.08/46.82  |   (5)  all_52_6 = e2
% 240.08/46.82  | 
% 240.08/46.82  | REDUCE: (4), (5) imply:
% 240.08/46.82  |   (6)  $false
% 240.08/46.82  | 
% 240.08/46.82  | CLOSE: (6) is inconsistent.
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #250 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)  all_58_6 = e2 & op(e1, e3) = e2
% 240.08/46.82    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.82    (3)  op(e1, e3) = all_52_2
% 240.08/46.82    (4)   ~ (all_52_2 = e2)
% 240.08/46.82  
% 240.08/46.82  Begin of proof
% 240.08/46.82  | 
% 240.08/46.82  | ALPHA: (1) implies:
% 240.08/46.82  |   (5)  op(e1, e3) = e2
% 240.08/46.82  | 
% 240.08/46.82  | GROUND_INST: instantiating (2) with all_52_2, e2, e3, e1, simplifying with
% 240.08/46.82  |              (3), (5) gives:
% 240.08/46.82  |   (6)  all_52_2 = e2
% 240.08/46.82  | 
% 240.08/46.82  | REDUCE: (4), (6) imply:
% 240.08/46.82  |   (7)  $false
% 240.08/46.82  | 
% 240.08/46.82  | CLOSE: (7) is inconsistent.
% 240.08/46.82  | 
% 240.08/46.82  End of proof
% 240.08/46.82  
% 240.08/46.82  Sub-proof #251 shows that the following formulas are inconsistent:
% 240.08/46.82  ----------------------------------------------------------------
% 240.08/46.82    (1)  op(e1, e0) = all_52_14
% 240.08/46.82    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.82             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.08/46.82           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.08/46.82             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.08/46.82           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 240.08/46.82           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.82           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.83    (3)   ~ (all_52_14 = e1)
% 240.08/46.83    (4)  all_56_31 = e2
% 240.08/46.83    (5)  all_56_21 = e1
% 240.08/46.83    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.83  
% 240.08/46.83  Begin of proof
% 240.08/46.83  | 
% 240.08/46.83  | BETA: splitting (2) gives:
% 240.08/46.83  | 
% 240.08/46.83  | Case 1:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (7)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.08/46.83  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 240.08/46.83  | |        & op(e0, e2) = e0
% 240.08/46.83  | | 
% 240.08/46.83  | | ALPHA: (7) implies:
% 240.08/46.83  | |   (8)   ~ (all_56_31 = e2)
% 240.08/46.83  | | 
% 240.08/46.83  | | REDUCE: (4), (8) imply:
% 240.08/46.83  | |   (9)  $false
% 240.08/46.83  | | 
% 240.08/46.83  | | CLOSE: (9) is inconsistent.
% 240.08/46.83  | | 
% 240.08/46.83  | Case 2:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.08/46.83  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.08/46.83  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.08/46.83  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.08/46.83  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.08/46.83  | | 
% 240.08/46.83  | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #1409.
% 240.08/46.83  | | 
% 240.08/46.83  | End of split
% 240.08/46.83  | 
% 240.08/46.83  End of proof
% 240.08/46.83  
% 240.08/46.83  Sub-proof #252 shows that the following formulas are inconsistent:
% 240.08/46.83  ----------------------------------------------------------------
% 240.08/46.83    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.08/46.83           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.08/46.83             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.08/46.83           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.08/46.83             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.83           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.83           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.83    (2)  op(e2, e3) = all_52_1
% 240.08/46.83    (3)   ~ (all_52_2 = e3)
% 240.08/46.83    (4)  op(e3, e2) = all_52_4
% 240.08/46.83    (5)   ~ (all_52_4 = e2)
% 240.08/46.83    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.83    (7)  op(e1, e3) = all_52_2
% 240.08/46.83    (8)   ~ (all_52_1 = e3)
% 240.08/46.83  
% 240.08/46.83  Begin of proof
% 240.08/46.83  | 
% 240.08/46.83  | BETA: splitting (1) gives:
% 240.08/46.83  | 
% 240.08/46.83  | Case 1:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (9)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.83  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.08/46.83  | |        op(e2, e3) = e3
% 240.08/46.83  | | 
% 240.08/46.83  | | ALPHA: (9) implies:
% 240.08/46.83  | |   (10)  op(e2, e3) = e3
% 240.08/46.83  | | 
% 240.08/46.83  | | REF_CLOSE: (2), (6), (8), (10) are inconsistent by sub-proof #2337.
% 240.08/46.83  | | 
% 240.08/46.83  | Case 2:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (11)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.08/46.83  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.08/46.83  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.08/46.83  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.08/46.83  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.08/46.83  | | 
% 240.08/46.83  | | REF_CLOSE: (3), (4), (5), (6), (7), (11) are inconsistent by sub-proof #253.
% 240.08/46.83  | | 
% 240.08/46.83  | End of split
% 240.08/46.83  | 
% 240.08/46.83  End of proof
% 240.08/46.83  
% 240.08/46.83  Sub-proof #253 shows that the following formulas are inconsistent:
% 240.08/46.83  ----------------------------------------------------------------
% 240.08/46.83    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 240.08/46.83           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 240.08/46.83             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.08/46.83           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 240.08/46.83             e1) = e3 & op(e1, e3) = e3)
% 240.08/46.83    (2)   ~ (all_52_2 = e3)
% 240.08/46.83    (3)  op(e3, e2) = all_52_4
% 240.08/46.83    (4)   ~ (all_52_4 = e2)
% 240.08/46.83    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.83    (6)  op(e1, e3) = all_52_2
% 240.08/46.83  
% 240.08/46.83  Begin of proof
% 240.08/46.83  | 
% 240.08/46.83  | BETA: splitting (1) gives:
% 240.08/46.83  | 
% 240.08/46.83  | Case 1:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.08/46.83  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.08/46.83  | |        op(e2, e3) = e2
% 240.08/46.83  | | 
% 240.08/46.83  | | ALPHA: (7) implies:
% 240.08/46.83  | |   (8)  op(e3, e2) = e2
% 240.08/46.83  | | 
% 240.08/46.83  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #254.
% 240.08/46.83  | | 
% 240.08/46.83  | Case 2:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.08/46.83  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.08/46.83  | |        op(e1, e3) = e3
% 240.08/46.83  | | 
% 240.08/46.83  | | ALPHA: (9) implies:
% 240.08/46.83  | |   (10)  op(e1, e3) = e3
% 240.08/46.83  | | 
% 240.08/46.83  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #2335.
% 240.08/46.83  | | 
% 240.08/46.83  | End of split
% 240.08/46.83  | 
% 240.08/46.83  End of proof
% 240.08/46.83  
% 240.08/46.83  Sub-proof #254 shows that the following formulas are inconsistent:
% 240.08/46.83  ----------------------------------------------------------------
% 240.08/46.83    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.83    (2)  op(e3, e2) = all_52_4
% 240.08/46.83    (3)  op(e3, e2) = e2
% 240.08/46.83    (4)   ~ (all_52_4 = e2)
% 240.08/46.83  
% 240.08/46.83  Begin of proof
% 240.08/46.83  | 
% 240.08/46.83  | GROUND_INST: instantiating (1) with all_52_4, e2, e2, e3, simplifying with
% 240.08/46.83  |              (2), (3) gives:
% 240.08/46.83  |   (5)  all_52_4 = e2
% 240.08/46.83  | 
% 240.08/46.83  | REDUCE: (4), (5) imply:
% 240.08/46.83  |   (6)  $false
% 240.08/46.83  | 
% 240.08/46.83  | CLOSE: (6) is inconsistent.
% 240.08/46.83  | 
% 240.08/46.83  End of proof
% 240.08/46.83  
% 240.08/46.83  Sub-proof #255 shows that the following formulas are inconsistent:
% 240.08/46.83  ----------------------------------------------------------------
% 240.08/46.83    (1)   ~ (e3 = e0)
% 240.08/46.83    (2)   ~ (e2 = e0)
% 240.08/46.83    (3)  all_58_6 = e2
% 240.08/46.83    (4)   ~ (e3 = e1)
% 240.08/46.83    (5)  op(e1, e3) = e2
% 240.08/46.83    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 240.08/46.83         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 240.08/46.83    (7)   ~ (e3 = e2)
% 240.08/46.83    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.08/46.83         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.08/46.83    (9)  op(e2, e3) = all_52_1
% 240.08/46.83    (10)  op(e3, e3) = e2
% 240.08/46.83    (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.08/46.83          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.08/46.83    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.83    (13)   ~ (e1 = e0)
% 240.08/46.83    (14)   ~ (all_52_1 = e3)
% 240.08/46.83    (15)   ~ (e2 = e1)
% 240.08/46.83  
% 240.08/46.83  Begin of proof
% 240.08/46.83  | 
% 240.08/46.83  | BETA: splitting (6) gives:
% 240.08/46.83  | 
% 240.08/46.83  | Case 1:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 240.08/46.83  | |           e3)
% 240.08/46.83  | | 
% 240.08/46.83  | | REF_CLOSE: (7), (9), (10), (12), (14), (16) are inconsistent by sub-proof
% 240.08/46.83  | |            #1404.
% 240.08/46.83  | | 
% 240.08/46.83  | Case 2:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (17)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 240.08/46.83  | |           e3)
% 240.08/46.83  | | 
% 240.08/46.83  | | BETA: splitting (17) gives:
% 240.08/46.83  | | 
% 240.08/46.83  | | Case 1:
% 240.08/46.83  | | | 
% 240.08/46.83  | | |   (18)  all_58_6 = e3 & op(e1, e3) = e3
% 240.08/46.83  | | | 
% 240.08/46.83  | | | ALPHA: (18) implies:
% 240.08/46.83  | | |   (19)  all_58_6 = e3
% 240.08/46.83  | | | 
% 240.08/46.83  | | | REF_CLOSE: (3), (7), (19) are inconsistent by sub-proof #2024.
% 240.08/46.83  | | | 
% 240.08/46.83  | | Case 2:
% 240.08/46.83  | | | 
% 240.08/46.83  | | |   (20)  all_58_12 = e3 & op(e0, e3) = e3
% 240.08/46.83  | | | 
% 240.08/46.83  | | | ALPHA: (20) implies:
% 240.08/46.83  | | |   (21)  all_58_12 = e3
% 240.08/46.83  | | | 
% 240.08/46.83  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (11), (12), (13), (15),
% 240.08/46.83  | | |            (21) are inconsistent by sub-proof #256.
% 240.08/46.83  | | | 
% 240.08/46.83  | | End of split
% 240.08/46.83  | | 
% 240.08/46.83  | End of split
% 240.08/46.83  | 
% 240.08/46.83  End of proof
% 240.08/46.83  
% 240.08/46.83  Sub-proof #256 shows that the following formulas are inconsistent:
% 240.08/46.83  ----------------------------------------------------------------
% 240.08/46.83    (1)   ~ (e3 = e0)
% 240.08/46.83    (2)   ~ (e2 = e0)
% 240.08/46.83    (3)  all_58_6 = e2
% 240.08/46.83    (4)   ~ (e3 = e1)
% 240.08/46.83    (5)  op(e1, e3) = e2
% 240.08/46.83    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.08/46.83         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.08/46.83    (7)  op(e3, e3) = e2
% 240.08/46.83    (8)  all_58_12 = e3
% 240.08/46.83    (9)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.08/46.83         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.08/46.83    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.83    (11)   ~ (e1 = e0)
% 240.08/46.83    (12)   ~ (e2 = e1)
% 240.08/46.83  
% 240.08/46.83  Begin of proof
% 240.08/46.83  | 
% 240.08/46.83  | BETA: splitting (6) gives:
% 240.08/46.83  | 
% 240.08/46.83  | Case 1:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 240.08/46.83  | |           e0)
% 240.08/46.83  | | 
% 240.08/46.83  | | BETA: splitting (13) gives:
% 240.08/46.83  | | 
% 240.08/46.83  | | Case 1:
% 240.08/46.83  | | | 
% 240.08/46.83  | | |   (14)  all_58_0 = e0 & op(e3, e3) = e0
% 240.08/46.83  | | | 
% 240.08/46.83  | | | ALPHA: (14) implies:
% 240.08/46.83  | | |   (15)  op(e3, e3) = e0
% 240.08/46.83  | | | 
% 240.08/46.83  | | | REF_CLOSE: (2), (7), (10), (15) are inconsistent by sub-proof #2188.
% 240.08/46.83  | | | 
% 240.08/46.83  | | Case 2:
% 240.08/46.83  | | | 
% 240.08/46.83  | | |   (16)  all_58_2 = e0 & op(e2, e3) = e0
% 240.08/46.83  | | | 
% 240.08/46.83  | | | ALPHA: (16) implies:
% 240.08/46.83  | | |   (17)  all_58_2 = e0
% 240.08/46.83  | | | 
% 240.08/46.83  | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (12), (17) are
% 240.08/46.83  | | |            inconsistent by sub-proof #257.
% 240.08/46.83  | | | 
% 240.08/46.83  | | End of split
% 240.08/46.83  | | 
% 240.08/46.83  | Case 2:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (18)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 240.08/46.83  | |           e0)
% 240.08/46.83  | | 
% 240.08/46.83  | | BETA: splitting (18) gives:
% 240.08/46.83  | | 
% 240.08/46.83  | | Case 1:
% 240.08/46.83  | | | 
% 240.08/46.83  | | |   (19)  all_58_6 = e0 & op(e1, e3) = e0
% 240.08/46.83  | | | 
% 240.08/46.83  | | | REF_CLOSE: (2), (3), (19) are inconsistent by sub-proof #1678.
% 240.08/46.83  | | | 
% 240.08/46.83  | | Case 2:
% 240.08/46.83  | | | 
% 240.08/46.83  | | |   (20)  all_58_12 = e0 & op(e0, e3) = e0
% 240.08/46.83  | | | 
% 240.08/46.83  | | | ALPHA: (20) implies:
% 240.08/46.83  | | |   (21)  all_58_12 = e0
% 240.08/46.83  | | | 
% 240.08/46.83  | | | REF_CLOSE: (1), (8), (21) are inconsistent by sub-proof #1971.
% 240.08/46.83  | | | 
% 240.08/46.83  | | End of split
% 240.08/46.83  | | 
% 240.08/46.83  | End of split
% 240.08/46.83  | 
% 240.08/46.83  End of proof
% 240.08/46.83  
% 240.08/46.83  Sub-proof #257 shows that the following formulas are inconsistent:
% 240.08/46.83  ----------------------------------------------------------------
% 240.08/46.83    (1)   ~ (e3 = e1)
% 240.08/46.83    (2)  op(e1, e3) = e2
% 240.08/46.83    (3)  op(e3, e3) = e2
% 240.08/46.83    (4)  all_58_12 = e3
% 240.08/46.83    (5)  all_58_2 = e0
% 240.08/46.83    (6)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.08/46.83         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.08/46.83    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.83    (8)   ~ (e1 = e0)
% 240.08/46.83    (9)   ~ (e2 = e1)
% 240.08/46.83  
% 240.08/46.83  Begin of proof
% 240.08/46.83  | 
% 240.08/46.83  | BETA: splitting (6) gives:
% 240.08/46.83  | 
% 240.08/46.83  | Case 1:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 240.08/46.83  | |           e1)
% 240.08/46.83  | | 
% 240.08/46.83  | | REF_CLOSE: (3), (5), (7), (8), (9), (10) are inconsistent by sub-proof #796.
% 240.08/46.83  | | 
% 240.08/46.83  | Case 2:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (11)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 240.08/46.83  | |           e1)
% 240.08/46.83  | | 
% 240.08/46.83  | | BETA: splitting (11) gives:
% 240.08/46.83  | | 
% 240.08/46.83  | | Case 1:
% 240.08/46.83  | | | 
% 240.08/46.83  | | |   (12)  all_58_6 = e1 & op(e1, e3) = e1
% 240.08/46.83  | | | 
% 240.08/46.83  | | | ALPHA: (12) implies:
% 240.08/46.83  | | |   (13)  op(e1, e3) = e1
% 240.08/46.83  | | | 
% 240.08/46.83  | | | REF_CLOSE: (2), (7), (9), (13) are inconsistent by sub-proof #2226.
% 240.08/46.83  | | | 
% 240.08/46.83  | | Case 2:
% 240.08/46.83  | | | 
% 240.08/46.83  | | |   (14)  all_58_12 = e1 & op(e0, e3) = e1
% 240.08/46.83  | | | 
% 240.08/46.83  | | | ALPHA: (14) implies:
% 240.08/46.83  | | |   (15)  all_58_12 = e1
% 240.08/46.83  | | | 
% 240.08/46.83  | | | REF_CLOSE: (1), (4), (15) are inconsistent by sub-proof #1542.
% 240.08/46.83  | | | 
% 240.08/46.83  | | End of split
% 240.08/46.83  | | 
% 240.08/46.83  | End of split
% 240.08/46.83  | 
% 240.08/46.83  End of proof
% 240.08/46.83  
% 240.08/46.83  Sub-proof #258 shows that the following formulas are inconsistent:
% 240.08/46.83  ----------------------------------------------------------------
% 240.08/46.83    (1)  all_58_11 = e2 & op(e1, e0) = e2
% 240.08/46.83    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.83    (3)  op(e1, e0) = all_52_14
% 240.08/46.83    (4)   ~ (all_52_14 = e2)
% 240.08/46.83  
% 240.08/46.83  Begin of proof
% 240.08/46.83  | 
% 240.08/46.83  | ALPHA: (1) implies:
% 240.08/46.83  |   (5)  op(e1, e0) = e2
% 240.08/46.83  | 
% 240.08/46.83  | GROUND_INST: instantiating (2) with all_52_14, e2, e0, e1, simplifying with
% 240.08/46.83  |              (3), (5) gives:
% 240.08/46.83  |   (6)  all_52_14 = e2
% 240.08/46.83  | 
% 240.08/46.83  | REDUCE: (4), (6) imply:
% 240.08/46.83  |   (7)  $false
% 240.08/46.83  | 
% 240.08/46.83  | CLOSE: (7) is inconsistent.
% 240.08/46.83  | 
% 240.08/46.83  End of proof
% 240.08/46.83  
% 240.08/46.83  Sub-proof #259 shows that the following formulas are inconsistent:
% 240.08/46.83  ----------------------------------------------------------------
% 240.08/46.83    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.08/46.83         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.08/46.83    (2)   ~ (all_52_3 = e1)
% 240.08/46.83    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.08/46.83         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.83    (4)   ~ (e3 = e0)
% 240.08/46.83    (5)  op(e0, e1) = all_52_11
% 240.08/46.83    (6)  op(e2, e1) = e1
% 240.08/46.83    (7)   ~ (e2 = e0)
% 240.08/46.83    (8)   ~ (all_52_11 = e1)
% 240.08/46.83    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.08/46.83         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.08/46.83    (10)   ~ (all_52_7 = e3)
% 240.08/46.83    (11)  op(e0, e3) = all_52_3
% 240.08/46.83    (12)   ~ (e3 = e1)
% 240.08/46.83    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.08/46.83          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.83    (14)   ~ (all_52_8 = e1)
% 240.08/46.83    (15)  all_58_3 = e3
% 240.08/46.83    (16)  op(e3, e3) = e1
% 240.08/46.83    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.08/46.83              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.08/46.83                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.08/46.83                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.08/46.83    (18)   ~ (all_52_11 = e3)
% 240.08/46.83    (19)  op(e3, e1) = all_52_8
% 240.08/46.83    (20)  op(e2, e1) = all_52_9
% 240.08/46.83    (21)   ~ (e3 = e2)
% 240.08/46.83    (22)  op(e0, all_52_11) = e0
% 240.08/46.83    (23)   ~ (all_52_7 = e1)
% 240.08/46.83    (24)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.83    (25)  all_58_9 = e3
% 240.08/46.83    (26)  op(e3, e0) = e3
% 240.08/46.83    (27)  all_58_12 = e3
% 240.08/46.83    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.08/46.83          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.08/46.83    (29)  op(e0, e2) = all_52_7
% 240.08/46.83    (30)   ~ (all_52_8 = all_52_11)
% 240.08/46.83    (31)  all_58_7 = e1
% 240.08/46.83    (32)   ~ (all_52_9 = e3)
% 240.08/46.83    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.83    (34)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.08/46.83          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.83    (35)   ~ (e1 = e0)
% 240.08/46.83    (36)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.83          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.08/46.83            e1)
% 240.08/46.83    (37)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.83          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.08/46.83            e2)
% 240.08/46.83    (38)   ~ (e2 = e1)
% 240.08/46.83    (39)   ~ (all_52_8 = e3)
% 240.08/46.83  
% 240.08/46.83  Begin of proof
% 240.08/46.83  | 
% 240.08/46.83  | BETA: splitting (24) gives:
% 240.08/46.83  | 
% 240.08/46.83  | Case 1:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (40)  all_58_7 = e2 & op(e1, e2) = e2
% 240.08/46.83  | | 
% 240.08/46.83  | | ALPHA: (40) implies:
% 240.08/46.83  | |   (41)  all_58_7 = e2
% 240.08/46.83  | | 
% 240.08/46.83  | | REF_CLOSE: (31), (38), (41) are inconsistent by sub-proof #2134.
% 240.08/46.83  | | 
% 240.08/46.83  | Case 2:
% 240.08/46.83  | | 
% 240.08/46.83  | |   (42)  all_58_13 = e2 & op(e0, e2) = e2
% 240.08/46.83  | | 
% 240.08/46.83  | | ALPHA: (42) implies:
% 240.08/46.83  | |   (43)  op(e0, e2) = e2
% 240.08/46.83  | | 
% 240.08/46.83  | | BETA: splitting (1) gives:
% 240.08/46.83  | | 
% 240.08/46.83  | | Case 1:
% 240.08/46.83  | | | 
% 240.08/46.83  | | |   (44)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 240.08/46.83  | | |           e2)
% 240.08/46.83  | | | 
% 240.08/46.83  | | | REF_CLOSE: (4), (7), (9), (12), (15), (16), (23), (29), (33), (34), (35),
% 240.08/46.83  | | |            (38), (43), (44) are inconsistent by sub-proof #263.
% 240.08/46.83  | | | 
% 240.08/46.83  | | Case 2:
% 240.08/46.83  | | | 
% 240.08/46.83  | | |   (45)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 240.08/46.83  | | |           e2)
% 240.08/46.83  | | | 
% 240.08/46.83  | | | BETA: splitting (45) gives:
% 240.08/46.83  | | | 
% 240.08/46.83  | | | Case 1:
% 240.08/46.83  | | | | 
% 240.08/46.83  | | | |   (46)  all_58_4 = e2 & op(e3, e1) = e2
% 240.08/46.83  | | | | 
% 240.08/46.83  | | | | ALPHA: (46) implies:
% 240.08/46.83  | | | |   (47)  all_58_4 = e2
% 240.08/46.83  | | | |   (48)  op(e3, e1) = e2
% 240.08/46.83  | | | | 
% 240.08/46.83  | | | | BETA: splitting (13) gives:
% 240.08/46.83  | | | | 
% 240.08/46.83  | | | | Case 1:
% 240.08/46.83  | | | | | 
% 240.08/46.83  | | | | |   (49)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 240.08/46.83  | | | | |             e1) = e0)
% 240.08/46.83  | | | | | 
% 240.08/46.83  | | | | | REF_CLOSE: (1), (4), (6), (7), (9), (15), (16), (20), (21), (25),
% 240.08/46.83  | | | | |            (31), (33), (35), (38), (43), (49) are inconsistent by
% 240.08/46.83  | | | | |            sub-proof #262.
% 240.08/46.83  | | | | | 
% 240.08/46.83  | | | | Case 2:
% 240.08/46.83  | | | | | 
% 240.08/46.83  | | | | |   (50)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 240.08/46.83  | | | | |             e1) = e0)
% 240.08/46.83  | | | | | 
% 240.08/46.83  | | | | | BETA: splitting (50) gives:
% 240.08/46.83  | | | | | 
% 240.08/46.83  | | | | | Case 1:
% 240.08/46.83  | | | | | | 
% 240.08/46.83  | | | | | |   (51)  all_58_8 = e0 & op(e1, e1) = e0
% 240.08/46.83  | | | | | | 
% 240.08/46.83  | | | | | | ALPHA: (51) implies:
% 240.08/46.83  | | | | | |   (52)  op(e1, e1) = e0
% 240.08/46.83  | | | | | | 
% 240.08/46.83  | | | | | | REF_CLOSE: (4), (5), (18), (20), (21), (28), (32), (33), (47), (52)
% 240.08/46.83  | | | | | |            are inconsistent by sub-proof #1493.
% 240.08/46.83  | | | | | | 
% 240.08/46.83  | | | | | Case 2:
% 240.08/46.83  | | | | | | 
% 240.08/46.83  | | | | | |   (53)  all_58_14 = e0 & op(e0, e1) = e0
% 240.08/46.83  | | | | | | 
% 240.08/46.83  | | | | | | ALPHA: (53) implies:
% 240.08/46.83  | | | | | |   (54)  all_58_14 = e0
% 240.08/46.83  | | | | | |   (55)  op(e0, e1) = e0
% 240.08/46.83  | | | | | | 
% 240.08/46.83  | | | | | | BETA: splitting (17) gives:
% 240.08/46.83  | | | | | | 
% 240.08/46.83  | | | | | | Case 1:
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | |   (56)  all_58_15 = e0 & op(e0, e0) = e0
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | | ALPHA: (56) implies:
% 240.08/46.83  | | | | | | |   (57)  all_58_15 = e0
% 240.08/46.83  | | | | | | |   (58)  op(e0, e0) = e0
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | | REF_CLOSE: (3), (4), (7), (10), (12), (21), (27), (29), (33),
% 240.08/46.83  | | | | | | |            (35), (36), (37), (38), (54), (55), (57), (58) are
% 240.08/46.83  | | | | | | |            inconsistent by sub-proof #859.
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | Case 2:
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | |   (59)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 240.08/46.83  | | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0))
% 240.08/46.83  | | | | | | |         & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.08/46.83  | | | | | | |             op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | | ALPHA: (59) implies:
% 240.08/46.83  | | | | | | |   (60)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.08/46.83  | | | | | | |           op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | | GROUND_INST: instantiating (33) with all_52_11, e0, e1, e0,
% 240.08/46.83  | | | | | | |              simplifying with (5), (55) gives:
% 240.08/46.83  | | | | | | |   (61)  all_52_11 = e0
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | | GROUND_INST: instantiating (33) with all_52_8, e2, e1, e3,
% 240.08/46.83  | | | | | | |              simplifying with (19), (48) gives:
% 240.08/46.83  | | | | | | |   (62)  all_52_8 = e2
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | | REDUCE: (39), (62) imply:
% 240.08/46.83  | | | | | | |   (63)   ~ (e3 = e2)
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | | REDUCE: (18), (61) imply:
% 240.08/46.83  | | | | | | |   (64)   ~ (e3 = e0)
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | | REDUCE: (8), (61) imply:
% 240.08/46.83  | | | | | | |   (65)   ~ (e1 = e0)
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | | REDUCE: (22), (61) imply:
% 240.08/46.83  | | | | | | |   (66)  op(e0, e0) = e0
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | | REF_CLOSE: (2), (3), (4), (7), (11), (12), (21), (33), (35), (36),
% 240.08/46.83  | | | | | | |            (37), (38), (54), (55), (60), (66) are inconsistent by
% 240.08/46.83  | | | | | | |            sub-proof #2073.
% 240.08/46.83  | | | | | | | 
% 240.08/46.83  | | | | | | End of split
% 240.08/46.83  | | | | | | 
% 240.08/46.83  | | | | | End of split
% 240.08/46.83  | | | | | 
% 240.08/46.83  | | | | End of split
% 240.08/46.83  | | | | 
% 240.08/46.83  | | | Case 2:
% 240.08/46.83  | | | | 
% 240.08/46.83  | | | |   (67)  all_58_9 = e2 & op(e3, e0) = e2
% 240.08/46.83  | | | | 
% 240.08/46.83  | | | | ALPHA: (67) implies:
% 240.08/46.83  | | | |   (68)  op(e3, e0) = e2
% 240.08/46.83  | | | | 
% 240.08/46.83  | | | | REF_CLOSE: (21), (26), (33), (68) are inconsistent by sub-proof #2125.
% 240.08/46.83  | | | | 
% 240.08/46.83  | | | End of split
% 240.08/46.83  | | | 
% 240.08/46.83  | | End of split
% 240.08/46.83  | | 
% 240.08/46.83  | End of split
% 240.08/46.83  | 
% 240.08/46.83  End of proof
% 240.08/46.83  
% 240.08/46.83  Sub-proof #260 shows that the following formulas are inconsistent:
% 240.08/46.83  ----------------------------------------------------------------
% 240.08/46.83    (1)  op(e2, e2) = e3
% 240.08/46.83    (2)   ~ (all_52_3 = e1)
% 240.08/46.83    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.08/46.83         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.83    (4)   ~ (e3 = e0)
% 240.08/46.83    (5)  op(e1, e2) = e1
% 240.08/46.83    (6)   ~ (e2 = e0)
% 240.08/46.83    (7)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.08/46.83           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 240.08/46.83           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 240.08/46.83         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.08/46.83           $i(all_56_15))
% 240.08/46.83    (8)  op(e1, e2) = all_52_6
% 240.08/46.83    (9)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.83         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.83    (10)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 240.08/46.83            all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3,
% 240.08/46.83              e1) = all_38_1 & $i(all_38_1))
% 240.08/46.83    (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.08/46.83          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.08/46.83    (12)   ~ (all_52_1 = all_52_2)
% 240.08/46.83    (13)   ~ (all_52_13 = e1)
% 240.08/46.83    (14)   ~ (all_52_7 = e3)
% 240.08/46.83    (15)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 240.08/46.83    (16)  op(e0, e3) = all_52_3
% 240.08/46.83    (17)   ~ (e3 = e1)
% 240.08/46.83    (18)  all_58_3 = e3
% 240.08/46.83    (19)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 240.08/46.83            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 240.08/46.83              e1) = all_10_1 & $i(all_10_1))
% 240.08/46.83    (20)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.08/46.83          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.08/46.83    (21)   ~ (all_52_2 = e1)
% 240.08/46.83    (22)  op(e3, e2) = e2
% 240.08/46.83    (23)  op(e3, e3) = e1
% 240.08/46.83    (24)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.08/46.83    (25)  op(e1, all_52_2) = e1
% 240.08/46.83    (26)   ~ (e3 = e2)
% 240.08/46.83    (27)  all_58_15 = e1
% 240.08/46.83    (28)  all_58_9 = e3
% 240.08/46.83    (29)  op(e2, e3) = all_52_1
% 240.08/46.83    (30)  all_58_12 = e3
% 240.08/46.83    (31)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.08/46.83          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.08/46.83    (32)  op(e1, e1) = e3
% 240.08/46.83    (33)   ~ (all_52_1 = all_52_13)
% 240.08/46.83    (34)  all_54_7 = all_52_13
% 240.08/46.83    (35)  op(e0, e2) = all_52_7
% 240.08/46.83    (36)   ~ (all_52_4 = e3)
% 240.08/46.83    (37)  op(e3, e2) = all_52_4
% 240.08/46.83    (38)  all_58_7 = e1
% 240.08/46.83    (39)  all_58_1 = e2
% 240.08/46.83    (40)  all_54_8 = all_52_2
% 240.08/46.83    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.84    (42)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.08/46.84          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.08/46.84    (43)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.08/46.84          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.84    (44)  all_56_11 = e3
% 240.08/46.84    (45)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.08/46.84          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.08/46.84    (46)   ~ (e1 = e0)
% 240.08/46.84    (47)  op(e2, e0) = all_52_13
% 240.08/46.84    (48)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.84          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.08/46.84            e1)
% 240.08/46.84    (49)   ~ (all_52_1 = e3)
% 240.08/46.84    (50)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.84          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.08/46.84            e2)
% 240.08/46.84    (51)   ~ (e2 = e1)
% 240.08/46.84    (52)   ~ (all_52_1 = e1)
% 240.08/46.84  
% 240.08/46.84  Begin of proof
% 240.08/46.84  | 
% 240.08/46.84  | BETA: splitting (11) gives:
% 240.08/46.84  | 
% 240.08/46.84  | Case 1:
% 240.08/46.84  | | 
% 240.08/46.84  | |   (53)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 240.08/46.84  | |           e0)
% 240.08/46.84  | | 
% 240.08/46.84  | | REF_CLOSE: (3), (4), (5), (6), (8), (11), (14), (17), (18), (22), (26),
% 240.08/46.84  | |            (27), (30), (35), (39), (41), (46), (50), (51), (53) are
% 240.08/46.84  | |            inconsistent by sub-proof #268.
% 240.08/46.84  | | 
% 240.08/46.84  | Case 2:
% 240.08/46.84  | | 
% 240.08/46.84  | |   (54)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.08/46.84  | |           e0)
% 240.08/46.84  | | 
% 240.08/46.84  | | BETA: splitting (54) gives:
% 240.08/46.84  | | 
% 240.08/46.84  | | Case 1:
% 240.08/46.84  | | | 
% 240.08/46.84  | | |   (55)  all_58_7 = e0 & op(e1, e2) = e0
% 240.08/46.84  | | | 
% 240.08/46.84  | | | ALPHA: (55) implies:
% 240.08/46.84  | | |   (56)  op(e1, e2) = e0
% 240.08/46.84  | | | 
% 240.08/46.84  | | | REF_CLOSE: (5), (8), (41), (46), (56) are inconsistent by sub-proof #2136.
% 240.08/46.84  | | | 
% 240.08/46.84  | | Case 2:
% 240.08/46.84  | | | 
% 240.08/46.84  | | |   (57)  all_58_13 = e0 & op(e0, e2) = e0
% 240.08/46.84  | | | 
% 240.08/46.84  | | | ALPHA: (57) implies:
% 240.08/46.84  | | |   (58)  all_58_13 = e0
% 240.08/46.84  | | |   (59)  op(e0, e2) = e0
% 240.08/46.84  | | | 
% 240.08/46.84  | | | BETA: splitting (31) gives:
% 240.08/46.84  | | | 
% 240.08/46.84  | | | Case 1:
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | |   (60)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 240.08/46.84  | | | |           = e0)
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | | REF_CLOSE: (1), (6), (9), (17), (18), (23), (26), (41), (43), (46),
% 240.08/46.84  | | | |            (51), (59), (60) are inconsistent by sub-proof #267.
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | Case 2:
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | |   (61)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 240.08/46.84  | | | |           = e0)
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | | BETA: splitting (61) gives:
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | | Case 1:
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | |   (62)  all_58_4 = e0 & op(e3, e1) = e0
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | | ALPHA: (62) implies:
% 240.08/46.84  | | | | |   (63)  all_58_4 = e0
% 240.08/46.84  | | | | |   (64)  op(e3, e1) = e0
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | | BETA: splitting (7) gives:
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | | Case 1:
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | |   (65)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) =
% 240.08/46.84  | | | | | |           all_56_9 & $i(all_56_9)) | (all_56_10 = e2 & op(e2,
% 240.08/46.84  | | | | | |             all_56_11) = e2)
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | | BETA: splitting (65) gives:
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | | Case 1:
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | |   (66)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) =
% 240.08/46.84  | | | | | | |         all_56_9 & $i(all_56_9)
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | REF_CLOSE: (22), (36), (37), (41), (66) are inconsistent by
% 240.08/46.84  | | | | | | |            sub-proof #1358.
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | Case 2:
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | |   (67)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | ALPHA: (67) implies:
% 240.08/46.84  | | | | | | |   (68)  op(e2, all_56_11) = e2
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | REDUCE: (44), (68) imply:
% 240.08/46.84  | | | | | | |   (69)  op(e2, e3) = e2
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | GROUND_INST: instantiating (41) with all_52_1, e2, e3, e2,
% 240.08/46.84  | | | | | | |              simplifying with (29), (69) gives:
% 240.08/46.84  | | | | | | |   (70)  all_52_1 = e2
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | REDUCE: (12), (70) imply:
% 240.08/46.84  | | | | | | |   (71)   ~ (all_52_2 = e2)
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | SIMP: (71) implies:
% 240.08/46.84  | | | | | | |   (72)   ~ (all_52_2 = e2)
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | REDUCE: (33), (70) imply:
% 240.08/46.84  | | | | | | |   (73)   ~ (all_52_13 = e2)
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | SIMP: (73) implies:
% 240.08/46.84  | | | | | | |   (74)   ~ (all_52_13 = e2)
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | REDUCE: (49), (70) imply:
% 240.08/46.84  | | | | | | |   (75)   ~ (e3 = e2)
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | BETA: splitting (42) gives:
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | Case 1:
% 240.08/46.84  | | | | | | | | 
% 240.08/46.84  | | | | | | | |   (76)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 240.08/46.84  | | | | | | | |           op(e2, e0) = e2)
% 240.08/46.84  | | | | | | | | 
% 240.08/46.84  | | | | | | | | BETA: splitting (76) gives:
% 240.08/46.84  | | | | | | | | 
% 240.08/46.84  | | | | | | | | Case 1:
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | |   (77)  all_58_9 = e2 & op(e3, e0) = e2
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | ALPHA: (77) implies:
% 240.08/46.84  | | | | | | | | |   (78)  op(e3, e0) = e2
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | REF_CLOSE: (4), (17), (20), (23), (26), (36), (37), (41),
% 240.08/46.84  | | | | | | | | |            (63), (78) are inconsistent by sub-proof #1400.
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | Case 2:
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | |   (79)  all_58_10 = e2 & op(e2, e0) = e2
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | ALPHA: (79) implies:
% 240.08/46.84  | | | | | | | | |   (80)  op(e2, e0) = e2
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | REF_CLOSE: (13), (24), (34), (41), (47), (74), (80) are
% 240.08/46.84  | | | | | | | | |            inconsistent by sub-proof #1995.
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | End of split
% 240.08/46.84  | | | | | | | | 
% 240.08/46.84  | | | | | | | Case 2:
% 240.08/46.84  | | | | | | | | 
% 240.08/46.84  | | | | | | | |   (81)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 240.08/46.84  | | | | | | | |           op(e0, e0) = e2)
% 240.08/46.84  | | | | | | | | 
% 240.08/46.84  | | | | | | | | BETA: splitting (81) gives:
% 240.08/46.84  | | | | | | | | 
% 240.08/46.84  | | | | | | | | Case 1:
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | |   (82)  all_58_11 = e2 & op(e1, e0) = e2
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | ALPHA: (82) implies:
% 240.08/46.84  | | | | | | | | |   (83)  op(e1, e0) = e2
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | BETA: splitting (15) gives:
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | Case 1:
% 240.08/46.84  | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | |   (84)  all_54_8 = e2
% 240.08/46.84  | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | REF_CLOSE: (40), (72), (84) are inconsistent by sub-proof
% 240.08/46.84  | | | | | | | | | |            #2007.
% 240.08/46.84  | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | Case 2:
% 240.08/46.84  | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | |   (85)  all_54_8 = e1 | all_54_8 = e0
% 240.08/46.84  | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | BETA: splitting (85) gives:
% 240.08/46.84  | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | Case 1:
% 240.08/46.84  | | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | |   (86)  all_54_8 = e1
% 240.08/46.84  | | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | | REF_CLOSE: (21), (40), (86) are inconsistent by sub-proof
% 240.08/46.84  | | | | | | | | | | |            #1951.
% 240.08/46.84  | | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | Case 2:
% 240.08/46.84  | | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | |   (87)  all_54_8 = e0
% 240.08/46.84  | | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | | COMBINE_EQS: (40), (87) imply:
% 240.08/46.84  | | | | | | | | | | |   (88)  all_52_2 = e0
% 240.08/46.84  | | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | | SIMP: (88) implies:
% 240.08/46.84  | | | | | | | | | | |   (89)  all_52_2 = e0
% 240.08/46.84  | | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | | REDUCE: (25), (89) imply:
% 240.08/46.84  | | | | | | | | | | |   (90)  op(e1, e0) = e1
% 240.08/46.84  | | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | | REF_CLOSE: (41), (51), (83), (90) are inconsistent by
% 240.08/46.84  | | | | | | | | | | |            sub-proof #2019.
% 240.08/46.84  | | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | | End of split
% 240.08/46.84  | | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | End of split
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | Case 2:
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | |   (91)  all_58_15 = e2 & op(e0, e0) = e2
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (11), (18), (26),
% 240.08/46.84  | | | | | | | | |            (27), (38), (39), (41), (46), (51), (91) are
% 240.08/46.84  | | | | | | | | |            inconsistent by sub-proof #871.
% 240.08/46.84  | | | | | | | | | 
% 240.08/46.84  | | | | | | | | End of split
% 240.08/46.84  | | | | | | | | 
% 240.08/46.84  | | | | | | | End of split
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | End of split
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | Case 2:
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | |   (92)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 240.08/46.84  | | | | | |           all_56_13 & $i(all_56_13)) | (all_56_14 = e0 & op(e0,
% 240.08/46.84  | | | | | |             all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.08/46.84  | | | | | |           $i(all_56_15))
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | | BETA: splitting (92) gives:
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | | Case 1:
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | |   (93)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 240.08/46.84  | | | | | | |         all_56_13 & $i(all_56_13)
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | REF_CLOSE: (5), (17), (32), (41), (93) are inconsistent by
% 240.08/46.84  | | | | | | |            sub-proof #276.
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | Case 2:
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | |   (94)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 240.08/46.84  | | | | | | |         all_56_15 & $i(all_56_15)
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | REF_CLOSE: (2), (3), (4), (6), (10), (16), (17), (19), (26), (41),
% 240.08/46.84  | | | | | | |            (46), (48), (50), (51), (59), (64), (94) are
% 240.08/46.84  | | | | | | |            inconsistent by sub-proof #266.
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | End of split
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | End of split
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | Case 2:
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | |   (95)  all_58_9 = e0 & op(e3, e0) = e0
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | | REF_CLOSE: (4), (6), (9), (17), (18), (26), (28), (38), (41), (45),
% 240.08/46.84  | | | | |            (51), (58), (59), (95) are inconsistent by sub-proof #265.
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | End of split
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | End of split
% 240.08/46.84  | | | 
% 240.08/46.84  | | End of split
% 240.08/46.84  | | 
% 240.08/46.84  | End of split
% 240.08/46.84  | 
% 240.08/46.84  End of proof
% 240.08/46.84  
% 240.08/46.84  Sub-proof #261 shows that the following formulas are inconsistent:
% 240.08/46.84  ----------------------------------------------------------------
% 240.08/46.84    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.08/46.84         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.08/46.84    (2)   ~ (e3 = e0)
% 240.08/46.84    (3)  op(e0, e1) = all_52_11
% 240.08/46.84    (4)  op(e2, e1) = e1
% 240.08/46.84    (5)  op(e1, e2) = e1
% 240.08/46.84    (6)   ~ (e2 = e0)
% 240.08/46.84    (7)  op(e1, e2) = all_52_6
% 240.08/46.84    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.08/46.84         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.08/46.84    (9)  op(e0, e2) = e2
% 240.08/46.84    (10)   ~ (e3 = e1)
% 240.08/46.84    (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.08/46.84          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.84    (12)  all_58_3 = e3
% 240.08/46.84    (13)  op(e3, e3) = e1
% 240.08/46.84    (14)   ~ (all_52_11 = e3)
% 240.08/46.84    (15)  op(e3, e1) = all_52_8
% 240.08/46.84    (16)  op(e2, e1) = all_52_9
% 240.08/46.84    (17)   ~ (e3 = e2)
% 240.08/46.84    (18)   ~ (all_52_7 = e1)
% 240.08/46.84    (19)  all_58_9 = e3
% 240.08/46.84    (20)  op(e3, e0) = e3
% 240.08/46.84    (21)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.08/46.84          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.08/46.84    (22)  op(e0, e2) = all_52_7
% 240.08/46.84    (23)  op(e3, all_52_8) = e3
% 240.08/46.84    (24)  op(e3, e2) = all_52_4
% 240.08/46.84    (25)  all_58_7 = e1
% 240.08/46.84    (26)   ~ (all_52_9 = e3)
% 240.08/46.84    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.84    (28)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.08/46.84          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.84    (29)   ~ (e1 = e0)
% 240.08/46.84    (30)   ~ (e2 = e1)
% 240.08/46.84  
% 240.08/46.84  Begin of proof
% 240.08/46.84  | 
% 240.08/46.84  | BETA: splitting (8) gives:
% 240.08/46.84  | 
% 240.08/46.84  | Case 1:
% 240.08/46.84  | | 
% 240.08/46.84  | |   (31)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 240.08/46.84  | |           e0)
% 240.08/46.84  | | 
% 240.08/46.84  | | BETA: splitting (31) gives:
% 240.08/46.84  | | 
% 240.08/46.84  | | Case 1:
% 240.08/46.84  | | | 
% 240.08/46.84  | | |   (32)  all_58_1 = e0 & op(e3, e2) = e0
% 240.08/46.84  | | | 
% 240.08/46.84  | | | ALPHA: (32) implies:
% 240.08/46.84  | | |   (33)  op(e3, e2) = e0
% 240.08/46.84  | | | 
% 240.08/46.84  | | | BETA: splitting (1) gives:
% 240.08/46.84  | | | 
% 240.08/46.84  | | | Case 1:
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | |   (34)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 240.08/46.84  | | | |           = e2)
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | | REF_CLOSE: (2), (6), (8), (9), (10), (12), (13), (18), (22), (27), (28),
% 240.08/46.84  | | | |            (29), (30), (34) are inconsistent by sub-proof #263.
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | Case 2:
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | |   (35)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 240.08/46.84  | | | |           = e2)
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | | BETA: splitting (35) gives:
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | | Case 1:
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | |   (36)  all_58_4 = e2 & op(e3, e1) = e2
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | | ALPHA: (36) implies:
% 240.08/46.84  | | | | |   (37)  all_58_4 = e2
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | | BETA: splitting (11) gives:
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | | Case 1:
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | |   (38)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 240.08/46.84  | | | | | |             e1) = e0)
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (12), (13), (16), (17),
% 240.08/46.84  | | | | | |            (19), (25), (27), (29), (30), (38) are inconsistent by
% 240.08/46.84  | | | | | |            sub-proof #262.
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | Case 2:
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | |   (39)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 240.08/46.84  | | | | | |             e1) = e0)
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | | BETA: splitting (39) gives:
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | | Case 1:
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | |   (40)  all_58_8 = e0 & op(e1, e1) = e0
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | ALPHA: (40) implies:
% 240.08/46.84  | | | | | | |   (41)  op(e1, e1) = e0
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | REF_CLOSE: (2), (3), (14), (16), (17), (21), (26), (27), (37),
% 240.08/46.84  | | | | | | |            (41) are inconsistent by sub-proof #1493.
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | Case 2:
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | |   (42)  all_58_14 = e0 & op(e0, e1) = e0
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | ALPHA: (42) implies:
% 240.08/46.84  | | | | | | |   (43)  op(e0, e1) = e0
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | ALPHA: (36) implies:
% 240.08/46.84  | | | | | | |   (44)  op(e3, e1) = e2
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | GROUND_INST: instantiating (27) with all_52_11, e0, e1, e0,
% 240.08/46.84  | | | | | | |              simplifying with (3), (43) gives:
% 240.08/46.84  | | | | | | |   (45)  all_52_11 = e0
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | GROUND_INST: instantiating (27) with all_52_8, e2, e1, e3,
% 240.08/46.84  | | | | | | |              simplifying with (15), (44) gives:
% 240.08/46.84  | | | | | | |   (46)  all_52_8 = e2
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | GROUND_INST: instantiating (27) with all_52_4, e0, e2, e3,
% 240.08/46.84  | | | | | | |              simplifying with (24), (33) gives:
% 240.08/46.84  | | | | | | |   (47)  all_52_4 = e0
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | REDUCE: (14), (45) imply:
% 240.08/46.84  | | | | | | |   (48)   ~ (e3 = e0)
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | REDUCE: (23), (46) imply:
% 240.08/46.84  | | | | | | |   (49)  op(e3, e2) = e3
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | | REF_CLOSE: (2), (27), (33), (49) are inconsistent by sub-proof
% 240.08/46.84  | | | | | | |            #2099.
% 240.08/46.84  | | | | | | | 
% 240.08/46.84  | | | | | | End of split
% 240.08/46.84  | | | | | | 
% 240.08/46.84  | | | | | End of split
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | Case 2:
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | |   (50)  all_58_9 = e2 & op(e3, e0) = e2
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | | ALPHA: (50) implies:
% 240.08/46.84  | | | | |   (51)  op(e3, e0) = e2
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | | REF_CLOSE: (17), (20), (27), (51) are inconsistent by sub-proof #2125.
% 240.08/46.84  | | | | | 
% 240.08/46.84  | | | | End of split
% 240.08/46.84  | | | | 
% 240.08/46.84  | | | End of split
% 240.08/46.84  | | | 
% 240.08/46.84  | | Case 2:
% 240.08/46.84  | | | 
% 240.08/46.84  | | |   (52)  all_58_3 = e0 & op(e2, e2) = e0
% 240.08/46.84  | | | 
% 240.08/46.84  | | | REF_CLOSE: (2), (12), (52) are inconsistent by sub-proof #1719.
% 240.08/46.84  | | | 
% 240.08/46.84  | | End of split
% 240.08/46.84  | | 
% 240.08/46.84  | Case 2:
% 240.08/46.84  | | 
% 240.08/46.84  | |   (53)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.08/46.84  | |           e0)
% 240.08/46.84  | | 
% 240.08/46.84  | | REF_CLOSE: (5), (6), (7), (9), (27), (29), (53) are inconsistent by
% 240.08/46.84  | |            sub-proof #2131.
% 240.08/46.84  | | 
% 240.08/46.84  | End of split
% 240.08/46.84  | 
% 240.08/46.84  End of proof
% 240.08/46.84  
% 240.08/46.84  Sub-proof #262 shows that the following formulas are inconsistent:
% 240.08/46.84  ----------------------------------------------------------------
% 240.08/46.84    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.08/46.84         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.08/46.84    (2)   ~ (e3 = e0)
% 240.08/46.84    (3)  op(e2, e1) = e1
% 240.08/46.84    (4)   ~ (e2 = e0)
% 240.08/46.84    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.08/46.84         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.08/46.84    (6)  op(e0, e2) = e2
% 240.08/46.84    (7)  all_58_3 = e3
% 240.08/46.84    (8)  op(e3, e3) = e1
% 240.08/46.84    (9)  op(e2, e1) = all_52_9
% 240.08/46.84    (10)   ~ (e3 = e2)
% 240.08/46.84    (11)  all_58_9 = e3
% 240.08/46.84    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 240.08/46.84    (13)  all_58_7 = e1
% 240.08/46.84    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.84    (15)   ~ (e1 = e0)
% 240.08/46.84    (16)   ~ (e2 = e1)
% 240.08/46.84  
% 240.08/46.84  Begin of proof
% 240.08/46.84  | 
% 240.08/46.84  | BETA: splitting (12) gives:
% 240.08/46.84  | 
% 240.08/46.84  | Case 1:
% 240.08/46.84  | | 
% 240.08/46.84  | |   (17)  all_58_4 = e0 & op(e3, e1) = e0
% 240.08/46.84  | | 
% 240.08/46.84  | | ALPHA: (17) implies:
% 240.08/46.84  | |   (18)  all_58_4 = e0
% 240.08/46.84  | | 
% 240.08/46.84  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (13), (14), (15),
% 240.08/46.84  | |            (16), (18) are inconsistent by sub-proof #719.
% 240.08/46.84  | | 
% 240.08/46.84  | Case 2:
% 240.08/46.84  | | 
% 240.08/46.84  | |   (19)  all_58_5 = e0 & op(e2, e1) = e0
% 240.08/46.84  | | 
% 240.08/46.84  | | ALPHA: (19) implies:
% 240.08/46.84  | |   (20)  op(e2, e1) = e0
% 240.08/46.84  | | 
% 240.08/46.84  | | REF_CLOSE: (3), (9), (14), (15), (20) are inconsistent by sub-proof #2165.
% 240.08/46.84  | | 
% 240.08/46.84  | End of split
% 240.08/46.84  | 
% 240.08/46.84  End of proof
% 240.08/46.84  
% 240.08/46.84  Sub-proof #263 shows that the following formulas are inconsistent:
% 240.08/46.84  ----------------------------------------------------------------
% 240.08/46.84    (1)   ~ (e3 = e0)
% 240.08/46.84    (2)   ~ (e2 = e0)
% 240.08/46.84    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.08/46.84         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.08/46.84    (4)  op(e0, e2) = e2
% 240.08/46.84    (5)   ~ (e3 = e1)
% 240.08/46.84    (6)  all_58_3 = e3
% 240.08/46.84    (7)  op(e3, e3) = e1
% 240.08/46.84    (8)   ~ (all_52_7 = e1)
% 240.08/46.84    (9)  op(e0, e2) = all_52_7
% 240.08/46.84    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.84    (11)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.08/46.84          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.84    (12)   ~ (e1 = e0)
% 240.08/46.84    (13)   ~ (e2 = e1)
% 240.08/46.84    (14)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 240.08/46.84  
% 240.08/46.84  Begin of proof
% 240.08/46.84  | 
% 240.08/46.84  | BETA: splitting (14) gives:
% 240.08/46.84  | 
% 240.08/46.84  | Case 1:
% 240.08/46.84  | | 
% 240.08/46.84  | |   (15)  all_58_0 = e2 & op(e3, e3) = e2
% 240.08/46.84  | | 
% 240.08/46.84  | | ALPHA: (15) implies:
% 240.08/46.84  | |   (16)  op(e3, e3) = e2
% 240.08/46.84  | | 
% 240.08/46.84  | | REF_CLOSE: (7), (10), (13), (16) are inconsistent by sub-proof #2267.
% 240.08/46.84  | | 
% 240.08/46.84  | Case 2:
% 240.08/46.84  | | 
% 240.08/46.84  | |   (17)  all_58_1 = e2 & op(e3, e2) = e2
% 240.08/46.84  | | 
% 240.08/46.84  | | ALPHA: (17) implies:
% 240.08/46.84  | |   (18)  all_58_1 = e2
% 240.08/46.84  | | 
% 240.08/46.84  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 240.08/46.84  | |            (18) are inconsistent by sub-proof #1352.
% 240.08/46.84  | | 
% 240.08/46.84  | End of split
% 240.08/46.84  | 
% 240.08/46.84  End of proof
% 240.08/46.84  
% 240.08/46.84  Sub-proof #264 shows that the following formulas are inconsistent:
% 240.08/46.84  ----------------------------------------------------------------
% 240.08/46.84    (1)  op(e2, e2) = e3
% 240.08/46.84    (2)   ~ (all_52_3 = e1)
% 240.08/46.84    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.08/46.84         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.84    (4)   ~ (e3 = e0)
% 240.08/46.84    (5)  op(e2, all_52_1) = e2
% 240.08/46.84    (6)  op(e1, e2) = e1
% 240.08/46.84    (7)   ~ (e2 = e0)
% 240.08/46.84    (8)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.08/46.84           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 240.08/46.84           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 240.08/46.84         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.08/46.84           $i(all_56_15))
% 240.08/46.84    (9)  op(e1, e2) = all_52_6
% 240.08/46.84    (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.84          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.84    (11)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 240.08/46.84            all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3,
% 240.08/46.84              e1) = all_38_1 & $i(all_38_1))
% 240.08/46.84    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.08/46.84          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.08/46.84    (13)   ~ (all_52_7 = e3)
% 240.08/46.84    (14)  op(e0, e3) = all_52_3
% 240.08/46.84    (15)   ~ (e3 = e1)
% 240.08/46.84    (16)  all_58_3 = e3
% 240.08/46.84    (17)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 240.08/46.84            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 240.08/46.84              e1) = all_10_1 & $i(all_10_1))
% 240.08/46.84    (18)  op(e3, e2) = e2
% 240.08/46.84    (19)  op(e3, e3) = e1
% 240.08/46.84    (20)   ~ (e3 = e2)
% 240.08/46.84    (21)  all_58_15 = e1
% 240.08/46.84    (22)  all_58_9 = e3
% 240.08/46.84    (23)  op(e2, e3) = all_52_1
% 240.08/46.84    (24)  all_58_12 = e3
% 240.08/46.84    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.08/46.84          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.08/46.84    (26)  op(e1, e1) = e3
% 240.08/46.84    (27)  op(e0, e2) = all_52_7
% 240.08/46.84    (28)   ~ (all_52_4 = e3)
% 240.08/46.84    (29)  op(e3, e2) = all_52_4
% 240.08/46.84    (30)  all_58_7 = e1
% 240.08/46.84    (31)  all_58_1 = e2
% 240.08/46.84    (32)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.84    (33)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.08/46.84          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.84    (34)  all_56_11 = e3
% 240.08/46.84    (35)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.08/46.84          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.08/46.84    (36)   ~ (e1 = e0)
% 240.08/46.85    (37)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.85          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.08/46.85            e1)
% 240.08/46.85    (38)   ~ (all_52_1 = e3)
% 240.08/46.85    (39)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.85          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.08/46.85            e2)
% 240.08/46.85    (40)   ~ (e2 = e1)
% 240.08/46.85    (41)   ~ (all_52_1 = e1)
% 240.08/46.85  
% 240.08/46.85  Begin of proof
% 240.08/46.85  | 
% 240.08/46.85  | BETA: splitting (12) gives:
% 240.08/46.85  | 
% 240.08/46.85  | Case 1:
% 240.08/46.85  | | 
% 240.08/46.85  | |   (42)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 240.08/46.85  | |           e0)
% 240.08/46.85  | | 
% 240.08/46.85  | | REF_CLOSE: (3), (4), (6), (7), (9), (12), (13), (15), (16), (18), (20),
% 240.08/46.85  | |            (21), (24), (27), (31), (32), (36), (39), (40), (42) are
% 240.08/46.85  | |            inconsistent by sub-proof #268.
% 240.08/46.85  | | 
% 240.08/46.85  | Case 2:
% 240.08/46.85  | | 
% 240.08/46.85  | |   (43)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.08/46.85  | |           e0)
% 240.08/46.85  | | 
% 240.08/46.85  | | BETA: splitting (43) gives:
% 240.08/46.85  | | 
% 240.08/46.85  | | Case 1:
% 240.08/46.85  | | | 
% 240.08/46.85  | | |   (44)  all_58_7 = e0 & op(e1, e2) = e0
% 240.08/46.85  | | | 
% 240.08/46.85  | | | ALPHA: (44) implies:
% 240.08/46.85  | | |   (45)  op(e1, e2) = e0
% 240.08/46.85  | | | 
% 240.08/46.85  | | | REF_CLOSE: (6), (9), (32), (36), (45) are inconsistent by sub-proof #2136.
% 240.08/46.85  | | | 
% 240.08/46.85  | | Case 2:
% 240.08/46.85  | | | 
% 240.08/46.85  | | |   (46)  all_58_13 = e0 & op(e0, e2) = e0
% 240.08/46.85  | | | 
% 240.08/46.85  | | | ALPHA: (46) implies:
% 240.08/46.85  | | |   (47)  all_58_13 = e0
% 240.08/46.85  | | |   (48)  op(e0, e2) = e0
% 240.08/46.85  | | | 
% 240.08/46.85  | | | BETA: splitting (25) gives:
% 240.08/46.85  | | | 
% 240.08/46.85  | | | Case 1:
% 240.08/46.85  | | | | 
% 240.08/46.85  | | | |   (49)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 240.08/46.85  | | | |           = e0)
% 240.08/46.85  | | | | 
% 240.08/46.85  | | | | REF_CLOSE: (1), (7), (10), (15), (16), (19), (20), (32), (33), (36),
% 240.08/46.85  | | | |            (40), (48), (49) are inconsistent by sub-proof #267.
% 240.08/46.85  | | | | 
% 240.08/46.85  | | | Case 2:
% 240.08/46.85  | | | | 
% 240.08/46.85  | | | |   (50)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 240.08/46.85  | | | |           = e0)
% 240.08/46.85  | | | | 
% 240.08/46.85  | | | | BETA: splitting (50) gives:
% 240.08/46.85  | | | | 
% 240.08/46.85  | | | | Case 1:
% 240.08/46.85  | | | | | 
% 240.08/46.85  | | | | |   (51)  all_58_4 = e0 & op(e3, e1) = e0
% 240.08/46.85  | | | | | 
% 240.08/46.85  | | | | | ALPHA: (51) implies:
% 240.08/46.85  | | | | |   (52)  op(e3, e1) = e0
% 240.08/46.85  | | | | | 
% 240.08/46.85  | | | | | BETA: splitting (8) gives:
% 240.08/46.85  | | | | | 
% 240.08/46.85  | | | | | Case 1:
% 240.08/46.85  | | | | | | 
% 240.08/46.85  | | | | | |   (53)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) =
% 240.08/46.85  | | | | | |           all_56_9 & $i(all_56_9)) | (all_56_10 = e2 & op(e2,
% 240.08/46.85  | | | | | |             all_56_11) = e2)
% 240.08/46.85  | | | | | | 
% 240.08/46.85  | | | | | | BETA: splitting (53) gives:
% 240.08/46.85  | | | | | | 
% 240.08/46.85  | | | | | | Case 1:
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | |   (54)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) =
% 240.08/46.85  | | | | | | |         all_56_9 & $i(all_56_9)
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | | REF_CLOSE: (18), (28), (29), (32), (54) are inconsistent by
% 240.08/46.85  | | | | | | |            sub-proof #1358.
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | Case 2:
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | |   (55)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | | ALPHA: (55) implies:
% 240.08/46.85  | | | | | | |   (56)  op(e2, all_56_11) = e2
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | | REDUCE: (34), (56) imply:
% 240.08/46.85  | | | | | | |   (57)  op(e2, e3) = e2
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | | GROUND_INST: instantiating (32) with all_52_1, e2, e3, e2,
% 240.08/46.85  | | | | | | |              simplifying with (23), (57) gives:
% 240.08/46.85  | | | | | | |   (58)  all_52_1 = e2
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | | REDUCE: (38), (58) imply:
% 240.08/46.85  | | | | | | |   (59)   ~ (e3 = e2)
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | | REDUCE: (5), (58) imply:
% 240.08/46.85  | | | | | | |   (60)  op(e2, e2) = e2
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | | REF_CLOSE: (4), (7), (9), (12), (15), (20), (31), (32), (33),
% 240.08/46.85  | | | | | | |            (35), (36), (40), (48), (60) are inconsistent by
% 240.08/46.85  | | | | | | |            sub-proof #1811.
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | End of split
% 240.08/46.85  | | | | | | 
% 240.08/46.85  | | | | | Case 2:
% 240.08/46.85  | | | | | | 
% 240.08/46.85  | | | | | |   (61)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 240.08/46.85  | | | | | |           all_56_13 & $i(all_56_13)) | (all_56_14 = e0 & op(e0,
% 240.08/46.85  | | | | | |             all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.08/46.85  | | | | | |           $i(all_56_15))
% 240.08/46.85  | | | | | | 
% 240.08/46.85  | | | | | | BETA: splitting (61) gives:
% 240.08/46.85  | | | | | | 
% 240.08/46.85  | | | | | | Case 1:
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | |   (62)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 240.08/46.85  | | | | | | |         all_56_13 & $i(all_56_13)
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | | REF_CLOSE: (6), (15), (26), (32), (62) are inconsistent by
% 240.08/46.85  | | | | | | |            sub-proof #276.
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | Case 2:
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | |   (63)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 240.08/46.85  | | | | | | |         all_56_15 & $i(all_56_15)
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | | REF_CLOSE: (2), (3), (4), (7), (11), (14), (15), (17), (20), (32),
% 240.08/46.85  | | | | | | |            (36), (37), (39), (40), (48), (52), (63) are
% 240.08/46.85  | | | | | | |            inconsistent by sub-proof #266.
% 240.08/46.85  | | | | | | | 
% 240.08/46.85  | | | | | | End of split
% 240.08/46.85  | | | | | | 
% 240.08/46.85  | | | | | End of split
% 240.08/46.85  | | | | | 
% 240.08/46.85  | | | | Case 2:
% 240.08/46.85  | | | | | 
% 240.08/46.85  | | | | |   (64)  all_58_9 = e0 & op(e3, e0) = e0
% 240.08/46.85  | | | | | 
% 240.08/46.85  | | | | | REF_CLOSE: (4), (7), (10), (15), (16), (20), (22), (30), (32), (35),
% 240.08/46.85  | | | | |            (40), (47), (48), (64) are inconsistent by sub-proof #265.
% 240.08/46.85  | | | | | 
% 240.08/46.85  | | | | End of split
% 240.08/46.85  | | | | 
% 240.08/46.85  | | | End of split
% 240.08/46.85  | | | 
% 240.08/46.85  | | End of split
% 240.08/46.85  | | 
% 240.08/46.85  | End of split
% 240.08/46.85  | 
% 240.08/46.85  End of proof
% 240.08/46.85  
% 240.08/46.85  Sub-proof #265 shows that the following formulas are inconsistent:
% 240.08/46.85  ----------------------------------------------------------------
% 240.08/46.85    (1)   ~ (e3 = e0)
% 240.08/46.85    (2)   ~ (e2 = e0)
% 240.08/46.85    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.85         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.85    (4)  all_58_9 = e0 & op(e3, e0) = e0
% 240.08/46.85    (5)   ~ (e3 = e1)
% 240.08/46.85    (6)  all_58_3 = e3
% 240.08/46.85    (7)   ~ (e3 = e2)
% 240.08/46.85    (8)  all_58_13 = e0
% 240.08/46.85    (9)  all_58_9 = e3
% 240.08/46.85    (10)  op(e0, e2) = e0
% 240.08/46.85    (11)  all_58_7 = e1
% 240.08/46.85    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.85    (13)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.08/46.85          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.08/46.85    (14)   ~ (e2 = e1)
% 240.08/46.85  
% 240.08/46.85  Begin of proof
% 240.08/46.85  | 
% 240.08/46.85  | ALPHA: (4) implies:
% 240.08/46.85  |   (15)  all_58_9 = e0
% 240.08/46.85  | 
% 240.08/46.85  | COMBINE_EQS: (9), (15) imply:
% 240.08/46.85  |   (16)  e3 = e0
% 240.08/46.85  | 
% 240.08/46.85  | SIMP: (16) implies:
% 240.08/46.85  |   (17)  e3 = e0
% 240.08/46.85  | 
% 240.08/46.85  | COMBINE_EQS: (6), (17) imply:
% 240.08/46.85  |   (18)  all_58_3 = e0
% 240.08/46.85  | 
% 240.08/46.85  | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (12), (13), (14), (18)
% 240.08/46.85  |            are inconsistent by sub-proof #1375.
% 240.08/46.85  | 
% 240.08/46.85  End of proof
% 240.08/46.85  
% 240.08/46.85  Sub-proof #266 shows that the following formulas are inconsistent:
% 240.08/46.85  ----------------------------------------------------------------
% 240.08/46.85    (1)   ~ (all_52_3 = e1)
% 240.08/46.85    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.08/46.85         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.85    (3)   ~ (e3 = e0)
% 240.08/46.85    (4)   ~ (e2 = e0)
% 240.08/46.85    (5)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) = all_38_1
% 240.08/46.85           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 240.08/46.85           all_38_1 & $i(all_38_1))
% 240.08/46.85    (6)  op(e0, e3) = all_52_3
% 240.08/46.85    (7)   ~ (e3 = e1)
% 240.08/46.85    (8)  op(e3, e1) = e0
% 240.08/46.85    (9)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) = all_10_1
% 240.08/46.85           & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3, e1) =
% 240.08/46.85           all_10_1 & $i(all_10_1))
% 240.08/46.85    (10)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.08/46.85          $i(all_56_15)
% 240.08/46.85    (11)   ~ (e3 = e2)
% 240.08/46.85    (12)  op(e0, e2) = e0
% 240.08/46.85    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.85    (14)   ~ (e1 = e0)
% 240.08/46.85    (15)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.85          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.08/46.85            e1)
% 240.08/46.85    (16)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.85          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.08/46.85            e2)
% 240.08/46.85    (17)   ~ (e2 = e1)
% 240.08/46.85  
% 240.08/46.85  Begin of proof
% 240.08/46.85  | 
% 240.08/46.85  | ALPHA: (10) implies:
% 240.08/46.85  |   (18)  op(e0, e2) = all_56_15
% 240.08/46.85  |   (19)  op(e0, all_56_15) = e0
% 240.08/46.85  | 
% 240.08/46.85  | BETA: splitting (5) gives:
% 240.08/46.85  | 
% 240.08/46.85  | Case 1:
% 240.08/46.85  | | 
% 240.08/46.85  | | 
% 240.08/46.85  | | GROUND_INST: instantiating (13) with e0, all_56_15, e2, e0, simplifying with
% 240.08/46.85  | |              (12), (18) gives:
% 240.08/46.85  | |   (20)  all_56_15 = e0
% 240.08/46.85  | | 
% 240.08/46.85  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (11), (13), (14), (15), (16), (17),
% 240.08/46.85  | |            (18), (19), (20) are inconsistent by sub-proof #1769.
% 240.08/46.85  | | 
% 240.08/46.85  | Case 2:
% 240.08/46.85  | | 
% 240.08/46.85  | |   (21)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1)
% 240.08/46.85  | | 
% 240.08/46.85  | | ALPHA: (21) implies:
% 240.08/46.85  | |   (22)   ~ (all_38_1 = e0)
% 240.08/46.85  | |   (23)  op(e3, e1) = all_38_1
% 240.08/46.85  | | 
% 240.08/46.85  | | REF_CLOSE: (8), (9), (13), (22), (23) are inconsistent by sub-proof #1194.
% 240.08/46.85  | | 
% 240.08/46.85  | End of split
% 240.08/46.85  | 
% 240.08/46.85  End of proof
% 240.08/46.85  
% 240.08/46.85  Sub-proof #267 shows that the following formulas are inconsistent:
% 240.08/46.85  ----------------------------------------------------------------
% 240.08/46.85    (1)  op(e2, e2) = e3
% 240.08/46.85    (2)   ~ (e2 = e0)
% 240.08/46.85    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.08/46.85         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.85    (4)   ~ (e3 = e1)
% 240.08/46.85    (5)  all_58_3 = e3
% 240.08/46.85    (6)  op(e3, e3) = e1
% 240.08/46.85    (7)   ~ (e3 = e2)
% 240.08/46.85    (8)  op(e0, e2) = e0
% 240.08/46.85    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.85    (10)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.08/46.85          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.08/46.85    (11)   ~ (e1 = e0)
% 240.08/46.85    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 240.08/46.85    (13)   ~ (e2 = e1)
% 240.08/46.85  
% 240.08/46.85  Begin of proof
% 240.08/46.85  | 
% 240.08/46.85  | BETA: splitting (12) gives:
% 240.08/46.85  | 
% 240.08/46.85  | Case 1:
% 240.08/46.85  | | 
% 240.08/46.85  | |   (14)  all_58_0 = e0 & op(e3, e3) = e0
% 240.08/46.85  | | 
% 240.08/46.85  | | ALPHA: (14) implies:
% 240.08/46.85  | |   (15)  op(e3, e3) = e0
% 240.08/46.85  | | 
% 240.08/46.85  | | REF_CLOSE: (6), (9), (11), (15) are inconsistent by sub-proof #1828.
% 240.08/46.85  | | 
% 240.08/46.85  | Case 2:
% 240.08/46.85  | | 
% 240.08/46.85  | |   (16)  all_58_1 = e0 & op(e3, e2) = e0
% 240.08/46.85  | | 
% 240.08/46.85  | | ALPHA: (16) implies:
% 240.08/46.85  | |   (17)  all_58_1 = e0
% 240.08/46.85  | | 
% 240.08/46.85  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (17)
% 240.08/46.85  | |            are inconsistent by sub-proof #309.
% 240.08/46.85  | | 
% 240.08/46.85  | End of split
% 240.08/46.85  | 
% 240.08/46.85  End of proof
% 240.08/46.85  
% 240.08/46.85  Sub-proof #268 shows that the following formulas are inconsistent:
% 240.08/46.85  ----------------------------------------------------------------
% 240.08/46.85    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.08/46.85         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.08/46.85    (2)   ~ (e3 = e0)
% 240.08/46.85    (3)  op(e1, e2) = e1
% 240.08/46.85    (4)   ~ (e2 = e0)
% 240.08/46.85    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 240.08/46.85    (6)  op(e1, e2) = all_52_6
% 240.08/46.85    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.08/46.85         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.08/46.85    (8)   ~ (all_52_7 = e3)
% 240.08/46.85    (9)   ~ (e3 = e1)
% 240.08/46.85    (10)  all_58_3 = e3
% 240.08/46.85    (11)  op(e3, e2) = e2
% 240.08/46.85    (12)   ~ (e3 = e2)
% 240.08/46.85    (13)  all_58_15 = e1
% 240.08/46.85    (14)  all_58_12 = e3
% 240.08/46.85    (15)  op(e0, e2) = all_52_7
% 240.08/46.85    (16)  all_58_1 = e2
% 240.08/46.85    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.85    (18)   ~ (e1 = e0)
% 240.08/46.85    (19)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.08/46.85          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.08/46.85            e2)
% 240.08/46.85    (20)   ~ (e2 = e1)
% 240.08/46.85  
% 240.08/46.85  Begin of proof
% 240.08/46.85  | 
% 240.08/46.85  | BETA: splitting (5) gives:
% 240.08/46.85  | 
% 240.08/46.85  | Case 1:
% 240.08/46.85  | | 
% 240.08/46.85  | |   (21)  all_58_1 = e0 & op(e3, e2) = e0
% 240.08/46.85  | | 
% 240.08/46.85  | | ALPHA: (21) implies:
% 240.08/46.85  | |   (22)  op(e3, e2) = e0
% 240.08/46.85  | | 
% 240.08/46.85  | | REF_CLOSE: (4), (11), (17), (22) are inconsistent by sub-proof #2026.
% 240.08/46.85  | | 
% 240.08/46.85  | Case 2:
% 240.08/46.85  | | 
% 240.08/46.85  | |   (23)  all_58_3 = e0 & op(e2, e2) = e0
% 240.08/46.85  | | 
% 240.08/46.85  | | ALPHA: (23) implies:
% 240.08/46.85  | |   (24)  all_58_3 = e0
% 240.08/46.85  | | 
% 240.08/46.85  | | COMBINE_EQS: (10), (24) imply:
% 240.08/46.85  | |   (25)  e3 = e0
% 240.08/46.85  | | 
% 240.08/46.85  | | COMBINE_EQS: (14), (25) imply:
% 240.08/46.85  | |   (26)  all_58_12 = e0
% 240.08/46.85  | | 
% 240.08/46.85  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (15),
% 240.08/46.85  | |            (16), (17), (18), (19), (20), (26) are inconsistent by sub-proof
% 240.08/46.85  | |            #925.
% 240.08/46.85  | | 
% 240.08/46.85  | End of split
% 240.08/46.85  | 
% 240.08/46.85  End of proof
% 240.08/46.85  
% 240.08/46.85  Sub-proof #269 shows that the following formulas are inconsistent:
% 240.08/46.85  ----------------------------------------------------------------
% 240.08/46.85    (1)   ~ (all_52_3 = e1)
% 240.08/46.85    (2)  op(e0, e3) = all_52_3
% 240.08/46.85    (3)   ~ (e3 = e1)
% 240.08/46.85    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 240.08/46.85    (5)   ~ (all_52_2 = e1)
% 240.08/46.85    (6)  op(e2, e3) = all_52_1
% 240.08/46.85    (7)   ~ (all_52_4 = e3)
% 240.08/46.85    (8)  op(e3, e2) = all_52_4
% 240.08/46.85    (9)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.08/46.85         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.08/46.85    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.85    (11)  op(e1, e3) = all_52_2
% 240.08/46.85    (12)   ~ (all_52_1 = e1)
% 240.08/46.85  
% 240.08/46.85  Begin of proof
% 240.08/46.85  | 
% 240.08/46.85  | BETA: splitting (4) gives:
% 240.08/46.85  | 
% 240.08/46.85  | Case 1:
% 240.08/46.85  | | 
% 240.08/46.85  | |   (13)  all_58_0 = e3 & op(e3, e3) = e3
% 240.08/46.85  | | 
% 240.08/46.85  | | ALPHA: (13) implies:
% 240.08/46.85  | |   (14)  op(e3, e3) = e3
% 240.08/46.85  | | 
% 240.08/46.85  | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (11), (12), (14) are
% 240.08/46.85  | |            inconsistent by sub-proof #440.
% 240.08/46.85  | | 
% 240.08/46.85  | Case 2:
% 240.08/46.85  | | 
% 240.08/46.85  | |   (15)  all_58_1 = e3 & op(e3, e2) = e3
% 240.08/46.85  | | 
% 240.08/46.85  | | ALPHA: (15) implies:
% 240.08/46.85  | |   (16)  op(e3, e2) = e3
% 240.08/46.85  | | 
% 240.08/46.85  | | REF_CLOSE: (7), (8), (10), (16) are inconsistent by sub-proof #2192.
% 240.08/46.85  | | 
% 240.08/46.85  | End of split
% 240.08/46.85  | 
% 240.08/46.85  End of proof
% 240.08/46.85  
% 240.08/46.85  Sub-proof #270 shows that the following formulas are inconsistent:
% 240.08/46.85  ----------------------------------------------------------------
% 240.08/46.85    (1)   ~ (all_52_3 = e1)
% 240.08/46.86    (2)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 240.08/46.86    (3)  op(e0, e3) = all_52_3
% 240.08/46.86    (4)   ~ (e3 = e1)
% 240.08/46.86    (5)   ~ (all_52_2 = e1)
% 240.08/46.86    (6)  op(e2, e3) = all_52_1
% 240.08/46.86    (7)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.08/46.86         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.08/46.86    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.86    (9)  op(e1, e3) = all_52_2
% 240.08/46.86    (10)   ~ (all_52_1 = e3)
% 240.08/46.86    (11)   ~ (all_52_1 = e1)
% 240.08/46.86  
% 240.08/46.86  Begin of proof
% 240.08/46.86  | 
% 240.08/46.86  | BETA: splitting (2) gives:
% 240.08/46.86  | 
% 240.08/46.86  | Case 1:
% 240.08/46.86  | | 
% 240.08/46.86  | |   (12)  all_58_0 = e3 & op(e3, e3) = e3
% 240.08/46.86  | | 
% 240.08/46.86  | | ALPHA: (12) implies:
% 240.08/46.86  | |   (13)  op(e3, e3) = e3
% 240.08/46.86  | | 
% 240.08/46.86  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (13) are
% 240.08/46.86  | |            inconsistent by sub-proof #440.
% 240.08/46.86  | | 
% 240.08/46.86  | Case 2:
% 240.08/46.86  | | 
% 240.08/46.86  | |   (14)  all_58_2 = e3 & op(e2, e3) = e3
% 240.08/46.86  | | 
% 240.08/46.86  | | ALPHA: (14) implies:
% 240.08/46.86  | |   (15)  op(e2, e3) = e3
% 240.08/46.86  | | 
% 240.08/46.86  | | REF_CLOSE: (6), (8), (10), (15) are inconsistent by sub-proof #2337.
% 240.08/46.86  | | 
% 240.08/46.86  | End of split
% 240.08/46.86  | 
% 240.08/46.86  End of proof
% 240.08/46.86  
% 240.08/46.86  Sub-proof #271 shows that the following formulas are inconsistent:
% 240.08/46.86  ----------------------------------------------------------------
% 240.08/46.86    (1)   ~ (e2 = e0)
% 240.08/46.86    (2)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.08/46.86             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.08/46.86           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 240.08/46.86             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.08/46.86           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.08/46.86    (3)  op(e2, e1) = all_52_9
% 240.08/46.86    (4)  op(e0, e2) = e0
% 240.08/46.86    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.86    (6)   ~ (all_52_9 = e1)
% 240.08/46.86  
% 240.08/46.86  Begin of proof
% 240.08/46.86  | 
% 240.08/46.86  | BETA: splitting (2) gives:
% 240.08/46.86  | 
% 240.08/46.86  | Case 1:
% 240.08/46.86  | | 
% 240.08/46.86  | |   (7)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.08/46.86  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 240.08/46.86  | |        & op(e1, e2) = e1
% 240.08/46.86  | | 
% 240.08/46.86  | | ALPHA: (7) implies:
% 240.08/46.86  | |   (8)  op(e2, e1) = e1
% 240.08/46.86  | | 
% 240.08/46.86  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2306.
% 240.08/46.86  | | 
% 240.08/46.86  | Case 2:
% 240.08/46.86  | | 
% 240.08/46.86  | |   (9)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.08/46.86  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 240.08/46.86  | |        & op(e0, e2) = e2
% 240.08/46.86  | | 
% 240.08/46.86  | | ALPHA: (9) implies:
% 240.08/46.86  | |   (10)  op(e0, e2) = e2
% 240.08/46.86  | | 
% 240.08/46.86  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2132.
% 240.08/46.86  | | 
% 240.08/46.86  | End of split
% 240.08/46.86  | 
% 240.08/46.86  End of proof
% 240.08/46.86  
% 240.08/46.86  Sub-proof #272 shows that the following formulas are inconsistent:
% 240.08/46.86  ----------------------------------------------------------------
% 240.08/46.86    (1)   ~ (all_52_3 = e0)
% 240.08/46.86    (2)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 240.08/46.86           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 240.08/46.86           all_12_1 & $i(all_12_1))
% 240.08/46.86    (3)  op(e3, e2) = e1
% 240.08/46.86    (4)   ~ (all_52_3 = e1)
% 240.08/46.86    (5)   ~ (e3 = e0)
% 240.08/46.86    (6)  op(e2, e3) = e0
% 240.08/46.86    (7)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.08/46.86           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 240.08/46.86           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 240.08/46.86         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.08/46.86           $i(all_56_15))
% 240.08/46.86    (8)  all_54_13 = all_52_7
% 240.08/46.86    (9)   ~ (all_52_7 = e3)
% 240.08/46.86    (10)  op(e0, e3) = all_52_3
% 240.08/46.86    (11)   ~ (e3 = e1)
% 240.08/46.86    (12)  op(e2, e3) = all_42_1
% 240.08/46.86    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.08/46.86          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.08/46.86    (14)  op(e3, e1) = e0
% 240.08/46.86    (15)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 240.08/46.86            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 240.08/46.86              e3) = all_26_1 & $i(all_26_1))
% 240.08/46.86    (16)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 240.08/46.86    (17)   ~ (all_52_3 = all_52_7)
% 240.08/46.86    (18)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.08/46.86          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.08/46.86    (19)   ~ (all_52_7 = e1)
% 240.08/46.86    (20)  all_54_12 = all_52_3
% 240.08/46.86    (21)   ~ (all_52_3 = e3)
% 240.08/46.86    (22)  op(e0, e2) = e0
% 240.08/46.86    (23)  all_58_5 = e2
% 240.08/46.86    (24)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.08/46.86          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.08/46.86    (25)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.08/46.86    (26)  op(e0, e0) = e3
% 240.08/46.86    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.08/46.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.08/46.86    (28)  all_56_11 = e3
% 240.08/46.86    (29)  all_56_13 = e2
% 240.08/46.86    (30)  all_58_14 = e1
% 240.08/46.86    (31)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.08/46.86            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.08/46.86            & $i(all_8_1))
% 240.08/46.86    (32)  all_58_4 = e0
% 240.08/46.86  
% 240.08/46.86  Begin of proof
% 240.08/46.86  | 
% 240.08/46.86  | BETA: splitting (25) gives:
% 240.08/46.86  | 
% 240.08/46.86  | Case 1:
% 240.08/46.86  | | 
% 240.08/46.86  | |   (33)  all_54_12 = e2
% 240.08/46.86  | | 
% 240.08/46.86  | | COMBINE_EQS: (20), (33) imply:
% 240.08/46.86  | |   (34)  all_52_3 = e2
% 240.08/46.86  | | 
% 240.08/46.86  | | REDUCE: (17), (34) imply:
% 240.08/46.86  | |   (35)   ~ (all_52_7 = e2)
% 240.08/46.86  | | 
% 240.08/46.86  | | SIMP: (35) implies:
% 240.08/46.86  | |   (36)   ~ (all_52_7 = e2)
% 240.08/46.86  | | 
% 240.08/46.86  | | REDUCE: (21), (34) imply:
% 240.08/46.86  | |   (37)   ~ (e3 = e2)
% 240.08/46.86  | | 
% 240.08/46.86  | | SIMP: (37) implies:
% 240.08/46.86  | |   (38)   ~ (e3 = e2)
% 240.08/46.86  | | 
% 240.08/46.86  | | REDUCE: (4), (34) imply:
% 240.08/46.86  | |   (39)   ~ (e2 = e1)
% 240.08/46.86  | | 
% 240.08/46.86  | | REDUCE: (1), (34) imply:
% 240.08/46.86  | |   (40)   ~ (e2 = e0)
% 240.08/46.86  | | 
% 240.08/46.86  | | REDUCE: (10), (34) imply:
% 240.08/46.86  | |   (41)  op(e0, e3) = e2
% 240.08/46.86  | | 
% 240.08/46.86  | | BETA: splitting (16) gives:
% 240.08/46.86  | | 
% 240.08/46.86  | | Case 1:
% 240.08/46.86  | | | 
% 240.08/46.86  | | |   (42)  all_54_13 = e2
% 240.08/46.86  | | | 
% 240.08/46.86  | | | REF_CLOSE: (8), (36), (42) are inconsistent by sub-proof #2009.
% 240.08/46.86  | | | 
% 240.08/46.86  | | Case 2:
% 240.08/46.86  | | | 
% 240.08/46.86  | | |   (43)   ~ (all_54_13 = e2)
% 240.08/46.86  | | |   (44)  all_54_13 = e1 | all_54_13 = e0
% 240.08/46.86  | | | 
% 240.08/46.86  | | | BETA: splitting (7) gives:
% 240.08/46.86  | | | 
% 240.08/46.86  | | | Case 1:
% 240.08/46.86  | | | | 
% 240.08/46.86  | | | |   (45)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.08/46.86  | | | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 240.08/46.86  | | | | 
% 240.08/46.86  | | | | BETA: splitting (45) gives:
% 240.08/46.86  | | | | 
% 240.08/46.86  | | | | Case 1:
% 240.08/46.86  | | | | | 
% 240.08/46.86  | | | | |   (46)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9
% 240.08/46.86  | | | | |         & $i(all_56_9)
% 240.08/46.86  | | | | | 
% 240.08/46.86  | | | | | ALPHA: (46) implies:
% 240.08/46.86  | | | | |   (47)  op(e3, e2) = all_56_9
% 240.08/46.86  | | | | |   (48)  op(e3, all_56_9) = e3
% 240.08/46.86  | | | | | 
% 240.08/46.86  | | | | | BETA: splitting (44) gives:
% 240.08/46.86  | | | | | 
% 240.08/46.86  | | | | | Case 1:
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | |   (49)  all_54_13 = e1
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | | COMBINE_EQS: (8), (49) imply:
% 240.08/46.86  | | | | | |   (50)  all_52_7 = e1
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | | REDUCE: (19), (50) imply:
% 240.08/46.86  | | | | | |   (51)  $false
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | | CLOSE: (51) is inconsistent.
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | Case 2:
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | |   (52)  all_54_13 = e0
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | | COMBINE_EQS: (8), (52) imply:
% 240.08/46.86  | | | | | |   (53)  all_52_7 = e0
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | | REDUCE: (9), (53) imply:
% 240.08/46.86  | | | | | |   (54)   ~ (e3 = e0)
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | | GROUND_INST: instantiating (27) with e1, all_56_9, e2, e3,
% 240.08/46.86  | | | | | |              simplifying with (3), (47) gives:
% 240.08/46.86  | | | | | |   (55)  all_56_9 = e1
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | | REDUCE: (48), (55) imply:
% 240.08/46.86  | | | | | |   (56)  op(e3, e1) = e3
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | | REF_CLOSE: (5), (14), (27), (56) are inconsistent by sub-proof
% 240.08/46.86  | | | | | |            #2118.
% 240.08/46.86  | | | | | | 
% 240.08/46.86  | | | | | End of split
% 240.08/46.86  | | | | | 
% 240.08/46.86  | | | | Case 2:
% 240.08/46.86  | | | | | 
% 240.08/46.86  | | | | |   (57)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 240.08/46.86  | | | | | 
% 240.08/46.86  | | | | | REF_CLOSE: (6), (12), (27), (28), (31), (40), (57) are inconsistent by
% 240.08/46.86  | | | | |            sub-proof #884.
% 240.08/46.86  | | | | | 
% 240.08/46.86  | | | | End of split
% 240.08/46.86  | | | | 
% 240.08/46.86  | | | Case 2:
% 240.08/46.86  | | | | 
% 240.08/46.86  | | | |   (58)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 240.08/46.86  | | | |           all_56_13 & $i(all_56_13)) | (all_56_14 = e0 & op(e0,
% 240.08/46.86  | | | |             all_56_15) = e0 & op(e0, e2) = all_56_15 & $i(all_56_15))
% 240.08/46.86  | | | | 
% 240.08/46.86  | | | | BETA: splitting (58) gives:
% 240.08/46.86  | | | | 
% 240.08/46.86  | | | | Case 1:
% 240.08/46.86  | | | | | 
% 240.08/46.86  | | | | |   (59)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 240.08/46.86  | | | | |         all_56_13 & $i(all_56_13)
% 240.08/46.86  | | | | | 
% 240.08/46.86  | | | | | ALPHA: (59) implies:
% 240.25/46.86  | | | | |   (60)  op(e1, e2) = all_56_13
% 240.25/46.86  | | | | |   (61)  op(e1, all_56_13) = e1
% 240.25/46.86  | | | | | 
% 240.25/46.86  | | | | | REDUCE: (29), (61) imply:
% 240.25/46.86  | | | | |   (62)  op(e1, e2) = e1
% 240.25/46.86  | | | | | 
% 240.25/46.86  | | | | | REDUCE: (29), (60) imply:
% 240.25/46.86  | | | | |   (63)  op(e1, e2) = e2
% 240.25/46.86  | | | | | 
% 240.25/46.86  | | | | | BETA: splitting (44) gives:
% 240.25/46.86  | | | | | 
% 240.25/46.86  | | | | | Case 1:
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | |   (64)  all_54_13 = e1
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | | COMBINE_EQS: (8), (64) imply:
% 240.25/46.86  | | | | | |   (65)  all_52_7 = e1
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | | REDUCE: (19), (65) imply:
% 240.25/46.86  | | | | | |   (66)  $false
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | | CLOSE: (66) is inconsistent.
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | Case 2:
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | |   (67)  all_54_13 = e0
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | | COMBINE_EQS: (8), (67) imply:
% 240.25/46.86  | | | | | |   (68)  all_52_7 = e0
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | | REDUCE: (9), (68) imply:
% 240.25/46.86  | | | | | |   (69)   ~ (e3 = e0)
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | | REDUCE: (36), (68) imply:
% 240.25/46.86  | | | | | |   (70)   ~ (e2 = e0)
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | | REDUCE: (19), (68) imply:
% 240.25/46.86  | | | | | |   (71)   ~ (e1 = e0)
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | | SIMP: (71) implies:
% 240.25/46.86  | | | | | |   (72)   ~ (e1 = e0)
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | | GROUND_INST: instantiating (27) with e1, e2, e2, e1, simplifying
% 240.25/46.86  | | | | | |              with (62), (63) gives:
% 240.25/46.86  | | | | | |   (73)  e2 = e1
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | | COMBINE_EQS: (23), (73) imply:
% 240.25/46.86  | | | | | |   (74)  all_58_5 = e1
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | | REF_CLOSE: (5), (11), (13), (18), (24), (27), (30), (32), (38),
% 240.25/46.86  | | | | | |            (39), (40), (72), (74) are inconsistent by sub-proof
% 240.25/46.86  | | | | | |            #1248.
% 240.25/46.86  | | | | | | 
% 240.25/46.86  | | | | | End of split
% 240.25/46.86  | | | | | 
% 240.25/46.86  | | | | Case 2:
% 240.25/46.86  | | | | | 
% 240.25/46.86  | | | | |   (75)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 240.25/46.86  | | | | |         all_56_15 & $i(all_56_15)
% 240.25/46.86  | | | | | 
% 240.25/46.86  | | | | | REF_CLOSE: (2), (5), (15), (22), (26), (27), (41), (75) are
% 240.25/46.86  | | | | |            inconsistent by sub-proof #1022.
% 240.25/46.86  | | | | | 
% 240.25/46.86  | | | | End of split
% 240.25/46.86  | | | | 
% 240.25/46.86  | | | End of split
% 240.25/46.86  | | | 
% 240.25/46.86  | | End of split
% 240.25/46.86  | | 
% 240.25/46.86  | Case 2:
% 240.25/46.86  | | 
% 240.25/46.86  | |   (76)  all_54_12 = e1 | all_54_12 = e0
% 240.25/46.86  | | 
% 240.25/46.86  | | REF_CLOSE: (1), (4), (20), (76) are inconsistent by sub-proof #2067.
% 240.25/46.86  | | 
% 240.25/46.86  | End of split
% 240.25/46.86  | 
% 240.25/46.86  End of proof
% 240.25/46.86  
% 240.25/46.86  Sub-proof #273 shows that the following formulas are inconsistent:
% 240.25/46.86  ----------------------------------------------------------------
% 240.25/46.86    (1)  op(e3, e2) = e1
% 240.25/46.86    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.25/46.86           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.25/46.86             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.25/46.86           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.25/46.86             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.25/46.86           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.25/46.86           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.25/46.86    (3)   ~ (e3 = e1)
% 240.25/46.86    (4)  op(e1, e3) = e1
% 240.25/46.86    (5)  op(e2, e3) = all_52_1
% 240.25/46.86    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.25/46.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.25/46.86    (7)   ~ (all_52_1 = e3)
% 240.25/46.86    (8)   ~ (e2 = e1)
% 240.25/46.86  
% 240.25/46.86  Begin of proof
% 240.25/46.86  | 
% 240.25/46.86  | BETA: splitting (2) gives:
% 240.25/46.86  | 
% 240.25/46.86  | Case 1:
% 240.25/46.86  | | 
% 240.25/46.86  | |   (9)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.25/46.86  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.25/46.86  | |        op(e2, e3) = e3
% 240.25/46.86  | | 
% 240.25/46.86  | | ALPHA: (9) implies:
% 240.25/46.86  | |   (10)  op(e2, e3) = e3
% 240.25/46.86  | | 
% 240.25/46.86  | | REF_CLOSE: (5), (6), (7), (10) are inconsistent by sub-proof #2337.
% 240.25/46.86  | | 
% 240.25/46.86  | Case 2:
% 240.25/46.86  | | 
% 240.25/46.86  | |   (11)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.25/46.86  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.25/46.86  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.25/46.86  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.25/46.86  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.25/46.86  | | 
% 240.25/46.86  | | REF_CLOSE: (1), (3), (4), (6), (8), (11) are inconsistent by sub-proof #334.
% 240.25/46.86  | | 
% 240.25/46.86  | End of split
% 240.25/46.86  | 
% 240.25/46.86  End of proof
% 240.25/46.86  
% 240.25/46.86  Sub-proof #274 shows that the following formulas are inconsistent:
% 240.25/46.86  ----------------------------------------------------------------
% 240.25/46.86    (1)   ~ (all_52_1 = all_52_3)
% 240.25/46.86    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 240.25/46.86    (3)  op(e2, e2) = e3
% 240.25/46.86    (4)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 240.25/46.86           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 240.25/46.86           all_12_1 & $i(all_12_1))
% 240.25/46.86    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.25/46.86         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.25/46.86    (6)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.25/46.86           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.25/46.86           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.25/46.86           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.25/46.86           & $i(all_56_23))
% 240.25/46.86    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.25/46.86         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.25/46.86    (8)   ~ (e3 = e0)
% 240.25/46.86    (9)  op(e0, e1) = all_52_11
% 240.25/46.86    (10)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.25/46.86          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.25/46.86    (11)   ~ (all_52_8 = all_52_9)
% 240.25/46.86    (12)   ~ (e2 = e0)
% 240.25/46.86    (13)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.25/46.86            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 240.25/46.86            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 240.25/46.86            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 240.25/46.86            = all_56_15 & $i(all_56_15))
% 240.25/46.86    (14)  all_54_13 = all_52_7
% 240.25/46.86    (15)  op(e1, e2) = all_52_6
% 240.25/46.86    (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.25/46.86          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.25/46.87    (17)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 240.25/46.87          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.25/46.87    (18)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.25/46.87              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.25/46.87            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.25/46.87            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.25/46.87            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.25/46.87             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.25/46.87            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.25/46.87            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.25/46.87            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.25/46.87            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.87            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.25/46.87              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.25/46.87            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.25/46.87            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.25/46.87            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.25/46.87            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.25/46.87            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.25/46.87            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.25/46.87              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.25/46.87            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.87            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.25/46.87            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.25/46.87            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.25/46.87            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.87            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.25/46.87              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.25/46.87            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.25/46.87            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.25/46.87    (19)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.25/46.87          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.25/46.87    (20)   ~ (all_52_7 = all_52_11)
% 240.25/46.87    (21)  all_58_4 = e2
% 240.25/46.87    (22)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.25/46.87          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.25/46.87    (23)   ~ (all_52_1 = all_52_2)
% 240.25/46.87    (24)  op(e1, e0) = all_52_14
% 240.25/46.87    (25)   ~ (all_52_7 = e3)
% 240.25/46.87    (26)  all_58_15 = e3
% 240.25/46.87    (27)  op(e0, e3) = all_52_3
% 240.25/46.87    (28)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.25/46.87          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.25/46.87    (29)   ~ (e3 = e1)
% 240.25/46.87    (30)  all_54_11 = all_52_14
% 240.25/46.87    (31)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.25/46.87          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.25/46.87    (32)   ~ (all_52_2 = all_52_3)
% 240.25/46.87    (33)   ~ (all_52_8 = e1)
% 240.25/46.87    (34)  all_58_3 = e3
% 240.25/46.87    (35)   ~ (all_52_12 = all_52_13)
% 240.25/46.87    (36)  op(e0, e1) = e1
% 240.25/46.87    (37)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.25/46.87    (38)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.25/46.87          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.25/46.87    (39)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 240.25/46.87            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 240.25/46.87              e3) = all_26_1 & $i(all_26_1))
% 240.25/46.87    (40)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 240.25/46.87            $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e1, e3) = all_6_1
% 240.25/46.87            & $i(all_6_1))
% 240.25/46.87    (41)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 240.25/46.87          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 240.25/46.87    (42)   ~ (all_52_1 = all_52_9)
% 240.25/46.87    (43)   ~ (all_52_3 = all_52_7)
% 240.25/46.87    (44)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.25/46.87    (45)  all_54_4 = all_52_1
% 240.25/46.87    (46)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.25/46.87              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.25/46.87                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.25/46.87                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.25/46.87    (47)   ~ (all_52_11 = e3)
% 240.25/46.87    (48)   ~ (all_52_8 = all_52_12)
% 240.25/46.87    (49)  op(e3, e1) = all_52_8
% 240.25/46.87    (50)  op(e2, e1) = all_52_9
% 240.25/46.87    (51)  all_54_9 = all_52_6
% 240.25/46.87    (52)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.25/46.87          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.25/46.87    (53)   ~ (e3 = e2)
% 240.25/46.87    (54)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.25/46.87          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.25/46.87    (55)   ~ (all_52_7 = e1)
% 240.25/46.87    (56)   ~ (all_52_3 = all_52_11)
% 240.25/46.87    (57)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.25/46.87            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.25/46.87            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.25/46.87            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.25/46.87            op(e0, all_56_31) = e0)
% 240.25/46.87    (58)  all_54_12 = all_52_3
% 240.25/46.87    (59)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.25/46.87    (60)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.25/46.87          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.25/46.87    (61)  op(e3, e0) = all_52_12
% 240.25/46.87    (62)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.25/46.87          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.25/46.87    (63)   ~ (all_52_9 = all_52_13)
% 240.25/46.87    (64)   ~ (all_52_3 = e3)
% 240.25/46.87    (65)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.25/46.87            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.25/46.87              e3) = all_42_1 & $i(all_42_1))
% 240.25/46.87    (66)  op(e2, e3) = all_52_1
% 240.25/46.87    (67)   ~ (all_52_14 = e3)
% 240.25/46.87    (68)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.25/46.87          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.25/46.87    (69)  op(e1, e1) = e3
% 240.25/46.87    (70)   ~ (all_52_2 = e3)
% 240.25/46.87    (71)   ~ (all_52_6 = e3)
% 240.25/46.87    (72)   ~ (all_52_1 = all_52_13)
% 240.25/46.87    (73)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.25/46.87          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.25/46.87    (74)  op(e3, e1) = e2
% 240.25/46.87    (75)  all_54_7 = all_52_13
% 240.25/46.87    (76)  op(e0, e2) = all_52_7
% 240.25/46.87    (77)   ~ (all_52_13 = all_52_14)
% 240.25/46.87    (78)   ~ (all_52_4 = e3)
% 240.25/46.87    (79)  op(e3, e2) = all_52_4
% 240.25/46.87    (80)   ~ (all_52_8 = all_52_11)
% 240.25/46.87    (81)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.25/46.87    (82)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 240.25/46.87    (83)   ~ (all_52_9 = e3)
% 240.25/46.87    (84)  all_56_31 = e3
% 240.25/46.87    (85)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.25/46.87          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.25/46.87    (86)  op(e0, e0) = e3
% 240.25/46.87    (87)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.25/46.87          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.25/46.87    (88)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.25/46.87          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.25/46.87    (89)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.25/46.87          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.25/46.87    (90)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.25/46.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.25/46.87    (91)  all_58_8 = e3
% 240.25/46.87    (92)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.25/46.87          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.25/46.87    (93)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.25/46.87            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.25/46.87              e3) = all_46_1 & $i(all_46_1))
% 240.25/46.87    (94)  op(e1, e3) = all_52_2
% 240.25/46.87    (95)  all_56_21 = e3
% 240.25/46.87    (96)   ~ (all_52_6 = all_52_7)
% 240.25/46.87    (97)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.25/46.87          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.25/46.87    (98)   ~ (all_52_12 = e3)
% 240.25/46.87    (99)  all_56_11 = e3
% 240.25/46.87    (100)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.25/46.87           (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.25/46.87    (101)   ~ (e1 = e0)
% 240.25/46.87    (102)  op(e3, e3) = e3
% 240.25/46.87    (103)   ~ (all_52_13 = e3)
% 240.25/46.87    (104)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.25/46.87           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.25/46.87    (105)  op(e2, e0) = all_52_13
% 240.25/46.87    (106)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.25/46.87           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.25/46.87             e1)
% 240.25/46.87    (107)   ~ (all_52_1 = e3)
% 240.25/46.87    (108)   ~ (all_52_9 = e1)
% 240.25/46.87    (109)  all_58_14 = e1
% 240.25/46.87    (110)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.25/46.87           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.25/46.87             e2)
% 240.25/46.87    (111)   ~ (all_52_9 = all_52_11)
% 240.25/46.87    (112)   ~ (all_52_4 = all_52_8)
% 240.25/46.87    (113)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.25/46.87             $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) =
% 240.25/46.87             all_8_1 & $i(all_8_1))
% 240.25/46.87    (114)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.25/46.87           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.25/46.87    (115)   ~ (all_52_8 = e3)
% 240.25/46.87    (116)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 240.25/46.87  
% 240.25/46.87  Begin of proof
% 240.25/46.87  | 
% 240.25/46.87  | BETA: splitting (31) gives:
% 240.25/46.87  | 
% 240.25/46.87  | Case 1:
% 240.25/46.87  | | 
% 240.25/46.87  | |   (117)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 240.25/46.87  | |            e0)
% 240.25/46.87  | | 
% 240.25/46.87  | | BETA: splitting (117) gives:
% 240.25/46.87  | | 
% 240.25/46.87  | | Case 1:
% 240.25/46.87  | | | 
% 240.25/46.87  | | |   (118)  all_58_4 = e0 & op(e3, e1) = e0
% 240.25/46.87  | | | 
% 240.25/46.87  | | | ALPHA: (118) implies:
% 240.25/46.87  | | |   (119)  all_58_4 = e0
% 240.25/46.87  | | | 
% 240.25/46.87  | | | REF_CLOSE: (12), (21), (119) are inconsistent by sub-proof #1666.
% 240.25/46.87  | | | 
% 240.25/46.87  | | Case 2:
% 240.25/46.87  | | | 
% 240.25/46.87  | | |   (120)  all_58_5 = e0 & op(e2, e1) = e0
% 240.25/46.87  | | | 
% 240.25/46.87  | | | ALPHA: (120) implies:
% 240.25/46.87  | | |   (121)  op(e2, e1) = e0
% 240.25/46.87  | | | 
% 240.25/46.87  | | | GROUND_INST: instantiating (90) with all_52_9, e0, e1, e2, simplifying
% 240.25/46.87  | | |              with (50), (121) gives:
% 240.25/46.87  | | |   (122)  all_52_9 = e0
% 240.25/46.87  | | | 
% 240.25/46.87  | | | GROUND_INST: instantiating (90) with all_52_8, e2, e1, e3, simplifying
% 240.25/46.87  | | |              with (49), (74) gives:
% 240.25/46.87  | | |   (123)  all_52_8 = e2
% 240.25/46.87  | | | 
% 240.25/46.87  | | | REDUCE: (42), (122) imply:
% 240.25/46.87  | | |   (124)   ~ (all_52_1 = e0)
% 240.25/46.87  | | | 
% 240.25/46.87  | | | REDUCE: (115), (123) imply:
% 240.25/46.87  | | |   (125)   ~ (e3 = e2)
% 240.25/46.87  | | | 
% 240.25/46.87  | | | REDUCE: (33), (123) imply:
% 240.25/46.87  | | |   (126)   ~ (e2 = e1)
% 240.25/46.87  | | | 
% 240.25/46.87  | | | REDUCE: (63), (122) imply:
% 240.25/46.87  | | |   (127)   ~ (all_52_13 = e0)
% 240.25/46.87  | | | 
% 240.25/46.87  | | | SIMP: (127) implies:
% 240.25/46.87  | | |   (128)   ~ (all_52_13 = e0)
% 240.25/46.87  | | | 
% 240.25/46.87  | | | REDUCE: (83), (122) imply:
% 240.25/46.87  | | |   (129)   ~ (e3 = e0)
% 240.25/46.87  | | | 
% 240.25/46.87  | | | REDUCE: (108), (122) imply:
% 240.25/46.87  | | |   (130)   ~ (e1 = e0)
% 240.25/46.87  | | | 
% 240.25/46.87  | | | BETA: splitting (6) gives:
% 240.25/46.87  | | | 
% 240.25/46.87  | | | Case 1:
% 240.25/46.87  | | | | 
% 240.25/46.87  | | | |   (131)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 240.25/46.87  | | | |            all_56_17 & $i(all_56_17)) | (all_56_18 = e2 & op(e2,
% 240.25/46.87  | | | |              all_56_19) = e2 & op(e2, e1) = all_56_19 & $i(all_56_19))
% 240.25/46.87  | | | | 
% 240.25/46.87  | | | | BETA: splitting (131) gives:
% 240.25/46.87  | | | | 
% 240.25/46.87  | | | | Case 1:
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | |   (132)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 240.25/46.87  | | | | |          all_56_17 & $i(all_56_17)
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | | REF_CLOSE: (74), (78), (79), (90), (132) are inconsistent by sub-proof
% 240.25/46.87  | | | | |            #300.
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | Case 2:
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | |   (133)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 240.25/46.87  | | | | |          all_56_19 & $i(all_56_19)
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | | ALPHA: (133) implies:
% 240.25/46.87  | | | | |   (134)  op(e2, e1) = all_56_19
% 240.25/46.87  | | | | |   (135)  op(e2, all_56_19) = e2
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | | GROUND_INST: instantiating (90) with e0, all_56_19, e1, e2,
% 240.25/46.87  | | | | |              simplifying with (121), (134) gives:
% 240.25/46.87  | | | | |   (136)  all_56_19 = e0
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | | REDUCE: (135), (136) imply:
% 240.25/46.87  | | | | |   (137)  op(e2, e0) = e2
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | | GROUND_INST: instantiating (90) with all_52_13, e2, e0, e2,
% 240.25/46.87  | | | | |              simplifying with (105), (137) gives:
% 240.25/46.87  | | | | |   (138)  all_52_13 = e2
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | | REDUCE: (72), (138) imply:
% 240.25/46.87  | | | | |   (139)   ~ (all_52_1 = e2)
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | | REDUCE: (35), (138) imply:
% 240.25/46.87  | | | | |   (140)   ~ (all_52_12 = e2)
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | | REDUCE: (77), (138) imply:
% 240.25/46.87  | | | | |   (141)   ~ (all_52_14 = e2)
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | | SIMP: (141) implies:
% 240.25/46.87  | | | | |   (142)   ~ (all_52_14 = e2)
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | | BETA: splitting (114) gives:
% 240.25/46.87  | | | | | 
% 240.25/46.87  | | | | | Case 1:
% 240.25/46.87  | | | | | | 
% 240.25/46.87  | | | | | |   (143)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2,
% 240.25/46.87  | | | | | |              e2) = e1)
% 240.25/46.87  | | | | | | 
% 240.25/46.87  | | | | | | BETA: splitting (143) gives:
% 240.25/46.87  | | | | | | 
% 240.25/46.87  | | | | | | Case 1:
% 240.25/46.87  | | | | | | | 
% 240.25/46.87  | | | | | | |   (144)  all_58_2 = e1 & op(e2, e3) = e1
% 240.25/46.87  | | | | | | | 
% 240.25/46.87  | | | | | | | ALPHA: (144) implies:
% 240.25/46.87  | | | | | | |   (145)  all_58_2 = e1
% 240.25/46.87  | | | | | | | 
% 240.25/46.87  | | | | | | | BETA: splitting (2) gives:
% 240.25/46.87  | | | | | | | 
% 240.25/46.87  | | | | | | | Case 1:
% 240.25/46.87  | | | | | | | | 
% 240.25/46.88  | | | | | | | |   (146)  all_54_4 = e2
% 240.25/46.88  | | | | | | | | 
% 240.25/46.88  | | | | | | | | REF_CLOSE: (45), (139), (146) are inconsistent by sub-proof
% 240.25/46.88  | | | | | | | |            #2096.
% 240.25/46.88  | | | | | | | | 
% 240.25/46.88  | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | 
% 240.25/46.88  | | | | | | | |   (147)   ~ (all_54_4 = e2)
% 240.25/46.88  | | | | | | | |   (148)  all_54_4 = e1 | all_54_4 = e0
% 240.25/46.88  | | | | | | | | 
% 240.25/46.88  | | | | | | | | BETA: splitting (148) gives:
% 240.25/46.88  | | | | | | | | 
% 240.25/46.88  | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | 
% 240.25/46.88  | | | | | | | | |   (149)  all_54_4 = e1
% 240.25/46.88  | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | COMBINE_EQS: (45), (149) imply:
% 240.25/46.88  | | | | | | | | |   (150)  all_52_1 = e1
% 240.25/46.88  | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | SIMP: (150) implies:
% 240.25/46.88  | | | | | | | | |   (151)  all_52_1 = e1
% 240.25/46.88  | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | REDUCE: (23), (151) imply:
% 240.25/46.88  | | | | | | | | |   (152)   ~ (all_52_2 = e1)
% 240.25/46.88  | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | SIMP: (152) implies:
% 240.25/46.88  | | | | | | | | |   (153)   ~ (all_52_2 = e1)
% 240.25/46.88  | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | REDUCE: (107), (151) imply:
% 240.25/46.88  | | | | | | | | |   (154)   ~ (e3 = e1)
% 240.25/46.88  | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | REDUCE: (139), (151) imply:
% 240.25/46.88  | | | | | | | | |   (155)   ~ (e2 = e1)
% 240.25/46.88  | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | REDUCE: (66), (151) imply:
% 240.25/46.88  | | | | | | | | |   (156)  op(e2, e3) = e1
% 240.25/46.88  | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | BETA: splitting (65) gives:
% 240.25/46.88  | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | |   (157)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 240.25/46.88  | | | | | | | | | |          op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)
% 240.25/46.88  | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | ALPHA: (157) implies:
% 240.25/46.88  | | | | | | | | | |   (158)   ~ (all_42_0 = e0)
% 240.25/46.88  | | | | | | | | | |   (159)  op(e2, e3) = all_42_1
% 240.25/46.88  | | | | | | | | | |   (160)  op(all_42_1, e2) = all_42_0
% 240.25/46.88  | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | BETA: splitting (113) gives:
% 240.25/46.88  | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | |   (161)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 240.25/46.88  | | | | | | | | | | |          op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | ALPHA: (161) implies:
% 240.25/46.88  | | | | | | | | | | |   (162)   ~ (all_8_0 = e1)
% 240.25/46.88  | | | | | | | | | | |   (163)  op(e2, e3) = all_8_1
% 240.25/46.88  | | | | | | | | | | |   (164)  op(all_8_1, e2) = all_8_0
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | GROUND_INST: instantiating (90) with all_8_1, all_42_1, e3, e2,
% 240.25/46.88  | | | | | | | | | | |              simplifying with (159), (163) gives:
% 240.25/46.88  | | | | | | | | | | |   (165)  all_42_1 = all_8_1
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | GROUND_INST: instantiating (90) with e1, all_42_1, e3, e2,
% 240.25/46.88  | | | | | | | | | | |              simplifying with (156), (159) gives:
% 240.25/46.88  | | | | | | | | | | |   (166)  all_42_1 = e1
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | COMBINE_EQS: (165), (166) imply:
% 240.25/46.88  | | | | | | | | | | |   (167)  all_8_1 = e1
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | SIMP: (167) implies:
% 240.25/46.88  | | | | | | | | | | |   (168)  all_8_1 = e1
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | REDUCE: (160), (166) imply:
% 240.25/46.88  | | | | | | | | | | |   (169)  op(e1, e2) = all_42_0
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | REDUCE: (164), (168) imply:
% 240.25/46.88  | | | | | | | | | | |   (170)  op(e1, e2) = all_8_0
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | GROUND_INST: instantiating (90) with all_52_6, all_8_0, e2, e1,
% 240.25/46.88  | | | | | | | | | | |              simplifying with (15), (170) gives:
% 240.25/46.88  | | | | | | | | | | |   (171)  all_52_6 = all_8_0
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | GROUND_INST: instantiating (90) with all_52_6, all_42_0, e2,
% 240.25/46.88  | | | | | | | | | | |              e1, simplifying with (15), (169) gives:
% 240.25/46.88  | | | | | | | | | | |   (172)  all_52_6 = all_42_0
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | COMBINE_EQS: (171), (172) imply:
% 240.25/46.88  | | | | | | | | | | |   (173)  all_42_0 = all_8_0
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | SIMP: (173) implies:
% 240.25/46.88  | | | | | | | | | | |   (174)  all_42_0 = all_8_0
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | COMBINE_EQS: (51), (171) imply:
% 240.25/46.88  | | | | | | | | | | |   (175)  all_54_9 = all_8_0
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | REDUCE: (96), (171) imply:
% 240.25/46.88  | | | | | | | | | | |   (176)   ~ (all_52_7 = all_8_0)
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | SIMP: (176) implies:
% 240.25/46.88  | | | | | | | | | | |   (177)   ~ (all_52_7 = all_8_0)
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | REDUCE: (71), (171) imply:
% 240.25/46.88  | | | | | | | | | | |   (178)   ~ (all_8_0 = e3)
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | REDUCE: (158), (174) imply:
% 240.25/46.88  | | | | | | | | | | |   (179)   ~ (all_8_0 = e0)
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | BETA: splitting (97) gives:
% 240.25/46.88  | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | |   (180)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 240.25/46.88  | | | | | | | | | | | |            & op(e2, e2) = e1)
% 240.25/46.88  | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | BETA: splitting (180) gives:
% 240.25/46.88  | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | |   (181)  all_58_1 = e1 & op(e3, e2) = e1
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | ALPHA: (181) implies:
% 240.25/46.88  | | | | | | | | | | | | |   (182)  all_58_1 = e1
% 240.25/46.88  | | | | | | | | | | | | |   (183)  op(e3, e2) = e1
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | BETA: splitting (10) gives:
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | |   (184)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 240.25/46.88  | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 240.25/46.88  | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (12), (15), (16), (19), (34), (53),
% 240.25/46.88  | | | | | | | | | | | | | |            (90), (94), (101), (126), (153), (182), (184) are
% 240.25/46.88  | | | | | | | | | | | | | |            inconsistent by sub-proof #949.
% 240.25/46.88  | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | |   (185)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 240.25/46.88  | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 240.25/46.88  | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 240.25/46.88  | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | |   (186)  all_58_8 = e1 & op(e1, e1) = e1
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 240.25/46.88  | | | | | | | | | | | | | | |   (187)  op(e1, e1) = e1
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | REF_CLOSE: (29), (69), (90), (187) are inconsistent by
% 240.25/46.88  | | | | | | | | | | | | | | |            sub-proof #468.
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | |   (188)  all_58_11 = e1 & op(e1, e0) = e1
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 240.25/46.88  | | | | | | | | | | | | | | |   (189)  op(e1, e0) = e1
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | |   (190)  all_54_9 = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (190) imply:
% 240.25/46.88  | | | | | | | | | | | | | | | |   (191)  all_8_0 = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | SIMP: (191) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | |   (192)  all_8_0 = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | REDUCE: (177), (192) imply:
% 240.25/46.88  | | | | | | | | | | | | | | | |   (193)   ~ (all_52_7 = e2)
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | |   (194)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | |   (195)  all_58_0 = e2 & op(e3, e3) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | |   (196)  op(e3, e3) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (38), (49), (53), (61), (90), (98), (115),
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            (182), (196) are inconsistent by sub-proof #1327.
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | |   (197)  all_58_2 = e2 & op(e2, e3) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | |   (198)  op(e2, e3) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (126), (156), (198) are inconsistent by
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            sub-proof #1633.
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | |   (199)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 240.25/46.88  | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | |   (200)  all_58_6 = e2 & op(e1, e3) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | |   (201)  all_58_6 = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | |   (202)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (53), (90), (126), (183), (202) are
% 240.25/46.88  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #287.
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | |   (203)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 240.25/46.88  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | |   (204)  all_58_7 = e2 & op(e1, e2) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | |   (205)  all_58_7 = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | |   (206)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (207)  all_58_12 = e2 & op(e0, e3) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (208)  all_58_12 = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (209)  op(e0, e3) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (9), (10), (11), (12), (15),
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            (16), (18), (19), (20), (25), (26), (27), (28),
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            (29), (31), (32), (34), (36), (46), (47), (49),
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            (50), (53), (54), (56), (57), (60), (62), (63),
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            (64), (65), (66), (69), (70), (71), (73), (76),
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            (80), (83), (84), (86), (87), (88), (90), (91),
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            (93), (94), (95), (97), (101), (102), (104),
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            (105), (106), (107), (109), (110), (111), (113),
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            (114), (115), (121), (126), (128), (137), (139),
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            (145), (208), (209) are inconsistent by sub-proof
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            #281.
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (210)  all_58_13 = e2 & op(e0, e2) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (211)  all_58_13 = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (212)  op(e0, e2) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (16), (19), (29), (34), (53), (90),
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            (97), (101), (126), (205), (211), (212) are
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1454.
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | |   (213)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (214)  all_58_14 = e2 & op(e0, e1) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (215)  all_58_14 = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (215) imply:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (216)  e2 = e1
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (216) imply:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (217)  all_58_7 = e1
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (90), (91), (101), (104), (189), (201),
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            (217) are inconsistent by sub-proof #1420.
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (218)  all_58_15 = e2 & op(e0, e0) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |   (219)  op(e0, e0) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (86), (90), (219) are inconsistent by
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1388.
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | |   (220)  all_58_13 = e2 & op(e0, e2) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | |   (221)  op(e0, e2) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (55), (76), (82), (90), (193), (221)
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1816.
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | |   (222)  all_58_12 = e2 & op(e0, e3) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | |   (223)  all_58_12 = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | |   (224)  op(e0, e3) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (9), (10), (11), (12), (15),
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            (16), (18), (19), (20), (25), (26), (27), (28),
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            (29), (31), (32), (34), (36), (46), (47), (49),
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            (50), (53), (54), (56), (57), (60), (62), (63),
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            (64), (65), (66), (69), (70), (71), (73), (76),
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            (80), (83), (84), (86), (87), (88), (90), (91),
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            (93), (94), (95), (97), (101), (102), (104),
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            (105), (106), (107), (109), (110), (111), (113),
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            (114), (115), (121), (126), (128), (137), (139),
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            (145), (223), (224) are inconsistent by sub-proof
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            #281.
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | |   (225)  all_54_9 = e1 | all_54_9 = e0
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | REF_CLOSE: (162), (175), (179), (225) are inconsistent by
% 240.25/46.88  | | | | | | | | | | | | | | | |            sub-proof #945.
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | |   (226)  all_58_3 = e1 & op(e2, e2) = e1
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | REF_CLOSE: (29), (34), (226) are inconsistent by sub-proof
% 240.25/46.88  | | | | | | | | | | | | |            #2197.
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | |   (227)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 240.25/46.88  | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 240.25/46.88  | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | BETA: splitting (227) gives:
% 240.25/46.88  | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | |   (228)  all_58_7 = e1 & op(e1, e2) = e1
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | ALPHA: (228) implies:
% 240.25/46.88  | | | | | | | | | | | | |   (229)  all_58_7 = e1
% 240.25/46.88  | | | | | | | | | | | | |   (230)  op(e1, e2) = e1
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | BETA: splitting (16) gives:
% 240.25/46.88  | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | |   (231)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 240.25/46.88  | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 240.25/46.88  | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 240.25/46.88  | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | |   (232)  all_58_1 = e2 & op(e3, e2) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 240.25/46.88  | | | | | | | | | | | | | | |   (233)  op(e3, e2) = e2
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | |   (234)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 240.25/46.88  | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | |   (235)  all_58_0 = e1 & op(e3, e3) = e1
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | |   (236)  op(e3, e3) = e1
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (90), (102), (236) are inconsistent by
% 240.25/46.88  | | | | | | | | | | | | | | | | |            sub-proof #1578.
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | |   (237)  all_58_1 = e1 & op(e3, e2) = e1
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | |   (238)  all_58_1 = e1
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (12), (15), (16), (19), (34), (53),
% 240.25/46.88  | | | | | | | | | | | | | | | | |            (90), (101), (126), (229), (230), (238) are
% 240.25/46.88  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1717.
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | |   (239)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 240.25/46.88  | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | |   (240)  all_58_4 = e1 & op(e3, e1) = e1
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | |   (241)  all_58_4 = e1
% 240.25/46.88  | | | | | | | | | | | | | | | | |   (242)  op(e3, e1) = e1
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (9), (11), (12), (18), (20), (26),
% 240.25/46.88  | | | | | | | | | | | | | | | | |            (27), (31), (32), (47), (49), (50), (53), (54),
% 240.25/46.88  | | | | | | | | | | | | | | | | |            (56), (60), (63), (64), (65), (66), (69), (70),
% 240.25/46.88  | | | | | | | | | | | | | | | | |            (73), (76), (80), (83), (84), (86), (90), (94),
% 240.25/46.88  | | | | | | | | | | | | | | | | |            (95), (101), (102), (105), (106), (107), (111),
% 240.25/46.88  | | | | | | | | | | | | | | | | |            (113), (115), (126), (241), (242) are inconsistent
% 240.25/46.88  | | | | | | | | | | | | | | | | |            by sub-proof #301.
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | |   (243)  all_58_9 = e1 & op(e3, e0) = e1
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | |   (244)  all_58_9 = e1
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | |   (245)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 240.25/46.88  | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | |   (246)  all_58_0 = e0 & op(e3, e3) = e0
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | |   (247)  op(e3, e3) = e0
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (90), (102), (247) are inconsistent by
% 240.25/46.88  | | | | | | | | | | | | | | | | | | |            sub-proof #1940.
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | |   (248)  all_58_1 = e0 & op(e3, e2) = e0
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | |   (249)  op(e3, e2) = e0
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (90), (233), (249) are inconsistent by
% 240.25/46.88  | | | | | | | | | | | | | | | | | | |            sub-proof #2026.
% 240.25/46.88  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.88  | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.88  | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | |   (250)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (251)  all_58_4 = e0 & op(e3, e1) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (252)  all_58_4 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (21), (252) are inconsistent by sub-proof
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |            #1666.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (253)  all_58_9 = e0 & op(e3, e0) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (254)  all_58_9 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (254) imply:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (255)  e1 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | SIMP: (255) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (256)  e1 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (256) imply:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (257)  all_58_2 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (28), (29), (34), (50), (53), (66),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |            (90), (101), (114), (121), (126), (139), (257) are
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #286.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | |   (258)  all_58_3 = e2 & op(e2, e2) = e2
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 240.25/46.89  | | | | | | | | | | | | | | |   (259)  op(e2, e2) = e2
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | REF_CLOSE: (3), (53), (90), (259) are inconsistent by
% 240.25/46.89  | | | | | | | | | | | | | | |            sub-proof #2140.
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | |   (260)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 240.25/46.89  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 240.25/46.89  | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 240.25/46.89  | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | |   (261)  all_58_7 = e2 & op(e1, e2) = e2
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | REF_CLOSE: (126), (229), (261) are inconsistent by sub-proof
% 240.25/46.89  | | | | | | | | | | | | | | |            #2218.
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | |   (262)  all_58_13 = e2 & op(e0, e2) = e2
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 240.25/46.89  | | | | | | | | | | | | | | |   (263)  op(e0, e2) = e2
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (55), (76), (82), (90), (116), (162),
% 240.25/46.89  | | | | | | | | | | | | | | |            (175), (177), (179), (263) are inconsistent by
% 240.25/46.89  | | | | | | | | | | | | | | |            sub-proof #944.
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | |   (264)  all_58_13 = e1 & op(e0, e2) = e1
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | REF_CLOSE: (55), (76), (90), (264) are inconsistent by
% 240.25/46.89  | | | | | | | | | | | | |            sub-proof #2275.
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | |   (265)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 240.25/46.89  | | | | | | | | | | |          $i(all_8_1)
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | ALPHA: (265) implies:
% 240.25/46.89  | | | | | | | | | | |   (266)   ~ (all_8_1 = e0)
% 240.25/46.89  | | | | | | | | | | |   (267)  op(e2, e3) = all_8_1
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | GROUND_INST: instantiating (90) with all_8_1, all_42_1, e3, e2,
% 240.25/46.89  | | | | | | | | | | |              simplifying with (159), (267) gives:
% 240.25/46.89  | | | | | | | | | | |   (268)  all_42_1 = all_8_1
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | GROUND_INST: instantiating (90) with e1, all_42_1, e3, e2,
% 240.25/46.89  | | | | | | | | | | |              simplifying with (156), (159) gives:
% 240.25/46.89  | | | | | | | | | | |   (269)  all_42_1 = e1
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | COMBINE_EQS: (268), (269) imply:
% 240.25/46.89  | | | | | | | | | | |   (270)  all_8_1 = e1
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | SIMP: (270) implies:
% 240.25/46.89  | | | | | | | | | | |   (271)  all_8_1 = e1
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | REDUCE: (160), (269) imply:
% 240.25/46.89  | | | | | | | | | | |   (272)  op(e1, e2) = all_42_0
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | GROUND_INST: instantiating (90) with all_52_6, all_42_0, e2,
% 240.25/46.89  | | | | | | | | | | |              e1, simplifying with (15), (272) gives:
% 240.25/46.89  | | | | | | | | | | |   (273)  all_52_6 = all_42_0
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | REDUCE: (71), (273) imply:
% 240.25/46.89  | | | | | | | | | | |   (274)   ~ (all_42_0 = e3)
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | BETA: splitting (52) gives:
% 240.25/46.89  | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | |   (275)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 240.25/46.89  | | | | | | | | | | | |            & op(e2, e3) = e2)
% 240.25/46.89  | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | BETA: splitting (275) gives:
% 240.25/46.89  | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | |   (276)  all_58_0 = e2 & op(e3, e3) = e2
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | ALPHA: (276) implies:
% 240.25/46.89  | | | | | | | | | | | | |   (277)  op(e3, e3) = e2
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | REF_CLOSE: (53), (90), (102), (277) are inconsistent by
% 240.25/46.89  | | | | | | | | | | | | |            sub-proof #2194.
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | |   (278)  all_58_2 = e2 & op(e2, e3) = e2
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | ALPHA: (278) implies:
% 240.25/46.89  | | | | | | | | | | | | |   (279)  op(e2, e3) = e2
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | REF_CLOSE: (90), (126), (156), (279) are inconsistent by
% 240.25/46.89  | | | | | | | | | | | | |            sub-proof #1633.
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | |   (280)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 240.25/46.89  | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 240.25/46.89  | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | BETA: splitting (280) gives:
% 240.25/46.89  | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | |   (281)  all_58_6 = e2 & op(e1, e3) = e2
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | ALPHA: (281) implies:
% 240.25/46.89  | | | | | | | | | | | | |   (282)  all_58_6 = e2
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | BETA: splitting (60) gives:
% 240.25/46.89  | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | |   (283)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 240.25/46.89  | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 240.25/46.89  | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (12), (28), (29), (34), (50), (53),
% 240.25/46.89  | | | | | | | | | | | | | |            (66), (90), (101), (102), (114), (121), (126),
% 240.25/46.89  | | | | | | | | | | | | | |            (139), (283) are inconsistent by sub-proof #285.
% 240.25/46.89  | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | |   (284)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 240.25/46.89  | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 240.25/46.89  | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 240.25/46.89  | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | |   (285)  all_58_6 = e0 & op(e1, e3) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | REF_CLOSE: (12), (282), (285) are inconsistent by sub-proof
% 240.25/46.89  | | | | | | | | | | | | | | |            #1678.
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | |   (286)  all_58_12 = e0 & op(e0, e3) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 240.25/46.89  | | | | | | | | | | | | | | |   (287)  all_58_12 = e0
% 240.25/46.89  | | | | | | | | | | | | | | |   (288)  op(e0, e3) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | |   (289)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 240.25/46.89  | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 240.25/46.89  | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | |   (290)  all_58_12 = e2 & op(e0, e3) = e2
% 240.25/46.89  | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | |   (291)  op(e0, e3) = e2
% 240.25/46.89  | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (90), (288), (291) are inconsistent by
% 240.25/46.89  | | | | | | | | | | | | | | | | |            sub-proof #1896.
% 240.25/46.89  | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | |   (292)  all_58_13 = e2 & op(e0, e2) = e2
% 240.25/46.89  | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | ALPHA: (292) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | |   (293)  op(e0, e2) = e2
% 240.25/46.89  | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | |   (294)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (295)  all_58_6 = e0 & op(e1, e3) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (282), (295) are inconsistent by sub-proof
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |            #1678.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (296)  all_58_7 = e0 & op(e1, e2) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (297)  op(e1, e2) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (90) with all_42_0, e0, e2, e1,
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |              simplifying with (272), (297) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (298)  all_42_0 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | REDUCE: (158), (298) imply:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (299)  $false
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | CLOSE: (299) is inconsistent.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | |   (300)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 240.25/46.89  | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (301)  all_58_8 = e0 & op(e1, e1) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (302)  op(e1, e1) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (21), (47), (50), (53), (73), (83),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |            (90), (302) are inconsistent by sub-proof #1493.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (303)  all_58_11 = e0 & op(e1, e0) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | |   (304)  op(e1, e0) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | |   (305)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | |   (306)  all_58_9 = e1 & op(e3, e0) = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | |   (307)  all_58_9 = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | |   (308)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | |   (309)  all_58_0 = e0 & op(e3, e3) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | |   (310)  op(e3, e3) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (90), (102), (310) are inconsistent by
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1940.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | |   (311)  all_58_1 = e0 & op(e3, e2) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_58_1 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | |   (313)  op(e3, e2) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | |   (314)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  all_58_0 = e1 & op(e3, e3) = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  op(e3, e3) = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (66), (90), (107), (316), (317) are
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1208.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  all_58_6 = e3 & op(e1, e3) = e3
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (282), (319) are inconsistent by sub-proof
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1838.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)  all_58_12 = e3 & op(e0, e3) = e3
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (60), (66), (90), (101), (124), (282),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (316), (320) are inconsistent by sub-proof #280.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (321)  all_58_1 = e1 & op(e3, e2) = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (28), (29), (34), (50), (53), (66),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (90), (101), (114), (121), (126), (139), (145),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (312), (321) are inconsistent by sub-proof #279.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | |   (322)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (323)  all_58_4 = e1 & op(e3, e1) = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  all_58_4 = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  op(e3, e1) = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (9), (11), (12), (18), (20), (26),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (27), (31), (32), (47), (49), (50), (53), (54),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (56), (60), (63), (64), (65), (66), (69), (70),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (73), (76), (80), (83), (84), (86), (90), (94),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (95), (101), (102), (105), (106), (107), (111),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |            (113), (115), (126), (324), (325) are inconsistent
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #301.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  op(e3, e0) = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  all_58_1 = e1 & op(e3, e2) = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (28), (29), (34), (50), (53), (66),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (90), (101), (114), (121), (126), (139), (145),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (312), (328) are inconsistent by sub-proof #279.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  all_58_3 = e1 & op(e2, e2) = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_58_3 = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (330) imply:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  e3 = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (331) imply:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (332)  all_58_15 = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (27), (29), (47), (53), (64), (90),
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (293), (332) are inconsistent by sub-proof #474.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (333)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (334)  all_58_7 = e1 & op(e1, e2) = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (335)  all_58_7 = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (336)  op(e1, e2) = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (337)  all_58_15 = e0 & op(e0, e0) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (337) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (338)  op(e0, e0) = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (86), (90), (338) are inconsistent by
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2079.
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (339)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (340)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (90) with all_52_7, e2, e2, e0,
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (76), (293) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_52_7 = e2
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (90) with all_52_14, e0, e0, e1,
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (24), (304) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (342)  all_52_14 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (90) with all_42_0, e1, e2, e1,
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (272), (336) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (343)  all_42_0 = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (90) with all_52_12, e1, e0, e3,
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (61), (326) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (344)  all_52_12 = e1
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (90) with all_52_4, e0, e2, e3,
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (79), (313) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (345)  all_52_4 = e0
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (342) imply:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (346)   ~ (e2 = e0)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (347)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, all_56_11) = e2)
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (348)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_9 & $i(all_56_9)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (348) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (349)  op(e3, e2) = all_56_9
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (350)  op(e3, all_56_9) = e3
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (351)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (33), (49), (64), (66), (70), (84),
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (90), (94), (107), (313), (351) are inconsistent
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #278.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (352)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (353)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (353) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (354)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (354) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (355)  op(e2, e1) = e2
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (53), (65), (90), (113), (134), (135), (156),
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (355) are inconsistent by sub-proof #750.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (356)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (356) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (357)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (357) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (358)  op(e2, e1) = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (126), (134), (135), (358) are inconsistent
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #299.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (90) with e0, all_56_9, e2, e3,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (313), (349) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (359)  all_56_9 = e0
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (359) imply:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (360)  op(e3, e0) = e3
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (90), (98), (360) are inconsistent by
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2179.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (361)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (90), (101), (105), (128), (304), (361) are
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #277.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (362)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (362) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (363)  op(e2, all_56_11) = e2
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (363) imply:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (364)  op(e2, e3) = e2
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (126), (156), (364) are inconsistent by
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1633.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (365)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_15 & $i(all_56_15))
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (365) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (366)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_13 & $i(all_56_13)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (69), (90), (336), (366) are inconsistent by
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #276.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (367)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_15 & $i(all_56_15)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (367) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (368)  op(e0, all_56_15) = e0
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (369)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (33), (49), (64), (66), (70), (84),
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (90), (94), (107), (313), (369) are inconsistent
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #278.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (370)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (371)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (371) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (372)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (372) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (373)  op(e2, e1) = e2
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (53), (65), (90), (113), (134), (135), (156),
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373) are inconsistent by sub-proof #750.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (374)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (374) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (375)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (376)  op(e2, e1) = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (126), (134), (135), (376) are inconsistent
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #299.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (377)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (378)  all_56_15 = e2
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (379)   ~ (all_56_31 = e0)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (378) imply:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (380)  op(e0, e2) = e0
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (12), (15), (26), (28), (29), (34),
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (50), (53), (60), (62), (66), (71), (88), (90),
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (101), (102), (105), (109), (110), (114), (121),
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (126), (128), (139), (145), (307), (335), (340),
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (380) are inconsistent by sub-proof #282.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (381)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (90), (101), (105), (128), (304), (381) are
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #277.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (382)  all_58_13 = e1 & op(e0, e2) = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (382) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (383)  all_58_13 = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (26), (53), (109), (110), (126), (287),
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (383) are inconsistent by sub-proof #1230.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | |   (384)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (384) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | |   (385)  all_58_4 = e0 & op(e3, e1) = e0
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (21), (385) are inconsistent by sub-proof
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | |            #2170.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | |   (386)  all_58_9 = e0 & op(e3, e0) = e0
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (28), (29), (34), (50), (53), (66),
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | |            (90), (101), (114), (121), (126), (139), (145),
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | |            (307), (386) are inconsistent by sub-proof #283.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | |   (387)  all_58_10 = e1 & op(e2, e0) = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | ALPHA: (387) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | |   (388)  op(e2, e0) = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (126), (137), (388) are inconsistent by
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1659.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | |   (389)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | BETA: splitting (389) gives:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | |   (390)  all_58_11 = e1 & op(e1, e0) = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | ALPHA: (390) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | |   (391)  op(e1, e0) = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (101), (304), (391) are inconsistent by
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | |   (392)  all_58_15 = e1 & op(e0, e0) = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | ALPHA: (392) implies:
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | |   (393)  all_58_15 = e1
% 240.25/46.90  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (27), (29), (47), (53), (64), (90),
% 240.25/46.91  | | | | | | | | | | | | | | | | | | | | |            (293), (393) are inconsistent by sub-proof #474.
% 240.25/46.91  | | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | |   (394)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 240.25/46.91  | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | | REF_CLOSE: (53), (86), (90), (109), (126), (394) are
% 240.25/46.91  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1283.
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | |   (395)  all_58_12 = e2 & op(e0, e3) = e2
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | ALPHA: (395) implies:
% 240.25/46.91  | | | | | | | | | | | | |   (396)  all_58_12 = e2
% 240.25/46.91  | | | | | | | | | | | | |   (397)  op(e0, e3) = e2
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (9), (10), (11), (12), (15),
% 240.25/46.91  | | | | | | | | | | | | |            (16), (18), (19), (20), (25), (26), (27), (28),
% 240.25/46.91  | | | | | | | | | | | | |            (29), (31), (32), (34), (36), (46), (47), (49),
% 240.25/46.91  | | | | | | | | | | | | |            (50), (53), (54), (56), (57), (60), (62), (63),
% 240.25/46.91  | | | | | | | | | | | | |            (64), (65), (66), (69), (70), (71), (73), (76),
% 240.25/46.91  | | | | | | | | | | | | |            (80), (83), (84), (86), (87), (88), (90), (91),
% 240.25/46.91  | | | | | | | | | | | | |            (93), (94), (95), (97), (101), (102), (104),
% 240.25/46.91  | | | | | | | | | | | | |            (105), (106), (107), (109), (110), (111), (113),
% 240.25/46.91  | | | | | | | | | | | | |            (114), (115), (121), (126), (128), (137), (139),
% 240.25/46.91  | | | | | | | | | | | | |            (145), (396), (397) are inconsistent by sub-proof
% 240.25/46.91  | | | | | | | | | | | | |            #281.
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | |   (398)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 240.25/46.91  | | | | | | | | | |          $i(all_42_1)
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | ALPHA: (398) implies:
% 240.25/46.91  | | | | | | | | | |   (399)   ~ (all_42_1 = e1)
% 240.25/46.91  | | | | | | | | | |   (400)  op(e2, e3) = all_42_1
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | REF_CLOSE: (90), (113), (156), (399), (400) are inconsistent
% 240.25/46.91  | | | | | | | | | |            by sub-proof #934.
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | |   (401)  all_54_4 = e0
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | REF_CLOSE: (45), (124), (401) are inconsistent by sub-proof
% 240.25/46.91  | | | | | | | | |            #1923.
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | 
% 240.25/46.91  | | | | | | | End of split
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | Case 2:
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | |   (402)  all_58_3 = e1 & op(e2, e2) = e1
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | | REF_CLOSE: (29), (34), (402) are inconsistent by sub-proof #2197.
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | End of split
% 240.25/46.91  | | | | | | 
% 240.25/46.91  | | | | | Case 2:
% 240.25/46.91  | | | | | | 
% 240.25/46.91  | | | | | |   (403)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 240.25/46.91  | | | | | |            op(e2, e0) = e1)
% 240.25/46.91  | | | | | | 
% 240.25/46.91  | | | | | | BETA: splitting (403) gives:
% 240.25/46.91  | | | | | | 
% 240.25/46.91  | | | | | | Case 1:
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | |   (404)  all_58_5 = e1 & op(e2, e1) = e1
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | | ALPHA: (404) implies:
% 240.25/46.91  | | | | | | |   (405)  op(e2, e1) = e1
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | | REF_CLOSE: (90), (126), (134), (135), (405) are inconsistent by
% 240.25/46.91  | | | | | | |            sub-proof #299.
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | Case 2:
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | |   (406)  all_58_10 = e1 & op(e2, e0) = e1
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | | ALPHA: (406) implies:
% 240.25/46.91  | | | | | | |   (407)  op(e2, e0) = e1
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | | REF_CLOSE: (90), (126), (137), (407) are inconsistent by sub-proof
% 240.25/46.91  | | | | | | |            #1659.
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | End of split
% 240.25/46.91  | | | | | | 
% 240.25/46.91  | | | | | End of split
% 240.25/46.91  | | | | | 
% 240.25/46.91  | | | | End of split
% 240.25/46.91  | | | | 
% 240.25/46.91  | | | Case 2:
% 240.25/46.91  | | | | 
% 240.25/46.91  | | | |   (408)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 = e0 &
% 240.25/46.91  | | | |            op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 240.25/46.91  | | | |            $i(all_56_23))
% 240.25/46.91  | | | | 
% 240.25/46.91  | | | | BETA: splitting (408) gives:
% 240.25/46.91  | | | | 
% 240.25/46.91  | | | | Case 1:
% 240.25/46.91  | | | | | 
% 240.25/46.91  | | | | |   (409)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 240.25/46.91  | | | | | 
% 240.25/46.91  | | | | | ALPHA: (409) implies:
% 240.25/46.91  | | | | |   (410)  op(e1, all_56_21) = e1
% 240.25/46.91  | | | | | 
% 240.25/46.91  | | | | | REDUCE: (95), (410) imply:
% 240.25/46.91  | | | | |   (411)  op(e1, e3) = e1
% 240.25/46.91  | | | | | 
% 240.25/46.91  | | | | | GROUND_INST: instantiating (90) with all_52_2, e1, e3, e1, simplifying
% 240.25/46.91  | | | | |              with (94), (411) gives:
% 240.25/46.91  | | | | |   (412)  all_52_2 = e1
% 240.25/46.91  | | | | | 
% 240.25/46.91  | | | | | REDUCE: (23), (412) imply:
% 240.25/46.91  | | | | |   (413)   ~ (all_52_1 = e1)
% 240.25/46.91  | | | | | 
% 240.25/46.91  | | | | | REDUCE: (32), (412) imply:
% 240.25/46.91  | | | | |   (414)   ~ (all_52_3 = e1)
% 240.25/46.91  | | | | | 
% 240.25/46.91  | | | | | SIMP: (414) implies:
% 240.25/46.91  | | | | |   (415)   ~ (all_52_3 = e1)
% 240.25/46.91  | | | | | 
% 240.25/46.91  | | | | | REDUCE: (70), (412) imply:
% 240.25/46.91  | | | | |   (416)   ~ (e3 = e1)
% 240.25/46.91  | | | | | 
% 240.25/46.91  | | | | | BETA: splitting (97) gives:
% 240.25/46.91  | | | | | 
% 240.25/46.91  | | | | | Case 1:
% 240.25/46.91  | | | | | | 
% 240.25/46.91  | | | | | |   (417)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 240.25/46.91  | | | | | |              e2) = e1)
% 240.25/46.91  | | | | | | 
% 240.25/46.91  | | | | | | BETA: splitting (417) gives:
% 240.25/46.91  | | | | | | 
% 240.25/46.91  | | | | | | Case 1:
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | |   (418)  all_58_1 = e1 & op(e3, e2) = e1
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | | ALPHA: (418) implies:
% 240.25/46.91  | | | | | | |   (419)  op(e3, e2) = e1
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | | BETA: splitting (114) gives:
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | | Case 1:
% 240.25/46.91  | | | | | | | | 
% 240.25/46.91  | | | | | | | |   (420)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 240.25/46.91  | | | | | | | |            op(e2, e2) = e1)
% 240.25/46.91  | | | | | | | | 
% 240.25/46.91  | | | | | | | | BETA: splitting (420) gives:
% 240.25/46.91  | | | | | | | | 
% 240.25/46.91  | | | | | | | | Case 1:
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | |   (421)  all_58_2 = e1 & op(e2, e3) = e1
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | REF_CLOSE: (66), (90), (413), (421) are inconsistent by
% 240.25/46.91  | | | | | | | | |            sub-proof #2229.
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | |   (422)  all_58_3 = e1 & op(e2, e2) = e1
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | REF_CLOSE: (29), (34), (422) are inconsistent by sub-proof
% 240.25/46.91  | | | | | | | | |            #2197.
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | 
% 240.25/46.91  | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | 
% 240.25/46.91  | | | | | | | |   (423)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 240.25/46.91  | | | | | | | |            op(e2, e0) = e1)
% 240.25/46.91  | | | | | | | | 
% 240.25/46.91  | | | | | | | | BETA: splitting (423) gives:
% 240.25/46.91  | | | | | | | | 
% 240.25/46.91  | | | | | | | | Case 1:
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | |   (424)  all_58_5 = e1 & op(e2, e1) = e1
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | ALPHA: (424) implies:
% 240.25/46.91  | | | | | | | | |   (425)  all_58_5 = e1
% 240.25/46.91  | | | | | | | | |   (426)  op(e2, e1) = e1
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 240.25/46.91  | | | | | | | | |            (11), (12), (15), (16), (17), (18), (19), (20),
% 240.25/46.91  | | | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (30),
% 240.25/46.91  | | | | | | | | |            (31), (32), (34), (37), (38), (39), (40), (43),
% 240.25/46.91  | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (52),
% 240.25/46.91  | | | | | | | | |            (53), (54), (56), (57), (58), (59), (60), (61),
% 240.25/46.91  | | | | | | | | |            (62), (63), (64), (65), (66), (67), (69), (70),
% 240.25/46.91  | | | | | | | | |            (71), (72), (73), (75), (76), (77), (78), (79),
% 240.25/46.91  | | | | | | | | |            (80), (81), (83), (84), (85), (86), (87), (88),
% 240.25/46.91  | | | | | | | | |            (89), (90), (91), (92), (93), (94), (95), (96),
% 240.25/46.91  | | | | | | | | |            (97), (98), (100), (101), (102), (103), (104),
% 240.25/46.91  | | | | | | | | |            (105), (106), (107), (110), (111), (112), (113),
% 240.25/46.91  | | | | | | | | |            (115), (126), (425), (426) are inconsistent by
% 240.25/46.91  | | | | | | | | |            sub-proof #288.
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | |   (427)  all_58_10 = e1 & op(e2, e0) = e1
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | ALPHA: (427) implies:
% 240.25/46.91  | | | | | | | | |   (428)  op(e2, e0) = e1
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | BETA: splitting (92) gives:
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | Case 1:
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | |   (429)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2
% 240.25/46.91  | | | | | | | | | |            & op(e2, e0) = e2)
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | REF_CLOSE: (8), (12), (21), (29), (68), (87), (90), (101),
% 240.25/46.91  | | | | | | | | | |            (102), (126), (428), (429) are inconsistent by
% 240.25/46.91  | | | | | | | | | |            sub-proof #275.
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | |   (430)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 240.25/46.91  | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | BETA: splitting (430) gives:
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | Case 1:
% 240.25/46.91  | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | |   (431)  all_58_11 = e2 & op(e1, e0) = e2
% 240.25/46.91  | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | ALPHA: (431) implies:
% 240.25/46.91  | | | | | | | | | | |   (432)  op(e1, e0) = e2
% 240.25/46.91  | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | BETA: splitting (2) gives:
% 240.25/46.91  | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | Case 1:
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | |   (433)  all_54_4 = e2
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | COMBINE_EQS: (45), (433) imply:
% 240.25/46.91  | | | | | | | | | | | |   (434)  all_52_1 = e2
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | SIMP: (434) implies:
% 240.25/46.91  | | | | | | | | | | | |   (435)  all_52_1 = e2
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | REDUCE: (72), (435) imply:
% 240.25/46.91  | | | | | | | | | | | |   (436)   ~ (all_52_13 = e2)
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | SIMP: (436) implies:
% 240.25/46.91  | | | | | | | | | | | |   (437)   ~ (all_52_13 = e2)
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | REDUCE: (66), (435) imply:
% 240.25/46.91  | | | | | | | | | | | |   (438)  op(e2, e3) = e2
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | BETA: splitting (18) gives:
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | Case 1:
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | |   (439)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.25/46.91  | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.25/46.91  | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.25/46.91  | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.25/46.91  | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.25/46.91  | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.25/46.91  | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.25/46.91  | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.25/46.91  | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.25/46.91  | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.25/46.91  | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 240.25/46.91  | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.25/46.91  | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | BETA: splitting (439) gives:
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | Case 1:
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | |   (440)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.25/46.91  | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.25/46.91  | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.25/46.91  | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.25/46.91  | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.25/46.91  | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.25/46.91  | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.25/46.91  | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.25/46.91  | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.25/46.91  | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.25/46.91  | | | | | | | | | | | | | |            = e3)
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | REF_CLOSE: (29), (53), (90), (126), (411), (419), (438),
% 240.25/46.91  | | | | | | | | | | | | | |            (440) are inconsistent by sub-proof #313.
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | |   (441)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.25/46.91  | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.25/46.91  | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.25/46.91  | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 240.25/46.91  | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.25/46.91  | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.25/46.91  | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 240.25/46.91  | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.25/46.91  | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.25/46.91  | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 240.25/46.91  | | | | | | | | | | | | | |            = e0)
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | REF_CLOSE: (27), (33), (49), (64), (84), (90), (441) are
% 240.25/46.91  | | | | | | | | | | | | | |            inconsistent by sub-proof #1411.
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | |   (442)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.25/46.91  | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.25/46.91  | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.25/46.91  | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.25/46.91  | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.25/46.91  | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.25/46.91  | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.25/46.91  | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.25/46.91  | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.25/46.91  | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.25/46.91  | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.25/46.91  | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.25/46.91  | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.25/46.91  | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | BETA: splitting (442) gives:
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | Case 1:
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | |   (443)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.25/46.91  | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.25/46.91  | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.25/46.91  | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.25/46.91  | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.25/46.91  | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.25/46.91  | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.25/46.91  | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.25/46.91  | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.25/46.91  | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.25/46.91  | | | | | | | | | | | | | |            = e2)
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | BETA: splitting (443) gives:
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | Case 1:
% 240.25/46.91  | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | |   (444)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.25/46.91  | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.25/46.91  | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 240.25/46.91  | | | | | | | | | | | | | | |            e2) = e2
% 240.25/46.91  | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | ALPHA: (444) implies:
% 240.25/46.91  | | | | | | | | | | | | | | |   (445)  op(e2, e1) = e2
% 240.25/46.91  | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | REF_CLOSE: (12), (90), (121), (445) are inconsistent by
% 240.25/46.91  | | | | | | | | | | | | | | |            sub-proof #1906.
% 240.25/46.91  | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | |   (446)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.25/46.91  | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.25/46.91  | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.25/46.91  | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.25/46.91  | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.25/46.91  | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.25/46.91  | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.25/46.91  | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | BETA: splitting (446) gives:
% 240.25/46.91  | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | Case 1:
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | |   (447)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.25/46.91  | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.25/46.91  | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 240.25/46.91  | | | | | | | | | | | | | | | |            e2) = e1
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | | ALPHA: (447) implies:
% 240.25/46.91  | | | | | | | | | | | | | | | |   (448)  op(e2, e1) = e1
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | | REF_CLOSE: (50), (90), (101), (121), (448) are inconsistent
% 240.25/46.91  | | | | | | | | | | | | | | | |            by sub-proof #2165.
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | |   (449)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 240.25/46.91  | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.25/46.91  | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 240.25/46.91  | | | | | | | | | | | | | | | |            e2) = e2
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | | ALPHA: (449) implies:
% 240.25/46.91  | | | | | | | | | | | | | | | |   (450)  op(e2, e0) = e2
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | | REF_CLOSE: (90), (105), (437), (450) are inconsistent by
% 240.25/46.91  | | | | | | | | | | | | | | | |            sub-proof #2317.
% 240.25/46.91  | | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | |   (451)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.25/46.91  | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.25/46.91  | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.25/46.91  | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.25/46.91  | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.25/46.91  | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.25/46.91  | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.25/46.91  | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.25/46.91  | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.25/46.91  | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.25/46.91  | | | | | | | | | | | | | |            = e0)
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | | REF_CLOSE: (12), (90), (101), (105), (126), (428), (432),
% 240.25/46.91  | | | | | | | | | | | | | |            (451) are inconsistent by sub-proof #384.
% 240.25/46.91  | | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | |   (452)  all_54_4 = e1 | all_54_4 = e0
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | | REF_CLOSE: (45), (124), (413), (452) are inconsistent by
% 240.25/46.91  | | | | | | | | | | | |            sub-proof #1922.
% 240.25/46.91  | | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | Case 2:
% 240.25/46.91  | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | |   (453)  all_58_15 = e2 & op(e0, e0) = e2
% 240.25/46.91  | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | ALPHA: (453) implies:
% 240.25/46.91  | | | | | | | | | | |   (454)  op(e0, e0) = e2
% 240.25/46.91  | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | | REF_CLOSE: (53), (86), (90), (454) are inconsistent by
% 240.25/46.91  | | | | | | | | | | |            sub-proof #1388.
% 240.25/46.91  | | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | | 
% 240.25/46.91  | | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | | 
% 240.25/46.91  | | | | | | | | End of split
% 240.25/46.91  | | | | | | | | 
% 240.25/46.91  | | | | | | | End of split
% 240.25/46.91  | | | | | | | 
% 240.25/46.91  | | | | | | Case 2:
% 240.25/46.91  | | | | | | | 
% 240.25/46.92  | | | | | | |   (455)  all_58_3 = e1 & op(e2, e2) = e1
% 240.25/46.92  | | | | | | | 
% 240.25/46.92  | | | | | | | REF_CLOSE: (29), (34), (455) are inconsistent by sub-proof #2197.
% 240.25/46.92  | | | | | | | 
% 240.25/46.92  | | | | | | End of split
% 240.25/46.92  | | | | | | 
% 240.25/46.92  | | | | | Case 2:
% 240.25/46.92  | | | | | | 
% 240.37/46.92  | | | | | |   (456)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 240.37/46.92  | | | | | |            op(e0, e2) = e1)
% 240.37/46.92  | | | | | | 
% 240.37/46.92  | | | | | | BETA: splitting (456) gives:
% 240.37/46.92  | | | | | | 
% 240.37/46.92  | | | | | | Case 1:
% 240.37/46.92  | | | | | | | 
% 240.37/46.92  | | | | | | |   (457)  all_58_7 = e1 & op(e1, e2) = e1
% 240.37/46.92  | | | | | | | 
% 240.37/46.92  | | | | | | | ALPHA: (457) implies:
% 240.37/46.92  | | | | | | |   (458)  all_58_7 = e1
% 240.37/46.92  | | | | | | |   (459)  op(e1, e2) = e1
% 240.37/46.92  | | | | | | | 
% 240.37/46.92  | | | | | | | BETA: splitting (114) gives:
% 240.37/46.92  | | | | | | | 
% 240.37/46.92  | | | | | | | Case 1:
% 240.37/46.92  | | | | | | | | 
% 240.37/46.92  | | | | | | | |   (460)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 240.37/46.92  | | | | | | | |            op(e2, e2) = e1)
% 240.37/46.92  | | | | | | | | 
% 240.37/46.92  | | | | | | | | BETA: splitting (460) gives:
% 240.37/46.92  | | | | | | | | 
% 240.37/46.92  | | | | | | | | Case 1:
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | |   (461)  all_58_2 = e1 & op(e2, e3) = e1
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | REF_CLOSE: (66), (90), (413), (461) are inconsistent by
% 240.37/46.92  | | | | | | | | |            sub-proof #2229.
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | Case 2:
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | |   (462)  all_58_3 = e1 & op(e2, e2) = e1
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | REF_CLOSE: (29), (34), (462) are inconsistent by sub-proof
% 240.37/46.92  | | | | | | | | |            #2197.
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | End of split
% 240.37/46.92  | | | | | | | | 
% 240.37/46.92  | | | | | | | Case 2:
% 240.37/46.92  | | | | | | | | 
% 240.37/46.92  | | | | | | | |   (463)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 240.37/46.92  | | | | | | | |            op(e2, e0) = e1)
% 240.37/46.92  | | | | | | | | 
% 240.37/46.92  | | | | | | | | BETA: splitting (463) gives:
% 240.37/46.92  | | | | | | | | 
% 240.37/46.92  | | | | | | | | Case 1:
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | |   (464)  all_58_5 = e1 & op(e2, e1) = e1
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | ALPHA: (464) implies:
% 240.37/46.92  | | | | | | | | |   (465)  all_58_5 = e1
% 240.37/46.92  | | | | | | | | |   (466)  op(e2, e1) = e1
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 240.37/46.92  | | | | | | | | |            (11), (12), (15), (16), (17), (18), (19), (20),
% 240.37/46.92  | | | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (30),
% 240.37/46.92  | | | | | | | | |            (31), (32), (34), (37), (38), (39), (40), (43),
% 240.37/46.92  | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (52),
% 240.37/46.92  | | | | | | | | |            (53), (54), (56), (57), (58), (59), (60), (61),
% 240.37/46.92  | | | | | | | | |            (62), (63), (64), (65), (66), (67), (69), (70),
% 240.37/46.92  | | | | | | | | |            (71), (72), (73), (75), (76), (77), (78), (79),
% 240.37/46.92  | | | | | | | | |            (80), (81), (83), (84), (85), (86), (87), (88),
% 240.37/46.92  | | | | | | | | |            (89), (90), (91), (92), (93), (94), (95), (96),
% 240.37/46.92  | | | | | | | | |            (97), (98), (100), (101), (102), (103), (104),
% 240.37/46.92  | | | | | | | | |            (105), (106), (107), (110), (111), (112), (113),
% 240.37/46.92  | | | | | | | | |            (115), (126), (465), (466) are inconsistent by
% 240.37/46.92  | | | | | | | | |            sub-proof #288.
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | Case 2:
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | |   (467)  all_58_10 = e1 & op(e2, e0) = e1
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | ALPHA: (467) implies:
% 240.37/46.92  | | | | | | | | |   (468)  op(e2, e0) = e1
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | BETA: splitting (85) gives:
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | Case 1:
% 240.37/46.92  | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | |   (469)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 240.37/46.92  | | | | | | | | | |            & op(e2, e3) = e1)
% 240.37/46.92  | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | REF_CLOSE: (29), (66), (90), (102), (413), (469) are
% 240.37/46.92  | | | | | | | | | |            inconsistent by sub-proof #1370.
% 240.37/46.92  | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | Case 2:
% 240.37/46.92  | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | |   (470)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 240.37/46.92  | | | | | | | | | |            & op(e0, e3) = e1)
% 240.37/46.92  | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | BETA: splitting (470) gives:
% 240.37/46.92  | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | Case 1:
% 240.37/46.92  | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | |   (471)  all_58_6 = e1 & op(e1, e3) = e1
% 240.37/46.92  | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | ALPHA: (471) implies:
% 240.37/46.92  | | | | | | | | | | |   (472)  all_58_6 = e1
% 240.37/46.92  | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | BETA: splitting (92) gives:
% 240.37/46.92  | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | Case 1:
% 240.37/46.92  | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | |   (473)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 240.37/46.92  | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 240.37/46.92  | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | | REF_CLOSE: (8), (12), (21), (29), (68), (87), (90), (101),
% 240.37/46.92  | | | | | | | | | | | |            (102), (126), (468), (473) are inconsistent by
% 240.37/46.92  | | | | | | | | | | | |            sub-proof #275.
% 240.37/46.92  | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | Case 2:
% 240.37/46.92  | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | |   (474)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 240.37/46.92  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 240.37/46.92  | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | | BETA: splitting (474) gives:
% 240.37/46.92  | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | | Case 1:
% 240.37/46.92  | | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | | |   (475)  all_58_11 = e2 & op(e1, e0) = e2
% 240.37/46.92  | | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | | | ALPHA: (475) implies:
% 240.37/46.92  | | | | | | | | | | | | |   (476)  op(e1, e0) = e2
% 240.37/46.92  | | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | | | REF_CLOSE: (8), (12), (15), (29), (53), (62), (88), (90),
% 240.37/46.92  | | | | | | | | | | | | |            (101), (104), (126), (411), (458), (459), (472),
% 240.37/46.92  | | | | | | | | | | | | |            (476) are inconsistent by sub-proof #418.
% 240.37/46.92  | | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | | Case 2:
% 240.37/46.92  | | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | | |   (477)  all_58_15 = e2 & op(e0, e0) = e2
% 240.37/46.92  | | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | | | ALPHA: (477) implies:
% 240.37/46.92  | | | | | | | | | | | | |   (478)  op(e0, e0) = e2
% 240.37/46.92  | | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | | | REF_CLOSE: (53), (86), (90), (478) are inconsistent by
% 240.37/46.92  | | | | | | | | | | | | |            sub-proof #1388.
% 240.37/46.92  | | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | | End of split
% 240.37/46.92  | | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | End of split
% 240.37/46.92  | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | Case 2:
% 240.37/46.92  | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | |   (479)  all_58_12 = e1 & op(e0, e3) = e1
% 240.37/46.92  | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | | REF_CLOSE: (27), (90), (415), (479) are inconsistent by
% 240.37/46.92  | | | | | | | | | | |            sub-proof #2276.
% 240.37/46.92  | | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | | End of split
% 240.37/46.92  | | | | | | | | | | 
% 240.37/46.92  | | | | | | | | | End of split
% 240.37/46.92  | | | | | | | | | 
% 240.37/46.92  | | | | | | | | End of split
% 240.37/46.92  | | | | | | | | 
% 240.37/46.92  | | | | | | | End of split
% 240.37/46.92  | | | | | | | 
% 240.37/46.92  | | | | | | Case 2:
% 240.37/46.92  | | | | | | | 
% 240.37/46.92  | | | | | | |   (480)  all_58_13 = e1 & op(e0, e2) = e1
% 240.37/46.92  | | | | | | | 
% 240.37/46.92  | | | | | | | REF_CLOSE: (55), (76), (90), (480) are inconsistent by sub-proof
% 240.37/46.92  | | | | | | |            #2275.
% 240.37/46.92  | | | | | | | 
% 240.37/46.92  | | | | | | End of split
% 240.37/46.92  | | | | | | 
% 240.37/46.92  | | | | | End of split
% 240.37/46.92  | | | | | 
% 240.37/46.92  | | | | Case 2:
% 240.37/46.92  | | | | | 
% 240.37/46.92  | | | | |   (481)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 240.37/46.92  | | | | |          all_56_23 & $i(all_56_23)
% 240.37/46.92  | | | | | 
% 240.37/46.92  | | | | | REF_CLOSE: (8), (36), (86), (90), (481) are inconsistent by sub-proof
% 240.37/46.92  | | | | |            #349.
% 240.37/46.92  | | | | | 
% 240.37/46.92  | | | | End of split
% 240.37/46.92  | | | | 
% 240.37/46.92  | | | End of split
% 240.37/46.92  | | | 
% 240.37/46.92  | | End of split
% 240.37/46.92  | | 
% 240.37/46.92  | Case 2:
% 240.37/46.92  | | 
% 240.37/46.92  | |   (482)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 240.37/46.92  | |            e0)
% 240.37/46.92  | | 
% 240.37/46.92  | | REF_CLOSE: (8), (9), (21), (36), (47), (50), (53), (73), (83), (90), (101),
% 240.37/46.92  | |            (482) are inconsistent by sub-proof #401.
% 240.37/46.92  | | 
% 240.37/46.92  | End of split
% 240.37/46.92  | 
% 240.37/46.92  End of proof
% 240.37/46.92  
% 240.37/46.92  Sub-proof #275 shows that the following formulas are inconsistent:
% 240.37/46.92  ----------------------------------------------------------------
% 240.37/46.92    (1)   ~ (e3 = e0)
% 240.37/46.92    (2)   ~ (e2 = e0)
% 240.37/46.92    (3)  all_58_4 = e2
% 240.37/46.92    (4)   ~ (e3 = e1)
% 240.37/46.92    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.37/46.92         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.37/46.92    (6)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.37/46.92         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.37/46.92    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.92    (8)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.37/46.92    (9)   ~ (e1 = e0)
% 240.37/46.92    (10)  op(e3, e3) = e3
% 240.37/46.92    (11)  op(e2, e0) = e1
% 240.37/46.92    (12)   ~ (e2 = e1)
% 240.37/46.92  
% 240.37/46.92  Begin of proof
% 240.37/46.92  | 
% 240.37/46.92  | BETA: splitting (8) gives:
% 240.37/46.92  | 
% 240.37/46.92  | Case 1:
% 240.37/46.92  | | 
% 240.37/46.92  | |   (13)  all_58_9 = e2 & op(e3, e0) = e2
% 240.37/46.92  | | 
% 240.37/46.92  | | ALPHA: (13) implies:
% 240.37/46.92  | |   (14)  all_58_9 = e2
% 240.37/46.92  | |   (15)  op(e3, e0) = e2
% 240.37/46.92  | | 
% 240.37/46.92  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (14), (15)
% 240.37/46.92  | |            are inconsistent by sub-proof #1402.
% 240.37/46.92  | | 
% 240.37/46.92  | Case 2:
% 240.37/46.92  | | 
% 240.37/46.92  | |   (16)  all_58_10 = e2 & op(e2, e0) = e2
% 240.37/46.92  | | 
% 240.37/46.92  | | ALPHA: (16) implies:
% 240.37/46.92  | |   (17)  op(e2, e0) = e2
% 240.37/46.92  | | 
% 240.37/46.92  | | REF_CLOSE: (7), (11), (12), (17) are inconsistent by sub-proof #1659.
% 240.37/46.92  | | 
% 240.37/46.92  | End of split
% 240.37/46.92  | 
% 240.37/46.92  End of proof
% 240.37/46.92  
% 240.37/46.92  Sub-proof #276 shows that the following formulas are inconsistent:
% 240.37/46.92  ----------------------------------------------------------------
% 240.37/46.92    (1)  op(e1, e2) = e1
% 240.37/46.92    (2)   ~ (e3 = e1)
% 240.37/46.92    (3)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 240.37/46.92         $i(all_56_13)
% 240.37/46.92    (4)  op(e1, e1) = e3
% 240.37/46.92    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.92  
% 240.37/46.92  Begin of proof
% 240.37/46.92  | 
% 240.37/46.92  | ALPHA: (3) implies:
% 240.37/46.92  |   (6)  op(e1, e2) = all_56_13
% 240.37/46.92  |   (7)  op(e1, all_56_13) = e1
% 240.37/46.92  | 
% 240.37/46.92  | GROUND_INST: instantiating (5) with e1, all_56_13, e2, e1, simplifying with
% 240.37/46.92  |              (1), (6) gives:
% 240.37/46.92  |   (8)  all_56_13 = e1
% 240.37/46.92  | 
% 240.37/46.92  | REDUCE: (7), (8) imply:
% 240.37/46.92  |   (9)  op(e1, e1) = e1
% 240.37/46.92  | 
% 240.37/46.92  | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #468.
% 240.37/46.92  | 
% 240.37/46.92  End of proof
% 240.37/46.92  
% 240.37/46.92  Sub-proof #277 shows that the following formulas are inconsistent:
% 240.37/46.92  ----------------------------------------------------------------
% 240.37/46.92    (1)  op(e1, e0) = e0
% 240.37/46.92    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.37/46.92             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.37/46.92           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.37/46.92             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.37/46.92           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 240.37/46.92           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.37/46.92           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.37/46.92    (3)  op(e0, e1) = e1
% 240.37/46.92    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.92    (5)   ~ (e1 = e0)
% 240.37/46.92    (6)  op(e2, e0) = all_52_13
% 240.37/46.92    (7)   ~ (all_52_13 = e0)
% 240.37/46.92  
% 240.37/46.92  Begin of proof
% 240.37/46.92  | 
% 240.37/46.92  | BETA: splitting (2) gives:
% 240.37/46.92  | 
% 240.37/46.92  | Case 1:
% 240.37/46.92  | | 
% 240.37/46.92  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.37/46.92  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 240.37/46.92  | |        & op(e0, e2) = e0
% 240.37/46.92  | | 
% 240.37/46.92  | | ALPHA: (8) implies:
% 240.37/46.92  | |   (9)  op(e2, e0) = e0
% 240.37/46.92  | | 
% 240.37/46.92  | | REF_CLOSE: (4), (6), (7), (9) are inconsistent by sub-proof #2324.
% 240.37/46.92  | | 
% 240.37/46.92  | Case 2:
% 240.37/46.92  | | 
% 240.37/46.92  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.37/46.92  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.37/46.92  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.37/46.92  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.37/46.92  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.37/46.92  | | 
% 240.37/46.92  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #496.
% 240.37/46.92  | | 
% 240.37/46.92  | End of split
% 240.37/46.92  | 
% 240.37/46.92  End of proof
% 240.37/46.92  
% 240.37/46.92  Sub-proof #278 shows that the following formulas are inconsistent:
% 240.37/46.92  ----------------------------------------------------------------
% 240.37/46.92    (1)   ~ (e2 = e0)
% 240.37/46.92    (2)  op(e0, e3) = all_52_3
% 240.37/46.92    (3)   ~ (all_52_8 = e1)
% 240.37/46.92    (4)  op(e3, e1) = all_52_8
% 240.37/46.92    (5)   ~ (all_52_3 = e3)
% 240.37/46.92    (6)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.37/46.92           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.37/46.92             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.37/46.92           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.37/46.92             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.37/46.92           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.37/46.92           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.37/46.92           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.37/46.92           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.37/46.92           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.37/46.92           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.37/46.92             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.37/46.92           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.37/46.92           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.37/46.92    (7)  op(e3, e2) = e0
% 240.37/46.92    (8)  op(e2, e3) = all_52_1
% 240.37/46.92    (9)   ~ (all_52_2 = e3)
% 240.37/46.92    (10)  all_56_31 = e3
% 240.37/46.92    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.92    (12)  op(e1, e3) = all_52_2
% 240.37/46.92    (13)   ~ (all_52_1 = e3)
% 240.37/46.92  
% 240.37/46.92  Begin of proof
% 240.37/46.92  | 
% 240.37/46.92  | BETA: splitting (6) gives:
% 240.37/46.92  | 
% 240.37/46.92  | Case 1:
% 240.37/46.92  | | 
% 240.37/46.92  | |   (14)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.37/46.92  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 240.37/46.92  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 240.37/46.92  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.37/46.92  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 240.37/46.92  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 240.37/46.92  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.37/46.92  | |           op(e1, e3) = e3)
% 240.37/46.92  | | 
% 240.37/46.92  | | BETA: splitting (14) gives:
% 240.37/46.92  | | 
% 240.37/46.92  | | Case 1:
% 240.37/46.92  | | | 
% 240.37/46.92  | | |   (15)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.37/46.92  | | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 240.37/46.92  | | |         e3 & op(e2, e3) = e3
% 240.37/46.92  | | | 
% 240.37/46.92  | | | ALPHA: (15) implies:
% 240.37/46.92  | | |   (16)  op(e2, e3) = e3
% 240.37/46.92  | | | 
% 240.37/46.92  | | | REF_CLOSE: (8), (11), (13), (16) are inconsistent by sub-proof #2337.
% 240.37/46.92  | | | 
% 240.37/46.92  | | Case 2:
% 240.37/46.92  | | | 
% 240.37/46.92  | | |   (17)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.37/46.92  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.37/46.92  | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17
% 240.37/46.92  | | |           = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 240.37/46.92  | | |             = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 240.37/46.92  | | |           e3)
% 240.37/46.92  | | | 
% 240.37/46.92  | | | REF_CLOSE: (1), (7), (9), (11), (12), (17) are inconsistent by sub-proof
% 240.37/46.92  | | |            #2025.
% 240.37/46.92  | | | 
% 240.37/46.92  | | End of split
% 240.37/46.92  | | 
% 240.37/46.92  | Case 2:
% 240.37/46.92  | | 
% 240.37/46.92  | |   (18)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.37/46.92  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 240.37/46.92  | |           e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 240.37/46.92  | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.37/46.92  | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7
% 240.37/46.92  | |           = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &
% 240.37/46.92  | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 240.37/46.92  | |           op(e0, e3) = e0)
% 240.37/46.92  | | 
% 240.37/46.92  | | REF_CLOSE: (2), (3), (4), (5), (10), (11), (18) are inconsistent by
% 240.37/46.92  | |            sub-proof #1411.
% 240.37/46.92  | | 
% 240.37/46.92  | End of split
% 240.37/46.92  | 
% 240.37/46.92  End of proof
% 240.37/46.92  
% 240.37/46.92  Sub-proof #279 shows that the following formulas are inconsistent:
% 240.37/46.92  ----------------------------------------------------------------
% 240.37/46.92    (1)  op(e2, e2) = e3
% 240.37/46.92    (2)   ~ (e2 = e0)
% 240.37/46.92    (3)  all_58_1 = e0
% 240.37/46.92    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.37/46.92         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.37/46.92    (5)   ~ (e3 = e1)
% 240.37/46.92    (6)  all_58_3 = e3
% 240.37/46.92    (7)  op(e2, e1) = all_52_9
% 240.37/46.92    (8)   ~ (e3 = e2)
% 240.37/46.92    (9)  op(e2, e3) = all_52_1
% 240.37/46.92    (10)  op(e2, e1) = e0
% 240.37/46.92    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.92    (12)  all_58_1 = e1 & op(e3, e2) = e1
% 240.37/46.92    (13)   ~ (e1 = e0)
% 240.37/46.93    (14)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.37/46.93          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.37/46.93    (15)  all_58_2 = e1
% 240.37/46.93    (16)   ~ (all_52_1 = e2)
% 240.37/46.93    (17)   ~ (e2 = e1)
% 240.37/46.93  
% 240.37/46.93  Begin of proof
% 240.37/46.93  | 
% 240.37/46.93  | ALPHA: (12) implies:
% 240.37/46.93  |   (18)  all_58_1 = e1
% 240.37/46.93  | 
% 240.37/46.93  | COMBINE_EQS: (3), (18) imply:
% 240.37/46.93  |   (19)  e1 = e0
% 240.37/46.93  | 
% 240.37/46.93  | SIMP: (19) implies:
% 240.37/46.93  |   (20)  e1 = e0
% 240.37/46.93  | 
% 240.37/46.93  | COMBINE_EQS: (15), (20) imply:
% 240.37/46.93  |   (21)  all_58_2 = e0
% 240.37/46.93  | 
% 240.37/46.93  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 240.37/46.93  |            (16), (17), (21) are inconsistent by sub-proof #286.
% 240.37/46.93  | 
% 240.37/46.93  End of proof
% 240.37/46.93  
% 240.37/46.93  Sub-proof #280 shows that the following formulas are inconsistent:
% 240.37/46.93  ----------------------------------------------------------------
% 240.37/46.93    (1)   ~ (e3 = e0)
% 240.37/46.93    (2)   ~ (e2 = e0)
% 240.37/46.93    (3)  all_58_12 = e3 & op(e0, e3) = e3
% 240.37/46.93    (4)  all_58_6 = e2
% 240.37/46.93    (5)  op(e3, e3) = e1
% 240.37/46.93    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.37/46.93         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.37/46.93    (7)   ~ (all_52_1 = e0)
% 240.37/46.93    (8)  op(e2, e3) = all_52_1
% 240.37/46.93    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.93    (10)   ~ (e1 = e0)
% 240.37/46.93  
% 240.37/46.93  Begin of proof
% 240.37/46.93  | 
% 240.37/46.93  | ALPHA: (3) implies:
% 240.37/46.93  |   (11)  all_58_12 = e3
% 240.37/46.93  | 
% 240.37/46.93  | BETA: splitting (6) gives:
% 240.37/46.93  | 
% 240.37/46.93  | Case 1:
% 240.37/46.93  | | 
% 240.37/46.93  | |   (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 240.37/46.93  | |           e0)
% 240.37/46.93  | | 
% 240.37/46.93  | | REF_CLOSE: (5), (7), (8), (9), (10), (12) are inconsistent by sub-proof
% 240.37/46.93  | |            #1272.
% 240.37/46.93  | | 
% 240.37/46.93  | Case 2:
% 240.37/46.93  | | 
% 240.37/46.93  | |   (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 240.37/46.93  | |           e0)
% 240.37/46.93  | | 
% 240.37/46.93  | | BETA: splitting (13) gives:
% 240.37/46.93  | | 
% 240.37/46.93  | | Case 1:
% 240.37/46.93  | | | 
% 240.37/46.93  | | |   (14)  all_58_6 = e0 & op(e1, e3) = e0
% 240.37/46.93  | | | 
% 240.37/46.93  | | | REF_CLOSE: (2), (4), (14) are inconsistent by sub-proof #1678.
% 240.37/46.93  | | | 
% 240.37/46.93  | | Case 2:
% 240.37/46.93  | | | 
% 240.37/46.93  | | |   (15)  all_58_12 = e0 & op(e0, e3) = e0
% 240.37/46.93  | | | 
% 240.37/46.93  | | | REF_CLOSE: (1), (11), (15) are inconsistent by sub-proof #1641.
% 240.37/46.93  | | | 
% 240.37/46.93  | | End of split
% 240.37/46.93  | | 
% 240.37/46.93  | End of split
% 240.37/46.93  | 
% 240.37/46.93  End of proof
% 240.37/46.93  
% 240.37/46.93  Sub-proof #281 shows that the following formulas are inconsistent:
% 240.37/46.93  ----------------------------------------------------------------
% 240.37/46.93    (1)  op(e2, e2) = e3
% 240.37/46.93    (2)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.37/46.93           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.37/46.93           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.37/46.93           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.37/46.93           & $i(all_56_23))
% 240.37/46.93    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.37/46.93         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.37/46.93    (4)   ~ (e3 = e0)
% 240.37/46.93    (5)  op(e0, e1) = all_52_11
% 240.37/46.93    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.37/46.93         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.37/46.93    (7)   ~ (all_52_8 = all_52_9)
% 240.37/46.93    (8)   ~ (e2 = e0)
% 240.37/46.93    (9)  op(e1, e2) = all_52_6
% 240.37/46.93    (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.37/46.93          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.37/46.93    (11)  all_58_12 = e2
% 240.37/46.93    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.37/46.93              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.37/46.93            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.37/46.93            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.37/46.93            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.37/46.93             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.37/46.93            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.37/46.93            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.37/46.93            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.37/46.93            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.37/46.93            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.37/46.93              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.37/46.93            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.37/46.93            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.37/46.93            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.37/46.93            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.37/46.93            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.37/46.93            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.37/46.93              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.37/46.93            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.37/46.93            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.37/46.93            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.37/46.93            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.37/46.93            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.37/46.93            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.37/46.93              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.37/46.93            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.37/46.93            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.37/46.93    (13)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.37/46.93          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.37/46.93    (14)   ~ (all_52_7 = all_52_11)
% 240.37/46.93    (15)   ~ (all_52_7 = e3)
% 240.37/46.93    (16)  all_58_15 = e3
% 240.37/46.93    (17)  op(e0, e3) = all_52_3
% 240.37/46.93    (18)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.37/46.93          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.37/46.93    (19)   ~ (e3 = e1)
% 240.37/46.93    (20)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.37/46.93          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.37/46.93    (21)   ~ (all_52_2 = all_52_3)
% 240.37/46.93    (22)  all_58_3 = e3
% 240.37/46.93    (23)  op(e0, e1) = e1
% 240.37/46.93    (24)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.37/46.93              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.37/46.93                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.37/46.93                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.37/46.93    (25)   ~ (all_52_11 = e3)
% 240.37/46.93    (26)  op(e3, e1) = all_52_8
% 240.37/46.93    (27)  op(e2, e1) = all_52_9
% 240.37/46.93    (28)   ~ (e3 = e2)
% 240.37/46.93    (29)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.37/46.93          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.37/46.93    (30)   ~ (all_52_3 = all_52_11)
% 240.37/46.93    (31)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.37/46.93            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.37/46.93            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.37/46.93            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.37/46.93            op(e0, all_56_31) = e0)
% 240.37/46.93    (32)  op(e2, e0) = e2
% 240.37/46.93    (33)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.37/46.93          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.37/46.93    (34)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.37/46.93          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.37/46.93    (35)   ~ (all_52_9 = all_52_13)
% 240.37/46.93    (36)   ~ (all_52_3 = e3)
% 240.37/46.93    (37)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.37/46.93            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.37/46.93              e3) = all_42_1 & $i(all_42_1))
% 240.37/46.93    (38)  op(e0, e3) = e2
% 240.37/46.93    (39)  op(e2, e3) = all_52_1
% 240.37/46.93    (40)  op(e1, e1) = e3
% 240.37/46.93    (41)   ~ (all_52_2 = e3)
% 240.37/46.93    (42)   ~ (all_52_6 = e3)
% 240.37/46.93    (43)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.37/46.93          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.37/46.93    (44)  op(e0, e2) = all_52_7
% 240.37/46.93    (45)  op(e2, e1) = e0
% 240.37/46.93    (46)   ~ (all_52_8 = all_52_11)
% 240.37/46.93    (47)   ~ (all_52_9 = e3)
% 240.37/46.93    (48)  all_56_31 = e3
% 240.37/46.93    (49)  op(e0, e0) = e3
% 240.37/46.93    (50)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.37/46.93          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.37/46.93    (51)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.37/46.93          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.37/46.93    (52)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.93    (53)  all_58_8 = e3
% 240.37/46.93    (54)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.37/46.93            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.37/46.93              e3) = all_46_1 & $i(all_46_1))
% 240.37/46.93    (55)  op(e1, e3) = all_52_2
% 240.37/46.93    (56)  all_56_21 = e3
% 240.37/46.93    (57)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.37/46.93          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.37/46.93    (58)   ~ (e1 = e0)
% 240.37/46.93    (59)  op(e3, e3) = e3
% 240.37/46.93    (60)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.37/46.93          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.37/46.93    (61)  op(e2, e0) = all_52_13
% 240.37/46.93    (62)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.37/46.93          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.37/46.93            e1)
% 240.37/46.93    (63)   ~ (all_52_1 = e3)
% 240.37/46.93    (64)  all_58_14 = e1
% 240.37/46.93    (65)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.37/46.93          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.37/46.93            e2)
% 240.37/46.93    (66)   ~ (all_52_9 = all_52_11)
% 240.37/46.93    (67)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.37/46.93            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.37/46.93            & $i(all_8_1))
% 240.37/46.93    (68)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.37/46.93          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.37/46.93    (69)   ~ (all_52_13 = e0)
% 240.37/46.93    (70)  all_58_2 = e1
% 240.37/46.93    (71)   ~ (all_52_1 = e2)
% 240.37/46.93    (72)   ~ (e2 = e1)
% 240.37/46.93    (73)   ~ (all_52_8 = e3)
% 240.37/46.93  
% 240.37/46.93  Begin of proof
% 240.37/46.93  | 
% 240.37/46.93  | BETA: splitting (24) gives:
% 240.37/46.93  | 
% 240.37/46.93  | Case 1:
% 240.37/46.93  | | 
% 240.37/46.93  | |   (74)  all_58_15 = e0 & op(e0, e0) = e0
% 240.37/46.93  | | 
% 240.37/46.93  | | ALPHA: (74) implies:
% 240.37/46.93  | |   (75)  op(e0, e0) = e0
% 240.37/46.93  | | 
% 240.37/46.93  | | REF_CLOSE: (3), (4), (11), (15), (19), (28), (44), (52), (64), (75) are
% 240.37/46.93  | |            inconsistent by sub-proof #1550.
% 240.37/46.93  | | 
% 240.37/46.93  | Case 2:
% 240.37/46.93  | | 
% 240.37/46.93  | |   (76)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 240.37/46.93  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 240.37/46.93  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 240.37/46.93  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 240.37/46.93  | | 
% 240.37/46.93  | | ALPHA: (76) implies:
% 240.37/46.93  | |   (77)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.37/46.93  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.37/46.93  | |   (78)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 240.37/46.93  | |           e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.37/46.93  | | 
% 240.37/46.93  | | BETA: splitting (77) gives:
% 240.37/46.93  | | 
% 240.37/46.93  | | Case 1:
% 240.37/46.93  | | | 
% 240.37/46.93  | | |   (79)  all_58_12 = e0 & op(e0, e3) = e0
% 240.37/46.93  | | | 
% 240.37/46.93  | | | ALPHA: (79) implies:
% 240.37/46.93  | | |   (80)  op(e0, e3) = e0
% 240.37/46.93  | | | 
% 240.37/46.93  | | | REF_CLOSE: (8), (38), (52), (80) are inconsistent by sub-proof #1896.
% 240.37/46.93  | | | 
% 240.37/46.93  | | Case 2:
% 240.37/46.93  | | | 
% 240.37/46.93  | | |   (81)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 240.37/46.93  | | |           = e0)
% 240.37/46.93  | | | 
% 240.37/46.93  | | | BETA: splitting (81) gives:
% 240.37/46.93  | | | 
% 240.37/46.93  | | | Case 1:
% 240.37/46.93  | | | | 
% 240.37/46.93  | | | |   (82)  all_58_13 = e0 & op(e0, e2) = e0
% 240.37/46.93  | | | | 
% 240.37/46.93  | | | | ALPHA: (82) implies:
% 240.37/46.93  | | | |   (83)  op(e0, e2) = e0
% 240.37/46.93  | | | | 
% 240.37/46.93  | | | | BETA: splitting (50) gives:
% 240.37/46.93  | | | | 
% 240.37/46.93  | | | | Case 1:
% 240.37/46.93  | | | | | 
% 240.37/46.93  | | | | |   (84)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3,
% 240.37/46.93  | | | | |             e2) = e1)
% 240.37/46.93  | | | | | 
% 240.37/46.93  | | | | | BETA: splitting (84) gives:
% 240.37/46.93  | | | | | 
% 240.37/46.93  | | | | | Case 1:
% 240.37/46.93  | | | | | | 
% 240.37/46.93  | | | | | |   (85)  all_58_0 = e1 & op(e3, e3) = e1
% 240.37/46.93  | | | | | | 
% 240.37/46.93  | | | | | | ALPHA: (85) implies:
% 240.37/46.93  | | | | | |   (86)  op(e3, e3) = e1
% 240.37/46.93  | | | | | | 
% 240.37/46.93  | | | | | | REF_CLOSE: (19), (52), (59), (86) are inconsistent by sub-proof
% 240.37/46.93  | | | | | |            #1578.
% 240.37/46.93  | | | | | | 
% 240.37/46.93  | | | | | Case 2:
% 240.37/46.93  | | | | | | 
% 240.37/46.93  | | | | | |   (87)  all_58_1 = e1 & op(e3, e2) = e1
% 240.37/46.93  | | | | | | 
% 240.37/46.93  | | | | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (13), (16), (18), (19),
% 240.37/46.93  | | | | | |            (22), (27), (28), (31), (32), (33), (34), (38), (39),
% 240.37/46.93  | | | | | |            (40), (42), (45), (48), (51), (52), (53), (54), (58),
% 240.37/46.93  | | | | | |            (59), (60), (61), (64), (65), (68), (69), (71), (72),
% 240.37/46.93  | | | | | |            (78), (83), (87) are inconsistent by sub-proof #284.
% 240.37/46.93  | | | | | | 
% 240.37/46.93  | | | | | End of split
% 240.37/46.93  | | | | | 
% 240.37/46.93  | | | | Case 2:
% 240.37/46.93  | | | | | 
% 240.37/46.93  | | | | |   (88)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3,
% 240.37/46.93  | | | | |             e0) = e1)
% 240.37/46.93  | | | | | 
% 240.37/46.93  | | | | | BETA: splitting (88) gives:
% 240.37/46.93  | | | | | 
% 240.37/46.93  | | | | | Case 1:
% 240.37/46.93  | | | | | | 
% 240.37/46.93  | | | | | |   (89)  all_58_4 = e1 & op(e3, e1) = e1
% 240.37/46.93  | | | | | | 
% 240.37/46.93  | | | | | | ALPHA: (89) implies:
% 240.37/46.93  | | | | | |   (90)  all_58_4 = e1
% 240.37/46.93  | | | | | |   (91)  op(e3, e1) = e1
% 240.37/46.93  | | | | | | 
% 240.37/46.94  | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (12), (14), (16), (17),
% 240.37/46.94  | | | | | |            (20), (21), (25), (26), (27), (28), (29), (30), (33),
% 240.37/46.94  | | | | | |            (35), (36), (37), (39), (40), (41), (43), (44), (46),
% 240.37/46.94  | | | | | |            (47), (48), (49), (52), (55), (56), (58), (59), (61),
% 240.37/46.94  | | | | | |            (62), (63), (66), (67), (72), (73), (90), (91) are
% 240.37/46.94  | | | | | |            inconsistent by sub-proof #301.
% 240.37/46.94  | | | | | | 
% 240.37/46.94  | | | | | Case 2:
% 240.37/46.94  | | | | | | 
% 240.37/46.94  | | | | | |   (92)  all_58_9 = e1 & op(e3, e0) = e1
% 240.37/46.94  | | | | | | 
% 240.37/46.94  | | | | | | ALPHA: (92) implies:
% 240.37/46.94  | | | | | |   (93)  all_58_9 = e1
% 240.37/46.94  | | | | | | 
% 240.37/46.94  | | | | | | BETA: splitting (57) gives:
% 240.37/46.94  | | | | | | 
% 240.37/46.94  | | | | | | Case 1:
% 240.37/46.94  | | | | | | | 
% 240.37/46.94  | | | | | | |   (94)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 240.37/46.94  | | | | | | |           op(e2, e2) = e1)
% 240.37/46.94  | | | | | | | 
% 240.37/46.94  | | | | | | | BETA: splitting (94) gives:
% 240.37/46.94  | | | | | | | 
% 240.37/46.94  | | | | | | | Case 1:
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | |   (95)  all_58_1 = e1 & op(e3, e2) = e1
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (13), (16), (18),
% 240.37/46.94  | | | | | | | |            (19), (22), (27), (28), (31), (32), (33), (34), (38),
% 240.37/46.94  | | | | | | | |            (39), (40), (42), (45), (48), (51), (52), (53), (54),
% 240.37/46.94  | | | | | | | |            (58), (59), (60), (61), (64), (65), (68), (69), (71),
% 240.37/46.94  | | | | | | | |            (72), (78), (83), (95) are inconsistent by sub-proof
% 240.37/46.94  | | | | | | | |            #284.
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | Case 2:
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | |   (96)  all_58_3 = e1 & op(e2, e2) = e1
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | | REF_CLOSE: (3), (11), (15), (16), (19), (22), (28), (44), (52),
% 240.37/46.94  | | | | | | | |            (64), (96) are inconsistent by sub-proof #772.
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | End of split
% 240.37/46.94  | | | | | | | 
% 240.37/46.94  | | | | | | Case 2:
% 240.37/46.94  | | | | | | | 
% 240.37/46.94  | | | | | | |   (97)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 240.37/46.94  | | | | | | |           op(e0, e2) = e1)
% 240.37/46.94  | | | | | | | 
% 240.37/46.94  | | | | | | | BETA: splitting (97) gives:
% 240.37/46.94  | | | | | | | 
% 240.37/46.94  | | | | | | | Case 1:
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | |   (98)  all_58_7 = e1 & op(e1, e2) = e1
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | | ALPHA: (98) implies:
% 240.37/46.94  | | | | | | | |   (99)  all_58_7 = e1
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | | REF_CLOSE: (1), (4), (8), (9), (16), (18), (19), (22), (27),
% 240.37/46.94  | | | | | | | |            (28), (33), (34), (39), (42), (45), (51), (52), (58),
% 240.37/46.94  | | | | | | | |            (59), (61), (64), (65), (68), (69), (70), (71), (72),
% 240.37/46.94  | | | | | | | |            (78), (83), (93), (99) are inconsistent by sub-proof
% 240.37/46.94  | | | | | | | |            #282.
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | Case 2:
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | |   (100)  all_58_13 = e1 & op(e0, e2) = e1
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | | ALPHA: (100) implies:
% 240.37/46.94  | | | | | | | |   (101)  all_58_13 = e1
% 240.37/46.94  | | | | | | | |   (102)  op(e0, e2) = e1
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | | REF_CLOSE: (8), (16), (23), (28), (52), (58), (64), (65), (72),
% 240.37/46.94  | | | | | | | |            (77), (101), (102) are inconsistent by sub-proof
% 240.37/46.94  | | | | | | | |            #765.
% 240.37/46.94  | | | | | | | | 
% 240.37/46.94  | | | | | | | End of split
% 240.37/46.94  | | | | | | | 
% 240.37/46.94  | | | | | | End of split
% 240.37/46.94  | | | | | | 
% 240.37/46.94  | | | | | End of split
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | End of split
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | Case 2:
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | |   (103)  all_58_14 = e0 & op(e0, e1) = e0
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | | ALPHA: (103) implies:
% 240.37/46.94  | | | |   (104)  op(e0, e1) = e0
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | | REF_CLOSE: (23), (52), (58), (104) are inconsistent by sub-proof #2158.
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | End of split
% 240.37/46.94  | | | 
% 240.37/46.94  | | End of split
% 240.37/46.94  | | 
% 240.37/46.94  | End of split
% 240.37/46.94  | 
% 240.37/46.94  End of proof
% 240.37/46.94  
% 240.37/46.94  Sub-proof #282 shows that the following formulas are inconsistent:
% 240.37/46.94  ----------------------------------------------------------------
% 240.37/46.94    (1)  op(e2, e2) = e3
% 240.37/46.94    (2)   ~ (e3 = e0)
% 240.37/46.94    (3)   ~ (e2 = e0)
% 240.37/46.94    (4)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 240.37/46.94         (all_58_11 = e0 & op(e1, e0) = e0)
% 240.37/46.94    (5)  op(e1, e2) = all_52_6
% 240.37/46.94    (6)  all_58_15 = e3
% 240.37/46.94    (7)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.37/46.94         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.37/46.94    (8)   ~ (e3 = e1)
% 240.37/46.94    (9)  all_58_3 = e3
% 240.37/46.94    (10)  op(e2, e1) = all_52_9
% 240.37/46.94    (11)   ~ (e3 = e2)
% 240.37/46.94    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.37/46.94          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.37/46.94    (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.37/46.94          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.37/46.94    (14)  op(e2, e3) = all_52_1
% 240.37/46.94    (15)  op(e0, e2) = e0
% 240.37/46.94    (16)   ~ (all_52_6 = e3)
% 240.37/46.94    (17)  op(e2, e1) = e0
% 240.37/46.94    (18)  all_58_7 = e1
% 240.37/46.94    (19)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.37/46.94          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.37/46.94    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.94    (21)   ~ (e1 = e0)
% 240.37/46.94    (22)  op(e3, e3) = e3
% 240.37/46.94    (23)  all_58_9 = e1
% 240.37/46.94    (24)  op(e2, e0) = all_52_13
% 240.37/46.94    (25)  all_58_14 = e1
% 240.37/46.94    (26)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.37/46.94          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.37/46.94            e2)
% 240.37/46.94    (27)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.37/46.94          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.37/46.94    (28)   ~ (all_52_13 = e0)
% 240.37/46.94    (29)  all_58_2 = e1
% 240.37/46.94    (30)   ~ (all_52_1 = e2)
% 240.37/46.94    (31)   ~ (e2 = e1)
% 240.37/46.94  
% 240.37/46.94  Begin of proof
% 240.37/46.94  | 
% 240.37/46.94  | BETA: splitting (4) gives:
% 240.37/46.94  | 
% 240.37/46.94  | Case 1:
% 240.37/46.94  | | 
% 240.37/46.94  | |   (32)  all_58_9 = e0 & op(e3, e0) = e0
% 240.37/46.94  | | 
% 240.37/46.94  | | REF_CLOSE: (1), (3), (7), (8), (9), (10), (11), (14), (17), (20), (21),
% 240.37/46.94  | |            (23), (27), (29), (30), (31), (32) are inconsistent by sub-proof
% 240.37/46.94  | |            #283.
% 240.37/46.94  | | 
% 240.37/46.94  | Case 2:
% 240.37/46.94  | | 
% 240.37/46.94  | |   (33)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.37/46.94  | |           e0)
% 240.37/46.94  | | 
% 240.37/46.94  | | BETA: splitting (33) gives:
% 240.37/46.94  | | 
% 240.37/46.94  | | Case 1:
% 240.37/46.94  | | | 
% 240.37/46.94  | | |   (34)  all_58_10 = e0 & op(e2, e0) = e0
% 240.37/46.94  | | | 
% 240.37/46.94  | | | ALPHA: (34) implies:
% 240.37/46.94  | | |   (35)  op(e2, e0) = e0
% 240.37/46.94  | | | 
% 240.37/46.94  | | | REF_CLOSE: (20), (24), (28), (35) are inconsistent by sub-proof #2324.
% 240.37/46.94  | | | 
% 240.37/46.94  | | Case 2:
% 240.37/46.94  | | | 
% 240.37/46.94  | | |   (36)  all_58_11 = e0 & op(e1, e0) = e0
% 240.37/46.94  | | | 
% 240.37/46.94  | | | ALPHA: (36) implies:
% 240.37/46.94  | | |   (37)  all_58_11 = e0
% 240.37/46.94  | | | 
% 240.37/46.94  | | | BETA: splitting (12) gives:
% 240.37/46.94  | | | 
% 240.37/46.94  | | | Case 1:
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | |   (38)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 240.37/46.94  | | | |           = e0)
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (11), (14), (17), (20),
% 240.37/46.94  | | | |            (21), (22), (27), (30), (31), (38) are inconsistent by
% 240.37/46.94  | | | |            sub-proof #285.
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | Case 2:
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | |   (39)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 240.37/46.94  | | | |           = e0)
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | | BETA: splitting (39) gives:
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | | Case 1:
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | |   (40)  all_58_6 = e0 & op(e1, e3) = e0
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | | ALPHA: (40) implies:
% 240.37/46.94  | | | | |   (41)  all_58_6 = e0
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | | REF_CLOSE: (2), (3), (5), (11), (13), (16), (18), (19), (20), (31),
% 240.37/46.94  | | | | |            (37), (41) are inconsistent by sub-proof #960.
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | Case 2:
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | |   (42)  all_58_12 = e0 & op(e0, e3) = e0
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | | ALPHA: (42) implies:
% 240.37/46.94  | | | | |   (43)  all_58_12 = e0
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | | REF_CLOSE: (3), (6), (11), (15), (20), (25), (26), (31), (43) are
% 240.37/46.94  | | | | |            inconsistent by sub-proof #1012.
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | End of split
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | End of split
% 240.37/46.94  | | | 
% 240.37/46.94  | | End of split
% 240.37/46.94  | | 
% 240.37/46.94  | End of split
% 240.37/46.94  | 
% 240.37/46.94  End of proof
% 240.37/46.94  
% 240.37/46.94  Sub-proof #283 shows that the following formulas are inconsistent:
% 240.37/46.94  ----------------------------------------------------------------
% 240.37/46.94    (1)  op(e2, e2) = e3
% 240.37/46.94    (2)   ~ (e2 = e0)
% 240.37/46.94    (3)  all_58_9 = e0 & op(e3, e0) = e0
% 240.37/46.94    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.37/46.94         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.37/46.94    (5)   ~ (e3 = e1)
% 240.37/46.94    (6)  all_58_3 = e3
% 240.37/46.94    (7)  op(e2, e1) = all_52_9
% 240.37/46.94    (8)   ~ (e3 = e2)
% 240.37/46.94    (9)  op(e2, e3) = all_52_1
% 240.37/46.94    (10)  op(e2, e1) = e0
% 240.37/46.94    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.94    (12)   ~ (e1 = e0)
% 240.37/46.94    (13)  all_58_9 = e1
% 240.37/46.94    (14)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.37/46.94          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.37/46.94    (15)  all_58_2 = e1
% 240.37/46.94    (16)   ~ (all_52_1 = e2)
% 240.37/46.94    (17)   ~ (e2 = e1)
% 240.37/46.94  
% 240.37/46.94  Begin of proof
% 240.37/46.94  | 
% 240.37/46.94  | ALPHA: (3) implies:
% 240.37/46.94  |   (18)  all_58_9 = e0
% 240.37/46.94  | 
% 240.37/46.94  | COMBINE_EQS: (13), (18) imply:
% 240.37/46.94  |   (19)  e1 = e0
% 240.37/46.94  | 
% 240.37/46.94  | COMBINE_EQS: (15), (19) imply:
% 240.37/46.94  |   (20)  all_58_2 = e0
% 240.37/46.94  | 
% 240.37/46.94  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 240.37/46.94  |            (16), (17), (20) are inconsistent by sub-proof #286.
% 240.37/46.94  | 
% 240.37/46.94  End of proof
% 240.37/46.94  
% 240.37/46.94  Sub-proof #284 shows that the following formulas are inconsistent:
% 240.37/46.94  ----------------------------------------------------------------
% 240.37/46.94    (1)  op(e2, e2) = e3
% 240.37/46.94    (2)   ~ (e3 = e0)
% 240.37/46.94    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.37/46.94         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.37/46.94    (4)   ~ (e2 = e0)
% 240.37/46.94    (5)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 240.37/46.94         (all_58_11 = e0 & op(e1, e0) = e0)
% 240.37/46.94    (6)  op(e1, e2) = all_52_6
% 240.37/46.94    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.37/46.94         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.37/46.94    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.37/46.94         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.37/46.94    (9)  all_58_15 = e3
% 240.37/46.94    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.37/46.94          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.37/46.94    (11)   ~ (e3 = e1)
% 240.37/46.94    (12)  all_58_3 = e3
% 240.37/46.94    (13)  op(e2, e1) = all_52_9
% 240.37/46.94    (14)   ~ (e3 = e2)
% 240.37/46.94    (15)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.37/46.94            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.37/46.94            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.37/46.94            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.37/46.94            op(e0, all_56_31) = e0)
% 240.37/46.94    (16)  op(e2, e0) = e2
% 240.37/46.94    (17)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.37/46.94          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.37/46.94    (18)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.37/46.94          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.37/46.94    (19)  op(e0, e3) = e2
% 240.37/46.94    (20)  op(e2, e3) = all_52_1
% 240.37/46.94    (21)  op(e0, e2) = e0
% 240.37/46.94    (22)  op(e1, e1) = e3
% 240.37/46.94    (23)   ~ (all_52_6 = e3)
% 240.37/46.94    (24)  op(e2, e1) = e0
% 240.37/46.94    (25)  all_56_31 = e3
% 240.37/46.94    (26)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.37/46.94          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.37/46.94    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.94    (28)  all_58_8 = e3
% 240.37/46.94    (29)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.37/46.94            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.37/46.94              e3) = all_46_1 & $i(all_46_1))
% 240.37/46.94    (30)  all_58_1 = e1 & op(e3, e2) = e1
% 240.37/46.94    (31)   ~ (e1 = e0)
% 240.37/46.94    (32)  op(e3, e3) = e3
% 240.37/46.94    (33)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.37/46.94          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.37/46.94    (34)  op(e2, e0) = all_52_13
% 240.37/46.94    (35)  all_58_14 = e1
% 240.37/46.94    (36)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.37/46.94          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.37/46.94            e2)
% 240.37/46.94    (37)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.37/46.94          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.37/46.94    (38)   ~ (all_52_13 = e0)
% 240.37/46.94    (39)   ~ (all_52_1 = e2)
% 240.37/46.94    (40)   ~ (e2 = e1)
% 240.37/46.94  
% 240.37/46.94  Begin of proof
% 240.37/46.94  | 
% 240.37/46.94  | ALPHA: (30) implies:
% 240.37/46.94  |   (41)  all_58_1 = e1
% 240.37/46.94  | 
% 240.37/46.94  | BETA: splitting (17) gives:
% 240.37/46.94  | 
% 240.37/46.94  | Case 1:
% 240.37/46.94  | | 
% 240.37/46.94  | |   (42)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 240.37/46.94  | |           e0)
% 240.37/46.94  | | 
% 240.37/46.94  | | REF_CLOSE: (1), (2), (4), (10), (11), (12), (13), (14), (20), (24), (27),
% 240.37/46.94  | |            (31), (32), (37), (39), (40), (42) are inconsistent by sub-proof
% 240.37/46.94  | |            #285.
% 240.37/46.94  | | 
% 240.37/46.94  | Case 2:
% 240.37/46.94  | | 
% 240.37/46.94  | |   (43)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 240.37/46.94  | |           e0)
% 240.37/46.94  | | 
% 240.37/46.94  | | BETA: splitting (43) gives:
% 240.37/46.94  | | 
% 240.37/46.94  | | Case 1:
% 240.37/46.94  | | | 
% 240.37/46.94  | | |   (44)  all_58_6 = e0 & op(e1, e3) = e0
% 240.37/46.94  | | | 
% 240.37/46.94  | | | ALPHA: (44) implies:
% 240.37/46.94  | | |   (45)  op(e1, e3) = e0
% 240.37/46.94  | | | 
% 240.37/46.94  | | | BETA: splitting (3) gives:
% 240.37/46.94  | | | 
% 240.37/46.94  | | | Case 1:
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | |   (46)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 240.37/46.94  | | | |           = e1)
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | | BETA: splitting (46) gives:
% 240.37/46.94  | | | | 
% 240.37/46.94  | | | | Case 1:
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | |   (47)  all_58_6 = e1 & op(e1, e3) = e1
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | | ALPHA: (47) implies:
% 240.37/46.94  | | | | |   (48)  op(e1, e3) = e1
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | | REF_CLOSE: (27), (31), (45), (48) are inconsistent by sub-proof #449.
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | Case 2:
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | |   (49)  all_58_7 = e1 & op(e1, e2) = e1
% 240.37/46.94  | | | | | 
% 240.37/46.94  | | | | | ALPHA: (49) implies:
% 240.37/46.94  | | | | |   (50)  all_58_7 = e1
% 240.37/46.94  | | | | |   (51)  op(e1, e2) = e1
% 240.37/46.94  | | | | | 
% 240.37/46.95  | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (12), (14), (27), (31), (40),
% 240.37/46.95  | | | | |            (41), (50), (51) are inconsistent by sub-proof #1717.
% 240.37/46.95  | | | | | 
% 240.37/46.95  | | | | End of split
% 240.37/46.95  | | | | 
% 240.37/46.95  | | | Case 2:
% 240.37/46.95  | | | | 
% 240.37/46.95  | | | |   (52)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0)
% 240.37/46.95  | | | |           = e1)
% 240.37/46.95  | | | | 
% 240.37/46.95  | | | | BETA: splitting (52) gives:
% 240.37/46.95  | | | | 
% 240.37/46.95  | | | | Case 1:
% 240.37/46.95  | | | | | 
% 240.37/46.95  | | | | |   (53)  all_58_8 = e1 & op(e1, e1) = e1
% 240.37/46.95  | | | | | 
% 240.37/46.95  | | | | | ALPHA: (53) implies:
% 240.37/46.95  | | | | |   (54)  op(e1, e1) = e1
% 240.37/46.95  | | | | | 
% 240.37/46.95  | | | | | REF_CLOSE: (11), (22), (27), (54) are inconsistent by sub-proof #468.
% 240.37/46.95  | | | | | 
% 240.37/46.95  | | | | Case 2:
% 240.37/46.95  | | | | | 
% 240.37/46.95  | | | | |   (55)  all_58_11 = e1 & op(e1, e0) = e1
% 240.37/46.95  | | | | | 
% 240.37/46.95  | | | | | ALPHA: (55) implies:
% 240.37/46.95  | | | | |   (56)  all_58_11 = e1
% 240.37/46.95  | | | | |   (57)  op(e1, e0) = e1
% 240.37/46.95  | | | | | 
% 240.37/46.95  | | | | | BETA: splitting (5) gives:
% 240.37/46.95  | | | | | 
% 240.37/46.95  | | | | | Case 1:
% 240.37/46.95  | | | | | | 
% 240.37/46.95  | | | | | |   (58)  all_58_9 = e0 & op(e3, e0) = e0
% 240.37/46.95  | | | | | | 
% 240.37/46.95  | | | | | | ALPHA: (58) implies:
% 240.37/46.95  | | | | | |   (59)  op(e3, e0) = e0
% 240.37/46.95  | | | | | | 
% 240.37/46.95  | | | | | | BETA: splitting (15) gives:
% 240.37/46.95  | | | | | | 
% 240.37/46.95  | | | | | | Case 1:
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | |   (60)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 240.37/46.95  | | | | | | |           all_56_25 & $i(all_56_25)) | (all_56_26 = e2 & op(e2,
% 240.37/46.95  | | | | | | |             all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 240.37/46.95  | | | | | | |           $i(all_56_27))
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | | BETA: splitting (60) gives:
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | | Case 1:
% 240.37/46.95  | | | | | | | | 
% 240.37/46.95  | | | | | | | |   (61)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 240.37/46.95  | | | | | | | |         all_56_25 & $i(all_56_25)
% 240.37/46.95  | | | | | | | | 
% 240.37/46.95  | | | | | | | | ALPHA: (61) implies:
% 240.37/46.95  | | | | | | | |   (62)  op(e3, e0) = all_56_25
% 240.37/46.95  | | | | | | | |   (63)  op(e3, all_56_25) = e3
% 240.37/46.95  | | | | | | | | 
% 240.37/46.95  | | | | | | | | REF_CLOSE: (2), (27), (59), (62), (63) are inconsistent by
% 240.37/46.95  | | | | | | | |            sub-proof #1926.
% 240.37/46.95  | | | | | | | | 
% 240.37/46.95  | | | | | | | Case 2:
% 240.37/46.95  | | | | | | | | 
% 240.37/46.95  | | | | | | | |   (64)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 240.37/46.95  | | | | | | | |         all_56_27 & $i(all_56_27)
% 240.37/46.95  | | | | | | | | 
% 240.37/46.95  | | | | | | | | ALPHA: (64) implies:
% 240.37/46.95  | | | | | | | |   (65)  op(e2, e0) = all_56_27
% 240.37/46.95  | | | | | | | |   (66)  op(e2, all_56_27) = e2
% 240.37/46.95  | | | | | | | | 
% 240.37/46.95  | | | | | | | | REF_CLOSE: (1), (14), (16), (27), (65), (66) are inconsistent by
% 240.37/46.95  | | | | | | | |            sub-proof #954.
% 240.37/46.95  | | | | | | | | 
% 240.37/46.95  | | | | | | | End of split
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | Case 2:
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | |   (67)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 240.37/46.95  | | | | | | |           all_56_29 & $i(all_56_29)) | (all_56_30 = e0 & op(e0,
% 240.37/46.95  | | | | | | |             all_56_31) = e0)
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | | REF_CLOSE: (2), (4), (6), (11), (14), (18), (19), (22), (23),
% 240.37/46.95  | | | | | | |            (25), (26), (27), (28), (29), (31), (33), (40), (45),
% 240.37/46.95  | | | | | | |            (56), (57), (67) are inconsistent by sub-proof #344.
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | End of split
% 240.37/46.95  | | | | | | 
% 240.37/46.95  | | | | | Case 2:
% 240.37/46.95  | | | | | | 
% 240.37/46.95  | | | | | |   (68)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.37/46.95  | | | | | |           op(e1, e0) = e0)
% 240.37/46.95  | | | | | | 
% 240.37/46.95  | | | | | | BETA: splitting (68) gives:
% 240.37/46.95  | | | | | | 
% 240.37/46.95  | | | | | | Case 1:
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | |   (69)  all_58_10 = e0 & op(e2, e0) = e0
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | | ALPHA: (69) implies:
% 240.37/46.95  | | | | | | |   (70)  op(e2, e0) = e0
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | | REF_CLOSE: (27), (34), (38), (70) are inconsistent by sub-proof
% 240.37/46.95  | | | | | | |            #2324.
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | Case 2:
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | |   (71)  all_58_11 = e0 & op(e1, e0) = e0
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | | ALPHA: (71) implies:
% 240.37/46.95  | | | | | | |   (72)  op(e1, e0) = e0
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | | REF_CLOSE: (27), (31), (57), (72) are inconsistent by sub-proof
% 240.37/46.95  | | | | | | |            #2284.
% 240.37/46.95  | | | | | | | 
% 240.37/46.95  | | | | | | End of split
% 240.37/46.95  | | | | | | 
% 240.37/46.95  | | | | | End of split
% 240.37/46.95  | | | | | 
% 240.37/46.95  | | | | End of split
% 240.37/46.95  | | | | 
% 240.37/46.95  | | | End of split
% 240.37/46.95  | | | 
% 240.37/46.95  | | Case 2:
% 240.37/46.95  | | | 
% 240.37/46.95  | | |   (73)  all_58_12 = e0 & op(e0, e3) = e0
% 240.37/46.95  | | | 
% 240.37/46.95  | | | ALPHA: (73) implies:
% 240.37/46.95  | | |   (74)  all_58_12 = e0
% 240.37/46.95  | | | 
% 240.37/46.95  | | | REF_CLOSE: (4), (9), (14), (21), (27), (35), (36), (40), (74) are
% 240.37/46.95  | | |            inconsistent by sub-proof #1012.
% 240.37/46.95  | | | 
% 240.37/46.95  | | End of split
% 240.37/46.95  | | 
% 240.37/46.95  | End of split
% 240.37/46.95  | 
% 240.37/46.95  End of proof
% 240.37/46.95  
% 240.37/46.95  Sub-proof #285 shows that the following formulas are inconsistent:
% 240.37/46.95  ----------------------------------------------------------------
% 240.37/46.95    (1)  op(e2, e2) = e3
% 240.37/46.95    (2)   ~ (e3 = e0)
% 240.37/46.95    (3)   ~ (e2 = e0)
% 240.37/46.95    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.37/46.95         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.37/46.95    (5)   ~ (e3 = e1)
% 240.37/46.95    (6)  all_58_3 = e3
% 240.37/46.95    (7)  op(e2, e1) = all_52_9
% 240.37/46.95    (8)   ~ (e3 = e2)
% 240.37/46.95    (9)  op(e2, e3) = all_52_1
% 240.37/46.95    (10)  op(e2, e1) = e0
% 240.37/46.95    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.95    (12)   ~ (e1 = e0)
% 240.37/46.95    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 240.37/46.95    (14)  op(e3, e3) = e3
% 240.37/46.95    (15)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.37/46.95          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.37/46.95    (16)   ~ (all_52_1 = e2)
% 240.37/46.95    (17)   ~ (e2 = e1)
% 240.37/46.95  
% 240.37/46.95  Begin of proof
% 240.37/46.95  | 
% 240.37/46.95  | BETA: splitting (13) gives:
% 240.37/46.95  | 
% 240.37/46.95  | Case 1:
% 240.37/46.95  | | 
% 240.37/46.95  | |   (18)  all_58_0 = e0 & op(e3, e3) = e0
% 240.37/46.95  | | 
% 240.37/46.95  | | ALPHA: (18) implies:
% 240.37/46.95  | |   (19)  op(e3, e3) = e0
% 240.37/46.95  | | 
% 240.37/46.95  | | REF_CLOSE: (2), (11), (14), (19) are inconsistent by sub-proof #1940.
% 240.37/46.95  | | 
% 240.37/46.95  | Case 2:
% 240.37/46.95  | | 
% 240.37/46.95  | |   (20)  all_58_2 = e0 & op(e2, e3) = e0
% 240.37/46.95  | | 
% 240.37/46.95  | | ALPHA: (20) implies:
% 240.37/46.95  | |   (21)  all_58_2 = e0
% 240.37/46.95  | | 
% 240.37/46.95  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (15),
% 240.37/46.95  | |            (16), (17), (21) are inconsistent by sub-proof #286.
% 240.37/46.95  | | 
% 240.37/46.95  | End of split
% 240.37/46.95  | 
% 240.37/46.95  End of proof
% 240.37/46.95  
% 240.37/46.95  Sub-proof #286 shows that the following formulas are inconsistent:
% 240.37/46.95  ----------------------------------------------------------------
% 240.37/46.95    (1)  op(e2, e2) = e3
% 240.37/46.95    (2)   ~ (e2 = e0)
% 240.37/46.95    (3)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.37/46.95         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.37/46.95    (4)   ~ (e3 = e1)
% 240.37/46.95    (5)  all_58_3 = e3
% 240.37/46.95    (6)  op(e2, e1) = all_52_9
% 240.37/46.95    (7)   ~ (e3 = e2)
% 240.37/46.95    (8)  op(e2, e3) = all_52_1
% 240.37/46.95    (9)  op(e2, e1) = e0
% 240.37/46.95    (10)  all_58_2 = e0
% 240.37/46.95    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.95    (12)   ~ (e1 = e0)
% 240.37/46.95    (13)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.37/46.95          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.37/46.95    (14)   ~ (all_52_1 = e2)
% 240.37/46.95    (15)   ~ (e2 = e1)
% 240.37/46.95  
% 240.37/46.95  Begin of proof
% 240.37/46.95  | 
% 240.37/46.95  | BETA: splitting (3) gives:
% 240.37/46.95  | 
% 240.37/46.95  | Case 1:
% 240.37/46.95  | | 
% 240.37/46.95  | |   (16)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 240.37/46.95  | |           e2)
% 240.37/46.95  | | 
% 240.37/46.95  | | REF_CLOSE: (1), (7), (8), (11), (14), (16) are inconsistent by sub-proof
% 240.37/46.95  | |            #998.
% 240.37/46.95  | | 
% 240.37/46.95  | Case 2:
% 240.37/46.95  | | 
% 240.37/46.95  | |   (17)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 240.37/46.95  | |           e2)
% 240.37/46.95  | | 
% 240.37/46.95  | | REF_CLOSE: (2), (4), (5), (6), (9), (10), (11), (12), (13), (15), (17) are
% 240.37/46.95  | |            inconsistent by sub-proof #862.
% 240.37/46.95  | | 
% 240.37/46.95  | End of split
% 240.37/46.95  | 
% 240.37/46.95  End of proof
% 240.37/46.95  
% 240.37/46.95  Sub-proof #287 shows that the following formulas are inconsistent:
% 240.37/46.95  ----------------------------------------------------------------
% 240.37/46.95    (1)  op(e2, e2) = e3
% 240.37/46.95    (2)  op(e3, e2) = e1
% 240.37/46.95    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 240.37/46.95    (4)   ~ (e3 = e2)
% 240.37/46.95    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.95    (6)   ~ (e2 = e1)
% 240.37/46.95  
% 240.37/46.95  Begin of proof
% 240.37/46.95  | 
% 240.37/46.95  | BETA: splitting (3) gives:
% 240.37/46.95  | 
% 240.37/46.95  | Case 1:
% 240.37/46.95  | | 
% 240.37/46.95  | |   (7)  all_58_1 = e2 & op(e3, e2) = e2
% 240.37/46.95  | | 
% 240.37/46.95  | | ALPHA: (7) implies:
% 240.37/46.95  | |   (8)  op(e3, e2) = e2
% 240.37/46.95  | | 
% 240.37/46.95  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2261.
% 240.37/46.95  | | 
% 240.37/46.95  | Case 2:
% 240.37/46.95  | | 
% 240.37/46.95  | |   (9)  all_58_3 = e2 & op(e2, e2) = e2
% 240.37/46.95  | | 
% 240.37/46.95  | | ALPHA: (9) implies:
% 240.37/46.95  | |   (10)  op(e2, e2) = e2
% 240.37/46.95  | | 
% 240.37/46.95  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2140.
% 240.37/46.95  | | 
% 240.37/46.95  | End of split
% 240.37/46.95  | 
% 240.37/46.95  End of proof
% 240.37/46.95  
% 240.37/46.95  Sub-proof #288 shows that the following formulas are inconsistent:
% 240.37/46.95  ----------------------------------------------------------------
% 240.37/46.95    (1)   ~ (all_52_1 = all_52_3)
% 240.37/46.95    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 240.37/46.95    (3)  op(e2, e2) = e3
% 240.37/46.95    (4)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 240.37/46.95           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 240.37/46.95           all_12_1 & $i(all_12_1))
% 240.37/46.95    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.37/46.95         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.37/46.95    (6)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.37/46.95           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.37/46.95           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.37/46.95           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.37/46.95           & $i(all_56_23))
% 240.37/46.95    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.37/46.95         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.37/46.95    (8)   ~ (e3 = e0)
% 240.37/46.95    (9)  op(e0, e1) = all_52_11
% 240.37/46.95    (10)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.37/46.95          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.37/46.95    (11)   ~ (all_52_8 = all_52_9)
% 240.37/46.95    (12)  op(e2, e1) = e1
% 240.37/46.95    (13)   ~ (e2 = e0)
% 240.37/46.95    (14)  op(e1, e2) = all_52_6
% 240.37/46.95    (15)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.37/46.95          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.37/46.95    (16)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 240.37/46.95          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.37/46.95    (17)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.37/46.95              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.37/46.95            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.37/46.95            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.37/46.95            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.37/46.95             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.37/46.95            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.37/46.95            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.37/46.95            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.37/46.95            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.37/46.95            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.37/46.95              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.37/46.95            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.37/46.95            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.37/46.95            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.37/46.95            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.37/46.95            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.37/46.95            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.37/46.95              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.37/46.95            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.37/46.95            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.37/46.95            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.37/46.95            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.37/46.95            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.37/46.95            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.37/46.95              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.37/46.95            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.37/46.95            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.37/46.95    (18)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.37/46.95          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.37/46.95    (19)   ~ (all_52_7 = all_52_11)
% 240.37/46.95    (20)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.37/46.95          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.37/46.95    (21)   ~ (all_52_1 = all_52_2)
% 240.37/46.95    (22)  op(e1, e0) = all_52_14
% 240.37/46.95    (23)   ~ (all_52_7 = e3)
% 240.37/46.95    (24)  all_58_15 = e3
% 240.37/46.95    (25)  op(e0, e3) = all_52_3
% 240.37/46.95    (26)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.37/46.95          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.37/46.95    (27)  all_54_11 = all_52_14
% 240.37/46.95    (28)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.37/46.95          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.37/46.95    (29)   ~ (all_52_2 = all_52_3)
% 240.37/46.95    (30)  all_58_3 = e3
% 240.37/46.95    (31)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.37/46.95    (32)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.37/46.95          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.37/46.95    (33)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 240.37/46.95            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 240.37/46.95              e3) = all_26_1 & $i(all_26_1))
% 240.37/46.95    (34)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 240.37/46.95            $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e1, e3) = all_6_1
% 240.37/46.95            & $i(all_6_1))
% 240.37/46.95    (35)   ~ (all_52_3 = all_52_7)
% 240.37/46.95    (36)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.37/46.95    (37)  all_54_4 = all_52_1
% 240.37/46.95    (38)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.37/46.95              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.37/46.95                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.37/46.95                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.37/46.95    (39)   ~ (all_52_11 = e3)
% 240.37/46.95    (40)   ~ (all_52_8 = all_52_12)
% 240.37/46.95    (41)  op(e3, e1) = all_52_8
% 240.37/46.95    (42)  op(e2, e1) = all_52_9
% 240.37/46.95    (43)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.37/46.95          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.37/46.95    (44)   ~ (e3 = e2)
% 240.37/46.96    (45)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.37/46.96          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.37/46.96    (46)   ~ (all_52_3 = all_52_11)
% 240.37/46.96    (47)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.37/46.96            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.37/46.96            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.37/46.96            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.37/46.96            op(e0, all_56_31) = e0)
% 240.37/46.96    (48)  all_54_12 = all_52_3
% 240.37/46.96    (49)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.37/46.96    (50)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.37/46.96          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.37/46.96    (51)  op(e3, e0) = all_52_12
% 240.37/46.96    (52)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.37/46.96          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.37/46.96    (53)   ~ (all_52_9 = all_52_13)
% 240.37/46.96    (54)   ~ (all_52_3 = e3)
% 240.37/46.96    (55)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.37/46.96            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.37/46.96              e3) = all_42_1 & $i(all_42_1))
% 240.37/46.96    (56)  op(e2, e3) = all_52_1
% 240.37/46.96    (57)   ~ (all_52_14 = e3)
% 240.37/46.96    (58)  op(e1, e1) = e3
% 240.37/46.96    (59)   ~ (all_52_2 = e3)
% 240.37/46.96    (60)   ~ (all_52_6 = e3)
% 240.37/46.96    (61)   ~ (all_52_1 = all_52_13)
% 240.37/46.96    (62)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.37/46.96          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.37/46.96    (63)  all_54_7 = all_52_13
% 240.37/46.96    (64)  op(e0, e2) = all_52_7
% 240.37/46.96    (65)   ~ (all_52_13 = all_52_14)
% 240.37/46.96    (66)   ~ (all_52_4 = e3)
% 240.37/46.96    (67)  op(e3, e2) = all_52_4
% 240.37/46.96    (68)   ~ (all_52_8 = all_52_11)
% 240.37/46.96    (69)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.37/46.96    (70)  all_58_5 = e1
% 240.37/46.96    (71)   ~ (all_52_9 = e3)
% 240.37/46.96    (72)  all_56_31 = e3
% 240.37/46.96    (73)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.37/46.96          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.37/46.96    (74)  op(e0, e0) = e3
% 240.37/46.96    (75)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.37/46.96          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.37/46.96    (76)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.37/46.96          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.37/46.96    (77)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.37/46.96          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.37/46.96    (78)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.37/46.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.37/46.96    (79)  all_58_8 = e3
% 240.37/46.96    (80)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.37/46.96          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.37/46.96    (81)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.37/46.96            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.37/46.96              e3) = all_46_1 & $i(all_46_1))
% 240.37/46.96    (82)  op(e1, e3) = all_52_2
% 240.37/46.96    (83)  all_56_21 = e3
% 240.37/46.96    (84)   ~ (all_52_6 = all_52_7)
% 240.37/46.96    (85)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.37/46.96          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.37/46.96    (86)   ~ (all_52_12 = e3)
% 240.37/46.96    (87)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.37/46.96          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.37/46.96    (88)   ~ (e1 = e0)
% 240.37/46.96    (89)  op(e3, e3) = e3
% 240.37/46.96    (90)   ~ (all_52_13 = e3)
% 240.37/46.96    (91)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.37/46.96          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.37/46.96    (92)  op(e2, e0) = all_52_13
% 240.37/46.96    (93)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.37/46.96          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.37/46.96            e1)
% 240.37/46.96    (94)   ~ (all_52_1 = e3)
% 240.37/46.96    (95)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.37/46.96          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.37/46.96            e2)
% 240.37/46.96    (96)   ~ (all_52_9 = all_52_11)
% 240.37/46.96    (97)   ~ (all_52_4 = all_52_8)
% 240.37/46.96    (98)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.37/46.96            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.37/46.96            & $i(all_8_1))
% 240.37/46.96    (99)   ~ (e2 = e1)
% 240.37/46.96    (100)   ~ (all_52_8 = e3)
% 240.37/46.96  
% 240.37/46.96  Begin of proof
% 240.37/46.96  | 
% 240.37/46.96  | GROUND_INST: instantiating (78) with all_52_9, e1, e1, e2, simplifying with
% 240.37/46.96  |              (12), (42) gives:
% 240.37/46.96  |   (101)  all_52_9 = e1
% 240.37/46.96  | 
% 240.37/46.96  | REDUCE: (11), (101) imply:
% 240.37/46.96  |   (102)   ~ (all_52_8 = e1)
% 240.37/46.96  | 
% 240.37/46.96  | REDUCE: (96), (101) imply:
% 240.37/46.96  |   (103)   ~ (all_52_11 = e1)
% 240.37/46.96  | 
% 240.37/46.96  | SIMP: (103) implies:
% 240.37/46.96  |   (104)   ~ (all_52_11 = e1)
% 240.37/46.96  | 
% 240.37/46.96  | REDUCE: (53), (101) imply:
% 240.37/46.96  |   (105)   ~ (all_52_13 = e1)
% 240.37/46.96  | 
% 240.37/46.96  | SIMP: (105) implies:
% 240.37/46.96  |   (106)   ~ (all_52_13 = e1)
% 240.37/46.96  | 
% 240.37/46.96  | REDUCE: (71), (101) imply:
% 240.37/46.96  |   (107)   ~ (e3 = e1)
% 240.37/46.96  | 
% 240.37/46.96  | SIMP: (107) implies:
% 240.37/46.96  |   (108)   ~ (e3 = e1)
% 240.37/46.96  | 
% 240.37/46.96  | BETA: splitting (45) gives:
% 240.37/46.96  | 
% 240.37/46.96  | Case 1:
% 240.37/46.96  | | 
% 240.37/46.96  | |   (109)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 240.37/46.96  | |            e2)
% 240.37/46.96  | | 
% 240.37/46.96  | | BETA: splitting (109) gives:
% 240.37/46.96  | | 
% 240.37/46.96  | | Case 1:
% 240.37/46.96  | | | 
% 240.37/46.96  | | |   (110)  all_58_4 = e2 & op(e3, e1) = e2
% 240.37/46.96  | | | 
% 240.37/46.96  | | | ALPHA: (110) implies:
% 240.37/46.96  | | |   (111)  all_58_4 = e2
% 240.37/46.96  | | |   (112)  op(e3, e1) = e2
% 240.37/46.96  | | | 
% 240.37/46.96  | | | BETA: splitting (28) gives:
% 240.37/46.96  | | | 
% 240.37/46.96  | | | Case 1:
% 240.37/46.96  | | | | 
% 240.37/46.96  | | | |   (113)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1)
% 240.37/46.96  | | | |            = e0)
% 240.37/46.96  | | | | 
% 240.37/46.96  | | | | BETA: splitting (113) gives:
% 240.37/46.96  | | | | 
% 240.37/46.96  | | | | Case 1:
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | |   (114)  all_58_4 = e0 & op(e3, e1) = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | ALPHA: (114) implies:
% 240.37/46.96  | | | | |   (115)  all_58_4 = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REF_CLOSE: (13), (111), (115) are inconsistent by sub-proof #1666.
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | Case 2:
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | |   (116)  all_58_5 = e0 & op(e2, e1) = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | ALPHA: (116) implies:
% 240.37/46.96  | | | | |   (117)  op(e2, e1) = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REF_CLOSE: (12), (42), (78), (88), (117) are inconsistent by sub-proof
% 240.37/46.96  | | | | |            #2165.
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | End of split
% 240.37/46.96  | | | | 
% 240.37/46.96  | | | Case 2:
% 240.37/46.96  | | | | 
% 240.37/46.96  | | | |   (118)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 240.37/46.96  | | | |              e1) = e0)
% 240.37/46.96  | | | | 
% 240.37/46.96  | | | | BETA: splitting (118) gives:
% 240.37/46.96  | | | | 
% 240.37/46.96  | | | | Case 1:
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | |   (119)  all_58_8 = e0 & op(e1, e1) = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | ALPHA: (119) implies:
% 240.37/46.96  | | | | |   (120)  op(e1, e1) = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REF_CLOSE: (8), (9), (39), (42), (44), (62), (71), (78), (111), (120)
% 240.37/46.96  | | | | |            are inconsistent by sub-proof #1493.
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | Case 2:
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | |   (121)  all_58_14 = e0 & op(e0, e1) = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | ALPHA: (121) implies:
% 240.37/46.96  | | | | |   (122)  op(e0, e1) = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | GROUND_INST: instantiating (78) with all_52_11, e0, e1, e0,
% 240.37/46.96  | | | | |              simplifying with (9), (122) gives:
% 240.37/46.96  | | | | |   (123)  all_52_11 = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | GROUND_INST: instantiating (78) with all_52_8, e2, e1, e3, simplifying
% 240.37/46.96  | | | | |              with (41), (112) gives:
% 240.37/46.96  | | | | |   (124)  all_52_8 = e2
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REDUCE: (46), (123) imply:
% 240.37/46.96  | | | | |   (125)   ~ (all_52_3 = e0)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REDUCE: (39), (123) imply:
% 240.37/46.96  | | | | |   (126)   ~ (e3 = e0)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REDUCE: (104), (123) imply:
% 240.37/46.96  | | | | |   (127)   ~ (e1 = e0)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | BETA: splitting (6) gives:
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | Case 1:
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | |   (128)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 240.37/46.96  | | | | | |            all_56_17 & $i(all_56_17)) | (all_56_18 = e2 & op(e2,
% 240.37/46.96  | | | | | |              all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 240.37/46.96  | | | | | |            $i(all_56_19))
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | | BETA: splitting (128) gives:
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | | Case 1:
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | |   (129)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 240.37/46.96  | | | | | | |          all_56_17 & $i(all_56_17)
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | REF_CLOSE: (66), (67), (78), (112), (129) are inconsistent by
% 240.37/46.96  | | | | | | |            sub-proof #300.
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | Case 2:
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | |   (130)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 240.37/46.96  | | | | | | |          all_56_19 & $i(all_56_19)
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | ALPHA: (130) implies:
% 240.37/46.96  | | | | | | |   (131)  op(e2, e1) = all_56_19
% 240.37/46.96  | | | | | | |   (132)  op(e2, all_56_19) = e2
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | REF_CLOSE: (12), (78), (99), (131), (132) are inconsistent by
% 240.37/46.96  | | | | | | |            sub-proof #299.
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | End of split
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | Case 2:
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | |   (133)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 = e0
% 240.37/46.96  | | | | | |            & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 240.37/46.96  | | | | | |            $i(all_56_23))
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | | BETA: splitting (133) gives:
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | | Case 1:
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | |   (134)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | ALPHA: (134) implies:
% 240.37/46.96  | | | | | | |   (135)  op(e1, all_56_21) = e1
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | REDUCE: (83), (135) imply:
% 240.37/46.96  | | | | | | |   (136)  op(e1, e3) = e1
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | REF_CLOSE: (8), (9), (24), (25), (29), (50), (55), (59), (78),
% 240.37/46.96  | | | | | | |            (82), (88), (89), (93), (98), (104), (125), (136) are
% 240.37/46.96  | | | | | | |            inconsistent by sub-proof #302.
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | Case 2:
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | |   (137)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 240.37/46.96  | | | | | | |          all_56_23 & $i(all_56_23)
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | ALPHA: (137) implies:
% 240.37/46.96  | | | | | | |   (138)  op(e0, e1) = all_56_23
% 240.37/46.96  | | | | | | |   (139)  op(e0, all_56_23) = e0
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | REF_CLOSE: (8), (74), (78), (122), (138), (139) are inconsistent
% 240.37/46.96  | | | | | | |            by sub-proof #1395.
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | End of split
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | End of split
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | End of split
% 240.37/46.96  | | | | 
% 240.37/46.96  | | | End of split
% 240.37/46.96  | | | 
% 240.37/46.96  | | Case 2:
% 240.37/46.96  | | | 
% 240.37/46.96  | | |   (140)  all_58_5 = e2 & op(e2, e1) = e2
% 240.37/46.96  | | | 
% 240.37/46.96  | | | REF_CLOSE: (70), (99), (140) are inconsistent by sub-proof #703.
% 240.37/46.96  | | | 
% 240.37/46.96  | | End of split
% 240.37/46.96  | | 
% 240.37/46.96  | Case 2:
% 240.37/46.96  | | 
% 240.37/46.96  | |   (141)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 240.37/46.96  | |            e2)
% 240.37/46.96  | | 
% 240.37/46.96  | | BETA: splitting (141) gives:
% 240.37/46.96  | | 
% 240.37/46.96  | | Case 1:
% 240.37/46.96  | | | 
% 240.37/46.96  | | |   (142)  all_58_8 = e2 & op(e1, e1) = e2
% 240.37/46.96  | | | 
% 240.37/46.96  | | | ALPHA: (142) implies:
% 240.37/46.96  | | |   (143)  op(e1, e1) = e2
% 240.37/46.96  | | | 
% 240.37/46.96  | | | REF_CLOSE: (44), (58), (78), (143) are inconsistent by sub-proof #2206.
% 240.37/46.96  | | | 
% 240.37/46.96  | | Case 2:
% 240.37/46.96  | | | 
% 240.37/46.96  | | |   (144)  all_58_14 = e2 & op(e0, e1) = e2
% 240.37/46.96  | | | 
% 240.37/46.96  | | | ALPHA: (144) implies:
% 240.37/46.96  | | |   (145)  all_58_14 = e2
% 240.37/46.96  | | |   (146)  op(e0, e1) = e2
% 240.37/46.96  | | | 
% 240.37/46.96  | | | BETA: splitting (28) gives:
% 240.37/46.96  | | | 
% 240.37/46.96  | | | Case 1:
% 240.37/46.96  | | | | 
% 240.37/46.96  | | | |   (147)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1)
% 240.37/46.96  | | | |            = e0)
% 240.37/46.96  | | | | 
% 240.37/46.96  | | | | BETA: splitting (147) gives:
% 240.37/46.96  | | | | 
% 240.37/46.96  | | | | Case 1:
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | |   (148)  all_58_4 = e0 & op(e3, e1) = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | ALPHA: (148) implies:
% 240.37/46.96  | | | | |   (149)  all_58_4 = e0
% 240.37/46.96  | | | | |   (150)  op(e3, e1) = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | GROUND_INST: instantiating (78) with all_52_11, e2, e1, e0,
% 240.37/46.96  | | | | |              simplifying with (9), (146) gives:
% 240.37/46.96  | | | | |   (151)  all_52_11 = e2
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | GROUND_INST: instantiating (78) with all_52_8, e0, e1, e3, simplifying
% 240.37/46.96  | | | | |              with (41), (150) gives:
% 240.37/46.96  | | | | |   (152)  all_52_8 = e0
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REDUCE: (46), (151) imply:
% 240.37/46.96  | | | | |   (153)   ~ (all_52_3 = e2)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REDUCE: (97), (152) imply:
% 240.37/46.96  | | | | |   (154)   ~ (all_52_4 = e0)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REDUCE: (19), (151) imply:
% 240.37/46.96  | | | | |   (155)   ~ (all_52_7 = e2)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REDUCE: (68), (151), (152) imply:
% 240.37/46.96  | | | | |   (156)   ~ (e2 = e0)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REDUCE: (40), (152) imply:
% 240.37/46.96  | | | | |   (157)   ~ (all_52_12 = e0)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | SIMP: (157) implies:
% 240.37/46.96  | | | | |   (158)   ~ (all_52_12 = e0)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REDUCE: (100), (152) imply:
% 240.37/46.96  | | | | |   (159)   ~ (e3 = e0)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REDUCE: (102), (152) imply:
% 240.37/46.96  | | | | |   (160)   ~ (e1 = e0)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | REDUCE: (39), (151) imply:
% 240.37/46.96  | | | | |   (161)   ~ (e3 = e2)
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | BETA: splitting (6) gives:
% 240.37/46.96  | | | | | 
% 240.37/46.96  | | | | | Case 1:
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | |   (162)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 240.37/46.96  | | | | | |            all_56_17 & $i(all_56_17)) | (all_56_18 = e2 & op(e2,
% 240.37/46.96  | | | | | |              all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 240.37/46.96  | | | | | |            $i(all_56_19))
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | | BETA: splitting (162) gives:
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | | Case 1:
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | |   (163)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 240.37/46.96  | | | | | | |          all_56_17 & $i(all_56_17)
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | REF_CLOSE: (51), (78), (86), (150), (163) are inconsistent by
% 240.37/46.96  | | | | | | |            sub-proof #298.
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | Case 2:
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | |   (164)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 240.37/46.96  | | | | | | |          all_56_19 & $i(all_56_19)
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | ALPHA: (164) implies:
% 240.37/46.96  | | | | | | |   (165)  op(e2, e1) = all_56_19
% 240.37/46.96  | | | | | | |   (166)  op(e2, all_56_19) = e2
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | GROUND_INST: instantiating (78) with e1, all_56_19, e1, e2,
% 240.37/46.96  | | | | | | |              simplifying with (12), (165) gives:
% 240.37/46.96  | | | | | | |   (167)  all_56_19 = e1
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | REDUCE: (166), (167) imply:
% 240.37/46.96  | | | | | | |   (168)  op(e2, e1) = e2
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | GROUND_INST: instantiating (78) with e1, e2, e1, e2, simplifying
% 240.37/46.96  | | | | | | |              with (12), (168) gives:
% 240.37/46.96  | | | | | | |   (169)  e2 = e1
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | COMBINE_EQS: (145), (169) imply:
% 240.37/46.96  | | | | | | |   (170)  all_58_14 = e1
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | | REF_CLOSE: (8), (13), (28), (44), (45), (62), (70), (78), (88),
% 240.37/46.96  | | | | | | |            (99), (108), (149), (170) are inconsistent by sub-proof
% 240.37/46.96  | | | | | | |            #1248.
% 240.37/46.96  | | | | | | | 
% 240.37/46.96  | | | | | | End of split
% 240.37/46.96  | | | | | | 
% 240.37/46.96  | | | | | Case 2:
% 240.37/46.96  | | | | | | 
% 240.37/46.97  | | | | | |   (171)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 = e0
% 240.37/46.97  | | | | | |            & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 240.37/46.97  | | | | | |            $i(all_56_23))
% 240.37/46.97  | | | | | | 
% 240.37/46.97  | | | | | | BETA: splitting (171) gives:
% 240.37/46.97  | | | | | | 
% 240.37/46.97  | | | | | | Case 1:
% 240.37/46.97  | | | | | | | 
% 240.37/46.97  | | | | | | |   (172)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 240.37/46.97  | | | | | | | 
% 240.37/46.97  | | | | | | | ALPHA: (172) implies:
% 240.37/46.97  | | | | | | |   (173)  op(e1, all_56_21) = e1
% 240.37/46.97  | | | | | | | 
% 240.37/46.97  | | | | | | | REDUCE: (83), (173) imply:
% 240.37/46.97  | | | | | | |   (174)  op(e1, e3) = e1
% 240.37/46.97  | | | | | | | 
% 240.37/46.97  | | | | | | | GROUND_INST: instantiating (78) with all_52_2, e1, e3, e1,
% 240.37/46.97  | | | | | | |              simplifying with (82), (174) gives:
% 240.37/46.97  | | | | | | |   (175)  all_52_2 = e1
% 240.37/46.97  | | | | | | | 
% 240.37/46.97  | | | | | | | REDUCE: (21), (175) imply:
% 240.37/46.97  | | | | | | |   (176)   ~ (all_52_1 = e1)
% 240.37/46.97  | | | | | | | 
% 240.37/46.97  | | | | | | | REDUCE: (29), (175) imply:
% 240.37/46.97  | | | | | | |   (177)   ~ (all_52_3 = e1)
% 240.37/46.97  | | | | | | | 
% 240.37/46.97  | | | | | | | SIMP: (177) implies:
% 240.37/46.97  | | | | | | |   (178)   ~ (all_52_3 = e1)
% 240.37/46.97  | | | | | | | 
% 240.37/46.97  | | | | | | | BETA: splitting (93) gives:
% 240.37/46.97  | | | | | | | 
% 240.37/46.97  | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | 
% 240.37/46.97  | | | | | | | |   (179)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 240.37/46.97  | | | | | | | |            op(e0, e2) = e1)
% 240.37/46.97  | | | | | | | | 
% 240.37/46.97  | | | | | | | | BETA: splitting (179) gives:
% 240.37/46.97  | | | | | | | | 
% 240.37/46.97  | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | 
% 240.37/46.97  | | | | | | | | |   (180)  all_58_12 = e1 & op(e0, e3) = e1
% 240.37/46.97  | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | REF_CLOSE: (25), (78), (178), (180) are inconsistent by
% 240.37/46.97  | | | | | | | | |            sub-proof #2276.
% 240.37/46.97  | | | | | | | | | 
% 240.37/46.97  | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | 
% 240.37/46.97  | | | | | | | | |   (181)  all_58_13 = e1 & op(e0, e2) = e1
% 240.37/46.97  | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | ALPHA: (181) implies:
% 240.37/46.97  | | | | | | | | |   (182)  all_58_13 = e1
% 240.37/46.97  | | | | | | | | |   (183)  op(e0, e2) = e1
% 240.37/46.97  | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | BETA: splitting (73) gives:
% 240.37/46.97  | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | |   (184)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 240.37/46.97  | | | | | | | | | |            & op(e2, e3) = e1)
% 240.37/46.97  | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | REF_CLOSE: (56), (78), (89), (108), (176), (184) are
% 240.37/46.97  | | | | | | | | | |            inconsistent by sub-proof #1370.
% 240.37/46.97  | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | |   (185)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 240.37/46.97  | | | | | | | | | |            & op(e0, e3) = e1)
% 240.37/46.97  | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | BETA: splitting (185) gives:
% 240.37/46.97  | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | |   (186)  all_58_6 = e1 & op(e1, e3) = e1
% 240.37/46.97  | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | ALPHA: (186) implies:
% 240.37/46.97  | | | | | | | | | | |   (187)  all_58_6 = e1
% 240.37/46.97  | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | BETA: splitting (43) gives:
% 240.37/46.97  | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | |   (188)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 240.37/46.97  | | | | | | | | | | | |            & op(e2, e3) = e2)
% 240.37/46.97  | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | BETA: splitting (188) gives:
% 240.37/46.97  | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | |   (189)  all_58_0 = e2 & op(e3, e3) = e2
% 240.37/46.97  | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | ALPHA: (189) implies:
% 240.37/46.97  | | | | | | | | | | | | |   (190)  op(e3, e3) = e2
% 240.37/46.97  | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | REF_CLOSE: (44), (78), (89), (190) are inconsistent by
% 240.37/46.97  | | | | | | | | | | | | |            sub-proof #2194.
% 240.37/46.97  | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | |   (191)  all_58_2 = e2 & op(e2, e3) = e2
% 240.37/46.97  | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | ALPHA: (191) implies:
% 240.37/46.97  | | | | | | | | | | | | |   (192)  all_58_2 = e2
% 240.37/46.97  | | | | | | | | | | | | |   (193)  op(e2, e3) = e2
% 240.37/46.97  | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | BETA: splitting (69) gives:
% 240.37/46.97  | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | |   (194)  all_54_12 = e2
% 240.37/46.97  | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | COMBINE_EQS: (48), (194) imply:
% 240.37/46.97  | | | | | | | | | | | | | |   (195)  all_52_3 = e2
% 240.37/46.97  | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | REDUCE: (153), (195) imply:
% 240.37/46.97  | | | | | | | | | | | | | |   (196)  $false
% 240.37/46.97  | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | CLOSE: (196) is inconsistent.
% 240.37/46.97  | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | |   (197)   ~ (all_54_12 = e2)
% 240.37/46.97  | | | | | | | | | | | | | |   (198)  all_54_12 = e1 | all_54_12 = e0
% 240.37/46.97  | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 240.37/46.97  | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | |   (199)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 240.37/46.97  | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 240.37/46.97  | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | |   (200)  all_58_1 = e0 & op(e3, e2) = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | REF_CLOSE: (67), (78), (154), (200) are inconsistent by
% 240.37/46.97  | | | | | | | | | | | | | | | |            sub-proof #1968.
% 240.37/46.97  | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | |   (201)  all_58_3 = e0 & op(e2, e2) = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (30), (201) are inconsistent by sub-proof
% 240.37/46.97  | | | | | | | | | | | | | | | |            #1719.
% 240.37/46.97  | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | End of split
% 240.37/46.97  | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | |   (202)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 240.37/46.97  | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 240.37/46.97  | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | |   (203)  all_58_7 = e0 & op(e1, e2) = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | |   (204)  all_58_7 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | |   (205)  op(e1, e2) = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | |   (206)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 240.37/46.97  | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | |   (207)  all_58_6 = e2 & op(e1, e3) = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | |   (208)  op(e1, e3) = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (99), (174), (208) are inconsistent by
% 240.37/46.97  | | | | | | | | | | | | | | | | | |            sub-proof #2226.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | |   (209)  all_58_7 = e2 & op(e1, e2) = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | |   (210)  all_58_7 = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (204), (210) are inconsistent by sub-proof
% 240.37/46.97  | | | | | | | | | | | | | | | | | |            #1587.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | End of split
% 240.37/46.97  | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | |   (211)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 240.37/46.97  | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 240.37/46.97  | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | |   (212)  all_58_8 = e2 & op(e1, e1) = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | |   (213)  op(e1, e1) = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (22), (44), (52), (57), (78), (108), (174),
% 240.37/46.97  | | | | | | | | | | | | | | | | | |            (204), (213) are inconsistent by sub-proof #2147.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | |   (214)  all_58_11 = e2 & op(e1, e0) = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | |   (215)  op(e1, e0) = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | |   (216)  all_54_12 = e1
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (178), (216) are inconsistent by sub-proof
% 240.37/46.97  | | | | | | | | | | | | | | | | | | |            #2263.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | |   (217)  all_54_12 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (217) imply:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | |   (218)  all_52_3 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | SIMP: (218) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | |   (219)  all_52_3 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | REDUCE: (1), (219) imply:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | |   (220)   ~ (all_52_1 = e0)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |   (221)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |   (222)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            = e3)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |   (223)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |          e3
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |   (224)  op(e2, e3) = e3
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (78), (193), (224) are inconsistent by
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1897.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |   (225)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (78), (108), (174), (225) are inconsistent
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1369.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |   (226)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |   (227)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |   (228)  op(e3, e1) = e1
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (88), (150), (228) are inconsistent by
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2089.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |   (229)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (51), (54), (78), (158), (229) are
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2257.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |   (230)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |   (231)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | |            = e2)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |   (232)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |   (233)   ~ (all_56_31 = e1)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |   (234)  op(e1, e2) = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | |   (235)  op(e2, e1) = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | |   (236)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (13), (32), (44), (56), (66), (67),
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | |            (75), (78), (88), (99), (108), (149), (220), (236)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #297.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | |   (237)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | |   (238)  all_58_6 = e0 & op(e1, e3) = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | |   (239)  op(e1, e3) = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (88), (174), (239) are inconsistent by
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #449.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | |   (240)  all_58_12 = e0 & op(e0, e3) = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | |   (241)  all_58_12 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_54_4 = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (242) imply:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (243)  all_52_1 = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (243) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_52_1 = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (244) imply:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (245)   ~ (all_52_13 = e2)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (245) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (246)   ~ (all_52_13 = e2)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  all_54_7 = e2
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (246), (247) are inconsistent by sub-proof
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1997.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)   ~ (all_54_7 = e2)
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (249)  all_54_7 = e1 | all_54_7 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (250)  all_54_7 = e1
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (106), (250) are inconsistent by sub-proof
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2295.
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  all_54_7 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (251) imply:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)  all_52_13 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (252) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)  all_52_13 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with e0, e2, e2, e1,
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (205), (234) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)  e2 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with e1, e2, e1, e2,
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (12), (235) gives:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (255)  e2 = e1
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (255) imply:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  e1 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (256) implies:
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  e1 = e0
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (257) imply:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  all_58_6 = e0
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (259) gives:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_58_0 = e1 & op(e3, e3) = e1
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (260) implies:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  op(e3, e3) = e1
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (89), (108), (261) are inconsistent by
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1578.
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_58_2 = e1 & op(e2, e3) = e1
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  all_58_2 = e1
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (263) imply:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  e2 = e1
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (255) imply:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_58_14 = e1
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (24), (44), (95), (99), (182), (241), (265)
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1230.
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (186), (258) are inconsistent by sub-proof
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1682.
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_58_12 = e1 & op(e0, e3) = e1
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (241), (266) are inconsistent by sub-proof
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #805.
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_54_4 = e1 | all_54_4 = e0
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (176), (220), (267) are inconsistent by
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1922.
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |   (268)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (64), (78), (88), (155), (205), (268) are
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #296.
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | |   (269)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |   (270)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (270) implies:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |   (271)  op(e0, e2) = e0
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (88), (183), (271) are inconsistent by
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1872.
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |   (272)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (78), (99), (215), (272) are inconsistent by
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #477.
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | |   (273)  all_58_13 = e0 & op(e0, e2) = e0
% 240.37/46.98  | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 240.37/46.98  | | | | | | | | | | | | | | | |   (274)  op(e0, e2) = e0
% 240.37/46.98  | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | REF_CLOSE: (78), (88), (183), (274) are inconsistent by
% 240.37/46.98  | | | | | | | | | | | | | | | |            sub-proof #1872.
% 240.37/46.98  | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | |   (275)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 240.37/46.98  | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | BETA: splitting (275) gives:
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | |   (276)  all_58_6 = e2 & op(e1, e3) = e2
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | ALPHA: (276) implies:
% 240.37/46.98  | | | | | | | | | | | | |   (277)  op(e1, e3) = e2
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | REF_CLOSE: (78), (99), (174), (277) are inconsistent by
% 240.37/46.98  | | | | | | | | | | | | |            sub-proof #2226.
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | |   (278)  all_58_12 = e2 & op(e0, e3) = e2
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | ALPHA: (278) implies:
% 240.37/46.98  | | | | | | | | | | | | |   (279)  all_58_12 = e2
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | REF_CLOSE: (8), (13), (24), (38), (74), (78), (88), (93),
% 240.37/46.98  | | | | | | | | | | | | |            (99), (108), (145), (279) are inconsistent by
% 240.37/46.98  | | | | | | | | | | | | |            sub-proof #1391.
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | |   (280)  all_58_12 = e1 & op(e0, e3) = e1
% 240.37/46.98  | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | REF_CLOSE: (25), (78), (178), (280) are inconsistent by
% 240.37/46.98  | | | | | | | | | | |            sub-proof #2276.
% 240.37/46.98  | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | 
% 240.37/46.98  | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | 
% 240.37/46.98  | | | | | | | |   (281)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 240.37/46.98  | | | | | | | |            op(e0, e0) = e1)
% 240.37/46.98  | | | | | | | | 
% 240.37/46.98  | | | | | | | | BETA: splitting (281) gives:
% 240.37/46.98  | | | | | | | | 
% 240.37/46.98  | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | |   (282)  all_58_14 = e1 & op(e0, e1) = e1
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | ALPHA: (282) implies:
% 240.37/46.98  | | | | | | | | |   (283)  all_58_14 = e1
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | REF_CLOSE: (8), (13), (28), (44), (45), (62), (70), (78),
% 240.37/46.98  | | | | | | | | |            (88), (99), (108), (149), (283) are inconsistent by
% 240.37/46.98  | | | | | | | | |            sub-proof #1248.
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | |   (284)  all_58_15 = e1 & op(e0, e0) = e1
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | ALPHA: (284) implies:
% 240.37/46.98  | | | | | | | | |   (285)  all_58_15 = e1
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | REF_CLOSE: (24), (108), (285) are inconsistent by sub-proof
% 240.37/46.98  | | | | | | | | |            #2249.
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | End of split
% 240.37/46.98  | | | | | | | | 
% 240.37/46.98  | | | | | | | End of split
% 240.37/46.98  | | | | | | | 
% 240.37/46.98  | | | | | | Case 2:
% 240.37/46.98  | | | | | | | 
% 240.37/46.98  | | | | | | |   (286)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 240.37/46.98  | | | | | | |          all_56_23 & $i(all_56_23)
% 240.37/46.98  | | | | | | | 
% 240.37/46.98  | | | | | | | ALPHA: (286) implies:
% 240.37/46.98  | | | | | | |   (287)  op(e0, e1) = all_56_23
% 240.37/46.98  | | | | | | |   (288)  op(e0, all_56_23) = e0
% 240.37/46.98  | | | | | | | 
% 240.37/46.98  | | | | | | | GROUND_INST: instantiating (78) with e2, all_56_23, e1, e0,
% 240.37/46.98  | | | | | | |              simplifying with (146), (287) gives:
% 240.37/46.98  | | | | | | |   (289)  all_56_23 = e2
% 240.37/46.98  | | | | | | | 
% 240.37/46.98  | | | | | | | REDUCE: (288), (289) imply:
% 240.37/46.98  | | | | | | |   (290)  op(e0, e2) = e0
% 240.37/46.98  | | | | | | | 
% 240.37/46.98  | | | | | | | GROUND_INST: instantiating (78) with all_52_7, e0, e2, e0,
% 240.37/46.98  | | | | | | |              simplifying with (64), (290) gives:
% 240.37/46.98  | | | | | | |   (291)  all_52_7 = e0
% 240.37/46.98  | | | | | | | 
% 240.37/46.98  | | | | | | | REDUCE: (35), (291) imply:
% 240.37/46.98  | | | | | | |   (292)   ~ (all_52_3 = e0)
% 240.37/46.98  | | | | | | | 
% 240.37/46.98  | | | | | | | REDUCE: (84), (291) imply:
% 240.37/46.98  | | | | | | |   (293)   ~ (all_52_6 = e0)
% 240.37/46.98  | | | | | | | 
% 240.37/46.98  | | | | | | | BETA: splitting (93) gives:
% 240.37/46.98  | | | | | | | 
% 240.37/46.98  | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | 
% 240.37/46.98  | | | | | | | |   (294)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 240.37/46.98  | | | | | | | |            op(e0, e2) = e1)
% 240.37/46.98  | | | | | | | | 
% 240.37/46.98  | | | | | | | | BETA: splitting (294) gives:
% 240.37/46.98  | | | | | | | | 
% 240.37/46.98  | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | |   (295)  all_58_12 = e1 & op(e0, e3) = e1
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | ALPHA: (295) implies:
% 240.37/46.98  | | | | | | | | |   (296)  all_58_12 = e1
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | BETA: splitting (38) gives:
% 240.37/46.98  | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | |   (297)  all_58_15 = e0 & op(e0, e0) = e0
% 240.37/46.98  | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | ALPHA: (297) implies:
% 240.37/46.98  | | | | | | | | | |   (298)  op(e0, e0) = e0
% 240.37/46.98  | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | REF_CLOSE: (8), (74), (78), (298) are inconsistent by
% 240.37/46.98  | | | | | | | | | |            sub-proof #2079.
% 240.37/46.98  | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | |   (299)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.37/46.98  | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.37/46.98  | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 240.37/46.98  | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.37/46.98  | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.37/46.98  | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | ALPHA: (299) implies:
% 240.37/46.98  | | | | | | | | | |   (300)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 240.37/46.98  | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 240.37/46.98  | | | | | | | | | |              e1) = e0)
% 240.37/46.98  | | | | | | | | | |   (301)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 240.37/46.98  | | | | | | | | | |            & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.37/46.98  | | | | | | | | | |            = e0)
% 240.37/46.98  | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | BETA: splitting (69) gives:
% 240.37/46.98  | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | |   (302)  all_54_12 = e2
% 240.37/46.98  | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | REF_CLOSE: (48), (153), (302) are inconsistent by sub-proof
% 240.37/46.98  | | | | | | | | | | |            #2264.
% 240.37/46.98  | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | |   (303)   ~ (all_54_12 = e2)
% 240.37/46.98  | | | | | | | | | | |   (304)  all_54_12 = e1 | all_54_12 = e0
% 240.37/46.98  | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | BETA: splitting (304) gives:
% 240.37/46.98  | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | |   (305)  all_54_12 = e1
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | COMBINE_EQS: (48), (305) imply:
% 240.37/46.98  | | | | | | | | | | | |   (306)  all_52_3 = e1
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | SIMP: (306) implies:
% 240.37/46.98  | | | | | | | | | | | |   (307)  all_52_3 = e1
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | REDUCE: (29), (307) imply:
% 240.37/46.98  | | | | | | | | | | | |   (308)   ~ (all_52_2 = e1)
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | REDUCE: (153), (307) imply:
% 240.37/46.98  | | | | | | | | | | | |   (309)   ~ (e2 = e1)
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | REDUCE: (25), (307) imply:
% 240.37/46.98  | | | | | | | | | | | |   (310)  op(e0, e3) = e1
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | BETA: splitting (33) gives:
% 240.37/46.98  | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | |   (311)   ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 240.37/46.98  | | | | | | | | | | | | |          op(e0, e3) = all_26_1 & $i(all_26_0) &
% 240.37/46.98  | | | | | | | | | | | | |          $i(all_26_1)
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | ALPHA: (311) implies:
% 240.37/46.98  | | | | | | | | | | | | |   (312)   ~ (all_26_0 = e2)
% 240.37/46.98  | | | | | | | | | | | | |   (313)  op(e0, e3) = all_26_1
% 240.37/46.98  | | | | | | | | | | | | |   (314)  op(all_26_1, e0) = all_26_0
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | BETA: splitting (4) gives:
% 240.37/46.98  | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | |   (315)   ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 &
% 240.37/46.98  | | | | | | | | | | | | | |          op(e0, e3) = all_12_1 & $i(all_12_0) &
% 240.37/46.98  | | | | | | | | | | | | | |          $i(all_12_1)
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | ALPHA: (315) implies:
% 240.37/46.98  | | | | | | | | | | | | | |   (316)   ~ (all_12_0 = e1)
% 240.37/46.98  | | | | | | | | | | | | | |   (317)  op(e0, e3) = all_12_1
% 240.37/46.98  | | | | | | | | | | | | | |   (318)  op(all_12_1, e0) = all_12_0
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_12_1, all_26_1, e3,
% 240.37/46.98  | | | | | | | | | | | | | |              e0, simplifying with (313), (317) gives:
% 240.37/46.98  | | | | | | | | | | | | | |   (319)  all_26_1 = all_12_1
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with e1, all_26_1, e3, e0,
% 240.37/46.98  | | | | | | | | | | | | | |              simplifying with (310), (313) gives:
% 240.37/46.98  | | | | | | | | | | | | | |   (320)  all_26_1 = e1
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | COMBINE_EQS: (319), (320) imply:
% 240.37/46.98  | | | | | | | | | | | | | |   (321)  all_12_1 = e1
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | SIMP: (321) implies:
% 240.37/46.98  | | | | | | | | | | | | | |   (322)  all_12_1 = e1
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | REDUCE: (314), (320) imply:
% 240.37/46.98  | | | | | | | | | | | | | |   (323)  op(e1, e0) = all_26_0
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | REDUCE: (318), (322) imply:
% 240.37/46.98  | | | | | | | | | | | | | |   (324)  op(e1, e0) = all_12_0
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_14, all_12_0, e0,
% 240.37/46.98  | | | | | | | | | | | | | |              e1, simplifying with (22), (324) gives:
% 240.37/46.98  | | | | | | | | | | | | | |   (325)  all_52_14 = all_12_0
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_14, all_26_0, e0,
% 240.37/46.98  | | | | | | | | | | | | | |              e1, simplifying with (22), (323) gives:
% 240.37/46.98  | | | | | | | | | | | | | |   (326)  all_52_14 = all_26_0
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | COMBINE_EQS: (325), (326) imply:
% 240.37/46.98  | | | | | | | | | | | | | |   (327)  all_26_0 = all_12_0
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | SIMP: (327) implies:
% 240.37/46.98  | | | | | | | | | | | | | |   (328)  all_26_0 = all_12_0
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | COMBINE_EQS: (27), (325) imply:
% 240.37/46.98  | | | | | | | | | | | | | |   (329)  all_54_11 = all_12_0
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | REDUCE: (65), (325) imply:
% 240.37/46.98  | | | | | | | | | | | | | |   (330)   ~ (all_52_13 = all_12_0)
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | REDUCE: (312), (328) imply:
% 240.37/46.98  | | | | | | | | | | | | | |   (331)   ~ (all_12_0 = e2)
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 240.37/46.98  | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | |   (332)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 240.37/46.98  | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 240.37/46.98  | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 240.37/46.98  | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | |   (333)  all_58_9 = e1 & op(e3, e0) = e1
% 240.37/46.98  | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | ALPHA: (333) implies:
% 240.37/46.98  | | | | | | | | | | | | | | | |   (334)  op(e3, e0) = e1
% 240.37/46.98  | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 240.37/46.98  | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | |   (335)  all_54_11 = e2
% 240.37/46.98  | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (335) imply:
% 240.37/46.98  | | | | | | | | | | | | | | | | |   (336)  all_12_0 = e2
% 240.37/46.98  | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | REDUCE: (331), (336) imply:
% 240.37/46.98  | | | | | | | | | | | | | | | | |   (337)  $false
% 240.37/46.98  | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | CLOSE: (337) is inconsistent.
% 240.37/46.98  | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.98  | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | |   (338)  all_54_11 = e1 | all_54_11 = e0
% 240.37/46.98  | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 240.37/46.98  | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | |   (339)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 240.37/46.98  | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 240.37/46.98  | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | 
% 240.37/46.98  | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.98  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.99  | | | | | | | | | | | | | | | | | | |   (340)  all_58_6 = e1 & op(e1, e3) = e1
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | ALPHA: (340) implies:
% 240.37/46.99  | | | | | | | | | | | | | | | | | | |   (341)  op(e1, e3) = e1
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (82), (308), (341) are inconsistent by
% 240.37/46.99  | | | | | | | | | | | | | | | | | | |            sub-proof #1948.
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.99  | | | | | | | | | | | | | | | | | | Case 2:
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.99  | | | | | | | | | | | | | | | | | | |   (342)  all_58_7 = e1 & op(e1, e2) = e1
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 240.37/46.99  | | | | | | | | | | | | | | | | | | |   (343)  all_58_7 = e1
% 240.37/46.99  | | | | | | | | | | | | | | | | | | |   (344)  op(e1, e2) = e1
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.37/46.99  | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | |   (345)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |   (346)  all_58_1 = e2 & op(e3, e2) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (346) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |   (347)  all_58_1 = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |   (348)  op(e3, e2) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | |   (349)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (349) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | |   (350)  all_58_6 = e2 & op(e1, e3) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (350) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | |   (351)  all_58_6 = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | |   (352)  op(e1, e3) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | |   (353)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (353) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (354)  all_58_6 = e0 & op(e1, e3) = e0
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (354) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (355)  all_58_6 = e0
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (24), (43), (44), (49), (56), (61), (63),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (88), (89), (90), (93), (99), (106), (108),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |            (145), (300), (316), (329), (330), (338), (355)
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #295.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (356)  all_58_7 = e0 & op(e1, e2) = e0
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (356) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (357)  op(e1, e2) = e0
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (78), (88), (344), (357) are inconsistent by
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2136.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | |   (358)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (358) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (359)  all_58_8 = e0 & op(e1, e1) = e0
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (359) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (360)  op(e1, e1) = e0
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (20), (42), (44), (45), (62), (71),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (88), (99), (108), (149), (360) are
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1662.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (361)  all_58_11 = e0 & op(e1, e0) = e0
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (361) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (362)  op(e1, e0) = e0
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (363)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (363) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (364)  all_58_2 = e2 & op(e2, e3) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (56), (61), (63), (78), (90), (106), (316),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (329), (330), (338), (364) are inconsistent by
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1304.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (365)  all_58_3 = e2 & op(e2, e2) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (365) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (366)  op(e2, e2) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (14), (18), (23), (44), (64), (78),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (85), (87), (88), (99), (108), (347), (348), (366)
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1809.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (367)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (368)  all_58_5 = e2 & op(e2, e1) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (369)  all_58_5 = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (369) imply:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (370)  e2 = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (370) imply:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (371)  all_58_1 = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (13), (14), (15), (18), (30), (44),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (88), (99), (343), (344), (371) are
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1717.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (372)  all_58_10 = e2 & op(e2, e0) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (372) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (373)  op(e2, e0) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (13), (44), (47), (72), (78), (79),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (81), (88), (91), (150), (310), (313), (317),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (334), (343), (351), (352), (362), (373) are
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #294.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | |   (374)  all_58_7 = e2 & op(e1, e2) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (13), (14), (15), (18), (30), (44),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | |            (78), (88), (99), (343), (344), (347), (374) are
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #874.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | |   (375)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (375) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | |   (376)  all_58_8 = e2 & op(e1, e1) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (376) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | |   (377)  op(e1, e1) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (44), (62), (70), (78), (108), (145), (150),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | |            (377) are inconsistent by sub-proof #2115.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | |   (378)  all_58_11 = e2 & op(e1, e0) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (312), (323), (378) are inconsistent by
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #293.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |   (379)  all_58_3 = e2 & op(e2, e2) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (379) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |   (380)  op(e2, e2) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (44), (78), (380) are inconsistent by
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2140.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | |   (381)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | BETA: splitting (381) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |   (382)  all_58_7 = e2 & op(e1, e2) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (382) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |   (383)  all_58_7 = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (343), (383) imply:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |   (384)  e2 = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (384) imply:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |   (385)  all_58_14 = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (44), (74), (78), (95), (99), (290), (296),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |            (385) are inconsistent by sub-proof #417.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |   (386)  all_58_13 = e2 & op(e0, e2) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (386) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |   (387)  op(e0, e2) = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (78), (290), (387) are inconsistent by
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | |   (388)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 240.46/46.99  | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 240.46/46.99  | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | BETA: splitting (388) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | |   (389)  all_58_8 = e1 & op(e1, e1) = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | ALPHA: (389) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | |   (390)  op(e1, e1) = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (78), (108), (390) are inconsistent by
% 240.46/46.99  | | | | | | | | | | | | | | | | | | |            sub-proof #468.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | |   (391)  all_58_11 = e1 & op(e1, e0) = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | | | | |   (392)  op(e1, e0) = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (14), (20), (24), (42), (43), (44),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | |            (45), (49), (56), (61), (62), (63), (71), (78),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | |            (88), (89), (90), (91), (93), (99), (106), (108),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | |            (145), (149), (293), (300), (316), (329), (330),
% 240.46/46.99  | | | | | | | | | | | | | | | | | | |            (338), (392) are inconsistent by sub-proof #291.
% 240.46/46.99  | | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | |   (393)  all_58_10 = e1 & op(e2, e0) = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | ALPHA: (393) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | |   (394)  all_58_10 = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (26), (30), (44), (70), (77), (88),
% 240.46/46.99  | | | | | | | | | | | | | | | |            (99), (394) are inconsistent by sub-proof #992.
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | |   (395)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 240.46/46.99  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.46/46.99  | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | BETA: splitting (395) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | |   (396)  all_58_11 = e1 & op(e1, e0) = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | ALPHA: (396) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | |   (397)  op(e1, e0) = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | Case 1:
% 240.46/46.99  | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | |   (398)  all_54_11 = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (398) imply:
% 240.46/46.99  | | | | | | | | | | | | | | | | |   (399)  all_12_0 = e2
% 240.46/46.99  | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | REDUCE: (331), (399) imply:
% 240.46/46.99  | | | | | | | | | | | | | | | | |   (400)  $false
% 240.46/46.99  | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | CLOSE: (400) is inconsistent.
% 240.46/46.99  | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | |   (401)  all_54_11 = e1 | all_54_11 = e0
% 240.46/46.99  | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (14), (20), (24), (42), (43), (44),
% 240.46/46.99  | | | | | | | | | | | | | | | | |            (45), (49), (56), (61), (62), (63), (71), (78),
% 240.46/46.99  | | | | | | | | | | | | | | | | |            (88), (89), (90), (91), (93), (99), (106), (108),
% 240.46/46.99  | | | | | | | | | | | | | | | | |            (145), (149), (293), (300), (316), (329), (330),
% 240.46/46.99  | | | | | | | | | | | | | | | | |            (397), (401) are inconsistent by sub-proof #291.
% 240.46/46.99  | | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | |   (402)  all_58_15 = e1 & op(e0, e0) = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | ALPHA: (402) implies:
% 240.46/46.99  | | | | | | | | | | | | | | | |   (403)  all_58_15 = e1
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (25), (44), (54), (78), (108), (145),
% 240.46/46.99  | | | | | | | | | | | | | | | |            (290), (403) are inconsistent by sub-proof #1746.
% 240.46/46.99  | | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | End of split
% 240.46/46.99  | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | Case 2:
% 240.46/46.99  | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | |   (404)   ~ (all_12_1 = e2) & op(e0, e3) = all_12_1 &
% 240.46/46.99  | | | | | | | | | | | | | |          $i(all_12_1)
% 240.46/46.99  | | | | | | | | | | | | | | 
% 240.46/46.99  | | | | | | | | | | | | | | ALPHA: (404) implies:
% 240.46/46.99  | | | | | | | | | | | | | |   (405)   ~ (all_12_1 = e2)
% 240.46/46.99  | | | | | | | | | | | | | |   (406)  op(e0, e3) = all_12_1
% 240.46/46.99  | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_12_1, all_26_1, e3,
% 240.46/47.00  | | | | | | | | | | | | | |              e0, simplifying with (313), (406) gives:
% 240.46/47.00  | | | | | | | | | | | | | |   (407)  all_26_1 = all_12_1
% 240.46/47.00  | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with e1, all_26_1, e3, e0,
% 240.46/47.00  | | | | | | | | | | | | | |              simplifying with (310), (313) gives:
% 240.46/47.00  | | | | | | | | | | | | | |   (408)  all_26_1 = e1
% 240.46/47.00  | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | COMBINE_EQS: (407), (408) imply:
% 240.46/47.00  | | | | | | | | | | | | | |   (409)  all_12_1 = e1
% 240.46/47.00  | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | SIMP: (409) implies:
% 240.46/47.00  | | | | | | | | | | | | | |   (410)  all_12_1 = e1
% 240.46/47.00  | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | REDUCE: (314), (408) imply:
% 240.46/47.00  | | | | | | | | | | | | | |   (411)  op(e1, e0) = all_26_0
% 240.46/47.00  | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_14, all_26_0, e0,
% 240.46/47.00  | | | | | | | | | | | | | |              e1, simplifying with (22), (411) gives:
% 240.46/47.00  | | | | | | | | | | | | | |   (412)  all_52_14 = all_26_0
% 240.46/47.00  | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | REDUCE: (57), (412) imply:
% 240.46/47.00  | | | | | | | | | | | | | |   (413)   ~ (all_26_0 = e3)
% 240.46/47.00  | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 240.46/47.00  | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | |   (414)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 240.46/47.00  | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 240.46/47.00  | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | BETA: splitting (414) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | |   (415)  all_58_2 = e2 & op(e2, e3) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | ALPHA: (415) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | |   (416)  all_58_2 = e2
% 240.46/47.00  | | | | | | | | | | | | | | | |   (417)  op(e2, e3) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | |   (418)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | BETA: splitting (418) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (419)  all_58_2 = e0 & op(e2, e3) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | ALPHA: (419) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (420)  op(e2, e3) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (55), (78), (98), (417), (420) are
% 240.46/47.00  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #733.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (421)  all_58_3 = e0 & op(e2, e2) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | ALPHA: (421) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (422)  all_58_3 = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (30), (422) are inconsistent by sub-proof
% 240.46/47.00  | | | | | | | | | | | | | | | | | |            #1460.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | |   (423)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 240.46/47.00  | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | BETA: splitting (423) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (424)  all_58_5 = e0 & op(e2, e1) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | ALPHA: (424) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (425)  op(e2, e1) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (42), (78), (88), (425) are inconsistent by
% 240.46/47.00  | | | | | | | | | | | | | | | | | |            sub-proof #2165.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (426)  all_58_10 = e0 & op(e2, e0) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | ALPHA: (426) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (427)  op(e2, e0) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | |   (428)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 240.46/47.00  | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | BETA: splitting (428) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |   (429)  all_58_9 = e2 & op(e3, e0) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | ALPHA: (429) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |   (430)  all_58_9 = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |   (431)  op(e3, e0) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | |   (432)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (432) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |   (433)  all_58_9 = e1 & op(e3, e0) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (433) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |   (434)  all_58_9 = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (430), (434) are inconsistent by sub-proof
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |            #1605.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |   (435)  all_58_10 = e1 & op(e2, e0) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (435) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |   (436)  all_58_10 = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (26), (30), (44), (70), (77), (88),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |            (99), (436) are inconsistent by sub-proof #992.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | |   (437)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (437) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |   (438)  all_58_11 = e1 & op(e1, e0) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (438) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |   (439)  all_58_11 = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |   (440)  op(e1, e0) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | |   (441)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (441) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |   (442)  all_58_0 = e1 & op(e3, e3) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (442) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |   (443)  op(e3, e3) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (32), (44), (66), (67), (78), (108), (149),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |            (431), (443) are inconsistent by sub-proof #1400.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |   (444)  all_58_1 = e1 & op(e3, e2) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (444) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |   (445)  op(e3, e2) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (446)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (446) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (447)  all_58_6 = e0 & op(e1, e3) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (448)  op(e1, e3) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_26_0, e1, e0, e1,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (411), (440) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (449)  all_26_0 = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_2, e0, e3, e1,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (82), (448) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (450)  all_52_2 = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_13, e0, e0, e2,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (92), (427) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (451)  all_52_13 = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_1, e2, e3, e2,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (56), (417) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (452)  all_52_1 = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_12, e2, e0, e3,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (51), (431) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (453)  all_52_12 = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_4, e1, e2, e3,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (67), (445) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (454)  all_52_4 = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (455)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (455) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (456)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_25 & $i(all_56_25)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (456) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (457)  op(e3, e0) = all_56_25
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (458)  op(e3, all_56_25) = e3
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with e2, all_56_25, e0, e3,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (431), (457) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)  all_56_25 = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (458), (459) imply:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (460)  op(e3, e2) = e3
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (108), (445), (460) are inconsistent by
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2265.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (461)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 &
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_6_1)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (81), (448), (461) are inconsistent by
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #443.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (462)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_27 & $i(all_56_27)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (30), (55), (70), (77), (78), (88),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (98), (416), (417), (427), (462) are inconsistent
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #778.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (463)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (463) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (464)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_29 & $i(all_56_29)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (14), (44), (52), (58), (60), (76),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (79), (81), (88), (91), (99), (108), (439),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (440), (448), (464) are inconsistent by sub-proof
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #412.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (465)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (465) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (466)  op(e0, all_56_31) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (466) imply:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (467)  op(e0, e3) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (88), (310), (313), (406), (467) are
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1387.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (468)  all_58_7 = e0 & op(e1, e2) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (78), (293), (468) are inconsistent by
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2022.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (469)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (20), (42), (44), (45), (62), (71),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (88), (99), (108), (149), (440), (469) are
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #292.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | |   (470)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (470) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |   (471)  all_58_4 = e1 & op(e3, e1) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (471) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |   (472)  all_58_4 = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |   (473)  op(e3, e1) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (9), (11), (13), (17), (19), (24),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |            (25), (28), (29), (39), (41), (42), (44), (45),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |            (46), (50), (53), (54), (55), (56), (58), (59),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |            (62), (64), (68), (71), (72), (74), (78), (82),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |            (83), (88), (89), (92), (93), (94), (96), (98),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |            (99), (100), (472), (473) are inconsistent by
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #301.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |   (474)  all_58_9 = e1 & op(e3, e0) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (474) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |   (475)  all_58_9 = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (430), (475) are inconsistent by sub-proof
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | |            #1605.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |   (476)  all_58_15 = e1 & op(e0, e0) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (476) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |   (477)  all_58_15 = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (25), (44), (54), (78), (108), (145),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |            (290), (477) are inconsistent by sub-proof #1746.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |   (478)  all_58_10 = e2 & op(e2, e0) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | ALPHA: (478) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |   (479)  op(e2, e0) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (30), (70), (77), (78), (88), (416),
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |            (479) are inconsistent by sub-proof #840.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | |   (480)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 240.46/47.00  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | BETA: splitting (480) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |   (481)  all_58_11 = e2 & op(e1, e0) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (312), (411), (481) are inconsistent by
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |            sub-proof #293.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |   (482)  all_58_15 = e2 & op(e0, e0) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | ALPHA: (482) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |   (483)  op(e0, e0) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (74), (78), (483) are inconsistent by
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |            sub-proof #1388.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | |   (484)  all_58_3 = e2 & op(e2, e2) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | ALPHA: (484) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | |   (485)  op(e2, e2) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (44), (78), (485) are inconsistent by
% 240.46/47.00  | | | | | | | | | | | | | | | |            sub-proof #2140.
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | End of split
% 240.46/47.00  | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | |   (486)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 240.46/47.00  | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 240.46/47.00  | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | BETA: splitting (486) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | |   (487)  all_58_5 = e2 & op(e2, e1) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | ALPHA: (487) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | |   (488)  all_58_5 = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | REF_CLOSE: (70), (99), (488) are inconsistent by sub-proof
% 240.46/47.00  | | | | | | | | | | | | | | | |            #1665.
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | |   (489)  all_58_10 = e2 & op(e2, e0) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | ALPHA: (489) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | |   (490)  all_58_10 = e2
% 240.46/47.00  | | | | | | | | | | | | | | | |   (491)  op(e2, e0) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | |   (492)  all_58_9 = e0 & op(e3, e0) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | ALPHA: (492) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | |   (493)  op(e3, e0) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (78), (158), (493) are inconsistent by
% 240.46/47.00  | | | | | | | | | | | | | | | | |            sub-proof #2258.
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | |   (494)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 240.46/47.00  | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | BETA: splitting (494) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (495)  all_58_10 = e0 & op(e2, e0) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | ALPHA: (495) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (496)  op(e2, e0) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (78), (491), (496) are inconsistent by
% 240.46/47.00  | | | | | | | | | | | | | | | | | |            sub-proof #2121.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (497)  all_58_11 = e0 & op(e1, e0) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | ALPHA: (497) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | |   (498)  op(e1, e0) = e0
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | |   (499)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 240.46/47.00  | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | BETA: splitting (499) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |   (500)  all_58_9 = e1 & op(e3, e0) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | ALPHA: (500) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |   (501)  all_58_9 = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | |   (502)  op(e3, e0) = e1
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | |   (503)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (503) gives:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |   (504)  all_58_0 = e2 & op(e3, e3) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (504) implies:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |   (505)  op(e3, e3) = e2
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (78), (89), (505) are inconsistent by
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2194.
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.00  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | |   (506)  all_58_1 = e2 & op(e3, e2) = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (506) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | |   (507)  all_58_1 = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | |   (508)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (508) gives:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | |   (509)  all_58_6 = e1 & op(e1, e3) = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (509) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | |   (510)  op(e1, e3) = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (82), (308), (510) are inconsistent by
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1948.
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | |   (511)  all_58_7 = e1 & op(e1, e2) = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (511) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | |   (512)  all_58_7 = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | |   (513)  op(e1, e2) = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (514)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (514) gives:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (515)  all_58_6 = e2 & op(e1, e3) = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (515) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (516)  all_58_6 = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (517)  op(e1, e3) = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_26_0, e0, e0, e1,
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (411), (498) gives:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (518)  all_26_0 = e0
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_2, e2, e3, e1,
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (82), (517) gives:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (519)  all_52_2 = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_13, e2, e0, e2,
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (92), (491) gives:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (520)  all_52_13 = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_12, e1, e0, e3,
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (51), (502) gives:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (521)  all_52_12 = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (13), (44), (47), (72), (78), (79),
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            (81), (88), (91), (150), (310), (313), (406),
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            (491), (498), (502), (512), (516), (517) are
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #294.
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (522)  all_58_7 = e2 & op(e1, e2) = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (13), (14), (15), (18), (30), (44),
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (88), (99), (507), (512), (513), (522) are
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #290.
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (523)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (523) gives:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (524)  all_58_8 = e2 & op(e1, e1) = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (524) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (525)  op(e1, e1) = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (44), (62), (70), (78), (108), (145), (150),
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            (525) are inconsistent by sub-proof #2115.
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (526)  all_58_11 = e2 & op(e1, e0) = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (526) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (527)  all_58_11 = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (16), (24), (38), (74), (78), (88),
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            (99), (108), (491), (527) are inconsistent by
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1344.
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | |   (528)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (78), (88), (108), (498), (528) are
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #289.
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | |   (529)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (529) gives:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | |   (530)  all_58_4 = e2 & op(e3, e1) = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (530) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | |   (531)  all_58_4 = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (28), (70), (79), (88), (145), (531)
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #848.
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | |   (532)  all_58_9 = e2 & op(e3, e0) = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (532) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | |   (533)  all_58_9 = e2
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (501), (533) imply:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | |   (534)  e2 = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | SIMP: (534) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | |   (535)  e2 = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (490), (535) imply:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | |   (536)  all_58_10 = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (26), (30), (44), (70), (77), (88),
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | |            (99), (536) are inconsistent by sub-proof #992.
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | |   (537)  all_58_10 = e1 & op(e2, e0) = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | ALPHA: (537) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | |   (538)  all_58_10 = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (26), (30), (44), (70), (77), (88),
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | |            (99), (538) are inconsistent by sub-proof #992.
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | |   (539)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 240.46/47.01  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | BETA: splitting (539) gives:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | |   (540)  all_58_11 = e1 & op(e1, e0) = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | ALPHA: (540) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | |   (541)  op(e1, e0) = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (88), (498), (541) are inconsistent by
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | |   (542)  all_58_15 = e1 & op(e0, e0) = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | ALPHA: (542) implies:
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | |   (543)  all_58_15 = e1
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (25), (44), (54), (78), (108), (145),
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | |            (290), (543) are inconsistent by sub-proof #1746.
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | |   (544)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 &
% 240.46/47.01  | | | | | | | | | | | | |          $i(all_26_1)
% 240.46/47.01  | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | | REF_CLOSE: (78), (310), (544) are inconsistent by sub-proof
% 240.46/47.01  | | | | | | | | | | | | |            #1386.
% 240.46/47.01  | | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | |   (545)  all_54_12 = e0
% 240.46/47.01  | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | | REF_CLOSE: (48), (292), (545) are inconsistent by sub-proof
% 240.46/47.01  | | | | | | | | | | | |            #2068.
% 240.46/47.01  | | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | |   (546)  all_58_13 = e1 & op(e0, e2) = e1
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | ALPHA: (546) implies:
% 240.46/47.01  | | | | | | | | |   (547)  op(e0, e2) = e1
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | REF_CLOSE: (78), (88), (290), (547) are inconsistent by
% 240.46/47.01  | | | | | | | | |            sub-proof #1872.
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | 
% 240.46/47.01  | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | 
% 240.46/47.01  | | | | | | | |   (548)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 240.46/47.01  | | | | | | | |            op(e0, e0) = e1)
% 240.46/47.01  | | | | | | | | 
% 240.46/47.01  | | | | | | | | BETA: splitting (548) gives:
% 240.46/47.01  | | | | | | | | 
% 240.46/47.01  | | | | | | | | Case 1:
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | |   (549)  all_58_14 = e1 & op(e0, e1) = e1
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | ALPHA: (549) implies:
% 240.46/47.01  | | | | | | | | |   (550)  all_58_14 = e1
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | REF_CLOSE: (8), (13), (28), (44), (45), (62), (70), (78),
% 240.46/47.01  | | | | | | | | |            (88), (99), (108), (149), (550) are inconsistent by
% 240.46/47.01  | | | | | | | | |            sub-proof #1248.
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | Case 2:
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | |   (551)  all_58_15 = e1 & op(e0, e0) = e1
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | ALPHA: (551) implies:
% 240.46/47.01  | | | | | | | | |   (552)  all_58_15 = e1
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | | REF_CLOSE: (7), (8), (25), (44), (54), (78), (108), (145),
% 240.46/47.01  | | | | | | | | |            (290), (552) are inconsistent by sub-proof #1746.
% 240.46/47.01  | | | | | | | | | 
% 240.46/47.01  | | | | | | | | End of split
% 240.46/47.01  | | | | | | | | 
% 240.46/47.01  | | | | | | | End of split
% 240.46/47.01  | | | | | | | 
% 240.46/47.01  | | | | | | End of split
% 240.46/47.01  | | | | | | 
% 240.46/47.01  | | | | | End of split
% 240.46/47.01  | | | | | 
% 240.46/47.01  | | | | Case 2:
% 240.46/47.01  | | | | | 
% 240.46/47.01  | | | | |   (553)  all_58_5 = e0 & op(e2, e1) = e0
% 240.46/47.01  | | | | | 
% 240.46/47.01  | | | | | ALPHA: (553) implies:
% 240.46/47.01  | | | | |   (554)  op(e2, e1) = e0
% 240.46/47.01  | | | | | 
% 240.46/47.01  | | | | | REF_CLOSE: (12), (42), (78), (88), (554) are inconsistent by sub-proof
% 240.46/47.01  | | | | |            #2165.
% 240.46/47.01  | | | | | 
% 240.46/47.01  | | | | End of split
% 240.46/47.01  | | | | 
% 240.46/47.01  | | | Case 2:
% 240.46/47.01  | | | | 
% 240.46/47.01  | | | |   (555)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 240.46/47.01  | | | |              e1) = e0)
% 240.46/47.01  | | | | 
% 240.46/47.01  | | | | REF_CLOSE: (8), (9), (13), (39), (41), (42), (62), (71), (78), (100),
% 240.46/47.01  | | | |            (146), (555) are inconsistent by sub-proof #306.
% 240.46/47.01  | | | | 
% 240.46/47.01  | | | End of split
% 240.46/47.01  | | | 
% 240.46/47.01  | | End of split
% 240.46/47.01  | | 
% 240.46/47.01  | End of split
% 240.46/47.01  | 
% 240.46/47.01  End of proof
% 240.46/47.01  
% 240.46/47.01  Sub-proof #289 shows that the following formulas are inconsistent:
% 240.46/47.01  ----------------------------------------------------------------
% 240.46/47.01    (1)  op(e1, e0) = e0
% 240.46/47.01    (2)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.46/47.01    (3)   ~ (e3 = e1)
% 240.46/47.01    (4)  op(e1, e1) = e3
% 240.46/47.01    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.01    (6)   ~ (e1 = e0)
% 240.46/47.01  
% 240.46/47.01  Begin of proof
% 240.46/47.01  | 
% 240.46/47.01  | BETA: splitting (2) gives:
% 240.46/47.01  | 
% 240.46/47.01  | Case 1:
% 240.46/47.01  | | 
% 240.46/47.01  | |   (7)  all_58_8 = e1 & op(e1, e1) = e1
% 240.46/47.01  | | 
% 240.46/47.01  | | ALPHA: (7) implies:
% 240.46/47.01  | |   (8)  op(e1, e1) = e1
% 240.46/47.01  | | 
% 240.46/47.01  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #468.
% 240.46/47.01  | | 
% 240.46/47.01  | Case 2:
% 240.46/47.01  | | 
% 240.46/47.01  | |   (9)  all_58_11 = e1 & op(e1, e0) = e1
% 240.46/47.01  | | 
% 240.46/47.01  | | ALPHA: (9) implies:
% 240.46/47.01  | |   (10)  op(e1, e0) = e1
% 240.46/47.01  | | 
% 240.46/47.01  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #2284.
% 240.46/47.01  | | 
% 240.46/47.01  | End of split
% 240.46/47.01  | 
% 240.46/47.01  End of proof
% 240.46/47.01  
% 240.46/47.01  Sub-proof #290 shows that the following formulas are inconsistent:
% 240.46/47.01  ----------------------------------------------------------------
% 240.46/47.01    (1)  op(e2, e2) = e3
% 240.46/47.01    (2)   ~ (e3 = e0)
% 240.46/47.01    (3)  op(e1, e2) = e1
% 240.46/47.01    (4)   ~ (e2 = e0)
% 240.46/47.01    (5)  op(e1, e2) = all_52_6
% 240.46/47.01    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.46/47.01         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.46/47.01    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.46/47.01         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.46/47.01    (8)  all_58_3 = e3
% 240.46/47.01    (9)   ~ (e3 = e2)
% 240.46/47.01    (10)  all_58_7 = e1
% 240.46/47.01    (11)  all_58_1 = e2
% 240.46/47.01    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.01    (13)   ~ (e1 = e0)
% 240.46/47.01    (14)  all_58_7 = e2 & op(e1, e2) = e2
% 240.46/47.01    (15)   ~ (e2 = e1)
% 240.46/47.01  
% 240.46/47.01  Begin of proof
% 240.46/47.01  | 
% 240.46/47.01  | ALPHA: (14) implies:
% 240.46/47.01  |   (16)  all_58_7 = e2
% 240.46/47.01  | 
% 240.46/47.01  | COMBINE_EQS: (10), (16) imply:
% 240.46/47.01  |   (17)  e2 = e1
% 240.46/47.01  | 
% 240.46/47.01  | SIMP: (17) implies:
% 240.46/47.01  |   (18)  e2 = e1
% 240.46/47.01  | 
% 240.46/47.01  | COMBINE_EQS: (11), (18) imply:
% 240.46/47.01  |   (19)  all_58_1 = e1
% 240.46/47.01  | 
% 240.46/47.01  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 240.46/47.01  |            (15), (19) are inconsistent by sub-proof #1717.
% 240.46/47.01  | 
% 240.46/47.01  End of proof
% 240.46/47.01  
% 240.46/47.01  Sub-proof #291 shows that the following formulas are inconsistent:
% 240.46/47.01  ----------------------------------------------------------------
% 240.46/47.01    (1)   ~ (e3 = e0)
% 240.46/47.01    (2)   ~ (e2 = e0)
% 240.46/47.01    (3)  op(e1, e2) = all_52_6
% 240.46/47.01    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.46/47.01         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.46/47.01    (5)   ~ (all_52_13 = e1)
% 240.46/47.01    (6)  all_58_14 = e2
% 240.46/47.01    (7)  all_58_15 = e3
% 240.46/47.01    (8)   ~ (all_52_6 = e0)
% 240.46/47.01    (9)   ~ (e3 = e1)
% 240.46/47.01    (10)  op(e1, e0) = e1
% 240.46/47.01    (11)   ~ (all_12_0 = e1)
% 240.46/47.01    (12)  all_54_11 = all_12_0
% 240.46/47.01    (13)  op(e2, e1) = all_52_9
% 240.46/47.01    (14)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.46/47.01          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.46/47.01    (15)   ~ (e3 = e2)
% 240.46/47.01    (16)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.46/47.01          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.46/47.01    (17)  all_54_11 = e1 | all_54_11 = e0
% 240.46/47.01    (18)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.46/47.01    (19)   ~ (all_52_13 = all_12_0)
% 240.46/47.01    (20)  op(e2, e3) = all_52_1
% 240.46/47.01    (21)   ~ (all_52_1 = all_52_13)
% 240.46/47.01    (22)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.46/47.01          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.46/47.01    (23)  all_54_7 = all_52_13
% 240.46/47.01    (24)   ~ (all_52_9 = e3)
% 240.46/47.01    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.01    (26)   ~ (e1 = e0)
% 240.46/47.01    (27)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.46/47.01          | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.46/47.01    (28)  op(e3, e3) = e3
% 240.46/47.01    (29)   ~ (all_52_13 = e3)
% 240.46/47.01    (30)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.46/47.01          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.46/47.01    (31)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.46/47.01          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.46/47.01            e1)
% 240.46/47.01    (32)  all_58_4 = e0
% 240.46/47.01    (33)   ~ (e2 = e1)
% 240.46/47.01  
% 240.46/47.01  Begin of proof
% 240.46/47.01  | 
% 240.46/47.01  | BETA: splitting (30) gives:
% 240.46/47.01  | 
% 240.46/47.01  | Case 1:
% 240.46/47.01  | | 
% 240.46/47.01  | |   (34)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 240.46/47.01  | |           e0)
% 240.46/47.01  | | 
% 240.46/47.01  | | BETA: splitting (34) gives:
% 240.46/47.01  | | 
% 240.46/47.01  | | Case 1:
% 240.46/47.01  | | | 
% 240.46/47.01  | | |   (35)  all_58_6 = e0 & op(e1, e3) = e0
% 240.46/47.01  | | | 
% 240.46/47.01  | | | ALPHA: (35) implies:
% 240.46/47.01  | | |   (36)  all_58_6 = e0
% 240.46/47.01  | | | 
% 240.46/47.01  | | | REF_CLOSE: (2), (5), (6), (7), (9), (11), (12), (14), (15), (17), (18),
% 240.46/47.01  | | |            (19), (20), (21), (23), (25), (26), (27), (28), (29), (31),
% 240.46/47.01  | | |            (33), (36) are inconsistent by sub-proof #295.
% 240.46/47.01  | | | 
% 240.46/47.01  | | Case 2:
% 240.46/47.01  | | | 
% 240.46/47.01  | | |   (37)  all_58_7 = e0 & op(e1, e2) = e0
% 240.46/47.01  | | | 
% 240.46/47.01  | | | REF_CLOSE: (3), (8), (25), (37) are inconsistent by sub-proof #2022.
% 240.46/47.01  | | | 
% 240.46/47.01  | | End of split
% 240.46/47.01  | | 
% 240.46/47.01  | Case 2:
% 240.46/47.01  | | 
% 240.46/47.01  | |   (38)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.46/47.01  | |           e0)
% 240.46/47.01  | | 
% 240.46/47.01  | | REF_CLOSE: (1), (2), (4), (9), (10), (13), (15), (16), (22), (24), (25),
% 240.46/47.01  | |            (26), (32), (33), (38) are inconsistent by sub-proof #292.
% 240.46/47.01  | | 
% 240.46/47.01  | End of split
% 240.46/47.01  | 
% 240.46/47.01  End of proof
% 240.46/47.01  
% 240.46/47.01  Sub-proof #292 shows that the following formulas are inconsistent:
% 240.46/47.01  ----------------------------------------------------------------
% 240.46/47.01    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.46/47.01    (2)   ~ (e3 = e0)
% 240.46/47.01    (3)   ~ (e2 = e0)
% 240.46/47.02    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.46/47.02         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.46/47.02    (5)   ~ (e3 = e1)
% 240.46/47.02    (6)  op(e1, e0) = e1
% 240.46/47.02    (7)  op(e2, e1) = all_52_9
% 240.46/47.02    (8)   ~ (e3 = e2)
% 240.46/47.02    (9)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.46/47.02         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.46/47.02    (10)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.46/47.02          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.46/47.02    (11)   ~ (all_52_9 = e3)
% 240.46/47.02    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.02    (13)   ~ (e1 = e0)
% 240.46/47.02    (14)  all_58_4 = e0
% 240.46/47.02    (15)   ~ (e2 = e1)
% 240.46/47.02  
% 240.46/47.02  Begin of proof
% 240.46/47.02  | 
% 240.46/47.02  | BETA: splitting (1) gives:
% 240.46/47.02  | 
% 240.46/47.02  | Case 1:
% 240.46/47.02  | | 
% 240.46/47.02  | |   (16)  all_58_8 = e0 & op(e1, e1) = e0
% 240.46/47.02  | | 
% 240.46/47.02  | | ALPHA: (16) implies:
% 240.46/47.02  | |   (17)  op(e1, e1) = e0
% 240.46/47.02  | | 
% 240.46/47.02  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 240.46/47.02  | |            (15), (17) are inconsistent by sub-proof #1662.
% 240.46/47.02  | | 
% 240.46/47.02  | Case 2:
% 240.46/47.02  | | 
% 240.46/47.02  | |   (18)  all_58_11 = e0 & op(e1, e0) = e0
% 240.46/47.02  | | 
% 240.46/47.02  | | ALPHA: (18) implies:
% 240.46/47.02  | |   (19)  op(e1, e0) = e0
% 240.46/47.02  | | 
% 240.46/47.02  | | REF_CLOSE: (6), (12), (13), (19) are inconsistent by sub-proof #2284.
% 240.46/47.02  | | 
% 240.46/47.02  | End of split
% 240.46/47.02  | 
% 240.46/47.02  End of proof
% 240.46/47.02  
% 240.46/47.02  Sub-proof #293 shows that the following formulas are inconsistent:
% 240.46/47.02  ----------------------------------------------------------------
% 240.46/47.02    (1)  all_58_11 = e2 & op(e1, e0) = e2
% 240.46/47.02    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.02    (3)  op(e1, e0) = all_26_0
% 240.46/47.02    (4)   ~ (all_26_0 = e2)
% 240.46/47.02  
% 240.46/47.02  Begin of proof
% 240.46/47.02  | 
% 240.46/47.02  | ALPHA: (1) implies:
% 240.46/47.02  |   (5)  op(e1, e0) = e2
% 240.46/47.02  | 
% 240.46/47.02  | GROUND_INST: instantiating (2) with all_26_0, e2, e0, e1, simplifying with
% 240.46/47.02  |              (3), (5) gives:
% 240.46/47.02  |   (6)  all_26_0 = e2
% 240.46/47.02  | 
% 240.46/47.02  | REDUCE: (4), (6) imply:
% 240.46/47.02  |   (7)  $false
% 240.46/47.02  | 
% 240.46/47.02  | CLOSE: (7) is inconsistent.
% 240.46/47.02  | 
% 240.46/47.02  End of proof
% 240.46/47.02  
% 240.46/47.02  Sub-proof #294 shows that the following formulas are inconsistent:
% 240.46/47.02  ----------------------------------------------------------------
% 240.46/47.02    (1)  op(e2, e2) = e3
% 240.46/47.02    (2)   ~ (e3 = e0)
% 240.46/47.02    (3)  op(e1, e0) = e0
% 240.46/47.02    (4)   ~ (e2 = e0)
% 240.46/47.02    (5)  all_58_6 = e2
% 240.46/47.02    (6)  op(e3, e0) = e1
% 240.46/47.02    (7)  op(e3, e1) = e0
% 240.46/47.02    (8)  op(e1, e3) = e2
% 240.46/47.02    (9)   ~ (e3 = e2)
% 240.46/47.02    (10)  op(e0, e3) = e1
% 240.46/47.02    (11)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.46/47.02            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.46/47.02            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.46/47.02            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.46/47.02            op(e0, all_56_31) = e0)
% 240.46/47.02    (12)  op(e2, e0) = e2
% 240.46/47.02    (13)  op(e0, e3) = all_26_1
% 240.46/47.02    (14)  op(e0, e3) = all_12_1
% 240.46/47.02    (15)  all_58_7 = e1
% 240.46/47.02    (16)  all_56_31 = e3
% 240.46/47.02    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.02    (18)  all_58_8 = e3
% 240.46/47.02    (19)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.46/47.02            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.46/47.02              e3) = all_46_1 & $i(all_46_1))
% 240.46/47.02    (20)   ~ (e1 = e0)
% 240.46/47.02    (21)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.46/47.02          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.46/47.02  
% 240.46/47.02  Begin of proof
% 240.46/47.02  | 
% 240.46/47.02  | BETA: splitting (11) gives:
% 240.46/47.02  | 
% 240.46/47.02  | Case 1:
% 240.46/47.02  | | 
% 240.46/47.02  | |   (22)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.46/47.02  | |           $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 240.46/47.02  | |             e0) = all_56_27 & $i(all_56_27))
% 240.46/47.02  | | 
% 240.46/47.02  | | BETA: splitting (22) gives:
% 240.46/47.02  | | 
% 240.46/47.02  | | Case 1:
% 240.46/47.02  | | | 
% 240.46/47.02  | | |   (23)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.46/47.02  | | |         $i(all_56_25)
% 240.46/47.02  | | | 
% 240.46/47.02  | | | ALPHA: (23) implies:
% 240.46/47.02  | | |   (24)  op(e3, e0) = all_56_25
% 240.46/47.02  | | |   (25)  op(e3, all_56_25) = e3
% 240.46/47.02  | | | 
% 240.46/47.02  | | | BETA: splitting (19) gives:
% 240.46/47.02  | | | 
% 240.46/47.02  | | | Case 1:
% 240.46/47.02  | | | | 
% 240.46/47.02  | | | | 
% 240.46/47.02  | | | | GROUND_INST: instantiating (17) with e1, all_56_25, e0, e3, simplifying
% 240.46/47.02  | | | |              with (6), (24) gives:
% 240.46/47.02  | | | |   (26)  all_56_25 = e1
% 240.46/47.02  | | | | 
% 240.46/47.02  | | | | REDUCE: (25), (26) imply:
% 240.46/47.02  | | | |   (27)  op(e3, e1) = e3
% 240.46/47.02  | | | | 
% 240.46/47.02  | | | | REF_CLOSE: (2), (7), (17), (27) are inconsistent by sub-proof #2118.
% 240.46/47.02  | | | | 
% 240.46/47.02  | | | Case 2:
% 240.46/47.02  | | | | 
% 240.46/47.02  | | | |   (28)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.46/47.02  | | | | 
% 240.46/47.02  | | | | REF_CLOSE: (8), (17), (28) are inconsistent by sub-proof #395.
% 240.46/47.02  | | | | 
% 240.46/47.02  | | | End of split
% 240.46/47.02  | | | 
% 240.46/47.02  | | Case 2:
% 240.46/47.02  | | | 
% 240.46/47.02  | | |   (29)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 240.46/47.02  | | |         $i(all_56_27)
% 240.46/47.02  | | | 
% 240.46/47.02  | | | ALPHA: (29) implies:
% 240.46/47.02  | | |   (30)  op(e2, e0) = all_56_27
% 240.46/47.02  | | |   (31)  op(e2, all_56_27) = e2
% 240.46/47.02  | | | 
% 240.46/47.02  | | | REF_CLOSE: (1), (9), (12), (17), (30), (31) are inconsistent by sub-proof
% 240.46/47.02  | | |            #954.
% 240.46/47.02  | | | 
% 240.46/47.02  | | End of split
% 240.46/47.02  | | 
% 240.46/47.02  | Case 2:
% 240.46/47.02  | | 
% 240.46/47.02  | |   (32)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 240.46/47.02  | |           $i(all_56_29)) | (all_56_30 = e0 & op(e0, all_56_31) = e0)
% 240.46/47.02  | | 
% 240.46/47.02  | | BETA: splitting (32) gives:
% 240.46/47.02  | | 
% 240.46/47.02  | | Case 1:
% 240.46/47.02  | | | 
% 240.46/47.02  | | |   (33)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 240.46/47.02  | | |         $i(all_56_29)
% 240.46/47.02  | | | 
% 240.46/47.02  | | | REF_CLOSE: (2), (3), (4), (5), (8), (15), (17), (18), (19), (20), (21),
% 240.46/47.02  | | |            (33) are inconsistent by sub-proof #308.
% 240.46/47.02  | | | 
% 240.46/47.02  | | Case 2:
% 240.46/47.02  | | | 
% 240.46/47.02  | | |   (34)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.46/47.02  | | | 
% 240.46/47.02  | | | ALPHA: (34) implies:
% 240.46/47.02  | | |   (35)  op(e0, all_56_31) = e0
% 240.46/47.02  | | | 
% 240.46/47.02  | | | REDUCE: (16), (35) imply:
% 240.46/47.02  | | |   (36)  op(e0, e3) = e0
% 240.46/47.02  | | | 
% 240.46/47.02  | | | REF_CLOSE: (10), (13), (14), (17), (20), (36) are inconsistent by
% 240.46/47.02  | | |            sub-proof #1387.
% 240.46/47.02  | | | 
% 240.46/47.02  | | End of split
% 240.46/47.02  | | 
% 240.46/47.02  | End of split
% 240.46/47.02  | 
% 240.46/47.02  End of proof
% 240.46/47.02  
% 240.46/47.02  Sub-proof #295 shows that the following formulas are inconsistent:
% 240.46/47.02  ----------------------------------------------------------------
% 240.46/47.02    (1)   ~ (e2 = e0)
% 240.46/47.02    (2)   ~ (all_52_13 = e1)
% 240.46/47.02    (3)  all_58_14 = e2
% 240.46/47.02    (4)  all_58_15 = e3
% 240.46/47.02    (5)   ~ (e3 = e1)
% 240.46/47.02    (6)   ~ (all_12_0 = e1)
% 240.46/47.02    (7)  all_54_11 = all_12_0
% 240.46/47.02    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.46/47.02         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.46/47.02    (9)   ~ (e3 = e2)
% 240.46/47.02    (10)  all_58_6 = e0
% 240.46/47.02    (11)  all_54_11 = e1 | all_54_11 = e0
% 240.46/47.02    (12)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.46/47.02    (13)   ~ (all_52_13 = all_12_0)
% 240.46/47.02    (14)  op(e2, e3) = all_52_1
% 240.46/47.02    (15)   ~ (all_52_1 = all_52_13)
% 240.46/47.02    (16)  all_54_7 = all_52_13
% 240.46/47.02    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.02    (18)   ~ (e1 = e0)
% 240.46/47.02    (19)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.46/47.02          | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.46/47.02    (20)  op(e3, e3) = e3
% 240.46/47.02    (21)   ~ (all_52_13 = e3)
% 240.46/47.02    (22)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.46/47.02          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.46/47.02            e1)
% 240.46/47.02    (23)   ~ (e2 = e1)
% 240.46/47.02  
% 240.46/47.02  Begin of proof
% 240.46/47.02  | 
% 240.46/47.02  | BETA: splitting (8) gives:
% 240.46/47.02  | 
% 240.46/47.02  | Case 1:
% 240.46/47.02  | | 
% 240.46/47.02  | |   (24)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 240.46/47.02  | |           e2)
% 240.46/47.02  | | 
% 240.46/47.02  | | BETA: splitting (24) gives:
% 240.46/47.02  | | 
% 240.46/47.02  | | Case 1:
% 240.46/47.02  | | | 
% 240.46/47.02  | | |   (25)  all_58_0 = e2 & op(e3, e3) = e2
% 240.46/47.02  | | | 
% 240.46/47.02  | | | ALPHA: (25) implies:
% 240.46/47.02  | | |   (26)  op(e3, e3) = e2
% 240.46/47.02  | | | 
% 240.46/47.02  | | | REF_CLOSE: (9), (17), (20), (26) are inconsistent by sub-proof #2194.
% 240.46/47.02  | | | 
% 240.46/47.02  | | Case 2:
% 240.46/47.02  | | | 
% 240.46/47.02  | | |   (27)  all_58_2 = e2 & op(e2, e3) = e2
% 240.46/47.02  | | | 
% 240.46/47.02  | | | REF_CLOSE: (2), (6), (7), (11), (12), (13), (14), (15), (16), (17), (21),
% 240.46/47.02  | | |            (27) are inconsistent by sub-proof #1304.
% 240.46/47.02  | | | 
% 240.46/47.02  | | End of split
% 240.46/47.02  | | 
% 240.46/47.02  | Case 2:
% 240.46/47.02  | | 
% 240.46/47.02  | |   (28)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 240.46/47.02  | |           e2)
% 240.46/47.02  | | 
% 240.46/47.02  | | BETA: splitting (28) gives:
% 240.46/47.02  | | 
% 240.46/47.02  | | Case 1:
% 240.46/47.02  | | | 
% 240.46/47.02  | | |   (29)  all_58_6 = e2 & op(e1, e3) = e2
% 240.46/47.02  | | | 
% 240.46/47.02  | | | REF_CLOSE: (1), (10), (29) are inconsistent by sub-proof #1444.
% 240.46/47.02  | | | 
% 240.46/47.02  | | Case 2:
% 240.46/47.02  | | | 
% 240.46/47.02  | | |   (30)  all_58_12 = e2 & op(e0, e3) = e2
% 240.46/47.02  | | | 
% 240.46/47.02  | | | ALPHA: (30) implies:
% 240.46/47.02  | | |   (31)  all_58_12 = e2
% 240.46/47.02  | | | 
% 240.46/47.02  | | | REF_CLOSE: (1), (3), (4), (5), (17), (18), (19), (22), (23), (31) are
% 240.46/47.02  | | |            inconsistent by sub-proof #1392.
% 240.46/47.02  | | | 
% 240.46/47.02  | | End of split
% 240.46/47.02  | | 
% 240.46/47.02  | End of split
% 240.46/47.02  | 
% 240.46/47.02  End of proof
% 240.46/47.02  
% 240.46/47.02  Sub-proof #296 shows that the following formulas are inconsistent:
% 240.46/47.02  ----------------------------------------------------------------
% 240.46/47.02    (1)   ~ (all_52_7 = e2)
% 240.46/47.02    (2)  op(e1, e2) = all_52_6
% 240.46/47.02    (3)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.46/47.02             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.46/47.02           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 240.46/47.02             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.46/47.02           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.46/47.02    (4)  op(e1, e2) = e0
% 240.46/47.02    (5)  op(e0, e2) = all_52_7
% 240.46/47.02    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.02    (7)   ~ (e1 = e0)
% 240.46/47.02  
% 240.46/47.02  Begin of proof
% 240.46/47.02  | 
% 240.46/47.02  | BETA: splitting (3) gives:
% 240.46/47.02  | 
% 240.46/47.02  | Case 1:
% 240.46/47.02  | | 
% 240.46/47.02  | |   (8)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.46/47.02  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 240.46/47.02  | |        & op(e1, e2) = e1
% 240.46/47.02  | | 
% 240.46/47.02  | | ALPHA: (8) implies:
% 240.46/47.02  | |   (9)  op(e1, e2) = e1
% 240.46/47.02  | | 
% 240.46/47.02  | | REF_CLOSE: (2), (4), (6), (7), (9) are inconsistent by sub-proof #2136.
% 240.46/47.02  | | 
% 240.46/47.02  | Case 2:
% 240.46/47.02  | | 
% 240.46/47.02  | |   (10)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.46/47.02  | |           = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) =
% 240.46/47.02  | |         e2 & op(e0, e2) = e2
% 240.46/47.02  | | 
% 240.46/47.02  | | ALPHA: (10) implies:
% 240.46/47.02  | |   (11)  op(e0, e2) = e2
% 240.46/47.02  | | 
% 240.46/47.02  | | REF_CLOSE: (1), (5), (6), (11) are inconsistent by sub-proof #2327.
% 240.46/47.02  | | 
% 240.46/47.02  | End of split
% 240.46/47.02  | 
% 240.46/47.02  End of proof
% 240.46/47.02  
% 240.46/47.02  Sub-proof #297 shows that the following formulas are inconsistent:
% 240.46/47.02  ----------------------------------------------------------------
% 240.46/47.02    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.46/47.02         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.46/47.02    (2)   ~ (e3 = e0)
% 240.46/47.02    (3)   ~ (e2 = e0)
% 240.46/47.02    (4)   ~ (e3 = e1)
% 240.46/47.02    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.46/47.02         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.46/47.02    (6)   ~ (e3 = e2)
% 240.46/47.02    (7)   ~ (all_52_1 = e0)
% 240.46/47.02    (8)  op(e2, e3) = all_52_1
% 240.46/47.02    (9)   ~ (all_52_4 = e3)
% 240.46/47.02    (10)  op(e3, e2) = all_52_4
% 240.46/47.02    (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.46/47.02          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.46/47.02    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.02    (13)   ~ (e1 = e0)
% 240.46/47.02    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 240.46/47.02    (15)  all_58_4 = e0
% 240.46/47.02    (16)   ~ (e2 = e1)
% 240.46/47.02  
% 240.46/47.02  Begin of proof
% 240.46/47.02  | 
% 240.46/47.02  | BETA: splitting (14) gives:
% 240.46/47.02  | 
% 240.46/47.02  | Case 1:
% 240.46/47.02  | | 
% 240.46/47.02  | |   (17)  all_58_0 = e0 & op(e3, e3) = e0
% 240.46/47.02  | | 
% 240.46/47.02  | | ALPHA: (17) implies:
% 240.46/47.02  | |   (18)  op(e3, e3) = e0
% 240.46/47.02  | | 
% 240.46/47.02  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (13), (15),
% 240.46/47.02  | |            (16), (18) are inconsistent by sub-proof #1512.
% 240.46/47.02  | | 
% 240.46/47.02  | Case 2:
% 240.46/47.02  | | 
% 240.46/47.02  | |   (19)  all_58_2 = e0 & op(e2, e3) = e0
% 240.46/47.02  | | 
% 240.46/47.02  | | REF_CLOSE: (7), (8), (12), (19) are inconsistent by sub-proof #1985.
% 240.46/47.02  | | 
% 240.46/47.02  | End of split
% 240.46/47.02  | 
% 240.46/47.02  End of proof
% 240.46/47.02  
% 240.46/47.02  Sub-proof #298 shows that the following formulas are inconsistent:
% 240.46/47.02  ----------------------------------------------------------------
% 240.46/47.02    (1)  op(e3, e1) = e0
% 240.46/47.02    (2)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.46/47.02         $i(all_56_17)
% 240.46/47.02    (3)  op(e3, e0) = all_52_12
% 240.46/47.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.02    (5)   ~ (all_52_12 = e3)
% 240.46/47.02  
% 240.46/47.02  Begin of proof
% 240.46/47.02  | 
% 240.46/47.02  | ALPHA: (2) implies:
% 240.46/47.02  |   (6)  op(e3, e1) = all_56_17
% 240.46/47.02  |   (7)  op(e3, all_56_17) = e3
% 240.46/47.02  | 
% 240.46/47.02  | GROUND_INST: instantiating (4) with e0, all_56_17, e1, e3, simplifying with
% 240.46/47.02  |              (1), (6) gives:
% 240.46/47.02  |   (8)  all_56_17 = e0
% 240.46/47.02  | 
% 240.46/47.02  | REDUCE: (7), (8) imply:
% 240.46/47.02  |   (9)  op(e3, e0) = e3
% 240.46/47.02  | 
% 240.46/47.02  | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #2179.
% 240.46/47.02  | 
% 240.46/47.02  End of proof
% 240.46/47.02  
% 240.46/47.02  Sub-proof #299 shows that the following formulas are inconsistent:
% 240.46/47.02  ----------------------------------------------------------------
% 240.46/47.02    (1)  op(e2, e1) = e1
% 240.46/47.02    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.02    (3)  op(e2, e1) = all_56_19
% 240.46/47.02    (4)  op(e2, all_56_19) = e2
% 240.46/47.02    (5)   ~ (e2 = e1)
% 240.46/47.02  
% 240.46/47.02  Begin of proof
% 240.46/47.02  | 
% 240.46/47.02  | GROUND_INST: instantiating (2) with e1, all_56_19, e1, e2, simplifying with
% 240.46/47.02  |              (1), (3) gives:
% 240.46/47.02  |   (6)  all_56_19 = e1
% 240.46/47.02  | 
% 240.46/47.02  | REDUCE: (4), (6) imply:
% 240.46/47.02  |   (7)  op(e2, e1) = e2
% 240.46/47.02  | 
% 240.46/47.02  | GROUND_INST: instantiating (2) with e1, e2, e1, e2, simplifying with (1), (7)
% 240.46/47.02  |              gives:
% 240.46/47.02  |   (8)  e2 = e1
% 240.46/47.02  | 
% 240.46/47.02  | REDUCE: (5), (8) imply:
% 240.46/47.03  |   (9)  $false
% 240.46/47.03  | 
% 240.46/47.03  | CLOSE: (9) is inconsistent.
% 240.46/47.03  | 
% 240.46/47.03  End of proof
% 240.46/47.03  
% 240.46/47.03  Sub-proof #300 shows that the following formulas are inconsistent:
% 240.46/47.03  ----------------------------------------------------------------
% 240.46/47.03    (1)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.46/47.03         $i(all_56_17)
% 240.46/47.03    (2)  op(e3, e1) = e2
% 240.46/47.03    (3)   ~ (all_52_4 = e3)
% 240.46/47.03    (4)  op(e3, e2) = all_52_4
% 240.46/47.03    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.03  
% 240.46/47.03  Begin of proof
% 240.46/47.03  | 
% 240.46/47.03  | ALPHA: (1) implies:
% 240.46/47.03  |   (6)  op(e3, e1) = all_56_17
% 240.46/47.03  |   (7)  op(e3, all_56_17) = e3
% 240.46/47.03  | 
% 240.46/47.03  | GROUND_INST: instantiating (5) with e2, all_56_17, e1, e3, simplifying with
% 240.46/47.03  |              (2), (6) gives:
% 240.46/47.03  |   (8)  all_56_17 = e2
% 240.46/47.03  | 
% 240.46/47.03  | REDUCE: (7), (8) imply:
% 240.46/47.03  |   (9)  op(e3, e2) = e3
% 240.46/47.03  | 
% 240.46/47.03  | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #2192.
% 240.46/47.03  | 
% 240.46/47.03  End of proof
% 240.46/47.03  
% 240.46/47.03  Sub-proof #301 shows that the following formulas are inconsistent:
% 240.46/47.03  ----------------------------------------------------------------
% 240.46/47.03    (1)  op(e2, e2) = e3
% 240.46/47.03    (2)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.46/47.03           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.46/47.03           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.46/47.03           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.46/47.03           & $i(all_56_23))
% 240.46/47.03    (3)   ~ (e3 = e0)
% 240.46/47.03    (4)  op(e0, e1) = all_52_11
% 240.46/47.03    (5)   ~ (all_52_8 = all_52_9)
% 240.46/47.03    (6)   ~ (e2 = e0)
% 240.46/47.03    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.46/47.03           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.46/47.03             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.46/47.03           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.46/47.03             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.46/47.03           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.03           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.46/47.03           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.46/47.03           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.46/47.03           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.46/47.03           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.46/47.03             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.46/47.03           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.46/47.03           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 240.46/47.03           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.46/47.03           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.46/47.03           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.46/47.03           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.46/47.03             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.46/47.03           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.46/47.03           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 240.46/47.03           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.46/47.03           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.46/47.03           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.46/47.03           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.46/47.03             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.46/47.03           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.03           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.46/47.03    (8)   ~ (all_52_7 = all_52_11)
% 240.46/47.03    (9)  all_58_15 = e3
% 240.46/47.03    (10)  op(e0, e3) = all_52_3
% 240.46/47.03    (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.46/47.03          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.46/47.03    (12)   ~ (all_52_2 = all_52_3)
% 240.46/47.03    (13)   ~ (all_52_11 = e3)
% 240.46/47.03    (14)  op(e3, e1) = all_52_8
% 240.46/47.03    (15)  op(e2, e1) = all_52_9
% 240.46/47.03    (16)   ~ (e3 = e2)
% 240.46/47.03    (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.46/47.03          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.46/47.03    (18)  op(e3, e1) = e1
% 240.46/47.03    (19)   ~ (all_52_3 = all_52_11)
% 240.46/47.03    (20)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.46/47.03          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.46/47.03    (21)   ~ (all_52_9 = all_52_13)
% 240.46/47.03    (22)   ~ (all_52_3 = e3)
% 240.46/47.03    (23)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.46/47.03            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.46/47.03              e3) = all_42_1 & $i(all_42_1))
% 240.46/47.03    (24)  all_58_4 = e1
% 240.46/47.03    (25)  op(e2, e3) = all_52_1
% 240.46/47.03    (26)  op(e1, e1) = e3
% 240.46/47.03    (27)   ~ (all_52_2 = e3)
% 240.46/47.03    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.46/47.03          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.46/47.03    (29)  op(e0, e2) = all_52_7
% 240.46/47.03    (30)   ~ (all_52_8 = all_52_11)
% 240.46/47.03    (31)   ~ (all_52_9 = e3)
% 240.46/47.03    (32)  all_56_31 = e3
% 240.46/47.03    (33)  op(e0, e0) = e3
% 240.46/47.03    (34)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.03    (35)  op(e1, e3) = all_52_2
% 240.46/47.03    (36)  all_56_21 = e3
% 240.46/47.03    (37)   ~ (e1 = e0)
% 240.46/47.03    (38)  op(e3, e3) = e3
% 240.46/47.03    (39)  op(e2, e0) = all_52_13
% 240.46/47.03    (40)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.46/47.03          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.46/47.03            e1)
% 240.46/47.03    (41)   ~ (all_52_1 = e3)
% 240.46/47.03    (42)   ~ (all_52_9 = all_52_11)
% 240.46/47.03    (43)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.46/47.03            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.46/47.03            & $i(all_8_1))
% 240.46/47.03    (44)   ~ (e2 = e1)
% 240.46/47.03    (45)   ~ (all_52_8 = e3)
% 240.46/47.03  
% 240.46/47.03  Begin of proof
% 240.46/47.03  | 
% 240.46/47.03  | GROUND_INST: instantiating (34) with all_52_8, e1, e1, e3, simplifying with
% 240.46/47.03  |              (14), (18) gives:
% 240.46/47.03  |   (46)  all_52_8 = e1
% 240.46/47.03  | 
% 240.46/47.03  | REDUCE: (5), (46) imply:
% 240.46/47.03  |   (47)   ~ (all_52_9 = e1)
% 240.46/47.03  | 
% 240.46/47.03  | SIMP: (47) implies:
% 240.46/47.03  |   (48)   ~ (all_52_9 = e1)
% 240.46/47.03  | 
% 240.46/47.03  | REDUCE: (30), (46) imply:
% 240.46/47.03  |   (49)   ~ (all_52_11 = e1)
% 240.46/47.03  | 
% 240.46/47.03  | SIMP: (49) implies:
% 240.46/47.03  |   (50)   ~ (all_52_11 = e1)
% 240.46/47.03  | 
% 240.46/47.03  | BETA: splitting (17) gives:
% 240.46/47.03  | 
% 240.46/47.03  | Case 1:
% 240.46/47.03  | | 
% 240.46/47.03  | |   (51)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 240.46/47.03  | |           e2)
% 240.46/47.03  | | 
% 240.46/47.03  | | BETA: splitting (51) gives:
% 240.46/47.03  | | 
% 240.46/47.03  | | Case 1:
% 240.46/47.03  | | | 
% 240.46/47.03  | | |   (52)  all_58_4 = e2 & op(e3, e1) = e2
% 240.46/47.03  | | | 
% 240.46/47.03  | | | REF_CLOSE: (24), (44), (52) are inconsistent by sub-proof #1471.
% 240.46/47.03  | | | 
% 240.46/47.03  | | Case 2:
% 240.46/47.03  | | | 
% 240.46/47.03  | | |   (53)  all_58_5 = e2 & op(e2, e1) = e2
% 240.46/47.03  | | | 
% 240.46/47.03  | | | ALPHA: (53) implies:
% 240.46/47.03  | | |   (54)  op(e2, e1) = e2
% 240.46/47.03  | | | 
% 240.46/47.03  | | | BETA: splitting (11) gives:
% 240.46/47.03  | | | 
% 240.46/47.03  | | | Case 1:
% 240.46/47.03  | | | | 
% 240.46/47.03  | | | |   (55)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1)
% 240.46/47.03  | | | |           = e0)
% 240.46/47.03  | | | | 
% 240.46/47.03  | | | | BETA: splitting (55) gives:
% 240.46/47.03  | | | | 
% 240.46/47.03  | | | | Case 1:
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | |   (56)  all_58_4 = e0 & op(e3, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | ALPHA: (56) implies:
% 240.46/47.03  | | | | |   (57)  op(e3, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REF_CLOSE: (18), (34), (37), (57) are inconsistent by sub-proof #2089.
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | Case 2:
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | |   (58)  all_58_5 = e0 & op(e2, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | ALPHA: (58) implies:
% 240.46/47.03  | | | | |   (59)  op(e2, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REF_CLOSE: (6), (34), (54), (59) are inconsistent by sub-proof #1906.
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | End of split
% 240.46/47.03  | | | | 
% 240.46/47.03  | | | Case 2:
% 240.46/47.03  | | | | 
% 240.46/47.03  | | | |   (60)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1)
% 240.46/47.03  | | | |           = e0)
% 240.46/47.03  | | | | 
% 240.46/47.03  | | | | BETA: splitting (60) gives:
% 240.46/47.03  | | | | 
% 240.46/47.03  | | | | Case 1:
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | |   (61)  all_58_8 = e0 & op(e1, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | ALPHA: (61) implies:
% 240.46/47.03  | | | | |   (62)  op(e1, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REF_CLOSE: (3), (4), (13), (14), (15), (28), (31), (34), (45), (62)
% 240.46/47.03  | | | | |            are inconsistent by sub-proof #1010.
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | Case 2:
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | |   (63)  all_58_14 = e0 & op(e0, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | ALPHA: (63) implies:
% 240.46/47.03  | | | | |   (64)  op(e0, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | GROUND_INST: instantiating (34) with all_52_11, e0, e1, e0,
% 240.46/47.03  | | | | |              simplifying with (4), (64) gives:
% 240.46/47.03  | | | | |   (65)  all_52_11 = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | GROUND_INST: instantiating (34) with all_52_9, e2, e1, e2, simplifying
% 240.46/47.03  | | | | |              with (15), (54) gives:
% 240.46/47.03  | | | | |   (66)  all_52_9 = e2
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REDUCE: (19), (65) imply:
% 240.46/47.03  | | | | |   (67)   ~ (all_52_3 = e0)
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REDUCE: (31), (66) imply:
% 240.46/47.03  | | | | |   (68)   ~ (e3 = e2)
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REDUCE: (13), (65) imply:
% 240.46/47.03  | | | | |   (69)   ~ (e3 = e0)
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REDUCE: (50), (65) imply:
% 240.46/47.03  | | | | |   (70)   ~ (e1 = e0)
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | BETA: splitting (2) gives:
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | Case 1:
% 240.46/47.03  | | | | | | 
% 240.46/47.03  | | | | | |   (71)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 240.46/47.03  | | | | | |           all_56_17 & $i(all_56_17)) | (all_56_18 = e2 & op(e2,
% 240.46/47.03  | | | | | |             all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 240.46/47.03  | | | | | |           $i(all_56_19))
% 240.46/47.03  | | | | | | 
% 240.46/47.03  | | | | | | BETA: splitting (71) gives:
% 240.46/47.03  | | | | | | 
% 240.46/47.03  | | | | | | Case 1:
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | |   (72)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 240.46/47.03  | | | | | | |         all_56_17 & $i(all_56_17)
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | | ALPHA: (72) implies:
% 240.46/47.03  | | | | | | |   (73)  op(e3, e1) = all_56_17
% 240.46/47.03  | | | | | | |   (74)  op(e3, all_56_17) = e3
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | | GROUND_INST: instantiating (34) with e1, all_56_17, e1, e3,
% 240.46/47.03  | | | | | | |              simplifying with (18), (73) gives:
% 240.46/47.03  | | | | | | |   (75)  all_56_17 = e1
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | | REDUCE: (74), (75) imply:
% 240.46/47.03  | | | | | | |   (76)  op(e3, e1) = e3
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | | REF_CLOSE: (14), (34), (45), (76) are inconsistent by sub-proof
% 240.46/47.03  | | | | | | |            #2260.
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | Case 2:
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | |   (77)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 240.46/47.03  | | | | | | |         all_56_19 & $i(all_56_19)
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | | REF_CLOSE: (1), (16), (34), (54), (77) are inconsistent by
% 240.46/47.03  | | | | | | |            sub-proof #758.
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | End of split
% 240.46/47.03  | | | | | | 
% 240.46/47.03  | | | | | Case 2:
% 240.46/47.03  | | | | | | 
% 240.46/47.03  | | | | | |   (78)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 = e0
% 240.46/47.03  | | | | | |           & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 240.46/47.03  | | | | | |           $i(all_56_23))
% 240.46/47.03  | | | | | | 
% 240.46/47.03  | | | | | | BETA: splitting (78) gives:
% 240.46/47.03  | | | | | | 
% 240.46/47.03  | | | | | | Case 1:
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | |   (79)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | | ALPHA: (79) implies:
% 240.46/47.03  | | | | | | |   (80)  op(e1, all_56_21) = e1
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | | REDUCE: (36), (80) imply:
% 240.46/47.03  | | | | | | |   (81)  op(e1, e3) = e1
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | | REF_CLOSE: (3), (4), (9), (10), (12), (20), (23), (27), (34),
% 240.46/47.03  | | | | | | |            (35), (37), (38), (40), (43), (50), (67), (81) are
% 240.46/47.03  | | | | | | |            inconsistent by sub-proof #302.
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | Case 2:
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | |   (82)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 240.46/47.03  | | | | | | |         all_56_23 & $i(all_56_23)
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | | ALPHA: (82) implies:
% 240.46/47.03  | | | | | | |   (83)  op(e0, e1) = all_56_23
% 240.46/47.03  | | | | | | |   (84)  op(e0, all_56_23) = e0
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | | REF_CLOSE: (3), (33), (34), (64), (83), (84) are inconsistent by
% 240.46/47.03  | | | | | | |            sub-proof #1395.
% 240.46/47.03  | | | | | | | 
% 240.46/47.03  | | | | | | End of split
% 240.46/47.03  | | | | | | 
% 240.46/47.03  | | | | | End of split
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | End of split
% 240.46/47.03  | | | | 
% 240.46/47.03  | | | End of split
% 240.46/47.03  | | | 
% 240.46/47.03  | | End of split
% 240.46/47.03  | | 
% 240.46/47.03  | Case 2:
% 240.46/47.03  | | 
% 240.46/47.03  | |   (85)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 240.46/47.03  | |           e2)
% 240.46/47.03  | | 
% 240.46/47.03  | | BETA: splitting (85) gives:
% 240.46/47.03  | | 
% 240.46/47.03  | | Case 1:
% 240.46/47.03  | | | 
% 240.46/47.03  | | |   (86)  all_58_8 = e2 & op(e1, e1) = e2
% 240.46/47.03  | | | 
% 240.46/47.03  | | | ALPHA: (86) implies:
% 240.46/47.03  | | |   (87)  op(e1, e1) = e2
% 240.46/47.03  | | | 
% 240.46/47.03  | | | REF_CLOSE: (16), (26), (34), (87) are inconsistent by sub-proof #2206.
% 240.46/47.03  | | | 
% 240.46/47.03  | | Case 2:
% 240.46/47.03  | | | 
% 240.46/47.03  | | |   (88)  all_58_14 = e2 & op(e0, e1) = e2
% 240.46/47.03  | | | 
% 240.46/47.03  | | | ALPHA: (88) implies:
% 240.46/47.03  | | |   (89)  op(e0, e1) = e2
% 240.46/47.03  | | | 
% 240.46/47.03  | | | BETA: splitting (11) gives:
% 240.46/47.03  | | | 
% 240.46/47.03  | | | Case 1:
% 240.46/47.03  | | | | 
% 240.46/47.03  | | | |   (90)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1)
% 240.46/47.03  | | | |           = e0)
% 240.46/47.03  | | | | 
% 240.46/47.03  | | | | BETA: splitting (90) gives:
% 240.46/47.03  | | | | 
% 240.46/47.03  | | | | Case 1:
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | |   (91)  all_58_4 = e0 & op(e3, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | ALPHA: (91) implies:
% 240.46/47.03  | | | | |   (92)  op(e3, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REF_CLOSE: (18), (34), (37), (92) are inconsistent by sub-proof #2089.
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | Case 2:
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | |   (93)  all_58_5 = e0 & op(e2, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | ALPHA: (93) implies:
% 240.46/47.03  | | | | |   (94)  op(e2, e1) = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | GROUND_INST: instantiating (34) with all_52_11, e2, e1, e0,
% 240.46/47.03  | | | | |              simplifying with (4), (89) gives:
% 240.46/47.03  | | | | |   (95)  all_52_11 = e2
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | GROUND_INST: instantiating (34) with all_52_9, e0, e1, e2, simplifying
% 240.46/47.03  | | | | |              with (15), (94) gives:
% 240.46/47.03  | | | | |   (96)  all_52_9 = e0
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REDUCE: (8), (95) imply:
% 240.46/47.03  | | | | |   (97)   ~ (all_52_7 = e2)
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REDUCE: (42), (95), (96) imply:
% 240.46/47.03  | | | | |   (98)   ~ (e2 = e0)
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REDUCE: (21), (96) imply:
% 240.46/47.03  | | | | |   (99)   ~ (all_52_13 = e0)
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | SIMP: (99) implies:
% 240.46/47.03  | | | | |   (100)   ~ (all_52_13 = e0)
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | REDUCE: (48), (96) imply:
% 240.46/47.03  | | | | |   (101)   ~ (e1 = e0)
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | BETA: splitting (7) gives:
% 240.46/47.03  | | | | | 
% 240.46/47.03  | | | | | Case 1:
% 240.46/47.03  | | | | | | 
% 240.46/47.03  | | | | | |   (102)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.46/47.03  | | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.46/47.03  | | | | | |              e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 =
% 240.46/47.03  | | | | | |            e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.46/47.03  | | | | | |              e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.46/47.03  | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 240.46/47.03  | | | | | |            all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1)
% 240.46/47.03  | | | | | |            &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 240.46/47.03  | | | | | |            = e3 & op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1
% 240.46/47.03  | | | | | |            &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.46/47.03  | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1
% 240.46/47.03  | | | | | |            & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 240.46/47.03  | | | | | |            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.46/47.03  | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 240.46/47.03  | | | | | |              e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.46/47.03  | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.46/47.03  | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 240.46/47.03  | | | | | |              e3) = e0)
% 240.46/47.03  | | | | | | 
% 240.46/47.03  | | | | | | BETA: splitting (102) gives:
% 240.46/47.03  | | | | | | 
% 240.46/47.03  | | | | | | Case 1:
% 240.46/47.03  | | | | | | | 
% 240.46/47.04  | | | | | | |   (103)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.46/47.04  | | | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 240.46/47.04  | | | | | | |              = e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 240.46/47.04  | | | | | | |          (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.46/47.04  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 240.46/47.04  | | | | | | |              = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 240.46/47.04  | | | | | | |          (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.46/47.04  | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 240.46/47.04  | | | | | | |              = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | | BETA: splitting (103) gives:
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | | Case 1:
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | |   (104)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.46/47.04  | | | | | | | |          (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 240.46/47.04  | | | | | | | |            = e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | | ALPHA: (104) implies:
% 240.46/47.04  | | | | | | | |   (105)  op(e2, e3) = e3
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | | REF_CLOSE: (25), (34), (41), (105) are inconsistent by sub-proof
% 240.46/47.04  | | | | | | | |            #2337.
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | Case 2:
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | |   (106)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) & 
% 240.46/47.04  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.46/47.04  | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 240.46/47.04  | | | | | | | |          | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1)
% 240.46/47.04  | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.04  | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | | BETA: splitting (106) gives:
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | | Case 1:
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | |   (107)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) & 
% 240.46/47.04  | | | | | | | | |          ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.46/47.04  | | | | | | | | |          (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | | ALPHA: (107) implies:
% 240.46/47.04  | | | | | | | | |   (108)   ~ (all_56_31 = e3)
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | | REDUCE: (32), (108) imply:
% 240.46/47.04  | | | | | | | | |   (109)  $false
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | | CLOSE: (109) is inconsistent.
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | Case 2:
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | |   (110)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &
% 240.46/47.04  | | | | | | | | |           ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.04  | | | | | | | | |          (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | | ALPHA: (110) implies:
% 240.46/47.04  | | | | | | | | |   (111)  op(e1, e3) = e3
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | | REF_CLOSE: (27), (34), (35), (111) are inconsistent by
% 240.46/47.04  | | | | | | | | |            sub-proof #2335.
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | End of split
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | End of split
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | Case 2:
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | |   (112)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.46/47.04  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 240.46/47.04  | | | | | | |              = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 240.46/47.04  | | | | | | |          (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.46/47.04  | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31
% 240.46/47.04  | | | | | | |              = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 240.46/47.04  | | | | | | |          (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.46/47.04  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 240.46/47.04  | | | | | | |              = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | | REF_CLOSE: (10), (22), (32), (34), (112) are inconsistent by
% 240.46/47.04  | | | | | | |            sub-proof #1389.
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | End of split
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | Case 2:
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | |   (113)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.46/47.04  | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 240.46/47.04  | | | | | |              e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 =
% 240.46/47.04  | | | | | |            e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.46/47.04  | | | | | |              = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.46/47.04  | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 240.46/47.04  | | | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0)
% 240.46/47.04  | | | | | |            &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0)
% 240.46/47.04  | | | | | |            = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 240.46/47.04  | | | | | |            e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.46/47.04  | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 240.46/47.04  | | | | | |            & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 & 
% 240.46/47.04  | | | | | |            ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.46/47.04  | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 240.46/47.04  | | | | | |              e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.46/47.04  | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.46/47.04  | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 240.46/47.04  | | | | | |              e1) = e0)
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | | BETA: splitting (113) gives:
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | | Case 1:
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | |   (114)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) & 
% 240.46/47.04  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.04  | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 240.46/47.04  | | | | | | |          (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) & 
% 240.46/47.04  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.46/47.04  | | | | | | |            (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 240.46/47.04  | | | | | | |          (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) & 
% 240.46/47.04  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.46/47.04  | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | | REF_CLOSE: (6), (15), (29), (34), (37), (94), (97), (114) are
% 240.46/47.04  | | | | | | |            inconsistent by sub-proof #1895.
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | Case 2:
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | |   (115)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) & 
% 240.46/47.04  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.46/47.04  | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 240.46/47.04  | | | | | | |          (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) & 
% 240.46/47.04  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.46/47.04  | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 240.46/47.04  | | | | | | |          (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) & 
% 240.46/47.04  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.04  | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | | BETA: splitting (115) gives:
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | | Case 1:
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | |   (116)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) & 
% 240.46/47.04  | | | | | | | |          ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.46/47.04  | | | | | | | |          (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | | ALPHA: (116) implies:
% 240.46/47.04  | | | | | | | |   (117)  op(e2, e0) = e0
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | | REF_CLOSE: (34), (39), (100), (117) are inconsistent by
% 240.46/47.04  | | | | | | | |            sub-proof #2324.
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | Case 2:
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | |   (118)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &
% 240.46/47.04  | | | | | | | |             ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.46/47.04  | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1)
% 240.46/47.04  | | | | | | | |          | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1)
% 240.46/47.04  | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.04  | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | | BETA: splitting (118) gives:
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | | Case 1:
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | |   (119)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0)
% 240.46/47.04  | | | | | | | | |          &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.46/47.04  | | | | | | | | |          (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | | ALPHA: (119) implies:
% 240.46/47.04  | | | | | | | | |   (120)  op(e0, e1) = e1
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | | REF_CLOSE: (4), (34), (50), (120) are inconsistent by
% 240.46/47.04  | | | | | | | | |            sub-proof #2272.
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | Case 2:
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | |   (121)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1)
% 240.46/47.04  | | | | | | | | |          &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.04  | | | | | | | | |          (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | | ALPHA: (121) implies:
% 240.46/47.04  | | | | | | | | |   (122)  op(e0, e1) = e0
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | | REF_CLOSE: (6), (34), (89), (122) are inconsistent by
% 240.46/47.04  | | | | | | | | |            sub-proof #458.
% 240.46/47.04  | | | | | | | | | 
% 240.46/47.04  | | | | | | | | End of split
% 240.46/47.04  | | | | | | | | 
% 240.46/47.04  | | | | | | | End of split
% 240.46/47.04  | | | | | | | 
% 240.46/47.04  | | | | | | End of split
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | End of split
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | End of split
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | Case 2:
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | |   (123)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 240.46/47.04  | | | |              e1) = e0)
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | | REF_CLOSE: (3), (4), (6), (13), (14), (15), (28), (31), (34), (45),
% 240.46/47.04  | | | |            (89), (123) are inconsistent by sub-proof #306.
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | End of split
% 240.46/47.04  | | | 
% 240.46/47.04  | | End of split
% 240.46/47.04  | | 
% 240.46/47.04  | End of split
% 240.46/47.04  | 
% 240.46/47.04  End of proof
% 240.46/47.04  
% 240.46/47.04  Sub-proof #302 shows that the following formulas are inconsistent:
% 240.46/47.04  ----------------------------------------------------------------
% 240.46/47.04    (1)   ~ (all_52_3 = e0)
% 240.46/47.04    (2)   ~ (e3 = e0)
% 240.46/47.04    (3)  op(e0, e1) = all_52_11
% 240.46/47.04    (4)   ~ (all_52_11 = e1)
% 240.46/47.04    (5)  all_58_15 = e3
% 240.46/47.04    (6)  op(e0, e3) = all_52_3
% 240.46/47.04    (7)   ~ (all_52_2 = all_52_3)
% 240.46/47.04    (8)  op(e1, e3) = e1
% 240.46/47.04    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.46/47.04         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.46/47.04    (10)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.46/47.04            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.46/47.04              e3) = all_42_1 & $i(all_42_1))
% 240.46/47.04    (11)   ~ (all_52_2 = e3)
% 240.46/47.04    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.04            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.04    (13)  op(e1, e3) = all_52_2
% 240.46/47.04    (14)   ~ (e1 = e0)
% 240.46/47.04    (15)  op(e3, e3) = e3
% 240.46/47.04    (16)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.46/47.04          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.46/47.04            e1)
% 240.46/47.04    (17)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.46/47.04            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.46/47.04            & $i(all_8_1))
% 240.46/47.04  
% 240.46/47.04  Begin of proof
% 240.46/47.04  | 
% 240.46/47.04  | GROUND_INST: instantiating (12) with all_52_2, e1, e3, e1, simplifying with
% 240.46/47.04  |              (8), (13) gives:
% 240.46/47.04  |   (18)  all_52_2 = e1
% 240.46/47.04  | 
% 240.46/47.04  | REDUCE: (7), (18) imply:
% 240.46/47.04  |   (19)   ~ (all_52_3 = e1)
% 240.46/47.04  | 
% 240.46/47.04  | SIMP: (19) implies:
% 240.46/47.04  |   (20)   ~ (all_52_3 = e1)
% 240.46/47.04  | 
% 240.46/47.04  | REDUCE: (11), (18) imply:
% 240.46/47.04  |   (21)   ~ (e3 = e1)
% 240.46/47.04  | 
% 240.46/47.04  | SIMP: (21) implies:
% 240.46/47.04  |   (22)   ~ (e3 = e1)
% 240.46/47.04  | 
% 240.46/47.04  | BETA: splitting (16) gives:
% 240.46/47.04  | 
% 240.46/47.04  | Case 1:
% 240.46/47.04  | | 
% 240.46/47.04  | |   (23)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 240.46/47.04  | |           e1)
% 240.46/47.04  | | 
% 240.46/47.04  | | BETA: splitting (23) gives:
% 240.46/47.04  | | 
% 240.46/47.04  | | Case 1:
% 240.46/47.04  | | | 
% 240.46/47.04  | | |   (24)  all_58_12 = e1 & op(e0, e3) = e1
% 240.46/47.04  | | | 
% 240.46/47.04  | | | REF_CLOSE: (6), (12), (20), (24) are inconsistent by sub-proof #2276.
% 240.46/47.04  | | | 
% 240.46/47.04  | | Case 2:
% 240.46/47.04  | | | 
% 240.46/47.04  | | |   (25)  all_58_13 = e1 & op(e0, e2) = e1
% 240.46/47.04  | | | 
% 240.46/47.04  | | | ALPHA: (25) implies:
% 240.46/47.04  | | |   (26)  op(e0, e2) = e1
% 240.46/47.04  | | | 
% 240.46/47.04  | | | BETA: splitting (9) gives:
% 240.46/47.04  | | | 
% 240.46/47.04  | | | Case 1:
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | |   (27)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 240.46/47.04  | | | |           = e0)
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | | BETA: splitting (27) gives:
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | | Case 1:
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | |   (28)  all_58_0 = e0 & op(e3, e3) = e0
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | | ALPHA: (28) implies:
% 240.46/47.04  | | | | |   (29)  op(e3, e3) = e0
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | | REF_CLOSE: (2), (12), (15), (29) are inconsistent by sub-proof #1940.
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | Case 2:
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | |   (30)  all_58_2 = e0 & op(e2, e3) = e0
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | | ALPHA: (30) implies:
% 240.46/47.04  | | | | |   (31)  op(e2, e3) = e0
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | | BETA: splitting (10) gives:
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | | Case 1:
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | |   (32)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2,
% 240.46/47.04  | | | | | |           e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | | ALPHA: (32) implies:
% 240.46/47.04  | | | | | |   (33)  op(e2, e3) = all_42_1
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | | REF_CLOSE: (12), (17), (26), (31), (33) are inconsistent by
% 240.46/47.04  | | | | | |            sub-proof #303.
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | Case 2:
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | |   (34)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | | ALPHA: (34) implies:
% 240.46/47.04  | | | | | |   (35)  op(e2, e3) = all_42_1
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | | REF_CLOSE: (12), (17), (26), (31), (35) are inconsistent by
% 240.46/47.04  | | | | | |            sub-proof #303.
% 240.46/47.04  | | | | | | 
% 240.46/47.04  | | | | | End of split
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | End of split
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | Case 2:
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | |   (36)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 240.46/47.04  | | | |           = e0)
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | | BETA: splitting (36) gives:
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | | Case 1:
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | |   (37)  all_58_6 = e0 & op(e1, e3) = e0
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | | ALPHA: (37) implies:
% 240.46/47.04  | | | | |   (38)  op(e1, e3) = e0
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | | REF_CLOSE: (8), (12), (14), (38) are inconsistent by sub-proof #449.
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | Case 2:
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | |   (39)  all_58_12 = e0 & op(e0, e3) = e0
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | | ALPHA: (39) implies:
% 240.46/47.04  | | | | |   (40)  op(e0, e3) = e0
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | | REF_CLOSE: (1), (6), (12), (40) are inconsistent by sub-proof #2331.
% 240.46/47.04  | | | | | 
% 240.46/47.04  | | | | End of split
% 240.46/47.04  | | | | 
% 240.46/47.04  | | | End of split
% 240.46/47.04  | | | 
% 240.46/47.04  | | End of split
% 240.46/47.04  | | 
% 240.46/47.04  | Case 2:
% 240.46/47.04  | | 
% 240.46/47.04  | |   (41)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.46/47.04  | |           e1)
% 240.46/47.04  | | 
% 240.46/47.04  | | BETA: splitting (41) gives:
% 240.46/47.04  | | 
% 240.46/47.04  | | Case 1:
% 240.46/47.04  | | | 
% 240.46/47.04  | | |   (42)  all_58_14 = e1 & op(e0, e1) = e1
% 240.46/47.04  | | | 
% 240.46/47.04  | | | ALPHA: (42) implies:
% 240.46/47.04  | | |   (43)  op(e0, e1) = e1
% 240.46/47.04  | | | 
% 240.46/47.04  | | | REF_CLOSE: (3), (4), (12), (43) are inconsistent by sub-proof #2272.
% 240.46/47.04  | | | 
% 240.46/47.04  | | Case 2:
% 240.46/47.04  | | | 
% 240.46/47.04  | | |   (44)  all_58_15 = e1 & op(e0, e0) = e1
% 240.46/47.04  | | | 
% 240.46/47.04  | | | ALPHA: (44) implies:
% 240.46/47.04  | | |   (45)  all_58_15 = e1
% 240.46/47.04  | | | 
% 240.46/47.04  | | | REF_CLOSE: (5), (22), (45) are inconsistent by sub-proof #2249.
% 240.46/47.04  | | | 
% 240.46/47.04  | | End of split
% 240.46/47.04  | | 
% 240.46/47.04  | End of split
% 240.46/47.04  | 
% 240.46/47.04  End of proof
% 240.46/47.04  
% 240.46/47.04  Sub-proof #303 shows that the following formulas are inconsistent:
% 240.46/47.04  ----------------------------------------------------------------
% 240.46/47.04    (1)  op(e2, e3) = e0
% 240.46/47.04    (2)  op(e2, e3) = all_42_1
% 240.46/47.04    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.04    (4)  op(e0, e2) = e1
% 240.46/47.04    (5)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.46/47.04           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.46/47.04           & $i(all_8_1))
% 240.46/47.04  
% 240.46/47.04  Begin of proof
% 240.46/47.04  | 
% 240.46/47.04  | BETA: splitting (5) gives:
% 240.46/47.04  | 
% 240.46/47.04  | Case 1:
% 240.46/47.04  | | 
% 240.46/47.04  | |   (6)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1
% 240.46/47.04  | |        & $i(all_8_0) & $i(all_8_1)
% 240.46/47.04  | | 
% 240.46/47.04  | | ALPHA: (6) implies:
% 240.46/47.04  | |   (7)   ~ (all_8_0 = e1)
% 240.46/47.04  | |   (8)  op(e2, e3) = all_8_1
% 240.46/47.04  | |   (9)  op(all_8_1, e2) = all_8_0
% 240.46/47.04  | | 
% 240.46/47.04  | | GROUND_INST: instantiating (3) with all_8_1, all_42_1, e3, e2, simplifying
% 240.46/47.04  | |              with (2), (8) gives:
% 240.46/47.04  | |   (10)  all_42_1 = all_8_1
% 240.46/47.04  | | 
% 240.46/47.04  | | GROUND_INST: instantiating (3) with e0, all_42_1, e3, e2, simplifying with
% 240.46/47.04  | |              (1), (2) gives:
% 240.46/47.04  | |   (11)  all_42_1 = e0
% 240.46/47.04  | | 
% 240.46/47.04  | | COMBINE_EQS: (10), (11) imply:
% 240.46/47.04  | |   (12)  all_8_1 = e0
% 240.46/47.04  | | 
% 240.46/47.04  | | SIMP: (12) implies:
% 240.46/47.04  | |   (13)  all_8_1 = e0
% 240.46/47.04  | | 
% 240.46/47.04  | | REDUCE: (9), (13) imply:
% 240.46/47.04  | |   (14)  op(e0, e2) = all_8_0
% 240.46/47.04  | | 
% 240.46/47.04  | | GROUND_INST: instantiating (3) with e1, all_8_0, e2, e0, simplifying with
% 240.46/47.04  | |              (4), (14) gives:
% 240.46/47.04  | |   (15)  all_8_0 = e1
% 240.46/47.04  | | 
% 240.46/47.04  | | REDUCE: (7), (15) imply:
% 240.46/47.04  | |   (16)  $false
% 240.46/47.04  | | 
% 240.46/47.04  | | CLOSE: (16) is inconsistent.
% 240.46/47.04  | | 
% 240.46/47.04  | Case 2:
% 240.46/47.04  | | 
% 240.46/47.04  | |   (17)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 240.46/47.04  | | 
% 240.46/47.04  | | ALPHA: (17) implies:
% 240.46/47.04  | |   (18)   ~ (all_8_1 = e0)
% 240.46/47.04  | |   (19)  op(e2, e3) = all_8_1
% 240.46/47.04  | | 
% 240.46/47.04  | | REF_CLOSE: (1), (2), (3), (18), (19) are inconsistent by sub-proof #898.
% 240.46/47.04  | | 
% 240.46/47.04  | End of split
% 240.46/47.04  | 
% 240.46/47.04  End of proof
% 240.46/47.04  
% 240.46/47.04  Sub-proof #304 shows that the following formulas are inconsistent:
% 240.46/47.04  ----------------------------------------------------------------
% 240.46/47.04    (1)  op(e0, e0) = e1
% 240.46/47.04    (2)  op(e2, e2) = e3
% 240.46/47.04    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.46/47.04         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.46/47.04    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.46/47.05           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.46/47.05           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.46/47.05           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.46/47.05           & $i(all_56_23))
% 240.46/47.05    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.46/47.05         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.46/47.05    (6)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 240.46/47.05           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 240.46/47.05             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 240.46/47.05    (7)   ~ (e3 = e0)
% 240.46/47.05    (8)  op(e0, e1) = all_52_11
% 240.46/47.05    (9)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.46/47.05         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.46/47.05    (10)  all_42_2 = e3
% 240.46/47.05    (11)   ~ (e2 = e0)
% 240.46/47.05    (12)  op(e1, e2) = all_52_6
% 240.46/47.05    (13)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.46/47.05          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.46/47.05    (14)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 240.46/47.05          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.46/47.05    (15)   ~ (all_52_11 = e1)
% 240.46/47.05    (16)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.46/47.05              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.46/47.05            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.46/47.05            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.46/47.05            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.46/47.05             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.05            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.46/47.05            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.46/47.05            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.46/47.05            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.46/47.05            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.46/47.05              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.46/47.05            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.46/47.05            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.46/47.05            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.46/47.05            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.46/47.05            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.46/47.05            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.46/47.05              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.46/47.05            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.46/47.05            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.46/47.05            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.46/47.05            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.46/47.05            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.46/47.05            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.46/47.05              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.46/47.05            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.05            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.46/47.05    (17)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.46/47.05          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.46/47.05    (18)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 240.46/47.05            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 240.46/47.05              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 240.46/47.05    (19)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.46/47.05          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.46/47.05    (20)  op(e1, e0) = all_52_14
% 240.46/47.05    (21)   ~ (all_52_13 = e1)
% 240.46/47.05    (22)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 240.46/47.05            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 240.46/47.05              e1) = all_20_1 & $i(all_20_1))
% 240.46/47.05    (23)   ~ (all_52_7 = e3)
% 240.46/47.05    (24)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.46/47.05          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.46/47.05    (25)   ~ (e3 = e1)
% 240.46/47.05    (26)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 240.46/47.05            op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 240.46/47.05              e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.46/47.05    (27)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.46/47.05          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.46/47.05    (28)  all_58_3 = e3
% 240.46/47.05    (29)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.46/47.05          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.46/47.05    (30)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.46/47.05              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.46/47.05                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.46/47.05                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.46/47.05    (31)   ~ (all_52_11 = e3)
% 240.46/47.05    (32)  op(e3, e1) = all_52_8
% 240.46/47.05    (33)  op(e2, e1) = all_52_9
% 240.46/47.05    (34)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.46/47.05          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.46/47.05    (35)   ~ (e3 = e2)
% 240.46/47.05    (36)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.46/47.05          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.46/47.05    (37)   ~ (all_52_14 = e1)
% 240.46/47.05    (38)   ~ (all_52_7 = e1)
% 240.46/47.05    (39)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.46/47.05            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.46/47.05            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.46/47.05            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.46/47.05            op(e0, all_56_31) = e0)
% 240.46/47.05    (40)  all_56_31 = e1
% 240.46/47.05    (41)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.46/47.05          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.46/47.05    (42)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.46/47.05          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.46/47.05    (43)  all_58_9 = e3
% 240.46/47.05    (44)  all_46_2 = e3
% 240.46/47.05    (45)  op(e3, e0) = e3
% 240.46/47.05    (46)  op(e2, e3) = all_52_1
% 240.46/47.05    (47)   ~ (all_52_14 = e3)
% 240.46/47.05    (48)  all_58_12 = e3
% 240.46/47.05    (49)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.46/47.05          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.46/47.05    (50)  all_34_2 = e1
% 240.46/47.05    (51)   ~ (all_50_1 = e2)
% 240.46/47.05    (52)  op(e1, e1) = e3
% 240.46/47.05    (53)   ~ (all_52_2 = e3)
% 240.46/47.05    (54)  op(e3, e0) = all_50_1
% 240.46/47.05    (55)   ~ (all_52_6 = e3)
% 240.46/47.05    (56)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.46/47.05          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.46/47.05    (57)  op(e0, e2) = all_52_7
% 240.46/47.05    (58)   ~ (all_52_4 = e3)
% 240.46/47.05    (59)  op(e3, e2) = all_52_4
% 240.46/47.05    (60)   ~ (all_52_9 = e3)
% 240.46/47.05    (61)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.46/47.05          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.46/47.05    (62)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.46/47.05          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.46/47.05    (63)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.46/47.05          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.46/47.05    (64)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.46/47.05          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.46/47.05    (65)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.46/47.05          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.46/47.05    (66)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.46/47.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.46/47.05    (67)  all_58_8 = e3
% 240.46/47.05    (68)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.46/47.05          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.46/47.05    (69)  op(e1, e3) = all_52_2
% 240.46/47.05    (70)  all_56_21 = e3
% 240.46/47.05    (71)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.46/47.05          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.46/47.05    (72)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.46/47.05          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.46/47.05    (73)   ~ (e1 = e0)
% 240.46/47.05    (74)  op(e3, e3) = e0
% 240.46/47.05    (75)   ~ (all_52_13 = e3)
% 240.46/47.05    (76)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.46/47.05          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.46/47.05    (77)  all_56_1 = e0
% 240.46/47.05    (78)  op(e2, e0) = all_52_13
% 240.46/47.05    (79)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.46/47.05          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.46/47.05            e1)
% 240.46/47.05    (80)   ~ (all_52_1 = e3)
% 240.46/47.05    (81)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.46/47.05          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.46/47.05            e2)
% 240.46/47.05    (82)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.46/47.05            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.46/47.05            & $i(all_8_1))
% 240.46/47.05    (83)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.46/47.05          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.46/47.05    (84)   ~ (all_52_4 = e0)
% 240.46/47.05    (85)   ~ (e2 = e1)
% 240.46/47.05    (86)   ~ (all_52_8 = e3)
% 240.46/47.05  
% 240.46/47.05  Begin of proof
% 240.46/47.05  | 
% 240.46/47.05  | BETA: splitting (14) gives:
% 240.46/47.05  | 
% 240.46/47.05  | Case 1:
% 240.46/47.05  | | 
% 240.46/47.05  | |   (87)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 240.46/47.05  | |           e1)
% 240.46/47.05  | | 
% 240.46/47.05  | | REF_CLOSE: (1), (7), (11), (21), (25), (30), (35), (62), (66), (68), (73),
% 240.46/47.05  | |            (75), (78), (85), (87) are inconsistent by sub-proof #878.
% 240.46/47.05  | | 
% 240.46/47.05  | Case 2:
% 240.46/47.05  | | 
% 240.46/47.05  | |   (88)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.46/47.05  | |           e1)
% 240.46/47.05  | | 
% 240.46/47.05  | | BETA: splitting (88) gives:
% 240.46/47.05  | | 
% 240.46/47.05  | | Case 1:
% 240.46/47.05  | | | 
% 240.46/47.05  | | |   (89)  all_58_11 = e1 & op(e1, e0) = e1
% 240.46/47.05  | | | 
% 240.46/47.05  | | | ALPHA: (89) implies:
% 240.46/47.05  | | |   (90)  op(e1, e0) = e1
% 240.46/47.05  | | | 
% 240.46/47.05  | | | REF_CLOSE: (20), (37), (66), (90) are inconsistent by sub-proof #2304.
% 240.46/47.05  | | | 
% 240.46/47.05  | | Case 2:
% 240.46/47.05  | | | 
% 240.46/47.05  | | |   (91)  all_58_15 = e1 & op(e0, e0) = e1
% 240.46/47.05  | | | 
% 240.46/47.05  | | | ALPHA: (91) implies:
% 240.46/47.05  | | |   (92)  all_58_15 = e1
% 240.46/47.05  | | | 
% 240.46/47.05  | | | BETA: splitting (6) gives:
% 240.46/47.05  | | | 
% 240.46/47.05  | | | Case 1:
% 240.46/47.05  | | | | 
% 240.46/47.05  | | | |   (93)   ~ (all_34_2 = e1)
% 240.46/47.05  | | | | 
% 240.46/47.05  | | | | REDUCE: (50), (93) imply:
% 240.46/47.05  | | | |   (94)  $false
% 240.46/47.05  | | | | 
% 240.46/47.05  | | | | CLOSE: (94) is inconsistent.
% 240.46/47.05  | | | | 
% 240.46/47.05  | | | Case 2:
% 240.46/47.05  | | | | 
% 240.46/47.05  | | | |   (95)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 240.46/47.05  | | | |           all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2)
% 240.46/47.05  | | | |           & op(e0, e1) = all_34_1 & $i(all_34_1))
% 240.46/47.05  | | | | 
% 240.46/47.05  | | | | BETA: splitting (18) gives:
% 240.46/47.05  | | | | 
% 240.46/47.05  | | | | Case 1:
% 240.46/47.05  | | | | | 
% 240.46/47.05  | | | | |   (96)   ~ (all_42_2 = e3)
% 240.46/47.05  | | | | | 
% 240.46/47.05  | | | | | REDUCE: (10), (96) imply:
% 240.46/47.05  | | | | |   (97)  $false
% 240.46/47.05  | | | | | 
% 240.46/47.05  | | | | | CLOSE: (97) is inconsistent.
% 240.46/47.05  | | | | | 
% 240.46/47.05  | | | | Case 2:
% 240.46/47.05  | | | | | 
% 240.46/47.05  | | | | |   (98)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3)
% 240.46/47.05  | | | | |           = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 240.46/47.05  | | | | |             e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 240.46/47.05  | | | | | 
% 240.46/47.05  | | | | | BETA: splitting (26) gives:
% 240.46/47.05  | | | | | 
% 240.46/47.05  | | | | | Case 1:
% 240.46/47.05  | | | | | | 
% 240.46/47.05  | | | | | |   (99)   ~ (all_46_2 = e3)
% 240.46/47.05  | | | | | | 
% 240.46/47.05  | | | | | | REDUCE: (44), (99) imply:
% 240.46/47.05  | | | | | |   (100)  $false
% 240.46/47.05  | | | | | | 
% 240.46/47.05  | | | | | | CLOSE: (100) is inconsistent.
% 240.46/47.05  | | | | | | 
% 240.46/47.05  | | | | | Case 2:
% 240.46/47.05  | | | | | | 
% 240.46/47.05  | | | | | |   (101)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1,
% 240.46/47.05  | | | | | |              e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 240.46/47.05  | | | | | |            (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.46/47.05  | | | | | | 
% 240.46/47.05  | | | | | | BETA: splitting (81) gives:
% 240.46/47.05  | | | | | | 
% 240.46/47.05  | | | | | | Case 1:
% 240.46/47.05  | | | | | | | 
% 240.46/47.05  | | | | | | |   (102)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 240.46/47.05  | | | | | | |            op(e0, e2) = e2)
% 240.46/47.05  | | | | | | | 
% 240.46/47.05  | | | | | | | BETA: splitting (102) gives:
% 240.46/47.05  | | | | | | | 
% 240.46/47.05  | | | | | | | Case 1:
% 240.46/47.05  | | | | | | | | 
% 240.46/47.05  | | | | | | | |   (103)  all_58_12 = e2 & op(e0, e3) = e2
% 240.46/47.05  | | | | | | | | 
% 240.46/47.05  | | | | | | | | REF_CLOSE: (35), (48), (103) are inconsistent by sub-proof
% 240.46/47.05  | | | | | | | |            #1974.
% 240.46/47.05  | | | | | | | | 
% 240.46/47.05  | | | | | | | Case 2:
% 240.46/47.05  | | | | | | | | 
% 240.46/47.05  | | | | | | | |   (104)  all_58_13 = e2 & op(e0, e2) = e2
% 240.46/47.05  | | | | | | | | 
% 240.46/47.05  | | | | | | | | ALPHA: (104) implies:
% 240.46/47.05  | | | | | | | |   (105)  all_58_13 = e2
% 240.46/47.05  | | | | | | | |   (106)  op(e0, e2) = e2
% 240.46/47.05  | | | | | | | | 
% 240.46/47.05  | | | | | | | | BETA: splitting (17) gives:
% 240.46/47.05  | | | | | | | | 
% 240.46/47.05  | | | | | | | | Case 1:
% 240.46/47.05  | | | | | | | | | 
% 240.46/47.05  | | | | | | | | |   (107)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 240.46/47.05  | | | | | | | | |            op(e2, e2) = e0)
% 240.46/47.05  | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | BETA: splitting (107) gives:
% 240.46/47.05  | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | Case 1:
% 240.46/47.05  | | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | |   (108)  all_58_1 = e0 & op(e3, e2) = e0
% 240.46/47.05  | | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | | REF_CLOSE: (59), (66), (84), (108) are inconsistent by
% 240.46/47.05  | | | | | | | | | |            sub-proof #1968.
% 240.46/47.05  | | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | Case 2:
% 240.46/47.05  | | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | |   (109)  all_58_3 = e0 & op(e2, e2) = e0
% 240.46/47.05  | | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | | REF_CLOSE: (3), (7), (11), (25), (28), (29), (35), (43),
% 240.46/47.05  | | | | | | | | | |            (58), (59), (63), (66), (73), (74), (85), (109)
% 240.46/47.05  | | | | | | | | | |            are inconsistent by sub-proof #318.
% 240.46/47.05  | | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | End of split
% 240.46/47.05  | | | | | | | | | 
% 240.46/47.05  | | | | | | | | Case 2:
% 240.46/47.05  | | | | | | | | | 
% 240.46/47.05  | | | | | | | | |   (110)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 240.46/47.05  | | | | | | | | |            op(e0, e2) = e0)
% 240.46/47.05  | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | BETA: splitting (110) gives:
% 240.46/47.05  | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | Case 1:
% 240.46/47.05  | | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | |   (111)  all_58_7 = e0 & op(e1, e2) = e0
% 240.46/47.05  | | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | | ALPHA: (111) implies:
% 240.46/47.05  | | | | | | | | | |   (112)  op(e1, e2) = e0
% 240.46/47.05  | | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | | BETA: splitting (9) gives:
% 240.46/47.05  | | | | | | | | | | 
% 240.46/47.05  | | | | | | | | | | Case 1:
% 240.46/47.05  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | |   (113)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 240.46/47.06  | | | | | | | | | | |            & op(e1, e2) = e1)
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | BETA: splitting (113) gives:
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | |   (114)  all_58_6 = e1 & op(e1, e3) = e1
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | ALPHA: (114) implies:
% 240.46/47.06  | | | | | | | | | | | |   (115)  op(e1, e3) = e1
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | BETA: splitting (30) gives:
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | |   (116)  all_58_15 = e0 & op(e0, e0) = e0
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | ALPHA: (116) implies:
% 240.46/47.06  | | | | | | | | | | | | |   (117)  op(e0, e0) = e0
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | REF_CLOSE: (1), (66), (73), (117) are inconsistent by
% 240.46/47.06  | | | | | | | | | | | | |            sub-proof #2274.
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | |   (118)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.46/47.06  | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.46/47.06  | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 240.46/47.06  | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.46/47.06  | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | ALPHA: (118) implies:
% 240.46/47.06  | | | | | | | | | | | | |   (119)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.46/47.06  | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 240.46/47.06  | | | | | | | | | | | | |              e0) = e0)
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | BETA: splitting (34) gives:
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | |   (120)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 240.46/47.06  | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | |   (121)  all_58_0 = e2 & op(e3, e3) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 240.46/47.06  | | | | | | | | | | | | | | |   (122)  op(e3, e3) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | REF_CLOSE: (11), (66), (74), (122) are inconsistent by
% 240.46/47.06  | | | | | | | | | | | | | | |            sub-proof #2188.
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | |   (123)  all_58_2 = e2 & op(e2, e3) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 240.46/47.06  | | | | | | | | | | | | | | |   (124)  op(e2, e3) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | |   (125)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 240.46/47.06  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 240.46/47.06  | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (11), (25), (28), (30), (35), (43),
% 240.46/47.06  | | | | | | | | | | | | | | | |            (62), (66), (68), (73), (75), (78), (85), (124),
% 240.46/47.06  | | | | | | | | | | | | | | | |            (125) are inconsistent by sub-proof #317.
% 240.46/47.06  | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | |   (126)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 240.46/47.06  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 240.46/47.06  | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 240.46/47.06  | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | |   (127)  all_58_5 = e1 & op(e2, e1) = e1
% 240.46/47.06  | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 240.46/47.06  | | | | | | | | | | | | | | | | |   (128)  op(e2, e1) = e1
% 240.46/47.06  | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 240.46/47.06  | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | |   (129)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 240.46/47.06  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 240.46/47.06  | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (11), (25), (29), (33), (35), (58),
% 240.46/47.06  | | | | | | | | | | | | | | | | | |            (59), (63), (66), (73), (74), (85), (128), (129)
% 240.46/47.06  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #316.
% 240.46/47.06  | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | |   (130)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 240.46/47.06  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 240.46/47.06  | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | |   (131)  all_58_8 = e0 & op(e1, e1) = e0
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | |   (132)  op(e1, e1) = e0
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (20), (25), (42), (47), (55), (66),
% 240.46/47.06  | | | | | | | | | | | | | | | | | | |            (115), (132) are inconsistent by sub-proof #457.
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | |   (133)  all_58_14 = e0 & op(e0, e1) = e0
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | |   (134)  op(e0, e1) = e0
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | |   (135)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | |   (136)  all_58_1 = e1 & op(e3, e2) = e1
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | |   (137)  op(e3, e2) = e1
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | |   (138)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (17), (25), (28), (38), (57), (66),
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | |            (71), (73), (74), (85), (106), (138) are
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #315.
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | |   (139)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | |   (140)  all_58_4 = e2 & op(e3, e1) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (11), (12), (13), (16), (17), (19),
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | |            (20), (25), (27), (28), (29), (33), (35), (37),
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | |            (40), (43), (56), (58), (59), (63), (64), (65),
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | |            (66), (70), (71), (72), (73), (74), (77), (82),
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | |            (85), (98), (105), (106), (112), (115), (124),
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | |            (128), (134), (137), (140) are inconsistent by
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #312.
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | |   (141)  all_58_9 = e2 & op(e3, e0) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | |   (142)  op(e3, e0) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (54), (66), (142) are inconsistent by
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | |   (143)  all_58_3 = e1 & op(e2, e2) = e1
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (11), (25), (28), (30), (35), (43),
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | |            (62), (66), (68), (73), (75), (78), (85), (143)
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #331.
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | |   (144)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (38), (57), (66), (73), (112), (144) are
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1840.
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | |   (145)  all_58_10 = e1 & op(e2, e0) = e1
% 240.46/47.06  | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 240.46/47.06  | | | | | | | | | | | | | | | | |   (146)  all_58_10 = e1
% 240.46/47.06  | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (25), (35), (62), (66), (68), (73),
% 240.46/47.06  | | | | | | | | | | | | | | | | |            (85), (92), (119), (146) are inconsistent by
% 240.46/47.06  | | | | | | | | | | | | | | | | |            sub-proof #910.
% 240.46/47.06  | | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | |   (147)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 240.46/47.06  | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | REF_CLOSE: (35), (48), (66), (85), (115), (147) are
% 240.46/47.06  | | | | | | | | | | | | | |            inconsistent by sub-proof #311.
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | |   (148)  all_58_7 = e1 & op(e1, e2) = e1
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | ALPHA: (148) implies:
% 240.46/47.06  | | | | | | | | | | | |   (149)  op(e1, e2) = e1
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | REF_CLOSE: (12), (66), (73), (112), (149) are inconsistent by
% 240.46/47.06  | | | | | | | | | | | |            sub-proof #2136.
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | |   (150)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 240.46/47.06  | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | REF_CLOSE: (20), (25), (37), (52), (66), (150) are
% 240.46/47.06  | | | | | | | | | | |            inconsistent by sub-proof #453.
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | |   (151)  all_58_13 = e0 & op(e0, e2) = e0
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | ALPHA: (151) implies:
% 240.46/47.06  | | | | | | | | | |   (152)  op(e0, e2) = e0
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | REF_CLOSE: (11), (66), (106), (152) are inconsistent by
% 240.46/47.06  | | | | | | | | | |            sub-proof #2132.
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | 
% 240.46/47.06  | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | 
% 240.46/47.06  | | | | | | | End of split
% 240.46/47.06  | | | | | | | 
% 240.46/47.06  | | | | | | Case 2:
% 240.46/47.06  | | | | | | | 
% 240.46/47.06  | | | | | | |   (153)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 240.46/47.06  | | | | | | |            op(e0, e0) = e2)
% 240.46/47.06  | | | | | | | 
% 240.46/47.06  | | | | | | | BETA: splitting (153) gives:
% 240.46/47.06  | | | | | | | 
% 240.46/47.06  | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | 
% 240.46/47.06  | | | | | | | |   (154)  all_58_14 = e2 & op(e0, e1) = e2
% 240.46/47.06  | | | | | | | | 
% 240.46/47.06  | | | | | | | | ALPHA: (154) implies:
% 240.46/47.06  | | | | | | | |   (155)  all_58_14 = e2
% 240.46/47.06  | | | | | | | |   (156)  op(e0, e1) = e2
% 240.46/47.06  | | | | | | | | 
% 240.46/47.06  | | | | | | | | BETA: splitting (27) gives:
% 240.46/47.06  | | | | | | | | 
% 240.46/47.06  | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | 
% 240.46/47.06  | | | | | | | | |   (157)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 240.46/47.06  | | | | | | | | |            op(e2, e1) = e0)
% 240.46/47.06  | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | BETA: splitting (157) gives:
% 240.46/47.06  | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | |   (158)  all_58_4 = e0 & op(e3, e1) = e0
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | ALPHA: (158) implies:
% 240.46/47.06  | | | | | | | | | |   (159)  all_58_4 = e0
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | REF_CLOSE: (3), (7), (11), (25), (29), (35), (58), (59),
% 240.46/47.06  | | | | | | | | | |            (63), (66), (73), (74), (85), (159) are
% 240.46/47.06  | | | | | | | | | |            inconsistent by sub-proof #1512.
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | |   (160)  all_58_5 = e0 & op(e2, e1) = e0
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | ALPHA: (160) implies:
% 240.46/47.06  | | | | | | | | | |   (161)  op(e2, e1) = e0
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | BETA: splitting (30) gives:
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | |   (162)  all_58_15 = e0 & op(e0, e0) = e0
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | ALPHA: (162) implies:
% 240.46/47.06  | | | | | | | | | | |   (163)  op(e0, e0) = e0
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | REF_CLOSE: (1), (66), (73), (163) are inconsistent by
% 240.46/47.06  | | | | | | | | | | |            sub-proof #2274.
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | |   (164)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.46/47.06  | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.46/47.06  | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 240.46/47.06  | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.46/47.06  | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | ALPHA: (164) implies:
% 240.46/47.06  | | | | | | | | | | |   (165)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 240.46/47.06  | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 240.46/47.06  | | | | | | | | | | |              e1) = e0)
% 240.46/47.06  | | | | | | | | | | |   (166)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.46/47.06  | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 240.46/47.06  | | | | | | | | | | |              e0) = e0)
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | BETA: splitting (19) gives:
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | |   (167)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 240.46/47.06  | | | | | | | | | | | |            & op(e2, e1) = e1)
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | BETA: splitting (167) gives:
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | |   (168)  all_58_4 = e1 & op(e3, e1) = e1
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | ALPHA: (168) implies:
% 240.46/47.06  | | | | | | | | | | | | |   (169)  all_58_4 = e1
% 240.46/47.06  | | | | | | | | | | | | |   (170)  op(e3, e1) = e1
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | BETA: splitting (3) gives:
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | |   (171)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 240.46/47.06  | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | |   (172)  all_58_0 = e2 & op(e3, e3) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 240.46/47.06  | | | | | | | | | | | | | | |   (173)  op(e3, e3) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (12),
% 240.46/47.06  | | | | | | | | | | | | | | |            (13), (17), (22), (23), (25), (28), (29), (30),
% 240.46/47.06  | | | | | | | | | | | | | | |            (31), (32), (33), (35), (36), (38), (41), (42),
% 240.46/47.06  | | | | | | | | | | | | | | |            (43), (45), (48), (49), (52), (55), (56), (57),
% 240.46/47.06  | | | | | | | | | | | | | | |            (58), (59), (60), (61), (62), (63), (64), (65),
% 240.46/47.06  | | | | | | | | | | | | | | |            (66), (68), (70), (71), (72), (73), (75), (76),
% 240.46/47.06  | | | | | | | | | | | | | | |            (78), (79), (82), (85), (86), (92), (95), (98),
% 240.46/47.06  | | | | | | | | | | | | | | |            (169), (170), (173) are inconsistent by sub-proof
% 240.46/47.06  | | | | | | | | | | | | | | |            #322.
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | |   (174)  all_58_1 = e2 & op(e3, e2) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 240.46/47.06  | | | | | | | | | | | | | | |   (175)  all_58_1 = e2
% 240.46/47.06  | | | | | | | | | | | | | | |   (176)  op(e3, e2) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (12),
% 240.46/47.06  | | | | | | | | | | | | | | |            (13), (16), (17), (22), (23), (24), (25), (28),
% 240.46/47.06  | | | | | | | | | | | | | | |            (29), (30), (31), (32), (33), (34), (35), (36),
% 240.46/47.06  | | | | | | | | | | | | | | |            (38), (39), (40), (41), (42), (43), (45), (46),
% 240.46/47.06  | | | | | | | | | | | | | | |            (48), (49), (52), (53), (55), (56), (57), (58),
% 240.46/47.06  | | | | | | | | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66),
% 240.46/47.06  | | | | | | | | | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (74),
% 240.46/47.06  | | | | | | | | | | | | | | |            (75), (76), (77), (78), (79), (80), (82), (83),
% 240.46/47.06  | | | | | | | | | | | | | | |            (85), (86), (92), (95), (98), (101), (155), (156),
% 240.46/47.06  | | | | | | | | | | | | | | |            (161), (165), (166), (169), (170), (175), (176)
% 240.46/47.06  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #307.
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | |   (177)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 240.46/47.06  | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | Case 1:
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | |   (178)  all_58_4 = e2 & op(e3, e1) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 240.46/47.06  | | | | | | | | | | | | | | |   (179)  all_58_4 = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | REF_CLOSE: (85), (169), (179) are inconsistent by sub-proof
% 240.46/47.06  | | | | | | | | | | | | | | |            #1786.
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | |   (180)  all_58_9 = e2 & op(e3, e0) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 240.46/47.06  | | | | | | | | | | | | | | |   (181)  op(e3, e0) = e2
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | | REF_CLOSE: (51), (54), (66), (181) are inconsistent by
% 240.46/47.06  | | | | | | | | | | | | | | |            sub-proof #1884.
% 240.46/47.06  | | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | |   (182)  all_58_5 = e1 & op(e2, e1) = e1
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | ALPHA: (182) implies:
% 240.46/47.06  | | | | | | | | | | | | |   (183)  op(e2, e1) = e1
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | | REF_CLOSE: (33), (66), (73), (161), (183) are inconsistent by
% 240.46/47.06  | | | | | | | | | | | | |            sub-proof #2165.
% 240.46/47.06  | | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | |   (184)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 240.46/47.06  | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | | REF_CLOSE: (8), (15), (25), (52), (66), (184) are
% 240.46/47.06  | | | | | | | | | | | |            inconsistent by sub-proof #467.
% 240.46/47.06  | | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | | 
% 240.46/47.06  | | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | | 
% 240.46/47.06  | | | | | | | | |   (185)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 240.46/47.06  | | | | | | | | |            op(e0, e1) = e0)
% 240.46/47.06  | | | | | | | | | 
% 240.46/47.06  | | | | | | | | | REF_CLOSE: (7), (8), (11), (31), (32), (33), (56), (60), (66),
% 240.46/47.06  | | | | | | | | |            (86), (156), (185) are inconsistent by sub-proof
% 240.46/47.06  | | | | | | | | |            #306.
% 240.46/47.06  | | | | | | | | | 
% 240.46/47.06  | | | | | | | | End of split
% 240.46/47.06  | | | | | | | | 
% 240.46/47.06  | | | | | | | Case 2:
% 240.46/47.06  | | | | | | | | 
% 240.46/47.06  | | | | | | | |   (186)  all_58_15 = e2 & op(e0, e0) = e2
% 240.46/47.06  | | | | | | | | 
% 240.46/47.06  | | | | | | | | REF_CLOSE: (85), (92), (186) are inconsistent by sub-proof
% 240.46/47.06  | | | | | | | |            #1917.
% 240.46/47.06  | | | | | | | | 
% 240.46/47.06  | | | | | | | End of split
% 240.46/47.06  | | | | | | | 
% 240.46/47.06  | | | | | | End of split
% 240.46/47.06  | | | | | | 
% 240.46/47.06  | | | | | End of split
% 240.46/47.06  | | | | | 
% 240.46/47.06  | | | | End of split
% 240.46/47.06  | | | | 
% 240.46/47.06  | | | End of split
% 240.46/47.06  | | | 
% 240.46/47.06  | | End of split
% 240.46/47.06  | | 
% 240.46/47.06  | End of split
% 240.46/47.06  | 
% 240.46/47.06  End of proof
% 240.46/47.06  
% 240.46/47.06  Sub-proof #305 shows that the following formulas are inconsistent:
% 240.46/47.06  ----------------------------------------------------------------
% 240.46/47.06    (1)  op(e0, e0) = e1
% 240.46/47.06    (2)  op(e2, e2) = e3
% 240.46/47.07    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.46/47.07         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.46/47.07    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.46/47.07           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.46/47.07           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.46/47.07           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.46/47.07           & $i(all_56_23))
% 240.46/47.07    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.46/47.07         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.46/47.07    (6)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 240.46/47.07           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 240.46/47.07             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 240.46/47.07    (7)   ~ (e3 = e0)
% 240.46/47.07    (8)  op(e0, e1) = all_52_11
% 240.46/47.07    (9)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.46/47.07         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.46/47.07    (10)  all_42_2 = e3
% 240.46/47.07    (11)   ~ (e2 = e0)
% 240.46/47.07    (12)  op(e1, e2) = all_52_6
% 240.46/47.07    (13)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.46/47.07          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.46/47.07    (14)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 240.46/47.07          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.46/47.07    (15)   ~ (all_52_11 = e1)
% 240.46/47.07    (16)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.46/47.07              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.46/47.07            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.46/47.07            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.46/47.07            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.46/47.07             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.07            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.46/47.07            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.46/47.07            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.46/47.07            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.46/47.07            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.46/47.07              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.46/47.07            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.46/47.07            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.46/47.07            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.46/47.07            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.46/47.07            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.46/47.07            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.46/47.07              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.46/47.07            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.46/47.07            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.46/47.07            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.46/47.07            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.46/47.07            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.46/47.07            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.46/47.07              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.46/47.07            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.46/47.07            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.46/47.07    (17)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.46/47.07          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.46/47.07    (18)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 240.46/47.07            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 240.46/47.07              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 240.46/47.07    (19)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.46/47.07          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.46/47.07    (20)  op(e1, e0) = all_52_14
% 240.46/47.07    (21)   ~ (all_52_13 = e1)
% 240.46/47.07    (22)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 240.46/47.07            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 240.46/47.07              e1) = all_20_1 & $i(all_20_1))
% 240.46/47.07    (23)   ~ (all_52_7 = e3)
% 240.46/47.07    (24)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.46/47.07          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.46/47.07    (25)   ~ (e3 = e1)
% 240.46/47.07    (26)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 240.46/47.07            op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 240.46/47.07              e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.46/47.07    (27)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.46/47.07          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.46/47.07    (28)  all_58_3 = e3
% 240.46/47.07    (29)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.46/47.07          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.46/47.07    (30)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.46/47.07              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.46/47.07                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.46/47.07                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.46/47.07    (31)   ~ (all_52_11 = e3)
% 240.46/47.07    (32)  op(e3, e1) = all_52_8
% 240.46/47.07    (33)  op(e2, e1) = all_52_9
% 240.46/47.07    (34)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.46/47.07          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.46/47.07    (35)   ~ (e3 = e2)
% 240.46/47.07    (36)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.46/47.07          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.46/47.07    (37)   ~ (all_52_14 = e1)
% 240.46/47.07    (38)   ~ (all_52_7 = e1)
% 240.54/47.07    (39)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.54/47.07            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.54/47.07            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.54/47.07            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.54/47.07            op(e0, all_56_31) = e0)
% 240.54/47.07    (40)  all_56_31 = e1
% 240.54/47.07    (41)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.54/47.07          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.54/47.07    (42)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.54/47.07          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.54/47.07    (43)  all_58_9 = e3
% 240.54/47.07    (44)  all_46_2 = e3
% 240.54/47.07    (45)  op(e3, e0) = e3
% 240.54/47.07    (46)  op(e2, e3) = all_52_1
% 240.54/47.07    (47)   ~ (all_52_14 = e3)
% 240.54/47.07    (48)  all_58_12 = e3
% 240.54/47.07    (49)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.54/47.07          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.54/47.07    (50)  all_34_2 = e1
% 240.54/47.07    (51)  op(e1, e1) = e3
% 240.54/47.07    (52)   ~ (all_52_2 = e3)
% 240.54/47.07    (53)   ~ (all_52_6 = e3)
% 240.54/47.07    (54)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.54/47.07          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.54/47.07    (55)  op(e0, e2) = all_52_7
% 240.54/47.07    (56)   ~ (all_52_4 = e3)
% 240.54/47.07    (57)  op(e3, e2) = all_52_4
% 240.54/47.07    (58)   ~ (all_52_9 = e3)
% 240.54/47.07    (59)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.54/47.07          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.54/47.07    (60)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.54/47.07          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.54/47.07    (61)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.54/47.07          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.54/47.07    (62)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.54/47.07          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.54/47.07    (63)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.54/47.07          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.54/47.07    (64)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.54/47.07            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.54/47.07    (65)  all_58_8 = e3
% 240.54/47.07    (66)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.54/47.07          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.54/47.07    (67)  op(e1, e3) = all_52_2
% 240.54/47.07    (68)  all_56_21 = e3
% 240.54/47.07    (69)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.54/47.07          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.54/47.07    (70)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.54/47.07          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.54/47.07    (71)   ~ (e1 = e0)
% 240.54/47.07    (72)  op(e3, e3) = e0
% 240.54/47.07    (73)   ~ (all_52_13 = e3)
% 240.54/47.07    (74)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.54/47.07          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.54/47.07    (75)  all_56_1 = e0
% 240.54/47.07    (76)  op(e2, e0) = all_52_13
% 240.54/47.07    (77)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.54/47.07          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.54/47.07            e1)
% 240.54/47.07    (78)   ~ (all_52_1 = e3)
% 240.54/47.07    (79)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.54/47.07          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.54/47.07            e2)
% 240.54/47.07    (80)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.54/47.07            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.54/47.07            & $i(all_8_1))
% 240.54/47.07    (81)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.54/47.07          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.54/47.07    (82)   ~ (all_52_4 = e0)
% 240.54/47.07    (83)   ~ (e2 = e1)
% 240.54/47.07    (84)   ~ (all_52_8 = e3)
% 240.54/47.07  
% 240.54/47.07  Begin of proof
% 240.54/47.07  | 
% 240.54/47.07  | BETA: splitting (14) gives:
% 240.54/47.07  | 
% 240.54/47.07  | Case 1:
% 240.54/47.07  | | 
% 240.54/47.07  | |   (85)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 240.54/47.07  | |           e1)
% 240.54/47.07  | | 
% 240.54/47.07  | | REF_CLOSE: (1), (7), (11), (21), (25), (30), (35), (60), (64), (66), (71),
% 240.54/47.07  | |            (73), (76), (83), (85) are inconsistent by sub-proof #878.
% 240.54/47.07  | | 
% 240.54/47.07  | Case 2:
% 240.54/47.07  | | 
% 240.54/47.07  | |   (86)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.54/47.07  | |           e1)
% 240.54/47.07  | | 
% 240.54/47.07  | | BETA: splitting (86) gives:
% 240.54/47.07  | | 
% 240.54/47.07  | | Case 1:
% 240.54/47.07  | | | 
% 240.54/47.07  | | |   (87)  all_58_11 = e1 & op(e1, e0) = e1
% 240.54/47.07  | | | 
% 240.54/47.07  | | | ALPHA: (87) implies:
% 240.54/47.07  | | |   (88)  op(e1, e0) = e1
% 240.54/47.07  | | | 
% 240.54/47.07  | | | REF_CLOSE: (20), (37), (64), (88) are inconsistent by sub-proof #2304.
% 240.54/47.07  | | | 
% 240.54/47.07  | | Case 2:
% 240.54/47.07  | | | 
% 240.54/47.07  | | |   (89)  all_58_15 = e1 & op(e0, e0) = e1
% 240.54/47.07  | | | 
% 240.54/47.07  | | | ALPHA: (89) implies:
% 240.54/47.07  | | |   (90)  all_58_15 = e1
% 240.54/47.07  | | | 
% 240.54/47.07  | | | BETA: splitting (6) gives:
% 240.54/47.07  | | | 
% 240.54/47.07  | | | Case 1:
% 240.54/47.07  | | | | 
% 240.54/47.07  | | | |   (91)   ~ (all_34_2 = e1)
% 240.54/47.07  | | | | 
% 240.54/47.07  | | | | REDUCE: (50), (91) imply:
% 240.54/47.07  | | | |   (92)  $false
% 240.54/47.07  | | | | 
% 240.54/47.07  | | | | CLOSE: (92) is inconsistent.
% 240.54/47.07  | | | | 
% 240.54/47.07  | | | Case 2:
% 240.54/47.07  | | | | 
% 240.54/47.07  | | | |   (93)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 240.54/47.07  | | | |           all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2)
% 240.54/47.07  | | | |           & op(e0, e1) = all_34_1 & $i(all_34_1))
% 240.54/47.07  | | | | 
% 240.54/47.07  | | | | BETA: splitting (18) gives:
% 240.54/47.07  | | | | 
% 240.54/47.07  | | | | Case 1:
% 240.54/47.07  | | | | | 
% 240.54/47.07  | | | | |   (94)   ~ (all_42_2 = e3)
% 240.54/47.07  | | | | | 
% 240.54/47.07  | | | | | REDUCE: (10), (94) imply:
% 240.54/47.07  | | | | |   (95)  $false
% 240.54/47.07  | | | | | 
% 240.54/47.07  | | | | | CLOSE: (95) is inconsistent.
% 240.54/47.07  | | | | | 
% 240.54/47.07  | | | | Case 2:
% 240.54/47.07  | | | | | 
% 240.54/47.07  | | | | |   (96)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3)
% 240.54/47.07  | | | | |           = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 240.54/47.07  | | | | |             e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 240.54/47.07  | | | | | 
% 240.54/47.07  | | | | | BETA: splitting (26) gives:
% 240.54/47.07  | | | | | 
% 240.54/47.07  | | | | | Case 1:
% 240.54/47.07  | | | | | | 
% 240.54/47.07  | | | | | |   (97)   ~ (all_46_2 = e3)
% 240.54/47.07  | | | | | | 
% 240.54/47.07  | | | | | | REDUCE: (44), (97) imply:
% 240.54/47.07  | | | | | |   (98)  $false
% 240.54/47.07  | | | | | | 
% 240.54/47.07  | | | | | | CLOSE: (98) is inconsistent.
% 240.54/47.07  | | | | | | 
% 240.54/47.07  | | | | | Case 2:
% 240.54/47.07  | | | | | | 
% 240.54/47.07  | | | | | |   (99)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1,
% 240.54/47.07  | | | | | |             e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 240.54/47.07  | | | | | |           (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.54/47.07  | | | | | | 
% 240.54/47.07  | | | | | | BETA: splitting (79) gives:
% 240.54/47.07  | | | | | | 
% 240.54/47.07  | | | | | | Case 1:
% 240.54/47.07  | | | | | | | 
% 240.54/47.07  | | | | | | |   (100)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 240.54/47.07  | | | | | | |            op(e0, e2) = e2)
% 240.54/47.07  | | | | | | | 
% 240.54/47.07  | | | | | | | BETA: splitting (100) gives:
% 240.54/47.07  | | | | | | | 
% 240.54/47.07  | | | | | | | Case 1:
% 240.54/47.07  | | | | | | | | 
% 240.54/47.07  | | | | | | | |   (101)  all_58_12 = e2 & op(e0, e3) = e2
% 240.54/47.07  | | | | | | | | 
% 240.54/47.07  | | | | | | | | REF_CLOSE: (35), (48), (101) are inconsistent by sub-proof
% 240.54/47.07  | | | | | | | |            #1974.
% 240.54/47.07  | | | | | | | | 
% 240.54/47.07  | | | | | | | Case 2:
% 240.54/47.07  | | | | | | | | 
% 240.54/47.07  | | | | | | | |   (102)  all_58_13 = e2 & op(e0, e2) = e2
% 240.54/47.07  | | | | | | | | 
% 240.54/47.07  | | | | | | | | ALPHA: (102) implies:
% 240.54/47.07  | | | | | | | |   (103)  all_58_13 = e2
% 240.54/47.07  | | | | | | | |   (104)  op(e0, e2) = e2
% 240.54/47.07  | | | | | | | | 
% 240.54/47.07  | | | | | | | | BETA: splitting (17) gives:
% 240.54/47.07  | | | | | | | | 
% 240.54/47.07  | | | | | | | | Case 1:
% 240.54/47.07  | | | | | | | | | 
% 240.54/47.07  | | | | | | | | |   (105)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 240.54/47.07  | | | | | | | | |            op(e2, e2) = e0)
% 240.54/47.07  | | | | | | | | | 
% 240.54/47.07  | | | | | | | | | BETA: splitting (105) gives:
% 240.54/47.07  | | | | | | | | | 
% 240.54/47.07  | | | | | | | | | Case 1:
% 240.54/47.07  | | | | | | | | | | 
% 240.54/47.07  | | | | | | | | | |   (106)  all_58_1 = e0 & op(e3, e2) = e0
% 240.54/47.07  | | | | | | | | | | 
% 240.54/47.07  | | | | | | | | | | REF_CLOSE: (57), (64), (82), (106) are inconsistent by
% 240.54/47.07  | | | | | | | | | |            sub-proof #1968.
% 240.54/47.07  | | | | | | | | | | 
% 240.54/47.07  | | | | | | | | | Case 2:
% 240.54/47.07  | | | | | | | | | | 
% 240.54/47.07  | | | | | | | | | |   (107)  all_58_3 = e0 & op(e2, e2) = e0
% 240.54/47.07  | | | | | | | | | | 
% 240.54/47.07  | | | | | | | | | | REF_CLOSE: (3), (7), (11), (25), (28), (29), (35), (43),
% 240.54/47.07  | | | | | | | | | |            (56), (57), (61), (64), (71), (72), (83), (107)
% 240.54/47.07  | | | | | | | | | |            are inconsistent by sub-proof #318.
% 240.54/47.07  | | | | | | | | | | 
% 240.54/47.07  | | | | | | | | | End of split
% 240.54/47.07  | | | | | | | | | 
% 240.54/47.07  | | | | | | | | Case 2:
% 240.54/47.07  | | | | | | | | | 
% 240.54/47.07  | | | | | | | | |   (108)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 240.54/47.07  | | | | | | | | |            op(e0, e2) = e0)
% 240.54/47.08  | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | BETA: splitting (108) gives:
% 240.54/47.08  | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | |   (109)  all_58_7 = e0 & op(e1, e2) = e0
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | ALPHA: (109) implies:
% 240.54/47.08  | | | | | | | | | |   (110)  op(e1, e2) = e0
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | BETA: splitting (9) gives:
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | |   (111)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 240.54/47.08  | | | | | | | | | | |            & op(e1, e2) = e1)
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | BETA: splitting (111) gives:
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | |   (112)  all_58_6 = e1 & op(e1, e3) = e1
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | ALPHA: (112) implies:
% 240.54/47.08  | | | | | | | | | | | |   (113)  op(e1, e3) = e1
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | BETA: splitting (30) gives:
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | |   (114)  all_58_15 = e0 & op(e0, e0) = e0
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | ALPHA: (114) implies:
% 240.54/47.08  | | | | | | | | | | | | |   (115)  op(e0, e0) = e0
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | REF_CLOSE: (1), (64), (71), (115) are inconsistent by
% 240.54/47.08  | | | | | | | | | | | | |            sub-proof #2274.
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | |   (116)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.54/47.08  | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.54/47.08  | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 240.54/47.08  | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.54/47.08  | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | ALPHA: (116) implies:
% 240.54/47.08  | | | | | | | | | | | | |   (117)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.54/47.08  | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 240.54/47.08  | | | | | | | | | | | | |              e0) = e0)
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | BETA: splitting (34) gives:
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | |   (118)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 240.54/47.08  | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | |   (119)  all_58_0 = e2 & op(e3, e3) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 240.54/47.08  | | | | | | | | | | | | | | |   (120)  op(e3, e3) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | REF_CLOSE: (11), (64), (72), (120) are inconsistent by
% 240.54/47.08  | | | | | | | | | | | | | | |            sub-proof #2188.
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | |   (121)  all_58_2 = e2 & op(e2, e3) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 240.54/47.08  | | | | | | | | | | | | | | |   (122)  op(e2, e3) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | |   (123)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 240.54/47.08  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 240.54/47.08  | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (11), (25), (28), (30), (35), (43),
% 240.54/47.08  | | | | | | | | | | | | | | | |            (60), (64), (66), (71), (73), (76), (83), (122),
% 240.54/47.08  | | | | | | | | | | | | | | | |            (123) are inconsistent by sub-proof #317.
% 240.54/47.08  | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | |   (124)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 240.54/47.08  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 240.54/47.08  | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 240.54/47.08  | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | |   (125)  all_58_5 = e1 & op(e2, e1) = e1
% 240.54/47.08  | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 240.54/47.08  | | | | | | | | | | | | | | | | |   (126)  op(e2, e1) = e1
% 240.54/47.08  | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 240.54/47.08  | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | |   (127)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 240.54/47.08  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 240.54/47.08  | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (11), (25), (29), (33), (35), (56),
% 240.54/47.08  | | | | | | | | | | | | | | | | | |            (57), (61), (64), (71), (72), (83), (126), (127)
% 240.54/47.08  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #316.
% 240.54/47.08  | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | |   (128)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 240.54/47.08  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 240.54/47.08  | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | |   (129)  all_58_8 = e0 & op(e1, e1) = e0
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | |   (130)  op(e1, e1) = e0
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (20), (25), (42), (47), (53), (64),
% 240.54/47.08  | | | | | | | | | | | | | | | | | | |            (113), (130) are inconsistent by sub-proof #457.
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | |   (131)  all_58_14 = e0 & op(e0, e1) = e0
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | |   (132)  op(e0, e1) = e0
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | |   (133)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | |   (134)  all_58_1 = e1 & op(e3, e2) = e1
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | |   (135)  op(e3, e2) = e1
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | |   (136)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (17), (25), (28), (38), (55), (64),
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | |            (69), (71), (72), (83), (104), (136) are
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #315.
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | |   (137)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | |   (138)  all_58_4 = e2 & op(e3, e1) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (11), (12), (13), (16), (17), (19),
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | |            (20), (25), (27), (28), (29), (33), (35), (37),
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | |            (40), (43), (54), (56), (57), (61), (62), (63),
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | |            (64), (68), (69), (70), (71), (72), (75), (80),
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | |            (83), (96), (103), (104), (110), (113), (122),
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | |            (126), (132), (135), (138) are inconsistent by
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #312.
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | |   (139)  all_58_9 = e2 & op(e3, e0) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | |   (140)  op(e3, e0) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (45), (64), (140) are inconsistent by
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2125.
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | |   (141)  all_58_3 = e1 & op(e2, e2) = e1
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (11), (25), (28), (30), (35), (43),
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | |            (60), (64), (66), (71), (73), (76), (83), (141)
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #331.
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | |   (142)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (38), (55), (64), (71), (110), (142) are
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1840.
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | |   (143)  all_58_10 = e1 & op(e2, e0) = e1
% 240.54/47.08  | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 240.54/47.08  | | | | | | | | | | | | | | | | |   (144)  all_58_10 = e1
% 240.54/47.08  | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (25), (35), (60), (64), (66), (71),
% 240.54/47.08  | | | | | | | | | | | | | | | | |            (83), (90), (117), (144) are inconsistent by
% 240.54/47.08  | | | | | | | | | | | | | | | | |            sub-proof #910.
% 240.54/47.08  | | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | |   (145)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 240.54/47.08  | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | REF_CLOSE: (35), (48), (64), (83), (113), (145) are
% 240.54/47.08  | | | | | | | | | | | | | |            inconsistent by sub-proof #311.
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | |   (146)  all_58_7 = e1 & op(e1, e2) = e1
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | ALPHA: (146) implies:
% 240.54/47.08  | | | | | | | | | | | |   (147)  op(e1, e2) = e1
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | REF_CLOSE: (12), (64), (71), (110), (147) are inconsistent by
% 240.54/47.08  | | | | | | | | | | | |            sub-proof #2136.
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | |   (148)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 240.54/47.08  | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | REF_CLOSE: (20), (25), (37), (51), (64), (148) are
% 240.54/47.08  | | | | | | | | | | |            inconsistent by sub-proof #453.
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | |   (149)  all_58_13 = e0 & op(e0, e2) = e0
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | ALPHA: (149) implies:
% 240.54/47.08  | | | | | | | | | |   (150)  op(e0, e2) = e0
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | REF_CLOSE: (11), (64), (104), (150) are inconsistent by
% 240.54/47.08  | | | | | | | | | |            sub-proof #2132.
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | 
% 240.54/47.08  | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | 
% 240.54/47.08  | | | | | | | End of split
% 240.54/47.08  | | | | | | | 
% 240.54/47.08  | | | | | | Case 2:
% 240.54/47.08  | | | | | | | 
% 240.54/47.08  | | | | | | |   (151)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 240.54/47.08  | | | | | | |            op(e0, e0) = e2)
% 240.54/47.08  | | | | | | | 
% 240.54/47.08  | | | | | | | BETA: splitting (151) gives:
% 240.54/47.08  | | | | | | | 
% 240.54/47.08  | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | 
% 240.54/47.08  | | | | | | | |   (152)  all_58_14 = e2 & op(e0, e1) = e2
% 240.54/47.08  | | | | | | | | 
% 240.54/47.08  | | | | | | | | ALPHA: (152) implies:
% 240.54/47.08  | | | | | | | |   (153)  all_58_14 = e2
% 240.54/47.08  | | | | | | | |   (154)  op(e0, e1) = e2
% 240.54/47.08  | | | | | | | | 
% 240.54/47.08  | | | | | | | | BETA: splitting (27) gives:
% 240.54/47.08  | | | | | | | | 
% 240.54/47.08  | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | 
% 240.54/47.08  | | | | | | | | |   (155)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 240.54/47.08  | | | | | | | | |            op(e2, e1) = e0)
% 240.54/47.08  | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | BETA: splitting (155) gives:
% 240.54/47.08  | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | |   (156)  all_58_4 = e0 & op(e3, e1) = e0
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | ALPHA: (156) implies:
% 240.54/47.08  | | | | | | | | | |   (157)  all_58_4 = e0
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | REF_CLOSE: (3), (7), (11), (25), (29), (35), (56), (57),
% 240.54/47.08  | | | | | | | | | |            (61), (64), (71), (72), (83), (157) are
% 240.54/47.08  | | | | | | | | | |            inconsistent by sub-proof #1512.
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | |   (158)  all_58_5 = e0 & op(e2, e1) = e0
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | ALPHA: (158) implies:
% 240.54/47.08  | | | | | | | | | |   (159)  op(e2, e1) = e0
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | BETA: splitting (30) gives:
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | |   (160)  all_58_15 = e0 & op(e0, e0) = e0
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | ALPHA: (160) implies:
% 240.54/47.08  | | | | | | | | | | |   (161)  op(e0, e0) = e0
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | REF_CLOSE: (1), (64), (71), (161) are inconsistent by
% 240.54/47.08  | | | | | | | | | | |            sub-proof #2274.
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | |   (162)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.54/47.08  | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.54/47.08  | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 240.54/47.08  | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.54/47.08  | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | ALPHA: (162) implies:
% 240.54/47.08  | | | | | | | | | | |   (163)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 240.54/47.08  | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 240.54/47.08  | | | | | | | | | | |              e1) = e0)
% 240.54/47.08  | | | | | | | | | | |   (164)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.54/47.08  | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 240.54/47.08  | | | | | | | | | | |              e0) = e0)
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | BETA: splitting (19) gives:
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | |   (165)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 240.54/47.08  | | | | | | | | | | | |            & op(e2, e1) = e1)
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | BETA: splitting (165) gives:
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | |   (166)  all_58_4 = e1 & op(e3, e1) = e1
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | ALPHA: (166) implies:
% 240.54/47.08  | | | | | | | | | | | | |   (167)  all_58_4 = e1
% 240.54/47.08  | | | | | | | | | | | | |   (168)  op(e3, e1) = e1
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | BETA: splitting (3) gives:
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | |   (169)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 240.54/47.08  | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | |   (170)  all_58_0 = e2 & op(e3, e3) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 240.54/47.08  | | | | | | | | | | | | | | |   (171)  op(e3, e3) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (12),
% 240.54/47.08  | | | | | | | | | | | | | | |            (13), (17), (22), (23), (25), (28), (29), (30),
% 240.54/47.08  | | | | | | | | | | | | | | |            (31), (32), (33), (35), (36), (38), (41), (42),
% 240.54/47.08  | | | | | | | | | | | | | | |            (43), (45), (48), (49), (51), (53), (54), (55),
% 240.54/47.08  | | | | | | | | | | | | | | |            (56), (57), (58), (59), (60), (61), (62), (63),
% 240.54/47.08  | | | | | | | | | | | | | | |            (64), (66), (68), (69), (70), (71), (73), (74),
% 240.54/47.08  | | | | | | | | | | | | | | |            (76), (77), (80), (83), (84), (90), (93), (96),
% 240.54/47.08  | | | | | | | | | | | | | | |            (167), (168), (171) are inconsistent by sub-proof
% 240.54/47.08  | | | | | | | | | | | | | | |            #322.
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | |   (172)  all_58_1 = e2 & op(e3, e2) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 240.54/47.08  | | | | | | | | | | | | | | |   (173)  all_58_1 = e2
% 240.54/47.08  | | | | | | | | | | | | | | |   (174)  op(e3, e2) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (12),
% 240.54/47.08  | | | | | | | | | | | | | | |            (13), (16), (17), (22), (23), (24), (25), (28),
% 240.54/47.08  | | | | | | | | | | | | | | |            (29), (30), (31), (32), (33), (34), (35), (36),
% 240.54/47.08  | | | | | | | | | | | | | | |            (38), (39), (40), (41), (42), (43), (45), (46),
% 240.54/47.08  | | | | | | | | | | | | | | |            (48), (49), (51), (52), (53), (54), (55), (56),
% 240.54/47.08  | | | | | | | | | | | | | | |            (57), (58), (59), (60), (61), (62), (63), (64),
% 240.54/47.08  | | | | | | | | | | | | | | |            (65), (66), (67), (68), (69), (70), (71), (72),
% 240.54/47.08  | | | | | | | | | | | | | | |            (73), (74), (75), (76), (77), (78), (80), (81),
% 240.54/47.08  | | | | | | | | | | | | | | |            (83), (84), (90), (93), (96), (99), (153), (154),
% 240.54/47.08  | | | | | | | | | | | | | | |            (159), (163), (164), (167), (168), (173), (174)
% 240.54/47.08  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #307.
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | |   (175)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 240.54/47.08  | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | Case 1:
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | |   (176)  all_58_4 = e2 & op(e3, e1) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 240.54/47.08  | | | | | | | | | | | | | | |   (177)  all_58_4 = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | REF_CLOSE: (83), (167), (177) are inconsistent by sub-proof
% 240.54/47.08  | | | | | | | | | | | | | | |            #1786.
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | |   (178)  all_58_9 = e2 & op(e3, e0) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 240.54/47.08  | | | | | | | | | | | | | | |   (179)  op(e3, e0) = e2
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | | REF_CLOSE: (35), (45), (64), (179) are inconsistent by
% 240.54/47.08  | | | | | | | | | | | | | | |            sub-proof #2125.
% 240.54/47.08  | | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | |   (180)  all_58_5 = e1 & op(e2, e1) = e1
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | ALPHA: (180) implies:
% 240.54/47.08  | | | | | | | | | | | | |   (181)  op(e2, e1) = e1
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | | REF_CLOSE: (33), (64), (71), (159), (181) are inconsistent by
% 240.54/47.08  | | | | | | | | | | | | |            sub-proof #2165.
% 240.54/47.08  | | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | |   (182)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 240.54/47.08  | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | | REF_CLOSE: (8), (15), (25), (51), (64), (182) are
% 240.54/47.08  | | | | | | | | | | | |            inconsistent by sub-proof #467.
% 240.54/47.08  | | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | | 
% 240.54/47.08  | | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | | 
% 240.54/47.08  | | | | | | | | |   (183)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 240.54/47.08  | | | | | | | | |            op(e0, e1) = e0)
% 240.54/47.08  | | | | | | | | | 
% 240.54/47.08  | | | | | | | | | REF_CLOSE: (7), (8), (11), (31), (32), (33), (54), (58), (64),
% 240.54/47.08  | | | | | | | | |            (84), (154), (183) are inconsistent by sub-proof
% 240.54/47.08  | | | | | | | | |            #306.
% 240.54/47.08  | | | | | | | | | 
% 240.54/47.08  | | | | | | | | End of split
% 240.54/47.08  | | | | | | | | 
% 240.54/47.08  | | | | | | | Case 2:
% 240.54/47.08  | | | | | | | | 
% 240.54/47.08  | | | | | | | |   (184)  all_58_15 = e2 & op(e0, e0) = e2
% 240.54/47.08  | | | | | | | | 
% 240.54/47.09  | | | | | | | | REF_CLOSE: (83), (90), (184) are inconsistent by sub-proof
% 240.54/47.09  | | | | | | | |            #1917.
% 240.54/47.09  | | | | | | | | 
% 240.54/47.09  | | | | | | | End of split
% 240.54/47.09  | | | | | | | 
% 240.54/47.09  | | | | | | End of split
% 240.54/47.09  | | | | | | 
% 240.54/47.09  | | | | | End of split
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | End of split
% 240.54/47.09  | | | | 
% 240.54/47.09  | | | End of split
% 240.54/47.09  | | | 
% 240.54/47.09  | | End of split
% 240.54/47.09  | | 
% 240.54/47.09  | End of split
% 240.54/47.09  | 
% 240.54/47.09  End of proof
% 240.54/47.09  
% 240.54/47.09  Sub-proof #306 shows that the following formulas are inconsistent:
% 240.54/47.09  ----------------------------------------------------------------
% 240.54/47.09    (1)   ~ (e3 = e0)
% 240.54/47.09    (2)  op(e0, e1) = all_52_11
% 240.54/47.09    (3)  op(e0, e1) = e2
% 240.54/47.09    (4)   ~ (e2 = e0)
% 240.54/47.09    (5)   ~ (all_52_11 = e3)
% 240.54/47.09    (6)  op(e3, e1) = all_52_8
% 240.54/47.09    (7)  op(e2, e1) = all_52_9
% 240.54/47.09    (8)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.54/47.09    (9)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.54/47.09         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.54/47.09    (10)   ~ (all_52_9 = e3)
% 240.54/47.09    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.54/47.09            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.54/47.09    (12)   ~ (all_52_8 = e3)
% 240.54/47.09  
% 240.54/47.09  Begin of proof
% 240.54/47.09  | 
% 240.54/47.09  | BETA: splitting (8) gives:
% 240.54/47.09  | 
% 240.54/47.09  | Case 1:
% 240.54/47.09  | | 
% 240.54/47.09  | |   (13)  all_58_8 = e0 & op(e1, e1) = e0
% 240.54/47.09  | | 
% 240.54/47.09  | | ALPHA: (13) implies:
% 240.54/47.09  | |   (14)  op(e1, e1) = e0
% 240.54/47.09  | | 
% 240.54/47.09  | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (14) are
% 240.54/47.09  | |            inconsistent by sub-proof #1010.
% 240.54/47.09  | | 
% 240.54/47.09  | Case 2:
% 240.54/47.09  | | 
% 240.54/47.09  | |   (15)  all_58_14 = e0 & op(e0, e1) = e0
% 240.54/47.09  | | 
% 240.54/47.09  | | ALPHA: (15) implies:
% 240.54/47.09  | |   (16)  op(e0, e1) = e0
% 240.54/47.09  | | 
% 240.54/47.09  | | REF_CLOSE: (3), (4), (11), (16) are inconsistent by sub-proof #458.
% 240.54/47.09  | | 
% 240.54/47.09  | End of split
% 240.54/47.09  | 
% 240.54/47.09  End of proof
% 240.54/47.09  
% 240.54/47.09  Sub-proof #307 shows that the following formulas are inconsistent:
% 240.54/47.09  ----------------------------------------------------------------
% 240.54/47.09    (1)  op(e0, e0) = e1
% 240.54/47.09    (2)  op(e2, e2) = e3
% 240.54/47.09    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.54/47.09         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.54/47.09    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.54/47.09           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.54/47.09           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.54/47.09           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.54/47.09           & $i(all_56_23))
% 240.54/47.09    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.54/47.09         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.54/47.09    (6)   ~ (e3 = e0)
% 240.54/47.09    (7)  op(e0, e1) = all_52_11
% 240.54/47.09    (8)  op(e0, e1) = e2
% 240.54/47.09    (9)   ~ (e2 = e0)
% 240.54/47.09    (10)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 240.54/47.09          (all_58_11 = e0 & op(e1, e0) = e0)
% 240.54/47.09    (11)  op(e1, e2) = all_52_6
% 240.54/47.09    (12)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.54/47.09          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.54/47.09    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.54/47.09              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.54/47.09            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.54/47.09            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.54/47.09            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.54/47.09             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.54/47.09            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.54/47.09            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.54/47.09            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.54/47.09            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.54/47.09            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.54/47.09              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.54/47.09            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.54/47.09            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.54/47.09            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.54/47.09            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.54/47.09            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.54/47.09            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.54/47.09              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.54/47.09            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.54/47.09            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.54/47.09            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.54/47.09            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.54/47.09            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.54/47.09            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.54/47.09              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.54/47.09            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.54/47.09            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.54/47.09    (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.54/47.09          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.54/47.09    (15)  all_58_14 = e2
% 240.54/47.09    (16)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 240.54/47.09            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 240.54/47.09              e1) = all_20_1 & $i(all_20_1))
% 240.54/47.09    (17)   ~ (all_52_7 = e3)
% 240.54/47.09    (18)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.54/47.09          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.54/47.09    (19)   ~ (e3 = e1)
% 240.54/47.09    (20)  all_58_3 = e3
% 240.54/47.09    (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.54/47.09          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.54/47.09    (22)  op(e3, e2) = e2
% 240.54/47.09    (23)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.54/47.09              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.54/47.09                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.54/47.09                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.54/47.09    (24)   ~ (all_52_11 = e3)
% 240.54/47.09    (25)  op(e3, e1) = all_52_8
% 240.54/47.09    (26)  op(e2, e1) = all_52_9
% 240.54/47.09    (27)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.54/47.09          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.54/47.09    (28)   ~ (e3 = e2)
% 240.54/47.09    (29)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.54/47.09          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.54/47.09    (30)   ~ (all_52_7 = e1)
% 240.54/47.09    (31)  op(e3, e1) = e1
% 240.54/47.09    (32)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.54/47.09            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.54/47.09            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.54/47.09            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.54/47.09            op(e0, all_56_31) = e0)
% 240.54/47.09    (33)  all_56_31 = e1
% 240.54/47.09    (34)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.54/47.09          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.54/47.09    (35)  all_58_15 = e1
% 240.54/47.09    (36)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.54/47.09          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.54/47.09    (37)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.54/47.09            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.54/47.09              e3) = all_42_1 & $i(all_42_1))
% 240.54/47.09    (38)  all_58_9 = e3
% 240.54/47.09    (39)  op(e3, e0) = e3
% 240.54/47.09    (40)  all_58_4 = e1
% 240.54/47.09    (41)  op(e2, e3) = all_52_1
% 240.54/47.09    (42)  all_58_12 = e3
% 240.54/47.09    (43)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.54/47.09          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.54/47.09    (44)  op(e1, e1) = e3
% 240.54/47.09    (45)   ~ (all_52_2 = e3)
% 240.54/47.09    (46)   ~ (all_52_6 = e3)
% 240.54/47.09    (47)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.54/47.09          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.54/47.09    (48)  op(e0, e2) = all_52_7
% 240.54/47.09    (49)  op(e2, e1) = e0
% 240.54/47.09    (50)   ~ (all_52_4 = e3)
% 240.54/47.09    (51)  op(e3, e2) = all_52_4
% 240.54/47.09    (52)  all_58_1 = e2
% 240.54/47.09    (53)   ~ (all_52_9 = e3)
% 240.54/47.09    (54)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.54/47.09          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.54/47.09    (55)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 240.54/47.09            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 240.54/47.09              e1) = all_34_1 & $i(all_34_1))
% 240.54/47.09    (56)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.54/47.09          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.54/47.09    (57)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.54/47.09          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.54/47.09    (58)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.54/47.09          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.54/47.09    (59)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.54/47.09          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.54/47.09    (60)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.54/47.09            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.54/47.09    (61)  all_58_8 = e3
% 240.54/47.09    (62)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.54/47.09          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.54/47.09    (63)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.54/47.09            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.54/47.09              e3) = all_46_1 & $i(all_46_1))
% 240.54/47.09    (64)  op(e1, e3) = all_52_2
% 240.54/47.09    (65)  all_56_21 = e3
% 240.54/47.09    (66)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.54/47.09          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.54/47.09    (67)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.54/47.09          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.54/47.09    (68)   ~ (e1 = e0)
% 240.54/47.09    (69)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.54/47.09          | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.54/47.09    (70)  op(e3, e3) = e0
% 240.54/47.09    (71)   ~ (all_52_13 = e3)
% 240.54/47.09    (72)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.54/47.09          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.54/47.09    (73)  all_56_1 = e0
% 240.54/47.09    (74)  op(e2, e0) = all_52_13
% 240.54/47.09    (75)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.54/47.09          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.54/47.09            e1)
% 240.54/47.09    (76)   ~ (all_52_1 = e3)
% 240.54/47.09    (77)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.54/47.09            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.54/47.09            & $i(all_8_1))
% 240.54/47.09    (78)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.54/47.09          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.54/47.09    (79)   ~ (e2 = e1)
% 240.54/47.09    (80)   ~ (all_52_8 = e3)
% 240.54/47.09  
% 240.54/47.09  Begin of proof
% 240.54/47.09  | 
% 240.54/47.09  | BETA: splitting (78) gives:
% 240.54/47.09  | 
% 240.54/47.09  | Case 1:
% 240.54/47.09  | | 
% 240.54/47.09  | |   (81)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 240.54/47.09  | |           e1)
% 240.54/47.09  | | 
% 240.54/47.09  | | BETA: splitting (81) gives:
% 240.54/47.09  | | 
% 240.54/47.09  | | Case 1:
% 240.54/47.09  | | | 
% 240.54/47.09  | | |   (82)  all_58_2 = e1 & op(e2, e3) = e1
% 240.54/47.09  | | | 
% 240.54/47.09  | | | ALPHA: (82) implies:
% 240.54/47.09  | | |   (83)  all_58_2 = e1
% 240.54/47.09  | | |   (84)  op(e2, e3) = e1
% 240.54/47.09  | | | 
% 240.54/47.09  | | | BETA: splitting (18) gives:
% 240.54/47.09  | | | 
% 240.54/47.09  | | | Case 1:
% 240.54/47.09  | | | | 
% 240.54/47.09  | | | |   (85)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2)
% 240.54/47.09  | | | |           = e2)
% 240.54/47.09  | | | | 
% 240.54/47.09  | | | | BETA: splitting (85) gives:
% 240.54/47.09  | | | | 
% 240.54/47.09  | | | | Case 1:
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | |   (86)  all_58_2 = e2 & op(e2, e3) = e2
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | | ALPHA: (86) implies:
% 240.54/47.09  | | | | |   (87)  op(e2, e3) = e2
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | | REF_CLOSE: (60), (79), (84), (87) are inconsistent by sub-proof #1633.
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | Case 2:
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | |   (88)  all_58_3 = e2 & op(e2, e2) = e2
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | | ALPHA: (88) implies:
% 240.54/47.09  | | | | |   (89)  op(e2, e2) = e2
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | | REF_CLOSE: (6), (9), (11), (14), (17), (19), (22), (28), (48), (52),
% 240.54/47.09  | | | | |            (60), (66), (67), (68), (79), (89) are inconsistent by
% 240.54/47.09  | | | | |            sub-proof #1809.
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | End of split
% 240.54/47.09  | | | | 
% 240.54/47.09  | | | Case 2:
% 240.54/47.09  | | | | 
% 240.54/47.09  | | | |   (90)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0)
% 240.54/47.09  | | | |           = e2)
% 240.54/47.09  | | | | 
% 240.54/47.09  | | | | BETA: splitting (90) gives:
% 240.54/47.09  | | | | 
% 240.54/47.09  | | | | Case 1:
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | |   (91)  all_58_5 = e2 & op(e2, e1) = e2
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | | ALPHA: (91) implies:
% 240.54/47.09  | | | | |   (92)  op(e2, e1) = e2
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | | REF_CLOSE: (9), (49), (60), (92) are inconsistent by sub-proof #1906.
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | Case 2:
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | |   (93)  all_58_10 = e2 & op(e2, e0) = e2
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | | ALPHA: (93) implies:
% 240.54/47.09  | | | | |   (94)  op(e2, e0) = e2
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | | BETA: splitting (66) gives:
% 240.54/47.09  | | | | | 
% 240.54/47.09  | | | | | Case 1:
% 240.54/47.09  | | | | | | 
% 240.54/47.09  | | | | | |   (95)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 240.54/47.09  | | | | | |             e2) = e1)
% 240.54/47.09  | | | | | | 
% 240.54/47.09  | | | | | | BETA: splitting (95) gives:
% 240.54/47.09  | | | | | | 
% 240.54/47.09  | | | | | | Case 1:
% 240.54/47.09  | | | | | | | 
% 240.54/47.09  | | | | | | |   (96)  all_58_1 = e1 & op(e3, e2) = e1
% 240.54/47.09  | | | | | | | 
% 240.54/47.09  | | | | | | | ALPHA: (96) implies:
% 240.54/47.09  | | | | | | |   (97)  all_58_1 = e1
% 240.54/47.09  | | | | | | | 
% 240.54/47.10  | | | | | | | REF_CLOSE: (3), (6), (9), (19), (21), (28), (39), (40), (43),
% 240.54/47.10  | | | | | | |            (50), (51), (60), (68), (79), (97) are inconsistent by
% 240.54/47.10  | | | | | | |            sub-proof #1437.
% 240.54/47.10  | | | | | | | 
% 240.54/47.10  | | | | | | Case 2:
% 240.54/47.10  | | | | | | | 
% 240.54/47.10  | | | | | | |   (98)  all_58_3 = e1 & op(e2, e2) = e1
% 240.54/47.10  | | | | | | | 
% 240.54/47.10  | | | | | | | ALPHA: (98) implies:
% 240.54/47.10  | | | | | | |   (99)  all_58_3 = e1
% 240.54/47.10  | | | | | | | 
% 240.54/47.10  | | | | | | | COMBINE_EQS: (20), (99) imply:
% 240.54/47.10  | | | | | | |   (100)  e3 = e1
% 240.54/47.10  | | | | | | | 
% 240.54/47.10  | | | | | | | COMBINE_EQS: (38), (100) imply:
% 240.54/47.10  | | | | | | |   (101)  all_58_9 = e1
% 240.54/47.10  | | | | | | | 
% 240.54/47.10  | | | | | | | REF_CLOSE: (1), (6), (9), (19), (23), (35), (56), (60), (68),
% 240.54/47.10  | | | | | | |            (71), (74), (94), (101) are inconsistent by sub-proof
% 240.54/47.10  | | | | | | |            #971.
% 240.54/47.10  | | | | | | | 
% 240.54/47.10  | | | | | | End of split
% 240.54/47.10  | | | | | | 
% 240.54/47.10  | | | | | Case 2:
% 240.54/47.10  | | | | | | 
% 240.54/47.10  | | | | | |   (102)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 240.54/47.10  | | | | | |            op(e0, e2) = e1)
% 240.54/47.10  | | | | | | 
% 240.54/47.10  | | | | | | BETA: splitting (102) gives:
% 240.54/47.10  | | | | | | 
% 240.54/47.10  | | | | | | Case 1:
% 240.54/47.10  | | | | | | | 
% 240.54/47.10  | | | | | | |   (103)  all_58_7 = e1 & op(e1, e2) = e1
% 240.54/47.10  | | | | | | | 
% 240.54/47.10  | | | | | | | ALPHA: (103) implies:
% 240.54/47.10  | | | | | | |   (104)  all_58_7 = e1
% 240.54/47.10  | | | | | | |   (105)  op(e1, e2) = e1
% 240.54/47.10  | | | | | | | 
% 240.54/47.10  | | | | | | | BETA: splitting (27) gives:
% 240.54/47.10  | | | | | | | 
% 240.54/47.10  | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | 
% 240.54/47.10  | | | | | | | |   (106)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 &
% 240.54/47.10  | | | | | | | |            op(e2, e3) = e2)
% 240.54/47.10  | | | | | | | | 
% 240.54/47.10  | | | | | | | | BETA: splitting (106) gives:
% 240.54/47.10  | | | | | | | | 
% 240.54/47.10  | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | |   (107)  all_58_0 = e2 & op(e3, e3) = e2
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | ALPHA: (107) implies:
% 240.54/47.10  | | | | | | | | |   (108)  op(e3, e3) = e2
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12),
% 240.54/47.10  | | | | | | | | |            (14), (16), (17), (19), (20), (21), (23), (24),
% 240.54/47.10  | | | | | | | | |            (25), (26), (28), (29), (31), (34), (35), (36),
% 240.54/47.10  | | | | | | | | |            (37), (38), (39), (40), (42), (43), (44), (46),
% 240.54/47.10  | | | | | | | | |            (47), (48), (50), (51), (53), (54), (55), (56),
% 240.54/47.10  | | | | | | | | |            (57), (58), (59), (60), (62), (65), (66), (67),
% 240.54/47.10  | | | | | | | | |            (68), (71), (72), (74), (75), (77), (79), (80),
% 240.54/47.10  | | | | | | | | |            (104), (105), (108) are inconsistent by sub-proof
% 240.54/47.10  | | | | | | | | |            #323.
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | |   (109)  all_58_2 = e2 & op(e2, e3) = e2
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | ALPHA: (109) implies:
% 240.54/47.10  | | | | | | | | |   (110)  op(e2, e3) = e2
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | REF_CLOSE: (60), (79), (84), (110) are inconsistent by
% 240.54/47.10  | | | | | | | | |            sub-proof #1633.
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | End of split
% 240.54/47.10  | | | | | | | | 
% 240.54/47.10  | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | 
% 240.54/47.10  | | | | | | | |   (111)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 &
% 240.54/47.10  | | | | | | | |            op(e0, e3) = e2)
% 240.54/47.10  | | | | | | | | 
% 240.54/47.10  | | | | | | | | BETA: splitting (111) gives:
% 240.54/47.10  | | | | | | | | 
% 240.54/47.10  | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | |   (112)  all_58_6 = e2 & op(e1, e3) = e2
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | ALPHA: (112) implies:
% 240.54/47.10  | | | | | | | | |   (113)  all_58_6 = e2
% 240.54/47.10  | | | | | | | | |   (114)  op(e1, e3) = e2
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | BETA: splitting (14) gives:
% 240.54/47.10  | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | |   (115)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 240.54/47.10  | | | | | | | | | |            & op(e2, e2) = e0)
% 240.54/47.10  | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | BETA: splitting (115) gives:
% 240.54/47.10  | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | |   (116)  all_58_1 = e0 & op(e3, e2) = e0
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | ALPHA: (116) implies:
% 240.54/47.10  | | | | | | | | | | |   (117)  op(e3, e2) = e0
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | REF_CLOSE: (9), (22), (60), (117) are inconsistent by
% 240.54/47.10  | | | | | | | | | | |            sub-proof #2026.
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | |   (118)  all_58_3 = e0 & op(e2, e2) = e0
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | ALPHA: (118) implies:
% 240.54/47.10  | | | | | | | | | | |   (119)  all_58_3 = e0
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | REF_CLOSE: (6), (9), (12), (15), (19), (28), (42), (60),
% 240.54/47.10  | | | | | | | | | | |            (67), (69), (79), (104), (119) are inconsistent by
% 240.54/47.10  | | | | | | | | | | |            sub-proof #1067.
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | End of split
% 240.54/47.10  | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | |   (120)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0
% 240.54/47.10  | | | | | | | | | |            & op(e0, e2) = e0)
% 240.54/47.10  | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | BETA: splitting (120) gives:
% 240.54/47.10  | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | |   (121)  all_58_7 = e0 & op(e1, e2) = e0
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | ALPHA: (121) implies:
% 240.54/47.10  | | | | | | | | | | |   (122)  op(e1, e2) = e0
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | REF_CLOSE: (11), (60), (68), (105), (122) are inconsistent by
% 240.54/47.10  | | | | | | | | | | |            sub-proof #2136.
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | |   (123)  all_58_13 = e0 & op(e0, e2) = e0
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | ALPHA: (123) implies:
% 240.54/47.10  | | | | | | | | | | |   (124)  op(e0, e2) = e0
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | BETA: splitting (72) gives:
% 240.54/47.10  | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | |   (125)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 240.54/47.10  | | | | | | | | | | | |            & op(e1, e2) = e0)
% 240.54/47.10  | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | BETA: splitting (125) gives:
% 240.54/47.10  | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | |   (126)  all_58_6 = e0 & op(e1, e3) = e0
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | ALPHA: (126) implies:
% 240.54/47.10  | | | | | | | | | | | | |   (127)  all_58_6 = e0
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | REF_CLOSE: (9), (27), (28), (42), (60), (70), (79), (83),
% 240.54/47.10  | | | | | | | | | | | | |            (127) are inconsistent by sub-proof #1443.
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | |   (128)  all_58_7 = e0 & op(e1, e2) = e0
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | ALPHA: (128) implies:
% 240.54/47.10  | | | | | | | | | | | | |   (129)  op(e1, e2) = e0
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | REF_CLOSE: (11), (60), (68), (105), (129) are inconsistent by
% 240.54/47.10  | | | | | | | | | | | | |            sub-proof #2136.
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | End of split
% 240.54/47.10  | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | |   (130)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 240.54/47.10  | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 240.54/47.10  | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | BETA: splitting (130) gives:
% 240.54/47.10  | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | |   (131)  all_58_8 = e0 & op(e1, e1) = e0
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | ALPHA: (131) implies:
% 240.54/47.10  | | | | | | | | | | | | |   (132)  op(e1, e1) = e0
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (24), (25), (26), (47), (53), (60),
% 240.54/47.10  | | | | | | | | | | | | |            (80), (132) are inconsistent by sub-proof #1010.
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | |   (133)  all_58_11 = e0 & op(e1, e0) = e0
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | ALPHA: (133) implies:
% 240.54/47.10  | | | | | | | | | | | | |   (134)  all_58_11 = e0
% 240.54/47.10  | | | | | | | | | | | | |   (135)  op(e1, e0) = e0
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | BETA: splitting (32) gives:
% 240.54/47.10  | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | |   (136)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.54/47.10  | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 240.54/47.10  | | | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 240.54/47.10  | | | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 240.54/47.10  | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 240.54/47.10  | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | |   (137)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.54/47.10  | | | | | | | | | | | | | | |            e0) = all_56_25 & $i(all_56_25)
% 240.54/47.10  | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 240.54/47.10  | | | | | | | | | | | | | | |   (138)  op(e3, e0) = all_56_25
% 240.54/47.10  | | | | | | | | | | | | | | |   (139)  op(e3, all_56_25) = e3
% 240.54/47.10  | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 240.54/47.10  | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | |   (140)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.54/47.10  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.54/47.10  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.54/47.10  | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.54/47.10  | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.54/47.10  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.54/47.10  | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.54/47.10  | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.54/47.10  | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.54/47.10  | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.54/47.10  | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 240.54/47.10  | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.54/47.10  | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 240.54/47.10  | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 240.54/47.10  | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | |   (141)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.54/47.10  | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.54/47.10  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.54/47.10  | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.54/47.10  | | | | | | | | | | | | | | | | |            = e3)
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (45), (60), (64), (76), (79), (84), (141)
% 240.54/47.10  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #436.
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | |   (142)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.54/47.10  | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.54/47.10  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.54/47.10  | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 240.54/47.10  | | | | | | | | | | | | | | | | |            = e0)
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | |   (143)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.54/47.10  | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 240.54/47.10  | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 240.54/47.10  | | | | | | | | | | | | | | | | | |            e3) = e1
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 240.54/47.10  | | | | | | | | | | | | | | | | | |   (144)  op(e1, e3) = e1
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (79), (114), (144) are inconsistent by
% 240.54/47.10  | | | | | | | | | | | | | | | | | |            sub-proof #2226.
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | |   (145)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 240.54/47.10  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.54/47.10  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.54/47.10  | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 240.54/47.10  | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.54/47.10  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.54/47.10  | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |   (146)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |            e3) = e3
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |   (147)   ~ (all_56_1 = e0)
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | REDUCE: (73), (147) imply:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |   (148)  $false
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | CLOSE: (148) is inconsistent.
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |   (149)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |            e3) = e0
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |   (150)  op(e3, e0) = e0
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (60), (138), (139), (150) are inconsistent by
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |            sub-proof #1926.
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | End of split
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | End of split
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | End of split
% 240.54/47.10  | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | |   (151)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.54/47.10  | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.54/47.10  | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.54/47.10  | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.54/47.10  | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.54/47.10  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.54/47.10  | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.54/47.10  | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.54/47.10  | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.54/47.10  | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.54/47.10  | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.54/47.10  | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.54/47.10  | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.54/47.10  | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 240.54/47.10  | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | |   (152)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.54/47.10  | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.54/47.10  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.54/47.10  | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.54/47.10  | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.54/47.10  | | | | | | | | | | | | | | | | |            = e2)
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (26), (49), (60), (68), (124), (152) are
% 240.54/47.10  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #310.
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | |   (153)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.54/47.10  | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.54/47.10  | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.54/47.10  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.54/47.10  | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.54/47.10  | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.54/47.10  | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.54/47.10  | | | | | | | | | | | | | | | | |            = e0)
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 240.54/47.10  | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | |   (154)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.54/47.10  | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.54/47.10  | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 240.54/47.10  | | | | | | | | | | | | | | | | | |            e2) = e0
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 240.54/47.10  | | | | | | | | | | | | | | | | | |   (155)  op(e2, e0) = e0
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |   (156)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (28), (39), (60), (155), (156) are
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1182.
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |   (157)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 240.54/47.10  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | |   (158)  all_58_11 = e2 & op(e1, e0) = e2
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | |   (159)  all_58_11 = e2
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (159) imply:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | |   (160)  e2 = e0
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (160) imply:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | |   (161)  all_58_1 = e0
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (9), (12), (19), (20), (28), (60), (66),
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | |            (68), (79), (124), (161) are inconsistent by
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | |            sub-proof #309.
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | |   (162)  all_58_15 = e2 & op(e0, e0) = e2
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (9), (11), (12), (14), (20), (28), (35),
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | |            (52), (60), (68), (79), (104), (105), (162) are
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #871.
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | End of split
% 240.54/47.10  | | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | | End of split
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.54/47.10  | | | | | | | | | | | | | | | | | Case 2:
% 240.54/47.10  | | | | | | | | | | | | | | | | | | 
% 240.62/47.10  | | | | | | | | | | | | | | | | | |   (163)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.62/47.10  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.62/47.10  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.62/47.10  | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.62/47.10  | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.62/47.10  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.62/47.10  | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.62/47.10  | | | | | | | | | | | | | | | | | | 
% 240.62/47.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (60), (68), (135), (163) are
% 240.62/47.10  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #390.
% 240.62/47.10  | | | | | | | | | | | | | | | | | | 
% 240.62/47.10  | | | | | | | | | | | | | | | | | End of split
% 240.62/47.10  | | | | | | | | | | | | | | | | | 
% 240.62/47.10  | | | | | | | | | | | | | | | | End of split
% 240.62/47.11  | | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | | End of split
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | Case 2:
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | |   (164)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 240.62/47.11  | | | | | | | | | | | | | | |            e0) = all_56_27 & $i(all_56_27)
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 240.62/47.11  | | | | | | | | | | | | | | |   (165)  op(e2, e0) = all_56_27
% 240.62/47.11  | | | | | | | | | | | | | | |   (166)  op(e2, all_56_27) = e2
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | | REF_CLOSE: (2), (28), (60), (94), (165), (166) are
% 240.62/47.11  | | | | | | | | | | | | | | |            inconsistent by sub-proof #954.
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | End of split
% 240.62/47.11  | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | Case 2:
% 240.62/47.11  | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | |   (167)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.62/47.11  | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 240.62/47.11  | | | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 240.62/47.11  | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 240.62/47.11  | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | Case 1:
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | |   (168)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.62/47.11  | | | | | | | | | | | | | | |            e0) = all_56_29 & $i(all_56_29)
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (60), (61), (63), (68), (72), (104),
% 240.62/47.11  | | | | | | | | | | | | | | |            (113), (114), (135), (168) are inconsistent by
% 240.62/47.11  | | | | | | | | | | | | | | |            sub-proof #308.
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | Case 2:
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | |   (169)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 240.62/47.11  | | | | | | | | | | | | | | |   (170)  op(e0, all_56_31) = e0
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | | REDUCE: (33), (170) imply:
% 240.62/47.11  | | | | | | | | | | | | | | |   (171)  op(e0, e1) = e0
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (60), (171) are inconsistent by
% 240.62/47.11  | | | | | | | | | | | | | | |            sub-proof #458.
% 240.62/47.11  | | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | | End of split
% 240.62/47.11  | | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | | End of split
% 240.62/47.11  | | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | | End of split
% 240.62/47.11  | | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | | End of split
% 240.62/47.11  | | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | | End of split
% 240.62/47.11  | | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | End of split
% 240.62/47.11  | | | | | | | | | 
% 240.62/47.11  | | | | | | | | Case 2:
% 240.62/47.11  | | | | | | | | | 
% 240.62/47.11  | | | | | | | | |   (172)  all_58_12 = e2 & op(e0, e3) = e2
% 240.62/47.11  | | | | | | | | | 
% 240.62/47.11  | | | | | | | | | REF_CLOSE: (28), (42), (172) are inconsistent by sub-proof
% 240.62/47.11  | | | | | | | | |            #1974.
% 240.62/47.11  | | | | | | | | | 
% 240.62/47.11  | | | | | | | | End of split
% 240.62/47.11  | | | | | | | | 
% 240.62/47.11  | | | | | | | End of split
% 240.62/47.11  | | | | | | | 
% 240.62/47.11  | | | | | | Case 2:
% 240.62/47.11  | | | | | | | 
% 240.62/47.11  | | | | | | |   (173)  all_58_13 = e1 & op(e0, e2) = e1
% 240.62/47.11  | | | | | | | 
% 240.62/47.11  | | | | | | | REF_CLOSE: (30), (48), (60), (173) are inconsistent by sub-proof
% 240.62/47.11  | | | | | | |            #2275.
% 240.62/47.11  | | | | | | | 
% 240.62/47.11  | | | | | | End of split
% 240.62/47.11  | | | | | | 
% 240.62/47.11  | | | | | End of split
% 240.62/47.11  | | | | | 
% 240.62/47.11  | | | | End of split
% 240.62/47.11  | | | | 
% 240.62/47.11  | | | End of split
% 240.62/47.11  | | | 
% 240.62/47.11  | | Case 2:
% 240.62/47.11  | | | 
% 240.62/47.11  | | |   (174)  all_58_3 = e1 & op(e2, e2) = e1
% 240.62/47.11  | | | 
% 240.62/47.11  | | | REF_CLOSE: (1), (6), (9), (19), (20), (23), (28), (38), (56), (60), (62),
% 240.62/47.11  | | |            (68), (71), (74), (79), (174) are inconsistent by sub-proof
% 240.62/47.11  | | |            #331.
% 240.62/47.11  | | | 
% 240.62/47.11  | | End of split
% 240.62/47.11  | | 
% 240.62/47.11  | Case 2:
% 240.62/47.11  | | 
% 240.62/47.11  | |   (175)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 240.62/47.11  | |            e1)
% 240.62/47.11  | | 
% 240.62/47.11  | | BETA: splitting (175) gives:
% 240.62/47.11  | | 
% 240.62/47.11  | | Case 1:
% 240.62/47.11  | | | 
% 240.62/47.11  | | |   (176)  all_58_5 = e1 & op(e2, e1) = e1
% 240.62/47.11  | | | 
% 240.62/47.11  | | | ALPHA: (176) implies:
% 240.62/47.11  | | |   (177)  op(e2, e1) = e1
% 240.62/47.11  | | | 
% 240.62/47.11  | | | REF_CLOSE: (26), (49), (60), (68), (177) are inconsistent by sub-proof
% 240.62/47.11  | | |            #2165.
% 240.62/47.11  | | | 
% 240.62/47.11  | | Case 2:
% 240.62/47.11  | | | 
% 240.62/47.11  | | |   (178)  all_58_10 = e1 & op(e2, e0) = e1
% 240.62/47.11  | | | 
% 240.62/47.11  | | | ALPHA: (178) implies:
% 240.62/47.11  | | |   (179)  all_58_10 = e1
% 240.62/47.11  | | | 
% 240.62/47.11  | | | REF_CLOSE: (6), (9), (10), (19), (28), (35), (56), (60), (62), (68), (79),
% 240.62/47.11  | | |            (179) are inconsistent by sub-proof #910.
% 240.62/47.11  | | | 
% 240.62/47.11  | | End of split
% 240.62/47.11  | | 
% 240.62/47.11  | End of split
% 240.62/47.11  | 
% 240.62/47.11  End of proof
% 240.62/47.11  
% 240.62/47.11  Sub-proof #308 shows that the following formulas are inconsistent:
% 240.62/47.11  ----------------------------------------------------------------
% 240.62/47.11    (1)   ~ (e3 = e0)
% 240.62/47.11    (2)  op(e1, e0) = e0
% 240.62/47.11    (3)   ~ (e2 = e0)
% 240.62/47.11    (4)  all_58_6 = e2
% 240.62/47.11    (5)  op(e1, e3) = e2
% 240.62/47.11    (6)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 240.62/47.11         $i(all_56_29)
% 240.62/47.11    (7)  all_58_7 = e1
% 240.62/47.11    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.62/47.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.62/47.11    (9)  all_58_8 = e3
% 240.62/47.11    (10)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.62/47.11            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.62/47.11              e3) = all_46_1 & $i(all_46_1))
% 240.62/47.11    (11)   ~ (e1 = e0)
% 240.62/47.11    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.62/47.11          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.62/47.11  
% 240.62/47.11  Begin of proof
% 240.62/47.11  | 
% 240.62/47.11  | ALPHA: (6) implies:
% 240.62/47.11  |   (13)  op(e1, e0) = all_56_29
% 240.62/47.11  |   (14)  op(e1, all_56_29) = e1
% 240.62/47.11  | 
% 240.62/47.11  | BETA: splitting (10) gives:
% 240.62/47.11  | 
% 240.62/47.11  | Case 1:
% 240.62/47.11  | | 
% 240.62/47.11  | | 
% 240.62/47.11  | | GROUND_INST: instantiating (8) with e0, all_56_29, e0, e1, simplifying with
% 240.62/47.11  | |              (2), (13) gives:
% 240.62/47.11  | |   (15)  all_56_29 = e0
% 240.62/47.11  | | 
% 240.62/47.11  | | REDUCE: (14), (15) imply:
% 240.62/47.11  | |   (16)  op(e1, e0) = e1
% 240.62/47.11  | | 
% 240.62/47.11  | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (11), (12), (16) are inconsistent
% 240.62/47.11  | |            by sub-proof #1420.
% 240.62/47.11  | | 
% 240.62/47.11  | Case 2:
% 240.62/47.11  | | 
% 240.62/47.11  | |   (17)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.62/47.11  | | 
% 240.62/47.11  | | REF_CLOSE: (5), (8), (17) are inconsistent by sub-proof #395.
% 240.62/47.11  | | 
% 240.62/47.11  | End of split
% 240.62/47.11  | 
% 240.62/47.11  End of proof
% 240.62/47.11  
% 240.62/47.11  Sub-proof #309 shows that the following formulas are inconsistent:
% 240.62/47.11  ----------------------------------------------------------------
% 240.62/47.11    (1)  op(e2, e2) = e3
% 240.62/47.11    (2)   ~ (e2 = e0)
% 240.62/47.11    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.62/47.11         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.62/47.11    (4)  all_58_1 = e0
% 240.62/47.11    (5)   ~ (e3 = e1)
% 240.62/47.11    (6)  all_58_3 = e3
% 240.62/47.11    (7)   ~ (e3 = e2)
% 240.62/47.11    (8)  op(e0, e2) = e0
% 240.62/47.11    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.62/47.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.62/47.11    (10)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.62/47.11          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.62/47.11    (11)   ~ (e1 = e0)
% 240.62/47.11    (12)   ~ (e2 = e1)
% 240.62/47.11  
% 240.62/47.11  Begin of proof
% 240.62/47.11  | 
% 240.62/47.11  | BETA: splitting (10) gives:
% 240.62/47.11  | 
% 240.62/47.11  | Case 1:
% 240.62/47.11  | | 
% 240.62/47.11  | |   (13)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 240.62/47.11  | |           e1)
% 240.62/47.11  | | 
% 240.62/47.11  | | REF_CLOSE: (4), (5), (6), (11), (13) are inconsistent by sub-proof #892.
% 240.62/47.11  | | 
% 240.62/47.11  | Case 2:
% 240.62/47.11  | | 
% 240.62/47.11  | |   (14)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 240.62/47.11  | |           e1)
% 240.62/47.11  | | 
% 240.62/47.11  | | BETA: splitting (14) gives:
% 240.62/47.11  | | 
% 240.62/47.11  | | Case 1:
% 240.62/47.11  | | | 
% 240.62/47.11  | | |   (15)  all_58_7 = e1 & op(e1, e2) = e1
% 240.62/47.11  | | | 
% 240.62/47.11  | | | ALPHA: (15) implies:
% 240.62/47.11  | | |   (16)  all_58_7 = e1
% 240.62/47.11  | | | 
% 240.62/47.11  | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (12), (16) are inconsistent
% 240.62/47.11  | | |            by sub-proof #882.
% 240.62/47.11  | | | 
% 240.62/47.11  | | Case 2:
% 240.62/47.11  | | | 
% 240.62/47.11  | | |   (17)  all_58_13 = e1 & op(e0, e2) = e1
% 240.62/47.11  | | | 
% 240.62/47.11  | | | ALPHA: (17) implies:
% 240.62/47.11  | | |   (18)  op(e0, e2) = e1
% 240.62/47.11  | | | 
% 240.62/47.11  | | | REF_CLOSE: (8), (9), (11), (18) are inconsistent by sub-proof #1872.
% 240.62/47.11  | | | 
% 240.62/47.11  | | End of split
% 240.62/47.11  | | 
% 240.62/47.11  | End of split
% 240.62/47.11  | 
% 240.62/47.11  End of proof
% 240.62/47.11  
% 240.62/47.11  Sub-proof #310 shows that the following formulas are inconsistent:
% 240.62/47.11  ----------------------------------------------------------------
% 240.62/47.11    (1)   ~ (e2 = e0)
% 240.62/47.11    (2)  op(e2, e1) = all_52_9
% 240.62/47.11    (3)  op(e0, e2) = e0
% 240.62/47.11    (4)  op(e2, e1) = e0
% 240.62/47.11    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.62/47.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.62/47.11    (6)   ~ (e1 = e0)
% 240.62/47.11    (7)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.62/47.11             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.62/47.11           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.62/47.11             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 240.62/47.11           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 240.62/47.11           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.62/47.11           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.62/47.11  
% 240.62/47.11  Begin of proof
% 240.62/47.11  | 
% 240.62/47.11  | BETA: splitting (7) gives:
% 240.62/47.11  | 
% 240.62/47.11  | Case 1:
% 240.62/47.11  | | 
% 240.62/47.11  | |   (8)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 240.62/47.11  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 240.62/47.11  | |        & op(e1, e2) = e2
% 240.62/47.11  | | 
% 240.62/47.11  | | ALPHA: (8) implies:
% 240.62/47.11  | |   (9)  op(e2, e1) = e2
% 240.62/47.11  | | 
% 240.62/47.11  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1906.
% 240.62/47.11  | | 
% 240.62/47.11  | Case 2:
% 240.62/47.11  | | 
% 240.62/47.11  | |   (10)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.62/47.11  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.62/47.11  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.62/47.11  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.62/47.11  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.62/47.11  | | 
% 240.62/47.11  | | BETA: splitting (10) gives:
% 240.62/47.11  | | 
% 240.62/47.11  | | Case 1:
% 240.62/47.11  | | | 
% 240.62/47.11  | | |   (11)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.62/47.11  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.62/47.11  | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 240.62/47.11  | | | 
% 240.62/47.11  | | | ALPHA: (11) implies:
% 240.62/47.11  | | |   (12)  op(e2, e1) = e1
% 240.62/47.11  | | | 
% 240.62/47.11  | | | REF_CLOSE: (2), (4), (5), (6), (12) are inconsistent by sub-proof #2165.
% 240.62/47.11  | | | 
% 240.62/47.11  | | Case 2:
% 240.62/47.11  | | | 
% 240.62/47.11  | | |   (13)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.62/47.11  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.62/47.11  | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 240.62/47.11  | | | 
% 240.62/47.11  | | | ALPHA: (13) implies:
% 240.62/47.11  | | |   (14)  op(e0, e2) = e2
% 240.62/47.11  | | | 
% 240.62/47.11  | | | REF_CLOSE: (1), (3), (5), (14) are inconsistent by sub-proof #2132.
% 240.62/47.11  | | | 
% 240.62/47.11  | | End of split
% 240.62/47.11  | | 
% 240.62/47.11  | End of split
% 240.62/47.11  | 
% 240.62/47.11  End of proof
% 240.62/47.11  
% 240.62/47.11  Sub-proof #311 shows that the following formulas are inconsistent:
% 240.62/47.11  ----------------------------------------------------------------
% 240.62/47.11    (1)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.62/47.11    (2)   ~ (e3 = e2)
% 240.62/47.11    (3)  op(e1, e3) = e1
% 240.62/47.11    (4)  all_58_12 = e3
% 240.62/47.11    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.62/47.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.62/47.11    (6)   ~ (e2 = e1)
% 240.62/47.11  
% 240.62/47.11  Begin of proof
% 240.62/47.11  | 
% 240.62/47.11  | BETA: splitting (1) gives:
% 240.62/47.11  | 
% 240.62/47.11  | Case 1:
% 240.62/47.11  | | 
% 240.62/47.11  | |   (7)  all_58_6 = e2 & op(e1, e3) = e2
% 240.62/47.11  | | 
% 240.62/47.11  | | ALPHA: (7) implies:
% 240.62/47.11  | |   (8)  op(e1, e3) = e2
% 240.62/47.11  | | 
% 240.62/47.11  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2226.
% 240.62/47.11  | | 
% 240.62/47.11  | Case 2:
% 240.62/47.11  | | 
% 240.62/47.11  | |   (9)  all_58_12 = e2 & op(e0, e3) = e2
% 240.62/47.11  | | 
% 240.62/47.11  | | ALPHA: (9) implies:
% 240.62/47.11  | |   (10)  all_58_12 = e2
% 240.62/47.11  | | 
% 240.62/47.11  | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #1552.
% 240.62/47.11  | | 
% 240.62/47.11  | End of split
% 240.62/47.11  | 
% 240.62/47.11  End of proof
% 240.62/47.11  
% 240.62/47.11  Sub-proof #312 shows that the following formulas are inconsistent:
% 240.62/47.11  ----------------------------------------------------------------
% 240.62/47.11    (1)  op(e3, e2) = e1
% 240.62/47.11    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.62/47.11         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.62/47.11    (3)   ~ (e3 = e0)
% 240.62/47.11    (4)  op(e2, e1) = e1
% 240.62/47.11    (5)   ~ (e2 = e0)
% 240.62/47.11    (6)  op(e1, e2) = all_52_6
% 240.62/47.11    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.62/47.11         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.62/47.11    (8)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.62/47.11           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.62/47.11             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.62/47.11           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.62/47.11             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.62/47.11           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.62/47.11           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.62/47.11           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.62/47.11           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.62/47.11           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.62/47.11           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.62/47.11             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.62/47.11           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.62/47.11           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 240.62/47.11           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.62/47.11           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.62/47.11           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.62/47.11           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.62/47.11             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.62/47.11           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.62/47.11           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 240.62/47.11           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.62/47.11           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.62/47.11           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.62/47.11           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.62/47.11             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.62/47.11           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.62/47.11           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.62/47.11    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.62/47.11         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.62/47.11    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.62/47.11          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.62/47.11    (11)  op(e1, e0) = all_52_14
% 240.62/47.11    (12)  op(e0, e2) = e2
% 240.62/47.11    (13)   ~ (e3 = e1)
% 240.62/47.11    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.62/47.11          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.62/47.11    (15)  all_58_3 = e3
% 240.62/47.11    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.62/47.11          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.62/47.11    (17)  op(e2, e1) = all_52_9
% 240.62/47.11    (18)  op(e1, e2) = e0
% 240.62/47.11    (19)   ~ (e3 = e2)
% 240.62/47.11    (20)   ~ (all_52_14 = e1)
% 240.62/47.11    (21)  op(e2, e3) = e2
% 240.62/47.11    (22)  op(e1, e3) = e1
% 240.62/47.11    (23)  all_56_31 = e1
% 240.62/47.11    (24)  op(e0, e1) = e0
% 240.62/47.11    (25)  all_58_13 = e2
% 240.62/47.11    (26)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.62/47.11            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.62/47.11              e3) = all_42_1 & $i(all_42_1))
% 240.62/47.11    (27)  all_58_9 = e3
% 240.62/47.11    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.62/47.11          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.62/47.11    (29)   ~ (all_52_4 = e3)
% 240.62/47.11    (30)  op(e3, e2) = all_52_4
% 240.62/47.11    (31)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.62/47.11          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.62/47.12    (32)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.62/47.12          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.62/47.12    (33)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.62/47.12          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.62/47.12    (34)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.62/47.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.62/47.12    (35)  all_56_21 = e3
% 240.62/47.12    (36)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.62/47.12          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.62/47.12    (37)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.62/47.12          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.62/47.12    (38)   ~ (e1 = e0)
% 240.62/47.12    (39)  all_58_4 = e2 & op(e3, e1) = e2
% 240.62/47.12    (40)  op(e3, e3) = e0
% 240.62/47.12    (41)  all_56_1 = e0
% 240.62/47.12    (42)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.62/47.12            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.62/47.12            & $i(all_8_1))
% 240.62/47.12    (43)   ~ (e2 = e1)
% 240.62/47.12  
% 240.62/47.12  Begin of proof
% 240.62/47.12  | 
% 240.62/47.12  | ALPHA: (39) implies:
% 240.62/47.12  |   (44)  all_58_4 = e2
% 240.62/47.12  | 
% 240.62/47.12  | BETA: splitting (32) gives:
% 240.62/47.12  | 
% 240.62/47.12  | Case 1:
% 240.62/47.12  | | 
% 240.62/47.12  | |   (45)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 240.62/47.12  | |           e2)
% 240.62/47.12  | | 
% 240.62/47.12  | | BETA: splitting (45) gives:
% 240.62/47.12  | | 
% 240.62/47.12  | | Case 1:
% 240.62/47.12  | | | 
% 240.62/47.12  | | |   (46)  all_58_6 = e2 & op(e1, e3) = e2
% 240.62/47.12  | | | 
% 240.62/47.12  | | | ALPHA: (46) implies:
% 240.62/47.12  | | |   (47)  op(e1, e3) = e2
% 240.62/47.12  | | | 
% 240.62/47.12  | | | REF_CLOSE: (22), (34), (43), (47) are inconsistent by sub-proof #2226.
% 240.62/47.12  | | | 
% 240.62/47.12  | | Case 2:
% 240.62/47.12  | | | 
% 240.62/47.12  | | |   (48)  all_58_7 = e2 & op(e1, e2) = e2
% 240.62/47.12  | | | 
% 240.62/47.12  | | | ALPHA: (48) implies:
% 240.62/47.12  | | |   (49)  all_58_7 = e2
% 240.62/47.12  | | | 
% 240.62/47.12  | | | REF_CLOSE: (3), (5), (7), (9), (12), (13), (19), (25), (34), (36), (37),
% 240.62/47.12  | | |            (38), (43), (49) are inconsistent by sub-proof #1453.
% 240.62/47.12  | | | 
% 240.62/47.12  | | End of split
% 240.62/47.12  | | 
% 240.62/47.12  | Case 2:
% 240.62/47.12  | | 
% 240.62/47.12  | |   (50)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 240.62/47.12  | |           e2)
% 240.62/47.12  | | 
% 240.62/47.12  | | BETA: splitting (50) gives:
% 240.62/47.12  | | 
% 240.62/47.12  | | Case 1:
% 240.62/47.12  | | | 
% 240.62/47.12  | | |   (51)  all_58_8 = e2 & op(e1, e1) = e2
% 240.62/47.12  | | | 
% 240.62/47.12  | | | ALPHA: (51) implies:
% 240.62/47.12  | | |   (52)  op(e1, e1) = e2
% 240.62/47.12  | | | 
% 240.62/47.12  | | | REF_CLOSE: (3), (5), (10), (13), (14), (17), (19), (24), (28), (34), (38),
% 240.62/47.12  | | |            (43), (44), (52) are inconsistent by sub-proof #2156.
% 240.62/47.12  | | | 
% 240.62/47.12  | | Case 2:
% 240.62/47.12  | | | 
% 240.62/47.12  | | |   (53)  all_58_11 = e2 & op(e1, e0) = e2
% 240.62/47.12  | | | 
% 240.62/47.12  | | | ALPHA: (53) implies:
% 240.62/47.12  | | |   (54)  op(e1, e0) = e2
% 240.62/47.12  | | | 
% 240.62/47.12  | | | BETA: splitting (33) gives:
% 240.62/47.12  | | | 
% 240.62/47.12  | | | Case 1:
% 240.62/47.12  | | | | 
% 240.62/47.12  | | | |   (55)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2)
% 240.62/47.12  | | | |           = e0)
% 240.62/47.12  | | | | 
% 240.62/47.12  | | | | REF_CLOSE: (2), (3), (5), (13), (15), (16), (19), (21), (26), (27),
% 240.62/47.12  | | | |            (29), (30), (31), (34), (38), (40), (42), (43), (55) are
% 240.62/47.12  | | | |            inconsistent by sub-proof #314.
% 240.62/47.12  | | | | 
% 240.62/47.12  | | | Case 2:
% 240.62/47.12  | | | | 
% 240.62/47.12  | | | |   (56)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0)
% 240.62/47.12  | | | |           = e0)
% 240.62/47.12  | | | | 
% 240.62/47.12  | | | | BETA: splitting (56) gives:
% 240.62/47.12  | | | | 
% 240.62/47.12  | | | | Case 1:
% 240.62/47.12  | | | | | 
% 240.62/47.12  | | | | |   (57)  all_58_5 = e0 & op(e2, e1) = e0
% 240.62/47.12  | | | | | 
% 240.62/47.12  | | | | | ALPHA: (57) implies:
% 240.62/47.12  | | | | |   (58)  op(e2, e1) = e0
% 240.62/47.12  | | | | | 
% 240.62/47.12  | | | | | REF_CLOSE: (4), (17), (34), (38), (58) are inconsistent by sub-proof
% 240.62/47.12  | | | | |            #2165.
% 240.62/47.12  | | | | | 
% 240.62/47.12  | | | | Case 2:
% 240.62/47.12  | | | | | 
% 240.62/47.12  | | | | |   (59)  all_58_10 = e0 & op(e2, e0) = e0
% 240.62/47.12  | | | | | 
% 240.62/47.12  | | | | | ALPHA: (59) implies:
% 240.62/47.12  | | | | |   (60)  op(e2, e0) = e0
% 240.62/47.12  | | | | | 
% 240.62/47.12  | | | | | BETA: splitting (8) gives:
% 240.62/47.12  | | | | | 
% 240.62/47.12  | | | | | Case 1:
% 240.62/47.12  | | | | | | 
% 240.62/47.12  | | | | | |   (61)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.62/47.12  | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | |             e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 =
% 240.62/47.12  | | | | | |           e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.62/47.12  | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.62/47.12  | | | | | |             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17
% 240.62/47.12  | | | | | |           = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.62/47.12  | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.62/47.12  | | | | | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 240.62/47.12  | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.62/47.12  | | | | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.62/47.12  | | | | | |           = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 240.62/47.12  | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.62/47.12  | | | | | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 240.62/47.12  | | | | | |         (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.62/47.12  | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | |             e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.62/47.12  | | | | | | 
% 240.62/47.12  | | | | | | BETA: splitting (61) gives:
% 240.62/47.12  | | | | | | 
% 240.62/47.12  | | | | | | Case 1:
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | |   (62)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.62/47.12  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | | |             e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 =
% 240.62/47.12  | | | | | | |           e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.62/47.12  | | | | | | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.62/47.12  | | | | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 240.62/47.12  | | | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.62/47.12  | | | | | | |             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.62/47.12  | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | | REF_CLOSE: (1), (13), (19), (21), (22), (34), (43), (62) are
% 240.62/47.12  | | | | | | |            inconsistent by sub-proof #313.
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | Case 2:
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | |   (63)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.62/47.12  | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | | |             e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 =
% 240.62/47.12  | | | | | | |           e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.62/47.12  | | | | | | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.62/47.12  | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 240.62/47.12  | | | | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.62/47.12  | | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.62/47.12  | | | | | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | | BETA: splitting (63) gives:
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | | Case 1:
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | |   (64)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.62/47.12  | | | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | | | |           e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | ALPHA: (64) implies:
% 240.62/47.12  | | | | | | | |   (65)   ~ (all_56_21 = e3)
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | REDUCE: (35), (65) imply:
% 240.62/47.12  | | | | | | | |   (66)  $false
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | CLOSE: (66) is inconsistent.
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | Case 2:
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | |   (67)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) & 
% 240.62/47.12  | | | | | | | |           ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.62/47.12  | | | | | | | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3)
% 240.62/47.12  | | | | | | | |         | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &
% 240.62/47.12  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.62/47.12  | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | BETA: splitting (67) gives:
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | Case 1:
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | |   (68)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) & 
% 240.62/47.12  | | | | | | | | |         ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.62/47.12  | | | | | | | | |         (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | | ALPHA: (68) implies:
% 240.62/47.12  | | | | | | | | |   (69)   ~ (all_56_1 = e0)
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | | REDUCE: (41), (69) imply:
% 240.62/47.12  | | | | | | | | |   (70)  $false
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | | CLOSE: (70) is inconsistent.
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | Case 2:
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | |   (71)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) & 
% 240.62/47.12  | | | | | | | | |         ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.62/47.12  | | | | | | | | |         (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | | ALPHA: (71) implies:
% 240.62/47.12  | | | | | | | | |   (72)   ~ (all_56_21 = e3)
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | | REDUCE: (35), (72) imply:
% 240.62/47.12  | | | | | | | | |   (73)  $false
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | | CLOSE: (73) is inconsistent.
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | End of split
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | End of split
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | End of split
% 240.62/47.12  | | | | | | 
% 240.62/47.12  | | | | | Case 2:
% 240.62/47.12  | | | | | | 
% 240.62/47.12  | | | | | |   (74)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.62/47.12  | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | |             e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 =
% 240.62/47.12  | | | | | |           e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.62/47.12  | | | | | |             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.62/47.12  | | | | | |             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 240.62/47.12  | | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0)
% 240.62/47.12  | | | | | |           &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) =
% 240.62/47.12  | | | | | |           e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 = e0 &
% 240.62/47.12  | | | | | |            ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.62/47.12  | | | | | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.62/47.12  | | | | | |           = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.62/47.12  | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.62/47.12  | | | | | |           (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 240.62/47.12  | | | | | |         (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.62/47.12  | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | |             e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.62/47.12  | | | | | | 
% 240.62/47.12  | | | | | | BETA: splitting (74) gives:
% 240.62/47.12  | | | | | | 
% 240.62/47.12  | | | | | | Case 1:
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | |   (75)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.62/47.12  | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | | |             e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13
% 240.62/47.12  | | | | | | |           = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.62/47.12  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | | |             e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.62/47.12  | | | | | | |           = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.62/47.12  | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | | |             e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | | BETA: splitting (75) gives:
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | | Case 1:
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | |   (76)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) & 
% 240.62/47.12  | | | | | | | |         ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 240.62/47.12  | | | | | | | |           = e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | ALPHA: (76) implies:
% 240.62/47.12  | | | | | | | |   (77)   ~ (all_56_31 = e1)
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | REDUCE: (23), (77) imply:
% 240.62/47.12  | | | | | | | |   (78)  $false
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | CLOSE: (78) is inconsistent.
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | Case 2:
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | |   (79)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) & 
% 240.62/47.12  | | | | | | | |           ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.62/47.12  | | | | | | | |           (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1)
% 240.62/47.12  | | | | | | | |         | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0)
% 240.62/47.12  | | | | | | | |           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.62/47.12  | | | | | | | |           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | REF_CLOSE: (5), (6), (18), (34), (38), (60), (79) are
% 240.62/47.12  | | | | | | | |            inconsistent by sub-proof #781.
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | End of split
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | Case 2:
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | |   (80)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.62/47.12  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | | |             e2) & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23
% 240.62/47.12  | | | | | | |           = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.62/47.12  | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | | |             e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.62/47.12  | | | | | | |           = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.62/47.12  | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 240.62/47.12  | | | | | | |             e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | | BETA: splitting (80) gives:
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | | Case 1:
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | |   (81)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) & 
% 240.62/47.12  | | | | | | | |         ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 240.62/47.12  | | | | | | | |           = e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | ALPHA: (81) implies:
% 240.62/47.12  | | | | | | | |   (82)  op(e0, e2) = e0
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | REF_CLOSE: (5), (12), (34), (82) are inconsistent by sub-proof
% 240.62/47.12  | | | | | | | |            #2132.
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | Case 2:
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | |   (83)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) & 
% 240.62/47.12  | | | | | | | |           ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.62/47.12  | | | | | | | |           (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1)
% 240.62/47.12  | | | | | | | |         | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1)
% 240.62/47.12  | | | | | | | |           &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.62/47.12  | | | | | | | |           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | BETA: splitting (83) gives:
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | | Case 1:
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | |   (84)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &
% 240.62/47.12  | | | | | | | | |          ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.62/47.12  | | | | | | | | |         (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | | ALPHA: (84) implies:
% 240.62/47.12  | | | | | | | | |   (85)  op(e1, e0) = e1
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | | REF_CLOSE: (11), (20), (34), (85) are inconsistent by
% 240.62/47.12  | | | | | | | | |            sub-proof #2304.
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | Case 2:
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | |   (86)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &
% 240.62/47.12  | | | | | | | | |          ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.62/47.12  | | | | | | | | |         (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | | ALPHA: (86) implies:
% 240.62/47.12  | | | | | | | | |   (87)  op(e1, e0) = e0
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | | REF_CLOSE: (5), (34), (54), (87) are inconsistent by sub-proof
% 240.62/47.12  | | | | | | | | |            #478.
% 240.62/47.12  | | | | | | | | | 
% 240.62/47.12  | | | | | | | | End of split
% 240.62/47.12  | | | | | | | | 
% 240.62/47.12  | | | | | | | End of split
% 240.62/47.12  | | | | | | | 
% 240.62/47.12  | | | | | | End of split
% 240.62/47.12  | | | | | | 
% 240.62/47.12  | | | | | End of split
% 240.62/47.12  | | | | | 
% 240.62/47.12  | | | | End of split
% 240.62/47.12  | | | | 
% 240.62/47.12  | | | End of split
% 240.62/47.12  | | | 
% 240.62/47.12  | | End of split
% 240.62/47.12  | | 
% 240.62/47.12  | End of split
% 240.62/47.12  | 
% 240.62/47.12  End of proof
% 240.62/47.12  
% 240.62/47.12  Sub-proof #313 shows that the following formulas are inconsistent:
% 240.62/47.12  ----------------------------------------------------------------
% 240.62/47.12    (1)  op(e3, e2) = e1
% 240.64/47.12    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.64/47.12           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.64/47.12             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.64/47.12           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.64/47.12             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.64/47.12           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.64/47.12           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.64/47.12    (3)   ~ (e3 = e1)
% 240.64/47.12    (4)   ~ (e3 = e2)
% 240.64/47.12    (5)  op(e2, e3) = e2
% 240.64/47.12    (6)  op(e1, e3) = e1
% 240.64/47.12    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.12    (8)   ~ (e2 = e1)
% 240.64/47.12  
% 240.64/47.12  Begin of proof
% 240.64/47.12  | 
% 240.64/47.12  | BETA: splitting (2) gives:
% 240.64/47.12  | 
% 240.64/47.12  | Case 1:
% 240.64/47.12  | | 
% 240.64/47.12  | |   (9)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.64/47.12  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.64/47.12  | |        op(e2, e3) = e3
% 240.64/47.12  | | 
% 240.64/47.12  | | ALPHA: (9) implies:
% 240.64/47.12  | |   (10)  op(e2, e3) = e3
% 240.64/47.12  | | 
% 240.64/47.12  | | REF_CLOSE: (4), (5), (7), (10) are inconsistent by sub-proof #1897.
% 240.64/47.12  | | 
% 240.64/47.12  | Case 2:
% 240.64/47.12  | | 
% 240.64/47.12  | |   (11)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.64/47.12  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.64/47.12  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.64/47.12  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.64/47.12  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.64/47.12  | | 
% 240.64/47.12  | | REF_CLOSE: (1), (3), (6), (7), (8), (11) are inconsistent by sub-proof #334.
% 240.64/47.12  | | 
% 240.64/47.12  | End of split
% 240.64/47.12  | 
% 240.64/47.12  End of proof
% 240.64/47.12  
% 240.64/47.12  Sub-proof #314 shows that the following formulas are inconsistent:
% 240.64/47.12  ----------------------------------------------------------------
% 240.64/47.12    (1)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 240.64/47.12    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.64/47.12         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.64/47.12    (3)   ~ (e3 = e0)
% 240.64/47.12    (4)   ~ (e2 = e0)
% 240.64/47.12    (5)   ~ (e3 = e1)
% 240.64/47.12    (6)  all_58_3 = e3
% 240.64/47.12    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.64/47.12         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.64/47.12    (8)   ~ (e3 = e2)
% 240.64/47.12    (9)  op(e2, e3) = e2
% 240.64/47.13    (10)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.64/47.13            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.64/47.13              e3) = all_42_1 & $i(all_42_1))
% 240.64/47.13    (11)  all_58_9 = e3
% 240.64/47.13    (12)   ~ (all_52_4 = e3)
% 240.64/47.13    (13)  op(e3, e2) = all_52_4
% 240.64/47.13    (14)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.64/47.13          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.64/47.13    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.13    (16)   ~ (e1 = e0)
% 240.64/47.13    (17)  op(e3, e3) = e0
% 240.64/47.13    (18)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.64/47.13            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.64/47.13            & $i(all_8_1))
% 240.64/47.13    (19)   ~ (e2 = e1)
% 240.64/47.13  
% 240.64/47.13  Begin of proof
% 240.64/47.13  | 
% 240.64/47.13  | BETA: splitting (1) gives:
% 240.64/47.13  | 
% 240.64/47.13  | Case 1:
% 240.64/47.13  | | 
% 240.64/47.13  | |   (20)  all_58_2 = e0 & op(e2, e3) = e0
% 240.64/47.13  | | 
% 240.64/47.13  | | ALPHA: (20) implies:
% 240.64/47.13  | |   (21)  op(e2, e3) = e0
% 240.64/47.13  | | 
% 240.64/47.13  | | REF_CLOSE: (4), (9), (10), (15), (18), (21) are inconsistent by sub-proof
% 240.64/47.13  | |            #733.
% 240.64/47.13  | | 
% 240.64/47.13  | Case 2:
% 240.64/47.13  | | 
% 240.64/47.13  | |   (22)  all_58_3 = e0 & op(e2, e2) = e0
% 240.64/47.13  | | 
% 240.64/47.13  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14), (15),
% 240.64/47.13  | |            (16), (17), (19), (22) are inconsistent by sub-proof #318.
% 240.64/47.13  | | 
% 240.64/47.13  | End of split
% 240.64/47.13  | 
% 240.64/47.13  End of proof
% 240.64/47.13  
% 240.64/47.13  Sub-proof #315 shows that the following formulas are inconsistent:
% 240.64/47.13  ----------------------------------------------------------------
% 240.64/47.13    (1)   ~ (e3 = e0)
% 240.64/47.13    (2)   ~ (e2 = e0)
% 240.64/47.13    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.64/47.13         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.64/47.13    (4)  op(e0, e2) = e2
% 240.64/47.13    (5)   ~ (e3 = e1)
% 240.64/47.13    (6)  all_58_3 = e3
% 240.64/47.13    (7)   ~ (all_52_7 = e1)
% 240.64/47.13    (8)  op(e0, e2) = all_52_7
% 240.64/47.13    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.13    (10)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.64/47.13          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.13    (11)   ~ (e1 = e0)
% 240.64/47.13    (12)  op(e3, e3) = e0
% 240.64/47.13    (13)   ~ (e2 = e1)
% 240.64/47.13    (14)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 240.64/47.13  
% 240.64/47.13  Begin of proof
% 240.64/47.13  | 
% 240.64/47.13  | BETA: splitting (14) gives:
% 240.64/47.13  | 
% 240.64/47.13  | Case 1:
% 240.64/47.13  | | 
% 240.64/47.13  | |   (15)  all_58_0 = e2 & op(e3, e3) = e2
% 240.64/47.13  | | 
% 240.64/47.13  | | ALPHA: (15) implies:
% 240.64/47.13  | |   (16)  op(e3, e3) = e2
% 240.64/47.13  | | 
% 240.64/47.13  | | REF_CLOSE: (2), (9), (12), (16) are inconsistent by sub-proof #2188.
% 240.64/47.13  | | 
% 240.64/47.13  | Case 2:
% 240.64/47.13  | | 
% 240.64/47.13  | |   (17)  all_58_1 = e2 & op(e3, e2) = e2
% 240.64/47.13  | | 
% 240.64/47.13  | | ALPHA: (17) implies:
% 240.64/47.13  | |   (18)  all_58_1 = e2
% 240.64/47.13  | | 
% 240.64/47.13  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 240.64/47.13  | |            (18) are inconsistent by sub-proof #1352.
% 240.64/47.13  | | 
% 240.64/47.13  | End of split
% 240.64/47.13  | 
% 240.64/47.13  End of proof
% 240.64/47.13  
% 240.64/47.13  Sub-proof #316 shows that the following formulas are inconsistent:
% 240.64/47.13  ----------------------------------------------------------------
% 240.64/47.13    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.64/47.13         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.64/47.13    (2)   ~ (e3 = e0)
% 240.64/47.13    (3)  op(e2, e1) = e1
% 240.64/47.13    (4)   ~ (e2 = e0)
% 240.64/47.13    (5)   ~ (e3 = e1)
% 240.64/47.13    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.64/47.13         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.64/47.13    (7)  op(e2, e1) = all_52_9
% 240.64/47.13    (8)   ~ (e3 = e2)
% 240.64/47.13    (9)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 240.64/47.13    (10)   ~ (all_52_4 = e3)
% 240.64/47.13    (11)  op(e3, e2) = all_52_4
% 240.64/47.13    (12)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.64/47.13          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.64/47.13    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.13    (14)   ~ (e1 = e0)
% 240.64/47.13    (15)  op(e3, e3) = e0
% 240.64/47.13    (16)   ~ (e2 = e1)
% 240.64/47.13  
% 240.64/47.13  Begin of proof
% 240.64/47.13  | 
% 240.64/47.13  | BETA: splitting (9) gives:
% 240.64/47.13  | 
% 240.64/47.13  | Case 1:
% 240.64/47.13  | | 
% 240.64/47.13  | |   (17)  all_58_4 = e0 & op(e3, e1) = e0
% 240.64/47.13  | | 
% 240.64/47.13  | | ALPHA: (17) implies:
% 240.64/47.13  | |   (18)  all_58_4 = e0
% 240.64/47.13  | | 
% 240.64/47.13  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (11), (12), (13), (14), (15),
% 240.64/47.13  | |            (16), (18) are inconsistent by sub-proof #1512.
% 240.64/47.13  | | 
% 240.64/47.13  | Case 2:
% 240.64/47.13  | | 
% 240.64/47.13  | |   (19)  all_58_5 = e0 & op(e2, e1) = e0
% 240.64/47.13  | | 
% 240.64/47.13  | | ALPHA: (19) implies:
% 240.64/47.13  | |   (20)  op(e2, e1) = e0
% 240.64/47.13  | | 
% 240.64/47.13  | | REF_CLOSE: (3), (7), (13), (14), (20) are inconsistent by sub-proof #2165.
% 240.64/47.13  | | 
% 240.64/47.13  | End of split
% 240.64/47.13  | 
% 240.64/47.13  End of proof
% 240.64/47.13  
% 240.64/47.13  Sub-proof #317 shows that the following formulas are inconsistent:
% 240.64/47.13  ----------------------------------------------------------------
% 240.64/47.13    (1)  op(e0, e0) = e1
% 240.64/47.13    (2)   ~ (e3 = e0)
% 240.64/47.13    (3)   ~ (e2 = e0)
% 240.64/47.13    (4)   ~ (e3 = e1)
% 240.64/47.13    (5)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 240.64/47.13    (6)  all_58_3 = e3
% 240.64/47.13    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.64/47.13             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.64/47.13               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.64/47.13               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.64/47.13    (8)   ~ (e3 = e2)
% 240.64/47.13    (9)  op(e2, e3) = e2
% 240.64/47.13    (10)  all_58_9 = e3
% 240.64/47.13    (11)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.64/47.13          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.13    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.13    (13)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.64/47.13          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.64/47.13    (14)   ~ (e1 = e0)
% 240.64/47.13    (15)   ~ (all_52_13 = e3)
% 240.64/47.13    (16)  op(e2, e0) = all_52_13
% 240.64/47.13    (17)   ~ (e2 = e1)
% 240.64/47.13  
% 240.64/47.13  Begin of proof
% 240.64/47.13  | 
% 240.64/47.13  | BETA: splitting (5) gives:
% 240.64/47.13  | 
% 240.64/47.13  | Case 1:
% 240.64/47.13  | | 
% 240.64/47.13  | |   (18)  all_58_2 = e1 & op(e2, e3) = e1
% 240.64/47.13  | | 
% 240.64/47.13  | | ALPHA: (18) implies:
% 240.64/47.13  | |   (19)  op(e2, e3) = e1
% 240.64/47.13  | | 
% 240.64/47.13  | | REF_CLOSE: (9), (12), (17), (19) are inconsistent by sub-proof #1633.
% 240.64/47.13  | | 
% 240.64/47.13  | Case 2:
% 240.64/47.13  | | 
% 240.64/47.13  | |   (20)  all_58_3 = e1 & op(e2, e2) = e1
% 240.64/47.13  | | 
% 240.64/47.13  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (13), (14),
% 240.64/47.13  | |            (15), (16), (17), (20) are inconsistent by sub-proof #331.
% 240.64/47.13  | | 
% 240.64/47.13  | End of split
% 240.64/47.13  | 
% 240.64/47.13  End of proof
% 240.64/47.13  
% 240.64/47.13  Sub-proof #318 shows that the following formulas are inconsistent:
% 240.64/47.13  ----------------------------------------------------------------
% 240.64/47.13    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.64/47.13         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.64/47.13    (2)   ~ (e3 = e0)
% 240.64/47.13    (3)   ~ (e2 = e0)
% 240.64/47.13    (4)   ~ (e3 = e1)
% 240.64/47.13    (5)  all_58_3 = e3
% 240.64/47.13    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.64/47.13         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.64/47.13    (7)  all_58_3 = e0 & op(e2, e2) = e0
% 240.64/47.13    (8)   ~ (e3 = e2)
% 240.64/47.13    (9)  all_58_9 = e3
% 240.64/47.13    (10)   ~ (all_52_4 = e3)
% 240.64/47.13    (11)  op(e3, e2) = all_52_4
% 240.64/47.13    (12)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.64/47.13          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.64/47.13    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.13    (14)   ~ (e1 = e0)
% 240.64/47.13    (15)  op(e3, e3) = e0
% 240.64/47.13    (16)   ~ (e2 = e1)
% 240.64/47.13  
% 240.64/47.13  Begin of proof
% 240.64/47.13  | 
% 240.64/47.13  | ALPHA: (7) implies:
% 240.64/47.13  |   (17)  all_58_3 = e0
% 240.64/47.13  | 
% 240.64/47.13  | COMBINE_EQS: (5), (17) imply:
% 240.64/47.13  |   (18)  e3 = e0
% 240.64/47.13  | 
% 240.64/47.13  | COMBINE_EQS: (9), (18) imply:
% 240.64/47.13  |   (19)  all_58_9 = e0
% 240.64/47.13  | 
% 240.64/47.13  | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (11), (12), (13), (14), (15),
% 240.64/47.13  |            (16), (19) are inconsistent by sub-proof #319.
% 240.64/47.13  | 
% 240.64/47.13  End of proof
% 240.64/47.13  
% 240.64/47.13  Sub-proof #319 shows that the following formulas are inconsistent:
% 240.64/47.13  ----------------------------------------------------------------
% 240.64/47.13    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.64/47.13         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.64/47.13    (2)   ~ (e3 = e0)
% 240.64/47.13    (3)   ~ (e2 = e0)
% 240.64/47.13    (4)  all_58_9 = e0
% 240.64/47.13    (5)   ~ (e3 = e1)
% 240.64/47.13    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.64/47.13         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.64/47.13    (7)   ~ (e3 = e2)
% 240.64/47.13    (8)   ~ (all_52_4 = e3)
% 240.64/47.13    (9)  op(e3, e2) = all_52_4
% 240.64/47.13    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.64/47.13          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.64/47.13    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.13    (12)   ~ (e1 = e0)
% 240.64/47.13    (13)  op(e3, e3) = e0
% 240.64/47.13    (14)   ~ (e2 = e1)
% 240.64/47.13  
% 240.64/47.13  Begin of proof
% 240.64/47.13  | 
% 240.64/47.13  | BETA: splitting (6) gives:
% 240.64/47.13  | 
% 240.64/47.13  | Case 1:
% 240.64/47.13  | | 
% 240.64/47.13  | |   (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 240.64/47.13  | |           e3)
% 240.64/47.13  | | 
% 240.64/47.13  | | REF_CLOSE: (2), (8), (9), (11), (13), (15) are inconsistent by sub-proof
% 240.64/47.13  | |            #1513.
% 240.64/47.13  | | 
% 240.64/47.13  | Case 2:
% 240.64/47.13  | | 
% 240.64/47.13  | |   (16)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 240.64/47.13  | |           e3)
% 240.64/47.13  | | 
% 240.64/47.13  | | BETA: splitting (16) gives:
% 240.64/47.13  | | 
% 240.64/47.13  | | Case 1:
% 240.64/47.13  | | | 
% 240.64/47.13  | | |   (17)  all_58_4 = e3 & op(e3, e1) = e3
% 240.64/47.13  | | | 
% 240.64/47.13  | | | ALPHA: (17) implies:
% 240.64/47.13  | | |   (18)  all_58_4 = e3
% 240.64/47.13  | | | 
% 240.64/47.13  | | | BETA: splitting (10) gives:
% 240.64/47.13  | | | 
% 240.64/47.13  | | | Case 1:
% 240.64/47.13  | | | | 
% 240.64/47.13  | | | |   (19)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 240.64/47.13  | | | |           = e1)
% 240.64/47.13  | | | | 
% 240.64/47.13  | | | | BETA: splitting (19) gives:
% 240.64/47.13  | | | | 
% 240.64/47.13  | | | | Case 1:
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | |   (20)  all_58_0 = e1 & op(e3, e3) = e1
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | | ALPHA: (20) implies:
% 240.64/47.13  | | | | |   (21)  op(e3, e3) = e1
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | | REF_CLOSE: (11), (12), (13), (21) are inconsistent by sub-proof #1828.
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | Case 2:
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | |   (22)  all_58_1 = e1 & op(e3, e2) = e1
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | | ALPHA: (22) implies:
% 240.64/47.13  | | | | |   (23)  all_58_1 = e1
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | | BETA: splitting (1) gives:
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | | Case 1:
% 240.64/47.13  | | | | | | 
% 240.64/47.13  | | | | | |   (24)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3,
% 240.64/47.13  | | | | | |             e2) = e2)
% 240.64/47.13  | | | | | | 
% 240.64/47.13  | | | | | | REF_CLOSE: (3), (11), (13), (14), (23), (24) are inconsistent by
% 240.64/47.13  | | | | | |            sub-proof #785.
% 240.64/47.13  | | | | | | 
% 240.64/47.13  | | | | | Case 2:
% 240.64/47.13  | | | | | | 
% 240.64/47.13  | | | | | |   (25)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3,
% 240.64/47.13  | | | | | |             e0) = e2)
% 240.64/47.13  | | | | | | 
% 240.64/47.13  | | | | | | BETA: splitting (25) gives:
% 240.64/47.13  | | | | | | 
% 240.64/47.13  | | | | | | Case 1:
% 240.64/47.13  | | | | | | | 
% 240.64/47.13  | | | | | | |   (26)  all_58_4 = e2 & op(e3, e1) = e2
% 240.64/47.13  | | | | | | | 
% 240.64/47.13  | | | | | | | REF_CLOSE: (7), (18), (26) are inconsistent by sub-proof #1476.
% 240.64/47.13  | | | | | | | 
% 240.64/47.13  | | | | | | Case 2:
% 240.64/47.13  | | | | | | | 
% 240.64/47.13  | | | | | | |   (27)  all_58_9 = e2 & op(e3, e0) = e2
% 240.64/47.13  | | | | | | | 
% 240.64/47.13  | | | | | | | REF_CLOSE: (3), (4), (27) are inconsistent by sub-proof #1655.
% 240.64/47.13  | | | | | | | 
% 240.64/47.13  | | | | | | End of split
% 240.64/47.13  | | | | | | 
% 240.64/47.13  | | | | | End of split
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | End of split
% 240.64/47.13  | | | | 
% 240.64/47.13  | | | Case 2:
% 240.64/47.13  | | | | 
% 240.64/47.13  | | | |   (28)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 240.64/47.13  | | | |           = e1)
% 240.64/47.13  | | | | 
% 240.64/47.13  | | | | BETA: splitting (28) gives:
% 240.64/47.13  | | | | 
% 240.64/47.13  | | | | Case 1:
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | |   (29)  all_58_4 = e1 & op(e3, e1) = e1
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | | REF_CLOSE: (5), (18), (29) are inconsistent by sub-proof #2042.
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | Case 2:
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | |   (30)  all_58_9 = e1 & op(e3, e0) = e1
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | | REF_CLOSE: (4), (12), (30) are inconsistent by sub-proof #2183.
% 240.64/47.13  | | | | | 
% 240.64/47.13  | | | | End of split
% 240.64/47.13  | | | | 
% 240.64/47.13  | | | End of split
% 240.64/47.13  | | | 
% 240.64/47.13  | | Case 2:
% 240.64/47.13  | | | 
% 240.64/47.13  | | |   (31)  all_58_9 = e3 & op(e3, e0) = e3
% 240.64/47.13  | | | 
% 240.64/47.13  | | | ALPHA: (31) implies:
% 240.64/47.13  | | |   (32)  all_58_9 = e3
% 240.64/47.13  | | | 
% 240.64/47.13  | | | REF_CLOSE: (2), (4), (32) are inconsistent by sub-proof #1958.
% 240.64/47.13  | | | 
% 240.64/47.13  | | End of split
% 240.64/47.13  | | 
% 240.64/47.13  | End of split
% 240.64/47.13  | 
% 240.64/47.13  End of proof
% 240.64/47.13  
% 240.64/47.13  Sub-proof #320 shows that the following formulas are inconsistent:
% 240.64/47.13  ----------------------------------------------------------------
% 240.64/47.13    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.64/47.13         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.64/47.13    (2)  all_56_31 = all_4_2
% 240.64/47.13    (3)  op(e0, e1) = all_52_11
% 240.64/47.13    (4)   ~ (all_4_2 = e2)
% 240.64/47.13    (5)  op(e1, e2) = all_52_6
% 240.64/47.13    (6)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 240.64/47.13         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.64/47.14    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.64/47.14           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.64/47.14             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.64/47.14           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.64/47.14             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.64/47.14           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.64/47.14           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.64/47.14           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.64/47.14           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.64/47.14           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.64/47.14           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.64/47.14             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.64/47.14           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.64/47.14           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 240.64/47.14           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.64/47.14           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.64/47.14           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.64/47.14           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.64/47.14             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.64/47.14           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.64/47.14           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 240.64/47.14           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.64/47.14           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.64/47.14           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.64/47.14           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.64/47.14             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.64/47.14           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.64/47.14           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.64/47.14    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.64/47.14         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.64/47.14    (9)  op(e1, e0) = all_52_14
% 240.64/47.14    (10)   ~ (e3 = e1)
% 240.64/47.14    (11)  op(e0, e0) = all_4_2
% 240.64/47.14    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.64/47.14          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.64/47.14    (13)  all_58_3 = e3
% 240.64/47.14    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.64/47.14          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.64/47.14    (15)   ~ (all_52_11 = e3)
% 240.64/47.14    (16)  op(e3, e1) = all_52_8
% 240.64/47.14    (17)  op(e2, e1) = all_52_9
% 240.64/47.14    (18)   ~ (e3 = e2)
% 240.64/47.14    (19)   ~ (all_4_2 = e3)
% 240.64/47.14    (20)   ~ (all_52_7 = all_4_2)
% 240.64/47.14    (21)   ~ (all_52_9 = all_52_13)
% 240.64/47.14    (22)  all_54_15 = all_4_2
% 240.64/47.14    (23)  all_58_9 = e3
% 240.64/47.14    (24)   ~ (all_52_6 = all_52_14)
% 240.64/47.14    (25)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 240.64/47.14    (26)  op(e2, e3) = all_52_1
% 240.64/47.14    (27)   ~ (all_52_2 = e3)
% 240.64/47.14    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.64/47.14          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.64/47.14    (29)  op(e0, e2) = all_52_7
% 240.64/47.14    (30)   ~ (all_52_4 = e3)
% 240.64/47.14    (31)  op(e3, e2) = all_52_4
% 240.64/47.14    (32)   ~ (all_4_2 = e1)
% 240.64/47.14    (33)   ~ (all_52_9 = e3)
% 240.64/47.14    (34)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.64/47.14          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.14    (35)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.64/47.14          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.64/47.14    (36)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.14    (37)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.64/47.14          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.64/47.14    (38)  op(e1, e3) = all_52_2
% 240.64/47.14    (39)  all_56_21 = e3
% 240.64/47.14    (40)  op(e3, e3) = e0
% 240.64/47.14    (41)   ~ (all_52_13 = e3)
% 240.64/47.14    (42)   ~ (all_52_11 = all_4_2)
% 240.64/47.14    (43)  op(e2, e0) = all_52_13
% 240.64/47.14    (44)   ~ (all_52_1 = e3)
% 240.64/47.14    (45)   ~ (all_52_4 = e0)
% 240.64/47.14    (46)   ~ (e2 = e1)
% 240.64/47.14    (47)   ~ (all_52_8 = e3)
% 240.64/47.14  
% 240.64/47.14  Begin of proof
% 240.64/47.14  | 
% 240.64/47.14  | BETA: splitting (25) gives:
% 240.64/47.14  | 
% 240.64/47.14  | Case 1:
% 240.64/47.14  | | 
% 240.64/47.14  | |   (48)  all_54_15 = e3
% 240.64/47.14  | | 
% 240.64/47.14  | | REF_CLOSE: (19), (22), (48) are inconsistent by sub-proof #2340.
% 240.64/47.14  | | 
% 240.64/47.14  | Case 2:
% 240.64/47.14  | | 
% 240.64/47.14  | |   (49)   ~ (all_54_15 = e3)
% 240.64/47.14  | |   (50)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 240.64/47.14  | | 
% 240.64/47.14  | | BETA: splitting (50) gives:
% 240.64/47.14  | | 
% 240.64/47.14  | | Case 1:
% 240.64/47.14  | | | 
% 240.64/47.14  | | |   (51)  all_54_15 = e2
% 240.64/47.14  | | | 
% 240.64/47.14  | | | REF_CLOSE: (4), (22), (51) are inconsistent by sub-proof #2339.
% 240.64/47.14  | | | 
% 240.64/47.14  | | Case 2:
% 240.64/47.14  | | | 
% 240.64/47.14  | | |   (52)   ~ (all_54_15 = e2)
% 240.64/47.14  | | |   (53)  all_54_15 = e1 | all_54_15 = e0
% 240.64/47.14  | | | 
% 240.64/47.14  | | | BETA: splitting (53) gives:
% 240.64/47.14  | | | 
% 240.64/47.14  | | | Case 1:
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | |   (54)  all_54_15 = e1
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | REF_CLOSE: (22), (32), (54) are inconsistent by sub-proof #2338.
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | Case 2:
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | |   (55)  all_54_15 = e0
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | COMBINE_EQS: (22), (55) imply:
% 240.64/47.14  | | | |   (56)  all_4_2 = e0
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | SIMP: (56) implies:
% 240.64/47.14  | | | |   (57)  all_4_2 = e0
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | COMBINE_EQS: (2), (57) imply:
% 240.64/47.14  | | | |   (58)  all_56_31 = e0
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | REDUCE: (20), (57) imply:
% 240.64/47.14  | | | |   (59)   ~ (all_52_7 = e0)
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | REDUCE: (42), (57) imply:
% 240.64/47.14  | | | |   (60)   ~ (all_52_11 = e0)
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | REDUCE: (19), (57) imply:
% 240.64/47.14  | | | |   (61)   ~ (e3 = e0)
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | SIMP: (61) implies:
% 240.64/47.14  | | | |   (62)   ~ (e3 = e0)
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | REDUCE: (4), (57) imply:
% 240.64/47.14  | | | |   (63)   ~ (e2 = e0)
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | SIMP: (63) implies:
% 240.64/47.14  | | | |   (64)   ~ (e2 = e0)
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | REDUCE: (32), (57) imply:
% 240.64/47.14  | | | |   (65)   ~ (e1 = e0)
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | SIMP: (65) implies:
% 240.64/47.14  | | | |   (66)   ~ (e1 = e0)
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | REDUCE: (11), (57) imply:
% 240.64/47.14  | | | |   (67)  op(e0, e0) = e0
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | BETA: splitting (12) gives:
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | | Case 1:
% 240.64/47.14  | | | | | 
% 240.64/47.14  | | | | |   (68)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 240.64/47.14  | | | | |             e1) = e0)
% 240.64/47.14  | | | | | 
% 240.64/47.14  | | | | | BETA: splitting (68) gives:
% 240.64/47.14  | | | | | 
% 240.64/47.14  | | | | | Case 1:
% 240.64/47.14  | | | | | | 
% 240.64/47.14  | | | | | |   (69)  all_58_4 = e0 & op(e3, e1) = e0
% 240.64/47.14  | | | | | | 
% 240.64/47.14  | | | | | | ALPHA: (69) implies:
% 240.64/47.14  | | | | | |   (70)  all_58_4 = e0
% 240.64/47.14  | | | | | | 
% 240.64/47.14  | | | | | | REF_CLOSE: (1), (10), (14), (18), (30), (31), (35), (36), (40),
% 240.64/47.14  | | | | | |            (46), (62), (64), (66), (70) are inconsistent by
% 240.64/47.14  | | | | | |            sub-proof #1512.
% 240.64/47.14  | | | | | | 
% 240.64/47.14  | | | | | Case 2:
% 240.64/47.14  | | | | | | 
% 240.64/47.14  | | | | | |   (71)  all_58_5 = e0 & op(e2, e1) = e0
% 240.64/47.14  | | | | | | 
% 240.64/47.14  | | | | | | ALPHA: (71) implies:
% 240.64/47.14  | | | | | |   (72)  op(e2, e1) = e0
% 240.64/47.14  | | | | | | 
% 240.64/47.14  | | | | | | BETA: splitting (8) gives:
% 240.64/47.14  | | | | | | 
% 240.64/47.14  | | | | | | Case 1:
% 240.64/47.14  | | | | | | | 
% 240.64/47.14  | | | | | | |   (73)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 240.64/47.14  | | | | | | |           op(e2, e2) = e0)
% 240.64/47.14  | | | | | | | 
% 240.64/47.14  | | | | | | | BETA: splitting (73) gives:
% 240.64/47.14  | | | | | | | 
% 240.64/47.14  | | | | | | | Case 1:
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | |   (74)  all_58_1 = e0 & op(e3, e2) = e0
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | REF_CLOSE: (31), (36), (45), (74) are inconsistent by sub-proof
% 240.64/47.14  | | | | | | | |            #1968.
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | Case 2:
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | |   (75)  all_58_3 = e0 & op(e2, e2) = e0
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | ALPHA: (75) implies:
% 240.64/47.14  | | | | | | | |   (76)  all_58_3 = e0
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | COMBINE_EQS: (13), (76) imply:
% 240.64/47.14  | | | | | | | |   (77)  e3 = e0
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | COMBINE_EQS: (23), (77) imply:
% 240.64/47.14  | | | | | | | |   (78)  all_58_9 = e0
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | REF_CLOSE: (6), (10), (18), (34), (36), (37), (41), (43), (46),
% 240.64/47.14  | | | | | | | |            (62), (64), (66), (67), (78) are inconsistent by
% 240.64/47.14  | | | | | | | |            sub-proof #1650.
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | End of split
% 240.64/47.14  | | | | | | | 
% 240.64/47.14  | | | | | | Case 2:
% 240.64/47.14  | | | | | | | 
% 240.64/47.14  | | | | | | |   (79)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 240.64/47.14  | | | | | | |           op(e0, e2) = e0)
% 240.64/47.14  | | | | | | | 
% 240.64/47.14  | | | | | | | BETA: splitting (79) gives:
% 240.64/47.14  | | | | | | | 
% 240.64/47.14  | | | | | | | Case 1:
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | |   (80)  all_58_7 = e0 & op(e1, e2) = e0
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | ALPHA: (80) implies:
% 240.64/47.14  | | | | | | | |   (81)  op(e1, e2) = e0
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | GROUND_INST: instantiating (36) with all_52_6, e0, e2, e1,
% 240.64/47.14  | | | | | | | |              simplifying with (5), (81) gives:
% 240.64/47.14  | | | | | | | |   (82)  all_52_6 = e0
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | GROUND_INST: instantiating (36) with all_52_9, e0, e1, e2,
% 240.64/47.14  | | | | | | | |              simplifying with (17), (72) gives:
% 240.64/47.14  | | | | | | | |   (83)  all_52_9 = e0
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | REDUCE: (24), (82) imply:
% 240.64/47.14  | | | | | | | |   (84)   ~ (all_52_14 = e0)
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | SIMP: (84) implies:
% 240.64/47.14  | | | | | | | |   (85)   ~ (all_52_14 = e0)
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | REDUCE: (21), (83) imply:
% 240.64/47.14  | | | | | | | |   (86)   ~ (all_52_13 = e0)
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | SIMP: (86) implies:
% 240.64/47.14  | | | | | | | |   (87)   ~ (all_52_13 = e0)
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | BETA: splitting (7) gives:
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | Case 1:
% 240.64/47.14  | | | | | | | | | 
% 240.64/47.14  | | | | | | | | |   (88)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 240.64/47.14  | | | | | | | | |           ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 240.64/47.14  | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 240.64/47.14  | | | | | | | | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 240.64/47.14  | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3)
% 240.64/47.14  | | | | | | | | |           = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 240.64/47.14  | | | | | | | | |           = e3 & op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17
% 240.64/47.14  | | | | | | | | |           = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1)
% 240.64/47.14  | | | | | | | | |           = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 240.64/47.14  | | | | | | | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0)
% 240.64/47.14  | | | | | | | | |           = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 240.64/47.14  | | | | | | | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 240.64/47.14  | | | | | | | | |           = e0 & op(e0, e3) = e0)
% 240.64/47.14  | | | | | | | | | 
% 240.64/47.14  | | | | | | | | | BETA: splitting (88) gives:
% 240.64/47.14  | | | | | | | | | 
% 240.64/47.14  | | | | | | | | | Case 1:
% 240.64/47.14  | | | | | | | | | | 
% 240.64/47.14  | | | | | | | | | |   (89)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 240.64/47.14  | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.64/47.14  | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 240.64/47.14  | | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 240.64/47.14  | | | | | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.64/47.14  | | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.64/47.14  | | | | | | | | | |             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 240.64/47.14  | | | | | | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.64/47.14  | | | | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.64/47.14  | | | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 240.64/47.14  | | | | | | | | | |           e3)
% 240.64/47.14  | | | | | | | | | | 
% 240.64/47.14  | | | | | | | | | | REF_CLOSE: (26), (27), (36), (38), (39), (44), (89) are
% 240.64/47.14  | | | | | | | | | |            inconsistent by sub-proof #441.
% 240.64/47.14  | | | | | | | | | | 
% 240.64/47.14  | | | | | | | | | Case 2:
% 240.64/47.14  | | | | | | | | | | 
% 240.64/47.14  | | | | | | | | | |   (90)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3)
% 240.64/47.14  | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.64/47.14  | | | | | | | | | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.64/47.14  | | | | | | | | | |           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 240.64/47.14  | | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 240.64/47.14  | | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.64/47.14  | | | | | | | | | |             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 240.64/47.14  | | | | | | | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.64/47.14  | | | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.64/47.14  | | | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 240.64/47.14  | | | | | | | | | |           e0)
% 240.64/47.14  | | | | | | | | | | 
% 240.64/47.14  | | | | | | | | | | REF_CLOSE: (39), (58), (90) are inconsistent by sub-proof
% 240.64/47.14  | | | | | | | | | |            #342.
% 240.64/47.14  | | | | | | | | | | 
% 240.64/47.14  | | | | | | | | | End of split
% 240.64/47.14  | | | | | | | | | 
% 240.64/47.14  | | | | | | | | Case 2:
% 240.64/47.14  | | | | | | | | | 
% 240.64/47.14  | | | | | | | | |   (91)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 240.64/47.14  | | | | | | | | |           &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.64/47.14  | | | | | | | | |           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1)
% 240.64/47.14  | | | | | | | | |           = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 240.64/47.14  | | | | | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.64/47.14  | | | | | | | | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.64/47.14  | | | | | | | | |           & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.64/47.14  | | | | | | | | |           e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.64/47.14  | | | | | | | | |           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 240.64/47.14  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0)
% 240.64/47.14  | | | | | | | | |           = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 240.64/47.14  | | | | | | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 240.64/47.14  | | | | | | | | |             = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 240.64/47.14  | | | | | | | | |           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.64/47.14  | | | | | | | | | 
% 240.64/47.14  | | | | | | | | | REF_CLOSE: (9), (17), (36), (43), (58), (64), (66), (72),
% 240.64/47.14  | | | | | | | | |            (85), (87), (91) are inconsistent by sub-proof
% 240.64/47.14  | | | | | | | | |            #858.
% 240.64/47.14  | | | | | | | | | 
% 240.64/47.14  | | | | | | | | End of split
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | Case 2:
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | |   (92)  all_58_13 = e0 & op(e0, e2) = e0
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | ALPHA: (92) implies:
% 240.64/47.14  | | | | | | | |   (93)  op(e0, e2) = e0
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | | REF_CLOSE: (29), (36), (59), (93) are inconsistent by sub-proof
% 240.64/47.14  | | | | | | | |            #2252.
% 240.64/47.14  | | | | | | | | 
% 240.64/47.14  | | | | | | | End of split
% 240.64/47.14  | | | | | | | 
% 240.64/47.14  | | | | | | End of split
% 240.64/47.14  | | | | | | 
% 240.64/47.14  | | | | | End of split
% 240.64/47.14  | | | | | 
% 240.64/47.14  | | | | Case 2:
% 240.64/47.14  | | | | | 
% 240.64/47.14  | | | | |   (94)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 240.64/47.14  | | | | |             e1) = e0)
% 240.64/47.14  | | | | | 
% 240.64/47.14  | | | | | REF_CLOSE: (3), (15), (16), (17), (28), (33), (36), (47), (60), (62),
% 240.64/47.14  | | | | |            (94) are inconsistent by sub-proof #360.
% 240.64/47.14  | | | | | 
% 240.64/47.14  | | | | End of split
% 240.64/47.14  | | | | 
% 240.64/47.14  | | | End of split
% 240.64/47.14  | | | 
% 240.64/47.14  | | End of split
% 240.64/47.14  | | 
% 240.64/47.14  | End of split
% 240.64/47.14  | 
% 240.64/47.14  End of proof
% 240.64/47.14  
% 240.64/47.14  Sub-proof #321 shows that the following formulas are inconsistent:
% 240.64/47.14  ----------------------------------------------------------------
% 240.64/47.14    (1)  op(e0, e0) = e1
% 240.64/47.14    (2)  op(e2, e2) = e3
% 240.64/47.14    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.64/47.14         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.64/47.14    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.64/47.14           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.64/47.14           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.64/47.14           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.64/47.14           & $i(all_56_23))
% 240.64/47.14    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.64/47.14         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.14    (6)   ~ (e3 = e0)
% 240.64/47.14    (7)  op(e0, e1) = all_52_11
% 240.64/47.14    (8)   ~ (e2 = e0)
% 240.64/47.14    (9)  op(e1, e2) = all_52_6
% 240.64/47.14    (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.64/47.14          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.64/47.14    (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.64/47.14          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.64/47.14    (12)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 240.64/47.14            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 240.64/47.14              e1) = all_20_1 & $i(all_20_1))
% 240.64/47.14    (13)   ~ (all_52_7 = e3)
% 240.64/47.14    (14)   ~ (e3 = e1)
% 240.64/47.14    (15)  all_58_3 = e3
% 240.64/47.14    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.64/47.14          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.64/47.14    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.64/47.14              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.64/47.14                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.64/47.14                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.64/47.14    (18)   ~ (all_52_11 = e3)
% 240.64/47.14    (19)  op(e3, e1) = all_52_8
% 240.64/47.14    (20)  op(e2, e1) = all_52_9
% 240.64/47.14    (21)   ~ (e3 = e2)
% 240.64/47.14    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.64/47.14          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.64/47.14    (23)   ~ (all_52_7 = e1)
% 240.64/47.14    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.64/47.14          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.64/47.14    (25)  all_58_15 = e1
% 240.64/47.15    (26)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.64/47.15          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.64/47.15    (27)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.64/47.15            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.64/47.15              e3) = all_42_1 & $i(all_42_1))
% 240.64/47.15    (28)  all_58_9 = e3
% 240.64/47.15    (29)  op(e3, e0) = e3
% 240.64/47.15    (30)  op(e3, e3) = e2
% 240.64/47.15    (31)  all_58_12 = e3
% 240.64/47.15    (32)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.64/47.15          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.64/47.15    (33)  op(e1, e1) = e3
% 240.64/47.15    (34)   ~ (all_52_6 = e3)
% 240.64/47.15    (35)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.64/47.15          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.64/47.15    (36)  op(e0, e2) = all_52_7
% 240.64/47.15    (37)   ~ (all_52_4 = e3)
% 240.64/47.15    (38)  op(e3, e2) = all_52_4
% 240.64/47.15    (39)   ~ (all_52_9 = e3)
% 240.64/47.15    (40)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.64/47.15          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.64/47.15    (41)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 240.64/47.15            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 240.64/47.15              e1) = all_34_1 & $i(all_34_1))
% 240.64/47.15    (42)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.64/47.15          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.15    (43)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.64/47.15          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.64/47.15    (44)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.64/47.15          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.64/47.15    (45)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.64/47.15          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.64/47.15    (46)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.15    (47)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.64/47.15          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.64/47.15    (48)  all_56_21 = e3
% 240.64/47.15    (49)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.64/47.15          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.15    (50)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.64/47.15          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.64/47.15    (51)   ~ (e1 = e0)
% 240.64/47.15    (52)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.64/47.15    (53)   ~ (all_52_13 = e3)
% 240.64/47.15    (54)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.64/47.15          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.64/47.15    (55)  op(e2, e0) = all_52_13
% 240.64/47.15    (56)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.15          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.64/47.15            e1)
% 240.64/47.15    (57)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.64/47.15            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.64/47.15            & $i(all_8_1))
% 240.64/47.15    (58)   ~ (e2 = e1)
% 240.64/47.15    (59)   ~ (all_52_8 = e3)
% 240.64/47.15  
% 240.64/47.15  Begin of proof
% 240.64/47.15  | 
% 240.64/47.15  | BETA: splitting (52) gives:
% 240.64/47.15  | 
% 240.64/47.15  | Case 1:
% 240.64/47.15  | | 
% 240.64/47.15  | |   (60)  all_58_4 = e1 & op(e3, e1) = e1
% 240.64/47.15  | | 
% 240.64/47.15  | | ALPHA: (60) implies:
% 240.64/47.15  | |   (61)  all_58_4 = e1
% 240.64/47.15  | |   (62)  op(e3, e1) = e1
% 240.64/47.15  | | 
% 240.64/47.15  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 240.64/47.15  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 240.64/47.15  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 240.64/47.15  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 240.64/47.15  | |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56), (57),
% 240.64/47.15  | |            (58), (59), (61), (62) are inconsistent by sub-proof #322.
% 240.64/47.15  | | 
% 240.64/47.15  | Case 2:
% 240.64/47.15  | | 
% 240.64/47.15  | |   (63)  all_58_9 = e1 & op(e3, e0) = e1
% 240.64/47.15  | | 
% 240.64/47.15  | | ALPHA: (63) implies:
% 240.64/47.15  | |   (64)  all_58_9 = e1
% 240.64/47.15  | | 
% 240.64/47.15  | | REF_CLOSE: (1), (6), (8), (14), (17), (21), (42), (46), (47), (51), (53),
% 240.64/47.15  | |            (55), (58), (64) are inconsistent by sub-proof #1600.
% 240.64/47.15  | | 
% 240.64/47.15  | End of split
% 240.64/47.15  | 
% 240.64/47.15  End of proof
% 240.64/47.15  
% 240.64/47.15  Sub-proof #322 shows that the following formulas are inconsistent:
% 240.64/47.15  ----------------------------------------------------------------
% 240.64/47.15    (1)  op(e0, e0) = e1
% 240.64/47.15    (2)  op(e2, e2) = e3
% 240.64/47.15    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.64/47.15         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.64/47.15    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.64/47.15           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.64/47.15           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.64/47.15           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.64/47.15           & $i(all_56_23))
% 240.64/47.15    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.64/47.15         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.15    (6)   ~ (e3 = e0)
% 240.64/47.15    (7)  op(e0, e1) = all_52_11
% 240.64/47.15    (8)   ~ (e2 = e0)
% 240.64/47.15    (9)  op(e1, e2) = all_52_6
% 240.64/47.15    (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.64/47.15          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.64/47.15    (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.64/47.15          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.64/47.15    (12)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 240.64/47.15            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 240.64/47.15              e1) = all_20_1 & $i(all_20_1))
% 240.64/47.15    (13)   ~ (all_52_7 = e3)
% 240.64/47.15    (14)   ~ (e3 = e1)
% 240.64/47.15    (15)  all_58_3 = e3
% 240.64/47.15    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.64/47.15          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.64/47.15    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.64/47.15              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.64/47.15                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.64/47.15                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.64/47.15    (18)   ~ (all_52_11 = e3)
% 240.64/47.15    (19)  op(e3, e1) = all_52_8
% 240.64/47.15    (20)  op(e2, e1) = all_52_9
% 240.64/47.15    (21)   ~ (e3 = e2)
% 240.64/47.15    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.64/47.15          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.64/47.15    (23)   ~ (all_52_7 = e1)
% 240.64/47.15    (24)  op(e3, e1) = e1
% 240.64/47.15    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.64/47.15          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.64/47.15    (26)  all_58_15 = e1
% 240.64/47.15    (27)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.64/47.15          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.64/47.15    (28)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.64/47.15            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.64/47.15              e3) = all_42_1 & $i(all_42_1))
% 240.64/47.15    (29)  all_58_9 = e3
% 240.64/47.15    (30)  op(e3, e0) = e3
% 240.64/47.15    (31)  all_58_4 = e1
% 240.64/47.15    (32)  op(e3, e3) = e2
% 240.64/47.15    (33)  all_58_12 = e3
% 240.64/47.15    (34)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.64/47.15          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.64/47.15    (35)  op(e1, e1) = e3
% 240.64/47.15    (36)   ~ (all_52_6 = e3)
% 240.64/47.15    (37)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.64/47.15          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.64/47.15    (38)  op(e0, e2) = all_52_7
% 240.64/47.15    (39)   ~ (all_52_4 = e3)
% 240.64/47.15    (40)  op(e3, e2) = all_52_4
% 240.64/47.15    (41)   ~ (all_52_9 = e3)
% 240.64/47.15    (42)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.64/47.15          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.64/47.15    (43)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 240.64/47.15            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 240.64/47.15              e1) = all_34_1 & $i(all_34_1))
% 240.64/47.15    (44)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.64/47.15          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.15    (45)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.64/47.15          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.64/47.15    (46)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.64/47.15          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.64/47.15    (47)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.64/47.15          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.64/47.15    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.15    (49)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.64/47.15          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.64/47.15    (50)  all_56_21 = e3
% 240.64/47.15    (51)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.64/47.15          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.15    (52)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.64/47.15          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.64/47.15    (53)   ~ (e1 = e0)
% 240.64/47.15    (54)   ~ (all_52_13 = e3)
% 240.64/47.15    (55)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.64/47.15          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.64/47.15    (56)  op(e2, e0) = all_52_13
% 240.64/47.15    (57)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.15          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.64/47.15            e1)
% 240.64/47.15    (58)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.64/47.15            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.64/47.15            & $i(all_8_1))
% 240.64/47.15    (59)   ~ (e2 = e1)
% 240.64/47.15    (60)   ~ (all_52_8 = e3)
% 240.64/47.15  
% 240.64/47.15  Begin of proof
% 240.64/47.15  | 
% 240.64/47.15  | BETA: splitting (51) gives:
% 240.64/47.15  | 
% 240.64/47.15  | Case 1:
% 240.64/47.15  | | 
% 240.64/47.15  | |   (61)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 240.64/47.15  | |           e1)
% 240.64/47.15  | | 
% 240.64/47.15  | | BETA: splitting (61) gives:
% 240.64/47.15  | | 
% 240.64/47.15  | | Case 1:
% 240.64/47.15  | | | 
% 240.64/47.15  | | |   (62)  all_58_1 = e1 & op(e3, e2) = e1
% 240.64/47.15  | | | 
% 240.64/47.15  | | | ALPHA: (62) implies:
% 240.64/47.15  | | |   (63)  all_58_1 = e1
% 240.64/47.15  | | | 
% 240.64/47.15  | | | REF_CLOSE: (6), (8), (14), (16), (21), (31), (32), (34), (39), (40), (48),
% 240.64/47.15  | | |            (53), (63) are inconsistent by sub-proof #1645.
% 240.64/47.15  | | | 
% 240.64/47.15  | | Case 2:
% 240.64/47.15  | | | 
% 240.64/47.15  | | |   (64)  all_58_3 = e1 & op(e2, e2) = e1
% 240.64/47.15  | | | 
% 240.64/47.15  | | | REF_CLOSE: (1), (6), (8), (14), (15), (17), (21), (29), (44), (48), (49),
% 240.64/47.15  | | |            (53), (54), (56), (59), (64) are inconsistent by sub-proof
% 240.64/47.15  | | |            #331.
% 240.64/47.15  | | | 
% 240.64/47.15  | | End of split
% 240.64/47.15  | | 
% 240.64/47.15  | Case 2:
% 240.64/47.15  | | 
% 240.64/47.15  | |   (65)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 240.64/47.15  | |           e1)
% 240.64/47.15  | | 
% 240.64/47.15  | | BETA: splitting (65) gives:
% 240.64/47.15  | | 
% 240.64/47.15  | | Case 1:
% 240.64/47.15  | | | 
% 240.64/47.15  | | |   (66)  all_58_7 = e1 & op(e1, e2) = e1
% 240.64/47.15  | | | 
% 240.64/47.15  | | | ALPHA: (66) implies:
% 240.64/47.15  | | |   (67)  all_58_7 = e1
% 240.64/47.15  | | |   (68)  op(e1, e2) = e1
% 240.64/47.15  | | | 
% 240.64/47.15  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 240.64/47.15  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 240.64/47.15  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 240.64/47.15  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 240.64/47.15  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 240.64/47.15  | | |            (54), (55), (56), (57), (58), (59), (60), (67), (68) are
% 240.64/47.15  | | |            inconsistent by sub-proof #323.
% 240.64/47.15  | | | 
% 240.64/47.15  | | Case 2:
% 240.64/47.15  | | | 
% 240.64/47.15  | | |   (69)  all_58_13 = e1 & op(e0, e2) = e1
% 240.64/47.15  | | | 
% 240.64/47.15  | | | REF_CLOSE: (23), (38), (48), (69) are inconsistent by sub-proof #2275.
% 240.64/47.15  | | | 
% 240.64/47.15  | | End of split
% 240.64/47.15  | | 
% 240.64/47.15  | End of split
% 240.64/47.15  | 
% 240.64/47.15  End of proof
% 240.64/47.15  
% 240.64/47.15  Sub-proof #323 shows that the following formulas are inconsistent:
% 240.64/47.15  ----------------------------------------------------------------
% 240.64/47.15    (1)  op(e0, e0) = e1
% 240.64/47.15    (2)  op(e2, e2) = e3
% 240.64/47.16    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.64/47.16         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.64/47.16    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.64/47.16           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.64/47.16           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.64/47.16           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.64/47.16           & $i(all_56_23))
% 240.64/47.16    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.64/47.16         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.16    (6)   ~ (e3 = e0)
% 240.64/47.16    (7)  op(e0, e1) = all_52_11
% 240.64/47.16    (8)  op(e1, e2) = e1
% 240.64/47.16    (9)   ~ (e2 = e0)
% 240.64/47.16    (10)  op(e1, e2) = all_52_6
% 240.64/47.16    (11)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.64/47.16          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.64/47.16    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.64/47.16          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.64/47.16    (13)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 240.64/47.16            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 240.64/47.16              e1) = all_20_1 & $i(all_20_1))
% 240.64/47.16    (14)   ~ (all_52_7 = e3)
% 240.64/47.16    (15)   ~ (e3 = e1)
% 240.64/47.16    (16)  all_58_3 = e3
% 240.64/47.16    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.64/47.16          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.64/47.16    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.64/47.16              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.64/47.16                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.64/47.16                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.64/47.16    (19)   ~ (all_52_11 = e3)
% 240.64/47.16    (20)  op(e3, e1) = all_52_8
% 240.64/47.16    (21)  op(e2, e1) = all_52_9
% 240.64/47.16    (22)   ~ (e3 = e2)
% 240.64/47.16    (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.64/47.16          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.64/47.16    (24)  op(e3, e1) = e1
% 240.64/47.16    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.64/47.16          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.64/47.16    (26)  all_58_15 = e1
% 240.64/47.16    (27)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.64/47.16          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.64/47.16    (28)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.64/47.16            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.64/47.16              e3) = all_42_1 & $i(all_42_1))
% 240.64/47.16    (29)  all_58_9 = e3
% 240.64/47.16    (30)  op(e3, e0) = e3
% 240.64/47.16    (31)  all_58_4 = e1
% 240.64/47.16    (32)  op(e3, e3) = e2
% 240.64/47.16    (33)  all_58_12 = e3
% 240.64/47.16    (34)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.64/47.16          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.64/47.16    (35)  op(e1, e1) = e3
% 240.64/47.16    (36)   ~ (all_52_6 = e3)
% 240.64/47.16    (37)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.64/47.16          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.64/47.16    (38)  op(e0, e2) = all_52_7
% 240.64/47.16    (39)   ~ (all_52_4 = e3)
% 240.64/47.16    (40)  op(e3, e2) = all_52_4
% 240.64/47.16    (41)  all_58_7 = e1
% 240.64/47.16    (42)   ~ (all_52_9 = e3)
% 240.64/47.16    (43)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.64/47.16          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.64/47.16    (44)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 240.64/47.16            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 240.64/47.16              e1) = all_34_1 & $i(all_34_1))
% 240.64/47.16    (45)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.64/47.16          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.16    (46)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.64/47.16          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.64/47.16    (47)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.64/47.16          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.64/47.16    (48)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.64/47.16          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.64/47.16    (49)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.16    (50)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.64/47.16          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.64/47.16    (51)  all_56_21 = e3
% 240.64/47.16    (52)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.64/47.16          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.16    (53)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.64/47.16          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.64/47.16    (54)   ~ (e1 = e0)
% 240.64/47.16    (55)   ~ (all_52_13 = e3)
% 240.64/47.16    (56)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.64/47.16          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.64/47.16    (57)  op(e2, e0) = all_52_13
% 240.64/47.16    (58)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.16          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.64/47.16            e1)
% 240.64/47.16    (59)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.64/47.16            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.64/47.16            & $i(all_8_1))
% 240.64/47.16    (60)   ~ (e2 = e1)
% 240.64/47.16    (61)   ~ (all_52_8 = e3)
% 240.64/47.16  
% 240.64/47.16  Begin of proof
% 240.64/47.16  | 
% 240.64/47.16  | BETA: splitting (11) gives:
% 240.64/47.16  | 
% 240.64/47.16  | Case 1:
% 240.64/47.16  | | 
% 240.64/47.16  | |   (62)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 240.64/47.16  | |           e2)
% 240.64/47.16  | | 
% 240.64/47.16  | | BETA: splitting (62) gives:
% 240.64/47.16  | | 
% 240.64/47.16  | | Case 1:
% 240.64/47.16  | | | 
% 240.64/47.16  | | |   (63)  all_58_1 = e2 & op(e3, e2) = e2
% 240.64/47.16  | | | 
% 240.64/47.16  | | | REF_CLOSE: (6), (9), (15), (17), (22), (24), (32), (34), (46), (49), (54),
% 240.64/47.16  | | |            (60), (63) are inconsistent by sub-proof #387.
% 240.64/47.16  | | | 
% 240.64/47.16  | | Case 2:
% 240.64/47.16  | | | 
% 240.64/47.16  | | |   (64)  all_58_3 = e2 & op(e2, e2) = e2
% 240.64/47.16  | | | 
% 240.64/47.16  | | | ALPHA: (64) implies:
% 240.64/47.16  | | |   (65)  op(e2, e2) = e2
% 240.64/47.16  | | | 
% 240.64/47.16  | | | REF_CLOSE: (2), (22), (49), (65) are inconsistent by sub-proof #2140.
% 240.64/47.16  | | | 
% 240.64/47.16  | | End of split
% 240.64/47.16  | | 
% 240.64/47.16  | Case 2:
% 240.64/47.16  | | 
% 240.64/47.16  | |   (66)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 240.64/47.16  | |           e2)
% 240.64/47.16  | | 
% 240.64/47.16  | | BETA: splitting (66) gives:
% 240.64/47.16  | | 
% 240.64/47.16  | | Case 1:
% 240.64/47.16  | | | 
% 240.64/47.16  | | |   (67)  all_58_7 = e2 & op(e1, e2) = e2
% 240.64/47.16  | | | 
% 240.64/47.16  | | | ALPHA: (67) implies:
% 240.64/47.16  | | |   (68)  all_58_7 = e2
% 240.64/47.16  | | | 
% 240.64/47.16  | | | REF_CLOSE: (41), (60), (68) are inconsistent by sub-proof #2134.
% 240.64/47.16  | | | 
% 240.64/47.16  | | Case 2:
% 240.64/47.16  | | | 
% 240.64/47.16  | | |   (69)  all_58_13 = e2 & op(e0, e2) = e2
% 240.64/47.16  | | | 
% 240.64/47.16  | | | ALPHA: (69) implies:
% 240.64/47.16  | | |   (70)  all_58_13 = e2
% 240.64/47.16  | | |   (71)  op(e0, e2) = e2
% 240.64/47.16  | | | 
% 240.64/47.16  | | | BETA: splitting (47) gives:
% 240.64/47.16  | | | 
% 240.64/47.16  | | | Case 1:
% 240.64/47.16  | | | | 
% 240.64/47.16  | | | |   (72)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 240.64/47.16  | | | |           = e2)
% 240.64/47.16  | | | | 
% 240.64/47.16  | | | | BETA: splitting (72) gives:
% 240.64/47.16  | | | | 
% 240.64/47.16  | | | | Case 1:
% 240.64/47.16  | | | | | 
% 240.64/47.16  | | | | |   (73)  all_58_6 = e2 & op(e1, e3) = e2
% 240.64/47.16  | | | | | 
% 240.64/47.16  | | | | | ALPHA: (73) implies:
% 240.64/47.16  | | | | |   (74)  all_58_6 = e2
% 240.64/47.16  | | | | |   (75)  op(e1, e3) = e2
% 240.64/47.16  | | | | | 
% 240.64/47.16  | | | | | BETA: splitting (43) gives:
% 240.64/47.16  | | | | | 
% 240.64/47.16  | | | | | Case 1:
% 240.64/47.16  | | | | | | 
% 240.64/47.16  | | | | | |   (76)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 240.64/47.16  | | | | | |             e3) = e1)
% 240.64/47.16  | | | | | | 
% 240.64/47.16  | | | | | | BETA: splitting (76) gives:
% 240.64/47.16  | | | | | | 
% 240.64/47.16  | | | | | | Case 1:
% 240.64/47.16  | | | | | | | 
% 240.64/47.16  | | | | | | |   (77)  all_58_0 = e1 & op(e3, e3) = e1
% 240.64/47.16  | | | | | | | 
% 240.64/47.16  | | | | | | | ALPHA: (77) implies:
% 240.64/47.16  | | | | | | |   (78)  op(e3, e3) = e1
% 240.64/47.16  | | | | | | | 
% 240.64/47.16  | | | | | | | REF_CLOSE: (3), (6), (9), (15), (17), (22), (31), (34), (39),
% 240.64/47.16  | | | | | | |            (40), (49), (54), (60), (78) are inconsistent by
% 240.64/47.16  | | | | | | |            sub-proof #1468.
% 240.64/47.16  | | | | | | | 
% 240.64/47.16  | | | | | | Case 2:
% 240.64/47.16  | | | | | | | 
% 240.64/47.16  | | | | | | |   (79)  all_58_2 = e1 & op(e2, e3) = e1
% 240.64/47.16  | | | | | | | 
% 240.64/47.16  | | | | | | | ALPHA: (79) implies:
% 240.64/47.16  | | | | | | |   (80)  all_58_2 = e1
% 240.64/47.16  | | | | | | | 
% 240.64/47.16  | | | | | | | BETA: splitting (23) gives:
% 240.64/47.16  | | | | | | | 
% 240.64/47.16  | | | | | | | Case 1:
% 240.64/47.16  | | | | | | | | 
% 240.64/47.16  | | | | | | | |   (81)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 240.64/47.16  | | | | | | | |           op(e2, e1) = e2)
% 240.64/47.16  | | | | | | | | 
% 240.64/47.16  | | | | | | | | BETA: splitting (81) gives:
% 240.64/47.16  | | | | | | | | 
% 240.64/47.16  | | | | | | | | Case 1:
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | |   (82)  all_58_4 = e2 & op(e3, e1) = e2
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | REF_CLOSE: (6), (9), (11), (12), (16), (22), (31), (41), (54),
% 240.64/47.16  | | | | | | | | |            (60), (70), (82) are inconsistent by sub-proof
% 240.64/47.16  | | | | | | | | |            #330.
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | Case 2:
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | |   (83)  all_58_5 = e2 & op(e2, e1) = e2
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | ALPHA: (83) implies:
% 240.64/47.16  | | | | | | | | |   (84)  op(e2, e1) = e2
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | BETA: splitting (48) gives:
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | Case 1:
% 240.64/47.16  | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | |   (85)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 240.64/47.16  | | | | | | | | | |           op(e2, e2) = e0)
% 240.64/47.16  | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | BETA: splitting (85) gives:
% 240.64/47.16  | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | Case 1:
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | |   (86)  all_58_2 = e0 & op(e2, e3) = e0
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | REF_CLOSE: (54), (80), (86) are inconsistent by sub-proof
% 240.64/47.16  | | | | | | | | | | |            #1972.
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | Case 2:
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | |   (87)  all_58_3 = e0 & op(e2, e2) = e0
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | REF_CLOSE: (6), (16), (17), (20), (22), (29), (32), (39),
% 240.64/47.16  | | | | | | | | | | |            (40), (49), (61), (87) are inconsistent by
% 240.64/47.16  | | | | | | | | | | |            sub-proof #332.
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | End of split
% 240.64/47.16  | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | Case 2:
% 240.64/47.16  | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | |   (88)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0
% 240.64/47.16  | | | | | | | | | |           & op(e2, e0) = e0)
% 240.64/47.16  | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | BETA: splitting (88) gives:
% 240.64/47.16  | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | Case 1:
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | |   (89)  all_58_5 = e0 & op(e2, e1) = e0
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | ALPHA: (89) implies:
% 240.64/47.16  | | | | | | | | | | |   (90)  op(e2, e1) = e0
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | REF_CLOSE: (9), (49), (84), (90) are inconsistent by
% 240.64/47.16  | | | | | | | | | | |            sub-proof #1906.
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | Case 2:
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | |   (91)  all_58_10 = e0 & op(e2, e0) = e0
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | ALPHA: (91) implies:
% 240.64/47.16  | | | | | | | | | | |   (92)  op(e2, e0) = e0
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | BETA: splitting (50) gives:
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | Case 1:
% 240.64/47.16  | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | |   (93)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 240.64/47.16  | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 240.64/47.16  | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | REF_CLOSE: (9), (22), (30), (49), (92), (93) are inconsistent
% 240.64/47.16  | | | | | | | | | | | |            by sub-proof #1182.
% 240.64/47.16  | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | Case 2:
% 240.64/47.16  | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | |   (94)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 240.64/47.16  | | | | | | | | | | | |           e2 & op(e0, e0) = e2)
% 240.64/47.16  | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | BETA: splitting (94) gives:
% 240.64/47.16  | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | Case 1:
% 240.64/47.16  | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | |   (95)  all_58_11 = e2 & op(e1, e0) = e2
% 240.64/47.16  | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | ALPHA: (95) implies:
% 240.64/47.16  | | | | | | | | | | | | |   (96)  all_58_11 = e2
% 240.64/47.16  | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | BETA: splitting (25) gives:
% 240.64/47.16  | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | Case 1:
% 240.64/47.16  | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | |   (97)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 240.64/47.16  | | | | | | | | | | | | | |           & op(e2, e3) = e0)
% 240.64/47.16  | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | REF_CLOSE: (9), (32), (49), (54), (80), (97) are inconsistent
% 240.64/47.16  | | | | | | | | | | | | | |            by sub-proof #806.
% 240.64/47.16  | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | Case 2:
% 240.64/47.16  | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | |   (98)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 240.64/47.16  | | | | | | | | | | | | | |           e0 & op(e0, e3) = e0)
% 240.64/47.16  | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 240.64/47.16  | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | Case 1:
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | |   (99)  all_58_6 = e0 & op(e1, e3) = e0
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 240.64/47.16  | | | | | | | | | | | | | | |   (100)  all_58_6 = e0
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | | COMBINE_EQS: (74), (100) imply:
% 240.64/47.16  | | | | | | | | | | | | | | |   (101)  e2 = e0
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | | SIMP: (101) implies:
% 240.64/47.16  | | | | | | | | | | | | | | |   (102)  e2 = e0
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | | COMBINE_EQS: (96), (102) imply:
% 240.64/47.16  | | | | | | | | | | | | | | |   (103)  all_58_11 = e0
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (10), (22), (27), (36), (41), (47),
% 240.64/47.16  | | | | | | | | | | | | | | |            (49), (60), (100), (103) are inconsistent by
% 240.64/47.16  | | | | | | | | | | | | | | |            sub-proof #960.
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | Case 2:
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | |   (104)  all_58_12 = e0 & op(e0, e3) = e0
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 240.64/47.16  | | | | | | | | | | | | | | |   (105)  all_58_12 = e0
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | | COMBINE_EQS: (33), (105) imply:
% 240.64/47.16  | | | | | | | | | | | | | | |   (106)  e3 = e0
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | | SIMP: (106) implies:
% 240.64/47.16  | | | | | | | | | | | | | | |   (107)  e3 = e0
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | | COMBINE_EQS: (29), (107) imply:
% 240.64/47.16  | | | | | | | | | | | | | | |   (108)  all_58_9 = e0
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (20), (22), (32), (39), (40), (49),
% 240.64/47.16  | | | | | | | | | | | | | | |            (61), (108) are inconsistent by sub-proof #1956.
% 240.64/47.16  | | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | | End of split
% 240.64/47.16  | | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | End of split
% 240.64/47.16  | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | Case 2:
% 240.64/47.16  | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | |   (109)  all_58_15 = e2 & op(e0, e0) = e2
% 240.64/47.16  | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | | REF_CLOSE: (6), (9), (11), (12), (16), (22), (26), (41),
% 240.64/47.16  | | | | | | | | | | | | |            (54), (60), (70), (109) are inconsistent by
% 240.64/47.16  | | | | | | | | | | | | |            sub-proof #565.
% 240.64/47.16  | | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | | End of split
% 240.64/47.16  | | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | | End of split
% 240.64/47.16  | | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | | End of split
% 240.64/47.16  | | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | End of split
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | End of split
% 240.64/47.16  | | | | | | | | 
% 240.64/47.16  | | | | | | | Case 2:
% 240.64/47.16  | | | | | | | | 
% 240.64/47.16  | | | | | | | |   (110)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 240.64/47.16  | | | | | | | |            op(e0, e1) = e2)
% 240.64/47.16  | | | | | | | | 
% 240.64/47.16  | | | | | | | | BETA: splitting (110) gives:
% 240.64/47.16  | | | | | | | | 
% 240.64/47.16  | | | | | | | | Case 1:
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | |   (111)  all_58_8 = e2 & op(e1, e1) = e2
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | ALPHA: (111) implies:
% 240.64/47.16  | | | | | | | | |   (112)  op(e1, e1) = e2
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (22), (27), (36), (49), (54),
% 240.64/47.16  | | | | | | | | |            (56), (74), (112) are inconsistent by sub-proof
% 240.64/47.16  | | | | | | | | |            #917.
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | Case 2:
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | |   (113)  all_58_14 = e2 & op(e0, e1) = e2
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | ALPHA: (113) implies:
% 240.64/47.16  | | | | | | | | |   (114)  all_58_14 = e2
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | | REF_CLOSE: (1), (5), (6), (9), (14), (15), (18), (22), (26),
% 240.64/47.16  | | | | | | | | |            (38), (49), (54), (71), (114) are inconsistent by
% 240.64/47.16  | | | | | | | | |            sub-proof #1636.
% 240.64/47.16  | | | | | | | | | 
% 240.64/47.16  | | | | | | | | End of split
% 240.64/47.16  | | | | | | | | 
% 240.64/47.16  | | | | | | | End of split
% 240.64/47.16  | | | | | | | 
% 240.64/47.16  | | | | | | End of split
% 240.64/47.16  | | | | | | 
% 240.64/47.16  | | | | | Case 2:
% 240.64/47.16  | | | | | | 
% 240.64/47.16  | | | | | |   (115)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 240.64/47.16  | | | | | |            op(e0, e3) = e1)
% 240.64/47.16  | | | | | | 
% 240.64/47.16  | | | | | | BETA: splitting (115) gives:
% 240.64/47.16  | | | | | | 
% 240.64/47.16  | | | | | | Case 1:
% 240.64/47.16  | | | | | | | 
% 240.64/47.16  | | | | | | |   (116)  all_58_6 = e1 & op(e1, e3) = e1
% 240.64/47.16  | | | | | | | 
% 240.64/47.16  | | | | | | | ALPHA: (116) implies:
% 240.64/47.16  | | | | | | |   (117)  op(e1, e3) = e1
% 240.64/47.16  | | | | | | | 
% 240.64/47.17  | | | | | | | REF_CLOSE: (49), (60), (75), (117) are inconsistent by sub-proof
% 240.64/47.17  | | | | | | |            #2226.
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | Case 2:
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | |   (118)  all_58_12 = e1 & op(e0, e3) = e1
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | | REF_CLOSE: (1), (6), (9), (15), (18), (22), (29), (33), (45),
% 240.64/47.17  | | | | | | |            (49), (50), (54), (55), (57), (60), (118) are
% 240.64/47.17  | | | | | | |            inconsistent by sub-proof #329.
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | End of split
% 240.64/47.17  | | | | | | 
% 240.64/47.17  | | | | | End of split
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | Case 2:
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | |   (119)  all_58_7 = e2 & op(e1, e2) = e2
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | | ALPHA: (119) implies:
% 240.64/47.17  | | | | |   (120)  all_58_7 = e2
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | | REF_CLOSE: (6), (9), (11), (12), (15), (22), (49), (52), (53), (54),
% 240.64/47.17  | | | | |            (60), (70), (71), (120) are inconsistent by sub-proof
% 240.64/47.17  | | | | |            #1453.
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | End of split
% 240.64/47.17  | | | | 
% 240.64/47.17  | | | Case 2:
% 240.64/47.17  | | | | 
% 240.64/47.17  | | | |   (121)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 240.64/47.17  | | | |              e0) = e2)
% 240.64/47.17  | | | | 
% 240.64/47.17  | | | | BETA: splitting (121) gives:
% 240.64/47.17  | | | | 
% 240.64/47.17  | | | | Case 1:
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | |   (122)  all_58_8 = e2 & op(e1, e1) = e2
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | | ALPHA: (122) implies:
% 240.64/47.17  | | | | |   (123)  op(e1, e1) = e2
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | | REF_CLOSE: (22), (35), (49), (123) are inconsistent by sub-proof
% 240.64/47.17  | | | | |            #2206.
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | Case 2:
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | |   (124)  all_58_11 = e2 & op(e1, e0) = e2
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | | ALPHA: (124) implies:
% 240.64/47.17  | | | | |   (125)  all_58_11 = e2
% 240.64/47.17  | | | | |   (126)  op(e1, e0) = e2
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | | BETA: splitting (56) gives:
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | | Case 1:
% 240.64/47.17  | | | | | | 
% 240.64/47.17  | | | | | |   (127)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1,
% 240.64/47.17  | | | | | |              e2) = e0)
% 240.64/47.17  | | | | | | 
% 240.64/47.17  | | | | | | BETA: splitting (127) gives:
% 240.64/47.17  | | | | | | 
% 240.64/47.17  | | | | | | Case 1:
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | |   (128)  all_58_6 = e0 & op(e1, e3) = e0
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | | ALPHA: (128) implies:
% 240.64/47.17  | | | | | | |   (129)  all_58_6 = e0
% 240.64/47.17  | | | | | | |   (130)  op(e1, e3) = e0
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | | BETA: splitting (43) gives:
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | 
% 240.64/47.17  | | | | | | | |   (131)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 240.64/47.17  | | | | | | | |            op(e2, e3) = e1)
% 240.64/47.17  | | | | | | | | 
% 240.64/47.17  | | | | | | | | BETA: splitting (131) gives:
% 240.64/47.17  | | | | | | | | 
% 240.64/47.17  | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | |   (132)  all_58_0 = e1 & op(e3, e3) = e1
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | ALPHA: (132) implies:
% 240.64/47.17  | | | | | | | | |   (133)  op(e3, e3) = e1
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | REF_CLOSE: (3), (6), (9), (15), (17), (22), (31), (34), (39),
% 240.64/47.17  | | | | | | | | |            (40), (49), (54), (60), (133) are inconsistent by
% 240.64/47.17  | | | | | | | | |            sub-proof #1468.
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | |   (134)  all_58_2 = e1 & op(e2, e3) = e1
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | ALPHA: (134) implies:
% 240.64/47.17  | | | | | | | | |   (135)  op(e2, e3) = e1
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | BETA: splitting (18) gives:
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | |   (136)  all_58_15 = e0 & op(e0, e0) = e0
% 240.64/47.17  | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | ALPHA: (136) implies:
% 240.64/47.17  | | | | | | | | | |   (137)  op(e0, e0) = e0
% 240.64/47.17  | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | REF_CLOSE: (1), (49), (54), (137) are inconsistent by
% 240.64/47.17  | | | | | | | | | |            sub-proof #2274.
% 240.64/47.17  | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | |   (138)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.64/47.17  | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.64/47.17  | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 240.64/47.17  | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.64/47.17  | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.64/47.17  | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | ALPHA: (138) implies:
% 240.64/47.17  | | | | | | | | | |   (139)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 240.64/47.17  | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 240.64/47.17  | | | | | | | | | |              e1) = e0)
% 240.64/47.17  | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | BETA: splitting (139) gives:
% 240.64/47.17  | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | |   (140)  all_58_12 = e0 & op(e0, e3) = e0
% 240.64/47.17  | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | REF_CLOSE: (6), (17), (20), (22), (29), (32), (33), (39),
% 240.64/47.17  | | | | | | | | | | |            (40), (49), (61), (140) are inconsistent by
% 240.64/47.17  | | | | | | | | | | |            sub-proof #337.
% 240.64/47.17  | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | |   (141)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 240.64/47.17  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 240.64/47.17  | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | BETA: splitting (141) gives:
% 240.64/47.17  | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | |   (142)  all_58_13 = e0 & op(e0, e2) = e0
% 240.64/47.17  | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | ALPHA: (142) implies:
% 240.64/47.17  | | | | | | | | | | | |   (143)  op(e0, e2) = e0
% 240.64/47.17  | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | REF_CLOSE: (9), (49), (71), (143) are inconsistent by
% 240.64/47.17  | | | | | | | | | | | |            sub-proof #2132.
% 240.64/47.17  | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | |   (144)  all_58_14 = e0 & op(e0, e1) = e0
% 240.64/47.17  | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | ALPHA: (144) implies:
% 240.64/47.17  | | | | | | | | | | | |   (145)  op(e0, e1) = e0
% 240.64/47.17  | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | BETA: splitting (23) gives:
% 240.64/47.17  | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | |   (146)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 240.64/47.17  | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 240.64/47.17  | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | BETA: splitting (146) gives:
% 240.64/47.17  | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | |   (147)  all_58_4 = e2 & op(e3, e1) = e2
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (11), (12), (16), (22), (31), (41),
% 240.64/47.17  | | | | | | | | | | | | | |            (54), (60), (70), (147) are inconsistent by
% 240.64/47.17  | | | | | | | | | | | | | |            sub-proof #330.
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | |   (148)  all_58_5 = e2 & op(e2, e1) = e2
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | ALPHA: (148) implies:
% 240.64/47.17  | | | | | | | | | | | | | |   (149)  op(e2, e1) = e2
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | |   (150)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 240.64/47.17  | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 240.64/47.17  | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 240.64/47.17  | | | | | | | | | | | | | | |            all_56_19 & $i(all_56_19))
% 240.64/47.17  | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 240.64/47.17  | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | |   (151)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 240.64/47.17  | | | | | | | | | | | | | | | |            e1) = all_56_17 & $i(all_56_17)
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 240.64/47.17  | | | | | | | | | | | | | | | |   (152)  op(e3, e1) = all_56_17
% 240.64/47.17  | | | | | | | | | | | | | | | |   (153)  op(e3, all_56_17) = e3
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | |   (154)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 240.64/47.17  | | | | | | | | | | | | | | | | |          op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 240.64/47.17  | | | | | | | | | | | | | | | | |   (155)  op(e2, e3) = all_8_1
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (24), (28), (32), (49), (135), (152), (153),
% 240.64/47.17  | | | | | | | | | | | | | | | | |            (155) are inconsistent by sub-proof #328.
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | |   (156)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 240.64/47.17  | | | | | | | | | | | | | | | | |          $i(all_8_1)
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 240.64/47.17  | | | | | | | | | | | | | | | | |   (157)  op(e2, e3) = all_8_1
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (24), (28), (32), (49), (135), (152), (153),
% 240.64/47.17  | | | | | | | | | | | | | | | | |            (157) are inconsistent by sub-proof #328.
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | |   (158)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 240.64/47.17  | | | | | | | | | | | | | | | |            e1) = all_56_19 & $i(all_56_19)
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 240.64/47.17  | | | | | | | | | | | | | | | |   (159)  op(e2, e1) = all_56_19
% 240.64/47.17  | | | | | | | | | | | | | | | |   (160)  op(e2, all_56_19) = e2
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (22), (28), (49), (59), (135), (149), (159),
% 240.64/47.17  | | | | | | | | | | | | | | | |            (160) are inconsistent by sub-proof #750.
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | |   (161)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 240.64/47.17  | | | | | | | | | | | | | | |          (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 240.64/47.17  | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23))
% 240.64/47.17  | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 240.64/47.17  | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | |   (162)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 240.64/47.17  | | | | | | | | | | | | | | | |   (163)  op(e1, all_56_21) = e1
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | REDUCE: (51), (163) imply:
% 240.64/47.17  | | | | | | | | | | | | | | | |   (164)  op(e1, e3) = e1
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | REF_CLOSE: (49), (54), (130), (164) are inconsistent by
% 240.64/47.17  | | | | | | | | | | | | | | | |            sub-proof #449.
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | |   (165)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 240.64/47.17  | | | | | | | | | | | | | | | |            e1) = all_56_23 & $i(all_56_23)
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 240.64/47.17  | | | | | | | | | | | | | | | |   (166)  op(e0, e1) = all_56_23
% 240.64/47.17  | | | | | | | | | | | | | | | |   (167)  op(e0, all_56_23) = e0
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | |   (168)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 240.64/47.17  | | | | | | | | | | | | | | | | |          op(e0, e1) = all_20_1 & $i(all_20_0) &
% 240.64/47.17  | | | | | | | | | | | | | | | | |          $i(all_20_1)
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 240.64/47.17  | | | | | | | | | | | | | | | | |   (169)  op(e0, e1) = all_20_1
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14), (15), (28), (38), (44), (49),
% 240.64/47.17  | | | | | | | | | | | | | | | | |            (54), (58), (59), (60), (70), (135), (145), (166),
% 240.64/47.17  | | | | | | | | | | | | | | | | |            (167), (169) are inconsistent by sub-proof #324.
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | |   (170)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 240.64/47.17  | | | | | | | | | | | | | | | | |          $i(all_20_1)
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 240.64/47.17  | | | | | | | | | | | | | | | | |   (171)  op(e0, e1) = all_20_1
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14), (15), (28), (38), (44), (49),
% 240.64/47.17  | | | | | | | | | | | | | | | | |            (54), (58), (59), (60), (70), (135), (145), (166),
% 240.64/47.17  | | | | | | | | | | | | | | | | |            (167), (171) are inconsistent by sub-proof #324.
% 240.64/47.17  | | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | |   (172)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 240.64/47.17  | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 240.64/47.17  | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | BETA: splitting (172) gives:
% 240.64/47.17  | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | |   (173)  all_58_8 = e2 & op(e1, e1) = e2
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | ALPHA: (173) implies:
% 240.64/47.17  | | | | | | | | | | | | | |   (174)  op(e1, e1) = e2
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (22), (27), (36), (49), (125), (129),
% 240.64/47.17  | | | | | | | | | | | | | |            (174) are inconsistent by sub-proof #997.
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | |   (175)  all_58_14 = e2 & op(e0, e1) = e2
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | ALPHA: (175) implies:
% 240.64/47.17  | | | | | | | | | | | | | |   (176)  all_58_14 = e2
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (9), (14), (15), (18), (22), (26),
% 240.64/47.17  | | | | | | | | | | | | | |            (38), (49), (54), (71), (176) are inconsistent by
% 240.64/47.17  | | | | | | | | | | | | | |            sub-proof #1636.
% 240.64/47.17  | | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | 
% 240.64/47.17  | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | 
% 240.64/47.17  | | | | | | | |   (177)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 240.64/47.17  | | | | | | | |            op(e0, e3) = e1)
% 240.64/47.17  | | | | | | | | 
% 240.64/47.17  | | | | | | | | BETA: splitting (177) gives:
% 240.64/47.17  | | | | | | | | 
% 240.64/47.17  | | | | | | | | Case 1:
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | |   (178)  all_58_6 = e1 & op(e1, e3) = e1
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | ALPHA: (178) implies:
% 240.64/47.17  | | | | | | | | |   (179)  op(e1, e3) = e1
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | REF_CLOSE: (49), (54), (130), (179) are inconsistent by
% 240.64/47.17  | | | | | | | | |            sub-proof #449.
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | Case 2:
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | |   (180)  all_58_12 = e1 & op(e0, e3) = e1
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | | REF_CLOSE: (1), (6), (9), (15), (18), (22), (29), (33), (45),
% 240.64/47.17  | | | | | | | | |            (49), (50), (54), (55), (57), (60), (180) are
% 240.64/47.17  | | | | | | | | |            inconsistent by sub-proof #329.
% 240.64/47.17  | | | | | | | | | 
% 240.64/47.17  | | | | | | | | End of split
% 240.64/47.17  | | | | | | | | 
% 240.64/47.17  | | | | | | | End of split
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | Case 2:
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | |   (181)  all_58_7 = e0 & op(e1, e2) = e0
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | | ALPHA: (181) implies:
% 240.64/47.17  | | | | | | |   (182)  op(e1, e2) = e0
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | | REF_CLOSE: (8), (10), (49), (54), (182) are inconsistent by
% 240.64/47.17  | | | | | | |            sub-proof #2136.
% 240.64/47.17  | | | | | | | 
% 240.64/47.17  | | | | | | End of split
% 240.64/47.17  | | | | | | 
% 240.64/47.17  | | | | | Case 2:
% 240.64/47.17  | | | | | | 
% 240.64/47.17  | | | | | |   (183)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 240.64/47.17  | | | | | |            op(e1, e0) = e0)
% 240.64/47.17  | | | | | | 
% 240.64/47.17  | | | | | | REF_CLOSE: (6), (7), (9), (19), (20), (21), (37), (42), (49), (61),
% 240.64/47.17  | | | | | |            (126), (183) are inconsistent by sub-proof #383.
% 240.64/47.17  | | | | | | 
% 240.64/47.17  | | | | | End of split
% 240.64/47.17  | | | | | 
% 240.64/47.17  | | | | End of split
% 240.64/47.17  | | | | 
% 240.64/47.17  | | | End of split
% 240.64/47.17  | | | 
% 240.64/47.17  | | End of split
% 240.64/47.17  | | 
% 240.64/47.17  | End of split
% 240.64/47.17  | 
% 240.64/47.17  End of proof
% 240.64/47.17  
% 240.64/47.17  Sub-proof #324 shows that the following formulas are inconsistent:
% 240.64/47.17  ----------------------------------------------------------------
% 240.64/47.17    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.64/47.17         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.17    (2)   ~ (e3 = e0)
% 240.64/47.17    (3)  op(e0, e1) = all_56_23
% 240.64/47.17    (4)   ~ (all_52_7 = e3)
% 240.64/47.17    (5)   ~ (e3 = e1)
% 240.64/47.17    (6)  op(e2, e3) = e1
% 240.64/47.17    (7)  op(e0, e1) = e0
% 240.64/47.17    (8)  all_58_13 = e2
% 240.64/47.17    (9)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 240.64/47.17           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 240.64/47.17           all_42_1 & $i(all_42_1))
% 240.64/47.17    (10)  op(e0, e2) = all_52_7
% 240.64/47.17    (11)  op(e0, e1) = all_20_1
% 240.64/47.17    (12)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 240.64/47.17            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 240.64/47.17              e1) = all_34_1 & $i(all_34_1))
% 240.64/47.17    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.17    (14)  op(e0, all_56_23) = e0
% 240.64/47.17    (15)   ~ (e1 = e0)
% 240.64/47.17    (16)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.17          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.64/47.17            e1)
% 240.64/47.17    (17)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 240.64/47.17            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 240.64/47.17            & $i(all_8_1))
% 240.64/47.17    (18)   ~ (e2 = e1)
% 240.64/47.17  
% 240.64/47.17  Begin of proof
% 240.64/47.17  | 
% 240.64/47.17  | BETA: splitting (17) gives:
% 240.64/47.17  | 
% 240.64/47.17  | Case 1:
% 240.64/47.17  | | 
% 240.64/47.17  | |   (19)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1
% 240.64/47.17  | |         & $i(all_8_0) & $i(all_8_1)
% 240.64/47.17  | | 
% 240.64/47.17  | | ALPHA: (19) implies:
% 240.64/47.17  | |   (20)  op(e2, e3) = all_8_1
% 240.64/47.17  | | 
% 240.64/47.17  | | BETA: splitting (12) gives:
% 240.64/47.17  | | 
% 240.64/47.17  | | Case 1:
% 240.64/47.17  | | | 
% 240.64/47.17  | | |   (21)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 240.64/47.17  | | |         all_34_1 & $i(all_34_0) & $i(all_34_1)
% 240.64/47.17  | | | 
% 240.64/47.17  | | | ALPHA: (21) implies:
% 240.64/47.17  | | |   (22)  op(e0, e1) = all_34_1
% 240.64/47.17  | | | 
% 240.64/47.17  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 240.64/47.17  | | |            (14), (15), (16), (18), (20), (22) are inconsistent by
% 240.64/47.17  | | |            sub-proof #326.
% 240.64/47.17  | | | 
% 240.64/47.17  | | Case 2:
% 240.64/47.17  | | | 
% 240.64/47.17  | | |   (23)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 240.64/47.17  | | | 
% 240.64/47.17  | | | ALPHA: (23) implies:
% 240.64/47.17  | | |   (24)  op(e0, e1) = all_34_1
% 240.64/47.17  | | | 
% 240.64/47.17  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 240.64/47.17  | | |            (14), (15), (16), (18), (20), (24) are inconsistent by
% 240.64/47.17  | | |            sub-proof #326.
% 240.64/47.17  | | | 
% 240.64/47.17  | | End of split
% 240.64/47.17  | | 
% 240.64/47.17  | Case 2:
% 240.64/47.17  | | 
% 240.64/47.17  | |   (25)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 240.64/47.17  | | 
% 240.64/47.17  | | ALPHA: (25) implies:
% 240.64/47.17  | |   (26)   ~ (all_8_1 = e0)
% 240.64/47.17  | |   (27)  op(e2, e3) = all_8_1
% 240.64/47.17  | | 
% 240.64/47.17  | | BETA: splitting (12) gives:
% 240.64/47.17  | | 
% 240.64/47.17  | | Case 1:
% 240.64/47.17  | | | 
% 240.64/47.17  | | |   (28)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 240.64/47.17  | | |         all_34_1 & $i(all_34_0) & $i(all_34_1)
% 240.64/47.17  | | | 
% 240.64/47.17  | | | ALPHA: (28) implies:
% 240.64/47.17  | | |   (29)  op(e0, e1) = all_34_1
% 240.64/47.17  | | | 
% 240.64/47.17  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 240.64/47.17  | | |            (14), (16), (18), (26), (27), (29) are inconsistent by
% 240.64/47.17  | | |            sub-proof #325.
% 240.64/47.17  | | | 
% 240.64/47.17  | | Case 2:
% 240.64/47.17  | | | 
% 240.64/47.17  | | |   (30)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 240.64/47.18  | | | 
% 240.64/47.18  | | | ALPHA: (30) implies:
% 240.64/47.18  | | |   (31)  op(e0, e1) = all_34_1
% 240.64/47.18  | | | 
% 240.64/47.18  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 240.64/47.18  | | |            (14), (16), (18), (26), (27), (31) are inconsistent by
% 240.64/47.18  | | |            sub-proof #325.
% 240.64/47.18  | | | 
% 240.64/47.18  | | End of split
% 240.64/47.18  | | 
% 240.64/47.18  | End of split
% 240.64/47.18  | 
% 240.64/47.18  End of proof
% 240.64/47.18  
% 240.64/47.18  Sub-proof #325 shows that the following formulas are inconsistent:
% 240.64/47.18  ----------------------------------------------------------------
% 240.64/47.18    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.64/47.18         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.18    (2)   ~ (e3 = e0)
% 240.64/47.18    (3)  op(e0, e1) = all_56_23
% 240.64/47.18    (4)  op(e0, e1) = all_34_1
% 240.64/47.18    (5)   ~ (all_52_7 = e3)
% 240.64/47.18    (6)   ~ (e3 = e1)
% 240.64/47.18    (7)   ~ (all_8_1 = e0)
% 240.64/47.18    (8)  op(e2, e3) = e1
% 240.64/47.18    (9)  op(e0, e1) = e0
% 240.64/47.18    (10)  all_58_13 = e2
% 240.64/47.18    (11)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.64/47.18            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.64/47.18              e3) = all_42_1 & $i(all_42_1))
% 240.64/47.18    (12)  op(e0, e2) = all_52_7
% 240.64/47.18    (13)  op(e0, e1) = all_20_1
% 240.64/47.18    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.18    (15)  op(e2, e3) = all_8_1
% 240.64/47.18    (16)  op(e0, all_56_23) = e0
% 240.64/47.18    (17)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.18          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.64/47.18            e1)
% 240.64/47.18    (18)   ~ (e2 = e1)
% 240.64/47.18  
% 240.64/47.18  Begin of proof
% 240.64/47.18  | 
% 240.64/47.18  | BETA: splitting (11) gives:
% 240.64/47.18  | 
% 240.64/47.18  | Case 1:
% 240.64/47.18  | | 
% 240.64/47.18  | |   (19)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.64/47.18  | |         all_42_1 & $i(all_42_0) & $i(all_42_1)
% 240.64/47.18  | | 
% 240.64/47.18  | | ALPHA: (19) implies:
% 240.64/47.18  | |   (20)  op(e2, e3) = all_42_1
% 240.64/47.18  | | 
% 240.64/47.18  | | GROUND_INST: instantiating (14) with e0, all_34_1, e1, e0, simplifying with
% 240.64/47.18  | |              (4), (9) gives:
% 240.64/47.18  | |   (21)  all_34_1 = e0
% 240.64/47.18  | | 
% 240.64/47.18  | | GROUND_INST: instantiating (14) with all_34_1, all_56_23, e1, e0,
% 240.64/47.18  | |              simplifying with (3), (4) gives:
% 240.64/47.18  | |   (22)  all_56_23 = all_34_1
% 240.64/47.18  | | 
% 240.64/47.18  | | GROUND_INST: instantiating (14) with all_20_1, all_56_23, e1, e0,
% 240.64/47.18  | |              simplifying with (3), (13) gives:
% 240.64/47.18  | |   (23)  all_56_23 = all_20_1
% 240.64/47.18  | | 
% 240.64/47.18  | | GROUND_INST: instantiating (14) with e1, all_42_1, e3, e2, simplifying with
% 240.64/47.18  | |              (8), (20) gives:
% 240.64/47.18  | |   (24)  all_42_1 = e1
% 240.64/47.18  | | 
% 240.64/47.18  | | GROUND_INST: instantiating (14) with all_8_1, all_42_1, e3, e2, simplifying
% 240.64/47.18  | |              with (15), (20) gives:
% 240.64/47.18  | |   (25)  all_42_1 = all_8_1
% 240.64/47.18  | | 
% 240.64/47.18  | | COMBINE_EQS: (22), (23) imply:
% 240.64/47.18  | |   (26)  all_34_1 = all_20_1
% 240.64/47.18  | | 
% 240.64/47.18  | | SIMP: (26) implies:
% 240.64/47.18  | |   (27)  all_34_1 = all_20_1
% 240.64/47.18  | | 
% 240.64/47.18  | | COMBINE_EQS: (24), (25) imply:
% 240.64/47.18  | |   (28)  all_8_1 = e1
% 240.64/47.18  | | 
% 240.64/47.18  | | SIMP: (28) implies:
% 240.64/47.18  | |   (29)  all_8_1 = e1
% 240.64/47.18  | | 
% 240.64/47.18  | | COMBINE_EQS: (21), (27) imply:
% 240.64/47.18  | |   (30)  all_20_1 = e0
% 240.64/47.18  | | 
% 240.64/47.18  | | COMBINE_EQS: (23), (30) imply:
% 240.64/47.18  | |   (31)  all_56_23 = e0
% 240.64/47.18  | | 
% 240.64/47.18  | | REDUCE: (7), (29) imply:
% 240.64/47.18  | |   (32)   ~ (e1 = e0)
% 240.64/47.18  | | 
% 240.64/47.18  | | REF_CLOSE: (1), (2), (5), (6), (10), (12), (13), (14), (16), (17), (18),
% 240.64/47.18  | |            (30), (31), (32) are inconsistent by sub-proof #327.
% 240.64/47.18  | | 
% 240.64/47.18  | Case 2:
% 240.64/47.18  | | 
% 240.64/47.18  | |   (33)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 240.64/47.18  | | 
% 240.64/47.18  | | ALPHA: (33) implies:
% 240.64/47.18  | |   (34)   ~ (all_42_1 = e1)
% 240.64/47.18  | |   (35)  op(e2, e3) = all_42_1
% 240.64/47.18  | | 
% 240.64/47.18  | | REF_CLOSE: (8), (14), (15), (34), (35) are inconsistent by sub-proof #935.
% 240.64/47.18  | | 
% 240.64/47.18  | End of split
% 240.64/47.18  | 
% 240.64/47.18  End of proof
% 240.64/47.18  
% 240.64/47.18  Sub-proof #326 shows that the following formulas are inconsistent:
% 240.64/47.18  ----------------------------------------------------------------
% 240.64/47.18    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.64/47.18         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.18    (2)   ~ (e3 = e0)
% 240.64/47.18    (3)  op(e0, e1) = all_56_23
% 240.64/47.18    (4)  op(e0, e1) = all_34_1
% 240.64/47.18    (5)   ~ (all_52_7 = e3)
% 240.64/47.18    (6)   ~ (e3 = e1)
% 240.64/47.18    (7)  op(e2, e3) = e1
% 240.64/47.18    (8)  op(e0, e1) = e0
% 240.64/47.18    (9)  all_58_13 = e2
% 240.64/47.18    (10)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 240.64/47.18            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 240.64/47.18              e3) = all_42_1 & $i(all_42_1))
% 240.64/47.18    (11)  op(e0, e2) = all_52_7
% 240.64/47.18    (12)  op(e0, e1) = all_20_1
% 240.64/47.18    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.18    (14)  op(e2, e3) = all_8_1
% 240.64/47.18    (15)  op(e0, all_56_23) = e0
% 240.64/47.18    (16)   ~ (e1 = e0)
% 240.64/47.18    (17)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.18          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.64/47.18            e1)
% 240.64/47.18    (18)   ~ (e2 = e1)
% 240.64/47.18  
% 240.64/47.18  Begin of proof
% 240.64/47.18  | 
% 240.64/47.18  | BETA: splitting (10) gives:
% 240.64/47.18  | 
% 240.64/47.18  | Case 1:
% 240.64/47.18  | | 
% 240.64/47.18  | | 
% 240.64/47.18  | | GROUND_INST: instantiating (13) with e0, all_34_1, e1, e0, simplifying with
% 240.64/47.18  | |              (4), (8) gives:
% 240.64/47.18  | |   (19)  all_34_1 = e0
% 240.64/47.18  | | 
% 240.64/47.18  | | GROUND_INST: instantiating (13) with all_34_1, all_56_23, e1, e0,
% 240.64/47.18  | |              simplifying with (3), (4) gives:
% 240.64/47.18  | |   (20)  all_56_23 = all_34_1
% 240.64/47.18  | | 
% 240.64/47.18  | | GROUND_INST: instantiating (13) with all_20_1, all_56_23, e1, e0,
% 240.64/47.18  | |              simplifying with (3), (12) gives:
% 240.64/47.18  | |   (21)  all_56_23 = all_20_1
% 240.64/47.18  | | 
% 240.64/47.18  | | COMBINE_EQS: (20), (21) imply:
% 240.64/47.18  | |   (22)  all_34_1 = all_20_1
% 240.64/47.18  | | 
% 240.64/47.18  | | SIMP: (22) implies:
% 240.64/47.18  | |   (23)  all_34_1 = all_20_1
% 240.64/47.18  | | 
% 240.64/47.18  | | COMBINE_EQS: (19), (23) imply:
% 240.64/47.18  | |   (24)  all_20_1 = e0
% 240.64/47.18  | | 
% 240.64/47.18  | | COMBINE_EQS: (21), (24) imply:
% 240.64/47.18  | |   (25)  all_56_23 = e0
% 240.64/47.18  | | 
% 240.64/47.18  | | REF_CLOSE: (1), (2), (5), (6), (9), (11), (12), (13), (15), (16), (17),
% 240.64/47.18  | |            (18), (24), (25) are inconsistent by sub-proof #327.
% 240.64/47.18  | | 
% 240.64/47.18  | Case 2:
% 240.64/47.18  | | 
% 240.64/47.18  | |   (26)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 240.64/47.18  | | 
% 240.64/47.18  | | ALPHA: (26) implies:
% 240.64/47.18  | |   (27)   ~ (all_42_1 = e1)
% 240.64/47.18  | |   (28)  op(e2, e3) = all_42_1
% 240.64/47.18  | | 
% 240.64/47.18  | | REF_CLOSE: (7), (13), (14), (27), (28) are inconsistent by sub-proof #935.
% 240.64/47.18  | | 
% 240.64/47.18  | End of split
% 240.64/47.18  | 
% 240.64/47.18  End of proof
% 240.64/47.18  
% 240.64/47.18  Sub-proof #327 shows that the following formulas are inconsistent:
% 240.64/47.18  ----------------------------------------------------------------
% 240.64/47.18    (1)  all_56_23 = e0
% 240.64/47.18    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.64/47.18         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.18    (3)   ~ (e3 = e0)
% 240.64/47.18    (4)   ~ (all_52_7 = e3)
% 240.64/47.18    (5)   ~ (e3 = e1)
% 240.64/47.18    (6)  all_20_1 = e0
% 240.64/47.18    (7)  all_58_13 = e2
% 240.64/47.18    (8)  op(e0, e2) = all_52_7
% 240.64/47.18    (9)  op(e0, e1) = all_20_1
% 240.64/47.18    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.18    (11)  op(e0, all_56_23) = e0
% 240.64/47.18    (12)   ~ (e1 = e0)
% 240.64/47.18    (13)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.18          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.64/47.18            e1)
% 240.64/47.18    (14)   ~ (e2 = e1)
% 240.64/47.18  
% 240.64/47.18  Begin of proof
% 240.64/47.18  | 
% 240.64/47.18  | REDUCE: (1), (11) imply:
% 240.64/47.18  |   (15)  op(e0, e0) = e0
% 240.64/47.18  | 
% 240.64/47.18  | REDUCE: (6), (9) imply:
% 240.64/47.18  |   (16)  op(e0, e1) = e0
% 240.64/47.18  | 
% 240.64/47.18  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (12), (13), (14), (15), (16)
% 240.64/47.18  |            are inconsistent by sub-proof #860.
% 240.64/47.18  | 
% 240.64/47.18  End of proof
% 240.64/47.18  
% 240.64/47.18  Sub-proof #328 shows that the following formulas are inconsistent:
% 240.64/47.18  ----------------------------------------------------------------
% 240.64/47.18    (1)  op(e3, e1) = all_56_17
% 240.64/47.18    (2)   ~ (e3 = e2)
% 240.64/47.18    (3)  op(e3, e1) = e1
% 240.64/47.18    (4)  op(e2, e3) = e1
% 240.64/47.18    (5)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 240.64/47.18           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 240.64/47.18           all_42_1 & $i(all_42_1))
% 240.64/47.18    (6)  op(e3, e3) = e2
% 240.64/47.18    (7)  op(e3, all_56_17) = e3
% 240.64/47.18    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.18    (9)  op(e2, e3) = all_8_1
% 240.64/47.18  
% 240.64/47.18  Begin of proof
% 240.64/47.18  | 
% 240.64/47.18  | BETA: splitting (5) gives:
% 240.64/47.18  | 
% 240.64/47.18  | Case 1:
% 240.64/47.18  | | 
% 240.64/47.18  | | 
% 240.64/47.18  | | GROUND_INST: instantiating (8) with e1, all_56_17, e1, e3, simplifying with
% 240.64/47.18  | |              (1), (3) gives:
% 240.64/47.18  | |   (10)  all_56_17 = e1
% 240.64/47.18  | | 
% 240.64/47.18  | | REDUCE: (7), (10) imply:
% 240.64/47.18  | |   (11)  op(e3, e1) = e3
% 240.64/47.18  | | 
% 240.64/47.18  | | REF_CLOSE: (1), (2), (6), (7), (8), (11) are inconsistent by sub-proof
% 240.64/47.18  | |            #2098.
% 240.64/47.18  | | 
% 240.64/47.18  | Case 2:
% 240.64/47.18  | | 
% 240.64/47.18  | |   (12)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 240.64/47.18  | | 
% 240.64/47.18  | | ALPHA: (12) implies:
% 240.64/47.18  | |   (13)   ~ (all_42_1 = e1)
% 240.64/47.18  | |   (14)  op(e2, e3) = all_42_1
% 240.64/47.18  | | 
% 240.64/47.18  | | REF_CLOSE: (4), (8), (9), (13), (14) are inconsistent by sub-proof #935.
% 240.64/47.18  | | 
% 240.64/47.18  | End of split
% 240.64/47.18  | 
% 240.64/47.18  End of proof
% 240.64/47.18  
% 240.64/47.18  Sub-proof #329 shows that the following formulas are inconsistent:
% 240.64/47.18  ----------------------------------------------------------------
% 240.64/47.18    (1)  op(e0, e0) = e1
% 240.64/47.18    (2)   ~ (e3 = e0)
% 240.64/47.18    (3)   ~ (e2 = e0)
% 240.64/47.18    (4)   ~ (e3 = e1)
% 240.64/47.18    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.64/47.18             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.64/47.18               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.64/47.18               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.64/47.18    (6)   ~ (e3 = e2)
% 240.64/47.18    (7)  all_58_9 = e3
% 240.64/47.18    (8)  all_58_12 = e3
% 240.64/47.18    (9)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.64/47.18         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.18    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.18    (11)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.64/47.18          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.64/47.18    (12)   ~ (e1 = e0)
% 240.64/47.18    (13)   ~ (all_52_13 = e3)
% 240.64/47.18    (14)  op(e2, e0) = all_52_13
% 240.64/47.18    (15)  all_58_12 = e1 & op(e0, e3) = e1
% 240.64/47.18    (16)   ~ (e2 = e1)
% 240.64/47.18  
% 240.64/47.18  Begin of proof
% 240.64/47.18  | 
% 240.64/47.18  | ALPHA: (15) implies:
% 240.64/47.18  |   (17)  all_58_12 = e1
% 240.64/47.18  | 
% 240.64/47.18  | COMBINE_EQS: (8), (17) imply:
% 240.64/47.18  |   (18)  e3 = e1
% 240.64/47.18  | 
% 240.64/47.18  | COMBINE_EQS: (7), (18) imply:
% 240.64/47.18  |   (19)  all_58_9 = e1
% 240.64/47.18  | 
% 240.64/47.18  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (13), (14),
% 240.64/47.18  |            (16), (19) are inconsistent by sub-proof #1600.
% 240.64/47.18  | 
% 240.64/47.18  End of proof
% 240.64/47.18  
% 240.64/47.18  Sub-proof #330 shows that the following formulas are inconsistent:
% 240.64/47.18  ----------------------------------------------------------------
% 240.64/47.18    (1)   ~ (e3 = e0)
% 240.64/47.18    (2)   ~ (e2 = e0)
% 240.64/47.18    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.64/47.18         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.64/47.18    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.64/47.18         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.64/47.18    (5)  all_58_3 = e3
% 240.64/47.18    (6)   ~ (e3 = e2)
% 240.64/47.18    (7)  all_58_13 = e2
% 240.64/47.18    (8)  all_58_4 = e1
% 240.64/47.18    (9)  all_58_7 = e1
% 240.64/47.18    (10)   ~ (e1 = e0)
% 240.64/47.18    (11)  all_58_4 = e2 & op(e3, e1) = e2
% 240.64/47.18    (12)   ~ (e2 = e1)
% 240.64/47.18  
% 240.64/47.18  Begin of proof
% 240.64/47.18  | 
% 240.64/47.18  | ALPHA: (11) implies:
% 240.64/47.18  |   (13)  all_58_4 = e2
% 240.64/47.18  | 
% 240.64/47.18  | COMBINE_EQS: (8), (13) imply:
% 240.64/47.18  |   (14)  e2 = e1
% 240.64/47.18  | 
% 240.64/47.18  | SIMP: (14) implies:
% 240.64/47.18  |   (15)  e2 = e1
% 240.64/47.18  | 
% 240.64/47.18  | COMBINE_EQS: (7), (15) imply:
% 240.64/47.18  |   (16)  all_58_13 = e1
% 240.64/47.18  | 
% 240.64/47.18  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (12), (16) are
% 240.64/47.18  |            inconsistent by sub-proof #1457.
% 240.64/47.18  | 
% 240.64/47.18  End of proof
% 240.64/47.18  
% 240.64/47.18  Sub-proof #331 shows that the following formulas are inconsistent:
% 240.64/47.18  ----------------------------------------------------------------
% 240.64/47.18    (1)  op(e0, e0) = e1
% 240.64/47.18    (2)   ~ (e3 = e0)
% 240.64/47.18    (3)   ~ (e2 = e0)
% 240.64/47.18    (4)   ~ (e3 = e1)
% 240.64/47.18    (5)  all_58_3 = e3
% 240.64/47.18    (6)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.64/47.18             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.64/47.18               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.64/47.18               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.64/47.18    (7)   ~ (e3 = e2)
% 240.64/47.18    (8)  all_58_9 = e3
% 240.64/47.18    (9)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.64/47.18         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.18    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.18    (11)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.64/47.18          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.64/47.18    (12)  all_58_3 = e1 & op(e2, e2) = e1
% 240.64/47.18    (13)   ~ (e1 = e0)
% 240.64/47.18    (14)   ~ (all_52_13 = e3)
% 240.64/47.18    (15)  op(e2, e0) = all_52_13
% 240.64/47.18    (16)   ~ (e2 = e1)
% 240.64/47.18  
% 240.64/47.18  Begin of proof
% 240.64/47.18  | 
% 240.64/47.18  | ALPHA: (12) implies:
% 240.64/47.18  |   (17)  all_58_3 = e1
% 240.64/47.18  | 
% 240.64/47.18  | COMBINE_EQS: (5), (17) imply:
% 240.64/47.18  |   (18)  e3 = e1
% 240.64/47.18  | 
% 240.64/47.18  | COMBINE_EQS: (8), (18) imply:
% 240.64/47.18  |   (19)  all_58_9 = e1
% 240.64/47.18  | 
% 240.64/47.18  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (13), (14), (15),
% 240.64/47.18  |            (16), (19) are inconsistent by sub-proof #1600.
% 240.64/47.18  | 
% 240.64/47.18  End of proof
% 240.64/47.18  
% 240.64/47.18  Sub-proof #332 shows that the following formulas are inconsistent:
% 240.64/47.18  ----------------------------------------------------------------
% 240.64/47.18    (1)   ~ (e3 = e0)
% 240.64/47.19    (2)  all_58_3 = e3
% 240.64/47.19    (3)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.64/47.19         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.64/47.19    (4)  all_58_3 = e0 & op(e2, e2) = e0
% 240.64/47.19    (5)  op(e3, e1) = all_52_8
% 240.64/47.19    (6)   ~ (e3 = e2)
% 240.64/47.19    (7)  all_58_9 = e3
% 240.64/47.19    (8)  op(e3, e3) = e2
% 240.64/47.19    (9)   ~ (all_52_4 = e3)
% 240.64/47.19    (10)  op(e3, e2) = all_52_4
% 240.64/47.19    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.19    (12)   ~ (all_52_8 = e3)
% 240.64/47.19  
% 240.64/47.19  Begin of proof
% 240.64/47.19  | 
% 240.64/47.19  | ALPHA: (4) implies:
% 240.64/47.19  |   (13)  all_58_3 = e0
% 240.64/47.19  | 
% 240.64/47.19  | COMBINE_EQS: (2), (13) imply:
% 240.64/47.19  |   (14)  e3 = e0
% 240.64/47.19  | 
% 240.64/47.19  | COMBINE_EQS: (7), (14) imply:
% 240.64/47.19  |   (15)  all_58_9 = e0
% 240.64/47.19  | 
% 240.64/47.19  | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (12), (15) are
% 240.64/47.19  |            inconsistent by sub-proof #1956.
% 240.64/47.19  | 
% 240.64/47.19  End of proof
% 240.64/47.19  
% 240.64/47.19  Sub-proof #333 shows that the following formulas are inconsistent:
% 240.64/47.19  ----------------------------------------------------------------
% 240.64/47.19    (1)  op(e0, e0) = e1
% 240.64/47.19    (2)   ~ (e3 = e0)
% 240.64/47.19    (3)   ~ (e2 = e0)
% 240.64/47.19    (4)   ~ (e3 = e1)
% 240.64/47.19    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.64/47.19             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.64/47.19               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.64/47.19               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.64/47.19    (6)  op(e2, e0) = e2
% 240.64/47.19    (7)  all_58_15 = e1
% 240.64/47.19    (8)  all_58_9 = e3
% 240.64/47.19    (9)  all_58_12 = e3
% 240.64/47.19    (10)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.64/47.19          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.19    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.19    (12)   ~ (e1 = e0)
% 240.64/47.19    (13)   ~ (all_52_13 = e3)
% 240.64/47.19    (14)  op(e2, e0) = all_52_13
% 240.64/47.19    (15)  all_58_12 = e1 & op(e0, e3) = e1
% 240.64/47.19  
% 240.64/47.19  Begin of proof
% 240.64/47.19  | 
% 240.64/47.19  | ALPHA: (15) implies:
% 240.64/47.19  |   (16)  all_58_12 = e1
% 240.64/47.19  | 
% 240.64/47.19  | COMBINE_EQS: (9), (16) imply:
% 240.64/47.19  |   (17)  e3 = e1
% 240.64/47.19  | 
% 240.64/47.19  | COMBINE_EQS: (8), (17) imply:
% 240.64/47.19  |   (18)  all_58_9 = e1
% 240.64/47.19  | 
% 240.64/47.19  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 240.64/47.19  |            (18) are inconsistent by sub-proof #971.
% 240.64/47.19  | 
% 240.64/47.19  End of proof
% 240.64/47.19  
% 240.64/47.19  Sub-proof #334 shows that the following formulas are inconsistent:
% 240.64/47.19  ----------------------------------------------------------------
% 240.64/47.19    (1)  op(e3, e2) = e1
% 240.64/47.19    (2)   ~ (e3 = e1)
% 240.64/47.19    (3)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 240.64/47.19           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 240.64/47.19             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.64/47.19           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 240.64/47.19             e1) = e3 & op(e1, e3) = e3)
% 240.64/47.19    (4)  op(e1, e3) = e1
% 240.64/47.19    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.19    (6)   ~ (e2 = e1)
% 240.64/47.19  
% 240.64/47.19  Begin of proof
% 240.64/47.19  | 
% 240.64/47.19  | BETA: splitting (3) gives:
% 240.64/47.19  | 
% 240.64/47.19  | Case 1:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.64/47.19  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.64/47.19  | |        op(e2, e3) = e2
% 240.64/47.19  | | 
% 240.64/47.19  | | ALPHA: (7) implies:
% 240.64/47.19  | |   (8)  op(e3, e2) = e2
% 240.64/47.19  | | 
% 240.64/47.19  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2261.
% 240.64/47.19  | | 
% 240.64/47.19  | Case 2:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.64/47.19  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.64/47.19  | |        op(e1, e3) = e3
% 240.64/47.19  | | 
% 240.64/47.19  | | ALPHA: (9) implies:
% 240.64/47.19  | |   (10)  op(e1, e3) = e3
% 240.64/47.19  | | 
% 240.64/47.19  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #2225.
% 240.64/47.19  | | 
% 240.64/47.19  | End of split
% 240.64/47.19  | 
% 240.64/47.19  End of proof
% 240.64/47.19  
% 240.64/47.19  Sub-proof #335 shows that the following formulas are inconsistent:
% 240.64/47.19  ----------------------------------------------------------------
% 240.64/47.19    (1)   ~ (e2 = e0)
% 240.64/47.19    (2)  all_58_7 = e2
% 240.64/47.19    (3)  op(e1, e3) = e1
% 240.64/47.19    (4)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 240.64/47.19    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.19    (6)   ~ (e1 = e0)
% 240.64/47.19  
% 240.64/47.19  Begin of proof
% 240.64/47.19  | 
% 240.64/47.19  | BETA: splitting (4) gives:
% 240.64/47.19  | 
% 240.64/47.19  | Case 1:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (7)  all_58_6 = e0 & op(e1, e3) = e0
% 240.64/47.19  | | 
% 240.64/47.19  | | ALPHA: (7) implies:
% 240.64/47.19  | |   (8)  op(e1, e3) = e0
% 240.64/47.19  | | 
% 240.64/47.19  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #449.
% 240.64/47.19  | | 
% 240.64/47.19  | Case 2:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (9)  all_58_7 = e0 & op(e1, e2) = e0
% 240.64/47.19  | | 
% 240.64/47.19  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #2212.
% 240.64/47.19  | | 
% 240.64/47.19  | End of split
% 240.64/47.19  | 
% 240.64/47.19  End of proof
% 240.64/47.19  
% 240.64/47.19  Sub-proof #336 shows that the following formulas are inconsistent:
% 240.64/47.19  ----------------------------------------------------------------
% 240.64/47.19    (1)  op(e3, e2) = e1
% 240.64/47.19    (2)   ~ (e3 = e0)
% 240.64/47.19    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.64/47.19         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.64/47.19    (4)   ~ (e3 = e1)
% 240.64/47.19    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 240.64/47.19    (6)   ~ (e3 = e2)
% 240.64/47.19    (7)  op(e2, e0) = e2
% 240.64/47.19    (8)  all_58_2 = e0
% 240.64/47.19    (9)  all_58_5 = e1
% 240.64/47.19    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.19    (11)   ~ (e2 = e1)
% 240.64/47.19  
% 240.64/47.19  Begin of proof
% 240.64/47.19  | 
% 240.64/47.19  | BETA: splitting (5) gives:
% 240.64/47.19  | 
% 240.64/47.19  | Case 1:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (12)  all_58_1 = e2 & op(e3, e2) = e2
% 240.64/47.19  | | 
% 240.64/47.19  | | ALPHA: (12) implies:
% 240.64/47.19  | |   (13)  op(e3, e2) = e2
% 240.64/47.19  | | 
% 240.64/47.19  | | REF_CLOSE: (1), (10), (11), (13) are inconsistent by sub-proof #2261.
% 240.64/47.19  | | 
% 240.64/47.19  | Case 2:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (14)  all_58_3 = e2 & op(e2, e2) = e2
% 240.64/47.19  | | 
% 240.64/47.19  | | ALPHA: (14) implies:
% 240.64/47.19  | |   (15)  op(e2, e2) = e2
% 240.64/47.19  | | 
% 240.64/47.19  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (15) are inconsistent by
% 240.64/47.19  | |            sub-proof #2122.
% 240.64/47.19  | | 
% 240.64/47.19  | End of split
% 240.64/47.19  | 
% 240.64/47.19  End of proof
% 240.64/47.19  
% 240.64/47.19  Sub-proof #337 shows that the following formulas are inconsistent:
% 240.64/47.19  ----------------------------------------------------------------
% 240.64/47.19    (1)   ~ (e3 = e0)
% 240.64/47.19    (2)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.64/47.19         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.64/47.19    (3)  op(e3, e1) = all_52_8
% 240.64/47.19    (4)   ~ (e3 = e2)
% 240.64/47.19    (5)  all_58_9 = e3
% 240.64/47.19    (6)  op(e3, e3) = e2
% 240.64/47.19    (7)  all_58_12 = e3
% 240.64/47.19    (8)  all_58_12 = e0 & op(e0, e3) = e0
% 240.64/47.19    (9)   ~ (all_52_4 = e3)
% 240.64/47.19    (10)  op(e3, e2) = all_52_4
% 240.64/47.19    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.19    (12)   ~ (all_52_8 = e3)
% 240.64/47.19  
% 240.64/47.19  Begin of proof
% 240.64/47.19  | 
% 240.64/47.19  | ALPHA: (8) implies:
% 240.64/47.19  |   (13)  all_58_12 = e0
% 240.64/47.19  | 
% 240.64/47.19  | COMBINE_EQS: (7), (13) imply:
% 240.64/47.19  |   (14)  e3 = e0
% 240.64/47.19  | 
% 240.64/47.19  | COMBINE_EQS: (5), (14) imply:
% 240.64/47.19  |   (15)  all_58_9 = e0
% 240.64/47.19  | 
% 240.64/47.19  | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (11), (12), (15) are
% 240.64/47.19  |            inconsistent by sub-proof #1956.
% 240.64/47.19  | 
% 240.64/47.19  End of proof
% 240.64/47.19  
% 240.64/47.19  Sub-proof #338 shows that the following formulas are inconsistent:
% 240.64/47.19  ----------------------------------------------------------------
% 240.64/47.19    (1)   ~ (e3 = e0)
% 240.64/47.19    (2)  all_58_5 = e2 & op(e2, e1) = e2
% 240.64/47.19    (3)   ~ (e2 = e0)
% 240.64/47.19    (4)  all_58_14 = e2
% 240.64/47.19    (5)   ~ (e3 = e1)
% 240.64/47.19    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.64/47.19         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.64/47.19    (7)   ~ (e3 = e2)
% 240.64/47.19    (8)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.64/47.19         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.64/47.19    (9)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.64/47.19         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.64/47.19    (10)  all_58_5 = e1
% 240.64/47.19    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.19    (12)   ~ (e1 = e0)
% 240.64/47.19    (13)  all_58_4 = e0
% 240.64/47.19    (14)   ~ (e2 = e1)
% 240.64/47.19  
% 240.64/47.19  Begin of proof
% 240.64/47.19  | 
% 240.64/47.19  | ALPHA: (2) implies:
% 240.64/47.19  |   (15)  all_58_5 = e2
% 240.64/47.19  | 
% 240.64/47.19  | COMBINE_EQS: (10), (15) imply:
% 240.64/47.19  |   (16)  e2 = e1
% 240.64/47.19  | 
% 240.64/47.19  | SIMP: (16) implies:
% 240.64/47.19  |   (17)  e2 = e1
% 240.64/47.19  | 
% 240.64/47.19  | COMBINE_EQS: (4), (17) imply:
% 240.64/47.19  |   (18)  all_58_14 = e1
% 240.64/47.19  | 
% 240.64/47.19  | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 240.64/47.19  |            (18) are inconsistent by sub-proof #1248.
% 240.64/47.19  | 
% 240.64/47.19  End of proof
% 240.64/47.19  
% 240.64/47.19  Sub-proof #339 shows that the following formulas are inconsistent:
% 240.64/47.19  ----------------------------------------------------------------
% 240.64/47.19    (1)   ~ (e2 = e0)
% 240.64/47.19    (2)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2)
% 240.64/47.19    (3)  all_58_5 = e1
% 240.64/47.19    (4)  all_58_4 = e0
% 240.64/47.19    (5)   ~ (e2 = e1)
% 240.64/47.19  
% 240.64/47.19  Begin of proof
% 240.64/47.19  | 
% 240.64/47.19  | BETA: splitting (2) gives:
% 240.64/47.19  | 
% 240.64/47.19  | Case 1:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (6)  all_58_4 = e2 & op(e3, e1) = e2
% 240.64/47.19  | | 
% 240.64/47.19  | | ALPHA: (6) implies:
% 240.64/47.19  | |   (7)  all_58_4 = e2
% 240.64/47.19  | | 
% 240.64/47.19  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #1666.
% 240.64/47.19  | | 
% 240.64/47.19  | Case 2:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (8)  all_58_5 = e2 & op(e2, e1) = e2
% 240.64/47.19  | | 
% 240.64/47.19  | | ALPHA: (8) implies:
% 240.64/47.19  | |   (9)  all_58_5 = e2
% 240.64/47.19  | | 
% 240.64/47.19  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #1665.
% 240.64/47.19  | | 
% 240.64/47.19  | End of split
% 240.64/47.19  | 
% 240.64/47.19  End of proof
% 240.64/47.19  
% 240.64/47.19  Sub-proof #340 shows that the following formulas are inconsistent:
% 240.64/47.19  ----------------------------------------------------------------
% 240.64/47.19    (1)  op(e1, e2) = all_52_6
% 240.64/47.19    (2)  all_54_11 = all_52_14
% 240.64/47.19    (3)  op(e2, e1) = e2
% 240.64/47.19    (4)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.64/47.19    (5)  op(e2, e1) = all_52_9
% 240.64/47.19    (6)   ~ (all_52_14 = e0)
% 240.64/47.19    (7)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.64/47.19    (8)   ~ (all_52_9 = all_52_13)
% 240.64/47.19    (9)   ~ (all_52_6 = all_52_14)
% 240.64/47.19    (10)   ~ (all_52_14 = e3)
% 240.64/47.19    (11)  op(e1, e2) = e2
% 240.64/47.19    (12)  all_54_7 = all_52_13
% 240.64/47.19    (13)   ~ (all_52_13 = all_52_14)
% 240.64/47.19    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.19    (15)   ~ (all_52_13 = e3)
% 240.64/47.19    (16)   ~ (all_52_13 = e0)
% 240.64/47.19  
% 240.64/47.19  Begin of proof
% 240.64/47.19  | 
% 240.64/47.19  | GROUND_INST: instantiating (14) with all_52_6, e2, e2, e1, simplifying with
% 240.64/47.19  |              (1), (11) gives:
% 240.64/47.19  |   (17)  all_52_6 = e2
% 240.64/47.19  | 
% 240.64/47.19  | GROUND_INST: instantiating (14) with all_52_9, e2, e1, e2, simplifying with
% 240.64/47.19  |              (3), (5) gives:
% 240.64/47.19  |   (18)  all_52_9 = e2
% 240.64/47.19  | 
% 240.64/47.19  | REDUCE: (9), (17) imply:
% 240.64/47.19  |   (19)   ~ (all_52_14 = e2)
% 240.64/47.19  | 
% 240.64/47.19  | SIMP: (19) implies:
% 240.64/47.19  |   (20)   ~ (all_52_14 = e2)
% 240.64/47.19  | 
% 240.64/47.19  | REDUCE: (8), (18) imply:
% 240.64/47.19  |   (21)   ~ (all_52_13 = e2)
% 240.64/47.19  | 
% 240.64/47.19  | SIMP: (21) implies:
% 240.64/47.19  |   (22)   ~ (all_52_13 = e2)
% 240.64/47.19  | 
% 240.64/47.19  | BETA: splitting (4) gives:
% 240.64/47.19  | 
% 240.64/47.19  | Case 1:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (23)  all_54_11 = e3
% 240.64/47.19  | | 
% 240.64/47.19  | | REF_CLOSE: (2), (10), (23) are inconsistent by sub-proof #1998.
% 240.64/47.19  | | 
% 240.64/47.19  | Case 2:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (24)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.64/47.19  | | 
% 240.64/47.19  | | BETA: splitting (7) gives:
% 240.64/47.19  | | 
% 240.64/47.19  | | Case 1:
% 240.64/47.19  | | | 
% 240.64/47.19  | | |   (25)  all_54_7 = e3
% 240.64/47.19  | | | 
% 240.64/47.19  | | | REF_CLOSE: (12), (15), (25) are inconsistent by sub-proof #2296.
% 240.64/47.19  | | | 
% 240.64/47.19  | | Case 2:
% 240.64/47.19  | | | 
% 240.64/47.19  | | |   (26)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.64/47.19  | | | 
% 240.64/47.19  | | | REF_CLOSE: (2), (6), (12), (13), (16), (20), (22), (24), (26) are
% 240.64/47.19  | | |            inconsistent by sub-proof #341.
% 240.64/47.19  | | | 
% 240.64/47.19  | | End of split
% 240.64/47.19  | | 
% 240.64/47.19  | End of split
% 240.64/47.19  | 
% 240.64/47.19  End of proof
% 240.64/47.19  
% 240.64/47.19  Sub-proof #341 shows that the following formulas are inconsistent:
% 240.64/47.19  ----------------------------------------------------------------
% 240.64/47.19    (1)  all_54_11 = all_52_14
% 240.64/47.19    (2)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.64/47.19    (3)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.64/47.19    (4)   ~ (all_52_14 = e2)
% 240.64/47.19    (5)   ~ (all_52_14 = e0)
% 240.64/47.19    (6)   ~ (all_52_13 = e2)
% 240.64/47.19    (7)  all_54_7 = all_52_13
% 240.64/47.19    (8)   ~ (all_52_13 = all_52_14)
% 240.64/47.19    (9)   ~ (all_52_13 = e0)
% 240.64/47.19  
% 240.64/47.19  Begin of proof
% 240.64/47.19  | 
% 240.64/47.19  | BETA: splitting (3) gives:
% 240.64/47.19  | 
% 240.64/47.19  | Case 1:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (10)  all_54_7 = e2
% 240.64/47.19  | | 
% 240.64/47.19  | | REF_CLOSE: (6), (7), (10) are inconsistent by sub-proof #1997.
% 240.64/47.19  | | 
% 240.64/47.19  | Case 2:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (11)  all_54_7 = e1 | all_54_7 = e0
% 240.64/47.19  | | 
% 240.64/47.19  | | BETA: splitting (11) gives:
% 240.64/47.19  | | 
% 240.64/47.19  | | Case 1:
% 240.64/47.19  | | | 
% 240.64/47.19  | | |   (12)  all_54_7 = e1
% 240.64/47.19  | | | 
% 240.64/47.19  | | | COMBINE_EQS: (7), (12) imply:
% 240.64/47.19  | | |   (13)  all_52_13 = e1
% 240.64/47.19  | | | 
% 240.64/47.19  | | | SIMP: (13) implies:
% 240.64/47.19  | | |   (14)  all_52_13 = e1
% 240.64/47.19  | | | 
% 240.64/47.19  | | | REDUCE: (8), (14) imply:
% 240.64/47.19  | | |   (15)   ~ (all_52_14 = e1)
% 240.64/47.19  | | | 
% 240.64/47.19  | | | SIMP: (15) implies:
% 240.64/47.19  | | |   (16)   ~ (all_52_14 = e1)
% 240.64/47.19  | | | 
% 240.64/47.19  | | | BETA: splitting (2) gives:
% 240.64/47.19  | | | 
% 240.64/47.19  | | | Case 1:
% 240.64/47.19  | | | | 
% 240.64/47.19  | | | |   (17)  all_54_11 = e2
% 240.64/47.19  | | | | 
% 240.64/47.19  | | | | REF_CLOSE: (1), (4), (17) are inconsistent by sub-proof #2177.
% 240.64/47.19  | | | | 
% 240.64/47.19  | | | Case 2:
% 240.64/47.19  | | | | 
% 240.64/47.19  | | | |   (18)  all_54_11 = e1 | all_54_11 = e0
% 240.64/47.19  | | | | 
% 240.64/47.19  | | | | REF_CLOSE: (1), (5), (16), (18) are inconsistent by sub-proof #2174.
% 240.64/47.19  | | | | 
% 240.64/47.19  | | | End of split
% 240.64/47.19  | | | 
% 240.64/47.19  | | Case 2:
% 240.64/47.19  | | | 
% 240.64/47.19  | | |   (19)  all_54_7 = e0
% 240.64/47.19  | | | 
% 240.64/47.19  | | | REF_CLOSE: (7), (9), (19) are inconsistent by sub-proof #2294.
% 240.64/47.19  | | | 
% 240.64/47.19  | | End of split
% 240.64/47.19  | | 
% 240.64/47.19  | End of split
% 240.64/47.19  | 
% 240.64/47.19  End of proof
% 240.64/47.19  
% 240.64/47.19  Sub-proof #342 shows that the following formulas are inconsistent:
% 240.64/47.19  ----------------------------------------------------------------
% 240.64/47.19    (1)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.64/47.19             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.64/47.19           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 240.64/47.19           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.64/47.19           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 240.64/47.19           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.64/47.19           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.64/47.19    (2)  all_56_21 = e3
% 240.64/47.19    (3)  all_56_31 = e0
% 240.64/47.19  
% 240.64/47.19  Begin of proof
% 240.64/47.19  | 
% 240.64/47.19  | BETA: splitting (1) gives:
% 240.64/47.19  | 
% 240.64/47.19  | Case 1:
% 240.64/47.19  | | 
% 240.64/47.19  | |   (4)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.64/47.19  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.64/47.19  | |        op(e1, e3) = e1
% 240.64/47.19  | | 
% 240.64/47.19  | | ALPHA: (4) implies:
% 240.64/47.19  | |   (5)   ~ (all_56_21 = e3)
% 240.64/47.19  | | 
% 240.64/47.19  | | REDUCE: (2), (5) imply:
% 240.64/47.19  | |   (6)  $false
% 240.64/47.19  | | 
% 240.64/47.19  | | CLOSE: (6) is inconsistent.
% 240.64/47.19  | | 
% 240.64/47.19  | Case 2:
% 240.64/47.19  | | 
% 240.64/47.20  | |   (7)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.64/47.20  | |            = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 240.64/47.20  | |          e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.64/47.20  | |          (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.64/47.20  | |          (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.64/47.20  | | 
% 240.64/47.20  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #343.
% 240.64/47.20  | | 
% 240.64/47.20  | End of split
% 240.64/47.20  | 
% 240.64/47.20  End of proof
% 240.64/47.20  
% 240.64/47.20  Sub-proof #343 shows that the following formulas are inconsistent:
% 240.64/47.20  ----------------------------------------------------------------
% 240.64/47.20    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.64/47.20             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.64/47.20           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 240.64/47.20           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.64/47.20           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.64/47.20    (2)  all_56_31 = e0
% 240.64/47.20    (3)  all_56_21 = e3
% 240.64/47.20  
% 240.64/47.20  Begin of proof
% 240.64/47.20  | 
% 240.64/47.20  | BETA: splitting (1) gives:
% 240.64/47.20  | 
% 240.64/47.20  | Case 1:
% 240.64/47.20  | | 
% 240.64/47.20  | |   (4)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.64/47.20  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.64/47.20  | |        op(e0, e3) = e3
% 240.64/47.20  | | 
% 240.64/47.20  | | ALPHA: (4) implies:
% 240.64/47.20  | |   (5)   ~ (all_56_31 = e0)
% 240.64/47.20  | | 
% 240.64/47.20  | | REDUCE: (2), (5) imply:
% 240.64/47.20  | |   (6)  $false
% 240.64/47.20  | | 
% 240.64/47.20  | | CLOSE: (6) is inconsistent.
% 240.64/47.20  | | 
% 240.64/47.20  | Case 2:
% 240.64/47.20  | | 
% 240.64/47.20  | |   (7)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.64/47.20  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 240.64/47.20  | |        op(e0, e3) = e0
% 240.64/47.20  | | 
% 240.64/47.20  | | ALPHA: (7) implies:
% 240.64/47.20  | |   (8)   ~ (all_56_21 = e3)
% 240.64/47.20  | | 
% 240.64/47.20  | | REDUCE: (3), (8) imply:
% 240.64/47.20  | |   (9)  $false
% 240.64/47.20  | | 
% 240.64/47.20  | | CLOSE: (9) is inconsistent.
% 240.64/47.20  | | 
% 240.64/47.20  | End of split
% 240.64/47.20  | 
% 240.64/47.20  End of proof
% 240.64/47.20  
% 240.64/47.20  Sub-proof #344 shows that the following formulas are inconsistent:
% 240.64/47.20  ----------------------------------------------------------------
% 240.64/47.20    (1)   ~ (e3 = e0)
% 240.64/47.20    (2)   ~ (e2 = e0)
% 240.64/47.20    (3)  op(e1, e2) = all_52_6
% 240.64/47.20    (4)  all_58_11 = e1
% 240.64/47.20    (5)   ~ (e3 = e1)
% 240.64/47.20    (6)  op(e1, e0) = e1
% 240.64/47.20    (7)   ~ (e3 = e2)
% 240.64/47.20    (8)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 240.64/47.20           $i(all_56_29)) | (all_56_30 = e0 & op(e0, all_56_31) = e0)
% 240.64/47.20    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.64/47.20         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.64/47.20    (10)  op(e0, e3) = e2
% 240.64/47.20    (11)  op(e1, e3) = e0
% 240.64/47.20    (12)  op(e1, e1) = e3
% 240.64/47.20    (13)   ~ (all_52_6 = e3)
% 240.64/47.20    (14)  all_56_31 = e3
% 240.64/47.20    (15)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.64/47.20          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.64/47.20    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.20    (17)  all_58_8 = e3
% 240.64/47.20    (18)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.64/47.20            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.64/47.20              e3) = all_46_1 & $i(all_46_1))
% 240.64/47.20    (19)   ~ (e1 = e0)
% 240.64/47.20    (20)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.64/47.20          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.64/47.20    (21)   ~ (e2 = e1)
% 240.64/47.20  
% 240.64/47.20  Begin of proof
% 240.64/47.20  | 
% 240.64/47.20  | BETA: splitting (8) gives:
% 240.64/47.20  | 
% 240.64/47.20  | Case 1:
% 240.64/47.20  | | 
% 240.64/47.20  | |   (22)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 240.64/47.20  | |         $i(all_56_29)
% 240.64/47.20  | | 
% 240.64/47.20  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (13), (15),
% 240.64/47.20  | |            (16), (17), (18), (19), (20), (21), (22) are inconsistent by
% 240.64/47.20  | |            sub-proof #412.
% 240.64/47.20  | | 
% 240.64/47.20  | Case 2:
% 240.64/47.20  | | 
% 240.64/47.20  | |   (23)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.64/47.20  | | 
% 240.64/47.20  | | ALPHA: (23) implies:
% 240.64/47.20  | |   (24)  op(e0, all_56_31) = e0
% 240.64/47.20  | | 
% 240.64/47.20  | | REDUCE: (14), (24) imply:
% 240.64/47.20  | |   (25)  op(e0, e3) = e0
% 240.64/47.20  | | 
% 240.64/47.20  | | REF_CLOSE: (2), (10), (16), (25) are inconsistent by sub-proof #1896.
% 240.64/47.20  | | 
% 240.64/47.20  | End of split
% 240.64/47.20  | 
% 240.64/47.20  End of proof
% 240.64/47.20  
% 240.64/47.20  Sub-proof #345 shows that the following formulas are inconsistent:
% 240.64/47.20  ----------------------------------------------------------------
% 240.64/47.20    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.64/47.20         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.64/47.20    (2)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.64/47.20           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.64/47.20           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.64/47.20           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.64/47.20           & $i(all_56_23))
% 240.64/47.20    (3)   ~ (e3 = e0)
% 240.64/47.20    (4)  op(e0, e1) = all_52_11
% 240.64/47.20    (5)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.64/47.20         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.64/47.20    (6)   ~ (e2 = e0)
% 240.64/47.20    (7)  op(e1, e2) = all_52_6
% 240.64/47.20    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.64/47.20         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.64/47.20    (9)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) = all_38_1
% 240.64/47.20           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 240.64/47.20           all_38_1 & $i(all_38_1))
% 240.64/47.20    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.64/47.20          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.64/47.20    (11)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.64/47.20          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.64/47.20    (12)  all_58_15 = e3
% 240.64/47.20    (13)  op(e2, e3) = e3
% 240.64/47.20    (14)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.64/47.20          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.64/47.20    (15)   ~ (e3 = e1)
% 240.64/47.20    (16)   ~ (all_52_12 = e1)
% 240.64/47.20    (17)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.64/47.20          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.64/47.20    (18)  op(e2, e2) = e0
% 240.64/47.20    (19)   ~ (all_52_8 = e1)
% 240.64/47.20    (20)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 240.64/47.20            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 240.64/47.20              e1) = all_10_1 & $i(all_10_1))
% 240.64/47.20    (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.64/47.20          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.64/47.20    (22)   ~ (all_52_2 = e1)
% 240.64/47.20    (23)  op(e3, e3) = e1
% 240.64/47.20    (24)   ~ (all_52_9 = e0)
% 240.64/47.20    (25)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.64/47.20              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.64/47.20                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.64/47.20                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.64/47.20    (26)   ~ (all_52_11 = e3)
% 240.64/47.20    (27)  op(e3, e1) = all_52_8
% 240.64/47.20    (28)  op(e2, e1) = all_52_9
% 240.64/47.20    (29)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.64/47.20          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.64/47.20    (30)   ~ (e3 = e2)
% 240.64/47.20    (31)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 240.64/47.20            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 240.64/47.20              e0) = all_14_1 & $i(all_14_1))
% 240.64/47.20    (32)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 240.64/47.20            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 240.64/47.20              e0) = all_48_1 & $i(all_48_1))
% 240.64/47.20    (33)  op(e3, e0) = all_52_12
% 240.64/47.20    (34)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.64/47.20          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.64/47.20    (35)  op(e3, e2) = all_52_4
% 240.64/47.20    (36)   ~ (all_52_9 = e3)
% 240.64/47.20    (37)  op(e0, e0) = e3
% 240.64/47.20    (38)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.64/47.20          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.64/47.20    (39)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.64/47.20          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.64/47.20    (40)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.20    (41)  all_58_8 = e3
% 240.64/47.20    (42)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.64/47.20          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.64/47.20    (43)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.64/47.20            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.64/47.20              e3) = all_46_1 & $i(all_46_1))
% 240.64/47.20    (44)  op(e1, e3) = all_52_2
% 240.64/47.20    (45)  all_56_21 = e3
% 240.64/47.20    (46)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.64/47.20          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.64/47.20    (47)   ~ (all_52_4 = e1)
% 240.64/47.20    (48)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.64/47.20          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.64/47.20    (49)   ~ (e1 = e0)
% 240.64/47.20    (50)  op(e2, e0) = e1
% 240.64/47.20    (51)  op(e3, e2) = e3
% 240.64/47.20    (52)  op(e2, e0) = all_52_13
% 240.64/47.20    (53)  all_58_3 = e0
% 240.64/47.20    (54)  all_58_10 = e1
% 240.64/47.20    (55)   ~ (e2 = e1)
% 240.64/47.20    (56)   ~ (all_52_8 = e3)
% 240.64/47.20  
% 240.64/47.20  Begin of proof
% 240.64/47.20  | 
% 240.64/47.20  | BETA: splitting (14) gives:
% 240.64/47.20  | 
% 240.64/47.20  | Case 1:
% 240.64/47.20  | | 
% 240.64/47.20  | |   (57)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 240.64/47.20  | |           e2)
% 240.64/47.20  | | 
% 240.64/47.20  | | REF_CLOSE: (6), (13), (18), (30), (40), (57) are inconsistent by sub-proof
% 240.64/47.20  | |            #1509.
% 240.64/47.20  | | 
% 240.64/47.20  | Case 2:
% 240.64/47.20  | | 
% 240.64/47.20  | |   (58)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 240.64/47.20  | |           e2)
% 240.64/47.20  | | 
% 240.64/47.20  | | BETA: splitting (58) gives:
% 240.64/47.20  | | 
% 240.64/47.20  | | Case 1:
% 240.64/47.20  | | | 
% 240.64/47.20  | | |   (59)  all_58_5 = e2 & op(e2, e1) = e2
% 240.64/47.20  | | | 
% 240.64/47.20  | | | ALPHA: (59) implies:
% 240.64/47.20  | | |   (60)  all_58_5 = e2
% 240.64/47.20  | | |   (61)  op(e2, e1) = e2
% 240.64/47.20  | | | 
% 240.64/47.20  | | | BETA: splitting (11) gives:
% 240.64/47.20  | | | 
% 240.64/47.20  | | | Case 1:
% 240.64/47.20  | | | | 
% 240.64/47.20  | | | |   (62)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 240.64/47.20  | | | |           = e1)
% 240.64/47.20  | | | | 
% 240.64/47.20  | | | | BETA: splitting (62) gives:
% 240.64/47.20  | | | | 
% 240.64/47.20  | | | | Case 1:
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | |   (63)  all_58_4 = e1 & op(e3, e1) = e1
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | | ALPHA: (63) implies:
% 240.64/47.20  | | | | |   (64)  op(e3, e1) = e1
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | | REF_CLOSE: (19), (27), (40), (64) are inconsistent by sub-proof #2309.
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | Case 2:
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | |   (65)  all_58_5 = e1 & op(e2, e1) = e1
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | | REF_CLOSE: (55), (60), (65) are inconsistent by sub-proof #1548.
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | End of split
% 240.64/47.20  | | | | 
% 240.64/47.20  | | | Case 2:
% 240.64/47.20  | | | | 
% 240.64/47.20  | | | |   (66)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 240.64/47.20  | | | |           = e1)
% 240.64/47.20  | | | | 
% 240.64/47.20  | | | | BETA: splitting (66) gives:
% 240.64/47.20  | | | | 
% 240.64/47.20  | | | | Case 1:
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | |   (67)  all_58_8 = e1 & op(e1, e1) = e1
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | | REF_CLOSE: (15), (41), (67) are inconsistent by sub-proof #406.
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | Case 2:
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | |   (68)  all_58_14 = e1 & op(e0, e1) = e1
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | | ALPHA: (68) implies:
% 240.64/47.20  | | | | |   (69)  op(e0, e1) = e1
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | | BETA: splitting (25) gives:
% 240.64/47.20  | | | | | 
% 240.64/47.20  | | | | | Case 1:
% 240.64/47.20  | | | | | | 
% 240.64/47.20  | | | | | |   (70)  all_58_15 = e0 & op(e0, e0) = e0
% 240.64/47.20  | | | | | | 
% 240.64/47.20  | | | | | | ALPHA: (70) implies:
% 240.64/47.20  | | | | | |   (71)  op(e0, e0) = e0
% 240.64/47.20  | | | | | | 
% 240.64/47.20  | | | | | | REF_CLOSE: (3), (37), (40), (71) are inconsistent by sub-proof
% 240.64/47.20  | | | | | |            #2079.
% 240.64/47.20  | | | | | | 
% 240.64/47.20  | | | | | Case 2:
% 240.64/47.20  | | | | | | 
% 240.64/47.20  | | | | | |   (72)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 240.64/47.20  | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 240.64/47.20  | | | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.64/47.20  | | | | | |             op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.64/47.20  | | | | | | 
% 240.64/47.20  | | | | | | ALPHA: (72) implies:
% 240.64/47.20  | | | | | |   (73)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.64/47.20  | | | | | |           op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.64/47.20  | | | | | |   (74)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 240.64/47.20  | | | | | |             e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.64/47.20  | | | | | | 
% 240.64/47.20  | | | | | | BETA: splitting (17) gives:
% 240.64/47.20  | | | | | | 
% 240.64/47.20  | | | | | | Case 1:
% 240.64/47.20  | | | | | | | 
% 240.64/47.20  | | | | | | |   (75)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 240.64/47.20  | | | | | | |           op(e2, e1) = e0)
% 240.64/47.20  | | | | | | | 
% 240.64/47.20  | | | | | | | BETA: splitting (75) gives:
% 240.64/47.20  | | | | | | | 
% 240.64/47.20  | | | | | | | Case 1:
% 240.64/47.20  | | | | | | | | 
% 240.64/47.20  | | | | | | | |   (76)  all_58_4 = e0 & op(e3, e1) = e0
% 240.64/47.20  | | | | | | | | 
% 240.64/47.20  | | | | | | | | ALPHA: (76) implies:
% 240.64/47.20  | | | | | | | |   (77)  all_58_4 = e0
% 240.64/47.20  | | | | | | | |   (78)  op(e3, e1) = e0
% 240.64/47.20  | | | | | | | | 
% 240.64/47.20  | | | | | | | | BETA: splitting (73) gives:
% 240.64/47.20  | | | | | | | | 
% 240.64/47.20  | | | | | | | | Case 1:
% 240.64/47.20  | | | | | | | | | 
% 240.64/47.20  | | | | | | | | |   (79)  all_58_12 = e0 & op(e0, e3) = e0
% 240.64/47.20  | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | ALPHA: (79) implies:
% 240.64/47.20  | | | | | | | | |   (80)  op(e0, e3) = e0
% 240.64/47.20  | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | BETA: splitting (1) gives:
% 240.64/47.20  | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | Case 1:
% 240.64/47.20  | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | |   (81)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 &
% 240.64/47.20  | | | | | | | | | |           op(e3, e2) = e2)
% 240.64/47.20  | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | REF_CLOSE: (23), (30), (40), (51), (55), (81) are
% 240.64/47.20  | | | | | | | | | |            inconsistent by sub-proof #348.
% 240.64/47.20  | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | Case 2:
% 240.64/47.20  | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | |   (82)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 &
% 240.64/47.20  | | | | | | | | | |           op(e3, e0) = e2)
% 240.64/47.20  | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | BETA: splitting (82) gives:
% 240.64/47.20  | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | Case 1:
% 240.64/47.20  | | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | |   (83)  all_58_4 = e2 & op(e3, e1) = e2
% 240.64/47.20  | | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | | ALPHA: (83) implies:
% 240.64/47.20  | | | | | | | | | | |   (84)  all_58_4 = e2
% 240.64/47.20  | | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | | REF_CLOSE: (6), (77), (84) are inconsistent by sub-proof
% 240.64/47.20  | | | | | | | | | | |            #1666.
% 240.64/47.20  | | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | Case 2:
% 240.64/47.20  | | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | |   (85)  all_58_9 = e2 & op(e3, e0) = e2
% 240.64/47.20  | | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | | ALPHA: (85) implies:
% 240.64/47.20  | | | | | | | | | | |   (86)  op(e3, e0) = e2
% 240.64/47.20  | | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | | BETA: splitting (74) gives:
% 240.64/47.20  | | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | | Case 1:
% 240.64/47.20  | | | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | | |   (87)  all_58_9 = e0 & op(e3, e0) = e0
% 240.64/47.20  | | | | | | | | | | | | 
% 240.64/47.20  | | | | | | | | | | | | ALPHA: (87) implies:
% 240.64/47.20  | | | | | | | | | | | |   (88)  all_58_9 = e0
% 240.64/47.20  | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (15), (21), (23), (30), (40), (55),
% 240.64/47.21  | | | | | | | | | | | |            (77), (88) are inconsistent by sub-proof #1190.
% 240.64/47.21  | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | |   (89)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 240.64/47.21  | | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 240.64/47.21  | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | BETA: splitting (89) gives:
% 240.64/47.21  | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | |   (90)  all_58_10 = e0 & op(e2, e0) = e0
% 240.64/47.21  | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | ALPHA: (90) implies:
% 240.64/47.21  | | | | | | | | | | | | |   (91)  op(e2, e0) = e0
% 240.64/47.21  | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | REF_CLOSE: (40), (49), (50), (52), (91) are inconsistent by
% 240.64/47.21  | | | | | | | | | | | | |            sub-proof #1778.
% 240.64/47.21  | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | |   (92)  all_58_11 = e0 & op(e1, e0) = e0
% 240.64/47.21  | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | ALPHA: (92) implies:
% 240.64/47.21  | | | | | | | | | | | | |   (93)  all_58_11 = e0
% 240.64/47.21  | | | | | | | | | | | | |   (94)  op(e1, e0) = e0
% 240.64/47.21  | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | BETA: splitting (5) gives:
% 240.64/47.21  | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | |   (95)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 240.64/47.21  | | | | | | | | | | | | | |           & op(e1, e2) = e1)
% 240.64/47.21  | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 240.64/47.21  | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | |   (96)  all_58_6 = e1 & op(e1, e3) = e1
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 240.64/47.21  | | | | | | | | | | | | | | |   (97)  op(e1, e3) = e1
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | REF_CLOSE: (22), (40), (44), (97) are inconsistent by
% 240.64/47.21  | | | | | | | | | | | | | | |            sub-proof #1948.
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | |   (98)  all_58_7 = e1 & op(e1, e2) = e1
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 240.64/47.21  | | | | | | | | | | | | | | |   (99)  all_58_7 = e1
% 240.64/47.21  | | | | | | | | | | | | | | |   (100)  op(e1, e2) = e1
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | |   (101)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 240.64/47.21  | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 240.64/47.21  | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 240.64/47.21  | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | |   (102)  all_58_0 = e2 & op(e3, e3) = e2
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 240.64/47.21  | | | | | | | | | | | | | | | | |   (103)  op(e3, e3) = e2
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (10), (15), (16), (18), (19),
% 240.64/47.21  | | | | | | | | | | | | | | | | |            (27), (30), (33), (39), (40), (48), (49), (55),
% 240.64/47.21  | | | | | | | | | | | | | | | | |            (99), (100), (103) are inconsistent by sub-proof
% 240.64/47.21  | | | | | | | | | | | | | | | | |            #1712.
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | |   (104)  all_58_2 = e2 & op(e2, e3) = e2
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 240.64/47.21  | | | | | | | | | | | | | | | | |   (105)  op(e2, e3) = e2
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (40), (105) are inconsistent by
% 240.64/47.21  | | | | | | | | | | | | | | | | |            sub-proof #1897.
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | |   (106)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 240.64/47.21  | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 240.64/47.21  | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 240.64/47.21  | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | |   (107)  all_58_6 = e2 & op(e1, e3) = e2
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 240.64/47.21  | | | | | | | | | | | | | | | | |   (108)  op(e1, e3) = e2
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | |   (109)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 240.64/47.21  | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 240.64/47.21  | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 240.64/47.21  | | | | | | | | | | | | | | | | | |            all_56_19 & $i(all_56_19))
% 240.64/47.21  | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |   (110)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |            e1) = all_56_17 & $i(all_56_17)
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |   (111)  op(e3, e1) = all_56_17
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |   (112)  op(e3, all_56_17) = e3
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |   (113)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |          op(e3, e1) = all_10_1 & $i(all_10_0) &
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |          $i(all_10_1)
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |   (114)  op(e3, e1) = all_10_1
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (30), (40), (43), (78), (86), (108),
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |            (111), (112), (114) are inconsistent by sub-proof
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |            #347.
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |   (115)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |          $i(all_10_1)
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |   (116)  op(e3, e1) = all_10_1
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (30), (40), (43), (78), (86), (108),
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |            (111), (112), (116) are inconsistent by sub-proof
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |            #347.
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |   (117)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |            e1) = all_56_19 & $i(all_56_19)
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18), (31), (32), (40), (50), (61), (117) are
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1520.
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | |   (118)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 240.64/47.21  | | | | | | | | | | | | | | | | | |          (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 240.64/47.21  | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23))
% 240.64/47.21  | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |   (119)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |   (120)  op(e1, all_56_21) = e1
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | REDUCE: (45), (120) imply:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |   (121)  op(e1, e3) = e1
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (40), (44), (121) are inconsistent by
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |            sub-proof #1948.
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |   (122)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |            e1) = all_56_23 & $i(all_56_23)
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |   (123)  op(e0, e1) = all_56_23
% 240.64/47.21  | | | | | | | | | | | | | | | | | | |   (124)  op(e0, all_56_23) = e0
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (40) with e1, all_56_23, e1, e0,
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |              simplifying with (69), (123) gives:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |   (125)  all_56_23 = e1
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (125) imply:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |   (126)  op(e0, e1) = e0
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (37), (40), (123), (124), (126) are
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1395.
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |   (127)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 &
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |          $i(all_46_1)
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (108), (127) are inconsistent by sub-proof
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | |            #395.
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | |   (128)  all_58_12 = e2 & op(e0, e3) = e2
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 240.64/47.21  | | | | | | | | | | | | | | | | |   (129)  op(e0, e3) = e2
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (40), (80), (129) are inconsistent by
% 240.64/47.21  | | | | | | | | | | | | | | | | |            sub-proof #1896.
% 240.64/47.21  | | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | |   (130)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 240.64/47.21  | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 240.64/47.21  | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 240.64/47.21  | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | |   (131)  all_58_8 = e1 & op(e1, e1) = e1
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 240.64/47.21  | | | | | | | | | | | | | | |   (132)  all_58_8 = e1
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | COMBINE_EQS: (41), (132) imply:
% 240.64/47.21  | | | | | | | | | | | | | | |   (133)  e3 = e1
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | COMBINE_EQS: (12), (133) imply:
% 240.64/47.21  | | | | | | | | | | | | | | |   (134)  all_58_15 = e1
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (15), (30), (38), (40), (42), (54),
% 240.64/47.21  | | | | | | | | | | | | | | |            (55), (93), (134) are inconsistent by sub-proof
% 240.64/47.21  | | | | | | | | | | | | | | |            #1597.
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | |   (135)  all_58_11 = e1 & op(e1, e0) = e1
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 240.64/47.21  | | | | | | | | | | | | | | |   (136)  op(e1, e0) = e1
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | | REF_CLOSE: (40), (49), (94), (136) are inconsistent by
% 240.64/47.21  | | | | | | | | | | | | | | |            sub-proof #2284.
% 240.64/47.21  | | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | 
% 240.64/47.21  | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | 
% 240.64/47.21  | | | | | | | | |   (137)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0
% 240.64/47.21  | | | | | | | | |            & op(e0, e1) = e0)
% 240.64/47.21  | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | BETA: splitting (137) gives:
% 240.64/47.21  | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | Case 1:
% 240.64/47.21  | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | |   (138)  all_58_13 = e0 & op(e0, e2) = e0
% 240.64/47.21  | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | ALPHA: (138) implies:
% 240.64/47.21  | | | | | | | | | |   (139)  all_58_13 = e0
% 240.64/47.21  | | | | | | | | | |   (140)  op(e0, e2) = e0
% 240.64/47.21  | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | REF_CLOSE: (3), (6), (8), (15), (30), (35), (40), (46), (47),
% 240.64/47.21  | | | | | | | | | |            (48), (49), (53), (55), (139), (140) are
% 240.64/47.21  | | | | | | | | | |            inconsistent by sub-proof #1374.
% 240.64/47.21  | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | |   (141)  all_58_14 = e0 & op(e0, e1) = e0
% 240.64/47.21  | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | ALPHA: (141) implies:
% 240.64/47.21  | | | | | | | | | |   (142)  op(e0, e1) = e0
% 240.64/47.21  | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | | REF_CLOSE: (40), (49), (69), (142) are inconsistent by
% 240.64/47.21  | | | | | | | | | |            sub-proof #2158.
% 240.64/47.21  | | | | | | | | | | 
% 240.64/47.21  | | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | | 
% 240.64/47.21  | | | | | | | | End of split
% 240.64/47.21  | | | | | | | | 
% 240.64/47.21  | | | | | | | Case 2:
% 240.64/47.21  | | | | | | | | 
% 240.64/47.21  | | | | | | | |   (143)  all_58_5 = e0 & op(e2, e1) = e0
% 240.64/47.21  | | | | | | | | 
% 240.64/47.21  | | | | | | | | REF_CLOSE: (24), (28), (40), (143) are inconsistent by sub-proof
% 240.64/47.21  | | | | | | | |            #2088.
% 240.64/47.21  | | | | | | | | 
% 240.64/47.21  | | | | | | | End of split
% 240.64/47.21  | | | | | | | 
% 240.64/47.21  | | | | | | Case 2:
% 240.64/47.21  | | | | | | | 
% 240.64/47.21  | | | | | | |   (144)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 240.64/47.21  | | | | | | |            op(e0, e1) = e0)
% 240.64/47.21  | | | | | | | 
% 240.64/47.21  | | | | | | | REF_CLOSE: (3), (4), (26), (27), (28), (34), (36), (40), (49),
% 240.64/47.21  | | | | | | |            (56), (69), (144) are inconsistent by sub-proof #346.
% 240.64/47.21  | | | | | | | 
% 240.64/47.21  | | | | | | End of split
% 240.64/47.21  | | | | | | 
% 240.64/47.21  | | | | | End of split
% 240.64/47.21  | | | | | 
% 240.64/47.21  | | | | End of split
% 240.64/47.21  | | | | 
% 240.64/47.21  | | | End of split
% 240.64/47.21  | | | 
% 240.64/47.21  | | Case 2:
% 240.64/47.21  | | | 
% 240.64/47.21  | | |   (145)  all_58_10 = e2 & op(e2, e0) = e2
% 240.64/47.21  | | | 
% 240.64/47.21  | | | ALPHA: (145) implies:
% 240.64/47.21  | | |   (146)  op(e2, e0) = e2
% 240.64/47.21  | | | 
% 240.64/47.21  | | | REF_CLOSE: (40), (50), (55), (146) are inconsistent by sub-proof #1659.
% 240.64/47.21  | | | 
% 240.64/47.21  | | End of split
% 240.64/47.21  | | 
% 240.64/47.21  | End of split
% 240.64/47.21  | 
% 240.64/47.21  End of proof
% 240.64/47.21  
% 240.64/47.21  Sub-proof #346 shows that the following formulas are inconsistent:
% 240.64/47.21  ----------------------------------------------------------------
% 240.64/47.21    (1)   ~ (e3 = e0)
% 240.64/47.21    (2)  op(e0, e1) = all_52_11
% 240.64/47.21    (3)  op(e0, e1) = e1
% 240.64/47.21    (4)   ~ (all_52_11 = e3)
% 240.64/47.21    (5)  op(e3, e1) = all_52_8
% 240.64/47.21    (6)  op(e2, e1) = all_52_9
% 240.64/47.21    (7)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.64/47.21    (8)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.64/47.21         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.64/47.21    (9)   ~ (all_52_9 = e3)
% 240.64/47.21    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.21    (11)   ~ (e1 = e0)
% 240.64/47.21    (12)   ~ (all_52_8 = e3)
% 240.64/47.21  
% 240.64/47.21  Begin of proof
% 240.64/47.21  | 
% 240.64/47.21  | BETA: splitting (7) gives:
% 240.64/47.21  | 
% 240.64/47.21  | Case 1:
% 240.64/47.21  | | 
% 240.64/47.21  | |   (13)  all_58_8 = e0 & op(e1, e1) = e0
% 240.64/47.21  | | 
% 240.64/47.21  | | ALPHA: (13) implies:
% 240.64/47.21  | |   (14)  op(e1, e1) = e0
% 240.64/47.21  | | 
% 240.64/47.21  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (12), (14) are
% 240.64/47.21  | |            inconsistent by sub-proof #1010.
% 240.64/47.21  | | 
% 240.64/47.21  | Case 2:
% 240.64/47.21  | | 
% 240.64/47.21  | |   (15)  all_58_14 = e0 & op(e0, e1) = e0
% 240.64/47.21  | | 
% 240.64/47.21  | | ALPHA: (15) implies:
% 240.64/47.21  | |   (16)  op(e0, e1) = e0
% 240.64/47.21  | | 
% 240.64/47.21  | | REF_CLOSE: (3), (10), (11), (16) are inconsistent by sub-proof #2158.
% 240.64/47.21  | | 
% 240.64/47.21  | End of split
% 240.64/47.21  | 
% 240.64/47.21  End of proof
% 240.64/47.21  
% 240.64/47.21  Sub-proof #347 shows that the following formulas are inconsistent:
% 240.64/47.21  ----------------------------------------------------------------
% 240.64/47.21    (1)  op(e3, e1) = all_56_17
% 240.64/47.21    (2)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) = all_38_1
% 240.64/47.21           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 240.64/47.21           all_38_1 & $i(all_38_1))
% 240.64/47.21    (3)  op(e3, e1) = e0
% 240.64/47.21    (4)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) = all_10_1
% 240.64/47.21           & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3, e1) =
% 240.64/47.21           all_10_1 & $i(all_10_1))
% 240.64/47.21    (5)  op(e1, e3) = e2
% 240.64/47.21    (6)   ~ (e3 = e2)
% 240.64/47.21    (7)  op(e3, e0) = e2
% 240.64/47.21    (8)  op(e3, all_56_17) = e3
% 240.64/47.21    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.21    (10)  op(e3, e1) = all_10_1
% 240.64/47.21    (11)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.64/47.21            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.64/47.21              e3) = all_46_1 & $i(all_46_1))
% 240.64/47.21  
% 240.64/47.21  Begin of proof
% 240.64/47.21  | 
% 240.64/47.21  | BETA: splitting (2) gives:
% 240.64/47.21  | 
% 240.64/47.21  | Case 1:
% 240.64/47.21  | | 
% 240.64/47.21  | |   (12)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 240.64/47.21  | |         all_38_1 & $i(all_38_0) & $i(all_38_1)
% 240.64/47.21  | | 
% 240.64/47.21  | | ALPHA: (12) implies:
% 240.64/47.21  | |   (13)  op(e3, e1) = all_38_1
% 240.64/47.21  | | 
% 240.64/47.21  | | BETA: splitting (11) gives:
% 240.64/47.21  | | 
% 240.64/47.21  | | Case 1:
% 240.64/47.21  | | | 
% 240.64/47.21  | | | 
% 240.64/47.21  | | | GROUND_INST: instantiating (9) with e0, all_38_1, e1, e3, simplifying with
% 240.64/47.21  | | |              (3), (13) gives:
% 240.64/47.21  | | |   (14)  all_38_1 = e0
% 240.64/47.21  | | | 
% 240.64/47.21  | | | GROUND_INST: instantiating (9) with all_38_1, all_56_17, e1, e3,
% 240.64/47.21  | | |              simplifying with (1), (13) gives:
% 240.64/47.21  | | |   (15)  all_56_17 = all_38_1
% 240.64/47.21  | | | 
% 240.64/47.21  | | | GROUND_INST: instantiating (9) with all_10_1, all_56_17, e1, e3,
% 240.64/47.21  | | |              simplifying with (1), (10) gives:
% 240.64/47.21  | | |   (16)  all_56_17 = all_10_1
% 240.64/47.21  | | | 
% 240.64/47.21  | | | COMBINE_EQS: (15), (16) imply:
% 240.64/47.21  | | |   (17)  all_38_1 = all_10_1
% 240.64/47.21  | | | 
% 240.64/47.21  | | | SIMP: (17) implies:
% 240.64/47.21  | | |   (18)  all_38_1 = all_10_1
% 240.64/47.21  | | | 
% 240.64/47.21  | | | COMBINE_EQS: (14), (18) imply:
% 240.64/47.21  | | |   (19)  all_10_1 = e0
% 240.64/47.21  | | | 
% 240.64/47.21  | | | SIMP: (19) implies:
% 240.64/47.21  | | |   (20)  all_10_1 = e0
% 240.64/47.21  | | | 
% 240.64/47.21  | | | COMBINE_EQS: (16), (20) imply:
% 240.64/47.21  | | |   (21)  all_56_17 = e0
% 240.64/47.21  | | | 
% 240.64/47.21  | | | REDUCE: (8), (21) imply:
% 240.64/47.21  | | |   (22)  op(e3, e0) = e3
% 240.64/47.21  | | | 
% 240.64/47.21  | | | REF_CLOSE: (6), (7), (9), (22) are inconsistent by sub-proof #2125.
% 240.64/47.21  | | | 
% 240.64/47.21  | | Case 2:
% 240.64/47.21  | | | 
% 240.64/47.21  | | |   (23)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.64/47.21  | | | 
% 240.64/47.21  | | | REF_CLOSE: (5), (9), (23) are inconsistent by sub-proof #395.
% 240.64/47.21  | | | 
% 240.64/47.21  | | End of split
% 240.64/47.21  | | 
% 240.64/47.21  | Case 2:
% 240.64/47.21  | | 
% 240.64/47.21  | |   (24)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1)
% 240.64/47.21  | | 
% 240.64/47.21  | | ALPHA: (24) implies:
% 240.64/47.21  | |   (25)   ~ (all_38_1 = e0)
% 240.64/47.21  | |   (26)  op(e3, e1) = all_38_1
% 240.64/47.21  | | 
% 240.64/47.21  | | REF_CLOSE: (3), (4), (9), (25), (26) are inconsistent by sub-proof #1194.
% 240.64/47.21  | | 
% 240.64/47.21  | End of split
% 240.64/47.21  | 
% 240.64/47.21  End of proof
% 240.64/47.21  
% 240.64/47.21  Sub-proof #348 shows that the following formulas are inconsistent:
% 240.64/47.21  ----------------------------------------------------------------
% 240.64/47.21    (1)  op(e3, e3) = e1
% 240.64/47.21    (2)   ~ (e3 = e2)
% 240.64/47.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.64/47.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.64/47.21    (4)  op(e3, e2) = e3
% 240.64/47.21    (5)   ~ (e2 = e1)
% 240.64/47.21    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 240.64/47.21  
% 240.64/47.21  Begin of proof
% 240.64/47.21  | 
% 240.64/47.21  | BETA: splitting (6) gives:
% 240.64/47.21  | 
% 240.64/47.21  | Case 1:
% 240.64/47.21  | | 
% 240.64/47.21  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 240.64/47.21  | | 
% 240.64/47.21  | | ALPHA: (7) implies:
% 240.64/47.21  | |   (8)  op(e3, e3) = e2
% 240.64/47.21  | | 
% 240.64/47.21  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #2267.
% 240.64/47.21  | | 
% 240.64/47.21  | Case 2:
% 240.64/47.21  | | 
% 240.64/47.21  | |   (9)  all_58_1 = e2 & op(e3, e2) = e2
% 240.64/47.21  | | 
% 240.64/47.21  | | ALPHA: (9) implies:
% 240.64/47.21  | |   (10)  op(e3, e2) = e2
% 240.64/47.21  | | 
% 240.64/47.21  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #2193.
% 240.64/47.21  | | 
% 240.64/47.21  | End of split
% 240.64/47.21  | 
% 240.64/47.21  End of proof
% 240.64/47.21  
% 240.64/47.21  Sub-proof #349 shows that the following formulas are inconsistent:
% 240.64/47.21  ----------------------------------------------------------------
% 240.64/47.21    (1)   ~ (e3 = e0)
% 240.73/47.22    (2)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 240.73/47.22         $i(all_56_23)
% 240.73/47.22    (3)  op(e0, e1) = e1
% 240.73/47.22    (4)  op(e0, e0) = e3
% 240.73/47.22    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.22  
% 240.73/47.22  Begin of proof
% 240.73/47.22  | 
% 240.73/47.22  | ALPHA: (2) implies:
% 240.73/47.22  |   (6)  op(e0, e1) = all_56_23
% 240.73/47.22  |   (7)  op(e0, all_56_23) = e0
% 240.73/47.22  | 
% 240.73/47.22  | GROUND_INST: instantiating (5) with e1, all_56_23, e1, e0, simplifying with
% 240.73/47.22  |              (3), (6) gives:
% 240.73/47.22  |   (8)  all_56_23 = e1
% 240.73/47.22  | 
% 240.73/47.22  | REDUCE: (7), (8) imply:
% 240.73/47.22  |   (9)  op(e0, e1) = e0
% 240.73/47.22  | 
% 240.73/47.22  | REF_CLOSE: (1), (4), (5), (6), (7), (9) are inconsistent by sub-proof #1395.
% 240.73/47.22  | 
% 240.73/47.22  End of proof
% 240.73/47.22  
% 240.73/47.22  Sub-proof #350 shows that the following formulas are inconsistent:
% 240.73/47.22  ----------------------------------------------------------------
% 240.73/47.22    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 240.73/47.22           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 240.73/47.22           all_12_1 & $i(all_12_1))
% 240.73/47.22    (2)   ~ (all_8_2 = e0)
% 240.73/47.22    (3)   ~ (e3 = e0)
% 240.73/47.22    (4)  all_56_11 = e1
% 240.73/47.22    (5)   ~ (e2 = e0)
% 240.73/47.22    (6)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.73/47.22           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 240.73/47.22           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 240.73/47.22         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.73/47.22           $i(all_56_15))
% 240.73/47.22    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.73/47.22         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.73/47.22    (8)  all_58_11 = e1
% 240.73/47.22    (9)  op(e1, e0) = all_52_14
% 240.73/47.22    (10)   ~ (e3 = e1)
% 240.73/47.22    (11)  op(e1, e0) = e1
% 240.73/47.22    (12)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 240.73/47.22            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 240.73/47.22              e3) = all_26_1 & $i(all_26_1))
% 240.73/47.22    (13)  op(e3, e3) = e1
% 240.73/47.22    (14)  op(e2, e1) = all_52_9
% 240.73/47.22    (15)   ~ (e3 = e2)
% 240.73/47.22    (16)  op(e2, all_52_9) = e2
% 240.73/47.22    (17)  op(e2, e2) = e1
% 240.73/47.22    (18)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.73/47.22          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.73/47.22    (19)  op(e0, e3) = e2
% 240.73/47.22    (20)  op(e2, e2) = all_8_2
% 240.73/47.22    (21)   ~ (all_52_14 = e3)
% 240.73/47.22    (22)  op(e0, e0) = e3
% 240.73/47.22    (23)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.73/47.22          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.73/47.22    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.22    (25)   ~ (e1 = e0)
% 240.73/47.22    (26)  all_58_7 = e2 & op(e1, e2) = e2
% 240.73/47.22    (27)  op(e3, e2) = e3
% 240.73/47.22    (28)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.73/47.22          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.73/47.22    (29)   ~ (all_52_9 = e1)
% 240.73/47.22    (30)   ~ (e2 = e1)
% 240.73/47.22  
% 240.73/47.22  Begin of proof
% 240.73/47.22  | 
% 240.73/47.22  | ALPHA: (26) implies:
% 240.73/47.22  |   (31)  all_58_7 = e2
% 240.73/47.22  |   (32)  op(e1, e2) = e2
% 240.73/47.22  | 
% 240.73/47.22  | BETA: splitting (7) gives:
% 240.73/47.22  | 
% 240.73/47.22  | Case 1:
% 240.73/47.22  | | 
% 240.73/47.22  | |   (33)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 240.73/47.22  | |           e0)
% 240.73/47.22  | | 
% 240.73/47.22  | | REF_CLOSE: (2), (3), (20), (24), (27), (33) are inconsistent by sub-proof
% 240.73/47.22  | |            #1323.
% 240.73/47.22  | | 
% 240.73/47.22  | Case 2:
% 240.73/47.22  | | 
% 240.73/47.22  | |   (34)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.73/47.22  | |           e0)
% 240.73/47.22  | | 
% 240.73/47.22  | | BETA: splitting (34) gives:
% 240.73/47.22  | | 
% 240.73/47.22  | | Case 1:
% 240.73/47.22  | | | 
% 240.73/47.22  | | |   (35)  all_58_7 = e0 & op(e1, e2) = e0
% 240.73/47.22  | | | 
% 240.73/47.22  | | | REF_CLOSE: (5), (31), (35) are inconsistent by sub-proof #2212.
% 240.73/47.22  | | | 
% 240.73/47.22  | | Case 2:
% 240.73/47.22  | | | 
% 240.73/47.22  | | |   (36)  all_58_13 = e0 & op(e0, e2) = e0
% 240.73/47.22  | | | 
% 240.73/47.22  | | | ALPHA: (36) implies:
% 240.73/47.22  | | |   (37)  op(e0, e2) = e0
% 240.73/47.22  | | | 
% 240.73/47.22  | | | BETA: splitting (6) gives:
% 240.73/47.22  | | | 
% 240.73/47.22  | | | Case 1:
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | |   (38)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.73/47.22  | | | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | | BETA: splitting (38) gives:
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | | Case 1:
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | |   (39)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9
% 240.73/47.22  | | | | |         & $i(all_56_9)
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | | REF_CLOSE: (10), (13), (24), (27), (39) are inconsistent by sub-proof
% 240.73/47.22  | | | | |            #1135.
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | Case 2:
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | |   (40)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | | ALPHA: (40) implies:
% 240.73/47.22  | | | | |   (41)  op(e2, all_56_11) = e2
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | | REDUCE: (4), (41) imply:
% 240.73/47.22  | | | | |   (42)  op(e2, e1) = e2
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | | GROUND_INST: instantiating (24) with all_52_9, e2, e1, e2, simplifying
% 240.73/47.22  | | | | |              with (14), (42) gives:
% 240.73/47.22  | | | | |   (43)  all_52_9 = e2
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | | REDUCE: (16), (43) imply:
% 240.73/47.22  | | | | |   (44)  op(e2, e2) = e2
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | | REF_CLOSE: (17), (24), (30), (44) are inconsistent by sub-proof #2235.
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | End of split
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | Case 2:
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | |   (45)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 240.73/47.22  | | | |           all_56_13 & $i(all_56_13)) | (all_56_14 = e0 & op(e0,
% 240.73/47.22  | | | |             all_56_15) = e0 & op(e0, e2) = all_56_15 & $i(all_56_15))
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | | BETA: splitting (45) gives:
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | | Case 1:
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | |   (46)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 240.73/47.22  | | | | |         all_56_13 & $i(all_56_13)
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | | ALPHA: (46) implies:
% 240.73/47.22  | | | | |   (47)  op(e1, e2) = all_56_13
% 240.73/47.22  | | | | |   (48)  op(e1, all_56_13) = e1
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | | GROUND_INST: instantiating (24) with e2, all_56_13, e2, e1,
% 240.73/47.22  | | | | |              simplifying with (32), (47) gives:
% 240.73/47.22  | | | | |   (49)  all_56_13 = e2
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | | REF_CLOSE: (3), (5), (8), (9), (10), (11), (15), (18), (21), (23),
% 240.73/47.22  | | | | |            (24), (25), (28), (30), (31), (47), (48), (49) are
% 240.73/47.22  | | | | |            inconsistent by sub-proof #354.
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | Case 2:
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | |   (50)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 240.73/47.22  | | | | |         all_56_15 & $i(all_56_15)
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | | REF_CLOSE: (1), (3), (12), (19), (22), (24), (37), (50) are
% 240.73/47.22  | | | | |            inconsistent by sub-proof #1022.
% 240.73/47.22  | | | | | 
% 240.73/47.22  | | | | End of split
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | End of split
% 240.73/47.22  | | | 
% 240.73/47.22  | | End of split
% 240.73/47.22  | | 
% 240.73/47.22  | End of split
% 240.73/47.22  | 
% 240.73/47.22  End of proof
% 240.73/47.22  
% 240.73/47.22  Sub-proof #351 shows that the following formulas are inconsistent:
% 240.73/47.22  ----------------------------------------------------------------
% 240.73/47.22    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 240.73/47.22           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 240.73/47.22           all_12_1 & $i(all_12_1))
% 240.73/47.22    (2)   ~ (all_8_2 = e0)
% 240.73/47.22    (3)   ~ (e3 = e0)
% 240.73/47.22    (4)  all_56_11 = e1
% 240.73/47.22    (5)   ~ (all_52_8 = all_52_9)
% 240.73/47.22    (6)   ~ (e2 = e0)
% 240.73/47.22    (7)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.73/47.22           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 240.73/47.22           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 240.73/47.22         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.73/47.22           $i(all_56_15))
% 240.73/47.22    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.73/47.22         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.73/47.22    (9)  all_58_11 = e1
% 240.73/47.22    (10)  op(e1, e0) = all_52_14
% 240.73/47.22    (11)   ~ (all_52_13 = e1)
% 240.73/47.22    (12)   ~ (e3 = e1)
% 240.73/47.22    (13)  op(e1, e0) = e1
% 240.73/47.22    (14)   ~ (all_52_8 = e1)
% 240.73/47.22    (15)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 240.73/47.22            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 240.73/47.22              e3) = all_26_1 & $i(all_26_1))
% 240.73/47.22    (16)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 240.73/47.22            $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e1, e3) = all_6_1
% 240.73/47.22            & $i(all_6_1))
% 240.73/47.22    (17)  all_54_2 = all_52_8
% 240.73/47.22    (18)  op(e3, e3) = e1
% 240.73/47.22    (19)  op(e2, e1) = all_52_9
% 240.73/47.22    (20)   ~ (e3 = e2)
% 240.73/47.22    (21)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 240.73/47.22    (22)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.73/47.22    (23)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.73/47.22          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.73/47.22    (24)   ~ (all_52_9 = all_52_13)
% 240.73/47.22    (25)  op(e0, e3) = e2
% 240.73/47.22    (26)  op(e2, e2) = all_8_2
% 240.73/47.22    (27)  op(e1, e3) = e0
% 240.73/47.22    (28)   ~ (all_52_14 = e3)
% 240.73/47.22    (29)  all_54_7 = all_52_13
% 240.73/47.22    (30)  op(e3, all_52_8) = e3
% 240.73/47.22    (31)   ~ (all_52_9 = e3)
% 240.73/47.22    (32)  op(e0, e0) = e3
% 240.73/47.22    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.73/47.22          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.73/47.22    (34)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.22    (35)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.73/47.22          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.73/47.22    (36)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.73/47.22            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.73/47.22              e3) = all_46_1 & $i(all_46_1))
% 240.73/47.22    (37)   ~ (e1 = e0)
% 240.73/47.22    (38)  all_58_7 = e2 & op(e1, e2) = e2
% 240.73/47.22    (39)  op(e3, e2) = e3
% 240.73/47.22    (40)   ~ (all_52_13 = e3)
% 240.73/47.22    (41)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.73/47.22          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.73/47.22    (42)  op(e2, e0) = all_52_13
% 240.73/47.22    (43)   ~ (all_52_9 = e1)
% 240.73/47.22    (44)   ~ (e2 = e1)
% 240.73/47.22  
% 240.73/47.22  Begin of proof
% 240.73/47.22  | 
% 240.73/47.22  | ALPHA: (38) implies:
% 240.73/47.22  |   (45)  all_58_7 = e2
% 240.73/47.22  |   (46)  op(e1, e2) = e2
% 240.73/47.22  | 
% 240.73/47.22  | BETA: splitting (8) gives:
% 240.73/47.22  | 
% 240.73/47.22  | Case 1:
% 240.73/47.22  | | 
% 240.73/47.22  | |   (47)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 240.73/47.22  | |           e0)
% 240.73/47.22  | | 
% 240.73/47.22  | | REF_CLOSE: (2), (3), (26), (34), (39), (47) are inconsistent by sub-proof
% 240.73/47.22  | |            #1323.
% 240.73/47.22  | | 
% 240.73/47.22  | Case 2:
% 240.73/47.22  | | 
% 240.73/47.22  | |   (48)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.73/47.22  | |           e0)
% 240.73/47.22  | | 
% 240.73/47.22  | | BETA: splitting (48) gives:
% 240.73/47.22  | | 
% 240.73/47.22  | | Case 1:
% 240.73/47.22  | | | 
% 240.73/47.22  | | |   (49)  all_58_7 = e0 & op(e1, e2) = e0
% 240.73/47.22  | | | 
% 240.73/47.22  | | | REF_CLOSE: (6), (45), (49) are inconsistent by sub-proof #2212.
% 240.73/47.22  | | | 
% 240.73/47.22  | | Case 2:
% 240.73/47.22  | | | 
% 240.73/47.22  | | |   (50)  all_58_13 = e0 & op(e0, e2) = e0
% 240.73/47.22  | | | 
% 240.73/47.22  | | | ALPHA: (50) implies:
% 240.73/47.22  | | |   (51)  op(e0, e2) = e0
% 240.73/47.22  | | | 
% 240.73/47.22  | | | BETA: splitting (16) gives:
% 240.73/47.22  | | | 
% 240.73/47.22  | | | Case 1:
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | |   (52)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) =
% 240.73/47.22  | | | |         all_6_1 & $i(all_6_0) & $i(all_6_1)
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | | ALPHA: (52) implies:
% 240.73/47.22  | | | |   (53)  op(e1, e3) = all_6_1
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 240.73/47.22  | | | |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 240.73/47.22  | | | |            (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 240.73/47.22  | | | |            (36), (37), (39), (40), (41), (42), (43), (44), (45), (46),
% 240.73/47.22  | | | |            (51), (53) are inconsistent by sub-proof #352.
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | Case 2:
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | |   (54)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 & $i(all_6_1)
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | | ALPHA: (54) implies:
% 240.73/47.22  | | | |   (55)  op(e1, e3) = all_6_1
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 240.73/47.22  | | | |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 240.73/47.22  | | | |            (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 240.73/47.22  | | | |            (36), (37), (39), (40), (41), (42), (43), (44), (45), (46),
% 240.73/47.22  | | | |            (51), (55) are inconsistent by sub-proof #352.
% 240.73/47.22  | | | | 
% 240.73/47.22  | | | End of split
% 240.73/47.22  | | | 
% 240.73/47.22  | | End of split
% 240.73/47.22  | | 
% 240.73/47.22  | End of split
% 240.73/47.22  | 
% 240.73/47.22  End of proof
% 240.73/47.22  
% 240.73/47.22  Sub-proof #352 shows that the following formulas are inconsistent:
% 240.73/47.22  ----------------------------------------------------------------
% 240.73/47.22    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 240.73/47.22           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 240.73/47.22           all_12_1 & $i(all_12_1))
% 240.73/47.22    (2)   ~ (e3 = e0)
% 240.73/47.22    (3)  all_56_11 = e1
% 240.73/47.22    (4)   ~ (all_52_8 = all_52_9)
% 240.73/47.22    (5)   ~ (e2 = e0)
% 240.73/47.22    (6)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.73/47.22           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 240.73/47.22           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 240.73/47.22         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.73/47.22           $i(all_56_15))
% 240.73/47.22    (7)  all_58_11 = e1
% 240.73/47.22    (8)  op(e1, e3) = all_6_1
% 240.73/47.22    (9)  op(e1, e0) = all_52_14
% 240.73/47.22    (10)   ~ (all_52_13 = e1)
% 240.73/47.22    (11)   ~ (e3 = e1)
% 240.73/47.22    (12)  all_58_7 = e2
% 240.73/47.22    (13)  op(e1, e0) = e1
% 240.73/47.22    (14)   ~ (all_52_8 = e1)
% 240.73/47.22    (15)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 240.73/47.22            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 240.73/47.22              e3) = all_26_1 & $i(all_26_1))
% 240.73/47.22    (16)  all_54_2 = all_52_8
% 240.73/47.23    (17)  op(e3, e3) = e1
% 240.73/47.23    (18)  op(e2, e1) = all_52_9
% 240.73/47.23    (19)   ~ (e3 = e2)
% 240.73/47.23    (20)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 240.73/47.23    (21)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.73/47.23    (22)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.73/47.23          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.73/47.23    (23)   ~ (all_52_9 = all_52_13)
% 240.73/47.23    (24)  op(e0, e3) = e2
% 240.73/47.23    (25)  op(e1, e3) = e0
% 240.73/47.23    (26)   ~ (all_52_14 = e3)
% 240.73/47.23    (27)  op(e0, e2) = e0
% 240.73/47.23    (28)  op(e1, e2) = e2
% 240.73/47.23    (29)  all_54_7 = all_52_13
% 240.73/47.23    (30)  op(e3, all_52_8) = e3
% 240.73/47.23    (31)   ~ (all_52_9 = e3)
% 240.73/47.23    (32)  op(e0, e0) = e3
% 240.73/47.23    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.73/47.23          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.73/47.23    (34)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.23    (35)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.73/47.23          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.73/47.23    (36)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.73/47.23            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.73/47.23              e3) = all_46_1 & $i(all_46_1))
% 240.73/47.23    (37)   ~ (e1 = e0)
% 240.73/47.23    (38)  op(e3, e2) = e3
% 240.73/47.23    (39)   ~ (all_52_13 = e3)
% 240.73/47.23    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.73/47.23          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.73/47.23    (41)  op(e2, e0) = all_52_13
% 240.73/47.23    (42)   ~ (all_52_9 = e1)
% 240.73/47.23    (43)   ~ (e2 = e1)
% 240.73/47.23  
% 240.73/47.23  Begin of proof
% 240.73/47.23  | 
% 240.73/47.23  | BETA: splitting (6) gives:
% 240.73/47.23  | 
% 240.73/47.23  | Case 1:
% 240.73/47.23  | | 
% 240.73/47.23  | |   (44)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.73/47.23  | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 240.73/47.23  | | 
% 240.73/47.23  | | BETA: splitting (44) gives:
% 240.73/47.23  | | 
% 240.73/47.23  | | Case 1:
% 240.73/47.23  | | | 
% 240.73/47.23  | | |   (45)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.73/47.23  | | |         $i(all_56_9)
% 240.73/47.23  | | | 
% 240.73/47.23  | | | REF_CLOSE: (11), (17), (34), (38), (45) are inconsistent by sub-proof
% 240.73/47.23  | | |            #1135.
% 240.73/47.23  | | | 
% 240.73/47.23  | | Case 2:
% 240.73/47.23  | | | 
% 240.73/47.23  | | |   (46)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 240.73/47.23  | | | 
% 240.73/47.23  | | | ALPHA: (46) implies:
% 240.73/47.23  | | |   (47)  op(e2, all_56_11) = e2
% 240.73/47.23  | | | 
% 240.73/47.23  | | | REDUCE: (3), (47) imply:
% 240.73/47.23  | | |   (48)  op(e2, e1) = e2
% 240.73/47.23  | | | 
% 240.73/47.23  | | | GROUND_INST: instantiating (34) with all_52_9, e2, e1, e2, simplifying
% 240.73/47.23  | | |              with (18), (48) gives:
% 240.73/47.23  | | |   (49)  all_52_9 = e2
% 240.73/47.23  | | | 
% 240.73/47.23  | | | REDUCE: (4), (49) imply:
% 240.73/47.23  | | |   (50)   ~ (all_52_8 = e2)
% 240.73/47.23  | | | 
% 240.73/47.23  | | | REDUCE: (23), (49) imply:
% 240.73/47.23  | | |   (51)   ~ (all_52_13 = e2)
% 240.73/47.23  | | | 
% 240.73/47.23  | | | SIMP: (51) implies:
% 240.73/47.23  | | |   (52)   ~ (all_52_13 = e2)
% 240.73/47.23  | | | 
% 240.73/47.23  | | | REDUCE: (31), (49) imply:
% 240.73/47.23  | | |   (53)   ~ (e3 = e2)
% 240.73/47.23  | | | 
% 240.73/47.23  | | | BETA: splitting (35) gives:
% 240.73/47.23  | | | 
% 240.73/47.23  | | | Case 1:
% 240.73/47.23  | | | | 
% 240.73/47.23  | | | |   (54)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 240.73/47.23  | | | |           = e2)
% 240.73/47.23  | | | | 
% 240.73/47.23  | | | | BETA: splitting (54) gives:
% 240.73/47.23  | | | | 
% 240.73/47.23  | | | | Case 1:
% 240.73/47.23  | | | | | 
% 240.73/47.23  | | | | |   (55)  all_58_9 = e2 & op(e3, e0) = e2
% 240.73/47.23  | | | | | 
% 240.73/47.23  | | | | | ALPHA: (55) implies:
% 240.73/47.23  | | | | |   (56)  op(e3, e0) = e2
% 240.73/47.23  | | | | | 
% 240.73/47.23  | | | | | BETA: splitting (20) gives:
% 240.73/47.23  | | | | | 
% 240.73/47.23  | | | | | Case 1:
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | |   (57)  all_54_2 = e2
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | | REF_CLOSE: (16), (50), (57) are inconsistent by sub-proof #1986.
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | Case 2:
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | |   (58)  all_54_2 = e1 | all_54_2 = e0
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | | BETA: splitting (58) gives:
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | | Case 1:
% 240.73/47.23  | | | | | | | 
% 240.73/47.23  | | | | | | |   (59)  all_54_2 = e1
% 240.73/47.23  | | | | | | | 
% 240.73/47.23  | | | | | | | REF_CLOSE: (14), (16), (59) are inconsistent by sub-proof #1337.
% 240.73/47.23  | | | | | | | 
% 240.73/47.23  | | | | | | Case 2:
% 240.73/47.23  | | | | | | | 
% 240.73/47.23  | | | | | | |   (60)  all_54_2 = e0
% 240.73/47.23  | | | | | | | 
% 240.73/47.23  | | | | | | | COMBINE_EQS: (16), (60) imply:
% 240.73/47.23  | | | | | | |   (61)  all_52_8 = e0
% 240.73/47.23  | | | | | | | 
% 240.73/47.23  | | | | | | | SIMP: (61) implies:
% 240.73/47.23  | | | | | | |   (62)  all_52_8 = e0
% 240.73/47.23  | | | | | | | 
% 240.73/47.23  | | | | | | | REDUCE: (30), (62) imply:
% 240.73/47.23  | | | | | | |   (63)  op(e3, e0) = e3
% 240.73/47.23  | | | | | | | 
% 240.73/47.23  | | | | | | | REF_CLOSE: (19), (34), (56), (63) are inconsistent by sub-proof
% 240.73/47.23  | | | | | | |            #2125.
% 240.73/47.23  | | | | | | | 
% 240.73/47.23  | | | | | | End of split
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | End of split
% 240.73/47.23  | | | | | 
% 240.73/47.23  | | | | Case 2:
% 240.73/47.23  | | | | | 
% 240.73/47.23  | | | | |   (64)  all_58_10 = e2 & op(e2, e0) = e2
% 240.73/47.23  | | | | | 
% 240.73/47.23  | | | | | ALPHA: (64) implies:
% 240.73/47.23  | | | | |   (65)  op(e2, e0) = e2
% 240.73/47.23  | | | | | 
% 240.73/47.23  | | | | | BETA: splitting (21) gives:
% 240.73/47.23  | | | | | 
% 240.73/47.23  | | | | | Case 1:
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | |   (66)  all_54_7 = e3
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | | REF_CLOSE: (29), (39), (66) are inconsistent by sub-proof #2296.
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | Case 2:
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | |   (67)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | | REF_CLOSE: (10), (29), (34), (41), (52), (65), (67) are inconsistent
% 240.73/47.23  | | | | | |            by sub-proof #1995.
% 240.73/47.23  | | | | | | 
% 240.73/47.23  | | | | | End of split
% 240.73/47.23  | | | | | 
% 240.73/47.23  | | | | End of split
% 240.73/47.23  | | | | 
% 240.73/47.23  | | | Case 2:
% 240.73/47.23  | | | | 
% 240.73/47.23  | | | |   (68)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 240.73/47.23  | | | |             e0) = e2)
% 240.73/47.23  | | | | 
% 240.73/47.23  | | | | REF_CLOSE: (13), (19), (32), (34), (43), (68) are inconsistent by
% 240.73/47.23  | | | |            sub-proof #1281.
% 240.73/47.23  | | | | 
% 240.73/47.23  | | | End of split
% 240.73/47.23  | | | 
% 240.73/47.23  | | End of split
% 240.73/47.23  | | 
% 240.73/47.23  | Case 2:
% 240.73/47.23  | | 
% 240.73/47.23  | |   (69)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 240.73/47.23  | |           $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 240.73/47.23  | |             e2) = all_56_15 & $i(all_56_15))
% 240.73/47.23  | | 
% 240.73/47.23  | | BETA: splitting (69) gives:
% 240.73/47.23  | | 
% 240.73/47.23  | | Case 1:
% 240.73/47.23  | | | 
% 240.73/47.23  | | |   (70)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 240.73/47.23  | | |         $i(all_56_13)
% 240.73/47.23  | | | 
% 240.73/47.23  | | | ALPHA: (70) implies:
% 240.73/47.23  | | |   (71)  op(e1, e2) = all_56_13
% 240.73/47.23  | | |   (72)  op(e1, all_56_13) = e1
% 240.73/47.23  | | | 
% 240.73/47.23  | | | REF_CLOSE: (2), (5), (7), (8), (9), (11), (12), (13), (19), (22), (25),
% 240.73/47.23  | | |            (26), (28), (33), (34), (36), (37), (40), (43), (71), (72) are
% 240.73/47.23  | | |            inconsistent by sub-proof #353.
% 240.73/47.23  | | | 
% 240.73/47.23  | | Case 2:
% 240.73/47.23  | | | 
% 240.73/47.23  | | |   (73)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.73/47.23  | | |         $i(all_56_15)
% 240.73/47.23  | | | 
% 240.73/47.23  | | | REF_CLOSE: (1), (2), (15), (24), (27), (32), (34), (73) are inconsistent
% 240.73/47.23  | | |            by sub-proof #1022.
% 240.73/47.23  | | | 
% 240.73/47.23  | | End of split
% 240.73/47.23  | | 
% 240.73/47.23  | End of split
% 240.73/47.23  | 
% 240.73/47.23  End of proof
% 240.73/47.23  
% 240.73/47.23  Sub-proof #353 shows that the following formulas are inconsistent:
% 240.73/47.23  ----------------------------------------------------------------
% 240.73/47.23    (1)  op(e1, e2) = all_56_13
% 240.73/47.23    (2)   ~ (e3 = e0)
% 240.73/47.23    (3)   ~ (e2 = e0)
% 240.73/47.23    (4)  all_58_11 = e1
% 240.73/47.23    (5)  op(e1, e3) = all_6_1
% 240.73/47.23    (6)  op(e1, e0) = all_52_14
% 240.73/47.23    (7)   ~ (e3 = e1)
% 240.73/47.23    (8)  all_58_7 = e2
% 240.73/47.23    (9)  op(e1, e0) = e1
% 240.73/47.23    (10)   ~ (e3 = e2)
% 240.73/47.23    (11)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.73/47.23          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.73/47.23    (12)  op(e1, e3) = e0
% 240.73/47.23    (13)   ~ (all_52_14 = e3)
% 240.73/47.23    (14)  op(e1, e2) = e2
% 240.73/47.23    (15)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.73/47.23          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.73/47.23    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.23    (17)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.73/47.23            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.73/47.23              e3) = all_46_1 & $i(all_46_1))
% 240.73/47.23    (18)  op(e1, all_56_13) = e1
% 240.73/47.23    (19)   ~ (e1 = e0)
% 240.73/47.23    (20)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.73/47.23          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.73/47.23    (21)   ~ (e2 = e1)
% 240.73/47.23  
% 240.73/47.23  Begin of proof
% 240.73/47.23  | 
% 240.73/47.23  | BETA: splitting (17) gives:
% 240.73/47.23  | 
% 240.73/47.23  | Case 1:
% 240.73/47.23  | | 
% 240.73/47.23  | | 
% 240.73/47.23  | | GROUND_INST: instantiating (16) with e2, all_56_13, e2, e1, simplifying with
% 240.73/47.23  | |              (1), (14) gives:
% 240.73/47.23  | |   (22)  all_56_13 = e2
% 240.73/47.23  | | 
% 240.73/47.23  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (15),
% 240.73/47.23  | |            (16), (18), (19), (20), (21), (22) are inconsistent by sub-proof
% 240.73/47.23  | |            #354.
% 240.73/47.23  | | 
% 240.73/47.23  | Case 2:
% 240.73/47.23  | | 
% 240.73/47.23  | |   (23)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.73/47.23  | | 
% 240.73/47.23  | | ALPHA: (23) implies:
% 240.73/47.23  | |   (24)   ~ (all_46_1 = e2)
% 240.73/47.23  | |   (25)  op(e1, e3) = all_46_1
% 240.73/47.23  | | 
% 240.73/47.23  | | GROUND_INST: instantiating (16) with e2, all_56_13, e2, e1, simplifying with
% 240.73/47.23  | |              (1), (14) gives:
% 240.73/47.23  | |   (26)  all_56_13 = e2
% 240.73/47.23  | | 
% 240.73/47.23  | | GROUND_INST: instantiating (16) with e0, all_46_1, e3, e1, simplifying with
% 240.73/47.23  | |              (12), (25) gives:
% 240.73/47.23  | |   (27)  all_46_1 = e0
% 240.73/47.23  | | 
% 240.73/47.23  | | GROUND_INST: instantiating (16) with all_6_1, all_46_1, e3, e1, simplifying
% 240.73/47.23  | |              with (5), (25) gives:
% 240.73/47.23  | |   (28)  all_46_1 = all_6_1
% 240.73/47.23  | | 
% 240.73/47.23  | | COMBINE_EQS: (27), (28) imply:
% 240.73/47.23  | |   (29)  all_6_1 = e0
% 240.73/47.23  | | 
% 240.73/47.23  | | REDUCE: (24), (27) imply:
% 240.73/47.23  | |   (30)   ~ (e2 = e0)
% 240.73/47.23  | | 
% 240.73/47.23  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (15),
% 240.73/47.23  | |            (16), (18), (19), (20), (21), (26) are inconsistent by sub-proof
% 240.73/47.23  | |            #354.
% 240.73/47.23  | | 
% 240.73/47.23  | End of split
% 240.73/47.23  | 
% 240.73/47.23  End of proof
% 240.73/47.23  
% 240.73/47.23  Sub-proof #354 shows that the following formulas are inconsistent:
% 240.73/47.23  ----------------------------------------------------------------
% 240.73/47.23    (1)  op(e1, e2) = all_56_13
% 240.73/47.23    (2)   ~ (e3 = e0)
% 240.73/47.23    (3)   ~ (e2 = e0)
% 240.73/47.23    (4)  all_58_11 = e1
% 240.73/47.23    (5)  op(e1, e0) = all_52_14
% 240.73/47.23    (6)   ~ (e3 = e1)
% 240.73/47.23    (7)  all_58_7 = e2
% 240.73/47.23    (8)  op(e1, e0) = e1
% 240.73/47.23    (9)   ~ (e3 = e2)
% 240.73/47.23    (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.73/47.23          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.73/47.23    (11)   ~ (all_52_14 = e3)
% 240.73/47.23    (12)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.73/47.23          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.73/47.23    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.23    (14)  op(e1, all_56_13) = e1
% 240.73/47.23    (15)   ~ (e1 = e0)
% 240.73/47.23    (16)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.73/47.23          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.73/47.23    (17)  all_56_13 = e2
% 240.73/47.23    (18)   ~ (e2 = e1)
% 240.73/47.23  
% 240.73/47.23  Begin of proof
% 240.73/47.23  | 
% 240.73/47.23  | REDUCE: (14), (17) imply:
% 240.73/47.23  |   (19)  op(e1, e2) = e1
% 240.73/47.23  | 
% 240.73/47.23  | REDUCE: (1), (17) imply:
% 240.73/47.23  |   (20)  op(e1, e2) = e2
% 240.73/47.23  | 
% 240.73/47.23  | GROUND_INST: instantiating (13) with e2, e1, e2, e1, simplifying with (19),
% 240.73/47.23  |              (20) gives:
% 240.73/47.23  |   (21)  e2 = e1
% 240.73/47.23  | 
% 240.73/47.23  | COMBINE_EQS: (7), (21) imply:
% 240.73/47.23  |   (22)  all_58_7 = e1
% 240.73/47.23  | 
% 240.73/47.23  | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 240.73/47.23  |            (16), (18), (22) are inconsistent by sub-proof #1417.
% 240.73/47.23  | 
% 240.73/47.23  End of proof
% 240.73/47.23  
% 240.73/47.23  Sub-proof #355 shows that the following formulas are inconsistent:
% 240.73/47.23  ----------------------------------------------------------------
% 240.73/47.23    (1)  op(e2, e3) = e3
% 240.73/47.23    (2)  op(e3, e3) = e1
% 240.73/47.23    (3)   ~ (e3 = e2)
% 240.73/47.23    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 240.73/47.23    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.23    (6)   ~ (e2 = e1)
% 240.73/47.23  
% 240.73/47.23  Begin of proof
% 240.73/47.23  | 
% 240.73/47.23  | BETA: splitting (4) gives:
% 240.73/47.23  | 
% 240.73/47.23  | Case 1:
% 240.73/47.23  | | 
% 240.73/47.23  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 240.73/47.23  | | 
% 240.73/47.23  | | ALPHA: (7) implies:
% 240.73/47.23  | |   (8)  op(e3, e3) = e2
% 240.73/47.23  | | 
% 240.73/47.23  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2267.
% 240.73/47.23  | | 
% 240.73/47.23  | Case 2:
% 240.73/47.23  | | 
% 240.73/47.23  | |   (9)  all_58_2 = e2 & op(e2, e3) = e2
% 240.73/47.23  | | 
% 240.73/47.23  | | ALPHA: (9) implies:
% 240.73/47.23  | |   (10)  op(e2, e3) = e2
% 240.73/47.23  | | 
% 240.73/47.23  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #1897.
% 240.73/47.23  | | 
% 240.73/47.23  | End of split
% 240.73/47.23  | 
% 240.73/47.23  End of proof
% 240.73/47.23  
% 240.73/47.23  Sub-proof #356 shows that the following formulas are inconsistent:
% 240.73/47.23  ----------------------------------------------------------------
% 240.73/47.23    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 240.73/47.23             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 240.73/47.23           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 240.73/47.23         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 240.73/47.23           $i(all_56_7))
% 240.73/47.23    (2)   ~ (e3 = e0)
% 240.73/47.23    (3)  all_58_1 = e3
% 240.73/47.23    (4)  op(e1, e2) = e1
% 240.73/47.23    (5)   ~ (e2 = e0)
% 240.73/47.23    (6)  op(e1, e2) = all_52_6
% 240.73/47.23    (7)   ~ (all_52_11 = e1)
% 240.73/47.23    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.73/47.23         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.73/47.23    (9)  op(e1, e3) = all_6_1
% 240.73/47.23    (10)  op(e1, e0) = all_52_14
% 240.73/47.23    (11)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 240.73/47.23            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 240.73/47.23              e1) = all_20_1 & $i(all_20_1))
% 240.73/47.23    (12)  op(e0, e2) = e2
% 240.73/47.23    (13)  all_54_11 = all_52_14
% 240.73/47.23    (14)   ~ (all_52_12 = e1)
% 240.73/47.23    (15)   ~ (all_52_12 = all_52_14)
% 240.73/47.23    (16)   ~ (all_52_8 = e1)
% 240.73/47.23    (17)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 240.73/47.23    (18)  all_54_2 = all_52_8
% 240.73/47.23    (19)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 240.73/47.23    (20)   ~ (all_52_11 = e3)
% 240.73/47.23    (21)   ~ (all_52_8 = all_52_12)
% 240.73/47.23    (22)  op(e3, e1) = all_52_8
% 240.73/47.23    (23)   ~ (all_52_14 = e1)
% 240.73/47.23    (24)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.73/47.23    (25)  op(e2, e3) = e2
% 240.73/47.23    (26)   ~ (all_52_14 = e0)
% 240.73/47.23    (27)  op(e0, e3) = e3
% 240.73/47.24    (28)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 240.73/47.24    (29)  op(e0, e1) = e0
% 240.73/47.24    (30)  op(e1, e3) = all_46_1
% 240.73/47.24    (31)  op(e1, e3) = e0
% 240.73/47.24    (32)   ~ (all_52_8 = all_52_11)
% 240.73/47.24    (33)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 240.73/47.24            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 240.73/47.24              e1) = all_34_1 & $i(all_34_1))
% 240.73/47.24    (34)  all_54_3 = all_52_12
% 240.73/47.24    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.24    (36)   ~ (all_52_12 = e3)
% 240.73/47.24    (37)   ~ (e1 = e0)
% 240.73/47.24    (38)  all_54_14 = all_52_11
% 240.73/47.24    (39)  all_56_1 = e1
% 240.73/47.24    (40)   ~ (all_52_8 = e3)
% 240.73/47.24  
% 240.73/47.24  Begin of proof
% 240.73/47.24  | 
% 240.73/47.24  | BETA: splitting (1) gives:
% 240.73/47.24  | 
% 240.73/47.24  | Case 1:
% 240.73/47.24  | | 
% 240.73/47.24  | |   (41)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 240.73/47.24  | |             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 240.73/47.24  | | 
% 240.73/47.24  | | BETA: splitting (41) gives:
% 240.73/47.24  | | 
% 240.73/47.24  | | Case 1:
% 240.73/47.24  | | | 
% 240.73/47.24  | | |   (42)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 240.73/47.24  | | | 
% 240.73/47.24  | | | ALPHA: (42) implies:
% 240.73/47.24  | | |   (43)  op(e3, all_56_1) = e3
% 240.73/47.24  | | | 
% 240.73/47.24  | | | REDUCE: (39), (43) imply:
% 240.73/47.24  | | |   (44)  op(e3, e1) = e3
% 240.73/47.24  | | | 
% 240.73/47.24  | | | REF_CLOSE: (22), (35), (40), (44) are inconsistent by sub-proof #2260.
% 240.73/47.24  | | | 
% 240.73/47.24  | | Case 2:
% 240.73/47.24  | | | 
% 240.73/47.24  | | |   (45)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 240.73/47.24  | | |         $i(all_56_3)
% 240.73/47.24  | | | 
% 240.73/47.24  | | | ALPHA: (45) implies:
% 240.73/47.24  | | |   (46)  op(e2, e3) = all_56_3
% 240.73/47.24  | | |   (47)  op(e2, all_56_3) = e2
% 240.73/47.24  | | | 
% 240.73/47.24  | | | BETA: splitting (11) gives:
% 240.73/47.24  | | | 
% 240.73/47.24  | | | Case 1:
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | GROUND_INST: instantiating (35) with e2, all_56_3, e3, e2, simplifying
% 240.73/47.24  | | | |              with (25), (46) gives:
% 240.73/47.24  | | | |   (48)  all_56_3 = e2
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | REDUCE: (47), (48) imply:
% 240.73/47.24  | | | |   (49)  op(e2, e2) = e2
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (12), (35), (37), (49) are
% 240.73/47.24  | | | |            inconsistent by sub-proof #2130.
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | Case 2:
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | |   (50)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 & $i(all_20_1)
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | ALPHA: (50) implies:
% 240.73/47.24  | | | |   (51)   ~ (all_20_1 = e3)
% 240.73/47.24  | | | |   (52)  op(e0, e1) = all_20_1
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | BETA: splitting (33) gives:
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | Case 1:
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | |   (53)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1)
% 240.73/47.24  | | | | |         = all_34_1 & $i(all_34_0) & $i(all_34_1)
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | ALPHA: (53) implies:
% 240.73/47.24  | | | | |   (54)  op(e0, e1) = all_34_1
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | GROUND_INST: instantiating (35) with all_20_1, all_34_1, e1, e0,
% 240.73/47.24  | | | | |              simplifying with (52), (54) gives:
% 240.73/47.24  | | | | |   (55)  all_34_1 = all_20_1
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | GROUND_INST: instantiating (35) with e0, all_34_1, e1, e0, simplifying
% 240.73/47.24  | | | | |              with (29), (54) gives:
% 240.73/47.24  | | | | |   (56)  all_34_1 = e0
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | GROUND_INST: instantiating (35) with e2, all_56_3, e3, e2, simplifying
% 240.73/47.24  | | | | |              with (25), (46) gives:
% 240.73/47.24  | | | | |   (57)  all_56_3 = e2
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | COMBINE_EQS: (55), (56) imply:
% 240.73/47.24  | | | | |   (58)  all_20_1 = e0
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (12), (35), (37), (47), (51),
% 240.73/47.24  | | | | |            (57), (58) are inconsistent by sub-proof #357.
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | Case 2:
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | |   (59)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | ALPHA: (59) implies:
% 240.73/47.24  | | | | |   (60)   ~ (all_34_1 = e2)
% 240.73/47.24  | | | | |   (61)  op(e0, e1) = all_34_1
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | GROUND_INST: instantiating (35) with all_20_1, all_34_1, e1, e0,
% 240.73/47.24  | | | | |              simplifying with (52), (61) gives:
% 240.73/47.24  | | | | |   (62)  all_34_1 = all_20_1
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | GROUND_INST: instantiating (35) with e0, all_34_1, e1, e0, simplifying
% 240.73/47.24  | | | | |              with (29), (61) gives:
% 240.73/47.24  | | | | |   (63)  all_34_1 = e0
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | GROUND_INST: instantiating (35) with e2, all_56_3, e3, e2, simplifying
% 240.73/47.24  | | | | |              with (25), (46) gives:
% 240.73/47.24  | | | | |   (64)  all_56_3 = e2
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | COMBINE_EQS: (62), (63) imply:
% 240.73/47.24  | | | | |   (65)  all_20_1 = e0
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | REDUCE: (60), (63) imply:
% 240.73/47.24  | | | | |   (66)   ~ (e2 = e0)
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (12), (35), (37), (47), (51),
% 240.73/47.24  | | | | |            (64), (65) are inconsistent by sub-proof #357.
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | End of split
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | End of split
% 240.73/47.24  | | | 
% 240.73/47.24  | | End of split
% 240.73/47.24  | | 
% 240.73/47.24  | Case 2:
% 240.73/47.24  | | 
% 240.73/47.24  | |   (67)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 240.73/47.24  | |           $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0,
% 240.73/47.24  | |             e3) = all_56_7 & $i(all_56_7))
% 240.73/47.24  | | 
% 240.73/47.24  | | BETA: splitting (67) gives:
% 240.73/47.24  | | 
% 240.73/47.24  | | Case 1:
% 240.73/47.24  | | | 
% 240.73/47.24  | | |   (68)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 240.73/47.24  | | |         $i(all_56_5)
% 240.73/47.24  | | | 
% 240.73/47.24  | | | ALPHA: (68) implies:
% 240.73/47.24  | | |   (69)  op(e1, e3) = all_56_5
% 240.73/47.24  | | |   (70)  op(e1, all_56_5) = e1
% 240.73/47.24  | | | 
% 240.73/47.24  | | | BETA: splitting (17) gives:
% 240.73/47.24  | | | 
% 240.73/47.24  | | | Case 1:
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | |   (71)  all_54_11 = e2
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | COMBINE_EQS: (13), (71) imply:
% 240.73/47.24  | | | |   (72)  all_52_14 = e2
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | SIMP: (72) implies:
% 240.73/47.24  | | | |   (73)  all_52_14 = e2
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | REDUCE: (15), (73) imply:
% 240.73/47.24  | | | |   (74)   ~ (all_52_12 = e2)
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | REDUCE: (10), (73) imply:
% 240.73/47.24  | | | |   (75)  op(e1, e0) = e2
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | BETA: splitting (19) gives:
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | Case 1:
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | |   (76)  all_54_3 = e3
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | REF_CLOSE: (34), (36), (76) are inconsistent by sub-proof #2057.
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | Case 2:
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | |   (77)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | BETA: splitting (77) gives:
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | | Case 1:
% 240.73/47.24  | | | | | | 
% 240.73/47.24  | | | | | |   (78)  all_54_3 = e2
% 240.73/47.24  | | | | | | 
% 240.73/47.24  | | | | | | REF_CLOSE: (34), (74), (78) are inconsistent by sub-proof #2290.
% 240.73/47.24  | | | | | | 
% 240.73/47.24  | | | | | Case 2:
% 240.73/47.24  | | | | | | 
% 240.73/47.24  | | | | | |   (79)  all_54_3 = e1 | all_54_3 = e0
% 240.73/47.24  | | | | | | 
% 240.73/47.24  | | | | | | BETA: splitting (79) gives:
% 240.73/47.24  | | | | | | 
% 240.73/47.24  | | | | | | Case 1:
% 240.73/47.24  | | | | | | | 
% 240.73/47.24  | | | | | | |   (80)  all_54_3 = e1
% 240.73/47.24  | | | | | | | 
% 240.73/47.24  | | | | | | | REF_CLOSE: (14), (34), (80) are inconsistent by sub-proof #2289.
% 240.73/47.24  | | | | | | | 
% 240.73/47.24  | | | | | | Case 2:
% 240.73/47.24  | | | | | | | 
% 240.73/47.24  | | | | | | |   (81)  all_54_3 = e0
% 240.73/47.24  | | | | | | | 
% 240.73/47.24  | | | | | | | COMBINE_EQS: (34), (81) imply:
% 240.73/47.24  | | | | | | |   (82)  all_52_12 = e0
% 240.73/47.24  | | | | | | | 
% 240.73/47.24  | | | | | | | SIMP: (82) implies:
% 240.73/47.24  | | | | | | |   (83)  all_52_12 = e0
% 240.73/47.24  | | | | | | | 
% 240.73/47.24  | | | | | | | REDUCE: (21), (83) imply:
% 240.73/47.24  | | | | | | |   (84)   ~ (all_52_8 = e0)
% 240.73/47.24  | | | | | | | 
% 240.73/47.24  | | | | | | | BETA: splitting (28) gives:
% 240.73/47.24  | | | | | | | 
% 240.73/47.24  | | | | | | | Case 1:
% 240.73/47.24  | | | | | | | | 
% 240.73/47.24  | | | | | | | |   (85)  all_54_2 = e3
% 240.73/47.24  | | | | | | | | 
% 240.73/47.24  | | | | | | | | REF_CLOSE: (18), (40), (85) are inconsistent by sub-proof #1987.
% 240.73/47.24  | | | | | | | | 
% 240.73/47.24  | | | | | | | Case 2:
% 240.73/47.24  | | | | | | | | 
% 240.73/47.24  | | | | | | | |   (86)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 240.73/47.24  | | | | | | | | 
% 240.73/47.24  | | | | | | | | BETA: splitting (86) gives:
% 240.73/47.24  | | | | | | | | 
% 240.73/47.24  | | | | | | | | Case 1:
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | |   (87)  all_54_2 = e2
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | COMBINE_EQS: (18), (87) imply:
% 240.73/47.24  | | | | | | | | |   (88)  all_52_8 = e2
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | SIMP: (88) implies:
% 240.73/47.24  | | | | | | | | |   (89)  all_52_8 = e2
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | REDUCE: (32), (89) imply:
% 240.73/47.24  | | | | | | | | |   (90)   ~ (all_52_11 = e2)
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | SIMP: (90) implies:
% 240.73/47.24  | | | | | | | | |   (91)   ~ (all_52_11 = e2)
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | REDUCE: (16), (89) imply:
% 240.73/47.24  | | | | | | | | |   (92)   ~ (e2 = e1)
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | BETA: splitting (24) gives:
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | Case 1:
% 240.73/47.24  | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | |   (93)  all_54_14 = e3
% 240.73/47.24  | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | COMBINE_EQS: (38), (93) imply:
% 240.73/47.24  | | | | | | | | | |   (94)  all_52_11 = e3
% 240.73/47.24  | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | REDUCE: (20), (94) imply:
% 240.73/47.24  | | | | | | | | | |   (95)  $false
% 240.73/47.24  | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | CLOSE: (95) is inconsistent.
% 240.73/47.24  | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | Case 2:
% 240.73/47.24  | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | |   (96)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.73/47.24  | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | BETA: splitting (96) gives:
% 240.73/47.24  | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | Case 1:
% 240.73/47.24  | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | |   (97)  all_54_14 = e2
% 240.73/47.24  | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | REF_CLOSE: (38), (91), (97) are inconsistent by sub-proof
% 240.73/47.24  | | | | | | | | | | |            #1856.
% 240.73/47.24  | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | Case 2:
% 240.73/47.24  | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | |   (98)  all_54_14 = e1 | all_54_14 = e0
% 240.73/47.24  | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | BETA: splitting (98) gives:
% 240.73/47.24  | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | Case 1:
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | |   (99)  all_54_14 = e1
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | COMBINE_EQS: (38), (99) imply:
% 240.73/47.24  | | | | | | | | | | | |   (100)  all_52_11 = e1
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | REDUCE: (7), (100) imply:
% 240.73/47.24  | | | | | | | | | | | |   (101)  $false
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | CLOSE: (101) is inconsistent.
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | Case 2:
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | GROUND_INST: instantiating (35) with e0, all_46_1, e3, e1,
% 240.73/47.24  | | | | | | | | | | | |              simplifying with (30), (31) gives:
% 240.73/47.24  | | | | | | | | | | | |   (102)  all_46_1 = e0
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_46_1, all_56_5, e3,
% 240.73/47.24  | | | | | | | | | | | |              e1, simplifying with (30), (69) gives:
% 240.73/47.24  | | | | | | | | | | | |   (103)  all_56_5 = all_46_1
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_6_1, all_56_5, e3, e1,
% 240.73/47.24  | | | | | | | | | | | |              simplifying with (9), (69) gives:
% 240.73/47.24  | | | | | | | | | | | |   (104)  all_56_5 = all_6_1
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | COMBINE_EQS: (103), (104) imply:
% 240.73/47.24  | | | | | | | | | | | |   (105)  all_46_1 = all_6_1
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | SIMP: (105) implies:
% 240.73/47.24  | | | | | | | | | | | |   (106)  all_46_1 = all_6_1
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | COMBINE_EQS: (102), (106) imply:
% 240.73/47.24  | | | | | | | | | | | |   (107)  all_6_1 = e0
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | SIMP: (107) implies:
% 240.73/47.24  | | | | | | | | | | | |   (108)  all_6_1 = e0
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | COMBINE_EQS: (104), (108) imply:
% 240.73/47.24  | | | | | | | | | | | |   (109)  all_56_5 = e0
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | REDUCE: (70), (109) imply:
% 240.73/47.24  | | | | | | | | | | | |   (110)  op(e1, e0) = e1
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | | REF_CLOSE: (35), (75), (92), (110) are inconsistent by
% 240.73/47.24  | | | | | | | | | | | |            sub-proof #2019.
% 240.73/47.24  | | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | | End of split
% 240.73/47.24  | | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | | End of split
% 240.73/47.24  | | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | End of split
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | Case 2:
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | |   (111)  all_54_2 = e1 | all_54_2 = e0
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | | REF_CLOSE: (16), (18), (84), (111) are inconsistent by
% 240.73/47.24  | | | | | | | | |            sub-proof #1336.
% 240.73/47.24  | | | | | | | | | 
% 240.73/47.24  | | | | | | | | End of split
% 240.73/47.24  | | | | | | | | 
% 240.73/47.24  | | | | | | | End of split
% 240.73/47.24  | | | | | | | 
% 240.73/47.24  | | | | | | End of split
% 240.73/47.24  | | | | | | 
% 240.73/47.24  | | | | | End of split
% 240.73/47.24  | | | | | 
% 240.73/47.24  | | | | End of split
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | Case 2:
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | |   (112)  all_54_11 = e1 | all_54_11 = e0
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | | REF_CLOSE: (13), (23), (26), (112) are inconsistent by sub-proof #2174.
% 240.73/47.24  | | | | 
% 240.73/47.24  | | | End of split
% 240.73/47.24  | | | 
% 240.73/47.24  | | Case 2:
% 240.73/47.24  | | | 
% 240.73/47.24  | | |   (113)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 240.73/47.24  | | |          $i(all_56_7)
% 240.73/47.24  | | | 
% 240.73/47.24  | | | ALPHA: (113) implies:
% 240.73/47.24  | | |   (114)  op(e0, e3) = all_56_7
% 240.73/47.24  | | |   (115)  op(e0, all_56_7) = e0
% 240.73/47.24  | | | 
% 240.73/47.24  | | | REF_CLOSE: (2), (27), (35), (114), (115) are inconsistent by sub-proof
% 240.73/47.24  | | |            #2070.
% 240.73/47.24  | | | 
% 240.73/47.24  | | End of split
% 240.73/47.24  | | 
% 240.73/47.24  | End of split
% 240.73/47.24  | 
% 240.73/47.24  End of proof
% 240.73/47.24  
% 240.73/47.24  Sub-proof #357 shows that the following formulas are inconsistent:
% 240.73/47.24  ----------------------------------------------------------------
% 240.73/47.24    (1)  all_58_1 = e3
% 240.73/47.24    (2)  op(e1, e2) = e1
% 240.73/47.24    (3)   ~ (e2 = e0)
% 240.73/47.24    (4)  op(e1, e2) = all_52_6
% 240.73/47.24    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.73/47.24         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.73/47.24    (6)  all_56_3 = e2
% 240.73/47.24    (7)  op(e0, e2) = e2
% 240.73/47.24    (8)  all_20_1 = e0
% 240.73/47.24    (9)  op(e2, all_56_3) = e2
% 240.73/47.24    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.24    (11)   ~ (e1 = e0)
% 240.73/47.24    (12)   ~ (all_20_1 = e3)
% 240.73/47.24  
% 240.73/47.24  Begin of proof
% 240.73/47.24  | 
% 240.73/47.24  | REDUCE: (8), (12) imply:
% 240.73/47.24  |   (13)   ~ (e3 = e0)
% 240.73/47.24  | 
% 240.73/47.24  | SIMP: (13) implies:
% 240.73/47.24  |   (14)   ~ (e3 = e0)
% 240.73/47.24  | 
% 240.73/47.24  | REDUCE: (6), (9) imply:
% 240.73/47.24  |   (15)  op(e2, e2) = e2
% 240.73/47.24  | 
% 240.73/47.24  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (10), (11), (14), (15) are
% 240.73/47.24  |            inconsistent by sub-proof #2130.
% 240.73/47.24  | 
% 240.73/47.24  End of proof
% 240.73/47.24  
% 240.73/47.24  Sub-proof #358 shows that the following formulas are inconsistent:
% 240.73/47.24  ----------------------------------------------------------------
% 240.73/47.24    (1)   ~ (e3 = e0)
% 240.73/47.24    (2)   ~ (e2 = e0)
% 240.73/47.24    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 240.73/47.24         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.73/47.24    (4)  op(e1, e0) = all_52_14
% 240.73/47.24    (5)   ~ (all_52_13 = e1)
% 240.73/47.24    (6)  all_58_15 = e3
% 240.73/47.24    (7)   ~ (e3 = e1)
% 240.73/47.24    (8)   ~ (all_52_12 = e1)
% 240.73/47.24    (9)   ~ (e3 = e2)
% 240.73/47.24    (10)  op(e3, e0) = all_52_12
% 240.73/47.24    (11)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.73/47.24          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.73/47.24    (12)   ~ (all_52_14 = e3)
% 240.73/47.24    (13)  all_58_7 = e1
% 240.73/47.24    (14)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.73/47.24          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.73/47.24    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.24    (16)   ~ (e1 = e0)
% 240.73/47.24    (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.73/47.24          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.73/47.24    (18)  op(e2, e0) = all_52_13
% 240.73/47.24    (19)   ~ (e2 = e1)
% 240.73/47.24  
% 240.73/47.24  Begin of proof
% 240.73/47.24  | 
% 240.73/47.24  | BETA: splitting (3) gives:
% 240.73/47.24  | 
% 240.73/47.24  | Case 1:
% 240.73/47.24  | | 
% 240.73/47.24  | |   (20)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 240.73/47.24  | |           e1)
% 240.73/47.24  | | 
% 240.73/47.24  | | BETA: splitting (20) gives:
% 240.73/47.24  | | 
% 240.73/47.24  | | Case 1:
% 240.73/47.24  | | | 
% 240.73/47.24  | | |   (21)  all_58_9 = e1 & op(e3, e0) = e1
% 240.73/47.24  | | | 
% 240.73/47.24  | | | REF_CLOSE: (8), (10), (15), (21) are inconsistent by sub-proof #2278.
% 240.73/47.24  | | | 
% 240.73/47.24  | | Case 2:
% 240.73/47.24  | | | 
% 240.73/47.24  | | |   (22)  all_58_10 = e1 & op(e2, e0) = e1
% 240.73/47.24  | | | 
% 240.73/47.24  | | | REF_CLOSE: (5), (15), (18), (22) are inconsistent by sub-proof #2277.
% 240.73/47.24  | | | 
% 240.73/47.24  | | End of split
% 240.73/47.24  | | 
% 240.73/47.24  | Case 2:
% 240.73/47.24  | | 
% 240.73/47.24  | |   (23)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.73/47.24  | |           e1)
% 240.73/47.24  | | 
% 240.73/47.24  | | BETA: splitting (23) gives:
% 240.73/47.24  | | 
% 240.73/47.24  | | Case 1:
% 240.73/47.24  | | | 
% 240.73/47.24  | | |   (24)  all_58_11 = e1 & op(e1, e0) = e1
% 240.73/47.24  | | | 
% 240.73/47.24  | | | ALPHA: (24) implies:
% 240.73/47.24  | | |   (25)  all_58_11 = e1
% 240.73/47.24  | | |   (26)  op(e1, e0) = e1
% 240.73/47.24  | | | 
% 240.73/47.24  | | | REF_CLOSE: (1), (2), (4), (7), (9), (11), (12), (13), (14), (15), (16),
% 240.73/47.24  | | |            (17), (19), (25), (26) are inconsistent by sub-proof #1417.
% 240.73/47.24  | | | 
% 240.73/47.24  | | Case 2:
% 240.73/47.24  | | | 
% 240.73/47.24  | | |   (27)  all_58_15 = e1 & op(e0, e0) = e1
% 240.73/47.24  | | | 
% 240.73/47.24  | | | REF_CLOSE: (6), (7), (27) are inconsistent by sub-proof #1393.
% 240.73/47.24  | | | 
% 240.73/47.24  | | End of split
% 240.73/47.24  | | 
% 240.73/47.24  | End of split
% 240.73/47.24  | 
% 240.73/47.24  End of proof
% 240.73/47.24  
% 240.73/47.24  Sub-proof #359 shows that the following formulas are inconsistent:
% 240.73/47.24  ----------------------------------------------------------------
% 240.73/47.24    (1)   ~ (e3 = e0)
% 240.73/47.24    (2)  op(e1, e2) = e1
% 240.73/47.24    (3)   ~ (e2 = e0)
% 240.73/47.24    (4)  op(e1, e2) = all_52_6
% 240.73/47.24    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.73/47.24         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.73/47.24    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.73/47.24         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.73/47.24    (7)   ~ (e3 = e1)
% 240.73/47.25    (8)  op(e2, e2) = e0
% 240.73/47.25    (9)  all_58_15 = e2
% 240.73/47.25    (10)   ~ (e3 = e2)
% 240.73/47.25    (11)  all_58_15 = e1
% 240.73/47.25    (12)  all_58_7 = e1
% 240.73/47.25    (13)  all_58_1 = e2
% 240.73/47.25    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.25    (15)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.73/47.25          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.73/47.25    (16)   ~ (e1 = e0)
% 240.73/47.25    (17)   ~ (e2 = e1)
% 240.73/47.25  
% 240.73/47.25  Begin of proof
% 240.73/47.25  | 
% 240.73/47.25  | COMBINE_EQS: (9), (11) imply:
% 240.73/47.25  |   (18)  e2 = e1
% 240.73/47.25  | 
% 240.73/47.25  | COMBINE_EQS: (13), (18) imply:
% 240.73/47.25  |   (19)  all_58_1 = e1
% 240.73/47.25  | 
% 240.73/47.25  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (14), (15),
% 240.73/47.25  |            (16), (17), (19) are inconsistent by sub-proof #1714.
% 240.73/47.25  | 
% 240.73/47.25  End of proof
% 240.73/47.25  
% 240.73/47.25  Sub-proof #360 shows that the following formulas are inconsistent:
% 240.73/47.25  ----------------------------------------------------------------
% 240.73/47.25    (1)   ~ (e3 = e0)
% 240.73/47.25    (2)  op(e0, e1) = all_52_11
% 240.73/47.25    (3)   ~ (all_52_11 = e3)
% 240.73/47.25    (4)  op(e3, e1) = all_52_8
% 240.73/47.25    (5)  op(e2, e1) = all_52_9
% 240.73/47.25    (6)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.73/47.25    (7)   ~ (all_52_11 = e0)
% 240.73/47.25    (8)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.73/47.25         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.73/47.25    (9)   ~ (all_52_9 = e3)
% 240.73/47.25    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.25    (11)   ~ (all_52_8 = e3)
% 240.73/47.25  
% 240.73/47.25  Begin of proof
% 240.73/47.25  | 
% 240.73/47.25  | BETA: splitting (6) gives:
% 240.73/47.25  | 
% 240.73/47.25  | Case 1:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (12)  all_58_8 = e0 & op(e1, e1) = e0
% 240.73/47.25  | | 
% 240.73/47.25  | | ALPHA: (12) implies:
% 240.73/47.25  | |   (13)  op(e1, e1) = e0
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (13) are
% 240.73/47.25  | |            inconsistent by sub-proof #1010.
% 240.73/47.25  | | 
% 240.73/47.25  | Case 2:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (14)  all_58_14 = e0 & op(e0, e1) = e0
% 240.73/47.25  | | 
% 240.73/47.25  | | ALPHA: (14) implies:
% 240.73/47.25  | |   (15)  op(e0, e1) = e0
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (2), (7), (10), (15) are inconsistent by sub-proof #1911.
% 240.73/47.25  | | 
% 240.73/47.25  | End of split
% 240.73/47.25  | 
% 240.73/47.25  End of proof
% 240.73/47.25  
% 240.73/47.25  Sub-proof #361 shows that the following formulas are inconsistent:
% 240.73/47.25  ----------------------------------------------------------------
% 240.73/47.25    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.73/47.25           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.73/47.25             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.73/47.25           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.73/47.25             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.73/47.25           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.73/47.25           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.73/47.25    (2)  op(e2, e3) = e3
% 240.73/47.25    (3)  op(e3, e2) = e2
% 240.73/47.25    (4)   ~ (e3 = e2)
% 240.73/47.25    (5)   ~ (all_52_2 = e3)
% 240.73/47.25    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.25    (7)  op(e1, e3) = all_52_2
% 240.73/47.25  
% 240.73/47.25  Begin of proof
% 240.73/47.25  | 
% 240.73/47.25  | BETA: splitting (1) gives:
% 240.73/47.25  | 
% 240.73/47.25  | Case 1:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.73/47.25  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.73/47.25  | |        op(e2, e3) = e3
% 240.73/47.25  | | 
% 240.73/47.25  | | ALPHA: (8) implies:
% 240.73/47.25  | |   (9)  op(e3, e2) = e3
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #2193.
% 240.73/47.25  | | 
% 240.73/47.25  | Case 2:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.73/47.25  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.73/47.25  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.73/47.25  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.73/47.25  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (2), (4), (5), (6), (7), (10) are inconsistent by sub-proof
% 240.73/47.25  | |            #1889.
% 240.73/47.25  | | 
% 240.73/47.25  | End of split
% 240.73/47.25  | 
% 240.73/47.25  End of proof
% 240.73/47.25  
% 240.73/47.25  Sub-proof #362 shows that the following formulas are inconsistent:
% 240.73/47.25  ----------------------------------------------------------------
% 240.73/47.25    (1)  all_58_3 = e3 & op(e2, e2) = e3
% 240.73/47.25    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.73/47.25         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.73/47.25    (3)   ~ (e3 = e0)
% 240.73/47.25    (4)   ~ (e2 = e0)
% 240.73/47.25    (5)   ~ (e3 = e1)
% 240.73/47.25    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.73/47.25         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.73/47.25    (7)  op(e3, e3) = e1
% 240.73/47.25    (8)   ~ (e3 = e2)
% 240.73/47.25    (9)  all_58_9 = e3
% 240.73/47.25    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.25    (11)  all_58_3 = e0
% 240.73/47.25    (12)  all_58_4 = e0
% 240.73/47.25    (13)   ~ (e2 = e1)
% 240.73/47.25  
% 240.73/47.25  Begin of proof
% 240.73/47.25  | 
% 240.73/47.25  | ALPHA: (1) implies:
% 240.73/47.25  |   (14)  all_58_3 = e3
% 240.73/47.25  | 
% 240.73/47.25  | COMBINE_EQS: (11), (14) imply:
% 240.73/47.25  |   (15)  e3 = e0
% 240.73/47.25  | 
% 240.73/47.25  | SIMP: (15) implies:
% 240.73/47.25  |   (16)  e3 = e0
% 240.73/47.25  | 
% 240.73/47.25  | COMBINE_EQS: (9), (16) imply:
% 240.73/47.25  |   (17)  all_58_9 = e0
% 240.73/47.25  | 
% 240.73/47.25  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (12), (13), (17) are
% 240.73/47.25  |            inconsistent by sub-proof #1190.
% 240.73/47.25  | 
% 240.73/47.25  End of proof
% 240.73/47.25  
% 240.73/47.25  Sub-proof #363 shows that the following formulas are inconsistent:
% 240.73/47.25  ----------------------------------------------------------------
% 240.73/47.25    (1)  op(e1, e0) = all_52_14
% 240.73/47.25    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.73/47.25             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.73/47.25           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.73/47.25             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.73/47.25           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 240.73/47.25           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.73/47.25           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.73/47.25    (3)   ~ (all_52_14 = e0)
% 240.73/47.25    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.25    (5)  op(e1, e0) = e2
% 240.73/47.25    (6)   ~ (e1 = e0)
% 240.73/47.25    (7)  op(e2, e0) = e1
% 240.73/47.25    (8)  op(e2, e0) = all_52_13
% 240.73/47.25    (9)   ~ (e2 = e1)
% 240.73/47.25  
% 240.73/47.25  Begin of proof
% 240.73/47.25  | 
% 240.73/47.25  | BETA: splitting (2) gives:
% 240.73/47.25  | 
% 240.73/47.25  | Case 1:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (10)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.73/47.25  | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) =
% 240.73/47.25  | |         e0 & op(e0, e2) = e0
% 240.73/47.25  | | 
% 240.73/47.25  | | ALPHA: (10) implies:
% 240.73/47.25  | |   (11)  op(e2, e0) = e0
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (4), (6), (7), (8), (11) are inconsistent by sub-proof #1778.
% 240.73/47.25  | | 
% 240.73/47.25  | Case 2:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (12)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.73/47.25  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.73/47.25  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.73/47.25  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.73/47.25  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (1), (3), (4), (5), (9), (12) are inconsistent by sub-proof
% 240.73/47.25  | |            #1960.
% 240.73/47.25  | | 
% 240.73/47.25  | End of split
% 240.73/47.25  | 
% 240.73/47.25  End of proof
% 240.73/47.25  
% 240.73/47.25  Sub-proof #364 shows that the following formulas are inconsistent:
% 240.73/47.25  ----------------------------------------------------------------
% 240.73/47.25    (1)   ~ (all_52_3 = e0)
% 240.73/47.25    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.73/47.25             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.73/47.25           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 240.73/47.25           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.73/47.25           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 240.73/47.25           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.73/47.25           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.73/47.25    (3)  op(e0, e3) = all_52_3
% 240.73/47.25    (4)  op(e3, e1) = e0
% 240.73/47.25    (5)  all_56_31 = e0
% 240.73/47.25    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.25    (7)   ~ (e1 = e0)
% 240.73/47.25  
% 240.73/47.25  Begin of proof
% 240.73/47.25  | 
% 240.73/47.25  | BETA: splitting (2) gives:
% 240.73/47.25  | 
% 240.73/47.25  | Case 1:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (8)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.73/47.25  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.73/47.25  | |        op(e1, e3) = e1
% 240.73/47.25  | | 
% 240.73/47.25  | | ALPHA: (8) implies:
% 240.73/47.25  | |   (9)  op(e3, e1) = e1
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (4), (6), (7), (9) are inconsistent by sub-proof #2089.
% 240.73/47.25  | | 
% 240.73/47.25  | Case 2:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.73/47.25  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 240.73/47.25  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.73/47.25  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.73/47.25  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #2308.
% 240.73/47.25  | | 
% 240.73/47.25  | End of split
% 240.73/47.25  | 
% 240.73/47.25  End of proof
% 240.73/47.25  
% 240.73/47.25  Sub-proof #365 shows that the following formulas are inconsistent:
% 240.73/47.25  ----------------------------------------------------------------
% 240.73/47.25    (1)  all_58_8 = e1 & op(e1, e1) = e1
% 240.73/47.25    (2)  all_58_8 = e3
% 240.73/47.25    (3)   ~ (e3 = e1)
% 240.73/47.25  
% 240.73/47.25  Begin of proof
% 240.73/47.25  | 
% 240.73/47.25  | ALPHA: (1) implies:
% 240.73/47.25  |   (4)  all_58_8 = e1
% 240.73/47.25  | 
% 240.73/47.25  | COMBINE_EQS: (2), (4) imply:
% 240.73/47.25  |   (5)  e3 = e1
% 240.73/47.25  | 
% 240.73/47.25  | SIMP: (5) implies:
% 240.73/47.25  |   (6)  e3 = e1
% 240.73/47.25  | 
% 240.73/47.25  | REDUCE: (3), (6) imply:
% 240.73/47.25  |   (7)  $false
% 240.73/47.25  | 
% 240.73/47.25  | CLOSE: (7) is inconsistent.
% 240.73/47.25  | 
% 240.73/47.25  End of proof
% 240.73/47.25  
% 240.73/47.25  Sub-proof #366 shows that the following formulas are inconsistent:
% 240.73/47.25  ----------------------------------------------------------------
% 240.73/47.25    (1)  all_54_14 = all_6_0
% 240.73/47.25    (2)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 240.73/47.25    (3)  op(e3, e1) = e0
% 240.73/47.25    (4)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.73/47.25    (5)  op(e2, e1) = all_52_9
% 240.73/47.25    (6)   ~ (all_52_9 = all_6_0)
% 240.73/47.25    (7)   ~ (all_6_0 = e0)
% 240.73/47.25    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.25    (9)   ~ (e1 = e0)
% 240.73/47.25    (10)   ~ (all_6_0 = e2)
% 240.73/47.25  
% 240.73/47.25  Begin of proof
% 240.73/47.25  | 
% 240.73/47.25  | BETA: splitting (2) gives:
% 240.73/47.25  | 
% 240.73/47.25  | Case 1:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (11)  all_58_4 = e1 & op(e3, e1) = e1
% 240.73/47.25  | | 
% 240.73/47.25  | | ALPHA: (11) implies:
% 240.73/47.25  | |   (12)  op(e3, e1) = e1
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (3), (8), (9), (12) are inconsistent by sub-proof #2089.
% 240.73/47.25  | | 
% 240.73/47.25  | Case 2:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (13)  all_58_5 = e1 & op(e2, e1) = e1
% 240.73/47.25  | | 
% 240.73/47.25  | | ALPHA: (13) implies:
% 240.73/47.25  | |   (14)  op(e2, e1) = e1
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (10), (14) are inconsistent by
% 240.73/47.25  | |            sub-proof #446.
% 240.73/47.25  | | 
% 240.73/47.25  | End of split
% 240.73/47.25  | 
% 240.73/47.25  End of proof
% 240.73/47.25  
% 240.73/47.25  Sub-proof #367 shows that the following formulas are inconsistent:
% 240.73/47.25  ----------------------------------------------------------------
% 240.73/47.25    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.73/47.25    (2)  op(e1, e0) = all_52_14
% 240.73/47.25    (3)   ~ (e3 = e1)
% 240.73/47.25    (4)   ~ (all_52_14 = e1)
% 240.73/47.25    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.25    (6)  all_58_8 = e3
% 240.73/47.25  
% 240.73/47.25  Begin of proof
% 240.73/47.25  | 
% 240.73/47.25  | BETA: splitting (1) gives:
% 240.73/47.25  | 
% 240.73/47.25  | Case 1:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (7)  all_58_8 = e1 & op(e1, e1) = e1
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (3), (6), (7) are inconsistent by sub-proof #406.
% 240.73/47.25  | | 
% 240.73/47.25  | Case 2:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (8)  all_58_11 = e1 & op(e1, e0) = e1
% 240.73/47.25  | | 
% 240.73/47.25  | | ALPHA: (8) implies:
% 240.73/47.25  | |   (9)  op(e1, e0) = e1
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2304.
% 240.73/47.25  | | 
% 240.73/47.25  | End of split
% 240.73/47.25  | 
% 240.73/47.25  End of proof
% 240.73/47.25  
% 240.73/47.25  Sub-proof #368 shows that the following formulas are inconsistent:
% 240.73/47.25  ----------------------------------------------------------------
% 240.73/47.25    (1)   ~ (e2 = e0)
% 240.73/47.25    (2)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.73/47.25         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.73/47.25    (3)  op(e0, e2) = e3
% 240.73/47.25    (4)   ~ (e3 = e2)
% 240.73/47.25    (5)  op(e2, e2) = e1
% 240.73/47.25    (6)  op(e3, e2) = e0
% 240.73/47.25    (7)  all_58_7 = e1
% 240.73/47.25    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.25    (9)   ~ (e2 = e1)
% 240.73/47.25  
% 240.73/47.25  Begin of proof
% 240.73/47.25  | 
% 240.73/47.25  | BETA: splitting (2) gives:
% 240.73/47.25  | 
% 240.73/47.25  | Case 1:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 240.73/47.25  | |           e2)
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (1), (5), (6), (8), (9), (10) are inconsistent by sub-proof #369.
% 240.73/47.25  | | 
% 240.73/47.25  | Case 2:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (11)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 240.73/47.25  | |           e2)
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (3), (4), (7), (8), (9), (11) are inconsistent by sub-proof
% 240.73/47.25  | |            #1716.
% 240.73/47.25  | | 
% 240.73/47.25  | End of split
% 240.73/47.25  | 
% 240.73/47.25  End of proof
% 240.73/47.25  
% 240.73/47.25  Sub-proof #369 shows that the following formulas are inconsistent:
% 240.73/47.25  ----------------------------------------------------------------
% 240.73/47.25    (1)   ~ (e2 = e0)
% 240.73/47.25    (2)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 240.73/47.25    (3)  op(e2, e2) = e1
% 240.73/47.25    (4)  op(e3, e2) = e0
% 240.73/47.25    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.25    (6)   ~ (e2 = e1)
% 240.73/47.25  
% 240.73/47.25  Begin of proof
% 240.73/47.25  | 
% 240.73/47.25  | BETA: splitting (2) gives:
% 240.73/47.25  | 
% 240.73/47.25  | Case 1:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (7)  all_58_1 = e2 & op(e3, e2) = e2
% 240.73/47.25  | | 
% 240.73/47.25  | | ALPHA: (7) implies:
% 240.73/47.25  | |   (8)  op(e3, e2) = e2
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2026.
% 240.73/47.25  | | 
% 240.73/47.25  | Case 2:
% 240.73/47.25  | | 
% 240.73/47.25  | |   (9)  all_58_3 = e2 & op(e2, e2) = e2
% 240.73/47.25  | | 
% 240.73/47.25  | | ALPHA: (9) implies:
% 240.73/47.25  | |   (10)  op(e2, e2) = e2
% 240.73/47.25  | | 
% 240.73/47.25  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #2235.
% 240.73/47.25  | | 
% 240.73/47.25  | End of split
% 240.73/47.25  | 
% 240.73/47.25  End of proof
% 240.73/47.25  
% 240.73/47.25  Sub-proof #370 shows that the following formulas are inconsistent:
% 240.73/47.25  ----------------------------------------------------------------
% 240.73/47.25    (1)  op(e1, e0) = e0
% 240.73/47.25    (2)   ~ (e2 = e0)
% 240.73/47.25    (3)  all_58_12 = e2
% 240.73/47.25    (4)  op(e0, e3) = all_52_3
% 240.73/47.25    (5)   ~ (e3 = e1)
% 240.73/47.25    (6)  op(e0, all_52_3) = e0
% 240.73/47.25    (7)   ~ (e3 = e2)
% 240.73/47.25    (8)  op(e1, e1) = e3
% 240.73/47.26    (9)  op(e0, e2) = all_52_7
% 240.73/47.26    (10)   ~ (all_52_7 = e0)
% 240.73/47.26    (11)  all_58_12 = e2 & op(e0, e3) = e2
% 240.73/47.26    (12)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.73/47.26          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.73/47.26    (13)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.73/47.26          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.73/47.26    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.26    (15)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.73/47.26          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.73/47.26    (16)   ~ (e1 = e0)
% 240.73/47.26    (17)  op(e3, e3) = e0
% 240.73/47.26    (18)  op(e3, e2) = e3
% 240.73/47.26    (19)  all_58_2 = e3
% 240.73/47.26    (20)  all_58_3 = e0
% 240.73/47.26    (21)   ~ (e2 = e1)
% 240.73/47.26  
% 240.73/47.26  Begin of proof
% 240.73/47.26  | 
% 240.73/47.26  | BETA: splitting (12) gives:
% 240.73/47.26  | 
% 240.73/47.26  | Case 1:
% 240.73/47.26  | | 
% 240.73/47.26  | |   (22)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 240.73/47.26  | |           e1)
% 240.73/47.26  | | 
% 240.73/47.26  | | REF_CLOSE: (5), (14), (16), (17), (19), (22) are inconsistent by sub-proof
% 240.73/47.26  | |            #1486.
% 240.73/47.26  | | 
% 240.73/47.26  | Case 2:
% 240.73/47.26  | | 
% 240.73/47.26  | |   (23)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 240.73/47.26  | |           e1)
% 240.73/47.26  | | 
% 240.73/47.26  | | BETA: splitting (23) gives:
% 240.73/47.26  | | 
% 240.73/47.26  | | Case 1:
% 240.73/47.26  | | | 
% 240.73/47.26  | | |   (24)  all_58_6 = e1 & op(e1, e3) = e1
% 240.73/47.26  | | | 
% 240.73/47.26  | | | ALPHA: (24) implies:
% 240.73/47.26  | | |   (25)  op(e1, e3) = e1
% 240.73/47.26  | | | 
% 240.73/47.26  | | | BETA: splitting (13) gives:
% 240.73/47.26  | | | 
% 240.73/47.26  | | | Case 1:
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | |   (26)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 240.73/47.26  | | | |           = e2)
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | | BETA: splitting (26) gives:
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | | Case 1:
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | |   (27)  all_58_6 = e2 & op(e1, e3) = e2
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | | ALPHA: (27) implies:
% 240.73/47.26  | | | | |   (28)  op(e1, e3) = e2
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | | REF_CLOSE: (14), (21), (25), (28) are inconsistent by sub-proof #2226.
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | Case 2:
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | |   (29)  all_58_7 = e2 & op(e1, e2) = e2
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | | ALPHA: (29) implies:
% 240.73/47.26  | | | | |   (30)  all_58_7 = e2
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | | BETA: splitting (15) gives:
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | | Case 1:
% 240.73/47.26  | | | | | | 
% 240.73/47.26  | | | | | |   (31)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 240.73/47.26  | | | | | |             e2) = e1)
% 240.73/47.26  | | | | | | 
% 240.73/47.26  | | | | | | REF_CLOSE: (5), (14), (16), (18), (20), (31) are inconsistent by
% 240.73/47.26  | | | | | |            sub-proof #380.
% 240.73/47.26  | | | | | | 
% 240.73/47.26  | | | | | Case 2:
% 240.73/47.26  | | | | | | 
% 240.73/47.26  | | | | | |   (32)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 240.73/47.26  | | | | | |             e2) = e1)
% 240.73/47.26  | | | | | | 
% 240.73/47.26  | | | | | | BETA: splitting (32) gives:
% 240.73/47.26  | | | | | | 
% 240.73/47.26  | | | | | | Case 1:
% 240.73/47.26  | | | | | | | 
% 240.73/47.26  | | | | | | |   (33)  all_58_7 = e1 & op(e1, e2) = e1
% 240.73/47.26  | | | | | | | 
% 240.73/47.26  | | | | | | | REF_CLOSE: (21), (30), (33) are inconsistent by sub-proof #2224.
% 240.73/47.26  | | | | | | | 
% 240.73/47.26  | | | | | | Case 2:
% 240.73/47.26  | | | | | | | 
% 240.73/47.26  | | | | | | | 
% 240.73/47.26  | | | | | | | ALPHA: (11) implies:
% 240.73/47.26  | | | | | | |   (34)  op(e0, e3) = e2
% 240.73/47.26  | | | | | | | 
% 240.73/47.26  | | | | | | | GROUND_INST: instantiating (14) with all_52_3, e2, e3, e0,
% 240.73/47.26  | | | | | | |              simplifying with (4), (34) gives:
% 240.73/47.26  | | | | | | |   (35)  all_52_3 = e2
% 240.73/47.26  | | | | | | | 
% 240.73/47.26  | | | | | | | REDUCE: (6), (35) imply:
% 240.73/47.26  | | | | | | |   (36)  op(e0, e2) = e0
% 240.73/47.26  | | | | | | | 
% 240.73/47.26  | | | | | | | REF_CLOSE: (9), (10), (14), (36) are inconsistent by sub-proof
% 240.73/47.26  | | | | | | |            #2252.
% 240.73/47.26  | | | | | | | 
% 240.73/47.26  | | | | | | End of split
% 240.73/47.26  | | | | | | 
% 240.73/47.26  | | | | | End of split
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | End of split
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | Case 2:
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | |   (37)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0)
% 240.73/47.26  | | | |           = e2)
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | | REF_CLOSE: (1), (2), (7), (8), (14), (37) are inconsistent by sub-proof
% 240.73/47.26  | | | |            #379.
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | End of split
% 240.73/47.26  | | | 
% 240.73/47.26  | | Case 2:
% 240.73/47.26  | | | 
% 240.73/47.26  | | |   (38)  all_58_12 = e1 & op(e0, e3) = e1
% 240.73/47.26  | | | 
% 240.73/47.26  | | | ALPHA: (38) implies:
% 240.73/47.26  | | |   (39)  all_58_12 = e1
% 240.73/47.26  | | | 
% 240.73/47.26  | | | REF_CLOSE: (3), (21), (39) are inconsistent by sub-proof #1757.
% 240.73/47.26  | | | 
% 240.73/47.26  | | End of split
% 240.73/47.26  | | 
% 240.73/47.26  | End of split
% 240.73/47.26  | 
% 240.73/47.26  End of proof
% 240.73/47.26  
% 240.73/47.26  Sub-proof #371 shows that the following formulas are inconsistent:
% 240.73/47.26  ----------------------------------------------------------------
% 240.73/47.26    (1)   ~ (all_52_3 = e0)
% 240.73/47.26    (2)  op(e1, e0) = e0
% 240.73/47.26    (3)  op(e0, e3) = all_52_3
% 240.73/47.26    (4)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 240.73/47.26           $i(all_56_29)) | (all_56_30 = e0 & op(e0, all_56_31) = e0)
% 240.73/47.26    (5)  all_56_31 = e3
% 240.73/47.26    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.26    (7)   ~ (e1 = e0)
% 240.73/47.26  
% 240.73/47.26  Begin of proof
% 240.73/47.26  | 
% 240.73/47.26  | BETA: splitting (4) gives:
% 240.73/47.26  | 
% 240.73/47.26  | Case 1:
% 240.73/47.26  | | 
% 240.73/47.26  | |   (8)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 240.73/47.26  | |        $i(all_56_29)
% 240.73/47.26  | | 
% 240.73/47.26  | | ALPHA: (8) implies:
% 240.73/47.26  | |   (9)  op(e1, e0) = all_56_29
% 240.73/47.26  | |   (10)  op(e1, all_56_29) = e1
% 240.73/47.26  | | 
% 240.73/47.26  | | REF_CLOSE: (2), (6), (7), (9), (10) are inconsistent by sub-proof #372.
% 240.73/47.26  | | 
% 240.73/47.26  | Case 2:
% 240.73/47.26  | | 
% 240.73/47.26  | |   (11)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.73/47.26  | | 
% 240.73/47.26  | | ALPHA: (11) implies:
% 240.73/47.26  | |   (12)  op(e0, all_56_31) = e0
% 240.73/47.26  | | 
% 240.73/47.26  | | REDUCE: (5), (12) imply:
% 240.73/47.26  | |   (13)  op(e0, e3) = e0
% 240.73/47.26  | | 
% 240.73/47.26  | | REF_CLOSE: (1), (3), (6), (13) are inconsistent by sub-proof #2331.
% 240.73/47.26  | | 
% 240.73/47.26  | End of split
% 240.73/47.26  | 
% 240.73/47.26  End of proof
% 240.73/47.26  
% 240.73/47.26  Sub-proof #372 shows that the following formulas are inconsistent:
% 240.73/47.26  ----------------------------------------------------------------
% 240.73/47.26    (1)  op(e1, e0) = e0
% 240.73/47.26    (2)  op(e1, all_56_29) = e1
% 240.73/47.26    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.26    (4)   ~ (e1 = e0)
% 240.73/47.26    (5)  op(e1, e0) = all_56_29
% 240.73/47.26  
% 240.73/47.26  Begin of proof
% 240.73/47.26  | 
% 240.73/47.26  | GROUND_INST: instantiating (3) with e0, all_56_29, e0, e1, simplifying with
% 240.73/47.26  |              (1), (5) gives:
% 240.73/47.26  |   (6)  all_56_29 = e0
% 240.73/47.26  | 
% 240.73/47.26  | REDUCE: (2), (6) imply:
% 240.73/47.26  |   (7)  op(e1, e0) = e1
% 240.73/47.26  | 
% 240.73/47.26  | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #2284.
% 240.73/47.26  | 
% 240.73/47.26  End of proof
% 240.73/47.26  
% 240.73/47.26  Sub-proof #373 shows that the following formulas are inconsistent:
% 240.73/47.26  ----------------------------------------------------------------
% 240.73/47.26    (1)  op(e2, e0) = all_56_27
% 240.73/47.26    (2)   ~ (e3 = e0)
% 240.73/47.26    (3)  all_58_1 = e3
% 240.73/47.26    (4)  all_58_13 = e2 & op(e0, e2) = e2
% 240.73/47.26    (5)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.73/47.26           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 240.73/47.26           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 240.73/47.26         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.73/47.26           $i(all_56_15))
% 240.73/47.26    (6)  op(e1, e2) = all_52_6
% 240.73/47.26    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.73/47.26         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.73/47.26    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.73/47.26         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.73/47.26    (9)  op(e2, all_56_27) = e2
% 240.73/47.26    (10)   ~ (all_52_7 = e3)
% 240.73/47.26    (11)  op(e0, e3) = all_52_3
% 240.73/47.26    (12)   ~ (all_52_6 = e0)
% 240.73/47.26    (13)   ~ (e3 = e1)
% 240.73/47.26    (14)  op(e2, e2) = e0
% 240.73/47.26    (15)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 240.73/47.26            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 240.73/47.26              e3) = all_26_1 & $i(all_26_1))
% 240.73/47.26    (16)  op(e1, e3) = e2
% 240.73/47.26    (17)  op(e0, e3) = e1
% 240.73/47.26    (18)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 240.73/47.26            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 240.73/47.26              e0) = all_48_1 & $i(all_48_1))
% 240.73/47.26    (19)  all_56_11 = e0
% 240.73/47.26    (20)  op(e1, e1) = e3
% 240.73/47.26    (21)   ~ (all_52_6 = e3)
% 240.73/47.26    (22)  op(e0, e2) = all_52_7
% 240.73/47.26    (23)   ~ (all_52_7 = e0)
% 240.73/47.26    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.26    (25)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.73/47.26            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.73/47.26              e3) = all_46_1 & $i(all_46_1))
% 240.73/47.26    (26)  op(e1, e3) = all_52_2
% 240.73/47.26    (27)   ~ (all_52_6 = all_52_7)
% 240.73/47.26    (28)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.73/47.26          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.73/47.26    (29)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.73/47.26          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.73/47.26    (30)   ~ (e1 = e0)
% 240.73/47.26    (31)  op(e3, e3) = e0
% 240.73/47.26    (32)  op(e3, e2) = e3
% 240.73/47.26    (33)  all_58_3 = e0
% 240.73/47.26    (34)   ~ (e2 = e1)
% 240.73/47.26  
% 240.73/47.26  Begin of proof
% 240.73/47.26  | 
% 240.73/47.26  | ALPHA: (4) implies:
% 240.73/47.26  |   (35)  all_58_13 = e2
% 240.73/47.26  |   (36)  op(e0, e2) = e2
% 240.73/47.26  | 
% 240.73/47.26  | BETA: splitting (28) gives:
% 240.73/47.26  | 
% 240.73/47.26  | Case 1:
% 240.73/47.26  | | 
% 240.73/47.26  | |   (37)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 240.73/47.26  | |           e1)
% 240.73/47.26  | | 
% 240.73/47.26  | | REF_CLOSE: (13), (24), (30), (32), (33), (37) are inconsistent by sub-proof
% 240.73/47.26  | |            #380.
% 240.73/47.26  | | 
% 240.73/47.26  | Case 2:
% 240.73/47.26  | | 
% 240.73/47.26  | |   (38)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 240.73/47.26  | |           e1)
% 240.73/47.26  | | 
% 240.73/47.26  | | BETA: splitting (38) gives:
% 240.73/47.26  | | 
% 240.73/47.26  | | Case 1:
% 240.73/47.26  | | | 
% 240.73/47.26  | | |   (39)  all_58_7 = e1 & op(e1, e2) = e1
% 240.73/47.26  | | | 
% 240.73/47.26  | | | ALPHA: (39) implies:
% 240.73/47.26  | | |   (40)  all_58_7 = e1
% 240.73/47.26  | | |   (41)  op(e1, e2) = e1
% 240.73/47.26  | | | 
% 240.73/47.26  | | | GROUND_INST: instantiating (24) with all_52_7, e2, e2, e0, simplifying
% 240.73/47.26  | | |              with (22), (36) gives:
% 240.73/47.26  | | |   (42)  all_52_7 = e2
% 240.73/47.26  | | | 
% 240.73/47.26  | | | GROUND_INST: instantiating (24) with all_52_3, e1, e3, e0, simplifying
% 240.73/47.26  | | |              with (11), (17) gives:
% 240.73/47.26  | | |   (43)  all_52_3 = e1
% 240.73/47.26  | | | 
% 240.73/47.26  | | | GROUND_INST: instantiating (24) with all_52_6, e1, e2, e1, simplifying
% 240.73/47.26  | | |              with (6), (41) gives:
% 240.73/47.26  | | |   (44)  all_52_6 = e1
% 240.73/47.26  | | | 
% 240.73/47.26  | | | GROUND_INST: instantiating (24) with all_52_2, e2, e3, e1, simplifying
% 240.73/47.26  | | |              with (16), (26) gives:
% 240.73/47.26  | | |   (45)  all_52_2 = e2
% 240.73/47.26  | | | 
% 240.73/47.26  | | | REDUCE: (27), (42), (44) imply:
% 240.73/47.26  | | |   (46)   ~ (e2 = e1)
% 240.73/47.26  | | | 
% 240.73/47.26  | | | REDUCE: (21), (44) imply:
% 240.73/47.26  | | |   (47)   ~ (e3 = e1)
% 240.73/47.26  | | | 
% 240.73/47.26  | | | REDUCE: (10), (42) imply:
% 240.73/47.26  | | |   (48)   ~ (e3 = e2)
% 240.73/47.26  | | | 
% 240.73/47.26  | | | SIMP: (48) implies:
% 240.73/47.26  | | |   (49)   ~ (e3 = e2)
% 240.73/47.26  | | | 
% 240.73/47.26  | | | REDUCE: (23), (42) imply:
% 240.73/47.26  | | |   (50)   ~ (e2 = e0)
% 240.73/47.26  | | | 
% 240.73/47.26  | | | BETA: splitting (5) gives:
% 240.73/47.26  | | | 
% 240.73/47.26  | | | Case 1:
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | |   (51)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.73/47.26  | | | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | | BETA: splitting (51) gives:
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | | Case 1:
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | |   (52)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9
% 240.73/47.26  | | | | |         & $i(all_56_9)
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | | REF_CLOSE: (2), (15), (17), (24), (31), (32), (52) are inconsistent by
% 240.73/47.26  | | | | |            sub-proof #377.
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | Case 2:
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | |   (53)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | | ALPHA: (53) implies:
% 240.73/47.26  | | | | |   (54)  op(e2, all_56_11) = e2
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | | REDUCE: (19), (54) imply:
% 240.73/47.26  | | | | |   (55)  op(e2, e0) = e2
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | | REF_CLOSE: (1), (9), (14), (18), (24), (50), (55) are inconsistent by
% 240.73/47.26  | | | | |            sub-proof #1059.
% 240.73/47.26  | | | | | 
% 240.73/47.26  | | | | End of split
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | Case 2:
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | |   (56)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 240.73/47.26  | | | |           all_56_13 & $i(all_56_13)) | (all_56_14 = e0 & op(e0,
% 240.73/47.26  | | | |             all_56_15) = e0 & op(e0, e2) = all_56_15 & $i(all_56_15))
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | | REF_CLOSE: (2), (3), (6), (7), (8), (13), (14), (16), (20), (22), (23),
% 240.73/47.26  | | | |            (24), (25), (29), (30), (34), (36), (40), (41), (49), (50),
% 240.73/47.26  | | | |            (56) are inconsistent by sub-proof #376.
% 240.73/47.26  | | | | 
% 240.73/47.26  | | | End of split
% 240.73/47.26  | | | 
% 240.73/47.26  | | Case 2:
% 240.73/47.26  | | | 
% 240.73/47.26  | | |   (57)  all_58_13 = e1 & op(e0, e2) = e1
% 240.73/47.26  | | | 
% 240.73/47.26  | | | REF_CLOSE: (34), (35), (57) are inconsistent by sub-proof #1751.
% 240.73/47.26  | | | 
% 240.73/47.26  | | End of split
% 240.73/47.26  | | 
% 240.73/47.26  | End of split
% 240.73/47.26  | 
% 240.73/47.26  End of proof
% 240.73/47.26  
% 240.73/47.26  Sub-proof #374 shows that the following formulas are inconsistent:
% 240.73/47.26  ----------------------------------------------------------------
% 240.73/47.26    (1)   ~ (e2 = e0)
% 240.73/47.26    (2)   ~ (e3 = e2)
% 240.73/47.26    (3)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.73/47.26    (4)  all_58_14 = e0
% 240.73/47.26    (5)  op(e0, e0) = e3
% 240.73/47.26    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.26  
% 240.73/47.26  Begin of proof
% 240.73/47.26  | 
% 240.73/47.26  | BETA: splitting (3) gives:
% 240.73/47.26  | 
% 240.73/47.26  | Case 1:
% 240.73/47.26  | | 
% 240.73/47.26  | |   (7)  all_58_14 = e2 & op(e0, e1) = e2
% 240.73/47.26  | | 
% 240.73/47.26  | | ALPHA: (7) implies:
% 240.73/47.26  | |   (8)  all_58_14 = e2
% 240.73/47.26  | | 
% 240.73/47.26  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #2114.
% 240.73/47.26  | | 
% 240.73/47.26  | Case 2:
% 240.73/47.26  | | 
% 240.73/47.26  | |   (9)  all_58_15 = e2 & op(e0, e0) = e2
% 240.73/47.26  | | 
% 240.73/47.26  | | ALPHA: (9) implies:
% 240.73/47.26  | |   (10)  op(e0, e0) = e2
% 240.73/47.26  | | 
% 240.73/47.26  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1388.
% 240.73/47.26  | | 
% 240.73/47.26  | End of split
% 240.73/47.26  | 
% 240.73/47.26  End of proof
% 240.73/47.26  
% 240.73/47.26  Sub-proof #375 shows that the following formulas are inconsistent:
% 240.73/47.26  ----------------------------------------------------------------
% 240.73/47.26    (1)  op(e3, all_52_12) = e3
% 240.73/47.26    (2)   ~ (e3 = e0)
% 240.73/47.26    (3)  all_58_1 = e3
% 240.73/47.26    (4)  all_58_13 = e2 & op(e0, e2) = e2
% 240.73/47.26    (5)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.73/47.26           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 240.73/47.26           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 240.73/47.26         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.73/47.26           $i(all_56_15))
% 240.73/47.26    (6)  op(e1, e2) = all_52_6
% 240.73/47.26    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.73/47.26         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.73/47.27    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.73/47.27         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.73/47.27    (9)   ~ (all_52_12 = e0)
% 240.73/47.27    (10)   ~ (all_52_7 = e3)
% 240.73/47.27    (11)  op(e0, e3) = all_52_3
% 240.73/47.27    (12)   ~ (all_52_6 = e0)
% 240.73/47.27    (13)   ~ (e3 = e1)
% 240.73/47.27    (14)  op(e2, e2) = e0
% 240.73/47.27    (15)   ~ (all_52_12 = all_52_13)
% 240.73/47.27    (16)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 240.73/47.27            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 240.73/47.27              e3) = all_26_1 & $i(all_26_1))
% 240.73/47.27    (17)  op(e1, e3) = e2
% 240.73/47.27    (18)  op(e3, e1) = all_52_8
% 240.73/47.27    (19)  op(e0, e3) = e1
% 240.73/47.27    (20)  all_56_11 = e0
% 240.73/47.27    (21)  op(e1, e1) = e3
% 240.73/47.27    (22)   ~ (all_52_6 = e3)
% 240.73/47.27    (23)  op(e0, e2) = all_52_7
% 240.73/47.27    (24)   ~ (all_52_7 = e0)
% 240.73/47.27    (25)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 240.73/47.27    (26)  all_54_3 = all_52_12
% 240.73/47.27    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.27            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.27    (28)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.73/47.27            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.73/47.27              e3) = all_46_1 & $i(all_46_1))
% 240.73/47.27    (29)  op(e1, e3) = all_52_2
% 240.73/47.27    (30)   ~ (all_52_6 = all_52_7)
% 240.73/47.27    (31)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.73/47.27          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.73/47.27    (32)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.73/47.27          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.73/47.27    (33)   ~ (e1 = e0)
% 240.73/47.27    (34)  op(e3, e3) = e0
% 240.73/47.27    (35)  op(e3, e2) = e3
% 240.73/47.27    (36)  op(e2, e0) = all_52_13
% 240.73/47.27    (37)  all_58_3 = e0
% 240.73/47.27    (38)   ~ (e2 = e1)
% 240.73/47.27    (39)   ~ (all_52_8 = e3)
% 240.73/47.27  
% 240.73/47.27  Begin of proof
% 240.73/47.27  | 
% 240.73/47.27  | ALPHA: (4) implies:
% 240.73/47.27  |   (40)  all_58_13 = e2
% 240.73/47.27  |   (41)  op(e0, e2) = e2
% 240.73/47.27  | 
% 240.73/47.27  | BETA: splitting (31) gives:
% 240.73/47.27  | 
% 240.73/47.27  | Case 1:
% 240.73/47.27  | | 
% 240.73/47.27  | |   (42)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 240.73/47.27  | |           e1)
% 240.73/47.27  | | 
% 240.73/47.27  | | REF_CLOSE: (13), (27), (33), (35), (37), (42) are inconsistent by sub-proof
% 240.73/47.27  | |            #380.
% 240.73/47.27  | | 
% 240.73/47.27  | Case 2:
% 240.73/47.27  | | 
% 240.73/47.27  | |   (43)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 240.73/47.27  | |           e1)
% 240.73/47.27  | | 
% 240.73/47.27  | | BETA: splitting (43) gives:
% 240.73/47.27  | | 
% 240.73/47.27  | | Case 1:
% 240.73/47.27  | | | 
% 240.73/47.27  | | |   (44)  all_58_7 = e1 & op(e1, e2) = e1
% 240.73/47.27  | | | 
% 240.73/47.27  | | | ALPHA: (44) implies:
% 240.73/47.27  | | |   (45)  all_58_7 = e1
% 240.73/47.27  | | |   (46)  op(e1, e2) = e1
% 240.73/47.27  | | | 
% 240.73/47.27  | | | GROUND_INST: instantiating (27) with all_52_7, e2, e2, e0, simplifying
% 240.73/47.27  | | |              with (23), (41) gives:
% 240.73/47.27  | | |   (47)  all_52_7 = e2
% 240.73/47.27  | | | 
% 240.73/47.27  | | | GROUND_INST: instantiating (27) with all_52_3, e1, e3, e0, simplifying
% 240.73/47.27  | | |              with (11), (19) gives:
% 240.73/47.27  | | |   (48)  all_52_3 = e1
% 240.73/47.27  | | | 
% 240.73/47.27  | | | GROUND_INST: instantiating (27) with all_52_6, e1, e2, e1, simplifying
% 240.73/47.27  | | |              with (6), (46) gives:
% 240.73/47.27  | | |   (49)  all_52_6 = e1
% 240.73/47.27  | | | 
% 240.73/47.27  | | | GROUND_INST: instantiating (27) with all_52_2, e2, e3, e1, simplifying
% 240.73/47.27  | | |              with (17), (29) gives:
% 240.73/47.27  | | |   (50)  all_52_2 = e2
% 240.73/47.27  | | | 
% 240.73/47.27  | | | REDUCE: (30), (47), (49) imply:
% 240.73/47.27  | | |   (51)   ~ (e2 = e1)
% 240.73/47.27  | | | 
% 240.73/47.27  | | | REDUCE: (22), (49) imply:
% 240.73/47.27  | | |   (52)   ~ (e3 = e1)
% 240.73/47.27  | | | 
% 240.73/47.27  | | | REDUCE: (10), (47) imply:
% 240.73/47.27  | | |   (53)   ~ (e3 = e2)
% 240.73/47.27  | | | 
% 240.73/47.27  | | | SIMP: (53) implies:
% 240.73/47.27  | | |   (54)   ~ (e3 = e2)
% 240.73/47.27  | | | 
% 240.73/47.27  | | | REDUCE: (24), (47) imply:
% 240.73/47.27  | | |   (55)   ~ (e2 = e0)
% 240.73/47.27  | | | 
% 240.73/47.27  | | | BETA: splitting (5) gives:
% 240.73/47.27  | | | 
% 240.73/47.27  | | | Case 1:
% 240.73/47.27  | | | | 
% 240.73/47.27  | | | |   (56)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.73/47.27  | | | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 240.73/47.27  | | | | 
% 240.73/47.27  | | | | BETA: splitting (56) gives:
% 240.73/47.27  | | | | 
% 240.73/47.27  | | | | Case 1:
% 240.73/47.27  | | | | | 
% 240.73/47.27  | | | | |   (57)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9
% 240.73/47.27  | | | | |         & $i(all_56_9)
% 240.73/47.27  | | | | | 
% 240.73/47.27  | | | | | REF_CLOSE: (2), (16), (19), (27), (34), (35), (57) are inconsistent by
% 240.73/47.27  | | | | |            sub-proof #377.
% 240.73/47.27  | | | | | 
% 240.73/47.27  | | | | Case 2:
% 240.73/47.27  | | | | | 
% 240.73/47.27  | | | | |   (58)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 240.73/47.27  | | | | | 
% 240.73/47.27  | | | | | ALPHA: (58) implies:
% 240.73/47.27  | | | | |   (59)  op(e2, all_56_11) = e2
% 240.73/47.27  | | | | | 
% 240.73/47.27  | | | | | REDUCE: (20), (59) imply:
% 240.73/47.27  | | | | |   (60)  op(e2, e0) = e2
% 240.73/47.27  | | | | | 
% 240.73/47.27  | | | | | BETA: splitting (28) gives:
% 240.73/47.27  | | | | | 
% 240.73/47.27  | | | | | Case 1:
% 240.73/47.27  | | | | | | 
% 240.73/47.27  | | | | | | 
% 240.73/47.27  | | | | | | GROUND_INST: instantiating (27) with all_52_13, e2, e0, e2,
% 240.73/47.27  | | | | | |              simplifying with (36), (60) gives:
% 240.73/47.27  | | | | | |   (61)  all_52_13 = e2
% 240.73/47.27  | | | | | | 
% 240.73/47.27  | | | | | | REDUCE: (15), (61) imply:
% 240.73/47.27  | | | | | |   (62)   ~ (all_52_12 = e2)
% 240.73/47.27  | | | | | | 
% 240.73/47.27  | | | | | | BETA: splitting (25) gives:
% 240.73/47.27  | | | | | | 
% 240.73/47.27  | | | | | | Case 1:
% 240.73/47.27  | | | | | | | 
% 240.73/47.27  | | | | | | |   (63)  all_54_3 = e2
% 240.73/47.27  | | | | | | | 
% 240.73/47.27  | | | | | | | COMBINE_EQS: (26), (63) imply:
% 240.73/47.27  | | | | | | |   (64)  all_52_12 = e2
% 240.73/47.27  | | | | | | | 
% 240.73/47.27  | | | | | | | REDUCE: (62), (64) imply:
% 240.73/47.27  | | | | | | |   (65)  $false
% 240.73/47.27  | | | | | | | 
% 240.73/47.27  | | | | | | | CLOSE: (65) is inconsistent.
% 240.73/47.27  | | | | | | | 
% 240.73/47.27  | | | | | | Case 2:
% 240.73/47.27  | | | | | | | 
% 240.73/47.27  | | | | | | |   (66)  all_54_3 = e1 | all_54_3 = e0
% 240.73/47.27  | | | | | | | 
% 240.73/47.27  | | | | | | | BETA: splitting (66) gives:
% 240.73/47.27  | | | | | | | 
% 240.73/47.27  | | | | | | | Case 1:
% 240.73/47.27  | | | | | | | | 
% 240.73/47.27  | | | | | | | |   (67)  all_54_3 = e1
% 240.73/47.27  | | | | | | | | 
% 240.73/47.27  | | | | | | | | COMBINE_EQS: (26), (67) imply:
% 240.73/47.27  | | | | | | | |   (68)  all_52_12 = e1
% 240.73/47.27  | | | | | | | | 
% 240.73/47.27  | | | | | | | | SIMP: (68) implies:
% 240.73/47.27  | | | | | | | |   (69)  all_52_12 = e1
% 240.73/47.27  | | | | | | | | 
% 240.73/47.27  | | | | | | | | REDUCE: (1), (69) imply:
% 240.73/47.27  | | | | | | | |   (70)  op(e3, e1) = e3
% 240.73/47.27  | | | | | | | | 
% 240.73/47.27  | | | | | | | | REF_CLOSE: (18), (27), (39), (70) are inconsistent by sub-proof
% 240.73/47.27  | | | | | | | |            #2260.
% 240.73/47.27  | | | | | | | | 
% 240.73/47.27  | | | | | | | Case 2:
% 240.73/47.27  | | | | | | | | 
% 240.73/47.27  | | | | | | | |   (71)  all_54_3 = e0
% 240.73/47.27  | | | | | | | | 
% 240.73/47.27  | | | | | | | | REF_CLOSE: (9), (26), (71) are inconsistent by sub-proof #2288.
% 240.73/47.27  | | | | | | | | 
% 240.73/47.27  | | | | | | | End of split
% 240.73/47.27  | | | | | | | 
% 240.73/47.27  | | | | | | End of split
% 240.73/47.27  | | | | | | 
% 240.73/47.27  | | | | | Case 2:
% 240.73/47.27  | | | | | | 
% 240.73/47.27  | | | | | |   (72)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.73/47.27  | | | | | | 
% 240.73/47.27  | | | | | | REF_CLOSE: (17), (27), (72) are inconsistent by sub-proof #395.
% 240.73/47.27  | | | | | | 
% 240.73/47.27  | | | | | End of split
% 240.73/47.27  | | | | | 
% 240.73/47.27  | | | | End of split
% 240.73/47.27  | | | | 
% 240.73/47.27  | | | Case 2:
% 240.73/47.27  | | | | 
% 240.73/47.27  | | | |   (73)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 240.73/47.27  | | | |           all_56_13 & $i(all_56_13)) | (all_56_14 = e0 & op(e0,
% 240.73/47.27  | | | |             all_56_15) = e0 & op(e0, e2) = all_56_15 & $i(all_56_15))
% 240.73/47.27  | | | | 
% 240.73/47.27  | | | | REF_CLOSE: (2), (3), (6), (7), (8), (13), (14), (17), (21), (23), (24),
% 240.73/47.27  | | | |            (27), (28), (32), (33), (38), (41), (45), (46), (54), (55),
% 240.73/47.27  | | | |            (73) are inconsistent by sub-proof #376.
% 240.73/47.27  | | | | 
% 240.73/47.27  | | | End of split
% 240.73/47.27  | | | 
% 240.73/47.27  | | Case 2:
% 240.73/47.27  | | | 
% 240.73/47.27  | | |   (74)  all_58_13 = e1 & op(e0, e2) = e1
% 240.73/47.27  | | | 
% 240.73/47.27  | | | REF_CLOSE: (38), (40), (74) are inconsistent by sub-proof #1751.
% 240.73/47.27  | | | 
% 240.73/47.27  | | End of split
% 240.73/47.27  | | 
% 240.73/47.27  | End of split
% 240.73/47.27  | 
% 240.73/47.27  End of proof
% 240.73/47.27  
% 240.73/47.27  Sub-proof #376 shows that the following formulas are inconsistent:
% 240.73/47.27  ----------------------------------------------------------------
% 240.73/47.27    (1)   ~ (e3 = e0)
% 240.73/47.27    (2)  all_58_1 = e3
% 240.73/47.27    (3)  op(e1, e2) = e1
% 240.73/47.27    (4)   ~ (e2 = e0)
% 240.73/47.27    (5)  op(e1, e2) = all_52_6
% 240.73/47.27    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.73/47.27         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.73/47.27    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.73/47.27         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.73/47.27    (8)  op(e0, e2) = e2
% 240.73/47.27    (9)   ~ (e3 = e1)
% 240.73/47.27    (10)  op(e2, e2) = e0
% 240.73/47.27    (11)  op(e1, e3) = e2
% 240.73/47.27    (12)   ~ (e3 = e2)
% 240.73/47.27    (13)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 240.73/47.27            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 240.73/47.27            = all_56_15 & $i(all_56_15))
% 240.73/47.27    (14)  op(e1, e1) = e3
% 240.73/47.27    (15)  op(e0, e2) = all_52_7
% 240.73/47.27    (16)   ~ (all_52_7 = e0)
% 240.73/47.27    (17)  all_58_7 = e1
% 240.73/47.27    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.27            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.27    (19)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.73/47.27            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.73/47.27              e3) = all_46_1 & $i(all_46_1))
% 240.73/47.27    (20)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.73/47.27          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.73/47.27    (21)   ~ (e1 = e0)
% 240.73/47.27    (22)   ~ (e2 = e1)
% 240.73/47.27  
% 240.73/47.27  Begin of proof
% 240.73/47.27  | 
% 240.73/47.27  | BETA: splitting (13) gives:
% 240.73/47.27  | 
% 240.73/47.27  | Case 1:
% 240.73/47.27  | | 
% 240.73/47.27  | |   (23)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 240.73/47.27  | |         $i(all_56_13)
% 240.73/47.27  | | 
% 240.73/47.27  | | ALPHA: (23) implies:
% 240.73/47.27  | |   (24)  op(e1, e2) = all_56_13
% 240.73/47.27  | |   (25)  op(e1, all_56_13) = e1
% 240.73/47.27  | | 
% 240.73/47.27  | | BETA: splitting (19) gives:
% 240.73/47.27  | | 
% 240.73/47.27  | | Case 1:
% 240.73/47.27  | | | 
% 240.73/47.27  | | | 
% 240.73/47.27  | | | GROUND_INST: instantiating (18) with e1, all_56_13, e2, e1, simplifying
% 240.73/47.27  | | |              with (3), (24) gives:
% 240.73/47.27  | | |   (26)  all_56_13 = e1
% 240.73/47.27  | | | 
% 240.73/47.27  | | | REDUCE: (25), (26) imply:
% 240.73/47.27  | | |   (27)  op(e1, e1) = e1
% 240.73/47.27  | | | 
% 240.73/47.27  | | | GROUND_INST: instantiating (18) with e3, e1, e1, e1, simplifying with
% 240.73/47.27  | | |              (14), (27) gives:
% 240.73/47.27  | | |   (28)  e3 = e1
% 240.73/47.27  | | | 
% 240.73/47.27  | | | COMBINE_EQS: (2), (28) imply:
% 240.73/47.27  | | |   (29)  all_58_1 = e1
% 240.73/47.27  | | | 
% 240.73/47.27  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (12), (17), (18),
% 240.73/47.27  | | |            (20), (21), (22), (29) are inconsistent by sub-proof #1714.
% 240.73/47.27  | | | 
% 240.73/47.27  | | Case 2:
% 240.73/47.27  | | | 
% 240.73/47.27  | | |   (30)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.73/47.27  | | | 
% 240.73/47.27  | | | REF_CLOSE: (11), (18), (30) are inconsistent by sub-proof #395.
% 240.73/47.27  | | | 
% 240.73/47.27  | | End of split
% 240.73/47.27  | | 
% 240.73/47.27  | Case 2:
% 240.73/47.27  | | 
% 240.73/47.27  | |   (31)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 240.73/47.27  | |         $i(all_56_15)
% 240.73/47.27  | | 
% 240.73/47.27  | | ALPHA: (31) implies:
% 240.73/47.27  | |   (32)  op(e0, e2) = all_56_15
% 240.73/47.27  | |   (33)  op(e0, all_56_15) = e0
% 240.73/47.27  | | 
% 240.73/47.27  | | BETA: splitting (19) gives:
% 240.73/47.27  | | 
% 240.73/47.27  | | Case 1:
% 240.73/47.27  | | | 
% 240.73/47.27  | | | 
% 240.73/47.27  | | | GROUND_INST: instantiating (18) with e2, all_56_15, e2, e0, simplifying
% 240.73/47.27  | | |              with (8), (32) gives:
% 240.73/47.27  | | |   (34)  all_56_15 = e2
% 240.73/47.27  | | | 
% 240.73/47.27  | | | REDUCE: (33), (34) imply:
% 240.73/47.27  | | |   (35)  op(e0, e2) = e0
% 240.73/47.27  | | | 
% 240.73/47.27  | | | REF_CLOSE: (15), (16), (18), (35) are inconsistent by sub-proof #2252.
% 240.73/47.27  | | | 
% 240.73/47.27  | | Case 2:
% 240.73/47.27  | | | 
% 240.73/47.27  | | |   (36)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.73/47.27  | | | 
% 240.73/47.27  | | | REF_CLOSE: (11), (18), (36) are inconsistent by sub-proof #395.
% 240.73/47.27  | | | 
% 240.73/47.27  | | End of split
% 240.73/47.27  | | 
% 240.73/47.27  | End of split
% 240.73/47.27  | 
% 240.73/47.27  End of proof
% 240.73/47.27  
% 240.73/47.27  Sub-proof #377 shows that the following formulas are inconsistent:
% 240.73/47.27  ----------------------------------------------------------------
% 240.73/47.27    (1)   ~ (e3 = e0)
% 240.73/47.27    (2)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 240.73/47.27         $i(all_56_9)
% 240.73/47.27    (3)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 240.73/47.27           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 240.73/47.27           all_26_1 & $i(all_26_1))
% 240.73/47.27    (4)  op(e0, e3) = e1
% 240.73/47.27    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.27    (6)  op(e3, e3) = e0
% 240.73/47.27    (7)  op(e3, e2) = e3
% 240.73/47.27  
% 240.73/47.27  Begin of proof
% 240.73/47.27  | 
% 240.73/47.27  | ALPHA: (2) implies:
% 240.73/47.27  |   (8)  op(e3, e2) = all_56_9
% 240.73/47.27  |   (9)  op(e3, all_56_9) = e3
% 240.73/47.27  | 
% 240.73/47.27  | BETA: splitting (3) gives:
% 240.73/47.27  | 
% 240.73/47.27  | Case 1:
% 240.73/47.27  | | 
% 240.73/47.27  | | 
% 240.73/47.27  | | GROUND_INST: instantiating (5) with e3, all_56_9, e2, e3, simplifying with
% 240.73/47.27  | |              (7), (8) gives:
% 240.73/47.27  | |   (10)  all_56_9 = e3
% 240.73/47.27  | | 
% 240.73/47.27  | | REDUCE: (9), (10) imply:
% 240.73/47.27  | |   (11)  op(e3, e3) = e3
% 240.73/47.27  | | 
% 240.73/47.27  | | REF_CLOSE: (1), (5), (6), (11) are inconsistent by sub-proof #1940.
% 240.73/47.27  | | 
% 240.73/47.27  | Case 2:
% 240.73/47.27  | | 
% 240.73/47.27  | |   (12)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 240.73/47.27  | | 
% 240.73/47.27  | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #1386.
% 240.73/47.27  | | 
% 240.73/47.27  | End of split
% 240.73/47.27  | 
% 240.73/47.27  End of proof
% 240.73/47.27  
% 240.73/47.27  Sub-proof #378 shows that the following formulas are inconsistent:
% 240.73/47.27  ----------------------------------------------------------------
% 240.73/47.27    (1)  all_58_1 = e3
% 240.73/47.27    (2)  op(e1, e0) = e0
% 240.73/47.27    (3)   ~ (e2 = e0)
% 240.73/47.27    (4)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.73/47.27         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.73/47.27    (5)  all_58_12 = e2
% 240.73/47.27    (6)   ~ (all_52_7 = e3)
% 240.73/47.27    (7)  all_58_15 = e3
% 240.73/47.27    (8)   ~ (e3 = e1)
% 240.73/47.27    (9)  op(e2, e2) = e0
% 240.73/47.27    (10)  op(e1, all_52_2) = e1
% 240.73/47.27    (11)   ~ (e3 = e2)
% 240.73/47.27    (12)  op(e1, e1) = e3
% 240.73/47.27    (13)  op(e0, e2) = all_52_7
% 240.73/47.27    (14)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.73/47.27          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.73/47.27    (15)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.73/47.27          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.73/47.27    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.27            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.27    (17)  op(e1, e3) = all_52_2
% 240.73/47.27    (18)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.73/47.27          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.73/47.27    (19)   ~ (e1 = e0)
% 240.73/47.27    (20)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.73/47.27          | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.73/47.27    (21)  op(e3, e3) = e0
% 240.73/47.27    (22)  op(e3, e2) = e3
% 240.73/47.27    (23)  all_58_2 = e3
% 240.73/47.28    (24)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.73/47.28          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.73/47.28            e1)
% 240.73/47.28    (25)  all_58_3 = e0
% 240.73/47.28    (26)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.73/47.28          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.73/47.28            e2)
% 240.73/47.28    (27)   ~ (e2 = e1)
% 240.73/47.28  
% 240.73/47.28  Begin of proof
% 240.73/47.28  | 
% 240.73/47.28  | BETA: splitting (14) gives:
% 240.73/47.28  | 
% 240.73/47.28  | Case 1:
% 240.73/47.28  | | 
% 240.73/47.28  | |   (28)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 240.73/47.28  | |           e1)
% 240.73/47.28  | | 
% 240.73/47.28  | | REF_CLOSE: (8), (16), (19), (21), (23), (28) are inconsistent by sub-proof
% 240.73/47.28  | |            #1486.
% 240.73/47.28  | | 
% 240.73/47.28  | Case 2:
% 240.73/47.28  | | 
% 240.73/47.28  | |   (29)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 240.73/47.28  | |           e1)
% 240.73/47.28  | | 
% 240.73/47.28  | | BETA: splitting (29) gives:
% 240.73/47.28  | | 
% 240.73/47.28  | | Case 1:
% 240.73/47.28  | | | 
% 240.73/47.28  | | |   (30)  all_58_6 = e1 & op(e1, e3) = e1
% 240.73/47.28  | | | 
% 240.73/47.28  | | | ALPHA: (30) implies:
% 240.73/47.28  | | |   (31)  op(e1, e3) = e1
% 240.73/47.28  | | | 
% 240.73/47.28  | | | BETA: splitting (15) gives:
% 240.73/47.28  | | | 
% 240.73/47.28  | | | Case 1:
% 240.73/47.28  | | | | 
% 240.73/47.28  | | | |   (32)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 240.73/47.28  | | | |           = e2)
% 240.73/47.28  | | | | 
% 240.73/47.28  | | | | BETA: splitting (32) gives:
% 240.73/47.28  | | | | 
% 240.73/47.28  | | | | Case 1:
% 240.73/47.28  | | | | | 
% 240.73/47.28  | | | | |   (33)  all_58_6 = e2 & op(e1, e3) = e2
% 240.73/47.28  | | | | | 
% 240.73/47.28  | | | | | ALPHA: (33) implies:
% 240.73/47.28  | | | | |   (34)  op(e1, e3) = e2
% 240.73/47.28  | | | | | 
% 240.73/47.28  | | | | | REF_CLOSE: (16), (27), (31), (34) are inconsistent by sub-proof #2226.
% 240.73/47.28  | | | | | 
% 240.73/47.28  | | | | Case 2:
% 240.73/47.28  | | | | | 
% 240.73/47.28  | | | | |   (35)  all_58_7 = e2 & op(e1, e2) = e2
% 240.73/47.28  | | | | | 
% 240.73/47.28  | | | | | ALPHA: (35) implies:
% 240.73/47.28  | | | | |   (36)  all_58_7 = e2
% 240.73/47.28  | | | | | 
% 240.73/47.28  | | | | | BETA: splitting (18) gives:
% 240.73/47.28  | | | | | 
% 240.73/47.28  | | | | | Case 1:
% 240.73/47.28  | | | | | | 
% 240.73/47.28  | | | | | |   (37)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 240.73/47.28  | | | | | |             e2) = e1)
% 240.73/47.28  | | | | | | 
% 240.73/47.28  | | | | | | REF_CLOSE: (8), (16), (19), (22), (25), (37) are inconsistent by
% 240.73/47.28  | | | | | |            sub-proof #380.
% 240.73/47.28  | | | | | | 
% 240.73/47.28  | | | | | Case 2:
% 240.73/47.28  | | | | | | 
% 240.73/47.28  | | | | | |   (38)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 240.73/47.28  | | | | | |             e2) = e1)
% 240.73/47.28  | | | | | | 
% 240.73/47.28  | | | | | | BETA: splitting (38) gives:
% 240.73/47.28  | | | | | | 
% 240.73/47.28  | | | | | | Case 1:
% 240.73/47.28  | | | | | | | 
% 240.73/47.28  | | | | | | |   (39)  all_58_7 = e1 & op(e1, e2) = e1
% 240.73/47.28  | | | | | | | 
% 240.73/47.28  | | | | | | | REF_CLOSE: (27), (36), (39) are inconsistent by sub-proof #2224.
% 240.73/47.28  | | | | | | | 
% 240.73/47.28  | | | | | | Case 2:
% 240.73/47.28  | | | | | | | 
% 240.73/47.28  | | | | | | |   (40)  all_58_13 = e1 & op(e0, e2) = e1
% 240.73/47.28  | | | | | | | 
% 240.73/47.28  | | | | | | | ALPHA: (40) implies:
% 240.73/47.28  | | | | | | |   (41)  all_58_13 = e1
% 240.73/47.28  | | | | | | |   (42)  op(e0, e2) = e1
% 240.73/47.28  | | | | | | | 
% 240.73/47.28  | | | | | | | BETA: splitting (24) gives:
% 240.73/47.28  | | | | | | | 
% 240.73/47.28  | | | | | | | Case 1:
% 240.73/47.28  | | | | | | | | 
% 240.73/47.28  | | | | | | | |   (43)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 240.73/47.28  | | | | | | | |           op(e0, e2) = e1)
% 240.73/47.28  | | | | | | | | 
% 240.73/47.28  | | | | | | | | BETA: splitting (43) gives:
% 240.73/47.28  | | | | | | | | 
% 240.73/47.28  | | | | | | | | Case 1:
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | |   (44)  all_58_12 = e1 & op(e0, e3) = e1
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | ALPHA: (44) implies:
% 240.73/47.28  | | | | | | | | |   (45)  all_58_12 = e1
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | COMBINE_EQS: (5), (45) imply:
% 240.73/47.28  | | | | | | | | |   (46)  e2 = e1
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | COMBINE_EQS: (36), (46) imply:
% 240.73/47.28  | | | | | | | | |   (47)  all_58_7 = e1
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | REF_CLOSE: (1), (3), (4), (9), (11), (16), (27), (41), (47)
% 240.73/47.28  | | | | | | | | |            are inconsistent by sub-proof #1588.
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | Case 2:
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | GROUND_INST: instantiating (16) with all_52_7, e1, e2, e0,
% 240.73/47.28  | | | | | | | | |              simplifying with (13), (42) gives:
% 240.73/47.28  | | | | | | | | |   (48)  all_52_7 = e1
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | GROUND_INST: instantiating (16) with all_52_2, e1, e3, e1,
% 240.73/47.28  | | | | | | | | |              simplifying with (17), (31) gives:
% 240.73/47.28  | | | | | | | | |   (49)  all_52_2 = e1
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | REDUCE: (6), (48) imply:
% 240.73/47.28  | | | | | | | | |   (50)   ~ (e3 = e1)
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | REDUCE: (10), (49) imply:
% 240.73/47.28  | | | | | | | | |   (51)  op(e1, e1) = e1
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | REF_CLOSE: (8), (12), (16), (51) are inconsistent by sub-proof
% 240.73/47.28  | | | | | | | | |            #468.
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | End of split
% 240.73/47.28  | | | | | | | | 
% 240.73/47.28  | | | | | | | Case 2:
% 240.73/47.28  | | | | | | | | 
% 240.73/47.28  | | | | | | | |   (52)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 240.73/47.28  | | | | | | | |           op(e0, e0) = e1)
% 240.73/47.28  | | | | | | | | 
% 240.73/47.28  | | | | | | | | BETA: splitting (52) gives:
% 240.73/47.28  | | | | | | | | 
% 240.73/47.28  | | | | | | | | Case 1:
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | |   (53)  all_58_14 = e1 & op(e0, e1) = e1
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | ALPHA: (53) implies:
% 240.73/47.28  | | | | | | | | |   (54)  all_58_14 = e1
% 240.73/47.28  | | | | | | | | |   (55)  op(e0, e1) = e1
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | REF_CLOSE: (3), (7), (11), (16), (19), (20), (26), (27), (41),
% 240.73/47.28  | | | | | | | | |            (42), (54), (55) are inconsistent by sub-proof
% 240.73/47.28  | | | | | | | | |            #765.
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | Case 2:
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | |   (56)  all_58_15 = e1 & op(e0, e0) = e1
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | | REF_CLOSE: (7), (8), (56) are inconsistent by sub-proof #1393.
% 240.73/47.28  | | | | | | | | | 
% 240.73/47.28  | | | | | | | | End of split
% 240.73/47.28  | | | | | | | | 
% 240.73/47.28  | | | | | | | End of split
% 240.73/47.28  | | | | | | | 
% 240.73/47.28  | | | | | | End of split
% 240.73/47.28  | | | | | | 
% 240.73/47.28  | | | | | End of split
% 240.73/47.28  | | | | | 
% 240.73/47.28  | | | | End of split
% 240.73/47.28  | | | | 
% 240.73/47.28  | | | Case 2:
% 240.73/47.28  | | | | 
% 240.73/47.28  | | | |   (57)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0)
% 240.73/47.28  | | | |           = e2)
% 240.73/47.28  | | | | 
% 240.73/47.28  | | | | REF_CLOSE: (2), (3), (11), (12), (16), (57) are inconsistent by
% 240.73/47.28  | | | |            sub-proof #379.
% 240.73/47.28  | | | | 
% 240.73/47.28  | | | End of split
% 240.73/47.28  | | | 
% 240.73/47.28  | | Case 2:
% 240.73/47.28  | | | 
% 240.73/47.28  | | |   (58)  all_58_12 = e1 & op(e0, e3) = e1
% 240.73/47.28  | | | 
% 240.73/47.28  | | | ALPHA: (58) implies:
% 240.73/47.28  | | |   (59)  all_58_12 = e1
% 240.73/47.28  | | | 
% 240.73/47.28  | | | REF_CLOSE: (5), (27), (59) are inconsistent by sub-proof #1757.
% 240.73/47.28  | | | 
% 240.73/47.28  | | End of split
% 240.73/47.28  | | 
% 240.73/47.28  | End of split
% 240.73/47.28  | 
% 240.73/47.28  End of proof
% 240.73/47.28  
% 240.73/47.28  Sub-proof #379 shows that the following formulas are inconsistent:
% 240.73/47.28  ----------------------------------------------------------------
% 240.73/47.28    (1)  op(e1, e0) = e0
% 240.73/47.28    (2)   ~ (e2 = e0)
% 240.73/47.28    (3)   ~ (e3 = e2)
% 240.73/47.28    (4)  op(e1, e1) = e3
% 240.73/47.28    (5)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.73/47.28    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.28  
% 240.73/47.28  Begin of proof
% 240.73/47.28  | 
% 240.73/47.28  | BETA: splitting (5) gives:
% 240.73/47.28  | 
% 240.73/47.28  | Case 1:
% 240.73/47.28  | | 
% 240.73/47.28  | |   (7)  all_58_8 = e2 & op(e1, e1) = e2
% 240.73/47.28  | | 
% 240.73/47.28  | | ALPHA: (7) implies:
% 240.73/47.28  | |   (8)  op(e1, e1) = e2
% 240.73/47.28  | | 
% 240.73/47.28  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #2206.
% 240.73/47.28  | | 
% 240.73/47.28  | Case 2:
% 240.73/47.28  | | 
% 240.73/47.28  | |   (9)  all_58_11 = e2 & op(e1, e0) = e2
% 240.73/47.28  | | 
% 240.73/47.28  | | ALPHA: (9) implies:
% 240.73/47.28  | |   (10)  op(e1, e0) = e2
% 240.73/47.28  | | 
% 240.73/47.28  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #478.
% 240.73/47.28  | | 
% 240.73/47.28  | End of split
% 240.73/47.28  | 
% 240.73/47.28  End of proof
% 240.73/47.28  
% 240.73/47.28  Sub-proof #380 shows that the following formulas are inconsistent:
% 240.73/47.28  ----------------------------------------------------------------
% 240.73/47.28    (1)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 240.73/47.28    (2)   ~ (e3 = e1)
% 240.73/47.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.28    (4)   ~ (e1 = e0)
% 240.73/47.28    (5)  op(e3, e2) = e3
% 240.73/47.28    (6)  all_58_3 = e0
% 240.73/47.28  
% 240.73/47.28  Begin of proof
% 240.73/47.28  | 
% 240.73/47.28  | BETA: splitting (1) gives:
% 240.73/47.28  | 
% 240.73/47.28  | Case 1:
% 240.73/47.28  | | 
% 240.73/47.28  | |   (7)  all_58_1 = e1 & op(e3, e2) = e1
% 240.73/47.28  | | 
% 240.73/47.28  | | ALPHA: (7) implies:
% 240.73/47.28  | |   (8)  op(e3, e2) = e1
% 240.73/47.28  | | 
% 240.73/47.28  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #2265.
% 240.73/47.28  | | 
% 240.73/47.28  | Case 2:
% 240.73/47.28  | | 
% 240.73/47.28  | |   (9)  all_58_3 = e1 & op(e2, e2) = e1
% 240.73/47.28  | | 
% 240.73/47.28  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #1752.
% 240.73/47.28  | | 
% 240.73/47.28  | End of split
% 240.73/47.28  | 
% 240.73/47.28  End of proof
% 240.73/47.28  
% 240.73/47.28  Sub-proof #381 shows that the following formulas are inconsistent:
% 240.73/47.28  ----------------------------------------------------------------
% 240.73/47.28    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 240.73/47.28           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 240.73/47.28           all_12_1 & $i(all_12_1))
% 240.73/47.28    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.73/47.28         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.73/47.28    (3)   ~ (e3 = e0)
% 240.73/47.28    (4)  all_58_1 = e3
% 240.73/47.28    (5)  op(e0, e1) = all_52_11
% 240.73/47.28    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.73/47.28         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.73/47.28    (7)   ~ (e2 = e0)
% 240.73/47.28    (8)  all_48_2 = e0
% 240.73/47.28    (9)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.73/47.28         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.73/47.28    (10)  op(e1, e2) = all_52_6
% 240.73/47.28    (11)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.73/47.28          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.73/47.28    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.73/47.28              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.73/47.28            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.73/47.28            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.73/47.28            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.73/47.28             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.73/47.28            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.73/47.28            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.73/47.28            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.73/47.28            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.73/47.28            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.73/47.28              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.73/47.28            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.73/47.28            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.73/47.28            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.73/47.28            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.73/47.28            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.73/47.28            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.73/47.28              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.73/47.28            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.73/47.28            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.73/47.28            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.73/47.28            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.73/47.28            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.73/47.28            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.73/47.28              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.73/47.28            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.73/47.28            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.73/47.28    (13)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.73/47.28          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.73/47.28    (14)  op(e1, e0) = all_52_14
% 240.73/47.28    (15)   ~ (all_52_7 = e3)
% 240.73/47.28    (16)  all_58_15 = e3
% 240.73/47.28    (17)  op(e2, e3) = e3
% 240.73/47.28    (18)  op(e0, e3) = all_52_3
% 240.73/47.28    (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.73/47.28          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.73/47.28    (20)   ~ (all_52_6 = e0)
% 240.73/47.28    (21)   ~ (e3 = e1)
% 240.73/47.28    (22)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 240.73/47.28            op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 240.73/47.28              e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.73/47.28    (23)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.73/47.28          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.73/47.28    (24)  op(e2, e2) = e0
% 240.73/47.28    (25)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 240.73/47.28            op(e2, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 240.73/47.28              e3) & op(e2, e0) = all_48_1 & $i(all_48_1))
% 240.73/47.28    (26)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.73/47.28          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.73/47.28    (27)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 240.73/47.28            $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e1, e3) = all_6_1
% 240.73/47.28            & $i(all_6_1))
% 240.73/47.28    (28)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.73/47.28              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.73/47.28                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.73/47.28                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.73/47.28    (29)   ~ (all_52_11 = e3)
% 240.73/47.28    (30)  op(e3, e1) = all_52_8
% 240.73/47.28    (31)  op(e2, e1) = all_52_9
% 240.73/47.28    (32)   ~ (e3 = e2)
% 240.73/47.28    (33)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.73/47.28          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.73/47.28    (34)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 240.73/47.28            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 240.73/47.28              e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 240.73/47.28    (35)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 240.73/47.28            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 240.73/47.28              e0) = all_14_1 & $i(all_14_1))
% 240.73/47.28    (36)  op(e3, e0) = all_52_12
% 240.73/47.28    (37)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.73/47.28          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.73/47.28    (38)   ~ (all_52_3 = e3)
% 240.73/47.28    (39)  all_46_2 = e3
% 240.73/47.28    (40)  all_56_11 = e0
% 240.73/47.28    (41)  op(e3, e3) = e2
% 240.73/47.28    (42)   ~ (all_52_14 = e3)
% 240.73/47.28    (43)   ~ (all_52_12 = e2)
% 240.73/47.28    (44)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.73/47.28          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.73/47.28    (45)  op(e1, e1) = e3
% 240.73/47.28    (46)   ~ (all_52_2 = e3)
% 240.73/47.28    (47)   ~ (all_52_6 = e3)
% 240.73/47.28    (48)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.73/47.28          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.73/47.28    (49)  op(e0, e2) = all_52_7
% 240.73/47.28    (50)  all_56_1 = e2
% 240.73/47.28    (51)   ~ (all_52_7 = e0)
% 240.73/47.28    (52)   ~ (all_52_9 = e3)
% 240.73/47.28    (53)  all_56_31 = e3
% 240.73/47.28    (54)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.73/47.28          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.73/47.28    (55)  op(e0, e0) = e3
% 240.73/47.28    (56)  all_26_2 = e3
% 240.73/47.28    (57)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.73/47.28          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.73/47.29    (58)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.73/47.29          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.73/47.29    (59)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.73/47.29          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.73/47.29    (60)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.73/47.29          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.73/47.29    (61)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.73/47.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.73/47.29    (62)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.73/47.29          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.73/47.29    (63)  op(e1, e3) = all_52_2
% 240.73/47.29    (64)   ~ (all_52_12 = e3)
% 240.73/47.29    (65)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.73/47.29          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.73/47.29    (66)   ~ (e1 = e0)
% 240.73/47.29    (67)  op(e3, e2) = e3
% 240.73/47.29    (68)  all_58_2 = e3
% 240.73/47.29    (69)   ~ (all_52_13 = e3)
% 240.73/47.29    (70)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.73/47.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.73/47.29    (71)  op(e2, e0) = all_52_13
% 240.73/47.29    (72)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.73/47.29          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.73/47.29            e1)
% 240.73/47.29    (73)  all_58_3 = e0
% 240.73/47.29    (74)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.73/47.29          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.73/47.29            e2)
% 240.73/47.29    (75)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.73/47.29          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.73/47.29    (76)   ~ (e2 = e1)
% 240.73/47.29    (77)   ~ (all_52_8 = e3)
% 240.73/47.29  
% 240.73/47.29  Begin of proof
% 240.73/47.29  | 
% 240.73/47.29  | BETA: splitting (34) gives:
% 240.73/47.29  | 
% 240.73/47.29  | Case 1:
% 240.73/47.29  | | 
% 240.73/47.29  | |   (78)   ~ (all_26_2 = e3)
% 240.73/47.29  | | 
% 240.73/47.29  | | REDUCE: (56), (78) imply:
% 240.73/47.29  | |   (79)  $false
% 240.73/47.29  | | 
% 240.73/47.29  | | CLOSE: (79) is inconsistent.
% 240.73/47.29  | | 
% 240.73/47.29  | Case 2:
% 240.73/47.29  | | 
% 240.73/47.29  | |   (80)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 240.73/47.29  | |           all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) &
% 240.73/47.29  | |           op(e0, e3) = all_26_1 & $i(all_26_1))
% 240.73/47.29  | | 
% 240.73/47.29  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 240.73/47.29  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 240.73/47.29  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 240.73/47.29  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 240.73/47.29  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (57), (58),
% 240.73/47.29  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 240.73/47.29  | |            (70), (71), (72), (73), (74), (75), (76), (77), (80) are
% 240.73/47.29  | |            inconsistent by sub-proof #382.
% 240.73/47.29  | | 
% 240.73/47.29  | End of split
% 240.73/47.29  | 
% 240.73/47.29  End of proof
% 240.73/47.29  
% 240.73/47.29  Sub-proof #382 shows that the following formulas are inconsistent:
% 240.73/47.29  ----------------------------------------------------------------
% 240.73/47.29    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 240.73/47.29           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 240.73/47.29           all_12_1 & $i(all_12_1))
% 240.73/47.29    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.73/47.29         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.73/47.29    (3)   ~ (e3 = e0)
% 240.73/47.29    (4)  all_58_1 = e3
% 240.73/47.29    (5)  op(e0, e1) = all_52_11
% 240.73/47.29    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.73/47.29         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.73/47.29    (7)   ~ (e2 = e0)
% 240.80/47.29    (8)  all_48_2 = e0
% 240.80/47.29    (9)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.80/47.29         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.80/47.29    (10)  op(e1, e2) = all_52_6
% 240.80/47.29    (11)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.80/47.29          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.80/47.29    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.80/47.29              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.80/47.29            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.80/47.29            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.80/47.29            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.80/47.29             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.80/47.29            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.80/47.29            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.80/47.29            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.80/47.29            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.29            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.80/47.29              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.80/47.29            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.80/47.29            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.80/47.29            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.80/47.29            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.80/47.29            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.80/47.29            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.80/47.29              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.80/47.29            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.29            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.80/47.29            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.80/47.29            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.80/47.29            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.29            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.80/47.29              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.80/47.29            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.80/47.29            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.80/47.29    (13)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.80/47.29          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.80/47.29    (14)  op(e1, e0) = all_52_14
% 240.80/47.29    (15)   ~ (all_52_7 = e3)
% 240.80/47.29    (16)  all_58_15 = e3
% 240.80/47.29    (17)  op(e2, e3) = e3
% 240.80/47.29    (18)  op(e0, e3) = all_52_3
% 240.80/47.29    (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.80/47.29          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.80/47.29    (20)   ~ (all_52_6 = e0)
% 240.80/47.29    (21)   ~ (e3 = e1)
% 240.80/47.29    (22)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 240.80/47.29            op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 240.80/47.29              e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.80/47.29    (23)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.80/47.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.80/47.29    (24)  op(e2, e2) = e0
% 240.80/47.29    (25)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 240.80/47.29            op(e2, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 240.80/47.29              e3) & op(e2, e0) = all_48_1 & $i(all_48_1))
% 240.80/47.29    (26)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.80/47.29          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.80/47.29    (27)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 240.80/47.29            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 240.80/47.29              e3) = all_26_1 & $i(all_26_1))
% 240.80/47.29    (28)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 240.80/47.29            $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e1, e3) = all_6_1
% 240.80/47.29            & $i(all_6_1))
% 240.80/47.29    (29)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.80/47.29              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.80/47.29                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.80/47.29                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.80/47.29    (30)   ~ (all_52_11 = e3)
% 240.80/47.29    (31)  op(e3, e1) = all_52_8
% 240.80/47.29    (32)  op(e2, e1) = all_52_9
% 240.80/47.29    (33)   ~ (e3 = e2)
% 240.80/47.29    (34)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.80/47.29          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.80/47.29    (35)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 240.80/47.29            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 240.80/47.29              e0) = all_14_1 & $i(all_14_1))
% 240.80/47.29    (36)  op(e3, e0) = all_52_12
% 240.80/47.29    (37)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.80/47.29          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.80/47.29    (38)   ~ (all_52_3 = e3)
% 240.80/47.29    (39)  all_46_2 = e3
% 240.80/47.29    (40)  all_56_11 = e0
% 240.80/47.29    (41)  op(e3, e3) = e2
% 240.80/47.29    (42)   ~ (all_52_14 = e3)
% 240.80/47.29    (43)   ~ (all_52_12 = e2)
% 240.80/47.29    (44)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.80/47.29          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.80/47.29    (45)  op(e1, e1) = e3
% 240.80/47.29    (46)   ~ (all_52_2 = e3)
% 240.80/47.29    (47)   ~ (all_52_6 = e3)
% 240.80/47.29    (48)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.80/47.29          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.80/47.29    (49)  op(e0, e2) = all_52_7
% 240.80/47.29    (50)  all_56_1 = e2
% 240.80/47.29    (51)   ~ (all_52_7 = e0)
% 240.80/47.29    (52)   ~ (all_52_9 = e3)
% 240.80/47.29    (53)  all_56_31 = e3
% 240.80/47.29    (54)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.80/47.29          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.80/47.29    (55)  op(e0, e0) = e3
% 240.80/47.29    (56)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.80/47.29          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.80/47.29    (57)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.80/47.29          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.80/47.29    (58)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.80/47.29          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.80/47.29    (59)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.80/47.29          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.80/47.29    (60)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.29    (61)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.80/47.29          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.80/47.29    (62)  op(e1, e3) = all_52_2
% 240.80/47.29    (63)   ~ (all_52_12 = e3)
% 240.80/47.29    (64)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.80/47.29          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.80/47.29    (65)   ~ (e1 = e0)
% 240.80/47.29    (66)  op(e3, e2) = e3
% 240.80/47.29    (67)  all_58_2 = e3
% 240.80/47.29    (68)   ~ (all_52_13 = e3)
% 240.80/47.29    (69)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.80/47.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.80/47.29    (70)  op(e2, e0) = all_52_13
% 240.80/47.29    (71)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.80/47.29          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.80/47.29            e1)
% 240.80/47.29    (72)  all_58_3 = e0
% 240.80/47.29    (73)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.80/47.29          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.80/47.29            e2)
% 240.80/47.29    (74)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.80/47.29          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.80/47.29    (75)   ~ (e2 = e1)
% 240.80/47.29    (76)   ~ (all_52_8 = e3)
% 240.80/47.29  
% 240.80/47.29  Begin of proof
% 240.80/47.29  | 
% 240.80/47.29  | BETA: splitting (22) gives:
% 240.80/47.29  | 
% 240.80/47.29  | Case 1:
% 240.80/47.29  | | 
% 240.80/47.29  | |   (77)   ~ (all_46_2 = e3)
% 240.80/47.29  | | 
% 240.80/47.29  | | REDUCE: (39), (77) imply:
% 240.80/47.29  | |   (78)  $false
% 240.80/47.29  | | 
% 240.80/47.29  | | CLOSE: (78) is inconsistent.
% 240.80/47.29  | | 
% 240.80/47.29  | Case 2:
% 240.80/47.29  | | 
% 240.80/47.29  | |   (79)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.80/47.29  | |           all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) &
% 240.80/47.29  | |           op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.80/47.29  | | 
% 240.80/47.29  | | BETA: splitting (25) gives:
% 240.80/47.29  | | 
% 240.80/47.29  | | Case 1:
% 240.80/47.29  | | | 
% 240.80/47.29  | | |   (80)   ~ (all_48_2 = e0)
% 240.80/47.29  | | | 
% 240.80/47.29  | | | REDUCE: (8), (80) imply:
% 240.80/47.29  | | |   (81)  $false
% 240.80/47.29  | | | 
% 240.80/47.29  | | | CLOSE: (81) is inconsistent.
% 240.80/47.29  | | | 
% 240.80/47.29  | | Case 2:
% 240.80/47.29  | | | 
% 240.80/47.29  | | |   (82)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 240.80/47.29  | | |           all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) &
% 240.80/47.29  | | |           op(e2, e0) = all_48_1 & $i(all_48_1))
% 240.80/47.29  | | | 
% 240.80/47.29  | | | BETA: splitting (74) gives:
% 240.80/47.29  | | | 
% 240.80/47.29  | | | Case 1:
% 240.80/47.29  | | | | 
% 240.80/47.29  | | | |   (83)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 240.80/47.29  | | | |           = e1)
% 240.80/47.29  | | | | 
% 240.80/47.29  | | | | BETA: splitting (83) gives:
% 240.80/47.29  | | | | 
% 240.80/47.29  | | | | Case 1:
% 240.80/47.29  | | | | | 
% 240.80/47.29  | | | | |   (84)  all_58_2 = e1 & op(e2, e3) = e1
% 240.80/47.29  | | | | | 
% 240.80/47.29  | | | | | ALPHA: (84) implies:
% 240.80/47.29  | | | | |   (85)  all_58_2 = e1
% 240.80/47.29  | | | | | 
% 240.80/47.29  | | | | | COMBINE_EQS: (67), (85) imply:
% 240.80/47.29  | | | | |   (86)  e3 = e1
% 240.80/47.29  | | | | | 
% 240.80/47.30  | | | | | REF_CLOSE: (4), (21), (26), (31), (33), (36), (41), (60), (63), (76),
% 240.80/47.30  | | | | |            (86) are inconsistent by sub-proof #419.
% 240.80/47.30  | | | | | 
% 240.80/47.30  | | | | Case 2:
% 240.80/47.30  | | | | | 
% 240.80/47.30  | | | | |   (87)  all_58_3 = e1 & op(e2, e2) = e1
% 240.80/47.30  | | | | | 
% 240.80/47.30  | | | | | REF_CLOSE: (65), (72), (87) are inconsistent by sub-proof #1752.
% 240.80/47.30  | | | | | 
% 240.80/47.30  | | | | End of split
% 240.80/47.30  | | | | 
% 240.80/47.30  | | | Case 2:
% 240.80/47.30  | | | | 
% 240.80/47.30  | | | |   (88)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 240.80/47.30  | | | |           = e1)
% 240.80/47.30  | | | | 
% 240.80/47.30  | | | | BETA: splitting (88) gives:
% 240.80/47.30  | | | | 
% 240.80/47.30  | | | | Case 1:
% 240.80/47.30  | | | | | 
% 240.80/47.30  | | | | |   (89)  all_58_5 = e1 & op(e2, e1) = e1
% 240.80/47.30  | | | | | 
% 240.80/47.30  | | | | | ALPHA: (89) implies:
% 240.80/47.30  | | | | |   (90)  all_58_5 = e1
% 240.80/47.30  | | | | |   (91)  op(e2, e1) = e1
% 240.80/47.30  | | | | | 
% 240.80/47.30  | | | | | BETA: splitting (19) gives:
% 240.80/47.30  | | | | | 
% 240.80/47.30  | | | | | Case 1:
% 240.80/47.30  | | | | | | 
% 240.80/47.30  | | | | | |   (92)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2,
% 240.80/47.30  | | | | | |             e2) = e2)
% 240.80/47.30  | | | | | | 
% 240.80/47.30  | | | | | | BETA: splitting (92) gives:
% 240.80/47.30  | | | | | | 
% 240.80/47.30  | | | | | | Case 1:
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | |   (93)  all_58_2 = e2 & op(e2, e3) = e2
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | | ALPHA: (93) implies:
% 240.80/47.30  | | | | | | |   (94)  op(e2, e3) = e2
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | | REF_CLOSE: (17), (33), (60), (94) are inconsistent by sub-proof
% 240.80/47.30  | | | | | | |            #1897.
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | Case 2:
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | |   (95)  all_58_3 = e2 & op(e2, e2) = e2
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | | ALPHA: (95) implies:
% 240.80/47.30  | | | | | | |   (96)  op(e2, e2) = e2
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | | REF_CLOSE: (3), (7), (10), (13), (20), (49), (51), (60), (66),
% 240.80/47.30  | | | | | | |            (96) are inconsistent by sub-proof #408.
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | End of split
% 240.80/47.30  | | | | | | 
% 240.80/47.30  | | | | | Case 2:
% 240.80/47.30  | | | | | | 
% 240.80/47.30  | | | | | |   (97)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2,
% 240.80/47.30  | | | | | |             e0) = e2)
% 240.80/47.30  | | | | | | 
% 240.80/47.30  | | | | | | BETA: splitting (97) gives:
% 240.80/47.30  | | | | | | 
% 240.80/47.30  | | | | | | Case 1:
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | |   (98)  all_58_5 = e2 & op(e2, e1) = e2
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | | ALPHA: (98) implies:
% 240.80/47.30  | | | | | | |   (99)  all_58_5 = e2
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | | REF_CLOSE: (75), (90), (99) are inconsistent by sub-proof #1665.
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | Case 2:
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | |   (100)  all_58_10 = e2 & op(e2, e0) = e2
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | | ALPHA: (100) implies:
% 240.80/47.30  | | | | | | |   (101)  op(e2, e0) = e2
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | | BETA: splitting (34) gives:
% 240.80/47.30  | | | | | | | 
% 240.80/47.30  | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | 
% 240.80/47.30  | | | | | | | |   (102)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 240.80/47.30  | | | | | | | |            op(e2, e1) = e2)
% 240.80/47.30  | | | | | | | | 
% 240.80/47.30  | | | | | | | | BETA: splitting (102) gives:
% 240.80/47.30  | | | | | | | | 
% 240.80/47.30  | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | |   (103)  all_58_4 = e2 & op(e3, e1) = e2
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | REF_CLOSE: (3), (7), (21), (26), (31), (33), (36), (41), (44),
% 240.80/47.30  | | | | | | | | |            (57), (60), (63), (65), (66), (75), (76), (103) are
% 240.80/47.30  | | | | | | | | |            inconsistent by sub-proof #415.
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | |   (104)  all_58_5 = e2 & op(e2, e1) = e2
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | ALPHA: (104) implies:
% 240.80/47.30  | | | | | | | | |   (105)  all_58_5 = e2
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | REF_CLOSE: (75), (90), (105) are inconsistent by sub-proof
% 240.80/47.30  | | | | | | | | |            #1665.
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | End of split
% 240.80/47.30  | | | | | | | | 
% 240.80/47.30  | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | 
% 240.80/47.30  | | | | | | | |   (106)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 240.80/47.30  | | | | | | | |            op(e0, e1) = e2)
% 240.80/47.30  | | | | | | | | 
% 240.80/47.30  | | | | | | | | BETA: splitting (106) gives:
% 240.80/47.30  | | | | | | | | 
% 240.80/47.30  | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | |   (107)  all_58_8 = e2 & op(e1, e1) = e2
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | ALPHA: (107) implies:
% 240.80/47.30  | | | | | | | | |   (108)  op(e1, e1) = e2
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | REF_CLOSE: (33), (45), (60), (108) are inconsistent by
% 240.80/47.30  | | | | | | | | |            sub-proof #2206.
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | |   (109)  all_58_14 = e2 & op(e0, e1) = e2
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | ALPHA: (109) implies:
% 240.80/47.30  | | | | | | | | |   (110)  all_58_14 = e2
% 240.80/47.30  | | | | | | | | |   (111)  op(e0, e1) = e2
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | BETA: splitting (29) gives:
% 240.80/47.30  | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | |   (112)  all_58_15 = e0 & op(e0, e0) = e0
% 240.80/47.30  | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | ALPHA: (112) implies:
% 240.80/47.30  | | | | | | | | | |   (113)  op(e0, e0) = e0
% 240.80/47.30  | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | REF_CLOSE: (3), (55), (60), (113) are inconsistent by
% 240.80/47.30  | | | | | | | | | |            sub-proof #2079.
% 240.80/47.30  | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | |   (114)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.80/47.30  | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.80/47.30  | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 240.80/47.30  | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.80/47.30  | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.80/47.30  | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | ALPHA: (114) implies:
% 240.80/47.30  | | | | | | | | | |   (115)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 240.80/47.30  | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 240.80/47.30  | | | | | | | | | |              e1) = e0)
% 240.80/47.30  | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | BETA: splitting (23) gives:
% 240.80/47.30  | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | |   (116)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 240.80/47.30  | | | | | | | | | | |            & op(e2, e1) = e0)
% 240.80/47.30  | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | BETA: splitting (116) gives:
% 240.80/47.30  | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | |   (117)  all_58_4 = e0 & op(e3, e1) = e0
% 240.80/47.30  | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | ALPHA: (117) implies:
% 240.80/47.30  | | | | | | | | | | | |   (118)  all_58_4 = e0
% 240.80/47.30  | | | | | | | | | | | |   (119)  op(e3, e1) = e0
% 240.80/47.30  | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | BETA: splitting (57) gives:
% 240.80/47.30  | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | |   (120)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 240.80/47.30  | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 240.80/47.30  | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | REF_CLOSE: (21), (26), (31), (33), (36), (41), (60), (63),
% 240.80/47.30  | | | | | | | | | | | | |            (75), (76), (120) are inconsistent by sub-proof
% 240.80/47.30  | | | | | | | | | | | | |            #416.
% 240.80/47.30  | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | |   (121)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 240.80/47.30  | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 240.80/47.30  | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | BETA: splitting (121) gives:
% 240.80/47.30  | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | |   (122)  all_58_4 = e1 & op(e3, e1) = e1
% 240.80/47.30  | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | ALPHA: (122) implies:
% 240.80/47.30  | | | | | | | | | | | | | |   (123)  op(e3, e1) = e1
% 240.80/47.30  | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | REF_CLOSE: (60), (65), (119), (123) are inconsistent by
% 240.80/47.30  | | | | | | | | | | | | | |            sub-proof #2089.
% 240.80/47.30  | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | |   (124)  all_58_9 = e1 & op(e3, e0) = e1
% 240.80/47.30  | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | ALPHA: (124) implies:
% 240.80/47.30  | | | | | | | | | | | | | |   (125)  all_58_9 = e1
% 240.80/47.30  | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 240.80/47.30  | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | |   (126)  all_58_12 = e0 & op(e0, e3) = e0
% 240.80/47.30  | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 240.80/47.30  | | | | | | | | | | | | | | |   (127)  all_58_12 = e0
% 240.80/47.30  | | | | | | | | | | | | | | |   (128)  op(e0, e3) = e0
% 240.80/47.30  | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | |   (129)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 240.80/47.30  | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 240.80/47.30  | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (26), (31), (33), (36), (41), (60),
% 240.80/47.30  | | | | | | | | | | | | | | | |            (63), (67), (75), (76), (129) are inconsistent by
% 240.80/47.30  | | | | | | | | | | | | | | | |            sub-proof #391.
% 240.80/47.30  | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | |   (130)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 240.80/47.30  | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 240.80/47.30  | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | |   (131)  all_58_6 = e1 & op(e1, e3) = e1
% 240.80/47.30  | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 240.80/47.30  | | | | | | | | | | | | | | | | |   (132)  all_58_6 = e1
% 240.80/47.30  | | | | | | | | | | | | | | | | |   (133)  op(e1, e3) = e1
% 240.80/47.30  | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | |   (134)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 240.80/47.30  | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | |   (135)  all_58_6 = e0 & op(e1, e3) = e0
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (132), (135) are inconsistent by sub-proof
% 240.80/47.30  | | | | | | | | | | | | | | | | | | |            #2205.
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | |   (136)  all_58_7 = e0 & op(e1, e2) = e0
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (20), (60), (136) are inconsistent by
% 240.80/47.30  | | | | | | | | | | | | | | | | | | |            sub-proof #2022.
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.30  | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | |   (137)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | |   (138)  all_58_8 = e0 & op(e1, e1) = e0
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | |   (139)  op(e1, e1) = e0
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (10), (14), (21), (37), (42), (47), (60),
% 240.80/47.30  | | | | | | | | | | | | | | | | | | |            (133), (139) are inconsistent by sub-proof #457.
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | |   (140)  all_58_11 = e0 & op(e1, e0) = e0
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | |   (141)  op(e1, e0) = e0
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | |   (142)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | |   (143)  all_58_12 = e1 & op(e0, e3) = e1
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | |   (144)  op(e0, e3) = e1
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (27), (60), (65), (128), (144) are
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1384.
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | |   (145)  all_58_13 = e1 & op(e0, e2) = e1
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | |   (146)  all_58_13 = e1
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | |   (147)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | |   (148)  all_58_1 = e2 & op(e3, e2) = e2
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | |   (149)  op(e3, e2) = e2
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (60), (66), (149) are inconsistent by
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2193.
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | |   (150)  all_58_3 = e2 & op(e2, e2) = e2
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | |   (151)  op(e2, e2) = e2
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (21), (32), (33), (59), (60), (65),
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | |            (90), (91), (101), (151) are inconsistent by
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2119.
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | |   (152)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | |   (153)  all_58_7 = e2 & op(e1, e2) = e2
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | |   (154)  all_58_7 = e2
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |   (155)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (33), (38), (50), (53), (60), (65),
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (66), (119), (133), (155) are inconsistent by
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #425.
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |   (156)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (157)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (158)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (159)   ~ (all_56_1 = e1)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (160)  op(e2, e1) = e2
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (60) with e1, e2, e1, e2,
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (91), (160) gives:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (161)  e2 = e1
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (154), (161) imply:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (162)  all_58_7 = e1
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (11), (24), (33), (60), (75), (146),
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (162) are inconsistent by sub-proof #1588.
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (163)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (50), (163) are inconsistent by sub-proof
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            #438.
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (164)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (60), (65), (101), (111), (141), (164) are
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #389.
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |   (165)  all_58_13 = e2 & op(e0, e2) = e2
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |   (166)  all_58_13 = e2
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |   (167)  op(e0, e2) = e2
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (168)  all_58_12 = e1 & op(e0, e3) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (169)  all_58_12 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (16), (29), (60), (65), (110), (167),
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            (169) are inconsistent by sub-proof #1537.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (146), (166) imply:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (170)  e2 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (170) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (171)  e2 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (171) imply:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (172)  all_58_14 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16), (33), (73), (75), (127), (146), (172)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1230.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |   (173)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (174)  all_58_14 = e1 & op(e0, e1) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (175)  all_58_14 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (175) imply:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (176)  e2 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (176) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (177)  e2 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16), (33), (73), (75), (127), (146), (175)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1230.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (178)  all_58_15 = e1 & op(e0, e0) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (179)  all_58_15 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (7), (15), (21), (33), (49), (60),
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            (110), (115), (167), (179) are inconsistent by
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1637.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | |   (180)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |   (181)  all_58_14 = e1 & op(e0, e1) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |   (182)  all_58_14 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (21), (23), (33), (34), (48), (60),
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            (65), (75), (90), (118), (182) are inconsistent by
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1248.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |   (183)  all_58_15 = e1 & op(e0, e0) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |   (184)  all_58_15 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |   (185)  op(e0, e0) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (21), (29), (56), (60), (65), (68),
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            (70), (101), (125), (184), (185) are inconsistent
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #971.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | |   (186)  all_58_12 = e1 & op(e0, e3) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | |   (187)  op(e0, e3) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (27), (60), (65), (128), (187) are
% 240.80/47.31  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1384.
% 240.80/47.31  | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | |   (188)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 240.80/47.31  | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 240.80/47.31  | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | REF_CLOSE: (7), (49), (51), (60), (110), (188) are
% 240.80/47.31  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1228.
% 240.80/47.31  | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | |   (189)  all_58_5 = e0 & op(e2, e1) = e0
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | ALPHA: (189) implies:
% 240.80/47.31  | | | | | | | | | | | |   (190)  op(e2, e1) = e0
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | REF_CLOSE: (32), (60), (65), (91), (190) are inconsistent by
% 240.80/47.31  | | | | | | | | | | | |            sub-proof #2165.
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | |   (191)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 240.80/47.31  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 240.80/47.31  | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | BETA: splitting (191) gives:
% 240.80/47.31  | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | |   (192)  all_58_8 = e0 & op(e1, e1) = e0
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | ALPHA: (192) implies:
% 240.80/47.31  | | | | | | | | | | | |   (193)  op(e1, e1) = e0
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | REF_CLOSE: (3), (5), (30), (31), (32), (48), (52), (60),
% 240.80/47.31  | | | | | | | | | | | |            (76), (193) are inconsistent by sub-proof #1010.
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | |   (194)  all_58_14 = e0 & op(e0, e1) = e0
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | REF_CLOSE: (7), (110), (194) are inconsistent by sub-proof
% 240.80/47.31  | | | | | | | | | | | |            #2036.
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | 
% 240.80/47.31  | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | 
% 240.80/47.31  | | | | | | | End of split
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | End of split
% 240.80/47.31  | | | | | | 
% 240.80/47.31  | | | | | End of split
% 240.80/47.31  | | | | | 
% 240.80/47.31  | | | | Case 2:
% 240.80/47.31  | | | | | 
% 240.80/47.31  | | | | |   (195)  all_58_10 = e1 & op(e2, e0) = e1
% 240.80/47.31  | | | | | 
% 240.80/47.31  | | | | | ALPHA: (195) implies:
% 240.80/47.31  | | | | |   (196)  op(e2, e0) = e1
% 240.80/47.31  | | | | | 
% 240.80/47.31  | | | | | BETA: splitting (61) gives:
% 240.80/47.31  | | | | | 
% 240.80/47.31  | | | | | Case 1:
% 240.80/47.31  | | | | | | 
% 240.80/47.31  | | | | | |   (197)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 240.80/47.31  | | | | | |            op(e2, e0) = e2)
% 240.80/47.31  | | | | | | 
% 240.80/47.31  | | | | | | BETA: splitting (197) gives:
% 240.80/47.31  | | | | | | 
% 240.80/47.31  | | | | | | Case 1:
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | |   (198)  all_58_9 = e2 & op(e3, e0) = e2
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | | REF_CLOSE: (36), (43), (60), (198) are inconsistent by sub-proof
% 240.80/47.31  | | | | | | |            #2318.
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | Case 2:
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | |   (199)  all_58_10 = e2 & op(e2, e0) = e2
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | | ALPHA: (199) implies:
% 240.80/47.31  | | | | | | |   (200)  op(e2, e0) = e2
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | | REF_CLOSE: (60), (75), (196), (200) are inconsistent by sub-proof
% 240.80/47.31  | | | | | | |            #1659.
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | End of split
% 240.80/47.31  | | | | | | 
% 240.80/47.31  | | | | | Case 2:
% 240.80/47.31  | | | | | | 
% 240.80/47.31  | | | | | |   (201)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 240.80/47.31  | | | | | |            op(e0, e0) = e2)
% 240.80/47.31  | | | | | | 
% 240.80/47.31  | | | | | | BETA: splitting (201) gives:
% 240.80/47.31  | | | | | | 
% 240.80/47.31  | | | | | | Case 1:
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | |   (202)  all_58_11 = e2 & op(e1, e0) = e2
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | | ALPHA: (202) implies:
% 240.80/47.31  | | | | | | |   (203)  all_58_11 = e2
% 240.80/47.31  | | | | | | |   (204)  op(e1, e0) = e2
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | | BETA: splitting (29) gives:
% 240.80/47.31  | | | | | | | 
% 240.80/47.31  | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | 
% 240.80/47.31  | | | | | | | |   (205)  all_58_15 = e0 & op(e0, e0) = e0
% 240.80/47.31  | | | | | | | | 
% 240.80/47.31  | | | | | | | | ALPHA: (205) implies:
% 240.80/47.31  | | | | | | | |   (206)  op(e0, e0) = e0
% 240.80/47.31  | | | | | | | | 
% 240.80/47.31  | | | | | | | | REF_CLOSE: (3), (55), (60), (206) are inconsistent by sub-proof
% 240.80/47.31  | | | | | | | |            #2079.
% 240.80/47.31  | | | | | | | | 
% 240.80/47.31  | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | 
% 240.80/47.31  | | | | | | | |   (207)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 240.80/47.31  | | | | | | | |              op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.80/47.31  | | | | | | | |              e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 240.80/47.31  | | | | | | | |            (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0
% 240.80/47.31  | | | | | | | |              & op(e0, e1) = e0))
% 240.80/47.31  | | | | | | | | 
% 240.80/47.31  | | | | | | | | ALPHA: (207) implies:
% 240.80/47.31  | | | | | | | |   (208)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 240.80/47.31  | | | | | | | |            op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.80/47.31  | | | | | | | | 
% 240.80/47.31  | | | | | | | | BETA: splitting (69) gives:
% 240.80/47.31  | | | | | | | | 
% 240.80/47.31  | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | 
% 240.80/47.31  | | | | | | | | |   (209)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 240.80/47.31  | | | | | | | | |            op(e1, e2) = e0)
% 240.80/47.31  | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | BETA: splitting (209) gives:
% 240.80/47.31  | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | |   (210)  all_58_6 = e0 & op(e1, e3) = e0
% 240.80/47.31  | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | ALPHA: (210) implies:
% 240.80/47.31  | | | | | | | | | |   (211)  all_58_6 = e0
% 240.80/47.31  | | | | | | | | | |   (212)  op(e1, e3) = e0
% 240.80/47.31  | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | BETA: splitting (54) gives:
% 240.80/47.31  | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | |   (213)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 240.80/47.31  | | | | | | | | | | |            & op(e2, e3) = e1)
% 240.80/47.31  | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | REF_CLOSE: (4), (21), (26), (31), (33), (36), (41), (60),
% 240.80/47.31  | | | | | | | | | | |            (63), (67), (75), (76), (213) are inconsistent by
% 240.80/47.31  | | | | | | | | | | |            sub-proof #391.
% 240.80/47.31  | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | |   (214)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 240.80/47.31  | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 240.80/47.31  | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | BETA: splitting (214) gives:
% 240.80/47.31  | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | |   (215)  all_58_6 = e1 & op(e1, e3) = e1
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | ALPHA: (215) implies:
% 240.80/47.31  | | | | | | | | | | | |   (216)  all_58_6 = e1
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | REF_CLOSE: (65), (211), (216) are inconsistent by sub-proof
% 240.80/47.31  | | | | | | | | | | | |            #1981.
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | |   (217)  all_58_12 = e1 & op(e0, e3) = e1
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | ALPHA: (217) implies:
% 240.80/47.31  | | | | | | | | | | | |   (218)  op(e0, e3) = e1
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | BETA: splitting (6) gives:
% 240.80/47.31  | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | |   (219)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 240.80/47.31  | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 240.80/47.31  | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | BETA: splitting (219) gives:
% 240.80/47.31  | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | |   (220)  all_58_6 = e1 & op(e1, e3) = e1
% 240.80/47.31  | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | ALPHA: (220) implies:
% 240.80/47.31  | | | | | | | | | | | | | |   (221)  all_58_6 = e1
% 240.80/47.31  | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | REF_CLOSE: (65), (211), (221) are inconsistent by sub-proof
% 240.80/47.31  | | | | | | | | | | | | | |            #1981.
% 240.80/47.31  | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | |   (222)  all_58_7 = e1 & op(e1, e2) = e1
% 240.80/47.31  | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | ALPHA: (222) implies:
% 240.80/47.31  | | | | | | | | | | | | | |   (223)  all_58_7 = e1
% 240.80/47.31  | | | | | | | | | | | | | |   (224)  op(e1, e2) = e1
% 240.80/47.31  | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 240.80/47.31  | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | |   (225)  all_58_9 = e0 & op(e3, e0) = e0
% 240.80/47.31  | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 240.80/47.31  | | | | | | | | | | | | | | |   (226)  all_58_9 = e0
% 240.80/47.31  | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | |   (227)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 240.80/47.31  | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (10), (11), (13), (21), (24), (33),
% 240.80/47.31  | | | | | | | | | | | | | | | |            (41), (60), (64), (65), (75), (223), (224), (227)
% 240.80/47.31  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1713.
% 240.80/47.31  | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | |   (228)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 240.80/47.31  | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | |   (229)  all_58_4 = e1 & op(e3, e1) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | |   (230)  op(e3, e1) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | |   (231)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 240.80/47.31  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | |   (232)  all_58_1 = e2 & op(e3, e2) = e2
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (21), (26), (33), (41), (44), (57),
% 240.80/47.31  | | | | | | | | | | | | | | | | | | |            (60), (65), (75), (230), (232) are inconsistent by
% 240.80/47.31  | | | | | | | | | | | | | | | | | | |            sub-proof #387.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | |   (233)  all_58_3 = e2 & op(e2, e2) = e2
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | ALPHA: (233) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | |   (234)  op(e2, e2) = e2
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (10), (13), (20), (49), (51), (60),
% 240.80/47.31  | | | | | | | | | | | | | | | | | | |            (66), (234) are inconsistent by sub-proof #408.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | |   (235)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | |   (236)  all_58_7 = e2 & op(e1, e2) = e2
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | |   (237)  all_58_7 = e2
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (223), (237) are inconsistent by sub-proof
% 240.80/47.31  | | | | | | | | | | | | | | | | | | |            #2134.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | |   (238)  all_58_13 = e2 & op(e0, e2) = e2
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | |   (239)  all_58_13 = e2
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | |   (240)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | |          op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | |   (241)  op(e1, e3) = all_6_1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |   (242)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |   (243)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |          e3
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |   (245)   ~ (all_56_1 = e2)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (245) imply:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |   (246)  $false
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |   (247)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (46), (60), (62), (66), (247) are
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1685.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |   (248)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |   (249)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | |   (250)  op(e1, e3) = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (33), (50), (60), (66), (250), (251) are
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #426.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)   ~ (all_56_31 = e3)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (252) imply:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)  $false
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (27), (38), (60), (65), (218), (254)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #386.
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |   (255)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.80/47.31  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)   ~ (all_56_1 = e1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  op(e1, e2) = e2
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e3) = all_46_1 & $i(all_46_0) &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_46_1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (260) implies:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  op(e1, e3) = all_46_1
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (10), (33), (37), (47), (58), (60),
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (75), (203), (211), (212), (223), (224), (241),
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (250), (259), (261) are inconsistent by sub-proof
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #385.
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_46_1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  op(e1, e3) = all_46_1
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (10), (33), (37), (47), (58), (60),
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (75), (203), (211), (212), (223), (224), (241),
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (250), (259), (263) are inconsistent by sub-proof
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #385.
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (60), (75), (196), (264) are inconsistent by
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1217.
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (60), (65), (70), (75), (196), (204), (265)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #384.
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |   (266)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (27), (38), (60), (65), (218), (266)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #386.
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |   (267)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |   (268)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |   (270)   ~ (all_56_1 = e1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |   (271)  op(e1, e2) = e2
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (60) with e1, e2, e2, e1,
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (224), (271) gives:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | |   (272)  e2 = e1
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (272) imply:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | |   (273)  all_58_13 = e1
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (11), (24), (33), (60), (75), (223),
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | |            (273) are inconsistent by sub-proof #1588.
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | |   (274)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_14_1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | |   (275)   ~ (all_14_1 = e1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | |   (276)  op(e2, e0) = all_14_1
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (82), (196), (275), (276) are inconsistent
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1584.
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |   (277)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (60), (75), (196), (277) are inconsistent by
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1217.
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |   (278)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (60), (65), (70), (75), (196), (204), (278)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #384.
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | |   (279)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 &
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | |          $i(all_6_1)
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (79), (212), (279) are inconsistent by
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | |            sub-proof #443.
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | |   (280)  all_58_9 = e1 & op(e3, e0) = e1
% 240.80/47.32  | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 240.80/47.32  | | | | | | | | | | | | | | | | |   (281)  all_58_9 = e1
% 240.80/47.32  | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (226), (281) are inconsistent by sub-proof
% 240.80/47.32  | | | | | | | | | | | | | | | | |            #1744.
% 240.80/47.32  | | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | End of split
% 240.80/47.32  | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | |   (282)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 240.80/47.32  | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 240.80/47.32  | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 240.80/47.32  | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | Case 1:
% 240.80/47.32  | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | |   (283)  all_58_10 = e0 & op(e2, e0) = e0
% 240.80/47.32  | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | ALPHA: (283) implies:
% 240.80/47.32  | | | | | | | | | | | | | | | |   (284)  op(e2, e0) = e0
% 240.80/47.32  | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | REF_CLOSE: (60), (65), (70), (196), (284) are inconsistent by
% 240.80/47.32  | | | | | | | | | | | | | | | |            sub-proof #1778.
% 240.80/47.32  | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | Case 2:
% 240.80/47.32  | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | |   (285)  all_58_11 = e0 & op(e1, e0) = e0
% 240.80/47.32  | | | | | | | | | | | | | | | | 
% 240.80/47.32  | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 240.80/47.32  | | | | | | | | | | | | | | | |   (286)  all_58_11 = e0
% 240.80/47.32  | | | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (10), (33), (37), (47), (58), (60),
% 240.80/47.33  | | | | | | | | | | | | | | | |            (75), (211), (223), (286) are inconsistent by
% 240.80/47.33  | | | | | | | | | | | | | | | |            sub-proof #960.
% 240.80/47.33  | | | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | | | End of split
% 240.80/47.33  | | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | | End of split
% 240.80/47.33  | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | End of split
% 240.80/47.33  | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | Case 2:
% 240.80/47.33  | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | |   (287)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 240.80/47.33  | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 240.80/47.33  | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | BETA: splitting (287) gives:
% 240.80/47.33  | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | Case 1:
% 240.80/47.33  | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | |   (288)  all_58_8 = e1 & op(e1, e1) = e1
% 240.80/47.33  | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | | ALPHA: (288) implies:
% 240.80/47.33  | | | | | | | | | | | | | |   (289)  op(e1, e1) = e1
% 240.80/47.33  | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | | REF_CLOSE: (21), (45), (60), (289) are inconsistent by
% 240.80/47.33  | | | | | | | | | | | | | |            sub-proof #468.
% 240.80/47.33  | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | Case 2:
% 240.80/47.33  | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | |   (290)  all_58_11 = e1 & op(e1, e0) = e1
% 240.80/47.33  | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | | ALPHA: (290) implies:
% 240.80/47.33  | | | | | | | | | | | | | |   (291)  op(e1, e0) = e1
% 240.80/47.33  | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | | REF_CLOSE: (60), (75), (204), (291) are inconsistent by
% 240.80/47.33  | | | | | | | | | | | | | |            sub-proof #2019.
% 240.80/47.33  | | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | | End of split
% 240.80/47.33  | | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | | End of split
% 240.80/47.33  | | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | | End of split
% 240.80/47.33  | | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | End of split
% 240.80/47.33  | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | Case 2:
% 240.80/47.33  | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | |   (292)  all_58_7 = e0 & op(e1, e2) = e0
% 240.80/47.33  | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | | REF_CLOSE: (10), (20), (60), (292) are inconsistent by
% 240.80/47.33  | | | | | | | | | |            sub-proof #2022.
% 240.80/47.33  | | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | End of split
% 240.80/47.33  | | | | | | | | | 
% 240.80/47.33  | | | | | | | | Case 2:
% 240.80/47.33  | | | | | | | | | 
% 240.80/47.33  | | | | | | | | |   (293)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 240.80/47.33  | | | | | | | | |            op(e1, e0) = e0)
% 240.80/47.33  | | | | | | | | | 
% 240.80/47.33  | | | | | | | | | REF_CLOSE: (3), (5), (7), (30), (31), (32), (48), (52), (60),
% 240.80/47.33  | | | | | | | | |            (76), (204), (293) are inconsistent by sub-proof
% 240.80/47.33  | | | | | | | | |            #383.
% 240.80/47.33  | | | | | | | | | 
% 240.80/47.33  | | | | | | | | End of split
% 240.80/47.33  | | | | | | | | 
% 240.80/47.33  | | | | | | | End of split
% 240.80/47.33  | | | | | | | 
% 240.80/47.33  | | | | | | Case 2:
% 240.80/47.33  | | | | | | | 
% 240.80/47.33  | | | | | | |   (294)  all_58_15 = e2 & op(e0, e0) = e2
% 240.80/47.33  | | | | | | | 
% 240.80/47.33  | | | | | | | ALPHA: (294) implies:
% 240.80/47.33  | | | | | | |   (295)  op(e0, e0) = e2
% 240.80/47.33  | | | | | | | 
% 240.80/47.33  | | | | | | | REF_CLOSE: (33), (55), (60), (295) are inconsistent by sub-proof
% 240.80/47.33  | | | | | | |            #1388.
% 240.80/47.33  | | | | | | | 
% 240.80/47.33  | | | | | | End of split
% 240.80/47.33  | | | | | | 
% 240.80/47.33  | | | | | End of split
% 240.80/47.33  | | | | | 
% 240.80/47.33  | | | | End of split
% 240.80/47.33  | | | | 
% 240.80/47.33  | | | End of split
% 240.80/47.33  | | | 
% 240.80/47.33  | | End of split
% 240.80/47.33  | | 
% 240.80/47.33  | End of split
% 240.80/47.33  | 
% 240.80/47.33  End of proof
% 240.80/47.33  
% 240.80/47.33  Sub-proof #383 shows that the following formulas are inconsistent:
% 240.80/47.33  ----------------------------------------------------------------
% 240.80/47.33    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.80/47.33    (2)   ~ (e3 = e0)
% 240.80/47.33    (3)  op(e0, e1) = all_52_11
% 240.80/47.33    (4)   ~ (e2 = e0)
% 240.80/47.33    (5)   ~ (all_52_11 = e3)
% 240.80/47.33    (6)  op(e3, e1) = all_52_8
% 240.80/47.33    (7)  op(e2, e1) = all_52_9
% 240.80/47.33    (8)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.80/47.33         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.80/47.33    (9)   ~ (all_52_9 = e3)
% 240.80/47.33    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.33    (11)  op(e1, e0) = e2
% 240.80/47.33    (12)   ~ (all_52_8 = e3)
% 240.80/47.33  
% 240.80/47.33  Begin of proof
% 240.80/47.33  | 
% 240.80/47.33  | BETA: splitting (1) gives:
% 240.80/47.33  | 
% 240.80/47.33  | Case 1:
% 240.80/47.33  | | 
% 240.80/47.33  | |   (13)  all_58_8 = e0 & op(e1, e1) = e0
% 240.80/47.33  | | 
% 240.80/47.33  | | ALPHA: (13) implies:
% 240.80/47.33  | |   (14)  op(e1, e1) = e0
% 240.80/47.33  | | 
% 240.80/47.33  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (12), (14) are
% 240.80/47.33  | |            inconsistent by sub-proof #1010.
% 240.80/47.33  | | 
% 240.80/47.33  | Case 2:
% 240.80/47.33  | | 
% 240.80/47.33  | |   (15)  all_58_11 = e0 & op(e1, e0) = e0
% 240.80/47.33  | | 
% 240.80/47.33  | | ALPHA: (15) implies:
% 240.80/47.33  | |   (16)  op(e1, e0) = e0
% 240.80/47.33  | | 
% 240.80/47.33  | | REF_CLOSE: (4), (10), (11), (16) are inconsistent by sub-proof #478.
% 240.80/47.33  | | 
% 240.80/47.33  | End of split
% 240.80/47.33  | 
% 240.80/47.33  End of proof
% 240.80/47.33  
% 240.80/47.33  Sub-proof #384 shows that the following formulas are inconsistent:
% 240.80/47.33  ----------------------------------------------------------------
% 240.80/47.33    (1)   ~ (e2 = e0)
% 240.80/47.33    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.80/47.33             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.80/47.33           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.80/47.33             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.80/47.33           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 240.80/47.33           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.80/47.33           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.80/47.33    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.33    (4)  op(e1, e0) = e2
% 240.80/47.33    (5)   ~ (e1 = e0)
% 240.80/47.33    (6)  op(e2, e0) = e1
% 240.80/47.33    (7)  op(e2, e0) = all_52_13
% 240.80/47.33    (8)   ~ (e2 = e1)
% 240.80/47.33  
% 240.80/47.33  Begin of proof
% 240.80/47.33  | 
% 240.80/47.33  | BETA: splitting (2) gives:
% 240.80/47.33  | 
% 240.80/47.33  | Case 1:
% 240.80/47.33  | | 
% 240.80/47.33  | |   (9)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.80/47.33  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 240.80/47.33  | |        & op(e0, e2) = e0
% 240.80/47.33  | | 
% 240.80/47.33  | | ALPHA: (9) implies:
% 240.80/47.33  | |   (10)  op(e2, e0) = e0
% 240.80/47.33  | | 
% 240.80/47.33  | | REF_CLOSE: (3), (5), (6), (7), (10) are inconsistent by sub-proof #1778.
% 240.80/47.33  | | 
% 240.80/47.33  | Case 2:
% 240.80/47.33  | | 
% 240.80/47.33  | |   (11)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.33  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.80/47.33  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.80/47.33  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.80/47.33  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.80/47.33  | | 
% 240.80/47.33  | | REF_CLOSE: (1), (3), (4), (8), (11) are inconsistent by sub-proof #477.
% 240.80/47.33  | | 
% 240.80/47.33  | End of split
% 240.80/47.33  | 
% 240.80/47.33  End of proof
% 240.80/47.33  
% 240.80/47.33  Sub-proof #385 shows that the following formulas are inconsistent:
% 240.80/47.33  ----------------------------------------------------------------
% 240.80/47.33    (1)   ~ (e3 = e0)
% 240.80/47.33    (2)  op(e1, e2) = e1
% 240.80/47.33    (3)   ~ (e2 = e0)
% 240.80/47.33    (4)  op(e1, e2) = all_52_6
% 240.80/47.33    (5)  op(e1, e3) = all_6_1
% 240.80/47.33    (6)   ~ (e3 = e2)
% 240.80/47.33    (7)  all_58_6 = e0
% 240.80/47.33    (8)  op(e1, e3) = e1
% 240.80/47.33    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.80/47.33         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.80/47.33    (10)  op(e1, e3) = all_46_1
% 240.80/47.33    (11)  all_58_11 = e2
% 240.80/47.33    (12)  op(e1, e3) = e0
% 240.80/47.33    (13)   ~ (all_52_6 = e3)
% 240.80/47.33    (14)  op(e1, e2) = e2
% 240.80/47.33    (15)  all_58_7 = e1
% 240.80/47.33    (16)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.80/47.33          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.80/47.33    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.33    (18)   ~ (e2 = e1)
% 240.80/47.33  
% 240.80/47.33  Begin of proof
% 240.80/47.33  | 
% 240.80/47.33  | GROUND_INST: instantiating (17) with e1, e2, e2, e1, simplifying with (2),
% 240.80/47.33  |              (14) gives:
% 240.80/47.33  |   (19)  e2 = e1
% 240.80/47.33  | 
% 240.80/47.33  | GROUND_INST: instantiating (17) with e0, all_46_1, e3, e1, simplifying with
% 240.80/47.33  |              (10), (12) gives:
% 240.80/47.33  |   (20)  all_46_1 = e0
% 240.80/47.33  | 
% 240.80/47.33  | GROUND_INST: instantiating (17) with all_6_1, all_46_1, e3, e1, simplifying
% 240.80/47.33  |              with (5), (10) gives:
% 240.80/47.33  |   (21)  all_46_1 = all_6_1
% 240.80/47.33  | 
% 240.80/47.33  | GROUND_INST: instantiating (17) with e1, all_46_1, e3, e1, simplifying with
% 240.80/47.33  |              (8), (10) gives:
% 240.80/47.33  |   (22)  all_46_1 = e1
% 240.80/47.33  | 
% 240.80/47.33  | COMBINE_EQS: (21), (22) imply:
% 240.80/47.33  |   (23)  all_6_1 = e1
% 240.80/47.33  | 
% 240.80/47.33  | COMBINE_EQS: (20), (21) imply:
% 240.80/47.33  |   (24)  all_6_1 = e0
% 240.80/47.33  | 
% 240.80/47.33  | COMBINE_EQS: (23), (24) imply:
% 240.80/47.33  |   (25)  e1 = e0
% 240.80/47.33  | 
% 240.80/47.33  | COMBINE_EQS: (19), (25) imply:
% 240.80/47.33  |   (26)  e2 = e0
% 240.80/47.33  | 
% 240.80/47.33  | COMBINE_EQS: (11), (26) imply:
% 240.80/47.33  |   (27)  all_58_11 = e0
% 240.80/47.33  | 
% 240.80/47.33  | REF_CLOSE: (1), (3), (4), (6), (7), (9), (13), (15), (16), (17), (18), (27)
% 240.80/47.33  |            are inconsistent by sub-proof #960.
% 240.80/47.33  | 
% 240.80/47.33  End of proof
% 240.80/47.33  
% 240.80/47.33  Sub-proof #386 shows that the following formulas are inconsistent:
% 240.80/47.33  ----------------------------------------------------------------
% 240.80/47.33    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.80/47.33             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.80/47.33           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 240.80/47.33           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.80/47.33           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.80/47.33    (2)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 240.80/47.33           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 240.80/47.33           all_12_1 & $i(all_12_1))
% 240.80/47.33    (3)  op(e0, e3) = all_52_3
% 240.80/47.33    (4)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 240.80/47.33           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 240.80/47.33           all_26_1 & $i(all_26_1))
% 240.80/47.33    (5)  op(e0, e3) = e1
% 240.80/47.33    (6)   ~ (all_52_3 = e3)
% 240.80/47.33    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.33    (8)   ~ (e1 = e0)
% 240.80/47.33  
% 240.80/47.33  Begin of proof
% 240.80/47.33  | 
% 240.80/47.33  | BETA: splitting (1) gives:
% 240.80/47.33  | 
% 240.80/47.33  | Case 1:
% 240.80/47.33  | | 
% 240.80/47.33  | |   (9)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.80/47.33  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.80/47.33  | |        op(e0, e3) = e3
% 240.80/47.33  | | 
% 240.80/47.33  | | ALPHA: (9) implies:
% 240.80/47.33  | |   (10)  op(e0, e3) = e3
% 240.80/47.33  | | 
% 240.80/47.33  | | REF_CLOSE: (3), (6), (7), (10) are inconsistent by sub-proof #2332.
% 240.80/47.33  | | 
% 240.80/47.33  | Case 2:
% 240.80/47.33  | | 
% 240.80/47.33  | |   (11)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.80/47.34  | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) =
% 240.80/47.34  | |         e0 & op(e0, e3) = e0
% 240.80/47.34  | | 
% 240.80/47.34  | | ALPHA: (11) implies:
% 240.80/47.34  | |   (12)  op(e0, e3) = e0
% 240.80/47.34  | | 
% 240.80/47.34  | | REF_CLOSE: (2), (4), (5), (7), (8), (12) are inconsistent by sub-proof
% 240.80/47.34  | |            #1384.
% 240.80/47.34  | | 
% 240.80/47.34  | End of split
% 240.80/47.34  | 
% 240.80/47.34  End of proof
% 240.80/47.34  
% 240.80/47.34  Sub-proof #387 shows that the following formulas are inconsistent:
% 240.80/47.34  ----------------------------------------------------------------
% 240.80/47.34    (1)   ~ (e3 = e0)
% 240.80/47.34    (2)   ~ (e2 = e0)
% 240.80/47.34    (3)  all_58_1 = e2 & op(e3, e2) = e2
% 240.80/47.34    (4)   ~ (e3 = e1)
% 240.80/47.34    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.80/47.34         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.80/47.34    (6)   ~ (e3 = e2)
% 240.80/47.34    (7)  op(e3, e1) = e1
% 240.80/47.34    (8)  op(e3, e3) = e2
% 240.80/47.34    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.80/47.34         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.80/47.34    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.80/47.34          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.80/47.34    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.34    (12)   ~ (e1 = e0)
% 240.80/47.34    (13)   ~ (e2 = e1)
% 240.80/47.34  
% 240.80/47.34  Begin of proof
% 240.80/47.34  | 
% 240.80/47.34  | ALPHA: (3) implies:
% 240.80/47.34  |   (14)  all_58_1 = e2
% 240.80/47.34  |   (15)  op(e3, e2) = e2
% 240.80/47.34  | 
% 240.80/47.34  | BETA: splitting (5) gives:
% 240.80/47.34  | 
% 240.80/47.34  | Case 1:
% 240.80/47.34  | | 
% 240.80/47.34  | |   (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 240.80/47.34  | |           e3)
% 240.80/47.34  | | 
% 240.80/47.34  | | BETA: splitting (16) gives:
% 240.80/47.34  | | 
% 240.80/47.34  | | Case 1:
% 240.80/47.34  | | | 
% 240.80/47.34  | | |   (17)  all_58_0 = e3 & op(e3, e3) = e3
% 240.80/47.34  | | | 
% 240.80/47.34  | | | ALPHA: (17) implies:
% 240.80/47.34  | | |   (18)  op(e3, e3) = e3
% 240.80/47.34  | | | 
% 240.80/47.34  | | | REF_CLOSE: (6), (8), (11), (18) are inconsistent by sub-proof #2194.
% 240.80/47.34  | | | 
% 240.80/47.34  | | Case 2:
% 240.80/47.34  | | | 
% 240.80/47.34  | | |   (19)  all_58_1 = e3 & op(e3, e2) = e3
% 240.80/47.34  | | | 
% 240.80/47.34  | | | ALPHA: (19) implies:
% 240.80/47.34  | | |   (20)  op(e3, e2) = e3
% 240.80/47.34  | | | 
% 240.80/47.34  | | | REF_CLOSE: (6), (11), (15), (20) are inconsistent by sub-proof #2193.
% 240.80/47.34  | | | 
% 240.80/47.34  | | End of split
% 240.80/47.34  | | 
% 240.80/47.34  | Case 2:
% 240.80/47.34  | | 
% 240.80/47.34  | |   (21)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 240.80/47.34  | |           e3)
% 240.80/47.34  | | 
% 240.80/47.34  | | BETA: splitting (21) gives:
% 240.80/47.34  | | 
% 240.80/47.34  | | Case 1:
% 240.80/47.34  | | | 
% 240.80/47.34  | | |   (22)  all_58_4 = e3 & op(e3, e1) = e3
% 240.80/47.34  | | | 
% 240.80/47.34  | | | ALPHA: (22) implies:
% 240.80/47.34  | | |   (23)  all_58_4 = e3
% 240.80/47.34  | | | 
% 240.80/47.34  | | | REF_CLOSE: (1), (2), (4), (8), (9), (10), (11), (12), (13), (14), (23) are
% 240.80/47.34  | | |            inconsistent by sub-proof #2180.
% 240.80/47.34  | | | 
% 240.80/47.34  | | Case 2:
% 240.80/47.34  | | | 
% 240.80/47.34  | | |   (24)  all_58_9 = e3 & op(e3, e0) = e3
% 240.80/47.34  | | | 
% 240.80/47.34  | | | ALPHA: (24) implies:
% 240.80/47.34  | | |   (25)  all_58_9 = e3
% 240.80/47.34  | | | 
% 240.80/47.34  | | | REF_CLOSE: (1), (2), (7), (8), (9), (11), (12), (15), (25) are
% 240.80/47.34  | | |            inconsistent by sub-proof #388.
% 240.80/47.34  | | | 
% 240.80/47.34  | | End of split
% 240.80/47.34  | | 
% 240.80/47.34  | End of split
% 240.80/47.34  | 
% 240.80/47.34  End of proof
% 240.80/47.34  
% 240.80/47.34  Sub-proof #388 shows that the following formulas are inconsistent:
% 240.80/47.34  ----------------------------------------------------------------
% 240.80/47.34    (1)   ~ (e3 = e0)
% 240.80/47.34    (2)   ~ (e2 = e0)
% 240.80/47.34    (3)  op(e3, e2) = e2
% 240.80/47.34    (4)  op(e3, e1) = e1
% 240.80/47.34    (5)  all_58_9 = e3
% 240.80/47.34    (6)  op(e3, e3) = e2
% 240.80/47.34    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.80/47.34         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.80/47.34    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.34    (9)   ~ (e1 = e0)
% 240.80/47.34  
% 240.80/47.34  Begin of proof
% 240.80/47.34  | 
% 240.80/47.34  | BETA: splitting (7) gives:
% 240.80/47.34  | 
% 240.80/47.34  | Case 1:
% 240.80/47.34  | | 
% 240.80/47.34  | |   (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 240.80/47.34  | |           e0)
% 240.80/47.34  | | 
% 240.80/47.34  | | BETA: splitting (10) gives:
% 240.80/47.34  | | 
% 240.80/47.34  | | Case 1:
% 240.80/47.34  | | | 
% 240.80/47.34  | | |   (11)  all_58_0 = e0 & op(e3, e3) = e0
% 240.80/47.34  | | | 
% 240.80/47.34  | | | ALPHA: (11) implies:
% 240.80/47.34  | | |   (12)  op(e3, e3) = e0
% 240.80/47.34  | | | 
% 240.80/47.34  | | | REF_CLOSE: (2), (6), (8), (12) are inconsistent by sub-proof #2188.
% 240.80/47.34  | | | 
% 240.80/47.34  | | Case 2:
% 240.80/47.34  | | | 
% 240.80/47.34  | | |   (13)  all_58_1 = e0 & op(e3, e2) = e0
% 240.80/47.34  | | | 
% 240.80/47.34  | | | ALPHA: (13) implies:
% 240.80/47.34  | | |   (14)  op(e3, e2) = e0
% 240.80/47.34  | | | 
% 240.80/47.34  | | | REF_CLOSE: (2), (3), (8), (14) are inconsistent by sub-proof #2026.
% 240.80/47.34  | | | 
% 240.80/47.34  | | End of split
% 240.80/47.34  | | 
% 240.80/47.34  | Case 2:
% 240.80/47.34  | | 
% 240.80/47.34  | |   (15)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 240.80/47.34  | |           e0)
% 240.80/47.34  | | 
% 240.80/47.34  | | BETA: splitting (15) gives:
% 240.80/47.34  | | 
% 240.80/47.34  | | Case 1:
% 240.80/47.34  | | | 
% 240.80/47.34  | | |   (16)  all_58_4 = e0 & op(e3, e1) = e0
% 240.80/47.34  | | | 
% 240.80/47.34  | | | ALPHA: (16) implies:
% 240.80/47.34  | | |   (17)  op(e3, e1) = e0
% 240.80/47.34  | | | 
% 240.80/47.34  | | | REF_CLOSE: (4), (8), (9), (17) are inconsistent by sub-proof #2089.
% 240.80/47.34  | | | 
% 240.80/47.34  | | Case 2:
% 240.80/47.34  | | | 
% 240.80/47.34  | | |   (18)  all_58_9 = e0 & op(e3, e0) = e0
% 240.80/47.34  | | | 
% 240.80/47.34  | | | REF_CLOSE: (1), (5), (18) are inconsistent by sub-proof #2103.
% 240.80/47.34  | | | 
% 240.80/47.34  | | End of split
% 240.80/47.34  | | 
% 240.80/47.34  | End of split
% 240.80/47.34  | 
% 240.80/47.34  End of proof
% 240.80/47.34  
% 240.80/47.34  Sub-proof #389 shows that the following formulas are inconsistent:
% 240.80/47.34  ----------------------------------------------------------------
% 240.80/47.34    (1)  op(e1, e0) = e0
% 240.80/47.34    (2)  op(e0, e1) = e2
% 240.80/47.34    (3)   ~ (e2 = e0)
% 240.80/47.34    (4)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.80/47.34             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.80/47.34           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.80/47.34             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.80/47.34           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 240.80/47.34           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.80/47.34           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.80/47.34    (5)  op(e2, e0) = e2
% 240.80/47.34    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.34    (7)   ~ (e1 = e0)
% 240.80/47.34  
% 240.80/47.34  Begin of proof
% 240.80/47.34  | 
% 240.80/47.34  | BETA: splitting (4) gives:
% 240.80/47.34  | 
% 240.80/47.34  | Case 1:
% 240.80/47.34  | | 
% 240.80/47.34  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.80/47.34  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 240.80/47.34  | |        & op(e0, e2) = e0
% 240.80/47.34  | | 
% 240.80/47.34  | | ALPHA: (8) implies:
% 240.80/47.34  | |   (9)  op(e2, e0) = e0
% 240.80/47.34  | | 
% 240.80/47.34  | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #2121.
% 240.80/47.34  | | 
% 240.80/47.34  | Case 2:
% 240.80/47.34  | | 
% 240.80/47.34  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.80/47.34  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.80/47.34  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.80/47.34  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.80/47.34  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.80/47.34  | | 
% 240.80/47.34  | | REF_CLOSE: (1), (2), (3), (6), (7), (10) are inconsistent by sub-proof #390.
% 240.80/47.34  | | 
% 240.80/47.34  | End of split
% 240.80/47.34  | 
% 240.80/47.34  End of proof
% 240.80/47.34  
% 240.80/47.34  Sub-proof #390 shows that the following formulas are inconsistent:
% 240.80/47.34  ----------------------------------------------------------------
% 240.80/47.34    (1)  op(e1, e0) = e0
% 240.80/47.34    (2)  op(e0, e1) = e2
% 240.80/47.34    (3)   ~ (e2 = e0)
% 240.80/47.34    (4)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.80/47.34             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.80/47.34           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 240.80/47.34             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 240.80/47.34           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.80/47.34    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.34    (6)   ~ (e1 = e0)
% 240.80/47.34  
% 240.80/47.34  Begin of proof
% 240.80/47.34  | 
% 240.80/47.34  | BETA: splitting (4) gives:
% 240.80/47.34  | 
% 240.80/47.34  | Case 1:
% 240.80/47.34  | | 
% 240.80/47.34  | |   (7)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.80/47.34  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 240.80/47.34  | |        & op(e0, e1) = e1
% 240.80/47.34  | | 
% 240.80/47.34  | | ALPHA: (7) implies:
% 240.80/47.34  | |   (8)  op(e1, e0) = e1
% 240.80/47.34  | | 
% 240.80/47.34  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2284.
% 240.80/47.34  | | 
% 240.80/47.34  | Case 2:
% 240.80/47.34  | | 
% 240.80/47.34  | |   (9)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 240.80/47.34  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 240.80/47.34  | |        & op(e0, e1) = e0
% 240.80/47.34  | | 
% 240.80/47.34  | | ALPHA: (9) implies:
% 240.80/47.34  | |   (10)  op(e0, e1) = e0
% 240.80/47.34  | | 
% 240.80/47.34  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #458.
% 240.80/47.34  | | 
% 240.80/47.34  | End of split
% 240.80/47.34  | 
% 240.80/47.34  End of proof
% 240.80/47.34  
% 240.80/47.34  Sub-proof #391 shows that the following formulas are inconsistent:
% 240.80/47.34  ----------------------------------------------------------------
% 240.80/47.34    (1)  all_58_1 = e3
% 240.80/47.34    (2)   ~ (e3 = e1)
% 240.80/47.35    (3)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.80/47.35         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.80/47.35    (4)  op(e3, e1) = all_52_8
% 240.80/47.35    (5)   ~ (e3 = e2)
% 240.80/47.35    (6)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 240.80/47.35    (7)  op(e3, e0) = all_52_12
% 240.80/47.35    (8)  op(e3, e3) = e2
% 240.80/47.35    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.35    (10)   ~ (all_52_12 = e3)
% 240.80/47.35    (11)  all_58_2 = e3
% 240.80/47.35    (12)   ~ (e2 = e1)
% 240.80/47.35    (13)   ~ (all_52_8 = e3)
% 240.80/47.35  
% 240.80/47.35  Begin of proof
% 240.80/47.35  | 
% 240.80/47.35  | BETA: splitting (6) gives:
% 240.80/47.35  | 
% 240.80/47.35  | Case 1:
% 240.80/47.35  | | 
% 240.80/47.35  | |   (14)  all_58_0 = e1 & op(e3, e3) = e1
% 240.80/47.35  | | 
% 240.80/47.35  | | ALPHA: (14) implies:
% 240.80/47.35  | |   (15)  op(e3, e3) = e1
% 240.80/47.35  | | 
% 240.80/47.35  | | REF_CLOSE: (8), (9), (12), (15) are inconsistent by sub-proof #2267.
% 240.80/47.35  | | 
% 240.80/47.35  | Case 2:
% 240.80/47.35  | | 
% 240.80/47.35  | |   (16)  all_58_2 = e1 & op(e2, e3) = e1
% 240.80/47.35  | | 
% 240.80/47.35  | | ALPHA: (16) implies:
% 240.80/47.35  | |   (17)  all_58_2 = e1
% 240.80/47.35  | | 
% 240.80/47.35  | | COMBINE_EQS: (11), (17) imply:
% 240.80/47.35  | |   (18)  e3 = e1
% 240.80/47.35  | | 
% 240.80/47.35  | | COMBINE_EQS: (1), (18) imply:
% 240.80/47.35  | |   (19)  all_58_1 = e1
% 240.80/47.35  | | 
% 240.80/47.35  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (13), (19) are
% 240.80/47.35  | |            inconsistent by sub-proof #1327.
% 240.80/47.35  | | 
% 240.80/47.35  | End of split
% 240.80/47.35  | 
% 240.80/47.35  End of proof
% 240.80/47.35  
% 240.80/47.35  Sub-proof #392 shows that the following formulas are inconsistent:
% 240.80/47.35  ----------------------------------------------------------------
% 240.80/47.35    (1)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) = all_22_1
% 240.80/47.35           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1) =
% 240.80/47.35           all_22_1 & $i(all_22_1))
% 240.80/47.35    (2)  op(e2, e1) = e2
% 240.80/47.35    (3)  op(e2, e2) = e1
% 240.80/47.35    (4)  op(e3, e0) = e2
% 240.80/47.35    (5)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) = all_50_1
% 240.80/47.35           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0) =
% 240.80/47.35           all_50_1 & $i(all_50_1))
% 240.80/47.35    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.35    (7)  op(e2, e1) = all_56_19
% 240.80/47.35    (8)  op(e2, all_56_19) = e2
% 240.80/47.35    (9)   ~ (e2 = e1)
% 240.80/47.35    (10)  op(e2, e1) = all_30_1
% 240.80/47.35  
% 240.80/47.35  Begin of proof
% 240.80/47.35  | 
% 240.80/47.35  | BETA: splitting (1) gives:
% 240.80/47.35  | 
% 240.80/47.35  | Case 1:
% 240.80/47.35  | | 
% 240.80/47.35  | |   (11)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) =
% 240.80/47.35  | |         all_22_1 & $i(all_22_0) & $i(all_22_1)
% 240.80/47.35  | | 
% 240.80/47.35  | | ALPHA: (11) implies:
% 240.80/47.35  | |   (12)  op(e2, e1) = all_22_1
% 240.80/47.35  | | 
% 240.80/47.35  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12) are
% 240.80/47.35  | |            inconsistent by sub-proof #393.
% 240.80/47.35  | | 
% 240.80/47.35  | Case 2:
% 240.80/47.35  | | 
% 240.80/47.35  | |   (13)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 & $i(all_22_1)
% 240.80/47.35  | | 
% 240.80/47.35  | | ALPHA: (13) implies:
% 240.80/47.35  | |   (14)  op(e2, e1) = all_22_1
% 240.80/47.35  | | 
% 240.80/47.35  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (14) are
% 240.80/47.35  | |            inconsistent by sub-proof #393.
% 240.80/47.35  | | 
% 240.80/47.35  | End of split
% 240.80/47.35  | 
% 240.80/47.35  End of proof
% 240.80/47.35  
% 240.80/47.35  Sub-proof #393 shows that the following formulas are inconsistent:
% 240.80/47.35  ----------------------------------------------------------------
% 240.80/47.35    (1)  op(e2, e1) = e2
% 240.80/47.35    (2)  op(e2, e2) = e1
% 240.80/47.35    (3)  op(e3, e0) = e2
% 240.80/47.35    (4)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) = all_50_1
% 240.80/47.35           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0) =
% 240.80/47.35           all_50_1 & $i(all_50_1))
% 240.80/47.35    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.35    (6)  op(e2, e1) = all_56_19
% 240.80/47.35    (7)  op(e2, e1) = all_22_1
% 240.80/47.35    (8)  op(e2, all_56_19) = e2
% 240.80/47.35    (9)   ~ (e2 = e1)
% 240.80/47.35    (10)  op(e2, e1) = all_30_1
% 240.80/47.35  
% 240.80/47.35  Begin of proof
% 240.80/47.35  | 
% 240.80/47.35  | BETA: splitting (4) gives:
% 240.80/47.35  | 
% 240.80/47.35  | Case 1:
% 240.80/47.35  | | 
% 240.80/47.35  | | 
% 240.80/47.35  | | GROUND_INST: instantiating (5) with e2, all_30_1, e1, e2, simplifying with
% 240.80/47.35  | |              (1), (10) gives:
% 240.80/47.35  | |   (11)  all_30_1 = e2
% 240.80/47.35  | | 
% 240.80/47.35  | | GROUND_INST: instantiating (5) with all_30_1, all_56_19, e1, e2, simplifying
% 240.80/47.35  | |              with (6), (10) gives:
% 240.80/47.35  | |   (12)  all_56_19 = all_30_1
% 240.80/47.35  | | 
% 240.80/47.35  | | GROUND_INST: instantiating (5) with all_22_1, all_56_19, e1, e2, simplifying
% 240.80/47.35  | |              with (6), (7) gives:
% 240.80/47.35  | |   (13)  all_56_19 = all_22_1
% 240.80/47.35  | | 
% 240.80/47.35  | | COMBINE_EQS: (12), (13) imply:
% 240.80/47.35  | |   (14)  all_30_1 = all_22_1
% 240.80/47.35  | | 
% 240.80/47.35  | | SIMP: (14) implies:
% 240.80/47.35  | |   (15)  all_30_1 = all_22_1
% 240.80/47.35  | | 
% 240.80/47.35  | | COMBINE_EQS: (11), (15) imply:
% 240.80/47.35  | |   (16)  all_22_1 = e2
% 240.80/47.35  | | 
% 240.80/47.35  | | COMBINE_EQS: (13), (16) imply:
% 240.80/47.35  | |   (17)  all_56_19 = e2
% 240.80/47.35  | | 
% 240.80/47.35  | | REDUCE: (8), (17) imply:
% 240.80/47.35  | |   (18)  op(e2, e2) = e2
% 240.80/47.35  | | 
% 240.80/47.35  | | REF_CLOSE: (2), (5), (9), (18) are inconsistent by sub-proof #2235.
% 240.80/47.35  | | 
% 240.80/47.35  | Case 2:
% 240.80/47.35  | | 
% 240.80/47.35  | |   (19)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 & $i(all_50_1)
% 240.80/47.35  | | 
% 240.80/47.35  | | ALPHA: (19) implies:
% 240.80/47.35  | |   (20)   ~ (all_50_1 = e2)
% 240.80/47.35  | |   (21)  op(e3, e0) = all_50_1
% 240.80/47.35  | | 
% 240.80/47.35  | | REF_CLOSE: (3), (5), (20), (21) are inconsistent by sub-proof #1884.
% 240.80/47.35  | | 
% 240.80/47.35  | End of split
% 240.80/47.35  | 
% 240.80/47.35  End of proof
% 240.80/47.35  
% 240.80/47.35  Sub-proof #394 shows that the following formulas are inconsistent:
% 240.80/47.35  ----------------------------------------------------------------
% 240.80/47.35    (1)  op(e1, e3) = e2
% 240.80/47.35    (2)  op(e3, e1) = all_52_8
% 240.80/47.35    (3)  op(e3, e1) = e1
% 240.80/47.35    (4)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.80/47.35         $i(all_56_17)
% 240.80/47.35    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.35    (6)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) = all_46_1
% 240.80/47.35           & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3) =
% 240.80/47.35           all_46_1 & $i(all_46_1))
% 240.80/47.35    (7)   ~ (all_52_8 = e3)
% 240.80/47.35  
% 240.80/47.35  Begin of proof
% 240.80/47.35  | 
% 240.80/47.35  | ALPHA: (4) implies:
% 240.80/47.35  |   (8)  op(e3, e1) = all_56_17
% 240.80/47.35  |   (9)  op(e3, all_56_17) = e3
% 240.80/47.35  | 
% 240.80/47.35  | BETA: splitting (6) gives:
% 240.80/47.35  | 
% 240.80/47.35  | Case 1:
% 240.80/47.35  | | 
% 240.80/47.35  | | 
% 240.80/47.35  | | GROUND_INST: instantiating (5) with e1, all_56_17, e1, e3, simplifying with
% 240.80/47.35  | |              (3), (8) gives:
% 240.80/47.35  | |   (10)  all_56_17 = e1
% 240.80/47.35  | | 
% 240.80/47.35  | | REDUCE: (9), (10) imply:
% 240.80/47.35  | |   (11)  op(e3, e1) = e3
% 240.80/47.35  | | 
% 240.80/47.35  | | REF_CLOSE: (2), (5), (7), (11) are inconsistent by sub-proof #2260.
% 240.80/47.35  | | 
% 240.80/47.35  | Case 2:
% 240.80/47.35  | | 
% 240.80/47.36  | |   (12)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.80/47.36  | | 
% 240.80/47.36  | | REF_CLOSE: (1), (5), (12) are inconsistent by sub-proof #395.
% 240.80/47.36  | | 
% 240.80/47.36  | End of split
% 240.80/47.36  | 
% 240.80/47.36  End of proof
% 240.80/47.36  
% 240.80/47.36  Sub-proof #395 shows that the following formulas are inconsistent:
% 240.80/47.36  ----------------------------------------------------------------
% 240.80/47.36    (1)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.80/47.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.36    (3)  op(e1, e3) = e2
% 240.80/47.36  
% 240.80/47.36  Begin of proof
% 240.80/47.36  | 
% 240.80/47.36  | ALPHA: (1) implies:
% 240.80/47.36  |   (4)   ~ (all_46_1 = e2)
% 240.80/47.36  |   (5)  op(e1, e3) = all_46_1
% 240.80/47.36  | 
% 240.80/47.36  | GROUND_INST: instantiating (2) with e2, all_46_1, e3, e1, simplifying with
% 240.80/47.36  |              (3), (5) gives:
% 240.80/47.36  |   (6)  all_46_1 = e2
% 240.80/47.36  | 
% 240.80/47.36  | REDUCE: (4), (6) imply:
% 240.80/47.36  |   (7)  $false
% 240.80/47.36  | 
% 240.80/47.36  | CLOSE: (7) is inconsistent.
% 240.80/47.36  | 
% 240.80/47.36  End of proof
% 240.80/47.36  
% 240.80/47.36  Sub-proof #396 shows that the following formulas are inconsistent:
% 240.80/47.36  ----------------------------------------------------------------
% 240.80/47.36    (1)   ~ (e3 = e0)
% 240.80/47.36    (2)  op(e0, e1) = all_52_11
% 240.80/47.36    (3)   ~ (e2 = e0)
% 240.80/47.36    (4)  op(e1, e2) = all_52_6
% 240.80/47.36    (5)  all_58_6 = e2
% 240.80/47.36    (6)  op(e0, e3) = all_52_3
% 240.80/47.36    (7)  op(e1, e0) = e1
% 240.80/47.36    (8)  op(e0, all_52_3) = e0
% 240.80/47.36    (9)  op(e3, e3) = e1
% 240.80/47.36    (10)   ~ (all_52_11 = e3)
% 240.80/47.36    (11)  op(e3, e1) = all_52_8
% 240.80/47.36    (12)  op(e2, e1) = all_52_9
% 240.80/47.36    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.80/47.36          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.80/47.36    (14)   ~ (all_52_6 = e3)
% 240.80/47.36    (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.80/47.36          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.80/47.36    (16)   ~ (all_52_9 = e3)
% 240.80/47.36    (17)  op(e0, e0) = e3
% 240.80/47.36    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.36    (19)   ~ (e1 = e0)
% 240.80/47.36    (20)  all_58_2 = e3
% 240.80/47.36    (21)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.80/47.36          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.80/47.36    (22)   ~ (all_52_8 = e3)
% 240.80/47.36  
% 240.80/47.36  Begin of proof
% 240.80/47.36  | 
% 240.80/47.36  | BETA: splitting (21) gives:
% 240.80/47.36  | 
% 240.80/47.36  | Case 1:
% 240.80/47.36  | | 
% 240.80/47.36  | |   (23)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 240.80/47.36  | |           e0)
% 240.80/47.36  | | 
% 240.80/47.36  | | BETA: splitting (23) gives:
% 240.80/47.36  | | 
% 240.80/47.36  | | Case 1:
% 240.80/47.36  | | | 
% 240.80/47.36  | | |   (24)  all_58_6 = e0 & op(e1, e3) = e0
% 240.80/47.36  | | | 
% 240.80/47.36  | | | REF_CLOSE: (3), (5), (24) are inconsistent by sub-proof #1678.
% 240.80/47.36  | | | 
% 240.80/47.36  | | Case 2:
% 240.80/47.36  | | | 
% 240.80/47.36  | | |   (25)  all_58_7 = e0 & op(e1, e2) = e0
% 240.80/47.36  | | | 
% 240.80/47.36  | | | ALPHA: (25) implies:
% 240.80/47.36  | | |   (26)  op(e1, e2) = e0
% 240.80/47.36  | | | 
% 240.80/47.36  | | | BETA: splitting (13) gives:
% 240.80/47.36  | | | 
% 240.80/47.36  | | | Case 1:
% 240.80/47.36  | | | | 
% 240.80/47.36  | | | |   (27)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 240.80/47.36  | | | |           = e0)
% 240.80/47.36  | | | | 
% 240.80/47.36  | | | | REF_CLOSE: (1), (9), (18), (19), (20), (27) are inconsistent by
% 240.80/47.36  | | | |            sub-proof #1222.
% 240.80/47.36  | | | | 
% 240.80/47.36  | | | Case 2:
% 240.80/47.36  | | | | 
% 240.80/47.36  | | | |   (28)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 240.80/47.36  | | | |           = e0)
% 240.80/47.36  | | | | 
% 240.80/47.36  | | | | BETA: splitting (28) gives:
% 240.80/47.36  | | | | 
% 240.80/47.36  | | | | Case 1:
% 240.80/47.36  | | | | | 
% 240.80/47.36  | | | | |   (29)  all_58_6 = e0 & op(e1, e3) = e0
% 240.80/47.36  | | | | | 
% 240.80/47.36  | | | | | REF_CLOSE: (3), (5), (29) are inconsistent by sub-proof #1678.
% 240.80/47.36  | | | | | 
% 240.80/47.36  | | | | Case 2:
% 240.80/47.36  | | | | | 
% 240.80/47.36  | | | | |   (30)  all_58_12 = e0 & op(e0, e3) = e0
% 240.80/47.36  | | | | | 
% 240.80/47.36  | | | | | ALPHA: (30) implies:
% 240.80/47.36  | | | | |   (31)  op(e0, e3) = e0
% 240.80/47.36  | | | | | 
% 240.80/47.36  | | | | | GROUND_INST: instantiating (18) with all_52_3, e0, e3, e0, simplifying
% 240.80/47.36  | | | | |              with (6), (31) gives:
% 240.80/47.36  | | | | |   (32)  all_52_3 = e0
% 240.80/47.36  | | | | | 
% 240.80/47.36  | | | | | GROUND_INST: instantiating (18) with all_52_6, e0, e2, e1, simplifying
% 240.80/47.36  | | | | |              with (4), (26) gives:
% 240.80/47.36  | | | | |   (33)  all_52_6 = e0
% 240.80/47.36  | | | | | 
% 240.80/47.36  | | | | | REDUCE: (14), (33) imply:
% 240.80/47.36  | | | | |   (34)   ~ (e3 = e0)
% 240.80/47.36  | | | | | 
% 240.80/47.36  | | | | | REDUCE: (8), (32) imply:
% 240.80/47.36  | | | | |   (35)  op(e0, e0) = e0
% 240.80/47.36  | | | | | 
% 240.80/47.36  | | | | | REF_CLOSE: (1), (17), (18), (35) are inconsistent by sub-proof #2079.
% 240.80/47.36  | | | | | 
% 240.80/47.36  | | | | End of split
% 240.80/47.36  | | | | 
% 240.80/47.36  | | | End of split
% 240.80/47.36  | | | 
% 240.80/47.36  | | End of split
% 240.80/47.36  | | 
% 240.80/47.36  | Case 2:
% 240.80/47.36  | | 
% 240.80/47.36  | |   (36)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.80/47.36  | |           e0)
% 240.80/47.36  | | 
% 240.80/47.36  | | REF_CLOSE: (1), (2), (7), (10), (11), (12), (15), (16), (18), (19), (22),
% 240.80/47.36  | |            (36) are inconsistent by sub-proof #400.
% 240.80/47.36  | | 
% 240.80/47.36  | End of split
% 240.80/47.36  | 
% 240.80/47.36  End of proof
% 240.80/47.36  
% 240.80/47.36  Sub-proof #397 shows that the following formulas are inconsistent:
% 240.80/47.36  ----------------------------------------------------------------
% 240.80/47.36    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.80/47.36         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.80/47.36    (2)   ~ (e3 = e0)
% 240.80/47.36    (3)  op(e0, e1) = all_52_11
% 240.80/47.36    (4)   ~ (e2 = e0)
% 240.80/47.36    (5)   ~ (all_52_12 = e0)
% 240.80/47.36    (6)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.80/47.36         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.80/47.36    (7)  op(e3, e0) = e1
% 240.80/47.36    (8)   ~ (all_52_8 = e0)
% 240.80/47.36    (9)  all_58_15 = e3
% 240.80/47.36    (10)  op(e2, e3) = e3
% 240.80/47.36    (11)  op(e0, e3) = all_52_3
% 240.80/47.36    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.80/47.36          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.80/47.36    (13)   ~ (e3 = e1)
% 240.80/47.36    (14)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) =
% 240.80/47.36            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2,
% 240.80/47.36              e1) = all_22_1 & $i(all_22_1))
% 240.80/47.36    (15)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.80/47.36          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.80/47.36    (16)  op(e0, all_52_3) = e0
% 240.80/47.36    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.80/47.36              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.80/47.36                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.80/47.36                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.80/47.36    (18)   ~ (all_52_11 = e3)
% 240.80/47.36    (19)  op(e3, e1) = all_52_8
% 240.80/47.36    (20)  op(e2, e1) = all_52_9
% 240.80/47.36    (21)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) =
% 240.80/47.36            all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2,
% 240.80/47.36              e1) = all_30_1 & $i(all_30_1))
% 240.80/47.36    (22)   ~ (e3 = e2)
% 240.80/47.36    (23)  op(e2, e2) = e1
% 240.80/47.37    (24)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.80/47.37            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.80/47.37            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.80/47.37            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.80/47.37            op(e0, all_56_31) = e0)
% 240.80/47.37    (25)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 240.80/47.37            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 240.80/47.37              e0) = all_16_1 & $i(all_16_1))
% 240.80/47.37    (26)  op(e3, e0) = all_52_12
% 240.80/47.37    (27)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 240.80/47.37            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 240.80/47.37              e0) = all_50_1 & $i(all_50_1))
% 240.80/47.37    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.80/47.37          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.80/47.37    (29)   ~ (all_52_9 = e3)
% 240.80/47.37    (30)  all_56_31 = e3
% 240.80/47.37    (31)  op(e0, e0) = e3
% 240.80/47.37    (32)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.80/47.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.80/47.37    (33)  all_58_8 = e3
% 240.80/47.37    (34)   ~ (e1 = e0)
% 240.80/47.37    (35)  op(e3, e3) = e0
% 240.80/47.37    (36)  op(e3, e2) = e3
% 240.80/47.37    (37)  all_58_9 = e1
% 240.80/47.37    (38)   ~ (all_52_9 = e1)
% 240.80/47.37    (39)   ~ (e2 = e1)
% 240.80/47.37    (40)   ~ (all_52_8 = e3)
% 240.80/47.37  
% 240.80/47.37  Begin of proof
% 240.80/47.37  | 
% 240.80/47.37  | BETA: splitting (1) gives:
% 240.80/47.37  | 
% 240.80/47.37  | Case 1:
% 240.80/47.37  | | 
% 240.80/47.37  | |   (41)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 240.80/47.37  | |           e2)
% 240.80/47.37  | | 
% 240.80/47.37  | | REF_CLOSE: (4), (22), (32), (35), (36), (41) are inconsistent by sub-proof
% 240.80/47.37  | |            #1857.
% 240.80/47.37  | | 
% 240.80/47.37  | Case 2:
% 240.80/47.37  | | 
% 240.80/47.37  | |   (42)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 240.80/47.37  | |           e2)
% 240.80/47.37  | | 
% 240.80/47.37  | | BETA: splitting (42) gives:
% 240.80/47.37  | | 
% 240.80/47.37  | | Case 1:
% 240.80/47.37  | | | 
% 240.80/47.37  | | |   (43)  all_58_4 = e2 & op(e3, e1) = e2
% 240.80/47.37  | | | 
% 240.80/47.37  | | | ALPHA: (43) implies:
% 240.80/47.37  | | |   (44)  all_58_4 = e2
% 240.80/47.37  | | | 
% 240.80/47.37  | | | BETA: splitting (6) gives:
% 240.80/47.37  | | | 
% 240.80/47.37  | | | Case 1:
% 240.80/47.37  | | | | 
% 240.80/47.37  | | | |   (45)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 240.80/47.37  | | | |           = e1)
% 240.80/47.37  | | | | 
% 240.80/47.37  | | | | REF_CLOSE: (20), (32), (38), (39), (44), (45) are inconsistent by
% 240.80/47.37  | | | |            sub-proof #407.
% 240.80/47.37  | | | | 
% 240.80/47.37  | | | Case 2:
% 240.80/47.37  | | | | 
% 240.80/47.37  | | | |   (46)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 240.80/47.37  | | | |           = e1)
% 240.80/47.37  | | | | 
% 240.80/47.37  | | | | BETA: splitting (46) gives:
% 240.80/47.37  | | | | 
% 240.80/47.37  | | | | Case 1:
% 240.80/47.37  | | | | | 
% 240.80/47.37  | | | | |   (47)  all_58_8 = e1 & op(e1, e1) = e1
% 240.80/47.37  | | | | | 
% 240.80/47.37  | | | | | REF_CLOSE: (13), (33), (47) are inconsistent by sub-proof #406.
% 240.80/47.37  | | | | | 
% 240.80/47.37  | | | | Case 2:
% 240.80/47.37  | | | | | 
% 240.80/47.37  | | | | |   (48)  all_58_14 = e1 & op(e0, e1) = e1
% 240.80/47.37  | | | | | 
% 240.80/47.37  | | | | | ALPHA: (48) implies:
% 240.80/47.37  | | | | |   (49)  op(e0, e1) = e1
% 240.80/47.37  | | | | | 
% 240.80/47.37  | | | | | BETA: splitting (17) gives:
% 240.86/47.37  | | | | | 
% 240.86/47.37  | | | | | Case 1:
% 240.86/47.37  | | | | | | 
% 240.86/47.37  | | | | | |   (50)  all_58_15 = e0 & op(e0, e0) = e0
% 240.86/47.37  | | | | | | 
% 240.86/47.37  | | | | | | ALPHA: (50) implies:
% 240.86/47.37  | | | | | |   (51)  op(e0, e0) = e0
% 240.86/47.37  | | | | | | 
% 240.86/47.37  | | | | | | REF_CLOSE: (2), (31), (32), (51) are inconsistent by sub-proof
% 240.86/47.37  | | | | | |            #2079.
% 240.86/47.37  | | | | | | 
% 240.86/47.37  | | | | | Case 2:
% 240.86/47.37  | | | | | | 
% 240.86/47.37  | | | | | |   (52)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 240.86/47.37  | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 240.86/47.37  | | | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.86/47.37  | | | | | |             op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.86/47.37  | | | | | | 
% 240.86/47.37  | | | | | | ALPHA: (52) implies:
% 240.86/47.37  | | | | | |   (53)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 240.86/47.37  | | | | | |             e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.86/47.37  | | | | | | 
% 240.86/47.37  | | | | | | BETA: splitting (15) gives:
% 240.86/47.37  | | | | | | 
% 240.86/47.37  | | | | | | Case 1:
% 240.86/47.37  | | | | | | | 
% 240.86/47.37  | | | | | | |   (54)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 240.86/47.37  | | | | | | |           op(e2, e1) = e0)
% 240.86/47.37  | | | | | | | 
% 240.86/47.37  | | | | | | | BETA: splitting (54) gives:
% 240.86/47.37  | | | | | | | 
% 240.86/47.37  | | | | | | | Case 1:
% 240.86/47.37  | | | | | | | | 
% 240.86/47.37  | | | | | | | |   (55)  all_58_4 = e0 & op(e3, e1) = e0
% 240.86/47.37  | | | | | | | | 
% 240.86/47.37  | | | | | | | | REF_CLOSE: (8), (19), (32), (55) are inconsistent by sub-proof
% 240.86/47.37  | | | | | | | |            #1908.
% 240.86/47.37  | | | | | | | | 
% 240.86/47.37  | | | | | | | Case 2:
% 240.86/47.37  | | | | | | | | 
% 240.86/47.37  | | | | | | | |   (56)  all_58_5 = e0 & op(e2, e1) = e0
% 240.86/47.37  | | | | | | | | 
% 240.86/47.37  | | | | | | | | ALPHA: (56) implies:
% 240.86/47.37  | | | | | | | |   (57)  op(e2, e1) = e0
% 240.86/47.37  | | | | | | | | 
% 240.86/47.37  | | | | | | | | BETA: splitting (12) gives:
% 240.86/47.37  | | | | | | | | 
% 240.86/47.37  | | | | | | | | Case 1:
% 240.86/47.37  | | | | | | | | | 
% 240.86/47.37  | | | | | | | | |   (58)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 240.86/47.37  | | | | | | | | |           op(e2, e2) = e2)
% 240.86/47.37  | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | REF_CLOSE: (10), (22), (23), (32), (39), (58) are inconsistent
% 240.86/47.37  | | | | | | | | |            by sub-proof #428.
% 240.86/47.37  | | | | | | | | | 
% 240.86/47.37  | | | | | | | | Case 2:
% 240.86/47.37  | | | | | | | | | 
% 240.86/47.37  | | | | | | | | |   (59)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 240.86/47.37  | | | | | | | | |           op(e2, e0) = e2)
% 240.86/47.37  | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | BETA: splitting (59) gives:
% 240.86/47.37  | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | Case 1:
% 240.86/47.37  | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | |   (60)  all_58_5 = e2 & op(e2, e1) = e2
% 240.86/47.37  | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | ALPHA: (60) implies:
% 240.86/47.37  | | | | | | | | | |   (61)  op(e2, e1) = e2
% 240.86/47.37  | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | REF_CLOSE: (4), (32), (57), (61) are inconsistent by
% 240.86/47.37  | | | | | | | | | |            sub-proof #1906.
% 240.86/47.37  | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | Case 2:
% 240.86/47.37  | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | |   (62)  all_58_10 = e2 & op(e2, e0) = e2
% 240.86/47.37  | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | ALPHA: (62) implies:
% 240.86/47.37  | | | | | | | | | |   (63)  op(e2, e0) = e2
% 240.86/47.37  | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | BETA: splitting (53) gives:
% 240.86/47.37  | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | Case 1:
% 240.86/47.37  | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | |   (64)  all_58_9 = e0 & op(e3, e0) = e0
% 240.86/47.37  | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | ALPHA: (64) implies:
% 240.86/47.37  | | | | | | | | | | |   (65)  op(e3, e0) = e0
% 240.86/47.37  | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | REF_CLOSE: (5), (26), (32), (65) are inconsistent by
% 240.86/47.37  | | | | | | | | | | |            sub-proof #2258.
% 240.86/47.37  | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | Case 2:
% 240.86/47.37  | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | |   (66)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 240.86/47.37  | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 240.86/47.37  | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | BETA: splitting (66) gives:
% 240.86/47.37  | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | Case 1:
% 240.86/47.37  | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | |   (67)  all_58_10 = e0 & op(e2, e0) = e0
% 240.86/47.37  | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | ALPHA: (67) implies:
% 240.86/47.37  | | | | | | | | | | | |   (68)  op(e2, e0) = e0
% 240.86/47.37  | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | REF_CLOSE: (4), (32), (63), (68) are inconsistent by
% 240.86/47.37  | | | | | | | | | | | |            sub-proof #2121.
% 240.86/47.37  | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | Case 2:
% 240.86/47.37  | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | |   (69)  all_58_11 = e0 & op(e1, e0) = e0
% 240.86/47.37  | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | ALPHA: (69) implies:
% 240.86/47.37  | | | | | | | | | | | |   (70)  op(e1, e0) = e0
% 240.86/47.37  | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | BETA: splitting (24) gives:
% 240.86/47.37  | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | Case 1:
% 240.86/47.37  | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | |   (71)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.86/47.37  | | | | | | | | | | | | |             e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 240.86/47.37  | | | | | | | | | | | | |           = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 240.86/47.37  | | | | | | | | | | | | |           all_56_27 & $i(all_56_27))
% 240.86/47.37  | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | | REF_CLOSE: (7), (14), (19), (21), (23), (25), (27), (32),
% 240.86/47.37  | | | | | | | | | | | | |            (39), (40), (57), (63), (71) are inconsistent by
% 240.86/47.37  | | | | | | | | | | | | |            sub-proof #404.
% 240.86/47.37  | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | Case 2:
% 240.86/47.37  | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | |   (72)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.86/47.37  | | | | | | | | | | | | |             e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 240.86/47.37  | | | | | | | | | | | | |           = e0 & op(e0, all_56_31) = e0)
% 240.86/47.37  | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | | BETA: splitting (72) gives:
% 240.86/47.37  | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | | Case 1:
% 240.86/47.37  | | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | | |   (73)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.86/47.37  | | | | | | | | | | | | | |           e0) = all_56_29 & $i(all_56_29)
% 240.86/47.37  | | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | | | REF_CLOSE: (7), (25), (27), (32), (34), (70), (73) are
% 240.86/47.37  | | | | | | | | | | | | | |            inconsistent by sub-proof #402.
% 240.86/47.37  | | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | | Case 2:
% 240.86/47.37  | | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | | |   (74)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.86/47.37  | | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | | | ALPHA: (74) implies:
% 240.86/47.37  | | | | | | | | | | | | | |   (75)  op(e0, all_56_31) = e0
% 240.86/47.37  | | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | | | REDUCE: (30), (75) imply:
% 240.86/47.37  | | | | | | | | | | | | | |   (76)  op(e0, e3) = e0
% 240.86/47.37  | | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | | | REF_CLOSE: (2), (9), (11), (16), (17), (20), (29), (31),
% 240.86/47.37  | | | | | | | | | | | | | |            (32), (57), (76) are inconsistent by sub-proof
% 240.86/47.37  | | | | | | | | | | | | | |            #813.
% 240.86/47.37  | | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | | End of split
% 240.86/47.37  | | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | | End of split
% 240.86/47.37  | | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | | End of split
% 240.86/47.37  | | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | | End of split
% 240.86/47.37  | | | | | | | | | | 
% 240.86/47.37  | | | | | | | | | End of split
% 240.86/47.37  | | | | | | | | | 
% 240.86/47.37  | | | | | | | | End of split
% 240.86/47.37  | | | | | | | | 
% 240.86/47.37  | | | | | | | End of split
% 240.86/47.37  | | | | | | | 
% 240.86/47.37  | | | | | | Case 2:
% 240.86/47.37  | | | | | | | 
% 240.86/47.37  | | | | | | |   (77)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 240.86/47.37  | | | | | | |           op(e0, e1) = e0)
% 240.86/47.37  | | | | | | | 
% 240.86/47.37  | | | | | | | REF_CLOSE: (2), (3), (18), (20), (22), (28), (29), (32), (34),
% 240.86/47.37  | | | | | | |            (44), (49), (77) are inconsistent by sub-proof #401.
% 240.86/47.37  | | | | | | | 
% 240.86/47.37  | | | | | | End of split
% 240.86/47.37  | | | | | | 
% 240.86/47.37  | | | | | End of split
% 240.86/47.37  | | | | | 
% 240.86/47.37  | | | | End of split
% 240.86/47.37  | | | | 
% 240.86/47.38  | | | End of split
% 240.86/47.38  | | | 
% 240.86/47.38  | | Case 2:
% 240.86/47.38  | | | 
% 240.86/47.38  | | |   (78)  all_58_9 = e2 & op(e3, e0) = e2
% 240.86/47.38  | | | 
% 240.86/47.38  | | | REF_CLOSE: (37), (39), (78) are inconsistent by sub-proof #1745.
% 240.86/47.38  | | | 
% 240.86/47.38  | | End of split
% 240.86/47.38  | | 
% 240.86/47.38  | End of split
% 240.86/47.38  | 
% 240.86/47.38  End of proof
% 240.86/47.38  
% 240.86/47.38  Sub-proof #398 shows that the following formulas are inconsistent:
% 240.86/47.38  ----------------------------------------------------------------
% 240.86/47.38    (1)  op(e1, e0) = e1
% 240.86/47.38    (2)   ~ (e3 = e2)
% 240.86/47.38    (3)  op(e1, e1) = e3
% 240.86/47.38    (4)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.86/47.38    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.38    (6)   ~ (e2 = e1)
% 240.86/47.38  
% 240.86/47.38  Begin of proof
% 240.86/47.38  | 
% 240.86/47.38  | BETA: splitting (4) gives:
% 240.86/47.38  | 
% 240.86/47.38  | Case 1:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (7)  all_58_8 = e2 & op(e1, e1) = e2
% 240.86/47.38  | | 
% 240.86/47.38  | | ALPHA: (7) implies:
% 240.86/47.38  | |   (8)  op(e1, e1) = e2
% 240.86/47.38  | | 
% 240.86/47.38  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #2206.
% 240.86/47.38  | | 
% 240.86/47.38  | Case 2:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (9)  all_58_11 = e2 & op(e1, e0) = e2
% 240.86/47.38  | | 
% 240.86/47.38  | | ALPHA: (9) implies:
% 240.86/47.38  | |   (10)  op(e1, e0) = e2
% 240.86/47.38  | | 
% 240.86/47.38  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #2019.
% 240.86/47.38  | | 
% 240.86/47.38  | End of split
% 240.86/47.38  | 
% 240.86/47.38  End of proof
% 240.86/47.38  
% 240.86/47.38  Sub-proof #399 shows that the following formulas are inconsistent:
% 240.86/47.38  ----------------------------------------------------------------
% 240.86/47.38    (1)   ~ (all_52_6 = e1)
% 240.86/47.38    (2)   ~ (all_8_2 = e0)
% 240.86/47.38    (3)   ~ (e3 = e0)
% 240.86/47.38    (4)  op(e0, e1) = all_52_11
% 240.86/47.38    (5)   ~ (e2 = e0)
% 240.86/47.38    (6)  op(e1, e2) = all_52_6
% 240.86/47.38    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.86/47.38         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.86/47.38    (8)  all_58_6 = e2
% 240.86/47.38    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.86/47.38         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.86/47.38    (10)  op(e1, e0) = e1
% 240.86/47.38    (11)  op(e1, e3) = e2
% 240.86/47.38    (12)   ~ (all_52_11 = e3)
% 240.86/47.38    (13)  op(e3, e1) = all_52_8
% 240.86/47.38    (14)  op(e1, all_52_2) = e1
% 240.86/47.38    (15)  op(e2, e1) = all_52_9
% 240.86/47.38    (16)   ~ (e3 = e2)
% 240.86/47.38    (17)  op(e2, e2) = e1
% 240.86/47.38    (18)  op(e2, e2) = all_8_2
% 240.86/47.38    (19)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.86/47.38          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.86/47.38    (20)   ~ (all_52_9 = e3)
% 240.86/47.38    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.38    (22)  op(e1, e3) = all_52_2
% 240.86/47.38    (23)   ~ (e1 = e0)
% 240.86/47.38    (24)  op(e3, e2) = e3
% 240.86/47.38    (25)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.86/47.38          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.86/47.38    (26)   ~ (e2 = e1)
% 240.86/47.38    (27)   ~ (all_52_8 = e3)
% 240.86/47.38  
% 240.86/47.38  Begin of proof
% 240.86/47.38  | 
% 240.86/47.38  | BETA: splitting (25) gives:
% 240.86/47.38  | 
% 240.86/47.38  | Case 1:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (28)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 240.86/47.38  | |           e0)
% 240.86/47.38  | | 
% 240.86/47.38  | | BETA: splitting (28) gives:
% 240.86/47.38  | | 
% 240.86/47.38  | | Case 1:
% 240.86/47.38  | | | 
% 240.86/47.38  | | |   (29)  all_58_6 = e0 & op(e1, e3) = e0
% 240.86/47.38  | | | 
% 240.86/47.38  | | | REF_CLOSE: (5), (8), (29) are inconsistent by sub-proof #1678.
% 240.86/47.38  | | | 
% 240.86/47.38  | | Case 2:
% 240.86/47.38  | | | 
% 240.86/47.38  | | |   (30)  all_58_7 = e0 & op(e1, e2) = e0
% 240.86/47.38  | | | 
% 240.86/47.38  | | | ALPHA: (30) implies:
% 240.86/47.38  | | |   (31)  all_58_7 = e0
% 240.86/47.38  | | | 
% 240.86/47.38  | | | BETA: splitting (7) gives:
% 240.86/47.38  | | | 
% 240.86/47.38  | | | Case 1:
% 240.86/47.38  | | | | 
% 240.86/47.38  | | | |   (32)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2)
% 240.86/47.38  | | | |           = e2)
% 240.86/47.38  | | | | 
% 240.86/47.38  | | | | REF_CLOSE: (16), (17), (21), (24), (26), (32) are inconsistent by
% 240.86/47.38  | | | |            sub-proof #1785.
% 240.86/47.38  | | | | 
% 240.86/47.38  | | | Case 2:
% 240.86/47.38  | | | | 
% 240.86/47.38  | | | |   (33)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2)
% 240.86/47.38  | | | |           = e2)
% 240.86/47.38  | | | | 
% 240.86/47.38  | | | | BETA: splitting (33) gives:
% 240.86/47.38  | | | | 
% 240.86/47.38  | | | | Case 1:
% 240.86/47.38  | | | | | 
% 240.86/47.38  | | | | |   (34)  all_58_7 = e2 & op(e1, e2) = e2
% 240.86/47.38  | | | | | 
% 240.86/47.38  | | | | | ALPHA: (34) implies:
% 240.86/47.38  | | | | |   (35)  all_58_7 = e2
% 240.86/47.38  | | | | | 
% 240.86/47.38  | | | | | REF_CLOSE: (5), (31), (35) are inconsistent by sub-proof #1587.
% 240.86/47.38  | | | | | 
% 240.86/47.38  | | | | Case 2:
% 240.86/47.38  | | | | | 
% 240.86/47.38  | | | | |   (36)  all_58_13 = e2 & op(e0, e2) = e2
% 240.86/47.38  | | | | | 
% 240.86/47.38  | | | | | ALPHA: (36) implies:
% 240.86/47.38  | | | | |   (37)  op(e0, e2) = e2
% 240.86/47.38  | | | | | 
% 240.86/47.38  | | | | | BETA: splitting (9) gives:
% 240.86/47.38  | | | | | 
% 240.86/47.38  | | | | | Case 1:
% 240.86/47.38  | | | | | | 
% 240.86/47.38  | | | | | |   (38)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 240.86/47.38  | | | | | |             e2) = e0)
% 240.86/47.38  | | | | | | 
% 240.86/47.38  | | | | | | REF_CLOSE: (2), (3), (18), (21), (24), (38) are inconsistent by
% 240.86/47.38  | | | | | |            sub-proof #1323.
% 240.86/47.38  | | | | | | 
% 240.86/47.38  | | | | | Case 2:
% 240.86/47.38  | | | | | | 
% 240.86/47.38  | | | | | |   (39)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0,
% 240.86/47.38  | | | | | |             e2) = e0)
% 240.86/47.38  | | | | | | 
% 240.86/47.38  | | | | | | BETA: splitting (39) gives:
% 240.86/47.38  | | | | | | 
% 240.86/47.38  | | | | | | Case 1:
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | | ALPHA: (30) implies:
% 240.86/47.38  | | | | | | |   (40)  op(e1, e2) = e0
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | | GROUND_INST: instantiating (21) with all_52_6, e0, e2, e1,
% 240.86/47.38  | | | | | | |              simplifying with (6), (40) gives:
% 240.86/47.38  | | | | | | |   (41)  all_52_6 = e0
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | | GROUND_INST: instantiating (21) with all_52_2, e2, e3, e1,
% 240.86/47.38  | | | | | | |              simplifying with (11), (22) gives:
% 240.86/47.38  | | | | | | |   (42)  all_52_2 = e2
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | | REDUCE: (1), (41) imply:
% 240.86/47.38  | | | | | | |   (43)   ~ (e1 = e0)
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | | REDUCE: (14), (42) imply:
% 240.86/47.38  | | | | | | |   (44)  op(e1, e2) = e1
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | | REF_CLOSE: (6), (21), (23), (40), (44) are inconsistent by
% 240.86/47.38  | | | | | | |            sub-proof #2136.
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | Case 2:
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | |   (45)  all_58_13 = e0 & op(e0, e2) = e0
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | | ALPHA: (45) implies:
% 240.86/47.38  | | | | | | |   (46)  op(e0, e2) = e0
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | | REF_CLOSE: (5), (21), (37), (46) are inconsistent by sub-proof
% 240.86/47.38  | | | | | | |            #2132.
% 240.86/47.38  | | | | | | | 
% 240.86/47.38  | | | | | | End of split
% 240.86/47.38  | | | | | | 
% 240.86/47.38  | | | | | End of split
% 240.86/47.38  | | | | | 
% 240.86/47.38  | | | | End of split
% 240.86/47.38  | | | | 
% 240.86/47.38  | | | End of split
% 240.86/47.38  | | | 
% 240.86/47.38  | | End of split
% 240.86/47.38  | | 
% 240.86/47.38  | Case 2:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (47)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.86/47.38  | |           e0)
% 240.86/47.38  | | 
% 240.86/47.38  | | REF_CLOSE: (3), (4), (10), (12), (13), (15), (19), (20), (21), (23), (27),
% 240.86/47.38  | |            (47) are inconsistent by sub-proof #400.
% 240.86/47.38  | | 
% 240.86/47.38  | End of split
% 240.86/47.38  | 
% 240.86/47.38  End of proof
% 240.86/47.38  
% 240.86/47.38  Sub-proof #400 shows that the following formulas are inconsistent:
% 240.86/47.38  ----------------------------------------------------------------
% 240.86/47.38    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.86/47.38    (2)   ~ (e3 = e0)
% 240.86/47.38    (3)  op(e0, e1) = all_52_11
% 240.86/47.38    (4)  op(e1, e0) = e1
% 240.86/47.38    (5)   ~ (all_52_11 = e3)
% 240.86/47.38    (6)  op(e3, e1) = all_52_8
% 240.86/47.38    (7)  op(e2, e1) = all_52_9
% 240.86/47.38    (8)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.86/47.38         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.86/47.38    (9)   ~ (all_52_9 = e3)
% 240.86/47.38    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.38    (11)   ~ (e1 = e0)
% 240.86/47.38    (12)   ~ (all_52_8 = e3)
% 240.86/47.38  
% 240.86/47.38  Begin of proof
% 240.86/47.38  | 
% 240.86/47.38  | BETA: splitting (1) gives:
% 240.86/47.38  | 
% 240.86/47.38  | Case 1:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (13)  all_58_8 = e0 & op(e1, e1) = e0
% 240.86/47.38  | | 
% 240.86/47.38  | | ALPHA: (13) implies:
% 240.86/47.38  | |   (14)  op(e1, e1) = e0
% 240.86/47.38  | | 
% 240.86/47.38  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (12), (14) are
% 240.86/47.38  | |            inconsistent by sub-proof #1010.
% 240.86/47.38  | | 
% 240.86/47.38  | Case 2:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (15)  all_58_11 = e0 & op(e1, e0) = e0
% 240.86/47.38  | | 
% 240.86/47.38  | | ALPHA: (15) implies:
% 240.86/47.38  | |   (16)  op(e1, e0) = e0
% 240.86/47.38  | | 
% 240.86/47.38  | | REF_CLOSE: (4), (10), (11), (16) are inconsistent by sub-proof #2284.
% 240.86/47.38  | | 
% 240.86/47.38  | End of split
% 240.86/47.38  | 
% 240.86/47.38  End of proof
% 240.86/47.38  
% 240.86/47.38  Sub-proof #401 shows that the following formulas are inconsistent:
% 240.86/47.38  ----------------------------------------------------------------
% 240.86/47.38    (1)   ~ (e3 = e0)
% 240.86/47.38    (2)  op(e0, e1) = all_52_11
% 240.86/47.38    (3)  all_58_4 = e2
% 240.86/47.38    (4)  op(e0, e1) = e1
% 240.86/47.38    (5)   ~ (all_52_11 = e3)
% 240.86/47.38    (6)  op(e2, e1) = all_52_9
% 240.86/47.38    (7)   ~ (e3 = e2)
% 240.86/47.38    (8)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.86/47.38    (9)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.86/47.38         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.86/47.38    (10)   ~ (all_52_9 = e3)
% 240.86/47.38    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.38    (12)   ~ (e1 = e0)
% 240.86/47.38  
% 240.86/47.38  Begin of proof
% 240.86/47.38  | 
% 240.86/47.38  | BETA: splitting (8) gives:
% 240.86/47.38  | 
% 240.86/47.38  | Case 1:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (13)  all_58_8 = e0 & op(e1, e1) = e0
% 240.86/47.38  | | 
% 240.86/47.38  | | ALPHA: (13) implies:
% 240.86/47.38  | |   (14)  op(e1, e1) = e0
% 240.86/47.38  | | 
% 240.86/47.38  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (14) are
% 240.86/47.38  | |            inconsistent by sub-proof #1493.
% 240.86/47.38  | | 
% 240.86/47.38  | Case 2:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (15)  all_58_14 = e0 & op(e0, e1) = e0
% 240.86/47.38  | | 
% 240.86/47.38  | | ALPHA: (15) implies:
% 240.86/47.38  | |   (16)  op(e0, e1) = e0
% 240.86/47.38  | | 
% 240.86/47.38  | | REF_CLOSE: (4), (11), (12), (16) are inconsistent by sub-proof #2158.
% 240.86/47.38  | | 
% 240.86/47.38  | End of split
% 240.86/47.38  | 
% 240.86/47.38  End of proof
% 240.86/47.38  
% 240.86/47.38  Sub-proof #402 shows that the following formulas are inconsistent:
% 240.86/47.38  ----------------------------------------------------------------
% 240.86/47.38    (1)  op(e1, e0) = e0
% 240.86/47.38    (2)  op(e3, e0) = e1
% 240.86/47.38    (3)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) = all_16_1
% 240.86/47.38           & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0) =
% 240.86/47.38           all_16_1 & $i(all_16_1))
% 240.86/47.38    (4)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 240.86/47.38         $i(all_56_29)
% 240.86/47.38    (5)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) = all_50_1
% 240.86/47.38           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0) =
% 240.86/47.38           all_50_1 & $i(all_50_1))
% 240.86/47.38    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.38    (7)   ~ (e1 = e0)
% 240.86/47.38  
% 240.86/47.38  Begin of proof
% 240.86/47.38  | 
% 240.86/47.38  | ALPHA: (4) implies:
% 240.86/47.38  |   (8)  op(e1, e0) = all_56_29
% 240.86/47.38  |   (9)  op(e1, all_56_29) = e1
% 240.86/47.38  | 
% 240.86/47.38  | BETA: splitting (5) gives:
% 240.86/47.38  | 
% 240.86/47.38  | Case 1:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (10)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 240.86/47.38  | |         all_50_1 & $i(all_50_0) & $i(all_50_1)
% 240.86/47.38  | | 
% 240.86/47.38  | | ALPHA: (10) implies:
% 240.86/47.38  | |   (11)  op(e3, e0) = all_50_1
% 240.86/47.38  | | 
% 240.86/47.38  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (11) are inconsistent by
% 240.86/47.38  | |            sub-proof #403.
% 240.86/47.38  | | 
% 240.86/47.38  | Case 2:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (12)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 & $i(all_50_1)
% 240.86/47.38  | | 
% 240.86/47.38  | | ALPHA: (12) implies:
% 240.86/47.38  | |   (13)  op(e3, e0) = all_50_1
% 240.86/47.38  | | 
% 240.86/47.38  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (13) are inconsistent by
% 240.86/47.38  | |            sub-proof #403.
% 240.86/47.38  | | 
% 240.86/47.38  | End of split
% 240.86/47.38  | 
% 240.86/47.38  End of proof
% 240.86/47.38  
% 240.86/47.38  Sub-proof #403 shows that the following formulas are inconsistent:
% 240.86/47.38  ----------------------------------------------------------------
% 240.86/47.38    (1)  op(e1, e0) = e0
% 240.86/47.38    (2)  op(e3, e0) = e1
% 240.86/47.38    (3)  op(e1, all_56_29) = e1
% 240.86/47.38    (4)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) = all_16_1
% 240.86/47.38           & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0) =
% 240.86/47.38           all_16_1 & $i(all_16_1))
% 240.86/47.38    (5)  op(e3, e0) = all_50_1
% 240.86/47.38    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.38    (7)   ~ (e1 = e0)
% 240.86/47.38    (8)  op(e1, e0) = all_56_29
% 240.86/47.38  
% 240.86/47.38  Begin of proof
% 240.86/47.38  | 
% 240.86/47.38  | BETA: splitting (4) gives:
% 240.86/47.38  | 
% 240.86/47.38  | Case 1:
% 240.86/47.38  | | 
% 240.86/47.38  | | 
% 240.86/47.38  | | REF_CLOSE: (1), (3), (6), (7), (8) are inconsistent by sub-proof #766.
% 240.86/47.38  | | 
% 240.86/47.38  | Case 2:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (9)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 & $i(all_16_1)
% 240.86/47.38  | | 
% 240.86/47.38  | | ALPHA: (9) implies:
% 240.86/47.38  | |   (10)   ~ (all_16_1 = e1)
% 240.86/47.38  | |   (11)  op(e3, e0) = all_16_1
% 240.86/47.38  | | 
% 240.86/47.38  | | REF_CLOSE: (2), (5), (6), (10), (11) are inconsistent by sub-proof #1570.
% 240.86/47.38  | | 
% 240.86/47.38  | End of split
% 240.86/47.38  | 
% 240.86/47.38  End of proof
% 240.86/47.38  
% 240.86/47.38  Sub-proof #404 shows that the following formulas are inconsistent:
% 240.86/47.38  ----------------------------------------------------------------
% 240.86/47.38    (1)  op(e3, e0) = e1
% 240.86/47.38    (2)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.86/47.38           $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.86/47.38           = all_56_27 & $i(all_56_27))
% 240.86/47.38    (3)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) = all_22_1
% 240.86/47.38           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1) =
% 240.86/47.38           all_22_1 & $i(all_22_1))
% 240.86/47.38    (4)  op(e3, e1) = all_52_8
% 240.86/47.38    (5)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 240.86/47.38           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 240.86/47.38           all_30_1 & $i(all_30_1))
% 240.86/47.38    (6)  op(e2, e2) = e1
% 240.86/47.38    (7)  op(e2, e0) = e2
% 240.86/47.38    (8)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) = all_16_1
% 240.86/47.38           & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0) =
% 240.86/47.38           all_16_1 & $i(all_16_1))
% 240.86/47.38    (9)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) = all_50_1
% 240.86/47.38           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0) =
% 240.86/47.38           all_50_1 & $i(all_50_1))
% 240.86/47.38    (10)  op(e2, e1) = e0
% 240.86/47.38    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.38    (12)   ~ (e2 = e1)
% 240.86/47.38    (13)   ~ (all_52_8 = e3)
% 240.86/47.38  
% 240.86/47.38  Begin of proof
% 240.86/47.38  | 
% 240.86/47.38  | BETA: splitting (2) gives:
% 240.86/47.38  | 
% 240.86/47.38  | Case 1:
% 240.86/47.38  | | 
% 240.86/47.38  | |   (14)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.86/47.38  | |         $i(all_56_25)
% 240.86/47.38  | | 
% 240.86/47.38  | | ALPHA: (14) implies:
% 240.86/47.38  | |   (15)  op(e3, e0) = all_56_25
% 240.86/47.38  | |   (16)  op(e3, all_56_25) = e3
% 240.86/47.38  | | 
% 240.86/47.38  | | BETA: splitting (9) gives:
% 240.86/47.38  | | 
% 240.86/47.38  | | Case 1:
% 240.86/47.38  | | | 
% 240.86/47.38  | | |   (17)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 240.86/47.38  | | |         all_50_1 & $i(all_50_0) & $i(all_50_1)
% 240.86/47.38  | | | 
% 240.86/47.38  | | | ALPHA: (17) implies:
% 240.86/47.38  | | |   (18)  op(e3, e0) = all_50_1
% 240.86/47.38  | | | 
% 240.86/47.38  | | | REF_CLOSE: (1), (3), (4), (5), (8), (10), (11), (13), (15), (16), (18) are
% 240.86/47.38  | | |            inconsistent by sub-proof #405.
% 240.86/47.39  | | | 
% 240.86/47.39  | | Case 2:
% 240.86/47.39  | | | 
% 240.86/47.39  | | |   (19)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 & $i(all_50_1)
% 240.86/47.39  | | | 
% 240.86/47.39  | | | ALPHA: (19) implies:
% 240.86/47.39  | | |   (20)  op(e3, e0) = all_50_1
% 240.86/47.39  | | | 
% 240.86/47.39  | | | REF_CLOSE: (1), (3), (4), (5), (8), (10), (11), (13), (15), (16), (20) are
% 240.86/47.39  | | |            inconsistent by sub-proof #405.
% 240.86/47.39  | | | 
% 240.86/47.39  | | End of split
% 240.86/47.39  | | 
% 240.86/47.39  | Case 2:
% 240.86/47.39  | | 
% 240.86/47.39  | |   (21)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 240.86/47.39  | |         $i(all_56_27)
% 240.86/47.39  | | 
% 240.86/47.39  | | REF_CLOSE: (3), (5), (6), (7), (10), (11), (12), (21) are inconsistent by
% 240.86/47.39  | |            sub-proof #414.
% 240.86/47.39  | | 
% 240.86/47.39  | End of split
% 240.86/47.39  | 
% 240.86/47.39  End of proof
% 240.86/47.39  
% 240.86/47.39  Sub-proof #405 shows that the following formulas are inconsistent:
% 240.86/47.39  ----------------------------------------------------------------
% 240.86/47.39    (1)  op(e3, e0) = e1
% 240.86/47.39    (2)  op(e3, all_56_25) = e3
% 240.86/47.39    (3)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) = all_22_1
% 240.86/47.39           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1) =
% 240.86/47.39           all_22_1 & $i(all_22_1))
% 240.86/47.39    (4)  op(e3, e1) = all_52_8
% 240.86/47.39    (5)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 240.86/47.39           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 240.86/47.39           all_30_1 & $i(all_30_1))
% 240.86/47.39    (6)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) = all_16_1
% 240.86/47.39           & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0) =
% 240.86/47.39           all_16_1 & $i(all_16_1))
% 240.86/47.39    (7)  op(e3, e0) = all_50_1
% 240.86/47.39    (8)  op(e3, e0) = all_56_25
% 240.86/47.39    (9)  op(e2, e1) = e0
% 240.86/47.39    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.39    (11)   ~ (all_52_8 = e3)
% 240.86/47.39  
% 240.86/47.39  Begin of proof
% 240.86/47.39  | 
% 240.86/47.39  | BETA: splitting (6) gives:
% 240.86/47.39  | 
% 240.86/47.39  | Case 1:
% 240.86/47.39  | | 
% 240.86/47.39  | |   (12)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 240.86/47.39  | |         all_16_1 & $i(all_16_0) & $i(all_16_1)
% 240.86/47.39  | | 
% 240.86/47.39  | | ALPHA: (12) implies:
% 240.86/47.39  | |   (13)  op(e3, e0) = all_16_1
% 240.86/47.39  | | 
% 240.86/47.39  | | BETA: splitting (3) gives:
% 240.86/47.39  | | 
% 240.86/47.39  | | Case 1:
% 240.86/47.39  | | | 
% 240.86/47.39  | | | 
% 240.86/47.39  | | | GROUND_INST: instantiating (10) with e1, all_50_1, e0, e3, simplifying
% 240.86/47.39  | | |              with (1), (7) gives:
% 240.86/47.39  | | |   (14)  all_50_1 = e1
% 240.86/47.39  | | | 
% 240.86/47.39  | | | GROUND_INST: instantiating (10) with all_50_1, all_56_25, e0, e3,
% 240.86/47.39  | | |              simplifying with (7), (8) gives:
% 240.86/47.39  | | |   (15)  all_56_25 = all_50_1
% 240.86/47.39  | | | 
% 240.86/47.39  | | | GROUND_INST: instantiating (10) with all_16_1, all_56_25, e0, e3,
% 240.86/47.39  | | |              simplifying with (8), (13) gives:
% 240.86/47.39  | | |   (16)  all_56_25 = all_16_1
% 240.86/47.39  | | | 
% 240.86/47.39  | | | COMBINE_EQS: (15), (16) imply:
% 240.86/47.39  | | |   (17)  all_50_1 = all_16_1
% 240.86/47.39  | | | 
% 240.86/47.39  | | | SIMP: (17) implies:
% 240.86/47.39  | | |   (18)  all_50_1 = all_16_1
% 240.86/47.39  | | | 
% 240.86/47.39  | | | COMBINE_EQS: (14), (18) imply:
% 240.86/47.39  | | |   (19)  all_16_1 = e1
% 240.86/47.39  | | | 
% 240.86/47.39  | | | SIMP: (19) implies:
% 240.86/47.39  | | |   (20)  all_16_1 = e1
% 240.86/47.39  | | | 
% 240.86/47.39  | | | COMBINE_EQS: (16), (20) imply:
% 240.86/47.39  | | |   (21)  all_56_25 = e1
% 240.86/47.39  | | | 
% 240.86/47.39  | | | REDUCE: (2), (21) imply:
% 240.86/47.39  | | |   (22)  op(e3, e1) = e3
% 240.86/47.39  | | | 
% 240.86/47.39  | | | REF_CLOSE: (4), (10), (11), (22) are inconsistent by sub-proof #2260.
% 240.86/47.39  | | | 
% 240.86/47.39  | | Case 2:
% 240.86/47.39  | | | 
% 240.86/47.39  | | |   (23)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 & $i(all_22_1)
% 240.86/47.39  | | | 
% 240.86/47.39  | | | ALPHA: (23) implies:
% 240.86/47.39  | | |   (24)   ~ (all_22_1 = e0)
% 240.86/47.39  | | |   (25)  op(e2, e1) = all_22_1
% 240.86/47.39  | | | 
% 240.86/47.39  | | | REF_CLOSE: (5), (9), (10), (24), (25) are inconsistent by sub-proof #1356.
% 240.86/47.39  | | | 
% 240.86/47.39  | | End of split
% 240.86/47.39  | | 
% 240.86/47.39  | Case 2:
% 240.86/47.39  | | 
% 240.86/47.39  | |   (26)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 & $i(all_16_1)
% 240.86/47.39  | | 
% 240.86/47.39  | | ALPHA: (26) implies:
% 240.86/47.39  | |   (27)   ~ (all_16_1 = e1)
% 240.86/47.39  | |   (28)  op(e3, e0) = all_16_1
% 240.86/47.39  | | 
% 240.86/47.39  | | REF_CLOSE: (1), (7), (10), (27), (28) are inconsistent by sub-proof #1570.
% 240.86/47.39  | | 
% 240.86/47.39  | End of split
% 240.86/47.39  | 
% 240.86/47.39  End of proof
% 240.86/47.39  
% 240.86/47.39  Sub-proof #406 shows that the following formulas are inconsistent:
% 240.86/47.39  ----------------------------------------------------------------
% 240.86/47.39    (1)  all_58_8 = e1 & op(e1, e1) = e1
% 240.86/47.39    (2)  all_58_8 = e3
% 240.86/47.39    (3)   ~ (e3 = e1)
% 240.86/47.39  
% 240.86/47.39  Begin of proof
% 240.86/47.39  | 
% 240.86/47.39  | ALPHA: (1) implies:
% 240.86/47.39  |   (4)  all_58_8 = e1
% 240.86/47.39  | 
% 240.86/47.39  | COMBINE_EQS: (2), (4) imply:
% 240.86/47.39  |   (5)  e3 = e1
% 240.86/47.39  | 
% 240.86/47.39  | REDUCE: (3), (5) imply:
% 240.86/47.39  |   (6)  $false
% 240.86/47.39  | 
% 240.86/47.39  | CLOSE: (6) is inconsistent.
% 240.86/47.39  | 
% 240.86/47.39  End of proof
% 240.86/47.39  
% 240.86/47.39  Sub-proof #407 shows that the following formulas are inconsistent:
% 240.86/47.39  ----------------------------------------------------------------
% 240.86/47.39    (1)  all_58_4 = e2
% 240.86/47.39    (2)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 240.86/47.39    (3)  op(e2, e1) = all_52_9
% 240.86/47.39    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.39    (5)   ~ (all_52_9 = e1)
% 240.86/47.39    (6)   ~ (e2 = e1)
% 240.86/47.39  
% 240.86/47.39  Begin of proof
% 240.86/47.39  | 
% 240.86/47.39  | BETA: splitting (2) gives:
% 240.86/47.39  | 
% 240.86/47.39  | Case 1:
% 240.86/47.39  | | 
% 240.86/47.39  | |   (7)  all_58_4 = e1 & op(e3, e1) = e1
% 240.86/47.39  | | 
% 240.86/47.39  | | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #2168.
% 240.86/47.39  | | 
% 240.86/47.39  | Case 2:
% 240.86/47.39  | | 
% 240.86/47.39  | |   (8)  all_58_5 = e1 & op(e2, e1) = e1
% 240.86/47.39  | | 
% 240.86/47.39  | | ALPHA: (8) implies:
% 240.86/47.39  | |   (9)  op(e2, e1) = e1
% 240.86/47.39  | | 
% 240.86/47.39  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #2306.
% 240.86/47.39  | | 
% 240.86/47.39  | End of split
% 240.86/47.39  | 
% 240.86/47.39  End of proof
% 240.86/47.39  
% 240.86/47.39  Sub-proof #408 shows that the following formulas are inconsistent:
% 240.86/47.39  ----------------------------------------------------------------
% 240.86/47.39    (1)   ~ (e3 = e0)
% 240.86/47.39    (2)   ~ (e2 = e0)
% 240.86/47.39    (3)  op(e1, e2) = all_52_6
% 240.86/47.39    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.86/47.39         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.86/47.39    (5)   ~ (all_52_6 = e0)
% 240.86/47.39    (6)  op(e0, e2) = all_52_7
% 240.86/47.39    (7)   ~ (all_52_7 = e0)
% 240.86/47.39    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.39    (9)  op(e3, e2) = e3
% 240.86/47.39    (10)  op(e2, e2) = e2
% 240.86/47.39  
% 240.86/47.39  Begin of proof
% 240.86/47.39  | 
% 240.86/47.39  | BETA: splitting (4) gives:
% 240.86/47.39  | 
% 240.86/47.39  | Case 1:
% 240.86/47.39  | | 
% 240.86/47.39  | |   (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 240.86/47.39  | |           e0)
% 240.86/47.39  | | 
% 240.86/47.39  | | REF_CLOSE: (1), (2), (8), (9), (10), (11) are inconsistent by sub-proof
% 240.86/47.39  | |            #409.
% 240.86/47.39  | | 
% 240.86/47.39  | Case 2:
% 240.86/47.39  | | 
% 240.86/47.39  | |   (12)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.86/47.39  | |           e0)
% 240.86/47.39  | | 
% 240.86/47.39  | | REF_CLOSE: (3), (5), (6), (7), (8), (12) are inconsistent by sub-proof
% 240.86/47.39  | |            #1990.
% 240.86/47.39  | | 
% 240.86/47.39  | End of split
% 240.86/47.39  | 
% 240.86/47.39  End of proof
% 240.86/47.39  
% 240.86/47.39  Sub-proof #409 shows that the following formulas are inconsistent:
% 240.86/47.39  ----------------------------------------------------------------
% 240.86/47.39    (1)   ~ (e3 = e0)
% 240.86/47.39    (2)   ~ (e2 = e0)
% 240.86/47.39    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 240.86/47.39    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.39    (5)  op(e3, e2) = e3
% 240.86/47.39    (6)  op(e2, e2) = e2
% 240.86/47.39  
% 240.86/47.39  Begin of proof
% 240.86/47.39  | 
% 240.86/47.39  | BETA: splitting (3) gives:
% 240.86/47.39  | 
% 240.86/47.39  | Case 1:
% 240.86/47.39  | | 
% 240.86/47.39  | |   (7)  all_58_1 = e0 & op(e3, e2) = e0
% 240.86/47.39  | | 
% 240.86/47.39  | | ALPHA: (7) implies:
% 240.86/47.39  | |   (8)  op(e3, e2) = e0
% 240.86/47.39  | | 
% 240.86/47.39  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2099.
% 240.86/47.39  | | 
% 240.86/47.39  | Case 2:
% 240.86/47.39  | | 
% 240.86/47.39  | |   (9)  all_58_3 = e0 & op(e2, e2) = e0
% 240.86/47.39  | | 
% 240.86/47.39  | | ALPHA: (9) implies:
% 240.86/47.39  | |   (10)  op(e2, e2) = e0
% 240.86/47.39  | | 
% 240.86/47.39  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #2137.
% 240.86/47.39  | | 
% 240.86/47.39  | End of split
% 240.86/47.39  | 
% 240.86/47.39  End of proof
% 240.86/47.39  
% 240.86/47.39  Sub-proof #410 shows that the following formulas are inconsistent:
% 240.86/47.39  ----------------------------------------------------------------
% 240.86/47.39    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 240.86/47.39           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 240.86/47.39           all_12_1 & $i(all_12_1))
% 240.86/47.39    (2)   ~ (all_52_9 = all_8_2)
% 240.86/47.39    (3)   ~ (all_52_13 = all_8_2)
% 240.86/47.39    (4)   ~ (all_8_2 = e0)
% 240.86/47.39    (5)   ~ (e3 = e0)
% 240.86/47.39    (6)  all_58_1 = e3
% 240.86/47.39    (7)  all_22_2 = all_8_2
% 240.86/47.39    (8)  op(e0, e1) = all_52_11
% 240.86/47.39    (9)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.86/47.39         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.86/47.39    (10)   ~ (e2 = e0)
% 240.86/47.39    (11)  op(e1, e2) = all_52_6
% 240.86/47.39    (12)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 240.86/47.39          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.86/47.39    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.39              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.39            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.86/47.39            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.39            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.86/47.39             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.39            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.86/47.39            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.39            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.86/47.39            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.39            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.86/47.39              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.39            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.39            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.86/47.39            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.39            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.86/47.39            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.39            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.86/47.39              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.86/47.39            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.39            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.86/47.39            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.39            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.86/47.39            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.39            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.86/47.39              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.39            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.39            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.39    (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.86/47.39          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.86/47.39    (15)   ~ (all_52_7 = all_52_11)
% 240.86/47.39    (16)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.86/47.39          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.86/47.39    (17)  op(e1, e0) = all_52_14
% 240.86/47.39    (18)  all_58_15 = e3
% 240.86/47.39    (19)  op(e2, e3) = e3
% 240.86/47.39    (20)  op(e0, e3) = all_52_3
% 240.86/47.39    (21)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.86/47.39          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.86/47.39    (22)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 240.86/47.39            op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 240.86/47.39              e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.86/47.39    (23)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.86/47.39          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.86/47.39    (24)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.86/47.39          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.86/47.39    (25)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 240.86/47.39          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 240.86/47.39    (26)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.86/47.39              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.86/47.39                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.86/47.39                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.86/47.39    (27)  op(e3, e1) = all_52_8
% 240.86/47.39    (28)  op(e2, e1) = all_52_9
% 240.86/47.39    (29)   ~ (e3 = e2)
% 240.86/47.39    (30)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.86/47.39          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.86/47.39    (31)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 240.86/47.39            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 240.86/47.39              e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 240.86/47.39    (32)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.86/47.39            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.86/47.39            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.86/47.39            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.86/47.39            op(e0, all_56_31) = e0)
% 240.86/47.39    (33)   ~ (all_22_2 = e1) | ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 240.86/47.39            op(e2, e1) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 240.86/47.39              e0) & op(e2, e1) = all_22_1 & $i(all_22_1))
% 240.86/47.39    (34)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.86/47.39          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.86/47.39    (35)  op(e3, e0) = all_52_12
% 240.86/47.39    (36)   ~ (all_52_3 = e2)
% 240.86/47.39    (37)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.86/47.39          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.86/47.39    (38)   ~ (all_52_3 = e3)
% 240.86/47.39    (39)  all_46_2 = e3
% 240.86/47.39    (40)  op(e2, e2) = all_8_2
% 240.86/47.39    (41)  all_54_5 = all_8_2
% 240.86/47.39    (42)  op(e3, e3) = e2
% 240.86/47.39    (43)   ~ (all_52_14 = e3)
% 240.86/47.39    (44)   ~ (all_52_12 = e2)
% 240.86/47.39    (45)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.86/47.39          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.86/47.39    (46)  op(e1, e1) = e3
% 240.86/47.39    (47)   ~ (all_52_2 = e3)
% 240.86/47.39    (48)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 240.86/47.39    (49)   ~ (all_52_6 = e3)
% 240.86/47.39    (50)   ~ (all_52_7 = all_8_2)
% 240.86/47.39    (51)  op(e0, e2) = all_52_7
% 240.86/47.39    (52)   ~ (all_52_13 = all_52_14)
% 240.86/47.40    (53)  all_56_1 = e2
% 240.86/47.40    (54)  all_56_31 = e3
% 240.86/47.40    (55)  all_30_2 = all_8_2
% 240.86/47.40    (56)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.86/47.40          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.86/47.40    (57)  op(e0, e0) = e3
% 240.86/47.40    (58)  all_26_2 = e3
% 240.86/47.40    (59)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.86/47.40          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.86/47.40    (60)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.86/47.40          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.86/47.40    (61)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.86/47.40          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.86/47.40    (62)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.86/47.40          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.86/47.40    (63)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.40    (64)  all_58_8 = e3
% 240.86/47.40    (65)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.86/47.40          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.86/47.40    (66)  op(e1, e3) = all_52_2
% 240.86/47.40    (67)   ~ (all_30_2 = e1) | ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 240.86/47.40            op(e2, e1) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 240.86/47.40              e3) & op(e2, e1) = all_30_1 & $i(all_30_1))
% 240.86/47.40    (68)   ~ (all_52_12 = e3)
% 240.86/47.40    (69)   ~ (all_8_2 = e3)
% 240.86/47.40    (70)  all_56_11 = all_8_2
% 240.86/47.40    (71)  op(e3, e2) = e3
% 240.86/47.40    (72)  all_58_2 = e3
% 240.86/47.40    (73)   ~ (all_52_13 = e3)
% 240.86/47.40    (74)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.86/47.40          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.86/47.40    (75)  op(e2, e0) = all_52_13
% 240.86/47.40    (76)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.86/47.40          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.86/47.40            e1)
% 240.86/47.40    (77)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.86/47.40          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.86/47.40            e2)
% 240.86/47.40    (78)   ~ (all_52_9 = all_52_11)
% 240.86/47.40    (79)   ~ (e2 = e1)
% 240.86/47.40    (80)   ~ (all_52_8 = e3)
% 240.86/47.40  
% 240.86/47.40  Begin of proof
% 240.86/47.40  | 
% 240.86/47.40  | BETA: splitting (33) gives:
% 240.86/47.40  | 
% 240.86/47.40  | Case 1:
% 240.86/47.40  | | 
% 240.86/47.40  | |   (81)   ~ (all_22_2 = e1)
% 240.86/47.40  | | 
% 240.86/47.40  | | REDUCE: (7), (81) imply:
% 240.86/47.40  | |   (82)   ~ (all_8_2 = e1)
% 240.86/47.40  | | 
% 240.86/47.40  | | REF_CLOSE: (3), (4), (8), (13), (15), (17), (20), (28), (35), (36), (38),
% 240.86/47.40  | |            (41), (43), (44), (47), (48), (50), (51), (54), (57), (63), (65),
% 240.86/47.40  | |            (66), (69), (70), (71), (75), (77), (78), (82) are inconsistent
% 240.86/47.40  | |            by sub-proof #429.
% 240.86/47.40  | | 
% 240.86/47.40  | Case 2:
% 240.86/47.40  | | 
% 240.86/47.40  | |   (83)  all_22_2 = e1
% 240.86/47.40  | |   (84)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) =
% 240.86/47.40  | |           all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) &
% 240.86/47.40  | |           op(e2, e1) = all_22_1 & $i(all_22_1))
% 240.86/47.40  | | 
% 240.86/47.40  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 240.86/47.40  | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 240.86/47.40  | |            (26), (27), (28), (29), (30), (31), (32), (34), (35), (36), (37),
% 240.86/47.40  | |            (38), (39), (40), (42), (43), (44), (45), (46), (49), (50), (51),
% 240.86/47.40  | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 240.86/47.40  | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 240.86/47.40  | |            (74), (75), (76), (77), (79), (80), (83), (84) are inconsistent
% 240.86/47.40  | |            by sub-proof #411.
% 240.86/47.40  | | 
% 240.86/47.40  | End of split
% 240.86/47.40  | 
% 240.86/47.40  End of proof
% 240.86/47.40  
% 240.86/47.40  Sub-proof #411 shows that the following formulas are inconsistent:
% 240.86/47.40  ----------------------------------------------------------------
% 240.86/47.40    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 240.86/47.40           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 240.86/47.40           all_12_1 & $i(all_12_1))
% 240.86/47.40    (2)   ~ (all_52_9 = all_8_2)
% 240.86/47.40    (3)   ~ (all_52_13 = all_8_2)
% 240.86/47.40    (4)   ~ (all_8_2 = e0)
% 240.86/47.40    (5)   ~ (e3 = e0)
% 240.86/47.40    (6)  all_58_1 = e3
% 240.86/47.40    (7)  all_22_2 = all_8_2
% 240.86/47.40    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.86/47.40         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.86/47.40    (9)   ~ (e2 = e0)
% 240.86/47.40    (10)  op(e1, e2) = all_52_6
% 240.86/47.40    (11)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 240.86/47.40          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.86/47.40    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.40              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.40            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.86/47.40            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.40            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.86/47.40             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.40            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.86/47.40            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.40            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.86/47.40            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.40            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.86/47.40              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.40            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.40            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.86/47.40            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.40            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.86/47.40            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.40            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.86/47.40              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.86/47.40            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.40            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.86/47.40            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.40            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.86/47.40            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.40            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.86/47.40              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.40            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.40            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.40    (13)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.86/47.40          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.86/47.40    (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.86/47.40          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.86/47.40    (15)  op(e1, e0) = all_52_14
% 240.86/47.40    (16)  all_58_15 = e3
% 240.86/47.40    (17)  op(e2, e3) = e3
% 240.86/47.40    (18)  op(e0, e3) = all_52_3
% 240.86/47.40    (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.86/47.40          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.86/47.40    (20)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 240.86/47.40            op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 240.86/47.40              e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.86/47.40    (21)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) =
% 240.86/47.40            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2,
% 240.86/47.40              e1) = all_22_1 & $i(all_22_1))
% 240.86/47.40    (22)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 240.86/47.40          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.86/47.40    (23)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.86/47.40          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.86/47.40    (24)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 240.86/47.40          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 240.86/47.40    (25)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.86/47.40              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.86/47.40                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.86/47.40                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.86/47.40    (26)  op(e3, e1) = all_52_8
% 240.86/47.40    (27)  op(e2, e1) = all_52_9
% 240.86/47.40    (28)   ~ (e3 = e2)
% 240.86/47.40    (29)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.86/47.40          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.86/47.40    (30)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 240.86/47.40            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 240.86/47.40              e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 240.86/47.40    (31)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 240.86/47.40            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 240.86/47.40            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 240.86/47.40            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 240.86/47.40            op(e0, all_56_31) = e0)
% 240.86/47.40    (32)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.86/47.40          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.86/47.40    (33)  op(e3, e0) = all_52_12
% 240.86/47.40    (34)  all_22_2 = e1
% 240.86/47.40    (35)   ~ (all_52_3 = e2)
% 240.86/47.40    (36)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.86/47.40          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.86/47.40    (37)   ~ (all_52_3 = e3)
% 240.86/47.40    (38)  all_46_2 = e3
% 240.86/47.40    (39)  op(e2, e2) = all_8_2
% 240.86/47.40    (40)  op(e3, e3) = e2
% 240.86/47.40    (41)   ~ (all_52_14 = e3)
% 240.86/47.40    (42)   ~ (all_52_12 = e2)
% 240.86/47.40    (43)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.86/47.40          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.86/47.40    (44)  op(e1, e1) = e3
% 240.86/47.40    (45)   ~ (all_52_6 = e3)
% 240.86/47.40    (46)   ~ (all_52_7 = all_8_2)
% 240.86/47.40    (47)  op(e0, e2) = all_52_7
% 240.86/47.40    (48)   ~ (all_52_13 = all_52_14)
% 240.86/47.40    (49)  all_56_1 = e2
% 240.86/47.40    (50)  all_56_31 = e3
% 240.86/47.40    (51)  all_30_2 = all_8_2
% 240.86/47.40    (52)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.86/47.40          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.86/47.40    (53)  op(e0, e0) = e3
% 240.86/47.40    (54)  all_26_2 = e3
% 240.86/47.40    (55)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.86/47.40          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.86/47.40    (56)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.86/47.40          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.86/47.40    (57)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.86/47.40          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.86/47.40    (58)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.86/47.40          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.86/47.40    (59)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.40    (60)  all_58_8 = e3
% 240.86/47.40    (61)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.86/47.40          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.86/47.40    (62)  op(e1, e3) = all_52_2
% 240.86/47.40    (63)   ~ (all_30_2 = e1) | ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 &
% 240.86/47.40            op(e2, e1) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 240.86/47.40              e3) & op(e2, e1) = all_30_1 & $i(all_30_1))
% 240.86/47.40    (64)   ~ (all_52_12 = e3)
% 240.86/47.40    (65)   ~ (all_8_2 = e3)
% 240.86/47.40    (66)  all_56_11 = all_8_2
% 240.86/47.40    (67)  op(e3, e2) = e3
% 240.86/47.40    (68)  all_58_2 = e3
% 240.86/47.40    (69)   ~ (all_52_13 = e3)
% 240.86/47.40    (70)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.86/47.40          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.86/47.40    (71)  op(e2, e0) = all_52_13
% 240.86/47.40    (72)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 240.86/47.40          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 240.86/47.40            e1)
% 240.86/47.40    (73)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.86/47.40          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.86/47.40            e2)
% 240.86/47.40    (74)   ~ (e2 = e1)
% 240.86/47.40    (75)   ~ (all_52_8 = e3)
% 240.86/47.40  
% 240.86/47.40  Begin of proof
% 240.86/47.40  | 
% 240.86/47.40  | COMBINE_EQS: (7), (34) imply:
% 240.86/47.40  |   (76)  all_8_2 = e1
% 240.86/47.40  | 
% 240.86/47.40  | SIMP: (76) implies:
% 240.86/47.40  |   (77)  all_8_2 = e1
% 240.86/47.40  | 
% 240.86/47.40  | COMBINE_EQS: (51), (77) imply:
% 240.86/47.40  |   (78)  all_30_2 = e1
% 240.86/47.40  | 
% 240.86/47.40  | COMBINE_EQS: (66), (77) imply:
% 240.86/47.40  |   (79)  all_56_11 = e1
% 240.86/47.40  | 
% 240.86/47.40  | REDUCE: (46), (77) imply:
% 240.86/47.40  |   (80)   ~ (all_52_7 = e1)
% 240.86/47.40  | 
% 240.86/47.40  | REDUCE: (2), (77) imply:
% 240.86/47.41  |   (81)   ~ (all_52_9 = e1)
% 240.86/47.41  | 
% 240.86/47.41  | REDUCE: (3), (77) imply:
% 240.86/47.41  |   (82)   ~ (all_52_13 = e1)
% 240.86/47.41  | 
% 240.86/47.41  | REDUCE: (65), (77) imply:
% 240.86/47.41  |   (83)   ~ (e3 = e1)
% 240.86/47.41  | 
% 240.86/47.41  | SIMP: (83) implies:
% 240.86/47.41  |   (84)   ~ (e3 = e1)
% 240.86/47.41  | 
% 240.86/47.41  | REDUCE: (4), (77) imply:
% 240.86/47.41  |   (85)   ~ (e1 = e0)
% 240.86/47.41  | 
% 240.86/47.41  | REDUCE: (39), (77) imply:
% 240.86/47.41  |   (86)  op(e2, e2) = e1
% 240.86/47.41  | 
% 240.86/47.41  | BETA: splitting (30) gives:
% 240.86/47.41  | 
% 240.86/47.41  | Case 1:
% 240.86/47.41  | | 
% 240.86/47.41  | |   (87)   ~ (all_26_2 = e3)
% 240.86/47.41  | | 
% 240.86/47.41  | | REDUCE: (54), (87) imply:
% 240.86/47.41  | |   (88)  $false
% 240.86/47.41  | | 
% 240.86/47.41  | | CLOSE: (88) is inconsistent.
% 240.86/47.41  | | 
% 240.86/47.41  | Case 2:
% 240.86/47.41  | | 
% 240.86/47.41  | |   (89)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 240.86/47.41  | |           all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) &
% 240.86/47.41  | |           op(e0, e3) = all_26_1 & $i(all_26_1))
% 240.86/47.41  | | 
% 240.86/47.41  | | BETA: splitting (63) gives:
% 240.86/47.41  | | 
% 240.86/47.41  | | Case 1:
% 240.86/47.41  | | | 
% 240.86/47.41  | | |   (90)   ~ (all_30_2 = e1)
% 240.86/47.41  | | | 
% 240.86/47.41  | | | REDUCE: (78), (90) imply:
% 240.86/47.41  | | |   (91)  $false
% 240.86/47.41  | | | 
% 240.86/47.41  | | | CLOSE: (91) is inconsistent.
% 240.86/47.41  | | | 
% 240.86/47.41  | | Case 2:
% 240.86/47.41  | | | 
% 240.86/47.41  | | |   (92)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) =
% 240.86/47.41  | | |           all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) &
% 240.86/47.41  | | |           op(e2, e1) = all_30_1 & $i(all_30_1))
% 240.86/47.41  | | | 
% 240.86/47.41  | | | BETA: splitting (20) gives:
% 240.86/47.41  | | | 
% 240.86/47.41  | | | Case 1:
% 240.86/47.41  | | | | 
% 240.86/47.41  | | | |   (93)   ~ (all_46_2 = e3)
% 240.86/47.41  | | | | 
% 240.86/47.41  | | | | REDUCE: (38), (93) imply:
% 240.86/47.41  | | | |   (94)  $false
% 240.86/47.41  | | | | 
% 240.86/47.41  | | | | CLOSE: (94) is inconsistent.
% 240.86/47.41  | | | | 
% 240.86/47.41  | | | Case 2:
% 240.86/47.41  | | | | 
% 240.86/47.41  | | | |   (95)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.86/47.41  | | | |           all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2)
% 240.86/47.41  | | | |           & op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.86/47.41  | | | | 
% 240.86/47.41  | | | | BETA: splitting (19) gives:
% 240.86/47.41  | | | | 
% 240.86/47.41  | | | | Case 1:
% 240.86/47.41  | | | | | 
% 240.86/47.41  | | | | |   (96)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2,
% 240.86/47.41  | | | | |             e2) = e2)
% 240.86/47.41  | | | | | 
% 240.86/47.41  | | | | | REF_CLOSE: (17), (28), (59), (74), (86), (96) are inconsistent by
% 240.86/47.41  | | | | |            sub-proof #428.
% 240.86/47.41  | | | | | 
% 240.86/47.41  | | | | Case 2:
% 240.86/47.41  | | | | | 
% 240.86/47.41  | | | | |   (97)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2,
% 240.86/47.41  | | | | |             e0) = e2)
% 240.86/47.41  | | | | | 
% 240.86/47.41  | | | | | BETA: splitting (97) gives:
% 240.86/47.41  | | | | | 
% 240.86/47.41  | | | | | Case 1:
% 240.86/47.41  | | | | | | 
% 240.86/47.41  | | | | | |   (98)  all_58_5 = e2 & op(e2, e1) = e2
% 240.86/47.41  | | | | | | 
% 240.86/47.41  | | | | | | ALPHA: (98) implies:
% 240.86/47.41  | | | | | |   (99)  op(e2, e1) = e2
% 240.86/47.41  | | | | | | 
% 240.86/47.41  | | | | | | BETA: splitting (58) gives:
% 240.86/47.41  | | | | | | 
% 240.86/47.41  | | | | | | Case 1:
% 240.86/47.41  | | | | | | | 
% 240.86/47.41  | | | | | | |   (100)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 240.86/47.41  | | | | | | |            op(e2, e2) = e0)
% 240.86/47.41  | | | | | | | 
% 240.86/47.41  | | | | | | | REF_CLOSE: (4), (5), (39), (59), (68), (100) are inconsistent by
% 240.86/47.41  | | | | | | |            sub-proof #427.
% 240.86/47.41  | | | | | | | 
% 240.86/47.41  | | | | | | Case 2:
% 240.86/47.41  | | | | | | | 
% 240.86/47.41  | | | | | | |   (101)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 240.86/47.41  | | | | | | |            op(e2, e0) = e0)
% 240.86/47.41  | | | | | | | 
% 240.86/47.41  | | | | | | | BETA: splitting (101) gives:
% 240.86/47.41  | | | | | | | 
% 240.86/47.41  | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | 
% 240.86/47.41  | | | | | | | |   (102)  all_58_5 = e0 & op(e2, e1) = e0
% 240.86/47.41  | | | | | | | | 
% 240.86/47.41  | | | | | | | | ALPHA: (102) implies:
% 240.86/47.41  | | | | | | | |   (103)  op(e2, e1) = e0
% 240.86/47.41  | | | | | | | | 
% 240.86/47.41  | | | | | | | | REF_CLOSE: (9), (59), (99), (103) are inconsistent by sub-proof
% 240.86/47.41  | | | | | | | |            #1906.
% 240.86/47.41  | | | | | | | | 
% 240.86/47.41  | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | 
% 240.86/47.41  | | | | | | | |   (104)  all_58_10 = e0 & op(e2, e0) = e0
% 240.86/47.41  | | | | | | | | 
% 240.86/47.41  | | | | | | | | ALPHA: (104) implies:
% 240.86/47.41  | | | | | | | |   (105)  op(e2, e0) = e0
% 240.86/47.41  | | | | | | | | 
% 240.86/47.41  | | | | | | | | BETA: splitting (61) gives:
% 240.86/47.41  | | | | | | | | 
% 240.86/47.41  | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | 
% 240.86/47.41  | | | | | | | | |   (106)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 240.86/47.41  | | | | | | | | |            op(e2, e0) = e2)
% 240.86/47.41  | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | REF_CLOSE: (9), (33), (42), (59), (105), (106) are
% 240.86/47.41  | | | | | | | | |            inconsistent by sub-proof #1364.
% 240.86/47.41  | | | | | | | | | 
% 240.86/47.41  | | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | | 
% 240.86/47.41  | | | | | | | | |   (107)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2
% 240.86/47.41  | | | | | | | | |            & op(e0, e0) = e2)
% 240.86/47.41  | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | BETA: splitting (107) gives:
% 240.86/47.41  | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | |   (108)  all_58_11 = e2 & op(e1, e0) = e2
% 240.86/47.41  | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | ALPHA: (108) implies:
% 240.86/47.41  | | | | | | | | | |   (109)  all_58_11 = e2
% 240.86/47.41  | | | | | | | | | |   (110)  op(e1, e0) = e2
% 240.86/47.41  | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | BETA: splitting (8) gives:
% 240.86/47.41  | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | |   (111)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 240.86/47.41  | | | | | | | | | | |            & op(e1, e2) = e1)
% 240.86/47.41  | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | BETA: splitting (111) gives:
% 240.86/47.41  | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | |   (112)  all_58_6 = e1 & op(e1, e3) = e1
% 240.86/47.41  | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | ALPHA: (112) implies:
% 240.86/47.41  | | | | | | | | | | | |   (113)  all_58_6 = e1
% 240.86/47.41  | | | | | | | | | | | |   (114)  op(e1, e3) = e1
% 240.86/47.41  | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | BETA: splitting (32) gives:
% 240.86/47.41  | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | |   (115)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 240.86/47.41  | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 240.86/47.41  | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | REF_CLOSE: (5), (9), (40), (59), (68), (115) are inconsistent
% 240.86/47.41  | | | | | | | | | | | | |            by sub-proof #1350.
% 240.86/47.41  | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | |   (116)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 240.86/47.41  | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 240.86/47.41  | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | BETA: splitting (116) gives:
% 240.86/47.41  | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | |   (117)  all_58_6 = e0 & op(e1, e3) = e0
% 240.86/47.41  | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | REF_CLOSE: (85), (113), (117) are inconsistent by sub-proof
% 240.86/47.41  | | | | | | | | | | | | | |            #2205.
% 240.86/47.41  | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | |   (118)  all_58_12 = e0 & op(e0, e3) = e0
% 240.86/47.41  | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | ALPHA: (118) implies:
% 240.86/47.41  | | | | | | | | | | | | | |   (119)  op(e0, e3) = e0
% 240.86/47.41  | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 240.86/47.41  | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | |   (120)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 240.86/47.41  | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 240.86/47.41  | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | |   (121)  all_58_9 = e1 & op(e3, e0) = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 240.86/47.41  | | | | | | | | | | | | | | | |   (122)  all_58_9 = e1
% 240.86/47.41  | | | | | | | | | | | | | | | |   (123)  op(e3, e0) = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | |   (124)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 240.86/47.41  | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 240.86/47.41  | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | |   (125)  all_58_12 = e1 & op(e0, e3) = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 240.86/47.41  | | | | | | | | | | | | | | | | | |   (126)  op(e0, e3) = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (59), (85), (89), (119), (126) are
% 240.86/47.41  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1384.
% 240.86/47.41  | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | |   (127)  all_58_13 = e1 & op(e0, e2) = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (59), (80), (127) are inconsistent by
% 240.86/47.41  | | | | | | | | | | | | | | | | | |            sub-proof #2275.
% 240.86/47.41  | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | End of split
% 240.86/47.41  | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | |   (128)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 240.86/47.41  | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.86/47.41  | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | |   (129)  all_58_14 = e1 & op(e0, e1) = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 240.86/47.41  | | | | | | | | | | | | | | | | | |   (130)  all_58_14 = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | | |   (131)  op(e0, e1) = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | |   (132)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | |   (133)  all_58_12 = e2 & op(e0, e3) = e2
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | |   (134)  op(e0, e3) = e2
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (59), (119), (134) are inconsistent by
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | |            sub-proof #1896.
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | |   (135)  all_58_13 = e2 & op(e0, e2) = e2
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | |   (136)  op(e0, e2) = e2
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | |   (137)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | |   (138)  all_58_4 = e0 & op(e3, e1) = e0
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | |   (139)  op(e3, e1) = e0
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (140)  all_58_15 = e0 & op(e0, e0) = e0
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (141)  op(e0, e0) = e0
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (53), (59), (141) are inconsistent by
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2079.
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (142)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (143)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (59) with all_52_7, e2, e2, e0,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (47), (136) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (144)  all_52_7 = e2
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (59) with all_52_14, e2, e0, e1,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (15), (110) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (145)  all_52_14 = e2
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (59) with all_52_2, e1, e3, e1,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (62), (114) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (146)  all_52_2 = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (59) with all_52_13, e0, e0, e2,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (71), (105) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (147)  all_52_13 = e0
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (59) with all_52_12, e1, e0, e3,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (33), (123) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (148)  all_52_12 = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (59) with all_52_8, e0, e1, e3,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (26), (139) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (149)  all_52_8 = e0
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (148) imply:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (150)   ~ (e2 = e1)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (145), (147) imply:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (151)   ~ (e2 = e0)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (82), (147) imply:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (152)   ~ (e1 = e0)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (145) imply:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | |   (153)   ~ (e3 = e2)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |   (154)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (28), (37), (49), (50), (59), (67), (84),
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (85), (114), (139), (154) are inconsistent by
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #425.
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |   (155)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (156)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (157)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (158)   ~ (all_56_11 = e1)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (79), (158) imply:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (159)  $false
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (160)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (161)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (162)  op(e2, e1) = e1
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (59), (81), (162) are inconsistent by
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2306.
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (163)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (164)  op(e2, e0) = e2
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (59), (85), (109), (122), (143), (164) are
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1347.
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (165)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (166)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (167)  op(e0, e2) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (59), (136), (167) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (168)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (59), (74), (110), (168) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #477.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (169)  all_58_5 = e0 & op(e2, e1) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (170)  op(e2, e1) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (59), (99), (170) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1906.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |   (171)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (172)  all_58_8 = e0 & op(e1, e1) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (173)  op(e1, e1) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (15), (36), (41), (45), (59), (84),
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |            (114), (173) are inconsistent by sub-proof #457.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (174)  all_58_14 = e0 & op(e0, e1) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (175)  op(e0, e1) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (85), (131), (175) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2158.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |   (176)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (53), (59), (74), (130), (176) are
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1283.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | |   (177)  all_58_15 = e1 & op(e0, e0) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | |   (178)  all_58_15 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | |   (179)  op(e0, e0) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (25), (28), (55), (59), (61), (69),
% 240.86/47.42  | | | | | | | | | | | | | | | | | |            (71), (74), (84), (85), (122), (178), (179) are
% 240.86/47.42  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1601.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | |   (180)  all_58_10 = e1 & op(e2, e0) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | REF_CLOSE: (59), (71), (82), (180) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | |            sub-proof #2277.
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | |   (181)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 240.86/47.42  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | |   (182)  all_58_11 = e1 & op(e1, e0) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | |   (183)  op(e1, e0) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | REF_CLOSE: (59), (74), (110), (183) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | |            sub-proof #2019.
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | |   (184)  all_58_15 = e1 & op(e0, e0) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (23), (26), (28), (33), (40), (59),
% 240.86/47.42  | | | | | | | | | | | | | | | |            (64), (75), (84), (184) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | |            sub-proof #424.
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | |   (185)  all_58_7 = e1 & op(e1, e2) = e1
% 240.86/47.42  | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | ALPHA: (185) implies:
% 240.86/47.42  | | | | | | | | | | | |   (186)  all_58_7 = e1
% 240.86/47.42  | | | | | | | | | | | |   (187)  op(e1, e2) = e1
% 240.86/47.42  | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | BETA: splitting (57) gives:
% 240.86/47.42  | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | |   (188)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 240.86/47.42  | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 240.86/47.42  | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | BETA: splitting (188) gives:
% 240.86/47.42  | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | |   (189)  all_58_6 = e2 & op(e1, e3) = e2
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | ALPHA: (189) implies:
% 240.86/47.42  | | | | | | | | | | | | | |   (190)  all_58_6 = e2
% 240.86/47.42  | | | | | | | | | | | | | |   (191)  op(e1, e3) = e2
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | |   (192)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 240.86/47.42  | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | |   (193)  all_58_9 = e1 & op(e3, e0) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | |   (194)  all_58_9 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | |   (195)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (40), (59), (67), (195) are inconsistent
% 240.86/47.42  | | | | | | | | | | | | | | | | |            by sub-proof #423.
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | |   (196)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | |   (197)  all_58_4 = e0 & op(e3, e1) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | |   (198)  op(e3, e1) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |   (199)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (59), (81), (85), (198), (199) are
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #422.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |   (200)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (201)  all_58_8 = e1 & op(e1, e1) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (23), (26), (28), (33), (40), (59), (60),
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |            (64), (75), (84), (201) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |            sub-proof #421.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (202)  all_58_14 = e1 & op(e0, e1) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (203)  all_58_14 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (204)  op(e0, e1) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |   (205)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (206)  all_58_12 = e2 & op(e0, e3) = e2
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (35), (59), (206) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2315.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (207)  all_58_13 = e2 & op(e0, e2) = e2
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (208)  op(e0, e2) = e2
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_58_15 = e0 & op(e0, e0) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | |   (210)  op(e0, e0) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (53), (59), (210) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2079.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | |   (211)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | |   (212)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_58_12 = e0 & op(e0, e3) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_58_12 = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (24), (28), (37), (40), (59), (74), (84),
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (215) are inconsistent by sub-proof #1341.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  all_58_6 = e1 & op(e1, e3) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  op(e1, e3) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (74), (191), (218) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2226.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  all_58_12 = e1 & op(e0, e3) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (214), (219) are inconsistent by sub-proof
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            #805.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | |   (220)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (59), (85), (204), (208), (220) are
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1333.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |   (221)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (53), (59), (74), (203), (221) are
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | |   (222)  all_58_9 = e0 & op(e3, e0) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (194), (222) are inconsistent by sub-proof
% 240.86/47.42  | | | | | | | | | | | | | | | | | |            #1696.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | |   (223)  all_58_10 = e1 & op(e2, e0) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | REF_CLOSE: (59), (71), (82), (223) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | |            sub-proof #2277.
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | |   (224)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 240.86/47.42  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (16), (23), (26), (28), (33), (40),
% 240.86/47.42  | | | | | | | | | | | | | | |            (44), (57), (59), (60), (64), (70), (74), (75),
% 240.86/47.42  | | | | | | | | | | | | | | |            (84), (85), (186), (224) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | |            sub-proof #420.
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | |   (225)  all_58_7 = e2 & op(e1, e2) = e2
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | ALPHA: (225) implies:
% 240.86/47.42  | | | | | | | | | | | | | |   (226)  all_58_7 = e2
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | REF_CLOSE: (74), (186), (226) are inconsistent by sub-proof
% 240.86/47.42  | | | | | | | | | | | | | |            #2134.
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | |   (227)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 240.86/47.42  | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 240.86/47.42  | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | BETA: splitting (227) gives:
% 240.86/47.42  | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | |   (228)  all_58_8 = e2 & op(e1, e1) = e2
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | ALPHA: (228) implies:
% 240.86/47.42  | | | | | | | | | | | | | |   (229)  op(e1, e1) = e2
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | REF_CLOSE: (28), (44), (59), (229) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | |            sub-proof #2206.
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 240.86/47.42  | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | |   (230)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 240.86/47.42  | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | |   (231)  all_58_9 = e1 & op(e3, e0) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | |   (232)  all_58_9 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | |   (233)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (40), (59), (67), (233) are inconsistent
% 240.86/47.42  | | | | | | | | | | | | | | | | |            by sub-proof #423.
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | |   (234)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | |   (235)  all_58_4 = e0 & op(e3, e1) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | |   (236)  op(e3, e1) = e0
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |   (237)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (238)  all_58_0 = e1 & op(e3, e3) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (239)  op(e3, e3) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (59), (74), (239) are inconsistent by
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |            sub-proof #2267.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (240)  all_58_2 = e1 & op(e2, e3) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (241)  all_58_2 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (241) imply:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (242)  e3 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (23), (26), (28), (33), (40), (59), (64),
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |            (75), (84), (242) are inconsistent by sub-proof
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |            #419.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |   (243)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (244)  all_58_6 = e1 & op(e1, e3) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (245)  all_58_6 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (246)  op(e1, e3) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (10), (28), (36), (57), (59), (70),
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |            (74), (84), (85), (110), (186), (187), (245),
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |            (246) are inconsistent by sub-proof #418.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (247)  all_58_12 = e1 & op(e0, e3) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | |   (248)  all_58_12 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |   (249)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (59), (81), (85), (236), (249) are
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #422.
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |   (250)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (251)  all_58_8 = e1 & op(e1, e1) = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (252)  all_58_8 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (252) imply:
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |   (253)  e3 = e1
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (23), (26), (28), (33), (40), (59), (64),
% 240.86/47.42  | | | | | | | | | | | | | | | | | | | | | |            (75), (84), (253) are inconsistent by sub-proof
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |            #419.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |   (254)  all_58_14 = e1 & op(e0, e1) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |   (255)  all_58_14 = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | |   (256)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (39), (59), (67), (256) are inconsistent
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1323.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | |   (257)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | |   (258)  all_58_7 = e0 & op(e1, e2) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | |   (259)  op(e1, e2) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (59), (85), (187), (259) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2136.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_58_13 = e0 & op(e0, e2) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (260) implies:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | |   (261)  op(e0, e2) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (28), (53), (59), (73), (74), (248), (255),
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | |            (261) are inconsistent by sub-proof #417.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | |   (262)  all_58_9 = e0 & op(e3, e0) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (232), (262) are inconsistent by sub-proof
% 240.86/47.43  | | | | | | | | | | | | | | | | | |            #1696.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | |   (263)  all_58_10 = e1 & op(e2, e0) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | REF_CLOSE: (59), (71), (82), (263) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | | | | | |            sub-proof #2277.
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | |   (264)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 240.86/47.43  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (16), (23), (26), (28), (33), (40),
% 240.86/47.43  | | | | | | | | | | | | | | |            (44), (57), (59), (60), (64), (70), (74), (75),
% 240.86/47.43  | | | | | | | | | | | | | | |            (84), (85), (186), (264) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | | | | |            sub-proof #420.
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | |   (265)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 240.86/47.43  | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | BETA: splitting (265) gives:
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | |   (266)  all_58_8 = e1 & op(e1, e1) = e1
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | REF_CLOSE: (6), (23), (26), (28), (33), (40), (59), (60),
% 240.86/47.43  | | | | | | | | | | | |            (64), (75), (84), (266) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | |            sub-proof #421.
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | |   (267)  all_58_11 = e1 & op(e1, e0) = e1
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | ALPHA: (267) implies:
% 240.86/47.43  | | | | | | | | | | | |   (268)  op(e1, e0) = e1
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | REF_CLOSE: (59), (74), (110), (268) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | |            sub-proof #2019.
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | |   (269)  all_58_15 = e2 & op(e0, e0) = e2
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | ALPHA: (269) implies:
% 240.86/47.43  | | | | | | | | | |   (270)  op(e0, e0) = e2
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | REF_CLOSE: (28), (53), (59), (270) are inconsistent by
% 240.86/47.43  | | | | | | | | | |            sub-proof #1388.
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | 
% 240.86/47.43  | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | 
% 240.86/47.43  | | | | | | | End of split
% 240.86/47.43  | | | | | | | 
% 240.86/47.43  | | | | | | End of split
% 240.86/47.43  | | | | | | 
% 240.86/47.43  | | | | | Case 2:
% 240.86/47.43  | | | | | | 
% 240.86/47.43  | | | | | |   (271)  all_58_10 = e2 & op(e2, e0) = e2
% 240.86/47.43  | | | | | | 
% 240.86/47.43  | | | | | | ALPHA: (271) implies:
% 240.86/47.43  | | | | | |   (272)  op(e2, e0) = e2
% 240.86/47.43  | | | | | | 
% 240.86/47.43  | | | | | | BETA: splitting (58) gives:
% 240.86/47.43  | | | | | | 
% 240.86/47.43  | | | | | | Case 1:
% 240.86/47.43  | | | | | | | 
% 240.86/47.43  | | | | | | |   (273)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 240.86/47.43  | | | | | | |            op(e2, e2) = e0)
% 240.86/47.43  | | | | | | | 
% 240.86/47.43  | | | | | | | REF_CLOSE: (4), (5), (39), (59), (68), (273) are inconsistent by
% 240.86/47.43  | | | | | | |            sub-proof #427.
% 240.86/47.43  | | | | | | | 
% 240.86/47.43  | | | | | | Case 2:
% 240.86/47.43  | | | | | | | 
% 240.86/47.43  | | | | | | |   (274)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 240.86/47.43  | | | | | | |            op(e2, e0) = e0)
% 240.86/47.43  | | | | | | | 
% 240.86/47.43  | | | | | | | BETA: splitting (274) gives:
% 240.86/47.43  | | | | | | | 
% 240.86/47.43  | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | 
% 240.86/47.43  | | | | | | | |   (275)  all_58_5 = e0 & op(e2, e1) = e0
% 240.86/47.43  | | | | | | | | 
% 240.86/47.43  | | | | | | | | ALPHA: (275) implies:
% 240.86/47.43  | | | | | | | |   (276)  op(e2, e1) = e0
% 240.86/47.43  | | | | | | | | 
% 240.86/47.43  | | | | | | | | BETA: splitting (29) gives:
% 240.86/47.43  | | | | | | | | 
% 240.86/47.43  | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | 
% 240.86/47.43  | | | | | | | | |   (277)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 240.86/47.43  | | | | | | | | |            op(e2, e1) = e2)
% 240.86/47.43  | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | BETA: splitting (277) gives:
% 240.86/47.43  | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | |   (278)  all_58_4 = e2 & op(e3, e1) = e2
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | REF_CLOSE: (5), (9), (23), (26), (28), (33), (40), (43),
% 240.86/47.43  | | | | | | | | | |            (56), (59), (64), (67), (74), (75), (84), (85),
% 240.86/47.43  | | | | | | | | | |            (278) are inconsistent by sub-proof #415.
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | |   (279)  all_58_5 = e2 & op(e2, e1) = e2
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | ALPHA: (279) implies:
% 240.86/47.43  | | | | | | | | | |   (280)  op(e2, e1) = e2
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | REF_CLOSE: (9), (59), (276), (280) are inconsistent by
% 240.86/47.43  | | | | | | | | | |            sub-proof #1906.
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | 
% 240.86/47.43  | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | 
% 240.86/47.43  | | | | | | | | |   (281)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 240.86/47.43  | | | | | | | | |            op(e0, e1) = e2)
% 240.86/47.43  | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | BETA: splitting (281) gives:
% 240.86/47.43  | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | |   (282)  all_58_8 = e2 & op(e1, e1) = e2
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | ALPHA: (282) implies:
% 240.86/47.43  | | | | | | | | | |   (283)  op(e1, e1) = e2
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | REF_CLOSE: (28), (44), (59), (283) are inconsistent by
% 240.86/47.43  | | | | | | | | | |            sub-proof #2206.
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | |   (284)  all_58_14 = e2 & op(e0, e1) = e2
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | ALPHA: (284) implies:
% 240.86/47.43  | | | | | | | | | |   (285)  all_58_14 = e2
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | BETA: splitting (14) gives:
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | |   (286)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 240.86/47.43  | | | | | | | | | | |            & op(e2, e1) = e1)
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | BETA: splitting (286) gives:
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | |   (287)  all_58_4 = e1 & op(e3, e1) = e1
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | ALPHA: (287) implies:
% 240.86/47.43  | | | | | | | | | | | |   (288)  op(e3, e1) = e1
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | BETA: splitting (43) gives:
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | |   (289)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 240.86/47.43  | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 240.86/47.43  | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | REF_CLOSE: (5), (9), (40), (59), (67), (289) are inconsistent
% 240.86/47.43  | | | | | | | | | | | | |            by sub-proof #423.
% 240.86/47.43  | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | |   (290)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 240.86/47.43  | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 240.86/47.43  | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | BETA: splitting (290) gives:
% 240.86/47.43  | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | |   (291)  all_58_4 = e0 & op(e3, e1) = e0
% 240.86/47.43  | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | ALPHA: (291) implies:
% 240.86/47.43  | | | | | | | | | | | | | |   (292)  op(e3, e1) = e0
% 240.86/47.43  | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | REF_CLOSE: (59), (85), (288), (292) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | | | |            sub-proof #2089.
% 240.86/47.43  | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | |   (293)  all_58_9 = e0 & op(e3, e0) = e0
% 240.86/47.43  | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | ALPHA: (293) implies:
% 240.86/47.43  | | | | | | | | | | | | | |   (294)  all_58_9 = e0
% 240.86/47.43  | | | | | | | | | | | | | |   (295)  op(e3, e0) = e0
% 240.86/47.43  | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 240.86/47.43  | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | |   (296)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 240.86/47.43  | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | |   (297)  all_58_9 = e1 & op(e3, e0) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 240.86/47.43  | | | | | | | | | | | | | | | |   (298)  all_58_9 = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | REF_CLOSE: (85), (294), (298) are inconsistent by sub-proof
% 240.86/47.43  | | | | | | | | | | | | | | | |            #1744.
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | |   (299)  all_58_10 = e1 & op(e2, e0) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 240.86/47.43  | | | | | | | | | | | | | | | |   (300)  op(e2, e0) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | REF_CLOSE: (59), (74), (272), (300) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | | | | | |            sub-proof #1659.
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | |   (301)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 240.86/47.43  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | |   (302)  all_58_11 = e1 & op(e1, e0) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 240.86/47.43  | | | | | | | | | | | | | | | |   (303)  all_58_11 = e1
% 240.86/47.43  | | | | | | | | | | | | | | | |   (304)  op(e1, e0) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | |   (305)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 240.86/47.43  | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 240.86/47.43  | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | |   (306)  all_58_12 = e1 & op(e0, e3) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 240.86/47.43  | | | | | | | | | | | | | | | | | |   (307)  op(e0, e3) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | |   (308)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (40), (59), (68), (308) are inconsistent
% 240.86/47.43  | | | | | | | | | | | | | | | | | | |            by sub-proof #1350.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | |   (309)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 240.86/47.43  | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | |   (310)  all_58_6 = e0 & op(e1, e3) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | |   (311)  op(e1, e3) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | |   (312)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |   (313)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_25 & $i(all_56_25)
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |   (314)  op(e3, e0) = all_56_25
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |   (315)  op(e3, all_56_25) = e3
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (59), (295), (314), (315) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1926.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |   (316)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_27 & $i(all_56_27)
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (59), (74), (86), (92), (272), (276), (316)
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #414.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | |   (317)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |   (318)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_29 & $i(all_56_29)
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (10), (28), (36), (44), (45), (57),
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |            (59), (60), (70), (74), (84), (85), (95), (303),
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |            (304), (311), (318) are inconsistent by sub-proof
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |            #412.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |   (319)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (319) implies:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |   (320)  op(e0, all_56_31) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (320) imply:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |   (321)  op(e0, e3) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (59), (85), (89), (307), (321) are
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1384.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | |   (322)  all_58_12 = e0 & op(e0, e3) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | ALPHA: (322) implies:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | |   (323)  op(e0, e3) = e0
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (59), (85), (89), (307), (323) are
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1384.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | |   (324)  all_58_13 = e1 & op(e0, e2) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (59), (80), (324) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | | | | | | | |            sub-proof #2275.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | |   (325)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 240.86/47.43  | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 240.86/47.43  | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 240.86/47.43  | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | |   (326)  all_58_14 = e1 & op(e0, e1) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (285), (326) are inconsistent by sub-proof
% 240.86/47.43  | | | | | | | | | | | | | | | | | |            #2040.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | |   (327)  all_58_15 = e1 & op(e0, e0) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (23), (26), (28), (33), (40), (59),
% 240.86/47.43  | | | | | | | | | | | | | | | | | |            (64), (75), (84), (327) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | | | | | | | |            sub-proof #424.
% 240.86/47.43  | | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | |   (328)  all_58_15 = e1 & op(e0, e0) = e1
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (23), (26), (28), (33), (40), (59),
% 240.86/47.43  | | | | | | | | | | | | | | | |            (64), (75), (84), (328) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | | | | | |            sub-proof #424.
% 240.86/47.43  | | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | |   (329)  all_58_5 = e1 & op(e2, e1) = e1
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | ALPHA: (329) implies:
% 240.86/47.43  | | | | | | | | | | | |   (330)  op(e2, e1) = e1
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | REF_CLOSE: (27), (59), (85), (276), (330) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | |            sub-proof #2165.
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | |   (331)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 240.86/47.43  | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | BETA: splitting (331) gives:
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | Case 1:
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | |   (332)  all_58_8 = e1 & op(e1, e1) = e1
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | REF_CLOSE: (6), (23), (26), (28), (33), (40), (59), (60),
% 240.86/47.43  | | | | | | | | | | | |            (64), (75), (84), (332) are inconsistent by
% 240.86/47.43  | | | | | | | | | | | |            sub-proof #421.
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | |   (333)  all_58_14 = e1 & op(e0, e1) = e1
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | | REF_CLOSE: (74), (285), (333) are inconsistent by sub-proof
% 240.86/47.43  | | | | | | | | | | | |            #2040.
% 240.86/47.43  | | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | | 
% 240.86/47.43  | | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | | 
% 240.86/47.43  | | | | | | | | End of split
% 240.86/47.43  | | | | | | | | 
% 240.86/47.43  | | | | | | | Case 2:
% 240.86/47.43  | | | | | | | | 
% 240.86/47.43  | | | | | | | |   (334)  all_58_10 = e0 & op(e2, e0) = e0
% 240.86/47.43  | | | | | | | | 
% 240.86/47.43  | | | | | | | | ALPHA: (334) implies:
% 240.86/47.43  | | | | | | | |   (335)  op(e2, e0) = e0
% 240.86/47.43  | | | | | | | | 
% 240.86/47.43  | | | | | | | | REF_CLOSE: (9), (59), (272), (335) are inconsistent by sub-proof
% 240.86/47.43  | | | | | | | |            #2121.
% 240.86/47.43  | | | | | | | | 
% 240.86/47.43  | | | | | | | End of split
% 240.86/47.43  | | | | | | | 
% 240.86/47.43  | | | | | | End of split
% 240.86/47.43  | | | | | | 
% 240.86/47.43  | | | | | End of split
% 240.86/47.43  | | | | | 
% 240.86/47.43  | | | | End of split
% 240.86/47.43  | | | | 
% 240.86/47.43  | | | End of split
% 240.86/47.43  | | | 
% 240.86/47.43  | | End of split
% 240.86/47.43  | | 
% 240.86/47.43  | End of split
% 240.86/47.43  | 
% 240.86/47.43  End of proof
% 240.86/47.43  
% 240.86/47.43  Sub-proof #412 shows that the following formulas are inconsistent:
% 240.86/47.43  ----------------------------------------------------------------
% 240.86/47.43    (1)   ~ (e3 = e0)
% 240.86/47.43    (2)   ~ (e2 = e0)
% 240.86/47.43    (3)  op(e1, e2) = all_52_6
% 240.86/47.43    (4)  all_58_11 = e1
% 240.86/47.43    (5)   ~ (e3 = e1)
% 240.86/47.43    (6)  op(e1, e0) = e1
% 240.86/47.43    (7)   ~ (e3 = e2)
% 240.86/47.43    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.86/47.43         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.86/47.43    (9)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 240.86/47.43         $i(all_56_29)
% 240.86/47.43    (10)  op(e1, e3) = e0
% 240.86/47.43    (11)  op(e1, e1) = e3
% 240.86/47.43    (12)   ~ (all_52_6 = e3)
% 240.86/47.43    (13)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.86/47.43          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.86/47.43    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.44    (15)  all_58_8 = e3
% 240.86/47.44    (16)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.86/47.44            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1,
% 240.86/47.44              e3) = all_46_1 & $i(all_46_1))
% 240.86/47.44    (17)   ~ (e1 = e0)
% 240.86/47.44    (18)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.86/47.44          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.86/47.44    (19)   ~ (e2 = e1)
% 240.86/47.44  
% 240.86/47.44  Begin of proof
% 240.86/47.44  | 
% 240.86/47.44  | ALPHA: (9) implies:
% 240.86/47.44  |   (20)  op(e1, e0) = all_56_29
% 240.86/47.44  |   (21)  op(e1, all_56_29) = e1
% 240.86/47.44  | 
% 240.86/47.44  | BETA: splitting (16) gives:
% 240.86/47.44  | 
% 240.86/47.44  | Case 1:
% 240.86/47.44  | | 
% 240.86/47.44  | | 
% 240.86/47.44  | | GROUND_INST: instantiating (14) with e1, all_56_29, e0, e1, simplifying with
% 240.86/47.44  | |              (6), (20) gives:
% 240.86/47.44  | |   (22)  all_56_29 = e1
% 240.86/47.44  | | 
% 240.86/47.44  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (12), (13), (14), (15),
% 240.86/47.44  | |            (17), (18), (19), (20), (21), (22) are inconsistent by sub-proof
% 240.86/47.44  | |            #413.
% 240.86/47.44  | | 
% 240.86/47.44  | Case 2:
% 240.86/47.44  | | 
% 240.86/47.44  | |   (23)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.86/47.44  | | 
% 240.86/47.44  | | ALPHA: (23) implies:
% 240.86/47.44  | |   (24)   ~ (all_46_1 = e2)
% 240.86/47.44  | |   (25)  op(e1, e3) = all_46_1
% 240.86/47.44  | | 
% 240.86/47.44  | | GROUND_INST: instantiating (14) with e1, all_56_29, e0, e1, simplifying with
% 240.86/47.44  | |              (6), (20) gives:
% 240.86/47.44  | |   (26)  all_56_29 = e1
% 240.86/47.44  | | 
% 240.86/47.44  | | GROUND_INST: instantiating (14) with e0, all_46_1, e3, e1, simplifying with
% 240.86/47.44  | |              (10), (25) gives:
% 240.86/47.44  | |   (27)  all_46_1 = e0
% 240.86/47.44  | | 
% 240.86/47.44  | | REDUCE: (24), (27) imply:
% 240.86/47.44  | |   (28)   ~ (e2 = e0)
% 240.86/47.44  | | 
% 240.86/47.44  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (12), (13), (14), (15),
% 240.86/47.44  | |            (17), (18), (19), (20), (21), (26) are inconsistent by sub-proof
% 240.86/47.44  | |            #413.
% 240.86/47.44  | | 
% 240.86/47.44  | End of split
% 240.86/47.44  | 
% 240.86/47.44  End of proof
% 240.86/47.44  
% 240.86/47.44  Sub-proof #413 shows that the following formulas are inconsistent:
% 240.86/47.44  ----------------------------------------------------------------
% 240.86/47.44    (1)  all_56_29 = e1
% 240.86/47.44    (2)   ~ (e3 = e0)
% 240.86/47.44    (3)   ~ (e2 = e0)
% 240.86/47.44    (4)  op(e1, e2) = all_52_6
% 240.86/47.44    (5)  all_58_11 = e1
% 240.86/47.44    (6)  op(e1, all_56_29) = e1
% 240.86/47.44    (7)   ~ (e3 = e1)
% 240.86/47.44    (8)   ~ (e3 = e2)
% 240.86/47.44    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.86/47.44         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.86/47.44    (10)  op(e1, e1) = e3
% 240.86/47.44    (11)   ~ (all_52_6 = e3)
% 240.86/47.44    (12)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.86/47.44          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.86/47.44    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.44    (14)  all_58_8 = e3
% 240.86/47.44    (15)   ~ (e1 = e0)
% 240.86/47.44    (16)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.86/47.44          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.86/47.44    (17)  op(e1, e0) = all_56_29
% 240.86/47.44    (18)   ~ (e2 = e1)
% 240.86/47.44  
% 240.86/47.44  Begin of proof
% 240.86/47.44  | 
% 240.86/47.44  | REDUCE: (1), (6) imply:
% 240.86/47.44  |   (19)  op(e1, e1) = e1
% 240.86/47.44  | 
% 240.86/47.44  | REDUCE: (1), (17) imply:
% 240.86/47.44  |   (20)  op(e1, e0) = e1
% 240.86/47.44  | 
% 240.86/47.44  | GROUND_INST: instantiating (13) with e3, e1, e1, e1, simplifying with (10),
% 240.86/47.44  |              (19) gives:
% 240.86/47.44  |   (21)  e3 = e1
% 240.86/47.44  | 
% 240.86/47.44  | COMBINE_EQS: (14), (21) imply:
% 240.86/47.44  |   (22)  all_58_8 = e1
% 240.86/47.44  | 
% 240.86/47.44  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (15), (16),
% 240.86/47.44  |            (18), (19), (20), (22) are inconsistent by sub-proof #787.
% 240.86/47.44  | 
% 240.86/47.44  End of proof
% 240.86/47.44  
% 240.86/47.44  Sub-proof #414 shows that the following formulas are inconsistent:
% 240.86/47.44  ----------------------------------------------------------------
% 240.86/47.44    (1)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) = all_22_1
% 240.86/47.44           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1) =
% 240.86/47.44           all_22_1 & $i(all_22_1))
% 240.86/47.44    (2)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 240.86/47.44           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 240.86/47.44           all_30_1 & $i(all_30_1))
% 240.86/47.44    (3)  op(e2, e2) = e1
% 240.86/47.44    (4)  op(e2, e0) = e2
% 240.86/47.44    (5)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 240.86/47.44         $i(all_56_27)
% 240.86/47.44    (6)  op(e2, e1) = e0
% 240.86/47.44    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.44    (8)   ~ (e2 = e1)
% 240.86/47.44  
% 240.86/47.44  Begin of proof
% 240.86/47.44  | 
% 240.86/47.44  | ALPHA: (5) implies:
% 240.86/47.44  |   (9)  op(e2, e0) = all_56_27
% 240.86/47.44  |   (10)  op(e2, all_56_27) = e2
% 240.86/47.44  | 
% 240.86/47.44  | BETA: splitting (1) gives:
% 240.86/47.44  | 
% 240.86/47.44  | Case 1:
% 240.86/47.44  | | 
% 240.86/47.44  | | 
% 240.86/47.44  | | GROUND_INST: instantiating (7) with e2, all_56_27, e0, e2, simplifying with
% 240.86/47.44  | |              (4), (9) gives:
% 240.86/47.44  | |   (11)  all_56_27 = e2
% 240.86/47.44  | | 
% 240.86/47.44  | | REDUCE: (10), (11) imply:
% 240.86/47.44  | |   (12)  op(e2, e2) = e2
% 240.86/47.44  | | 
% 240.86/47.44  | | REF_CLOSE: (3), (7), (8), (12) are inconsistent by sub-proof #2235.
% 240.86/47.44  | | 
% 240.86/47.44  | Case 2:
% 240.86/47.44  | | 
% 240.86/47.44  | |   (13)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 & $i(all_22_1)
% 240.86/47.44  | | 
% 240.86/47.44  | | ALPHA: (13) implies:
% 240.86/47.44  | |   (14)   ~ (all_22_1 = e0)
% 240.86/47.44  | |   (15)  op(e2, e1) = all_22_1
% 240.86/47.44  | | 
% 240.86/47.44  | | REF_CLOSE: (2), (6), (7), (14), (15) are inconsistent by sub-proof #1356.
% 240.86/47.44  | | 
% 240.86/47.44  | End of split
% 240.86/47.44  | 
% 240.86/47.44  End of proof
% 240.86/47.44  
% 240.86/47.44  Sub-proof #415 shows that the following formulas are inconsistent:
% 240.86/47.44  ----------------------------------------------------------------
% 240.86/47.44    (1)   ~ (e3 = e0)
% 240.86/47.44    (2)   ~ (e2 = e0)
% 240.86/47.44    (3)   ~ (e3 = e1)
% 240.86/47.44    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.86/47.44         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.86/47.44    (5)  op(e3, e1) = all_52_8
% 240.86/47.44    (6)   ~ (e3 = e2)
% 240.86/47.44    (7)  op(e3, e0) = all_52_12
% 240.86/47.44    (8)  op(e3, e3) = e2
% 240.86/47.44    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.86/47.44         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.86/47.44    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 240.86/47.44          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 240.86/47.44    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.44    (12)   ~ (all_52_12 = e3)
% 240.86/47.44    (13)   ~ (e1 = e0)
% 240.86/47.44    (14)  all_58_4 = e2 & op(e3, e1) = e2
% 240.86/47.44    (15)  op(e3, e2) = e3
% 240.86/47.44    (16)   ~ (e2 = e1)
% 240.86/47.44    (17)   ~ (all_52_8 = e3)
% 240.86/47.44  
% 240.86/47.44  Begin of proof
% 240.86/47.44  | 
% 240.86/47.44  | ALPHA: (14) implies:
% 240.86/47.44  |   (18)  all_58_4 = e2
% 240.86/47.44  | 
% 240.86/47.44  | BETA: splitting (9) gives:
% 240.86/47.44  | 
% 240.86/47.44  | Case 1:
% 240.86/47.44  | | 
% 240.86/47.44  | |   (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 240.86/47.44  | |           e0)
% 240.86/47.44  | | 
% 240.86/47.44  | | REF_CLOSE: (1), (2), (8), (11), (15), (19) are inconsistent by sub-proof
% 240.86/47.44  | |            #423.
% 240.86/47.44  | | 
% 240.86/47.44  | Case 2:
% 240.86/47.44  | | 
% 240.86/47.44  | |   (20)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 240.86/47.44  | |           e0)
% 240.86/47.44  | | 
% 240.86/47.44  | | BETA: splitting (20) gives:
% 240.86/47.44  | | 
% 240.86/47.44  | | Case 1:
% 240.86/47.44  | | | 
% 240.86/47.44  | | |   (21)  all_58_4 = e0 & op(e3, e1) = e0
% 240.86/47.44  | | | 
% 240.86/47.44  | | | REF_CLOSE: (2), (18), (21) are inconsistent by sub-proof #2170.
% 240.86/47.44  | | | 
% 240.86/47.44  | | Case 2:
% 240.86/47.44  | | | 
% 240.86/47.44  | | |   (22)  all_58_9 = e0 & op(e3, e0) = e0
% 240.86/47.44  | | | 
% 240.86/47.44  | | | ALPHA: (22) implies:
% 240.86/47.44  | | |   (23)  all_58_9 = e0
% 240.86/47.44  | | | 
% 240.86/47.44  | | | BETA: splitting (10) gives:
% 240.86/47.44  | | | 
% 240.86/47.44  | | | Case 1:
% 240.86/47.44  | | | | 
% 240.86/47.44  | | | |   (24)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 240.86/47.44  | | | |           = e1)
% 240.86/47.44  | | | | 
% 240.86/47.44  | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (11), (12), (16), (17), (24)
% 240.86/47.44  | | | |            are inconsistent by sub-proof #416.
% 240.86/47.44  | | | | 
% 240.86/47.44  | | | Case 2:
% 240.86/47.44  | | | | 
% 240.86/47.44  | | | |   (25)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 240.86/47.44  | | | |           = e1)
% 240.86/47.44  | | | | 
% 240.86/47.44  | | | | BETA: splitting (25) gives:
% 240.86/47.44  | | | | 
% 240.86/47.44  | | | | Case 1:
% 240.86/47.44  | | | | | 
% 240.86/47.44  | | | | |   (26)  all_58_4 = e1 & op(e3, e1) = e1
% 240.86/47.44  | | | | | 
% 240.86/47.44  | | | | | REF_CLOSE: (16), (18), (26) are inconsistent by sub-proof #2168.
% 240.86/47.44  | | | | | 
% 240.86/47.44  | | | | Case 2:
% 240.86/47.44  | | | | | 
% 240.86/47.44  | | | | |   (27)  all_58_9 = e1 & op(e3, e0) = e1
% 240.86/47.44  | | | | | 
% 240.86/47.44  | | | | | ALPHA: (27) implies:
% 240.86/47.44  | | | | |   (28)  all_58_9 = e1
% 240.86/47.44  | | | | | 
% 240.86/47.44  | | | | | REF_CLOSE: (13), (23), (28) are inconsistent by sub-proof #1744.
% 240.86/47.44  | | | | | 
% 240.86/47.44  | | | | End of split
% 240.86/47.44  | | | | 
% 240.86/47.44  | | | End of split
% 240.86/47.44  | | | 
% 240.86/47.44  | | End of split
% 240.86/47.44  | | 
% 240.86/47.44  | End of split
% 240.86/47.44  | 
% 240.86/47.44  End of proof
% 240.86/47.44  
% 240.86/47.44  Sub-proof #416 shows that the following formulas are inconsistent:
% 240.86/47.44  ----------------------------------------------------------------
% 240.86/47.44    (1)   ~ (e3 = e1)
% 240.86/47.44    (2)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.86/47.44         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.86/47.44    (3)  op(e3, e1) = all_52_8
% 240.86/47.44    (4)   ~ (e3 = e2)
% 240.86/47.44    (5)  op(e3, e0) = all_52_12
% 240.86/47.44    (6)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 240.86/47.44    (7)  op(e3, e3) = e2
% 240.86/47.44    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.44    (9)   ~ (all_52_12 = e3)
% 240.86/47.44    (10)   ~ (e2 = e1)
% 240.86/47.44    (11)   ~ (all_52_8 = e3)
% 240.86/47.44  
% 240.86/47.44  Begin of proof
% 240.86/47.44  | 
% 240.86/47.44  | BETA: splitting (6) gives:
% 240.86/47.44  | 
% 240.86/47.44  | Case 1:
% 240.86/47.44  | | 
% 240.86/47.44  | |   (12)  all_58_0 = e1 & op(e3, e3) = e1
% 240.86/47.44  | | 
% 240.86/47.44  | | ALPHA: (12) implies:
% 240.86/47.44  | |   (13)  op(e3, e3) = e1
% 240.86/47.44  | | 
% 240.86/47.44  | | REF_CLOSE: (7), (8), (10), (13) are inconsistent by sub-proof #2267.
% 240.86/47.44  | | 
% 240.86/47.44  | Case 2:
% 240.86/47.44  | | 
% 240.86/47.44  | |   (14)  all_58_1 = e1 & op(e3, e2) = e1
% 240.86/47.44  | | 
% 240.86/47.44  | | ALPHA: (14) implies:
% 240.86/47.44  | |   (15)  all_58_1 = e1
% 240.86/47.44  | | 
% 240.86/47.44  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (15) are
% 240.86/47.44  | |            inconsistent by sub-proof #1327.
% 240.86/47.44  | | 
% 240.86/47.44  | End of split
% 240.86/47.44  | 
% 240.86/47.44  End of proof
% 240.86/47.44  
% 240.86/47.44  Sub-proof #417 shows that the following formulas are inconsistent:
% 240.86/47.44  ----------------------------------------------------------------
% 240.86/47.44    (1)   ~ (e2 = e0)
% 240.86/47.44    (2)  all_58_12 = e1
% 240.86/47.44    (3)   ~ (e3 = e2)
% 240.86/47.44    (4)  op(e0, e2) = e0
% 240.86/47.44    (5)  op(e0, e0) = e3
% 240.86/47.44    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.44    (7)  all_58_14 = e1
% 240.86/47.44    (8)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 240.86/47.44         (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.86/47.44    (9)   ~ (e2 = e1)
% 240.86/47.44  
% 240.86/47.44  Begin of proof
% 240.86/47.44  | 
% 240.86/47.44  | BETA: splitting (8) gives:
% 240.86/47.44  | 
% 240.86/47.44  | Case 1:
% 240.86/47.44  | | 
% 240.86/47.44  | |   (10)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 240.86/47.44  | |           e2)
% 240.86/47.44  | | 
% 240.86/47.44  | | REF_CLOSE: (1), (2), (4), (6), (9), (10) are inconsistent by sub-proof #849.
% 240.86/47.44  | | 
% 240.86/47.44  | Case 2:
% 240.86/47.44  | | 
% 240.86/47.44  | |   (11)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.86/47.44  | |           e2)
% 240.86/47.44  | | 
% 240.86/47.44  | | REF_CLOSE: (3), (5), (6), (7), (9), (11) are inconsistent by sub-proof
% 240.86/47.44  | |            #1037.
% 240.86/47.44  | | 
% 240.86/47.44  | End of split
% 240.86/47.44  | 
% 240.86/47.44  End of proof
% 240.86/47.44  
% 240.86/47.44  Sub-proof #418 shows that the following formulas are inconsistent:
% 240.86/47.44  ----------------------------------------------------------------
% 240.86/47.44    (1)   ~ (e3 = e0)
% 240.86/47.44    (2)  op(e1, e2) = e1
% 240.86/47.44    (3)   ~ (e2 = e0)
% 240.86/47.44    (4)  op(e1, e2) = all_52_6
% 240.86/47.44    (5)   ~ (e3 = e1)
% 240.86/47.44    (6)   ~ (e3 = e2)
% 240.86/47.44    (7)  op(e1, e3) = e1
% 240.86/47.44    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.86/47.44         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.86/47.44    (9)  all_58_6 = e1
% 240.86/47.44    (10)  all_58_7 = e1
% 240.86/47.44    (11)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.86/47.44          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.86/47.44    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.44    (13)  op(e1, e0) = e2
% 240.86/47.44    (14)   ~ (e1 = e0)
% 240.86/47.44    (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.86/47.44          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.86/47.44    (16)   ~ (e2 = e1)
% 240.86/47.44  
% 240.86/47.44  Begin of proof
% 240.86/47.44  | 
% 240.86/47.44  | BETA: splitting (15) gives:
% 240.86/47.44  | 
% 240.86/47.44  | Case 1:
% 240.86/47.44  | | 
% 240.86/47.44  | |   (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 240.86/47.44  | |           e0)
% 240.86/47.44  | | 
% 240.86/47.44  | | BETA: splitting (17) gives:
% 240.86/47.44  | | 
% 240.86/47.44  | | Case 1:
% 240.86/47.44  | | | 
% 240.86/47.44  | | |   (18)  all_58_6 = e0 & op(e1, e3) = e0
% 240.86/47.44  | | | 
% 240.86/47.44  | | | REF_CLOSE: (9), (14), (18) are inconsistent by sub-proof #2205.
% 240.86/47.44  | | | 
% 240.86/47.44  | | Case 2:
% 240.86/47.44  | | | 
% 240.86/47.44  | | |   (19)  all_58_7 = e0 & op(e1, e2) = e0
% 240.86/47.44  | | | 
% 240.86/47.44  | | | ALPHA: (19) implies:
% 240.86/47.44  | | |   (20)  op(e1, e2) = e0
% 240.86/47.44  | | | 
% 240.86/47.44  | | | REF_CLOSE: (2), (4), (12), (14), (20) are inconsistent by sub-proof #2136.
% 240.86/47.44  | | | 
% 240.86/47.44  | | End of split
% 240.86/47.44  | | 
% 240.86/47.44  | Case 2:
% 240.86/47.44  | | 
% 240.86/47.44  | |   (21)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.86/47.44  | |           e0)
% 240.86/47.44  | | 
% 240.86/47.44  | | BETA: splitting (21) gives:
% 240.86/47.44  | | 
% 240.86/47.44  | | Case 1:
% 240.86/47.44  | | | 
% 240.86/47.44  | | |   (22)  all_58_8 = e0 & op(e1, e1) = e0
% 240.86/47.44  | | | 
% 240.86/47.44  | | | ALPHA: (22) implies:
% 240.86/47.44  | | |   (23)  op(e1, e1) = e0
% 240.86/47.44  | | | 
% 240.86/47.44  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (16), (23)
% 240.86/47.44  | | |            are inconsistent by sub-proof #1993.
% 240.86/47.44  | | | 
% 240.86/47.44  | | Case 2:
% 240.86/47.44  | | | 
% 240.86/47.44  | | |   (24)  all_58_11 = e0 & op(e1, e0) = e0
% 240.86/47.44  | | | 
% 240.86/47.44  | | | ALPHA: (24) implies:
% 240.86/47.44  | | |   (25)  op(e1, e0) = e0
% 240.86/47.44  | | | 
% 240.86/47.44  | | | REF_CLOSE: (3), (12), (13), (25) are inconsistent by sub-proof #478.
% 240.86/47.44  | | | 
% 240.86/47.44  | | End of split
% 240.86/47.44  | | 
% 240.86/47.44  | End of split
% 240.86/47.44  | 
% 240.86/47.44  End of proof
% 240.86/47.44  
% 240.86/47.44  Sub-proof #419 shows that the following formulas are inconsistent:
% 240.86/47.44  ----------------------------------------------------------------
% 240.86/47.44    (1)  e3 = e1
% 240.86/47.44    (2)  all_58_1 = e3
% 240.86/47.44    (3)   ~ (e3 = e1)
% 240.86/47.45    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.86/47.45         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.86/47.45    (5)  op(e3, e1) = all_52_8
% 240.86/47.45    (6)   ~ (e3 = e2)
% 240.86/47.45    (7)  op(e3, e0) = all_52_12
% 240.86/47.45    (8)  op(e3, e3) = e2
% 240.86/47.45    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.45    (10)   ~ (all_52_12 = e3)
% 240.86/47.45    (11)   ~ (all_52_8 = e3)
% 240.86/47.45  
% 240.86/47.45  Begin of proof
% 240.86/47.45  | 
% 240.86/47.45  | SIMP: (1) implies:
% 240.86/47.45  |   (12)  e3 = e1
% 240.86/47.45  | 
% 240.86/47.45  | COMBINE_EQS: (2), (12) imply:
% 240.86/47.45  |   (13)  all_58_1 = e1
% 240.86/47.45  | 
% 240.86/47.45  | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (13) are
% 240.86/47.45  |            inconsistent by sub-proof #1327.
% 240.86/47.45  | 
% 240.86/47.45  End of proof
% 240.86/47.45  
% 240.86/47.45  Sub-proof #420 shows that the following formulas are inconsistent:
% 240.86/47.45  ----------------------------------------------------------------
% 240.86/47.45    (1)   ~ (e3 = e0)
% 240.86/47.45    (2)  all_58_1 = e3
% 240.86/47.45    (3)   ~ (e2 = e0)
% 240.86/47.45    (4)  all_58_15 = e3
% 240.86/47.45    (5)   ~ (e3 = e1)
% 240.86/47.45    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.86/47.45         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.86/47.45    (7)  op(e3, e1) = all_52_8
% 240.86/47.45    (8)   ~ (e3 = e2)
% 240.86/47.45    (9)  op(e3, e0) = all_52_12
% 240.86/47.45    (10)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.86/47.45    (11)  op(e3, e3) = e2
% 240.86/47.45    (12)  op(e1, e1) = e3
% 240.86/47.45    (13)  all_58_7 = e1
% 240.86/47.45    (14)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 240.86/47.45          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 240.86/47.45    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.45    (16)  all_58_8 = e3
% 240.86/47.45    (17)   ~ (all_52_12 = e3)
% 240.86/47.45    (18)   ~ (e1 = e0)
% 240.86/47.45    (19)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.86/47.45          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 240.86/47.45    (20)   ~ (e2 = e1)
% 240.86/47.45    (21)   ~ (all_52_8 = e3)
% 240.86/47.45  
% 240.86/47.45  Begin of proof
% 240.86/47.45  | 
% 240.86/47.45  | BETA: splitting (10) gives:
% 240.86/47.45  | 
% 240.86/47.45  | Case 1:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (22)  all_58_11 = e1 & op(e1, e0) = e1
% 240.86/47.45  | | 
% 240.86/47.45  | | ALPHA: (22) implies:
% 240.86/47.45  | |   (23)  all_58_11 = e1
% 240.86/47.45  | |   (24)  op(e1, e0) = e1
% 240.86/47.45  | | 
% 240.86/47.45  | | REF_CLOSE: (1), (3), (8), (12), (13), (14), (15), (16), (18), (19), (20),
% 240.86/47.45  | |            (23), (24) are inconsistent by sub-proof #1419.
% 240.86/47.45  | | 
% 240.86/47.45  | Case 2:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (25)  all_58_15 = e1 & op(e0, e0) = e1
% 240.86/47.45  | | 
% 240.86/47.45  | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (15), (17), (21), (25)
% 240.86/47.45  | |            are inconsistent by sub-proof #424.
% 240.86/47.45  | | 
% 240.86/47.45  | End of split
% 240.86/47.45  | 
% 240.86/47.45  End of proof
% 240.86/47.45  
% 240.86/47.45  Sub-proof #421 shows that the following formulas are inconsistent:
% 240.86/47.45  ----------------------------------------------------------------
% 240.86/47.45    (1)  all_58_1 = e3
% 240.86/47.45    (2)   ~ (e3 = e1)
% 240.86/47.45    (3)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.86/47.45         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.86/47.45    (4)  op(e3, e1) = all_52_8
% 240.86/47.45    (5)   ~ (e3 = e2)
% 240.86/47.45    (6)  all_58_8 = e1 & op(e1, e1) = e1
% 240.86/47.45    (7)  op(e3, e0) = all_52_12
% 240.86/47.45    (8)  op(e3, e3) = e2
% 240.86/47.45    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.45    (10)  all_58_8 = e3
% 240.86/47.45    (11)   ~ (all_52_12 = e3)
% 240.86/47.45    (12)   ~ (all_52_8 = e3)
% 240.86/47.45  
% 240.86/47.45  Begin of proof
% 240.86/47.45  | 
% 240.86/47.45  | ALPHA: (6) implies:
% 240.86/47.45  |   (13)  all_58_8 = e1
% 240.86/47.45  | 
% 240.86/47.45  | COMBINE_EQS: (10), (13) imply:
% 240.86/47.45  |   (14)  e3 = e1
% 240.86/47.45  | 
% 240.86/47.45  | COMBINE_EQS: (1), (14) imply:
% 240.86/47.45  |   (15)  all_58_1 = e1
% 240.86/47.45  | 
% 240.86/47.45  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (11), (12), (15) are
% 240.86/47.45  |            inconsistent by sub-proof #1327.
% 240.86/47.45  | 
% 240.86/47.45  End of proof
% 240.86/47.45  
% 240.86/47.45  Sub-proof #422 shows that the following formulas are inconsistent:
% 240.86/47.45  ----------------------------------------------------------------
% 240.86/47.45    (1)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 240.86/47.45    (2)  op(e3, e1) = e0
% 240.86/47.45    (3)  op(e2, e1) = all_52_9
% 240.86/47.45    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.45    (5)   ~ (e1 = e0)
% 240.86/47.45    (6)   ~ (all_52_9 = e1)
% 240.86/47.45  
% 240.86/47.45  Begin of proof
% 240.86/47.45  | 
% 240.86/47.45  | BETA: splitting (1) gives:
% 240.86/47.45  | 
% 240.86/47.45  | Case 1:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (7)  all_58_4 = e1 & op(e3, e1) = e1
% 240.86/47.45  | | 
% 240.86/47.45  | | ALPHA: (7) implies:
% 240.86/47.45  | |   (8)  op(e3, e1) = e1
% 240.86/47.45  | | 
% 240.86/47.45  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2089.
% 240.86/47.45  | | 
% 240.86/47.45  | Case 2:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (9)  all_58_5 = e1 & op(e2, e1) = e1
% 240.86/47.45  | | 
% 240.86/47.45  | | ALPHA: (9) implies:
% 240.86/47.45  | |   (10)  op(e2, e1) = e1
% 240.86/47.45  | | 
% 240.86/47.45  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #2306.
% 240.86/47.45  | | 
% 240.86/47.45  | End of split
% 240.86/47.45  | 
% 240.86/47.45  End of proof
% 240.86/47.45  
% 240.86/47.45  Sub-proof #423 shows that the following formulas are inconsistent:
% 240.86/47.45  ----------------------------------------------------------------
% 240.86/47.45    (1)   ~ (e3 = e0)
% 240.86/47.45    (2)   ~ (e2 = e0)
% 240.86/47.45    (3)  op(e3, e3) = e2
% 240.86/47.45    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.45    (5)  op(e3, e2) = e3
% 240.86/47.45    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 240.86/47.45  
% 240.86/47.45  Begin of proof
% 240.86/47.45  | 
% 240.86/47.45  | BETA: splitting (6) gives:
% 240.86/47.45  | 
% 240.86/47.45  | Case 1:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 240.86/47.45  | | 
% 240.86/47.45  | | ALPHA: (7) implies:
% 240.86/47.45  | |   (8)  op(e3, e3) = e0
% 240.86/47.45  | | 
% 240.86/47.45  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2188.
% 240.86/47.45  | | 
% 240.86/47.45  | Case 2:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (9)  all_58_1 = e0 & op(e3, e2) = e0
% 240.86/47.45  | | 
% 240.86/47.45  | | ALPHA: (9) implies:
% 240.86/47.45  | |   (10)  op(e3, e2) = e0
% 240.86/47.45  | | 
% 240.86/47.45  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2099.
% 240.86/47.45  | | 
% 240.86/47.45  | End of split
% 240.86/47.45  | 
% 240.86/47.45  End of proof
% 240.86/47.45  
% 240.86/47.45  Sub-proof #424 shows that the following formulas are inconsistent:
% 240.86/47.45  ----------------------------------------------------------------
% 240.86/47.45    (1)  all_58_1 = e3
% 240.86/47.45    (2)  all_58_15 = e3
% 240.86/47.45    (3)   ~ (e3 = e1)
% 240.86/47.45    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.86/47.45         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.86/47.45    (5)  op(e3, e1) = all_52_8
% 240.86/47.45    (6)   ~ (e3 = e2)
% 240.86/47.45    (7)  op(e3, e0) = all_52_12
% 240.86/47.45    (8)  op(e3, e3) = e2
% 240.86/47.45    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.45    (10)   ~ (all_52_12 = e3)
% 240.86/47.45    (11)  all_58_15 = e1 & op(e0, e0) = e1
% 240.86/47.45    (12)   ~ (all_52_8 = e3)
% 240.86/47.45  
% 240.86/47.45  Begin of proof
% 240.86/47.45  | 
% 240.86/47.45  | ALPHA: (11) implies:
% 240.86/47.45  |   (13)  all_58_15 = e1
% 240.86/47.45  | 
% 240.86/47.45  | COMBINE_EQS: (2), (13) imply:
% 240.86/47.45  |   (14)  e3 = e1
% 240.86/47.45  | 
% 240.86/47.45  | COMBINE_EQS: (1), (14) imply:
% 240.86/47.45  |   (15)  all_58_1 = e1
% 240.86/47.45  | 
% 240.86/47.45  | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12), (15) are
% 240.86/47.45  |            inconsistent by sub-proof #1327.
% 240.86/47.45  | 
% 240.86/47.45  End of proof
% 240.86/47.45  
% 240.86/47.45  Sub-proof #425 shows that the following formulas are inconsistent:
% 240.86/47.45  ----------------------------------------------------------------
% 240.86/47.45    (1)  op(e0, e3) = all_52_3
% 240.86/47.45    (2)   ~ (e3 = e1)
% 240.86/47.45    (3)  op(e3, e1) = e0
% 240.86/47.45    (4)   ~ (e3 = e2)
% 240.86/47.45    (5)  op(e1, e3) = e1
% 240.86/47.45    (6)   ~ (all_52_3 = e3)
% 240.86/47.45    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.86/47.45           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.86/47.45             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.45           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.86/47.45             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.45           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.45           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.86/47.45           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.45           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.86/47.45           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.45           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.86/47.45             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.45           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.45           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.86/47.45    (8)  all_56_1 = e2
% 240.86/47.45    (9)  all_56_31 = e3
% 240.86/47.45    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.45    (11)   ~ (e1 = e0)
% 240.86/47.45    (12)  op(e3, e2) = e3
% 240.86/47.45  
% 240.86/47.45  Begin of proof
% 240.86/47.45  | 
% 240.86/47.45  | BETA: splitting (7) gives:
% 240.86/47.45  | 
% 240.86/47.45  | Case 1:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.86/47.45  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 240.86/47.45  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 240.86/47.45  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.45  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 240.86/47.45  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 240.86/47.45  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.86/47.45  | |           op(e1, e3) = e3)
% 240.86/47.45  | | 
% 240.86/47.45  | | REF_CLOSE: (2), (4), (5), (8), (10), (12), (13) are inconsistent by
% 240.86/47.45  | |            sub-proof #426.
% 240.86/47.45  | | 
% 240.86/47.45  | Case 2:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (14)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.86/47.45  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 240.86/47.45  | |           e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 240.86/47.45  | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.45  | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7
% 240.86/47.45  | |           = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &
% 240.86/47.45  | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 240.86/47.45  | |           op(e0, e3) = e0)
% 240.86/47.45  | | 
% 240.86/47.45  | | BETA: splitting (14) gives:
% 240.86/47.45  | | 
% 240.86/47.45  | | Case 1:
% 240.86/47.45  | | | 
% 240.86/47.45  | | |   (15)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.45  | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.45  | | |         op(e3, e1) = e1 & op(e1, e3) = e1
% 240.86/47.45  | | | 
% 240.86/47.45  | | | ALPHA: (15) implies:
% 240.86/47.45  | | |   (16)  op(e3, e1) = e1
% 240.86/47.45  | | | 
% 240.86/47.45  | | | REF_CLOSE: (3), (10), (11), (16) are inconsistent by sub-proof #2089.
% 240.86/47.45  | | | 
% 240.86/47.45  | | Case 2:
% 240.86/47.45  | | | 
% 240.86/47.45  | | |   (17)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.45  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.86/47.45  | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 240.86/47.45  | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 240.86/47.45  | | |             = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 240.86/47.45  | | |           e0)
% 240.86/47.45  | | | 
% 240.86/47.45  | | | REF_CLOSE: (1), (6), (9), (10), (17) are inconsistent by sub-proof #1412.
% 240.86/47.45  | | | 
% 240.86/47.45  | | End of split
% 240.86/47.45  | | 
% 240.86/47.45  | End of split
% 240.86/47.45  | 
% 240.86/47.45  End of proof
% 240.86/47.45  
% 240.86/47.45  Sub-proof #426 shows that the following formulas are inconsistent:
% 240.86/47.45  ----------------------------------------------------------------
% 240.86/47.45    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.86/47.45           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.86/47.45             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.45           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.86/47.45             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.45           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.45           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.45    (2)   ~ (e3 = e1)
% 240.86/47.45    (3)   ~ (e3 = e2)
% 240.86/47.45    (4)  op(e1, e3) = e1
% 240.86/47.45    (5)  all_56_1 = e2
% 240.86/47.45    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.45    (7)  op(e3, e2) = e3
% 240.86/47.45  
% 240.86/47.45  Begin of proof
% 240.86/47.45  | 
% 240.86/47.45  | BETA: splitting (1) gives:
% 240.86/47.45  | 
% 240.86/47.45  | Case 1:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.45  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.45  | |        op(e2, e3) = e3
% 240.86/47.45  | | 
% 240.86/47.45  | | ALPHA: (8) implies:
% 240.86/47.45  | |   (9)   ~ (all_56_1 = e2)
% 240.86/47.45  | | 
% 240.86/47.45  | | REDUCE: (5), (9) imply:
% 240.86/47.45  | |   (10)  $false
% 240.86/47.45  | | 
% 240.86/47.45  | | CLOSE: (10) is inconsistent.
% 240.86/47.45  | | 
% 240.86/47.45  | Case 2:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (11)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.86/47.45  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.86/47.45  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.45  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.45  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.45  | | 
% 240.86/47.45  | | REF_CLOSE: (2), (3), (4), (6), (7), (11) are inconsistent by sub-proof #479.
% 240.86/47.45  | | 
% 240.86/47.45  | End of split
% 240.86/47.45  | 
% 240.86/47.45  End of proof
% 240.86/47.45  
% 240.86/47.45  Sub-proof #427 shows that the following formulas are inconsistent:
% 240.86/47.45  ----------------------------------------------------------------
% 240.86/47.45    (1)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 240.86/47.45    (2)   ~ (all_8_2 = e0)
% 240.86/47.45    (3)   ~ (e3 = e0)
% 240.86/47.45    (4)  op(e2, e2) = all_8_2
% 240.86/47.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.45    (6)  all_58_2 = e3
% 240.86/47.45  
% 240.86/47.45  Begin of proof
% 240.86/47.45  | 
% 240.86/47.45  | BETA: splitting (1) gives:
% 240.86/47.45  | 
% 240.86/47.45  | Case 1:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (7)  all_58_2 = e0 & op(e2, e3) = e0
% 240.86/47.45  | | 
% 240.86/47.45  | | ALPHA: (7) implies:
% 240.86/47.45  | |   (8)  all_58_2 = e0
% 240.86/47.45  | | 
% 240.86/47.45  | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #2124.
% 240.86/47.45  | | 
% 240.86/47.45  | Case 2:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (9)  all_58_3 = e0 & op(e2, e2) = e0
% 240.86/47.45  | | 
% 240.86/47.45  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #1992.
% 240.86/47.45  | | 
% 240.86/47.45  | End of split
% 240.86/47.45  | 
% 240.86/47.45  End of proof
% 240.86/47.45  
% 240.86/47.45  Sub-proof #428 shows that the following formulas are inconsistent:
% 240.86/47.45  ----------------------------------------------------------------
% 240.86/47.45    (1)  op(e2, e3) = e3
% 240.86/47.45    (2)   ~ (e3 = e2)
% 240.86/47.45    (3)  op(e2, e2) = e1
% 240.86/47.45    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 240.86/47.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.45    (6)   ~ (e2 = e1)
% 240.86/47.45  
% 240.86/47.45  Begin of proof
% 240.86/47.45  | 
% 240.86/47.45  | BETA: splitting (4) gives:
% 240.86/47.45  | 
% 240.86/47.45  | Case 1:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (7)  all_58_2 = e2 & op(e2, e3) = e2
% 240.86/47.45  | | 
% 240.86/47.45  | | ALPHA: (7) implies:
% 240.86/47.45  | |   (8)  op(e2, e3) = e2
% 240.86/47.45  | | 
% 240.86/47.45  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1897.
% 240.86/47.45  | | 
% 240.86/47.45  | Case 2:
% 240.86/47.45  | | 
% 240.86/47.45  | |   (9)  all_58_3 = e2 & op(e2, e2) = e2
% 240.86/47.46  | | 
% 240.86/47.46  | | ALPHA: (9) implies:
% 240.86/47.46  | |   (10)  op(e2, e2) = e2
% 240.86/47.46  | | 
% 240.86/47.46  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #2235.
% 240.86/47.46  | | 
% 240.86/47.46  | End of split
% 240.86/47.46  | 
% 240.86/47.46  End of proof
% 240.86/47.46  
% 240.86/47.46  Sub-proof #429 shows that the following formulas are inconsistent:
% 240.86/47.46  ----------------------------------------------------------------
% 240.86/47.46    (1)   ~ (all_8_2 = e1)
% 240.86/47.46    (2)   ~ (all_52_13 = all_8_2)
% 240.86/47.46    (3)   ~ (all_8_2 = e0)
% 240.86/47.46    (4)  op(e0, e1) = all_52_11
% 240.86/47.46    (5)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.86/47.46           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.86/47.46             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.46           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.86/47.46             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.46           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.46           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.86/47.46           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.46           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.86/47.46           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.46           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.86/47.46             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.46           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.46           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 240.86/47.46           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.46           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.86/47.46           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.46           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.86/47.46             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.86/47.46           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.46           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 240.86/47.46           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.46           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.86/47.46           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.46           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.86/47.46             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.46           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.46           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.46    (6)   ~ (all_52_7 = all_52_11)
% 240.86/47.46    (7)  op(e1, e0) = all_52_14
% 240.86/47.46    (8)  op(e0, e3) = all_52_3
% 240.86/47.46    (9)  op(e2, e1) = all_52_9
% 240.86/47.46    (10)  op(e3, e0) = all_52_12
% 240.86/47.46    (11)   ~ (all_52_3 = e2)
% 240.86/47.46    (12)   ~ (all_52_3 = e3)
% 240.86/47.46    (13)  all_54_5 = all_8_2
% 240.86/47.46    (14)   ~ (all_52_14 = e3)
% 240.86/47.46    (15)   ~ (all_52_12 = e2)
% 240.86/47.46    (16)   ~ (all_52_2 = e3)
% 240.86/47.46    (17)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 240.86/47.46    (18)   ~ (all_52_7 = all_8_2)
% 240.86/47.46    (19)  op(e0, e2) = all_52_7
% 240.86/47.46    (20)  all_56_31 = e3
% 240.86/47.46    (21)  op(e0, e0) = e3
% 240.86/47.46    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.46    (23)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.86/47.46          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.86/47.46    (24)  op(e1, e3) = all_52_2
% 240.86/47.46    (25)   ~ (all_8_2 = e3)
% 240.86/47.46    (26)  all_56_11 = all_8_2
% 240.86/47.46    (27)  op(e3, e2) = e3
% 240.86/47.46    (28)  op(e2, e0) = all_52_13
% 240.86/47.46    (29)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.86/47.46          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 240.86/47.46            e2)
% 240.86/47.46    (30)   ~ (all_52_9 = all_52_11)
% 240.86/47.46  
% 240.86/47.46  Begin of proof
% 240.86/47.46  | 
% 240.86/47.46  | BETA: splitting (17) gives:
% 240.86/47.46  | 
% 240.86/47.46  | Case 1:
% 240.86/47.46  | | 
% 240.86/47.46  | |   (31)  all_54_5 = e3
% 240.86/47.46  | | 
% 240.86/47.46  | | REF_CLOSE: (13), (25), (31) are inconsistent by sub-proof #1907.
% 240.86/47.46  | | 
% 240.86/47.46  | Case 2:
% 240.86/47.46  | | 
% 240.86/47.46  | |   (32)   ~ (all_54_5 = e3)
% 240.86/47.46  | |   (33)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 240.86/47.46  | | 
% 240.86/47.46  | | BETA: splitting (33) gives:
% 240.86/47.46  | | 
% 240.86/47.46  | | Case 1:
% 240.86/47.46  | | | 
% 240.86/47.46  | | |   (34)  all_54_5 = e2
% 240.86/47.46  | | | 
% 240.86/47.46  | | | COMBINE_EQS: (13), (34) imply:
% 240.86/47.46  | | |   (35)  all_8_2 = e2
% 240.86/47.46  | | | 
% 240.86/47.46  | | | SIMP: (35) implies:
% 240.86/47.46  | | |   (36)  all_8_2 = e2
% 240.86/47.46  | | | 
% 240.86/47.46  | | | COMBINE_EQS: (26), (36) imply:
% 240.86/47.46  | | |   (37)  all_56_11 = e2
% 240.86/47.46  | | | 
% 240.86/47.46  | | | REDUCE: (18), (36) imply:
% 240.86/47.46  | | |   (38)   ~ (all_52_7 = e2)
% 240.86/47.46  | | | 
% 240.86/47.46  | | | REDUCE: (2), (36) imply:
% 240.86/47.46  | | |   (39)   ~ (all_52_13 = e2)
% 240.86/47.46  | | | 
% 240.86/47.46  | | | REDUCE: (25), (36) imply:
% 240.86/47.46  | | |   (40)   ~ (e3 = e2)
% 240.86/47.46  | | | 
% 240.86/47.46  | | | SIMP: (40) implies:
% 240.86/47.46  | | |   (41)   ~ (e3 = e2)
% 240.86/47.46  | | | 
% 240.86/47.46  | | | REDUCE: (1), (36) imply:
% 240.86/47.46  | | |   (42)   ~ (e2 = e1)
% 240.86/47.46  | | | 
% 240.86/47.46  | | | REDUCE: (3), (36) imply:
% 240.86/47.46  | | |   (43)   ~ (e2 = e0)
% 240.86/47.46  | | | 
% 240.86/47.46  | | | BETA: splitting (23) gives:
% 240.86/47.46  | | | 
% 240.86/47.46  | | | Case 1:
% 240.86/47.46  | | | | 
% 240.86/47.46  | | | |   (44)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 240.86/47.46  | | | |           = e2)
% 240.86/47.46  | | | | 
% 240.86/47.46  | | | | REF_CLOSE: (10), (15), (22), (28), (39), (44) are inconsistent by
% 240.86/47.46  | | | |            sub-proof #2316.
% 240.86/47.46  | | | | 
% 240.86/47.46  | | | Case 2:
% 240.86/47.46  | | | | 
% 240.86/47.46  | | | |   (45)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 240.86/47.46  | | | |             e0) = e2)
% 240.86/47.46  | | | | 
% 240.86/47.46  | | | | BETA: splitting (45) gives:
% 240.86/47.46  | | | | 
% 240.86/47.46  | | | | Case 1:
% 240.86/47.46  | | | | | 
% 240.86/47.46  | | | | |   (46)  all_58_11 = e2 & op(e1, e0) = e2
% 240.86/47.46  | | | | | 
% 240.86/47.46  | | | | | ALPHA: (46) implies:
% 240.86/47.46  | | | | |   (47)  op(e1, e0) = e2
% 240.86/47.46  | | | | | 
% 240.86/47.46  | | | | | BETA: splitting (29) gives:
% 240.86/47.46  | | | | | 
% 240.86/47.46  | | | | | Case 1:
% 240.86/47.46  | | | | | | 
% 240.86/47.46  | | | | | |   (48)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 240.86/47.46  | | | | | |           op(e0, e2) = e2)
% 240.86/47.46  | | | | | | 
% 240.86/47.46  | | | | | | REF_CLOSE: (8), (11), (19), (22), (38), (48) are inconsistent by
% 240.86/47.46  | | | | | |            sub-proof #2314.
% 240.86/47.46  | | | | | | 
% 240.86/47.46  | | | | | Case 2:
% 240.86/47.46  | | | | | | 
% 240.86/47.46  | | | | | |   (49)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 240.86/47.46  | | | | | |           op(e0, e0) = e2)
% 240.86/47.46  | | | | | | 
% 240.86/47.46  | | | | | | BETA: splitting (49) gives:
% 240.86/47.46  | | | | | | 
% 240.86/47.46  | | | | | | Case 1:
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | |   (50)  all_58_14 = e2 & op(e0, e1) = e2
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | | ALPHA: (50) implies:
% 240.86/47.46  | | | | | | |   (51)  op(e0, e1) = e2
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | | GROUND_INST: instantiating (22) with all_52_11, e2, e1, e0,
% 240.86/47.46  | | | | | | |              simplifying with (4), (51) gives:
% 240.86/47.46  | | | | | | |   (52)  all_52_11 = e2
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | | GROUND_INST: instantiating (22) with all_52_14, e2, e0, e1,
% 240.86/47.46  | | | | | | |              simplifying with (7), (47) gives:
% 240.86/47.46  | | | | | | |   (53)  all_52_14 = e2
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | | REDUCE: (30), (52) imply:
% 240.86/47.46  | | | | | | |   (54)   ~ (all_52_9 = e2)
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | | BETA: splitting (5) gives:
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | | Case 1:
% 240.86/47.46  | | | | | | | | 
% 240.86/47.46  | | | | | | | |   (55)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 240.86/47.46  | | | | | | | |             = e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 240.86/47.46  | | | | | | | |         (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 240.86/47.46  | | | | | | | |             = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 240.86/47.46  | | | | | | | |         (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) & 
% 240.86/47.46  | | | | | | | |           ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.46  | | | | | | | |         | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &
% 240.86/47.46  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1)
% 240.86/47.46  | | | | | | | |         | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &
% 240.86/47.46  | | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3)
% 240.86/47.46  | | | | | | | |         | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &
% 240.86/47.46  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.86/47.46  | | | | | | | | 
% 240.86/47.46  | | | | | | | | BETA: splitting (55) gives:
% 240.86/47.46  | | | | | | | | 
% 240.86/47.46  | | | | | | | | Case 1:
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | |   (56)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 240.86/47.46  | | | | | | | | |           ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 240.86/47.46  | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 240.86/47.46  | | | | | | | | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 240.86/47.46  | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3)
% 240.86/47.46  | | | | | | | | |           = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 240.86/47.46  | | | | | | | | |           = e3 & op(e1, e3) = e3)
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | REF_CLOSE: (16), (22), (24), (27), (37), (41), (56) are
% 240.86/47.46  | | | | | | | | |            inconsistent by sub-proof #430.
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | Case 2:
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | |   (57)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &
% 240.86/47.46  | | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.86/47.46  | | | | | | | | |           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1
% 240.86/47.46  | | | | | | | | |             = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.86/47.46  | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 240.86/47.46  | | | | | | | | |           = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 240.86/47.46  | | | | | | | | |           = e0 & op(e0, e3) = e0)
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | REF_CLOSE: (8), (12), (20), (22), (57) are inconsistent by
% 240.86/47.46  | | | | | | | | |            sub-proof #1389.
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | End of split
% 240.86/47.46  | | | | | | | | 
% 240.86/47.46  | | | | | | | Case 2:
% 240.86/47.46  | | | | | | | | 
% 240.86/47.46  | | | | | | | |   (58)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) & 
% 240.86/47.46  | | | | | | | |           ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2)
% 240.86/47.46  | | | | | | | |         | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2)
% 240.86/47.46  | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1)
% 240.86/47.46  | | | | | | | |         | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0)
% 240.86/47.46  | | | | | | | |           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.86/47.46  | | | | | | | |         | (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2)
% 240.86/47.46  | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0)
% 240.86/47.46  | | | | | | | |         | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0)
% 240.86/47.46  | | | | | | | |           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1)
% 240.86/47.46  | | | | | | | |         | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1)
% 240.86/47.46  | | | | | | | |           &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.46  | | | | | | | |           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.46  | | | | | | | | 
% 240.86/47.46  | | | | | | | | BETA: splitting (58) gives:
% 240.86/47.46  | | | | | | | | 
% 240.86/47.46  | | | | | | | | Case 1:
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | |   (59)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 240.86/47.46  | | | | | | | | |           &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.86/47.46  | | | | | | | | |           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1)
% 240.86/47.46  | | | | | | | | |           = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 240.86/47.46  | | | | | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.86/47.46  | | | | | | | | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.86/47.46  | | | | | | | | |           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | REF_CLOSE: (9), (19), (22), (37), (38), (54), (59) are
% 240.86/47.46  | | | | | | | | |            inconsistent by sub-proof #2325.
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | Case 2:
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | |   (60)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2)
% 240.86/47.46  | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.86/47.46  | | | | | | | | |           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 240.86/47.46  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0)
% 240.86/47.46  | | | | | | | | |           = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 240.86/47.46  | | | | | | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 240.86/47.46  | | | | | | | | |             = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 240.86/47.46  | | | | | | | | |           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | BETA: splitting (60) gives:
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | Case 1:
% 240.86/47.46  | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | |   (61)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2)
% 240.86/47.46  | | | | | | | | | |         &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.86/47.46  | | | | | | | | | |         (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 240.86/47.46  | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | ALPHA: (61) implies:
% 240.86/47.46  | | | | | | | | | |   (62)   ~ (all_56_11 = e2)
% 240.86/47.46  | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | REDUCE: (37), (62) imply:
% 240.86/47.46  | | | | | | | | | |   (63)  $false
% 240.86/47.46  | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | CLOSE: (63) is inconsistent.
% 240.86/47.46  | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | Case 2:
% 240.86/47.46  | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | |   (64)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.86/47.46  | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.86/47.46  | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 240.86/47.46  | | | | | | | | | |             e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 & 
% 240.86/47.46  | | | | | | | | | |           ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.46  | | | | | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.86/47.46  | | | | | | | | | |             e0) = e0 & op(e0, e1) = e0)
% 240.86/47.46  | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | BETA: splitting (64) gives:
% 240.86/47.46  | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | Case 1:
% 240.86/47.46  | | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | |   (65)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.86/47.46  | | | | | | | | | | |           e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.86/47.46  | | | | | | | | | | |         &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 240.86/47.46  | | | | | | | | | | |           e1) = e1
% 240.86/47.46  | | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | | ALPHA: (65) implies:
% 240.86/47.46  | | | | | | | | | | |   (66)  op(e1, e0) = e1
% 240.86/47.46  | | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | | REF_CLOSE: (22), (42), (47), (66) are inconsistent by
% 240.86/47.46  | | | | | | | | | | |            sub-proof #2019.
% 240.86/47.46  | | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | Case 2:
% 240.86/47.46  | | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | |   (67)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 240.86/47.46  | | | | | | | | | | |           e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.86/47.46  | | | | | | | | | | |         &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 240.86/47.46  | | | | | | | | | | |           e1) = e0
% 240.86/47.46  | | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | | ALPHA: (67) implies:
% 240.86/47.46  | | | | | | | | | | |   (68)  op(e1, e0) = e0
% 240.86/47.46  | | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | | GROUND_INST: instantiating (22) with e2, e0, e0, e1,
% 240.86/47.46  | | | | | | | | | | |              simplifying with (47), (68) gives:
% 240.86/47.46  | | | | | | | | | | |   (69)  e2 = e0
% 240.86/47.46  | | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | | REDUCE: (43), (69) imply:
% 240.86/47.46  | | | | | | | | | | |   (70)  $false
% 240.86/47.46  | | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | | CLOSE: (70) is inconsistent.
% 240.86/47.46  | | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | | End of split
% 240.86/47.46  | | | | | | | | | | 
% 240.86/47.46  | | | | | | | | | End of split
% 240.86/47.46  | | | | | | | | | 
% 240.86/47.46  | | | | | | | | End of split
% 240.86/47.46  | | | | | | | | 
% 240.86/47.46  | | | | | | | End of split
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | Case 2:
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | |   (71)  all_58_15 = e2 & op(e0, e0) = e2
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | | ALPHA: (71) implies:
% 240.86/47.46  | | | | | | |   (72)  op(e0, e0) = e2
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | | REF_CLOSE: (21), (22), (41), (72) are inconsistent by sub-proof
% 240.86/47.46  | | | | | | |            #1388.
% 240.86/47.46  | | | | | | | 
% 240.86/47.46  | | | | | | End of split
% 240.86/47.46  | | | | | | 
% 240.86/47.46  | | | | | End of split
% 240.86/47.46  | | | | | 
% 240.86/47.46  | | | | Case 2:
% 240.86/47.46  | | | | | 
% 240.86/47.46  | | | | |   (73)  all_58_15 = e2 & op(e0, e0) = e2
% 240.86/47.46  | | | | | 
% 240.86/47.46  | | | | | ALPHA: (73) implies:
% 240.86/47.46  | | | | |   (74)  op(e0, e0) = e2
% 240.86/47.46  | | | | | 
% 240.86/47.46  | | | | | REF_CLOSE: (21), (22), (41), (74) are inconsistent by sub-proof #1388.
% 240.86/47.46  | | | | | 
% 240.86/47.46  | | | | End of split
% 240.86/47.46  | | | | 
% 240.86/47.46  | | | End of split
% 240.86/47.46  | | | 
% 240.86/47.46  | | Case 2:
% 240.86/47.46  | | | 
% 240.86/47.46  | | |   (75)  all_54_5 = e1 | all_54_5 = e0
% 240.86/47.46  | | | 
% 240.86/47.46  | | | REF_CLOSE: (1), (3), (13), (75) are inconsistent by sub-proof #2300.
% 240.86/47.46  | | | 
% 240.86/47.46  | | End of split
% 240.86/47.46  | | 
% 240.86/47.46  | End of split
% 240.86/47.46  | 
% 240.86/47.46  End of proof
% 240.86/47.46  
% 240.86/47.46  Sub-proof #430 shows that the following formulas are inconsistent:
% 240.86/47.46  ----------------------------------------------------------------
% 240.86/47.46    (1)  all_56_11 = e2
% 240.86/47.46    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.86/47.46           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.86/47.46             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.46           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.86/47.46             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.46           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.46           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.46    (3)   ~ (e3 = e2)
% 240.86/47.46    (4)   ~ (all_52_2 = e3)
% 240.86/47.46    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.46    (6)  op(e1, e3) = all_52_2
% 240.86/47.46    (7)  op(e3, e2) = e3
% 240.86/47.46  
% 240.86/47.46  Begin of proof
% 240.86/47.46  | 
% 240.86/47.46  | BETA: splitting (2) gives:
% 240.86/47.46  | 
% 240.86/47.46  | Case 1:
% 240.86/47.46  | | 
% 240.86/47.47  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.47  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.47  | |        op(e2, e3) = e3
% 240.86/47.47  | | 
% 240.86/47.47  | | ALPHA: (8) implies:
% 240.86/47.47  | |   (9)   ~ (all_56_11 = e2)
% 240.86/47.47  | | 
% 240.86/47.47  | | REDUCE: (1), (9) imply:
% 240.86/47.47  | |   (10)  $false
% 240.86/47.47  | | 
% 240.86/47.47  | | CLOSE: (10) is inconsistent.
% 240.86/47.47  | | 
% 240.86/47.47  | Case 2:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (11)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.86/47.47  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.86/47.47  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.47  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.47  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.47  | | 
% 240.86/47.47  | | REF_CLOSE: (3), (4), (5), (6), (7), (11) are inconsistent by sub-proof
% 240.86/47.47  | |            #1685.
% 240.86/47.47  | | 
% 240.86/47.47  | End of split
% 240.86/47.47  | 
% 240.86/47.47  End of proof
% 240.86/47.47  
% 240.86/47.47  Sub-proof #431 shows that the following formulas are inconsistent:
% 240.86/47.47  ----------------------------------------------------------------
% 240.86/47.47    (1)   ~ (all_52_3 = e0)
% 240.86/47.47    (2)   ~ (e3 = e0)
% 240.86/47.47    (3)   ~ (e2 = e0)
% 240.86/47.47    (4)  op(e0, e3) = all_52_3
% 240.86/47.47    (5)  op(e0, e2) = e3
% 240.86/47.47    (6)  op(e2, e1) = all_52_9
% 240.86/47.47    (7)   ~ (e3 = e2)
% 240.86/47.47    (8)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.86/47.47         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.86/47.47    (9)  all_58_4 = e1
% 240.86/47.47    (10)  op(e1, e1) = e3
% 240.86/47.47    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.47    (12)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.86/47.47          | (all_58_14 = e0 & op(e0, e1) = e0)
% 240.86/47.47    (13)   ~ (e2 = e1)
% 240.86/47.47    (14)   ~ (all_52_9 = e2)
% 240.86/47.47  
% 240.86/47.47  Begin of proof
% 240.86/47.47  | 
% 240.86/47.47  | BETA: splitting (12) gives:
% 240.86/47.47  | 
% 240.86/47.47  | Case 1:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (15)  all_58_12 = e0 & op(e0, e3) = e0
% 240.86/47.47  | | 
% 240.86/47.47  | | ALPHA: (15) implies:
% 240.86/47.47  | |   (16)  op(e0, e3) = e0
% 240.86/47.47  | | 
% 240.86/47.47  | | REF_CLOSE: (1), (4), (11), (16) are inconsistent by sub-proof #2331.
% 240.86/47.47  | | 
% 240.86/47.47  | Case 2:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (17)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 240.86/47.47  | |           e0)
% 240.86/47.47  | | 
% 240.86/47.47  | | BETA: splitting (17) gives:
% 240.86/47.47  | | 
% 240.86/47.47  | | Case 1:
% 240.86/47.47  | | | 
% 240.86/47.47  | | |   (18)  all_58_13 = e0 & op(e0, e2) = e0
% 240.86/47.47  | | | 
% 240.86/47.47  | | | ALPHA: (18) implies:
% 240.86/47.47  | | |   (19)  op(e0, e2) = e0
% 240.86/47.47  | | | 
% 240.86/47.47  | | | REF_CLOSE: (2), (5), (11), (19) are inconsistent by sub-proof #1961.
% 240.86/47.47  | | | 
% 240.86/47.47  | | Case 2:
% 240.86/47.47  | | | 
% 240.86/47.47  | | |   (20)  all_58_14 = e0 & op(e0, e1) = e0
% 240.86/47.47  | | | 
% 240.86/47.47  | | | ALPHA: (20) implies:
% 240.86/47.47  | | |   (21)  op(e0, e1) = e0
% 240.86/47.47  | | | 
% 240.86/47.47  | | | BETA: splitting (8) gives:
% 240.86/47.47  | | | 
% 240.86/47.47  | | | Case 1:
% 240.86/47.47  | | | | 
% 240.86/47.47  | | | |   (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 240.86/47.47  | | | |           = e2)
% 240.86/47.47  | | | | 
% 240.86/47.47  | | | | REF_CLOSE: (6), (9), (11), (13), (14), (22) are inconsistent by
% 240.86/47.47  | | | |            sub-proof #464.
% 240.86/47.47  | | | | 
% 240.86/47.47  | | | Case 2:
% 240.86/47.47  | | | | 
% 240.86/47.47  | | | |   (23)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 240.86/47.47  | | | |           = e2)
% 240.86/47.47  | | | | 
% 240.86/47.47  | | | | REF_CLOSE: (3), (7), (10), (11), (21), (23) are inconsistent by
% 240.86/47.47  | | | |            sub-proof #433.
% 240.86/47.47  | | | | 
% 240.86/47.47  | | | End of split
% 240.86/47.47  | | | 
% 240.86/47.47  | | End of split
% 240.86/47.47  | | 
% 240.86/47.47  | End of split
% 240.86/47.47  | 
% 240.86/47.47  End of proof
% 240.86/47.47  
% 240.86/47.47  Sub-proof #432 shows that the following formulas are inconsistent:
% 240.86/47.47  ----------------------------------------------------------------
% 240.86/47.47    (1)  op(e0, e0) = e1
% 240.86/47.47    (2)   ~ (e3 = e0)
% 240.86/47.47    (3)   ~ (e2 = e0)
% 240.86/47.47    (4)   ~ (e3 = e1)
% 240.86/47.47    (5)  all_58_2 = e1 & op(e2, e3) = e1
% 240.86/47.47    (6)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.86/47.47             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 240.86/47.47               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.86/47.47               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.86/47.47    (7)  op(e2, e0) = e2
% 240.86/47.47    (8)  all_58_15 = e1
% 240.86/47.47    (9)  all_58_9 = e3
% 240.86/47.47    (10)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.86/47.47          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.86/47.47    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.47    (12)   ~ (e1 = e0)
% 240.86/47.47    (13)  all_58_2 = e3
% 240.86/47.47    (14)   ~ (all_52_13 = e3)
% 240.86/47.47    (15)  op(e2, e0) = all_52_13
% 240.86/47.47  
% 240.86/47.47  Begin of proof
% 240.86/47.47  | 
% 240.86/47.47  | ALPHA: (5) implies:
% 240.86/47.47  |   (16)  all_58_2 = e1
% 240.86/47.47  | 
% 240.86/47.47  | COMBINE_EQS: (13), (16) imply:
% 240.86/47.47  |   (17)  e3 = e1
% 240.86/47.47  | 
% 240.86/47.47  | COMBINE_EQS: (9), (17) imply:
% 240.86/47.47  |   (18)  all_58_9 = e1
% 240.86/47.47  | 
% 240.86/47.47  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (14), (15),
% 240.86/47.47  |            (18) are inconsistent by sub-proof #971.
% 240.86/47.47  | 
% 240.86/47.47  End of proof
% 240.86/47.47  
% 240.86/47.47  Sub-proof #433 shows that the following formulas are inconsistent:
% 240.86/47.47  ----------------------------------------------------------------
% 240.86/47.47    (1)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.86/47.47    (2)   ~ (e2 = e0)
% 240.86/47.47    (3)   ~ (e3 = e2)
% 240.86/47.47    (4)  op(e0, e1) = e0
% 240.86/47.47    (5)  op(e1, e1) = e3
% 240.86/47.47    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.47  
% 240.86/47.47  Begin of proof
% 240.86/47.47  | 
% 240.86/47.47  | BETA: splitting (1) gives:
% 240.86/47.47  | 
% 240.86/47.47  | Case 1:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (7)  all_58_8 = e2 & op(e1, e1) = e2
% 240.86/47.47  | | 
% 240.86/47.47  | | ALPHA: (7) implies:
% 240.86/47.47  | |   (8)  op(e1, e1) = e2
% 240.86/47.47  | | 
% 240.86/47.47  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2206.
% 240.86/47.47  | | 
% 240.86/47.47  | Case 2:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (9)  all_58_14 = e2 & op(e0, e1) = e2
% 240.86/47.47  | | 
% 240.86/47.47  | | ALPHA: (9) implies:
% 240.86/47.47  | |   (10)  op(e0, e1) = e2
% 240.86/47.47  | | 
% 240.86/47.47  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #458.
% 240.86/47.47  | | 
% 240.86/47.47  | End of split
% 240.86/47.47  | 
% 240.86/47.47  End of proof
% 240.86/47.47  
% 240.86/47.47  Sub-proof #434 shows that the following formulas are inconsistent:
% 240.86/47.47  ----------------------------------------------------------------
% 240.86/47.47    (1)   ~ (all_52_8 = all_52_9)
% 240.86/47.47    (2)  op(e2, e1) = e1
% 240.86/47.47    (3)   ~ (all_52_8 = e0)
% 240.86/47.47    (4)  all_54_2 = all_52_8
% 240.86/47.47    (5)  op(e2, e1) = all_52_9
% 240.86/47.47    (6)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 240.86/47.47    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.47    (8)   ~ (all_52_8 = e2)
% 240.86/47.47  
% 240.86/47.47  Begin of proof
% 240.86/47.47  | 
% 240.86/47.47  | BETA: splitting (6) gives:
% 240.86/47.47  | 
% 240.86/47.47  | Case 1:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (9)  all_54_2 = e2
% 240.86/47.47  | | 
% 240.86/47.47  | | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #1986.
% 240.86/47.47  | | 
% 240.86/47.47  | Case 2:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (10)  all_54_2 = e1 | all_54_2 = e0
% 240.86/47.47  | | 
% 240.86/47.47  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (10) are inconsistent by sub-proof
% 240.86/47.47  | |            #435.
% 240.86/47.47  | | 
% 240.86/47.47  | End of split
% 240.86/47.47  | 
% 240.86/47.47  End of proof
% 240.86/47.47  
% 240.86/47.47  Sub-proof #435 shows that the following formulas are inconsistent:
% 240.86/47.47  ----------------------------------------------------------------
% 240.86/47.47    (1)  all_54_2 = e1 | all_54_2 = e0
% 240.86/47.47    (2)   ~ (all_52_8 = all_52_9)
% 240.86/47.47    (3)  op(e2, e1) = e1
% 240.86/47.47    (4)   ~ (all_52_8 = e0)
% 240.86/47.47    (5)  all_54_2 = all_52_8
% 240.86/47.47    (6)  op(e2, e1) = all_52_9
% 240.86/47.47    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.47  
% 240.86/47.47  Begin of proof
% 240.86/47.47  | 
% 240.86/47.47  | BETA: splitting (1) gives:
% 240.86/47.47  | 
% 240.86/47.47  | Case 1:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (8)  all_54_2 = e1
% 240.86/47.47  | | 
% 240.86/47.47  | | COMBINE_EQS: (5), (8) imply:
% 240.86/47.47  | |   (9)  all_52_8 = e1
% 240.86/47.47  | | 
% 240.86/47.47  | | SIMP: (9) implies:
% 240.86/47.47  | |   (10)  all_52_8 = e1
% 240.86/47.47  | | 
% 240.86/47.47  | | REDUCE: (2), (10) imply:
% 240.86/47.47  | |   (11)   ~ (all_52_9 = e1)
% 240.86/47.47  | | 
% 240.86/47.47  | | SIMP: (11) implies:
% 240.86/47.47  | |   (12)   ~ (all_52_9 = e1)
% 240.86/47.47  | | 
% 240.86/47.47  | | REF_CLOSE: (3), (6), (7), (12) are inconsistent by sub-proof #2306.
% 240.86/47.47  | | 
% 240.86/47.47  | Case 2:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (13)  all_54_2 = e0
% 240.86/47.47  | | 
% 240.86/47.47  | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #1643.
% 240.86/47.47  | | 
% 240.86/47.47  | End of split
% 240.86/47.47  | 
% 240.86/47.47  End of proof
% 240.86/47.47  
% 240.86/47.47  Sub-proof #436 shows that the following formulas are inconsistent:
% 240.86/47.47  ----------------------------------------------------------------
% 240.86/47.47    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.86/47.47           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.86/47.47             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.47           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.86/47.47             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.47           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.47           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.47    (2)  op(e2, e3) = e1
% 240.86/47.47    (3)  op(e2, e3) = all_52_1
% 240.86/47.47    (4)   ~ (all_52_2 = e3)
% 240.86/47.47    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.47    (6)  op(e1, e3) = all_52_2
% 240.86/47.47    (7)   ~ (all_52_1 = e3)
% 240.86/47.47    (8)   ~ (e2 = e1)
% 240.86/47.47  
% 240.86/47.47  Begin of proof
% 240.86/47.47  | 
% 240.86/47.47  | BETA: splitting (1) gives:
% 240.86/47.47  | 
% 240.86/47.47  | Case 1:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (9)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.47  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.47  | |        op(e2, e3) = e3
% 240.86/47.47  | | 
% 240.86/47.47  | | ALPHA: (9) implies:
% 240.86/47.47  | |   (10)  op(e2, e3) = e3
% 240.86/47.47  | | 
% 240.86/47.47  | | REF_CLOSE: (3), (5), (7), (10) are inconsistent by sub-proof #2337.
% 240.86/47.47  | | 
% 240.86/47.47  | Case 2:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (11)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.86/47.47  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.86/47.47  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.47  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.47  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.47  | | 
% 240.86/47.47  | | BETA: splitting (11) gives:
% 240.86/47.47  | | 
% 240.86/47.47  | | Case 1:
% 240.86/47.47  | | | 
% 240.86/47.47  | | |   (12)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.86/47.47  | | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.86/47.47  | | |         e2 & op(e2, e3) = e2
% 240.86/47.47  | | | 
% 240.86/47.47  | | | ALPHA: (12) implies:
% 240.86/47.47  | | |   (13)  op(e2, e3) = e2
% 240.86/47.47  | | | 
% 240.86/47.47  | | | REF_CLOSE: (2), (5), (8), (13) are inconsistent by sub-proof #1633.
% 240.86/47.47  | | | 
% 240.86/47.47  | | Case 2:
% 240.86/47.47  | | | 
% 240.86/47.47  | | |   (14)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.47  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.86/47.47  | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 240.86/47.47  | | | 
% 240.86/47.47  | | | ALPHA: (14) implies:
% 240.86/47.47  | | |   (15)  op(e1, e3) = e3
% 240.86/47.47  | | | 
% 240.86/47.47  | | | REF_CLOSE: (4), (5), (6), (15) are inconsistent by sub-proof #2335.
% 240.86/47.47  | | | 
% 240.86/47.47  | | End of split
% 240.86/47.47  | | 
% 240.86/47.47  | End of split
% 240.86/47.47  | 
% 240.86/47.47  End of proof
% 240.86/47.47  
% 240.86/47.47  Sub-proof #437 shows that the following formulas are inconsistent:
% 240.86/47.47  ----------------------------------------------------------------
% 240.86/47.47    (1)   ~ (e3 = e0)
% 240.86/47.47    (2)   ~ (e2 = e0)
% 240.86/47.47    (3)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.86/47.47         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.86/47.47    (4)   ~ (e3 = e1)
% 240.86/47.47    (5)  op(e2, e1) = all_52_9
% 240.86/47.47    (6)   ~ (e3 = e2)
% 240.86/47.47    (7)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.86/47.47         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.86/47.47    (8)  op(e0, e1) = e0
% 240.86/47.47    (9)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 240.86/47.47         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 240.86/47.47    (10)  all_58_14 = e0
% 240.86/47.47    (11)   ~ (all_52_9 = e3)
% 240.86/47.47    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.47    (13)  op(e1, e1) = e0
% 240.86/47.47    (14)   ~ (e1 = e0)
% 240.86/47.47    (15)   ~ (e2 = e1)
% 240.86/47.47  
% 240.86/47.47  Begin of proof
% 240.86/47.47  | 
% 240.86/47.47  | BETA: splitting (9) gives:
% 240.86/47.47  | 
% 240.86/47.47  | Case 1:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (16)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 240.86/47.47  | |           e3)
% 240.86/47.47  | | 
% 240.86/47.47  | | BETA: splitting (16) gives:
% 240.86/47.47  | | 
% 240.86/47.47  | | Case 1:
% 240.86/47.47  | | | 
% 240.86/47.47  | | |   (17)  all_58_4 = e3 & op(e3, e1) = e3
% 240.86/47.47  | | | 
% 240.86/47.47  | | | ALPHA: (17) implies:
% 240.86/47.47  | | |   (18)  all_58_4 = e3
% 240.86/47.47  | | | 
% 240.86/47.47  | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (12), (13), (14), (15),
% 240.86/47.47  | | |            (18) are inconsistent by sub-proof #1241.
% 240.86/47.47  | | | 
% 240.86/47.47  | | Case 2:
% 240.86/47.47  | | | 
% 240.86/47.47  | | |   (19)  all_58_5 = e3 & op(e2, e1) = e3
% 240.86/47.47  | | | 
% 240.86/47.47  | | | REF_CLOSE: (5), (11), (12), (19) are inconsistent by sub-proof #1822.
% 240.86/47.47  | | | 
% 240.86/47.47  | | End of split
% 240.86/47.47  | | 
% 240.86/47.47  | Case 2:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (20)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 240.86/47.47  | |           e3)
% 240.86/47.47  | | 
% 240.86/47.47  | | BETA: splitting (20) gives:
% 240.86/47.47  | | 
% 240.86/47.47  | | Case 1:
% 240.86/47.47  | | | 
% 240.86/47.47  | | |   (21)  all_58_8 = e3 & op(e1, e1) = e3
% 240.86/47.47  | | | 
% 240.86/47.47  | | | REF_CLOSE: (1), (12), (13), (21) are inconsistent by sub-proof #2018.
% 240.86/47.47  | | | 
% 240.86/47.47  | | Case 2:
% 240.86/47.47  | | | 
% 240.86/47.47  | | |   (22)  all_58_14 = e3 & op(e0, e1) = e3
% 240.86/47.47  | | | 
% 240.86/47.47  | | | ALPHA: (22) implies:
% 240.86/47.47  | | |   (23)  op(e0, e1) = e3
% 240.86/47.47  | | | 
% 240.86/47.47  | | | REF_CLOSE: (1), (8), (12), (23) are inconsistent by sub-proof #2164.
% 240.86/47.47  | | | 
% 240.86/47.47  | | End of split
% 240.86/47.47  | | 
% 240.86/47.47  | End of split
% 240.86/47.47  | 
% 240.86/47.47  End of proof
% 240.86/47.47  
% 240.86/47.47  Sub-proof #438 shows that the following formulas are inconsistent:
% 240.86/47.47  ----------------------------------------------------------------
% 240.86/47.47    (1)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.47             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.86/47.47           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 240.86/47.47             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 240.86/47.47           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.86/47.47    (2)  all_56_1 = e2
% 240.86/47.47    (3)  all_56_11 = e0
% 240.86/47.47  
% 240.86/47.47  Begin of proof
% 240.86/47.47  | 
% 240.86/47.47  | BETA: splitting (1) gives:
% 240.86/47.47  | 
% 240.86/47.47  | Case 1:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (4)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 240.86/47.47  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 240.86/47.47  | |        & op(e1, e2) = e1
% 240.86/47.47  | | 
% 240.86/47.47  | | ALPHA: (4) implies:
% 240.86/47.47  | |   (5)   ~ (all_56_1 = e2)
% 240.86/47.47  | | 
% 240.86/47.47  | | REDUCE: (2), (5) imply:
% 240.86/47.47  | |   (6)  $false
% 240.86/47.47  | | 
% 240.86/47.47  | | CLOSE: (6) is inconsistent.
% 240.86/47.47  | | 
% 240.86/47.47  | Case 2:
% 240.86/47.47  | | 
% 240.86/47.47  | |   (7)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.86/47.47  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 240.86/47.47  | |        & op(e0, e2) = e2
% 240.86/47.47  | | 
% 240.86/47.47  | | ALPHA: (7) implies:
% 240.86/47.47  | |   (8)   ~ (all_56_11 = e0)
% 240.86/47.47  | | 
% 240.86/47.47  | | REDUCE: (3), (8) imply:
% 240.86/47.47  | |   (9)  $false
% 240.86/47.47  | | 
% 240.86/47.47  | | CLOSE: (9) is inconsistent.
% 240.86/47.47  | | 
% 240.86/47.47  | End of split
% 240.86/47.47  | 
% 240.86/47.47  End of proof
% 240.86/47.47  
% 240.86/47.47  Sub-proof #439 shows that the following formulas are inconsistent:
% 240.86/47.47  ----------------------------------------------------------------
% 240.86/47.47    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.86/47.47             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.86/47.47           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 240.86/47.47           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.47           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.86/47.47    (2)  all_56_11 = e0
% 240.86/47.47    (3)  all_56_21 = e3
% 240.86/47.47  
% 240.86/47.47  Begin of proof
% 240.86/47.47  | 
% 240.86/47.47  | BETA: splitting (1) gives:
% 240.86/47.47  | 
% 240.86/47.47  | Case 1:
% 240.86/47.47  | | 
% 240.86/47.48  | |   (4)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.86/47.48  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.86/47.48  | |        op(e0, e3) = e3
% 240.86/47.48  | | 
% 240.86/47.48  | | ALPHA: (4) implies:
% 240.86/47.48  | |   (5)   ~ (all_56_11 = e0)
% 240.86/47.48  | | 
% 240.86/47.48  | | REDUCE: (2), (5) imply:
% 240.86/47.48  | |   (6)  $false
% 240.86/47.48  | | 
% 240.86/47.48  | | CLOSE: (6) is inconsistent.
% 240.86/47.48  | | 
% 240.86/47.48  | Case 2:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (7)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.86/47.48  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 240.86/47.48  | |        op(e0, e3) = e0
% 240.86/47.48  | | 
% 240.86/47.48  | | ALPHA: (7) implies:
% 240.86/47.48  | |   (8)   ~ (all_56_21 = e3)
% 240.86/47.48  | | 
% 240.86/47.48  | | REDUCE: (3), (8) imply:
% 240.86/47.48  | |   (9)  $false
% 240.86/47.48  | | 
% 240.86/47.48  | | CLOSE: (9) is inconsistent.
% 240.86/47.48  | | 
% 240.86/47.48  | End of split
% 240.86/47.48  | 
% 240.86/47.48  End of proof
% 240.86/47.48  
% 240.86/47.48  Sub-proof #440 shows that the following formulas are inconsistent:
% 240.86/47.48  ----------------------------------------------------------------
% 240.86/47.48    (1)   ~ (all_52_3 = e1)
% 240.86/47.48    (2)  op(e0, e3) = all_52_3
% 240.86/47.48    (3)   ~ (e3 = e1)
% 240.86/47.48    (4)   ~ (all_52_2 = e1)
% 240.86/47.48    (5)  op(e2, e3) = all_52_1
% 240.86/47.48    (6)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.86/47.48         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.86/47.48    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.48    (8)  op(e1, e3) = all_52_2
% 240.86/47.48    (9)  op(e3, e3) = e3
% 240.86/47.48    (10)   ~ (all_52_1 = e1)
% 240.86/47.48  
% 240.86/47.48  Begin of proof
% 240.86/47.48  | 
% 240.86/47.48  | BETA: splitting (6) gives:
% 240.86/47.48  | 
% 240.86/47.48  | Case 1:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 240.86/47.48  | |           e1)
% 240.86/47.48  | | 
% 240.86/47.48  | | REF_CLOSE: (3), (5), (7), (9), (10), (11) are inconsistent by sub-proof
% 240.86/47.48  | |            #1370.
% 240.86/47.48  | | 
% 240.86/47.48  | Case 2:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (12)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 240.86/47.48  | |           e1)
% 240.86/47.48  | | 
% 240.86/47.48  | | REF_CLOSE: (1), (2), (4), (7), (8), (12) are inconsistent by sub-proof
% 240.86/47.48  | |            #1947.
% 240.86/47.48  | | 
% 240.86/47.48  | End of split
% 240.86/47.48  | 
% 240.86/47.48  End of proof
% 240.86/47.48  
% 240.86/47.48  Sub-proof #441 shows that the following formulas are inconsistent:
% 240.86/47.48  ----------------------------------------------------------------
% 240.86/47.48    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.86/47.48           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.86/47.48             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.48           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.86/47.48             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.48           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.48           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.48    (2)  op(e2, e3) = all_52_1
% 240.86/47.48    (3)   ~ (all_52_2 = e3)
% 240.86/47.48    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.48    (5)  op(e1, e3) = all_52_2
% 240.86/47.48    (6)  all_56_21 = e3
% 240.86/47.48    (7)   ~ (all_52_1 = e3)
% 240.86/47.48  
% 240.86/47.48  Begin of proof
% 240.86/47.48  | 
% 240.86/47.48  | BETA: splitting (1) gives:
% 240.86/47.48  | 
% 240.86/47.48  | Case 1:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.48  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.48  | |        op(e2, e3) = e3
% 240.86/47.48  | | 
% 240.86/47.48  | | ALPHA: (8) implies:
% 240.86/47.48  | |   (9)  op(e2, e3) = e3
% 240.86/47.48  | | 
% 240.86/47.48  | | REF_CLOSE: (2), (4), (7), (9) are inconsistent by sub-proof #2337.
% 240.86/47.48  | | 
% 240.86/47.48  | Case 2:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.86/47.48  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.86/47.48  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.48  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.48  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.48  | | 
% 240.86/47.48  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #483.
% 240.86/47.48  | | 
% 240.86/47.48  | End of split
% 240.86/47.48  | 
% 240.86/47.48  End of proof
% 240.86/47.48  
% 240.86/47.48  Sub-proof #442 shows that the following formulas are inconsistent:
% 240.86/47.48  ----------------------------------------------------------------
% 240.86/47.48    (1)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 240.86/47.48    (2)  op(e2, e2) = all_8_2
% 240.86/47.48    (3)   ~ (all_52_4 = e3)
% 240.86/47.48    (4)  op(e3, e2) = all_52_4
% 240.86/47.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.48    (6)   ~ (all_8_2 = e3)
% 240.86/47.48  
% 240.86/47.48  Begin of proof
% 240.86/47.48  | 
% 240.86/47.48  | BETA: splitting (1) gives:
% 240.86/47.48  | 
% 240.86/47.48  | Case 1:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (7)  all_58_1 = e3 & op(e3, e2) = e3
% 240.86/47.48  | | 
% 240.86/47.48  | | ALPHA: (7) implies:
% 240.86/47.48  | |   (8)  op(e3, e2) = e3
% 240.86/47.48  | | 
% 240.86/47.48  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2192.
% 240.86/47.48  | | 
% 240.86/47.48  | Case 2:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (9)  all_58_3 = e3 & op(e2, e2) = e3
% 240.86/47.48  | | 
% 240.86/47.48  | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #450.
% 240.86/47.48  | | 
% 240.86/47.48  | End of split
% 240.86/47.48  | 
% 240.86/47.48  End of proof
% 240.86/47.48  
% 240.86/47.48  Sub-proof #443 shows that the following formulas are inconsistent:
% 240.86/47.48  ----------------------------------------------------------------
% 240.86/47.48    (1)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 & $i(all_6_1)
% 240.86/47.48    (2)  op(e1, e3) = e0
% 240.86/47.48    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.48    (4)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) = all_46_1
% 240.86/47.48           & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e1, e3) =
% 240.86/47.48           all_46_1 & $i(all_46_1))
% 240.86/47.48  
% 240.86/47.48  Begin of proof
% 240.86/47.48  | 
% 240.86/47.48  | ALPHA: (1) implies:
% 240.86/47.48  |   (5)   ~ (all_6_1 = e0)
% 240.86/47.48  |   (6)  op(e1, e3) = all_6_1
% 240.86/47.48  | 
% 240.86/47.48  | BETA: splitting (4) gives:
% 240.86/47.48  | 
% 240.86/47.48  | Case 1:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (7)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.86/47.48  | |        all_46_1 & $i(all_46_0) & $i(all_46_1)
% 240.86/47.48  | | 
% 240.86/47.48  | | ALPHA: (7) implies:
% 240.86/47.48  | |   (8)  op(e1, e3) = all_46_1
% 240.86/47.48  | | 
% 240.86/47.48  | | REF_CLOSE: (2), (3), (5), (6), (8) are inconsistent by sub-proof #444.
% 240.86/47.48  | | 
% 240.86/47.48  | Case 2:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (9)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.86/47.48  | | 
% 240.86/47.48  | | ALPHA: (9) implies:
% 240.86/47.48  | |   (10)  op(e1, e3) = all_46_1
% 240.86/47.48  | | 
% 240.86/47.48  | | REF_CLOSE: (2), (3), (5), (6), (10) are inconsistent by sub-proof #444.
% 240.86/47.48  | | 
% 240.86/47.48  | End of split
% 240.86/47.48  | 
% 240.86/47.48  End of proof
% 240.86/47.48  
% 240.86/47.48  Sub-proof #444 shows that the following formulas are inconsistent:
% 240.86/47.48  ----------------------------------------------------------------
% 240.86/47.48    (1)   ~ (all_6_1 = e0)
% 240.86/47.48    (2)  op(e1, e3) = all_6_1
% 240.86/47.48    (3)  op(e1, e3) = all_46_1
% 240.86/47.48    (4)  op(e1, e3) = e0
% 240.86/47.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.48  
% 240.86/47.48  Begin of proof
% 240.86/47.48  | 
% 240.86/47.48  | GROUND_INST: instantiating (5) with e0, all_46_1, e3, e1, simplifying with
% 240.86/47.48  |              (3), (4) gives:
% 240.86/47.48  |   (6)  all_46_1 = e0
% 240.86/47.48  | 
% 240.86/47.48  | GROUND_INST: instantiating (5) with all_6_1, all_46_1, e3, e1, simplifying
% 240.86/47.48  |              with (2), (3) gives:
% 240.86/47.48  |   (7)  all_46_1 = all_6_1
% 240.86/47.48  | 
% 240.86/47.48  | COMBINE_EQS: (6), (7) imply:
% 240.86/47.48  |   (8)  all_6_1 = e0
% 240.86/47.48  | 
% 240.86/47.48  | SIMP: (8) implies:
% 240.86/47.48  |   (9)  all_6_1 = e0
% 240.86/47.48  | 
% 240.86/47.48  | REDUCE: (1), (9) imply:
% 240.86/47.48  |   (10)  $false
% 240.86/47.48  | 
% 240.86/47.48  | CLOSE: (10) is inconsistent.
% 240.86/47.48  | 
% 240.86/47.48  End of proof
% 240.86/47.48  
% 240.86/47.48  Sub-proof #445 shows that the following formulas are inconsistent:
% 240.86/47.48  ----------------------------------------------------------------
% 240.86/47.48    (1)  all_54_14 = all_6_0
% 240.86/47.48    (2)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 240.86/47.48         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.86/47.48    (3)  all_58_14 = e2
% 240.86/47.48    (4)   ~ (e3 = e1)
% 240.86/47.48    (5)  op(e3, e1) = e0
% 240.86/47.48    (6)  op(e2, e1) = all_52_9
% 240.86/47.48    (7)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.86/47.48    (8)  op(e1, e1) = e3
% 240.86/47.48    (9)   ~ (all_6_0 = e3)
% 240.86/47.48    (10)   ~ (all_52_9 = all_6_0)
% 240.86/47.48    (11)   ~ (all_6_0 = e0)
% 240.86/47.48    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.48    (13)   ~ (e1 = e0)
% 240.86/47.48    (14)   ~ (all_6_0 = e2)
% 240.86/47.48    (15)   ~ (e2 = e1)
% 240.86/47.48  
% 240.86/47.48  Begin of proof
% 240.86/47.48  | 
% 240.86/47.48  | BETA: splitting (2) gives:
% 240.86/47.48  | 
% 240.86/47.48  | Case 1:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (16)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 240.86/47.48  | |           e1)
% 240.86/47.48  | | 
% 240.86/47.48  | | BETA: splitting (16) gives:
% 240.86/47.48  | | 
% 240.86/47.48  | | Case 1:
% 240.86/47.48  | | | 
% 240.86/47.48  | | |   (17)  all_58_4 = e1 & op(e3, e1) = e1
% 240.86/47.48  | | | 
% 240.86/47.48  | | | ALPHA: (17) implies:
% 240.86/47.48  | | |   (18)  op(e3, e1) = e1
% 240.86/47.48  | | | 
% 240.86/47.48  | | | REF_CLOSE: (5), (12), (13), (18) are inconsistent by sub-proof #2089.
% 240.86/47.48  | | | 
% 240.86/47.48  | | Case 2:
% 240.86/47.48  | | | 
% 240.86/47.48  | | |   (19)  all_58_5 = e1 & op(e2, e1) = e1
% 240.86/47.48  | | | 
% 240.86/47.48  | | | ALPHA: (19) implies:
% 240.86/47.48  | | |   (20)  op(e2, e1) = e1
% 240.86/47.48  | | | 
% 240.86/47.48  | | | BETA: splitting (7) gives:
% 240.86/47.48  | | | 
% 240.86/47.48  | | | Case 1:
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | |   (21)  all_54_14 = e3
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | | REF_CLOSE: (1), (9), (21) are inconsistent by sub-proof #452.
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | Case 2:
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | |   (22)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | | REF_CLOSE: (1), (6), (10), (11), (12), (14), (20), (22) are inconsistent
% 240.86/47.48  | | | |            by sub-proof #446.
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | End of split
% 240.86/47.48  | | | 
% 240.86/47.48  | | End of split
% 240.86/47.48  | | 
% 240.86/47.48  | Case 2:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (23)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 240.86/47.48  | |           e1)
% 240.86/47.48  | | 
% 240.86/47.48  | | BETA: splitting (23) gives:
% 240.86/47.48  | | 
% 240.86/47.48  | | Case 1:
% 240.86/47.48  | | | 
% 240.86/47.48  | | |   (24)  all_58_8 = e1 & op(e1, e1) = e1
% 240.86/47.48  | | | 
% 240.86/47.48  | | | ALPHA: (24) implies:
% 240.86/47.48  | | |   (25)  op(e1, e1) = e1
% 240.86/47.48  | | | 
% 240.86/47.48  | | | REF_CLOSE: (4), (8), (12), (25) are inconsistent by sub-proof #468.
% 240.86/47.48  | | | 
% 240.86/47.48  | | Case 2:
% 240.86/47.48  | | | 
% 240.86/47.48  | | |   (26)  all_58_14 = e1 & op(e0, e1) = e1
% 240.86/47.48  | | | 
% 240.86/47.48  | | | ALPHA: (26) implies:
% 240.86/47.48  | | |   (27)  all_58_14 = e1
% 240.86/47.48  | | | 
% 240.86/47.48  | | | REF_CLOSE: (3), (15), (27) are inconsistent by sub-proof #2044.
% 240.86/47.48  | | | 
% 240.86/47.48  | | End of split
% 240.86/47.48  | | 
% 240.86/47.48  | End of split
% 240.86/47.48  | 
% 240.86/47.48  End of proof
% 240.86/47.48  
% 240.86/47.48  Sub-proof #446 shows that the following formulas are inconsistent:
% 240.86/47.48  ----------------------------------------------------------------
% 240.86/47.48    (1)  all_54_14 = all_6_0
% 240.86/47.48    (2)  op(e2, e1) = e1
% 240.86/47.48    (3)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.86/47.48    (4)  op(e2, e1) = all_52_9
% 240.86/47.48    (5)   ~ (all_52_9 = all_6_0)
% 240.86/47.48    (6)   ~ (all_6_0 = e0)
% 240.86/47.48    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.48    (8)   ~ (all_6_0 = e2)
% 240.86/47.48  
% 240.86/47.48  Begin of proof
% 240.86/47.48  | 
% 240.86/47.48  | BETA: splitting (3) gives:
% 240.86/47.48  | 
% 240.86/47.48  | Case 1:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (9)  all_54_14 = e2
% 240.86/47.48  | | 
% 240.86/47.48  | | REF_CLOSE: (1), (8), (9) are inconsistent by sub-proof #451.
% 240.86/47.48  | | 
% 240.86/47.48  | Case 2:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (10)  all_54_14 = e1 | all_54_14 = e0
% 240.86/47.48  | | 
% 240.86/47.48  | | BETA: splitting (10) gives:
% 240.86/47.48  | | 
% 240.86/47.48  | | Case 1:
% 240.86/47.48  | | | 
% 240.86/47.48  | | |   (11)  all_54_14 = e1
% 240.86/47.48  | | | 
% 240.86/47.48  | | | COMBINE_EQS: (1), (11) imply:
% 240.86/47.48  | | |   (12)  all_6_0 = e1
% 240.86/47.48  | | | 
% 240.86/47.48  | | | SIMP: (12) implies:
% 240.86/47.48  | | |   (13)  all_6_0 = e1
% 240.86/47.48  | | | 
% 240.86/47.48  | | | REDUCE: (5), (13) imply:
% 240.86/47.48  | | |   (14)   ~ (all_52_9 = e1)
% 240.86/47.48  | | | 
% 240.86/47.48  | | | REF_CLOSE: (2), (4), (7), (14) are inconsistent by sub-proof #2306.
% 240.86/47.48  | | | 
% 240.86/47.48  | | Case 2:
% 240.86/47.48  | | | 
% 240.86/47.48  | | |   (15)  all_54_14 = e0
% 240.86/47.48  | | | 
% 240.86/47.48  | | | REF_CLOSE: (1), (6), (15) are inconsistent by sub-proof #448.
% 240.86/47.48  | | | 
% 240.86/47.48  | | End of split
% 240.86/47.48  | | 
% 240.86/47.48  | End of split
% 240.86/47.48  | 
% 240.86/47.48  End of proof
% 240.86/47.48  
% 240.86/47.48  Sub-proof #447 shows that the following formulas are inconsistent:
% 240.86/47.48  ----------------------------------------------------------------
% 240.86/47.48    (1)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 240.86/47.48           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 240.86/47.48           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 240.86/47.48           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 240.86/47.48           & $i(all_56_23))
% 240.86/47.48    (2)  op(e0, e1) = all_6_0
% 240.86/47.48    (3)  all_54_14 = all_6_0
% 240.86/47.48    (4)   ~ (e2 = e0)
% 240.86/47.48    (5)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.48         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.86/47.48    (6)   ~ (all_10_2 = e1)
% 240.86/47.48    (7)  op(e0, e3) = all_52_3
% 240.86/47.48    (8)  op(e2, e2) = e0
% 240.86/47.48    (9)  op(e3, e1) = e0
% 240.86/47.48    (10)   ~ (all_52_12 = all_52_13)
% 240.86/47.48    (11)   ~ (e3 = e2)
% 240.86/47.48    (12)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.86/47.48    (13)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2)
% 240.86/47.48    (14)  op(e3, e0) = all_52_12
% 240.86/47.48    (15)   ~ (all_52_1 = e0)
% 240.86/47.48    (16)  op(e2, e2) = all_8_2
% 240.86/47.48    (17)  op(e2, e3) = all_52_1
% 240.86/47.48    (18)  op(e1, e3) = e0
% 240.86/47.48    (19)   ~ (all_6_0 = e3)
% 240.86/47.48    (20)   ~ (all_6_0 = e0)
% 240.86/47.48    (21)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 240.86/47.48          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 240.86/47.48    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.48    (23)  op(e3, e3) = all_10_2
% 240.86/47.48    (24)  all_56_21 = e3
% 240.86/47.48    (25)   ~ (all_8_2 = e3)
% 240.86/47.48    (26)   ~ (all_6_0 = e2)
% 240.86/47.48    (27)  op(e2, e0) = all_52_13
% 240.86/47.48    (28)   ~ (all_52_3 = all_6_0)
% 240.86/47.48    (29)  all_58_4 = e0
% 240.86/47.48  
% 240.86/47.48  Begin of proof
% 240.86/47.48  | 
% 240.86/47.48  | BETA: splitting (13) gives:
% 240.86/47.48  | 
% 240.86/47.48  | Case 1:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (30)  all_58_4 = e2 & op(e3, e1) = e2
% 240.86/47.48  | | 
% 240.86/47.48  | | ALPHA: (30) implies:
% 240.86/47.48  | |   (31)  all_58_4 = e2
% 240.86/47.48  | | 
% 240.86/47.48  | | REF_CLOSE: (4), (29), (31) are inconsistent by sub-proof #1666.
% 240.86/47.48  | | 
% 240.86/47.48  | Case 2:
% 240.86/47.48  | | 
% 240.86/47.48  | |   (32)  all_58_5 = e2 & op(e2, e1) = e2
% 240.86/47.48  | | 
% 240.86/47.48  | | ALPHA: (32) implies:
% 240.86/47.48  | |   (33)  op(e2, e1) = e2
% 240.86/47.48  | | 
% 240.86/47.48  | | BETA: splitting (12) gives:
% 240.86/47.48  | | 
% 240.86/47.48  | | Case 1:
% 240.86/47.48  | | | 
% 240.86/47.48  | | |   (34)  all_54_14 = e3
% 240.86/47.48  | | | 
% 240.86/47.48  | | | REF_CLOSE: (3), (19), (34) are inconsistent by sub-proof #452.
% 240.86/47.48  | | | 
% 240.86/47.48  | | Case 2:
% 240.86/47.48  | | | 
% 240.86/47.48  | | |   (35)   ~ (all_54_14 = e3)
% 240.86/47.48  | | |   (36)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 240.86/47.48  | | | 
% 240.86/47.48  | | | BETA: splitting (36) gives:
% 240.86/47.48  | | | 
% 240.86/47.48  | | | Case 1:
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | |   (37)  all_54_14 = e2
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | | REF_CLOSE: (3), (26), (37) are inconsistent by sub-proof #451.
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | Case 2:
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | |   (38)  all_54_14 = e1 | all_54_14 = e0
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | | BETA: splitting (38) gives:
% 240.86/47.48  | | | | 
% 240.86/47.48  | | | | Case 1:
% 240.86/47.48  | | | | | 
% 240.86/47.48  | | | | |   (39)  all_54_14 = e1
% 240.86/47.48  | | | | | 
% 240.86/47.48  | | | | | COMBINE_EQS: (3), (39) imply:
% 240.86/47.48  | | | | |   (40)  all_6_0 = e1
% 240.86/47.48  | | | | | 
% 240.86/47.48  | | | | | SIMP: (40) implies:
% 240.86/47.48  | | | | |   (41)  all_6_0 = e1
% 240.86/47.48  | | | | | 
% 240.86/47.48  | | | | | REDUCE: (28), (41) imply:
% 240.86/47.48  | | | | |   (42)   ~ (all_52_3 = e1)
% 240.86/47.48  | | | | | 
% 240.86/47.48  | | | | | REDUCE: (19), (41) imply:
% 240.86/47.48  | | | | |   (43)   ~ (e3 = e1)
% 240.86/47.48  | | | | | 
% 240.86/47.48  | | | | | SIMP: (43) implies:
% 240.86/47.48  | | | | |   (44)   ~ (e3 = e1)
% 240.86/47.48  | | | | | 
% 240.86/47.48  | | | | | REDUCE: (20), (41) imply:
% 240.86/47.48  | | | | |   (45)   ~ (e1 = e0)
% 240.86/47.48  | | | | | 
% 240.86/47.48  | | | | | REDUCE: (2), (41) imply:
% 240.86/47.48  | | | | |   (46)  op(e0, e1) = e1
% 240.86/47.48  | | | | | 
% 240.86/47.49  | | | | | BETA: splitting (21) gives:
% 240.86/47.49  | | | | | 
% 240.86/47.49  | | | | | Case 1:
% 240.86/47.49  | | | | | | 
% 240.86/47.49  | | | | | |   (47)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 240.86/47.49  | | | | | |             e3) = e1)
% 240.86/47.49  | | | | | | 
% 240.86/47.49  | | | | | | BETA: splitting (47) gives:
% 240.86/47.49  | | | | | | 
% 240.86/47.49  | | | | | | Case 1:
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | |   (48)  all_58_0 = e1 & op(e3, e3) = e1
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | | REF_CLOSE: (6), (22), (23), (48) are inconsistent by sub-proof
% 240.86/47.49  | | | | | | |            #2230.
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | Case 2:
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | |   (49)  all_58_2 = e1 & op(e2, e3) = e1
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | | ALPHA: (49) implies:
% 240.86/47.49  | | | | | | |   (50)  all_58_2 = e1
% 240.86/47.49  | | | | | | |   (51)  op(e2, e3) = e1
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | | BETA: splitting (5) gives:
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | | Case 1:
% 240.86/47.49  | | | | | | | | 
% 240.86/47.49  | | | | | | | |   (52)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 &
% 240.86/47.49  | | | | | | | |           op(e2, e2) = e3)
% 240.86/47.49  | | | | | | | | 
% 240.86/47.49  | | | | | | | | BETA: splitting (52) gives:
% 240.86/47.49  | | | | | | | | 
% 240.86/47.49  | | | | | | | | Case 1:
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | |   (53)  all_58_2 = e3 & op(e2, e3) = e3
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | ALPHA: (53) implies:
% 240.86/47.49  | | | | | | | | |   (54)  all_58_2 = e3
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | REF_CLOSE: (44), (50), (54) are inconsistent by sub-proof
% 240.86/47.49  | | | | | | | | |            #1691.
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | Case 2:
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | |   (55)  all_58_3 = e3 & op(e2, e2) = e3
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | REF_CLOSE: (16), (22), (25), (55) are inconsistent by
% 240.86/47.49  | | | | | | | | |            sub-proof #450.
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | End of split
% 240.86/47.49  | | | | | | | | 
% 240.86/47.49  | | | | | | | Case 2:
% 240.86/47.49  | | | | | | | | 
% 240.86/47.49  | | | | | | | |   (56)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 &
% 240.86/47.49  | | | | | | | |           op(e2, e0) = e3)
% 240.86/47.49  | | | | | | | | 
% 240.86/47.49  | | | | | | | | BETA: splitting (56) gives:
% 240.86/47.49  | | | | | | | | 
% 240.86/47.49  | | | | | | | | Case 1:
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | |   (57)  all_58_5 = e3 & op(e2, e1) = e3
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | ALPHA: (57) implies:
% 240.86/47.49  | | | | | | | | |   (58)  op(e2, e1) = e3
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | REF_CLOSE: (11), (22), (33), (58) are inconsistent by
% 240.86/47.49  | | | | | | | | |            sub-proof #2256.
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | Case 2:
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | |   (59)  all_58_10 = e3 & op(e2, e0) = e3
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | ALPHA: (59) implies:
% 240.86/47.49  | | | | | | | | |   (60)  op(e2, e0) = e3
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | BETA: splitting (1) gives:
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | Case 1:
% 240.86/47.49  | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | |   (61)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 240.86/47.49  | | | | | | | | | |             e1) = all_56_17 & $i(all_56_17)) | (all_56_18 =
% 240.86/47.49  | | | | | | | | | |           e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 240.86/47.49  | | | | | | | | | |           all_56_19 & $i(all_56_19))
% 240.86/47.49  | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | BETA: splitting (61) gives:
% 240.86/47.49  | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | Case 1:
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | |   (62)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 240.86/47.49  | | | | | | | | | | |           e1) = all_56_17 & $i(all_56_17)
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | ALPHA: (62) implies:
% 240.86/47.49  | | | | | | | | | | |   (63)  op(e3, e1) = all_56_17
% 240.86/47.49  | | | | | | | | | | |   (64)  op(e3, all_56_17) = e3
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | GROUND_INST: instantiating (22) with all_52_13, e3, e0, e2,
% 240.86/47.49  | | | | | | | | | | |              simplifying with (27), (60) gives:
% 240.86/47.49  | | | | | | | | | | |   (65)  all_52_13 = e3
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | GROUND_INST: instantiating (22) with e0, all_56_17, e1, e3,
% 240.86/47.49  | | | | | | | | | | |              simplifying with (9), (63) gives:
% 240.86/47.49  | | | | | | | | | | |   (66)  all_56_17 = e0
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | REDUCE: (10), (65) imply:
% 240.86/47.49  | | | | | | | | | | |   (67)   ~ (all_52_12 = e3)
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | REDUCE: (64), (66) imply:
% 240.86/47.49  | | | | | | | | | | |   (68)  op(e3, e0) = e3
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | REF_CLOSE: (14), (22), (67), (68) are inconsistent by
% 240.86/47.49  | | | | | | | | | | |            sub-proof #2179.
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | Case 2:
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | |   (69)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 240.86/47.49  | | | | | | | | | | |           e1) = all_56_19 & $i(all_56_19)
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | ALPHA: (69) implies:
% 240.86/47.49  | | | | | | | | | | |   (70)  op(e2, e1) = all_56_19
% 240.86/47.49  | | | | | | | | | | |   (71)  op(e2, all_56_19) = e2
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | GROUND_INST: instantiating (22) with e2, all_56_19, e1, e2,
% 240.86/47.49  | | | | | | | | | | |              simplifying with (33), (70) gives:
% 240.86/47.49  | | | | | | | | | | |   (72)  all_56_19 = e2
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | REDUCE: (71), (72) imply:
% 240.86/47.49  | | | | | | | | | | |   (73)  op(e2, e2) = e2
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | REF_CLOSE: (4), (8), (22), (73) are inconsistent by sub-proof
% 240.86/47.49  | | | | | | | | | | |            #2137.
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | End of split
% 240.86/47.49  | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | Case 2:
% 240.86/47.49  | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | |   (74)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 240.86/47.49  | | | | | | | | | |         (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 240.86/47.49  | | | | | | | | | |             e1) = all_56_23 & $i(all_56_23))
% 240.86/47.49  | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | BETA: splitting (74) gives:
% 240.86/47.49  | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | Case 1:
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | |   (75)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | ALPHA: (75) implies:
% 240.86/47.49  | | | | | | | | | | |   (76)  op(e1, all_56_21) = e1
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | REDUCE: (24), (76) imply:
% 240.86/47.49  | | | | | | | | | | |   (77)  op(e1, e3) = e1
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | GROUND_INST: instantiating (22) with e0, e1, e3, e1,
% 240.86/47.49  | | | | | | | | | | |              simplifying with (18), (77) gives:
% 240.86/47.49  | | | | | | | | | | |   (78)  e1 = e0
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | REDUCE: (45), (78) imply:
% 240.86/47.49  | | | | | | | | | | |   (79)  $false
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | CLOSE: (79) is inconsistent.
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | Case 2:
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | |   (80)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 240.86/47.49  | | | | | | | | | | |           e1) = all_56_23 & $i(all_56_23)
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | ALPHA: (80) implies:
% 240.86/47.49  | | | | | | | | | | |   (81)  op(e0, e1) = all_56_23
% 240.86/47.49  | | | | | | | | | | |   (82)  op(e0, all_56_23) = e0
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | GROUND_INST: instantiating (22) with e1, all_56_23, e1, e0,
% 240.86/47.49  | | | | | | | | | | |              simplifying with (46), (81) gives:
% 240.86/47.49  | | | | | | | | | | |   (83)  all_56_23 = e1
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | GROUND_INST: instantiating (22) with all_52_1, e1, e3, e2,
% 240.86/47.49  | | | | | | | | | | |              simplifying with (17), (51) gives:
% 240.86/47.49  | | | | | | | | | | |   (84)  all_52_1 = e1
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | REDUCE: (82), (83) imply:
% 240.86/47.49  | | | | | | | | | | |   (85)  op(e0, e1) = e0
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | | REF_CLOSE: (22), (45), (46), (85) are inconsistent by
% 240.86/47.49  | | | | | | | | | | |            sub-proof #2158.
% 240.86/47.49  | | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | | End of split
% 240.86/47.49  | | | | | | | | | | 
% 240.86/47.49  | | | | | | | | | End of split
% 240.86/47.49  | | | | | | | | | 
% 240.86/47.49  | | | | | | | | End of split
% 240.86/47.49  | | | | | | | | 
% 240.86/47.49  | | | | | | | End of split
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | End of split
% 240.86/47.49  | | | | | | 
% 240.86/47.49  | | | | | Case 2:
% 240.86/47.49  | | | | | | 
% 240.86/47.49  | | | | | |   (86)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 240.86/47.49  | | | | | |             e3) = e1)
% 240.86/47.49  | | | | | | 
% 240.86/47.49  | | | | | | BETA: splitting (86) gives:
% 240.86/47.49  | | | | | | 
% 240.86/47.49  | | | | | | Case 1:
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | |   (87)  all_58_6 = e1 & op(e1, e3) = e1
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | | ALPHA: (87) implies:
% 240.86/47.49  | | | | | | |   (88)  op(e1, e3) = e1
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | | REF_CLOSE: (18), (22), (45), (88) are inconsistent by sub-proof
% 240.86/47.49  | | | | | | |            #449.
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | Case 2:
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | |   (89)  all_58_12 = e1 & op(e0, e3) = e1
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | | REF_CLOSE: (7), (22), (42), (89) are inconsistent by sub-proof
% 240.86/47.49  | | | | | | |            #2276.
% 240.86/47.49  | | | | | | | 
% 240.86/47.49  | | | | | | End of split
% 240.86/47.49  | | | | | | 
% 240.86/47.49  | | | | | End of split
% 240.86/47.49  | | | | | 
% 240.86/47.49  | | | | Case 2:
% 240.86/47.49  | | | | | 
% 240.86/47.49  | | | | |   (90)  all_54_14 = e0
% 240.86/47.49  | | | | | 
% 240.86/47.49  | | | | | REF_CLOSE: (3), (20), (90) are inconsistent by sub-proof #448.
% 240.86/47.49  | | | | | 
% 240.86/47.49  | | | | End of split
% 240.86/47.49  | | | | 
% 240.86/47.49  | | | End of split
% 240.86/47.49  | | | 
% 240.86/47.49  | | End of split
% 240.86/47.49  | | 
% 240.86/47.49  | End of split
% 240.86/47.49  | 
% 240.86/47.49  End of proof
% 240.86/47.49  
% 240.86/47.49  Sub-proof #448 shows that the following formulas are inconsistent:
% 240.86/47.49  ----------------------------------------------------------------
% 240.86/47.49    (1)  all_54_14 = all_6_0
% 240.86/47.49    (2)  all_54_14 = e0
% 240.86/47.49    (3)   ~ (all_6_0 = e0)
% 240.86/47.49  
% 240.86/47.49  Begin of proof
% 240.86/47.49  | 
% 240.86/47.49  | COMBINE_EQS: (1), (2) imply:
% 240.86/47.49  |   (4)  all_6_0 = e0
% 240.86/47.49  | 
% 240.86/47.49  | SIMP: (4) implies:
% 240.86/47.49  |   (5)  all_6_0 = e0
% 240.86/47.49  | 
% 240.86/47.49  | REDUCE: (3), (5) imply:
% 240.86/47.49  |   (6)  $false
% 240.86/47.49  | 
% 240.86/47.49  | CLOSE: (6) is inconsistent.
% 240.86/47.49  | 
% 240.86/47.49  End of proof
% 240.86/47.49  
% 240.86/47.49  Sub-proof #449 shows that the following formulas are inconsistent:
% 240.86/47.49  ----------------------------------------------------------------
% 240.86/47.49    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.49    (2)  op(e1, e3) = e1
% 240.86/47.49    (3)  op(e1, e3) = e0
% 240.86/47.49    (4)   ~ (e1 = e0)
% 240.86/47.49  
% 240.86/47.49  Begin of proof
% 240.86/47.49  | 
% 240.86/47.49  | GROUND_INST: instantiating (1) with e0, e1, e3, e1, simplifying with (2), (3)
% 240.86/47.49  |              gives:
% 240.86/47.49  |   (5)  e1 = e0
% 240.86/47.49  | 
% 240.86/47.49  | REDUCE: (4), (5) imply:
% 240.86/47.49  |   (6)  $false
% 240.86/47.49  | 
% 240.86/47.49  | CLOSE: (6) is inconsistent.
% 240.86/47.49  | 
% 240.86/47.49  End of proof
% 240.86/47.49  
% 240.86/47.49  Sub-proof #450 shows that the following formulas are inconsistent:
% 240.86/47.49  ----------------------------------------------------------------
% 240.86/47.49    (1)  all_58_3 = e3 & op(e2, e2) = e3
% 240.86/47.49    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.49    (3)  op(e2, e2) = all_8_2
% 240.86/47.49    (4)   ~ (all_8_2 = e3)
% 240.86/47.49  
% 240.86/47.49  Begin of proof
% 240.86/47.49  | 
% 240.86/47.49  | ALPHA: (1) implies:
% 240.86/47.49  |   (5)  op(e2, e2) = e3
% 240.86/47.49  | 
% 240.86/47.49  | GROUND_INST: instantiating (2) with all_8_2, e3, e2, e2, simplifying with (3),
% 240.86/47.49  |              (5) gives:
% 240.86/47.49  |   (6)  all_8_2 = e3
% 240.86/47.49  | 
% 240.86/47.49  | REDUCE: (4), (6) imply:
% 240.86/47.49  |   (7)  $false
% 240.86/47.49  | 
% 240.86/47.49  | CLOSE: (7) is inconsistent.
% 240.86/47.49  | 
% 240.86/47.49  End of proof
% 240.86/47.49  
% 240.86/47.49  Sub-proof #451 shows that the following formulas are inconsistent:
% 240.86/47.49  ----------------------------------------------------------------
% 240.86/47.49    (1)  all_54_14 = all_6_0
% 240.86/47.49    (2)  all_54_14 = e2
% 240.86/47.49    (3)   ~ (all_6_0 = e2)
% 240.86/47.49  
% 240.86/47.49  Begin of proof
% 240.86/47.49  | 
% 240.86/47.49  | COMBINE_EQS: (1), (2) imply:
% 240.86/47.49  |   (4)  all_6_0 = e2
% 240.86/47.49  | 
% 240.86/47.49  | SIMP: (4) implies:
% 240.86/47.49  |   (5)  all_6_0 = e2
% 240.86/47.49  | 
% 240.86/47.49  | REDUCE: (3), (5) imply:
% 240.86/47.49  |   (6)  $false
% 240.86/47.49  | 
% 240.86/47.49  | CLOSE: (6) is inconsistent.
% 240.86/47.49  | 
% 240.86/47.49  End of proof
% 240.86/47.49  
% 240.86/47.49  Sub-proof #452 shows that the following formulas are inconsistent:
% 240.86/47.49  ----------------------------------------------------------------
% 240.86/47.49    (1)  all_54_14 = all_6_0
% 240.86/47.49    (2)  all_54_14 = e3
% 240.86/47.49    (3)   ~ (all_6_0 = e3)
% 240.86/47.49  
% 240.86/47.49  Begin of proof
% 240.86/47.49  | 
% 240.86/47.49  | COMBINE_EQS: (1), (2) imply:
% 240.86/47.49  |   (4)  all_6_0 = e3
% 240.86/47.49  | 
% 240.86/47.49  | SIMP: (4) implies:
% 240.86/47.49  |   (5)  all_6_0 = e3
% 240.86/47.49  | 
% 240.86/47.49  | REDUCE: (3), (5) imply:
% 240.86/47.49  |   (6)  $false
% 240.86/47.49  | 
% 240.86/47.49  | CLOSE: (6) is inconsistent.
% 240.86/47.49  | 
% 240.86/47.49  End of proof
% 240.86/47.49  
% 240.86/47.49  Sub-proof #453 shows that the following formulas are inconsistent:
% 240.86/47.49  ----------------------------------------------------------------
% 240.86/47.49    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.86/47.49    (2)  op(e1, e0) = all_52_14
% 240.86/47.49    (3)   ~ (e3 = e1)
% 240.86/47.49    (4)   ~ (all_52_14 = e1)
% 240.86/47.49    (5)  op(e1, e1) = e3
% 240.86/47.49    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.49  
% 240.86/47.49  Begin of proof
% 240.86/47.49  | 
% 240.86/47.49  | BETA: splitting (1) gives:
% 240.86/47.49  | 
% 240.86/47.49  | Case 1:
% 240.86/47.49  | | 
% 240.86/47.49  | |   (7)  all_58_8 = e1 & op(e1, e1) = e1
% 240.86/47.49  | | 
% 240.86/47.49  | | ALPHA: (7) implies:
% 240.86/47.49  | |   (8)  op(e1, e1) = e1
% 240.86/47.49  | | 
% 240.86/47.49  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #468.
% 240.86/47.49  | | 
% 240.86/47.49  | Case 2:
% 240.86/47.49  | | 
% 240.86/47.49  | |   (9)  all_58_11 = e1 & op(e1, e0) = e1
% 240.86/47.49  | | 
% 240.86/47.49  | | ALPHA: (9) implies:
% 240.86/47.49  | |   (10)  op(e1, e0) = e1
% 240.86/47.49  | | 
% 240.86/47.49  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #2304.
% 240.86/47.49  | | 
% 240.86/47.49  | End of split
% 240.86/47.49  | 
% 240.86/47.49  End of proof
% 240.86/47.49  
% 240.86/47.49  Sub-proof #454 shows that the following formulas are inconsistent:
% 240.86/47.49  ----------------------------------------------------------------
% 240.86/47.49    (1)   ~ (all_52_1 = all_52_3)
% 240.86/47.49    (2)   ~ (all_52_9 = all_8_2)
% 240.86/47.49    (3)   ~ (all_52_13 = all_8_2)
% 240.86/47.49    (4)   ~ (all_8_2 = e0)
% 240.86/47.49    (5)   ~ (all_52_8 = all_52_9)
% 240.86/47.49    (6)  op(e1, e2) = e1
% 240.86/47.49    (7)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.49         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.86/47.49    (8)  op(e1, e2) = all_52_6
% 240.86/47.49    (9)   ~ (all_52_1 = all_8_2)
% 240.86/47.49    (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.49              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.49            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.86/47.49            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.49            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.86/47.49             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.49            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.86/47.49            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.49            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.86/47.49            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.49            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.86/47.49              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.49            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.49            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.86/47.49            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.49            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.86/47.49            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.49            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.86/47.49              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.86/47.49            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.49            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.86/47.49            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.49            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.86/47.49            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.49            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.86/47.49              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.49            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.49            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.49    (11)  all_58_5 = e1 & op(e2, e1) = e1
% 240.86/47.49    (12)  op(e1, e0) = all_52_14
% 240.86/47.49    (13)  op(e0, e3) = all_52_3
% 240.86/47.49    (14)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.86/47.49          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.86/47.49    (15)   ~ (all_52_12 = all_52_13)
% 240.86/47.49    (16)  op(e3, e1) = all_52_8
% 240.86/47.49    (17)  op(e2, e1) = all_52_9
% 240.86/47.49    (18)  all_56_31 = e1
% 240.86/47.49    (19)  op(e3, e0) = all_52_12
% 240.86/47.49    (20)   ~ (all_52_6 = all_52_14)
% 240.86/47.49    (21)  all_54_5 = all_8_2
% 240.86/47.49    (22)  op(e2, e3) = all_52_1
% 240.86/47.49    (23)   ~ (all_52_2 = e3)
% 240.86/47.49    (24)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 240.86/47.49    (25)   ~ (all_52_7 = all_8_2)
% 240.86/47.49    (26)  op(e0, e2) = all_52_7
% 240.86/47.49    (27)   ~ (all_52_9 = e3)
% 240.86/47.49    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.50    (29)  op(e1, e3) = all_52_2
% 240.86/47.50    (30)  all_56_21 = e3
% 240.86/47.50    (31)   ~ (all_8_2 = e3)
% 240.86/47.50    (32)  all_56_11 = all_8_2
% 240.86/47.50    (33)  op(e2, e0) = all_52_13
% 240.86/47.50  
% 240.86/47.50  Begin of proof
% 240.86/47.50  | 
% 240.86/47.50  | ALPHA: (11) implies:
% 240.86/47.50  |   (34)  all_58_5 = e1
% 240.86/47.50  |   (35)  op(e2, e1) = e1
% 240.86/47.50  | 
% 240.86/47.50  | GROUND_INST: instantiating (28) with all_52_6, e1, e2, e1, simplifying with
% 240.86/47.50  |              (6), (8) gives:
% 240.86/47.50  |   (36)  all_52_6 = e1
% 240.86/47.50  | 
% 240.86/47.50  | GROUND_INST: instantiating (28) with all_52_9, e1, e1, e2, simplifying with
% 240.86/47.50  |              (17), (35) gives:
% 240.86/47.50  |   (37)  all_52_9 = e1
% 240.86/47.50  | 
% 240.86/47.50  | REDUCE: (20), (36) imply:
% 240.86/47.50  |   (38)   ~ (all_52_14 = e1)
% 240.86/47.50  | 
% 240.86/47.50  | SIMP: (38) implies:
% 240.86/47.50  |   (39)   ~ (all_52_14 = e1)
% 240.86/47.50  | 
% 240.86/47.50  | REDUCE: (5), (37) imply:
% 240.86/47.50  |   (40)   ~ (all_52_8 = e1)
% 240.86/47.50  | 
% 240.86/47.50  | REDUCE: (2), (37) imply:
% 240.86/47.50  |   (41)   ~ (all_8_2 = e1)
% 240.86/47.50  | 
% 240.86/47.50  | SIMP: (41) implies:
% 240.86/47.50  |   (42)   ~ (all_8_2 = e1)
% 240.86/47.50  | 
% 240.86/47.50  | BETA: splitting (24) gives:
% 240.86/47.50  | 
% 240.86/47.50  | Case 1:
% 240.86/47.50  | | 
% 240.86/47.50  | |   (43)  all_54_5 = e3
% 240.86/47.50  | | 
% 240.86/47.50  | | REF_CLOSE: (21), (31), (43) are inconsistent by sub-proof #1907.
% 240.86/47.50  | | 
% 240.86/47.50  | Case 2:
% 240.86/47.50  | | 
% 240.86/47.50  | |   (44)   ~ (all_54_5 = e3)
% 240.86/47.50  | |   (45)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 240.86/47.50  | | 
% 240.86/47.50  | | BETA: splitting (45) gives:
% 240.86/47.50  | | 
% 240.86/47.50  | | Case 1:
% 240.86/47.50  | | | 
% 240.86/47.50  | | |   (46)  all_54_5 = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | COMBINE_EQS: (21), (46) imply:
% 240.86/47.50  | | |   (47)  all_8_2 = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | SIMP: (47) implies:
% 240.86/47.50  | | |   (48)  all_8_2 = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | COMBINE_EQS: (32), (48) imply:
% 240.86/47.50  | | |   (49)  all_56_11 = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | REDUCE: (9), (48) imply:
% 240.86/47.50  | | |   (50)   ~ (all_52_1 = e2)
% 240.86/47.50  | | | 
% 240.86/47.50  | | | REDUCE: (25), (48) imply:
% 240.86/47.50  | | |   (51)   ~ (all_52_7 = e2)
% 240.86/47.50  | | | 
% 240.86/47.50  | | | REDUCE: (3), (48) imply:
% 240.86/47.50  | | |   (52)   ~ (all_52_13 = e2)
% 240.86/47.50  | | | 
% 240.86/47.50  | | | REDUCE: (31), (48) imply:
% 240.86/47.50  | | |   (53)   ~ (e3 = e2)
% 240.86/47.50  | | | 
% 240.86/47.50  | | | SIMP: (53) implies:
% 240.86/47.50  | | |   (54)   ~ (e3 = e2)
% 240.86/47.50  | | | 
% 240.86/47.50  | | | REDUCE: (42), (48) imply:
% 240.86/47.50  | | |   (55)   ~ (e2 = e1)
% 240.86/47.50  | | | 
% 240.86/47.50  | | | BETA: splitting (10) gives:
% 240.86/47.50  | | | 
% 240.86/47.50  | | | Case 1:
% 240.86/47.50  | | | | 
% 240.86/47.50  | | | |   (56)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.50  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.86/47.50  | | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9
% 240.86/47.50  | | | |           = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.50  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.86/47.50  | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.50  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 240.86/47.50  | | | |           ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 240.86/47.50  | | | |         (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.50  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.50  | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.86/47.50  | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 240.86/47.50  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.86/47.50  | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.50  | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) & 
% 240.86/47.50  | | | |           ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.86/47.50  | | | | 
% 240.86/47.50  | | | | BETA: splitting (56) gives:
% 240.86/47.50  | | | | 
% 240.86/47.50  | | | | Case 1:
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | |   (57)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.50  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 240.86/47.50  | | | | |           & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 &
% 240.86/47.50  | | | | |           all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.86/47.50  | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.86/47.50  | | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.50  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.86/47.50  | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | | REF_CLOSE: (22), (23), (28), (29), (49), (50), (57) are inconsistent
% 240.86/47.50  | | | | |            by sub-proof #486.
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | Case 2:
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | |   (58)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.50  | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 240.86/47.50  | | | | |           & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.86/47.50  | | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.86/47.50  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.86/47.50  | | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.50  | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 240.86/47.50  | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | | BETA: splitting (58) gives:
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | | Case 1:
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | |   (59)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.50  | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 240.86/47.50  | | | | | |         & op(e3, e1) = e1 & op(e1, e3) = e1
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | | ALPHA: (59) implies:
% 240.86/47.50  | | | | | |   (60)  op(e3, e1) = e1
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | | REF_CLOSE: (16), (28), (40), (60) are inconsistent by sub-proof
% 240.86/47.50  | | | | | |            #2309.
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | Case 2:
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | |   (61)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.50  | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 240.86/47.50  | | | | | |             e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 240.86/47.50  | | | | | |           e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.86/47.50  | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.86/47.50  | | | | | |             e0) = e0 & op(e0, e3) = e0)
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | | BETA: splitting (61) gives:
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | | Case 1:
% 240.86/47.50  | | | | | | | 
% 240.86/47.50  | | | | | | |   (62)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.50  | | | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 240.86/47.50  | | | | | | |           e0) & op(e3, e0) = e3 & op(e0, e3) = e3
% 240.86/47.50  | | | | | | | 
% 240.86/47.50  | | | | | | | ALPHA: (62) implies:
% 240.86/47.50  | | | | | | |   (63)  op(e0, e3) = e3
% 240.86/47.50  | | | | | | |   (64)  op(e3, e0) = e3
% 240.86/47.50  | | | | | | | 
% 240.86/47.50  | | | | | | | REF_CLOSE: (1), (7), (13), (14), (15), (17), (19), (22), (27),
% 240.86/47.50  | | | | | | |            (28), (33), (34), (50), (52), (54), (55), (63), (64)
% 240.86/47.50  | | | | | | |            are inconsistent by sub-proof #455.
% 240.86/47.50  | | | | | | | 
% 240.86/47.50  | | | | | | Case 2:
% 240.86/47.50  | | | | | | | 
% 240.86/47.50  | | | | | | |   (65)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.50  | | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 240.86/47.50  | | | | | | |           e3) & op(e3, e0) = e0 & op(e0, e3) = e0
% 240.86/47.50  | | | | | | | 
% 240.86/47.50  | | | | | | | ALPHA: (65) implies:
% 240.86/47.50  | | | | | | |   (66)   ~ (all_56_21 = e3)
% 240.86/47.50  | | | | | | | 
% 240.86/47.50  | | | | | | | REDUCE: (30), (66) imply:
% 240.86/47.50  | | | | | | |   (67)  $false
% 240.86/47.50  | | | | | | | 
% 240.86/47.50  | | | | | | | CLOSE: (67) is inconsistent.
% 240.86/47.50  | | | | | | | 
% 240.86/47.50  | | | | | | End of split
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | End of split
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | End of split
% 240.86/47.50  | | | | 
% 240.86/47.50  | | | Case 2:
% 240.86/47.50  | | | | 
% 240.86/47.50  | | | |   (68)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.50  | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.86/47.50  | | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 240.86/47.50  | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.50  | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.86/47.50  | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.86/47.50  | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) & 
% 240.86/47.50  | | | |           ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 240.86/47.50  | | | |         (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.50  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.86/47.50  | | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 240.86/47.50  | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 240.86/47.50  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.86/47.50  | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.50  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 240.86/47.50  | | | |           ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.50  | | | | 
% 240.86/47.50  | | | | BETA: splitting (68) gives:
% 240.86/47.50  | | | | 
% 240.86/47.50  | | | | Case 1:
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | |   (69)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.50  | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 240.86/47.50  | | | | |           & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 240.86/47.50  | | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.86/47.50  | | | | |           ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.86/47.50  | | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.86/47.50  | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.86/47.50  | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | | BETA: splitting (69) gives:
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | | Case 1:
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | |   (70)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.50  | | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 240.86/47.50  | | | | | |         & op(e2, e1) = e2 & op(e1, e2) = e2
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | | ALPHA: (70) implies:
% 240.86/47.50  | | | | | |   (71)   ~ (all_56_31 = e1)
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | | REDUCE: (18), (71) imply:
% 240.86/47.50  | | | | | |   (72)  $false
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | | CLOSE: (72) is inconsistent.
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | Case 2:
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | |   (73)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.50  | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.86/47.50  | | | | | |             e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 =
% 240.86/47.50  | | | | | |           e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.86/47.50  | | | | | |             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2,
% 240.86/47.50  | | | | | |             e0) = e2 & op(e0, e2) = e2)
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | | REF_CLOSE: (26), (28), (49), (51), (73) are inconsistent by
% 240.86/47.50  | | | | | |            sub-proof #2326.
% 240.86/47.50  | | | | | | 
% 240.86/47.50  | | | | | End of split
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | Case 2:
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | |   (74)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.50  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 240.86/47.50  | | | | |           & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 240.86/47.50  | | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.86/47.50  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.86/47.50  | | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.50  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.86/47.50  | | | | |           &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | | REF_CLOSE: (12), (18), (28), (39), (49), (74) are inconsistent by
% 240.86/47.50  | | | | |            sub-proof #2268.
% 240.86/47.50  | | | | | 
% 240.86/47.50  | | | | End of split
% 240.86/47.50  | | | | 
% 240.86/47.50  | | | End of split
% 240.86/47.50  | | | 
% 240.86/47.50  | | Case 2:
% 240.86/47.50  | | | 
% 240.86/47.50  | | |   (75)  all_54_5 = e1 | all_54_5 = e0
% 240.86/47.50  | | | 
% 240.86/47.50  | | | REF_CLOSE: (4), (21), (42), (75) are inconsistent by sub-proof #2300.
% 240.86/47.50  | | | 
% 240.86/47.50  | | End of split
% 240.86/47.50  | | 
% 240.86/47.50  | End of split
% 240.86/47.50  | 
% 240.86/47.50  End of proof
% 240.86/47.50  
% 240.86/47.50  Sub-proof #455 shows that the following formulas are inconsistent:
% 240.86/47.50  ----------------------------------------------------------------
% 240.86/47.50    (1)   ~ (all_52_1 = all_52_3)
% 240.86/47.50    (2)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.50         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.86/47.50    (3)  op(e0, e3) = all_52_3
% 240.86/47.50    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.86/47.50         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.86/47.50    (5)   ~ (all_52_12 = all_52_13)
% 240.86/47.50    (6)  op(e2, e1) = all_52_9
% 240.86/47.50    (7)   ~ (e3 = e2)
% 240.86/47.50    (8)  op(e0, e3) = e3
% 240.86/47.50    (9)  op(e3, e0) = all_52_12
% 240.86/47.50    (10)  op(e3, e0) = e3
% 240.86/47.50    (11)  op(e2, e3) = all_52_1
% 240.86/47.50    (12)   ~ (all_52_13 = e2)
% 240.86/47.50    (13)  all_58_5 = e1
% 240.86/47.50    (14)   ~ (all_52_9 = e3)
% 240.86/47.50    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.50    (16)  op(e2, e0) = all_52_13
% 240.86/47.50    (17)   ~ (all_52_1 = e2)
% 240.86/47.50    (18)   ~ (e2 = e1)
% 240.86/47.50  
% 240.86/47.50  Begin of proof
% 240.86/47.50  | 
% 240.86/47.50  | BETA: splitting (4) gives:
% 240.86/47.50  | 
% 240.86/47.50  | Case 1:
% 240.86/47.50  | | 
% 240.86/47.50  | |   (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 240.86/47.50  | |           e2)
% 240.86/47.50  | | 
% 240.86/47.50  | | BETA: splitting (19) gives:
% 240.86/47.50  | | 
% 240.86/47.50  | | Case 1:
% 240.86/47.50  | | | 
% 240.86/47.50  | | |   (20)  all_58_2 = e2 & op(e2, e3) = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | ALPHA: (20) implies:
% 240.86/47.50  | | |   (21)  op(e2, e3) = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | REF_CLOSE: (11), (15), (17), (21) are inconsistent by sub-proof #2336.
% 240.86/47.50  | | | 
% 240.86/47.50  | | Case 2:
% 240.86/47.50  | | | 
% 240.86/47.50  | | |   (22)  all_58_3 = e2 & op(e2, e2) = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | ALPHA: (22) implies:
% 240.86/47.50  | | |   (23)  op(e2, e2) = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (14), (15),
% 240.86/47.50  | | |            (16), (23) are inconsistent by sub-proof #469.
% 240.86/47.50  | | | 
% 240.86/47.50  | | End of split
% 240.86/47.50  | | 
% 240.86/47.50  | Case 2:
% 240.86/47.50  | | 
% 240.86/47.50  | |   (24)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 240.86/47.50  | |           e2)
% 240.86/47.50  | | 
% 240.86/47.50  | | BETA: splitting (24) gives:
% 240.86/47.50  | | 
% 240.86/47.50  | | Case 1:
% 240.86/47.50  | | | 
% 240.86/47.50  | | |   (25)  all_58_5 = e2 & op(e2, e1) = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | ALPHA: (25) implies:
% 240.86/47.50  | | |   (26)  all_58_5 = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | REF_CLOSE: (13), (18), (26) are inconsistent by sub-proof #1665.
% 240.86/47.50  | | | 
% 240.86/47.50  | | Case 2:
% 240.86/47.50  | | | 
% 240.86/47.50  | | |   (27)  all_58_10 = e2 & op(e2, e0) = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | ALPHA: (27) implies:
% 240.86/47.50  | | |   (28)  op(e2, e0) = e2
% 240.86/47.50  | | | 
% 240.86/47.50  | | | REF_CLOSE: (12), (15), (16), (28) are inconsistent by sub-proof #2317.
% 240.86/47.50  | | | 
% 240.86/47.50  | | End of split
% 240.86/47.50  | | 
% 240.86/47.50  | End of split
% 240.86/47.50  | 
% 240.86/47.50  End of proof
% 240.86/47.50  
% 240.86/47.50  Sub-proof #456 shows that the following formulas are inconsistent:
% 240.86/47.50  ----------------------------------------------------------------
% 240.86/47.50    (1)   ~ (all_52_7 = e2)
% 240.86/47.50    (2)  all_54_13 = all_52_7
% 240.86/47.50    (3)   ~ (all_52_7 = e1)
% 240.86/47.50    (4)  op(e3, e2) = all_52_4
% 240.86/47.50    (5)   ~ (all_52_7 = e0)
% 240.86/47.50    (6)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 240.86/47.50    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.50    (8)  op(e3, e2) = e3
% 240.86/47.50    (9)   ~ (all_52_4 = all_52_7)
% 240.86/47.50  
% 240.86/47.50  Begin of proof
% 240.86/47.50  | 
% 240.86/47.50  | BETA: splitting (6) gives:
% 240.86/47.50  | 
% 240.86/47.50  | Case 1:
% 240.86/47.50  | | 
% 240.86/47.50  | |   (10)  all_54_13 = e3
% 240.86/47.50  | | 
% 240.86/47.50  | | COMBINE_EQS: (2), (10) imply:
% 240.86/47.50  | |   (11)  all_52_7 = e3
% 240.86/47.50  | | 
% 240.86/47.50  | | REDUCE: (9), (11) imply:
% 240.86/47.51  | |   (12)   ~ (all_52_4 = e3)
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (4), (7), (8), (12) are inconsistent by sub-proof #2192.
% 240.86/47.51  | | 
% 240.86/47.51  | Case 2:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (13)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (1), (2), (3), (5), (13) are inconsistent by sub-proof #1648.
% 240.86/47.51  | | 
% 240.86/47.51  | End of split
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #457 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)   ~ (e3 = e0)
% 240.86/47.51    (2)  op(e1, e2) = all_52_6
% 240.86/47.51    (3)  op(e1, e0) = all_52_14
% 240.86/47.51    (4)   ~ (e3 = e1)
% 240.86/47.51    (5)  op(e1, e3) = e1
% 240.86/47.51    (6)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.86/47.51         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.86/47.51    (7)   ~ (all_52_14 = e3)
% 240.86/47.51    (8)   ~ (all_52_6 = e3)
% 240.86/47.51    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (10)  op(e1, e1) = e0
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | BETA: splitting (6) gives:
% 240.86/47.51  | 
% 240.86/47.51  | Case 1:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (11)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 240.86/47.51  | |           e3)
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (2), (4), (5), (8), (9), (11) are inconsistent by sub-proof
% 240.86/47.51  | |            #1969.
% 240.86/47.51  | | 
% 240.86/47.51  | Case 2:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (12)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 240.86/47.51  | |           e3)
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (1), (3), (7), (9), (10), (12) are inconsistent by sub-proof
% 240.86/47.51  | |            #1909.
% 240.86/47.51  | | 
% 240.86/47.51  | End of split
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #458 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (2)  op(e0, e1) = e2
% 240.86/47.51    (3)  op(e0, e1) = e0
% 240.86/47.51    (4)   ~ (e2 = e0)
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | GROUND_INST: instantiating (1) with e2, e0, e1, e0, simplifying with (2), (3)
% 240.86/47.51  |              gives:
% 240.86/47.51  |   (5)  e2 = e0
% 240.86/47.51  | 
% 240.86/47.51  | REDUCE: (4), (5) imply:
% 240.86/47.51  |   (6)  $false
% 240.86/47.51  | 
% 240.86/47.51  | CLOSE: (6) is inconsistent.
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #459 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)  all_54_6 = all_52_9
% 240.86/47.51    (2)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 240.86/47.51    (3)  op(e2, e0) = e0
% 240.86/47.51    (4)   ~ (all_52_9 = all_52_13)
% 240.86/47.51    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (6)  op(e2, e0) = all_52_13
% 240.86/47.51    (7)   ~ (all_52_9 = e1)
% 240.86/47.51    (8)   ~ (all_52_9 = e2)
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | BETA: splitting (2) gives:
% 240.86/47.51  | 
% 240.86/47.51  | Case 1:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (9)  all_54_6 = e2
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (1), (8), (9) are inconsistent by sub-proof #2247.
% 240.86/47.51  | | 
% 240.86/47.51  | Case 2:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (10)  all_54_6 = e1 | all_54_6 = e0
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10) are inconsistent by sub-proof
% 240.86/47.51  | |            #460.
% 240.86/47.51  | | 
% 240.86/47.51  | End of split
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #460 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)  all_54_6 = all_52_9
% 240.86/47.51    (2)  op(e2, e0) = e0
% 240.86/47.51    (3)   ~ (all_52_9 = all_52_13)
% 240.86/47.51    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (5)  all_54_6 = e1 | all_54_6 = e0
% 240.86/47.51    (6)  op(e2, e0) = all_52_13
% 240.86/47.51    (7)   ~ (all_52_9 = e1)
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | BETA: splitting (5) gives:
% 240.86/47.51  | 
% 240.86/47.51  | Case 1:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (8)  all_54_6 = e1
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (1), (7), (8) are inconsistent by sub-proof #2246.
% 240.86/47.51  | | 
% 240.86/47.51  | Case 2:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (9)  all_54_6 = e0
% 240.86/47.51  | | 
% 240.86/47.51  | | COMBINE_EQS: (1), (9) imply:
% 240.86/47.51  | |   (10)  all_52_9 = e0
% 240.86/47.51  | | 
% 240.86/47.51  | | SIMP: (10) implies:
% 240.86/47.51  | |   (11)  all_52_9 = e0
% 240.86/47.51  | | 
% 240.86/47.51  | | REDUCE: (3), (11) imply:
% 240.86/47.51  | |   (12)   ~ (all_52_13 = e0)
% 240.86/47.51  | | 
% 240.86/47.51  | | SIMP: (12) implies:
% 240.86/47.51  | |   (13)   ~ (all_52_13 = e0)
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (2), (4), (6), (13) are inconsistent by sub-proof #2324.
% 240.86/47.51  | | 
% 240.86/47.51  | End of split
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #461 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)   ~ (all_52_3 = e0)
% 240.86/47.51    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.86/47.51             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.86/47.51           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 240.86/47.51           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.86/47.51           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 240.86/47.51           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.51           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.86/47.51    (3)  op(e0, e3) = all_52_3
% 240.86/47.51    (4)   ~ (e3 = e2)
% 240.86/47.51    (5)  op(e3, e0) = e2
% 240.86/47.51    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (7)  all_56_21 = e3
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | BETA: splitting (2) gives:
% 240.86/47.51  | 
% 240.86/47.51  | Case 1:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (8)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.86/47.51  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.86/47.51  | |        op(e1, e3) = e1
% 240.86/47.51  | | 
% 240.86/47.51  | | ALPHA: (8) implies:
% 240.86/47.51  | |   (9)   ~ (all_56_21 = e3)
% 240.86/47.51  | | 
% 240.86/47.51  | | REDUCE: (7), (9) imply:
% 240.86/47.51  | |   (10)  $false
% 240.86/47.51  | | 
% 240.86/47.51  | | CLOSE: (10) is inconsistent.
% 240.86/47.51  | | 
% 240.86/47.51  | Case 2:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (11)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.86/47.51  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 240.86/47.51  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.51  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.51  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (1), (3), (4), (5), (6), (11) are inconsistent by sub-proof
% 240.86/47.51  | |            #1849.
% 240.86/47.51  | | 
% 240.86/47.51  | End of split
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #462 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)   ~ (all_52_3 = e0)
% 240.86/47.51    (2)   ~ (e3 = e0)
% 240.86/47.51    (3)  op(e0, e3) = all_52_3
% 240.86/47.51    (4)   ~ (e3 = e1)
% 240.86/47.51    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.86/47.51         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.86/47.51    (6)  op(e3, e2) = e2
% 240.86/47.51    (7)   ~ (e3 = e2)
% 240.86/47.51    (8)  op(e3, e1) = e1
% 240.86/47.51    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.86/47.51         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.86/47.51    (10)   ~ (all_52_1 = e0)
% 240.86/47.51    (11)  op(e2, e3) = all_52_1
% 240.86/47.51    (12)  op(e3, e0) = e2
% 240.86/47.51    (13)   ~ (all_52_2 = e0)
% 240.86/47.51    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (15)  op(e1, e3) = all_52_2
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | BETA: splitting (5) gives:
% 240.86/47.51  | 
% 240.86/47.51  | Case 1:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 240.86/47.51  | |           e3)
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (10), (11), (13), (14), (15), (16)
% 240.86/47.51  | |            are inconsistent by sub-proof #463.
% 240.86/47.51  | | 
% 240.86/47.51  | Case 2:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (17)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 240.86/47.51  | |           e3)
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (4), (7), (8), (12), (14), (17) are inconsistent by sub-proof
% 240.86/47.51  | |            #1792.
% 240.86/47.51  | | 
% 240.86/47.51  | End of split
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #463 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)   ~ (all_52_3 = e0)
% 240.86/47.51    (2)   ~ (e3 = e0)
% 240.86/47.51    (3)  op(e0, e3) = all_52_3
% 240.86/47.51    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 240.86/47.51    (5)  op(e3, e2) = e2
% 240.86/47.51    (6)   ~ (e3 = e2)
% 240.86/47.51    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.86/47.51         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.86/47.51    (8)   ~ (all_52_1 = e0)
% 240.86/47.51    (9)  op(e2, e3) = all_52_1
% 240.86/47.51    (10)   ~ (all_52_2 = e0)
% 240.86/47.51    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (12)  op(e1, e3) = all_52_2
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | BETA: splitting (4) gives:
% 240.86/47.51  | 
% 240.86/47.51  | Case 1:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (13)  all_58_0 = e3 & op(e3, e3) = e3
% 240.86/47.51  | | 
% 240.86/47.51  | | ALPHA: (13) implies:
% 240.86/47.51  | |   (14)  op(e3, e3) = e3
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (11), (12), (14) are
% 240.86/47.51  | |            inconsistent by sub-proof #1938.
% 240.86/47.51  | | 
% 240.86/47.51  | Case 2:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (15)  all_58_1 = e3 & op(e3, e2) = e3
% 240.86/47.51  | | 
% 240.86/47.51  | | ALPHA: (15) implies:
% 240.86/47.51  | |   (16)  op(e3, e2) = e3
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (5), (6), (11), (16) are inconsistent by sub-proof #2193.
% 240.86/47.51  | | 
% 240.86/47.51  | End of split
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #464 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)  op(e2, e1) = all_52_9
% 240.86/47.51    (2)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2)
% 240.86/47.51    (3)  all_58_4 = e1
% 240.86/47.51    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (5)   ~ (e2 = e1)
% 240.86/47.51    (6)   ~ (all_52_9 = e2)
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | BETA: splitting (2) gives:
% 240.86/47.51  | 
% 240.86/47.51  | Case 1:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (7)  all_58_4 = e2 & op(e3, e1) = e2
% 240.86/47.51  | | 
% 240.86/47.51  | | ALPHA: (7) implies:
% 240.86/47.51  | |   (8)  all_58_4 = e2
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #1786.
% 240.86/47.51  | | 
% 240.86/47.51  | Case 2:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (9)  all_58_5 = e2 & op(e2, e1) = e2
% 240.86/47.51  | | 
% 240.86/47.51  | | ALPHA: (9) implies:
% 240.86/47.51  | |   (10)  op(e2, e1) = e2
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #2328.
% 240.86/47.51  | | 
% 240.86/47.51  | End of split
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #465 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)   ~ (all_52_3 = e0)
% 240.86/47.51    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.86/47.51             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.86/47.51           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 240.86/47.51           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.86/47.51           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 240.86/47.51           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.51           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.86/47.51    (3)  op(e0, e3) = all_52_3
% 240.86/47.51    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (5)  all_56_21 = e3
% 240.86/47.51    (6)  all_56_1 = e0
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | BETA: splitting (2) gives:
% 240.86/47.51  | 
% 240.86/47.51  | Case 1:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (7)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.86/47.51  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.86/47.51  | |        op(e1, e3) = e1
% 240.86/47.51  | | 
% 240.86/47.51  | | ALPHA: (7) implies:
% 240.86/47.51  | |   (8)   ~ (all_56_21 = e3)
% 240.86/47.51  | | 
% 240.86/47.51  | | REDUCE: (5), (8) imply:
% 240.86/47.51  | |   (9)  $false
% 240.86/47.51  | | 
% 240.86/47.51  | | CLOSE: (9) is inconsistent.
% 240.86/47.51  | | 
% 240.86/47.51  | Case 2:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.86/47.51  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 240.86/47.51  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.51  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.51  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (1), (3), (4), (6), (10) are inconsistent by sub-proof #1829.
% 240.86/47.51  | | 
% 240.86/47.51  | End of split
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #466 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.86/47.51         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.86/47.51    (2)   ~ (e3 = e0)
% 240.86/47.51    (3)  op(e0, e1) = all_52_11
% 240.86/47.51    (4)  op(e0, e3) = all_52_3
% 240.86/47.51    (5)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) = all_22_1
% 240.86/47.51           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1) =
% 240.86/47.51           all_22_1 & $i(all_22_1))
% 240.86/47.51    (6)   ~ (all_52_11 = e3)
% 240.86/47.51    (7)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 240.86/47.51           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 240.86/47.51           all_30_1 & $i(all_30_1))
% 240.86/47.51    (8)   ~ (all_52_3 = e3)
% 240.86/47.51    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (10)  op(e0, e0) = e0
% 240.86/47.51    (11)  all_30_1 = e0
% 240.86/47.51    (12)  op(e2, e1) = all_30_1
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | REDUCE: (11), (12) imply:
% 240.86/47.51  |   (13)  op(e2, e1) = e0
% 240.86/47.51  | 
% 240.86/47.51  | BETA: splitting (1) gives:
% 240.86/47.51  | 
% 240.86/47.51  | Case 1:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (14)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 240.86/47.51  | |           e3)
% 240.86/47.51  | | 
% 240.86/47.51  | | BETA: splitting (14) gives:
% 240.86/47.51  | | 
% 240.86/47.51  | | Case 1:
% 240.86/47.51  | | | 
% 240.86/47.51  | | |   (15)  all_58_12 = e3 & op(e0, e3) = e3
% 240.86/47.51  | | | 
% 240.86/47.51  | | | ALPHA: (15) implies:
% 240.86/47.51  | | |   (16)  op(e0, e3) = e3
% 240.86/47.51  | | | 
% 240.86/47.51  | | | REF_CLOSE: (4), (8), (9), (16) are inconsistent by sub-proof #2332.
% 240.86/47.51  | | | 
% 240.86/47.51  | | Case 2:
% 240.86/47.51  | | | 
% 240.86/47.51  | | |   (17)  all_58_13 = e3 & op(e0, e2) = e3
% 240.86/47.51  | | | 
% 240.86/47.51  | | | ALPHA: (17) implies:
% 240.86/47.51  | | |   (18)  op(e0, e2) = e3
% 240.86/47.51  | | | 
% 240.86/47.51  | | | REF_CLOSE: (5), (7), (9), (13), (18) are inconsistent by sub-proof #1110.
% 240.86/47.51  | | | 
% 240.86/47.51  | | End of split
% 240.86/47.51  | | 
% 240.86/47.51  | Case 2:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (19)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 240.86/47.51  | |           e3)
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (2), (3), (6), (9), (10), (19) are inconsistent by sub-proof
% 240.86/47.51  | |            #1580.
% 240.86/47.51  | | 
% 240.86/47.51  | End of split
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #467 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 240.86/47.51    (2)  op(e0, e1) = all_52_11
% 240.86/47.51    (3)   ~ (all_52_11 = e1)
% 240.86/47.51    (4)   ~ (e3 = e1)
% 240.86/47.51    (5)  op(e1, e1) = e3
% 240.86/47.51    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | BETA: splitting (1) gives:
% 240.86/47.51  | 
% 240.86/47.51  | Case 1:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (7)  all_58_8 = e1 & op(e1, e1) = e1
% 240.86/47.51  | | 
% 240.86/47.51  | | ALPHA: (7) implies:
% 240.86/47.51  | |   (8)  op(e1, e1) = e1
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #468.
% 240.86/47.51  | | 
% 240.86/47.51  | Case 2:
% 240.86/47.51  | | 
% 240.86/47.51  | |   (9)  all_58_14 = e1 & op(e0, e1) = e1
% 240.86/47.51  | | 
% 240.86/47.51  | | ALPHA: (9) implies:
% 240.86/47.51  | |   (10)  op(e0, e1) = e1
% 240.86/47.51  | | 
% 240.86/47.51  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #2272.
% 240.86/47.51  | | 
% 240.86/47.51  | End of split
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #468 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (2)  op(e1, e1) = e3
% 240.86/47.51    (3)  op(e1, e1) = e1
% 240.86/47.51    (4)   ~ (e3 = e1)
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | GROUND_INST: instantiating (1) with e3, e1, e1, e1, simplifying with (2), (3)
% 240.86/47.51  |              gives:
% 240.86/47.51  |   (5)  e3 = e1
% 240.86/47.51  | 
% 240.86/47.51  | REDUCE: (4), (5) imply:
% 240.86/47.51  |   (6)  $false
% 240.86/47.51  | 
% 240.86/47.51  | CLOSE: (6) is inconsistent.
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #469 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)   ~ (all_52_1 = all_52_3)
% 240.86/47.51    (2)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.51         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.86/47.51    (3)  op(e0, e3) = all_52_3
% 240.86/47.51    (4)   ~ (all_52_12 = all_52_13)
% 240.86/47.51    (5)  op(e2, e1) = all_52_9
% 240.86/47.51    (6)   ~ (e3 = e2)
% 240.86/47.51    (7)  op(e0, e3) = e3
% 240.86/47.51    (8)  op(e3, e0) = all_52_12
% 240.86/47.51    (9)  op(e3, e0) = e3
% 240.86/47.51    (10)  op(e2, e3) = all_52_1
% 240.86/47.51    (11)   ~ (all_52_9 = e3)
% 240.86/47.51    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.51    (13)  op(e2, e0) = all_52_13
% 240.86/47.51    (14)  op(e2, e2) = e2
% 240.86/47.51  
% 240.86/47.51  Begin of proof
% 240.86/47.51  | 
% 240.86/47.51  | GROUND_INST: instantiating (12) with all_52_3, e3, e3, e0, simplifying with
% 240.86/47.51  |              (3), (7) gives:
% 240.86/47.51  |   (15)  all_52_3 = e3
% 240.86/47.51  | 
% 240.86/47.51  | GROUND_INST: instantiating (12) with all_52_12, e3, e0, e3, simplifying with
% 240.86/47.51  |              (8), (9) gives:
% 240.86/47.51  |   (16)  all_52_12 = e3
% 240.86/47.51  | 
% 240.86/47.51  | REDUCE: (1), (15) imply:
% 240.86/47.51  |   (17)   ~ (all_52_1 = e3)
% 240.86/47.51  | 
% 240.86/47.51  | REDUCE: (4), (16) imply:
% 240.86/47.51  |   (18)   ~ (all_52_13 = e3)
% 240.86/47.51  | 
% 240.86/47.51  | SIMP: (18) implies:
% 240.86/47.51  |   (19)   ~ (all_52_13 = e3)
% 240.86/47.51  | 
% 240.86/47.51  | REF_CLOSE: (2), (5), (6), (10), (11), (12), (13), (14), (17), (19) are
% 240.86/47.51  |            inconsistent by sub-proof #1321.
% 240.86/47.51  | 
% 240.86/47.51  End of proof
% 240.86/47.51  
% 240.86/47.51  Sub-proof #470 shows that the following formulas are inconsistent:
% 240.86/47.51  ----------------------------------------------------------------
% 240.86/47.51    (1)   ~ (all_52_4 = all_10_2)
% 240.86/47.51    (2)   ~ (all_52_1 = all_52_3)
% 240.86/47.51    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.86/47.51    (4)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 240.86/47.52    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.86/47.52         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.86/47.52    (6)   ~ (e3 = e0)
% 240.86/47.52    (7)  op(e0, e1) = all_52_11
% 240.86/47.52    (8)   ~ (all_52_8 = all_52_9)
% 240.86/47.52    (9)   ~ (e2 = e0)
% 240.86/47.52    (10)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.52          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.86/47.52    (11)  op(e1, e2) = all_52_6
% 240.86/47.52    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.52              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.52            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.86/47.52            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.52            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.86/47.52             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.52            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.86/47.52            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.52            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.86/47.52            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.52            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.86/47.52              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.52            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.52            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.86/47.52            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.52            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.86/47.52            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.52            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.86/47.52              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.86/47.52            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.52            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.86/47.52            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.52            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.86/47.52            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.52            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.86/47.52              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.52            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.52            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.52    (13)   ~ (all_10_2 = e0)
% 240.86/47.52    (14)   ~ (all_52_1 = all_52_2)
% 240.86/47.52    (15)  op(e1, e0) = all_52_14
% 240.86/47.52    (16)   ~ (all_52_13 = e1)
% 240.86/47.52    (17)   ~ (all_52_8 = all_10_2)
% 240.86/47.52    (18)  op(e0, e3) = all_52_3
% 240.86/47.52    (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.86/47.52          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.86/47.52    (20)   ~ (all_52_1 = all_10_2)
% 240.86/47.52    (21)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 &
% 240.86/47.52            op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 240.86/47.52              e2) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.86/47.52    (22)   ~ (all_52_2 = all_52_3)
% 240.86/47.52    (23)  all_54_6 = all_52_9
% 240.86/47.52    (24)   ~ (all_52_12 = all_52_13)
% 240.86/47.52    (25)   ~ (all_52_3 = all_10_2)
% 240.86/47.52    (26)  ( ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 240.86/47.52            $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e1, e3) = all_6_1
% 240.86/47.52            & $i(all_6_1))
% 240.86/47.52    (27)   ~ (all_52_2 = all_52_14)
% 240.86/47.52    (28)   ~ (all_52_1 = all_52_9)
% 240.86/47.52    (29)   ~ (all_52_3 = all_52_7)
% 240.86/47.52    (30)  all_54_4 = all_52_1
% 240.86/47.52    (31)   ~ (all_52_11 = e3)
% 240.86/47.52    (32)  op(e3, e1) = all_52_8
% 240.86/47.52    (33)  op(e2, e1) = all_52_9
% 240.86/47.52    (34)   ~ (e3 = e2)
% 240.86/47.52    (35)   ~ (all_52_12 = all_10_2)
% 240.86/47.52    (36)  op(e3, e1) = e1
% 240.86/47.52    (37)  op(e1, e3) = e1
% 240.86/47.52    (38)  all_56_31 = e1
% 240.86/47.52    (39)  all_54_12 = all_52_3
% 240.86/47.52    (40)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.86/47.52    (41)  all_58_15 = e1
% 240.86/47.52    (42)  op(e3, e0) = all_52_12
% 240.86/47.52    (43)   ~ (all_52_9 = all_52_13)
% 240.86/47.52    (44)  all_24_2 = all_10_2
% 240.86/47.52    (45)  all_46_2 = e3
% 240.86/47.52    (46)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 240.86/47.52    (47)  op(e2, e3) = all_52_1
% 240.86/47.52    (48)  op(e1, e1) = e3
% 240.86/47.52    (49)   ~ (all_52_6 = e3)
% 240.86/47.52    (50)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 240.86/47.52    (51)   ~ (all_52_1 = all_52_13)
% 240.86/47.52    (52)  all_54_7 = all_52_13
% 240.86/47.52    (53)  op(e0, e2) = all_52_7
% 240.86/47.52    (54)  op(e3, e2) = all_52_4
% 240.86/47.52    (55)   ~ (all_52_9 = e3)
% 240.86/47.52    (56)  all_56_1 = all_10_2
% 240.86/47.52    (57)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.86/47.52          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.86/47.52    (58)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.52    (59)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.86/47.52          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.86/47.52    (60)  op(e1, e3) = all_52_2
% 240.86/47.52    (61)  all_56_21 = e3
% 240.86/47.52    (62)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.52          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.86/47.52    (63)   ~ (e1 = e0)
% 240.86/47.52    (64)  op(e2, e0) = all_52_13
% 240.86/47.52    (65)  all_54_0 = all_10_2
% 240.86/47.52    (66)   ~ (all_24_2 = e2) | ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 240.86/47.52            op(e3, e2) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 240.86/47.52              e1) & op(e3, e2) = all_24_1 & $i(all_24_1))
% 240.86/47.52    (67)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.86/47.52          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.86/47.52    (68)   ~ (e2 = e1)
% 240.86/47.52    (69)   ~ (all_52_8 = e3)
% 240.86/47.52  
% 240.86/47.52  Begin of proof
% 240.86/47.52  | 
% 240.86/47.52  | GROUND_INST: instantiating (58) with all_52_2, e1, e3, e1, simplifying with
% 240.86/47.52  |              (37), (60) gives:
% 240.86/47.52  |   (70)  all_52_2 = e1
% 240.86/47.52  | 
% 240.86/47.52  | GROUND_INST: instantiating (58) with all_52_8, e1, e1, e3, simplifying with
% 240.86/47.52  |              (32), (36) gives:
% 240.86/47.52  |   (71)  all_52_8 = e1
% 240.86/47.52  | 
% 240.86/47.52  | REDUCE: (14), (70) imply:
% 240.86/47.52  |   (72)   ~ (all_52_1 = e1)
% 240.86/47.52  | 
% 240.86/47.52  | REDUCE: (22), (70) imply:
% 240.86/47.52  |   (73)   ~ (all_52_3 = e1)
% 240.86/47.52  | 
% 240.86/47.52  | SIMP: (73) implies:
% 240.86/47.52  |   (74)   ~ (all_52_3 = e1)
% 240.86/47.52  | 
% 240.86/47.52  | REDUCE: (27), (70) imply:
% 240.86/47.52  |   (75)   ~ (all_52_14 = e1)
% 240.86/47.52  | 
% 240.86/47.52  | SIMP: (75) implies:
% 240.86/47.52  |   (76)   ~ (all_52_14 = e1)
% 240.86/47.52  | 
% 240.86/47.52  | REDUCE: (8), (71) imply:
% 240.86/47.52  |   (77)   ~ (all_52_9 = e1)
% 240.86/47.52  | 
% 240.86/47.52  | SIMP: (77) implies:
% 240.86/47.52  |   (78)   ~ (all_52_9 = e1)
% 240.86/47.52  | 
% 240.86/47.52  | REDUCE: (17), (71) imply:
% 240.86/47.52  |   (79)   ~ (all_10_2 = e1)
% 240.86/47.52  | 
% 240.86/47.52  | SIMP: (79) implies:
% 240.86/47.52  |   (80)   ~ (all_10_2 = e1)
% 240.86/47.52  | 
% 240.86/47.52  | REDUCE: (69), (71) imply:
% 240.86/47.52  |   (81)   ~ (e3 = e1)
% 240.86/47.52  | 
% 240.86/47.52  | SIMP: (81) implies:
% 240.86/47.52  |   (82)   ~ (e3 = e1)
% 240.86/47.52  | 
% 240.86/47.52  | BETA: splitting (26) gives:
% 240.86/47.52  | 
% 240.86/47.52  | Case 1:
% 240.86/47.52  | | 
% 240.86/47.52  | |   (83)   ~ (all_6_0 = e2) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1
% 240.86/47.52  | |         & $i(all_6_0) & $i(all_6_1)
% 240.86/47.52  | | 
% 240.86/47.52  | | ALPHA: (83) implies:
% 240.86/47.52  | |   (84)  op(e1, e3) = all_6_1
% 240.86/47.52  | | 
% 240.86/47.52  | | BETA: splitting (21) gives:
% 240.86/47.52  | | 
% 240.86/47.52  | | Case 1:
% 240.86/47.52  | | | 
% 240.86/47.52  | | |   (85)   ~ (all_46_2 = e3)
% 240.86/47.52  | | | 
% 240.86/47.52  | | | REDUCE: (45), (85) imply:
% 240.86/47.52  | | |   (86)  $false
% 240.86/47.52  | | | 
% 240.86/47.52  | | | CLOSE: (86) is inconsistent.
% 240.86/47.52  | | | 
% 240.86/47.52  | | Case 2:
% 240.86/47.52  | | | 
% 240.86/47.52  | | |   (87)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.86/47.52  | | |           all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) &
% 240.86/47.52  | | |           op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.86/47.52  | | | 
% 240.86/47.52  | | | GROUND_INST: instantiating (58) with e1, all_6_1, e3, e1, simplifying with
% 240.86/47.52  | | |              (37), (84) gives:
% 240.86/47.52  | | |   (88)  all_6_1 = e1
% 240.86/47.52  | | | 
% 240.86/47.52  | | | BETA: splitting (87) gives:
% 240.86/47.52  | | | 
% 240.86/47.52  | | | Case 1:
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | |   (89)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.86/47.52  | | | |         all_46_1 & $i(all_46_0) & $i(all_46_1)
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | | ALPHA: (89) implies:
% 240.86/47.52  | | | |   (90)   ~ (all_46_0 = e0)
% 240.86/47.52  | | | |   (91)  op(e1, e3) = all_46_1
% 240.86/47.52  | | | |   (92)  op(all_46_1, e1) = all_46_0
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13),
% 240.86/47.52  | | | |            (15), (16), (18), (19), (20), (23), (24), (25), (28), (29),
% 240.86/47.52  | | | |            (30), (31), (33), (34), (35), (37), (38), (39), (40), (41),
% 240.86/47.52  | | | |            (42), (43), (44), (46), (47), (48), (49), (50), (51), (52),
% 240.86/47.52  | | | |            (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 240.86/47.52  | | | |            (64), (65), (66), (67), (68), (72), (74), (76), (78), (80),
% 240.86/47.52  | | | |            (82), (90), (91), (92) are inconsistent by sub-proof #472.
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | Case 2:
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | |   (93)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | | ALPHA: (93) implies:
% 240.86/47.52  | | | |   (94)   ~ (all_46_1 = e2)
% 240.86/47.52  | | | |   (95)  op(e1, e3) = all_46_1
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 240.86/47.52  | | | |            (13), (15), (16), (18), (19), (20), (23), (24), (25), (28),
% 240.86/47.52  | | | |            (29), (30), (31), (33), (34), (35), (37), (38), (39), (40),
% 240.86/47.52  | | | |            (41), (42), (43), (44), (46), (47), (49), (50), (51), (52),
% 240.86/47.52  | | | |            (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 240.86/47.52  | | | |            (64), (65), (66), (67), (72), (74), (76), (78), (80), (82),
% 240.86/47.52  | | | |            (94), (95) are inconsistent by sub-proof #471.
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | End of split
% 240.86/47.52  | | | 
% 240.86/47.52  | | End of split
% 240.86/47.52  | | 
% 240.86/47.52  | Case 2:
% 240.86/47.52  | | 
% 240.86/47.52  | |   (96)   ~ (all_6_1 = e0) & op(e1, e3) = all_6_1 & $i(all_6_1)
% 240.86/47.52  | | 
% 240.86/47.52  | | ALPHA: (96) implies:
% 240.86/47.52  | |   (97)   ~ (all_6_1 = e0)
% 240.86/47.52  | |   (98)  op(e1, e3) = all_6_1
% 240.86/47.52  | | 
% 240.86/47.52  | | BETA: splitting (21) gives:
% 240.86/47.52  | | 
% 240.86/47.52  | | Case 1:
% 240.86/47.52  | | | 
% 240.86/47.52  | | |   (99)   ~ (all_46_2 = e3)
% 240.86/47.52  | | | 
% 240.86/47.52  | | | REDUCE: (45), (99) imply:
% 240.86/47.52  | | |   (100)  $false
% 240.86/47.52  | | | 
% 240.86/47.52  | | | CLOSE: (100) is inconsistent.
% 240.86/47.52  | | | 
% 240.86/47.52  | | Case 2:
% 240.86/47.52  | | | 
% 240.86/47.52  | | |   (101)  ( ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.86/47.52  | | |            all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) &
% 240.86/47.52  | | |            op(e1, e3) = all_46_1 & $i(all_46_1))
% 240.86/47.52  | | | 
% 240.86/47.52  | | | GROUND_INST: instantiating (58) with e1, all_6_1, e3, e1, simplifying with
% 240.86/47.52  | | |              (37), (98) gives:
% 240.86/47.52  | | |   (102)  all_6_1 = e1
% 240.86/47.52  | | | 
% 240.86/47.52  | | | BETA: splitting (101) gives:
% 240.86/47.52  | | | 
% 240.86/47.52  | | | Case 1:
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | |   (103)   ~ (all_46_0 = e0) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 240.86/47.52  | | | |          all_46_1 & $i(all_46_0) & $i(all_46_1)
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | | ALPHA: (103) implies:
% 240.86/47.52  | | | |   (104)   ~ (all_46_0 = e0)
% 240.86/47.52  | | | |   (105)  op(e1, e3) = all_46_1
% 240.86/47.52  | | | |   (106)  op(all_46_1, e1) = all_46_0
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13),
% 240.86/47.52  | | | |            (15), (16), (18), (19), (20), (23), (24), (25), (28), (29),
% 240.86/47.52  | | | |            (30), (31), (33), (34), (35), (37), (38), (39), (40), (41),
% 240.86/47.52  | | | |            (42), (43), (44), (46), (47), (48), (49), (50), (51), (52),
% 240.86/47.52  | | | |            (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 240.86/47.52  | | | |            (64), (65), (66), (67), (68), (72), (74), (76), (78), (80),
% 240.86/47.52  | | | |            (82), (104), (105), (106) are inconsistent by sub-proof #472.
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | Case 2:
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | |   (107)   ~ (all_46_1 = e2) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | | ALPHA: (107) implies:
% 240.86/47.52  | | | |   (108)   ~ (all_46_1 = e2)
% 240.86/47.52  | | | |   (109)  op(e1, e3) = all_46_1
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 240.86/47.52  | | | |            (13), (15), (16), (18), (19), (20), (23), (24), (25), (28),
% 240.86/47.52  | | | |            (29), (30), (31), (33), (34), (35), (37), (38), (39), (40),
% 240.86/47.52  | | | |            (41), (42), (43), (44), (46), (47), (49), (50), (51), (52),
% 240.86/47.52  | | | |            (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 240.86/47.52  | | | |            (64), (65), (66), (67), (72), (74), (76), (78), (80), (82),
% 240.86/47.52  | | | |            (108), (109) are inconsistent by sub-proof #471.
% 240.86/47.52  | | | | 
% 240.86/47.52  | | | End of split
% 240.86/47.52  | | | 
% 240.86/47.52  | | End of split
% 240.86/47.52  | | 
% 240.86/47.52  | End of split
% 240.86/47.52  | 
% 240.86/47.52  End of proof
% 240.86/47.52  
% 240.86/47.52  Sub-proof #471 shows that the following formulas are inconsistent:
% 240.86/47.52  ----------------------------------------------------------------
% 240.86/47.52    (1)   ~ (all_52_4 = all_10_2)
% 240.86/47.52    (2)   ~ (all_52_1 = all_52_3)
% 240.86/47.52    (3)   ~ (all_46_1 = e2)
% 240.86/47.52    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.86/47.52    (5)   ~ (all_52_3 = e1)
% 240.86/47.53    (6)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 240.86/47.53    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.86/47.53         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.86/47.53    (8)   ~ (e3 = e0)
% 240.86/47.53    (9)  op(e0, e1) = all_52_11
% 240.86/47.53    (10)   ~ (e2 = e0)
% 240.86/47.53    (11)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.53          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.86/47.53    (12)  op(e1, e2) = all_52_6
% 240.86/47.53    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.53              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.53            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.86/47.53            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.53            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.86/47.53             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.53            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.86/47.53            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.53            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.86/47.53            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.53            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.86/47.53              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.53            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.53            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.86/47.53            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.53            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.86/47.53            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.53            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.86/47.53              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.86/47.53            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.53            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.86/47.53            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.53            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.86/47.53            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.53            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.86/47.53              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.53            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.53            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.53    (14)   ~ (all_10_2 = e0)
% 240.86/47.53    (15)  op(e1, e0) = all_52_14
% 240.86/47.53    (16)   ~ (all_52_13 = e1)
% 240.86/47.53    (17)   ~ (all_10_2 = e1)
% 240.86/47.53    (18)  op(e0, e3) = all_52_3
% 240.86/47.53    (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.86/47.53          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.86/47.53    (20)   ~ (all_52_1 = all_10_2)
% 240.86/47.53    (21)   ~ (e3 = e1)
% 240.86/47.53    (22)  all_54_6 = all_52_9
% 240.86/47.53    (23)   ~ (all_52_12 = all_52_13)
% 240.86/47.53    (24)   ~ (all_52_3 = all_10_2)
% 240.86/47.53    (25)   ~ (all_52_1 = all_52_9)
% 240.86/47.53    (26)   ~ (all_52_3 = all_52_7)
% 240.86/47.53    (27)  all_54_4 = all_52_1
% 240.86/47.53    (28)   ~ (all_52_11 = e3)
% 240.86/47.53    (29)  op(e2, e1) = all_52_9
% 240.86/47.53    (30)   ~ (e3 = e2)
% 240.86/47.53    (31)   ~ (all_52_12 = all_10_2)
% 240.86/47.53    (32)   ~ (all_52_14 = e1)
% 240.86/47.53    (33)  op(e1, e3) = e1
% 240.86/47.53    (34)  all_56_31 = e1
% 240.86/47.53    (35)  all_54_12 = all_52_3
% 240.86/47.53    (36)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.86/47.53    (37)  all_58_15 = e1
% 240.86/47.53    (38)  op(e3, e0) = all_52_12
% 240.86/47.53    (39)   ~ (all_52_9 = all_52_13)
% 240.86/47.53    (40)  op(e1, e3) = all_46_1
% 240.86/47.53    (41)  all_24_2 = all_10_2
% 240.86/47.53    (42)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 240.86/47.53    (43)  op(e2, e3) = all_52_1
% 240.86/47.53    (44)   ~ (all_52_6 = e3)
% 240.86/47.53    (45)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 240.86/47.53    (46)   ~ (all_52_1 = all_52_13)
% 240.86/47.53    (47)  all_54_7 = all_52_13
% 240.86/47.53    (48)  op(e0, e2) = all_52_7
% 240.86/47.53    (49)  op(e3, e2) = all_52_4
% 240.86/47.53    (50)   ~ (all_52_9 = e3)
% 240.86/47.53    (51)  all_56_1 = all_10_2
% 240.86/47.53    (52)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.86/47.53          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.86/47.53    (53)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.53            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.53    (54)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.86/47.53          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.86/47.53    (55)  all_56_21 = e3
% 240.86/47.53    (56)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.53          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.86/47.53    (57)   ~ (e1 = e0)
% 240.86/47.53    (58)  op(e2, e0) = all_52_13
% 240.86/47.53    (59)  all_54_0 = all_10_2
% 240.86/47.53    (60)   ~ (all_52_9 = e1)
% 240.86/47.53    (61)   ~ (all_24_2 = e2) | ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 240.86/47.53            op(e3, e2) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 240.86/47.53              e1) & op(e3, e2) = all_24_1 & $i(all_24_1))
% 240.86/47.53    (62)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.86/47.53          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.86/47.53    (63)   ~ (all_52_1 = e1)
% 240.86/47.53  
% 240.86/47.53  Begin of proof
% 240.86/47.53  | 
% 240.86/47.53  | GROUND_INST: instantiating (53) with e1, all_46_1, e3, e1, simplifying with
% 240.86/47.53  |              (33), (40) gives:
% 240.86/47.53  |   (64)  all_46_1 = e1
% 240.86/47.53  | 
% 240.86/47.53  | REDUCE: (3), (64) imply:
% 240.86/47.53  |   (65)   ~ (e2 = e1)
% 240.86/47.53  | 
% 240.86/47.53  | SIMP: (65) implies:
% 240.86/47.53  |   (66)   ~ (e2 = e1)
% 240.86/47.53  | 
% 240.86/47.53  | BETA: splitting (61) gives:
% 240.86/47.53  | 
% 240.86/47.53  | Case 1:
% 240.86/47.53  | | 
% 240.86/47.53  | |   (67)   ~ (all_24_2 = e2)
% 240.86/47.53  | | 
% 240.86/47.53  | | REDUCE: (41), (67) imply:
% 240.86/47.53  | |   (68)   ~ (all_10_2 = e2)
% 240.86/47.53  | | 
% 240.86/47.53  | | REF_CLOSE: (1), (6), (10), (11), (12), (13), (14), (15), (16), (17), (18),
% 240.86/47.53  | |            (19), (20), (26), (29), (32), (33), (34), (43), (44), (46), (48),
% 240.86/47.53  | |            (49), (50), (52), (53), (55), (56), (57), (58), (59), (60), (62),
% 240.86/47.53  | |            (63), (66), (68) are inconsistent by sub-proof #480.
% 240.86/47.53  | | 
% 240.86/47.53  | Case 2:
% 240.86/47.53  | | 
% 240.86/47.53  | |   (69)  all_24_2 = e2
% 240.86/47.53  | | 
% 240.86/47.53  | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (11), (12), (13), (14), (15), (16),
% 240.86/47.53  | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 240.86/47.53  | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 240.86/47.53  | |            (39), (41), (42), (43), (44), (45), (46), (47), (48), (50), (51),
% 240.86/47.53  | |            (52), (53), (54), (55), (56), (57), (58), (60), (62), (63), (69)
% 240.86/47.53  | |            are inconsistent by sub-proof #473.
% 240.86/47.53  | | 
% 240.86/47.53  | End of split
% 240.86/47.53  | 
% 240.86/47.53  End of proof
% 240.86/47.53  
% 240.86/47.53  Sub-proof #472 shows that the following formulas are inconsistent:
% 240.86/47.53  ----------------------------------------------------------------
% 240.86/47.53    (1)   ~ (all_52_4 = all_10_2)
% 240.86/47.53    (2)   ~ (all_52_1 = all_52_3)
% 240.86/47.53    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.86/47.53    (4)   ~ (all_52_3 = e1)
% 240.86/47.53    (5)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 240.86/47.53    (6)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.86/47.53         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.86/47.53    (7)  op(e0, e1) = all_52_11
% 240.86/47.53    (8)   ~ (e2 = e0)
% 240.86/47.53    (9)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.53         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.86/47.53    (10)  op(e1, e2) = all_52_6
% 240.86/47.53    (11)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.53              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.53            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.86/47.53            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.53            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.86/47.53             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.53            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.86/47.53            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.53            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.86/47.53            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.53            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.86/47.53              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.53            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.53            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.86/47.53            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.53            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.86/47.53            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.53            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.86/47.53              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.86/47.53            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.53            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.86/47.53            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.53            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.86/47.53            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.53            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.86/47.53              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.53            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.53            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.53    (12)   ~ (all_10_2 = e0)
% 240.86/47.53    (13)  op(e1, e0) = all_52_14
% 240.86/47.53    (14)   ~ (all_52_13 = e1)
% 240.86/47.53    (15)   ~ (all_46_0 = e0)
% 240.86/47.53    (16)   ~ (all_10_2 = e1)
% 240.86/47.53    (17)  op(e0, e3) = all_52_3
% 240.86/47.53    (18)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.86/47.53          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.86/47.53    (19)   ~ (all_52_1 = all_10_2)
% 240.86/47.53    (20)   ~ (e3 = e1)
% 240.86/47.53    (21)  all_54_6 = all_52_9
% 240.86/47.53    (22)   ~ (all_52_12 = all_52_13)
% 240.86/47.53    (23)   ~ (all_52_3 = all_10_2)
% 240.86/47.53    (24)   ~ (all_52_1 = all_52_9)
% 240.86/47.53    (25)   ~ (all_52_3 = all_52_7)
% 240.86/47.53    (26)  all_54_4 = all_52_1
% 240.86/47.53    (27)   ~ (all_52_11 = e3)
% 240.86/47.53    (28)  op(e2, e1) = all_52_9
% 240.86/47.53    (29)   ~ (e3 = e2)
% 240.86/47.53    (30)   ~ (all_52_12 = all_10_2)
% 240.86/47.53    (31)   ~ (all_52_14 = e1)
% 240.86/47.53    (32)  op(e1, e3) = e1
% 240.86/47.53    (33)  all_56_31 = e1
% 240.86/47.53    (34)  all_54_12 = all_52_3
% 240.86/47.53    (35)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.86/47.53    (36)  all_58_15 = e1
% 240.86/47.53    (37)  op(e3, e0) = all_52_12
% 240.86/47.53    (38)   ~ (all_52_9 = all_52_13)
% 240.86/47.53    (39)  op(all_46_1, e1) = all_46_0
% 240.86/47.53    (40)  op(e1, e3) = all_46_1
% 240.86/47.53    (41)  all_24_2 = all_10_2
% 240.86/47.53    (42)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 240.86/47.53    (43)  op(e2, e3) = all_52_1
% 240.86/47.53    (44)  op(e1, e1) = e3
% 240.86/47.53    (45)   ~ (all_52_6 = e3)
% 240.86/47.53    (46)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 240.86/47.53    (47)   ~ (all_52_1 = all_52_13)
% 240.86/47.53    (48)  all_54_7 = all_52_13
% 240.86/47.53    (49)  op(e0, e2) = all_52_7
% 240.86/47.53    (50)  op(e3, e2) = all_52_4
% 240.86/47.53    (51)   ~ (all_52_9 = e3)
% 240.86/47.53    (52)  all_56_1 = all_10_2
% 240.86/47.53    (53)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.86/47.53          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.86/47.53    (54)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.53            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.53    (55)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.86/47.53          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.86/47.53    (56)  all_56_21 = e3
% 240.86/47.53    (57)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.53          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.86/47.53    (58)   ~ (e1 = e0)
% 240.86/47.53    (59)  op(e2, e0) = all_52_13
% 240.86/47.53    (60)  all_54_0 = all_10_2
% 240.86/47.53    (61)   ~ (all_52_9 = e1)
% 240.86/47.53    (62)   ~ (all_24_2 = e2) | ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 240.86/47.53            op(e3, e2) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 240.86/47.53              e1) & op(e3, e2) = all_24_1 & $i(all_24_1))
% 240.86/47.53    (63)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.86/47.53          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.86/47.53    (64)   ~ (e2 = e1)
% 240.86/47.53    (65)   ~ (all_52_1 = e1)
% 240.86/47.53  
% 240.86/47.53  Begin of proof
% 240.86/47.53  | 
% 240.86/47.53  | GROUND_INST: instantiating (54) with e1, all_46_1, e3, e1, simplifying with
% 240.86/47.53  |              (32), (40) gives:
% 240.86/47.53  |   (66)  all_46_1 = e1
% 240.86/47.53  | 
% 240.86/47.53  | REDUCE: (39), (66) imply:
% 240.86/47.53  |   (67)  op(e1, e1) = all_46_0
% 240.86/47.53  | 
% 240.86/47.53  | GROUND_INST: instantiating (54) with e3, all_46_0, e1, e1, simplifying with
% 240.86/47.53  |              (44), (67) gives:
% 240.86/47.53  |   (68)  all_46_0 = e3
% 240.86/47.53  | 
% 240.86/47.53  | REDUCE: (15), (68) imply:
% 240.86/47.53  |   (69)   ~ (e3 = e0)
% 240.86/47.53  | 
% 240.86/47.53  | BETA: splitting (62) gives:
% 240.86/47.53  | 
% 240.86/47.53  | Case 1:
% 240.86/47.53  | | 
% 240.86/47.53  | |   (70)   ~ (all_24_2 = e2)
% 240.86/47.53  | | 
% 240.86/47.53  | | REDUCE: (41), (70) imply:
% 240.86/47.53  | |   (71)   ~ (all_10_2 = e2)
% 240.86/47.53  | | 
% 240.86/47.53  | | REF_CLOSE: (1), (5), (8), (9), (10), (11), (12), (13), (14), (16), (17),
% 240.86/47.53  | |            (18), (19), (25), (28), (31), (32), (33), (43), (45), (47), (49),
% 240.86/47.53  | |            (50), (51), (53), (54), (56), (57), (58), (59), (60), (61), (63),
% 240.86/47.53  | |            (64), (65), (71) are inconsistent by sub-proof #480.
% 240.86/47.53  | | 
% 240.86/47.53  | Case 2:
% 240.86/47.53  | | 
% 240.86/47.53  | |   (72)  all_24_2 = e2
% 240.86/47.53  | | 
% 240.86/47.54  | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14), (16),
% 240.86/47.54  | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 240.86/47.54  | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 240.86/47.54  | |            (41), (42), (43), (45), (46), (47), (48), (49), (51), (52), (53),
% 240.86/47.54  | |            (54), (55), (56), (57), (58), (59), (61), (63), (65), (69), (72)
% 240.86/47.54  | |            are inconsistent by sub-proof #473.
% 240.86/47.54  | | 
% 240.86/47.54  | End of split
% 240.86/47.54  | 
% 240.86/47.54  End of proof
% 240.86/47.54  
% 240.86/47.54  Sub-proof #473 shows that the following formulas are inconsistent:
% 240.86/47.54  ----------------------------------------------------------------
% 240.86/47.54    (1)   ~ (all_52_1 = all_52_3)
% 240.86/47.54    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 240.86/47.54    (3)   ~ (all_52_3 = e1)
% 240.86/47.54    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.86/47.54         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.86/47.54    (5)   ~ (e3 = e0)
% 240.86/47.54    (6)  op(e0, e1) = all_52_11
% 240.86/47.54    (7)  all_24_2 = e2
% 240.86/47.54    (8)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.54         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.86/47.54    (9)  op(e1, e2) = all_52_6
% 240.86/47.54    (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.54              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.54            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 240.86/47.54            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.54            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 240.86/47.54             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.54            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.86/47.54            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.54            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 240.86/47.54            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.54            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.86/47.54              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.54            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.54            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 240.86/47.54            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.54            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 240.86/47.54            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.54            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.86/47.54              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.86/47.54            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.54            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 240.86/47.54            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.54            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 240.86/47.54            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.54            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.86/47.54              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.54            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.54            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.54    (11)   ~ (all_10_2 = e0)
% 240.86/47.54    (12)  op(e1, e0) = all_52_14
% 240.86/47.54    (13)   ~ (all_52_13 = e1)
% 240.86/47.54    (14)   ~ (all_10_2 = e1)
% 240.86/47.54    (15)  op(e0, e3) = all_52_3
% 240.86/47.54    (16)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.86/47.54          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.86/47.54    (17)   ~ (all_52_1 = all_10_2)
% 240.86/47.54    (18)   ~ (e3 = e1)
% 240.86/47.54    (19)  all_54_6 = all_52_9
% 240.86/47.54    (20)   ~ (all_52_12 = all_52_13)
% 240.86/47.54    (21)   ~ (all_52_3 = all_10_2)
% 240.86/47.54    (22)   ~ (all_52_1 = all_52_9)
% 240.86/47.54    (23)   ~ (all_52_3 = all_52_7)
% 240.86/47.54    (24)  all_54_4 = all_52_1
% 240.86/47.54    (25)   ~ (all_52_11 = e3)
% 240.86/47.54    (26)  op(e2, e1) = all_52_9
% 240.86/47.54    (27)   ~ (e3 = e2)
% 240.86/47.54    (28)   ~ (all_52_12 = all_10_2)
% 240.86/47.54    (29)   ~ (all_52_14 = e1)
% 240.86/47.54    (30)  op(e1, e3) = e1
% 240.86/47.54    (31)  all_56_31 = e1
% 240.86/47.54    (32)  all_54_12 = all_52_3
% 240.86/47.54    (33)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 240.86/47.54    (34)  all_58_15 = e1
% 240.86/47.54    (35)  op(e3, e0) = all_52_12
% 240.86/47.54    (36)   ~ (all_52_9 = all_52_13)
% 240.86/47.54    (37)  all_24_2 = all_10_2
% 240.86/47.54    (38)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 240.86/47.54    (39)  op(e2, e3) = all_52_1
% 240.86/47.54    (40)   ~ (all_52_6 = e3)
% 240.86/47.54    (41)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 240.86/47.54    (42)   ~ (all_52_1 = all_52_13)
% 240.86/47.54    (43)  all_54_7 = all_52_13
% 240.86/47.54    (44)  op(e0, e2) = all_52_7
% 240.86/47.54    (45)   ~ (all_52_9 = e3)
% 240.86/47.54    (46)  all_56_1 = all_10_2
% 240.86/47.54    (47)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.86/47.54          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.86/47.54    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.54    (49)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.86/47.54          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.86/47.54    (50)  all_56_21 = e3
% 240.86/47.54    (51)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.86/47.54          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.86/47.54    (52)   ~ (e1 = e0)
% 240.86/47.54    (53)  op(e2, e0) = all_52_13
% 240.86/47.54    (54)   ~ (all_52_9 = e1)
% 240.86/47.54    (55)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.86/47.54          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.86/47.54    (56)   ~ (all_52_1 = e1)
% 240.86/47.54  
% 240.86/47.54  Begin of proof
% 240.86/47.54  | 
% 240.86/47.54  | COMBINE_EQS: (7), (37) imply:
% 240.86/47.54  |   (57)  all_10_2 = e2
% 240.86/47.54  | 
% 240.86/47.54  | SIMP: (57) implies:
% 240.86/47.54  |   (58)  all_10_2 = e2
% 240.86/47.54  | 
% 240.86/47.54  | COMBINE_EQS: (46), (58) imply:
% 240.86/47.54  |   (59)  all_56_1 = e2
% 240.86/47.54  | 
% 240.86/47.54  | REDUCE: (17), (58) imply:
% 240.86/47.54  |   (60)   ~ (all_52_1 = e2)
% 240.86/47.54  | 
% 240.86/47.54  | REDUCE: (21), (58) imply:
% 240.86/47.54  |   (61)   ~ (all_52_3 = e2)
% 240.86/47.54  | 
% 240.86/47.54  | REDUCE: (28), (58) imply:
% 240.86/47.54  |   (62)   ~ (all_52_12 = e2)
% 240.86/47.54  | 
% 240.86/47.54  | REDUCE: (14), (58) imply:
% 240.86/47.54  |   (63)   ~ (e2 = e1)
% 240.86/47.54  | 
% 240.86/47.54  | REDUCE: (11), (58) imply:
% 240.86/47.54  |   (64)   ~ (e2 = e0)
% 240.86/47.54  | 
% 240.86/47.54  | BETA: splitting (38) gives:
% 240.86/47.54  | 
% 240.86/47.54  | Case 1:
% 240.86/47.54  | | 
% 240.86/47.54  | |   (65)  all_54_6 = e3
% 240.86/47.54  | | 
% 240.86/47.54  | | REF_CLOSE: (19), (45), (65) are inconsistent by sub-proof #1825.
% 240.86/47.54  | | 
% 240.86/47.54  | Case 2:
% 240.86/47.54  | | 
% 240.86/47.54  | |   (66)   ~ (all_54_6 = e3)
% 240.86/47.54  | |   (67)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 240.86/47.54  | | 
% 240.86/47.54  | | BETA: splitting (2) gives:
% 240.86/47.54  | | 
% 240.86/47.54  | | Case 1:
% 240.86/47.54  | | | 
% 240.86/47.54  | | |   (68)  all_54_12 = e3
% 240.86/47.54  | | | 
% 240.86/47.54  | | | COMBINE_EQS: (32), (68) imply:
% 240.86/47.54  | | |   (69)  all_52_3 = e3
% 240.86/47.54  | | | 
% 240.86/47.54  | | | SIMP: (69) implies:
% 240.86/47.54  | | |   (70)  all_52_3 = e3
% 240.86/47.54  | | | 
% 240.86/47.54  | | | REDUCE: (1), (70) imply:
% 240.86/47.54  | | |   (71)   ~ (all_52_1 = e3)
% 240.86/47.54  | | | 
% 240.86/47.54  | | | REDUCE: (23), (70) imply:
% 240.86/47.54  | | |   (72)   ~ (all_52_7 = e3)
% 240.86/47.54  | | | 
% 240.86/47.54  | | | SIMP: (72) implies:
% 240.86/47.54  | | |   (73)   ~ (all_52_7 = e3)
% 240.86/47.54  | | | 
% 240.86/47.54  | | | BETA: splitting (41) gives:
% 240.86/47.54  | | | 
% 240.86/47.54  | | | Case 1:
% 240.86/47.54  | | | | 
% 240.86/47.54  | | | |   (74)  all_54_4 = e3
% 240.86/47.54  | | | | 
% 240.86/47.54  | | | | REF_CLOSE: (24), (71), (74) are inconsistent by sub-proof #2100.
% 240.86/47.54  | | | | 
% 240.86/47.54  | | | Case 2:
% 240.86/47.54  | | | | 
% 240.86/47.54  | | | |   (75)   ~ (all_54_4 = e3)
% 240.86/47.54  | | | |   (76)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 240.86/47.54  | | | | 
% 240.86/47.54  | | | | BETA: splitting (8) gives:
% 240.86/47.54  | | | | 
% 240.86/47.54  | | | | Case 1:
% 240.86/47.54  | | | | | 
% 240.86/47.54  | | | | |   (77)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2,
% 240.86/47.54  | | | | |             e2) = e3)
% 240.86/47.54  | | | | | 
% 240.86/47.54  | | | | | REF_CLOSE: (13), (18), (26), (39), (48), (53), (54), (55), (56), (71),
% 240.86/47.54  | | | | |            (77) are inconsistent by sub-proof #2195.
% 240.86/47.54  | | | | | 
% 240.86/47.54  | | | | Case 2:
% 240.86/47.54  | | | | | 
% 240.86/47.54  | | | | |   (78)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2,
% 240.86/47.54  | | | | |             e0) = e3)
% 240.86/47.54  | | | | | 
% 240.86/47.54  | | | | | BETA: splitting (78) gives:
% 240.86/47.54  | | | | | 
% 240.86/47.54  | | | | | Case 1:
% 240.86/47.54  | | | | | | 
% 240.86/47.54  | | | | | |   (79)  all_58_5 = e3 & op(e2, e1) = e3
% 240.86/47.54  | | | | | | 
% 240.86/47.54  | | | | | | REF_CLOSE: (26), (45), (48), (79) are inconsistent by sub-proof
% 240.86/47.54  | | | | | |            #1822.
% 240.86/47.54  | | | | | | 
% 240.86/47.54  | | | | | Case 2:
% 240.86/47.54  | | | | | | 
% 240.86/47.54  | | | | | |   (80)  all_58_10 = e3 & op(e2, e0) = e3
% 240.86/47.54  | | | | | | 
% 240.86/47.54  | | | | | | ALPHA: (80) implies:
% 240.86/47.54  | | | | | |   (81)  all_58_10 = e3
% 240.86/47.54  | | | | | |   (82)  op(e2, e0) = e3
% 240.86/47.54  | | | | | | 
% 240.86/47.54  | | | | | | BETA: splitting (49) gives:
% 240.86/47.54  | | | | | | 
% 240.86/47.54  | | | | | | Case 1:
% 240.86/47.54  | | | | | | | 
% 240.86/47.54  | | | | | | |   (83)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 240.86/47.54  | | | | | | |           op(e2, e0) = e2)
% 240.86/47.54  | | | | | | | 
% 240.86/47.54  | | | | | | | BETA: splitting (83) gives:
% 240.86/47.54  | | | | | | | 
% 240.86/47.54  | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | 
% 240.86/47.54  | | | | | | | |   (84)  all_58_9 = e2 & op(e3, e0) = e2
% 240.86/47.54  | | | | | | | | 
% 240.86/47.54  | | | | | | | | REF_CLOSE: (35), (48), (62), (84) are inconsistent by sub-proof
% 240.86/47.54  | | | | | | | |            #2318.
% 240.86/47.54  | | | | | | | | 
% 240.86/47.54  | | | | | | | Case 2:
% 240.86/47.54  | | | | | | | | 
% 240.86/47.54  | | | | | | | |   (85)  all_58_10 = e2 & op(e2, e0) = e2
% 240.86/47.54  | | | | | | | | 
% 240.86/47.54  | | | | | | | | ALPHA: (85) implies:
% 240.86/47.54  | | | | | | | |   (86)  op(e2, e0) = e2
% 240.86/47.54  | | | | | | | | 
% 240.86/47.54  | | | | | | | | REF_CLOSE: (27), (48), (82), (86) are inconsistent by sub-proof
% 240.86/47.54  | | | | | | | |            #2152.
% 240.86/47.54  | | | | | | | | 
% 240.86/47.54  | | | | | | | End of split
% 240.86/47.54  | | | | | | | 
% 240.86/47.54  | | | | | | Case 2:
% 240.86/47.54  | | | | | | | 
% 240.86/47.54  | | | | | | |   (87)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 240.86/47.54  | | | | | | |           op(e0, e0) = e2)
% 240.86/47.54  | | | | | | | 
% 240.86/47.54  | | | | | | | BETA: splitting (87) gives:
% 240.86/47.54  | | | | | | | 
% 240.86/47.54  | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | 
% 240.86/47.54  | | | | | | | |   (88)  all_58_11 = e2 & op(e1, e0) = e2
% 240.86/47.54  | | | | | | | | 
% 240.86/47.54  | | | | | | | | ALPHA: (88) implies:
% 240.86/47.54  | | | | | | | |   (89)  op(e1, e0) = e2
% 240.86/47.54  | | | | | | | | 
% 240.86/47.54  | | | | | | | | BETA: splitting (76) gives:
% 240.86/47.54  | | | | | | | | 
% 240.86/47.54  | | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | | 
% 240.86/47.54  | | | | | | | | |   (90)  all_54_4 = e2
% 240.86/47.54  | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | COMBINE_EQS: (24), (90) imply:
% 240.86/47.54  | | | | | | | | |   (91)  all_52_1 = e2
% 240.86/47.54  | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | REDUCE: (60), (91) imply:
% 240.86/47.54  | | | | | | | | |   (92)  $false
% 240.86/47.54  | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | CLOSE: (92) is inconsistent.
% 240.86/47.54  | | | | | | | | | 
% 240.86/47.54  | | | | | | | | Case 2:
% 240.86/47.54  | | | | | | | | | 
% 240.86/47.54  | | | | | | | | |   (93)  all_54_4 = e1 | all_54_4 = e0
% 240.86/47.54  | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | BETA: splitting (51) gives:
% 240.86/47.54  | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | |   (94)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 &
% 240.86/47.54  | | | | | | | | | |           op(e2, e2) = e3)
% 240.86/47.54  | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | BETA: splitting (94) gives:
% 240.86/47.54  | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | |   (95)  all_58_1 = e3 & op(e3, e2) = e3
% 240.86/47.54  | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | ALPHA: (95) implies:
% 240.86/47.54  | | | | | | | | | | |   (96)  op(e3, e2) = e3
% 240.86/47.54  | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | BETA: splitting (93) gives:
% 240.86/47.54  | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | |   (97)  all_54_4 = e1
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | COMBINE_EQS: (24), (97) imply:
% 240.86/47.54  | | | | | | | | | | | |   (98)  all_52_1 = e1
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | REDUCE: (56), (98) imply:
% 240.86/47.54  | | | | | | | | | | | |   (99)  $false
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | CLOSE: (99) is inconsistent.
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | Case 2:
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | |   (100)  all_54_4 = e0
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | COMBINE_EQS: (24), (100) imply:
% 240.86/47.54  | | | | | | | | | | | |   (101)  all_52_1 = e0
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | REDUCE: (22), (101) imply:
% 240.86/47.54  | | | | | | | | | | | |   (102)   ~ (all_52_9 = e0)
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | SIMP: (102) implies:
% 240.86/47.54  | | | | | | | | | | | |   (103)   ~ (all_52_9 = e0)
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | REDUCE: (42), (101) imply:
% 240.86/47.54  | | | | | | | | | | | |   (104)   ~ (all_52_13 = e0)
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | SIMP: (104) implies:
% 240.86/47.54  | | | | | | | | | | | |   (105)   ~ (all_52_13 = e0)
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | BETA: splitting (67) gives:
% 240.86/47.54  | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | |   (106)  all_54_6 = e2
% 240.86/47.54  | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | COMBINE_EQS: (19), (106) imply:
% 240.86/47.54  | | | | | | | | | | | | |   (107)  all_52_9 = e2
% 240.86/47.54  | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | REDUCE: (36), (107) imply:
% 240.86/47.54  | | | | | | | | | | | | |   (108)   ~ (all_52_13 = e2)
% 240.86/47.54  | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | SIMP: (108) implies:
% 240.86/47.54  | | | | | | | | | | | | |   (109)   ~ (all_52_13 = e2)
% 240.86/47.54  | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | BETA: splitting (33) gives:
% 240.86/47.54  | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | |   (110)  all_54_7 = e3
% 240.86/47.54  | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | COMBINE_EQS: (43), (110) imply:
% 240.86/47.54  | | | | | | | | | | | | | |   (111)  all_52_13 = e3
% 240.86/47.54  | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | SIMP: (111) implies:
% 240.86/47.54  | | | | | | | | | | | | | |   (112)  all_52_13 = e3
% 240.86/47.54  | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | REDUCE: (20), (112) imply:
% 240.86/47.54  | | | | | | | | | | | | | |   (113)   ~ (all_52_12 = e3)
% 240.86/47.54  | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 240.86/47.54  | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | |   (114)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.86/47.54  | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.86/47.54  | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.54  | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.86/47.54  | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.86/47.54  | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.54  | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.86/47.54  | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.54  | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.54  | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.86/47.54  | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 240.86/47.54  | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.54  | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.86/47.54  | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.86/47.54  | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.54  | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.54  | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 240.86/47.54  | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.54  | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.54  | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.86/47.54  | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 240.86/47.54  | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 240.86/47.54  | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | |   (115)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 240.86/47.54  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.86/47.54  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.86/47.54  | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 240.86/47.54  | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.86/47.54  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.54  | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.86/47.54  | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.54  | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.54  | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.86/47.54  | | | | | | | | | | | | | | | |            = e3)
% 240.86/47.54  | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 240.86/47.54  | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | |   (116)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 240.86/47.54  | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.86/47.54  | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 240.86/47.54  | | | | | | | | | | | | | | | | |          e3
% 240.86/47.54  | | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 240.86/47.54  | | | | | | | | | | | | | | | | |   (117)  op(e2, e3) = e3
% 240.86/47.54  | | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (48), (71), (117) are inconsistent by
% 240.86/47.54  | | | | | | | | | | | | | | | | |            sub-proof #2337.
% 240.86/47.54  | | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.54  | | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | |   (118)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 240.86/47.54  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.86/47.54  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.86/47.54  | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 240.86/47.54  | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.86/47.54  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.86/47.54  | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.54  | | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (27), (30), (48), (96), (118) are
% 240.86/47.54  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #479.
% 240.86/47.54  | | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | End of split
% 240.86/47.54  | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | Case 2:
% 240.86/47.54  | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | |   (119)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.86/47.54  | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.86/47.54  | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.86/47.54  | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 240.86/47.54  | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.86/47.54  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.86/47.54  | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 240.86/47.54  | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.54  | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.86/47.54  | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 240.86/47.54  | | | | | | | | | | | | | | | |            = e0)
% 240.86/47.54  | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 240.86/47.54  | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.54  | | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | |   (120)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 240.86/47.54  | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 240.86/47.54  | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 240.86/47.54  | | | | | | | | | | | | | | | | |            e3) = e1
% 240.86/47.54  | | | | | | | | | | | | | | | | | 
% 240.86/47.54  | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 240.86/47.54  | | | | | | | | | | | | | | | | |   (121)   ~ (all_56_21 = e3)
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | REDUCE: (50), (121) imply:
% 240.86/47.55  | | | | | | | | | | | | | | | | |   (122)  $false
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | CLOSE: (122) is inconsistent.
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | |   (123)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.86/47.55  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.86/47.55  | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 240.86/47.55  | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 240.86/47.55  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.86/47.55  | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | |   (124)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.86/47.55  | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 240.86/47.55  | | | | | | | | | | | | | | | | | |            e3) = e3
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 240.86/47.55  | | | | | | | | | | | | | | | | | |   (125)  op(e3, e0) = e3
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (48), (113), (125) are inconsistent by
% 240.86/47.55  | | | | | | | | | | | | | | | | | |            sub-proof #2179.
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | |   (126)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 240.86/47.55  | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 240.86/47.55  | | | | | | | | | | | | | | | | | |            e3) = e0
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 240.86/47.55  | | | | | | | | | | | | | | | | | |   (127)   ~ (all_56_21 = e3)
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | | REDUCE: (50), (127) imply:
% 240.86/47.55  | | | | | | | | | | | | | | | | | |   (128)  $false
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | | CLOSE: (128) is inconsistent.
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | |   (129)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.86/47.55  | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.86/47.55  | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.86/47.55  | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.86/47.55  | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.86/47.55  | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.86/47.55  | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.55  | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.55  | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.86/47.55  | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 240.86/47.55  | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.86/47.55  | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.86/47.55  | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 240.86/47.55  | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.55  | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.55  | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 240.86/47.55  | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.55  | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.55  | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 240.86/47.55  | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 240.86/47.55  | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 240.86/47.55  | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | Case 1:
% 240.86/47.55  | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | |   (130)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.86/47.55  | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 240.86/47.55  | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 240.86/47.55  | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.86/47.55  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 240.86/47.55  | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.86/47.55  | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.55  | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.86/47.55  | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 240.86/47.55  | | | | | | | | | | | | | | | |            = e2)
% 240.86/47.55  | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 240.86/47.55  | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | |   (131)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.86/47.55  | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 240.86/47.55  | | | | | | | | | | | | | | | | |            e2) = e2
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 240.86/47.55  | | | | | | | | | | | | | | | | |   (132)   ~ (all_56_31 = e1)
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | REDUCE: (31), (132) imply:
% 240.86/47.55  | | | | | | | | | | | | | | | | |   (133)  $false
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | CLOSE: (133) is inconsistent.
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | |   (134)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.86/47.55  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.86/47.55  | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 240.86/47.55  | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.86/47.55  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.86/47.55  | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | |   (135)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.86/47.55  | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 240.86/47.55  | | | | | | | | | | | | | | | | | |            e2) = e1
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 240.86/47.55  | | | | | | | | | | | | | | | | | |   (136)  op(e2, e1) = e1
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (48), (54), (136) are inconsistent by
% 240.86/47.55  | | | | | | | | | | | | | | | | | |            sub-proof #2306.
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | |   (137)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 240.86/47.55  | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 240.86/47.55  | | | | | | | | | | | | | | | | | |            e2) = e2
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 240.86/47.55  | | | | | | | | | | | | | | | | | |   (138)  op(e2, e0) = e2
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (53), (109), (138) are inconsistent by
% 240.86/47.55  | | | | | | | | | | | | | | | | | |            sub-proof #2317.
% 240.86/47.55  | | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | |   (139)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 240.86/47.55  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 240.86/47.55  | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 240.86/47.55  | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.86/47.55  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.86/47.55  | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.86/47.55  | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.55  | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.86/47.55  | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 240.86/47.55  | | | | | | | | | | | | | | | |            = e0)
% 240.86/47.55  | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 240.86/47.55  | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | Case 1:
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | |   (140)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 240.86/47.55  | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 240.86/47.55  | | | | | | | | | | | | | | | | |            e2) = e0
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 240.86/47.55  | | | | | | | | | | | | | | | | |   (141)  op(e2, e0) = e0
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (53), (105), (141) are inconsistent by
% 240.86/47.55  | | | | | | | | | | | | | | | | |            sub-proof #2324.
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | |   (142)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 240.86/47.55  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 240.86/47.55  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.86/47.55  | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 240.86/47.55  | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 240.86/47.55  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.86/47.55  | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (63), (64), (89), (142) are inconsistent by
% 240.86/47.55  | | | | | | | | | | | | | | | | |            sub-proof #477.
% 240.86/47.55  | | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | |   (143)   ~ (all_54_7 = e3)
% 240.86/47.55  | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | REDUCE: (43), (143) imply:
% 240.86/47.55  | | | | | | | | | | | | | |   (144)   ~ (all_52_13 = e3)
% 240.86/47.55  | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | | REF_CLOSE: (48), (53), (82), (144) are inconsistent by
% 240.86/47.55  | | | | | | | | | | | | | |            sub-proof #1994.
% 240.86/47.55  | | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | |   (145)  all_54_6 = e1 | all_54_6 = e0
% 240.86/47.55  | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | | REF_CLOSE: (19), (54), (103), (145) are inconsistent by
% 240.86/47.55  | | | | | | | | | | | | |            sub-proof #476.
% 240.86/47.55  | | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | |   (146)  all_58_3 = e3 & op(e2, e2) = e3
% 240.86/47.55  | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | ALPHA: (146) implies:
% 240.86/47.55  | | | | | | | | | | |   (147)  all_58_3 = e3
% 240.86/47.55  | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | | REF_CLOSE: (5), (16), (18), (27), (39), (47), (48), (52),
% 240.86/47.55  | | | | | | | | | | |            (55), (56), (63), (64), (81), (147) are
% 240.86/47.55  | | | | | | | | | | |            inconsistent by sub-proof #1099.
% 240.86/47.55  | | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | |   (148)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3
% 240.86/47.55  | | | | | | | | | |            & op(e0, e2) = e3)
% 240.86/47.55  | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | | REF_CLOSE: (9), (40), (44), (48), (73), (148) are
% 240.86/47.55  | | | | | | | | | |            inconsistent by sub-proof #475.
% 240.86/47.55  | | | | | | | | | | 
% 240.86/47.55  | | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | | 
% 240.86/47.55  | | | | | | | | End of split
% 240.86/47.55  | | | | | | | | 
% 240.86/47.55  | | | | | | | Case 2:
% 240.86/47.55  | | | | | | | | 
% 240.86/47.55  | | | | | | | |   (149)  all_58_15 = e2 & op(e0, e0) = e2
% 240.86/47.55  | | | | | | | | 
% 240.86/47.55  | | | | | | | | ALPHA: (149) implies:
% 240.86/47.55  | | | | | | | |   (150)  all_58_15 = e2
% 240.86/47.55  | | | | | | | | 
% 240.86/47.55  | | | | | | | | REF_CLOSE: (34), (63), (150) are inconsistent by sub-proof
% 240.86/47.55  | | | | | | | |            #2231.
% 240.86/47.55  | | | | | | | | 
% 240.86/47.55  | | | | | | | End of split
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | End of split
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | End of split
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | End of split
% 240.86/47.55  | | | | 
% 240.86/47.55  | | | End of split
% 240.86/47.55  | | | 
% 240.86/47.55  | | Case 2:
% 240.86/47.55  | | | 
% 240.86/47.55  | | |   (151)   ~ (all_54_12 = e3)
% 240.86/47.55  | | | 
% 240.86/47.55  | | | REDUCE: (32), (151) imply:
% 240.86/47.55  | | |   (152)   ~ (all_52_3 = e3)
% 240.86/47.55  | | | 
% 240.86/47.55  | | | BETA: splitting (10) gives:
% 240.86/47.55  | | | 
% 240.86/47.55  | | | Case 1:
% 240.86/47.55  | | | | 
% 240.86/47.55  | | | |   (153)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.55  | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 240.86/47.55  | | | |            & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 &
% 240.86/47.55  | | | |            all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.86/47.55  | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.86/47.55  | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.86/47.55  | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &
% 240.86/47.55  | | | |             ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 240.86/47.55  | | | |          (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.55  | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 240.86/47.55  | | | |            & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.86/47.55  | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.86/47.55  | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.86/47.55  | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.86/47.55  | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &
% 240.86/47.55  | | | |             ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.86/47.55  | | | | 
% 240.86/47.55  | | | | BETA: splitting (153) gives:
% 240.86/47.55  | | | | 
% 240.86/47.55  | | | | Case 1:
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | |   (154)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.55  | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.86/47.55  | | | | |              e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2
% 240.86/47.55  | | | | |            & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 240.86/47.55  | | | | |            &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.86/47.55  | | | | |            e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 & 
% 240.86/47.55  | | | | |            ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 240.86/47.55  | | | | |              e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.86/47.55  | | | | |            = e3)
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | | BETA: splitting (154) gives:
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | | Case 1:
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | |   (155)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.55  | | | | | |          (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.86/47.55  | | | | | |            e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | | ALPHA: (155) implies:
% 240.86/47.55  | | | | | |   (156)   ~ (all_56_1 = e2)
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | | REDUCE: (59), (156) imply:
% 240.86/47.55  | | | | | |   (157)  $false
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | | CLOSE: (157) is inconsistent.
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | Case 2:
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | |   (158)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.55  | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 240.86/47.55  | | | | | |              e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 240.86/47.55  | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 240.86/47.55  | | | | | |              = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.86/47.55  | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | | BETA: splitting (158) gives:
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | | Case 1:
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | |   (159)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.55  | | | | | | |          (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 240.86/47.55  | | | | | | |            e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | | ALPHA: (159) implies:
% 240.86/47.55  | | | | | | |   (160)  op(e2, e3) = e2
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | | REF_CLOSE: (39), (48), (60), (160) are inconsistent by sub-proof
% 240.86/47.55  | | | | | | |            #2336.
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | Case 2:
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | |   (161)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.55  | | | | | | |          (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 240.86/47.55  | | | | | | |            e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | | ALPHA: (161) implies:
% 240.86/47.55  | | | | | | |   (162)  op(e1, e3) = e3
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | | REF_CLOSE: (18), (30), (48), (162) are inconsistent by sub-proof
% 240.86/47.55  | | | | | | |            #2225.
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | End of split
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | End of split
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | Case 2:
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | |   (163)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 240.86/47.55  | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 240.86/47.55  | | | | |              e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3
% 240.86/47.55  | | | | |            & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0)
% 240.86/47.55  | | | | |            &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 240.86/47.55  | | | | |            e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 240.86/47.55  | | | | |            ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 240.86/47.55  | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 240.86/47.55  | | | | |            = e0)
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | | REF_CLOSE: (15), (48), (50), (152), (163) are inconsistent by
% 240.86/47.55  | | | | |            sub-proof #481.
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | End of split
% 240.86/47.55  | | | | 
% 240.86/47.55  | | | Case 2:
% 240.86/47.55  | | | | 
% 240.86/47.55  | | | |   (164)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.55  | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 240.86/47.55  | | | |            & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 240.86/47.55  | | | |            all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 240.86/47.55  | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 240.86/47.55  | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.86/47.55  | | | |            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &
% 240.86/47.55  | | | |             ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 240.86/47.55  | | | |          (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.55  | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 240.86/47.55  | | | |            & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 240.86/47.55  | | | |            all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 240.86/47.55  | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.86/47.55  | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.86/47.55  | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &
% 240.86/47.55  | | | |             ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.55  | | | | 
% 240.86/47.55  | | | | BETA: splitting (164) gives:
% 240.86/47.55  | | | | 
% 240.86/47.55  | | | | Case 1:
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | |   (165)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.55  | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 240.86/47.55  | | | | |              e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 =
% 240.86/47.55  | | | | |            e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.86/47.55  | | | | |              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.86/47.55  | | | | |              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27
% 240.86/47.55  | | | | |            = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 240.86/47.55  | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 &
% 240.86/47.55  | | | | |            op(e0, e2) = e2)
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | | BETA: splitting (165) gives:
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | | Case 1:
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | |   (166)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.86/47.55  | | | | | |          (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 240.86/47.55  | | | | | |            e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | | ALPHA: (166) implies:
% 240.86/47.55  | | | | | |   (167)   ~ (all_56_31 = e1)
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | | REDUCE: (31), (167) imply:
% 240.86/47.55  | | | | | |   (168)  $false
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | | CLOSE: (168) is inconsistent.
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | Case 2:
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | |   (169)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.55  | | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.86/47.55  | | | | | |              e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 =
% 240.86/47.55  | | | | | |            e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.86/47.55  | | | | | |              = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.86/47.55  | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | | BETA: splitting (169) gives:
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | | Case 1:
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | |   (170)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.55  | | | | | | |          (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.86/47.55  | | | | | | |            e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | | ALPHA: (170) implies:
% 240.86/47.55  | | | | | | |   (171)  op(e2, e1) = e1
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | | REF_CLOSE: (26), (48), (54), (171) are inconsistent by sub-proof
% 240.86/47.55  | | | | | | |            #2306.
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | Case 2:
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | |   (172)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.55  | | | | | | |          (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 240.86/47.55  | | | | | | |            e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | | ALPHA: (172) implies:
% 240.86/47.55  | | | | | | |   (173)  op(e0, e2) = e2
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | | REF_CLOSE: (4), (6), (15), (18), (25), (27), (34), (48), (152),
% 240.86/47.55  | | | | | | |            (173) are inconsistent by sub-proof #474.
% 240.86/47.55  | | | | | | | 
% 240.86/47.55  | | | | | | End of split
% 240.86/47.55  | | | | | | 
% 240.86/47.55  | | | | | End of split
% 240.86/47.55  | | | | | 
% 240.86/47.55  | | | | Case 2:
% 240.86/47.55  | | | | | 
% 240.86/47.56  | | | | |   (174)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.56  | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.86/47.56  | | | | |              e2) & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 =
% 240.86/47.56  | | | | |            e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.86/47.56  | | | | |              e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.86/47.56  | | | | |              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29
% 240.86/47.56  | | | | |            = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.86/47.56  | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 &
% 240.86/47.56  | | | | |            op(e0, e1) = e0)
% 240.86/47.56  | | | | | 
% 240.86/47.56  | | | | | BETA: splitting (174) gives:
% 240.86/47.56  | | | | | 
% 240.86/47.56  | | | | | Case 1:
% 240.86/47.56  | | | | | | 
% 240.86/47.56  | | | | | |   (175)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.86/47.56  | | | | | |          (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.86/47.56  | | | | | |            e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 240.86/47.56  | | | | | | 
% 240.86/47.56  | | | | | | ALPHA: (175) implies:
% 240.86/47.56  | | | | | |   (176)   ~ (all_56_1 = e2)
% 240.86/47.56  | | | | | | 
% 240.86/47.56  | | | | | | REDUCE: (59), (176) imply:
% 240.86/47.56  | | | | | |   (177)  $false
% 240.86/47.56  | | | | | | 
% 240.86/47.56  | | | | | | CLOSE: (177) is inconsistent.
% 240.86/47.56  | | | | | | 
% 240.86/47.56  | | | | | Case 2:
% 240.86/47.56  | | | | | | 
% 240.86/47.56  | | | | | |   (178)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.86/47.56  | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 240.86/47.56  | | | | | |              e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 =
% 240.86/47.56  | | | | | |            e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 240.86/47.56  | | | | | |              = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.86/47.56  | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.86/47.56  | | | | | | 
% 240.86/47.56  | | | | | | REF_CLOSE: (12), (29), (31), (48), (178) are inconsistent by
% 240.86/47.56  | | | | | |            sub-proof #2269.
% 240.86/47.56  | | | | | | 
% 240.86/47.56  | | | | | End of split
% 240.86/47.56  | | | | | 
% 240.86/47.56  | | | | End of split
% 240.86/47.56  | | | | 
% 240.86/47.56  | | | End of split
% 240.86/47.56  | | | 
% 240.86/47.56  | | End of split
% 240.86/47.56  | | 
% 240.86/47.56  | End of split
% 240.86/47.56  | 
% 240.86/47.56  End of proof
% 240.86/47.56  
% 240.86/47.56  Sub-proof #474 shows that the following formulas are inconsistent:
% 240.86/47.56  ----------------------------------------------------------------
% 240.86/47.56    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.86/47.56         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.86/47.56    (2)  op(e0, e1) = all_52_11
% 240.86/47.56    (3)  op(e0, e3) = all_52_3
% 240.86/47.56    (4)  op(e0, e2) = e2
% 240.86/47.56    (5)   ~ (e3 = e1)
% 240.86/47.56    (6)   ~ (all_52_11 = e3)
% 240.86/47.56    (7)   ~ (e3 = e2)
% 240.86/47.56    (8)  all_58_15 = e1
% 240.86/47.56    (9)   ~ (all_52_3 = e3)
% 240.86/47.56    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.56  
% 240.86/47.56  Begin of proof
% 240.86/47.56  | 
% 240.86/47.56  | BETA: splitting (1) gives:
% 240.86/47.56  | 
% 240.86/47.56  | Case 1:
% 240.86/47.56  | | 
% 240.86/47.56  | |   (11)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 240.86/47.56  | |           e3)
% 240.86/47.56  | | 
% 240.86/47.56  | | BETA: splitting (11) gives:
% 240.86/47.56  | | 
% 240.86/47.56  | | Case 1:
% 240.86/47.56  | | | 
% 240.86/47.56  | | |   (12)  all_58_12 = e3 & op(e0, e3) = e3
% 240.86/47.56  | | | 
% 240.86/47.56  | | | ALPHA: (12) implies:
% 240.86/47.56  | | |   (13)  op(e0, e3) = e3
% 240.86/47.56  | | | 
% 240.86/47.56  | | | REF_CLOSE: (3), (9), (10), (13) are inconsistent by sub-proof #2332.
% 240.86/47.56  | | | 
% 240.86/47.56  | | Case 2:
% 240.86/47.56  | | | 
% 240.86/47.56  | | |   (14)  all_58_13 = e3 & op(e0, e2) = e3
% 240.86/47.56  | | | 
% 240.86/47.56  | | | ALPHA: (14) implies:
% 240.86/47.56  | | |   (15)  op(e0, e2) = e3
% 240.86/47.56  | | | 
% 240.86/47.56  | | | REF_CLOSE: (4), (7), (10), (15) are inconsistent by sub-proof #2254.
% 240.86/47.56  | | | 
% 240.86/47.56  | | End of split
% 240.86/47.56  | | 
% 240.86/47.56  | Case 2:
% 240.86/47.56  | | 
% 240.86/47.56  | |   (16)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 240.86/47.56  | |           e3)
% 240.86/47.56  | | 
% 240.86/47.56  | | BETA: splitting (16) gives:
% 240.86/47.56  | | 
% 240.86/47.56  | | Case 1:
% 240.86/47.56  | | | 
% 240.86/47.56  | | |   (17)  all_58_14 = e3 & op(e0, e1) = e3
% 240.86/47.56  | | | 
% 240.86/47.56  | | | REF_CLOSE: (2), (6), (10), (17) are inconsistent by sub-proof #1647.
% 240.86/47.56  | | | 
% 240.86/47.56  | | Case 2:
% 240.86/47.56  | | | 
% 240.86/47.56  | | |   (18)  all_58_15 = e3 & op(e0, e0) = e3
% 240.86/47.56  | | | 
% 240.86/47.56  | | | REF_CLOSE: (5), (8), (18) are inconsistent by sub-proof #1915.
% 240.86/47.56  | | | 
% 240.86/47.56  | | End of split
% 240.86/47.56  | | 
% 240.86/47.56  | End of split
% 240.86/47.56  | 
% 240.86/47.56  End of proof
% 240.86/47.56  
% 240.86/47.56  Sub-proof #475 shows that the following formulas are inconsistent:
% 240.86/47.56  ----------------------------------------------------------------
% 240.86/47.56    (1)  op(e1, e2) = all_52_6
% 240.86/47.56    (2)   ~ (all_52_7 = e3)
% 240.86/47.56    (3)   ~ (all_52_6 = e3)
% 240.86/47.56    (4)  op(e0, e2) = all_52_7
% 240.86/47.56    (5)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.86/47.56    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.86/47.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.86/47.56  
% 240.86/47.56  Begin of proof
% 240.86/47.56  | 
% 240.86/47.56  | BETA: splitting (5) gives:
% 240.86/47.56  | 
% 240.86/47.56  | Case 1:
% 240.86/47.56  | | 
% 240.86/47.56  | |   (7)  all_58_7 = e3 & op(e1, e2) = e3
% 240.86/47.56  | | 
% 240.86/47.56  | | ALPHA: (7) implies:
% 240.86/47.56  | |   (8)  op(e1, e2) = e3
% 240.86/47.56  | | 
% 240.86/47.56  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #2191.
% 240.86/47.56  | | 
% 240.86/47.56  | Case 2:
% 240.86/47.56  | | 
% 240.86/47.56  | |   (9)  all_58_13 = e3 & op(e0, e2) = e3
% 240.86/47.56  | | 
% 240.86/47.56  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #1919.
% 240.86/47.56  | | 
% 240.86/47.56  | End of split
% 240.86/47.56  | 
% 240.86/47.56  End of proof
% 240.86/47.56  
% 240.86/47.56  Sub-proof #476 shows that the following formulas are inconsistent:
% 240.86/47.56  ----------------------------------------------------------------
% 240.86/47.56    (1)  all_54_6 = e1 | all_54_6 = e0
% 240.86/47.56    (2)  all_54_6 = all_52_9
% 240.86/47.56    (3)   ~ (all_52_9 = e1)
% 240.86/47.56    (4)   ~ (all_52_9 = e0)
% 240.86/47.56  
% 240.86/47.56  Begin of proof
% 240.86/47.56  | 
% 240.86/47.56  | BETA: splitting (1) gives:
% 240.86/47.56  | 
% 240.86/47.56  | Case 1:
% 240.86/47.56  | | 
% 240.86/47.56  | |   (5)  all_54_6 = e1
% 240.86/47.56  | | 
% 240.86/47.56  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2246.
% 240.86/47.56  | | 
% 240.86/47.56  | Case 2:
% 240.86/47.56  | | 
% 240.86/47.56  | |   (6)  all_54_6 = e0
% 240.86/47.56  | | 
% 240.86/47.56  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2245.
% 240.86/47.56  | | 
% 240.86/47.56  | End of split
% 240.86/47.56  | 
% 240.86/47.56  End of proof
% 240.86/47.56  
% 240.86/47.56  Sub-proof #477 shows that the following formulas are inconsistent:
% 240.86/47.56  ----------------------------------------------------------------
% 240.86/47.56    (1)   ~ (e2 = e0)
% 240.86/47.56    (2)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.86/47.56             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 240.86/47.56           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 240.86/47.56             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 240.86/47.56           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.98/47.56    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.98/47.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.98/47.56    (4)  op(e1, e0) = e2
% 240.98/47.56    (5)   ~ (e2 = e1)
% 240.98/47.56  
% 240.98/47.56  Begin of proof
% 240.98/47.56  | 
% 240.98/47.56  | BETA: splitting (2) gives:
% 240.98/47.56  | 
% 240.98/47.56  | Case 1:
% 240.98/47.56  | | 
% 240.98/47.56  | |   (6)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.98/47.56  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 240.98/47.56  | |        & op(e0, e1) = e1
% 240.98/47.56  | | 
% 240.98/47.56  | | ALPHA: (6) implies:
% 240.98/47.56  | |   (7)  op(e1, e0) = e1
% 240.98/47.56  | | 
% 240.98/47.56  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #2019.
% 240.98/47.56  | | 
% 240.98/47.56  | Case 2:
% 240.98/47.56  | | 
% 240.98/47.56  | |   (8)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 240.98/47.56  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 240.98/47.56  | |        & op(e0, e1) = e0
% 240.98/47.56  | | 
% 240.98/47.56  | | ALPHA: (8) implies:
% 240.98/47.56  | |   (9)  op(e1, e0) = e0
% 240.98/47.56  | | 
% 240.98/47.56  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #478.
% 240.98/47.56  | | 
% 240.98/47.56  | End of split
% 240.98/47.56  | 
% 240.98/47.56  End of proof
% 240.98/47.56  
% 240.98/47.56  Sub-proof #478 shows that the following formulas are inconsistent:
% 240.98/47.56  ----------------------------------------------------------------
% 240.98/47.56    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.98/47.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.98/47.56    (2)  op(e1, e0) = e2
% 240.98/47.56    (3)  op(e1, e0) = e0
% 240.98/47.56    (4)   ~ (e2 = e0)
% 240.98/47.56  
% 240.98/47.56  Begin of proof
% 240.98/47.56  | 
% 240.98/47.56  | GROUND_INST: instantiating (1) with e2, e0, e0, e1, simplifying with (2), (3)
% 240.98/47.56  |              gives:
% 240.98/47.56  |   (5)  e2 = e0
% 240.98/47.56  | 
% 240.98/47.56  | REDUCE: (4), (5) imply:
% 240.98/47.56  |   (6)  $false
% 240.98/47.56  | 
% 240.98/47.56  | CLOSE: (6) is inconsistent.
% 240.98/47.56  | 
% 240.98/47.56  End of proof
% 240.98/47.56  
% 240.98/47.56  Sub-proof #479 shows that the following formulas are inconsistent:
% 240.98/47.56  ----------------------------------------------------------------
% 240.98/47.56    (1)   ~ (e3 = e1)
% 240.98/47.56    (2)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 240.98/47.56           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 240.98/47.56             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.98/47.56           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 240.98/47.56             e1) = e3 & op(e1, e3) = e3)
% 240.98/47.56    (3)   ~ (e3 = e2)
% 240.98/47.56    (4)  op(e1, e3) = e1
% 240.98/47.56    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.98/47.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.98/47.56    (6)  op(e3, e2) = e3
% 240.98/47.56  
% 240.98/47.56  Begin of proof
% 240.98/47.56  | 
% 240.98/47.56  | BETA: splitting (2) gives:
% 240.98/47.56  | 
% 240.98/47.56  | Case 1:
% 240.98/47.56  | | 
% 240.98/47.56  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.98/47.56  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.98/47.56  | |        op(e2, e3) = e2
% 240.98/47.56  | | 
% 240.98/47.56  | | ALPHA: (7) implies:
% 240.98/47.56  | |   (8)  op(e3, e2) = e2
% 240.98/47.56  | | 
% 240.98/47.56  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2193.
% 240.98/47.56  | | 
% 240.98/47.56  | Case 2:
% 240.98/47.56  | | 
% 240.98/47.56  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.98/47.56  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.98/47.56  | |        op(e1, e3) = e3
% 240.98/47.56  | | 
% 240.98/47.56  | | ALPHA: (9) implies:
% 240.98/47.56  | |   (10)  op(e1, e3) = e3
% 240.98/47.56  | | 
% 240.98/47.56  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2225.
% 240.98/47.56  | | 
% 240.98/47.56  | End of split
% 240.98/47.56  | 
% 240.98/47.56  End of proof
% 240.98/47.56  
% 240.98/47.56  Sub-proof #480 shows that the following formulas are inconsistent:
% 240.98/47.56  ----------------------------------------------------------------
% 240.98/47.56    (1)   ~ (all_52_4 = all_10_2)
% 240.98/47.56    (2)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 240.98/47.56    (3)   ~ (e2 = e0)
% 240.98/47.56    (4)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.98/47.56         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 240.98/47.56    (5)  op(e1, e2) = all_52_6
% 240.98/47.56    (6)   ~ (all_10_2 = e2)
% 240.98/47.56    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.98/47.56           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.98/47.56             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.98/47.56           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.98/47.56             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.98/47.56           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.98/47.56           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 240.98/47.56           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 240.98/47.56           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 240.98/47.56           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 240.98/47.56           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 240.98/47.56             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.98/47.56           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.98/47.56           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 240.98/47.56           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 240.98/47.56           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 240.98/47.56           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.98/47.56           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 240.98/47.56             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 240.98/47.56           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.98/47.56           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 240.98/47.56           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 240.98/47.56           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 240.98/47.56           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.98/47.56           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 240.98/47.56             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 240.98/47.56           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.98/47.56           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.98/47.56    (8)   ~ (all_10_2 = e0)
% 240.98/47.56    (9)  op(e1, e0) = all_52_14
% 240.98/47.56    (10)   ~ (all_52_13 = e1)
% 240.98/47.56    (11)   ~ (all_10_2 = e1)
% 240.98/47.56    (12)  op(e0, e3) = all_52_3
% 240.98/47.56    (13)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.98/47.56          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.98/47.56    (14)   ~ (all_52_1 = all_10_2)
% 240.98/47.56    (15)   ~ (all_52_3 = all_52_7)
% 240.98/47.56    (16)  op(e2, e1) = all_52_9
% 240.98/47.56    (17)   ~ (all_52_14 = e1)
% 240.98/47.56    (18)  op(e1, e3) = e1
% 240.98/47.56    (19)  all_56_31 = e1
% 240.98/47.56    (20)  op(e2, e3) = all_52_1
% 240.98/47.56    (21)   ~ (all_52_6 = e3)
% 240.98/47.56    (22)   ~ (all_52_1 = all_52_13)
% 240.98/47.56    (23)  op(e0, e2) = all_52_7
% 240.98/47.56    (24)  op(e3, e2) = all_52_4
% 240.98/47.56    (25)   ~ (all_52_9 = e3)
% 240.98/47.56    (26)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.98/47.56          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.98/47.56    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.98/47.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.98/47.56    (28)  all_56_21 = e3
% 240.98/47.56    (29)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 240.98/47.56          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 240.98/47.56    (30)   ~ (e1 = e0)
% 240.98/47.56    (31)  op(e2, e0) = all_52_13
% 240.98/47.56    (32)  all_54_0 = all_10_2
% 240.98/47.56    (33)   ~ (all_52_9 = e1)
% 240.98/47.56    (34)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 240.98/47.56          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 240.98/47.56    (35)   ~ (e2 = e1)
% 240.98/47.56    (36)   ~ (all_52_1 = e1)
% 240.98/47.56  
% 240.98/47.56  Begin of proof
% 240.98/47.56  | 
% 240.98/47.56  | BETA: splitting (2) gives:
% 240.98/47.56  | 
% 240.98/47.56  | Case 1:
% 240.98/47.56  | | 
% 240.98/47.56  | |   (37)  all_54_0 = e3
% 240.98/47.56  | | 
% 240.98/47.56  | | COMBINE_EQS: (32), (37) imply:
% 240.98/47.56  | |   (38)  all_10_2 = e3
% 240.98/47.56  | | 
% 240.98/47.56  | | REDUCE: (14), (38) imply:
% 240.98/47.56  | |   (39)   ~ (all_52_1 = e3)
% 240.98/47.56  | | 
% 240.98/47.56  | | REDUCE: (1), (38) imply:
% 240.98/47.56  | |   (40)   ~ (all_52_4 = e3)
% 240.98/47.56  | | 
% 240.98/47.56  | | REDUCE: (6), (38) imply:
% 240.98/47.56  | |   (41)   ~ (e3 = e2)
% 240.98/47.56  | | 
% 240.98/47.56  | | REDUCE: (11), (38) imply:
% 240.98/47.56  | |   (42)   ~ (e3 = e1)
% 240.98/47.56  | | 
% 240.98/47.56  | | REDUCE: (8), (38) imply:
% 240.98/47.56  | |   (43)   ~ (e3 = e0)
% 240.98/47.56  | | 
% 240.98/47.56  | | BETA: splitting (4) gives:
% 240.98/47.56  | | 
% 240.98/47.56  | | Case 1:
% 240.98/47.56  | | | 
% 240.98/47.56  | | |   (44)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 240.98/47.56  | | |           e3)
% 240.98/47.56  | | | 
% 240.98/47.56  | | | REF_CLOSE: (10), (16), (20), (27), (31), (33), (34), (36), (39), (42),
% 240.98/47.56  | | |            (44) are inconsistent by sub-proof #2195.
% 240.98/47.56  | | | 
% 240.98/47.56  | | Case 2:
% 240.98/47.56  | | | 
% 240.98/47.56  | | |   (45)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 240.98/47.56  | | |           e3)
% 240.98/47.56  | | | 
% 240.98/47.56  | | | BETA: splitting (45) gives:
% 240.98/47.56  | | | 
% 240.98/47.56  | | | Case 1:
% 240.98/47.56  | | | | 
% 240.98/47.56  | | | |   (46)  all_58_5 = e3 & op(e2, e1) = e3
% 240.98/47.56  | | | | 
% 240.98/47.56  | | | | REF_CLOSE: (16), (25), (27), (46) are inconsistent by sub-proof #1822.
% 240.98/47.56  | | | | 
% 240.98/47.56  | | | Case 2:
% 240.98/47.56  | | | | 
% 240.98/47.56  | | | |   (47)  all_58_10 = e3 & op(e2, e0) = e3
% 240.98/47.56  | | | | 
% 240.98/47.56  | | | | ALPHA: (47) implies:
% 240.98/47.56  | | | |   (48)  all_58_10 = e3
% 240.98/47.56  | | | |   (49)  op(e2, e0) = e3
% 240.98/47.56  | | | | 
% 240.98/47.56  | | | | BETA: splitting (29) gives:
% 240.98/47.56  | | | | 
% 240.98/47.56  | | | | Case 1:
% 240.98/47.56  | | | | | 
% 240.98/47.56  | | | | |   (50)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2,
% 240.98/47.56  | | | | |             e2) = e3)
% 240.98/47.56  | | | | | 
% 240.98/47.56  | | | | | REF_CLOSE: (3), (13), (20), (24), (26), (27), (30), (34), (35), (36),
% 240.98/47.56  | | | | |            (40), (41), (42), (43), (48), (50) are inconsistent by
% 240.98/47.56  | | | | |            sub-proof #1098.
% 240.98/47.56  | | | | | 
% 240.98/47.56  | | | | Case 2:
% 240.98/47.56  | | | | | 
% 240.98/47.56  | | | | |   (51)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0,
% 240.98/47.56  | | | | |             e2) = e3)
% 240.98/47.56  | | | | | 
% 240.98/47.56  | | | | | BETA: splitting (51) gives:
% 240.98/47.56  | | | | | 
% 240.98/47.56  | | | | | Case 1:
% 240.98/47.56  | | | | | | 
% 240.98/47.56  | | | | | |   (52)  all_58_7 = e3 & op(e1, e2) = e3
% 240.98/47.56  | | | | | | 
% 240.98/47.56  | | | | | | ALPHA: (52) implies:
% 240.98/47.56  | | | | | |   (53)  op(e1, e2) = e3
% 240.98/47.56  | | | | | | 
% 240.98/47.56  | | | | | | REF_CLOSE: (5), (21), (27), (53) are inconsistent by sub-proof
% 240.98/47.56  | | | | | |            #2191.
% 240.98/47.56  | | | | | | 
% 240.98/47.56  | | | | | Case 2:
% 240.98/47.56  | | | | | | 
% 240.98/47.57  | | | | | |   (54)  all_58_13 = e3 & op(e0, e2) = e3
% 240.98/47.57  | | | | | | 
% 240.98/47.57  | | | | | | ALPHA: (54) implies:
% 240.98/47.57  | | | | | |   (55)  op(e0, e2) = e3
% 240.98/47.57  | | | | | | 
% 240.98/47.57  | | | | | | GROUND_INST: instantiating (27) with all_52_7, e3, e2, e0,
% 240.98/47.57  | | | | | |              simplifying with (23), (55) gives:
% 240.98/47.57  | | | | | |   (56)  all_52_7 = e3
% 240.98/47.57  | | | | | | 
% 240.98/47.57  | | | | | | GROUND_INST: instantiating (27) with all_52_13, e3, e0, e2,
% 240.98/47.57  | | | | | |              simplifying with (31), (49) gives:
% 240.98/47.57  | | | | | |   (57)  all_52_13 = e3
% 240.98/47.57  | | | | | | 
% 240.98/47.57  | | | | | | REDUCE: (15), (56) imply:
% 240.98/47.57  | | | | | |   (58)   ~ (all_52_3 = e3)
% 240.98/47.57  | | | | | | 
% 240.98/47.57  | | | | | | BETA: splitting (7) gives:
% 240.98/47.57  | | | | | | 
% 240.98/47.57  | | | | | | Case 1:
% 240.98/47.57  | | | | | | | 
% 240.98/47.57  | | | | | | |   (59)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.98/47.57  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.98/47.57  | | | | | | |             e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 =
% 240.98/47.57  | | | | | | |           e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.98/47.57  | | | | | | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.98/47.57  | | | | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 240.98/47.57  | | | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.98/47.57  | | | | | | |             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 240.98/47.57  | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1 &
% 240.98/47.57  | | | | | | |           all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.98/47.57  | | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.98/47.57  | | | | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 240.98/47.57  | | | | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.98/47.57  | | | | | | |             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.98/47.57  | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 240.98/47.57  | | | | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.98/47.57  | | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.98/47.57  | | | | | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.98/47.57  | | | | | | | 
% 240.98/47.57  | | | | | | | BETA: splitting (59) gives:
% 240.98/47.57  | | | | | | | 
% 240.98/47.57  | | | | | | | Case 1:
% 240.98/47.57  | | | | | | | | 
% 240.98/47.57  | | | | | | | |   (60)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 240.98/47.57  | | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 240.98/47.57  | | | | | | | |             = e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 240.98/47.57  | | | | | | | |         (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.98/47.57  | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 240.98/47.57  | | | | | | | |             = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 240.98/47.57  | | | | | | | |         (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) & 
% 240.98/47.57  | | | | | | | |           ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.98/47.57  | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.98/47.57  | | | | | | | | 
% 240.98/47.57  | | | | | | | | BETA: splitting (60) gives:
% 240.98/47.57  | | | | | | | | 
% 240.98/47.57  | | | | | | | | Case 1:
% 240.98/47.57  | | | | | | | | | 
% 240.98/47.57  | | | | | | | | |   (61)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 240.98/47.57  | | | | | | | | |         ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 240.98/47.57  | | | | | | | | |         (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 240.98/47.57  | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | ALPHA: (61) implies:
% 240.98/47.57  | | | | | | | | |   (62)  op(e2, e3) = e3
% 240.98/47.57  | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | REF_CLOSE: (20), (27), (39), (62) are inconsistent by
% 240.98/47.57  | | | | | | | | |            sub-proof #2337.
% 240.98/47.57  | | | | | | | | | 
% 240.98/47.57  | | | | | | | | Case 2:
% 240.98/47.57  | | | | | | | | | 
% 240.98/47.57  | | | | | | | | |   (63)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) & 
% 240.98/47.57  | | | | | | | | |           ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.98/47.57  | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 240.98/47.57  | | | | | | | | |           e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1
% 240.98/47.57  | | | | | | | | |             = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 240.98/47.57  | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 240.98/47.57  | | | | | | | | |           = e3)
% 240.98/47.57  | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | BETA: splitting (63) gives:
% 240.98/47.57  | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | Case 1:
% 240.98/47.57  | | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | |   (64)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &
% 240.98/47.57  | | | | | | | | | |          ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.98/47.57  | | | | | | | | | |         (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 240.98/47.57  | | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | | ALPHA: (64) implies:
% 240.98/47.57  | | | | | | | | | |   (65)   ~ (all_56_21 = e3)
% 240.98/47.57  | | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | | REDUCE: (28), (65) imply:
% 240.98/47.57  | | | | | | | | | |   (66)  $false
% 240.98/47.57  | | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | | CLOSE: (66) is inconsistent.
% 240.98/47.57  | | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | Case 2:
% 240.98/47.57  | | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | |   (67)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1)
% 240.98/47.57  | | | | | | | | | |         &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.98/47.57  | | | | | | | | | |         (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 240.98/47.57  | | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | | ALPHA: (67) implies:
% 240.98/47.57  | | | | | | | | | |   (68)  op(e1, e3) = e3
% 240.98/47.57  | | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | | REF_CLOSE: (18), (27), (42), (68) are inconsistent by
% 240.98/47.57  | | | | | | | | | |            sub-proof #2225.
% 240.98/47.57  | | | | | | | | | | 
% 240.98/47.57  | | | | | | | | | End of split
% 240.98/47.57  | | | | | | | | | 
% 240.98/47.57  | | | | | | | | End of split
% 240.98/47.57  | | | | | | | | 
% 240.98/47.57  | | | | | | | Case 2:
% 240.98/47.57  | | | | | | | | 
% 240.98/47.57  | | | | | | | |   (69)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) & 
% 240.98/47.57  | | | | | | | |           ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.98/47.57  | | | | | | | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1)
% 240.98/47.57  | | | | | | | |         | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &
% 240.98/47.57  | | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 240.98/47.57  | | | | | | | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3)
% 240.98/47.57  | | | | | | | |         | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &
% 240.98/47.57  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.98/47.57  | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.98/47.57  | | | | | | | | 
% 240.98/47.57  | | | | | | | | REF_CLOSE: (12), (27), (28), (58), (69) are inconsistent by
% 240.98/47.57  | | | | | | | |            sub-proof #481.
% 240.98/47.57  | | | | | | | | 
% 240.98/47.57  | | | | | | | End of split
% 240.98/47.57  | | | | | | | 
% 240.98/47.57  | | | | | | Case 2:
% 240.98/47.57  | | | | | | | 
% 240.98/47.57  | | | | | | |   (70)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 240.98/47.57  | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 240.98/47.57  | | | | | | |             e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13
% 240.98/47.57  | | | | | | |           = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 240.98/47.57  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.98/47.57  | | | | | | |             e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 240.98/47.57  | | | | | | |           = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 240.98/47.57  | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 240.98/47.57  | | | | | | |             e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15
% 240.98/47.57  | | | | | | |           = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 240.98/47.57  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 240.98/47.57  | | | | | | |             e2) & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23
% 240.98/47.57  | | | | | | |           = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 240.98/47.57  | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 240.98/47.57  | | | | | | |             e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 240.98/47.57  | | | | | | |           = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 240.98/47.57  | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 240.98/47.57  | | | | | | |             e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 240.98/47.57  | | | | | | | 
% 240.98/47.57  | | | | | | | REF_CLOSE: (9), (16), (17), (19), (27), (33), (41), (43), (55),
% 240.98/47.57  | | | | | | |            (70) are inconsistent by sub-proof #1107.
% 240.98/47.57  | | | | | | | 
% 240.98/47.57  | | | | | | End of split
% 240.98/47.57  | | | | | | 
% 240.98/47.57  | | | | | End of split
% 240.98/47.57  | | | | | 
% 240.98/47.57  | | | | End of split
% 240.98/47.57  | | | | 
% 240.98/47.57  | | | End of split
% 240.98/47.57  | | | 
% 240.98/47.57  | | End of split
% 240.98/47.57  | | 
% 240.98/47.57  | Case 2:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (71)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 240.98/47.57  | | 
% 240.98/47.57  | | REF_CLOSE: (6), (8), (11), (32), (71) are inconsistent by sub-proof #2319.
% 240.98/47.57  | | 
% 240.98/47.57  | End of split
% 240.98/47.57  | 
% 240.98/47.57  End of proof
% 240.98/47.57  
% 240.98/47.57  Sub-proof #481 shows that the following formulas are inconsistent:
% 240.98/47.57  ----------------------------------------------------------------
% 240.98/47.57    (1)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.98/47.57             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.98/47.57           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 240.98/47.57           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.98/47.57           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 240.98/47.57           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.98/47.57           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.98/47.57    (2)  op(e0, e3) = all_52_3
% 240.98/47.57    (3)   ~ (all_52_3 = e3)
% 240.98/47.57    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.98/47.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.98/47.57    (5)  all_56_21 = e3
% 240.98/47.57  
% 240.98/47.57  Begin of proof
% 240.98/47.57  | 
% 240.98/47.57  | BETA: splitting (1) gives:
% 240.98/47.57  | 
% 240.98/47.57  | Case 1:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (6)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.98/47.57  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.98/47.57  | |        op(e1, e3) = e1
% 240.98/47.57  | | 
% 240.98/47.57  | | ALPHA: (6) implies:
% 240.98/47.57  | |   (7)   ~ (all_56_21 = e3)
% 240.98/47.57  | | 
% 240.98/47.57  | | REDUCE: (5), (7) imply:
% 240.98/47.57  | |   (8)  $false
% 240.98/47.57  | | 
% 240.98/47.57  | | CLOSE: (8) is inconsistent.
% 240.98/47.57  | | 
% 240.98/47.57  | Case 2:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (9)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.98/47.57  | |            = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 240.98/47.57  | |          e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.98/47.57  | |          (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.98/47.57  | |          (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.98/47.57  | | 
% 240.98/47.57  | | REF_CLOSE: (2), (3), (4), (5), (9) are inconsistent by sub-proof #482.
% 240.98/47.57  | | 
% 240.98/47.57  | End of split
% 240.98/47.57  | 
% 240.98/47.57  End of proof
% 240.98/47.57  
% 240.98/47.57  Sub-proof #482 shows that the following formulas are inconsistent:
% 240.98/47.57  ----------------------------------------------------------------
% 240.98/47.57    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.98/47.57             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.98/47.57           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 240.98/47.57           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 240.98/47.57           op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.98/47.57    (2)  op(e0, e3) = all_52_3
% 240.98/47.57    (3)   ~ (all_52_3 = e3)
% 240.98/47.57    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.98/47.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.98/47.57    (5)  all_56_21 = e3
% 240.98/47.57  
% 240.98/47.57  Begin of proof
% 240.98/47.57  | 
% 240.98/47.57  | BETA: splitting (1) gives:
% 240.98/47.57  | 
% 240.98/47.57  | Case 1:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (6)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 240.98/47.57  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 240.98/47.57  | |        op(e0, e3) = e3
% 240.98/47.57  | | 
% 240.98/47.57  | | ALPHA: (6) implies:
% 240.98/47.57  | |   (7)  op(e0, e3) = e3
% 240.98/47.57  | | 
% 240.98/47.57  | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #2332.
% 240.98/47.57  | | 
% 240.98/47.57  | Case 2:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (8)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.98/47.57  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 240.98/47.57  | |        op(e0, e3) = e0
% 240.98/47.57  | | 
% 240.98/47.57  | | ALPHA: (8) implies:
% 240.98/47.57  | |   (9)   ~ (all_56_21 = e3)
% 240.98/47.57  | | 
% 240.98/47.57  | | REDUCE: (5), (9) imply:
% 240.98/47.57  | |   (10)  $false
% 240.98/47.57  | | 
% 240.98/47.57  | | CLOSE: (10) is inconsistent.
% 240.98/47.57  | | 
% 240.98/47.57  | End of split
% 240.98/47.57  | 
% 240.98/47.57  End of proof
% 240.98/47.57  
% 240.98/47.57  Sub-proof #483 shows that the following formulas are inconsistent:
% 240.98/47.57  ----------------------------------------------------------------
% 240.98/47.57    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 240.98/47.57           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 240.98/47.57             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 240.98/47.57           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 240.98/47.57             e1) = e3 & op(e1, e3) = e3)
% 240.98/47.57    (2)   ~ (all_52_2 = e3)
% 240.98/47.57    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.98/47.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.98/47.57    (4)  op(e1, e3) = all_52_2
% 240.98/47.57    (5)  all_56_21 = e3
% 240.98/47.57  
% 240.98/47.57  Begin of proof
% 240.98/47.57  | 
% 240.98/47.57  | BETA: splitting (1) gives:
% 240.98/47.57  | 
% 240.98/47.57  | Case 1:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (6)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.98/47.57  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 240.98/47.57  | |        op(e2, e3) = e2
% 240.98/47.57  | | 
% 240.98/47.57  | | ALPHA: (6) implies:
% 240.98/47.57  | |   (7)   ~ (all_56_21 = e3)
% 240.98/47.57  | | 
% 240.98/47.57  | | REDUCE: (5), (7) imply:
% 240.98/47.57  | |   (8)  $false
% 240.98/47.57  | | 
% 240.98/47.57  | | CLOSE: (8) is inconsistent.
% 240.98/47.57  | | 
% 240.98/47.57  | Case 2:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 240.98/47.57  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 240.98/47.57  | |        op(e1, e3) = e3
% 240.98/47.57  | | 
% 240.98/47.57  | | ALPHA: (9) implies:
% 240.98/47.57  | |   (10)  op(e1, e3) = e3
% 240.98/47.57  | | 
% 240.98/47.57  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #2335.
% 240.98/47.57  | | 
% 240.98/47.57  | End of split
% 240.98/47.57  | 
% 240.98/47.57  End of proof
% 240.98/47.57  
% 240.98/47.57  Sub-proof #484 shows that the following formulas are inconsistent:
% 240.98/47.57  ----------------------------------------------------------------
% 240.98/47.57    (1)   ~ (all_52_4 = all_10_2)
% 240.98/47.57    (2)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 240.98/47.57    (3)   ~ (all_10_2 = e2)
% 240.98/47.57    (4)   ~ (all_10_2 = e0)
% 240.98/47.57    (5)   ~ (all_10_2 = e1)
% 240.98/47.57    (6)  op(e3, e2) = all_52_4
% 240.98/47.57    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.98/47.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.98/47.57    (8)  op(e3, e2) = e3
% 240.98/47.57    (9)  all_54_0 = all_10_2
% 240.98/47.57  
% 240.98/47.57  Begin of proof
% 240.98/47.57  | 
% 240.98/47.57  | BETA: splitting (2) gives:
% 240.98/47.57  | 
% 240.98/47.57  | Case 1:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (10)  all_54_0 = e3
% 240.98/47.57  | | 
% 240.98/47.57  | | COMBINE_EQS: (9), (10) imply:
% 240.98/47.57  | |   (11)  all_10_2 = e3
% 240.98/47.57  | | 
% 240.98/47.57  | | REDUCE: (1), (11) imply:
% 240.98/47.57  | |   (12)   ~ (all_52_4 = e3)
% 240.98/47.57  | | 
% 240.98/47.57  | | REF_CLOSE: (6), (7), (8), (12) are inconsistent by sub-proof #2192.
% 240.98/47.57  | | 
% 240.98/47.57  | Case 2:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (13)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 240.98/47.57  | | 
% 240.98/47.57  | | REF_CLOSE: (3), (4), (5), (9), (13) are inconsistent by sub-proof #2319.
% 240.98/47.57  | | 
% 240.98/47.57  | End of split
% 240.98/47.57  | 
% 240.98/47.57  End of proof
% 240.98/47.57  
% 240.98/47.57  Sub-proof #485 shows that the following formulas are inconsistent:
% 240.98/47.57  ----------------------------------------------------------------
% 240.98/47.57    (1)   ~ (all_52_3 = e0)
% 240.98/47.57    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.98/47.57             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.98/47.57           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 240.98/47.57           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 240.98/47.57           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 240.98/47.57           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.98/47.57           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.98/47.57    (3)  op(e0, e3) = all_52_3
% 240.98/47.57    (4)  all_56_31 = e0
% 240.98/47.57    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.98/47.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.98/47.57    (6)  all_56_21 = e3
% 240.98/47.57  
% 240.98/47.57  Begin of proof
% 240.98/47.57  | 
% 240.98/47.57  | BETA: splitting (2) gives:
% 240.98/47.57  | 
% 240.98/47.57  | Case 1:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (7)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 240.98/47.57  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 240.98/47.57  | |        op(e1, e3) = e1
% 240.98/47.57  | | 
% 240.98/47.57  | | ALPHA: (7) implies:
% 240.98/47.57  | |   (8)   ~ (all_56_21 = e3)
% 240.98/47.57  | | 
% 240.98/47.57  | | REDUCE: (6), (8) imply:
% 240.98/47.57  | |   (9)  $false
% 240.98/47.57  | | 
% 240.98/47.57  | | CLOSE: (9) is inconsistent.
% 240.98/47.57  | | 
% 240.98/47.57  | Case 2:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 240.98/47.57  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 240.98/47.57  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 240.98/47.57  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 240.98/47.57  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 240.98/47.57  | | 
% 240.98/47.57  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #2308.
% 240.98/47.57  | | 
% 240.98/47.57  | End of split
% 240.98/47.57  | 
% 240.98/47.57  End of proof
% 240.98/47.57  
% 240.98/47.57  Sub-proof #486 shows that the following formulas are inconsistent:
% 240.98/47.57  ----------------------------------------------------------------
% 240.98/47.57    (1)  all_56_11 = e2
% 240.98/47.57    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 240.98/47.57           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 240.98/47.57             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 240.98/47.57           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 240.98/47.57             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.98/47.57           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.98/47.57           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.98/47.57    (3)  op(e2, e3) = all_52_1
% 240.98/47.57    (4)   ~ (all_52_2 = e3)
% 240.98/47.57    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.98/47.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.98/47.57    (6)  op(e1, e3) = all_52_2
% 240.98/47.57    (7)   ~ (all_52_1 = e2)
% 240.98/47.57  
% 240.98/47.57  Begin of proof
% 240.98/47.57  | 
% 240.98/47.57  | BETA: splitting (2) gives:
% 240.98/47.57  | 
% 240.98/47.57  | Case 1:
% 240.98/47.57  | | 
% 240.98/47.57  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 240.98/47.57  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 240.98/47.57  | |        op(e2, e3) = e3
% 240.98/47.57  | | 
% 240.98/47.57  | | ALPHA: (8) implies:
% 240.98/47.57  | |   (9)   ~ (all_56_11 = e2)
% 240.98/47.57  | | 
% 240.98/47.57  | | REDUCE: (1), (9) imply:
% 240.98/47.57  | |   (10)  $false
% 240.98/47.57  | | 
% 240.98/47.57  | | CLOSE: (10) is inconsistent.
% 240.98/47.57  | | 
% 240.98/47.57  | Case 2:
% 240.98/47.57  | | 
% 240.98/47.58  | |   (11)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 240.98/47.58  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 240.98/47.58  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 240.98/47.58  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 240.98/47.58  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 240.98/47.58  | | 
% 240.98/47.58  | | REF_CLOSE: (3), (4), (5), (6), (7), (11) are inconsistent by sub-proof
% 240.98/47.58  | |            #2334.
% 240.98/47.58  | | 
% 240.98/47.58  | End of split
% 240.98/47.58  | 
% 240.98/47.58  End of proof
% 240.98/47.58  
% 240.98/47.58  Sub-proof #487 shows that the following formulas are inconsistent:
% 240.98/47.58  ----------------------------------------------------------------
% 240.98/47.58    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 240.98/47.58         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 240.98/47.58    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 240.98/47.58         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.98/47.58    (3)   ~ (e3 = e0)
% 240.98/47.58    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 240.98/47.58         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 240.98/47.58    (5)   ~ (e2 = e0)
% 240.98/47.58    (6)  op(e1, e2) = all_52_6
% 240.98/47.58    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.98/47.58         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 240.98/47.58    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 240.98/47.58         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 240.98/47.58    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.98/47.58         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 240.98/47.58    (10)  op(e1, e1) = all_6_2
% 240.98/47.58    (11)   ~ (all_52_7 = e3)
% 240.98/47.58    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 240.98/47.58          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 240.98/47.58    (13)   ~ (e3 = e1)
% 240.98/47.58    (14)  all_58_3 = e3
% 240.98/47.58    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 240.98/47.58          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 240.98/47.58    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 240.98/47.58          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 240.98/47.58    (17)  op(e3, e3) = e1
% 240.98/47.58    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 240.98/47.58              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 240.98/47.58                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 240.98/47.58                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 240.98/47.58    (19)   ~ (all_6_2 = e3)
% 240.98/47.58    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 240.98/47.58          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 240.98/47.58    (21)   ~ (e3 = e2)
% 240.98/47.58    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 240.98/47.58          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 240.98/47.58    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 240.98/47.58          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 240.98/47.58    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 240.98/47.58          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 240.98/47.58    (25)  op(e2, e3) = all_52_1
% 240.98/47.58    (26)  all_58_12 = e3
% 240.98/47.58    (27)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 240.98/47.58          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 240.98/47.58    (28)   ~ (all_52_6 = e3)
% 240.98/47.58    (29)  op(e0, e2) = all_52_7
% 240.98/47.58    (30)   ~ (all_52_4 = e3)
% 240.98/47.58    (31)  op(e3, e2) = all_52_4
% 240.98/47.58    (32)  op(e0, e0) = e3
% 240.98/47.58    (33)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 240.98/47.58          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 240.98/47.58    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 240.98/47.58          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 240.98/47.58    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 240.98/47.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 240.98/47.58    (36)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 240.98/47.58          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 240.98/47.58    (37)   ~ (e1 = e0)
% 240.98/47.58    (38)  all_58_4 = e3
% 240.98/47.58    (39)  all_58_4 = e3 & op(e3, e1) = e3
% 240.98/47.58    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 240.98/47.58          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.07/47.58    (41)  op(e2, e0) = all_52_13
% 241.07/47.58    (42)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.07/47.58          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.07/47.58            e1)
% 241.07/47.58    (43)   ~ (all_52_1 = e3)
% 241.07/47.58    (44)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.07/47.58          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.07/47.58    (45)   ~ (e2 = e1)
% 241.07/47.58    (46)   ~ (all_52_1 = e1)
% 241.07/47.58  
% 241.07/47.58  Begin of proof
% 241.07/47.58  | 
% 241.07/47.58  | BETA: splitting (24) gives:
% 241.07/47.58  | 
% 241.07/47.58  | Case 1:
% 241.07/47.58  | | 
% 241.07/47.58  | |   (47)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 241.07/47.58  | |           e3)
% 241.07/47.58  | | 
% 241.07/47.58  | | REF_CLOSE: (3), (5), (6), (17), (20), (21), (23), (26), (28), (35), (37),
% 241.07/47.58  | |            (45), (47) are inconsistent by sub-proof #1136.
% 241.07/47.58  | | 
% 241.07/47.58  | Case 2:
% 241.07/47.58  | | 
% 241.07/47.58  | |   (48)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 241.07/47.58  | |           e3)
% 241.07/47.58  | | 
% 241.07/47.58  | | BETA: splitting (48) gives:
% 241.07/47.58  | | 
% 241.07/47.58  | | Case 1:
% 241.07/47.58  | | | 
% 241.07/47.58  | | |   (49)  all_58_8 = e3 & op(e1, e1) = e3
% 241.07/47.58  | | | 
% 241.07/47.58  | | | REF_CLOSE: (10), (19), (35), (49) are inconsistent by sub-proof #2092.
% 241.07/47.58  | | | 
% 241.07/47.58  | | Case 2:
% 241.07/47.58  | | | 
% 241.07/47.58  | | |   (50)  all_58_11 = e3 & op(e1, e0) = e3
% 241.07/47.58  | | | 
% 241.07/47.58  | | | ALPHA: (50) implies:
% 241.07/47.58  | | |   (51)  all_58_11 = e3
% 241.07/47.58  | | | 
% 241.07/47.58  | | | BETA: splitting (8) gives:
% 241.07/47.58  | | | 
% 241.07/47.58  | | | Case 1:
% 241.07/47.58  | | | | 
% 241.07/47.58  | | | |   (52)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 241.07/47.58  | | | |           = e1)
% 241.07/47.58  | | | | 
% 241.07/47.58  | | | | BETA: splitting (52) gives:
% 241.07/47.58  | | | | 
% 241.07/47.58  | | | | Case 1:
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | |   (53)  all_58_9 = e1 & op(e3, e0) = e1
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | | ALPHA: (53) implies:
% 241.07/47.58  | | | | |   (54)  all_58_9 = e1
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | | REF_CLOSE: (1), (3), (5), (17), (21), (27), (35), (37), (38), (45),
% 241.07/47.58  | | | | |            (54) are inconsistent by sub-proof #1292.
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | Case 2:
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | |   (55)  all_58_10 = e1 & op(e2, e0) = e1
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | | ALPHA: (55) implies:
% 241.07/47.58  | | | | |   (56)  op(e2, e0) = e1
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | | BETA: splitting (36) gives:
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | | Case 1:
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | |   (57)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 241.07/47.58  | | | | | |             e0) = e2)
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | | BETA: splitting (57) gives:
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | | Case 1:
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | |   (58)  all_58_9 = e2 & op(e3, e0) = e2
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | ALPHA: (58) implies:
% 241.07/47.58  | | | | | | |   (59)  all_58_9 = e2
% 241.07/47.58  | | | | | | |   (60)  op(e3, e0) = e2
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | BETA: splitting (27) gives:
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | Case 1:
% 241.07/47.58  | | | | | | | | 
% 241.07/47.58  | | | | | | | |   (61)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 241.07/47.58  | | | | | | | |           op(e3, e2) = e0)
% 241.07/47.58  | | | | | | | | 
% 241.07/47.58  | | | | | | | | BETA: splitting (61) gives:
% 241.07/47.58  | | | | | | | | 
% 241.07/47.58  | | | | | | | | Case 1:
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | |   (62)  all_58_0 = e0 & op(e3, e3) = e0
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | ALPHA: (62) implies:
% 241.07/47.58  | | | | | | | | |   (63)  op(e3, e3) = e0
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | REF_CLOSE: (17), (35), (37), (63) are inconsistent by
% 241.07/47.58  | | | | | | | | |            sub-proof #1828.
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | Case 2:
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | |   (64)  all_58_1 = e0 & op(e3, e2) = e0
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | ALPHA: (64) implies:
% 241.07/47.58  | | | | | | | | |   (65)  all_58_1 = e0
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | BETA: splitting (18) gives:
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | Case 1:
% 241.07/47.58  | | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | |   (66)  all_58_15 = e0 & op(e0, e0) = e0
% 241.07/47.58  | | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | | ALPHA: (66) implies:
% 241.07/47.58  | | | | | | | | | |   (67)  op(e0, e0) = e0
% 241.07/47.58  | | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | | GROUND_INST: instantiating (35) with e0, e3, e0, e0,
% 241.07/47.58  | | | | | | | | | |              simplifying with (32), (67) gives:
% 241.07/47.58  | | | | | | | | | |   (68)  e3 = e0
% 241.07/47.58  | | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | | COMBINE_EQS: (38), (68) imply:
% 241.07/47.58  | | | | | | | | | |   (69)  all_58_4 = e0
% 241.07/47.58  | | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | | REF_CLOSE: (3), (13), (15), (17), (21), (30), (31), (35),
% 241.07/47.58  | | | | | | | | | |            (60), (69) are inconsistent by sub-proof #1400.
% 241.07/47.58  | | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | Case 2:
% 241.07/47.58  | | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | |   (70)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 241.07/47.58  | | | | | | | | | |             & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 241.07/47.58  | | | | | | | | | |               e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) =
% 241.07/47.58  | | | | | | | | | |             e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 241.07/47.58  | | | | | | | | | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 241.07/47.58  | | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | | ALPHA: (70) implies:
% 241.07/47.58  | | | | | | | | | |   (71)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 241.07/47.58  | | | | | | | | | |           & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.07/47.58  | | | | | | | | | |           = e0)
% 241.07/47.58  | | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | | REF_CLOSE: (1), (3), (5), (13), (15), (17), (21), (30), (31),
% 241.07/47.58  | | | | | | | | | |            (35), (37), (38), (41), (45), (51), (56), (60),
% 241.07/47.58  | | | | | | | | | |            (65), (71) are inconsistent by sub-proof #534.
% 241.07/47.58  | | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | End of split
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | End of split
% 241.07/47.58  | | | | | | | | 
% 241.07/47.58  | | | | | | | Case 2:
% 241.07/47.58  | | | | | | | | 
% 241.07/47.58  | | | | | | | |   (72)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 241.07/47.58  | | | | | | | |           op(e3, e0) = e0)
% 241.07/47.58  | | | | | | | | 
% 241.07/47.58  | | | | | | | | BETA: splitting (72) gives:
% 241.07/47.58  | | | | | | | | 
% 241.07/47.58  | | | | | | | | Case 1:
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | |   (73)  all_58_4 = e0 & op(e3, e1) = e0
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | ALPHA: (73) implies:
% 241.07/47.58  | | | | | | | | |   (74)  all_58_4 = e0
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | REF_CLOSE: (3), (13), (15), (17), (21), (30), (31), (35),
% 241.07/47.58  | | | | | | | | |            (60), (74) are inconsistent by sub-proof #1400.
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | Case 2:
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | |   (75)  all_58_9 = e0 & op(e3, e0) = e0
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | | REF_CLOSE: (5), (59), (75) are inconsistent by sub-proof
% 241.07/47.58  | | | | | | | | |            #1563.
% 241.07/47.58  | | | | | | | | | 
% 241.07/47.58  | | | | | | | | End of split
% 241.07/47.58  | | | | | | | | 
% 241.07/47.58  | | | | | | | End of split
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | Case 2:
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | |   (76)  all_58_10 = e2 & op(e2, e0) = e2
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | ALPHA: (76) implies:
% 241.07/47.58  | | | | | | |   (77)  op(e2, e0) = e2
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | REF_CLOSE: (35), (45), (56), (77) are inconsistent by sub-proof
% 241.07/47.58  | | | | | | |            #1659.
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | End of split
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | Case 2:
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | |   (78)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 241.07/47.58  | | | | | |           op(e0, e0) = e2)
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | | BETA: splitting (78) gives:
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | | Case 1:
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | |   (79)  all_58_11 = e2 & op(e1, e0) = e2
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | ALPHA: (79) implies:
% 241.07/47.58  | | | | | | |   (80)  all_58_11 = e2
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | REF_CLOSE: (21), (51), (80) are inconsistent by sub-proof #2030.
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | Case 2:
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | |   (81)  all_58_15 = e2 & op(e0, e0) = e2
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | ALPHA: (81) implies:
% 241.07/47.58  | | | | | | |   (82)  op(e0, e0) = e2
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | REF_CLOSE: (21), (32), (35), (82) are inconsistent by sub-proof
% 241.07/47.58  | | | | | | |            #1388.
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | End of split
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | End of split
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | End of split
% 241.07/47.58  | | | | 
% 241.07/47.58  | | | Case 2:
% 241.07/47.58  | | | | 
% 241.07/47.58  | | | |   (83)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 241.07/47.58  | | | |             e0) = e1)
% 241.07/47.58  | | | | 
% 241.07/47.58  | | | | BETA: splitting (83) gives:
% 241.07/47.58  | | | | 
% 241.07/47.58  | | | | Case 1:
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | |   (84)  all_58_11 = e1 & op(e1, e0) = e1
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | | REF_CLOSE: (1), (3), (5), (13), (15), (17), (21), (27), (30), (31),
% 241.07/47.58  | | | | |            (35), (37), (38), (45), (51), (84) are inconsistent by
% 241.07/47.58  | | | | |            sub-proof #1467.
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | Case 2:
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | |   (85)  all_58_15 = e1 & op(e0, e0) = e1
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | | ALPHA: (85) implies:
% 241.07/47.58  | | | | |   (86)  op(e0, e0) = e1
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | | BETA: splitting (24) gives:
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | | Case 1:
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | |   (87)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 241.07/47.58  | | | | | |             e2) = e3)
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | | BETA: splitting (87) gives:
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | | Case 1:
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | |   (88)  all_58_6 = e3 & op(e1, e3) = e3
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | ALPHA: (88) implies:
% 241.07/47.58  | | | | | | |   (89)  all_58_6 = e3
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12),
% 241.07/47.58  | | | | | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22),
% 241.07/47.58  | | | | | | |            (23), (25), (27), (29), (30), (31), (32), (33), (34),
% 241.07/47.58  | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 241.07/47.58  | | | | | | |            (44), (45), (46), (51), (89) are inconsistent by
% 241.07/47.58  | | | | | | |            sub-proof #529.
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | Case 2:
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | |   (90)  all_58_7 = e3 & op(e1, e2) = e3
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | ALPHA: (90) implies:
% 241.07/47.58  | | | | | | |   (91)  op(e1, e2) = e3
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | REF_CLOSE: (6), (28), (35), (91) are inconsistent by sub-proof
% 241.07/47.58  | | | | | | |            #2191.
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | End of split
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | Case 2:
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | | BETA: splitting (48) gives:
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | | Case 1:
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | |   (92)  all_58_8 = e3 & op(e1, e1) = e3
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | REF_CLOSE: (10), (19), (35), (92) are inconsistent by sub-proof
% 241.07/47.58  | | | | | | |            #2092.
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | Case 2:
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | GROUND_INST: instantiating (35) with e1, e3, e0, e0, simplifying
% 241.07/47.58  | | | | | | |              with (32), (86) gives:
% 241.07/47.58  | | | | | | |   (93)  e3 = e1
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | COMBINE_EQS: (38), (93) imply:
% 241.07/47.58  | | | | | | |   (94)  all_58_4 = e1
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | | REF_CLOSE: (1), (3), (5), (13), (15), (17), (21), (27), (30),
% 241.07/47.58  | | | | | | |            (31), (35), (37), (45), (94) are inconsistent by
% 241.07/47.58  | | | | | | |            sub-proof #1468.
% 241.07/47.58  | | | | | | | 
% 241.07/47.58  | | | | | | End of split
% 241.07/47.58  | | | | | | 
% 241.07/47.58  | | | | | End of split
% 241.07/47.58  | | | | | 
% 241.07/47.58  | | | | End of split
% 241.07/47.58  | | | | 
% 241.07/47.58  | | | End of split
% 241.07/47.58  | | | 
% 241.07/47.58  | | End of split
% 241.07/47.58  | | 
% 241.07/47.58  | End of split
% 241.07/47.58  | 
% 241.07/47.58  End of proof
% 241.07/47.58  
% 241.07/47.58  Sub-proof #488 shows that the following formulas are inconsistent:
% 241.07/47.58  ----------------------------------------------------------------
% 241.07/47.58    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.07/47.58         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.07/47.58    (2)   ~ (all_52_9 = all_6_2)
% 241.07/47.58    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.07/47.58         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.07/47.58    (4)   ~ (e3 = e0)
% 241.07/47.58    (5)  op(e0, e1) = all_52_11
% 241.07/47.58    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.07/47.58         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.07/47.58    (7)  all_42_2 = e3
% 241.07/47.58    (8)  all_58_6 = e3
% 241.07/47.59    (9)   ~ (e2 = e0)
% 241.07/47.59    (10)  op(e1, e2) = all_52_6
% 241.07/47.59    (11)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.07/47.59          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.07/47.59    (12)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.07/47.59          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.07/47.59    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.07/47.59              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.07/47.59            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.07/47.59            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.07/47.59            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.07/47.59             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.59            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.07/47.59            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.07/47.59            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.07/47.59            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.59            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.07/47.59              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.07/47.59            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.07/47.59            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.07/47.59            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.07/47.59            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.07/47.59            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.07/47.59            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.07/47.59              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.07/47.59            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.59            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.07/47.59            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.07/47.59            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.07/47.59            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.59            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.07/47.59              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.07/47.59            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.59            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.07/47.59    (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.07/47.59          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.07/47.59    (15)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.07/47.59            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.07/47.59              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.07/47.59    (16)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.07/47.59          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.07/47.59    (17)  op(e1, e1) = all_6_2
% 241.07/47.59    (18)  op(e1, e0) = all_52_14
% 241.07/47.59    (19)   ~ (all_52_7 = e3)
% 241.07/47.59    (20)  all_58_15 = e3
% 241.07/47.59    (21)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.07/47.59          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.07/47.59    (22)   ~ (e3 = e1)
% 241.07/47.59    (23)   ~ (all_52_12 = e1)
% 241.07/47.59    (24)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.07/47.59          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.07/47.59    (25)  all_58_3 = e3
% 241.07/47.59    (26)   ~ (all_52_12 = all_52_13)
% 241.07/47.59    (27)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.07/47.59          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.07/47.59    (28)  all_54_10 = all_6_2
% 241.07/47.59    (29)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.07/47.59          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.07/47.59    (30)  op(e3, e3) = e1
% 241.07/47.59    (31)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.07/47.59              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.07/47.59                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.07/47.59                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.07/47.59    (32)   ~ (all_6_2 = e3)
% 241.07/47.59    (33)  op(e2, e1) = all_52_9
% 241.07/47.59    (34)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.07/47.59          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.07/47.59    (35)   ~ (e3 = e2)
% 241.07/47.59    (36)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.07/47.59          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.07/47.59    (37)   ~ (all_52_14 = all_6_2)
% 241.07/47.59    (38)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.07/47.59          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.07/47.59    (39)  op(e3, e0) = all_52_12
% 241.07/47.59    (40)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.07/47.59          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.07/47.59    (41)   ~ (all_52_9 = all_52_13)
% 241.07/47.59    (42)  op(e2, e3) = all_52_1
% 241.07/47.59    (43)   ~ (all_52_14 = e3)
% 241.07/47.59    (44)  all_36_2 = all_6_2
% 241.07/47.59    (45)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 241.07/47.59    (46)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.07/47.59          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.07/47.59    (47)   ~ (all_52_6 = e3)
% 241.07/47.59    (48)  all_18_2 = all_6_2
% 241.07/47.59    (49)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 241.07/47.59            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 241.07/47.59              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 241.07/47.59    (50)   ~ (all_52_1 = all_52_13)
% 241.07/47.59    (51)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.07/47.59          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.07/47.59    (52)  op(e0, e2) = all_52_7
% 241.07/47.59    (53)   ~ (all_52_13 = all_52_14)
% 241.07/47.59    (54)   ~ (all_52_4 = e3)
% 241.07/47.59    (55)  op(e3, e2) = all_52_4
% 241.07/47.59    (56)   ~ (all_52_9 = e3)
% 241.07/47.59    (57)  all_56_31 = e3
% 241.07/47.59    (58)   ~ (all_18_2 = e0) | ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 &
% 241.07/47.59            op(e1, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 =
% 241.07/47.59              e3) & op(e1, e0) = all_18_1 & $i(all_18_1))
% 241.07/47.59    (59)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.07/47.59          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.07/47.59    (60)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.07/47.59          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.07/47.59    (61)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.07/47.59          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.07/47.59    (62)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.07/47.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.07/47.59    (63)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.07/47.59          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.07/47.59    (64)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.07/47.59          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.07/47.59    (65)   ~ (all_52_12 = e3)
% 241.07/47.59    (66)  all_56_11 = e3
% 241.07/47.59    (67)   ~ (all_52_4 = e1)
% 241.07/47.59    (68)   ~ (e1 = e0)
% 241.07/47.59    (69)  all_56_21 = all_6_2
% 241.07/47.59    (70)  all_58_4 = e3
% 241.07/47.59    (71)   ~ (all_52_13 = e3)
% 241.07/47.59    (72)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.07/47.59          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.07/47.59    (73)  op(e2, e0) = all_52_13
% 241.07/47.59    (74)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.07/47.59          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.07/47.59            e1)
% 241.07/47.59    (75)   ~ (all_52_1 = e3)
% 241.07/47.59    (76)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.07/47.59          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.07/47.59            e2)
% 241.07/47.59    (77)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.07/47.59            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 241.07/47.59            & $i(all_8_1))
% 241.07/47.59    (78)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.07/47.59          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.07/47.59    (79)  all_56_1 = e1
% 241.07/47.59    (80)   ~ (e2 = e1)
% 241.07/47.59    (81)   ~ (all_52_1 = e1)
% 241.07/47.59  
% 241.07/47.59  Begin of proof
% 241.07/47.59  | 
% 241.07/47.59  | BETA: splitting (58) gives:
% 241.07/47.59  | 
% 241.07/47.59  | Case 1:
% 241.07/47.59  | | 
% 241.07/47.59  | |   (82)   ~ (all_18_2 = e0)
% 241.07/47.59  | | 
% 241.07/47.59  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.07/47.59  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 241.07/47.59  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 241.07/47.59  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 241.07/47.59  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 241.07/47.59  | |            (57), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 241.07/47.59  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 241.07/47.59  | |            (80), (81), (82) are inconsistent by sub-proof #489.
% 241.07/47.59  | | 
% 241.07/47.59  | Case 2:
% 241.07/47.59  | | 
% 241.07/47.59  | |   (83)  all_18_2 = e0
% 241.07/47.59  | | 
% 241.07/47.59  | | COMBINE_EQS: (48), (83) imply:
% 241.07/47.59  | |   (84)  all_6_2 = e0
% 241.07/47.59  | | 
% 241.07/47.59  | | SIMP: (84) implies:
% 241.07/47.59  | |   (85)  all_6_2 = e0
% 241.07/47.59  | | 
% 241.07/47.59  | | COMBINE_EQS: (69), (85) imply:
% 241.07/47.59  | |   (86)  all_56_21 = e0
% 241.07/47.59  | | 
% 241.07/47.59  | | REDUCE: (32), (85) imply:
% 241.07/47.59  | |   (87)   ~ (e3 = e0)
% 241.07/47.59  | | 
% 241.07/47.59  | | REDUCE: (17), (85) imply:
% 241.07/47.59  | |   (88)  op(e1, e1) = e0
% 241.07/47.59  | | 
% 241.07/47.59  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 241.07/47.59  | |            (15), (16), (19), (20), (21), (22), (24), (25), (27), (29), (30),
% 241.07/47.59  | |            (31), (33), (34), (35), (36), (38), (40), (42), (46), (47), (51),
% 241.07/47.59  | |            (52), (54), (55), (56), (57), (59), (60), (61), (62), (63), (64),
% 241.07/47.59  | |            (67), (68), (70), (72), (73), (74), (75), (76), (77), (78), (79),
% 241.07/47.59  | |            (80), (81), (86), (88) are inconsistent by sub-proof #497.
% 241.07/47.59  | | 
% 241.07/47.59  | End of split
% 241.07/47.59  | 
% 241.07/47.59  End of proof
% 241.07/47.59  
% 241.07/47.59  Sub-proof #489 shows that the following formulas are inconsistent:
% 241.07/47.59  ----------------------------------------------------------------
% 241.07/47.59    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.07/47.59         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.07/47.59    (2)   ~ (all_52_9 = all_6_2)
% 241.07/47.59    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.07/47.59         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.07/47.59    (4)   ~ (e3 = e0)
% 241.07/47.59    (5)  op(e0, e1) = all_52_11
% 241.07/47.59    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.07/47.59         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.07/47.59    (7)  all_42_2 = e3
% 241.07/47.59    (8)  all_58_6 = e3
% 241.07/47.59    (9)   ~ (e2 = e0)
% 241.07/47.59    (10)  op(e1, e2) = all_52_6
% 241.07/47.59    (11)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.07/47.59          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.07/47.59    (12)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.07/47.59          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.07/47.59    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.07/47.59              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.07/47.59            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.07/47.59            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.07/47.59            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.07/47.59             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.59            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.07/47.59            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.07/47.59            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.07/47.59            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.59            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.07/47.59              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.07/47.59            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.07/47.59            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.07/47.59            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.07/47.59            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.07/47.59            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.07/47.59            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.07/47.59              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.07/47.59            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.59            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.07/47.59            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.07/47.59            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.07/47.59            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.59            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.07/47.59              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.07/47.59            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.59            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.07/47.59    (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.07/47.59          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.07/47.60    (15)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.07/47.60            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.07/47.60              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.07/47.60    (16)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.07/47.60          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.07/47.60    (17)  op(e1, e1) = all_6_2
% 241.07/47.60    (18)  op(e1, e0) = all_52_14
% 241.07/47.60    (19)   ~ (all_52_7 = e3)
% 241.07/47.60    (20)  all_58_15 = e3
% 241.07/47.60    (21)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.07/47.60          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.07/47.60    (22)   ~ (e3 = e1)
% 241.07/47.60    (23)   ~ (all_52_12 = e1)
% 241.07/47.60    (24)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.07/47.60          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.07/47.60    (25)  all_58_3 = e3
% 241.07/47.60    (26)   ~ (all_52_12 = all_52_13)
% 241.07/47.60    (27)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.07/47.60          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.07/47.60    (28)  all_54_10 = all_6_2
% 241.07/47.60    (29)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.07/47.60          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.07/47.60    (30)  op(e3, e3) = e1
% 241.07/47.60    (31)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.07/47.60              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.07/47.60                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.07/47.60                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.07/47.60    (32)   ~ (all_6_2 = e3)
% 241.07/47.60    (33)  op(e2, e1) = all_52_9
% 241.07/47.60    (34)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.07/47.60          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.07/47.60    (35)   ~ (e3 = e2)
% 241.07/47.60    (36)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.07/47.60          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.07/47.60    (37)   ~ (all_52_14 = all_6_2)
% 241.07/47.60    (38)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.07/47.60          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.07/47.60    (39)  op(e3, e0) = all_52_12
% 241.07/47.60    (40)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.07/47.60          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.07/47.60    (41)   ~ (all_52_9 = all_52_13)
% 241.07/47.60    (42)  op(e2, e3) = all_52_1
% 241.07/47.60    (43)   ~ (all_52_14 = e3)
% 241.07/47.60    (44)  all_36_2 = all_6_2
% 241.07/47.60    (45)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 241.07/47.60    (46)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.07/47.60          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.07/47.60    (47)   ~ (all_52_6 = e3)
% 241.07/47.60    (48)  all_18_2 = all_6_2
% 241.07/47.60    (49)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 241.07/47.60            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 241.07/47.60              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 241.07/47.60    (50)   ~ (all_52_1 = all_52_13)
% 241.07/47.60    (51)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.07/47.60          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.07/47.60    (52)  op(e0, e2) = all_52_7
% 241.07/47.60    (53)   ~ (all_52_13 = all_52_14)
% 241.07/47.60    (54)   ~ (all_52_4 = e3)
% 241.07/47.60    (55)  op(e3, e2) = all_52_4
% 241.07/47.60    (56)   ~ (all_52_9 = e3)
% 241.07/47.60    (57)  all_56_31 = e3
% 241.07/47.60    (58)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.07/47.60          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.07/47.60    (59)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.07/47.60          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.07/47.60    (60)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.07/47.60          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.07/47.60    (61)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.07/47.60            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.07/47.60    (62)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.07/47.60          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.07/47.60    (63)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.07/47.60          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.07/47.60    (64)   ~ (all_52_12 = e3)
% 241.07/47.60    (65)  all_56_11 = e3
% 241.07/47.60    (66)   ~ (all_52_4 = e1)
% 241.07/47.60    (67)   ~ (e1 = e0)
% 241.07/47.60    (68)  all_56_21 = all_6_2
% 241.07/47.60    (69)  all_58_4 = e3
% 241.07/47.60    (70)   ~ (all_18_2 = e0)
% 241.07/47.60    (71)   ~ (all_52_13 = e3)
% 241.07/47.60    (72)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.07/47.60          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.07/47.60    (73)  op(e2, e0) = all_52_13
% 241.07/47.60    (74)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.07/47.60          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.07/47.60            e1)
% 241.07/47.60    (75)   ~ (all_52_1 = e3)
% 241.07/47.60    (76)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.07/47.60          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.07/47.60            e2)
% 241.07/47.60    (77)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.07/47.60            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 241.07/47.60            & $i(all_8_1))
% 241.07/47.60    (78)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.07/47.60          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.07/47.60    (79)  all_56_1 = e1
% 241.07/47.60    (80)   ~ (e2 = e1)
% 241.07/47.60    (81)   ~ (all_52_1 = e1)
% 241.07/47.60  
% 241.07/47.60  Begin of proof
% 241.07/47.60  | 
% 241.07/47.60  | REDUCE: (48), (70) imply:
% 241.07/47.60  |   (82)   ~ (all_6_2 = e0)
% 241.07/47.60  | 
% 241.07/47.60  | BETA: splitting (49) gives:
% 241.07/47.60  | 
% 241.07/47.60  | Case 1:
% 241.07/47.60  | | 
% 241.07/47.60  | |   (83)   ~ (all_36_2 = e2)
% 241.07/47.60  | | 
% 241.07/47.60  | | REDUCE: (44), (83) imply:
% 241.07/47.60  | |   (84)   ~ (all_6_2 = e2)
% 241.07/47.60  | | 
% 241.07/47.60  | | BETA: splitting (45) gives:
% 241.07/47.60  | | 
% 241.07/47.60  | | Case 1:
% 241.07/47.60  | | | 
% 241.07/47.60  | | |   (85)  all_54_10 = e3
% 241.07/47.60  | | | 
% 241.07/47.60  | | | REF_CLOSE: (28), (32), (85) are inconsistent by sub-proof #2313.
% 241.07/47.60  | | | 
% 241.07/47.60  | | Case 2:
% 241.07/47.60  | | | 
% 241.07/47.60  | | |   (86)   ~ (all_54_10 = e3)
% 241.07/47.60  | | |   (87)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 241.07/47.60  | | | 
% 241.07/47.60  | | | BETA: splitting (87) gives:
% 241.07/47.60  | | | 
% 241.07/47.60  | | | Case 1:
% 241.07/47.60  | | | | 
% 241.07/47.60  | | | |   (88)  all_54_10 = e2
% 241.07/47.60  | | | | 
% 241.07/47.60  | | | | REF_CLOSE: (28), (84), (88) are inconsistent by sub-proof #2312.
% 241.07/47.60  | | | | 
% 241.07/47.60  | | | Case 2:
% 241.07/47.60  | | | | 
% 241.07/47.60  | | | |   (89)   ~ (all_54_10 = e2)
% 241.07/47.60  | | | |   (90)  all_54_10 = e1 | all_54_10 = e0
% 241.07/47.60  | | | | 
% 241.07/47.60  | | | | BETA: splitting (90) gives:
% 241.07/47.60  | | | | 
% 241.07/47.60  | | | | Case 1:
% 241.07/47.60  | | | | | 
% 241.07/47.60  | | | | |   (91)  all_54_10 = e1
% 241.07/47.60  | | | | | 
% 241.07/47.60  | | | | | COMBINE_EQS: (28), (91) imply:
% 241.07/47.60  | | | | |   (92)  all_6_2 = e1
% 241.07/47.60  | | | | | 
% 241.07/47.60  | | | | | SIMP: (92) implies:
% 241.07/47.60  | | | | |   (93)  all_6_2 = e1
% 241.07/47.60  | | | | | 
% 241.07/47.60  | | | | | COMBINE_EQS: (68), (93) imply:
% 241.07/47.60  | | | | |   (94)  all_56_21 = e1
% 241.07/47.60  | | | | | 
% 241.07/47.60  | | | | | REDUCE: (2), (93) imply:
% 241.07/47.60  | | | | |   (95)   ~ (all_52_9 = e1)
% 241.07/47.60  | | | | | 
% 241.07/47.60  | | | | | REDUCE: (32), (93) imply:
% 241.07/47.60  | | | | |   (96)   ~ (e3 = e1)
% 241.07/47.60  | | | | | 
% 241.07/47.60  | | | | | REDUCE: (84), (93) imply:
% 241.07/47.60  | | | | |   (97)   ~ (e2 = e1)
% 241.07/47.60  | | | | | 
% 241.07/47.60  | | | | | BETA: splitting (78) gives:
% 241.07/47.60  | | | | | 
% 241.07/47.60  | | | | | Case 1:
% 241.07/47.60  | | | | | | 
% 241.07/47.60  | | | | | |   (98)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2,
% 241.07/47.60  | | | | | |             e2) = e1)
% 241.07/47.60  | | | | | | 
% 241.07/47.60  | | | | | | BETA: splitting (98) gives:
% 241.07/47.60  | | | | | | 
% 241.07/47.60  | | | | | | Case 1:
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | |   (99)  all_58_2 = e1 & op(e2, e3) = e1
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | | REF_CLOSE: (42), (61), (81), (99) are inconsistent by sub-proof
% 241.07/47.60  | | | | | | |            #2229.
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | Case 2:
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | |   (100)  all_58_3 = e1 & op(e2, e2) = e1
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | | REF_CLOSE: (1), (4), (9), (22), (25), (27), (30), (35), (46),
% 241.07/47.60  | | | | | | |            (54), (55), (61), (67), (69), (80), (100) are
% 241.07/47.60  | | | | | | |            inconsistent by sub-proof #1030.
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | End of split
% 241.07/47.60  | | | | | | 
% 241.07/47.60  | | | | | Case 2:
% 241.07/47.60  | | | | | | 
% 241.07/47.60  | | | | | |   (101)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 241.07/47.60  | | | | | |            op(e2, e0) = e1)
% 241.07/47.60  | | | | | | 
% 241.07/47.60  | | | | | | BETA: splitting (101) gives:
% 241.07/47.60  | | | | | | 
% 241.07/47.60  | | | | | | Case 1:
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | |   (102)  all_58_5 = e1 & op(e2, e1) = e1
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | | ALPHA: (102) implies:
% 241.07/47.60  | | | | | | |   (103)  op(e2, e1) = e1
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | | REF_CLOSE: (33), (61), (95), (103) are inconsistent by sub-proof
% 241.07/47.60  | | | | | | |            #2306.
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | Case 2:
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | |   (104)  all_58_10 = e1 & op(e2, e0) = e1
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | | ALPHA: (104) implies:
% 241.07/47.60  | | | | | | |   (105)  op(e2, e0) = e1
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | | GROUND_INST: instantiating (61) with all_52_13, e1, e0, e2,
% 241.07/47.60  | | | | | | |              simplifying with (73), (105) gives:
% 241.07/47.60  | | | | | | |   (106)  all_52_13 = e1
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | | REDUCE: (53), (106) imply:
% 241.07/47.60  | | | | | | |   (107)   ~ (all_52_14 = e1)
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | | SIMP: (107) implies:
% 241.07/47.60  | | | | | | |   (108)   ~ (all_52_14 = e1)
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | | BETA: splitting (13) gives:
% 241.07/47.60  | | | | | | | 
% 241.07/47.60  | | | | | | | Case 1:
% 241.07/47.60  | | | | | | | | 
% 241.07/47.60  | | | | | | | |   (109)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 241.07/47.60  | | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.07/47.60  | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) = e3)
% 241.07/47.60  | | | | | | | |          | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &
% 241.07/47.60  | | | | | | | |             ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.07/47.60  | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 241.07/47.60  | | | | | | | |          | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1)
% 241.07/47.60  | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.60  | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 241.07/47.60  | | | | | | | |          | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3)
% 241.07/47.60  | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.07/47.60  | | | | | | | |            (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1)
% 241.07/47.60  | | | | | | | |          | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 241.07/47.60  | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.60  | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3)
% 241.07/47.60  | | | | | | | |          | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 241.07/47.60  | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.07/47.60  | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 241.07/47.60  | | | | | | | | 
% 241.07/47.60  | | | | | | | | BETA: splitting (109) gives:
% 241.07/47.60  | | | | | | | | 
% 241.07/47.60  | | | | | | | | Case 1:
% 241.07/47.60  | | | | | | | | | 
% 241.07/47.60  | | | | | | | | |   (110)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &
% 241.07/47.60  | | | | | | | | |             ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.07/47.60  | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 241.07/47.60  | | | | | | | | |            e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 241.07/47.60  | | | | | | | | |              = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 241.07/47.60  | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 241.07/47.60  | | | | | | | | |              e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.07/47.60  | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.07/47.60  | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 241.07/47.60  | | | | | | | | |            = e3 & op(e1, e3) = e3)
% 241.07/47.60  | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | REF_CLOSE: (42), (57), (61), (75), (94), (110) are
% 241.07/47.60  | | | | | | | | |            inconsistent by sub-proof #791.
% 241.07/47.60  | | | | | | | | | 
% 241.07/47.60  | | | | | | | | Case 2:
% 241.07/47.60  | | | | | | | | | 
% 241.07/47.60  | | | | | | | | |   (111)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3)
% 241.07/47.60  | | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.07/47.60  | | | | | | | | |            (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.07/47.60  | | | | | | | | |            e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 241.07/47.60  | | | | | | | | |            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 241.07/47.60  | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0)
% 241.07/47.60  | | | | | | | | |            = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 241.07/47.60  | | | | | | | | |            all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 241.07/47.60  | | | | | | | | |              = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 241.07/47.60  | | | | | | | | |            & op(e3, e0) = e0 & op(e0, e3) = e0)
% 241.07/47.60  | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | BETA: splitting (111) gives:
% 241.07/47.60  | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | Case 1:
% 241.07/47.60  | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | |   (112)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3)
% 241.07/47.60  | | | | | | | | | |          &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.07/47.60  | | | | | | | | | |          (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.07/47.60  | | | | | | | | | |          e1
% 241.07/47.60  | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | ALPHA: (112) implies:
% 241.07/47.60  | | | | | | | | | |   (113)   ~ (all_56_31 = e3)
% 241.07/47.60  | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | REDUCE: (57), (113) imply:
% 241.07/47.60  | | | | | | | | | |   (114)  $false
% 241.07/47.60  | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | CLOSE: (114) is inconsistent.
% 241.07/47.60  | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | Case 2:
% 241.07/47.60  | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | |   (115)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 241.07/47.60  | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.07/47.60  | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 241.07/47.60  | | | | | | | | | |              e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 241.07/47.60  | | | | | | | | | |            ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.07/47.60  | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.07/47.60  | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 241.07/47.60  | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | BETA: splitting (115) gives:
% 241.07/47.60  | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | Case 1:
% 241.07/47.60  | | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | |   (116)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 241.07/47.60  | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.07/47.60  | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 241.07/47.60  | | | | | | | | | | |            e3) = e3
% 241.07/47.60  | | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | | ALPHA: (116) implies:
% 241.07/47.60  | | | | | | | | | | |   (117)  op(e3, e0) = e3
% 241.07/47.60  | | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_12, e3, e0, e3,
% 241.07/47.60  | | | | | | | | | | |              simplifying with (39), (117) gives:
% 241.07/47.60  | | | | | | | | | | |   (118)  all_52_12 = e3
% 241.07/47.60  | | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | | REDUCE: (64), (118) imply:
% 241.07/47.60  | | | | | | | | | | |   (119)  $false
% 241.07/47.60  | | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | | CLOSE: (119) is inconsistent.
% 241.07/47.60  | | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | Case 2:
% 241.07/47.60  | | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | |   (120)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 241.07/47.60  | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 241.07/47.60  | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 241.07/47.60  | | | | | | | | | | |            e3) = e0
% 241.07/47.60  | | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | | ALPHA: (120) implies:
% 241.07/47.60  | | | | | | | | | | |   (121)   ~ (all_56_31 = e3)
% 241.07/47.60  | | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | | REDUCE: (57), (121) imply:
% 241.07/47.60  | | | | | | | | | | |   (122)  $false
% 241.07/47.60  | | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | | CLOSE: (122) is inconsistent.
% 241.07/47.60  | | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | | End of split
% 241.07/47.60  | | | | | | | | | | 
% 241.07/47.60  | | | | | | | | | End of split
% 241.07/47.60  | | | | | | | | | 
% 241.07/47.60  | | | | | | | | End of split
% 241.07/47.60  | | | | | | | | 
% 241.07/47.60  | | | | | | | Case 2:
% 241.07/47.60  | | | | | | | | 
% 241.07/47.61  | | | | | | | |   (123)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &
% 241.07/47.61  | | | | | | | |             ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.61  | | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2)
% 241.07/47.61  | | | | | | | |          | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2)
% 241.07/47.61  | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.07/47.61  | | | | | | | |            (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1)
% 241.07/47.61  | | | | | | | |          | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0)
% 241.07/47.61  | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.61  | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.07/47.61  | | | | | | | |          | (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2)
% 241.07/47.61  | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.07/47.61  | | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0)
% 241.07/47.61  | | | | | | | |          | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0)
% 241.07/47.61  | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.61  | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1)
% 241.07/47.61  | | | | | | | |          | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1)
% 241.07/47.61  | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.61  | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | | BETA: splitting (123) gives:
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | |   (124)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 241.07/47.61  | | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.61  | | | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.07/47.61  | | | | | | | | |            e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~
% 241.07/47.61  | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.07/47.61  | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1)
% 241.07/47.61  | | | | | | | | |            = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 241.07/47.61  | | | | | | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 241.07/47.61  | | | | | | | | |              = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 241.07/47.61  | | | | | | | | |            & op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | BETA: splitting (124) gives:
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | |   (125)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.07/47.61  | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &
% 241.07/47.61  | | | | | | | | | |           ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.07/47.61  | | | | | | | | | |          = e2
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | ALPHA: (125) implies:
% 241.07/47.61  | | | | | | | | | |   (126)   ~ (all_56_21 = e1)
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | REDUCE: (94), (126) imply:
% 241.07/47.61  | | | | | | | | | |   (127)  $false
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | CLOSE: (127) is inconsistent.
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | |   (128)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.07/47.61  | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.07/47.61  | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 241.07/47.61  | | | | | | | | | |              e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 & 
% 241.07/47.61  | | | | | | | | | |            ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 241.07/47.61  | | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2,
% 241.07/47.61  | | | | | | | | | |              e0) = e2 & op(e0, e2) = e2)
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | BETA: splitting (128) gives:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | |   (129)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.07/47.61  | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.07/47.61  | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 241.07/47.61  | | | | | | | | | | |            e2) = e1
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | ALPHA: (129) implies:
% 241.07/47.61  | | | | | | | | | | |   (130)  op(e2, e1) = e1
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | REF_CLOSE: (33), (61), (95), (130) are inconsistent by
% 241.07/47.61  | | | | | | | | | | |            sub-proof #2306.
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | |   (131)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 241.07/47.61  | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.07/47.61  | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 241.07/47.61  | | | | | | | | | | |            e2) = e2
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | ALPHA: (131) implies:
% 241.07/47.61  | | | | | | | | | | |   (132)  op(e2, e0) = e2
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | GROUND_INST: instantiating (61) with e1, e2, e0, e2,
% 241.07/47.61  | | | | | | | | | | |              simplifying with (105), (132) gives:
% 241.07/47.61  | | | | | | | | | | |   (133)  e2 = e1
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | REDUCE: (80), (133) imply:
% 241.07/47.61  | | | | | | | | | | |   (134)  $false
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | |   (135)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2)
% 241.07/47.61  | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.07/47.61  | | | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.07/47.61  | | | | | | | | |            e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 241.07/47.61  | | | | | | | | |            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 241.07/47.61  | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0)
% 241.07/47.61  | | | | | | | | |            = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 241.07/47.61  | | | | | | | | |            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 241.07/47.61  | | | | | | | | |              = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 241.07/47.61  | | | | | | | | |            & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | BETA: splitting (135) gives:
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | |   (136)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.07/47.61  | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &
% 241.07/47.61  | | | | | | | | | |           ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.07/47.61  | | | | | | | | | |          = e0
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | ALPHA: (136) implies:
% 241.07/47.61  | | | | | | | | | |   (137)  op(e2, e0) = e0
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | REF_CLOSE: (22), (25), (33), (42), (61), (67), (73), (78),
% 241.07/47.61  | | | | | | | | | |            (81), (95), (137) are inconsistent by sub-proof
% 241.07/47.61  | | | | | | | | | |            #1777.
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | |   (138)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.07/47.61  | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.07/47.61  | | | | | | | | | |            &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 241.07/47.61  | | | | | | | | | |              e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 & 
% 241.07/47.61  | | | | | | | | | |            ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.07/47.61  | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 241.07/47.61  | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | BETA: splitting (138) gives:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | |   (139)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.07/47.61  | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.07/47.61  | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 241.07/47.61  | | | | | | | | | | |            e1) = e1
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | ALPHA: (139) implies:
% 241.07/47.61  | | | | | | | | | | |   (140)  op(e1, e0) = e1
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_14, e1, e0, e1,
% 241.07/47.61  | | | | | | | | | | |              simplifying with (18), (140) gives:
% 241.07/47.61  | | | | | | | | | | |   (141)  all_52_14 = e1
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | REDUCE: (108), (141) imply:
% 241.07/47.61  | | | | | | | | | | |   (142)  $false
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | CLOSE: (142) is inconsistent.
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | |   (143)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 241.07/47.61  | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 241.07/47.61  | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 241.07/47.61  | | | | | | | | | | |            e1) = e0
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | ALPHA: (143) implies:
% 241.07/47.61  | | | | | | | | | | |   (144)   ~ (all_56_21 = e1)
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | REDUCE: (94), (144) imply:
% 241.07/47.61  | | | | | | | | | | |   (145)  $false
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | CLOSE: (145) is inconsistent.
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | End of split
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | End of split
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | End of split
% 241.07/47.61  | | | | | 
% 241.07/47.61  | | | | Case 2:
% 241.07/47.61  | | | | | 
% 241.07/47.61  | | | | |   (146)  all_54_10 = e0
% 241.07/47.61  | | | | | 
% 241.07/47.61  | | | | | REF_CLOSE: (28), (82), (146) are inconsistent by sub-proof #2303.
% 241.07/47.61  | | | | | 
% 241.07/47.61  | | | | End of split
% 241.07/47.61  | | | | 
% 241.07/47.61  | | | End of split
% 241.07/47.61  | | | 
% 241.07/47.61  | | End of split
% 241.07/47.61  | | 
% 241.07/47.61  | Case 2:
% 241.07/47.61  | | 
% 241.07/47.61  | |   (147)  all_36_2 = e2
% 241.07/47.61  | | 
% 241.07/47.61  | | COMBINE_EQS: (44), (147) imply:
% 241.07/47.61  | |   (148)  all_6_2 = e2
% 241.07/47.61  | | 
% 241.07/47.61  | | COMBINE_EQS: (68), (148) imply:
% 241.07/47.61  | |   (149)  all_56_21 = e2
% 241.07/47.61  | | 
% 241.07/47.61  | | REDUCE: (37), (148) imply:
% 241.07/47.61  | |   (150)   ~ (all_52_14 = e2)
% 241.07/47.61  | | 
% 241.07/47.61  | | REDUCE: (32), (148) imply:
% 241.07/47.61  | |   (151)   ~ (e3 = e2)
% 241.07/47.61  | | 
% 241.07/47.61  | | REDUCE: (17), (148) imply:
% 241.07/47.61  | |   (152)  op(e1, e1) = e2
% 241.07/47.61  | | 
% 241.07/47.61  | | BETA: splitting (59) gives:
% 241.07/47.61  | | 
% 241.07/47.61  | | Case 1:
% 241.07/47.61  | | | 
% 241.07/47.61  | | |   (153)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 241.07/47.61  | | |            e2)
% 241.07/47.61  | | | 
% 241.07/47.61  | | | BETA: splitting (153) gives:
% 241.07/47.61  | | | 
% 241.07/47.61  | | | Case 1:
% 241.07/47.61  | | | | 
% 241.07/47.61  | | | |   (154)  all_58_6 = e2 & op(e1, e3) = e2
% 241.07/47.61  | | | | 
% 241.07/47.61  | | | | REF_CLOSE: (8), (35), (154) are inconsistent by sub-proof #2219.
% 241.07/47.61  | | | | 
% 241.07/47.61  | | | Case 2:
% 241.07/47.61  | | | | 
% 241.07/47.61  | | | |   (155)  all_58_7 = e2 & op(e1, e2) = e2
% 241.07/47.61  | | | | 
% 241.07/47.61  | | | | ALPHA: (155) implies:
% 241.07/47.61  | | | |   (156)  all_58_7 = e2
% 241.07/47.61  | | | | 
% 241.07/47.61  | | | | BETA: splitting (6) gives:
% 241.07/47.61  | | | | 
% 241.07/47.61  | | | | Case 1:
% 241.07/47.61  | | | | | 
% 241.07/47.61  | | | | |   (157)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1,
% 241.07/47.61  | | | | |              e2) = e1)
% 241.07/47.61  | | | | | 
% 241.07/47.61  | | | | | BETA: splitting (157) gives:
% 241.07/47.61  | | | | | 
% 241.07/47.61  | | | | | Case 1:
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | |   (158)  all_58_6 = e1 & op(e1, e3) = e1
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | | ALPHA: (158) implies:
% 241.07/47.61  | | | | | |   (159)  all_58_6 = e1
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | | REF_CLOSE: (4), (9), (22), (29), (30), (34), (35), (38), (42), (61),
% 241.07/47.61  | | | | | |            (67), (75), (80), (159) are inconsistent by sub-proof
% 241.07/47.61  | | | | | |            #1161.
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | Case 2:
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | |   (160)  all_58_7 = e1 & op(e1, e2) = e1
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | | REF_CLOSE: (80), (156), (160) are inconsistent by sub-proof #2224.
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | End of split
% 241.07/47.61  | | | | | 
% 241.07/47.61  | | | | Case 2:
% 241.07/47.61  | | | | | 
% 241.07/47.61  | | | | |   (161)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1,
% 241.07/47.61  | | | | |              e0) = e1)
% 241.07/47.61  | | | | | 
% 241.07/47.61  | | | | | BETA: splitting (161) gives:
% 241.07/47.61  | | | | | 
% 241.07/47.61  | | | | | Case 1:
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | |   (162)  all_58_8 = e1 & op(e1, e1) = e1
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | | ALPHA: (162) implies:
% 241.07/47.61  | | | | | |   (163)  all_58_8 = e1
% 241.07/47.61  | | | | | |   (164)  op(e1, e1) = e1
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | | BETA: splitting (63) gives:
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | | Case 1:
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | |   (165)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 241.07/47.61  | | | | | | |            op(e2, e2) = e1)
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | | REF_CLOSE: (1), (4), (9), (22), (25), (27), (30), (35), (46),
% 241.07/47.61  | | | | | | |            (54), (55), (61), (66), (67), (69), (80), (165) are
% 241.07/47.61  | | | | | | |            inconsistent by sub-proof #528.
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | Case 2:
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | |   (166)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 241.07/47.61  | | | | | | |            op(e0, e2) = e1)
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | | BETA: splitting (166) gives:
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | |   (167)  all_58_7 = e1 & op(e1, e2) = e1
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | | REF_CLOSE: (80), (156), (167) are inconsistent by sub-proof
% 241.07/47.61  | | | | | | | |            #2224.
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | |   (168)  all_58_13 = e1 & op(e0, e2) = e1
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | | ALPHA: (168) implies:
% 241.07/47.61  | | | | | | | |   (169)  all_58_13 = e1
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | | BETA: splitting (36) gives:
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | |   (170)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 241.07/47.61  | | | | | | | | |            op(e2, e1) = e2)
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | BETA: splitting (170) gives:
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | |   (171)  all_58_4 = e2 & op(e3, e1) = e2
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | REF_CLOSE: (35), (69), (171) are inconsistent by sub-proof
% 241.07/47.61  | | | | | | | | | |            #1476.
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | |   (172)  all_58_5 = e2 & op(e2, e1) = e2
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | ALPHA: (172) implies:
% 241.07/47.61  | | | | | | | | | |   (173)  all_58_5 = e2
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | BETA: splitting (72) gives:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | |   (174)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 241.07/47.61  | | | | | | | | | | |            & op(e1, e2) = e0)
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | BETA: splitting (174) gives:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | |   (175)  all_58_6 = e0 & op(e1, e3) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | REF_CLOSE: (2), (8), (13), (25), (28), (32), (33), (42),
% 241.07/47.61  | | | | | | | | | | | |            (45), (57), (61), (65), (68), (73), (75), (78),
% 241.07/47.61  | | | | | | | | | | | |            (79), (81), (82), (175) are inconsistent by
% 241.07/47.61  | | | | | | | | | | | |            sub-proof #527.
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | |   (176)  all_58_7 = e0 & op(e1, e2) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | REF_CLOSE: (9), (156), (176) are inconsistent by sub-proof
% 241.07/47.61  | | | | | | | | | | | |            #2212.
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | |   (177)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 241.07/47.61  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | BETA: splitting (177) gives:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | |   (178)  all_58_8 = e0 & op(e1, e1) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | ALPHA: (178) implies:
% 241.07/47.61  | | | | | | | | | | | |   (179)  op(e1, e1) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | REF_CLOSE: (61), (67), (164), (179) are inconsistent by
% 241.07/47.61  | | | | | | | | | | | |            sub-proof #2220.
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | |   (180)  all_58_11 = e0 & op(e1, e0) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | ALPHA: (180) implies:
% 241.07/47.61  | | | | | | | | | | | |   (181)  all_58_11 = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | BETA: splitting (78) gives:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | |   (182)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 241.07/47.61  | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | BETA: splitting (182) gives:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | |   (183)  all_58_2 = e1 & op(e2, e3) = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | REF_CLOSE: (42), (61), (81), (183) are inconsistent by
% 241.07/47.61  | | | | | | | | | | | | | |            sub-proof #2229.
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | |   (184)  all_58_3 = e1 & op(e2, e2) = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (22), (25), (27), (30), (35), (46),
% 241.07/47.61  | | | | | | | | | | | | | |            (54), (55), (61), (67), (69), (80), (184) are
% 241.07/47.61  | | | | | | | | | | | | | |            inconsistent by sub-proof #1030.
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | |   (185)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 241.07/47.61  | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | |   (186)  all_58_5 = e1 & op(e2, e1) = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | ALPHA: (186) implies:
% 241.07/47.61  | | | | | | | | | | | | | |   (187)  all_58_5 = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | COMBINE_EQS: (173), (187) imply:
% 241.07/47.61  | | | | | | | | | | | | | |   (188)  e2 = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | COMBINE_EQS: (156), (188) imply:
% 241.07/47.61  | | | | | | | | | | | | | |   (189)  all_58_7 = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (35), (59), (80), (163), (181), (189)
% 241.07/47.61  | | | | | | | | | | | | | |            are inconsistent by sub-proof #2215.
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | |   (190)  all_58_10 = e1 & op(e2, e0) = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (9), (10), (11), (14), (16), (20),
% 241.07/47.61  | | | | | | | | | | | | | |            (21), (22), (24), (25), (27), (29), (30), (31),
% 241.07/47.61  | | | | | | | | | | | | | |            (34), (35), (38), (40), (42), (46), (47), (54),
% 241.07/47.61  | | | | | | | | | | | | | |            (55), (58), (59), (60), (61), (62), (67), (69),
% 241.07/47.61  | | | | | | | | | | | | | |            (74), (75), (76), (80), (152), (155), (164),
% 241.07/47.61  | | | | | | | | | | | | | |            (181), (190) are inconsistent by sub-proof #524.
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | |   (191)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 241.07/47.61  | | | | | | | | |            op(e0, e1) = e2)
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | BETA: splitting (191) gives:
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | |   (192)  all_58_8 = e2 & op(e1, e1) = e2
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | ALPHA: (192) implies:
% 241.07/47.61  | | | | | | | | | |   (193)  all_58_8 = e2
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | REF_CLOSE: (2), (4), (6), (8), (9), (10), (11), (13), (14),
% 241.07/47.61  | | | | | | | | | |            (22), (25), (28), (29), (30), (32), (33), (34),
% 241.07/47.61  | | | | | | | | | |            (35), (38), (40), (42), (45), (47), (57), (59),
% 241.07/47.61  | | | | | | | | | |            (61), (65), (67), (68), (72), (73), (75), (78),
% 241.07/47.61  | | | | | | | | | |            (79), (80), (81), (82), (156), (169), (193) are
% 241.07/47.61  | | | | | | | | | |            inconsistent by sub-proof #521.
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | |   (194)  all_58_14 = e2 & op(e0, e1) = e2
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | ALPHA: (194) implies:
% 241.07/47.61  | | | | | | | | | |   (195)  all_58_14 = e2
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | BETA: splitting (72) gives:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | |   (196)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 241.07/47.61  | | | | | | | | | | |            & op(e1, e2) = e0)
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | BETA: splitting (196) gives:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | |   (197)  all_58_6 = e0 & op(e1, e3) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | REF_CLOSE: (2), (8), (13), (25), (28), (32), (33), (42),
% 241.07/47.61  | | | | | | | | | | | |            (45), (57), (61), (65), (68), (73), (75), (78),
% 241.07/47.61  | | | | | | | | | | | |            (79), (81), (82), (197) are inconsistent by
% 241.07/47.61  | | | | | | | | | | | |            sub-proof #527.
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | |   (198)  all_58_7 = e0 & op(e1, e2) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | REF_CLOSE: (9), (156), (198) are inconsistent by sub-proof
% 241.07/47.61  | | | | | | | | | | | |            #2212.
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | |   (199)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 241.07/47.61  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | BETA: splitting (199) gives:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | |   (200)  all_58_8 = e0 & op(e1, e1) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | ALPHA: (200) implies:
% 241.07/47.61  | | | | | | | | | | | |   (201)  op(e1, e1) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | REF_CLOSE: (61), (67), (164), (201) are inconsistent by
% 241.07/47.61  | | | | | | | | | | | |            sub-proof #2220.
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | |   (202)  all_58_11 = e0 & op(e1, e0) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | ALPHA: (202) implies:
% 241.07/47.61  | | | | | | | | | | | |   (203)  all_58_11 = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | BETA: splitting (12) gives:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | |   (204)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 241.07/47.61  | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | BETA: splitting (204) gives:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | |   (205)  all_58_9 = e1 & op(e3, e0) = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | ALPHA: (205) implies:
% 241.07/47.61  | | | | | | | | | | | | | |   (206)  all_58_9 = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (30), (35), (46), (61), (67), (69),
% 241.07/47.61  | | | | | | | | | | | | | |            (80), (206) are inconsistent by sub-proof #1292.
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | |   (207)  all_58_10 = e1 & op(e2, e0) = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (9), (10), (11), (14), (16), (20),
% 241.07/47.61  | | | | | | | | | | | | | |            (21), (22), (24), (25), (27), (29), (30), (31),
% 241.07/47.61  | | | | | | | | | | | | | |            (34), (35), (38), (40), (42), (46), (47), (54),
% 241.07/47.61  | | | | | | | | | | | | | |            (55), (58), (59), (60), (61), (62), (67), (69),
% 241.07/47.61  | | | | | | | | | | | | | |            (74), (75), (76), (80), (152), (155), (164),
% 241.07/47.61  | | | | | | | | | | | | | |            (203), (207) are inconsistent by sub-proof #524.
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | |   (208)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 241.07/47.61  | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | BETA: splitting (208) gives:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | |   (209)  all_58_11 = e1 & op(e1, e0) = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | ALPHA: (209) implies:
% 241.07/47.61  | | | | | | | | | | | | | |   (210)  all_58_11 = e1
% 241.07/47.61  | | | | | | | | | | | | | |   (211)  op(e1, e0) = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (35), (59), (61), (67), (72), (80),
% 241.07/47.61  | | | | | | | | | | | | | |            (163), (164), (210), (211) are inconsistent by
% 241.07/47.61  | | | | | | | | | | | | | |            sub-proof #804.
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | |   (212)  all_58_15 = e1 & op(e0, e0) = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | ALPHA: (212) implies:
% 241.07/47.61  | | | | | | | | | | | | | |   (213)  all_58_15 = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (8), (9), (19), (22), (29), (30), (31),
% 241.07/47.61  | | | | | | | | | | | | | |            (34), (35), (38), (42), (52), (61), (67), (75),
% 241.07/47.61  | | | | | | | | | | | | | |            (76), (80), (195), (213) are inconsistent by
% 241.07/47.61  | | | | | | | | | | | | | |            sub-proof #1159.
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | End of split
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | End of split
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | Case 2:
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | |   (214)  all_58_11 = e1 & op(e1, e0) = e1
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | | ALPHA: (214) implies:
% 241.07/47.61  | | | | | |   (215)  all_58_11 = e1
% 241.07/47.61  | | | | | |   (216)  op(e1, e0) = e1
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | | BETA: splitting (63) gives:
% 241.07/47.61  | | | | | | 
% 241.07/47.61  | | | | | | Case 1:
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | |   (217)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 241.07/47.61  | | | | | | |            op(e2, e2) = e1)
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | | REF_CLOSE: (1), (4), (9), (22), (25), (27), (30), (35), (46),
% 241.07/47.61  | | | | | | |            (54), (55), (61), (66), (67), (69), (80), (217) are
% 241.07/47.61  | | | | | | |            inconsistent by sub-proof #528.
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | Case 2:
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | |   (218)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 241.07/47.61  | | | | | | |            op(e0, e2) = e1)
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | | BETA: splitting (218) gives:
% 241.07/47.61  | | | | | | | 
% 241.07/47.61  | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | |   (219)  all_58_7 = e1 & op(e1, e2) = e1
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | | REF_CLOSE: (80), (156), (219) are inconsistent by sub-proof
% 241.07/47.61  | | | | | | | |            #2224.
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | |   (220)  all_58_13 = e1 & op(e0, e2) = e1
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | | ALPHA: (220) implies:
% 241.07/47.61  | | | | | | | |   (221)  all_58_13 = e1
% 241.07/47.61  | | | | | | | |   (222)  op(e0, e2) = e1
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | | BETA: splitting (36) gives:
% 241.07/47.61  | | | | | | | | 
% 241.07/47.61  | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | |   (223)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 241.07/47.61  | | | | | | | | |            op(e2, e1) = e2)
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | BETA: splitting (223) gives:
% 241.07/47.61  | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | |   (224)  all_58_4 = e2 & op(e3, e1) = e2
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | REF_CLOSE: (35), (69), (224) are inconsistent by sub-proof
% 241.07/47.61  | | | | | | | | | |            #1476.
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | |   (225)  all_58_5 = e2 & op(e2, e1) = e2
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | ALPHA: (225) implies:
% 241.07/47.61  | | | | | | | | | |   (226)  all_58_5 = e2
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | BETA: splitting (72) gives:
% 241.07/47.61  | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | |   (227)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 241.07/47.61  | | | | | | | | | | |            & op(e1, e2) = e0)
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | BETA: splitting (227) gives:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | |   (228)  all_58_6 = e0 & op(e1, e3) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | REF_CLOSE: (2), (8), (13), (25), (28), (32), (33), (42),
% 241.07/47.61  | | | | | | | | | | | |            (45), (57), (61), (65), (68), (73), (75), (78),
% 241.07/47.61  | | | | | | | | | | | |            (79), (81), (82), (228) are inconsistent by
% 241.07/47.61  | | | | | | | | | | | |            sub-proof #527.
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | |   (229)  all_58_7 = e0 & op(e1, e2) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | REF_CLOSE: (9), (156), (229) are inconsistent by sub-proof
% 241.07/47.61  | | | | | | | | | | | |            #2212.
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | |   (230)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 241.07/47.61  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | BETA: splitting (230) gives:
% 241.07/47.61  | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | |   (231)  all_58_8 = e0 & op(e1, e1) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | ALPHA: (231) implies:
% 241.07/47.61  | | | | | | | | | | | |   (232)  op(e1, e1) = e0
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | BETA: splitting (16) gives:
% 241.07/47.61  | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | |   (233)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.07/47.61  | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | BETA: splitting (233) gives:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | |   (234)  all_58_4 = e1 & op(e3, e1) = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | ALPHA: (234) implies:
% 241.07/47.61  | | | | | | | | | | | | | |   (235)  all_58_4 = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (22), (27), (30), (35), (46), (54),
% 241.07/47.61  | | | | | | | | | | | | | |            (55), (61), (67), (80), (235) are inconsistent by
% 241.07/47.61  | | | | | | | | | | | | | |            sub-proof #1468.
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | |   (236)  all_58_5 = e1 & op(e2, e1) = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | ALPHA: (236) implies:
% 241.07/47.61  | | | | | | | | | | | | | |   (237)  all_58_5 = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | COMBINE_EQS: (226), (237) imply:
% 241.07/47.61  | | | | | | | | | | | | | |   (238)  e2 = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | COMBINE_EQS: (156), (238) imply:
% 241.07/47.61  | | | | | | | | | | | | | |   (239)  all_58_7 = e1
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (11), (14), (25), (35), (67), (80),
% 241.07/47.61  | | | | | | | | | | | | | |            (221), (239) are inconsistent by sub-proof #1457.
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | End of split
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | Case 2:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | |   (240)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.07/47.61  | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | BETA: splitting (240) gives:
% 241.07/47.61  | | | | | | | | | | | | | 
% 241.07/47.61  | | | | | | | | | | | | | Case 1:
% 241.07/47.61  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | |   (241)  all_58_8 = e1 & op(e1, e1) = e1
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | ALPHA: (241) implies:
% 241.07/47.62  | | | | | | | | | | | | | |   (242)  all_58_8 = e1
% 241.07/47.62  | | | | | | | | | | | | | |   (243)  op(e1, e1) = e1
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (10), (22), (35), (40), (47), (59),
% 241.07/47.62  | | | | | | | | | | | | | |            (61), (67), (72), (80), (215), (216), (242), (243)
% 241.07/47.62  | | | | | | | | | | | | | |            are inconsistent by sub-proof #787.
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | |   (244)  all_58_14 = e1 & op(e0, e1) = e1
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | ALPHA: (244) implies:
% 241.07/47.62  | | | | | | | | | | | | | |   (245)  all_58_14 = e1
% 241.07/47.62  | | | | | | | | | | | | | |   (246)  op(e0, e1) = e1
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | |   (247)  all_58_15 = e0 & op(e0, e0) = e0
% 241.07/47.62  | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (11), (12), (14),
% 241.07/47.62  | | | | | | | | | | | | | | |            (16), (20), (21), (22), (24), (25), (27), (29),
% 241.07/47.62  | | | | | | | | | | | | | | |            (30), (31), (33), (34), (35), (36), (38), (40),
% 241.07/47.62  | | | | | | | | | | | | | | |            (42), (46), (47), (51), (54), (55), (56), (58),
% 241.07/47.62  | | | | | | | | | | | | | | |            (59), (60), (61), (62), (67), (69), (72), (73),
% 241.07/47.62  | | | | | | | | | | | | | | |            (74), (75), (76), (78), (80), (81), (232), (245),
% 241.07/47.62  | | | | | | | | | | | | | | |            (247) are inconsistent by sub-proof #520.
% 241.07/47.62  | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | |   (248)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.07/47.62  | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 241.07/47.62  | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 241.07/47.62  | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 241.07/47.62  | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.07/47.62  | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 241.07/47.62  | | | | | | | | | | | | | | |   (249)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 241.07/47.62  | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 241.07/47.62  | | | | | | | | | | | | | | |              e1) = e0)
% 241.07/47.62  | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (35), (61), (67), (76), (80), (221),
% 241.07/47.62  | | | | | | | | | | | | | | |            (222), (245), (246), (249) are inconsistent by
% 241.07/47.62  | | | | | | | | | | | | | | |            sub-proof #765.
% 241.07/47.62  | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | |   (250)  all_58_11 = e0 & op(e1, e0) = e0
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | ALPHA: (250) implies:
% 241.07/47.62  | | | | | | | | | | | |   (251)  op(e1, e0) = e0
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | REF_CLOSE: (61), (67), (216), (251) are inconsistent by
% 241.07/47.62  | | | | | | | | | | | |            sub-proof #2284.
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | 
% 241.07/47.62  | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | 
% 241.07/47.62  | | | | | | | | |   (252)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 241.07/47.62  | | | | | | | | |            op(e0, e1) = e2)
% 241.07/47.62  | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | BETA: splitting (252) gives:
% 241.07/47.62  | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | |   (253)  all_58_8 = e2 & op(e1, e1) = e2
% 241.07/47.62  | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | ALPHA: (253) implies:
% 241.07/47.62  | | | | | | | | | |   (254)  all_58_8 = e2
% 241.07/47.62  | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | REF_CLOSE: (2), (4), (6), (8), (9), (10), (11), (13), (14),
% 241.07/47.62  | | | | | | | | | |            (22), (25), (28), (29), (30), (32), (33), (34),
% 241.07/47.62  | | | | | | | | | |            (35), (38), (40), (42), (45), (47), (57), (59),
% 241.07/47.62  | | | | | | | | | |            (61), (65), (67), (68), (72), (73), (75), (78),
% 241.07/47.62  | | | | | | | | | |            (79), (80), (81), (82), (156), (221), (254) are
% 241.07/47.62  | | | | | | | | | |            inconsistent by sub-proof #521.
% 241.07/47.62  | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | |   (255)  all_58_14 = e2 & op(e0, e1) = e2
% 241.07/47.62  | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | ALPHA: (255) implies:
% 241.07/47.62  | | | | | | | | | |   (256)  all_58_14 = e2
% 241.07/47.62  | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | BETA: splitting (72) gives:
% 241.07/47.62  | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | |   (257)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 241.07/47.62  | | | | | | | | | | |            & op(e1, e2) = e0)
% 241.07/47.62  | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | BETA: splitting (257) gives:
% 241.07/47.62  | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | |   (258)  all_58_6 = e0 & op(e1, e3) = e0
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | REF_CLOSE: (2), (8), (13), (25), (28), (32), (33), (42),
% 241.07/47.62  | | | | | | | | | | | |            (45), (57), (61), (65), (68), (73), (75), (78),
% 241.07/47.62  | | | | | | | | | | | |            (79), (81), (82), (258) are inconsistent by
% 241.07/47.62  | | | | | | | | | | | |            sub-proof #527.
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | |   (259)  all_58_7 = e0 & op(e1, e2) = e0
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | REF_CLOSE: (9), (156), (259) are inconsistent by sub-proof
% 241.07/47.62  | | | | | | | | | | | |            #2212.
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | |   (260)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 241.07/47.62  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 241.07/47.62  | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | BETA: splitting (260) gives:
% 241.07/47.62  | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | |   (261)  all_58_8 = e0 & op(e1, e1) = e0
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | ALPHA: (261) implies:
% 241.07/47.62  | | | | | | | | | | | |   (262)  all_58_8 = e0
% 241.07/47.62  | | | | | | | | | | | |   (263)  op(e1, e1) = e0
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | BETA: splitting (16) gives:
% 241.07/47.62  | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | |   (264)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.07/47.62  | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 241.07/47.62  | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | BETA: splitting (264) gives:
% 241.07/47.62  | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | |   (265)  all_58_4 = e1 & op(e3, e1) = e1
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | ALPHA: (265) implies:
% 241.07/47.62  | | | | | | | | | | | | | |   (266)  all_58_4 = e1
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (22), (27), (30), (35), (46), (54),
% 241.07/47.62  | | | | | | | | | | | | | |            (55), (61), (67), (80), (266) are inconsistent by
% 241.07/47.62  | | | | | | | | | | | | | |            sub-proof #1468.
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | |   (267)  all_58_5 = e1 & op(e2, e1) = e1
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | ALPHA: (267) implies:
% 241.07/47.62  | | | | | | | | | | | | | |   (268)  all_58_5 = e1
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 241.07/47.62  | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | |   (269)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 241.07/47.62  | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 241.07/47.62  | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | |   (270)  all_58_1 = e0 & op(e3, e2) = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | ALPHA: (270) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | |   (271)  all_58_1 = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | |   (272)  all_58_15 = e0 & op(e0, e0) = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | |   (273)  all_58_15 = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (273) imply:
% 241.07/47.62  | | | | | | | | | | | | | | | | |   (274)  e3 = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (11), (12), (14),
% 241.07/47.62  | | | | | | | | | | | | | | | | |            (16), (21), (22), (24), (25), (27), (29), (30),
% 241.07/47.62  | | | | | | | | | | | | | | | | |            (31), (33), (34), (35), (36), (38), (40), (42),
% 241.07/47.62  | | | | | | | | | | | | | | | | |            (46), (47), (51), (54), (55), (56), (58), (59),
% 241.07/47.62  | | | | | | | | | | | | | | | | |            (60), (61), (62), (67), (72), (73), (74), (75),
% 241.07/47.62  | | | | | | | | | | | | | | | | |            (76), (78), (80), (81), (263), (274) are
% 241.07/47.62  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #642.
% 241.07/47.62  | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | |   (275)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.07/47.62  | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 241.07/47.62  | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 241.07/47.62  | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 241.07/47.62  | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.07/47.62  | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | |   (276)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 241.07/47.62  | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 241.07/47.62  | | | | | | | | | | | | | | | | |              e1) = e0)
% 241.07/47.62  | | | | | | | | | | | | | | | | |   (277)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.07/47.62  | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 241.07/47.62  | | | | | | | | | | | | | | | | |              e0) = e0)
% 241.07/47.62  | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | |   (278)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 241.07/47.62  | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |   (279)  all_58_0 = e2 & op(e3, e3) = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |   (280)  op(e3, e3) = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (61), (80), (280) are inconsistent by
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |            sub-proof #2267.
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |   (281)  all_58_1 = e2 & op(e3, e2) = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |   (282)  all_58_1 = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (282) imply:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |   (283)  e2 = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (10), (11), (14), (22), (25), (29),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |            (30), (34), (35), (38), (40), (42), (47), (59),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |            (61), (67), (75), (80), (156), (221), (262),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |            (263), (283) are inconsistent by sub-proof #518.
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | |   (284)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 241.07/47.62  | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |   (285)  all_58_4 = e2 & op(e3, e1) = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (10), (22), (29), (30), (34), (35),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |            (38), (40), (42), (47), (61), (67), (69), (75),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |            (80), (215), (263), (285) are inconsistent by
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |            sub-proof #517.
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |   (286)  all_58_9 = e2 & op(e3, e0) = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | |   (287)  all_58_9 = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | |   (288)  all_58_12 = e0 & op(e0, e3) = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | |   (289)  all_58_12 = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | |   (290)  all_58_9 = e0 & op(e3, e0) = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | |   (291)  all_58_9 = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (9), (20), (22), (25), (30), (34),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | |            (35), (42), (60), (61), (62), (67), (69), (78),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | |            (80), (81), (215), (289), (291) are inconsistent
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #613.
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | |   (292)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | |   (293)  all_58_10 = e0 & op(e2, e0) = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | |   (294)  all_58_10 = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | |   (295)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_58_0 = e2 & op(e3, e3) = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |   (297)  op(e3, e3) = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (61), (80), (297) are inconsistent by
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2267.
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |   (298)  all_58_2 = e2 & op(e2, e3) = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_58_2 = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (300)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  all_58_9 = e1 & op(e3, e0) = e1
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_58_9 = e1
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (9), (10), (11), (12), (14), (16),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (21), (22), (24), (25), (27), (29), (30), (31),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (33), (34), (35), (36), (38), (40), (42), (46),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (47), (51), (54), (55), (56), (58), (59), (60),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (61), (62), (67), (72), (73), (74), (75), (76),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (80), (81), (263), (289), (302) are
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #639.
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  all_58_10 = e1 & op(e2, e0) = e1
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_58_10 = e1
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (20), (21), (22), (25), (27), (30),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (35), (46), (54), (55), (58), (60), (61), (62),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (67), (80), (268), (277), (287), (304) are
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #516.
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e0, e2, e1, e1,
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (152), (263) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  e2 = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (21), (22), (25), (29), (30), (34),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (35), (38), (42), (60), (61), (67), (75), (78),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (80), (81), (289), (294), (299), (306) are
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #632.
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  all_58_15 = e1 & op(e0, e0) = e1
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_58_15 = e1
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (8), (9), (19), (22), (29), (30), (31),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (34), (35), (38), (42), (52), (61), (67), (75),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (76), (80), (256), (308) are inconsistent by
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1159.
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | |   (309)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |   (310)  all_58_6 = e2 & op(e1, e3) = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |   (311)  all_58_6 = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (10), (22), (29), (30), (34), (35),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |            (38), (40), (42), (47), (61), (67), (75), (80),
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |            (215), (263), (311) are inconsistent by sub-proof
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |            #661.
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_58_12 = e2 & op(e0, e3) = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (312) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_58_12 = e2
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  all_58_0 = e0 & op(e3, e3) = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  op(e3, e3) = e0
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (61), (67), (316) are inconsistent by
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1828.
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  all_58_2 = e0 & op(e2, e3) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  all_58_2 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  all_58_15 = e0 & op(e0, e0) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (319) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)  all_58_15 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (320) imply:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)  e3 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (11), (12), (14),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16), (21), (22), (24), (25), (27), (29), (30),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (31), (33), (34), (35), (36), (38), (40), (42),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (51), (54), (55), (56), (58), (59),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (60), (61), (62), (67), (72), (73), (74), (75),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (76), (78), (80), (81), (263), (321) are
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #642.
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (21), (25), (30), (34), (35), (60),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (61), (67), (80), (268), (289), (318) are
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #633.
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (322)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (323)  all_58_13 = e0 & op(e0, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  op(e0, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (67), (222), (324) are inconsistent by
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1872.
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  all_58_14 = e0 & op(e0, e1) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (325) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  all_58_14 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (326) imply:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  e2 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (10), (11), (14), (22), (25), (29),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (30), (34), (35), (38), (40), (42), (47), (59),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (61), (67), (75), (80), (156), (221), (262),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (263), (327) are inconsistent by sub-proof #518.
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  all_58_6 = e0 & op(e1, e3) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_58_6 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (9), (10), (11), (12), (14), (16),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (21), (22), (24), (25), (27), (29), (30), (31),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (33), (34), (35), (36), (38), (40), (42), (46),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (47), (51), (54), (55), (56), (58), (59), (60),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (61), (62), (67), (72), (73), (74), (75), (76),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (80), (81), (263), (330) are inconsistent by
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #664.
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (313) imply:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  e2 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (10), (11), (14), (22), (25), (29),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (30), (34), (35), (38), (40), (42), (47), (59),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (61), (67), (75), (80), (156), (221), (262),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (263), (331) are inconsistent by sub-proof #518.
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | |   (332)  all_58_11 = e0 & op(e1, e0) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | |   (333)  op(e1, e0) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (67), (216), (333) are inconsistent by
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | |   (334)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | |   (335)  all_58_13 = e0 & op(e0, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | |   (336)  op(e0, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (67), (222), (336) are inconsistent by
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1872.
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | |   (337)  all_58_14 = e0 & op(e0, e1) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | ALPHA: (337) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | |   (338)  all_58_14 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (12), (16), (20),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | |            (21), (22), (25), (27), (29), (30), (34), (35),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | |            (36), (38), (40), (42), (46), (47), (54), (55),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | |            (59), (60), (61), (67), (69), (72), (73), (75),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | |            (76), (80), (221), (262), (263), (271), (277),
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | |            (287), (338) are inconsistent by sub-proof #512.
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | |   (339)  all_58_3 = e0 & op(e2, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (11), (12), (14),
% 241.07/47.63  | | | | | | | | | | | | | | | |            (16), (21), (22), (24), (25), (27), (29), (30),
% 241.07/47.63  | | | | | | | | | | | | | | | |            (31), (33), (34), (35), (36), (38), (40), (42),
% 241.07/47.63  | | | | | | | | | | | | | | | |            (46), (47), (51), (54), (55), (56), (58), (59),
% 241.07/47.63  | | | | | | | | | | | | | | | |            (60), (61), (62), (67), (72), (73), (74), (75),
% 241.07/47.63  | | | | | | | | | | | | | | | |            (76), (78), (80), (81), (263), (339) are
% 241.07/47.63  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #578.
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | |   (340)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 241.07/47.63  | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | |   (341)  all_58_7 = e0 & op(e1, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | |   (342)  all_58_7 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (10), (11), (14), (22), (25), (29),
% 241.07/47.63  | | | | | | | | | | | | | | | |            (30), (34), (35), (38), (40), (42), (47), (59),
% 241.07/47.63  | | | | | | | | | | | | | | | |            (61), (67), (75), (80), (221), (262), (263), (342)
% 241.07/47.63  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #519.
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | |   (343)  all_58_13 = e0 & op(e0, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | ALPHA: (343) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | |   (344)  op(e0, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | REF_CLOSE: (61), (67), (222), (344) are inconsistent by
% 241.07/47.63  | | | | | | | | | | | | | | | |            sub-proof #1872.
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | |   (345)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.07/47.63  | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | BETA: splitting (345) gives:
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | |   (346)  all_58_8 = e1 & op(e1, e1) = e1
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | ALPHA: (346) implies:
% 241.07/47.63  | | | | | | | | | | | | | |   (347)  all_58_8 = e1
% 241.07/47.63  | | | | | | | | | | | | | |   (348)  op(e1, e1) = e1
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (10), (22), (35), (40), (47), (59),
% 241.07/47.63  | | | | | | | | | | | | | |            (61), (67), (72), (80), (215), (216), (347), (348)
% 241.07/47.63  | | | | | | | | | | | | | |            are inconsistent by sub-proof #787.
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | |   (349)  all_58_14 = e1 & op(e0, e1) = e1
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | ALPHA: (349) implies:
% 241.07/47.63  | | | | | | | | | | | | | |   (350)  all_58_14 = e1
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | COMBINE_EQS: (256), (350) imply:
% 241.07/47.63  | | | | | | | | | | | | | |   (351)  e2 = e1
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | COMBINE_EQS: (156), (351) imply:
% 241.07/47.63  | | | | | | | | | | | | | |   (352)  all_58_7 = e1
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (11), (14), (25), (35), (67), (80),
% 241.07/47.63  | | | | | | | | | | | | | |            (221), (352) are inconsistent by sub-proof #1457.
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | |   (353)  all_58_11 = e0 & op(e1, e0) = e0
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | ALPHA: (353) implies:
% 241.07/47.63  | | | | | | | | | | | |   (354)  op(e1, e0) = e0
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | REF_CLOSE: (61), (67), (216), (354) are inconsistent by
% 241.07/47.63  | | | | | | | | | | | |            sub-proof #2284.
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | 
% 241.07/47.63  | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | 
% 241.07/47.63  | | | | | | | End of split
% 241.07/47.63  | | | | | | | 
% 241.07/47.63  | | | | | | End of split
% 241.07/47.63  | | | | | | 
% 241.07/47.63  | | | | | End of split
% 241.07/47.63  | | | | | 
% 241.07/47.63  | | | | End of split
% 241.07/47.63  | | | | 
% 241.07/47.63  | | | End of split
% 241.07/47.63  | | | 
% 241.07/47.63  | | Case 2:
% 241.07/47.63  | | | 
% 241.07/47.63  | | |   (355)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0)
% 241.07/47.63  | | |            = e2)
% 241.07/47.63  | | | 
% 241.07/47.63  | | | BETA: splitting (355) gives:
% 241.07/47.63  | | | 
% 241.07/47.63  | | | Case 1:
% 241.07/47.63  | | | | 
% 241.07/47.63  | | | |   (356)  all_58_8 = e2 & op(e1, e1) = e2
% 241.07/47.63  | | | | 
% 241.07/47.63  | | | | ALPHA: (356) implies:
% 241.07/47.63  | | | |   (357)  all_58_8 = e2
% 241.07/47.63  | | | | 
% 241.07/47.63  | | | | BETA: splitting (15) gives:
% 241.07/47.63  | | | | 
% 241.07/47.63  | | | | Case 1:
% 241.07/47.63  | | | | | 
% 241.07/47.63  | | | | |   (358)   ~ (all_42_2 = e3)
% 241.07/47.63  | | | | | 
% 241.07/47.63  | | | | | REDUCE: (7), (358) imply:
% 241.07/47.63  | | | | |   (359)  $false
% 241.07/47.63  | | | | | 
% 241.07/47.63  | | | | | CLOSE: (359) is inconsistent.
% 241.07/47.63  | | | | | 
% 241.07/47.63  | | | | Case 2:
% 241.07/47.63  | | | | | 
% 241.07/47.63  | | | | |   (360)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2,
% 241.07/47.63  | | | | |              e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 241.07/47.63  | | | | |            (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.07/47.63  | | | | | 
% 241.07/47.63  | | | | | BETA: splitting (74) gives:
% 241.07/47.63  | | | | | 
% 241.07/47.63  | | | | | Case 1:
% 241.07/47.63  | | | | | | 
% 241.07/47.63  | | | | | |   (361)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 241.07/47.63  | | | | | |            op(e0, e2) = e1)
% 241.07/47.63  | | | | | | 
% 241.07/47.63  | | | | | | BETA: splitting (361) gives:
% 241.07/47.63  | | | | | | 
% 241.07/47.63  | | | | | | Case 1:
% 241.07/47.63  | | | | | | | 
% 241.07/47.63  | | | | | | |   (362)  all_58_12 = e1 & op(e0, e3) = e1
% 241.07/47.63  | | | | | | | 
% 241.07/47.63  | | | | | | | ALPHA: (362) implies:
% 241.07/47.63  | | | | | | |   (363)  all_58_12 = e1
% 241.07/47.63  | | | | | | | 
% 241.07/47.63  | | | | | | | REF_CLOSE: (4), (8), (9), (30), (34), (35), (38), (61), (67),
% 241.07/47.63  | | | | | | |            (80), (363) are inconsistent by sub-proof #1206.
% 241.07/47.63  | | | | | | | 
% 241.07/47.63  | | | | | | Case 2:
% 241.07/47.63  | | | | | | | 
% 241.07/47.63  | | | | | | |   (364)  all_58_13 = e1 & op(e0, e2) = e1
% 241.07/47.63  | | | | | | | 
% 241.07/47.63  | | | | | | | ALPHA: (364) implies:
% 241.07/47.63  | | | | | | |   (365)  all_58_13 = e1
% 241.07/47.63  | | | | | | |   (366)  op(e0, e2) = e1
% 241.07/47.63  | | | | | | | 
% 241.07/47.63  | | | | | | | BETA: splitting (76) gives:
% 241.07/47.63  | | | | | | | 
% 241.07/47.63  | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | 
% 241.07/47.63  | | | | | | | |   (367)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 241.07/47.63  | | | | | | | |            op(e0, e2) = e2)
% 241.07/47.63  | | | | | | | | 
% 241.07/47.63  | | | | | | | | BETA: splitting (367) gives:
% 241.07/47.63  | | | | | | | | 
% 241.07/47.63  | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | 
% 241.07/47.63  | | | | | | | | |   (368)  all_58_12 = e2 & op(e0, e3) = e2
% 241.07/47.63  | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | ALPHA: (368) implies:
% 241.07/47.63  | | | | | | | | |   (369)  all_58_12 = e2
% 241.07/47.63  | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | BETA: splitting (11) gives:
% 241.07/47.63  | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | |   (370)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 241.07/47.63  | | | | | | | | | |            & op(e2, e2) = e2)
% 241.07/47.63  | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | BETA: splitting (370) gives:
% 241.07/47.63  | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | |   (371)  all_58_1 = e2 & op(e3, e2) = e2
% 241.07/47.63  | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | ALPHA: (371) implies:
% 241.07/47.63  | | | | | | | | | | |   (372)  all_58_1 = e2
% 241.07/47.63  | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | BETA: splitting (31) gives:
% 241.07/47.63  | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | |   (373)  all_58_15 = e0 & op(e0, e0) = e0
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | ALPHA: (373) implies:
% 241.07/47.63  | | | | | | | | | | | |   (374)  all_58_15 = e0
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | COMBINE_EQS: (20), (374) imply:
% 241.07/47.63  | | | | | | | | | | | |   (375)  e3 = e0
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | COMBINE_EQS: (57), (375) imply:
% 241.07/47.63  | | | | | | | | | | | |   (376)  all_56_31 = e0
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | REF_CLOSE: (2), (13), (25), (28), (32), (33), (42), (45),
% 241.07/47.63  | | | | | | | | | | | |            (61), (65), (68), (73), (75), (78), (79), (81),
% 241.07/47.63  | | | | | | | | | | | |            (82), (376) are inconsistent by sub-proof #742.
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | |   (377)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.07/47.63  | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 241.07/47.63  | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 241.07/47.63  | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 241.07/47.63  | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | ALPHA: (377) implies:
% 241.07/47.63  | | | | | | | | | | | |   (378)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 241.07/47.63  | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 241.07/47.63  | | | | | | | | | | | |              e1) = e0)
% 241.07/47.63  | | | | | | | | | | | |   (379)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.07/47.63  | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 241.07/47.63  | | | | | | | | | | | |              e0) = e0)
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | BETA: splitting (378) gives:
% 241.07/47.63  | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | |   (380)  all_58_12 = e0 & op(e0, e3) = e0
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | ALPHA: (380) implies:
% 241.07/47.63  | | | | | | | | | | | | |   (381)  all_58_12 = e0
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | REF_CLOSE: (9), (369), (381) are inconsistent by sub-proof
% 241.07/47.63  | | | | | | | | | | | | |            #2083.
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | |   (382)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 241.07/47.63  | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | BETA: splitting (382) gives:
% 241.07/47.63  | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | |   (383)  all_58_13 = e0 & op(e0, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | ALPHA: (383) implies:
% 241.07/47.63  | | | | | | | | | | | | | |   (384)  op(e0, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | REF_CLOSE: (61), (67), (366), (384) are inconsistent by
% 241.07/47.63  | | | | | | | | | | | | | |            sub-proof #1872.
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | |   (385)  all_58_14 = e0 & op(e0, e1) = e0
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | ALPHA: (385) implies:
% 241.07/47.63  | | | | | | | | | | | | | |   (386)  all_58_14 = e0
% 241.07/47.63  | | | | | | | | | | | | | |   (387)  op(e0, e1) = e0
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 241.07/47.63  | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | |   (388)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 241.07/47.63  | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | BETA: splitting (388) gives:
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | |   (389)  all_58_1 = e0 & op(e3, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (372), (389) are inconsistent by sub-proof
% 241.07/47.63  | | | | | | | | | | | | | | | |            #2187.
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | |   (390)  all_58_3 = e0 & op(e2, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | ALPHA: (390) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | |   (391)  all_58_3 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (391) imply:
% 241.07/47.63  | | | | | | | | | | | | | | | |   (392)  e3 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (392) imply:
% 241.07/47.63  | | | | | | | | | | | | | | | |   (393)  all_56_31 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (13), (25), (28), (32), (33), (42), (45),
% 241.07/47.63  | | | | | | | | | | | | | | | |            (61), (65), (68), (73), (75), (78), (79), (81),
% 241.07/47.63  | | | | | | | | | | | | | | | |            (82), (393) are inconsistent by sub-proof #742.
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | End of split
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | Case 2:
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | |   (394)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 241.07/47.63  | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | BETA: splitting (394) gives:
% 241.07/47.63  | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | |   (395)  all_58_7 = e0 & op(e1, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | ALPHA: (395) implies:
% 241.07/47.63  | | | | | | | | | | | | | | | |   (396)  all_58_7 = e0
% 241.07/47.63  | | | | | | | | | | | | | | | |   (397)  op(e1, e2) = e0
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 241.07/47.63  | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.63  | | | | | | | | | | | | | | | | | 
% 241.07/47.63  | | | | | | | | | | | | | | | | |   (398)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 241.07/47.63  | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 241.07/47.63  | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (14), (22), (25), (29), (30), (34),
% 241.07/47.64  | | | | | | | | | | | | | | | | |            (35), (38), (42), (61), (67), (75), (80), (365),
% 241.07/47.64  | | | | | | | | | | | | | | | | |            (372), (398) are inconsistent by sub-proof #530.
% 241.07/47.64  | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | |   (399)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 241.07/47.64  | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 241.07/47.64  | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | BETA: splitting (399) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | |   (400)  all_58_8 = e1 & op(e1, e1) = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | ALPHA: (400) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | |   (401)  all_58_8 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (401) imply:
% 241.07/47.64  | | | | | | | | | | | | | | | | | |   (402)  e2 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (30), (34), (35), (38), (61), (67),
% 241.07/47.64  | | | | | | | | | | | | | | | | | |            (80), (369), (402) are inconsistent by sub-proof
% 241.07/47.64  | | | | | | | | | | | | | | | | | |            #585.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | |   (403)  all_58_11 = e1 & op(e1, e0) = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | ALPHA: (403) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | |   (404)  all_58_11 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | |   (405)  op(e1, e0) = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | |   (406)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | BETA: splitting (406) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | |   (407)  all_58_0 = e0 & op(e3, e3) = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | ALPHA: (407) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | |   (408)  op(e3, e3) = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (61), (67), (408) are inconsistent by
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | |            sub-proof #1828.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | |   (409)  all_58_2 = e0 & op(e2, e3) = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | ALPHA: (409) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | |   (410)  op(e2, e3) = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | |   (411)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (25), (35), (61), (77), (360), (410), (411)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #511.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | |   (412)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (412) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | |   (413)  all_58_5 = e2 & op(e2, e1) = e2
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (413) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | |   (414)  all_58_5 = e2
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | |   (415)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (415) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (416)  all_58_4 = e1 & op(e3, e1) = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (416) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (417)  all_58_4 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (22), (27), (30), (35), (46), (54),
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |            (55), (61), (67), (80), (417) are inconsistent by
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1468.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (418)  all_58_5 = e1 & op(e2, e1) = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (418) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (419)  all_58_5 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (414), (419) imply:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (420)  e2 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (420) imply:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (421)  all_58_8 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (35), (59), (80), (396), (404), (421)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #988.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | |   (422)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (35), (59), (67), (80), (386), (396),
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | |            (404), (422) are inconsistent by sub-proof #510.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | |   (423)  all_58_10 = e2 & op(e2, e0) = e2
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (423) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | |   (424)  all_58_10 = e2
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | |   (425)  op(e2, e0) = e2
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | |   (426)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (426) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (427)  all_58_0 = e0 & op(e3, e3) = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (427) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (428)  op(e3, e3) = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (61), (67), (428) are inconsistent by
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1828.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (429)  all_58_1 = e0 & op(e3, e2) = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (429) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (430)  all_58_1 = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (430) imply:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (431)  e2 = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (369), (431) imply:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (432)  all_58_12 = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (22), (25), (30), (34), (35), (42),
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |            (60), (61), (67), (78), (80), (81), (424), (425),
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |            (432) are inconsistent by sub-proof #616.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | |   (433)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (433) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (434)  all_58_4 = e0 & op(e3, e1) = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (13), (25), (28), (32), (33), (42), (45),
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |            (57), (61), (65), (68), (69), (73), (75), (78),
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |            (79), (81), (82), (434) are inconsistent by
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #509.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (435)  all_58_9 = e0 & op(e3, e0) = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (435) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (436)  all_58_9 = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | |   (437)  op(e3, e0) = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (438)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (438) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (439)  all_58_4 = e1 & op(e3, e1) = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (439) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (440)  all_58_4 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (22), (27), (30), (35), (46), (54),
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |            (55), (61), (67), (80), (440) are inconsistent by
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1468.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (441)  all_58_5 = e1 & op(e2, e1) = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (441) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (442)  all_58_5 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_11, e0, e1, e0,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (5), (387) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (443)  all_52_11 = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_7, e1, e2, e0,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (52), (366) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (444)  all_52_7 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_14, e1, e0, e1,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (18), (405) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (445)  all_52_14 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_6, e0, e2, e1,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (10), (397) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (446)  all_52_6 = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_13, e2, e0, e2,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (73), (425) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (447)  all_52_13 = e2
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_1, e0, e3, e2,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (42), (410) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (448)  all_52_1 = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_12, e0, e0, e3,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (39), (437) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (449)  all_52_12 = e0
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (447), (449) imply:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (450)   ~ (e2 = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (449) imply:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (451)   ~ (e1 = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (445) imply:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (452)   ~ (e3 = e1)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (445) imply:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (453)   ~ (e2 = e1)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (454)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (454) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (455)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (61), (75), (77), (79), (360), (410),
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (455) are inconsistent by sub-proof #508.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (456)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (57), (61), (64), (456) are inconsistent by
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #838.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (457)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (457) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (458)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (459) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (460)   ~ (all_56_1 = e1)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (79), (460) imply:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (461)  $false
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (461) is inconsistent.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (462)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (462) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (463)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (463) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (464)  op(e1, e2) = e1
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (61), (67), (397), (464) are inconsistent by
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2136.
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (465)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (465) implies:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (466)   ~ (all_56_31 = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (467)   ~ (all_56_21 = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (468)   ~ (all_56_1 = e0)
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (469)  op(e0, e2) = e2
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e1, e2, e2, e0,
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (366), (469) gives:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (470)  e2 = e1
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (470) imply:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (471)  all_58_8 = e1
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (472)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (8), (9), (30), (35), (61), (69), (80),
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (372), (396), (436), (472) are inconsistent by
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #552.
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (471) imply:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (473)  e2 = e1
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (470) imply:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (474)  all_58_10 = e1
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (20), (21), (22), (25), (30), (34),
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (35), (38), (58), (60), (61), (62), (67), (80),
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (369), (379), (442), (474) are inconsistent by
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #584.
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (475)  all_58_11 = e2 & op(e1, e0) = e2
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (475) implies:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (476)  all_58_11 = e2
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (470) imply:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (477)  all_58_10 = e1
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (20), (21), (22), (25), (30), (34),
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (35), (38), (58), (60), (61), (62), (67), (80),
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (369), (379), (442), (477) are inconsistent by
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #584.
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (478)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_8_1)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (478) implies:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (479)   ~ (all_8_1 = e0)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (480)  op(e2, e3) = all_8_1
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (360), (410), (479), (480) are inconsistent
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #897.
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (481)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (481) gives:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (482)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (482) implies:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (483)  op(e2, e0) = e0
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (61), (425), (483) are inconsistent by
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2121.
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (484)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (484) gives:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (485)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e1
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (485) implies:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (486)   ~ (all_56_1 = e0)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  op(e0, e1) = e1
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (67), (387), (487) are inconsistent by
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2158.
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (488)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e0
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (488) implies:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  op(e1, e0) = e0
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (67), (405), (489) are inconsistent by
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (490)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (35), (59), (67), (80), (386), (396),
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (404), (490) are inconsistent by sub-proof #510.
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | |   (491)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 241.07/47.65  | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | BETA: splitting (491) gives:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | |   (492)  all_58_6 = e0 & op(e1, e3) = e0
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (13), (25), (28), (32), (33), (42),
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | |            (45), (57), (61), (65), (68), (73), (75), (78),
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | |            (79), (81), (82), (492) are inconsistent by
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | |            sub-proof #527.
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | |   (493)  all_58_12 = e0 & op(e0, e3) = e0
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (369), (493) are inconsistent by sub-proof
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | |            #1760.
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | |   (494)  all_58_13 = e0 & op(e0, e2) = e0
% 241.07/47.65  | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | ALPHA: (494) implies:
% 241.07/47.65  | | | | | | | | | | | | | | | |   (495)  op(e0, e2) = e0
% 241.07/47.65  | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | | REF_CLOSE: (61), (67), (366), (495) are inconsistent by
% 241.07/47.65  | | | | | | | | | | | | | | | |            sub-proof #1872.
% 241.07/47.65  | | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | |   (496)  all_58_3 = e2 & op(e2, e2) = e2
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | REF_CLOSE: (25), (35), (496) are inconsistent by sub-proof
% 241.07/47.65  | | | | | | | | | | |            #1458.
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | |   (497)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2
% 241.07/47.65  | | | | | | | | | |            & op(e0, e2) = e2)
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | BETA: splitting (497) gives:
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | |   (498)  all_58_7 = e2 & op(e1, e2) = e2
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | ALPHA: (498) implies:
% 241.07/47.65  | | | | | | | | | | |   (499)  all_58_7 = e2
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (8), (9), (10), (11), (13), (14),
% 241.07/47.65  | | | | | | | | | | |            (22), (25), (28), (29), (30), (32), (33), (34),
% 241.07/47.65  | | | | | | | | | | |            (35), (38), (40), (42), (45), (47), (57), (59),
% 241.07/47.65  | | | | | | | | | | |            (61), (65), (67), (68), (72), (73), (75), (78),
% 241.07/47.65  | | | | | | | | | | |            (79), (80), (81), (82), (357), (365), (499) are
% 241.07/47.65  | | | | | | | | | | |            inconsistent by sub-proof #521.
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | |   (500)  all_58_13 = e2 & op(e0, e2) = e2
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | ALPHA: (500) implies:
% 241.07/47.65  | | | | | | | | | | |   (501)  all_58_13 = e2
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | COMBINE_EQS: (365), (501) imply:
% 241.07/47.65  | | | | | | | | | | |   (502)  e2 = e1
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | COMBINE_EQS: (369), (502) imply:
% 241.07/47.65  | | | | | | | | | | |   (503)  all_58_12 = e1
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (30), (34), (35), (38), (61), (67),
% 241.07/47.65  | | | | | | | | | | |            (80), (503) are inconsistent by sub-proof #1206.
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | |   (504)  all_58_13 = e2 & op(e0, e2) = e2
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | REF_CLOSE: (80), (365), (504) are inconsistent by sub-proof
% 241.07/47.65  | | | | | | | | |            #2078.
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | 
% 241.07/47.65  | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | 
% 241.07/47.65  | | | | | | | |   (505)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 241.07/47.65  | | | | | | | |            op(e0, e0) = e2)
% 241.07/47.65  | | | | | | | | 
% 241.07/47.65  | | | | | | | | BETA: splitting (505) gives:
% 241.07/47.65  | | | | | | | | 
% 241.07/47.65  | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | |   (506)  all_58_14 = e2 & op(e0, e1) = e2
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | ALPHA: (506) implies:
% 241.07/47.65  | | | | | | | | |   (507)  all_58_14 = e2
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | BETA: splitting (16) gives:
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | |   (508)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.07/47.65  | | | | | | | | | |            & op(e2, e1) = e1)
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | BETA: splitting (508) gives:
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | |   (509)  all_58_4 = e1 & op(e3, e1) = e1
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | ALPHA: (509) implies:
% 241.07/47.65  | | | | | | | | | | |   (510)  all_58_4 = e1
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (22), (27), (30), (35), (46), (54),
% 241.07/47.65  | | | | | | | | | | |            (55), (61), (67), (80), (510) are inconsistent by
% 241.07/47.65  | | | | | | | | | | |            sub-proof #1468.
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | |   (511)  all_58_5 = e1 & op(e2, e1) = e1
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | ALPHA: (511) implies:
% 241.07/47.65  | | | | | | | | | | |   (512)  op(e2, e1) = e1
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | BETA: splitting (24) gives:
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | |   (513)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 241.07/47.65  | | | | | | | | | | | |            & op(e2, e1) = e0)
% 241.07/47.65  | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | BETA: splitting (513) gives:
% 241.07/47.65  | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | |   (514)  all_58_4 = e0 & op(e3, e1) = e0
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | REF_CLOSE: (2), (13), (25), (28), (32), (33), (42), (45),
% 241.07/47.65  | | | | | | | | | | | | |            (57), (61), (65), (68), (69), (73), (75), (78),
% 241.07/47.65  | | | | | | | | | | | | |            (79), (81), (82), (514) are inconsistent by
% 241.07/47.65  | | | | | | | | | | | | |            sub-proof #509.
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | |   (515)  all_58_5 = e0 & op(e2, e1) = e0
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | ALPHA: (515) implies:
% 241.07/47.65  | | | | | | | | | | | | |   (516)  op(e2, e1) = e0
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | REF_CLOSE: (33), (61), (67), (512), (516) are inconsistent by
% 241.07/47.65  | | | | | | | | | | | | |            sub-proof #2165.
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | |   (517)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 241.07/47.65  | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 241.07/47.65  | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | BETA: splitting (517) gives:
% 241.07/47.65  | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | |   (518)  all_58_8 = e0 & op(e1, e1) = e0
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | ALPHA: (518) implies:
% 241.07/47.65  | | | | | | | | | | | | |   (519)  all_58_8 = e0
% 241.07/47.65  | | | | | | | | | | | | |   (520)  op(e1, e1) = e0
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | COMBINE_EQS: (357), (519) imply:
% 241.07/47.65  | | | | | | | | | | | | |   (521)  e2 = e0
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | SIMP: (521) implies:
% 241.07/47.65  | | | | | | | | | | | | |   (522)  e2 = e0
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | COMBINE_EQS: (149), (522) imply:
% 241.07/47.65  | | | | | | | | | | | | |   (523)  all_56_21 = e0
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11),
% 241.07/47.65  | | | | | | | | | | | | |            (12), (13), (14), (15), (16), (19), (20), (21),
% 241.07/47.65  | | | | | | | | | | | | |            (22), (24), (25), (27), (29), (30), (31), (33),
% 241.07/47.65  | | | | | | | | | | | | |            (34), (35), (36), (38), (40), (42), (46), (47),
% 241.07/47.65  | | | | | | | | | | | | |            (51), (52), (54), (55), (56), (57), (58), (59),
% 241.07/47.65  | | | | | | | | | | | | |            (60), (61), (62), (63), (66), (67), (69), (72),
% 241.07/47.65  | | | | | | | | | | | | |            (73), (74), (75), (76), (77), (78), (79), (80),
% 241.07/47.65  | | | | | | | | | | | | |            (81), (520), (523) are inconsistent by sub-proof
% 241.07/47.65  | | | | | | | | | | | | |            #497.
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | |   (524)  all_58_14 = e0 & op(e0, e1) = e0
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | | REF_CLOSE: (9), (507), (524) are inconsistent by sub-proof
% 241.07/47.65  | | | | | | | | | | | | |            #2036.
% 241.07/47.65  | | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | |   (525)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1
% 241.07/47.65  | | | | | | | | | |            & op(e0, e1) = e1)
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | BETA: splitting (525) gives:
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | |   (526)  all_58_8 = e1 & op(e1, e1) = e1
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | REF_CLOSE: (80), (357), (526) are inconsistent by sub-proof
% 241.07/47.65  | | | | | | | | | | |            #2045.
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | |   (527)  all_58_14 = e1 & op(e0, e1) = e1
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | REF_CLOSE: (80), (507), (527) are inconsistent by sub-proof
% 241.07/47.65  | | | | | | | | | | |            #2040.
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | |   (528)  all_58_15 = e2 & op(e0, e0) = e2
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | ALPHA: (528) implies:
% 241.07/47.65  | | | | | | | | |   (529)  all_58_15 = e2
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | REF_CLOSE: (20), (35), (529) are inconsistent by sub-proof
% 241.07/47.65  | | | | | | | | |            #615.
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | 
% 241.07/47.65  | | | | | | | End of split
% 241.07/47.65  | | | | | | | 
% 241.07/47.65  | | | | | | End of split
% 241.07/47.65  | | | | | | 
% 241.07/47.65  | | | | | Case 2:
% 241.07/47.65  | | | | | | 
% 241.07/47.65  | | | | | |   (530)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 241.07/47.65  | | | | | |            op(e0, e0) = e1)
% 241.07/47.65  | | | | | | 
% 241.07/47.65  | | | | | | BETA: splitting (530) gives:
% 241.07/47.65  | | | | | | 
% 241.07/47.65  | | | | | | Case 1:
% 241.07/47.65  | | | | | | | 
% 241.07/47.65  | | | | | | |   (531)  all_58_14 = e1 & op(e0, e1) = e1
% 241.07/47.65  | | | | | | | 
% 241.07/47.65  | | | | | | | ALPHA: (531) implies:
% 241.07/47.65  | | | | | | |   (532)  all_58_14 = e1
% 241.07/47.65  | | | | | | |   (533)  op(e0, e1) = e1
% 241.07/47.65  | | | | | | | 
% 241.07/47.65  | | | | | | | BETA: splitting (24) gives:
% 241.07/47.65  | | | | | | | 
% 241.07/47.65  | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | 
% 241.07/47.65  | | | | | | | |   (534)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 241.07/47.65  | | | | | | | |            op(e2, e1) = e0)
% 241.07/47.65  | | | | | | | | 
% 241.07/47.65  | | | | | | | | BETA: splitting (534) gives:
% 241.07/47.65  | | | | | | | | 
% 241.07/47.65  | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | |   (535)  all_58_4 = e0 & op(e3, e1) = e0
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | ALPHA: (535) implies:
% 241.07/47.65  | | | | | | | | |   (536)  all_58_4 = e0
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | COMBINE_EQS: (69), (536) imply:
% 241.07/47.65  | | | | | | | | |   (537)  e3 = e0
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | SIMP: (537) implies:
% 241.07/47.65  | | | | | | | | |   (538)  e3 = e0
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | COMBINE_EQS: (8), (538) imply:
% 241.07/47.65  | | | | | | | | |   (539)  all_58_6 = e0
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | REF_CLOSE: (4), (9), (20), (22), (29), (30), (31), (35), (42),
% 241.07/47.65  | | | | | | | | |            (61), (67), (75), (76), (80), (532), (539) are
% 241.07/47.65  | | | | | | | | |            inconsistent by sub-proof #542.
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | |   (540)  all_58_5 = e0 & op(e2, e1) = e0
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | ALPHA: (540) implies:
% 241.07/47.65  | | | | | | | | |   (541)  all_58_5 = e0
% 241.07/47.65  | | | | | | | | |   (542)  op(e2, e1) = e0
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | BETA: splitting (78) gives:
% 241.07/47.65  | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | |   (543)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 241.07/47.65  | | | | | | | | | |            & op(e2, e2) = e1)
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | BETA: splitting (543) gives:
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | |   (544)  all_58_2 = e1 & op(e2, e3) = e1
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | REF_CLOSE: (42), (61), (81), (544) are inconsistent by
% 241.07/47.65  | | | | | | | | | | |            sub-proof #2229.
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | |   (545)  all_58_3 = e1 & op(e2, e2) = e1
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (22), (25), (27), (30), (35), (46),
% 241.07/47.65  | | | | | | | | | | |            (54), (55), (61), (67), (69), (80), (545) are
% 241.07/47.65  | | | | | | | | | | |            inconsistent by sub-proof #1030.
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | End of split
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | Case 2:
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | |   (546)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1
% 241.07/47.65  | | | | | | | | | |            & op(e2, e0) = e1)
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | BETA: splitting (546) gives:
% 241.07/47.65  | | | | | | | | | | 
% 241.07/47.65  | | | | | | | | | | Case 1:
% 241.07/47.65  | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | |   (547)  all_58_5 = e1 & op(e2, e1) = e1
% 241.07/47.66  | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | ALPHA: (547) implies:
% 241.07/47.66  | | | | | | | | | | |   (548)  all_58_5 = e1
% 241.07/47.66  | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | REF_CLOSE: (4), (9), (24), (67), (69), (357), (532), (548)
% 241.07/47.66  | | | | | | | | | | |            are inconsistent by sub-proof #1482.
% 241.07/47.66  | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | |   (549)  all_58_10 = e1 & op(e2, e0) = e1
% 241.07/47.66  | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | ALPHA: (549) implies:
% 241.07/47.66  | | | | | | | | | | |   (550)  op(e2, e0) = e1
% 241.07/47.66  | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | BETA: splitting (62) gives:
% 241.07/47.66  | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | |   (551)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 241.07/47.66  | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 241.07/47.66  | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | BETA: splitting (551) gives:
% 241.07/47.66  | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | |   (552)  all_58_9 = e2 & op(e3, e0) = e2
% 241.07/47.66  | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | ALPHA: (552) implies:
% 241.07/47.66  | | | | | | | | | | | | |   (553)  all_58_9 = e2
% 241.07/47.66  | | | | | | | | | | | | |   (554)  op(e3, e0) = e2
% 241.07/47.66  | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | BETA: splitting (46) gives:
% 241.07/47.66  | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | |   (555)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 241.07/47.66  | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 241.07/47.66  | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | BETA: splitting (555) gives:
% 241.07/47.66  | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | |   (556)  all_58_0 = e0 & op(e3, e3) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | ALPHA: (556) implies:
% 241.07/47.66  | | | | | | | | | | | | | | |   (557)  op(e3, e3) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | REF_CLOSE: (30), (61), (67), (557) are inconsistent by
% 241.07/47.66  | | | | | | | | | | | | | | |            sub-proof #1828.
% 241.07/47.66  | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | |   (558)  all_58_1 = e0 & op(e3, e2) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | ALPHA: (558) implies:
% 241.07/47.66  | | | | | | | | | | | | | | |   (559)  all_58_1 = e0
% 241.07/47.66  | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | |   (560)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 241.07/47.66  | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 241.07/47.66  | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | BETA: splitting (560) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | |   (561)  all_58_1 = e2 & op(e3, e2) = e2
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (9), (30), (35), (61), (69), (80), (553),
% 241.07/47.66  | | | | | | | | | | | | | | | | |            (559), (561) are inconsistent by sub-proof #603.
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | |   (562)  all_58_3 = e2 & op(e2, e2) = e2
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (35), (562) are inconsistent by sub-proof
% 241.07/47.66  | | | | | | | | | | | | | | | | |            #1458.
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | End of split
% 241.07/47.66  | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | |   (563)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 241.07/47.66  | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.07/47.66  | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | BETA: splitting (563) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | |   (564)  all_58_7 = e2 & op(e1, e2) = e2
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | ALPHA: (564) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | |   (565)  all_58_7 = e2
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | |   (566)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | BETA: splitting (566) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (567)  all_58_6 = e1 & op(e1, e3) = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | ALPHA: (567) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (568)  all_58_6 = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (22), (29), (30), (34), (35), (38),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |            (42), (61), (67), (75), (80), (568) are
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1161.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (569)  all_58_7 = e1 & op(e1, e2) = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | ALPHA: (569) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (570)  all_58_7 = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (565), (570) imply:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (571)  e2 = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | SIMP: (571) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (572)  e2 = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (572) imply:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (573)  all_58_9 = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (9), (30), (35), (61), (69), (80), (559),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |            (573) are inconsistent by sub-proof #1338.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | |   (574)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | BETA: splitting (574) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (575)  all_58_8 = e1 & op(e1, e1) = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | ALPHA: (575) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (576)  all_58_8 = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (357), (576) imply:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (577)  e2 = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (577) imply:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (578)  all_58_9 = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (9), (30), (35), (61), (69), (80), (559),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |            (578) are inconsistent by sub-proof #1338.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (579)  all_58_11 = e1 & op(e1, e0) = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | ALPHA: (579) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (580)  all_58_11 = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (581)  op(e1, e0) = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (9), (10), (13), (22), (25), (28),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (34), (35), (38), (40),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |            (42), (45), (47), (57), (59), (61), (65), (67),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |            (68), (72), (73), (75), (78), (79), (80), (81),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |            (82), (357), (565), (580), (581) are inconsistent
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |            by sub-proof #522.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | End of split
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | |   (582)  all_58_13 = e2 & op(e0, e2) = e2
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | ALPHA: (582) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | |   (583)  op(e0, e2) = e2
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | |   (584)  all_58_15 = e0 & op(e0, e0) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (22), (27), (30), (35), (54), (55),
% 241.07/47.66  | | | | | | | | | | | | | | | | | |            (61), (69), (554), (584) are inconsistent by
% 241.07/47.66  | | | | | | | | | | | | | | | | | |            sub-proof #533.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | |   (585)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 241.07/47.66  | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 241.07/47.66  | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 241.07/47.66  | | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | ALPHA: (585) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | |   (586)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 241.07/47.66  | | | | | | | | | | | | | | | | | |              e1) = e0)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | BETA: splitting (586) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (587)  all_58_12 = e0 & op(e0, e3) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | |   (588)  all_58_12 = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | |   (589)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (22), (25), (27), (30), (35), (46),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | |            (54), (55), (61), (66), (67), (69), (80), (589)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #528.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | |   (590)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | BETA: splitting (590) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | |   (591)  all_58_7 = e1 & op(e1, e2) = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | ALPHA: (591) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | |   (592)  op(e1, e2) = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | |   (593)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (593) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |   (594)  all_58_6 = e0 & op(e1, e3) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (594) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |   (595)  all_58_6 = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (20), (22), (29), (30), (31), (35),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |            (42), (61), (67), (75), (76), (80), (532), (595)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #542.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |   (596)  all_58_7 = e0 & op(e1, e2) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (596) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |   (597)  op(e1, e2) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (61), (67), (592), (597) are inconsistent by
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2136.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | |   (598)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (598) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |   (599)  all_58_8 = e0 & op(e1, e1) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (599) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |   (600)  all_58_8 = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |   (601)  op(e1, e1) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (22), (29), (30), (33), (34), (35),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (42), (51), (56), (61), (67), (75),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |            (80), (532), (541), (588), (600), (601) are
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #643.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |   (602)  all_58_11 = e0 & op(e1, e0) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (602) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |   (603)  all_58_11 = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | |   (604)  op(e1, e0) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |   (605)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (605) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (606)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (57), (61), (75), (79), (606) are
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (607)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (607) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (608)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (608) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (609)   ~ (all_56_31 = e3)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (609) imply:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (610)  $false
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (610) is inconsistent.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (611)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (611) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (612)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (612) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (613)  op(e3, e0) = e3
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (551) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (61), (554), (613) are inconsistent by
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2125.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (614)  all_58_10 = e2 & op(e2, e0) = e2
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (614) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (615)  all_58_10 = e2
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (616)  op(e2, e0) = e2
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (22), (25), (30), (34), (35), (42),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (60), (61), (67), (78), (80), (81), (588), (615),
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (616) are inconsistent by sub-proof #616.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (617)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (617) gives:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (618)  all_58_11 = e2 & op(e1, e0) = e2
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (603), (618) are inconsistent by sub-proof
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2216.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (619)  all_58_15 = e2 & op(e0, e0) = e2
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (35), (619) are inconsistent by sub-proof
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1231.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (620)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e0
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (620) implies:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (621)   ~ (all_56_31 = e3)
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (621) imply:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (622)  $false
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (622) is inconsistent.
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |   (623)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (623) gives:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (624)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (624) gives:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (625)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (625) implies:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (626)   ~ (all_56_1 = e1)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (79), (626) imply:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (627)  $false
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (627) is inconsistent.
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (628)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (628) gives:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (629)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (629) implies:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (630)  op(e2, e1) = e1
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (61), (67), (542), (630) are inconsistent by
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2165.
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (631)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (631) implies:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (632)  op(e2, e0) = e2
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (80), (550), (632) are inconsistent by
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1659.
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (633)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (67), (73), (533), (550), (604), (633) are
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #495.
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | |   (634)  all_58_13 = e1 & op(e0, e2) = e1
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | ALPHA: (634) implies:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | |   (635)  all_58_13 = e1
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (35), (76), (80), (532), (588), (635)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1230.
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | Case 2:
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | |   (636)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 241.07/47.67  | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (61), (67), (533), (583), (636) are
% 241.07/47.67  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1333.
% 241.07/47.67  | | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | Case 2:
% 241.07/47.67  | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | |   (637)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 241.07/47.67  | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 241.07/47.67  | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (22), (27), (30), (35), (54), (55),
% 241.07/47.67  | | | | | | | | | | | | | |            (61), (553), (554), (637) are inconsistent by
% 241.07/47.67  | | | | | | | | | | | | | |            sub-proof #532.
% 241.07/47.67  | | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | Case 2:
% 241.07/47.67  | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | |   (638)  all_58_10 = e2 & op(e2, e0) = e2
% 241.07/47.67  | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | ALPHA: (638) implies:
% 241.07/47.67  | | | | | | | | | | | | |   (639)  op(e2, e0) = e2
% 241.07/47.67  | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | REF_CLOSE: (61), (80), (550), (639) are inconsistent by
% 241.07/47.67  | | | | | | | | | | | | |            sub-proof #1659.
% 241.07/47.67  | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | End of split
% 241.07/47.67  | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | Case 2:
% 241.07/47.67  | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | |   (640)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 241.07/47.67  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.07/47.67  | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | BETA: splitting (640) gives:
% 241.07/47.67  | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | Case 1:
% 241.07/47.67  | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | |   (641)  all_58_11 = e2 & op(e1, e0) = e2
% 241.07/47.67  | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | ALPHA: (641) implies:
% 241.07/47.67  | | | | | | | | | | | | |   (642)  all_58_11 = e2
% 241.07/47.67  | | | | | | | | | | | | | 
% 241.07/47.67  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11),
% 241.16/47.67  | | | | | | | | | | | | |            (12), (13), (14), (15), (16), (19), (20), (21),
% 241.16/47.67  | | | | | | | | | | | | |            (22), (24), (25), (27), (29), (30), (31), (33),
% 241.16/47.67  | | | | | | | | | | | | |            (34), (35), (36), (38), (40), (42), (46), (47),
% 241.16/47.67  | | | | | | | | | | | | |            (51), (52), (54), (55), (56), (57), (58), (59),
% 241.16/47.67  | | | | | | | | | | | | |            (60), (61), (62), (63), (66), (67), (69), (72),
% 241.16/47.67  | | | | | | | | | | | | |            (73), (74), (75), (76), (77), (78), (79), (80),
% 241.16/47.67  | | | | | | | | | | | | |            (81), (149), (152), (642) are inconsistent by
% 241.16/47.67  | | | | | | | | | | | | |            sub-proof #490.
% 241.16/47.67  | | | | | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | | | | Case 2:
% 241.16/47.67  | | | | | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | | | | |   (643)  all_58_15 = e2 & op(e0, e0) = e2
% 241.16/47.67  | | | | | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | | | | | REF_CLOSE: (20), (35), (643) are inconsistent by sub-proof
% 241.16/47.67  | | | | | | | | | | | | |            #1231.
% 241.16/47.67  | | | | | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | | | | End of split
% 241.16/47.67  | | | | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | | | End of split
% 241.16/47.67  | | | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | | End of split
% 241.16/47.67  | | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | End of split
% 241.16/47.67  | | | | | | | | | 
% 241.16/47.67  | | | | | | | | End of split
% 241.16/47.67  | | | | | | | | 
% 241.16/47.67  | | | | | | | Case 2:
% 241.16/47.67  | | | | | | | | 
% 241.16/47.67  | | | | | | | |   (644)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 241.16/47.67  | | | | | | | |            op(e0, e1) = e0)
% 241.16/47.67  | | | | | | | | 
% 241.16/47.67  | | | | | | | | BETA: splitting (644) gives:
% 241.16/47.67  | | | | | | | | 
% 241.16/47.67  | | | | | | | | Case 1:
% 241.16/47.67  | | | | | | | | | 
% 241.16/47.67  | | | | | | | | |   (645)  all_58_8 = e0 & op(e1, e1) = e0
% 241.16/47.67  | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | ALPHA: (645) implies:
% 241.16/47.67  | | | | | | | | |   (646)  all_58_8 = e0
% 241.16/47.67  | | | | | | | | |   (647)  op(e1, e1) = e0
% 241.16/47.67  | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | COMBINE_EQS: (357), (646) imply:
% 241.16/47.67  | | | | | | | | |   (648)  e2 = e0
% 241.16/47.67  | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | COMBINE_EQS: (149), (648) imply:
% 241.16/47.67  | | | | | | | | |   (649)  all_56_21 = e0
% 241.16/47.67  | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11),
% 241.16/47.67  | | | | | | | | |            (12), (13), (14), (15), (16), (19), (20), (21),
% 241.16/47.67  | | | | | | | | |            (22), (24), (25), (27), (29), (30), (31), (33),
% 241.16/47.67  | | | | | | | | |            (34), (35), (36), (38), (40), (42), (46), (47),
% 241.16/47.67  | | | | | | | | |            (51), (52), (54), (55), (56), (57), (58), (59),
% 241.16/47.67  | | | | | | | | |            (60), (61), (62), (63), (66), (67), (69), (72),
% 241.16/47.67  | | | | | | | | |            (73), (74), (75), (76), (77), (78), (79), (80),
% 241.16/47.67  | | | | | | | | |            (81), (647), (649) are inconsistent by sub-proof
% 241.16/47.67  | | | | | | | | |            #497.
% 241.16/47.67  | | | | | | | | | 
% 241.16/47.67  | | | | | | | | Case 2:
% 241.16/47.67  | | | | | | | | | 
% 241.16/47.67  | | | | | | | | |   (650)  all_58_14 = e0 & op(e0, e1) = e0
% 241.16/47.67  | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | ALPHA: (650) implies:
% 241.16/47.67  | | | | | | | | |   (651)  op(e0, e1) = e0
% 241.16/47.67  | | | | | | | | | 
% 241.16/47.67  | | | | | | | | | REF_CLOSE: (61), (67), (533), (651) are inconsistent by
% 241.16/47.67  | | | | | | | | |            sub-proof #2158.
% 241.16/47.67  | | | | | | | | | 
% 241.16/47.67  | | | | | | | | End of split
% 241.16/47.67  | | | | | | | | 
% 241.16/47.67  | | | | | | | End of split
% 241.16/47.67  | | | | | | | 
% 241.16/47.67  | | | | | | Case 2:
% 241.16/47.67  | | | | | | | 
% 241.16/47.67  | | | | | | |   (652)  all_58_15 = e1 & op(e0, e0) = e1
% 241.16/47.67  | | | | | | | 
% 241.16/47.67  | | | | | | | ALPHA: (652) implies:
% 241.16/47.67  | | | | | | |   (653)  all_58_15 = e1
% 241.16/47.67  | | | | | | | 
% 241.16/47.67  | | | | | | | REF_CLOSE: (1), (4), (9), (20), (22), (27), (30), (35), (46),
% 241.16/47.67  | | | | | | |            (54), (55), (61), (67), (69), (80), (653) are
% 241.16/47.67  | | | | | | |            inconsistent by sub-proof #1093.
% 241.16/47.67  | | | | | | | 
% 241.16/47.67  | | | | | | End of split
% 241.16/47.67  | | | | | | 
% 241.16/47.67  | | | | | End of split
% 241.16/47.67  | | | | | 
% 241.16/47.67  | | | | End of split
% 241.16/47.67  | | | | 
% 241.16/47.67  | | | Case 2:
% 241.16/47.67  | | | | 
% 241.16/47.67  | | | |   (654)  all_58_11 = e2 & op(e1, e0) = e2
% 241.16/47.67  | | | | 
% 241.16/47.67  | | | | ALPHA: (654) implies:
% 241.16/47.67  | | | |   (655)  all_58_11 = e2
% 241.16/47.67  | | | | 
% 241.16/47.67  | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.16/47.67  | | | |            (14), (15), (16), (19), (20), (21), (22), (24), (25), (27),
% 241.16/47.67  | | | |            (29), (30), (31), (33), (34), (35), (36), (38), (40), (42),
% 241.16/47.67  | | | |            (46), (47), (51), (52), (54), (55), (56), (57), (58), (59),
% 241.16/47.67  | | | |            (60), (61), (62), (63), (66), (67), (69), (72), (73), (74),
% 241.16/47.67  | | | |            (75), (76), (77), (78), (79), (80), (81), (149), (152), (655)
% 241.16/47.67  | | | |            are inconsistent by sub-proof #490.
% 241.16/47.67  | | | | 
% 241.16/47.67  | | | End of split
% 241.16/47.67  | | | 
% 241.16/47.67  | | End of split
% 241.16/47.67  | | 
% 241.16/47.67  | End of split
% 241.16/47.67  | 
% 241.16/47.67  End of proof
% 241.16/47.67  
% 241.16/47.67  Sub-proof #490 shows that the following formulas are inconsistent:
% 241.16/47.67  ----------------------------------------------------------------
% 241.16/47.67    (1)  all_56_21 = e2
% 241.16/47.67    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.16/47.67         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.16/47.67    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.16/47.67         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.16/47.67    (4)   ~ (e3 = e0)
% 241.16/47.67    (5)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.16/47.67         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.16/47.67    (6)  all_42_2 = e3
% 241.16/47.67    (7)  all_58_6 = e3
% 241.16/47.67    (8)   ~ (e2 = e0)
% 241.16/47.67    (9)  op(e1, e2) = all_52_6
% 241.16/47.67    (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.16/47.67          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.16/47.67    (11)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.16/47.67          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.16/47.67    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.16/47.67              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.16/47.67            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.16/47.67            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.16/47.67            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.16/47.67             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.16/47.67            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.16/47.67            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.16/47.67            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.16/47.67            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.16/47.67            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.16/47.67              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.16/47.67            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.16/47.67            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.16/47.67            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.16/47.67            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.16/47.67            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.16/47.67            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.16/47.67              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.16/47.67            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.16/47.67            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.16/47.67            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.16/47.67            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.16/47.67            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.16/47.67            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.16/47.67              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.16/47.67            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.16/47.67            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.16/47.67    (13)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.16/47.67          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.16/47.67    (14)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.16/47.67            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.16/47.67              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.16/47.67    (15)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.16/47.67          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.16/47.67    (16)   ~ (all_52_7 = e3)
% 241.16/47.67    (17)  all_58_15 = e3
% 241.16/47.67    (18)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.16/47.67          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.16/47.67    (19)   ~ (e3 = e1)
% 241.16/47.67    (20)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.16/47.67          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.16/47.67    (21)  all_58_3 = e3
% 241.16/47.67    (22)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.16/47.67          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.16/47.67    (23)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.16/47.67          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.16/47.67    (24)  op(e3, e3) = e1
% 241.16/47.67    (25)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.16/47.67              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.16/47.67                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.16/47.67                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.16/47.67    (26)  op(e2, e1) = all_52_9
% 241.16/47.68    (27)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.16/47.68          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.16/47.68    (28)   ~ (e3 = e2)
% 241.16/47.68    (29)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.16/47.68          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.16/47.68    (30)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.16/47.68          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.16/47.68    (31)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.16/47.68          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.16/47.68    (32)  all_58_11 = e2
% 241.16/47.68    (33)  op(e2, e3) = all_52_1
% 241.16/47.68    (34)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.16/47.68          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.16/47.68    (35)   ~ (all_52_6 = e3)
% 241.16/47.68    (36)  op(e1, e1) = e2
% 241.16/47.68    (37)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.16/47.68          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.16/47.68    (38)  op(e0, e2) = all_52_7
% 241.16/47.68    (39)   ~ (all_52_4 = e3)
% 241.16/47.68    (40)  op(e3, e2) = all_52_4
% 241.16/47.68    (41)   ~ (all_52_9 = e3)
% 241.16/47.68    (42)  all_56_31 = e3
% 241.16/47.68    (43)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.16/47.68          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.16/47.68    (44)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.16/47.68          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.16/47.68    (45)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.16/47.68          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.16/47.68    (46)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.16/47.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.16/47.68    (47)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.16/47.68          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.16/47.68    (48)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.16/47.68          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.16/47.68    (49)   ~ (all_52_4 = e1)
% 241.16/47.68    (50)   ~ (e1 = e0)
% 241.16/47.68    (51)  all_58_4 = e3
% 241.16/47.68    (52)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.16/47.68          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.16/47.68    (53)  op(e2, e0) = all_52_13
% 241.16/47.68    (54)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.16/47.68          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.16/47.68            e1)
% 241.16/47.68    (55)   ~ (all_52_1 = e3)
% 241.16/47.68    (56)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.16/47.68          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.16/47.68            e2)
% 241.16/47.68    (57)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.16/47.68            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 241.16/47.68            & $i(all_8_1))
% 241.16/47.68    (58)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.16/47.68          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.16/47.68    (59)  all_56_1 = e1
% 241.16/47.68    (60)   ~ (e2 = e1)
% 241.16/47.68    (61)   ~ (all_52_1 = e1)
% 241.16/47.68  
% 241.16/47.68  Begin of proof
% 241.16/47.68  | 
% 241.16/47.68  | BETA: splitting (5) gives:
% 241.16/47.68  | 
% 241.16/47.68  | Case 1:
% 241.16/47.68  | | 
% 241.16/47.68  | |   (62)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 241.16/47.68  | |           e1)
% 241.16/47.68  | | 
% 241.16/47.68  | | BETA: splitting (62) gives:
% 241.16/47.68  | | 
% 241.16/47.68  | | Case 1:
% 241.16/47.68  | | | 
% 241.16/47.68  | | |   (63)  all_58_6 = e1 & op(e1, e3) = e1
% 241.16/47.68  | | | 
% 241.16/47.68  | | | ALPHA: (63) implies:
% 241.16/47.68  | | |   (64)  all_58_6 = e1
% 241.16/47.68  | | | 
% 241.16/47.68  | | | REF_CLOSE: (4), (8), (19), (23), (24), (27), (28), (30), (33), (46), (50),
% 241.16/47.68  | | |            (55), (60), (64) are inconsistent by sub-proof #1161.
% 241.16/47.68  | | | 
% 241.16/47.68  | | Case 2:
% 241.16/47.68  | | | 
% 241.16/47.68  | | |   (65)  all_58_7 = e1 & op(e1, e2) = e1
% 241.16/47.68  | | | 
% 241.16/47.68  | | | ALPHA: (65) implies:
% 241.16/47.68  | | |   (66)  all_58_7 = e1
% 241.16/47.68  | | |   (67)  op(e1, e2) = e1
% 241.16/47.68  | | | 
% 241.16/47.68  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.16/47.68  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.16/47.68  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 241.16/47.68  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 241.16/47.68  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 241.16/47.68  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (66),
% 241.16/47.68  | | |            (67) are inconsistent by sub-proof #492.
% 241.16/47.68  | | | 
% 241.16/47.68  | | End of split
% 241.16/47.68  | | 
% 241.16/47.68  | Case 2:
% 241.16/47.68  | | 
% 241.16/47.68  | |   (68)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 241.16/47.68  | |           e1)
% 241.16/47.68  | | 
% 241.16/47.68  | | BETA: splitting (68) gives:
% 241.16/47.68  | | 
% 241.16/47.68  | | Case 1:
% 241.16/47.68  | | | 
% 241.16/47.68  | | |   (69)  all_58_8 = e1 & op(e1, e1) = e1
% 241.16/47.68  | | | 
% 241.16/47.68  | | | ALPHA: (69) implies:
% 241.16/47.68  | | |   (70)  all_58_8 = e1
% 241.16/47.68  | | |   (71)  op(e1, e1) = e1
% 241.16/47.68  | | | 
% 241.16/47.68  | | | BETA: splitting (11) gives:
% 241.16/47.68  | | | 
% 241.16/47.68  | | | Case 1:
% 241.16/47.68  | | | | 
% 241.16/47.68  | | | |   (72)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 241.16/47.68  | | | |           = e1)
% 241.16/47.68  | | | | 
% 241.16/47.68  | | | | BETA: splitting (72) gives:
% 241.16/47.68  | | | | 
% 241.16/47.68  | | | | Case 1:
% 241.16/47.68  | | | | | 
% 241.16/47.68  | | | | |   (73)  all_58_9 = e1 & op(e3, e0) = e1
% 241.16/47.68  | | | | | 
% 241.16/47.68  | | | | | ALPHA: (73) implies:
% 241.16/47.68  | | | | |   (74)  all_58_9 = e1
% 241.16/47.68  | | | | | 
% 241.16/47.68  | | | | | REF_CLOSE: (2), (4), (8), (24), (28), (34), (46), (50), (51), (60),
% 241.16/47.68  | | | | |            (74) are inconsistent by sub-proof #1292.
% 241.16/47.68  | | | | | 
% 241.16/47.68  | | | | Case 2:
% 241.16/47.68  | | | | | 
% 241.16/47.68  | | | | |   (75)  all_58_10 = e1 & op(e2, e0) = e1
% 241.16/47.68  | | | | | 
% 241.16/47.68  | | | | | ALPHA: (75) implies:
% 241.16/47.68  | | | | |   (76)  all_58_10 = e1
% 241.16/47.68  | | | | |   (77)  op(e2, e0) = e1
% 241.16/47.68  | | | | | 
% 241.16/47.68  | | | | | BETA: splitting (18) gives:
% 241.16/47.68  | | | | | 
% 241.16/47.68  | | | | | Case 1:
% 241.16/47.68  | | | | | | 
% 241.16/47.68  | | | | | |   (78)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2,
% 241.16/47.68  | | | | | |             e2) = e2)
% 241.16/47.68  | | | | | | 
% 241.16/47.68  | | | | | | BETA: splitting (78) gives:
% 241.16/47.68  | | | | | | 
% 241.16/47.68  | | | | | | Case 1:
% 241.16/47.68  | | | | | | | 
% 241.16/47.68  | | | | | | |   (79)  all_58_2 = e2 & op(e2, e3) = e2
% 241.16/47.68  | | | | | | | 
% 241.16/47.68  | | | | | | | ALPHA: (79) implies:
% 241.16/47.68  | | | | | | |   (80)  all_58_2 = e2
% 241.16/47.68  | | | | | | | 
% 241.16/47.68  | | | | | | | BETA: splitting (52) gives:
% 241.16/47.68  | | | | | | | 
% 241.16/47.68  | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | 
% 241.16/47.68  | | | | | | | |   (81)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 241.16/47.68  | | | | | | | |           op(e1, e2) = e0)
% 241.16/47.68  | | | | | | | | 
% 241.16/47.68  | | | | | | | | BETA: splitting (81) gives:
% 241.16/47.68  | | | | | | | | 
% 241.16/47.68  | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | 
% 241.16/47.68  | | | | | | | | |   (82)  all_58_6 = e0 & op(e1, e3) = e0
% 241.16/47.68  | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | ALPHA: (82) implies:
% 241.16/47.68  | | | | | | | | |   (83)  all_58_6 = e0
% 241.16/47.68  | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | REF_CLOSE: (4), (9), (28), (31), (32), (35), (36), (46), (83)
% 241.16/47.68  | | | | | | | | |            are inconsistent by sub-proof #997.
% 241.16/47.68  | | | | | | | | | 
% 241.16/47.68  | | | | | | | | Case 2:
% 241.16/47.68  | | | | | | | | | 
% 241.16/47.68  | | | | | | | | |   (84)  all_58_7 = e0 & op(e1, e2) = e0
% 241.16/47.68  | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | ALPHA: (84) implies:
% 241.16/47.68  | | | | | | | | |   (85)  all_58_7 = e0
% 241.16/47.68  | | | | | | | | |   (86)  op(e1, e2) = e0
% 241.16/47.68  | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | BETA: splitting (25) gives:
% 241.16/47.68  | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | |   (87)  all_58_15 = e0 & op(e0, e0) = e0
% 241.16/47.68  | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | ALPHA: (87) implies:
% 241.16/47.68  | | | | | | | | | |   (88)  all_58_15 = e0
% 241.16/47.68  | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | COMBINE_EQS: (17), (88) imply:
% 241.16/47.68  | | | | | | | | | |   (89)  e3 = e0
% 241.16/47.68  | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | COMBINE_EQS: (7), (89) imply:
% 241.16/47.68  | | | | | | | | | |   (90)  all_58_6 = e0
% 241.16/47.68  | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | REF_CLOSE: (4), (9), (28), (31), (32), (35), (36), (46), (90)
% 241.16/47.68  | | | | | | | | | |            are inconsistent by sub-proof #997.
% 241.16/47.68  | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | Case 2:
% 241.16/47.68  | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | |   (91)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 241.16/47.68  | | | | | | | | | |             & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 241.16/47.68  | | | | | | | | | |               e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) =
% 241.16/47.68  | | | | | | | | | |             e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 241.16/47.68  | | | | | | | | | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 241.16/47.68  | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | ALPHA: (91) implies:
% 241.16/47.68  | | | | | | | | | |   (92)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 241.16/47.68  | | | | | | | | | |           & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.16/47.68  | | | | | | | | | |           = e0)
% 241.16/47.68  | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | BETA: splitting (92) gives:
% 241.16/47.68  | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | |   (93)  all_58_9 = e0 & op(e3, e0) = e0
% 241.16/47.68  | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | ALPHA: (93) implies:
% 241.16/47.68  | | | | | | | | | | |   (94)  all_58_9 = e0
% 241.16/47.68  | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | BETA: splitting (48) gives:
% 241.16/47.68  | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | |   (95)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 241.16/47.68  | | | | | | | | | | | |           & op(e2, e2) = e1)
% 241.16/47.68  | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | BETA: splitting (95) gives:
% 241.16/47.68  | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | |   (96)  all_58_1 = e1 & op(e3, e2) = e1
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | ALPHA: (96) implies:
% 241.16/47.68  | | | | | | | | | | | | |   (97)  op(e3, e2) = e1
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | REF_CLOSE: (40), (46), (49), (97) are inconsistent by
% 241.16/47.68  | | | | | | | | | | | | |            sub-proof #2228.
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | Case 2:
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | |   (98)  all_58_3 = e1 & op(e2, e2) = e1
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | ALPHA: (98) implies:
% 241.16/47.68  | | | | | | | | | | | | |   (99)  all_58_3 = e1
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (19), (21), (22), (24), (28), (34),
% 241.16/47.68  | | | | | | | | | | | | |            (39), (40), (46), (50), (51), (60), (99) are
% 241.16/47.68  | | | | | | | | | | | | |            inconsistent by sub-proof #1111.
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | End of split
% 241.16/47.68  | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | Case 2:
% 241.16/47.68  | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | |   (100)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 241.16/47.68  | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 241.16/47.68  | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | BETA: splitting (100) gives:
% 241.16/47.68  | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | |   (101)  all_58_7 = e1 & op(e1, e2) = e1
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | ALPHA: (101) implies:
% 241.16/47.68  | | | | | | | | | | | | |   (102)  all_58_7 = e1
% 241.16/47.68  | | | | | | | | | | | | |   (103)  op(e1, e2) = e1
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 241.16/47.68  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 241.16/47.68  | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 241.16/47.68  | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 241.16/47.68  | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 241.16/47.68  | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 241.16/47.68  | | | | | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58),
% 241.16/47.68  | | | | | | | | | | | | |            (59), (60), (61), (102), (103) are inconsistent by
% 241.16/47.68  | | | | | | | | | | | | |            sub-proof #492.
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | Case 2:
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | |   (104)  all_58_13 = e1 & op(e0, e2) = e1
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | ALPHA: (104) implies:
% 241.16/47.68  | | | | | | | | | | | | |   (105)  all_58_13 = e1
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | BETA: splitting (10) gives:
% 241.16/47.68  | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | |   (106)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 241.16/47.68  | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 241.16/47.68  | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 241.16/47.68  | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | |   (107)  all_58_1 = e2 & op(e3, e2) = e2
% 241.16/47.68  | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 241.16/47.68  | | | | | | | | | | | | | | |   (108)  all_58_1 = e2
% 241.16/47.68  | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 241.16/47.68  | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | |   (109)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 241.16/47.68  | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 241.16/47.68  | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 241.16/47.68  | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | |   (110)  all_58_0 = e0 & op(e3, e3) = e0
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 241.16/47.68  | | | | | | | | | | | | | | | | |   (111)  op(e3, e3) = e0
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (46), (50), (111) are inconsistent by
% 241.16/47.68  | | | | | | | | | | | | | | | | |            sub-proof #1828.
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | Case 2:
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | |   (112)  all_58_2 = e0 & op(e2, e3) = e0
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 241.16/47.68  | | | | | | | | | | | | | | | | |   (113)  all_58_2 = e0
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (113) imply:
% 241.16/47.68  | | | | | | | | | | | | | | | | |   (114)  e2 = e0
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | SIMP: (114) implies:
% 241.16/47.68  | | | | | | | | | | | | | | | | |   (115)  e2 = e0
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (115) imply:
% 241.16/47.68  | | | | | | | | | | | | | | | | |   (116)  all_58_1 = e0
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (24), (28), (46), (51), (60), (94),
% 241.16/47.68  | | | | | | | | | | | | | | | | |            (116) are inconsistent by sub-proof #1097.
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | End of split
% 241.16/47.68  | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | Case 2:
% 241.16/47.68  | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | |   (117)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 241.16/47.68  | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 241.16/47.68  | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 241.16/47.68  | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | |   (118)  all_58_6 = e0 & op(e1, e3) = e0
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 241.16/47.68  | | | | | | | | | | | | | | | | |   (119)  all_58_6 = e0
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (28), (31), (32), (35), (36), (46),
% 241.16/47.68  | | | | | | | | | | | | | | | | |            (119) are inconsistent by sub-proof #997.
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | Case 2:
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | |   (120)  all_58_12 = e0 & op(e0, e3) = e0
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 241.16/47.68  | | | | | | | | | | | | | | | | |   (121)  all_58_12 = e0
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 241.16/47.68  | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | |   (122)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 241.16/47.68  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 241.16/47.68  | | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 241.16/47.68  | | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | | Case 1:
% 241.16/47.68  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | | |   (123)  all_58_4 = e2 & op(e3, e1) = e2
% 241.16/47.68  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 241.16/47.68  | | | | | | | | | | | | | | | | | | |   (124)  all_58_4 = e2
% 241.16/47.68  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (51), (124) are inconsistent by sub-proof
% 241.16/47.68  | | | | | | | | | | | | | | | | | | |            #1902.
% 241.16/47.68  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | | Case 2:
% 241.16/47.68  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | | |   (125)  all_58_5 = e2 & op(e2, e1) = e2
% 241.16/47.68  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.68  | | | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 241.16/47.68  | | | | | | | | | | | | | | | | | | |   (126)  all_58_5 = e2
% 241.16/47.68  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            (13), (15), (16), (17), (18), (19), (20), (21),
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29),
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            (38), (39), (40), (41), (43), (44), (45), (46),
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            (55), (56), (58), (60), (61), (71), (76), (77),
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            (85), (86), (126) are inconsistent by sub-proof
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            #491.
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | Case 2:
% 241.16/47.69  | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | |   (127)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 241.16/47.69  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 241.16/47.69  | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 241.16/47.69  | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | Case 1:
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |   (128)  all_58_8 = e2 & op(e1, e1) = e2
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |   (129)  all_58_8 = e2
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (129) imply:
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |   (130)  e2 = e1
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | SIMP: (130) implies:
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |   (131)  e2 = e1
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (131) imply:
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |   (132)  all_58_11 = e1
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (8), (17), (19), (21), (24), (27),
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            (28), (33), (45), (46), (47), (50), (51), (58),
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            (60), (61), (94), (121), (132) are inconsistent by
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            sub-proof #613.
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | Case 2:
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (46) with e1, e2, e1, e1,
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |              simplifying with (36), (71) gives:
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |   (133)  e2 = e1
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (133) imply:
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |   (134)  all_58_11 = e1
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (8), (17), (19), (21), (24), (27),
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            (28), (33), (45), (46), (47), (50), (51), (58),
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            (60), (61), (94), (121), (134) are inconsistent by
% 241.16/47.69  | | | | | | | | | | | | | | | | | | |            sub-proof #613.
% 241.16/47.69  | | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | Case 2:
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | |   (135)  all_58_3 = e2 & op(e2, e2) = e2
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | REF_CLOSE: (21), (28), (135) are inconsistent by sub-proof
% 241.16/47.69  | | | | | | | | | | | | | | |            #1106.
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | Case 2:
% 241.16/47.69  | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | |   (136)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 241.16/47.69  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.16/47.69  | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 241.16/47.69  | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | Case 1:
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | |   (137)  all_58_7 = e2 & op(e1, e2) = e2
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | REF_CLOSE: (8), (85), (137) are inconsistent by sub-proof
% 241.16/47.69  | | | | | | | | | | | | | | |            #1326.
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | Case 2:
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | |   (138)  all_58_13 = e2 & op(e0, e2) = e2
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 241.16/47.69  | | | | | | | | | | | | | | |   (139)  all_58_13 = e2
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | COMBINE_EQS: (105), (139) imply:
% 241.16/47.69  | | | | | | | | | | | | | | |   (140)  e2 = e1
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | COMBINE_EQS: (32), (140) imply:
% 241.16/47.69  | | | | | | | | | | | | | | |   (141)  all_58_11 = e1
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (28), (44), (60), (70), (85), (141) are
% 241.16/47.69  | | | | | | | | | | | | | | |            inconsistent by sub-proof #988.
% 241.16/47.69  | | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | Case 2:
% 241.16/47.69  | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | |   (142)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 241.16/47.69  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 241.16/47.69  | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | BETA: splitting (142) gives:
% 241.16/47.69  | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | Case 1:
% 241.16/47.69  | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | |   (143)  all_58_10 = e0 & op(e2, e0) = e0
% 241.16/47.69  | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | ALPHA: (143) implies:
% 241.16/47.69  | | | | | | | | | | | |   (144)  op(e2, e0) = e0
% 241.16/47.69  | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | REF_CLOSE: (46), (50), (53), (77), (144) are inconsistent by
% 241.16/47.69  | | | | | | | | | | | |            sub-proof #1778.
% 241.16/47.69  | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | Case 2:
% 241.16/47.69  | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | |   (145)  all_58_11 = e0 & op(e1, e0) = e0
% 241.16/47.69  | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | | REF_CLOSE: (8), (32), (145) are inconsistent by sub-proof
% 241.16/47.69  | | | | | | | | | | | |            #2033.
% 241.16/47.69  | | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | | 
% 241.16/47.69  | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | 
% 241.16/47.69  | | | | | | | Case 2:
% 241.16/47.69  | | | | | | | | 
% 241.16/47.69  | | | | | | | |   (146)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 241.16/47.69  | | | | | | | |            op(e1, e0) = e0)
% 241.16/47.69  | | | | | | | | 
% 241.16/47.69  | | | | | | | | BETA: splitting (146) gives:
% 241.16/47.69  | | | | | | | | 
% 241.16/47.69  | | | | | | | | Case 1:
% 241.16/47.69  | | | | | | | | | 
% 241.16/47.69  | | | | | | | | |   (147)  all_58_8 = e0 & op(e1, e1) = e0
% 241.16/47.69  | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | ALPHA: (147) implies:
% 241.16/47.69  | | | | | | | | |   (148)  all_58_8 = e0
% 241.16/47.69  | | | | | | | | |   (149)  op(e1, e1) = e0
% 241.16/47.69  | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 241.16/47.69  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 241.16/47.69  | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 241.16/47.69  | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 241.16/47.69  | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 241.16/47.69  | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 241.16/47.69  | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58),
% 241.16/47.69  | | | | | | | | |            (59), (60), (61), (76), (77), (80), (148), (149)
% 241.16/47.69  | | | | | | | | |            are inconsistent by sub-proof #493.
% 241.16/47.69  | | | | | | | | | 
% 241.16/47.69  | | | | | | | | Case 2:
% 241.16/47.69  | | | | | | | | | 
% 241.16/47.69  | | | | | | | | |   (150)  all_58_11 = e0 & op(e1, e0) = e0
% 241.16/47.69  | | | | | | | | | 
% 241.16/47.69  | | | | | | | | | REF_CLOSE: (8), (32), (150) are inconsistent by sub-proof
% 241.16/47.69  | | | | | | | | |            #2033.
% 241.16/47.69  | | | | | | | | | 
% 241.16/47.69  | | | | | | | | End of split
% 241.16/47.69  | | | | | | | | 
% 241.16/47.69  | | | | | | | End of split
% 241.16/47.69  | | | | | | | 
% 241.16/47.69  | | | | | | Case 2:
% 241.16/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | |   (151)  all_58_3 = e2 & op(e2, e2) = e2
% 241.19/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | | REF_CLOSE: (21), (28), (151) are inconsistent by sub-proof #1458.
% 241.19/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | End of split
% 241.19/47.69  | | | | | | 
% 241.19/47.69  | | | | | Case 2:
% 241.19/47.69  | | | | | | 
% 241.19/47.69  | | | | | |   (152)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 241.19/47.69  | | | | | |            op(e2, e0) = e2)
% 241.19/47.69  | | | | | | 
% 241.19/47.69  | | | | | | BETA: splitting (152) gives:
% 241.19/47.69  | | | | | | 
% 241.19/47.69  | | | | | | Case 1:
% 241.19/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | |   (153)  all_58_5 = e2 & op(e2, e1) = e2
% 241.19/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | | ALPHA: (153) implies:
% 241.19/47.69  | | | | | | |   (154)  all_58_5 = e2
% 241.19/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | | BETA: splitting (52) gives:
% 241.19/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | | Case 1:
% 241.19/47.69  | | | | | | | | 
% 241.19/47.69  | | | | | | | |   (155)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 241.19/47.69  | | | | | | | |            op(e1, e2) = e0)
% 241.19/47.69  | | | | | | | | 
% 241.19/47.69  | | | | | | | | BETA: splitting (155) gives:
% 241.19/47.69  | | | | | | | | 
% 241.19/47.69  | | | | | | | | Case 1:
% 241.19/47.69  | | | | | | | | | 
% 241.19/47.69  | | | | | | | | |   (156)  all_58_6 = e0 & op(e1, e3) = e0
% 241.19/47.69  | | | | | | | | | 
% 241.19/47.69  | | | | | | | | | ALPHA: (156) implies:
% 241.19/47.69  | | | | | | | | |   (157)  all_58_6 = e0
% 241.19/47.69  | | | | | | | | | 
% 241.19/47.69  | | | | | | | | | REF_CLOSE: (4), (9), (28), (31), (32), (35), (36), (46), (157)
% 241.19/47.69  | | | | | | | | |            are inconsistent by sub-proof #997.
% 241.19/47.69  | | | | | | | | | 
% 241.19/47.69  | | | | | | | | Case 2:
% 241.19/47.69  | | | | | | | | | 
% 241.19/47.69  | | | | | | | | |   (158)  all_58_7 = e0 & op(e1, e2) = e0
% 241.19/47.69  | | | | | | | | | 
% 241.19/47.69  | | | | | | | | | ALPHA: (158) implies:
% 241.19/47.69  | | | | | | | | |   (159)  all_58_7 = e0
% 241.19/47.69  | | | | | | | | |   (160)  op(e1, e2) = e0
% 241.19/47.69  | | | | | | | | | 
% 241.19/47.69  | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 241.19/47.69  | | | | | | | | |            (13), (15), (16), (17), (18), (19), (20), (21),
% 241.19/47.69  | | | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29),
% 241.19/47.69  | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 241.19/47.69  | | | | | | | | |            (38), (39), (40), (41), (43), (44), (45), (46),
% 241.19/47.69  | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 241.19/47.69  | | | | | | | | |            (55), (56), (58), (60), (61), (71), (76), (77),
% 241.19/47.69  | | | | | | | | |            (154), (159), (160) are inconsistent by sub-proof
% 241.19/47.69  | | | | | | | | |            #491.
% 241.19/47.69  | | | | | | | | | 
% 241.19/47.69  | | | | | | | | End of split
% 241.19/47.69  | | | | | | | | 
% 241.19/47.69  | | | | | | | Case 2:
% 241.19/47.69  | | | | | | | | 
% 241.19/47.69  | | | | | | | |   (161)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 241.19/47.69  | | | | | | | |            op(e1, e0) = e0)
% 241.19/47.69  | | | | | | | | 
% 241.19/47.69  | | | | | | | | REF_CLOSE: (8), (32), (46), (50), (71), (161) are inconsistent
% 241.19/47.69  | | | | | | | |            by sub-proof #986.
% 241.19/47.69  | | | | | | | | 
% 241.19/47.69  | | | | | | | End of split
% 241.19/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | Case 2:
% 241.19/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | |   (162)  all_58_10 = e2 & op(e2, e0) = e2
% 241.19/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | | ALPHA: (162) implies:
% 241.19/47.69  | | | | | | |   (163)  op(e2, e0) = e2
% 241.19/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | | REF_CLOSE: (46), (60), (77), (163) are inconsistent by sub-proof
% 241.19/47.69  | | | | | | |            #1659.
% 241.19/47.69  | | | | | | | 
% 241.19/47.69  | | | | | | End of split
% 241.19/47.69  | | | | | | 
% 241.19/47.69  | | | | | End of split
% 241.19/47.69  | | | | | 
% 241.19/47.69  | | | | End of split
% 241.19/47.69  | | | | 
% 241.19/47.69  | | | Case 2:
% 241.19/47.69  | | | | 
% 241.19/47.69  | | | |   (164)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 241.19/47.69  | | | |              e0) = e1)
% 241.19/47.69  | | | | 
% 241.19/47.69  | | | | BETA: splitting (164) gives:
% 241.19/47.69  | | | | 
% 241.19/47.69  | | | | Case 1:
% 241.19/47.69  | | | | | 
% 241.19/47.69  | | | | |   (165)  all_58_11 = e1 & op(e1, e0) = e1
% 241.19/47.69  | | | | | 
% 241.19/47.69  | | | | | ALPHA: (165) implies:
% 241.19/47.69  | | | | |   (166)  all_58_11 = e1
% 241.19/47.69  | | | | |   (167)  op(e1, e0) = e1
% 241.19/47.69  | | | | | 
% 241.19/47.69  | | | | | REF_CLOSE: (4), (8), (9), (19), (28), (31), (35), (44), (46), (50),
% 241.19/47.69  | | | | |            (52), (60), (70), (71), (166), (167) are inconsistent by
% 241.19/47.69  | | | | |            sub-proof #787.
% 241.19/47.69  | | | | | 
% 241.19/47.69  | | | | Case 2:
% 241.19/47.69  | | | | | 
% 241.19/47.69  | | | | |   (168)  all_58_15 = e1 & op(e0, e0) = e1
% 241.19/47.69  | | | | | 
% 241.19/47.69  | | | | | ALPHA: (168) implies:
% 241.19/47.69  | | | | |   (169)  all_58_15 = e1
% 241.19/47.69  | | | | | 
% 241.19/47.69  | | | | | REF_CLOSE: (2), (4), (8), (17), (19), (22), (24), (28), (34), (39),
% 241.19/47.69  | | | | |            (40), (46), (50), (51), (60), (169) are inconsistent by
% 241.19/47.69  | | | | |            sub-proof #1093.
% 241.19/47.69  | | | | | 
% 241.19/47.69  | | | | End of split
% 241.19/47.69  | | | | 
% 241.19/47.69  | | | End of split
% 241.19/47.69  | | | 
% 241.19/47.69  | | Case 2:
% 241.19/47.69  | | | 
% 241.19/47.69  | | |   (170)  all_58_11 = e1 & op(e1, e0) = e1
% 241.19/47.69  | | | 
% 241.19/47.69  | | | REF_CLOSE: (32), (60), (170) are inconsistent by sub-proof #1346.
% 241.19/47.69  | | | 
% 241.19/47.69  | | End of split
% 241.19/47.69  | | 
% 241.19/47.69  | End of split
% 241.19/47.69  | 
% 241.19/47.69  End of proof
% 241.19/47.69  
% 241.19/47.69  Sub-proof #491 shows that the following formulas are inconsistent:
% 241.19/47.69  ----------------------------------------------------------------
% 241.19/47.69    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.19/47.69         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.19/47.69    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.19/47.69         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.19/47.69    (3)   ~ (e3 = e0)
% 241.19/47.69    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.19/47.69         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.19/47.69    (5)  op(e1, e1) = e1
% 241.19/47.69    (6)  all_58_6 = e3
% 241.19/47.69    (7)   ~ (e2 = e0)
% 241.19/47.69    (8)  all_58_7 = e0
% 241.19/47.69    (9)  op(e1, e2) = all_52_6
% 241.19/47.69    (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.19/47.69          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.19/47.69    (11)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.19/47.69          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.19/47.69    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.19/47.69          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.19/47.69    (13)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.19/47.69          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.19/47.69    (14)   ~ (all_52_7 = e3)
% 241.19/47.69    (15)  all_58_15 = e3
% 241.19/47.69    (16)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.19/47.69          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.19/47.69    (17)   ~ (e3 = e1)
% 241.19/47.69    (18)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.19/47.69          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.19/47.69    (19)  all_58_3 = e3
% 241.19/47.69    (20)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.19/47.69          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.19/47.69    (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.19/47.69          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.19/47.69    (22)  op(e3, e3) = e1
% 241.19/47.69    (23)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.19/47.69              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.19/47.69                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.19/47.69                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.19/47.69    (24)  op(e2, e1) = all_52_9
% 241.19/47.69    (25)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.19/47.69          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.19/47.69    (26)  op(e1, e2) = e0
% 241.19/47.69    (27)   ~ (e3 = e2)
% 241.19/47.69    (28)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.19/47.69          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.19/47.69    (29)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.19/47.69          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.19/47.69    (30)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.19/47.69          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.19/47.69    (31)  all_58_11 = e2
% 241.19/47.69    (32)  op(e2, e3) = all_52_1
% 241.19/47.69    (33)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.19/47.69          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.19/47.69    (34)   ~ (all_52_6 = e3)
% 241.19/47.69    (35)  op(e1, e1) = e2
% 241.19/47.69    (36)  all_58_5 = e2
% 241.19/47.69    (37)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.19/47.69          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.19/47.69    (38)  op(e0, e2) = all_52_7
% 241.19/47.69    (39)   ~ (all_52_4 = e3)
% 241.19/47.69    (40)  op(e3, e2) = all_52_4
% 241.19/47.69    (41)   ~ (all_52_9 = e3)
% 241.19/47.69    (42)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.19/47.69          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.19/47.69    (43)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.19/47.69          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.19/47.69    (44)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.19/47.69          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.19/47.70    (45)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.19/47.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.19/47.70    (46)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.19/47.70          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.19/47.70    (47)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.19/47.70          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.19/47.70    (48)   ~ (all_52_4 = e1)
% 241.19/47.70    (49)   ~ (e1 = e0)
% 241.19/47.70    (50)  all_58_4 = e3
% 241.19/47.70    (51)  op(e2, e0) = e1
% 241.19/47.70    (52)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.19/47.70          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.19/47.70    (53)  op(e2, e0) = all_52_13
% 241.19/47.70    (54)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.19/47.70          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.19/47.70            e1)
% 241.19/47.70    (55)   ~ (all_52_1 = e3)
% 241.19/47.70    (56)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.19/47.70          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.19/47.70            e2)
% 241.19/47.70    (57)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.19/47.70          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.19/47.70    (58)  all_58_10 = e1
% 241.19/47.70    (59)   ~ (e2 = e1)
% 241.19/47.70    (60)   ~ (all_52_1 = e1)
% 241.19/47.70  
% 241.19/47.70  Begin of proof
% 241.19/47.70  | 
% 241.19/47.70  | BETA: splitting (44) gives:
% 241.19/47.70  | 
% 241.19/47.70  | Case 1:
% 241.19/47.70  | | 
% 241.19/47.70  | |   (61)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 241.19/47.70  | |           e0)
% 241.19/47.70  | | 
% 241.19/47.70  | | BETA: splitting (61) gives:
% 241.19/47.70  | | 
% 241.19/47.70  | | Case 1:
% 241.19/47.70  | | | 
% 241.19/47.70  | | |   (62)  all_58_2 = e0 & op(e2, e3) = e0
% 241.19/47.70  | | | 
% 241.19/47.70  | | | ALPHA: (62) implies:
% 241.19/47.70  | | |   (63)  all_58_2 = e0
% 241.19/47.70  | | | 
% 241.19/47.70  | | | BETA: splitting (18) gives:
% 241.19/47.70  | | | 
% 241.19/47.70  | | | Case 1:
% 241.19/47.70  | | | | 
% 241.19/47.70  | | | |   (64)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1)
% 241.19/47.70  | | | |           = e0)
% 241.19/47.70  | | | | 
% 241.19/47.70  | | | | BETA: splitting (64) gives:
% 241.19/47.70  | | | | 
% 241.19/47.70  | | | | Case 1:
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | |   (65)  all_58_4 = e0 & op(e3, e1) = e0
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | | REF_CLOSE: (3), (6), (9), (27), (30), (31), (34), (35), (45), (50),
% 241.19/47.70  | | | | |            (65) are inconsistent by sub-proof #786.
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | Case 2:
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | |   (66)  all_58_5 = e0 & op(e2, e1) = e0
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | | REF_CLOSE: (7), (36), (66) are inconsistent by sub-proof #836.
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | End of split
% 241.19/47.70  | | | | 
% 241.19/47.70  | | | Case 2:
% 241.19/47.70  | | | | 
% 241.19/47.70  | | | |   (67)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1)
% 241.19/47.70  | | | |           = e0)
% 241.19/47.70  | | | | 
% 241.19/47.70  | | | | BETA: splitting (67) gives:
% 241.19/47.70  | | | | 
% 241.19/47.70  | | | | Case 1:
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | |   (68)  all_58_8 = e0 & op(e1, e1) = e0
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | | ALPHA: (68) implies:
% 241.19/47.70  | | | | |   (69)  op(e1, e1) = e0
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12),
% 241.19/47.70  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.19/47.70  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (32), (33),
% 241.19/47.70  | | | | |            (34), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 241.19/47.70  | | | | |            (46), (47), (48), (49), (50), (52), (53), (54), (55), (56),
% 241.19/47.70  | | | | |            (57), (59), (60), (69) are inconsistent by sub-proof #507.
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | Case 2:
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | |   (70)  all_58_14 = e0 & op(e0, e1) = e0
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | | ALPHA: (70) implies:
% 241.19/47.70  | | | | |   (71)  all_58_14 = e0
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (15), (16), (17),
% 241.19/47.70  | | | | |            (19), (20), (21), (22), (23), (24), (25), (27), (29), (30),
% 241.19/47.70  | | | | |            (31), (32), (33), (34), (35), (36), (37), (39), (40), (41),
% 241.19/47.70  | | | | |            (42), (44), (45), (46), (49), (50), (54), (55), (58), (59),
% 241.19/47.70  | | | | |            (63), (71) are inconsistent by sub-proof #827.
% 241.19/47.70  | | | | | 
% 241.19/47.70  | | | | End of split
% 241.19/47.70  | | | | 
% 241.19/47.70  | | | End of split
% 241.19/47.70  | | | 
% 241.19/47.70  | | Case 2:
% 241.19/47.70  | | | 
% 241.19/47.70  | | |   (72)  all_58_3 = e0 & op(e2, e2) = e0
% 241.19/47.70  | | | 
% 241.19/47.70  | | | REF_CLOSE: (3), (6), (9), (19), (27), (30), (31), (34), (35), (45), (72)
% 241.19/47.70  | | |            are inconsistent by sub-proof #916.
% 241.19/47.70  | | | 
% 241.19/47.70  | | End of split
% 241.19/47.70  | | 
% 241.19/47.70  | Case 2:
% 241.19/47.70  | | 
% 241.19/47.70  | |   (73)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 241.19/47.70  | |           e0)
% 241.19/47.70  | | 
% 241.19/47.70  | | BETA: splitting (73) gives:
% 241.19/47.70  | | 
% 241.19/47.70  | | Case 1:
% 241.19/47.70  | | | 
% 241.19/47.70  | | |   (74)  all_58_5 = e0 & op(e2, e1) = e0
% 241.19/47.70  | | | 
% 241.19/47.70  | | | REF_CLOSE: (7), (36), (74) are inconsistent by sub-proof #836.
% 241.19/47.70  | | | 
% 241.19/47.70  | | Case 2:
% 241.19/47.70  | | | 
% 241.19/47.70  | | |   (75)  all_58_10 = e0 & op(e2, e0) = e0
% 241.19/47.70  | | | 
% 241.19/47.70  | | | ALPHA: (75) implies:
% 241.19/47.70  | | |   (76)  op(e2, e0) = e0
% 241.19/47.70  | | | 
% 241.19/47.70  | | | REF_CLOSE: (45), (49), (51), (53), (76) are inconsistent by sub-proof
% 241.19/47.70  | | |            #1778.
% 241.19/47.70  | | | 
% 241.19/47.70  | | End of split
% 241.19/47.70  | | 
% 241.19/47.70  | End of split
% 241.19/47.70  | 
% 241.19/47.70  End of proof
% 241.19/47.70  
% 241.19/47.70  Sub-proof #492 shows that the following formulas are inconsistent:
% 241.19/47.70  ----------------------------------------------------------------
% 241.19/47.70    (1)  all_56_21 = e2
% 241.19/47.70    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.19/47.70         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.19/47.70    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.19/47.70         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.19/47.70    (4)   ~ (e3 = e0)
% 241.19/47.70    (5)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.19/47.70         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.19/47.70    (6)  all_42_2 = e3
% 241.19/47.70    (7)  all_58_6 = e3
% 241.19/47.70    (8)  op(e1, e2) = e1
% 241.19/47.70    (9)   ~ (e2 = e0)
% 241.19/47.70    (10)  op(e1, e2) = all_52_6
% 241.19/47.70    (11)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.19/47.70          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.19/47.70    (12)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.19/47.70          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.19/47.70    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.19/47.70              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.19/47.70            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.19/47.70            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.19/47.70            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.19/47.70             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.19/47.70            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.19/47.70            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.19/47.70            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.19/47.70            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.19/47.70            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.19/47.70              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.19/47.70            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.19/47.70            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.19/47.70            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.19/47.70            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.19/47.70            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.19/47.70            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.19/47.70              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.19/47.70            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.19/47.70            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.19/47.70            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.19/47.70            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.19/47.70            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.19/47.70            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.19/47.70              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.19/47.70            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.19/47.70            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.19/47.70    (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.19/47.70          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.19/47.70    (15)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.19/47.70            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.19/47.70              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.19/47.70    (16)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.19/47.70          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.19/47.70    (17)   ~ (all_52_7 = e3)
% 241.19/47.70    (18)  all_58_15 = e3
% 241.19/47.70    (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.19/47.70          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.19/47.70    (20)   ~ (e3 = e1)
% 241.19/47.70    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.19/47.70          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.19/47.70    (22)  all_58_3 = e3
% 241.19/47.70    (23)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.19/47.70          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.19/47.70    (24)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.19/47.70          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.19/47.70    (25)  op(e3, e3) = e1
% 241.19/47.70    (26)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.19/47.70              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.19/47.70                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.19/47.70                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.19/47.70    (27)  op(e2, e1) = all_52_9
% 241.19/47.70    (28)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.19/47.70          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.19/47.70    (29)   ~ (e3 = e2)
% 241.19/47.70    (30)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.19/47.70          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.19/47.70    (31)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.19/47.70          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.19/47.70    (32)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.19/47.70          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.19/47.70    (33)  all_58_11 = e2
% 241.19/47.70    (34)  op(e2, e3) = all_52_1
% 241.19/47.70    (35)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.19/47.70          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.19/47.70    (36)   ~ (all_52_6 = e3)
% 241.19/47.70    (37)  op(e1, e1) = e2
% 241.19/47.70    (38)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.19/47.70          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.19/47.70    (39)  op(e0, e2) = all_52_7
% 241.19/47.70    (40)   ~ (all_52_4 = e3)
% 241.19/47.70    (41)  op(e3, e2) = all_52_4
% 241.19/47.70    (42)  all_58_7 = e1
% 241.19/47.70    (43)   ~ (all_52_9 = e3)
% 241.19/47.70    (44)  all_56_31 = e3
% 241.19/47.70    (45)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.19/47.70          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.19/47.70    (46)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.19/47.70          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.19/47.70    (47)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.19/47.70          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.19/47.70    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.19/47.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.19/47.70    (49)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.19/47.70          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.19/47.70    (50)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.19/47.70          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.19/47.70    (51)   ~ (all_52_4 = e1)
% 241.19/47.70    (52)   ~ (e1 = e0)
% 241.19/47.70    (53)  all_58_4 = e3
% 241.19/47.70    (54)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.19/47.70          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.19/47.70    (55)  op(e2, e0) = all_52_13
% 241.19/47.70    (56)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.19/47.70          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.19/47.70            e1)
% 241.19/47.70    (57)   ~ (all_52_1 = e3)
% 241.19/47.70    (58)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.19/47.70          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.19/47.70            e2)
% 241.19/47.70    (59)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.19/47.70            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 241.19/47.70            & $i(all_8_1))
% 241.19/47.70    (60)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.19/47.70          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.19/47.70    (61)  all_56_1 = e1
% 241.19/47.70    (62)   ~ (e2 = e1)
% 241.19/47.70    (63)   ~ (all_52_1 = e1)
% 241.19/47.70  
% 241.19/47.70  Begin of proof
% 241.19/47.70  | 
% 241.19/47.70  | BETA: splitting (12) gives:
% 241.19/47.70  | 
% 241.19/47.70  | Case 1:
% 241.19/47.70  | | 
% 241.19/47.70  | |   (64)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 241.19/47.70  | |           e1)
% 241.19/47.70  | | 
% 241.19/47.70  | | BETA: splitting (64) gives:
% 241.19/47.70  | | 
% 241.19/47.70  | | Case 1:
% 241.19/47.70  | | | 
% 241.19/47.70  | | |   (65)  all_58_9 = e1 & op(e3, e0) = e1
% 241.19/47.70  | | | 
% 241.19/47.70  | | | ALPHA: (65) implies:
% 241.19/47.70  | | |   (66)  all_58_9 = e1
% 241.19/47.70  | | | 
% 241.19/47.71  | | | REF_CLOSE: (2), (4), (9), (25), (29), (35), (48), (52), (53), (62), (66)
% 241.19/47.71  | | |            are inconsistent by sub-proof #1292.
% 241.19/47.71  | | | 
% 241.19/47.71  | | Case 2:
% 241.19/47.71  | | | 
% 241.19/47.71  | | |   (67)  all_58_10 = e1 & op(e2, e0) = e1
% 241.19/47.71  | | | 
% 241.19/47.71  | | | ALPHA: (67) implies:
% 241.19/47.71  | | |   (68)  all_58_10 = e1
% 241.19/47.71  | | |   (69)  op(e2, e0) = e1
% 241.19/47.71  | | | 
% 241.19/47.71  | | | BETA: splitting (19) gives:
% 241.19/47.71  | | | 
% 241.19/47.71  | | | Case 1:
% 241.19/47.71  | | | | 
% 241.19/47.71  | | | |   (70)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2)
% 241.19/47.71  | | | |           = e2)
% 241.19/47.71  | | | | 
% 241.19/47.71  | | | | BETA: splitting (70) gives:
% 241.19/47.71  | | | | 
% 241.19/47.71  | | | | Case 1:
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | |   (71)  all_58_2 = e2 & op(e2, e3) = e2
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | | ALPHA: (71) implies:
% 241.19/47.71  | | | | |   (72)  all_58_2 = e2
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | | BETA: splitting (54) gives:
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | | Case 1:
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | |   (73)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1,
% 241.19/47.71  | | | | | |             e2) = e0)
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | | REF_CLOSE: (4), (8), (10), (29), (32), (33), (36), (37), (48), (52),
% 241.19/47.71  | | | | | |            (73) are inconsistent by sub-proof #989.
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | Case 2:
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | |   (74)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1,
% 241.19/47.71  | | | | | |             e0) = e0)
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | | BETA: splitting (74) gives:
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | | Case 1:
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | |   (75)  all_58_8 = e0 & op(e1, e1) = e0
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | | ALPHA: (75) implies:
% 241.19/47.71  | | | | | | |   (76)  all_58_8 = e0
% 241.19/47.71  | | | | | | |   (77)  op(e1, e1) = e0
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11),
% 241.19/47.71  | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 241.19/47.71  | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 241.19/47.71  | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 241.19/47.71  | | | | | | |            (39), (40), (41), (43), (44), (45), (46), (47), (48),
% 241.19/47.71  | | | | | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 241.19/47.71  | | | | | | |            (58), (59), (60), (61), (62), (63), (68), (69), (72),
% 241.19/47.71  | | | | | | |            (76), (77) are inconsistent by sub-proof #493.
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | Case 2:
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | |   (78)  all_58_11 = e0 & op(e1, e0) = e0
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | | REF_CLOSE: (9), (33), (78) are inconsistent by sub-proof #2033.
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | End of split
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | End of split
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | Case 2:
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | |   (79)  all_58_3 = e2 & op(e2, e2) = e2
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | | REF_CLOSE: (22), (29), (79) are inconsistent by sub-proof #1458.
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | End of split
% 241.19/47.71  | | | | 
% 241.19/47.71  | | | Case 2:
% 241.19/47.71  | | | | 
% 241.19/47.71  | | | |   (80)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0)
% 241.19/47.71  | | | |           = e2)
% 241.19/47.71  | | | | 
% 241.19/47.71  | | | | BETA: splitting (80) gives:
% 241.19/47.71  | | | | 
% 241.19/47.71  | | | | Case 1:
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | |   (81)  all_58_5 = e2 & op(e2, e1) = e2
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | | ALPHA: (81) implies:
% 241.19/47.71  | | | | |   (82)  all_58_5 = e2
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | | BETA: splitting (54) gives:
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | | Case 1:
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | |   (83)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1,
% 241.19/47.71  | | | | | |             e2) = e0)
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | | REF_CLOSE: (4), (8), (10), (29), (32), (33), (36), (37), (48), (52),
% 241.19/47.71  | | | | | |            (83) are inconsistent by sub-proof #989.
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | Case 2:
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | |   (84)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1,
% 241.19/47.71  | | | | | |             e0) = e0)
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | | BETA: splitting (84) gives:
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | | Case 1:
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | |   (85)  all_58_8 = e0 & op(e1, e1) = e0
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | | ALPHA: (85) implies:
% 241.19/47.71  | | | | | | |   (86)  all_58_8 = e0
% 241.19/47.71  | | | | | | |   (87)  op(e1, e1) = e0
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | | BETA: splitting (47) gives:
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | 
% 241.19/47.71  | | | | | | | |   (88)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 241.19/47.71  | | | | | | | |           op(e2, e2) = e0)
% 241.19/47.71  | | | | | | | | 
% 241.19/47.71  | | | | | | | | BETA: splitting (88) gives:
% 241.19/47.71  | | | | | | | | 
% 241.19/47.71  | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | 
% 241.19/47.71  | | | | | | | | |   (89)  all_58_2 = e0 & op(e2, e3) = e0
% 241.19/47.71  | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | ALPHA: (89) implies:
% 241.19/47.71  | | | | | | | | |   (90)  all_58_2 = e0
% 241.19/47.71  | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | BETA: splitting (28) gives:
% 241.19/47.71  | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | |   (91)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 &
% 241.19/47.71  | | | | | | | | | |           op(e2, e3) = e2)
% 241.19/47.71  | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | BETA: splitting (91) gives:
% 241.19/47.71  | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | |   (92)  all_58_0 = e2 & op(e3, e3) = e2
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | ALPHA: (92) implies:
% 241.19/47.71  | | | | | | | | | | |   (93)  op(e3, e3) = e2
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | REF_CLOSE: (25), (48), (62), (93) are inconsistent by
% 241.19/47.71  | | | | | | | | | | |            sub-proof #2267.
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | |   (94)  all_58_2 = e2 & op(e2, e3) = e2
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | ALPHA: (94) implies:
% 241.19/47.71  | | | | | | | | | | |   (95)  all_58_2 = e2
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 241.19/47.71  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 241.19/47.71  | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 241.19/47.71  | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 241.19/47.71  | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (43),
% 241.19/47.71  | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 241.19/47.71  | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 241.19/47.71  | | | | | | | | | | |            (60), (61), (62), (63), (68), (69), (86), (87),
% 241.19/47.71  | | | | | | | | | | |            (95) are inconsistent by sub-proof #493.
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | |   (96)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2
% 241.19/47.71  | | | | | | | | | |           & op(e0, e3) = e2)
% 241.19/47.71  | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | BETA: splitting (96) gives:
% 241.19/47.71  | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | |   (97)  all_58_6 = e2 & op(e1, e3) = e2
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | REF_CLOSE: (7), (29), (97) are inconsistent by sub-proof
% 241.19/47.71  | | | | | | | | | | |            #2219.
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | |   (98)  all_58_12 = e2 & op(e0, e3) = e2
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | ALPHA: (98) implies:
% 241.19/47.71  | | | | | | | | | | |   (99)  all_58_12 = e2
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | BETA: splitting (16) gives:
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | |   (100)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.19/47.71  | | | | | | | | | | | |            & op(e2, e1) = e1)
% 241.19/47.71  | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | REF_CLOSE: (2), (4), (9), (19), (20), (22), (23), (25), (29),
% 241.19/47.71  | | | | | | | | | | | |            (35), (40), (41), (47), (48), (52), (62), (68),
% 241.19/47.71  | | | | | | | | | | | |            (100) are inconsistent by sub-proof #647.
% 241.19/47.71  | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | |   (101)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.19/47.71  | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 241.19/47.71  | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | BETA: splitting (101) gives:
% 241.19/47.71  | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | |   (102)  all_58_8 = e1 & op(e1, e1) = e1
% 241.19/47.71  | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | ALPHA: (102) implies:
% 241.19/47.71  | | | | | | | | | | | | |   (103)  op(e1, e1) = e1
% 241.19/47.71  | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | REF_CLOSE: (48), (52), (87), (103) are inconsistent by
% 241.19/47.71  | | | | | | | | | | | | |            sub-proof #2220.
% 241.19/47.71  | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | |   (104)  all_58_14 = e1 & op(e0, e1) = e1
% 241.19/47.71  | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | ALPHA: (104) implies:
% 241.19/47.71  | | | | | | | | | | | | |   (105)  all_58_14 = e1
% 241.19/47.71  | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | BETA: splitting (26) gives:
% 241.19/47.71  | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | |   (106)  all_58_15 = e0 & op(e0, e0) = e0
% 241.19/47.71  | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (7), (9), (10), (11), (12), (14),
% 241.19/47.71  | | | | | | | | | | | | | |            (16), (18), (19), (20), (21), (22), (23), (24),
% 241.19/47.71  | | | | | | | | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32),
% 241.19/47.71  | | | | | | | | | | | | | |            (34), (35), (36), (38), (40), (41), (43), (45),
% 241.19/47.71  | | | | | | | | | | | | | |            (46), (47), (48), (49), (52), (53), (54), (55),
% 241.19/47.71  | | | | | | | | | | | | | |            (56), (57), (58), (60), (62), (63), (87), (105),
% 241.19/47.71  | | | | | | | | | | | | | |            (106) are inconsistent by sub-proof #520.
% 241.19/47.71  | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | |   (107)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.19/47.71  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 241.19/47.71  | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 241.19/47.71  | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 241.19/47.71  | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.19/47.71  | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | ALPHA: (107) implies:
% 241.19/47.71  | | | | | | | | | | | | | |   (108)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 241.19/47.71  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 241.19/47.71  | | | | | | | | | | | | | |              e1) = e0)
% 241.19/47.71  | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 241.19/47.71  | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | |   (109)  all_58_12 = e0 & op(e0, e3) = e0
% 241.19/47.71  | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 241.19/47.71  | | | | | | | | | | | | | | |   (110)  all_58_12 = e0
% 241.19/47.71  | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (20), (24), (25), (28), (29), (34),
% 241.19/47.71  | | | | | | | | | | | | | | |            (48), (57), (62), (90), (110) are inconsistent by
% 241.19/47.71  | | | | | | | | | | | | | | |            sub-proof #1149.
% 241.19/47.71  | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | |   (111)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 241.19/47.71  | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 241.19/47.71  | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 241.19/47.71  | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | |   (112)  all_58_13 = e0 & op(e0, e2) = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 241.19/47.71  | | | | | | | | | | | | | | | |   (113)  op(e0, e2) = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 241.19/47.71  | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | |   (114)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 241.19/47.71  | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 241.19/47.71  | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 241.19/47.71  | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | |   (115)  all_58_0 = e2 & op(e3, e3) = e2
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 241.19/47.71  | | | | | | | | | | | | | | | | | |   (116)  op(e3, e3) = e2
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (48), (62), (116) are inconsistent by
% 241.19/47.71  | | | | | | | | | | | | | | | | | |            sub-proof #2267.
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | |   (117)  all_58_1 = e2 & op(e3, e2) = e2
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 241.19/47.71  | | | | | | | | | | | | | | | | | |   (118)  all_58_1 = e2
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (48) with e0, e2, e1, e1,
% 241.19/47.71  | | | | | | | | | | | | | | | | | |              simplifying with (37), (87) gives:
% 241.19/47.71  | | | | | | | | | | | | | | | | | |   (119)  e2 = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (119) imply:
% 241.19/47.71  | | | | | | | | | | | | | | | | | |   (120)  all_58_1 = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (9), (11), (22), (25), (28), (29),
% 241.19/47.71  | | | | | | | | | | | | | | | | | |            (31), (42), (48), (52), (53), (62), (99), (113),
% 241.19/47.71  | | | | | | | | | | | | | | | | | |            (120) are inconsistent by sub-proof #586.
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | |   (121)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 241.19/47.71  | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 241.19/47.71  | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 241.19/47.71  | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | |   (122)  all_58_4 = e2 & op(e3, e1) = e2
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 241.19/47.71  | | | | | | | | | | | | | | | | | |   (123)  all_58_4 = e2
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (20), (24), (25), (27), (28), (29),
% 241.19/47.71  | | | | | | | | | | | | | | | | | |            (31), (34), (38), (43), (48), (52), (57), (62),
% 241.19/47.71  | | | | | | | | | | | | | | | | | |            (87), (105), (123) are inconsistent by sub-proof
% 241.19/47.71  | | | | | | | | | | | | | | | | | |            #645.
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | |   (124)  all_58_9 = e2 & op(e3, e0) = e2
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 241.19/47.71  | | | | | | | | | | | | | | | | | |   (125)  all_58_9 = e2
% 241.19/47.71  | | | | | | | | | | | | | | | | | |   (126)  op(e3, e0) = e2
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | |   (127)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (9), (11), (22), (25), (28), (29),
% 241.19/47.71  | | | | | | | | | | | | | | | | | | |            (31), (42), (48), (52), (53), (62), (99), (113),
% 241.19/47.71  | | | | | | | | | | | | | | | | | | |            (127) are inconsistent by sub-proof #506.
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | |   (128)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | |   (129)  all_58_4 = e0 & op(e3, e1) = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | |   (130)  all_58_4 = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (23), (25), (29), (40), (41), (48),
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | |            (126), (130) are inconsistent by sub-proof #1400.
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | |   (131)  all_58_9 = e0 & op(e3, e0) = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | |   (132)  all_58_9 = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (132) imply:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | |   (133)  e2 = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | SIMP: (133) implies:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | |   (134)  e2 = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (134) imply:
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | |   (135)  all_58_5 = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (20), (24), (25), (27), (28), (29),
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | |            (30), (31), (34), (38), (43), (48), (52), (57),
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | |            (62), (86), (87), (105), (135) are inconsistent by
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | |            sub-proof #505.
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | |   (136)  all_58_14 = e0 & op(e0, e1) = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 241.19/47.71  | | | | | | | | | | | | | | | |   (137)  all_58_14 = e0
% 241.19/47.71  | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | | REF_CLOSE: (52), (105), (137) are inconsistent by sub-proof
% 241.19/47.71  | | | | | | | | | | | | | | | |            #1033.
% 241.19/47.71  | | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | | 
% 241.19/47.71  | | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | | 
% 241.19/47.71  | | | | | | | | |   (138)  all_58_3 = e0 & op(e2, e2) = e0
% 241.19/47.71  | | | | | | | | | 
% 241.19/47.71  | | | | | | | | | REF_CLOSE: (4), (7), (10), (22), (29), (32), (33), (36), (37),
% 241.19/47.71  | | | | | | | | |            (48), (138) are inconsistent by sub-proof #916.
% 241.19/47.71  | | | | | | | | | 
% 241.19/47.71  | | | | | | | | End of split
% 241.19/47.71  | | | | | | | | 
% 241.19/47.71  | | | | | | | Case 2:
% 241.19/47.71  | | | | | | | | 
% 241.19/47.71  | | | | | | | |   (139)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 241.19/47.71  | | | | | | | |            op(e2, e0) = e0)
% 241.19/47.71  | | | | | | | | 
% 241.19/47.71  | | | | | | | | REF_CLOSE: (2), (4), (7), (9), (16), (19), (20), (22), (23),
% 241.19/47.71  | | | | | | | |            (24), (25), (27), (28), (29), (30), (31), (34), (35),
% 241.19/47.71  | | | | | | | |            (38), (40), (41), (43), (47), (48), (52), (55), (57),
% 241.19/47.71  | | | | | | | |            (62), (68), (69), (86), (87), (139) are inconsistent
% 241.19/47.71  | | | | | | | |            by sub-proof #494.
% 241.19/47.71  | | | | | | | | 
% 241.19/47.71  | | | | | | | End of split
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | Case 2:
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | |   (140)  all_58_11 = e0 & op(e1, e0) = e0
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | | REF_CLOSE: (9), (33), (140) are inconsistent by sub-proof #2033.
% 241.19/47.71  | | | | | | | 
% 241.19/47.71  | | | | | | End of split
% 241.19/47.71  | | | | | | 
% 241.19/47.71  | | | | | End of split
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | Case 2:
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | |   (141)  all_58_10 = e2 & op(e2, e0) = e2
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | | ALPHA: (141) implies:
% 241.19/47.71  | | | | |   (142)  op(e2, e0) = e2
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | | REF_CLOSE: (48), (62), (69), (142) are inconsistent by sub-proof
% 241.19/47.71  | | | | |            #1659.
% 241.19/47.71  | | | | | 
% 241.19/47.71  | | | | End of split
% 241.19/47.71  | | | | 
% 241.19/47.71  | | | End of split
% 241.19/47.71  | | | 
% 241.19/47.71  | | End of split
% 241.19/47.71  | | 
% 241.19/47.71  | Case 2:
% 241.19/47.71  | | 
% 241.19/47.71  | |   (143)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.19/47.71  | |            e1)
% 241.19/47.71  | | 
% 241.19/47.71  | | BETA: splitting (143) gives:
% 241.19/47.71  | | 
% 241.19/47.71  | | Case 1:
% 241.19/47.71  | | | 
% 241.19/47.71  | | |   (144)  all_58_11 = e1 & op(e1, e0) = e1
% 241.19/47.71  | | | 
% 241.19/47.71  | | | REF_CLOSE: (33), (62), (144) are inconsistent by sub-proof #1346.
% 241.19/47.71  | | | 
% 241.19/47.71  | | Case 2:
% 241.19/47.71  | | | 
% 241.19/47.71  | | |   (145)  all_58_15 = e1 & op(e0, e0) = e1
% 241.19/47.71  | | | 
% 241.19/47.71  | | | ALPHA: (145) implies:
% 241.19/47.72  | | |   (146)  all_58_15 = e1
% 241.19/47.72  | | | 
% 241.19/47.72  | | | REF_CLOSE: (2), (4), (9), (18), (20), (23), (25), (29), (35), (40), (41),
% 241.19/47.72  | | |            (48), (52), (53), (62), (146) are inconsistent by sub-proof
% 241.19/47.72  | | |            #1093.
% 241.19/47.72  | | | 
% 241.19/47.72  | | End of split
% 241.19/47.72  | | 
% 241.19/47.72  | End of split
% 241.19/47.72  | 
% 241.19/47.72  End of proof
% 241.19/47.72  
% 241.19/47.72  Sub-proof #493 shows that the following formulas are inconsistent:
% 241.19/47.72  ----------------------------------------------------------------
% 241.19/47.72    (1)  all_56_21 = e2
% 241.19/47.72    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.19/47.72         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.19/47.72    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.19/47.72         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.19/47.72    (4)   ~ (e3 = e0)
% 241.19/47.72    (5)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.19/47.72         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.19/47.72    (6)  all_42_2 = e3
% 241.19/47.72    (7)  all_58_6 = e3
% 241.19/47.72    (8)   ~ (e2 = e0)
% 241.19/47.72    (9)  op(e1, e2) = all_52_6
% 241.19/47.72    (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.19/47.72          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.19/47.72    (11)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.19/47.72          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.22/47.72    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.22/47.72              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.22/47.72            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.22/47.72            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.22/47.72            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.22/47.72             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.72            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.22/47.72            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.22/47.72            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.22/47.72            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.72            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.22/47.72              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.22/47.72            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.22/47.72            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.22/47.72            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.22/47.72            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.22/47.72            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.22/47.72            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.22/47.72              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.22/47.72            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.22/47.72            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.22/47.72            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.22/47.72            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.22/47.72            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.72            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.22/47.72              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.22/47.72            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.72            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.22/47.72    (13)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.72          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.22/47.72    (14)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.22/47.72            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.22/47.72              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.22/47.72    (15)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.22/47.72          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.22/47.72    (16)   ~ (all_52_7 = e3)
% 241.22/47.72    (17)  all_58_8 = e0
% 241.22/47.72    (18)  all_58_15 = e3
% 241.22/47.72    (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.72          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.22/47.72    (20)   ~ (e3 = e1)
% 241.22/47.72    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.22/47.72          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.22/47.72    (22)  all_58_2 = e2
% 241.22/47.72    (23)  all_58_3 = e3
% 241.22/47.72    (24)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.22/47.72          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.22/47.72    (25)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.22/47.72          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.22/47.72    (26)  op(e3, e3) = e1
% 241.22/47.72    (27)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.72              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.22/47.72                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.22/47.72                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.22/47.72    (28)  op(e2, e1) = all_52_9
% 241.22/47.72    (29)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.22/47.72          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.22/47.72    (30)   ~ (e3 = e2)
% 241.22/47.72    (31)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.22/47.72          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.22/47.72    (32)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.22/47.72          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.22/47.72    (33)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.22/47.72          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.22/47.72    (34)  all_58_11 = e2
% 241.22/47.72    (35)  op(e2, e3) = all_52_1
% 241.22/47.72    (36)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.22/47.72          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.72    (37)   ~ (all_52_6 = e3)
% 241.22/47.72    (38)  op(e1, e1) = e2
% 241.22/47.72    (39)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.22/47.72          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.22/47.72    (40)  op(e0, e2) = all_52_7
% 241.22/47.72    (41)   ~ (all_52_4 = e3)
% 241.22/47.72    (42)  op(e3, e2) = all_52_4
% 241.22/47.72    (43)   ~ (all_52_9 = e3)
% 241.22/47.72    (44)  all_56_31 = e3
% 241.22/47.72    (45)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.22/47.72          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.22/47.72    (46)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.22/47.72          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.22/47.72    (47)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.72          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.22/47.72    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.72    (49)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.22/47.72          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.22/47.72    (50)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.22/47.72          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.22/47.72    (51)  op(e1, e1) = e0
% 241.22/47.72    (52)   ~ (all_52_4 = e1)
% 241.22/47.72    (53)   ~ (e1 = e0)
% 241.22/47.72    (54)  all_58_4 = e3
% 241.22/47.72    (55)  op(e2, e0) = e1
% 241.22/47.72    (56)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.22/47.72          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.22/47.72    (57)  op(e2, e0) = all_52_13
% 241.22/47.72    (58)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.22/47.72          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.22/47.72            e1)
% 241.22/47.72    (59)   ~ (all_52_1 = e3)
% 241.22/47.72    (60)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.22/47.72          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.22/47.72            e2)
% 241.22/47.72    (61)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.22/47.72            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 241.22/47.72            & $i(all_8_1))
% 241.22/47.72    (62)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.22/47.72          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.22/47.72    (63)  all_58_10 = e1
% 241.22/47.72    (64)  all_56_1 = e1
% 241.22/47.72    (65)   ~ (e2 = e1)
% 241.22/47.72    (66)   ~ (all_52_1 = e1)
% 241.22/47.72  
% 241.22/47.72  Begin of proof
% 241.22/47.72  | 
% 241.22/47.72  | BETA: splitting (47) gives:
% 241.22/47.72  | 
% 241.22/47.72  | Case 1:
% 241.22/47.72  | | 
% 241.22/47.72  | |   (67)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 241.22/47.72  | |           e0)
% 241.22/47.72  | | 
% 241.22/47.72  | | BETA: splitting (67) gives:
% 241.22/47.72  | | 
% 241.22/47.72  | | Case 1:
% 241.22/47.72  | | | 
% 241.22/47.72  | | |   (68)  all_58_2 = e0 & op(e2, e3) = e0
% 241.22/47.72  | | | 
% 241.22/47.72  | | | ALPHA: (68) implies:
% 241.22/47.72  | | |   (69)  all_58_2 = e0
% 241.22/47.72  | | | 
% 241.22/47.72  | | | COMBINE_EQS: (22), (69) imply:
% 241.22/47.72  | | |   (70)  e2 = e0
% 241.22/47.72  | | | 
% 241.22/47.72  | | | COMBINE_EQS: (1), (70) imply:
% 241.22/47.72  | | |   (71)  all_56_21 = e0
% 241.22/47.72  | | | 
% 241.22/47.72  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.22/47.72  | | |            (14), (15), (16), (18), (19), (20), (21), (23), (24), (25),
% 241.22/47.72  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (35), (36),
% 241.22/47.72  | | |            (37), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 241.22/47.72  | | |            (48), (49), (50), (51), (52), (53), (54), (56), (57), (58),
% 241.22/47.72  | | |            (59), (60), (61), (62), (64), (65), (66), (71) are inconsistent
% 241.22/47.72  | | |            by sub-proof #497.
% 241.22/47.72  | | | 
% 241.22/47.72  | | Case 2:
% 241.22/47.72  | | | 
% 241.22/47.72  | | |   (72)  all_58_3 = e0 & op(e2, e2) = e0
% 241.22/47.72  | | | 
% 241.22/47.72  | | | REF_CLOSE: (4), (7), (9), (23), (30), (33), (34), (37), (38), (48), (72)
% 241.22/47.72  | | |            are inconsistent by sub-proof #916.
% 241.22/47.72  | | | 
% 241.22/47.72  | | End of split
% 241.22/47.72  | | 
% 241.22/47.72  | Case 2:
% 241.22/47.72  | | 
% 241.22/47.72  | |   (73)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 241.22/47.72  | |           e0)
% 241.22/47.72  | | 
% 241.22/47.72  | | REF_CLOSE: (2), (4), (7), (8), (15), (17), (19), (20), (23), (24), (25),
% 241.22/47.72  | |            (26), (28), (29), (30), (31), (32), (35), (36), (39), (41), (42),
% 241.22/47.72  | |            (43), (47), (48), (51), (53), (55), (57), (59), (63), (65), (73)
% 241.22/47.72  | |            are inconsistent by sub-proof #494.
% 241.22/47.72  | | 
% 241.22/47.72  | End of split
% 241.22/47.72  | 
% 241.22/47.72  End of proof
% 241.22/47.72  
% 241.22/47.72  Sub-proof #494 shows that the following formulas are inconsistent:
% 241.22/47.72  ----------------------------------------------------------------
% 241.22/47.72    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.22/47.72         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.22/47.72    (2)   ~ (e3 = e0)
% 241.22/47.72    (3)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.22/47.72    (4)  all_58_6 = e3
% 241.22/47.72    (5)   ~ (e2 = e0)
% 241.22/47.72    (6)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.22/47.72         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.22/47.72    (7)  all_58_8 = e0
% 241.22/47.72    (8)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.72         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.22/47.72    (9)   ~ (e3 = e1)
% 241.22/47.72    (10)  all_58_3 = e3
% 241.22/47.72    (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.22/47.72          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.22/47.72    (12)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.22/47.72          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.22/47.72    (13)  op(e3, e3) = e1
% 241.22/47.72    (14)  op(e2, e1) = all_52_9
% 241.22/47.72    (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.22/47.72          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.22/47.72    (16)   ~ (e3 = e2)
% 241.22/47.72    (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.22/47.72          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.22/47.72    (18)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.22/47.72          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.22/47.72    (19)  op(e2, e3) = all_52_1
% 241.22/47.72    (20)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.22/47.72          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.72    (21)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.22/47.72          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.22/47.72    (22)   ~ (all_52_4 = e3)
% 241.22/47.72    (23)  op(e3, e2) = all_52_4
% 241.22/47.72    (24)   ~ (all_52_9 = e3)
% 241.22/47.72    (25)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.72          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.22/47.73    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.73    (27)  op(e1, e1) = e0
% 241.22/47.73    (28)   ~ (e1 = e0)
% 241.22/47.73    (29)  op(e2, e0) = e1
% 241.22/47.73    (30)  op(e2, e0) = all_52_13
% 241.22/47.73    (31)   ~ (all_52_1 = e3)
% 241.22/47.73    (32)  all_58_10 = e1
% 241.22/47.73    (33)   ~ (e2 = e1)
% 241.22/47.73  
% 241.22/47.73  Begin of proof
% 241.22/47.73  | 
% 241.22/47.73  | BETA: splitting (3) gives:
% 241.22/47.73  | 
% 241.22/47.73  | Case 1:
% 241.22/47.73  | | 
% 241.22/47.73  | |   (34)  all_58_5 = e0 & op(e2, e1) = e0
% 241.22/47.73  | | 
% 241.22/47.73  | | ALPHA: (34) implies:
% 241.22/47.73  | |   (35)  all_58_5 = e0
% 241.22/47.73  | | 
% 241.22/47.73  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.22/47.73  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 241.22/47.73  | |            (25), (26), (27), (28), (31), (32), (33), (35) are inconsistent
% 241.22/47.73  | |            by sub-proof #504.
% 241.22/47.73  | | 
% 241.22/47.73  | Case 2:
% 241.22/47.73  | | 
% 241.22/47.73  | |   (36)  all_58_10 = e0 & op(e2, e0) = e0
% 241.22/47.73  | | 
% 241.22/47.73  | | ALPHA: (36) implies:
% 241.22/47.73  | |   (37)  op(e2, e0) = e0
% 241.22/47.73  | | 
% 241.22/47.73  | | REF_CLOSE: (26), (28), (29), (30), (37) are inconsistent by sub-proof #1778.
% 241.22/47.73  | | 
% 241.22/47.73  | End of split
% 241.22/47.73  | 
% 241.22/47.73  End of proof
% 241.22/47.73  
% 241.22/47.73  Sub-proof #495 shows that the following formulas are inconsistent:
% 241.22/47.73  ----------------------------------------------------------------
% 241.22/47.73    (1)  op(e1, e0) = e0
% 241.22/47.73    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.22/47.73             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 241.22/47.73           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.22/47.73             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 241.22/47.73           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 241.22/47.73           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.73           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.22/47.73    (3)  op(e0, e1) = e1
% 241.22/47.73    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.73    (5)   ~ (e1 = e0)
% 241.22/47.73    (6)  op(e2, e0) = e1
% 241.22/47.73    (7)  op(e2, e0) = all_52_13
% 241.22/47.73  
% 241.22/47.73  Begin of proof
% 241.22/47.73  | 
% 241.22/47.73  | BETA: splitting (2) gives:
% 241.22/47.73  | 
% 241.22/47.73  | Case 1:
% 241.22/47.73  | | 
% 241.22/47.73  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 241.22/47.73  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 241.22/47.73  | |        & op(e0, e2) = e0
% 241.22/47.73  | | 
% 241.22/47.73  | | ALPHA: (8) implies:
% 241.22/47.73  | |   (9)  op(e2, e0) = e0
% 241.22/47.73  | | 
% 241.22/47.73  | | REF_CLOSE: (4), (5), (6), (7), (9) are inconsistent by sub-proof #1778.
% 241.22/47.73  | | 
% 241.22/47.73  | Case 2:
% 241.22/47.73  | | 
% 241.22/47.73  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.73  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.22/47.73  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 241.22/47.73  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.22/47.73  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.22/47.73  | | 
% 241.22/47.73  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #496.
% 241.22/47.73  | | 
% 241.22/47.73  | End of split
% 241.22/47.73  | 
% 241.22/47.73  End of proof
% 241.22/47.73  
% 241.22/47.73  Sub-proof #496 shows that the following formulas are inconsistent:
% 241.22/47.73  ----------------------------------------------------------------
% 241.22/47.73    (1)  op(e1, e0) = e0
% 241.22/47.73    (2)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 241.22/47.73             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 241.22/47.73           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 241.22/47.73             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 241.22/47.73           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.22/47.73    (3)  op(e0, e1) = e1
% 241.22/47.73    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.73    (5)   ~ (e1 = e0)
% 241.22/47.73  
% 241.22/47.73  Begin of proof
% 241.22/47.73  | 
% 241.22/47.73  | BETA: splitting (2) gives:
% 241.22/47.73  | 
% 241.22/47.73  | Case 1:
% 241.22/47.73  | | 
% 241.22/47.73  | |   (6)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 241.22/47.73  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 241.22/47.73  | |        & op(e0, e1) = e1
% 241.22/47.73  | | 
% 241.22/47.73  | | ALPHA: (6) implies:
% 241.22/47.73  | |   (7)  op(e1, e0) = e1
% 241.22/47.73  | | 
% 241.22/47.73  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #2284.
% 241.22/47.73  | | 
% 241.22/47.73  | Case 2:
% 241.22/47.73  | | 
% 241.22/47.73  | |   (8)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 241.22/47.73  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 241.22/47.73  | |        & op(e0, e1) = e0
% 241.22/47.73  | | 
% 241.22/47.73  | | ALPHA: (8) implies:
% 241.22/47.73  | |   (9)  op(e0, e1) = e0
% 241.22/47.73  | | 
% 241.22/47.73  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #2158.
% 241.22/47.73  | | 
% 241.22/47.73  | End of split
% 241.22/47.73  | 
% 241.22/47.73  End of proof
% 241.22/47.73  
% 241.22/47.73  Sub-proof #497 shows that the following formulas are inconsistent:
% 241.22/47.73  ----------------------------------------------------------------
% 241.22/47.73    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.22/47.73         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.22/47.73    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.22/47.73         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.22/47.73    (3)   ~ (e3 = e0)
% 241.22/47.73    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.22/47.73         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.22/47.73    (5)  all_42_2 = e3
% 241.22/47.73    (6)  all_58_6 = e3
% 241.22/47.73    (7)   ~ (e2 = e0)
% 241.22/47.73    (8)  op(e1, e2) = all_52_6
% 241.22/47.73    (9)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.73         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.22/47.73    (10)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.22/47.73          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.22/47.73    (11)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.22/47.73              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.22/47.73            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.22/47.73            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.22/47.73            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.22/47.73             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.73            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.22/47.73            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.22/47.73            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.22/47.73            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.73            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.22/47.73              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.22/47.73            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.22/47.73            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.22/47.73            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.22/47.73            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.22/47.73            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.22/47.73            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.22/47.73              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.22/47.73            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.22/47.73            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.22/47.73            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.22/47.73            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.22/47.73            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.73            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.22/47.73              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.22/47.73            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.73            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.22/47.73    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.73          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.22/47.73    (13)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.22/47.73            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.22/47.73              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.22/47.73    (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.22/47.73          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.22/47.73    (15)   ~ (all_52_7 = e3)
% 241.22/47.73    (16)  all_58_15 = e3
% 241.22/47.73    (17)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.73          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.22/47.73    (18)   ~ (e3 = e1)
% 241.22/47.73    (19)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.22/47.73          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.22/47.73    (20)  all_58_3 = e3
% 241.22/47.73    (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.22/47.73          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.22/47.73    (22)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.22/47.73          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.22/47.73    (23)  op(e3, e3) = e1
% 241.22/47.73    (24)  all_56_21 = e0
% 241.22/47.73    (25)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.73              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.22/47.73                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.22/47.73                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.22/47.73    (26)  op(e2, e1) = all_52_9
% 241.22/47.73    (27)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.22/47.73          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.22/47.73    (28)   ~ (e3 = e2)
% 241.22/47.73    (29)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.22/47.73          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.22/47.73    (30)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.22/47.73          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.22/47.73    (31)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.22/47.73          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.22/47.73    (32)  op(e2, e3) = all_52_1
% 241.22/47.73    (33)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.22/47.73          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.73    (34)   ~ (all_52_6 = e3)
% 241.22/47.73    (35)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.22/47.73          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.22/47.73    (36)  op(e0, e2) = all_52_7
% 241.22/47.73    (37)   ~ (all_52_4 = e3)
% 241.22/47.73    (38)  op(e3, e2) = all_52_4
% 241.22/47.73    (39)   ~ (all_52_9 = e3)
% 241.22/47.73    (40)  all_56_31 = e3
% 241.22/47.73    (41)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.22/47.73          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.22/47.73    (42)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.22/47.73          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.22/47.73    (43)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.73          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.22/47.73    (44)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.73    (45)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.22/47.73          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.22/47.73    (46)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.22/47.73          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.22/47.73    (47)  op(e1, e1) = e0
% 241.22/47.73    (48)   ~ (all_52_4 = e1)
% 241.22/47.73    (49)   ~ (e1 = e0)
% 241.22/47.73    (50)  all_58_4 = e3
% 241.22/47.73    (51)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.22/47.73          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.22/47.73    (52)  op(e2, e0) = all_52_13
% 241.22/47.73    (53)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.22/47.73          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.22/47.73            e1)
% 241.22/47.73    (54)   ~ (all_52_1 = e3)
% 241.22/47.73    (55)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.22/47.73          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.22/47.73            e2)
% 241.22/47.73    (56)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.22/47.73            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 241.22/47.73            & $i(all_8_1))
% 241.22/47.73    (57)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.22/47.73          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.22/47.73    (58)  all_56_1 = e1
% 241.22/47.73    (59)   ~ (e2 = e1)
% 241.22/47.73    (60)   ~ (all_52_1 = e1)
% 241.22/47.73  
% 241.22/47.73  Begin of proof
% 241.22/47.73  | 
% 241.22/47.73  | BETA: splitting (51) gives:
% 241.22/47.73  | 
% 241.22/47.73  | Case 1:
% 241.22/47.73  | | 
% 241.22/47.73  | |   (61)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 241.22/47.73  | |           e0)
% 241.22/47.73  | | 
% 241.22/47.73  | | BETA: splitting (61) gives:
% 241.22/47.73  | | 
% 241.22/47.73  | | Case 1:
% 241.22/47.73  | | | 
% 241.22/47.73  | | |   (62)  all_58_6 = e0 & op(e1, e3) = e0
% 241.22/47.73  | | | 
% 241.22/47.73  | | | ALPHA: (62) implies:
% 241.22/47.73  | | |   (63)  all_58_6 = e0
% 241.22/47.73  | | | 
% 241.22/47.73  | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (12), (14), (17), (18),
% 241.22/47.73  | | |            (19), (20), (21), (22), (23), (25), (26), (27), (28), (29),
% 241.22/47.73  | | |            (30), (31), (32), (33), (34), (35), (37), (38), (39), (41),
% 241.22/47.73  | | |            (42), (43), (44), (45), (47), (49), (51), (52), (53), (54),
% 241.22/47.73  | | |            (55), (57), (59), (60), (63) are inconsistent by sub-proof
% 241.22/47.73  | | |            #664.
% 241.22/47.73  | | | 
% 241.22/47.73  | | Case 2:
% 241.22/47.74  | | | 
% 241.22/47.74  | | |   (64)  all_58_7 = e0 & op(e1, e2) = e0
% 241.22/47.74  | | | 
% 241.22/47.74  | | | ALPHA: (64) implies:
% 241.22/47.74  | | |   (65)  all_58_7 = e0
% 241.22/47.74  | | |   (66)  op(e1, e2) = e0
% 241.22/47.74  | | | 
% 241.22/47.74  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (14), (15),
% 241.22/47.74  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 241.22/47.74  | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 241.22/47.74  | | |            (37), (38), (39), (41), (42), (43), (44), (45), (46), (47),
% 241.22/47.74  | | |            (48), (49), (50), (51), (52), (53), (54), (55), (57), (59),
% 241.22/47.74  | | |            (60), (65), (66) are inconsistent by sub-proof #507.
% 241.22/47.74  | | | 
% 241.22/47.74  | | End of split
% 241.22/47.74  | | 
% 241.22/47.74  | Case 2:
% 241.22/47.74  | | 
% 241.22/47.74  | |   (67)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 241.22/47.74  | |           e0)
% 241.22/47.74  | | 
% 241.22/47.74  | | BETA: splitting (67) gives:
% 241.22/47.74  | | 
% 241.22/47.74  | | Case 1:
% 241.22/47.74  | | | 
% 241.22/47.74  | | |   (68)  all_58_8 = e0 & op(e1, e1) = e0
% 241.22/47.74  | | | 
% 241.22/47.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.22/47.74  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.22/47.74  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 241.22/47.74  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 241.22/47.74  | | |            (43), (44), (45), (46), (48), (49), (50), (51), (52), (53),
% 241.22/47.74  | | |            (54), (55), (56), (57), (58), (59), (60), (68) are inconsistent
% 241.22/47.74  | | |            by sub-proof #499.
% 241.22/47.74  | | | 
% 241.22/47.74  | | Case 2:
% 241.22/47.74  | | | 
% 241.22/47.74  | | |   (69)  all_58_11 = e0 & op(e1, e0) = e0
% 241.22/47.74  | | | 
% 241.22/47.74  | | | ALPHA: (69) implies:
% 241.22/47.74  | | |   (70)  all_58_11 = e0
% 241.22/47.74  | | |   (71)  op(e1, e0) = e0
% 241.22/47.74  | | | 
% 241.22/47.74  | | | BETA: splitting (10) gives:
% 241.22/47.74  | | | 
% 241.22/47.74  | | | Case 1:
% 241.22/47.74  | | | | 
% 241.22/47.74  | | | |   (72)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 241.22/47.74  | | | |           = e1)
% 241.22/47.74  | | | | 
% 241.22/47.74  | | | | BETA: splitting (72) gives:
% 241.22/47.74  | | | | 
% 241.22/47.74  | | | | Case 1:
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | |   (73)  all_58_9 = e1 & op(e3, e0) = e1
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | | ALPHA: (73) implies:
% 241.22/47.74  | | | | |   (74)  all_58_9 = e1
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12), (14), (17),
% 241.22/47.74  | | | | |            (18), (19), (20), (21), (22), (23), (25), (26), (27), (28),
% 241.22/47.74  | | | | |            (29), (30), (31), (32), (33), (34), (35), (37), (38), (39),
% 241.22/47.74  | | | | |            (41), (42), (43), (44), (45), (47), (49), (51), (52), (53),
% 241.22/47.74  | | | | |            (54), (55), (57), (59), (60), (74) are inconsistent by
% 241.22/47.74  | | | | |            sub-proof #640.
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | Case 2:
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | |   (75)  all_58_10 = e1 & op(e2, e0) = e1
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | | ALPHA: (75) implies:
% 241.22/47.74  | | | | |   (76)  all_58_10 = e1
% 241.22/47.74  | | | | |   (77)  op(e2, e0) = e1
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | | BETA: splitting (43) gives:
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | | Case 1:
% 241.22/47.74  | | | | | | 
% 241.22/47.74  | | | | | |   (78)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2,
% 241.22/47.74  | | | | | |             e2) = e0)
% 241.22/47.74  | | | | | | 
% 241.22/47.74  | | | | | | BETA: splitting (78) gives:
% 241.22/47.74  | | | | | | 
% 241.22/47.74  | | | | | | Case 1:
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | |   (79)  all_58_2 = e0 & op(e2, e3) = e0
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | | ALPHA: (79) implies:
% 241.22/47.74  | | | | | | |   (80)  all_58_2 = e0
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | | BETA: splitting (19) gives:
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | | Case 1:
% 241.22/47.74  | | | | | | | | 
% 241.22/47.74  | | | | | | | |   (81)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 241.22/47.74  | | | | | | | |           op(e2, e1) = e0)
% 241.22/47.74  | | | | | | | | 
% 241.22/47.74  | | | | | | | | BETA: splitting (81) gives:
% 241.22/47.74  | | | | | | | | 
% 241.22/47.74  | | | | | | | | Case 1:
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | |   (82)  all_58_4 = e0 & op(e3, e1) = e0
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | ALPHA: (82) implies:
% 241.22/47.74  | | | | | | | | |   (83)  all_58_4 = e0
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12),
% 241.22/47.74  | | | | | | | | |            (14), (17), (18), (19), (20), (21), (22), (23),
% 241.22/47.74  | | | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32),
% 241.22/47.74  | | | | | | | | |            (33), (34), (35), (37), (38), (39), (41), (42),
% 241.22/47.74  | | | | | | | | |            (43), (44), (45), (47), (49), (50), (51), (52),
% 241.22/47.74  | | | | | | | | |            (53), (54), (55), (57), (59), (60), (83) are
% 241.22/47.74  | | | | | | | | |            inconsistent by sub-proof #583.
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | Case 2:
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | |   (84)  all_58_5 = e0 & op(e2, e1) = e0
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | ALPHA: (84) implies:
% 241.22/47.74  | | | | | | | | |   (85)  all_58_5 = e0
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12),
% 241.22/47.74  | | | | | | | | |            (14), (16), (17), (18), (19), (20), (21), (22),
% 241.22/47.74  | | | | | | | | |            (23), (25), (26), (27), (28), (29), (30), (31),
% 241.22/47.74  | | | | | | | | |            (32), (33), (34), (35), (37), (38), (39), (41),
% 241.22/47.74  | | | | | | | | |            (42), (43), (44), (45), (47), (49), (50), (51),
% 241.22/47.74  | | | | | | | | |            (52), (53), (54), (55), (57), (59), (60), (70),
% 241.22/47.74  | | | | | | | | |            (71), (76), (85) are inconsistent by sub-proof
% 241.22/47.74  | | | | | | | | |            #498.
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | End of split
% 241.22/47.74  | | | | | | | | 
% 241.22/47.74  | | | | | | | Case 2:
% 241.22/47.74  | | | | | | | | 
% 241.22/47.74  | | | | | | | |   (86)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 241.22/47.74  | | | | | | | |           op(e0, e1) = e0)
% 241.22/47.74  | | | | | | | | 
% 241.22/47.74  | | | | | | | | BETA: splitting (86) gives:
% 241.22/47.74  | | | | | | | | 
% 241.22/47.74  | | | | | | | | Case 1:
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | |   (87)  all_58_8 = e0 & op(e1, e1) = e0
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 241.22/47.74  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 241.22/47.74  | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 241.22/47.74  | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 241.22/47.74  | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 241.22/47.74  | | | | | | | | |            (43), (44), (45), (46), (48), (49), (50), (51),
% 241.22/47.74  | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 241.22/47.74  | | | | | | | | |            (60), (87) are inconsistent by sub-proof #499.
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | Case 2:
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | |   (88)  all_58_14 = e0 & op(e0, e1) = e0
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | ALPHA: (88) implies:
% 241.22/47.74  | | | | | | | | |   (89)  all_58_14 = e0
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | BETA: splitting (53) gives:
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | Case 1:
% 241.22/47.74  | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | |   (90)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1
% 241.22/47.74  | | | | | | | | | |           & op(e0, e2) = e1)
% 241.22/47.74  | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | BETA: splitting (90) gives:
% 241.22/47.74  | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | Case 1:
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | |   (91)  all_58_12 = e1 & op(e0, e3) = e1
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | | ALPHA: (91) implies:
% 241.22/47.74  | | | | | | | | | | |   (92)  all_58_12 = e1
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | | REF_CLOSE: (6), (7), (23), (27), (28), (44), (59), (80), (92)
% 241.22/47.74  | | | | | | | | | | |            are inconsistent by sub-proof #1328.
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | Case 2:
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | |   (93)  all_58_13 = e1 & op(e0, e2) = e1
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | | ALPHA: (93) implies:
% 241.22/47.74  | | | | | | | | | | |   (94)  all_58_13 = e1
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (9), (12), (18), (20), (22), (23),
% 241.22/47.74  | | | | | | | | | | |            (27), (28), (30), (32), (44), (47), (49), (54),
% 241.22/47.74  | | | | | | | | | | |            (59), (71), (94) are inconsistent by sub-proof
% 241.22/47.74  | | | | | | | | | | |            #500.
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | End of split
% 241.22/47.74  | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | Case 2:
% 241.22/47.74  | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | |   (95)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1
% 241.22/47.74  | | | | | | | | | |           & op(e0, e0) = e1)
% 241.22/47.74  | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | BETA: splitting (95) gives:
% 241.22/47.74  | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | Case 1:
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | |   (96)  all_58_14 = e1 & op(e0, e1) = e1
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | | REF_CLOSE: (49), (89), (96) are inconsistent by sub-proof
% 241.22/47.74  | | | | | | | | | | |            #828.
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | Case 2:
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | |   (97)  all_58_15 = e1 & op(e0, e0) = e1
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | | ALPHA: (97) implies:
% 241.22/47.74  | | | | | | | | | | |   (98)  all_58_15 = e1
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | | REF_CLOSE: (3), (7), (18), (28), (41), (44), (45), (59),
% 241.22/47.74  | | | | | | | | | | |            (70), (76), (98) are inconsistent by sub-proof
% 241.22/47.74  | | | | | | | | | | |            #1597.
% 241.22/47.74  | | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | | End of split
% 241.22/47.74  | | | | | | | | | | 
% 241.22/47.74  | | | | | | | | | End of split
% 241.22/47.74  | | | | | | | | | 
% 241.22/47.74  | | | | | | | | End of split
% 241.22/47.74  | | | | | | | | 
% 241.22/47.74  | | | | | | | End of split
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | Case 2:
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | |   (99)  all_58_3 = e0 & op(e2, e2) = e0
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12), (14),
% 241.22/47.74  | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 241.22/47.74  | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 241.22/47.74  | | | | | | |            (37), (38), (39), (41), (42), (43), (44), (45), (47),
% 241.22/47.74  | | | | | | |            (49), (51), (52), (53), (54), (55), (57), (59), (60),
% 241.22/47.74  | | | | | | |            (99) are inconsistent by sub-proof #578.
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | End of split
% 241.22/47.74  | | | | | | 
% 241.22/47.74  | | | | | Case 2:
% 241.22/47.74  | | | | | | 
% 241.22/47.74  | | | | | |   (100)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 241.22/47.74  | | | | | |            op(e2, e0) = e0)
% 241.22/47.74  | | | | | | 
% 241.22/47.74  | | | | | | BETA: splitting (100) gives:
% 241.22/47.74  | | | | | | 
% 241.22/47.74  | | | | | | Case 1:
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | |   (101)  all_58_5 = e0 & op(e2, e1) = e0
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | | ALPHA: (101) implies:
% 241.22/47.74  | | | | | | |   (102)  all_58_5 = e0
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12), (14),
% 241.22/47.74  | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 241.22/47.74  | | | | | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 241.22/47.74  | | | | | | |            (35), (37), (38), (39), (41), (42), (43), (44), (45),
% 241.22/47.74  | | | | | | |            (47), (49), (50), (51), (52), (53), (54), (55), (57),
% 241.22/47.74  | | | | | | |            (59), (60), (70), (71), (76), (102) are inconsistent by
% 241.22/47.74  | | | | | | |            sub-proof #498.
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | Case 2:
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | |   (103)  all_58_10 = e0 & op(e2, e0) = e0
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | | ALPHA: (103) implies:
% 241.22/47.74  | | | | | | |   (104)  op(e2, e0) = e0
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | | REF_CLOSE: (44), (49), (52), (77), (104) are inconsistent by
% 241.22/47.74  | | | | | | |            sub-proof #1778.
% 241.22/47.74  | | | | | | | 
% 241.22/47.74  | | | | | | End of split
% 241.22/47.74  | | | | | | 
% 241.22/47.74  | | | | | End of split
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | End of split
% 241.22/47.74  | | | | 
% 241.22/47.74  | | | Case 2:
% 241.22/47.74  | | | | 
% 241.22/47.74  | | | |   (105)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 241.22/47.74  | | | |              e0) = e1)
% 241.22/47.74  | | | | 
% 241.22/47.74  | | | | BETA: splitting (105) gives:
% 241.22/47.74  | | | | 
% 241.22/47.74  | | | | Case 1:
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | |   (106)  all_58_11 = e1 & op(e1, e0) = e1
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | | ALPHA: (106) implies:
% 241.22/47.74  | | | | |   (107)  op(e1, e0) = e1
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | | REF_CLOSE: (44), (49), (71), (107) are inconsistent by sub-proof
% 241.22/47.74  | | | | |            #2284.
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | Case 2:
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | |   (108)  all_58_15 = e1 & op(e0, e0) = e1
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | | REF_CLOSE: (1), (3), (7), (16), (18), (21), (23), (28), (33), (37),
% 241.22/47.74  | | | | |            (38), (44), (49), (50), (59), (108) are inconsistent by
% 241.22/47.74  | | | | |            sub-proof #513.
% 241.22/47.74  | | | | | 
% 241.22/47.74  | | | | End of split
% 241.22/47.74  | | | | 
% 241.22/47.74  | | | End of split
% 241.22/47.74  | | | 
% 241.22/47.74  | | End of split
% 241.22/47.74  | | 
% 241.22/47.74  | End of split
% 241.22/47.74  | 
% 241.22/47.74  End of proof
% 241.22/47.74  
% 241.22/47.74  Sub-proof #498 shows that the following formulas are inconsistent:
% 241.22/47.74  ----------------------------------------------------------------
% 241.22/47.74    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.22/47.74         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.22/47.74    (2)  all_58_5 = e0
% 241.22/47.74    (3)   ~ (e3 = e0)
% 241.22/47.74    (4)  op(e1, e0) = e0
% 241.22/47.74    (5)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.22/47.74         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.22/47.74    (6)  all_58_6 = e3
% 241.22/47.74    (7)   ~ (e2 = e0)
% 241.22/47.74    (8)  op(e1, e2) = all_52_6
% 241.22/47.74    (9)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.74         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.22/47.74    (10)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.22/47.74          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.22/47.74    (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.74          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.22/47.74    (12)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.22/47.74          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.22/47.74    (13)  all_58_15 = e3
% 241.22/47.74    (14)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.74          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.22/47.74    (15)   ~ (e3 = e1)
% 241.22/47.74    (16)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.22/47.74          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.22/47.74    (17)  all_58_3 = e3
% 241.22/47.74    (18)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.22/47.74          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.22/47.74    (19)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.22/47.74          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.22/47.74    (20)  op(e3, e3) = e1
% 241.22/47.74    (21)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.74              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.22/47.74                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.22/47.74                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.22/47.74    (22)  op(e2, e1) = all_52_9
% 241.22/47.74    (23)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.22/47.74          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.22/47.74    (24)   ~ (e3 = e2)
% 241.22/47.74    (25)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.22/47.74          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.22/47.74    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.22/47.74          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.22/47.74    (27)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.22/47.74          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.22/47.74    (28)  op(e2, e3) = all_52_1
% 241.22/47.74    (29)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.22/47.74          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.74    (30)   ~ (all_52_6 = e3)
% 241.22/47.74    (31)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.22/47.74          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.22/47.74    (32)   ~ (all_52_4 = e3)
% 241.22/47.74    (33)  op(e3, e2) = all_52_4
% 241.22/47.74    (34)   ~ (all_52_9 = e3)
% 241.22/47.74    (35)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.22/47.74          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.22/47.74    (36)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.22/47.74          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.22/47.74    (37)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.74          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.22/47.75    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.75    (39)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.22/47.75          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.22/47.75    (40)  op(e1, e1) = e0
% 241.22/47.75    (41)  all_58_11 = e0
% 241.22/47.75    (42)   ~ (e1 = e0)
% 241.22/47.75    (43)  all_58_4 = e3
% 241.22/47.75    (44)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.22/47.75          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.22/47.75    (45)  op(e2, e0) = all_52_13
% 241.22/47.75    (46)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.22/47.75          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.22/47.75            e1)
% 241.22/47.75    (47)   ~ (all_52_1 = e3)
% 241.22/47.75    (48)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.22/47.75          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.22/47.75            e2)
% 241.22/47.75    (49)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.22/47.75          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.22/47.75    (50)  all_58_10 = e1
% 241.22/47.75    (51)   ~ (e2 = e1)
% 241.22/47.75    (52)   ~ (all_52_1 = e1)
% 241.22/47.75  
% 241.22/47.75  Begin of proof
% 241.22/47.75  | 
% 241.22/47.75  | BETA: splitting (14) gives:
% 241.22/47.75  | 
% 241.22/47.75  | Case 1:
% 241.22/47.75  | | 
% 241.22/47.75  | |   (53)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 241.22/47.75  | |           e2)
% 241.22/47.75  | | 
% 241.22/47.75  | | BETA: splitting (53) gives:
% 241.22/47.75  | | 
% 241.22/47.75  | | Case 1:
% 241.22/47.75  | | | 
% 241.22/47.75  | | |   (54)  all_58_2 = e2 & op(e2, e3) = e2
% 241.22/47.75  | | | 
% 241.22/47.75  | | | ALPHA: (54) implies:
% 241.22/47.75  | | |   (55)  all_58_2 = e2
% 241.22/47.75  | | | 
% 241.22/47.75  | | | BETA: splitting (21) gives:
% 241.22/47.75  | | | 
% 241.22/47.75  | | | Case 1:
% 241.22/47.75  | | | | 
% 241.22/47.75  | | | |   (56)  all_58_15 = e0 & op(e0, e0) = e0
% 241.22/47.75  | | | | 
% 241.22/47.75  | | | | ALPHA: (56) implies:
% 241.22/47.75  | | | |   (57)  all_58_15 = e0
% 241.22/47.75  | | | | 
% 241.22/47.75  | | | | COMBINE_EQS: (13), (57) imply:
% 241.22/47.75  | | | |   (58)  e3 = e0
% 241.22/47.75  | | | | 
% 241.22/47.75  | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 241.22/47.75  | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 241.22/47.75  | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 241.22/47.75  | | | |            (35), (36), (37), (38), (39), (40), (42), (44), (45), (46),
% 241.22/47.75  | | | |            (47), (48), (49), (51), (52), (58) are inconsistent by
% 241.22/47.75  | | | |            sub-proof #642.
% 241.22/47.75  | | | | 
% 241.22/47.75  | | | Case 2:
% 241.22/47.75  | | | | 
% 241.22/47.75  | | | |   (59)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 241.22/47.75  | | | |               e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 241.22/47.75  | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 241.22/47.75  | | | |               e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.22/47.75  | | | | 
% 241.22/47.75  | | | | ALPHA: (59) implies:
% 241.22/47.75  | | | |   (60)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 241.22/47.75  | | | |             e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.22/47.75  | | | | 
% 241.22/47.75  | | | | BETA: splitting (26) gives:
% 241.22/47.75  | | | | 
% 241.22/47.75  | | | | Case 1:
% 241.22/47.75  | | | | | 
% 241.22/47.75  | | | | |   (61)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 241.22/47.75  | | | | |             e3) = e0)
% 241.22/47.75  | | | | | 
% 241.22/47.75  | | | | | REF_CLOSE: (7), (20), (38), (42), (55), (61) are inconsistent by
% 241.22/47.75  | | | | |            sub-proof #1534.
% 241.22/47.75  | | | | | 
% 241.22/47.75  | | | | Case 2:
% 241.22/47.75  | | | | | 
% 241.22/47.75  | | | | |   (62)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0,
% 241.22/47.75  | | | | |             e3) = e0)
% 241.22/47.75  | | | | | 
% 241.22/47.75  | | | | | BETA: splitting (62) gives:
% 241.22/47.75  | | | | | 
% 241.22/47.75  | | | | | Case 1:
% 241.22/47.75  | | | | | | 
% 241.22/47.75  | | | | | |   (63)  all_58_6 = e0 & op(e1, e3) = e0
% 241.22/47.75  | | | | | | 
% 241.22/47.75  | | | | | | ALPHA: (63) implies:
% 241.22/47.75  | | | | | |   (64)  all_58_6 = e0
% 241.22/47.75  | | | | | | 
% 241.22/47.75  | | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12), (14),
% 241.22/47.75  | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 241.22/47.75  | | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 241.22/47.75  | | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (42),
% 241.22/47.75  | | | | | |            (44), (45), (46), (47), (48), (49), (51), (52), (64) are
% 241.22/47.75  | | | | | |            inconsistent by sub-proof #664.
% 241.22/47.75  | | | | | | 
% 241.22/47.75  | | | | | Case 2:
% 241.22/47.75  | | | | | | 
% 241.22/47.75  | | | | | |   (65)  all_58_12 = e0 & op(e0, e3) = e0
% 241.22/47.75  | | | | | | 
% 241.22/47.75  | | | | | | ALPHA: (65) implies:
% 241.22/47.75  | | | | | |   (66)  all_58_12 = e0
% 241.22/47.75  | | | | | | 
% 241.22/47.75  | | | | | | BETA: splitting (5) gives:
% 241.22/47.75  | | | | | | 
% 241.22/47.75  | | | | | | Case 1:
% 241.22/47.75  | | | | | | | 
% 241.22/47.75  | | | | | | |   (67)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 241.22/47.75  | | | | | | |           op(e1, e2) = e1)
% 241.22/47.75  | | | | | | | 
% 241.22/47.75  | | | | | | | BETA: splitting (67) gives:
% 241.22/47.75  | | | | | | | 
% 241.22/47.75  | | | | | | | Case 1:
% 241.22/47.75  | | | | | | | | 
% 241.22/47.75  | | | | | | | |   (68)  all_58_6 = e1 & op(e1, e3) = e1
% 241.22/47.75  | | | | | | | | 
% 241.22/47.75  | | | | | | | | ALPHA: (68) implies:
% 241.22/47.75  | | | | | | | |   (69)  all_58_6 = e1
% 241.22/47.75  | | | | | | | | 
% 241.22/47.75  | | | | | | | | REF_CLOSE: (3), (7), (15), (19), (20), (23), (24), (26), (28),
% 241.22/47.75  | | | | | | | |            (38), (42), (47), (51), (69) are inconsistent by
% 241.22/47.75  | | | | | | | |            sub-proof #1161.
% 241.22/47.75  | | | | | | | | 
% 241.22/47.75  | | | | | | | Case 2:
% 241.22/47.75  | | | | | | | | 
% 241.22/47.75  | | | | | | | |   (70)  all_58_7 = e1 & op(e1, e2) = e1
% 241.22/47.75  | | | | | | | | 
% 241.22/47.75  | | | | | | | | ALPHA: (70) implies:
% 241.22/47.75  | | | | | | | |   (71)  all_58_7 = e1
% 241.22/47.75  | | | | | | | | 
% 241.22/47.75  | | | | | | | | BETA: splitting (36) gives:
% 241.22/47.75  | | | | | | | | 
% 241.22/47.75  | | | | | | | | Case 1:
% 241.22/47.75  | | | | | | | | | 
% 241.22/47.75  | | | | | | | | |   (72)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 241.22/47.75  | | | | | | | | |           op(e1, e2) = e2)
% 241.22/47.75  | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | BETA: splitting (72) gives:
% 241.22/47.75  | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | Case 1:
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | |   (73)  all_58_6 = e2 & op(e1, e3) = e2
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | ALPHA: (73) implies:
% 241.22/47.75  | | | | | | | | | |   (74)  all_58_6 = e2
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12),
% 241.22/47.75  | | | | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21),
% 241.22/47.75  | | | | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29),
% 241.22/47.75  | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 241.22/47.75  | | | | | | | | | |            (38), (39), (40), (41), (42), (44), (45), (46),
% 241.22/47.75  | | | | | | | | | |            (47), (48), (49), (51), (52), (74) are
% 241.22/47.75  | | | | | | | | | |            inconsistent by sub-proof #548.
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | Case 2:
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | |   (75)  all_58_7 = e2 & op(e1, e2) = e2
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | REF_CLOSE: (51), (71), (75) are inconsistent by sub-proof
% 241.22/47.75  | | | | | | | | | |            #2218.
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | End of split
% 241.22/47.75  | | | | | | | | | 
% 241.22/47.75  | | | | | | | | Case 2:
% 241.22/47.75  | | | | | | | | | 
% 241.22/47.75  | | | | | | | | |   (76)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 241.22/47.75  | | | | | | | | |           op(e1, e0) = e2)
% 241.22/47.75  | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | BETA: splitting (76) gives:
% 241.22/47.75  | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | Case 1:
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | |   (77)  all_58_8 = e2 & op(e1, e1) = e2
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | ALPHA: (77) implies:
% 241.22/47.75  | | | | | | | | | |   (78)  all_58_8 = e2
% 241.22/47.75  | | | | | | | | | |   (79)  op(e1, e1) = e2
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | BETA: splitting (12) gives:
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | Case 1:
% 241.22/47.75  | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | |   (80)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.22/47.75  | | | | | | | | | | |           & op(e2, e1) = e1)
% 241.22/47.75  | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | | REF_CLOSE: (1), (3), (7), (15), (17), (18), (20), (24), (29),
% 241.22/47.75  | | | | | | | | | | |            (32), (33), (37), (38), (42), (50), (51), (55),
% 241.22/47.75  | | | | | | | | | | |            (80) are inconsistent by sub-proof #672.
% 241.22/47.75  | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | Case 2:
% 241.22/47.75  | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | |   (81)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.22/47.75  | | | | | | | | | | |           e1 & op(e0, e1) = e1)
% 241.22/47.75  | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | | BETA: splitting (81) gives:
% 241.22/47.75  | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | | Case 1:
% 241.22/47.75  | | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | | |   (82)  all_58_8 = e1 & op(e1, e1) = e1
% 241.22/47.75  | | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | | | ALPHA: (82) implies:
% 241.22/47.75  | | | | | | | | | | | |   (83)  all_58_8 = e1
% 241.22/47.75  | | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | | | REF_CLOSE: (6), (7), (24), (36), (41), (51), (71), (83) are
% 241.22/47.75  | | | | | | | | | | | |            inconsistent by sub-proof #2215.
% 241.22/47.75  | | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | | Case 2:
% 241.22/47.75  | | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | | |   (84)  all_58_14 = e1 & op(e0, e1) = e1
% 241.22/47.75  | | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | | | ALPHA: (84) implies:
% 241.22/47.75  | | | | | | | | | | | |   (85)  all_58_14 = e1
% 241.22/47.75  | | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (12), (13), (14),
% 241.22/47.75  | | | | | | | | | | | |            (15), (17), (18), (19), (20), (22), (23), (24),
% 241.22/47.75  | | | | | | | | | | | |            (26), (27), (28), (29), (30), (31), (32), (33),
% 241.22/47.75  | | | | | | | | | | | |            (34), (36), (37), (38), (39), (40), (41), (42),
% 241.22/47.75  | | | | | | | | | | | |            (43), (47), (49), (50), (51), (52), (55), (60),
% 241.22/47.75  | | | | | | | | | | | |            (66), (70), (71), (78), (79), (85) are
% 241.22/47.75  | | | | | | | | | | | |            inconsistent by sub-proof #539.
% 241.22/47.75  | | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | | End of split
% 241.22/47.75  | | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | End of split
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | Case 2:
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | |   (86)  all_58_11 = e2 & op(e1, e0) = e2
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | ALPHA: (86) implies:
% 241.22/47.75  | | | | | | | | | |   (87)  all_58_11 = e2
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | COMBINE_EQS: (41), (87) imply:
% 241.22/47.75  | | | | | | | | | |   (88)  e2 = e0
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (20), (23), (24), (27), (30),
% 241.22/47.75  | | | | | | | | | |            (36), (38), (41), (51), (55), (66), (71), (88) are
% 241.22/47.75  | | | | | | | | | |            inconsistent by sub-proof #541.
% 241.22/47.75  | | | | | | | | | | 
% 241.22/47.75  | | | | | | | | | End of split
% 241.22/47.75  | | | | | | | | | 
% 241.22/47.75  | | | | | | | | End of split
% 241.22/47.75  | | | | | | | | 
% 241.22/47.75  | | | | | | | End of split
% 241.22/47.75  | | | | | | | 
% 241.22/47.75  | | | | | | Case 2:
% 241.22/47.75  | | | | | | | 
% 241.22/47.75  | | | | | | |   (89)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 241.22/47.75  | | | | | | |           op(e1, e0) = e1)
% 241.22/47.75  | | | | | | | 
% 241.22/47.75  | | | | | | | REF_CLOSE: (4), (38), (40), (42), (89) are inconsistent by
% 241.22/47.75  | | | | | | |            sub-proof #795.
% 241.22/47.75  | | | | | | | 
% 241.22/47.75  | | | | | | End of split
% 241.22/47.75  | | | | | | 
% 241.22/47.75  | | | | | End of split
% 241.22/47.75  | | | | | 
% 241.22/47.75  | | | | End of split
% 241.22/47.75  | | | | 
% 241.22/47.75  | | | End of split
% 241.22/47.75  | | | 
% 241.22/47.75  | | Case 2:
% 241.22/47.75  | | | 
% 241.22/47.75  | | |   (90)  all_58_3 = e2 & op(e2, e2) = e2
% 241.22/47.75  | | | 
% 241.22/47.75  | | | ALPHA: (90) implies:
% 241.22/47.75  | | |   (91)  all_58_3 = e2
% 241.22/47.75  | | | 
% 241.22/47.75  | | | COMBINE_EQS: (17), (91) imply:
% 241.22/47.75  | | |   (92)  e3 = e2
% 241.22/47.75  | | | 
% 241.22/47.75  | | | COMBINE_EQS: (6), (92) imply:
% 241.22/47.75  | | |   (93)  all_58_6 = e2
% 241.22/47.75  | | | 
% 241.22/47.75  | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12), (14), (15),
% 241.22/47.75  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 241.22/47.75  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 241.22/47.75  | | |            (36), (37), (38), (39), (40), (41), (42), (44), (45), (46),
% 241.22/47.75  | | |            (47), (48), (49), (51), (52), (93) are inconsistent by
% 241.22/47.75  | | |            sub-proof #548.
% 241.22/47.75  | | | 
% 241.22/47.75  | | End of split
% 241.22/47.75  | | 
% 241.22/47.75  | Case 2:
% 241.22/47.75  | | 
% 241.22/47.75  | |   (94)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 241.22/47.75  | |           e2)
% 241.22/47.75  | | 
% 241.22/47.75  | | REF_CLOSE: (2), (7), (50), (51), (94) are inconsistent by sub-proof #525.
% 241.22/47.75  | | 
% 241.22/47.75  | End of split
% 241.22/47.75  | 
% 241.22/47.75  End of proof
% 241.22/47.75  
% 241.22/47.75  Sub-proof #499 shows that the following formulas are inconsistent:
% 241.22/47.75  ----------------------------------------------------------------
% 241.22/47.75    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.22/47.75         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.22/47.75    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.22/47.75         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.22/47.75    (3)   ~ (e3 = e0)
% 241.22/47.75    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.22/47.75         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.22/47.75    (5)  all_42_2 = e3
% 241.22/47.75    (6)  all_58_6 = e3
% 241.22/47.75    (7)   ~ (e2 = e0)
% 241.22/47.75    (8)  op(e1, e2) = all_52_6
% 241.22/47.75    (9)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.75         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.22/47.75    (10)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.22/47.75          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.22/47.75    (11)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.22/47.75              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.22/47.75            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.22/47.75            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.22/47.75            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.22/47.75             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.75            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.22/47.75            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.22/47.75            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.22/47.75            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.75            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.22/47.75              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.22/47.75            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.22/47.75            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.22/47.75            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.22/47.75            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.22/47.75            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.22/47.75            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.22/47.75              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.22/47.75            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.22/47.75            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.22/47.75            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.22/47.75            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.22/47.75            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.75            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.22/47.75              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.22/47.75            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.75            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.22/47.75    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.75          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.22/47.75    (13)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.22/47.75            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.22/47.75              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.22/47.75    (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.22/47.75          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.22/47.75    (15)   ~ (all_52_7 = e3)
% 241.22/47.75    (16)  all_58_15 = e3
% 241.22/47.75    (17)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.75          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.22/47.75    (18)   ~ (e3 = e1)
% 241.22/47.75    (19)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.22/47.75          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.22/47.75    (20)  all_58_3 = e3
% 241.22/47.75    (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.22/47.75          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.22/47.76    (22)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.22/47.76          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.22/47.76    (23)  op(e3, e3) = e1
% 241.22/47.76    (24)  all_56_21 = e0
% 241.22/47.76    (25)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.76              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.22/47.76                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.22/47.76                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.22/47.76    (26)  op(e2, e1) = all_52_9
% 241.22/47.76    (27)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.22/47.76          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.22/47.76    (28)   ~ (e3 = e2)
% 241.22/47.76    (29)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.22/47.76          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.22/47.76    (30)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.22/47.76          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.22/47.76    (31)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.22/47.76          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.22/47.76    (32)  op(e2, e3) = all_52_1
% 241.22/47.76    (33)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.22/47.76          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.76    (34)   ~ (all_52_6 = e3)
% 241.22/47.76    (35)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.22/47.76          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.22/47.76    (36)  op(e0, e2) = all_52_7
% 241.22/47.76    (37)   ~ (all_52_4 = e3)
% 241.22/47.76    (38)  op(e3, e2) = all_52_4
% 241.22/47.76    (39)   ~ (all_52_9 = e3)
% 241.22/47.76    (40)  all_56_31 = e3
% 241.22/47.76    (41)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.22/47.76          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.22/47.76    (42)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.22/47.76          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.22/47.76    (43)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.76          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.22/47.76    (44)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.76            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.76    (45)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.22/47.76          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.22/47.76    (46)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.22/47.76          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.22/47.76    (47)   ~ (all_52_4 = e1)
% 241.22/47.76    (48)   ~ (e1 = e0)
% 241.22/47.76    (49)  all_58_8 = e0 & op(e1, e1) = e0
% 241.22/47.76    (50)  all_58_4 = e3
% 241.22/47.76    (51)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.22/47.76          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.22/47.76    (52)  op(e2, e0) = all_52_13
% 241.22/47.76    (53)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.22/47.76          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.22/47.76            e1)
% 241.22/47.76    (54)   ~ (all_52_1 = e3)
% 241.22/47.76    (55)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.22/47.76          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.22/47.76            e2)
% 241.22/47.76    (56)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.22/47.76            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 241.22/47.76            & $i(all_8_1))
% 241.22/47.76    (57)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.22/47.76          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.22/47.76    (58)  all_56_1 = e1
% 241.22/47.76    (59)   ~ (e2 = e1)
% 241.22/47.76    (60)   ~ (all_52_1 = e1)
% 241.22/47.76  
% 241.22/47.76  Begin of proof
% 241.22/47.76  | 
% 241.22/47.76  | ALPHA: (49) implies:
% 241.22/47.76  |   (61)  all_58_8 = e0
% 241.22/47.76  |   (62)  op(e1, e1) = e0
% 241.22/47.76  | 
% 241.22/47.76  | BETA: splitting (13) gives:
% 241.22/47.76  | 
% 241.22/47.76  | Case 1:
% 241.22/47.76  | | 
% 241.22/47.76  | |   (63)   ~ (all_42_2 = e3)
% 241.22/47.76  | | 
% 241.22/47.76  | | REDUCE: (5), (63) imply:
% 241.22/47.76  | |   (64)  $false
% 241.22/47.76  | | 
% 241.22/47.76  | | CLOSE: (64) is inconsistent.
% 241.22/47.76  | | 
% 241.22/47.76  | Case 2:
% 241.22/47.76  | | 
% 241.22/47.76  | |   (65)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 241.22/47.76  | |           all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) &
% 241.22/47.76  | |           op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.22/47.76  | | 
% 241.22/47.76  | | BETA: splitting (46) gives:
% 241.22/47.76  | | 
% 241.22/47.76  | | Case 1:
% 241.22/47.76  | | | 
% 241.22/47.76  | | |   (66)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 241.22/47.76  | | |           e1)
% 241.22/47.76  | | | 
% 241.22/47.76  | | | REF_CLOSE: (1), (3), (7), (18), (20), (21), (23), (28), (33), (37), (38),
% 241.22/47.76  | | |            (44), (47), (48), (50), (59), (66) are inconsistent by
% 241.22/47.76  | | |            sub-proof #528.
% 241.22/47.76  | | | 
% 241.22/47.76  | | Case 2:
% 241.22/47.76  | | | 
% 241.22/47.76  | | |   (67)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 241.22/47.76  | | |           e1)
% 241.22/47.76  | | | 
% 241.22/47.76  | | | BETA: splitting (67) gives:
% 241.22/47.76  | | | 
% 241.22/47.76  | | | Case 1:
% 241.22/47.76  | | | | 
% 241.22/47.76  | | | |   (68)  all_58_7 = e1 & op(e1, e2) = e1
% 241.22/47.76  | | | | 
% 241.22/47.76  | | | | ALPHA: (68) implies:
% 241.22/47.76  | | | |   (69)  all_58_7 = e1
% 241.22/47.76  | | | | 
% 241.22/47.76  | | | | BETA: splitting (42) gives:
% 241.22/47.76  | | | | 
% 241.22/47.76  | | | | Case 1:
% 241.22/47.76  | | | | | 
% 241.22/47.76  | | | | |   (70)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 241.22/47.76  | | | | |             e2) = e2)
% 241.22/47.76  | | | | | 
% 241.22/47.76  | | | | | REF_CLOSE: (6), (28), (59), (69), (70) are inconsistent by sub-proof
% 241.22/47.76  | | | | |            #547.
% 241.22/47.76  | | | | | 
% 241.22/47.76  | | | | Case 2:
% 241.22/47.76  | | | | | 
% 241.22/47.76  | | | | |   (71)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 241.22/47.76  | | | | |             e0) = e2)
% 241.22/47.76  | | | | | 
% 241.22/47.76  | | | | | BETA: splitting (71) gives:
% 241.22/47.76  | | | | | 
% 241.22/47.76  | | | | | Case 1:
% 241.22/47.76  | | | | | | 
% 241.22/47.76  | | | | | |   (72)  all_58_8 = e2 & op(e1, e1) = e2
% 241.22/47.76  | | | | | | 
% 241.22/47.76  | | | | | | REF_CLOSE: (7), (61), (72) are inconsistent by sub-proof #683.
% 241.22/47.76  | | | | | | 
% 241.22/47.76  | | | | | Case 2:
% 241.22/47.76  | | | | | | 
% 241.22/47.76  | | | | | |   (73)  all_58_11 = e2 & op(e1, e0) = e2
% 241.22/47.76  | | | | | | 
% 241.22/47.76  | | | | | | ALPHA: (73) implies:
% 241.22/47.76  | | | | | |   (74)  all_58_11 = e2
% 241.22/47.76  | | | | | | 
% 241.22/47.76  | | | | | | BETA: splitting (10) gives:
% 241.22/47.76  | | | | | | 
% 241.22/47.76  | | | | | | Case 1:
% 241.22/47.76  | | | | | | | 
% 241.22/47.76  | | | | | | |   (75)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 &
% 241.22/47.76  | | | | | | |           op(e2, e0) = e1)
% 241.22/47.76  | | | | | | | 
% 241.22/47.76  | | | | | | | BETA: splitting (75) gives:
% 241.22/47.76  | | | | | | | 
% 241.22/47.76  | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | 
% 241.22/47.76  | | | | | | | |   (76)  all_58_9 = e1 & op(e3, e0) = e1
% 241.22/47.76  | | | | | | | | 
% 241.22/47.76  | | | | | | | | ALPHA: (76) implies:
% 241.22/47.76  | | | | | | | |   (77)  all_58_9 = e1
% 241.22/47.76  | | | | | | | | 
% 241.22/47.76  | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12), (14),
% 241.22/47.76  | | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 241.22/47.76  | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 241.22/47.76  | | | | | | | |            (37), (38), (39), (41), (42), (43), (44), (45), (48),
% 241.22/47.76  | | | | | | | |            (51), (52), (53), (54), (55), (57), (59), (60), (62),
% 241.22/47.76  | | | | | | | |            (77) are inconsistent by sub-proof #640.
% 241.22/47.76  | | | | | | | | 
% 241.22/47.76  | | | | | | | Case 2:
% 241.22/47.76  | | | | | | | | 
% 241.22/47.76  | | | | | | | |   (78)  all_58_10 = e1 & op(e2, e0) = e1
% 241.22/47.76  | | | | | | | | 
% 241.22/47.76  | | | | | | | | ALPHA: (78) implies:
% 241.22/47.76  | | | | | | | |   (79)  all_58_10 = e1
% 241.22/47.76  | | | | | | | |   (80)  op(e2, e0) = e1
% 241.22/47.76  | | | | | | | | 
% 241.22/47.76  | | | | | | | | BETA: splitting (43) gives:
% 241.22/47.76  | | | | | | | | 
% 241.22/47.76  | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | 
% 241.22/47.76  | | | | | | | | |   (81)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 241.22/47.76  | | | | | | | | |           op(e2, e2) = e0)
% 241.22/47.76  | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | BETA: splitting (81) gives:
% 241.22/47.76  | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | |   (82)  all_58_2 = e0 & op(e2, e3) = e0
% 241.22/47.76  | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | ALPHA: (82) implies:
% 241.22/47.76  | | | | | | | | | |   (83)  all_58_2 = e0
% 241.22/47.76  | | | | | | | | | |   (84)  op(e2, e3) = e0
% 241.22/47.76  | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | BETA: splitting (27) gives:
% 241.22/47.76  | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | |   (85)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 241.22/47.76  | | | | | | | | | | |           & op(e2, e3) = e2)
% 241.22/47.76  | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | BETA: splitting (85) gives:
% 241.22/47.76  | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | |   (86)  all_58_0 = e2 & op(e3, e3) = e2
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | ALPHA: (86) implies:
% 241.22/47.76  | | | | | | | | | | | |   (87)  op(e3, e3) = e2
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | REF_CLOSE: (23), (44), (59), (87) are inconsistent by
% 241.22/47.76  | | | | | | | | | | | |            sub-proof #2267.
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | Case 2:
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | |   (88)  all_58_2 = e2 & op(e2, e3) = e2
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | ALPHA: (88) implies:
% 241.22/47.76  | | | | | | | | | | | |   (89)  op(e2, e3) = e2
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | REF_CLOSE: (7), (44), (56), (65), (84), (89) are inconsistent
% 241.22/47.76  | | | | | | | | | | | |            by sub-proof #733.
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | End of split
% 241.22/47.76  | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | Case 2:
% 241.22/47.76  | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | |   (90)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 241.22/47.76  | | | | | | | | | | |           e2 & op(e0, e3) = e2)
% 241.22/47.76  | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | BETA: splitting (90) gives:
% 241.22/47.76  | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | |   (91)  all_58_6 = e2 & op(e1, e3) = e2
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | REF_CLOSE: (6), (28), (91) are inconsistent by sub-proof
% 241.22/47.76  | | | | | | | | | | | |            #2219.
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | Case 2:
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | |   (92)  all_58_12 = e2 & op(e0, e3) = e2
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | ALPHA: (92) implies:
% 241.22/47.76  | | | | | | | | | | | |   (93)  all_58_12 = e2
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | BETA: splitting (17) gives:
% 241.22/47.76  | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | |   (94)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 241.22/47.76  | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 241.22/47.76  | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | REF_CLOSE: (7), (20), (28), (44), (56), (65), (84), (94) are
% 241.22/47.76  | | | | | | | | | | | | |            inconsistent by sub-proof #511.
% 241.22/47.76  | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | Case 2:
% 241.22/47.76  | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | |   (95)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 241.22/47.76  | | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 241.22/47.76  | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | BETA: splitting (95) gives:
% 241.22/47.76  | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | |   (96)  all_58_5 = e2 & op(e2, e1) = e2
% 241.22/47.76  | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | ALPHA: (96) implies:
% 241.22/47.76  | | | | | | | | | | | | | |   (97)  all_58_5 = e2
% 241.22/47.76  | | | | | | | | | | | | | |   (98)  op(e2, e1) = e2
% 241.22/47.76  | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 241.22/47.76  | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | |   (99)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.22/47.76  | | | | | | | | | | | | | | |           & op(e2, e1) = e1)
% 241.22/47.76  | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (7), (17), (18), (20), (21), (23), (28),
% 241.22/47.76  | | | | | | | | | | | | | | |            (33), (37), (38), (43), (44), (48), (59), (79),
% 241.22/47.76  | | | | | | | | | | | | | | |            (99) are inconsistent by sub-proof #647.
% 241.22/47.76  | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | Case 2:
% 241.22/47.76  | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | |   (100)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.22/47.76  | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 241.22/47.76  | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 241.22/47.76  | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | |   (101)  all_58_8 = e1 & op(e1, e1) = e1
% 241.22/47.76  | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 241.22/47.76  | | | | | | | | | | | | | | | |   (102)  op(e1, e1) = e1
% 241.22/47.76  | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | REF_CLOSE: (44), (48), (62), (102) are inconsistent by
% 241.22/47.76  | | | | | | | | | | | | | | | |            sub-proof #2220.
% 241.22/47.76  | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | Case 2:
% 241.22/47.76  | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | |   (103)  all_58_14 = e1 & op(e0, e1) = e1
% 241.22/47.76  | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 241.22/47.76  | | | | | | | | | | | | | | | |   (104)  all_58_14 = e1
% 241.22/47.76  | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 241.22/47.76  | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | |   (105)  all_58_15 = e0 & op(e0, e0) = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 241.22/47.76  | | | | | | | | | | | | | | | | |   (106)  all_58_15 = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (106) imply:
% 241.22/47.76  | | | | | | | | | | | | | | | | |   (107)  e3 = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (107) imply:
% 241.22/47.76  | | | | | | | | | | | | | | | | |   (108)  all_58_4 = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12),
% 241.22/47.76  | | | | | | | | | | | | | | | | |            (14), (17), (18), (19), (20), (21), (22), (23),
% 241.22/47.76  | | | | | | | | | | | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32),
% 241.22/47.76  | | | | | | | | | | | | | | | | |            (33), (34), (35), (37), (38), (39), (41), (42),
% 241.22/47.76  | | | | | | | | | | | | | | | | |            (43), (44), (45), (48), (51), (52), (53), (54),
% 241.22/47.76  | | | | | | | | | | | | | | | | |            (55), (57), (59), (60), (62), (104), (108) are
% 241.22/47.76  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #582.
% 241.22/47.76  | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.76  | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | |   (109)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.22/47.76  | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 241.22/47.76  | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 241.22/47.76  | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 241.22/47.76  | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.22/47.76  | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 241.22/47.76  | | | | | | | | | | | | | | | | |   (110)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 241.22/47.76  | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 241.22/47.76  | | | | | | | | | | | | | | | | |              e1) = e0)
% 241.22/47.76  | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 241.22/47.76  | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | |   (111)  all_58_12 = e0 & op(e0, e3) = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 241.22/47.76  | | | | | | | | | | | | | | | | | |   (112)  all_58_12 = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (18), (22), (23), (27), (28), (32),
% 241.22/47.76  | | | | | | | | | | | | | | | | | |            (44), (54), (59), (83), (112) are inconsistent by
% 241.22/47.76  | | | | | | | | | | | | | | | | | |            sub-proof #1149.
% 241.22/47.76  | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.76  | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | |   (113)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 241.22/47.76  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 241.22/47.76  | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 241.22/47.76  | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | |   (114)  all_58_13 = e0 & op(e0, e2) = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 241.22/47.76  | | | | | | | | | | | | | | | | | | |   (115)  op(e0, e2) = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | |   (116)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (7), (9), (20), (23), (27), (28),
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | |            (30), (44), (48), (50), (59), (69), (93), (115),
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | |            (116) are inconsistent by sub-proof #506.
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | |   (117)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | |   (118)  all_58_4 = e0 & op(e3, e1) = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | |   (119)  all_58_4 = e0
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12),
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | |            (14), (17), (18), (19), (20), (21), (22), (23),
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32),
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | |            (33), (34), (35), (37), (38), (39), (41), (42),
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | |            (43), (44), (45), (48), (51), (52), (53), (54),
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | |            (55), (57), (59), (60), (62), (104), (119) are
% 241.22/47.76  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #582.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | |   (120)  all_58_9 = e0 & op(e3, e0) = e0
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | |   (121)  all_58_9 = e0
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |   (122)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |   (123)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (32), (44), (54), (56), (58), (65), (84),
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            (123) are inconsistent by sub-proof #508.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |   (124)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |   (125)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |   (126)   ~ (all_56_31 = e3)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (126) imply:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |   (127)  $false
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |   (128)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (129)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (130)   ~ (all_56_21 = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (130) imply:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (131)  $false
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (131) is inconsistent.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (132)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e0
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (133)   ~ (all_56_31 = e3)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (133) imply:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (134)  $false
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |   (135)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |   (136)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |   (137)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |   (138)   ~ (all_56_1 = e1)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (138) imply:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |   (139)  $false
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (139) is inconsistent.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |   (140)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (141)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (142)   ~ (all_56_31 = e2)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (143)   ~ (all_56_21 = e2)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (144)   ~ (all_56_1 = e2)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (145)  op(e2, e1) = e1
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (144) imply:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (146)   ~ (e2 = e1)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (143) imply:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (147)   ~ (e2 = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (44) with e2, e1, e1, e2,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (98), (145) gives:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (148)  e2 = e1
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (148) imply:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (149)  all_58_5 = e1
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (18), (19), (21), (23), (28), (29),
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            (37), (38), (44), (48), (59), (104), (121), (149)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1044.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (150)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (151)  op(e0, e2) = e2
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (44), (115), (151) are inconsistent by
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |   (152)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |   (153)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |   (154)  op(e2, e0) = e0
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (48), (52), (80), (154) are inconsistent by
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1778.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |   (155)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (156)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e1
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (157)   ~ (all_56_21 = e0)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (157) imply:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (158)  $false
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (158) is inconsistent.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (159)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e0
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (160)   ~ (all_56_1 = e1)
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (160) imply:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (161)  $false
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | |   (162)  all_58_14 = e0 & op(e0, e1) = e0
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (104), (162) are inconsistent by sub-proof
% 241.22/47.77  | | | | | | | | | | | | | | | | | | |            #1483.
% 241.22/47.77  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | |   (163)  all_58_10 = e2 & op(e2, e0) = e2
% 241.22/47.77  | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | ALPHA: (163) implies:
% 241.22/47.77  | | | | | | | | | | | | | |   (164)  all_58_10 = e2
% 241.22/47.77  | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | COMBINE_EQS: (79), (164) imply:
% 241.22/47.77  | | | | | | | | | | | | | |   (165)  e2 = e1
% 241.22/47.77  | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | SIMP: (165) implies:
% 241.22/47.77  | | | | | | | | | | | | | |   (166)  e2 = e1
% 241.22/47.77  | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | COMBINE_EQS: (93), (166) imply:
% 241.22/47.77  | | | | | | | | | | | | | |   (167)  all_58_12 = e1
% 241.22/47.77  | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (23), (27), (28), (44), (59), (83),
% 241.22/47.77  | | | | | | | | | | | | | |            (167) are inconsistent by sub-proof #1328.
% 241.22/47.77  | | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | |   (168)  all_58_3 = e0 & op(e2, e2) = e0
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12),
% 241.22/47.77  | | | | | | | | | |            (14), (17), (18), (19), (20), (21), (22), (23),
% 241.22/47.77  | | | | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32),
% 241.22/47.77  | | | | | | | | | |            (33), (34), (35), (37), (38), (39), (41), (42),
% 241.22/47.77  | | | | | | | | | |            (43), (44), (45), (48), (51), (52), (53), (54),
% 241.22/47.77  | | | | | | | | | |            (55), (57), (59), (60), (62), (168) are
% 241.22/47.77  | | | | | | | | | |            inconsistent by sub-proof #578.
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | 
% 241.22/47.77  | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | 
% 241.22/47.77  | | | | | | | | |   (169)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 241.22/47.77  | | | | | | | | |            op(e2, e0) = e0)
% 241.22/47.77  | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | BETA: splitting (169) gives:
% 241.22/47.77  | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | Case 1:
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | |   (170)  all_58_5 = e0 & op(e2, e1) = e0
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | ALPHA: (170) implies:
% 241.22/47.77  | | | | | | | | | |   (171)  all_58_5 = e0
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | REF_CLOSE: (1), (3), (6), (7), (14), (17), (18), (20), (21),
% 241.22/47.77  | | | | | | | | | |            (22), (23), (26), (27), (28), (29), (30), (32),
% 241.22/47.77  | | | | | | | | | |            (33), (35), (37), (38), (39), (43), (44), (48),
% 241.22/47.77  | | | | | | | | | |            (54), (59), (61), (62), (79), (171) are
% 241.22/47.77  | | | | | | | | | |            inconsistent by sub-proof #504.
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | |   (172)  all_58_10 = e0 & op(e2, e0) = e0
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | ALPHA: (172) implies:
% 241.22/47.77  | | | | | | | | | |   (173)  op(e2, e0) = e0
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | | REF_CLOSE: (44), (48), (52), (80), (173) are inconsistent by
% 241.22/47.77  | | | | | | | | | |            sub-proof #1778.
% 241.22/47.77  | | | | | | | | | | 
% 241.22/47.77  | | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | | 
% 241.22/47.77  | | | | | | | | End of split
% 241.22/47.77  | | | | | | | | 
% 241.22/47.77  | | | | | | | End of split
% 241.22/47.77  | | | | | | | 
% 241.22/47.77  | | | | | | Case 2:
% 241.22/47.77  | | | | | | | 
% 241.22/47.77  | | | | | | |   (174)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 241.22/47.77  | | | | | | |            op(e0, e0) = e1)
% 241.22/47.77  | | | | | | | 
% 241.22/47.77  | | | | | | | BETA: splitting (174) gives:
% 241.22/47.77  | | | | | | | 
% 241.22/47.77  | | | | | | | Case 1:
% 241.22/47.77  | | | | | | | | 
% 241.22/47.77  | | | | | | | |   (175)  all_58_11 = e1 & op(e1, e0) = e1
% 241.22/47.77  | | | | | | | | 
% 241.22/47.77  | | | | | | | | ALPHA: (175) implies:
% 241.22/47.77  | | | | | | | |   (176)  all_58_11 = e1
% 241.22/47.77  | | | | | | | | 
% 241.22/47.77  | | | | | | | | REF_CLOSE: (59), (74), (176) are inconsistent by sub-proof
% 241.22/47.77  | | | | | | | |            #1020.
% 241.22/47.77  | | | | | | | | 
% 241.22/47.77  | | | | | | | Case 2:
% 241.22/47.77  | | | | | | | | 
% 241.22/47.77  | | | | | | | |   (177)  all_58_15 = e1 & op(e0, e0) = e1
% 241.22/47.77  | | | | | | | | 
% 241.22/47.77  | | | | | | | | REF_CLOSE: (1), (3), (7), (16), (18), (21), (23), (28), (33),
% 241.22/47.77  | | | | | | | |            (37), (38), (44), (48), (50), (59), (177) are
% 241.22/47.77  | | | | | | | |            inconsistent by sub-proof #513.
% 241.22/47.77  | | | | | | | | 
% 241.22/47.77  | | | | | | | End of split
% 241.22/47.77  | | | | | | | 
% 241.22/47.77  | | | | | | End of split
% 241.22/47.77  | | | | | | 
% 241.22/47.77  | | | | | End of split
% 241.22/47.77  | | | | | 
% 241.22/47.77  | | | | End of split
% 241.22/47.77  | | | | 
% 241.22/47.77  | | | Case 2:
% 241.22/47.77  | | | | 
% 241.22/47.77  | | | |   (178)  all_58_13 = e1 & op(e0, e2) = e1
% 241.22/47.77  | | | | 
% 241.22/47.77  | | | | ALPHA: (178) implies:
% 241.22/47.77  | | | |   (179)  all_58_13 = e1
% 241.22/47.77  | | | |   (180)  op(e0, e2) = e1
% 241.22/47.77  | | | | 
% 241.22/47.77  | | | | BETA: splitting (12) gives:
% 241.22/47.77  | | | | 
% 241.22/47.77  | | | | Case 1:
% 241.22/47.77  | | | | | 
% 241.22/47.77  | | | | |   (181)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 241.22/47.77  | | | | |              e2) = e0)
% 241.22/47.77  | | | | | 
% 241.22/47.77  | | | | | BETA: splitting (181) gives:
% 241.22/47.77  | | | | | 
% 241.22/47.77  | | | | | Case 1:
% 241.22/47.77  | | | | | | 
% 241.22/47.77  | | | | | |   (182)  all_58_1 = e0 & op(e3, e2) = e0
% 241.22/47.77  | | | | | | 
% 241.22/47.77  | | | | | | ALPHA: (182) implies:
% 241.22/47.77  | | | | | |   (183)  all_58_1 = e0
% 241.22/47.77  | | | | | | 
% 241.22/47.78  | | | | | | BETA: splitting (1) gives:
% 241.22/47.78  | | | | | | 
% 241.22/47.78  | | | | | | Case 1:
% 241.22/47.78  | | | | | | | 
% 241.22/47.78  | | | | | | |   (184)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 &
% 241.22/47.78  | | | | | | |            op(e3, e2) = e2)
% 241.22/47.78  | | | | | | | 
% 241.22/47.78  | | | | | | | REF_CLOSE: (7), (23), (44), (59), (183), (184) are inconsistent by
% 241.22/47.78  | | | | | | |            sub-proof #1477.
% 241.22/47.78  | | | | | | | 
% 241.22/47.78  | | | | | | Case 2:
% 241.22/47.78  | | | | | | | 
% 241.22/47.78  | | | | | | |   (185)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 &
% 241.22/47.78  | | | | | | |            op(e3, e0) = e2)
% 241.22/47.78  | | | | | | | 
% 241.22/47.78  | | | | | | | BETA: splitting (185) gives:
% 241.22/47.78  | | | | | | | 
% 241.22/47.78  | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | 
% 241.22/47.78  | | | | | | | |   (186)  all_58_4 = e2 & op(e3, e1) = e2
% 241.22/47.78  | | | | | | | | 
% 241.22/47.78  | | | | | | | | REF_CLOSE: (28), (50), (186) are inconsistent by sub-proof
% 241.22/47.78  | | | | | | | |            #1476.
% 241.22/47.78  | | | | | | | | 
% 241.22/47.78  | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | 
% 241.22/47.78  | | | | | | | |   (187)  all_58_9 = e2 & op(e3, e0) = e2
% 241.22/47.78  | | | | | | | | 
% 241.22/47.78  | | | | | | | | ALPHA: (187) implies:
% 241.22/47.78  | | | | | | | |   (188)  all_58_9 = e2
% 241.22/47.78  | | | | | | | |   (189)  op(e3, e0) = e2
% 241.22/47.78  | | | | | | | | 
% 241.22/47.78  | | | | | | | | BETA: splitting (25) gives:
% 241.22/47.78  | | | | | | | | 
% 241.22/47.78  | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | 
% 241.22/47.78  | | | | | | | | |   (190)  all_58_15 = e0 & op(e0, e0) = e0
% 241.22/47.78  | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | ALPHA: (190) implies:
% 241.22/47.78  | | | | | | | | |   (191)  all_58_15 = e0
% 241.22/47.78  | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (9), (12), (17), (18), (20),
% 241.22/47.78  | | | | | | | | |            (21), (22), (23), (27), (28), (30), (32), (33),
% 241.22/47.78  | | | | | | | | |            (37), (38), (41), (43), (44), (48), (50), (54),
% 241.22/47.78  | | | | | | | | |            (57), (59), (60), (62), (179), (189), (191) are
% 241.22/47.78  | | | | | | | | |            inconsistent by sub-proof #537.
% 241.22/47.78  | | | | | | | | | 
% 241.22/47.78  | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | 
% 241.22/47.78  | | | | | | | | |   (192)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 241.22/47.78  | | | | | | | | |              & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.22/47.78  | | | | | | | | |              = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 241.22/47.78  | | | | | | | | |            (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 241.22/47.78  | | | | | | | | |              e0 & op(e0, e1) = e0))
% 241.22/47.78  | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | ALPHA: (192) implies:
% 241.22/47.78  | | | | | | | | |   (193)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0
% 241.22/47.78  | | | | | | | | |            & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 241.22/47.78  | | | | | | | | |            e0)
% 241.22/47.78  | | | | | | | | |   (194)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 241.22/47.78  | | | | | | | | |            op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 241.22/47.78  | | | | | | | | |            e0)
% 241.22/47.78  | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | BETA: splitting (193) gives:
% 241.22/47.78  | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | |   (195)  all_58_12 = e0 & op(e0, e3) = e0
% 241.22/47.78  | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | ALPHA: (195) implies:
% 241.22/47.78  | | | | | | | | | |   (196)  all_58_12 = e0
% 241.22/47.78  | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | BETA: splitting (55) gives:
% 241.22/47.78  | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | |   (197)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 241.22/47.78  | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.22/47.78  | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | BETA: splitting (197) gives:
% 241.22/47.78  | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | |   (198)  all_58_12 = e2 & op(e0, e3) = e2
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | ALPHA: (198) implies:
% 241.22/47.78  | | | | | | | | | | | |   (199)  all_58_12 = e2
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | COMBINE_EQS: (196), (199) imply:
% 241.22/47.78  | | | | | | | | | | | |   (200)  e2 = e0
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | SIMP: (200) implies:
% 241.22/47.78  | | | | | | | | | | | |   (201)  e2 = e0
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | COMBINE_EQS: (188), (201) imply:
% 241.22/47.78  | | | | | | | | | | | |   (202)  all_58_9 = e0
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | REF_CLOSE: (1), (7), (23), (28), (44), (50), (59), (183),
% 241.22/47.78  | | | | | | | | | | | |            (202) are inconsistent by sub-proof #1097.
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | |   (203)  all_58_13 = e2 & op(e0, e2) = e2
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | ALPHA: (203) implies:
% 241.22/47.78  | | | | | | | | | | | |   (204)  all_58_13 = e2
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | COMBINE_EQS: (179), (204) imply:
% 241.22/47.78  | | | | | | | | | | | |   (205)  e2 = e1
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (12), (14),
% 241.22/47.78  | | | | | | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (25),
% 241.22/47.78  | | | | | | | | | | | |            (26), (27), (28), (29), (30), (31), (32), (33),
% 241.22/47.78  | | | | | | | | | | | |            (34), (35), (37), (38), (39), (41), (42), (43),
% 241.22/47.78  | | | | | | | | | | | |            (44), (45), (48), (51), (52), (53), (54), (55),
% 241.22/47.78  | | | | | | | | | | | |            (57), (59), (60), (62), (188), (196), (205) are
% 241.22/47.78  | | | | | | | | | | | |            inconsistent by sub-proof #503.
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | End of split
% 241.22/47.78  | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | |   (206)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 241.22/47.78  | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.22/47.78  | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | BETA: splitting (206) gives:
% 241.22/47.78  | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | |   (207)  all_58_14 = e2 & op(e0, e1) = e2
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | ALPHA: (207) implies:
% 241.22/47.78  | | | | | | | | | | | |   (208)  all_58_14 = e2
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | BETA: splitting (194) gives:
% 241.22/47.78  | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | |   (209)  all_58_9 = e0 & op(e3, e0) = e0
% 241.22/47.78  | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | ALPHA: (209) implies:
% 241.22/47.78  | | | | | | | | | | | | |   (210)  all_58_9 = e0
% 241.22/47.78  | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | REF_CLOSE: (1), (7), (23), (28), (44), (50), (59), (183),
% 241.22/47.78  | | | | | | | | | | | | |            (210) are inconsistent by sub-proof #1097.
% 241.22/47.78  | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | |   (211)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 241.22/47.78  | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 241.22/47.78  | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | BETA: splitting (211) gives:
% 241.22/47.78  | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | |   (212)  all_58_10 = e0 & op(e2, e0) = e0
% 241.22/47.78  | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | ALPHA: (212) implies:
% 241.22/47.78  | | | | | | | | | | | | | |   (213)  all_58_10 = e0
% 241.22/47.78  | | | | | | | | | | | | | |   (214)  op(e2, e0) = e0
% 241.22/47.78  | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 241.22/47.78  | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | |   (215)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 241.22/47.78  | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 241.22/47.78  | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | |   (216)  all_58_9 = e1 & op(e3, e0) = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | |   (217)  all_58_9 = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (12), (14),
% 241.22/47.78  | | | | | | | | | | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (25),
% 241.22/47.78  | | | | | | | | | | | | | | | |            (26), (27), (28), (29), (30), (31), (32), (33),
% 241.22/47.78  | | | | | | | | | | | | | | | |            (34), (35), (37), (38), (39), (41), (42), (43),
% 241.22/47.78  | | | | | | | | | | | | | | | |            (44), (45), (48), (51), (52), (53), (54), (55),
% 241.22/47.78  | | | | | | | | | | | | | | | |            (57), (59), (60), (62), (196), (217) are
% 241.22/47.78  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #639.
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | |   (218)  all_58_10 = e1 & op(e2, e0) = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | |   (219)  op(e2, e0) = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | REF_CLOSE: (44), (48), (52), (214), (219) are inconsistent by
% 241.22/47.78  | | | | | | | | | | | | | | | |            sub-proof #1778.
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | End of split
% 241.22/47.78  | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | |   (220)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 241.22/47.78  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.22/47.78  | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | |   (221)  all_58_11 = e1 & op(e1, e0) = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | |   (222)  all_58_11 = e1
% 241.22/47.78  | | | | | | | | | | | | | | | |   (223)  op(e1, e0) = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | |   (224)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 241.22/47.78  | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | |   (225)  all_58_4 = e1 & op(e3, e1) = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | | | |   (226)  all_58_4 = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (7), (18), (21), (23), (28), (33), (37),
% 241.22/47.78  | | | | | | | | | | | | | | | | | |            (38), (44), (48), (59), (226) are inconsistent by
% 241.22/47.78  | | | | | | | | | | | | | | | | | |            sub-proof #1468.
% 241.22/47.78  | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | |   (227)  all_58_5 = e1 & op(e2, e1) = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | | | |   (228)  all_58_5 = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | |   (229)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | |   (230)  all_58_0 = e2 & op(e3, e3) = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | |   (231)  op(e3, e3) = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (44), (59), (231) are inconsistent by
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | |            sub-proof #2267.
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | |   (232)  all_58_2 = e2 & op(e2, e3) = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | |   (233)  all_58_2 = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | |   (234)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | |   (235)  all_58_6 = e2 & op(e1, e3) = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | |   (236)  all_58_6 = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (8), (18), (22), (23), (27), (28), (30),
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | |            (31), (32), (34), (44), (48), (54), (59), (62),
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | |            (222), (236) are inconsistent by sub-proof #661.
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | |   (237)  all_58_7 = e2 & op(e1, e2) = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | |   (238)  all_58_7 = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | |   (239)  op(e1, e2) = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |   (240)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |   (241)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (40), (44), (54), (58), (241) are
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |   (242)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (243)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (244)   ~ (all_56_31 = e3)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (244) imply:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  $false
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent.
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)  op(e3, e0) = e3
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (44), (189), (248) are inconsistent by
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2125.
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (249)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e0
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (250)   ~ (all_56_31 = e3)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (250) imply:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  $false
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (251) is inconsistent.
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |   (252)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |   (253)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (254)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (255)   ~ (all_56_1 = e1)
% 241.22/47.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (255) imply:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  $false
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent.
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)   ~ (all_56_31 = e2)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)   ~ (all_56_21 = e2)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)   ~ (all_56_1 = e2)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  op(e1, e2) = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (261) imply:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)   ~ (e2 = e1)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (260) imply:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)   ~ (e2 = e0)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (44) with e2, e1, e2, e1,
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (239), (262) gives:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  e2 = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (265) imply:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_58_7 = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (20), (28), (48), (59),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |            (179), (266) are inconsistent by sub-proof #1457.
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  op(e2, e0) = e2
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (20), (43), (44), (48), (228), (233),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | |            (268) are inconsistent by sub-proof #840.
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | |   (269)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (270) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  op(e0, e2) = e0
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (48), (180), (271) are inconsistent by
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1872.
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (44), (48), (223), (272) are inconsistent by
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #501.
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | |   (273)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |   (274)  all_58_8 = e2 & op(e1, e1) = e2
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |   (275)  all_58_8 = e2
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (275) imply:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |   (276)  e2 = e0
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | SIMP: (276) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |   (277)  e2 = e0
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (17), (18), (20), (22), (23), (27),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |            (28), (30), (32), (43), (44), (48), (54), (57),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |            (59), (60), (196), (213), (233), (277) are
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #632.
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |   (278)  all_58_11 = e2 & op(e1, e0) = e2
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |   (279)  all_58_11 = e2
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (222), (279) imply:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |   (280)  e2 = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (12), (14),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (25),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |            (26), (27), (28), (29), (30), (31), (32), (33),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |            (34), (35), (37), (38), (39), (41), (42), (43),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |            (44), (45), (48), (51), (52), (53), (54), (55),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |            (57), (59), (60), (62), (188), (196), (280) are
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #503.
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | |   (281)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 241.22/47.79  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |   (282)  all_58_6 = e2 & op(e1, e3) = e2
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |   (283)  all_58_6 = e2
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (8), (18), (22), (23), (27), (28), (30),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |            (31), (32), (34), (44), (48), (54), (59), (62),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |            (222), (283) are inconsistent by sub-proof #661.
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |   (284)  all_58_12 = e2 & op(e0, e3) = e2
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |   (285)  all_58_12 = e2
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (285) imply:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |   (286)  e2 = e0
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | SIMP: (286) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |   (287)  e2 = e0
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (287) imply:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |   (288)  all_58_9 = e0
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (7), (16), (18), (20), (23), (27),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |            (28), (32), (43), (44), (45), (48), (50), (57),
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |            (59), (60), (196), (222), (288) are inconsistent
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | |            by sub-proof #613.
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | |   (289)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.22/47.79  | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 241.22/47.79  | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 241.22/47.79  | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | Case 1:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | |   (290)  all_58_8 = e1 & op(e1, e1) = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | | | |   (291)  all_58_8 = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | |   (292)  op(e1, e1) = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (28), (42), (44), (48), (51), (59),
% 241.22/47.79  | | | | | | | | | | | | | | | | | |            (222), (223), (291), (292) are inconsistent by
% 241.22/47.79  | | | | | | | | | | | | | | | | | |            sub-proof #804.
% 241.22/47.79  | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | |   (293)  all_58_14 = e1 & op(e0, e1) = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | | | |   (294)  all_58_14 = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (294) imply:
% 241.22/47.79  | | | | | | | | | | | | | | | | | |   (295)  e2 = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (295) imply:
% 241.22/47.79  | | | | | | | | | | | | | | | | | |   (296)  all_58_9 = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (12), (14),
% 241.22/47.79  | | | | | | | | | | | | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (25),
% 241.22/47.79  | | | | | | | | | | | | | | | | | |            (26), (27), (28), (29), (30), (31), (32), (33),
% 241.22/47.79  | | | | | | | | | | | | | | | | | |            (34), (35), (37), (38), (39), (41), (42), (43),
% 241.22/47.79  | | | | | | | | | | | | | | | | | |            (44), (45), (48), (51), (52), (53), (54), (55),
% 241.22/47.79  | | | | | | | | | | | | | | | | | |            (57), (59), (60), (62), (196), (296) are
% 241.22/47.79  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #639.
% 241.22/47.79  | | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | |   (297)  all_58_15 = e1 & op(e0, e0) = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 241.22/47.79  | | | | | | | | | | | | | | | |   (298)  all_58_15 = e1
% 241.22/47.79  | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (7), (15), (18), (22), (23), (25),
% 241.22/47.79  | | | | | | | | | | | | | | | |            (27), (28), (30), (32), (36), (44), (48), (54),
% 241.22/47.79  | | | | | | | | | | | | | | | |            (55), (59), (208), (298) are inconsistent by
% 241.22/47.79  | | | | | | | | | | | | | | | |            sub-proof #1159.
% 241.22/47.79  | | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | |   (299)  all_58_11 = e0 & op(e1, e0) = e0
% 241.22/47.79  | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | ALPHA: (299) implies:
% 241.22/47.79  | | | | | | | | | | | | | |   (300)  op(e1, e0) = e0
% 241.22/47.79  | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (9), (12), (18), (20), (22), (23),
% 241.22/47.79  | | | | | | | | | | | | | |            (27), (28), (30), (32), (44), (48), (54), (59),
% 241.22/47.79  | | | | | | | | | | | | | |            (62), (179), (300) are inconsistent by sub-proof
% 241.22/47.79  | | | | | | | | | | | | | |            #500.
% 241.22/47.79  | | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | |   (301)  all_58_15 = e2 & op(e0, e0) = e2
% 241.22/47.79  | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | | REF_CLOSE: (16), (28), (301) are inconsistent by sub-proof
% 241.22/47.79  | | | | | | | | | | | |            #1231.
% 241.22/47.79  | | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | |   (302)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 241.22/47.79  | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 241.22/47.79  | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | BETA: splitting (302) gives:
% 241.22/47.79  | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | Case 1:
% 241.22/47.79  | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | |   (303)  all_58_13 = e0 & op(e0, e2) = e0
% 241.22/47.79  | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | REF_CLOSE: (48), (179), (303) are inconsistent by sub-proof
% 241.22/47.79  | | | | | | | | | | |            #609.
% 241.22/47.79  | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | Case 2:
% 241.22/47.79  | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | |   (304)  all_58_14 = e0 & op(e0, e1) = e0
% 241.22/47.79  | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | ALPHA: (304) implies:
% 241.22/47.79  | | | | | | | | | | |   (305)  all_58_14 = e0
% 241.22/47.79  | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (14), (16),
% 241.22/47.79  | | | | | | | | | | |            (17), (18), (20), (21), (22), (23), (27), (28),
% 241.22/47.79  | | | | | | | | | | |            (29), (30), (31), (32), (33), (34), (37), (38),
% 241.22/47.79  | | | | | | | | | | |            (42), (43), (44), (48), (50), (51), (52), (54),
% 241.22/47.79  | | | | | | | | | | |            (55), (59), (61), (62), (179), (183), (188),
% 241.22/47.79  | | | | | | | | | | |            (194), (305) are inconsistent by sub-proof #512.
% 241.22/47.79  | | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | | 
% 241.22/47.79  | | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | | 
% 241.22/47.79  | | | | | | | | End of split
% 241.22/47.79  | | | | | | | | 
% 241.22/47.79  | | | | | | | End of split
% 241.22/47.79  | | | | | | | 
% 241.22/47.79  | | | | | | End of split
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | Case 2:
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | |   (306)  all_58_3 = e0 & op(e2, e2) = e0
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12), (14),
% 241.22/47.79  | | | | | |            (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 241.22/47.79  | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 241.22/47.79  | | | | | |            (37), (38), (39), (41), (42), (43), (44), (45), (48),
% 241.22/47.79  | | | | | |            (51), (52), (53), (54), (55), (57), (59), (60), (62),
% 241.22/47.79  | | | | | |            (306) are inconsistent by sub-proof #578.
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | End of split
% 241.22/47.79  | | | | | 
% 241.22/47.79  | | | | Case 2:
% 241.22/47.79  | | | | | 
% 241.22/47.79  | | | | |   (307)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0,
% 241.22/47.79  | | | | |              e2) = e0)
% 241.22/47.79  | | | | | 
% 241.22/47.79  | | | | | BETA: splitting (307) gives:
% 241.22/47.79  | | | | | 
% 241.22/47.79  | | | | | Case 1:
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | |   (308)  all_58_7 = e0 & op(e1, e2) = e0
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | | ALPHA: (308) implies:
% 241.22/47.79  | | | | | |   (309)  all_58_7 = e0
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | | REF_CLOSE: (3), (4), (7), (8), (9), (12), (18), (20), (22), (23),
% 241.22/47.79  | | | | | |            (27), (28), (30), (31), (32), (34), (42), (44), (48),
% 241.22/47.79  | | | | | |            (54), (59), (61), (62), (179), (309) are inconsistent by
% 241.22/47.79  | | | | | |            sub-proof #519.
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | Case 2:
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | |   (310)  all_58_13 = e0 & op(e0, e2) = e0
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | | ALPHA: (310) implies:
% 241.22/47.79  | | | | | |   (311)  op(e0, e2) = e0
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | | REF_CLOSE: (44), (48), (180), (311) are inconsistent by sub-proof
% 241.22/47.79  | | | | | |            #1872.
% 241.22/47.79  | | | | | | 
% 241.22/47.79  | | | | | End of split
% 241.22/47.79  | | | | | 
% 241.22/47.79  | | | | End of split
% 241.22/47.79  | | | | 
% 241.22/47.79  | | | End of split
% 241.22/47.79  | | | 
% 241.22/47.79  | | End of split
% 241.22/47.79  | | 
% 241.22/47.79  | End of split
% 241.22/47.79  | 
% 241.22/47.79  End of proof
% 241.22/47.79  
% 241.22/47.79  Sub-proof #500 shows that the following formulas are inconsistent:
% 241.22/47.79  ----------------------------------------------------------------
% 241.22/47.79    (1)   ~ (e3 = e0)
% 241.22/47.79    (2)  op(e1, e0) = e0
% 241.22/47.79    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.22/47.79         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.22/47.79    (4)   ~ (e2 = e0)
% 241.22/47.79    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.79         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.22/47.79    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.79         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.22/47.79    (7)   ~ (e3 = e1)
% 241.22/47.79    (8)  all_58_3 = e3
% 241.22/47.79    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.22/47.79         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.22/47.79    (10)  op(e3, e3) = e1
% 241.22/47.79    (11)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.22/47.79          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.22/47.79    (12)   ~ (e3 = e2)
% 241.22/47.79    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.22/47.79          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.22/47.79    (14)  op(e2, e3) = all_52_1
% 241.22/47.79    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.79    (16)  op(e1, e1) = e0
% 241.22/47.79    (17)   ~ (e1 = e0)
% 241.22/47.79    (18)  all_58_13 = e1
% 241.22/47.79    (19)   ~ (all_52_1 = e3)
% 241.22/47.79    (20)   ~ (e2 = e1)
% 241.22/47.79  
% 241.22/47.79  Begin of proof
% 241.22/47.79  | 
% 241.22/47.79  | BETA: splitting (3) gives:
% 241.22/47.79  | 
% 241.22/47.79  | Case 1:
% 241.22/47.79  | | 
% 241.22/47.79  | |   (21)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 241.22/47.79  | |           e1)
% 241.22/47.79  | | 
% 241.22/47.80  | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 241.22/47.80  | |            (15), (17), (18), (19), (20), (21) are inconsistent by sub-proof
% 241.22/47.80  | |            #538.
% 241.22/47.80  | | 
% 241.22/47.80  | Case 2:
% 241.22/47.80  | | 
% 241.22/47.80  | |   (22)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 241.22/47.80  | |           e1)
% 241.22/47.80  | | 
% 241.22/47.80  | | REF_CLOSE: (2), (15), (16), (17), (22) are inconsistent by sub-proof #795.
% 241.22/47.80  | | 
% 241.22/47.80  | End of split
% 241.22/47.80  | 
% 241.22/47.80  End of proof
% 241.22/47.80  
% 241.22/47.80  Sub-proof #501 shows that the following formulas are inconsistent:
% 241.22/47.80  ----------------------------------------------------------------
% 241.22/47.80    (1)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 241.22/47.80             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 241.22/47.80           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 241.22/47.80             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 241.22/47.80           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.22/47.80    (2)  op(e1, e0) = e1
% 241.22/47.80    (3)  all_56_21 = e0
% 241.22/47.80    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.80    (5)   ~ (e1 = e0)
% 241.22/47.80  
% 241.22/47.80  Begin of proof
% 241.22/47.80  | 
% 241.22/47.80  | BETA: splitting (1) gives:
% 241.22/47.80  | 
% 241.22/47.80  | Case 1:
% 241.22/47.80  | | 
% 241.22/47.80  | |   (6)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 241.22/47.80  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 241.22/47.80  | |        & op(e0, e1) = e1
% 241.22/47.80  | | 
% 241.22/47.80  | | ALPHA: (6) implies:
% 241.22/47.80  | |   (7)   ~ (all_56_21 = e0)
% 241.22/47.80  | | 
% 241.22/47.80  | | REDUCE: (3), (7) imply:
% 241.22/47.80  | |   (8)  $false
% 241.22/47.80  | | 
% 241.22/47.80  | | CLOSE: (8) is inconsistent.
% 241.22/47.80  | | 
% 241.22/47.80  | Case 2:
% 241.22/47.80  | | 
% 241.22/47.80  | |   (9)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 241.22/47.80  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 241.22/47.80  | |        & op(e0, e1) = e0
% 241.22/47.80  | | 
% 241.22/47.80  | | ALPHA: (9) implies:
% 241.22/47.80  | |   (10)  op(e1, e0) = e0
% 241.22/47.80  | | 
% 241.22/47.80  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #2284.
% 241.22/47.80  | | 
% 241.22/47.80  | End of split
% 241.22/47.80  | 
% 241.22/47.80  End of proof
% 241.22/47.80  
% 241.22/47.80  Sub-proof #502 shows that the following formulas are inconsistent:
% 241.22/47.80  ----------------------------------------------------------------
% 241.22/47.80    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.22/47.80           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.22/47.80             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.22/47.80           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.22/47.80             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.22/47.80           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.22/47.80           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 241.22/47.80    (2)  op(e2, e3) = all_52_1
% 241.22/47.80    (3)  all_56_31 = e3
% 241.22/47.80    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.80    (5)   ~ (all_52_1 = e3)
% 241.22/47.80    (6)  all_56_1 = e1
% 241.22/47.80  
% 241.22/47.80  Begin of proof
% 241.22/47.80  | 
% 241.22/47.80  | BETA: splitting (1) gives:
% 241.22/47.80  | 
% 241.22/47.80  | Case 1:
% 241.22/47.80  | | 
% 241.22/47.80  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.22/47.80  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.22/47.80  | |        op(e2, e3) = e3
% 241.22/47.80  | | 
% 241.22/47.80  | | ALPHA: (7) implies:
% 241.22/47.80  | |   (8)  op(e2, e3) = e3
% 241.22/47.80  | | 
% 241.22/47.80  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2337.
% 241.22/47.80  | | 
% 241.22/47.80  | Case 2:
% 241.22/47.80  | | 
% 241.22/47.80  | |   (9)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 241.22/47.80  | |            e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2
% 241.22/47.80  | |          & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1
% 241.22/47.80  | |            = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 241.22/47.80  | |            = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 241.22/47.80  | | 
% 241.22/47.80  | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #1239.
% 241.22/47.80  | | 
% 241.22/47.80  | End of split
% 241.22/47.80  | 
% 241.22/47.80  End of proof
% 241.22/47.80  
% 241.22/47.80  Sub-proof #503 shows that the following formulas are inconsistent:
% 241.22/47.80  ----------------------------------------------------------------
% 241.22/47.80    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.22/47.80         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.22/47.80    (2)   ~ (e3 = e0)
% 241.22/47.80    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.22/47.80         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.22/47.80    (4)   ~ (e2 = e0)
% 241.22/47.80    (5)  op(e1, e2) = all_52_6
% 241.22/47.80    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.80         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.22/47.80    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.22/47.80         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.22/47.80    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.80         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.22/47.80    (9)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.22/47.80         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.22/47.80    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.80          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.22/47.80    (11)   ~ (e3 = e1)
% 241.22/47.80    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.22/47.80          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.22/47.80    (13)  all_58_3 = e3
% 241.22/47.80    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.22/47.80          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.22/47.80    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.22/47.80          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.22/47.80    (16)  op(e3, e3) = e1
% 241.22/47.80    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.80              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.22/47.80                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.22/47.80                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.22/47.80    (18)  op(e2, e1) = all_52_9
% 241.22/47.80    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.22/47.80          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.22/47.80    (20)   ~ (e3 = e2)
% 241.22/47.80    (21)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.22/47.80          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.22/47.80    (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.22/47.80          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.22/47.80    (23)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.22/47.80          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.22/47.80    (24)  all_58_12 = e0
% 241.22/47.80    (25)  op(e2, e3) = all_52_1
% 241.22/47.80    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.22/47.80          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.80    (27)   ~ (all_52_6 = e3)
% 241.22/47.80    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.22/47.80          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.22/47.80    (29)   ~ (all_52_4 = e3)
% 241.22/47.80    (30)  op(e3, e2) = all_52_4
% 241.22/47.80    (31)   ~ (all_52_9 = e3)
% 241.22/47.80    (32)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.22/47.80          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.22/47.80    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.22/47.80          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.22/47.80    (34)  e2 = e1
% 241.22/47.80    (35)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.80          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.22/47.80    (36)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.80            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.80    (37)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.22/47.80          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.22/47.80    (38)  op(e1, e1) = e0
% 241.22/47.80    (39)   ~ (e1 = e0)
% 241.22/47.80    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.22/47.80          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.22/47.80    (41)  op(e2, e0) = all_52_13
% 241.22/47.80    (42)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.22/47.80          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.22/47.80            e1)
% 241.22/47.80    (43)  all_58_9 = e2
% 241.22/47.80    (44)   ~ (all_52_1 = e3)
% 241.22/47.80    (45)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.22/47.80          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.22/47.80            e2)
% 241.22/47.80    (46)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.22/47.80          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.22/47.80    (47)   ~ (e2 = e1)
% 241.22/47.80    (48)   ~ (all_52_1 = e1)
% 241.22/47.80  
% 241.22/47.80  Begin of proof
% 241.22/47.80  | 
% 241.22/47.80  | SIMP: (34) implies:
% 241.22/47.80  |   (49)  e2 = e1
% 241.22/47.80  | 
% 241.22/47.80  | COMBINE_EQS: (43), (49) imply:
% 241.22/47.80  |   (50)  all_58_9 = e1
% 241.22/47.80  | 
% 241.22/47.80  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.22/47.80  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 241.22/47.80  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 241.22/47.80  |            (36), (37), (38), (39), (40), (41), (42), (44), (45), (46), (47),
% 241.22/47.80  |            (48), (50) are inconsistent by sub-proof #639.
% 241.22/47.80  | 
% 241.22/47.80  End of proof
% 241.22/47.80  
% 241.22/47.80  Sub-proof #504 shows that the following formulas are inconsistent:
% 241.22/47.80  ----------------------------------------------------------------
% 241.22/47.80    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.22/47.80         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.22/47.80    (2)  all_58_5 = e0
% 241.22/47.80    (3)   ~ (e3 = e0)
% 241.22/47.80    (4)  all_58_6 = e3
% 241.22/47.80    (5)   ~ (e2 = e0)
% 241.22/47.80    (6)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.22/47.80         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.22/47.80    (7)  all_58_8 = e0
% 241.22/47.80    (8)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.22/47.80         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.22/47.80    (9)   ~ (e3 = e1)
% 241.22/47.80    (10)  all_58_3 = e3
% 241.22/47.80    (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.22/47.80          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.22/47.80    (12)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.22/47.80          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.22/47.80    (13)  op(e3, e3) = e1
% 241.22/47.80    (14)  op(e2, e1) = all_52_9
% 241.22/47.80    (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.22/47.80          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.22/47.80    (16)   ~ (e3 = e2)
% 241.22/47.80    (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.22/47.80          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.22/47.80    (18)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.22/47.80          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.22/47.80    (19)  op(e2, e3) = all_52_1
% 241.22/47.80    (20)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.22/47.80          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.22/47.80    (21)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.22/47.80          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.22/47.80    (22)   ~ (all_52_4 = e3)
% 241.22/47.80    (23)  op(e3, e2) = all_52_4
% 241.22/47.80    (24)   ~ (all_52_9 = e3)
% 241.22/47.80    (25)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.22/47.80          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.22/47.80    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.22/47.80            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.22/47.80    (27)  op(e1, e1) = e0
% 241.22/47.80    (28)   ~ (e1 = e0)
% 241.22/47.80    (29)   ~ (all_52_1 = e3)
% 241.22/47.80    (30)  all_58_10 = e1
% 241.22/47.80    (31)   ~ (e2 = e1)
% 241.22/47.80  
% 241.22/47.80  Begin of proof
% 241.22/47.80  | 
% 241.22/47.80  | BETA: splitting (6) gives:
% 241.22/47.80  | 
% 241.22/47.80  | Case 1:
% 241.22/47.80  | | 
% 241.22/47.80  | |   (32)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 241.22/47.80  | |           e1)
% 241.22/47.80  | | 
% 241.30/47.80  | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (11), (13), (16), (20), (22),
% 241.30/47.80  | |            (23), (25), (26), (28), (30), (31), (32) are inconsistent by
% 241.30/47.80  | |            sub-proof #647.
% 241.30/47.80  | | 
% 241.30/47.80  | Case 2:
% 241.30/47.80  | | 
% 241.30/47.80  | |   (33)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 241.30/47.80  | |           e1)
% 241.30/47.80  | | 
% 241.30/47.80  | | BETA: splitting (33) gives:
% 241.30/47.80  | | 
% 241.30/47.80  | | Case 1:
% 241.30/47.80  | | | 
% 241.30/47.80  | | |   (34)  all_58_8 = e1 & op(e1, e1) = e1
% 241.30/47.80  | | | 
% 241.30/47.80  | | | ALPHA: (34) implies:
% 241.30/47.80  | | |   (35)  op(e1, e1) = e1
% 241.30/47.80  | | | 
% 241.30/47.80  | | | REF_CLOSE: (26), (27), (28), (35) are inconsistent by sub-proof #2220.
% 241.30/47.80  | | | 
% 241.30/47.80  | | Case 2:
% 241.30/47.80  | | | 
% 241.30/47.80  | | |   (36)  all_58_14 = e1 & op(e0, e1) = e1
% 241.30/47.80  | | | 
% 241.30/47.80  | | | ALPHA: (36) implies:
% 241.30/47.81  | | |   (37)  all_58_14 = e1
% 241.30/47.81  | | | 
% 241.30/47.81  | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (12), (13), (14), (15), (16),
% 241.30/47.81  | | |            (17), (18), (19), (21), (24), (26), (27), (28), (29), (31),
% 241.30/47.81  | | |            (37) are inconsistent by sub-proof #505.
% 241.30/47.81  | | | 
% 241.30/47.81  | | End of split
% 241.30/47.81  | | 
% 241.30/47.81  | End of split
% 241.30/47.81  | 
% 241.30/47.81  End of proof
% 241.30/47.81  
% 241.30/47.81  Sub-proof #505 shows that the following formulas are inconsistent:
% 241.30/47.81  ----------------------------------------------------------------
% 241.30/47.81    (1)  all_58_5 = e0
% 241.30/47.81    (2)   ~ (e3 = e0)
% 241.30/47.81    (3)  all_58_6 = e3
% 241.30/47.81    (4)   ~ (e2 = e0)
% 241.30/47.81    (5)  all_58_8 = e0
% 241.30/47.81    (6)   ~ (e3 = e1)
% 241.30/47.81    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.30/47.81         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.30/47.81    (8)  op(e3, e3) = e1
% 241.30/47.81    (9)  op(e2, e1) = all_52_9
% 241.30/47.81    (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.30/47.81          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.30/47.81    (11)   ~ (e3 = e2)
% 241.30/47.81    (12)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.30/47.81          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.30/47.81    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.30/47.81          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.30/47.81    (14)  op(e2, e3) = all_52_1
% 241.30/47.81    (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.30/47.81          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.30/47.81    (16)   ~ (all_52_9 = e3)
% 241.30/47.81    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.81    (18)  op(e1, e1) = e0
% 241.30/47.81    (19)   ~ (e1 = e0)
% 241.30/47.81    (20)   ~ (all_52_1 = e3)
% 241.30/47.81    (21)  all_58_14 = e1
% 241.30/47.81    (22)   ~ (e2 = e1)
% 241.30/47.81  
% 241.30/47.81  Begin of proof
% 241.30/47.81  | 
% 241.30/47.81  | BETA: splitting (12) gives:
% 241.30/47.81  | 
% 241.30/47.81  | Case 1:
% 241.30/47.81  | | 
% 241.30/47.81  | |   (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 241.30/47.81  | |           e2)
% 241.30/47.81  | | 
% 241.30/47.81  | | BETA: splitting (23) gives:
% 241.30/47.81  | | 
% 241.30/47.81  | | Case 1:
% 241.30/47.81  | | | 
% 241.30/47.81  | | |   (24)  all_58_4 = e2 & op(e3, e1) = e2
% 241.30/47.81  | | | 
% 241.30/47.81  | | | ALPHA: (24) implies:
% 241.30/47.81  | | |   (25)  all_58_4 = e2
% 241.30/47.81  | | | 
% 241.30/47.81  | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 241.30/47.81  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (25) are
% 241.30/47.81  | | |            inconsistent by sub-proof #645.
% 241.30/47.81  | | | 
% 241.30/47.81  | | Case 2:
% 241.30/47.81  | | | 
% 241.30/47.81  | | |   (26)  all_58_5 = e2 & op(e2, e1) = e2
% 241.30/47.81  | | | 
% 241.30/47.81  | | | ALPHA: (26) implies:
% 241.30/47.81  | | |   (27)  all_58_5 = e2
% 241.30/47.81  | | | 
% 241.30/47.81  | | | REF_CLOSE: (1), (4), (27) are inconsistent by sub-proof #835.
% 241.30/47.81  | | | 
% 241.30/47.81  | | End of split
% 241.30/47.81  | | 
% 241.30/47.81  | Case 2:
% 241.30/47.81  | | 
% 241.30/47.81  | |   (28)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 241.30/47.81  | |           e2)
% 241.30/47.81  | | 
% 241.30/47.81  | | BETA: splitting (28) gives:
% 241.30/47.81  | | 
% 241.30/47.81  | | Case 1:
% 241.30/47.81  | | | 
% 241.30/47.81  | | |   (29)  all_58_8 = e2 & op(e1, e1) = e2
% 241.30/47.81  | | | 
% 241.30/47.81  | | | REF_CLOSE: (4), (5), (29) are inconsistent by sub-proof #683.
% 241.30/47.81  | | | 
% 241.30/47.81  | | Case 2:
% 241.30/47.81  | | | 
% 241.30/47.81  | | |   (30)  all_58_14 = e2 & op(e0, e1) = e2
% 241.30/47.81  | | | 
% 241.30/47.81  | | | ALPHA: (30) implies:
% 241.30/47.81  | | |   (31)  all_58_14 = e2
% 241.30/47.81  | | | 
% 241.30/47.81  | | | REF_CLOSE: (21), (22), (31) are inconsistent by sub-proof #2044.
% 241.30/47.81  | | | 
% 241.30/47.81  | | End of split
% 241.30/47.81  | | 
% 241.30/47.81  | End of split
% 241.30/47.81  | 
% 241.30/47.81  End of proof
% 241.30/47.81  
% 241.30/47.81  Sub-proof #506 shows that the following formulas are inconsistent:
% 241.30/47.81  ----------------------------------------------------------------
% 241.30/47.81    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.30/47.81         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.30/47.81    (2)   ~ (e3 = e0)
% 241.30/47.81    (3)  all_58_6 = e3
% 241.30/47.81    (4)   ~ (e2 = e0)
% 241.30/47.81    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.30/47.81         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.30/47.81    (6)  all_58_12 = e2
% 241.30/47.81    (7)  all_58_3 = e3
% 241.30/47.81    (8)  op(e3, e3) = e1
% 241.30/47.81    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.30/47.81         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.30/47.81    (10)   ~ (e3 = e2)
% 241.30/47.81    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.30/47.81          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.30/47.81    (12)  op(e0, e2) = e0
% 241.30/47.81    (13)  all_58_7 = e1
% 241.30/47.81    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.81    (15)   ~ (e1 = e0)
% 241.30/47.81    (16)  all_58_4 = e3
% 241.30/47.81    (17)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 241.30/47.81    (18)   ~ (e2 = e1)
% 241.30/47.81  
% 241.30/47.81  Begin of proof
% 241.30/47.81  | 
% 241.30/47.81  | BETA: splitting (17) gives:
% 241.30/47.81  | 
% 241.30/47.81  | Case 1:
% 241.30/47.81  | | 
% 241.30/47.81  | |   (19)  all_58_0 = e0 & op(e3, e3) = e0
% 241.30/47.81  | | 
% 241.30/47.81  | | ALPHA: (19) implies:
% 241.30/47.81  | |   (20)  op(e3, e3) = e0
% 241.30/47.81  | | 
% 241.30/47.81  | | REF_CLOSE: (8), (14), (15), (20) are inconsistent by sub-proof #1828.
% 241.30/47.81  | | 
% 241.30/47.81  | Case 2:
% 241.30/47.81  | | 
% 241.30/47.81  | |   (21)  all_58_1 = e0 & op(e3, e2) = e0
% 241.30/47.81  | | 
% 241.30/47.81  | | ALPHA: (21) implies:
% 241.30/47.81  | |   (22)  all_58_1 = e0
% 241.30/47.81  | | 
% 241.30/47.81  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.30/47.81  | |            (13), (14), (15), (16), (18), (22) are inconsistent by sub-proof
% 241.30/47.81  | |            #586.
% 241.30/47.81  | | 
% 241.30/47.81  | End of split
% 241.30/47.81  | 
% 241.30/47.81  End of proof
% 241.30/47.81  
% 241.30/47.81  Sub-proof #507 shows that the following formulas are inconsistent:
% 241.30/47.81  ----------------------------------------------------------------
% 241.30/47.81    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.30/47.81         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.30/47.81    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.30/47.81         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.30/47.81    (3)   ~ (e3 = e0)
% 241.30/47.81    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.30/47.81         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.30/47.81    (5)  all_58_6 = e3
% 241.30/47.81    (6)   ~ (e2 = e0)
% 241.30/47.81    (7)  all_58_7 = e0
% 241.30/47.81    (8)  op(e1, e2) = all_52_6
% 241.30/47.81    (9)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.30/47.81         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.30/47.81    (10)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.30/47.81          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.30/47.81    (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.30/47.81          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.30/47.81    (12)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.30/47.81          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.30/47.81    (13)   ~ (all_52_7 = e3)
% 241.30/47.81    (14)  all_58_15 = e3
% 241.30/47.81    (15)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.30/47.81          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.30/47.81    (16)   ~ (e3 = e1)
% 241.30/47.81    (17)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.30/47.81          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.30/47.81    (18)  all_58_3 = e3
% 241.30/47.81    (19)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.30/47.81          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.30/47.81    (20)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.30/47.81          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.30/47.81    (21)  op(e3, e3) = e1
% 241.30/47.81    (22)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.30/47.81              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.30/47.81                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.30/47.81                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.30/47.81    (23)  op(e2, e1) = all_52_9
% 241.30/47.81    (24)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.30/47.81          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.30/47.81    (25)  op(e1, e2) = e0
% 241.30/47.81    (26)   ~ (e3 = e2)
% 241.30/47.81    (27)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.30/47.81          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.30/47.81    (28)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.30/47.81          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.30/47.81    (29)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.30/47.81          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.30/47.81    (30)  op(e2, e3) = all_52_1
% 241.30/47.81    (31)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.30/47.81          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.30/47.81    (32)   ~ (all_52_6 = e3)
% 241.30/47.81    (33)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.30/47.81          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.30/47.81    (34)  op(e0, e2) = all_52_7
% 241.30/47.81    (35)   ~ (all_52_4 = e3)
% 241.30/47.81    (36)  op(e3, e2) = all_52_4
% 241.30/47.81    (37)   ~ (all_52_9 = e3)
% 241.30/47.81    (38)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.30/47.81          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.30/47.81    (39)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.30/47.81          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.30/47.81    (40)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.30/47.81          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.30/47.81    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.81    (42)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.30/47.81          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.30/47.81    (43)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.30/47.81          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.30/47.81    (44)  op(e1, e1) = e0
% 241.30/47.81    (45)   ~ (all_52_4 = e1)
% 241.30/47.81    (46)   ~ (e1 = e0)
% 241.30/47.81    (47)  all_58_4 = e3
% 241.30/47.81    (48)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.30/47.81          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.30/47.81    (49)  op(e2, e0) = all_52_13
% 241.30/47.81    (50)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.30/47.81          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.30/47.81            e1)
% 241.30/47.81    (51)   ~ (all_52_1 = e3)
% 241.30/47.81    (52)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.30/47.81          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.30/47.81            e2)
% 241.30/47.81    (53)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.30/47.81          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.30/47.81    (54)   ~ (e2 = e1)
% 241.30/47.81    (55)   ~ (all_52_1 = e1)
% 241.30/47.81  
% 241.30/47.81  Begin of proof
% 241.30/47.81  | 
% 241.30/47.81  | BETA: splitting (43) gives:
% 241.30/47.81  | 
% 241.30/47.81  | Case 1:
% 241.30/47.81  | | 
% 241.30/47.81  | |   (56)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 241.30/47.81  | |           e1)
% 241.30/47.81  | | 
% 241.30/47.81  | | REF_CLOSE: (1), (3), (6), (16), (18), (19), (21), (26), (31), (35), (36),
% 241.30/47.81  | |            (41), (45), (46), (47), (54), (56) are inconsistent by sub-proof
% 241.30/47.81  | |            #528.
% 241.30/47.81  | | 
% 241.30/47.81  | Case 2:
% 241.30/47.81  | | 
% 241.30/47.81  | |   (57)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 241.30/47.81  | |           e1)
% 241.30/47.81  | | 
% 241.30/47.81  | | BETA: splitting (57) gives:
% 241.30/47.81  | | 
% 241.30/47.81  | | Case 1:
% 241.30/47.81  | | | 
% 241.30/47.81  | | |   (58)  all_58_7 = e1 & op(e1, e2) = e1
% 241.30/47.81  | | | 
% 241.30/47.81  | | | ALPHA: (58) implies:
% 241.30/47.81  | | |   (59)  op(e1, e2) = e1
% 241.30/47.81  | | | 
% 241.30/47.81  | | | REF_CLOSE: (8), (25), (41), (46), (59) are inconsistent by sub-proof
% 241.30/47.81  | | |            #2136.
% 241.30/47.81  | | | 
% 241.30/47.81  | | Case 2:
% 241.30/47.81  | | | 
% 241.30/47.81  | | |   (60)  all_58_13 = e1 & op(e0, e2) = e1
% 241.30/47.81  | | | 
% 241.30/47.81  | | | ALPHA: (60) implies:
% 241.30/47.81  | | |   (61)  all_58_13 = e1
% 241.30/47.81  | | | 
% 241.30/47.81  | | | BETA: splitting (9) gives:
% 241.30/47.81  | | | 
% 241.30/47.81  | | | Case 1:
% 241.30/47.81  | | | | 
% 241.30/47.81  | | | |   (62)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2)
% 241.30/47.81  | | | |           = e2)
% 241.30/47.81  | | | | 
% 241.30/47.81  | | | | BETA: splitting (62) gives:
% 241.30/47.81  | | | | 
% 241.30/47.81  | | | | Case 1:
% 241.30/47.81  | | | | | 
% 241.30/47.81  | | | | |   (63)  all_58_1 = e2 & op(e3, e2) = e2
% 241.30/47.81  | | | | | 
% 241.30/47.81  | | | | | ALPHA: (63) implies:
% 241.30/47.81  | | | | |   (64)  all_58_1 = e2
% 241.30/47.81  | | | | | 
% 241.30/47.81  | | | | | BETA: splitting (4) gives:
% 241.30/47.81  | | | | | 
% 241.30/47.81  | | | | | Case 1:
% 241.30/47.81  | | | | | | 
% 241.30/47.81  | | | | | |   (65)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1,
% 241.30/47.81  | | | | | |             e2) = e1)
% 241.30/47.81  | | | | | | 
% 241.30/47.81  | | | | | | REF_CLOSE: (3), (6), (9), (11), (16), (18), (20), (21), (24), (26),
% 241.30/47.81  | | | | | |            (28), (30), (41), (46), (51), (54), (61), (65) are
% 241.30/47.81  | | | | | |            inconsistent by sub-proof #538.
% 241.30/47.81  | | | | | | 
% 241.30/47.81  | | | | | Case 2:
% 241.30/47.81  | | | | | | 
% 241.30/47.82  | | | | | |   (66)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1,
% 241.30/47.82  | | | | | |             e0) = e1)
% 241.30/47.82  | | | | | | 
% 241.30/47.82  | | | | | | BETA: splitting (66) gives:
% 241.30/47.82  | | | | | | 
% 241.30/47.82  | | | | | | Case 1:
% 241.30/47.82  | | | | | | | 
% 241.30/47.82  | | | | | | |   (67)  all_58_8 = e1 & op(e1, e1) = e1
% 241.30/47.82  | | | | | | | 
% 241.30/47.82  | | | | | | | ALPHA: (67) implies:
% 241.30/47.82  | | | | | | |   (68)  op(e1, e1) = e1
% 241.30/47.82  | | | | | | | 
% 241.30/47.82  | | | | | | | REF_CLOSE: (41), (44), (46), (68) are inconsistent by sub-proof
% 241.30/47.82  | | | | | | |            #2220.
% 241.30/47.82  | | | | | | | 
% 241.30/47.82  | | | | | | Case 2:
% 241.30/47.82  | | | | | | | 
% 241.30/47.82  | | | | | | |   (69)  all_58_11 = e1 & op(e1, e0) = e1
% 241.30/47.82  | | | | | | | 
% 241.30/47.82  | | | | | | | ALPHA: (69) implies:
% 241.30/47.82  | | | | | | |   (70)  all_58_11 = e1
% 241.30/47.82  | | | | | | |   (71)  op(e1, e0) = e1
% 241.30/47.82  | | | | | | | 
% 241.30/47.82  | | | | | | | BETA: splitting (17) gives:
% 241.30/47.82  | | | | | | | 
% 241.30/47.82  | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | 
% 241.30/47.82  | | | | | | | |   (72)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 241.30/47.82  | | | | | | | |           op(e2, e1) = e0)
% 241.30/47.82  | | | | | | | | 
% 241.30/47.82  | | | | | | | | BETA: splitting (72) gives:
% 241.30/47.82  | | | | | | | | 
% 241.30/47.82  | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | |   (73)  all_58_4 = e0 & op(e3, e1) = e0
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | ALPHA: (73) implies:
% 241.30/47.82  | | | | | | | | |   (74)  all_58_4 = e0
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11),
% 241.30/47.82  | | | | | | | | |            (12), (15), (16), (17), (18), (19), (20), (21),
% 241.30/47.82  | | | | | | | | |            (22), (23), (24), (26), (27), (28), (29), (30),
% 241.30/47.82  | | | | | | | | |            (31), (32), (33), (35), (36), (37), (38), (39),
% 241.30/47.82  | | | | | | | | |            (40), (41), (42), (44), (46), (47), (48), (49),
% 241.30/47.82  | | | | | | | | |            (50), (51), (52), (53), (54), (55), (74) are
% 241.30/47.82  | | | | | | | | |            inconsistent by sub-proof #583.
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | |   (75)  all_58_5 = e0 & op(e2, e1) = e0
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | ALPHA: (75) implies:
% 241.30/47.82  | | | | | | | | |   (76)  op(e2, e1) = e0
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | BETA: splitting (53) gives:
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | |   (77)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 241.30/47.82  | | | | | | | | | |           op(e2, e2) = e1)
% 241.30/47.82  | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | BETA: splitting (77) gives:
% 241.30/47.82  | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | |   (78)  all_58_2 = e1 & op(e2, e3) = e1
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | REF_CLOSE: (30), (41), (55), (78) are inconsistent by
% 241.30/47.82  | | | | | | | | | | |            sub-proof #2229.
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | |   (79)  all_58_3 = e1 & op(e2, e2) = e1
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | ALPHA: (79) implies:
% 241.30/47.82  | | | | | | | | | | |   (80)  all_58_3 = e1
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (16), (18), (19), (21), (26), (31),
% 241.30/47.82  | | | | | | | | | | |            (35), (36), (41), (46), (47), (54), (80) are
% 241.30/47.82  | | | | | | | | | | |            inconsistent by sub-proof #1111.
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | |   (81)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1
% 241.30/47.82  | | | | | | | | | |           & op(e2, e0) = e1)
% 241.30/47.82  | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | BETA: splitting (81) gives:
% 241.30/47.82  | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | |   (82)  all_58_5 = e1 & op(e2, e1) = e1
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | ALPHA: (82) implies:
% 241.30/47.82  | | | | | | | | | | |   (83)  op(e2, e1) = e1
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | REF_CLOSE: (23), (41), (46), (76), (83) are inconsistent by
% 241.30/47.82  | | | | | | | | | | |            sub-proof #2165.
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | |   (84)  all_58_10 = e1 & op(e2, e0) = e1
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | ALPHA: (84) implies:
% 241.30/47.82  | | | | | | | | | | |   (85)  all_58_10 = e1
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | BETA: splitting (42) gives:
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | |   (86)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 241.30/47.82  | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 241.30/47.82  | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | BETA: splitting (86) gives:
% 241.30/47.82  | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | |   (87)  all_58_9 = e2 & op(e3, e0) = e2
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | ALPHA: (87) implies:
% 241.30/47.82  | | | | | | | | | | | | |   (88)  all_58_9 = e2
% 241.30/47.82  | | | | | | | | | | | | |   (89)  op(e3, e0) = e2
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | BETA: splitting (39) gives:
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | |   (90)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.30/47.82  | | | | | | | | | | | | | |           & op(e1, e2) = e2)
% 241.30/47.82  | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 241.30/47.82  | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | |   (91)  all_58_6 = e2 & op(e1, e3) = e2
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | ALPHA: (91) implies:
% 241.30/47.82  | | | | | | | | | | | | | | |   (92)  all_58_6 = e2
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (16), (20), (21), (24), (26), (28),
% 241.30/47.82  | | | | | | | | | | | | | | |            (29), (30), (32), (41), (44), (46), (51), (54),
% 241.30/47.82  | | | | | | | | | | | | | | |            (70), (92) are inconsistent by sub-proof #661.
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | |   (93)  all_58_7 = e2 & op(e1, e2) = e2
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 241.30/47.82  | | | | | | | | | | | | | | |   (94)  all_58_7 = e2
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | COMBINE_EQS: (7), (94) imply:
% 241.30/47.82  | | | | | | | | | | | | | | |   (95)  e2 = e0
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | SIMP: (95) implies:
% 241.30/47.82  | | | | | | | | | | | | | | |   (96)  e2 = e0
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | COMBINE_EQS: (88), (96) imply:
% 241.30/47.82  | | | | | | | | | | | | | | |   (97)  all_58_9 = e0
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | COMBINE_EQS: (64), (96) imply:
% 241.30/47.82  | | | | | | | | | | | | | | |   (98)  all_58_1 = e0
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (21), (26), (41), (47), (54), (97), (98)
% 241.30/47.82  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1097.
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | |   (99)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.30/47.82  | | | | | | | | | | | | | |           e2 & op(e1, e0) = e2)
% 241.30/47.82  | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 241.30/47.82  | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | |   (100)  all_58_8 = e2 & op(e1, e1) = e2
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 241.30/47.82  | | | | | | | | | | | | | | |   (101)  all_58_8 = e2
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | |   (102)  all_58_15 = e0 & op(e0, e0) = e0
% 241.30/47.82  | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | |   (103)  all_58_15 = e0
% 241.30/47.82  | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (15), (16), (18), (19), (21), (26),
% 241.30/47.82  | | | | | | | | | | | | | | | |            (30), (31), (35), (36), (38), (40), (41), (46),
% 241.30/47.82  | | | | | | | | | | | | | | | |            (47), (53), (54), (55), (70), (89), (103) are
% 241.30/47.82  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #650.
% 241.30/47.82  | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | |   (104)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.30/47.82  | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 241.30/47.82  | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 241.30/47.82  | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 241.30/47.82  | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.30/47.82  | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | |   (105)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.30/47.82  | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 241.30/47.82  | | | | | | | | | | | | | | | |              e0) = e0)
% 241.30/47.82  | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | |   (106)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.30/47.82  | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 241.30/47.82  | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | |   (107)  all_58_4 = e1 & op(e3, e1) = e1
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | | | |   (108)  all_58_4 = e1
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (16), (19), (21), (26), (31), (35),
% 241.30/47.82  | | | | | | | | | | | | | | | | | |            (36), (41), (46), (54), (108) are inconsistent by
% 241.30/47.82  | | | | | | | | | | | | | | | | | |            sub-proof #1468.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | |   (109)  all_58_5 = e1 & op(e2, e1) = e1
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | | | |   (110)  all_58_5 = e1
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (14), (15), (16), (18), (19), (21),
% 241.30/47.82  | | | | | | | | | | | | | | | | | |            (26), (31), (35), (36), (38), (40), (41), (42),
% 241.30/47.82  | | | | | | | | | | | | | | | | | |            (46), (54), (85), (88), (105), (110) are
% 241.30/47.82  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #516.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | |   (111)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.30/47.82  | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 241.30/47.82  | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | |   (112)  all_58_8 = e1 & op(e1, e1) = e1
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | | | |   (113)  all_58_8 = e1
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (26), (39), (54), (70), (113) are
% 241.30/47.82  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #988.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | |   (114)  all_58_14 = e1 & op(e0, e1) = e1
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | | | |   (115)  all_58_14 = e1
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | |   (116)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 241.30/47.82  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |   (117)  all_58_12 = e2 & op(e0, e3) = e2
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |   (118)  all_58_12 = e2
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | |   (119)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | |   (120)  all_58_12 = e3 & op(e0, e3) = e3
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (118), (120) are inconsistent by sub-proof
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | |            #2085.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | |   (121)  all_58_13 = e3 & op(e0, e2) = e3
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (34), (41), (121) are inconsistent by
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1919.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | |   (122)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | |   (123)  all_58_14 = e3 & op(e0, e1) = e3
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | |   (124)  all_58_14 = e3
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (115), (124) are inconsistent by sub-proof
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | |            #1844.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | |   (125)  all_58_15 = e3 & op(e0, e0) = e3
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | |   (126)  all_58_9 = e0 & op(e3, e0) = e0
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | |   (127)  all_58_9 = e0
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (14), (21), (24), (26), (28), (41),
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | |            (42), (46), (54), (70), (85), (118), (127) are
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #550.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | |   (128)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | |   (129)  all_58_10 = e0 & op(e2, e0) = e0
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (85), (129) are inconsistent by sub-proof
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | |            #995.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | |   (130)  all_58_11 = e0 & op(e1, e0) = e0
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | |   (131)  op(e1, e0) = e0
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (46), (71), (131) are inconsistent by
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |   (132)  all_58_13 = e2 & op(e0, e2) = e2
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (26), (39), (54), (61), (70),
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |            (101), (132) are inconsistent by sub-proof #559.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | |   (133)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 241.30/47.82  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |   (134)  all_58_14 = e2 & op(e0, e1) = e2
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |   (135)  all_58_14 = e2
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (115), (135) imply:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |   (136)  e2 = e1
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (136) imply:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |   (137)  all_58_8 = e1
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (26), (39), (54), (70), (137) are
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #988.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |   (138)  all_58_15 = e2 & op(e0, e0) = e2
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |   (139)  all_58_15 = e2
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (139) imply:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |   (140)  e3 = e2
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (140) imply:
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |   (141)  all_58_4 = e2
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (16), (20), (21), (23), (24), (26),
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |            (28), (30), (33), (37), (41), (44), (46), (51),
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |            (54), (115), (141) are inconsistent by sub-proof
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | |            #645.
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | |   (142)  all_58_11 = e2 & op(e1, e0) = e2
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 241.30/47.82  | | | | | | | | | | | | | | |   (143)  all_58_11 = e2
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | COMBINE_EQS: (70), (143) imply:
% 241.30/47.82  | | | | | | | | | | | | | | |   (144)  e2 = e1
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | COMBINE_EQS: (88), (144) imply:
% 241.30/47.82  | | | | | | | | | | | | | | |   (145)  all_58_9 = e1
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11),
% 241.30/47.82  | | | | | | | | | | | | | | |            (12), (15), (16), (17), (18), (19), (20), (21),
% 241.30/47.82  | | | | | | | | | | | | | | |            (22), (23), (24), (26), (27), (28), (29), (30),
% 241.30/47.82  | | | | | | | | | | | | | | |            (31), (32), (33), (35), (36), (37), (38), (39),
% 241.30/47.82  | | | | | | | | | | | | | | |            (40), (41), (42), (44), (46), (48), (49), (50),
% 241.30/47.82  | | | | | | | | | | | | | | |            (51), (52), (53), (54), (55), (145) are
% 241.30/47.82  | | | | | | | | | | | | | | |            inconsistent by sub-proof #640.
% 241.30/47.82  | | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | |   (146)  all_58_10 = e2 & op(e2, e0) = e2
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | REF_CLOSE: (54), (85), (146) are inconsistent by sub-proof
% 241.30/47.82  | | | | | | | | | | | | |            #1622.
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | |   (147)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 241.30/47.82  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.30/47.82  | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | BETA: splitting (147) gives:
% 241.30/47.82  | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | |   (148)  all_58_11 = e2 & op(e1, e0) = e2
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | REF_CLOSE: (54), (70), (148) are inconsistent by sub-proof
% 241.30/47.82  | | | | | | | | | | | | |            #1554.
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | |   (149)  all_58_15 = e2 & op(e0, e0) = e2
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | ALPHA: (149) implies:
% 241.30/47.82  | | | | | | | | | | | | |   (150)  all_58_15 = e2
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | COMBINE_EQS: (14), (150) imply:
% 241.30/47.82  | | | | | | | | | | | | |   (151)  e3 = e2
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (8), (16), (20), (21), (24), (26),
% 241.30/47.82  | | | | | | | | | | | | |            (28), (29), (30), (32), (41), (44), (46), (51),
% 241.30/47.82  | | | | | | | | | | | | |            (54), (70), (151) are inconsistent by sub-proof
% 241.30/47.82  | | | | | | | | | | | | |            #561.
% 241.30/47.82  | | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | End of split
% 241.30/47.82  | | | | | | | | 
% 241.30/47.82  | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | 
% 241.30/47.82  | | | | | | | |   (152)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 241.30/47.82  | | | | | | | |            op(e0, e1) = e0)
% 241.30/47.82  | | | | | | | | 
% 241.30/47.82  | | | | | | | | BETA: splitting (152) gives:
% 241.30/47.82  | | | | | | | | 
% 241.30/47.82  | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | |   (153)  all_58_8 = e0 & op(e1, e1) = e0
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | ALPHA: (153) implies:
% 241.30/47.82  | | | | | | | | |   (154)  all_58_8 = e0
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (16), (20), (21), (24), (26),
% 241.30/47.82  | | | | | | | | |            (28), (29), (30), (32), (39), (41), (44), (46),
% 241.30/47.82  | | | | | | | | |            (51), (54), (70), (154) are inconsistent by
% 241.30/47.82  | | | | | | | | |            sub-proof #523.
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | Case 2:
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | |   (155)  all_58_14 = e0 & op(e0, e1) = e0
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | ALPHA: (155) implies:
% 241.30/47.82  | | | | | | | | |   (156)  all_58_14 = e0
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | BETA: splitting (31) gives:
% 241.30/47.82  | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | Case 1:
% 241.30/47.82  | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | |   (157)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 241.30/47.82  | | | | | | | | | |            & op(e3, e2) = e0)
% 241.30/47.82  | | | | | | | | | | 
% 241.30/47.82  | | | | | | | | | | REF_CLOSE: (6), (21), (41), (46), (64), (157) are
% 241.30/47.83  | | | | | | | | | |            inconsistent by sub-proof #709.
% 241.30/47.83  | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | Case 2:
% 241.30/47.83  | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | |   (158)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 241.30/47.83  | | | | | | | | | |            & op(e3, e0) = e0)
% 241.30/47.83  | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | BETA: splitting (158) gives:
% 241.30/47.83  | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | Case 1:
% 241.30/47.83  | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | |   (159)  all_58_4 = e0 & op(e3, e1) = e0
% 241.30/47.83  | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | ALPHA: (159) implies:
% 241.30/47.83  | | | | | | | | | | |   (160)  all_58_4 = e0
% 241.30/47.83  | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11),
% 241.30/47.83  | | | | | | | | | | |            (12), (15), (16), (17), (18), (19), (20), (21),
% 241.30/47.83  | | | | | | | | | | |            (22), (23), (24), (26), (27), (28), (29), (30),
% 241.30/47.83  | | | | | | | | | | |            (31), (32), (33), (35), (36), (37), (38), (39),
% 241.30/47.83  | | | | | | | | | | |            (40), (41), (42), (44), (46), (47), (48), (49),
% 241.30/47.83  | | | | | | | | | | |            (50), (51), (52), (53), (54), (55), (160) are
% 241.30/47.83  | | | | | | | | | | |            inconsistent by sub-proof #583.
% 241.30/47.83  | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | Case 2:
% 241.30/47.83  | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | |   (161)  all_58_9 = e0 & op(e3, e0) = e0
% 241.30/47.83  | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | ALPHA: (161) implies:
% 241.30/47.83  | | | | | | | | | | |   (162)  all_58_9 = e0
% 241.30/47.83  | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | BETA: splitting (39) gives:
% 241.30/47.83  | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | Case 1:
% 241.30/47.83  | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | |   (163)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.30/47.83  | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.30/47.83  | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | BETA: splitting (163) gives:
% 241.30/47.83  | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | Case 1:
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | |   (164)  all_58_6 = e2 & op(e1, e3) = e2
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | ALPHA: (164) implies:
% 241.30/47.83  | | | | | | | | | | | | |   (165)  all_58_6 = e2
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (16), (20), (21), (24), (26), (28),
% 241.30/47.83  | | | | | | | | | | | | |            (29), (30), (32), (41), (44), (46), (51), (54),
% 241.30/47.83  | | | | | | | | | | | | |            (70), (165) are inconsistent by sub-proof #661.
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | Case 2:
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | |   (166)  all_58_7 = e2 & op(e1, e2) = e2
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | ALPHA: (166) implies:
% 241.30/47.83  | | | | | | | | | | | | |   (167)  all_58_7 = e2
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | COMBINE_EQS: (7), (167) imply:
% 241.30/47.83  | | | | | | | | | | | | |   (168)  e2 = e0
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | COMBINE_EQS: (64), (168) imply:
% 241.30/47.83  | | | | | | | | | | | | |   (169)  all_58_1 = e0
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | REF_CLOSE: (1), (6), (21), (26), (41), (47), (54), (162),
% 241.30/47.83  | | | | | | | | | | | | |            (169) are inconsistent by sub-proof #1097.
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | End of split
% 241.30/47.83  | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | Case 2:
% 241.30/47.83  | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | |   (170)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.30/47.83  | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.30/47.83  | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | BETA: splitting (170) gives:
% 241.30/47.83  | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | Case 1:
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | |   (171)  all_58_8 = e2 & op(e1, e1) = e2
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | ALPHA: (171) implies:
% 241.30/47.83  | | | | | | | | | | | | |   (172)  all_58_8 = e2
% 241.30/47.83  | | | | | | | | | | | | |   (173)  op(e1, e1) = e2
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | BETA: splitting (12) gives:
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | Case 1:
% 241.30/47.83  | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | |   (174)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.30/47.83  | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 241.30/47.83  | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 241.30/47.83  | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | | Case 1:
% 241.30/47.83  | | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | | |   (175)  all_58_4 = e1 & op(e3, e1) = e1
% 241.30/47.83  | | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 241.30/47.83  | | | | | | | | | | | | | | |   (176)  all_58_4 = e1
% 241.30/47.83  | | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (16), (19), (21), (26), (31), (35),
% 241.30/47.83  | | | | | | | | | | | | | | |            (36), (41), (46), (54), (176) are inconsistent by
% 241.30/47.83  | | | | | | | | | | | | | | |            sub-proof #1468.
% 241.30/47.83  | | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | | Case 2:
% 241.30/47.83  | | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | | |   (177)  all_58_5 = e1 & op(e2, e1) = e1
% 241.30/47.83  | | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 241.30/47.83  | | | | | | | | | | | | | | |   (178)  all_58_5 = e1
% 241.30/47.83  | | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (14), (16), (18),
% 241.30/47.83  | | | | | | | | | | | | | | |            (20), (21), (24), (26), (28), (29), (30), (32),
% 241.30/47.83  | | | | | | | | | | | | | | |            (39), (40), (41), (42), (44), (46), (47), (51),
% 241.30/47.83  | | | | | | | | | | | | | | |            (54), (64), (70), (162), (172), (173), (178) are
% 241.30/47.83  | | | | | | | | | | | | | | |            inconsistent by sub-proof #553.
% 241.30/47.83  | | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | | End of split
% 241.30/47.83  | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | Case 2:
% 241.30/47.83  | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | |   (179)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.30/47.83  | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 241.30/47.83  | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (26), (39), (46), (54), (70),
% 241.30/47.83  | | | | | | | | | | | | | |            (156), (179) are inconsistent by sub-proof #549.
% 241.30/47.83  | | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | End of split
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | Case 2:
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | |   (180)  all_58_11 = e2 & op(e1, e0) = e2
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | ALPHA: (180) implies:
% 241.30/47.83  | | | | | | | | | | | | |   (181)  all_58_11 = e2
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | | REF_CLOSE: (54), (70), (181) are inconsistent by sub-proof
% 241.30/47.83  | | | | | | | | | | | | |            #1020.
% 241.30/47.83  | | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | | End of split
% 241.30/47.83  | | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | | End of split
% 241.30/47.83  | | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | | End of split
% 241.30/47.83  | | | | | | | | | | 
% 241.30/47.83  | | | | | | | | | End of split
% 241.30/47.83  | | | | | | | | | 
% 241.30/47.83  | | | | | | | | End of split
% 241.30/47.83  | | | | | | | | 
% 241.30/47.83  | | | | | | | End of split
% 241.30/47.83  | | | | | | | 
% 241.30/47.83  | | | | | | End of split
% 241.30/47.83  | | | | | | 
% 241.30/47.83  | | | | | End of split
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | Case 2:
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | |   (182)  all_58_3 = e2 & op(e2, e2) = e2
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | | REF_CLOSE: (18), (26), (182) are inconsistent by sub-proof #1458.
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | End of split
% 241.30/47.83  | | | | 
% 241.30/47.83  | | | Case 2:
% 241.30/47.83  | | | | 
% 241.30/47.83  | | | |   (183)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0,
% 241.30/47.83  | | | |              e2) = e2)
% 241.30/47.83  | | | | 
% 241.30/47.83  | | | | BETA: splitting (183) gives:
% 241.30/47.83  | | | | 
% 241.30/47.83  | | | | Case 1:
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | |   (184)  all_58_7 = e2 & op(e1, e2) = e2
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | | ALPHA: (184) implies:
% 241.30/47.83  | | | | |   (185)  all_58_7 = e2
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | | REF_CLOSE: (6), (7), (185) are inconsistent by sub-proof #1587.
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | Case 2:
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | |   (186)  all_58_13 = e2 & op(e0, e2) = e2
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | | ALPHA: (186) implies:
% 241.30/47.83  | | | | |   (187)  all_58_13 = e2
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | | REF_CLOSE: (54), (61), (187) are inconsistent by sub-proof #1544.
% 241.30/47.83  | | | | | 
% 241.30/47.83  | | | | End of split
% 241.30/47.83  | | | | 
% 241.30/47.83  | | | End of split
% 241.30/47.83  | | | 
% 241.30/47.83  | | End of split
% 241.30/47.83  | | 
% 241.30/47.83  | End of split
% 241.30/47.83  | 
% 241.30/47.83  End of proof
% 241.30/47.83  
% 241.30/47.83  Sub-proof #508 shows that the following formulas are inconsistent:
% 241.30/47.83  ----------------------------------------------------------------
% 241.30/47.83    (1)  op(e2, e3) = e0
% 241.30/47.83    (2)   ~ (e2 = e0)
% 241.30/47.83    (3)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.30/47.83           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.30/47.83             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.30/47.83           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.30/47.83             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.30/47.83           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.30/47.83           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 241.30/47.83    (4)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 241.30/47.83           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 241.30/47.83           all_42_1 & $i(all_42_1))
% 241.30/47.83    (5)  op(e2, e3) = all_52_1
% 241.30/47.83    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.83    (7)   ~ (all_52_1 = e3)
% 241.30/47.83    (8)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.30/47.83           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 241.30/47.83           & $i(all_8_1))
% 241.30/47.83    (9)  all_56_1 = e1
% 241.30/47.83  
% 241.30/47.83  Begin of proof
% 241.30/47.83  | 
% 241.30/47.83  | BETA: splitting (3) gives:
% 241.30/47.83  | 
% 241.30/47.83  | Case 1:
% 241.30/47.83  | | 
% 241.30/47.83  | |   (10)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.30/47.83  | |           e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3
% 241.30/47.83  | |         & op(e2, e3) = e3
% 241.30/47.83  | | 
% 241.30/47.83  | | ALPHA: (10) implies:
% 241.30/47.83  | |   (11)  op(e2, e3) = e3
% 241.30/47.83  | | 
% 241.30/47.83  | | REF_CLOSE: (5), (6), (7), (11) are inconsistent by sub-proof #2337.
% 241.30/47.83  | | 
% 241.30/47.83  | Case 2:
% 241.30/47.83  | | 
% 241.30/47.83  | |   (12)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 241.30/47.83  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 241.30/47.83  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.30/47.83  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.30/47.83  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 241.30/47.83  | | 
% 241.30/47.83  | | BETA: splitting (12) gives:
% 241.30/47.83  | | 
% 241.30/47.83  | | Case 1:
% 241.30/47.83  | | | 
% 241.30/47.83  | | |   (13)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 241.30/47.83  | | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 241.30/47.83  | | |         e2 & op(e2, e3) = e2
% 241.30/47.83  | | | 
% 241.30/47.83  | | | ALPHA: (13) implies:
% 241.30/47.83  | | |   (14)  op(e2, e3) = e2
% 241.30/47.83  | | | 
% 241.30/47.83  | | | REF_CLOSE: (1), (2), (4), (6), (8), (14) are inconsistent by sub-proof
% 241.30/47.83  | | |            #733.
% 241.30/47.83  | | | 
% 241.30/47.83  | | Case 2:
% 241.30/47.83  | | | 
% 241.30/47.83  | | |   (15)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.30/47.83  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.30/47.83  | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 241.30/47.83  | | | 
% 241.30/47.83  | | | ALPHA: (15) implies:
% 241.30/47.83  | | |   (16)   ~ (all_56_1 = e1)
% 241.30/47.83  | | | 
% 241.30/47.83  | | | REDUCE: (9), (16) imply:
% 241.30/47.83  | | |   (17)  $false
% 241.30/47.83  | | | 
% 241.30/47.83  | | | CLOSE: (17) is inconsistent.
% 241.30/47.83  | | | 
% 241.30/47.83  | | End of split
% 241.30/47.83  | | 
% 241.30/47.83  | End of split
% 241.30/47.83  | 
% 241.30/47.83  End of proof
% 241.30/47.83  
% 241.30/47.83  Sub-proof #509 shows that the following formulas are inconsistent:
% 241.30/47.83  ----------------------------------------------------------------
% 241.30/47.83    (1)   ~ (all_52_9 = all_6_2)
% 241.30/47.83    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.30/47.83           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.30/47.83             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.30/47.83           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.30/47.83             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.30/47.83           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.30/47.83           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.30/47.83           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.30/47.83           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.30/47.83           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.30/47.83           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.30/47.83             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.30/47.83           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.30/47.83           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 241.30/47.83           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.30/47.83           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.30/47.83           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.30/47.83           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.30/47.83             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.30/47.83           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.30/47.83           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 241.30/47.83           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.30/47.83           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.30/47.83           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.30/47.83           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.30/47.83             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.30/47.83           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.30/47.83           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.30/47.83    (3)  all_58_3 = e3
% 241.30/47.83    (4)  all_54_10 = all_6_2
% 241.30/47.83    (5)   ~ (all_6_2 = e3)
% 241.30/47.83    (6)  op(e2, e1) = all_52_9
% 241.30/47.83    (7)  all_58_4 = e0 & op(e3, e1) = e0
% 241.30/47.83    (8)   ~ (all_6_2 = e0)
% 241.30/47.83    (9)  op(e2, e3) = all_52_1
% 241.30/47.83    (10)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 241.30/47.83    (11)  all_56_31 = e3
% 241.30/47.83    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.83    (13)  all_56_11 = e3
% 241.30/47.83    (14)  all_56_21 = all_6_2
% 241.30/47.83    (15)  all_58_4 = e3
% 241.30/47.83    (16)  op(e2, e0) = all_52_13
% 241.30/47.83    (17)   ~ (all_52_1 = e3)
% 241.30/47.83    (18)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.30/47.83          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.30/47.83    (19)  all_56_1 = e1
% 241.30/47.83    (20)   ~ (all_52_1 = e1)
% 241.30/47.83  
% 241.30/47.83  Begin of proof
% 241.30/47.83  | 
% 241.30/47.83  | ALPHA: (7) implies:
% 241.30/47.83  |   (21)  all_58_4 = e0
% 241.30/47.83  | 
% 241.30/47.83  | COMBINE_EQS: (15), (21) imply:
% 241.30/47.83  |   (22)  e3 = e0
% 241.30/47.83  | 
% 241.30/47.83  | COMBINE_EQS: (11), (22) imply:
% 241.30/47.83  |   (23)  all_56_31 = e0
% 241.30/47.83  | 
% 241.30/47.83  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14),
% 241.30/47.83  |            (16), (17), (18), (19), (20), (23) are inconsistent by sub-proof
% 241.30/47.83  |            #742.
% 241.30/47.83  | 
% 241.30/47.83  End of proof
% 241.30/47.83  
% 241.30/47.83  Sub-proof #510 shows that the following formulas are inconsistent:
% 241.30/47.83  ----------------------------------------------------------------
% 241.30/47.83    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.30/47.83    (2)  all_58_6 = e3
% 241.30/47.83    (3)   ~ (e2 = e0)
% 241.30/47.83    (4)  all_58_7 = e0
% 241.30/47.83    (5)  all_58_11 = e1
% 241.30/47.83    (6)   ~ (e3 = e2)
% 241.30/47.83    (7)  all_58_14 = e0
% 241.30/47.83    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.30/47.83         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.30/47.83    (9)   ~ (e1 = e0)
% 241.30/47.83    (10)   ~ (e2 = e1)
% 241.30/47.83  
% 241.30/47.83  Begin of proof
% 241.30/47.83  | 
% 241.30/47.83  | BETA: splitting (1) gives:
% 241.30/47.83  | 
% 241.30/47.83  | Case 1:
% 241.30/47.83  | | 
% 241.30/47.83  | |   (11)  all_58_8 = e1 & op(e1, e1) = e1
% 241.30/47.83  | | 
% 241.30/47.83  | | ALPHA: (11) implies:
% 241.30/47.83  | |   (12)  all_58_8 = e1
% 241.30/47.83  | | 
% 241.30/47.83  | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (12) are inconsistent by
% 241.30/47.83  | |            sub-proof #988.
% 241.30/47.83  | | 
% 241.30/47.83  | Case 2:
% 241.30/47.83  | | 
% 241.30/47.83  | |   (13)  all_58_14 = e1 & op(e0, e1) = e1
% 241.30/47.83  | | 
% 241.30/47.83  | | ALPHA: (13) implies:
% 241.30/47.83  | |   (14)  all_58_14 = e1
% 241.30/47.83  | | 
% 241.30/47.83  | | REF_CLOSE: (7), (9), (14) are inconsistent by sub-proof #1033.
% 241.30/47.83  | | 
% 241.30/47.83  | End of split
% 241.30/47.83  | 
% 241.30/47.83  End of proof
% 241.30/47.83  
% 241.30/47.83  Sub-proof #511 shows that the following formulas are inconsistent:
% 241.30/47.83  ----------------------------------------------------------------
% 241.30/47.83    (1)  op(e2, e3) = e0
% 241.30/47.83    (2)   ~ (e2 = e0)
% 241.30/47.83    (3)  all_58_3 = e3
% 241.30/47.83    (4)   ~ (e3 = e2)
% 241.30/47.83    (5)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 241.30/47.83           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 241.30/47.83           all_42_1 & $i(all_42_1))
% 241.30/47.83    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 241.30/47.83    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.83    (8)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.30/47.83           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 241.30/47.83           & $i(all_8_1))
% 241.30/47.83  
% 241.30/47.83  Begin of proof
% 241.30/47.83  | 
% 241.30/47.83  | BETA: splitting (6) gives:
% 241.30/47.83  | 
% 241.30/47.83  | Case 1:
% 241.30/47.83  | | 
% 241.30/47.83  | |   (9)  all_58_2 = e2 & op(e2, e3) = e2
% 241.30/47.83  | | 
% 241.30/47.83  | | ALPHA: (9) implies:
% 241.30/47.83  | |   (10)  op(e2, e3) = e2
% 241.30/47.83  | | 
% 241.30/47.83  | | REF_CLOSE: (1), (2), (5), (7), (8), (10) are inconsistent by sub-proof #733.
% 241.30/47.83  | | 
% 241.30/47.83  | Case 2:
% 241.30/47.83  | | 
% 241.30/47.83  | |   (11)  all_58_3 = e2 & op(e2, e2) = e2
% 241.30/47.83  | | 
% 241.30/47.83  | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #1458.
% 241.30/47.83  | | 
% 241.30/47.83  | End of split
% 241.30/47.83  | 
% 241.30/47.83  End of proof
% 241.30/47.83  
% 241.30/47.83  Sub-proof #512 shows that the following formulas are inconsistent:
% 241.30/47.83  ----------------------------------------------------------------
% 241.30/47.83    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.30/47.83         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.30/47.83    (2)   ~ (e3 = e0)
% 241.30/47.83    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.30/47.83         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.30/47.83    (4)  all_58_6 = e3
% 241.30/47.83    (5)   ~ (e2 = e0)
% 241.30/47.84    (6)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 241.30/47.84         (all_58_11 = e0 & op(e1, e0) = e0)
% 241.30/47.84    (7)  op(e1, e2) = all_52_6
% 241.30/47.84    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.30/47.84         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.30/47.84    (9)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.30/47.84         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.30/47.84    (10)  all_58_1 = e0
% 241.30/47.84    (11)  all_58_8 = e0
% 241.30/47.84    (12)  all_58_15 = e3
% 241.30/47.84    (13)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.30/47.84          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.30/47.84    (14)   ~ (e3 = e1)
% 241.30/47.84    (15)  all_58_3 = e3
% 241.30/47.84    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.30/47.84          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.30/47.84    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.30/47.84          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.30/47.84    (18)  op(e3, e3) = e1
% 241.30/47.84    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.30/47.84          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.30/47.84    (20)   ~ (e3 = e2)
% 241.30/47.84    (21)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.30/47.84          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.30/47.84    (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.30/47.84          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.30/47.84    (23)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.30/47.84          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.30/47.84    (24)  op(e2, e3) = all_52_1
% 241.30/47.84    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.30/47.84          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.30/47.84    (26)   ~ (all_52_6 = e3)
% 241.30/47.84    (27)   ~ (all_52_4 = e3)
% 241.30/47.84    (28)  op(e3, e2) = all_52_4
% 241.30/47.84    (29)  all_58_14 = e0
% 241.30/47.84    (30)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.30/47.84          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.30/47.84    (31)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.30/47.84          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.30/47.84    (32)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.84    (33)  op(e1, e1) = e0
% 241.30/47.84    (34)   ~ (e1 = e0)
% 241.30/47.84    (35)  all_58_13 = e1
% 241.30/47.84    (36)  all_58_4 = e3
% 241.30/47.84    (37)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.30/47.84          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.30/47.84    (38)  op(e2, e0) = all_52_13
% 241.30/47.84    (39)  all_58_9 = e2
% 241.30/47.84    (40)   ~ (all_52_1 = e3)
% 241.30/47.84    (41)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.30/47.84          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.30/47.84            e2)
% 241.30/47.84    (42)   ~ (e2 = e1)
% 241.30/47.84  
% 241.30/47.84  Begin of proof
% 241.30/47.84  | 
% 241.30/47.84  | BETA: splitting (41) gives:
% 241.30/47.84  | 
% 241.30/47.84  | Case 1:
% 241.30/47.84  | | 
% 241.30/47.84  | |   (43)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 241.30/47.84  | |           e2)
% 241.30/47.84  | | 
% 241.30/47.84  | | BETA: splitting (43) gives:
% 241.30/47.84  | | 
% 241.30/47.84  | | Case 1:
% 241.30/47.84  | | | 
% 241.30/47.84  | | |   (44)  all_58_12 = e2 & op(e0, e3) = e2
% 241.30/47.84  | | | 
% 241.30/47.84  | | | ALPHA: (44) implies:
% 241.30/47.84  | | |   (45)  all_58_12 = e2
% 241.30/47.84  | | | 
% 241.30/47.84  | | | BETA: splitting (6) gives:
% 241.30/47.84  | | | 
% 241.30/47.84  | | | Case 1:
% 241.30/47.84  | | | | 
% 241.30/47.84  | | | |   (46)  all_58_9 = e0 & op(e3, e0) = e0
% 241.30/47.84  | | | | 
% 241.30/47.84  | | | | ALPHA: (46) implies:
% 241.30/47.84  | | | |   (47)  all_58_9 = e0
% 241.30/47.84  | | | | 
% 241.30/47.84  | | | | REF_CLOSE: (1), (5), (10), (18), (20), (32), (36), (42), (47) are
% 241.30/47.84  | | | |            inconsistent by sub-proof #1097.
% 241.30/47.84  | | | | 
% 241.30/47.84  | | | Case 2:
% 241.30/47.84  | | | | 
% 241.30/47.84  | | | |   (48)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 241.30/47.84  | | | |             e0) = e0)
% 241.30/47.84  | | | | 
% 241.30/47.84  | | | | BETA: splitting (48) gives:
% 241.30/47.84  | | | | 
% 241.30/47.84  | | | | Case 1:
% 241.30/47.84  | | | | | 
% 241.30/47.84  | | | | |   (49)  all_58_10 = e0 & op(e2, e0) = e0
% 241.30/47.84  | | | | | 
% 241.30/47.84  | | | | | ALPHA: (49) implies:
% 241.30/47.84  | | | | |   (50)  op(e2, e0) = e0
% 241.30/47.84  | | | | | 
% 241.30/47.84  | | | | | BETA: splitting (8) gives:
% 241.30/47.84  | | | | | 
% 241.30/47.84  | | | | | Case 1:
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | |   (51)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 241.30/47.84  | | | | | |             e0) = e1)
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | | BETA: splitting (51) gives:
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | | Case 1:
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | |   (52)  all_58_9 = e1 & op(e3, e0) = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | ALPHA: (52) implies:
% 241.30/47.84  | | | | | | |   (53)  all_58_9 = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (14), (16), (18), (19), (20), (22),
% 241.30/47.84  | | | | | | |            (25), (27), (28), (32), (34), (42), (45), (53) are
% 241.30/47.84  | | | | | | |            inconsistent by sub-proof #1147.
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | Case 2:
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | |   (54)  all_58_10 = e1 & op(e2, e0) = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | ALPHA: (54) implies:
% 241.30/47.84  | | | | | | |   (55)  op(e2, e0) = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | REF_CLOSE: (32), (34), (38), (50), (55) are inconsistent by
% 241.30/47.84  | | | | | | |            sub-proof #1778.
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | End of split
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | Case 2:
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | |   (56)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 241.30/47.84  | | | | | |           op(e0, e0) = e1)
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | | BETA: splitting (56) gives:
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | | Case 1:
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | |   (57)  all_58_11 = e1 & op(e1, e0) = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | ALPHA: (57) implies:
% 241.30/47.84  | | | | | | |   (58)  all_58_11 = e1
% 241.30/47.84  | | | | | | |   (59)  op(e1, e0) = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (14), (16),
% 241.30/47.84  | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 241.30/47.84  | | | | | | |            (26), (27), (28), (29), (30), (32), (33), (34), (36),
% 241.30/47.84  | | | | | | |            (37), (39), (40), (42), (45), (58), (59) are
% 241.30/47.84  | | | | | | |            inconsistent by sub-proof #514.
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | Case 2:
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | |   (60)  all_58_15 = e1 & op(e0, e0) = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | REF_CLOSE: (1), (2), (5), (12), (14), (16), (18), (20), (25),
% 241.30/47.84  | | | | | | |            (27), (28), (32), (34), (36), (42), (60) are
% 241.30/47.84  | | | | | | |            inconsistent by sub-proof #513.
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | End of split
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | End of split
% 241.30/47.84  | | | | | 
% 241.30/47.84  | | | | Case 2:
% 241.30/47.84  | | | | | 
% 241.30/47.84  | | | | |   (61)  all_58_11 = e0 & op(e1, e0) = e0
% 241.30/47.84  | | | | | 
% 241.30/47.84  | | | | | ALPHA: (61) implies:
% 241.30/47.84  | | | | |   (62)  all_58_11 = e0
% 241.30/47.84  | | | | | 
% 241.30/47.84  | | | | | BETA: splitting (8) gives:
% 241.30/47.84  | | | | | 
% 241.30/47.84  | | | | | Case 1:
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | |   (63)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 241.30/47.84  | | | | | |             e0) = e1)
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | | BETA: splitting (63) gives:
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | | Case 1:
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | |   (64)  all_58_9 = e1 & op(e3, e0) = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | ALPHA: (64) implies:
% 241.30/47.84  | | | | | | |   (65)  all_58_9 = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (14), (16), (18), (19), (20), (22),
% 241.30/47.84  | | | | | | |            (25), (27), (28), (32), (34), (42), (45), (65) are
% 241.30/47.84  | | | | | | |            inconsistent by sub-proof #1147.
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | Case 2:
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | |   (66)  all_58_10 = e1 & op(e2, e0) = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | ALPHA: (66) implies:
% 241.30/47.84  | | | | | | |   (67)  all_58_10 = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | BETA: splitting (3) gives:
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | Case 1:
% 241.30/47.84  | | | | | | | | 
% 241.30/47.84  | | | | | | | |   (68)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 241.30/47.84  | | | | | | | |           op(e1, e2) = e1)
% 241.30/47.84  | | | | | | | | 
% 241.30/47.84  | | | | | | | | BETA: splitting (68) gives:
% 241.30/47.84  | | | | | | | | 
% 241.30/47.84  | | | | | | | | Case 1:
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | |   (69)  all_58_6 = e1 & op(e1, e3) = e1
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | | ALPHA: (69) implies:
% 241.30/47.84  | | | | | | | | |   (70)  all_58_6 = e1
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | | REF_CLOSE: (2), (5), (14), (17), (18), (19), (20), (22), (24),
% 241.30/47.84  | | | | | | | | |            (32), (34), (40), (42), (70) are inconsistent by
% 241.30/47.84  | | | | | | | | |            sub-proof #1161.
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | Case 2:
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | |   (71)  all_58_7 = e1 & op(e1, e2) = e1
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | | ALPHA: (71) implies:
% 241.30/47.84  | | | | | | | | |   (72)  all_58_7 = e1
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (9), (13), (14), (15), (16),
% 241.30/47.84  | | | | | | | | |            (18), (20), (25), (27), (28), (29), (30), (31),
% 241.30/47.84  | | | | | | | | |            (32), (34), (42), (62), (67), (72) are inconsistent
% 241.30/47.84  | | | | | | | | |            by sub-proof #540.
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | End of split
% 241.30/47.84  | | | | | | | | 
% 241.30/47.84  | | | | | | | Case 2:
% 241.30/47.84  | | | | | | | | 
% 241.30/47.84  | | | | | | | |   (73)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 241.30/47.84  | | | | | | | |           op(e1, e0) = e1)
% 241.30/47.84  | | | | | | | | 
% 241.30/47.84  | | | | | | | | BETA: splitting (73) gives:
% 241.30/47.84  | | | | | | | | 
% 241.30/47.84  | | | | | | | | Case 1:
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | |   (74)  all_58_8 = e1 & op(e1, e1) = e1
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | | ALPHA: (74) implies:
% 241.30/47.84  | | | | | | | | |   (75)  op(e1, e1) = e1
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | | REF_CLOSE: (32), (33), (34), (75) are inconsistent by
% 241.30/47.84  | | | | | | | | |            sub-proof #2220.
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | Case 2:
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | |   (76)  all_58_11 = e1 & op(e1, e0) = e1
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | | ALPHA: (76) implies:
% 241.30/47.84  | | | | | | | | |   (77)  all_58_11 = e1
% 241.30/47.84  | | | | | | | | |   (78)  op(e1, e0) = e1
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (14),
% 241.30/47.84  | | | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23),
% 241.30/47.84  | | | | | | | | |            (24), (25), (26), (27), (28), (29), (30), (32),
% 241.30/47.84  | | | | | | | | |            (33), (34), (36), (37), (39), (40), (42), (45),
% 241.30/47.84  | | | | | | | | |            (77), (78) are inconsistent by sub-proof #514.
% 241.30/47.84  | | | | | | | | | 
% 241.30/47.84  | | | | | | | | End of split
% 241.30/47.84  | | | | | | | | 
% 241.30/47.84  | | | | | | | End of split
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | End of split
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | Case 2:
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | |   (79)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 241.30/47.84  | | | | | |           op(e0, e0) = e1)
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | | BETA: splitting (79) gives:
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | | Case 1:
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | |   (80)  all_58_11 = e1 & op(e1, e0) = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | ALPHA: (80) implies:
% 241.30/47.84  | | | | | | |   (81)  all_58_11 = e1
% 241.30/47.84  | | | | | | |   (82)  op(e1, e0) = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (14), (16),
% 241.30/47.84  | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 241.30/47.84  | | | | | | |            (26), (27), (28), (29), (30), (32), (33), (34), (36),
% 241.30/47.84  | | | | | | |            (37), (39), (40), (42), (45), (81), (82) are
% 241.30/47.84  | | | | | | |            inconsistent by sub-proof #514.
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | Case 2:
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | |   (83)  all_58_15 = e1 & op(e0, e0) = e1
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | | REF_CLOSE: (1), (2), (5), (12), (14), (16), (18), (20), (25),
% 241.30/47.84  | | | | | | |            (27), (28), (32), (34), (36), (42), (83) are
% 241.30/47.84  | | | | | | |            inconsistent by sub-proof #513.
% 241.30/47.84  | | | | | | | 
% 241.30/47.84  | | | | | | End of split
% 241.30/47.84  | | | | | | 
% 241.30/47.84  | | | | | End of split
% 241.30/47.84  | | | | | 
% 241.30/47.84  | | | | End of split
% 241.30/47.84  | | | | 
% 241.30/47.84  | | | End of split
% 241.30/47.84  | | | 
% 241.30/47.84  | | Case 2:
% 241.30/47.84  | | | 
% 241.30/47.84  | | |   (84)  all_58_13 = e2 & op(e0, e2) = e2
% 241.30/47.84  | | | 
% 241.30/47.84  | | | ALPHA: (84) implies:
% 241.30/47.84  | | |   (85)  all_58_13 = e2
% 241.30/47.84  | | | 
% 241.30/47.84  | | | COMBINE_EQS: (35), (85) imply:
% 241.30/47.84  | | |   (86)  e2 = e1
% 241.30/47.84  | | | 
% 241.30/47.84  | | | SIMP: (86) implies:
% 241.30/47.84  | | |   (87)  e2 = e1
% 241.30/47.84  | | | 
% 241.30/47.84  | | | COMBINE_EQS: (39), (87) imply:
% 241.30/47.84  | | |   (88)  all_58_9 = e1
% 241.30/47.84  | | | 
% 241.30/47.84  | | | REF_CLOSE: (1), (5), (10), (18), (20), (32), (36), (42), (88) are
% 241.30/47.84  | | |            inconsistent by sub-proof #1338.
% 241.30/47.84  | | | 
% 241.30/47.84  | | End of split
% 241.30/47.84  | | 
% 241.30/47.84  | Case 2:
% 241.30/47.84  | | 
% 241.30/47.84  | |   (89)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.30/47.84  | |           e2)
% 241.30/47.84  | | 
% 241.30/47.84  | | BETA: splitting (89) gives:
% 241.30/47.84  | | 
% 241.30/47.84  | | Case 1:
% 241.30/47.84  | | | 
% 241.30/47.84  | | |   (90)  all_58_14 = e2 & op(e0, e1) = e2
% 241.30/47.84  | | | 
% 241.30/47.84  | | | REF_CLOSE: (1), (5), (10), (18), (20), (29), (32), (36), (39), (42), (90)
% 241.30/47.84  | | |            are inconsistent by sub-proof #515.
% 241.30/47.84  | | | 
% 241.30/47.84  | | Case 2:
% 241.30/47.84  | | | 
% 241.30/47.84  | | |   (91)  all_58_15 = e2 & op(e0, e0) = e2
% 241.30/47.84  | | | 
% 241.30/47.84  | | | REF_CLOSE: (12), (20), (91) are inconsistent by sub-proof #1231.
% 241.30/47.84  | | | 
% 241.30/47.84  | | End of split
% 241.30/47.84  | | 
% 241.30/47.84  | End of split
% 241.30/47.84  | 
% 241.30/47.84  End of proof
% 241.30/47.84  
% 241.30/47.84  Sub-proof #513 shows that the following formulas are inconsistent:
% 241.30/47.84  ----------------------------------------------------------------
% 241.30/47.84    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.30/47.84         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.30/47.84    (2)   ~ (e3 = e0)
% 241.30/47.84    (3)   ~ (e2 = e0)
% 241.30/47.84    (4)  all_58_15 = e3
% 241.30/47.84    (5)   ~ (e3 = e1)
% 241.30/47.84    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.30/47.84         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.30/47.84    (7)  op(e3, e3) = e1
% 241.30/47.84    (8)   ~ (e3 = e2)
% 241.30/47.84    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.30/47.84         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.30/47.84    (10)   ~ (all_52_4 = e3)
% 241.30/47.84    (11)  op(e3, e2) = all_52_4
% 241.30/47.84    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.84    (13)   ~ (e1 = e0)
% 241.30/47.84    (14)  all_58_4 = e3
% 241.30/47.84    (15)  all_58_15 = e1 & op(e0, e0) = e1
% 241.30/47.84    (16)   ~ (e2 = e1)
% 241.30/47.84  
% 241.30/47.84  Begin of proof
% 241.30/47.84  | 
% 241.30/47.84  | ALPHA: (15) implies:
% 241.30/47.84  |   (17)  all_58_15 = e1
% 241.30/47.84  | 
% 241.30/47.84  | COMBINE_EQS: (4), (17) imply:
% 241.30/47.84  |   (18)  e3 = e1
% 241.30/47.84  | 
% 241.30/47.84  | COMBINE_EQS: (14), (18) imply:
% 241.30/47.84  |   (19)  all_58_4 = e1
% 241.30/47.84  | 
% 241.30/47.84  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.30/47.84  |            (16), (19) are inconsistent by sub-proof #1468.
% 241.30/47.84  | 
% 241.30/47.84  End of proof
% 241.30/47.84  
% 241.30/47.84  Sub-proof #514 shows that the following formulas are inconsistent:
% 241.30/47.84  ----------------------------------------------------------------
% 241.30/47.84    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.30/47.84         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.30/47.84    (2)   ~ (e3 = e0)
% 241.30/47.84    (3)  all_58_6 = e3
% 241.30/47.84    (4)   ~ (e2 = e0)
% 241.30/47.84    (5)  op(e1, e2) = all_52_6
% 241.30/47.84    (6)  all_58_12 = e2
% 241.30/47.84    (7)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.30/47.84         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.30/47.85    (8)  all_58_11 = e1
% 241.30/47.85    (9)  all_58_1 = e0
% 241.30/47.85    (10)  all_58_8 = e0
% 241.30/47.85    (11)   ~ (e3 = e1)
% 241.30/47.85    (12)  op(e1, e0) = e1
% 241.30/47.85    (13)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.30/47.85          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.30/47.85    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.30/47.85          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.30/47.85    (15)  op(e3, e3) = e1
% 241.30/47.85    (16)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.30/47.85          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.30/47.85    (17)   ~ (e3 = e2)
% 241.30/47.85    (18)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.30/47.85          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.30/47.85    (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.30/47.85          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.30/47.85    (20)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.30/47.85          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.30/47.85    (21)  op(e2, e3) = all_52_1
% 241.30/47.85    (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.30/47.85          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.30/47.85    (23)   ~ (all_52_6 = e3)
% 241.30/47.85    (24)   ~ (all_52_4 = e3)
% 241.30/47.85    (25)  op(e3, e2) = all_52_4
% 241.30/47.85    (26)  all_58_14 = e0
% 241.30/47.85    (27)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.30/47.85          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.30/47.85    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.85    (29)  op(e1, e1) = e0
% 241.30/47.85    (30)   ~ (e1 = e0)
% 241.30/47.85    (31)  all_58_4 = e3
% 241.30/47.85    (32)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.30/47.85          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.30/47.85    (33)  all_58_9 = e2
% 241.30/47.85    (34)   ~ (all_52_1 = e3)
% 241.30/47.85    (35)   ~ (e2 = e1)
% 241.30/47.85  
% 241.30/47.85  Begin of proof
% 241.30/47.85  | 
% 241.30/47.85  | BETA: splitting (7) gives:
% 241.30/47.85  | 
% 241.30/47.85  | Case 1:
% 241.30/47.85  | | 
% 241.30/47.85  | |   (36)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 241.30/47.85  | |           e1)
% 241.30/47.85  | | 
% 241.30/47.85  | | BETA: splitting (36) gives:
% 241.30/47.85  | | 
% 241.30/47.85  | | Case 1:
% 241.30/47.85  | | | 
% 241.30/47.85  | | |   (37)  all_58_4 = e1 & op(e3, e1) = e1
% 241.30/47.85  | | | 
% 241.30/47.85  | | | ALPHA: (37) implies:
% 241.30/47.85  | | |   (38)  all_58_4 = e1
% 241.30/47.85  | | | 
% 241.30/47.85  | | | REF_CLOSE: (1), (2), (4), (11), (13), (15), (17), (22), (24), (25), (28),
% 241.30/47.85  | | |            (30), (35), (38) are inconsistent by sub-proof #1468.
% 241.30/47.85  | | | 
% 241.30/47.85  | | Case 2:
% 241.30/47.85  | | | 
% 241.30/47.85  | | |   (39)  all_58_5 = e1 & op(e2, e1) = e1
% 241.30/47.85  | | | 
% 241.30/47.85  | | | ALPHA: (39) implies:
% 241.30/47.85  | | |   (40)  all_58_5 = e1
% 241.30/47.85  | | | 
% 241.30/47.85  | | | BETA: splitting (18) gives:
% 241.30/47.85  | | | 
% 241.30/47.85  | | | Case 1:
% 241.30/47.85  | | | | 
% 241.30/47.85  | | | |   (41)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 241.30/47.85  | | | |           = e2)
% 241.30/47.85  | | | | 
% 241.30/47.85  | | | | BETA: splitting (41) gives:
% 241.30/47.85  | | | | 
% 241.30/47.85  | | | | Case 1:
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | |   (42)  all_58_4 = e2 & op(e3, e1) = e2
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | | REF_CLOSE: (2), (3), (4), (5), (8), (11), (14), (15), (16), (17),
% 241.30/47.85  | | | | |            (19), (20), (21), (23), (28), (29), (30), (31), (34), (35),
% 241.30/47.85  | | | | |            (42) are inconsistent by sub-proof #517.
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | Case 2:
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | |   (43)  all_58_5 = e2 & op(e2, e1) = e2
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | | ALPHA: (43) implies:
% 241.30/47.85  | | | | |   (44)  all_58_5 = e2
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | | COMBINE_EQS: (40), (44) imply:
% 241.30/47.85  | | | | |   (45)  e2 = e1
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | | SIMP: (45) implies:
% 241.30/47.85  | | | | |   (46)  e2 = e1
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | | COMBINE_EQS: (33), (46) imply:
% 241.30/47.85  | | | | |   (47)  all_58_9 = e1
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (11), (13), (15), (16), (17),
% 241.30/47.85  | | | | |            (19), (22), (24), (25), (28), (30), (35), (47) are
% 241.30/47.85  | | | | |            inconsistent by sub-proof #1147.
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | End of split
% 241.30/47.85  | | | | 
% 241.30/47.85  | | | Case 2:
% 241.30/47.85  | | | | 
% 241.30/47.85  | | | |   (48)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 241.30/47.85  | | | |           = e2)
% 241.30/47.85  | | | | 
% 241.30/47.85  | | | | BETA: splitting (48) gives:
% 241.30/47.85  | | | | 
% 241.30/47.85  | | | | Case 1:
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | |   (49)  all_58_8 = e2 & op(e1, e1) = e2
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | | REF_CLOSE: (1), (4), (9), (10), (15), (17), (28), (31), (33), (35),
% 241.30/47.85  | | | | |            (49) are inconsistent by sub-proof #599.
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | Case 2:
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | |   (50)  all_58_14 = e2 & op(e0, e1) = e2
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | | REF_CLOSE: (1), (4), (9), (15), (17), (26), (28), (31), (33), (35),
% 241.30/47.85  | | | | |            (50) are inconsistent by sub-proof #515.
% 241.30/47.85  | | | | | 
% 241.30/47.85  | | | | End of split
% 241.30/47.85  | | | | 
% 241.30/47.85  | | | End of split
% 241.30/47.85  | | | 
% 241.30/47.85  | | End of split
% 241.30/47.85  | | 
% 241.30/47.85  | Case 2:
% 241.30/47.85  | | 
% 241.30/47.85  | |   (51)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 241.30/47.85  | |           e1)
% 241.30/47.85  | | 
% 241.30/47.85  | | BETA: splitting (51) gives:
% 241.30/47.85  | | 
% 241.30/47.85  | | Case 1:
% 241.30/47.85  | | | 
% 241.30/47.85  | | |   (52)  all_58_8 = e1 & op(e1, e1) = e1
% 241.30/47.85  | | | 
% 241.30/47.85  | | | ALPHA: (52) implies:
% 241.30/47.85  | | |   (53)  all_58_8 = e1
% 241.30/47.85  | | |   (54)  op(e1, e1) = e1
% 241.30/47.85  | | | 
% 241.30/47.85  | | | REF_CLOSE: (2), (3), (4), (8), (12), (17), (27), (28), (30), (32), (35),
% 241.30/47.85  | | |            (53), (54) are inconsistent by sub-proof #804.
% 241.30/47.85  | | | 
% 241.30/47.85  | | Case 2:
% 241.30/47.85  | | | 
% 241.30/47.85  | | |   (55)  all_58_14 = e1 & op(e0, e1) = e1
% 241.30/47.85  | | | 
% 241.30/47.85  | | | ALPHA: (55) implies:
% 241.30/47.85  | | |   (56)  all_58_14 = e1
% 241.30/47.85  | | | 
% 241.30/47.85  | | | REF_CLOSE: (26), (30), (56) are inconsistent by sub-proof #1033.
% 241.30/47.85  | | | 
% 241.30/47.85  | | End of split
% 241.30/47.85  | | 
% 241.30/47.85  | End of split
% 241.30/47.85  | 
% 241.30/47.85  End of proof
% 241.30/47.85  
% 241.30/47.85  Sub-proof #515 shows that the following formulas are inconsistent:
% 241.30/47.85  ----------------------------------------------------------------
% 241.30/47.85    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.30/47.85         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.30/47.85    (2)   ~ (e2 = e0)
% 241.30/47.85    (3)  all_58_1 = e0
% 241.30/47.85    (4)  all_58_14 = e2 & op(e0, e1) = e2
% 241.30/47.85    (5)  op(e3, e3) = e1
% 241.30/47.85    (6)   ~ (e3 = e2)
% 241.30/47.85    (7)  all_58_14 = e0
% 241.30/47.85    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.85    (9)  all_58_4 = e3
% 241.30/47.85    (10)  all_58_9 = e2
% 241.30/47.85    (11)   ~ (e2 = e1)
% 241.30/47.85  
% 241.30/47.85  Begin of proof
% 241.30/47.85  | 
% 241.30/47.85  | ALPHA: (4) implies:
% 241.30/47.85  |   (12)  all_58_14 = e2
% 241.30/47.85  | 
% 241.30/47.85  | COMBINE_EQS: (7), (12) imply:
% 241.30/47.85  |   (13)  e2 = e0
% 241.30/47.85  | 
% 241.30/47.85  | SIMP: (13) implies:
% 241.30/47.85  |   (14)  e2 = e0
% 241.30/47.85  | 
% 241.30/47.85  | COMBINE_EQS: (10), (14) imply:
% 241.30/47.85  |   (15)  all_58_9 = e0
% 241.30/47.85  | 
% 241.30/47.85  | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (11), (15) are inconsistent by
% 241.30/47.85  |            sub-proof #1097.
% 241.30/47.85  | 
% 241.30/47.85  End of proof
% 241.30/47.85  
% 241.30/47.85  Sub-proof #516 shows that the following formulas are inconsistent:
% 241.30/47.85  ----------------------------------------------------------------
% 241.30/47.85    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.30/47.85         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.30/47.85    (2)   ~ (e3 = e0)
% 241.30/47.85    (3)   ~ (e2 = e0)
% 241.30/47.85    (4)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 241.30/47.85         (all_58_11 = e0 & op(e1, e0) = e0)
% 241.30/47.85    (5)  all_58_15 = e3
% 241.30/47.85    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.30/47.85         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.30/47.85    (7)   ~ (e3 = e1)
% 241.30/47.85    (8)  all_58_3 = e3
% 241.30/47.86    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.30/47.86         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.30/47.86    (10)  op(e3, e3) = e1
% 241.30/47.86    (11)   ~ (e3 = e2)
% 241.30/47.86    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.30/47.86          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.30/47.86    (13)   ~ (all_52_4 = e3)
% 241.30/47.86    (14)  op(e3, e2) = all_52_4
% 241.30/47.86    (15)  all_58_5 = e1
% 241.30/47.86    (16)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.30/47.86          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.30/47.86    (17)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.30/47.86          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.30/47.86    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.86    (19)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.30/47.86          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.30/47.86    (20)   ~ (e1 = e0)
% 241.30/47.86    (21)  all_58_9 = e2
% 241.30/47.86    (22)  all_58_10 = e1
% 241.30/47.86    (23)   ~ (e2 = e1)
% 241.30/47.86  
% 241.30/47.86  Begin of proof
% 241.30/47.86  | 
% 241.30/47.86  | BETA: splitting (6) gives:
% 241.30/47.86  | 
% 241.30/47.86  | Case 1:
% 241.30/47.86  | | 
% 241.30/47.86  | |   (24)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 241.30/47.86  | |           e2)
% 241.30/47.86  | | 
% 241.30/47.86  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11), (15), (16), (17), (18),
% 241.30/47.86  | |            (19), (20), (22), (23), (24) are inconsistent by sub-proof #830.
% 241.30/47.86  | | 
% 241.30/47.86  | Case 2:
% 241.30/47.86  | | 
% 241.30/47.86  | |   (25)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 241.30/47.86  | |           e2)
% 241.30/47.86  | | 
% 241.30/47.86  | | BETA: splitting (25) gives:
% 241.30/47.86  | | 
% 241.30/47.86  | | Case 1:
% 241.30/47.86  | | | 
% 241.30/47.86  | | |   (26)  all_58_5 = e2 & op(e2, e1) = e2
% 241.30/47.86  | | | 
% 241.30/47.86  | | | ALPHA: (26) implies:
% 241.30/47.86  | | |   (27)  all_58_5 = e2
% 241.30/47.86  | | | 
% 241.30/47.86  | | | COMBINE_EQS: (15), (27) imply:
% 241.30/47.86  | | |   (28)  e2 = e1
% 241.30/47.86  | | | 
% 241.30/47.86  | | | SIMP: (28) implies:
% 241.30/47.86  | | |   (29)  e2 = e1
% 241.30/47.86  | | | 
% 241.30/47.86  | | | COMBINE_EQS: (21), (29) imply:
% 241.30/47.86  | | |   (30)  all_58_9 = e1
% 241.30/47.86  | | | 
% 241.30/47.86  | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (12), (13), (14),
% 241.30/47.86  | | |            (16), (18), (19), (20), (22), (23), (30) are inconsistent by
% 241.30/47.86  | | |            sub-proof #1168.
% 241.30/47.86  | | | 
% 241.30/47.86  | | Case 2:
% 241.30/47.86  | | | 
% 241.30/47.86  | | |   (31)  all_58_10 = e2 & op(e2, e0) = e2
% 241.30/47.86  | | | 
% 241.30/47.86  | | | ALPHA: (31) implies:
% 241.30/47.86  | | |   (32)  all_58_10 = e2
% 241.30/47.86  | | | 
% 241.30/47.86  | | | COMBINE_EQS: (22), (32) imply:
% 241.30/47.86  | | |   (33)  e2 = e1
% 241.30/47.86  | | | 
% 241.30/47.86  | | | SIMP: (33) implies:
% 241.30/47.86  | | |   (34)  e2 = e1
% 241.30/47.86  | | | 
% 241.30/47.86  | | | COMBINE_EQS: (21), (34) imply:
% 241.30/47.86  | | |   (35)  all_58_9 = e1
% 241.30/47.86  | | | 
% 241.30/47.86  | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (12), (13), (14),
% 241.30/47.86  | | |            (16), (18), (19), (20), (22), (23), (35) are inconsistent by
% 241.30/47.86  | | |            sub-proof #1168.
% 241.30/47.86  | | | 
% 241.30/47.86  | | End of split
% 241.30/47.86  | | 
% 241.30/47.86  | End of split
% 241.30/47.86  | 
% 241.30/47.86  End of proof
% 241.30/47.86  
% 241.30/47.86  Sub-proof #517 shows that the following formulas are inconsistent:
% 241.30/47.86  ----------------------------------------------------------------
% 241.30/47.86    (1)   ~ (e3 = e0)
% 241.30/47.86    (2)  all_58_6 = e3
% 241.30/47.86    (3)   ~ (e2 = e0)
% 241.30/47.86    (4)  op(e1, e2) = all_52_6
% 241.30/47.86    (5)  all_58_11 = e1
% 241.30/47.86    (6)   ~ (e3 = e1)
% 241.30/47.86    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.30/47.86         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.30/47.86    (8)  op(e3, e3) = e1
% 241.30/47.86    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.30/47.86         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.30/47.86    (10)   ~ (e3 = e2)
% 241.30/47.86    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.30/47.86          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.30/47.86    (12)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.30/47.86          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.30/47.86    (13)  op(e2, e3) = all_52_1
% 241.30/47.86    (14)   ~ (all_52_6 = e3)
% 241.30/47.86    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.86    (16)  op(e1, e1) = e0
% 241.30/47.86    (17)   ~ (e1 = e0)
% 241.30/47.86    (18)  all_58_4 = e2 & op(e3, e1) = e2
% 241.30/47.86    (19)  all_58_4 = e3
% 241.30/47.86    (20)   ~ (all_52_1 = e3)
% 241.30/47.86    (21)   ~ (e2 = e1)
% 241.30/47.86  
% 241.30/47.86  Begin of proof
% 241.30/47.86  | 
% 241.30/47.86  | ALPHA: (18) implies:
% 241.30/47.86  |   (22)  all_58_4 = e2
% 241.30/47.86  | 
% 241.30/47.86  | COMBINE_EQS: (19), (22) imply:
% 241.30/47.86  |   (23)  e3 = e2
% 241.30/47.86  | 
% 241.30/47.86  | COMBINE_EQS: (2), (23) imply:
% 241.30/47.86  |   (24)  all_58_6 = e2
% 241.30/47.86  | 
% 241.30/47.86  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.30/47.86  |            (14), (15), (16), (17), (20), (21), (24) are inconsistent by
% 241.30/47.86  |            sub-proof #661.
% 241.30/47.86  | 
% 241.30/47.86  End of proof
% 241.30/47.86  
% 241.30/47.86  Sub-proof #518 shows that the following formulas are inconsistent:
% 241.30/47.86  ----------------------------------------------------------------
% 241.30/47.86    (1)   ~ (e3 = e0)
% 241.30/47.86    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.30/47.86         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.30/47.86    (3)   ~ (e2 = e0)
% 241.30/47.86    (4)  op(e1, e2) = all_52_6
% 241.30/47.86    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.30/47.86         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.30/47.86    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.30/47.86         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.30/47.86    (7)  all_58_8 = e0
% 241.30/47.86    (8)   ~ (e3 = e1)
% 241.30/47.86    (9)  all_58_7 = e2
% 241.30/47.86    (10)  all_58_3 = e3
% 241.30/47.86    (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.30/47.86          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.30/47.86    (12)  op(e3, e3) = e1
% 241.30/47.86    (13)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.30/47.86          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.30/47.86    (14)   ~ (e3 = e2)
% 241.30/47.86    (15)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.30/47.86          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.30/47.86    (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.30/47.86          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.30/47.86    (17)  e2 = e0
% 241.30/47.86    (18)  op(e2, e3) = all_52_1
% 241.30/47.86    (19)   ~ (all_52_6 = e3)
% 241.30/47.86    (20)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.30/47.86          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.30/47.86    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.86    (22)  op(e1, e1) = e0
% 241.30/47.86    (23)   ~ (e1 = e0)
% 241.30/47.86    (24)  all_58_13 = e1
% 241.30/47.86    (25)   ~ (all_52_1 = e3)
% 241.30/47.86    (26)   ~ (e2 = e1)
% 241.30/47.86  
% 241.30/47.86  Begin of proof
% 241.30/47.86  | 
% 241.30/47.86  | SIMP: (17) implies:
% 241.30/47.86  |   (27)  e2 = e0
% 241.30/47.86  | 
% 241.30/47.86  | COMBINE_EQS: (9), (27) imply:
% 241.30/47.86  |   (28)  all_58_7 = e0
% 241.30/47.86  | 
% 241.30/47.86  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 241.30/47.86  |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 241.30/47.86  |            (26), (28) are inconsistent by sub-proof #519.
% 241.30/47.86  | 
% 241.30/47.86  End of proof
% 241.30/47.86  
% 241.30/47.86  Sub-proof #519 shows that the following formulas are inconsistent:
% 241.30/47.86  ----------------------------------------------------------------
% 241.30/47.86    (1)   ~ (e3 = e0)
% 241.30/47.86    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.30/47.86         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.30/47.86    (3)   ~ (e2 = e0)
% 241.30/47.86    (4)  all_58_7 = e0
% 241.30/47.86    (5)  op(e1, e2) = all_52_6
% 241.30/47.86    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.30/47.86         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.30/47.86    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.30/47.86         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.30/47.86    (8)  all_58_8 = e0
% 241.30/47.86    (9)   ~ (e3 = e1)
% 241.30/47.86    (10)  all_58_3 = e3
% 241.30/47.86    (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.30/47.86          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.30/47.86    (12)  op(e3, e3) = e1
% 241.30/47.86    (13)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.30/47.86          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.30/47.86    (14)   ~ (e3 = e2)
% 241.30/47.86    (15)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.30/47.86          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.30/47.86    (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.30/47.86          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.30/47.86    (17)  op(e2, e3) = all_52_1
% 241.30/47.86    (18)   ~ (all_52_6 = e3)
% 241.30/47.87    (19)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.30/47.87          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.30/47.87    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.87    (21)  op(e1, e1) = e0
% 241.30/47.87    (22)   ~ (e1 = e0)
% 241.30/47.87    (23)  all_58_13 = e1
% 241.30/47.87    (24)   ~ (all_52_1 = e3)
% 241.30/47.87    (25)   ~ (e2 = e1)
% 241.30/47.87  
% 241.30/47.87  Begin of proof
% 241.30/47.87  | 
% 241.30/47.87  | BETA: splitting (2) gives:
% 241.30/47.87  | 
% 241.30/47.87  | Case 1:
% 241.30/47.87  | | 
% 241.30/47.87  | |   (26)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 241.30/47.87  | |           e1)
% 241.30/47.87  | | 
% 241.30/47.87  | | REF_CLOSE: (1), (3), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 241.30/47.87  | |            (17), (20), (22), (23), (24), (25), (26) are inconsistent by
% 241.30/47.87  | |            sub-proof #538.
% 241.30/47.87  | | 
% 241.30/47.87  | Case 2:
% 241.30/47.87  | | 
% 241.30/47.87  | |   (27)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 241.30/47.87  | |           e1)
% 241.30/47.87  | | 
% 241.30/47.87  | | BETA: splitting (27) gives:
% 241.30/47.87  | | 
% 241.30/47.87  | | Case 1:
% 241.30/47.87  | | | 
% 241.30/47.87  | | |   (28)  all_58_8 = e1 & op(e1, e1) = e1
% 241.30/47.87  | | | 
% 241.30/47.87  | | | ALPHA: (28) implies:
% 241.30/47.87  | | |   (29)  op(e1, e1) = e1
% 241.30/47.87  | | | 
% 241.30/47.87  | | | REF_CLOSE: (20), (21), (22), (29) are inconsistent by sub-proof #2220.
% 241.30/47.87  | | | 
% 241.30/47.87  | | Case 2:
% 241.30/47.87  | | | 
% 241.30/47.87  | | |   (30)  all_58_11 = e1 & op(e1, e0) = e1
% 241.30/47.87  | | | 
% 241.30/47.87  | | | ALPHA: (30) implies:
% 241.30/47.87  | | |   (31)  all_58_11 = e1
% 241.30/47.87  | | | 
% 241.30/47.87  | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (11), (12), (13), (14), (15),
% 241.30/47.87  | | |            (16), (17), (18), (19), (20), (21), (22), (24), (25), (31) are
% 241.30/47.87  | | |            inconsistent by sub-proof #523.
% 241.30/47.87  | | | 
% 241.30/47.87  | | End of split
% 241.30/47.87  | | 
% 241.30/47.87  | End of split
% 241.30/47.87  | 
% 241.30/47.87  End of proof
% 241.30/47.87  
% 241.30/47.87  Sub-proof #520 shows that the following formulas are inconsistent:
% 241.30/47.87  ----------------------------------------------------------------
% 241.30/47.87    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.30/47.87         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.30/47.87    (2)   ~ (e3 = e0)
% 241.30/47.87    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.30/47.87         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.30/47.87    (4)  all_58_6 = e3
% 241.30/47.87    (5)   ~ (e2 = e0)
% 241.30/47.87    (6)  op(e1, e2) = all_52_6
% 241.30/47.87    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.30/47.87         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.30/47.87    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.30/47.87         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.30/47.87    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.30/47.87         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.30/47.87    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.30/47.87          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.30/47.87    (11)  all_58_15 = e3
% 241.30/47.87    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.30/47.87          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.30/47.87    (13)   ~ (e3 = e1)
% 241.30/47.87    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.30/47.87          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.30/47.87    (15)  all_58_3 = e3
% 241.30/47.87    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.30/47.87          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.30/47.87    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.30/47.87          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.30/47.87    (18)  op(e3, e3) = e1
% 241.30/47.87    (19)  all_58_15 = e0 & op(e0, e0) = e0
% 241.30/47.87    (20)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.30/47.87              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.30/47.87                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.30/47.87                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.30/47.87    (21)  op(e2, e1) = all_52_9
% 241.30/47.87    (22)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.30/47.87          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.30/47.87    (23)   ~ (e3 = e2)
% 241.30/47.87    (24)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.30/47.87          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.30/47.87    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.30/47.87          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.30/47.87    (26)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.30/47.87          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.30/47.87    (27)  op(e2, e3) = all_52_1
% 241.30/47.87    (28)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.30/47.87          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.30/47.87    (29)   ~ (all_52_6 = e3)
% 241.30/47.87    (30)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.30/47.87          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.30/47.87    (31)   ~ (all_52_4 = e3)
% 241.30/47.87    (32)  op(e3, e2) = all_52_4
% 241.30/47.87    (33)   ~ (all_52_9 = e3)
% 241.30/47.87    (34)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.30/47.87          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.30/47.87    (35)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.30/47.87          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.30/47.87    (36)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.30/47.87          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.30/47.87    (37)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.87    (38)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.30/47.87          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.30/47.87    (39)  op(e1, e1) = e0
% 241.30/47.87    (40)   ~ (e1 = e0)
% 241.30/47.87    (41)  all_58_4 = e3
% 241.30/47.87    (42)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.30/47.87          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.30/47.87    (43)  op(e2, e0) = all_52_13
% 241.30/47.87    (44)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.30/47.87          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.30/47.87            e1)
% 241.30/47.87    (45)   ~ (all_52_1 = e3)
% 241.30/47.87    (46)  all_58_14 = e1
% 241.30/47.87    (47)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.30/47.87          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.30/47.87            e2)
% 241.30/47.87    (48)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.30/47.87          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.30/47.87    (49)   ~ (e2 = e1)
% 241.30/47.87    (50)   ~ (all_52_1 = e1)
% 241.30/47.87  
% 241.30/47.87  Begin of proof
% 241.30/47.87  | 
% 241.30/47.87  | ALPHA: (19) implies:
% 241.30/47.87  |   (51)  all_58_15 = e0
% 241.30/47.87  | 
% 241.30/47.87  | COMBINE_EQS: (11), (51) imply:
% 241.30/47.87  |   (52)  e3 = e0
% 241.30/47.87  | 
% 241.30/47.87  | SIMP: (52) implies:
% 241.30/47.87  |   (53)  e3 = e0
% 241.30/47.87  | 
% 241.30/47.87  | COMBINE_EQS: (41), (53) imply:
% 241.30/47.87  |   (54)  all_58_4 = e0
% 241.30/47.87  | 
% 241.30/47.87  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 241.30/47.87  |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), (25),
% 241.30/47.87  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 241.30/47.87  |            (37), (38), (39), (40), (42), (43), (44), (45), (46), (47), (48),
% 241.30/47.87  |            (49), (50), (54) are inconsistent by sub-proof #582.
% 241.30/47.87  | 
% 241.30/47.87  End of proof
% 241.30/47.87  
% 241.30/47.87  Sub-proof #521 shows that the following formulas are inconsistent:
% 241.30/47.87  ----------------------------------------------------------------
% 241.30/47.87    (1)   ~ (all_52_9 = all_6_2)
% 241.30/47.87    (2)   ~ (e3 = e0)
% 241.30/47.87    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.30/47.87         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.30/47.87    (4)  all_58_6 = e3
% 241.30/47.87    (5)   ~ (e2 = e0)
% 241.30/47.87    (6)  op(e1, e2) = all_52_6
% 241.30/47.87    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.30/47.87         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.30/47.87    (8)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.30/47.87           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.30/47.87             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.30/47.87           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.30/47.87             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.30/47.87           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.30/47.87           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.30/47.87           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.30/47.87           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.30/47.87           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.30/47.87           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.30/47.87             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.30/47.87           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.30/47.87           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 241.30/47.87           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.30/47.87           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.30/47.87           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.30/47.87           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.30/47.87             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.30/47.87           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.30/47.87           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 241.30/47.87           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.30/47.87           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.30/47.87           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.30/47.87           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.30/47.87             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.30/47.87           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.30/47.87           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.30/47.87    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.30/47.87         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.30/47.87    (10)   ~ (e3 = e1)
% 241.30/47.87    (11)  all_58_8 = e2
% 241.30/47.87    (12)  all_58_7 = e2
% 241.30/47.87    (13)  all_58_3 = e3
% 241.30/47.87    (14)  all_54_10 = all_6_2
% 241.30/47.87    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.30/47.87          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.30/47.87    (16)  op(e3, e3) = e1
% 241.30/47.87    (17)   ~ (all_6_2 = e3)
% 241.30/47.87    (18)  op(e2, e1) = all_52_9
% 241.30/47.87    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.30/47.87          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.30/47.87    (20)   ~ (e3 = e2)
% 241.30/47.87    (21)   ~ (all_6_2 = e0)
% 241.30/47.87    (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.30/47.87          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.30/47.87    (23)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.30/47.87          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.30/47.87    (24)  op(e2, e3) = all_52_1
% 241.30/47.87    (25)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 241.30/47.87    (26)   ~ (all_52_6 = e3)
% 241.30/47.87    (27)  all_56_31 = e3
% 241.30/47.87    (28)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.30/47.87          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.30/47.87    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.30/47.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.30/47.87    (30)  all_56_11 = e3
% 241.30/47.87    (31)   ~ (e1 = e0)
% 241.30/47.87    (32)  all_56_21 = all_6_2
% 241.30/47.87    (33)  all_58_13 = e1
% 241.30/47.87    (34)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.30/47.87          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.30/47.87    (35)  op(e2, e0) = all_52_13
% 241.30/47.87    (36)   ~ (all_52_1 = e3)
% 241.30/47.87    (37)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.30/47.87          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.30/47.87    (38)  all_56_1 = e1
% 241.30/47.87    (39)   ~ (e2 = e1)
% 241.30/47.87    (40)   ~ (all_52_1 = e1)
% 241.30/47.87  
% 241.30/47.87  Begin of proof
% 241.30/47.87  | 
% 241.30/47.87  | BETA: splitting (3) gives:
% 241.30/47.87  | 
% 241.30/47.87  | Case 1:
% 241.30/47.87  | | 
% 241.30/47.87  | |   (41)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 241.30/47.87  | |           e1)
% 241.30/47.87  | | 
% 241.30/47.88  | | REF_CLOSE: (2), (5), (7), (9), (10), (13), (15), (16), (19), (20), (22),
% 241.30/47.88  | |            (24), (29), (31), (33), (36), (39), (41) are inconsistent by
% 241.30/47.88  | |            sub-proof #538.
% 241.30/47.88  | | 
% 241.30/47.88  | Case 2:
% 241.30/47.88  | | 
% 241.30/47.88  | |   (42)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 241.30/47.88  | |           e1)
% 241.30/47.88  | | 
% 241.30/47.88  | | BETA: splitting (42) gives:
% 241.30/47.88  | | 
% 241.30/47.88  | | Case 1:
% 241.30/47.88  | | | 
% 241.30/47.88  | | |   (43)  all_58_8 = e1 & op(e1, e1) = e1
% 241.30/47.88  | | | 
% 241.30/47.88  | | | ALPHA: (43) implies:
% 241.30/47.88  | | |   (44)  all_58_8 = e1
% 241.30/47.88  | | | 
% 241.30/47.88  | | | COMBINE_EQS: (11), (44) imply:
% 241.30/47.88  | | |   (45)  e2 = e1
% 241.30/47.88  | | | 
% 241.30/47.88  | | | COMBINE_EQS: (12), (45) imply:
% 241.30/47.88  | | |   (46)  all_58_7 = e1
% 241.30/47.88  | | | 
% 241.30/47.88  | | | REF_CLOSE: (2), (5), (7), (9), (13), (20), (31), (33), (39), (46) are
% 241.30/47.88  | | |            inconsistent by sub-proof #1457.
% 241.30/47.88  | | | 
% 241.30/47.88  | | Case 2:
% 241.30/47.88  | | | 
% 241.30/47.88  | | |   (47)  all_58_11 = e1 & op(e1, e0) = e1
% 241.30/47.88  | | | 
% 241.30/47.88  | | | ALPHA: (47) implies:
% 241.30/47.88  | | |   (48)  all_58_11 = e1
% 241.30/47.88  | | |   (49)  op(e1, e0) = e1
% 241.30/47.88  | | | 
% 241.30/47.88  | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (11), (12), (13), (14),
% 241.30/47.88  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 241.30/47.88  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (34), (35),
% 241.30/47.88  | | |            (36), (37), (38), (39), (40), (48), (49) are inconsistent by
% 241.30/47.88  | | |            sub-proof #522.
% 241.30/47.88  | | | 
% 241.30/47.88  | | End of split
% 241.30/47.88  | | 
% 241.30/47.88  | End of split
% 241.30/47.88  | 
% 241.30/47.88  End of proof
% 241.30/47.88  
% 241.30/47.88  Sub-proof #522 shows that the following formulas are inconsistent:
% 241.30/47.88  ----------------------------------------------------------------
% 241.30/47.88    (1)   ~ (all_52_9 = all_6_2)
% 241.30/47.88    (2)   ~ (e3 = e0)
% 241.30/47.88    (3)  all_58_6 = e3
% 241.30/47.88    (4)   ~ (e2 = e0)
% 241.30/47.88    (5)  op(e1, e2) = all_52_6
% 241.39/47.88    (6)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.39/47.88           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.39/47.88             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.39/47.88           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.39/47.88             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.39/47.88           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.39/47.88           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.39/47.88           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.39/47.88           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.39/47.88           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.39/47.88           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.39/47.88             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.39/47.88           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.39/47.88           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 241.39/47.88           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.39/47.88           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.39/47.88           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.39/47.88           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.39/47.88             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.39/47.88           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.39/47.88           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 241.39/47.88           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.39/47.88           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.39/47.88           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.39/47.88           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.39/47.88             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.39/47.88           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.39/47.88           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.39/47.88    (7)  all_58_11 = e1
% 241.39/47.88    (8)   ~ (e3 = e1)
% 241.39/47.88    (9)  all_58_8 = e2
% 241.39/47.88    (10)  all_58_7 = e2
% 241.39/47.88    (11)  op(e1, e0) = e1
% 241.39/47.88    (12)  all_58_3 = e3
% 241.39/47.88    (13)  all_54_10 = all_6_2
% 241.39/47.88    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.39/47.88          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.39/47.88    (15)  op(e3, e3) = e1
% 241.39/47.88    (16)   ~ (all_6_2 = e3)
% 241.39/47.88    (17)  op(e2, e1) = all_52_9
% 241.39/47.88    (18)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.39/47.88          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.39/47.88    (19)   ~ (e3 = e2)
% 241.39/47.88    (20)   ~ (all_6_2 = e0)
% 241.39/47.88    (21)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.39/47.88          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.39/47.88    (22)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.39/47.88          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.39/47.88    (23)  op(e2, e3) = all_52_1
% 241.39/47.88    (24)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 241.39/47.88    (25)   ~ (all_52_6 = e3)
% 241.39/47.88    (26)  all_56_31 = e3
% 241.39/47.88    (27)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.39/47.88          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.39/47.88    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.88    (29)  all_56_11 = e3
% 241.39/47.88    (30)   ~ (e1 = e0)
% 241.39/47.88    (31)  all_56_21 = all_6_2
% 241.39/47.88    (32)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.39/47.88          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.39/47.88    (33)  op(e2, e0) = all_52_13
% 241.39/47.88    (34)   ~ (all_52_1 = e3)
% 241.39/47.88    (35)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.39/47.88          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.39/47.88    (36)  all_56_1 = e1
% 241.39/47.88    (37)   ~ (e2 = e1)
% 241.39/47.88    (38)   ~ (all_52_1 = e1)
% 241.39/47.88  
% 241.39/47.88  Begin of proof
% 241.39/47.88  | 
% 241.39/47.88  | BETA: splitting (32) gives:
% 241.39/47.88  | 
% 241.39/47.88  | Case 1:
% 241.39/47.88  | | 
% 241.39/47.88  | |   (39)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 241.39/47.88  | |           e0)
% 241.39/47.88  | | 
% 241.39/47.88  | | BETA: splitting (39) gives:
% 241.39/47.88  | | 
% 241.39/47.88  | | Case 1:
% 241.39/47.88  | | | 
% 241.39/47.88  | | |   (40)  all_58_6 = e0 & op(e1, e3) = e0
% 241.39/47.88  | | | 
% 241.39/47.88  | | | REF_CLOSE: (1), (3), (6), (12), (13), (16), (17), (20), (23), (24), (26),
% 241.39/47.88  | | |            (28), (29), (31), (33), (34), (35), (36), (38), (40) are
% 241.39/47.88  | | |            inconsistent by sub-proof #527.
% 241.39/47.88  | | | 
% 241.39/47.88  | | Case 2:
% 241.39/47.88  | | | 
% 241.39/47.88  | | |   (41)  all_58_7 = e0 & op(e1, e2) = e0
% 241.39/47.88  | | | 
% 241.39/47.88  | | | REF_CLOSE: (4), (10), (41) are inconsistent by sub-proof #2212.
% 241.39/47.88  | | | 
% 241.39/47.88  | | End of split
% 241.39/47.88  | | 
% 241.39/47.88  | Case 2:
% 241.39/47.88  | | 
% 241.39/47.88  | |   (42)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 241.39/47.88  | |           e0)
% 241.39/47.88  | | 
% 241.39/47.88  | | BETA: splitting (42) gives:
% 241.39/47.88  | | 
% 241.39/47.88  | | Case 1:
% 241.39/47.88  | | | 
% 241.39/47.88  | | |   (43)  all_58_8 = e0 & op(e1, e1) = e0
% 241.39/47.88  | | | 
% 241.39/47.88  | | | ALPHA: (43) implies:
% 241.39/47.88  | | |   (44)  all_58_8 = e0
% 241.39/47.88  | | |   (45)  op(e1, e1) = e0
% 241.39/47.88  | | | 
% 241.39/47.88  | | | COMBINE_EQS: (9), (44) imply:
% 241.39/47.88  | | |   (46)  e2 = e0
% 241.39/47.88  | | | 
% 241.39/47.88  | | | COMBINE_EQS: (10), (46) imply:
% 241.39/47.88  | | |   (47)  all_58_7 = e0
% 241.39/47.88  | | | 
% 241.39/47.88  | | | REF_CLOSE: (2), (4), (5), (7), (8), (14), (15), (18), (19), (21), (22),
% 241.39/47.88  | | |            (23), (25), (27), (28), (30), (34), (37), (44), (45), (47) are
% 241.39/47.88  | | |            inconsistent by sub-proof #523.
% 241.39/47.88  | | | 
% 241.39/47.88  | | Case 2:
% 241.39/47.88  | | | 
% 241.39/47.88  | | |   (48)  all_58_11 = e0 & op(e1, e0) = e0
% 241.39/47.88  | | | 
% 241.39/47.88  | | | ALPHA: (48) implies:
% 241.39/47.88  | | |   (49)  op(e1, e0) = e0
% 241.39/47.88  | | | 
% 241.39/47.88  | | | REF_CLOSE: (11), (28), (30), (49) are inconsistent by sub-proof #2284.
% 241.39/47.88  | | | 
% 241.39/47.88  | | End of split
% 241.39/47.88  | | 
% 241.39/47.88  | End of split
% 241.39/47.88  | 
% 241.39/47.88  End of proof
% 241.39/47.88  
% 241.39/47.88  Sub-proof #523 shows that the following formulas are inconsistent:
% 241.39/47.88  ----------------------------------------------------------------
% 241.39/47.88    (1)   ~ (e3 = e0)
% 241.39/47.88    (2)   ~ (e2 = e0)
% 241.39/47.88    (3)  all_58_7 = e0
% 241.39/47.88    (4)  op(e1, e2) = all_52_6
% 241.39/47.88    (5)  all_58_11 = e1
% 241.39/47.88    (6)  all_58_8 = e0
% 241.39/47.88    (7)   ~ (e3 = e1)
% 241.39/47.88    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.39/47.88         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.39/47.88    (9)  op(e3, e3) = e1
% 241.39/47.88    (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.39/47.88          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.39/47.88    (11)   ~ (e3 = e2)
% 241.39/47.88    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.39/47.88          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.39/47.88    (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.39/47.88          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.39/47.88    (14)  op(e2, e3) = all_52_1
% 241.39/47.88    (15)   ~ (all_52_6 = e3)
% 241.39/47.88    (16)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.39/47.88          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.39/47.88    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.88    (18)  op(e1, e1) = e0
% 241.39/47.88    (19)   ~ (e1 = e0)
% 241.39/47.88    (20)   ~ (all_52_1 = e3)
% 241.39/47.88    (21)   ~ (e2 = e1)
% 241.39/47.88  
% 241.39/47.88  Begin of proof
% 241.39/47.88  | 
% 241.39/47.88  | BETA: splitting (16) gives:
% 241.39/47.88  | 
% 241.39/47.88  | Case 1:
% 241.39/47.88  | | 
% 241.39/47.88  | |   (22)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 241.39/47.88  | |           e2)
% 241.39/47.88  | | 
% 241.39/47.88  | | BETA: splitting (22) gives:
% 241.39/47.88  | | 
% 241.39/47.88  | | Case 1:
% 241.39/47.88  | | | 
% 241.39/47.88  | | |   (23)  all_58_6 = e2 & op(e1, e3) = e2
% 241.39/47.88  | | | 
% 241.39/47.88  | | | ALPHA: (23) implies:
% 241.39/47.88  | | |   (24)  all_58_6 = e2
% 241.39/47.88  | | | 
% 241.39/47.88  | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 241.39/47.88  | | |            (14), (15), (17), (18), (19), (20), (21), (24) are inconsistent
% 241.39/47.88  | | |            by sub-proof #661.
% 241.39/47.88  | | | 
% 241.39/47.88  | | Case 2:
% 241.39/47.88  | | | 
% 241.39/47.88  | | |   (25)  all_58_7 = e2 & op(e1, e2) = e2
% 241.39/47.88  | | | 
% 241.39/47.88  | | | ALPHA: (25) implies:
% 241.39/47.88  | | |   (26)  all_58_7 = e2
% 241.39/47.88  | | | 
% 241.39/47.88  | | | REF_CLOSE: (2), (3), (26) are inconsistent by sub-proof #1587.
% 241.39/47.88  | | | 
% 241.39/47.88  | | End of split
% 241.39/47.88  | | 
% 241.39/47.88  | Case 2:
% 241.39/47.88  | | 
% 241.39/47.88  | |   (27)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 241.39/47.88  | |           e2)
% 241.39/47.88  | | 
% 241.39/47.88  | | BETA: splitting (27) gives:
% 241.39/47.88  | | 
% 241.39/47.88  | | Case 1:
% 241.39/47.88  | | | 
% 241.39/47.88  | | |   (28)  all_58_8 = e2 & op(e1, e1) = e2
% 241.39/47.88  | | | 
% 241.39/47.88  | | | ALPHA: (28) implies:
% 241.39/47.88  | | |   (29)  all_58_8 = e2
% 241.39/47.88  | | | 
% 241.39/47.88  | | | REF_CLOSE: (2), (6), (29) are inconsistent by sub-proof #1556.
% 241.39/47.88  | | | 
% 241.39/47.88  | | Case 2:
% 241.39/47.88  | | | 
% 241.39/47.88  | | |   (30)  all_58_11 = e2 & op(e1, e0) = e2
% 241.39/47.88  | | | 
% 241.39/47.88  | | | REF_CLOSE: (5), (21), (30) are inconsistent by sub-proof #1554.
% 241.39/47.88  | | | 
% 241.39/47.88  | | End of split
% 241.39/47.88  | | 
% 241.39/47.88  | End of split
% 241.39/47.88  | 
% 241.39/47.88  End of proof
% 241.39/47.88  
% 241.39/47.88  Sub-proof #524 shows that the following formulas are inconsistent:
% 241.39/47.88  ----------------------------------------------------------------
% 241.39/47.88    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.39/47.88         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.39/47.88    (2)   ~ (e3 = e0)
% 241.39/47.88    (3)  op(e1, e1) = e1
% 241.39/47.88    (4)  all_58_6 = e3
% 241.39/47.88    (5)   ~ (e2 = e0)
% 241.39/47.88    (6)  op(e1, e2) = all_52_6
% 241.39/47.88    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.39/47.88         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.39/47.88    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.39/47.88         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.39/47.88    (9)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.39/47.88         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.39/47.88    (10)  all_58_15 = e3
% 241.39/47.88    (11)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.39/47.88          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.39/47.88    (12)   ~ (e3 = e1)
% 241.39/47.88    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.39/47.88          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.39/47.88    (14)  all_58_3 = e3
% 241.39/47.88    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.88          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.88    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.39/47.88          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.39/47.88    (17)  op(e3, e3) = e1
% 241.39/47.88    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.88              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.39/47.88                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.39/47.88                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.39/47.88    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.39/47.88          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.39/47.88    (20)   ~ (e3 = e2)
% 241.39/47.88    (21)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.39/47.88          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.39/47.88    (22)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.39/47.88          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.39/47.88    (23)  op(e2, e3) = all_52_1
% 241.39/47.89    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.39/47.89          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.89    (25)   ~ (all_52_6 = e3)
% 241.39/47.89    (26)  op(e1, e1) = e2
% 241.39/47.89    (27)   ~ (all_52_4 = e3)
% 241.39/47.89    (28)  op(e3, e2) = all_52_4
% 241.39/47.89    (29)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.39/47.89          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.39/47.89    (30)  all_58_10 = e1 & op(e2, e0) = e1
% 241.39/47.89    (31)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.39/47.89          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.39/47.89    (32)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.39/47.89          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.39/47.89    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.89    (34)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.39/47.89          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.39/47.89    (35)  all_58_11 = e0
% 241.39/47.89    (36)   ~ (e1 = e0)
% 241.39/47.89    (37)  all_58_7 = e2 & op(e1, e2) = e2
% 241.39/47.89    (38)  all_58_4 = e3
% 241.39/47.89    (39)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.39/47.89          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.39/47.89            e1)
% 241.39/47.89    (40)   ~ (all_52_1 = e3)
% 241.39/47.89    (41)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.39/47.89          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.39/47.89            e2)
% 241.39/47.89    (42)   ~ (e2 = e1)
% 241.39/47.89  
% 241.39/47.89  Begin of proof
% 241.39/47.89  | 
% 241.39/47.89  | BETA: splitting (18) gives:
% 241.39/47.89  | 
% 241.39/47.89  | Case 1:
% 241.39/47.89  | | 
% 241.39/47.89  | |   (43)  all_58_15 = e0 & op(e0, e0) = e0
% 241.39/47.89  | | 
% 241.39/47.89  | | ALPHA: (43) implies:
% 241.39/47.89  | |   (44)  all_58_15 = e0
% 241.39/47.89  | | 
% 241.39/47.89  | | COMBINE_EQS: (10), (44) imply:
% 241.39/47.89  | |   (45)  e3 = e0
% 241.39/47.89  | | 
% 241.39/47.89  | | SIMP: (45) implies:
% 241.39/47.89  | |   (46)  e3 = e0
% 241.39/47.89  | | 
% 241.39/47.89  | | COMBINE_EQS: (4), (46) imply:
% 241.39/47.89  | |   (47)  all_58_6 = e0
% 241.39/47.89  | | 
% 241.39/47.89  | | REF_CLOSE: (2), (6), (20), (22), (25), (26), (33), (35), (47) are
% 241.39/47.89  | |            inconsistent by sub-proof #1686.
% 241.39/47.89  | | 
% 241.39/47.89  | Case 2:
% 241.39/47.89  | | 
% 241.39/47.89  | | 
% 241.39/47.89  | | ALPHA: (37) implies:
% 241.39/47.89  | |   (48)  all_58_7 = e2
% 241.39/47.89  | | 
% 241.39/47.89  | | ALPHA: (30) implies:
% 241.39/47.89  | |   (49)  all_58_10 = e1
% 241.39/47.89  | | 
% 241.39/47.89  | | GROUND_INST: instantiating (33) with e1, e2, e1, e1, simplifying with (3),
% 241.39/47.89  | |              (26) gives:
% 241.39/47.89  | |   (50)  e2 = e1
% 241.39/47.89  | | 
% 241.39/47.89  | | COMBINE_EQS: (48), (50) imply:
% 241.39/47.89  | |   (51)  all_58_7 = e1
% 241.39/47.89  | | 
% 241.39/47.89  | | BETA: splitting (39) gives:
% 241.39/47.89  | | 
% 241.39/47.89  | | Case 1:
% 241.39/47.89  | | | 
% 241.39/47.89  | | |   (52)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2)
% 241.39/47.89  | | |           = e1)
% 241.39/47.89  | | | 
% 241.39/47.89  | | | BETA: splitting (52) gives:
% 241.39/47.89  | | | 
% 241.39/47.89  | | | Case 1:
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | |   (53)  all_58_12 = e1 & op(e0, e3) = e1
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | | ALPHA: (53) implies:
% 241.39/47.89  | | | |   (54)  all_58_12 = e1
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | | REF_CLOSE: (2), (4), (5), (17), (19), (20), (21), (33), (36), (42), (54)
% 241.39/47.89  | | | |            are inconsistent by sub-proof #1206.
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | Case 2:
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | |   (55)  all_58_13 = e1 & op(e0, e2) = e1
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | | ALPHA: (55) implies:
% 241.39/47.89  | | | |   (56)  all_58_13 = e1
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | | REF_CLOSE: (2), (5), (7), (8), (14), (20), (36), (42), (51), (56) are
% 241.39/47.89  | | | |            inconsistent by sub-proof #1457.
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | End of split
% 241.39/47.89  | | | 
% 241.39/47.89  | | Case 2:
% 241.39/47.89  | | | 
% 241.39/47.89  | | |   (57)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0)
% 241.39/47.89  | | |           = e1)
% 241.39/47.89  | | | 
% 241.39/47.89  | | | BETA: splitting (57) gives:
% 241.39/47.89  | | | 
% 241.39/47.89  | | | Case 1:
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | |   (58)  all_58_14 = e1 & op(e0, e1) = e1
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | | ALPHA: (58) implies:
% 241.39/47.89  | | | |   (59)  all_58_14 = e1
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | | BETA: splitting (13) gives:
% 241.39/47.89  | | | | 
% 241.39/47.89  | | | | Case 1:
% 241.39/47.89  | | | | | 
% 241.39/47.89  | | | | |   (60)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 241.39/47.89  | | | | |             e1) = e0)
% 241.39/47.89  | | | | | 
% 241.39/47.89  | | | | | BETA: splitting (60) gives:
% 241.39/47.89  | | | | | 
% 241.39/47.89  | | | | | Case 1:
% 241.39/47.89  | | | | | | 
% 241.39/47.89  | | | | | |   (61)  all_58_4 = e0 & op(e3, e1) = e0
% 241.39/47.89  | | | | | | 
% 241.39/47.89  | | | | | | ALPHA: (61) implies:
% 241.39/47.89  | | | | | |   (62)  all_58_4 = e0
% 241.39/47.89  | | | | | | 
% 241.39/47.89  | | | | | | COMBINE_EQS: (38), (62) imply:
% 241.39/47.89  | | | | | |   (63)  e3 = e0
% 241.39/47.89  | | | | | | 
% 241.39/47.89  | | | | | | COMBINE_EQS: (4), (63) imply:
% 241.39/47.89  | | | | | |   (64)  all_58_6 = e0
% 241.39/47.89  | | | | | | 
% 241.39/47.89  | | | | | | REF_CLOSE: (2), (5), (10), (12), (16), (17), (18), (20), (23), (33),
% 241.39/47.89  | | | | | |            (36), (40), (41), (42), (59), (64) are inconsistent by
% 241.39/47.89  | | | | | |            sub-proof #542.
% 241.39/47.89  | | | | | | 
% 241.39/47.89  | | | | | Case 2:
% 241.39/47.89  | | | | | | 
% 241.39/47.89  | | | | | |   (65)  all_58_5 = e0 & op(e2, e1) = e0
% 241.39/47.89  | | | | | | 
% 241.39/47.89  | | | | | | ALPHA: (65) implies:
% 241.39/47.89  | | | | | |   (66)  all_58_5 = e0
% 241.39/47.89  | | | | | | 
% 241.39/47.89  | | | | | | BETA: splitting (11) gives:
% 241.39/47.89  | | | | | | 
% 241.39/47.89  | | | | | | Case 1:
% 241.39/47.89  | | | | | | | 
% 241.39/47.89  | | | | | | |   (67)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 241.39/47.89  | | | | | | |           op(e2, e2) = e2)
% 241.39/47.89  | | | | | | | 
% 241.39/47.89  | | | | | | | BETA: splitting (67) gives:
% 241.39/47.89  | | | | | | | 
% 241.39/47.89  | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | 
% 241.39/47.89  | | | | | | | |   (68)  all_58_2 = e2 & op(e2, e3) = e2
% 241.39/47.89  | | | | | | | | 
% 241.39/47.89  | | | | | | | | ALPHA: (68) implies:
% 241.39/47.89  | | | | | | | |   (69)  all_58_2 = e2
% 241.39/47.89  | | | | | | | | 
% 241.39/47.89  | | | | | | | | BETA: splitting (34) gives:
% 241.39/47.89  | | | | | | | | 
% 241.39/47.89  | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | 
% 241.39/47.89  | | | | | | | | |   (70)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 241.39/47.89  | | | | | | | | |           op(e2, e0) = e2)
% 241.39/47.89  | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | BETA: splitting (70) gives:
% 241.39/47.89  | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | |   (71)  all_58_9 = e2 & op(e3, e0) = e2
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | ALPHA: (71) implies:
% 241.39/47.89  | | | | | | | | | |   (72)  all_58_9 = e2
% 241.39/47.89  | | | | | | | | | |   (73)  op(e3, e0) = e2
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | BETA: splitting (18) gives:
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | |   (74)  all_58_15 = e0 & op(e0, e0) = e0
% 241.39/47.89  | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | ALPHA: (74) implies:
% 241.39/47.89  | | | | | | | | | | |   (75)  all_58_15 = e0
% 241.39/47.89  | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | REF_CLOSE: (2), (10), (12), (15), (17), (20), (27), (28),
% 241.39/47.89  | | | | | | | | | | |            (33), (38), (73), (75) are inconsistent by
% 241.39/47.89  | | | | | | | | | | |            sub-proof #651.
% 241.39/47.89  | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | |   (76)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.39/47.89  | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 241.39/47.89  | | | | | | | | | | |             op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 241.39/47.89  | | | | | | | | | | |               e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 241.39/47.89  | | | | | | | | | | |             e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.39/47.89  | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | ALPHA: (76) implies:
% 241.39/47.89  | | | | | | | | | | |   (77)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.39/47.89  | | | | | | | | | | |           e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 241.39/47.89  | | | | | | | | | | |             e0) = e0)
% 241.39/47.89  | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | BETA: splitting (21) gives:
% 241.39/47.89  | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | |   (78)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 241.39/47.89  | | | | | | | | | | | |           & op(e2, e3) = e0)
% 241.39/47.89  | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | REF_CLOSE: (5), (17), (33), (36), (69), (78) are inconsistent
% 241.39/47.89  | | | | | | | | | | | |            by sub-proof #1534.
% 241.39/47.89  | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | |   (79)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 241.39/47.89  | | | | | | | | | | | |           e0 & op(e0, e3) = e0)
% 241.39/47.89  | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | BETA: splitting (79) gives:
% 241.39/47.89  | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | |   (80)  all_58_6 = e0 & op(e1, e3) = e0
% 241.39/47.89  | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | ALPHA: (80) implies:
% 241.39/47.89  | | | | | | | | | | | | |   (81)  all_58_6 = e0
% 241.39/47.89  | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (12), (16), (17), (18), (20),
% 241.39/47.89  | | | | | | | | | | | | |            (23), (33), (36), (40), (41), (42), (59), (81) are
% 241.39/47.89  | | | | | | | | | | | | |            inconsistent by sub-proof #542.
% 241.39/47.89  | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | |   (82)  all_58_12 = e0 & op(e0, e3) = e0
% 241.39/47.89  | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | ALPHA: (82) implies:
% 241.39/47.89  | | | | | | | | | | | | |   (83)  all_58_12 = e0
% 241.39/47.89  | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | BETA: splitting (41) gives:
% 241.39/47.89  | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | |   (84)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 241.39/47.89  | | | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 241.39/47.89  | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 241.39/47.89  | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | |   (85)  all_58_12 = e2 & op(e0, e3) = e2
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | ALPHA: (85) implies:
% 241.39/47.89  | | | | | | | | | | | | | | |   (86)  all_58_12 = e2
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | COMBINE_EQS: (83), (86) imply:
% 241.39/47.89  | | | | | | | | | | | | | | |   (87)  e2 = e0
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | COMBINE_EQS: (69), (87) imply:
% 241.39/47.89  | | | | | | | | | | | | | | |   (88)  all_58_2 = e0
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17), (19), (20), (33), (42), (83), (88)
% 241.39/47.89  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1150.
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | |   (89)  all_58_13 = e2 & op(e0, e2) = e2
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 241.39/47.89  | | | | | | | | | | | | | | |   (90)  all_58_13 = e2
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | |   (91)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.39/47.89  | | | | | | | | | | | | | | | |           & op(e1, e2) = e2)
% 241.39/47.89  | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 241.39/47.89  | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (92)  all_58_6 = e2 & op(e1, e3) = e2
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (93)  all_58_6 = e2
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (93) imply:
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (94)  e3 = e2
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | SIMP: (94) implies:
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (95)  e3 = e2
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (95) imply:
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (96)  all_58_15 = e2
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (12), (15), (17), (20), (24), (27),
% 241.39/47.89  | | | | | | | | | | | | | | | | |            (28), (29), (33), (35), (36), (42), (49), (73),
% 241.39/47.89  | | | | | | | | | | | | | | | | |            (96) are inconsistent by sub-proof #526.
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (72) imply:
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (97)  all_58_9 = e1
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (12), (15), (17), (20), (24), (27),
% 241.39/47.89  | | | | | | | | | | | | | | | | |            (28), (29), (33), (34), (36), (42), (49), (77),
% 241.39/47.89  | | | | | | | | | | | | | | | | |            (97) are inconsistent by sub-proof #1168.
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | |   (98)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.39/47.89  | | | | | | | | | | | | | | | |           e2 & op(e1, e0) = e2)
% 241.39/47.89  | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 241.39/47.89  | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (99)  all_58_8 = e2 & op(e1, e1) = e2
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (100)  all_58_8 = e2
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (14), (20),
% 241.39/47.89  | | | | | | | | | | | | | | | | |            (22), (25), (26), (31), (33), (35), (36), (42),
% 241.39/47.89  | | | | | | | | | | | | | | | | |            (51), (90), (100) are inconsistent by sub-proof
% 241.39/47.89  | | | | | | | | | | | | | | | | |            #964.
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (101)  all_58_11 = e2 & op(e1, e0) = e2
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (102)  all_58_11 = e2
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (102) imply:
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (103)  e2 = e0
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (103) imply:
% 241.39/47.89  | | | | | | | | | | | | | | | | |   (104)  all_58_2 = e0
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17), (19), (20), (33), (42), (83),
% 241.39/47.89  | | | | | | | | | | | | | | | | |            (104) are inconsistent by sub-proof #1150.
% 241.39/47.89  | | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | |   (105)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 241.39/47.89  | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.39/47.89  | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 241.39/47.89  | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | |   (106)  all_58_14 = e2 & op(e0, e1) = e2
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 241.39/47.89  | | | | | | | | | | | | | | |   (107)  all_58_14 = e2
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | COMBINE_EQS: (50), (72) imply:
% 241.39/47.89  | | | | | | | | | | | | | | |   (108)  all_58_9 = e1
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (12), (15), (17), (20), (24), (27),
% 241.39/47.89  | | | | | | | | | | | | | | |            (28), (29), (33), (34), (36), (42), (49), (77),
% 241.39/47.89  | | | | | | | | | | | | | | |            (108) are inconsistent by sub-proof #1168.
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | |   (109)  all_58_15 = e2 & op(e0, e0) = e2
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 241.39/47.89  | | | | | | | | | | | | | | |   (110)  all_58_15 = e2
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (12), (15), (17), (20), (24), (27),
% 241.39/47.89  | | | | | | | | | | | | | | |            (28), (29), (33), (35), (36), (42), (49), (73),
% 241.39/47.89  | | | | | | | | | | | | | | |            (110) are inconsistent by sub-proof #526.
% 241.39/47.89  | | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | |   (111)  all_58_10 = e2 & op(e2, e0) = e2
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | ALPHA: (111) implies:
% 241.39/47.89  | | | | | | | | | |   (112)  all_58_10 = e2
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | REF_CLOSE: (42), (49), (112) are inconsistent by sub-proof
% 241.39/47.89  | | | | | | | | | |            #1598.
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | | 
% 241.39/47.89  | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | 
% 241.39/47.89  | | | | | | | | |   (113)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2
% 241.39/47.89  | | | | | | | | |            & op(e0, e0) = e2)
% 241.39/47.89  | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | BETA: splitting (113) gives:
% 241.39/47.89  | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | Case 1:
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | |   (114)  all_58_11 = e2 & op(e1, e0) = e2
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | ALPHA: (114) implies:
% 241.39/47.89  | | | | | | | | | |   (115)  all_58_11 = e2
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | REF_CLOSE: (5), (35), (115) are inconsistent by sub-proof
% 241.39/47.89  | | | | | | | | | |            #2110.
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | |   (116)  all_58_15 = e2 & op(e0, e0) = e2
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | | REF_CLOSE: (10), (20), (116) are inconsistent by sub-proof
% 241.39/47.89  | | | | | | | | | |            #1231.
% 241.39/47.89  | | | | | | | | | | 
% 241.39/47.89  | | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | | 
% 241.39/47.89  | | | | | | | | End of split
% 241.39/47.89  | | | | | | | | 
% 241.39/47.89  | | | | | | | Case 2:
% 241.39/47.89  | | | | | | | | 
% 241.39/47.89  | | | | | | | |   (117)  all_58_3 = e2 & op(e2, e2) = e2
% 241.39/47.89  | | | | | | | | 
% 241.39/47.89  | | | | | | | | REF_CLOSE: (14), (20), (117) are inconsistent by sub-proof
% 241.39/47.89  | | | | | | | |            #1458.
% 241.39/47.89  | | | | | | | | 
% 241.39/47.89  | | | | | | | End of split
% 241.39/47.89  | | | | | | | 
% 241.39/47.89  | | | | | | Case 2:
% 241.39/47.89  | | | | | | | 
% 241.39/47.89  | | | | | | |   (118)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 241.39/47.89  | | | | | | |            op(e2, e0) = e2)
% 241.39/47.89  | | | | | | | 
% 241.39/47.90  | | | | | | | REF_CLOSE: (5), (42), (49), (66), (118) are inconsistent by
% 241.39/47.90  | | | | | | |            sub-proof #525.
% 241.39/47.90  | | | | | | | 
% 241.39/47.90  | | | | | | End of split
% 241.39/47.90  | | | | | | 
% 241.39/47.90  | | | | | End of split
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | Case 2:
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | |   (119)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 241.39/47.90  | | | | |              e1) = e0)
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | | BETA: splitting (119) gives:
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | | Case 1:
% 241.39/47.90  | | | | | | 
% 241.39/47.90  | | | | | |   (120)  all_58_8 = e0 & op(e1, e1) = e0
% 241.39/47.90  | | | | | | 
% 241.39/47.90  | | | | | | ALPHA: (120) implies:
% 241.39/47.90  | | | | | |   (121)  op(e1, e1) = e0
% 241.39/47.90  | | | | | | 
% 241.39/47.90  | | | | | | REF_CLOSE: (3), (33), (36), (121) are inconsistent by sub-proof
% 241.39/47.90  | | | | | |            #2220.
% 241.39/47.90  | | | | | | 
% 241.39/47.90  | | | | | Case 2:
% 241.39/47.90  | | | | | | 
% 241.39/47.90  | | | | | |   (122)  all_58_14 = e0 & op(e0, e1) = e0
% 241.39/47.90  | | | | | | 
% 241.39/47.90  | | | | | | ALPHA: (122) implies:
% 241.39/47.90  | | | | | |   (123)  all_58_14 = e0
% 241.39/47.90  | | | | | | 
% 241.39/47.90  | | | | | | REF_CLOSE: (1), (2), (4), (5), (9), (11), (12), (14), (15), (17),
% 241.39/47.90  | | | | | |            (20), (24), (27), (28), (31), (32), (33), (35), (36),
% 241.39/47.90  | | | | | |            (42), (49), (51), (123) are inconsistent by sub-proof
% 241.39/47.90  | | | | | |            #540.
% 241.39/47.90  | | | | | | 
% 241.39/47.90  | | | | | End of split
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | End of split
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | Case 2:
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | |   (124)  all_58_15 = e1 & op(e0, e0) = e1
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | | ALPHA: (124) implies:
% 241.39/47.90  | | | |   (125)  all_58_15 = e1
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | | REF_CLOSE: (2), (5), (12), (20), (29), (33), (34), (35), (42), (49),
% 241.39/47.90  | | | |            (125) are inconsistent by sub-proof #1597.
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | End of split
% 241.39/47.90  | | | 
% 241.39/47.90  | | End of split
% 241.39/47.90  | | 
% 241.39/47.90  | End of split
% 241.39/47.90  | 
% 241.39/47.90  End of proof
% 241.39/47.90  
% 241.39/47.90  Sub-proof #525 shows that the following formulas are inconsistent:
% 241.39/47.90  ----------------------------------------------------------------
% 241.39/47.90    (1)  all_58_5 = e0
% 241.39/47.90    (2)   ~ (e2 = e0)
% 241.39/47.90    (3)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.39/47.90    (4)  all_58_10 = e1
% 241.39/47.90    (5)   ~ (e2 = e1)
% 241.39/47.90  
% 241.39/47.90  Begin of proof
% 241.39/47.90  | 
% 241.39/47.90  | BETA: splitting (3) gives:
% 241.39/47.90  | 
% 241.39/47.90  | Case 1:
% 241.39/47.90  | | 
% 241.39/47.90  | |   (6)  all_58_5 = e2 & op(e2, e1) = e2
% 241.39/47.90  | | 
% 241.39/47.90  | | ALPHA: (6) implies:
% 241.39/47.90  | |   (7)  all_58_5 = e2
% 241.39/47.90  | | 
% 241.39/47.90  | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #835.
% 241.39/47.90  | | 
% 241.39/47.90  | Case 2:
% 241.39/47.90  | | 
% 241.39/47.90  | |   (8)  all_58_10 = e2 & op(e2, e0) = e2
% 241.39/47.90  | | 
% 241.39/47.90  | | ALPHA: (8) implies:
% 241.39/47.90  | |   (9)  all_58_10 = e2
% 241.39/47.90  | | 
% 241.39/47.90  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #1598.
% 241.39/47.90  | | 
% 241.39/47.90  | End of split
% 241.39/47.90  | 
% 241.39/47.90  End of proof
% 241.39/47.90  
% 241.39/47.90  Sub-proof #526 shows that the following formulas are inconsistent:
% 241.39/47.90  ----------------------------------------------------------------
% 241.39/47.90    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.39/47.90         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.39/47.90    (2)   ~ (e3 = e0)
% 241.39/47.90    (3)   ~ (e2 = e0)
% 241.39/47.90    (4)   ~ (e3 = e1)
% 241.39/47.90    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.90         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.90    (6)  op(e3, e3) = e1
% 241.39/47.90    (7)  all_58_15 = e2
% 241.39/47.90    (8)   ~ (e3 = e2)
% 241.39/47.90    (9)  op(e3, e0) = e2
% 241.39/47.90    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.39/47.90          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.90    (11)   ~ (all_52_4 = e3)
% 241.39/47.90    (12)  op(e3, e2) = all_52_4
% 241.39/47.90    (13)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.39/47.90          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.39/47.90    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.90    (15)  all_58_11 = e0
% 241.39/47.90    (16)   ~ (e1 = e0)
% 241.39/47.90    (17)  all_58_10 = e1
% 241.39/47.90    (18)   ~ (e2 = e1)
% 241.39/47.90  
% 241.39/47.90  Begin of proof
% 241.39/47.90  | 
% 241.39/47.90  | BETA: splitting (5) gives:
% 241.39/47.90  | 
% 241.39/47.90  | Case 1:
% 241.39/47.90  | | 
% 241.39/47.90  | |   (19)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 241.39/47.90  | |           e3)
% 241.39/47.90  | | 
% 241.39/47.90  | | REF_CLOSE: (4), (6), (11), (12), (14), (19) are inconsistent by sub-proof
% 241.39/47.90  | |            #1401.
% 241.39/47.90  | | 
% 241.39/47.90  | Case 2:
% 241.39/47.90  | | 
% 241.39/47.90  | |   (20)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 241.39/47.90  | |           e3)
% 241.39/47.90  | | 
% 241.39/47.90  | | BETA: splitting (20) gives:
% 241.39/47.90  | | 
% 241.39/47.90  | | Case 1:
% 241.39/47.90  | | | 
% 241.39/47.90  | | |   (21)  all_58_4 = e3 & op(e3, e1) = e3
% 241.39/47.90  | | | 
% 241.39/47.90  | | | ALPHA: (21) implies:
% 241.39/47.90  | | |   (22)  all_58_4 = e3
% 241.39/47.90  | | | 
% 241.39/47.90  | | | BETA: splitting (13) gives:
% 241.39/47.90  | | | 
% 241.39/47.90  | | | Case 1:
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | |   (23)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0)
% 241.39/47.90  | | | |           = e3)
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | | BETA: splitting (23) gives:
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | | Case 1:
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | |   (24)  all_58_9 = e3 & op(e3, e0) = e3
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | | ALPHA: (24) implies:
% 241.39/47.90  | | | | |   (25)  op(e3, e0) = e3
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | | REF_CLOSE: (8), (9), (14), (25) are inconsistent by sub-proof #2125.
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | Case 2:
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | |   (26)  all_58_10 = e3 & op(e2, e0) = e3
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (14),
% 241.39/47.90  | | | | |            (16), (17), (18), (22), (26) are inconsistent by sub-proof
% 241.39/47.90  | | | | |            #1171.
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | End of split
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | Case 2:
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | |   (27)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 241.39/47.90  | | | |             e0) = e3)
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | | BETA: splitting (27) gives:
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | | Case 1:
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | |   (28)  all_58_11 = e3 & op(e1, e0) = e3
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (11), (12), (14), (15), (22),
% 241.39/47.90  | | | | |            (28) are inconsistent by sub-proof #1064.
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | Case 2:
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | |   (29)  all_58_15 = e3 & op(e0, e0) = e3
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | | REF_CLOSE: (7), (8), (29) are inconsistent by sub-proof #1170.
% 241.39/47.90  | | | | | 
% 241.39/47.90  | | | | End of split
% 241.39/47.90  | | | | 
% 241.39/47.90  | | | End of split
% 241.39/47.90  | | | 
% 241.39/47.90  | | Case 2:
% 241.39/47.90  | | | 
% 241.39/47.90  | | |   (30)  all_58_9 = e3 & op(e3, e0) = e3
% 241.39/47.90  | | | 
% 241.39/47.90  | | | ALPHA: (30) implies:
% 241.39/47.90  | | |   (31)  op(e3, e0) = e3
% 241.39/47.90  | | | 
% 241.39/47.90  | | | REF_CLOSE: (8), (9), (14), (31) are inconsistent by sub-proof #2125.
% 241.39/47.90  | | | 
% 241.39/47.90  | | End of split
% 241.39/47.90  | | 
% 241.39/47.90  | End of split
% 241.39/47.90  | 
% 241.39/47.90  End of proof
% 241.39/47.90  
% 241.39/47.90  Sub-proof #527 shows that the following formulas are inconsistent:
% 241.39/47.90  ----------------------------------------------------------------
% 241.39/47.90    (1)   ~ (all_52_9 = all_6_2)
% 241.39/47.90    (2)  all_58_6 = e3
% 241.39/47.90    (3)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.39/47.90           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.39/47.90             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.39/47.90           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.39/47.90             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.39/47.90           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.39/47.90           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.39/47.90           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.39/47.90           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.39/47.90           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.39/47.90           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.39/47.90             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.39/47.90           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.39/47.90           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 241.39/47.90           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.39/47.90           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.39/47.90           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.39/47.90           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.39/47.90             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.39/47.90           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.39/47.90           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 241.39/47.90           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.39/47.90           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.39/47.90           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.39/47.90           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.39/47.90             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.39/47.90           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.39/47.90           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.39/47.90    (4)  all_58_3 = e3
% 241.39/47.90    (5)  all_54_10 = all_6_2
% 241.39/47.90    (6)   ~ (all_6_2 = e3)
% 241.39/47.90    (7)  op(e2, e1) = all_52_9
% 241.39/47.90    (8)   ~ (all_6_2 = e0)
% 241.39/47.90    (9)  op(e2, e3) = all_52_1
% 241.39/47.90    (10)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 241.39/47.90    (11)  all_56_31 = e3
% 241.39/47.90    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.90    (13)  all_56_11 = e3
% 241.39/47.90    (14)  all_56_21 = all_6_2
% 241.39/47.90    (15)  all_58_6 = e0 & op(e1, e3) = e0
% 241.39/47.90    (16)  op(e2, e0) = all_52_13
% 241.39/47.90    (17)   ~ (all_52_1 = e3)
% 241.39/47.90    (18)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.39/47.90          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.39/47.90    (19)  all_56_1 = e1
% 241.39/47.90    (20)   ~ (all_52_1 = e1)
% 241.39/47.90  
% 241.39/47.90  Begin of proof
% 241.39/47.90  | 
% 241.39/47.90  | ALPHA: (15) implies:
% 241.39/47.90  |   (21)  all_58_6 = e0
% 241.39/47.90  | 
% 241.39/47.90  | COMBINE_EQS: (2), (21) imply:
% 241.39/47.90  |   (22)  e3 = e0
% 241.39/47.90  | 
% 241.39/47.90  | COMBINE_EQS: (11), (22) imply:
% 241.39/47.90  |   (23)  all_56_31 = e0
% 241.39/47.90  | 
% 241.39/47.90  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 241.39/47.90  |            (16), (17), (18), (19), (20), (23) are inconsistent by sub-proof
% 241.39/47.90  |            #742.
% 241.39/47.90  | 
% 241.39/47.90  End of proof
% 241.39/47.90  
% 241.39/47.90  Sub-proof #528 shows that the following formulas are inconsistent:
% 241.39/47.90  ----------------------------------------------------------------
% 241.39/47.90    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.39/47.90         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.39/47.90    (2)   ~ (e3 = e0)
% 241.39/47.90    (3)   ~ (e2 = e0)
% 241.39/47.90    (4)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 241.39/47.90    (5)   ~ (e3 = e1)
% 241.39/47.90    (6)  all_58_3 = e3
% 241.39/47.90    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.90         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.90    (8)  op(e3, e3) = e1
% 241.39/47.90    (9)   ~ (e3 = e2)
% 241.39/47.90    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.39/47.90          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.90    (11)   ~ (all_52_4 = e3)
% 241.39/47.90    (12)  op(e3, e2) = all_52_4
% 241.39/47.90    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.90    (14)   ~ (all_52_4 = e1)
% 241.39/47.90    (15)   ~ (e1 = e0)
% 241.39/47.90    (16)  all_58_4 = e3
% 241.39/47.90    (17)   ~ (e2 = e1)
% 241.39/47.90  
% 241.39/47.90  Begin of proof
% 241.39/47.90  | 
% 241.39/47.90  | BETA: splitting (4) gives:
% 241.39/47.90  | 
% 241.39/47.90  | Case 1:
% 241.39/47.90  | | 
% 241.39/47.90  | |   (18)  all_58_1 = e1 & op(e3, e2) = e1
% 241.39/47.90  | | 
% 241.39/47.90  | | ALPHA: (18) implies:
% 241.39/47.90  | |   (19)  op(e3, e2) = e1
% 241.39/47.90  | | 
% 241.39/47.90  | | REF_CLOSE: (12), (13), (14), (19) are inconsistent by sub-proof #2228.
% 241.39/47.90  | | 
% 241.39/47.90  | Case 2:
% 241.39/47.90  | | 
% 241.39/47.90  | |   (20)  all_58_3 = e1 & op(e2, e2) = e1
% 241.39/47.90  | | 
% 241.39/47.90  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.39/47.90  | |            (15), (16), (17), (20) are inconsistent by sub-proof #1030.
% 241.39/47.90  | | 
% 241.39/47.90  | End of split
% 241.39/47.90  | 
% 241.39/47.90  End of proof
% 241.39/47.90  
% 241.39/47.90  Sub-proof #529 shows that the following formulas are inconsistent:
% 241.39/47.90  ----------------------------------------------------------------
% 241.39/47.90    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.39/47.90         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.39/47.90    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.39/47.90         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.39/47.90    (3)   ~ (e3 = e0)
% 241.39/47.90    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.39/47.90         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.39/47.90    (5)  all_58_6 = e3
% 241.39/47.90    (6)   ~ (e2 = e0)
% 241.39/47.90    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.39/47.90         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.39/47.90    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.39/47.90         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.39/47.90    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.39/47.90         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.39/47.90    (10)   ~ (all_52_7 = e3)
% 241.39/47.91    (11)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.39/47.91          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.39/47.91    (12)   ~ (e3 = e1)
% 241.39/47.91    (13)  all_58_3 = e3
% 241.39/47.91    (14)  all_58_11 = e3
% 241.39/47.91    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.91          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.91    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.39/47.91          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.39/47.91    (17)  op(e3, e3) = e1
% 241.39/47.91    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.91              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.39/47.91                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.39/47.91                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.39/47.91    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.39/47.91          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.39/47.91    (20)   ~ (e3 = e2)
% 241.39/47.91    (21)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.39/47.91          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.39/47.91    (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.39/47.91          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.39/47.91    (23)  op(e2, e3) = all_52_1
% 241.39/47.91    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.39/47.91          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.91    (25)  op(e0, e2) = all_52_7
% 241.39/47.91    (26)   ~ (all_52_4 = e3)
% 241.39/47.91    (27)  op(e3, e2) = all_52_4
% 241.39/47.91    (28)  op(e0, e0) = e3
% 241.39/47.91    (29)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.39/47.91          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.39/47.91    (30)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.39/47.91          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.39/47.91    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.91    (32)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.39/47.91          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.39/47.91    (33)   ~ (e1 = e0)
% 241.39/47.91    (34)  all_58_4 = e3
% 241.39/47.91    (35)  all_58_4 = e3 & op(e3, e1) = e3
% 241.39/47.91    (36)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.39/47.91          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.39/47.91    (37)  op(e2, e0) = all_52_13
% 241.39/47.91    (38)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.39/47.91          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.39/47.91            e1)
% 241.39/47.91    (39)   ~ (all_52_1 = e3)
% 241.39/47.91    (40)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.39/47.91          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.39/47.91    (41)   ~ (e2 = e1)
% 241.39/47.91    (42)   ~ (all_52_1 = e1)
% 241.39/47.91  
% 241.39/47.91  Begin of proof
% 241.39/47.91  | 
% 241.39/47.91  | BETA: splitting (8) gives:
% 241.39/47.91  | 
% 241.39/47.91  | Case 1:
% 241.39/47.91  | | 
% 241.39/47.91  | |   (43)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 241.39/47.91  | |           e1)
% 241.39/47.91  | | 
% 241.39/47.91  | | BETA: splitting (43) gives:
% 241.39/47.91  | | 
% 241.39/47.91  | | Case 1:
% 241.39/47.91  | | | 
% 241.39/47.91  | | |   (44)  all_58_9 = e1 & op(e3, e0) = e1
% 241.39/47.91  | | | 
% 241.39/47.91  | | | ALPHA: (44) implies:
% 241.39/47.91  | | |   (45)  all_58_9 = e1
% 241.39/47.91  | | | 
% 241.39/47.91  | | | REF_CLOSE: (1), (3), (6), (17), (20), (24), (31), (33), (34), (41), (45)
% 241.39/47.91  | | |            are inconsistent by sub-proof #1292.
% 241.39/47.91  | | | 
% 241.39/47.91  | | Case 2:
% 241.39/47.91  | | | 
% 241.39/47.91  | | |   (46)  all_58_10 = e1 & op(e2, e0) = e1
% 241.39/47.91  | | | 
% 241.39/47.91  | | | ALPHA: (46) implies:
% 241.39/47.91  | | |   (47)  all_58_10 = e1
% 241.39/47.91  | | |   (48)  op(e2, e0) = e1
% 241.39/47.91  | | | 
% 241.39/47.91  | | | BETA: splitting (32) gives:
% 241.39/47.91  | | | 
% 241.39/47.91  | | | Case 1:
% 241.39/47.91  | | | | 
% 241.39/47.91  | | | |   (49)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 241.39/47.91  | | | |           = e2)
% 241.39/47.91  | | | | 
% 241.39/47.91  | | | | BETA: splitting (49) gives:
% 241.39/47.91  | | | | 
% 241.39/47.91  | | | | Case 1:
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | |   (50)  all_58_9 = e2 & op(e3, e0) = e2
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 241.39/47.91  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 241.39/47.91  | | | | |            (24), (25), (26), (27), (29), (30), (31), (32), (33), (34),
% 241.39/47.91  | | | | |            (36), (37), (38), (39), (40), (41), (42), (47), (48), (50)
% 241.39/47.91  | | | | |            are inconsistent by sub-proof #531.
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | Case 2:
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | |   (51)  all_58_10 = e2 & op(e2, e0) = e2
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | | REF_CLOSE: (41), (47), (51) are inconsistent by sub-proof #1622.
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | End of split
% 241.39/47.91  | | | | 
% 241.39/47.91  | | | Case 2:
% 241.39/47.91  | | | | 
% 241.39/47.91  | | | |   (52)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 241.39/47.91  | | | |             e0) = e2)
% 241.39/47.91  | | | | 
% 241.39/47.91  | | | | BETA: splitting (52) gives:
% 241.39/47.91  | | | | 
% 241.39/47.91  | | | | Case 1:
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | |   (53)  all_58_11 = e2 & op(e1, e0) = e2
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | | ALPHA: (53) implies:
% 241.39/47.91  | | | | |   (54)  all_58_11 = e2
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | | REF_CLOSE: (14), (20), (54) are inconsistent by sub-proof #2030.
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | Case 2:
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | |   (55)  all_58_15 = e2 & op(e0, e0) = e2
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | | ALPHA: (55) implies:
% 241.39/47.91  | | | | |   (56)  all_58_15 = e2
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | | BETA: splitting (2) gives:
% 241.39/47.91  | | | | | 
% 241.39/47.91  | | | | | Case 1:
% 241.39/47.91  | | | | | | 
% 241.39/47.91  | | | | | |   (57)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 241.39/47.91  | | | | | |           op(e0, e2) = e3)
% 241.39/47.91  | | | | | | 
% 241.39/47.91  | | | | | | REF_CLOSE: (3), (5), (6), (10), (17), (19), (20), (22), (25), (31),
% 241.39/47.91  | | | | | |            (33), (41), (57) are inconsistent by sub-proof #1167.
% 241.39/47.91  | | | | | | 
% 241.39/47.91  | | | | | Case 2:
% 241.39/47.91  | | | | | | 
% 241.39/47.91  | | | | | |   (58)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 241.39/47.91  | | | | | |           op(e0, e0) = e3)
% 241.39/47.91  | | | | | | 
% 241.39/47.91  | | | | | | BETA: splitting (58) gives:
% 241.39/47.91  | | | | | | 
% 241.39/47.91  | | | | | | Case 1:
% 241.39/47.91  | | | | | | | 
% 241.39/47.91  | | | | | | |   (59)  all_58_14 = e3 & op(e0, e1) = e3
% 241.39/47.91  | | | | | | | 
% 241.39/47.91  | | | | | | | ALPHA: (59) implies:
% 241.39/47.91  | | | | | | |   (60)  all_58_14 = e3
% 241.39/47.91  | | | | | | | 
% 241.39/47.91  | | | | | | | BETA: splitting (18) gives:
% 241.39/47.91  | | | | | | | 
% 241.39/47.91  | | | | | | | Case 1:
% 241.39/47.91  | | | | | | | | 
% 241.39/47.91  | | | | | | | |   (61)  all_58_15 = e0 & op(e0, e0) = e0
% 241.39/47.91  | | | | | | | | 
% 241.39/47.91  | | | | | | | | REF_CLOSE: (6), (56), (61) are inconsistent by sub-proof #1873.
% 241.39/47.91  | | | | | | | | 
% 241.39/47.91  | | | | | | | Case 2:
% 241.39/47.91  | | | | | | | | 
% 241.39/47.91  | | | | | | | |   (62)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 241.39/47.91  | | | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 241.39/47.91  | | | | | | | |             e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 241.39/47.91  | | | | | | | |           (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 241.39/47.91  | | | | | | | |             op(e0, e1) = e0))
% 241.39/47.91  | | | | | | | | 
% 241.39/47.91  | | | | | | | | ALPHA: (62) implies:
% 241.39/47.91  | | | | | | | |   (63)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.39/47.91  | | | | | | | |           op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.39/47.92  | | | | | | | |   (64)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 241.39/47.92  | | | | | | | |           op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.39/47.92  | | | | | | | | 
% 241.39/47.92  | | | | | | | | BETA: splitting (64) gives:
% 241.39/47.92  | | | | | | | | 
% 241.39/47.92  | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | 
% 241.39/47.92  | | | | | | | | |   (65)  all_58_9 = e0 & op(e3, e0) = e0
% 241.39/47.92  | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | ALPHA: (65) implies:
% 241.39/47.92  | | | | | | | | |   (66)  all_58_9 = e0
% 241.39/47.92  | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | BETA: splitting (1) gives:
% 241.39/47.92  | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | |   (67)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 &
% 241.39/47.92  | | | | | | | | | |           op(e3, e2) = e2)
% 241.39/47.92  | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | BETA: splitting (67) gives:
% 241.39/47.92  | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | |   (68)  all_58_0 = e2 & op(e3, e3) = e2
% 241.39/47.92  | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | ALPHA: (68) implies:
% 241.39/47.92  | | | | | | | | | | |   (69)  op(e3, e3) = e2
% 241.39/47.92  | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | REF_CLOSE: (17), (31), (41), (69) are inconsistent by
% 241.39/47.92  | | | | | | | | | | |            sub-proof #2267.
% 241.39/47.92  | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | Case 2:
% 241.39/47.92  | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | |   (70)  all_58_1 = e2 & op(e3, e2) = e2
% 241.39/47.92  | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | ALPHA: (70) implies:
% 241.39/47.92  | | | | | | | | | | |   (71)  all_58_1 = e2
% 241.39/47.92  | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | BETA: splitting (38) gives:
% 241.39/47.92  | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | |   (72)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 241.39/47.92  | | | | | | | | | | | |           e1 & op(e0, e2) = e1)
% 241.39/47.92  | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | BETA: splitting (72) gives:
% 241.39/47.92  | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | |   (73)  all_58_12 = e1 & op(e0, e3) = e1
% 241.39/47.92  | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | ALPHA: (73) implies:
% 241.39/47.92  | | | | | | | | | | | | |   (74)  all_58_12 = e1
% 241.39/47.92  | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (17), (19), (20), (22), (31), (33),
% 241.39/47.92  | | | | | | | | | | | | |            (41), (74) are inconsistent by sub-proof #1206.
% 241.39/47.92  | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | Case 2:
% 241.39/47.92  | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | |   (75)  all_58_13 = e1 & op(e0, e2) = e1
% 241.39/47.92  | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | ALPHA: (75) implies:
% 241.39/47.92  | | | | | | | | | | | | |   (76)  all_58_13 = e1
% 241.39/47.92  | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | BETA: splitting (63) gives:
% 241.39/47.92  | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | |   (77)  all_58_12 = e0 & op(e0, e3) = e0
% 241.39/47.92  | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | ALPHA: (77) implies:
% 241.39/47.92  | | | | | | | | | | | | | |   (78)  all_58_12 = e0
% 241.39/47.92  | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 241.39/47.92  | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | |   (79)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 241.39/47.92  | | | | | | | | | | | | | | |           & op(e2, e2) = e0)
% 241.39/47.92  | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 241.39/47.92  | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | |   (80)  all_58_2 = e0 & op(e2, e3) = e0
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | ALPHA: (80) implies:
% 241.39/47.92  | | | | | | | | | | | | | | | |   (81)  all_58_2 = e0
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (17), (19), (20), (31), (41), (78), (81)
% 241.39/47.92  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1150.
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | Case 2:
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | |   (82)  all_58_3 = e0 & op(e2, e2) = e0
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (82) are inconsistent by sub-proof
% 241.39/47.92  | | | | | | | | | | | | | | | |            #1719.
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | End of split
% 241.39/47.92  | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | Case 2:
% 241.39/47.92  | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | |   (83)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 241.39/47.92  | | | | | | | | | | | | | | |           e0 & op(e2, e0) = e0)
% 241.39/47.92  | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 241.39/47.92  | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | |   (84)  all_58_5 = e0 & op(e2, e1) = e0
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 241.39/47.92  | | | | | | | | | | | | | | | |   (85)  all_58_5 = e0
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | |   (86)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 241.39/47.92  | | | | | | | | | | | | | | | | |           & op(e1, e2) = e1)
% 241.39/47.92  | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (12), (13), (16), (17), (19), (20),
% 241.39/47.92  | | | | | | | | | | | | | | | | |            (22), (23), (31), (33), (39), (41), (71), (76),
% 241.39/47.92  | | | | | | | | | | | | | | | | |            (86) are inconsistent by sub-proof #530.
% 241.39/47.92  | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | Case 2:
% 241.39/47.92  | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | |   (87)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 241.39/47.92  | | | | | | | | | | | | | | | | |           e1 & op(e1, e0) = e1)
% 241.39/47.92  | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 241.39/47.92  | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | |   (88)  all_58_8 = e1 & op(e1, e1) = e1
% 241.39/47.92  | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | ALPHA: (88) implies:
% 241.39/47.92  | | | | | | | | | | | | | | | | | |   (89)  all_58_8 = e1
% 241.39/47.92  | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | |   (90)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 241.39/47.92  | | | | | | | | | | | | | | | | | | |           & op(e2, e1) = e2)
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |   (91)  all_58_4 = e2 & op(e3, e1) = e2
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (34), (91) are inconsistent by sub-proof
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |            #1476.
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |   (92)  all_58_5 = e2 & op(e2, e1) = e2
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |   (93)  all_58_5 = e2
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (85), (93) are inconsistent by sub-proof
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |            #835.
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | End of split
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | Case 2:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | |   (94)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 241.39/47.92  | | | | | | | | | | | | | | | | | | |           e2 & op(e0, e1) = e2)
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |   (95)  all_58_8 = e2 & op(e1, e1) = e2
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |   (96)  all_58_8 = e2
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (96) imply:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |   (97)  e2 = e1
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (97) imply:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |   (98)  all_58_15 = e1
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (12), (20), (29), (32), (41), (47),
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |            (66), (98) are inconsistent by sub-proof #1618.
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |   (99)  all_58_14 = e2 & op(e0, e1) = e2
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |   (100)  all_58_14 = e2
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (60), (100) are inconsistent by sub-proof
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | |            #2117.
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | End of split
% 241.39/47.92  | | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | End of split
% 241.39/47.92  | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | Case 2:
% 241.39/47.92  | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | |   (101)  all_58_11 = e1 & op(e1, e0) = e1
% 241.39/47.92  | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (12), (14), (15), (17), (20), (24),
% 241.39/47.92  | | | | | | | | | | | | | | | | | |            (26), (27), (31), (33), (34), (41), (101) are
% 241.39/47.92  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1467.
% 241.39/47.92  | | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | | End of split
% 241.39/47.92  | | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | End of split
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | Case 2:
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | |   (102)  all_58_10 = e0 & op(e2, e0) = e0
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 241.39/47.92  | | | | | | | | | | | | | | | |   (103)  op(e2, e0) = e0
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | | REF_CLOSE: (31), (33), (37), (48), (103) are inconsistent by
% 241.39/47.92  | | | | | | | | | | | | | | | |            sub-proof #1778.
% 241.39/47.92  | | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | | End of split
% 241.39/47.92  | | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | | End of split
% 241.39/47.92  | | | | | | | | | | | | | | 
% 241.39/47.92  | | | | | | | | | | | | | Case 2:
% 241.39/47.92  | | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | |   (104)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 241.39/47.93  | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 241.39/47.93  | | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 241.39/47.93  | | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | | Case 1:
% 241.39/47.93  | | | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | | |   (105)  all_58_13 = e0 & op(e0, e2) = e0
% 241.39/47.93  | | | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | | | REF_CLOSE: (33), (76), (105) are inconsistent by sub-proof
% 241.39/47.93  | | | | | | | | | | | | | | |            #609.
% 241.39/47.93  | | | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | | Case 2:
% 241.39/47.93  | | | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | | |   (106)  all_58_14 = e0 & op(e0, e1) = e0
% 241.39/47.93  | | | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 241.39/47.93  | | | | | | | | | | | | | | |   (107)  all_58_14 = e0
% 241.39/47.93  | | | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | | | REF_CLOSE: (3), (60), (107) are inconsistent by sub-proof
% 241.39/47.93  | | | | | | | | | | | | | | |            #1871.
% 241.39/47.93  | | | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | | End of split
% 241.39/47.93  | | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | End of split
% 241.39/47.93  | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | End of split
% 241.39/47.93  | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | Case 2:
% 241.39/47.93  | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | |   (108)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 241.39/47.93  | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.39/47.93  | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | BETA: splitting (108) gives:
% 241.39/47.93  | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | Case 1:
% 241.39/47.93  | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | |   (109)  all_58_14 = e1 & op(e0, e1) = e1
% 241.39/47.93  | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (12), (15), (17), (20), (24), (26),
% 241.39/47.93  | | | | | | | | | | | | |            (27), (31), (33), (34), (41), (60), (109) are
% 241.39/47.93  | | | | | | | | | | | | |            inconsistent by sub-proof #535.
% 241.39/47.93  | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | Case 2:
% 241.39/47.93  | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | |   (110)  all_58_15 = e1 & op(e0, e0) = e1
% 241.39/47.93  | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | ALPHA: (110) implies:
% 241.39/47.93  | | | | | | | | | | | | |   (111)  all_58_15 = e1
% 241.39/47.93  | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | | REF_CLOSE: (3), (6), (12), (20), (29), (31), (32), (33),
% 241.39/47.93  | | | | | | | | | | | | |            (41), (47), (64), (111) are inconsistent by
% 241.39/47.93  | | | | | | | | | | | | |            sub-proof #910.
% 241.39/47.93  | | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | | End of split
% 241.39/47.93  | | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | End of split
% 241.39/47.93  | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | End of split
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | Case 2:
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | |   (112)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 241.39/47.93  | | | | | | | | | |            & op(e3, e0) = e2)
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | BETA: splitting (112) gives:
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | Case 1:
% 241.39/47.93  | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | |   (113)  all_58_4 = e2 & op(e3, e1) = e2
% 241.39/47.93  | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | ALPHA: (113) implies:
% 241.39/47.93  | | | | | | | | | | |   (114)  all_58_4 = e2
% 241.39/47.93  | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | REF_CLOSE: (20), (34), (114) are inconsistent by sub-proof
% 241.39/47.93  | | | | | | | | | | |            #1902.
% 241.39/47.93  | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | Case 2:
% 241.39/47.93  | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | |   (115)  all_58_9 = e2 & op(e3, e0) = e2
% 241.39/47.93  | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 241.39/47.93  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 241.39/47.93  | | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 241.39/47.93  | | | | | | | | | | |            (29), (30), (31), (32), (33), (34), (36), (37),
% 241.39/47.93  | | | | | | | | | | |            (38), (39), (40), (41), (42), (47), (48), (115)
% 241.39/47.93  | | | | | | | | | | |            are inconsistent by sub-proof #531.
% 241.39/47.93  | | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | End of split
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | End of split
% 241.39/47.93  | | | | | | | | | 
% 241.39/47.93  | | | | | | | | Case 2:
% 241.39/47.93  | | | | | | | | | 
% 241.39/47.93  | | | | | | | | |   (116)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0
% 241.39/47.93  | | | | | | | | |            & op(e1, e0) = e0)
% 241.39/47.93  | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | BETA: splitting (116) gives:
% 241.39/47.93  | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | Case 1:
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | |   (117)  all_58_10 = e0 & op(e2, e0) = e0
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | ALPHA: (117) implies:
% 241.39/47.93  | | | | | | | | | |   (118)  op(e2, e0) = e0
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | REF_CLOSE: (31), (33), (37), (48), (118) are inconsistent by
% 241.39/47.93  | | | | | | | | | |            sub-proof #1778.
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | Case 2:
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | |   (119)  all_58_11 = e0 & op(e1, e0) = e0
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | ALPHA: (119) implies:
% 241.39/47.93  | | | | | | | | | |   (120)  all_58_11 = e0
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | | REF_CLOSE: (3), (14), (120) are inconsistent by sub-proof
% 241.39/47.93  | | | | | | | | | |            #1688.
% 241.39/47.93  | | | | | | | | | | 
% 241.39/47.93  | | | | | | | | | End of split
% 241.39/47.93  | | | | | | | | | 
% 241.39/47.93  | | | | | | | | End of split
% 241.39/47.93  | | | | | | | | 
% 241.39/47.93  | | | | | | | End of split
% 241.39/47.93  | | | | | | | 
% 241.39/47.93  | | | | | | Case 2:
% 241.39/47.93  | | | | | | | 
% 241.39/47.93  | | | | | | |   (121)  all_58_15 = e3 & op(e0, e0) = e3
% 241.39/47.93  | | | | | | | 
% 241.39/47.93  | | | | | | | REF_CLOSE: (20), (56), (121) are inconsistent by sub-proof #1170.
% 241.39/47.93  | | | | | | | 
% 241.39/47.93  | | | | | | End of split
% 241.39/47.93  | | | | | | 
% 241.39/47.93  | | | | | End of split
% 241.39/47.93  | | | | | 
% 241.39/47.93  | | | | End of split
% 241.39/47.93  | | | | 
% 241.39/47.93  | | | End of split
% 241.39/47.93  | | | 
% 241.39/47.93  | | End of split
% 241.39/47.93  | | 
% 241.39/47.93  | Case 2:
% 241.39/47.93  | | 
% 241.39/47.93  | |   (122)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.39/47.93  | |            e1)
% 241.39/47.93  | | 
% 241.39/47.93  | | BETA: splitting (122) gives:
% 241.39/47.93  | | 
% 241.39/47.93  | | Case 1:
% 241.39/47.93  | | | 
% 241.39/47.93  | | |   (123)  all_58_11 = e1 & op(e1, e0) = e1
% 241.39/47.93  | | | 
% 241.39/47.93  | | | ALPHA: (123) implies:
% 241.39/47.93  | | |   (124)  all_58_11 = e1
% 241.39/47.93  | | | 
% 241.39/47.93  | | | REF_CLOSE: (1), (3), (6), (12), (14), (15), (17), (20), (24), (26), (27),
% 241.39/47.93  | | |            (31), (33), (34), (41), (124) are inconsistent by sub-proof
% 241.39/47.93  | | |            #667.
% 241.39/47.93  | | | 
% 241.39/47.93  | | Case 2:
% 241.39/47.93  | | | 
% 241.39/47.93  | | |   (125)  all_58_15 = e1 & op(e0, e0) = e1
% 241.39/47.93  | | | 
% 241.39/47.93  | | | ALPHA: (125) implies:
% 241.39/47.93  | | |   (126)  op(e0, e0) = e1
% 241.39/47.93  | | | 
% 241.39/47.93  | | | GROUND_INST: instantiating (31) with e1, e3, e0, e0, simplifying with
% 241.39/47.93  | | |              (28), (126) gives:
% 241.39/47.93  | | |   (127)  e3 = e1
% 241.39/47.93  | | | 
% 241.39/47.93  | | | COMBINE_EQS: (34), (127) imply:
% 241.39/47.93  | | |   (128)  all_58_4 = e1
% 241.39/47.93  | | | 
% 241.39/47.93  | | | REF_CLOSE: (1), (3), (6), (12), (15), (17), (20), (24), (26), (27), (31),
% 241.39/47.93  | | |            (33), (41), (128) are inconsistent by sub-proof #1468.
% 241.39/47.93  | | | 
% 241.39/47.93  | | End of split
% 241.39/47.93  | | 
% 241.39/47.93  | End of split
% 241.39/47.93  | 
% 241.39/47.93  End of proof
% 241.39/47.93  
% 241.39/47.93  Sub-proof #530 shows that the following formulas are inconsistent:
% 241.39/47.93  ----------------------------------------------------------------
% 241.39/47.93    (1)   ~ (e3 = e0)
% 241.39/47.93    (2)   ~ (e2 = e0)
% 241.39/47.93    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.39/47.93         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.39/47.93    (4)   ~ (e3 = e1)
% 241.39/47.93    (5)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 241.39/47.93    (6)  all_58_3 = e3
% 241.39/47.93    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.39/47.93         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.39/47.93    (8)  op(e3, e3) = e1
% 241.39/47.93    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.39/47.93         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.39/47.93    (10)   ~ (e3 = e2)
% 241.39/47.93    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.39/47.93          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.39/47.93    (12)  op(e2, e3) = all_52_1
% 241.39/47.93    (13)  all_58_1 = e2
% 241.39/47.93    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.93    (15)   ~ (e1 = e0)
% 241.39/47.93    (16)  all_58_13 = e1
% 241.39/47.93    (17)   ~ (all_52_1 = e3)
% 241.39/47.93    (18)   ~ (e2 = e1)
% 241.39/47.93  
% 241.39/47.93  Begin of proof
% 241.39/47.93  | 
% 241.39/47.93  | BETA: splitting (5) gives:
% 241.39/47.93  | 
% 241.39/47.93  | Case 1:
% 241.39/47.93  | | 
% 241.39/47.93  | |   (19)  all_58_6 = e1 & op(e1, e3) = e1
% 241.39/47.93  | | 
% 241.39/47.93  | | ALPHA: (19) implies:
% 241.39/47.94  | |   (20)  all_58_6 = e1
% 241.39/47.94  | | 
% 241.39/47.94  | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (11), (12), (14), (15), (17),
% 241.39/47.94  | |            (18), (20) are inconsistent by sub-proof #1161.
% 241.39/47.94  | | 
% 241.39/47.94  | Case 2:
% 241.39/47.94  | | 
% 241.39/47.94  | |   (21)  all_58_7 = e1 & op(e1, e2) = e1
% 241.39/47.94  | | 
% 241.39/47.94  | | ALPHA: (21) implies:
% 241.39/47.94  | |   (22)  all_58_7 = e1
% 241.39/47.94  | | 
% 241.39/47.94  | | REF_CLOSE: (1), (2), (3), (6), (13), (15), (16), (22) are inconsistent by
% 241.39/47.94  | |            sub-proof #1459.
% 241.39/47.94  | | 
% 241.39/47.94  | End of split
% 241.39/47.94  | 
% 241.39/47.94  End of proof
% 241.39/47.94  
% 241.39/47.94  Sub-proof #531 shows that the following formulas are inconsistent:
% 241.39/47.94  ----------------------------------------------------------------
% 241.39/47.94    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.39/47.94         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.39/47.94    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.39/47.94         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.39/47.94    (3)   ~ (e3 = e0)
% 241.39/47.94    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.39/47.94         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.39/47.94    (5)  all_58_6 = e3
% 241.39/47.94    (6)   ~ (e2 = e0)
% 241.39/47.94    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.39/47.94         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.39/47.94    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.39/47.94         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.39/47.94    (9)   ~ (all_52_7 = e3)
% 241.39/47.94    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.39/47.94          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.39/47.94    (11)   ~ (e3 = e1)
% 241.39/47.94    (12)  all_58_3 = e3
% 241.39/47.94    (13)  all_58_11 = e3
% 241.39/47.94    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.94          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.94    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.39/47.94          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.39/47.94    (16)  op(e3, e3) = e1
% 241.39/47.94    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.94              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.39/47.94                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.39/47.94                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.39/47.94    (18)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.39/47.94          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.39/47.94    (19)   ~ (e3 = e2)
% 241.39/47.94    (20)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.39/47.94          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.39/47.94    (21)  op(e2, e3) = all_52_1
% 241.39/47.94    (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.39/47.94          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.94    (23)  op(e0, e2) = all_52_7
% 241.39/47.94    (24)   ~ (all_52_4 = e3)
% 241.39/47.94    (25)  op(e3, e2) = all_52_4
% 241.39/47.94    (26)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.39/47.94          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.39/47.94    (27)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.39/47.94          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.39/47.94    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.94    (29)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.39/47.94          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.39/47.94    (30)   ~ (e1 = e0)
% 241.39/47.94    (31)  all_58_4 = e3
% 241.39/47.94    (32)  op(e2, e0) = e1
% 241.39/47.94    (33)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.39/47.94          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.39/47.94    (34)  op(e2, e0) = all_52_13
% 241.39/47.94    (35)  all_58_9 = e2 & op(e3, e0) = e2
% 241.39/47.94    (36)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.39/47.94          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.39/47.94            e1)
% 241.39/47.94    (37)   ~ (all_52_1 = e3)
% 241.39/47.94    (38)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.39/47.94          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.39/47.94    (39)  all_58_10 = e1
% 241.39/47.94    (40)   ~ (e2 = e1)
% 241.39/47.94    (41)   ~ (all_52_1 = e1)
% 241.39/47.94  
% 241.39/47.94  Begin of proof
% 241.39/47.94  | 
% 241.39/47.94  | ALPHA: (35) implies:
% 241.39/47.94  |   (42)  all_58_9 = e2
% 241.39/47.94  |   (43)  op(e3, e0) = e2
% 241.39/47.94  | 
% 241.39/47.94  | BETA: splitting (22) gives:
% 241.39/47.94  | 
% 241.39/47.94  | Case 1:
% 241.39/47.94  | | 
% 241.39/47.94  | |   (44)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 241.39/47.94  | |           e0)
% 241.39/47.94  | | 
% 241.39/47.94  | | BETA: splitting (44) gives:
% 241.39/47.94  | | 
% 241.39/47.94  | | Case 1:
% 241.39/47.94  | | | 
% 241.39/47.94  | | |   (45)  all_58_0 = e0 & op(e3, e3) = e0
% 241.39/47.94  | | | 
% 241.39/47.94  | | | ALPHA: (45) implies:
% 241.39/47.94  | | |   (46)  op(e3, e3) = e0
% 241.39/47.94  | | | 
% 241.39/47.94  | | | REF_CLOSE: (16), (28), (30), (46) are inconsistent by sub-proof #1828.
% 241.39/47.94  | | | 
% 241.39/47.94  | | Case 2:
% 241.39/47.94  | | | 
% 241.39/47.94  | | |   (47)  all_58_1 = e0 & op(e3, e2) = e0
% 241.39/47.94  | | | 
% 241.39/47.94  | | | ALPHA: (47) implies:
% 241.39/47.94  | | |   (48)  all_58_1 = e0
% 241.39/47.94  | | | 
% 241.39/47.94  | | | BETA: splitting (2) gives:
% 241.39/47.94  | | | 
% 241.39/47.94  | | | Case 1:
% 241.39/47.94  | | | | 
% 241.39/47.94  | | | |   (49)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 241.39/47.94  | | | |             e2) = e3)
% 241.39/47.94  | | | | 
% 241.39/47.94  | | | | REF_CLOSE: (3), (5), (6), (9), (16), (18), (19), (20), (23), (28), (30),
% 241.39/47.94  | | | |            (40), (49) are inconsistent by sub-proof #1167.
% 241.39/47.94  | | | | 
% 241.39/47.94  | | | Case 2:
% 241.39/47.94  | | | | 
% 241.39/47.94  | | | |   (50)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 241.39/47.94  | | | |             e0) = e3)
% 241.39/47.94  | | | | 
% 241.39/47.94  | | | | BETA: splitting (50) gives:
% 241.39/47.94  | | | | 
% 241.39/47.94  | | | | Case 1:
% 241.39/47.94  | | | | | 
% 241.39/47.94  | | | | |   (51)  all_58_14 = e3 & op(e0, e1) = e3
% 241.39/47.94  | | | | | 
% 241.39/47.94  | | | | | ALPHA: (51) implies:
% 241.39/47.94  | | | | |   (52)  all_58_14 = e3
% 241.39/47.94  | | | | | 
% 241.39/47.94  | | | | | BETA: splitting (17) gives:
% 241.39/47.94  | | | | | 
% 241.39/47.94  | | | | | Case 1:
% 241.39/47.94  | | | | | | 
% 241.39/47.94  | | | | | |   (53)  all_58_15 = e0 & op(e0, e0) = e0
% 241.39/47.94  | | | | | | 
% 241.39/47.94  | | | | | | ALPHA: (53) implies:
% 241.39/47.94  | | | | | |   (54)  all_58_15 = e0
% 241.39/47.94  | | | | | |   (55)  op(e0, e0) = e0
% 241.39/47.94  | | | | | | 
% 241.39/47.94  | | | | | | BETA: splitting (36) gives:
% 241.39/47.94  | | | | | | 
% 241.39/47.94  | | | | | | Case 1:
% 241.39/47.94  | | | | | | | 
% 241.39/47.94  | | | | | | |   (56)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 241.39/47.94  | | | | | | |           op(e0, e2) = e1)
% 241.39/47.94  | | | | | | | 
% 241.39/47.94  | | | | | | | BETA: splitting (56) gives:
% 241.39/47.94  | | | | | | | 
% 241.39/47.94  | | | | | | | Case 1:
% 241.39/47.94  | | | | | | | | 
% 241.39/47.94  | | | | | | | |   (57)  all_58_12 = e1 & op(e0, e3) = e1
% 241.39/47.94  | | | | | | | | 
% 241.39/47.94  | | | | | | | | ALPHA: (57) implies:
% 241.39/47.94  | | | | | | | |   (58)  all_58_12 = e1
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | | REF_CLOSE: (3), (5), (6), (16), (18), (19), (20), (28), (30),
% 241.39/47.95  | | | | | | | |            (40), (58) are inconsistent by sub-proof #1206.
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | Case 2:
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | |   (59)  all_58_13 = e1 & op(e0, e2) = e1
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | | ALPHA: (59) implies:
% 241.39/47.95  | | | | | | | |   (60)  all_58_13 = e1
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | | BETA: splitting (7) gives:
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | | Case 1:
% 241.39/47.95  | | | | | | | | | 
% 241.39/47.95  | | | | | | | | |   (61)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 &
% 241.39/47.95  | | | | | | | | |           op(e2, e2) = e2)
% 241.39/47.95  | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | BETA: splitting (61) gives:
% 241.39/47.95  | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | Case 1:
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | |   (62)  all_58_1 = e2 & op(e3, e2) = e2
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | REF_CLOSE: (1), (6), (16), (19), (28), (31), (40), (42),
% 241.39/47.95  | | | | | | | | | |            (48), (62) are inconsistent by sub-proof #603.
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | Case 2:
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | |   (63)  all_58_3 = e2 & op(e2, e2) = e2
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | REF_CLOSE: (12), (19), (63) are inconsistent by sub-proof
% 241.39/47.95  | | | | | | | | | |            #1458.
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | End of split
% 241.39/47.95  | | | | | | | | | 
% 241.39/47.95  | | | | | | | | Case 2:
% 241.39/47.95  | | | | | | | | | 
% 241.39/47.95  | | | | | | | | |   (64)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 &
% 241.39/47.95  | | | | | | | | |           op(e0, e2) = e2)
% 241.39/47.95  | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | BETA: splitting (64) gives:
% 241.39/47.95  | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | Case 1:
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | |   (65)  all_58_7 = e2 & op(e1, e2) = e2
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | ALPHA: (65) implies:
% 241.39/47.95  | | | | | | | | | |   (66)  all_58_7 = e2
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | BETA: splitting (33) gives:
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | Case 1:
% 241.39/47.95  | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | |   (67)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 241.39/47.95  | | | | | | | | | | |           & op(e1, e2) = e0)
% 241.39/47.95  | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | BETA: splitting (67) gives:
% 241.39/47.95  | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | Case 1:
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | |   (68)  all_58_6 = e0 & op(e1, e3) = e0
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | | ALPHA: (68) implies:
% 241.39/47.95  | | | | | | | | | | | |   (69)  all_58_6 = e0
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | | REF_CLOSE: (3), (5), (11), (14), (16), (19), (24), (25),
% 241.39/47.95  | | | | | | | | | | | |            (28), (31), (43), (69) are inconsistent by
% 241.39/47.95  | | | | | | | | | | | |            sub-proof #1074.
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | Case 2:
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | |   (70)  all_58_7 = e0 & op(e1, e2) = e0
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | | ALPHA: (70) implies:
% 241.39/47.95  | | | | | | | | | | | |   (71)  all_58_7 = e0
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | | REF_CLOSE: (1), (6), (16), (19), (28), (31), (40), (42),
% 241.39/47.95  | | | | | | | | | | | |            (48), (66), (71) are inconsistent by sub-proof
% 241.39/47.95  | | | | | | | | | | | |            #602.
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | End of split
% 241.39/47.95  | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | Case 2:
% 241.39/47.95  | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | |   (72)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 241.39/47.95  | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 241.39/47.95  | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | BETA: splitting (72) gives:
% 241.39/47.95  | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | Case 1:
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | |   (73)  all_58_8 = e0 & op(e1, e1) = e0
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | | ALPHA: (73) implies:
% 241.39/47.95  | | | | | | | | | | | |   (74)  op(e1, e1) = e0
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (12),
% 241.39/47.95  | | | | | | | | | | | |            (14), (15), (16), (18), (19), (20), (21), (22),
% 241.39/47.95  | | | | | | | | | | | |            (24), (25), (26), (27), (28), (30), (31), (37),
% 241.39/47.95  | | | | | | | | | | | |            (38), (40), (41), (43), (54), (60), (74) are
% 241.39/47.95  | | | | | | | | | | | |            inconsistent by sub-proof #537.
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | Case 2:
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | |   (75)  all_58_11 = e0 & op(e1, e0) = e0
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | | REF_CLOSE: (3), (11), (13), (14), (16), (19), (24), (25),
% 241.39/47.95  | | | | | | | | | | | |            (28), (31), (43), (75) are inconsistent by
% 241.39/47.95  | | | | | | | | | | | |            sub-proof #536.
% 241.39/47.95  | | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | | End of split
% 241.39/47.95  | | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | End of split
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | Case 2:
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | |   (76)  all_58_13 = e2 & op(e0, e2) = e2
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | ALPHA: (76) implies:
% 241.39/47.95  | | | | | | | | | |   (77)  all_58_13 = e2
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | COMBINE_EQS: (60), (77) imply:
% 241.39/47.95  | | | | | | | | | |   (78)  e2 = e1
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | COMBINE_EQS: (42), (78) imply:
% 241.39/47.95  | | | | | | | | | |   (79)  all_58_9 = e1
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | | REF_CLOSE: (6), (13), (19), (29), (39), (40), (54), (79) are
% 241.39/47.95  | | | | | | | | | |            inconsistent by sub-proof #1506.
% 241.39/47.95  | | | | | | | | | | 
% 241.39/47.95  | | | | | | | | | End of split
% 241.39/47.95  | | | | | | | | | 
% 241.39/47.95  | | | | | | | | End of split
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | End of split
% 241.39/47.95  | | | | | | | 
% 241.39/47.95  | | | | | | Case 2:
% 241.39/47.95  | | | | | | | 
% 241.39/47.95  | | | | | | |   (80)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 241.39/47.95  | | | | | | |           op(e0, e0) = e1)
% 241.39/47.95  | | | | | | | 
% 241.39/47.95  | | | | | | | BETA: splitting (80) gives:
% 241.39/47.95  | | | | | | | 
% 241.39/47.95  | | | | | | | Case 1:
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | |   (81)  all_58_14 = e1 & op(e0, e1) = e1
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | | REF_CLOSE: (1), (3), (6), (11), (14), (16), (19), (22), (24),
% 241.39/47.95  | | | | | | | |            (25), (28), (30), (31), (40), (52), (81) are
% 241.39/47.95  | | | | | | | |            inconsistent by sub-proof #535.
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | Case 2:
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | |   (82)  all_58_15 = e1 & op(e0, e0) = e1
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | | ALPHA: (82) implies:
% 241.39/47.95  | | | | | | | |   (83)  op(e0, e0) = e1
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | | REF_CLOSE: (28), (30), (55), (83) are inconsistent by sub-proof
% 241.39/47.95  | | | | | | | |            #2274.
% 241.39/47.95  | | | | | | | | 
% 241.39/47.95  | | | | | | | End of split
% 241.39/47.95  | | | | | | | 
% 241.39/47.95  | | | | | | End of split
% 241.39/47.95  | | | | | | 
% 241.39/47.95  | | | | | Case 2:
% 241.39/47.95  | | | | | | 
% 241.39/47.95  | | | | | |   (84)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 241.39/47.95  | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 241.39/47.95  | | | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.39/47.95  | | | | | |             op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.39/47.95  | | | | | | 
% 241.39/47.95  | | | | | | ALPHA: (84) implies:
% 241.39/47.95  | | | | | |   (85)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 241.39/47.95  | | | | | |             e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.39/47.95  | | | | | | 
% 241.39/47.95  | | | | | | REF_CLOSE: (1), (3), (6), (11), (13), (14), (16), (19), (24), (25),
% 241.39/47.95  | | | | | |            (28), (30), (31), (32), (34), (40), (43), (48), (85) are
% 241.39/47.95  | | | | | |            inconsistent by sub-proof #534.
% 241.39/47.95  | | | | | | 
% 241.39/47.95  | | | | | End of split
% 241.39/47.95  | | | | | 
% 241.39/47.95  | | | | Case 2:
% 241.39/47.95  | | | | | 
% 241.39/47.95  | | | | |   (86)  all_58_15 = e3 & op(e0, e0) = e3
% 241.39/47.95  | | | | | 
% 241.39/47.95  | | | | | ALPHA: (86) implies:
% 241.39/47.95  | | | | |   (87)  all_58_15 = e3
% 241.39/47.95  | | | | | 
% 241.39/47.95  | | | | | BETA: splitting (17) gives:
% 241.39/47.95  | | | | | 
% 241.39/47.95  | | | | | Case 1:
% 241.39/47.95  | | | | | | 
% 241.39/47.95  | | | | | |   (88)  all_58_15 = e0 & op(e0, e0) = e0
% 241.39/47.95  | | | | | | 
% 241.39/47.95  | | | | | | REF_CLOSE: (3), (11), (14), (16), (19), (24), (25), (28), (31),
% 241.39/47.95  | | | | | |            (43), (87), (88) are inconsistent by sub-proof #533.
% 241.39/47.95  | | | | | | 
% 241.39/47.95  | | | | | Case 2:
% 241.39/47.95  | | | | | | 
% 241.39/47.95  | | | | | |   (89)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 241.39/47.95  | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 241.39/47.95  | | | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.39/47.95  | | | | | |             op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.39/47.95  | | | | | | 
% 241.39/47.95  | | | | | | ALPHA: (89) implies:
% 241.39/47.96  | | | | | |   (90)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 241.39/47.96  | | | | | |             e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.39/47.96  | | | | | | 
% 241.39/47.96  | | | | | | REF_CLOSE: (1), (3), (6), (11), (13), (14), (16), (19), (24), (25),
% 241.39/47.96  | | | | | |            (28), (30), (31), (32), (34), (40), (43), (48), (90) are
% 241.39/47.96  | | | | | |            inconsistent by sub-proof #534.
% 241.39/47.96  | | | | | | 
% 241.39/47.96  | | | | | End of split
% 241.39/47.96  | | | | | 
% 241.39/47.96  | | | | End of split
% 241.39/47.96  | | | | 
% 241.39/47.96  | | | End of split
% 241.39/47.96  | | | 
% 241.39/47.96  | | End of split
% 241.39/47.96  | | 
% 241.39/47.96  | Case 2:
% 241.39/47.96  | | 
% 241.39/47.96  | |   (91)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 241.39/47.96  | |           e0)
% 241.39/47.96  | | 
% 241.39/47.96  | | REF_CLOSE: (3), (6), (11), (14), (16), (19), (24), (25), (28), (42), (43),
% 241.39/47.96  | |            (91) are inconsistent by sub-proof #532.
% 241.39/47.96  | | 
% 241.39/47.96  | End of split
% 241.39/47.96  | 
% 241.39/47.96  End of proof
% 241.39/47.96  
% 241.39/47.96  Sub-proof #532 shows that the following formulas are inconsistent:
% 241.39/47.96  ----------------------------------------------------------------
% 241.39/47.96    (1)   ~ (e3 = e0)
% 241.39/47.96    (2)   ~ (e2 = e0)
% 241.39/47.96    (3)   ~ (e3 = e1)
% 241.39/47.96    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.96         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.96    (5)  op(e3, e3) = e1
% 241.39/47.96    (6)   ~ (e3 = e2)
% 241.39/47.96    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.96    (8)  op(e3, e0) = e2
% 241.39/47.96    (9)   ~ (all_52_4 = e3)
% 241.39/47.96    (10)  op(e3, e2) = all_52_4
% 241.39/47.96    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.96    (12)  all_58_9 = e2
% 241.39/47.96  
% 241.39/47.96  Begin of proof
% 241.39/47.96  | 
% 241.39/47.96  | BETA: splitting (7) gives:
% 241.39/47.96  | 
% 241.39/47.96  | Case 1:
% 241.39/47.96  | | 
% 241.39/47.96  | |   (13)  all_58_4 = e0 & op(e3, e1) = e0
% 241.39/47.96  | | 
% 241.39/47.96  | | ALPHA: (13) implies:
% 241.39/47.96  | |   (14)  all_58_4 = e0
% 241.39/47.96  | | 
% 241.39/47.96  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (14) are
% 241.39/47.96  | |            inconsistent by sub-proof #1400.
% 241.39/47.96  | | 
% 241.39/47.96  | Case 2:
% 241.39/47.96  | | 
% 241.39/47.96  | |   (15)  all_58_9 = e0 & op(e3, e0) = e0
% 241.39/47.96  | | 
% 241.39/47.96  | | ALPHA: (15) implies:
% 241.39/47.96  | |   (16)  all_58_9 = e0
% 241.39/47.96  | | 
% 241.39/47.96  | | REF_CLOSE: (2), (12), (16) are inconsistent by sub-proof #1660.
% 241.39/47.96  | | 
% 241.39/47.96  | End of split
% 241.39/47.96  | 
% 241.39/47.96  End of proof
% 241.39/47.96  
% 241.39/47.96  Sub-proof #533 shows that the following formulas are inconsistent:
% 241.39/47.96  ----------------------------------------------------------------
% 241.39/47.96    (1)   ~ (e3 = e0)
% 241.39/47.96    (2)  all_58_15 = e3
% 241.39/47.96    (3)   ~ (e3 = e1)
% 241.39/47.96    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.96         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.96    (5)  op(e3, e3) = e1
% 241.39/47.96    (6)  all_58_15 = e0 & op(e0, e0) = e0
% 241.39/47.96    (7)   ~ (e3 = e2)
% 241.39/47.96    (8)  op(e3, e0) = e2
% 241.39/47.96    (9)   ~ (all_52_4 = e3)
% 241.39/47.96    (10)  op(e3, e2) = all_52_4
% 241.39/47.96    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.96    (12)  all_58_4 = e3
% 241.39/47.96  
% 241.39/47.96  Begin of proof
% 241.39/47.96  | 
% 241.39/47.96  | ALPHA: (6) implies:
% 241.39/47.96  |   (13)  all_58_15 = e0
% 241.39/47.96  | 
% 241.39/47.96  | COMBINE_EQS: (2), (13) imply:
% 241.39/47.96  |   (14)  e3 = e0
% 241.39/47.96  | 
% 241.39/47.96  | COMBINE_EQS: (12), (14) imply:
% 241.39/47.96  |   (15)  all_58_4 = e0
% 241.39/47.96  | 
% 241.39/47.96  | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (15) are
% 241.39/47.96  |            inconsistent by sub-proof #1400.
% 241.39/47.96  | 
% 241.39/47.96  End of proof
% 241.39/47.96  
% 241.39/47.96  Sub-proof #534 shows that the following formulas are inconsistent:
% 241.39/47.96  ----------------------------------------------------------------
% 241.39/47.96    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.39/47.96         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.39/47.96    (2)   ~ (e3 = e0)
% 241.39/47.96    (3)   ~ (e2 = e0)
% 241.39/47.96    (4)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 241.39/47.96         (all_58_11 = e0 & op(e1, e0) = e0)
% 241.39/47.96    (5)  all_58_1 = e0
% 241.39/47.96    (6)   ~ (e3 = e1)
% 241.39/47.96    (7)  all_58_11 = e3
% 241.39/47.96    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.96         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.96    (9)  op(e3, e3) = e1
% 241.39/47.96    (10)   ~ (e3 = e2)
% 241.39/47.96    (11)  op(e3, e0) = e2
% 241.39/47.96    (12)   ~ (all_52_4 = e3)
% 241.39/47.96    (13)  op(e3, e2) = all_52_4
% 241.39/47.96    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.96    (15)   ~ (e1 = e0)
% 241.39/47.96    (16)  all_58_4 = e3
% 241.39/47.96    (17)  op(e2, e0) = e1
% 241.39/47.96    (18)  op(e2, e0) = all_52_13
% 241.39/47.96    (19)   ~ (e2 = e1)
% 241.39/47.96  
% 241.39/47.96  Begin of proof
% 241.39/47.96  | 
% 241.39/47.96  | BETA: splitting (4) gives:
% 241.39/47.96  | 
% 241.39/47.96  | Case 1:
% 241.39/47.96  | | 
% 241.39/47.96  | |   (20)  all_58_9 = e0 & op(e3, e0) = e0
% 241.39/47.96  | | 
% 241.39/47.96  | | ALPHA: (20) implies:
% 241.39/47.96  | |   (21)  all_58_9 = e0
% 241.39/47.96  | | 
% 241.39/47.96  | | REF_CLOSE: (1), (3), (5), (9), (10), (14), (16), (19), (21) are inconsistent
% 241.39/47.96  | |            by sub-proof #1097.
% 241.39/47.96  | | 
% 241.39/47.96  | Case 2:
% 241.39/47.96  | | 
% 241.39/47.96  | |   (22)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 241.39/47.96  | |           e0)
% 241.39/47.96  | | 
% 241.39/47.96  | | BETA: splitting (22) gives:
% 241.39/47.96  | | 
% 241.39/47.96  | | Case 1:
% 241.39/47.96  | | | 
% 241.39/47.96  | | |   (23)  all_58_10 = e0 & op(e2, e0) = e0
% 241.39/47.96  | | | 
% 241.39/47.96  | | | ALPHA: (23) implies:
% 241.39/47.96  | | |   (24)  op(e2, e0) = e0
% 241.39/47.96  | | | 
% 241.39/47.96  | | | REF_CLOSE: (14), (15), (17), (18), (24) are inconsistent by sub-proof
% 241.39/47.96  | | |            #1778.
% 241.39/47.96  | | | 
% 241.39/47.96  | | Case 2:
% 241.39/47.96  | | | 
% 241.39/47.96  | | |   (25)  all_58_11 = e0 & op(e1, e0) = e0
% 241.39/47.96  | | | 
% 241.39/47.96  | | | REF_CLOSE: (2), (6), (7), (8), (9), (10), (11), (12), (13), (14), (16),
% 241.39/47.96  | | |            (25) are inconsistent by sub-proof #536.
% 241.39/47.96  | | | 
% 241.39/47.96  | | End of split
% 241.39/47.96  | | 
% 241.39/47.96  | End of split
% 241.39/47.96  | 
% 241.39/47.96  End of proof
% 241.39/47.96  
% 241.39/47.96  Sub-proof #535 shows that the following formulas are inconsistent:
% 241.39/47.96  ----------------------------------------------------------------
% 241.39/47.96    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.39/47.96         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.39/47.96    (2)  all_58_14 = e1 & op(e0, e1) = e1
% 241.39/47.96    (3)   ~ (e3 = e0)
% 241.39/47.96    (4)   ~ (e2 = e0)
% 241.39/47.96    (5)   ~ (e3 = e1)
% 241.39/47.96    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.96         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.96    (7)  op(e3, e3) = e1
% 241.39/47.96    (8)   ~ (e3 = e2)
% 241.39/47.96    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.39/47.96         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.96    (10)   ~ (all_52_4 = e3)
% 241.39/47.96    (11)  op(e3, e2) = all_52_4
% 241.39/47.96    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.96    (13)  all_58_14 = e3
% 241.39/47.96    (14)   ~ (e1 = e0)
% 241.39/47.96    (15)  all_58_4 = e3
% 241.39/47.96    (16)   ~ (e2 = e1)
% 241.39/47.96  
% 241.39/47.96  Begin of proof
% 241.39/47.96  | 
% 241.39/47.96  | ALPHA: (2) implies:
% 241.39/47.96  |   (17)  all_58_14 = e1
% 241.39/47.96  | 
% 241.39/47.96  | COMBINE_EQS: (13), (17) imply:
% 241.39/47.96  |   (18)  e3 = e1
% 241.39/47.96  | 
% 241.39/47.96  | COMBINE_EQS: (15), (18) imply:
% 241.39/47.96  |   (19)  all_58_4 = e1
% 241.39/47.96  | 
% 241.39/47.96  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 241.39/47.96  |            (16), (19) are inconsistent by sub-proof #1468.
% 241.39/47.96  | 
% 241.39/47.96  End of proof
% 241.39/47.96  
% 241.39/47.96  Sub-proof #536 shows that the following formulas are inconsistent:
% 241.39/47.96  ----------------------------------------------------------------
% 241.39/47.96    (1)   ~ (e3 = e0)
% 241.39/47.96    (2)   ~ (e3 = e1)
% 241.39/47.96    (3)  all_58_11 = e3
% 241.39/47.96    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.96         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.96    (5)  op(e3, e3) = e1
% 241.39/47.96    (6)   ~ (e3 = e2)
% 241.39/47.96    (7)  all_58_11 = e0 & op(e1, e0) = e0
% 241.39/47.96    (8)  op(e3, e0) = e2
% 241.39/47.96    (9)   ~ (all_52_4 = e3)
% 241.39/47.96    (10)  op(e3, e2) = all_52_4
% 241.39/47.96    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.96    (12)  all_58_4 = e3
% 241.39/47.96  
% 241.39/47.96  Begin of proof
% 241.39/47.96  | 
% 241.39/47.96  | ALPHA: (7) implies:
% 241.39/47.96  |   (13)  all_58_11 = e0
% 241.39/47.96  | 
% 241.39/47.96  | COMBINE_EQS: (3), (13) imply:
% 241.39/47.96  |   (14)  e3 = e0
% 241.39/47.96  | 
% 241.39/47.96  | COMBINE_EQS: (12), (14) imply:
% 241.39/47.96  |   (15)  all_58_4 = e0
% 241.39/47.96  | 
% 241.39/47.96  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (15) are
% 241.39/47.96  |            inconsistent by sub-proof #1400.
% 241.39/47.96  | 
% 241.39/47.96  End of proof
% 241.39/47.96  
% 241.39/47.96  Sub-proof #537 shows that the following formulas are inconsistent:
% 241.39/47.96  ----------------------------------------------------------------
% 241.39/47.96    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.39/47.96         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.39/47.96    (2)   ~ (e3 = e0)
% 241.39/47.96    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.39/47.96         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.39/47.96    (4)   ~ (e2 = e0)
% 241.39/47.96    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.39/47.96         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.39/47.96    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.39/47.96         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.39/47.96    (7)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.39/47.96         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.39/47.96    (8)   ~ (e3 = e1)
% 241.39/47.96    (9)  all_58_3 = e3
% 241.39/47.96    (10)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.96          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.96    (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.39/47.96          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.39/47.96    (12)  op(e3, e3) = e1
% 241.39/47.96    (13)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.39/47.96          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.39/47.96    (14)   ~ (e3 = e2)
% 241.39/47.96    (15)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.39/47.96          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.39/47.96    (16)  op(e2, e3) = all_52_1
% 241.39/47.96    (17)  op(e3, e0) = e2
% 241.39/47.96    (18)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.39/47.96          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.96    (19)   ~ (all_52_4 = e3)
% 241.39/47.96    (20)  op(e3, e2) = all_52_4
% 241.39/47.96    (21)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.39/47.96          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.39/47.96    (22)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.39/47.96          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.39/47.96    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.96    (24)  op(e1, e1) = e0
% 241.39/47.96    (25)   ~ (e1 = e0)
% 241.39/47.96    (26)  all_58_13 = e1
% 241.39/47.96    (27)  all_58_4 = e3
% 241.39/47.96    (28)  all_58_15 = e0
% 241.39/47.96    (29)   ~ (all_52_1 = e3)
% 241.39/47.96    (30)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.39/47.96          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.39/47.96    (31)   ~ (e2 = e1)
% 241.39/47.96    (32)   ~ (all_52_1 = e1)
% 241.39/47.96  
% 241.39/47.96  Begin of proof
% 241.39/47.96  | 
% 241.39/47.96  | BETA: splitting (3) gives:
% 241.39/47.96  | 
% 241.39/47.96  | Case 1:
% 241.39/47.96  | | 
% 241.39/47.96  | |   (33)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 241.39/47.96  | |           e1)
% 241.39/47.96  | | 
% 241.39/47.96  | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (11), (12), (13), (14), (15), (16),
% 241.39/47.96  | |            (23), (25), (26), (29), (31), (33) are inconsistent by sub-proof
% 241.39/47.96  | |            #538.
% 241.39/47.96  | | 
% 241.39/47.96  | Case 2:
% 241.39/47.96  | | 
% 241.39/47.96  | |   (34)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 241.39/47.96  | |           e1)
% 241.39/47.96  | | 
% 241.39/47.96  | | BETA: splitting (34) gives:
% 241.39/47.96  | | 
% 241.39/47.96  | | Case 1:
% 241.39/47.96  | | | 
% 241.39/47.96  | | |   (35)  all_58_8 = e1 & op(e1, e1) = e1
% 241.39/47.96  | | | 
% 241.39/47.96  | | | ALPHA: (35) implies:
% 241.39/47.96  | | |   (36)  op(e1, e1) = e1
% 241.39/47.96  | | | 
% 241.39/47.96  | | | REF_CLOSE: (23), (24), (25), (36) are inconsistent by sub-proof #2220.
% 241.39/47.96  | | | 
% 241.39/47.96  | | Case 2:
% 241.39/47.96  | | | 
% 241.39/47.96  | | |   (37)  all_58_11 = e1 & op(e1, e0) = e1
% 241.39/47.96  | | | 
% 241.39/47.96  | | | ALPHA: (37) implies:
% 241.39/47.96  | | |   (38)  all_58_11 = e1
% 241.39/47.96  | | | 
% 241.39/47.96  | | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (12), (14), (16), (17),
% 241.39/47.96  | | |            (18), (19), (20), (21), (22), (23), (25), (27), (28), (30),
% 241.39/47.96  | | |            (31), (32), (38) are inconsistent by sub-proof #650.
% 241.39/47.96  | | | 
% 241.39/47.96  | | End of split
% 241.39/47.96  | | 
% 241.39/47.96  | End of split
% 241.39/47.96  | 
% 241.39/47.96  End of proof
% 241.39/47.96  
% 241.39/47.96  Sub-proof #538 shows that the following formulas are inconsistent:
% 241.39/47.96  ----------------------------------------------------------------
% 241.39/47.96    (1)   ~ (e3 = e0)
% 241.39/47.96    (2)   ~ (e2 = e0)
% 241.39/47.96    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.39/47.96         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.39/47.96    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.39/47.96         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.39/47.96    (5)   ~ (e3 = e1)
% 241.39/47.96    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 241.39/47.96    (7)  all_58_3 = e3
% 241.39/47.97    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.39/47.97         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.39/47.97    (9)  op(e3, e3) = e1
% 241.39/47.97    (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.39/47.97          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.39/47.97    (11)   ~ (e3 = e2)
% 241.39/47.97    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.39/47.97          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.39/47.97    (13)  op(e2, e3) = all_52_1
% 241.39/47.97    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.39/47.97            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.39/47.97    (15)   ~ (e1 = e0)
% 241.39/47.97    (16)  all_58_13 = e1
% 241.39/47.97    (17)   ~ (all_52_1 = e3)
% 241.39/47.97    (18)   ~ (e2 = e1)
% 241.39/47.97  
% 241.39/47.97  Begin of proof
% 241.39/47.97  | 
% 241.39/47.97  | BETA: splitting (6) gives:
% 241.39/47.97  | 
% 241.39/47.97  | Case 1:
% 241.39/47.97  | | 
% 241.39/47.97  | |   (19)  all_58_6 = e1 & op(e1, e3) = e1
% 241.39/47.97  | | 
% 241.39/47.97  | | ALPHA: (19) implies:
% 241.39/47.97  | |   (20)  all_58_6 = e1
% 241.39/47.97  | | 
% 241.39/47.97  | | REF_CLOSE: (1), (2), (5), (8), (9), (10), (11), (12), (13), (14), (15),
% 241.39/47.97  | |            (17), (18), (20) are inconsistent by sub-proof #1161.
% 241.39/47.97  | | 
% 241.39/47.97  | Case 2:
% 241.39/47.97  | | 
% 241.39/47.97  | |   (21)  all_58_7 = e1 & op(e1, e2) = e1
% 241.39/47.97  | | 
% 241.39/47.97  | | ALPHA: (21) implies:
% 241.39/47.97  | |   (22)  all_58_7 = e1
% 241.39/47.97  | | 
% 241.39/47.97  | | REF_CLOSE: (1), (2), (3), (4), (7), (11), (15), (16), (18), (22) are
% 241.39/47.97  | |            inconsistent by sub-proof #1457.
% 241.39/47.97  | | 
% 241.39/47.97  | End of split
% 241.39/47.97  | 
% 241.39/47.97  End of proof
% 241.39/47.97  
% 241.39/47.97  Sub-proof #539 shows that the following formulas are inconsistent:
% 241.39/47.97  ----------------------------------------------------------------
% 241.39/47.97    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.39/47.97         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.39/47.97    (2)   ~ (e3 = e0)
% 241.39/47.97    (3)  all_58_6 = e3
% 241.39/47.97    (4)   ~ (e2 = e0)
% 241.39/47.97    (5)  op(e1, e2) = all_52_6
% 241.39/47.97    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.39/47.97         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.39/47.97    (7)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.39/47.97         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.39/47.97    (8)  all_58_15 = e3
% 241.39/47.97    (9)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.39/47.97         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.39/47.97    (10)   ~ (e3 = e1)
% 241.39/47.97    (11)  all_58_8 = e2
% 241.39/47.97    (12)  all_58_2 = e2
% 241.39/47.97    (13)  all_58_3 = e3
% 241.39/47.97    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.39/47.97          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.39/47.97    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.39/47.97          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.39/47.97    (16)  op(e3, e3) = e1
% 241.39/47.97    (17)  op(e2, e1) = all_52_9
% 241.39/47.97    (18)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.39/47.97          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.39/47.97    (19)   ~ (e3 = e2)
% 241.39/47.97    (20)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.39/47.97          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.39/47.97    (21)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.39/47.97          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.39/47.97    (22)  all_58_12 = e0
% 241.39/47.97    (23)  op(e2, e3) = all_52_1
% 241.39/47.97    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.39/47.97          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.39/47.97    (25)   ~ (all_52_6 = e3)
% 241.39/47.97    (26)  op(e1, e1) = e2
% 241.39/47.97    (27)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.39/47.97          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.39/47.97    (28)   ~ (all_52_4 = e3)
% 241.39/47.97    (29)  op(e3, e2) = all_52_4
% 241.39/47.97    (30)  all_58_7 = e1
% 241.39/47.97    (31)   ~ (all_52_9 = e3)
% 241.39/47.97    (32)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.39/47.97          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.39/47.97    (33)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.39/47.97          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.46/47.97    (34)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.46/47.97            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.46/47.97    (35)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.46/47.97          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.46/47.97    (36)  op(e1, e1) = e0
% 241.46/47.97    (37)  all_58_11 = e0
% 241.46/47.97    (38)  all_58_7 = e1 & op(e1, e2) = e1
% 241.46/47.97    (39)   ~ (e1 = e0)
% 241.46/47.97    (40)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.46/47.97          | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.46/47.97    (41)  all_58_4 = e3
% 241.46/47.97    (42)   ~ (all_52_1 = e3)
% 241.46/47.97    (43)  all_58_14 = e1
% 241.46/47.97    (44)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.46/47.97          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.46/47.97    (45)  all_58_10 = e1
% 241.46/47.97    (46)   ~ (e2 = e1)
% 241.46/47.97    (47)   ~ (all_52_1 = e1)
% 241.46/47.97  
% 241.46/47.97  Begin of proof
% 241.46/47.97  | 
% 241.46/47.97  | BETA: splitting (35) gives:
% 241.46/47.97  | 
% 241.46/47.97  | Case 1:
% 241.46/47.97  | | 
% 241.46/47.97  | |   (48)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 241.46/47.97  | |           e2)
% 241.46/47.97  | | 
% 241.46/47.97  | | BETA: splitting (48) gives:
% 241.46/47.97  | | 
% 241.46/47.97  | | Case 1:
% 241.46/47.97  | | | 
% 241.46/47.97  | | |   (49)  all_58_9 = e2 & op(e3, e0) = e2
% 241.46/47.97  | | | 
% 241.46/47.97  | | | ALPHA: (49) implies:
% 241.46/47.97  | | |   (50)  all_58_9 = e2
% 241.46/47.97  | | |   (51)  op(e3, e0) = e2
% 241.46/47.97  | | | 
% 241.46/47.97  | | | BETA: splitting (24) gives:
% 241.46/47.97  | | | 
% 241.46/47.97  | | | Case 1:
% 241.46/47.97  | | | | 
% 241.46/47.97  | | | |   (52)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 241.46/47.97  | | | |           = e0)
% 241.46/47.97  | | | | 
% 241.46/47.97  | | | | BETA: splitting (52) gives:
% 241.46/47.97  | | | | 
% 241.46/47.97  | | | | Case 1:
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | |   (53)  all_58_0 = e0 & op(e3, e3) = e0
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | | ALPHA: (53) implies:
% 241.46/47.97  | | | | |   (54)  op(e3, e3) = e0
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | | REF_CLOSE: (16), (34), (39), (54) are inconsistent by sub-proof #1828.
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | Case 2:
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | |   (55)  all_58_1 = e0 & op(e3, e2) = e0
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | | ALPHA: (55) implies:
% 241.46/47.97  | | | | |   (56)  all_58_1 = e0
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | | BETA: splitting (6) gives:
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | | Case 1:
% 241.46/47.97  | | | | | | 
% 241.46/47.97  | | | | | |   (57)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2,
% 241.46/47.97  | | | | | |             e2) = e2)
% 241.46/47.97  | | | | | | 
% 241.46/47.97  | | | | | | BETA: splitting (57) gives:
% 241.46/47.97  | | | | | | 
% 241.46/47.97  | | | | | | Case 1:
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | |   (58)  all_58_1 = e2 & op(e3, e2) = e2
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | ALPHA: (58) implies:
% 241.46/47.97  | | | | | | |   (59)  all_58_1 = e2
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | COMBINE_EQS: (56), (59) imply:
% 241.46/47.97  | | | | | | |   (60)  e2 = e0
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | SIMP: (60) implies:
% 241.46/47.97  | | | | | | |   (61)  e2 = e0
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (12), (16), (18), (19), (21), (22),
% 241.46/47.97  | | | | | | |            (25), (30), (32), (34), (37), (46), (61) are
% 241.46/47.97  | | | | | | |            inconsistent by sub-proof #541.
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | Case 2:
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | |   (62)  all_58_3 = e2 & op(e2, e2) = e2
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | ALPHA: (62) implies:
% 241.46/47.97  | | | | | | |   (63)  all_58_3 = e2
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | COMBINE_EQS: (13), (63) imply:
% 241.46/47.97  | | | | | | |   (64)  e3 = e2
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | COMBINE_EQS: (41), (64) imply:
% 241.46/47.97  | | | | | | |   (65)  all_58_4 = e2
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | REF_CLOSE: (2), (3), (4), (10), (15), (16), (17), (18), (19),
% 241.46/47.97  | | | | | | |            (20), (23), (27), (31), (34), (36), (39), (42), (43),
% 241.46/47.97  | | | | | | |            (46), (65) are inconsistent by sub-proof #645.
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | End of split
% 241.46/47.97  | | | | | | 
% 241.46/47.97  | | | | | Case 2:
% 241.46/47.97  | | | | | | 
% 241.46/47.97  | | | | | |   (66)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0,
% 241.46/47.97  | | | | | |             e2) = e2)
% 241.46/47.97  | | | | | | 
% 241.46/47.97  | | | | | | BETA: splitting (66) gives:
% 241.46/47.97  | | | | | | 
% 241.46/47.97  | | | | | | Case 1:
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | |   (67)  all_58_7 = e2 & op(e1, e2) = e2
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | REF_CLOSE: (3), (4), (11), (19), (30), (32), (37), (46), (67) are
% 241.46/47.97  | | | | | | |            inconsistent by sub-proof #965.
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | Case 2:
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | |   (68)  all_58_13 = e2 & op(e0, e2) = e2
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | ALPHA: (68) implies:
% 241.46/47.97  | | | | | | |   (69)  op(e0, e2) = e2
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | BETA: splitting (40) gives:
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | | Case 1:
% 241.46/47.97  | | | | | | | | 
% 241.46/47.97  | | | | | | | |   (70)  all_58_12 = e0 & op(e0, e3) = e0
% 241.46/47.97  | | | | | | | | 
% 241.46/47.97  | | | | | | | | GROUND_INST: instantiating (34) with e0, e2, e1, e1, simplifying
% 241.46/47.97  | | | | | | | |              with (26), (36) gives:
% 241.46/47.97  | | | | | | | |   (71)  e2 = e0
% 241.46/47.97  | | | | | | | | 
% 241.46/47.97  | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (12), (16), (18), (19), (21),
% 241.46/47.97  | | | | | | | |            (22), (25), (30), (32), (34), (37), (46), (71) are
% 241.46/47.97  | | | | | | | |            inconsistent by sub-proof #541.
% 241.46/47.97  | | | | | | | | 
% 241.46/47.97  | | | | | | | Case 2:
% 241.46/47.97  | | | | | | | | 
% 241.46/47.97  | | | | | | | |   (72)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 241.46/47.97  | | | | | | | |           op(e0, e1) = e0)
% 241.46/47.97  | | | | | | | | 
% 241.46/47.97  | | | | | | | | BETA: splitting (72) gives:
% 241.46/47.97  | | | | | | | | 
% 241.46/47.97  | | | | | | | | Case 1:
% 241.46/47.97  | | | | | | | | | 
% 241.46/47.97  | | | | | | | | |   (73)  all_58_13 = e0 & op(e0, e2) = e0
% 241.46/47.97  | | | | | | | | | 
% 241.46/47.97  | | | | | | | | | ALPHA: (73) implies:
% 241.46/47.97  | | | | | | | | |   (74)  op(e0, e2) = e0
% 241.46/47.97  | | | | | | | | | 
% 241.46/47.97  | | | | | | | | | REF_CLOSE: (4), (34), (69), (74) are inconsistent by sub-proof
% 241.46/47.97  | | | | | | | | |            #2132.
% 241.46/47.97  | | | | | | | | | 
% 241.46/47.97  | | | | | | | | Case 2:
% 241.46/47.97  | | | | | | | | | 
% 241.46/47.97  | | | | | | | | |   (75)  all_58_14 = e0 & op(e0, e1) = e0
% 241.46/47.97  | | | | | | | | | 
% 241.46/47.97  | | | | | | | | | ALPHA: (75) implies:
% 241.46/47.97  | | | | | | | | |   (76)  all_58_14 = e0
% 241.46/47.97  | | | | | | | | | 
% 241.46/47.97  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (13), (14),
% 241.46/47.97  | | | | | | | | |            (16), (19), (24), (28), (29), (30), (32), (33),
% 241.46/47.97  | | | | | | | | |            (34), (37), (39), (45), (46), (76) are inconsistent
% 241.46/47.97  | | | | | | | | |            by sub-proof #540.
% 241.46/47.97  | | | | | | | | | 
% 241.46/47.97  | | | | | | | | End of split
% 241.46/47.97  | | | | | | | | 
% 241.46/47.97  | | | | | | | End of split
% 241.46/47.97  | | | | | | | 
% 241.46/47.97  | | | | | | End of split
% 241.46/47.97  | | | | | | 
% 241.46/47.97  | | | | | End of split
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | End of split
% 241.46/47.97  | | | | 
% 241.46/47.97  | | | Case 2:
% 241.46/47.97  | | | | 
% 241.46/47.97  | | | |   (77)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 241.46/47.97  | | | |           = e0)
% 241.46/47.97  | | | | 
% 241.46/47.97  | | | | BETA: splitting (77) gives:
% 241.46/47.97  | | | | 
% 241.46/47.97  | | | | Case 1:
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | |   (78)  all_58_4 = e0 & op(e3, e1) = e0
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | | ALPHA: (78) implies:
% 241.46/47.97  | | | | |   (79)  all_58_4 = e0
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | | REF_CLOSE: (2), (10), (14), (16), (19), (28), (29), (34), (51), (79)
% 241.46/47.97  | | | | |            are inconsistent by sub-proof #1400.
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | Case 2:
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | |   (80)  all_58_9 = e0 & op(e3, e0) = e0
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | | ALPHA: (80) implies:
% 241.46/47.97  | | | | |   (81)  all_58_9 = e0
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | | COMBINE_EQS: (50), (81) imply:
% 241.46/47.97  | | | | |   (82)  e2 = e0
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | | REF_CLOSE: (2), (3), (4), (5), (12), (16), (18), (19), (21), (22),
% 241.46/47.97  | | | | |            (25), (30), (32), (34), (37), (46), (82) are inconsistent
% 241.46/47.97  | | | | |            by sub-proof #541.
% 241.46/47.97  | | | | | 
% 241.46/47.97  | | | | End of split
% 241.46/47.97  | | | | 
% 241.46/47.97  | | | End of split
% 241.46/47.97  | | | 
% 241.46/47.97  | | Case 2:
% 241.46/47.97  | | | 
% 241.46/47.97  | | |   (83)  all_58_10 = e2 & op(e2, e0) = e2
% 241.46/47.97  | | | 
% 241.46/47.97  | | | ALPHA: (83) implies:
% 241.46/47.97  | | |   (84)  all_58_10 = e2
% 241.46/47.97  | | |   (85)  op(e2, e0) = e2
% 241.46/47.97  | | | 
% 241.46/47.97  | | | REF_CLOSE: (2), (3), (4), (10), (13), (16), (18), (19), (22), (23), (33),
% 241.46/47.97  | | |            (34), (39), (44), (46), (47), (84), (85) are inconsistent by
% 241.46/47.97  | | |            sub-proof #616.
% 241.46/47.97  | | | 
% 241.46/47.97  | | End of split
% 241.46/47.97  | | 
% 241.46/47.97  | Case 2:
% 241.46/47.97  | | 
% 241.46/47.97  | |   (86)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.46/47.97  | |           e2)
% 241.46/47.97  | | 
% 241.46/47.97  | | BETA: splitting (86) gives:
% 241.46/47.97  | | 
% 241.46/47.97  | | Case 1:
% 241.46/47.97  | | | 
% 241.46/47.97  | | |   (87)  all_58_11 = e2 & op(e1, e0) = e2
% 241.46/47.97  | | | 
% 241.46/47.97  | | | ALPHA: (87) implies:
% 241.46/47.97  | | |   (88)  all_58_11 = e2
% 241.46/47.97  | | | 
% 241.46/47.97  | | | COMBINE_EQS: (37), (88) imply:
% 241.46/47.97  | | |   (89)  e2 = e0
% 241.46/47.97  | | | 
% 241.46/47.97  | | | SIMP: (89) implies:
% 241.46/47.97  | | |   (90)  e2 = e0
% 241.46/47.97  | | | 
% 241.46/47.97  | | | REF_CLOSE: (2), (3), (4), (5), (12), (16), (18), (19), (21), (22), (25),
% 241.46/47.97  | | |            (30), (32), (34), (37), (46), (90) are inconsistent by
% 241.46/47.97  | | |            sub-proof #541.
% 241.46/47.97  | | | 
% 241.46/47.97  | | Case 2:
% 241.46/47.97  | | | 
% 241.46/47.97  | | |   (91)  all_58_15 = e2 & op(e0, e0) = e2
% 241.46/47.97  | | | 
% 241.46/47.97  | | | ALPHA: (91) implies:
% 241.46/47.97  | | |   (92)  all_58_15 = e2
% 241.46/47.97  | | | 
% 241.46/47.97  | | | COMBINE_EQS: (8), (92) imply:
% 241.46/47.97  | | |   (93)  e3 = e2
% 241.46/47.97  | | | 
% 241.46/47.97  | | | REF_CLOSE: (2), (3), (4), (10), (15), (16), (17), (18), (19), (20), (23),
% 241.46/47.97  | | |            (27), (31), (34), (36), (39), (41), (42), (43), (46), (93) are
% 241.46/47.97  | | |            inconsistent by sub-proof #588.
% 241.46/47.97  | | | 
% 241.46/47.97  | | End of split
% 241.46/47.97  | | 
% 241.46/47.97  | End of split
% 241.46/47.97  | 
% 241.46/47.97  End of proof
% 241.46/47.97  
% 241.46/47.97  Sub-proof #540 shows that the following formulas are inconsistent:
% 241.46/47.97  ----------------------------------------------------------------
% 241.46/47.97    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.46/47.97         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.46/47.97    (2)   ~ (e3 = e0)
% 241.46/47.97    (3)  all_58_6 = e3
% 241.46/47.97    (4)   ~ (e2 = e0)
% 241.46/47.97    (5)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.46/47.97         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.46/47.97    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.46/47.97         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.46/47.97    (7)   ~ (e3 = e1)
% 241.46/47.97    (8)  all_58_3 = e3
% 241.46/47.98    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.46/47.98         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.46/47.98    (10)  op(e3, e3) = e1
% 241.46/47.98    (11)   ~ (e3 = e2)
% 241.46/47.98    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.46/47.98          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.46/47.98    (13)   ~ (all_52_4 = e3)
% 241.46/47.98    (14)  op(e3, e2) = all_52_4
% 241.46/47.98    (15)  all_58_14 = e0
% 241.46/47.98    (16)  all_58_7 = e1
% 241.46/47.98    (17)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.46/47.98          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.46/47.98    (18)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.46/47.98          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.46/47.98    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.46/47.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.46/47.98    (20)  all_58_11 = e0
% 241.46/47.98    (21)   ~ (e1 = e0)
% 241.46/47.98    (22)  all_58_10 = e1
% 241.46/47.98    (23)   ~ (e2 = e1)
% 241.46/47.98  
% 241.46/47.98  Begin of proof
% 241.46/47.98  | 
% 241.46/47.98  | BETA: splitting (5) gives:
% 241.46/47.98  | 
% 241.46/47.98  | Case 1:
% 241.46/47.98  | | 
% 241.46/47.98  | |   (24)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 241.46/47.98  | |           e1)
% 241.46/47.98  | | 
% 241.46/47.98  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 241.46/47.98  | |            (18), (19), (21), (22), (23), (24) are inconsistent by sub-proof
% 241.46/47.98  | |            #647.
% 241.46/47.98  | | 
% 241.46/47.98  | Case 2:
% 241.46/47.98  | | 
% 241.46/47.98  | |   (25)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 241.46/47.98  | |           e1)
% 241.46/47.98  | | 
% 241.46/47.98  | | BETA: splitting (25) gives:
% 241.46/47.98  | | 
% 241.46/47.98  | | Case 1:
% 241.46/47.98  | | | 
% 241.46/47.98  | | |   (26)  all_58_8 = e1 & op(e1, e1) = e1
% 241.46/47.98  | | | 
% 241.46/47.98  | | | ALPHA: (26) implies:
% 241.46/47.98  | | |   (27)  all_58_8 = e1
% 241.46/47.98  | | | 
% 241.46/47.98  | | | REF_CLOSE: (3), (4), (11), (16), (17), (20), (23), (27) are inconsistent
% 241.46/47.98  | | |            by sub-proof #2215.
% 241.46/47.98  | | | 
% 241.46/47.98  | | Case 2:
% 241.46/47.98  | | | 
% 241.46/47.98  | | |   (28)  all_58_14 = e1 & op(e0, e1) = e1
% 241.46/47.98  | | | 
% 241.46/47.98  | | | ALPHA: (28) implies:
% 241.46/47.98  | | |   (29)  all_58_14 = e1
% 241.46/47.98  | | | 
% 241.46/47.98  | | | REF_CLOSE: (15), (21), (29) are inconsistent by sub-proof #1033.
% 241.46/47.98  | | | 
% 241.46/47.98  | | End of split
% 241.46/47.98  | | 
% 241.46/47.98  | End of split
% 241.46/47.98  | 
% 241.46/47.98  End of proof
% 241.46/47.98  
% 241.46/47.98  Sub-proof #541 shows that the following formulas are inconsistent:
% 241.46/47.98  ----------------------------------------------------------------
% 241.46/47.98    (1)   ~ (e3 = e0)
% 241.46/47.98    (2)  all_58_6 = e3
% 241.46/47.98    (3)   ~ (e2 = e0)
% 241.46/47.98    (4)  e2 = e0
% 241.46/47.98    (5)  op(e1, e2) = all_52_6
% 241.46/47.98    (6)  all_58_2 = e2
% 241.46/47.98    (7)  op(e3, e3) = e1
% 241.46/47.98    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.46/47.98         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.46/47.98    (9)   ~ (e3 = e2)
% 241.46/47.98    (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.46/47.98          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.46/47.98    (11)  all_58_12 = e0
% 241.46/47.98    (12)   ~ (all_52_6 = e3)
% 241.46/47.98    (13)  all_58_7 = e1
% 241.46/47.98    (14)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.46/47.98          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.46/47.98    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.46/47.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.46/47.98    (16)  all_58_11 = e0
% 241.46/47.98    (17)   ~ (e2 = e1)
% 241.46/47.98  
% 241.46/47.98  Begin of proof
% 241.46/47.98  | 
% 241.46/47.98  | COMBINE_EQS: (4), (6) imply:
% 241.46/47.98  |   (18)  all_58_2 = e0
% 241.46/47.98  | 
% 241.46/47.98  | BETA: splitting (14) gives:
% 241.46/47.98  | 
% 241.46/47.98  | Case 1:
% 241.46/47.98  | | 
% 241.46/47.98  | |   (19)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 241.46/47.98  | |           e2)
% 241.46/47.98  | | 
% 241.46/47.98  | | BETA: splitting (19) gives:
% 241.46/47.98  | | 
% 241.46/47.98  | | Case 1:
% 241.46/47.98  | | | 
% 241.46/47.98  | | |   (20)  all_58_6 = e2 & op(e1, e3) = e2
% 241.46/47.98  | | | 
% 241.46/47.98  | | | REF_CLOSE: (2), (9), (20) are inconsistent by sub-proof #2219.
% 241.46/47.98  | | | 
% 241.46/47.98  | | Case 2:
% 241.46/47.98  | | | 
% 241.46/47.98  | | |   (21)  all_58_7 = e2 & op(e1, e2) = e2
% 241.46/47.98  | | | 
% 241.46/47.98  | | | REF_CLOSE: (13), (17), (21) are inconsistent by sub-proof #2218.
% 241.46/47.98  | | | 
% 241.46/47.98  | | End of split
% 241.46/47.98  | | 
% 241.46/47.98  | Case 2:
% 241.46/47.98  | | 
% 241.46/47.98  | |   (22)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 241.46/47.98  | |           e2)
% 241.46/47.98  | | 
% 241.46/47.98  | | BETA: splitting (22) gives:
% 241.46/47.98  | | 
% 241.46/47.98  | | Case 1:
% 241.46/47.98  | | | 
% 241.46/47.98  | | |   (23)  all_58_8 = e2 & op(e1, e1) = e2
% 241.46/47.98  | | | 
% 241.46/47.98  | | | ALPHA: (23) implies:
% 241.46/47.98  | | |   (24)  op(e1, e1) = e2
% 241.46/47.98  | | | 
% 241.46/47.98  | | | BETA: splitting (8) gives:
% 241.46/47.98  | | | 
% 241.46/47.98  | | | Case 1:
% 241.46/47.98  | | | | 
% 241.46/47.98  | | | |   (25)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3)
% 241.46/47.98  | | | |           = e2)
% 241.46/47.98  | | | | 
% 241.46/47.98  | | | | REF_CLOSE: (3), (7), (15), (17), (18), (25) are inconsistent by
% 241.46/47.98  | | | |            sub-proof #1329.
% 241.46/47.98  | | | | 
% 241.46/47.98  | | | Case 2:
% 241.46/47.98  | | | | 
% 241.46/47.98  | | | |   (26)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3)
% 241.46/47.98  | | | |           = e2)
% 241.46/47.98  | | | | 
% 241.46/47.98  | | | | BETA: splitting (26) gives:
% 241.46/47.98  | | | | 
% 241.46/47.98  | | | | Case 1:
% 241.46/47.98  | | | | | 
% 241.46/47.98  | | | | |   (27)  all_58_6 = e2 & op(e1, e3) = e2
% 241.46/47.98  | | | | | 
% 241.46/47.98  | | | | | ALPHA: (27) implies:
% 241.46/47.98  | | | | |   (28)  all_58_6 = e2
% 241.46/47.98  | | | | | 
% 241.46/47.98  | | | | | REF_CLOSE: (1), (5), (9), (10), (12), (15), (16), (24), (28) are
% 241.46/47.98  | | | | |            inconsistent by sub-proof #967.
% 241.46/47.98  | | | | | 
% 241.46/47.98  | | | | Case 2:
% 241.46/47.98  | | | | | 
% 241.46/47.98  | | | | |   (29)  all_58_12 = e2 & op(e0, e3) = e2
% 241.46/47.98  | | | | | 
% 241.46/47.98  | | | | | ALPHA: (29) implies:
% 241.46/47.98  | | | | |   (30)  all_58_12 = e2
% 241.46/47.98  | | | | | 
% 241.46/47.98  | | | | | REF_CLOSE: (3), (11), (30) are inconsistent by sub-proof #2083.
% 241.46/47.98  | | | | | 
% 241.46/47.98  | | | | End of split
% 241.46/47.98  | | | | 
% 241.46/47.98  | | | End of split
% 241.46/47.98  | | | 
% 241.46/47.98  | | Case 2:
% 241.46/47.98  | | | 
% 241.46/47.98  | | |   (31)  all_58_11 = e2 & op(e1, e0) = e2
% 241.46/47.98  | | | 
% 241.46/47.98  | | | REF_CLOSE: (3), (16), (31) are inconsistent by sub-proof #2216.
% 241.46/47.98  | | | 
% 241.46/47.98  | | End of split
% 241.46/47.98  | | 
% 241.46/47.98  | End of split
% 241.46/47.98  | 
% 241.46/47.98  End of proof
% 241.46/47.98  
% 241.46/47.98  Sub-proof #542 shows that the following formulas are inconsistent:
% 241.46/47.98  ----------------------------------------------------------------
% 241.46/47.98    (1)   ~ (e3 = e0)
% 241.46/47.98    (2)   ~ (e2 = e0)
% 241.46/47.98    (3)  all_58_15 = e3
% 241.46/47.98    (4)   ~ (e3 = e1)
% 241.46/47.98    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.46/47.98         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.46/47.98    (6)  op(e3, e3) = e1
% 241.46/47.98    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.46/47.98             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 241.46/47.98               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.46/47.98               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.46/47.98    (8)   ~ (e3 = e2)
% 241.46/47.98    (9)  all_58_6 = e0
% 241.46/47.98    (10)  op(e2, e3) = all_52_1
% 241.46/47.98    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.46/47.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.46/47.98    (12)   ~ (e1 = e0)
% 241.46/47.98    (13)   ~ (all_52_1 = e3)
% 241.46/47.98    (14)  all_58_14 = e1
% 241.46/47.98    (15)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.46/47.98          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.46/47.98            e2)
% 241.46/47.98    (16)   ~ (e2 = e1)
% 241.46/47.98  
% 241.46/47.98  Begin of proof
% 241.46/47.98  | 
% 241.46/47.98  | BETA: splitting (5) gives:
% 241.46/47.98  | 
% 241.46/47.98  | Case 1:
% 241.46/47.98  | | 
% 241.46/47.98  | |   (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 241.46/47.98  | |           e3)
% 241.46/47.98  | | 
% 241.46/47.98  | | REF_CLOSE: (4), (6), (10), (11), (13), (17) are inconsistent by sub-proof
% 241.46/47.98  | |            #1208.
% 241.46/47.98  | | 
% 241.46/47.98  | Case 2:
% 241.46/47.98  | | 
% 241.46/47.98  | |   (18)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 241.46/47.98  | |           e3)
% 241.46/47.98  | | 
% 241.46/47.98  | | BETA: splitting (18) gives:
% 241.46/47.98  | | 
% 241.46/47.98  | | Case 1:
% 241.46/47.98  | | | 
% 241.46/47.98  | | |   (19)  all_58_6 = e3 & op(e1, e3) = e3
% 241.46/47.98  | | | 
% 241.46/47.98  | | | ALPHA: (19) implies:
% 241.46/47.98  | | |   (20)  all_58_6 = e3
% 241.46/47.98  | | | 
% 241.46/47.98  | | | REF_CLOSE: (1), (9), (20) are inconsistent by sub-proof #2222.
% 241.46/47.98  | | | 
% 241.46/47.98  | | Case 2:
% 241.46/47.98  | | | 
% 241.46/47.98  | | |   (21)  all_58_12 = e3 & op(e0, e3) = e3
% 241.46/47.98  | | | 
% 241.46/47.98  | | | ALPHA: (21) implies:
% 241.46/47.98  | | |   (22)  all_58_12 = e3
% 241.46/47.98  | | | 
% 241.46/47.98  | | | REF_CLOSE: (1), (2), (3), (7), (8), (11), (12), (14), (15), (16), (22) are
% 241.46/47.98  | | |            inconsistent by sub-proof #1031.
% 241.46/47.98  | | | 
% 241.46/47.98  | | End of split
% 241.46/47.98  | | 
% 241.46/47.98  | End of split
% 241.46/47.98  | 
% 241.46/47.98  End of proof
% 241.46/47.98  
% 241.46/47.98  Sub-proof #543 shows that the following formulas are inconsistent:
% 241.46/47.98  ----------------------------------------------------------------
% 241.46/47.98    (1)   ~ (all_52_12 = all_4_2)
% 241.46/47.98    (2)  op(e2, e2) = e3
% 241.46/47.98    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 241.46/47.98             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 241.46/47.98           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 241.46/47.98         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 241.46/47.98           $i(all_56_7))
% 241.46/47.98    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.46/47.98         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.46/47.98    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.46/47.98         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.46/47.98    (6)   ~ (e3 = e0)
% 241.46/47.98    (7)  all_56_31 = all_4_2
% 241.46/47.98    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.46/47.98         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.46/47.98    (9)   ~ (all_4_2 = e2)
% 241.46/47.98    (10)  all_42_2 = e3
% 241.46/47.98    (11)  all_58_6 = e3
% 241.46/47.98    (12)   ~ (e2 = e0)
% 241.46/47.98    (13)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 241.46/47.98            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 241.46/47.98            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 241.46/47.98            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 241.46/47.98            = all_56_15 & $i(all_56_15))
% 241.46/47.98    (14)  all_54_13 = all_52_7
% 241.46/47.98    (15)  op(e1, e2) = all_52_6
% 241.46/47.98    (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.46/47.98          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.46/47.98    (17)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.46/47.98          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.46/47.98    (18)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.46/47.98              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.46/47.98            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.46/47.98            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.46/47.98            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.46/47.98             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.46/47.98            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.46/47.98            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.46/47.98            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.46/47.98            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.46/47.98            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.46/47.98              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.46/47.98            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.46/47.98            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.46/47.98            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.46/47.98            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.46/47.98            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.46/47.98            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.46/47.98              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.46/47.98            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.46/47.98            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.46/47.98            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.46/47.98            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.46/47.98            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.46/47.98            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.46/47.98              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.46/47.98            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.46/47.98            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.46/47.98    (19)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.46/47.98          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.46/47.98    (20)   ~ (all_52_7 = all_52_11)
% 241.46/47.98    (21)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.46/47.98            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.46/47.98              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.46/47.98    (22)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.46/47.98          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.46/47.98    (23)  all_58_1 = e0
% 241.46/47.98    (24)   ~ (all_52_7 = e3)
% 241.46/47.98    (25)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 241.46/47.98    (26)   ~ (all_52_8 = e0)
% 241.46/47.98    (27)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.46/47.98          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.46/47.98    (28)   ~ (e3 = e1)
% 241.46/47.98    (29)  all_54_11 = all_52_14
% 241.46/47.98    (30)  all_58_8 = e2
% 241.46/47.98    (31)  op(e0, e0) = all_4_2
% 241.46/47.98    (32)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.46/47.98          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.46/47.98    (33)   ~ (all_52_12 = all_52_14)
% 241.46/47.98    (34)   ~ (all_52_8 = e1)
% 241.46/47.98    (35)  all_58_3 = e3
% 241.46/47.98    (36)   ~ (all_52_12 = all_52_13)
% 241.46/47.98    (37)   ~ (all_52_14 = all_4_2)
% 241.46/47.98    (38)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 241.46/47.98            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 241.46/47.98              e1) = all_10_1 & $i(all_10_1))
% 241.46/47.98    (39)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.46/47.98          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.46/47.98    (40)  all_54_2 = all_52_8
% 241.46/47.98    (41)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 241.46/47.98    (42)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.46/47.98          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.46/47.98    (43)  op(e3, e3) = e1
% 241.46/47.98    (44)   ~ (all_52_9 = e0)
% 241.46/47.98    (45)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.46/47.98    (46)  all_56_21 = e0
% 241.46/47.98    (47)  all_54_4 = all_52_1
% 241.46/47.99    (48)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.46/47.99              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.46/47.99                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.46/47.99                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.46/47.99    (49)   ~ (all_52_8 = all_52_12)
% 241.46/47.99    (50)  op(e2, e1) = all_52_9
% 241.46/47.99    (51)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.46/47.99          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.46/47.99    (52)   ~ (e3 = e2)
% 241.46/47.99    (53)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.46/47.99          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.46/47.99    (54)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 241.46/47.99    (55)   ~ (all_52_14 = e0)
% 241.46/47.99    (56)   ~ (all_52_13 = all_4_2)
% 241.46/47.99    (57)   ~ (all_4_2 = e3)
% 241.46/47.99    (58)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 241.46/47.99    (59)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 241.46/47.99    (60)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.46/47.99          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.46/47.99    (61)  op(e3, e0) = all_52_12
% 241.46/47.99    (62)   ~ (all_52_7 = all_4_2)
% 241.46/47.99    (63)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.46/47.99          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.46/47.99    (64)   ~ (all_52_9 = all_52_13)
% 241.46/47.99    (65)  all_54_15 = all_4_2
% 241.46/47.99    (66)  all_58_9 = e3
% 241.46/47.99    (67)   ~ (all_52_4 = all_52_12)
% 241.46/47.99    (68)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 241.46/47.99    (69)  all_38_2 = e1
% 241.46/47.99    (70)  op(e3, e0) = e3
% 241.46/47.99    (71)  op(e2, e3) = all_52_1
% 241.46/47.99    (72)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.46/47.99          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.46/47.99    (73)   ~ (all_52_6 = e3)
% 241.46/47.99    (74)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 241.46/47.99    (75)  op(e1, e1) = e2
% 241.46/47.99    (76)   ~ (all_52_1 = all_52_13)
% 241.46/47.99    (77)   ~ (all_52_11 = e0)
% 241.46/47.99    (78)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.46/47.99          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.46/47.99    (79)  all_54_7 = all_52_13
% 241.46/47.99    (80)  op(e0, e2) = all_52_7
% 241.46/47.99    (81)   ~ (all_52_13 = all_52_14)
% 241.46/47.99    (82)  all_54_1 = all_52_4
% 241.46/47.99    (83)   ~ (all_20_2 = e1) | ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 241.46/47.99            op(e0, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 241.46/47.99              e3) & op(e0, e1) = all_20_1 & $i(all_20_1))
% 241.46/47.99    (84)   ~ (all_52_4 = e3)
% 241.46/47.99    (85)  op(e3, e2) = all_52_4
% 241.46/47.99    (86)   ~ (all_52_8 = all_52_11)
% 241.46/47.99    (87)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.46/47.99    (88)  all_58_7 = e1
% 241.46/47.99    (89)   ~ (all_52_9 = e3)
% 241.46/47.99    (90)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.46/47.99          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.46/47.99    (91)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.46/47.99          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.46/47.99    (92)  all_54_3 = all_52_12
% 241.46/47.99    (93)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.46/47.99          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.46/47.99    (94)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.46/47.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.46/47.99    (95)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.46/47.99          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.46/47.99    (96)   ~ (all_52_6 = all_52_7)
% 241.46/47.99    (97)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.46/47.99          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.46/47.99    (98)  all_56_11 = e3
% 241.46/47.99    (99)  op(e1, e1) = e0
% 241.46/47.99    (100)   ~ (all_52_4 = e1)
% 241.46/47.99    (101)  all_58_11 = e0
% 241.46/47.99    (102)  all_20_2 = all_4_2
% 241.46/47.99    (103)   ~ (e1 = e0)
% 241.46/47.99    (104)   ~ (all_52_13 = e3)
% 241.46/47.99    (105)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.46/47.99           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.46/47.99    (106)   ~ (all_52_11 = all_4_2)
% 241.46/47.99    (107)  op(e2, e0) = all_52_13
% 241.48/47.99    (108)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.48/47.99           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.48/47.99             e1)
% 241.48/47.99    (109)   ~ (all_52_1 = e3)
% 241.48/47.99    (110)  all_54_14 = all_52_11
% 241.48/47.99    (111)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.48/47.99           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.48/47.99             e2)
% 241.48/47.99    (112)   ~ (all_52_4 = all_52_8)
% 241.48/47.99    (113)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.48/47.99             $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) =
% 241.48/47.99             all_8_1 & $i(all_8_1))
% 241.48/47.99    (114)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.48/47.99           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.48/47.99    (115)  all_56_1 = e1
% 241.48/47.99    (116)   ~ (e2 = e1)
% 241.48/47.99    (117)   ~ (all_52_1 = e1)
% 241.48/47.99    (118)   ~ (all_52_4 = all_52_7)
% 241.48/47.99    (119)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 241.48/47.99             & op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 241.48/47.99             (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 241.48/47.99  
% 241.48/47.99  Begin of proof
% 241.48/47.99  | 
% 241.48/47.99  | BETA: splitting (4) gives:
% 241.48/47.99  | 
% 241.48/47.99  | Case 1:
% 241.48/47.99  | | 
% 241.48/47.99  | |   (120)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 241.48/47.99  | |            e2)
% 241.48/47.99  | | 
% 241.48/47.99  | | BETA: splitting (120) gives:
% 241.48/47.99  | | 
% 241.48/47.99  | | Case 1:
% 241.48/47.99  | | | 
% 241.48/47.99  | | |   (121)  all_58_0 = e2 & op(e3, e3) = e2
% 241.48/47.99  | | | 
% 241.48/47.99  | | | ALPHA: (121) implies:
% 241.48/47.99  | | |   (122)  op(e3, e3) = e2
% 241.48/47.99  | | | 
% 241.48/47.99  | | | REF_CLOSE: (43), (94), (116), (122) are inconsistent by sub-proof #2267.
% 241.48/47.99  | | | 
% 241.48/47.99  | | Case 2:
% 241.48/47.99  | | | 
% 241.48/47.99  | | |   (123)  all_58_1 = e2 & op(e3, e2) = e2
% 241.48/47.99  | | | 
% 241.48/47.99  | | | ALPHA: (123) implies:
% 241.48/47.99  | | |   (124)  all_58_1 = e2
% 241.48/47.99  | | | 
% 241.48/47.99  | | | COMBINE_EQS: (23), (124) imply:
% 241.48/47.99  | | |   (125)  e2 = e0
% 241.48/47.99  | | | 
% 241.48/47.99  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 241.48/47.99  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 241.48/47.99  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 241.48/47.99  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 241.48/47.99  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 241.48/47.99  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 241.48/47.99  | | |            (65), (67), (68), (69), (71), (72), (73), (74), (76), (77),
% 241.48/47.99  | | |            (78), (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 241.48/47.99  | | |            (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 241.48/47.99  | | |            (99), (100), (102), (103), (104), (105), (106), (107), (108),
% 241.48/47.99  | | |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 241.48/47.99  | | |            (118), (119), (125) are inconsistent by sub-proof #562.
% 241.48/47.99  | | | 
% 241.48/47.99  | | End of split
% 241.48/47.99  | | 
% 241.48/47.99  | Case 2:
% 241.48/47.99  | | 
% 241.48/47.99  | |   (126)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 241.48/47.99  | |            e2)
% 241.48/47.99  | | 
% 241.48/47.99  | | BETA: splitting (126) gives:
% 241.48/47.99  | | 
% 241.48/47.99  | | Case 1:
% 241.48/47.99  | | | 
% 241.48/47.99  | | |   (127)  all_58_4 = e2 & op(e3, e1) = e2
% 241.48/47.99  | | | 
% 241.48/47.99  | | | ALPHA: (127) implies:
% 241.48/47.99  | | |   (128)  all_58_4 = e2
% 241.48/47.99  | | | 
% 241.48/47.99  | | | REF_CLOSE: (4), (6), (8), (11), (12), (15), (16), (17), (19), (22), (27),
% 241.48/47.99  | | |            (28), (30), (32), (35), (39), (42), (43), (48), (50), (51),
% 241.48/47.99  | | |            (52), (53), (60), (63), (66), (70), (71), (72), (73), (75),
% 241.48/47.99  | | |            (78), (84), (85), (88), (89), (90), (91), (93), (94), (95),
% 241.48/47.99  | | |            (99), (101), (103), (105), (107), (108), (109), (111), (114),
% 241.48/47.99  | | |            (116), (117), (128) are inconsistent by sub-proof #544.
% 241.48/47.99  | | | 
% 241.48/47.99  | | Case 2:
% 241.48/47.99  | | | 
% 241.48/47.99  | | |   (129)  all_58_9 = e2 & op(e3, e0) = e2
% 241.48/47.99  | | | 
% 241.48/47.99  | | | ALPHA: (129) implies:
% 241.48/47.99  | | |   (130)  op(e3, e0) = e2
% 241.48/47.99  | | | 
% 241.48/47.99  | | | REF_CLOSE: (52), (70), (94), (130) are inconsistent by sub-proof #2125.
% 241.48/47.99  | | | 
% 241.48/47.99  | | End of split
% 241.48/47.99  | | 
% 241.48/47.99  | End of split
% 241.48/47.99  | 
% 241.48/47.99  End of proof
% 241.48/47.99  
% 241.48/47.99  Sub-proof #544 shows that the following formulas are inconsistent:
% 241.48/47.99  ----------------------------------------------------------------
% 241.48/47.99    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.48/47.99         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.48/47.99    (2)   ~ (e3 = e0)
% 241.48/47.99    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.48/47.99         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.48/47.99    (4)  all_58_6 = e3
% 241.48/47.99    (5)   ~ (e2 = e0)
% 241.48/47.99    (6)  op(e1, e2) = all_52_6
% 241.48/47.99    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.48/47.99         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.48/47.99    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.48/47.99         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.48/47.99    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.48/47.99         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.48/47.99    (10)  all_58_4 = e2
% 241.48/47.99    (11)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.48/47.99          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.48/47.99    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.48/47.99          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.48/47.99    (13)   ~ (e3 = e1)
% 241.48/47.99    (14)  all_58_8 = e2
% 241.48/47.99    (15)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.48/47.99          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.48/47.99    (16)  all_58_3 = e3
% 241.48/47.99    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.48/47.99          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.48/47.99    (18)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.48/47.99          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.48/47.99    (19)  op(e3, e3) = e1
% 241.48/47.99    (20)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.48/47.99              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.48/47.99                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.48/47.99                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.48/47.99    (21)  op(e2, e1) = all_52_9
% 241.48/47.99    (22)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.48/47.99          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.48/47.99    (23)   ~ (e3 = e2)
% 241.48/47.99    (24)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.48/47.99          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.48/47.99    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.48/47.99          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.48/47.99    (26)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.48/47.99          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.48/47.99    (27)  all_58_9 = e3
% 241.48/47.99    (28)  op(e3, e0) = e3
% 241.48/47.99    (29)  op(e2, e3) = all_52_1
% 241.48/47.99    (30)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.48/47.99          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.48/47.99    (31)   ~ (all_52_6 = e3)
% 241.48/47.99    (32)  op(e1, e1) = e2
% 241.48/47.99    (33)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.48/47.99          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.48/47.99    (34)   ~ (all_52_4 = e3)
% 241.48/47.99    (35)  op(e3, e2) = all_52_4
% 241.48/47.99    (36)  all_58_7 = e1
% 241.48/47.99    (37)   ~ (all_52_9 = e3)
% 241.48/47.99    (38)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.48/47.99          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.48/47.99    (39)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.48/47.99          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.48/47.99    (40)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.48/47.99          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.48/47.99    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.48/47.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.48/47.99    (42)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.48/47.99          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.48/47.99    (43)  op(e1, e1) = e0
% 241.48/47.99    (44)  all_58_11 = e0
% 241.48/48.00    (45)   ~ (e1 = e0)
% 241.48/48.00    (46)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.48/48.00          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.48/48.00    (47)  op(e2, e0) = all_52_13
% 241.48/48.00    (48)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.48/48.00          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.48/48.00            e1)
% 241.48/48.00    (49)   ~ (all_52_1 = e3)
% 241.48/48.00    (50)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.48/48.00          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.48/48.00            e2)
% 241.48/48.00    (51)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.48/48.00          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.48/48.00    (52)   ~ (e2 = e1)
% 241.48/48.00    (53)   ~ (all_52_1 = e1)
% 241.48/48.00  
% 241.48/48.00  Begin of proof
% 241.48/48.00  | 
% 241.48/48.00  | BETA: splitting (7) gives:
% 241.48/48.00  | 
% 241.48/48.00  | Case 1:
% 241.48/48.00  | | 
% 241.48/48.00  | |   (54)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 241.48/48.00  | |           e2)
% 241.48/48.00  | | 
% 241.48/48.00  | | BETA: splitting (54) gives:
% 241.48/48.00  | | 
% 241.48/48.00  | | Case 1:
% 241.48/48.00  | | | 
% 241.48/48.00  | | |   (55)  all_58_1 = e2 & op(e3, e2) = e2
% 241.48/48.00  | | | 
% 241.48/48.00  | | | ALPHA: (55) implies:
% 241.48/48.00  | | |   (56)  all_58_1 = e2
% 241.48/48.00  | | | 
% 241.48/48.00  | | | REF_CLOSE: (2), (5), (10), (19), (27), (30), (41), (45), (56) are
% 241.48/48.00  | | |            inconsistent by sub-proof #708.
% 241.48/48.00  | | | 
% 241.48/48.00  | | Case 2:
% 241.48/48.00  | | | 
% 241.48/48.00  | | |   (57)  all_58_3 = e2 & op(e2, e2) = e2
% 241.48/48.00  | | | 
% 241.48/48.00  | | | ALPHA: (57) implies:
% 241.48/48.00  | | |   (58)  all_58_3 = e2
% 241.48/48.00  | | | 
% 241.48/48.00  | | | COMBINE_EQS: (16), (58) imply:
% 241.48/48.00  | | |   (59)  e3 = e2
% 241.48/48.00  | | | 
% 241.48/48.00  | | | SIMP: (59) implies:
% 241.48/48.00  | | |   (60)  e3 = e2
% 241.48/48.00  | | | 
% 241.48/48.00  | | | COMBINE_EQS: (4), (60) imply:
% 241.48/48.00  | | |   (61)  all_58_6 = e2
% 241.48/48.00  | | | 
% 241.48/48.00  | | | REF_CLOSE: (2), (6), (23), (26), (31), (32), (41), (44), (61) are
% 241.48/48.00  | | |            inconsistent by sub-proof #967.
% 241.48/48.00  | | | 
% 241.48/48.00  | | End of split
% 241.48/48.00  | | 
% 241.48/48.00  | Case 2:
% 241.48/48.00  | | 
% 241.48/48.00  | |   (62)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 241.48/48.00  | |           e2)
% 241.48/48.00  | | 
% 241.48/48.00  | | BETA: splitting (62) gives:
% 241.48/48.00  | | 
% 241.48/48.00  | | Case 1:
% 241.48/48.00  | | | 
% 241.48/48.00  | | |   (63)  all_58_7 = e2 & op(e1, e2) = e2
% 241.48/48.00  | | | 
% 241.48/48.00  | | | ALPHA: (63) implies:
% 241.48/48.00  | | |   (64)  all_58_7 = e2
% 241.48/48.00  | | | 
% 241.48/48.00  | | | REF_CLOSE: (1), (2), (5), (10), (19), (23), (27), (30), (36), (41), (45),
% 241.48/48.00  | | |            (52), (64) are inconsistent by sub-proof #571.
% 241.48/48.00  | | | 
% 241.48/48.00  | | Case 2:
% 241.48/48.00  | | | 
% 241.48/48.00  | | |   (65)  all_58_13 = e2 & op(e0, e2) = e2
% 241.48/48.00  | | | 
% 241.48/48.00  | | | ALPHA: (65) implies:
% 241.48/48.00  | | |   (66)  op(e0, e2) = e2
% 241.48/48.00  | | | 
% 241.48/48.00  | | | BETA: splitting (42) gives:
% 241.48/48.00  | | | 
% 241.48/48.00  | | | Case 1:
% 241.48/48.00  | | | | 
% 241.48/48.00  | | | |   (67)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 241.48/48.00  | | | |           = e2)
% 241.48/48.00  | | | | 
% 241.48/48.00  | | | | BETA: splitting (67) gives:
% 241.48/48.00  | | | | 
% 241.48/48.00  | | | | Case 1:
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | |   (68)  all_58_9 = e2 & op(e3, e0) = e2
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | ALPHA: (68) implies:
% 241.48/48.00  | | | | |   (69)  op(e3, e0) = e2
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | REF_CLOSE: (23), (28), (41), (69) are inconsistent by sub-proof #2125.
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | Case 2:
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | |   (70)  all_58_10 = e2 & op(e2, e0) = e2
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | ALPHA: (70) implies:
% 241.48/48.00  | | | | |   (71)  all_58_10 = e2
% 241.48/48.00  | | | | |   (72)  op(e2, e0) = e2
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | BETA: splitting (20) gives:
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | Case 1:
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | |   (73)  all_58_15 = e0 & op(e0, e0) = e0
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | ALPHA: (73) implies:
% 241.48/48.00  | | | | | |   (74)  op(e0, e0) = e0
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | BETA: splitting (8) gives:
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | Case 1:
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | |   (75)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 &
% 241.48/48.00  | | | | | | |           op(e2, e0) = e1)
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | BETA: splitting (75) gives:
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | Case 1:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | |   (76)  all_58_9 = e1 & op(e3, e0) = e1
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | ALPHA: (76) implies:
% 241.48/48.00  | | | | | | | |   (77)  all_58_9 = e1
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 241.48/48.00  | | | | | | | |            (12), (13), (15), (16), (17), (18), (19), (20), (21),
% 241.48/48.00  | | | | | | | |            (22), (23), (24), (25), (26), (29), (30), (31), (33),
% 241.48/48.00  | | | | | | | |            (34), (35), (37), (38), (39), (40), (41), (42), (43),
% 241.48/48.00  | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 241.48/48.00  | | | | | | | |            (77) are inconsistent by sub-proof #640.
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | Case 2:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | |   (78)  all_58_10 = e1 & op(e2, e0) = e1
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | ALPHA: (78) implies:
% 241.48/48.00  | | | | | | | |   (79)  all_58_10 = e1
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | COMBINE_EQS: (71), (79) imply:
% 241.48/48.00  | | | | | | | |   (80)  e2 = e1
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | COMBINE_EQS: (10), (80) imply:
% 241.48/48.00  | | | | | | | |   (81)  all_58_4 = e1
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | REF_CLOSE: (1), (2), (5), (19), (23), (27), (30), (41), (45),
% 241.48/48.00  | | | | | | | |            (52), (81) are inconsistent by sub-proof #1469.
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | End of split
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | Case 2:
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | |   (82)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 241.48/48.00  | | | | | | |           op(e0, e0) = e1)
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | BETA: splitting (82) gives:
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | Case 1:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | |   (83)  all_58_11 = e1 & op(e1, e0) = e1
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | ALPHA: (83) implies:
% 241.48/48.00  | | | | | | | |   (84)  op(e1, e0) = e1
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | REF_CLOSE: (2), (4), (5), (14), (36), (41), (45), (46), (84) are
% 241.48/48.00  | | | | | | | |            inconsistent by sub-proof #1555.
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | Case 2:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | |   (85)  all_58_15 = e1 & op(e0, e0) = e1
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | ALPHA: (85) implies:
% 241.48/48.00  | | | | | | | |   (86)  op(e0, e0) = e1
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | REF_CLOSE: (41), (45), (74), (86) are inconsistent by sub-proof
% 241.48/48.00  | | | | | | | |            #2274.
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | End of split
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | End of split
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | Case 2:
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | |   (87)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 241.48/48.00  | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 241.48/48.00  | | | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.48/48.00  | | | | | |             op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | ALPHA: (87) implies:
% 241.48/48.00  | | | | | |   (88)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.48/48.00  | | | | | |           op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | BETA: splitting (88) gives:
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | Case 1:
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | |   (89)  all_58_12 = e0 & op(e0, e3) = e0
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | ALPHA: (89) implies:
% 241.48/48.00  | | | | | | |   (90)  all_58_12 = e0
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | REF_CLOSE: (2), (4), (5), (13), (16), (19), (22), (23), (29),
% 241.48/48.00  | | | | | | |            (40), (41), (45), (51), (52), (53), (71), (72), (90)
% 241.48/48.00  | | | | | | |            are inconsistent by sub-proof #616.
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | Case 2:
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | |   (91)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 241.48/48.00  | | | | | | |           op(e0, e1) = e0)
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | BETA: splitting (91) gives:
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | Case 1:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | |   (92)  all_58_13 = e0 & op(e0, e2) = e0
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | ALPHA: (92) implies:
% 241.48/48.00  | | | | | | | |   (93)  op(e0, e2) = e0
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | REF_CLOSE: (5), (41), (66), (93) are inconsistent by sub-proof
% 241.48/48.00  | | | | | | | |            #2132.
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | Case 2:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | |   (94)  all_58_14 = e0 & op(e0, e1) = e0
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | ALPHA: (94) implies:
% 241.48/48.00  | | | | | | | |   (95)  all_58_14 = e0
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (10), (21), (23), (26), (31),
% 241.48/48.00  | | | | | | | |            (32), (33), (36), (37), (39), (41), (44), (52), (95)
% 241.48/48.00  | | | | | | | |            are inconsistent by sub-proof #545.
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | End of split
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | End of split
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | End of split
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | End of split
% 241.48/48.00  | | | | 
% 241.48/48.00  | | | Case 2:
% 241.48/48.00  | | | | 
% 241.48/48.00  | | | |   (96)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 241.48/48.00  | | | |             e0) = e2)
% 241.48/48.00  | | | | 
% 241.48/48.00  | | | | BETA: splitting (96) gives:
% 241.48/48.00  | | | | 
% 241.48/48.00  | | | | Case 1:
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | |   (97)  all_58_11 = e2 & op(e1, e0) = e2
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | ALPHA: (97) implies:
% 241.48/48.00  | | | | |   (98)  all_58_11 = e2
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | COMBINE_EQS: (44), (98) imply:
% 241.48/48.00  | | | | |   (99)  e2 = e0
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | SIMP: (99) implies:
% 241.48/48.00  | | | | |   (100)  e2 = e0
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | COMBINE_EQS: (10), (100) imply:
% 241.48/48.00  | | | | |   (101)  all_58_4 = e0
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | REF_CLOSE: (1), (2), (5), (9), (16), (19), (23), (27), (36), (41),
% 241.48/48.00  | | | | |            (45), (52), (66), (101) are inconsistent by sub-proof #719.
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | Case 2:
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | |   (102)  all_58_15 = e2 & op(e0, e0) = e2
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | ALPHA: (102) implies:
% 241.48/48.00  | | | | |   (103)  all_58_15 = e2
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | BETA: splitting (20) gives:
% 241.48/48.00  | | | | | 
% 241.48/48.00  | | | | | Case 1:
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | |   (104)  all_58_15 = e0 & op(e0, e0) = e0
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | ALPHA: (104) implies:
% 241.48/48.00  | | | | | |   (105)  all_58_15 = e0
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | COMBINE_EQS: (103), (105) imply:
% 241.48/48.00  | | | | | |   (106)  e2 = e0
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | SIMP: (106) implies:
% 241.48/48.00  | | | | | |   (107)  e2 = e0
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | COMBINE_EQS: (10), (107) imply:
% 241.48/48.00  | | | | | |   (108)  all_58_4 = e0
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | REF_CLOSE: (1), (2), (5), (9), (16), (19), (23), (27), (36), (41),
% 241.48/48.00  | | | | | |            (45), (52), (66), (108) are inconsistent by sub-proof
% 241.48/48.00  | | | | | |            #719.
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | Case 2:
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | |   (109)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 241.48/48.00  | | | | | |              op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0))
% 241.48/48.00  | | | | | |          & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.48/48.00  | | | | | |              op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | ALPHA: (109) implies:
% 241.48/48.00  | | | | | |   (110)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.48/48.00  | | | | | |            op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.48/48.00  | | | | | |   (111)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 241.48/48.00  | | | | | |            op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | BETA: splitting (110) gives:
% 241.48/48.00  | | | | | | 
% 241.48/48.00  | | | | | | Case 1:
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | |   (112)  all_58_12 = e0 & op(e0, e3) = e0
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | ALPHA: (112) implies:
% 241.48/48.00  | | | | | | |   (113)  all_58_12 = e0
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | BETA: splitting (11) gives:
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | Case 1:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | |   (114)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 &
% 241.48/48.00  | | | | | | | |            op(e2, e1) = e1)
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | BETA: splitting (114) gives:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | Case 1:
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | |   (115)  all_58_4 = e1 & op(e3, e1) = e1
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | ALPHA: (115) implies:
% 241.48/48.00  | | | | | | | | |   (116)  all_58_4 = e1
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | REF_CLOSE: (1), (2), (5), (19), (23), (27), (30), (41), (45),
% 241.48/48.00  | | | | | | | | |            (52), (116) are inconsistent by sub-proof #1469.
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | Case 2:
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | |   (117)  all_58_5 = e1 & op(e2, e1) = e1
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | ALPHA: (117) implies:
% 241.48/48.00  | | | | | | | | |   (118)  all_58_5 = e1
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | BETA: splitting (8) gives:
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | Case 1:
% 241.48/48.00  | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | |   (119)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1
% 241.48/48.00  | | | | | | | | | |            & op(e2, e0) = e1)
% 241.48/48.00  | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | BETA: splitting (119) gives:
% 241.48/48.00  | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | Case 1:
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | |   (120)  all_58_9 = e1 & op(e3, e0) = e1
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | | ALPHA: (120) implies:
% 241.48/48.00  | | | | | | | | | | |   (121)  all_58_9 = e1
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 241.48/48.00  | | | | | | | | | | |            (12), (13), (15), (16), (17), (18), (19), (20),
% 241.48/48.00  | | | | | | | | | | |            (21), (22), (23), (24), (25), (26), (29), (30),
% 241.48/48.00  | | | | | | | | | | |            (31), (33), (34), (35), (37), (38), (39), (40),
% 241.48/48.00  | | | | | | | | | | |            (41), (42), (43), (45), (46), (47), (48), (49),
% 241.48/48.00  | | | | | | | | | | |            (50), (51), (52), (53), (121) are inconsistent by
% 241.48/48.00  | | | | | | | | | | |            sub-proof #640.
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | Case 2:
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | |   (122)  all_58_10 = e1 & op(e2, e0) = e1
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | | ALPHA: (122) implies:
% 241.48/48.00  | | | | | | | | | | |   (123)  all_58_10 = e1
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | | REF_CLOSE: (2), (5), (12), (13), (16), (23), (38), (40),
% 241.48/48.00  | | | | | | | | | | |            (41), (42), (45), (52), (103), (111), (118), (123)
% 241.48/48.00  | | | | | | | | | | |            are inconsistent by sub-proof #831.
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | End of split
% 241.48/48.00  | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | Case 2:
% 241.48/48.00  | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | |   (124)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 241.48/48.00  | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.48/48.00  | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | BETA: splitting (124) gives:
% 241.48/48.00  | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | Case 1:
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | |   (125)  all_58_11 = e1 & op(e1, e0) = e1
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | | ALPHA: (125) implies:
% 241.48/48.00  | | | | | | | | | | |   (126)  op(e1, e0) = e1
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (14), (36), (41), (45), (46), (126)
% 241.48/48.00  | | | | | | | | | | |            are inconsistent by sub-proof #1555.
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | Case 2:
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | |   (127)  all_58_15 = e1 & op(e0, e0) = e1
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | | ALPHA: (127) implies:
% 241.48/48.00  | | | | | | | | | | |   (128)  all_58_15 = e1
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (10), (19), (23), (27), (30), (41),
% 241.48/48.00  | | | | | | | | | | |            (45), (52), (103), (128) are inconsistent by
% 241.48/48.00  | | | | | | | | | | |            sub-proof #691.
% 241.48/48.00  | | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | | End of split
% 241.48/48.00  | | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | End of split
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | End of split
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | Case 2:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | |   (129)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 241.48/48.00  | | | | | | | |            op(e0, e1) = e1)
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | BETA: splitting (129) gives:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | Case 1:
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | |   (130)  all_58_8 = e1 & op(e1, e1) = e1
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | ALPHA: (130) implies:
% 241.48/48.00  | | | | | | | | |   (131)  all_58_8 = e1
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | REF_CLOSE: (4), (5), (23), (36), (39), (44), (52), (131) are
% 241.48/48.00  | | | | | | | | |            inconsistent by sub-proof #2215.
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | Case 2:
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | |   (132)  all_58_14 = e1 & op(e0, e1) = e1
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | ALPHA: (132) implies:
% 241.48/48.00  | | | | | | | | |   (133)  all_58_14 = e1
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | | REF_CLOSE: (2), (5), (10), (13), (18), (19), (21), (22), (23),
% 241.48/48.00  | | | | | | | | |            (25), (29), (33), (37), (41), (43), (45), (49),
% 241.48/48.00  | | | | | | | | |            (52), (113), (133) are inconsistent by sub-proof
% 241.48/48.00  | | | | | | | | |            #644.
% 241.48/48.00  | | | | | | | | | 
% 241.48/48.00  | | | | | | | | End of split
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | End of split
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | Case 2:
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | |   (134)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 241.48/48.00  | | | | | | |            op(e0, e1) = e0)
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | BETA: splitting (134) gives:
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | | Case 1:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | |   (135)  all_58_13 = e0 & op(e0, e2) = e0
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | ALPHA: (135) implies:
% 241.48/48.00  | | | | | | | |   (136)  op(e0, e2) = e0
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | REF_CLOSE: (5), (41), (66), (136) are inconsistent by sub-proof
% 241.48/48.00  | | | | | | | |            #2132.
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | Case 2:
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | |   (137)  all_58_14 = e0 & op(e0, e1) = e0
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | ALPHA: (137) implies:
% 241.48/48.00  | | | | | | | |   (138)  all_58_14 = e0
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (10), (21), (23), (26), (31),
% 241.48/48.00  | | | | | | | |            (32), (33), (36), (37), (39), (41), (44), (52), (138)
% 241.48/48.00  | | | | | | | |            are inconsistent by sub-proof #545.
% 241.48/48.00  | | | | | | | | 
% 241.48/48.00  | | | | | | | End of split
% 241.48/48.00  | | | | | | | 
% 241.48/48.00  | | | | | | End of split
% 241.48/48.00  | | | | | | 
% 241.48/48.01  | | | | | End of split
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | End of split
% 241.48/48.01  | | | | 
% 241.48/48.01  | | | End of split
% 241.48/48.01  | | | 
% 241.48/48.01  | | End of split
% 241.48/48.01  | | 
% 241.48/48.01  | End of split
% 241.48/48.01  | 
% 241.48/48.01  End of proof
% 241.48/48.01  
% 241.48/48.01  Sub-proof #545 shows that the following formulas are inconsistent:
% 241.48/48.01  ----------------------------------------------------------------
% 241.48/48.01    (1)   ~ (e3 = e0)
% 241.48/48.01    (2)  all_58_6 = e3
% 241.48/48.01    (3)   ~ (e2 = e0)
% 241.48/48.01    (4)  op(e1, e2) = all_52_6
% 241.48/48.01    (5)  all_58_4 = e2
% 241.48/48.01    (6)  op(e2, e1) = all_52_9
% 241.48/48.01    (7)   ~ (e3 = e2)
% 241.48/48.01    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.48/48.01         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.48/48.01    (9)   ~ (all_52_6 = e3)
% 241.48/48.01    (10)  op(e1, e1) = e2
% 241.48/48.01    (11)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.48/48.01          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.48/48.01    (12)  all_58_14 = e0
% 241.48/48.01    (13)  all_58_7 = e1
% 241.48/48.01    (14)   ~ (all_52_9 = e3)
% 241.48/48.01    (15)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.48/48.01          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.48/48.01    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.48/48.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.48/48.01    (17)  all_58_11 = e0
% 241.48/48.01    (18)   ~ (e2 = e1)
% 241.48/48.01  
% 241.48/48.01  Begin of proof
% 241.48/48.01  | 
% 241.48/48.01  | BETA: splitting (11) gives:
% 241.48/48.01  | 
% 241.48/48.01  | Case 1:
% 241.48/48.01  | | 
% 241.48/48.01  | |   (19)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 241.48/48.01  | |           e3)
% 241.48/48.01  | | 
% 241.48/48.01  | | BETA: splitting (19) gives:
% 241.48/48.01  | | 
% 241.48/48.01  | | Case 1:
% 241.48/48.01  | | | 
% 241.48/48.01  | | |   (20)  all_58_4 = e3 & op(e3, e1) = e3
% 241.48/48.01  | | | 
% 241.48/48.01  | | | ALPHA: (20) implies:
% 241.48/48.01  | | |   (21)  all_58_4 = e3
% 241.48/48.01  | | | 
% 241.48/48.01  | | | COMBINE_EQS: (5), (21) imply:
% 241.48/48.01  | | |   (22)  e3 = e2
% 241.48/48.01  | | | 
% 241.48/48.01  | | | SIMP: (22) implies:
% 241.48/48.01  | | |   (23)  e3 = e2
% 241.48/48.01  | | | 
% 241.48/48.01  | | | COMBINE_EQS: (2), (23) imply:
% 241.48/48.01  | | |   (24)  all_58_6 = e2
% 241.48/48.01  | | | 
% 241.48/48.01  | | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (16), (17), (24) are
% 241.48/48.01  | | |            inconsistent by sub-proof #967.
% 241.48/48.01  | | | 
% 241.48/48.01  | | Case 2:
% 241.48/48.01  | | | 
% 241.48/48.01  | | |   (25)  all_58_5 = e3 & op(e2, e1) = e3
% 241.48/48.01  | | | 
% 241.48/48.01  | | | REF_CLOSE: (6), (14), (16), (25) are inconsistent by sub-proof #1822.
% 241.48/48.01  | | | 
% 241.48/48.01  | | End of split
% 241.48/48.01  | | 
% 241.48/48.01  | Case 2:
% 241.48/48.01  | | 
% 241.48/48.01  | |   (26)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 241.48/48.01  | |           e3)
% 241.48/48.01  | | 
% 241.48/48.01  | | BETA: splitting (26) gives:
% 241.48/48.01  | | 
% 241.48/48.01  | | Case 1:
% 241.48/48.01  | | | 
% 241.48/48.01  | | |   (27)  all_58_8 = e3 & op(e1, e1) = e3
% 241.48/48.01  | | | 
% 241.48/48.01  | | | ALPHA: (27) implies:
% 241.48/48.01  | | |   (28)  op(e1, e1) = e3
% 241.48/48.01  | | | 
% 241.48/48.01  | | | REF_CLOSE: (2), (3), (7), (13), (15), (16), (17), (18), (28) are
% 241.48/48.01  | | |            inconsistent by sub-proof #546.
% 241.48/48.01  | | | 
% 241.48/48.01  | | Case 2:
% 241.48/48.01  | | | 
% 241.48/48.01  | | |   (29)  all_58_14 = e3 & op(e0, e1) = e3
% 241.48/48.01  | | | 
% 241.48/48.01  | | | ALPHA: (29) implies:
% 241.48/48.01  | | |   (30)  all_58_14 = e3
% 241.48/48.01  | | | 
% 241.48/48.01  | | | COMBINE_EQS: (12), (30) imply:
% 241.48/48.01  | | |   (31)  e3 = e0
% 241.48/48.01  | | | 
% 241.48/48.01  | | | COMBINE_EQS: (2), (31) imply:
% 241.48/48.01  | | |   (32)  all_58_6 = e0
% 241.48/48.01  | | | 
% 241.48/48.01  | | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (16), (17), (32) are
% 241.48/48.01  | | |            inconsistent by sub-proof #1686.
% 241.48/48.01  | | | 
% 241.48/48.01  | | End of split
% 241.48/48.01  | | 
% 241.48/48.01  | End of split
% 241.48/48.01  | 
% 241.48/48.01  End of proof
% 241.48/48.01  
% 241.48/48.01  Sub-proof #546 shows that the following formulas are inconsistent:
% 241.48/48.01  ----------------------------------------------------------------
% 241.48/48.01    (1)  all_58_6 = e3
% 241.48/48.01    (2)   ~ (e2 = e0)
% 241.48/48.01    (3)   ~ (e3 = e2)
% 241.48/48.01    (4)  op(e1, e1) = e3
% 241.48/48.01    (5)  all_58_7 = e1
% 241.48/48.01    (6)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.48/48.01         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.48/48.01    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.48/48.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.48/48.01    (8)  all_58_11 = e0
% 241.48/48.01    (9)   ~ (e2 = e1)
% 241.48/48.01  
% 241.48/48.01  Begin of proof
% 241.48/48.01  | 
% 241.48/48.01  | BETA: splitting (6) gives:
% 241.48/48.01  | 
% 241.48/48.01  | Case 1:
% 241.48/48.01  | | 
% 241.48/48.01  | |   (10)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 241.48/48.01  | |           e2)
% 241.48/48.01  | | 
% 241.48/48.01  | | REF_CLOSE: (1), (3), (5), (9), (10) are inconsistent by sub-proof #547.
% 241.48/48.01  | | 
% 241.48/48.01  | Case 2:
% 241.48/48.01  | | 
% 241.48/48.01  | |   (11)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 241.48/48.01  | |           e2)
% 241.48/48.01  | | 
% 241.48/48.01  | | BETA: splitting (11) gives:
% 241.48/48.01  | | 
% 241.48/48.01  | | Case 1:
% 241.48/48.01  | | | 
% 241.48/48.01  | | |   (12)  all_58_8 = e2 & op(e1, e1) = e2
% 241.48/48.01  | | | 
% 241.48/48.01  | | | ALPHA: (12) implies:
% 241.48/48.01  | | |   (13)  op(e1, e1) = e2
% 241.48/48.01  | | | 
% 241.48/48.01  | | | REF_CLOSE: (3), (4), (7), (13) are inconsistent by sub-proof #2206.
% 241.48/48.01  | | | 
% 241.48/48.01  | | Case 2:
% 241.48/48.01  | | | 
% 241.48/48.01  | | |   (14)  all_58_11 = e2 & op(e1, e0) = e2
% 241.48/48.01  | | | 
% 241.48/48.01  | | | ALPHA: (14) implies:
% 241.48/48.01  | | |   (15)  all_58_11 = e2
% 241.48/48.01  | | | 
% 241.48/48.01  | | | REF_CLOSE: (2), (8), (15) are inconsistent by sub-proof #2110.
% 241.48/48.01  | | | 
% 241.48/48.01  | | End of split
% 241.48/48.01  | | 
% 241.48/48.01  | End of split
% 241.48/48.01  | 
% 241.48/48.01  End of proof
% 241.48/48.01  
% 241.48/48.01  Sub-proof #547 shows that the following formulas are inconsistent:
% 241.48/48.01  ----------------------------------------------------------------
% 241.48/48.01    (1)  all_58_6 = e3
% 241.48/48.01    (2)   ~ (e3 = e2)
% 241.48/48.01    (3)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 241.48/48.01    (4)  all_58_7 = e1
% 241.48/48.01    (5)   ~ (e2 = e1)
% 241.48/48.01  
% 241.48/48.01  Begin of proof
% 241.48/48.01  | 
% 241.48/48.01  | BETA: splitting (3) gives:
% 241.48/48.01  | 
% 241.48/48.01  | Case 1:
% 241.48/48.01  | | 
% 241.48/48.01  | |   (6)  all_58_6 = e2 & op(e1, e3) = e2
% 241.48/48.01  | | 
% 241.48/48.01  | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #2219.
% 241.48/48.01  | | 
% 241.48/48.01  | Case 2:
% 241.48/48.01  | | 
% 241.48/48.01  | |   (7)  all_58_7 = e2 & op(e1, e2) = e2
% 241.48/48.01  | | 
% 241.48/48.01  | | ALPHA: (7) implies:
% 241.48/48.01  | |   (8)  all_58_7 = e2
% 241.48/48.01  | | 
% 241.48/48.01  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #2134.
% 241.48/48.01  | | 
% 241.48/48.01  | End of split
% 241.48/48.01  | 
% 241.48/48.01  End of proof
% 241.48/48.01  
% 241.48/48.01  Sub-proof #548 shows that the following formulas are inconsistent:
% 241.48/48.01  ----------------------------------------------------------------
% 241.48/48.01    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.48/48.01         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.48/48.01    (2)   ~ (e3 = e0)
% 241.48/48.01    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.48/48.01         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.48/48.01    (4)   ~ (e2 = e0)
% 241.48/48.01    (5)  op(e1, e2) = all_52_6
% 241.48/48.01    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.48/48.01         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.48/48.01    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.48/48.01         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.48/48.01    (8)  all_58_6 = e2
% 241.48/48.01    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.48/48.01         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.48/48.01    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.48/48.01          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.48/48.01    (11)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.48/48.01          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.48/48.01    (12)   ~ (e3 = e1)
% 241.48/48.01    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.48/48.01          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.48/48.01    (14)  all_58_3 = e3
% 241.48/48.01    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.48/48.01          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.48/48.01    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.48/48.01          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.48/48.01    (17)  op(e3, e3) = e1
% 241.48/48.01    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.48/48.01              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.48/48.01                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.48/48.01                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.48/48.01    (19)  op(e2, e1) = all_52_9
% 241.48/48.01    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.48/48.01          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.48/48.01    (21)   ~ (e3 = e2)
% 241.48/48.01    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.48/48.01          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.48/48.01    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.48/48.01          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.48/48.01    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.48/48.01          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.48/48.01    (25)  op(e2, e3) = all_52_1
% 241.48/48.01    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.48/48.01          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.48/48.01    (27)   ~ (all_52_6 = e3)
% 241.48/48.01    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.48/48.01          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.48/48.01    (29)   ~ (all_52_4 = e3)
% 241.48/48.01    (30)  op(e3, e2) = all_52_4
% 241.48/48.01    (31)   ~ (all_52_9 = e3)
% 241.48/48.01    (32)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.48/48.01          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.48/48.01    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.48/48.01          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.48/48.01    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.48/48.01          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.48/48.01    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.48/48.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.48/48.01    (36)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.48/48.01          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.48/48.01    (37)  op(e1, e1) = e0
% 241.48/48.01    (38)  all_58_11 = e0
% 241.48/48.01    (39)   ~ (e1 = e0)
% 241.48/48.01    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.48/48.01          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.48/48.01    (41)  op(e2, e0) = all_52_13
% 241.48/48.01    (42)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.48/48.01          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.48/48.01            e1)
% 241.48/48.01    (43)   ~ (all_52_1 = e3)
% 241.48/48.01    (44)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.48/48.01          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.48/48.01            e2)
% 241.48/48.01    (45)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.48/48.01          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.48/48.01    (46)   ~ (e2 = e1)
% 241.48/48.01    (47)   ~ (all_52_1 = e1)
% 241.48/48.01  
% 241.48/48.01  Begin of proof
% 241.48/48.01  | 
% 241.48/48.01  | BETA: splitting (16) gives:
% 241.48/48.01  | 
% 241.48/48.01  | Case 1:
% 241.48/48.01  | | 
% 241.48/48.01  | |   (48)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 241.48/48.01  | |           e3)
% 241.48/48.01  | | 
% 241.48/48.01  | | REF_CLOSE: (12), (17), (25), (35), (43), (48) are inconsistent by sub-proof
% 241.48/48.01  | |            #1208.
% 241.48/48.01  | | 
% 241.48/48.01  | Case 2:
% 241.48/48.01  | | 
% 241.48/48.01  | |   (49)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 241.48/48.01  | |           e3)
% 241.48/48.01  | | 
% 241.48/48.01  | | BETA: splitting (49) gives:
% 241.48/48.01  | | 
% 241.48/48.01  | | Case 1:
% 241.48/48.01  | | | 
% 241.48/48.01  | | |   (50)  all_58_6 = e3 & op(e1, e3) = e3
% 241.48/48.01  | | | 
% 241.48/48.01  | | | REF_CLOSE: (8), (21), (50) are inconsistent by sub-proof #1838.
% 241.48/48.01  | | | 
% 241.48/48.01  | | Case 2:
% 241.48/48.01  | | | 
% 241.48/48.01  | | |   (51)  all_58_12 = e3 & op(e0, e3) = e3
% 241.48/48.01  | | | 
% 241.48/48.01  | | | ALPHA: (51) implies:
% 241.48/48.01  | | |   (52)  all_58_12 = e3
% 241.48/48.01  | | | 
% 241.48/48.01  | | | BETA: splitting (23) gives:
% 241.48/48.01  | | | 
% 241.48/48.01  | | | Case 1:
% 241.48/48.01  | | | | 
% 241.48/48.01  | | | |   (53)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 241.48/48.01  | | | |           = e0)
% 241.48/48.01  | | | | 
% 241.48/48.01  | | | | BETA: splitting (53) gives:
% 241.48/48.01  | | | | 
% 241.48/48.01  | | | | Case 1:
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | |   (54)  all_58_0 = e0 & op(e3, e3) = e0
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | | ALPHA: (54) implies:
% 241.48/48.01  | | | | |   (55)  op(e3, e3) = e0
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | | REF_CLOSE: (17), (35), (39), (55) are inconsistent by sub-proof #1828.
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | Case 2:
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | |   (56)  all_58_2 = e0 & op(e2, e3) = e0
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | | ALPHA: (56) implies:
% 241.48/48.01  | | | | |   (57)  all_58_2 = e0
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | | BETA: splitting (24) gives:
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | | Case 1:
% 241.48/48.01  | | | | | | 
% 241.48/48.01  | | | | | |   (58)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 241.48/48.01  | | | | | |             e2) = e3)
% 241.48/48.01  | | | | | | 
% 241.48/48.01  | | | | | | REF_CLOSE: (2), (4), (5), (17), (20), (21), (23), (27), (35), (39),
% 241.48/48.01  | | | | | |            (46), (52), (58) are inconsistent by sub-proof #1136.
% 241.48/48.01  | | | | | | 
% 241.48/48.01  | | | | | Case 2:
% 241.48/48.01  | | | | | | 
% 241.48/48.01  | | | | | |   (59)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 241.48/48.01  | | | | | |             e0) = e3)
% 241.48/48.01  | | | | | | 
% 241.48/48.01  | | | | | | BETA: splitting (59) gives:
% 241.48/48.01  | | | | | | 
% 241.48/48.01  | | | | | | Case 1:
% 241.48/48.01  | | | | | | | 
% 241.48/48.01  | | | | | | |   (60)  all_58_8 = e3 & op(e1, e1) = e3
% 241.48/48.01  | | | | | | | 
% 241.48/48.01  | | | | | | | REF_CLOSE: (2), (35), (37), (60) are inconsistent by sub-proof
% 241.48/48.01  | | | | | | |            #2018.
% 241.48/48.01  | | | | | | | 
% 241.48/48.01  | | | | | | Case 2:
% 241.48/48.01  | | | | | | | 
% 241.48/48.01  | | | | | | |   (61)  all_58_11 = e3 & op(e1, e0) = e3
% 241.48/48.01  | | | | | | | 
% 241.48/48.01  | | | | | | | REF_CLOSE: (2), (4), (12), (16), (17), (20), (21), (25), (35),
% 241.48/48.01  | | | | | | |            (38), (43), (46), (52), (57), (61) are inconsistent by
% 241.48/48.01  | | | | | | |            sub-proof #579.
% 241.48/48.01  | | | | | | | 
% 241.48/48.01  | | | | | | End of split
% 241.48/48.01  | | | | | | 
% 241.48/48.01  | | | | | End of split
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | End of split
% 241.48/48.01  | | | | 
% 241.48/48.01  | | | Case 2:
% 241.48/48.01  | | | | 
% 241.48/48.01  | | | |   (62)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 241.48/48.01  | | | |           = e0)
% 241.48/48.01  | | | | 
% 241.48/48.01  | | | | BETA: splitting (62) gives:
% 241.48/48.01  | | | | 
% 241.48/48.01  | | | | Case 1:
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | |   (63)  all_58_6 = e0 & op(e1, e3) = e0
% 241.48/48.01  | | | | | 
% 241.48/48.01  | | | | | ALPHA: (63) implies:
% 241.48/48.01  | | | | |   (64)  all_58_6 = e0
% 241.48/48.01  | | | | | 
% 241.48/48.02  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 241.48/48.02  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.48/48.02  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 241.48/48.02  | | | | |            (33), (34), (35), (36), (37), (39), (40), (41), (42), (43),
% 241.48/48.02  | | | | |            (44), (45), (46), (47), (52), (64) are inconsistent by
% 241.48/48.02  | | | | |            sub-proof #665.
% 241.48/48.02  | | | | | 
% 241.48/48.02  | | | | Case 2:
% 241.48/48.02  | | | | | 
% 241.48/48.02  | | | | |   (65)  all_58_12 = e0 & op(e0, e3) = e0
% 241.48/48.02  | | | | | 
% 241.48/48.02  | | | | | ALPHA: (65) implies:
% 241.48/48.02  | | | | |   (66)  all_58_12 = e0
% 241.48/48.02  | | | | | 
% 241.48/48.02  | | | | | REF_CLOSE: (2), (52), (66) are inconsistent by sub-proof #1971.
% 241.48/48.02  | | | | | 
% 241.48/48.02  | | | | End of split
% 241.48/48.02  | | | | 
% 241.48/48.02  | | | End of split
% 241.48/48.02  | | | 
% 241.48/48.02  | | End of split
% 241.48/48.02  | | 
% 241.48/48.02  | End of split
% 241.48/48.02  | 
% 241.48/48.02  End of proof
% 241.48/48.02  
% 241.48/48.02  Sub-proof #549 shows that the following formulas are inconsistent:
% 241.48/48.02  ----------------------------------------------------------------
% 241.48/48.02    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.48/48.02    (2)  all_58_6 = e3
% 241.48/48.02    (3)   ~ (e2 = e0)
% 241.48/48.02    (4)  all_58_7 = e0
% 241.48/48.02    (5)  all_58_11 = e1
% 241.48/48.02    (6)   ~ (e3 = e2)
% 241.48/48.02    (7)  all_58_14 = e0
% 241.48/48.02    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.48/48.02         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.48/48.02    (9)   ~ (e1 = e0)
% 241.48/48.02    (10)   ~ (e2 = e1)
% 241.48/48.02  
% 241.48/48.02  Begin of proof
% 241.48/48.02  | 
% 241.48/48.02  | BETA: splitting (1) gives:
% 241.48/48.02  | 
% 241.48/48.02  | Case 1:
% 241.48/48.02  | | 
% 241.48/48.02  | |   (11)  all_58_8 = e1 & op(e1, e1) = e1
% 241.48/48.02  | | 
% 241.48/48.02  | | ALPHA: (11) implies:
% 241.48/48.02  | |   (12)  all_58_8 = e1
% 241.48/48.02  | | 
% 241.48/48.02  | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (12) are inconsistent by
% 241.48/48.02  | |            sub-proof #988.
% 241.48/48.02  | | 
% 241.48/48.02  | Case 2:
% 241.48/48.02  | | 
% 241.48/48.02  | |   (13)  all_58_14 = e1 & op(e0, e1) = e1
% 241.48/48.02  | | 
% 241.48/48.02  | | REF_CLOSE: (7), (9), (13) are inconsistent by sub-proof #828.
% 241.48/48.02  | | 
% 241.48/48.02  | End of split
% 241.48/48.02  | 
% 241.48/48.02  End of proof
% 241.48/48.02  
% 241.48/48.02  Sub-proof #550 shows that the following formulas are inconsistent:
% 241.48/48.02  ----------------------------------------------------------------
% 241.48/48.02    (1)   ~ (e3 = e0)
% 241.48/48.02    (2)  all_58_6 = e3
% 241.48/48.02    (3)   ~ (e2 = e0)
% 241.48/48.02    (4)  all_58_12 = e2
% 241.48/48.02    (5)  all_58_9 = e0
% 241.48/48.02    (6)  all_58_11 = e1
% 241.48/48.02    (7)  all_58_15 = e3
% 241.48/48.02    (8)  op(e3, e3) = e1
% 241.51/48.02    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.02         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.02    (10)   ~ (e3 = e2)
% 241.51/48.02    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.02          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.02    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.02    (13)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.51/48.02          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.51/48.02    (14)   ~ (e1 = e0)
% 241.51/48.02    (15)  all_58_10 = e1
% 241.51/48.02    (16)   ~ (e2 = e1)
% 241.51/48.02  
% 241.51/48.02  Begin of proof
% 241.51/48.02  | 
% 241.51/48.02  | BETA: splitting (13) gives:
% 241.51/48.02  | 
% 241.51/48.02  | Case 1:
% 241.51/48.02  | | 
% 241.51/48.02  | |   (17)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 241.51/48.02  | |           e2)
% 241.51/48.02  | | 
% 241.51/48.02  | | BETA: splitting (17) gives:
% 241.51/48.02  | | 
% 241.51/48.02  | | Case 1:
% 241.51/48.02  | | | 
% 241.51/48.02  | | |   (18)  all_58_9 = e2 & op(e3, e0) = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | ALPHA: (18) implies:
% 241.51/48.02  | | |   (19)  all_58_9 = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | REF_CLOSE: (3), (5), (19) are inconsistent by sub-proof #1660.
% 241.51/48.02  | | | 
% 241.51/48.02  | | Case 2:
% 241.51/48.02  | | | 
% 241.51/48.02  | | |   (20)  all_58_10 = e2 & op(e2, e0) = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | ALPHA: (20) implies:
% 241.51/48.02  | | |   (21)  all_58_10 = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | COMBINE_EQS: (15), (21) imply:
% 241.51/48.02  | | |   (22)  e2 = e1
% 241.51/48.02  | | | 
% 241.51/48.02  | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (12), (14), (16),
% 241.51/48.02  | | |            (22) are inconsistent by sub-proof #585.
% 241.51/48.02  | | | 
% 241.51/48.02  | | End of split
% 241.51/48.02  | | 
% 241.51/48.02  | Case 2:
% 241.51/48.02  | | 
% 241.51/48.02  | |   (23)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.51/48.02  | |           e2)
% 241.51/48.02  | | 
% 241.51/48.02  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 241.51/48.02  | |            (16), (23) are inconsistent by sub-proof #551.
% 241.51/48.02  | | 
% 241.51/48.02  | End of split
% 241.51/48.02  | 
% 241.51/48.02  End of proof
% 241.51/48.02  
% 241.51/48.02  Sub-proof #551 shows that the following formulas are inconsistent:
% 241.51/48.02  ----------------------------------------------------------------
% 241.51/48.02    (1)   ~ (e3 = e0)
% 241.51/48.02    (2)  all_58_6 = e3
% 241.51/48.02    (3)   ~ (e2 = e0)
% 241.51/48.02    (4)  all_58_12 = e2
% 241.51/48.02    (5)  all_58_11 = e1
% 241.51/48.02    (6)  all_58_15 = e3
% 241.51/48.02    (7)  op(e3, e3) = e1
% 241.51/48.02    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.02         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.02    (9)   ~ (e3 = e2)
% 241.51/48.02    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.02          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.02    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.02    (12)   ~ (e1 = e0)
% 241.51/48.02    (13)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.51/48.02    (14)   ~ (e2 = e1)
% 241.51/48.02  
% 241.51/48.02  Begin of proof
% 241.51/48.02  | 
% 241.51/48.02  | BETA: splitting (13) gives:
% 241.51/48.02  | 
% 241.51/48.02  | Case 1:
% 241.51/48.02  | | 
% 241.51/48.02  | |   (15)  all_58_11 = e2 & op(e1, e0) = e2
% 241.51/48.02  | | 
% 241.51/48.02  | | ALPHA: (15) implies:
% 241.51/48.02  | |   (16)  all_58_11 = e2
% 241.51/48.02  | | 
% 241.51/48.02  | | COMBINE_EQS: (5), (16) imply:
% 241.51/48.02  | |   (17)  e2 = e1
% 241.51/48.02  | | 
% 241.51/48.02  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (14), (17)
% 241.51/48.02  | |            are inconsistent by sub-proof #585.
% 241.51/48.02  | | 
% 241.51/48.02  | Case 2:
% 241.51/48.02  | | 
% 241.51/48.02  | |   (18)  all_58_15 = e2 & op(e0, e0) = e2
% 241.51/48.02  | | 
% 241.51/48.02  | | ALPHA: (18) implies:
% 241.51/48.02  | |   (19)  all_58_15 = e2
% 241.51/48.02  | | 
% 241.51/48.02  | | REF_CLOSE: (6), (9), (19) are inconsistent by sub-proof #615.
% 241.51/48.02  | | 
% 241.51/48.02  | End of split
% 241.51/48.02  | 
% 241.51/48.02  End of proof
% 241.51/48.02  
% 241.51/48.02  Sub-proof #552 shows that the following formulas are inconsistent:
% 241.51/48.02  ----------------------------------------------------------------
% 241.51/48.02    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.51/48.02         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.51/48.02    (2)  all_58_6 = e3
% 241.51/48.02    (3)   ~ (e2 = e0)
% 241.51/48.02    (4)  all_58_7 = e0
% 241.51/48.02    (5)  all_58_9 = e0
% 241.51/48.02    (6)  op(e3, e3) = e1
% 241.51/48.02    (7)   ~ (e3 = e2)
% 241.51/48.02    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 241.51/48.02    (9)  all_58_1 = e2
% 241.51/48.02    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.02    (11)  all_58_4 = e3
% 241.51/48.02    (12)   ~ (e2 = e1)
% 241.51/48.02  
% 241.51/48.02  Begin of proof
% 241.51/48.02  | 
% 241.51/48.02  | BETA: splitting (8) gives:
% 241.51/48.02  | 
% 241.51/48.02  | Case 1:
% 241.51/48.02  | | 
% 241.51/48.02  | |   (13)  all_58_6 = e2 & op(e1, e3) = e2
% 241.51/48.02  | | 
% 241.51/48.02  | | ALPHA: (13) implies:
% 241.51/48.02  | |   (14)  all_58_6 = e2
% 241.51/48.02  | | 
% 241.51/48.02  | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #2024.
% 241.51/48.02  | | 
% 241.51/48.02  | Case 2:
% 241.51/48.02  | | 
% 241.51/48.02  | |   (15)  all_58_7 = e2 & op(e1, e2) = e2
% 241.51/48.02  | | 
% 241.51/48.02  | | ALPHA: (15) implies:
% 241.51/48.02  | |   (16)  all_58_7 = e2
% 241.51/48.02  | | 
% 241.51/48.02  | | COMBINE_EQS: (4), (16) imply:
% 241.51/48.02  | |   (17)  e2 = e0
% 241.51/48.02  | | 
% 241.51/48.02  | | SIMP: (17) implies:
% 241.51/48.02  | |   (18)  e2 = e0
% 241.51/48.02  | | 
% 241.51/48.02  | | COMBINE_EQS: (9), (18) imply:
% 241.51/48.02  | |   (19)  all_58_1 = e0
% 241.51/48.02  | | 
% 241.51/48.02  | | REF_CLOSE: (1), (3), (5), (6), (7), (10), (11), (12), (19) are inconsistent
% 241.51/48.02  | |            by sub-proof #1097.
% 241.51/48.02  | | 
% 241.51/48.02  | End of split
% 241.51/48.02  | 
% 241.51/48.02  End of proof
% 241.51/48.02  
% 241.51/48.02  Sub-proof #553 shows that the following formulas are inconsistent:
% 241.51/48.02  ----------------------------------------------------------------
% 241.51/48.02    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.51/48.02         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.51/48.02    (2)   ~ (e3 = e0)
% 241.51/48.02    (3)  all_58_6 = e3
% 241.51/48.02    (4)   ~ (e2 = e0)
% 241.51/48.02    (5)  all_58_7 = e0
% 241.51/48.02    (6)  op(e1, e2) = all_52_6
% 241.51/48.02    (7)  all_58_9 = e0
% 241.51/48.02    (8)  all_58_11 = e1
% 241.51/48.02    (9)  all_58_15 = e3
% 241.51/48.02    (10)   ~ (e3 = e1)
% 241.51/48.02    (11)  all_58_8 = e2
% 241.51/48.02    (12)  all_58_3 = e3
% 241.51/48.02    (13)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.51/48.02          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.51/48.02    (14)  op(e3, e3) = e1
% 241.51/48.02    (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.02          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.02    (16)   ~ (e3 = e2)
% 241.51/48.02    (17)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.02          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.02    (18)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.51/48.02          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.51/48.02    (19)  op(e2, e3) = all_52_1
% 241.51/48.02    (20)   ~ (all_52_6 = e3)
% 241.51/48.02    (21)  op(e1, e1) = e2
% 241.51/48.02    (22)  all_58_5 = e1
% 241.51/48.02    (23)  all_58_1 = e2
% 241.51/48.02    (24)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.51/48.02          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.51/48.02    (25)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.02          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.51/48.02    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.02    (27)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.51/48.02          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.51/48.02    (28)  op(e1, e1) = e0
% 241.51/48.02    (29)   ~ (e1 = e0)
% 241.51/48.02    (30)  all_58_4 = e3
% 241.51/48.02    (31)   ~ (all_52_1 = e3)
% 241.51/48.02    (32)   ~ (e2 = e1)
% 241.51/48.02  
% 241.51/48.02  Begin of proof
% 241.51/48.02  | 
% 241.51/48.02  | BETA: splitting (27) gives:
% 241.51/48.02  | 
% 241.51/48.02  | Case 1:
% 241.51/48.02  | | 
% 241.51/48.02  | |   (33)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 241.51/48.02  | |           e2)
% 241.51/48.02  | | 
% 241.51/48.02  | | BETA: splitting (33) gives:
% 241.51/48.02  | | 
% 241.51/48.02  | | Case 1:
% 241.51/48.02  | | | 
% 241.51/48.02  | | |   (34)  all_58_9 = e2 & op(e3, e0) = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | ALPHA: (34) implies:
% 241.51/48.02  | | |   (35)  all_58_9 = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | REF_CLOSE: (1), (4), (7), (14), (16), (23), (26), (30), (32), (35) are
% 241.51/48.02  | | |            inconsistent by sub-proof #1065.
% 241.51/48.02  | | | 
% 241.51/48.02  | | Case 2:
% 241.51/48.02  | | | 
% 241.51/48.02  | | |   (36)  all_58_10 = e2 & op(e2, e0) = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | ALPHA: (36) implies:
% 241.51/48.02  | | |   (37)  op(e2, e0) = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | BETA: splitting (15) gives:
% 241.51/48.02  | | | 
% 241.51/48.02  | | | Case 1:
% 241.51/48.02  | | | | 
% 241.51/48.02  | | | |   (38)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3)
% 241.51/48.02  | | | |           = e2)
% 241.51/48.02  | | | | 
% 241.51/48.02  | | | | REF_CLOSE: (2), (4), (12), (14), (22), (25), (26), (29), (32), (37),
% 241.51/48.02  | | | |            (38) are inconsistent by sub-proof #636.
% 241.51/48.02  | | | | 
% 241.51/48.02  | | | Case 2:
% 241.51/48.02  | | | | 
% 241.51/48.02  | | | |   (39)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3)
% 241.51/48.02  | | | |           = e2)
% 241.51/48.02  | | | | 
% 241.51/48.02  | | | | BETA: splitting (39) gives:
% 241.51/48.02  | | | | 
% 241.51/48.02  | | | | Case 1:
% 241.51/48.02  | | | | | 
% 241.51/48.02  | | | | |   (40)  all_58_6 = e2 & op(e1, e3) = e2
% 241.51/48.02  | | | | | 
% 241.51/48.02  | | | | | ALPHA: (40) implies:
% 241.51/48.02  | | | | |   (41)  all_58_6 = e2
% 241.51/48.02  | | | | | 
% 241.51/48.02  | | | | | REF_CLOSE: (2), (4), (6), (8), (10), (13), (14), (15), (16), (17),
% 241.51/48.02  | | | | |            (18), (19), (20), (26), (28), (29), (31), (32), (41) are
% 241.51/48.02  | | | | |            inconsistent by sub-proof #661.
% 241.51/48.02  | | | | | 
% 241.51/48.02  | | | | Case 2:
% 241.51/48.02  | | | | | 
% 241.51/48.02  | | | | | 
% 241.51/48.02  | | | | | GROUND_INST: instantiating (26) with e0, e2, e1, e1, simplifying with
% 241.51/48.02  | | | | |              (21), (28) gives:
% 241.51/48.02  | | | | |   (42)  e2 = e0
% 241.51/48.02  | | | | | 
% 241.51/48.02  | | | | | COMBINE_EQS: (23), (42) imply:
% 241.51/48.02  | | | | |   (43)  all_58_1 = e0
% 241.51/48.02  | | | | | 
% 241.51/48.02  | | | | | REF_CLOSE: (1), (4), (7), (14), (16), (26), (30), (32), (43) are
% 241.51/48.02  | | | | |            inconsistent by sub-proof #1097.
% 241.51/48.02  | | | | | 
% 241.51/48.02  | | | | End of split
% 241.51/48.02  | | | | 
% 241.51/48.02  | | | End of split
% 241.51/48.02  | | | 
% 241.51/48.02  | | End of split
% 241.51/48.02  | | 
% 241.51/48.02  | Case 2:
% 241.51/48.02  | | 
% 241.51/48.02  | |   (44)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.51/48.02  | |           e2)
% 241.51/48.02  | | 
% 241.51/48.02  | | BETA: splitting (44) gives:
% 241.51/48.02  | | 
% 241.51/48.02  | | Case 1:
% 241.51/48.02  | | | 
% 241.51/48.02  | | |   (45)  all_58_11 = e2 & op(e1, e0) = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | ALPHA: (45) implies:
% 241.51/48.02  | | |   (46)  all_58_11 = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | COMBINE_EQS: (8), (46) imply:
% 241.51/48.02  | | |   (47)  e2 = e1
% 241.51/48.02  | | | 
% 241.51/48.02  | | | SIMP: (47) implies:
% 241.51/48.02  | | |   (48)  e2 = e1
% 241.51/48.02  | | | 
% 241.51/48.02  | | | COMBINE_EQS: (11), (48) imply:
% 241.51/48.02  | | |   (49)  all_58_8 = e1
% 241.51/48.02  | | | 
% 241.51/48.02  | | | REF_CLOSE: (3), (4), (5), (8), (16), (24), (32), (49) are inconsistent by
% 241.51/48.02  | | |            sub-proof #988.
% 241.51/48.02  | | | 
% 241.51/48.02  | | Case 2:
% 241.51/48.02  | | | 
% 241.51/48.02  | | |   (50)  all_58_15 = e2 & op(e0, e0) = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | ALPHA: (50) implies:
% 241.51/48.02  | | |   (51)  all_58_15 = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | COMBINE_EQS: (9), (51) imply:
% 241.51/48.02  | | |   (52)  e3 = e2
% 241.51/48.02  | | | 
% 241.51/48.02  | | | REF_CLOSE: (2), (3), (4), (6), (8), (10), (13), (14), (15), (16), (17),
% 241.51/48.02  | | |            (18), (19), (20), (26), (28), (29), (31), (32), (52) are
% 241.51/48.02  | | |            inconsistent by sub-proof #561.
% 241.51/48.02  | | | 
% 241.51/48.02  | | End of split
% 241.51/48.02  | | 
% 241.51/48.02  | End of split
% 241.51/48.02  | 
% 241.51/48.02  End of proof
% 241.51/48.02  
% 241.51/48.02  Sub-proof #554 shows that the following formulas are inconsistent:
% 241.51/48.02  ----------------------------------------------------------------
% 241.51/48.02    (1)   ~ (all_52_12 = all_4_2)
% 241.51/48.02    (2)  op(e2, e2) = e3
% 241.51/48.02    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 241.51/48.02             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 241.51/48.02           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 241.51/48.02         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 241.51/48.02           $i(all_56_7))
% 241.51/48.02    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.51/48.02         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.51/48.02    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.51/48.02         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.02    (6)   ~ (e3 = e0)
% 241.51/48.02    (7)  all_56_31 = all_4_2
% 241.51/48.02    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.51/48.02         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.51/48.02    (9)   ~ (all_4_2 = e2)
% 241.51/48.02    (10)  all_42_2 = e3
% 241.51/48.02    (11)  all_58_6 = e3
% 241.51/48.02    (12)   ~ (e2 = e0)
% 241.51/48.02    (13)  all_58_7 = e0
% 241.51/48.02    (14)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 241.51/48.02            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 241.51/48.02            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 241.51/48.02            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 241.51/48.02            = all_56_15 & $i(all_56_15))
% 241.51/48.02    (15)  all_54_13 = all_52_7
% 241.51/48.02    (16)  op(e1, e2) = all_52_6
% 241.51/48.02    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.02          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.02    (18)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.51/48.02          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.51/48.02    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.51/48.02              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.51/48.02            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.51/48.02            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.51/48.02            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.51/48.02             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.02            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.51/48.02            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.51/48.02            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.51/48.02            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.02            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.51/48.02              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.51/48.02            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.51/48.02            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.51/48.02            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.51/48.02            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.51/48.02            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.51/48.02            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.51/48.02              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.51/48.02            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.02            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.51/48.02            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.51/48.02            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.51/48.02            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.02            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.51/48.02              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.51/48.02            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.02            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.51/48.02    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.02          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.51/48.02    (21)   ~ (all_52_7 = all_52_11)
% 241.51/48.02    (22)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.51/48.02            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.51/48.02              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.51/48.02    (23)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.51/48.02          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.51/48.02    (24)  all_58_11 = e1
% 241.51/48.02    (25)   ~ (all_52_7 = e3)
% 241.51/48.02    (26)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 241.51/48.02    (27)   ~ (all_52_8 = e0)
% 241.51/48.02    (28)  all_58_15 = e3
% 241.51/48.02    (29)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.02          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.51/48.02    (30)   ~ (e3 = e1)
% 241.51/48.02    (31)  all_54_11 = all_52_14
% 241.51/48.02    (32)  all_58_8 = e2
% 241.51/48.02    (33)  op(e0, e0) = all_4_2
% 241.51/48.02    (34)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.51/48.02          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.51/48.02    (35)   ~ (all_52_12 = all_52_14)
% 241.51/48.02    (36)   ~ (all_52_8 = e1)
% 241.51/48.02    (37)  all_58_3 = e3
% 241.51/48.02    (38)   ~ (all_52_12 = all_52_13)
% 241.51/48.02    (39)   ~ (all_52_14 = all_4_2)
% 241.51/48.02    (40)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 241.51/48.02            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 241.51/48.02              e1) = all_10_1 & $i(all_10_1))
% 241.51/48.02    (41)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.51/48.02          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.51/48.02    (42)  all_54_2 = all_52_8
% 241.51/48.02    (43)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 241.51/48.02    (44)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.51/48.02          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.51/48.02    (45)  op(e3, e3) = e1
% 241.51/48.02    (46)   ~ (all_52_9 = e0)
% 241.51/48.02    (47)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.51/48.02    (48)  all_56_21 = e0
% 241.51/48.02    (49)  all_54_4 = all_52_1
% 241.51/48.02    (50)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.02              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.51/48.02                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.51/48.02                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.51/48.02    (51)   ~ (all_52_8 = all_52_12)
% 241.51/48.02    (52)  op(e2, e1) = all_52_9
% 241.51/48.02    (53)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.02          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.02    (54)   ~ (e3 = e2)
% 241.51/48.02    (55)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.51/48.02          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.51/48.02    (56)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 241.51/48.02    (57)   ~ (all_52_14 = e0)
% 241.51/48.02    (58)   ~ (all_52_13 = all_4_2)
% 241.51/48.02    (59)   ~ (all_4_2 = e3)
% 241.51/48.02    (60)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 241.51/48.02    (61)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 241.51/48.02    (62)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.02          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.02    (63)  op(e3, e0) = all_52_12
% 241.51/48.02    (64)   ~ (all_52_7 = all_4_2)
% 241.51/48.02    (65)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.51/48.02          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.51/48.02    (66)   ~ (all_52_9 = all_52_13)
% 241.51/48.02    (67)  all_54_15 = all_4_2
% 241.51/48.02    (68)   ~ (all_52_4 = all_52_12)
% 241.51/48.02    (69)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 241.51/48.02    (70)  all_38_2 = e1
% 241.51/48.02    (71)  op(e2, e3) = all_52_1
% 241.51/48.02    (72)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.51/48.02          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.02    (73)   ~ (all_52_6 = e3)
% 241.51/48.02    (74)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 241.51/48.02    (75)   ~ (all_52_1 = all_52_13)
% 241.51/48.02    (76)   ~ (all_52_11 = e0)
% 241.51/48.02    (77)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.51/48.02          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.51/48.02    (78)  all_54_7 = all_52_13
% 241.51/48.02    (79)  op(e0, e2) = all_52_7
% 241.51/48.02    (80)   ~ (all_52_13 = all_52_14)
% 241.51/48.02    (81)  all_54_1 = all_52_4
% 241.51/48.03    (82)   ~ (all_20_2 = e1) | ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 241.51/48.03            op(e0, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 241.51/48.03              e3) & op(e0, e1) = all_20_1 & $i(all_20_1))
% 241.51/48.03    (83)   ~ (all_52_4 = e3)
% 241.51/48.03    (84)  op(e3, e2) = all_52_4
% 241.51/48.03    (85)   ~ (all_52_8 = all_52_11)
% 241.51/48.03    (86)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.51/48.03    (87)  all_58_1 = e2
% 241.51/48.03    (88)   ~ (all_52_9 = e3)
% 241.51/48.03    (89)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.51/48.03          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.03    (90)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.51/48.03          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.51/48.03    (91)  all_54_3 = all_52_12
% 241.51/48.03    (92)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.03          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.51/48.03    (93)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.03    (94)  all_58_14 = e3
% 241.51/48.03    (95)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.51/48.03          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.51/48.03    (96)   ~ (all_52_6 = all_52_7)
% 241.51/48.03    (97)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.03          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.03    (98)  all_56_11 = e3
% 241.51/48.03    (99)  op(e1, e1) = e0
% 241.51/48.03    (100)   ~ (all_52_4 = e1)
% 241.51/48.03    (101)  all_20_2 = all_4_2
% 241.51/48.03    (102)   ~ (e1 = e0)
% 241.51/48.03    (103)  all_58_13 = e1
% 241.51/48.03    (104)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.51/48.03           | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.51/48.03    (105)   ~ (all_52_13 = e3)
% 241.51/48.03    (106)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.51/48.03           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.51/48.03    (107)   ~ (all_52_11 = all_4_2)
% 241.51/48.03    (108)  op(e2, e0) = all_52_13
% 241.51/48.03    (109)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.03           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.51/48.03             e1)
% 241.51/48.03    (110)   ~ (all_52_1 = e3)
% 241.51/48.03    (111)  all_54_14 = all_52_11
% 241.51/48.03    (112)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.03           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.51/48.03             e2)
% 241.51/48.03    (113)   ~ (all_52_4 = all_52_8)
% 241.51/48.03    (114)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.51/48.03             $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) =
% 241.51/48.03             all_8_1 & $i(all_8_1))
% 241.51/48.03    (115)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.03           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.51/48.03    (116)  all_56_1 = e1
% 241.51/48.03    (117)   ~ (e2 = e1)
% 241.51/48.03    (118)   ~ (all_52_1 = e1)
% 241.51/48.03    (119)   ~ (all_52_4 = all_52_7)
% 241.51/48.03    (120)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 241.51/48.03             & op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 241.51/48.03             (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 241.51/48.03  
% 241.51/48.03  Begin of proof
% 241.51/48.03  | 
% 241.51/48.03  | BETA: splitting (104) gives:
% 241.51/48.03  | 
% 241.51/48.03  | Case 1:
% 241.51/48.03  | | 
% 241.51/48.03  | |   (121)  all_58_12 = e0 & op(e0, e3) = e0
% 241.51/48.03  | | 
% 241.51/48.03  | | ALPHA: (121) implies:
% 241.51/48.03  | |   (122)  all_58_12 = e0
% 241.51/48.03  | | 
% 241.51/48.03  | | BETA: splitting (112) gives:
% 241.51/48.03  | | 
% 241.51/48.03  | | Case 1:
% 241.51/48.03  | | | 
% 241.51/48.03  | | |   (123)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2)
% 241.51/48.03  | | |            = e2)
% 241.51/48.03  | | | 
% 241.51/48.03  | | | BETA: splitting (123) gives:
% 241.51/48.03  | | | 
% 241.51/48.03  | | | Case 1:
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | |   (124)  all_58_12 = e2 & op(e0, e3) = e2
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | ALPHA: (124) implies:
% 241.51/48.03  | | | |   (125)  all_58_12 = e2
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | COMBINE_EQS: (122), (125) imply:
% 241.51/48.03  | | | |   (126)  e2 = e0
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | SIMP: (126) implies:
% 241.51/48.03  | | | |   (127)  e2 = e0
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | COMBINE_EQS: (87), (127) imply:
% 241.51/48.03  | | | |   (128)  all_58_1 = e0
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 241.51/48.03  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 241.51/48.03  | | | |            (22), (23), (24), (25), (26), (27), (29), (30), (31), (32),
% 241.51/48.03  | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 241.51/48.03  | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 241.51/48.03  | | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 241.51/48.03  | | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 241.51/48.03  | | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 241.51/48.03  | | | |            (83), (84), (85), (86), (88), (89), (90), (91), (92), (93),
% 241.51/48.03  | | | |            (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 241.51/48.03  | | | |            (105), (106), (107), (108), (109), (110), (111), (112),
% 241.51/48.03  | | | |            (113), (114), (115), (116), (117), (118), (119), (120), (128)
% 241.51/48.03  | | | |            are inconsistent by sub-proof #558.
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | Case 2:
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | |   (129)  all_58_13 = e2 & op(e0, e2) = e2
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | REF_CLOSE: (11), (12), (13), (24), (32), (54), (90), (103), (117), (129)
% 241.51/48.03  | | | |            are inconsistent by sub-proof #559.
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | End of split
% 241.51/48.03  | | | 
% 241.51/48.03  | | Case 2:
% 241.51/48.03  | | | 
% 241.51/48.03  | | |   (130)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0)
% 241.51/48.03  | | |            = e2)
% 241.51/48.03  | | | 
% 241.51/48.03  | | | BETA: splitting (130) gives:
% 241.51/48.03  | | | 
% 241.51/48.03  | | | Case 1:
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | |   (131)  all_58_14 = e2 & op(e0, e1) = e2
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | ALPHA: (131) implies:
% 241.51/48.03  | | | |   (132)  all_58_14 = e2
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | COMBINE_EQS: (94), (132) imply:
% 241.51/48.03  | | | |   (133)  e3 = e2
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | REF_CLOSE: (6), (11), (12), (16), (24), (30), (44), (45), (53), (54),
% 241.51/48.03  | | | |            (62), (65), (71), (73), (93), (99), (102), (110), (117),
% 241.51/48.03  | | | |            (133) are inconsistent by sub-proof #561.
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | Case 2:
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | |   (134)  all_58_15 = e2 & op(e0, e0) = e2
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | ALPHA: (134) implies:
% 241.51/48.03  | | | |   (135)  all_58_15 = e2
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | COMBINE_EQS: (28), (135) imply:
% 241.51/48.03  | | | |   (136)  e3 = e2
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | | REF_CLOSE: (6), (11), (12), (16), (24), (30), (44), (45), (53), (54),
% 241.51/48.03  | | | |            (62), (65), (71), (73), (93), (99), (102), (110), (117),
% 241.51/48.03  | | | |            (136) are inconsistent by sub-proof #561.
% 241.51/48.03  | | | | 
% 241.51/48.03  | | | End of split
% 241.51/48.03  | | | 
% 241.51/48.03  | | End of split
% 241.51/48.03  | | 
% 241.51/48.03  | Case 2:
% 241.51/48.03  | | 
% 241.51/48.03  | |   (137)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 241.51/48.03  | |            e0)
% 241.51/48.03  | | 
% 241.51/48.03  | | BETA: splitting (137) gives:
% 241.51/48.03  | | 
% 241.51/48.03  | | Case 1:
% 241.51/48.03  | | | 
% 241.51/48.03  | | |   (138)  all_58_13 = e0 & op(e0, e2) = e0
% 241.51/48.03  | | | 
% 241.51/48.03  | | | REF_CLOSE: (102), (103), (138) are inconsistent by sub-proof #609.
% 241.51/48.03  | | | 
% 241.51/48.03  | | Case 2:
% 241.51/48.03  | | | 
% 241.51/48.03  | | |   (139)  all_58_14 = e0 & op(e0, e1) = e0
% 241.51/48.03  | | | 
% 241.51/48.03  | | | ALPHA: (139) implies:
% 241.51/48.03  | | |   (140)  all_58_14 = e0
% 241.51/48.03  | | | 
% 241.51/48.03  | | | COMBINE_EQS: (94), (140) imply:
% 241.51/48.03  | | |   (141)  e3 = e0
% 241.51/48.03  | | | 
% 241.51/48.03  | | | REF_CLOSE: (4), (6), (8), (11), (12), (16), (17), (18), (20), (23), (29),
% 241.51/48.03  | | |            (30), (34), (37), (41), (44), (45), (50), (52), (53), (54),
% 241.51/48.03  | | |            (55), (62), (65), (71), (72), (73), (77), (83), (84), (88),
% 241.51/48.03  | | |            (89), (90), (92), (93), (95), (99), (102), (106), (108), (109),
% 241.51/48.03  | | |            (110), (112), (115), (117), (118), (141) are inconsistent by
% 241.51/48.03  | | |            sub-proof #642.
% 241.51/48.03  | | | 
% 241.51/48.03  | | End of split
% 241.51/48.03  | | 
% 241.51/48.03  | End of split
% 241.51/48.03  | 
% 241.51/48.03  End of proof
% 241.51/48.03  
% 241.51/48.03  Sub-proof #555 shows that the following formulas are inconsistent:
% 241.51/48.03  ----------------------------------------------------------------
% 241.51/48.03    (1)  all_58_13 = e2 & op(e0, e2) = e2
% 241.51/48.03    (2)  all_58_6 = e3
% 241.51/48.03    (3)   ~ (e2 = e0)
% 241.51/48.03    (4)  all_58_7 = e0
% 241.51/48.03    (5)  all_58_11 = e1
% 241.51/48.03    (6)  all_58_8 = e2
% 241.51/48.03    (7)   ~ (e3 = e2)
% 241.51/48.03    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.51/48.03         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.51/48.03    (9)  all_58_13 = e1
% 241.51/48.03    (10)   ~ (e2 = e1)
% 241.51/48.03  
% 241.51/48.03  Begin of proof
% 241.51/48.03  | 
% 241.51/48.03  | ALPHA: (1) implies:
% 241.51/48.03  |   (11)  all_58_13 = e2
% 241.51/48.03  | 
% 241.51/48.03  | COMBINE_EQS: (9), (11) imply:
% 241.51/48.03  |   (12)  e2 = e1
% 241.51/48.03  | 
% 241.51/48.03  | SIMP: (12) implies:
% 241.51/48.03  |   (13)  e2 = e1
% 241.51/48.03  | 
% 241.51/48.03  | COMBINE_EQS: (6), (13) imply:
% 241.51/48.03  |   (14)  all_58_8 = e1
% 241.51/48.03  | 
% 241.51/48.03  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (14) are inconsistent by
% 241.51/48.03  |            sub-proof #988.
% 241.51/48.03  | 
% 241.51/48.03  End of proof
% 241.51/48.03  
% 241.51/48.03  Sub-proof #556 shows that the following formulas are inconsistent:
% 241.51/48.03  ----------------------------------------------------------------
% 241.51/48.03    (1)   ~ (e3 = e0)
% 241.51/48.03    (2)  all_58_6 = e3
% 241.51/48.03    (3)   ~ (e2 = e0)
% 241.51/48.03    (4)  op(e1, e2) = all_52_6
% 241.51/48.03    (5)  all_58_11 = e1
% 241.51/48.03    (6)   ~ (e3 = e1)
% 241.51/48.03    (7)  all_58_3 = e3
% 241.51/48.03    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.51/48.03         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.51/48.03    (9)  op(e3, e3) = e1
% 241.51/48.03    (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.03          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.03    (11)   ~ (e3 = e2)
% 241.51/48.03    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.03          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.03    (13)  all_58_3 = e2 & op(e2, e2) = e2
% 241.51/48.03    (14)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.51/48.03          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.51/48.03    (15)  op(e2, e3) = all_52_1
% 241.51/48.03    (16)   ~ (all_52_6 = e3)
% 241.51/48.03    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.03    (18)  op(e1, e1) = e0
% 241.51/48.03    (19)   ~ (e1 = e0)
% 241.51/48.03    (20)   ~ (all_52_1 = e3)
% 241.51/48.03    (21)   ~ (e2 = e1)
% 241.51/48.03  
% 241.51/48.03  Begin of proof
% 241.51/48.03  | 
% 241.51/48.03  | ALPHA: (13) implies:
% 241.51/48.03  |   (22)  all_58_3 = e2
% 241.51/48.03  | 
% 241.51/48.03  | COMBINE_EQS: (7), (22) imply:
% 241.51/48.03  |   (23)  e3 = e2
% 241.51/48.03  | 
% 241.51/48.03  | COMBINE_EQS: (2), (23) imply:
% 241.51/48.03  |   (24)  all_58_6 = e2
% 241.51/48.03  | 
% 241.51/48.03  | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14), (15),
% 241.51/48.03  |            (16), (17), (18), (19), (20), (21), (24) are inconsistent by
% 241.51/48.03  |            sub-proof #661.
% 241.51/48.03  | 
% 241.51/48.03  End of proof
% 241.51/48.03  
% 241.51/48.03  Sub-proof #557 shows that the following formulas are inconsistent:
% 241.51/48.03  ----------------------------------------------------------------
% 241.51/48.03    (1)   ~ (all_52_12 = all_4_2)
% 241.51/48.03    (2)  op(e2, e2) = e3
% 241.51/48.03    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 241.51/48.03             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 241.51/48.03           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 241.51/48.03         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 241.51/48.03           $i(all_56_7))
% 241.51/48.03    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.51/48.03         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.51/48.03    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.51/48.03         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.03    (6)   ~ (e3 = e0)
% 241.51/48.03    (7)  all_56_31 = all_4_2
% 241.51/48.03    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.51/48.03         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.51/48.03    (9)   ~ (all_4_2 = e2)
% 241.51/48.03    (10)  all_42_2 = e3
% 241.51/48.03    (11)  all_58_6 = e3
% 241.51/48.03    (12)   ~ (e2 = e0)
% 241.51/48.03    (13)  all_58_7 = e0
% 241.51/48.03    (14)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 241.51/48.03            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 241.51/48.03            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 241.51/48.03            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 241.51/48.03            = all_56_15 & $i(all_56_15))
% 241.51/48.03    (15)  all_54_13 = all_52_7
% 241.51/48.03    (16)  op(e1, e2) = all_52_6
% 241.51/48.03    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.03          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.03    (18)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.51/48.03          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.51/48.03    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.51/48.03              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.51/48.03            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.51/48.03            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.51/48.03            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.51/48.03             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.03            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.51/48.03            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.51/48.03            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.51/48.03            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.03            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.51/48.03              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.51/48.03            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.51/48.03            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.51/48.03            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.51/48.03            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.51/48.03            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.51/48.03            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.51/48.03              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.51/48.03            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.03            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.51/48.03            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.51/48.03            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.51/48.03            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.03            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.51/48.03              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.51/48.03            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.03            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.51/48.03    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.03          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.51/48.03    (21)   ~ (all_52_7 = all_52_11)
% 241.51/48.03    (22)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.51/48.03            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.51/48.03              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.51/48.03    (23)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.51/48.03          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.51/48.03    (24)  all_58_11 = e1
% 241.51/48.03    (25)   ~ (all_52_7 = e3)
% 241.51/48.03    (26)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 241.51/48.03    (27)   ~ (all_52_8 = e0)
% 241.51/48.03    (28)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.03          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.51/48.03    (29)   ~ (e3 = e1)
% 241.51/48.03    (30)  all_54_11 = all_52_14
% 241.51/48.03    (31)  all_58_8 = e2
% 241.51/48.03    (32)  op(e0, e0) = all_4_2
% 241.51/48.03    (33)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.51/48.03          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.51/48.03    (34)   ~ (all_52_12 = all_52_14)
% 241.51/48.03    (35)   ~ (all_52_8 = e1)
% 241.51/48.03    (36)  all_58_3 = e3
% 241.51/48.03    (37)   ~ (all_52_12 = all_52_13)
% 241.51/48.03    (38)   ~ (all_52_14 = all_4_2)
% 241.51/48.03    (39)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 241.51/48.03            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 241.51/48.03              e1) = all_10_1 & $i(all_10_1))
% 241.51/48.03    (40)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.51/48.03          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.51/48.03    (41)  all_54_2 = all_52_8
% 241.51/48.03    (42)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 241.51/48.03    (43)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.51/48.03          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.51/48.03    (44)  op(e3, e3) = e1
% 241.51/48.03    (45)   ~ (all_52_9 = e0)
% 241.51/48.03    (46)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.51/48.03    (47)  all_56_21 = e0
% 241.51/48.03    (48)  all_54_4 = all_52_1
% 241.51/48.03    (49)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.03              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.51/48.03                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.51/48.03                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.51/48.03    (50)   ~ (all_52_8 = all_52_12)
% 241.51/48.03    (51)  op(e2, e1) = all_52_9
% 241.51/48.03    (52)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.03          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.03    (53)   ~ (e3 = e2)
% 241.51/48.03    (54)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.51/48.03          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.51/48.03    (55)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 241.51/48.03    (56)   ~ (all_52_14 = e0)
% 241.51/48.03    (57)   ~ (all_52_13 = all_4_2)
% 241.51/48.03    (58)   ~ (all_4_2 = e3)
% 241.51/48.03    (59)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 241.51/48.03    (60)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 241.51/48.03    (61)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.03          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.03    (62)  op(e3, e0) = all_52_12
% 241.51/48.03    (63)   ~ (all_52_7 = all_4_2)
% 241.51/48.03    (64)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.51/48.03          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.51/48.03    (65)   ~ (all_52_9 = all_52_13)
% 241.51/48.03    (66)  all_54_15 = all_4_2
% 241.51/48.03    (67)   ~ (all_52_4 = all_52_12)
% 241.51/48.03    (68)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 241.51/48.03    (69)  all_38_2 = e1
% 241.51/48.03    (70)  op(e2, e3) = all_52_1
% 241.51/48.03    (71)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.51/48.03          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.03    (72)   ~ (all_52_6 = e3)
% 241.51/48.03    (73)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 241.51/48.03    (74)   ~ (all_52_1 = all_52_13)
% 241.51/48.03    (75)   ~ (all_52_11 = e0)
% 241.51/48.03    (76)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.51/48.03          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.51/48.03    (77)  all_54_7 = all_52_13
% 241.51/48.03    (78)  op(e0, e2) = all_52_7
% 241.51/48.03    (79)   ~ (all_52_13 = all_52_14)
% 241.51/48.03    (80)  all_54_1 = all_52_4
% 241.51/48.03    (81)   ~ (all_20_2 = e1) | ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 241.51/48.03            op(e0, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 241.51/48.03              e3) & op(e0, e1) = all_20_1 & $i(all_20_1))
% 241.51/48.03    (82)   ~ (all_52_4 = e3)
% 241.51/48.03    (83)  op(e3, e2) = all_52_4
% 241.51/48.03    (84)   ~ (all_52_8 = all_52_11)
% 241.51/48.03    (85)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.51/48.03    (86)   ~ (all_52_9 = e3)
% 241.51/48.03    (87)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.51/48.03          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.03    (88)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.51/48.03          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.51/48.03    (89)  all_54_3 = all_52_12
% 241.51/48.03    (90)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.03          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.51/48.03    (91)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.03    (92)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.51/48.03          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.51/48.03    (93)   ~ (all_52_6 = all_52_7)
% 241.51/48.03    (94)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.03          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.03    (95)  all_56_11 = e3
% 241.51/48.03    (96)  op(e1, e1) = e0
% 241.51/48.03    (97)   ~ (all_52_4 = e1)
% 241.51/48.03    (98)  all_20_2 = all_4_2
% 241.51/48.03    (99)   ~ (e1 = e0)
% 241.51/48.03    (100)  all_58_13 = e1
% 241.51/48.03    (101)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 241.51/48.03    (102)   ~ (all_52_13 = e3)
% 241.51/48.04    (103)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.51/48.04           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.51/48.04    (104)   ~ (all_52_11 = all_4_2)
% 241.51/48.04    (105)  op(e2, e0) = all_52_13
% 241.51/48.04    (106)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.04           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.51/48.04             e1)
% 241.51/48.04    (107)   ~ (all_52_1 = e3)
% 241.51/48.04    (108)  all_54_14 = all_52_11
% 241.51/48.04    (109)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.04           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.51/48.04             e2)
% 241.51/48.04    (110)   ~ (all_52_4 = all_52_8)
% 241.51/48.04    (111)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.51/48.04             $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) =
% 241.51/48.04             all_8_1 & $i(all_8_1))
% 241.51/48.04    (112)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.04           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.51/48.04    (113)  all_56_1 = e1
% 241.51/48.04    (114)   ~ (e2 = e1)
% 241.51/48.04    (115)   ~ (all_52_1 = e1)
% 241.51/48.04    (116)   ~ (all_52_4 = all_52_7)
% 241.51/48.04    (117)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 241.51/48.04             & op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 241.51/48.04             (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 241.51/48.04  
% 241.51/48.04  Begin of proof
% 241.51/48.04  | 
% 241.51/48.04  | BETA: splitting (101) gives:
% 241.51/48.04  | 
% 241.51/48.04  | Case 1:
% 241.51/48.04  | | 
% 241.51/48.04  | |   (118)  all_58_0 = e0 & op(e3, e3) = e0
% 241.51/48.04  | | 
% 241.51/48.04  | | ALPHA: (118) implies:
% 241.51/48.04  | |   (119)  op(e3, e3) = e0
% 241.51/48.04  | | 
% 241.51/48.04  | | REF_CLOSE: (44), (91), (99), (119) are inconsistent by sub-proof #1828.
% 241.51/48.04  | | 
% 241.51/48.04  | Case 2:
% 241.51/48.04  | | 
% 241.51/48.04  | |   (120)  all_58_1 = e0 & op(e3, e2) = e0
% 241.51/48.04  | | 
% 241.51/48.04  | | ALPHA: (120) implies:
% 241.51/48.04  | |   (121)  all_58_1 = e0
% 241.51/48.04  | | 
% 241.51/48.04  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.51/48.04  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 241.51/48.04  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 241.51/48.04  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 241.51/48.04  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 241.51/48.04  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 241.51/48.04  | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 241.51/48.04  | |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 241.51/48.04  | |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 241.51/48.04  | |            (100), (102), (103), (104), (105), (106), (107), (108), (109),
% 241.51/48.04  | |            (110), (111), (112), (113), (114), (115), (116), (117), (121) are
% 241.51/48.04  | |            inconsistent by sub-proof #558.
% 241.51/48.04  | | 
% 241.51/48.04  | End of split
% 241.51/48.04  | 
% 241.51/48.04  End of proof
% 241.51/48.04  
% 241.51/48.04  Sub-proof #558 shows that the following formulas are inconsistent:
% 241.51/48.04  ----------------------------------------------------------------
% 241.51/48.04    (1)   ~ (all_52_12 = all_4_2)
% 241.51/48.04    (2)  op(e2, e2) = e3
% 241.51/48.04    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 241.51/48.04             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 241.51/48.04           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 241.51/48.04         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 241.51/48.04           $i(all_56_7))
% 241.51/48.04    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.51/48.04         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.51/48.04    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.51/48.04         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.04    (6)   ~ (e3 = e0)
% 241.51/48.04    (7)  all_56_31 = all_4_2
% 241.51/48.04    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.51/48.04         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.51/48.04    (9)   ~ (all_4_2 = e2)
% 241.51/48.04    (10)  all_42_2 = e3
% 241.51/48.04    (11)  all_58_6 = e3
% 241.51/48.04    (12)   ~ (e2 = e0)
% 241.51/48.04    (13)  all_58_7 = e0
% 241.51/48.04    (14)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 241.51/48.04            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 241.51/48.04            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 241.51/48.04            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 241.51/48.04            = all_56_15 & $i(all_56_15))
% 241.51/48.04    (15)  all_54_13 = all_52_7
% 241.51/48.04    (16)  op(e1, e2) = all_52_6
% 241.51/48.04    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.04          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.04    (18)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.51/48.04          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.51/48.04    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.51/48.04              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.51/48.04            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.51/48.04            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.51/48.04            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.51/48.04             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.04            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.51/48.04            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.51/48.04            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.51/48.04            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.04            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.51/48.04              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.51/48.04            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.51/48.04            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.51/48.04            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.51/48.04            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.51/48.04            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.51/48.04            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.51/48.04              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.51/48.04            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.04            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.51/48.04            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.51/48.04            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.51/48.04            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.04            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.51/48.04              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.51/48.04            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.04            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.51/48.04    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.04          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.51/48.04    (21)   ~ (all_52_7 = all_52_11)
% 241.51/48.04    (22)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.51/48.04            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.51/48.04              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.51/48.04    (23)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.51/48.04          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.51/48.04    (24)  all_58_11 = e1
% 241.51/48.04    (25)  all_58_1 = e0
% 241.51/48.04    (26)   ~ (all_52_7 = e3)
% 241.51/48.04    (27)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 241.51/48.04    (28)   ~ (all_52_8 = e0)
% 241.51/48.04    (29)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.04          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.51/48.04    (30)   ~ (e3 = e1)
% 241.51/48.04    (31)  all_54_11 = all_52_14
% 241.51/48.04    (32)  all_58_8 = e2
% 241.51/48.04    (33)  op(e0, e0) = all_4_2
% 241.51/48.04    (34)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.51/48.04          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.51/48.04    (35)   ~ (all_52_12 = all_52_14)
% 241.51/48.04    (36)   ~ (all_52_8 = e1)
% 241.51/48.04    (37)  all_58_3 = e3
% 241.51/48.04    (38)   ~ (all_52_12 = all_52_13)
% 241.51/48.04    (39)   ~ (all_52_14 = all_4_2)
% 241.51/48.04    (40)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 241.51/48.04            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 241.51/48.04              e1) = all_10_1 & $i(all_10_1))
% 241.51/48.04    (41)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.51/48.04          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.51/48.04    (42)  all_54_2 = all_52_8
% 241.51/48.04    (43)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 241.51/48.04    (44)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.51/48.04          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.51/48.04    (45)  op(e3, e3) = e1
% 241.51/48.04    (46)   ~ (all_52_9 = e0)
% 241.51/48.04    (47)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.51/48.04    (48)  all_56_21 = e0
% 241.51/48.04    (49)  all_54_4 = all_52_1
% 241.51/48.04    (50)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.04              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.51/48.04                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.51/48.04                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.51/48.04    (51)   ~ (all_52_8 = all_52_12)
% 241.51/48.04    (52)  op(e2, e1) = all_52_9
% 241.51/48.04    (53)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.04          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.04    (54)   ~ (e3 = e2)
% 241.51/48.04    (55)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.51/48.04          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.51/48.04    (56)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 241.51/48.04    (57)   ~ (all_52_14 = e0)
% 241.51/48.04    (58)   ~ (all_52_13 = all_4_2)
% 241.51/48.04    (59)   ~ (all_4_2 = e3)
% 241.51/48.04    (60)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 241.51/48.04    (61)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 241.51/48.04    (62)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.04          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.04    (63)  op(e3, e0) = all_52_12
% 241.51/48.04    (64)   ~ (all_52_7 = all_4_2)
% 241.51/48.04    (65)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.51/48.04          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.51/48.04    (66)   ~ (all_52_9 = all_52_13)
% 241.51/48.04    (67)  all_54_15 = all_4_2
% 241.51/48.04    (68)   ~ (all_52_4 = all_52_12)
% 241.51/48.04    (69)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 241.51/48.04    (70)  all_38_2 = e1
% 241.51/48.04    (71)  op(e2, e3) = all_52_1
% 241.51/48.04    (72)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.51/48.04          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.04    (73)   ~ (all_52_6 = e3)
% 241.51/48.04    (74)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 241.51/48.04    (75)   ~ (all_52_1 = all_52_13)
% 241.51/48.04    (76)   ~ (all_52_11 = e0)
% 241.51/48.04    (77)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.51/48.04          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.51/48.04    (78)  all_54_7 = all_52_13
% 241.51/48.04    (79)  op(e0, e2) = all_52_7
% 241.51/48.04    (80)   ~ (all_52_13 = all_52_14)
% 241.51/48.04    (81)  all_54_1 = all_52_4
% 241.51/48.04    (82)   ~ (all_20_2 = e1) | ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 241.51/48.04            op(e0, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 241.51/48.04              e3) & op(e0, e1) = all_20_1 & $i(all_20_1))
% 241.51/48.04    (83)   ~ (all_52_4 = e3)
% 241.51/48.04    (84)  op(e3, e2) = all_52_4
% 241.51/48.04    (85)   ~ (all_52_8 = all_52_11)
% 241.51/48.04    (86)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.51/48.04    (87)   ~ (all_52_9 = e3)
% 241.51/48.04    (88)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.51/48.04          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.04    (89)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.51/48.04          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.51/48.04    (90)  all_54_3 = all_52_12
% 241.51/48.04    (91)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.04          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.51/48.04    (92)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.04            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.04    (93)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.51/48.04          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.51/48.04    (94)   ~ (all_52_6 = all_52_7)
% 241.51/48.04    (95)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.04          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.04    (96)  all_56_11 = e3
% 241.51/48.04    (97)  op(e1, e1) = e0
% 241.51/48.04    (98)   ~ (all_52_4 = e1)
% 241.51/48.04    (99)  all_20_2 = all_4_2
% 241.51/48.04    (100)   ~ (e1 = e0)
% 241.51/48.04    (101)  all_58_13 = e1
% 241.51/48.04    (102)   ~ (all_52_13 = e3)
% 241.51/48.04    (103)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.51/48.04           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.51/48.04    (104)   ~ (all_52_11 = all_4_2)
% 241.51/48.04    (105)  op(e2, e0) = all_52_13
% 241.51/48.04    (106)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.04           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.51/48.04             e1)
% 241.51/48.04    (107)   ~ (all_52_1 = e3)
% 241.51/48.04    (108)  all_54_14 = all_52_11
% 241.51/48.04    (109)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.04           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.51/48.04             e2)
% 241.51/48.04    (110)   ~ (all_52_4 = all_52_8)
% 241.51/48.04    (111)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.51/48.04             $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) =
% 241.51/48.04             all_8_1 & $i(all_8_1))
% 241.51/48.04    (112)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.04           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.51/48.04    (113)  all_56_1 = e1
% 241.51/48.04    (114)   ~ (e2 = e1)
% 241.51/48.04    (115)   ~ (all_52_1 = e1)
% 241.51/48.04    (116)   ~ (all_52_4 = all_52_7)
% 241.51/48.04    (117)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 241.51/48.04             & op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 241.51/48.04             (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 241.51/48.04  
% 241.51/48.04  Begin of proof
% 241.51/48.04  | 
% 241.51/48.04  | BETA: splitting (17) gives:
% 241.51/48.04  | 
% 241.51/48.04  | Case 1:
% 241.51/48.04  | | 
% 241.51/48.04  | |   (118)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 241.51/48.04  | |            e2)
% 241.51/48.04  | | 
% 241.51/48.04  | | BETA: splitting (118) gives:
% 241.51/48.04  | | 
% 241.51/48.04  | | Case 1:
% 241.51/48.04  | | | 
% 241.51/48.04  | | |   (119)  all_58_1 = e2 & op(e3, e2) = e2
% 241.51/48.04  | | | 
% 241.51/48.04  | | | ALPHA: (119) implies:
% 241.51/48.04  | | |   (120)  all_58_1 = e2
% 241.51/48.04  | | | 
% 241.51/48.04  | | | COMBINE_EQS: (25), (120) imply:
% 241.51/48.04  | | |   (121)  e2 = e0
% 241.51/48.04  | | | 
% 241.51/48.04  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 241.51/48.04  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (26),
% 241.51/48.04  | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 241.51/48.04  | | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 241.51/48.04  | | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 241.51/48.04  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 241.51/48.04  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 241.51/48.04  | | |            (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 241.51/48.04  | | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 241.51/48.04  | | |            (97), (98), (99), (100), (102), (103), (104), (105), (106),
% 241.51/48.04  | | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 241.51/48.04  | | |            (116), (117), (121) are inconsistent by sub-proof #562.
% 241.51/48.04  | | | 
% 241.51/48.04  | | Case 2:
% 241.51/48.04  | | | 
% 241.51/48.04  | | |   (122)  all_58_3 = e2 & op(e2, e2) = e2
% 241.51/48.04  | | | 
% 241.51/48.04  | | | ALPHA: (122) implies:
% 241.51/48.04  | | |   (123)  all_58_3 = e2
% 241.51/48.04  | | | 
% 241.51/48.04  | | | COMBINE_EQS: (37), (123) imply:
% 241.51/48.04  | | |   (124)  e3 = e2
% 241.51/48.04  | | | 
% 241.51/48.04  | | | REF_CLOSE: (6), (11), (12), (16), (24), (30), (44), (45), (53), (54),
% 241.51/48.04  | | |            (62), (65), (71), (73), (92), (97), (100), (107), (114), (124)
% 241.51/48.04  | | |            are inconsistent by sub-proof #561.
% 241.51/48.04  | | | 
% 241.51/48.04  | | End of split
% 241.51/48.04  | | 
% 241.51/48.04  | Case 2:
% 241.51/48.04  | | 
% 241.51/48.04  | |   (125)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 241.51/48.04  | |            e2)
% 241.51/48.04  | | 
% 241.51/48.04  | | BETA: splitting (125) gives:
% 241.51/48.04  | | 
% 241.51/48.04  | | Case 1:
% 241.51/48.04  | | | 
% 241.51/48.04  | | |   (126)  all_58_7 = e2 & op(e1, e2) = e2
% 241.51/48.04  | | | 
% 241.51/48.04  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 241.51/48.04  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 241.51/48.04  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 241.51/48.04  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 241.51/48.04  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 241.51/48.04  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 241.51/48.04  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 241.51/48.04  | | |            (76), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 241.51/48.04  | | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 241.51/48.04  | | |            (96), (97), (98), (99), (100), (102), (103), (104), (105),
% 241.51/48.04  | | |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 241.51/48.04  | | |            (115), (116), (117), (126) are inconsistent by sub-proof #560.
% 241.51/48.04  | | | 
% 241.51/48.04  | | Case 2:
% 241.51/48.04  | | | 
% 241.51/48.04  | | |   (127)  all_58_13 = e2 & op(e0, e2) = e2
% 241.51/48.04  | | | 
% 241.51/48.04  | | | REF_CLOSE: (11), (12), (13), (24), (32), (54), (89), (101), (114), (127)
% 241.51/48.04  | | |            are inconsistent by sub-proof #559.
% 241.51/48.04  | | | 
% 241.51/48.04  | | End of split
% 241.51/48.04  | | 
% 241.51/48.04  | End of split
% 241.51/48.04  | 
% 241.51/48.04  End of proof
% 241.51/48.04  
% 241.51/48.04  Sub-proof #559 shows that the following formulas are inconsistent:
% 241.51/48.04  ----------------------------------------------------------------
% 241.51/48.04    (1)  all_58_13 = e2 & op(e0, e2) = e2
% 241.51/48.04    (2)  all_58_6 = e3
% 241.51/48.04    (3)   ~ (e2 = e0)
% 241.51/48.04    (4)  all_58_7 = e0
% 241.51/48.04    (5)  all_58_11 = e1
% 241.51/48.04    (6)  all_58_8 = e2
% 241.51/48.04    (7)   ~ (e3 = e2)
% 241.51/48.04    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.51/48.04         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.51/48.04    (9)  all_58_13 = e1
% 241.51/48.04    (10)   ~ (e2 = e1)
% 241.51/48.04  
% 241.51/48.04  Begin of proof
% 241.51/48.04  | 
% 241.51/48.04  | ALPHA: (1) implies:
% 241.51/48.04  |   (11)  all_58_13 = e2
% 241.51/48.04  | 
% 241.51/48.04  | COMBINE_EQS: (9), (11) imply:
% 241.51/48.04  |   (12)  e2 = e1
% 241.51/48.04  | 
% 241.51/48.04  | COMBINE_EQS: (6), (12) imply:
% 241.51/48.04  |   (13)  all_58_8 = e1
% 241.51/48.04  | 
% 241.51/48.04  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (13) are inconsistent by
% 241.51/48.04  |            sub-proof #988.
% 241.51/48.04  | 
% 241.51/48.04  End of proof
% 241.51/48.04  
% 241.51/48.04  Sub-proof #560 shows that the following formulas are inconsistent:
% 241.51/48.04  ----------------------------------------------------------------
% 241.51/48.04    (1)   ~ (all_52_12 = all_4_2)
% 241.51/48.04    (2)  op(e2, e2) = e3
% 241.51/48.04    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 241.51/48.04             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 241.51/48.04           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 241.51/48.04         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 241.51/48.04           $i(all_56_7))
% 241.51/48.04    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.51/48.04         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.51/48.04    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.51/48.04         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.04    (6)   ~ (e3 = e0)
% 241.51/48.04    (7)  all_56_31 = all_4_2
% 241.51/48.04    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.51/48.04         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.51/48.04    (9)   ~ (all_4_2 = e2)
% 241.51/48.04    (10)  all_42_2 = e3
% 241.51/48.04    (11)   ~ (e2 = e0)
% 241.51/48.04    (12)  all_58_7 = e0
% 241.51/48.04    (13)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 241.51/48.04            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 241.51/48.04            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 241.51/48.04            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 241.51/48.04            = all_56_15 & $i(all_56_15))
% 241.51/48.04    (14)  all_54_13 = all_52_7
% 241.51/48.04    (15)  op(e1, e2) = all_52_6
% 241.51/48.04    (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.04          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.04    (17)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.51/48.04          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.51/48.04    (18)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.51/48.04              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.51/48.04            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.51/48.04            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.51/48.04            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.51/48.04             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.04            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.51/48.04            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.51/48.04            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.51/48.04            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.04            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.51/48.04              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.51/48.04            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.51/48.04            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.51/48.04            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.51/48.04            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.51/48.04            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.51/48.04            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.51/48.04              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.51/48.04            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.04            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.51/48.04            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.51/48.04            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.51/48.04            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.04            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.51/48.04              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.51/48.04            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.04            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.51/48.04    (19)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.04          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.51/48.04    (20)   ~ (all_52_7 = all_52_11)
% 241.51/48.05    (21)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.51/48.05            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.51/48.05              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.51/48.05    (22)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.51/48.05          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.51/48.05    (23)   ~ (all_52_7 = e3)
% 241.51/48.05    (24)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 241.51/48.05    (25)   ~ (all_52_8 = e0)
% 241.51/48.05    (26)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.05          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.51/48.05    (27)   ~ (e3 = e1)
% 241.51/48.05    (28)  all_54_11 = all_52_14
% 241.51/48.05    (29)  all_58_8 = e2
% 241.51/48.05    (30)  op(e0, e0) = all_4_2
% 241.51/48.05    (31)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.51/48.05          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.51/48.05    (32)   ~ (all_52_12 = all_52_14)
% 241.51/48.05    (33)   ~ (all_52_8 = e1)
% 241.51/48.05    (34)  all_58_3 = e3
% 241.51/48.05    (35)   ~ (all_52_12 = all_52_13)
% 241.51/48.05    (36)   ~ (all_52_14 = all_4_2)
% 241.51/48.05    (37)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 241.51/48.05            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 241.51/48.05              e1) = all_10_1 & $i(all_10_1))
% 241.51/48.05    (38)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.51/48.05          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.51/48.05    (39)  all_54_2 = all_52_8
% 241.51/48.05    (40)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 241.51/48.05    (41)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.51/48.05          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.51/48.05    (42)  op(e3, e3) = e1
% 241.51/48.05    (43)   ~ (all_52_9 = e0)
% 241.51/48.05    (44)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.51/48.05    (45)  all_56_21 = e0
% 241.51/48.05    (46)  all_54_4 = all_52_1
% 241.51/48.05    (47)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.05              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.51/48.05                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.51/48.05                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.51/48.05    (48)   ~ (all_52_8 = all_52_12)
% 241.51/48.05    (49)  op(e2, e1) = all_52_9
% 241.51/48.05    (50)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.05          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.05    (51)   ~ (e3 = e2)
% 241.51/48.05    (52)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.51/48.05          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.51/48.05    (53)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 241.51/48.05    (54)   ~ (all_52_14 = e0)
% 241.51/48.05    (55)   ~ (all_52_13 = all_4_2)
% 241.51/48.05    (56)   ~ (all_4_2 = e3)
% 241.51/48.05    (57)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 241.51/48.05    (58)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 241.51/48.05    (59)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.05          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.05    (60)  op(e3, e0) = all_52_12
% 241.51/48.05    (61)   ~ (all_52_7 = all_4_2)
% 241.51/48.05    (62)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.51/48.05          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.51/48.05    (63)   ~ (all_52_9 = all_52_13)
% 241.51/48.05    (64)  all_54_15 = all_4_2
% 241.51/48.05    (65)   ~ (all_52_4 = all_52_12)
% 241.51/48.05    (66)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 241.51/48.05    (67)  all_38_2 = e1
% 241.51/48.05    (68)  op(e2, e3) = all_52_1
% 241.51/48.05    (69)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.51/48.05          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.05    (70)   ~ (all_52_6 = e3)
% 241.51/48.05    (71)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 241.51/48.05    (72)   ~ (all_52_1 = all_52_13)
% 241.51/48.05    (73)   ~ (all_52_11 = e0)
% 241.51/48.05    (74)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.51/48.05          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.51/48.05    (75)  all_54_7 = all_52_13
% 241.51/48.05    (76)  op(e0, e2) = all_52_7
% 241.51/48.05    (77)   ~ (all_52_13 = all_52_14)
% 241.51/48.05    (78)  all_54_1 = all_52_4
% 241.51/48.05    (79)   ~ (all_20_2 = e1) | ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 241.51/48.05            op(e0, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 241.51/48.05              e3) & op(e0, e1) = all_20_1 & $i(all_20_1))
% 241.51/48.05    (80)   ~ (all_52_4 = e3)
% 241.51/48.05    (81)  op(e3, e2) = all_52_4
% 241.51/48.05    (82)   ~ (all_52_8 = all_52_11)
% 241.51/48.05    (83)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.51/48.05    (84)   ~ (all_52_9 = e3)
% 241.51/48.05    (85)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.51/48.05          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.05    (86)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.51/48.05          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.51/48.05    (87)  all_54_3 = all_52_12
% 241.51/48.05    (88)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.05          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.51/48.05    (89)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.05    (90)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.51/48.05          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.51/48.05    (91)   ~ (all_52_6 = all_52_7)
% 241.51/48.05    (92)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.05          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.05    (93)  all_56_11 = e3
% 241.51/48.05    (94)  op(e1, e1) = e0
% 241.51/48.05    (95)   ~ (all_52_4 = e1)
% 241.51/48.05    (96)  all_20_2 = all_4_2
% 241.51/48.05    (97)   ~ (e1 = e0)
% 241.51/48.05    (98)  all_58_7 = e2 & op(e1, e2) = e2
% 241.51/48.05    (99)   ~ (all_52_13 = e3)
% 241.51/48.05    (100)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.51/48.05           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.51/48.05    (101)   ~ (all_52_11 = all_4_2)
% 241.51/48.05    (102)  op(e2, e0) = all_52_13
% 241.51/48.05    (103)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.05           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.51/48.05             e1)
% 241.51/48.05    (104)   ~ (all_52_1 = e3)
% 241.51/48.05    (105)  all_54_14 = all_52_11
% 241.51/48.05    (106)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.05           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.51/48.05             e2)
% 241.51/48.05    (107)   ~ (all_52_4 = all_52_8)
% 241.51/48.05    (108)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.51/48.05             $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) =
% 241.51/48.05             all_8_1 & $i(all_8_1))
% 241.51/48.05    (109)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.05           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.51/48.05    (110)  all_56_1 = e1
% 241.51/48.05    (111)   ~ (e2 = e1)
% 241.51/48.05    (112)   ~ (all_52_1 = e1)
% 241.51/48.05    (113)   ~ (all_52_4 = all_52_7)
% 241.51/48.05    (114)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 241.51/48.05             & op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 241.51/48.05             (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 241.51/48.05  
% 241.51/48.05  Begin of proof
% 241.51/48.05  | 
% 241.51/48.05  | ALPHA: (98) implies:
% 241.51/48.05  |   (115)  all_58_7 = e2
% 241.51/48.05  | 
% 241.51/48.05  | COMBINE_EQS: (12), (115) imply:
% 241.51/48.05  |   (116)  e2 = e0
% 241.51/48.05  | 
% 241.51/48.05  | COMBINE_EQS: (29), (116) imply:
% 241.51/48.05  |   (117)  all_58_8 = e0
% 241.51/48.05  | 
% 241.51/48.05  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 241.51/48.05  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 241.51/48.05  |            (25), (26), (27), (28), (30), (31), (32), (33), (34), (35), (36),
% 241.51/48.05  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 241.51/48.05  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 241.51/48.05  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 241.51/48.05  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 241.51/48.05  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 241.51/48.05  |            (92), (93), (94), (95), (96), (97), (99), (100), (101), (102),
% 241.51/48.05  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 241.51/48.05  |            (112), (113), (114), (117) are inconsistent by sub-proof #563.
% 241.51/48.05  | 
% 241.51/48.05  End of proof
% 241.51/48.05  
% 241.51/48.05  Sub-proof #561 shows that the following formulas are inconsistent:
% 241.51/48.05  ----------------------------------------------------------------
% 241.51/48.05    (1)   ~ (e3 = e0)
% 241.51/48.05    (2)  all_58_6 = e3
% 241.51/48.05    (3)   ~ (e2 = e0)
% 241.51/48.05    (4)  op(e1, e2) = all_52_6
% 241.51/48.05    (5)  all_58_11 = e1
% 241.51/48.05    (6)   ~ (e3 = e1)
% 241.51/48.05    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.51/48.05         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.51/48.05    (8)  op(e3, e3) = e1
% 241.51/48.05    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.05         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.05    (10)   ~ (e3 = e2)
% 241.51/48.05    (11)  e3 = e2
% 241.51/48.05    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.05          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.05    (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.51/48.05          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.51/48.05    (14)  op(e2, e3) = all_52_1
% 241.51/48.05    (15)   ~ (all_52_6 = e3)
% 241.51/48.05    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.05    (17)  op(e1, e1) = e0
% 241.51/48.05    (18)   ~ (e1 = e0)
% 241.51/48.05    (19)   ~ (all_52_1 = e3)
% 241.51/48.05    (20)   ~ (e2 = e1)
% 241.51/48.05  
% 241.51/48.05  Begin of proof
% 241.51/48.05  | 
% 241.51/48.05  | SIMP: (11) implies:
% 241.51/48.05  |   (21)  e3 = e2
% 241.51/48.05  | 
% 241.51/48.05  | COMBINE_EQS: (2), (21) imply:
% 241.51/48.05  |   (22)  all_58_6 = e2
% 241.51/48.05  | 
% 241.51/48.05  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 241.51/48.05  |            (15), (16), (17), (18), (19), (20), (22) are inconsistent by
% 241.51/48.05  |            sub-proof #661.
% 241.51/48.05  | 
% 241.51/48.05  End of proof
% 241.51/48.05  
% 241.51/48.05  Sub-proof #562 shows that the following formulas are inconsistent:
% 241.51/48.05  ----------------------------------------------------------------
% 241.51/48.05    (1)   ~ (all_52_12 = all_4_2)
% 241.51/48.05    (2)  op(e2, e2) = e3
% 241.51/48.05    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 241.51/48.05             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 241.51/48.05           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 241.51/48.05         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 241.51/48.05           $i(all_56_7))
% 241.51/48.05    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.51/48.05         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.51/48.05    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.51/48.05         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.05    (6)   ~ (e3 = e0)
% 241.51/48.05    (7)  all_56_31 = all_4_2
% 241.51/48.05    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.51/48.05         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.51/48.05    (9)   ~ (all_4_2 = e2)
% 241.51/48.05    (10)  all_42_2 = e3
% 241.51/48.05    (11)   ~ (e2 = e0)
% 241.51/48.05    (12)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 241.51/48.05            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 241.51/48.05            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 241.51/48.05            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 241.51/48.05            = all_56_15 & $i(all_56_15))
% 241.51/48.05    (13)  all_54_13 = all_52_7
% 241.51/48.05    (14)  op(e1, e2) = all_52_6
% 241.51/48.05    (15)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.05          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.05    (16)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.51/48.05          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.51/48.05    (17)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.51/48.05              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.51/48.05            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.51/48.05            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.51/48.05            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.51/48.05             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.05            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.51/48.05            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.51/48.05            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.51/48.05            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.05            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.51/48.05              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.51/48.05            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.51/48.05            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.51/48.05            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.51/48.05            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.51/48.05            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.51/48.05            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.51/48.05              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.51/48.05            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.05            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.51/48.05            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.51/48.05            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.51/48.05            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.05            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.51/48.05              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.51/48.05            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.05            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.51/48.05    (18)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.05          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.51/48.05    (19)   ~ (all_52_7 = all_52_11)
% 241.51/48.05    (20)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.51/48.05            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.51/48.05              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.51/48.05    (21)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.51/48.05          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.51/48.05    (22)   ~ (all_52_7 = e3)
% 241.51/48.05    (23)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 241.51/48.05    (24)   ~ (all_52_8 = e0)
% 241.51/48.05    (25)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.05          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.51/48.05    (26)   ~ (e3 = e1)
% 241.51/48.05    (27)  all_54_11 = all_52_14
% 241.51/48.05    (28)  all_58_8 = e2
% 241.51/48.05    (29)  op(e0, e0) = all_4_2
% 241.51/48.05    (30)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.51/48.05          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.51/48.05    (31)   ~ (all_52_12 = all_52_14)
% 241.51/48.05    (32)   ~ (all_52_8 = e1)
% 241.51/48.05    (33)  all_58_3 = e3
% 241.51/48.05    (34)   ~ (all_52_12 = all_52_13)
% 241.51/48.05    (35)   ~ (all_52_14 = all_4_2)
% 241.51/48.05    (36)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 241.51/48.05            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 241.51/48.05              e1) = all_10_1 & $i(all_10_1))
% 241.51/48.05    (37)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.51/48.05          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.51/48.05    (38)  all_54_2 = all_52_8
% 241.51/48.05    (39)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 241.51/48.05    (40)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.51/48.05          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.51/48.05    (41)  op(e3, e3) = e1
% 241.51/48.05    (42)   ~ (all_52_9 = e0)
% 241.51/48.05    (43)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.51/48.05    (44)  all_56_21 = e0
% 241.51/48.05    (45)  all_54_4 = all_52_1
% 241.51/48.05    (46)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.05              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.51/48.05                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.51/48.05                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.51/48.05    (47)   ~ (all_52_8 = all_52_12)
% 241.51/48.05    (48)  op(e2, e1) = all_52_9
% 241.51/48.06    (49)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.06          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.06    (50)   ~ (e3 = e2)
% 241.51/48.06    (51)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.51/48.06          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.51/48.06    (52)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 241.51/48.06    (53)   ~ (all_52_14 = e0)
% 241.51/48.06    (54)   ~ (all_52_13 = all_4_2)
% 241.51/48.06    (55)   ~ (all_4_2 = e3)
% 241.51/48.06    (56)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 241.51/48.06    (57)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 241.51/48.06    (58)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.06          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.06    (59)  op(e3, e0) = all_52_12
% 241.51/48.06    (60)   ~ (all_52_7 = all_4_2)
% 241.51/48.06    (61)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.51/48.06          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.51/48.06    (62)   ~ (all_52_9 = all_52_13)
% 241.51/48.06    (63)  all_54_15 = all_4_2
% 241.51/48.06    (64)   ~ (all_52_4 = all_52_12)
% 241.51/48.06    (65)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 241.51/48.06    (66)  all_38_2 = e1
% 241.51/48.06    (67)  e2 = e0
% 241.51/48.06    (68)  op(e2, e3) = all_52_1
% 241.51/48.06    (69)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.51/48.06          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.06    (70)   ~ (all_52_6 = e3)
% 241.51/48.06    (71)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 241.51/48.06    (72)   ~ (all_52_1 = all_52_13)
% 241.51/48.06    (73)   ~ (all_52_11 = e0)
% 241.51/48.06    (74)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.51/48.06          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.51/48.06    (75)  all_54_7 = all_52_13
% 241.51/48.06    (76)  op(e0, e2) = all_52_7
% 241.51/48.06    (77)   ~ (all_52_13 = all_52_14)
% 241.51/48.06    (78)  all_54_1 = all_52_4
% 241.51/48.06    (79)   ~ (all_20_2 = e1) | ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 241.51/48.06            op(e0, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 241.51/48.06              e3) & op(e0, e1) = all_20_1 & $i(all_20_1))
% 241.51/48.06    (80)   ~ (all_52_4 = e3)
% 241.51/48.06    (81)  op(e3, e2) = all_52_4
% 241.51/48.06    (82)   ~ (all_52_8 = all_52_11)
% 241.51/48.06    (83)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.51/48.06    (84)   ~ (all_52_9 = e3)
% 241.51/48.06    (85)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.51/48.06          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.06    (86)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.51/48.06          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.51/48.06    (87)  all_54_3 = all_52_12
% 241.51/48.06    (88)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.06          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.51/48.06    (89)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.06    (90)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.51/48.06          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.51/48.06    (91)   ~ (all_52_6 = all_52_7)
% 241.51/48.06    (92)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.06          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.06    (93)  all_56_11 = e3
% 241.51/48.06    (94)  op(e1, e1) = e0
% 241.51/48.06    (95)   ~ (all_52_4 = e1)
% 241.51/48.06    (96)  all_20_2 = all_4_2
% 241.51/48.06    (97)   ~ (e1 = e0)
% 241.51/48.06    (98)   ~ (all_52_13 = e3)
% 241.51/48.06    (99)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.51/48.06          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.51/48.06    (100)   ~ (all_52_11 = all_4_2)
% 241.51/48.06    (101)  op(e2, e0) = all_52_13
% 241.51/48.06    (102)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.06           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.51/48.06             e1)
% 241.51/48.06    (103)   ~ (all_52_1 = e3)
% 241.51/48.06    (104)  all_54_14 = all_52_11
% 241.51/48.06    (105)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.06           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.51/48.06             e2)
% 241.51/48.06    (106)   ~ (all_52_4 = all_52_8)
% 241.51/48.06    (107)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.51/48.06             $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) =
% 241.51/48.06             all_8_1 & $i(all_8_1))
% 241.51/48.06    (108)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.06           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.51/48.06    (109)  all_56_1 = e1
% 241.51/48.06    (110)   ~ (e2 = e1)
% 241.51/48.06    (111)   ~ (all_52_1 = e1)
% 241.51/48.06    (112)   ~ (all_52_4 = all_52_7)
% 241.51/48.06    (113)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 241.51/48.06             & op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 241.51/48.06             (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 241.51/48.06  
% 241.51/48.06  Begin of proof
% 241.51/48.06  | 
% 241.51/48.06  | SIMP: (67) implies:
% 241.51/48.06  |   (114)  e2 = e0
% 241.51/48.06  | 
% 241.51/48.06  | COMBINE_EQS: (28), (114) imply:
% 241.51/48.06  |   (115)  all_58_8 = e0
% 241.51/48.06  | 
% 241.51/48.06  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.51/48.06  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 241.51/48.06  |            (24), (25), (26), (27), (29), (30), (31), (32), (33), (34), (35),
% 241.51/48.06  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 241.51/48.06  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 241.51/48.06  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (68), (69),
% 241.51/48.06  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 241.51/48.06  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 241.51/48.06  |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 241.51/48.06  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 241.51/48.06  |            (111), (112), (113), (115) are inconsistent by sub-proof #563.
% 241.51/48.06  | 
% 241.51/48.06  End of proof
% 241.51/48.06  
% 241.51/48.06  Sub-proof #563 shows that the following formulas are inconsistent:
% 241.51/48.06  ----------------------------------------------------------------
% 241.51/48.06    (1)   ~ (all_52_12 = all_4_2)
% 241.51/48.06    (2)  op(e2, e2) = e3
% 241.51/48.06    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 241.51/48.06             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 241.51/48.06           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 241.51/48.06         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 241.51/48.06           $i(all_56_7))
% 241.51/48.06    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.51/48.06         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.51/48.06    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.51/48.06         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.06    (6)   ~ (e3 = e0)
% 241.51/48.06    (7)  all_56_31 = all_4_2
% 241.51/48.06    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.51/48.06         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.51/48.06    (9)   ~ (all_4_2 = e2)
% 241.51/48.06    (10)  all_42_2 = e3
% 241.51/48.06    (11)   ~ (e2 = e0)
% 241.51/48.06    (12)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 241.51/48.06            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 241.51/48.06            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 241.51/48.06            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 241.51/48.06            = all_56_15 & $i(all_56_15))
% 241.51/48.06    (13)  all_54_13 = all_52_7
% 241.51/48.06    (14)  op(e1, e2) = all_52_6
% 241.51/48.06    (15)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.06          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.06    (16)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.51/48.06          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.51/48.06    (17)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.51/48.06              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.51/48.06            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.51/48.06            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.51/48.06            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.51/48.06             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.06            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.51/48.06            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.51/48.06            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.51/48.06            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.06            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.51/48.06              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.51/48.06            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.51/48.06            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.51/48.06            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.51/48.06            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.51/48.06            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.51/48.06            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.51/48.06              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.51/48.06            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.06            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.51/48.06            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.51/48.06            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.51/48.06            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.06            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.51/48.06              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.51/48.06            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.06            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.51/48.06    (18)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.06          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.51/48.06    (19)   ~ (all_52_7 = all_52_11)
% 241.51/48.06    (20)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.51/48.06            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 241.51/48.06              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 241.51/48.06    (21)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.51/48.06          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.51/48.06    (22)   ~ (all_52_7 = e3)
% 241.51/48.06    (23)  all_58_8 = e0
% 241.51/48.06    (24)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 241.51/48.06    (25)   ~ (all_52_8 = e0)
% 241.51/48.06    (26)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.06          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.51/48.06    (27)   ~ (e3 = e1)
% 241.51/48.06    (28)  all_54_11 = all_52_14
% 241.51/48.06    (29)  op(e0, e0) = all_4_2
% 241.51/48.06    (30)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.51/48.06          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.51/48.06    (31)   ~ (all_52_12 = all_52_14)
% 241.51/48.06    (32)   ~ (all_52_8 = e1)
% 241.51/48.06    (33)  all_58_3 = e3
% 241.51/48.06    (34)   ~ (all_52_12 = all_52_13)
% 241.51/48.06    (35)   ~ (all_52_14 = all_4_2)
% 241.51/48.06    (36)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 241.51/48.06            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 241.51/48.06              e1) = all_10_1 & $i(all_10_1))
% 241.51/48.06    (37)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.51/48.06          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.51/48.06    (38)  all_54_2 = all_52_8
% 241.51/48.06    (39)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 241.51/48.06    (40)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.51/48.06          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.51/48.06    (41)  op(e3, e3) = e1
% 241.51/48.06    (42)   ~ (all_52_9 = e0)
% 241.51/48.06    (43)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.51/48.06    (44)  all_56_21 = e0
% 241.51/48.06    (45)  all_54_4 = all_52_1
% 241.51/48.06    (46)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.06              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.51/48.06                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.51/48.06                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.51/48.06    (47)   ~ (all_52_8 = all_52_12)
% 241.51/48.06    (48)  op(e2, e1) = all_52_9
% 241.51/48.06    (49)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.06          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.06    (50)   ~ (e3 = e2)
% 241.51/48.06    (51)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.51/48.06          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.51/48.06    (52)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 241.51/48.06    (53)   ~ (all_52_14 = e0)
% 241.51/48.06    (54)   ~ (all_52_13 = all_4_2)
% 241.51/48.06    (55)   ~ (all_4_2 = e3)
% 241.51/48.06    (56)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 241.51/48.06    (57)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 241.51/48.06    (58)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.06          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.06    (59)  op(e3, e0) = all_52_12
% 241.51/48.06    (60)   ~ (all_52_7 = all_4_2)
% 241.51/48.06    (61)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.51/48.06          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.51/48.06    (62)   ~ (all_52_9 = all_52_13)
% 241.51/48.06    (63)  all_54_15 = all_4_2
% 241.51/48.06    (64)   ~ (all_52_4 = all_52_12)
% 241.51/48.06    (65)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 241.51/48.07    (66)  all_38_2 = e1
% 241.51/48.07    (67)  op(e2, e3) = all_52_1
% 241.51/48.07    (68)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.51/48.07          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.07    (69)   ~ (all_52_6 = e3)
% 241.51/48.07    (70)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 241.51/48.07    (71)   ~ (all_52_1 = all_52_13)
% 241.51/48.07    (72)   ~ (all_52_11 = e0)
% 241.51/48.07    (73)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.51/48.07          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.51/48.07    (74)  all_54_7 = all_52_13
% 241.51/48.07    (75)  op(e0, e2) = all_52_7
% 241.51/48.07    (76)   ~ (all_52_13 = all_52_14)
% 241.51/48.07    (77)  all_54_1 = all_52_4
% 241.51/48.07    (78)   ~ (all_20_2 = e1) | ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 241.51/48.07            op(e0, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 241.51/48.07              e3) & op(e0, e1) = all_20_1 & $i(all_20_1))
% 241.51/48.07    (79)   ~ (all_52_4 = e3)
% 241.51/48.07    (80)  op(e3, e2) = all_52_4
% 241.51/48.07    (81)   ~ (all_52_8 = all_52_11)
% 241.51/48.07    (82)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.51/48.07    (83)   ~ (all_52_9 = e3)
% 241.51/48.07    (84)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.51/48.07          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.07    (85)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.51/48.07          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.51/48.07    (86)  all_54_3 = all_52_12
% 241.51/48.07    (87)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.07          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.51/48.07    (88)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.07            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.07    (89)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.51/48.07          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.51/48.07    (90)   ~ (all_52_6 = all_52_7)
% 241.51/48.07    (91)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.07          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.07    (92)  all_56_11 = e3
% 241.51/48.07    (93)  op(e1, e1) = e0
% 241.51/48.07    (94)   ~ (all_52_4 = e1)
% 241.51/48.07    (95)  all_20_2 = all_4_2
% 241.51/48.07    (96)   ~ (e1 = e0)
% 241.51/48.07    (97)   ~ (all_52_13 = e3)
% 241.51/48.07    (98)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.51/48.07          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.51/48.07    (99)   ~ (all_52_11 = all_4_2)
% 241.51/48.07    (100)  op(e2, e0) = all_52_13
% 241.51/48.07    (101)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.07           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.51/48.07             e1)
% 241.51/48.07    (102)   ~ (all_52_1 = e3)
% 241.51/48.07    (103)  all_54_14 = all_52_11
% 241.51/48.07    (104)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.07           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.51/48.07             e2)
% 241.51/48.07    (105)   ~ (all_52_4 = all_52_8)
% 241.51/48.07    (106)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.51/48.07             $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) =
% 241.51/48.07             all_8_1 & $i(all_8_1))
% 241.51/48.07    (107)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.07           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.51/48.07    (108)  all_56_1 = e1
% 241.51/48.07    (109)   ~ (e2 = e1)
% 241.51/48.07    (110)   ~ (all_52_1 = e1)
% 241.51/48.07    (111)   ~ (all_52_4 = all_52_7)
% 241.51/48.07    (112)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0
% 241.51/48.07             & op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 241.51/48.07             (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 241.51/48.07  
% 241.51/48.07  Begin of proof
% 241.51/48.07  | 
% 241.51/48.07  | BETA: splitting (78) gives:
% 241.51/48.07  | 
% 241.51/48.07  | Case 1:
% 241.51/48.07  | | 
% 241.51/48.07  | |   (113)   ~ (all_20_2 = e1)
% 241.51/48.07  | | 
% 241.51/48.07  | | REDUCE: (95), (113) imply:
% 241.51/48.07  | |   (114)   ~ (all_4_2 = e1)
% 241.51/48.07  | | 
% 241.51/48.07  | | BETA: splitting (65) gives:
% 241.51/48.07  | | 
% 241.51/48.07  | | Case 1:
% 241.51/48.07  | | | 
% 241.51/48.07  | | |   (115)  all_54_15 = e3
% 241.51/48.07  | | | 
% 241.51/48.07  | | | REF_CLOSE: (55), (63), (115) are inconsistent by sub-proof #2340.
% 241.51/48.07  | | | 
% 241.51/48.07  | | Case 2:
% 241.51/48.07  | | | 
% 241.51/48.07  | | |   (116)   ~ (all_54_15 = e3)
% 241.51/48.07  | | |   (117)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 241.51/48.07  | | | 
% 241.51/48.07  | | | BETA: splitting (117) gives:
% 241.51/48.07  | | | 
% 241.51/48.07  | | | Case 1:
% 241.51/48.07  | | | | 
% 241.51/48.07  | | | |   (118)  all_54_15 = e2
% 241.51/48.07  | | | | 
% 241.51/48.07  | | | | REF_CLOSE: (9), (63), (118) are inconsistent by sub-proof #2339.
% 241.51/48.07  | | | | 
% 241.51/48.07  | | | Case 2:
% 241.51/48.07  | | | | 
% 241.51/48.07  | | | |   (119)   ~ (all_54_15 = e2)
% 241.51/48.07  | | | |   (120)  all_54_15 = e1 | all_54_15 = e0
% 241.51/48.07  | | | | 
% 241.51/48.07  | | | | BETA: splitting (120) gives:
% 241.51/48.07  | | | | 
% 241.51/48.07  | | | | Case 1:
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | |   (121)  all_54_15 = e1
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | | REF_CLOSE: (63), (114), (121) are inconsistent by sub-proof #2338.
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | Case 2:
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | |   (122)  all_54_15 = e0
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | | COMBINE_EQS: (63), (122) imply:
% 241.51/48.07  | | | | |   (123)  all_4_2 = e0
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | | SIMP: (123) implies:
% 241.51/48.07  | | | | |   (124)  all_4_2 = e0
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | | COMBINE_EQS: (7), (124) imply:
% 241.51/48.07  | | | | |   (125)  all_56_31 = e0
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | | REDUCE: (55), (124) imply:
% 241.51/48.07  | | | | |   (126)   ~ (e3 = e0)
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | | REDUCE: (9), (124) imply:
% 241.51/48.07  | | | | |   (127)   ~ (e2 = e0)
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | | REDUCE: (114), (124) imply:
% 241.51/48.07  | | | | |   (128)   ~ (e1 = e0)
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | | REDUCE: (29), (124) imply:
% 241.51/48.07  | | | | |   (129)  op(e0, e0) = e0
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | | BETA: splitting (46) gives:
% 241.51/48.07  | | | | | 
% 241.51/48.07  | | | | | Case 1:
% 241.51/48.07  | | | | | | 
% 241.51/48.07  | | | | | |   (130)  all_58_15 = e0 & op(e0, e0) = e0
% 241.51/48.07  | | | | | | 
% 241.51/48.07  | | | | | | ALPHA: (130) implies:
% 241.51/48.07  | | | | | |   (131)  all_58_15 = e0
% 241.51/48.07  | | | | | | 
% 241.51/48.07  | | | | | | REF_CLOSE: (4), (5), (6), (11), (14), (16), (17), (18), (22), (26),
% 241.51/48.07  | | | | | |            (27), (30), (33), (37), (40), (41), (42), (48), (49),
% 241.51/48.07  | | | | | |            (50), (51), (58), (62), (67), (68), (73), (75), (79),
% 241.51/48.07  | | | | | |            (80), (83), (84), (87), (88), (89), (90), (92), (93),
% 241.51/48.07  | | | | | |            (96), (100), (101), (102), (104), (107), (108), (109),
% 241.51/48.07  | | | | | |            (110), (125), (129), (131) are inconsistent by sub-proof
% 241.51/48.07  | | | | | |            #648.
% 241.51/48.07  | | | | | | 
% 241.51/48.07  | | | | | Case 2:
% 241.51/48.07  | | | | | | 
% 241.51/48.07  | | | | | |   (132)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 241.51/48.07  | | | | | |              op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0))
% 241.51/48.07  | | | | | |          & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.51/48.07  | | | | | |              op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.51/48.07  | | | | | | 
% 241.51/48.07  | | | | | | ALPHA: (132) implies:
% 241.51/48.07  | | | | | |   (133)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.51/48.07  | | | | | |            op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.51/48.07  | | | | | |   (134)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 241.51/48.07  | | | | | |            op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.51/48.07  | | | | | | 
% 241.51/48.07  | | | | | | BETA: splitting (133) gives:
% 241.51/48.07  | | | | | | 
% 241.51/48.07  | | | | | | Case 1:
% 241.51/48.07  | | | | | | | 
% 241.51/48.07  | | | | | | |   (135)  all_58_12 = e0 & op(e0, e3) = e0
% 241.51/48.07  | | | | | | | 
% 241.51/48.07  | | | | | | | REF_CLOSE: (4), (5), (6), (8), (11), (14), (15), (16), (17), (18),
% 241.51/48.07  | | | | | | |            (21), (22), (23), (26), (27), (30), (33), (37), (40),
% 241.51/48.07  | | | | | | |            (41), (46), (48), (49), (50), (51), (58), (61), (67),
% 241.51/48.07  | | | | | | |            (68), (69), (73), (75), (79), (80), (83), (84), (85),
% 241.51/48.07  | | | | | | |            (87), (88), (89), (91), (92), (93), (94), (96), (98),
% 241.51/48.07  | | | | | | |            (100), (101), (102), (104), (107), (108), (109), (110),
% 241.51/48.07  | | | | | | |            (125), (129), (135) are inconsistent by sub-proof #611.
% 241.51/48.07  | | | | | | | 
% 241.51/48.07  | | | | | | Case 2:
% 241.51/48.07  | | | | | | | 
% 241.51/48.07  | | | | | | |   (136)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 241.51/48.07  | | | | | | |            op(e0, e1) = e0)
% 241.51/48.07  | | | | | | | 
% 241.51/48.07  | | | | | | | BETA: splitting (136) gives:
% 241.51/48.07  | | | | | | | 
% 241.51/48.07  | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | 
% 241.51/48.07  | | | | | | | |   (137)  all_58_13 = e0 & op(e0, e2) = e0
% 241.51/48.07  | | | | | | | | 
% 241.51/48.07  | | | | | | | | ALPHA: (137) implies:
% 241.51/48.07  | | | | | | | |   (138)  all_58_13 = e0
% 241.51/48.07  | | | | | | | |   (139)  op(e0, e2) = e0
% 241.51/48.07  | | | | | | | | 
% 241.51/48.07  | | | | | | | | BETA: splitting (58) gives:
% 241.51/48.07  | | | | | | | | 
% 241.51/48.07  | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | 
% 241.51/48.07  | | | | | | | | |   (140)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 241.51/48.07  | | | | | | | | |            op(e2, e3) = e0)
% 241.51/48.07  | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | BETA: splitting (140) gives:
% 241.51/48.07  | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | |   (141)  all_58_0 = e0 & op(e3, e3) = e0
% 241.51/48.07  | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | ALPHA: (141) implies:
% 241.51/48.07  | | | | | | | | | |   (142)  op(e3, e3) = e0
% 241.51/48.07  | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | REF_CLOSE: (41), (88), (96), (142) are inconsistent by
% 241.51/48.07  | | | | | | | | | |            sub-proof #1828.
% 241.51/48.07  | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | Case 2:
% 241.51/48.07  | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | |   (143)  all_58_2 = e0 & op(e2, e3) = e0
% 241.51/48.07  | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | ALPHA: (143) implies:
% 241.51/48.07  | | | | | | | | | |   (144)  all_58_2 = e0
% 241.51/48.07  | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | BETA: splitting (101) gives:
% 241.51/48.07  | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | |   (145)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 241.51/48.07  | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 241.51/48.07  | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | BETA: splitting (145) gives:
% 241.51/48.07  | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | |   (146)  all_58_12 = e1 & op(e0, e3) = e1
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | ALPHA: (146) implies:
% 241.51/48.07  | | | | | | | | | | | |   (147)  all_58_12 = e1
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | REF_CLOSE: (6), (11), (27), (40), (41), (49), (50), (58),
% 241.51/48.07  | | | | | | | | | | | |            (67), (88), (96), (102), (109), (147) are
% 241.51/48.07  | | | | | | | | | | | |            inconsistent by sub-proof #1204.
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | Case 2:
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | |   (148)  all_58_13 = e1 & op(e0, e2) = e1
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | ALPHA: (148) implies:
% 241.51/48.07  | | | | | | | | | | | |   (149)  all_58_13 = e1
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | REF_CLOSE: (96), (138), (149) are inconsistent by sub-proof
% 241.51/48.07  | | | | | | | | | | | |            #2082.
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | End of split
% 241.51/48.07  | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | Case 2:
% 241.51/48.07  | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | |   (150)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 241.51/48.07  | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.51/48.07  | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | BETA: splitting (150) gives:
% 241.51/48.07  | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | |   (151)  all_58_14 = e1 & op(e0, e1) = e1
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | ALPHA: (151) implies:
% 241.51/48.07  | | | | | | | | | | | |   (152)  all_58_14 = e1
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | BETA: splitting (91) gives:
% 241.51/48.07  | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | |   (153)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 241.51/48.07  | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 241.51/48.07  | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | REF_CLOSE: (27), (33), (80), (88), (94), (153) are
% 241.51/48.07  | | | | | | | | | | | | |            inconsistent by sub-proof #741.
% 241.51/48.07  | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | Case 2:
% 241.51/48.07  | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | |   (154)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 241.51/48.07  | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 241.51/48.07  | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | BETA: splitting (154) gives:
% 241.51/48.07  | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | |   (155)  all_58_7 = e1 & op(e1, e2) = e1
% 241.51/48.07  | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | ALPHA: (155) implies:
% 241.51/48.07  | | | | | | | | | | | | | |   (156)  all_58_7 = e1
% 241.51/48.07  | | | | | | | | | | | | | |   (157)  op(e1, e2) = e1
% 241.51/48.07  | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 241.51/48.07  | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | |   (158)  all_58_9 = e0 & op(e3, e0) = e0
% 241.51/48.07  | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 241.51/48.07  | | | | | | | | | | | | | | |   (159)  all_58_9 = e0
% 241.51/48.07  | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 241.51/48.07  | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | |   (160)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 241.51/48.07  | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 241.51/48.07  | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 241.51/48.07  | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | |   (161)  all_58_4 = e3 & op(e3, e1) = e3
% 241.51/48.07  | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 241.51/48.07  | | | | | | | | | | | | | | | | |   (162)  all_58_4 = e3
% 241.51/48.07  | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 241.51/48.07  | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | |   (163)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 241.51/48.07  | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 241.51/48.07  | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | |   (164)  all_58_9 = e3 & op(e3, e0) = e3
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (164) are inconsistent by sub-proof
% 241.51/48.07  | | | | | | | | | | | | | | | | | | |            #1621.
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | |   (165)  all_58_10 = e3 & op(e2, e0) = e3
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | |   (166)  all_58_10 = e3
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (26), (27), (33), (37), (41),
% 241.51/48.07  | | | | | | | | | | | | | | | | | | |            (50), (67), (68), (79), (80), (87), (88), (96),
% 241.51/48.07  | | | | | | | | | | | | | | | | | | |            (107), (109), (110), (162), (166) are inconsistent
% 241.51/48.07  | | | | | | | | | | | | | | | | | | |            by sub-proof #653.
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.07  | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | |   (167)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 241.51/48.07  | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.51/48.07  | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | |   (168)  all_58_11 = e3 & op(e1, e0) = e3
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | |   (169)  all_58_11 = e3
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | |   (170)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |   (171)  all_58_9 = e1 & op(e3, e0) = e1
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |   (172)  all_58_9 = e1
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (172) imply:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |   (173)  e1 = e0
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (173) imply:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |   (174)  all_58_14 = e0
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (11), (14), (15), (16), (17),
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |            (18), (21), (22), (23), (26), (27), (30), (33),
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |            (37), (40), (41), (42), (46), (48), (49), (50),
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |            (51), (58), (61), (62), (67), (68), (69), (73),
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |            (75), (79), (80), (83), (84), (85), (87), (88),
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |            (89), (90), (92), (93), (96), (98), (100), (101),
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |            (102), (104), (107), (108), (109), (110), (125),
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |            (129), (134), (144), (174) are inconsistent by
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |            sub-proof #591.
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |   (175)  all_58_10 = e1 & op(e2, e0) = e1
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |   (176)  all_58_10 = e1
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | |   (177)  op(e2, e0) = e1
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | |   (178)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | | |   (179)  all_58_4 = e2 & op(e3, e1) = e2
% 241.51/48.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (162), (179) are inconsistent by sub-proof
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | |            #1476.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | |   (180)  all_58_5 = e2 & op(e2, e1) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | |   (181)  all_58_5 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | |   (182)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (183)  all_58_1 = e2 & op(e3, e2) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (184)  all_58_1 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (185)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_58_6 = e2 & op(e1, e3) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (187)  all_58_6 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (188)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (189)  all_58_9 = e2 & op(e3, e0) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (190)  all_58_9 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (191)  op(e3, e0) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (192)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (193)  all_58_0 = e0 & op(e3, e3) = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (194)  op(e3, e3) = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (88), (96), (194) are inconsistent by
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1828.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  all_58_1 = e0 & op(e3, e2) = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  all_58_1 = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (196) imply:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (197)  e2 = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (197) imply:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (198)  all_58_6 = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (14), (27), (37), (41), (50), (61),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (69), (79), (80), (85), (88), (96), (109),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (169), (184), (190), (191), (198) are
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #590.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (199)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_58_4 = e0 & op(e3, e1) = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_58_4 = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (27), (37), (41), (50), (79), (80), (88),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (201) are inconsistent by sub-proof #1400.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11), (41), (50), (88), (109), (159), (162),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (184), (190) are inconsistent by sub-proof #829.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (202)  all_58_10 = e2 & op(e2, e0) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_58_10 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (16), (27), (37), (41), (50),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (79), (80), (88), (96), (109), (129), (159),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (169), (203) are inconsistent by sub-proof
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1465.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (204)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_58_11 = e2 & op(e1, e0) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (206)  all_58_11 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (169), (206) are inconsistent by sub-proof
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2030.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (207)  all_58_15 = e2 & op(e0, e0) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (208)  op(e0, e0) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (88), (92), (102), (108), (125), (209) are
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #744.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  op(e1, e2) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (88), (96), (129), (157), (208), (213) are
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #627.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)   ~ (all_56_31 = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)   ~ (all_56_11 = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)   ~ (all_56_1 = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (218) imply:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)   ~ (e2 = e1)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (88) with e0, e2, e0, e0,
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (129), (208) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)  e2 = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (220) imply:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_58_1 = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11), (41), (50), (88), (109), (159), (162),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221) are inconsistent by sub-proof #1097.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  op(e0, e2) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (18), (33), (88), (96), (156), (184),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223) are inconsistent by sub-proof #1353.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  op(e2, e0) = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (96), (100), (177), (226) are inconsistent
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1778.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (108), (125), (227) are inconsistent by sub-proof
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #743.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  all_58_7 = e2 & op(e1, e2) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (26), (33), (50), (87), (96), (109),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (176), (181), (228) are inconsistent by
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #589.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  all_58_8 = e2 & op(e1, e1) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  all_58_8 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (231) imply:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  e2 = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (232) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  e2 = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (233) imply:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  all_58_1 = e0
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11), (41), (50), (88), (109), (159), (162),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234) are inconsistent by sub-proof #1097.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_58_11 = e2 & op(e1, e0) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  all_58_11 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (169), (236) are inconsistent by sub-proof
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2030.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  all_58_3 = e2 & op(e2, e2) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (50), (237) are inconsistent by sub-proof
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | |            #1106.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | |   (238)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (239)  all_58_7 = e2 & op(e1, e2) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (26), (33), (50), (87), (96), (109),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (176), (181), (239) are inconsistent by
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #589.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (240)  all_58_13 = e2 & op(e0, e2) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (241)  op(e0, e2) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (88), (139), (241) are inconsistent by
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | |   (242)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | |   (243)  all_58_8 = e2 & op(e1, e1) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (23), (243) are inconsistent by sub-proof
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | |            #683.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_58_14 = e2 & op(e0, e1) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (152), (244) are inconsistent by sub-proof
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | |            #1771.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | |   (245)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (27), (37), (41), (50), (68),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | |            (79), (80), (88), (96), (109), (129), (162),
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | |            (169), (245) are inconsistent by sub-proof #1466.
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | |   (246)  all_58_15 = e3 & op(e0, e0) = e3
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | |   (247)  all_58_15 = e3
% 241.51/48.08  | | | | | | | | | | | | | | | | | | |   (248)  op(e0, e0) = e3
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | |   (249)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | |   (250)  all_58_12 = e2 & op(e0, e3) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | |   (251)  all_58_12 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | |   (252)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | |   (253)  all_58_1 = e2 & op(e3, e2) = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | |   (254)  all_58_1 = e2
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | |   (255)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  all_58_4 = e2 & op(e3, e1) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_58_4 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (162), (257) are inconsistent by sub-proof
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |            #1902.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  all_58_5 = e2 & op(e2, e1) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  all_58_5 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (41), (67), (88), (102), (260) are
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1208.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_58_6 = e3 & op(e1, e3) = e3
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  all_58_6 = e3
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_58_6 = e2 & op(e1, e3) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_58_6 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (266) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  e3 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (27), (40), (41), (48), (49), (50),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (67), (73), (83), (88), (93), (96), (102),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (109), (152), (162), (263), (267) are inconsistent
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #588.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_58_7 = e2 & op(e1, e2) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_58_7 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (156), (269) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  e2 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (11), (14), (15), (16), (17), (18),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22), (26), (27), (30), (33), (37), (40), (41),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (42), (48), (49), (50), (51), (58), (62), (67),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (73), (75), (79), (80), (83), (84), (87),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (90), (92), (93), (96), (100), (101),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (102), (104), (107), (108), (109), (110), (125),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (129), (144), (159), (162), (259), (270) are
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #587.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  all_58_8 = e2 & op(e1, e1) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (273)  all_58_8 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (273) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (274)  e2 = e0
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (274) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (275)  e2 = e0
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (275) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (276)  all_58_1 = e0
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (15), (33), (41), (49), (50),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (88), (96), (109), (139), (156), (162),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (251), (263), (276) are inconsistent by sub-proof
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #586.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (277)  all_58_11 = e2 & op(e1, e0) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_58_11 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (279)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_58_9 = e1 & op(e3, e0) = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  all_58_9 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (11), (14), (15), (16), (18), (21),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (26), (27), (30), (33), (37), (40), (41), (46),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (48), (49), (50), (51), (58), (61), (67), (68),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (69), (73), (79), (80), (83), (84), (85), (87),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (93), (96), (98), (100), (101), (102),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (104), (107), (109), (110), (263), (281) are
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #640.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  all_58_10 = e1 & op(e2, e0) = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  all_58_10 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (285)  all_58_2 = e1 & op(e2, e3) = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (88), (110), (285) are inconsistent by
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2229.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (286)  all_58_3 = e1 & op(e2, e2) = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (27), (33), (37), (41), (50),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (79), (80), (88), (96), (109), (162), (286)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1030.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (288)  all_58_5 = e1 & op(e2, e1) = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_58_5 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (26), (27), (33), (41), (49), (50),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (84), (87), (88), (89), (96), (109), (134),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (251), (263), (283), (289) are inconsistent
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #584.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (88) with e0, e3, e0, e0,
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (129), (248) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)  e3 = e0
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (290) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)  all_58_4 = e0
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (11), (14), (15), (16), (18), (21),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (26), (27), (30), (33), (37), (40), (41), (46),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (48), (49), (50), (51), (58), (61), (67), (68),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (69), (73), (79), (80), (83), (84), (85), (87),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (93), (96), (98), (100), (101), (102),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (104), (107), (109), (110), (152), (263), (291)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #582.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)  all_58_11 = e1 & op(e1, e0) = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)  all_58_11 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (294) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)  e2 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (11), (14), (15), (16), (17), (18),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22), (26), (27), (30), (33), (37), (40), (41),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (42), (48), (49), (50), (51), (58), (62), (67),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (73), (75), (79), (80), (83), (84), (87),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (90), (92), (93), (96), (100), (101),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (102), (104), (107), (108), (109), (110), (125),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (129), (144), (159), (162), (259), (295) are
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #587.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_58_15 = e1 & op(e0, e0) = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  all_58_15 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22), (27), (50), (75), (88), (152), (251),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (297) are inconsistent by sub-proof #1814.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  all_58_12 = e3 & op(e0, e3) = e3
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_58_12 = e3
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (46), (50), (88), (96), (104), (109),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (152), (247), (299) are inconsistent by sub-proof
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1031.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | |   (300)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  all_58_8 = e2 & op(e1, e1) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_58_8 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (302) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  e2 = e0
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (303) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_58_1 = e0
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11), (41), (50), (88), (109), (159), (162),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |            (304) are inconsistent by sub-proof #1097.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_58_14 = e2 & op(e0, e1) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  all_58_14 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (152), (306) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  e2 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (307) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_58_12 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (27), (40), (41), (49), (50), (58),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |            (67), (88), (96), (102), (109), (308) are
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1204.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | |   (309)  all_58_3 = e2 & op(e2, e2) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (50), (309) are inconsistent by sub-proof
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | |            #1106.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | |   (310)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | |   (311)  all_58_7 = e2 & op(e1, e2) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_58_7 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (156), (312) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | |   (313)  e2 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (313) imply:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | |   (314)  all_58_12 = e1
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (27), (40), (41), (49), (50), (58),
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | |            (67), (88), (96), (102), (109), (314) are
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1204.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | |   (315)  all_58_13 = e2 & op(e0, e2) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | |   (316)  op(e0, e2) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (88), (139), (316) are inconsistent by
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | |   (317)  all_58_13 = e2 & op(e0, e2) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | |   (318)  op(e0, e2) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (88), (139), (318) are inconsistent by
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | |   (319)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | |   (320)  all_58_14 = e2 & op(e0, e1) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (152), (320) are inconsistent by sub-proof
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | |            #1771.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | |   (321)  all_58_15 = e2 & op(e0, e0) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | ALPHA: (321) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | |   (322)  all_58_15 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (247), (322) are inconsistent by sub-proof
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | |            #615.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | |   (323)  all_58_5 = e3 & op(e2, e1) = e3
% 241.51/48.09  | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (83), (88), (323) are inconsistent by
% 241.51/48.09  | | | | | | | | | | | | | | | | |            sub-proof #1822.
% 241.51/48.09  | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | |   (324)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 241.51/48.09  | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (27), (88), (93), (152), (324) are
% 241.51/48.09  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #658.
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | End of split
% 241.51/48.09  | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | |   (325)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 241.51/48.09  | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 241.51/48.09  | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | |   (326)  all_58_10 = e0 & op(e2, e0) = e0
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | |   (327)  all_58_10 = e0
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (15), (16), (18), (26), (27), (30),
% 241.51/48.09  | | | | | | | | | | | | | | | |            (33), (37), (40), (41), (48), (49), (50), (51),
% 241.51/48.09  | | | | | | | | | | | | | | | |            (58), (67), (73), (79), (80), (83), (85), (87),
% 241.51/48.09  | | | | | | | | | | | | | | | |            (88), (96), (98), (101), (102), (107), (109),
% 241.51/48.09  | | | | | | | | | | | | | | | |            (110), (129), (156), (327) are inconsistent by
% 241.51/48.09  | | | | | | | | | | | | | | | |            sub-proof #638.
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | |   (328)  all_58_11 = e0 & op(e1, e0) = e0
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | ALPHA: (328) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | |   (329)  all_58_11 = e0
% 241.51/48.09  | | | | | | | | | | | | | | | |   (330)  op(e1, e0) = e0
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | |   (331)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.51/48.09  | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | |   (332)  all_58_6 = e2 & op(e1, e3) = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | |   (333)  all_58_6 = e2
% 241.51/48.09  | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | |   (334)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 241.51/48.09  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (41), (67), (88), (102), (334) are
% 241.51/48.09  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1208.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | |   (335)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 241.51/48.09  | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | |   (336)  all_58_6 = e3 & op(e1, e3) = e3
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | ALPHA: (336) implies:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | |   (337)  all_58_6 = e3
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (333), (337) are inconsistent by sub-proof
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | |            #2024.
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.09  | | | | | | | | | | | | | | | | | | | |   (338)  all_58_12 = e3 & op(e0, e3) = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | |   (339)  all_58_12 = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | |   (340)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |   (341)  all_58_9 = e3 & op(e3, e0) = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |   (342)  all_58_9 = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | |   (343)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | |   (344)  all_58_9 = e1 & op(e3, e0) = e1
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (27), (40), (41), (49), (50), (58),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | |            (67), (88), (96), (102), (109), (339), (342),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | |            (344) are inconsistent by sub-proof #737.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | |   (345)  all_58_10 = e1 & op(e2, e0) = e1
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (345) implies:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | |   (346)  all_58_10 = e1
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (347)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (348)  all_58_4 = e3 & op(e3, e1) = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (348) implies:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (349)  all_58_4 = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (350)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (14), (41), (49), (50), (58), (69),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (96), (109), (339), (350) are inconsistent
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1136.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (351)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (351) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (352)  all_58_8 = e3 & op(e1, e1) = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (88), (93), (352) are inconsistent by
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2018.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (353)  all_58_11 = e3 & op(e1, e0) = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (354)  all_58_11 = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (354) imply:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (355)  e3 = e0
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (355) imply:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (356)  all_58_4 = e0
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (356) imply:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (357)  e3 = e0
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (355) imply:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (358)  all_58_12 = e0
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (359)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (26), (27), (33), (37), (41),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (50), (68), (79), (80), (87), (88), (96), (109),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (346), (359) are inconsistent by sub-proof #647.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (360)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (360) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (361)  all_58_8 = e1 & op(e1, e1) = e1
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (361) implies:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (362)  op(e1, e1) = e1
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (93), (96), (362) are inconsistent by
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2220.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (363)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (41), (67), (88), (102), (363) are
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1208.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (364)  all_58_6 = e3 & op(e1, e3) = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (364) implies:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (365)  all_58_6 = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (11), (14), (15), (16), (18), (21),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (26), (27), (30), (33), (37), (40), (41), (46),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (48), (49), (50), (51), (58), (61), (67), (68),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (69), (73), (79), (80), (83), (84), (85), (87),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (93), (96), (98), (100), (101), (102),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (104), (107), (109), (110), (152), (356), (365)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #582.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (338), (358) are inconsistent by sub-proof
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #581.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (366)  all_58_5 = e3 & op(e2, e1) = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (83), (88), (366) are inconsistent by
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1822.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (367)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (27), (37), (41), (50), (68),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (79), (80), (84), (88), (89), (93), (96), (109),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (152), (342), (346), (367) are inconsistent
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #580.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (368)  all_58_5 = e3 & op(e2, e1) = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (83), (88), (368) are inconsistent by
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1822.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (369)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (27), (37), (41), (50), (68),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (79), (80), (84), (88), (89), (93), (96), (109),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (152), (342), (346), (369) are inconsistent
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #580.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | |   (370)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (96), (129), (330), (370) are inconsistent
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #625.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |   (371)  all_58_10 = e3 & op(e2, e0) = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |   (372)  all_58_10 = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (26), (27), (33), (50), (67), (87),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |            (88), (96), (107), (109), (110), (372) are
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1099.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | |   (373)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (373) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |   (374)  all_58_11 = e3 & op(e1, e0) = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (27), (40), (41), (49), (50), (67),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |            (88), (102), (109), (144), (329), (339), (374) are
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #579.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |   (375)  all_58_15 = e3 & op(e0, e0) = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |   (376)  all_58_15 = e3
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (46), (50), (88), (96), (104), (109),
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |            (152), (339), (376) are inconsistent by sub-proof
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | |            #1031.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | |   (377)  all_58_7 = e2 & op(e1, e2) = e2
% 241.51/48.10  | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 241.51/48.10  | | | | | | | | | | | | | | | | | |   (378)  all_58_7 = e2
% 241.51/48.10  | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (156), (378) are inconsistent by sub-proof
% 241.51/48.10  | | | | | | | | | | | | | | | | | |            #2134.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | |   (379)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.51/48.10  | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.51/48.10  | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | BETA: splitting (379) gives:
% 241.51/48.10  | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | |   (380)  all_58_8 = e2 & op(e1, e1) = e2
% 241.51/48.10  | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (23), (380) are inconsistent by sub-proof
% 241.51/48.10  | | | | | | | | | | | | | | | | | |            #683.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | |   (381)  all_58_11 = e2 & op(e1, e0) = e2
% 241.51/48.10  | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (329), (381) are inconsistent by sub-proof
% 241.51/48.10  | | | | | | | | | | | | | | | | | |            #2216.
% 241.51/48.10  | | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | |   (382)  all_58_13 = e1 & op(e0, e2) = e1
% 241.51/48.10  | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | ALPHA: (382) implies:
% 241.51/48.10  | | | | | | | | | | | | | |   (383)  all_58_13 = e1
% 241.51/48.10  | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | COMBINE_EQS: (138), (383) imply:
% 241.51/48.10  | | | | | | | | | | | | | |   (384)  e1 = e0
% 241.51/48.10  | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | SIMP: (384) implies:
% 241.51/48.10  | | | | | | | | | | | | | |   (385)  e1 = e0
% 241.51/48.10  | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | COMBINE_EQS: (152), (385) imply:
% 241.51/48.10  | | | | | | | | | | | | | |   (386)  all_58_14 = e0
% 241.51/48.10  | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (11), (14), (15), (16), (17),
% 241.51/48.10  | | | | | | | | | | | | | |            (18), (21), (22), (23), (26), (27), (30), (33),
% 241.51/48.10  | | | | | | | | | | | | | |            (37), (40), (41), (42), (46), (48), (49), (50),
% 241.51/48.10  | | | | | | | | | | | | | |            (51), (58), (61), (62), (67), (68), (69), (73),
% 241.51/48.10  | | | | | | | | | | | | | |            (75), (79), (80), (83), (84), (85), (87), (88),
% 241.51/48.10  | | | | | | | | | | | | | |            (89), (90), (92), (93), (96), (98), (100), (101),
% 241.51/48.10  | | | | | | | | | | | | | |            (102), (104), (107), (108), (109), (110), (125),
% 241.51/48.10  | | | | | | | | | | | | | |            (129), (134), (144), (386) are inconsistent by
% 241.51/48.10  | | | | | | | | | | | | | |            sub-proof #591.
% 241.51/48.10  | | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | |   (387)  all_58_15 = e1 & op(e0, e0) = e1
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | ALPHA: (387) implies:
% 241.51/48.10  | | | | | | | | | | | |   (388)  op(e0, e0) = e1
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | REF_CLOSE: (88), (96), (129), (388) are inconsistent by
% 241.51/48.10  | | | | | | | | | | | |            sub-proof #2274.
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | |   (389)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 241.51/48.10  | | | | | | | | |            op(e0, e3) = e0)
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | BETA: splitting (389) gives:
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | |   (390)  all_58_6 = e0 & op(e1, e3) = e0
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | ALPHA: (390) implies:
% 241.51/48.10  | | | | | | | | | |   (391)  all_58_6 = e0
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | REF_CLOSE: (4), (6), (8), (11), (14), (15), (16), (18), (21),
% 241.51/48.10  | | | | | | | | | |            (26), (27), (30), (33), (37), (40), (41), (46),
% 241.51/48.10  | | | | | | | | | |            (48), (49), (50), (51), (58), (61), (67), (68),
% 241.51/48.10  | | | | | | | | | |            (69), (73), (79), (80), (83), (84), (85), (87),
% 241.51/48.10  | | | | | | | | | |            (88), (89), (93), (96), (98), (100), (101), (102),
% 241.51/48.10  | | | | | | | | | |            (104), (107), (109), (110), (391) are inconsistent
% 241.51/48.10  | | | | | | | | | |            by sub-proof #664.
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | |   (392)  all_58_12 = e0 & op(e0, e3) = e0
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (11), (14), (15), (16), (17),
% 241.51/48.10  | | | | | | | | | |            (18), (21), (22), (23), (26), (27), (30), (33),
% 241.51/48.10  | | | | | | | | | |            (37), (40), (41), (46), (48), (49), (50), (51),
% 241.51/48.10  | | | | | | | | | |            (58), (61), (67), (68), (69), (73), (75), (79),
% 241.51/48.10  | | | | | | | | | |            (80), (83), (84), (85), (87), (88), (89), (91),
% 241.51/48.10  | | | | | | | | | |            (92), (93), (94), (96), (98), (100), (101), (102),
% 241.51/48.10  | | | | | | | | | |            (104), (107), (108), (109), (110), (125), (129),
% 241.51/48.10  | | | | | | | | | |            (392) are inconsistent by sub-proof #611.
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | 
% 241.51/48.10  | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | 
% 241.51/48.10  | | | | | | | |   (393)  all_58_14 = e0 & op(e0, e1) = e0
% 241.51/48.10  | | | | | | | | 
% 241.51/48.10  | | | | | | | | ALPHA: (393) implies:
% 241.51/48.10  | | | | | | | |   (394)  all_58_14 = e0
% 241.51/48.10  | | | | | | | | 
% 241.51/48.10  | | | | | | | | BETA: splitting (58) gives:
% 241.51/48.10  | | | | | | | | 
% 241.51/48.10  | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | |   (395)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 241.51/48.10  | | | | | | | | |            op(e2, e3) = e0)
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | BETA: splitting (395) gives:
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | |   (396)  all_58_0 = e0 & op(e3, e3) = e0
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | ALPHA: (396) implies:
% 241.51/48.10  | | | | | | | | | |   (397)  op(e3, e3) = e0
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | REF_CLOSE: (41), (88), (96), (397) are inconsistent by
% 241.51/48.10  | | | | | | | | | |            sub-proof #1828.
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | |   (398)  all_58_2 = e0 & op(e2, e3) = e0
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | ALPHA: (398) implies:
% 241.51/48.10  | | | | | | | | | |   (399)  all_58_2 = e0
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (11), (14), (15), (16), (17),
% 241.51/48.10  | | | | | | | | | |            (18), (21), (22), (23), (26), (27), (30), (33),
% 241.51/48.10  | | | | | | | | | |            (37), (40), (41), (42), (46), (48), (49), (50),
% 241.51/48.10  | | | | | | | | | |            (51), (58), (61), (62), (67), (68), (69), (73),
% 241.51/48.10  | | | | | | | | | |            (75), (79), (80), (83), (84), (85), (87), (88),
% 241.51/48.10  | | | | | | | | | |            (89), (90), (92), (93), (96), (98), (100), (101),
% 241.51/48.10  | | | | | | | | | |            (102), (104), (107), (108), (109), (110), (125),
% 241.51/48.10  | | | | | | | | | |            (129), (134), (394), (399) are inconsistent by
% 241.51/48.10  | | | | | | | | | |            sub-proof #591.
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | End of split
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | |   (400)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 241.51/48.10  | | | | | | | | |            op(e0, e3) = e0)
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | BETA: splitting (400) gives:
% 241.51/48.10  | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | |   (401)  all_58_6 = e0 & op(e1, e3) = e0
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | ALPHA: (401) implies:
% 241.51/48.10  | | | | | | | | | |   (402)  all_58_6 = e0
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | REF_CLOSE: (4), (6), (8), (11), (14), (15), (16), (18), (21),
% 241.51/48.10  | | | | | | | | | |            (26), (27), (30), (33), (37), (40), (41), (46),
% 241.51/48.10  | | | | | | | | | |            (48), (49), (50), (51), (58), (61), (67), (68),
% 241.51/48.10  | | | | | | | | | |            (69), (73), (79), (80), (83), (84), (85), (87),
% 241.51/48.10  | | | | | | | | | |            (88), (89), (93), (96), (98), (100), (101), (102),
% 241.51/48.10  | | | | | | | | | |            (104), (107), (109), (110), (402) are inconsistent
% 241.51/48.10  | | | | | | | | | |            by sub-proof #664.
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | |   (403)  all_58_12 = e0 & op(e0, e3) = e0
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | ALPHA: (403) implies:
% 241.51/48.10  | | | | | | | | | |   (404)  all_58_12 = e0
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | BETA: splitting (21) gives:
% 241.51/48.10  | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | |   (405)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.51/48.10  | | | | | | | | | | |            & op(e2, e1) = e1)
% 241.51/48.10  | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | BETA: splitting (405) gives:
% 241.51/48.10  | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | Case 1:
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | |   (406)  all_58_4 = e1 & op(e3, e1) = e1
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | ALPHA: (406) implies:
% 241.51/48.10  | | | | | | | | | | | |   (407)  all_58_4 = e1
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (27), (37), (41), (50), (68),
% 241.51/48.10  | | | | | | | | | | | |            (79), (80), (88), (96), (109), (407) are
% 241.51/48.10  | | | | | | | | | | | |            inconsistent by sub-proof #1468.
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | Case 2:
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | |   (408)  all_58_5 = e1 & op(e2, e1) = e1
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.10  | | | | | | | | | | | | ALPHA: (408) implies:
% 241.51/48.10  | | | | | | | | | | | |   (409)  all_58_5 = e1
% 241.51/48.10  | | | | | | | | | | | |   (410)  op(e2, e1) = e1
% 241.51/48.10  | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | BETA: splitting (73) gives:
% 241.51/48.11  | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | |   (411)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 241.51/48.11  | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 241.51/48.11  | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | BETA: splitting (411) gives:
% 241.51/48.11  | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | |   (412)  all_58_4 = e3 & op(e3, e1) = e3
% 241.51/48.11  | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | ALPHA: (412) implies:
% 241.51/48.11  | | | | | | | | | | | | | |   (413)  all_58_4 = e3
% 241.51/48.11  | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 241.51/48.11  | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | |   (414)  all_58_9 = e0 & op(e3, e0) = e0
% 241.51/48.11  | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | ALPHA: (414) implies:
% 241.51/48.11  | | | | | | | | | | | | | | |   (415)  all_58_9 = e0
% 241.51/48.11  | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | |   (416)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 241.51/48.11  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | BETA: splitting (416) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | |   (417)  all_58_12 = e1 & op(e0, e3) = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | ALPHA: (417) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | |   (418)  all_58_12 = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (27), (40), (41), (49), (50), (58),
% 241.51/48.11  | | | | | | | | | | | | | | | | |            (67), (88), (96), (102), (109), (418) are
% 241.51/48.11  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1204.
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | |   (419)  all_58_13 = e1 & op(e0, e2) = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | ALPHA: (419) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | |   (420)  all_58_13 = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | |   (421)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 241.51/48.11  | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | BETA: splitting (421) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | |   (422)  all_58_9 = e3 & op(e3, e0) = e3
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (415), (422) are inconsistent by sub-proof
% 241.51/48.11  | | | | | | | | | | | | | | | | | | |            #1621.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | |   (423)  all_58_10 = e3 & op(e2, e0) = e3
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | ALPHA: (423) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | |   (424)  all_58_10 = e3
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (26), (33), (50), (87), (96), (109),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | |            (409), (424) are inconsistent by sub-proof #1101.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | |   (425)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 241.51/48.11  | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | BETA: splitting (425) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | |   (426)  all_58_11 = e3 & op(e1, e0) = e3
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (16), (26), (27), (33), (37),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | |            (41), (50), (68), (79), (80), (87), (88), (96),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | |            (109), (129), (409), (413), (426) are inconsistent
% 241.51/48.11  | | | | | | | | | | | | | | | | | | |            by sub-proof #610.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | |   (427)  all_58_15 = e3 & op(e0, e0) = e3
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | ALPHA: (427) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | |   (428)  all_58_15 = e3
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | |   (429)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (41), (67), (88), (102), (429) are
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1208.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | |   (430)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (430) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | |   (431)  all_58_6 = e3 & op(e1, e3) = e3
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (431) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | |   (432)  all_58_6 = e3
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | |   (433)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (433) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (434)  all_58_2 = e0 & op(e2, e3) = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (434) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (435)  all_58_2 = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (11), (14), (15), (16), (17), (18),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (22), (26), (27), (30), (33), (37), (40), (41),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (42), (48), (49), (50), (51), (58), (62), (67),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (68), (73), (75), (79), (80), (83), (84), (87),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (90), (92), (93), (96), (100), (101),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (102), (104), (107), (108), (109), (110), (125),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (129), (409), (413), (415), (420), (428), (435)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #608.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (436)  all_58_3 = e0 & op(e2, e2) = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (11), (14), (15), (16), (18), (21),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (26), (27), (30), (33), (37), (40), (41), (46),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (48), (49), (50), (51), (58), (61), (67), (68),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (69), (73), (79), (80), (83), (84), (85), (87),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (93), (96), (98), (100), (101), (102),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (104), (107), (109), (110), (432), (436) are
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #578.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | |   (437)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (437) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (438)  all_58_5 = e0 & op(e2, e1) = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (438) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (439)  op(e2, e1) = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (88), (96), (410), (439) are inconsistent by
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2165.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (440)  all_58_10 = e0 & op(e2, e0) = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (440) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (441)  all_58_10 = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (442)  op(e2, e0) = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (11), (14), (15), (16), (18),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (21), (22), (23), (26), (27), (30), (33), (37),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (40), (41), (46), (48), (49), (50), (51), (58),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (61), (67), (68), (69), (73), (75), (79), (80),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (87), (88), (89), (93), (96),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (98), (100), (101), (102), (104), (107), (109),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (110), (129), (394), (404), (409), (413), (441),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            (442) are inconsistent by sub-proof #577.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | |   (443)  all_58_12 = e3 & op(e0, e3) = e3
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (443) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | |   (444)  all_58_12 = e3
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | |   (445)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (445) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (446)  all_58_12 = e2 & op(e0, e3) = e2
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (446) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (447)  all_58_12 = e2
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (444), (447) are inconsistent by sub-proof
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            #1552.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (448)  all_58_13 = e2 & op(e0, e2) = e2
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (448) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (449)  all_58_13 = e2
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (450)  op(e0, e2) = e2
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | |   (451)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (27), (33), (40), (41), (49), (50),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | |            (58), (67), (80), (88), (94), (96), (102), (109),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | |            (444), (451) are inconsistent by sub-proof #576.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | |   (452)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (452) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (453)  all_58_7 = e1 & op(e1, e2) = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (453) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (454)  all_58_7 = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (15), (18), (27), (33), (40), (41),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (50), (58), (67), (88), (96), (102), (109),
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (416), (454) are inconsistent by sub-proof #740.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (455)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (455) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (456)  all_58_14 = e1 & op(e0, e1) = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (456) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (457)  all_58_14 = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (88), (96), (133), (444), (450), (457)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1032.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (458)  all_58_15 = e1 & op(e0, e0) = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (458) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)  op(e0, e0) = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (96), (129), (459) are inconsistent by
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (420), (449) are inconsistent by sub-proof
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | |            #1544.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | |   (460)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (460) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (461)  all_58_14 = e2 & op(e0, e1) = e2
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (394), (461) are inconsistent by sub-proof
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            #2077.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (462)  all_58_15 = e2 & op(e0, e0) = e2
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (462) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |   (463)  all_58_15 = e2
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (428), (463) are inconsistent by sub-proof
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | |            #615.
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | |   (464)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 241.51/48.11  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | BETA: splitting (464) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | |   (465)  all_58_14 = e1 & op(e0, e1) = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | ALPHA: (465) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | |   (466)  all_58_14 = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (27), (30), (37), (41), (50), (51),
% 241.51/48.11  | | | | | | | | | | | | | | | | |            (79), (80), (88), (96), (109), (409), (415), (466)
% 241.51/48.11  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1044.
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | |   (467)  all_58_15 = e1 & op(e0, e0) = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | ALPHA: (467) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | | |   (468)  op(e0, e0) = e1
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (96), (129), (468) are inconsistent by
% 241.51/48.11  | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 241.51/48.11  | | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | |   (469)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 241.51/48.11  | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 241.51/48.11  | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | BETA: splitting (469) gives:
% 241.51/48.11  | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | Case 1:
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | |   (470)  all_58_10 = e0 & op(e2, e0) = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | ALPHA: (470) implies:
% 241.51/48.11  | | | | | | | | | | | | | | | |   (471)  all_58_10 = e0
% 241.51/48.11  | | | | | | | | | | | | | | | |   (472)  op(e2, e0) = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (11), (14), (15), (16), (18),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (21), (22), (23), (26), (27), (30), (33), (37),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (40), (41), (46), (48), (49), (50), (51), (58),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (61), (67), (68), (69), (73), (75), (79), (80),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (83), (84), (85), (87), (88), (89), (93), (96),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (98), (100), (101), (102), (104), (107), (109),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (110), (129), (394), (404), (409), (413), (471),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (472) are inconsistent by sub-proof #577.
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | |   (473)  all_58_11 = e0 & op(e1, e0) = e0
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (11), (14), (15), (16), (18),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (21), (22), (26), (27), (30), (33), (37), (40),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (41), (46), (48), (49), (50), (51), (58), (61),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (67), (68), (69), (73), (75), (79), (80), (83),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (84), (85), (87), (88), (89), (93), (96), (98),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (100), (101), (102), (104), (107), (109), (110),
% 241.51/48.11  | | | | | | | | | | | | | | | |            (129), (394), (409), (413), (473) are inconsistent
% 241.51/48.11  | | | | | | | | | | | | | | | |            by sub-proof #594.
% 241.51/48.11  | | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | |   (474)  all_58_5 = e3 & op(e2, e1) = e3
% 241.51/48.11  | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | | REF_CLOSE: (48), (83), (88), (474) are inconsistent by
% 241.51/48.11  | | | | | | | | | | | | | |            sub-proof #1822.
% 241.51/48.11  | | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | |   (475)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 241.51/48.11  | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 241.51/48.11  | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | | REF_CLOSE: (6), (88), (93), (394), (475) are inconsistent by
% 241.51/48.11  | | | | | | | | | | | | |            sub-proof #593.
% 241.51/48.11  | | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | Case 2:
% 241.51/48.11  | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | |   (476)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.51/48.11  | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 241.51/48.11  | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | | REF_CLOSE: (88), (93), (96), (394), (476) are inconsistent by
% 241.51/48.11  | | | | | | | | | | |            sub-proof #592.
% 241.51/48.11  | | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | | 
% 241.51/48.11  | | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | | 
% 241.51/48.11  | | | | | | | | End of split
% 241.51/48.11  | | | | | | | | 
% 241.51/48.11  | | | | | | | End of split
% 241.51/48.11  | | | | | | | 
% 241.51/48.11  | | | | | | End of split
% 241.51/48.11  | | | | | | 
% 241.51/48.11  | | | | | End of split
% 241.51/48.11  | | | | | 
% 241.51/48.11  | | | | End of split
% 241.51/48.11  | | | | 
% 241.51/48.11  | | | End of split
% 241.51/48.11  | | | 
% 241.51/48.11  | | End of split
% 241.51/48.11  | | 
% 241.51/48.11  | Case 2:
% 241.51/48.11  | | 
% 241.51/48.11  | |   (477)  all_20_2 = e1
% 241.51/48.11  | | 
% 241.51/48.11  | | COMBINE_EQS: (95), (477) imply:
% 241.51/48.11  | |   (478)  all_4_2 = e1
% 241.51/48.11  | | 
% 241.51/48.11  | | COMBINE_EQS: (7), (478) imply:
% 241.51/48.11  | |   (479)  all_56_31 = e1
% 241.51/48.11  | | 
% 241.51/48.11  | | REDUCE: (60), (478) imply:
% 241.51/48.11  | |   (480)   ~ (all_52_7 = e1)
% 241.51/48.11  | | 
% 241.51/48.11  | | REDUCE: (99), (478) imply:
% 241.51/48.11  | |   (481)   ~ (all_52_11 = e1)
% 241.51/48.11  | | 
% 241.51/48.11  | | REDUCE: (1), (478) imply:
% 241.51/48.11  | |   (482)   ~ (all_52_12 = e1)
% 241.51/48.11  | | 
% 241.51/48.11  | | REDUCE: (54), (478) imply:
% 241.51/48.11  | |   (483)   ~ (all_52_13 = e1)
% 241.51/48.11  | | 
% 241.51/48.11  | | REDUCE: (35), (478) imply:
% 241.51/48.11  | |   (484)   ~ (all_52_14 = e1)
% 241.51/48.11  | | 
% 241.51/48.11  | | REDUCE: (55), (478) imply:
% 241.51/48.11  | |   (485)   ~ (e3 = e1)
% 241.51/48.11  | | 
% 241.51/48.11  | | REDUCE: (9), (478) imply:
% 241.51/48.11  | |   (486)   ~ (e2 = e1)
% 241.51/48.11  | | 
% 241.51/48.11  | | BETA: splitting (91) gives:
% 241.51/48.11  | | 
% 241.51/48.11  | | Case 1:
% 241.51/48.11  | | | 
% 241.51/48.11  | | |   (487)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 241.51/48.11  | | |            e1)
% 241.51/48.11  | | | 
% 241.51/48.11  | | | REF_CLOSE: (27), (33), (80), (88), (94), (487) are inconsistent by
% 241.51/48.11  | | |            sub-proof #741.
% 241.51/48.11  | | | 
% 241.51/48.11  | | Case 2:
% 241.51/48.11  | | | 
% 241.51/48.11  | | |   (488)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 241.51/48.11  | | |            = e1)
% 241.51/48.11  | | | 
% 241.51/48.11  | | | BETA: splitting (488) gives:
% 241.51/48.11  | | | 
% 241.51/48.11  | | | Case 1:
% 241.51/48.11  | | | | 
% 241.51/48.11  | | | |   (489)  all_58_7 = e1 & op(e1, e2) = e1
% 241.51/48.11  | | | | 
% 241.51/48.11  | | | | ALPHA: (489) implies:
% 241.51/48.11  | | | |   (490)  all_58_7 = e1
% 241.51/48.11  | | | | 
% 241.51/48.11  | | | | BETA: splitting (21) gives:
% 241.51/48.11  | | | | 
% 241.51/48.11  | | | | Case 1:
% 241.51/48.11  | | | | | 
% 241.51/48.12  | | | | |   (491)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 241.51/48.12  | | | | |              e1) = e1)
% 241.51/48.12  | | | | | 
% 241.51/48.12  | | | | | BETA: splitting (491) gives:
% 241.51/48.12  | | | | | 
% 241.51/48.12  | | | | | Case 1:
% 241.51/48.12  | | | | | | 
% 241.51/48.12  | | | | | |   (492)  all_58_4 = e1 & op(e3, e1) = e1
% 241.51/48.12  | | | | | | 
% 241.51/48.12  | | | | | | ALPHA: (492) implies:
% 241.51/48.12  | | | | | |   (493)  all_58_4 = e1
% 241.51/48.12  | | | | | | 
% 241.51/48.12  | | | | | | REF_CLOSE: (4), (6), (11), (27), (37), (41), (50), (68), (79), (80),
% 241.51/48.12  | | | | | |            (88), (96), (109), (493) are inconsistent by sub-proof
% 241.51/48.12  | | | | | |            #1468.
% 241.51/48.12  | | | | | | 
% 241.51/48.12  | | | | | Case 2:
% 241.51/48.12  | | | | | | 
% 241.51/48.12  | | | | | |   (494)  all_58_5 = e1 & op(e2, e1) = e1
% 241.51/48.12  | | | | | | 
% 241.51/48.12  | | | | | | ALPHA: (494) implies:
% 241.51/48.12  | | | | | |   (495)  all_58_5 = e1
% 241.51/48.12  | | | | | | 
% 241.51/48.12  | | | | | | BETA: splitting (101) gives:
% 241.51/48.12  | | | | | | 
% 241.51/48.12  | | | | | | Case 1:
% 241.51/48.12  | | | | | | | 
% 241.51/48.12  | | | | | | |   (496)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 241.51/48.12  | | | | | | |            op(e0, e2) = e1)
% 241.51/48.12  | | | | | | | 
% 241.51/48.12  | | | | | | | REF_CLOSE: (6), (11), (15), (18), (27), (33), (40), (41), (49),
% 241.51/48.12  | | | | | | |            (50), (58), (67), (88), (96), (102), (109), (490),
% 241.51/48.12  | | | | | | |            (496) are inconsistent by sub-proof #740.
% 241.51/48.12  | | | | | | | 
% 241.51/48.12  | | | | | | Case 2:
% 241.51/48.12  | | | | | | | 
% 241.51/48.12  | | | | | | |   (497)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 241.51/48.12  | | | | | | |            op(e0, e0) = e1)
% 241.51/48.12  | | | | | | | 
% 241.51/48.12  | | | | | | | BETA: splitting (497) gives:
% 241.51/48.12  | | | | | | | 
% 241.51/48.12  | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | 
% 241.51/48.12  | | | | | | | |   (498)  all_58_14 = e1 & op(e0, e1) = e1
% 241.51/48.12  | | | | | | | | 
% 241.51/48.12  | | | | | | | | ALPHA: (498) implies:
% 241.51/48.12  | | | | | | | |   (499)  all_58_14 = e1
% 241.51/48.12  | | | | | | | | 
% 241.51/48.12  | | | | | | | | REF_CLOSE: (4), (6), (11), (27), (30), (33), (37), (41), (48),
% 241.51/48.12  | | | | | | | |            (50), (51), (67), (68), (73), (79), (80), (83), (88),
% 241.51/48.12  | | | | | | | |            (93), (96), (100), (107), (109), (110), (483), (499)
% 241.51/48.12  | | | | | | | |            are inconsistent by sub-proof #657.
% 241.51/48.12  | | | | | | | | 
% 241.51/48.12  | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | 
% 241.51/48.12  | | | | | | | |   (500)  all_58_15 = e1 & op(e0, e0) = e1
% 241.51/48.12  | | | | | | | | 
% 241.51/48.12  | | | | | | | | ALPHA: (500) implies:
% 241.51/48.12  | | | | | | | |   (501)  all_58_15 = e1
% 241.51/48.12  | | | | | | | |   (502)  op(e0, e0) = e1
% 241.51/48.12  | | | | | | | | 
% 241.51/48.12  | | | | | | | | BETA: splitting (112) gives:
% 241.51/48.12  | | | | | | | | 
% 241.51/48.12  | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | 
% 241.51/48.12  | | | | | | | | |   (503)   ~ (all_38_2 = e1)
% 241.51/48.12  | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | REDUCE: (66), (503) imply:
% 241.51/48.12  | | | | | | | | |   (504)  $false
% 241.51/48.12  | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | CLOSE: (504) is inconsistent.
% 241.51/48.12  | | | | | | | | | 
% 241.51/48.12  | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | 
% 241.51/48.12  | | | | | | | | |   (505)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 241.51/48.12  | | | | | | | | |            op(e3, e1) = all_38_1 & $i(all_38_0) &
% 241.51/48.12  | | | | | | | | |            $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 241.51/48.12  | | | | | | | | |            all_38_1 & $i(all_38_1))
% 241.51/48.12  | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | BETA: splitting (20) gives:
% 241.51/48.12  | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | |   (506)   ~ (all_42_2 = e3)
% 241.51/48.12  | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | REDUCE: (10), (506) imply:
% 241.51/48.12  | | | | | | | | | |   (507)  $false
% 241.51/48.12  | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | CLOSE: (507) is inconsistent.
% 241.51/48.12  | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | |   (508)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.51/48.12  | | | | | | | | | |            op(e2, e3) = all_42_1 & $i(all_42_0) &
% 241.51/48.12  | | | | | | | | | |            $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3)
% 241.51/48.12  | | | | | | | | | |            = all_42_1 & $i(all_42_1))
% 241.51/48.12  | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | BETA: splitting (56) gives:
% 241.51/48.12  | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | |   (509)  all_54_7 = e3
% 241.51/48.12  | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | COMBINE_EQS: (74), (509) imply:
% 241.51/48.12  | | | | | | | | | | |   (510)  all_52_13 = e3
% 241.51/48.12  | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | REDUCE: (97), (510) imply:
% 241.51/48.12  | | | | | | | | | | |   (511)  $false
% 241.51/48.12  | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | CLOSE: (511) is inconsistent.
% 241.51/48.12  | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | |   (512)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 241.51/48.12  | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | BETA: splitting (57) gives:
% 241.51/48.12  | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | |   (513)  all_54_2 = e3
% 241.51/48.12  | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | COMBINE_EQS: (38), (513) imply:
% 241.51/48.12  | | | | | | | | | | | |   (514)  all_52_8 = e3
% 241.51/48.12  | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | SIMP: (514) implies:
% 241.51/48.12  | | | | | | | | | | | |   (515)  all_52_8 = e3
% 241.51/48.12  | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | REDUCE: (81), (515) imply:
% 241.51/48.12  | | | | | | | | | | | |   (516)   ~ (all_52_11 = e3)
% 241.51/48.12  | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | SIMP: (516) implies:
% 241.51/48.12  | | | | | | | | | | | |   (517)   ~ (all_52_11 = e3)
% 241.51/48.12  | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | REDUCE: (47), (515) imply:
% 241.51/48.12  | | | | | | | | | | | |   (518)   ~ (all_52_12 = e3)
% 241.51/48.12  | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | SIMP: (518) implies:
% 241.51/48.12  | | | | | | | | | | | |   (519)   ~ (all_52_12 = e3)
% 241.51/48.12  | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | BETA: splitting (51) gives:
% 241.51/48.12  | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | |   (520)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 241.51/48.12  | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 241.51/48.12  | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | BETA: splitting (520) gives:
% 241.51/48.12  | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | |   (521)  all_58_4 = e2 & op(e3, e1) = e2
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | ALPHA: (521) implies:
% 241.51/48.12  | | | | | | | | | | | | | |   (522)  all_58_4 = e2
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | |   (523)  all_54_14 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | COMBINE_EQS: (103), (523) imply:
% 241.51/48.12  | | | | | | | | | | | | | | |   (524)  all_52_11 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | REDUCE: (517), (524) imply:
% 241.51/48.12  | | | | | | | | | | | | | | |   (525)  $false
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | CLOSE: (525) is inconsistent.
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | |   (526)   ~ (all_54_14 = e3)
% 241.51/48.12  | | | | | | | | | | | | | | |   (527)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | |   (528)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 241.51/48.12  | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 241.51/48.12  | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | BETA: splitting (528) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | |   (529)  all_58_12 = e3 & op(e0, e3) = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | ALPHA: (529) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | |   (530)  all_58_12 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (46), (48), (50), (73), (83), (88),
% 241.51/48.12  | | | | | | | | | | | | | | | | |            (93), (96), (104), (109), (501), (522), (530) are
% 241.51/48.12  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #843.
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | |   (531)  all_58_13 = e3 & op(e0, e2) = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (75), (88), (531) are inconsistent by
% 241.51/48.12  | | | | | | | | | | | | | | | | |            sub-proof #1919.
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | |   (532)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 241.51/48.12  | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.51/48.12  | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | BETA: splitting (532) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | |   (533)  all_58_14 = e3 & op(e0, e1) = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | ALPHA: (533) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | |   (534)  all_58_14 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | |   (535)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 241.51/48.12  | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | BETA: splitting (535) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (536)  all_58_9 = e3 & op(e3, e0) = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | ALPHA: (536) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (537)  all_58_9 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (527) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (538)  all_54_14 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (538) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (539)  all_52_11 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | SIMP: (539) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (540)  all_52_11 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (540) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (541)   ~ (all_52_7 = e2)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | REDUCE: (517), (540) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (542)   ~ (e3 = e2)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (13), (15), (22), (33), (41),
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |            (50), (68), (75), (82), (88), (96), (109), (480),
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |            (490), (522), (537), (541) are inconsistent by
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |            sub-proof #575.
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (543)  all_54_14 = e1 | all_54_14 = e0
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (103), (481), (543) are inconsistent by
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |            sub-proof #1935.
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (544)  all_58_10 = e3 & op(e2, e0) = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | ALPHA: (544) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (545)  all_58_10 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (26), (33), (50), (87), (96), (109),
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |            (495), (545) are inconsistent by sub-proof #1101.
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | |   (546)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 241.51/48.12  | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | BETA: splitting (546) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (547)  all_58_11 = e3 & op(e1, e0) = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | ALPHA: (547) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (548)  all_58_11 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (549)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (27), (37), (40), (41), (46),
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |            (50), (67), (68), (79), (80), (88), (96), (102),
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |            (104), (109), (490), (501), (522), (534), (549)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #574.
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (550)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (550) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | |   (551)  all_58_8 = e2 & op(e1, e1) = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | ALPHA: (551) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | |   (552)  all_58_8 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (23), (552) are inconsistent by sub-proof
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | |            #1556.
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | |   (553)  all_58_11 = e2 & op(e1, e0) = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | ALPHA: (553) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | |   (554)  all_58_11 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (548), (554) are inconsistent by sub-proof
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | |            #2030.
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (555)  all_58_15 = e3 & op(e0, e0) = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | ALPHA: (555) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (556)  all_58_15 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (501), (556) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (557)  e3 = e1
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | SIMP: (557) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (558)  e3 = e1
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (534), (558) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (559)  all_58_14 = e1
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (27), (30), (33), (37), (41),
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |            (48), (50), (51), (67), (68), (73), (79), (80),
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |            (83), (88), (93), (96), (100), (107), (109),
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |            (110), (483), (559) are inconsistent by sub-proof
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |            #657.
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | |   (560)  all_58_15 = e3 & op(e0, e0) = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (501), (560) are inconsistent by sub-proof
% 241.51/48.12  | | | | | | | | | | | | | | | | |            #1915.
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | |   (561)  all_58_5 = e2 & op(e2, e1) = e2
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | REF_CLOSE: (109), (495), (561) are inconsistent by sub-proof
% 241.51/48.12  | | | | | | | | | | | | | |            #703.
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | |   (562)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 241.51/48.12  | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 241.51/48.12  | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | BETA: splitting (562) gives:
% 241.51/48.12  | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | |   (563)  all_58_8 = e2 & op(e1, e1) = e2
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | ALPHA: (563) implies:
% 241.51/48.12  | | | | | | | | | | | | | |   (564)  all_58_8 = e2
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | REF_CLOSE: (11), (23), (564) are inconsistent by sub-proof
% 241.51/48.12  | | | | | | | | | | | | | |            #1556.
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | |   (565)  all_58_14 = e2 & op(e0, e1) = e2
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | ALPHA: (565) implies:
% 241.51/48.12  | | | | | | | | | | | | | |   (566)  all_58_14 = e2
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 241.51/48.12  | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | |   (567)  all_54_14 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | COMBINE_EQS: (103), (567) imply:
% 241.51/48.12  | | | | | | | | | | | | | | |   (568)  all_52_11 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | REDUCE: (517), (568) imply:
% 241.51/48.12  | | | | | | | | | | | | | | |   (569)  $false
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | CLOSE: (569) is inconsistent.
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | |   (570)   ~ (all_54_14 = e3)
% 241.51/48.12  | | | | | | | | | | | | | | |   (571)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | |   (572)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 241.51/48.12  | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 241.51/48.12  | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | BETA: splitting (572) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | |   (573)  all_58_12 = e3 & op(e0, e3) = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | ALPHA: (573) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | |   (574)  all_58_12 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | |   (575)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 241.51/48.12  | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | BETA: splitting (575) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (576)  all_58_9 = e3 & op(e3, e0) = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | ALPHA: (576) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | |   (577)  all_58_9 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (571) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (578)  all_54_14 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (578) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (579)  all_52_11 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | SIMP: (579) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (580)  all_52_11 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (580) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (581)   ~ (all_52_7 = e2)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | REDUCE: (517), (580) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | |   (582)   ~ (e3 = e2)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | |   (583)  all_54_13 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (583) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | |   (584)  all_52_7 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (584) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | |   (585)  $false
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | CLOSE: (585) is inconsistent.
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | |   (586)   ~ (all_54_13 = e3)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | |   (587)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | |   (588)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (588) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | |   (589)  all_58_4 = e3 & op(e3, e1) = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (589) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | |   (590)  all_58_4 = e3
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | |   (591)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (591) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (592)  all_58_0 = e0 & op(e3, e3) = e0
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (592) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (593)  op(e3, e3) = e0
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (88), (96), (593) are inconsistent by
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1828.
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (594)  all_58_1 = e0 & op(e3, e2) = e0
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (594) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (595)  all_58_1 = e0
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (596)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (596) gives:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (597)  all_58_1 = e2 & op(e3, e2) = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (597) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (598)  all_58_1 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (595), (598) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (599)  e2 = e0
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (599) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (600)  e2 = e0
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (566), (600) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (601)  all_58_14 = e0
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (18), (33), (50), (96), (104), (109),
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (490), (501), (574), (598), (601) are inconsistent
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #735.
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (602)  all_58_3 = e2 & op(e2, e2) = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (602) implies:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (603)  all_58_3 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (603) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (604)  e3 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (590), (604) imply:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (605)  all_58_4 = e2
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (13), (15), (22), (33), (41),
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (50), (68), (75), (82), (88), (96), (109), (480),
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (490), (577), (581), (605) are inconsistent by
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #575.
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (606)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (606) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (607)  all_58_7 = e2 & op(e1, e2) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (27), (30), (33), (37), (41),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (50), (51), (67), (68), (79), (80), (88), (96),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (100), (107), (109), (110), (483), (490), (566),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (590), (607) are inconsistent by sub-proof #573.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (608)  all_58_13 = e2 & op(e0, e2) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (608) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (609)  op(e0, e2) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (75), (88), (480), (581), (587), (609) are
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1817.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | |   (610)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (610) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (611)  all_58_4 = e0 & op(e3, e1) = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (590), (611) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | |            #1697.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (612)  all_58_9 = e0 & op(e3, e0) = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (577), (612) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | |            #2103.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | |   (613)  all_58_5 = e3 & op(e2, e1) = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (83), (88), (613) are inconsistent by
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1822.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | |   (614)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (46), (50), (88), (93), (96), (104),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | |            (109), (501), (574), (614) are inconsistent by
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #844.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | |   (615)  all_54_14 = e1 | all_54_14 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (103), (481), (615) are inconsistent by
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | |            sub-proof #1935.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | |   (616)  all_58_10 = e3 & op(e2, e0) = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | ALPHA: (616) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | |   (617)  all_58_10 = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (26), (33), (50), (87), (96), (109),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | |            (495), (617) are inconsistent by sub-proof #1101.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | |   (618)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 241.51/48.13  | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | BETA: splitting (618) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | |   (619)  all_58_11 = e3 & op(e1, e0) = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | ALPHA: (619) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | |   (620)  all_58_11 = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | BETA: splitting (571) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | |   (621)  all_54_14 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (621) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | |   (622)  all_52_11 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | SIMP: (622) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | |   (623)  all_52_11 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (623) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | |   (624)   ~ (all_52_7 = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | REDUCE: (517), (623) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | |   (625)   ~ (e3 = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | |   (626)  all_54_13 = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (626) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | |   (627)  all_52_7 = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (627) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | |   (628)  $false
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | CLOSE: (628) is inconsistent.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | |   (629)   ~ (all_54_13 = e3)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | |   (630)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | |   (631)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (631) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | |   (632)  all_58_4 = e3 & op(e3, e1) = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (632) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | |   (633)  all_58_4 = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (630) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | |   (634)  all_54_13 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (634) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | |   (635)  all_52_7 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (624), (635) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | |   (636)  $false
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (636) is inconsistent.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | |   (637)   ~ (all_54_13 = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | |   (638)  all_54_13 = e1 | all_54_13 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (639)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (639) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (640)  all_58_6 = e2 & op(e1, e3) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (640) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (641)  all_58_6 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (642)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (642) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (643)  all_58_0 = e0 & op(e3, e3) = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (643) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (644)  op(e3, e3) = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (88), (96), (644) are inconsistent by
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1828.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (645)  all_58_2 = e0 & op(e2, e3) = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (645) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (646)  op(e2, e3) = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (647)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (647) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (648)  all_58_1 = e2 & op(e3, e2) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (648) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (649)  all_58_1 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (638) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (650)  all_54_13 = e1
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (480), (650) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1966.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (651)  all_54_13 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (651) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (652)  all_52_7 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (652) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (653)  all_52_7 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (653) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (654)   ~ (all_52_4 = e0)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (653) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (655)   ~ (e3 = e0)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (480), (653) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (656)   ~ (e1 = e0)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (653) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (657)  op(e0, e2) = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (658)  all_54_1 = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (79), (658) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1930.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (659)   ~ (all_54_1 = e3)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (660)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (660) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (661)  all_54_1 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (661) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (662)  all_52_4 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (662) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (663)  all_52_4 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (663) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (664)   ~ (all_52_12 = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (664) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (665)   ~ (all_52_12 = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (663) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (666)  op(e3, e2) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (667)  all_54_3 = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (519), (667) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2057.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (668)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (669)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (669) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (670)  all_58_2 = e2 & op(e2, e3) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (670) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (671)  all_58_2 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (41), (88), (96), (642), (671) are
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1534.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (672)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (672) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (673)  all_58_6 = e0 & op(e1, e3) = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (673) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (674)  all_58_6 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (675)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14), (69), (88), (674), (675) are
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1689.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (676)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (676) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (677)  all_58_8 = e3 & op(e1, e1) = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (23), (677) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #694.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (647) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (678)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (678) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (679)  all_58_9 = e2 & op(e3, e0) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (679) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (680)  all_58_9 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (681)  op(e3, e0) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (14), (27), (37), (41), (50), (61),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (69), (79), (80), (85), (88), (96), (109),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (490), (620), (649), (674), (680), (681) are
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #590.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (682)  all_58_10 = e2 & op(e2, e0) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (682) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (683)  op(e2, e0) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (33), (87), (88), (96), (495), (671),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (683) are inconsistent by sub-proof #840.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (684)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (684) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (685)  all_58_11 = e2 & op(e1, e0) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (620), (685) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1741.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (686)  all_58_15 = e2 & op(e0, e0) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (501), (686) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1917.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (687)  all_58_3 = e2 & op(e2, e2) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (50), (687) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1106.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (688)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (88), (109), (490), (657), (688) are
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1376.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (689)  all_58_12 = e0 & op(e0, e3) = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (689) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (690)  all_58_12 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (11), (22), (27), (50), (75), (88),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (104), (109), (501), (657), (690) are inconsistent
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1914.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (691)  all_58_3 = e2 & op(e2, e2) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (33), (46), (48), (50), (73), (83),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (93), (96), (104), (109), (501), (574),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (633), (691) are inconsistent by sub-proof #572.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (692)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (692) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (693)  all_58_5 = e2 & op(e2, e1) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (693) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (694)  all_58_5 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (495), (694) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (695)  e2 = e1
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (641), (695) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (696)  all_58_6 = e1
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (41), (49), (50), (58), (88), (96),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (109), (574), (696) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1162.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (697)  all_58_10 = e2 & op(e2, e0) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (697) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (698)  all_58_10 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (699)  op(e2, e0) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (700)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, all_56_11) = e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (700) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (701)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_9 & $i(all_56_9)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (701) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (702)  op(e3, e2) = all_56_9
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (703)  op(e3, all_56_9) = e3
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (668) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (704)  all_54_3 = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (665), (704) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2290.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (705)  all_54_3 = e1 | all_54_3 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (705) gives:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (706)  all_54_3 = e1
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (482), (706) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2289.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (707)  all_54_3 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (707) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (708)  all_52_12 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (708) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (709)  all_52_12 = e0
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (709) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (710)   ~ (all_52_13 = e0)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (710) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (711)   ~ (all_52_13 = e0)
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (79), (80), (88), (483), (512), (666),
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (702), (703), (711) are inconsistent by sub-proof
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1024.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (712)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (712) implies:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (713)  op(e2, all_56_11) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (713) imply:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (714)  op(e2, e3) = e2
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (88), (106), (508), (646), (714) are
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #733.
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (715)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_15 & $i(all_56_15))
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (715) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (716)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_13 & $i(all_56_13)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (716) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (717)  op(e1, all_56_13) = e1
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (718)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (718) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (719)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (719) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (720)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          e3
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (720) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (721)  op(e2, e3) = e3
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (88), (102), (721) are inconsistent by
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2337.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (722)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (722) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (723)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          e2
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (723) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (724)  op(e2, e3) = e2
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (88), (106), (508), (646), (724) are
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #733.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (725)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (725) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (726)   ~ (all_56_31 = e1)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (479), (726) imply:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (727)  $false
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (727) is inconsistent.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (728)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (92), (728) are inconsistent by sub-proof
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #863.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (729)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (729) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (730)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (730) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (731)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (731) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (732)   ~ (all_56_31 = e1)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (479), (732) imply:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (733)  $false
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (733) is inconsistent.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (734)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (734) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (735)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (735) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (736)  all_56_13 = e1
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (717), (736) imply:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (737)  op(e1, e1) = e1
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (93), (96), (737) are inconsistent by
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2220.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (738)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (738) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (739)  op(e0, e2) = e2
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (22), (75), (77), (82), (88), (94), (111),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (480), (654), (660), (739) are inconsistent by
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1815.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (740)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (740) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (741)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (741) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (742)  op(e2, e0) = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (88), (699), (742) are inconsistent by
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2121.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (743)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (743) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (744)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e1
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (744) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (745)   ~ (all_56_21 = e0)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (745) imply:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (746)  $false
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (746) is inconsistent.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (747)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (747) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (748)   ~ (all_56_31 = e1)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (479), (748) imply:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (749)  $false
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (749) is inconsistent.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (750)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_15 & $i(all_56_15)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (750) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (751)  op(e0, e2) = all_56_15
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (752)  op(e0, all_56_15) = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (753)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (754)  all_58_0 = e0 & op(e3, e3) = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (754) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (755)  op(e3, e3) = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (88), (96), (755) are inconsistent by
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1828.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (756)  all_58_1 = e0 & op(e3, e2) = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (756) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (757)  all_58_1 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (757) imply:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (758)  e2 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (641), (758) imply:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (759)  all_58_6 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (11), (14), (15), (16), (18), (21),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (26), (27), (30), (33), (37), (40), (41), (46),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (48), (49), (50), (51), (58), (61), (67), (68),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (69), (73), (79), (80), (83), (84), (85), (87),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (93), (96), (98), (100), (101), (102),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (104), (107), (109), (110), (574), (619), (620),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (759) are inconsistent by sub-proof #666.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (760)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (760) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (761)  all_58_4 = e0 & op(e3, e1) = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (761) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (762)  all_58_4 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (633), (762) imply:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (763)  e3 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (763) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (764)  e3 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (574), (764) imply:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (765)  all_58_12 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (11), (22), (27), (50), (75), (88),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (104), (109), (501), (657), (765) are inconsistent
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1914.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (766)  all_58_9 = e0 & op(e3, e0) = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (766) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (767)  all_58_9 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (508) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (88) with e0, all_56_15, e2, e0,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (657), (751) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (768)  all_56_15 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (752), (768) imply:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (769)  op(e0, e0) = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (16), (27), (37), (41), (50),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (79), (80), (88), (96), (109), (620), (633),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (698), (767), (769) are inconsistent by sub-proof
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1465.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (770)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_42_1)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (770) implies:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (771)   ~ (all_42_1 = e1)
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (772)  op(e2, e3) = all_42_1
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (88) with e0, all_56_15, e2, e0,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (657), (751) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (773)  all_56_15 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (88) with e0, all_42_1, e3, e2,
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (646), (772) gives:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (774)  all_42_1 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (752), (773) imply:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (775)  op(e0, e0) = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (16), (27), (37), (41), (50),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (79), (80), (88), (96), (109), (620), (633),
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (698), (767), (775) are inconsistent by sub-proof
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1465.
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (776)  all_54_1 = e1 | all_54_1 = e0
% 241.51/48.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (94), (654), (776) are inconsistent by
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2049.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (777)  all_58_3 = e2 & op(e2, e2) = e2
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (33), (46), (48), (50), (73), (83),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (93), (96), (104), (109), (501), (574),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (633), (777) are inconsistent by sub-proof #572.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (778)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (778) gives:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (779)  all_58_7 = e2 & op(e1, e2) = e2
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (779) implies:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (780)  all_58_7 = e2
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (490), (780) imply:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (781)  e2 = e1
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (781) implies:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (782)  e2 = e1
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (641), (782) imply:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (783)  all_58_6 = e1
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (41), (49), (50), (58), (88), (96),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (109), (574), (783) are inconsistent by sub-proof
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1162.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (784)  all_58_13 = e2 & op(e0, e2) = e2
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (784) implies:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (785)  op(e0, e2) = e2
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (75), (88), (480), (624), (630), (785) are
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1817.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (786)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (786) gives:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (787)  all_58_6 = e0 & op(e1, e3) = e0
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (787) implies:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (788)  all_58_6 = e0
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (11), (14), (15), (16), (18), (21),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (26), (27), (30), (33), (37), (40), (41), (46),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (48), (49), (50), (51), (58), (61), (67), (68),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (69), (73), (79), (80), (83), (84), (85), (87),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (93), (96), (98), (100), (101), (102),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (104), (107), (109), (110), (574), (619), (620),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (788) are inconsistent by sub-proof #666.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (789)  all_58_12 = e0 & op(e0, e3) = e0
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (574), (789) are inconsistent by sub-proof
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1641.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (790)  all_58_7 = e2 & op(e1, e2) = e2
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (27), (30), (33), (37), (41),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            (50), (51), (67), (68), (79), (80), (88), (96),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            (100), (107), (109), (110), (483), (490), (566),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            (633), (790) are inconsistent by sub-proof #573.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (791)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (791) gives:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (792)  all_58_8 = e2 & op(e1, e1) = e2
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (792) implies:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (793)  all_58_8 = e2
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (23), (793) are inconsistent by sub-proof
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1556.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | |   (794)  all_58_11 = e2 & op(e1, e0) = e2
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (46), (48), (50), (73), (83), (88),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (104), (109), (501), (574), (620),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | |            (633), (794) are inconsistent by sub-proof #842.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | |   (795)  all_58_5 = e3 & op(e2, e1) = e3
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (83), (88), (795) are inconsistent by
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1822.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | |   (796)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (46), (50), (88), (93), (96), (104),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | |            (109), (501), (574), (796) are inconsistent by
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #844.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | |   (797)  all_54_14 = e1 | all_54_14 = e0
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (103), (481), (797) are inconsistent by
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | |            sub-proof #1935.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | |   (798)  all_58_15 = e3 & op(e0, e0) = e3
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (27), (40), (41), (49), (50), (58),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | |            (67), (88), (96), (102), (109), (501), (574),
% 241.51/48.15  | | | | | | | | | | | | | | | | | | |            (798) are inconsistent by sub-proof #712.
% 241.51/48.15  | | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | |   (799)  all_58_13 = e3 & op(e0, e2) = e3
% 241.51/48.15  | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (75), (88), (799) are inconsistent by
% 241.51/48.15  | | | | | | | | | | | | | | | | |            sub-proof #1919.
% 241.51/48.15  | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | |   (800)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 241.51/48.15  | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.51/48.15  | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | BETA: splitting (800) gives:
% 241.51/48.15  | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | Case 1:
% 241.51/48.15  | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | |   (801)  all_58_14 = e3 & op(e0, e1) = e3
% 241.51/48.15  | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | ALPHA: (801) implies:
% 241.51/48.15  | | | | | | | | | | | | | | | | |   (802)  all_58_14 = e3
% 241.51/48.15  | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (566), (802) are inconsistent by sub-proof
% 241.51/48.15  | | | | | | | | | | | | | | | | |            #2117.
% 241.51/48.15  | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | |   (803)  all_58_15 = e3 & op(e0, e0) = e3
% 241.51/48.15  | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (501), (803) are inconsistent by sub-proof
% 241.51/48.15  | | | | | | | | | | | | | | | | |            #1915.
% 241.51/48.15  | | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | |   (804)   ~ (all_54_2 = e3)
% 241.51/48.15  | | | | | | | | | | | |   (805)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 241.51/48.15  | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | REDUCE: (38), (804) imply:
% 241.51/48.15  | | | | | | | | | | | |   (806)   ~ (all_52_8 = e3)
% 241.51/48.15  | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | BETA: splitting (805) gives:
% 241.51/48.15  | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | Case 1:
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | |   (807)  all_54_2 = e2
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | COMBINE_EQS: (38), (807) imply:
% 241.51/48.15  | | | | | | | | | | | | |   (808)  all_52_8 = e2
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | SIMP: (808) implies:
% 241.51/48.15  | | | | | | | | | | | | |   (809)  all_52_8 = e2
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | REDUCE: (105), (809) imply:
% 241.51/48.15  | | | | | | | | | | | | |   (810)   ~ (all_52_4 = e2)
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | REDUCE: (47), (809) imply:
% 241.51/48.15  | | | | | | | | | | | | |   (811)   ~ (all_52_12 = e2)
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | SIMP: (811) implies:
% 241.51/48.15  | | | | | | | | | | | | |   (812)   ~ (all_52_12 = e2)
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | REDUCE: (806), (809) imply:
% 241.51/48.15  | | | | | | | | | | | | |   (813)   ~ (e3 = e2)
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | BETA: splitting (36) gives:
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | Case 1:
% 241.51/48.15  | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | |   (814)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 241.51/48.15  | | | | | | | | | | | | | |          op(e3, e1) = all_10_1 & $i(all_10_0) &
% 241.51/48.15  | | | | | | | | | | | | | |          $i(all_10_1)
% 241.51/48.15  | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | ALPHA: (814) implies:
% 241.51/48.15  | | | | | | | | | | | | | |   (815)  op(e3, e1) = all_10_1
% 241.51/48.15  | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (11), (13), (14),
% 241.51/48.15  | | | | | | | | | | | | | |            (15), (16), (18), (21), (22), (23), (24), (26),
% 241.51/48.15  | | | | | | | | | | | | | |            (27), (28), (30), (31), (33), (34), (37), (39),
% 241.51/48.15  | | | | | | | | | | | | | |            (40), (41), (43), (45), (46), (48), (49), (50),
% 241.51/48.15  | | | | | | | | | | | | | |            (51), (53), (58), (59), (61), (64), (67), (68),
% 241.51/48.15  | | | | | | | | | | | | | |            (69), (70), (71), (73), (74), (75), (76), (77),
% 241.51/48.15  | | | | | | | | | | | | | |            (79), (80), (82), (83), (84), (85), (86), (87),
% 241.51/48.15  | | | | | | | | | | | | | |            (88), (89), (93), (94), (96), (98), (100), (101),
% 241.51/48.15  | | | | | | | | | | | | | |            (102), (104), (106), (107), (108), (109), (110),
% 241.51/48.15  | | | | | | | | | | | | | |            (111), (480), (482), (483), (484), (490), (495),
% 241.51/48.15  | | | | | | | | | | | | | |            (501), (502), (505), (508), (512), (810), (812),
% 241.51/48.15  | | | | | | | | | | | | | |            (815) are inconsistent by sub-proof #564.
% 241.51/48.15  | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | |   (816)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 241.51/48.15  | | | | | | | | | | | | | |          $i(all_10_1)
% 241.51/48.15  | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | ALPHA: (816) implies:
% 241.51/48.15  | | | | | | | | | | | | | |   (817)  op(e3, e1) = all_10_1
% 241.51/48.15  | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (11), (13), (14),
% 241.51/48.15  | | | | | | | | | | | | | |            (15), (16), (18), (21), (22), (23), (24), (26),
% 241.51/48.15  | | | | | | | | | | | | | |            (27), (28), (30), (31), (33), (34), (37), (39),
% 241.51/48.15  | | | | | | | | | | | | | |            (40), (41), (43), (45), (46), (48), (49), (50),
% 241.51/48.15  | | | | | | | | | | | | | |            (51), (53), (58), (59), (61), (64), (67), (68),
% 241.51/48.15  | | | | | | | | | | | | | |            (69), (70), (71), (73), (74), (75), (76), (77),
% 241.51/48.15  | | | | | | | | | | | | | |            (79), (80), (82), (83), (84), (85), (86), (87),
% 241.51/48.15  | | | | | | | | | | | | | |            (88), (89), (93), (94), (96), (98), (100), (101),
% 241.51/48.15  | | | | | | | | | | | | | |            (102), (104), (106), (107), (108), (109), (110),
% 241.51/48.15  | | | | | | | | | | | | | |            (111), (480), (482), (483), (484), (490), (495),
% 241.51/48.15  | | | | | | | | | | | | | |            (501), (502), (505), (508), (512), (810), (812),
% 241.51/48.15  | | | | | | | | | | | | | |            (817) are inconsistent by sub-proof #564.
% 241.51/48.15  | | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | Case 2:
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | |   (818)  all_54_2 = e1 | all_54_2 = e0
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | | REF_CLOSE: (25), (32), (38), (818) are inconsistent by
% 241.51/48.15  | | | | | | | | | | | | |            sub-proof #1336.
% 241.51/48.15  | | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | | 
% 241.51/48.15  | | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | | 
% 241.51/48.15  | | | | | | | | End of split
% 241.51/48.15  | | | | | | | | 
% 241.51/48.15  | | | | | | | End of split
% 241.51/48.15  | | | | | | | 
% 241.51/48.15  | | | | | | End of split
% 241.51/48.15  | | | | | | 
% 241.51/48.15  | | | | | End of split
% 241.51/48.15  | | | | | 
% 241.51/48.15  | | | | Case 2:
% 241.51/48.15  | | | | | 
% 241.51/48.15  | | | | |   (819)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0,
% 241.51/48.15  | | | | |              e1) = e1)
% 241.51/48.15  | | | | | 
% 241.51/48.15  | | | | | BETA: splitting (819) gives:
% 241.51/48.15  | | | | | 
% 241.51/48.15  | | | | | Case 1:
% 241.51/48.15  | | | | | | 
% 241.51/48.15  | | | | | |   (820)  all_58_8 = e1 & op(e1, e1) = e1
% 241.51/48.15  | | | | | | 
% 241.51/48.15  | | | | | | ALPHA: (820) implies:
% 241.51/48.15  | | | | | |   (821)  op(e1, e1) = e1
% 241.51/48.15  | | | | | | 
% 241.51/48.15  | | | | | | REF_CLOSE: (88), (93), (96), (821) are inconsistent by sub-proof
% 241.51/48.15  | | | | | |            #2220.
% 241.51/48.15  | | | | | | 
% 241.51/48.15  | | | | | Case 2:
% 241.51/48.15  | | | | | | 
% 241.51/48.15  | | | | | |   (822)  all_58_14 = e1 & op(e0, e1) = e1
% 241.51/48.15  | | | | | | 
% 241.51/48.15  | | | | | | ALPHA: (822) implies:
% 241.51/48.15  | | | | | |   (823)  all_58_14 = e1
% 241.51/48.15  | | | | | | 
% 241.51/48.15  | | | | | | REF_CLOSE: (4), (6), (11), (27), (30), (33), (37), (41), (48), (50),
% 241.51/48.15  | | | | | |            (51), (67), (68), (73), (79), (80), (83), (88), (93),
% 241.51/48.15  | | | | | |            (96), (100), (107), (109), (110), (483), (823) are
% 241.51/48.15  | | | | | |            inconsistent by sub-proof #657.
% 241.51/48.15  | | | | | | 
% 241.51/48.15  | | | | | End of split
% 241.51/48.15  | | | | | 
% 241.51/48.15  | | | | End of split
% 241.51/48.15  | | | | 
% 241.51/48.15  | | | Case 2:
% 241.51/48.15  | | | | 
% 241.51/48.15  | | | |   (824)  all_58_13 = e1 & op(e0, e2) = e1
% 241.51/48.15  | | | | 
% 241.51/48.15  | | | | REF_CLOSE: (75), (88), (480), (824) are inconsistent by sub-proof #2275.
% 241.51/48.15  | | | | 
% 241.51/48.15  | | | End of split
% 241.51/48.15  | | | 
% 241.51/48.15  | | End of split
% 241.51/48.15  | | 
% 241.51/48.15  | End of split
% 241.51/48.15  | 
% 241.51/48.15  End of proof
% 241.51/48.15  
% 241.51/48.15  Sub-proof #564 shows that the following formulas are inconsistent:
% 241.51/48.15  ----------------------------------------------------------------
% 241.51/48.15    (1)  op(e0, e0) = e1
% 241.51/48.15    (2)  op(e2, e2) = e3
% 241.51/48.15    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 241.51/48.15             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 241.51/48.15           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 241.51/48.15         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 241.51/48.15           $i(all_56_7))
% 241.51/48.15    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.51/48.15         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.51/48.15    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.51/48.15         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.15    (6)   ~ (e3 = e0)
% 241.51/48.15    (7)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.51/48.15         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.51/48.15    (8)   ~ (e2 = e0)
% 241.51/48.15    (9)  all_54_13 = all_52_7
% 241.51/48.15    (10)  op(e1, e2) = all_52_6
% 241.51/48.15    (11)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.15          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.15    (12)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.51/48.15          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.51/48.15    (13)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 241.51/48.15            all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3,
% 241.51/48.15              e1) = all_38_1 & $i(all_38_1))
% 241.51/48.15    (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.15          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.51/48.15    (15)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.51/48.15          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.51/48.15    (16)   ~ (all_52_13 = e1)
% 241.51/48.15    (17)   ~ (all_52_7 = e3)
% 241.51/48.15    (18)  all_58_8 = e0
% 241.51/48.15    (19)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 241.51/48.15    (20)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.51/48.15          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.51/48.15    (21)   ~ (e3 = e1)
% 241.51/48.15    (22)  all_54_11 = all_52_14
% 241.51/48.15    (23)   ~ (all_52_12 = e1)
% 241.51/48.15    (24)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.51/48.15          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.51/48.15    (25)   ~ (all_52_12 = all_52_14)
% 241.51/48.15    (26)  all_58_3 = e3
% 241.51/48.15    (27)   ~ (all_52_12 = all_52_13)
% 241.51/48.15    (28)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.51/48.16          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.51/48.16    (29)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 241.51/48.16    (30)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.51/48.16          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.51/48.16    (31)  op(e3, e3) = e1
% 241.51/48.16    (32)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 241.51/48.16    (33)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.51/48.16    (34)  all_54_4 = all_52_1
% 241.51/48.16    (35)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.16              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.51/48.16                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.51/48.16                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.51/48.16    (36)  op(e2, e1) = all_52_9
% 241.51/48.16    (37)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.51/48.16          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.51/48.16    (38)   ~ (e3 = e2)
% 241.51/48.16    (39)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.51/48.16          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.51/48.16    (40)   ~ (all_52_14 = e1)
% 241.51/48.16    (41)   ~ (all_52_7 = e1)
% 241.51/48.16    (42)   ~ (all_52_14 = e0)
% 241.51/48.16    (43)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.51/48.16          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.51/48.16    (44)  all_58_15 = e1
% 241.51/48.16    (45)  op(e3, e0) = all_52_12
% 241.51/48.16    (46)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.51/48.16          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.51/48.16    (47)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 241.51/48.16            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 241.51/48.16              e3) = all_42_1 & $i(all_42_1))
% 241.51/48.16    (48)   ~ (all_52_4 = all_52_12)
% 241.51/48.16    (49)  op(e2, e3) = all_52_1
% 241.51/48.16    (50)   ~ (all_52_12 = e2)
% 241.51/48.16    (51)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.51/48.16          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.51/48.16    (52)   ~ (all_52_6 = e3)
% 241.51/48.16    (53)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 241.51/48.16    (54)   ~ (all_52_1 = all_52_13)
% 241.51/48.16    (55)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.51/48.16          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.51/48.16    (56)  all_54_7 = all_52_13
% 241.51/48.16    (57)  op(e0, e2) = all_52_7
% 241.51/48.16    (58)   ~ (all_52_13 = all_52_14)
% 241.51/48.16    (59)  all_54_1 = all_52_4
% 241.51/48.16    (60)   ~ (all_52_4 = e3)
% 241.51/48.16    (61)  op(e3, e2) = all_52_4
% 241.51/48.16    (62)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.51/48.16    (63)  all_58_5 = e1
% 241.51/48.16    (64)  all_58_7 = e1
% 241.51/48.16    (65)   ~ (all_52_9 = e3)
% 241.51/48.16    (66)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.51/48.16          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.51/48.16    (67)   ~ (all_52_4 = e2)
% 241.51/48.16    (68)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.51/48.16          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.51/48.16    (69)  all_54_3 = all_52_12
% 241.51/48.16    (70)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.51/48.16          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.51/48.16    (71)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.51/48.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.51/48.16    (72)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.51/48.16          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.51/48.16    (73)  op(e3, e1) = all_10_1
% 241.51/48.16    (74)  op(e1, e1) = e0
% 241.51/48.16    (75)   ~ (all_52_4 = e1)
% 241.51/48.16    (76)   ~ (e1 = e0)
% 241.51/48.16    (77)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.51/48.16          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.51/48.16    (78)  op(e2, e0) = all_52_13
% 241.51/48.16    (79)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.51/48.16          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.51/48.16            e1)
% 241.51/48.16    (80)   ~ (all_52_1 = e3)
% 241.51/48.16    (81)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.51/48.16          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.51/48.16            e2)
% 241.51/48.16    (82)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 241.51/48.16            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 241.51/48.16            & $i(all_8_1))
% 241.51/48.16    (83)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.51/48.16          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.51/48.16    (84)  all_56_1 = e1
% 241.51/48.16    (85)   ~ (e2 = e1)
% 241.51/48.16    (86)   ~ (all_52_1 = e1)
% 241.51/48.16    (87)   ~ (all_52_4 = all_52_7)
% 241.51/48.16  
% 241.51/48.16  Begin of proof
% 241.51/48.16  | 
% 241.51/48.16  | BETA: splitting (19) gives:
% 241.51/48.16  | 
% 241.51/48.16  | Case 1:
% 241.51/48.16  | | 
% 241.51/48.16  | |   (88)  all_54_1 = e3
% 241.51/48.16  | | 
% 241.51/48.16  | | REF_CLOSE: (59), (60), (88) are inconsistent by sub-proof #1930.
% 241.51/48.16  | | 
% 241.51/48.16  | Case 2:
% 241.51/48.16  | | 
% 241.51/48.16  | |   (89)   ~ (all_54_1 = e3)
% 241.51/48.16  | |   (90)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 241.51/48.16  | | 
% 241.51/48.16  | | BETA: splitting (39) gives:
% 241.51/48.16  | | 
% 241.51/48.16  | | Case 1:
% 241.51/48.16  | | | 
% 241.51/48.16  | | |   (91)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 241.51/48.16  | | |           e2)
% 241.51/48.16  | | | 
% 241.51/48.16  | | | BETA: splitting (91) gives:
% 241.51/48.16  | | | 
% 241.51/48.16  | | | Case 1:
% 241.51/48.16  | | | | 
% 241.51/48.16  | | | |   (92)  all_58_4 = e2 & op(e3, e1) = e2
% 241.51/48.16  | | | | 
% 241.51/48.16  | | | | ALPHA: (92) implies:
% 241.51/48.16  | | | |   (93)  all_58_4 = e2
% 241.51/48.16  | | | |   (94)  op(e3, e1) = e2
% 241.51/48.16  | | | | 
% 241.51/48.16  | | | | BETA: splitting (30) gives:
% 241.51/48.16  | | | | 
% 241.51/48.16  | | | | Case 1:
% 241.51/48.16  | | | | | 
% 241.51/48.16  | | | | |   (95)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2,
% 241.51/48.16  | | | | |             e3) = e3)
% 241.51/48.16  | | | | | 
% 241.51/48.16  | | | | | REF_CLOSE: (21), (31), (49), (71), (80), (95) are inconsistent by
% 241.51/48.16  | | | | |            sub-proof #1208.
% 241.51/48.16  | | | | | 
% 241.51/48.16  | | | | Case 2:
% 241.51/48.16  | | | | | 
% 241.51/48.16  | | | | |   (96)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0,
% 241.51/48.16  | | | | |             e3) = e3)
% 241.51/48.16  | | | | | 
% 241.51/48.16  | | | | | BETA: splitting (96) gives:
% 241.51/48.16  | | | | | 
% 241.51/48.16  | | | | | Case 1:
% 241.51/48.16  | | | | | | 
% 241.51/48.16  | | | | | |   (97)  all_58_6 = e3 & op(e1, e3) = e3
% 241.51/48.16  | | | | | | 
% 241.51/48.16  | | | | | | ALPHA: (97) implies:
% 241.51/48.16  | | | | | |   (98)  all_58_6 = e3
% 241.51/48.16  | | | | | |   (99)  op(e1, e3) = e3
% 241.51/48.16  | | | | | | 
% 241.51/48.16  | | | | | | BETA: splitting (5) gives:
% 241.51/48.16  | | | | | | 
% 241.51/48.16  | | | | | | Case 1:
% 241.51/48.16  | | | | | | | 
% 241.51/48.16  | | | | | | |   (100)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 241.51/48.16  | | | | | | |            op(e0, e2) = e3)
% 241.51/48.16  | | | | | | | 
% 241.51/48.16  | | | | | | | REF_CLOSE: (6), (8), (17), (31), (37), (38), (43), (57), (71),
% 241.51/48.16  | | | | | | |            (76), (85), (98), (100) are inconsistent by sub-proof
% 241.51/48.16  | | | | | | |            #1167.
% 241.51/48.16  | | | | | | | 
% 241.51/48.16  | | | | | | Case 2:
% 241.51/48.16  | | | | | | | 
% 241.51/48.16  | | | | | | |   (101)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 241.51/48.16  | | | | | | |            op(e0, e0) = e3)
% 241.51/48.16  | | | | | | | 
% 241.51/48.16  | | | | | | | BETA: splitting (101) gives:
% 241.51/48.16  | | | | | | | 
% 241.51/48.16  | | | | | | | Case 1:
% 241.51/48.16  | | | | | | | | 
% 241.51/48.16  | | | | | | | |   (102)  all_58_14 = e3 & op(e0, e1) = e3
% 241.51/48.16  | | | | | | | | 
% 241.51/48.16  | | | | | | | | ALPHA: (102) implies:
% 241.51/48.16  | | | | | | | |   (103)  all_58_14 = e3
% 241.51/48.16  | | | | | | | | 
% 241.51/48.16  | | | | | | | | BETA: splitting (68) gives:
% 241.51/48.16  | | | | | | | | 
% 241.51/48.16  | | | | | | | | Case 1:
% 241.51/48.16  | | | | | | | | | 
% 241.51/48.16  | | | | | | | | |   (104)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 241.51/48.16  | | | | | | | | |            op(e1, e2) = e2)
% 241.51/48.16  | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | REF_CLOSE: (4), (6), (8), (21), (28), (30), (31), (35), (38),
% 241.51/48.16  | | | | | | | | |            (44), (49), (51), (60), (61), (64), (71), (76),
% 241.51/48.16  | | | | | | | | |            (80), (81), (85), (93), (103), (104) are
% 241.51/48.16  | | | | | | | | |            inconsistent by sub-proof #574.
% 241.51/48.16  | | | | | | | | | 
% 241.51/48.16  | | | | | | | | Case 2:
% 241.51/48.16  | | | | | | | | | 
% 241.51/48.16  | | | | | | | | |   (105)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 241.51/48.16  | | | | | | | | |            op(e1, e0) = e2)
% 241.51/48.16  | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | BETA: splitting (105) gives:
% 241.51/48.16  | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | Case 1:
% 241.51/48.16  | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | |   (106)  all_58_8 = e2 & op(e1, e1) = e2
% 241.51/48.16  | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | REF_CLOSE: (8), (18), (106) are inconsistent by sub-proof
% 241.51/48.16  | | | | | | | | | |            #683.
% 241.51/48.16  | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | Case 2:
% 241.51/48.16  | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | |   (107)  all_58_11 = e2 & op(e1, e0) = e2
% 241.51/48.16  | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | ALPHA: (107) implies:
% 241.51/48.16  | | | | | | | | | |   (108)  all_58_11 = e2
% 241.51/48.16  | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | BETA: splitting (90) gives:
% 241.51/48.16  | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | Case 1:
% 241.51/48.16  | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | |   (109)  all_54_1 = e2
% 241.51/48.16  | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | REF_CLOSE: (59), (67), (109) are inconsistent by sub-proof
% 241.51/48.16  | | | | | | | | | | |            #1928.
% 241.51/48.16  | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | Case 2:
% 241.51/48.16  | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | |   (110)   ~ (all_54_1 = e2)
% 241.51/48.16  | | | | | | | | | | |   (111)  all_54_1 = e1 | all_54_1 = e0
% 241.51/48.16  | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | BETA: splitting (111) gives:
% 241.51/48.16  | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | Case 1:
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | |   (112)  all_54_1 = e1
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | | REF_CLOSE: (59), (75), (112) are inconsistent by sub-proof
% 241.51/48.16  | | | | | | | | | | | |            #2051.
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | Case 2:
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | |   (113)  all_54_1 = e0
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | | COMBINE_EQS: (59), (113) imply:
% 241.51/48.16  | | | | | | | | | | | |   (114)  all_52_4 = e0
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | | SIMP: (114) implies:
% 241.51/48.16  | | | | | | | | | | | |   (115)  all_52_4 = e0
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | | REDUCE: (87), (115) imply:
% 241.51/48.16  | | | | | | | | | | | |   (116)   ~ (all_52_7 = e0)
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | | SIMP: (116) implies:
% 241.51/48.16  | | | | | | | | | | | |   (117)   ~ (all_52_7 = e0)
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | | REDUCE: (48), (115) imply:
% 241.51/48.16  | | | | | | | | | | | |   (118)   ~ (all_52_12 = e0)
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | | SIMP: (118) implies:
% 241.51/48.16  | | | | | | | | | | | |   (119)   ~ (all_52_12 = e0)
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | | REDUCE: (67), (115) imply:
% 241.51/48.16  | | | | | | | | | | | |   (120)   ~ (e2 = e0)
% 241.51/48.16  | | | | | | | | | | | | 
% 241.51/48.16  | | | | | | | | | | | | REDUCE: (75), (115) imply:
% 241.59/48.16  | | | | | | | | | | | |   (121)   ~ (e1 = e0)
% 241.59/48.16  | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | BETA: splitting (62) gives:
% 241.59/48.16  | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | |   (122)  all_54_13 = e3
% 241.59/48.16  | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | REF_CLOSE: (9), (17), (122) are inconsistent by sub-proof
% 241.59/48.16  | | | | | | | | | | | | |            #2010.
% 241.59/48.16  | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | Case 2:
% 241.59/48.16  | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | |   (123)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.59/48.16  | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | BETA: splitting (33) gives:
% 241.59/48.16  | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | |   (124)  all_54_3 = e3
% 241.59/48.16  | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | COMBINE_EQS: (69), (124) imply:
% 241.59/48.16  | | | | | | | | | | | | | |   (125)  all_52_12 = e3
% 241.59/48.16  | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | SIMP: (125) implies:
% 241.59/48.16  | | | | | | | | | | | | | |   (126)  all_52_12 = e3
% 241.59/48.16  | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | REDUCE: (27), (126) imply:
% 241.59/48.16  | | | | | | | | | | | | | |   (127)   ~ (all_52_13 = e3)
% 241.59/48.16  | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | SIMP: (127) implies:
% 241.59/48.16  | | | | | | | | | | | | | |   (128)   ~ (all_52_13 = e3)
% 241.59/48.16  | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | REDUCE: (25), (126) imply:
% 241.59/48.16  | | | | | | | | | | | | | |   (129)   ~ (all_52_14 = e3)
% 241.59/48.16  | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | SIMP: (129) implies:
% 241.59/48.16  | | | | | | | | | | | | | |   (130)   ~ (all_52_14 = e3)
% 241.59/48.16  | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | BETA: splitting (66) gives:
% 241.59/48.16  | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | |   (131)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 241.59/48.16  | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 241.59/48.16  | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 241.59/48.16  | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | |   (132)  all_58_9 = e3 & op(e3, e0) = e3
% 241.59/48.16  | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 241.59/48.16  | | | | | | | | | | | | | | | |   (133)  all_58_9 = e3
% 241.59/48.16  | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 241.59/48.16  | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | |   (134)  all_54_11 = e3
% 241.59/48.16  | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (130), (134) are inconsistent by sub-proof
% 241.59/48.16  | | | | | | | | | | | | | | | | |            #1998.
% 241.59/48.16  | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.16  | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | |   (135)   ~ (all_54_11 = e3)
% 241.59/48.16  | | | | | | | | | | | | | | | | |   (136)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 241.59/48.16  | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 241.59/48.16  | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | |   (137)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 241.59/48.16  | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21), (26), (30), (31), (35), (38),
% 241.59/48.16  | | | | | | | | | | | | | | | | | |            (44), (49), (51), (71), (76), (80), (81), (85),
% 241.59/48.16  | | | | | | | | | | | | | | | | | |            (93), (98), (103), (133), (137) are inconsistent
% 241.59/48.16  | | | | | | | | | | | | | | | | | |            by sub-proof #685.
% 241.59/48.16  | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | |   (138)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 241.59/48.16  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.59/48.16  | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | |   (139)  all_58_7 = e2 & op(e1, e2) = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | |   (140)  all_58_7 = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (31), (38), (51), (64), (71), (76),
% 241.59/48.16  | | | | | | | | | | | | | | | | | | |            (85), (93), (133), (140) are inconsistent by
% 241.59/48.16  | | | | | | | | | | | | | | | | | | |            sub-proof #571.
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | |   (141)  all_58_13 = e2 & op(e0, e2) = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | |   (142)  op(e0, e2) = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | |   (143)  all_58_15 = e0 & op(e0, e0) = e0
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | |   (144)  op(e0, e0) = e0
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (71), (76), (144) are inconsistent by
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | |   (145)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | |   (146)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | |   (147)  all_58_12 = e0 & op(e0, e3) = e0
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | |   (148)  all_58_12 = e0
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | |   (149)  op(e0, e3) = e0
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | |   (150)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | |   (151)  all_58_0 = e2 & op(e3, e3) = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | |   (152)  op(e3, e3) = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (71), (85), (152) are inconsistent by
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2267.
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | |   (153)  all_58_2 = e2 & op(e2, e3) = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | |   (154)  op(e2, e3) = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | |   (155)  all_54_11 = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (155) imply:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | |   (156)  all_52_14 = e2
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (156) imply:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | |   (157)   ~ (all_52_13 = e2)
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (130), (156) imply:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | |   (158)   ~ (e3 = e2)
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (159)  all_54_7 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (157), (159) are inconsistent by sub-proof
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | |            #1997.
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (160)   ~ (all_54_7 = e2)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (161)  all_54_7 = e1 | all_54_7 = e0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (162)  all_54_7 = e1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (56), (162) are inconsistent by sub-proof
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2295.
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (163)  all_54_7 = e0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (163) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (164)  all_52_13 = e0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (164) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (165)  all_52_13 = e0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (165) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (166)   ~ (all_52_1 = e0)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (165) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (167)   ~ (e3 = e0)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (168)  all_54_4 = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (80), (168) are inconsistent by sub-proof
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2100.
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (169)   ~ (all_54_4 = e3)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (170)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (171)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_3 & $i(all_56_3))
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (172)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (173)  op(e3, all_56_1) = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (173) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (174)  op(e3, e1) = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (175)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e1) = all_38_1 & $i(all_38_0) &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_38_1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (176)  op(e3, e1) = all_38_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (21), (30), (31), (34), (35), (44), (49),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (73), (76), (80), (81), (86), (94), (98),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (166), (170), (174), (176) are inconsistent
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #570.
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (177)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_38_1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (178)  op(e3, e1) = all_38_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (21), (30), (31), (34), (35), (44), (49),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (73), (76), (80), (81), (86), (94), (98),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (166), (170), (174), (178) are inconsistent
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #570.
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (179)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_3 & $i(all_56_3)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (180)  op(e2, e3) = all_56_3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (181)  op(e2, all_56_3) = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (182)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (183)  op(e2, e3) = all_8_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (184)  op(all_8_1, e2) = all_8_0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (185)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e3) = all_42_1 & $i(all_42_0) &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_42_1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (186)  op(e2, e3) = all_42_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (187)  op(all_42_1, e2) = all_42_0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_8_1, all_42_1, e3, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (183), (186) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_42_1 = all_8_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_42_1, all_56_3, e3,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (180), (186) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (189)  all_56_3 = all_42_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e2, all_56_3, e3, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (154), (180) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (190)  all_56_3 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (189), (190) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (191)  all_42_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (191) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (192)  all_42_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (188), (192) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (193)  all_8_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (193) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (194)  all_8_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (192) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  op(e2, e2) = all_42_0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (194) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  op(e2, e2) = all_8_0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (190) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (197)  op(e2, e2) = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e2, all_8_0, e2, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (196), (197) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (198)  all_8_0 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e3, all_42_0, e2, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (2), (195) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (199)  all_42_0 = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_8_0, all_42_0, e2, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (195), (196) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_42_0 = all_8_0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (200) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_8_0 = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (201) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (202)  all_8_0 = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21), (30), (31), (35), (38), (44),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (71), (76), (80), (81), (85), (98), (103),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (198), (202) are inconsistent by sub-proof #569.
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (203)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_42_1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (204)   ~ (all_42_1 = e1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (205)  op(e2, e3) = all_42_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_8_1, all_42_1, e3, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (183), (205) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (206)  all_42_1 = all_8_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_42_1, all_56_3, e3,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (180), (205) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (207)  all_56_3 = all_42_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e2, all_56_3, e3, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (154), (180) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (208)  all_56_3 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (208) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_42_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (209) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_42_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (210) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  all_8_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (211) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  all_8_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (212) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  op(e2, e2) = all_8_0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (208) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  op(e2, e2) = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e3, all_8_0, e2, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (2), (213) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_8_0 = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e2, all_8_0, e2, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (213), (214) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  all_8_0 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21), (30), (31), (35), (38), (44),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (71), (76), (80), (81), (85), (98), (103),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216) are inconsistent by sub-proof #569.
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_8_1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)   ~ (all_8_1 = e0)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  op(e2, e3) = all_8_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e3) = all_42_1 & $i(all_42_0) &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_42_1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  op(e2, e3) = all_42_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  op(all_42_1, e2) = all_42_0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_8_1, all_42_1, e3, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (219), (221) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  all_42_1 = all_8_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_42_1, all_56_3, e3,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (180), (221) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  all_56_3 = all_42_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e2, all_56_3, e3, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (154), (180) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  all_56_3 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (225) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  all_42_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (226) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  all_42_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (227) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  all_8_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  all_8_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (222), (227) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  op(e2, e2) = all_42_0
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (225) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  op(e2, e2) = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e3, all_42_0, e2, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (2), (230) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  all_42_0 = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e2, all_42_0, e2, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (230), (231) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  all_42_0 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (232), (233) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  e3 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (234) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_58_6 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21), (30), (31), (35), (38), (44),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (71), (76), (80), (81), (85), (103), (235)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1166.
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_42_1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (237)   ~ (all_42_1 = e1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (238)  op(e2, e3) = all_42_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_8_1, all_42_1, e3, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (219), (238) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (239)  all_42_1 = all_8_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_42_1, all_56_3, e3,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (180), (238) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (240)  all_56_3 = all_42_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e2, all_56_3, e3, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (154), (180) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (241)  all_56_3 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (240), (241) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_42_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (242) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (243)  all_42_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (243) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_8_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (244) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  all_8_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (241) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  op(e2, e2) = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e3, e2, e2, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (2), (246) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  e3 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (247) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)  all_58_6 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21), (30), (31), (35), (38), (44),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (71), (76), (80), (81), (85), (103), (248)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1166.
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (249)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_7 & $i(all_56_7))
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (250)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_5 & $i(all_56_5)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  op(e1, e3) = all_56_5
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)  op(e1, all_56_5) = e1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e3, all_56_5, e3, e1,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (99), (251) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)  all_56_5 = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21), (30), (31), (37), (38), (43),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (71), (76), (80), (85), (98), (251), (252),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (253) are inconsistent by sub-proof #568.
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_8_1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (255)   ~ (all_8_1 = e0)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  op(e2, e3) = all_8_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e3) = all_42_1 & $i(all_42_0) &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_42_1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  op(e2, e3) = all_42_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e3, all_56_5, e3, e1,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (99), (251) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  all_56_5 = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_8_1, all_42_1, e3, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (256), (258) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_42_1 = all_8_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e2, all_42_1, e3, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (154), (258) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  all_42_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (261) imply:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_8_1 = e2
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21), (30), (31), (37), (38), (43),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (71), (76), (80), (85), (98), (251), (252),
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (259) are inconsistent by sub-proof #568.
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_42_1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)   ~ (all_42_1 = e1)
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  op(e2, e3) = all_42_1
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e3, all_56_5, e3, e1,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (99), (251) gives:
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_56_5 = e3
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_8_1, all_42_1, e3, e2,
% 241.59/48.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (256), (265) gives:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_42_1 = all_8_1
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e2, all_42_1, e3, e2,
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (154), (265) gives:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_42_1 = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (268) imply:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_8_1 = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21), (30), (31), (37), (38), (43),
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (71), (76), (80), (85), (98), (251), (252),
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (266) are inconsistent by sub-proof #568.
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_7 & $i(all_56_7)
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (270) implies:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  op(e0, e3) = all_56_7
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  op(e0, all_56_7) = e0
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (34), (71), (76), (86), (149), (166), (170),
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (271), (272) are inconsistent by sub-proof #1153.
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | |   (273)  all_54_11 = e1 | all_54_11 = e0
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (40), (42), (273) are inconsistent by
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2174.
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |   (274)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_58_6 = e2 & op(e1, e3) = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | |   (276)  all_58_6 = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21), (30), (31), (35), (38), (44),
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | |            (49), (71), (76), (80), (81), (85), (103), (276)
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1166.
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | |   (277)  all_58_12 = e2 & op(e0, e3) = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_58_12 = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (278) imply:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | |   (279)  e2 = e0
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (279) imply:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_58_4 = e0
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (14), (26), (31), (38), (64), (71),
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | |            (76), (85), (133), (142), (280) are inconsistent
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #719.
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | |   (281)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |   (282)  all_58_13 = e0 & op(e0, e2) = e0
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |   (283)  op(e0, e2) = e0
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (57), (71), (117), (123), (283) are
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1965.
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |   (284)  all_58_14 = e0 & op(e0, e1) = e0
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |   (285)  all_58_14 = e0
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (285) imply:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |   (286)  e3 = e0
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (10), (11), (12), (14), (15),
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |            (20), (21), (24), (26), (28), (30), (31), (35),
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (43), (46), (49), (51),
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |            (52), (55), (60), (61), (65), (66), (68), (70),
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |            (71), (72), (74), (76), (77), (78), (79), (80),
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |            (81), (83), (85), (86), (98), (286) are
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #642.
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | |   (287)  all_58_10 = e3 & op(e2, e0) = e3
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 241.59/48.18  | | | | | | | | | | | | | | | |   (288)  all_58_10 = e3
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (20), (26), (38), (63), (70), (76),
% 241.59/48.18  | | | | | | | | | | | | | | | |            (85), (288) are inconsistent by sub-proof #1101.
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | |   (289)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 241.59/48.18  | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | |   (290)  all_58_11 = e3 & op(e1, e0) = e3
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 241.59/48.18  | | | | | | | | | | | | | | | |   (291)  all_58_11 = e3
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (291) imply:
% 241.59/48.18  | | | | | | | | | | | | | | | |   (292)  e3 = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | SIMP: (292) implies:
% 241.59/48.18  | | | | | | | | | | | | | | | |   (293)  e3 = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (293) imply:
% 241.59/48.18  | | | | | | | | | | | | | | | |   (294)  all_58_6 = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21), (30), (31), (35), (38), (44),
% 241.59/48.18  | | | | | | | | | | | | | | | |            (49), (71), (76), (80), (81), (85), (103), (294)
% 241.59/48.18  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1166.
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | |   (295)  all_58_15 = e3 & op(e0, e0) = e3
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (21), (30), (31), (37), (38), (43),
% 241.59/48.18  | | | | | | | | | | | | | | | |            (44), (49), (71), (76), (80), (85), (98), (295)
% 241.59/48.18  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1137.
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | |   (296)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.59/48.18  | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | REF_CLOSE: (23), (50), (69), (119), (296) are inconsistent by
% 241.59/48.18  | | | | | | | | | | | | | |            sub-proof #2286.
% 241.59/48.18  | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | 
% 241.59/48.18  | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | |   (297)  all_58_15 = e3 & op(e0, e0) = e3
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | | ALPHA: (297) implies:
% 241.59/48.18  | | | | | | | |   (298)  all_58_15 = e3
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | | REF_CLOSE: (6), (8), (21), (30), (31), (37), (38), (43), (44),
% 241.59/48.18  | | | | | | | |            (49), (71), (76), (80), (85), (98), (298) are
% 241.59/48.18  | | | | | | | |            inconsistent by sub-proof #1160.
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | End of split
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | End of split
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | Case 2:
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | |   (299)  all_58_12 = e3 & op(e0, e3) = e3
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | | ALPHA: (299) implies:
% 241.59/48.18  | | | | | |   (300)  all_58_12 = e3
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | | BETA: splitting (55) gives:
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | | Case 1:
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | |   (301)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 241.59/48.18  | | | | | | |            op(e2, e1) = e3)
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | | BETA: splitting (301) gives:
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | |   (302)  all_58_4 = e3 & op(e3, e1) = e3
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | | REF_CLOSE: (4), (9), (14), (17), (23), (26), (31), (33), (41),
% 241.59/48.18  | | | | | | | |            (45), (48), (50), (57), (59), (62), (64), (67), (69),
% 241.59/48.18  | | | | | | | |            (71), (75), (85), (87), (90), (302) are inconsistent
% 241.59/48.18  | | | | | | | |            by sub-proof #566.
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | |   (303)  all_58_5 = e3 & op(e2, e1) = e3
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | | REF_CLOSE: (36), (65), (71), (303) are inconsistent by sub-proof
% 241.59/48.18  | | | | | | | |            #1822.
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | End of split
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | Case 2:
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | |   (304)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 241.59/48.18  | | | | | | |            op(e0, e1) = e3)
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | | REF_CLOSE: (6), (8), (35), (38), (44), (71), (74), (76), (81),
% 241.59/48.18  | | | | | | |            (85), (300), (304) are inconsistent by sub-proof #844.
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | End of split
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | End of split
% 241.59/48.18  | | | | | 
% 241.59/48.18  | | | | End of split
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | Case 2:
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | |   (305)  all_58_5 = e2 & op(e2, e1) = e2
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | | ALPHA: (305) implies:
% 241.59/48.18  | | | |   (306)  all_58_5 = e2
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | | REF_CLOSE: (63), (85), (306) are inconsistent by sub-proof #1665.
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | End of split
% 241.59/48.18  | | | 
% 241.59/48.18  | | Case 2:
% 241.59/48.18  | | | 
% 241.59/48.18  | | |   (307)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 241.59/48.18  | | |            = e2)
% 241.59/48.18  | | | 
% 241.59/48.18  | | | BETA: splitting (307) gives:
% 241.59/48.18  | | | 
% 241.59/48.18  | | | Case 1:
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | |   (308)  all_58_8 = e2 & op(e1, e1) = e2
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | | ALPHA: (308) implies:
% 241.59/48.18  | | | |   (309)  all_58_8 = e2
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | | REF_CLOSE: (8), (18), (309) are inconsistent by sub-proof #1556.
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | Case 2:
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | |   (310)  all_58_14 = e2 & op(e0, e1) = e2
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | | ALPHA: (310) implies:
% 241.59/48.18  | | | |   (311)  all_58_14 = e2
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | | BETA: splitting (30) gives:
% 241.59/48.18  | | | | 
% 241.59/48.18  | | | | Case 1:
% 241.59/48.18  | | | | | 
% 241.59/48.18  | | | | |   (312)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2,
% 241.59/48.18  | | | | |              e3) = e3)
% 241.59/48.18  | | | | | 
% 241.59/48.18  | | | | | REF_CLOSE: (21), (31), (49), (71), (80), (312) are inconsistent by
% 241.59/48.18  | | | | |            sub-proof #1208.
% 241.59/48.18  | | | | | 
% 241.59/48.18  | | | | Case 2:
% 241.59/48.18  | | | | | 
% 241.59/48.18  | | | | |   (313)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0,
% 241.59/48.18  | | | | |              e3) = e3)
% 241.59/48.18  | | | | | 
% 241.59/48.18  | | | | | BETA: splitting (313) gives:
% 241.59/48.18  | | | | | 
% 241.59/48.18  | | | | | Case 1:
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | |   (314)  all_58_6 = e3 & op(e1, e3) = e3
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | | ALPHA: (314) implies:
% 241.59/48.18  | | | | | |   (315)  all_58_6 = e3
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | | REF_CLOSE: (5), (6), (8), (17), (21), (30), (31), (35), (37), (38),
% 241.59/48.18  | | | | | |            (43), (44), (49), (57), (71), (76), (80), (81), (85),
% 241.59/48.18  | | | | | |            (311), (315) are inconsistent by sub-proof #1159.
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | Case 2:
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | |   (316)  all_58_12 = e3 & op(e0, e3) = e3
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | | ALPHA: (316) implies:
% 241.59/48.18  | | | | | |   (317)  all_58_12 = e3
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | | BETA: splitting (28) gives:
% 241.59/48.18  | | | | | | 
% 241.59/48.18  | | | | | | Case 1:
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | |   (318)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 241.59/48.18  | | | | | | |            op(e3, e2) = e3)
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | | REF_CLOSE: (21), (31), (60), (61), (71), (318) are inconsistent by
% 241.59/48.18  | | | | | | |            sub-proof #1401.
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | Case 2:
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | |   (319)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 241.59/48.18  | | | | | | |            op(e3, e0) = e3)
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | | BETA: splitting (319) gives:
% 241.59/48.18  | | | | | | | 
% 241.59/48.18  | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | |   (320)  all_58_4 = e3 & op(e3, e1) = e3
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | | REF_CLOSE: (4), (9), (14), (17), (23), (26), (31), (33), (41),
% 241.59/48.18  | | | | | | | |            (45), (48), (50), (57), (59), (62), (64), (67), (69),
% 241.59/48.18  | | | | | | | |            (71), (75), (85), (87), (90), (320) are inconsistent
% 241.59/48.18  | | | | | | | |            by sub-proof #566.
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | |   (321)  all_58_9 = e3 & op(e3, e0) = e3
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | | ALPHA: (321) implies:
% 241.59/48.18  | | | | | | | |   (322)  all_58_9 = e3
% 241.59/48.18  | | | | | | | |   (323)  op(e3, e0) = e3
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | | BETA: splitting (55) gives:
% 241.59/48.18  | | | | | | | | 
% 241.59/48.18  | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | 
% 241.59/48.18  | | | | | | | | |   (324)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 241.59/48.18  | | | | | | | | |            op(e2, e1) = e3)
% 241.59/48.18  | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | BETA: splitting (324) gives:
% 241.59/48.18  | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | |   (325)  all_58_4 = e3 & op(e3, e1) = e3
% 241.59/48.18  | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | ALPHA: (325) implies:
% 241.59/48.18  | | | | | | | | | |   (326)  all_58_4 = e3
% 241.59/48.18  | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | BETA: splitting (90) gives:
% 241.59/48.18  | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | |   (327)  all_54_1 = e2
% 241.59/48.18  | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | REF_CLOSE: (59), (67), (327) are inconsistent by sub-proof
% 241.59/48.18  | | | | | | | | | | |            #1928.
% 241.59/48.18  | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | |   (328)   ~ (all_54_1 = e2)
% 241.59/48.18  | | | | | | | | | | |   (329)  all_54_1 = e1 | all_54_1 = e0
% 241.59/48.18  | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | BETA: splitting (329) gives:
% 241.59/48.18  | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | |   (330)  all_54_1 = e1
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | REF_CLOSE: (59), (75), (330) are inconsistent by sub-proof
% 241.59/48.18  | | | | | | | | | | | |            #2051.
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | |   (331)  all_54_1 = e0
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | COMBINE_EQS: (59), (331) imply:
% 241.59/48.18  | | | | | | | | | | | |   (332)  all_52_4 = e0
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | SIMP: (332) implies:
% 241.59/48.18  | | | | | | | | | | | |   (333)  all_52_4 = e0
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | REDUCE: (87), (333) imply:
% 241.59/48.18  | | | | | | | | | | | |   (334)   ~ (all_52_7 = e0)
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | SIMP: (334) implies:
% 241.59/48.18  | | | | | | | | | | | |   (335)   ~ (all_52_7 = e0)
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | REDUCE: (60), (333) imply:
% 241.59/48.18  | | | | | | | | | | | |   (336)   ~ (e3 = e0)
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | REDUCE: (67), (333) imply:
% 241.59/48.18  | | | | | | | | | | | |   (337)   ~ (e2 = e0)
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | REDUCE: (75), (333) imply:
% 241.59/48.18  | | | | | | | | | | | |   (338)   ~ (e1 = e0)
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | BETA: splitting (46) gives:
% 241.59/48.18  | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | |   (339)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 241.59/48.18  | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 241.59/48.18  | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (31), (37), (38), (43), (52),
% 241.59/48.18  | | | | | | | | | | | | |            (71), (76), (85), (317), (339) are inconsistent by
% 241.59/48.18  | | | | | | | | | | | | |            sub-proof #1136.
% 241.59/48.18  | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | |   (340)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 241.59/48.18  | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 241.59/48.18  | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | BETA: splitting (340) gives:
% 241.59/48.18  | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | |   (341)  all_58_8 = e3 & op(e1, e1) = e3
% 241.59/48.18  | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | REF_CLOSE: (6), (71), (74), (341) are inconsistent by
% 241.59/48.18  | | | | | | | | | | | | | |            sub-proof #2018.
% 241.59/48.18  | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | |   (342)  all_58_11 = e3 & op(e1, e0) = e3
% 241.59/48.18  | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | ALPHA: (342) implies:
% 241.59/48.18  | | | | | | | | | | | | | |   (343)  all_58_11 = e3
% 241.59/48.18  | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 241.59/48.18  | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | |   (344)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 241.59/48.18  | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | BETA: splitting (344) gives:
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | |   (345)  all_58_1 = e2 & op(e3, e2) = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | ALPHA: (345) implies:
% 241.59/48.18  | | | | | | | | | | | | | | | |   (346)  all_58_1 = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | |   (347)  all_54_13 = e3
% 241.59/48.18  | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17), (347) are inconsistent by sub-proof
% 241.59/48.18  | | | | | | | | | | | | | | | | |            #2010.
% 241.59/48.18  | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | |   (348)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.59/48.18  | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (14), (26), (41), (57), (64), (71),
% 241.59/48.18  | | | | | | | | | | | | | | | | |            (76), (335), (346), (348) are inconsistent by
% 241.59/48.18  | | | | | | | | | | | | | | | | |            sub-proof #567.
% 241.59/48.18  | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | |   (349)  all_58_3 = e2 & op(e2, e2) = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | REF_CLOSE: (26), (38), (349) are inconsistent by sub-proof
% 241.59/48.18  | | | | | | | | | | | | | | | |            #1458.
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | End of split
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | |   (350)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 241.59/48.18  | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | BETA: splitting (350) gives:
% 241.59/48.18  | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | |   (351)  all_58_7 = e2 & op(e1, e2) = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (16), (21), (24), (26), (28), (31),
% 241.59/48.18  | | | | | | | | | | | | | | | |            (38), (39), (49), (51), (60), (61), (64), (71),
% 241.59/48.18  | | | | | | | | | | | | | | | |            (76), (78), (83), (85), (86), (311), (326), (351)
% 241.59/48.18  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #573.
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | |   (352)  all_58_13 = e2 & op(e0, e2) = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | ALPHA: (352) implies:
% 241.59/48.18  | | | | | | | | | | | | | | | |   (353)  all_58_13 = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 241.59/48.18  | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | |   (354)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 241.59/48.18  | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 241.59/48.18  | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | BETA: splitting (354) gives:
% 241.59/48.18  | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | |   (355)  all_58_9 = e2 & op(e3, e0) = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | ALPHA: (355) implies:
% 241.59/48.18  | | | | | | | | | | | | | | | | | |   (356)  op(e3, e0) = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (71), (323), (356) are inconsistent by
% 241.59/48.18  | | | | | | | | | | | | | | | | | |            sub-proof #2125.
% 241.59/48.18  | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.18  | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | |   (357)  all_58_10 = e2 & op(e2, e0) = e2
% 241.59/48.18  | | | | | | | | | | | | | | | | | | 
% 241.59/48.18  | | | | | | | | | | | | | | | | | | ALPHA: (357) implies:
% 241.59/48.19  | | | | | | | | | | | | | | | | | |   (358)  op(e2, e0) = e2
% 241.59/48.19  | | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (35), (44), (71), (76), (322), (343),
% 241.59/48.19  | | | | | | | | | | | | | | | | | |            (358) are inconsistent by sub-proof #710.
% 241.59/48.19  | | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | | End of split
% 241.59/48.19  | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.19  | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | |   (359)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 241.59/48.19  | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.59/48.19  | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | | BETA: splitting (359) gives:
% 241.59/48.19  | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.19  | | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | | |   (360)  all_58_11 = e2 & op(e1, e0) = e2
% 241.59/48.19  | | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | | | ALPHA: (360) implies:
% 241.59/48.19  | | | | | | | | | | | | | | | | | |   (361)  all_58_11 = e2
% 241.59/48.19  | | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (343), (361) are inconsistent by sub-proof
% 241.59/48.19  | | | | | | | | | | | | | | | | | |            #2030.
% 241.59/48.19  | | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.19  | | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | | |   (362)  all_58_15 = e2 & op(e0, e0) = e2
% 241.59/48.19  | | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (11), (14), (26), (38), (44), (64),
% 241.59/48.19  | | | | | | | | | | | | | | | | | |            (76), (85), (353), (362) are inconsistent by
% 241.59/48.19  | | | | | | | | | | | | | | | | | |            sub-proof #565.
% 241.59/48.19  | | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | | End of split
% 241.59/48.19  | | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | | End of split
% 241.59/48.19  | | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | | End of split
% 241.59/48.19  | | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | | End of split
% 241.59/48.19  | | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | | End of split
% 241.59/48.19  | | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | | End of split
% 241.59/48.19  | | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | | End of split
% 241.59/48.19  | | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | End of split
% 241.59/48.19  | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | Case 2:
% 241.59/48.19  | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | |   (363)  all_58_5 = e3 & op(e2, e1) = e3
% 241.59/48.19  | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | | REF_CLOSE: (36), (65), (71), (363) are inconsistent by
% 241.59/48.19  | | | | | | | | | |            sub-proof #1822.
% 241.59/48.19  | | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | End of split
% 241.59/48.19  | | | | | | | | | 
% 241.59/48.19  | | | | | | | | Case 2:
% 241.59/48.19  | | | | | | | | | 
% 241.59/48.19  | | | | | | | | |   (364)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 241.59/48.19  | | | | | | | | |            op(e0, e1) = e3)
% 241.59/48.19  | | | | | | | | | 
% 241.59/48.19  | | | | | | | | | REF_CLOSE: (6), (8), (35), (38), (44), (71), (74), (76), (81),
% 241.59/48.19  | | | | | | | | |            (85), (317), (364) are inconsistent by sub-proof
% 241.59/48.19  | | | | | | | | |            #844.
% 241.59/48.19  | | | | | | | | | 
% 241.59/48.19  | | | | | | | | End of split
% 241.59/48.19  | | | | | | | | 
% 241.59/48.19  | | | | | | | End of split
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | End of split
% 241.59/48.19  | | | | | | 
% 241.59/48.19  | | | | | End of split
% 241.59/48.19  | | | | | 
% 241.59/48.19  | | | | End of split
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | End of split
% 241.59/48.19  | | | 
% 241.59/48.19  | | End of split
% 241.59/48.19  | | 
% 241.59/48.19  | End of split
% 241.59/48.19  | 
% 241.59/48.19  End of proof
% 241.59/48.19  
% 241.59/48.19  Sub-proof #565 shows that the following formulas are inconsistent:
% 241.59/48.19  ----------------------------------------------------------------
% 241.59/48.19    (1)   ~ (e3 = e0)
% 241.59/48.19    (2)   ~ (e2 = e0)
% 241.59/48.19    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.59/48.19         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.19    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.19         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.59/48.19    (5)  all_58_15 = e2 & op(e0, e0) = e2
% 241.59/48.19    (6)  all_58_3 = e3
% 241.59/48.19    (7)   ~ (e3 = e2)
% 241.59/48.19    (8)  all_58_15 = e1
% 241.59/48.19    (9)  all_58_13 = e2
% 241.59/48.19    (10)  all_58_7 = e1
% 241.59/48.19    (11)   ~ (e1 = e0)
% 241.59/48.19    (12)   ~ (e2 = e1)
% 241.59/48.19  
% 241.59/48.19  Begin of proof
% 241.59/48.19  | 
% 241.59/48.19  | ALPHA: (5) implies:
% 241.59/48.19  |   (13)  all_58_15 = e2
% 241.59/48.19  | 
% 241.59/48.19  | COMBINE_EQS: (8), (13) imply:
% 241.59/48.19  |   (14)  e2 = e1
% 241.59/48.19  | 
% 241.59/48.19  | COMBINE_EQS: (9), (14) imply:
% 241.59/48.19  |   (15)  all_58_13 = e1
% 241.59/48.19  | 
% 241.59/48.19  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (10), (11), (12), (15) are
% 241.59/48.19  |            inconsistent by sub-proof #1457.
% 241.59/48.19  | 
% 241.59/48.19  End of proof
% 241.59/48.19  
% 241.59/48.19  Sub-proof #566 shows that the following formulas are inconsistent:
% 241.59/48.19  ----------------------------------------------------------------
% 241.59/48.19    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.59/48.19         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.59/48.19    (2)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 241.59/48.19    (3)  all_54_13 = all_52_7
% 241.59/48.19    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.19         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.59/48.19    (5)   ~ (all_52_7 = e3)
% 241.59/48.19    (6)   ~ (all_52_12 = e1)
% 241.59/48.19    (7)  all_58_3 = e3
% 241.59/48.19    (8)  op(e3, e3) = e1
% 241.59/48.19    (9)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.59/48.19    (10)   ~ (all_52_7 = e1)
% 241.59/48.19    (11)  op(e3, e0) = all_52_12
% 241.59/48.19    (12)   ~ (all_52_4 = all_52_12)
% 241.59/48.19    (13)   ~ (all_52_12 = e2)
% 241.59/48.19    (14)  op(e0, e2) = all_52_7
% 241.59/48.19    (15)  all_54_1 = all_52_4
% 241.59/48.19    (16)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.59/48.19    (17)  all_58_7 = e1
% 241.59/48.19    (18)   ~ (all_52_4 = e2)
% 241.59/48.19    (19)  all_54_3 = all_52_12
% 241.59/48.19    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.19    (21)   ~ (all_52_4 = e1)
% 241.59/48.19    (22)  all_58_4 = e3 & op(e3, e1) = e3
% 241.59/48.19    (23)   ~ (e2 = e1)
% 241.59/48.19    (24)   ~ (all_52_4 = all_52_7)
% 241.59/48.19  
% 241.59/48.19  Begin of proof
% 241.59/48.19  | 
% 241.59/48.19  | ALPHA: (22) implies:
% 241.59/48.19  |   (25)  all_58_4 = e3
% 241.59/48.19  | 
% 241.59/48.19  | BETA: splitting (2) gives:
% 241.59/48.19  | 
% 241.59/48.19  | Case 1:
% 241.59/48.19  | | 
% 241.59/48.19  | |   (26)  all_54_1 = e2
% 241.59/48.19  | | 
% 241.59/48.19  | | REF_CLOSE: (15), (18), (26) are inconsistent by sub-proof #1928.
% 241.59/48.19  | | 
% 241.59/48.19  | Case 2:
% 241.59/48.19  | | 
% 241.59/48.19  | |   (27)  all_54_1 = e1 | all_54_1 = e0
% 241.59/48.19  | | 
% 241.59/48.19  | | BETA: splitting (27) gives:
% 241.59/48.19  | | 
% 241.59/48.19  | | Case 1:
% 241.59/48.19  | | | 
% 241.59/48.19  | | |   (28)  all_54_1 = e1
% 241.59/48.19  | | | 
% 241.59/48.19  | | | REF_CLOSE: (15), (21), (28) are inconsistent by sub-proof #2051.
% 241.59/48.19  | | | 
% 241.59/48.19  | | Case 2:
% 241.59/48.19  | | | 
% 241.59/48.19  | | |   (29)  all_54_1 = e0
% 241.59/48.19  | | | 
% 241.59/48.19  | | | COMBINE_EQS: (15), (29) imply:
% 241.59/48.19  | | |   (30)  all_52_4 = e0
% 241.59/48.19  | | | 
% 241.59/48.19  | | | SIMP: (30) implies:
% 241.59/48.19  | | |   (31)  all_52_4 = e0
% 241.59/48.19  | | | 
% 241.59/48.19  | | | REDUCE: (24), (31) imply:
% 241.59/48.19  | | |   (32)   ~ (all_52_7 = e0)
% 241.59/48.19  | | | 
% 241.59/48.19  | | | SIMP: (32) implies:
% 241.59/48.19  | | |   (33)   ~ (all_52_7 = e0)
% 241.59/48.19  | | | 
% 241.59/48.19  | | | REDUCE: (12), (31) imply:
% 241.59/48.19  | | |   (34)   ~ (all_52_12 = e0)
% 241.59/48.19  | | | 
% 241.59/48.19  | | | SIMP: (34) implies:
% 241.59/48.19  | | |   (35)   ~ (all_52_12 = e0)
% 241.59/48.19  | | | 
% 241.59/48.19  | | | REDUCE: (21), (31) imply:
% 241.59/48.19  | | |   (36)   ~ (e1 = e0)
% 241.59/48.19  | | | 
% 241.59/48.19  | | | SIMP: (36) implies:
% 241.59/48.19  | | |   (37)   ~ (e1 = e0)
% 241.59/48.19  | | | 
% 241.59/48.19  | | | BETA: splitting (9) gives:
% 241.59/48.19  | | | 
% 241.59/48.19  | | | Case 1:
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | |   (38)  all_54_3 = e3
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | | COMBINE_EQS: (19), (38) imply:
% 241.59/48.19  | | | |   (39)  all_52_12 = e3
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | | SIMP: (39) implies:
% 241.59/48.19  | | | |   (40)  all_52_12 = e3
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | | REDUCE: (13), (40) imply:
% 241.59/48.19  | | | |   (41)   ~ (e3 = e2)
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | | REDUCE: (35), (40) imply:
% 241.59/48.19  | | | |   (42)   ~ (e3 = e0)
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | | REDUCE: (11), (40) imply:
% 241.59/48.19  | | | |   (43)  op(e3, e0) = e3
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | | BETA: splitting (16) gives:
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | | Case 1:
% 241.59/48.19  | | | | | 
% 241.59/48.19  | | | | |   (44)  all_54_13 = e3
% 241.59/48.19  | | | | | 
% 241.59/48.19  | | | | | REF_CLOSE: (3), (5), (44) are inconsistent by sub-proof #2010.
% 241.59/48.19  | | | | | 
% 241.59/48.19  | | | | Case 2:
% 241.59/48.19  | | | | | 
% 241.59/48.19  | | | | |   (45)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.59/48.19  | | | | | 
% 241.59/48.19  | | | | | BETA: splitting (1) gives:
% 241.59/48.19  | | | | | 
% 241.59/48.19  | | | | | Case 1:
% 241.59/48.19  | | | | | | 
% 241.59/48.19  | | | | | |   (46)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3,
% 241.59/48.19  | | | | | |             e2) = e2)
% 241.59/48.19  | | | | | | 
% 241.59/48.19  | | | | | | BETA: splitting (46) gives:
% 241.59/48.19  | | | | | | 
% 241.59/48.19  | | | | | | Case 1:
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | |   (47)  all_58_0 = e2 & op(e3, e3) = e2
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | | ALPHA: (47) implies:
% 241.59/48.19  | | | | | | |   (48)  op(e3, e3) = e2
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | | REF_CLOSE: (8), (20), (23), (48) are inconsistent by sub-proof
% 241.59/48.19  | | | | | | |            #2267.
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | Case 2:
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | |   (49)  all_58_1 = e2 & op(e3, e2) = e2
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | | ALPHA: (49) implies:
% 241.59/48.19  | | | | | | |   (50)  all_58_1 = e2
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | | REF_CLOSE: (3), (4), (7), (10), (14), (17), (20), (33), (37),
% 241.59/48.19  | | | | | | |            (42), (45), (50) are inconsistent by sub-proof #567.
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | End of split
% 241.59/48.19  | | | | | | 
% 241.59/48.19  | | | | | Case 2:
% 241.59/48.19  | | | | | | 
% 241.59/48.19  | | | | | |   (51)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3,
% 241.59/48.19  | | | | | |             e0) = e2)
% 241.59/48.19  | | | | | | 
% 241.59/48.19  | | | | | | BETA: splitting (51) gives:
% 241.59/48.19  | | | | | | 
% 241.59/48.19  | | | | | | Case 1:
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | |   (52)  all_58_4 = e2 & op(e3, e1) = e2
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | | ALPHA: (52) implies:
% 241.59/48.19  | | | | | | |   (53)  all_58_4 = e2
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | | REF_CLOSE: (25), (41), (53) are inconsistent by sub-proof #1902.
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | Case 2:
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | |   (54)  all_58_9 = e2 & op(e3, e0) = e2
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | | ALPHA: (54) implies:
% 241.59/48.19  | | | | | | |   (55)  op(e3, e0) = e2
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | | REF_CLOSE: (20), (41), (43), (55) are inconsistent by sub-proof
% 241.59/48.19  | | | | | | |            #2125.
% 241.59/48.19  | | | | | | | 
% 241.59/48.19  | | | | | | End of split
% 241.59/48.19  | | | | | | 
% 241.59/48.19  | | | | | End of split
% 241.59/48.19  | | | | | 
% 241.59/48.19  | | | | End of split
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | Case 2:
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | |   (56)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | | REF_CLOSE: (6), (13), (19), (35), (56) are inconsistent by sub-proof
% 241.59/48.19  | | | |            #2286.
% 241.59/48.19  | | | | 
% 241.59/48.19  | | | End of split
% 241.59/48.19  | | | 
% 241.59/48.19  | | End of split
% 241.59/48.19  | | 
% 241.59/48.19  | End of split
% 241.59/48.19  | 
% 241.59/48.19  End of proof
% 241.59/48.19  
% 241.59/48.19  Sub-proof #567 shows that the following formulas are inconsistent:
% 241.59/48.19  ----------------------------------------------------------------
% 241.59/48.19    (1)   ~ (e3 = e0)
% 241.59/48.19    (2)  all_54_13 = all_52_7
% 241.59/48.19    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.19         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.59/48.19    (4)  all_58_3 = e3
% 241.59/48.19    (5)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.59/48.19    (6)   ~ (all_52_7 = e1)
% 241.59/48.19    (7)  op(e0, e2) = all_52_7
% 241.59/48.19    (8)   ~ (all_52_7 = e0)
% 241.59/48.19    (9)  all_58_7 = e1
% 241.59/48.19    (10)  all_58_1 = e2
% 241.59/48.19    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.19    (12)   ~ (e1 = e0)
% 241.59/48.19  
% 241.59/48.19  Begin of proof
% 241.59/48.19  | 
% 241.59/48.19  | BETA: splitting (5) gives:
% 241.59/48.19  | 
% 241.59/48.19  | Case 1:
% 241.59/48.19  | | 
% 241.59/48.19  | |   (13)  all_54_13 = e2
% 241.59/48.19  | | 
% 241.59/48.19  | | COMBINE_EQS: (2), (13) imply:
% 241.59/48.19  | |   (14)  all_52_7 = e2
% 241.59/48.19  | | 
% 241.59/48.19  | | SIMP: (14) implies:
% 241.59/48.19  | |   (15)  all_52_7 = e2
% 241.59/48.19  | | 
% 241.59/48.19  | | REDUCE: (8), (15) imply:
% 241.59/48.19  | |   (16)   ~ (e2 = e0)
% 241.59/48.19  | | 
% 241.59/48.19  | | REDUCE: (7), (15) imply:
% 241.59/48.19  | |   (17)  op(e0, e2) = e2
% 241.59/48.19  | | 
% 241.59/48.19  | | REF_CLOSE: (1), (3), (4), (9), (10), (11), (12), (16), (17) are inconsistent
% 241.59/48.19  | |            by sub-proof #1353.
% 241.59/48.19  | | 
% 241.59/48.19  | Case 2:
% 241.59/48.19  | | 
% 241.59/48.19  | |   (18)  all_54_13 = e1 | all_54_13 = e0
% 241.59/48.19  | | 
% 241.59/48.19  | | REF_CLOSE: (2), (6), (8), (18) are inconsistent by sub-proof #1793.
% 241.59/48.19  | | 
% 241.59/48.19  | End of split
% 241.59/48.19  | 
% 241.59/48.19  End of proof
% 241.59/48.19  
% 241.59/48.19  Sub-proof #568 shows that the following formulas are inconsistent:
% 241.59/48.19  ----------------------------------------------------------------
% 241.59/48.19    (1)   ~ (e3 = e0)
% 241.59/48.19    (2)  all_58_6 = e3
% 241.59/48.19    (3)   ~ (e2 = e0)
% 241.59/48.19    (4)  op(e1, all_56_5) = e1
% 241.59/48.19    (5)  op(e1, e3) = all_56_5
% 241.59/48.19    (6)   ~ (e3 = e1)
% 241.59/48.19    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.59/48.19         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.59/48.19    (8)  op(e3, e3) = e1
% 241.59/48.19    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.59/48.19         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.59/48.19    (10)   ~ (e3 = e2)
% 241.59/48.19    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.59/48.19          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.59/48.19    (12)  op(e2, e3) = all_52_1
% 241.59/48.19    (13)  all_56_5 = e3
% 241.59/48.19    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.19    (15)   ~ (e1 = e0)
% 241.59/48.19    (16)   ~ (all_52_1 = e3)
% 241.59/48.19    (17)   ~ (e2 = e1)
% 241.59/48.19  
% 241.59/48.19  Begin of proof
% 241.59/48.19  | 
% 241.59/48.19  | REDUCE: (4), (13) imply:
% 241.59/48.19  |   (18)  op(e1, e3) = e1
% 241.59/48.19  | 
% 241.59/48.19  | REDUCE: (5), (13) imply:
% 241.59/48.19  |   (19)  op(e1, e3) = e3
% 241.59/48.19  | 
% 241.59/48.19  | GROUND_INST: instantiating (14) with e3, e1, e3, e1, simplifying with (18),
% 241.59/48.19  |              (19) gives:
% 241.59/48.19  |   (20)  e3 = e1
% 241.59/48.19  | 
% 241.59/48.19  | COMBINE_EQS: (2), (20) imply:
% 241.59/48.19  |   (21)  all_58_6 = e1
% 241.59/48.19  | 
% 241.59/48.19  | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (12), (14), (15), (16),
% 241.59/48.19  |            (17), (21) are inconsistent by sub-proof #1161.
% 241.59/48.19  | 
% 241.59/48.19  End of proof
% 241.59/48.19  
% 241.59/48.19  Sub-proof #569 shows that the following formulas are inconsistent:
% 241.59/48.19  ----------------------------------------------------------------
% 241.59/48.19    (1)   ~ (e3 = e0)
% 241.59/48.19    (2)  all_58_6 = e3
% 241.59/48.19    (3)   ~ (e2 = e0)
% 241.59/48.19    (4)   ~ (e3 = e1)
% 241.59/48.19    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.59/48.19         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.59/48.19    (6)  op(e3, e3) = e1
% 241.59/48.19    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.19             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 241.59/48.19               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.59/48.19               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.59/48.19    (8)   ~ (e3 = e2)
% 241.59/48.19    (9)  all_8_0 = e2
% 241.59/48.19    (10)  all_8_0 = e3
% 241.59/48.19    (11)  all_58_15 = e1
% 241.59/48.19    (12)  op(e2, e3) = all_52_1
% 241.59/48.19    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.19    (14)  all_58_14 = e3
% 241.59/48.19    (15)   ~ (e1 = e0)
% 241.59/48.19    (16)   ~ (all_52_1 = e3)
% 241.59/48.19    (17)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.19          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.59/48.19            e2)
% 241.59/48.19    (18)   ~ (e2 = e1)
% 241.59/48.19  
% 241.59/48.19  Begin of proof
% 241.59/48.19  | 
% 241.59/48.19  | COMBINE_EQS: (9), (10) imply:
% 241.59/48.19  |   (19)  e3 = e2
% 241.59/48.19  | 
% 241.59/48.19  | SIMP: (19) implies:
% 241.59/48.19  |   (20)  e3 = e2
% 241.59/48.19  | 
% 241.59/48.19  | COMBINE_EQS: (2), (20) imply:
% 241.59/48.19  |   (21)  all_58_6 = e2
% 241.59/48.19  | 
% 241.59/48.19  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14), (15),
% 241.59/48.19  |            (16), (17), (18), (21) are inconsistent by sub-proof #1166.
% 241.59/48.19  | 
% 241.59/48.19  End of proof
% 241.59/48.19  
% 241.59/48.19  Sub-proof #570 shows that the following formulas are inconsistent:
% 241.59/48.19  ----------------------------------------------------------------
% 241.59/48.19    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 241.59/48.19    (2)   ~ (e3 = e0)
% 241.59/48.19    (3)  all_58_6 = e3
% 241.59/48.19    (4)   ~ (e3 = e1)
% 241.59/48.19    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.59/48.19         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.59/48.19    (6)  op(e3, e3) = e1
% 241.59/48.19    (7)  all_54_4 = all_52_1
% 241.59/48.19    (8)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.19             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 241.59/48.19               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.59/48.19               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.59/48.19    (9)  op(e3, e1) = all_38_1
% 241.59/48.19    (10)  all_58_15 = e1
% 241.59/48.19    (11)   ~ (all_52_1 = e0)
% 241.59/48.19    (12)  op(e2, e3) = all_52_1
% 241.59/48.19    (13)  op(e3, e1) = e2
% 241.59/48.19    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.19    (15)  all_58_14 = e3
% 241.59/48.19    (16)  op(e3, e1) = all_10_1
% 241.59/48.19    (17)  op(e3, e1) = e3
% 241.59/48.19    (18)   ~ (e1 = e0)
% 241.59/48.19    (19)   ~ (all_52_1 = e3)
% 241.59/48.19    (20)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.19          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.59/48.19            e2)
% 241.59/48.19    (21)   ~ (all_52_1 = e1)
% 241.59/48.19  
% 241.59/48.19  Begin of proof
% 241.59/48.19  | 
% 241.59/48.19  | BETA: splitting (1) gives:
% 241.59/48.19  | 
% 241.59/48.19  | Case 1:
% 241.59/48.19  | | 
% 241.59/48.19  | |   (22)  all_54_4 = e2
% 241.59/48.20  | | 
% 241.59/48.20  | | COMBINE_EQS: (7), (22) imply:
% 241.59/48.20  | |   (23)  all_52_1 = e2
% 241.59/48.20  | | 
% 241.59/48.20  | | SIMP: (23) implies:
% 241.59/48.20  | |   (24)  all_52_1 = e2
% 241.59/48.20  | | 
% 241.59/48.20  | | REDUCE: (19), (24) imply:
% 241.59/48.20  | |   (25)   ~ (e3 = e2)
% 241.59/48.20  | | 
% 241.59/48.20  | | SIMP: (25) implies:
% 241.59/48.20  | |   (26)   ~ (e3 = e2)
% 241.59/48.20  | | 
% 241.59/48.20  | | REDUCE: (21), (24) imply:
% 241.59/48.20  | |   (27)   ~ (e2 = e1)
% 241.59/48.20  | | 
% 241.59/48.20  | | REDUCE: (11), (24) imply:
% 241.59/48.20  | |   (28)   ~ (e2 = e0)
% 241.59/48.20  | | 
% 241.59/48.20  | | GROUND_INST: instantiating (14) with all_10_1, all_38_1, e1, e3, simplifying
% 241.59/48.20  | |              with (9), (16) gives:
% 241.59/48.20  | |   (29)  all_38_1 = all_10_1
% 241.59/48.20  | | 
% 241.59/48.20  | | GROUND_INST: instantiating (14) with e3, all_38_1, e1, e3, simplifying with
% 241.59/48.20  | |              (9), (17) gives:
% 241.59/48.20  | |   (30)  all_38_1 = e3
% 241.59/48.20  | | 
% 241.59/48.20  | | GROUND_INST: instantiating (14) with e2, all_38_1, e1, e3, simplifying with
% 241.59/48.20  | |              (9), (13) gives:
% 241.59/48.20  | |   (31)  all_38_1 = e2
% 241.59/48.20  | | 
% 241.59/48.20  | | COMBINE_EQS: (29), (31) imply:
% 241.59/48.20  | |   (32)  all_10_1 = e2
% 241.59/48.20  | | 
% 241.59/48.20  | | COMBINE_EQS: (29), (30) imply:
% 241.59/48.20  | |   (33)  all_10_1 = e3
% 241.59/48.20  | | 
% 241.59/48.20  | | COMBINE_EQS: (32), (33) imply:
% 241.59/48.20  | |   (34)  e3 = e2
% 241.59/48.20  | | 
% 241.59/48.20  | | COMBINE_EQS: (3), (34) imply:
% 241.59/48.20  | |   (35)  all_58_6 = e2
% 241.59/48.20  | | 
% 241.59/48.20  | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (12), (14), (15), (18), (19),
% 241.59/48.20  | |            (20), (26), (27), (28), (35) are inconsistent by sub-proof #1166.
% 241.59/48.20  | | 
% 241.59/48.20  | Case 2:
% 241.59/48.20  | | 
% 241.59/48.20  | |   (36)  all_54_4 = e1 | all_54_4 = e0
% 241.59/48.20  | | 
% 241.59/48.20  | | REF_CLOSE: (7), (11), (21), (36) are inconsistent by sub-proof #1922.
% 241.59/48.20  | | 
% 241.59/48.20  | End of split
% 241.59/48.20  | 
% 241.59/48.20  End of proof
% 241.59/48.20  
% 241.59/48.20  Sub-proof #571 shows that the following formulas are inconsistent:
% 241.59/48.20  ----------------------------------------------------------------
% 241.59/48.20    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.59/48.20         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.59/48.20    (2)   ~ (e3 = e0)
% 241.59/48.20    (3)   ~ (e2 = e0)
% 241.59/48.20    (4)  all_58_4 = e2
% 241.59/48.20    (5)  all_58_7 = e2
% 241.59/48.20    (6)  op(e3, e3) = e1
% 241.59/48.20    (7)   ~ (e3 = e2)
% 241.59/48.20    (8)  all_58_9 = e3
% 241.59/48.20    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.59/48.20         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.20    (10)  all_58_7 = e1
% 241.59/48.20    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.20    (12)   ~ (e1 = e0)
% 241.59/48.20    (13)   ~ (e2 = e1)
% 241.59/48.20  
% 241.59/48.20  Begin of proof
% 241.59/48.20  | 
% 241.59/48.20  | COMBINE_EQS: (5), (10) imply:
% 241.59/48.20  |   (14)  e2 = e1
% 241.59/48.20  | 
% 241.59/48.20  | COMBINE_EQS: (4), (14) imply:
% 241.59/48.20  |   (15)  all_58_4 = e1
% 241.59/48.20  | 
% 241.59/48.20  | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (11), (12), (13), (15) are
% 241.59/48.20  |            inconsistent by sub-proof #1469.
% 241.59/48.20  | 
% 241.59/48.20  End of proof
% 241.59/48.20  
% 241.59/48.20  Sub-proof #572 shows that the following formulas are inconsistent:
% 241.59/48.20  ----------------------------------------------------------------
% 241.59/48.20    (1)   ~ (e3 = e0)
% 241.59/48.20    (2)   ~ (e2 = e0)
% 241.59/48.20    (3)  all_58_3 = e3
% 241.59/48.20    (4)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.20             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 241.59/48.20               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.59/48.20               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.59/48.20    (5)  op(e2, e1) = all_52_9
% 241.59/48.20    (6)   ~ (e3 = e2)
% 241.59/48.20    (7)  all_58_15 = e1
% 241.59/48.20    (8)  all_58_3 = e2 & op(e2, e2) = e2
% 241.59/48.20    (9)  all_58_12 = e3
% 241.59/48.20    (10)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.59/48.20          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.59/48.20    (11)   ~ (all_52_9 = e3)
% 241.59/48.20    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.20    (13)  op(e1, e1) = e0
% 241.59/48.20    (14)   ~ (e1 = e0)
% 241.59/48.20    (15)  all_58_4 = e3
% 241.59/48.20    (16)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.20          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.59/48.20            e2)
% 241.59/48.20    (17)   ~ (e2 = e1)
% 241.59/48.20  
% 241.59/48.20  Begin of proof
% 241.59/48.20  | 
% 241.59/48.20  | ALPHA: (8) implies:
% 241.59/48.20  |   (18)  all_58_3 = e2
% 241.59/48.20  | 
% 241.59/48.20  | COMBINE_EQS: (3), (18) imply:
% 241.59/48.20  |   (19)  e3 = e2
% 241.59/48.20  | 
% 241.59/48.20  | COMBINE_EQS: (15), (19) imply:
% 241.59/48.20  |   (20)  all_58_4 = e2
% 241.59/48.20  | 
% 241.59/48.20  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 241.59/48.20  |            (16), (17), (20) are inconsistent by sub-proof #843.
% 241.59/48.20  | 
% 241.59/48.20  End of proof
% 241.59/48.20  
% 241.59/48.20  Sub-proof #573 shows that the following formulas are inconsistent:
% 241.59/48.20  ----------------------------------------------------------------
% 241.59/48.20    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.59/48.20         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.59/48.20    (2)   ~ (e3 = e0)
% 241.59/48.20    (3)   ~ (e2 = e0)
% 241.59/48.20    (4)   ~ (all_52_13 = e1)
% 241.59/48.20    (5)  all_58_14 = e2
% 241.59/48.20    (6)   ~ (e3 = e1)
% 241.59/48.20    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.59/48.20         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.59/48.20    (8)  all_58_3 = e3
% 241.59/48.20    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.59/48.20         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.59/48.20    (10)  op(e3, e3) = e1
% 241.59/48.20    (11)   ~ (e3 = e2)
% 241.59/48.20    (12)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.59/48.20          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.59/48.20    (13)  op(e2, e3) = all_52_1
% 241.59/48.20    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.59/48.20          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.20    (15)   ~ (all_52_4 = e3)
% 241.59/48.20    (16)  op(e3, e2) = all_52_4
% 241.59/48.20    (17)  all_58_7 = e1
% 241.59/48.20    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.20    (19)   ~ (e1 = e0)
% 241.59/48.20    (20)  all_58_7 = e2 & op(e1, e2) = e2
% 241.59/48.20    (21)  all_58_4 = e3
% 241.59/48.20    (22)  op(e2, e0) = all_52_13
% 241.59/48.20    (23)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.59/48.20          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.59/48.20    (24)   ~ (e2 = e1)
% 241.59/48.20    (25)   ~ (all_52_1 = e1)
% 241.59/48.20  
% 241.59/48.20  Begin of proof
% 241.59/48.20  | 
% 241.59/48.20  | ALPHA: (20) implies:
% 241.59/48.20  |   (26)  all_58_7 = e2
% 241.59/48.20  | 
% 241.59/48.20  | COMBINE_EQS: (17), (26) imply:
% 241.59/48.20  |   (27)  e2 = e1
% 241.59/48.20  | 
% 241.59/48.20  | SIMP: (27) implies:
% 241.59/48.20  |   (28)  e2 = e1
% 241.59/48.20  | 
% 241.59/48.20  | COMBINE_EQS: (5), (28) imply:
% 241.59/48.20  |   (29)  all_58_14 = e1
% 241.59/48.20  | 
% 241.59/48.20  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.59/48.20  |            (14), (15), (16), (18), (19), (21), (22), (23), (24), (25), (29)
% 241.59/48.20  |            are inconsistent by sub-proof #1029.
% 241.59/48.20  | 
% 241.59/48.20  End of proof
% 241.59/48.20  
% 241.59/48.20  Sub-proof #574 shows that the following formulas are inconsistent:
% 241.59/48.20  ----------------------------------------------------------------
% 241.59/48.20    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.59/48.20         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.59/48.20    (2)   ~ (e3 = e0)
% 241.59/48.20    (3)   ~ (e2 = e0)
% 241.59/48.20    (4)  all_58_4 = e2
% 241.59/48.20    (5)   ~ (e3 = e1)
% 241.59/48.20    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.59/48.20         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.59/48.20    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.59/48.20         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.59/48.20    (8)  op(e3, e3) = e1
% 241.59/48.20    (9)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.20             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 241.59/48.20               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.59/48.20               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.59/48.20    (10)   ~ (e3 = e2)
% 241.59/48.20    (11)  all_58_15 = e1
% 241.59/48.20    (12)  op(e2, e3) = all_52_1
% 241.59/48.20    (13)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 241.59/48.20    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.59/48.20          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.20    (15)   ~ (all_52_4 = e3)
% 241.59/48.20    (16)  op(e3, e2) = all_52_4
% 241.59/48.20    (17)  all_58_7 = e1
% 241.59/48.20    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.20    (19)  all_58_14 = e3
% 241.59/48.20    (20)   ~ (e1 = e0)
% 241.59/48.20    (21)   ~ (all_52_1 = e3)
% 241.59/48.20    (22)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.20          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.59/48.20            e2)
% 241.59/48.20    (23)   ~ (e2 = e1)
% 241.59/48.20  
% 241.59/48.20  Begin of proof
% 241.59/48.20  | 
% 241.59/48.20  | BETA: splitting (13) gives:
% 241.59/48.20  | 
% 241.59/48.20  | Case 1:
% 241.59/48.20  | | 
% 241.59/48.20  | |   (24)  all_58_6 = e2 & op(e1, e3) = e2
% 241.59/48.20  | | 
% 241.59/48.20  | | ALPHA: (24) implies:
% 241.59/48.20  | |   (25)  all_58_6 = e2
% 241.59/48.20  | | 
% 241.59/48.20  | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (11), (12), (18), (19), (20),
% 241.59/48.20  | |            (21), (22), (23), (25) are inconsistent by sub-proof #1166.
% 241.59/48.20  | | 
% 241.59/48.20  | Case 2:
% 241.59/48.20  | | 
% 241.59/48.20  | |   (26)  all_58_7 = e2 & op(e1, e2) = e2
% 241.59/48.20  | | 
% 241.59/48.20  | | ALPHA: (26) implies:
% 241.59/48.20  | |   (27)  all_58_7 = e2
% 241.59/48.20  | | 
% 241.59/48.20  | | COMBINE_EQS: (17), (27) imply:
% 241.59/48.20  | |   (28)  e2 = e1
% 241.59/48.20  | | 
% 241.59/48.20  | | SIMP: (28) implies:
% 241.59/48.20  | |   (29)  e2 = e1
% 241.59/48.20  | | 
% 241.59/48.20  | | COMBINE_EQS: (4), (29) imply:
% 241.59/48.20  | |   (30)  all_58_4 = e1
% 241.59/48.20  | | 
% 241.59/48.20  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10), (14), (15), (16), (18), (20),
% 241.59/48.20  | |            (23), (30) are inconsistent by sub-proof #1468.
% 241.59/48.20  | | 
% 241.59/48.20  | End of split
% 241.59/48.20  | 
% 241.59/48.20  End of proof
% 241.59/48.20  
% 241.59/48.20  Sub-proof #575 shows that the following formulas are inconsistent:
% 241.59/48.20  ----------------------------------------------------------------
% 241.59/48.20    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.59/48.20         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.59/48.20    (2)   ~ (e3 = e0)
% 241.59/48.20    (3)   ~ (all_52_7 = e2)
% 241.59/48.20    (4)   ~ (e2 = e0)
% 241.59/48.20    (5)  all_54_13 = all_52_7
% 241.59/48.20    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.59/48.20         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.20    (7)  all_58_4 = e2
% 241.59/48.20    (8)   ~ (all_52_7 = e3)
% 241.59/48.20    (9)  all_58_3 = e3
% 241.59/48.20    (10)  op(e3, e3) = e1
% 241.59/48.20    (11)   ~ (e3 = e2)
% 241.59/48.20    (12)   ~ (all_52_7 = e1)
% 241.59/48.20    (13)  all_58_9 = e3
% 241.59/48.20    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.59/48.20          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.20    (15)  op(e0, e2) = all_52_7
% 241.59/48.20    (16)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.59/48.20    (17)  all_58_7 = e1
% 241.59/48.20    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.20    (19)   ~ (e1 = e0)
% 241.59/48.20    (20)   ~ (e2 = e1)
% 241.59/48.20  
% 241.59/48.20  Begin of proof
% 241.59/48.20  | 
% 241.59/48.20  | BETA: splitting (16) gives:
% 241.59/48.20  | 
% 241.59/48.20  | Case 1:
% 241.59/48.20  | | 
% 241.59/48.20  | |   (21)  all_54_13 = e3
% 241.59/48.20  | | 
% 241.59/48.20  | | COMBINE_EQS: (5), (21) imply:
% 241.59/48.20  | |   (22)  all_52_7 = e3
% 241.59/48.20  | | 
% 241.59/48.20  | | REDUCE: (8), (22) imply:
% 241.59/48.20  | |   (23)  $false
% 241.59/48.20  | | 
% 241.59/48.20  | | CLOSE: (23) is inconsistent.
% 241.59/48.20  | | 
% 241.59/48.20  | Case 2:
% 241.59/48.20  | | 
% 241.59/48.20  | |   (24)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 241.59/48.20  | | 
% 241.59/48.20  | | BETA: splitting (6) gives:
% 241.59/48.20  | | 
% 241.59/48.20  | | Case 1:
% 241.59/48.20  | | | 
% 241.59/48.20  | | |   (25)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 241.59/48.20  | | |           e2)
% 241.59/48.20  | | | 
% 241.59/48.20  | | | BETA: splitting (25) gives:
% 241.59/48.20  | | | 
% 241.59/48.20  | | | Case 1:
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | |   (26)  all_58_1 = e2 & op(e3, e2) = e2
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | | ALPHA: (26) implies:
% 241.59/48.20  | | | |   (27)  all_58_1 = e2
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | | REF_CLOSE: (2), (4), (7), (10), (13), (14), (18), (19), (27) are
% 241.59/48.20  | | | |            inconsistent by sub-proof #708.
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | Case 2:
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | |   (28)  all_58_3 = e2 & op(e2, e2) = e2
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | | REF_CLOSE: (9), (11), (28) are inconsistent by sub-proof #1458.
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | End of split
% 241.59/48.20  | | | 
% 241.59/48.20  | | Case 2:
% 241.59/48.20  | | | 
% 241.59/48.20  | | |   (29)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 241.59/48.20  | | |           e2)
% 241.59/48.20  | | | 
% 241.59/48.20  | | | BETA: splitting (29) gives:
% 241.59/48.20  | | | 
% 241.59/48.20  | | | Case 1:
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | |   (30)  all_58_7 = e2 & op(e1, e2) = e2
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | | ALPHA: (30) implies:
% 241.59/48.20  | | | |   (31)  all_58_7 = e2
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | | COMBINE_EQS: (17), (31) imply:
% 241.59/48.20  | | | |   (32)  e2 = e1
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | | REF_CLOSE: (1), (2), (4), (7), (10), (11), (13), (14), (18), (19), (20),
% 241.59/48.20  | | | |            (32) are inconsistent by sub-proof #714.
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | Case 2:
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | |   (33)  all_58_13 = e2 & op(e0, e2) = e2
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | | ALPHA: (33) implies:
% 241.59/48.20  | | | |   (34)  op(e0, e2) = e2
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | | REF_CLOSE: (3), (5), (12), (15), (18), (24), (34) are inconsistent by
% 241.59/48.20  | | | |            sub-proof #1817.
% 241.59/48.20  | | | | 
% 241.59/48.20  | | | End of split
% 241.59/48.20  | | | 
% 241.59/48.20  | | End of split
% 241.59/48.20  | | 
% 241.59/48.20  | End of split
% 241.59/48.20  | 
% 241.59/48.20  End of proof
% 241.59/48.20  
% 241.59/48.20  Sub-proof #576 shows that the following formulas are inconsistent:
% 241.59/48.20  ----------------------------------------------------------------
% 241.59/48.20    (1)   ~ (e3 = e0)
% 241.59/48.20    (2)   ~ (e2 = e0)
% 241.59/48.20    (3)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 241.59/48.20    (4)   ~ (e3 = e1)
% 241.59/48.20    (5)  all_58_3 = e3
% 241.59/48.20    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.59/48.20         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.59/48.20    (7)  op(e3, e3) = e1
% 241.59/48.20    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.59/48.20         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.59/48.20    (9)   ~ (e3 = e2)
% 241.59/48.20    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.59/48.20          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.59/48.20    (11)  op(e2, e3) = all_52_1
% 241.59/48.20    (12)  all_58_12 = e3
% 241.59/48.21    (13)  op(e3, e2) = all_52_4
% 241.59/48.21    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.21    (15)   ~ (all_52_4 = e1)
% 241.59/48.21    (16)   ~ (e1 = e0)
% 241.59/48.21    (17)   ~ (all_52_1 = e3)
% 241.59/48.21    (18)   ~ (e2 = e1)
% 241.59/48.21  
% 241.59/48.21  Begin of proof
% 241.59/48.21  | 
% 241.59/48.21  | BETA: splitting (3) gives:
% 241.59/48.21  | 
% 241.59/48.21  | Case 1:
% 241.59/48.21  | | 
% 241.59/48.21  | |   (19)  all_58_1 = e1 & op(e3, e2) = e1
% 241.59/48.21  | | 
% 241.59/48.21  | | ALPHA: (19) implies:
% 241.59/48.21  | |   (20)  op(e3, e2) = e1
% 241.59/48.21  | | 
% 241.59/48.21  | | REF_CLOSE: (13), (14), (15), (20) are inconsistent by sub-proof #2228.
% 241.59/48.21  | | 
% 241.59/48.21  | Case 2:
% 241.59/48.21  | | 
% 241.59/48.21  | |   (21)  all_58_3 = e1 & op(e2, e2) = e1
% 241.59/48.21  | | 
% 241.59/48.21  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 241.59/48.21  | |            (16), (17), (18), (21) are inconsistent by sub-proof #738.
% 241.59/48.21  | | 
% 241.59/48.21  | End of split
% 241.59/48.21  | 
% 241.59/48.21  End of proof
% 241.59/48.21  
% 241.59/48.21  Sub-proof #577 shows that the following formulas are inconsistent:
% 241.59/48.21  ----------------------------------------------------------------
% 241.59/48.21    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.59/48.21         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.59/48.21    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.59/48.21         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.59/48.21    (3)   ~ (e3 = e0)
% 241.59/48.21    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.59/48.21         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.59/48.21    (5)   ~ (e2 = e0)
% 241.59/48.21    (6)  op(e1, e2) = all_52_6
% 241.59/48.21    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.59/48.21         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.21    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.59/48.21         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.59/48.21    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.21         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.59/48.21    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.59/48.21          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.59/48.21    (11)   ~ (all_52_7 = e3)
% 241.59/48.21    (12)  all_58_8 = e0
% 241.59/48.21    (13)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.59/48.21          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.59/48.21    (14)   ~ (e3 = e1)
% 241.59/48.21    (15)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.59/48.21          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.59/48.21    (16)  all_58_3 = e3
% 241.59/48.21    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.59/48.21          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.59/48.21    (18)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.59/48.21          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.59/48.21    (19)  op(e3, e3) = e1
% 241.59/48.21    (20)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.21              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.59/48.21                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.59/48.21                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.59/48.21    (21)  op(e2, e1) = all_52_9
% 241.59/48.21    (22)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.59/48.21          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.59/48.21    (23)   ~ (e3 = e2)
% 241.59/48.21    (24)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.59/48.21          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.59/48.21    (25)  op(e2, e0) = e0
% 241.59/48.21    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.59/48.21          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.59/48.21    (27)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.59/48.21          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.59/48.21    (28)  all_58_10 = e0
% 241.59/48.21    (29)  all_58_12 = e0
% 241.59/48.21    (30)  op(e2, e3) = all_52_1
% 241.59/48.21    (31)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.59/48.21          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.21    (32)   ~ (all_52_6 = e3)
% 241.59/48.21    (33)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.59/48.21          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.59/48.21    (34)  op(e0, e2) = all_52_7
% 241.59/48.21    (35)   ~ (all_52_4 = e3)
% 241.59/48.21    (36)  op(e3, e2) = all_52_4
% 241.59/48.21    (37)  all_58_14 = e0
% 241.59/48.21    (38)  all_58_5 = e1
% 241.59/48.21    (39)   ~ (all_52_9 = e3)
% 241.59/48.21    (40)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.59/48.21          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.59/48.21    (41)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.59/48.21          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.59/48.21    (42)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.21          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.59/48.21    (43)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.21    (44)  op(e0, e0) = e0
% 241.59/48.21    (45)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.59/48.21          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.59/48.21    (46)  op(e1, e1) = e0
% 241.59/48.21    (47)   ~ (e1 = e0)
% 241.59/48.21    (48)  all_58_4 = e3
% 241.59/48.21    (49)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.59/48.21          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.59/48.21    (50)  op(e2, e0) = all_52_13
% 241.59/48.21    (51)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.59/48.21          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.59/48.21            e1)
% 241.59/48.21    (52)   ~ (all_52_1 = e3)
% 241.59/48.21    (53)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.21          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.59/48.21            e2)
% 241.59/48.21    (54)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.59/48.21          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.59/48.21    (55)   ~ (e2 = e1)
% 241.59/48.21    (56)   ~ (all_52_1 = e1)
% 241.59/48.21  
% 241.59/48.21  Begin of proof
% 241.59/48.21  | 
% 241.59/48.21  | BETA: splitting (51) gives:
% 241.59/48.21  | 
% 241.59/48.21  | Case 1:
% 241.59/48.21  | | 
% 241.59/48.21  | |   (57)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 241.59/48.21  | |           e1)
% 241.59/48.21  | | 
% 241.59/48.21  | | BETA: splitting (57) gives:
% 241.59/48.21  | | 
% 241.59/48.21  | | Case 1:
% 241.59/48.21  | | | 
% 241.59/48.21  | | |   (58)  all_58_12 = e1 & op(e0, e3) = e1
% 241.59/48.21  | | | 
% 241.59/48.21  | | | ALPHA: (58) implies:
% 241.59/48.21  | | |   (59)  all_58_12 = e1
% 241.59/48.21  | | | 
% 241.59/48.21  | | | REF_CLOSE: (3), (5), (14), (18), (19), (22), (23), (26), (30), (43), (47),
% 241.59/48.21  | | |            (52), (55), (59) are inconsistent by sub-proof #1204.
% 241.59/48.21  | | | 
% 241.59/48.21  | | Case 2:
% 241.59/48.21  | | | 
% 241.59/48.21  | | |   (60)  all_58_13 = e1 & op(e0, e2) = e1
% 241.59/48.21  | | | 
% 241.59/48.21  | | | ALPHA: (60) implies:
% 241.59/48.21  | | |   (61)  all_58_13 = e1
% 241.59/48.21  | | | 
% 241.59/48.21  | | | BETA: splitting (18) gives:
% 241.59/48.21  | | | 
% 241.59/48.21  | | | Case 1:
% 241.59/48.21  | | | | 
% 241.59/48.21  | | | |   (62)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 241.59/48.21  | | | |           = e3)
% 241.59/48.21  | | | | 
% 241.59/48.21  | | | | REF_CLOSE: (14), (19), (30), (43), (52), (62) are inconsistent by
% 241.59/48.21  | | | |            sub-proof #1208.
% 241.59/48.21  | | | | 
% 241.59/48.21  | | | Case 2:
% 241.59/48.21  | | | | 
% 241.59/48.21  | | | |   (63)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 241.59/48.21  | | | |           = e3)
% 241.59/48.21  | | | | 
% 241.59/48.21  | | | | BETA: splitting (63) gives:
% 241.59/48.21  | | | | 
% 241.59/48.21  | | | | Case 1:
% 241.59/48.21  | | | | | 
% 241.59/48.21  | | | | |   (64)  all_58_6 = e3 & op(e1, e3) = e3
% 241.59/48.21  | | | | | 
% 241.59/48.21  | | | | | ALPHA: (64) implies:
% 241.59/48.21  | | | | |   (65)  all_58_6 = e3
% 241.59/48.21  | | | | | 
% 241.59/48.21  | | | | | BETA: splitting (8) gives:
% 241.59/48.21  | | | | | 
% 241.59/48.21  | | | | | Case 1:
% 241.59/48.21  | | | | | | 
% 241.59/48.21  | | | | | |   (66)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 241.59/48.21  | | | | | |             e0) = e1)
% 241.59/48.21  | | | | | | 
% 241.59/48.21  | | | | | | BETA: splitting (66) gives:
% 241.59/48.21  | | | | | | 
% 241.59/48.21  | | | | | | Case 1:
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | |   (67)  all_58_9 = e1 & op(e3, e0) = e1
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | | ALPHA: (67) implies:
% 241.59/48.21  | | | | | | |   (68)  all_58_9 = e1
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (13),
% 241.59/48.21  | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.59/48.21  | | | | | | |            (23), (24), (26), (27), (30), (31), (32), (33), (35),
% 241.59/48.21  | | | | | | |            (36), (39), (40), (41), (42), (43), (45), (46), (47),
% 241.59/48.21  | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 241.59/48.21  | | | | | | |            (65), (68) are inconsistent by sub-proof #641.
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | Case 2:
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | |   (69)  all_58_10 = e1 & op(e2, e0) = e1
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | | ALPHA: (69) implies:
% 241.59/48.21  | | | | | | |   (70)  all_58_10 = e1
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | | REF_CLOSE: (3), (5), (13), (16), (23), (38), (42), (47), (55),
% 241.59/48.21  | | | | | | |            (70) are inconsistent by sub-proof #992.
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | End of split
% 241.59/48.21  | | | | | | 
% 241.59/48.21  | | | | | Case 2:
% 241.59/48.21  | | | | | | 
% 241.59/48.21  | | | | | |   (71)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 241.59/48.21  | | | | | |           op(e0, e0) = e1)
% 241.59/48.21  | | | | | | 
% 241.59/48.21  | | | | | | BETA: splitting (71) gives:
% 241.59/48.21  | | | | | | 
% 241.59/48.21  | | | | | | Case 1:
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | |   (72)  all_58_11 = e1 & op(e1, e0) = e1
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | | ALPHA: (72) implies:
% 241.59/48.21  | | | | | | |   (73)  all_58_11 = e1
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | | BETA: splitting (31) gives:
% 241.59/48.21  | | | | | | | 
% 241.59/48.21  | | | | | | | Case 1:
% 241.59/48.21  | | | | | | | | 
% 241.59/48.21  | | | | | | | |   (74)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 241.59/48.21  | | | | | | | |           op(e3, e2) = e0)
% 241.59/48.21  | | | | | | | | 
% 241.59/48.21  | | | | | | | | BETA: splitting (74) gives:
% 241.59/48.21  | | | | | | | | 
% 241.59/48.21  | | | | | | | | Case 1:
% 241.59/48.21  | | | | | | | | | 
% 241.59/48.21  | | | | | | | | |   (75)  all_58_0 = e0 & op(e3, e3) = e0
% 241.59/48.21  | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | ALPHA: (75) implies:
% 241.59/48.21  | | | | | | | | |   (76)  op(e3, e3) = e0
% 241.59/48.21  | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | REF_CLOSE: (19), (43), (47), (76) are inconsistent by
% 241.59/48.21  | | | | | | | | |            sub-proof #1828.
% 241.59/48.21  | | | | | | | | | 
% 241.59/48.21  | | | | | | | | Case 2:
% 241.59/48.21  | | | | | | | | | 
% 241.59/48.21  | | | | | | | | |   (77)  all_58_1 = e0 & op(e3, e2) = e0
% 241.59/48.21  | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | ALPHA: (77) implies:
% 241.59/48.21  | | | | | | | | |   (78)  all_58_1 = e0
% 241.59/48.21  | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | BETA: splitting (2) gives:
% 241.59/48.21  | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | Case 1:
% 241.59/48.21  | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | |   (79)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3
% 241.59/48.21  | | | | | | | | | |           & op(e0, e2) = e3)
% 241.59/48.21  | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (11), (14), (17), (19), (22),
% 241.59/48.21  | | | | | | | | | |            (23), (26), (27), (31), (32), (34), (35), (36),
% 241.59/48.21  | | | | | | | | | |            (43), (46), (47), (48), (55), (73), (79) are
% 241.59/48.21  | | | | | | | | | |            inconsistent by sub-proof #617.
% 241.59/48.21  | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | Case 2:
% 241.59/48.21  | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | |   (80)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3
% 241.59/48.21  | | | | | | | | | |           & op(e0, e0) = e3)
% 241.59/48.21  | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | BETA: splitting (80) gives:
% 241.59/48.21  | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | Case 1:
% 241.59/48.21  | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | |   (81)  all_58_14 = e3 & op(e0, e1) = e3
% 241.59/48.21  | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 241.59/48.21  | | | | | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20),
% 241.59/48.21  | | | | | | | | | | |            (21), (22), (23), (24), (26), (27), (30), (31),
% 241.59/48.21  | | | | | | | | | | |            (32), (33), (35), (36), (37), (39), (40), (41),
% 241.59/48.21  | | | | | | | | | | |            (42), (43), (45), (46), (47), (49), (50), (51),
% 241.59/48.21  | | | | | | | | | | |            (52), (53), (54), (55), (56), (65), (81) are
% 241.59/48.21  | | | | | | | | | | |            inconsistent by sub-proof #595.
% 241.59/48.21  | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | Case 2:
% 241.59/48.21  | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | |   (82)  all_58_15 = e3 & op(e0, e0) = e3
% 241.59/48.21  | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | ALPHA: (82) implies:
% 241.59/48.21  | | | | | | | | | | |   (83)  all_58_15 = e3
% 241.59/48.21  | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | BETA: splitting (41) gives:
% 241.59/48.21  | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | Case 1:
% 241.59/48.21  | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | |   (84)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.59/48.21  | | | | | | | | | | | |           & op(e1, e2) = e2)
% 241.59/48.21  | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | BETA: splitting (84) gives:
% 241.59/48.21  | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | Case 1:
% 241.59/48.21  | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | |   (85)  all_58_6 = e2 & op(e1, e3) = e2
% 241.59/48.21  | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | ALPHA: (85) implies:
% 241.59/48.21  | | | | | | | | | | | | |   (86)  all_58_6 = e2
% 241.59/48.21  | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | REF_CLOSE: (23), (65), (86) are inconsistent by sub-proof
% 241.59/48.21  | | | | | | | | | | | | |            #2024.
% 241.59/48.21  | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | Case 2:
% 241.59/48.21  | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | |   (87)  all_58_7 = e2 & op(e1, e2) = e2
% 241.59/48.21  | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | ALPHA: (87) implies:
% 241.59/48.21  | | | | | | | | | | | | |   (88)  all_58_7 = e2
% 241.59/48.21  | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | BETA: splitting (22) gives:
% 241.59/48.21  | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | Case 1:
% 241.59/48.21  | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | |   (89)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 241.59/48.21  | | | | | | | | | | | | | |           & op(e2, e3) = e2)
% 241.59/48.21  | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 241.59/48.21  | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | Case 1:
% 241.59/48.21  | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | |   (90)  all_58_0 = e2 & op(e3, e3) = e2
% 241.59/48.21  | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | ALPHA: (90) implies:
% 241.59/48.21  | | | | | | | | | | | | | | |   (91)  op(e3, e3) = e2
% 241.59/48.21  | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | REF_CLOSE: (19), (43), (55), (91) are inconsistent by
% 241.59/48.21  | | | | | | | | | | | | | | |            sub-proof #2267.
% 241.59/48.21  | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | Case 2:
% 241.59/48.21  | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | |   (92)  all_58_2 = e2 & op(e2, e3) = e2
% 241.59/48.21  | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 241.59/48.21  | | | | | | | | | | | | | | |   (93)  all_58_2 = e2
% 241.59/48.21  | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 241.59/48.21  | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | Case 1:
% 241.59/48.21  | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | |   (94)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 241.59/48.21  | | | | | | | | | | | | | | | |           & op(e3, e2) = e2)
% 241.59/48.21  | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 241.59/48.21  | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.21  | | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | | |   (95)  all_58_0 = e2 & op(e3, e3) = e2
% 241.59/48.21  | | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 241.59/48.21  | | | | | | | | | | | | | | | | |   (96)  op(e3, e3) = e2
% 241.59/48.21  | | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (43), (55), (96) are inconsistent by
% 241.59/48.21  | | | | | | | | | | | | | | | | |            sub-proof #2267.
% 241.59/48.21  | | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.21  | | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | | |   (97)  all_58_1 = e2 & op(e3, e2) = e2
% 241.59/48.21  | | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 241.59/48.21  | | | | | | | | | | | | | | | | |   (98)  all_58_1 = e2
% 241.59/48.21  | | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (98) imply:
% 241.59/48.21  | | | | | | | | | | | | | | | | |   (99)  e2 = e0
% 241.59/48.21  | | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | | | SIMP: (99) implies:
% 241.59/48.21  | | | | | | | | | | | | | | | | |   (100)  e2 = e0
% 241.59/48.21  | | | | | | | | | | | | | | | | | 
% 241.59/48.21  | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (100) imply:
% 241.59/48.21  | | | | | | | | | | | | | | | | |   (101)  all_58_2 = e0
% 241.59/48.21  | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (12), (13), (14),
% 241.59/48.22  | | | | | | | | | | | | | | | | |            (15), (16), (17), (18), (19), (21), (22), (23),
% 241.59/48.22  | | | | | | | | | | | | | | | | |            (24), (25), (26), (28), (30), (31), (33), (35),
% 241.59/48.22  | | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 241.59/48.22  | | | | | | | | | | | | | | | | |            (44), (45), (47), (48), (49), (51), (52), (54),
% 241.59/48.22  | | | | | | | | | | | | | | | | |            (55), (56), (61), (65), (73), (78), (83), (101)
% 241.59/48.22  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #597.
% 241.59/48.22  | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | |   (102)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 241.59/48.22  | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 241.59/48.22  | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 241.59/48.22  | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.22  | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | |   (103)  all_58_4 = e2 & op(e3, e1) = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 241.59/48.22  | | | | | | | | | | | | | | | | |   (104)  all_58_4 = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (48), (104) are inconsistent by sub-proof
% 241.59/48.22  | | | | | | | | | | | | | | | | |            #1902.
% 241.59/48.22  | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | |   (105)  all_58_9 = e2 & op(e3, e0) = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 241.59/48.22  | | | | | | | | | | | | | | | | |   (106)  all_58_9 = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | |   (107)  op(e3, e0) = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 241.59/48.22  | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | |   (108)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 241.59/48.22  | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |   (109)  all_58_4 = e2 & op(e3, e1) = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (48), (109) are inconsistent by sub-proof
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            #1476.
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |   (110)  all_58_5 = e2 & op(e2, e1) = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (9), (13), (14), (15), (16),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (23), (24), (26),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (28), (30), (33), (35), (36), (38), (39), (41),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (42), (43), (44), (47), (49), (51), (52), (54),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (55), (56), (88), (110) are inconsistent by
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            sub-proof #623.
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | |   (111)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 241.59/48.22  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 241.59/48.22  | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | Case 1:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |   (112)  all_58_8 = e2 & op(e1, e1) = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |   (113)  all_58_8 = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (113) imply:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |   (114)  e2 = e0
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | SIMP: (114) implies:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |   (115)  e2 = e0
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (115) imply:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |   (116)  all_58_2 = e0
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (12), (13), (14),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (15), (16), (17), (18), (19), (21), (22), (23),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (24), (25), (26), (28), (30), (31), (33), (35),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (44), (45), (47), (48), (49), (51), (52), (54),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (55), (56), (61), (65), (73), (78), (83), (106),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (107), (116) are inconsistent by sub-proof #598.
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |   (117)  all_58_14 = e2 & op(e0, e1) = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |   (118)  all_58_14 = e2
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (118) imply:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |   (119)  e2 = e0
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (119) imply:
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |   (120)  all_58_2 = e0
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (12), (13), (14),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (15), (16), (17), (18), (19), (21), (22), (23),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (24), (25), (26), (28), (30), (31), (33), (35),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (44), (45), (47), (48), (49), (51), (52), (54),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (55), (56), (61), (65), (73), (78), (83), (106),
% 241.59/48.22  | | | | | | | | | | | | | | | | | | |            (107), (120) are inconsistent by sub-proof #598.
% 241.59/48.22  | | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | |   (121)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 241.59/48.22  | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 241.59/48.22  | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | | REF_CLOSE: (5), (23), (29), (65), (121) are inconsistent by
% 241.59/48.22  | | | | | | | | | | | | | |            sub-proof #635.
% 241.59/48.22  | | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | |   (122)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.59/48.22  | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | BETA: splitting (122) gives:
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | Case 1:
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | |   (123)  all_58_8 = e2 & op(e1, e1) = e2
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | REF_CLOSE: (5), (12), (123) are inconsistent by sub-proof
% 241.59/48.22  | | | | | | | | | | | | |            #683.
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | |   (124)  all_58_11 = e2 & op(e1, e0) = e2
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | ALPHA: (124) implies:
% 241.59/48.22  | | | | | | | | | | | | |   (125)  all_58_11 = e2
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | REF_CLOSE: (55), (73), (125) are inconsistent by sub-proof
% 241.59/48.22  | | | | | | | | | | | | |            #1020.
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | 
% 241.59/48.22  | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | 
% 241.59/48.22  | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | 
% 241.59/48.22  | | | | | | | |   (126)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 241.59/48.22  | | | | | | | |            op(e3, e0) = e0)
% 241.59/48.22  | | | | | | | | 
% 241.59/48.22  | | | | | | | | BETA: splitting (126) gives:
% 241.59/48.22  | | | | | | | | 
% 241.59/48.22  | | | | | | | | Case 1:
% 241.59/48.22  | | | | | | | | | 
% 241.59/48.22  | | | | | | | | |   (127)  all_58_4 = e0 & op(e3, e1) = e0
% 241.59/48.22  | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | ALPHA: (127) implies:
% 241.59/48.22  | | | | | | | | |   (128)  all_58_4 = e0
% 241.59/48.22  | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | COMBINE_EQS: (48), (128) imply:
% 241.59/48.22  | | | | | | | | |   (129)  e3 = e0
% 241.59/48.22  | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (13),
% 241.59/48.22  | | | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21),
% 241.59/48.22  | | | | | | | | |            (22), (23), (24), (26), (27), (30), (31), (32),
% 241.59/48.22  | | | | | | | | |            (33), (35), (36), (39), (40), (41), (42), (43),
% 241.59/48.22  | | | | | | | | |            (45), (46), (47), (49), (50), (51), (52), (53),
% 241.59/48.22  | | | | | | | | |            (54), (55), (56), (65), (129) are inconsistent by
% 241.59/48.22  | | | | | | | | |            sub-proof #642.
% 241.59/48.22  | | | | | | | | | 
% 241.59/48.22  | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | 
% 241.59/48.22  | | | | | | | | |   (130)  all_58_9 = e0 & op(e3, e0) = e0
% 241.59/48.22  | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | ALPHA: (130) implies:
% 241.59/48.22  | | | | | | | | |   (131)  all_58_9 = e0
% 241.59/48.22  | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | BETA: splitting (22) gives:
% 241.59/48.22  | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | Case 1:
% 241.59/48.22  | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | |   (132)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 241.59/48.22  | | | | | | | | | |            & op(e2, e3) = e2)
% 241.59/48.22  | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | BETA: splitting (132) gives:
% 241.59/48.22  | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | Case 1:
% 241.59/48.22  | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | |   (133)  all_58_0 = e2 & op(e3, e3) = e2
% 241.59/48.22  | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | ALPHA: (133) implies:
% 241.59/48.22  | | | | | | | | | | |   (134)  op(e3, e3) = e2
% 241.59/48.22  | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | REF_CLOSE: (19), (43), (55), (134) are inconsistent by
% 241.59/48.22  | | | | | | | | | | |            sub-proof #2267.
% 241.59/48.22  | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | |   (135)  all_58_2 = e2 & op(e2, e3) = e2
% 241.59/48.22  | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | ALPHA: (135) implies:
% 241.59/48.22  | | | | | | | | | | |   (136)  all_58_2 = e2
% 241.59/48.22  | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | BETA: splitting (2) gives:
% 241.59/48.22  | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | Case 1:
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | |   (137)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 241.59/48.22  | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | REF_CLOSE: (3), (5), (11), (19), (26), (34), (43), (47),
% 241.59/48.22  | | | | | | | | | | | |            (65), (136), (137) are inconsistent by sub-proof
% 241.59/48.22  | | | | | | | | | | | |            #630.
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | |   (138)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 241.59/48.22  | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | BETA: splitting (138) gives:
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | Case 1:
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | |   (139)  all_58_14 = e3 & op(e0, e1) = e3
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 241.59/48.22  | | | | | | | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20),
% 241.59/48.22  | | | | | | | | | | | | |            (21), (22), (23), (24), (26), (27), (30), (31),
% 241.59/48.22  | | | | | | | | | | | | |            (32), (33), (35), (36), (37), (39), (40), (41),
% 241.59/48.22  | | | | | | | | | | | | |            (42), (43), (45), (46), (47), (49), (50), (51),
% 241.59/48.22  | | | | | | | | | | | | |            (52), (53), (54), (55), (56), (65), (139) are
% 241.59/48.22  | | | | | | | | | | | | |            inconsistent by sub-proof #595.
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | |   (140)  all_58_15 = e3 & op(e0, e0) = e3
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | ALPHA: (140) implies:
% 241.59/48.22  | | | | | | | | | | | | |   (141)  all_58_15 = e3
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (14), (16), (19), (22), (23), (29),
% 241.59/48.22  | | | | | | | | | | | | |            (30), (42), (43), (45), (47), (48), (54), (55),
% 241.59/48.22  | | | | | | | | | | | | |            (56), (65), (73), (131), (141) are inconsistent by
% 241.59/48.22  | | | | | | | | | | | | |            sub-proof #613.
% 241.59/48.22  | | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | Case 2:
% 241.59/48.22  | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | |   (142)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2
% 241.59/48.22  | | | | | | | | | |            & op(e0, e3) = e2)
% 241.59/48.22  | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | | REF_CLOSE: (5), (23), (29), (65), (142) are inconsistent by
% 241.59/48.22  | | | | | | | | | |            sub-proof #635.
% 241.59/48.22  | | | | | | | | | | 
% 241.59/48.22  | | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | | 
% 241.59/48.22  | | | | | | | | End of split
% 241.59/48.22  | | | | | | | | 
% 241.59/48.22  | | | | | | | End of split
% 241.59/48.22  | | | | | | | 
% 241.59/48.22  | | | | | | Case 2:
% 241.59/48.22  | | | | | | | 
% 241.59/48.22  | | | | | | |   (143)  all_58_15 = e1 & op(e0, e0) = e1
% 241.59/48.22  | | | | | | | 
% 241.59/48.22  | | | | | | | ALPHA: (143) implies:
% 241.59/48.22  | | | | | | |   (144)  op(e0, e0) = e1
% 241.59/48.22  | | | | | | | 
% 241.59/48.22  | | | | | | | REF_CLOSE: (43), (44), (47), (144) are inconsistent by sub-proof
% 241.59/48.22  | | | | | | |            #2274.
% 241.59/48.22  | | | | | | | 
% 241.59/48.22  | | | | | | End of split
% 241.59/48.22  | | | | | | 
% 241.59/48.22  | | | | | End of split
% 241.59/48.22  | | | | | 
% 241.59/48.22  | | | | Case 2:
% 241.59/48.22  | | | | | 
% 241.59/48.22  | | | | |   (145)  all_58_12 = e3 & op(e0, e3) = e3
% 241.59/48.22  | | | | | 
% 241.59/48.22  | | | | | REF_CLOSE: (3), (29), (145) are inconsistent by sub-proof #581.
% 241.59/48.22  | | | | | 
% 241.59/48.22  | | | | End of split
% 241.59/48.22  | | | | 
% 241.59/48.22  | | | End of split
% 241.59/48.22  | | | 
% 241.59/48.22  | | End of split
% 241.59/48.22  | | 
% 241.59/48.22  | Case 2:
% 241.59/48.22  | | 
% 241.59/48.22  | |   (146)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.59/48.22  | |            e1)
% 241.59/48.22  | | 
% 241.59/48.22  | | REF_CLOSE: (3), (5), (15), (23), (24), (38), (43), (44), (47), (48), (55),
% 241.59/48.22  | |            (146) are inconsistent by sub-proof #607.
% 241.59/48.22  | | 
% 241.59/48.22  | End of split
% 241.59/48.22  | 
% 241.59/48.22  End of proof
% 241.59/48.22  
% 241.59/48.22  Sub-proof #578 shows that the following formulas are inconsistent:
% 241.59/48.22  ----------------------------------------------------------------
% 241.59/48.22    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.59/48.22         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.59/48.22    (2)   ~ (e3 = e0)
% 241.59/48.22    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.59/48.22         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.59/48.22    (4)  all_58_6 = e3
% 241.59/48.22    (5)   ~ (e2 = e0)
% 241.59/48.22    (6)  op(e1, e2) = all_52_6
% 241.59/48.22    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.59/48.22         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.22    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.59/48.22         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.59/48.22    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.22         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.59/48.22    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.59/48.22          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.59/48.22    (11)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.59/48.22          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.59/48.22    (12)   ~ (e3 = e1)
% 241.59/48.22    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.59/48.22          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.59/48.22    (14)  all_58_3 = e3
% 241.59/48.22    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.59/48.22          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.59/48.22    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.59/48.22          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.59/48.22    (17)  op(e3, e3) = e1
% 241.59/48.22    (18)  all_58_3 = e0 & op(e2, e2) = e0
% 241.59/48.22    (19)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.22              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.59/48.22                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.59/48.22                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.59/48.22    (20)  op(e2, e1) = all_52_9
% 241.59/48.22    (21)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.59/48.22          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.59/48.22    (22)   ~ (e3 = e2)
% 241.59/48.22    (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.59/48.22          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.59/48.22    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.59/48.22          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.59/48.22    (25)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.59/48.22          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.59/48.22    (26)  op(e2, e3) = all_52_1
% 241.59/48.22    (27)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.59/48.22          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.22    (28)   ~ (all_52_6 = e3)
% 241.59/48.22    (29)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.59/48.22          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.59/48.22    (30)   ~ (all_52_4 = e3)
% 241.59/48.22    (31)  op(e3, e2) = all_52_4
% 241.59/48.22    (32)   ~ (all_52_9 = e3)
% 241.59/48.22    (33)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.59/48.22          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.59/48.22    (34)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.59/48.22          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.59/48.22    (35)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.22          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.59/48.22    (36)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.23    (37)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.59/48.23          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.59/48.23    (38)  op(e1, e1) = e0
% 241.59/48.23    (39)   ~ (e1 = e0)
% 241.59/48.23    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.59/48.23          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.59/48.23    (41)  op(e2, e0) = all_52_13
% 241.59/48.23    (42)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.59/48.23          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.59/48.23            e1)
% 241.59/48.23    (43)   ~ (all_52_1 = e3)
% 241.59/48.23    (44)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.23          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.59/48.23            e2)
% 241.59/48.23    (45)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.59/48.23          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.59/48.23    (46)   ~ (e2 = e1)
% 241.59/48.23    (47)   ~ (all_52_1 = e1)
% 241.59/48.23  
% 241.59/48.23  Begin of proof
% 241.59/48.23  | 
% 241.59/48.23  | ALPHA: (18) implies:
% 241.59/48.23  |   (48)  all_58_3 = e0
% 241.59/48.23  | 
% 241.59/48.23  | COMBINE_EQS: (14), (48) imply:
% 241.59/48.23  |   (49)  e3 = e0
% 241.59/48.23  | 
% 241.59/48.23  | COMBINE_EQS: (4), (49) imply:
% 241.59/48.23  |   (50)  all_58_6 = e0
% 241.59/48.23  | 
% 241.59/48.23  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.59/48.23  |            (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 241.59/48.23  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 241.59/48.23  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 241.59/48.23  |            (50) are inconsistent by sub-proof #664.
% 241.59/48.23  | 
% 241.59/48.23  End of proof
% 241.59/48.23  
% 241.59/48.23  Sub-proof #579 shows that the following formulas are inconsistent:
% 241.59/48.23  ----------------------------------------------------------------
% 241.59/48.23    (1)   ~ (e3 = e0)
% 241.59/48.23    (2)   ~ (e2 = e0)
% 241.59/48.23    (3)   ~ (e3 = e1)
% 241.59/48.23    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.59/48.23         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.59/48.23    (5)  op(e3, e3) = e1
% 241.59/48.23    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.59/48.23         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.59/48.23    (7)   ~ (e3 = e2)
% 241.59/48.23    (8)  op(e2, e3) = all_52_1
% 241.59/48.23    (9)  all_58_12 = e3
% 241.59/48.23    (10)  all_58_2 = e0
% 241.59/48.23    (11)  all_58_11 = e3 & op(e1, e0) = e3
% 241.59/48.23    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.23    (13)  all_58_11 = e0
% 241.59/48.23    (14)   ~ (all_52_1 = e3)
% 241.59/48.23    (15)   ~ (e2 = e1)
% 241.59/48.23  
% 241.59/48.23  Begin of proof
% 241.59/48.23  | 
% 241.59/48.23  | ALPHA: (11) implies:
% 241.59/48.23  |   (16)  all_58_11 = e3
% 241.59/48.23  | 
% 241.59/48.23  | COMBINE_EQS: (13), (16) imply:
% 241.59/48.23  |   (17)  e3 = e0
% 241.59/48.23  | 
% 241.59/48.23  | COMBINE_EQS: (9), (17) imply:
% 241.59/48.23  |   (18)  all_58_12 = e0
% 241.59/48.23  | 
% 241.59/48.23  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (14), (15),
% 241.59/48.23  |            (18) are inconsistent by sub-proof #1149.
% 241.59/48.23  | 
% 241.59/48.23  End of proof
% 241.59/48.23  
% 241.59/48.23  Sub-proof #580 shows that the following formulas are inconsistent:
% 241.59/48.23  ----------------------------------------------------------------
% 241.59/48.23    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.59/48.23         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.59/48.23    (2)   ~ (e3 = e0)
% 241.59/48.23    (3)   ~ (e2 = e0)
% 241.59/48.23    (4)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 241.59/48.23         (all_58_11 = e0 & op(e1, e0) = e0)
% 241.59/48.23    (5)   ~ (e3 = e1)
% 241.59/48.23    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.59/48.23         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.59/48.23    (7)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.59/48.23    (8)  op(e3, e3) = e1
% 241.59/48.23    (9)   ~ (e3 = e2)
% 241.59/48.23    (10)  all_58_9 = e3
% 241.59/48.23    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.59/48.23          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.23    (12)   ~ (all_52_4 = e3)
% 241.59/48.23    (13)  op(e3, e2) = all_52_4
% 241.59/48.23    (14)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.59/48.23          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.59/48.23    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.23    (16)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.59/48.23          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.59/48.23    (17)  op(e1, e1) = e0
% 241.59/48.23    (18)   ~ (e1 = e0)
% 241.59/48.23    (19)  all_58_14 = e1
% 241.59/48.23    (20)  all_58_10 = e1
% 241.59/48.23    (21)   ~ (e2 = e1)
% 241.59/48.23  
% 241.59/48.23  Begin of proof
% 241.59/48.23  | 
% 241.59/48.23  | BETA: splitting (7) gives:
% 241.59/48.23  | 
% 241.59/48.23  | Case 1:
% 241.59/48.23  | | 
% 241.59/48.23  | |   (22)  all_58_8 = e3 & op(e1, e1) = e3
% 241.59/48.23  | | 
% 241.59/48.23  | | REF_CLOSE: (2), (15), (17), (22) are inconsistent by sub-proof #2018.
% 241.59/48.23  | | 
% 241.59/48.23  | Case 2:
% 241.59/48.23  | | 
% 241.59/48.23  | |   (23)  all_58_14 = e3 & op(e0, e1) = e3
% 241.59/48.23  | | 
% 241.59/48.23  | | ALPHA: (23) implies:
% 241.59/48.23  | |   (24)  all_58_14 = e3
% 241.59/48.23  | | 
% 241.59/48.23  | | COMBINE_EQS: (19), (24) imply:
% 241.59/48.23  | |   (25)  e3 = e1
% 241.59/48.23  | | 
% 241.59/48.23  | | COMBINE_EQS: (10), (25) imply:
% 241.59/48.23  | |   (26)  all_58_9 = e1
% 241.59/48.23  | | 
% 241.59/48.23  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 241.59/48.23  | |            (15), (16), (18), (20), (21), (26) are inconsistent by sub-proof
% 241.59/48.23  | |            #1168.
% 241.59/48.23  | | 
% 241.59/48.23  | End of split
% 241.59/48.23  | 
% 241.59/48.23  End of proof
% 241.59/48.23  
% 241.59/48.23  Sub-proof #581 shows that the following formulas are inconsistent:
% 241.59/48.23  ----------------------------------------------------------------
% 241.59/48.23    (1)  all_58_12 = e3 & op(e0, e3) = e3
% 241.59/48.23    (2)  all_58_12 = e0
% 241.59/48.23    (3)   ~ (e3 = e0)
% 241.59/48.23  
% 241.59/48.23  Begin of proof
% 241.59/48.23  | 
% 241.59/48.23  | ALPHA: (1) implies:
% 241.59/48.23  |   (4)  all_58_12 = e3
% 241.59/48.23  | 
% 241.59/48.23  | COMBINE_EQS: (2), (4) imply:
% 241.59/48.23  |   (5)  e3 = e0
% 241.59/48.23  | 
% 241.59/48.23  | REDUCE: (3), (5) imply:
% 241.59/48.23  |   (6)  $false
% 241.59/48.23  | 
% 241.59/48.23  | CLOSE: (6) is inconsistent.
% 241.59/48.23  | 
% 241.59/48.23  End of proof
% 241.59/48.23  
% 241.59/48.23  Sub-proof #582 shows that the following formulas are inconsistent:
% 241.59/48.23  ----------------------------------------------------------------
% 241.59/48.23    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.59/48.23         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.59/48.23    (2)   ~ (e3 = e0)
% 241.59/48.23    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.59/48.23         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.59/48.23    (4)  all_58_6 = e3
% 241.59/48.23    (5)   ~ (e2 = e0)
% 241.59/48.23    (6)  op(e1, e2) = all_52_6
% 241.59/48.23    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.59/48.23         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.23    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.59/48.23         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.59/48.23    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.23         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.59/48.23    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.59/48.23          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.59/48.23    (11)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.59/48.23          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.59/48.23    (12)   ~ (e3 = e1)
% 241.59/48.23    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.59/48.23          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.59/48.23    (14)  all_58_3 = e3
% 241.59/48.23    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.59/48.23          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.59/48.23    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.59/48.23          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.59/48.23    (17)  op(e3, e3) = e1
% 241.59/48.23    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.23              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.59/48.23                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.59/48.23                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.59/48.23    (19)  op(e2, e1) = all_52_9
% 241.59/48.23    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.59/48.23          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.59/48.23    (21)   ~ (e3 = e2)
% 241.59/48.23    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.59/48.23          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.59/48.23    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.59/48.23          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.59/48.23    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.59/48.23          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.59/48.23    (25)  op(e2, e3) = all_52_1
% 241.59/48.23    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.59/48.23          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.23    (27)   ~ (all_52_6 = e3)
% 241.59/48.23    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.59/48.23          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.59/48.23    (29)   ~ (all_52_4 = e3)
% 241.59/48.23    (30)  op(e3, e2) = all_52_4
% 241.59/48.23    (31)   ~ (all_52_9 = e3)
% 241.59/48.23    (32)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.59/48.23          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.59/48.23    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.59/48.23          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.59/48.23    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.23          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.59/48.23    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.23    (36)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.59/48.23          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.59/48.23    (37)  op(e1, e1) = e0
% 241.59/48.23    (38)   ~ (e1 = e0)
% 241.59/48.23    (39)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.59/48.23          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.59/48.23    (40)  op(e2, e0) = all_52_13
% 241.59/48.23    (41)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.59/48.23          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.59/48.23            e1)
% 241.59/48.23    (42)   ~ (all_52_1 = e3)
% 241.59/48.23    (43)  all_58_14 = e1
% 241.59/48.23    (44)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.23          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.59/48.23            e2)
% 241.59/48.23    (45)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.59/48.23          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.59/48.23    (46)  all_58_4 = e0
% 241.59/48.23    (47)   ~ (e2 = e1)
% 241.59/48.23    (48)   ~ (all_52_1 = e1)
% 241.59/48.23  
% 241.59/48.23  Begin of proof
% 241.59/48.23  | 
% 241.59/48.23  | BETA: splitting (28) gives:
% 241.59/48.23  | 
% 241.59/48.23  | Case 1:
% 241.59/48.23  | | 
% 241.59/48.23  | |   (49)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 241.59/48.23  | |           e3)
% 241.59/48.23  | | 
% 241.59/48.23  | | BETA: splitting (49) gives:
% 241.59/48.23  | | 
% 241.59/48.23  | | Case 1:
% 241.59/48.23  | | | 
% 241.59/48.23  | | |   (50)  all_58_4 = e3 & op(e3, e1) = e3
% 241.59/48.23  | | | 
% 241.59/48.23  | | | ALPHA: (50) implies:
% 241.59/48.23  | | |   (51)  all_58_4 = e3
% 241.59/48.23  | | | 
% 241.59/48.23  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.59/48.23  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.59/48.23  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 241.59/48.23  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 241.59/48.23  | | |            (44), (45), (46), (47), (48), (51) are inconsistent by
% 241.59/48.23  | | |            sub-proof #583.
% 241.59/48.23  | | | 
% 241.59/48.23  | | Case 2:
% 241.59/48.23  | | | 
% 241.59/48.23  | | |   (52)  all_58_5 = e3 & op(e2, e1) = e3
% 241.59/48.23  | | | 
% 241.59/48.23  | | | REF_CLOSE: (19), (31), (35), (52) are inconsistent by sub-proof #1822.
% 241.59/48.23  | | | 
% 241.59/48.23  | | End of split
% 241.59/48.23  | | 
% 241.59/48.23  | Case 2:
% 241.59/48.23  | | 
% 241.59/48.23  | |   (53)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 241.59/48.23  | |           e3)
% 241.59/48.23  | | 
% 241.59/48.23  | | BETA: splitting (53) gives:
% 241.59/48.23  | | 
% 241.59/48.23  | | Case 1:
% 241.59/48.23  | | | 
% 241.59/48.23  | | |   (54)  all_58_8 = e3 & op(e1, e1) = e3
% 241.59/48.23  | | | 
% 241.59/48.23  | | | REF_CLOSE: (2), (35), (37), (54) are inconsistent by sub-proof #2018.
% 241.59/48.23  | | | 
% 241.59/48.23  | | Case 2:
% 241.59/48.23  | | | 
% 241.59/48.23  | | |   (55)  all_58_14 = e3 & op(e0, e1) = e3
% 241.59/48.23  | | | 
% 241.59/48.23  | | | REF_CLOSE: (2), (4), (5), (12), (16), (17), (20), (21), (23), (25), (35),
% 241.59/48.23  | | |            (38), (42), (43), (47), (55) are inconsistent by sub-proof
% 241.59/48.23  | | |            #646.
% 241.59/48.23  | | | 
% 241.59/48.23  | | End of split
% 241.59/48.23  | | 
% 241.59/48.23  | End of split
% 241.59/48.23  | 
% 241.59/48.23  End of proof
% 241.59/48.23  
% 241.59/48.23  Sub-proof #583 shows that the following formulas are inconsistent:
% 241.59/48.23  ----------------------------------------------------------------
% 241.59/48.23    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.59/48.23         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.59/48.23    (2)   ~ (e3 = e0)
% 241.59/48.23    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.59/48.23         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.59/48.23    (4)  all_58_6 = e3
% 241.59/48.23    (5)   ~ (e2 = e0)
% 241.59/48.23    (6)  op(e1, e2) = all_52_6
% 241.59/48.23    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.59/48.23         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.24    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.59/48.24         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.59/48.24    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.24         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.59/48.24    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.59/48.24          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.59/48.24    (11)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.59/48.24          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.59/48.24    (12)   ~ (e3 = e1)
% 241.59/48.24    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.59/48.24          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.59/48.24    (14)  all_58_3 = e3
% 241.59/48.24    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.59/48.24          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.59/48.24    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.59/48.24          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.59/48.24    (17)  op(e3, e3) = e1
% 241.59/48.24    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.24              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.59/48.24                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.59/48.24                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.59/48.24    (19)  op(e2, e1) = all_52_9
% 241.59/48.24    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.59/48.24          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.59/48.24    (21)   ~ (e3 = e2)
% 241.59/48.24    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.59/48.24          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.59/48.24    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.59/48.24          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.59/48.24    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.59/48.24          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.59/48.24    (25)  op(e2, e3) = all_52_1
% 241.59/48.24    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.59/48.24          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.59/48.24    (27)   ~ (all_52_6 = e3)
% 241.59/48.24    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.59/48.24          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.59/48.24    (29)   ~ (all_52_4 = e3)
% 241.59/48.24    (30)  op(e3, e2) = all_52_4
% 241.59/48.24    (31)   ~ (all_52_9 = e3)
% 241.59/48.24    (32)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.59/48.24          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.59/48.24    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.59/48.24          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.59/48.24    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.24          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.59/48.24    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.24    (36)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.59/48.24          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.59/48.24    (37)  op(e1, e1) = e0
% 241.59/48.24    (38)   ~ (e1 = e0)
% 241.59/48.24    (39)  all_58_4 = e3
% 241.59/48.24    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.59/48.24          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.59/48.24    (41)  op(e2, e0) = all_52_13
% 241.59/48.24    (42)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.59/48.24          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.59/48.24            e1)
% 241.59/48.24    (43)   ~ (all_52_1 = e3)
% 241.59/48.24    (44)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.59/48.24          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.59/48.24            e2)
% 241.59/48.24    (45)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.59/48.24          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.59/48.24    (46)  all_58_4 = e0
% 241.59/48.24    (47)   ~ (e2 = e1)
% 241.59/48.24    (48)   ~ (all_52_1 = e1)
% 241.59/48.24  
% 241.59/48.24  Begin of proof
% 241.59/48.24  | 
% 241.59/48.24  | COMBINE_EQS: (39), (46) imply:
% 241.59/48.24  |   (49)  e3 = e0
% 241.59/48.24  | 
% 241.59/48.24  | COMBINE_EQS: (4), (49) imply:
% 241.59/48.24  |   (50)  all_58_6 = e0
% 241.59/48.24  | 
% 241.59/48.24  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.59/48.24  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 241.59/48.24  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 241.59/48.24  |            (36), (37), (38), (40), (41), (42), (43), (44), (45), (47), (48),
% 241.59/48.24  |            (50) are inconsistent by sub-proof #664.
% 241.59/48.24  | 
% 241.59/48.24  End of proof
% 241.59/48.24  
% 241.59/48.24  Sub-proof #584 shows that the following formulas are inconsistent:
% 241.59/48.24  ----------------------------------------------------------------
% 241.59/48.24    (1)   ~ (e3 = e0)
% 241.59/48.24    (2)  all_58_6 = e3
% 241.59/48.24    (3)   ~ (e2 = e0)
% 241.59/48.24    (4)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 241.59/48.24         (all_58_11 = e0 & op(e1, e0) = e0)
% 241.59/48.24    (5)  all_58_12 = e2
% 241.59/48.24    (6)  all_58_15 = e3
% 241.59/48.24    (7)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.59/48.24         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.59/48.24    (8)   ~ (e3 = e1)
% 241.59/48.24    (9)  all_58_3 = e3
% 241.59/48.24    (10)  op(e3, e3) = e1
% 241.59/48.24    (11)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.59/48.24          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.59/48.24    (12)   ~ (e3 = e2)
% 241.59/48.24    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.59/48.24          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.59/48.24    (14)  all_58_5 = e1
% 241.59/48.24    (15)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.59/48.24          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.59/48.24    (16)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.59/48.24          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.59/48.24    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.59/48.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.59/48.24    (18)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.59/48.24          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.59/48.24    (19)   ~ (e1 = e0)
% 241.59/48.24    (20)  all_58_10 = e1
% 241.59/48.24    (21)   ~ (e2 = e1)
% 241.59/48.24  
% 241.59/48.24  Begin of proof
% 241.59/48.24  | 
% 241.59/48.24  | BETA: splitting (7) gives:
% 241.59/48.24  | 
% 241.59/48.24  | Case 1:
% 241.59/48.24  | | 
% 241.59/48.24  | |   (22)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 241.59/48.24  | |           e2)
% 241.59/48.24  | | 
% 241.59/48.24  | | BETA: splitting (22) gives:
% 241.59/48.24  | | 
% 241.59/48.24  | | Case 1:
% 241.59/48.24  | | | 
% 241.59/48.24  | | |   (23)  all_58_2 = e2 & op(e2, e3) = e2
% 241.59/48.24  | | | 
% 241.59/48.24  | | | ALPHA: (23) implies:
% 241.59/48.24  | | |   (24)  all_58_2 = e2
% 241.59/48.24  | | | 
% 241.59/48.24  | | | REF_CLOSE: (1), (3), (9), (14), (16), (19), (20), (24) are inconsistent by
% 241.59/48.24  | | |            sub-proof #994.
% 241.59/48.24  | | | 
% 241.59/48.24  | | Case 2:
% 241.59/48.24  | | | 
% 241.59/48.24  | | |   (25)  all_58_3 = e2 & op(e2, e2) = e2
% 241.59/48.24  | | | 
% 241.59/48.24  | | | ALPHA: (25) implies:
% 241.59/48.24  | | |   (26)  all_58_3 = e2
% 241.59/48.24  | | | 
% 241.59/48.24  | | | COMBINE_EQS: (9), (26) imply:
% 241.59/48.24  | | |   (27)  e3 = e2
% 241.59/48.24  | | | 
% 241.59/48.24  | | | COMBINE_EQS: (6), (27) imply:
% 241.59/48.24  | | |   (28)  all_58_15 = e2
% 241.59/48.24  | | | 
% 241.59/48.24  | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (12), (14), (15), (16), (17),
% 241.59/48.24  | | |            (18), (19), (20), (21), (28) are inconsistent by sub-proof
% 241.59/48.24  | | |            #831.
% 241.59/48.24  | | | 
% 241.59/48.24  | | End of split
% 241.59/48.24  | | 
% 241.59/48.24  | Case 2:
% 241.59/48.24  | | 
% 241.59/48.24  | |   (29)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 241.59/48.24  | |           e2)
% 241.59/48.24  | | 
% 241.59/48.24  | | BETA: splitting (29) gives:
% 241.59/48.24  | | 
% 241.59/48.24  | | Case 1:
% 241.59/48.24  | | | 
% 241.59/48.24  | | |   (30)  all_58_5 = e2 & op(e2, e1) = e2
% 241.59/48.24  | | | 
% 241.59/48.24  | | | ALPHA: (30) implies:
% 241.59/48.24  | | |   (31)  all_58_5 = e2
% 241.59/48.24  | | | 
% 241.59/48.24  | | | COMBINE_EQS: (14), (31) imply:
% 241.59/48.24  | | |   (32)  e2 = e1
% 241.59/48.24  | | | 
% 241.59/48.24  | | | REF_CLOSE: (1), (2), (3), (5), (10), (11), (12), (13), (17), (19), (21),
% 241.59/48.24  | | |            (32) are inconsistent by sub-proof #585.
% 241.59/48.24  | | | 
% 241.59/48.24  | | Case 2:
% 241.59/48.24  | | | 
% 241.59/48.24  | | |   (33)  all_58_10 = e2 & op(e2, e0) = e2
% 241.59/48.24  | | | 
% 241.59/48.24  | | | ALPHA: (33) implies:
% 241.59/48.24  | | |   (34)  all_58_10 = e2
% 241.59/48.24  | | | 
% 241.59/48.24  | | | COMBINE_EQS: (20), (34) imply:
% 241.59/48.24  | | |   (35)  e2 = e1
% 241.59/48.24  | | | 
% 241.59/48.24  | | | REF_CLOSE: (1), (2), (3), (5), (10), (11), (12), (13), (17), (19), (21),
% 241.59/48.24  | | |            (35) are inconsistent by sub-proof #585.
% 241.59/48.24  | | | 
% 241.59/48.24  | | End of split
% 241.59/48.24  | | 
% 241.59/48.24  | End of split
% 241.59/48.24  | 
% 241.59/48.24  End of proof
% 241.59/48.24  
% 241.59/48.24  Sub-proof #585 shows that the following formulas are inconsistent:
% 241.59/48.24  ----------------------------------------------------------------
% 241.59/48.24    (1)   ~ (e3 = e0)
% 241.59/48.24    (2)  all_58_6 = e3
% 241.59/48.24    (3)   ~ (e2 = e0)
% 241.59/48.24    (4)  all_58_12 = e2
% 241.59/48.24    (5)  op(e3, e3) = e1
% 241.73/48.24    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.73/48.24         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.73/48.24    (7)   ~ (e3 = e2)
% 241.73/48.24    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.73/48.24         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.73/48.24    (9)  e2 = e1
% 241.73/48.24    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.24    (11)   ~ (e1 = e0)
% 241.73/48.24    (12)   ~ (e2 = e1)
% 241.73/48.24  
% 241.73/48.24  Begin of proof
% 241.73/48.24  | 
% 241.73/48.24  | SIMP: (9) implies:
% 241.73/48.24  |   (13)  e2 = e1
% 241.73/48.24  | 
% 241.73/48.24  | COMBINE_EQS: (4), (13) imply:
% 241.73/48.24  |   (14)  all_58_12 = e1
% 241.73/48.24  | 
% 241.73/48.24  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (14) are
% 241.73/48.24  |            inconsistent by sub-proof #1206.
% 241.73/48.24  | 
% 241.73/48.24  End of proof
% 241.73/48.24  
% 241.73/48.24  Sub-proof #586 shows that the following formulas are inconsistent:
% 241.73/48.24  ----------------------------------------------------------------
% 241.73/48.24    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.24         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.24    (2)   ~ (e3 = e0)
% 241.73/48.24    (3)  all_58_6 = e3
% 241.73/48.24    (4)   ~ (e2 = e0)
% 241.73/48.24    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.24         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.24    (6)  all_58_12 = e2
% 241.73/48.24    (7)  all_58_1 = e0
% 241.73/48.24    (8)  all_58_3 = e3
% 241.73/48.24    (9)  op(e3, e3) = e1
% 241.73/48.24    (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.73/48.24          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.73/48.24    (11)   ~ (e3 = e2)
% 241.73/48.24    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.73/48.24          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.73/48.24    (13)  op(e0, e2) = e0
% 241.73/48.24    (14)  all_58_7 = e1
% 241.73/48.24    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.24    (16)   ~ (e1 = e0)
% 241.73/48.24    (17)  all_58_4 = e3
% 241.73/48.24    (18)   ~ (e2 = e1)
% 241.73/48.24  
% 241.73/48.24  Begin of proof
% 241.73/48.24  | 
% 241.73/48.24  | BETA: splitting (1) gives:
% 241.73/48.24  | 
% 241.73/48.24  | Case 1:
% 241.73/48.24  | | 
% 241.73/48.24  | |   (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 241.73/48.24  | |           e2)
% 241.73/48.24  | | 
% 241.73/48.24  | | REF_CLOSE: (4), (7), (9), (15), (18), (19) are inconsistent by sub-proof
% 241.73/48.24  | |            #1477.
% 241.73/48.24  | | 
% 241.73/48.24  | Case 2:
% 241.73/48.24  | | 
% 241.73/48.24  | |   (20)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 241.73/48.24  | |           e2)
% 241.73/48.24  | | 
% 241.73/48.24  | | BETA: splitting (20) gives:
% 241.73/48.24  | | 
% 241.73/48.24  | | Case 1:
% 241.73/48.24  | | | 
% 241.73/48.24  | | |   (21)  all_58_4 = e2 & op(e3, e1) = e2
% 241.73/48.24  | | | 
% 241.73/48.24  | | | REF_CLOSE: (11), (17), (21) are inconsistent by sub-proof #1476.
% 241.73/48.24  | | | 
% 241.73/48.24  | | Case 2:
% 241.73/48.24  | | | 
% 241.73/48.24  | | |   (22)  all_58_9 = e2 & op(e3, e0) = e2
% 241.73/48.24  | | | 
% 241.73/48.24  | | | ALPHA: (22) implies:
% 241.73/48.24  | | |   (23)  all_58_9 = e2
% 241.73/48.24  | | | 
% 241.73/48.24  | | | BETA: splitting (5) gives:
% 241.73/48.24  | | | 
% 241.73/48.24  | | | Case 1:
% 241.73/48.24  | | | | 
% 241.73/48.24  | | | |   (24)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2)
% 241.73/48.24  | | | |           = e2)
% 241.73/48.24  | | | | 
% 241.73/48.24  | | | | BETA: splitting (24) gives:
% 241.73/48.24  | | | | 
% 241.73/48.24  | | | | Case 1:
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | |   (25)  all_58_1 = e2 & op(e3, e2) = e2
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | | REF_CLOSE: (1), (4), (7), (9), (11), (15), (17), (18), (23), (25) are
% 241.73/48.24  | | | | |            inconsistent by sub-proof #603.
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | Case 2:
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | |   (26)  all_58_3 = e2 & op(e2, e2) = e2
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | | REF_CLOSE: (8), (11), (26) are inconsistent by sub-proof #1458.
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | End of split
% 241.73/48.24  | | | | 
% 241.73/48.24  | | | Case 2:
% 241.73/48.24  | | | | 
% 241.73/48.24  | | | |   (27)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2)
% 241.73/48.24  | | | |           = e2)
% 241.73/48.24  | | | | 
% 241.73/48.24  | | | | BETA: splitting (27) gives:
% 241.73/48.24  | | | | 
% 241.73/48.24  | | | | Case 1:
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | |   (28)  all_58_7 = e2 & op(e1, e2) = e2
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | | ALPHA: (28) implies:
% 241.73/48.24  | | | | |   (29)  all_58_7 = e2
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | | COMBINE_EQS: (14), (29) imply:
% 241.73/48.24  | | | | |   (30)  e2 = e1
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | | SIMP: (30) implies:
% 241.73/48.24  | | | | |   (31)  e2 = e1
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | | COMBINE_EQS: (23), (31) imply:
% 241.73/48.24  | | | | |   (32)  all_58_9 = e1
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (15),
% 241.73/48.24  | | | | |            (16), (17), (18), (32) are inconsistent by sub-proof #1148.
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | Case 2:
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | |   (33)  all_58_13 = e2 & op(e0, e2) = e2
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | | ALPHA: (33) implies:
% 241.73/48.24  | | | | |   (34)  op(e0, e2) = e2
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | | REF_CLOSE: (4), (13), (15), (34) are inconsistent by sub-proof #2132.
% 241.73/48.24  | | | | | 
% 241.73/48.24  | | | | End of split
% 241.73/48.24  | | | | 
% 241.73/48.24  | | | End of split
% 241.73/48.24  | | | 
% 241.73/48.24  | | End of split
% 241.73/48.24  | | 
% 241.73/48.24  | End of split
% 241.73/48.24  | 
% 241.73/48.24  End of proof
% 241.73/48.24  
% 241.73/48.24  Sub-proof #587 shows that the following formulas are inconsistent:
% 241.73/48.24  ----------------------------------------------------------------
% 241.73/48.25    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.25         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.25    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.73/48.25         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.25    (3)   ~ (e3 = e0)
% 241.73/48.25    (4)   ~ (e2 = e0)
% 241.73/48.25    (5)  op(e1, e2) = all_52_6
% 241.73/48.25    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.25         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.25    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.73/48.25         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.73/48.25    (8)  all_58_9 = e0
% 241.73/48.25    (9)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.73/48.25           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.73/48.25             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.73/48.25           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.73/48.25             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.73/48.25           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.73/48.25           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.73/48.25           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.73/48.25           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.73/48.25           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.73/48.25           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.73/48.25             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.73/48.25           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.73/48.25           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 241.73/48.25           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.73/48.25           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.73/48.25           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.73/48.25           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.73/48.25             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.73/48.25           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.73/48.25           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 241.73/48.25           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.73/48.25           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.73/48.25           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.73/48.25           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.73/48.25             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.73/48.25           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.73/48.25           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.73/48.25    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.25          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.73/48.25    (11)   ~ (all_52_7 = e3)
% 241.73/48.25    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.25          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.73/48.25    (13)   ~ (e3 = e1)
% 241.73/48.25    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.73/48.25          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.73/48.25    (15)  all_58_3 = e3
% 241.73/48.25    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.73/48.25          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.73/48.25    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.73/48.25          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.73/48.25    (18)  op(e3, e3) = e1
% 241.73/48.25    (19)   ~ (all_52_9 = e0)
% 241.73/48.25    (20)  op(e2, e1) = all_52_9
% 241.73/48.25    (21)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.73/48.25          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.73/48.25    (22)   ~ (e3 = e2)
% 241.73/48.25    (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.73/48.25          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.73/48.25    (24)  all_56_31 = e0
% 241.73/48.25    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.73/48.25          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.73/48.25    (26)   ~ (all_52_9 = all_52_13)
% 241.73/48.25    (27)  op(e2, e3) = all_52_1
% 241.73/48.25    (28)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.73/48.25          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.25    (29)  all_58_5 = e2
% 241.73/48.25    (30)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.73/48.25          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.73/48.25    (31)  op(e0, e2) = all_52_7
% 241.73/48.25    (32)  all_58_2 = e0
% 241.73/48.25    (33)   ~ (all_52_4 = e3)
% 241.73/48.25    (34)  op(e3, e2) = all_52_4
% 241.73/48.25    (35)   ~ (all_52_9 = e3)
% 241.73/48.25    (36)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.73/48.25          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.25    (37)  e2 = e1
% 241.73/48.25    (38)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.25          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.73/48.25    (39)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.25    (40)  op(e0, e0) = e0
% 241.73/48.25    (41)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.73/48.25          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.73/48.25    (42)   ~ (all_52_6 = all_52_7)
% 241.73/48.25    (43)  all_56_11 = e3
% 241.73/48.25    (44)  op(e1, e1) = e0
% 241.73/48.25    (45)   ~ (e1 = e0)
% 241.73/48.25    (46)  all_58_4 = e3
% 241.73/48.25    (47)  op(e2, e0) = all_52_13
% 241.73/48.25    (48)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.73/48.25          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.73/48.25            e1)
% 241.73/48.25    (49)   ~ (all_52_1 = e3)
% 241.73/48.25    (50)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.25          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.73/48.25            e2)
% 241.73/48.25    (51)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.73/48.25          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.73/48.25    (52)  all_56_1 = e1
% 241.73/48.25    (53)   ~ (e2 = e1)
% 241.73/48.25    (54)   ~ (all_52_1 = e1)
% 241.73/48.25  
% 241.73/48.25  Begin of proof
% 241.73/48.25  | 
% 241.73/48.25  | SIMP: (37) implies:
% 241.73/48.25  |   (55)  e2 = e1
% 241.73/48.25  | 
% 241.73/48.25  | COMBINE_EQS: (29), (55) imply:
% 241.73/48.25  |   (56)  all_58_5 = e1
% 241.73/48.25  | 
% 241.73/48.25  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.73/48.25  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 241.73/48.25  |            (24), (25), (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 241.73/48.25  |            (36), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 241.73/48.25  |            (48), (49), (50), (51), (52), (53), (54), (56) are inconsistent by
% 241.73/48.25  |            sub-proof #606.
% 241.73/48.25  | 
% 241.73/48.25  End of proof
% 241.73/48.25  
% 241.73/48.25  Sub-proof #588 shows that the following formulas are inconsistent:
% 241.73/48.25  ----------------------------------------------------------------
% 241.73/48.25    (1)   ~ (e3 = e0)
% 241.73/48.25    (2)  all_58_6 = e3
% 241.73/48.25    (3)   ~ (e2 = e0)
% 241.73/48.25    (4)   ~ (e3 = e1)
% 241.73/48.25    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.73/48.25         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.73/48.25    (6)  op(e3, e3) = e1
% 241.73/48.25    (7)  op(e2, e1) = all_52_9
% 241.73/48.25    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.73/48.25         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.73/48.25    (9)   ~ (e3 = e2)
% 241.73/48.25    (10)  e3 = e2
% 241.73/48.25    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.73/48.25          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.73/48.25    (12)  op(e2, e3) = all_52_1
% 241.73/48.25    (13)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.73/48.25          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.73/48.25    (14)   ~ (all_52_9 = e3)
% 241.73/48.25    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.25    (16)  op(e1, e1) = e0
% 241.73/48.25    (17)   ~ (e1 = e0)
% 241.73/48.25    (18)  all_58_4 = e3
% 241.73/48.25    (19)   ~ (all_52_1 = e3)
% 241.73/48.25    (20)  all_58_14 = e1
% 241.73/48.25    (21)   ~ (e2 = e1)
% 241.73/48.25  
% 241.73/48.25  Begin of proof
% 241.73/48.25  | 
% 241.73/48.25  | SIMP: (10) implies:
% 241.73/48.25  |   (22)  e3 = e2
% 241.73/48.25  | 
% 241.73/48.25  | COMBINE_EQS: (18), (22) imply:
% 241.73/48.25  |   (23)  all_58_4 = e2
% 241.73/48.25  | 
% 241.73/48.25  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 241.73/48.25  |            (14), (15), (16), (17), (19), (20), (21), (23) are inconsistent by
% 241.73/48.25  |            sub-proof #645.
% 241.73/48.25  | 
% 241.73/48.25  End of proof
% 241.73/48.25  
% 241.73/48.25  Sub-proof #589 shows that the following formulas are inconsistent:
% 241.73/48.25  ----------------------------------------------------------------
% 241.73/48.25    (1)   ~ (e3 = e0)
% 241.73/48.25    (2)   ~ (e2 = e0)
% 241.73/48.25    (3)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.25         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.73/48.25    (4)  all_58_3 = e3
% 241.73/48.25    (5)   ~ (e3 = e2)
% 241.73/48.25    (6)  all_58_5 = e2
% 241.73/48.25    (7)  all_58_7 = e1
% 241.73/48.25    (8)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.25         (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.73/48.25    (9)   ~ (e1 = e0)
% 241.73/48.25    (10)  all_58_7 = e2 & op(e1, e2) = e2
% 241.73/48.25    (11)  all_58_10 = e1
% 241.73/48.25    (12)   ~ (e2 = e1)
% 241.73/48.25  
% 241.73/48.25  Begin of proof
% 241.73/48.25  | 
% 241.73/48.25  | ALPHA: (10) implies:
% 241.73/48.25  |   (13)  all_58_7 = e2
% 241.73/48.25  | 
% 241.73/48.25  | COMBINE_EQS: (7), (13) imply:
% 241.73/48.25  |   (14)  e2 = e1
% 241.73/48.25  | 
% 241.73/48.25  | COMBINE_EQS: (6), (14) imply:
% 241.73/48.25  |   (15)  all_58_5 = e1
% 241.73/48.25  | 
% 241.73/48.25  | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (12), (15) are
% 241.73/48.25  |            inconsistent by sub-proof #992.
% 241.73/48.25  | 
% 241.73/48.25  End of proof
% 241.73/48.25  
% 241.73/48.25  Sub-proof #590 shows that the following formulas are inconsistent:
% 241.73/48.25  ----------------------------------------------------------------
% 241.73/48.25    (1)   ~ (e3 = e0)
% 241.73/48.25    (2)   ~ (e2 = e0)
% 241.73/48.25    (3)  op(e1, e2) = all_52_6
% 241.73/48.25    (4)   ~ (e3 = e1)
% 241.73/48.25    (5)  all_58_11 = e3
% 241.73/48.25    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.73/48.25         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.73/48.25    (7)  op(e3, e3) = e1
% 241.73/48.25    (8)   ~ (e3 = e2)
% 241.73/48.25    (9)  all_58_6 = e0
% 241.73/48.25    (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.73/48.25          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.73/48.25    (11)  op(e3, e0) = e2
% 241.73/48.25    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.73/48.25          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.25    (13)   ~ (all_52_6 = e3)
% 241.73/48.25    (14)   ~ (all_52_4 = e3)
% 241.73/48.25    (15)  op(e3, e2) = all_52_4
% 241.73/48.25    (16)  all_58_7 = e1
% 241.73/48.25    (17)  all_58_1 = e2
% 241.73/48.25    (18)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.73/48.25          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.73/48.25    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.25    (20)   ~ (e1 = e0)
% 241.73/48.25    (21)  all_58_9 = e2
% 241.73/48.25    (22)   ~ (e2 = e1)
% 241.73/48.25  
% 241.73/48.25  Begin of proof
% 241.73/48.25  | 
% 241.73/48.25  | BETA: splitting (12) gives:
% 241.73/48.25  | 
% 241.73/48.25  | Case 1:
% 241.73/48.25  | | 
% 241.73/48.25  | |   (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 241.73/48.25  | |           e0)
% 241.73/48.25  | | 
% 241.73/48.25  | | REF_CLOSE: (2), (7), (17), (19), (20), (23) are inconsistent by sub-proof
% 241.73/48.25  | |            #709.
% 241.73/48.25  | | 
% 241.73/48.25  | Case 2:
% 241.73/48.25  | | 
% 241.73/48.25  | |   (24)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 241.73/48.25  | |           e0)
% 241.73/48.25  | | 
% 241.73/48.25  | | BETA: splitting (24) gives:
% 241.73/48.25  | | 
% 241.73/48.25  | | Case 1:
% 241.73/48.25  | | | 
% 241.73/48.25  | | |   (25)  all_58_4 = e0 & op(e3, e1) = e0
% 241.73/48.25  | | | 
% 241.73/48.25  | | | ALPHA: (25) implies:
% 241.73/48.25  | | |   (26)  all_58_4 = e0
% 241.73/48.25  | | | 
% 241.73/48.25  | | | BETA: splitting (6) gives:
% 241.73/48.25  | | | 
% 241.73/48.25  | | | Case 1:
% 241.73/48.25  | | | | 
% 241.73/48.25  | | | |   (27)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 241.73/48.25  | | | |           = e3)
% 241.73/48.25  | | | | 
% 241.73/48.25  | | | | REF_CLOSE: (4), (7), (14), (15), (19), (27) are inconsistent by
% 241.73/48.25  | | | |            sub-proof #1401.
% 241.73/48.25  | | | | 
% 241.73/48.25  | | | Case 2:
% 241.73/48.25  | | | | 
% 241.73/48.25  | | | |   (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 241.73/48.25  | | | |           = e3)
% 241.73/48.25  | | | | 
% 241.73/48.25  | | | | BETA: splitting (28) gives:
% 241.73/48.25  | | | | 
% 241.73/48.25  | | | | Case 1:
% 241.73/48.25  | | | | | 
% 241.73/48.25  | | | | |   (29)  all_58_4 = e3 & op(e3, e1) = e3
% 241.73/48.25  | | | | | 
% 241.73/48.25  | | | | | ALPHA: (29) implies:
% 241.73/48.25  | | | | |   (30)  all_58_4 = e3
% 241.73/48.25  | | | | | 
% 241.73/48.25  | | | | | COMBINE_EQS: (26), (30) imply:
% 241.73/48.25  | | | | |   (31)  e3 = e0
% 241.73/48.25  | | | | | 
% 241.73/48.25  | | | | | SIMP: (31) implies:
% 241.73/48.25  | | | | |   (32)  e3 = e0
% 241.73/48.25  | | | | | 
% 241.73/48.25  | | | | | COMBINE_EQS: (5), (32) imply:
% 241.73/48.25  | | | | |   (33)  all_58_11 = e0
% 241.73/48.25  | | | | | 
% 241.73/48.25  | | | | | REF_CLOSE: (1), (2), (3), (8), (9), (10), (13), (16), (18), (19),
% 241.73/48.25  | | | | |            (22), (33) are inconsistent by sub-proof #960.
% 241.73/48.25  | | | | | 
% 241.73/48.25  | | | | Case 2:
% 241.73/48.25  | | | | | 
% 241.73/48.25  | | | | |   (34)  all_58_9 = e3 & op(e3, e0) = e3
% 241.73/48.25  | | | | | 
% 241.73/48.25  | | | | | ALPHA: (34) implies:
% 241.73/48.25  | | | | |   (35)  op(e3, e0) = e3
% 241.73/48.25  | | | | | 
% 241.73/48.25  | | | | | REF_CLOSE: (8), (11), (19), (35) are inconsistent by sub-proof #2125.
% 241.73/48.25  | | | | | 
% 241.73/48.25  | | | | End of split
% 241.73/48.25  | | | | 
% 241.73/48.25  | | | End of split
% 241.73/48.25  | | | 
% 241.73/48.25  | | Case 2:
% 241.73/48.25  | | | 
% 241.73/48.25  | | |   (36)  all_58_9 = e0 & op(e3, e0) = e0
% 241.73/48.25  | | | 
% 241.73/48.25  | | | REF_CLOSE: (2), (21), (36) are inconsistent by sub-proof #1563.
% 241.73/48.25  | | | 
% 241.73/48.25  | | End of split
% 241.73/48.25  | | 
% 241.73/48.25  | End of split
% 241.73/48.25  | 
% 241.73/48.25  End of proof
% 241.73/48.25  
% 241.73/48.25  Sub-proof #591 shows that the following formulas are inconsistent:
% 241.73/48.25  ----------------------------------------------------------------
% 241.73/48.25    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.25         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.25    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.73/48.25         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.25    (3)   ~ (e3 = e0)
% 241.73/48.26    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.73/48.26         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.73/48.26    (5)   ~ (e2 = e0)
% 241.73/48.26    (6)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 241.73/48.26         (all_58_11 = e0 & op(e1, e0) = e0)
% 241.73/48.26    (7)  op(e1, e2) = all_52_6
% 241.73/48.26    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.26         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.26    (9)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.73/48.26         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.73/48.26    (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.73/48.26              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 241.73/48.26            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 241.73/48.26            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 241.73/48.26            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 241.73/48.26             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.73/48.26            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.73/48.26            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.73/48.26            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.73/48.26            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.73/48.26            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.73/48.26              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.73/48.26            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.73/48.26            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 241.73/48.26            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.73/48.26            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 241.73/48.26            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.73/48.26            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.73/48.26              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.73/48.26            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.73/48.26            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 241.73/48.26            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.73/48.26            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.73/48.26            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.73/48.26            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.73/48.26              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.73/48.26            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.73/48.26            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.73/48.26    (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.26          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.73/48.26    (12)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.73/48.26          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.73/48.26    (13)   ~ (all_52_7 = e3)
% 241.73/48.26    (14)  all_58_8 = e0
% 241.73/48.26    (15)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.26          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.73/48.26    (16)   ~ (e3 = e1)
% 241.73/48.26    (17)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.73/48.26          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.73/48.26    (18)  all_58_3 = e3
% 241.73/48.26    (19)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.73/48.26          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.73/48.26    (20)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.73/48.26          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.73/48.26    (21)  op(e3, e3) = e1
% 241.73/48.26    (22)   ~ (all_52_9 = e0)
% 241.73/48.26    (23)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.26              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.73/48.26                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.73/48.26                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.73/48.26    (24)  op(e2, e1) = all_52_9
% 241.73/48.26    (25)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.73/48.26          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.73/48.26    (26)   ~ (e3 = e2)
% 241.73/48.26    (27)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.73/48.26          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.73/48.26    (28)  all_56_31 = e0
% 241.73/48.26    (29)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.73/48.26          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.73/48.26    (30)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.73/48.26          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.73/48.26    (31)   ~ (all_52_9 = all_52_13)
% 241.73/48.26    (32)  op(e2, e3) = all_52_1
% 241.73/48.26    (33)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.73/48.26          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.26    (34)   ~ (all_52_6 = e3)
% 241.73/48.26    (35)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.73/48.26          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.73/48.26    (36)  op(e0, e2) = all_52_7
% 241.73/48.26    (37)  all_58_2 = e0
% 241.73/48.26    (38)   ~ (all_52_4 = e3)
% 241.73/48.26    (39)  op(e3, e2) = all_52_4
% 241.73/48.26    (40)  all_58_14 = e0
% 241.73/48.26    (41)   ~ (all_52_9 = e3)
% 241.73/48.26    (42)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.73/48.26          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.26    (43)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.73/48.26          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.73/48.26    (44)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.26          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.73/48.26    (45)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.26    (46)  op(e0, e0) = e0
% 241.73/48.26    (47)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.73/48.26          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.73/48.26    (48)   ~ (all_52_6 = all_52_7)
% 241.73/48.26    (49)  all_56_11 = e3
% 241.73/48.26    (50)  op(e1, e1) = e0
% 241.73/48.26    (51)   ~ (e1 = e0)
% 241.73/48.26    (52)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.73/48.26          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.73/48.26    (53)  op(e2, e0) = all_52_13
% 241.73/48.26    (54)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.73/48.26          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.73/48.26            e1)
% 241.73/48.26    (55)   ~ (all_52_1 = e3)
% 241.73/48.26    (56)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.26          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.73/48.26            e2)
% 241.73/48.26    (57)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.73/48.26          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.73/48.26    (58)  all_56_1 = e1
% 241.73/48.26    (59)   ~ (e2 = e1)
% 241.73/48.26    (60)   ~ (all_52_1 = e1)
% 241.73/48.26  
% 241.73/48.26  Begin of proof
% 241.73/48.26  | 
% 241.73/48.26  | BETA: splitting (12) gives:
% 241.73/48.26  | 
% 241.73/48.26  | Case 1:
% 241.73/48.26  | | 
% 241.73/48.26  | |   (61)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 241.73/48.26  | |           e1)
% 241.73/48.26  | | 
% 241.73/48.26  | | BETA: splitting (61) gives:
% 241.73/48.26  | | 
% 241.73/48.26  | | Case 1:
% 241.73/48.26  | | | 
% 241.73/48.26  | | |   (62)  all_58_4 = e1 & op(e3, e1) = e1
% 241.73/48.26  | | | 
% 241.73/48.26  | | | ALPHA: (62) implies:
% 241.73/48.26  | | |   (63)  all_58_4 = e1
% 241.73/48.26  | | | 
% 241.73/48.26  | | | REF_CLOSE: (1), (3), (5), (16), (19), (21), (26), (33), (38), (39), (45),
% 241.73/48.26  | | |            (51), (59), (63) are inconsistent by sub-proof #1468.
% 241.73/48.26  | | | 
% 241.73/48.26  | | Case 2:
% 241.73/48.26  | | | 
% 241.73/48.26  | | |   (64)  all_58_5 = e1 & op(e2, e1) = e1
% 241.73/48.26  | | | 
% 241.73/48.26  | | | ALPHA: (64) implies:
% 241.73/48.26  | | |   (65)  all_58_5 = e1
% 241.73/48.26  | | | 
% 241.73/48.26  | | | BETA: splitting (35) gives:
% 241.73/48.26  | | | 
% 241.73/48.26  | | | Case 1:
% 241.73/48.26  | | | | 
% 241.73/48.26  | | | |   (66)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 241.73/48.26  | | | |           = e3)
% 241.73/48.26  | | | | 
% 241.73/48.26  | | | | BETA: splitting (66) gives:
% 241.73/48.26  | | | | 
% 241.73/48.26  | | | | Case 1:
% 241.73/48.26  | | | | | 
% 241.73/48.26  | | | | |   (67)  all_58_4 = e3 & op(e3, e1) = e3
% 241.73/48.26  | | | | | 
% 241.73/48.26  | | | | | ALPHA: (67) implies:
% 241.73/48.26  | | | | |   (68)  all_58_4 = e3
% 241.73/48.26  | | | | | 
% 241.73/48.26  | | | | | BETA: splitting (6) gives:
% 241.73/48.26  | | | | | 
% 241.73/48.26  | | | | | Case 1:
% 241.73/48.26  | | | | | | 
% 241.73/48.26  | | | | | |   (69)  all_58_9 = e0 & op(e3, e0) = e0
% 241.73/48.26  | | | | | | 
% 241.73/48.26  | | | | | | ALPHA: (69) implies:
% 241.73/48.26  | | | | | |   (70)  all_58_9 = e0
% 241.73/48.26  | | | | | | 
% 241.73/48.26  | | | | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (13),
% 241.73/48.26  | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 241.73/48.26  | | | | | |            (25), (26), (27), (28), (29), (31), (32), (33), (35),
% 241.73/48.26  | | | | | |            (36), (37), (38), (39), (41), (42), (44), (45), (46),
% 241.73/48.26  | | | | | |            (47), (48), (49), (50), (51), (53), (54), (55), (56),
% 241.73/48.26  | | | | | |            (57), (58), (59), (60), (65), (68), (70) are inconsistent
% 241.73/48.26  | | | | | |            by sub-proof #606.
% 241.73/48.26  | | | | | | 
% 241.73/48.26  | | | | | Case 2:
% 241.73/48.26  | | | | | | 
% 241.73/48.26  | | | | | |   (71)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 241.73/48.26  | | | | | |           op(e1, e0) = e0)
% 241.73/48.26  | | | | | | 
% 241.73/48.26  | | | | | | BETA: splitting (71) gives:
% 241.73/48.26  | | | | | | 
% 241.73/48.26  | | | | | | Case 1:
% 241.73/48.26  | | | | | | | 
% 241.73/48.26  | | | | | | |   (72)  all_58_10 = e0 & op(e2, e0) = e0
% 241.73/48.26  | | | | | | | 
% 241.73/48.26  | | | | | | | ALPHA: (72) implies:
% 241.73/48.26  | | | | | | |   (73)  all_58_10 = e0
% 241.73/48.26  | | | | | | |   (74)  op(e2, e0) = e0
% 241.73/48.26  | | | | | | | 
% 241.73/48.26  | | | | | | | BETA: splitting (54) gives:
% 241.73/48.26  | | | | | | | 
% 241.73/48.26  | | | | | | | Case 1:
% 241.73/48.26  | | | | | | | | 
% 241.73/48.26  | | | | | | | |   (75)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 241.73/48.26  | | | | | | | |           op(e0, e2) = e1)
% 241.73/48.26  | | | | | | | | 
% 241.73/48.26  | | | | | | | | BETA: splitting (75) gives:
% 241.73/48.26  | | | | | | | | 
% 241.73/48.26  | | | | | | | | Case 1:
% 241.73/48.26  | | | | | | | | | 
% 241.73/48.26  | | | | | | | | |   (76)  all_58_12 = e1 & op(e0, e3) = e1
% 241.73/48.26  | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | ALPHA: (76) implies:
% 241.73/48.26  | | | | | | | | |   (77)  all_58_12 = e1
% 241.73/48.26  | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | REF_CLOSE: (3), (5), (16), (20), (21), (25), (26), (29), (32),
% 241.73/48.26  | | | | | | | | |            (45), (51), (55), (59), (77) are inconsistent by
% 241.73/48.26  | | | | | | | | |            sub-proof #1204.
% 241.73/48.26  | | | | | | | | | 
% 241.73/48.26  | | | | | | | | Case 2:
% 241.73/48.26  | | | | | | | | | 
% 241.73/48.26  | | | | | | | | |   (78)  all_58_13 = e1 & op(e0, e2) = e1
% 241.73/48.26  | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | ALPHA: (78) implies:
% 241.73/48.26  | | | | | | | | |   (79)  all_58_13 = e1
% 241.73/48.26  | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | BETA: splitting (2) gives:
% 241.73/48.26  | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | Case 1:
% 241.73/48.26  | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | |   (80)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3
% 241.73/48.26  | | | | | | | | | |           & op(e0, e2) = e3)
% 241.73/48.26  | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | BETA: splitting (80) gives:
% 241.73/48.26  | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | Case 1:
% 241.73/48.26  | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | |   (81)  all_58_12 = e3 & op(e0, e3) = e3
% 241.73/48.26  | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | ALPHA: (81) implies:
% 241.73/48.26  | | | | | | | | | | |   (82)  all_58_12 = e3
% 241.73/48.26  | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | BETA: splitting (9) gives:
% 241.73/48.26  | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | Case 1:
% 241.73/48.26  | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | |   (83)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 241.73/48.26  | | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 241.73/48.26  | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | BETA: splitting (83) gives:
% 241.73/48.26  | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | Case 1:
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | |   (84)  all_58_9 = e1 & op(e3, e0) = e1
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | ALPHA: (84) implies:
% 241.73/48.26  | | | | | | | | | | | | |   (85)  all_58_9 = e1
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | BETA: splitting (33) gives:
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | Case 1:
% 241.73/48.26  | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | |   (86)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 241.73/48.26  | | | | | | | | | | | | | |           & op(e3, e2) = e0)
% 241.73/48.26  | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (21), (26), (45), (51), (59), (68),
% 241.73/48.26  | | | | | | | | | | | | | |            (85), (86) are inconsistent by sub-proof #1293.
% 241.73/48.26  | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | Case 2:
% 241.73/48.26  | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | |   (87)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 241.73/48.26  | | | | | | | | | | | | | |           & op(e3, e0) = e0)
% 241.73/48.26  | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 241.73/48.26  | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | Case 1:
% 241.73/48.26  | | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | |   (88)  all_58_4 = e0 & op(e3, e1) = e0
% 241.73/48.26  | | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | | ALPHA: (88) implies:
% 241.73/48.26  | | | | | | | | | | | | | | |   (89)  all_58_4 = e0
% 241.73/48.26  | | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | | COMBINE_EQS: (68), (89) imply:
% 241.73/48.26  | | | | | | | | | | | | | | |   (90)  e3 = e0
% 241.73/48.26  | | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | | COMBINE_EQS: (82), (90) imply:
% 241.73/48.26  | | | | | | | | | | | | | | |   (91)  all_58_12 = e0
% 241.73/48.26  | | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (16), (20), (21), (25), (26), (32),
% 241.73/48.26  | | | | | | | | | | | | | | |            (37), (45), (55), (59), (91) are inconsistent by
% 241.73/48.26  | | | | | | | | | | | | | | |            sub-proof #1149.
% 241.73/48.26  | | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | Case 2:
% 241.73/48.26  | | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | |   (92)  all_58_9 = e0 & op(e3, e0) = e0
% 241.73/48.26  | | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 241.73/48.26  | | | | | | | | | | | | | | |   (93)  all_58_9 = e0
% 241.73/48.26  | | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | | REF_CLOSE: (51), (85), (93) are inconsistent by sub-proof
% 241.73/48.26  | | | | | | | | | | | | | | |            #1744.
% 241.73/48.26  | | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | | End of split
% 241.73/48.26  | | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | End of split
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | Case 2:
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | |   (94)  all_58_10 = e1 & op(e2, e0) = e1
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | ALPHA: (94) implies:
% 241.73/48.26  | | | | | | | | | | | | |   (95)  all_58_10 = e1
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (15), (18), (26), (44), (51), (59),
% 241.73/48.26  | | | | | | | | | | | | |            (65), (95) are inconsistent by sub-proof #992.
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | End of split
% 241.73/48.26  | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | Case 2:
% 241.73/48.26  | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | |   (96)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 241.73/48.26  | | | | | | | | | | | |           e1 & op(e0, e0) = e1)
% 241.73/48.26  | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | BETA: splitting (96) gives:
% 241.73/48.26  | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | Case 1:
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | |   (97)  all_58_11 = e1 & op(e1, e0) = e1
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | ALPHA: (97) implies:
% 241.73/48.26  | | | | | | | | | | | | |   (98)  all_58_11 = e1
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (16), (19), (21), (25), (26),
% 241.73/48.26  | | | | | | | | | | | | |            (29), (30), (33), (34), (38), (39), (45), (50),
% 241.73/48.26  | | | | | | | | | | | | |            (51), (59), (68), (82), (98) are inconsistent by
% 241.73/48.26  | | | | | | | | | | | | |            sub-proof #618.
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | Case 2:
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | |   (99)  all_58_15 = e1 & op(e0, e0) = e1
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | ALPHA: (99) implies:
% 241.73/48.26  | | | | | | | | | | | | |   (100)  op(e0, e0) = e1
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | | REF_CLOSE: (45), (46), (51), (100) are inconsistent by
% 241.73/48.26  | | | | | | | | | | | | |            sub-proof #2274.
% 241.73/48.26  | | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | | End of split
% 241.73/48.26  | | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | End of split
% 241.73/48.26  | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | Case 2:
% 241.73/48.26  | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | |   (101)  all_58_13 = e3 & op(e0, e2) = e3
% 241.73/48.26  | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | REF_CLOSE: (13), (36), (45), (101) are inconsistent by
% 241.73/48.26  | | | | | | | | | | |            sub-proof #1919.
% 241.73/48.26  | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | End of split
% 241.73/48.26  | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | Case 2:
% 241.73/48.26  | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | |   (102)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 241.73/48.26  | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.73/48.26  | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | BETA: splitting (102) gives:
% 241.73/48.26  | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | Case 1:
% 241.73/48.26  | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | |   (103)  all_58_14 = e3 & op(e0, e1) = e3
% 241.73/48.26  | | | | | | | | | | | 
% 241.73/48.26  | | | | | | | | | | | ALPHA: (103) implies:
% 241.73/48.27  | | | | | | | | | | |   (104)  all_58_14 = e3
% 241.73/48.27  | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | COMBINE_EQS: (40), (104) imply:
% 241.73/48.27  | | | | | | | | | | |   (105)  e3 = e0
% 241.73/48.27  | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | REDUCE: (3), (105) imply:
% 241.73/48.27  | | | | | | | | | | |   (106)  $false
% 241.73/48.27  | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | CLOSE: (106) is inconsistent.
% 241.73/48.27  | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | |   (107)  all_58_15 = e3 & op(e0, e0) = e3
% 241.73/48.27  | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | ALPHA: (107) implies:
% 241.73/48.27  | | | | | | | | | | |   (108)  all_58_15 = e3
% 241.73/48.27  | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | BETA: splitting (9) gives:
% 241.73/48.27  | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | |   (109)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 241.73/48.27  | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 241.73/48.27  | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | BETA: splitting (109) gives:
% 241.73/48.27  | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | |   (110)  all_58_9 = e1 & op(e3, e0) = e1
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | ALPHA: (110) implies:
% 241.73/48.27  | | | | | | | | | | | | |   (111)  all_58_9 = e1
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (9), (15), (16), (18), (19), (21),
% 241.73/48.27  | | | | | | | | | | | | |            (26), (33), (38), (39), (42), (44), (45), (46),
% 241.73/48.27  | | | | | | | | | | | | |            (51), (59), (65), (68), (108), (111) are
% 241.73/48.27  | | | | | | | | | | | | |            inconsistent by sub-proof #605.
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | |   (112)  all_58_10 = e1 & op(e2, e0) = e1
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | ALPHA: (112) implies:
% 241.73/48.27  | | | | | | | | | | | | |   (113)  all_58_10 = e1
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (15), (18), (26), (44), (51), (59),
% 241.73/48.27  | | | | | | | | | | | | |            (65), (113) are inconsistent by sub-proof #992.
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | |   (114)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 241.73/48.27  | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 241.73/48.27  | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | BETA: splitting (114) gives:
% 241.73/48.27  | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | |   (115)  all_58_11 = e1 & op(e1, e0) = e1
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | ALPHA: (115) implies:
% 241.73/48.27  | | | | | | | | | | | | |   (116)  all_58_11 = e1
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | BETA: splitting (33) gives:
% 241.73/48.27  | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | |   (117)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 241.73/48.27  | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 241.73/48.27  | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 241.73/48.27  | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | |   (118)  all_58_0 = e0 & op(e3, e3) = e0
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 241.73/48.27  | | | | | | | | | | | | | | |   (119)  op(e3, e3) = e0
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | REF_CLOSE: (21), (45), (51), (119) are inconsistent by
% 241.73/48.27  | | | | | | | | | | | | | | |            sub-proof #1828.
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | |   (120)  all_58_1 = e0 & op(e3, e2) = e0
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 241.73/48.27  | | | | | | | | | | | | | | |   (121)  all_58_1 = e0
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | |   (122)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 241.73/48.27  | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | |   (123)  all_58_6 = e3 & op(e1, e3) = e3
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | |   (124)  all_58_6 = e3
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (8), (9), (11), (14), (15), (16),
% 241.73/48.27  | | | | | | | | | | | | | | | | |            (17), (18), (19), (20), (21), (24), (25), (26),
% 241.73/48.27  | | | | | | | | | | | | | | | | |            (27), (29), (32), (33), (35), (37), (38), (39),
% 241.73/48.27  | | | | | | | | | | | | | | | | |            (40), (41), (42), (43), (44), (45), (46), (47),
% 241.73/48.27  | | | | | | | | | | | | | | | | |            (51), (52), (54), (55), (57), (59), (60), (65),
% 241.73/48.27  | | | | | | | | | | | | | | | | |            (68), (73), (74), (79), (108), (116), (121), (124)
% 241.73/48.27  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #597.
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | |   (125)  all_58_7 = e3 & op(e1, e2) = e3
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | |   (126)  op(e1, e2) = e3
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (34), (45), (126) are inconsistent by
% 241.73/48.27  | | | | | | | | | | | | | | | | |            sub-proof #2191.
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | |   (127)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 241.73/48.27  | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (16), (19), (21), (26), (33), (38),
% 241.73/48.27  | | | | | | | | | | | | | | | |            (39), (45), (50), (51), (59), (68), (116), (127)
% 241.73/48.27  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #619.
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | |   (128)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 241.73/48.27  | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 241.73/48.27  | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 241.73/48.27  | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | |   (129)  all_58_4 = e0 & op(e3, e1) = e0
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 241.73/48.27  | | | | | | | | | | | | | | |   (130)  all_58_4 = e0
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | COMBINE_EQS: (68), (130) imply:
% 241.73/48.27  | | | | | | | | | | | | | | |   (131)  e3 = e0
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | COMBINE_EQS: (108), (131) imply:
% 241.73/48.27  | | | | | | | | | | | | | | |   (132)  all_58_15 = e0
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (9), (15), (16), (18), (19), (21),
% 241.73/48.27  | | | | | | | | | | | | | | |            (26), (32), (33), (38), (39), (42), (44), (45),
% 241.73/48.27  | | | | | | | | | | | | | | |            (46), (47), (51), (53), (57), (59), (60), (74),
% 241.73/48.27  | | | | | | | | | | | | | | |            (132) are inconsistent by sub-proof #649.
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | |   (133)  all_58_9 = e0 & op(e3, e0) = e0
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 241.73/48.27  | | | | | | | | | | | | | | |   (134)  all_58_9 = e0
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | |   (135)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 241.73/48.27  | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | |   (136)  all_58_6 = e3 & op(e1, e3) = e3
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | |   (137)  all_58_6 = e3
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | |   (138)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |   (139)  all_58_6 = e2 & op(e1, e3) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (16), (19), (21), (26), (33), (38),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |            (39), (42), (45), (51), (59), (68), (73), (108),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |            (116), (134), (137), (139) are inconsistent by
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |            sub-proof #596.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |   (140)  all_58_7 = e2 & op(e1, e2) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |   (141)  all_58_7 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | |   (142)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (21), (37), (45), (59), (142) are
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1329.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | |   (143)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | |   (144)  all_58_6 = e2 & op(e1, e3) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (16), (19), (21), (26), (33), (38),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | |            (39), (42), (45), (51), (59), (68), (73), (108),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | |            (116), (134), (137), (144) are inconsistent by
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | |            sub-proof #596.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | |   (145)  all_58_12 = e2 & op(e0, e3) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | |   (146)  all_58_12 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | |   (147)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |   (148)  all_58_0 = e2 & op(e3, e3) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |   (149)  op(e3, e3) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (45), (59), (149) are inconsistent by
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2267.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |   (150)  all_58_1 = e2 & op(e3, e2) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |   (151)  all_58_1 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | |   (152)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (153)  all_58_9 = e2 & op(e3, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (154)  all_58_9 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (155)  op(e3, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (8), (9), (11), (14), (15), (16),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (20), (21), (24), (25), (26),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (27), (29), (32), (33), (35), (37), (38), (39),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (40), (41), (42), (43), (44), (45), (46), (47),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (51), (52), (54), (55), (57), (59), (60), (65),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (73), (74), (79), (108), (116), (137),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (141), (146), (154), (155) are inconsistent by
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #600.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (156)  all_58_10 = e2 & op(e2, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (157)  op(e2, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (45), (74), (157) are inconsistent by
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2121.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | |   (158)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (159)  all_58_11 = e2 & op(e1, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (160)  all_58_11 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (116), (160) imply:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (161)  e2 = e1
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (161) imply:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (162)  all_58_7 = e1
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (11), (18), (51), (79), (151), (162) are
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1459.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (163)  all_58_15 = e2 & op(e0, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (164)  all_58_15 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (16), (19), (21), (26), (33), (38),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (39), (42), (45), (51), (59), (68), (73), (116),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (164) are inconsistent by sub-proof #612.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | |   (165)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |   (166)  all_58_4 = e2 & op(e3, e1) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |   (167)  all_58_4 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (167) imply:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |   (168)  e3 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (108), (168) imply:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |   (169)  all_58_15 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (16), (19), (21), (26), (33), (38),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |            (39), (42), (45), (51), (59), (68), (73), (116),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |            (134), (169) are inconsistent by sub-proof #612.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |   (170)  all_58_9 = e2 & op(e3, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |   (171)  all_58_9 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |   (172)  op(e3, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (8), (9), (11), (14), (15), (16),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (20), (21), (24), (25), (26),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |            (27), (29), (32), (33), (35), (37), (38), (39),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |            (40), (41), (42), (43), (44), (45), (46), (47),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |            (51), (52), (54), (55), (57), (59), (60), (65),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |            (68), (73), (74), (79), (108), (116), (137),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |            (141), (146), (171), (172) are inconsistent by
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #600.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | |   (173)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.73/48.27  | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |   (174)  all_58_8 = e2 & op(e1, e1) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (174) are inconsistent by sub-proof
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |            #683.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |   (175)  all_58_11 = e2 & op(e1, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (116), (175) are inconsistent by sub-proof
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |            #1554.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | |   (176)  all_58_7 = e3 & op(e1, e2) = e3
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | |   (177)  op(e1, e2) = e3
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (34), (45), (177) are inconsistent by
% 241.73/48.27  | | | | | | | | | | | | | | | | |            sub-proof #2191.
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | |   (178)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 241.73/48.27  | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | |   (179)  all_58_8 = e3 & op(e1, e1) = e3
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (45), (50), (179) are inconsistent by
% 241.73/48.27  | | | | | | | | | | | | | | | | |            sub-proof #2018.
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | |   (180)  all_58_11 = e3 & op(e1, e0) = e3
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | |   (181)  all_58_11 = e3
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | |   (182)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 241.73/48.27  | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |   (183)  all_58_9 = e2 & op(e3, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |   (184)  all_58_9 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (134), (184) are inconsistent by sub-proof
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |            #1660.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |   (185)  all_58_10 = e2 & op(e2, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |   (186)  all_58_10 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (9), (16), (19), (21), (26), (33),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |            (38), (39), (45), (46), (51), (59), (68), (134),
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |            (181), (186) are inconsistent by sub-proof #1465.
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | |   (187)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 241.73/48.27  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | Case 1:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |   (188)  all_58_11 = e2 & op(e1, e0) = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 241.73/48.27  | | | | | | | | | | | | | | | | | | |   (189)  all_58_11 = e2
% 241.73/48.27  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (181), (189) are inconsistent by sub-proof
% 241.73/48.28  | | | | | | | | | | | | | | | | | | |            #2030.
% 241.73/48.28  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | | | | | | Case 2:
% 241.73/48.28  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | | | | | | |   (190)  all_58_15 = e2 & op(e0, e0) = e2
% 241.73/48.28  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 241.73/48.28  | | | | | | | | | | | | | | | | | | |   (191)  all_58_15 = e2
% 241.73/48.28  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (108), (191) are inconsistent by sub-proof
% 241.73/48.28  | | | | | | | | | | | | | | | | | | |            #615.
% 241.73/48.28  | | | | | | | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | | | | | | End of split
% 241.73/48.28  | | | | | | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | | | | | End of split
% 241.73/48.28  | | | | | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | | | | End of split
% 241.73/48.28  | | | | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | | | End of split
% 241.73/48.28  | | | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | | End of split
% 241.73/48.28  | | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | End of split
% 241.73/48.28  | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | Case 2:
% 241.73/48.28  | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | |   (192)  all_58_15 = e1 & op(e0, e0) = e1
% 241.73/48.28  | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | ALPHA: (192) implies:
% 241.73/48.28  | | | | | | | | | | | | |   (193)  op(e0, e0) = e1
% 241.73/48.28  | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | | REF_CLOSE: (45), (46), (51), (193) are inconsistent by
% 241.73/48.28  | | | | | | | | | | | | |            sub-proof #2274.
% 241.73/48.28  | | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | | End of split
% 241.73/48.28  | | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | | End of split
% 241.73/48.28  | | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | | End of split
% 241.73/48.28  | | | | | | | | | | 
% 241.73/48.28  | | | | | | | | | End of split
% 241.73/48.28  | | | | | | | | | 
% 241.73/48.28  | | | | | | | | End of split
% 241.73/48.28  | | | | | | | | 
% 241.73/48.28  | | | | | | | Case 2:
% 241.73/48.28  | | | | | | | | 
% 241.73/48.28  | | | | | | | |   (194)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 241.73/48.28  | | | | | | | |            op(e0, e0) = e1)
% 241.73/48.28  | | | | | | | | 
% 241.73/48.28  | | | | | | | | REF_CLOSE: (3), (5), (17), (26), (27), (45), (46), (51), (59),
% 241.73/48.28  | | | | | | | |            (65), (68), (194) are inconsistent by sub-proof #607.
% 241.73/48.28  | | | | | | | | 
% 241.73/48.28  | | | | | | | End of split
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | Case 2:
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | |   (195)  all_58_11 = e0 & op(e1, e0) = e0
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12),
% 241.73/48.28  | | | | | | |            (13), (15), (16), (17), (18), (19), (20), (21), (23),
% 241.73/48.28  | | | | | | |            (24), (25), (26), (27), (29), (30), (32), (33), (34),
% 241.73/48.28  | | | | | | |            (35), (36), (38), (39), (40), (41), (42), (43), (44),
% 241.73/48.28  | | | | | | |            (45), (46), (47), (50), (51), (52), (53), (54), (55),
% 241.73/48.28  | | | | | | |            (56), (57), (59), (60), (65), (68), (195) are
% 241.73/48.28  | | | | | | |            inconsistent by sub-proof #594.
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | End of split
% 241.73/48.28  | | | | | | 
% 241.73/48.28  | | | | | End of split
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | Case 2:
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | |   (196)  all_58_5 = e3 & op(e2, e1) = e3
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | | REF_CLOSE: (24), (41), (45), (196) are inconsistent by sub-proof
% 241.73/48.28  | | | | |            #1822.
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | End of split
% 241.73/48.28  | | | | 
% 241.73/48.28  | | | Case 2:
% 241.73/48.28  | | | | 
% 241.73/48.28  | | | |   (197)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0,
% 241.73/48.28  | | | |              e1) = e3)
% 241.73/48.28  | | | | 
% 241.73/48.28  | | | | REF_CLOSE: (3), (40), (45), (50), (197) are inconsistent by sub-proof
% 241.73/48.28  | | | |            #593.
% 241.73/48.28  | | | | 
% 241.73/48.28  | | | End of split
% 241.73/48.28  | | | 
% 241.73/48.28  | | End of split
% 241.73/48.28  | | 
% 241.73/48.28  | Case 2:
% 241.73/48.28  | | 
% 241.73/48.28  | |   (198)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 241.73/48.28  | |            e1)
% 241.73/48.28  | | 
% 241.73/48.28  | | REF_CLOSE: (40), (45), (50), (51), (198) are inconsistent by sub-proof #592.
% 241.73/48.28  | | 
% 241.73/48.28  | End of split
% 241.73/48.28  | 
% 241.73/48.28  End of proof
% 241.73/48.28  
% 241.73/48.28  Sub-proof #592 shows that the following formulas are inconsistent:
% 241.73/48.28  ----------------------------------------------------------------
% 241.73/48.28    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.73/48.28    (2)  all_58_14 = e0
% 241.73/48.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.28    (4)  op(e1, e1) = e0
% 241.73/48.28    (5)   ~ (e1 = e0)
% 241.73/48.28  
% 241.73/48.28  Begin of proof
% 241.73/48.28  | 
% 241.73/48.28  | BETA: splitting (1) gives:
% 241.73/48.28  | 
% 241.73/48.28  | Case 1:
% 241.73/48.28  | | 
% 241.73/48.28  | |   (6)  all_58_8 = e1 & op(e1, e1) = e1
% 241.73/48.28  | | 
% 241.73/48.28  | | ALPHA: (6) implies:
% 241.73/48.28  | |   (7)  op(e1, e1) = e1
% 241.73/48.28  | | 
% 241.73/48.28  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #2220.
% 241.73/48.28  | | 
% 241.73/48.28  | Case 2:
% 241.73/48.28  | | 
% 241.73/48.28  | |   (8)  all_58_14 = e1 & op(e0, e1) = e1
% 241.73/48.28  | | 
% 241.73/48.28  | | ALPHA: (8) implies:
% 241.73/48.28  | |   (9)  all_58_14 = e1
% 241.73/48.28  | | 
% 241.73/48.28  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #1033.
% 241.73/48.28  | | 
% 241.73/48.28  | End of split
% 241.73/48.28  | 
% 241.73/48.28  End of proof
% 241.73/48.28  
% 241.73/48.28  Sub-proof #593 shows that the following formulas are inconsistent:
% 241.73/48.28  ----------------------------------------------------------------
% 241.73/48.28    (1)   ~ (e3 = e0)
% 241.73/48.28    (2)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.73/48.28    (3)  all_58_14 = e0
% 241.73/48.28    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.28    (5)  op(e1, e1) = e0
% 241.73/48.28  
% 241.73/48.28  Begin of proof
% 241.73/48.28  | 
% 241.73/48.28  | BETA: splitting (2) gives:
% 241.73/48.28  | 
% 241.73/48.28  | Case 1:
% 241.73/48.28  | | 
% 241.73/48.28  | |   (6)  all_58_8 = e3 & op(e1, e1) = e3
% 241.73/48.28  | | 
% 241.73/48.28  | | REF_CLOSE: (1), (4), (5), (6) are inconsistent by sub-proof #2018.
% 241.73/48.28  | | 
% 241.73/48.28  | Case 2:
% 241.73/48.28  | | 
% 241.73/48.28  | |   (7)  all_58_14 = e3 & op(e0, e1) = e3
% 241.73/48.28  | | 
% 241.73/48.28  | | ALPHA: (7) implies:
% 241.73/48.28  | |   (8)  all_58_14 = e3
% 241.73/48.28  | | 
% 241.73/48.28  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #1871.
% 241.73/48.28  | | 
% 241.73/48.28  | End of split
% 241.73/48.28  | 
% 241.73/48.28  End of proof
% 241.73/48.28  
% 241.73/48.28  Sub-proof #594 shows that the following formulas are inconsistent:
% 241.73/48.28  ----------------------------------------------------------------
% 241.73/48.28    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.28         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.28    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.73/48.28         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.28    (3)   ~ (e3 = e0)
% 241.73/48.28    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.73/48.28         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.73/48.28    (5)   ~ (e2 = e0)
% 241.73/48.28    (6)  op(e1, e2) = all_52_6
% 241.73/48.28    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.28         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.28    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.73/48.28         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.73/48.28    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.28         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.73/48.28    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.73/48.28          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.73/48.28    (11)   ~ (all_52_7 = e3)
% 241.73/48.28    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.28          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.73/48.28    (13)   ~ (e3 = e1)
% 241.73/48.28    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.73/48.28          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.73/48.28    (15)  all_58_3 = e3
% 241.73/48.28    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.73/48.28          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.73/48.28    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.73/48.28          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.73/48.28    (18)  op(e3, e3) = e1
% 241.73/48.28    (19)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.28              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.73/48.28                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.73/48.28                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.73/48.28    (20)  op(e2, e1) = all_52_9
% 241.73/48.28    (21)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.73/48.28          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.73/48.28    (22)   ~ (e3 = e2)
% 241.73/48.28    (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.73/48.28          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.73/48.28    (24)  all_58_11 = e0 & op(e1, e0) = e0
% 241.73/48.28    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.73/48.28          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.73/48.28    (26)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.73/48.28          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.73/48.28    (27)  op(e2, e3) = all_52_1
% 241.73/48.28    (28)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.73/48.28          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.28    (29)   ~ (all_52_6 = e3)
% 241.73/48.28    (30)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.73/48.28          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.73/48.28    (31)  op(e0, e2) = all_52_7
% 241.73/48.28    (32)   ~ (all_52_4 = e3)
% 241.73/48.28    (33)  op(e3, e2) = all_52_4
% 241.73/48.28    (34)  all_58_14 = e0
% 241.73/48.28    (35)  all_58_5 = e1
% 241.73/48.28    (36)   ~ (all_52_9 = e3)
% 241.73/48.28    (37)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.73/48.28          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.28    (38)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.73/48.28          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.73/48.28    (39)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.28          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.73/48.28    (40)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.28    (41)  op(e0, e0) = e0
% 241.73/48.28    (42)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.73/48.28          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.73/48.28    (43)  op(e1, e1) = e0
% 241.73/48.28    (44)   ~ (e1 = e0)
% 241.73/48.28    (45)  all_58_4 = e3
% 241.73/48.28    (46)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.73/48.28          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.73/48.28    (47)  op(e2, e0) = all_52_13
% 241.73/48.28    (48)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.73/48.28          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.73/48.28            e1)
% 241.73/48.28    (49)   ~ (all_52_1 = e3)
% 241.73/48.28    (50)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.28          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.73/48.28            e2)
% 241.73/48.28    (51)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.73/48.28          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.73/48.28    (52)   ~ (e2 = e1)
% 241.73/48.28    (53)   ~ (all_52_1 = e1)
% 241.73/48.28  
% 241.73/48.28  Begin of proof
% 241.73/48.28  | 
% 241.73/48.28  | ALPHA: (24) implies:
% 241.73/48.28  |   (54)  op(e1, e0) = e0
% 241.73/48.28  | 
% 241.73/48.28  | BETA: splitting (26) gives:
% 241.73/48.28  | 
% 241.73/48.28  | Case 1:
% 241.73/48.28  | | 
% 241.73/48.28  | |   (55)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 241.73/48.28  | |           e3)
% 241.73/48.28  | | 
% 241.73/48.28  | | BETA: splitting (55) gives:
% 241.73/48.28  | | 
% 241.73/48.28  | | Case 1:
% 241.73/48.28  | | | 
% 241.73/48.28  | | |   (56)  all_58_6 = e3 & op(e1, e3) = e3
% 241.73/48.28  | | | 
% 241.73/48.28  | | | ALPHA: (56) implies:
% 241.73/48.28  | | |   (57)  all_58_6 = e3
% 241.73/48.28  | | | 
% 241.73/48.28  | | | BETA: splitting (2) gives:
% 241.73/48.28  | | | 
% 241.73/48.28  | | | Case 1:
% 241.73/48.28  | | | | 
% 241.73/48.28  | | | |   (58)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 241.73/48.28  | | | |             e2) = e3)
% 241.73/48.28  | | | | 
% 241.73/48.28  | | | | REF_CLOSE: (3), (5), (11), (18), (21), (22), (25), (31), (40), (44),
% 241.73/48.28  | | | |            (52), (57), (58) are inconsistent by sub-proof #1167.
% 241.73/48.28  | | | | 
% 241.73/48.28  | | | Case 2:
% 241.73/48.28  | | | | 
% 241.73/48.28  | | | |   (59)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 241.73/48.28  | | | |             e0) = e3)
% 241.73/48.28  | | | | 
% 241.73/48.28  | | | | BETA: splitting (59) gives:
% 241.73/48.28  | | | | 
% 241.73/48.28  | | | | Case 1:
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | |   (60)  all_58_14 = e3 & op(e0, e1) = e3
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 241.73/48.28  | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 241.73/48.28  | | | | |            (25), (26), (27), (28), (29), (30), (32), (33), (34), (36),
% 241.73/48.28  | | | | |            (37), (38), (39), (40), (42), (43), (44), (46), (47), (48),
% 241.73/48.28  | | | | |            (49), (50), (51), (52), (53), (57), (60) are inconsistent
% 241.73/48.28  | | | | |            by sub-proof #595.
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | Case 2:
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | |   (61)  all_58_15 = e3 & op(e0, e0) = e3
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | | ALPHA: (61) implies:
% 241.73/48.28  | | | | |   (62)  all_58_15 = e3
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | | BETA: splitting (8) gives:
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | | Case 1:
% 241.73/48.28  | | | | | | 
% 241.73/48.28  | | | | | |   (63)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 241.73/48.28  | | | | | |             e0) = e1)
% 241.73/48.28  | | | | | | 
% 241.73/48.28  | | | | | | BETA: splitting (63) gives:
% 241.73/48.28  | | | | | | 
% 241.73/48.28  | | | | | | Case 1:
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | |   (64)  all_58_9 = e1 & op(e3, e0) = e1
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | | ALPHA: (64) implies:
% 241.73/48.28  | | | | | | |   (65)  all_58_9 = e1
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | | REF_CLOSE: (1), (3), (5), (8), (12), (13), (15), (16), (18), (22),
% 241.73/48.28  | | | | | | |            (28), (32), (33), (35), (37), (39), (40), (41), (44),
% 241.73/48.28  | | | | | | |            (45), (52), (62), (65) are inconsistent by sub-proof
% 241.73/48.28  | | | | | | |            #605.
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | Case 2:
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | |   (66)  all_58_10 = e1 & op(e2, e0) = e1
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | | ALPHA: (66) implies:
% 241.73/48.28  | | | | | | |   (67)  all_58_10 = e1
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | | REF_CLOSE: (3), (5), (12), (15), (22), (35), (39), (44), (52),
% 241.73/48.28  | | | | | | |            (67) are inconsistent by sub-proof #992.
% 241.73/48.28  | | | | | | | 
% 241.73/48.28  | | | | | | End of split
% 241.73/48.28  | | | | | | 
% 241.73/48.28  | | | | | Case 2:
% 241.73/48.28  | | | | | | 
% 241.73/48.28  | | | | | |   (68)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 241.73/48.28  | | | | | |           op(e0, e0) = e1)
% 241.73/48.28  | | | | | | 
% 241.73/48.28  | | | | | | REF_CLOSE: (40), (41), (44), (54), (68) are inconsistent by
% 241.73/48.28  | | | | | |            sub-proof #625.
% 241.73/48.28  | | | | | | 
% 241.73/48.28  | | | | | End of split
% 241.73/48.28  | | | | | 
% 241.73/48.28  | | | | End of split
% 241.73/48.28  | | | | 
% 241.73/48.28  | | | End of split
% 241.73/48.28  | | | 
% 241.73/48.28  | | Case 2:
% 241.73/48.28  | | | 
% 241.73/48.28  | | |   (69)  all_58_7 = e3 & op(e1, e2) = e3
% 241.73/48.28  | | | 
% 241.73/48.28  | | | ALPHA: (69) implies:
% 241.73/48.28  | | |   (70)  op(e1, e2) = e3
% 241.73/48.28  | | | 
% 241.73/48.28  | | | REF_CLOSE: (6), (29), (40), (70) are inconsistent by sub-proof #2191.
% 241.73/48.28  | | | 
% 241.73/48.28  | | End of split
% 241.73/48.28  | | 
% 241.73/48.28  | Case 2:
% 241.73/48.28  | | 
% 241.73/48.28  | |   (71)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 241.73/48.28  | |           e3)
% 241.73/48.28  | | 
% 241.73/48.28  | | BETA: splitting (71) gives:
% 241.73/48.28  | | 
% 241.73/48.28  | | Case 1:
% 241.73/48.28  | | | 
% 241.73/48.28  | | |   (72)  all_58_8 = e3 & op(e1, e1) = e3
% 241.73/48.28  | | | 
% 241.73/48.28  | | | REF_CLOSE: (3), (40), (43), (72) are inconsistent by sub-proof #2018.
% 241.73/48.28  | | | 
% 241.73/48.28  | | Case 2:
% 241.73/48.28  | | | 
% 241.73/48.28  | | |   (73)  all_58_11 = e3 & op(e1, e0) = e3
% 241.73/48.28  | | | 
% 241.73/48.28  | | | REF_CLOSE: (1), (3), (5), (8), (12), (13), (15), (16), (18), (22), (28),
% 241.73/48.28  | | |            (32), (33), (35), (39), (40), (41), (44), (45), (52), (73) are
% 241.73/48.28  | | |            inconsistent by sub-proof #610.
% 241.73/48.28  | | | 
% 241.73/48.28  | | End of split
% 241.73/48.28  | | 
% 241.73/48.28  | End of split
% 241.73/48.28  | 
% 241.73/48.28  End of proof
% 241.73/48.28  
% 241.73/48.28  Sub-proof #595 shows that the following formulas are inconsistent:
% 241.73/48.28  ----------------------------------------------------------------
% 241.73/48.29    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.29         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.29    (2)   ~ (e3 = e0)
% 241.73/48.29    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.73/48.29         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.73/48.29    (4)  all_58_14 = e3 & op(e0, e1) = e3
% 241.73/48.29    (5)  all_58_6 = e3
% 241.73/48.29    (6)   ~ (e2 = e0)
% 241.73/48.29    (7)  op(e1, e2) = all_52_6
% 241.73/48.29    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.29         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.29    (9)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.73/48.29         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.73/48.29    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.29          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.73/48.29    (11)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.73/48.29          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.73/48.29    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.29          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.73/48.29    (13)   ~ (e3 = e1)
% 241.73/48.29    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.73/48.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.73/48.29    (15)  all_58_3 = e3
% 241.73/48.29    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.73/48.29          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.73/48.29    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.73/48.29          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.73/48.29    (18)  op(e3, e3) = e1
% 241.73/48.29    (19)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.29              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.73/48.29                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.73/48.29                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.73/48.29    (20)  op(e2, e1) = all_52_9
% 241.73/48.29    (21)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.73/48.29          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.73/48.29    (22)   ~ (e3 = e2)
% 241.73/48.29    (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.73/48.29          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.73/48.29    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.73/48.29          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.73/48.29    (25)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.73/48.29          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.73/48.29    (26)  op(e2, e3) = all_52_1
% 241.73/48.29    (27)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.73/48.29          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.29    (28)   ~ (all_52_6 = e3)
% 241.73/48.29    (29)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.73/48.29          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.73/48.29    (30)   ~ (all_52_4 = e3)
% 241.73/48.29    (31)  op(e3, e2) = all_52_4
% 241.73/48.29    (32)  all_58_14 = e0
% 241.73/48.29    (33)   ~ (all_52_9 = e3)
% 241.73/48.29    (34)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.73/48.29          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.29    (35)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.73/48.29          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.73/48.29    (36)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.29          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.73/48.29    (37)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.29    (38)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.73/48.29          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.73/48.29    (39)  op(e1, e1) = e0
% 241.73/48.29    (40)   ~ (e1 = e0)
% 241.73/48.29    (41)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.73/48.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.73/48.29    (42)  op(e2, e0) = all_52_13
% 241.73/48.29    (43)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.73/48.29          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.73/48.29            e1)
% 241.73/48.29    (44)   ~ (all_52_1 = e3)
% 241.73/48.29    (45)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.29          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.73/48.29            e2)
% 241.73/48.29    (46)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.73/48.29          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.73/48.29    (47)   ~ (e2 = e1)
% 241.73/48.29    (48)   ~ (all_52_1 = e1)
% 241.73/48.29  
% 241.73/48.29  Begin of proof
% 241.73/48.29  | 
% 241.73/48.29  | ALPHA: (4) implies:
% 241.73/48.29  |   (49)  all_58_14 = e3
% 241.73/48.29  | 
% 241.73/48.29  | COMBINE_EQS: (32), (49) imply:
% 241.73/48.29  |   (50)  e3 = e0
% 241.73/48.29  | 
% 241.73/48.29  | COMBINE_EQS: (5), (50) imply:
% 241.73/48.29  |   (51)  all_58_6 = e0
% 241.73/48.29  | 
% 241.73/48.29  | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 241.73/48.29  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 241.73/48.29  |            (26), (27), (28), (29), (30), (31), (33), (34), (35), (36), (37),
% 241.73/48.29  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 241.73/48.29  |            (51) are inconsistent by sub-proof #664.
% 241.73/48.29  | 
% 241.73/48.29  End of proof
% 241.73/48.29  
% 241.73/48.29  Sub-proof #596 shows that the following formulas are inconsistent:
% 241.73/48.29  ----------------------------------------------------------------
% 241.73/48.29    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.29         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.29    (2)   ~ (e3 = e0)
% 241.73/48.29    (3)  all_58_6 = e3
% 241.73/48.29    (4)   ~ (e2 = e0)
% 241.73/48.29    (5)  all_58_9 = e0
% 241.73/48.29    (6)  all_58_11 = e1
% 241.73/48.29    (7)  all_58_15 = e3
% 241.73/48.29    (8)  all_58_6 = e2 & op(e1, e3) = e2
% 241.73/48.29    (9)   ~ (e3 = e1)
% 241.73/48.29    (10)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.73/48.29          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.73/48.29    (11)  op(e3, e3) = e1
% 241.73/48.29    (12)   ~ (e3 = e2)
% 241.73/48.29    (13)  all_58_10 = e0
% 241.73/48.29    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.73/48.29          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.29    (15)   ~ (all_52_4 = e3)
% 241.73/48.29    (16)  op(e3, e2) = all_52_4
% 241.73/48.29    (17)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.73/48.29          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.29    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.29    (19)   ~ (e1 = e0)
% 241.73/48.29    (20)  all_58_4 = e3
% 241.73/48.29    (21)   ~ (e2 = e1)
% 241.73/48.29  
% 241.73/48.29  Begin of proof
% 241.73/48.29  | 
% 241.73/48.29  | ALPHA: (8) implies:
% 241.73/48.29  |   (22)  all_58_6 = e2
% 241.73/48.29  | 
% 241.73/48.29  | COMBINE_EQS: (3), (22) imply:
% 241.73/48.29  |   (23)  e3 = e2
% 241.73/48.29  | 
% 241.73/48.29  | SIMP: (23) implies:
% 241.73/48.29  |   (24)  e3 = e2
% 241.73/48.29  | 
% 241.73/48.29  | COMBINE_EQS: (7), (24) imply:
% 241.73/48.29  |   (25)  all_58_15 = e2
% 241.73/48.29  | 
% 241.73/48.29  | REF_CLOSE: (1), (2), (4), (5), (6), (9), (10), (11), (12), (13), (14), (15),
% 241.73/48.29  |            (16), (17), (18), (19), (20), (21), (25) are inconsistent by
% 241.73/48.29  |            sub-proof #612.
% 241.73/48.29  | 
% 241.73/48.29  End of proof
% 241.73/48.29  
% 241.73/48.29  Sub-proof #597 shows that the following formulas are inconsistent:
% 241.73/48.29  ----------------------------------------------------------------
% 241.73/48.29    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.29         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.29    (2)   ~ (e3 = e0)
% 241.73/48.29    (3)  all_58_6 = e3
% 241.73/48.29    (4)   ~ (e2 = e0)
% 241.73/48.29    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.29         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.29    (6)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.73/48.29         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.73/48.29    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.29         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.73/48.29    (8)  all_58_11 = e1
% 241.73/48.29    (9)  all_58_1 = e0
% 241.73/48.29    (10)  all_58_8 = e0
% 241.73/48.29    (11)  all_58_15 = e3
% 241.73/48.29    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.29          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.73/48.29    (13)   ~ (e3 = e1)
% 241.73/48.29    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.73/48.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.73/48.29    (15)  all_58_3 = e3
% 241.73/48.29    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.73/48.29          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.73/48.29    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.73/48.29          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.73/48.29    (18)  op(e3, e3) = e1
% 241.73/48.29    (19)  op(e2, e1) = all_52_9
% 241.73/48.29    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.73/48.29          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.73/48.29    (21)   ~ (e3 = e2)
% 241.73/48.29    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.73/48.29          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.73/48.29    (23)  op(e2, e0) = e0
% 241.73/48.29    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.73/48.29          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.73/48.29    (25)  all_58_10 = e0
% 241.73/48.29    (26)  op(e2, e3) = all_52_1
% 241.73/48.29    (27)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.73/48.29          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.29    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.73/48.29          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.73/48.29    (29)  all_58_2 = e0
% 241.73/48.29    (30)   ~ (all_52_4 = e3)
% 241.73/48.29    (31)  op(e3, e2) = all_52_4
% 241.73/48.29    (32)  all_58_14 = e0
% 241.73/48.29    (33)  all_58_5 = e1
% 241.73/48.29    (34)   ~ (all_52_9 = e3)
% 241.73/48.29    (35)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.73/48.29          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.29    (36)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.73/48.29          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.73/48.29    (37)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.29          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.73/48.29    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.29    (39)  op(e0, e0) = e0
% 241.73/48.29    (40)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.73/48.29          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.73/48.29    (41)   ~ (e1 = e0)
% 241.73/48.29    (42)  all_58_13 = e1
% 241.73/48.29    (43)  all_58_4 = e3
% 241.73/48.29    (44)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.73/48.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.73/48.29    (45)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.73/48.29          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.73/48.29            e1)
% 241.73/48.29    (46)   ~ (all_52_1 = e3)
% 241.73/48.29    (47)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.73/48.29          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.73/48.29    (48)   ~ (e2 = e1)
% 241.73/48.29    (49)   ~ (all_52_1 = e1)
% 241.73/48.29  
% 241.73/48.29  Begin of proof
% 241.73/48.29  | 
% 241.73/48.29  | BETA: splitting (40) gives:
% 241.73/48.29  | 
% 241.73/48.29  | Case 1:
% 241.73/48.29  | | 
% 241.73/48.29  | |   (50)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 241.73/48.29  | |           e2)
% 241.73/48.29  | | 
% 241.73/48.29  | | BETA: splitting (50) gives:
% 241.73/48.29  | | 
% 241.73/48.29  | | Case 1:
% 241.73/48.29  | | | 
% 241.73/48.29  | | |   (51)  all_58_9 = e2 & op(e3, e0) = e2
% 241.73/48.29  | | | 
% 241.73/48.29  | | | ALPHA: (51) implies:
% 241.73/48.29  | | |   (52)  all_58_9 = e2
% 241.73/48.29  | | |   (53)  op(e3, e0) = e2
% 241.73/48.29  | | | 
% 241.73/48.30  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.73/48.30  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.73/48.30  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 241.73/48.30  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 241.73/48.30  | | |            (43), (44), (45), (46), (47), (48), (49), (52), (53) are
% 241.73/48.30  | | |            inconsistent by sub-proof #598.
% 241.73/48.30  | | | 
% 241.73/48.30  | | Case 2:
% 241.73/48.30  | | | 
% 241.73/48.30  | | |   (54)  all_58_10 = e2 & op(e2, e0) = e2
% 241.73/48.30  | | | 
% 241.73/48.30  | | | ALPHA: (54) implies:
% 241.73/48.30  | | |   (55)  op(e2, e0) = e2
% 241.73/48.30  | | | 
% 241.73/48.30  | | | REF_CLOSE: (4), (23), (38), (55) are inconsistent by sub-proof #2121.
% 241.73/48.30  | | | 
% 241.73/48.30  | | End of split
% 241.73/48.30  | | 
% 241.73/48.30  | Case 2:
% 241.73/48.30  | | 
% 241.73/48.30  | |   (56)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.73/48.30  | |           e2)
% 241.73/48.30  | | 
% 241.73/48.30  | | BETA: splitting (56) gives:
% 241.73/48.30  | | 
% 241.73/48.30  | | Case 1:
% 241.73/48.30  | | | 
% 241.73/48.30  | | |   (57)  all_58_11 = e2 & op(e1, e0) = e2
% 241.73/48.30  | | | 
% 241.73/48.30  | | | REF_CLOSE: (8), (48), (57) are inconsistent by sub-proof #1554.
% 241.73/48.30  | | | 
% 241.73/48.30  | | Case 2:
% 241.73/48.30  | | | 
% 241.73/48.30  | | |   (58)  all_58_15 = e2 & op(e0, e0) = e2
% 241.73/48.30  | | | 
% 241.73/48.30  | | | ALPHA: (58) implies:
% 241.73/48.30  | | |   (59)  all_58_15 = e2
% 241.73/48.30  | | | 
% 241.73/48.30  | | | REF_CLOSE: (2), (4), (8), (12), (13), (15), (21), (23), (29), (33), (35),
% 241.73/48.30  | | |            (37), (38), (40), (41), (48), (59) are inconsistent by
% 241.73/48.30  | | |            sub-proof #626.
% 241.73/48.30  | | | 
% 241.73/48.30  | | End of split
% 241.73/48.30  | | 
% 241.73/48.30  | End of split
% 241.73/48.30  | 
% 241.73/48.30  End of proof
% 241.73/48.30  
% 241.73/48.30  Sub-proof #598 shows that the following formulas are inconsistent:
% 241.73/48.30  ----------------------------------------------------------------
% 241.73/48.30    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.30         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.30    (2)   ~ (e3 = e0)
% 241.73/48.30    (3)  all_58_6 = e3
% 241.73/48.30    (4)   ~ (e2 = e0)
% 241.73/48.30    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.30         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.30    (6)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.73/48.30         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.73/48.30    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.30         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.73/48.30    (8)  all_58_11 = e1
% 241.73/48.30    (9)  all_58_1 = e0
% 241.73/48.30    (10)  all_58_8 = e0
% 241.73/48.30    (11)  all_58_15 = e3
% 241.73/48.30    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.30          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.73/48.30    (13)   ~ (e3 = e1)
% 241.73/48.30    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.73/48.30          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.73/48.30    (15)  all_58_3 = e3
% 241.73/48.30    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.73/48.30          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.73/48.30    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.73/48.30          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.73/48.30    (18)  op(e3, e3) = e1
% 241.73/48.30    (19)  op(e2, e1) = all_52_9
% 241.73/48.30    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.73/48.30          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.73/48.30    (21)   ~ (e3 = e2)
% 241.73/48.30    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.73/48.30          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.73/48.30    (23)  op(e2, e0) = e0
% 241.73/48.30    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.73/48.30          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.73/48.30    (25)  all_58_10 = e0
% 241.73/48.30    (26)  op(e2, e3) = all_52_1
% 241.73/48.30    (27)  op(e3, e0) = e2
% 241.73/48.30    (28)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.73/48.30          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.30    (29)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.73/48.30          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.73/48.30    (30)  all_58_2 = e0
% 241.73/48.30    (31)   ~ (all_52_4 = e3)
% 241.73/48.30    (32)  op(e3, e2) = all_52_4
% 241.73/48.30    (33)  all_58_14 = e0
% 241.73/48.30    (34)  all_58_5 = e1
% 241.73/48.30    (35)   ~ (all_52_9 = e3)
% 241.73/48.30    (36)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.73/48.30          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.30    (37)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.73/48.30          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.73/48.30    (38)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.30          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.73/48.30    (39)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.30            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.30    (40)  op(e0, e0) = e0
% 241.73/48.30    (41)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.73/48.30          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.73/48.30    (42)   ~ (e1 = e0)
% 241.73/48.30    (43)  all_58_13 = e1
% 241.73/48.30    (44)  all_58_4 = e3
% 241.73/48.30    (45)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.73/48.30          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.73/48.30    (46)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.73/48.30          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.73/48.30            e1)
% 241.73/48.30    (47)  all_58_9 = e2
% 241.73/48.30    (48)   ~ (all_52_1 = e3)
% 241.73/48.30    (49)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.73/48.30          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.73/48.30    (50)   ~ (e2 = e1)
% 241.73/48.30    (51)   ~ (all_52_1 = e1)
% 241.73/48.30  
% 241.73/48.30  Begin of proof
% 241.73/48.30  | 
% 241.73/48.30  | BETA: splitting (37) gives:
% 241.73/48.30  | 
% 241.73/48.30  | Case 1:
% 241.73/48.30  | | 
% 241.73/48.30  | |   (52)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 241.73/48.30  | |           e2)
% 241.73/48.30  | | 
% 241.73/48.30  | | BETA: splitting (52) gives:
% 241.73/48.30  | | 
% 241.73/48.30  | | Case 1:
% 241.73/48.30  | | | 
% 241.73/48.30  | | |   (53)  all_58_6 = e2 & op(e1, e3) = e2
% 241.73/48.30  | | | 
% 241.73/48.30  | | | REF_CLOSE: (2), (3), (4), (8), (11), (12), (13), (15), (21), (23), (30),
% 241.73/48.30  | | |            (34), (36), (38), (39), (41), (42), (50), (53) are inconsistent
% 241.73/48.30  | | |            by sub-proof #604.
% 241.73/48.30  | | | 
% 241.73/48.30  | | Case 2:
% 241.73/48.30  | | | 
% 241.73/48.30  | | |   (54)  all_58_7 = e2 & op(e1, e2) = e2
% 241.73/48.30  | | | 
% 241.73/48.30  | | | ALPHA: (54) implies:
% 241.73/48.30  | | |   (55)  all_58_7 = e2
% 241.73/48.30  | | | 
% 241.73/48.30  | | | BETA: splitting (20) gives:
% 241.73/48.30  | | | 
% 241.73/48.30  | | | Case 1:
% 241.73/48.30  | | | | 
% 241.73/48.30  | | | |   (56)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3)
% 241.73/48.30  | | | |           = e2)
% 241.73/48.30  | | | | 
% 241.73/48.30  | | | | BETA: splitting (56) gives:
% 241.73/48.30  | | | | 
% 241.73/48.30  | | | | Case 1:
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | |   (57)  all_58_0 = e2 & op(e3, e3) = e2
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | | ALPHA: (57) implies:
% 241.73/48.30  | | | | |   (58)  op(e3, e3) = e2
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | | REF_CLOSE: (18), (39), (50), (58) are inconsistent by sub-proof #2267.
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | Case 2:
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | |   (59)  all_58_2 = e2 & op(e2, e3) = e2
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | | ALPHA: (59) implies:
% 241.73/48.30  | | | | |   (60)  all_58_2 = e2
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | | COMBINE_EQS: (30), (60) imply:
% 241.73/48.30  | | | | |   (61)  e2 = e0
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | | COMBINE_EQS: (47), (61) imply:
% 241.73/48.30  | | | | |   (62)  all_58_9 = e0
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | | REF_CLOSE: (1), (4), (9), (18), (21), (39), (44), (50), (62) are
% 241.73/48.30  | | | | |            inconsistent by sub-proof #1097.
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | End of split
% 241.73/48.30  | | | | 
% 241.73/48.30  | | | Case 2:
% 241.73/48.30  | | | | 
% 241.73/48.30  | | | |   (63)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3)
% 241.73/48.30  | | | |           = e2)
% 241.73/48.30  | | | | 
% 241.73/48.30  | | | | BETA: splitting (63) gives:
% 241.73/48.30  | | | | 
% 241.73/48.30  | | | | Case 1:
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | |   (64)  all_58_6 = e2 & op(e1, e3) = e2
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | | REF_CLOSE: (2), (3), (4), (8), (11), (12), (13), (15), (21), (23),
% 241.73/48.30  | | | | |            (30), (34), (36), (38), (39), (41), (42), (50), (64) are
% 241.73/48.30  | | | | |            inconsistent by sub-proof #604.
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | Case 2:
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | |   (65)  all_58_12 = e2 & op(e0, e3) = e2
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | | ALPHA: (65) implies:
% 241.73/48.30  | | | | |   (66)  all_58_12 = e2
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 241.73/48.30  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.73/48.30  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 241.73/48.30  | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 241.73/48.30  | | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (55),
% 241.73/48.30  | | | | |            (66) are inconsistent by sub-proof #600.
% 241.73/48.30  | | | | | 
% 241.73/48.30  | | | | End of split
% 241.73/48.30  | | | | 
% 241.73/48.30  | | | End of split
% 241.73/48.30  | | | 
% 241.73/48.30  | | End of split
% 241.73/48.30  | | 
% 241.73/48.30  | Case 2:
% 241.73/48.30  | | 
% 241.73/48.30  | |   (67)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 241.73/48.30  | |           e2)
% 241.73/48.30  | | 
% 241.73/48.30  | | BETA: splitting (67) gives:
% 241.73/48.30  | | 
% 241.73/48.30  | | Case 1:
% 241.73/48.30  | | | 
% 241.73/48.30  | | |   (68)  all_58_8 = e2 & op(e1, e1) = e2
% 241.73/48.30  | | | 
% 241.73/48.30  | | | REF_CLOSE: (1), (4), (9), (10), (18), (21), (39), (44), (47), (50), (68)
% 241.73/48.30  | | |            are inconsistent by sub-proof #599.
% 241.73/48.30  | | | 
% 241.73/48.30  | | Case 2:
% 241.73/48.30  | | | 
% 241.73/48.30  | | |   (69)  all_58_11 = e2 & op(e1, e0) = e2
% 241.73/48.30  | | | 
% 241.73/48.30  | | | ALPHA: (69) implies:
% 241.73/48.30  | | |   (70)  all_58_11 = e2
% 241.73/48.30  | | | 
% 241.73/48.30  | | | COMBINE_EQS: (8), (70) imply:
% 241.73/48.30  | | |   (71)  e2 = e1
% 241.73/48.30  | | | 
% 241.73/48.30  | | | COMBINE_EQS: (47), (71) imply:
% 241.73/48.30  | | |   (72)  all_58_9 = e1
% 241.73/48.30  | | | 
% 241.73/48.30  | | | REF_CLOSE: (1), (4), (9), (18), (21), (39), (44), (50), (72) are
% 241.73/48.30  | | |            inconsistent by sub-proof #1338.
% 241.73/48.30  | | | 
% 241.73/48.30  | | End of split
% 241.73/48.30  | | 
% 241.73/48.30  | End of split
% 241.73/48.30  | 
% 241.73/48.30  End of proof
% 241.73/48.30  
% 241.73/48.30  Sub-proof #599 shows that the following formulas are inconsistent:
% 241.73/48.30  ----------------------------------------------------------------
% 241.73/48.30    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.30         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.30    (2)   ~ (e2 = e0)
% 241.73/48.30    (3)  all_58_1 = e0
% 241.73/48.30    (4)  all_58_8 = e0
% 241.73/48.30    (5)  op(e3, e3) = e1
% 241.73/48.30    (6)   ~ (e3 = e2)
% 241.73/48.30    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.30    (8)  all_58_4 = e3
% 241.73/48.30    (9)  all_58_9 = e2
% 241.73/48.30    (10)  all_58_8 = e2 & op(e1, e1) = e2
% 241.73/48.30    (11)   ~ (e2 = e1)
% 241.73/48.30  
% 241.73/48.30  Begin of proof
% 241.73/48.30  | 
% 241.73/48.30  | ALPHA: (10) implies:
% 241.73/48.30  |   (12)  all_58_8 = e2
% 241.73/48.30  | 
% 241.73/48.30  | COMBINE_EQS: (4), (12) imply:
% 241.73/48.30  |   (13)  e2 = e0
% 241.73/48.30  | 
% 241.73/48.30  | SIMP: (13) implies:
% 241.73/48.30  |   (14)  e2 = e0
% 241.73/48.30  | 
% 241.73/48.30  | COMBINE_EQS: (9), (14) imply:
% 241.73/48.30  |   (15)  all_58_9 = e0
% 241.73/48.30  | 
% 241.73/48.30  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (11), (15) are inconsistent by
% 241.73/48.30  |            sub-proof #1097.
% 241.73/48.30  | 
% 241.73/48.30  End of proof
% 241.73/48.30  
% 241.73/48.30  Sub-proof #600 shows that the following formulas are inconsistent:
% 241.73/48.30  ----------------------------------------------------------------
% 241.73/48.30    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.30         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.30    (2)   ~ (e3 = e0)
% 241.73/48.30    (3)  all_58_6 = e3
% 241.73/48.30    (4)   ~ (e2 = e0)
% 241.73/48.30    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.30         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.30    (6)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.73/48.30         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.73/48.30    (7)  all_58_12 = e2
% 241.73/48.30    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.30         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.73/48.30    (9)  all_58_11 = e1
% 241.73/48.30    (10)  all_58_8 = e0
% 241.73/48.30    (11)  all_58_15 = e3
% 241.73/48.30    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.30          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.73/48.30    (13)   ~ (e3 = e1)
% 241.73/48.30    (14)  all_58_7 = e2
% 241.73/48.30    (15)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.73/48.30          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.73/48.30    (16)  all_58_3 = e3
% 241.73/48.30    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.73/48.30          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.73/48.30    (18)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.73/48.30          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.73/48.30    (19)  op(e3, e3) = e1
% 241.73/48.30    (20)  op(e2, e1) = all_52_9
% 241.73/48.30    (21)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.73/48.30          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.73/48.30    (22)   ~ (e3 = e2)
% 241.73/48.30    (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.73/48.30          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.73/48.30    (24)  op(e2, e0) = e0
% 241.73/48.30    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.73/48.30          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.73/48.30    (26)  all_58_10 = e0
% 241.73/48.30    (27)  op(e2, e3) = all_52_1
% 241.73/48.30    (28)  op(e3, e0) = e2
% 241.73/48.30    (29)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.73/48.30          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.30    (30)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.73/48.30          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.73/48.30    (31)  all_58_2 = e0
% 241.73/48.30    (32)   ~ (all_52_4 = e3)
% 241.73/48.31    (33)  op(e3, e2) = all_52_4
% 241.73/48.31    (34)  all_58_14 = e0
% 241.73/48.31    (35)  all_58_5 = e1
% 241.73/48.31    (36)   ~ (all_52_9 = e3)
% 241.73/48.31    (37)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.73/48.31          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.31    (38)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.73/48.31          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.73/48.31    (39)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.31          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.73/48.31    (40)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.31    (41)  op(e0, e0) = e0
% 241.73/48.31    (42)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.73/48.31          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.73/48.31    (43)   ~ (e1 = e0)
% 241.73/48.31    (44)  all_58_13 = e1
% 241.73/48.31    (45)  all_58_4 = e3
% 241.73/48.31    (46)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.73/48.31          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.73/48.31    (47)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.73/48.31          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.73/48.31            e1)
% 241.73/48.31    (48)  all_58_9 = e2
% 241.73/48.31    (49)   ~ (all_52_1 = e3)
% 241.73/48.31    (50)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.73/48.31          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.73/48.31    (51)   ~ (e2 = e1)
% 241.73/48.31    (52)   ~ (all_52_1 = e1)
% 241.73/48.31  
% 241.73/48.31  Begin of proof
% 241.73/48.31  | 
% 241.73/48.31  | BETA: splitting (23) gives:
% 241.73/48.31  | 
% 241.73/48.31  | Case 1:
% 241.73/48.31  | | 
% 241.73/48.31  | |   (53)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 241.73/48.31  | |           e2)
% 241.73/48.31  | | 
% 241.73/48.31  | | BETA: splitting (53) gives:
% 241.73/48.31  | | 
% 241.73/48.31  | | Case 1:
% 241.73/48.31  | | | 
% 241.73/48.31  | | |   (54)  all_58_4 = e2 & op(e3, e1) = e2
% 241.73/48.31  | | | 
% 241.73/48.31  | | | ALPHA: (54) implies:
% 241.73/48.31  | | |   (55)  all_58_4 = e2
% 241.73/48.31  | | | 
% 241.73/48.31  | | | COMBINE_EQS: (45), (55) imply:
% 241.73/48.31  | | |   (56)  e3 = e2
% 241.73/48.31  | | | 
% 241.73/48.31  | | | COMBINE_EQS: (11), (56) imply:
% 241.73/48.31  | | |   (57)  all_58_15 = e2
% 241.73/48.31  | | | 
% 241.73/48.31  | | | REF_CLOSE: (2), (4), (9), (12), (13), (16), (22), (24), (31), (35), (37),
% 241.73/48.31  | | |            (39), (40), (42), (43), (51), (57) are inconsistent by
% 241.73/48.31  | | |            sub-proof #626.
% 241.73/48.31  | | | 
% 241.73/48.31  | | Case 2:
% 241.73/48.31  | | | 
% 241.73/48.31  | | |   (58)  all_58_5 = e2 & op(e2, e1) = e2
% 241.73/48.31  | | | 
% 241.73/48.31  | | | REF_CLOSE: (2), (4), (5), (6), (8), (12), (13), (14), (15), (16), (17),
% 241.73/48.31  | | |            (18), (19), (20), (21), (22), (23), (25), (26), (27), (30),
% 241.73/48.31  | | |            (32), (33), (35), (36), (38), (39), (40), (41), (43), (46),
% 241.73/48.31  | | |            (47), (49), (50), (51), (52), (58) are inconsistent by
% 241.73/48.31  | | |            sub-proof #623.
% 241.73/48.31  | | | 
% 241.73/48.31  | | End of split
% 241.73/48.31  | | 
% 241.73/48.31  | Case 2:
% 241.73/48.31  | | 
% 241.73/48.31  | |   (59)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 241.73/48.31  | |           e2)
% 241.73/48.31  | | 
% 241.73/48.31  | | BETA: splitting (59) gives:
% 241.73/48.31  | | 
% 241.73/48.31  | | Case 1:
% 241.73/48.31  | | | 
% 241.73/48.31  | | |   (60)  all_58_8 = e2 & op(e1, e1) = e2
% 241.73/48.31  | | | 
% 241.73/48.31  | | | ALPHA: (60) implies:
% 241.73/48.31  | | |   (61)  all_58_8 = e2
% 241.73/48.31  | | | 
% 241.73/48.31  | | | COMBINE_EQS: (10), (61) imply:
% 241.73/48.31  | | |   (62)  e2 = e0
% 241.73/48.31  | | | 
% 241.73/48.31  | | | SIMP: (62) implies:
% 241.73/48.31  | | |   (63)  e2 = e0
% 241.73/48.31  | | | 
% 241.73/48.31  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (11), (12), (13), (14),
% 241.73/48.31  | | |            (16), (17), (19), (21), (22), (24), (25), (28), (29), (31),
% 241.73/48.31  | | |            (32), (33), (35), (37), (39), (40), (42), (43), (44), (48),
% 241.73/48.31  | | |            (51), (63) are inconsistent by sub-proof #601.
% 241.73/48.31  | | | 
% 241.73/48.31  | | Case 2:
% 241.73/48.31  | | | 
% 241.73/48.31  | | |   (64)  all_58_14 = e2 & op(e0, e1) = e2
% 241.73/48.31  | | | 
% 241.73/48.31  | | | ALPHA: (64) implies:
% 241.73/48.31  | | |   (65)  all_58_14 = e2
% 241.73/48.31  | | | 
% 241.73/48.31  | | | COMBINE_EQS: (34), (65) imply:
% 241.73/48.31  | | |   (66)  e2 = e0
% 241.73/48.31  | | | 
% 241.73/48.31  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (11), (12), (13), (14),
% 241.73/48.31  | | |            (16), (17), (19), (21), (22), (24), (25), (28), (29), (31),
% 241.73/48.31  | | |            (32), (33), (35), (37), (39), (40), (42), (43), (44), (48),
% 241.73/48.31  | | |            (51), (66) are inconsistent by sub-proof #601.
% 241.73/48.31  | | | 
% 241.73/48.31  | | End of split
% 241.73/48.31  | | 
% 241.73/48.31  | End of split
% 241.73/48.31  | 
% 241.73/48.31  End of proof
% 241.73/48.31  
% 241.73/48.31  Sub-proof #601 shows that the following formulas are inconsistent:
% 241.73/48.31  ----------------------------------------------------------------
% 241.73/48.31    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.31         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.31    (2)   ~ (e3 = e0)
% 241.73/48.31    (3)  all_58_6 = e3
% 241.73/48.31    (4)   ~ (e2 = e0)
% 241.73/48.31    (5)  e2 = e0
% 241.73/48.31    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.31         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.73/48.31    (7)  all_58_12 = e2
% 241.73/48.31    (8)  all_58_11 = e1
% 241.73/48.31    (9)  all_58_15 = e3
% 241.73/48.31    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.73/48.31          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.73/48.31    (11)   ~ (e3 = e1)
% 241.73/48.31    (12)  all_58_7 = e2
% 241.73/48.31    (13)  all_58_3 = e3
% 241.73/48.31    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.73/48.31          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.73/48.31    (15)  op(e3, e3) = e1
% 241.73/48.31    (16)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.73/48.31          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.73/48.31    (17)   ~ (e3 = e2)
% 241.73/48.31    (18)  op(e2, e0) = e0
% 241.73/48.31    (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.73/48.31          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.73/48.31    (20)  op(e3, e0) = e2
% 241.73/48.31    (21)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.73/48.31          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.73/48.31    (22)  all_58_2 = e0
% 241.73/48.31    (23)   ~ (all_52_4 = e3)
% 241.73/48.31    (24)  op(e3, e2) = all_52_4
% 241.73/48.31    (25)  all_58_5 = e1
% 241.73/48.31    (26)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.73/48.31          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.73/48.31    (27)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.73/48.31          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.73/48.31    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.31    (29)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.73/48.31          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.73/48.31    (30)   ~ (e1 = e0)
% 241.73/48.31    (31)  all_58_13 = e1
% 241.73/48.31    (32)  all_58_9 = e2
% 241.73/48.31    (33)   ~ (e2 = e1)
% 241.73/48.31  
% 241.73/48.31  Begin of proof
% 241.73/48.31  | 
% 241.73/48.31  | COMBINE_EQS: (5), (12) imply:
% 241.73/48.31  |   (34)  all_58_7 = e0
% 241.73/48.31  | 
% 241.73/48.31  | BETA: splitting (14) gives:
% 241.73/48.31  | 
% 241.73/48.31  | Case 1:
% 241.73/48.31  | | 
% 241.73/48.31  | |   (35)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 241.73/48.31  | |           e3)
% 241.73/48.31  | | 
% 241.73/48.31  | | REF_CLOSE: (11), (15), (23), (24), (28), (35) are inconsistent by sub-proof
% 241.73/48.31  | |            #1401.
% 241.73/48.31  | | 
% 241.73/48.31  | Case 2:
% 241.73/48.31  | | 
% 241.73/48.31  | |   (36)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 241.73/48.31  | |           e3)
% 241.73/48.31  | | 
% 241.73/48.31  | | BETA: splitting (36) gives:
% 241.73/48.31  | | 
% 241.73/48.31  | | Case 1:
% 241.73/48.31  | | | 
% 241.73/48.31  | | |   (37)  all_58_4 = e3 & op(e3, e1) = e3
% 241.73/48.31  | | | 
% 241.73/48.31  | | | ALPHA: (37) implies:
% 241.73/48.31  | | |   (38)  all_58_4 = e3
% 241.73/48.31  | | | 
% 241.73/48.31  | | | BETA: splitting (21) gives:
% 241.73/48.31  | | | 
% 241.73/48.31  | | | Case 1:
% 241.73/48.31  | | | | 
% 241.73/48.31  | | | |   (39)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 241.73/48.31  | | | |           = e0)
% 241.73/48.31  | | | | 
% 241.73/48.31  | | | | BETA: splitting (39) gives:
% 241.73/48.31  | | | | 
% 241.73/48.31  | | | | Case 1:
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | |   (40)  all_58_0 = e0 & op(e3, e3) = e0
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | | ALPHA: (40) implies:
% 241.73/48.31  | | | | |   (41)  op(e3, e3) = e0
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | | REF_CLOSE: (15), (28), (30), (41) are inconsistent by sub-proof #1828.
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | Case 2:
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | |   (42)  all_58_1 = e0 & op(e3, e2) = e0
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | | ALPHA: (42) implies:
% 241.73/48.31  | | | | |   (43)  all_58_1 = e0
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | | BETA: splitting (6) gives:
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | | Case 1:
% 241.73/48.31  | | | | | | 
% 241.73/48.31  | | | | | |   (44)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2,
% 241.73/48.31  | | | | | |             e2) = e2)
% 241.73/48.31  | | | | | | 
% 241.73/48.31  | | | | | | BETA: splitting (44) gives:
% 241.73/48.31  | | | | | | 
% 241.73/48.31  | | | | | | Case 1:
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | |   (45)  all_58_1 = e2 & op(e3, e2) = e2
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | | REF_CLOSE: (1), (4), (15), (17), (28), (32), (33), (38), (43),
% 241.73/48.31  | | | | | | |            (45) are inconsistent by sub-proof #603.
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | Case 2:
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | |   (46)  all_58_3 = e2 & op(e2, e2) = e2
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | | ALPHA: (46) implies:
% 241.73/48.31  | | | | | | |   (47)  all_58_3 = e2
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | | COMBINE_EQS: (13), (47) imply:
% 241.73/48.31  | | | | | | |   (48)  e3 = e2
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | | COMBINE_EQS: (9), (48) imply:
% 241.73/48.31  | | | | | | |   (49)  all_58_15 = e2
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | | REF_CLOSE: (2), (4), (8), (10), (11), (13), (17), (18), (22),
% 241.73/48.31  | | | | | | |            (25), (26), (27), (28), (29), (30), (33), (49) are
% 241.73/48.31  | | | | | | |            inconsistent by sub-proof #626.
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | End of split
% 241.73/48.31  | | | | | | 
% 241.73/48.31  | | | | | Case 2:
% 241.73/48.31  | | | | | | 
% 241.73/48.31  | | | | | |   (50)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0,
% 241.73/48.31  | | | | | |             e2) = e2)
% 241.73/48.31  | | | | | | 
% 241.73/48.31  | | | | | | BETA: splitting (50) gives:
% 241.73/48.31  | | | | | | 
% 241.73/48.31  | | | | | | Case 1:
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | |   (51)  all_58_7 = e2 & op(e1, e2) = e2
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | | REF_CLOSE: (1), (4), (12), (15), (17), (28), (32), (33), (34),
% 241.73/48.31  | | | | | | |            (38), (43) are inconsistent by sub-proof #602.
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | Case 2:
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | |   (52)  all_58_13 = e2 & op(e0, e2) = e2
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | | ALPHA: (52) implies:
% 241.73/48.31  | | | | | | |   (53)  all_58_13 = e2
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | | COMBINE_EQS: (31), (53) imply:
% 241.73/48.31  | | | | | | |   (54)  e2 = e1
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | | COMBINE_EQS: (32), (54) imply:
% 241.73/48.31  | | | | | | |   (55)  all_58_9 = e1
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (15), (16), (17), (19), (28),
% 241.73/48.31  | | | | | | |            (30), (33), (38), (43), (55) are inconsistent by
% 241.73/48.31  | | | | | | |            sub-proof #1148.
% 241.73/48.31  | | | | | | | 
% 241.73/48.31  | | | | | | End of split
% 241.73/48.31  | | | | | | 
% 241.73/48.31  | | | | | End of split
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | End of split
% 241.73/48.31  | | | | 
% 241.73/48.31  | | | Case 2:
% 241.73/48.31  | | | | 
% 241.73/48.31  | | | |   (56)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 241.73/48.31  | | | |           = e0)
% 241.73/48.31  | | | | 
% 241.73/48.31  | | | | BETA: splitting (56) gives:
% 241.73/48.31  | | | | 
% 241.73/48.31  | | | | Case 1:
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | |   (57)  all_58_4 = e0 & op(e3, e1) = e0
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | | REF_CLOSE: (2), (38), (57) are inconsistent by sub-proof #1697.
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | Case 2:
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | |   (58)  all_58_9 = e0 & op(e3, e0) = e0
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | | REF_CLOSE: (4), (32), (58) are inconsistent by sub-proof #1563.
% 241.73/48.31  | | | | | 
% 241.73/48.31  | | | | End of split
% 241.73/48.31  | | | | 
% 241.73/48.31  | | | End of split
% 241.73/48.31  | | | 
% 241.73/48.31  | | Case 2:
% 241.73/48.31  | | | 
% 241.73/48.31  | | |   (59)  all_58_9 = e3 & op(e3, e0) = e3
% 241.73/48.31  | | | 
% 241.73/48.31  | | | ALPHA: (59) implies:
% 241.73/48.31  | | |   (60)  op(e3, e0) = e3
% 241.73/48.31  | | | 
% 241.73/48.31  | | | REF_CLOSE: (17), (20), (28), (60) are inconsistent by sub-proof #2125.
% 241.73/48.31  | | | 
% 241.73/48.31  | | End of split
% 241.73/48.31  | | 
% 241.73/48.31  | End of split
% 241.73/48.31  | 
% 241.73/48.31  End of proof
% 241.73/48.31  
% 241.73/48.31  Sub-proof #602 shows that the following formulas are inconsistent:
% 241.73/48.31  ----------------------------------------------------------------
% 241.73/48.31    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.31         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.31    (2)   ~ (e2 = e0)
% 241.73/48.31    (3)  all_58_7 = e0
% 241.73/48.31    (4)  all_58_1 = e0
% 241.73/48.31    (5)  all_58_7 = e2
% 241.73/48.31    (6)  op(e3, e3) = e1
% 241.73/48.31    (7)   ~ (e3 = e2)
% 241.73/48.31    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.73/48.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.73/48.31    (9)  all_58_4 = e3
% 241.73/48.31    (10)  all_58_9 = e2
% 241.73/48.31    (11)   ~ (e2 = e1)
% 241.73/48.31  
% 241.73/48.31  Begin of proof
% 241.73/48.31  | 
% 241.73/48.31  | COMBINE_EQS: (3), (5) imply:
% 241.73/48.31  |   (12)  e2 = e0
% 241.73/48.31  | 
% 241.73/48.31  | SIMP: (12) implies:
% 241.73/48.31  |   (13)  e2 = e0
% 241.73/48.31  | 
% 241.73/48.31  | COMBINE_EQS: (10), (13) imply:
% 241.73/48.31  |   (14)  all_58_9 = e0
% 241.73/48.31  | 
% 241.73/48.31  | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (11), (14) are inconsistent by
% 241.73/48.31  |            sub-proof #1097.
% 241.73/48.31  | 
% 241.73/48.31  End of proof
% 241.73/48.31  
% 241.73/48.31  Sub-proof #603 shows that the following formulas are inconsistent:
% 241.73/48.31  ----------------------------------------------------------------
% 241.73/48.31    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.73/48.31         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.73/48.31    (2)   ~ (e2 = e0)
% 241.73/48.31    (3)  all_58_1 = e2 & op(e3, e2) = e2
% 241.73/48.31    (4)  all_58_1 = e0
% 241.80/48.31    (5)  op(e3, e3) = e1
% 241.80/48.31    (6)   ~ (e3 = e2)
% 241.80/48.31    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.80/48.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.80/48.31    (8)  all_58_4 = e3
% 241.80/48.31    (9)  all_58_9 = e2
% 241.80/48.31    (10)   ~ (e2 = e1)
% 241.80/48.31  
% 241.80/48.31  Begin of proof
% 241.80/48.31  | 
% 241.80/48.31  | ALPHA: (3) implies:
% 241.80/48.31  |   (11)  all_58_1 = e2
% 241.80/48.31  | 
% 241.80/48.31  | COMBINE_EQS: (4), (11) imply:
% 241.80/48.31  |   (12)  e2 = e0
% 241.80/48.31  | 
% 241.80/48.31  | SIMP: (12) implies:
% 241.80/48.31  |   (13)  e2 = e0
% 241.80/48.31  | 
% 241.80/48.31  | COMBINE_EQS: (9), (13) imply:
% 241.80/48.31  |   (14)  all_58_9 = e0
% 241.80/48.31  | 
% 241.80/48.31  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (14) are inconsistent by
% 241.80/48.31  |            sub-proof #1097.
% 241.80/48.31  | 
% 241.80/48.31  End of proof
% 241.80/48.31  
% 241.80/48.31  Sub-proof #604 shows that the following formulas are inconsistent:
% 241.80/48.31  ----------------------------------------------------------------
% 241.80/48.31    (1)   ~ (e3 = e0)
% 241.80/48.31    (2)  all_58_6 = e3
% 241.80/48.31    (3)   ~ (e2 = e0)
% 241.80/48.31    (4)  all_58_11 = e1
% 241.80/48.31    (5)  all_58_15 = e3
% 241.80/48.31    (6)  all_58_6 = e2 & op(e1, e3) = e2
% 241.80/48.31    (7)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.80/48.31         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.80/48.31    (8)   ~ (e3 = e1)
% 241.80/48.31    (9)  all_58_3 = e3
% 241.80/48.31    (10)   ~ (e3 = e2)
% 241.80/48.31    (11)  op(e2, e0) = e0
% 241.80/48.31    (12)  all_58_2 = e0
% 241.80/48.31    (13)  all_58_5 = e1
% 241.80/48.32    (14)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.80/48.32          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.80/48.32    (15)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.80/48.32          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.80/48.32    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.80/48.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.80/48.32    (17)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.80/48.32          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.80/48.32    (18)   ~ (e1 = e0)
% 241.80/48.32    (19)   ~ (e2 = e1)
% 241.80/48.32  
% 241.80/48.32  Begin of proof
% 241.80/48.32  | 
% 241.80/48.32  | ALPHA: (6) implies:
% 241.80/48.32  |   (20)  all_58_6 = e2
% 241.80/48.32  | 
% 241.80/48.32  | COMBINE_EQS: (2), (20) imply:
% 241.80/48.32  |   (21)  e3 = e2
% 241.80/48.32  | 
% 241.80/48.32  | SIMP: (21) implies:
% 241.80/48.32  |   (22)  e3 = e2
% 241.80/48.32  | 
% 241.80/48.32  | COMBINE_EQS: (5), (22) imply:
% 241.80/48.32  |   (23)  all_58_15 = e2
% 241.80/48.32  | 
% 241.80/48.32  | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 241.80/48.32  |            (16), (17), (18), (19), (23) are inconsistent by sub-proof #626.
% 241.80/48.32  | 
% 241.80/48.32  End of proof
% 241.80/48.32  
% 241.80/48.32  Sub-proof #605 shows that the following formulas are inconsistent:
% 241.80/48.32  ----------------------------------------------------------------
% 241.80/48.32    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.80/48.32         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.80/48.32    (2)   ~ (e3 = e0)
% 241.80/48.32    (3)   ~ (e2 = e0)
% 241.80/48.32    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.80/48.32         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.80/48.32    (5)  all_58_15 = e3
% 241.80/48.32    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.80/48.32         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.80/48.32    (7)   ~ (e3 = e1)
% 241.80/48.32    (8)  all_58_3 = e3
% 241.80/48.32    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.80/48.32         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.80/48.32    (10)  op(e3, e3) = e1
% 241.80/48.32    (11)   ~ (e3 = e2)
% 241.80/48.32    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.80/48.32          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.80/48.32    (13)   ~ (all_52_4 = e3)
% 241.80/48.32    (14)  op(e3, e2) = all_52_4
% 241.80/48.32    (15)  all_58_5 = e1
% 241.80/48.32    (16)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.80/48.32          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.80/48.32    (17)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.80/48.32          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.80/48.32    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.80/48.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.80/48.32    (19)  op(e0, e0) = e0
% 241.80/48.32    (20)   ~ (e1 = e0)
% 241.80/48.32    (21)  all_58_4 = e3
% 241.80/48.32    (22)  all_58_9 = e1
% 241.80/48.32    (23)   ~ (e2 = e1)
% 241.80/48.32  
% 241.80/48.32  Begin of proof
% 241.80/48.32  | 
% 241.80/48.32  | BETA: splitting (12) gives:
% 241.80/48.32  | 
% 241.80/48.32  | Case 1:
% 241.80/48.32  | | 
% 241.80/48.32  | |   (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 241.80/48.32  | |           e0)
% 241.80/48.32  | | 
% 241.80/48.32  | | REF_CLOSE: (1), (3), (10), (11), (18), (20), (21), (22), (23), (24) are
% 241.80/48.32  | |            inconsistent by sub-proof #1293.
% 241.80/48.32  | | 
% 241.80/48.32  | Case 2:
% 241.80/48.32  | | 
% 241.80/48.32  | |   (25)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 241.80/48.32  | |           e0)
% 241.80/48.32  | | 
% 241.80/48.32  | | BETA: splitting (25) gives:
% 241.80/48.32  | | 
% 241.80/48.32  | | Case 1:
% 241.80/48.32  | | | 
% 241.80/48.32  | | |   (26)  all_58_4 = e0 & op(e3, e1) = e0
% 241.80/48.32  | | | 
% 241.80/48.32  | | | ALPHA: (26) implies:
% 241.80/48.32  | | |   (27)  all_58_4 = e0
% 241.80/48.32  | | | 
% 241.80/48.32  | | | COMBINE_EQS: (21), (27) imply:
% 241.80/48.32  | | |   (28)  e3 = e0
% 241.80/48.32  | | | 
% 241.80/48.32  | | | COMBINE_EQS: (5), (28) imply:
% 241.80/48.32  | | |   (29)  all_58_15 = e0
% 241.80/48.32  | | | 
% 241.80/48.32  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.80/48.32  | | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (29) are
% 241.80/48.32  | | |            inconsistent by sub-proof #654.
% 241.80/48.32  | | | 
% 241.80/48.32  | | Case 2:
% 241.80/48.32  | | | 
% 241.80/48.32  | | |   (30)  all_58_9 = e0 & op(e3, e0) = e0
% 241.80/48.32  | | | 
% 241.80/48.32  | | | ALPHA: (30) implies:
% 241.80/48.32  | | |   (31)  all_58_9 = e0
% 241.80/48.32  | | | 
% 241.80/48.32  | | | REF_CLOSE: (20), (22), (31) are inconsistent by sub-proof #1744.
% 241.80/48.32  | | | 
% 241.80/48.32  | | End of split
% 241.80/48.32  | | 
% 241.80/48.32  | End of split
% 241.80/48.32  | 
% 241.80/48.32  End of proof
% 241.80/48.32  
% 241.80/48.32  Sub-proof #606 shows that the following formulas are inconsistent:
% 241.80/48.32  ----------------------------------------------------------------
% 241.80/48.32    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.80/48.32         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.80/48.32    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.80/48.32         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.80/48.32    (3)   ~ (e3 = e0)
% 241.80/48.32    (4)   ~ (e2 = e0)
% 241.80/48.32    (5)  op(e1, e2) = all_52_6
% 241.80/48.32    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.80/48.32         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.80/48.32    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.80/48.32         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.80/48.32    (8)  all_58_9 = e0
% 241.80/48.32    (9)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.80/48.32           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.80/48.32             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.80/48.32           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.80/48.32             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.80/48.32           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.80/48.32           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.80/48.32           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.80/48.32           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.80/48.32           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.80/48.32           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.80/48.32             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.80/48.32           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.80/48.32           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 241.80/48.32           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.80/48.32           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.80/48.32           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.80/48.32           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.80/48.32             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.80/48.32           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.80/48.32           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 241.80/48.32           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.80/48.32           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.80/48.32           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.80/48.32           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.80/48.32             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.80/48.32           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.80/48.32           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.80/48.32    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.80/48.32          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.80/48.32    (11)   ~ (all_52_7 = e3)
% 241.80/48.32    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.80/48.32          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.80/48.32    (13)   ~ (e3 = e1)
% 241.80/48.32    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.80/48.32          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.80/48.32    (15)  all_58_3 = e3
% 241.80/48.32    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.80/48.32          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.80/48.32    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.80/48.32          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.80/48.32    (18)  op(e3, e3) = e1
% 241.80/48.32    (19)   ~ (all_52_9 = e0)
% 241.80/48.32    (20)  op(e2, e1) = all_52_9
% 241.80/48.32    (21)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.80/48.32          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.80/48.32    (22)   ~ (e3 = e2)
% 241.80/48.32    (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.80/48.32          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.80/48.32    (24)  all_56_31 = e0
% 241.80/48.32    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.80/48.32          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.80/48.32    (26)   ~ (all_52_9 = all_52_13)
% 241.80/48.32    (27)  op(e2, e3) = all_52_1
% 241.80/48.32    (28)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.80/48.32          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.80/48.32    (29)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.80/48.32          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.80/48.32    (30)  op(e0, e2) = all_52_7
% 241.80/48.32    (31)  all_58_2 = e0
% 241.80/48.32    (32)   ~ (all_52_4 = e3)
% 241.80/48.32    (33)  op(e3, e2) = all_52_4
% 241.80/48.32    (34)  all_58_5 = e1
% 241.80/48.32    (35)   ~ (all_52_9 = e3)
% 241.80/48.32    (36)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.80/48.32          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.80/48.32    (37)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.80/48.32          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.80/48.32    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.80/48.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.80/48.32    (39)  op(e0, e0) = e0
% 241.80/48.32    (40)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.80/48.32          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.80/48.32    (41)   ~ (all_52_6 = all_52_7)
% 241.80/48.32    (42)  all_56_11 = e3
% 241.80/48.32    (43)  op(e1, e1) = e0
% 241.80/48.32    (44)   ~ (e1 = e0)
% 241.80/48.32    (45)  all_58_4 = e3
% 241.80/48.32    (46)  op(e2, e0) = all_52_13
% 241.80/48.32    (47)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.80/48.32          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.80/48.32            e1)
% 241.80/48.32    (48)   ~ (all_52_1 = e3)
% 241.80/48.32    (49)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.80/48.32          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.80/48.32            e2)
% 241.80/48.32    (50)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.80/48.32          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.80/48.32    (51)  all_56_1 = e1
% 241.80/48.32    (52)   ~ (e2 = e1)
% 241.80/48.32    (53)   ~ (all_52_1 = e1)
% 241.80/48.32  
% 241.80/48.32  Begin of proof
% 241.80/48.32  | 
% 241.80/48.32  | BETA: splitting (47) gives:
% 241.80/48.32  | 
% 241.80/48.32  | Case 1:
% 241.80/48.32  | | 
% 241.80/48.32  | |   (54)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 241.80/48.32  | |           e1)
% 241.80/48.32  | | 
% 241.80/48.32  | | BETA: splitting (54) gives:
% 241.80/48.32  | | 
% 241.80/48.32  | | Case 1:
% 241.80/48.32  | | | 
% 241.80/48.32  | | |   (55)  all_58_12 = e1 & op(e0, e3) = e1
% 241.80/48.32  | | | 
% 241.80/48.32  | | | ALPHA: (55) implies:
% 241.80/48.32  | | |   (56)  all_58_12 = e1
% 241.80/48.32  | | | 
% 241.80/48.32  | | | REF_CLOSE: (3), (4), (13), (17), (18), (21), (22), (25), (27), (38), (44),
% 241.80/48.32  | | |            (48), (52), (56) are inconsistent by sub-proof #1204.
% 241.80/48.32  | | | 
% 241.80/48.32  | | Case 2:
% 241.80/48.32  | | | 
% 241.80/48.32  | | |   (57)  all_58_13 = e1 & op(e0, e2) = e1
% 241.80/48.32  | | | 
% 241.80/48.32  | | | ALPHA: (57) implies:
% 241.80/48.32  | | |   (58)  all_58_13 = e1
% 241.80/48.32  | | | 
% 241.80/48.32  | | | BETA: splitting (36) gives:
% 241.80/48.32  | | | 
% 241.80/48.32  | | | Case 1:
% 241.80/48.32  | | | | 
% 241.80/48.32  | | | |   (59)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0)
% 241.80/48.32  | | | |           = e3)
% 241.80/48.32  | | | | 
% 241.80/48.32  | | | | BETA: splitting (59) gives:
% 241.80/48.32  | | | | 
% 241.80/48.32  | | | | Case 1:
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | |   (60)  all_58_9 = e3 & op(e3, e0) = e3
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | | REF_CLOSE: (3), (8), (60) are inconsistent by sub-proof #1621.
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | Case 2:
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | |   (61)  all_58_10 = e3 & op(e2, e0) = e3
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | | ALPHA: (61) implies:
% 241.80/48.32  | | | | |   (62)  all_58_10 = e3
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | | REF_CLOSE: (4), (12), (15), (22), (31), (34), (52), (62) are
% 241.80/48.32  | | | | |            inconsistent by sub-proof #1104.
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | End of split
% 241.80/48.32  | | | | 
% 241.80/48.32  | | | Case 2:
% 241.80/48.32  | | | | 
% 241.80/48.32  | | | |   (63)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 241.80/48.32  | | | |             e0) = e3)
% 241.80/48.32  | | | | 
% 241.80/48.32  | | | | BETA: splitting (63) gives:
% 241.80/48.32  | | | | 
% 241.80/48.32  | | | | Case 1:
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | |   (64)  all_58_11 = e3 & op(e1, e0) = e3
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | | REF_CLOSE: (1), (3), (4), (7), (12), (13), (15), (16), (18), (22),
% 241.80/48.32  | | | | |            (28), (32), (33), (34), (37), (38), (39), (44), (45), (52),
% 241.80/48.32  | | | | |            (64) are inconsistent by sub-proof #610.
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | Case 2:
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | |   (65)  all_58_15 = e3 & op(e0, e0) = e3
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | | ALPHA: (65) implies:
% 241.80/48.32  | | | | |   (66)  all_58_15 = e3
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 241.80/48.32  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 241.80/48.32  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 241.80/48.32  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 241.80/48.32  | | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 241.80/48.32  | | | | |            (52), (53), (58), (66) are inconsistent by sub-proof #608.
% 241.80/48.32  | | | | | 
% 241.80/48.32  | | | | End of split
% 241.80/48.32  | | | | 
% 241.80/48.32  | | | End of split
% 241.80/48.32  | | | 
% 241.80/48.32  | | End of split
% 241.80/48.32  | | 
% 241.80/48.32  | Case 2:
% 241.80/48.32  | | 
% 241.80/48.32  | |   (67)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.80/48.32  | |           e1)
% 241.80/48.32  | | 
% 241.80/48.32  | | REF_CLOSE: (3), (4), (14), (22), (23), (34), (38), (39), (44), (45), (52),
% 241.80/48.32  | |            (67) are inconsistent by sub-proof #607.
% 241.80/48.32  | | 
% 241.80/48.32  | End of split
% 241.80/48.32  | 
% 241.80/48.32  End of proof
% 241.80/48.32  
% 241.80/48.33  Sub-proof #607 shows that the following formulas are inconsistent:
% 241.80/48.33  ----------------------------------------------------------------
% 241.80/48.33    (1)   ~ (e3 = e0)
% 241.80/48.33    (2)   ~ (e2 = e0)
% 241.80/48.33    (3)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.80/48.33         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.80/48.33    (4)   ~ (e3 = e2)
% 241.80/48.33    (5)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.80/48.33         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.80/48.33    (6)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.80/48.33    (7)  all_58_5 = e1
% 241.80/48.33    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.80/48.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.80/48.33    (9)  op(e0, e0) = e0
% 241.80/48.33    (10)   ~ (e1 = e0)
% 241.80/48.33    (11)  all_58_4 = e3
% 241.80/48.33    (12)   ~ (e2 = e1)
% 241.80/48.33  
% 241.80/48.33  Begin of proof
% 241.80/48.33  | 
% 241.80/48.33  | BETA: splitting (6) gives:
% 241.80/48.33  | 
% 241.80/48.33  | Case 1:
% 241.80/48.33  | | 
% 241.80/48.33  | |   (13)  all_58_14 = e1 & op(e0, e1) = e1
% 241.80/48.33  | | 
% 241.80/48.33  | | ALPHA: (13) implies:
% 241.80/48.33  | |   (14)  all_58_14 = e1
% 241.80/48.33  | | 
% 241.80/48.33  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (10), (11), (12), (14) are
% 241.80/48.33  | |            inconsistent by sub-proof #1481.
% 241.80/48.33  | | 
% 241.80/48.33  | Case 2:
% 241.80/48.33  | | 
% 241.80/48.33  | |   (15)  all_58_15 = e1 & op(e0, e0) = e1
% 241.80/48.33  | | 
% 241.80/48.33  | | ALPHA: (15) implies:
% 241.80/48.33  | |   (16)  op(e0, e0) = e1
% 241.80/48.33  | | 
% 241.80/48.33  | | REF_CLOSE: (8), (9), (10), (16) are inconsistent by sub-proof #2274.
% 241.80/48.33  | | 
% 241.80/48.33  | End of split
% 241.80/48.33  | 
% 241.80/48.33  End of proof
% 241.80/48.33  
% 241.80/48.33  Sub-proof #608 shows that the following formulas are inconsistent:
% 241.80/48.33  ----------------------------------------------------------------
% 241.80/48.33    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.80/48.33         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.80/48.33    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.80/48.33         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.80/48.33    (3)   ~ (e3 = e0)
% 241.80/48.33    (4)   ~ (e2 = e0)
% 241.80/48.33    (5)  op(e1, e2) = all_52_6
% 241.80/48.33    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.80/48.33         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.80/48.33    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.80/48.33         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.80/48.33    (8)  all_58_9 = e0
% 241.80/48.33    (9)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.80/48.33           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.80/48.33             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.80/48.33           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.80/48.33             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.80/48.33           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.80/48.33           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.80/48.33           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.80/48.33           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.80/48.33           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.80/48.33           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.80/48.33             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.80/48.33           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.80/48.33           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 241.80/48.33           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.80/48.33           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.80/48.33           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.80/48.33           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.80/48.33             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.80/48.33           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.80/48.33           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 241.80/48.33           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.80/48.33           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.80/48.33           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.80/48.33           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.80/48.33             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.80/48.33           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.80/48.33           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.80/48.33    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.80/48.33          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.80/48.33    (11)   ~ (all_52_7 = e3)
% 241.80/48.33    (12)  all_58_15 = e3
% 241.80/48.33    (13)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.80/48.33          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.80/48.33    (14)   ~ (e3 = e1)
% 241.80/48.33    (15)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.80/48.33          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.80/48.33    (16)  all_58_3 = e3
% 241.80/48.33    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.80/48.33          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.80/48.33    (18)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.80/48.33          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.80/48.33    (19)  op(e3, e3) = e1
% 241.80/48.33    (20)   ~ (all_52_9 = e0)
% 241.80/48.33    (21)  op(e2, e1) = all_52_9
% 241.80/48.33    (22)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.80/48.33          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.80/48.33    (23)   ~ (e3 = e2)
% 241.80/48.33    (24)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.80/48.33          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.80/48.33    (25)  all_56_31 = e0
% 241.80/48.33    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.80/48.33          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.80/48.33    (27)   ~ (all_52_9 = all_52_13)
% 241.80/48.33    (28)  op(e2, e3) = all_52_1
% 241.80/48.33    (29)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.80/48.33          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.80/48.33    (30)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.80/48.33          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.80/48.33    (31)  op(e0, e2) = all_52_7
% 241.80/48.33    (32)  all_58_2 = e0
% 241.80/48.33    (33)   ~ (all_52_4 = e3)
% 241.80/48.33    (34)  op(e3, e2) = all_52_4
% 241.80/48.33    (35)  all_58_5 = e1
% 241.80/48.33    (36)   ~ (all_52_9 = e3)
% 241.80/48.33    (37)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.80/48.33          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.80/48.33    (38)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.80/48.33          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.80/48.33    (39)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.80/48.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.80/48.33    (40)  op(e0, e0) = e0
% 241.80/48.33    (41)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.80/48.33          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.80/48.33    (42)   ~ (all_52_6 = all_52_7)
% 241.80/48.33    (43)  all_56_11 = e3
% 241.80/48.33    (44)  op(e1, e1) = e0
% 241.80/48.33    (45)   ~ (e1 = e0)
% 241.80/48.33    (46)  all_58_13 = e1
% 241.80/48.33    (47)  all_58_4 = e3
% 241.80/48.33    (48)  op(e2, e0) = all_52_13
% 241.80/48.33    (49)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.80/48.33          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.80/48.33            e1)
% 241.80/48.33    (50)   ~ (all_52_1 = e3)
% 241.80/48.33    (51)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.80/48.33          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.80/48.33            e2)
% 241.80/48.33    (52)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.80/48.33          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.80/48.33    (53)  all_56_1 = e1
% 241.80/48.33    (54)   ~ (e2 = e1)
% 241.80/48.33    (55)   ~ (all_52_1 = e1)
% 241.80/48.33  
% 241.80/48.33  Begin of proof
% 241.80/48.33  | 
% 241.80/48.33  | BETA: splitting (10) gives:
% 241.80/48.33  | 
% 241.80/48.33  | Case 1:
% 241.80/48.33  | | 
% 241.80/48.33  | |   (56)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 241.80/48.33  | |           e0)
% 241.80/48.33  | | 
% 241.80/48.33  | | BETA: splitting (56) gives:
% 241.80/48.33  | | 
% 241.80/48.33  | | Case 1:
% 241.80/48.33  | | | 
% 241.80/48.33  | | |   (57)  all_58_1 = e0 & op(e3, e2) = e0
% 241.80/48.33  | | | 
% 241.80/48.33  | | | ALPHA: (57) implies:
% 241.80/48.33  | | |   (58)  all_58_1 = e0
% 241.80/48.33  | | | 
% 241.80/48.33  | | | REF_CLOSE: (1), (4), (8), (19), (23), (39), (47), (54), (58) are
% 241.80/48.33  | | |            inconsistent by sub-proof #1097.
% 241.80/48.33  | | | 
% 241.80/48.33  | | Case 2:
% 241.80/48.33  | | | 
% 241.80/48.33  | | |   (59)  all_58_3 = e0 & op(e2, e2) = e0
% 241.80/48.33  | | | 
% 241.80/48.33  | | | ALPHA: (59) implies:
% 241.80/48.33  | | |   (60)  all_58_3 = e0
% 241.80/48.33  | | | 
% 241.80/48.33  | | | COMBINE_EQS: (16), (60) imply:
% 241.80/48.33  | | |   (61)  e3 = e0
% 241.80/48.33  | | | 
% 241.80/48.33  | | | SIMP: (61) implies:
% 241.80/48.33  | | |   (62)  e3 = e0
% 241.80/48.33  | | | 
% 241.80/48.33  | | | COMBINE_EQS: (12), (62) imply:
% 241.80/48.33  | | |   (63)  all_58_15 = e0
% 241.80/48.33  | | | 
% 241.80/48.33  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (13), (14),
% 241.80/48.33  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 241.80/48.33  | | |            (25), (26), (27), (28), (29), (30), (31), (33), (34), (36),
% 241.80/48.33  | | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (48),
% 241.80/48.33  | | |            (49), (50), (51), (52), (53), (54), (55), (63) are inconsistent
% 241.80/48.33  | | |            by sub-proof #648.
% 241.80/48.33  | | | 
% 241.80/48.33  | | End of split
% 241.80/48.33  | | 
% 241.80/48.33  | Case 2:
% 241.80/48.33  | | 
% 241.80/48.33  | |   (64)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 241.80/48.33  | |           e0)
% 241.80/48.33  | | 
% 241.80/48.33  | | BETA: splitting (64) gives:
% 241.80/48.33  | | 
% 241.80/48.33  | | Case 1:
% 241.80/48.33  | | | 
% 241.80/48.33  | | |   (65)  all_58_7 = e0 & op(e1, e2) = e0
% 241.80/48.33  | | | 
% 241.80/48.33  | | | ALPHA: (65) implies:
% 241.80/48.33  | | |   (66)  all_58_7 = e0
% 241.80/48.33  | | |   (67)  op(e1, e2) = e0
% 241.80/48.33  | | | 
% 241.80/48.33  | | | BETA: splitting (6) gives:
% 241.80/48.33  | | | 
% 241.80/48.33  | | | Case 1:
% 241.80/48.33  | | | | 
% 241.80/48.33  | | | |   (68)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2)
% 241.80/48.33  | | | |           = e2)
% 241.80/48.33  | | | | 
% 241.80/48.33  | | | | BETA: splitting (68) gives:
% 241.80/48.33  | | | | 
% 241.80/48.33  | | | | Case 1:
% 241.80/48.33  | | | | | 
% 241.80/48.33  | | | | |   (69)  all_58_1 = e2 & op(e3, e2) = e2
% 241.80/48.33  | | | | | 
% 241.80/48.33  | | | | | ALPHA: (69) implies:
% 241.80/48.33  | | | | |   (70)  all_58_1 = e2
% 241.80/48.33  | | | | | 
% 241.80/48.33  | | | | | BETA: splitting (9) gives:
% 241.80/48.33  | | | | | 
% 241.80/48.33  | | | | | Case 1:
% 241.80/48.33  | | | | | | 
% 241.80/48.33  | | | | | |   (71)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 241.80/48.33  | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 241.80/48.33  | | | | | |             e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 =
% 241.80/48.33  | | | | | |           e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 241.80/48.33  | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.80/48.33  | | | | | |             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17
% 241.80/48.33  | | | | | |           = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.80/48.33  | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 241.80/48.33  | | | | | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 241.80/48.33  | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 241.80/48.33  | | | | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 241.80/48.33  | | | | | |           = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 241.80/48.33  | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.80/48.33  | | | | | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 241.80/48.33  | | | | | |         (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 241.80/48.33  | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 241.80/48.33  | | | | | |             e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 241.80/48.33  | | | | | | 
% 241.80/48.33  | | | | | | REF_CLOSE: (25), (28), (39), (43), (50), (53), (71) are inconsistent
% 241.80/48.33  | | | | | |            by sub-proof #744.
% 241.80/48.33  | | | | | | 
% 241.80/48.33  | | | | | Case 2:
% 241.80/48.33  | | | | | | 
% 241.80/48.33  | | | | | |   (72)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 241.80/48.33  | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 241.80/48.33  | | | | | |             e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 =
% 241.80/48.33  | | | | | |           e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 241.80/48.33  | | | | | |             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.80/48.33  | | | | | |             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 241.80/48.33  | | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0)
% 241.80/48.33  | | | | | |           &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) =
% 241.80/48.33  | | | | | |           e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 = e0 &
% 241.80/48.33  | | | | | |            ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.80/48.33  | | | | | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 241.80/48.33  | | | | | |           = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.80/48.33  | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.80/48.33  | | | | | |           (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 241.80/48.33  | | | | | |         (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 241.80/48.33  | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 241.80/48.33  | | | | | |             e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.80/48.33  | | | | | | 
% 241.80/48.33  | | | | | | BETA: splitting (72) gives:
% 241.80/48.33  | | | | | | 
% 241.80/48.33  | | | | | | Case 1:
% 241.80/48.33  | | | | | | | 
% 241.80/48.33  | | | | | | |   (73)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 241.80/48.33  | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 241.80/48.33  | | | | | | |             e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13
% 241.80/48.33  | | | | | | |           = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.80/48.33  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 241.80/48.33  | | | | | | |             e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 241.80/48.33  | | | | | | |           = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.80/48.33  | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 241.80/48.33  | | | | | | |             e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.80/48.33  | | | | | | | 
% 241.80/48.33  | | | | | | | BETA: splitting (73) gives:
% 241.80/48.33  | | | | | | | 
% 241.80/48.33  | | | | | | | Case 1:
% 241.80/48.33  | | | | | | | | 
% 241.80/48.33  | | | | | | | |   (74)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) & 
% 241.80/48.33  | | | | | | | |         ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 241.80/48.33  | | | | | | | |           = e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 241.80/48.33  | | | | | | | | 
% 241.80/48.33  | | | | | | | | ALPHA: (74) implies:
% 241.80/48.33  | | | | | | | |   (75)   ~ (all_56_1 = e1)
% 241.80/48.33  | | | | | | | | 
% 241.80/48.33  | | | | | | | | REDUCE: (53), (75) imply:
% 241.80/48.33  | | | | | | | |   (76)  $false
% 241.80/48.33  | | | | | | | | 
% 241.80/48.33  | | | | | | | | CLOSE: (76) is inconsistent.
% 241.80/48.33  | | | | | | | | 
% 241.80/48.33  | | | | | | | Case 2:
% 241.80/48.33  | | | | | | | | 
% 241.80/48.33  | | | | | | | |   (77)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) & 
% 241.80/48.33  | | | | | | | |           ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.80/48.33  | | | | | | | |           (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1)
% 241.80/48.33  | | | | | | | |         | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0)
% 241.80/48.33  | | | | | | | |           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.80/48.33  | | | | | | | |           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.80/48.33  | | | | | | | | 
% 241.80/48.33  | | | | | | | | BETA: splitting (77) gives:
% 241.80/48.33  | | | | | | | | 
% 241.80/48.33  | | | | | | | | Case 1:
% 241.80/48.33  | | | | | | | | | 
% 241.80/48.33  | | | | | | | | |   (78)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &
% 241.80/48.33  | | | | | | | | |          ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.80/48.33  | | | | | | | | |         (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 241.80/48.33  | | | | | | | | | 
% 241.80/48.33  | | | | | | | | | ALPHA: (78) implies:
% 241.80/48.33  | | | | | | | | |   (79)  op(e1, e2) = e1
% 241.80/48.33  | | | | | | | | | 
% 241.80/48.33  | | | | | | | | | REF_CLOSE: (5), (39), (45), (67), (79) are inconsistent by
% 241.80/48.33  | | | | | | | | |            sub-proof #2136.
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | Case 2:
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | |   (80)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &
% 241.80/48.34  | | | | | | | | |          ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.80/48.34  | | | | | | | | |         (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | ALPHA: (80) implies:
% 241.80/48.34  | | | | | | | | |   (81)   ~ (all_56_31 = e0)
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | REDUCE: (25), (81) imply:
% 241.80/48.34  | | | | | | | | |   (82)  $false
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | CLOSE: (82) is inconsistent.
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | End of split
% 241.80/48.34  | | | | | | | | 
% 241.80/48.34  | | | | | | | End of split
% 241.80/48.34  | | | | | | | 
% 241.80/48.34  | | | | | | Case 2:
% 241.80/48.34  | | | | | | | 
% 241.80/48.34  | | | | | | |   (83)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 241.80/48.34  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 241.80/48.34  | | | | | | |             e2) & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23
% 241.80/48.34  | | | | | | |           = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.80/48.34  | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 241.80/48.34  | | | | | | |             e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 241.80/48.34  | | | | | | |           = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 241.80/48.34  | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 241.80/48.34  | | | | | | |             e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.80/48.34  | | | | | | | 
% 241.80/48.34  | | | | | | | BETA: splitting (83) gives:
% 241.80/48.34  | | | | | | | 
% 241.80/48.34  | | | | | | | Case 1:
% 241.80/48.34  | | | | | | | | 
% 241.80/48.34  | | | | | | | |   (84)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) & 
% 241.80/48.34  | | | | | | | |         ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 241.80/48.34  | | | | | | | |           = e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 241.80/48.34  | | | | | | | | 
% 241.80/48.34  | | | | | | | | ALPHA: (84) implies:
% 241.80/48.34  | | | | | | | |   (85)   ~ (all_56_31 = e2)
% 241.80/48.34  | | | | | | | |   (86)   ~ (all_56_11 = e2)
% 241.80/48.34  | | | | | | | |   (87)   ~ (all_56_1 = e2)
% 241.80/48.34  | | | | | | | |   (88)  op(e2, e0) = e0
% 241.80/48.34  | | | | | | | | 
% 241.80/48.34  | | | | | | | | REDUCE: (53), (87) imply:
% 241.80/48.34  | | | | | | | |   (89)   ~ (e2 = e1)
% 241.80/48.34  | | | | | | | | 
% 241.80/48.34  | | | | | | | | REDUCE: (25), (85) imply:
% 241.80/48.34  | | | | | | | |   (90)   ~ (e2 = e0)
% 241.80/48.34  | | | | | | | | 
% 241.80/48.34  | | | | | | | | BETA: splitting (13) gives:
% 241.80/48.34  | | | | | | | | 
% 241.80/48.34  | | | | | | | | Case 1:
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | |   (91)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 241.80/48.34  | | | | | | | | |           op(e2, e2) = e2)
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | BETA: splitting (91) gives:
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | Case 1:
% 241.80/48.34  | | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | |   (92)  all_58_2 = e2 & op(e2, e3) = e2
% 241.80/48.34  | | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | | ALPHA: (92) implies:
% 241.80/48.34  | | | | | | | | | |   (93)  all_58_2 = e2
% 241.80/48.34  | | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | | COMBINE_EQS: (32), (93) imply:
% 241.80/48.34  | | | | | | | | | |   (94)  e2 = e0
% 241.80/48.34  | | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | | COMBINE_EQS: (70), (94) imply:
% 241.80/48.34  | | | | | | | | | |   (95)  all_58_1 = e0
% 241.80/48.34  | | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | | REF_CLOSE: (1), (4), (8), (19), (23), (39), (47), (54), (95)
% 241.80/48.34  | | | | | | | | | |            are inconsistent by sub-proof #1097.
% 241.80/48.34  | | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | Case 2:
% 241.80/48.34  | | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | |   (96)  all_58_3 = e2 & op(e2, e2) = e2
% 241.80/48.34  | | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | | REF_CLOSE: (16), (23), (96) are inconsistent by sub-proof
% 241.80/48.34  | | | | | | | | | |            #1458.
% 241.80/48.34  | | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | End of split
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | Case 2:
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | |   (97)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 241.80/48.34  | | | | | | | | |           op(e2, e0) = e2)
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | | REF_CLOSE: (4), (35), (39), (54), (88), (97) are inconsistent
% 241.80/48.34  | | | | | | | | |            by sub-proof #702.
% 241.80/48.34  | | | | | | | | | 
% 241.80/48.34  | | | | | | | | End of split
% 241.80/48.34  | | | | | | | | 
% 241.80/48.34  | | | | | | | Case 2:
% 241.80/48.34  | | | | | | | | 
% 241.80/48.34  | | | | | | | |   (98)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) & 
% 241.80/48.34  | | | | | | | |           ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.80/48.34  | | | | | | | |           (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1)
% 241.80/48.34  | | | | | | | |         | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1)
% 241.80/48.34  | | | | | | | |           &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.80/48.34  | | | | | | | |           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.80/48.34  | | | | | | | | 
% 241.80/48.34  | | | | | | | | REF_CLOSE: (25), (53), (98) are inconsistent by sub-proof #743.
% 241.80/48.34  | | | | | | | | 
% 241.80/48.34  | | | | | | | End of split
% 241.80/48.34  | | | | | | | 
% 241.80/48.34  | | | | | | End of split
% 241.80/48.34  | | | | | | 
% 241.80/48.34  | | | | | End of split
% 241.80/48.34  | | | | | 
% 241.80/48.34  | | | | Case 2:
% 241.80/48.34  | | | | | 
% 241.80/48.34  | | | | |   (99)  all_58_3 = e2 & op(e2, e2) = e2
% 241.80/48.34  | | | | | 
% 241.80/48.34  | | | | | REF_CLOSE: (16), (23), (99) are inconsistent by sub-proof #1106.
% 241.80/48.34  | | | | | 
% 241.80/48.34  | | | | End of split
% 241.80/48.34  | | | | 
% 241.80/48.34  | | | Case 2:
% 241.80/48.34  | | | | 
% 241.80/48.34  | | | |   (100)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0,
% 241.80/48.34  | | | |              e2) = e2)
% 241.80/48.34  | | | | 
% 241.80/48.34  | | | | BETA: splitting (100) gives:
% 241.80/48.34  | | | | 
% 241.80/48.34  | | | | Case 1:
% 241.80/48.34  | | | | | 
% 241.80/48.34  | | | | |   (101)  all_58_7 = e2 & op(e1, e2) = e2
% 241.80/48.34  | | | | | 
% 241.80/48.34  | | | | | REF_CLOSE: (4), (66), (101) are inconsistent by sub-proof #1326.
% 241.80/48.34  | | | | | 
% 241.80/48.34  | | | | Case 2:
% 241.80/48.34  | | | | | 
% 241.80/48.34  | | | | |   (102)  all_58_13 = e2 & op(e0, e2) = e2
% 241.80/48.34  | | | | | 
% 241.80/48.34  | | | | | REF_CLOSE: (46), (54), (102) are inconsistent by sub-proof #2078.
% 241.80/48.34  | | | | | 
% 241.80/48.34  | | | | End of split
% 241.80/48.34  | | | | 
% 241.80/48.34  | | | End of split
% 241.80/48.34  | | | 
% 241.80/48.34  | | Case 2:
% 241.80/48.34  | | | 
% 241.80/48.34  | | |   (103)  all_58_13 = e0 & op(e0, e2) = e0
% 241.80/48.34  | | | 
% 241.80/48.34  | | | REF_CLOSE: (45), (46), (103) are inconsistent by sub-proof #609.
% 241.80/48.34  | | | 
% 241.80/48.34  | | End of split
% 241.80/48.34  | | 
% 241.80/48.34  | End of split
% 241.80/48.34  | 
% 241.80/48.34  End of proof
% 241.80/48.34  
% 241.80/48.34  Sub-proof #609 shows that the following formulas are inconsistent:
% 241.80/48.34  ----------------------------------------------------------------
% 241.80/48.34    (1)  all_58_13 = e0 & op(e0, e2) = e0
% 241.80/48.34    (2)  all_58_13 = e1
% 241.80/48.34    (3)   ~ (e1 = e0)
% 241.80/48.34  
% 241.80/48.34  Begin of proof
% 241.80/48.34  | 
% 241.80/48.34  | ALPHA: (1) implies:
% 241.80/48.34  |   (4)  all_58_13 = e0
% 241.80/48.34  | 
% 241.80/48.34  | COMBINE_EQS: (2), (4) imply:
% 241.80/48.34  |   (5)  e1 = e0
% 241.80/48.34  | 
% 241.80/48.34  | REDUCE: (3), (5) imply:
% 241.80/48.34  |   (6)  $false
% 241.80/48.34  | 
% 241.80/48.34  | CLOSE: (6) is inconsistent.
% 241.80/48.34  | 
% 241.80/48.34  End of proof
% 241.80/48.34  
% 241.80/48.34  Sub-proof #610 shows that the following formulas are inconsistent:
% 241.80/48.34  ----------------------------------------------------------------
% 241.80/48.34    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.80/48.34         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.80/48.34    (2)   ~ (e3 = e0)
% 241.80/48.34    (3)   ~ (e2 = e0)
% 241.80/48.34    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.80/48.34         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.80/48.34    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.80/48.34         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.80/48.34    (6)   ~ (e3 = e1)
% 241.80/48.34    (7)  all_58_3 = e3
% 241.80/48.34    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.80/48.34         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.80/48.34    (9)  op(e3, e3) = e1
% 241.80/48.34    (10)   ~ (e3 = e2)
% 241.80/48.34    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.80/48.34          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.80/48.34    (12)  all_58_11 = e3 & op(e1, e0) = e3
% 241.80/48.34    (13)   ~ (all_52_4 = e3)
% 241.80/48.34    (14)  op(e3, e2) = all_52_4
% 241.80/48.34    (15)  all_58_5 = e1
% 241.80/48.34    (16)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.80/48.34          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.80/48.34    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.80/48.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.80/48.34    (18)  op(e0, e0) = e0
% 241.80/48.34    (19)   ~ (e1 = e0)
% 241.80/48.34    (20)  all_58_4 = e3
% 241.80/48.34    (21)   ~ (e2 = e1)
% 241.80/48.34  
% 241.80/48.34  Begin of proof
% 241.80/48.34  | 
% 241.80/48.34  | ALPHA: (12) implies:
% 241.80/48.34  |   (22)  all_58_11 = e3
% 241.80/48.34  | 
% 241.80/48.34  | BETA: splitting (4) gives:
% 241.80/48.34  | 
% 241.80/48.34  | Case 1:
% 241.80/48.34  | | 
% 241.80/48.34  | |   (23)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 241.80/48.34  | |           e1)
% 241.80/48.34  | | 
% 241.80/48.34  | | BETA: splitting (23) gives:
% 241.80/48.34  | | 
% 241.80/48.34  | | Case 1:
% 241.80/48.34  | | | 
% 241.80/48.34  | | |   (24)  all_58_9 = e1 & op(e3, e0) = e1
% 241.80/48.34  | | | 
% 241.80/48.34  | | | ALPHA: (24) implies:
% 241.80/48.34  | | |   (25)  all_58_9 = e1
% 241.80/48.34  | | | 
% 241.80/48.34  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 241.80/48.34  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (25) are
% 241.80/48.34  | | |            inconsistent by sub-proof #655.
% 241.80/48.34  | | | 
% 241.80/48.34  | | Case 2:
% 241.80/48.34  | | | 
% 241.80/48.34  | | |   (26)  all_58_10 = e1 & op(e2, e0) = e1
% 241.80/48.34  | | | 
% 241.80/48.34  | | | ALPHA: (26) implies:
% 241.80/48.34  | | |   (27)  all_58_10 = e1
% 241.80/48.34  | | | 
% 241.80/48.34  | | | REF_CLOSE: (2), (3), (5), (7), (10), (15), (16), (19), (21), (27) are
% 241.80/48.34  | | |            inconsistent by sub-proof #992.
% 241.80/48.34  | | | 
% 241.80/48.34  | | End of split
% 241.80/48.34  | | 
% 241.80/48.34  | Case 2:
% 241.80/48.34  | | 
% 241.80/48.34  | |   (28)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.80/48.34  | |           e1)
% 241.80/48.34  | | 
% 241.80/48.34  | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (11), (13), (14), (17), (18),
% 241.80/48.34  | |            (19), (20), (21), (22), (28) are inconsistent by sub-proof #1466.
% 241.80/48.34  | | 
% 241.80/48.34  | End of split
% 241.80/48.34  | 
% 241.80/48.34  End of proof
% 241.80/48.34  
% 241.80/48.34  Sub-proof #611 shows that the following formulas are inconsistent:
% 241.80/48.34  ----------------------------------------------------------------
% 241.80/48.34    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.80/48.34         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.80/48.34    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.80/48.34         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.80/48.34    (3)   ~ (e3 = e0)
% 241.80/48.34    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.80/48.34         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.80/48.34    (5)   ~ (e2 = e0)
% 241.80/48.34    (6)  op(e1, e2) = all_52_6
% 241.80/48.34    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.80/48.34         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.80/48.34    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.80/48.34         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.80/48.34    (9)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.80/48.34           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.80/48.34             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.80/48.34           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.80/48.34             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.80/48.34           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.80/48.34           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.80/48.34           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.80/48.34           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.80/48.34           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.80/48.34           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.80/48.34             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.80/48.34           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.80/48.34           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 241.80/48.34           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.80/48.34           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.80/48.34           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.80/48.34           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.80/48.34             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.80/48.34           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.80/48.34           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 241.80/48.34           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.80/48.34           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.80/48.34           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.80/48.34           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.80/48.34             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.80/48.34           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.80/48.34           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.80/48.34    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.80/48.34          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.80/48.34    (11)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.80/48.34          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.80/48.34    (12)   ~ (all_52_7 = e3)
% 241.80/48.34    (13)  all_58_8 = e0
% 241.80/48.34    (14)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.80/48.34          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.80/48.34    (15)   ~ (e3 = e1)
% 241.80/48.34    (16)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.80/48.34          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.80/48.34    (17)  all_58_3 = e3
% 241.80/48.34    (18)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.80/48.34          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.80/48.34    (19)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.80/48.34          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.80/48.34    (20)  op(e3, e3) = e1
% 241.80/48.34    (21)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.80/48.34              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.80/48.34                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.80/48.34                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.80/48.34    (22)  op(e2, e1) = all_52_9
% 241.80/48.34    (23)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.80/48.34          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.80/48.34    (24)   ~ (e3 = e2)
% 241.80/48.34    (25)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.80/48.34          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.80/48.34    (26)  all_56_31 = e0
% 241.80/48.34    (27)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.80/48.34          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.80/48.34    (28)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.80/48.34          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.80/48.34    (29)  op(e2, e3) = all_52_1
% 241.80/48.34    (30)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.80/48.34          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.80/48.34    (31)   ~ (all_52_6 = e3)
% 241.80/48.34    (32)  all_58_12 = e0 & op(e0, e3) = e0
% 241.80/48.34    (33)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.80/48.34          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.80/48.34    (34)  op(e0, e2) = all_52_7
% 241.80/48.34    (35)   ~ (all_52_4 = e3)
% 241.80/48.34    (36)  op(e3, e2) = all_52_4
% 241.80/48.34    (37)   ~ (all_52_9 = e3)
% 241.80/48.34    (38)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.80/48.34          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.80/48.34    (39)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.80/48.34          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.80/48.34    (40)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.80/48.34          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.80/48.35    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.80/48.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.80/48.35    (42)  op(e0, e0) = e0
% 241.80/48.35    (43)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.80/48.35          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.80/48.35    (44)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.80/48.35          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.80/48.35    (45)  all_56_11 = e3
% 241.80/48.35    (46)  op(e1, e1) = e0
% 241.80/48.35    (47)   ~ (all_52_4 = e1)
% 241.80/48.35    (48)   ~ (e1 = e0)
% 241.80/48.35    (49)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.80/48.35          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.80/48.35    (50)  op(e2, e0) = all_52_13
% 241.80/48.35    (51)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.80/48.35          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.80/48.35            e1)
% 241.80/48.35    (52)   ~ (all_52_1 = e3)
% 241.80/48.35    (53)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.80/48.35          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.80/48.35            e2)
% 241.80/48.35    (54)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.80/48.35          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.80/48.35    (55)  all_56_1 = e1
% 241.80/48.35    (56)   ~ (e2 = e1)
% 241.80/48.35    (57)   ~ (all_52_1 = e1)
% 241.80/48.35  
% 241.80/48.35  Begin of proof
% 241.80/48.35  | 
% 241.80/48.35  | ALPHA: (32) implies:
% 241.80/48.35  |   (58)  all_58_12 = e0
% 241.80/48.35  | 
% 241.80/48.35  | BETA: splitting (40) gives:
% 241.80/48.35  | 
% 241.80/48.35  | Case 1:
% 241.80/48.35  | | 
% 241.80/48.35  | |   (59)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 241.80/48.35  | |           e0)
% 241.80/48.35  | | 
% 241.80/48.35  | | BETA: splitting (59) gives:
% 241.80/48.35  | | 
% 241.80/48.35  | | Case 1:
% 241.80/48.35  | | | 
% 241.80/48.35  | | |   (60)  all_58_2 = e0 & op(e2, e3) = e0
% 241.80/48.35  | | | 
% 241.80/48.35  | | | ALPHA: (60) implies:
% 241.80/48.35  | | |   (61)  all_58_2 = e0
% 241.80/48.35  | | | 
% 241.80/48.35  | | | REF_CLOSE: (3), (5), (15), (19), (20), (23), (24), (29), (41), (52), (56),
% 241.80/48.35  | | |            (58), (61) are inconsistent by sub-proof #1149.
% 241.80/48.35  | | | 
% 241.80/48.35  | | Case 2:
% 241.80/48.35  | | | 
% 241.80/48.35  | | |   (62)  all_58_3 = e0 & op(e2, e2) = e0
% 241.80/48.35  | | | 
% 241.80/48.35  | | | REF_CLOSE: (3), (17), (62) are inconsistent by sub-proof #1719.
% 241.80/48.35  | | | 
% 241.80/48.35  | | End of split
% 241.80/48.35  | | 
% 241.80/48.35  | Case 2:
% 241.80/48.35  | | 
% 241.80/48.35  | |   (63)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 241.80/48.35  | |           e0)
% 241.80/48.35  | | 
% 241.80/48.35  | | BETA: splitting (63) gives:
% 241.80/48.35  | | 
% 241.80/48.35  | | Case 1:
% 241.80/48.35  | | | 
% 241.80/48.35  | | |   (64)  all_58_5 = e0 & op(e2, e1) = e0
% 241.80/48.35  | | | 
% 241.80/48.35  | | | ALPHA: (64) implies:
% 241.80/48.35  | | |   (65)  all_58_5 = e0
% 241.80/48.35  | | |   (66)  op(e2, e1) = e0
% 241.80/48.35  | | | 
% 241.80/48.35  | | | BETA: splitting (54) gives:
% 241.80/48.35  | | | 
% 241.80/48.35  | | | Case 1:
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | |   (67)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 241.80/48.35  | | | |           = e1)
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | | BETA: splitting (67) gives:
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | | Case 1:
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | |   (68)  all_58_2 = e1 & op(e2, e3) = e1
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | REF_CLOSE: (29), (41), (57), (68) are inconsistent by sub-proof #2229.
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | Case 2:
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | |   (69)  all_58_3 = e1 & op(e2, e2) = e1
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | REF_CLOSE: (15), (17), (69) are inconsistent by sub-proof #2197.
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | End of split
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | Case 2:
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | |   (70)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 241.80/48.35  | | | |           = e1)
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | | BETA: splitting (70) gives:
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | | Case 1:
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | |   (71)  all_58_5 = e1 & op(e2, e1) = e1
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | ALPHA: (71) implies:
% 241.80/48.35  | | | | |   (72)  op(e2, e1) = e1
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | REF_CLOSE: (22), (41), (48), (66), (72) are inconsistent by sub-proof
% 241.80/48.35  | | | | |            #2165.
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | Case 2:
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | |   (73)  all_58_10 = e1 & op(e2, e0) = e1
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | ALPHA: (73) implies:
% 241.80/48.35  | | | | |   (74)  all_58_10 = e1
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | BETA: splitting (11) gives:
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | Case 1:
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | |   (75)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 241.80/48.35  | | | | | |             e1) = e1)
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | | REF_CLOSE: (1), (3), (5), (14), (15), (17), (18), (20), (24), (30),
% 241.80/48.35  | | | | | |            (35), (36), (40), (41), (48), (56), (74), (75) are
% 241.80/48.35  | | | | | |            inconsistent by sub-proof #647.
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | Case 2:
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | |   (76)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0,
% 241.80/48.35  | | | | | |             e1) = e1)
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | | BETA: splitting (76) gives:
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | | Case 1:
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | |   (77)  all_58_8 = e1 & op(e1, e1) = e1
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | | ALPHA: (77) implies:
% 241.80/48.35  | | | | | | |   (78)  op(e1, e1) = e1
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | | REF_CLOSE: (41), (46), (48), (78) are inconsistent by sub-proof
% 241.80/48.35  | | | | | | |            #2220.
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | Case 2:
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | |   (79)  all_58_14 = e1 & op(e0, e1) = e1
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | | ALPHA: (79) implies:
% 241.80/48.35  | | | | | | |   (80)  all_58_14 = e1
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | | REF_CLOSE: (3), (5), (13), (15), (19), (20), (22), (23), (24),
% 241.80/48.35  | | | | | | |            (25), (27), (29), (33), (37), (41), (46), (48), (52),
% 241.80/48.35  | | | | | | |            (56), (58), (65), (80) are inconsistent by sub-proof
% 241.80/48.35  | | | | | | |            #643.
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | End of split
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | End of split
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | End of split
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | End of split
% 241.80/48.35  | | | 
% 241.80/48.35  | | Case 2:
% 241.80/48.35  | | | 
% 241.80/48.35  | | |   (81)  all_58_10 = e0 & op(e2, e0) = e0
% 241.80/48.35  | | | 
% 241.80/48.35  | | | ALPHA: (81) implies:
% 241.80/48.35  | | |   (82)  all_58_10 = e0
% 241.80/48.35  | | |   (83)  op(e2, e0) = e0
% 241.80/48.35  | | | 
% 241.80/48.35  | | | BETA: splitting (54) gives:
% 241.80/48.35  | | | 
% 241.80/48.35  | | | Case 1:
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | |   (84)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 241.80/48.35  | | | |           = e1)
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | | BETA: splitting (84) gives:
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | | Case 1:
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | |   (85)  all_58_2 = e1 & op(e2, e3) = e1
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | REF_CLOSE: (29), (41), (57), (85) are inconsistent by sub-proof #2229.
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | Case 2:
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | |   (86)  all_58_3 = e1 & op(e2, e2) = e1
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | REF_CLOSE: (15), (17), (86) are inconsistent by sub-proof #2197.
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | End of split
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | Case 2:
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | |   (87)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 241.80/48.35  | | | |           = e1)
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | | BETA: splitting (87) gives:
% 241.80/48.35  | | | | 
% 241.80/48.35  | | | | Case 1:
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | |   (88)  all_58_5 = e1 & op(e2, e1) = e1
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | ALPHA: (88) implies:
% 241.80/48.35  | | | | |   (89)  all_58_5 = e1
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | BETA: splitting (8) gives:
% 241.80/48.35  | | | | | 
% 241.80/48.35  | | | | | Case 1:
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | |   (90)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 241.80/48.35  | | | | | |             e0) = e1)
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | | BETA: splitting (90) gives:
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | | Case 1:
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | |   (91)  all_58_9 = e1 & op(e3, e0) = e1
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | | ALPHA: (91) implies:
% 241.80/48.35  | | | | | | |   (92)  all_58_9 = e1
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (14),
% 241.80/48.35  | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 241.80/48.35  | | | | | | |            (24), (25), (27), (28), (29), (30), (31), (33), (35),
% 241.80/48.35  | | | | | | |            (36), (37), (38), (39), (40), (41), (43), (46), (48),
% 241.80/48.35  | | | | | | |            (49), (50), (51), (52), (53), (54), (56), (57), (58),
% 241.80/48.35  | | | | | | |            (92) are inconsistent by sub-proof #639.
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | Case 2:
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | |   (93)  all_58_10 = e1 & op(e2, e0) = e1
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | | ALPHA: (93) implies:
% 241.80/48.35  | | | | | | |   (94)  all_58_10 = e1
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | | REF_CLOSE: (3), (5), (14), (17), (24), (40), (48), (56), (89),
% 241.80/48.35  | | | | | | |            (94) are inconsistent by sub-proof #992.
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | End of split
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | Case 2:
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | |   (95)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 241.80/48.35  | | | | | |           op(e0, e0) = e1)
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | | BETA: splitting (95) gives:
% 241.80/48.35  | | | | | | 
% 241.80/48.35  | | | | | | Case 1:
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | |   (96)  all_58_11 = e1 & op(e1, e0) = e1
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | | ALPHA: (96) implies:
% 241.80/48.35  | | | | | | |   (97)  all_58_11 = e1
% 241.80/48.35  | | | | | | |   (98)  op(e1, e0) = e1
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | | BETA: splitting (28) gives:
% 241.80/48.35  | | | | | | | 
% 241.80/48.35  | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | 
% 241.80/48.35  | | | | | | | |   (99)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 &
% 241.80/48.35  | | | | | | | |           op(e1, e2) = e3)
% 241.80/48.35  | | | | | | | | 
% 241.80/48.35  | | | | | | | | BETA: splitting (99) gives:
% 241.80/48.35  | | | | | | | | 
% 241.80/48.35  | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | 
% 241.80/48.35  | | | | | | | | |   (100)  all_58_6 = e3 & op(e1, e3) = e3
% 241.80/48.35  | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | ALPHA: (100) implies:
% 241.80/48.35  | | | | | | | | |   (101)  all_58_6 = e3
% 241.80/48.35  | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | BETA: splitting (23) gives:
% 241.80/48.35  | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | |   (102)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 241.80/48.35  | | | | | | | | | |            & op(e2, e3) = e2)
% 241.80/48.35  | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | BETA: splitting (102) gives:
% 241.80/48.35  | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | |   (103)  all_58_0 = e2 & op(e3, e3) = e2
% 241.80/48.35  | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | ALPHA: (103) implies:
% 241.80/48.35  | | | | | | | | | | |   (104)  op(e3, e3) = e2
% 241.80/48.35  | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | REF_CLOSE: (20), (41), (56), (104) are inconsistent by
% 241.80/48.35  | | | | | | | | | | |            sub-proof #2267.
% 241.80/48.35  | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | Case 2:
% 241.80/48.35  | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | |   (105)  all_58_2 = e2 & op(e2, e3) = e2
% 241.80/48.35  | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | ALPHA: (105) implies:
% 241.80/48.35  | | | | | | | | | | |   (106)  all_58_2 = e2
% 241.80/48.35  | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | BETA: splitting (30) gives:
% 241.80/48.35  | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | |   (107)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 241.80/48.35  | | | | | | | | | | | |            & op(e3, e2) = e0)
% 241.80/48.35  | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | BETA: splitting (107) gives:
% 241.80/48.35  | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | |   (108)  all_58_0 = e0 & op(e3, e3) = e0
% 241.80/48.35  | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | ALPHA: (108) implies:
% 241.80/48.35  | | | | | | | | | | | | |   (109)  op(e3, e3) = e0
% 241.80/48.35  | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | REF_CLOSE: (20), (41), (48), (109) are inconsistent by
% 241.80/48.35  | | | | | | | | | | | | |            sub-proof #1828.
% 241.80/48.35  | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | Case 2:
% 241.80/48.35  | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | |   (110)  all_58_1 = e0 & op(e3, e2) = e0
% 241.80/48.35  | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | ALPHA: (110) implies:
% 241.80/48.35  | | | | | | | | | | | | |   (111)  all_58_1 = e0
% 241.80/48.35  | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | BETA: splitting (39) gives:
% 241.80/48.35  | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | |   (112)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.80/48.35  | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.80/48.35  | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 241.80/48.35  | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | |   (113)  all_58_6 = e2 & op(e1, e3) = e2
% 241.80/48.35  | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 241.80/48.35  | | | | | | | | | | | | | | |   (114)  all_58_6 = e2
% 241.80/48.35  | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | REF_CLOSE: (24), (101), (114) are inconsistent by sub-proof
% 241.80/48.35  | | | | | | | | | | | | | | |            #2024.
% 241.80/48.35  | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | Case 2:
% 241.80/48.35  | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | |   (115)  all_58_7 = e2 & op(e1, e2) = e2
% 241.80/48.35  | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 241.80/48.35  | | | | | | | | | | | | | | |   (116)  all_58_7 = e2
% 241.80/48.35  | | | | | | | | | | | | | | |   (117)  op(e1, e2) = e2
% 241.80/48.35  | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 241.80/48.35  | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | |   (118)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 241.80/48.35  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 241.80/48.35  | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (15), (17), (19), (20), (23), (24),
% 241.80/48.35  | | | | | | | | | | | | | | | |            (27), (29), (36), (41), (47), (48), (52), (56),
% 241.80/48.35  | | | | | | | | | | | | | | | |            (101), (118) are inconsistent by sub-proof #659.
% 241.80/48.35  | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | Case 2:
% 241.80/48.35  | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | |   (119)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 241.80/48.35  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 241.80/48.35  | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 241.80/48.35  | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | |   (120)  all_58_7 = e1 & op(e1, e2) = e1
% 241.80/48.35  | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 241.80/48.35  | | | | | | | | | | | | | | | | |   (121)  all_58_7 = e1
% 241.80/48.35  | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (10), (14), (15), (16), (17),
% 241.80/48.35  | | | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (24), (25), (27),
% 241.80/48.35  | | | | | | | | | | | | | | | | |            (29), (33), (35), (36), (37), (39), (40), (41),
% 241.80/48.35  | | | | | | | | | | | | | | | | |            (42), (48), (49), (51), (52), (54), (56), (57),
% 241.80/48.35  | | | | | | | | | | | | | | | | |            (82), (121) are inconsistent by sub-proof #638.
% 241.80/48.35  | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.35  | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | |   (122)  all_58_13 = e1 & op(e0, e2) = e1
% 241.80/48.35  | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 241.80/48.35  | | | | | | | | | | | | | | | | |   (123)  all_58_13 = e1
% 241.80/48.35  | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 241.80/48.35  | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | |   (124)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 241.80/48.35  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.80/48.35  | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (10), (14), (15), (16), (17),
% 241.80/48.35  | | | | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (24), (25), (27),
% 241.80/48.35  | | | | | | | | | | | | | | | | | |            (29), (33), (35), (36), (37), (39), (40), (41),
% 241.80/48.35  | | | | | | | | | | | | | | | | | |            (42), (48), (49), (51), (52), (54), (56), (57),
% 241.80/48.35  | | | | | | | | | | | | | | | | | |            (58), (82), (101), (106), (116), (123), (124) are
% 241.80/48.35  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #631.
% 241.80/48.35  | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | |   (125)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 241.80/48.35  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.80/48.35  | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | |   (126)  all_58_14 = e2 & op(e0, e1) = e2
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | |   (127)  all_58_14 = e2
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (9), (12), (14), (15), (17),
% 241.80/48.35  | | | | | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (24), (26), (27),
% 241.80/48.35  | | | | | | | | | | | | | | | | | | |            (29), (33), (34), (35), (36), (37), (40), (41),
% 241.80/48.35  | | | | | | | | | | | | | | | | | | |            (42), (45), (46), (48), (52), (54), (55), (56),
% 241.80/48.35  | | | | | | | | | | | | | | | | | | |            (57), (58), (82), (89), (98), (101), (106), (111),
% 241.80/48.35  | | | | | | | | | | | | | | | | | | |            (127) are inconsistent by sub-proof #628.
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | |   (128)  all_58_15 = e2 & op(e0, e0) = e2
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | |   (129)  all_58_15 = e2
% 241.80/48.35  | | | | | | | | | | | | | | | | | | |   (130)  op(e0, e0) = e2
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | |   (131)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (12), (20), (27), (34), (41), (48),
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | |            (101), (106), (131) are inconsistent by sub-proof
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | |            #630.
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | |   (132)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | |   (133)  all_58_14 = e3 & op(e0, e1) = e3
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | |   (134)  all_58_14 = e3
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | |   (135)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | |   (136)  all_58_4 = e2 & op(e3, e1) = e2
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | |   (137)  all_58_4 = e2
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | |   (138)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (20), (35), (36), (41), (138) are
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1401.
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | |   (139)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (140)  all_58_4 = e3 & op(e3, e1) = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (141)  all_58_4 = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (137), (141) imply:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (142)  e3 = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (142) imply:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (143)  all_58_14 = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (9), (12), (14), (15), (17),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (24), (26), (27),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (33), (34), (35), (36), (37), (40), (41),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (42), (45), (46), (48), (52), (54), (55), (56),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (82), (89), (98), (101), (106), (111),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (143) are inconsistent by sub-proof #628.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (144)  all_58_9 = e3 & op(e3, e0) = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (8), (9), (14), (15), (16), (17),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (20), (24), (25), (26), (29), (35), (36),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (40), (41), (42), (43), (45), (48), (52),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (55), (56), (89), (97), (106), (117), (129),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (134), (144) are inconsistent by sub-proof
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | |            #624.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (145)  all_58_5 = e2 & op(e2, e1) = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (10), (14), (15), (16), (17),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (24), (25), (27),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (29), (33), (35), (36), (37), (39), (40), (41),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (42), (48), (49), (51), (52), (54), (56), (57),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (82), (89), (116), (145) are inconsistent by
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #623.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | |   (146)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (147)  all_58_8 = e2 & op(e1, e1) = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (148)  all_58_8 = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (148) imply:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (149)  e2 = e0
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (149) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (150)  e2 = e0
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (106), (150) imply:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (151)  all_58_2 = e0
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (14), (15), (17), (24), (38), (40),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (41), (43), (48), (56), (83), (89), (97), (129),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (151) are inconsistent by sub-proof #626.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (152)  all_58_14 = e2 & op(e0, e1) = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (153)  all_58_14 = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (9), (12), (14), (15), (17),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (24), (26), (27),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (29), (33), (34), (35), (36), (37), (40), (41),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (42), (45), (46), (48), (52), (54), (55), (56),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (82), (89), (98), (101), (106), (111),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (153) are inconsistent by sub-proof #628.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | |   (154)  all_58_15 = e3 & op(e0, e0) = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (129), (154) are inconsistent by sub-proof
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | |            #1170.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | |   (155)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.80/48.36  | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (13), (14), (15), (17), (19), (20),
% 241.80/48.36  | | | | | | | | | | | | | |            (23), (24), (27), (29), (40), (41), (48), (52),
% 241.80/48.36  | | | | | | | | | | | | | |            (54), (56), (57), (58), (82), (97), (101), (106),
% 241.80/48.36  | | | | | | | | | | | | | |            (155) are inconsistent by sub-proof #622.
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | |   (156)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 241.80/48.36  | | | | | | | | | | | |            & op(e3, e0) = e0)
% 241.80/48.36  | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | BETA: splitting (156) gives:
% 241.80/48.36  | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | |   (157)  all_58_4 = e0 & op(e3, e1) = e0
% 241.80/48.36  | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | ALPHA: (157) implies:
% 241.80/48.36  | | | | | | | | | | | | |   (158)  all_58_4 = e0
% 241.80/48.36  | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | BETA: splitting (39) gives:
% 241.80/48.36  | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | |   (159)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.80/48.36  | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | |   (160)  all_58_6 = e2 & op(e1, e3) = e2
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 241.80/48.36  | | | | | | | | | | | | | | |   (161)  all_58_6 = e2
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | REF_CLOSE: (24), (101), (161) are inconsistent by sub-proof
% 241.80/48.36  | | | | | | | | | | | | | | |            #2024.
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | |   (162)  all_58_7 = e2 & op(e1, e2) = e2
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 241.80/48.36  | | | | | | | | | | | | | | |   (163)  all_58_7 = e2
% 241.80/48.36  | | | | | | | | | | | | | | |   (164)  op(e1, e2) = e2
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | |   (165)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 241.80/48.36  | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11),
% 241.80/48.36  | | | | | | | | | | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21),
% 241.80/48.36  | | | | | | | | | | | | | | | |            (22), (23), (24), (25), (27), (28), (29), (30),
% 241.80/48.36  | | | | | | | | | | | | | | | |            (31), (33), (35), (36), (37), (38), (39), (40),
% 241.80/48.36  | | | | | | | | | | | | | | | |            (41), (43), (46), (48), (49), (50), (51), (52),
% 241.80/48.36  | | | | | | | | | | | | | | | |            (53), (54), (56), (57), (101), (158), (165) are
% 241.80/48.36  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #621.
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | |   (166)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 241.80/48.36  | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | |   (167)  all_58_8 = e3 & op(e1, e1) = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (41), (46), (167) are inconsistent by
% 241.80/48.36  | | | | | | | | | | | | | | | | |            sub-proof #2018.
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | |   (168)  all_58_14 = e3 & op(e0, e1) = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | |   (169)  all_58_14 = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | |   (170)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 241.80/48.36  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 241.80/48.36  | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (15), (17), (19), (20), (23), (24),
% 241.80/48.36  | | | | | | | | | | | | | | | | | |            (27), (29), (36), (41), (47), (48), (52), (56),
% 241.80/48.36  | | | | | | | | | | | | | | | | | |            (101), (170) are inconsistent by sub-proof #620.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | |   (171)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 241.80/48.36  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 241.80/48.36  | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | |   (172)  all_58_7 = e1 & op(e1, e2) = e1
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | |   (173)  all_58_7 = e1
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (10), (14), (15), (16), (17),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (24), (25), (27),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | |            (29), (33), (35), (36), (37), (39), (40), (41),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | |            (42), (48), (49), (51), (52), (54), (56), (57),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | |            (82), (173) are inconsistent by sub-proof #638.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | |   (174)  all_58_13 = e1 & op(e0, e2) = e1
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | |   (175)  all_58_13 = e1
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | |   (176)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (10), (14), (15), (16), (17),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (24), (25), (27),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | |            (29), (33), (35), (36), (37), (39), (40), (41),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | |            (42), (48), (49), (51), (52), (54), (56), (57),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | |            (58), (82), (101), (106), (163), (175), (176) are
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #631.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | |   (177)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | |   (178)  all_58_14 = e2 & op(e0, e1) = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | |   (179)  all_58_14 = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (169), (179) are inconsistent by sub-proof
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | |            #2117.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | |   (180)  all_58_15 = e2 & op(e0, e0) = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | |   (181)  all_58_15 = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | |   (182)  op(e0, e0) = e2
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | |   (183)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (20), (35), (36), (41), (183) are
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1401.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | |   (184)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (185)  all_58_4 = e3 & op(e3, e1) = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_58_4 = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (186) imply:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (187)  e3 = e0
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (22), (23), (24), (25), (27), (28), (29), (30),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (31), (33), (35), (36), (37), (38), (39), (40),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (41), (43), (46), (48), (49), (50), (51), (52),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (53), (54), (56), (57), (101), (187) are
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #642.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_58_9 = e3 & op(e3, e0) = e3
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (8), (9), (14), (15), (16), (17),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (18), (20), (24), (25), (26), (29), (35), (36),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (38), (40), (41), (42), (43), (45), (48), (52),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (55), (56), (89), (97), (106), (164), (169),
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (188) are inconsistent by sub-proof
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | |            #624.
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | |   (189)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.80/48.36  | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (13), (14), (15), (17), (19), (20),
% 241.80/48.36  | | | | | | | | | | | | | |            (23), (24), (27), (29), (40), (41), (48), (52),
% 241.80/48.36  | | | | | | | | | | | | | |            (54), (56), (57), (58), (82), (97), (101), (106),
% 241.80/48.36  | | | | | | | | | | | | | |            (189) are inconsistent by sub-proof #622.
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | End of split
% 241.80/48.36  | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | |   (190)  all_58_9 = e0 & op(e3, e0) = e0
% 241.80/48.36  | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | ALPHA: (190) implies:
% 241.80/48.36  | | | | | | | | | | | | |   (191)  all_58_9 = e0
% 241.80/48.36  | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | BETA: splitting (39) gives:
% 241.80/48.36  | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | |   (192)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 241.80/48.36  | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 241.80/48.36  | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | |   (193)  all_58_6 = e2 & op(e1, e3) = e2
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 241.80/48.36  | | | | | | | | | | | | | | |   (194)  all_58_6 = e2
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | REF_CLOSE: (24), (101), (194) are inconsistent by sub-proof
% 241.80/48.36  | | | | | | | | | | | | | | |            #2024.
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | |   (195)  all_58_7 = e2 & op(e1, e2) = e2
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 241.80/48.36  | | | | | | | | | | | | | | |   (196)  all_58_7 = e2
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | |   (197)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 241.80/48.36  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (15), (17), (19), (20), (23), (24),
% 241.80/48.36  | | | | | | | | | | | | | | | |            (27), (29), (36), (41), (47), (48), (52), (56),
% 241.80/48.36  | | | | | | | | | | | | | | | |            (101), (197) are inconsistent by sub-proof #620.
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | |   (198)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 241.80/48.36  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | |   (199)  all_58_7 = e1 & op(e1, e2) = e1
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | |   (200)  all_58_7 = e1
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (10), (14), (15), (16), (17),
% 241.80/48.36  | | | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (24), (25), (27),
% 241.80/48.36  | | | | | | | | | | | | | | | | |            (29), (33), (35), (36), (37), (39), (40), (41),
% 241.80/48.36  | | | | | | | | | | | | | | | | |            (42), (48), (49), (51), (52), (54), (56), (57),
% 241.80/48.36  | | | | | | | | | | | | | | | | |            (82), (200) are inconsistent by sub-proof #638.
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | |   (201)  all_58_13 = e1 & op(e0, e2) = e1
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 241.80/48.36  | | | | | | | | | | | | | | | | |   (202)  all_58_13 = e1
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 241.80/48.36  | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.36  | | | | | | | | | | | | | | | | | | 
% 241.80/48.36  | | | | | | | | | | | | | | | | | |   (203)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 241.80/48.36  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 241.80/48.36  | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (10), (14), (15), (16), (17),
% 241.80/48.37  | | | | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (24), (25), (27),
% 241.80/48.37  | | | | | | | | | | | | | | | | | |            (29), (33), (35), (36), (37), (39), (40), (41),
% 241.80/48.37  | | | | | | | | | | | | | | | | | |            (42), (48), (49), (51), (52), (54), (56), (57),
% 241.80/48.37  | | | | | | | | | | | | | | | | | |            (58), (82), (101), (106), (196), (202), (203) are
% 241.80/48.37  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #631.
% 241.80/48.37  | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | |   (204)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 241.80/48.37  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 241.80/48.37  | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | |   (205)  all_58_14 = e2 & op(e0, e1) = e2
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | |   (206)  all_58_14 = e2
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | |   (207)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (20), (35), (36), (41), (207) are
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1401.
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | |   (208)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |   (209)  all_58_4 = e3 & op(e3, e1) = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |   (210)  all_58_4 = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | |   (211)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (12), (15), (18), (20), (23),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | |            (24), (27), (28), (30), (31), (34), (35), (36),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | |            (41), (46), (48), (56), (97), (210), (211) are
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #617.
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | |   (212)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_58_14 = e3 & op(e0, e1) = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (206), (213) are inconsistent by sub-proof
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | |            #1747.
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_58_15 = e3 & op(e0, e0) = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_58_15 = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (15), (17), (20), (23), (24), (29),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | |            (40), (41), (43), (48), (54), (56), (57), (58),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | |            (97), (101), (191), (210), (215) are inconsistent
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #613.
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |   (216)  all_58_9 = e3 & op(e3, e0) = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |   (217)  all_58_9 = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (217) imply:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |   (218)  e3 = e0
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |            (22), (23), (24), (25), (27), (28), (29), (30),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |            (31), (33), (35), (36), (37), (38), (39), (40),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |            (41), (43), (46), (48), (49), (50), (51), (52),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |            (53), (54), (56), (57), (101), (218) are
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #642.
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | End of split
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | |   (219)  all_58_15 = e2 & op(e0, e0) = e2
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | |   (220)  all_58_15 = e2
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | |   (221)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (20), (35), (36), (41), (221) are
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1401.
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | |   (222)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | Case 1:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |   (223)  all_58_4 = e3 & op(e3, e1) = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |   (224)  all_58_4 = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (15), (18), (20), (24), (30), (35),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |            (36), (38), (41), (48), (56), (82), (97), (191),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |            (220), (224) are inconsistent by sub-proof #612.
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | Case 2:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |   (225)  all_58_9 = e3 & op(e3, e0) = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |   (226)  all_58_9 = e3
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (226) imply:
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |   (227)  e3 = e0
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11),
% 241.80/48.37  | | | | | | | | | | | | | | | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21),
% 241.88/48.37  | | | | | | | | | | | | | | | | | | | | |            (22), (23), (24), (25), (27), (28), (29), (30),
% 241.88/48.37  | | | | | | | | | | | | | | | | | | | | |            (31), (33), (35), (36), (37), (38), (39), (40),
% 241.88/48.37  | | | | | | | | | | | | | | | | | | | | |            (41), (43), (46), (48), (49), (50), (51), (52),
% 241.88/48.37  | | | | | | | | | | | | | | | | | | | | |            (53), (54), (56), (57), (101), (227) are
% 241.88/48.37  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #642.
% 241.88/48.37  | | | | | | | | | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | | Case 2:
% 241.88/48.37  | | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | | |   (228)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 241.88/48.37  | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 241.88/48.37  | | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (13), (14), (15), (17), (19), (20),
% 241.88/48.37  | | | | | | | | | | | | | |            (23), (24), (27), (29), (40), (41), (48), (52),
% 241.88/48.37  | | | | | | | | | | | | | |            (54), (56), (57), (58), (82), (97), (101), (106),
% 241.88/48.37  | | | | | | | | | | | | | |            (228) are inconsistent by sub-proof #622.
% 241.88/48.37  | | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | Case 2:
% 241.88/48.37  | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | |   (229)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2
% 241.88/48.37  | | | | | | | | | |            & op(e0, e3) = e2)
% 241.88/48.37  | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | | REF_CLOSE: (5), (24), (58), (101), (229) are inconsistent by
% 241.88/48.37  | | | | | | | | | |            sub-proof #1151.
% 241.88/48.37  | | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | Case 2:
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | |   (230)  all_58_7 = e3 & op(e1, e2) = e3
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | ALPHA: (230) implies:
% 241.88/48.37  | | | | | | | | |   (231)  op(e1, e2) = e3
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | REF_CLOSE: (6), (31), (41), (231) are inconsistent by
% 241.88/48.37  | | | | | | | | |            sub-proof #2191.
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | 
% 241.88/48.37  | | | | | | | Case 2:
% 241.88/48.37  | | | | | | | | 
% 241.88/48.37  | | | | | | | |   (232)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 &
% 241.88/48.37  | | | | | | | |            op(e1, e0) = e3)
% 241.88/48.37  | | | | | | | | 
% 241.88/48.37  | | | | | | | | BETA: splitting (232) gives:
% 241.88/48.37  | | | | | | | | 
% 241.88/48.37  | | | | | | | | Case 1:
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | |   (233)  all_58_8 = e3 & op(e1, e1) = e3
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | REF_CLOSE: (3), (41), (46), (233) are inconsistent by
% 241.88/48.37  | | | | | | | | |            sub-proof #2018.
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | Case 2:
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | |   (234)  all_58_11 = e3 & op(e1, e0) = e3
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | ALPHA: (234) implies:
% 241.88/48.37  | | | | | | | | |   (235)  all_58_11 = e3
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | | REF_CLOSE: (15), (97), (235) are inconsistent by sub-proof
% 241.88/48.37  | | | | | | | | |            #1980.
% 241.88/48.37  | | | | | | | | | 
% 241.88/48.37  | | | | | | | | End of split
% 241.88/48.37  | | | | | | | | 
% 241.88/48.37  | | | | | | | End of split
% 241.88/48.37  | | | | | | | 
% 241.88/48.37  | | | | | | Case 2:
% 241.88/48.37  | | | | | | | 
% 241.88/48.37  | | | | | | |   (236)  all_58_15 = e1 & op(e0, e0) = e1
% 241.88/48.37  | | | | | | | 
% 241.88/48.37  | | | | | | | ALPHA: (236) implies:
% 241.88/48.37  | | | | | | |   (237)  op(e0, e0) = e1
% 241.88/48.37  | | | | | | | 
% 241.88/48.37  | | | | | | | REF_CLOSE: (41), (42), (48), (237) are inconsistent by sub-proof
% 241.88/48.37  | | | | | | |            #2274.
% 241.88/48.37  | | | | | | | 
% 241.88/48.37  | | | | | | End of split
% 241.88/48.37  | | | | | | 
% 241.88/48.37  | | | | | End of split
% 241.88/48.37  | | | | | 
% 241.88/48.37  | | | | Case 2:
% 241.88/48.37  | | | | | 
% 241.88/48.37  | | | | |   (238)  all_58_10 = e1 & op(e2, e0) = e1
% 241.88/48.37  | | | | | 
% 241.88/48.37  | | | | | ALPHA: (238) implies:
% 241.88/48.37  | | | | |   (239)  op(e2, e0) = e1
% 241.88/48.37  | | | | | 
% 241.88/48.37  | | | | | REF_CLOSE: (41), (48), (50), (83), (239) are inconsistent by sub-proof
% 241.88/48.37  | | | | |            #1778.
% 241.88/48.37  | | | | | 
% 241.88/48.37  | | | | End of split
% 241.88/48.37  | | | | 
% 241.88/48.37  | | | End of split
% 241.88/48.37  | | | 
% 241.88/48.37  | | End of split
% 241.88/48.37  | | 
% 241.88/48.37  | End of split
% 241.88/48.37  | 
% 241.88/48.37  End of proof
% 241.88/48.37  
% 241.88/48.37  Sub-proof #612 shows that the following formulas are inconsistent:
% 241.88/48.37  ----------------------------------------------------------------
% 241.88/48.37    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.37         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.37    (2)   ~ (e3 = e0)
% 241.88/48.37    (3)   ~ (e2 = e0)
% 241.88/48.37    (4)  all_58_9 = e0
% 241.88/48.37    (5)  all_58_11 = e1
% 241.88/48.37    (6)   ~ (e3 = e1)
% 241.88/48.37    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.37         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.37    (8)  op(e3, e3) = e1
% 241.88/48.37    (9)  all_58_15 = e2
% 241.88/48.37    (10)   ~ (e3 = e2)
% 241.88/48.37    (11)  all_58_10 = e0
% 241.88/48.37    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.88/48.37          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.37    (13)   ~ (all_52_4 = e3)
% 241.88/48.37    (14)  op(e3, e2) = all_52_4
% 241.88/48.37    (15)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.88/48.37          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.88/48.37    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.37    (17)   ~ (e1 = e0)
% 241.88/48.37    (18)  all_58_4 = e3
% 241.88/48.37    (19)   ~ (e2 = e1)
% 241.88/48.37  
% 241.88/48.37  Begin of proof
% 241.88/48.37  | 
% 241.88/48.37  | BETA: splitting (15) gives:
% 241.88/48.37  | 
% 241.88/48.37  | Case 1:
% 241.88/48.37  | | 
% 241.88/48.37  | |   (20)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 241.88/48.37  | |           e3)
% 241.88/48.37  | | 
% 241.88/48.37  | | BETA: splitting (20) gives:
% 241.88/48.37  | | 
% 241.88/48.37  | | Case 1:
% 241.88/48.37  | | | 
% 241.88/48.37  | | |   (21)  all_58_9 = e3 & op(e3, e0) = e3
% 241.88/48.37  | | | 
% 241.88/48.37  | | | ALPHA: (21) implies:
% 241.88/48.37  | | |   (22)  all_58_9 = e3
% 241.88/48.37  | | | 
% 241.88/48.37  | | | REF_CLOSE: (2), (4), (22) are inconsistent by sub-proof #1958.
% 241.88/48.37  | | | 
% 241.88/48.37  | | Case 2:
% 241.88/48.37  | | | 
% 241.88/48.37  | | |   (23)  all_58_10 = e3 & op(e2, e0) = e3
% 241.88/48.37  | | | 
% 241.88/48.37  | | | ALPHA: (23) implies:
% 241.88/48.37  | | |   (24)  all_58_10 = e3
% 241.88/48.37  | | | 
% 241.88/48.37  | | | COMBINE_EQS: (11), (24) imply:
% 241.88/48.37  | | |   (25)  e3 = e0
% 241.88/48.37  | | | 
% 241.88/48.37  | | | REDUCE: (2), (25) imply:
% 241.88/48.37  | | |   (26)  $false
% 241.88/48.37  | | | 
% 241.88/48.37  | | | CLOSE: (26) is inconsistent.
% 241.88/48.37  | | | 
% 241.88/48.37  | | End of split
% 241.88/48.37  | | 
% 241.88/48.37  | Case 2:
% 241.88/48.37  | | 
% 241.88/48.37  | |   (27)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 241.88/48.37  | |           e3)
% 241.88/48.37  | | 
% 241.88/48.37  | | BETA: splitting (27) gives:
% 241.88/48.37  | | 
% 241.88/48.37  | | Case 1:
% 241.88/48.37  | | | 
% 241.88/48.37  | | |   (28)  all_58_11 = e3 & op(e1, e0) = e3
% 241.88/48.37  | | | 
% 241.88/48.37  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (12), (13), (14),
% 241.88/48.37  | | |            (16), (17), (18), (19), (28) are inconsistent by sub-proof
% 241.88/48.37  | | |            #652.
% 241.88/48.37  | | | 
% 241.88/48.37  | | Case 2:
% 241.88/48.37  | | | 
% 241.88/48.37  | | |   (29)  all_58_15 = e3 & op(e0, e0) = e3
% 241.88/48.37  | | | 
% 241.88/48.37  | | | REF_CLOSE: (9), (10), (29) are inconsistent by sub-proof #1170.
% 241.88/48.37  | | | 
% 241.88/48.37  | | End of split
% 241.88/48.37  | | 
% 241.88/48.37  | End of split
% 241.88/48.37  | 
% 241.88/48.37  End of proof
% 241.88/48.37  
% 241.88/48.37  Sub-proof #613 shows that the following formulas are inconsistent:
% 241.88/48.37  ----------------------------------------------------------------
% 241.88/48.37    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.37         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.37    (2)   ~ (e3 = e0)
% 241.88/48.37    (3)  all_58_6 = e3
% 241.88/48.37    (4)   ~ (e2 = e0)
% 241.88/48.37    (5)  all_58_9 = e0
% 241.88/48.37    (6)  all_58_11 = e1
% 241.88/48.37    (7)  all_58_15 = e3
% 241.88/48.37    (8)   ~ (e3 = e1)
% 241.88/48.37    (9)  all_58_3 = e3
% 241.88/48.37    (10)  op(e3, e3) = e1
% 241.88/48.37    (11)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.37          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.37    (12)   ~ (e3 = e2)
% 241.88/48.37    (13)  all_58_12 = e0
% 241.88/48.37    (14)  op(e2, e3) = all_52_1
% 241.88/48.37    (15)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.37          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.37    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.37    (17)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.88/48.37          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.88/48.37    (18)   ~ (e1 = e0)
% 241.88/48.37    (19)  all_58_4 = e3
% 241.88/48.37    (20)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.37          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.37    (21)   ~ (e2 = e1)
% 241.88/48.37    (22)   ~ (all_52_1 = e1)
% 241.88/48.37  
% 241.88/48.37  Begin of proof
% 241.88/48.37  | 
% 241.88/48.37  | BETA: splitting (1) gives:
% 241.88/48.37  | 
% 241.88/48.37  | Case 1:
% 241.88/48.37  | | 
% 241.88/48.37  | |   (23)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 241.88/48.37  | |           e2)
% 241.88/48.37  | | 
% 241.88/48.37  | | BETA: splitting (23) gives:
% 241.88/48.37  | | 
% 241.88/48.37  | | Case 1:
% 241.88/48.37  | | | 
% 241.88/48.37  | | |   (24)  all_58_0 = e2 & op(e3, e3) = e2
% 241.88/48.37  | | | 
% 241.88/48.37  | | | ALPHA: (24) implies:
% 241.88/48.37  | | |   (25)  op(e3, e3) = e2
% 241.88/48.37  | | | 
% 241.88/48.37  | | | REF_CLOSE: (10), (16), (21), (25) are inconsistent by sub-proof #2267.
% 241.88/48.37  | | | 
% 241.88/48.37  | | Case 2:
% 241.88/48.37  | | | 
% 241.88/48.37  | | |   (26)  all_58_1 = e2 & op(e3, e2) = e2
% 241.88/48.37  | | | 
% 241.88/48.37  | | | ALPHA: (26) implies:
% 241.88/48.37  | | |   (27)  all_58_1 = e2
% 241.88/48.37  | | | 
% 241.88/48.37  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.88/48.37  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.88/48.37  | | |            (27) are inconsistent by sub-proof #614.
% 241.88/48.37  | | | 
% 241.88/48.37  | | End of split
% 241.88/48.37  | | 
% 241.88/48.37  | Case 2:
% 241.88/48.37  | | 
% 241.88/48.37  | |   (28)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 241.88/48.37  | |           e2)
% 241.88/48.37  | | 
% 241.88/48.37  | | BETA: splitting (28) gives:
% 241.88/48.37  | | 
% 241.88/48.37  | | Case 1:
% 241.88/48.37  | | | 
% 241.88/48.37  | | |   (29)  all_58_4 = e2 & op(e3, e1) = e2
% 241.88/48.37  | | | 
% 241.88/48.37  | | | REF_CLOSE: (12), (19), (29) are inconsistent by sub-proof #1476.
% 241.88/48.37  | | | 
% 241.88/48.37  | | Case 2:
% 241.88/48.37  | | | 
% 241.88/48.37  | | |   (30)  all_58_9 = e2 & op(e3, e0) = e2
% 241.88/48.37  | | | 
% 241.88/48.37  | | | REF_CLOSE: (4), (5), (30) are inconsistent by sub-proof #1655.
% 241.88/48.37  | | | 
% 241.88/48.37  | | End of split
% 241.88/48.37  | | 
% 241.88/48.37  | End of split
% 241.88/48.37  | 
% 241.88/48.37  End of proof
% 241.88/48.37  
% 241.88/48.37  Sub-proof #614 shows that the following formulas are inconsistent:
% 241.88/48.37  ----------------------------------------------------------------
% 241.88/48.37    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.37         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.37    (2)   ~ (e3 = e0)
% 241.88/48.37    (3)  all_58_6 = e3
% 241.88/48.37    (4)   ~ (e2 = e0)
% 241.88/48.37    (5)  all_58_9 = e0
% 241.88/48.37    (6)  all_58_11 = e1
% 241.88/48.37    (7)  all_58_15 = e3
% 241.88/48.37    (8)   ~ (e3 = e1)
% 241.88/48.37    (9)  all_58_3 = e3
% 241.88/48.37    (10)  op(e3, e3) = e1
% 241.88/48.37    (11)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.37          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.37    (12)   ~ (e3 = e2)
% 241.88/48.37    (13)  all_58_12 = e0
% 241.88/48.37    (14)  op(e2, e3) = all_52_1
% 241.88/48.37    (15)  all_58_1 = e2
% 241.88/48.38    (16)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.38          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.38    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.38    (18)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.88/48.38          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.88/48.38    (19)   ~ (e1 = e0)
% 241.88/48.38    (20)  all_58_4 = e3
% 241.88/48.38    (21)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.38          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.38    (22)   ~ (e2 = e1)
% 241.88/48.38    (23)   ~ (all_52_1 = e1)
% 241.88/48.38  
% 241.88/48.38  Begin of proof
% 241.88/48.38  | 
% 241.88/48.38  | BETA: splitting (18) gives:
% 241.88/48.38  | 
% 241.88/48.38  | Case 1:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (24)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 241.88/48.38  | |           e2)
% 241.88/48.38  | | 
% 241.88/48.38  | | BETA: splitting (24) gives:
% 241.88/48.38  | | 
% 241.88/48.38  | | Case 1:
% 241.88/48.38  | | | 
% 241.88/48.38  | | |   (25)  all_58_9 = e2 & op(e3, e0) = e2
% 241.88/48.38  | | | 
% 241.88/48.38  | | | ALPHA: (25) implies:
% 241.88/48.38  | | |   (26)  all_58_9 = e2
% 241.88/48.38  | | | 
% 241.88/48.38  | | | REF_CLOSE: (1), (4), (5), (10), (12), (15), (17), (20), (22), (26) are
% 241.88/48.38  | | |            inconsistent by sub-proof #1065.
% 241.88/48.38  | | | 
% 241.88/48.38  | | Case 2:
% 241.88/48.38  | | | 
% 241.88/48.38  | | |   (27)  all_58_10 = e2 & op(e2, e0) = e2
% 241.88/48.38  | | | 
% 241.88/48.38  | | | ALPHA: (27) implies:
% 241.88/48.38  | | |   (28)  all_58_10 = e2
% 241.88/48.38  | | |   (29)  op(e2, e0) = e2
% 241.88/48.38  | | | 
% 241.88/48.38  | | | REF_CLOSE: (2), (3), (4), (8), (9), (10), (11), (12), (13), (14), (16),
% 241.88/48.38  | | |            (17), (19), (21), (22), (23), (28), (29) are inconsistent by
% 241.88/48.38  | | |            sub-proof #616.
% 241.88/48.38  | | | 
% 241.88/48.38  | | End of split
% 241.88/48.38  | | 
% 241.88/48.38  | Case 2:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (30)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.88/48.38  | |           e2)
% 241.88/48.38  | | 
% 241.88/48.38  | | BETA: splitting (30) gives:
% 241.88/48.38  | | 
% 241.88/48.38  | | Case 1:
% 241.88/48.38  | | | 
% 241.88/48.38  | | |   (31)  all_58_11 = e2 & op(e1, e0) = e2
% 241.88/48.38  | | | 
% 241.88/48.38  | | | ALPHA: (31) implies:
% 241.88/48.38  | | |   (32)  all_58_11 = e2
% 241.88/48.38  | | | 
% 241.88/48.38  | | | REF_CLOSE: (6), (22), (32) are inconsistent by sub-proof #1020.
% 241.88/48.38  | | | 
% 241.88/48.38  | | Case 2:
% 241.88/48.38  | | | 
% 241.88/48.38  | | |   (33)  all_58_15 = e2 & op(e0, e0) = e2
% 241.88/48.38  | | | 
% 241.88/48.38  | | | ALPHA: (33) implies:
% 241.88/48.38  | | |   (34)  all_58_15 = e2
% 241.88/48.38  | | | 
% 241.88/48.38  | | | REF_CLOSE: (7), (12), (34) are inconsistent by sub-proof #615.
% 241.88/48.38  | | | 
% 241.88/48.38  | | End of split
% 241.88/48.38  | | 
% 241.88/48.38  | End of split
% 241.88/48.38  | 
% 241.88/48.38  End of proof
% 241.88/48.38  
% 241.88/48.38  Sub-proof #615 shows that the following formulas are inconsistent:
% 241.88/48.38  ----------------------------------------------------------------
% 241.88/48.38    (1)  all_58_15 = e3
% 241.88/48.38    (2)  all_58_15 = e2
% 241.88/48.38    (3)   ~ (e3 = e2)
% 241.88/48.38  
% 241.88/48.38  Begin of proof
% 241.88/48.38  | 
% 241.88/48.38  | COMBINE_EQS: (1), (2) imply:
% 241.88/48.38  |   (4)  e3 = e2
% 241.88/48.38  | 
% 241.88/48.38  | SIMP: (4) implies:
% 241.88/48.38  |   (5)  e3 = e2
% 241.88/48.38  | 
% 241.88/48.38  | REDUCE: (3), (5) imply:
% 241.88/48.38  |   (6)  $false
% 241.88/48.38  | 
% 241.88/48.38  | CLOSE: (6) is inconsistent.
% 241.88/48.38  | 
% 241.88/48.38  End of proof
% 241.88/48.38  
% 241.88/48.38  Sub-proof #616 shows that the following formulas are inconsistent:
% 241.88/48.38  ----------------------------------------------------------------
% 241.88/48.38    (1)   ~ (e3 = e0)
% 241.88/48.38    (2)  all_58_6 = e3
% 241.88/48.38    (3)   ~ (e2 = e0)
% 241.88/48.38    (4)   ~ (e3 = e1)
% 241.88/48.38    (5)  all_58_3 = e3
% 241.88/48.38    (6)  op(e3, e3) = e1
% 241.88/48.38    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.38         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.38    (8)   ~ (e3 = e2)
% 241.88/48.38    (9)  all_58_10 = e2
% 241.88/48.38    (10)  op(e2, e0) = e2
% 241.88/48.38    (11)  all_58_12 = e0
% 241.88/48.38    (12)  op(e2, e3) = all_52_1
% 241.88/48.38    (13)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.38          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.38    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.38    (15)   ~ (e1 = e0)
% 241.88/48.38    (16)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.38          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.38    (17)   ~ (e2 = e1)
% 241.88/48.38    (18)   ~ (all_52_1 = e1)
% 241.88/48.38  
% 241.88/48.38  Begin of proof
% 241.88/48.38  | 
% 241.88/48.38  | BETA: splitting (16) gives:
% 241.88/48.38  | 
% 241.88/48.38  | Case 1:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (19)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 241.88/48.38  | |           e1)
% 241.88/48.38  | | 
% 241.88/48.38  | | BETA: splitting (19) gives:
% 241.88/48.38  | | 
% 241.88/48.38  | | Case 1:
% 241.88/48.38  | | | 
% 241.88/48.38  | | |   (20)  all_58_2 = e1 & op(e2, e3) = e1
% 241.88/48.38  | | | 
% 241.88/48.38  | | | REF_CLOSE: (12), (14), (18), (20) are inconsistent by sub-proof #2229.
% 241.88/48.38  | | | 
% 241.88/48.38  | | Case 2:
% 241.88/48.38  | | | 
% 241.88/48.38  | | |   (21)  all_58_3 = e1 & op(e2, e2) = e1
% 241.88/48.38  | | | 
% 241.88/48.38  | | | ALPHA: (21) implies:
% 241.88/48.38  | | |   (22)  all_58_3 = e1
% 241.88/48.38  | | | 
% 241.88/48.38  | | | REF_CLOSE: (4), (5), (22) are inconsistent by sub-proof #1999.
% 241.88/48.38  | | | 
% 241.88/48.38  | | End of split
% 241.88/48.38  | | 
% 241.88/48.38  | Case 2:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (23)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 241.88/48.38  | |           e1)
% 241.88/48.38  | | 
% 241.88/48.38  | | BETA: splitting (23) gives:
% 241.88/48.38  | | 
% 241.88/48.38  | | Case 1:
% 241.88/48.38  | | | 
% 241.88/48.38  | | |   (24)  all_58_5 = e1 & op(e2, e1) = e1
% 241.88/48.38  | | | 
% 241.88/48.38  | | | ALPHA: (24) implies:
% 241.88/48.38  | | |   (25)  all_58_5 = e1
% 241.88/48.38  | | | 
% 241.88/48.38  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (13), (14),
% 241.88/48.38  | | |            (15), (17), (25) are inconsistent by sub-proof #634.
% 241.88/48.38  | | | 
% 241.88/48.38  | | Case 2:
% 241.88/48.38  | | | 
% 241.88/48.38  | | |   (26)  all_58_10 = e1 & op(e2, e0) = e1
% 241.88/48.38  | | | 
% 241.88/48.38  | | | ALPHA: (26) implies:
% 241.88/48.38  | | |   (27)  all_58_10 = e1
% 241.88/48.38  | | | 
% 241.88/48.38  | | | COMBINE_EQS: (9), (27) imply:
% 241.88/48.38  | | |   (28)  e2 = e1
% 241.88/48.38  | | | 
% 241.88/48.38  | | | REDUCE: (17), (28) imply:
% 241.88/48.38  | | |   (29)  $false
% 241.88/48.38  | | | 
% 241.88/48.38  | | | CLOSE: (29) is inconsistent.
% 241.88/48.38  | | | 
% 241.88/48.38  | | End of split
% 241.88/48.38  | | 
% 241.88/48.38  | End of split
% 241.88/48.38  | 
% 241.88/48.38  End of proof
% 241.88/48.38  
% 241.88/48.38  Sub-proof #617 shows that the following formulas are inconsistent:
% 241.88/48.38  ----------------------------------------------------------------
% 241.88/48.38    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.38         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.38    (2)   ~ (e3 = e0)
% 241.88/48.38    (3)   ~ (e2 = e0)
% 241.88/48.38    (4)  op(e1, e2) = all_52_6
% 241.88/48.38    (5)  all_58_11 = e1
% 241.88/48.38    (6)   ~ (all_52_7 = e3)
% 241.88/48.38    (7)   ~ (e3 = e1)
% 241.88/48.38    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.38         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.38    (9)  op(e3, e3) = e1
% 241.88/48.38    (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.38          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.38    (11)   ~ (e3 = e2)
% 241.88/48.38    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.38          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.38    (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.88/48.38          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.88/48.38    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.88/48.38          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.38    (15)   ~ (all_52_6 = e3)
% 241.88/48.38    (16)  op(e0, e2) = all_52_7
% 241.88/48.38    (17)   ~ (all_52_4 = e3)
% 241.88/48.38    (18)  op(e3, e2) = all_52_4
% 241.88/48.38    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.38    (20)  op(e1, e1) = e0
% 241.88/48.38    (21)   ~ (e1 = e0)
% 241.88/48.38    (22)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 241.88/48.38    (23)  all_58_4 = e3
% 241.88/48.38    (24)   ~ (e2 = e1)
% 241.88/48.38  
% 241.88/48.38  Begin of proof
% 241.88/48.38  | 
% 241.88/48.38  | BETA: splitting (22) gives:
% 241.88/48.38  | 
% 241.88/48.38  | Case 1:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (25)  all_58_12 = e3 & op(e0, e3) = e3
% 241.88/48.38  | | 
% 241.88/48.38  | | ALPHA: (25) implies:
% 241.88/48.38  | |   (26)  all_58_12 = e3
% 241.88/48.38  | | 
% 241.88/48.38  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 241.88/48.38  | |            (14), (15), (17), (18), (19), (20), (21), (23), (24), (26) are
% 241.88/48.38  | |            inconsistent by sub-proof #618.
% 241.88/48.38  | | 
% 241.88/48.38  | Case 2:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (27)  all_58_13 = e3 & op(e0, e2) = e3
% 241.88/48.38  | | 
% 241.88/48.38  | | REF_CLOSE: (6), (16), (19), (27) are inconsistent by sub-proof #1919.
% 241.88/48.38  | | 
% 241.88/48.38  | End of split
% 241.88/48.38  | 
% 241.88/48.38  End of proof
% 241.88/48.38  
% 241.88/48.38  Sub-proof #618 shows that the following formulas are inconsistent:
% 241.88/48.38  ----------------------------------------------------------------
% 241.88/48.38    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.38         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.38    (2)   ~ (e3 = e0)
% 241.88/48.38    (3)   ~ (e2 = e0)
% 241.88/48.38    (4)  op(e1, e2) = all_52_6
% 241.88/48.38    (5)  all_58_11 = e1
% 241.88/48.38    (6)   ~ (e3 = e1)
% 241.88/48.38    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.38         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.38    (8)  op(e3, e3) = e1
% 241.88/48.38    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.38         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.38    (10)   ~ (e3 = e2)
% 241.88/48.38    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.38          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.38    (12)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.88/48.38          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.88/48.38    (13)  all_58_12 = e3
% 241.88/48.38    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.88/48.38          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.38    (15)   ~ (all_52_6 = e3)
% 241.88/48.38    (16)   ~ (all_52_4 = e3)
% 241.88/48.38    (17)  op(e3, e2) = all_52_4
% 241.88/48.38    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.38    (19)  op(e1, e1) = e0
% 241.88/48.38    (20)   ~ (e1 = e0)
% 241.88/48.38    (21)  all_58_4 = e3
% 241.88/48.38    (22)   ~ (e2 = e1)
% 241.88/48.38  
% 241.88/48.38  Begin of proof
% 241.88/48.38  | 
% 241.88/48.38  | BETA: splitting (12) gives:
% 241.88/48.38  | 
% 241.88/48.38  | Case 1:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (23)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 241.88/48.38  | |           e3)
% 241.88/48.38  | | 
% 241.88/48.38  | | REF_CLOSE: (2), (3), (4), (8), (9), (10), (11), (13), (15), (18), (20),
% 241.88/48.38  | |            (22), (23) are inconsistent by sub-proof #1136.
% 241.88/48.38  | | 
% 241.88/48.38  | Case 2:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (24)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 241.88/48.38  | |           e3)
% 241.88/48.38  | | 
% 241.88/48.38  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (14), (16), (17), (18),
% 241.88/48.38  | |            (19), (20), (21), (22), (24) are inconsistent by sub-proof #619.
% 241.88/48.38  | | 
% 241.88/48.38  | End of split
% 241.88/48.38  | 
% 241.88/48.38  End of proof
% 241.88/48.38  
% 241.88/48.38  Sub-proof #619 shows that the following formulas are inconsistent:
% 241.88/48.38  ----------------------------------------------------------------
% 241.88/48.38    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.38         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.38    (2)   ~ (e3 = e0)
% 241.88/48.38    (3)   ~ (e2 = e0)
% 241.88/48.38    (4)  all_58_11 = e1
% 241.88/48.38    (5)   ~ (e3 = e1)
% 241.88/48.38    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.38         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.38    (7)  op(e3, e3) = e1
% 241.88/48.38    (8)   ~ (e3 = e2)
% 241.88/48.38    (9)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.88/48.38    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.88/48.38          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.38    (11)   ~ (all_52_4 = e3)
% 241.88/48.38    (12)  op(e3, e2) = all_52_4
% 241.88/48.38    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.38    (14)  op(e1, e1) = e0
% 241.88/48.38    (15)   ~ (e1 = e0)
% 241.88/48.38    (16)  all_58_4 = e3
% 241.88/48.38    (17)   ~ (e2 = e1)
% 241.88/48.38  
% 241.88/48.38  Begin of proof
% 241.88/48.38  | 
% 241.88/48.38  | BETA: splitting (9) gives:
% 241.88/48.38  | 
% 241.88/48.38  | Case 1:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (18)  all_58_8 = e3 & op(e1, e1) = e3
% 241.88/48.38  | | 
% 241.88/48.38  | | REF_CLOSE: (2), (13), (14), (18) are inconsistent by sub-proof #2018.
% 241.88/48.38  | | 
% 241.88/48.38  | Case 2:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (19)  all_58_11 = e3 & op(e1, e0) = e3
% 241.88/48.38  | | 
% 241.88/48.38  | | ALPHA: (19) implies:
% 241.88/48.38  | |   (20)  all_58_11 = e3
% 241.88/48.38  | | 
% 241.88/48.38  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 241.88/48.38  | |            (15), (16), (17), (20) are inconsistent by sub-proof #667.
% 241.88/48.38  | | 
% 241.88/48.38  | End of split
% 241.88/48.38  | 
% 241.88/48.38  End of proof
% 241.88/48.38  
% 241.88/48.38  Sub-proof #620 shows that the following formulas are inconsistent:
% 241.88/48.38  ----------------------------------------------------------------
% 241.88/48.38    (1)   ~ (e3 = e0)
% 241.88/48.38    (2)  all_58_6 = e3
% 241.88/48.38    (3)   ~ (e2 = e0)
% 241.88/48.38    (4)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 241.88/48.38    (5)   ~ (e3 = e1)
% 241.88/48.38    (6)  all_58_3 = e3
% 241.88/48.38    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.38         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.38    (8)  op(e3, e3) = e1
% 241.88/48.38    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.38         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.38    (10)   ~ (e3 = e2)
% 241.88/48.38    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.38          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.38    (12)  op(e2, e3) = all_52_1
% 241.88/48.38    (13)  op(e3, e2) = all_52_4
% 241.88/48.38    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.38    (15)   ~ (all_52_4 = e1)
% 241.88/48.38    (16)   ~ (e1 = e0)
% 241.88/48.38    (17)   ~ (all_52_1 = e3)
% 241.88/48.38    (18)   ~ (e2 = e1)
% 241.88/48.38  
% 241.88/48.38  Begin of proof
% 241.88/48.38  | 
% 241.88/48.38  | BETA: splitting (4) gives:
% 241.88/48.38  | 
% 241.88/48.38  | Case 1:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (19)  all_58_1 = e1 & op(e3, e2) = e1
% 241.88/48.38  | | 
% 241.88/48.38  | | ALPHA: (19) implies:
% 241.88/48.38  | |   (20)  op(e3, e2) = e1
% 241.88/48.38  | | 
% 241.88/48.38  | | REF_CLOSE: (13), (14), (15), (20) are inconsistent by sub-proof #2228.
% 241.88/48.38  | | 
% 241.88/48.38  | Case 2:
% 241.88/48.38  | | 
% 241.88/48.38  | |   (21)  all_58_3 = e1 & op(e2, e2) = e1
% 241.88/48.38  | | 
% 241.88/48.39  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 241.88/48.39  | |            (16), (17), (18), (21) are inconsistent by sub-proof #637.
% 241.88/48.39  | | 
% 241.88/48.39  | End of split
% 241.88/48.39  | 
% 241.88/48.39  End of proof
% 241.88/48.39  
% 241.88/48.39  Sub-proof #621 shows that the following formulas are inconsistent:
% 241.88/48.39  ----------------------------------------------------------------
% 241.88/48.39    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 241.88/48.39    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.39         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.39    (3)   ~ (e3 = e0)
% 241.88/48.39    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.88/48.39         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.88/48.39    (5)  all_58_6 = e3
% 241.88/48.39    (6)   ~ (e2 = e0)
% 241.88/48.39    (7)  op(e1, e2) = all_52_6
% 241.88/48.39    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.39         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.39    (9)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.88/48.39         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.88/48.39    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.39          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.88/48.39    (11)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.88/48.39          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.88/48.39    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.39          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.39    (13)   ~ (e3 = e1)
% 241.88/48.39    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.88/48.39          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.88/48.39    (15)  all_58_3 = e3
% 241.88/48.39    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.39          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.39    (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.39          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.39    (18)  op(e3, e3) = e1
% 241.88/48.39    (19)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.39              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.88/48.39                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.88/48.39                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.88/48.39    (20)  op(e2, e1) = all_52_9
% 241.88/48.39    (21)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.39          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.39    (22)   ~ (e3 = e2)
% 241.88/48.39    (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.88/48.39          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.88/48.39    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.39          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.39    (25)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.88/48.39          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.88/48.39    (26)  op(e2, e3) = all_52_1
% 241.88/48.39    (27)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.88/48.39          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.39    (28)   ~ (all_52_6 = e3)
% 241.88/48.39    (29)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.88/48.39          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.88/48.39    (30)   ~ (all_52_4 = e3)
% 241.88/48.39    (31)  op(e3, e2) = all_52_4
% 241.88/48.39    (32)   ~ (all_52_9 = e3)
% 241.88/48.39    (33)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.88/48.39          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.88/48.39    (34)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.88/48.39          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.88/48.39    (35)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.39          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.39    (36)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.39    (37)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.88/48.39          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.88/48.39    (38)  op(e1, e1) = e0
% 241.88/48.39    (39)   ~ (e1 = e0)
% 241.88/48.39    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.88/48.39          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.88/48.39    (41)  op(e2, e0) = all_52_13
% 241.88/48.39    (42)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.88/48.39          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.88/48.39            e1)
% 241.88/48.39    (43)   ~ (all_52_1 = e3)
% 241.88/48.39    (44)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.39          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.88/48.39            e2)
% 241.88/48.39    (45)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.39          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.39    (46)  all_58_4 = e0
% 241.88/48.39    (47)   ~ (e2 = e1)
% 241.88/48.39    (48)   ~ (all_52_1 = e1)
% 241.88/48.39  
% 241.88/48.39  Begin of proof
% 241.88/48.39  | 
% 241.88/48.39  | BETA: splitting (1) gives:
% 241.88/48.39  | 
% 241.88/48.39  | Case 1:
% 241.88/48.39  | | 
% 241.88/48.39  | |   (49)  all_58_4 = e3 & op(e3, e1) = e3
% 241.88/48.39  | | 
% 241.88/48.39  | | ALPHA: (49) implies:
% 241.88/48.39  | |   (50)  all_58_4 = e3
% 241.88/48.39  | | 
% 241.88/48.39  | | COMBINE_EQS: (46), (50) imply:
% 241.88/48.39  | |   (51)  e3 = e0
% 241.88/48.39  | | 
% 241.88/48.39  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.88/48.39  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 241.88/48.39  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 241.88/48.39  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (47),
% 241.88/48.39  | |            (48), (51) are inconsistent by sub-proof #642.
% 241.88/48.39  | | 
% 241.88/48.39  | Case 2:
% 241.88/48.39  | | 
% 241.88/48.39  | |   (52)  all_58_5 = e3 & op(e2, e1) = e3
% 241.88/48.39  | | 
% 241.88/48.39  | | REF_CLOSE: (20), (32), (36), (52) are inconsistent by sub-proof #1822.
% 241.88/48.39  | | 
% 241.88/48.39  | End of split
% 241.88/48.39  | 
% 241.88/48.39  End of proof
% 241.88/48.39  
% 241.88/48.39  Sub-proof #622 shows that the following formulas are inconsistent:
% 241.88/48.39  ----------------------------------------------------------------
% 241.88/48.39    (1)   ~ (e3 = e0)
% 241.88/48.39    (2)  all_58_6 = e3
% 241.88/48.39    (3)   ~ (e2 = e0)
% 241.88/48.39    (4)  all_58_11 = e1
% 241.88/48.39    (5)  all_58_8 = e0
% 241.88/48.39    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.39         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.39    (7)   ~ (e3 = e1)
% 241.88/48.39    (8)  all_58_2 = e2
% 241.88/48.39    (9)  all_58_3 = e3
% 241.88/48.39    (10)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.39          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.39    (11)  op(e3, e3) = e1
% 241.88/48.39    (12)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.39          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.39    (13)   ~ (e3 = e2)
% 241.88/48.39    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.39          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.39    (15)  all_58_10 = e0
% 241.88/48.39    (16)  all_58_12 = e0
% 241.88/48.39    (17)  op(e2, e3) = all_52_1
% 241.88/48.39    (18)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.88/48.39    (19)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.39          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.39    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.39    (21)   ~ (e1 = e0)
% 241.88/48.39    (22)   ~ (all_52_1 = e3)
% 241.88/48.39    (23)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.39          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.39    (24)   ~ (e2 = e1)
% 241.88/48.39    (25)   ~ (all_52_1 = e1)
% 241.88/48.39  
% 241.88/48.39  Begin of proof
% 241.88/48.39  | 
% 241.88/48.39  | BETA: splitting (18) gives:
% 241.88/48.39  | 
% 241.88/48.39  | Case 1:
% 241.88/48.39  | | 
% 241.88/48.39  | |   (26)  all_58_8 = e2 & op(e1, e1) = e2
% 241.88/48.39  | | 
% 241.88/48.39  | | ALPHA: (26) implies:
% 241.88/48.39  | |   (27)  all_58_8 = e2
% 241.88/48.39  | | 
% 241.88/48.39  | | COMBINE_EQS: (5), (27) imply:
% 241.88/48.39  | |   (28)  e2 = e0
% 241.88/48.39  | | 
% 241.88/48.39  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 241.88/48.39  | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (28)
% 241.88/48.39  | |            are inconsistent by sub-proof #632.
% 241.88/48.39  | | 
% 241.88/48.39  | Case 2:
% 241.88/48.39  | | 
% 241.88/48.39  | |   (29)  all_58_11 = e2 & op(e1, e0) = e2
% 241.88/48.39  | | 
% 241.88/48.39  | | REF_CLOSE: (4), (24), (29) are inconsistent by sub-proof #1554.
% 241.88/48.39  | | 
% 241.88/48.39  | End of split
% 241.88/48.39  | 
% 241.88/48.39  End of proof
% 241.88/48.39  
% 241.88/48.39  Sub-proof #623 shows that the following formulas are inconsistent:
% 241.88/48.39  ----------------------------------------------------------------
% 241.88/48.39    (1)   ~ (e3 = e0)
% 241.88/48.39    (2)  all_58_5 = e2 & op(e2, e1) = e2
% 241.88/48.39    (3)   ~ (e2 = e0)
% 241.88/48.39    (4)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.39         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.39    (5)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.88/48.39         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.88/48.39    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.39         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.88/48.39    (7)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.39         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.39    (8)   ~ (e3 = e1)
% 241.88/48.39    (9)  all_58_7 = e2
% 241.88/48.39    (10)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.88/48.39          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.88/48.39    (11)  all_58_3 = e3
% 241.88/48.39    (12)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.39          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.39    (13)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.39          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.39    (14)  op(e3, e3) = e1
% 241.88/48.39    (15)  op(e2, e1) = all_52_9
% 241.88/48.39    (16)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.39          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.39    (17)   ~ (e3 = e2)
% 241.88/48.39    (18)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.88/48.39          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.88/48.39    (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.39          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.39    (20)  all_58_10 = e0
% 241.88/48.39    (21)  op(e2, e3) = all_52_1
% 241.88/48.39    (22)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.88/48.39          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.88/48.39    (23)   ~ (all_52_4 = e3)
% 241.88/48.39    (24)  op(e3, e2) = all_52_4
% 241.88/48.39    (25)  all_58_5 = e1
% 241.88/48.39    (26)   ~ (all_52_9 = e3)
% 241.88/48.39    (27)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.88/48.39          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.88/48.39    (28)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.39          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.39    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.39    (30)  op(e0, e0) = e0
% 241.88/48.39    (31)   ~ (e1 = e0)
% 241.88/48.39    (32)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.88/48.39          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.88/48.39    (33)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.88/48.39          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.88/48.39            e1)
% 241.88/48.39    (34)   ~ (all_52_1 = e3)
% 241.88/48.39    (35)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.39          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.39    (36)   ~ (e2 = e1)
% 241.88/48.39    (37)   ~ (all_52_1 = e1)
% 241.88/48.39  
% 241.88/48.39  Begin of proof
% 241.88/48.39  | 
% 241.88/48.39  | ALPHA: (2) implies:
% 241.88/48.39  |   (38)  all_58_5 = e2
% 241.88/48.39  | 
% 241.88/48.39  | COMBINE_EQS: (25), (38) imply:
% 241.88/48.39  |   (39)  e2 = e1
% 241.88/48.39  | 
% 241.88/48.39  | COMBINE_EQS: (9), (39) imply:
% 241.88/48.39  |   (40)  all_58_7 = e1
% 241.88/48.39  | 
% 241.88/48.39  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 241.88/48.39  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (26),
% 241.88/48.39  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 241.88/48.39  |            (40) are inconsistent by sub-proof #638.
% 241.88/48.39  | 
% 241.88/48.39  End of proof
% 241.88/48.39  
% 241.88/48.39  Sub-proof #624 shows that the following formulas are inconsistent:
% 241.88/48.39  ----------------------------------------------------------------
% 241.88/48.39    (1)   ~ (e3 = e0)
% 241.88/48.39    (2)   ~ (e2 = e0)
% 241.88/48.39    (3)  op(e1, e2) = all_52_6
% 241.88/48.40    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.88/48.40         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.88/48.40    (5)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.88/48.40           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.88/48.40             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.88/48.40           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.88/48.40             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.88/48.40           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.88/48.40           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.88/48.40           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.88/48.40           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.88/48.40           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.88/48.40           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.88/48.40             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.88/48.40           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.88/48.40           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 241.88/48.40           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.88/48.40           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.88/48.40           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.88/48.40           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.88/48.40             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.88/48.40           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.88/48.40           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 241.88/48.40           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.88/48.40           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.88/48.40           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.88/48.40           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.88/48.40             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.88/48.40           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.88/48.40           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.88/48.40    (6)  all_58_11 = e1
% 241.88/48.40    (7)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.40         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.40    (8)   ~ (e3 = e1)
% 241.88/48.40    (9)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.88/48.40         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.88/48.40    (10)  all_58_2 = e2
% 241.88/48.40    (11)  all_58_3 = e3
% 241.88/48.40    (12)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.40          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.40    (13)  all_58_9 = e3 & op(e3, e0) = e3
% 241.88/48.40    (14)  op(e3, e3) = e1
% 241.88/48.40    (15)  all_58_15 = e2
% 241.88/48.40    (16)   ~ (e3 = e2)
% 241.88/48.40    (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.88/48.40          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.88/48.40    (18)  all_56_31 = e0
% 241.88/48.40    (19)  op(e2, e3) = all_52_1
% 241.88/48.40    (20)  op(e1, e2) = e2
% 241.88/48.40    (21)   ~ (all_52_4 = e3)
% 241.88/48.40    (22)  op(e3, e2) = all_52_4
% 241.88/48.40    (23)  all_58_5 = e1
% 241.88/48.40    (24)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.88/48.40          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.88/48.40    (25)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.40          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.40    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.40    (27)  op(e0, e0) = e0
% 241.88/48.40    (28)  all_58_14 = e3
% 241.88/48.40    (29)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.88/48.40          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.88/48.40    (30)  all_56_11 = e3
% 241.88/48.40    (31)   ~ (e1 = e0)
% 241.88/48.40    (32)  op(e0, e0) = e2
% 241.88/48.40    (33)   ~ (all_52_1 = e3)
% 241.88/48.40    (34)  all_56_1 = e1
% 241.88/48.40    (35)   ~ (e2 = e1)
% 241.88/48.40  
% 241.88/48.40  Begin of proof
% 241.88/48.40  | 
% 241.88/48.40  | ALPHA: (13) implies:
% 241.88/48.40  |   (36)  all_58_9 = e3
% 241.88/48.40  | 
% 241.88/48.40  | BETA: splitting (5) gives:
% 241.88/48.40  | 
% 241.88/48.40  | Case 1:
% 241.88/48.40  | | 
% 241.88/48.40  | |   (37)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 241.88/48.40  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 241.88/48.40  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 241.88/48.40  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.88/48.40  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 241.88/48.40  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 241.88/48.40  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 241.88/48.40  | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 241.88/48.40  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.88/48.40  | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 241.88/48.40  | |           = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &
% 241.88/48.40  | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 241.88/48.40  | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 241.88/48.40  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.88/48.40  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 241.88/48.40  | | 
% 241.88/48.40  | | REF_CLOSE: (18), (19), (26), (30), (33), (34), (37) are inconsistent by
% 241.88/48.40  | |            sub-proof #744.
% 241.88/48.40  | | 
% 241.88/48.40  | Case 2:
% 241.88/48.40  | | 
% 241.88/48.40  | |   (38)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 241.88/48.40  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.88/48.40  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.88/48.40  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.88/48.40  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 241.88/48.40  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.88/48.40  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.88/48.40  | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 241.88/48.40  | |           e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.88/48.40  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 241.88/48.40  | |         (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.88/48.40  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.88/48.40  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 241.88/48.40  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.88/48.40  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.88/48.40  | | 
% 241.88/48.40  | | BETA: splitting (38) gives:
% 241.88/48.40  | | 
% 241.88/48.40  | | Case 1:
% 241.88/48.40  | | | 
% 241.88/48.40  | | |   (39)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 241.88/48.40  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.88/48.40  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 241.88/48.40  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 241.88/48.40  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 241.88/48.40  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.88/48.40  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.88/48.40  | | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.88/48.40  | | | 
% 241.88/48.40  | | | BETA: splitting (39) gives:
% 241.88/48.40  | | | 
% 241.88/48.40  | | | Case 1:
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | |   (40)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 241.88/48.40  | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.88/48.40  | | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | ALPHA: (40) implies:
% 241.88/48.40  | | | |   (41)   ~ (all_56_1 = e1)
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | REDUCE: (34), (41) imply:
% 241.88/48.40  | | | |   (42)  $false
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | CLOSE: (42) is inconsistent.
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | Case 2:
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | |   (43)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.88/48.40  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.88/48.40  | | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 241.88/48.40  | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 241.88/48.40  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 &
% 241.88/48.40  | | | |           op(e0, e2) = e2)
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | BETA: splitting (43) gives:
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | Case 1:
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | |   (44)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.88/48.40  | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.88/48.40  | | | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | | ALPHA: (44) implies:
% 241.88/48.40  | | | | |   (45)  op(e1, e2) = e1
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | | REF_CLOSE: (3), (20), (26), (27), (31), (32), (45) are inconsistent by
% 241.88/48.40  | | | | |            sub-proof #627.
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | Case 2:
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | |   (46)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.88/48.40  | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.88/48.40  | | | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | | ALPHA: (46) implies:
% 241.88/48.40  | | | | |   (47)  op(e2, e0) = e2
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | | REF_CLOSE: (1), (2), (10), (11), (23), (25), (26), (31), (47) are
% 241.88/48.40  | | | | |            inconsistent by sub-proof #840.
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | End of split
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | End of split
% 241.88/48.40  | | | 
% 241.88/48.40  | | Case 2:
% 241.88/48.40  | | | 
% 241.88/48.40  | | |   (48)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 241.88/48.40  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.88/48.40  | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29
% 241.88/48.40  | | |           = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 241.88/48.40  | | |             = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 241.88/48.40  | | |           e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 241.88/48.40  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.88/48.40  | | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.88/48.40  | | | 
% 241.88/48.40  | | | BETA: splitting (48) gives:
% 241.88/48.40  | | | 
% 241.88/48.40  | | | Case 1:
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | |   (49)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 241.88/48.40  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.88/48.40  | | | |         op(e2, e0) = e0 & op(e0, e2) = e0
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | ALPHA: (49) implies:
% 241.88/48.40  | | | |   (50)   ~ (all_56_31 = e2)
% 241.88/48.40  | | | |   (51)   ~ (all_56_11 = e2)
% 241.88/48.40  | | | |   (52)   ~ (all_56_1 = e2)
% 241.88/48.40  | | | |   (53)  op(e2, e0) = e0
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | REDUCE: (34), (52) imply:
% 241.88/48.40  | | | |   (54)   ~ (e2 = e1)
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | REDUCE: (18), (50) imply:
% 241.88/48.40  | | | |   (55)   ~ (e2 = e0)
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | GROUND_INST: instantiating (26) with e0, e2, e0, e0, simplifying with
% 241.88/48.40  | | | |              (27), (32) gives:
% 241.88/48.40  | | | |   (56)  e2 = e0
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | COMBINE_EQS: (10), (56) imply:
% 241.88/48.40  | | | |   (57)  all_58_2 = e0
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | REF_CLOSE: (1), (2), (6), (7), (8), (11), (15), (16), (23), (24), (25),
% 241.88/48.40  | | | |            (26), (29), (31), (35), (53), (57) are inconsistent by
% 241.88/48.40  | | | |            sub-proof #626.
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | Case 2:
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | |   (58)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.88/48.40  | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.88/48.40  | | | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 241.88/48.40  | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.88/48.40  | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 &
% 241.88/48.40  | | | |           op(e0, e1) = e0)
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | BETA: splitting (58) gives:
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | | Case 1:
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | |   (59)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.88/48.40  | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.88/48.40  | | | | |         op(e1, e0) = e1 & op(e0, e1) = e1
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | | ALPHA: (59) implies:
% 241.88/48.40  | | | | |   (60)   ~ (all_56_31 = e0)
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | | REDUCE: (18), (60) imply:
% 241.88/48.40  | | | | |   (61)  $false
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | | CLOSE: (61) is inconsistent.
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | Case 2:
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | |   (62)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 241.88/48.40  | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.88/48.40  | | | | |         op(e1, e0) = e0 & op(e0, e1) = e0
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | | ALPHA: (62) implies:
% 241.88/48.40  | | | | |   (63)  op(e1, e0) = e0
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | | BETA: splitting (4) gives:
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | | Case 1:
% 241.88/48.40  | | | | | | 
% 241.88/48.40  | | | | | |   (64)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 241.88/48.40  | | | | | |             e0) = e1)
% 241.88/48.40  | | | | | | 
% 241.88/48.40  | | | | | | BETA: splitting (64) gives:
% 241.88/48.40  | | | | | | 
% 241.88/48.40  | | | | | | Case 1:
% 241.88/48.40  | | | | | | | 
% 241.88/48.40  | | | | | | |   (65)  all_58_9 = e1 & op(e3, e0) = e1
% 241.88/48.40  | | | | | | | 
% 241.88/48.40  | | | | | | | ALPHA: (65) implies:
% 241.88/48.40  | | | | | | |   (66)  all_58_9 = e1
% 241.88/48.40  | | | | | | | 
% 241.88/48.40  | | | | | | | COMBINE_EQS: (36), (66) imply:
% 241.88/48.40  | | | | | | |   (67)  e3 = e1
% 241.88/48.40  | | | | | | | 
% 241.88/48.40  | | | | | | | SIMP: (67) implies:
% 241.88/48.40  | | | | | | |   (68)  e3 = e1
% 241.88/48.40  | | | | | | | 
% 241.88/48.40  | | | | | | | COMBINE_EQS: (28), (68) imply:
% 241.88/48.40  | | | | | | |   (69)  all_58_14 = e1
% 241.88/48.40  | | | | | | | 
% 241.88/48.40  | | | | | | | REF_CLOSE: (1), (2), (8), (9), (12), (14), (16), (17), (21), (22),
% 241.88/48.40  | | | | | | |            (23), (26), (31), (35), (66), (69) are inconsistent by
% 241.88/48.40  | | | | | | |            sub-proof #676.
% 241.88/48.40  | | | | | | | 
% 241.88/48.40  | | | | | | Case 2:
% 241.88/48.40  | | | | | | | 
% 241.88/48.40  | | | | | | |   (70)  all_58_10 = e1 & op(e2, e0) = e1
% 241.88/48.40  | | | | | | | 
% 241.88/48.40  | | | | | | | ALPHA: (70) implies:
% 241.88/48.40  | | | | | | |   (71)  all_58_10 = e1
% 241.88/48.40  | | | | | | | 
% 241.88/48.40  | | | | | | | REF_CLOSE: (1), (2), (10), (11), (23), (25), (31), (71) are
% 241.88/48.40  | | | | | | |            inconsistent by sub-proof #994.
% 241.88/48.40  | | | | | | | 
% 241.88/48.40  | | | | | | End of split
% 241.88/48.40  | | | | | | 
% 241.88/48.40  | | | | | Case 2:
% 241.88/48.40  | | | | | | 
% 241.88/48.40  | | | | | |   (72)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 241.88/48.40  | | | | | |           op(e0, e0) = e1)
% 241.88/48.40  | | | | | | 
% 241.88/48.40  | | | | | | REF_CLOSE: (26), (27), (31), (63), (72) are inconsistent by
% 241.88/48.40  | | | | | |            sub-proof #625.
% 241.88/48.40  | | | | | | 
% 241.88/48.40  | | | | | End of split
% 241.88/48.40  | | | | | 
% 241.88/48.40  | | | | End of split
% 241.88/48.40  | | | | 
% 241.88/48.40  | | | End of split
% 241.88/48.40  | | | 
% 241.88/48.40  | | End of split
% 241.88/48.40  | | 
% 241.88/48.40  | End of split
% 241.88/48.40  | 
% 241.88/48.40  End of proof
% 241.88/48.40  
% 241.88/48.40  Sub-proof #625 shows that the following formulas are inconsistent:
% 241.88/48.40  ----------------------------------------------------------------
% 241.88/48.40    (1)  op(e1, e0) = e0
% 241.88/48.40    (2)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.88/48.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.40    (4)  op(e0, e0) = e0
% 241.88/48.40    (5)   ~ (e1 = e0)
% 241.88/48.40  
% 241.88/48.40  Begin of proof
% 241.88/48.40  | 
% 241.88/48.40  | BETA: splitting (2) gives:
% 241.88/48.40  | 
% 241.88/48.40  | Case 1:
% 241.88/48.40  | | 
% 241.88/48.40  | |   (6)  all_58_11 = e1 & op(e1, e0) = e1
% 241.88/48.40  | | 
% 241.88/48.40  | | ALPHA: (6) implies:
% 241.88/48.40  | |   (7)  op(e1, e0) = e1
% 241.88/48.40  | | 
% 241.88/48.40  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #2284.
% 241.88/48.40  | | 
% 241.88/48.40  | Case 2:
% 241.88/48.40  | | 
% 241.88/48.40  | |   (8)  all_58_15 = e1 & op(e0, e0) = e1
% 241.88/48.40  | | 
% 241.88/48.40  | | ALPHA: (8) implies:
% 241.88/48.40  | |   (9)  op(e0, e0) = e1
% 241.88/48.40  | | 
% 241.88/48.40  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #2274.
% 241.88/48.40  | | 
% 241.88/48.40  | End of split
% 241.88/48.40  | 
% 241.88/48.40  End of proof
% 241.88/48.40  
% 241.88/48.40  Sub-proof #626 shows that the following formulas are inconsistent:
% 241.88/48.40  ----------------------------------------------------------------
% 241.88/48.40    (1)   ~ (e3 = e0)
% 241.88/48.40    (2)   ~ (e2 = e0)
% 241.88/48.40    (3)  all_58_11 = e1
% 241.88/48.40    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.40         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.40    (5)   ~ (e3 = e1)
% 241.88/48.40    (6)  all_58_3 = e3
% 241.88/48.40    (7)  all_58_15 = e2
% 241.88/48.40    (8)   ~ (e3 = e2)
% 241.88/48.40    (9)  op(e2, e0) = e0
% 241.88/48.40    (10)  all_58_2 = e0
% 241.88/48.40    (11)  all_58_5 = e1
% 241.88/48.40    (12)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.88/48.40          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.88/48.40    (13)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.40          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.41    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.41    (15)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.88/48.41          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.88/48.41    (16)   ~ (e1 = e0)
% 241.88/48.41    (17)   ~ (e2 = e1)
% 241.88/48.41  
% 241.88/48.41  Begin of proof
% 241.88/48.41  | 
% 241.88/48.41  | BETA: splitting (4) gives:
% 241.88/48.41  | 
% 241.88/48.41  | Case 1:
% 241.88/48.41  | | 
% 241.88/48.41  | |   (18)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 241.88/48.41  | |           e2)
% 241.88/48.41  | | 
% 241.88/48.41  | | BETA: splitting (18) gives:
% 241.88/48.41  | | 
% 241.88/48.41  | | Case 1:
% 241.88/48.41  | | | 
% 241.88/48.41  | | |   (19)  all_58_2 = e2 & op(e2, e3) = e2
% 241.88/48.41  | | | 
% 241.88/48.41  | | | REF_CLOSE: (2), (10), (19) are inconsistent by sub-proof #1575.
% 241.88/48.41  | | | 
% 241.88/48.41  | | Case 2:
% 241.88/48.41  | | | 
% 241.88/48.41  | | |   (20)  all_58_3 = e2 & op(e2, e2) = e2
% 241.88/48.41  | | | 
% 241.88/48.41  | | | REF_CLOSE: (6), (8), (20) are inconsistent by sub-proof #1106.
% 241.88/48.41  | | | 
% 241.88/48.41  | | End of split
% 241.88/48.41  | | 
% 241.88/48.41  | Case 2:
% 241.88/48.41  | | 
% 241.88/48.41  | |   (21)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 241.88/48.41  | |           e2)
% 241.88/48.41  | | 
% 241.88/48.41  | | BETA: splitting (21) gives:
% 241.88/48.41  | | 
% 241.88/48.41  | | Case 1:
% 241.88/48.41  | | | 
% 241.88/48.41  | | |   (22)  all_58_5 = e2 & op(e2, e1) = e2
% 241.88/48.41  | | | 
% 241.88/48.41  | | | ALPHA: (22) implies:
% 241.88/48.41  | | |   (23)  all_58_5 = e2
% 241.88/48.41  | | | 
% 241.88/48.41  | | | COMBINE_EQS: (11), (23) imply:
% 241.88/48.41  | | |   (24)  e2 = e1
% 241.88/48.41  | | | 
% 241.88/48.41  | | | SIMP: (24) implies:
% 241.88/48.41  | | |   (25)  e2 = e1
% 241.88/48.41  | | | 
% 241.88/48.41  | | | COMBINE_EQS: (7), (25) imply:
% 241.88/48.41  | | |   (26)  all_58_15 = e1
% 241.88/48.41  | | | 
% 241.88/48.41  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 241.88/48.41  | | |            (15), (16), (17), (26) are inconsistent by sub-proof #913.
% 241.88/48.41  | | | 
% 241.88/48.41  | | Case 2:
% 241.88/48.41  | | | 
% 241.88/48.41  | | |   (27)  all_58_10 = e2 & op(e2, e0) = e2
% 241.88/48.41  | | | 
% 241.88/48.41  | | | ALPHA: (27) implies:
% 241.88/48.41  | | |   (28)  op(e2, e0) = e2
% 241.88/48.41  | | | 
% 241.88/48.41  | | | REF_CLOSE: (2), (9), (14), (28) are inconsistent by sub-proof #2121.
% 241.88/48.41  | | | 
% 241.88/48.41  | | End of split
% 241.88/48.41  | | 
% 241.88/48.41  | End of split
% 241.88/48.41  | 
% 241.88/48.41  End of proof
% 241.88/48.41  
% 241.88/48.41  Sub-proof #627 shows that the following formulas are inconsistent:
% 241.88/48.41  ----------------------------------------------------------------
% 241.88/48.41    (1)  op(e1, e2) = e1
% 241.88/48.41    (2)  op(e1, e2) = all_52_6
% 241.88/48.41    (3)  op(e1, e2) = e2
% 241.88/48.41    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.41    (5)  op(e0, e0) = e0
% 241.88/48.41    (6)   ~ (e1 = e0)
% 241.88/48.41    (7)  op(e0, e0) = e2
% 241.88/48.41  
% 241.88/48.41  Begin of proof
% 241.88/48.41  | 
% 241.88/48.41  | GROUND_INST: instantiating (4) with e0, e2, e0, e0, simplifying with (5), (7)
% 241.88/48.41  |              gives:
% 241.88/48.41  |   (8)  e2 = e0
% 241.88/48.41  | 
% 241.88/48.41  | GROUND_INST: instantiating (4) with all_52_6, e1, e2, e1, simplifying with
% 241.88/48.41  |              (1), (2) gives:
% 241.88/48.41  |   (9)  all_52_6 = e1
% 241.88/48.41  | 
% 241.88/48.41  | GROUND_INST: instantiating (4) with all_52_6, e2, e2, e1, simplifying with
% 241.88/48.41  |              (2), (3) gives:
% 241.88/48.41  |   (10)  all_52_6 = e2
% 241.88/48.41  | 
% 241.88/48.41  | COMBINE_EQS: (9), (10) imply:
% 241.88/48.41  |   (11)  e2 = e1
% 241.88/48.41  | 
% 241.88/48.41  | SIMP: (11) implies:
% 241.88/48.41  |   (12)  e2 = e1
% 241.88/48.41  | 
% 241.88/48.41  | COMBINE_EQS: (8), (12) imply:
% 241.88/48.41  |   (13)  e1 = e0
% 241.88/48.41  | 
% 241.88/48.41  | REDUCE: (6), (13) imply:
% 241.88/48.41  |   (14)  $false
% 241.88/48.41  | 
% 241.88/48.41  | CLOSE: (14) is inconsistent.
% 241.88/48.41  | 
% 241.88/48.41  End of proof
% 241.88/48.41  
% 241.88/48.41  Sub-proof #628 shows that the following formulas are inconsistent:
% 241.88/48.41  ----------------------------------------------------------------
% 241.88/48.41    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.41         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.41    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.88/48.41         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.88/48.41    (3)   ~ (e3 = e0)
% 241.88/48.41    (4)  all_58_6 = e3
% 241.88/48.41    (5)   ~ (e2 = e0)
% 241.88/48.41    (6)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.88/48.41           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.88/48.41             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.88/48.41           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.88/48.41             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.88/48.41           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.88/48.41           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.88/48.41           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.88/48.41           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.88/48.41           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.88/48.41           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.88/48.41             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.88/48.41           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.88/48.41           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 241.88/48.41           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.88/48.41           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.88/48.41           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.88/48.41           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.88/48.41             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.88/48.41           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.88/48.41           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 241.88/48.41           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.88/48.41           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.88/48.41           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.88/48.41           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.88/48.41             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.88/48.41           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.88/48.41           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.88/48.41    (7)  all_58_1 = e0
% 241.88/48.41    (8)  all_58_14 = e2
% 241.88/48.41    (9)   ~ (all_52_7 = e3)
% 241.88/48.41    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.41          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.41    (11)   ~ (e3 = e1)
% 241.88/48.41    (12)  op(e1, e0) = e1
% 241.88/48.41    (13)  all_58_2 = e2
% 241.88/48.41    (14)  all_58_3 = e3
% 241.88/48.41    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.41          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.41    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.41          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.41    (17)  op(e3, e3) = e1
% 241.88/48.41    (18)  op(e2, e1) = all_52_9
% 241.88/48.41    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.41          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.41    (20)   ~ (e3 = e2)
% 241.88/48.41    (21)  all_56_31 = e0
% 241.88/48.41    (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.41          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.41    (23)  all_58_10 = e0
% 241.88/48.41    (24)  all_58_12 = e0
% 241.88/48.41    (25)  op(e2, e3) = all_52_1
% 241.88/48.41    (26)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.88/48.41          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.88/48.41    (27)  op(e0, e2) = all_52_7
% 241.88/48.41    (28)   ~ (all_52_4 = e3)
% 241.88/48.41    (29)  op(e3, e2) = all_52_4
% 241.88/48.41    (30)  all_58_5 = e1
% 241.88/48.41    (31)   ~ (all_52_9 = e3)
% 241.88/48.41    (32)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.41          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.41    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.41    (34)  op(e0, e0) = e0
% 241.88/48.41    (35)  all_56_11 = e3
% 241.88/48.41    (36)  op(e1, e1) = e0
% 241.88/48.41    (37)   ~ (e1 = e0)
% 241.88/48.41    (38)   ~ (all_52_1 = e3)
% 241.88/48.41    (39)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.41          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.41    (40)  all_56_1 = e1
% 241.88/48.41    (41)   ~ (e2 = e1)
% 241.88/48.41    (42)   ~ (all_52_1 = e1)
% 241.88/48.41  
% 241.88/48.41  Begin of proof
% 241.88/48.41  | 
% 241.88/48.41  | BETA: splitting (2) gives:
% 241.88/48.41  | 
% 241.88/48.41  | Case 1:
% 241.88/48.41  | | 
% 241.88/48.41  | |   (43)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 241.88/48.41  | |           e3)
% 241.88/48.41  | | 
% 241.88/48.41  | | REF_CLOSE: (3), (4), (5), (9), (13), (17), (22), (27), (33), (37), (43) are
% 241.88/48.41  | |            inconsistent by sub-proof #630.
% 241.88/48.41  | | 
% 241.88/48.41  | Case 2:
% 241.88/48.41  | | 
% 241.88/48.41  | |   (44)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 241.88/48.41  | |           e3)
% 241.88/48.41  | | 
% 241.88/48.41  | | BETA: splitting (44) gives:
% 241.88/48.41  | | 
% 241.88/48.41  | | Case 1:
% 241.88/48.41  | | | 
% 241.88/48.41  | | |   (45)  all_58_14 = e3 & op(e0, e1) = e3
% 241.88/48.41  | | | 
% 241.88/48.41  | | | REF_CLOSE: (8), (20), (45) are inconsistent by sub-proof #1747.
% 241.88/48.41  | | | 
% 241.88/48.41  | | Case 2:
% 241.88/48.41  | | | 
% 241.88/48.41  | | |   (46)  all_58_15 = e3 & op(e0, e0) = e3
% 241.88/48.41  | | | 
% 241.88/48.41  | | | ALPHA: (46) implies:
% 241.88/48.41  | | |   (47)  op(e0, e0) = e3
% 241.88/48.41  | | | 
% 241.88/48.41  | | | BETA: splitting (26) gives:
% 241.88/48.41  | | | 
% 241.88/48.41  | | | Case 1:
% 241.88/48.41  | | | | 
% 241.88/48.41  | | | |   (48)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 241.88/48.41  | | | |           = e3)
% 241.88/48.41  | | | | 
% 241.88/48.41  | | | | BETA: splitting (48) gives:
% 241.88/48.41  | | | | 
% 241.88/48.41  | | | | Case 1:
% 241.88/48.41  | | | | | 
% 241.88/48.41  | | | | |   (49)  all_58_4 = e3 & op(e3, e1) = e3
% 241.88/48.41  | | | | | 
% 241.88/48.41  | | | | | ALPHA: (49) implies:
% 241.88/48.41  | | | | |   (50)  all_58_4 = e3
% 241.88/48.41  | | | | | 
% 241.88/48.41  | | | | | BETA: splitting (1) gives:
% 241.88/48.41  | | | | | 
% 241.88/48.41  | | | | | Case 1:
% 241.88/48.41  | | | | | | 
% 241.88/48.41  | | | | | |   (51)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3,
% 241.88/48.41  | | | | | |             e2) = e2)
% 241.88/48.41  | | | | | | 
% 241.88/48.41  | | | | | | BETA: splitting (51) gives:
% 241.88/48.41  | | | | | | 
% 241.88/48.41  | | | | | | Case 1:
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | |   (52)  all_58_0 = e2 & op(e3, e3) = e2
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | | ALPHA: (52) implies:
% 241.88/48.41  | | | | | | |   (53)  op(e3, e3) = e2
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | | REF_CLOSE: (17), (33), (41), (53) are inconsistent by sub-proof
% 241.88/48.41  | | | | | | |            #2267.
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | Case 2:
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | |   (54)  all_58_1 = e2 & op(e3, e2) = e2
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | | ALPHA: (54) implies:
% 241.88/48.41  | | | | | | |   (55)  all_58_1 = e2
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | | COMBINE_EQS: (7), (55) imply:
% 241.88/48.41  | | | | | | |   (56)  e2 = e0
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | | SIMP: (56) implies:
% 241.88/48.41  | | | | | | |   (57)  e2 = e0
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | | REF_CLOSE: (3), (4), (5), (10), (11), (13), (14), (16), (17),
% 241.88/48.41  | | | | | | |            (19), (20), (22), (23), (24), (25), (32), (33), (37),
% 241.88/48.41  | | | | | | |            (38), (39), (41), (42), (57) are inconsistent by
% 241.88/48.41  | | | | | | |            sub-proof #632.
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | End of split
% 241.88/48.41  | | | | | | 
% 241.88/48.41  | | | | | Case 2:
% 241.88/48.41  | | | | | | 
% 241.88/48.41  | | | | | |   (58)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3,
% 241.88/48.41  | | | | | |             e0) = e2)
% 241.88/48.41  | | | | | | 
% 241.88/48.41  | | | | | | BETA: splitting (58) gives:
% 241.88/48.41  | | | | | | 
% 241.88/48.41  | | | | | | Case 1:
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | |   (59)  all_58_4 = e2 & op(e3, e1) = e2
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | | ALPHA: (59) implies:
% 241.88/48.41  | | | | | | |   (60)  all_58_4 = e2
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | | REF_CLOSE: (20), (50), (60) are inconsistent by sub-proof #1902.
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | Case 2:
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | |   (61)  all_58_9 = e2 & op(e3, e0) = e2
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | | ALPHA: (61) implies:
% 241.88/48.41  | | | | | | |   (62)  op(e3, e0) = e2
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | | BETA: splitting (6) gives:
% 241.88/48.41  | | | | | | | 
% 241.88/48.41  | | | | | | | Case 1:
% 241.88/48.41  | | | | | | | | 
% 241.88/48.41  | | | | | | | |   (63)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 241.88/48.41  | | | | | | | |             = e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 241.88/48.41  | | | | | | | |         (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 241.88/48.41  | | | | | | | |             = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 241.88/48.41  | | | | | | | |         (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) & 
% 241.88/48.41  | | | | | | | |           ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 241.88/48.41  | | | | | | | |         | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &
% 241.88/48.41  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1)
% 241.88/48.41  | | | | | | | |         | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &
% 241.88/48.41  | | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3)
% 241.88/48.41  | | | | | | | |         | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &
% 241.88/48.41  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 241.88/48.41  | | | | | | | | 
% 241.88/48.41  | | | | | | | | BETA: splitting (63) gives:
% 241.88/48.41  | | | | | | | | 
% 241.88/48.41  | | | | | | | | Case 1:
% 241.88/48.41  | | | | | | | | | 
% 241.88/48.41  | | | | | | | | |   (64)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 241.88/48.41  | | | | | | | | |           ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.88/48.41  | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 241.88/48.41  | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 241.88/48.41  | | | | | | | | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 241.88/48.41  | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3)
% 241.88/48.41  | | | | | | | | |           = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.88/48.41  | | | | | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.88/48.41  | | | | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 241.88/48.41  | | | | | | | | |           = e3 & op(e1, e3) = e3)
% 241.88/48.41  | | | | | | | | | 
% 241.88/48.41  | | | | | | | | | REF_CLOSE: (25), (33), (35), (38), (40), (64) are inconsistent
% 241.88/48.41  | | | | | | | | |            by sub-proof #745.
% 241.88/48.41  | | | | | | | | | 
% 241.88/48.41  | | | | | | | | Case 2:
% 241.88/48.41  | | | | | | | | | 
% 241.88/48.41  | | | | | | | | |   (65)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &
% 241.88/48.41  | | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.88/48.41  | | | | | | | | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.88/48.41  | | | | | | | | |           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1
% 241.88/48.41  | | | | | | | | |             = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.88/48.41  | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 241.88/48.41  | | | | | | | | |           = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.88/48.41  | | | | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.88/48.41  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 241.88/48.41  | | | | | | | | |           = e0 & op(e0, e3) = e0)
% 241.88/48.41  | | | | | | | | | 
% 241.88/48.41  | | | | | | | | | REF_CLOSE: (20), (33), (35), (62), (65) are inconsistent by
% 241.88/48.41  | | | | | | | | |            sub-proof #727.
% 241.88/48.41  | | | | | | | | | 
% 241.88/48.41  | | | | | | | | End of split
% 241.88/48.41  | | | | | | | | 
% 241.88/48.41  | | | | | | | Case 2:
% 241.88/48.41  | | | | | | | | 
% 241.88/48.41  | | | | | | | |   (66)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) & 
% 241.88/48.41  | | | | | | | |           ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2)
% 241.88/48.41  | | | | | | | |         | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2)
% 241.88/48.41  | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1)
% 241.88/48.41  | | | | | | | |         | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0)
% 241.88/48.41  | | | | | | | |           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.88/48.41  | | | | | | | |         | (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2)
% 241.88/48.41  | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0)
% 241.88/48.41  | | | | | | | |         | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0)
% 241.88/48.41  | | | | | | | |           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1)
% 241.88/48.41  | | | | | | | |         | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1)
% 241.88/48.41  | | | | | | | |           &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.88/48.41  | | | | | | | |           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.88/48.41  | | | | | | | | 
% 241.88/48.41  | | | | | | | | BETA: splitting (66) gives:
% 241.88/48.41  | | | | | | | | 
% 241.88/48.41  | | | | | | | | Case 1:
% 241.88/48.41  | | | | | | | | | 
% 241.88/48.42  | | | | | | | | |   (67)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 241.88/48.42  | | | | | | | | |           &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.88/48.42  | | | | | | | | |           (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.88/48.42  | | | | | | | | |           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~
% 241.88/48.42  | | | | | | | | |           (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.88/48.42  | | | | | | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1)
% 241.88/48.42  | | | | | | | | |           = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 241.88/48.42  | | | | | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 241.88/48.42  | | | | | | | | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 241.88/48.42  | | | | | | | | |           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.88/48.42  | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | BETA: splitting (67) gives:
% 241.88/48.42  | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | Case 1:
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | |   (68)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 241.88/48.42  | | | | | | | | | |         &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.88/48.42  | | | | | | | | | |         (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | ALPHA: (68) implies:
% 241.88/48.42  | | | | | | | | | |   (69)   ~ (all_56_1 = e1)
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | REDUCE: (40), (69) imply:
% 241.88/48.42  | | | | | | | | | |   (70)  $false
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | CLOSE: (70) is inconsistent.
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | Case 2:
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | |   (71)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.88/48.42  | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.88/48.42  | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 241.88/48.42  | | | | | | | | | |             e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 & 
% 241.88/48.42  | | | | | | | | | |           ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 241.88/48.42  | | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2,
% 241.88/48.42  | | | | | | | | | |             e0) = e2 & op(e0, e2) = e2)
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | BETA: splitting (71) gives:
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | Case 1:
% 241.88/48.42  | | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | |   (72)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 241.88/48.42  | | | | | | | | | | |           e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 241.88/48.42  | | | | | | | | | | |         &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 241.88/48.42  | | | | | | | | | | |           e2) = e1
% 241.88/48.42  | | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | | ALPHA: (72) implies:
% 241.88/48.42  | | | | | | | | | | |   (73)   ~ (all_56_11 = e2)
% 241.88/48.42  | | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | | REF_CLOSE: (3), (11), (15), (17), (28), (29), (33), (34),
% 241.88/48.42  | | | | | | | | | | |            (35), (47), (50), (62), (73) are inconsistent by
% 241.88/48.42  | | | | | | | | | | |            sub-proof #629.
% 241.88/48.42  | | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | Case 2:
% 241.88/48.42  | | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | |   (74)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 241.88/48.42  | | | | | | | | | | |           e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.88/48.42  | | | | | | | | | | |         &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 241.88/48.42  | | | | | | | | | | |           e2) = e2
% 241.88/48.42  | | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | | ALPHA: (74) implies:
% 241.88/48.42  | | | | | | | | | | |   (75)  op(e2, e0) = e2
% 241.88/48.42  | | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | | REF_CLOSE: (3), (5), (13), (14), (30), (32), (33), (37), (75)
% 241.88/48.42  | | | | | | | | | | |            are inconsistent by sub-proof #840.
% 241.88/48.42  | | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | End of split
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | End of split
% 241.88/48.42  | | | | | | | | | 
% 241.88/48.42  | | | | | | | | Case 2:
% 241.88/48.42  | | | | | | | | | 
% 241.88/48.42  | | | | | | | | |   (76)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2)
% 241.88/48.42  | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.88/48.42  | | | | | | | | |           (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.88/48.42  | | | | | | | | |           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 241.88/48.42  | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 241.88/48.42  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0)
% 241.88/48.42  | | | | | | | | |           = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 241.88/48.42  | | | | | | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 241.88/48.42  | | | | | | | | |             = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 241.88/48.42  | | | | | | | | |           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.88/48.42  | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | BETA: splitting (76) gives:
% 241.88/48.42  | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | Case 1:
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | |   (77)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2)
% 241.88/48.42  | | | | | | | | | |         &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 241.88/48.42  | | | | | | | | | |         (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | ALPHA: (77) implies:
% 241.88/48.42  | | | | | | | | | |   (78)   ~ (all_56_11 = e2)
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | REF_CLOSE: (3), (11), (15), (17), (28), (29), (33), (34),
% 241.88/48.42  | | | | | | | | | |            (35), (47), (50), (62), (78) are inconsistent by
% 241.88/48.42  | | | | | | | | | |            sub-proof #629.
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | Case 2:
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | |   (79)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 241.88/48.42  | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 241.88/48.42  | | | | | | | | | |           &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 241.88/48.42  | | | | | | | | | |             e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 & 
% 241.88/48.42  | | | | | | | | | |           ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.88/48.42  | | | | | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 241.88/48.42  | | | | | | | | | |             e0) = e0 & op(e0, e1) = e0)
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | | REF_CLOSE: (12), (21), (33), (37), (79) are inconsistent by
% 241.88/48.42  | | | | | | | | | |            sub-proof #2283.
% 241.88/48.42  | | | | | | | | | | 
% 241.88/48.42  | | | | | | | | | End of split
% 241.88/48.42  | | | | | | | | | 
% 241.88/48.42  | | | | | | | | End of split
% 241.88/48.42  | | | | | | | | 
% 241.88/48.42  | | | | | | | End of split
% 241.88/48.42  | | | | | | | 
% 241.88/48.42  | | | | | | End of split
% 241.88/48.42  | | | | | | 
% 241.88/48.42  | | | | | End of split
% 241.88/48.42  | | | | | 
% 241.88/48.42  | | | | Case 2:
% 241.88/48.42  | | | | | 
% 241.88/48.42  | | | | |   (80)  all_58_5 = e3 & op(e2, e1) = e3
% 241.88/48.42  | | | | | 
% 241.88/48.42  | | | | | REF_CLOSE: (18), (31), (33), (80) are inconsistent by sub-proof #1822.
% 241.88/48.42  | | | | | 
% 241.88/48.42  | | | | End of split
% 241.88/48.42  | | | | 
% 241.88/48.42  | | | Case 2:
% 241.88/48.42  | | | | 
% 241.88/48.42  | | | |   (81)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1)
% 241.88/48.42  | | | |           = e3)
% 241.88/48.42  | | | | 
% 241.88/48.42  | | | | BETA: splitting (81) gives:
% 241.88/48.42  | | | | 
% 241.88/48.42  | | | | Case 1:
% 241.88/48.42  | | | | | 
% 241.88/48.42  | | | | |   (82)  all_58_8 = e3 & op(e1, e1) = e3
% 241.88/48.42  | | | | | 
% 241.88/48.42  | | | | | REF_CLOSE: (3), (33), (36), (82) are inconsistent by sub-proof #2018.
% 241.88/48.42  | | | | | 
% 241.88/48.42  | | | | Case 2:
% 241.88/48.42  | | | | | 
% 241.88/48.42  | | | | |   (83)  all_58_14 = e3 & op(e0, e1) = e3
% 241.88/48.42  | | | | | 
% 241.88/48.42  | | | | | REF_CLOSE: (8), (20), (83) are inconsistent by sub-proof #1747.
% 241.88/48.42  | | | | | 
% 241.88/48.42  | | | | End of split
% 241.88/48.42  | | | | 
% 241.88/48.42  | | | End of split
% 241.88/48.42  | | | 
% 241.88/48.42  | | End of split
% 241.88/48.42  | | 
% 241.88/48.42  | End of split
% 241.88/48.42  | 
% 241.88/48.42  End of proof
% 241.88/48.42  
% 241.88/48.42  Sub-proof #629 shows that the following formulas are inconsistent:
% 241.88/48.42  ----------------------------------------------------------------
% 241.88/48.42    (1)   ~ (all_56_11 = e2)
% 241.88/48.42    (2)   ~ (e3 = e0)
% 241.88/48.42    (3)   ~ (e3 = e1)
% 241.88/48.42    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.42         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.42    (5)  op(e3, e3) = e1
% 241.88/48.42    (6)  op(e3, e0) = e2
% 241.88/48.42    (7)   ~ (all_52_4 = e3)
% 241.88/48.42    (8)  op(e3, e2) = all_52_4
% 241.88/48.42    (9)  op(e0, e0) = e3
% 241.88/48.42    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.42    (11)  op(e0, e0) = e0
% 241.88/48.42    (12)  all_56_11 = e3
% 241.88/48.42    (13)  all_58_4 = e3
% 241.88/48.42  
% 241.88/48.42  Begin of proof
% 241.88/48.42  | 
% 241.88/48.42  | REDUCE: (1), (12) imply:
% 241.88/48.42  |   (14)   ~ (e3 = e2)
% 241.88/48.42  | 
% 241.88/48.42  | GROUND_INST: instantiating (10) with e0, e3, e0, e0, simplifying with (9),
% 241.88/48.42  |              (11) gives:
% 241.88/48.42  |   (15)  e3 = e0
% 241.88/48.42  | 
% 241.88/48.42  | COMBINE_EQS: (13), (15) imply:
% 241.88/48.42  |   (16)  all_58_4 = e0
% 241.88/48.42  | 
% 241.88/48.42  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (14), (16) are
% 241.88/48.42  |            inconsistent by sub-proof #1400.
% 241.88/48.42  | 
% 241.88/48.42  End of proof
% 241.88/48.42  
% 241.88/48.42  Sub-proof #630 shows that the following formulas are inconsistent:
% 241.88/48.42  ----------------------------------------------------------------
% 241.88/48.42    (1)   ~ (e3 = e0)
% 241.88/48.42    (2)  all_58_6 = e3
% 241.88/48.42    (3)   ~ (e2 = e0)
% 241.88/48.42    (4)   ~ (all_52_7 = e3)
% 241.88/48.42    (5)  all_58_2 = e2
% 241.88/48.42    (6)  op(e3, e3) = e1
% 241.88/48.42    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.42         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.42    (8)  op(e0, e2) = all_52_7
% 241.88/48.42    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.42    (10)   ~ (e1 = e0)
% 241.88/48.42    (11)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 241.88/48.42  
% 241.88/48.42  Begin of proof
% 241.88/48.42  | 
% 241.88/48.42  | BETA: splitting (11) gives:
% 241.88/48.42  | 
% 241.88/48.42  | Case 1:
% 241.88/48.42  | | 
% 241.88/48.42  | |   (12)  all_58_12 = e3 & op(e0, e3) = e3
% 241.88/48.42  | | 
% 241.88/48.42  | | ALPHA: (12) implies:
% 241.88/48.42  | |   (13)  all_58_12 = e3
% 241.88/48.42  | | 
% 241.88/48.42  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (13) are inconsistent by
% 241.88/48.42  | |            sub-proof #1533.
% 241.88/48.42  | | 
% 241.88/48.42  | Case 2:
% 241.88/48.42  | | 
% 241.88/48.42  | |   (14)  all_58_13 = e3 & op(e0, e2) = e3
% 241.88/48.42  | | 
% 241.88/48.42  | | REF_CLOSE: (4), (8), (9), (14) are inconsistent by sub-proof #1919.
% 241.88/48.42  | | 
% 241.88/48.42  | End of split
% 241.88/48.42  | 
% 241.88/48.42  End of proof
% 241.88/48.42  
% 241.88/48.42  Sub-proof #631 shows that the following formulas are inconsistent:
% 241.88/48.42  ----------------------------------------------------------------
% 241.88/48.42    (1)   ~ (e3 = e0)
% 241.88/48.42    (2)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.42    (3)  all_58_6 = e3
% 241.88/48.42    (4)   ~ (e2 = e0)
% 241.88/48.42    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.42         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.42    (6)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.88/48.42         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.88/48.42    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.42         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.88/48.42    (8)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.42         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.42    (9)   ~ (e3 = e1)
% 241.88/48.42    (10)  all_58_7 = e2
% 241.88/48.42    (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.88/48.42          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.88/48.42    (12)  all_58_2 = e2
% 241.88/48.42    (13)  all_58_3 = e3
% 241.88/48.42    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.42          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.42    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.42          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.42    (16)  op(e3, e3) = e1
% 241.88/48.42    (17)  op(e2, e1) = all_52_9
% 241.88/48.42    (18)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.42          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.42    (19)   ~ (e3 = e2)
% 241.88/48.42    (20)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.88/48.42          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.88/48.42    (21)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.42          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.42    (22)  all_58_10 = e0
% 241.88/48.42    (23)  all_58_12 = e0
% 241.88/48.42    (24)  op(e2, e3) = all_52_1
% 241.88/48.42    (25)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.88/48.42          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.88/48.42    (26)   ~ (all_52_4 = e3)
% 241.88/48.42    (27)  op(e3, e2) = all_52_4
% 241.88/48.42    (28)   ~ (all_52_9 = e3)
% 241.88/48.42    (29)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.88/48.42          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.88/48.42    (30)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.42          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.42    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.42    (32)  op(e0, e0) = e0
% 241.88/48.42    (33)   ~ (e1 = e0)
% 241.88/48.42    (34)  all_58_13 = e1
% 241.88/48.42    (35)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.88/48.42          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.88/48.42    (36)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.88/48.42          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.88/48.42            e1)
% 241.88/48.42    (37)   ~ (all_52_1 = e3)
% 241.88/48.42    (38)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.42          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.42    (39)   ~ (e2 = e1)
% 241.88/48.42    (40)   ~ (all_52_1 = e1)
% 241.88/48.42  
% 241.88/48.42  Begin of proof
% 241.88/48.42  | 
% 241.88/48.42  | BETA: splitting (2) gives:
% 241.88/48.42  | 
% 241.88/48.42  | Case 1:
% 241.88/48.42  | | 
% 241.88/48.42  | |   (41)  all_58_12 = e2 & op(e0, e3) = e2
% 241.88/48.42  | | 
% 241.88/48.42  | | ALPHA: (41) implies:
% 241.88/48.42  | |   (42)  all_58_12 = e2
% 241.88/48.42  | | 
% 241.88/48.42  | | COMBINE_EQS: (23), (42) imply:
% 241.88/48.42  | |   (43)  e2 = e0
% 241.88/48.42  | | 
% 241.88/48.42  | | REF_CLOSE: (1), (3), (4), (8), (9), (12), (13), (15), (16), (18), (19),
% 241.88/48.42  | |            (21), (22), (23), (24), (30), (31), (33), (37), (38), (39), (40),
% 241.88/48.42  | |            (43) are inconsistent by sub-proof #632.
% 241.88/48.42  | | 
% 241.88/48.42  | Case 2:
% 241.88/48.42  | | 
% 241.88/48.42  | |   (44)  all_58_13 = e2 & op(e0, e2) = e2
% 241.88/48.42  | | 
% 241.88/48.42  | | ALPHA: (44) implies:
% 241.88/48.42  | |   (45)  all_58_13 = e2
% 241.88/48.42  | | 
% 241.88/48.42  | | COMBINE_EQS: (34), (45) imply:
% 241.88/48.42  | |   (46)  e2 = e1
% 241.88/48.42  | | 
% 241.88/48.42  | | COMBINE_EQS: (10), (46) imply:
% 241.88/48.42  | |   (47)  all_58_7 = e1
% 241.88/48.42  | | 
% 241.88/48.42  | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (11), (13), (14), (15), (16),
% 241.88/48.42  | |            (17), (18), (19), (20), (21), (22), (24), (25), (26), (27), (28),
% 241.88/48.42  | |            (29), (30), (31), (32), (33), (35), (36), (37), (38), (39), (40),
% 241.88/48.42  | |            (47) are inconsistent by sub-proof #638.
% 241.88/48.42  | | 
% 241.88/48.42  | End of split
% 241.88/48.42  | 
% 241.88/48.42  End of proof
% 241.88/48.42  
% 241.88/48.42  Sub-proof #632 shows that the following formulas are inconsistent:
% 241.88/48.42  ----------------------------------------------------------------
% 241.88/48.42    (1)   ~ (e3 = e0)
% 241.88/48.42    (2)  all_58_6 = e3
% 241.88/48.42    (3)   ~ (e2 = e0)
% 241.88/48.42    (4)  e2 = e0
% 241.88/48.42    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.42         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.42    (6)   ~ (e3 = e1)
% 241.88/48.42    (7)  all_58_2 = e2
% 241.88/48.42    (8)  all_58_3 = e3
% 241.88/48.42    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.42         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.42    (10)  op(e3, e3) = e1
% 241.88/48.42    (11)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.42          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.42    (12)   ~ (e3 = e2)
% 241.88/48.42    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.42          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.42    (14)  all_58_10 = e0
% 241.88/48.42    (15)  all_58_12 = e0
% 241.88/48.42    (16)  op(e2, e3) = all_52_1
% 241.88/48.42    (17)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.42          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.42    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.42    (19)   ~ (e1 = e0)
% 241.88/48.42    (20)   ~ (all_52_1 = e3)
% 241.88/48.42    (21)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.42          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.42    (22)   ~ (e2 = e1)
% 241.88/48.42    (23)   ~ (all_52_1 = e1)
% 241.88/48.42  
% 241.88/48.42  Begin of proof
% 241.88/48.42  | 
% 241.88/48.42  | COMBINE_EQS: (4), (7) imply:
% 241.88/48.42  |   (24)  all_58_2 = e0
% 241.88/48.42  | 
% 241.88/48.42  | BETA: splitting (21) gives:
% 241.88/48.42  | 
% 241.88/48.42  | Case 1:
% 241.88/48.42  | | 
% 241.88/48.42  | |   (25)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 241.88/48.42  | |           e1)
% 241.88/48.42  | | 
% 241.88/48.43  | | BETA: splitting (25) gives:
% 241.88/48.43  | | 
% 241.88/48.43  | | Case 1:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (26)  all_58_2 = e1 & op(e2, e3) = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REF_CLOSE: (16), (18), (23), (26) are inconsistent by sub-proof #2229.
% 241.88/48.43  | | | 
% 241.88/48.43  | | Case 2:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (27)  all_58_3 = e1 & op(e2, e2) = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (11), (12), (13), (16),
% 241.88/48.43  | | |            (18), (19), (20), (22), (27) are inconsistent by sub-proof
% 241.88/48.43  | | |            #637.
% 241.88/48.43  | | | 
% 241.88/48.43  | | End of split
% 241.88/48.43  | | 
% 241.88/48.43  | Case 2:
% 241.88/48.43  | | 
% 241.88/48.43  | |   (28)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 241.88/48.43  | |           e1)
% 241.88/48.43  | | 
% 241.88/48.43  | | BETA: splitting (28) gives:
% 241.88/48.43  | | 
% 241.88/48.43  | | Case 1:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (29)  all_58_5 = e1 & op(e2, e1) = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | ALPHA: (29) implies:
% 241.88/48.43  | | |   (30)  all_58_5 = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REF_CLOSE: (1), (2), (3), (5), (8), (10), (11), (12), (15), (17), (18),
% 241.88/48.43  | | |            (19), (22), (24), (30) are inconsistent by sub-proof #633.
% 241.88/48.43  | | | 
% 241.88/48.43  | | Case 2:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (31)  all_58_10 = e1 & op(e2, e0) = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | ALPHA: (31) implies:
% 241.88/48.43  | | |   (32)  all_58_10 = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | COMBINE_EQS: (14), (32) imply:
% 241.88/48.43  | | |   (33)  e1 = e0
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REDUCE: (19), (33) imply:
% 241.88/48.43  | | |   (34)  $false
% 241.88/48.43  | | | 
% 241.88/48.43  | | | CLOSE: (34) is inconsistent.
% 241.88/48.43  | | | 
% 241.88/48.43  | | End of split
% 241.88/48.43  | | 
% 241.88/48.43  | End of split
% 241.88/48.43  | 
% 241.88/48.43  End of proof
% 241.88/48.43  
% 241.88/48.43  Sub-proof #633 shows that the following formulas are inconsistent:
% 241.88/48.43  ----------------------------------------------------------------
% 241.88/48.43    (1)   ~ (e3 = e0)
% 241.88/48.43    (2)  all_58_6 = e3
% 241.88/48.43    (3)   ~ (e2 = e0)
% 241.88/48.43    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.43         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.43    (5)  all_58_3 = e3
% 241.88/48.43    (6)  op(e3, e3) = e1
% 241.88/48.43    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.43         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.43    (8)   ~ (e3 = e2)
% 241.88/48.43    (9)  all_58_12 = e0
% 241.88/48.43    (10)  all_58_2 = e0
% 241.88/48.43    (11)  all_58_5 = e1
% 241.88/48.43    (12)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.43          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.43    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.43    (14)   ~ (e1 = e0)
% 241.88/48.43    (15)   ~ (e2 = e1)
% 241.88/48.43  
% 241.88/48.43  Begin of proof
% 241.88/48.43  | 
% 241.88/48.43  | BETA: splitting (4) gives:
% 241.88/48.43  | 
% 241.88/48.43  | Case 1:
% 241.88/48.43  | | 
% 241.88/48.43  | |   (16)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 241.88/48.43  | |           e2)
% 241.88/48.43  | | 
% 241.88/48.43  | | BETA: splitting (16) gives:
% 241.88/48.43  | | 
% 241.88/48.43  | | Case 1:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (17)  all_58_2 = e2 & op(e2, e3) = e2
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REF_CLOSE: (3), (10), (17) are inconsistent by sub-proof #1575.
% 241.88/48.43  | | | 
% 241.88/48.43  | | Case 2:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (18)  all_58_3 = e2 & op(e2, e2) = e2
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REF_CLOSE: (5), (8), (18) are inconsistent by sub-proof #1106.
% 241.88/48.43  | | | 
% 241.88/48.43  | | End of split
% 241.88/48.43  | | 
% 241.88/48.43  | Case 2:
% 241.88/48.43  | | 
% 241.88/48.43  | |   (19)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 241.88/48.43  | |           e2)
% 241.88/48.43  | | 
% 241.88/48.43  | | BETA: splitting (19) gives:
% 241.88/48.43  | | 
% 241.88/48.43  | | Case 1:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (20)  all_58_5 = e2 & op(e2, e1) = e2
% 241.88/48.43  | | | 
% 241.88/48.43  | | | ALPHA: (20) implies:
% 241.88/48.43  | | |   (21)  all_58_5 = e2
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REF_CLOSE: (11), (15), (21) are inconsistent by sub-proof #1665.
% 241.88/48.43  | | | 
% 241.88/48.43  | | Case 2:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (22)  all_58_10 = e2 & op(e2, e0) = e2
% 241.88/48.43  | | | 
% 241.88/48.43  | | | ALPHA: (22) implies:
% 241.88/48.43  | | |   (23)  op(e2, e0) = e2
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 241.88/48.43  | | |            (15), (23) are inconsistent by sub-proof #634.
% 241.88/48.43  | | | 
% 241.88/48.43  | | End of split
% 241.88/48.43  | | 
% 241.88/48.43  | End of split
% 241.88/48.43  | 
% 241.88/48.43  End of proof
% 241.88/48.43  
% 241.88/48.43  Sub-proof #634 shows that the following formulas are inconsistent:
% 241.88/48.43  ----------------------------------------------------------------
% 241.88/48.43    (1)   ~ (e3 = e0)
% 241.88/48.43    (2)  all_58_6 = e3
% 241.88/48.43    (3)   ~ (e2 = e0)
% 241.88/48.43    (4)  all_58_3 = e3
% 241.88/48.43    (5)  op(e3, e3) = e1
% 241.88/48.43    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.43         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.43    (7)   ~ (e3 = e2)
% 241.88/48.43    (8)  op(e2, e0) = e2
% 241.88/48.43    (9)  all_58_12 = e0
% 241.88/48.43    (10)  all_58_5 = e1
% 241.88/48.43    (11)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.43          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.43    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.43    (13)   ~ (e1 = e0)
% 241.88/48.43    (14)   ~ (e2 = e1)
% 241.88/48.43  
% 241.88/48.43  Begin of proof
% 241.88/48.43  | 
% 241.88/48.43  | BETA: splitting (6) gives:
% 241.88/48.43  | 
% 241.88/48.43  | Case 1:
% 241.88/48.43  | | 
% 241.88/48.43  | |   (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 241.88/48.43  | |           e2)
% 241.88/48.43  | | 
% 241.88/48.43  | | REF_CLOSE: (1), (3), (4), (5), (8), (10), (11), (12), (13), (14), (15) are
% 241.88/48.43  | |            inconsistent by sub-proof #636.
% 241.88/48.43  | | 
% 241.88/48.43  | Case 2:
% 241.88/48.43  | | 
% 241.88/48.43  | |   (16)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 241.88/48.43  | |           e2)
% 241.88/48.43  | | 
% 241.88/48.43  | | REF_CLOSE: (2), (3), (7), (9), (16) are inconsistent by sub-proof #635.
% 241.88/48.43  | | 
% 241.88/48.43  | End of split
% 241.88/48.43  | 
% 241.88/48.43  End of proof
% 241.88/48.43  
% 241.88/48.43  Sub-proof #635 shows that the following formulas are inconsistent:
% 241.88/48.43  ----------------------------------------------------------------
% 241.88/48.43    (1)  all_58_6 = e3
% 241.88/48.43    (2)   ~ (e2 = e0)
% 241.88/48.43    (3)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.43    (4)   ~ (e3 = e2)
% 241.88/48.43    (5)  all_58_12 = e0
% 241.88/48.43  
% 241.88/48.43  Begin of proof
% 241.88/48.43  | 
% 241.88/48.43  | BETA: splitting (3) gives:
% 241.88/48.43  | 
% 241.88/48.43  | Case 1:
% 241.88/48.43  | | 
% 241.88/48.43  | |   (6)  all_58_6 = e2 & op(e1, e3) = e2
% 241.88/48.43  | | 
% 241.88/48.43  | | ALPHA: (6) implies:
% 241.88/48.43  | |   (7)  all_58_6 = e2
% 241.88/48.43  | | 
% 241.88/48.43  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #2024.
% 241.88/48.43  | | 
% 241.88/48.43  | Case 2:
% 241.88/48.43  | | 
% 241.88/48.43  | |   (8)  all_58_12 = e2 & op(e0, e3) = e2
% 241.88/48.43  | | 
% 241.88/48.43  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #1013.
% 241.88/48.43  | | 
% 241.88/48.43  | End of split
% 241.88/48.43  | 
% 241.88/48.43  End of proof
% 241.88/48.43  
% 241.88/48.43  Sub-proof #636 shows that the following formulas are inconsistent:
% 241.88/48.43  ----------------------------------------------------------------
% 241.88/48.43    (1)   ~ (e3 = e0)
% 241.88/48.43    (2)   ~ (e2 = e0)
% 241.88/48.43    (3)  all_58_3 = e3
% 241.88/48.43    (4)  op(e3, e3) = e1
% 241.88/48.43    (5)  op(e2, e0) = e2
% 241.88/48.43    (6)  all_58_5 = e1
% 241.88/48.43    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 241.88/48.43    (8)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.43         (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.43    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.43    (10)   ~ (e1 = e0)
% 241.88/48.43    (11)   ~ (e2 = e1)
% 241.88/48.43  
% 241.88/48.43  Begin of proof
% 241.88/48.43  | 
% 241.88/48.43  | BETA: splitting (7) gives:
% 241.88/48.43  | 
% 241.88/48.43  | Case 1:
% 241.88/48.43  | | 
% 241.88/48.43  | |   (12)  all_58_0 = e2 & op(e3, e3) = e2
% 241.88/48.43  | | 
% 241.88/48.43  | | ALPHA: (12) implies:
% 241.88/48.43  | |   (13)  op(e3, e3) = e2
% 241.88/48.43  | | 
% 241.88/48.43  | | REF_CLOSE: (4), (9), (11), (13) are inconsistent by sub-proof #2267.
% 241.88/48.43  | | 
% 241.88/48.43  | Case 2:
% 241.88/48.43  | | 
% 241.88/48.43  | |   (14)  all_58_2 = e2 & op(e2, e3) = e2
% 241.88/48.43  | | 
% 241.88/48.43  | | ALPHA: (14) implies:
% 241.88/48.43  | |   (15)  all_58_2 = e2
% 241.88/48.43  | | 
% 241.88/48.43  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (15) are inconsistent by
% 241.88/48.43  | |            sub-proof #840.
% 241.88/48.43  | | 
% 241.88/48.43  | End of split
% 241.88/48.43  | 
% 241.88/48.43  End of proof
% 241.88/48.43  
% 241.88/48.43  Sub-proof #637 shows that the following formulas are inconsistent:
% 241.88/48.43  ----------------------------------------------------------------
% 241.88/48.43    (1)   ~ (e3 = e0)
% 241.88/48.43    (2)  all_58_6 = e3
% 241.88/48.43    (3)   ~ (e2 = e0)
% 241.88/48.43    (4)   ~ (e3 = e1)
% 241.88/48.43    (5)  all_58_3 = e3
% 241.88/48.43    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.43         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.43    (7)  op(e3, e3) = e1
% 241.88/48.43    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.43         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.43    (9)   ~ (e3 = e2)
% 241.88/48.43    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.43          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.43    (11)  op(e2, e3) = all_52_1
% 241.88/48.43    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.43    (13)  all_58_3 = e1 & op(e2, e2) = e1
% 241.88/48.43    (14)   ~ (e1 = e0)
% 241.88/48.43    (15)   ~ (all_52_1 = e3)
% 241.88/48.43    (16)   ~ (e2 = e1)
% 241.88/48.43  
% 241.88/48.43  Begin of proof
% 241.88/48.43  | 
% 241.88/48.43  | ALPHA: (13) implies:
% 241.88/48.43  |   (17)  all_58_3 = e1
% 241.88/48.43  | 
% 241.88/48.43  | COMBINE_EQS: (5), (17) imply:
% 241.88/48.43  |   (18)  e3 = e1
% 241.88/48.43  | 
% 241.88/48.43  | SIMP: (18) implies:
% 241.88/48.43  |   (19)  e3 = e1
% 241.88/48.43  | 
% 241.88/48.43  | COMBINE_EQS: (2), (19) imply:
% 241.88/48.43  |   (20)  all_58_6 = e1
% 241.88/48.43  | 
% 241.88/48.43  | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 241.88/48.43  |            (16), (20) are inconsistent by sub-proof #1161.
% 241.88/48.43  | 
% 241.88/48.43  End of proof
% 241.88/48.43  
% 241.88/48.43  Sub-proof #638 shows that the following formulas are inconsistent:
% 241.88/48.43  ----------------------------------------------------------------
% 241.88/48.43    (1)   ~ (e3 = e0)
% 241.88/48.43    (2)   ~ (e2 = e0)
% 241.88/48.43    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.43         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.43    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.88/48.43         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.88/48.43    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.43         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.88/48.43    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.43         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.43    (7)   ~ (e3 = e1)
% 241.88/48.43    (8)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.88/48.43         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.88/48.43    (9)  all_58_3 = e3
% 241.88/48.43    (10)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.43          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.43    (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.43          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.43    (12)  op(e3, e3) = e1
% 241.88/48.43    (13)  op(e2, e1) = all_52_9
% 241.88/48.43    (14)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.43          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.43    (15)   ~ (e3 = e2)
% 241.88/48.43    (16)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.88/48.43          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.88/48.43    (17)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.43          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.43    (18)  all_58_10 = e0
% 241.88/48.43    (19)  op(e2, e3) = all_52_1
% 241.88/48.43    (20)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.88/48.43          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.88/48.43    (21)   ~ (all_52_4 = e3)
% 241.88/48.43    (22)  op(e3, e2) = all_52_4
% 241.88/48.43    (23)  all_58_7 = e1
% 241.88/48.43    (24)   ~ (all_52_9 = e3)
% 241.88/48.43    (25)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.88/48.43          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.88/48.43    (26)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.43          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.43    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.43    (28)  op(e0, e0) = e0
% 241.88/48.43    (29)   ~ (e1 = e0)
% 241.88/48.43    (30)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.88/48.43          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.88/48.43    (31)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.88/48.43          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.88/48.43            e1)
% 241.88/48.43    (32)   ~ (all_52_1 = e3)
% 241.88/48.43    (33)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.43          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.43    (34)   ~ (e2 = e1)
% 241.88/48.43    (35)   ~ (all_52_1 = e1)
% 241.88/48.43  
% 241.88/48.43  Begin of proof
% 241.88/48.43  | 
% 241.88/48.43  | BETA: splitting (33) gives:
% 241.88/48.43  | 
% 241.88/48.43  | Case 1:
% 241.88/48.43  | | 
% 241.88/48.43  | |   (36)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 241.88/48.43  | |           e1)
% 241.88/48.43  | | 
% 241.88/48.43  | | BETA: splitting (36) gives:
% 241.88/48.43  | | 
% 241.88/48.43  | | Case 1:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (37)  all_58_2 = e1 & op(e2, e3) = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REF_CLOSE: (19), (27), (35), (37) are inconsistent by sub-proof #2229.
% 241.88/48.43  | | | 
% 241.88/48.43  | | Case 2:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (38)  all_58_3 = e1 & op(e2, e2) = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REF_CLOSE: (7), (9), (38) are inconsistent by sub-proof #2197.
% 241.88/48.43  | | | 
% 241.88/48.43  | | End of split
% 241.88/48.43  | | 
% 241.88/48.43  | Case 2:
% 241.88/48.43  | | 
% 241.88/48.43  | |   (39)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 241.88/48.43  | |           e1)
% 241.88/48.43  | | 
% 241.88/48.43  | | BETA: splitting (39) gives:
% 241.88/48.43  | | 
% 241.88/48.43  | | Case 1:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (40)  all_58_5 = e1 & op(e2, e1) = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | ALPHA: (40) implies:
% 241.88/48.43  | | |   (41)  all_58_5 = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.88/48.43  | | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23),
% 241.88/48.43  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (34),
% 241.88/48.43  | | |            (41) are inconsistent by sub-proof #675.
% 241.88/48.43  | | | 
% 241.88/48.43  | | Case 2:
% 241.88/48.43  | | | 
% 241.88/48.43  | | |   (42)  all_58_10 = e1 & op(e2, e0) = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | ALPHA: (42) implies:
% 241.88/48.43  | | |   (43)  all_58_10 = e1
% 241.88/48.43  | | | 
% 241.88/48.43  | | | REF_CLOSE: (18), (29), (43) are inconsistent by sub-proof #1173.
% 241.88/48.43  | | | 
% 241.88/48.43  | | End of split
% 241.88/48.43  | | 
% 241.88/48.43  | End of split
% 241.88/48.43  | 
% 241.88/48.43  End of proof
% 241.88/48.43  
% 241.88/48.43  Sub-proof #639 shows that the following formulas are inconsistent:
% 241.88/48.43  ----------------------------------------------------------------
% 241.88/48.43    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.43         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.43    (2)   ~ (e3 = e0)
% 241.88/48.43    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.88/48.43         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.88/48.43    (4)   ~ (e2 = e0)
% 241.88/48.43    (5)  op(e1, e2) = all_52_6
% 241.88/48.44    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.44         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.44    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.88/48.44         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.88/48.44    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.44         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.88/48.44    (9)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.88/48.44         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.88/48.44    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.44          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.44    (11)   ~ (e3 = e1)
% 241.88/48.44    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.88/48.44          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.88/48.44    (13)  all_58_3 = e3
% 241.88/48.44    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.44          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.44    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.44          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.44    (16)  op(e3, e3) = e1
% 241.88/48.44    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.44              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.88/48.44                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.88/48.44                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.88/48.44    (18)  op(e2, e1) = all_52_9
% 241.88/48.44    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.44          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.44    (20)   ~ (e3 = e2)
% 241.88/48.44    (21)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.88/48.44          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.88/48.44    (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.44          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.44    (23)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.88/48.44          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.88/48.44    (24)  all_58_12 = e0
% 241.88/48.44    (25)  op(e2, e3) = all_52_1
% 241.88/48.44    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.88/48.44          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.44    (27)   ~ (all_52_6 = e3)
% 241.88/48.44    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.88/48.44          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.88/48.44    (29)   ~ (all_52_4 = e3)
% 241.88/48.44    (30)  op(e3, e2) = all_52_4
% 241.88/48.44    (31)   ~ (all_52_9 = e3)
% 241.88/48.44    (32)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.88/48.44          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.88/48.44    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.88/48.44          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.88/48.44    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.44          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.44    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.44    (36)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.88/48.44          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.88/48.44    (37)  op(e1, e1) = e0
% 241.88/48.44    (38)   ~ (e1 = e0)
% 241.88/48.44    (39)  all_58_9 = e1
% 241.88/48.44    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.88/48.44          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.88/48.44    (41)  op(e2, e0) = all_52_13
% 241.88/48.44    (42)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.88/48.44          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.88/48.44            e1)
% 241.88/48.44    (43)   ~ (all_52_1 = e3)
% 241.88/48.44    (44)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.44          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.88/48.44            e2)
% 241.88/48.44    (45)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.44          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.44    (46)   ~ (e2 = e1)
% 241.88/48.44    (47)   ~ (all_52_1 = e1)
% 241.88/48.44  
% 241.88/48.44  Begin of proof
% 241.88/48.44  | 
% 241.88/48.44  | BETA: splitting (15) gives:
% 241.88/48.44  | 
% 241.88/48.44  | Case 1:
% 241.88/48.44  | | 
% 241.88/48.44  | |   (48)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 241.88/48.44  | |           e3)
% 241.88/48.44  | | 
% 241.88/48.44  | | REF_CLOSE: (11), (16), (25), (35), (43), (48) are inconsistent by sub-proof
% 241.88/48.44  | |            #1208.
% 241.88/48.44  | | 
% 241.88/48.44  | Case 2:
% 241.88/48.44  | | 
% 241.88/48.44  | |   (49)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 241.88/48.44  | |           e3)
% 241.88/48.44  | | 
% 241.88/48.44  | | BETA: splitting (49) gives:
% 241.88/48.44  | | 
% 241.88/48.44  | | Case 1:
% 241.88/48.44  | | | 
% 241.88/48.44  | | |   (50)  all_58_6 = e3 & op(e1, e3) = e3
% 241.88/48.44  | | | 
% 241.88/48.44  | | | ALPHA: (50) implies:
% 241.88/48.44  | | |   (51)  all_58_6 = e3
% 241.88/48.44  | | | 
% 241.88/48.44  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.88/48.44  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.88/48.44  | | |            (23), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 241.88/48.44  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 241.88/48.44  | | |            (44), (45), (46), (47), (51) are inconsistent by sub-proof
% 241.88/48.44  | | |            #640.
% 241.88/48.44  | | | 
% 241.88/48.44  | | Case 2:
% 241.88/48.44  | | | 
% 241.88/48.44  | | |   (52)  all_58_12 = e3 & op(e0, e3) = e3
% 241.88/48.44  | | | 
% 241.88/48.44  | | | ALPHA: (52) implies:
% 241.88/48.44  | | |   (53)  all_58_12 = e3
% 241.88/48.44  | | | 
% 241.88/48.44  | | | REF_CLOSE: (2), (24), (53) are inconsistent by sub-proof #1971.
% 241.88/48.44  | | | 
% 241.88/48.44  | | End of split
% 241.88/48.44  | | 
% 241.88/48.44  | End of split
% 241.88/48.44  | 
% 241.88/48.44  End of proof
% 241.88/48.44  
% 241.88/48.44  Sub-proof #640 shows that the following formulas are inconsistent:
% 241.88/48.44  ----------------------------------------------------------------
% 241.88/48.44    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.44         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.44    (2)   ~ (e3 = e0)
% 241.88/48.44    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.88/48.44         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.88/48.44    (4)  all_58_6 = e3
% 241.88/48.44    (5)   ~ (e2 = e0)
% 241.88/48.44    (6)  op(e1, e2) = all_52_6
% 241.88/48.44    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.44         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.44    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.88/48.44         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.88/48.44    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.44         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.88/48.44    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.88/48.44          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.88/48.44    (11)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.44          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.44    (12)   ~ (e3 = e1)
% 241.88/48.44    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.88/48.44          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.88/48.44    (14)  all_58_3 = e3
% 241.88/48.44    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.44          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.44    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.44          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.44    (17)  op(e3, e3) = e1
% 241.88/48.44    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.44              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.88/48.44                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.88/48.44                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.88/48.44    (19)  op(e2, e1) = all_52_9
% 241.88/48.44    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.44          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.44    (21)   ~ (e3 = e2)
% 241.88/48.44    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.88/48.44          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.88/48.44    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.44          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.44    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.88/48.44          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.88/48.44    (25)  op(e2, e3) = all_52_1
% 241.88/48.44    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.88/48.44          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.44    (27)   ~ (all_52_6 = e3)
% 241.88/48.44    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.88/48.44          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.88/48.44    (29)   ~ (all_52_4 = e3)
% 241.88/48.44    (30)  op(e3, e2) = all_52_4
% 241.88/48.44    (31)   ~ (all_52_9 = e3)
% 241.88/48.44    (32)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.88/48.44          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.88/48.44    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.88/48.44          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.88/48.44    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.44          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.44    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.44    (36)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.88/48.44          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.88/48.44    (37)  op(e1, e1) = e0
% 241.88/48.44    (38)   ~ (e1 = e0)
% 241.88/48.44    (39)  all_58_9 = e1
% 241.88/48.44    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.88/48.44          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.88/48.44    (41)  op(e2, e0) = all_52_13
% 241.88/48.44    (42)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.88/48.44          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.88/48.44            e1)
% 241.88/48.44    (43)   ~ (all_52_1 = e3)
% 241.88/48.44    (44)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.44          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.88/48.44            e2)
% 241.88/48.44    (45)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.44          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.44    (46)   ~ (e2 = e1)
% 241.88/48.44    (47)   ~ (all_52_1 = e1)
% 241.88/48.44  
% 241.88/48.44  Begin of proof
% 241.88/48.44  | 
% 241.88/48.44  | BETA: splitting (15) gives:
% 241.88/48.44  | 
% 241.88/48.44  | Case 1:
% 241.88/48.44  | | 
% 241.88/48.44  | |   (48)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 241.88/48.44  | |           e3)
% 241.88/48.44  | | 
% 241.88/48.44  | | REF_CLOSE: (12), (17), (29), (30), (35), (48) are inconsistent by sub-proof
% 241.88/48.44  | |            #1401.
% 241.88/48.44  | | 
% 241.88/48.44  | Case 2:
% 241.88/48.44  | | 
% 241.88/48.44  | |   (49)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 241.88/48.44  | |           e3)
% 241.88/48.44  | | 
% 241.88/48.44  | | BETA: splitting (49) gives:
% 241.88/48.44  | | 
% 241.88/48.44  | | Case 1:
% 241.88/48.44  | | | 
% 241.88/48.44  | | |   (50)  all_58_4 = e3 & op(e3, e1) = e3
% 241.88/48.44  | | | 
% 241.88/48.44  | | | ALPHA: (50) implies:
% 241.88/48.44  | | |   (51)  all_58_4 = e3
% 241.88/48.44  | | | 
% 241.88/48.44  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.88/48.44  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.88/48.44  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 241.88/48.44  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 241.88/48.44  | | |            (43), (44), (45), (46), (47), (51) are inconsistent by
% 241.88/48.44  | | |            sub-proof #641.
% 241.88/48.44  | | | 
% 241.88/48.44  | | Case 2:
% 241.88/48.44  | | | 
% 241.88/48.44  | | |   (52)  all_58_9 = e3 & op(e3, e0) = e3
% 241.88/48.44  | | | 
% 241.88/48.44  | | | ALPHA: (52) implies:
% 241.88/48.44  | | |   (53)  all_58_9 = e3
% 241.88/48.44  | | | 
% 241.88/48.44  | | | COMBINE_EQS: (39), (53) imply:
% 241.88/48.44  | | |   (54)  e3 = e1
% 241.88/48.44  | | | 
% 241.88/48.44  | | | SIMP: (54) implies:
% 241.88/48.44  | | |   (55)  e3 = e1
% 241.88/48.44  | | | 
% 241.88/48.44  | | | COMBINE_EQS: (4), (55) imply:
% 241.88/48.44  | | |   (56)  all_58_6 = e1
% 241.88/48.44  | | | 
% 241.88/48.44  | | | REF_CLOSE: (2), (5), (12), (16), (17), (20), (21), (23), (25), (35), (38),
% 241.88/48.44  | | |            (43), (46), (56) are inconsistent by sub-proof #1161.
% 241.88/48.44  | | | 
% 241.88/48.44  | | End of split
% 241.88/48.44  | | 
% 241.88/48.44  | End of split
% 241.88/48.44  | 
% 241.88/48.44  End of proof
% 241.88/48.44  
% 241.88/48.44  Sub-proof #641 shows that the following formulas are inconsistent:
% 241.88/48.44  ----------------------------------------------------------------
% 241.88/48.44    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.44         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.44    (2)   ~ (e3 = e0)
% 241.88/48.45    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.88/48.45         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.88/48.45    (4)  all_58_6 = e3
% 241.88/48.45    (5)   ~ (e2 = e0)
% 241.88/48.45    (6)  op(e1, e2) = all_52_6
% 241.88/48.45    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.45         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.45    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.88/48.45         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.88/48.45    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.45         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.88/48.45    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.88/48.45          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.88/48.45    (11)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.45          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.45    (12)   ~ (e3 = e1)
% 241.88/48.45    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.88/48.45          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.88/48.45    (14)  all_58_3 = e3
% 241.88/48.45    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.45          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.45    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.45          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.45    (17)  op(e3, e3) = e1
% 241.88/48.45    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.45              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.88/48.45                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.88/48.45                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.88/48.45    (19)  op(e2, e1) = all_52_9
% 241.88/48.45    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.45          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.45    (21)   ~ (e3 = e2)
% 241.88/48.45    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.88/48.45          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.88/48.45    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.45          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.45    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.88/48.45          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.88/48.45    (25)  op(e2, e3) = all_52_1
% 241.88/48.45    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.88/48.45          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.45    (27)   ~ (all_52_6 = e3)
% 241.88/48.45    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.88/48.45          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.88/48.45    (29)   ~ (all_52_4 = e3)
% 241.88/48.45    (30)  op(e3, e2) = all_52_4
% 241.88/48.45    (31)   ~ (all_52_9 = e3)
% 241.88/48.45    (32)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.88/48.45          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.88/48.45    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.88/48.45          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.88/48.45    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.45          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.88/48.45    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.88/48.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.88/48.45    (36)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.88/48.45          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.88/48.45    (37)  op(e1, e1) = e0
% 241.88/48.45    (38)   ~ (e1 = e0)
% 241.88/48.45    (39)  all_58_4 = e3
% 241.88/48.45    (40)  all_58_9 = e1
% 241.88/48.45    (41)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.88/48.45          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.88/48.45    (42)  op(e2, e0) = all_52_13
% 241.88/48.45    (43)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.88/48.45          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.88/48.45            e1)
% 241.88/48.45    (44)   ~ (all_52_1 = e3)
% 241.88/48.45    (45)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.45          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.88/48.45            e2)
% 241.88/48.45    (46)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.88/48.45          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.88/48.45    (47)   ~ (e2 = e1)
% 241.88/48.45    (48)   ~ (all_52_1 = e1)
% 241.88/48.45  
% 241.88/48.45  Begin of proof
% 241.88/48.45  | 
% 241.88/48.45  | BETA: splitting (26) gives:
% 241.88/48.45  | 
% 241.88/48.45  | Case 1:
% 241.88/48.45  | | 
% 241.88/48.45  | |   (49)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 241.88/48.45  | |           e0)
% 241.88/48.45  | | 
% 241.88/48.45  | | REF_CLOSE: (1), (5), (17), (21), (35), (38), (39), (40), (47), (49) are
% 241.88/48.45  | |            inconsistent by sub-proof #1293.
% 241.88/48.45  | | 
% 241.88/48.45  | Case 2:
% 241.88/48.45  | | 
% 241.88/48.45  | |   (50)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 241.88/48.45  | |           e0)
% 241.88/48.45  | | 
% 241.88/48.45  | | BETA: splitting (50) gives:
% 241.88/48.45  | | 
% 241.88/48.45  | | Case 1:
% 241.88/48.45  | | | 
% 241.88/48.45  | | |   (51)  all_58_4 = e0 & op(e3, e1) = e0
% 241.88/48.45  | | | 
% 241.88/48.45  | | | ALPHA: (51) implies:
% 241.88/48.45  | | |   (52)  all_58_4 = e0
% 241.88/48.45  | | | 
% 241.88/48.45  | | | COMBINE_EQS: (39), (52) imply:
% 241.88/48.45  | | |   (53)  e3 = e0
% 241.88/48.45  | | | 
% 241.88/48.45  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.88/48.45  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.88/48.45  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 241.88/48.45  | | |            (33), (34), (35), (36), (37), (38), (41), (42), (43), (44),
% 241.88/48.45  | | |            (45), (46), (47), (48), (53) are inconsistent by sub-proof
% 241.88/48.45  | | |            #642.
% 241.88/48.45  | | | 
% 241.88/48.45  | | Case 2:
% 241.88/48.45  | | | 
% 241.88/48.45  | | |   (54)  all_58_9 = e0 & op(e3, e0) = e0
% 241.88/48.45  | | | 
% 241.88/48.45  | | | ALPHA: (54) implies:
% 241.88/48.45  | | |   (55)  all_58_9 = e0
% 241.88/48.45  | | | 
% 241.88/48.45  | | | REF_CLOSE: (38), (40), (55) are inconsistent by sub-proof #1744.
% 241.88/48.45  | | | 
% 241.88/48.45  | | End of split
% 241.88/48.45  | | 
% 241.88/48.45  | End of split
% 241.88/48.45  | 
% 241.88/48.45  End of proof
% 241.88/48.45  
% 241.88/48.45  Sub-proof #642 shows that the following formulas are inconsistent:
% 241.88/48.45  ----------------------------------------------------------------
% 241.88/48.45    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.88/48.45         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.88/48.45    (2)   ~ (e3 = e0)
% 241.88/48.45    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.88/48.45         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.88/48.45    (4)  all_58_6 = e3
% 241.88/48.45    (5)   ~ (e2 = e0)
% 241.88/48.45    (6)  op(e1, e2) = all_52_6
% 241.88/48.45    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.45         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.88/48.45    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.88/48.45         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.88/48.45    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.88/48.45         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.88/48.45    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.88/48.45          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.88/48.45    (11)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.88/48.45          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.88/48.45    (12)   ~ (e3 = e1)
% 241.88/48.45    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.88/48.45          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.88/48.45    (14)  all_58_3 = e3
% 241.88/48.45    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.88/48.45          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.88/48.45    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.88/48.45          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.88/48.45    (17)  op(e3, e3) = e1
% 241.88/48.45    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.45              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.88/48.45                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.88/48.45                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.88/48.45    (19)  op(e2, e1) = all_52_9
% 241.88/48.45    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.88/48.45          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.88/48.45    (21)   ~ (e3 = e2)
% 241.88/48.45    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.88/48.45          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.88/48.45    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.88/48.45          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.88/48.45    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.88/48.45          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.88/48.45    (25)  op(e2, e3) = all_52_1
% 241.88/48.45    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.88/48.45          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.88/48.45    (27)   ~ (all_52_6 = e3)
% 241.88/48.45    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.88/48.45          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.88/48.45    (29)   ~ (all_52_4 = e3)
% 241.88/48.45    (30)  op(e3, e2) = all_52_4
% 241.88/48.45    (31)   ~ (all_52_9 = e3)
% 241.96/48.45    (32)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.96/48.45          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.96/48.45    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.96/48.45          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.96/48.45    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.96/48.45          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.96/48.45    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.96/48.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.96/48.45    (36)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.96/48.45          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.96/48.45    (37)  e3 = e0
% 241.96/48.45    (38)  op(e1, e1) = e0
% 241.96/48.45    (39)   ~ (e1 = e0)
% 241.96/48.45    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.96/48.45          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.96/48.45    (41)  op(e2, e0) = all_52_13
% 241.96/48.45    (42)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.96/48.45          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.96/48.45            e1)
% 241.96/48.45    (43)   ~ (all_52_1 = e3)
% 241.96/48.45    (44)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.96/48.45          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.96/48.45            e2)
% 241.96/48.45    (45)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.96/48.45          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.96/48.45    (46)   ~ (e2 = e1)
% 241.96/48.45    (47)   ~ (all_52_1 = e1)
% 241.96/48.45  
% 241.96/48.45  Begin of proof
% 241.96/48.45  | 
% 241.96/48.45  | SIMP: (37) implies:
% 241.96/48.45  |   (48)  e3 = e0
% 241.96/48.45  | 
% 241.96/48.45  | COMBINE_EQS: (4), (48) imply:
% 241.96/48.45  |   (49)  all_58_6 = e0
% 241.96/48.45  | 
% 241.96/48.45  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.96/48.45  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 241.96/48.45  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 241.96/48.45  |            (36), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 241.96/48.45  |            (49) are inconsistent by sub-proof #664.
% 241.96/48.45  | 
% 241.96/48.45  End of proof
% 241.96/48.45  
% 241.96/48.45  Sub-proof #643 shows that the following formulas are inconsistent:
% 241.96/48.45  ----------------------------------------------------------------
% 241.96/48.45    (1)  all_58_5 = e0
% 241.96/48.45    (2)   ~ (e3 = e0)
% 241.96/48.45    (3)   ~ (e2 = e0)
% 241.96/48.45    (4)  all_58_8 = e0
% 241.96/48.45    (5)   ~ (e3 = e1)
% 241.96/48.45    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.96/48.45         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.96/48.45    (7)  op(e3, e3) = e1
% 241.96/48.45    (8)  op(e2, e1) = all_52_9
% 241.96/48.45    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.96/48.45         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.96/48.45    (10)   ~ (e3 = e2)
% 241.96/48.45    (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.96/48.45          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.96/48.46    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.96/48.46          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.96/48.46    (13)  all_58_12 = e0
% 241.96/48.46    (14)  op(e2, e3) = all_52_1
% 241.96/48.46    (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.96/48.46          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.96/48.46    (16)   ~ (all_52_9 = e3)
% 241.96/48.46    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.96/48.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.96/48.46    (18)  op(e1, e1) = e0
% 241.96/48.46    (19)   ~ (e1 = e0)
% 241.96/48.46    (20)   ~ (all_52_1 = e3)
% 241.96/48.46    (21)  all_58_14 = e1
% 241.96/48.46    (22)   ~ (e2 = e1)
% 241.96/48.46  
% 241.96/48.46  Begin of proof
% 241.96/48.46  | 
% 241.96/48.46  | BETA: splitting (11) gives:
% 241.96/48.46  | 
% 241.96/48.46  | Case 1:
% 241.96/48.46  | | 
% 241.96/48.46  | |   (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 241.96/48.46  | |           e2)
% 241.96/48.46  | | 
% 241.96/48.46  | | BETA: splitting (23) gives:
% 241.96/48.46  | | 
% 241.96/48.46  | | Case 1:
% 241.96/48.46  | | | 
% 241.96/48.46  | | |   (24)  all_58_4 = e2 & op(e3, e1) = e2
% 241.96/48.46  | | | 
% 241.96/48.46  | | | ALPHA: (24) implies:
% 241.96/48.46  | | |   (25)  all_58_4 = e2
% 241.96/48.46  | | | 
% 241.96/48.46  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 241.96/48.46  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (25) are
% 241.96/48.46  | | |            inconsistent by sub-proof #644.
% 241.96/48.46  | | | 
% 241.96/48.46  | | Case 2:
% 241.96/48.46  | | | 
% 241.96/48.46  | | |   (26)  all_58_5 = e2 & op(e2, e1) = e2
% 241.96/48.46  | | | 
% 241.96/48.46  | | | ALPHA: (26) implies:
% 241.96/48.46  | | |   (27)  all_58_5 = e2
% 241.96/48.46  | | | 
% 241.96/48.46  | | | COMBINE_EQS: (1), (27) imply:
% 241.96/48.46  | | |   (28)  e2 = e0
% 241.96/48.46  | | | 
% 241.96/48.46  | | | REDUCE: (3), (28) imply:
% 241.96/48.46  | | |   (29)  $false
% 241.96/48.46  | | | 
% 241.96/48.46  | | | CLOSE: (29) is inconsistent.
% 241.96/48.46  | | | 
% 241.96/48.46  | | End of split
% 241.96/48.46  | | 
% 241.96/48.46  | Case 2:
% 241.96/48.46  | | 
% 241.96/48.46  | |   (30)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 241.96/48.46  | |           e2)
% 241.96/48.46  | | 
% 241.96/48.46  | | BETA: splitting (30) gives:
% 241.96/48.46  | | 
% 241.96/48.46  | | Case 1:
% 241.96/48.46  | | | 
% 241.96/48.46  | | |   (31)  all_58_8 = e2 & op(e1, e1) = e2
% 241.96/48.46  | | | 
% 241.96/48.46  | | | ALPHA: (31) implies:
% 241.96/48.46  | | |   (32)  all_58_8 = e2
% 241.96/48.46  | | | 
% 241.96/48.46  | | | REF_CLOSE: (3), (4), (32) are inconsistent by sub-proof #1556.
% 241.96/48.46  | | | 
% 241.96/48.46  | | Case 2:
% 241.96/48.46  | | | 
% 241.96/48.46  | | |   (33)  all_58_14 = e2 & op(e0, e1) = e2
% 241.96/48.46  | | | 
% 241.96/48.46  | | | ALPHA: (33) implies:
% 241.96/48.46  | | |   (34)  all_58_14 = e2
% 241.96/48.46  | | | 
% 241.96/48.46  | | | REF_CLOSE: (21), (22), (34) are inconsistent by sub-proof #2044.
% 241.96/48.46  | | | 
% 241.96/48.46  | | End of split
% 241.96/48.46  | | 
% 241.96/48.46  | End of split
% 241.96/48.46  | 
% 241.96/48.46  End of proof
% 241.96/48.46  
% 241.96/48.46  Sub-proof #644 shows that the following formulas are inconsistent:
% 241.96/48.46  ----------------------------------------------------------------
% 241.96/48.46    (1)   ~ (e3 = e0)
% 241.96/48.46    (2)   ~ (e2 = e0)
% 241.96/48.46    (3)  all_58_4 = e2
% 241.96/48.46    (4)   ~ (e3 = e1)
% 241.96/48.46    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.96/48.46         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.96/48.46    (6)  op(e3, e3) = e1
% 241.96/48.46    (7)  op(e2, e1) = all_52_9
% 241.96/48.46    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.96/48.46         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.96/48.46    (9)   ~ (e3 = e2)
% 241.96/48.46    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.96/48.46          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.96/48.46    (11)  all_58_12 = e0
% 241.96/48.46    (12)  op(e2, e3) = all_52_1
% 241.96/48.46    (13)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.96/48.46          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.96/48.46    (14)   ~ (all_52_9 = e3)
% 241.96/48.46    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.96/48.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.96/48.46    (16)  op(e1, e1) = e0
% 241.96/48.46    (17)   ~ (e1 = e0)
% 241.96/48.46    (18)   ~ (all_52_1 = e3)
% 241.96/48.46    (19)  all_58_14 = e1
% 241.96/48.46    (20)   ~ (e2 = e1)
% 241.96/48.46  
% 241.96/48.46  Begin of proof
% 241.96/48.46  | 
% 241.96/48.46  | BETA: splitting (5) gives:
% 241.96/48.46  | 
% 241.96/48.46  | Case 1:
% 241.96/48.46  | | 
% 241.96/48.46  | |   (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 241.96/48.46  | |           e3)
% 241.96/48.46  | | 
% 241.96/48.46  | | REF_CLOSE: (4), (6), (12), (15), (18), (21) are inconsistent by sub-proof
% 241.96/48.46  | |            #1208.
% 241.96/48.46  | | 
% 241.96/48.46  | Case 2:
% 241.96/48.46  | | 
% 241.96/48.46  | |   (22)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 241.96/48.46  | |           e3)
% 241.96/48.46  | | 
% 241.96/48.46  | | BETA: splitting (22) gives:
% 241.96/48.46  | | 
% 241.96/48.46  | | Case 1:
% 241.96/48.46  | | | 
% 241.96/48.46  | | |   (23)  all_58_6 = e3 & op(e1, e3) = e3
% 241.96/48.46  | | | 
% 241.96/48.46  | | | ALPHA: (23) implies:
% 241.96/48.46  | | |   (24)  all_58_6 = e3
% 241.96/48.46  | | | 
% 241.96/48.46  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 241.96/48.46  | | |            (14), (15), (16), (17), (18), (19), (20), (24) are inconsistent
% 241.96/48.46  | | |            by sub-proof #645.
% 241.96/48.46  | | | 
% 241.96/48.46  | | Case 2:
% 241.96/48.46  | | | 
% 241.96/48.46  | | |   (25)  all_58_12 = e3 & op(e0, e3) = e3
% 241.96/48.46  | | | 
% 241.96/48.46  | | | ALPHA: (25) implies:
% 241.96/48.46  | | |   (26)  all_58_12 = e3
% 241.96/48.46  | | | 
% 241.96/48.46  | | | REF_CLOSE: (1), (11), (26) are inconsistent by sub-proof #1971.
% 241.96/48.46  | | | 
% 241.96/48.46  | | End of split
% 241.96/48.46  | | 
% 241.96/48.46  | End of split
% 241.96/48.46  | 
% 241.96/48.46  End of proof
% 241.96/48.46  
% 241.96/48.46  Sub-proof #645 shows that the following formulas are inconsistent:
% 241.96/48.46  ----------------------------------------------------------------
% 241.96/48.46    (1)   ~ (e3 = e0)
% 241.96/48.46    (2)  all_58_6 = e3
% 241.96/48.46    (3)   ~ (e2 = e0)
% 241.96/48.46    (4)  all_58_4 = e2
% 241.96/48.46    (5)   ~ (e3 = e1)
% 241.96/48.46    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.96/48.46         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.96/48.46    (7)  op(e3, e3) = e1
% 241.96/48.46    (8)  op(e2, e1) = all_52_9
% 241.96/48.46    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.96/48.46         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.96/48.46    (10)   ~ (e3 = e2)
% 241.96/48.46    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.96/48.46          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.96/48.46    (12)  op(e2, e3) = all_52_1
% 241.96/48.46    (13)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.96/48.46          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.96/48.46    (14)   ~ (all_52_9 = e3)
% 241.96/48.46    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.96/48.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.96/48.46    (16)  op(e1, e1) = e0
% 241.96/48.46    (17)   ~ (e1 = e0)
% 241.96/48.46    (18)   ~ (all_52_1 = e3)
% 241.96/48.46    (19)  all_58_14 = e1
% 241.96/48.46    (20)   ~ (e2 = e1)
% 241.96/48.46  
% 241.96/48.46  Begin of proof
% 241.96/48.46  | 
% 241.96/48.46  | BETA: splitting (13) gives:
% 241.96/48.46  | 
% 241.96/48.46  | Case 1:
% 241.96/48.46  | | 
% 241.96/48.46  | |   (21)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 241.96/48.46  | |           e3)
% 241.96/48.46  | | 
% 241.96/48.46  | | BETA: splitting (21) gives:
% 241.96/48.46  | | 
% 241.96/48.46  | | Case 1:
% 241.96/48.46  | | | 
% 241.96/48.46  | | |   (22)  all_58_4 = e3 & op(e3, e1) = e3
% 241.96/48.46  | | | 
% 241.96/48.46  | | | REF_CLOSE: (4), (10), (22) are inconsistent by sub-proof #2167.
% 241.96/48.46  | | | 
% 241.96/48.46  | | Case 2:
% 241.96/48.46  | | | 
% 241.96/48.46  | | |   (23)  all_58_5 = e3 & op(e2, e1) = e3
% 241.96/48.46  | | | 
% 241.96/48.46  | | | REF_CLOSE: (8), (14), (15), (23) are inconsistent by sub-proof #1822.
% 241.96/48.46  | | | 
% 241.96/48.46  | | End of split
% 241.96/48.46  | | 
% 241.96/48.46  | Case 2:
% 241.96/48.46  | | 
% 241.96/48.46  | |   (24)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 241.96/48.46  | |           e3)
% 241.96/48.46  | | 
% 241.96/48.46  | | BETA: splitting (24) gives:
% 241.96/48.46  | | 
% 241.96/48.46  | | Case 1:
% 241.96/48.46  | | | 
% 241.96/48.46  | | |   (25)  all_58_8 = e3 & op(e1, e1) = e3
% 241.96/48.46  | | | 
% 241.96/48.46  | | | REF_CLOSE: (1), (15), (16), (25) are inconsistent by sub-proof #2018.
% 241.96/48.46  | | | 
% 241.96/48.46  | | Case 2:
% 241.96/48.46  | | | 
% 241.96/48.46  | | |   (26)  all_58_14 = e3 & op(e0, e1) = e3
% 241.96/48.46  | | | 
% 241.96/48.46  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (12), (15),
% 241.96/48.46  | | |            (17), (18), (19), (20), (26) are inconsistent by sub-proof
% 241.96/48.46  | | |            #646.
% 241.96/48.46  | | | 
% 241.96/48.46  | | End of split
% 241.96/48.46  | | 
% 241.96/48.46  | End of split
% 241.96/48.46  | 
% 241.96/48.46  End of proof
% 241.96/48.46  
% 241.96/48.46  Sub-proof #646 shows that the following formulas are inconsistent:
% 241.96/48.46  ----------------------------------------------------------------
% 241.96/48.46    (1)   ~ (e3 = e0)
% 241.96/48.46    (2)  all_58_14 = e3 & op(e0, e1) = e3
% 241.96/48.46    (3)  all_58_6 = e3
% 241.96/48.46    (4)   ~ (e2 = e0)
% 241.96/48.46    (5)   ~ (e3 = e1)
% 241.96/48.46    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.96/48.46         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.96/48.46    (7)  op(e3, e3) = e1
% 241.96/48.46    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.96/48.46         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.96/48.46    (9)   ~ (e3 = e2)
% 241.96/48.46    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.96/48.46          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.96/48.46    (11)  op(e2, e3) = all_52_1
% 241.96/48.46    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.96/48.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.96/48.46    (13)   ~ (e1 = e0)
% 241.96/48.46    (14)   ~ (all_52_1 = e3)
% 241.96/48.46    (15)  all_58_14 = e1
% 241.96/48.46    (16)   ~ (e2 = e1)
% 241.96/48.46  
% 241.96/48.46  Begin of proof
% 241.96/48.46  | 
% 241.96/48.46  | ALPHA: (2) implies:
% 241.96/48.46  |   (17)  all_58_14 = e3
% 241.96/48.46  | 
% 241.96/48.46  | COMBINE_EQS: (15), (17) imply:
% 241.96/48.46  |   (18)  e3 = e1
% 241.96/48.46  | 
% 241.96/48.46  | COMBINE_EQS: (3), (18) imply:
% 241.96/48.46  |   (19)  all_58_6 = e1
% 241.96/48.46  | 
% 241.96/48.46  | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 241.96/48.46  |            (16), (19) are inconsistent by sub-proof #1161.
% 241.96/48.46  | 
% 241.96/48.46  End of proof
% 241.96/48.46  
% 241.96/48.46  Sub-proof #647 shows that the following formulas are inconsistent:
% 241.96/48.46  ----------------------------------------------------------------
% 241.96/48.46    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.96/48.46         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.96/48.46    (2)   ~ (e3 = e0)
% 241.96/48.46    (3)   ~ (e2 = e0)
% 241.96/48.46    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 241.96/48.46    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.96/48.46         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.96/48.46    (6)   ~ (e3 = e1)
% 241.96/48.46    (7)  all_58_3 = e3
% 241.96/48.46    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.96/48.46         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.96/48.46    (9)  op(e3, e3) = e1
% 241.96/48.46    (10)   ~ (e3 = e2)
% 241.96/48.46    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.96/48.46          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.96/48.46    (12)   ~ (all_52_4 = e3)
% 241.96/48.46    (13)  op(e3, e2) = all_52_4
% 241.96/48.46    (14)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.96/48.46          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.96/48.46    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.96/48.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.96/48.46    (16)   ~ (e1 = e0)
% 241.96/48.46    (17)  all_58_10 = e1
% 241.96/48.46    (18)   ~ (e2 = e1)
% 241.96/48.46  
% 241.96/48.46  Begin of proof
% 241.96/48.46  | 
% 241.96/48.46  | BETA: splitting (4) gives:
% 241.96/48.46  | 
% 241.96/48.46  | Case 1:
% 241.96/48.46  | | 
% 241.96/48.46  | |   (19)  all_58_4 = e1 & op(e3, e1) = e1
% 241.96/48.46  | | 
% 241.96/48.46  | | ALPHA: (19) implies:
% 241.96/48.46  | |   (20)  all_58_4 = e1
% 241.96/48.46  | | 
% 241.96/48.46  | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (11), (12), (13), (15), (16),
% 241.96/48.46  | |            (18), (20) are inconsistent by sub-proof #1468.
% 241.96/48.46  | | 
% 241.96/48.46  | Case 2:
% 241.96/48.46  | | 
% 241.96/48.46  | |   (21)  all_58_5 = e1 & op(e2, e1) = e1
% 241.96/48.46  | | 
% 241.96/48.46  | | ALPHA: (21) implies:
% 241.96/48.46  | |   (22)  all_58_5 = e1
% 241.96/48.46  | | 
% 241.96/48.46  | | REF_CLOSE: (2), (3), (5), (7), (10), (14), (16), (17), (18), (22) are
% 241.96/48.46  | |            inconsistent by sub-proof #992.
% 241.96/48.46  | | 
% 241.96/48.46  | End of split
% 241.96/48.46  | 
% 241.96/48.46  End of proof
% 241.96/48.46  
% 241.96/48.46  Sub-proof #648 shows that the following formulas are inconsistent:
% 241.96/48.46  ----------------------------------------------------------------
% 241.96/48.46    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.96/48.46         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.96/48.46    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 241.96/48.46         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.96/48.46    (3)   ~ (e3 = e0)
% 241.96/48.46    (4)   ~ (e2 = e0)
% 241.96/48.46    (5)  op(e1, e2) = all_52_6
% 241.96/48.46    (6)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.96/48.46         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.96/48.46    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 241.96/48.46           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 241.96/48.46             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 241.96/48.46           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 241.96/48.46             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 241.96/48.46           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.96/48.46           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 241.96/48.46           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 241.96/48.46           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 241.96/48.46           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 241.96/48.46           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 241.96/48.46             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 241.96/48.46           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.96/48.46           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 241.96/48.46           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 241.96/48.46           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 241.96/48.46           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.96/48.46           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 241.96/48.46             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 241.96/48.46           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 241.96/48.46           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 241.96/48.46           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 241.96/48.46           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 241.96/48.46           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.96/48.46           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 241.96/48.46             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 241.96/48.46           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 241.96/48.46           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.96/48.46    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.96/48.46         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.96/48.46    (9)   ~ (all_52_7 = e3)
% 241.96/48.47    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.96/48.47          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.96/48.47    (11)   ~ (e3 = e1)
% 241.96/48.47    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.96/48.47          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.96/48.47    (13)  all_58_3 = e3
% 241.96/48.47    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.96/48.47          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.96/48.47    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.96/48.47          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.96/48.47    (16)  op(e3, e3) = e1
% 241.96/48.47    (17)   ~ (all_52_9 = e0)
% 241.96/48.47    (18)  op(e2, e1) = all_52_9
% 241.96/48.47    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.96/48.47          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.96/48.47    (20)   ~ (e3 = e2)
% 241.96/48.47    (21)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.96/48.47          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.96/48.47    (22)  all_56_31 = e0
% 241.96/48.47    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.96/48.47          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.96/48.47    (24)   ~ (all_52_9 = all_52_13)
% 241.96/48.47    (25)  op(e2, e3) = all_52_1
% 241.96/48.47    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.96/48.47          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.96/48.47    (27)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.96/48.47          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.96/48.47    (28)  op(e0, e2) = all_52_7
% 241.96/48.47    (29)   ~ (all_52_4 = e3)
% 241.96/48.47    (30)  op(e3, e2) = all_52_4
% 241.96/48.47    (31)   ~ (all_52_9 = e3)
% 241.96/48.47    (32)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.96/48.47          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.96/48.47    (33)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.96/48.47          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.96/48.47    (34)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.96/48.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.96/48.47    (35)  op(e0, e0) = e0
% 241.96/48.47    (36)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.96/48.47          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.96/48.47    (37)   ~ (all_52_6 = all_52_7)
% 241.96/48.47    (38)  all_56_11 = e3
% 241.96/48.47    (39)  op(e1, e1) = e0
% 241.96/48.47    (40)   ~ (e1 = e0)
% 241.96/48.47    (41)  all_58_15 = e0
% 241.96/48.47    (42)  op(e2, e0) = all_52_13
% 241.96/48.47    (43)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.96/48.47          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.96/48.47            e1)
% 241.96/48.47    (44)   ~ (all_52_1 = e3)
% 241.96/48.47    (45)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.96/48.47          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.96/48.47            e2)
% 241.96/48.47    (46)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.96/48.47          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.96/48.47    (47)  all_56_1 = e1
% 241.96/48.47    (48)   ~ (e2 = e1)
% 241.96/48.47    (49)   ~ (all_52_1 = e1)
% 241.96/48.47  
% 241.96/48.47  Begin of proof
% 241.96/48.47  | 
% 241.96/48.47  | BETA: splitting (7) gives:
% 241.96/48.47  | 
% 241.96/48.47  | Case 1:
% 241.96/48.47  | | 
% 241.96/48.47  | |   (50)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 241.96/48.47  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 241.96/48.47  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 241.96/48.47  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.96/48.47  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 241.96/48.47  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 241.96/48.47  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 241.96/48.47  | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 241.96/48.47  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.96/48.47  | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 241.96/48.47  | |           = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &
% 241.96/48.47  | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 241.96/48.47  | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 241.96/48.47  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 241.96/48.47  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 241.96/48.47  | | 
% 241.96/48.47  | | REF_CLOSE: (22), (25), (34), (38), (44), (47), (50) are inconsistent by
% 241.96/48.47  | |            sub-proof #744.
% 241.96/48.47  | | 
% 241.96/48.47  | Case 2:
% 241.96/48.47  | | 
% 241.96/48.47  | |   (51)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 241.96/48.47  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.96/48.47  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 241.96/48.47  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.96/48.47  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 241.96/48.47  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.96/48.47  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.96/48.47  | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 241.96/48.47  | |           e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 241.96/48.47  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 241.96/48.47  | |         (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.96/48.47  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.96/48.47  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 241.96/48.47  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 241.96/48.47  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.96/48.47  | | 
% 241.96/48.47  | | BETA: splitting (51) gives:
% 241.96/48.47  | | 
% 241.96/48.47  | | Case 1:
% 241.96/48.47  | | | 
% 241.96/48.47  | | |   (52)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 241.96/48.47  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.96/48.47  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 241.96/48.47  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 241.96/48.47  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 241.96/48.47  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.96/48.47  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.96/48.47  | | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 241.96/48.47  | | | 
% 241.96/48.47  | | | BETA: splitting (52) gives:
% 241.96/48.47  | | | 
% 241.96/48.47  | | | Case 1:
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | |   (53)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 241.96/48.47  | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.96/48.47  | | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | | ALPHA: (53) implies:
% 241.96/48.47  | | | |   (54)   ~ (all_56_1 = e1)
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | | REDUCE: (47), (54) imply:
% 241.96/48.47  | | | |   (55)  $false
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | | CLOSE: (55) is inconsistent.
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | Case 2:
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | |   (56)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.96/48.47  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.96/48.47  | | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 241.96/48.47  | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 241.96/48.47  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 &
% 241.96/48.47  | | | |           op(e0, e2) = e2)
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | | BETA: splitting (56) gives:
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | | Case 1:
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | |   (57)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 241.96/48.47  | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.96/48.47  | | | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | | ALPHA: (57) implies:
% 241.96/48.47  | | | | |   (58)   ~ (all_56_31 = e2)
% 241.96/48.47  | | | | |   (59)   ~ (all_56_11 = e2)
% 241.96/48.47  | | | | |   (60)   ~ (all_56_1 = e2)
% 241.96/48.47  | | | | |   (61)  op(e1, e2) = e1
% 241.96/48.47  | | | | |   (62)  op(e2, e1) = e1
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | | REDUCE: (47), (60) imply:
% 241.96/48.47  | | | | |   (63)   ~ (e2 = e1)
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | | REDUCE: (22), (58) imply:
% 241.96/48.47  | | | | |   (64)   ~ (e2 = e0)
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | | BETA: splitting (8) gives:
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | | Case 1:
% 241.96/48.47  | | | | | | 
% 241.96/48.47  | | | | | |   (65)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 241.96/48.47  | | | | | |             e2) = e0)
% 241.96/48.47  | | | | | | 
% 241.96/48.47  | | | | | | BETA: splitting (65) gives:
% 241.96/48.47  | | | | | | 
% 241.96/48.47  | | | | | | Case 1:
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | |   (66)  all_58_1 = e0 & op(e3, e2) = e0
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | ALPHA: (66) implies:
% 241.96/48.47  | | | | | | |   (67)  op(e3, e2) = e0
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | GROUND_INST: instantiating (34) with all_52_6, e1, e2, e1,
% 241.96/48.47  | | | | | | |              simplifying with (5), (61) gives:
% 241.96/48.47  | | | | | | |   (68)  all_52_6 = e1
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | GROUND_INST: instantiating (34) with all_52_9, e1, e1, e2,
% 241.96/48.47  | | | | | | |              simplifying with (18), (62) gives:
% 241.96/48.47  | | | | | | |   (69)  all_52_9 = e1
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | GROUND_INST: instantiating (34) with all_52_4, e0, e2, e3,
% 241.96/48.47  | | | | | | |              simplifying with (30), (67) gives:
% 241.96/48.47  | | | | | | |   (70)  all_52_4 = e0
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | REDUCE: (29), (70) imply:
% 241.96/48.47  | | | | | | |   (71)   ~ (e3 = e0)
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | REDUCE: (37), (68) imply:
% 241.96/48.47  | | | | | | |   (72)   ~ (all_52_7 = e1)
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | SIMP: (72) implies:
% 241.96/48.47  | | | | | | |   (73)   ~ (all_52_7 = e1)
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | REDUCE: (24), (69) imply:
% 241.96/48.47  | | | | | | |   (74)   ~ (all_52_13 = e1)
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | SIMP: (74) implies:
% 241.96/48.47  | | | | | | |   (75)   ~ (all_52_13 = e1)
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | REDUCE: (31), (69) imply:
% 241.96/48.47  | | | | | | |   (76)   ~ (e3 = e1)
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | REF_CLOSE: (1), (3), (4), (11), (12), (13), (14), (15), (16),
% 241.96/48.47  | | | | | | |            (18), (19), (20), (21), (23), (25), (26), (27), (28),
% 241.96/48.47  | | | | | | |            (29), (30), (31), (34), (35), (39), (40), (42), (43),
% 241.96/48.47  | | | | | | |            (44), (46), (48), (49), (73), (75) are inconsistent by
% 241.96/48.47  | | | | | | |            sub-proof #656.
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | Case 2:
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | |   (77)  all_58_3 = e0 & op(e2, e2) = e0
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | REF_CLOSE: (3), (13), (77) are inconsistent by sub-proof #1719.
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | End of split
% 241.96/48.47  | | | | | | 
% 241.96/48.47  | | | | | Case 2:
% 241.96/48.47  | | | | | | 
% 241.96/48.47  | | | | | |   (78)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0,
% 241.96/48.47  | | | | | |             e2) = e0)
% 241.96/48.47  | | | | | | 
% 241.96/48.47  | | | | | | BETA: splitting (78) gives:
% 241.96/48.47  | | | | | | 
% 241.96/48.47  | | | | | | Case 1:
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | |   (79)  all_58_7 = e0 & op(e1, e2) = e0
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | ALPHA: (79) implies:
% 241.96/48.47  | | | | | | |   (80)  op(e1, e2) = e0
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | REF_CLOSE: (5), (34), (40), (61), (80) are inconsistent by
% 241.96/48.47  | | | | | | |            sub-proof #2136.
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | Case 2:
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | |   (81)  all_58_13 = e0 & op(e0, e2) = e0
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | ALPHA: (81) implies:
% 241.96/48.47  | | | | | | |   (82)  all_58_13 = e0
% 241.96/48.47  | | | | | | |   (83)  op(e0, e2) = e0
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | BETA: splitting (43) gives:
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | | Case 1:
% 241.96/48.47  | | | | | | | | 
% 241.96/48.47  | | | | | | | |   (84)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 241.96/48.47  | | | | | | | |           op(e0, e2) = e1)
% 241.96/48.47  | | | | | | | | 
% 241.96/48.47  | | | | | | | | BETA: splitting (84) gives:
% 241.96/48.47  | | | | | | | | 
% 241.96/48.47  | | | | | | | | Case 1:
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | |   (85)  all_58_12 = e1 & op(e0, e3) = e1
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | | ALPHA: (85) implies:
% 241.96/48.47  | | | | | | | | |   (86)  all_58_12 = e1
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | | REF_CLOSE: (3), (4), (11), (15), (16), (19), (20), (23), (25),
% 241.96/48.47  | | | | | | | | |            (34), (40), (44), (48), (86) are inconsistent by
% 241.96/48.47  | | | | | | | | |            sub-proof #1204.
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | Case 2:
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | |   (87)  all_58_13 = e1 & op(e0, e2) = e1
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | | ALPHA: (87) implies:
% 241.96/48.47  | | | | | | | | |   (88)  all_58_13 = e1
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | | COMBINE_EQS: (82), (88) imply:
% 241.96/48.47  | | | | | | | | |   (89)  e1 = e0
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | | REDUCE: (40), (89) imply:
% 241.96/48.47  | | | | | | | | |   (90)  $false
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | | CLOSE: (90) is inconsistent.
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | End of split
% 241.96/48.47  | | | | | | | | 
% 241.96/48.47  | | | | | | | Case 2:
% 241.96/48.47  | | | | | | | | 
% 241.96/48.47  | | | | | | | |   (91)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 241.96/48.47  | | | | | | | |           op(e0, e0) = e1)
% 241.96/48.47  | | | | | | | | 
% 241.96/48.47  | | | | | | | | BETA: splitting (91) gives:
% 241.96/48.47  | | | | | | | | 
% 241.96/48.47  | | | | | | | | Case 1:
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | |   (92)  all_58_14 = e1 & op(e0, e1) = e1
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | | ALPHA: (92) implies:
% 241.96/48.47  | | | | | | | | |   (93)  all_58_14 = e1
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | | REF_CLOSE: (2), (3), (4), (9), (11), (20), (28), (34), (41),
% 241.96/48.47  | | | | | | | | |            (45), (48), (83), (93) are inconsistent by
% 241.96/48.47  | | | | | | | | |            sub-proof #760.
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | Case 2:
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | |   (94)  all_58_15 = e1 & op(e0, e0) = e1
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | | ALPHA: (94) implies:
% 241.96/48.47  | | | | | | | | |   (95)  op(e0, e0) = e1
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | | REF_CLOSE: (34), (35), (40), (95) are inconsistent by
% 241.96/48.47  | | | | | | | | |            sub-proof #2274.
% 241.96/48.47  | | | | | | | | | 
% 241.96/48.47  | | | | | | | | End of split
% 241.96/48.47  | | | | | | | | 
% 241.96/48.47  | | | | | | | End of split
% 241.96/48.47  | | | | | | | 
% 241.96/48.47  | | | | | | End of split
% 241.96/48.47  | | | | | | 
% 241.96/48.47  | | | | | End of split
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | Case 2:
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | |   (96)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 241.96/48.47  | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 241.96/48.47  | | | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | | ALPHA: (96) implies:
% 241.96/48.47  | | | | |   (97)   ~ (all_56_31 = e0)
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | | REDUCE: (22), (97) imply:
% 241.96/48.47  | | | | |   (98)  $false
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | | CLOSE: (98) is inconsistent.
% 241.96/48.47  | | | | | 
% 241.96/48.47  | | | | End of split
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | End of split
% 241.96/48.47  | | | 
% 241.96/48.47  | | Case 2:
% 241.96/48.47  | | | 
% 241.96/48.47  | | |   (99)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 241.96/48.47  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.96/48.47  | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29
% 241.96/48.47  | | |           = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 241.96/48.47  | | |             = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 241.96/48.47  | | |           e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 241.96/48.47  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 241.96/48.47  | | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 241.96/48.47  | | | 
% 241.96/48.47  | | | BETA: splitting (99) gives:
% 241.96/48.47  | | | 
% 241.96/48.47  | | | Case 1:
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | |   (100)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 241.96/48.47  | | | |          (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 241.96/48.47  | | | |          op(e2, e0) = e0 & op(e0, e2) = e0
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | | ALPHA: (100) implies:
% 241.96/48.47  | | | |   (101)  op(e2, e0) = e0
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | | REF_CLOSE: (1), (3), (4), (6), (10), (11), (13), (14), (16), (20), (25),
% 241.96/48.47  | | | |            (26), (29), (30), (32), (33), (34), (35), (36), (40), (41),
% 241.96/48.47  | | | |            (42), (46), (48), (49), (101) are inconsistent by sub-proof
% 241.96/48.47  | | | |            #649.
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | Case 2:
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | |   (102)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 241.96/48.47  | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 241.96/48.47  | | | |            & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 241.96/48.47  | | | |            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 241.96/48.47  | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 &
% 241.96/48.47  | | | |            op(e0, e1) = e0)
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | | REF_CLOSE: (22), (47), (102) are inconsistent by sub-proof #743.
% 241.96/48.47  | | | | 
% 241.96/48.47  | | | End of split
% 241.96/48.47  | | | 
% 241.96/48.47  | | End of split
% 241.96/48.47  | | 
% 241.96/48.47  | End of split
% 241.96/48.47  | 
% 241.96/48.47  End of proof
% 241.96/48.47  
% 241.96/48.47  Sub-proof #649 shows that the following formulas are inconsistent:
% 241.96/48.47  ----------------------------------------------------------------
% 241.96/48.48    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.96/48.48         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.96/48.48    (2)   ~ (e3 = e0)
% 241.96/48.48    (3)   ~ (e2 = e0)
% 241.96/48.48    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.96/48.48         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.96/48.48    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.96/48.48         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.96/48.48    (6)   ~ (e3 = e1)
% 241.96/48.48    (7)  all_58_3 = e3
% 241.96/48.48    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.96/48.48         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.96/48.48    (9)  op(e3, e3) = e1
% 241.96/48.48    (10)   ~ (e3 = e2)
% 241.96/48.48    (11)  op(e2, e0) = e0
% 241.96/48.48    (12)  op(e2, e3) = all_52_1
% 241.96/48.48    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.96/48.48          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.96/48.48    (14)   ~ (all_52_4 = e3)
% 241.96/48.48    (15)  op(e3, e2) = all_52_4
% 241.96/48.48    (16)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.96/48.48          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.96/48.48    (17)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.96/48.48          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.96/48.48    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.96/48.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.96/48.48    (19)  op(e0, e0) = e0
% 241.96/48.48    (20)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.96/48.48          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.96/48.48    (21)   ~ (e1 = e0)
% 241.96/48.48    (22)  all_58_15 = e0
% 241.96/48.48    (23)  op(e2, e0) = all_52_13
% 241.96/48.48    (24)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.96/48.48          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.96/48.48    (25)   ~ (e2 = e1)
% 241.96/48.48    (26)   ~ (all_52_1 = e1)
% 241.96/48.48  
% 241.96/48.48  Begin of proof
% 241.96/48.48  | 
% 241.96/48.48  | BETA: splitting (24) gives:
% 241.96/48.48  | 
% 241.96/48.48  | Case 1:
% 241.96/48.48  | | 
% 241.96/48.48  | |   (27)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 241.96/48.48  | |           e1)
% 241.96/48.48  | | 
% 241.96/48.48  | | BETA: splitting (27) gives:
% 241.96/48.48  | | 
% 241.96/48.48  | | Case 1:
% 241.96/48.48  | | | 
% 241.96/48.48  | | |   (28)  all_58_2 = e1 & op(e2, e3) = e1
% 241.96/48.48  | | | 
% 241.96/48.48  | | | REF_CLOSE: (12), (18), (26), (28) are inconsistent by sub-proof #2229.
% 241.96/48.48  | | | 
% 241.96/48.48  | | Case 2:
% 241.96/48.48  | | | 
% 241.96/48.48  | | |   (29)  all_58_3 = e1 & op(e2, e2) = e1
% 241.96/48.48  | | | 
% 241.96/48.48  | | | REF_CLOSE: (6), (7), (29) are inconsistent by sub-proof #2197.
% 241.96/48.48  | | | 
% 241.96/48.48  | | End of split
% 241.96/48.48  | | 
% 241.96/48.48  | Case 2:
% 241.96/48.48  | | 
% 241.96/48.48  | |   (30)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 241.96/48.48  | |           e1)
% 241.96/48.48  | | 
% 241.96/48.48  | | BETA: splitting (30) gives:
% 241.96/48.48  | | 
% 241.96/48.48  | | Case 1:
% 241.96/48.48  | | | 
% 241.96/48.48  | | |   (31)  all_58_5 = e1 & op(e2, e1) = e1
% 241.96/48.48  | | | 
% 241.96/48.48  | | | ALPHA: (31) implies:
% 241.96/48.48  | | |   (32)  all_58_5 = e1
% 241.96/48.48  | | | 
% 241.96/48.48  | | | BETA: splitting (4) gives:
% 241.96/48.48  | | | 
% 241.96/48.48  | | | Case 1:
% 241.96/48.48  | | | | 
% 241.96/48.48  | | | |   (33)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 241.96/48.48  | | | |           = e1)
% 241.96/48.48  | | | | 
% 241.96/48.48  | | | | BETA: splitting (33) gives:
% 241.96/48.48  | | | | 
% 241.96/48.48  | | | | Case 1:
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | |   (34)  all_58_9 = e1 & op(e3, e0) = e1
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | | ALPHA: (34) implies:
% 241.96/48.48  | | | | |   (35)  all_58_9 = e1
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13),
% 241.96/48.48  | | | | |            (14), (15), (16), (17), (18), (19), (21), (22), (25), (32),
% 241.96/48.48  | | | | |            (35) are inconsistent by sub-proof #654.
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | Case 2:
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | |   (36)  all_58_10 = e1 & op(e2, e0) = e1
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | | ALPHA: (36) implies:
% 241.96/48.48  | | | | |   (37)  all_58_10 = e1
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | | REF_CLOSE: (2), (3), (5), (7), (10), (17), (21), (25), (32), (37) are
% 241.96/48.48  | | | | |            inconsistent by sub-proof #992.
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | End of split
% 241.96/48.48  | | | | 
% 241.96/48.48  | | | Case 2:
% 241.96/48.48  | | | | 
% 241.96/48.48  | | | |   (38)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 241.96/48.48  | | | |             e0) = e1)
% 241.96/48.48  | | | | 
% 241.96/48.48  | | | | BETA: splitting (38) gives:
% 241.96/48.48  | | | | 
% 241.96/48.48  | | | | Case 1:
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | |   (39)  all_58_11 = e1 & op(e1, e0) = e1
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | | ALPHA: (39) implies:
% 241.96/48.48  | | | | |   (40)  all_58_11 = e1
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | | BETA: splitting (20) gives:
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | | Case 1:
% 241.96/48.48  | | | | | | 
% 241.96/48.48  | | | | | |   (41)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 241.96/48.48  | | | | | |             e0) = e2)
% 241.96/48.48  | | | | | | 
% 241.96/48.48  | | | | | | BETA: splitting (41) gives:
% 241.96/48.48  | | | | | | 
% 241.96/48.48  | | | | | | Case 1:
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | |   (42)  all_58_9 = e2 & op(e3, e0) = e2
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | | ALPHA: (42) implies:
% 241.96/48.48  | | | | | | |   (43)  op(e3, e0) = e2
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | | BETA: splitting (8) gives:
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | | Case 1:
% 241.96/48.48  | | | | | | | | 
% 241.96/48.48  | | | | | | | |   (44)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 241.96/48.48  | | | | | | | |           op(e3, e2) = e3)
% 241.96/48.48  | | | | | | | | 
% 241.96/48.48  | | | | | | | | REF_CLOSE: (6), (9), (14), (15), (18), (44) are inconsistent by
% 241.96/48.48  | | | | | | | |            sub-proof #1401.
% 241.96/48.48  | | | | | | | | 
% 241.96/48.48  | | | | | | | Case 2:
% 241.96/48.48  | | | | | | | | 
% 241.96/48.48  | | | | | | | |   (45)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 241.96/48.48  | | | | | | | |           op(e3, e0) = e3)
% 241.96/48.48  | | | | | | | | 
% 241.96/48.48  | | | | | | | | BETA: splitting (45) gives:
% 241.96/48.48  | | | | | | | | 
% 241.96/48.48  | | | | | | | | Case 1:
% 241.96/48.48  | | | | | | | | | 
% 241.96/48.48  | | | | | | | | |   (46)  all_58_4 = e3 & op(e3, e1) = e3
% 241.96/48.48  | | | | | | | | | 
% 241.96/48.48  | | | | | | | | | ALPHA: (46) implies:
% 241.96/48.48  | | | | | | | | |   (47)  all_58_4 = e3
% 241.96/48.48  | | | | | | | | | 
% 241.96/48.48  | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12),
% 241.96/48.48  | | | | | | | | |            (13), (14), (15), (16), (17), (18), (21), (22),
% 241.96/48.48  | | | | | | | | |            (24), (25), (26), (40), (43), (47) are inconsistent
% 241.96/48.48  | | | | | | | | |            by sub-proof #650.
% 241.96/48.48  | | | | | | | | | 
% 241.96/48.48  | | | | | | | | Case 2:
% 241.96/48.48  | | | | | | | | | 
% 241.96/48.48  | | | | | | | | |   (48)  all_58_9 = e3 & op(e3, e0) = e3
% 241.96/48.48  | | | | | | | | | 
% 241.96/48.48  | | | | | | | | | ALPHA: (48) implies:
% 241.96/48.48  | | | | | | | | |   (49)  op(e3, e0) = e3
% 241.96/48.48  | | | | | | | | | 
% 241.96/48.48  | | | | | | | | | REF_CLOSE: (10), (18), (43), (49) are inconsistent by
% 241.96/48.48  | | | | | | | | |            sub-proof #2125.
% 241.96/48.48  | | | | | | | | | 
% 241.96/48.48  | | | | | | | | End of split
% 241.96/48.48  | | | | | | | | 
% 241.96/48.48  | | | | | | | End of split
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | Case 2:
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | |   (50)  all_58_10 = e2 & op(e2, e0) = e2
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | | ALPHA: (50) implies:
% 241.96/48.48  | | | | | | |   (51)  op(e2, e0) = e2
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | | REF_CLOSE: (3), (11), (18), (51) are inconsistent by sub-proof
% 241.96/48.48  | | | | | | |            #2121.
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | End of split
% 241.96/48.48  | | | | | | 
% 241.96/48.48  | | | | | Case 2:
% 241.96/48.48  | | | | | | 
% 241.96/48.48  | | | | | |   (52)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 241.96/48.48  | | | | | |           op(e0, e0) = e2)
% 241.96/48.48  | | | | | | 
% 241.96/48.48  | | | | | | BETA: splitting (52) gives:
% 241.96/48.48  | | | | | | 
% 241.96/48.48  | | | | | | Case 1:
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | |   (53)  all_58_11 = e2 & op(e1, e0) = e2
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | | ALPHA: (53) implies:
% 241.96/48.48  | | | | | | |   (54)  all_58_11 = e2
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | | REF_CLOSE: (25), (40), (54) are inconsistent by sub-proof #1020.
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | Case 2:
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | |   (55)  all_58_15 = e2 & op(e0, e0) = e2
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | | REF_CLOSE: (3), (22), (55) are inconsistent by sub-proof #1654.
% 241.96/48.48  | | | | | | | 
% 241.96/48.48  | | | | | | End of split
% 241.96/48.48  | | | | | | 
% 241.96/48.48  | | | | | End of split
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | Case 2:
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | |   (56)  all_58_15 = e1 & op(e0, e0) = e1
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | | ALPHA: (56) implies:
% 241.96/48.48  | | | | |   (57)  op(e0, e0) = e1
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | | REF_CLOSE: (18), (19), (21), (57) are inconsistent by sub-proof #2274.
% 241.96/48.48  | | | | | 
% 241.96/48.48  | | | | End of split
% 241.96/48.48  | | | | 
% 241.96/48.48  | | | End of split
% 241.96/48.48  | | | 
% 241.96/48.48  | | Case 2:
% 241.96/48.48  | | | 
% 241.96/48.48  | | |   (58)  all_58_10 = e1 & op(e2, e0) = e1
% 241.96/48.48  | | | 
% 241.96/48.48  | | | ALPHA: (58) implies:
% 241.96/48.48  | | |   (59)  op(e2, e0) = e1
% 241.96/48.48  | | | 
% 241.96/48.48  | | | REF_CLOSE: (11), (18), (21), (23), (59) are inconsistent by sub-proof
% 241.96/48.48  | | |            #1778.
% 241.96/48.48  | | | 
% 241.96/48.48  | | End of split
% 241.96/48.48  | | 
% 241.96/48.48  | End of split
% 241.96/48.48  | 
% 241.96/48.48  End of proof
% 241.96/48.48  
% 241.96/48.48  Sub-proof #650 shows that the following formulas are inconsistent:
% 241.96/48.48  ----------------------------------------------------------------
% 241.96/48.48    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.96/48.48         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.96/48.48    (2)   ~ (e3 = e0)
% 241.96/48.48    (3)   ~ (e2 = e0)
% 241.96/48.48    (4)  all_58_11 = e1
% 241.96/48.48    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.96/48.48         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.96/48.48    (6)   ~ (e3 = e1)
% 241.96/48.48    (7)  all_58_3 = e3
% 241.96/48.48    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.96/48.48         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.96/48.48    (9)  op(e3, e3) = e1
% 241.96/48.48    (10)   ~ (e3 = e2)
% 241.96/48.48    (11)  op(e2, e3) = all_52_1
% 241.96/48.48    (12)  op(e3, e0) = e2
% 241.96/48.48    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.96/48.48          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.96/48.48    (14)   ~ (all_52_4 = e3)
% 241.96/48.48    (15)  op(e3, e2) = all_52_4
% 241.96/48.48    (16)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.96/48.48          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.99/48.48    (17)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.99/48.48          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.99/48.48    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.48    (19)   ~ (e1 = e0)
% 241.99/48.48    (20)  all_58_4 = e3
% 241.99/48.48    (21)  all_58_15 = e0
% 241.99/48.48    (22)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.99/48.48          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.99/48.48    (23)   ~ (e2 = e1)
% 241.99/48.48    (24)   ~ (all_52_1 = e1)
% 241.99/48.48  
% 241.99/48.48  Begin of proof
% 241.99/48.48  | 
% 241.99/48.48  | BETA: splitting (16) gives:
% 241.99/48.48  | 
% 241.99/48.48  | Case 1:
% 241.99/48.48  | | 
% 241.99/48.48  | |   (25)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 241.99/48.48  | |           e3)
% 241.99/48.48  | | 
% 241.99/48.48  | | BETA: splitting (25) gives:
% 241.99/48.48  | | 
% 241.99/48.48  | | Case 1:
% 241.99/48.48  | | | 
% 241.99/48.48  | | |   (26)  all_58_9 = e3 & op(e3, e0) = e3
% 241.99/48.48  | | | 
% 241.99/48.48  | | | ALPHA: (26) implies:
% 241.99/48.48  | | |   (27)  op(e3, e0) = e3
% 241.99/48.48  | | | 
% 241.99/48.48  | | | REF_CLOSE: (10), (12), (18), (27) are inconsistent by sub-proof #2125.
% 241.99/48.48  | | | 
% 241.99/48.48  | | Case 2:
% 241.99/48.48  | | | 
% 241.99/48.48  | | |   (28)  all_58_10 = e3 & op(e2, e0) = e3
% 241.99/48.48  | | | 
% 241.99/48.48  | | | ALPHA: (28) implies:
% 241.99/48.48  | | |   (29)  all_58_10 = e3
% 241.99/48.48  | | | 
% 241.99/48.48  | | | BETA: splitting (8) gives:
% 241.99/48.48  | | | 
% 241.99/48.48  | | | Case 1:
% 241.99/48.48  | | | | 
% 241.99/48.48  | | | |   (30)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 241.99/48.48  | | | |           = e3)
% 241.99/48.48  | | | | 
% 241.99/48.48  | | | | REF_CLOSE: (6), (9), (14), (15), (18), (30) are inconsistent by
% 241.99/48.48  | | | |            sub-proof #1401.
% 241.99/48.48  | | | | 
% 241.99/48.48  | | | Case 2:
% 241.99/48.48  | | | | 
% 241.99/48.48  | | | |   (31)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 241.99/48.48  | | | |           = e3)
% 241.99/48.48  | | | | 
% 241.99/48.48  | | | | BETA: splitting (31) gives:
% 241.99/48.48  | | | | 
% 241.99/48.48  | | | | Case 1:
% 241.99/48.48  | | | | | 
% 241.99/48.48  | | | | |   (32)  all_58_4 = e3 & op(e3, e1) = e3
% 241.99/48.48  | | | | | 
% 241.99/48.48  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (13),
% 241.99/48.48  | | | | |            (14), (15), (17), (18), (19), (20), (22), (23), (24), (29)
% 241.99/48.48  | | | | |            are inconsistent by sub-proof #653.
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | Case 2:
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | |   (33)  all_58_9 = e3 & op(e3, e0) = e3
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | ALPHA: (33) implies:
% 241.99/48.49  | | | | |   (34)  op(e3, e0) = e3
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | REF_CLOSE: (10), (12), (18), (34) are inconsistent by sub-proof #2125.
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | End of split
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | End of split
% 241.99/48.49  | | | 
% 241.99/48.49  | | End of split
% 241.99/48.49  | | 
% 241.99/48.49  | Case 2:
% 241.99/48.49  | | 
% 241.99/48.49  | |   (35)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 241.99/48.49  | |           e3)
% 241.99/48.49  | | 
% 241.99/48.49  | | BETA: splitting (35) gives:
% 241.99/48.49  | | 
% 241.99/48.49  | | Case 1:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (36)  all_58_11 = e3 & op(e1, e0) = e3
% 241.99/48.49  | | | 
% 241.99/48.49  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (13), (14), (15),
% 241.99/48.49  | | |            (18), (19), (20), (23), (36) are inconsistent by sub-proof
% 241.99/48.49  | | |            #652.
% 241.99/48.49  | | | 
% 241.99/48.49  | | Case 2:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (37)  all_58_15 = e3 & op(e0, e0) = e3
% 241.99/48.49  | | | 
% 241.99/48.49  | | | ALPHA: (37) implies:
% 241.99/48.49  | | |   (38)  all_58_15 = e3
% 241.99/48.49  | | | 
% 241.99/48.49  | | | REF_CLOSE: (2), (6), (8), (9), (10), (12), (14), (15), (18), (20), (21),
% 241.99/48.49  | | |            (38) are inconsistent by sub-proof #651.
% 241.99/48.49  | | | 
% 241.99/48.49  | | End of split
% 241.99/48.49  | | 
% 241.99/48.49  | End of split
% 241.99/48.49  | 
% 241.99/48.49  End of proof
% 241.99/48.49  
% 241.99/48.49  Sub-proof #651 shows that the following formulas are inconsistent:
% 241.99/48.49  ----------------------------------------------------------------
% 241.99/48.49    (1)   ~ (e3 = e0)
% 241.99/48.49    (2)  all_58_15 = e3
% 241.99/48.49    (3)   ~ (e3 = e1)
% 241.99/48.49    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.99/48.49         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.99/48.49    (5)  op(e3, e3) = e1
% 241.99/48.49    (6)   ~ (e3 = e2)
% 241.99/48.49    (7)  op(e3, e0) = e2
% 241.99/48.49    (8)   ~ (all_52_4 = e3)
% 241.99/48.49    (9)  op(e3, e2) = all_52_4
% 241.99/48.49    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.49    (11)  all_58_4 = e3
% 241.99/48.49    (12)  all_58_15 = e0
% 241.99/48.49  
% 241.99/48.49  Begin of proof
% 241.99/48.49  | 
% 241.99/48.49  | COMBINE_EQS: (2), (12) imply:
% 241.99/48.49  |   (13)  e3 = e0
% 241.99/48.49  | 
% 241.99/48.49  | SIMP: (13) implies:
% 241.99/48.49  |   (14)  e3 = e0
% 241.99/48.49  | 
% 241.99/48.49  | COMBINE_EQS: (11), (14) imply:
% 241.99/48.49  |   (15)  all_58_4 = e0
% 241.99/48.49  | 
% 241.99/48.49  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (15) are inconsistent
% 241.99/48.49  |            by sub-proof #1400.
% 241.99/48.49  | 
% 241.99/48.49  End of proof
% 241.99/48.49  
% 241.99/48.49  Sub-proof #652 shows that the following formulas are inconsistent:
% 241.99/48.49  ----------------------------------------------------------------
% 241.99/48.49    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.99/48.49         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.99/48.49    (2)   ~ (e3 = e0)
% 241.99/48.49    (3)   ~ (e2 = e0)
% 241.99/48.49    (4)  all_58_11 = e1
% 241.99/48.49    (5)   ~ (e3 = e1)
% 241.99/48.49    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.99/48.49         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.99/48.49    (7)  op(e3, e3) = e1
% 241.99/48.49    (8)   ~ (e3 = e2)
% 241.99/48.49    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.99/48.49         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.49    (10)  all_58_11 = e3 & op(e1, e0) = e3
% 241.99/48.49    (11)   ~ (all_52_4 = e3)
% 241.99/48.49    (12)  op(e3, e2) = all_52_4
% 241.99/48.49    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.49    (14)   ~ (e1 = e0)
% 241.99/48.49    (15)  all_58_4 = e3
% 241.99/48.49    (16)   ~ (e2 = e1)
% 241.99/48.49  
% 241.99/48.49  Begin of proof
% 241.99/48.49  | 
% 241.99/48.49  | ALPHA: (10) implies:
% 241.99/48.49  |   (17)  all_58_11 = e3
% 241.99/48.49  | 
% 241.99/48.49  | COMBINE_EQS: (4), (17) imply:
% 241.99/48.49  |   (18)  e3 = e1
% 241.99/48.49  | 
% 241.99/48.49  | COMBINE_EQS: (15), (18) imply:
% 241.99/48.49  |   (19)  all_58_4 = e1
% 241.99/48.49  | 
% 241.99/48.49  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 241.99/48.49  |            (16), (19) are inconsistent by sub-proof #1468.
% 241.99/48.49  | 
% 241.99/48.49  End of proof
% 241.99/48.49  
% 241.99/48.49  Sub-proof #653 shows that the following formulas are inconsistent:
% 241.99/48.49  ----------------------------------------------------------------
% 241.99/48.49    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.99/48.49         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.99/48.49    (2)  all_58_10 = e3
% 241.99/48.49    (3)   ~ (e3 = e0)
% 241.99/48.49    (4)   ~ (e2 = e0)
% 241.99/48.49    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.99/48.49         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.99/48.49    (6)   ~ (e3 = e1)
% 241.99/48.49    (7)  all_58_3 = e3
% 241.99/48.49    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.99/48.49         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.99/48.49    (9)  op(e3, e3) = e1
% 241.99/48.49    (10)   ~ (e3 = e2)
% 241.99/48.49    (11)  op(e2, e3) = all_52_1
% 241.99/48.49    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.99/48.49          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.49    (13)   ~ (all_52_4 = e3)
% 241.99/48.49    (14)  op(e3, e2) = all_52_4
% 241.99/48.49    (15)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.99/48.49          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.99/48.49    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.49    (17)   ~ (e1 = e0)
% 241.99/48.49    (18)  all_58_4 = e3
% 241.99/48.49    (19)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.99/48.49          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.99/48.49    (20)   ~ (e2 = e1)
% 241.99/48.49    (21)   ~ (all_52_1 = e1)
% 241.99/48.49  
% 241.99/48.49  Begin of proof
% 241.99/48.49  | 
% 241.99/48.49  | BETA: splitting (19) gives:
% 241.99/48.49  | 
% 241.99/48.49  | Case 1:
% 241.99/48.49  | | 
% 241.99/48.49  | |   (22)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 241.99/48.49  | |           e1)
% 241.99/48.49  | | 
% 241.99/48.49  | | BETA: splitting (22) gives:
% 241.99/48.49  | | 
% 241.99/48.49  | | Case 1:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (23)  all_58_2 = e1 & op(e2, e3) = e1
% 241.99/48.49  | | | 
% 241.99/48.49  | | | REF_CLOSE: (11), (16), (21), (23) are inconsistent by sub-proof #2229.
% 241.99/48.49  | | | 
% 241.99/48.49  | | Case 2:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (24)  all_58_3 = e1 & op(e2, e2) = e1
% 241.99/48.49  | | | 
% 241.99/48.49  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14),
% 241.99/48.49  | | |            (16), (17), (18), (20), (24) are inconsistent by sub-proof
% 241.99/48.49  | | |            #1030.
% 241.99/48.49  | | | 
% 241.99/48.49  | | End of split
% 241.99/48.49  | | 
% 241.99/48.49  | Case 2:
% 241.99/48.49  | | 
% 241.99/48.49  | |   (25)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 241.99/48.49  | |           e1)
% 241.99/48.49  | | 
% 241.99/48.49  | | BETA: splitting (25) gives:
% 241.99/48.49  | | 
% 241.99/48.49  | | Case 1:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (26)  all_58_5 = e1 & op(e2, e1) = e1
% 241.99/48.49  | | | 
% 241.99/48.49  | | | ALPHA: (26) implies:
% 241.99/48.49  | | |   (27)  all_58_5 = e1
% 241.99/48.49  | | | 
% 241.99/48.49  | | | REF_CLOSE: (2), (3), (4), (5), (7), (10), (15), (17), (20), (27) are
% 241.99/48.49  | | |            inconsistent by sub-proof #1101.
% 241.99/48.49  | | | 
% 241.99/48.49  | | Case 2:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (28)  all_58_10 = e1 & op(e2, e0) = e1
% 241.99/48.49  | | | 
% 241.99/48.49  | | | ALPHA: (28) implies:
% 241.99/48.49  | | |   (29)  all_58_10 = e1
% 241.99/48.49  | | | 
% 241.99/48.49  | | | COMBINE_EQS: (2), (29) imply:
% 241.99/48.49  | | |   (30)  e3 = e1
% 241.99/48.49  | | | 
% 241.99/48.49  | | | COMBINE_EQS: (18), (30) imply:
% 241.99/48.49  | | |   (31)  all_58_4 = e1
% 241.99/48.49  | | | 
% 241.99/48.49  | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (12), (13), (14), (16),
% 241.99/48.49  | | |            (17), (20), (31) are inconsistent by sub-proof #1468.
% 241.99/48.49  | | | 
% 241.99/48.49  | | End of split
% 241.99/48.49  | | 
% 241.99/48.49  | End of split
% 241.99/48.49  | 
% 241.99/48.49  End of proof
% 241.99/48.49  
% 241.99/48.49  Sub-proof #654 shows that the following formulas are inconsistent:
% 241.99/48.49  ----------------------------------------------------------------
% 241.99/48.49    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.99/48.49         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.99/48.49    (2)   ~ (e3 = e0)
% 241.99/48.49    (3)   ~ (e2 = e0)
% 241.99/48.49    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.99/48.49         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.99/48.49    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.99/48.49         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.99/48.49    (6)   ~ (e3 = e1)
% 241.99/48.49    (7)  all_58_3 = e3
% 241.99/48.49    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.99/48.49         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.99/48.49    (9)  op(e3, e3) = e1
% 241.99/48.49    (10)   ~ (e3 = e2)
% 241.99/48.49    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.99/48.49          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.49    (12)   ~ (all_52_4 = e3)
% 241.99/48.49    (13)  op(e3, e2) = all_52_4
% 241.99/48.49    (14)  all_58_5 = e1
% 241.99/48.49    (15)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.99/48.49          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.99/48.49    (16)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.99/48.49          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.99/48.49    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.49    (18)  op(e0, e0) = e0
% 241.99/48.49    (19)   ~ (e1 = e0)
% 241.99/48.49    (20)  all_58_9 = e1
% 241.99/48.49    (21)  all_58_15 = e0
% 241.99/48.49    (22)   ~ (e2 = e1)
% 241.99/48.49  
% 241.99/48.49  Begin of proof
% 241.99/48.49  | 
% 241.99/48.49  | BETA: splitting (8) gives:
% 241.99/48.49  | 
% 241.99/48.49  | Case 1:
% 241.99/48.49  | | 
% 241.99/48.49  | |   (23)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 241.99/48.49  | |           e3)
% 241.99/48.49  | | 
% 241.99/48.49  | | REF_CLOSE: (6), (9), (12), (13), (17), (23) are inconsistent by sub-proof
% 241.99/48.49  | |            #1401.
% 241.99/48.49  | | 
% 241.99/48.49  | Case 2:
% 241.99/48.49  | | 
% 241.99/48.49  | |   (24)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 241.99/48.49  | |           e3)
% 241.99/48.49  | | 
% 241.99/48.49  | | BETA: splitting (24) gives:
% 241.99/48.49  | | 
% 241.99/48.49  | | Case 1:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (25)  all_58_4 = e3 & op(e3, e1) = e3
% 241.99/48.49  | | | 
% 241.99/48.49  | | | ALPHA: (25) implies:
% 241.99/48.49  | | |   (26)  all_58_4 = e3
% 241.99/48.49  | | | 
% 241.99/48.49  | | | BETA: splitting (15) gives:
% 241.99/48.49  | | | 
% 241.99/48.49  | | | Case 1:
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | |   (27)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0)
% 241.99/48.49  | | | |           = e3)
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | | BETA: splitting (27) gives:
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | | Case 1:
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | |   (28)  all_58_9 = e3 & op(e3, e0) = e3
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | REF_CLOSE: (1), (2), (3), (9), (10), (11), (17), (19), (20), (22),
% 241.99/48.49  | | | | |            (26), (28) are inconsistent by sub-proof #1172.
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | Case 2:
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | |   (29)  all_58_10 = e3 & op(e2, e0) = e3
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | ALPHA: (29) implies:
% 241.99/48.49  | | | | |   (30)  all_58_10 = e3
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | REF_CLOSE: (2), (3), (5), (7), (10), (14), (16), (19), (22), (30) are
% 241.99/48.49  | | | | |            inconsistent by sub-proof #1101.
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | End of split
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | Case 2:
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | |   (31)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 241.99/48.49  | | | |             e0) = e3)
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | | BETA: splitting (31) gives:
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | | Case 1:
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | |   (32)  all_58_11 = e3 & op(e1, e0) = e3
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | ALPHA: (32) implies:
% 241.99/48.49  | | | | |   (33)  all_58_11 = e3
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 241.99/48.49  | | | | |            (12), (13), (14), (16), (17), (18), (19), (20), (22), (26),
% 241.99/48.49  | | | | |            (33) are inconsistent by sub-proof #655.
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | Case 2:
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | |   (34)  all_58_15 = e3 & op(e0, e0) = e3
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | ALPHA: (34) implies:
% 241.99/48.49  | | | | |   (35)  all_58_15 = e3
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | REF_CLOSE: (2), (21), (35) are inconsistent by sub-proof #1540.
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | End of split
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | End of split
% 241.99/48.49  | | | 
% 241.99/48.49  | | Case 2:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (36)  all_58_9 = e3 & op(e3, e0) = e3
% 241.99/48.49  | | | 
% 241.99/48.49  | | | REF_CLOSE: (6), (20), (36) are inconsistent by sub-proof #1603.
% 241.99/48.49  | | | 
% 241.99/48.49  | | End of split
% 241.99/48.49  | | 
% 241.99/48.49  | End of split
% 241.99/48.49  | 
% 241.99/48.49  End of proof
% 241.99/48.49  
% 241.99/48.49  Sub-proof #655 shows that the following formulas are inconsistent:
% 241.99/48.49  ----------------------------------------------------------------
% 241.99/48.49    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.99/48.49         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.99/48.49    (2)   ~ (e3 = e0)
% 241.99/48.49    (3)   ~ (e2 = e0)
% 241.99/48.49    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.99/48.49         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.99/48.49    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.99/48.49         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.99/48.49    (6)   ~ (e3 = e1)
% 241.99/48.49    (7)  all_58_3 = e3
% 241.99/48.49    (8)  all_58_11 = e3
% 241.99/48.49    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.99/48.49         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.99/48.49    (10)  op(e3, e3) = e1
% 241.99/48.49    (11)   ~ (e3 = e2)
% 241.99/48.49    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.99/48.49          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.49    (13)   ~ (all_52_4 = e3)
% 241.99/48.49    (14)  op(e3, e2) = all_52_4
% 241.99/48.49    (15)  all_58_5 = e1
% 241.99/48.49    (16)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.99/48.49          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.99/48.49    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.49    (18)  op(e0, e0) = e0
% 241.99/48.49    (19)   ~ (e1 = e0)
% 241.99/48.49    (20)  all_58_4 = e3
% 241.99/48.49    (21)  all_58_9 = e1
% 241.99/48.49    (22)   ~ (e2 = e1)
% 241.99/48.49  
% 241.99/48.49  Begin of proof
% 241.99/48.49  | 
% 241.99/48.49  | BETA: splitting (5) gives:
% 241.99/48.49  | 
% 241.99/48.49  | Case 1:
% 241.99/48.49  | | 
% 241.99/48.49  | |   (23)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 241.99/48.49  | |           e2)
% 241.99/48.49  | | 
% 241.99/48.49  | | BETA: splitting (23) gives:
% 241.99/48.49  | | 
% 241.99/48.49  | | Case 1:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (24)  all_58_2 = e2 & op(e2, e3) = e2
% 241.99/48.49  | | | 
% 241.99/48.49  | | | ALPHA: (24) implies:
% 241.99/48.49  | | |   (25)  all_58_2 = e2
% 241.99/48.49  | | | 
% 241.99/48.49  | | | BETA: splitting (12) gives:
% 241.99/48.49  | | | 
% 241.99/48.49  | | | Case 1:
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | |   (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 241.99/48.49  | | | |           = e0)
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | | REF_CLOSE: (1), (3), (10), (11), (17), (19), (20), (21), (22), (26) are
% 241.99/48.49  | | | |            inconsistent by sub-proof #1293.
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | Case 2:
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | |   (27)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 241.99/48.49  | | | |           = e0)
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | | BETA: splitting (27) gives:
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | | Case 1:
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | |   (28)  all_58_4 = e0 & op(e3, e1) = e0
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | REF_CLOSE: (2), (20), (28) are inconsistent by sub-proof #1697.
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | Case 2:
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | |   (29)  all_58_9 = e0 & op(e3, e0) = e0
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | ALPHA: (29) implies:
% 241.99/48.49  | | | | |   (30)  all_58_9 = e0
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | BETA: splitting (4) gives:
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | | Case 1:
% 241.99/48.49  | | | | | | 
% 241.99/48.49  | | | | | |   (31)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 241.99/48.49  | | | | | |             e0) = e1)
% 241.99/48.49  | | | | | | 
% 241.99/48.49  | | | | | | BETA: splitting (31) gives:
% 241.99/48.49  | | | | | | 
% 241.99/48.49  | | | | | | Case 1:
% 241.99/48.49  | | | | | | | 
% 241.99/48.49  | | | | | | |   (32)  all_58_9 = e1 & op(e3, e0) = e1
% 241.99/48.49  | | | | | | | 
% 241.99/48.49  | | | | | | | REF_CLOSE: (19), (30), (32) are inconsistent by sub-proof #2183.
% 241.99/48.49  | | | | | | | 
% 241.99/48.49  | | | | | | Case 2:
% 241.99/48.49  | | | | | | | 
% 241.99/48.49  | | | | | | |   (33)  all_58_10 = e1 & op(e2, e0) = e1
% 241.99/48.49  | | | | | | | 
% 241.99/48.49  | | | | | | | ALPHA: (33) implies:
% 241.99/48.49  | | | | | | |   (34)  all_58_10 = e1
% 241.99/48.49  | | | | | | | 
% 241.99/48.49  | | | | | | | REF_CLOSE: (2), (3), (7), (15), (16), (19), (25), (34) are
% 241.99/48.49  | | | | | | |            inconsistent by sub-proof #994.
% 241.99/48.49  | | | | | | | 
% 241.99/48.49  | | | | | | End of split
% 241.99/48.49  | | | | | | 
% 241.99/48.49  | | | | | Case 2:
% 241.99/48.49  | | | | | | 
% 241.99/48.49  | | | | | |   (35)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 241.99/48.49  | | | | | |           op(e0, e0) = e1)
% 241.99/48.49  | | | | | | 
% 241.99/48.49  | | | | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (11), (12), (13),
% 241.99/48.49  | | | | | |            (14), (17), (18), (19), (20), (22), (35) are inconsistent
% 241.99/48.49  | | | | | |            by sub-proof #1466.
% 241.99/48.49  | | | | | | 
% 241.99/48.49  | | | | | End of split
% 241.99/48.49  | | | | | 
% 241.99/48.49  | | | | End of split
% 241.99/48.49  | | | | 
% 241.99/48.49  | | | End of split
% 241.99/48.49  | | | 
% 241.99/48.49  | | Case 2:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (36)  all_58_3 = e2 & op(e2, e2) = e2
% 241.99/48.49  | | | 
% 241.99/48.49  | | | REF_CLOSE: (7), (11), (36) are inconsistent by sub-proof #1458.
% 241.99/48.49  | | | 
% 241.99/48.49  | | End of split
% 241.99/48.49  | | 
% 241.99/48.49  | Case 2:
% 241.99/48.49  | | 
% 241.99/48.49  | |   (37)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 241.99/48.49  | |           e2)
% 241.99/48.49  | | 
% 241.99/48.49  | | BETA: splitting (37) gives:
% 241.99/48.49  | | 
% 241.99/48.49  | | Case 1:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (38)  all_58_5 = e2 & op(e2, e1) = e2
% 241.99/48.49  | | | 
% 241.99/48.49  | | | ALPHA: (38) implies:
% 241.99/48.49  | | |   (39)  all_58_5 = e2
% 241.99/48.49  | | | 
% 241.99/48.49  | | | REF_CLOSE: (15), (22), (39) are inconsistent by sub-proof #1665.
% 241.99/48.49  | | | 
% 241.99/48.49  | | Case 2:
% 241.99/48.49  | | | 
% 241.99/48.49  | | |   (40)  all_58_10 = e2 & op(e2, e0) = e2
% 241.99/48.49  | | | 
% 241.99/48.49  | | | ALPHA: (40) implies:
% 241.99/48.49  | | |   (41)  all_58_10 = e2
% 241.99/48.49  | | | 
% 241.99/48.49  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13),
% 241.99/48.49  | | |            (14), (17), (18), (19), (20), (21), (22), (41) are inconsistent
% 241.99/48.49  | | |            by sub-proof #1464.
% 241.99/48.49  | | | 
% 241.99/48.49  | | End of split
% 241.99/48.49  | | 
% 241.99/48.49  | End of split
% 241.99/48.49  | 
% 241.99/48.49  End of proof
% 241.99/48.49  
% 241.99/48.49  Sub-proof #656 shows that the following formulas are inconsistent:
% 241.99/48.49  ----------------------------------------------------------------
% 241.99/48.50    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.99/48.50         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.99/48.50    (2)   ~ (e3 = e0)
% 241.99/48.50    (3)   ~ (e2 = e0)
% 241.99/48.50    (4)   ~ (all_52_13 = e1)
% 241.99/48.50    (5)   ~ (e3 = e1)
% 241.99/48.50    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.99/48.50         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.99/48.50    (7)  all_58_3 = e3
% 241.99/48.50    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.99/48.50         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.99/48.50    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.99/48.50         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.99/48.50    (10)  op(e3, e3) = e1
% 241.99/48.50    (11)  op(e2, e1) = all_52_9
% 241.99/48.50    (12)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.99/48.50          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.99/48.50    (13)   ~ (e3 = e2)
% 241.99/48.50    (14)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.99/48.50          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.99/48.50    (15)   ~ (all_52_7 = e1)
% 241.99/48.50    (16)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.99/48.50          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.99/48.50    (17)  op(e2, e3) = all_52_1
% 241.99/48.50    (18)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.99/48.50          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.50    (19)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.99/48.50          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.99/48.50    (20)  op(e0, e2) = all_52_7
% 241.99/48.50    (21)   ~ (all_52_4 = e3)
% 241.99/48.50    (22)  op(e3, e2) = all_52_4
% 241.99/48.50    (23)   ~ (all_52_9 = e3)
% 241.99/48.50    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.50    (25)  op(e0, e0) = e0
% 241.99/48.50    (26)  op(e1, e1) = e0
% 241.99/48.50    (27)   ~ (e1 = e0)
% 241.99/48.50    (28)  op(e2, e0) = all_52_13
% 241.99/48.50    (29)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.99/48.50          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.99/48.50            e1)
% 241.99/48.50    (30)   ~ (all_52_1 = e3)
% 241.99/48.50    (31)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.99/48.50          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.99/48.50    (32)   ~ (e2 = e1)
% 241.99/48.50    (33)   ~ (all_52_1 = e1)
% 241.99/48.50  
% 241.99/48.50  Begin of proof
% 241.99/48.50  | 
% 241.99/48.50  | BETA: splitting (29) gives:
% 241.99/48.50  | 
% 241.99/48.50  | Case 1:
% 241.99/48.50  | | 
% 241.99/48.50  | |   (34)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 241.99/48.50  | |           e1)
% 241.99/48.50  | | 
% 241.99/48.50  | | BETA: splitting (34) gives:
% 241.99/48.50  | | 
% 241.99/48.50  | | Case 1:
% 241.99/48.50  | | | 
% 241.99/48.50  | | |   (35)  all_58_12 = e1 & op(e0, e3) = e1
% 241.99/48.50  | | | 
% 241.99/48.50  | | | ALPHA: (35) implies:
% 241.99/48.50  | | |   (36)  all_58_12 = e1
% 241.99/48.50  | | | 
% 241.99/48.50  | | | REF_CLOSE: (2), (3), (5), (9), (10), (12), (13), (16), (17), (24), (27),
% 241.99/48.50  | | |            (30), (32), (36) are inconsistent by sub-proof #1204.
% 241.99/48.50  | | | 
% 241.99/48.50  | | Case 2:
% 241.99/48.50  | | | 
% 241.99/48.50  | | |   (37)  all_58_13 = e1 & op(e0, e2) = e1
% 241.99/48.50  | | | 
% 241.99/48.50  | | | REF_CLOSE: (15), (20), (24), (37) are inconsistent by sub-proof #2275.
% 241.99/48.50  | | | 
% 241.99/48.50  | | End of split
% 241.99/48.50  | | 
% 241.99/48.50  | Case 2:
% 241.99/48.50  | | 
% 241.99/48.50  | |   (38)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.99/48.50  | |           e1)
% 241.99/48.50  | | 
% 241.99/48.50  | | BETA: splitting (38) gives:
% 241.99/48.50  | | 
% 241.99/48.50  | | Case 1:
% 241.99/48.50  | | | 
% 241.99/48.50  | | |   (39)  all_58_14 = e1 & op(e0, e1) = e1
% 241.99/48.50  | | | 
% 241.99/48.50  | | | ALPHA: (39) implies:
% 241.99/48.50  | | |   (40)  all_58_14 = e1
% 241.99/48.50  | | | 
% 241.99/48.50  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (14),
% 241.99/48.50  | | |            (17), (18), (19), (21), (22), (23), (24), (26), (27), (28),
% 241.99/48.50  | | |            (31), (32), (33), (40) are inconsistent by sub-proof #657.
% 241.99/48.50  | | | 
% 241.99/48.50  | | Case 2:
% 241.99/48.50  | | | 
% 241.99/48.50  | | |   (41)  all_58_15 = e1 & op(e0, e0) = e1
% 241.99/48.50  | | | 
% 241.99/48.50  | | | ALPHA: (41) implies:
% 241.99/48.50  | | |   (42)  op(e0, e0) = e1
% 241.99/48.50  | | | 
% 241.99/48.50  | | | REF_CLOSE: (24), (25), (27), (42) are inconsistent by sub-proof #2274.
% 241.99/48.50  | | | 
% 241.99/48.50  | | End of split
% 241.99/48.50  | | 
% 241.99/48.50  | End of split
% 241.99/48.50  | 
% 241.99/48.50  End of proof
% 241.99/48.50  
% 241.99/48.50  Sub-proof #657 shows that the following formulas are inconsistent:
% 241.99/48.50  ----------------------------------------------------------------
% 241.99/48.50    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.99/48.50         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.99/48.50    (2)   ~ (e3 = e0)
% 241.99/48.50    (3)   ~ (e2 = e0)
% 241.99/48.50    (4)   ~ (all_52_13 = e1)
% 241.99/48.50    (5)   ~ (e3 = e1)
% 241.99/48.50    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.99/48.50         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.99/48.50    (7)  all_58_3 = e3
% 241.99/48.50    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.99/48.50         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.99/48.50    (9)  op(e3, e3) = e1
% 241.99/48.50    (10)  op(e2, e1) = all_52_9
% 241.99/48.50    (11)   ~ (e3 = e2)
% 241.99/48.50    (12)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.99/48.50          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.99/48.50    (13)  op(e2, e3) = all_52_1
% 241.99/48.50    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.99/48.50          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.50    (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.99/48.50          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.99/48.50    (16)   ~ (all_52_4 = e3)
% 241.99/48.50    (17)  op(e3, e2) = all_52_4
% 241.99/48.50    (18)   ~ (all_52_9 = e3)
% 241.99/48.50    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.50    (20)  op(e1, e1) = e0
% 241.99/48.50    (21)   ~ (e1 = e0)
% 241.99/48.50    (22)  op(e2, e0) = all_52_13
% 241.99/48.50    (23)  all_58_14 = e1
% 241.99/48.50    (24)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.99/48.50          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.99/48.50    (25)   ~ (e2 = e1)
% 241.99/48.50    (26)   ~ (all_52_1 = e1)
% 241.99/48.50  
% 241.99/48.50  Begin of proof
% 241.99/48.50  | 
% 241.99/48.50  | BETA: splitting (15) gives:
% 241.99/48.50  | 
% 241.99/48.50  | Case 1:
% 241.99/48.50  | | 
% 241.99/48.50  | |   (27)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 241.99/48.50  | |           e3)
% 241.99/48.50  | | 
% 241.99/48.50  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.99/48.50  | |            (13), (14), (16), (17), (18), (19), (21), (22), (23), (24), (25),
% 241.99/48.50  | |            (26), (27) are inconsistent by sub-proof #739.
% 241.99/48.50  | | 
% 241.99/48.50  | Case 2:
% 241.99/48.50  | | 
% 241.99/48.50  | |   (28)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 241.99/48.50  | |           e3)
% 241.99/48.50  | | 
% 241.99/48.50  | | REF_CLOSE: (2), (5), (19), (20), (23), (28) are inconsistent by sub-proof
% 241.99/48.50  | |            #658.
% 241.99/48.50  | | 
% 241.99/48.50  | End of split
% 241.99/48.50  | 
% 241.99/48.50  End of proof
% 241.99/48.50  
% 241.99/48.50  Sub-proof #658 shows that the following formulas are inconsistent:
% 241.99/48.50  ----------------------------------------------------------------
% 241.99/48.50    (1)   ~ (e3 = e0)
% 241.99/48.50    (2)   ~ (e3 = e1)
% 241.99/48.50    (3)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.99/48.50    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.50    (5)  op(e1, e1) = e0
% 241.99/48.50    (6)  all_58_14 = e1
% 241.99/48.50  
% 241.99/48.50  Begin of proof
% 241.99/48.50  | 
% 241.99/48.50  | BETA: splitting (3) gives:
% 241.99/48.50  | 
% 241.99/48.50  | Case 1:
% 241.99/48.50  | | 
% 241.99/48.50  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 241.99/48.50  | | 
% 241.99/48.50  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #2018.
% 241.99/48.50  | | 
% 241.99/48.50  | Case 2:
% 241.99/48.50  | | 
% 241.99/48.50  | |   (8)  all_58_14 = e3 & op(e0, e1) = e3
% 241.99/48.50  | | 
% 241.99/48.50  | | ALPHA: (8) implies:
% 241.99/48.50  | |   (9)  all_58_14 = e3
% 241.99/48.50  | | 
% 241.99/48.50  | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #1844.
% 241.99/48.50  | | 
% 241.99/48.50  | End of split
% 241.99/48.50  | 
% 241.99/48.50  End of proof
% 241.99/48.50  
% 241.99/48.50  Sub-proof #659 shows that the following formulas are inconsistent:
% 241.99/48.50  ----------------------------------------------------------------
% 241.99/48.50    (1)   ~ (e3 = e0)
% 241.99/48.50    (2)  all_58_6 = e3
% 241.99/48.50    (3)   ~ (e2 = e0)
% 241.99/48.50    (4)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 241.99/48.50    (5)   ~ (e3 = e1)
% 241.99/48.50    (6)  all_58_3 = e3
% 241.99/48.50    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.99/48.50         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.99/48.50    (8)  op(e3, e3) = e1
% 241.99/48.50    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.99/48.50         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.99/48.50    (10)   ~ (e3 = e2)
% 241.99/48.50    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.99/48.50          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.99/48.50    (12)  op(e2, e3) = all_52_1
% 241.99/48.50    (13)  op(e3, e2) = all_52_4
% 241.99/48.50    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.50    (15)   ~ (all_52_4 = e1)
% 241.99/48.50    (16)   ~ (e1 = e0)
% 241.99/48.50    (17)   ~ (all_52_1 = e3)
% 241.99/48.50    (18)   ~ (e2 = e1)
% 241.99/48.50  
% 241.99/48.50  Begin of proof
% 241.99/48.50  | 
% 241.99/48.50  | BETA: splitting (4) gives:
% 241.99/48.50  | 
% 241.99/48.50  | Case 1:
% 241.99/48.50  | | 
% 241.99/48.50  | |   (19)  all_58_1 = e1 & op(e3, e2) = e1
% 241.99/48.50  | | 
% 241.99/48.50  | | ALPHA: (19) implies:
% 241.99/48.50  | |   (20)  op(e3, e2) = e1
% 241.99/48.50  | | 
% 241.99/48.50  | | REF_CLOSE: (13), (14), (15), (20) are inconsistent by sub-proof #2228.
% 241.99/48.50  | | 
% 241.99/48.50  | Case 2:
% 241.99/48.50  | | 
% 241.99/48.50  | |   (21)  all_58_3 = e1 & op(e2, e2) = e1
% 241.99/48.50  | | 
% 241.99/48.50  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 241.99/48.50  | |            (16), (17), (18), (21) are inconsistent by sub-proof #660.
% 241.99/48.50  | | 
% 241.99/48.50  | End of split
% 241.99/48.50  | 
% 241.99/48.50  End of proof
% 241.99/48.50  
% 241.99/48.50  Sub-proof #660 shows that the following formulas are inconsistent:
% 241.99/48.50  ----------------------------------------------------------------
% 241.99/48.50    (1)   ~ (e3 = e0)
% 241.99/48.50    (2)  all_58_6 = e3
% 241.99/48.50    (3)   ~ (e2 = e0)
% 241.99/48.50    (4)   ~ (e3 = e1)
% 241.99/48.50    (5)  all_58_3 = e3
% 241.99/48.50    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.99/48.50         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.99/48.50    (7)  op(e3, e3) = e1
% 241.99/48.50    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.99/48.50         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.99/48.50    (9)   ~ (e3 = e2)
% 241.99/48.50    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.99/48.50          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.99/48.50    (11)  op(e2, e3) = all_52_1
% 241.99/48.50    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.50    (13)  all_58_3 = e1 & op(e2, e2) = e1
% 241.99/48.50    (14)   ~ (e1 = e0)
% 241.99/48.50    (15)   ~ (all_52_1 = e3)
% 241.99/48.50    (16)   ~ (e2 = e1)
% 241.99/48.50  
% 241.99/48.50  Begin of proof
% 241.99/48.50  | 
% 241.99/48.50  | ALPHA: (13) implies:
% 241.99/48.50  |   (17)  all_58_3 = e1
% 241.99/48.50  | 
% 241.99/48.50  | COMBINE_EQS: (5), (17) imply:
% 241.99/48.50  |   (18)  e3 = e1
% 241.99/48.50  | 
% 241.99/48.50  | COMBINE_EQS: (2), (18) imply:
% 241.99/48.50  |   (19)  all_58_6 = e1
% 241.99/48.50  | 
% 241.99/48.50  | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 241.99/48.50  |            (16), (19) are inconsistent by sub-proof #1161.
% 241.99/48.50  | 
% 241.99/48.50  End of proof
% 241.99/48.50  
% 241.99/48.50  Sub-proof #661 shows that the following formulas are inconsistent:
% 241.99/48.50  ----------------------------------------------------------------
% 241.99/48.50    (1)   ~ (e3 = e0)
% 241.99/48.50    (2)   ~ (e2 = e0)
% 241.99/48.50    (3)  op(e1, e2) = all_52_6
% 241.99/48.50    (4)  all_58_6 = e2
% 241.99/48.50    (5)  all_58_11 = e1
% 241.99/48.50    (6)   ~ (e3 = e1)
% 241.99/48.50    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.99/48.50         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.99/48.50    (8)  op(e3, e3) = e1
% 241.99/48.50    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.99/48.50         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.99/48.50    (10)   ~ (e3 = e2)
% 241.99/48.50    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.99/48.50          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.99/48.50    (12)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.99/48.50          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.99/48.50    (13)  op(e2, e3) = all_52_1
% 241.99/48.50    (14)   ~ (all_52_6 = e3)
% 241.99/48.50    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.50    (16)  op(e1, e1) = e0
% 241.99/48.50    (17)   ~ (e1 = e0)
% 241.99/48.50    (18)   ~ (all_52_1 = e3)
% 241.99/48.50    (19)   ~ (e2 = e1)
% 241.99/48.50  
% 241.99/48.50  Begin of proof
% 241.99/48.50  | 
% 241.99/48.50  | BETA: splitting (7) gives:
% 241.99/48.50  | 
% 241.99/48.50  | Case 1:
% 241.99/48.50  | | 
% 241.99/48.50  | |   (20)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 241.99/48.50  | |           e3)
% 241.99/48.50  | | 
% 241.99/48.50  | | REF_CLOSE: (6), (8), (13), (15), (18), (20) are inconsistent by sub-proof
% 241.99/48.50  | |            #1208.
% 241.99/48.50  | | 
% 241.99/48.50  | Case 2:
% 241.99/48.50  | | 
% 241.99/48.50  | |   (21)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 241.99/48.50  | |           e3)
% 241.99/48.50  | | 
% 241.99/48.50  | | BETA: splitting (21) gives:
% 241.99/48.50  | | 
% 241.99/48.50  | | Case 1:
% 241.99/48.50  | | | 
% 241.99/48.50  | | |   (22)  all_58_6 = e3 & op(e1, e3) = e3
% 241.99/48.50  | | | 
% 241.99/48.50  | | | REF_CLOSE: (4), (10), (22) are inconsistent by sub-proof #1838.
% 241.99/48.50  | | | 
% 241.99/48.50  | | Case 2:
% 241.99/48.50  | | | 
% 241.99/48.50  | | |   (23)  all_58_12 = e3 & op(e0, e3) = e3
% 241.99/48.50  | | | 
% 241.99/48.50  | | | ALPHA: (23) implies:
% 241.99/48.50  | | |   (24)  all_58_12 = e3
% 241.99/48.50  | | | 
% 241.99/48.50  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 241.99/48.50  | | |            (14), (15), (16), (17), (18), (19), (24) are inconsistent by
% 241.99/48.50  | | |            sub-proof #662.
% 241.99/48.50  | | | 
% 241.99/48.50  | | End of split
% 241.99/48.50  | | 
% 241.99/48.50  | End of split
% 241.99/48.50  | 
% 241.99/48.50  End of proof
% 241.99/48.50  
% 241.99/48.50  Sub-proof #662 shows that the following formulas are inconsistent:
% 241.99/48.50  ----------------------------------------------------------------
% 241.99/48.50    (1)   ~ (e3 = e0)
% 241.99/48.50    (2)   ~ (e2 = e0)
% 241.99/48.51    (3)  op(e1, e2) = all_52_6
% 241.99/48.51    (4)  all_58_11 = e1
% 241.99/48.51    (5)   ~ (e3 = e1)
% 241.99/48.51    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.99/48.51         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.99/48.51    (7)  op(e3, e3) = e1
% 241.99/48.51    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.99/48.51         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.99/48.51    (9)   ~ (e3 = e2)
% 241.99/48.51    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.99/48.51          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.99/48.51    (11)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.99/48.51          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.99/48.51    (12)  op(e2, e3) = all_52_1
% 241.99/48.51    (13)  all_58_12 = e3
% 241.99/48.51    (14)   ~ (all_52_6 = e3)
% 241.99/48.51    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.51    (16)  op(e1, e1) = e0
% 241.99/48.51    (17)   ~ (e1 = e0)
% 241.99/48.51    (18)   ~ (all_52_1 = e3)
% 241.99/48.51    (19)   ~ (e2 = e1)
% 241.99/48.51  
% 241.99/48.51  Begin of proof
% 241.99/48.51  | 
% 241.99/48.51  | BETA: splitting (11) gives:
% 241.99/48.51  | 
% 241.99/48.51  | Case 1:
% 241.99/48.51  | | 
% 241.99/48.51  | |   (20)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 241.99/48.51  | |           e3)
% 241.99/48.51  | | 
% 241.99/48.51  | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (13), (14), (15), (17), (19),
% 241.99/48.51  | |            (20) are inconsistent by sub-proof #1136.
% 241.99/48.51  | | 
% 241.99/48.51  | Case 2:
% 241.99/48.51  | | 
% 241.99/48.51  | |   (21)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 241.99/48.51  | |           e3)
% 241.99/48.51  | | 
% 241.99/48.51  | | BETA: splitting (21) gives:
% 241.99/48.51  | | 
% 241.99/48.51  | | Case 1:
% 241.99/48.51  | | | 
% 241.99/48.51  | | |   (22)  all_58_8 = e3 & op(e1, e1) = e3
% 241.99/48.51  | | | 
% 241.99/48.51  | | | REF_CLOSE: (1), (15), (16), (22) are inconsistent by sub-proof #2018.
% 241.99/48.51  | | | 
% 241.99/48.51  | | Case 2:
% 241.99/48.51  | | | 
% 241.99/48.51  | | |   (23)  all_58_11 = e3 & op(e1, e0) = e3
% 241.99/48.51  | | | 
% 241.99/48.51  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (13), (15),
% 241.99/48.51  | | |            (17), (18), (19), (23) are inconsistent by sub-proof #663.
% 241.99/48.51  | | | 
% 241.99/48.51  | | End of split
% 241.99/48.51  | | 
% 241.99/48.51  | End of split
% 241.99/48.51  | 
% 241.99/48.51  End of proof
% 241.99/48.51  
% 241.99/48.51  Sub-proof #663 shows that the following formulas are inconsistent:
% 241.99/48.51  ----------------------------------------------------------------
% 241.99/48.51    (1)   ~ (e3 = e0)
% 241.99/48.51    (2)   ~ (e2 = e0)
% 241.99/48.51    (3)  all_58_11 = e1
% 241.99/48.51    (4)   ~ (e3 = e1)
% 241.99/48.51    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.99/48.51         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.99/48.51    (6)  op(e3, e3) = e1
% 241.99/48.51    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.99/48.51         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.99/48.51    (8)   ~ (e3 = e2)
% 241.99/48.51    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.99/48.51         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.99/48.51    (10)  op(e2, e3) = all_52_1
% 241.99/48.51    (11)  all_58_12 = e3
% 241.99/48.51    (12)  all_58_11 = e3 & op(e1, e0) = e3
% 241.99/48.51    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.51    (14)   ~ (e1 = e0)
% 241.99/48.51    (15)   ~ (all_52_1 = e3)
% 241.99/48.51    (16)   ~ (e2 = e1)
% 241.99/48.51  
% 241.99/48.51  Begin of proof
% 241.99/48.51  | 
% 241.99/48.51  | ALPHA: (12) implies:
% 241.99/48.51  |   (17)  all_58_11 = e3
% 241.99/48.51  | 
% 241.99/48.51  | COMBINE_EQS: (3), (17) imply:
% 241.99/48.51  |   (18)  e3 = e1
% 241.99/48.51  | 
% 241.99/48.51  | COMBINE_EQS: (11), (18) imply:
% 241.99/48.51  |   (19)  all_58_12 = e1
% 241.99/48.51  | 
% 241.99/48.51  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (13), (14), (15),
% 241.99/48.51  |            (16), (19) are inconsistent by sub-proof #1204.
% 241.99/48.51  | 
% 241.99/48.51  End of proof
% 241.99/48.51  
% 241.99/48.51  Sub-proof #664 shows that the following formulas are inconsistent:
% 241.99/48.51  ----------------------------------------------------------------
% 241.99/48.51    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.99/48.51         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.99/48.51    (2)   ~ (e3 = e0)
% 241.99/48.51    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.99/48.51         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.99/48.51    (4)   ~ (e2 = e0)
% 241.99/48.51    (5)  op(e1, e2) = all_52_6
% 241.99/48.51    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.99/48.51         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.99/48.51    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.99/48.51         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.99/48.51    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.99/48.51         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.99/48.51    (9)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.99/48.51         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.99/48.51    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.99/48.51          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.99/48.51    (11)   ~ (e3 = e1)
% 241.99/48.51    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.99/48.51          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.99/48.51    (13)  all_58_3 = e3
% 241.99/48.51    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.99/48.51          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.99/48.51    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.99/48.51          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.99/48.51    (16)  op(e3, e3) = e1
% 241.99/48.51    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.51              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.99/48.51                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.99/48.51                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.99/48.51    (18)  op(e2, e1) = all_52_9
% 241.99/48.51    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.99/48.51          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.99/48.51    (20)   ~ (e3 = e2)
% 241.99/48.51    (21)  all_58_6 = e0
% 241.99/48.51    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.99/48.51          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.99/48.51    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.99/48.51          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.99/48.51    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.99/48.51          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.99/48.51    (25)  op(e2, e3) = all_52_1
% 241.99/48.51    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.99/48.51          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.51    (27)   ~ (all_52_6 = e3)
% 241.99/48.51    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.99/48.51          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.99/48.51    (29)   ~ (all_52_4 = e3)
% 241.99/48.51    (30)  op(e3, e2) = all_52_4
% 241.99/48.51    (31)   ~ (all_52_9 = e3)
% 241.99/48.51    (32)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.99/48.51          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.99/48.51    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.99/48.51          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.99/48.51    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.99/48.51          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.99/48.51    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.51    (36)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.99/48.51          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.99/48.51    (37)  op(e1, e1) = e0
% 241.99/48.51    (38)   ~ (e1 = e0)
% 241.99/48.51    (39)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.99/48.51          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.99/48.51    (40)  op(e2, e0) = all_52_13
% 241.99/48.51    (41)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.99/48.51          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.99/48.51            e1)
% 241.99/48.51    (42)   ~ (all_52_1 = e3)
% 241.99/48.51    (43)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.99/48.51          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.99/48.51            e2)
% 241.99/48.51    (44)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.99/48.51          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.99/48.51    (45)   ~ (e2 = e1)
% 241.99/48.51    (46)   ~ (all_52_1 = e1)
% 241.99/48.51  
% 241.99/48.51  Begin of proof
% 241.99/48.51  | 
% 241.99/48.51  | BETA: splitting (15) gives:
% 241.99/48.51  | 
% 241.99/48.51  | Case 1:
% 241.99/48.51  | | 
% 241.99/48.51  | |   (47)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 241.99/48.51  | |           e3)
% 241.99/48.51  | | 
% 241.99/48.51  | | REF_CLOSE: (11), (16), (25), (35), (42), (47) are inconsistent by sub-proof
% 241.99/48.51  | |            #1208.
% 241.99/48.51  | | 
% 241.99/48.51  | Case 2:
% 241.99/48.51  | | 
% 241.99/48.51  | |   (48)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 241.99/48.51  | |           e3)
% 241.99/48.51  | | 
% 241.99/48.51  | | BETA: splitting (48) gives:
% 241.99/48.51  | | 
% 241.99/48.51  | | Case 1:
% 241.99/48.51  | | | 
% 241.99/48.51  | | |   (49)  all_58_6 = e3 & op(e1, e3) = e3
% 241.99/48.51  | | | 
% 241.99/48.51  | | | ALPHA: (49) implies:
% 241.99/48.51  | | |   (50)  all_58_6 = e3
% 241.99/48.51  | | | 
% 241.99/48.51  | | | REF_CLOSE: (2), (21), (50) are inconsistent by sub-proof #2222.
% 241.99/48.51  | | | 
% 241.99/48.51  | | Case 2:
% 241.99/48.51  | | | 
% 241.99/48.51  | | |   (51)  all_58_12 = e3 & op(e0, e3) = e3
% 241.99/48.51  | | | 
% 241.99/48.51  | | | ALPHA: (51) implies:
% 241.99/48.51  | | |   (52)  all_58_12 = e3
% 241.99/48.51  | | | 
% 241.99/48.51  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.99/48.51  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.99/48.51  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 241.99/48.51  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 241.99/48.51  | | |            (43), (44), (45), (46), (52) are inconsistent by sub-proof
% 241.99/48.51  | | |            #665.
% 241.99/48.51  | | | 
% 241.99/48.51  | | End of split
% 241.99/48.51  | | 
% 241.99/48.51  | End of split
% 241.99/48.51  | 
% 241.99/48.51  End of proof
% 241.99/48.51  
% 241.99/48.51  Sub-proof #665 shows that the following formulas are inconsistent:
% 241.99/48.51  ----------------------------------------------------------------
% 241.99/48.51    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.99/48.51         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.99/48.51    (2)   ~ (e3 = e0)
% 241.99/48.51    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.99/48.51         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.99/48.51    (4)   ~ (e2 = e0)
% 241.99/48.51    (5)  op(e1, e2) = all_52_6
% 241.99/48.51    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.99/48.51         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.99/48.51    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.99/48.51         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.99/48.51    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.99/48.51         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.99/48.51    (9)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.99/48.51         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.99/48.51    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.99/48.51          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.99/48.51    (11)   ~ (e3 = e1)
% 241.99/48.51    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.99/48.51          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.99/48.51    (13)  all_58_3 = e3
% 241.99/48.51    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.99/48.51          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.99/48.51    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.99/48.51          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.99/48.51    (16)  op(e3, e3) = e1
% 241.99/48.51    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.51              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.99/48.51                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.99/48.51                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.99/48.51    (18)  op(e2, e1) = all_52_9
% 241.99/48.51    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.99/48.51          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.99/48.51    (20)   ~ (e3 = e2)
% 241.99/48.51    (21)  all_58_6 = e0
% 241.99/48.51    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.99/48.51          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.99/48.51    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.99/48.51          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.99/48.52    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.99/48.52          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.99/48.52    (25)  op(e2, e3) = all_52_1
% 241.99/48.52    (26)  all_58_12 = e3
% 241.99/48.52    (27)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.99/48.52          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.52    (28)   ~ (all_52_6 = e3)
% 241.99/48.52    (29)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.99/48.52          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.99/48.52    (30)   ~ (all_52_4 = e3)
% 241.99/48.52    (31)  op(e3, e2) = all_52_4
% 241.99/48.52    (32)   ~ (all_52_9 = e3)
% 241.99/48.52    (33)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.99/48.52          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.99/48.52    (34)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.99/48.52          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.99/48.52    (35)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.99/48.52          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.99/48.52    (36)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.52    (37)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.99/48.52          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.99/48.52    (38)  op(e1, e1) = e0
% 241.99/48.52    (39)   ~ (e1 = e0)
% 241.99/48.52    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.99/48.52          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.99/48.52    (41)  op(e2, e0) = all_52_13
% 241.99/48.52    (42)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.99/48.52          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.99/48.52            e1)
% 241.99/48.52    (43)   ~ (all_52_1 = e3)
% 241.99/48.52    (44)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.99/48.52          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.99/48.52            e2)
% 241.99/48.52    (45)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.99/48.52          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.99/48.52    (46)   ~ (e2 = e1)
% 241.99/48.52    (47)   ~ (all_52_1 = e1)
% 241.99/48.52  
% 241.99/48.52  Begin of proof
% 241.99/48.52  | 
% 241.99/48.52  | BETA: splitting (24) gives:
% 241.99/48.52  | 
% 241.99/48.52  | Case 1:
% 241.99/48.52  | | 
% 241.99/48.52  | |   (48)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 241.99/48.52  | |           e3)
% 241.99/48.52  | | 
% 241.99/48.52  | | REF_CLOSE: (2), (4), (5), (16), (19), (20), (23), (26), (28), (36), (39),
% 241.99/48.52  | |            (46), (48) are inconsistent by sub-proof #1136.
% 241.99/48.52  | | 
% 241.99/48.52  | Case 2:
% 241.99/48.52  | | 
% 241.99/48.52  | |   (49)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 241.99/48.52  | |           e3)
% 241.99/48.52  | | 
% 241.99/48.52  | | BETA: splitting (49) gives:
% 241.99/48.52  | | 
% 241.99/48.52  | | Case 1:
% 241.99/48.52  | | | 
% 241.99/48.52  | | |   (50)  all_58_8 = e3 & op(e1, e1) = e3
% 241.99/48.52  | | | 
% 241.99/48.52  | | | REF_CLOSE: (2), (36), (38), (50) are inconsistent by sub-proof #2018.
% 241.99/48.52  | | | 
% 241.99/48.52  | | Case 2:
% 241.99/48.52  | | | 
% 241.99/48.52  | | |   (51)  all_58_11 = e3 & op(e1, e0) = e3
% 241.99/48.52  | | | 
% 241.99/48.52  | | | ALPHA: (51) implies:
% 241.99/48.52  | | |   (52)  all_58_11 = e3
% 241.99/48.52  | | | 
% 241.99/48.52  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 241.99/48.52  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 241.99/48.52  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 241.99/48.52  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 241.99/48.52  | | |            (43), (44), (45), (46), (47), (51), (52) are inconsistent by
% 241.99/48.52  | | |            sub-proof #666.
% 241.99/48.52  | | | 
% 241.99/48.52  | | End of split
% 241.99/48.52  | | 
% 241.99/48.52  | End of split
% 241.99/48.52  | 
% 241.99/48.52  End of proof
% 241.99/48.52  
% 241.99/48.52  Sub-proof #666 shows that the following formulas are inconsistent:
% 241.99/48.52  ----------------------------------------------------------------
% 241.99/48.52    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 241.99/48.52         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 241.99/48.52    (2)   ~ (e3 = e0)
% 241.99/48.52    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 241.99/48.52         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 241.99/48.52    (4)   ~ (e2 = e0)
% 241.99/48.52    (5)  op(e1, e2) = all_52_6
% 241.99/48.52    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.99/48.52         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.99/48.52    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 241.99/48.52         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 241.99/48.52    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.99/48.52         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 241.99/48.52    (9)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 241.99/48.52         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 241.99/48.52    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 241.99/48.52          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 241.99/48.52    (11)   ~ (e3 = e1)
% 241.99/48.52    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 241.99/48.52          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 241.99/48.52    (13)  all_58_3 = e3
% 241.99/48.52    (14)  all_58_11 = e3
% 241.99/48.52    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 241.99/48.52          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 241.99/48.52    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 241.99/48.52          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 241.99/48.52    (17)  op(e3, e3) = e1
% 241.99/48.52    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.52              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 241.99/48.52                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 241.99/48.52                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 241.99/48.52    (19)  op(e2, e1) = all_52_9
% 241.99/48.52    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 241.99/48.52          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 241.99/48.52    (21)   ~ (e3 = e2)
% 241.99/48.52    (22)  all_58_6 = e0
% 241.99/48.52    (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 241.99/48.52          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 241.99/48.52    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 241.99/48.52          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 241.99/48.52    (25)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 241.99/48.52          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 241.99/48.52    (26)  op(e2, e3) = all_52_1
% 241.99/48.52    (27)  all_58_12 = e3
% 241.99/48.52    (28)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 241.99/48.52          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 241.99/48.52    (29)   ~ (all_52_6 = e3)
% 241.99/48.52    (30)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 241.99/48.52          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 241.99/48.52    (31)  all_58_11 = e3 & op(e1, e0) = e3
% 241.99/48.52    (32)   ~ (all_52_4 = e3)
% 241.99/48.52    (33)  op(e3, e2) = all_52_4
% 241.99/48.52    (34)   ~ (all_52_9 = e3)
% 241.99/48.52    (35)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 241.99/48.52          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 241.99/48.52    (36)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 241.99/48.52          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 241.99/48.52    (37)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 241.99/48.52          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 241.99/48.52    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 241.99/48.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 241.99/48.52    (39)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 241.99/48.52          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 241.99/48.52    (40)  op(e1, e1) = e0
% 241.99/48.52    (41)   ~ (e1 = e0)
% 241.99/48.52    (42)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 241.99/48.52          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 241.99/48.52    (43)  op(e2, e0) = all_52_13
% 241.99/48.52    (44)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 241.99/48.52          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 241.99/48.52            e1)
% 241.99/48.52    (45)   ~ (all_52_1 = e3)
% 241.99/48.52    (46)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 241.99/48.52          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 241.99/48.52            e2)
% 241.99/48.52    (47)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 241.99/48.52          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 241.99/48.52    (48)   ~ (e2 = e1)
% 241.99/48.52    (49)   ~ (all_52_1 = e1)
% 241.99/48.52  
% 241.99/48.52  Begin of proof
% 241.99/48.52  | 
% 241.99/48.52  | BETA: splitting (20) gives:
% 241.99/48.52  | 
% 241.99/48.52  | Case 1:
% 241.99/48.52  | | 
% 241.99/48.52  | |   (50)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 241.99/48.52  | |           e2)
% 241.99/48.52  | | 
% 241.99/48.52  | | BETA: splitting (50) gives:
% 241.99/48.52  | | 
% 241.99/48.52  | | Case 1:
% 241.99/48.52  | | | 
% 241.99/48.52  | | |   (51)  all_58_0 = e2 & op(e3, e3) = e2
% 241.99/48.52  | | | 
% 241.99/48.52  | | | ALPHA: (51) implies:
% 241.99/48.52  | | |   (52)  op(e3, e3) = e2
% 241.99/48.52  | | | 
% 241.99/48.52  | | | REF_CLOSE: (17), (38), (48), (52) are inconsistent by sub-proof #2267.
% 241.99/48.52  | | | 
% 241.99/48.52  | | Case 2:
% 241.99/48.52  | | | 
% 241.99/48.52  | | |   (53)  all_58_2 = e2 & op(e2, e3) = e2
% 241.99/48.52  | | | 
% 241.99/48.52  | | | ALPHA: (53) implies:
% 241.99/48.52  | | |   (54)  all_58_2 = e2
% 241.99/48.52  | | | 
% 241.99/48.52  | | | BETA: splitting (3) gives:
% 241.99/48.52  | | | 
% 241.99/48.52  | | | Case 1:
% 241.99/48.52  | | | | 
% 241.99/48.52  | | | |   (55)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 241.99/48.52  | | | |           = e1)
% 241.99/48.52  | | | | 
% 241.99/48.52  | | | | BETA: splitting (55) gives:
% 241.99/48.52  | | | | 
% 241.99/48.52  | | | | Case 1:
% 241.99/48.52  | | | | | 
% 241.99/48.52  | | | | |   (56)  all_58_6 = e1 & op(e1, e3) = e1
% 241.99/48.52  | | | | | 
% 241.99/48.52  | | | | | ALPHA: (56) implies:
% 241.99/48.52  | | | | |   (57)  all_58_6 = e1
% 241.99/48.52  | | | | | 
% 241.99/48.52  | | | | | REF_CLOSE: (2), (4), (17), (24), (27), (38), (41), (54), (57) are
% 241.99/48.52  | | | | |            inconsistent by sub-proof #1164.
% 241.99/48.52  | | | | | 
% 241.99/48.52  | | | | Case 2:
% 241.99/48.52  | | | | | 
% 241.99/48.52  | | | | |   (58)  all_58_7 = e1 & op(e1, e2) = e1
% 241.99/48.52  | | | | | 
% 241.99/48.52  | | | | | ALPHA: (58) implies:
% 241.99/48.52  | | | | |   (59)  all_58_7 = e1
% 241.99/48.52  | | | | |   (60)  op(e1, e2) = e1
% 241.99/48.52  | | | | | 
% 241.99/48.52  | | | | | BETA: splitting (36) gives:
% 241.99/48.52  | | | | | 
% 241.99/48.52  | | | | | Case 1:
% 241.99/48.52  | | | | | | 
% 241.99/48.52  | | | | | |   (61)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 241.99/48.52  | | | | | |             e2) = e2)
% 241.99/48.52  | | | | | | 
% 241.99/48.52  | | | | | | BETA: splitting (61) gives:
% 241.99/48.52  | | | | | | 
% 241.99/48.52  | | | | | | Case 1:
% 241.99/48.52  | | | | | | | 
% 241.99/48.52  | | | | | | |   (62)  all_58_6 = e2 & op(e1, e3) = e2
% 241.99/48.52  | | | | | | | 
% 241.99/48.52  | | | | | | | ALPHA: (62) implies:
% 241.99/48.52  | | | | | | |   (63)  all_58_6 = e2
% 241.99/48.52  | | | | | | | 
% 241.99/48.52  | | | | | | | REF_CLOSE: (4), (22), (63) are inconsistent by sub-proof #1982.
% 241.99/48.52  | | | | | | | 
% 241.99/48.52  | | | | | | Case 2:
% 241.99/48.52  | | | | | | | 
% 241.99/48.52  | | | | | | |   (64)  all_58_7 = e2 & op(e1, e2) = e2
% 241.99/48.52  | | | | | | | 
% 241.99/48.52  | | | | | | | REF_CLOSE: (48), (59), (64) are inconsistent by sub-proof #2218.
% 241.99/48.52  | | | | | | | 
% 241.99/48.52  | | | | | | End of split
% 241.99/48.52  | | | | | | 
% 241.99/48.52  | | | | | Case 2:
% 241.99/48.52  | | | | | | 
% 241.99/48.52  | | | | | |   (65)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 241.99/48.52  | | | | | |             e0) = e2)
% 241.99/48.52  | | | | | | 
% 241.99/48.52  | | | | | | BETA: splitting (65) gives:
% 241.99/48.52  | | | | | | 
% 241.99/48.52  | | | | | | Case 1:
% 241.99/48.52  | | | | | | | 
% 241.99/48.52  | | | | | | |   (66)  all_58_8 = e2 & op(e1, e1) = e2
% 241.99/48.52  | | | | | | | 
% 241.99/48.52  | | | | | | | ALPHA: (66) implies:
% 241.99/48.52  | | | | | | |   (67)  all_58_8 = e2
% 241.99/48.52  | | | | | | |   (68)  op(e1, e1) = e2
% 241.99/48.52  | | | | | | | 
% 241.99/48.52  | | | | | | | BETA: splitting (12) gives:
% 241.99/48.52  | | | | | | | 
% 241.99/48.52  | | | | | | | Case 1:
% 241.99/48.52  | | | | | | | | 
% 241.99/48.52  | | | | | | | |   (69)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 241.99/48.52  | | | | | | | |           op(e2, e1) = e0)
% 241.99/48.52  | | | | | | | | 
% 241.99/48.52  | | | | | | | | BETA: splitting (69) gives:
% 241.99/48.52  | | | | | | | | 
% 241.99/48.52  | | | | | | | | Case 1:
% 241.99/48.52  | | | | | | | | | 
% 241.99/48.52  | | | | | | | | |   (70)  all_58_4 = e0 & op(e3, e1) = e0
% 241.99/48.52  | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | ALPHA: (70) implies:
% 241.99/48.52  | | | | | | | | |   (71)  all_58_4 = e0
% 241.99/48.52  | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11),
% 241.99/48.52  | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 241.99/48.52  | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 241.99/48.52  | | | | | | | | |            (28), (29), (30), (32), (33), (34), (35), (36),
% 241.99/48.52  | | | | | | | | |            (37), (38), (39), (40), (41), (42), (44), (45),
% 241.99/48.52  | | | | | | | | |            (46), (48), (59), (68), (71) are inconsistent by
% 241.99/48.52  | | | | | | | | |            sub-proof #673.
% 241.99/48.52  | | | | | | | | | 
% 241.99/48.52  | | | | | | | | Case 2:
% 241.99/48.52  | | | | | | | | | 
% 241.99/48.52  | | | | | | | | |   (72)  all_58_5 = e0 & op(e2, e1) = e0
% 241.99/48.52  | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | ALPHA: (72) implies:
% 241.99/48.52  | | | | | | | | |   (73)  op(e2, e1) = e0
% 241.99/48.52  | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | BETA: splitting (47) gives:
% 241.99/48.52  | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | Case 1:
% 241.99/48.52  | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | |   (74)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 241.99/48.52  | | | | | | | | | |           op(e2, e2) = e1)
% 241.99/48.52  | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | BETA: splitting (74) gives:
% 241.99/48.52  | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | Case 1:
% 241.99/48.52  | | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | |   (75)  all_58_2 = e1 & op(e2, e3) = e1
% 241.99/48.52  | | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | | REF_CLOSE: (26), (38), (49), (75) are inconsistent by
% 241.99/48.52  | | | | | | | | | | |            sub-proof #2229.
% 241.99/48.52  | | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | Case 2:
% 241.99/48.52  | | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | |   (76)  all_58_3 = e1 & op(e2, e2) = e1
% 241.99/48.52  | | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | | ALPHA: (76) implies:
% 241.99/48.52  | | | | | | | | | | |   (77)  all_58_3 = e1
% 241.99/48.52  | | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | | COMBINE_EQS: (13), (77) imply:
% 241.99/48.52  | | | | | | | | | | |   (78)  e3 = e1
% 241.99/48.52  | | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | | SIMP: (78) implies:
% 241.99/48.52  | | | | | | | | | | |   (79)  e3 = e1
% 241.99/48.52  | | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | | COMBINE_EQS: (27), (79) imply:
% 241.99/48.52  | | | | | | | | | | |   (80)  all_58_12 = e1
% 241.99/48.52  | | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | | REF_CLOSE: (2), (4), (11), (16), (17), (20), (21), (24),
% 241.99/48.52  | | | | | | | | | | |            (26), (38), (41), (45), (48), (80) are
% 241.99/48.52  | | | | | | | | | | |            inconsistent by sub-proof #1204.
% 241.99/48.52  | | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | | End of split
% 241.99/48.52  | | | | | | | | | | 
% 241.99/48.52  | | | | | | | | | Case 2:
% 241.99/48.52  | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | |   (81)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1
% 241.99/48.53  | | | | | | | | | |           & op(e2, e0) = e1)
% 241.99/48.53  | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | BETA: splitting (81) gives:
% 241.99/48.53  | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | Case 1:
% 241.99/48.53  | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | |   (82)  all_58_5 = e1 & op(e2, e1) = e1
% 241.99/48.53  | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | ALPHA: (82) implies:
% 241.99/48.53  | | | | | | | | | | |   (83)  op(e2, e1) = e1
% 241.99/48.53  | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | REF_CLOSE: (19), (38), (41), (73), (83) are inconsistent by
% 241.99/48.53  | | | | | | | | | | |            sub-proof #2165.
% 241.99/48.53  | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | Case 2:
% 241.99/48.53  | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | |   (84)  all_58_10 = e1 & op(e2, e0) = e1
% 241.99/48.53  | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | ALPHA: (84) implies:
% 241.99/48.53  | | | | | | | | | | |   (85)  all_58_10 = e1
% 241.99/48.53  | | | | | | | | | | |   (86)  op(e2, e0) = e1
% 241.99/48.53  | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | BETA: splitting (9) gives:
% 241.99/48.53  | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | Case 1:
% 241.99/48.53  | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | |   (87)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 241.99/48.53  | | | | | | | | | | | |           & op(e2, e1) = e1)
% 241.99/48.53  | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (11), (13), (15), (17), (21), (28),
% 241.99/48.53  | | | | | | | | | | | |            (32), (33), (37), (38), (41), (48), (54), (85),
% 241.99/48.53  | | | | | | | | | | | |            (87) are inconsistent by sub-proof #672.
% 241.99/48.53  | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | Case 2:
% 241.99/48.53  | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | |   (88)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 241.99/48.53  | | | | | | | | | | | |           e1 & op(e0, e1) = e1)
% 241.99/48.53  | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | BETA: splitting (88) gives:
% 241.99/48.53  | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | Case 1:
% 241.99/48.53  | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | |   (89)  all_58_8 = e1 & op(e1, e1) = e1
% 241.99/48.53  | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | ALPHA: (89) implies:
% 241.99/48.53  | | | | | | | | | | | | |   (90)  op(e1, e1) = e1
% 241.99/48.53  | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | REF_CLOSE: (38), (40), (41), (90) are inconsistent by
% 241.99/48.53  | | | | | | | | | | | | |            sub-proof #2220.
% 241.99/48.53  | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | Case 2:
% 241.99/48.53  | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | |   (91)  all_58_14 = e1 & op(e0, e1) = e1
% 241.99/48.53  | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | ALPHA: (91) implies:
% 241.99/48.53  | | | | | | | | | | | | |   (92)  all_58_14 = e1
% 241.99/48.53  | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | BETA: splitting (30) gives:
% 241.99/48.53  | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | Case 1:
% 241.99/48.53  | | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | |   (93)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 241.99/48.53  | | | | | | | | | | | | | |           & op(e2, e1) = e3)
% 241.99/48.53  | | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 241.99/48.53  | | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | | Case 1:
% 241.99/48.53  | | | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | | |   (94)  all_58_4 = e3 & op(e3, e1) = e3
% 241.99/48.53  | | | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 241.99/48.53  | | | | | | | | | | | | | | |   (95)  all_58_4 = e3
% 241.99/48.53  | | | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 241.99/48.53  | | | | | | | | | | | | | | | 
% 241.99/48.53  | | | | | | | | | | | | | | | Case 1:
% 241.99/48.53  | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | |   (96)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 242.03/48.53  | | | | | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 242.03/48.53  | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | |   (97)  all_58_12 = e2 & op(e0, e3) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (14), (21), (22), (25), (27), (29),
% 242.03/48.53  | | | | | | | | | | | | | | | | |            (38), (68), (97) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | |            #677.
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | |   (98)  all_58_13 = e2 & op(e0, e2) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | |   (99)  op(e0, e2) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | |   (100)  all_58_15 = e0 & op(e0, e0) = e0
% 242.03/48.53  | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | | |   (101)  all_58_15 = e0
% 242.03/48.53  | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | |   (102)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 242.03/48.53  | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (103)  all_58_9 = e2 & op(e3, e0) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (104)  all_58_9 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with e0, e2, e1, e1,
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |              simplifying with (40), (68) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (105)  e2 = e0
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (105) imply:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (106)  all_58_9 = e0
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |   (107)  all_58_12 = e2 & op(e0, e3) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (27), (107) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |            #1974.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |   (108)  all_58_13 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | |   (109)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (8), (13), (21), (22), (41), (48),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | |            (59), (108), (109) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | |            #671.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (110)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (13), (17), (38), (41), (48), (59),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | |            (99), (110) are inconsistent by sub-proof #720.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (111)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (112)  all_58_4 = e2 & op(e3, e1) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (113)  all_58_4 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (113) imply:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (114)  e3 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (114) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (115)  e3 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (115) imply:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (116)  all_58_11 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (21), (22), (25), (29), (38), (68),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | |            (116) are inconsistent by sub-proof #997.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (103), (106) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1655.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | |   (117)  all_58_11 = e2 & op(e1, e0) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (21), (117) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | |            #1741.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | |   (118)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |   (119)  all_58_14 = e2 & op(e0, e1) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |   (120)  all_58_14 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (92), (120) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |            #2044.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |   (121)  all_58_15 = e2 & op(e0, e0) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (101), (121) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |            #1654.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (122)  all_58_10 = e2 & op(e2, e0) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (123)  all_58_10 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (123) imply:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (124)  e2 = e1
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | SIMP: (124) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (125)  e2 = e1
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (125) imply:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (126)  all_58_8 = e1
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |   (127)  all_58_12 = e2 & op(e0, e3) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (27), (127) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |            #1974.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |   (128)  all_58_13 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | |   (129)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (8), (13), (21), (22), (41), (48),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | |            (59), (128), (129) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | |            #671.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (128) imply:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | |   (130)  all_58_13 = e1
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (8), (13), (21), (41), (48), (59),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | |            (130) are inconsistent by sub-proof #1457.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | |   (131)  all_58_11 = e2 & op(e1, e0) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (21), (131) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | |            #1741.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | |   (132)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |   (133)  all_58_14 = e2 & op(e0, e1) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (92), (133) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |            #1771.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |   (134)  all_58_15 = e2 & op(e0, e0) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (101), (134) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | |            #1654.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | |   (135)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 242.03/48.53  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (136)  all_58_11 = e2 & op(e1, e0) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (137)  all_58_11 = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (21), (22), (25), (29), (38), (68),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |            (137) are inconsistent by sub-proof #997.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |   (138)  all_58_15 = e2 & op(e0, e0) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (32), (33), (34), (35),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |            (44), (45), (46), (48), (59), (68), (85), (86),
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |            (92), (94), (95), (138) are inconsistent by
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | |            sub-proof #669.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | |   (139)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.03/48.53  | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.03/48.53  | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 242.03/48.53  | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.03/48.53  | | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.03/48.53  | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 242.03/48.53  | | | | | | | | | | | | | | | | | |   (140)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 242.03/48.53  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 242.03/48.53  | | | | | | | | | | | | | | | | | |              e1) = e0)
% 242.03/48.53  | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (27), (38), (41), (92), (99), (140) are
% 242.03/48.53  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1032.
% 242.03/48.53  | | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | |   (141)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 242.03/48.53  | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 242.03/48.53  | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | |   (142)  all_58_14 = e2 & op(e0, e1) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (92), (142) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | | | |            #1771.
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | |   (143)  all_58_15 = e2 & op(e0, e0) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10),
% 242.03/48.53  | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 242.03/48.53  | | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 242.03/48.53  | | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (32), (33), (34), (35),
% 242.03/48.53  | | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 242.03/48.53  | | | | | | | | | | | | | | | | |            (44), (45), (46), (48), (59), (68), (85), (86),
% 242.03/48.53  | | | | | | | | | | | | | | | | |            (92), (94), (95), (143) are inconsistent by
% 242.03/48.53  | | | | | | | | | | | | | | | | |            sub-proof #669.
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | |   (144)  all_58_5 = e3 & op(e2, e1) = e3
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | REF_CLOSE: (19), (34), (38), (144) are inconsistent by
% 242.03/48.53  | | | | | | | | | | | | | | |            sub-proof #1822.
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | |   (145)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 242.03/48.53  | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 242.03/48.53  | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 242.03/48.53  | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | |   (146)  all_58_8 = e3 & op(e1, e1) = e3
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 242.03/48.53  | | | | | | | | | | | | | | |   (147)  op(e1, e1) = e3
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | REF_CLOSE: (21), (38), (68), (147) are inconsistent by
% 242.03/48.53  | | | | | | | | | | | | | | |            sub-proof #2206.
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | |   (148)  all_58_14 = e3 & op(e0, e1) = e3
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 242.03/48.53  | | | | | | | | | | | | | | |   (149)  all_58_14 = e3
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | COMBINE_EQS: (92), (149) imply:
% 242.03/48.53  | | | | | | | | | | | | | | |   (150)  e3 = e1
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | COMBINE_EQS: (27), (150) imply:
% 242.03/48.53  | | | | | | | | | | | | | | |   (151)  all_58_12 = e1
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (11), (16), (17), (20), (21), (24),
% 242.03/48.53  | | | | | | | | | | | | | | |            (26), (38), (41), (45), (48), (151) are
% 242.03/48.53  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1204.
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | | 
% 242.03/48.53  | | | | | | | | End of split
% 242.03/48.53  | | | | | | | | 
% 242.03/48.53  | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | 
% 242.03/48.53  | | | | | | | |   (152)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 242.03/48.53  | | | | | | | |            op(e0, e1) = e0)
% 242.03/48.53  | | | | | | | | 
% 242.03/48.53  | | | | | | | | BETA: splitting (152) gives:
% 242.03/48.53  | | | | | | | | 
% 242.03/48.53  | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | 
% 242.03/48.53  | | | | | | | | |   (153)  all_58_8 = e0 & op(e1, e1) = e0
% 242.03/48.53  | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | ALPHA: (153) implies:
% 242.03/48.53  | | | | | | | | |   (154)  all_58_8 = e0
% 242.03/48.53  | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | REF_CLOSE: (4), (67), (154) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | |            #1556.
% 242.03/48.53  | | | | | | | | | 
% 242.03/48.53  | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | 
% 242.03/48.53  | | | | | | | | |   (155)  all_58_14 = e0 & op(e0, e1) = e0
% 242.03/48.53  | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | ALPHA: (155) implies:
% 242.03/48.53  | | | | | | | | |   (156)  all_58_14 = e0
% 242.03/48.53  | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | BETA: splitting (30) gives:
% 242.03/48.53  | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | |   (157)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 242.03/48.53  | | | | | | | | | |            & op(e2, e1) = e3)
% 242.03/48.53  | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | BETA: splitting (157) gives:
% 242.03/48.53  | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | |   (158)  all_58_4 = e3 & op(e3, e1) = e3
% 242.03/48.53  | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | ALPHA: (158) implies:
% 242.03/48.53  | | | | | | | | | | |   (159)  all_58_4 = e3
% 242.03/48.53  | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | BETA: splitting (9) gives:
% 242.03/48.53  | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | |   (160)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 242.03/48.53  | | | | | | | | | | | |            & op(e2, e1) = e1)
% 242.03/48.53  | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | BETA: splitting (160) gives:
% 242.03/48.53  | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | |   (161)  all_58_4 = e1 & op(e3, e1) = e1
% 242.03/48.53  | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | ALPHA: (161) implies:
% 242.03/48.53  | | | | | | | | | | | | |   (162)  all_58_4 = e1
% 242.03/48.53  | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (11), (15), (17), (21), (28), (32),
% 242.03/48.53  | | | | | | | | | | | | |            (33), (38), (41), (48), (162) are inconsistent by
% 242.03/48.53  | | | | | | | | | | | | |            sub-proof #1468.
% 242.03/48.53  | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | |   (163)  all_58_5 = e1 & op(e2, e1) = e1
% 242.03/48.53  | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | ALPHA: (163) implies:
% 242.03/48.53  | | | | | | | | | | | | |   (164)  all_58_5 = e1
% 242.03/48.53  | | | | | | | | | | | | |   (165)  op(e2, e1) = e1
% 242.03/48.53  | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | BETA: splitting (46) gives:
% 242.03/48.53  | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | |   (166)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 242.03/48.53  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 242.03/48.53  | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 242.03/48.53  | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | |   (167)  all_58_12 = e2 & op(e0, e3) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (14), (21), (22), (25), (27), (29),
% 242.03/48.53  | | | | | | | | | | | | | | |            (38), (68), (167) are inconsistent by sub-proof
% 242.03/48.53  | | | | | | | | | | | | | | |            #677.
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | Case 2:
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | |   (168)  all_58_13 = e2 & op(e0, e2) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 242.03/48.53  | | | | | | | | | | | | | | |   (169)  op(e0, e2) = e2
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | |   (170)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 242.03/48.53  | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 242.03/48.53  | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 242.03/48.53  | | | | | | | | | | | | | | | | 
% 242.03/48.53  | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.53  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (171)  all_58_1 = e0 & op(e3, e2) = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (172)  all_58_1 = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | |   (173)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 242.03/48.54  | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (13), (17), (38), (41), (48), (59),
% 242.03/48.54  | | | | | | | | | | | | | | | | | |            (169), (173) are inconsistent by sub-proof #720.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | |   (174)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 242.03/48.54  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (175)  all_58_4 = e2 & op(e3, e1) = e2
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (176)  all_58_4 = e2
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (176) imply:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (177)  e3 = e2
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (177) imply:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (178)  all_58_11 = e2
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (21), (22), (25), (29), (38), (68),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            (178) are inconsistent by sub-proof #997.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (179)  all_58_9 = e2 & op(e3, e0) = e2
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |   (180)  all_58_15 = e0 & op(e0, e0) = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |   (181)  op(e0, e0) = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (10), (11), (12), (13),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |            (15), (16), (17), (19), (20), (21), (23), (24),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |            (26), (30), (32), (33), (34), (36), (37), (38),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |            (41), (42), (44), (45), (48), (59), (164), (181)
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #675.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |   (182)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |   (183)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | |              e0) = e0)
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | |   (184)  all_58_9 = e0 & op(e3, e0) = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | |   (185)  all_58_9 = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (17), (21), (38), (48), (159), (172),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | |            (185) are inconsistent by sub-proof #1097.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | |   (186)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | |   (187)  all_58_9 = e2
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with e0, e2, e1, e1,
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | |              simplifying with (40), (68) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | |   (188)  e2 = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (188) imply:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | |   (189)  all_58_9 = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (17), (21), (38), (48), (159), (172),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | |            (189) are inconsistent by sub-proof #1097.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | |   (190)  all_58_11 = e0 & op(e1, e0) = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | |   (191)  all_58_11 = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (21), (22), (25), (29), (38), (68),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | |            (191) are inconsistent by sub-proof #1686.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (192)  all_58_3 = e0 & op(e2, e2) = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (193)  all_58_3 = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (193) imply:
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (194)  e3 = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10),
% 242.03/48.54  | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 242.03/48.54  | | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 242.03/48.54  | | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (32), (33), (34), (35),
% 242.03/48.54  | | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (44),
% 242.03/48.54  | | | | | | | | | | | | | | | | |            (45), (46), (48), (59), (68), (159), (194) are
% 242.03/48.54  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | |   (195)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 242.03/48.54  | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (38), (41), (60), (169), (195) are
% 242.03/48.54  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | |   (196)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 242.03/48.54  | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 242.03/48.54  | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 242.03/48.54  | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | |   (197)  all_58_14 = e2 & op(e0, e1) = e2
% 242.03/48.54  | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (197) are inconsistent by sub-proof
% 242.03/48.54  | | | | | | | | | | | | | | |            #2077.
% 242.03/48.54  | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | |   (198)  all_58_15 = e2 & op(e0, e0) = e2
% 242.03/48.54  | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | ALPHA: (198) implies:
% 242.03/48.54  | | | | | | | | | | | | | | |   (199)  all_58_15 = e2
% 242.03/48.54  | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | |   (200)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 242.03/48.54  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (201)  all_58_9 = e1 & op(e3, e0) = e1
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (202)  all_58_9 = e1
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | |   (203)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (17), (21), (38), (41), (48), (159),
% 242.03/48.54  | | | | | | | | | | | | | | | | | |            (202), (203) are inconsistent by sub-proof #1293.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | |   (204)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (205)  all_58_4 = e0 & op(e3, e1) = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (206)  all_58_4 = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (32), (33), (34), (35),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (44),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            (45), (46), (48), (59), (68), (206) are
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #673.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (207)  all_58_9 = e0 & op(e3, e0) = e0
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (202), (207) are inconsistent by sub-proof
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            #1696.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (208)  all_58_10 = e1 & op(e2, e0) = e1
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (209)  all_58_10 = e1
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (13), (14), (19), (21), (22), (25),
% 242.03/48.54  | | | | | | | | | | | | | | | | |            (29), (36), (37), (38), (41), (48), (54), (59),
% 242.03/48.54  | | | | | | | | | | | | | | | | |            (165), (209) are inconsistent by sub-proof #668.
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | |   (210)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 242.03/48.54  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (211)  all_58_11 = e1 & op(e1, e0) = e1
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (212)  all_58_11 = e1
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (213)  op(e1, e0) = e1
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | |   (214)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 242.03/48.54  | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (215)  all_58_6 = e3 & op(e1, e3) = e3
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (216)  all_58_6 = e3
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (38), (41), (42), (59), (67), (213),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            (216) are inconsistent by sub-proof #1555.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (217)  all_58_7 = e3 & op(e1, e2) = e3
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (218)  op(e1, e2) = e3
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (29), (38), (218) are inconsistent by
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            sub-proof #2191.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | |   (219)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 242.03/48.54  | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (220)  all_58_8 = e3 & op(e1, e1) = e3
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |   (221)  op(e1, e1) = e3
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (38), (68), (221) are inconsistent by
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            sub-proof #2206.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (11), (14), (15), (17), (21), (28),
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            (32), (33), (38), (41), (48), (159), (212) are
% 242.03/48.54  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #667.
% 242.03/48.54  | | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (222)  all_58_15 = e1 & op(e0, e0) = e1
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 242.03/48.54  | | | | | | | | | | | | | | | | |   (223)  all_58_15 = e1
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (199), (223) are inconsistent by sub-proof
% 242.03/48.54  | | | | | | | | | | | | | | | | |            #2231.
% 242.03/48.54  | | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | |   (224)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 242.03/48.54  | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 242.03/48.54  | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | BETA: splitting (224) gives:
% 242.03/48.54  | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | |   (225)  all_58_8 = e1 & op(e1, e1) = e1
% 242.03/48.54  | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | ALPHA: (225) implies:
% 242.03/48.54  | | | | | | | | | | | | |   (226)  op(e1, e1) = e1
% 242.03/48.54  | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | REF_CLOSE: (38), (40), (41), (226) are inconsistent by
% 242.03/48.54  | | | | | | | | | | | | |            sub-proof #2220.
% 242.03/48.54  | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | |   (227)  all_58_14 = e1 & op(e0, e1) = e1
% 242.03/48.54  | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | | REF_CLOSE: (41), (156), (227) are inconsistent by sub-proof
% 242.03/48.54  | | | | | | | | | | | | |            #828.
% 242.03/48.54  | | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | |   (228)  all_58_5 = e3 & op(e2, e1) = e3
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | REF_CLOSE: (19), (34), (38), (228) are inconsistent by
% 242.03/48.54  | | | | | | | | | | |            sub-proof #1822.
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | End of split
% 242.03/48.54  | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | |   (229)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3
% 242.03/48.54  | | | | | | | | | |            & op(e0, e1) = e3)
% 242.03/48.54  | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | BETA: splitting (229) gives:
% 242.03/48.54  | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | Case 1:
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | |   (230)  all_58_8 = e3 & op(e1, e1) = e3
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | ALPHA: (230) implies:
% 242.03/48.54  | | | | | | | | | | |   (231)  op(e1, e1) = e3
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | REF_CLOSE: (21), (38), (68), (231) are inconsistent by
% 242.03/48.54  | | | | | | | | | | |            sub-proof #2206.
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | Case 2:
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | |   (232)  all_58_14 = e3 & op(e0, e1) = e3
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | ALPHA: (232) implies:
% 242.03/48.54  | | | | | | | | | | |   (233)  all_58_14 = e3
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | COMBINE_EQS: (156), (233) imply:
% 242.03/48.54  | | | | | | | | | | |   (234)  e3 = e0
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | SIMP: (234) implies:
% 242.03/48.54  | | | | | | | | | | |   (235)  e3 = e0
% 242.03/48.54  | | | | | | | | | | | 
% 242.03/48.54  | | | | | | | | | | | COMBINE_EQS: (14), (235) imply:
% 242.05/48.54  | | | | | | | | | | |   (236)  all_58_11 = e0
% 242.05/48.54  | | | | | | | | | | | 
% 242.05/48.54  | | | | | | | | | | | REF_CLOSE: (2), (5), (21), (22), (25), (29), (38), (68),
% 242.05/48.54  | | | | | | | | | | |            (236) are inconsistent by sub-proof #1686.
% 242.05/48.54  | | | | | | | | | | | 
% 242.05/48.54  | | | | | | | | | | End of split
% 242.05/48.54  | | | | | | | | | | 
% 242.05/48.54  | | | | | | | | | End of split
% 242.05/48.54  | | | | | | | | | 
% 242.05/48.54  | | | | | | | | End of split
% 242.05/48.54  | | | | | | | | 
% 242.05/48.54  | | | | | | | End of split
% 242.05/48.54  | | | | | | | 
% 242.05/48.54  | | | | | | Case 2:
% 242.05/48.54  | | | | | | | 
% 242.05/48.54  | | | | | | |   (237)  all_58_11 = e2 & op(e1, e0) = e2
% 242.05/48.54  | | | | | | | 
% 242.05/48.54  | | | | | | | ALPHA: (237) implies:
% 242.05/48.54  | | | | | | |   (238)  all_58_11 = e2
% 242.05/48.54  | | | | | | | 
% 242.05/48.54  | | | | | | | REF_CLOSE: (14), (21), (238) are inconsistent by sub-proof #2030.
% 242.05/48.54  | | | | | | | 
% 242.05/48.54  | | | | | | End of split
% 242.05/48.54  | | | | | | 
% 242.05/48.54  | | | | | End of split
% 242.05/48.54  | | | | | 
% 242.05/48.54  | | | | End of split
% 242.05/48.54  | | | | 
% 242.05/48.54  | | | Case 2:
% 242.05/48.54  | | | | 
% 242.05/48.54  | | | |   (239)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1,
% 242.05/48.54  | | | |              e0) = e1)
% 242.05/48.54  | | | | 
% 242.05/48.54  | | | | BETA: splitting (239) gives:
% 242.05/48.54  | | | | 
% 242.05/48.54  | | | | Case 1:
% 242.05/48.54  | | | | | 
% 242.05/48.54  | | | | |   (240)  all_58_8 = e1 & op(e1, e1) = e1
% 242.05/48.54  | | | | | 
% 242.05/48.54  | | | | | ALPHA: (240) implies:
% 242.05/48.54  | | | | |   (241)  op(e1, e1) = e1
% 242.05/48.54  | | | | | 
% 242.05/48.54  | | | | | REF_CLOSE: (38), (40), (41), (241) are inconsistent by sub-proof
% 242.05/48.54  | | | | |            #2220.
% 242.05/48.54  | | | | | 
% 242.05/48.54  | | | | Case 2:
% 242.05/48.54  | | | | | 
% 242.05/48.54  | | | | |   (242)  all_58_11 = e1 & op(e1, e0) = e1
% 242.05/48.54  | | | | | 
% 242.05/48.54  | | | | | REF_CLOSE: (2), (4), (11), (14), (16), (17), (20), (21), (24), (26),
% 242.05/48.54  | | | | |            (27), (38), (41), (45), (48), (242) are inconsistent by
% 242.05/48.54  | | | | |            sub-proof #674.
% 242.05/48.54  | | | | | 
% 242.05/48.54  | | | | End of split
% 242.05/48.54  | | | | 
% 242.05/48.54  | | | End of split
% 242.05/48.54  | | | 
% 242.05/48.54  | | End of split
% 242.05/48.54  | | 
% 242.05/48.54  | Case 2:
% 242.05/48.54  | | 
% 242.05/48.54  | |   (243)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 242.05/48.54  | |            e2)
% 242.05/48.54  | | 
% 242.05/48.54  | | BETA: splitting (243) gives:
% 242.05/48.54  | | 
% 242.05/48.54  | | Case 1:
% 242.05/48.54  | | | 
% 242.05/48.54  | | |   (244)  all_58_6 = e2 & op(e1, e3) = e2
% 242.05/48.54  | | | 
% 242.05/48.54  | | | REF_CLOSE: (4), (22), (244) are inconsistent by sub-proof #1444.
% 242.05/48.54  | | | 
% 242.05/48.54  | | Case 2:
% 242.05/48.54  | | | 
% 242.05/48.54  | | |   (245)  all_58_12 = e2 & op(e0, e3) = e2
% 242.05/48.54  | | | 
% 242.05/48.54  | | | ALPHA: (245) implies:
% 242.05/48.54  | | |   (246)  all_58_12 = e2
% 242.05/48.54  | | | 
% 242.05/48.54  | | | REF_CLOSE: (21), (27), (246) are inconsistent by sub-proof #1552.
% 242.05/48.54  | | | 
% 242.05/48.54  | | End of split
% 242.05/48.54  | | 
% 242.05/48.54  | End of split
% 242.05/48.54  | 
% 242.05/48.54  End of proof
% 242.05/48.54  
% 242.05/48.54  Sub-proof #667 shows that the following formulas are inconsistent:
% 242.05/48.54  ----------------------------------------------------------------
% 242.05/48.54    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.05/48.54         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.05/48.54    (2)   ~ (e3 = e0)
% 242.05/48.54    (3)   ~ (e2 = e0)
% 242.05/48.54    (4)  all_58_11 = e1
% 242.05/48.54    (5)   ~ (e3 = e1)
% 242.05/48.54    (6)  all_58_11 = e3
% 242.05/48.54    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.05/48.54         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.05/48.54    (8)  op(e3, e3) = e1
% 242.05/48.54    (9)   ~ (e3 = e2)
% 242.05/48.54    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.05/48.54          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.54    (11)   ~ (all_52_4 = e3)
% 242.05/48.54    (12)  op(e3, e2) = all_52_4
% 242.05/48.54    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.54    (14)   ~ (e1 = e0)
% 242.05/48.54    (15)  all_58_4 = e3
% 242.05/48.54    (16)   ~ (e2 = e1)
% 242.05/48.54  
% 242.05/48.54  Begin of proof
% 242.05/48.54  | 
% 242.05/48.54  | COMBINE_EQS: (4), (6) imply:
% 242.05/48.54  |   (17)  e3 = e1
% 242.05/48.54  | 
% 242.05/48.54  | SIMP: (17) implies:
% 242.05/48.54  |   (18)  e3 = e1
% 242.05/48.54  | 
% 242.05/48.54  | COMBINE_EQS: (15), (18) imply:
% 242.05/48.54  |   (19)  all_58_4 = e1
% 242.05/48.54  | 
% 242.05/48.54  | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 242.05/48.54  |            (16), (19) are inconsistent by sub-proof #1468.
% 242.05/48.54  | 
% 242.05/48.54  End of proof
% 242.05/48.54  
% 242.05/48.54  Sub-proof #668 shows that the following formulas are inconsistent:
% 242.05/48.54  ----------------------------------------------------------------
% 242.05/48.54    (1)   ~ (e3 = e0)
% 242.05/48.54    (2)  op(e2, e1) = e1
% 242.05/48.54    (3)   ~ (e2 = e0)
% 242.05/48.54    (4)  op(e1, e2) = all_52_6
% 242.05/48.54    (5)  all_58_2 = e2
% 242.05/48.54    (6)  all_58_3 = e3
% 242.05/48.54    (7)  all_58_11 = e3
% 242.05/48.54    (8)  op(e2, e1) = all_52_9
% 242.05/48.54    (9)   ~ (e3 = e2)
% 242.05/48.54    (10)  all_58_6 = e0
% 242.05/48.55    (11)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.05/48.55          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.05/48.55    (12)   ~ (all_52_6 = e3)
% 242.05/48.55    (13)  all_58_7 = e1
% 242.05/48.55    (14)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.05/48.55          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.05/48.55    (15)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.55          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.05/48.55    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.55    (17)   ~ (e1 = e0)
% 242.05/48.55    (18)  all_58_10 = e1
% 242.05/48.55    (19)   ~ (e2 = e1)
% 242.05/48.55  
% 242.05/48.55  Begin of proof
% 242.05/48.55  | 
% 242.05/48.55  | BETA: splitting (15) gives:
% 242.05/48.55  | 
% 242.05/48.55  | Case 1:
% 242.05/48.55  | | 
% 242.05/48.55  | |   (20)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 242.05/48.55  | |           e0)
% 242.05/48.55  | | 
% 242.05/48.55  | | BETA: splitting (20) gives:
% 242.05/48.55  | | 
% 242.05/48.55  | | Case 1:
% 242.05/48.55  | | | 
% 242.05/48.55  | | |   (21)  all_58_2 = e0 & op(e2, e3) = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | REF_CLOSE: (3), (5), (21) are inconsistent by sub-proof #1535.
% 242.05/48.55  | | | 
% 242.05/48.55  | | Case 2:
% 242.05/48.55  | | | 
% 242.05/48.55  | | |   (22)  all_58_3 = e0 & op(e2, e2) = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | ALPHA: (22) implies:
% 242.05/48.55  | | |   (23)  all_58_3 = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | COMBINE_EQS: (6), (23) imply:
% 242.05/48.55  | | |   (24)  e3 = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | SIMP: (24) implies:
% 242.05/48.55  | | |   (25)  e3 = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | COMBINE_EQS: (7), (25) imply:
% 242.05/48.55  | | |   (26)  all_58_11 = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | REF_CLOSE: (1), (3), (4), (9), (10), (11), (12), (13), (14), (16), (19),
% 242.05/48.55  | | |            (26) are inconsistent by sub-proof #960.
% 242.05/48.55  | | | 
% 242.05/48.55  | | End of split
% 242.05/48.55  | | 
% 242.05/48.55  | Case 2:
% 242.05/48.55  | | 
% 242.05/48.55  | |   (27)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 242.05/48.55  | |           e0)
% 242.05/48.55  | | 
% 242.05/48.55  | | BETA: splitting (27) gives:
% 242.05/48.55  | | 
% 242.05/48.55  | | Case 1:
% 242.05/48.55  | | | 
% 242.05/48.55  | | |   (28)  all_58_5 = e0 & op(e2, e1) = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | ALPHA: (28) implies:
% 242.05/48.55  | | |   (29)  op(e2, e1) = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | REF_CLOSE: (2), (8), (16), (17), (29) are inconsistent by sub-proof #2165.
% 242.05/48.55  | | | 
% 242.05/48.55  | | Case 2:
% 242.05/48.55  | | | 
% 242.05/48.55  | | |   (30)  all_58_10 = e0 & op(e2, e0) = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | REF_CLOSE: (17), (18), (30) are inconsistent by sub-proof #995.
% 242.05/48.55  | | | 
% 242.05/48.55  | | End of split
% 242.05/48.55  | | 
% 242.05/48.55  | End of split
% 242.05/48.55  | 
% 242.05/48.55  End of proof
% 242.05/48.55  
% 242.05/48.55  Sub-proof #669 shows that the following formulas are inconsistent:
% 242.05/48.55  ----------------------------------------------------------------
% 242.05/48.55    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.05/48.55         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.05/48.55    (2)   ~ (e3 = e0)
% 242.05/48.55    (3)   ~ (e2 = e0)
% 242.05/48.55    (4)  op(e1, e2) = all_52_6
% 242.05/48.55    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.55         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.55    (6)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 242.05/48.55         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 242.05/48.55    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.55         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.05/48.55    (8)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.05/48.55         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.05/48.55    (9)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.55         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.05/48.55    (10)   ~ (e3 = e1)
% 242.05/48.55    (11)  all_58_15 = e2 & op(e0, e0) = e2
% 242.05/48.55    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.05/48.55          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.05/48.55    (13)  all_58_3 = e3
% 242.05/48.55    (14)  all_58_11 = e3
% 242.05/48.55    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.05/48.55          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.05/48.55    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.05/48.55          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.05/48.55    (17)  op(e3, e3) = e1
% 242.05/48.55    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.55              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.05/48.55                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.05/48.55                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.05/48.55    (19)  op(e2, e1) = all_52_9
% 242.05/48.55    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.05/48.55          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.05/48.55    (21)   ~ (e3 = e2)
% 242.05/48.55    (22)  all_58_6 = e0
% 242.05/48.55    (23)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.05/48.55          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.05/48.55    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.05/48.55          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.05/48.55    (25)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.05/48.55          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.05/48.55    (26)  op(e2, e3) = all_52_1
% 242.05/48.55    (27)  all_58_12 = e3
% 242.05/48.55    (28)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.05/48.55          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.55    (29)   ~ (all_52_6 = e3)
% 242.05/48.55    (30)  op(e1, e1) = e2
% 242.05/48.55    (31)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.05/48.55          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.05/48.55    (32)   ~ (all_52_4 = e3)
% 242.05/48.55    (33)  op(e3, e2) = all_52_4
% 242.05/48.55    (34)  all_58_7 = e1
% 242.05/48.55    (35)   ~ (all_52_9 = e3)
% 242.05/48.55    (36)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.05/48.55          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.05/48.55    (37)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.05/48.55          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.05/48.55    (38)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.55          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.05/48.55    (39)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.55    (40)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.05/48.55          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.05/48.55    (41)  op(e1, e1) = e0
% 242.05/48.55    (42)   ~ (e1 = e0)
% 242.05/48.55    (43)  all_58_4 = e3
% 242.05/48.55    (44)  op(e2, e0) = e1
% 242.05/48.55    (45)  all_58_4 = e3 & op(e3, e1) = e3
% 242.05/48.55    (46)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.05/48.55          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.05/48.55    (47)  op(e2, e0) = all_52_13
% 242.05/48.55    (48)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.05/48.55          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.05/48.55            e1)
% 242.05/48.55    (49)   ~ (all_52_1 = e3)
% 242.05/48.55    (50)  all_58_14 = e1
% 242.05/48.55    (51)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.55          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.05/48.55            e2)
% 242.05/48.55    (52)  all_58_10 = e1
% 242.05/48.55    (53)   ~ (e2 = e1)
% 242.05/48.55  
% 242.05/48.55  Begin of proof
% 242.05/48.55  | 
% 242.05/48.55  | ALPHA: (11) implies:
% 242.05/48.55  |   (54)  all_58_15 = e2
% 242.05/48.55  | 
% 242.05/48.55  | BETA: splitting (18) gives:
% 242.05/48.55  | 
% 242.05/48.55  | Case 1:
% 242.05/48.55  | | 
% 242.05/48.55  | |   (55)  all_58_15 = e0 & op(e0, e0) = e0
% 242.05/48.55  | | 
% 242.05/48.55  | | ALPHA: (55) implies:
% 242.05/48.55  | |   (56)  all_58_15 = e0
% 242.05/48.55  | | 
% 242.05/48.55  | | REF_CLOSE: (3), (54), (56) are inconsistent by sub-proof #1507.
% 242.05/48.55  | | 
% 242.05/48.55  | Case 2:
% 242.05/48.55  | | 
% 242.05/48.55  | |   (57)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 242.05/48.55  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 242.05/48.55  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 242.05/48.55  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 242.05/48.55  | | 
% 242.05/48.55  | | ALPHA: (57) implies:
% 242.05/48.55  | |   (58)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.05/48.55  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.05/48.55  | |   (59)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 242.05/48.55  | |           e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.05/48.55  | | 
% 242.05/48.55  | | BETA: splitting (58) gives:
% 242.05/48.55  | | 
% 242.05/48.55  | | Case 1:
% 242.05/48.55  | | | 
% 242.05/48.55  | | |   (60)  all_58_12 = e0 & op(e0, e3) = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | ALPHA: (60) implies:
% 242.05/48.55  | | |   (61)  all_58_12 = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | COMBINE_EQS: (27), (61) imply:
% 242.05/48.55  | | |   (62)  e3 = e0
% 242.05/48.55  | | | 
% 242.05/48.55  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 242.05/48.55  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 242.05/48.55  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 242.05/48.55  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 242.05/48.55  | | |            (46), (48), (49), (51), (53), (62) are inconsistent by
% 242.05/48.55  | | |            sub-proof #670.
% 242.05/48.55  | | | 
% 242.05/48.55  | | Case 2:
% 242.05/48.55  | | | 
% 242.05/48.55  | | |   (63)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 242.05/48.55  | | |           = e0)
% 242.05/48.55  | | | 
% 242.05/48.55  | | | BETA: splitting (63) gives:
% 242.05/48.55  | | | 
% 242.05/48.55  | | | Case 1:
% 242.05/48.55  | | | | 
% 242.05/48.55  | | | |   (64)  all_58_13 = e0 & op(e0, e2) = e0
% 242.05/48.55  | | | | 
% 242.05/48.55  | | | | ALPHA: (64) implies:
% 242.05/48.55  | | | |   (65)  op(e0, e2) = e0
% 242.05/48.55  | | | | 
% 242.05/48.55  | | | | BETA: splitting (5) gives:
% 242.05/48.55  | | | | 
% 242.05/48.55  | | | | Case 1:
% 242.05/48.55  | | | | | 
% 242.05/48.55  | | | | |   (66)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2,
% 242.05/48.55  | | | | |             e2) = e2)
% 242.05/48.55  | | | | | 
% 242.05/48.55  | | | | | BETA: splitting (66) gives:
% 242.05/48.55  | | | | | 
% 242.05/48.55  | | | | | Case 1:
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | |   (67)  all_58_1 = e2 & op(e3, e2) = e2
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | BETA: splitting (59) gives:
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | Case 1:
% 242.05/48.55  | | | | | | | 
% 242.05/48.55  | | | | | | |   (68)  all_58_9 = e0 & op(e3, e0) = e0
% 242.05/48.55  | | | | | | | 
% 242.05/48.55  | | | | | | | ALPHA: (68) implies:
% 242.05/48.55  | | | | | | |   (69)  all_58_9 = e0
% 242.05/48.55  | | | | | | | 
% 242.05/48.55  | | | | | | | ALPHA: (67) implies:
% 242.05/48.55  | | | | | | |   (70)  all_58_1 = e2
% 242.05/48.55  | | | | | | | 
% 242.05/48.55  | | | | | | | GROUND_INST: instantiating (39) with e0, e2, e1, e1, simplifying
% 242.05/48.55  | | | | | | |              with (30), (41) gives:
% 242.05/48.55  | | | | | | |   (71)  e2 = e0
% 242.05/48.55  | | | | | | | 
% 242.05/48.55  | | | | | | | COMBINE_EQS: (70), (71) imply:
% 242.05/48.55  | | | | | | |   (72)  all_58_1 = e0
% 242.05/48.55  | | | | | | | 
% 242.05/48.55  | | | | | | | REF_CLOSE: (1), (3), (17), (21), (39), (43), (53), (69), (72) are
% 242.05/48.55  | | | | | | |            inconsistent by sub-proof #1097.
% 242.05/48.55  | | | | | | | 
% 242.05/48.55  | | | | | | Case 2:
% 242.05/48.55  | | | | | | | 
% 242.05/48.55  | | | | | | |   (73)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.05/48.55  | | | | | | |           op(e1, e0) = e0)
% 242.05/48.55  | | | | | | | 
% 242.05/48.55  | | | | | | | BETA: splitting (73) gives:
% 242.05/48.55  | | | | | | | 
% 242.05/48.55  | | | | | | | Case 1:
% 242.05/48.55  | | | | | | | | 
% 242.05/48.55  | | | | | | | |   (74)  all_58_10 = e0 & op(e2, e0) = e0
% 242.05/48.55  | | | | | | | | 
% 242.05/48.55  | | | | | | | | ALPHA: (74) implies:
% 242.05/48.55  | | | | | | | |   (75)  op(e2, e0) = e0
% 242.05/48.55  | | | | | | | | 
% 242.05/48.55  | | | | | | | | REF_CLOSE: (39), (42), (44), (47), (75) are inconsistent by
% 242.05/48.55  | | | | | | | |            sub-proof #1778.
% 242.05/48.55  | | | | | | | | 
% 242.05/48.55  | | | | | | | Case 2:
% 242.05/48.55  | | | | | | | | 
% 242.05/48.55  | | | | | | | |   (76)  all_58_11 = e0 & op(e1, e0) = e0
% 242.05/48.55  | | | | | | | | 
% 242.05/48.55  | | | | | | | | ALPHA: (76) implies:
% 242.05/48.55  | | | | | | | |   (77)  all_58_11 = e0
% 242.05/48.55  | | | | | | | | 
% 242.05/48.55  | | | | | | | | REF_CLOSE: (2), (4), (21), (22), (25), (29), (30), (39), (77)
% 242.05/48.55  | | | | | | | |            are inconsistent by sub-proof #1686.
% 242.05/48.55  | | | | | | | | 
% 242.05/48.55  | | | | | | | End of split
% 242.05/48.55  | | | | | | | 
% 242.05/48.55  | | | | | | End of split
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | Case 2:
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | |   (78)  all_58_3 = e2 & op(e2, e2) = e2
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | ALPHA: (78) implies:
% 242.05/48.55  | | | | | |   (79)  all_58_3 = e2
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | COMBINE_EQS: (13), (79) imply:
% 242.05/48.55  | | | | | |   (80)  e3 = e2
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | SIMP: (80) implies:
% 242.05/48.55  | | | | | |   (81)  e3 = e2
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | COMBINE_EQS: (14), (81) imply:
% 242.05/48.55  | | | | | |   (82)  all_58_11 = e2
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | REF_CLOSE: (2), (4), (21), (22), (25), (29), (30), (39), (82) are
% 242.05/48.55  | | | | | |            inconsistent by sub-proof #997.
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | End of split
% 242.05/48.55  | | | | | 
% 242.05/48.55  | | | | Case 2:
% 242.05/48.55  | | | | | 
% 242.05/48.55  | | | | |   (83)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0,
% 242.05/48.55  | | | | |             e2) = e2)
% 242.05/48.55  | | | | | 
% 242.05/48.55  | | | | | BETA: splitting (83) gives:
% 242.05/48.55  | | | | | 
% 242.05/48.55  | | | | | Case 1:
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | |   (84)  all_58_7 = e2 & op(e1, e2) = e2
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | ALPHA: (84) implies:
% 242.05/48.55  | | | | | |   (85)  all_58_7 = e2
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | COMBINE_EQS: (34), (85) imply:
% 242.05/48.55  | | | | | |   (86)  e2 = e1
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | COMBINE_EQS: (54), (86) imply:
% 242.05/48.55  | | | | | |   (87)  all_58_15 = e1
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | REF_CLOSE: (2), (3), (10), (21), (36), (39), (40), (42), (52), (53),
% 242.05/48.55  | | | | | |            (59), (87) are inconsistent by sub-proof #910.
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | Case 2:
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | |   (88)  all_58_13 = e2 & op(e0, e2) = e2
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | ALPHA: (88) implies:
% 242.05/48.55  | | | | | |   (89)  op(e0, e2) = e2
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | | REF_CLOSE: (3), (39), (65), (89) are inconsistent by sub-proof
% 242.05/48.55  | | | | | |            #2132.
% 242.05/48.55  | | | | | | 
% 242.05/48.55  | | | | | End of split
% 242.05/48.55  | | | | | 
% 242.05/48.55  | | | | End of split
% 242.05/48.55  | | | | 
% 242.05/48.55  | | | Case 2:
% 242.05/48.55  | | | | 
% 242.05/48.55  | | | |   (90)  all_58_14 = e0 & op(e0, e1) = e0
% 242.05/48.55  | | | | 
% 242.05/48.55  | | | | ALPHA: (90) implies:
% 242.05/48.55  | | | |   (91)  all_58_14 = e0
% 242.05/48.55  | | | | 
% 242.05/48.55  | | | | REF_CLOSE: (42), (50), (91) are inconsistent by sub-proof #1033.
% 242.05/48.55  | | | | 
% 242.05/48.55  | | | End of split
% 242.05/48.55  | | | 
% 242.05/48.55  | | End of split
% 242.05/48.55  | | 
% 242.05/48.55  | End of split
% 242.05/48.55  | 
% 242.05/48.55  End of proof
% 242.05/48.55  
% 242.05/48.55  Sub-proof #670 shows that the following formulas are inconsistent:
% 242.05/48.55  ----------------------------------------------------------------
% 242.05/48.55    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.05/48.55         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.05/48.55    (2)   ~ (e3 = e0)
% 242.05/48.55    (3)   ~ (e2 = e0)
% 242.05/48.55    (4)  op(e1, e2) = all_52_6
% 242.05/48.55    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.55         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.55    (6)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 242.05/48.55         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 242.05/48.55    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.55         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.05/48.56    (8)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.05/48.56         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.05/48.56    (9)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.56         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.05/48.56    (10)   ~ (e3 = e1)
% 242.05/48.56    (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.05/48.56          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.05/48.56    (12)  all_58_3 = e3
% 242.05/48.56    (13)  all_58_11 = e3
% 242.05/48.56    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.05/48.56          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.05/48.56    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.05/48.56          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.05/48.56    (16)  op(e3, e3) = e1
% 242.05/48.56    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.56              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.05/48.56                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.05/48.56                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.05/48.56    (18)  op(e2, e1) = all_52_9
% 242.05/48.56    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.05/48.56          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.05/48.56    (20)   ~ (e3 = e2)
% 242.05/48.56    (21)  all_58_6 = e0
% 242.05/48.56    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.05/48.56          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.05/48.56    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.05/48.56          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.05/48.56    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.05/48.56          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.05/48.56    (25)  op(e2, e3) = all_52_1
% 242.05/48.56    (26)  all_58_12 = e3
% 242.05/48.56    (27)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.05/48.56          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.56    (28)   ~ (all_52_6 = e3)
% 242.05/48.56    (29)  op(e1, e1) = e2
% 242.05/48.56    (30)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.05/48.56          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.05/48.56    (31)   ~ (all_52_4 = e3)
% 242.05/48.56    (32)  op(e3, e2) = all_52_4
% 242.05/48.56    (33)  all_58_7 = e1
% 242.05/48.56    (34)   ~ (all_52_9 = e3)
% 242.05/48.56    (35)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.05/48.56          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.05/48.56    (36)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.05/48.56          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.05/48.56    (37)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.56          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.05/48.56    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.56    (39)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.05/48.56          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.05/48.56    (40)  e3 = e0
% 242.05/48.56    (41)  op(e1, e1) = e0
% 242.05/48.56    (42)   ~ (e1 = e0)
% 242.05/48.56    (43)  all_58_4 = e3
% 242.05/48.56    (44)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.05/48.56          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.05/48.56    (45)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.05/48.56          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.05/48.56            e1)
% 242.05/48.56    (46)   ~ (all_52_1 = e3)
% 242.05/48.56    (47)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.56          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.05/48.56            e2)
% 242.05/48.56    (48)   ~ (e2 = e1)
% 242.05/48.56  
% 242.05/48.56  Begin of proof
% 242.05/48.56  | 
% 242.05/48.56  | SIMP: (40) implies:
% 242.05/48.56  |   (49)  e3 = e0
% 242.05/48.56  | 
% 242.05/48.56  | COMBINE_EQS: (43), (49) imply:
% 242.05/48.56  |   (50)  all_58_4 = e0
% 242.05/48.56  | 
% 242.05/48.56  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.05/48.56  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 242.05/48.56  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 242.05/48.56  |            (35), (36), (37), (38), (39), (41), (42), (44), (45), (46), (47),
% 242.05/48.56  |            (48), (50) are inconsistent by sub-proof #673.
% 242.05/48.56  | 
% 242.05/48.56  End of proof
% 242.05/48.56  
% 242.05/48.56  Sub-proof #671 shows that the following formulas are inconsistent:
% 242.05/48.56  ----------------------------------------------------------------
% 242.05/48.56    (1)   ~ (e3 = e0)
% 242.05/48.56    (2)   ~ (e2 = e0)
% 242.05/48.56    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.56         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.56    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.56         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.05/48.56    (5)  all_58_3 = e3
% 242.05/48.56    (6)   ~ (e3 = e2)
% 242.05/48.56    (7)  all_58_6 = e0
% 242.05/48.56    (8)  all_58_13 = e2
% 242.05/48.56    (9)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 242.05/48.56    (10)  all_58_7 = e1
% 242.05/48.56    (11)   ~ (e1 = e0)
% 242.05/48.56    (12)   ~ (e2 = e1)
% 242.05/48.56  
% 242.05/48.56  Begin of proof
% 242.05/48.56  | 
% 242.05/48.56  | BETA: splitting (9) gives:
% 242.05/48.56  | 
% 242.05/48.56  | Case 1:
% 242.05/48.56  | | 
% 242.05/48.56  | |   (13)  all_58_6 = e2 & op(e1, e3) = e2
% 242.05/48.56  | | 
% 242.05/48.56  | | ALPHA: (13) implies:
% 242.05/48.56  | |   (14)  all_58_6 = e2
% 242.05/48.56  | | 
% 242.05/48.56  | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #1982.
% 242.05/48.56  | | 
% 242.05/48.56  | Case 2:
% 242.05/48.56  | | 
% 242.05/48.56  | |   (15)  all_58_7 = e2 & op(e1, e2) = e2
% 242.05/48.56  | | 
% 242.05/48.56  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (15) are
% 242.05/48.56  | |            inconsistent by sub-proof #802.
% 242.05/48.56  | | 
% 242.05/48.56  | End of split
% 242.05/48.56  | 
% 242.05/48.56  End of proof
% 242.05/48.56  
% 242.05/48.56  Sub-proof #672 shows that the following formulas are inconsistent:
% 242.05/48.56  ----------------------------------------------------------------
% 242.05/48.56    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.05/48.56         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.05/48.56    (2)   ~ (e3 = e0)
% 242.05/48.56    (3)   ~ (e2 = e0)
% 242.05/48.56    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 242.05/48.56    (5)   ~ (e3 = e1)
% 242.05/48.56    (6)  all_58_2 = e2
% 242.05/48.56    (7)  all_58_3 = e3
% 242.05/48.56    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.05/48.56         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.05/48.56    (9)  op(e3, e3) = e1
% 242.05/48.56    (10)   ~ (e3 = e2)
% 242.05/48.56    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.05/48.56          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.56    (12)   ~ (all_52_4 = e3)
% 242.05/48.56    (13)  op(e3, e2) = all_52_4
% 242.05/48.56    (14)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.56          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.05/48.56    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.56    (16)   ~ (e1 = e0)
% 242.05/48.56    (17)  all_58_10 = e1
% 242.05/48.56    (18)   ~ (e2 = e1)
% 242.05/48.56  
% 242.05/48.56  Begin of proof
% 242.05/48.56  | 
% 242.05/48.56  | BETA: splitting (4) gives:
% 242.05/48.56  | 
% 242.05/48.56  | Case 1:
% 242.05/48.56  | | 
% 242.05/48.56  | |   (19)  all_58_4 = e1 & op(e3, e1) = e1
% 242.05/48.56  | | 
% 242.05/48.56  | | ALPHA: (19) implies:
% 242.05/48.56  | |   (20)  all_58_4 = e1
% 242.05/48.56  | | 
% 242.05/48.56  | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (10), (11), (12), (13), (15), (16),
% 242.05/48.56  | |            (18), (20) are inconsistent by sub-proof #1468.
% 242.05/48.56  | | 
% 242.05/48.56  | Case 2:
% 242.05/48.56  | | 
% 242.05/48.56  | |   (21)  all_58_5 = e1 & op(e2, e1) = e1
% 242.05/48.56  | | 
% 242.05/48.56  | | ALPHA: (21) implies:
% 242.05/48.56  | |   (22)  all_58_5 = e1
% 242.05/48.56  | | 
% 242.05/48.56  | | REF_CLOSE: (2), (3), (6), (7), (14), (16), (17), (22) are inconsistent by
% 242.05/48.56  | |            sub-proof #994.
% 242.05/48.56  | | 
% 242.05/48.56  | End of split
% 242.05/48.56  | 
% 242.05/48.56  End of proof
% 242.05/48.56  
% 242.05/48.56  Sub-proof #673 shows that the following formulas are inconsistent:
% 242.05/48.56  ----------------------------------------------------------------
% 242.05/48.56    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.05/48.56         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.05/48.56    (2)   ~ (e3 = e0)
% 242.05/48.56    (3)   ~ (e2 = e0)
% 242.05/48.56    (4)  op(e1, e2) = all_52_6
% 242.05/48.56    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.56         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.56    (6)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 242.05/48.56         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 242.05/48.56    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.56         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.05/48.56    (8)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.05/48.56         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.05/48.56    (9)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.56         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.05/48.56    (10)   ~ (e3 = e1)
% 242.05/48.56    (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.05/48.56          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.05/48.56    (12)  all_58_3 = e3
% 242.05/48.56    (13)  all_58_11 = e3
% 242.05/48.56    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.05/48.56          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.05/48.56    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.05/48.56          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.05/48.56    (16)  op(e3, e3) = e1
% 242.05/48.56    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.56              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.05/48.56                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.05/48.56                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.05/48.56    (18)  op(e2, e1) = all_52_9
% 242.05/48.56    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.05/48.56          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.05/48.56    (20)   ~ (e3 = e2)
% 242.05/48.56    (21)  all_58_6 = e0
% 242.05/48.56    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.05/48.56          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.05/48.56    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.05/48.56          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.05/48.56    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.05/48.56          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.05/48.56    (25)  op(e2, e3) = all_52_1
% 242.05/48.56    (26)  all_58_12 = e3
% 242.05/48.56    (27)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.05/48.56          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.56    (28)   ~ (all_52_6 = e3)
% 242.05/48.56    (29)  op(e1, e1) = e2
% 242.05/48.56    (30)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.05/48.56          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.05/48.56    (31)   ~ (all_52_4 = e3)
% 242.05/48.56    (32)  op(e3, e2) = all_52_4
% 242.05/48.56    (33)  all_58_7 = e1
% 242.05/48.56    (34)   ~ (all_52_9 = e3)
% 242.05/48.56    (35)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.05/48.56          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.05/48.56    (36)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.05/48.56          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.05/48.56    (37)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.56          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.05/48.56    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.56    (39)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.05/48.56          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.05/48.56    (40)  op(e1, e1) = e0
% 242.05/48.56    (41)   ~ (e1 = e0)
% 242.05/48.56    (42)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.05/48.56          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.05/48.56    (43)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.05/48.56          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.05/48.56            e1)
% 242.05/48.56    (44)   ~ (all_52_1 = e3)
% 242.05/48.56    (45)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.56          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.05/48.56            e2)
% 242.05/48.56    (46)  all_58_4 = e0
% 242.05/48.56    (47)   ~ (e2 = e1)
% 242.05/48.56  
% 242.05/48.56  Begin of proof
% 242.05/48.56  | 
% 242.05/48.56  | BETA: splitting (30) gives:
% 242.05/48.56  | 
% 242.05/48.56  | Case 1:
% 242.05/48.56  | | 
% 242.05/48.57  | |   (48)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 242.05/48.57  | |           e3)
% 242.05/48.57  | | 
% 242.05/48.57  | | BETA: splitting (48) gives:
% 242.05/48.57  | | 
% 242.05/48.57  | | Case 1:
% 242.05/48.57  | | | 
% 242.05/48.57  | | |   (49)  all_58_4 = e3 & op(e3, e1) = e3
% 242.05/48.57  | | | 
% 242.05/48.57  | | | REF_CLOSE: (2), (4), (13), (20), (21), (24), (28), (29), (38), (46), (49)
% 242.05/48.57  | | |            are inconsistent by sub-proof #678.
% 242.05/48.57  | | | 
% 242.05/48.57  | | Case 2:
% 242.05/48.57  | | | 
% 242.05/48.57  | | |   (50)  all_58_5 = e3 & op(e2, e1) = e3
% 242.05/48.57  | | | 
% 242.05/48.57  | | | REF_CLOSE: (18), (34), (38), (50) are inconsistent by sub-proof #1822.
% 242.05/48.57  | | | 
% 242.05/48.57  | | End of split
% 242.05/48.57  | | 
% 242.05/48.57  | Case 2:
% 242.05/48.57  | | 
% 242.05/48.57  | |   (51)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 242.05/48.57  | |           e3)
% 242.05/48.57  | | 
% 242.05/48.57  | | BETA: splitting (51) gives:
% 242.05/48.57  | | 
% 242.05/48.57  | | Case 1:
% 242.05/48.57  | | | 
% 242.05/48.57  | | |   (52)  all_58_8 = e3 & op(e1, e1) = e3
% 242.05/48.57  | | | 
% 242.05/48.57  | | | ALPHA: (52) implies:
% 242.05/48.57  | | |   (53)  op(e1, e1) = e3
% 242.05/48.57  | | | 
% 242.05/48.57  | | | REF_CLOSE: (20), (29), (38), (53) are inconsistent by sub-proof #2206.
% 242.05/48.57  | | | 
% 242.05/48.57  | | Case 2:
% 242.05/48.57  | | | 
% 242.05/48.57  | | |   (54)  all_58_14 = e3 & op(e0, e1) = e3
% 242.05/48.57  | | | 
% 242.05/48.57  | | | ALPHA: (54) implies:
% 242.05/48.57  | | |   (55)  all_58_14 = e3
% 242.05/48.57  | | | 
% 242.05/48.57  | | | BETA: splitting (8) gives:
% 242.05/48.57  | | | 
% 242.05/48.57  | | | Case 1:
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | |   (56)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 242.05/48.57  | | | |           = e1)
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | | BETA: splitting (56) gives:
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | | Case 1:
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | |   (57)  all_58_4 = e1 & op(e3, e1) = e1
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | | ALPHA: (57) implies:
% 242.05/48.57  | | | | |   (58)  all_58_4 = e1
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | | REF_CLOSE: (1), (2), (3), (10), (14), (16), (20), (27), (31), (32),
% 242.05/48.57  | | | | |            (38), (41), (47), (58) are inconsistent by sub-proof #1468.
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | Case 2:
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | |   (59)  all_58_5 = e1 & op(e2, e1) = e1
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | | ALPHA: (59) implies:
% 242.05/48.57  | | | | |   (60)  all_58_5 = e1
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | | BETA: splitting (14) gives:
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | | Case 1:
% 242.05/48.57  | | | | | | 
% 242.05/48.57  | | | | | |   (61)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3,
% 242.05/48.57  | | | | | |             e2) = e3)
% 242.05/48.57  | | | | | | 
% 242.05/48.57  | | | | | | REF_CLOSE: (10), (16), (31), (32), (38), (61) are inconsistent by
% 242.05/48.57  | | | | | |            sub-proof #1401.
% 242.05/48.57  | | | | | | 
% 242.05/48.57  | | | | | Case 2:
% 242.05/48.57  | | | | | | 
% 242.05/48.57  | | | | | |   (62)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 242.05/48.57  | | | | | |             e0) = e3)
% 242.05/48.57  | | | | | | 
% 242.05/48.57  | | | | | | BETA: splitting (62) gives:
% 242.05/48.57  | | | | | | 
% 242.05/48.57  | | | | | | Case 1:
% 242.05/48.57  | | | | | | | 
% 242.05/48.57  | | | | | | |   (63)  all_58_4 = e3 & op(e3, e1) = e3
% 242.05/48.57  | | | | | | | 
% 242.05/48.57  | | | | | | | REF_CLOSE: (2), (4), (13), (20), (21), (24), (28), (29), (38),
% 242.05/48.57  | | | | | | |            (46), (63) are inconsistent by sub-proof #678.
% 242.05/48.57  | | | | | | | 
% 242.05/48.57  | | | | | | Case 2:
% 242.05/48.57  | | | | | | | 
% 242.05/48.57  | | | | | | |   (64)  all_58_9 = e3 & op(e3, e0) = e3
% 242.05/48.57  | | | | | | | 
% 242.05/48.57  | | | | | | | ALPHA: (64) implies:
% 242.05/48.57  | | | | | | |   (65)  all_58_9 = e3
% 242.05/48.57  | | | | | | | 
% 242.05/48.57  | | | | | | | BETA: splitting (45) gives:
% 242.05/48.57  | | | | | | | 
% 242.05/48.57  | | | | | | | Case 1:
% 242.05/48.57  | | | | | | | | 
% 242.05/48.57  | | | | | | | |   (66)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 242.05/48.57  | | | | | | | |           op(e0, e2) = e2)
% 242.05/48.57  | | | | | | | | 
% 242.05/48.57  | | | | | | | | BETA: splitting (66) gives:
% 242.05/48.57  | | | | | | | | 
% 242.05/48.57  | | | | | | | | Case 1:
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | |   (67)  all_58_12 = e2 & op(e0, e3) = e2
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | REF_CLOSE: (2), (4), (13), (20), (21), (24), (26), (28), (29),
% 242.05/48.57  | | | | | | | | |            (38), (67) are inconsistent by sub-proof #677.
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | Case 2:
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | |   (68)  all_58_13 = e2 & op(e0, e2) = e2
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | ALPHA: (68) implies:
% 242.05/48.57  | | | | | | | | |   (69)  op(e0, e2) = e2
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | REF_CLOSE: (1), (2), (3), (7), (12), (16), (20), (33), (38),
% 242.05/48.57  | | | | | | | | |            (41), (46), (47), (65), (69) are inconsistent by
% 242.05/48.57  | | | | | | | | |            sub-proof #719.
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | End of split
% 242.05/48.57  | | | | | | | | 
% 242.05/48.57  | | | | | | | Case 2:
% 242.05/48.57  | | | | | | | | 
% 242.05/48.57  | | | | | | | |   (70)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 242.05/48.57  | | | | | | | |           op(e0, e0) = e2)
% 242.05/48.57  | | | | | | | | 
% 242.05/48.57  | | | | | | | | BETA: splitting (70) gives:
% 242.05/48.57  | | | | | | | | 
% 242.05/48.57  | | | | | | | | Case 1:
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | |   (71)  all_58_14 = e2 & op(e0, e1) = e2
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | ALPHA: (71) implies:
% 242.05/48.57  | | | | | | | | |   (72)  all_58_14 = e2
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | COMBINE_EQS: (55), (72) imply:
% 242.05/48.57  | | | | | | | | |   (73)  e3 = e2
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | SIMP: (73) implies:
% 242.05/48.57  | | | | | | | | |   (74)  e3 = e2
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | COMBINE_EQS: (13), (74) imply:
% 242.05/48.57  | | | | | | | | |   (75)  all_58_11 = e2
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | REF_CLOSE: (2), (4), (20), (21), (24), (28), (29), (38), (75)
% 242.05/48.57  | | | | | | | | |            are inconsistent by sub-proof #997.
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | Case 2:
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | |   (76)  all_58_15 = e2 & op(e0, e0) = e2
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | ALPHA: (76) implies:
% 242.05/48.57  | | | | | | | | |   (77)  all_58_15 = e2
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | BETA: splitting (17) gives:
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | Case 1:
% 242.05/48.57  | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | |   (78)  all_58_15 = e0 & op(e0, e0) = e0
% 242.05/48.57  | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | ALPHA: (78) implies:
% 242.05/48.57  | | | | | | | | | |   (79)  op(e0, e0) = e0
% 242.05/48.57  | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (10), (11), (12),
% 242.05/48.57  | | | | | | | | | |            (14), (15), (16), (18), (19), (20), (22), (23),
% 242.05/48.57  | | | | | | | | | |            (25), (30), (31), (32), (33), (34), (36), (37),
% 242.05/48.57  | | | | | | | | | |            (38), (41), (42), (43), (44), (47), (60), (79) are
% 242.05/48.57  | | | | | | | | | |            inconsistent by sub-proof #675.
% 242.05/48.57  | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | Case 2:
% 242.05/48.57  | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | |   (80)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 242.05/48.57  | | | | | | | | | |             & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 242.05/48.57  | | | | | | | | | |               e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) =
% 242.05/48.57  | | | | | | | | | |             e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 242.05/48.57  | | | | | | | | | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 242.05/48.57  | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | ALPHA: (80) implies:
% 242.05/48.57  | | | | | | | | | |   (81)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 242.05/48.57  | | | | | | | | | |           & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.05/48.57  | | | | | | | | | |           = e0)
% 242.05/48.57  | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | BETA: splitting (6) gives:
% 242.05/48.57  | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | Case 1:
% 242.05/48.57  | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | |   (82)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 242.05/48.57  | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 242.05/48.57  | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | BETA: splitting (82) gives:
% 242.05/48.57  | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | Case 1:
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | |   (83)  all_58_9 = e1 & op(e3, e0) = e1
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | | REF_CLOSE: (2), (3), (10), (15), (16), (19), (20), (23),
% 242.05/48.57  | | | | | | | | | | | |            (25), (26), (38), (41), (44), (47), (65), (83) are
% 242.05/48.57  | | | | | | | | | | | |            inconsistent by sub-proof #737.
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | Case 2:
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | |   (84)  all_58_10 = e1 & op(e2, e0) = e1
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | | ALPHA: (84) implies:
% 242.05/48.57  | | | | | | | | | | | |   (85)  all_58_10 = e1
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | | REF_CLOSE: (2), (3), (9), (10), (12), (20), (35), (37), (38),
% 242.05/48.57  | | | | | | | | | | | |            (39), (41), (47), (60), (77), (81), (85) are
% 242.05/48.57  | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | End of split
% 242.05/48.57  | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | Case 2:
% 242.05/48.57  | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | |   (86)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 242.05/48.57  | | | | | | | | | | |           e1 & op(e0, e0) = e1)
% 242.05/48.57  | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | BETA: splitting (86) gives:
% 242.05/48.57  | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | Case 1:
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | |   (87)  all_58_11 = e1 & op(e1, e0) = e1
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | | REF_CLOSE: (2), (3), (10), (13), (15), (16), (19), (20),
% 242.05/48.57  | | | | | | | | | | | |            (23), (25), (26), (38), (41), (44), (47), (87) are
% 242.05/48.57  | | | | | | | | | | | |            inconsistent by sub-proof #674.
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | Case 2:
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | |   (88)  all_58_15 = e1 & op(e0, e0) = e1
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | | ALPHA: (88) implies:
% 242.05/48.57  | | | | | | | | | | | |   (89)  all_58_15 = e1
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | | REF_CLOSE: (2), (3), (17), (20), (26), (41), (45), (47),
% 242.05/48.57  | | | | | | | | | | | |            (55), (89) are inconsistent by sub-proof #1863.
% 242.05/48.57  | | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | | End of split
% 242.05/48.57  | | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | | End of split
% 242.05/48.57  | | | | | | | | | | 
% 242.05/48.57  | | | | | | | | | End of split
% 242.05/48.57  | | | | | | | | | 
% 242.05/48.57  | | | | | | | | End of split
% 242.05/48.57  | | | | | | | | 
% 242.05/48.57  | | | | | | | End of split
% 242.05/48.57  | | | | | | | 
% 242.05/48.57  | | | | | | End of split
% 242.05/48.57  | | | | | | 
% 242.05/48.57  | | | | | End of split
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | End of split
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | Case 2:
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | |   (90)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 242.05/48.57  | | | |           = e1)
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | | BETA: splitting (90) gives:
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | | Case 1:
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | |   (91)  all_58_8 = e1 & op(e1, e1) = e1
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | | ALPHA: (91) implies:
% 242.05/48.57  | | | | |   (92)  op(e1, e1) = e1
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | | REF_CLOSE: (38), (40), (41), (92) are inconsistent by sub-proof #2220.
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | Case 2:
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | |   (93)  all_58_14 = e1 & op(e0, e1) = e1
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | | REF_CLOSE: (2), (3), (10), (15), (16), (19), (20), (23), (25), (26),
% 242.05/48.57  | | | | |            (38), (41), (44), (47), (55), (93) are inconsistent by
% 242.05/48.57  | | | | |            sub-proof #1201.
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | End of split
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | End of split
% 242.05/48.57  | | | 
% 242.05/48.57  | | End of split
% 242.05/48.57  | | 
% 242.05/48.57  | End of split
% 242.05/48.57  | 
% 242.05/48.57  End of proof
% 242.05/48.57  
% 242.05/48.57  Sub-proof #674 shows that the following formulas are inconsistent:
% 242.05/48.57  ----------------------------------------------------------------
% 242.05/48.57    (1)   ~ (e3 = e0)
% 242.05/48.57    (2)   ~ (e2 = e0)
% 242.05/48.57    (3)  all_58_11 = e1 & op(e1, e0) = e1
% 242.05/48.57    (4)   ~ (e3 = e1)
% 242.05/48.57    (5)  all_58_11 = e3
% 242.05/48.57    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.05/48.57         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.05/48.57    (7)  op(e3, e3) = e1
% 242.05/48.57    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.05/48.57         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.05/48.57    (9)   ~ (e3 = e2)
% 242.05/48.57    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.05/48.57          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.05/48.57    (11)  op(e2, e3) = all_52_1
% 242.05/48.57    (12)  all_58_12 = e3
% 242.05/48.57    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.57    (14)   ~ (e1 = e0)
% 242.05/48.57    (15)   ~ (all_52_1 = e3)
% 242.05/48.57    (16)   ~ (e2 = e1)
% 242.05/48.57  
% 242.05/48.57  Begin of proof
% 242.05/48.57  | 
% 242.05/48.57  | ALPHA: (3) implies:
% 242.05/48.57  |   (17)  all_58_11 = e1
% 242.05/48.57  | 
% 242.05/48.57  | COMBINE_EQS: (5), (17) imply:
% 242.05/48.57  |   (18)  e3 = e1
% 242.05/48.57  | 
% 242.05/48.57  | SIMP: (18) implies:
% 242.05/48.57  |   (19)  e3 = e1
% 242.05/48.57  | 
% 242.05/48.57  | COMBINE_EQS: (12), (19) imply:
% 242.05/48.57  |   (20)  all_58_12 = e1
% 242.05/48.57  | 
% 242.05/48.57  | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (13), (14), (15),
% 242.05/48.57  |            (16), (20) are inconsistent by sub-proof #1204.
% 242.05/48.57  | 
% 242.05/48.57  End of proof
% 242.05/48.57  
% 242.05/48.57  Sub-proof #675 shows that the following formulas are inconsistent:
% 242.05/48.57  ----------------------------------------------------------------
% 242.05/48.57    (1)   ~ (e3 = e0)
% 242.05/48.57    (2)   ~ (e2 = e0)
% 242.05/48.57    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.57         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.57    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 242.05/48.57         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 242.05/48.57    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.57         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.05/48.57    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.57         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.05/48.57    (7)   ~ (e3 = e1)
% 242.05/48.57    (8)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.05/48.57         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.05/48.57    (9)  all_58_3 = e3
% 242.05/48.57    (10)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.05/48.57          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.05/48.57    (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.05/48.57          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.05/48.57    (12)  op(e3, e3) = e1
% 242.05/48.57    (13)  op(e2, e1) = all_52_9
% 242.05/48.57    (14)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.05/48.57          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.05/48.57    (15)   ~ (e3 = e2)
% 242.05/48.57    (16)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.05/48.57          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.05/48.57    (17)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.05/48.57          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.05/48.57    (18)  op(e2, e3) = all_52_1
% 242.05/48.57    (19)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.05/48.57          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.05/48.57    (20)   ~ (all_52_4 = e3)
% 242.05/48.57    (21)  op(e3, e2) = all_52_4
% 242.05/48.57    (22)  all_58_5 = e1
% 242.05/48.57    (23)  all_58_7 = e1
% 242.05/48.57    (24)   ~ (all_52_9 = e3)
% 242.05/48.57    (25)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.05/48.57          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.05/48.57    (26)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.57          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.05/48.57    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.57    (28)  op(e0, e0) = e0
% 242.05/48.57    (29)   ~ (e1 = e0)
% 242.05/48.57    (30)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.05/48.57          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.05/48.57    (31)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.05/48.57          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.05/48.57            e1)
% 242.05/48.57    (32)   ~ (all_52_1 = e3)
% 242.05/48.57    (33)   ~ (e2 = e1)
% 242.05/48.57  
% 242.05/48.57  Begin of proof
% 242.05/48.57  | 
% 242.05/48.57  | BETA: splitting (31) gives:
% 242.05/48.57  | 
% 242.05/48.57  | Case 1:
% 242.05/48.57  | | 
% 242.05/48.57  | |   (34)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 242.05/48.57  | |           e1)
% 242.05/48.57  | | 
% 242.05/48.57  | | REF_CLOSE: (1), (2), (3), (5), (7), (9), (11), (12), (14), (15), (17), (18),
% 242.05/48.57  | |            (23), (27), (29), (32), (33), (34) are inconsistent by sub-proof
% 242.05/48.57  | |            #740.
% 242.05/48.57  | | 
% 242.05/48.57  | Case 2:
% 242.05/48.57  | | 
% 242.05/48.57  | |   (35)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.05/48.57  | |           e1)
% 242.05/48.57  | | 
% 242.05/48.57  | | BETA: splitting (35) gives:
% 242.05/48.57  | | 
% 242.05/48.57  | | Case 1:
% 242.05/48.57  | | | 
% 242.05/48.57  | | |   (36)  all_58_14 = e1 & op(e0, e1) = e1
% 242.05/48.57  | | | 
% 242.05/48.57  | | | ALPHA: (36) implies:
% 242.05/48.57  | | |   (37)  all_58_14 = e1
% 242.05/48.57  | | | 
% 242.05/48.57  | | | BETA: splitting (19) gives:
% 242.05/48.57  | | | 
% 242.05/48.57  | | | Case 1:
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | |   (38)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 242.05/48.57  | | | |           = e3)
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | | BETA: splitting (38) gives:
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | | Case 1:
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | |   (39)  all_58_4 = e3 & op(e3, e1) = e3
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | | ALPHA: (39) implies:
% 242.05/48.57  | | | | |   (40)  all_58_4 = e3
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | | REF_CLOSE: (1), (2), (8), (15), (16), (22), (29), (33), (37), (40) are
% 242.05/48.57  | | | | |            inconsistent by sub-proof #1481.
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | Case 2:
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | |   (41)  all_58_5 = e3 & op(e2, e1) = e3
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | | REF_CLOSE: (13), (24), (27), (41) are inconsistent by sub-proof #1822.
% 242.05/48.57  | | | | | 
% 242.05/48.57  | | | | End of split
% 242.05/48.57  | | | | 
% 242.05/48.57  | | | Case 2:
% 242.05/48.57  | | | | 
% 242.05/48.58  | | | |   (42)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1)
% 242.05/48.58  | | | |           = e3)
% 242.05/48.58  | | | | 
% 242.05/48.58  | | | | BETA: splitting (42) gives:
% 242.05/48.58  | | | | 
% 242.05/48.58  | | | | Case 1:
% 242.05/48.58  | | | | | 
% 242.05/48.58  | | | | |   (43)  all_58_8 = e3 & op(e1, e1) = e3
% 242.05/48.58  | | | | | 
% 242.05/48.58  | | | | | ALPHA: (43) implies:
% 242.05/48.58  | | | | |   (44)  all_58_8 = e3
% 242.05/48.58  | | | | |   (45)  op(e1, e1) = e3
% 242.05/48.58  | | | | | 
% 242.05/48.58  | | | | | BETA: splitting (4) gives:
% 242.05/48.58  | | | | | 
% 242.05/48.58  | | | | | Case 1:
% 242.05/48.58  | | | | | | 
% 242.05/48.58  | | | | | |   (46)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 242.05/48.58  | | | | | |             e0) = e1)
% 242.05/48.58  | | | | | | 
% 242.05/48.58  | | | | | | BETA: splitting (46) gives:
% 242.05/48.58  | | | | | | 
% 242.05/48.58  | | | | | | Case 1:
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | |   (47)  all_58_9 = e1 & op(e3, e0) = e1
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | | ALPHA: (47) implies:
% 242.05/48.58  | | | | | | |   (48)  all_58_9 = e1
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | | REF_CLOSE: (1), (2), (7), (8), (10), (12), (15), (16), (20), (21),
% 242.05/48.58  | | | | | | |            (22), (27), (29), (33), (37), (48) are inconsistent by
% 242.05/48.58  | | | | | | |            sub-proof #676.
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | Case 2:
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | |   (49)  all_58_10 = e1 & op(e2, e0) = e1
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | | ALPHA: (49) implies:
% 242.05/48.58  | | | | | | |   (50)  all_58_10 = e1
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | | REF_CLOSE: (1), (2), (6), (9), (15), (22), (26), (29), (33), (50)
% 242.05/48.58  | | | | | | |            are inconsistent by sub-proof #992.
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | End of split
% 242.05/48.58  | | | | | | 
% 242.05/48.58  | | | | | Case 2:
% 242.05/48.58  | | | | | | 
% 242.05/48.58  | | | | | |   (51)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 242.05/48.58  | | | | | |           op(e0, e0) = e1)
% 242.05/48.58  | | | | | | 
% 242.05/48.58  | | | | | | BETA: splitting (51) gives:
% 242.05/48.58  | | | | | | 
% 242.05/48.58  | | | | | | Case 1:
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | |   (52)  all_58_11 = e1 & op(e1, e0) = e1
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | | ALPHA: (52) implies:
% 242.05/48.58  | | | | | | |   (53)  all_58_11 = e1
% 242.05/48.58  | | | | | | |   (54)  op(e1, e0) = e1
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | | REF_CLOSE: (1), (2), (15), (23), (25), (27), (29), (30), (33),
% 242.05/48.58  | | | | | | |            (44), (45), (53), (54) are inconsistent by sub-proof
% 242.05/48.58  | | | | | | |            #1419.
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | Case 2:
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | |   (55)  all_58_15 = e1 & op(e0, e0) = e1
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | | ALPHA: (55) implies:
% 242.05/48.58  | | | | | | |   (56)  op(e0, e0) = e1
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | | REF_CLOSE: (27), (28), (29), (56) are inconsistent by sub-proof
% 242.05/48.58  | | | | | | |            #2274.
% 242.05/48.58  | | | | | | | 
% 242.05/48.58  | | | | | | End of split
% 242.05/48.58  | | | | | | 
% 242.05/48.58  | | | | | End of split
% 242.05/48.58  | | | | | 
% 242.05/48.58  | | | | Case 2:
% 242.05/48.58  | | | | | 
% 242.05/48.58  | | | | |   (57)  all_58_14 = e3 & op(e0, e1) = e3
% 242.05/48.58  | | | | | 
% 242.05/48.58  | | | | | REF_CLOSE: (7), (37), (57) are inconsistent by sub-proof #1773.
% 242.05/48.58  | | | | | 
% 242.05/48.58  | | | | End of split
% 242.05/48.58  | | | | 
% 242.05/48.58  | | | End of split
% 242.05/48.58  | | | 
% 242.05/48.58  | | Case 2:
% 242.05/48.58  | | | 
% 242.05/48.58  | | |   (58)  all_58_15 = e1 & op(e0, e0) = e1
% 242.05/48.58  | | | 
% 242.05/48.58  | | | ALPHA: (58) implies:
% 242.05/48.58  | | |   (59)  op(e0, e0) = e1
% 242.05/48.58  | | | 
% 242.05/48.58  | | | REF_CLOSE: (27), (28), (29), (59) are inconsistent by sub-proof #2274.
% 242.05/48.58  | | | 
% 242.05/48.58  | | End of split
% 242.05/48.58  | | 
% 242.05/48.58  | End of split
% 242.05/48.58  | 
% 242.05/48.58  End of proof
% 242.05/48.58  
% 242.05/48.58  Sub-proof #676 shows that the following formulas are inconsistent:
% 242.05/48.58  ----------------------------------------------------------------
% 242.05/48.58    (1)   ~ (e3 = e0)
% 242.05/48.58    (2)   ~ (e2 = e0)
% 242.05/48.58    (3)   ~ (e3 = e1)
% 242.05/48.58    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.05/48.58         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.05/48.58    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.05/48.58         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.05/48.58    (6)  op(e3, e3) = e1
% 242.05/48.58    (7)   ~ (e3 = e2)
% 242.05/48.58    (8)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.05/48.58         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.05/48.58    (9)   ~ (all_52_4 = e3)
% 242.05/48.58    (10)  op(e3, e2) = all_52_4
% 242.05/48.58    (11)  all_58_5 = e1
% 242.05/48.58    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.58    (13)   ~ (e1 = e0)
% 242.05/48.58    (14)  all_58_9 = e1
% 242.05/48.58    (15)  all_58_14 = e1
% 242.05/48.58    (16)   ~ (e2 = e1)
% 242.05/48.58  
% 242.05/48.58  Begin of proof
% 242.05/48.58  | 
% 242.05/48.58  | BETA: splitting (5) gives:
% 242.05/48.58  | 
% 242.05/48.58  | Case 1:
% 242.05/48.58  | | 
% 242.05/48.58  | |   (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 242.05/48.58  | |           e3)
% 242.05/48.58  | | 
% 242.05/48.58  | | REF_CLOSE: (3), (6), (9), (10), (12), (17) are inconsistent by sub-proof
% 242.05/48.58  | |            #1401.
% 242.05/48.58  | | 
% 242.05/48.58  | Case 2:
% 242.05/48.58  | | 
% 242.05/48.58  | |   (18)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 242.05/48.58  | |           e3)
% 242.05/48.58  | | 
% 242.05/48.58  | | BETA: splitting (18) gives:
% 242.05/48.58  | | 
% 242.05/48.58  | | Case 1:
% 242.05/48.58  | | | 
% 242.05/48.58  | | |   (19)  all_58_4 = e3 & op(e3, e1) = e3
% 242.05/48.58  | | | 
% 242.05/48.58  | | | ALPHA: (19) implies:
% 242.05/48.58  | | |   (20)  all_58_4 = e3
% 242.05/48.58  | | | 
% 242.05/48.58  | | | REF_CLOSE: (1), (2), (4), (7), (8), (11), (13), (15), (16), (20) are
% 242.05/48.58  | | |            inconsistent by sub-proof #1481.
% 242.05/48.58  | | | 
% 242.05/48.58  | | Case 2:
% 242.05/48.58  | | | 
% 242.05/48.58  | | |   (21)  all_58_9 = e3 & op(e3, e0) = e3
% 242.05/48.58  | | | 
% 242.05/48.58  | | | REF_CLOSE: (3), (14), (21) are inconsistent by sub-proof #1603.
% 242.05/48.58  | | | 
% 242.05/48.58  | | End of split
% 242.05/48.58  | | 
% 242.05/48.58  | End of split
% 242.05/48.58  | 
% 242.05/48.58  End of proof
% 242.05/48.58  
% 242.05/48.58  Sub-proof #677 shows that the following formulas are inconsistent:
% 242.05/48.58  ----------------------------------------------------------------
% 242.05/48.58    (1)   ~ (e3 = e0)
% 242.05/48.58    (2)  op(e1, e2) = all_52_6
% 242.05/48.58    (3)  all_58_11 = e3
% 242.05/48.58    (4)   ~ (e3 = e2)
% 242.05/48.58    (5)  all_58_6 = e0
% 242.05/48.58    (6)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.05/48.58         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.05/48.58    (7)  all_58_12 = e3
% 242.05/48.58    (8)   ~ (all_52_6 = e3)
% 242.05/48.58    (9)  op(e1, e1) = e2
% 242.05/48.58    (10)  all_58_12 = e2 & op(e0, e3) = e2
% 242.05/48.58    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.58  
% 242.05/48.58  Begin of proof
% 242.05/48.58  | 
% 242.05/48.58  | ALPHA: (10) implies:
% 242.05/48.58  |   (12)  all_58_12 = e2
% 242.05/48.58  | 
% 242.05/48.58  | COMBINE_EQS: (7), (12) imply:
% 242.05/48.58  |   (13)  e3 = e2
% 242.05/48.58  | 
% 242.05/48.58  | SIMP: (13) implies:
% 242.05/48.58  |   (14)  e3 = e2
% 242.05/48.58  | 
% 242.05/48.58  | COMBINE_EQS: (3), (14) imply:
% 242.05/48.58  |   (15)  all_58_11 = e2
% 242.05/48.58  | 
% 242.05/48.58  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (15) are inconsistent by
% 242.05/48.58  |            sub-proof #997.
% 242.05/48.58  | 
% 242.05/48.58  End of proof
% 242.05/48.58  
% 242.05/48.58  Sub-proof #678 shows that the following formulas are inconsistent:
% 242.05/48.58  ----------------------------------------------------------------
% 242.05/48.58    (1)   ~ (e3 = e0)
% 242.05/48.58    (2)  op(e1, e2) = all_52_6
% 242.05/48.58    (3)  all_58_11 = e3
% 242.05/48.58    (4)   ~ (e3 = e2)
% 242.05/48.58    (5)  all_58_6 = e0
% 242.05/48.58    (6)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.05/48.58         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.05/48.58    (7)   ~ (all_52_6 = e3)
% 242.05/48.58    (8)  op(e1, e1) = e2
% 242.05/48.58    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.58    (10)  all_58_4 = e3 & op(e3, e1) = e3
% 242.05/48.58    (11)  all_58_4 = e0
% 242.05/48.58  
% 242.05/48.58  Begin of proof
% 242.05/48.58  | 
% 242.05/48.58  | ALPHA: (10) implies:
% 242.05/48.58  |   (12)  all_58_4 = e3
% 242.05/48.58  | 
% 242.05/48.58  | COMBINE_EQS: (11), (12) imply:
% 242.05/48.58  |   (13)  e3 = e0
% 242.05/48.58  | 
% 242.05/48.58  | SIMP: (13) implies:
% 242.05/48.58  |   (14)  e3 = e0
% 242.05/48.58  | 
% 242.05/48.58  | COMBINE_EQS: (3), (14) imply:
% 242.05/48.58  |   (15)  all_58_11 = e0
% 242.05/48.58  | 
% 242.05/48.58  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (15) are inconsistent by
% 242.05/48.58  |            sub-proof #1686.
% 242.05/48.58  | 
% 242.05/48.58  End of proof
% 242.05/48.58  
% 242.05/48.58  Sub-proof #679 shows that the following formulas are inconsistent:
% 242.05/48.58  ----------------------------------------------------------------
% 242.05/48.58    (1)   ~ (all_52_1 = all_52_3)
% 242.05/48.58    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.05/48.58    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.05/48.58         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.05/48.58    (4)   ~ (all_52_3 = e1)
% 242.05/48.58    (5)   ~ (all_52_9 = all_6_2)
% 242.05/48.58    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.05/48.58    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.05/48.58         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.05/48.58    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.05/48.58           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.05/48.58             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.05/48.58    (9)   ~ (e3 = e0)
% 242.05/48.58    (10)  op(e0, e1) = all_52_11
% 242.05/48.58    (11)   ~ (all_52_8 = all_52_9)
% 242.05/48.58    (12)  all_42_2 = e3
% 242.05/48.58    (13)  op(e1, e2) = e1
% 242.05/48.58    (14)  all_54_13 = all_52_7
% 242.05/48.58    (15)   ~ (all_52_8 = all_6_2)
% 242.05/48.58    (16)  op(e1, e2) = all_52_6
% 242.05/48.58    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.58          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.58    (18)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.05/48.58              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.05/48.58            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.05/48.58            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.05/48.58            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.05/48.58             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.05/48.58            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.05/48.58            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.05/48.58            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.05/48.58            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.05/48.58            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.05/48.58              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.05/48.58            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.05/48.58            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.05/48.58            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.05/48.58            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.05/48.58            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.05/48.58            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.05/48.58              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.05/48.58            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.05/48.58            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.05/48.58            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.05/48.58            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.05/48.58            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.05/48.58            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.05/48.58              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.05/48.58            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.05/48.58            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.05/48.58    (19)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.58          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.05/48.58    (20)   ~ (all_52_7 = all_52_11)
% 242.05/48.58    (21)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.05/48.58            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.05/48.58              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.05/48.58    (22)  all_40_2 = all_6_2
% 242.05/48.58    (23)  op(e1, e1) = all_6_2
% 242.05/48.58    (24)   ~ (all_52_1 = all_52_2)
% 242.05/48.58    (25)   ~ (all_52_13 = e1)
% 242.05/48.58    (26)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.05/48.58            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.05/48.58              e1) = all_20_1 & $i(all_20_1))
% 242.05/48.58    (27)   ~ (all_52_7 = e3)
% 242.05/48.58    (28)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.05/48.58    (29)  op(e0, e3) = all_52_3
% 242.05/48.58    (30)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.58          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.05/48.58    (31)   ~ (e3 = e1)
% 242.05/48.58    (32)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.05/48.58          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.05/48.58    (33)   ~ (all_52_2 = all_52_3)
% 242.05/48.58    (34)  all_58_3 = e3
% 242.05/48.58    (35)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.05/48.58          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.05/48.58    (36)  all_54_10 = all_6_2
% 242.05/48.58    (37)  all_54_2 = all_52_8
% 242.05/48.58    (38)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.05/48.58          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.05/48.58    (39)  op(e3, e3) = e1
% 242.05/48.58    (40)   ~ (all_52_1 = all_52_9)
% 242.05/48.58    (41)   ~ (all_52_3 = all_52_7)
% 242.05/48.58    (42)  all_54_4 = all_52_1
% 242.05/48.58    (43)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.58              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.05/48.58                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.05/48.58                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.05/48.58    (44)   ~ (all_6_2 = e3)
% 242.05/48.58    (45)  op(e2, e1) = all_52_9
% 242.05/48.58    (46)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.05/48.58          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.05/48.58    (47)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.05/48.58          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.05/48.58    (48)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.05/48.58    (49)   ~ (all_52_3 = all_52_11)
% 242.05/48.58    (50)   ~ (all_6_2 = e0)
% 242.05/48.58    (51)  all_56_31 = e1
% 242.05/48.58    (52)  all_54_12 = all_52_3
% 242.05/48.58    (53)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.05/48.58    (54)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.05/48.58          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.05/48.58    (55)  all_58_15 = e1
% 242.05/48.58    (56)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.05/48.58          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.05/48.58    (57)   ~ (all_52_2 = all_6_2)
% 242.05/48.58    (58)  op(e2, e3) = all_52_1
% 242.05/48.58    (59)  all_36_2 = all_6_2
% 242.05/48.58    (60)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 242.05/48.58    (61)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.05/48.58          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.58    (62)  all_34_2 = e1
% 242.05/48.58    (63)   ~ (all_52_6 = e3)
% 242.05/48.58    (64)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.05/48.58    (65)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 242.05/48.58            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 242.05/48.58              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 242.05/48.59    (66)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.05/48.59          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.05/48.59    (67)  op(e0, e2) = all_52_7
% 242.05/48.59    (68)  all_54_1 = all_52_4
% 242.05/48.59    (69)   ~ (all_52_4 = e3)
% 242.05/48.59    (70)  op(e3, e2) = all_52_4
% 242.05/48.59    (71)   ~ (all_52_8 = all_52_11)
% 242.05/48.59    (72)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.05/48.59    (73)  all_58_7 = e1
% 242.05/48.59    (74)   ~ (all_52_9 = e3)
% 242.05/48.59    (75)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.05/48.59          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.05/48.59    (76)  all_54_8 = all_52_2
% 242.05/48.59    (77)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.05/48.59          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.05/48.59    (78)   ~ (all_52_2 = all_52_6)
% 242.05/48.59    (79)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.59          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.05/48.59    (80)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.59    (81)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.05/48.59          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.05/48.59    (82)   ~ (all_52_6 = all_52_7)
% 242.05/48.59    (83)  all_56_11 = e3
% 242.05/48.59    (84)   ~ (e1 = e0)
% 242.05/48.59    (85)  all_56_21 = all_6_2
% 242.05/48.59    (86)   ~ (all_52_11 = all_6_2)
% 242.05/48.59    (87)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.05/48.59          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.05/48.59    (88)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 242.05/48.59            op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 242.05/48.59              e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 242.05/48.59    (89)  op(e2, e0) = all_52_13
% 242.05/48.59    (90)   ~ (all_52_1 = e3)
% 242.05/48.59    (91)  all_54_14 = all_52_11
% 242.05/48.59    (92)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.59          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.05/48.59            e2)
% 242.05/48.59    (93)   ~ (all_52_9 = all_52_11)
% 242.05/48.59    (94)   ~ (all_52_4 = all_52_8)
% 242.05/48.59    (95)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.05/48.59            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.05/48.59            & $i(all_8_1))
% 242.05/48.59    (96)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.05/48.59          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.05/48.59    (97)   ~ (all_52_4 = all_52_6)
% 242.05/48.59    (98)   ~ (all_52_1 = e1)
% 242.05/48.59    (99)   ~ (all_52_4 = all_52_7)
% 242.05/48.59  
% 242.05/48.59  Begin of proof
% 242.05/48.59  | 
% 242.05/48.59  | BETA: splitting (96) gives:
% 242.05/48.59  | 
% 242.05/48.59  | Case 1:
% 242.05/48.59  | | 
% 242.05/48.59  | |   (100)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 242.05/48.59  | |            e1)
% 242.05/48.59  | | 
% 242.05/48.59  | | BETA: splitting (100) gives:
% 242.05/48.59  | | 
% 242.05/48.59  | | Case 1:
% 242.05/48.59  | | | 
% 242.05/48.59  | | |   (101)  all_58_2 = e1 & op(e2, e3) = e1
% 242.05/48.59  | | | 
% 242.05/48.59  | | | REF_CLOSE: (58), (80), (98), (101) are inconsistent by sub-proof #2229.
% 242.05/48.59  | | | 
% 242.05/48.59  | | Case 2:
% 242.05/48.59  | | | 
% 242.05/48.59  | | |   (102)  all_58_3 = e1 & op(e2, e2) = e1
% 242.05/48.59  | | | 
% 242.05/48.59  | | | REF_CLOSE: (31), (34), (102) are inconsistent by sub-proof #2197.
% 242.05/48.59  | | | 
% 242.05/48.59  | | End of split
% 242.05/48.59  | | 
% 242.05/48.59  | Case 2:
% 242.05/48.59  | | 
% 242.05/48.59  | |   (103)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 242.05/48.59  | |            e1)
% 242.05/48.59  | | 
% 242.05/48.59  | | BETA: splitting (103) gives:
% 242.05/48.59  | | 
% 242.05/48.59  | | Case 1:
% 242.05/48.59  | | | 
% 242.05/48.59  | | |   (104)  all_58_5 = e1 & op(e2, e1) = e1
% 242.05/48.59  | | | 
% 242.05/48.59  | | | ALPHA: (104) implies:
% 242.05/48.59  | | |   (105)  all_58_5 = e1
% 242.05/48.59  | | |   (106)  op(e2, e1) = e1
% 242.05/48.59  | | | 
% 242.05/48.59  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.05/48.59  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 242.05/48.59  | | |            (23), (24), (26), (27), (28), (29), (30), (32), (33), (34),
% 242.05/48.59  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 242.05/48.59  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 242.05/48.59  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 242.05/48.59  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 242.05/48.59  | | |            (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 242.05/48.59  | | |            (85), (86), (87), (88), (90), (91), (92), (93), (94), (95),
% 242.05/48.59  | | |            (97), (99), (105), (106) are inconsistent by sub-proof #680.
% 242.05/48.59  | | | 
% 242.05/48.59  | | Case 2:
% 242.05/48.59  | | | 
% 242.05/48.59  | | |   (107)  all_58_10 = e1 & op(e2, e0) = e1
% 242.05/48.59  | | | 
% 242.05/48.59  | | | ALPHA: (107) implies:
% 242.05/48.59  | | |   (108)  op(e2, e0) = e1
% 242.05/48.59  | | | 
% 242.05/48.59  | | | GROUND_INST: instantiating (80) with all_52_13, e1, e0, e2, simplifying
% 242.05/48.59  | | |              with (89), (108) gives:
% 242.05/48.59  | | |   (109)  all_52_13 = e1
% 242.05/48.59  | | | 
% 242.05/48.59  | | | REDUCE: (25), (109) imply:
% 242.05/48.59  | | |   (110)  $false
% 242.05/48.59  | | | 
% 242.05/48.59  | | | CLOSE: (110) is inconsistent.
% 242.05/48.59  | | | 
% 242.05/48.59  | | End of split
% 242.05/48.59  | | 
% 242.05/48.59  | End of split
% 242.05/48.59  | 
% 242.05/48.59  End of proof
% 242.05/48.59  
% 242.05/48.59  Sub-proof #680 shows that the following formulas are inconsistent:
% 242.05/48.59  ----------------------------------------------------------------
% 242.05/48.59    (1)   ~ (all_52_1 = all_52_3)
% 242.05/48.59    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.05/48.59    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.05/48.59         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.05/48.59    (4)   ~ (all_52_3 = e1)
% 242.05/48.59    (5)   ~ (all_52_9 = all_6_2)
% 242.05/48.59    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.05/48.59    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.05/48.59         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.05/48.59    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.05/48.59           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.05/48.59             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.05/48.59    (9)   ~ (e3 = e0)
% 242.05/48.59    (10)  op(e0, e1) = all_52_11
% 242.05/48.59    (11)   ~ (all_52_8 = all_52_9)
% 242.05/48.59    (12)  all_42_2 = e3
% 242.05/48.59    (13)  op(e2, e1) = e1
% 242.05/48.59    (14)  op(e1, e2) = e1
% 242.05/48.59    (15)  all_54_13 = all_52_7
% 242.05/48.59    (16)   ~ (all_52_8 = all_6_2)
% 242.05/48.59    (17)  op(e1, e2) = all_52_6
% 242.05/48.59    (18)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.59          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.59    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.05/48.59              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.05/48.59            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.05/48.59            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.05/48.59            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.05/48.59             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.05/48.59            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.05/48.59            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.05/48.59            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.05/48.59            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.05/48.59            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.05/48.59              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.05/48.59            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.05/48.59            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.05/48.59            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.05/48.59            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.05/48.59            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.05/48.59            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.05/48.59              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.05/48.59            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.05/48.59            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.05/48.59            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.05/48.59            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.05/48.59            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.05/48.59            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.05/48.59              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.05/48.59            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.05/48.59            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.05/48.59    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.59          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.05/48.59    (21)   ~ (all_52_7 = all_52_11)
% 242.05/48.59    (22)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.05/48.59            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.05/48.59              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.05/48.59    (23)  all_40_2 = all_6_2
% 242.05/48.59    (24)  op(e1, e1) = all_6_2
% 242.05/48.59    (25)   ~ (all_52_1 = all_52_2)
% 242.05/48.59    (26)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.05/48.59            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.05/48.59              e1) = all_20_1 & $i(all_20_1))
% 242.05/48.59    (27)   ~ (all_52_7 = e3)
% 242.05/48.59    (28)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.05/48.59    (29)  op(e0, e3) = all_52_3
% 242.05/48.59    (30)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.05/48.59          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.05/48.59    (31)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.05/48.59          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.05/48.59    (32)   ~ (all_52_2 = all_52_3)
% 242.05/48.59    (33)  all_58_3 = e3
% 242.05/48.59    (34)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.05/48.59          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.05/48.59    (35)  all_54_10 = all_6_2
% 242.05/48.59    (36)  all_54_2 = all_52_8
% 242.05/48.59    (37)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.05/48.59          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.05/48.59    (38)  op(e3, e3) = e1
% 242.05/48.59    (39)   ~ (all_52_1 = all_52_9)
% 242.05/48.59    (40)   ~ (all_52_3 = all_52_7)
% 242.05/48.59    (41)  all_54_4 = all_52_1
% 242.05/48.59    (42)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.59              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.05/48.59                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.05/48.59                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.05/48.59    (43)   ~ (all_6_2 = e3)
% 242.05/48.59    (44)  op(e2, e1) = all_52_9
% 242.05/48.59    (45)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.05/48.59          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.05/48.59    (46)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.05/48.59          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.05/48.59    (47)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.05/48.59    (48)   ~ (all_52_3 = all_52_11)
% 242.05/48.59    (49)   ~ (all_6_2 = e0)
% 242.05/48.59    (50)  all_56_31 = e1
% 242.05/48.59    (51)  all_54_12 = all_52_3
% 242.05/48.59    (52)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.05/48.59    (53)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.05/48.59          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.05/48.59    (54)  all_58_15 = e1
% 242.05/48.59    (55)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.05/48.59          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.05/48.59    (56)   ~ (all_52_2 = all_6_2)
% 242.05/48.59    (57)  op(e2, e3) = all_52_1
% 242.05/48.59    (58)  all_36_2 = all_6_2
% 242.05/48.59    (59)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 242.05/48.59    (60)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.05/48.59          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.05/48.59    (61)  all_34_2 = e1
% 242.05/48.59    (62)   ~ (all_52_6 = e3)
% 242.05/48.59    (63)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.05/48.59    (64)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 242.05/48.59            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 242.05/48.59              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 242.05/48.59    (65)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.05/48.59          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.05/48.59    (66)  op(e0, e2) = all_52_7
% 242.05/48.59    (67)  all_54_1 = all_52_4
% 242.05/48.59    (68)   ~ (all_52_4 = e3)
% 242.05/48.59    (69)  op(e3, e2) = all_52_4
% 242.05/48.59    (70)   ~ (all_52_8 = all_52_11)
% 242.05/48.59    (71)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.05/48.59    (72)  all_58_5 = e1
% 242.05/48.59    (73)  all_58_7 = e1
% 242.05/48.59    (74)   ~ (all_52_9 = e3)
% 242.05/48.59    (75)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.05/48.59          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.05/48.59    (76)  all_54_8 = all_52_2
% 242.05/48.59    (77)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.05/48.59          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.05/48.59    (78)   ~ (all_52_2 = all_52_6)
% 242.05/48.59    (79)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.05/48.59          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.05/48.59    (80)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.05/48.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.05/48.59    (81)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.05/48.59          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.05/48.59    (82)   ~ (all_52_6 = all_52_7)
% 242.05/48.59    (83)  all_56_11 = e3
% 242.05/48.60    (84)   ~ (e1 = e0)
% 242.05/48.60    (85)  all_56_21 = all_6_2
% 242.05/48.60    (86)   ~ (all_52_11 = all_6_2)
% 242.05/48.60    (87)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.05/48.60          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.05/48.60    (88)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 242.05/48.60            op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 242.05/48.60              e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 242.05/48.60    (89)   ~ (all_52_1 = e3)
% 242.05/48.60    (90)  all_54_14 = all_52_11
% 242.05/48.60    (91)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.05/48.60          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.05/48.60            e2)
% 242.05/48.60    (92)   ~ (all_52_9 = all_52_11)
% 242.05/48.60    (93)   ~ (all_52_4 = all_52_8)
% 242.05/48.60    (94)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.05/48.60            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.05/48.60            & $i(all_8_1))
% 242.05/48.60    (95)   ~ (all_52_4 = all_52_6)
% 242.05/48.60    (96)   ~ (all_52_4 = all_52_7)
% 242.05/48.60  
% 242.05/48.60  Begin of proof
% 242.05/48.60  | 
% 242.05/48.60  | GROUND_INST: instantiating (80) with all_52_6, e1, e2, e1, simplifying with
% 242.05/48.60  |              (14), (17) gives:
% 242.05/48.60  |   (97)  all_52_6 = e1
% 242.05/48.60  | 
% 242.05/48.60  | GROUND_INST: instantiating (80) with all_52_9, e1, e1, e2, simplifying with
% 242.05/48.60  |              (13), (44) gives:
% 242.05/48.60  |   (98)  all_52_9 = e1
% 242.05/48.60  | 
% 242.05/48.60  | REDUCE: (39), (98) imply:
% 242.05/48.60  |   (99)   ~ (all_52_1 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | REDUCE: (78), (97) imply:
% 242.05/48.60  |   (100)   ~ (all_52_2 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | REDUCE: (95), (97) imply:
% 242.05/48.60  |   (101)   ~ (all_52_4 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | REDUCE: (82), (97) imply:
% 242.05/48.60  |   (102)   ~ (all_52_7 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | SIMP: (102) implies:
% 242.05/48.60  |   (103)   ~ (all_52_7 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | REDUCE: (11), (98) imply:
% 242.05/48.60  |   (104)   ~ (all_52_8 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | REDUCE: (92), (98) imply:
% 242.05/48.60  |   (105)   ~ (all_52_11 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | SIMP: (105) implies:
% 242.05/48.60  |   (106)   ~ (all_52_11 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | REDUCE: (5), (98) imply:
% 242.05/48.60  |   (107)   ~ (all_6_2 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | SIMP: (107) implies:
% 242.05/48.60  |   (108)   ~ (all_6_2 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | REDUCE: (74), (98) imply:
% 242.05/48.60  |   (109)   ~ (e3 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | SIMP: (109) implies:
% 242.05/48.60  |   (110)   ~ (e3 = e1)
% 242.05/48.60  | 
% 242.05/48.60  | BETA: splitting (59) gives:
% 242.05/48.60  | 
% 242.05/48.60  | Case 1:
% 242.05/48.60  | | 
% 242.05/48.60  | |   (111)  all_54_10 = e3
% 242.05/48.60  | | 
% 242.05/48.60  | | REF_CLOSE: (35), (43), (111) are inconsistent by sub-proof #2313.
% 242.05/48.60  | | 
% 242.05/48.60  | Case 2:
% 242.05/48.60  | | 
% 242.05/48.60  | |   (112)   ~ (all_54_10 = e3)
% 242.05/48.60  | |   (113)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 242.05/48.60  | | 
% 242.05/48.60  | | BETA: splitting (113) gives:
% 242.05/48.60  | | 
% 242.05/48.60  | | Case 1:
% 242.05/48.60  | | | 
% 242.05/48.60  | | |   (114)  all_54_10 = e2
% 242.05/48.60  | | | 
% 242.05/48.60  | | | COMBINE_EQS: (35), (114) imply:
% 242.05/48.60  | | |   (115)  all_6_2 = e2
% 242.05/48.60  | | | 
% 242.05/48.60  | | | SIMP: (115) implies:
% 242.05/48.60  | | |   (116)  all_6_2 = e2
% 242.05/48.60  | | | 
% 242.05/48.60  | | | COMBINE_EQS: (58), (116) imply:
% 242.05/48.60  | | |   (117)  all_36_2 = e2
% 242.05/48.60  | | | 
% 242.05/48.60  | | | COMBINE_EQS: (23), (116) imply:
% 242.05/48.60  | | |   (118)  all_40_2 = e2
% 242.05/48.60  | | | 
% 242.05/48.60  | | | COMBINE_EQS: (85), (116) imply:
% 242.05/48.60  | | |   (119)  all_56_21 = e2
% 242.05/48.60  | | | 
% 242.05/48.60  | | | REDUCE: (56), (116) imply:
% 242.05/48.60  | | |   (120)   ~ (all_52_2 = e2)
% 242.05/48.60  | | | 
% 242.05/48.60  | | | REDUCE: (16), (116) imply:
% 242.05/48.60  | | |   (121)   ~ (all_52_8 = e2)
% 242.05/48.60  | | | 
% 242.05/48.60  | | | REDUCE: (86), (116) imply:
% 242.05/48.60  | | |   (122)   ~ (all_52_11 = e2)
% 242.05/48.60  | | | 
% 242.05/48.60  | | | REDUCE: (43), (116) imply:
% 242.05/48.60  | | |   (123)   ~ (e3 = e2)
% 242.05/48.60  | | | 
% 242.05/48.60  | | | SIMP: (123) implies:
% 242.05/48.60  | | |   (124)   ~ (e3 = e2)
% 242.05/48.60  | | | 
% 242.05/48.60  | | | REDUCE: (108), (116) imply:
% 242.05/48.60  | | |   (125)   ~ (e2 = e1)
% 242.05/48.60  | | | 
% 242.05/48.60  | | | REDUCE: (49), (116) imply:
% 242.05/48.60  | | |   (126)   ~ (e2 = e0)
% 242.05/48.60  | | | 
% 242.05/48.60  | | | REDUCE: (24), (116) imply:
% 242.05/48.60  | | |   (127)  op(e1, e1) = e2
% 242.05/48.60  | | | 
% 242.05/48.60  | | | BETA: splitting (88) gives:
% 242.05/48.60  | | | 
% 242.05/48.60  | | | Case 1:
% 242.05/48.60  | | | | 
% 242.05/48.60  | | | |   (128)   ~ (all_40_2 = e2)
% 242.05/48.60  | | | | 
% 242.05/48.60  | | | | REDUCE: (118), (128) imply:
% 242.05/48.60  | | | |   (129)  $false
% 242.05/48.60  | | | | 
% 242.05/48.60  | | | | CLOSE: (129) is inconsistent.
% 242.05/48.60  | | | | 
% 242.05/48.60  | | | Case 2:
% 242.05/48.60  | | | | 
% 242.05/48.60  | | | |   (130)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2)
% 242.05/48.60  | | | |            = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 242.05/48.60  | | | |              e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 242.05/48.60  | | | | 
% 242.05/48.60  | | | | BETA: splitting (130) gives:
% 242.05/48.60  | | | | 
% 242.05/48.60  | | | | Case 1:
% 242.05/48.60  | | | | | 
% 242.05/48.60  | | | | |   (131)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2)
% 242.05/48.60  | | | | |          = all_40_1 & $i(all_40_0) & $i(all_40_1)
% 242.05/48.60  | | | | | 
% 242.05/48.60  | | | | | ALPHA: (131) implies:
% 242.05/48.60  | | | | |   (132)   ~ (all_40_0 = e0)
% 242.05/48.60  | | | | |   (133)  op(e1, e2) = all_40_1
% 242.05/48.60  | | | | |   (134)  op(all_40_1, e1) = all_40_0
% 242.05/48.60  | | | | | 
% 242.05/48.60  | | | | | BETA: splitting (64) gives:
% 242.05/48.60  | | | | | 
% 242.05/48.60  | | | | | Case 1:
% 242.05/48.60  | | | | | | 
% 242.05/48.60  | | | | | |   (135)   ~ (all_36_2 = e2)
% 242.05/48.60  | | | | | | 
% 242.05/48.60  | | | | | | REDUCE: (117), (135) imply:
% 242.05/48.60  | | | | | |   (136)  $false
% 242.05/48.60  | | | | | | 
% 242.05/48.60  | | | | | | CLOSE: (136) is inconsistent.
% 242.05/48.60  | | | | | | 
% 242.05/48.60  | | | | | Case 2:
% 242.05/48.60  | | | | | | 
% 242.05/48.60  | | | | | |   (137)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1,
% 242.05/48.60  | | | | | |              e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~
% 242.05/48.60  | | | | | |            (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 242.05/48.60  | | | | | | 
% 242.05/48.60  | | | | | | BETA: splitting (77) gives:
% 242.05/48.60  | | | | | | 
% 242.05/48.60  | | | | | | Case 1:
% 242.05/48.60  | | | | | | | 
% 242.05/48.60  | | | | | | |   (138)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 242.05/48.60  | | | | | | |            op(e1, e2) = e2)
% 242.05/48.60  | | | | | | | 
% 242.05/48.60  | | | | | | | BETA: splitting (138) gives:
% 242.05/48.60  | | | | | | | 
% 242.05/48.60  | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | 
% 242.05/48.60  | | | | | | | |   (139)  all_58_6 = e2 & op(e1, e3) = e2
% 242.05/48.60  | | | | | | | | 
% 242.05/48.60  | | | | | | | | ALPHA: (139) implies:
% 242.05/48.60  | | | | | | | |   (140)  all_58_6 = e2
% 242.05/48.60  | | | | | | | | 
% 242.05/48.60  | | | | | | | | BETA: splitting (37) gives:
% 242.05/48.60  | | | | | | | | 
% 242.05/48.60  | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | 
% 242.05/48.60  | | | | | | | | |   (141)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 242.05/48.60  | | | | | | | | |            op(e2, e3) = e3)
% 242.05/48.60  | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | REF_CLOSE: (38), (57), (80), (89), (110), (141) are
% 242.05/48.60  | | | | | | | | |            inconsistent by sub-proof #1208.
% 242.05/48.60  | | | | | | | | | 
% 242.05/48.60  | | | | | | | | Case 2:
% 242.05/48.60  | | | | | | | | | 
% 242.05/48.60  | | | | | | | | |   (142)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 242.05/48.60  | | | | | | | | |            op(e0, e3) = e3)
% 242.05/48.60  | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | BETA: splitting (142) gives:
% 242.05/48.60  | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | |   (143)  all_58_6 = e3 & op(e1, e3) = e3
% 242.05/48.60  | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | ALPHA: (143) implies:
% 242.05/48.60  | | | | | | | | | |   (144)  all_58_6 = e3
% 242.05/48.60  | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | REF_CLOSE: (124), (140), (144) are inconsistent by sub-proof
% 242.05/48.60  | | | | | | | | | |            #2024.
% 242.05/48.60  | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | Case 2:
% 242.05/48.60  | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | |   (145)  all_58_12 = e3 & op(e0, e3) = e3
% 242.05/48.60  | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | ALPHA: (145) implies:
% 242.05/48.60  | | | | | | | | | |   (146)  all_58_12 = e3
% 242.05/48.60  | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | BETA: splitting (87) gives:
% 242.05/48.60  | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | |   (147)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 242.05/48.60  | | | | | | | | | | |            & op(e1, e2) = e0)
% 242.05/48.60  | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | REF_CLOSE: (73), (84), (126), (140), (147) are inconsistent
% 242.05/48.60  | | | | | | | | | | |            by sub-proof #736.
% 242.05/48.60  | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | Case 2:
% 242.05/48.60  | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | |   (148)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 242.05/48.60  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 242.05/48.60  | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | BETA: splitting (148) gives:
% 242.05/48.60  | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | |   (149)  all_58_8 = e0 & op(e1, e1) = e0
% 242.05/48.60  | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | ALPHA: (149) implies:
% 242.05/48.60  | | | | | | | | | | | |   (150)  all_58_8 = e0
% 242.05/48.60  | | | | | | | | | | | |   (151)  op(e1, e1) = e0
% 242.05/48.60  | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | BETA: splitting (46) gives:
% 242.05/48.60  | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | |   (152)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 242.05/48.60  | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 242.05/48.60  | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | BETA: splitting (152) gives:
% 242.05/48.60  | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | |   (153)  all_58_4 = e2 & op(e3, e1) = e2
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | ALPHA: (153) implies:
% 242.05/48.60  | | | | | | | | | | | | | |   (154)  all_58_4 = e2
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 242.05/48.60  | | | | | | | | | | | | | |            (12), (14), (15), (17), (18), (19), (20), (21),
% 242.05/48.60  | | | | | | | | | | | | | |            (22), (25), (26), (27), (28), (29), (30), (31),
% 242.05/48.60  | | | | | | | | | | | | | |            (32), (33), (34), (36), (37), (38), (40), (41),
% 242.05/48.60  | | | | | | | | | | | | | |            (42), (44), (45), (46), (47), (48), (50), (51),
% 242.05/48.60  | | | | | | | | | | | | | |            (52), (53), (54), (55), (57), (60), (61), (62),
% 242.05/48.60  | | | | | | | | | | | | | |            (63), (65), (66), (67), (68), (69), (70), (71),
% 242.05/48.60  | | | | | | | | | | | | | |            (72), (73), (74), (75), (76), (79), (80), (81),
% 242.05/48.60  | | | | | | | | | | | | | |            (83), (84), (87), (89), (90), (91), (93), (94),
% 242.05/48.60  | | | | | | | | | | | | | |            (96), (99), (100), (101), (103), (104), (106),
% 242.05/48.60  | | | | | | | | | | | | | |            (110), (119), (120), (121), (122), (124), (125),
% 242.05/48.60  | | | | | | | | | | | | | |            (126), (127), (132), (133), (134), (137), (140),
% 242.05/48.60  | | | | | | | | | | | | | |            (146), (150), (151), (154) are inconsistent by
% 242.05/48.60  | | | | | | | | | | | | | |            sub-proof #690.
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | Case 2:
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | |   (155)  all_58_5 = e2 & op(e2, e1) = e2
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | REF_CLOSE: (72), (125), (155) are inconsistent by sub-proof
% 242.05/48.60  | | | | | | | | | | | | | |            #703.
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | End of split
% 242.05/48.60  | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | Case 2:
% 242.05/48.60  | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | |   (156)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 242.05/48.60  | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 242.05/48.60  | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | BETA: splitting (156) gives:
% 242.05/48.60  | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | |   (157)  all_58_8 = e2 & op(e1, e1) = e2
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | ALPHA: (157) implies:
% 242.05/48.60  | | | | | | | | | | | | | |   (158)  all_58_8 = e2
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 242.05/48.60  | | | | | | | | | | | | | |            (12), (14), (15), (17), (18), (19), (20), (21),
% 242.05/48.60  | | | | | | | | | | | | | |            (22), (25), (26), (27), (28), (29), (31), (32),
% 242.05/48.60  | | | | | | | | | | | | | |            (33), (34), (36), (37), (38), (40), (41), (42),
% 242.05/48.60  | | | | | | | | | | | | | |            (44), (45), (47), (48), (50), (51), (52), (54),
% 242.05/48.60  | | | | | | | | | | | | | |            (55), (57), (60), (61), (62), (63), (65), (66),
% 242.05/48.60  | | | | | | | | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (74),
% 242.05/48.60  | | | | | | | | | | | | | |            (75), (76), (79), (80), (81), (83), (84), (87),
% 242.05/48.60  | | | | | | | | | | | | | |            (89), (90), (91), (93), (94), (96), (99), (100),
% 242.05/48.60  | | | | | | | | | | | | | |            (101), (103), (104), (106), (110), (119), (120),
% 242.05/48.60  | | | | | | | | | | | | | |            (121), (122), (124), (125), (127), (132), (133),
% 242.05/48.60  | | | | | | | | | | | | | |            (134), (137), (158) are inconsistent by sub-proof
% 242.05/48.60  | | | | | | | | | | | | | |            #715.
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | Case 2:
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | |   (159)  all_58_14 = e2 & op(e0, e1) = e2
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | ALPHA: (159) implies:
% 242.05/48.60  | | | | | | | | | | | | | |   (160)  all_58_14 = e2
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 242.05/48.60  | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | |   (161)  all_58_15 = e0 & op(e0, e0) = e0
% 242.05/48.60  | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | REF_CLOSE: (54), (84), (161) are inconsistent by sub-proof
% 242.05/48.60  | | | | | | | | | | | | | | |            #689.
% 242.05/48.60  | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | Case 2:
% 242.05/48.60  | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | |   (162)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.05/48.60  | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.05/48.60  | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 242.05/48.60  | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.05/48.60  | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.05/48.60  | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 242.05/48.60  | | | | | | | | | | | | | | |   (163)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 242.05/48.60  | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 242.05/48.60  | | | | | | | | | | | | | | |              e1) = e0)
% 242.05/48.60  | | | | | | | | | | | | | | |   (164)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.05/48.60  | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 242.05/48.60  | | | | | | | | | | | | | | |              e0) = e0)
% 242.05/48.60  | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 242.05/48.60  | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | |   (165)  all_58_12 = e0 & op(e0, e3) = e0
% 242.05/48.60  | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 242.05/48.60  | | | | | | | | | | | | | | | |   (166)  all_58_12 = e0
% 242.05/48.60  | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (146), (166) are inconsistent by sub-proof
% 242.05/48.60  | | | | | | | | | | | | | | | |            #1971.
% 242.05/48.60  | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | Case 2:
% 242.05/48.60  | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | |   (167)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 242.05/48.60  | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 242.05/48.60  | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 242.05/48.60  | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | |   (168)  all_58_13 = e0 & op(e0, e2) = e0
% 242.05/48.60  | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 242.05/48.60  | | | | | | | | | | | | | | | | |   (169)  op(e0, e2) = e0
% 242.05/48.60  | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 242.05/48.60  | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | |   (170)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 242.05/48.60  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 242.05/48.60  | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | |   (171)  all_58_1 = e2 & op(e3, e2) = e2
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | |   (172)  all_58_1 = e2
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | |   (173)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (62), (80), (124), (140), (173) are
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #933.
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | |   (174)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | |   (175)  all_58_8 = e3 & op(e1, e1) = e3
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (150), (175) are inconsistent by sub-proof
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | |            #694.
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | |   (176)  all_58_11 = e3 & op(e1, e0) = e3
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | |   (177)  all_58_11 = e3
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | |   (178)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | |   (179)  all_58_0 = e0 & op(e3, e3) = e0
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | |   (180)  op(e3, e3) = e0
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (80), (84), (180) are inconsistent by
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1828.
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | |   (181)  all_58_2 = e0 & op(e2, e3) = e0
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | |   (182)  all_58_2 = e0
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | |   (183)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (184)  all_58_4 = e3 & op(e3, e1) = e3
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.60  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (185)  all_58_4 = e3
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (186)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (187)  all_58_2 = e2 & op(e2, e3) = e2
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (33), (54), (73), (84), (91), (124),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (126), (146), (160), (172), (182), (187)
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #688.
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_58_3 = e2 & op(e2, e2) = e2
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (189)  all_58_3 = e2
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (189) imply:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (190)  e3 = e2
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (190) imply:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (191)  all_58_4 = e2
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12), (14), (15), (17), (18), (19), (20), (21),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (22), (25), (26), (27), (28), (29), (30), (31),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (32), (33), (34), (36), (37), (38), (40), (41),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (42), (44), (45), (46), (47), (48), (50), (51),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (53), (54), (55), (57), (60), (61), (62),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (63), (65), (66), (67), (68), (69), (70), (71),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (72), (73), (74), (75), (76), (79), (80), (81),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (87), (89), (90), (91), (93), (94),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (96), (99), (100), (101), (103), (104), (106),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (110), (119), (120), (121), (122), (124), (125),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (126), (127), (132), (133), (134), (137), (140),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (146), (150), (151), (191) are inconsistent by
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #690.
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (192)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (33), (54), (72), (73), (80), (84),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (124), (125), (126), (127), (146), (151),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (164), (171), (177), (192) are inconsistent
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #687.
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (193)  all_58_5 = e3 & op(e2, e1) = e3
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (74), (80), (193) are inconsistent by
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1822.
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | |   (194)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  all_58_8 = e3 & op(e1, e1) = e3
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  all_58_8 = e3
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (196) imply:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (197)  e3 = e0
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (197) implies:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (198)  e3 = e0
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (198) imply:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (199)  $false
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent.
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_58_14 = e3 & op(e0, e1) = e3
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_58_14 = e3
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (54), (84), (91), (124), (125), (126),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | |            (146), (201) are inconsistent by sub-proof #1863.
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | |   (202)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (33), (54), (73), (84), (91), (124),
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | |            (125), (126), (140), (146), (160), (172), (202)
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #686.
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | |   (203)  all_58_3 = e2 & op(e2, e2) = e2
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (124), (203) are inconsistent by sub-proof
% 242.05/48.61  | | | | | | | | | | | | | | | | | | |            #1458.
% 242.05/48.61  | | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | |   (204)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 242.05/48.61  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 242.05/48.61  | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (80), (125), (126), (169), (204) are
% 242.05/48.61  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1376.
% 242.05/48.61  | | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | |   (205)  all_58_14 = e0 & op(e0, e1) = e0
% 242.05/48.61  | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (160), (205) are inconsistent by sub-proof
% 242.05/48.61  | | | | | | | | | | | | | | | | |            #2036.
% 242.05/48.61  | | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | |   (206)  all_58_11 = e0 & op(e1, e0) = e0
% 242.05/48.61  | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | ALPHA: (206) implies:
% 242.05/48.61  | | | | | | | | | | | |   (207)  all_58_11 = e0
% 242.05/48.61  | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | BETA: splitting (55) gives:
% 242.05/48.61  | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | Case 1:
% 242.05/48.61  | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | |   (208)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 242.05/48.61  | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 242.05/48.61  | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | REF_CLOSE: (17), (62), (80), (124), (140), (208) are
% 242.05/48.61  | | | | | | | | | | | | |            inconsistent by sub-proof #968.
% 242.05/48.61  | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | |   (209)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 242.05/48.61  | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 242.05/48.61  | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | BETA: splitting (209) gives:
% 242.05/48.61  | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | Case 1:
% 242.05/48.61  | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | |   (210)  all_58_8 = e3 & op(e1, e1) = e3
% 242.05/48.61  | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | ALPHA: (210) implies:
% 242.05/48.61  | | | | | | | | | | | | | |   (211)  all_58_8 = e3
% 242.05/48.61  | | | | | | | | | | | | | |   (212)  op(e1, e1) = e3
% 242.05/48.61  | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 242.05/48.61  | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | Case 1:
% 242.05/48.61  | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | |   (213)  all_58_15 = e0 & op(e0, e0) = e0
% 242.05/48.61  | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | REF_CLOSE: (54), (84), (213) are inconsistent by sub-proof
% 242.05/48.61  | | | | | | | | | | | | | | |            #689.
% 242.05/48.61  | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 242.05/48.61  | | | | | | | | | | | | | | |            (12), (14), (15), (17), (18), (19), (20), (21),
% 242.05/48.61  | | | | | | | | | | | | | | |            (22), (25), (26), (27), (28), (29), (31), (32),
% 242.05/48.61  | | | | | | | | | | | | | | |            (33), (34), (36), (37), (38), (40), (41), (42),
% 242.05/48.61  | | | | | | | | | | | | | | |            (44), (45), (47), (48), (50), (51), (52), (54),
% 242.05/48.61  | | | | | | | | | | | | | | |            (55), (57), (60), (61), (62), (63), (65), (66),
% 242.05/48.61  | | | | | | | | | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (74),
% 242.05/48.61  | | | | | | | | | | | | | | |            (75), (76), (79), (80), (81), (83), (84), (87),
% 242.05/48.61  | | | | | | | | | | | | | | |            (89), (90), (91), (93), (94), (96), (99), (100),
% 242.05/48.61  | | | | | | | | | | | | | | |            (101), (103), (104), (106), (110), (119), (120),
% 242.05/48.61  | | | | | | | | | | | | | | |            (121), (122), (124), (125), (127), (132), (133),
% 242.05/48.61  | | | | | | | | | | | | | | |            (134), (137), (211), (212) are inconsistent by
% 242.05/48.61  | | | | | | | | | | | | | | |            sub-proof #713.
% 242.05/48.61  | | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | |   (214)  all_58_11 = e3 & op(e1, e0) = e3
% 242.05/48.61  | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | ALPHA: (214) implies:
% 242.05/48.61  | | | | | | | | | | | | | |   (215)  all_58_11 = e3
% 242.05/48.61  | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | | REF_CLOSE: (9), (207), (215) are inconsistent by sub-proof
% 242.05/48.61  | | | | | | | | | | | | | |            #1688.
% 242.05/48.61  | | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | | 
% 242.05/48.61  | | | | | | | | End of split
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | |   (216)  all_58_7 = e2 & op(e1, e2) = e2
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | | ALPHA: (216) implies:
% 242.05/48.61  | | | | | | | |   (217)  all_58_7 = e2
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | | REF_CLOSE: (73), (125), (217) are inconsistent by sub-proof
% 242.05/48.61  | | | | | | | |            #2134.
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | End of split
% 242.05/48.61  | | | | | | | 
% 242.05/48.61  | | | | | | Case 2:
% 242.05/48.61  | | | | | | | 
% 242.05/48.61  | | | | | | |   (218)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 242.05/48.61  | | | | | | |            op(e1, e0) = e2)
% 242.05/48.61  | | | | | | | 
% 242.05/48.61  | | | | | | | BETA: splitting (218) gives:
% 242.05/48.61  | | | | | | | 
% 242.05/48.61  | | | | | | | Case 1:
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | |   (219)  all_58_8 = e2 & op(e1, e1) = e2
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | | ALPHA: (219) implies:
% 242.05/48.61  | | | | | | | |   (220)  all_58_8 = e2
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12),
% 242.05/48.61  | | | | | | | |            (14), (15), (17), (18), (19), (20), (21), (22), (25),
% 242.05/48.61  | | | | | | | |            (26), (27), (28), (29), (31), (32), (33), (34), (36),
% 242.05/48.61  | | | | | | | |            (37), (38), (40), (41), (42), (44), (45), (47), (48),
% 242.05/48.61  | | | | | | | |            (50), (51), (52), (54), (55), (57), (60), (61), (62),
% 242.05/48.61  | | | | | | | |            (63), (65), (66), (67), (68), (69), (70), (71), (72),
% 242.05/48.61  | | | | | | | |            (73), (74), (75), (76), (79), (80), (81), (83), (84),
% 242.05/48.61  | | | | | | | |            (87), (89), (90), (91), (93), (94), (96), (99),
% 242.05/48.61  | | | | | | | |            (100), (101), (103), (104), (106), (110), (119),
% 242.05/48.61  | | | | | | | |            (120), (121), (122), (124), (125), (127), (132),
% 242.05/48.61  | | | | | | | |            (133), (134), (137), (220) are inconsistent by
% 242.05/48.61  | | | | | | | |            sub-proof #715.
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | Case 2:
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | |   (221)  all_58_11 = e2 & op(e1, e0) = e2
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | | ALPHA: (221) implies:
% 242.05/48.61  | | | | | | | |   (222)  all_58_11 = e2
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | | BETA: splitting (75) gives:
% 242.05/48.61  | | | | | | | | 
% 242.05/48.61  | | | | | | | | Case 1:
% 242.05/48.61  | | | | | | | | | 
% 242.05/48.61  | | | | | | | | |   (223)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 242.05/48.61  | | | | | | | | |            op(e2, e0) = e3)
% 242.05/48.61  | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | BETA: splitting (223) gives:
% 242.05/48.61  | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | Case 1:
% 242.05/48.61  | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | |   (224)  all_58_9 = e3 & op(e3, e0) = e3
% 242.05/48.61  | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | ALPHA: (224) implies:
% 242.05/48.61  | | | | | | | | | |   (225)  all_58_9 = e3
% 242.05/48.61  | | | | | | | | | |   (226)  op(e3, e0) = e3
% 242.05/48.61  | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | BETA: splitting (87) gives:
% 242.05/48.61  | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | Case 1:
% 242.05/48.61  | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | |   (227)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 242.05/48.61  | | | | | | | | | | |            & op(e1, e2) = e0)
% 242.05/48.61  | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | BETA: splitting (227) gives:
% 242.05/48.61  | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | Case 1:
% 242.05/48.61  | | | | | | | | | | | | 
% 242.05/48.61  | | | | | | | | | | | |   (228)  all_58_6 = e0 & op(e1, e3) = e0
% 242.12/48.61  | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | ALPHA: (228) implies:
% 242.12/48.61  | | | | | | | | | | | |   (229)  all_58_6 = e0
% 242.12/48.61  | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 242.12/48.61  | | | | | | | | | | | |            (12), (14), (15), (17), (18), (19), (20), (21),
% 242.12/48.61  | | | | | | | | | | | |            (22), (25), (26), (27), (28), (29), (31), (32),
% 242.12/48.61  | | | | | | | | | | | |            (33), (34), (36), (37), (38), (40), (41), (42),
% 242.12/48.61  | | | | | | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52),
% 242.12/48.61  | | | | | | | | | | | |            (53), (54), (55), (57), (60), (61), (62), (63),
% 242.12/48.61  | | | | | | | | | | | |            (65), (66), (67), (68), (69), (70), (71), (72),
% 242.12/48.61  | | | | | | | | | | | |            (73), (74), (75), (76), (79), (80), (81), (83),
% 242.12/48.61  | | | | | | | | | | | |            (84), (87), (89), (90), (91), (93), (94), (96),
% 242.12/48.61  | | | | | | | | | | | |            (99), (100), (101), (103), (104), (106), (110),
% 242.12/48.61  | | | | | | | | | | | |            (119), (120), (121), (122), (124), (125), (126),
% 242.12/48.61  | | | | | | | | | | | |            (127), (132), (133), (134), (137), (222), (225),
% 242.12/48.61  | | | | | | | | | | | |            (226), (229) are inconsistent by sub-proof #705.
% 242.12/48.61  | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | Case 2:
% 242.12/48.61  | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | |   (230)  all_58_7 = e0 & op(e1, e2) = e0
% 242.12/48.61  | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | REF_CLOSE: (73), (84), (230) are inconsistent by sub-proof
% 242.12/48.61  | | | | | | | | | | | |            #1558.
% 242.12/48.61  | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | End of split
% 242.12/48.61  | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | Case 2:
% 242.12/48.61  | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | |   (231)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 242.12/48.61  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 242.12/48.61  | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | BETA: splitting (231) gives:
% 242.12/48.61  | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | Case 1:
% 242.12/48.61  | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | |   (232)  all_58_8 = e0 & op(e1, e1) = e0
% 242.12/48.61  | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | ALPHA: (232) implies:
% 242.12/48.61  | | | | | | | | | | | |   (233)  all_58_8 = e0
% 242.12/48.61  | | | | | | | | | | | |   (234)  op(e1, e1) = e0
% 242.12/48.61  | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | BETA: splitting (3) gives:
% 242.12/48.61  | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | Case 1:
% 242.12/48.61  | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | |   (235)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 242.12/48.61  | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 242.12/48.61  | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | BETA: splitting (235) gives:
% 242.12/48.61  | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | Case 1:
% 242.12/48.61  | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | |   (236)  all_58_0 = e2 & op(e3, e3) = e2
% 242.12/48.61  | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | ALPHA: (236) implies:
% 242.12/48.61  | | | | | | | | | | | | | |   (237)  op(e3, e3) = e2
% 242.12/48.61  | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | REF_CLOSE: (38), (80), (125), (237) are inconsistent by
% 242.12/48.61  | | | | | | | | | | | | | |            sub-proof #2267.
% 242.12/48.61  | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | Case 2:
% 242.12/48.61  | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | |   (238)  all_58_1 = e2 & op(e3, e2) = e2
% 242.12/48.61  | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | ALPHA: (238) implies:
% 242.12/48.61  | | | | | | | | | | | | | |   (239)  all_58_1 = e2
% 242.12/48.61  | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 242.12/48.61  | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | Case 1:
% 242.12/48.61  | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | |   (240)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 242.12/48.61  | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 242.12/48.61  | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 242.12/48.61  | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | | Case 1:
% 242.12/48.61  | | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | | |   (241)  all_58_6 = e3 & op(e1, e3) = e3
% 242.12/48.61  | | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | | | ALPHA: (241) implies:
% 242.12/48.61  | | | | | | | | | | | | | | | |   (242)  all_58_6 = e3
% 242.12/48.61  | | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 242.12/48.61  | | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.61  | | | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | | | |   (243)  all_58_15 = e0 & op(e0, e0) = e0
% 242.12/48.61  | | | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (84), (243) are inconsistent by sub-proof
% 242.12/48.61  | | | | | | | | | | | | | | | | |            #1867.
% 242.12/48.61  | | | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.61  | | | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | | | |   (244)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.12/48.61  | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.12/48.61  | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 242.12/48.61  | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.12/48.61  | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.12/48.61  | | | | | | | | | | | | | | | | | 
% 242.12/48.61  | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 242.12/48.61  | | | | | | | | | | | | | | | | |   (245)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.12/48.61  | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 242.12/48.61  | | | | | | | | | | | | | | | | |              e0) = e0)
% 242.12/48.61  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (12), (14), (15), (17), (18), (19), (20), (21),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (22), (25), (26), (27), (28), (29), (30), (31),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (32), (33), (34), (36), (37), (38), (40), (41),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (42), (44), (45), (46), (47), (48), (50), (51),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (52), (53), (54), (55), (57), (60), (61), (62),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (63), (65), (66), (67), (68), (69), (70), (71),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (72), (73), (74), (75), (76), (79), (80), (81),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (83), (84), (87), (89), (90), (91), (93), (94),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (96), (99), (100), (101), (103), (104), (106),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (110), (119), (120), (121), (122), (124), (125),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (126), (127), (132), (133), (134), (137), (222),
% 242.12/48.62  | | | | | | | | | | | | | | | | |            (225), (226), (233), (239), (242), (245) are
% 242.12/48.62  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #700.
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | |   (246)  all_58_7 = e3 & op(e1, e2) = e3
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 242.12/48.62  | | | | | | | | | | | | | | | |   (247)  op(e1, e2) = e3
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | REF_CLOSE: (17), (62), (80), (247) are inconsistent by
% 242.12/48.62  | | | | | | | | | | | | | | | |            sub-proof #2191.
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | |   (248)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 242.12/48.62  | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | REF_CLOSE: (9), (124), (222), (233), (248) are inconsistent
% 242.12/48.62  | | | | | | | | | | | | | | |            by sub-proof #693.
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | |   (249)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 242.12/48.62  | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | BETA: splitting (249) gives:
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | |   (250)  all_58_4 = e2 & op(e3, e1) = e2
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | ALPHA: (250) implies:
% 242.12/48.62  | | | | | | | | | | | | | |   (251)  all_58_4 = e2
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 242.12/48.62  | | | | | | | | | | | | | |            (12), (14), (15), (17), (18), (19), (20), (21),
% 242.12/48.62  | | | | | | | | | | | | | |            (22), (25), (26), (27), (28), (29), (30), (31),
% 242.12/48.62  | | | | | | | | | | | | | |            (32), (33), (34), (36), (37), (38), (40), (41),
% 242.12/48.62  | | | | | | | | | | | | | |            (42), (44), (45), (46), (47), (48), (50), (51),
% 242.12/48.62  | | | | | | | | | | | | | |            (52), (53), (54), (55), (57), (60), (61), (62),
% 242.12/48.62  | | | | | | | | | | | | | |            (63), (65), (66), (67), (68), (69), (70), (71),
% 242.12/48.62  | | | | | | | | | | | | | |            (72), (73), (74), (75), (76), (79), (80), (81),
% 242.12/48.62  | | | | | | | | | | | | | |            (83), (84), (87), (89), (90), (91), (93), (94),
% 242.12/48.62  | | | | | | | | | | | | | |            (96), (99), (100), (101), (103), (104), (106),
% 242.12/48.62  | | | | | | | | | | | | | |            (110), (119), (120), (121), (122), (124), (125),
% 242.12/48.62  | | | | | | | | | | | | | |            (126), (127), (132), (133), (134), (137), (222),
% 242.12/48.62  | | | | | | | | | | | | | |            (225), (226), (233), (234), (251) are inconsistent
% 242.12/48.62  | | | | | | | | | | | | | |            by sub-proof #692.
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | |   (252)  all_58_9 = e2 & op(e3, e0) = e2
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | ALPHA: (252) implies:
% 242.12/48.62  | | | | | | | | | | | | | |   (253)  op(e3, e0) = e2
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | REF_CLOSE: (80), (124), (226), (253) are inconsistent by
% 242.12/48.62  | | | | | | | | | | | | | |            sub-proof #2125.
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | |   (254)  all_58_11 = e0 & op(e1, e0) = e0
% 242.12/48.62  | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | ALPHA: (254) implies:
% 242.12/48.62  | | | | | | | | | | | |   (255)  all_58_11 = e0
% 242.12/48.62  | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | REF_CLOSE: (126), (222), (255) are inconsistent by sub-proof
% 242.12/48.62  | | | | | | | | | | | |            #2110.
% 242.12/48.62  | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | |   (256)  all_58_10 = e3 & op(e2, e0) = e3
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | ALPHA: (256) implies:
% 242.12/48.62  | | | | | | | | | |   (257)  all_58_10 = e3
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | REF_CLOSE: (9), (30), (33), (72), (79), (84), (124), (125),
% 242.12/48.62  | | | | | | | | | |            (126), (257) are inconsistent by sub-proof #1101.
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | 
% 242.12/48.62  | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | 
% 242.12/48.62  | | | | | | | | |   (258)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3
% 242.12/48.62  | | | | | | | | |            & op(e0, e0) = e3)
% 242.12/48.62  | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | BETA: splitting (258) gives:
% 242.12/48.62  | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | |   (259)  all_58_11 = e3 & op(e1, e0) = e3
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | REF_CLOSE: (124), (222), (259) are inconsistent by sub-proof
% 242.12/48.62  | | | | | | | | | |            #2108.
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | |   (260)  all_58_15 = e3 & op(e0, e0) = e3
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | REF_CLOSE: (54), (110), (260) are inconsistent by sub-proof
% 242.12/48.62  | | | | | | | | | |            #1915.
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | 
% 242.12/48.62  | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | 
% 242.12/48.62  | | | | | | | End of split
% 242.12/48.62  | | | | | | | 
% 242.12/48.62  | | | | | | End of split
% 242.12/48.62  | | | | | | 
% 242.12/48.62  | | | | | End of split
% 242.12/48.62  | | | | | 
% 242.12/48.62  | | | | Case 2:
% 242.12/48.62  | | | | | 
% 242.12/48.62  | | | | |   (261)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 242.12/48.62  | | | | | 
% 242.12/48.62  | | | | | ALPHA: (261) implies:
% 242.12/48.62  | | | | |   (262)   ~ (all_40_1 = e3)
% 242.12/48.62  | | | | |   (263)  op(e1, e2) = all_40_1
% 242.12/48.62  | | | | | 
% 242.12/48.62  | | | | | BETA: splitting (64) gives:
% 242.12/48.62  | | | | | 
% 242.12/48.62  | | | | | Case 1:
% 242.12/48.62  | | | | | | 
% 242.12/48.62  | | | | | |   (264)   ~ (all_36_2 = e2)
% 242.12/48.62  | | | | | | 
% 242.12/48.62  | | | | | | REDUCE: (117), (264) imply:
% 242.12/48.62  | | | | | |   (265)  $false
% 242.12/48.62  | | | | | | 
% 242.12/48.62  | | | | | | CLOSE: (265) is inconsistent.
% 242.12/48.62  | | | | | | 
% 242.12/48.62  | | | | | Case 2:
% 242.12/48.62  | | | | | | 
% 242.12/48.62  | | | | | |   (266)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1,
% 242.12/48.62  | | | | | |              e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~
% 242.12/48.62  | | | | | |            (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 242.12/48.62  | | | | | | 
% 242.12/48.62  | | | | | | BETA: splitting (77) gives:
% 242.12/48.62  | | | | | | 
% 242.12/48.62  | | | | | | Case 1:
% 242.12/48.62  | | | | | | | 
% 242.12/48.62  | | | | | | |   (267)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 242.12/48.62  | | | | | | |            op(e1, e2) = e2)
% 242.12/48.62  | | | | | | | 
% 242.12/48.62  | | | | | | | BETA: splitting (267) gives:
% 242.12/48.62  | | | | | | | 
% 242.12/48.62  | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | 
% 242.12/48.62  | | | | | | | |   (268)  all_58_6 = e2 & op(e1, e3) = e2
% 242.12/48.62  | | | | | | | | 
% 242.12/48.62  | | | | | | | | ALPHA: (268) implies:
% 242.12/48.62  | | | | | | | |   (269)  all_58_6 = e2
% 242.12/48.62  | | | | | | | | 
% 242.12/48.62  | | | | | | | | BETA: splitting (37) gives:
% 242.12/48.62  | | | | | | | | 
% 242.12/48.62  | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | 
% 242.12/48.62  | | | | | | | | |   (270)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 242.12/48.62  | | | | | | | | |            op(e2, e3) = e3)
% 242.12/48.62  | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | REF_CLOSE: (38), (57), (80), (89), (110), (270) are
% 242.12/48.62  | | | | | | | | |            inconsistent by sub-proof #1208.
% 242.12/48.62  | | | | | | | | | 
% 242.12/48.62  | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | 
% 242.12/48.62  | | | | | | | | |   (271)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 242.12/48.62  | | | | | | | | |            op(e0, e3) = e3)
% 242.12/48.62  | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | BETA: splitting (271) gives:
% 242.12/48.62  | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | |   (272)  all_58_6 = e3 & op(e1, e3) = e3
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | ALPHA: (272) implies:
% 242.12/48.62  | | | | | | | | | |   (273)  all_58_6 = e3
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | REF_CLOSE: (124), (269), (273) are inconsistent by sub-proof
% 242.12/48.62  | | | | | | | | | |            #2024.
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | |   (274)  all_58_12 = e3 & op(e0, e3) = e3
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | ALPHA: (274) implies:
% 242.12/48.62  | | | | | | | | | |   (275)  all_58_12 = e3
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | BETA: splitting (87) gives:
% 242.12/48.62  | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | |   (276)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 242.12/48.62  | | | | | | | | | | |            & op(e1, e2) = e0)
% 242.12/48.62  | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | REF_CLOSE: (73), (84), (126), (269), (276) are inconsistent
% 242.12/48.62  | | | | | | | | | | |            by sub-proof #736.
% 242.12/48.62  | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | |   (277)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 242.12/48.62  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 242.12/48.62  | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | BETA: splitting (277) gives:
% 242.12/48.62  | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | |   (278)  all_58_8 = e0 & op(e1, e1) = e0
% 242.12/48.62  | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | ALPHA: (278) implies:
% 242.12/48.62  | | | | | | | | | | | |   (279)  all_58_8 = e0
% 242.12/48.62  | | | | | | | | | | | |   (280)  op(e1, e1) = e0
% 242.12/48.62  | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | BETA: splitting (46) gives:
% 242.12/48.62  | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | |   (281)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 242.12/48.62  | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | BETA: splitting (281) gives:
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | |   (282)  all_58_4 = e2 & op(e3, e1) = e2
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | ALPHA: (282) implies:
% 242.12/48.62  | | | | | | | | | | | | | |   (283)  all_58_4 = e2
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | |   (284)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 242.12/48.62  | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | REF_CLOSE: (38), (68), (69), (80), (110), (284) are
% 242.12/48.62  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1401.
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | |   (285)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 242.12/48.62  | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | |   (286)  all_58_4 = e3 & op(e3, e1) = e3
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | REF_CLOSE: (124), (283), (286) are inconsistent by sub-proof
% 242.12/48.62  | | | | | | | | | | | | | | | |            #2167.
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | |   (287)  all_58_9 = e3 & op(e3, e0) = e3
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 242.12/48.62  | | | | | | | | | | | | | | | |   (288)  all_58_9 = e3
% 242.12/48.62  | | | | | | | | | | | | | | | |   (289)  op(e3, e0) = e3
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | |   (290)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 242.12/48.62  | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | |   (291)  all_58_9 = e2 & op(e3, e0) = e2
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | ALPHA: (291) implies:
% 242.12/48.62  | | | | | | | | | | | | | | | | | |   (292)  op(e3, e0) = e2
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (124), (289), (292) are inconsistent by
% 242.12/48.62  | | | | | | | | | | | | | | | | | |            sub-proof #2125.
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | |   (293)  all_58_10 = e2 & op(e2, e0) = e2
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 242.12/48.62  | | | | | | | | | | | | | | | | | |   (294)  op(e2, e0) = e2
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | |   (295)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 242.12/48.62  | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (62), (80), (124), (269), (295) are
% 242.12/48.62  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #933.
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | |   (296)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 242.12/48.62  | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | |   (297)  all_58_8 = e3 & op(e1, e1) = e3
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | |   (298)  op(e1, e1) = e3
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (124), (127), (298) are inconsistent by
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | |            sub-proof #2206.
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | |   (299)  all_58_11 = e3 & op(e1, e0) = e3
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | |   (300)  all_58_11 = e3
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (54), (80), (84), (126), (288), (294),
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | |            (300) are inconsistent by sub-proof #710.
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | |   (301)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 242.12/48.62  | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | |   (302)  all_58_11 = e2 & op(e1, e0) = e2
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 242.12/48.62  | | | | | | | | | | | | | | | | | |   (303)  all_58_11 = e2
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (17), (18), (20), (27), (30), (33),
% 242.12/48.62  | | | | | | | | | | | | | | | | | |            (37), (38), (42), (44), (46), (53), (54), (55),
% 242.12/48.62  | | | | | | | | | | | | | | | | | |            (57), (60), (62), (65), (66), (72), (73), (74),
% 242.12/48.62  | | | | | | | | | | | | | | | | | |            (79), (80), (84), (89), (91), (110), (124), (125),
% 242.12/48.62  | | | | | | | | | | | | | | | | | |            (126), (127), (279), (280), (288), (289), (303)
% 242.12/48.62  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #682.
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | |   (304)  all_58_15 = e2 & op(e0, e0) = e2
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | ALPHA: (304) implies:
% 242.12/48.62  | | | | | | | | | | | | | | | | | |   (305)  all_58_15 = e2
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (9), (38), (54), (60), (80), (84), (124),
% 242.12/48.62  | | | | | | | | | | | | | | | | | |            (125), (126), (283), (288), (305) are inconsistent
% 242.12/48.62  | | | | | | | | | | | | | | | | | |            by sub-proof #691.
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | |   (306)  all_58_5 = e2 & op(e2, e1) = e2
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | REF_CLOSE: (72), (125), (306) are inconsistent by sub-proof
% 242.12/48.62  | | | | | | | | | | | | | |            #703.
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | End of split
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | |   (307)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 242.12/48.62  | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | BETA: splitting (307) gives:
% 242.12/48.62  | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | |   (308)  all_58_8 = e2 & op(e1, e1) = e2
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | REF_CLOSE: (126), (279), (308) are inconsistent by sub-proof
% 242.12/48.62  | | | | | | | | | | | | | |            #683.
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | |   (309)  all_58_14 = e2 & op(e0, e1) = e2
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | ALPHA: (309) implies:
% 242.12/48.62  | | | | | | | | | | | | | |   (310)  all_58_14 = e2
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 242.12/48.62  | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | |   (311)  all_58_15 = e0 & op(e0, e0) = e0
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | REF_CLOSE: (54), (84), (311) are inconsistent by sub-proof
% 242.12/48.62  | | | | | | | | | | | | | | |            #689.
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | |   (312)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.12/48.62  | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.12/48.62  | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 242.12/48.62  | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.12/48.62  | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | ALPHA: (312) implies:
% 242.12/48.62  | | | | | | | | | | | | | | |   (313)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 242.12/48.62  | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 242.12/48.62  | | | | | | | | | | | | | | |              e1) = e0)
% 242.12/48.62  | | | | | | | | | | | | | | |   (314)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.12/48.62  | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 242.12/48.62  | | | | | | | | | | | | | | |              e0) = e0)
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 242.12/48.62  | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | |   (315)  all_58_12 = e0 & op(e0, e3) = e0
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 242.12/48.62  | | | | | | | | | | | | | | | |   (316)  all_58_12 = e0
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (275), (316) are inconsistent by sub-proof
% 242.12/48.62  | | | | | | | | | | | | | | | |            #1971.
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | Case 2:
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | |   (317)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 242.12/48.62  | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 242.12/48.62  | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | |   (318)  all_58_13 = e0 & op(e0, e2) = e0
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 242.12/48.62  | | | | | | | | | | | | | | | | |   (319)  op(e0, e2) = e0
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 242.12/48.62  | | | | | | | | | | | | | | | | | 
% 242.12/48.62  | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.62  | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | |   (320)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 242.12/48.63  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 242.12/48.63  | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | |   (321)  all_58_1 = e2 & op(e3, e2) = e2
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | ALPHA: (321) implies:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | |   (322)  all_58_1 = e2
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | |   (323)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (62), (80), (124), (269), (323) are
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #933.
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | |   (324)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | |   (325)  all_58_8 = e3 & op(e1, e1) = e3
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | ALPHA: (325) implies:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | |   (326)  op(e1, e1) = e3
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (124), (127), (326) are inconsistent by
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2206.
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | |   (327)  all_58_11 = e3 & op(e1, e0) = e3
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | ALPHA: (327) implies:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | |   (328)  all_58_11 = e3
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | |   (329)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_58_0 = e0 & op(e3, e3) = e0
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | |   (331)  op(e3, e3) = e0
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (80), (84), (331) are inconsistent by
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1828.
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | |   (332)  all_58_2 = e0 & op(e2, e3) = e0
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | |   (333)  all_58_2 = e0
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | |   (334)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (335)  all_58_2 = e2 & op(e2, e3) = e2
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (33), (54), (73), (84), (91), (124),
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (126), (275), (310), (322), (333), (335)
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #688.
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (336)  all_58_3 = e2 & op(e2, e2) = e2
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (336) implies:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (337)  all_58_3 = e2
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (337) imply:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (338)  e3 = e2
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (338) imply:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (339)  all_58_11 = e2
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (17), (18), (20), (27), (30), (33),
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (37), (38), (42), (44), (46), (53), (54), (55),
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (60), (62), (65), (66), (72), (73), (74),
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (75), (79), (80), (84), (87), (89), (91), (110),
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (124), (125), (126), (127), (339) are inconsistent
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #681.
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | |   (340)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (33), (54), (72), (73), (80), (84),
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | |            (91), (124), (125), (126), (127), (275), (280),
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | |            (310), (314), (321), (328), (340) are inconsistent
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #687.
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | |   (341)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (20), (33), (54), (73), (84), (91), (124),
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | |            (125), (126), (269), (275), (310), (322), (341)
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #686.
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | |   (342)  all_58_3 = e2 & op(e2, e2) = e2
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (124), (342) are inconsistent by sub-proof
% 242.12/48.63  | | | | | | | | | | | | | | | | | | |            #1458.
% 242.12/48.63  | | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | |   (343)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 242.12/48.63  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 242.12/48.63  | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (80), (125), (126), (319), (343) are
% 242.12/48.63  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1376.
% 242.12/48.63  | | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | |   (344)  all_58_14 = e0 & op(e0, e1) = e0
% 242.12/48.63  | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (310), (344) are inconsistent by sub-proof
% 242.12/48.63  | | | | | | | | | | | | | | | | |            #2036.
% 242.12/48.63  | | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | |   (345)  all_58_11 = e0 & op(e1, e0) = e0
% 242.12/48.63  | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | ALPHA: (345) implies:
% 242.12/48.63  | | | | | | | | | | | |   (346)  all_58_11 = e0
% 242.12/48.63  | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | | REF_CLOSE: (9), (17), (55), (62), (80), (124), (127), (269),
% 242.12/48.63  | | | | | | | | | | | |            (346) are inconsistent by sub-proof #967.
% 242.12/48.63  | | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | | 
% 242.12/48.63  | | | | | | | | End of split
% 242.12/48.63  | | | | | | | | 
% 242.12/48.63  | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | 
% 242.12/48.63  | | | | | | | |   (347)  all_58_7 = e2 & op(e1, e2) = e2
% 242.12/48.63  | | | | | | | | 
% 242.12/48.63  | | | | | | | | ALPHA: (347) implies:
% 242.12/48.63  | | | | | | | |   (348)  all_58_7 = e2
% 242.12/48.63  | | | | | | | | 
% 242.12/48.63  | | | | | | | | REF_CLOSE: (73), (125), (348) are inconsistent by sub-proof
% 242.12/48.63  | | | | | | | |            #2134.
% 242.12/48.63  | | | | | | | | 
% 242.12/48.63  | | | | | | | End of split
% 242.12/48.63  | | | | | | | 
% 242.12/48.63  | | | | | | Case 2:
% 242.12/48.63  | | | | | | | 
% 242.12/48.63  | | | | | | |   (349)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 242.12/48.63  | | | | | | |            op(e1, e0) = e2)
% 242.12/48.63  | | | | | | | 
% 242.12/48.63  | | | | | | | BETA: splitting (349) gives:
% 242.12/48.63  | | | | | | | 
% 242.12/48.63  | | | | | | | Case 1:
% 242.12/48.63  | | | | | | | | 
% 242.12/48.63  | | | | | | | |   (350)  all_58_8 = e2 & op(e1, e1) = e2
% 242.12/48.63  | | | | | | | | 
% 242.12/48.63  | | | | | | | | ALPHA: (350) implies:
% 242.12/48.63  | | | | | | | |   (351)  all_58_8 = e2
% 242.12/48.63  | | | | | | | | 
% 242.12/48.63  | | | | | | | | GROUND_INST: instantiating (80) with e1, all_40_1, e2, e1,
% 242.12/48.63  | | | | | | | |              simplifying with (14), (263) gives:
% 242.12/48.63  | | | | | | | |   (352)  all_40_1 = e1
% 242.12/48.63  | | | | | | | | 
% 242.12/48.63  | | | | | | | | BETA: splitting (266) gives:
% 242.12/48.63  | | | | | | | | 
% 242.12/48.63  | | | | | | | | Case 1:
% 242.12/48.63  | | | | | | | | | 
% 242.12/48.63  | | | | | | | | |   (353)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 242.12/48.63  | | | | | | | | |          op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)
% 242.12/48.63  | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | ALPHA: (353) implies:
% 242.12/48.63  | | | | | | | | |   (354)   ~ (all_36_0 = e3)
% 242.12/48.63  | | | | | | | | |   (355)  op(e1, e2) = all_36_1
% 242.12/48.63  | | | | | | | | |   (356)  op(all_36_1, e1) = all_36_0
% 242.12/48.63  | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | GROUND_INST: instantiating (80) with e1, all_36_1, e2, e1,
% 242.12/48.63  | | | | | | | | |              simplifying with (14), (355) gives:
% 242.12/48.63  | | | | | | | | |   (357)  all_36_1 = e1
% 242.12/48.63  | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | REDUCE: (356), (357) imply:
% 242.12/48.63  | | | | | | | | |   (358)  op(e1, e1) = all_36_0
% 242.12/48.63  | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12),
% 242.12/48.63  | | | | | | | | |            (15), (17), (18), (19), (20), (21), (22), (25),
% 242.12/48.63  | | | | | | | | |            (26), (27), (28), (29), (31), (32), (33), (34),
% 242.12/48.63  | | | | | | | | |            (36), (37), (38), (40), (41), (42), (44), (45),
% 242.12/48.63  | | | | | | | | |            (47), (48), (50), (51), (52), (54), (55), (57),
% 242.12/48.63  | | | | | | | | |            (60), (61), (62), (63), (65), (66), (67), (68),
% 242.12/48.63  | | | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76),
% 242.12/48.63  | | | | | | | | |            (79), (80), (81), (83), (84), (87), (89), (90),
% 242.12/48.63  | | | | | | | | |            (91), (93), (94), (96), (99), (100), (101), (103),
% 242.12/48.63  | | | | | | | | |            (104), (106), (110), (119), (120), (121), (122),
% 242.12/48.63  | | | | | | | | |            (125), (126), (127), (351), (354), (358) are
% 242.12/48.63  | | | | | | | | |            inconsistent by sub-proof #716.
% 242.12/48.63  | | | | | | | | | 
% 242.12/48.63  | | | | | | | | Case 2:
% 242.12/48.63  | | | | | | | | | 
% 242.12/48.63  | | | | | | | | |   (359)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 242.12/48.63  | | | | | | | | |          $i(all_36_1)
% 242.12/48.63  | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | ALPHA: (359) implies:
% 242.12/48.63  | | | | | | | | |   (360)   ~ (all_36_1 = e0)
% 242.12/48.63  | | | | | | | | |   (361)  op(e1, e2) = all_36_1
% 242.12/48.63  | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | GROUND_INST: instantiating (80) with e1, all_36_1, e2, e1,
% 242.12/48.63  | | | | | | | | |              simplifying with (14), (361) gives:
% 242.12/48.63  | | | | | | | | |   (362)  all_36_1 = e1
% 242.12/48.63  | | | | | | | | | 
% 242.12/48.63  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12),
% 242.12/48.63  | | | | | | | | |            (15), (17), (18), (19), (20), (21), (22), (25),
% 242.12/48.63  | | | | | | | | |            (26), (27), (28), (29), (31), (32), (33), (34),
% 242.12/48.63  | | | | | | | | |            (36), (37), (38), (40), (41), (42), (44), (45),
% 242.12/48.64  | | | | | | | | |            (47), (48), (50), (51), (52), (54), (55), (57),
% 242.12/48.64  | | | | | | | | |            (60), (61), (62), (63), (65), (66), (67), (68),
% 242.12/48.64  | | | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76),
% 242.12/48.64  | | | | | | | | |            (79), (80), (81), (83), (84), (87), (89), (90),
% 242.12/48.64  | | | | | | | | |            (91), (93), (94), (96), (99), (100), (101), (103),
% 242.12/48.64  | | | | | | | | |            (104), (106), (110), (119), (120), (121), (122),
% 242.12/48.64  | | | | | | | | |            (124), (125), (126), (351) are inconsistent by
% 242.12/48.64  | | | | | | | | |            sub-proof #717.
% 242.12/48.64  | | | | | | | | | 
% 242.12/48.64  | | | | | | | | End of split
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | Case 2:
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | |   (363)  all_58_11 = e2 & op(e1, e0) = e2
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | | ALPHA: (363) implies:
% 242.12/48.64  | | | | | | | |   (364)  all_58_11 = e2
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | | REF_CLOSE: (3), (7), (9), (17), (18), (20), (27), (30), (33),
% 242.12/48.64  | | | | | | | |            (37), (38), (42), (44), (46), (53), (54), (55), (57),
% 242.12/48.64  | | | | | | | |            (60), (62), (65), (66), (72), (73), (74), (75), (79),
% 242.12/48.64  | | | | | | | |            (80), (84), (87), (89), (91), (110), (124), (125),
% 242.12/48.64  | | | | | | | |            (126), (127), (364) are inconsistent by sub-proof
% 242.12/48.64  | | | | | | | |            #681.
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | End of split
% 242.12/48.64  | | | | | | | 
% 242.12/48.64  | | | | | | End of split
% 242.12/48.64  | | | | | | 
% 242.12/48.64  | | | | | End of split
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | End of split
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | End of split
% 242.12/48.64  | | | 
% 242.12/48.64  | | Case 2:
% 242.12/48.64  | | | 
% 242.12/48.64  | | |   (365)  all_54_10 = e1 | all_54_10 = e0
% 242.12/48.64  | | | 
% 242.12/48.64  | | | REF_CLOSE: (35), (49), (108), (365) are inconsistent by sub-proof #2282.
% 242.12/48.64  | | | 
% 242.12/48.64  | | End of split
% 242.12/48.64  | | 
% 242.12/48.64  | End of split
% 242.12/48.64  | 
% 242.12/48.64  End of proof
% 242.12/48.64  
% 242.12/48.64  Sub-proof #681 shows that the following formulas are inconsistent:
% 242.12/48.64  ----------------------------------------------------------------
% 242.12/48.64    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.12/48.64         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.12/48.64    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.12/48.64         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.12/48.64    (3)   ~ (e3 = e0)
% 242.12/48.64    (4)   ~ (e2 = e0)
% 242.12/48.64    (5)  op(e1, e2) = all_52_6
% 242.12/48.64    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.12/48.64         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.12/48.64    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.12/48.64         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.12/48.64    (8)   ~ (all_52_7 = e3)
% 242.12/48.64    (9)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.12/48.64         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.12/48.64    (10)   ~ (e3 = e1)
% 242.12/48.64    (11)  all_58_3 = e3
% 242.12/48.64    (12)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.12/48.64          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.12/48.64    (13)  op(e3, e3) = e1
% 242.12/48.64    (14)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.12/48.64              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.12/48.64                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.12/48.64                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.12/48.64    (15)  op(e2, e1) = all_52_9
% 242.12/48.64    (16)   ~ (e3 = e2)
% 242.12/48.64    (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.12/48.64          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.12/48.64    (18)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.12/48.64          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.12/48.64    (19)  all_58_15 = e1
% 242.12/48.64    (20)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.12/48.64          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.12/48.64    (21)  all_58_11 = e2
% 242.12/48.64    (22)  op(e2, e3) = all_52_1
% 242.12/48.64    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.12/48.64          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.12/48.64    (24)   ~ (all_52_6 = e3)
% 242.12/48.64    (25)  op(e1, e1) = e2
% 242.12/48.64    (26)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.12/48.64          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.12/48.64    (27)  op(e0, e2) = all_52_7
% 242.12/48.64    (28)  all_58_5 = e1
% 242.12/48.64    (29)  all_58_7 = e1
% 242.12/48.64    (30)   ~ (all_52_9 = e3)
% 242.12/48.64    (31)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.12/48.64          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.12/48.64    (32)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.12/48.64          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.12/48.64    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.12/48.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.12/48.64    (34)   ~ (e1 = e0)
% 242.12/48.64    (35)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.12/48.64          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.12/48.64    (36)   ~ (all_52_1 = e3)
% 242.12/48.64    (37)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.12/48.64          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.12/48.64            e2)
% 242.12/48.64    (38)   ~ (e2 = e1)
% 242.12/48.64  
% 242.12/48.64  Begin of proof
% 242.12/48.64  | 
% 242.12/48.64  | BETA: splitting (31) gives:
% 242.12/48.64  | 
% 242.12/48.64  | Case 1:
% 242.12/48.64  | | 
% 242.12/48.64  | |   (39)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 242.12/48.64  | |           e3)
% 242.12/48.64  | | 
% 242.12/48.64  | | BETA: splitting (39) gives:
% 242.12/48.64  | | 
% 242.12/48.64  | | Case 1:
% 242.12/48.64  | | | 
% 242.12/48.64  | | |   (40)  all_58_9 = e3 & op(e3, e0) = e3
% 242.12/48.64  | | | 
% 242.12/48.64  | | | ALPHA: (40) implies:
% 242.12/48.64  | | |   (41)  all_58_9 = e3
% 242.12/48.64  | | |   (42)  op(e3, e0) = e3
% 242.12/48.64  | | | 
% 242.12/48.64  | | | BETA: splitting (35) gives:
% 242.12/48.64  | | | 
% 242.12/48.64  | | | Case 1:
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | |   (43)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2)
% 242.12/48.64  | | | |           = e0)
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | | BETA: splitting (43) gives:
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | | Case 1:
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | |   (44)  all_58_6 = e0 & op(e1, e3) = e0
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | | ALPHA: (44) implies:
% 242.12/48.64  | | | | |   (45)  all_58_6 = e0
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | | REF_CLOSE: (3), (5), (16), (20), (21), (24), (25), (33), (45) are
% 242.12/48.64  | | | | |            inconsistent by sub-proof #997.
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | Case 2:
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | |   (46)  all_58_7 = e0 & op(e1, e2) = e0
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | | REF_CLOSE: (29), (34), (46) are inconsistent by sub-proof #1558.
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | End of split
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | Case 2:
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | |   (47)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.12/48.64  | | | |           = e0)
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | | BETA: splitting (47) gives:
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | | Case 1:
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | |   (48)  all_58_8 = e0 & op(e1, e1) = e0
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | | ALPHA: (48) implies:
% 242.12/48.64  | | | | |   (49)  all_58_8 = e0
% 242.12/48.64  | | | | |   (50)  op(e1, e1) = e0
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 242.12/48.64  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 242.12/48.64  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (32),
% 242.12/48.64  | | | | |            (33), (34), (36), (37), (38), (41), (42), (49), (50) are
% 242.12/48.64  | | | | |            inconsistent by sub-proof #682.
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | Case 2:
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | |   (51)  all_58_11 = e0 & op(e1, e0) = e0
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | | ALPHA: (51) implies:
% 242.12/48.64  | | | | |   (52)  all_58_11 = e0
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | | REF_CLOSE: (4), (21), (52) are inconsistent by sub-proof #2110.
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | End of split
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | End of split
% 242.12/48.64  | | | 
% 242.12/48.64  | | Case 2:
% 242.12/48.64  | | | 
% 242.12/48.64  | | |   (53)  all_58_10 = e3 & op(e2, e0) = e3
% 242.12/48.64  | | | 
% 242.12/48.64  | | | ALPHA: (53) implies:
% 242.12/48.64  | | |   (54)  all_58_10 = e3
% 242.12/48.64  | | | 
% 242.12/48.64  | | | REF_CLOSE: (3), (4), (9), (11), (16), (28), (32), (34), (38), (54) are
% 242.12/48.64  | | |            inconsistent by sub-proof #1101.
% 242.12/48.64  | | | 
% 242.12/48.64  | | End of split
% 242.12/48.64  | | 
% 242.12/48.64  | Case 2:
% 242.12/48.64  | | 
% 242.12/48.64  | |   (55)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 242.12/48.64  | |           e3)
% 242.12/48.64  | | 
% 242.12/48.64  | | BETA: splitting (55) gives:
% 242.12/48.64  | | 
% 242.12/48.64  | | Case 1:
% 242.12/48.64  | | | 
% 242.12/48.64  | | |   (56)  all_58_11 = e3 & op(e1, e0) = e3
% 242.12/48.64  | | | 
% 242.12/48.64  | | | REF_CLOSE: (16), (21), (56) are inconsistent by sub-proof #2108.
% 242.12/48.64  | | | 
% 242.12/48.64  | | Case 2:
% 242.12/48.64  | | | 
% 242.12/48.64  | | |   (57)  all_58_15 = e3 & op(e0, e0) = e3
% 242.12/48.64  | | | 
% 242.12/48.64  | | | REF_CLOSE: (10), (19), (57) are inconsistent by sub-proof #1915.
% 242.12/48.64  | | | 
% 242.12/48.64  | | End of split
% 242.12/48.64  | | 
% 242.12/48.64  | End of split
% 242.12/48.64  | 
% 242.12/48.64  End of proof
% 242.12/48.64  
% 242.12/48.64  Sub-proof #682 shows that the following formulas are inconsistent:
% 242.12/48.64  ----------------------------------------------------------------
% 242.12/48.64    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.12/48.64         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.12/48.64    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.12/48.64         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.12/48.64    (3)   ~ (e3 = e0)
% 242.12/48.64    (4)   ~ (e2 = e0)
% 242.12/48.64    (5)  op(e1, e2) = all_52_6
% 242.12/48.64    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.12/48.64         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.12/48.64    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.12/48.64         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.12/48.64    (8)   ~ (all_52_7 = e3)
% 242.12/48.64    (9)  all_58_8 = e0
% 242.12/48.64    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.12/48.64          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.12/48.64    (11)   ~ (e3 = e1)
% 242.12/48.64    (12)  all_58_3 = e3
% 242.12/48.64    (13)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.12/48.64          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.12/48.64    (14)  op(e3, e3) = e1
% 242.12/48.64    (15)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.12/48.64              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.12/48.64                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.12/48.64                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.12/48.64    (16)  op(e2, e1) = all_52_9
% 242.12/48.64    (17)   ~ (e3 = e2)
% 242.12/48.64    (18)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.12/48.64          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.12/48.64    (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.12/48.64          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.12/48.64    (20)  all_58_15 = e1
% 242.12/48.64    (21)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.12/48.64          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.12/48.64    (22)  all_58_9 = e3
% 242.12/48.64    (23)  op(e3, e0) = e3
% 242.12/48.64    (24)  all_58_11 = e2
% 242.12/48.64    (25)  op(e2, e3) = all_52_1
% 242.12/48.64    (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.12/48.64          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.12/48.64    (27)   ~ (all_52_6 = e3)
% 242.12/48.64    (28)  op(e1, e1) = e2
% 242.12/48.64    (29)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.12/48.64          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.12/48.64    (30)  op(e0, e2) = all_52_7
% 242.12/48.64    (31)  all_58_5 = e1
% 242.12/48.64    (32)  all_58_7 = e1
% 242.12/48.64    (33)   ~ (all_52_9 = e3)
% 242.12/48.64    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.12/48.64          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.12/48.64    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.12/48.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.12/48.64    (36)  op(e1, e1) = e0
% 242.12/48.64    (37)   ~ (e1 = e0)
% 242.12/48.64    (38)   ~ (all_52_1 = e3)
% 242.12/48.64    (39)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.12/48.64          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.12/48.64            e2)
% 242.12/48.64    (40)   ~ (e2 = e1)
% 242.12/48.64  
% 242.12/48.64  Begin of proof
% 242.12/48.64  | 
% 242.12/48.64  | BETA: splitting (1) gives:
% 242.12/48.64  | 
% 242.12/48.64  | Case 1:
% 242.12/48.64  | | 
% 242.12/48.64  | |   (41)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 242.12/48.64  | |           e2)
% 242.12/48.64  | | 
% 242.12/48.64  | | BETA: splitting (41) gives:
% 242.12/48.64  | | 
% 242.12/48.64  | | Case 1:
% 242.12/48.64  | | | 
% 242.12/48.64  | | |   (42)  all_58_0 = e2 & op(e3, e3) = e2
% 242.12/48.64  | | | 
% 242.12/48.64  | | | ALPHA: (42) implies:
% 242.12/48.64  | | |   (43)  op(e3, e3) = e2
% 242.12/48.64  | | | 
% 242.12/48.64  | | | REF_CLOSE: (14), (35), (40), (43) are inconsistent by sub-proof #2267.
% 242.12/48.64  | | | 
% 242.12/48.64  | | Case 2:
% 242.12/48.64  | | | 
% 242.12/48.64  | | |   (44)  all_58_1 = e2 & op(e3, e2) = e2
% 242.12/48.64  | | | 
% 242.12/48.64  | | | ALPHA: (44) implies:
% 242.12/48.64  | | |   (45)  all_58_1 = e2
% 242.12/48.64  | | | 
% 242.12/48.64  | | | BETA: splitting (21) gives:
% 242.12/48.64  | | | 
% 242.12/48.64  | | | Case 1:
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | |   (46)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 242.12/48.64  | | | |           = e3)
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | | BETA: splitting (46) gives:
% 242.12/48.64  | | | | 
% 242.12/48.64  | | | | Case 1:
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | |   (47)  all_58_6 = e3 & op(e1, e3) = e3
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | | ALPHA: (47) implies:
% 242.12/48.64  | | | | |   (48)  all_58_6 = e3
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | | BETA: splitting (15) gives:
% 242.12/48.64  | | | | | 
% 242.12/48.64  | | | | | Case 1:
% 242.12/48.64  | | | | | | 
% 242.12/48.64  | | | | | |   (49)  all_58_15 = e0 & op(e0, e0) = e0
% 242.12/48.64  | | | | | | 
% 242.12/48.64  | | | | | | REF_CLOSE: (20), (37), (49) are inconsistent by sub-proof #1867.
% 242.12/48.64  | | | | | | 
% 242.12/48.64  | | | | | Case 2:
% 242.12/48.64  | | | | | | 
% 242.12/48.64  | | | | | |   (50)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 242.12/48.64  | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 242.12/48.64  | | | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.12/48.64  | | | | | |             op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.12/48.64  | | | | | | 
% 242.12/48.64  | | | | | | ALPHA: (50) implies:
% 242.12/48.64  | | | | | |   (51)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 242.12/48.64  | | | | | |             e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.12/48.64  | | | | | | 
% 242.12/48.64  | | | | | | BETA: splitting (18) gives:
% 242.12/48.64  | | | | | | 
% 242.12/48.64  | | | | | | Case 1:
% 242.12/48.64  | | | | | | | 
% 242.12/48.64  | | | | | | |   (52)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 242.12/48.64  | | | | | | |           op(e2, e1) = e2)
% 242.12/48.64  | | | | | | | 
% 242.12/48.64  | | | | | | | BETA: splitting (52) gives:
% 242.12/48.64  | | | | | | | 
% 242.12/48.64  | | | | | | | Case 1:
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | |   (53)  all_58_4 = e2 & op(e3, e1) = e2
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | | ALPHA: (53) implies:
% 242.12/48.64  | | | | | | | |   (54)  all_58_4 = e2
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (12), (13),
% 242.12/48.64  | | | | | | | |            (14), (15), (16), (17), (20), (21), (22), (24), (25),
% 242.12/48.64  | | | | | | | |            (26), (27), (28), (29), (31), (32), (33), (34), (35),
% 242.12/48.64  | | | | | | | |            (36), (37), (38), (39), (40), (48), (51), (54) are
% 242.12/48.64  | | | | | | | |            inconsistent by sub-proof #684.
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | Case 2:
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | |   (55)  all_58_5 = e2 & op(e2, e1) = e2
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | | ALPHA: (55) implies:
% 242.12/48.64  | | | | | | | |   (56)  all_58_5 = e2
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | | REF_CLOSE: (31), (40), (56) are inconsistent by sub-proof #1665.
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | End of split
% 242.12/48.64  | | | | | | | 
% 242.12/48.64  | | | | | | Case 2:
% 242.12/48.64  | | | | | | | 
% 242.12/48.64  | | | | | | |   (57)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 242.12/48.64  | | | | | | |           op(e0, e1) = e2)
% 242.12/48.64  | | | | | | | 
% 242.12/48.64  | | | | | | | BETA: splitting (57) gives:
% 242.12/48.64  | | | | | | | 
% 242.12/48.64  | | | | | | | Case 1:
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | |   (58)  all_58_8 = e2 & op(e1, e1) = e2
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | | REF_CLOSE: (4), (9), (58) are inconsistent by sub-proof #683.
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | Case 2:
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | |   (59)  all_58_14 = e2 & op(e0, e1) = e2
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | | ALPHA: (59) implies:
% 242.12/48.64  | | | | | | | |   (60)  all_58_14 = e2
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | | BETA: splitting (51) gives:
% 242.12/48.64  | | | | | | | | 
% 242.12/48.64  | | | | | | | | Case 1:
% 242.12/48.64  | | | | | | | | | 
% 242.12/48.64  | | | | | | | | |   (61)  all_58_9 = e0 & op(e3, e0) = e0
% 242.12/48.64  | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | REF_CLOSE: (3), (5), (17), (21), (22), (24), (27), (28), (35),
% 242.12/48.64  | | | | | | | | |            (48), (61) are inconsistent by sub-proof #912.
% 242.12/48.64  | | | | | | | | | 
% 242.12/48.64  | | | | | | | | Case 2:
% 242.12/48.64  | | | | | | | | | 
% 242.12/48.64  | | | | | | | | |   (62)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.12/48.64  | | | | | | | | |           op(e1, e0) = e0)
% 242.12/48.64  | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | BETA: splitting (62) gives:
% 242.12/48.64  | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | Case 1:
% 242.12/48.64  | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | |   (63)  all_58_10 = e0 & op(e2, e0) = e0
% 242.12/48.64  | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | ALPHA: (63) implies:
% 242.12/48.64  | | | | | | | | | |   (64)  op(e2, e0) = e0
% 242.12/48.64  | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | BETA: splitting (2) gives:
% 242.12/48.64  | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | Case 1:
% 242.12/48.64  | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | |   (65)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 242.12/48.64  | | | | | | | | | | |           e3 & op(e0, e2) = e3)
% 242.12/48.64  | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | BETA: splitting (65) gives:
% 242.12/48.64  | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | Case 1:
% 242.12/48.64  | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | |   (66)  all_58_12 = e3 & op(e0, e3) = e3
% 242.12/48.64  | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | ALPHA: (66) implies:
% 242.12/48.64  | | | | | | | | | | | |   (67)  all_58_12 = e3
% 242.12/48.64  | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | BETA: splitting (29) gives:
% 242.12/48.64  | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | Case 1:
% 242.12/48.64  | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | |   (68)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 242.12/48.64  | | | | | | | | | | | | |           & op(e2, e1) = e3)
% 242.12/48.64  | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | BETA: splitting (68) gives:
% 242.12/48.64  | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | Case 1:
% 242.12/48.64  | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | |   (69)  all_58_4 = e3 & op(e3, e1) = e3
% 242.12/48.64  | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | ALPHA: (69) implies:
% 242.12/48.64  | | | | | | | | | | | | | |   (70)  all_58_4 = e3
% 242.12/48.64  | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 242.12/48.64  | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | Case 1:
% 242.12/48.64  | | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | |   (71)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 242.12/48.64  | | | | | | | | | | | | | | |           & op(e2, e3) = e0)
% 242.12/48.64  | | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (10), (12), (14), (17), (20),
% 242.12/48.64  | | | | | | | | | | | | | | |            (22), (26), (31), (32), (35), (37), (39), (40),
% 242.12/48.64  | | | | | | | | | | | | | | |            (45), (60), (64), (67), (70), (71) are
% 242.12/48.64  | | | | | | | | | | | | | | |            inconsistent by sub-proof #701.
% 242.12/48.64  | | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | Case 2:
% 242.12/48.64  | | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | |   (72)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 242.12/48.64  | | | | | | | | | | | | | | |           e0 & op(e0, e3) = e0)
% 242.12/48.64  | | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 242.12/48.64  | | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | | Case 1:
% 242.12/48.64  | | | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | | |   (73)  all_58_6 = e0 & op(e1, e3) = e0
% 242.12/48.64  | | | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | | | ALPHA: (73) implies:
% 242.12/48.64  | | | | | | | | | | | | | | | |   (74)  all_58_6 = e0
% 242.12/48.64  | | | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (17), (21), (24), (27), (28), (35), (74)
% 242.12/48.64  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #997.
% 242.12/48.64  | | | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | | Case 2:
% 242.12/48.64  | | | | | | | | | | | | | | | | 
% 242.12/48.64  | | | | | | | | | | | | | | | |   (75)  all_58_12 = e0 & op(e0, e3) = e0
% 242.12/48.65  | | | | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | | | | ALPHA: (75) implies:
% 242.12/48.65  | | | | | | | | | | | | | | | |   (76)  all_58_12 = e0
% 242.12/48.65  | | | | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (76) imply:
% 242.12/48.65  | | | | | | | | | | | | | | | |   (77)  e3 = e0
% 242.12/48.65  | | | | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | | | | SIMP: (77) implies:
% 242.12/48.65  | | | | | | | | | | | | | | | |   (78)  e3 = e0
% 242.12/48.65  | | | | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (78) imply:
% 242.12/48.65  | | | | | | | | | | | | | | | |   (79)  all_58_6 = e0
% 242.12/48.65  | | | | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (17), (21), (24), (27), (28), (35), (79)
% 242.12/48.65  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #997.
% 242.12/48.65  | | | | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | Case 2:
% 242.12/48.65  | | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | |   (80)  all_58_5 = e3 & op(e2, e1) = e3
% 242.12/48.65  | | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | | REF_CLOSE: (16), (33), (35), (80) are inconsistent by
% 242.12/48.65  | | | | | | | | | | | | | |            sub-proof #1822.
% 242.12/48.65  | | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | Case 2:
% 242.12/48.65  | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | |   (81)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 242.12/48.65  | | | | | | | | | | | | |           e3 & op(e0, e1) = e3)
% 242.12/48.65  | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | | REF_CLOSE: (3), (4), (15), (17), (20), (28), (35), (37),
% 242.12/48.65  | | | | | | | | | | | | |            (39), (40), (67), (81) are inconsistent by
% 242.12/48.65  | | | | | | | | | | | | |            sub-proof #930.
% 242.12/48.65  | | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | Case 2:
% 242.12/48.65  | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | |   (82)  all_58_13 = e3 & op(e0, e2) = e3
% 242.12/48.65  | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | REF_CLOSE: (8), (30), (35), (82) are inconsistent by
% 242.12/48.65  | | | | | | | | | | | |            sub-proof #1919.
% 242.12/48.65  | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | Case 2:
% 242.12/48.65  | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | |   (83)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 242.12/48.65  | | | | | | | | | | |           e3 & op(e0, e0) = e3)
% 242.12/48.65  | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | BETA: splitting (83) gives:
% 242.12/48.65  | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | Case 1:
% 242.12/48.65  | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | |   (84)  all_58_14 = e3 & op(e0, e1) = e3
% 242.12/48.65  | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | REF_CLOSE: (3), (4), (11), (13), (14), (15), (17), (20),
% 242.12/48.65  | | | | | | | | | | | |            (25), (35), (37), (38), (39), (40), (48), (60),
% 242.12/48.65  | | | | | | | | | | | |            (84) are inconsistent by sub-proof #1165.
% 242.12/48.65  | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | Case 2:
% 242.12/48.65  | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | |   (85)  all_58_15 = e3 & op(e0, e0) = e3
% 242.12/48.65  | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | | REF_CLOSE: (11), (20), (85) are inconsistent by sub-proof
% 242.12/48.65  | | | | | | | | | | | |            #1915.
% 242.12/48.65  | | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | Case 2:
% 242.12/48.65  | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | |   (86)  all_58_11 = e0 & op(e1, e0) = e0
% 242.12/48.65  | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | REF_CLOSE: (4), (24), (86) are inconsistent by sub-proof
% 242.12/48.65  | | | | | | | | | |            #2033.
% 242.12/48.65  | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | | 
% 242.12/48.65  | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | 
% 242.12/48.65  | | | | | | | End of split
% 242.12/48.65  | | | | | | | 
% 242.12/48.65  | | | | | | End of split
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | End of split
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | Case 2:
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | |   (87)  all_58_7 = e3 & op(e1, e2) = e3
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | | ALPHA: (87) implies:
% 242.12/48.65  | | | | |   (88)  op(e1, e2) = e3
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | | REF_CLOSE: (5), (27), (35), (88) are inconsistent by sub-proof #2191.
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | End of split
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | Case 2:
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | |   (89)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 242.12/48.65  | | | |           = e3)
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | | REF_CLOSE: (17), (24), (28), (35), (89) are inconsistent by sub-proof
% 242.12/48.65  | | | |            #2029.
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | End of split
% 242.12/48.65  | | | 
% 242.12/48.65  | | End of split
% 242.12/48.65  | | 
% 242.12/48.65  | Case 2:
% 242.12/48.65  | | 
% 242.12/48.65  | |   (90)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 242.12/48.65  | |           e2)
% 242.12/48.65  | | 
% 242.12/48.65  | | BETA: splitting (90) gives:
% 242.12/48.65  | | 
% 242.12/48.65  | | Case 1:
% 242.12/48.65  | | | 
% 242.12/48.65  | | |   (91)  all_58_4 = e2 & op(e3, e1) = e2
% 242.12/48.65  | | | 
% 242.12/48.65  | | | ALPHA: (91) implies:
% 242.12/48.65  | | |   (92)  all_58_4 = e2
% 242.12/48.65  | | | 
% 242.12/48.65  | | | BETA: splitting (21) gives:
% 242.12/48.65  | | | 
% 242.12/48.65  | | | Case 1:
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | |   (93)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 242.12/48.65  | | | |           = e3)
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | | BETA: splitting (93) gives:
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | | Case 1:
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | |   (94)  all_58_6 = e3 & op(e1, e3) = e3
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | | ALPHA: (94) implies:
% 242.12/48.65  | | | | |   (95)  all_58_6 = e3
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | | BETA: splitting (15) gives:
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | | Case 1:
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | |   (96)  all_58_15 = e0 & op(e0, e0) = e0
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | | REF_CLOSE: (20), (37), (96) are inconsistent by sub-proof #1867.
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | Case 2:
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | |   (97)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 242.12/48.65  | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 242.12/48.65  | | | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.12/48.65  | | | | | |             op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | | ALPHA: (97) implies:
% 242.12/48.65  | | | | | |   (98)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 242.12/48.65  | | | | | |             e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (12), (13),
% 242.12/48.65  | | | | | |            (14), (15), (16), (17), (20), (21), (22), (24), (25),
% 242.12/48.65  | | | | | |            (26), (27), (28), (29), (31), (32), (33), (34), (35),
% 242.12/48.65  | | | | | |            (36), (37), (38), (39), (40), (92), (95), (98) are
% 242.12/48.65  | | | | | |            inconsistent by sub-proof #684.
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | End of split
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | Case 2:
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | |   (99)  all_58_7 = e3 & op(e1, e2) = e3
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | | ALPHA: (99) implies:
% 242.12/48.65  | | | | |   (100)  op(e1, e2) = e3
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | | REF_CLOSE: (5), (27), (35), (100) are inconsistent by sub-proof #2191.
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | End of split
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | Case 2:
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | |   (101)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 242.12/48.65  | | | |              e0) = e3)
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | | REF_CLOSE: (17), (24), (28), (35), (101) are inconsistent by sub-proof
% 242.12/48.65  | | | |            #2029.
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | End of split
% 242.12/48.65  | | | 
% 242.12/48.65  | | Case 2:
% 242.12/48.65  | | | 
% 242.12/48.65  | | |   (102)  all_58_9 = e2 & op(e3, e0) = e2
% 242.12/48.65  | | | 
% 242.12/48.65  | | | ALPHA: (102) implies:
% 242.12/48.65  | | |   (103)  op(e3, e0) = e2
% 242.12/48.65  | | | 
% 242.12/48.65  | | | REF_CLOSE: (17), (23), (35), (103) are inconsistent by sub-proof #2125.
% 242.12/48.65  | | | 
% 242.12/48.65  | | End of split
% 242.12/48.65  | | 
% 242.12/48.65  | End of split
% 242.12/48.65  | 
% 242.12/48.65  End of proof
% 242.12/48.65  
% 242.12/48.65  Sub-proof #683 shows that the following formulas are inconsistent:
% 242.12/48.65  ----------------------------------------------------------------
% 242.12/48.65    (1)  all_58_8 = e2 & op(e1, e1) = e2
% 242.12/48.65    (2)  all_58_8 = e0
% 242.12/48.65    (3)   ~ (e2 = e0)
% 242.12/48.65  
% 242.12/48.65  Begin of proof
% 242.12/48.65  | 
% 242.12/48.65  | ALPHA: (1) implies:
% 242.12/48.65  |   (4)  all_58_8 = e2
% 242.12/48.65  | 
% 242.12/48.65  | COMBINE_EQS: (2), (4) imply:
% 242.12/48.65  |   (5)  e2 = e0
% 242.12/48.65  | 
% 242.12/48.65  | REDUCE: (3), (5) imply:
% 242.12/48.65  |   (6)  $false
% 242.12/48.65  | 
% 242.12/48.65  | CLOSE: (6) is inconsistent.
% 242.12/48.65  | 
% 242.12/48.65  End of proof
% 242.12/48.65  
% 242.12/48.65  Sub-proof #684 shows that the following formulas are inconsistent:
% 242.12/48.65  ----------------------------------------------------------------
% 242.12/48.65    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.12/48.65         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.12/48.65    (2)   ~ (e3 = e0)
% 242.12/48.65    (3)  all_58_6 = e3
% 242.12/48.65    (4)   ~ (e2 = e0)
% 242.12/48.65    (5)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.12/48.65         (all_58_11 = e0 & op(e1, e0) = e0)
% 242.12/48.65    (6)  op(e1, e2) = all_52_6
% 242.12/48.65    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.12/48.65         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.12/48.65    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.12/48.65         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.12/48.65    (9)  all_58_4 = e2
% 242.12/48.65    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.12/48.65          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.12/48.65    (11)   ~ (e3 = e1)
% 242.12/48.65    (12)  all_58_3 = e3
% 242.12/48.65    (13)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.12/48.65          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.12/48.65    (14)  op(e3, e3) = e1
% 242.12/48.65    (15)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.12/48.65              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.12/48.65                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.12/48.65                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.12/48.65    (16)  op(e2, e1) = all_52_9
% 242.12/48.65    (17)   ~ (e3 = e2)
% 242.12/48.65    (18)  all_58_15 = e1
% 242.12/48.65    (19)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.12/48.65          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.12/48.65    (20)  all_58_9 = e3
% 242.12/48.65    (21)  all_58_11 = e2
% 242.12/48.65    (22)  op(e2, e3) = all_52_1
% 242.12/48.65    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.12/48.65          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.12/48.65    (24)   ~ (all_52_6 = e3)
% 242.12/48.65    (25)  op(e1, e1) = e2
% 242.12/48.65    (26)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.12/48.65          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.12/48.65    (27)  all_58_5 = e1
% 242.12/48.65    (28)  all_58_7 = e1
% 242.12/48.65    (29)   ~ (all_52_9 = e3)
% 242.12/48.65    (30)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.12/48.65          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.12/48.65    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.12/48.65            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.12/48.65    (32)  op(e1, e1) = e0
% 242.12/48.65    (33)   ~ (e1 = e0)
% 242.12/48.65    (34)   ~ (all_52_1 = e3)
% 242.12/48.65    (35)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.12/48.65          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.12/48.65            e2)
% 242.12/48.65    (36)   ~ (e2 = e1)
% 242.12/48.65  
% 242.12/48.65  Begin of proof
% 242.12/48.65  | 
% 242.12/48.65  | BETA: splitting (26) gives:
% 242.12/48.65  | 
% 242.12/48.65  | Case 1:
% 242.12/48.65  | | 
% 242.12/48.65  | |   (37)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 242.12/48.65  | |           e3)
% 242.12/48.65  | | 
% 242.12/48.65  | | BETA: splitting (37) gives:
% 242.12/48.65  | | 
% 242.12/48.65  | | Case 1:
% 242.12/48.65  | | | 
% 242.12/48.65  | | |   (38)  all_58_4 = e3 & op(e3, e1) = e3
% 242.12/48.65  | | | 
% 242.12/48.65  | | | REF_CLOSE: (9), (17), (38) are inconsistent by sub-proof #2167.
% 242.12/48.65  | | | 
% 242.12/48.65  | | Case 2:
% 242.12/48.65  | | | 
% 242.12/48.65  | | |   (39)  all_58_5 = e3 & op(e2, e1) = e3
% 242.12/48.65  | | | 
% 242.12/48.65  | | | REF_CLOSE: (16), (29), (31), (39) are inconsistent by sub-proof #1822.
% 242.12/48.65  | | | 
% 242.12/48.65  | | End of split
% 242.12/48.65  | | 
% 242.12/48.65  | Case 2:
% 242.12/48.65  | | 
% 242.12/48.65  | |   (40)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 242.12/48.65  | |           e3)
% 242.12/48.65  | | 
% 242.12/48.65  | | BETA: splitting (40) gives:
% 242.12/48.65  | | 
% 242.12/48.65  | | Case 1:
% 242.12/48.65  | | | 
% 242.12/48.65  | | |   (41)  all_58_8 = e3 & op(e1, e1) = e3
% 242.12/48.65  | | | 
% 242.12/48.65  | | | ALPHA: (41) implies:
% 242.12/48.65  | | |   (42)  op(e1, e1) = e3
% 242.12/48.65  | | | 
% 242.12/48.65  | | | REF_CLOSE: (17), (25), (31), (42) are inconsistent by sub-proof #2206.
% 242.12/48.65  | | | 
% 242.12/48.65  | | Case 2:
% 242.12/48.65  | | | 
% 242.12/48.65  | | |   (43)  all_58_14 = e3 & op(e0, e1) = e3
% 242.12/48.65  | | | 
% 242.12/48.65  | | | ALPHA: (43) implies:
% 242.12/48.65  | | |   (44)  all_58_14 = e3
% 242.12/48.65  | | | 
% 242.12/48.65  | | | BETA: splitting (5) gives:
% 242.12/48.65  | | | 
% 242.12/48.65  | | | Case 1:
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | |   (45)  all_58_9 = e0 & op(e3, e0) = e0
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | | REF_CLOSE: (2), (3), (6), (17), (19), (20), (21), (24), (25), (31), (45)
% 242.12/48.65  | | | |            are inconsistent by sub-proof #912.
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | Case 2:
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | |   (46)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 242.12/48.65  | | | |             e0) = e0)
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | | BETA: splitting (46) gives:
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | | Case 1:
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | |   (47)  all_58_10 = e0 & op(e2, e0) = e0
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | | ALPHA: (47) implies:
% 242.12/48.65  | | | | |   (48)  op(e2, e0) = e0
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | | BETA: splitting (10) gives:
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | | Case 1:
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | |   (49)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2,
% 242.12/48.65  | | | | | |             e2) = e2)
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | | BETA: splitting (49) gives:
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | | Case 1:
% 242.12/48.65  | | | | | | | 
% 242.12/48.65  | | | | | | |   (50)  all_58_2 = e2 & op(e2, e3) = e2
% 242.12/48.65  | | | | | | | 
% 242.12/48.65  | | | | | | | ALPHA: (50) implies:
% 242.12/48.65  | | | | | | |   (51)  all_58_2 = e2
% 242.12/48.65  | | | | | | | 
% 242.12/48.65  | | | | | | | BETA: splitting (7) gives:
% 242.12/48.65  | | | | | | | 
% 242.12/48.65  | | | | | | | Case 1:
% 242.12/48.65  | | | | | | | | 
% 242.12/48.65  | | | | | | | |   (52)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 &
% 242.12/48.65  | | | | | | | |           op(e2, e2) = e2)
% 242.12/48.65  | | | | | | | | 
% 242.12/48.65  | | | | | | | | REF_CLOSE: (2), (3), (4), (9), (11), (12), (13), (14), (15),
% 242.12/48.65  | | | | | | | |            (17), (18), (20), (22), (23), (31), (33), (34), (35),
% 242.12/48.65  | | | | | | | |            (36), (44), (52) are inconsistent by sub-proof #685.
% 242.12/48.65  | | | | | | | | 
% 242.12/48.65  | | | | | | | Case 2:
% 242.12/48.65  | | | | | | | | 
% 242.12/48.65  | | | | | | | |   (53)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 &
% 242.12/48.65  | | | | | | | |           op(e0, e2) = e2)
% 242.12/48.65  | | | | | | | | 
% 242.12/48.65  | | | | | | | | BETA: splitting (53) gives:
% 242.12/48.65  | | | | | | | | 
% 242.12/48.65  | | | | | | | | Case 1:
% 242.12/48.65  | | | | | | | | | 
% 242.12/48.65  | | | | | | | | |   (54)  all_58_7 = e2 & op(e1, e2) = e2
% 242.12/48.65  | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | ALPHA: (54) implies:
% 242.12/48.65  | | | | | | | | |   (55)  all_58_7 = e2
% 242.12/48.65  | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | COMBINE_EQS: (28), (55) imply:
% 242.12/48.65  | | | | | | | | |   (56)  e2 = e1
% 242.12/48.65  | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | REF_CLOSE: (1), (2), (4), (9), (14), (17), (20), (23), (31),
% 242.12/48.65  | | | | | | | | |            (33), (36), (56) are inconsistent by sub-proof
% 242.12/48.65  | | | | | | | | |            #714.
% 242.12/48.65  | | | | | | | | | 
% 242.12/48.65  | | | | | | | | Case 2:
% 242.12/48.65  | | | | | | | | | 
% 242.12/48.65  | | | | | | | | |   (57)  all_58_13 = e2 & op(e0, e2) = e2
% 242.12/48.65  | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | ALPHA: (57) implies:
% 242.12/48.65  | | | | | | | | |   (58)  op(e0, e2) = e2
% 242.12/48.65  | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | BETA: splitting (30) gives:
% 242.12/48.65  | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | Case 1:
% 242.12/48.65  | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | |   (59)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 242.12/48.65  | | | | | | | | | |           op(e2, e2) = e0)
% 242.12/48.65  | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | BETA: splitting (59) gives:
% 242.12/48.65  | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | Case 1:
% 242.12/48.65  | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | |   (60)  all_58_2 = e0 & op(e2, e3) = e0
% 242.12/48.65  | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (8), (9), (12), (14), (17), (20),
% 242.12/48.65  | | | | | | | | | | |            (28), (31), (33), (36), (51), (58), (60) are
% 242.12/48.65  | | | | | | | | | | |            inconsistent by sub-proof #698.
% 242.12/48.65  | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | Case 2:
% 242.12/48.65  | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | |   (61)  all_58_3 = e0 & op(e2, e2) = e0
% 242.12/48.65  | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (12), (17), (19), (21), (24), (25),
% 242.12/48.65  | | | | | | | | | | |            (31), (61) are inconsistent by sub-proof #916.
% 242.12/48.65  | | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | Case 2:
% 242.12/48.65  | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | |   (62)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0
% 242.12/48.65  | | | | | | | | | |           & op(e2, e0) = e0)
% 242.12/48.65  | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | | REF_CLOSE: (1), (2), (4), (8), (9), (12), (14), (17), (20),
% 242.12/48.65  | | | | | | | | | |            (25), (27), (28), (31), (32), (33), (36), (58),
% 242.12/48.65  | | | | | | | | | |            (62) are inconsistent by sub-proof #697.
% 242.12/48.65  | | | | | | | | | | 
% 242.12/48.65  | | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | | 
% 242.12/48.65  | | | | | | | | End of split
% 242.12/48.65  | | | | | | | | 
% 242.12/48.65  | | | | | | | End of split
% 242.12/48.65  | | | | | | | 
% 242.12/48.65  | | | | | | Case 2:
% 242.12/48.65  | | | | | | | 
% 242.12/48.65  | | | | | | |   (63)  all_58_3 = e2 & op(e2, e2) = e2
% 242.12/48.65  | | | | | | | 
% 242.12/48.65  | | | | | | | REF_CLOSE: (2), (3), (4), (11), (12), (13), (14), (15), (17),
% 242.12/48.65  | | | | | | |            (18), (22), (31), (33), (34), (35), (36), (44), (63)
% 242.12/48.65  | | | | | | |            are inconsistent by sub-proof #696.
% 242.12/48.65  | | | | | | | 
% 242.12/48.65  | | | | | | End of split
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | Case 2:
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | |   (64)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2,
% 242.12/48.65  | | | | | |             e0) = e2)
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | | REF_CLOSE: (1), (2), (4), (9), (14), (17), (20), (23), (27), (31),
% 242.12/48.65  | | | | | |            (33), (36), (48), (64) are inconsistent by sub-proof
% 242.12/48.65  | | | | | |            #695.
% 242.12/48.65  | | | | | | 
% 242.12/48.65  | | | | | End of split
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | Case 2:
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | |   (65)  all_58_11 = e0 & op(e1, e0) = e0
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | | REF_CLOSE: (4), (21), (65) are inconsistent by sub-proof #2033.
% 242.12/48.65  | | | | | 
% 242.12/48.65  | | | | End of split
% 242.12/48.65  | | | | 
% 242.12/48.65  | | | End of split
% 242.12/48.65  | | | 
% 242.12/48.65  | | End of split
% 242.12/48.65  | | 
% 242.12/48.65  | End of split
% 242.12/48.65  | 
% 242.12/48.65  End of proof
% 242.12/48.65  
% 242.12/48.65  Sub-proof #685 shows that the following formulas are inconsistent:
% 242.12/48.65  ----------------------------------------------------------------
% 242.12/48.65    (1)   ~ (e3 = e0)
% 242.12/48.65    (2)  all_58_6 = e3
% 242.12/48.65    (3)   ~ (e2 = e0)
% 242.12/48.65    (4)  all_58_4 = e2
% 242.12/48.65    (5)   ~ (e3 = e1)
% 242.12/48.65    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 242.12/48.65    (7)  all_58_3 = e3
% 242.12/48.66    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.12/48.66         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.12/48.66    (9)  op(e3, e3) = e1
% 242.12/48.66    (10)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.12/48.66              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.12/48.66                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.12/48.66                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.12/48.66    (11)   ~ (e3 = e2)
% 242.12/48.66    (12)  all_58_15 = e1
% 242.12/48.66    (13)  all_58_9 = e3
% 242.12/48.66    (14)  op(e2, e3) = all_52_1
% 242.12/48.66    (15)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.12/48.66          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.12/48.66    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.12/48.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.12/48.66    (17)  all_58_14 = e3
% 242.12/48.66    (18)   ~ (e1 = e0)
% 242.12/48.66    (19)   ~ (all_52_1 = e3)
% 242.12/48.66    (20)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.12/48.66          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.12/48.66            e2)
% 242.12/48.66    (21)   ~ (e2 = e1)
% 242.12/48.66  
% 242.12/48.66  Begin of proof
% 242.12/48.66  | 
% 242.12/48.66  | BETA: splitting (6) gives:
% 242.12/48.66  | 
% 242.12/48.66  | Case 1:
% 242.12/48.66  | | 
% 242.12/48.66  | |   (22)  all_58_1 = e2 & op(e3, e2) = e2
% 242.12/48.66  | | 
% 242.12/48.66  | | ALPHA: (22) implies:
% 242.12/48.66  | |   (23)  all_58_1 = e2
% 242.12/48.66  | | 
% 242.12/48.66  | | REF_CLOSE: (1), (3), (4), (9), (13), (15), (16), (18), (23) are inconsistent
% 242.12/48.66  | |            by sub-proof #708.
% 242.12/48.66  | | 
% 242.12/48.66  | Case 2:
% 242.12/48.66  | | 
% 242.12/48.66  | |   (24)  all_58_3 = e2 & op(e2, e2) = e2
% 242.12/48.66  | | 
% 242.12/48.66  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (14), (16),
% 242.12/48.66  | |            (17), (18), (19), (20), (21), (24) are inconsistent by sub-proof
% 242.12/48.66  | |            #699.
% 242.12/48.66  | | 
% 242.12/48.66  | End of split
% 242.12/48.66  | 
% 242.12/48.66  End of proof
% 242.12/48.66  
% 242.12/48.66  Sub-proof #686 shows that the following formulas are inconsistent:
% 242.12/48.66  ----------------------------------------------------------------
% 242.12/48.66    (1)   ~ (e3 = e0)
% 242.12/48.66    (2)   ~ (e2 = e0)
% 242.12/48.66    (3)  all_58_6 = e2
% 242.12/48.66    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.12/48.66         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.12/48.66    (5)  all_58_14 = e2
% 242.12/48.66    (6)  all_58_3 = e3
% 242.12/48.66    (7)   ~ (e3 = e2)
% 242.12/48.66    (8)  all_58_15 = e1
% 242.12/48.66    (9)  all_58_12 = e3
% 242.12/48.66    (10)  all_58_7 = e1
% 242.12/48.66    (11)  all_58_1 = e2
% 242.12/48.66    (12)   ~ (e1 = e0)
% 242.12/48.66    (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.12/48.66    (14)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.12/48.66          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.12/48.66            e2)
% 242.12/48.66    (15)   ~ (e2 = e1)
% 242.12/48.66  
% 242.12/48.66  Begin of proof
% 242.12/48.66  | 
% 242.12/48.66  | BETA: splitting (13) gives:
% 242.12/48.66  | 
% 242.12/48.66  | Case 1:
% 242.12/48.66  | | 
% 242.12/48.66  | |   (16)  all_58_6 = e0 & op(e1, e3) = e0
% 242.12/48.66  | | 
% 242.12/48.66  | | ALPHA: (16) implies:
% 242.12/48.66  | |   (17)  all_58_6 = e0
% 242.12/48.66  | | 
% 242.12/48.66  | | COMBINE_EQS: (3), (17) imply:
% 242.12/48.66  | |   (18)  e2 = e0
% 242.12/48.66  | | 
% 242.12/48.66  | | COMBINE_EQS: (5), (18) imply:
% 242.12/48.66  | |   (19)  all_58_14 = e0
% 242.12/48.66  | | 
% 242.12/48.66  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 242.12/48.66  | |            (19) are inconsistent by sub-proof #735.
% 242.12/48.66  | | 
% 242.12/48.66  | Case 2:
% 242.12/48.66  | | 
% 242.12/48.66  | |   (20)  all_58_12 = e0 & op(e0, e3) = e0
% 242.12/48.66  | | 
% 242.12/48.66  | | REF_CLOSE: (1), (9), (20) are inconsistent by sub-proof #1641.
% 242.12/48.66  | | 
% 242.12/48.66  | End of split
% 242.12/48.66  | 
% 242.12/48.66  End of proof
% 242.12/48.66  
% 242.12/48.66  Sub-proof #687 shows that the following formulas are inconsistent:
% 242.12/48.66  ----------------------------------------------------------------
% 242.12/48.66    (1)   ~ (e3 = e0)
% 242.12/48.66    (2)   ~ (e2 = e0)
% 242.12/48.66    (3)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.12/48.66         (all_58_11 = e0 & op(e1, e0) = e0)
% 242.12/48.66    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.12/48.66         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.12/48.66    (5)  all_58_1 = e2 & op(e3, e2) = e2
% 242.12/48.66    (6)  all_58_14 = e2
% 242.12/48.66    (7)  all_58_3 = e3
% 242.12/48.66    (8)  all_58_11 = e3
% 242.12/48.66    (9)   ~ (e3 = e2)
% 242.12/48.66    (10)  all_58_15 = e1
% 242.12/48.66    (11)  all_58_12 = e3
% 242.12/48.66    (12)  op(e1, e1) = e2
% 242.12/48.66    (13)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.12/48.66    (14)  all_58_5 = e1
% 242.12/48.66    (15)  all_58_7 = e1
% 242.12/48.66    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.12/48.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.12/48.66    (17)  op(e1, e1) = e0
% 242.12/48.66    (18)   ~ (e1 = e0)
% 242.12/48.66    (19)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.12/48.66          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.12/48.66            e2)
% 242.12/48.66    (20)   ~ (e2 = e1)
% 242.12/48.66  
% 242.12/48.66  Begin of proof
% 242.12/48.66  | 
% 242.12/48.66  | BETA: splitting (13) gives:
% 242.12/48.66  | 
% 242.12/48.66  | Case 1:
% 242.12/48.66  | | 
% 242.12/48.66  | |   (21)  all_58_5 = e2 & op(e2, e1) = e2
% 242.12/48.66  | | 
% 242.12/48.66  | | REF_CLOSE: (14), (20), (21) are inconsistent by sub-proof #703.
% 242.12/48.66  | | 
% 242.12/48.66  | Case 2:
% 242.12/48.66  | | 
% 242.12/48.66  | |   (22)  all_58_10 = e2 & op(e2, e0) = e2
% 242.12/48.66  | | 
% 242.12/48.66  | | ALPHA: (22) implies:
% 242.12/48.66  | |   (23)  op(e2, e0) = e2
% 242.12/48.66  | | 
% 242.12/48.66  | | BETA: splitting (3) gives:
% 242.12/48.66  | | 
% 242.12/48.66  | | Case 1:
% 242.12/48.66  | | | 
% 242.12/48.66  | | | 
% 242.12/48.66  | | | ALPHA: (5) implies:
% 242.12/48.66  | | |   (24)  all_58_1 = e2
% 242.12/48.66  | | | 
% 242.12/48.66  | | | GROUND_INST: instantiating (16) with e0, e2, e1, e1, simplifying with
% 242.12/48.66  | | |              (12), (17) gives:
% 242.12/48.66  | | |   (25)  e2 = e0
% 242.12/48.66  | | | 
% 242.12/48.66  | | | COMBINE_EQS: (6), (25) imply:
% 242.12/48.66  | | |   (26)  all_58_14 = e0
% 242.12/48.66  | | | 
% 242.12/48.66  | | | REF_CLOSE: (1), (2), (4), (7), (9), (10), (11), (15), (18), (19), (20),
% 242.12/48.66  | | |            (24), (26) are inconsistent by sub-proof #735.
% 242.12/48.66  | | | 
% 242.12/48.66  | | Case 2:
% 242.12/48.67  | | | 
% 242.12/48.67  | | |   (27)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.12/48.67  | | |           = e0)
% 242.12/48.67  | | | 
% 242.12/48.67  | | | REF_CLOSE: (1), (2), (8), (16), (23), (27) are inconsistent by sub-proof
% 242.12/48.67  | | |            #955.
% 242.12/48.67  | | | 
% 242.12/48.67  | | End of split
% 242.12/48.67  | | 
% 242.12/48.67  | End of split
% 242.12/48.67  | 
% 242.12/48.67  End of proof
% 242.12/48.67  
% 242.12/48.67  Sub-proof #688 shows that the following formulas are inconsistent:
% 242.12/48.67  ----------------------------------------------------------------
% 242.12/48.67    (1)   ~ (e3 = e0)
% 242.12/48.67    (2)   ~ (e2 = e0)
% 242.12/48.67    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.12/48.67         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.12/48.67    (4)  all_58_14 = e2
% 242.12/48.67    (5)  all_58_3 = e3
% 242.12/48.67    (6)   ~ (e3 = e2)
% 242.12/48.67    (7)  all_58_2 = e2 & op(e2, e3) = e2
% 242.12/48.67    (8)  all_58_15 = e1
% 242.12/48.67    (9)  all_58_12 = e3
% 242.12/48.67    (10)  all_58_2 = e0
% 242.12/48.67    (11)  all_58_7 = e1
% 242.12/48.67    (12)  all_58_1 = e2
% 242.12/48.67    (13)   ~ (e1 = e0)
% 242.12/48.67    (14)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.12/48.67          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.12/48.67            e2)
% 242.12/48.67    (15)   ~ (e2 = e1)
% 242.12/48.67  
% 242.12/48.67  Begin of proof
% 242.12/48.67  | 
% 242.12/48.67  | ALPHA: (7) implies:
% 242.12/48.67  |   (16)  all_58_2 = e2
% 242.12/48.67  | 
% 242.12/48.67  | COMBINE_EQS: (10), (16) imply:
% 242.12/48.67  |   (17)  e2 = e0
% 242.12/48.67  | 
% 242.12/48.67  | COMBINE_EQS: (4), (17) imply:
% 242.12/48.67  |   (18)  all_58_14 = e0
% 242.12/48.67  | 
% 242.12/48.67  | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (11), (12), (13), (14), (15),
% 242.12/48.67  |            (18) are inconsistent by sub-proof #735.
% 242.12/48.67  | 
% 242.12/48.67  End of proof
% 242.12/48.67  
% 242.12/48.67  Sub-proof #689 shows that the following formulas are inconsistent:
% 242.12/48.67  ----------------------------------------------------------------
% 242.12/48.67    (1)  all_58_15 = e0 & op(e0, e0) = e0
% 242.12/48.67    (2)  all_58_15 = e1
% 242.12/48.67    (3)   ~ (e1 = e0)
% 242.12/48.67  
% 242.12/48.67  Begin of proof
% 242.12/48.67  | 
% 242.12/48.67  | ALPHA: (1) implies:
% 242.12/48.67  |   (4)  all_58_15 = e0
% 242.12/48.67  | 
% 242.12/48.67  | COMBINE_EQS: (2), (4) imply:
% 242.12/48.67  |   (5)  e1 = e0
% 242.12/48.67  | 
% 242.12/48.67  | REDUCE: (3), (5) imply:
% 242.12/48.67  |   (6)  $false
% 242.12/48.67  | 
% 242.12/48.67  | CLOSE: (6) is inconsistent.
% 242.12/48.67  | 
% 242.12/48.67  End of proof
% 242.12/48.67  
% 242.12/48.67  Sub-proof #690 shows that the following formulas are inconsistent:
% 242.12/48.67  ----------------------------------------------------------------
% 242.12/48.67    (1)   ~ (all_52_1 = all_52_3)
% 242.12/48.67    (2)  all_56_21 = e2
% 242.18/48.67    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.18/48.67    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.67         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.67    (5)   ~ (all_52_3 = e1)
% 242.18/48.67    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.18/48.67    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.18/48.67         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.67    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.18/48.67           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.18/48.67             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.18/48.67    (9)   ~ (e3 = e0)
% 242.18/48.67    (10)  op(e0, e1) = all_52_11
% 242.18/48.67    (11)  all_42_2 = e3
% 242.18/48.67    (12)  op(e1, e2) = e1
% 242.18/48.67    (13)   ~ (e2 = e0)
% 242.18/48.67    (14)   ~ (all_52_11 = e2)
% 242.18/48.67    (15)  all_54_13 = all_52_7
% 242.18/48.67    (16)  op(e1, e2) = all_52_6
% 242.18/48.67    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.18/48.67          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.67    (18)  all_58_6 = e2
% 242.18/48.67    (19)   ~ (all_52_11 = e1)
% 242.18/48.67    (20)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.18/48.67              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.18/48.67            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.18/48.67            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.18/48.67            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.18/48.67             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.67            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.18/48.67            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.18/48.67            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.18/48.67            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.67            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.18/48.67              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.18/48.67            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.18/48.67            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.18/48.67            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.18/48.67            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.18/48.67            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.18/48.67            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.18/48.67              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.18/48.67            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.18/48.67            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.18/48.67            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.18/48.67            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.18/48.67            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.67            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.18/48.67              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.18/48.67            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.67            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.18/48.67    (21)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.67          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.18/48.67    (22)   ~ (all_52_7 = all_52_11)
% 242.18/48.67    (23)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.18/48.67            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.18/48.67              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.18/48.67    (24)  all_58_4 = e2
% 242.18/48.67    (25)   ~ (all_52_1 = all_52_2)
% 242.18/48.67    (26)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.18/48.67            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.18/48.67              e1) = all_20_1 & $i(all_20_1))
% 242.18/48.67    (27)   ~ (all_52_7 = e3)
% 242.18/48.67    (28)  all_58_8 = e0
% 242.18/48.67    (29)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.18/48.67    (30)  op(e0, e3) = all_52_3
% 242.18/48.67    (31)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.18/48.67          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.18/48.67    (32)   ~ (e3 = e1)
% 242.18/48.67    (33)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.18/48.67          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.18/48.67    (34)   ~ (all_52_2 = all_52_3)
% 242.18/48.67    (35)   ~ (all_52_8 = e1)
% 242.18/48.67    (36)  all_58_3 = e3
% 242.18/48.67    (37)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.18/48.67          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.18/48.67    (38)   ~ (all_52_2 = e1)
% 242.18/48.67    (39)  op(all_40_1, e1) = all_40_0
% 242.18/48.67    (40)  all_54_2 = all_52_8
% 242.18/48.67    (41)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.18/48.67          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.18/48.67    (42)  op(e3, e3) = e1
% 242.18/48.67    (43)   ~ (all_52_3 = all_52_7)
% 242.18/48.67    (44)  all_54_4 = all_52_1
% 242.18/48.67    (45)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.67              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.18/48.67                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.18/48.67                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.18/48.67    (46)  op(e2, e1) = all_52_9
% 242.18/48.67    (47)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.18/48.67          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.18/48.67    (48)   ~ (e3 = e2)
% 242.18/48.67    (49)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.18/48.67          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.18/48.67    (50)   ~ (all_52_7 = e1)
% 242.18/48.67    (51)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.18/48.67    (52)   ~ (all_52_3 = all_52_11)
% 242.18/48.67    (53)  all_56_31 = e1
% 242.18/48.67    (54)  all_54_12 = all_52_3
% 242.18/48.67    (55)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.18/48.67    (56)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.18/48.67          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.18/48.67    (57)  all_58_15 = e1
% 242.18/48.67    (58)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.18/48.67          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.18/48.67    (59)  op(e2, e3) = all_52_1
% 242.18/48.67    (60)  all_58_12 = e3
% 242.18/48.67    (61)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.18/48.67          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.67    (62)  all_34_2 = e1
% 242.18/48.67    (63)   ~ (all_52_6 = e3)
% 242.18/48.67    (64)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.18/48.67    (65)  op(e1, e1) = e2
% 242.18/48.67    (66)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.18/48.67          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.18/48.67    (67)  op(e0, e2) = all_52_7
% 242.18/48.67    (68)  all_54_1 = all_52_4
% 242.18/48.67    (69)   ~ (all_52_4 = e3)
% 242.18/48.67    (70)  op(e3, e2) = all_52_4
% 242.18/48.67    (71)   ~ (all_52_8 = all_52_11)
% 242.18/48.67    (72)   ~ (all_40_0 = e0)
% 242.18/48.67    (73)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.18/48.67    (74)  all_58_5 = e1
% 242.18/48.67    (75)  all_58_7 = e1
% 242.18/48.67    (76)   ~ (all_52_2 = e2)
% 242.18/48.67    (77)   ~ (all_52_9 = e3)
% 242.18/48.67    (78)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.18/48.67          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.67    (79)  all_54_8 = all_52_2
% 242.18/48.67    (80)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.67          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.18/48.67    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.67    (82)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.18/48.67          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.18/48.67    (83)  all_56_11 = e3
% 242.18/48.67    (84)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.18/48.67            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.18/48.67              e2) = all_36_1 & $i(all_36_1))
% 242.18/48.67    (85)  op(e1, e1) = e0
% 242.18/48.67    (86)  op(e1, e2) = all_40_1
% 242.18/48.67    (87)   ~ (all_52_4 = e1)
% 242.18/48.67    (88)   ~ (e1 = e0)
% 242.18/48.67    (89)   ~ (all_52_8 = e2)
% 242.18/48.67    (90)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.18/48.67          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.18/48.67    (91)   ~ (all_52_1 = e3)
% 242.18/48.67    (92)  all_54_14 = all_52_11
% 242.18/48.67    (93)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.67          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.18/48.67            e2)
% 242.18/48.67    (94)   ~ (all_52_4 = all_52_8)
% 242.18/48.67    (95)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.18/48.67            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.18/48.67            & $i(all_8_1))
% 242.18/48.67    (96)   ~ (e2 = e1)
% 242.18/48.67    (97)   ~ (all_52_1 = e1)
% 242.18/48.67    (98)   ~ (all_52_4 = all_52_7)
% 242.18/48.67  
% 242.18/48.67  Begin of proof
% 242.18/48.67  | 
% 242.18/48.67  | BETA: splitting (37) gives:
% 242.18/48.67  | 
% 242.18/48.67  | Case 1:
% 242.18/48.67  | | 
% 242.18/48.67  | |   (99)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 242.18/48.67  | |           e3)
% 242.18/48.67  | | 
% 242.18/48.67  | | REF_CLOSE: (32), (42), (69), (70), (81), (99) are inconsistent by sub-proof
% 242.18/48.67  | |            #1401.
% 242.18/48.67  | | 
% 242.18/48.67  | Case 2:
% 242.18/48.67  | | 
% 242.18/48.67  | |   (100)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 242.18/48.67  | |            e3)
% 242.18/48.67  | | 
% 242.18/48.67  | | BETA: splitting (100) gives:
% 242.18/48.67  | | 
% 242.18/48.67  | | Case 1:
% 242.18/48.67  | | | 
% 242.18/48.67  | | |   (101)  all_58_4 = e3 & op(e3, e1) = e3
% 242.18/48.67  | | | 
% 242.18/48.67  | | | REF_CLOSE: (24), (48), (101) are inconsistent by sub-proof #2167.
% 242.18/48.67  | | | 
% 242.18/48.67  | | Case 2:
% 242.18/48.67  | | | 
% 242.18/48.67  | | |   (102)  all_58_9 = e3 & op(e3, e0) = e3
% 242.18/48.67  | | | 
% 242.18/48.67  | | | ALPHA: (102) implies:
% 242.18/48.67  | | |   (103)  all_58_9 = e3
% 242.18/48.67  | | |   (104)  op(e3, e0) = e3
% 242.18/48.67  | | | 
% 242.18/48.67  | | | BETA: splitting (82) gives:
% 242.18/48.67  | | | 
% 242.18/48.67  | | | Case 1:
% 242.18/48.67  | | | | 
% 242.18/48.67  | | | |   (105)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 242.18/48.67  | | | |              e0) = e2)
% 242.18/48.67  | | | | 
% 242.18/48.67  | | | | BETA: splitting (105) gives:
% 242.18/48.67  | | | | 
% 242.18/48.67  | | | | Case 1:
% 242.18/48.67  | | | | | 
% 242.18/48.67  | | | | |   (106)  all_58_9 = e2 & op(e3, e0) = e2
% 242.18/48.67  | | | | | 
% 242.18/48.67  | | | | | ALPHA: (106) implies:
% 242.18/48.67  | | | | |   (107)  op(e3, e0) = e2
% 242.18/48.67  | | | | | 
% 242.18/48.67  | | | | | REF_CLOSE: (48), (81), (104), (107) are inconsistent by sub-proof
% 242.18/48.67  | | | | |            #2125.
% 242.18/48.67  | | | | | 
% 242.18/48.67  | | | | Case 2:
% 242.18/48.67  | | | | | 
% 242.18/48.67  | | | | |   (108)  all_58_10 = e2 & op(e2, e0) = e2
% 242.18/48.67  | | | | | 
% 242.18/48.67  | | | | | ALPHA: (108) implies:
% 242.18/48.67  | | | | |   (109)  op(e2, e0) = e2
% 242.18/48.67  | | | | | 
% 242.18/48.67  | | | | | BETA: splitting (58) gives:
% 242.18/48.67  | | | | | 
% 242.18/48.67  | | | | | Case 1:
% 242.18/48.67  | | | | | | 
% 242.18/48.67  | | | | | |   (110)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 242.18/48.67  | | | | | |              e2) = e3)
% 242.18/48.67  | | | | | | 
% 242.18/48.67  | | | | | | REF_CLOSE: (16), (18), (48), (63), (81), (110) are inconsistent by
% 242.18/48.67  | | | | | |            sub-proof #933.
% 242.18/48.67  | | | | | | 
% 242.18/48.67  | | | | | Case 2:
% 242.18/48.67  | | | | | | 
% 242.18/48.67  | | | | | |   (111)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 &
% 242.18/48.67  | | | | | |            op(e1, e0) = e3)
% 242.18/48.67  | | | | | | 
% 242.18/48.67  | | | | | | BETA: splitting (111) gives:
% 242.18/48.67  | | | | | | 
% 242.18/48.67  | | | | | | Case 1:
% 242.18/48.67  | | | | | | | 
% 242.18/48.67  | | | | | | |   (112)  all_58_8 = e3 & op(e1, e1) = e3
% 242.18/48.67  | | | | | | | 
% 242.18/48.67  | | | | | | | ALPHA: (112) implies:
% 242.18/48.67  | | | | | | |   (113)  all_58_8 = e3
% 242.18/48.67  | | | | | | |   (114)  op(e1, e1) = e3
% 242.18/48.67  | | | | | | | 
% 242.18/48.68  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 242.18/48.68  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (19), (20),
% 242.18/48.68  | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (29), (30),
% 242.18/48.68  | | | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 242.18/48.68  | | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (50),
% 242.18/48.68  | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 242.18/48.68  | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 242.18/48.68  | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 242.18/48.68  | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (86), (87),
% 242.18/48.68  | | | | | | |            (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 242.18/48.68  | | | | | | |            (97), (98), (103), (113), (114) are inconsistent by
% 242.18/48.68  | | | | | | |            sub-proof #711.
% 242.18/48.68  | | | | | | | 
% 242.18/48.68  | | | | | | Case 2:
% 242.18/48.68  | | | | | | | 
% 242.18/48.68  | | | | | | |   (115)  all_58_11 = e3 & op(e1, e0) = e3
% 242.18/48.68  | | | | | | | 
% 242.18/48.68  | | | | | | | ALPHA: (115) implies:
% 242.18/48.68  | | | | | | |   (116)  all_58_11 = e3
% 242.18/48.68  | | | | | | | 
% 242.18/48.68  | | | | | | | REF_CLOSE: (9), (13), (45), (57), (81), (88), (103), (109), (116)
% 242.18/48.68  | | | | | | |            are inconsistent by sub-proof #710.
% 242.18/48.68  | | | | | | | 
% 242.18/48.68  | | | | | | End of split
% 242.18/48.68  | | | | | | 
% 242.18/48.68  | | | | | End of split
% 242.18/48.68  | | | | | 
% 242.18/48.68  | | | | End of split
% 242.18/48.68  | | | | 
% 242.18/48.68  | | | Case 2:
% 242.18/48.68  | | | | 
% 242.18/48.68  | | | |   (117)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 242.18/48.68  | | | |              e0) = e2)
% 242.18/48.68  | | | | 
% 242.18/48.68  | | | | BETA: splitting (117) gives:
% 242.18/48.68  | | | | 
% 242.18/48.68  | | | | Case 1:
% 242.18/48.68  | | | | | 
% 242.18/48.68  | | | | |   (118)  all_58_11 = e2 & op(e1, e0) = e2
% 242.18/48.68  | | | | | 
% 242.18/48.68  | | | | | ALPHA: (118) implies:
% 242.18/48.68  | | | | |   (119)  all_58_11 = e2
% 242.18/48.68  | | | | | 
% 242.18/48.68  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 242.18/48.68  | | | | |            (12), (13), (14), (15), (16), (17), (19), (20), (21), (22),
% 242.18/48.68  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 242.18/48.68  | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 242.18/48.68  | | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 242.18/48.68  | | | | |            (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 242.18/48.68  | | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 242.18/48.68  | | | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 242.18/48.68  | | | | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 242.18/48.68  | | | | |            (94), (95), (96), (97), (98), (103), (104), (119) are
% 242.18/48.68  | | | | |            inconsistent by sub-proof #692.
% 242.18/48.68  | | | | | 
% 242.18/48.68  | | | | Case 2:
% 242.18/48.68  | | | | | 
% 242.18/48.68  | | | | |   (120)  all_58_15 = e2 & op(e0, e0) = e2
% 242.18/48.68  | | | | | 
% 242.18/48.68  | | | | | ALPHA: (120) implies:
% 242.18/48.68  | | | | |   (121)  all_58_15 = e2
% 242.18/48.68  | | | | | 
% 242.18/48.68  | | | | | REF_CLOSE: (4), (9), (13), (24), (42), (48), (57), (61), (81), (88),
% 242.18/48.68  | | | | |            (96), (103), (121) are inconsistent by sub-proof #691.
% 242.18/48.68  | | | | | 
% 242.18/48.68  | | | | End of split
% 242.18/48.68  | | | | 
% 242.18/48.68  | | | End of split
% 242.18/48.68  | | | 
% 242.18/48.68  | | End of split
% 242.18/48.68  | | 
% 242.18/48.68  | End of split
% 242.18/48.68  | 
% 242.18/48.68  End of proof
% 242.18/48.68  
% 242.18/48.68  Sub-proof #691 shows that the following formulas are inconsistent:
% 242.18/48.68  ----------------------------------------------------------------
% 242.18/48.68    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.68         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.68    (2)   ~ (e3 = e0)
% 242.18/48.68    (3)   ~ (e2 = e0)
% 242.18/48.68    (4)  all_58_4 = e2
% 242.18/48.68    (5)  op(e3, e3) = e1
% 242.18/48.68    (6)  all_58_15 = e2
% 242.18/48.68    (7)   ~ (e3 = e2)
% 242.18/48.68    (8)  all_58_15 = e1
% 242.18/48.68    (9)  all_58_9 = e3
% 242.18/48.68    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.18/48.68          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.68    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.68    (12)   ~ (e1 = e0)
% 242.18/48.68    (13)   ~ (e2 = e1)
% 242.18/48.68  
% 242.18/48.68  Begin of proof
% 242.18/48.68  | 
% 242.18/48.68  | COMBINE_EQS: (6), (8) imply:
% 242.18/48.68  |   (14)  e2 = e1
% 242.18/48.68  | 
% 242.18/48.68  | COMBINE_EQS: (4), (14) imply:
% 242.18/48.68  |   (15)  all_58_4 = e1
% 242.18/48.68  | 
% 242.18/48.68  | REF_CLOSE: (1), (2), (3), (5), (7), (9), (10), (11), (12), (13), (15) are
% 242.18/48.68  |            inconsistent by sub-proof #1469.
% 242.18/48.68  | 
% 242.18/48.68  End of proof
% 242.18/48.68  
% 242.18/48.68  Sub-proof #692 shows that the following formulas are inconsistent:
% 242.18/48.68  ----------------------------------------------------------------
% 242.18/48.68    (1)   ~ (all_52_1 = all_52_3)
% 242.18/48.68    (2)  all_56_21 = e2
% 242.18/48.68    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.18/48.68    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.68         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.68    (5)   ~ (all_52_3 = e1)
% 242.18/48.68    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.18/48.68    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.18/48.68         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.68    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.18/48.68           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.18/48.68             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.18/48.68    (9)   ~ (e3 = e0)
% 242.18/48.68    (10)  op(e0, e1) = all_52_11
% 242.18/48.68    (11)  all_42_2 = e3
% 242.18/48.68    (12)  op(e1, e2) = e1
% 242.18/48.68    (13)   ~ (e2 = e0)
% 242.18/48.68    (14)   ~ (all_52_11 = e2)
% 242.18/48.68    (15)  all_54_13 = all_52_7
% 242.18/48.68    (16)  op(e1, e2) = all_52_6
% 242.18/48.68    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.18/48.68          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.68    (18)   ~ (all_52_11 = e1)
% 242.18/48.68    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.18/48.68              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.18/48.68            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.18/48.68            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.18/48.68            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.18/48.68             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.68            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.18/48.68            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.18/48.68            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.18/48.68            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.68            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.18/48.68              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.18/48.68            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.18/48.68            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.18/48.68            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.18/48.68            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.18/48.68            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.18/48.68            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.18/48.68              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.18/48.68            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.18/48.68            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.18/48.68            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.18/48.68            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.18/48.68            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.68            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.18/48.68              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.18/48.68            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.68            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.18/48.68    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.68          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.18/48.68    (21)   ~ (all_52_7 = all_52_11)
% 242.18/48.68    (22)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.18/48.68            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.18/48.68              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.18/48.68    (23)  all_58_4 = e2
% 242.18/48.68    (24)   ~ (all_52_1 = all_52_2)
% 242.18/48.68    (25)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.18/48.68            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.18/48.68              e1) = all_20_1 & $i(all_20_1))
% 242.18/48.68    (26)   ~ (all_52_7 = e3)
% 242.18/48.68    (27)  all_58_8 = e0
% 242.18/48.68    (28)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.18/48.68    (29)  op(e0, e3) = all_52_3
% 242.18/48.68    (30)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.18/48.68          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.18/48.68    (31)   ~ (e3 = e1)
% 242.18/48.68    (32)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.18/48.68          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.18/48.68    (33)   ~ (all_52_2 = all_52_3)
% 242.18/48.68    (34)   ~ (all_52_8 = e1)
% 242.18/48.68    (35)  all_58_3 = e3
% 242.18/48.68    (36)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.18/48.68          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.18/48.68    (37)   ~ (all_52_2 = e1)
% 242.18/48.68    (38)  op(all_40_1, e1) = all_40_0
% 242.18/48.68    (39)  all_54_2 = all_52_8
% 242.18/48.68    (40)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.18/48.68          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.18/48.68    (41)  op(e3, e3) = e1
% 242.18/48.68    (42)   ~ (all_52_3 = all_52_7)
% 242.18/48.68    (43)  all_54_4 = all_52_1
% 242.18/48.68    (44)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.68              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.18/48.68                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.18/48.68                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.18/48.68    (45)  op(e2, e1) = all_52_9
% 242.18/48.68    (46)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.18/48.68          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.18/48.68    (47)   ~ (e3 = e2)
% 242.18/48.68    (48)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.18/48.68          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.18/48.68    (49)   ~ (all_52_7 = e1)
% 242.18/48.68    (50)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.18/48.68    (51)   ~ (all_52_3 = all_52_11)
% 242.18/48.68    (52)  all_56_31 = e1
% 242.18/48.68    (53)  all_54_12 = all_52_3
% 242.18/48.68    (54)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.18/48.68    (55)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.18/48.68          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.18/48.68    (56)  all_58_15 = e1
% 242.18/48.68    (57)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.18/48.68          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.18/48.68    (58)  all_58_9 = e3
% 242.18/48.68    (59)  op(e3, e0) = e3
% 242.18/48.68    (60)  all_58_11 = e2
% 242.18/48.68    (61)  op(e2, e3) = all_52_1
% 242.18/48.68    (62)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.18/48.68          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.68    (63)  all_34_2 = e1
% 242.18/48.68    (64)   ~ (all_52_6 = e3)
% 242.18/48.68    (65)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.18/48.68    (66)  op(e1, e1) = e2
% 242.18/48.68    (67)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.18/48.68          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.18/48.68    (68)  op(e0, e2) = all_52_7
% 242.18/48.68    (69)  all_54_1 = all_52_4
% 242.18/48.68    (70)   ~ (all_52_4 = e3)
% 242.18/48.68    (71)  op(e3, e2) = all_52_4
% 242.18/48.68    (72)   ~ (all_52_8 = all_52_11)
% 242.18/48.68    (73)   ~ (all_40_0 = e0)
% 242.18/48.68    (74)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.18/48.68    (75)  all_58_5 = e1
% 242.18/48.68    (76)  all_58_7 = e1
% 242.18/48.68    (77)   ~ (all_52_2 = e2)
% 242.18/48.68    (78)   ~ (all_52_9 = e3)
% 242.18/48.68    (79)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.18/48.68          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.68    (80)  all_54_8 = all_52_2
% 242.18/48.68    (81)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.68          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.18/48.68    (82)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.68    (83)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.18/48.68          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.18/48.68    (84)  all_56_11 = e3
% 242.18/48.68    (85)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.18/48.68            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.18/48.68              e2) = all_36_1 & $i(all_36_1))
% 242.18/48.68    (86)  op(e1, e1) = e0
% 242.18/48.68    (87)  op(e1, e2) = all_40_1
% 242.18/48.68    (88)   ~ (all_52_4 = e1)
% 242.18/48.68    (89)   ~ (e1 = e0)
% 242.18/48.68    (90)   ~ (all_52_8 = e2)
% 242.18/48.68    (91)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.18/48.68          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.18/48.68    (92)   ~ (all_52_1 = e3)
% 242.18/48.68    (93)  all_54_14 = all_52_11
% 242.18/48.68    (94)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.68          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.18/48.68            e2)
% 242.18/48.68    (95)   ~ (all_52_4 = all_52_8)
% 242.18/48.68    (96)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.18/48.68            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.18/48.68            & $i(all_8_1))
% 242.18/48.68    (97)   ~ (e2 = e1)
% 242.18/48.68    (98)   ~ (all_52_1 = e1)
% 242.18/48.68    (99)   ~ (all_52_4 = all_52_7)
% 242.18/48.68  
% 242.18/48.68  Begin of proof
% 242.18/48.68  | 
% 242.18/48.68  | BETA: splitting (57) gives:
% 242.18/48.68  | 
% 242.18/48.68  | Case 1:
% 242.18/48.68  | | 
% 242.18/48.68  | |   (100)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 242.18/48.68  | |            e3)
% 242.18/48.68  | | 
% 242.18/48.68  | | BETA: splitting (100) gives:
% 242.18/48.68  | | 
% 242.18/48.68  | | Case 1:
% 242.18/48.68  | | | 
% 242.18/48.68  | | |   (101)  all_58_6 = e3 & op(e1, e3) = e3
% 242.18/48.68  | | | 
% 242.18/48.68  | | | ALPHA: (101) implies:
% 242.18/48.68  | | |   (102)  all_58_6 = e3
% 242.18/48.68  | | | 
% 242.18/48.68  | | | BETA: splitting (44) gives:
% 242.18/48.68  | | | 
% 242.18/48.68  | | | Case 1:
% 242.18/48.68  | | | | 
% 242.18/48.68  | | | |   (103)  all_58_15 = e0 & op(e0, e0) = e0
% 242.18/48.68  | | | | 
% 242.18/48.68  | | | | REF_CLOSE: (56), (89), (103) are inconsistent by sub-proof #1867.
% 242.18/48.68  | | | | 
% 242.18/48.68  | | | Case 2:
% 242.18/48.68  | | | | 
% 242.18/48.69  | | | |   (104)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 242.18/48.69  | | | |                e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 242.18/48.69  | | | |          ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 242.18/48.69  | | | |                e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.18/48.69  | | | | 
% 242.18/48.69  | | | | ALPHA: (104) implies:
% 242.18/48.69  | | | |   (105)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 242.18/48.69  | | | |              e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.18/48.69  | | | | 
% 242.18/48.69  | | | | BETA: splitting (67) gives:
% 242.18/48.69  | | | | 
% 242.18/48.69  | | | | Case 1:
% 242.18/48.69  | | | | | 
% 242.18/48.69  | | | | |   (106)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2,
% 242.18/48.69  | | | | |              e1) = e3)
% 242.18/48.69  | | | | | 
% 242.18/48.69  | | | | | BETA: splitting (106) gives:
% 242.18/48.69  | | | | | 
% 242.18/48.69  | | | | | Case 1:
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | |   (107)  all_58_4 = e3 & op(e3, e1) = e3
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | | REF_CLOSE: (23), (47), (107) are inconsistent by sub-proof #2167.
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | Case 2:
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | |   (108)  all_58_5 = e3 & op(e2, e1) = e3
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | | REF_CLOSE: (45), (78), (82), (108) are inconsistent by sub-proof
% 242.18/48.69  | | | | | |            #1822.
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | End of split
% 242.18/48.69  | | | | | 
% 242.18/48.69  | | | | Case 2:
% 242.18/48.69  | | | | | 
% 242.18/48.69  | | | | |   (109)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0,
% 242.18/48.69  | | | | |              e1) = e3)
% 242.18/48.69  | | | | | 
% 242.18/48.69  | | | | | BETA: splitting (109) gives:
% 242.18/48.69  | | | | | 
% 242.18/48.69  | | | | | Case 1:
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | |   (110)  all_58_8 = e3 & op(e1, e1) = e3
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | | ALPHA: (110) implies:
% 242.18/48.69  | | | | | |   (111)  all_58_8 = e3
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | | COMBINE_EQS: (27), (111) imply:
% 242.18/48.69  | | | | | |   (112)  e3 = e0
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | | COMBINE_EQS: (102), (112) imply:
% 242.18/48.69  | | | | | |   (113)  all_58_6 = e0
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 242.18/48.69  | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 242.18/48.69  | | | | | |            (21), (22), (24), (25), (26), (28), (29), (31), (32),
% 242.18/48.69  | | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 242.18/48.69  | | | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 242.18/48.69  | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 242.18/48.69  | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 242.18/48.69  | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 242.18/48.69  | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85), (87),
% 242.18/48.69  | | | | | |            (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 242.18/48.69  | | | | | |            (97), (98), (99), (113) are inconsistent by sub-proof
% 242.18/48.69  | | | | | |            #705.
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | Case 2:
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | |   (114)  all_58_14 = e3 & op(e0, e1) = e3
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | | ALPHA: (114) implies:
% 242.18/48.69  | | | | | |   (115)  all_58_14 = e3
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | | BETA: splitting (105) gives:
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | | Case 1:
% 242.18/48.69  | | | | | | | 
% 242.18/48.69  | | | | | | |   (116)  all_58_9 = e0 & op(e3, e0) = e0
% 242.18/48.69  | | | | | | | 
% 242.18/48.69  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 242.18/48.69  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 242.18/48.69  | | | | | | |            (20), (21), (22), (24), (25), (26), (28), (29), (31),
% 242.18/48.69  | | | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 242.18/48.69  | | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 242.18/48.69  | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 242.18/48.69  | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 242.18/48.69  | | | | | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 242.18/48.69  | | | | | | |            (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 242.18/48.69  | | | | | | |            (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 242.18/48.69  | | | | | | |            (96), (97), (98), (99), (102), (116) are inconsistent
% 242.18/48.69  | | | | | | |            by sub-proof #704.
% 242.18/48.69  | | | | | | | 
% 242.18/48.69  | | | | | | Case 2:
% 242.18/48.69  | | | | | | | 
% 242.18/48.69  | | | | | | |   (117)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.18/48.69  | | | | | | |            op(e1, e0) = e0)
% 242.18/48.69  | | | | | | | 
% 242.18/48.69  | | | | | | | BETA: splitting (117) gives:
% 242.18/48.69  | | | | | | | 
% 242.18/48.69  | | | | | | | Case 1:
% 242.18/48.69  | | | | | | | | 
% 242.18/48.69  | | | | | | | |   (118)  all_58_10 = e0 & op(e2, e0) = e0
% 242.18/48.69  | | | | | | | | 
% 242.18/48.69  | | | | | | | | ALPHA: (118) implies:
% 242.18/48.69  | | | | | | | |   (119)  op(e2, e0) = e0
% 242.18/48.69  | | | | | | | | 
% 242.18/48.69  | | | | | | | | BETA: splitting (30) gives:
% 242.18/48.69  | | | | | | | | 
% 242.18/48.69  | | | | | | | | Case 1:
% 242.18/48.69  | | | | | | | | | 
% 242.18/48.69  | | | | | | | | |   (120)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 242.18/48.69  | | | | | | | | |            op(e2, e2) = e2)
% 242.18/48.69  | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | BETA: splitting (120) gives:
% 242.18/48.69  | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | Case 1:
% 242.18/48.69  | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | |   (121)  all_58_2 = e2 & op(e2, e3) = e2
% 242.18/48.69  | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | ALPHA: (121) implies:
% 242.18/48.69  | | | | | | | | | |   (122)  all_58_2 = e2
% 242.18/48.69  | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | BETA: splitting (17) gives:
% 242.18/48.69  | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | Case 1:
% 242.18/48.69  | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | |   (123)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 242.18/48.69  | | | | | | | | | | |            & op(e2, e2) = e2)
% 242.18/48.69  | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | BETA: splitting (123) gives:
% 242.18/48.69  | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | Case 1:
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | |   (124)  all_58_1 = e2 & op(e3, e2) = e2
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | ALPHA: (124) implies:
% 242.18/48.69  | | | | | | | | | | | |   (125)  all_58_1 = e2
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 242.18/48.69  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 242.18/48.69  | | | | | | | | | | | |            (19), (20), (21), (22), (24), (25), (26), (27),
% 242.18/48.69  | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 242.18/48.69  | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 242.18/48.69  | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 242.18/48.69  | | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 242.18/48.69  | | | | | | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67),
% 242.18/48.69  | | | | | | | | | | | |            (68), (69), (70), (71), (72), (73), (74), (75),
% 242.18/48.69  | | | | | | | | | | | |            (76), (77), (78), (79), (80), (81), (82), (83),
% 242.18/48.69  | | | | | | | | | | | |            (84), (85), (87), (88), (89), (90), (91), (92),
% 242.18/48.69  | | | | | | | | | | | |            (93), (94), (95), (96), (97), (98), (99), (102),
% 242.18/48.69  | | | | | | | | | | | |            (105), (125) are inconsistent by sub-proof #700.
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | Case 2:
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | |   (126)  all_58_3 = e2 & op(e2, e2) = e2
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | REF_CLOSE: (9), (13), (31), (35), (40), (41), (44), (47),
% 242.18/48.69  | | | | | | | | | | | |            (56), (61), (82), (89), (92), (94), (97), (102),
% 242.18/48.69  | | | | | | | | | | | |            (115), (126) are inconsistent by sub-proof #699.
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | End of split
% 242.18/48.69  | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | Case 2:
% 242.18/48.69  | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | |   (127)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 242.18/48.69  | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 242.18/48.69  | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | BETA: splitting (127) gives:
% 242.18/48.69  | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | Case 1:
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | |   (128)  all_58_7 = e2 & op(e1, e2) = e2
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | ALPHA: (128) implies:
% 242.18/48.69  | | | | | | | | | | | |   (129)  all_58_7 = e2
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | COMBINE_EQS: (76), (129) imply:
% 242.18/48.69  | | | | | | | | | | | |   (130)  e2 = e1
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | REF_CLOSE: (4), (9), (13), (23), (41), (47), (58), (62),
% 242.18/48.69  | | | | | | | | | | | |            (82), (89), (97), (130) are inconsistent by
% 242.18/48.69  | | | | | | | | | | | |            sub-proof #714.
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | Case 2:
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | |   (131)  all_58_13 = e2 & op(e0, e2) = e2
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | ALPHA: (131) implies:
% 242.18/48.69  | | | | | | | | | | | |   (132)  op(e0, e2) = e2
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | BETA: splitting (81) gives:
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | Case 1:
% 242.18/48.69  | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | |   (133)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 242.18/48.69  | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 242.18/48.69  | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | BETA: splitting (133) gives:
% 242.18/48.69  | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | Case 1:
% 242.18/48.69  | | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | |   (134)  all_58_2 = e0 & op(e2, e3) = e0
% 242.18/48.69  | | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (13), (20), (23), (35), (41), (47),
% 242.18/48.69  | | | | | | | | | | | | | |            (58), (76), (82), (89), (97), (122), (132), (134)
% 242.18/48.69  | | | | | | | | | | | | | |            are inconsistent by sub-proof #698.
% 242.18/48.69  | | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | Case 2:
% 242.18/48.69  | | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | |   (135)  all_58_3 = e0 & op(e2, e2) = e0
% 242.18/48.69  | | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | | ALPHA: (135) implies:
% 242.18/48.69  | | | | | | | | | | | | | |   (136)  all_58_3 = e0
% 242.18/48.69  | | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | | COMBINE_EQS: (35), (136) imply:
% 242.18/48.69  | | | | | | | | | | | | | |   (137)  e3 = e0
% 242.18/48.69  | | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | | COMBINE_EQS: (102), (137) imply:
% 242.18/48.69  | | | | | | | | | | | | | |   (138)  all_58_6 = e0
% 242.18/48.69  | | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 242.18/48.69  | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 242.18/48.69  | | | | | | | | | | | | | |            (19), (20), (21), (22), (24), (25), (26), (28),
% 242.18/48.69  | | | | | | | | | | | | | |            (29), (31), (32), (33), (34), (35), (36), (37),
% 242.18/48.69  | | | | | | | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45),
% 242.18/48.69  | | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 242.18/48.69  | | | | | | | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61),
% 242.18/48.69  | | | | | | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 242.18/48.69  | | | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 242.18/48.69  | | | | | | | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85),
% 242.18/48.69  | | | | | | | | | | | | | |            (87), (88), (89), (90), (91), (92), (93), (94),
% 242.18/48.69  | | | | | | | | | | | | | |            (95), (96), (97), (98), (99), (138) are
% 242.18/48.69  | | | | | | | | | | | | | |            inconsistent by sub-proof #705.
% 242.18/48.69  | | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | End of split
% 242.18/48.69  | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | Case 2:
% 242.18/48.69  | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | |   (139)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 242.18/48.69  | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 242.18/48.69  | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | | REF_CLOSE: (4), (9), (13), (20), (23), (35), (41), (47),
% 242.18/48.69  | | | | | | | | | | | | |            (58), (66), (75), (76), (82), (86), (89), (97),
% 242.18/48.69  | | | | | | | | | | | | |            (132), (139) are inconsistent by sub-proof #697.
% 242.18/48.69  | | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | | End of split
% 242.18/48.69  | | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | | End of split
% 242.18/48.69  | | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | End of split
% 242.18/48.69  | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | Case 2:
% 242.18/48.69  | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | |   (140)  all_58_3 = e2 & op(e2, e2) = e2
% 242.18/48.69  | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | | REF_CLOSE: (9), (13), (31), (35), (40), (41), (44), (47),
% 242.18/48.69  | | | | | | | | | |            (56), (61), (82), (89), (92), (94), (97), (102),
% 242.18/48.69  | | | | | | | | | |            (115), (140) are inconsistent by sub-proof #696.
% 242.18/48.69  | | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | End of split
% 242.18/48.69  | | | | | | | | | 
% 242.18/48.69  | | | | | | | | Case 2:
% 242.18/48.69  | | | | | | | | | 
% 242.18/48.69  | | | | | | | | |   (141)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 242.18/48.69  | | | | | | | | |            op(e2, e0) = e2)
% 242.18/48.69  | | | | | | | | | 
% 242.18/48.69  | | | | | | | | | REF_CLOSE: (4), (9), (13), (23), (41), (47), (58), (62), (75),
% 242.18/48.69  | | | | | | | | |            (82), (89), (97), (119), (141) are inconsistent by
% 242.18/48.69  | | | | | | | | |            sub-proof #695.
% 242.18/48.69  | | | | | | | | | 
% 242.18/48.69  | | | | | | | | End of split
% 242.18/48.69  | | | | | | | | 
% 242.18/48.69  | | | | | | | Case 2:
% 242.18/48.69  | | | | | | | | 
% 242.18/48.69  | | | | | | | |   (142)  all_58_11 = e0 & op(e1, e0) = e0
% 242.18/48.69  | | | | | | | | 
% 242.18/48.69  | | | | | | | | REF_CLOSE: (13), (60), (142) are inconsistent by sub-proof
% 242.18/48.69  | | | | | | | |            #2033.
% 242.18/48.69  | | | | | | | | 
% 242.18/48.69  | | | | | | | End of split
% 242.18/48.69  | | | | | | | 
% 242.18/48.69  | | | | | | End of split
% 242.18/48.69  | | | | | | 
% 242.18/48.69  | | | | | End of split
% 242.18/48.69  | | | | | 
% 242.18/48.69  | | | | End of split
% 242.18/48.69  | | | | 
% 242.18/48.69  | | | End of split
% 242.18/48.69  | | | 
% 242.18/48.69  | | Case 2:
% 242.18/48.69  | | | 
% 242.18/48.69  | | |   (143)  all_58_7 = e3 & op(e1, e2) = e3
% 242.18/48.69  | | | 
% 242.18/48.69  | | | ALPHA: (143) implies:
% 242.18/48.69  | | |   (144)  op(e1, e2) = e3
% 242.18/48.69  | | | 
% 242.18/48.69  | | | REF_CLOSE: (16), (64), (82), (144) are inconsistent by sub-proof #2191.
% 242.18/48.69  | | | 
% 242.18/48.69  | | End of split
% 242.18/48.69  | | 
% 242.18/48.69  | Case 2:
% 242.18/48.69  | | 
% 242.18/48.69  | |   (145)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 242.18/48.69  | |            e3)
% 242.18/48.69  | | 
% 242.18/48.69  | | REF_CLOSE: (9), (27), (47), (60), (145) are inconsistent by sub-proof #693.
% 242.18/48.69  | | 
% 242.18/48.69  | End of split
% 242.18/48.69  | 
% 242.18/48.69  End of proof
% 242.18/48.69  
% 242.18/48.69  Sub-proof #693 shows that the following formulas are inconsistent:
% 242.18/48.69  ----------------------------------------------------------------
% 242.18/48.69    (1)   ~ (e3 = e0)
% 242.18/48.69    (2)  all_58_8 = e0
% 242.18/48.69    (3)   ~ (e3 = e2)
% 242.18/48.69    (4)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.18/48.69    (5)  all_58_11 = e2
% 242.18/48.69  
% 242.18/48.69  Begin of proof
% 242.18/48.69  | 
% 242.18/48.69  | BETA: splitting (4) gives:
% 242.18/48.69  | 
% 242.18/48.69  | Case 1:
% 242.18/48.69  | | 
% 242.18/48.69  | |   (6)  all_58_8 = e3 & op(e1, e1) = e3
% 242.18/48.69  | | 
% 242.18/48.69  | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #694.
% 242.18/48.69  | | 
% 242.18/48.69  | Case 2:
% 242.18/48.69  | | 
% 242.18/48.69  | |   (7)  all_58_11 = e3 & op(e1, e0) = e3
% 242.18/48.69  | | 
% 242.18/48.69  | | ALPHA: (7) implies:
% 242.18/48.69  | |   (8)  all_58_11 = e3
% 242.18/48.69  | | 
% 242.18/48.69  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #2030.
% 242.18/48.69  | | 
% 242.18/48.69  | End of split
% 242.18/48.69  | 
% 242.18/48.69  End of proof
% 242.18/48.69  
% 242.18/48.69  Sub-proof #694 shows that the following formulas are inconsistent:
% 242.18/48.69  ----------------------------------------------------------------
% 242.18/48.69    (1)  all_58_8 = e3 & op(e1, e1) = e3
% 242.18/48.69    (2)  all_58_8 = e0
% 242.18/48.69    (3)   ~ (e3 = e0)
% 242.18/48.69  
% 242.18/48.69  Begin of proof
% 242.18/48.69  | 
% 242.18/48.69  | ALPHA: (1) implies:
% 242.18/48.69  |   (4)  all_58_8 = e3
% 242.18/48.69  | 
% 242.18/48.69  | COMBINE_EQS: (2), (4) imply:
% 242.18/48.69  |   (5)  e3 = e0
% 242.18/48.69  | 
% 242.18/48.69  | REDUCE: (3), (5) imply:
% 242.18/48.69  |   (6)  $false
% 242.18/48.69  | 
% 242.18/48.69  | CLOSE: (6) is inconsistent.
% 242.18/48.69  | 
% 242.18/48.69  End of proof
% 242.18/48.69  
% 242.18/48.69  Sub-proof #695 shows that the following formulas are inconsistent:
% 242.18/48.69  ----------------------------------------------------------------
% 242.18/48.69    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.69         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.69    (2)   ~ (e3 = e0)
% 242.18/48.69    (3)   ~ (e2 = e0)
% 242.18/48.69    (4)  all_58_4 = e2
% 242.18/48.69    (5)  op(e3, e3) = e1
% 242.18/48.69    (6)   ~ (e3 = e2)
% 242.18/48.69    (7)  op(e2, e0) = e0
% 242.18/48.69    (8)  all_58_9 = e3
% 242.18/48.69    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.18/48.69         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.69    (10)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.18/48.69    (11)  all_58_5 = e1
% 242.18/48.69    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.69    (13)   ~ (e1 = e0)
% 242.18/48.69    (14)   ~ (e2 = e1)
% 242.18/48.69  
% 242.18/48.69  Begin of proof
% 242.18/48.69  | 
% 242.18/48.69  | BETA: splitting (10) gives:
% 242.18/48.69  | 
% 242.18/48.69  | Case 1:
% 242.18/48.69  | | 
% 242.18/48.69  | |   (15)  all_58_5 = e2 & op(e2, e1) = e2
% 242.18/48.69  | | 
% 242.18/48.69  | | ALPHA: (15) implies:
% 242.18/48.69  | |   (16)  all_58_5 = e2
% 242.18/48.69  | | 
% 242.18/48.69  | | COMBINE_EQS: (11), (16) imply:
% 242.18/48.69  | |   (17)  e2 = e1
% 242.18/48.69  | | 
% 242.18/48.69  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (12), (13), (14), (17)
% 242.18/48.69  | |            are inconsistent by sub-proof #714.
% 242.18/48.69  | | 
% 242.18/48.69  | Case 2:
% 242.18/48.69  | | 
% 242.18/48.69  | |   (18)  all_58_10 = e2 & op(e2, e0) = e2
% 242.18/48.69  | | 
% 242.18/48.69  | | ALPHA: (18) implies:
% 242.18/48.69  | |   (19)  op(e2, e0) = e2
% 242.18/48.69  | | 
% 242.18/48.69  | | REF_CLOSE: (3), (7), (12), (19) are inconsistent by sub-proof #2121.
% 242.18/48.69  | | 
% 242.18/48.69  | End of split
% 242.18/48.69  | 
% 242.18/48.69  End of proof
% 242.18/48.69  
% 242.18/48.69  Sub-proof #696 shows that the following formulas are inconsistent:
% 242.18/48.69  ----------------------------------------------------------------
% 242.18/48.69    (1)   ~ (e3 = e0)
% 242.18/48.69    (2)  all_58_6 = e3
% 242.18/48.69    (3)   ~ (e2 = e0)
% 242.18/48.69    (4)   ~ (e3 = e1)
% 242.18/48.69    (5)  all_58_3 = e3
% 242.18/48.69    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.18/48.69         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.18/48.69    (7)  op(e3, e3) = e1
% 242.18/48.69    (8)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.69             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.18/48.69               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.18/48.69               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.18/48.69    (9)   ~ (e3 = e2)
% 242.18/48.69    (10)  all_58_15 = e1
% 242.18/48.69    (11)  all_58_3 = e2 & op(e2, e2) = e2
% 242.18/48.69    (12)  op(e2, e3) = all_52_1
% 242.18/48.69    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.69    (14)  all_58_14 = e3
% 242.18/48.69    (15)   ~ (e1 = e0)
% 242.18/48.69    (16)   ~ (all_52_1 = e3)
% 242.18/48.69    (17)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.69          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.18/48.69            e2)
% 242.18/48.69    (18)   ~ (e2 = e1)
% 242.18/48.69  
% 242.18/48.69  Begin of proof
% 242.18/48.69  | 
% 242.18/48.69  | ALPHA: (11) implies:
% 242.18/48.69  |   (19)  all_58_3 = e2
% 242.18/48.69  | 
% 242.18/48.69  | COMBINE_EQS: (5), (19) imply:
% 242.18/48.69  |   (20)  e3 = e2
% 242.18/48.69  | 
% 242.18/48.69  | SIMP: (20) implies:
% 242.18/48.69  |   (21)  e3 = e2
% 242.18/48.69  | 
% 242.18/48.69  | COMBINE_EQS: (2), (21) imply:
% 242.18/48.69  |   (22)  all_58_6 = e2
% 242.18/48.69  | 
% 242.18/48.69  | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14), (15),
% 242.18/48.69  |            (16), (17), (18), (22) are inconsistent by sub-proof #1166.
% 242.18/48.69  | 
% 242.18/48.69  End of proof
% 242.18/48.69  
% 242.18/48.69  Sub-proof #697 shows that the following formulas are inconsistent:
% 242.18/48.69  ----------------------------------------------------------------
% 242.18/48.69    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.69         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.69    (2)   ~ (e3 = e0)
% 242.18/48.69    (3)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.18/48.69    (4)   ~ (e2 = e0)
% 242.18/48.69    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.70         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.18/48.70    (6)  all_58_4 = e2
% 242.18/48.70    (7)  op(e0, e2) = e2
% 242.18/48.70    (8)  all_58_3 = e3
% 242.18/48.70    (9)  op(e3, e3) = e1
% 242.18/48.70    (10)   ~ (e3 = e2)
% 242.18/48.70    (11)  all_58_9 = e3
% 242.18/48.70    (12)  op(e1, e1) = e2
% 242.18/48.70    (13)  all_58_5 = e1
% 242.18/48.70    (14)  all_58_7 = e1
% 242.18/48.70    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.70    (16)  op(e1, e1) = e0
% 242.18/48.70    (17)   ~ (e1 = e0)
% 242.18/48.70    (18)   ~ (e2 = e1)
% 242.18/48.70  
% 242.18/48.70  Begin of proof
% 242.18/48.70  | 
% 242.18/48.70  | BETA: splitting (3) gives:
% 242.18/48.70  | 
% 242.18/48.70  | Case 1:
% 242.18/48.70  | | 
% 242.18/48.70  | |   (19)  all_58_5 = e0 & op(e2, e1) = e0
% 242.18/48.70  | | 
% 242.18/48.70  | | REF_CLOSE: (13), (17), (19) are inconsistent by sub-proof #1103.
% 242.18/48.70  | | 
% 242.18/48.70  | Case 2:
% 242.18/48.70  | | 
% 242.18/48.70  | | 
% 242.18/48.70  | | GROUND_INST: instantiating (15) with e0, e2, e1, e1, simplifying with (12),
% 242.18/48.70  | |              (16) gives:
% 242.18/48.70  | |   (20)  e2 = e0
% 242.18/48.70  | | 
% 242.18/48.70  | | COMBINE_EQS: (6), (20) imply:
% 242.18/48.70  | |   (21)  all_58_4 = e0
% 242.18/48.70  | | 
% 242.18/48.70  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (14), (15), (17),
% 242.18/48.70  | |            (18), (21) are inconsistent by sub-proof #719.
% 242.18/48.70  | | 
% 242.18/48.70  | End of split
% 242.18/48.70  | 
% 242.18/48.70  End of proof
% 242.18/48.70  
% 242.18/48.70  Sub-proof #698 shows that the following formulas are inconsistent:
% 242.18/48.70  ----------------------------------------------------------------
% 242.18/48.70    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.70         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.70    (2)   ~ (e3 = e0)
% 242.18/48.70    (3)   ~ (e2 = e0)
% 242.18/48.70    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.70         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.18/48.70    (5)  all_58_4 = e2
% 242.18/48.70    (6)  op(e0, e2) = e2
% 242.18/48.70    (7)  all_58_2 = e2
% 242.18/48.70    (8)  all_58_3 = e3
% 242.18/48.70    (9)  op(e3, e3) = e1
% 242.18/48.70    (10)   ~ (e3 = e2)
% 242.18/48.70    (11)  all_58_2 = e0 & op(e2, e3) = e0
% 242.18/48.70    (12)  all_58_9 = e3
% 242.18/48.70    (13)  all_58_7 = e1
% 242.18/48.70    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.70    (15)   ~ (e1 = e0)
% 242.18/48.70    (16)   ~ (e2 = e1)
% 242.18/48.70  
% 242.18/48.70  Begin of proof
% 242.18/48.70  | 
% 242.18/48.70  | ALPHA: (11) implies:
% 242.18/48.70  |   (17)  all_58_2 = e0
% 242.18/48.70  | 
% 242.18/48.70  | COMBINE_EQS: (7), (17) imply:
% 242.18/48.70  |   (18)  e2 = e0
% 242.18/48.70  | 
% 242.18/48.70  | SIMP: (18) implies:
% 242.18/48.70  |   (19)  e2 = e0
% 242.18/48.70  | 
% 242.18/48.70  | COMBINE_EQS: (5), (19) imply:
% 242.18/48.70  |   (20)  all_58_4 = e0
% 242.18/48.70  | 
% 242.18/48.70  | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (13), (14), (15),
% 242.18/48.70  |            (16), (20) are inconsistent by sub-proof #719.
% 242.18/48.70  | 
% 242.18/48.70  End of proof
% 242.18/48.70  
% 242.18/48.70  Sub-proof #699 shows that the following formulas are inconsistent:
% 242.18/48.70  ----------------------------------------------------------------
% 242.18/48.70    (1)   ~ (e3 = e0)
% 242.18/48.70    (2)  all_58_6 = e3
% 242.18/48.70    (3)   ~ (e2 = e0)
% 242.18/48.70    (4)   ~ (e3 = e1)
% 242.18/48.70    (5)  all_58_3 = e3
% 242.18/48.70    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.18/48.70         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.18/48.70    (7)  op(e3, e3) = e1
% 242.18/48.70    (8)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.70             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.18/48.70               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.18/48.70               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.18/48.70    (9)   ~ (e3 = e2)
% 242.18/48.70    (10)  all_58_15 = e1
% 242.18/48.70    (11)  all_58_3 = e2 & op(e2, e2) = e2
% 242.18/48.70    (12)  op(e2, e3) = all_52_1
% 242.18/48.70    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.70    (14)  all_58_14 = e3
% 242.18/48.70    (15)   ~ (e1 = e0)
% 242.18/48.70    (16)   ~ (all_52_1 = e3)
% 242.18/48.70    (17)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.70          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.18/48.70            e2)
% 242.18/48.70    (18)   ~ (e2 = e1)
% 242.18/48.70  
% 242.18/48.70  Begin of proof
% 242.18/48.70  | 
% 242.18/48.70  | ALPHA: (11) implies:
% 242.18/48.70  |   (19)  all_58_3 = e2
% 242.18/48.70  | 
% 242.18/48.70  | COMBINE_EQS: (5), (19) imply:
% 242.18/48.70  |   (20)  e3 = e2
% 242.18/48.70  | 
% 242.18/48.70  | COMBINE_EQS: (2), (20) imply:
% 242.18/48.70  |   (21)  all_58_6 = e2
% 242.18/48.70  | 
% 242.18/48.70  | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14), (15),
% 242.18/48.70  |            (16), (17), (18), (21) are inconsistent by sub-proof #1166.
% 242.18/48.70  | 
% 242.18/48.70  End of proof
% 242.18/48.70  
% 242.18/48.70  Sub-proof #700 shows that the following formulas are inconsistent:
% 242.18/48.70  ----------------------------------------------------------------
% 242.18/48.70    (1)   ~ (all_52_1 = all_52_3)
% 242.18/48.70    (2)  all_56_21 = e2
% 242.18/48.70    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.18/48.70    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.70         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.70    (5)   ~ (all_52_3 = e1)
% 242.18/48.70    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.18/48.70    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.18/48.70         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.70    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.18/48.70           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.18/48.70             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.18/48.70    (9)   ~ (e3 = e0)
% 242.18/48.70    (10)  op(e0, e1) = all_52_11
% 242.18/48.70    (11)  all_42_2 = e3
% 242.18/48.70    (12)  all_58_6 = e3
% 242.18/48.70    (13)  op(e1, e2) = e1
% 242.18/48.70    (14)   ~ (e2 = e0)
% 242.18/48.70    (15)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.18/48.70          (all_58_11 = e0 & op(e1, e0) = e0)
% 242.18/48.70    (16)   ~ (all_52_11 = e2)
% 242.18/48.70    (17)  all_54_13 = all_52_7
% 242.18/48.70    (18)  op(e1, e2) = all_52_6
% 242.18/48.70    (19)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.18/48.70          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.70    (20)   ~ (all_52_11 = e1)
% 242.18/48.70    (21)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.18/48.70              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.18/48.70            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.18/48.70            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.18/48.70            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.18/48.70             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.70            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.18/48.70            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.18/48.70            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.18/48.70            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.70            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.18/48.70              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.18/48.70            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.18/48.70            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.18/48.70            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.18/48.70            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.18/48.70            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.18/48.70            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.18/48.70              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.18/48.70            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.18/48.70            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.18/48.70            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.18/48.70            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.18/48.70            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.70            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.18/48.70              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.18/48.70            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.70            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.18/48.70    (22)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.70          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.18/48.70    (23)   ~ (all_52_7 = all_52_11)
% 242.18/48.70    (24)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.18/48.70            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.18/48.70              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.18/48.70    (25)   ~ (all_52_1 = all_52_2)
% 242.18/48.70    (26)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.18/48.70            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.18/48.70              e1) = all_20_1 & $i(all_20_1))
% 242.18/48.70    (27)   ~ (all_52_7 = e3)
% 242.18/48.70    (28)  all_58_8 = e0
% 242.18/48.70    (29)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.18/48.70    (30)  op(e0, e3) = all_52_3
% 242.18/48.70    (31)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.18/48.70          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.18/48.70    (32)   ~ (e3 = e1)
% 242.18/48.70    (33)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.18/48.70          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.18/48.70    (34)   ~ (all_52_2 = all_52_3)
% 242.18/48.70    (35)   ~ (all_52_8 = e1)
% 242.18/48.70    (36)  all_58_3 = e3
% 242.18/48.70    (37)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.18/48.70          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.18/48.70    (38)   ~ (all_52_2 = e1)
% 242.18/48.70    (39)  op(all_40_1, e1) = all_40_0
% 242.18/48.70    (40)  all_54_2 = all_52_8
% 242.18/48.70    (41)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.18/48.70          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.18/48.70    (42)  op(e3, e3) = e1
% 242.18/48.70    (43)   ~ (all_52_3 = all_52_7)
% 242.18/48.70    (44)  all_54_4 = all_52_1
% 242.18/48.70    (45)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.70              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.18/48.70                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.18/48.70                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.18/48.70    (46)  op(e2, e1) = all_52_9
% 242.18/48.70    (47)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.18/48.70          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.18/48.70    (48)   ~ (e3 = e2)
% 242.18/48.70    (49)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.18/48.70          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.18/48.70    (50)   ~ (all_52_7 = e1)
% 242.18/48.70    (51)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.18/48.70    (52)   ~ (all_52_3 = all_52_11)
% 242.18/48.70    (53)  all_56_31 = e1
% 242.18/48.70    (54)  all_54_12 = all_52_3
% 242.18/48.70    (55)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.18/48.70    (56)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.18/48.70          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.18/48.70    (57)  all_58_15 = e1
% 242.18/48.70    (58)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.18/48.70          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.18/48.70    (59)  all_58_9 = e3
% 242.18/48.70    (60)  op(e3, e0) = e3
% 242.18/48.70    (61)  all_58_11 = e2
% 242.18/48.70    (62)  op(e2, e3) = all_52_1
% 242.18/48.70    (63)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.18/48.70          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.70    (64)  all_34_2 = e1
% 242.18/48.70    (65)   ~ (all_52_6 = e3)
% 242.18/48.70    (66)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.18/48.70    (67)  op(e1, e1) = e2
% 242.18/48.70    (68)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.18/48.70          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.18/48.70    (69)  op(e0, e2) = all_52_7
% 242.18/48.70    (70)  all_54_1 = all_52_4
% 242.18/48.70    (71)   ~ (all_52_4 = e3)
% 242.18/48.70    (72)  op(e3, e2) = all_52_4
% 242.18/48.70    (73)   ~ (all_52_8 = all_52_11)
% 242.18/48.70    (74)   ~ (all_40_0 = e0)
% 242.18/48.70    (75)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.18/48.70    (76)  all_58_5 = e1
% 242.18/48.70    (77)  all_58_7 = e1
% 242.18/48.70    (78)  all_58_1 = e2
% 242.18/48.70    (79)   ~ (all_52_2 = e2)
% 242.18/48.70    (80)   ~ (all_52_9 = e3)
% 242.18/48.70    (81)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.18/48.70          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.70    (82)  all_54_8 = all_52_2
% 242.18/48.70    (83)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.70          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.18/48.70    (84)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.70    (85)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.18/48.70          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.18/48.70    (86)  all_56_11 = e3
% 242.18/48.70    (87)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.18/48.70            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.18/48.70              e2) = all_36_1 & $i(all_36_1))
% 242.18/48.70    (88)  op(e1, e2) = all_40_1
% 242.18/48.70    (89)   ~ (all_52_4 = e1)
% 242.18/48.70    (90)   ~ (e1 = e0)
% 242.18/48.70    (91)   ~ (all_52_8 = e2)
% 242.18/48.70    (92)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.18/48.70          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.18/48.70    (93)   ~ (all_52_1 = e3)
% 242.18/48.70    (94)  all_54_14 = all_52_11
% 242.18/48.71    (95)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.71          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.18/48.71            e2)
% 242.18/48.71    (96)   ~ (all_52_4 = all_52_8)
% 242.18/48.71    (97)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.18/48.71            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.18/48.71            & $i(all_8_1))
% 242.18/48.71    (98)   ~ (e2 = e1)
% 242.18/48.71    (99)   ~ (all_52_1 = e1)
% 242.18/48.71    (100)   ~ (all_52_4 = all_52_7)
% 242.18/48.71  
% 242.18/48.71  Begin of proof
% 242.18/48.71  | 
% 242.18/48.71  | BETA: splitting (49) gives:
% 242.18/48.71  | 
% 242.18/48.71  | Case 1:
% 242.18/48.71  | | 
% 242.18/48.71  | |   (101)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 242.18/48.71  | |            e2)
% 242.18/48.71  | | 
% 242.18/48.71  | | BETA: splitting (101) gives:
% 242.18/48.71  | | 
% 242.18/48.71  | | Case 1:
% 242.18/48.71  | | | 
% 242.18/48.71  | | |   (102)  all_58_4 = e2 & op(e3, e1) = e2
% 242.18/48.71  | | | 
% 242.18/48.71  | | | ALPHA: (102) implies:
% 242.18/48.71  | | |   (103)  all_58_4 = e2
% 242.18/48.71  | | | 
% 242.18/48.71  | | | REF_CLOSE: (9), (14), (42), (59), (63), (78), (84), (90), (103) are
% 242.18/48.71  | | |            inconsistent by sub-proof #708.
% 242.18/48.71  | | | 
% 242.18/48.71  | | Case 2:
% 242.18/48.71  | | | 
% 242.18/48.71  | | |   (104)  all_58_5 = e2 & op(e2, e1) = e2
% 242.18/48.71  | | | 
% 242.18/48.71  | | | ALPHA: (104) implies:
% 242.18/48.71  | | |   (105)  all_58_5 = e2
% 242.18/48.71  | | | 
% 242.18/48.71  | | | REF_CLOSE: (76), (98), (105) are inconsistent by sub-proof #1665.
% 242.18/48.71  | | | 
% 242.18/48.71  | | End of split
% 242.18/48.71  | | 
% 242.18/48.71  | Case 2:
% 242.18/48.71  | | 
% 242.18/48.71  | |   (106)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 242.18/48.71  | |            e2)
% 242.18/48.71  | | 
% 242.18/48.71  | | BETA: splitting (106) gives:
% 242.18/48.71  | | 
% 242.18/48.71  | | Case 1:
% 242.18/48.71  | | | 
% 242.18/48.71  | | |   (107)  all_58_8 = e2 & op(e1, e1) = e2
% 242.18/48.71  | | | 
% 242.18/48.71  | | | ALPHA: (107) implies:
% 242.18/48.71  | | |   (108)  all_58_8 = e2
% 242.18/48.71  | | | 
% 242.18/48.71  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 242.18/48.71  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 242.18/48.71  | | |            (26), (27), (29), (30), (32), (33), (34), (35), (36), (37),
% 242.18/48.71  | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 242.18/48.71  | | |            (48), (50), (51), (52), (53), (54), (55), (57), (58), (62),
% 242.18/48.71  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 242.18/48.71  | | |            (73), (74), (75), (76), (77), (79), (80), (81), (82), (83),
% 242.18/48.71  | | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 242.18/48.71  | | |            (94), (95), (96), (97), (98), (99), (100), (108) are
% 242.18/48.71  | | |            inconsistent by sub-proof #715.
% 242.18/48.71  | | | 
% 242.18/48.71  | | Case 2:
% 242.18/48.71  | | | 
% 242.18/48.71  | | |   (109)  all_58_14 = e2 & op(e0, e1) = e2
% 242.18/48.71  | | | 
% 242.18/48.71  | | | ALPHA: (109) implies:
% 242.18/48.71  | | |   (110)  all_58_14 = e2
% 242.18/48.71  | | | 
% 242.18/48.71  | | | BETA: splitting (15) gives:
% 242.18/48.71  | | | 
% 242.18/48.71  | | | Case 1:
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | |   (111)  all_58_9 = e0 & op(e3, e0) = e0
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 242.18/48.71  | | | |            (12), (13), (14), (16), (17), (18), (19), (20), (21), (22),
% 242.18/48.71  | | | |            (23), (24), (25), (26), (27), (29), (30), (32), (33), (34),
% 242.18/48.71  | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 242.18/48.71  | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 242.18/48.71  | | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 242.18/48.71  | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 242.18/48.71  | | | |            (75), (76), (77), (79), (80), (81), (82), (83), (84), (85),
% 242.18/48.71  | | | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 242.18/48.71  | | | |            (96), (97), (98), (99), (100), (111) are inconsistent by
% 242.18/48.71  | | | |            sub-proof #704.
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | Case 2:
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | |   (112)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 242.18/48.71  | | | |              e0) = e0)
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | BETA: splitting (112) gives:
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | Case 1:
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | |   (113)  all_58_10 = e0 & op(e2, e0) = e0
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | | ALPHA: (113) implies:
% 242.18/48.71  | | | | |   (114)  op(e2, e0) = e0
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | | BETA: splitting (7) gives:
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | | Case 1:
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | |   (115)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 242.18/48.71  | | | | | |            op(e0, e2) = e3)
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | | BETA: splitting (115) gives:
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | | Case 1:
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | |   (116)  all_58_12 = e3 & op(e0, e3) = e3
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | | ALPHA: (116) implies:
% 242.18/48.71  | | | | | | |   (117)  all_58_12 = e3
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | | BETA: splitting (68) gives:
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | | Case 1:
% 242.18/48.71  | | | | | | | | 
% 242.18/48.71  | | | | | | | |   (118)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 242.18/48.71  | | | | | | | |            op(e2, e1) = e3)
% 242.18/48.71  | | | | | | | | 
% 242.18/48.71  | | | | | | | | BETA: splitting (118) gives:
% 242.18/48.71  | | | | | | | | 
% 242.18/48.71  | | | | | | | | Case 1:
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | |   (119)  all_58_4 = e3 & op(e3, e1) = e3
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | ALPHA: (119) implies:
% 242.18/48.71  | | | | | | | | |   (120)  all_58_4 = e3
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | BETA: splitting (56) gives:
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | Case 1:
% 242.18/48.71  | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | |   (121)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 242.18/48.71  | | | | | | | | | |            & op(e2, e3) = e0)
% 242.18/48.71  | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | REF_CLOSE: (4), (9), (14), (22), (31), (36), (42), (48),
% 242.18/48.71  | | | | | | | | | |            (57), (59), (63), (76), (77), (78), (84), (90),
% 242.18/48.71  | | | | | | | | | |            (95), (98), (110), (114), (117), (120), (121) are
% 242.18/48.71  | | | | | | | | | |            inconsistent by sub-proof #701.
% 242.18/48.71  | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | Case 2:
% 242.18/48.71  | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | |   (122)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0
% 242.18/48.71  | | | | | | | | | |            & op(e0, e3) = e0)
% 242.18/48.71  | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | BETA: splitting (122) gives:
% 242.18/48.71  | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | Case 1:
% 242.18/48.71  | | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | |   (123)  all_58_6 = e0 & op(e1, e3) = e0
% 242.18/48.71  | | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | | ALPHA: (123) implies:
% 242.18/48.71  | | | | | | | | | | |   (124)  all_58_6 = e0
% 242.18/48.71  | | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 242.18/48.71  | | | | | | | | | | |            (11), (13), (14), (16), (17), (18), (19), (20),
% 242.18/48.71  | | | | | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (29),
% 242.18/48.71  | | | | | | | | | | |            (30), (32), (33), (34), (35), (36), (37), (38),
% 242.18/48.71  | | | | | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46),
% 242.18/48.71  | | | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 242.18/48.71  | | | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 242.18/48.71  | | | | | | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70),
% 242.18/48.71  | | | | | | | | | | |            (71), (72), (73), (74), (75), (76), (77), (79),
% 242.18/48.71  | | | | | | | | | | |            (80), (81), (82), (83), (84), (85), (86), (87),
% 242.18/48.71  | | | | | | | | | | |            (88), (89), (90), (91), (92), (93), (94), (95),
% 242.18/48.71  | | | | | | | | | | |            (96), (97), (98), (99), (100), (117), (124) are
% 242.18/48.71  | | | | | | | | | | |            inconsistent by sub-proof #706.
% 242.18/48.71  | | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | Case 2:
% 242.18/48.71  | | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | |   (125)  all_58_12 = e0 & op(e0, e3) = e0
% 242.18/48.71  | | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | | ALPHA: (125) implies:
% 242.18/48.71  | | | | | | | | | | |   (126)  all_58_12 = e0
% 242.18/48.71  | | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | | COMBINE_EQS: (117), (126) imply:
% 242.18/48.71  | | | | | | | | | | |   (127)  e3 = e0
% 242.18/48.71  | | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | | SIMP: (127) implies:
% 242.18/48.71  | | | | | | | | | | |   (128)  e3 = e0
% 242.18/48.71  | | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | | COMBINE_EQS: (12), (128) imply:
% 242.18/48.71  | | | | | | | | | | |   (129)  all_58_6 = e0
% 242.18/48.71  | | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 242.18/48.71  | | | | | | | | | | |            (11), (13), (14), (16), (17), (18), (19), (20),
% 242.18/48.71  | | | | | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (29),
% 242.18/48.71  | | | | | | | | | | |            (30), (32), (33), (34), (35), (36), (37), (38),
% 242.18/48.71  | | | | | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46),
% 242.18/48.71  | | | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 242.18/48.71  | | | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 242.18/48.71  | | | | | | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70),
% 242.18/48.71  | | | | | | | | | | |            (71), (72), (73), (74), (75), (76), (77), (79),
% 242.18/48.71  | | | | | | | | | | |            (80), (81), (82), (83), (84), (85), (86), (87),
% 242.18/48.71  | | | | | | | | | | |            (88), (89), (90), (91), (92), (93), (94), (95),
% 242.18/48.71  | | | | | | | | | | |            (96), (97), (98), (99), (100), (117), (129) are
% 242.18/48.71  | | | | | | | | | | |            inconsistent by sub-proof #706.
% 242.18/48.71  | | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | | End of split
% 242.18/48.71  | | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | End of split
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | Case 2:
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | |   (130)  all_58_5 = e3 & op(e2, e1) = e3
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | REF_CLOSE: (46), (80), (84), (130) are inconsistent by
% 242.18/48.71  | | | | | | | | |            sub-proof #1822.
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | End of split
% 242.18/48.71  | | | | | | | | 
% 242.18/48.71  | | | | | | | Case 2:
% 242.18/48.71  | | | | | | | | 
% 242.18/48.71  | | | | | | | |   (131)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 242.18/48.71  | | | | | | | |            op(e0, e1) = e3)
% 242.18/48.71  | | | | | | | | 
% 242.18/48.71  | | | | | | | | BETA: splitting (131) gives:
% 242.18/48.71  | | | | | | | | 
% 242.18/48.71  | | | | | | | | Case 1:
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | |   (132)  all_58_8 = e3 & op(e1, e1) = e3
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | ALPHA: (132) implies:
% 242.18/48.71  | | | | | | | | |   (133)  all_58_8 = e3
% 242.18/48.71  | | | | | | | | |   (134)  op(e1, e1) = e3
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | COMBINE_EQS: (28), (133) imply:
% 242.18/48.71  | | | | | | | | |   (135)  e3 = e0
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | COMBINE_EQS: (12), (135) imply:
% 242.18/48.71  | | | | | | | | |   (136)  all_58_6 = e0
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 242.18/48.71  | | | | | | | | |            (11), (13), (14), (16), (17), (18), (19), (20),
% 242.18/48.71  | | | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (29),
% 242.18/48.71  | | | | | | | | |            (30), (32), (33), (34), (35), (36), (37), (38),
% 242.18/48.71  | | | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46),
% 242.18/48.71  | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 242.18/48.71  | | | | | | | | |            (55), (56), (57), (58), (59), (60), (62), (63),
% 242.18/48.71  | | | | | | | | |            (64), (65), (66), (67), (68), (69), (70), (71),
% 242.18/48.71  | | | | | | | | |            (72), (73), (74), (75), (76), (77), (79), (80),
% 242.18/48.71  | | | | | | | | |            (81), (82), (83), (84), (85), (86), (87), (88),
% 242.18/48.71  | | | | | | | | |            (89), (90), (91), (92), (93), (94), (95), (96),
% 242.18/48.71  | | | | | | | | |            (97), (98), (99), (100), (117), (133), (134), (136)
% 242.18/48.71  | | | | | | | | |            are inconsistent by sub-proof #707.
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | Case 2:
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | |   (137)  all_58_14 = e3 & op(e0, e1) = e3
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | ALPHA: (137) implies:
% 242.18/48.71  | | | | | | | | |   (138)  all_58_14 = e3
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | | REF_CLOSE: (9), (14), (45), (48), (57), (90), (95), (98),
% 242.18/48.71  | | | | | | | | |            (117), (138) are inconsistent by sub-proof #1863.
% 242.18/48.71  | | | | | | | | | 
% 242.18/48.71  | | | | | | | | End of split
% 242.18/48.71  | | | | | | | | 
% 242.18/48.71  | | | | | | | End of split
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | Case 2:
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | |   (139)  all_58_13 = e3 & op(e0, e2) = e3
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | | REF_CLOSE: (27), (69), (84), (139) are inconsistent by sub-proof
% 242.18/48.71  | | | | | | |            #1919.
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | End of split
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | Case 2:
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | |   (140)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 242.18/48.71  | | | | | |            op(e0, e0) = e3)
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | | BETA: splitting (140) gives:
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | | Case 1:
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | |   (141)  all_58_14 = e3 & op(e0, e1) = e3
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | | REF_CLOSE: (9), (12), (14), (32), (41), (42), (45), (48), (57),
% 242.18/48.71  | | | | | | |            (62), (84), (90), (93), (95), (98), (110), (141) are
% 242.18/48.71  | | | | | | |            inconsistent by sub-proof #1165.
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | Case 2:
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | |   (142)  all_58_15 = e3 & op(e0, e0) = e3
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | | REF_CLOSE: (32), (57), (142) are inconsistent by sub-proof #1915.
% 242.18/48.71  | | | | | | | 
% 242.18/48.71  | | | | | | End of split
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | End of split
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | Case 2:
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | |   (143)  all_58_11 = e0 & op(e1, e0) = e0
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | | REF_CLOSE: (14), (61), (143) are inconsistent by sub-proof #2033.
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | End of split
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | End of split
% 242.18/48.71  | | | 
% 242.18/48.71  | | End of split
% 242.18/48.71  | | 
% 242.18/48.71  | End of split
% 242.18/48.71  | 
% 242.18/48.71  End of proof
% 242.18/48.71  
% 242.18/48.71  Sub-proof #701 shows that the following formulas are inconsistent:
% 242.18/48.71  ----------------------------------------------------------------
% 242.18/48.71    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.71         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.71    (2)   ~ (e3 = e0)
% 242.18/48.71    (3)   ~ (e2 = e0)
% 242.18/48.71    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.71         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.18/48.71    (5)  all_58_14 = e2
% 242.18/48.71    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.18/48.71         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.18/48.71    (7)  all_58_3 = e3
% 242.18/48.71    (8)  op(e3, e3) = e1
% 242.18/48.71    (9)   ~ (e3 = e2)
% 242.18/48.71    (10)  op(e2, e0) = e0
% 242.18/48.71    (11)  all_58_15 = e1
% 242.18/48.71    (12)  all_58_9 = e3
% 242.18/48.71    (13)  all_58_12 = e3
% 242.18/48.71    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.18/48.71          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.71    (15)  all_58_5 = e1
% 242.18/48.71    (16)  all_58_7 = e1
% 242.18/48.71    (17)  all_58_1 = e2
% 242.18/48.71    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.71    (19)   ~ (e1 = e0)
% 242.18/48.71    (20)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 242.18/48.71    (21)  all_58_4 = e3
% 242.18/48.71    (22)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.71          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.18/48.71            e2)
% 242.18/48.71    (23)   ~ (e2 = e1)
% 242.18/48.71  
% 242.18/48.71  Begin of proof
% 242.18/48.71  | 
% 242.18/48.71  | BETA: splitting (20) gives:
% 242.18/48.71  | 
% 242.18/48.71  | Case 1:
% 242.18/48.71  | | 
% 242.18/48.71  | |   (24)  all_58_0 = e0 & op(e3, e3) = e0
% 242.18/48.71  | | 
% 242.18/48.71  | | ALPHA: (24) implies:
% 242.18/48.71  | |   (25)  op(e3, e3) = e0
% 242.18/48.71  | | 
% 242.18/48.71  | | REF_CLOSE: (8), (18), (19), (25) are inconsistent by sub-proof #1828.
% 242.18/48.71  | | 
% 242.18/48.71  | Case 2:
% 242.18/48.71  | | 
% 242.18/48.71  | |   (26)  all_58_2 = e0 & op(e2, e3) = e0
% 242.18/48.71  | | 
% 242.18/48.71  | | ALPHA: (26) implies:
% 242.18/48.71  | |   (27)  all_58_2 = e0
% 242.18/48.71  | | 
% 242.18/48.71  | | BETA: splitting (6) gives:
% 242.18/48.71  | | 
% 242.18/48.71  | | Case 1:
% 242.18/48.71  | | | 
% 242.18/48.71  | | |   (28)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 242.18/48.71  | | |           e2)
% 242.18/48.71  | | | 
% 242.18/48.71  | | | BETA: splitting (28) gives:
% 242.18/48.71  | | | 
% 242.18/48.71  | | | Case 1:
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | |   (29)  all_58_2 = e2 & op(e2, e3) = e2
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | ALPHA: (29) implies:
% 242.18/48.71  | | | |   (30)  all_58_2 = e2
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | COMBINE_EQS: (27), (30) imply:
% 242.18/48.71  | | | |   (31)  e2 = e0
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | COMBINE_EQS: (5), (31) imply:
% 242.18/48.71  | | | |   (32)  all_58_14 = e0
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | BETA: splitting (1) gives:
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | Case 1:
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | |   (33)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3,
% 242.18/48.71  | | | | |             e2) = e2)
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | | BETA: splitting (33) gives:
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | | Case 1:
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | |   (34)  all_58_0 = e2 & op(e3, e3) = e2
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | | ALPHA: (34) implies:
% 242.18/48.71  | | | | | |   (35)  op(e3, e3) = e2
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | | REF_CLOSE: (8), (18), (23), (35) are inconsistent by sub-proof
% 242.18/48.71  | | | | | |            #2267.
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | Case 2:
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | |   (36)  all_58_1 = e2 & op(e3, e2) = e2
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | | REF_CLOSE: (2), (3), (4), (7), (9), (11), (13), (16), (17), (19),
% 242.18/48.71  | | | | | |            (22), (23), (32) are inconsistent by sub-proof #735.
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | End of split
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | Case 2:
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | |   (37)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3,
% 242.18/48.71  | | | | |             e0) = e2)
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | | BETA: splitting (37) gives:
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | | Case 1:
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | |   (38)  all_58_4 = e2 & op(e3, e1) = e2
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | | REF_CLOSE: (9), (21), (38) are inconsistent by sub-proof #1476.
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | Case 2:
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | |   (39)  all_58_9 = e2 & op(e3, e0) = e2
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | | REF_CLOSE: (9), (12), (39) are inconsistent by sub-proof #732.
% 242.18/48.71  | | | | | | 
% 242.18/48.71  | | | | | End of split
% 242.18/48.71  | | | | | 
% 242.18/48.71  | | | | End of split
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | Case 2:
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | |   (40)  all_58_3 = e2 & op(e2, e2) = e2
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | ALPHA: (40) implies:
% 242.18/48.71  | | | |   (41)  all_58_3 = e2
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | COMBINE_EQS: (7), (41) imply:
% 242.18/48.71  | | | |   (42)  e3 = e2
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | COMBINE_EQS: (21), (42) imply:
% 242.18/48.71  | | | |   (43)  all_58_4 = e2
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | | REF_CLOSE: (2), (3), (8), (12), (14), (17), (18), (19), (43) are
% 242.18/48.71  | | | |            inconsistent by sub-proof #708.
% 242.18/48.71  | | | | 
% 242.18/48.71  | | | End of split
% 242.18/48.71  | | | 
% 242.18/48.71  | | Case 2:
% 242.18/48.71  | | | 
% 242.18/48.71  | | |   (44)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 242.18/48.71  | | |           e2)
% 242.18/48.71  | | | 
% 242.18/48.71  | | | REF_CLOSE: (3), (10), (15), (18), (23), (44) are inconsistent by sub-proof
% 242.18/48.71  | | |            #702.
% 242.18/48.71  | | | 
% 242.18/48.71  | | End of split
% 242.18/48.71  | | 
% 242.18/48.71  | End of split
% 242.18/48.71  | 
% 242.18/48.71  End of proof
% 242.18/48.71  
% 242.18/48.71  Sub-proof #702 shows that the following formulas are inconsistent:
% 242.18/48.71  ----------------------------------------------------------------
% 242.18/48.71    (1)   ~ (e2 = e0)
% 242.18/48.71    (2)  op(e2, e0) = e0
% 242.18/48.72    (3)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.18/48.72    (4)  all_58_5 = e1
% 242.18/48.72    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.72    (6)   ~ (e2 = e1)
% 242.18/48.72  
% 242.18/48.72  Begin of proof
% 242.18/48.72  | 
% 242.18/48.72  | BETA: splitting (3) gives:
% 242.18/48.72  | 
% 242.18/48.72  | Case 1:
% 242.18/48.72  | | 
% 242.18/48.72  | |   (7)  all_58_5 = e2 & op(e2, e1) = e2
% 242.18/48.72  | | 
% 242.18/48.72  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #703.
% 242.18/48.72  | | 
% 242.18/48.72  | Case 2:
% 242.18/48.72  | | 
% 242.18/48.72  | |   (8)  all_58_10 = e2 & op(e2, e0) = e2
% 242.18/48.72  | | 
% 242.18/48.72  | | ALPHA: (8) implies:
% 242.18/48.72  | |   (9)  op(e2, e0) = e2
% 242.18/48.72  | | 
% 242.18/48.72  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2121.
% 242.18/48.72  | | 
% 242.18/48.72  | End of split
% 242.18/48.72  | 
% 242.18/48.72  End of proof
% 242.18/48.72  
% 242.18/48.72  Sub-proof #703 shows that the following formulas are inconsistent:
% 242.18/48.72  ----------------------------------------------------------------
% 242.18/48.72    (1)  all_58_5 = e2 & op(e2, e1) = e2
% 242.18/48.72    (2)  all_58_5 = e1
% 242.18/48.72    (3)   ~ (e2 = e1)
% 242.18/48.72  
% 242.18/48.72  Begin of proof
% 242.18/48.72  | 
% 242.18/48.72  | ALPHA: (1) implies:
% 242.18/48.72  |   (4)  all_58_5 = e2
% 242.18/48.72  | 
% 242.18/48.72  | COMBINE_EQS: (2), (4) imply:
% 242.18/48.72  |   (5)  e2 = e1
% 242.18/48.72  | 
% 242.18/48.72  | REDUCE: (3), (5) imply:
% 242.18/48.72  |   (6)  $false
% 242.18/48.72  | 
% 242.18/48.72  | CLOSE: (6) is inconsistent.
% 242.18/48.72  | 
% 242.18/48.72  End of proof
% 242.18/48.72  
% 242.18/48.72  Sub-proof #704 shows that the following formulas are inconsistent:
% 242.18/48.72  ----------------------------------------------------------------
% 242.18/48.72    (1)   ~ (all_52_1 = all_52_3)
% 242.18/48.72    (2)  all_56_21 = e2
% 242.18/48.72    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.18/48.72    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.72         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.72    (5)   ~ (all_52_3 = e1)
% 242.18/48.72    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.18/48.72    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.18/48.72         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.72    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.18/48.72           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.18/48.72             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.18/48.72    (9)   ~ (e3 = e0)
% 242.18/48.72    (10)  op(e0, e1) = all_52_11
% 242.18/48.72    (11)  all_42_2 = e3
% 242.18/48.72    (12)  all_58_6 = e3
% 242.18/48.72    (13)  op(e1, e2) = e1
% 242.18/48.72    (14)   ~ (e2 = e0)
% 242.18/48.72    (15)   ~ (all_52_11 = e2)
% 242.18/48.72    (16)  all_54_13 = all_52_7
% 242.18/48.72    (17)  op(e1, e2) = all_52_6
% 242.18/48.72    (18)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.18/48.72          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.72    (19)   ~ (all_52_11 = e1)
% 242.18/48.72    (20)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.18/48.72              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.18/48.72            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.18/48.72            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.18/48.72            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.18/48.72             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.72            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.18/48.72            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.18/48.72            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.18/48.72            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.72            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.18/48.72              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.18/48.72            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.18/48.72            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.18/48.72            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.18/48.72            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.18/48.72            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.18/48.72            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.18/48.72              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.18/48.72            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.18/48.72            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.18/48.72            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.18/48.72            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.18/48.72            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.72            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.18/48.72              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.18/48.72            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.72            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.18/48.72    (21)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.72          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.18/48.72    (22)   ~ (all_52_7 = all_52_11)
% 242.18/48.72    (23)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.18/48.72            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.18/48.72              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.18/48.72    (24)   ~ (all_52_1 = all_52_2)
% 242.18/48.72    (25)  all_58_9 = e0 & op(e3, e0) = e0
% 242.18/48.72    (26)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.18/48.72            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.18/48.72              e1) = all_20_1 & $i(all_20_1))
% 242.18/48.72    (27)   ~ (all_52_7 = e3)
% 242.18/48.72    (28)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.18/48.72    (29)  op(e0, e3) = all_52_3
% 242.18/48.72    (30)   ~ (e3 = e1)
% 242.18/48.72    (31)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.18/48.72          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.18/48.72    (32)   ~ (all_52_2 = all_52_3)
% 242.18/48.72    (33)   ~ (all_52_8 = e1)
% 242.18/48.72    (34)  all_58_3 = e3
% 242.18/48.72    (35)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.18/48.72          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.18/48.72    (36)   ~ (all_52_2 = e1)
% 242.18/48.72    (37)  op(all_40_1, e1) = all_40_0
% 242.18/48.72    (38)  all_54_2 = all_52_8
% 242.18/48.72    (39)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.18/48.72          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.18/48.72    (40)  op(e3, e3) = e1
% 242.18/48.72    (41)   ~ (all_52_3 = all_52_7)
% 242.18/48.72    (42)  all_54_4 = all_52_1
% 242.18/48.72    (43)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.72              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.18/48.72                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.18/48.72                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.18/48.72    (44)  op(e2, e1) = all_52_9
% 242.18/48.72    (45)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.18/48.72          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.18/48.72    (46)   ~ (e3 = e2)
% 242.18/48.72    (47)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.18/48.72          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.18/48.72    (48)   ~ (all_52_7 = e1)
% 242.18/48.72    (49)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.18/48.72    (50)   ~ (all_52_3 = all_52_11)
% 242.18/48.72    (51)  all_56_31 = e1
% 242.18/48.72    (52)  all_54_12 = all_52_3
% 242.18/48.72    (53)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.18/48.72    (54)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.18/48.72          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.18/48.72    (55)  all_58_15 = e1
% 242.18/48.72    (56)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.18/48.72          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.18/48.72    (57)  all_58_9 = e3
% 242.18/48.72    (58)  op(e3, e0) = e3
% 242.18/48.72    (59)  all_58_11 = e2
% 242.18/48.72    (60)  op(e2, e3) = all_52_1
% 242.18/48.72    (61)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.18/48.72          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.72    (62)  all_34_2 = e1
% 242.18/48.72    (63)   ~ (all_52_6 = e3)
% 242.18/48.72    (64)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.18/48.72    (65)  op(e1, e1) = e2
% 242.18/48.72    (66)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.18/48.72          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.18/48.72    (67)  op(e0, e2) = all_52_7
% 242.18/48.72    (68)  all_54_1 = all_52_4
% 242.18/48.72    (69)   ~ (all_52_4 = e3)
% 242.18/48.72    (70)  op(e3, e2) = all_52_4
% 242.18/48.72    (71)   ~ (all_52_8 = all_52_11)
% 242.18/48.72    (72)   ~ (all_40_0 = e0)
% 242.18/48.72    (73)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.18/48.72    (74)  all_58_5 = e1
% 242.18/48.72    (75)  all_58_7 = e1
% 242.18/48.72    (76)   ~ (all_52_2 = e2)
% 242.18/48.72    (77)   ~ (all_52_9 = e3)
% 242.18/48.72    (78)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.18/48.72          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.72    (79)  all_54_8 = all_52_2
% 242.18/48.72    (80)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.72          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.18/48.72    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.72    (82)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.18/48.72          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.18/48.72    (83)  all_56_11 = e3
% 242.18/48.72    (84)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.18/48.72            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.18/48.72              e2) = all_36_1 & $i(all_36_1))
% 242.18/48.72    (85)  op(e1, e2) = all_40_1
% 242.18/48.72    (86)   ~ (all_52_4 = e1)
% 242.18/48.72    (87)   ~ (e1 = e0)
% 242.18/48.72    (88)   ~ (all_52_8 = e2)
% 242.18/48.72    (89)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.18/48.72          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.18/48.72    (90)   ~ (all_52_1 = e3)
% 242.18/48.72    (91)  all_54_14 = all_52_11
% 242.18/48.72    (92)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.72          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.18/48.72            e2)
% 242.18/48.72    (93)   ~ (all_52_4 = all_52_8)
% 242.18/48.72    (94)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.18/48.72            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.18/48.72            & $i(all_8_1))
% 242.18/48.72    (95)   ~ (e2 = e1)
% 242.18/48.72    (96)   ~ (all_52_1 = e1)
% 242.18/48.72    (97)   ~ (all_52_4 = all_52_7)
% 242.18/48.72  
% 242.18/48.72  Begin of proof
% 242.18/48.72  | 
% 242.18/48.72  | ALPHA: (25) implies:
% 242.18/48.72  |   (98)  all_58_9 = e0
% 242.18/48.72  | 
% 242.18/48.72  | COMBINE_EQS: (57), (98) imply:
% 242.18/48.72  |   (99)  e3 = e0
% 242.18/48.72  | 
% 242.18/48.72  | COMBINE_EQS: (12), (99) imply:
% 242.18/48.72  |   (100)  all_58_6 = e0
% 242.18/48.72  | 
% 242.18/48.72  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 242.18/48.72  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 242.18/48.72  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 242.18/48.72  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 242.18/48.72  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 242.18/48.72  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 242.18/48.72  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 242.18/48.72  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 242.18/48.72  |            (92), (93), (94), (95), (96), (97), (100) are inconsistent by
% 242.18/48.72  |            sub-proof #705.
% 242.18/48.72  | 
% 242.18/48.72  End of proof
% 242.18/48.72  
% 242.18/48.72  Sub-proof #705 shows that the following formulas are inconsistent:
% 242.18/48.72  ----------------------------------------------------------------
% 242.18/48.72    (1)   ~ (all_52_1 = all_52_3)
% 242.18/48.72    (2)  all_56_21 = e2
% 242.18/48.72    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.18/48.72    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.72         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.72    (5)   ~ (all_52_3 = e1)
% 242.18/48.72    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.18/48.72    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.18/48.72         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.72    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.18/48.72           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.18/48.72             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.18/48.72    (9)   ~ (e3 = e0)
% 242.18/48.72    (10)  op(e0, e1) = all_52_11
% 242.18/48.72    (11)  all_42_2 = e3
% 242.18/48.72    (12)  op(e1, e2) = e1
% 242.18/48.72    (13)   ~ (e2 = e0)
% 242.18/48.72    (14)   ~ (all_52_11 = e2)
% 242.18/48.72    (15)  all_54_13 = all_52_7
% 242.18/48.72    (16)  op(e1, e2) = all_52_6
% 242.18/48.72    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.18/48.72          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.72    (18)   ~ (all_52_11 = e1)
% 242.18/48.73    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.18/48.73              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.18/48.73            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.18/48.73            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.18/48.73            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.18/48.73             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.73            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.18/48.73            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.18/48.73            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.18/48.73            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.73            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.18/48.73              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.18/48.73            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.18/48.73            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.18/48.73            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.18/48.73            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.18/48.73            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.18/48.73            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.18/48.73              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.18/48.73            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.18/48.73            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.18/48.73            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.18/48.73            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.18/48.73            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.73            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.18/48.73              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.18/48.73            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.73            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.18/48.73    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.73          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.18/48.73    (21)   ~ (all_52_7 = all_52_11)
% 242.18/48.73    (22)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.18/48.73            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.18/48.73              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.18/48.73    (23)   ~ (all_52_1 = all_52_2)
% 242.18/48.73    (24)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.18/48.73            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.18/48.73              e1) = all_20_1 & $i(all_20_1))
% 242.18/48.73    (25)   ~ (all_52_7 = e3)
% 242.18/48.73    (26)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.18/48.73    (27)  op(e0, e3) = all_52_3
% 242.18/48.73    (28)   ~ (e3 = e1)
% 242.18/48.73    (29)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.18/48.73          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.18/48.73    (30)   ~ (all_52_2 = all_52_3)
% 242.18/48.73    (31)   ~ (all_52_8 = e1)
% 242.18/48.73    (32)  all_58_3 = e3
% 242.18/48.73    (33)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.18/48.73          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.18/48.73    (34)   ~ (all_52_2 = e1)
% 242.18/48.73    (35)  op(all_40_1, e1) = all_40_0
% 242.18/48.73    (36)  all_54_2 = all_52_8
% 242.18/48.73    (37)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.18/48.73          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.18/48.73    (38)  op(e3, e3) = e1
% 242.18/48.73    (39)   ~ (all_52_3 = all_52_7)
% 242.18/48.73    (40)  all_54_4 = all_52_1
% 242.18/48.73    (41)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.73              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.18/48.73                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.18/48.73                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.18/48.73    (42)  op(e2, e1) = all_52_9
% 242.18/48.73    (43)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.18/48.73          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.18/48.73    (44)   ~ (e3 = e2)
% 242.18/48.73    (45)  all_58_6 = e0
% 242.18/48.73    (46)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.18/48.73          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.18/48.73    (47)   ~ (all_52_7 = e1)
% 242.18/48.73    (48)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.18/48.73    (49)   ~ (all_52_3 = all_52_11)
% 242.18/48.73    (50)  all_56_31 = e1
% 242.18/48.73    (51)  all_54_12 = all_52_3
% 242.18/48.73    (52)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.18/48.73    (53)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.18/48.73          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.18/48.73    (54)  all_58_15 = e1
% 242.18/48.73    (55)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.18/48.73          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.18/48.73    (56)  all_58_9 = e3
% 242.18/48.73    (57)  op(e3, e0) = e3
% 242.18/48.73    (58)  all_58_11 = e2
% 242.18/48.73    (59)  op(e2, e3) = all_52_1
% 242.18/48.73    (60)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.18/48.73          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.73    (61)  all_34_2 = e1
% 242.18/48.73    (62)   ~ (all_52_6 = e3)
% 242.18/48.73    (63)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.18/48.73    (64)  op(e1, e1) = e2
% 242.18/48.73    (65)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.18/48.73          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.18/48.73    (66)  op(e0, e2) = all_52_7
% 242.18/48.73    (67)  all_54_1 = all_52_4
% 242.18/48.73    (68)   ~ (all_52_4 = e3)
% 242.18/48.73    (69)  op(e3, e2) = all_52_4
% 242.18/48.73    (70)   ~ (all_52_8 = all_52_11)
% 242.18/48.73    (71)   ~ (all_40_0 = e0)
% 242.18/48.73    (72)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.18/48.73    (73)  all_58_5 = e1
% 242.18/48.73    (74)  all_58_7 = e1
% 242.18/48.73    (75)   ~ (all_52_2 = e2)
% 242.18/48.73    (76)   ~ (all_52_9 = e3)
% 242.18/48.73    (77)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.18/48.73          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.73    (78)  all_54_8 = all_52_2
% 242.18/48.73    (79)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.73          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.18/48.73    (80)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.73    (81)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.18/48.73          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.18/48.73    (82)  all_56_11 = e3
% 242.18/48.73    (83)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.18/48.73            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.18/48.73              e2) = all_36_1 & $i(all_36_1))
% 242.18/48.73    (84)  op(e1, e2) = all_40_1
% 242.18/48.73    (85)   ~ (all_52_4 = e1)
% 242.18/48.73    (86)   ~ (e1 = e0)
% 242.18/48.73    (87)   ~ (all_52_8 = e2)
% 242.18/48.73    (88)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.18/48.73          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.18/48.73    (89)   ~ (all_52_1 = e3)
% 242.18/48.73    (90)  all_54_14 = all_52_11
% 242.18/48.73    (91)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.73          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.18/48.73            e2)
% 242.18/48.73    (92)   ~ (all_52_4 = all_52_8)
% 242.18/48.73    (93)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.18/48.73            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.18/48.73            & $i(all_8_1))
% 242.18/48.73    (94)   ~ (e2 = e1)
% 242.18/48.73    (95)   ~ (all_52_1 = e1)
% 242.18/48.73    (96)   ~ (all_52_4 = all_52_7)
% 242.18/48.73  
% 242.18/48.73  Begin of proof
% 242.18/48.73  | 
% 242.18/48.73  | BETA: splitting (37) gives:
% 242.18/48.73  | 
% 242.18/48.73  | Case 1:
% 242.18/48.73  | | 
% 242.18/48.73  | |   (97)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 242.18/48.73  | |           e3)
% 242.18/48.73  | | 
% 242.18/48.73  | | REF_CLOSE: (28), (38), (59), (80), (89), (97) are inconsistent by sub-proof
% 242.18/48.73  | |            #1208.
% 242.18/48.73  | | 
% 242.18/48.73  | Case 2:
% 242.18/48.73  | | 
% 242.18/48.73  | |   (98)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 242.18/48.73  | |           e3)
% 242.18/48.73  | | 
% 242.18/48.73  | | BETA: splitting (98) gives:
% 242.18/48.73  | | 
% 242.18/48.73  | | Case 1:
% 242.18/48.73  | | | 
% 242.18/48.73  | | |   (99)  all_58_6 = e3 & op(e1, e3) = e3
% 242.18/48.73  | | | 
% 242.18/48.73  | | | ALPHA: (99) implies:
% 242.18/48.73  | | |   (100)  all_58_6 = e3
% 242.18/48.73  | | | 
% 242.18/48.73  | | | REF_CLOSE: (9), (45), (100) are inconsistent by sub-proof #2222.
% 242.18/48.73  | | | 
% 242.18/48.73  | | Case 2:
% 242.18/48.73  | | | 
% 242.18/48.73  | | |   (101)  all_58_12 = e3 & op(e0, e3) = e3
% 242.18/48.73  | | | 
% 242.18/48.73  | | | ALPHA: (101) implies:
% 242.18/48.73  | | |   (102)  all_58_12 = e3
% 242.18/48.73  | | | 
% 242.18/48.73  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.18/48.73  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 242.18/48.73  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 242.18/48.73  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 242.18/48.73  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 242.18/48.73  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 242.18/48.73  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 242.18/48.73  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 242.18/48.73  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 242.18/48.73  | | |            (93), (94), (95), (96), (102) are inconsistent by sub-proof
% 242.18/48.73  | | |            #706.
% 242.18/48.73  | | | 
% 242.18/48.73  | | End of split
% 242.18/48.73  | | 
% 242.18/48.73  | End of split
% 242.18/48.73  | 
% 242.18/48.73  End of proof
% 242.18/48.73  
% 242.18/48.73  Sub-proof #706 shows that the following formulas are inconsistent:
% 242.18/48.73  ----------------------------------------------------------------
% 242.18/48.73    (1)   ~ (all_52_1 = all_52_3)
% 242.18/48.73    (2)  all_56_21 = e2
% 242.18/48.73    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.18/48.73    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.73         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.73    (5)   ~ (all_52_3 = e1)
% 242.18/48.73    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.18/48.73    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.18/48.73         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.73    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.18/48.73           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.18/48.73             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.18/48.73    (9)   ~ (e3 = e0)
% 242.18/48.73    (10)  op(e0, e1) = all_52_11
% 242.18/48.73    (11)  all_42_2 = e3
% 242.18/48.73    (12)  op(e1, e2) = e1
% 242.18/48.73    (13)   ~ (e2 = e0)
% 242.18/48.73    (14)   ~ (all_52_11 = e2)
% 242.18/48.73    (15)  all_54_13 = all_52_7
% 242.18/48.73    (16)  op(e1, e2) = all_52_6
% 242.18/48.73    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.18/48.73          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.73    (18)   ~ (all_52_11 = e1)
% 242.18/48.73    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.18/48.73              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.18/48.73            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.18/48.73            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.18/48.73            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.18/48.73             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.73            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.18/48.73            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.18/48.73            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.18/48.73            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.73            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.18/48.73              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.18/48.73            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.18/48.73            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.18/48.73            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.18/48.73            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.18/48.73            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.18/48.73            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.18/48.73              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.18/48.73            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.18/48.73            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.18/48.73            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.18/48.73            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.18/48.73            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.73            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.18/48.73              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.18/48.73            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.73            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.18/48.73    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.73          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.18/48.73    (21)   ~ (all_52_7 = all_52_11)
% 242.18/48.73    (22)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.18/48.73            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.18/48.73              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.18/48.73    (23)   ~ (all_52_1 = all_52_2)
% 242.18/48.73    (24)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.18/48.73            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.18/48.73              e1) = all_20_1 & $i(all_20_1))
% 242.18/48.73    (25)   ~ (all_52_7 = e3)
% 242.18/48.73    (26)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.18/48.73    (27)  op(e0, e3) = all_52_3
% 242.18/48.73    (28)   ~ (e3 = e1)
% 242.18/48.73    (29)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.18/48.73          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.18/48.73    (30)   ~ (all_52_2 = all_52_3)
% 242.18/48.73    (31)   ~ (all_52_8 = e1)
% 242.18/48.73    (32)  all_58_3 = e3
% 242.18/48.73    (33)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.18/48.73          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.18/48.73    (34)   ~ (all_52_2 = e1)
% 242.18/48.73    (35)  op(all_40_1, e1) = all_40_0
% 242.18/48.73    (36)  all_54_2 = all_52_8
% 242.18/48.73    (37)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.18/48.73          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.18/48.73    (38)  op(e3, e3) = e1
% 242.18/48.73    (39)   ~ (all_52_3 = all_52_7)
% 242.18/48.73    (40)  all_54_4 = all_52_1
% 242.18/48.73    (41)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.73              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.18/48.73                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.18/48.73                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.18/48.73    (42)  op(e2, e1) = all_52_9
% 242.18/48.73    (43)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.18/48.73          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.18/48.73    (44)   ~ (e3 = e2)
% 242.18/48.73    (45)  all_58_6 = e0
% 242.18/48.74    (46)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.18/48.74          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.18/48.74    (47)   ~ (all_52_7 = e1)
% 242.18/48.74    (48)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.18/48.74    (49)   ~ (all_52_3 = all_52_11)
% 242.18/48.74    (50)  all_56_31 = e1
% 242.18/48.74    (51)  all_54_12 = all_52_3
% 242.18/48.74    (52)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.18/48.74    (53)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.18/48.74          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.18/48.74    (54)  all_58_15 = e1
% 242.18/48.74    (55)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.18/48.74          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.18/48.74    (56)  all_58_9 = e3
% 242.18/48.74    (57)  op(e3, e0) = e3
% 242.18/48.74    (58)  all_58_11 = e2
% 242.18/48.74    (59)  op(e2, e3) = all_52_1
% 242.18/48.74    (60)  all_58_12 = e3
% 242.18/48.74    (61)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.18/48.74          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.74    (62)  all_34_2 = e1
% 242.18/48.74    (63)   ~ (all_52_6 = e3)
% 242.18/48.74    (64)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.18/48.74    (65)  op(e1, e1) = e2
% 242.18/48.74    (66)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.18/48.74          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.18/48.74    (67)  op(e0, e2) = all_52_7
% 242.18/48.74    (68)  all_54_1 = all_52_4
% 242.18/48.74    (69)   ~ (all_52_4 = e3)
% 242.18/48.74    (70)  op(e3, e2) = all_52_4
% 242.18/48.74    (71)   ~ (all_52_8 = all_52_11)
% 242.18/48.74    (72)   ~ (all_40_0 = e0)
% 242.18/48.74    (73)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.18/48.74    (74)  all_58_5 = e1
% 242.18/48.74    (75)  all_58_7 = e1
% 242.18/48.74    (76)   ~ (all_52_2 = e2)
% 242.18/48.74    (77)   ~ (all_52_9 = e3)
% 242.18/48.74    (78)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.18/48.74          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.74    (79)  all_54_8 = all_52_2
% 242.18/48.74    (80)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.74          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.18/48.74    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.74            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.74    (82)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.18/48.74          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.18/48.74    (83)  all_56_11 = e3
% 242.18/48.74    (84)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.18/48.74            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.18/48.74              e2) = all_36_1 & $i(all_36_1))
% 242.18/48.74    (85)  op(e1, e2) = all_40_1
% 242.18/48.74    (86)   ~ (all_52_4 = e1)
% 242.18/48.74    (87)   ~ (e1 = e0)
% 242.18/48.74    (88)   ~ (all_52_8 = e2)
% 242.18/48.74    (89)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.18/48.74          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.18/48.74    (90)   ~ (all_52_1 = e3)
% 242.18/48.74    (91)  all_54_14 = all_52_11
% 242.18/48.74    (92)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.74          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.18/48.74            e2)
% 242.18/48.74    (93)   ~ (all_52_4 = all_52_8)
% 242.18/48.74    (94)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.18/48.74            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.18/48.74            & $i(all_8_1))
% 242.18/48.74    (95)   ~ (e2 = e1)
% 242.18/48.74    (96)   ~ (all_52_1 = e1)
% 242.18/48.74    (97)   ~ (all_52_4 = all_52_7)
% 242.18/48.74  
% 242.18/48.74  Begin of proof
% 242.18/48.74  | 
% 242.18/48.74  | BETA: splitting (55) gives:
% 242.18/48.74  | 
% 242.18/48.74  | Case 1:
% 242.18/48.74  | | 
% 242.18/48.74  | |   (98)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 242.18/48.74  | |           e3)
% 242.18/48.74  | | 
% 242.18/48.74  | | REF_CLOSE: (9), (16), (45), (63), (81), (98) are inconsistent by sub-proof
% 242.18/48.74  | |            #1983.
% 242.18/48.74  | | 
% 242.18/48.74  | Case 2:
% 242.18/48.74  | | 
% 242.18/48.74  | |   (99)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 242.18/48.74  | |           e3)
% 242.18/48.74  | | 
% 242.18/48.74  | | BETA: splitting (99) gives:
% 242.18/48.74  | | 
% 242.18/48.74  | | Case 1:
% 242.18/48.74  | | | 
% 242.18/48.74  | | |   (100)  all_58_8 = e3 & op(e1, e1) = e3
% 242.18/48.74  | | | 
% 242.18/48.74  | | | ALPHA: (100) implies:
% 242.18/48.74  | | |   (101)  all_58_8 = e3
% 242.18/48.74  | | |   (102)  op(e1, e1) = e3
% 242.18/48.74  | | | 
% 242.18/48.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.18/48.74  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 242.18/48.74  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 242.18/48.74  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 242.18/48.74  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 242.18/48.74  | | |            (53), (54), (55), (56), (57), (59), (60), (61), (62), (63),
% 242.18/48.74  | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 242.18/48.74  | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 242.18/48.74  | | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 242.18/48.74  | | |            (94), (95), (96), (97), (101), (102) are inconsistent by
% 242.18/48.74  | | |            sub-proof #707.
% 242.18/48.74  | | | 
% 242.18/48.74  | | Case 2:
% 242.18/48.74  | | | 
% 242.18/48.74  | | |   (103)  all_58_11 = e3 & op(e1, e0) = e3
% 242.18/48.74  | | | 
% 242.18/48.74  | | | REF_CLOSE: (44), (58), (103) are inconsistent by sub-proof #2108.
% 242.18/48.74  | | | 
% 242.18/48.74  | | End of split
% 242.18/48.74  | | 
% 242.18/48.74  | End of split
% 242.18/48.74  | 
% 242.18/48.74  End of proof
% 242.18/48.74  
% 242.18/48.74  Sub-proof #707 shows that the following formulas are inconsistent:
% 242.18/48.74  ----------------------------------------------------------------
% 242.18/48.74    (1)   ~ (all_52_1 = all_52_3)
% 242.18/48.74    (2)  all_56_21 = e2
% 242.18/48.74    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.18/48.74    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.18/48.74         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.18/48.74    (5)   ~ (all_52_3 = e1)
% 242.18/48.74    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.18/48.74    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.18/48.74         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.74    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.18/48.74           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.18/48.74             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.18/48.74    (9)   ~ (e3 = e0)
% 242.18/48.74    (10)  op(e0, e1) = all_52_11
% 242.18/48.74    (11)  all_42_2 = e3
% 242.18/48.74    (12)  op(e1, e2) = e1
% 242.18/48.74    (13)   ~ (e2 = e0)
% 242.18/48.74    (14)   ~ (all_52_11 = e2)
% 242.18/48.74    (15)  all_54_13 = all_52_7
% 242.18/48.74    (16)  op(e1, e2) = all_52_6
% 242.18/48.74    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.18/48.74          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.74    (18)   ~ (all_52_11 = e1)
% 242.18/48.74    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.18/48.74              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.18/48.74            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.18/48.74            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.18/48.74            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.18/48.74             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.74            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.18/48.74            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.18/48.74            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.18/48.74            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.74            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.18/48.74              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.18/48.74            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.18/48.74            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.18/48.74            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.18/48.74            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.18/48.74            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.18/48.74            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.18/48.74              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.18/48.74            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.18/48.74            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.18/48.74            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.18/48.74            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.18/48.74            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.18/48.74            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.18/48.74              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.18/48.74            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.18/48.74            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.18/48.74    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.74          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.18/48.74    (21)   ~ (all_52_7 = all_52_11)
% 242.18/48.74    (22)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.18/48.74            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.18/48.74              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.18/48.74    (23)   ~ (all_52_1 = all_52_2)
% 242.18/48.74    (24)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.18/48.74            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.18/48.74              e1) = all_20_1 & $i(all_20_1))
% 242.18/48.74    (25)   ~ (all_52_7 = e3)
% 242.18/48.74    (26)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.18/48.74    (27)  op(e0, e3) = all_52_3
% 242.18/48.74    (28)   ~ (e3 = e1)
% 242.18/48.74    (29)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.18/48.74          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.18/48.74    (30)   ~ (all_52_2 = all_52_3)
% 242.18/48.74    (31)   ~ (all_52_8 = e1)
% 242.18/48.74    (32)  all_58_3 = e3
% 242.18/48.74    (33)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.18/48.74          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.18/48.74    (34)   ~ (all_52_2 = e1)
% 242.18/48.74    (35)  op(all_40_1, e1) = all_40_0
% 242.18/48.74    (36)  all_54_2 = all_52_8
% 242.18/48.74    (37)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.18/48.74          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.18/48.74    (38)  op(e3, e3) = e1
% 242.18/48.74    (39)   ~ (all_52_3 = all_52_7)
% 242.18/48.74    (40)  all_54_4 = all_52_1
% 242.18/48.74    (41)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.74              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.18/48.74                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.18/48.74                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.18/48.74    (42)  op(e2, e1) = all_52_9
% 242.18/48.74    (43)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.18/48.74          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.18/48.74    (44)   ~ (e3 = e2)
% 242.18/48.74    (45)  all_58_6 = e0
% 242.18/48.74    (46)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.18/48.74          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.18/48.74    (47)   ~ (all_52_7 = e1)
% 242.18/48.74    (48)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.18/48.74    (49)   ~ (all_52_3 = all_52_11)
% 242.18/48.74    (50)  all_56_31 = e1
% 242.18/48.74    (51)  all_54_12 = all_52_3
% 242.18/48.74    (52)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.18/48.74    (53)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.18/48.74          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.18/48.74    (54)  all_58_15 = e1
% 242.18/48.74    (55)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.18/48.74          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.18/48.74    (56)  all_58_9 = e3
% 242.18/48.74    (57)  op(e3, e0) = e3
% 242.18/48.74    (58)  op(e2, e3) = all_52_1
% 242.18/48.74    (59)  all_58_12 = e3
% 242.18/48.74    (60)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.18/48.74          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.18/48.74    (61)  all_34_2 = e1
% 242.18/48.74    (62)  op(e1, e1) = e3
% 242.18/48.74    (63)   ~ (all_52_6 = e3)
% 242.18/48.74    (64)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.18/48.74    (65)  op(e1, e1) = e2
% 242.18/48.74    (66)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.18/48.74          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.18/48.74    (67)  op(e0, e2) = all_52_7
% 242.18/48.74    (68)  all_54_1 = all_52_4
% 242.18/48.74    (69)   ~ (all_52_4 = e3)
% 242.18/48.74    (70)  op(e3, e2) = all_52_4
% 242.18/48.74    (71)   ~ (all_52_8 = all_52_11)
% 242.18/48.74    (72)   ~ (all_40_0 = e0)
% 242.18/48.74    (73)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.18/48.74    (74)  all_58_5 = e1
% 242.18/48.74    (75)  all_58_7 = e1
% 242.18/48.74    (76)   ~ (all_52_2 = e2)
% 242.18/48.74    (77)   ~ (all_52_9 = e3)
% 242.18/48.74    (78)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.18/48.74          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.18/48.74    (79)  all_54_8 = all_52_2
% 242.18/48.74    (80)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.18/48.74          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.18/48.74    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.18/48.74            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.18/48.74    (82)  all_58_8 = e3
% 242.18/48.74    (83)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.18/48.74          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.18/48.74    (84)  all_56_11 = e3
% 242.18/48.75    (85)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.18/48.75            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.18/48.75              e2) = all_36_1 & $i(all_36_1))
% 242.18/48.75    (86)  op(e1, e2) = all_40_1
% 242.18/48.75    (87)   ~ (all_52_4 = e1)
% 242.18/48.75    (88)   ~ (e1 = e0)
% 242.18/48.75    (89)   ~ (all_52_8 = e2)
% 242.18/48.75    (90)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.18/48.75          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.18/48.75    (91)   ~ (all_52_1 = e3)
% 242.18/48.75    (92)  all_54_14 = all_52_11
% 242.18/48.75    (93)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.18/48.75          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.18/48.75            e2)
% 242.18/48.75    (94)   ~ (all_52_4 = all_52_8)
% 242.18/48.75    (95)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.18/48.75            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.18/48.75            & $i(all_8_1))
% 242.18/48.75    (96)   ~ (e2 = e1)
% 242.18/48.75    (97)   ~ (all_52_1 = e1)
% 242.18/48.75    (98)   ~ (all_52_4 = all_52_7)
% 242.18/48.75  
% 242.18/48.75  Begin of proof
% 242.18/48.75  | 
% 242.18/48.75  | BETA: splitting (43) gives:
% 242.18/48.75  | 
% 242.18/48.75  | Case 1:
% 242.18/48.75  | | 
% 242.18/48.75  | |   (99)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 242.18/48.75  | |           e2)
% 242.18/48.75  | | 
% 242.18/48.75  | | BETA: splitting (99) gives:
% 242.18/48.75  | | 
% 242.18/48.75  | | Case 1:
% 242.18/48.75  | | | 
% 242.18/48.75  | | |   (100)  all_58_0 = e2 & op(e3, e3) = e2
% 242.18/48.75  | | | 
% 242.18/48.75  | | | ALPHA: (100) implies:
% 242.18/48.75  | | |   (101)  op(e3, e3) = e2
% 242.18/48.75  | | | 
% 242.18/48.75  | | | REF_CLOSE: (38), (81), (96), (101) are inconsistent by sub-proof #2267.
% 242.18/48.75  | | | 
% 242.18/48.75  | | Case 2:
% 242.18/48.75  | | | 
% 242.18/48.75  | | |   (102)  all_58_2 = e2 & op(e2, e3) = e2
% 242.18/48.75  | | | 
% 242.18/48.75  | | | ALPHA: (102) implies:
% 242.18/48.75  | | |   (103)  all_58_2 = e2
% 242.18/48.75  | | | 
% 242.18/48.75  | | | BETA: splitting (4) gives:
% 242.18/48.75  | | | 
% 242.18/48.75  | | | Case 1:
% 242.18/48.75  | | | | 
% 242.18/48.75  | | | |   (104)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 242.18/48.75  | | | |            = e2)
% 242.18/48.75  | | | | 
% 242.18/48.75  | | | | BETA: splitting (104) gives:
% 242.18/48.75  | | | | 
% 242.18/48.75  | | | | Case 1:
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | |   (105)  all_58_0 = e2 & op(e3, e3) = e2
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | | ALPHA: (105) implies:
% 242.18/48.75  | | | | |   (106)  op(e3, e3) = e2
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | | REF_CLOSE: (38), (81), (96), (106) are inconsistent by sub-proof
% 242.18/48.75  | | | | |            #2267.
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | Case 2:
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | |   (107)  all_58_1 = e2 & op(e3, e2) = e2
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | | ALPHA: (107) implies:
% 242.18/48.75  | | | | |   (108)  all_58_1 = e2
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | | BETA: splitting (46) gives:
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | | Case 1:
% 242.18/48.75  | | | | | | 
% 242.18/48.75  | | | | | |   (109)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 242.18/48.75  | | | | | |              e1) = e2)
% 242.18/48.75  | | | | | | 
% 242.18/48.75  | | | | | | BETA: splitting (109) gives:
% 242.18/48.75  | | | | | | 
% 242.18/48.75  | | | | | | Case 1:
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | |   (110)  all_58_4 = e2 & op(e3, e1) = e2
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | | ALPHA: (110) implies:
% 242.18/48.75  | | | | | | |   (111)  all_58_4 = e2
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | | REF_CLOSE: (9), (13), (38), (56), (60), (81), (88), (108), (111)
% 242.18/48.75  | | | | | | |            are inconsistent by sub-proof #708.
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | Case 2:
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | |   (112)  all_58_5 = e2 & op(e2, e1) = e2
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | | ALPHA: (112) implies:
% 242.18/48.75  | | | | | | |   (113)  all_58_5 = e2
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | | REF_CLOSE: (74), (96), (113) are inconsistent by sub-proof #1665.
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | End of split
% 242.18/48.75  | | | | | | 
% 242.18/48.75  | | | | | Case 2:
% 242.18/48.75  | | | | | | 
% 242.18/48.75  | | | | | |   (114)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 242.18/48.75  | | | | | |            op(e0, e1) = e2)
% 242.18/48.75  | | | | | | 
% 242.18/48.75  | | | | | | BETA: splitting (114) gives:
% 242.18/48.75  | | | | | | 
% 242.18/48.75  | | | | | | Case 1:
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | |   (115)  all_58_8 = e2 & op(e1, e1) = e2
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | | ALPHA: (115) implies:
% 242.18/48.75  | | | | | | |   (116)  all_58_8 = e2
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 242.18/48.75  | | | | | | |            (11), (12), (14), (15), (16), (17), (18), (19), (20),
% 242.18/48.75  | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 242.18/48.75  | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 242.18/48.75  | | | | | | |            (39), (40), (41), (42), (43), (44), (47), (48), (49),
% 242.18/48.75  | | | | | | |            (50), (51), (52), (54), (55), (58), (60), (61), (63),
% 242.18/48.75  | | | | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 242.18/48.75  | | | | | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 242.18/48.75  | | | | | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 242.18/48.75  | | | | | | |            (92), (93), (94), (95), (96), (97), (98), (116) are
% 242.18/48.75  | | | | | | |            inconsistent by sub-proof #715.
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | Case 2:
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | |   (117)  all_58_14 = e2 & op(e0, e1) = e2
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | | ALPHA: (117) implies:
% 242.18/48.75  | | | | | | |   (118)  all_58_14 = e2
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | | BETA: splitting (80) gives:
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | | Case 1:
% 242.18/48.75  | | | | | | | | 
% 242.18/48.75  | | | | | | | |   (119)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 242.18/48.75  | | | | | | | |            op(e2, e2) = e0)
% 242.18/48.75  | | | | | | | | 
% 242.18/48.75  | | | | | | | | BETA: splitting (119) gives:
% 242.18/48.75  | | | | | | | | 
% 242.18/48.75  | | | | | | | | Case 1:
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | |   (120)  all_58_2 = e0 & op(e2, e3) = e0
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | | ALPHA: (120) implies:
% 242.18/48.75  | | | | | | | | |   (121)  all_58_2 = e0
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | | COMBINE_EQS: (103), (121) imply:
% 242.18/48.75  | | | | | | | | |   (122)  e2 = e0
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | | SIMP: (122) implies:
% 242.18/48.75  | | | | | | | | |   (123)  e2 = e0
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | | COMBINE_EQS: (118), (123) imply:
% 242.18/48.75  | | | | | | | | |   (124)  all_58_14 = e0
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | | REF_CLOSE: (9), (13), (20), (32), (44), (54), (59), (75),
% 242.18/48.75  | | | | | | | | |            (88), (93), (96), (108), (124) are inconsistent by
% 242.18/48.75  | | | | | | | | |            sub-proof #735.
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | Case 2:
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | |   (125)  all_58_3 = e0 & op(e2, e2) = e0
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | | REF_CLOSE: (9), (32), (125) are inconsistent by sub-proof
% 242.18/48.75  | | | | | | | | |            #1719.
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | End of split
% 242.18/48.75  | | | | | | | | 
% 242.18/48.75  | | | | | | | Case 2:
% 242.18/48.75  | | | | | | | | 
% 242.18/48.75  | | | | | | | |   (126)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 242.18/48.75  | | | | | | | |            op(e2, e0) = e0)
% 242.18/48.75  | | | | | | | | 
% 242.18/48.75  | | | | | | | | BETA: splitting (126) gives:
% 242.18/48.75  | | | | | | | | 
% 242.18/48.75  | | | | | | | | Case 1:
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | |   (127)  all_58_5 = e0 & op(e2, e1) = e0
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | | REF_CLOSE: (74), (88), (127) are inconsistent by sub-proof
% 242.18/48.75  | | | | | | | | |            #1103.
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | Case 2:
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 242.18/48.75  | | | | | | | | |            (11), (12), (14), (15), (16), (17), (18), (19),
% 242.18/48.75  | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 242.18/48.75  | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 242.18/48.75  | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 242.18/48.75  | | | | | | | | |            (44), (47), (48), (49), (50), (51), (52), (54),
% 242.18/48.75  | | | | | | | | |            (55), (58), (60), (61), (62), (63), (64), (65),
% 242.18/48.75  | | | | | | | | |            (66), (67), (68), (69), (70), (71), (72), (73),
% 242.18/48.75  | | | | | | | | |            (74), (75), (76), (77), (78), (79), (80), (81),
% 242.18/48.75  | | | | | | | | |            (82), (83), (84), (85), (86), (87), (88), (89),
% 242.18/48.75  | | | | | | | | |            (90), (91), (92), (93), (94), (95), (96), (97),
% 242.18/48.75  | | | | | | | | |            (98) are inconsistent by sub-proof #713.
% 242.18/48.75  | | | | | | | | | 
% 242.18/48.75  | | | | | | | | End of split
% 242.18/48.75  | | | | | | | | 
% 242.18/48.75  | | | | | | | End of split
% 242.18/48.75  | | | | | | | 
% 242.18/48.75  | | | | | | End of split
% 242.18/48.75  | | | | | | 
% 242.18/48.75  | | | | | End of split
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | End of split
% 242.18/48.75  | | | | 
% 242.18/48.75  | | | Case 2:
% 242.18/48.75  | | | | 
% 242.18/48.75  | | | |   (128)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 242.18/48.75  | | | |            = e2)
% 242.18/48.75  | | | | 
% 242.18/48.75  | | | | BETA: splitting (128) gives:
% 242.18/48.75  | | | | 
% 242.18/48.75  | | | | Case 1:
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | |   (129)  all_58_4 = e2 & op(e3, e1) = e2
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | | ALPHA: (129) implies:
% 242.18/48.75  | | | | |   (130)  all_58_4 = e2
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 242.18/48.75  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 242.18/48.75  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 242.18/48.75  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 242.18/48.75  | | | | |            (42), (43), (44), (47), (48), (49), (50), (51), (52), (53),
% 242.18/48.75  | | | | |            (54), (55), (56), (58), (59), (60), (61), (62), (63), (64),
% 242.18/48.75  | | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 242.18/48.75  | | | | |            (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 242.18/48.75  | | | | |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 242.18/48.75  | | | | |            (95), (96), (97), (98), (130) are inconsistent by sub-proof
% 242.18/48.75  | | | | |            #711.
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | Case 2:
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | |   (131)  all_58_9 = e2 & op(e3, e0) = e2
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | | ALPHA: (131) implies:
% 242.18/48.75  | | | | |   (132)  op(e3, e0) = e2
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | | REF_CLOSE: (44), (57), (81), (132) are inconsistent by sub-proof
% 242.18/48.75  | | | | |            #2125.
% 242.18/48.75  | | | | | 
% 242.18/48.75  | | | | End of split
% 242.18/48.75  | | | | 
% 242.18/48.75  | | | End of split
% 242.18/48.75  | | | 
% 242.18/48.75  | | End of split
% 242.18/48.75  | | 
% 242.18/48.75  | Case 2:
% 242.18/48.75  | | 
% 242.18/48.75  | |   (133)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 242.18/48.75  | |            e2)
% 242.18/48.75  | | 
% 242.18/48.75  | | BETA: splitting (133) gives:
% 242.18/48.75  | | 
% 242.18/48.75  | | Case 1:
% 242.18/48.75  | | | 
% 242.18/48.75  | | |   (134)  all_58_6 = e2 & op(e1, e3) = e2
% 242.18/48.75  | | | 
% 242.26/48.75  | | | ALPHA: (134) implies:
% 242.26/48.75  | | |   (135)  all_58_6 = e2
% 242.26/48.75  | | | 
% 242.26/48.75  | | | REF_CLOSE: (13), (45), (135) are inconsistent by sub-proof #1982.
% 242.26/48.75  | | | 
% 242.26/48.75  | | Case 2:
% 242.26/48.75  | | | 
% 242.26/48.75  | | |   (136)  all_58_12 = e2 & op(e0, e3) = e2
% 242.26/48.75  | | | 
% 242.26/48.75  | | | ALPHA: (136) implies:
% 242.26/48.75  | | |   (137)  all_58_12 = e2
% 242.26/48.75  | | | 
% 242.26/48.75  | | | COMBINE_EQS: (59), (137) imply:
% 242.26/48.75  | | |   (138)  e3 = e2
% 242.26/48.75  | | | 
% 242.26/48.75  | | | COMBINE_EQS: (82), (138) imply:
% 242.26/48.75  | | |   (139)  all_58_8 = e2
% 242.26/48.75  | | | 
% 242.26/48.75  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.26/48.75  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 242.26/48.75  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 242.26/48.75  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 242.26/48.75  | | |            (44), (47), (48), (49), (50), (51), (52), (54), (55), (58),
% 242.26/48.75  | | |            (60), (61), (63), (64), (65), (66), (67), (68), (69), (70),
% 242.26/48.75  | | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 242.26/48.75  | | |            (81), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 242.26/48.75  | | |            (92), (93), (94), (95), (96), (97), (98), (139) are
% 242.26/48.75  | | |            inconsistent by sub-proof #715.
% 242.26/48.75  | | | 
% 242.26/48.75  | | End of split
% 242.26/48.75  | | 
% 242.26/48.75  | End of split
% 242.26/48.75  | 
% 242.26/48.75  End of proof
% 242.26/48.75  
% 242.26/48.75  Sub-proof #708 shows that the following formulas are inconsistent:
% 242.26/48.75  ----------------------------------------------------------------
% 242.26/48.75    (1)   ~ (e3 = e0)
% 242.26/48.75    (2)   ~ (e2 = e0)
% 242.26/48.75    (3)  all_58_4 = e2
% 242.26/48.75    (4)  op(e3, e3) = e1
% 242.26/48.75    (5)  all_58_9 = e3
% 242.26/48.75    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.26/48.75         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.75    (7)  all_58_1 = e2
% 242.26/48.75    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.75    (9)   ~ (e1 = e0)
% 242.26/48.75  
% 242.26/48.75  Begin of proof
% 242.26/48.75  | 
% 242.26/48.75  | BETA: splitting (6) gives:
% 242.26/48.75  | 
% 242.26/48.75  | Case 1:
% 242.26/48.75  | | 
% 242.26/48.75  | |   (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 242.26/48.75  | |           e0)
% 242.26/48.75  | | 
% 242.26/48.75  | | REF_CLOSE: (2), (4), (7), (8), (9), (10) are inconsistent by sub-proof #709.
% 242.26/48.75  | | 
% 242.26/48.75  | Case 2:
% 242.26/48.75  | | 
% 242.26/48.75  | |   (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 242.26/48.75  | |           e0)
% 242.26/48.75  | | 
% 242.26/48.75  | | BETA: splitting (11) gives:
% 242.26/48.75  | | 
% 242.26/48.75  | | Case 1:
% 242.26/48.75  | | | 
% 242.26/48.75  | | |   (12)  all_58_4 = e0 & op(e3, e1) = e0
% 242.26/48.75  | | | 
% 242.26/48.75  | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #2170.
% 242.26/48.75  | | | 
% 242.26/48.75  | | Case 2:
% 242.26/48.75  | | | 
% 242.26/48.75  | | |   (13)  all_58_9 = e0 & op(e3, e0) = e0
% 242.26/48.75  | | | 
% 242.26/48.75  | | | REF_CLOSE: (1), (5), (13) are inconsistent by sub-proof #2103.
% 242.26/48.75  | | | 
% 242.26/48.75  | | End of split
% 242.26/48.75  | | 
% 242.26/48.75  | End of split
% 242.26/48.75  | 
% 242.26/48.75  End of proof
% 242.26/48.75  
% 242.26/48.75  Sub-proof #709 shows that the following formulas are inconsistent:
% 242.26/48.75  ----------------------------------------------------------------
% 242.26/48.75    (1)   ~ (e2 = e0)
% 242.26/48.75    (2)  op(e3, e3) = e1
% 242.26/48.75    (3)  all_58_1 = e2
% 242.26/48.75    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.75    (5)   ~ (e1 = e0)
% 242.26/48.75    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 242.26/48.75  
% 242.26/48.75  Begin of proof
% 242.26/48.75  | 
% 242.26/48.75  | BETA: splitting (6) gives:
% 242.26/48.75  | 
% 242.26/48.75  | Case 1:
% 242.26/48.75  | | 
% 242.26/48.75  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 242.26/48.75  | | 
% 242.26/48.76  | | ALPHA: (7) implies:
% 242.26/48.76  | |   (8)  op(e3, e3) = e0
% 242.26/48.76  | | 
% 242.26/48.76  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #1828.
% 242.26/48.76  | | 
% 242.26/48.76  | Case 2:
% 242.26/48.76  | | 
% 242.26/48.76  | |   (9)  all_58_1 = e0 & op(e3, e2) = e0
% 242.26/48.76  | | 
% 242.26/48.76  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #2187.
% 242.26/48.76  | | 
% 242.26/48.76  | End of split
% 242.26/48.76  | 
% 242.26/48.76  End of proof
% 242.26/48.76  
% 242.26/48.76  Sub-proof #710 shows that the following formulas are inconsistent:
% 242.26/48.76  ----------------------------------------------------------------
% 242.26/48.76    (1)   ~ (e3 = e0)
% 242.26/48.76    (2)   ~ (e2 = e0)
% 242.26/48.76    (3)  all_58_11 = e3
% 242.26/48.76    (4)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.76             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.26/48.76               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.26/48.76               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.26/48.76    (5)  op(e2, e0) = e2
% 242.26/48.76    (6)  all_58_15 = e1
% 242.26/48.76    (7)  all_58_9 = e3
% 242.26/48.76    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.76    (9)   ~ (e1 = e0)
% 242.26/48.76  
% 242.26/48.76  Begin of proof
% 242.26/48.76  | 
% 242.26/48.76  | BETA: splitting (4) gives:
% 242.26/48.76  | 
% 242.26/48.76  | Case 1:
% 242.26/48.76  | | 
% 242.26/48.76  | |   (10)  all_58_15 = e0 & op(e0, e0) = e0
% 242.26/48.76  | | 
% 242.26/48.76  | | REF_CLOSE: (6), (9), (10) are inconsistent by sub-proof #1867.
% 242.26/48.76  | | 
% 242.26/48.76  | Case 2:
% 242.26/48.76  | | 
% 242.26/48.76  | |   (11)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 242.26/48.76  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 242.26/48.76  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 242.26/48.76  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 242.26/48.76  | | 
% 242.26/48.76  | | ALPHA: (11) implies:
% 242.26/48.76  | |   (12)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 242.26/48.76  | |           e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.26/48.76  | | 
% 242.26/48.76  | | BETA: splitting (12) gives:
% 242.26/48.76  | | 
% 242.26/48.76  | | Case 1:
% 242.26/48.76  | | | 
% 242.26/48.76  | | |   (13)  all_58_9 = e0 & op(e3, e0) = e0
% 242.26/48.76  | | | 
% 242.26/48.76  | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #2103.
% 242.26/48.76  | | | 
% 242.26/48.76  | | Case 2:
% 242.26/48.76  | | | 
% 242.26/48.76  | | |   (14)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.26/48.76  | | |           = e0)
% 242.26/48.76  | | | 
% 242.26/48.76  | | | REF_CLOSE: (1), (2), (3), (5), (8), (14) are inconsistent by sub-proof
% 242.26/48.76  | | |            #955.
% 242.26/48.76  | | | 
% 242.26/48.76  | | End of split
% 242.26/48.76  | | 
% 242.26/48.76  | End of split
% 242.26/48.76  | 
% 242.26/48.76  End of proof
% 242.26/48.76  
% 242.26/48.76  Sub-proof #711 shows that the following formulas are inconsistent:
% 242.26/48.76  ----------------------------------------------------------------
% 242.26/48.76    (1)   ~ (all_52_1 = all_52_3)
% 242.26/48.76    (2)  all_56_21 = e2
% 242.26/48.76    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.26/48.76    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.76         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.76    (5)   ~ (all_52_3 = e1)
% 242.26/48.76    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.26/48.76    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.26/48.76         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.76    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.26/48.76           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.26/48.76             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.26/48.76    (9)   ~ (e3 = e0)
% 242.26/48.76    (10)  op(e0, e1) = all_52_11
% 242.26/48.76    (11)  all_42_2 = e3
% 242.26/48.76    (12)  op(e1, e2) = e1
% 242.26/48.76    (13)   ~ (e2 = e0)
% 242.26/48.76    (14)   ~ (all_52_11 = e2)
% 242.26/48.76    (15)  all_54_13 = all_52_7
% 242.26/48.76    (16)  op(e1, e2) = all_52_6
% 242.26/48.76    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.26/48.76          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.76    (18)   ~ (all_52_11 = e1)
% 242.26/48.76    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.26/48.76              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.26/48.76            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.26/48.76            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.76            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.26/48.76             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.76            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.26/48.76            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.76            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.26/48.76            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.76            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.26/48.76              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.76            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.76            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.26/48.76            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.76            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.26/48.76            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.76            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.26/48.76              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.26/48.76            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.76            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.26/48.76            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.76            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.26/48.76            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.76            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.26/48.76              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.26/48.76            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.76            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.76    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.76          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.76    (21)   ~ (all_52_7 = all_52_11)
% 242.26/48.76    (22)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.26/48.76            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.26/48.76              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.26/48.76    (23)  all_58_4 = e2
% 242.26/48.76    (24)   ~ (all_52_1 = all_52_2)
% 242.26/48.76    (25)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.26/48.76            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.26/48.76              e1) = all_20_1 & $i(all_20_1))
% 242.26/48.76    (26)   ~ (all_52_7 = e3)
% 242.26/48.76    (27)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.26/48.76    (28)  op(e0, e3) = all_52_3
% 242.26/48.76    (29)   ~ (e3 = e1)
% 242.26/48.76    (30)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.76          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.76    (31)   ~ (all_52_2 = all_52_3)
% 242.26/48.76    (32)   ~ (all_52_8 = e1)
% 242.26/48.76    (33)  all_58_3 = e3
% 242.26/48.76    (34)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.76          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.76    (35)   ~ (all_52_2 = e1)
% 242.26/48.76    (36)  op(all_40_1, e1) = all_40_0
% 242.26/48.76    (37)  all_54_2 = all_52_8
% 242.26/48.76    (38)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.26/48.76          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.26/48.76    (39)  op(e3, e3) = e1
% 242.26/48.76    (40)   ~ (all_52_3 = all_52_7)
% 242.26/48.76    (41)  all_54_4 = all_52_1
% 242.26/48.76    (42)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.76              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.26/48.76                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.26/48.76                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.26/48.76    (43)  op(e2, e1) = all_52_9
% 242.26/48.76    (44)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.76          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.76    (45)   ~ (e3 = e2)
% 242.26/48.76    (46)   ~ (all_52_7 = e1)
% 242.26/48.76    (47)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.76    (48)   ~ (all_52_3 = all_52_11)
% 242.26/48.76    (49)  all_56_31 = e1
% 242.26/48.76    (50)  all_54_12 = all_52_3
% 242.26/48.76    (51)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.26/48.76    (52)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.26/48.76          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.26/48.76    (53)  all_58_15 = e1
% 242.26/48.76    (54)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.26/48.76          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.26/48.76    (55)  all_58_9 = e3
% 242.26/48.76    (56)  op(e2, e3) = all_52_1
% 242.26/48.76    (57)  all_58_12 = e3
% 242.26/48.76    (58)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.26/48.76          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.76    (59)  all_34_2 = e1
% 242.26/48.76    (60)  op(e1, e1) = e3
% 242.26/48.76    (61)   ~ (all_52_6 = e3)
% 242.26/48.76    (62)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.26/48.76    (63)  op(e1, e1) = e2
% 242.26/48.76    (64)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.26/48.76          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.26/48.76    (65)  op(e0, e2) = all_52_7
% 242.26/48.76    (66)  all_54_1 = all_52_4
% 242.26/48.76    (67)   ~ (all_52_4 = e3)
% 242.26/48.76    (68)  op(e3, e2) = all_52_4
% 242.26/48.76    (69)   ~ (all_52_8 = all_52_11)
% 242.26/48.76    (70)   ~ (all_40_0 = e0)
% 242.26/48.76    (71)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.76    (72)  all_58_5 = e1
% 242.26/48.76    (73)  all_58_7 = e1
% 242.26/48.76    (74)   ~ (all_52_2 = e2)
% 242.26/48.76    (75)   ~ (all_52_9 = e3)
% 242.26/48.76    (76)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.26/48.76          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.76    (77)  all_54_8 = all_52_2
% 242.26/48.76    (78)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.76          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.26/48.76    (79)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.76            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.76    (80)  all_58_8 = e3
% 242.26/48.76    (81)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.26/48.76          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.26/48.76    (82)  all_56_11 = e3
% 242.26/48.76    (83)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.26/48.76            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.26/48.76              e2) = all_36_1 & $i(all_36_1))
% 242.26/48.76    (84)  op(e1, e2) = all_40_1
% 242.26/48.76    (85)   ~ (all_52_4 = e1)
% 242.26/48.76    (86)   ~ (e1 = e0)
% 242.26/48.76    (87)   ~ (all_52_8 = e2)
% 242.26/48.76    (88)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.26/48.76          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.26/48.76    (89)   ~ (all_52_1 = e3)
% 242.26/48.76    (90)  all_54_14 = all_52_11
% 242.26/48.76    (91)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.76          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.76            e2)
% 242.26/48.76    (92)   ~ (all_52_4 = all_52_8)
% 242.26/48.76    (93)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.76            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.76            & $i(all_8_1))
% 242.26/48.76    (94)   ~ (e2 = e1)
% 242.26/48.76    (95)   ~ (all_52_1 = e1)
% 242.26/48.76    (96)   ~ (all_52_4 = all_52_7)
% 242.26/48.76  
% 242.26/48.76  Begin of proof
% 242.26/48.76  | 
% 242.26/48.76  | BETA: splitting (30) gives:
% 242.26/48.76  | 
% 242.26/48.76  | Case 1:
% 242.26/48.76  | | 
% 242.26/48.76  | |   (97)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 242.26/48.76  | |           e0)
% 242.26/48.76  | | 
% 242.26/48.76  | | BETA: splitting (97) gives:
% 242.26/48.76  | | 
% 242.26/48.76  | | Case 1:
% 242.26/48.76  | | | 
% 242.26/48.76  | | |   (98)  all_58_4 = e0 & op(e3, e1) = e0
% 242.26/48.76  | | | 
% 242.26/48.76  | | | REF_CLOSE: (13), (23), (98) are inconsistent by sub-proof #2170.
% 242.26/48.76  | | | 
% 242.26/48.76  | | Case 2:
% 242.26/48.76  | | | 
% 242.26/48.76  | | |   (99)  all_58_5 = e0 & op(e2, e1) = e0
% 242.26/48.76  | | | 
% 242.26/48.76  | | | REF_CLOSE: (72), (86), (99) are inconsistent by sub-proof #1485.
% 242.26/48.76  | | | 
% 242.26/48.76  | | End of split
% 242.26/48.76  | | 
% 242.26/48.76  | Case 2:
% 242.26/48.76  | | 
% 242.26/48.76  | |   (100)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 242.26/48.76  | |            e0)
% 242.26/48.76  | | 
% 242.26/48.76  | | BETA: splitting (100) gives:
% 242.26/48.76  | | 
% 242.26/48.76  | | Case 1:
% 242.26/48.76  | | | 
% 242.26/48.76  | | |   (101)  all_58_8 = e0 & op(e1, e1) = e0
% 242.26/48.76  | | | 
% 242.26/48.76  | | | REF_CLOSE: (9), (80), (101) are inconsistent by sub-proof #1421.
% 242.26/48.76  | | | 
% 242.26/48.76  | | Case 2:
% 242.26/48.76  | | | 
% 242.26/48.76  | | |   (102)  all_58_14 = e0 & op(e0, e1) = e0
% 242.26/48.76  | | | 
% 242.26/48.76  | | | ALPHA: (102) implies:
% 242.26/48.76  | | |   (103)  all_58_14 = e0
% 242.26/48.76  | | | 
% 242.26/48.76  | | | BETA: splitting (17) gives:
% 242.26/48.76  | | | 
% 242.26/48.76  | | | Case 1:
% 242.26/48.76  | | | | 
% 242.26/48.76  | | | |   (104)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2)
% 242.26/48.76  | | | |            = e2)
% 242.26/48.76  | | | | 
% 242.26/48.76  | | | | BETA: splitting (104) gives:
% 242.26/48.76  | | | | 
% 242.26/48.76  | | | | Case 1:
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | |   (105)  all_58_1 = e2 & op(e3, e2) = e2
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | ALPHA: (105) implies:
% 242.26/48.76  | | | | |   (106)  all_58_1 = e2
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | REF_CLOSE: (9), (13), (20), (33), (45), (53), (57), (73), (86), (91),
% 242.26/48.76  | | | | |            (94), (103), (106) are inconsistent by sub-proof #735.
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | Case 2:
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | |   (107)  all_58_3 = e2 & op(e2, e2) = e2
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | ALPHA: (107) implies:
% 242.26/48.76  | | | | |   (108)  all_58_3 = e2
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | COMBINE_EQS: (33), (108) imply:
% 242.26/48.76  | | | | |   (109)  e3 = e2
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | COMBINE_EQS: (80), (109) imply:
% 242.26/48.76  | | | | |   (110)  all_58_8 = e2
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 242.26/48.76  | | | | |            (12), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 242.26/48.76  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 242.26/48.76  | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 242.26/48.76  | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (53), (54),
% 242.26/48.76  | | | | |            (56), (58), (59), (61), (62), (63), (64), (65), (66), (67),
% 242.26/48.76  | | | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 242.26/48.76  | | | | |            (78), (79), (81), (82), (83), (84), (85), (86), (87), (88),
% 242.26/48.76  | | | | |            (89), (90), (91), (92), (93), (94), (95), (96), (110) are
% 242.26/48.76  | | | | |            inconsistent by sub-proof #715.
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | End of split
% 242.26/48.76  | | | | 
% 242.26/48.76  | | | Case 2:
% 242.26/48.76  | | | | 
% 242.26/48.76  | | | |   (111)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0,
% 242.26/48.76  | | | |              e2) = e2)
% 242.26/48.76  | | | | 
% 242.26/48.76  | | | | BETA: splitting (111) gives:
% 242.26/48.76  | | | | 
% 242.26/48.76  | | | | Case 1:
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | |   (112)  all_58_7 = e2 & op(e1, e2) = e2
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | ALPHA: (112) implies:
% 242.26/48.76  | | | | |   (113)  all_58_7 = e2
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | COMBINE_EQS: (73), (113) imply:
% 242.26/48.76  | | | | |   (114)  e2 = e1
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | REF_CLOSE: (4), (9), (13), (23), (39), (45), (55), (58), (79), (86),
% 242.26/48.76  | | | | |            (94), (114) are inconsistent by sub-proof #714.
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | Case 2:
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | |   (115)  all_58_13 = e2 & op(e0, e2) = e2
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | ALPHA: (115) implies:
% 242.26/48.76  | | | | |   (116)  all_58_13 = e2
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | BETA: splitting (7) gives:
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | | Case 1:
% 242.26/48.76  | | | | | | 
% 242.26/48.76  | | | | | |   (117)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 242.26/48.76  | | | | | |            op(e0, e2) = e3)
% 242.26/48.76  | | | | | | 
% 242.26/48.76  | | | | | | BETA: splitting (117) gives:
% 242.26/48.76  | | | | | | 
% 242.26/48.76  | | | | | | Case 1:
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 242.26/48.76  | | | | | | |            (11), (12), (14), (15), (16), (17), (18), (19), (20),
% 242.26/48.76  | | | | | | |            (21), (22), (24), (25), (26), (27), (28), (29), (30),
% 242.26/48.76  | | | | | | |            (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 242.26/48.76  | | | | | | |            (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 242.26/48.76  | | | | | | |            (49), (50), (51), (53), (54), (56), (58), (59), (60),
% 242.26/48.76  | | | | | | |            (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 242.26/48.76  | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 242.26/48.76  | | | | | | |            (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 242.26/48.76  | | | | | | |            (88), (89), (90), (91), (92), (93), (94), (95), (96)
% 242.26/48.76  | | | | | | |            are inconsistent by sub-proof #713.
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | Case 2:
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | |   (118)  all_58_13 = e3 & op(e0, e2) = e3
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | | REF_CLOSE: (26), (65), (79), (118) are inconsistent by sub-proof
% 242.26/48.76  | | | | | | |            #1919.
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | End of split
% 242.26/48.76  | | | | | | 
% 242.26/48.76  | | | | | Case 2:
% 242.26/48.76  | | | | | | 
% 242.26/48.76  | | | | | |   (119)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 242.26/48.76  | | | | | |            op(e0, e0) = e3)
% 242.26/48.76  | | | | | | 
% 242.26/48.76  | | | | | | BETA: splitting (119) gives:
% 242.26/48.76  | | | | | | 
% 242.26/48.76  | | | | | | Case 1:
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | |   (120)  all_58_14 = e3 & op(e0, e1) = e3
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | | ALPHA: (120) implies:
% 242.26/48.76  | | | | | | |   (121)  all_58_14 = e3
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | | REF_CLOSE: (9), (13), (42), (53), (57), (86), (116), (121) are
% 242.26/48.76  | | | | | | |            inconsistent by sub-proof #1865.
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | Case 2:
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | |   (122)  all_58_15 = e3 & op(e0, e0) = e3
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | | REF_CLOSE: (9), (13), (29), (38), (39), (44), (45), (52), (53),
% 242.26/48.76  | | | | | | |            (56), (57), (79), (86), (89), (94), (122) are
% 242.26/48.76  | | | | | | |            inconsistent by sub-proof #712.
% 242.26/48.76  | | | | | | | 
% 242.26/48.76  | | | | | | End of split
% 242.26/48.76  | | | | | | 
% 242.26/48.76  | | | | | End of split
% 242.26/48.76  | | | | | 
% 242.26/48.76  | | | | End of split
% 242.26/48.76  | | | | 
% 242.26/48.76  | | | End of split
% 242.26/48.76  | | | 
% 242.26/48.76  | | End of split
% 242.26/48.76  | | 
% 242.26/48.76  | End of split
% 242.26/48.76  | 
% 242.26/48.76  End of proof
% 242.26/48.76  
% 242.26/48.76  Sub-proof #712 shows that the following formulas are inconsistent:
% 242.26/48.76  ----------------------------------------------------------------
% 242.26/48.76    (1)   ~ (e3 = e0)
% 242.26/48.76    (2)   ~ (e2 = e0)
% 242.26/48.76    (3)   ~ (e3 = e1)
% 242.26/48.76    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.26/48.76         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.26/48.76    (5)  op(e3, e3) = e1
% 242.26/48.76    (6)  all_58_15 = e3 & op(e0, e0) = e3
% 242.26/48.76    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.76         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.76    (8)   ~ (e3 = e2)
% 242.26/48.77    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.26/48.77         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.26/48.77    (10)  all_58_15 = e1
% 242.26/48.77    (11)  op(e2, e3) = all_52_1
% 242.26/48.77    (12)  all_58_12 = e3
% 242.26/48.77    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.77    (14)   ~ (e1 = e0)
% 242.26/48.77    (15)   ~ (all_52_1 = e3)
% 242.26/48.77    (16)   ~ (e2 = e1)
% 242.26/48.77  
% 242.26/48.77  Begin of proof
% 242.26/48.77  | 
% 242.26/48.77  | ALPHA: (6) implies:
% 242.26/48.77  |   (17)  all_58_15 = e3
% 242.26/48.77  | 
% 242.26/48.77  | COMBINE_EQS: (10), (17) imply:
% 242.26/48.77  |   (18)  e3 = e1
% 242.26/48.77  | 
% 242.26/48.77  | SIMP: (18) implies:
% 242.26/48.77  |   (19)  e3 = e1
% 242.26/48.77  | 
% 242.26/48.77  | COMBINE_EQS: (12), (19) imply:
% 242.26/48.77  |   (20)  all_58_12 = e1
% 242.26/48.77  | 
% 242.26/48.77  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (13), (14), (15),
% 242.26/48.77  |            (16), (20) are inconsistent by sub-proof #1204.
% 242.26/48.77  | 
% 242.26/48.77  End of proof
% 242.26/48.77  
% 242.26/48.77  Sub-proof #713 shows that the following formulas are inconsistent:
% 242.26/48.77  ----------------------------------------------------------------
% 242.26/48.77    (1)   ~ (all_52_1 = all_52_3)
% 242.26/48.77    (2)  all_56_21 = e2
% 242.26/48.77    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.26/48.77    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.77         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.77    (5)   ~ (all_52_3 = e1)
% 242.26/48.77    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.26/48.77    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.26/48.77         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.77    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.26/48.77           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.26/48.77             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.26/48.77    (9)   ~ (e3 = e0)
% 242.26/48.77    (10)  op(e0, e1) = all_52_11
% 242.26/48.77    (11)  all_42_2 = e3
% 242.26/48.77    (12)  op(e1, e2) = e1
% 242.26/48.77    (13)   ~ (all_52_11 = e2)
% 242.26/48.77    (14)  all_54_13 = all_52_7
% 242.26/48.77    (15)  op(e1, e2) = all_52_6
% 242.26/48.77    (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.26/48.77          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.77    (17)   ~ (all_52_11 = e1)
% 242.26/48.77    (18)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.26/48.77              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.26/48.77            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.26/48.77            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.77            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.26/48.77             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.77            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.26/48.77            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.77            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.26/48.77            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.77            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.26/48.77              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.77            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.77            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.26/48.77            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.77            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.26/48.77            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.77            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.26/48.77              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.26/48.77            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.77            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.26/48.77            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.77            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.26/48.77            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.77            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.26/48.77              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.26/48.77            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.77            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.77    (19)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.77          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.77    (20)   ~ (all_52_7 = all_52_11)
% 242.26/48.77    (21)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.26/48.77            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.26/48.77              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.26/48.77    (22)   ~ (all_52_1 = all_52_2)
% 242.26/48.77    (23)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.26/48.77            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.26/48.77              e1) = all_20_1 & $i(all_20_1))
% 242.26/48.77    (24)   ~ (all_52_7 = e3)
% 242.26/48.77    (25)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.26/48.77    (26)  op(e0, e3) = all_52_3
% 242.26/48.77    (27)   ~ (e3 = e1)
% 242.26/48.77    (28)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.77          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.77    (29)   ~ (all_52_2 = all_52_3)
% 242.26/48.77    (30)   ~ (all_52_8 = e1)
% 242.26/48.77    (31)  all_58_3 = e3
% 242.26/48.77    (32)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.77          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.77    (33)   ~ (all_52_2 = e1)
% 242.26/48.77    (34)  op(all_40_1, e1) = all_40_0
% 242.26/48.77    (35)  all_54_2 = all_52_8
% 242.26/48.77    (36)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.26/48.77          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.26/48.77    (37)  op(e3, e3) = e1
% 242.26/48.77    (38)   ~ (all_52_3 = all_52_7)
% 242.26/48.77    (39)  all_54_4 = all_52_1
% 242.26/48.77    (40)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.77              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.26/48.77                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.26/48.77                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.26/48.77    (41)  op(e2, e1) = all_52_9
% 242.26/48.77    (42)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.77          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.77    (43)   ~ (e3 = e2)
% 242.26/48.77    (44)   ~ (all_52_7 = e1)
% 242.26/48.77    (45)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.77    (46)   ~ (all_52_3 = all_52_11)
% 242.26/48.77    (47)  all_56_31 = e1
% 242.26/48.77    (48)  all_54_12 = all_52_3
% 242.26/48.77    (49)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.26/48.77    (50)  all_58_15 = e1
% 242.26/48.77    (51)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.26/48.77          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.26/48.77    (52)  op(e2, e3) = all_52_1
% 242.26/48.77    (53)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.26/48.77          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.77    (54)  all_34_2 = e1
% 242.26/48.77    (55)  op(e1, e1) = e3
% 242.26/48.77    (56)   ~ (all_52_6 = e3)
% 242.26/48.77    (57)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.26/48.77    (58)  op(e1, e1) = e2
% 242.26/48.77    (59)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.26/48.77          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.26/48.77    (60)  op(e0, e2) = all_52_7
% 242.26/48.77    (61)  all_54_1 = all_52_4
% 242.26/48.77    (62)   ~ (all_52_4 = e3)
% 242.26/48.77    (63)  op(e3, e2) = all_52_4
% 242.26/48.77    (64)   ~ (all_52_8 = all_52_11)
% 242.26/48.77    (65)   ~ (all_40_0 = e0)
% 242.26/48.77    (66)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.77    (67)  all_58_5 = e1
% 242.26/48.77    (68)  all_58_7 = e1
% 242.26/48.77    (69)   ~ (all_52_2 = e2)
% 242.26/48.77    (70)   ~ (all_52_9 = e3)
% 242.26/48.77    (71)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.26/48.77          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.77    (72)  all_54_8 = all_52_2
% 242.26/48.77    (73)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.77          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.26/48.77    (74)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.77    (75)  all_58_8 = e3
% 242.26/48.77    (76)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.26/48.77          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.26/48.77    (77)  all_56_11 = e3
% 242.26/48.77    (78)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.26/48.77            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.26/48.77              e2) = all_36_1 & $i(all_36_1))
% 242.26/48.77    (79)  op(e1, e2) = all_40_1
% 242.26/48.77    (80)   ~ (all_52_4 = e1)
% 242.26/48.77    (81)   ~ (e1 = e0)
% 242.26/48.77    (82)   ~ (all_52_8 = e2)
% 242.26/48.77    (83)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.26/48.77          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.26/48.77    (84)   ~ (all_52_1 = e3)
% 242.26/48.77    (85)  all_54_14 = all_52_11
% 242.26/48.77    (86)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.77          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.77            e2)
% 242.26/48.77    (87)   ~ (all_52_4 = all_52_8)
% 242.26/48.77    (88)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.77            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.77            & $i(all_8_1))
% 242.26/48.77    (89)   ~ (e2 = e1)
% 242.26/48.77    (90)   ~ (all_52_1 = e1)
% 242.26/48.77    (91)   ~ (all_52_4 = all_52_7)
% 242.26/48.77  
% 242.26/48.77  Begin of proof
% 242.26/48.77  | 
% 242.26/48.77  | GROUND_INST: instantiating (74) with e2, e3, e1, e1, simplifying with (55),
% 242.26/48.77  |              (58) gives:
% 242.26/48.77  |   (92)  e3 = e2
% 242.26/48.77  | 
% 242.26/48.77  | COMBINE_EQS: (75), (92) imply:
% 242.26/48.77  |   (93)  all_58_8 = e2
% 242.26/48.77  | 
% 242.26/48.77  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.26/48.77  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 242.26/48.77  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 242.26/48.77  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 242.26/48.77  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 242.26/48.77  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 242.26/48.77  |            (69), (70), (71), (72), (73), (74), (76), (77), (78), (79), (80),
% 242.26/48.77  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 242.26/48.77  |            (93) are inconsistent by sub-proof #715.
% 242.26/48.77  | 
% 242.26/48.77  End of proof
% 242.26/48.77  
% 242.26/48.77  Sub-proof #714 shows that the following formulas are inconsistent:
% 242.26/48.77  ----------------------------------------------------------------
% 242.26/48.77    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.77         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.77    (2)   ~ (e3 = e0)
% 242.26/48.77    (3)   ~ (e2 = e0)
% 242.26/48.77    (4)  all_58_4 = e2
% 242.26/48.77    (5)  op(e3, e3) = e1
% 242.26/48.77    (6)   ~ (e3 = e2)
% 242.26/48.77    (7)  all_58_9 = e3
% 242.26/48.77    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.26/48.77         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.77    (9)  e2 = e1
% 242.26/48.77    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.77    (11)   ~ (e1 = e0)
% 242.26/48.77    (12)   ~ (e2 = e1)
% 242.26/48.77  
% 242.26/48.77  Begin of proof
% 242.26/48.77  | 
% 242.26/48.77  | SIMP: (9) implies:
% 242.26/48.77  |   (13)  e2 = e1
% 242.26/48.77  | 
% 242.26/48.77  | COMBINE_EQS: (4), (13) imply:
% 242.26/48.77  |   (14)  all_58_4 = e1
% 242.26/48.77  | 
% 242.26/48.77  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (14) are
% 242.26/48.77  |            inconsistent by sub-proof #1469.
% 242.26/48.77  | 
% 242.26/48.77  End of proof
% 242.26/48.77  
% 242.26/48.77  Sub-proof #715 shows that the following formulas are inconsistent:
% 242.26/48.77  ----------------------------------------------------------------
% 242.26/48.77    (1)   ~ (all_52_1 = all_52_3)
% 242.26/48.77    (2)  all_56_21 = e2
% 242.26/48.77    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.26/48.77    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.77         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.77    (5)   ~ (all_52_3 = e1)
% 242.26/48.77    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.26/48.77    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.26/48.77         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.77    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.26/48.77           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.26/48.77             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.26/48.77    (9)   ~ (e3 = e0)
% 242.26/48.77    (10)  op(e0, e1) = all_52_11
% 242.26/48.77    (11)  all_42_2 = e3
% 242.26/48.77    (12)  op(e1, e2) = e1
% 242.26/48.77    (13)   ~ (all_52_11 = e2)
% 242.26/48.77    (14)  all_54_13 = all_52_7
% 242.26/48.77    (15)  op(e1, e2) = all_52_6
% 242.26/48.77    (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.26/48.77          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.77    (17)   ~ (all_52_11 = e1)
% 242.26/48.78    (18)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.26/48.78              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.26/48.78            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.26/48.78            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.78            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.26/48.78             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.78            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.26/48.78            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.78            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.26/48.78            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.78            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.26/48.78              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.78            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.78            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.26/48.78            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.78            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.26/48.78            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.78            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.26/48.78              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.26/48.78            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.78            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.26/48.78            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.78            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.26/48.78            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.78            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.26/48.78              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.26/48.78            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.78            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.78    (19)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.78          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.78    (20)   ~ (all_52_7 = all_52_11)
% 242.26/48.78    (21)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.26/48.78            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.26/48.78              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.26/48.78    (22)   ~ (all_52_1 = all_52_2)
% 242.26/48.78    (23)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.26/48.78            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.26/48.78              e1) = all_20_1 & $i(all_20_1))
% 242.26/48.78    (24)   ~ (all_52_7 = e3)
% 242.26/48.78    (25)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.26/48.78    (26)  op(e0, e3) = all_52_3
% 242.26/48.78    (27)   ~ (e3 = e1)
% 242.26/48.78    (28)  all_58_8 = e2
% 242.26/48.78    (29)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.78          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.78    (30)   ~ (all_52_2 = all_52_3)
% 242.26/48.78    (31)   ~ (all_52_8 = e1)
% 242.26/48.78    (32)  all_58_3 = e3
% 242.26/48.78    (33)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.78          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.78    (34)   ~ (all_52_2 = e1)
% 242.26/48.78    (35)  op(all_40_1, e1) = all_40_0
% 242.26/48.78    (36)  all_54_2 = all_52_8
% 242.26/48.78    (37)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.26/48.78          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.26/48.78    (38)  op(e3, e3) = e1
% 242.26/48.78    (39)   ~ (all_52_3 = all_52_7)
% 242.26/48.78    (40)  all_54_4 = all_52_1
% 242.26/48.78    (41)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.78              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.26/48.78                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.26/48.78                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.26/48.78    (42)  op(e2, e1) = all_52_9
% 242.26/48.78    (43)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.78          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.78    (44)   ~ (e3 = e2)
% 242.26/48.78    (45)   ~ (all_52_7 = e1)
% 242.26/48.78    (46)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.78    (47)   ~ (all_52_3 = all_52_11)
% 242.26/48.78    (48)  all_56_31 = e1
% 242.26/48.78    (49)  all_54_12 = all_52_3
% 242.26/48.78    (50)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.26/48.78    (51)  all_58_15 = e1
% 242.26/48.78    (52)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.26/48.78          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.26/48.78    (53)  op(e2, e3) = all_52_1
% 242.26/48.78    (54)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.26/48.78          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.78    (55)  all_34_2 = e1
% 242.26/48.78    (56)   ~ (all_52_6 = e3)
% 242.26/48.78    (57)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.26/48.78    (58)  op(e1, e1) = e2
% 242.26/48.78    (59)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.26/48.78          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.26/48.78    (60)  op(e0, e2) = all_52_7
% 242.26/48.78    (61)  all_54_1 = all_52_4
% 242.26/48.78    (62)   ~ (all_52_4 = e3)
% 242.26/48.78    (63)  op(e3, e2) = all_52_4
% 242.26/48.78    (64)   ~ (all_52_8 = all_52_11)
% 242.26/48.78    (65)   ~ (all_40_0 = e0)
% 242.26/48.78    (66)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.78    (67)  all_58_5 = e1
% 242.26/48.78    (68)  all_58_7 = e1
% 242.26/48.78    (69)   ~ (all_52_2 = e2)
% 242.26/48.78    (70)   ~ (all_52_9 = e3)
% 242.26/48.78    (71)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.26/48.78          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.78    (72)  all_54_8 = all_52_2
% 242.26/48.78    (73)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.78          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.26/48.78    (74)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.78            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.78    (75)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.26/48.78          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.26/48.78    (76)  all_56_11 = e3
% 242.26/48.78    (77)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.26/48.78            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.26/48.78              e2) = all_36_1 & $i(all_36_1))
% 242.26/48.78    (78)  op(e1, e2) = all_40_1
% 242.26/48.78    (79)   ~ (all_52_4 = e1)
% 242.26/48.78    (80)   ~ (e1 = e0)
% 242.26/48.78    (81)   ~ (all_52_8 = e2)
% 242.26/48.78    (82)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.26/48.78          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.26/48.78    (83)   ~ (all_52_1 = e3)
% 242.26/48.78    (84)  all_54_14 = all_52_11
% 242.26/48.78    (85)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.78          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.78            e2)
% 242.26/48.78    (86)   ~ (all_52_4 = all_52_8)
% 242.26/48.78    (87)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.78            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.78            & $i(all_8_1))
% 242.26/48.78    (88)   ~ (e2 = e1)
% 242.26/48.78    (89)   ~ (all_52_1 = e1)
% 242.26/48.79    (90)   ~ (all_52_4 = all_52_7)
% 242.26/48.79  
% 242.26/48.79  Begin of proof
% 242.26/48.79  | 
% 242.26/48.79  | GROUND_INST: instantiating (74) with e1, all_40_1, e2, e1, simplifying with
% 242.26/48.79  |              (12), (78) gives:
% 242.26/48.79  |   (91)  all_40_1 = e1
% 242.26/48.79  | 
% 242.26/48.79  | REDUCE: (35), (91) imply:
% 242.26/48.79  |   (92)  op(e1, e1) = all_40_0
% 242.26/48.79  | 
% 242.26/48.79  | BETA: splitting (77) gives:
% 242.26/48.79  | 
% 242.26/48.79  | Case 1:
% 242.26/48.79  | | 
% 242.26/48.79  | |   (93)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.26/48.79  | |         all_36_1 & $i(all_36_0) & $i(all_36_1)
% 242.26/48.79  | | 
% 242.26/48.79  | | ALPHA: (93) implies:
% 242.26/48.79  | |   (94)   ~ (all_36_0 = e3)
% 242.26/48.79  | |   (95)  op(e1, e2) = all_36_1
% 242.26/48.79  | |   (96)  op(all_36_1, e1) = all_36_0
% 242.26/48.79  | | 
% 242.26/48.79  | | GROUND_INST: instantiating (74) with e2, all_40_0, e1, e1, simplifying with
% 242.26/48.79  | |              (58), (92) gives:
% 242.26/48.79  | |   (97)  all_40_0 = e2
% 242.26/48.79  | | 
% 242.26/48.79  | | GROUND_INST: instantiating (74) with e1, all_36_1, e2, e1, simplifying with
% 242.26/48.79  | |              (12), (95) gives:
% 242.26/48.79  | |   (98)  all_36_1 = e1
% 242.26/48.79  | | 
% 242.26/48.79  | | REDUCE: (65), (97) imply:
% 242.26/48.79  | |   (99)   ~ (e2 = e0)
% 242.26/48.79  | | 
% 242.26/48.79  | | REDUCE: (96), (98) imply:
% 242.26/48.79  | |   (100)  op(e1, e1) = all_36_0
% 242.26/48.79  | | 
% 242.26/48.79  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 242.26/48.79  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 242.26/48.79  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36),
% 242.26/48.79  | |            (37), (38), (39), (40), (41), (42), (43), (45), (46), (47), (48),
% 242.26/48.79  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 242.26/48.79  | |            (60), (61), (62), (63), (64), (66), (67), (68), (69), (70), (71),
% 242.26/48.79  | |            (72), (73), (74), (75), (76), (79), (80), (81), (82), (83), (84),
% 242.26/48.79  | |            (85), (86), (87), (88), (89), (90), (94), (99), (100) are
% 242.26/48.79  | |            inconsistent by sub-proof #716.
% 242.26/48.79  | | 
% 242.26/48.79  | Case 2:
% 242.26/48.79  | | 
% 242.26/48.79  | |   (101)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1)
% 242.26/48.79  | | 
% 242.26/48.79  | | ALPHA: (101) implies:
% 242.26/48.79  | |   (102)   ~ (all_36_1 = e0)
% 242.26/48.79  | |   (103)  op(e1, e2) = all_36_1
% 242.26/48.79  | | 
% 242.26/48.79  | | GROUND_INST: instantiating (74) with e2, all_40_0, e1, e1, simplifying with
% 242.26/48.79  | |              (58), (92) gives:
% 242.26/48.79  | |   (104)  all_40_0 = e2
% 242.26/48.79  | | 
% 242.26/48.79  | | GROUND_INST: instantiating (74) with e1, all_36_1, e2, e1, simplifying with
% 242.26/48.79  | |              (12), (103) gives:
% 242.26/48.79  | |   (105)  all_36_1 = e1
% 242.26/48.79  | | 
% 242.26/48.79  | | REDUCE: (65), (104) imply:
% 242.26/48.79  | |   (106)   ~ (e2 = e0)
% 242.26/48.79  | | 
% 242.26/48.79  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 242.26/48.79  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 242.26/48.79  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36),
% 242.26/48.79  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 242.26/48.79  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (59),
% 242.26/48.79  | |            (60), (61), (62), (63), (64), (66), (67), (68), (69), (70), (71),
% 242.26/48.79  | |            (72), (73), (74), (75), (76), (79), (80), (81), (82), (83), (84),
% 242.26/48.79  | |            (85), (86), (87), (88), (89), (90), (106) are inconsistent by
% 242.26/48.79  | |            sub-proof #717.
% 242.26/48.79  | | 
% 242.26/48.79  | End of split
% 242.26/48.79  | 
% 242.26/48.79  End of proof
% 242.26/48.79  
% 242.26/48.79  Sub-proof #716 shows that the following formulas are inconsistent:
% 242.26/48.79  ----------------------------------------------------------------
% 242.26/48.79    (1)   ~ (all_52_1 = all_52_3)
% 242.26/48.79    (2)  all_56_21 = e2
% 242.26/48.79    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.26/48.79    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.79         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.79    (5)   ~ (all_52_3 = e1)
% 242.26/48.79    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.26/48.79    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.26/48.79         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.79    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.26/48.79           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.26/48.79             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.26/48.79    (9)   ~ (e3 = e0)
% 242.26/48.79    (10)  op(e0, e1) = all_52_11
% 242.26/48.79    (11)  all_42_2 = e3
% 242.26/48.79    (12)   ~ (e2 = e0)
% 242.26/48.79    (13)   ~ (all_52_11 = e2)
% 242.26/48.79    (14)  all_54_13 = all_52_7
% 242.26/48.79    (15)  op(e1, e2) = all_52_6
% 242.26/48.79    (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.26/48.79          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.79    (17)   ~ (all_52_11 = e1)
% 242.26/48.79    (18)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.26/48.79              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.26/48.79            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.26/48.79            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.79            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.26/48.79             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.79            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.26/48.79            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.79            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.26/48.79            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.79            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.26/48.79              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.79            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.79            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.26/48.79            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.79            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.26/48.79            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.79            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.26/48.79              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.26/48.79            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.79            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.26/48.79            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.79            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.26/48.79            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.79            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.26/48.79              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.26/48.79            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.79            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.79    (19)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.79          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.79    (20)   ~ (all_52_7 = all_52_11)
% 242.26/48.79    (21)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.26/48.79            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.26/48.79              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.26/48.79    (22)   ~ (all_52_1 = all_52_2)
% 242.26/48.79    (23)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.26/48.79            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.26/48.79              e1) = all_20_1 & $i(all_20_1))
% 242.26/48.79    (24)   ~ (all_52_7 = e3)
% 242.26/48.79    (25)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.26/48.79    (26)  op(e0, e3) = all_52_3
% 242.26/48.79    (27)   ~ (e3 = e1)
% 242.26/48.79    (28)  all_58_8 = e2
% 242.26/48.79    (29)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.79          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.79    (30)   ~ (all_52_2 = all_52_3)
% 242.26/48.79    (31)   ~ (all_52_8 = e1)
% 242.26/48.79    (32)  all_58_3 = e3
% 242.26/48.79    (33)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.79          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.79    (34)   ~ (all_52_2 = e1)
% 242.26/48.79    (35)  all_54_2 = all_52_8
% 242.26/48.79    (36)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.26/48.79          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.26/48.79    (37)  op(e3, e3) = e1
% 242.26/48.79    (38)  op(e1, e1) = all_36_0
% 242.26/48.79    (39)   ~ (all_52_3 = all_52_7)
% 242.26/48.79    (40)  all_54_4 = all_52_1
% 242.26/48.79    (41)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.79              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.26/48.79                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.26/48.79                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.26/48.79    (42)  op(e2, e1) = all_52_9
% 242.26/48.79    (43)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.79          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.79    (44)   ~ (all_52_7 = e1)
% 242.26/48.79    (45)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.79    (46)   ~ (all_52_3 = all_52_11)
% 242.26/48.79    (47)  all_56_31 = e1
% 242.26/48.79    (48)  all_54_12 = all_52_3
% 242.26/48.79    (49)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.26/48.79    (50)  all_58_15 = e1
% 242.26/48.79    (51)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.26/48.79          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.26/48.79    (52)  op(e2, e3) = all_52_1
% 242.26/48.79    (53)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.26/48.79          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.79    (54)  all_34_2 = e1
% 242.26/48.79    (55)   ~ (all_52_6 = e3)
% 242.26/48.79    (56)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.26/48.79    (57)  op(e1, e1) = e2
% 242.26/48.79    (58)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.26/48.79          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.26/48.79    (59)  op(e0, e2) = all_52_7
% 242.26/48.79    (60)  all_54_1 = all_52_4
% 242.26/48.79    (61)   ~ (all_52_4 = e3)
% 242.26/48.79    (62)  op(e3, e2) = all_52_4
% 242.26/48.79    (63)   ~ (all_52_8 = all_52_11)
% 242.26/48.79    (64)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.79    (65)  all_58_5 = e1
% 242.26/48.79    (66)  all_58_7 = e1
% 242.26/48.79    (67)   ~ (all_52_2 = e2)
% 242.26/48.79    (68)   ~ (all_52_9 = e3)
% 242.26/48.79    (69)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.26/48.79          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.79    (70)  all_54_8 = all_52_2
% 242.26/48.79    (71)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.79          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.26/48.79    (72)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.79    (73)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.26/48.79          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.26/48.79    (74)  all_56_11 = e3
% 242.26/48.79    (75)   ~ (all_52_4 = e1)
% 242.26/48.79    (76)   ~ (e1 = e0)
% 242.26/48.79    (77)   ~ (all_36_0 = e3)
% 242.26/48.79    (78)   ~ (all_52_8 = e2)
% 242.26/48.79    (79)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.26/48.79          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.26/48.79    (80)   ~ (all_52_1 = e3)
% 242.26/48.79    (81)  all_54_14 = all_52_11
% 242.26/48.79    (82)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.79          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.79            e2)
% 242.26/48.79    (83)   ~ (all_52_4 = all_52_8)
% 242.26/48.79    (84)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.79            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.79            & $i(all_8_1))
% 242.26/48.79    (85)   ~ (e2 = e1)
% 242.26/48.79    (86)   ~ (all_52_1 = e1)
% 242.26/48.79    (87)   ~ (all_52_4 = all_52_7)
% 242.26/48.79  
% 242.26/48.79  Begin of proof
% 242.26/48.79  | 
% 242.26/48.79  | GROUND_INST: instantiating (72) with e2, all_36_0, e1, e1, simplifying with
% 242.26/48.79  |              (38), (57) gives:
% 242.26/48.79  |   (88)  all_36_0 = e2
% 242.26/48.79  | 
% 242.26/48.79  | REDUCE: (77), (88) imply:
% 242.26/48.79  |   (89)   ~ (e3 = e2)
% 242.26/48.79  | 
% 242.26/48.79  | SIMP: (89) implies:
% 242.26/48.79  |   (90)   ~ (e3 = e2)
% 242.26/48.79  | 
% 242.26/48.79  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.26/48.79  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 242.26/48.79  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 242.26/48.79  |            (35), (36), (37), (39), (40), (41), (42), (43), (44), (45), (46),
% 242.26/48.79  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (58),
% 242.26/48.79  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 242.26/48.79  |            (70), (71), (72), (73), (74), (75), (76), (78), (79), (80), (81),
% 242.26/48.79  |            (82), (83), (84), (85), (86), (87), (90) are inconsistent by
% 242.26/48.79  |            sub-proof #717.
% 242.26/48.79  | 
% 242.26/48.79  End of proof
% 242.26/48.79  
% 242.26/48.79  Sub-proof #717 shows that the following formulas are inconsistent:
% 242.26/48.79  ----------------------------------------------------------------
% 242.26/48.79    (1)   ~ (all_52_1 = all_52_3)
% 242.26/48.79    (2)  all_56_21 = e2
% 242.26/48.79    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.26/48.79    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.79         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.79    (5)   ~ (all_52_3 = e1)
% 242.26/48.79    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.26/48.79    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.26/48.79         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.79    (8)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.26/48.79           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.26/48.79             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.26/48.79    (9)   ~ (e3 = e0)
% 242.26/48.79    (10)  op(e0, e1) = all_52_11
% 242.26/48.79    (11)  all_42_2 = e3
% 242.26/48.79    (12)   ~ (e2 = e0)
% 242.26/48.79    (13)   ~ (all_52_11 = e2)
% 242.26/48.79    (14)  all_54_13 = all_52_7
% 242.26/48.79    (15)  op(e1, e2) = all_52_6
% 242.26/48.79    (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.26/48.79          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.79    (17)   ~ (all_52_11 = e1)
% 242.26/48.79    (18)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.26/48.79              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.26/48.79            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.26/48.79            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.79            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.26/48.79             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.79            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.26/48.79            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.79            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.26/48.79            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.79            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.26/48.79              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.79            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.79            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.26/48.79            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.79            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.26/48.79            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.79            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.26/48.79              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.26/48.79            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.79            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.26/48.79            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.79            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.26/48.79            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.79            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.26/48.79              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.26/48.79            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.79            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.79    (19)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.79          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.79    (20)   ~ (all_52_7 = all_52_11)
% 242.26/48.79    (21)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.26/48.79            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.26/48.79              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.26/48.79    (22)   ~ (all_52_1 = all_52_2)
% 242.26/48.79    (23)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.26/48.79            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.26/48.79              e1) = all_20_1 & $i(all_20_1))
% 242.26/48.79    (24)   ~ (all_52_7 = e3)
% 242.26/48.79    (25)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.26/48.79    (26)  op(e0, e3) = all_52_3
% 242.26/48.79    (27)   ~ (e3 = e1)
% 242.26/48.79    (28)  all_58_8 = e2
% 242.26/48.79    (29)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.79          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.79    (30)   ~ (all_52_2 = all_52_3)
% 242.26/48.79    (31)   ~ (all_52_8 = e1)
% 242.26/48.79    (32)  all_58_3 = e3
% 242.26/48.79    (33)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.79          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.79    (34)   ~ (all_52_2 = e1)
% 242.26/48.79    (35)  all_54_2 = all_52_8
% 242.26/48.79    (36)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.26/48.79          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.26/48.80    (37)  op(e3, e3) = e1
% 242.26/48.80    (38)   ~ (all_52_3 = all_52_7)
% 242.26/48.80    (39)  all_54_4 = all_52_1
% 242.26/48.80    (40)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.80              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.26/48.80                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.26/48.80                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.26/48.80    (41)  op(e2, e1) = all_52_9
% 242.26/48.80    (42)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.80          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.80    (43)   ~ (e3 = e2)
% 242.26/48.80    (44)   ~ (all_52_7 = e1)
% 242.26/48.80    (45)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.80    (46)   ~ (all_52_3 = all_52_11)
% 242.26/48.80    (47)  all_56_31 = e1
% 242.26/48.80    (48)  all_54_12 = all_52_3
% 242.26/48.80    (49)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.26/48.80    (50)  all_58_15 = e1
% 242.26/48.80    (51)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.26/48.80          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.26/48.80    (52)  op(e2, e3) = all_52_1
% 242.26/48.80    (53)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.26/48.80          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.80    (54)  all_34_2 = e1
% 242.26/48.80    (55)   ~ (all_52_6 = e3)
% 242.26/48.80    (56)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.26/48.80    (57)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.26/48.80          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.26/48.80    (58)  op(e0, e2) = all_52_7
% 242.26/48.80    (59)  all_54_1 = all_52_4
% 242.26/48.80    (60)   ~ (all_52_4 = e3)
% 242.26/48.80    (61)  op(e3, e2) = all_52_4
% 242.26/48.80    (62)   ~ (all_52_8 = all_52_11)
% 242.26/48.80    (63)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.80    (64)  all_58_5 = e1
% 242.26/48.80    (65)  all_58_7 = e1
% 242.26/48.80    (66)   ~ (all_52_2 = e2)
% 242.26/48.80    (67)   ~ (all_52_9 = e3)
% 242.26/48.80    (68)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.26/48.80          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.80    (69)  all_54_8 = all_52_2
% 242.26/48.80    (70)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.80          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.26/48.80    (71)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.80            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.80    (72)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.26/48.80          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.26/48.80    (73)  all_56_11 = e3
% 242.26/48.80    (74)   ~ (all_52_4 = e1)
% 242.26/48.80    (75)   ~ (e1 = e0)
% 242.26/48.80    (76)   ~ (all_52_8 = e2)
% 242.26/48.80    (77)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.26/48.80          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.26/48.80    (78)   ~ (all_52_1 = e3)
% 242.26/48.80    (79)  all_54_14 = all_52_11
% 242.26/48.80    (80)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.80          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.80            e2)
% 242.26/48.80    (81)   ~ (all_52_4 = all_52_8)
% 242.26/48.80    (82)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.80            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.80            & $i(all_8_1))
% 242.26/48.80    (83)   ~ (e2 = e1)
% 242.26/48.80    (84)   ~ (all_52_1 = e1)
% 242.26/48.80    (85)   ~ (all_52_4 = all_52_7)
% 242.26/48.80  
% 242.26/48.80  Begin of proof
% 242.26/48.80  | 
% 242.26/48.80  | BETA: splitting (8) gives:
% 242.26/48.80  | 
% 242.26/48.80  | Case 1:
% 242.26/48.80  | | 
% 242.26/48.80  | |   (86)   ~ (all_34_2 = e1)
% 242.26/48.80  | | 
% 242.26/48.80  | | REDUCE: (54), (86) imply:
% 242.26/48.80  | |   (87)  $false
% 242.26/48.80  | | 
% 242.26/48.80  | | CLOSE: (87) is inconsistent.
% 242.26/48.80  | | 
% 242.26/48.80  | Case 2:
% 242.26/48.80  | | 
% 242.26/48.80  | |   (88)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 242.26/48.80  | |           all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) &
% 242.26/48.80  | |           op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.26/48.80  | | 
% 242.26/48.80  | | BETA: splitting (21) gives:
% 242.26/48.80  | | 
% 242.26/48.80  | | Case 1:
% 242.26/48.80  | | | 
% 242.26/48.80  | | |   (89)   ~ (all_42_2 = e3)
% 242.26/48.80  | | | 
% 242.26/48.80  | | | REDUCE: (11), (89) imply:
% 242.26/48.80  | | |   (90)  $false
% 242.26/48.80  | | | 
% 242.26/48.80  | | | CLOSE: (90) is inconsistent.
% 242.26/48.80  | | | 
% 242.26/48.80  | | Case 2:
% 242.26/48.80  | | | 
% 242.26/48.80  | | |   (91)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.26/48.80  | | |           all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) &
% 242.26/48.80  | | |           op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.26/48.80  | | | 
% 242.26/48.80  | | | BETA: splitting (56) gives:
% 242.26/48.80  | | | 
% 242.26/48.80  | | | Case 1:
% 242.26/48.80  | | | | 
% 242.26/48.80  | | | |   (92)  all_54_4 = e3
% 242.26/48.80  | | | | 
% 242.26/48.80  | | | | REF_CLOSE: (39), (78), (92) are inconsistent by sub-proof #2100.
% 242.26/48.80  | | | | 
% 242.26/48.80  | | | Case 2:
% 242.26/48.80  | | | | 
% 242.26/48.80  | | | |   (93)   ~ (all_54_4 = e3)
% 242.26/48.80  | | | |   (94)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.26/48.80  | | | | 
% 242.26/48.80  | | | | BETA: splitting (25) gives:
% 242.26/48.80  | | | | 
% 242.26/48.80  | | | | Case 1:
% 242.26/48.80  | | | | | 
% 242.26/48.80  | | | | |   (95)  all_54_1 = e3
% 242.26/48.80  | | | | | 
% 242.26/48.80  | | | | | REF_CLOSE: (59), (60), (95) are inconsistent by sub-proof #1930.
% 242.26/48.80  | | | | | 
% 242.26/48.80  | | | | Case 2:
% 242.26/48.80  | | | | | 
% 242.26/48.80  | | | | |   (96)   ~ (all_54_1 = e3)
% 242.26/48.80  | | | | |   (97)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.26/48.80  | | | | | 
% 242.26/48.80  | | | | | BETA: splitting (49) gives:
% 242.26/48.80  | | | | | 
% 242.26/48.80  | | | | | Case 1:
% 242.26/48.80  | | | | | | 
% 242.26/48.80  | | | | | |   (98)  all_54_2 = e3
% 242.26/48.80  | | | | | | 
% 242.26/48.80  | | | | | | COMBINE_EQS: (35), (98) imply:
% 242.26/48.80  | | | | | |   (99)  all_52_8 = e3
% 242.26/48.80  | | | | | | 
% 242.26/48.80  | | | | | | SIMP: (99) implies:
% 242.26/48.80  | | | | | |   (100)  all_52_8 = e3
% 242.26/48.80  | | | | | | 
% 242.26/48.80  | | | | | | REDUCE: (62), (100) imply:
% 242.26/48.80  | | | | | |   (101)   ~ (all_52_11 = e3)
% 242.26/48.80  | | | | | | 
% 242.26/48.80  | | | | | | SIMP: (101) implies:
% 242.26/48.80  | | | | | |   (102)   ~ (all_52_11 = e3)
% 242.26/48.80  | | | | | | 
% 242.26/48.80  | | | | | | BETA: splitting (57) gives:
% 242.26/48.80  | | | | | | 
% 242.26/48.80  | | | | | | Case 1:
% 242.26/48.80  | | | | | | | 
% 242.26/48.80  | | | | | | |   (103)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 242.26/48.80  | | | | | | |            op(e2, e1) = e3)
% 242.26/48.80  | | | | | | | 
% 242.26/48.80  | | | | | | | BETA: splitting (103) gives:
% 242.26/48.80  | | | | | | | 
% 242.26/48.80  | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | 
% 242.26/48.80  | | | | | | | |   (104)  all_58_4 = e3 & op(e3, e1) = e3
% 242.26/48.80  | | | | | | | | 
% 242.26/48.80  | | | | | | | | ALPHA: (104) implies:
% 242.26/48.80  | | | | | | | |   (105)  all_58_4 = e3
% 242.26/48.80  | | | | | | | | 
% 242.26/48.80  | | | | | | | | BETA: splitting (45) gives:
% 242.26/48.80  | | | | | | | | 
% 242.26/48.80  | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | 
% 242.26/48.80  | | | | | | | | |   (106)  all_54_14 = e3
% 242.26/48.80  | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | COMBINE_EQS: (79), (106) imply:
% 242.26/48.80  | | | | | | | | |   (107)  all_52_11 = e3
% 242.26/48.80  | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | REDUCE: (102), (107) imply:
% 242.26/48.80  | | | | | | | | |   (108)  $false
% 242.26/48.80  | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | CLOSE: (108) is inconsistent.
% 242.26/48.80  | | | | | | | | | 
% 242.26/48.80  | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | 
% 242.26/48.80  | | | | | | | | |   (109)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.80  | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | BETA: splitting (68) gives:
% 242.26/48.80  | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | |   (110)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3
% 242.26/48.80  | | | | | | | | | |            & op(e2, e0) = e3)
% 242.26/48.80  | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | BETA: splitting (110) gives:
% 242.26/48.80  | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | |   (111)  all_58_9 = e3 & op(e3, e0) = e3
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | ALPHA: (111) implies:
% 242.26/48.80  | | | | | | | | | | |   (112)  op(e3, e0) = e3
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | BETA: splitting (4) gives:
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | |   (113)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 242.26/48.80  | | | | | | | | | | | |            & op(e3, e2) = e2)
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | REF_CLOSE: (9), (12), (13), (14), (17), (19), (20), (24),
% 242.26/48.80  | | | | | | | | | | | |            (32), (37), (44), (58), (63), (65), (71), (75),
% 242.26/48.80  | | | | | | | | | | | |            (79), (83), (109), (113) are inconsistent by
% 242.26/48.80  | | | | | | | | | | | |            sub-proof #734.
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | |   (114)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 242.26/48.80  | | | | | | | | | | | |            & op(e3, e0) = e2)
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | BETA: splitting (114) gives:
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | |   (115)  all_58_4 = e2 & op(e3, e1) = e2
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | REF_CLOSE: (43), (105), (115) are inconsistent by sub-proof
% 242.26/48.80  | | | | | | | | | | | | |            #1476.
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | |   (116)  all_58_9 = e2 & op(e3, e0) = e2
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | ALPHA: (116) implies:
% 242.26/48.80  | | | | | | | | | | | | |   (117)  op(e3, e0) = e2
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | REF_CLOSE: (43), (71), (112), (117) are inconsistent by
% 242.26/48.80  | | | | | | | | | | | | |            sub-proof #2125.
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | |   (118)  all_58_10 = e3 & op(e2, e0) = e3
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | ALPHA: (118) implies:
% 242.26/48.80  | | | | | | | | | | |   (119)  all_58_10 = e3
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | BETA: splitting (7) gives:
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | |   (120)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 242.26/48.80  | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | BETA: splitting (120) gives:
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | |   (121)  all_58_12 = e3 & op(e0, e3) = e3
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | ALPHA: (121) implies:
% 242.26/48.80  | | | | | | | | | | | | |   (122)  all_58_12 = e3
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | BETA: splitting (42) gives:
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | |   (123)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 242.26/48.80  | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 242.26/48.80  | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 242.26/48.80  | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | |   (124)  all_58_0 = e2 & op(e3, e3) = e2
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 242.26/48.80  | | | | | | | | | | | | | | |   (125)  op(e3, e3) = e2
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | REF_CLOSE: (37), (71), (83), (125) are inconsistent by
% 242.26/48.80  | | | | | | | | | | | | | | |            sub-proof #2267.
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | |   (126)  all_58_2 = e2 & op(e2, e3) = e2
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 242.26/48.80  | | | | | | | | | | | | | | |   (127)  op(e2, e3) = e2
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | |   (128)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 242.26/48.80  | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (12), (13), (14), (17), (19), (20),
% 242.26/48.80  | | | | | | | | | | | | | | | |            (24), (27), (32), (33), (37), (43), (44), (58),
% 242.26/48.80  | | | | | | | | | | | | | | | |            (60), (61), (63), (65), (71), (75), (79), (82),
% 242.26/48.80  | | | | | | | | | | | | | | | |            (83), (91), (105), (109), (127), (128) are
% 242.26/48.80  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #730.
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | |   (129)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 242.26/48.80  | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | |   (130)  all_58_5 = e0 & op(e2, e1) = e0
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (75), (130) are inconsistent by sub-proof
% 242.26/48.80  | | | | | | | | | | | | | | | | |            #1485.
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | |   (131)  all_58_10 = e0 & op(e2, e0) = e0
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 242.26/48.80  | | | | | | | | | | | | | | | | |   (132)  all_58_10 = e0
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (132) imply:
% 242.26/48.80  | | | | | | | | | | | | | | | | |   (133)  e3 = e0
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (133) imply:
% 242.26/48.80  | | | | | | | | | | | | | | | | |   (134)  all_58_4 = e0
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (12), (13), (14), (17), (19), (20),
% 242.26/48.80  | | | | | | | | | | | | | | | | |            (24), (27), (32), (33), (37), (43), (44), (58),
% 242.26/48.80  | | | | | | | | | | | | | | | | |            (60), (61), (63), (65), (71), (75), (79), (83),
% 242.26/48.80  | | | | | | | | | | | | | | | | |            (109), (134) are inconsistent by sub-proof #731.
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | |   (135)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 242.26/48.80  | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 242.26/48.80  | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 242.26/48.80  | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | |   (136)  all_58_6 = e2 & op(e1, e3) = e2
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 242.26/48.80  | | | | | | | | | | | | | | |   (137)  all_58_6 = e2
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | |   (138)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 242.26/48.80  | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (43), (55), (71), (137), (138) are
% 242.26/48.80  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #933.
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | |   (139)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 242.26/48.80  | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | |   (140)  all_58_8 = e3 & op(e1, e1) = e3
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (43), (140) are inconsistent by sub-proof
% 242.26/48.80  | | | | | | | | | | | | | | | | |            #729.
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | |   (141)  all_58_11 = e3 & op(e1, e0) = e3
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 242.26/48.80  | | | | | | | | | | | | | | | | |   (142)  all_58_11 = e3
% 242.26/48.80  | | | | | | | | | | | | | | | | |   (143)  op(e1, e0) = e3
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (12),
% 242.26/48.80  | | | | | | | | | | | | | | | | |            (13), (14), (16), (17), (18), (19), (20), (22),
% 242.26/48.80  | | | | | | | | | | | | | | | | |            (23), (24), (27), (28), (29), (30), (32), (33),
% 242.26/48.80  | | | | | | | | | | | | | | | | |            (34), (36), (37), (38), (39), (42), (43), (44),
% 242.26/48.80  | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (58), (60), (61),
% 242.26/48.80  | | | | | | | | | | | | | | | | |            (63), (64), (65), (66), (69), (70), (71), (72),
% 242.26/48.80  | | | | | | | | | | | | | | | | |            (73), (75), (77), (78), (79), (80), (82), (83),
% 242.26/48.80  | | | | | | | | | | | | | | | | |            (84), (88), (91), (94), (105), (109), (142), (143)
% 242.26/48.80  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #723.
% 242.26/48.80  | | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | |   (144)  all_58_12 = e2 & op(e0, e3) = e2
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | | REF_CLOSE: (43), (122), (144) are inconsistent by sub-proof
% 242.26/48.80  | | | | | | | | | | | | | | |            #1974.
% 242.26/48.80  | | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | |   (145)  all_58_13 = e3 & op(e0, e2) = e3
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | REF_CLOSE: (24), (58), (71), (145) are inconsistent by
% 242.26/48.80  | | | | | | | | | | | | |            sub-proof #1919.
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | |   (146)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 242.26/48.80  | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | BETA: splitting (146) gives:
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | |   (147)  all_58_14 = e3 & op(e0, e1) = e3
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | ALPHA: (147) implies:
% 242.26/48.80  | | | | | | | | | | | | |   (148)  all_58_14 = e3
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | REF_CLOSE: (4), (9), (12), (13), (14), (17), (19), (20),
% 242.26/48.80  | | | | | | | | | | | | |            (24), (27), (28), (29), (32), (33), (37), (43),
% 242.26/48.80  | | | | | | | | | | | | |            (44), (58), (60), (61), (63), (64), (65), (71),
% 242.26/48.80  | | | | | | | | | | | | |            (75), (79), (83), (109), (148) are inconsistent by
% 242.26/48.80  | | | | | | | | | | | | |            sub-proof #721.
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | |   (149)  all_58_15 = e3 & op(e0, e0) = e3
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | ALPHA: (149) implies:
% 242.26/48.80  | | | | | | | | | | | | |   (150)  all_58_15 = e3
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | | REF_CLOSE: (4), (9), (12), (27), (33), (37), (43), (50),
% 242.26/48.80  | | | | | | | | | | | | |            (53), (60), (61), (71), (75), (83), (105), (150)
% 242.26/48.80  | | | | | | | | | | | | |            are inconsistent by sub-proof #1093.
% 242.26/48.80  | | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | End of split
% 242.26/48.80  | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | |   (151)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 242.26/48.80  | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 242.26/48.80  | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | BETA: splitting (151) gives:
% 242.26/48.80  | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | Case 1:
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | |   (152)  all_58_11 = e3 & op(e1, e0) = e3
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | ALPHA: (152) implies:
% 242.26/48.80  | | | | | | | | | | |   (153)  all_58_11 = e3
% 242.26/48.80  | | | | | | | | | | |   (154)  op(e1, e0) = e3
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (12),
% 242.26/48.80  | | | | | | | | | | |            (13), (14), (16), (17), (18), (19), (20), (22),
% 242.26/48.80  | | | | | | | | | | |            (23), (24), (27), (28), (29), (30), (32), (33),
% 242.26/48.80  | | | | | | | | | | |            (34), (36), (37), (38), (39), (42), (43), (44),
% 242.26/48.80  | | | | | | | | | | |            (46), (47), (48), (50), (52), (58), (60), (61),
% 242.26/48.80  | | | | | | | | | | |            (63), (64), (65), (66), (69), (70), (71), (72),
% 242.26/48.80  | | | | | | | | | | |            (73), (75), (77), (78), (79), (80), (82), (83),
% 242.26/48.80  | | | | | | | | | | |            (84), (88), (91), (94), (105), (109), (153), (154)
% 242.26/48.80  | | | | | | | | | | |            are inconsistent by sub-proof #723.
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.80  | | | | | | | | | | Case 2:
% 242.26/48.80  | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | |   (155)  all_58_15 = e3 & op(e0, e0) = e3
% 242.26/48.81  | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | REF_CLOSE: (4), (9), (12), (27), (33), (37), (43), (50),
% 242.26/48.81  | | | | | | | | | | |            (53), (60), (61), (71), (75), (83), (105), (155)
% 242.26/48.81  | | | | | | | | | | |            are inconsistent by sub-proof #1091.
% 242.26/48.81  | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | |   (156)  all_58_5 = e3 & op(e2, e1) = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | REF_CLOSE: (41), (67), (71), (156) are inconsistent by sub-proof
% 242.26/48.81  | | | | | | | |            #1822.
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | End of split
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | Case 2:
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | |   (157)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 242.26/48.81  | | | | | | |            op(e0, e1) = e3)
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | BETA: splitting (157) gives:
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | |   (158)  all_58_8 = e3 & op(e1, e1) = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | REF_CLOSE: (28), (43), (158) are inconsistent by sub-proof #729.
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | |   (159)  all_58_14 = e3 & op(e0, e1) = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | ALPHA: (159) implies:
% 242.26/48.81  | | | | | | | |   (160)  all_58_14 = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | BETA: splitting (45) gives:
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | |   (161)  all_54_14 = e3
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | COMBINE_EQS: (79), (161) imply:
% 242.26/48.81  | | | | | | | | |   (162)  all_52_11 = e3
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | REDUCE: (102), (162) imply:
% 242.26/48.81  | | | | | | | | |   (163)  $false
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | CLOSE: (163) is inconsistent.
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | |   (164)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | REF_CLOSE: (4), (9), (12), (13), (14), (17), (19), (20), (24),
% 242.26/48.81  | | | | | | | | |            (27), (28), (29), (32), (33), (37), (43), (44),
% 242.26/48.81  | | | | | | | | |            (58), (60), (61), (63), (64), (65), (71), (75),
% 242.26/48.81  | | | | | | | | |            (79), (83), (160), (164) are inconsistent by
% 242.26/48.81  | | | | | | | | |            sub-proof #721.
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | End of split
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | End of split
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | Case 2:
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | |   (165)   ~ (all_54_2 = e3)
% 242.26/48.81  | | | | | |   (166)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | | REDUCE: (35), (165) imply:
% 242.26/48.81  | | | | | |   (167)   ~ (all_52_8 = e3)
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | | BETA: splitting (57) gives:
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | | Case 1:
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | |   (168)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 242.26/48.81  | | | | | | |            op(e2, e1) = e3)
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | BETA: splitting (168) gives:
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | |   (169)  all_58_4 = e3 & op(e3, e1) = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | ALPHA: (169) implies:
% 242.26/48.81  | | | | | | | |   (170)  all_58_4 = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | BETA: splitting (29) gives:
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | |   (171)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 242.26/48.81  | | | | | | | | |            op(e2, e1) = e0)
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | REF_CLOSE: (9), (64), (75), (170), (171) are inconsistent by
% 242.26/48.81  | | | | | | | | |            sub-proof #1484.
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | |   (172)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 242.26/48.81  | | | | | | | | |            op(e0, e1) = e0)
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | BETA: splitting (172) gives:
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | |   (173)  all_58_8 = e0 & op(e1, e1) = e0
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | ALPHA: (173) implies:
% 242.26/48.81  | | | | | | | | | |   (174)  all_58_8 = e0
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | REF_CLOSE: (12), (28), (174) are inconsistent by sub-proof
% 242.26/48.81  | | | | | | | | | |            #1556.
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | |   (175)  all_58_14 = e0 & op(e0, e1) = e0
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | ALPHA: (175) implies:
% 242.26/48.81  | | | | | | | | | |   (176)  all_58_14 = e0
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | BETA: splitting (166) gives:
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | |   (177)  all_54_2 = e2
% 242.26/48.81  | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | REF_CLOSE: (35), (76), (177) are inconsistent by sub-proof
% 242.26/48.81  | | | | | | | | | | |            #1986.
% 242.26/48.81  | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | |   (178)   ~ (all_54_2 = e2)
% 242.26/48.81  | | | | | | | | | | |   (179)  all_54_2 = e1 | all_54_2 = e0
% 242.26/48.81  | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | BETA: splitting (179) gives:
% 242.26/48.81  | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | |   (180)  all_54_2 = e1
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | REF_CLOSE: (31), (35), (180) are inconsistent by sub-proof
% 242.26/48.81  | | | | | | | | | | | |            #1337.
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | |   (181)  all_54_2 = e0
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | COMBINE_EQS: (35), (181) imply:
% 242.26/48.81  | | | | | | | | | | | |   (182)  all_52_8 = e0
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | SIMP: (182) implies:
% 242.26/48.81  | | | | | | | | | | | |   (183)  all_52_8 = e0
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | REDUCE: (81), (183) imply:
% 242.26/48.81  | | | | | | | | | | | |   (184)   ~ (all_52_4 = e0)
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | REDUCE: (167), (183) imply:
% 242.26/48.81  | | | | | | | | | | | |   (185)   ~ (e3 = e0)
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | REDUCE: (76), (183) imply:
% 242.26/48.81  | | | | | | | | | | | |   (186)   ~ (e2 = e0)
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | REDUCE: (31), (183) imply:
% 242.26/48.81  | | | | | | | | | | | |   (187)   ~ (e1 = e0)
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | BETA: splitting (7) gives:
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | |   (188)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 242.26/48.81  | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 242.26/48.81  | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | BETA: splitting (188) gives:
% 242.26/48.81  | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | |   (189)  all_58_12 = e3 & op(e0, e3) = e3
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | ALPHA: (189) implies:
% 242.26/48.81  | | | | | | | | | | | | | |   (190)  all_58_12 = e3
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | |   (191)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 242.26/48.81  | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 242.26/48.81  | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 242.26/48.81  | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | |   (192)  all_58_12 = e2 & op(e0, e3) = e2
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 242.26/48.81  | | | | | | | | | | | | | | | |   (193)  all_58_12 = e2
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | | REF_CLOSE: (43), (190), (193) are inconsistent by sub-proof
% 242.26/48.81  | | | | | | | | | | | | | | | |            #1552.
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | |   (194)  all_58_13 = e2 & op(e0, e2) = e2
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 242.26/48.81  | | | | | | | | | | | | | | | |   (195)  op(e0, e2) = e2
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | | REF_CLOSE: (14), (24), (44), (58), (59), (63), (71), (74),
% 242.26/48.81  | | | | | | | | | | | | | | | |            (85), (97), (184), (195) are inconsistent by
% 242.26/48.81  | | | | | | | | | | | | | | | |            sub-proof #1815.
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | |   (196)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 242.26/48.81  | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 242.26/48.81  | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 242.26/48.81  | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | |   (197)  all_58_14 = e2 & op(e0, e1) = e2
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 242.26/48.81  | | | | | | | | | | | | | | | |   (198)  all_58_14 = e2
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | | REF_CLOSE: (12), (176), (198) are inconsistent by sub-proof
% 242.26/48.81  | | | | | | | | | | | | | | | |            #2114.
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | |   (199)  all_58_15 = e2 & op(e0, e0) = e2
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 242.26/48.81  | | | | | | | | | | | | | | | |   (200)  all_58_15 = e2
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | | REF_CLOSE: (50), (83), (200) are inconsistent by sub-proof
% 242.26/48.81  | | | | | | | | | | | | | | | |            #2231.
% 242.26/48.81  | | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | |   (201)  all_58_13 = e3 & op(e0, e2) = e3
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | REF_CLOSE: (24), (58), (71), (201) are inconsistent by
% 242.26/48.81  | | | | | | | | | | | | | |            sub-proof #1919.
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | |   (202)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 242.26/48.81  | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 242.26/48.81  | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | BETA: splitting (202) gives:
% 242.26/48.81  | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | |   (203)  all_58_14 = e3 & op(e0, e1) = e3
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | ALPHA: (203) implies:
% 242.26/48.81  | | | | | | | | | | | | | |   (204)  all_58_14 = e3
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (9), (12), (13), (14), (17),
% 242.26/48.81  | | | | | | | | | | | | | |            (18), (19), (20), (26), (27), (28), (29), (31),
% 242.26/48.81  | | | | | | | | | | | | | |            (32), (33), (35), (36), (37), (38), (40), (44),
% 242.26/48.81  | | | | | | | | | | | | | |            (45), (46), (47), (48), (50), (52), (59), (60),
% 242.26/48.81  | | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (71), (73), (74),
% 242.26/48.81  | | | | | | | | | | | | | |            (75), (76), (77), (78), (79), (80), (81), (83),
% 242.26/48.81  | | | | | | | | | | | | | |            (85), (97), (166), (204) are inconsistent by
% 242.26/48.81  | | | | | | | | | | | | | |            sub-proof #718.
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | |   (205)  all_58_15 = e3 & op(e0, e0) = e3
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | ALPHA: (205) implies:
% 242.26/48.81  | | | | | | | | | | | | | |   (206)  all_58_15 = e3
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (12), (27), (33), (37), (43), (50),
% 242.26/48.81  | | | | | | | | | | | | | |            (53), (60), (61), (71), (75), (83), (170), (206)
% 242.26/48.81  | | | | | | | | | | | | | |            are inconsistent by sub-proof #1093.
% 242.26/48.81  | | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | End of split
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | |   (207)  all_58_5 = e3 & op(e2, e1) = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | REF_CLOSE: (41), (67), (71), (207) are inconsistent by sub-proof
% 242.26/48.81  | | | | | | | |            #1822.
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | End of split
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | Case 2:
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | |   (208)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 242.26/48.81  | | | | | | |            op(e0, e1) = e3)
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | BETA: splitting (208) gives:
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | |   (209)  all_58_8 = e3 & op(e1, e1) = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | REF_CLOSE: (28), (43), (209) are inconsistent by sub-proof #729.
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | |   (210)  all_58_14 = e3 & op(e0, e1) = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | ALPHA: (210) implies:
% 242.26/48.81  | | | | | | | |   (211)  all_58_14 = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (9), (12), (13), (14), (17),
% 242.26/48.81  | | | | | | | |            (18), (19), (20), (26), (27), (28), (29), (31), (32),
% 242.26/48.81  | | | | | | | |            (33), (35), (36), (37), (38), (40), (44), (45), (46),
% 242.26/48.81  | | | | | | | |            (47), (48), (50), (52), (59), (60), (61), (62), (63),
% 242.26/48.81  | | | | | | | |            (64), (65), (71), (73), (74), (75), (76), (77), (78),
% 242.26/48.81  | | | | | | | |            (79), (80), (81), (83), (85), (97), (166), (211) are
% 242.26/48.81  | | | | | | | |            inconsistent by sub-proof #718.
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | End of split
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | End of split
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | End of split
% 242.26/48.81  | | | | | 
% 242.26/48.81  | | | | End of split
% 242.26/48.81  | | | | 
% 242.26/48.81  | | | End of split
% 242.26/48.81  | | | 
% 242.26/48.81  | | End of split
% 242.26/48.81  | | 
% 242.26/48.81  | End of split
% 242.26/48.81  | 
% 242.26/48.81  End of proof
% 242.26/48.81  
% 242.26/48.81  Sub-proof #718 shows that the following formulas are inconsistent:
% 242.26/48.81  ----------------------------------------------------------------
% 242.26/48.81    (1)  all_56_21 = e2
% 242.26/48.81    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.26/48.81    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.81         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.81    (4)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.26/48.81    (5)   ~ (all_52_3 = e1)
% 242.26/48.81    (6)   ~ (e3 = e0)
% 242.26/48.81    (7)   ~ (e2 = e0)
% 242.26/48.81    (8)   ~ (all_52_11 = e2)
% 242.26/48.81    (9)  all_54_13 = all_52_7
% 242.26/48.81    (10)   ~ (all_52_11 = e1)
% 242.26/48.81    (11)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.26/48.81              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.26/48.81            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.26/48.81            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.81            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.26/48.81             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.81            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.26/48.81            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.81            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.26/48.81            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.81            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.26/48.81              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.81            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.81            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.26/48.81            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.81            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.26/48.81            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.81            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.26/48.81              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.26/48.81            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.81            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.26/48.81            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.81            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.26/48.81            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.81            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.26/48.81              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.26/48.81            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.81            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.81    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.81          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.81    (13)   ~ (all_52_7 = all_52_11)
% 242.26/48.81    (14)  op(e0, e3) = all_52_3
% 242.26/48.81    (15)   ~ (e3 = e1)
% 242.26/48.81    (16)  all_58_8 = e2
% 242.26/48.81    (17)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.81          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.81    (18)   ~ (all_52_8 = e1)
% 242.26/48.81    (19)  all_58_3 = e3
% 242.26/48.81    (20)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.81          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.81    (21)  all_54_2 = all_52_8
% 242.26/48.81    (22)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.26/48.81          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.26/48.81    (23)  op(e3, e3) = e1
% 242.26/48.81    (24)   ~ (all_52_3 = all_52_7)
% 242.26/48.81    (25)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.81              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.26/48.81                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.26/48.81                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.26/48.81    (26)   ~ (all_52_7 = e1)
% 242.26/48.81    (27)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.81    (28)   ~ (all_52_3 = all_52_11)
% 242.26/48.81    (29)  all_56_31 = e1
% 242.26/48.81    (30)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.26/48.81    (31)  all_54_12 = all_52_3
% 242.26/48.81    (32)  all_58_15 = e1
% 242.26/48.81    (33)  op(e2, e3) = all_52_1
% 242.26/48.81    (34)  all_54_1 = all_52_4
% 242.26/48.81    (35)   ~ (all_52_4 = e3)
% 242.26/48.81    (36)  op(e3, e2) = all_52_4
% 242.26/48.81    (37)   ~ (all_52_8 = all_52_11)
% 242.26/48.81    (38)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.81    (39)  all_58_5 = e1
% 242.26/48.81    (40)  all_58_7 = e1
% 242.26/48.81    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.81    (42)  all_58_14 = e3
% 242.26/48.81    (43)  all_56_11 = e3
% 242.26/48.81    (44)   ~ (all_52_4 = e1)
% 242.26/48.81    (45)   ~ (e1 = e0)
% 242.26/48.81    (46)   ~ (all_52_8 = e2)
% 242.26/48.81    (47)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.26/48.81          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.26/48.81    (48)   ~ (all_52_1 = e3)
% 242.26/48.81    (49)  all_54_14 = all_52_11
% 242.26/48.81    (50)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.81          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.81            e2)
% 242.26/48.81    (51)   ~ (all_52_4 = all_52_8)
% 242.26/48.81    (52)   ~ (e2 = e1)
% 242.26/48.81    (53)   ~ (all_52_4 = all_52_7)
% 242.26/48.81  
% 242.26/48.81  Begin of proof
% 242.26/48.81  | 
% 242.26/48.81  | BETA: splitting (17) gives:
% 242.26/48.81  | 
% 242.26/48.81  | Case 1:
% 242.26/48.81  | | 
% 242.26/48.81  | |   (54)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 242.26/48.81  | |           e0)
% 242.26/48.81  | | 
% 242.26/48.81  | | BETA: splitting (54) gives:
% 242.26/48.81  | | 
% 242.26/48.81  | | Case 1:
% 242.26/48.81  | | | 
% 242.26/48.81  | | |   (55)  all_58_4 = e0 & op(e3, e1) = e0
% 242.26/48.81  | | | 
% 242.26/48.81  | | | ALPHA: (55) implies:
% 242.26/48.81  | | |   (56)  all_58_4 = e0
% 242.26/48.81  | | | 
% 242.26/48.81  | | | BETA: splitting (20) gives:
% 242.26/48.81  | | | 
% 242.26/48.81  | | | Case 1:
% 242.26/48.81  | | | | 
% 242.26/48.81  | | | |   (57)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 242.26/48.81  | | | |           = e3)
% 242.26/48.81  | | | | 
% 242.26/48.81  | | | | REF_CLOSE: (15), (23), (35), (36), (41), (57) are inconsistent by
% 242.26/48.81  | | | |            sub-proof #1401.
% 242.26/48.81  | | | | 
% 242.26/48.81  | | | Case 2:
% 242.26/48.81  | | | | 
% 242.26/48.81  | | | |   (58)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 242.26/48.81  | | | |           = e3)
% 242.26/48.81  | | | | 
% 242.26/48.81  | | | | BETA: splitting (58) gives:
% 242.26/48.81  | | | | 
% 242.26/48.81  | | | | Case 1:
% 242.26/48.81  | | | | | 
% 242.26/48.81  | | | | |   (59)  all_58_4 = e3 & op(e3, e1) = e3
% 242.26/48.81  | | | | | 
% 242.26/48.81  | | | | | REF_CLOSE: (6), (56), (59) are inconsistent by sub-proof #1244.
% 242.26/48.81  | | | | | 
% 242.26/48.81  | | | | Case 2:
% 242.26/48.81  | | | | | 
% 242.26/48.81  | | | | |   (60)  all_58_9 = e3 & op(e3, e0) = e3
% 242.26/48.81  | | | | | 
% 242.26/48.81  | | | | | ALPHA: (60) implies:
% 242.26/48.81  | | | | |   (61)  all_58_9 = e3
% 242.26/48.81  | | | | | 
% 242.26/48.81  | | | | | BETA: splitting (30) gives:
% 242.26/48.81  | | | | | 
% 242.26/48.81  | | | | | Case 1:
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | |   (62)  all_54_2 = e2
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | | COMBINE_EQS: (21), (62) imply:
% 242.26/48.81  | | | | | |   (63)  all_52_8 = e2
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | | REDUCE: (46), (63) imply:
% 242.26/48.81  | | | | | |   (64)  $false
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | | CLOSE: (64) is inconsistent.
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | Case 2:
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | |   (65)  all_54_2 = e1 | all_54_2 = e0
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | | BETA: splitting (65) gives:
% 242.26/48.81  | | | | | | 
% 242.26/48.81  | | | | | | Case 1:
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | |   (66)  all_54_2 = e1
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | COMBINE_EQS: (21), (66) imply:
% 242.26/48.81  | | | | | | |   (67)  all_52_8 = e1
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | REDUCE: (18), (67) imply:
% 242.26/48.81  | | | | | | |   (68)  $false
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | CLOSE: (68) is inconsistent.
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | Case 2:
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | |   (69)  all_54_2 = e0
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | COMBINE_EQS: (21), (69) imply:
% 242.26/48.81  | | | | | | |   (70)  all_52_8 = e0
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | REDUCE: (51), (70) imply:
% 242.26/48.81  | | | | | | |   (71)   ~ (all_52_4 = e0)
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | REDUCE: (37), (70) imply:
% 242.26/48.81  | | | | | | |   (72)   ~ (all_52_11 = e0)
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | SIMP: (72) implies:
% 242.26/48.81  | | | | | | |   (73)   ~ (all_52_11 = e0)
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | BETA: splitting (27) gives:
% 242.26/48.81  | | | | | | | 
% 242.26/48.81  | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | |   (74)  all_54_14 = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | COMBINE_EQS: (49), (74) imply:
% 242.26/48.81  | | | | | | | |   (75)  all_52_11 = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | SIMP: (75) implies:
% 242.26/48.81  | | | | | | | |   (76)  all_52_11 = e3
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | REDUCE: (28), (76) imply:
% 242.26/48.81  | | | | | | | |   (77)   ~ (all_52_3 = e3)
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | REDUCE: (13), (76) imply:
% 242.26/48.81  | | | | | | | |   (78)   ~ (all_52_7 = e3)
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | REDUCE: (8), (76) imply:
% 242.26/48.81  | | | | | | | |   (79)   ~ (e3 = e2)
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | BETA: splitting (11) gives:
% 242.26/48.81  | | | | | | | | 
% 242.26/48.81  | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | |   (80)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 242.26/48.81  | | | | | | | | |           ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 242.26/48.81  | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 242.26/48.81  | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 242.26/48.81  | | | | | | | | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 242.26/48.81  | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3)
% 242.26/48.81  | | | | | | | | |           = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 242.26/48.81  | | | | | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.81  | | | | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 242.26/48.81  | | | | | | | | |           = e3 & op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17
% 242.26/48.81  | | | | | | | | |           = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.81  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1)
% 242.26/48.81  | | | | | | | | |           = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 242.26/48.81  | | | | | | | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 242.26/48.81  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0)
% 242.26/48.81  | | | | | | | | |           = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 242.26/48.81  | | | | | | | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.81  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 242.26/48.81  | | | | | | | | |           = e0 & op(e0, e3) = e0)
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | BETA: splitting (80) gives:
% 242.26/48.81  | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | Case 1:
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | |   (81)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 242.26/48.81  | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 242.26/48.81  | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 242.26/48.81  | | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 242.26/48.81  | | | | | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.81  | | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.26/48.81  | | | | | | | | | |             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 242.26/48.81  | | | | | | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.26/48.81  | | | | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.81  | | | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 242.26/48.81  | | | | | | | | | |           e3)
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | | REF_CLOSE: (29), (33), (41), (43), (48), (81) are
% 242.26/48.81  | | | | | | | | | |            inconsistent by sub-proof #857.
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.81  | | | | | | | | | Case 2:
% 242.26/48.81  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | |   (82)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3)
% 242.26/48.82  | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.82  | | | | | | | | | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 242.26/48.82  | | | | | | | | | |           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 242.26/48.82  | | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 242.26/48.82  | | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.26/48.82  | | | | | | | | | |             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 242.26/48.82  | | | | | | | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 242.26/48.82  | | | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.82  | | | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 242.26/48.82  | | | | | | | | | |           e0)
% 242.26/48.82  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | BETA: splitting (82) gives:
% 242.26/48.82  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | |   (83)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | |           e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 242.26/48.82  | | | | | | | | | | |         &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 242.26/48.82  | | | | | | | | | | |           e3) = e1
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | ALPHA: (83) implies:
% 242.26/48.82  | | | | | | | | | | |   (84)   ~ (all_56_11 = e3)
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | REDUCE: (43), (84) imply:
% 242.26/48.82  | | | | | | | | | | |   (85)  $false
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | CLOSE: (85) is inconsistent.
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | |   (86)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 242.26/48.82  | | | | | | | | | | |             e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 242.26/48.82  | | | | | | | | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 242.26/48.82  | | | | | | | | | | |           e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 242.26/48.82  | | | | | | | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.82  | | | | | | | | | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | BETA: splitting (86) gives:
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | |   (87)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | | |           e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 242.26/48.82  | | | | | | | | | | | |         &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 242.26/48.82  | | | | | | | | | | | |           e3) = e3
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | ALPHA: (87) implies:
% 242.26/48.82  | | | | | | | | | | | |   (88)   ~ (all_56_31 = e0)
% 242.26/48.82  | | | | | | | | | | | |   (89)   ~ (all_56_21 = e0)
% 242.26/48.82  | | | | | | | | | | | |   (90)   ~ (all_56_11 = e0)
% 242.26/48.82  | | | | | | | | | | | |   (91)  op(e0, e3) = e3
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | BETA: splitting (22) gives:
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | |   (92)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 242.26/48.82  | | | | | | | | | | | | |           & op(e2, e3) = e3)
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | REF_CLOSE: (15), (23), (33), (41), (48), (92) are
% 242.26/48.82  | | | | | | | | | | | | |            inconsistent by sub-proof #1208.
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | |   (93)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 242.26/48.82  | | | | | | | | | | | | |           e3 & op(e0, e3) = e3)
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | BETA: splitting (93) gives:
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | |   (94)  all_58_6 = e3 & op(e1, e3) = e3
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | ALPHA: (94) implies:
% 242.26/48.82  | | | | | | | | | | | | | |   (95)  all_58_6 = e3
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | |   (96)  all_54_1 = e2
% 242.26/48.82  | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | COMBINE_EQS: (34), (96) imply:
% 242.26/48.82  | | | | | | | | | | | | | | |   (97)  all_52_4 = e2
% 242.26/48.82  | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | SIMP: (97) implies:
% 242.26/48.82  | | | | | | | | | | | | | | |   (98)  all_52_4 = e2
% 242.26/48.82  | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | REDUCE: (53), (98) imply:
% 242.26/48.82  | | | | | | | | | | | | | | |   (99)   ~ (all_52_7 = e2)
% 242.26/48.82  | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | SIMP: (99) implies:
% 242.26/48.82  | | | | | | | | | | | | | | |   (100)   ~ (all_52_7 = e2)
% 242.26/48.82  | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 242.26/48.82  | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | |   (101)  all_54_13 = e3
% 242.26/48.82  | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (78), (101) are inconsistent by sub-proof
% 242.26/48.82  | | | | | | | | | | | | | | | |            #2010.
% 242.26/48.82  | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | |   (102)   ~ (all_54_13 = e3)
% 242.26/48.82  | | | | | | | | | | | | | | | |   (103)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.82  | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 242.26/48.82  | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | |   (104)  all_54_13 = e2
% 242.26/48.82  | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (100), (104) are inconsistent by sub-proof
% 242.26/48.82  | | | | | | | | | | | | | | | | |            #2009.
% 242.26/48.82  | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | |   (105)  all_54_13 = e1 | all_54_13 = e0
% 242.26/48.82  | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 242.26/48.82  | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | |   (106)  all_54_13 = e1
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (26), (106) are inconsistent by sub-proof
% 242.26/48.82  | | | | | | | | | | | | | | | | | |            #1966.
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | |   (107)  all_54_13 = e0
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (107) imply:
% 242.26/48.82  | | | | | | | | | | | | | | | | | |   (108)  all_52_7 = e0
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | SIMP: (108) implies:
% 242.26/48.82  | | | | | | | | | | | | | | | | | |   (109)  all_52_7 = e0
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | REDUCE: (24), (109) imply:
% 242.26/48.82  | | | | | | | | | | | | | | | | | |   (110)   ~ (all_52_3 = e0)
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | REDUCE: (78), (109) imply:
% 242.26/48.82  | | | | | | | | | | | | | | | | | |   (111)   ~ (e3 = e0)
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | REDUCE: (26), (109) imply:
% 242.26/48.82  | | | | | | | | | | | | | | | | | |   (112)   ~ (e1 = e0)
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | |   (113)  all_54_12 = e3
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (77), (113) are inconsistent by sub-proof
% 242.26/48.82  | | | | | | | | | | | | | | | | | | |            #2266.
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | |   (114)   ~ (all_54_12 = e3)
% 242.26/48.82  | | | | | | | | | | | | | | | | | | |   (115)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |   (116)  all_54_12 = e2
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (116) imply:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |   (117)  all_52_3 = e2
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | SIMP: (117) implies:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |   (118)  all_52_3 = e2
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (118) imply:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |   (119)   ~ (e3 = e2)
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (118) imply:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |   (120)  op(e0, e3) = e2
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (41) with e2, e3, e3, e0,
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |              simplifying with (91), (120) gives:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |   (121)  e3 = e2
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (121) imply:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |   (122)  all_58_6 = e2
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (15), (22), (23), (25), (32), (33),
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |            (41), (42), (45), (48), (50), (52), (79), (122)
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1166.
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |   (123)  all_54_12 = e1 | all_54_12 = e0
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (31), (110), (123) are inconsistent by
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | |            sub-proof #2067.
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | |   (124)  all_54_1 = e1 | all_54_1 = e0
% 242.26/48.82  | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | | REF_CLOSE: (34), (44), (71), (124) are inconsistent by
% 242.26/48.82  | | | | | | | | | | | | | | |            sub-proof #2049.
% 242.26/48.82  | | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | |   (125)  all_58_12 = e3 & op(e0, e3) = e3
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | ALPHA: (125) implies:
% 242.26/48.82  | | | | | | | | | | | | | |   (126)  all_58_12 = e3
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (25), (32), (42), (45), (50), (52),
% 242.26/48.82  | | | | | | | | | | | | | |            (79), (126) are inconsistent by sub-proof #1863.
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | |   (127)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 242.26/48.82  | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 242.26/48.82  | | | | | | | | | | | |            e3) = e0
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | ALPHA: (127) implies:
% 242.26/48.82  | | | | | | | | | | | |   (128)   ~ (all_56_11 = e3)
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | REDUCE: (43), (128) imply:
% 242.26/48.82  | | | | | | | | | | | |   (129)  $false
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | CLOSE: (129) is inconsistent.
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | 
% 242.26/48.82  | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | 
% 242.26/48.82  | | | | | | | | |   (130)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 242.26/48.82  | | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.82  | | | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 242.26/48.82  | | | | | | | | |            e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~
% 242.26/48.82  | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.82  | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1)
% 242.26/48.82  | | | | | | | | |            = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 242.26/48.82  | | | | | | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 242.26/48.82  | | | | | | | | |              = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 242.26/48.82  | | | | | | | | |            & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.26/48.82  | | | | | | | | |            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.82  | | | | | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 242.26/48.82  | | | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 242.26/48.82  | | | | | | | | |            e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 242.26/48.82  | | | | | | | | |            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 242.26/48.82  | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0)
% 242.26/48.82  | | | | | | | | |            = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 242.26/48.82  | | | | | | | | |            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 242.26/48.82  | | | | | | | | |              = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 242.26/48.82  | | | | | | | | |            & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.82  | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | BETA: splitting (130) gives:
% 242.26/48.82  | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | |   (131)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 242.26/48.82  | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 242.26/48.82  | | | | | | | | | |              e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 & 
% 242.26/48.82  | | | | | | | | | |            ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.82  | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.26/48.82  | | | | | | | | | |              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 242.26/48.82  | | | | | | | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.82  | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.82  | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 242.26/48.82  | | | | | | | | | |            e2)
% 242.26/48.82  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | BETA: splitting (131) gives:
% 242.26/48.82  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | |   (132)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 242.26/48.82  | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 242.26/48.82  | | | | | | | | | | |            e2) = e2
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | ALPHA: (132) implies:
% 242.26/48.82  | | | | | | | | | | |   (133)   ~ (all_56_31 = e1)
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | REDUCE: (29), (133) imply:
% 242.26/48.82  | | | | | | | | | | |   (134)  $false
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | |   (135)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.26/48.82  | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 242.26/48.82  | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 242.26/48.82  | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 242.26/48.82  | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.82  | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | BETA: splitting (135) gives:
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | |   (136)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 242.26/48.82  | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 242.26/48.82  | | | | | | | | | | | |            e2) = e1
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | ALPHA: (136) implies:
% 242.26/48.82  | | | | | | | | | | | |   (137)   ~ (all_56_21 = e2)
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | REDUCE: (1), (137) imply:
% 242.26/48.82  | | | | | | | | | | | |   (138)  $false
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | CLOSE: (138) is inconsistent.
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | |   (139)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 242.26/48.82  | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 242.26/48.82  | | | | | | | | | | | |            e2) = e2
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | ALPHA: (139) implies:
% 242.26/48.82  | | | | | | | | | | | |   (140)   ~ (all_56_31 = e0)
% 242.26/48.82  | | | | | | | | | | | |   (141)   ~ (all_56_21 = e0)
% 242.26/48.82  | | | | | | | | | | | |   (142)   ~ (all_56_11 = e0)
% 242.26/48.82  | | | | | | | | | | | |   (143)  op(e0, e2) = e2
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (12), (19), (23), (40), (41), (45),
% 242.26/48.82  | | | | | | | | | | | |            (52), (56), (61), (79), (143) are inconsistent by
% 242.26/48.82  | | | | | | | | | | | |            sub-proof #719.
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | |   (144)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 242.26/48.82  | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 242.26/48.82  | | | | | | | | | |              e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 & 
% 242.26/48.82  | | | | | | | | | |            ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 242.26/48.82  | | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.26/48.82  | | | | | | | | | |              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 242.26/48.82  | | | | | | | | | |            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 242.26/48.82  | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.82  | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 242.26/48.82  | | | | | | | | | |            e0)
% 242.26/48.82  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | BETA: splitting (144) gives:
% 242.26/48.82  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | |   (145)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 242.26/48.82  | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 242.26/48.82  | | | | | | | | | | |            e2) = e0
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | ALPHA: (145) implies:
% 242.26/48.82  | | | | | | | | | | |   (146)   ~ (all_56_21 = e2)
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | REDUCE: (1), (146) imply:
% 242.26/48.82  | | | | | | | | | | |   (147)  $false
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | |   (148)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 242.26/48.82  | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 242.26/48.82  | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 242.26/48.82  | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 242.26/48.82  | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.26/48.82  | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | BETA: splitting (148) gives:
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | |   (149)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 242.26/48.82  | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 242.26/48.82  | | | | | | | | | | | |            e1) = e1
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | ALPHA: (149) implies:
% 242.26/48.82  | | | | | | | | | | | |   (150)   ~ (all_56_31 = e0)
% 242.26/48.82  | | | | | | | | | | | |   (151)   ~ (all_56_21 = e0)
% 242.26/48.82  | | | | | | | | | | | |   (152)   ~ (all_56_11 = e0)
% 242.26/48.82  | | | | | | | | | | | |   (153)  op(e1, e0) = e1
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | BETA: splitting (22) gives:
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | |   (154)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 242.26/48.82  | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | REF_CLOSE: (15), (23), (33), (41), (48), (154) are
% 242.26/48.82  | | | | | | | | | | | | |            inconsistent by sub-proof #1208.
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | |   (155)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 242.26/48.82  | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | BETA: splitting (155) gives:
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | |   (156)  all_58_6 = e3 & op(e1, e3) = e3
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | ALPHA: (156) implies:
% 242.26/48.82  | | | | | | | | | | | | | |   (157)  all_58_6 = e3
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (16), (40), (41), (45), (47), (153),
% 242.26/48.82  | | | | | | | | | | | | | |            (157) are inconsistent by sub-proof #1555.
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | |   (158)  all_58_12 = e3 & op(e0, e3) = e3
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | ALPHA: (158) implies:
% 242.26/48.82  | | | | | | | | | | | | | |   (159)  all_58_12 = e3
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (25), (32), (42), (45), (50), (52),
% 242.26/48.82  | | | | | | | | | | | | | |            (79), (159) are inconsistent by sub-proof #1863.
% 242.26/48.82  | | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | |   (160)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 242.26/48.82  | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 242.26/48.82  | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 242.26/48.82  | | | | | | | | | | | |            e1) = e0
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | ALPHA: (160) implies:
% 242.26/48.82  | | | | | | | | | | | |   (161)   ~ (all_56_31 = e1)
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | REDUCE: (29), (161) imply:
% 242.26/48.82  | | | | | | | | | | | |   (162)  $false
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | | CLOSE: (162) is inconsistent.
% 242.26/48.82  | | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | | 
% 242.26/48.82  | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | 
% 242.26/48.82  | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | 
% 242.26/48.82  | | | | | | | |   (163)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.82  | | | | | | | | 
% 242.26/48.82  | | | | | | | | BETA: splitting (163) gives:
% 242.26/48.82  | | | | | | | | 
% 242.26/48.82  | | | | | | | | Case 1:
% 242.26/48.82  | | | | | | | | | 
% 242.26/48.82  | | | | | | | | |   (164)  all_54_14 = e2
% 242.26/48.82  | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | REF_CLOSE: (8), (49), (164) are inconsistent by sub-proof
% 242.26/48.82  | | | | | | | | |            #1856.
% 242.26/48.82  | | | | | | | | | 
% 242.26/48.82  | | | | | | | | Case 2:
% 242.26/48.82  | | | | | | | | | 
% 242.26/48.82  | | | | | | | | |   (165)  all_54_14 = e1 | all_54_14 = e0
% 242.26/48.82  | | | | | | | | | 
% 242.26/48.82  | | | | | | | | | REF_CLOSE: (10), (49), (73), (165) are inconsistent by
% 242.26/48.82  | | | | | | | | |            sub-proof #1935.
% 242.26/48.82  | | | | | | | | | 
% 242.26/48.82  | | | | | | | | End of split
% 242.26/48.82  | | | | | | | | 
% 242.26/48.82  | | | | | | | End of split
% 242.26/48.82  | | | | | | | 
% 242.26/48.82  | | | | | | End of split
% 242.26/48.82  | | | | | | 
% 242.26/48.82  | | | | | End of split
% 242.26/48.82  | | | | | 
% 242.26/48.82  | | | | End of split
% 242.26/48.82  | | | | 
% 242.26/48.82  | | | End of split
% 242.26/48.82  | | | 
% 242.26/48.82  | | Case 2:
% 242.26/48.82  | | | 
% 242.26/48.82  | | |   (166)  all_58_5 = e0 & op(e2, e1) = e0
% 242.26/48.82  | | | 
% 242.26/48.82  | | | REF_CLOSE: (39), (45), (166) are inconsistent by sub-proof #1103.
% 242.26/48.82  | | | 
% 242.26/48.82  | | End of split
% 242.26/48.82  | | 
% 242.26/48.82  | Case 2:
% 242.26/48.82  | | 
% 242.26/48.82  | |   (167)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 242.26/48.82  | |            e0)
% 242.26/48.82  | | 
% 242.26/48.82  | | REF_CLOSE: (6), (7), (16), (42), (167) are inconsistent by sub-proof #722.
% 242.26/48.82  | | 
% 242.26/48.82  | End of split
% 242.26/48.82  | 
% 242.26/48.82  End of proof
% 242.26/48.82  
% 242.26/48.82  Sub-proof #719 shows that the following formulas are inconsistent:
% 242.26/48.82  ----------------------------------------------------------------
% 242.26/48.82    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.82         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.82    (2)   ~ (e3 = e0)
% 242.26/48.82    (3)   ~ (e2 = e0)
% 242.26/48.83    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.83         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.83    (5)  op(e0, e2) = e2
% 242.26/48.83    (6)  all_58_3 = e3
% 242.26/48.83    (7)  op(e3, e3) = e1
% 242.26/48.83    (8)   ~ (e3 = e2)
% 242.26/48.83    (9)  all_58_9 = e3
% 242.26/48.83    (10)  all_58_7 = e1
% 242.26/48.83    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.83    (12)   ~ (e1 = e0)
% 242.26/48.83    (13)  all_58_4 = e0
% 242.26/48.83    (14)   ~ (e2 = e1)
% 242.26/48.83  
% 242.26/48.83  Begin of proof
% 242.26/48.83  | 
% 242.26/48.83  | BETA: splitting (1) gives:
% 242.26/48.83  | 
% 242.26/48.83  | Case 1:
% 242.26/48.83  | | 
% 242.26/48.83  | |   (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 242.26/48.83  | |           e2)
% 242.26/48.83  | | 
% 242.26/48.83  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (12), (14), (15) are
% 242.26/48.83  | |            inconsistent by sub-proof #720.
% 242.26/48.83  | | 
% 242.26/48.83  | Case 2:
% 242.26/48.83  | | 
% 242.26/48.83  | |   (16)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 242.26/48.83  | |           e2)
% 242.26/48.83  | | 
% 242.26/48.83  | | BETA: splitting (16) gives:
% 242.26/48.83  | | 
% 242.26/48.83  | | Case 1:
% 242.26/48.83  | | | 
% 242.26/48.83  | | |   (17)  all_58_4 = e2 & op(e3, e1) = e2
% 242.26/48.83  | | | 
% 242.26/48.83  | | | ALPHA: (17) implies:
% 242.26/48.83  | | |   (18)  all_58_4 = e2
% 242.26/48.83  | | | 
% 242.26/48.83  | | | REF_CLOSE: (3), (13), (18) are inconsistent by sub-proof #1666.
% 242.26/48.83  | | | 
% 242.26/48.83  | | Case 2:
% 242.26/48.83  | | | 
% 242.26/48.83  | | |   (19)  all_58_9 = e2 & op(e3, e0) = e2
% 242.26/48.83  | | | 
% 242.26/48.83  | | | REF_CLOSE: (8), (9), (19) are inconsistent by sub-proof #1470.
% 242.26/48.83  | | | 
% 242.26/48.83  | | End of split
% 242.26/48.83  | | 
% 242.26/48.83  | End of split
% 242.26/48.83  | 
% 242.26/48.83  End of proof
% 242.26/48.83  
% 242.26/48.83  Sub-proof #720 shows that the following formulas are inconsistent:
% 242.26/48.83  ----------------------------------------------------------------
% 242.26/48.83    (1)   ~ (e3 = e0)
% 242.26/48.83    (2)   ~ (e2 = e0)
% 242.26/48.83    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.83         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.83    (4)  op(e0, e2) = e2
% 242.26/48.83    (5)  all_58_3 = e3
% 242.26/48.83    (6)  op(e3, e3) = e1
% 242.26/48.83    (7)  all_58_7 = e1
% 242.26/48.83    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.83    (9)   ~ (e1 = e0)
% 242.26/48.83    (10)   ~ (e2 = e1)
% 242.26/48.83    (11)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 242.26/48.83  
% 242.26/48.83  Begin of proof
% 242.26/48.83  | 
% 242.26/48.83  | BETA: splitting (11) gives:
% 242.26/48.83  | 
% 242.26/48.83  | Case 1:
% 242.26/48.83  | | 
% 242.26/48.83  | |   (12)  all_58_0 = e2 & op(e3, e3) = e2
% 242.26/48.83  | | 
% 242.26/48.83  | | ALPHA: (12) implies:
% 242.26/48.83  | |   (13)  op(e3, e3) = e2
% 242.26/48.83  | | 
% 242.26/48.83  | | REF_CLOSE: (6), (8), (10), (13) are inconsistent by sub-proof #2267.
% 242.26/48.83  | | 
% 242.26/48.83  | Case 2:
% 242.26/48.83  | | 
% 242.26/48.83  | |   (14)  all_58_1 = e2 & op(e3, e2) = e2
% 242.26/48.83  | | 
% 242.26/48.83  | | ALPHA: (14) implies:
% 242.26/48.83  | |   (15)  all_58_1 = e2
% 242.26/48.83  | | 
% 242.26/48.83  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (15) are inconsistent by
% 242.26/48.83  | |            sub-proof #1353.
% 242.26/48.83  | | 
% 242.26/48.83  | End of split
% 242.26/48.83  | 
% 242.26/48.83  End of proof
% 242.26/48.83  
% 242.26/48.83  Sub-proof #721 shows that the following formulas are inconsistent:
% 242.26/48.83  ----------------------------------------------------------------
% 242.26/48.83    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.83         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.83    (2)   ~ (e3 = e0)
% 242.26/48.83    (3)   ~ (e2 = e0)
% 242.26/48.83    (4)   ~ (all_52_11 = e2)
% 242.26/48.83    (5)  all_54_13 = all_52_7
% 242.26/48.83    (6)   ~ (all_52_11 = e1)
% 242.26/48.83    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.83         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.83    (8)   ~ (all_52_7 = all_52_11)
% 242.26/48.83    (9)   ~ (all_52_7 = e3)
% 242.26/48.83    (10)   ~ (e3 = e1)
% 242.26/48.83    (11)  all_58_8 = e2
% 242.26/48.83    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.83          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.83    (13)  all_58_3 = e3
% 242.26/48.83    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.83          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.83    (15)  op(e3, e3) = e1
% 242.26/48.83    (16)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.83    (17)   ~ (e3 = e2)
% 242.26/48.83    (18)   ~ (all_52_7 = e1)
% 242.26/48.83    (19)  op(e0, e2) = all_52_7
% 242.26/48.83    (20)   ~ (all_52_4 = e3)
% 242.26/48.83    (21)  op(e3, e2) = all_52_4
% 242.26/48.83    (22)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.83    (23)  all_58_5 = e1
% 242.26/48.83    (24)  all_58_7 = e1
% 242.26/48.83    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.83    (26)  all_58_14 = e3
% 242.26/48.83    (27)   ~ (e1 = e0)
% 242.26/48.83    (28)  all_54_14 = all_52_11
% 242.26/48.83    (29)   ~ (e2 = e1)
% 242.26/48.83  
% 242.26/48.83  Begin of proof
% 242.26/48.83  | 
% 242.26/48.83  | BETA: splitting (12) gives:
% 242.26/48.83  | 
% 242.26/48.83  | Case 1:
% 242.26/48.83  | | 
% 242.26/48.83  | |   (30)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 242.26/48.83  | |           e0)
% 242.26/48.83  | | 
% 242.26/48.83  | | BETA: splitting (30) gives:
% 242.26/48.83  | | 
% 242.26/48.83  | | Case 1:
% 242.26/48.83  | | | 
% 242.26/48.83  | | |   (31)  all_58_4 = e0 & op(e3, e1) = e0
% 242.26/48.83  | | | 
% 242.26/48.83  | | | ALPHA: (31) implies:
% 242.26/48.83  | | |   (32)  all_58_4 = e0
% 242.26/48.83  | | | 
% 242.26/48.83  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 242.26/48.83  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 242.26/48.83  | | |            (27), (28), (29), (32) are inconsistent by sub-proof #731.
% 242.26/48.83  | | | 
% 242.26/48.83  | | Case 2:
% 242.26/48.83  | | | 
% 242.26/48.83  | | |   (33)  all_58_5 = e0 & op(e2, e1) = e0
% 242.26/48.83  | | | 
% 242.26/48.83  | | | REF_CLOSE: (23), (27), (33) are inconsistent by sub-proof #1485.
% 242.26/48.83  | | | 
% 242.26/48.83  | | End of split
% 242.26/48.83  | | 
% 242.26/48.83  | Case 2:
% 242.26/48.83  | | 
% 242.26/48.83  | |   (34)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 242.26/48.83  | |           e0)
% 242.26/48.83  | | 
% 242.26/48.83  | | REF_CLOSE: (2), (3), (11), (26), (34) are inconsistent by sub-proof #722.
% 242.26/48.83  | | 
% 242.26/48.83  | End of split
% 242.26/48.83  | 
% 242.26/48.83  End of proof
% 242.26/48.83  
% 242.26/48.83  Sub-proof #722 shows that the following formulas are inconsistent:
% 242.26/48.83  ----------------------------------------------------------------
% 242.26/48.83    (1)   ~ (e3 = e0)
% 242.26/48.83    (2)   ~ (e2 = e0)
% 242.26/48.83    (3)  all_58_8 = e2
% 242.26/48.83    (4)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.83    (5)  all_58_14 = e3
% 242.26/48.83  
% 242.26/48.83  Begin of proof
% 242.26/48.83  | 
% 242.26/48.83  | BETA: splitting (4) gives:
% 242.26/48.83  | 
% 242.26/48.83  | Case 1:
% 242.26/48.83  | | 
% 242.26/48.83  | |   (6)  all_58_8 = e0 & op(e1, e1) = e0
% 242.26/48.83  | | 
% 242.26/48.83  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #728.
% 242.26/48.83  | | 
% 242.26/48.83  | Case 2:
% 242.26/48.83  | | 
% 242.26/48.83  | |   (7)  all_58_14 = e0 & op(e0, e1) = e0
% 242.26/48.83  | | 
% 242.26/48.83  | | ALPHA: (7) implies:
% 242.26/48.83  | |   (8)  all_58_14 = e0
% 242.26/48.83  | | 
% 242.26/48.83  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #1871.
% 242.26/48.83  | | 
% 242.26/48.83  | End of split
% 242.26/48.83  | 
% 242.26/48.83  End of proof
% 242.26/48.83  
% 242.26/48.83  Sub-proof #723 shows that the following formulas are inconsistent:
% 242.26/48.83  ----------------------------------------------------------------
% 242.26/48.83    (1)   ~ (all_52_1 = all_52_3)
% 242.26/48.83    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.26/48.83    (3)  all_56_21 = e2
% 242.26/48.83    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.26/48.83    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.83         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.83    (6)   ~ (all_52_3 = e1)
% 242.26/48.83    (7)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.26/48.83    (8)   ~ (e3 = e0)
% 242.26/48.83    (9)  op(e0, e1) = all_52_11
% 242.26/48.83    (10)   ~ (e2 = e0)
% 242.26/48.83    (11)   ~ (all_52_11 = e2)
% 242.26/48.83    (12)  all_54_13 = all_52_7
% 242.26/48.83    (13)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.26/48.83          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.83    (14)   ~ (all_52_11 = e1)
% 242.26/48.83    (15)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.26/48.83              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.26/48.83            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.26/48.83            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.83            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.26/48.83             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.83            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.26/48.83            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.83            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.26/48.83            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.83            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.26/48.83              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.83            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.83            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.26/48.83            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.83            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.26/48.83            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.83            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.26/48.83              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.26/48.83            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.83            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.26/48.83            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.83            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.26/48.83            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.83            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.26/48.83              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.26/48.83            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.83            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.83    (16)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.83          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.83    (17)   ~ (all_52_7 = all_52_11)
% 242.26/48.83    (18)   ~ (all_52_1 = all_52_2)
% 242.26/48.83    (19)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.26/48.83            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.26/48.83              e1) = all_20_1 & $i(all_20_1))
% 242.26/48.83    (20)   ~ (all_52_7 = e3)
% 242.26/48.83    (21)   ~ (e3 = e1)
% 242.26/48.83    (22)  all_58_8 = e2
% 242.26/48.83    (23)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.83          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.83    (24)   ~ (all_52_2 = all_52_3)
% 242.26/48.83    (25)  all_58_3 = e3
% 242.26/48.83    (26)  all_58_11 = e3
% 242.26/48.83    (27)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.83          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.83    (28)   ~ (all_52_2 = e1)
% 242.26/48.83    (29)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.26/48.83          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.26/48.83    (30)  op(e3, e3) = e1
% 242.26/48.83    (31)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.83    (32)   ~ (all_52_3 = all_52_7)
% 242.26/48.83    (33)  all_54_4 = all_52_1
% 242.26/48.83    (34)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.83          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.83    (35)   ~ (e3 = e2)
% 242.26/48.83    (36)  op(e1, e0) = e3
% 242.26/48.83    (37)   ~ (all_52_7 = e1)
% 242.26/48.83    (38)   ~ (all_52_3 = all_52_11)
% 242.26/48.83    (39)  all_56_31 = e1
% 242.26/48.83    (40)  all_54_12 = all_52_3
% 242.26/48.83    (41)  all_58_15 = e1
% 242.26/48.83    (42)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.26/48.83            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.26/48.83              e3) = all_42_1 & $i(all_42_1))
% 242.26/48.83    (43)  op(e2, e3) = all_52_1
% 242.26/48.83    (44)  op(e0, e2) = all_52_7
% 242.26/48.83    (45)   ~ (all_52_4 = e3)
% 242.26/48.83    (46)  op(e3, e2) = all_52_4
% 242.26/48.83    (47)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.83    (48)  all_58_5 = e1
% 242.26/48.83    (49)  all_58_7 = e1
% 242.26/48.83    (50)   ~ (all_52_2 = e2)
% 242.26/48.83    (51)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 242.26/48.83            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 242.26/48.83              e1) = all_34_1 & $i(all_34_1))
% 242.26/48.83    (52)  all_54_8 = all_52_2
% 242.26/48.83    (53)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.83          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.26/48.83    (54)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.83    (55)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.26/48.83          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.26/48.83    (56)  all_56_11 = e3
% 242.26/48.83    (57)   ~ (e1 = e0)
% 242.26/48.83    (58)  all_58_4 = e3
% 242.26/48.83    (59)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.26/48.83          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.26/48.83    (60)   ~ (all_52_1 = e3)
% 242.26/48.83    (61)  all_54_14 = all_52_11
% 242.26/48.83    (62)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.83          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.83            e2)
% 242.26/48.83    (63)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.83            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.83            & $i(all_8_1))
% 242.26/48.83    (64)   ~ (e2 = e1)
% 242.26/48.83    (65)   ~ (all_52_1 = e1)
% 242.26/48.83  
% 242.26/48.83  Begin of proof
% 242.26/48.83  | 
% 242.26/48.83  | BETA: splitting (59) gives:
% 242.26/48.83  | 
% 242.26/48.83  | Case 1:
% 242.26/48.83  | | 
% 242.26/48.83  | |   (66)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 242.26/48.83  | |           e0)
% 242.26/48.83  | | 
% 242.26/48.83  | | BETA: splitting (66) gives:
% 242.26/48.83  | | 
% 242.26/48.83  | | Case 1:
% 242.26/48.83  | | | 
% 242.26/48.83  | | |   (67)  all_58_6 = e0 & op(e1, e3) = e0
% 242.26/48.83  | | | 
% 242.26/48.83  | | | ALPHA: (67) implies:
% 242.26/48.83  | | |   (68)  all_58_6 = e0
% 242.26/48.83  | | | 
% 242.26/48.83  | | | BETA: splitting (29) gives:
% 242.26/48.83  | | | 
% 242.26/48.83  | | | Case 1:
% 242.26/48.83  | | | | 
% 242.26/48.83  | | | |   (69)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 242.26/48.83  | | | |           = e3)
% 242.26/48.83  | | | | 
% 242.26/48.83  | | | | REF_CLOSE: (21), (30), (43), (54), (60), (69) are inconsistent by
% 242.26/48.83  | | | |            sub-proof #1208.
% 242.26/48.83  | | | | 
% 242.26/48.83  | | | Case 2:
% 242.26/48.83  | | | | 
% 242.26/48.83  | | | |   (70)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 242.26/48.83  | | | |           = e3)
% 242.26/48.83  | | | | 
% 242.26/48.83  | | | | BETA: splitting (70) gives:
% 242.26/48.83  | | | | 
% 242.26/48.83  | | | | Case 1:
% 242.26/48.83  | | | | | 
% 242.26/48.83  | | | | |   (71)  all_58_6 = e3 & op(e1, e3) = e3
% 242.26/48.83  | | | | | 
% 242.26/48.83  | | | | | ALPHA: (71) implies:
% 242.26/48.84  | | | | |   (72)  all_58_6 = e3
% 242.26/48.84  | | | | | 
% 242.26/48.84  | | | | | REF_CLOSE: (8), (10), (22), (26), (49), (57), (59), (72) are
% 242.26/48.84  | | | | |            inconsistent by sub-proof #909.
% 242.26/48.84  | | | | | 
% 242.26/48.84  | | | | Case 2:
% 242.26/48.84  | | | | | 
% 242.26/48.84  | | | | |   (73)  all_58_12 = e3 & op(e0, e3) = e3
% 242.26/48.84  | | | | | 
% 242.26/48.84  | | | | | ALPHA: (73) implies:
% 242.26/48.84  | | | | |   (74)  all_58_12 = e3
% 242.26/48.84  | | | | | 
% 242.26/48.84  | | | | | BETA: splitting (34) gives:
% 242.26/48.84  | | | | | 
% 242.26/48.84  | | | | | Case 1:
% 242.26/48.84  | | | | | | 
% 242.26/48.84  | | | | | |   (75)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2,
% 242.26/48.84  | | | | | |             e3) = e2)
% 242.26/48.84  | | | | | | 
% 242.26/48.84  | | | | | | BETA: splitting (75) gives:
% 242.26/48.84  | | | | | | 
% 242.26/48.84  | | | | | | Case 1:
% 242.26/48.84  | | | | | | | 
% 242.26/48.84  | | | | | | |   (76)  all_58_0 = e2 & op(e3, e3) = e2
% 242.26/48.84  | | | | | | | 
% 242.26/48.84  | | | | | | | ALPHA: (76) implies:
% 242.26/48.84  | | | | | | |   (77)  op(e3, e3) = e2
% 242.26/48.84  | | | | | | | 
% 242.26/48.84  | | | | | | | REF_CLOSE: (30), (54), (64), (77) are inconsistent by sub-proof
% 242.26/48.84  | | | | | | |            #2267.
% 242.26/48.84  | | | | | | | 
% 242.26/48.84  | | | | | | Case 2:
% 242.26/48.84  | | | | | | | 
% 242.26/48.84  | | | | | | |   (78)  all_58_2 = e2 & op(e2, e3) = e2
% 242.26/48.84  | | | | | | | 
% 242.26/48.84  | | | | | | | ALPHA: (78) implies:
% 242.26/48.84  | | | | | | |   (79)  op(e2, e3) = e2
% 242.26/48.84  | | | | | | | 
% 242.26/48.84  | | | | | | | BETA: splitting (23) gives:
% 242.26/48.84  | | | | | | | 
% 242.26/48.84  | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | 
% 242.26/48.84  | | | | | | | |   (80)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 242.26/48.84  | | | | | | | |           op(e2, e1) = e0)
% 242.26/48.84  | | | | | | | | 
% 242.26/48.84  | | | | | | | | BETA: splitting (80) gives:
% 242.26/48.84  | | | | | | | | 
% 242.26/48.84  | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | |   (81)  all_58_4 = e0 & op(e3, e1) = e0
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | ALPHA: (81) implies:
% 242.26/48.84  | | | | | | | | |   (82)  all_58_4 = e0
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | REF_CLOSE: (5), (8), (10), (11), (12), (14), (16), (17), (20),
% 242.26/48.84  | | | | | | | | |            (21), (25), (27), (30), (31), (35), (37), (44),
% 242.26/48.84  | | | | | | | | |            (45), (46), (47), (49), (54), (57), (61), (64),
% 242.26/48.84  | | | | | | | | |            (82) are inconsistent by sub-proof #731.
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | |   (83)  all_58_5 = e0 & op(e2, e1) = e0
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | REF_CLOSE: (48), (57), (83) are inconsistent by sub-proof
% 242.26/48.84  | | | | | | | | |            #1485.
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | End of split
% 242.26/48.84  | | | | | | | | 
% 242.26/48.84  | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | 
% 242.26/48.84  | | | | | | | |   (84)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 242.26/48.84  | | | | | | | |           op(e0, e1) = e0)
% 242.26/48.84  | | | | | | | | 
% 242.26/48.84  | | | | | | | | BETA: splitting (84) gives:
% 242.26/48.84  | | | | | | | | 
% 242.26/48.84  | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | |   (85)  all_58_8 = e0 & op(e1, e1) = e0
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | REF_CLOSE: (10), (22), (85) are inconsistent by sub-proof
% 242.26/48.84  | | | | | | | | |            #728.
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | |   (86)  all_58_14 = e0 & op(e0, e1) = e0
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | ALPHA: (86) implies:
% 242.26/48.84  | | | | | | | | |   (87)  all_58_14 = e0
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | BETA: splitting (31) gives:
% 242.26/48.84  | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | |   (88)  all_54_14 = e2
% 242.26/48.84  | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | COMBINE_EQS: (61), (88) imply:
% 242.26/48.84  | | | | | | | | | |   (89)  all_52_11 = e2
% 242.26/48.84  | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | REDUCE: (11), (89) imply:
% 242.26/48.84  | | | | | | | | | |   (90)  $false
% 242.26/48.84  | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | CLOSE: (90) is inconsistent.
% 242.26/48.84  | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | |   (91)   ~ (all_54_14 = e2)
% 242.26/48.84  | | | | | | | | | |   (92)  all_54_14 = e1 | all_54_14 = e0
% 242.26/48.84  | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | BETA: splitting (53) gives:
% 242.26/48.84  | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | |   (93)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 242.26/48.84  | | | | | | | | | | |           & op(e2, e2) = e0)
% 242.26/48.84  | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | REF_CLOSE: (5), (8), (10), (11), (12), (14), (16), (17),
% 242.26/48.84  | | | | | | | | | | |            (20), (21), (25), (27), (30), (31), (35), (37),
% 242.26/48.84  | | | | | | | | | | |            (42), (44), (45), (46), (47), (49), (54), (57),
% 242.26/48.84  | | | | | | | | | | |            (58), (61), (63), (64), (79), (93) are
% 242.26/48.84  | | | | | | | | | | |            inconsistent by sub-proof #730.
% 242.26/48.84  | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | |   (94)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 242.26/48.84  | | | | | | | | | | |           e0 & op(e2, e0) = e0)
% 242.26/48.84  | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | BETA: splitting (94) gives:
% 242.26/48.84  | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | |   (95)  all_58_5 = e0 & op(e2, e1) = e0
% 242.26/48.84  | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | REF_CLOSE: (48), (57), (95) are inconsistent by sub-proof
% 242.26/48.84  | | | | | | | | | | | |            #1485.
% 242.26/48.84  | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | |   (96)  all_58_10 = e0 & op(e2, e0) = e0
% 242.26/48.84  | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | ALPHA: (96) implies:
% 242.26/48.84  | | | | | | | | | | | |   (97)  all_58_10 = e0
% 242.26/48.84  | | | | | | | | | | | |   (98)  op(e2, e0) = e0
% 242.26/48.84  | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | BETA: splitting (55) gives:
% 242.26/48.84  | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | |   (99)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 242.26/48.84  | | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 242.26/48.84  | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | BETA: splitting (99) gives:
% 242.26/48.84  | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | |   (100)  all_58_9 = e2 & op(e3, e0) = e2
% 242.26/48.84  | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | ALPHA: (100) implies:
% 242.26/48.84  | | | | | | | | | | | | | |   (101)  op(e3, e0) = e2
% 242.26/48.84  | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 242.26/48.84  | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | |   (102)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 242.26/48.84  | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 242.26/48.84  | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | |   (103)  all_58_1 = e2 & op(e3, e2) = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 242.26/48.84  | | | | | | | | | | | | | | | |   (104)  all_58_1 = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (16), (25), (35), (41), (49), (57),
% 242.26/48.84  | | | | | | | | | | | | | | | |            (62), (64), (74), (87), (104) are inconsistent by
% 242.26/48.84  | | | | | | | | | | | | | | | |            sub-proof #735.
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | |   (105)  all_58_3 = e2 & op(e2, e2) = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | REF_CLOSE: (25), (35), (105) are inconsistent by sub-proof
% 242.26/48.84  | | | | | | | | | | | | | | | |            #1458.
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | End of split
% 242.26/48.84  | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | |   (106)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 242.26/48.84  | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 242.26/48.84  | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | |   (107)  all_58_7 = e2 & op(e1, e2) = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 242.26/48.84  | | | | | | | | | | | | | | | |   (108)  all_58_7 = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | REF_CLOSE: (49), (64), (108) are inconsistent by sub-proof
% 242.26/48.84  | | | | | | | | | | | | | | | |            #2134.
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | |   (109)  all_58_13 = e2 & op(e0, e2) = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 242.26/48.84  | | | | | | | | | | | | | | | |   (110)  op(e0, e2) = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | |   (111)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.26/48.84  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.26/48.84  | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 242.26/48.84  | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 242.26/48.84  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.84  | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 242.26/48.84  | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 242.26/48.84  | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.26/48.84  | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 242.26/48.84  | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 242.26/48.84  | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.26/48.84  | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 242.26/48.84  | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | |   (112)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            = e3)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (43), (54), (56), (60), (112) are
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #857.
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | |   (113)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            = e0)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (54), (56), (101), (113) are inconsistent by
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            sub-proof #727.
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | End of split
% 242.26/48.84  | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | |   (114)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 242.26/48.84  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 242.26/48.84  | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 242.26/48.84  | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 242.26/48.84  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.26/48.84  | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 242.26/48.84  | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 242.26/48.84  | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.26/48.84  | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 242.26/48.84  | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 242.26/48.84  | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 242.26/48.84  | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 242.26/48.84  | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | |   (115)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            = e2)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |   (116)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            e2) = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |   (117)   ~ (all_56_31 = e1)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (117) imply:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |   (118)  $false
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | CLOSE: (118) is inconsistent.
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |   (119)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |   (120)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |   (121)   ~ (all_56_21 = e2)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (121) imply:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |   (122)  $false
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | CLOSE: (122) is inconsistent.
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |   (123)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |   (124)   ~ (all_56_21 = e0)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |   (125)  op(e2, e0) = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (54), (98), (125) are inconsistent by
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |            sub-proof #2121.
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | End of split
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | End of split
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | |   (126)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 242.26/48.84  | | | | | | | | | | | | | | | | | |            = e0)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |   (127)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            e2) = e0
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |   (128)  op(e0, e2) = e0
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (54), (110), (128) are inconsistent by
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |   (129)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.26/48.84  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |   (130)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |            e1) = e1
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |   (131)  op(e0, e1) = e1
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | |   (132)  op(e1, e0) = e1
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | |   (133)  all_54_14 = e1
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (61), (133) are inconsistent by sub-proof
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | |            #1937.
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | |   (134)  all_54_14 = e0
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (134) imply:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | |   (135)  all_52_11 = e0
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | SIMP: (135) implies:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | |   (136)  all_52_11 = e0
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (136) imply:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | |   (137)   ~ (all_52_3 = e0)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (136) imply:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | |   (138)   ~ (all_52_7 = e0)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (136) imply:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | |   (139)  op(e0, e1) = e0
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | |   (140)  all_54_13 = e3
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (20), (140) are inconsistent by sub-proof
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | |   (141)   ~ (all_54_13 = e3)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | |   (142)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | |   (143)  all_54_13 = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (143) imply:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | |   (144)  all_52_7 = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (144) implies:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | |   (145)  all_52_7 = e2
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (145) imply:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | |   (146)   ~ (all_52_3 = e2)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | |   (147)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | |          op(e0, e1) = all_34_1 & $i(all_34_0) &
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_34_1)
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.84  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |   (148)  op(e0, e1) = all_34_1
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (11), (12), (14),
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |            (16), (17), (18), (19), (20), (24), (25), (27),
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |            (28), (30), (31), (33), (36), (37), (40), (44),
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |            (45), (46), (47), (49), (50), (52), (54), (58),
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |            (61), (65), (131), (132), (137), (139), (146),
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |            (148) are inconsistent by sub-proof #725.
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |   (149)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 &
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_34_1)
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |   (150)  op(e0, e1) = all_34_1
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (11), (12), (14),
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |            (16), (17), (18), (19), (20), (24), (25), (27),
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |            (28), (30), (31), (33), (36), (37), (40), (44),
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |            (45), (46), (47), (49), (50), (52), (54), (58),
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |            (61), (65), (131), (132), (137), (139), (146),
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | |            (150) are inconsistent by sub-proof #725.
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | |   (151)  all_54_13 = e1 | all_54_13 = e0
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (37), (138), (151) are inconsistent by
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1793.
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | |   (152)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | |            e1) = e0
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | |   (153)   ~ (all_56_31 = e1)
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (153) imply:
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | |   (154)  $false
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent.
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | Case 2:
% 242.26/48.85  | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | |   (155)  all_58_10 = e2 & op(e2, e0) = e2
% 242.26/48.85  | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | ALPHA: (155) implies:
% 242.26/48.85  | | | | | | | | | | | | | |   (156)  all_58_10 = e2
% 242.26/48.85  | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | COMBINE_EQS: (97), (156) imply:
% 242.26/48.85  | | | | | | | | | | | | | |   (157)  e2 = e0
% 242.26/48.85  | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | SIMP: (157) implies:
% 242.26/48.85  | | | | | | | | | | | | | |   (158)  e2 = e0
% 242.26/48.85  | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | REDUCE: (10), (158) imply:
% 242.26/48.85  | | | | | | | | | | | | | |   (159)  $false
% 242.26/48.85  | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 242.26/48.85  | | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | Case 2:
% 242.26/48.85  | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | |   (160)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 242.26/48.85  | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 242.26/48.85  | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | | REF_CLOSE: (26), (35), (41), (64), (160) are inconsistent by
% 242.26/48.85  | | | | | | | | | | | | |            sub-proof #1058.
% 242.26/48.85  | | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | | 
% 242.26/48.85  | | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | | 
% 242.26/48.85  | | | | | | | | End of split
% 242.26/48.85  | | | | | | | | 
% 242.26/48.85  | | | | | | | End of split
% 242.26/48.85  | | | | | | | 
% 242.26/48.85  | | | | | | End of split
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | Case 2:
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | |   (161)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 &
% 242.26/48.85  | | | | | |            op(e0, e3) = e2)
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | REF_CLOSE: (10), (35), (68), (74), (161) are inconsistent by
% 242.26/48.85  | | | | | |            sub-proof #724.
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | End of split
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | End of split
% 242.26/48.85  | | | | 
% 242.26/48.85  | | | End of split
% 242.26/48.85  | | | 
% 242.26/48.85  | | Case 2:
% 242.26/48.85  | | | 
% 242.26/48.85  | | |   (162)  all_58_7 = e0 & op(e1, e2) = e0
% 242.26/48.85  | | | 
% 242.26/48.85  | | | REF_CLOSE: (49), (57), (162) are inconsistent by sub-proof #1558.
% 242.26/48.85  | | | 
% 242.26/48.85  | | End of split
% 242.26/48.85  | | 
% 242.26/48.85  | Case 2:
% 242.26/48.85  | | 
% 242.26/48.85  | |   (163)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.26/48.85  | |            e0)
% 242.26/48.85  | | 
% 242.26/48.85  | | BETA: splitting (163) gives:
% 242.26/48.85  | | 
% 242.26/48.85  | | Case 1:
% 242.26/48.85  | | | 
% 242.26/48.85  | | |   (164)  all_58_8 = e0 & op(e1, e1) = e0
% 242.26/48.85  | | | 
% 242.26/48.85  | | | REF_CLOSE: (10), (22), (164) are inconsistent by sub-proof #728.
% 242.26/48.85  | | | 
% 242.26/48.85  | | Case 2:
% 242.26/48.85  | | | 
% 242.26/48.85  | | |   (165)  all_58_11 = e0 & op(e1, e0) = e0
% 242.26/48.85  | | | 
% 242.26/48.85  | | | ALPHA: (165) implies:
% 242.26/48.85  | | |   (166)  all_58_11 = e0
% 242.26/48.85  | | | 
% 242.26/48.85  | | | COMBINE_EQS: (26), (166) imply:
% 242.26/48.85  | | |   (167)  e3 = e0
% 242.26/48.85  | | | 
% 242.26/48.85  | | | SIMP: (167) implies:
% 242.26/48.85  | | |   (168)  e3 = e0
% 242.26/48.85  | | | 
% 242.26/48.85  | | | COMBINE_EQS: (58), (168) imply:
% 242.26/48.85  | | |   (169)  all_58_4 = e0
% 242.26/48.85  | | | 
% 242.26/48.85  | | | REF_CLOSE: (5), (8), (10), (11), (12), (14), (16), (17), (20), (21), (25),
% 242.26/48.85  | | |            (27), (30), (31), (35), (37), (44), (45), (46), (47), (49),
% 242.26/48.85  | | |            (54), (57), (61), (64), (169) are inconsistent by sub-proof
% 242.26/48.85  | | |            #731.
% 242.26/48.85  | | | 
% 242.26/48.85  | | End of split
% 242.26/48.85  | | 
% 242.26/48.85  | End of split
% 242.26/48.85  | 
% 242.26/48.85  End of proof
% 242.26/48.85  
% 242.26/48.85  Sub-proof #724 shows that the following formulas are inconsistent:
% 242.26/48.85  ----------------------------------------------------------------
% 242.26/48.85    (1)   ~ (e2 = e0)
% 242.26/48.85    (2)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.85    (3)   ~ (e3 = e2)
% 242.26/48.85    (4)  all_58_6 = e0
% 242.26/48.85    (5)  all_58_12 = e3
% 242.26/48.85  
% 242.26/48.85  Begin of proof
% 242.26/48.85  | 
% 242.26/48.85  | BETA: splitting (2) gives:
% 242.26/48.85  | 
% 242.26/48.85  | Case 1:
% 242.26/48.85  | | 
% 242.26/48.85  | |   (6)  all_58_6 = e2 & op(e1, e3) = e2
% 242.26/48.85  | | 
% 242.26/48.85  | | ALPHA: (6) implies:
% 242.26/48.85  | |   (7)  all_58_6 = e2
% 242.26/48.85  | | 
% 242.26/48.85  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #1982.
% 242.26/48.85  | | 
% 242.26/48.85  | Case 2:
% 242.26/48.85  | | 
% 242.26/48.85  | |   (8)  all_58_12 = e2 & op(e0, e3) = e2
% 242.26/48.85  | | 
% 242.26/48.85  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #1974.
% 242.26/48.85  | | 
% 242.26/48.85  | End of split
% 242.26/48.85  | 
% 242.26/48.85  End of proof
% 242.26/48.85  
% 242.26/48.85  Sub-proof #725 shows that the following formulas are inconsistent:
% 242.26/48.85  ----------------------------------------------------------------
% 242.26/48.85    (1)   ~ (all_52_3 = e0)
% 242.26/48.85    (2)   ~ (all_52_1 = all_52_3)
% 242.26/48.85    (3)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.26/48.85    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.26/48.85    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.85         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.85    (6)   ~ (all_52_3 = e1)
% 242.26/48.85    (7)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.26/48.85    (8)   ~ (all_52_11 = e2)
% 242.26/48.85    (9)  all_54_13 = all_52_7
% 242.26/48.85    (10)   ~ (all_52_11 = e1)
% 242.26/48.85    (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.85          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.85    (12)   ~ (all_52_7 = all_52_11)
% 242.26/48.85    (13)   ~ (all_52_1 = all_52_2)
% 242.26/48.85    (14)  op(e0, e1) = all_34_1
% 242.26/48.85    (15)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.26/48.85            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.26/48.85              e1) = all_20_1 & $i(all_20_1))
% 242.26/48.85    (16)   ~ (all_52_7 = e3)
% 242.26/48.85    (17)  op(e1, e0) = e1
% 242.26/48.85    (18)   ~ (all_52_2 = all_52_3)
% 242.26/48.85    (19)  all_58_3 = e3
% 242.26/48.85    (20)  op(e0, e1) = e1
% 242.26/48.85    (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.85          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.85    (22)   ~ (all_52_2 = e1)
% 242.26/48.85    (23)  op(e3, e3) = e1
% 242.26/48.85    (24)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.85    (25)  all_54_4 = all_52_1
% 242.26/48.85    (26)  op(e1, e0) = e3
% 242.26/48.85    (27)   ~ (all_52_7 = e1)
% 242.26/48.85    (28)  all_54_12 = all_52_3
% 242.26/48.85    (29)  op(e0, e1) = e0
% 242.26/48.85    (30)   ~ (all_52_3 = e2)
% 242.26/48.85    (31)  op(e0, e2) = all_52_7
% 242.26/48.85    (32)   ~ (all_52_4 = e3)
% 242.26/48.85    (33)  op(e3, e2) = all_52_4
% 242.26/48.85    (34)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.85    (35)  all_58_7 = e1
% 242.26/48.85    (36)   ~ (all_52_2 = e2)
% 242.26/48.85    (37)  all_54_8 = all_52_2
% 242.26/48.85    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.85    (39)  all_58_4 = e3
% 242.26/48.85    (40)  all_54_14 = all_52_11
% 242.26/48.85    (41)   ~ (all_52_1 = e1)
% 242.26/48.85  
% 242.26/48.85  Begin of proof
% 242.26/48.85  | 
% 242.26/48.85  | BETA: splitting (15) gives:
% 242.26/48.85  | 
% 242.26/48.85  | Case 1:
% 242.26/48.85  | | 
% 242.26/48.85  | |   (42)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.26/48.85  | |         all_20_1 & $i(all_20_0) & $i(all_20_1)
% 242.26/48.85  | | 
% 242.26/48.85  | | ALPHA: (42) implies:
% 242.26/48.85  | |   (43)  op(e0, e1) = all_20_1
% 242.26/48.85  | | 
% 242.26/48.85  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.26/48.85  | |            (13), (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 242.26/48.85  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 242.26/48.85  | |            (36), (37), (38), (39), (40), (41), (43) are inconsistent by
% 242.26/48.85  | |            sub-proof #726.
% 242.26/48.85  | | 
% 242.26/48.85  | Case 2:
% 242.26/48.85  | | 
% 242.26/48.85  | |   (44)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 & $i(all_20_1)
% 242.26/48.85  | | 
% 242.26/48.85  | | ALPHA: (44) implies:
% 242.26/48.85  | |   (45)  op(e0, e1) = all_20_1
% 242.26/48.85  | | 
% 242.26/48.85  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.26/48.85  | |            (13), (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 242.26/48.85  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 242.26/48.85  | |            (36), (37), (38), (39), (40), (41), (45) are inconsistent by
% 242.26/48.85  | |            sub-proof #726.
% 242.26/48.85  | | 
% 242.26/48.85  | End of split
% 242.26/48.85  | 
% 242.26/48.85  End of proof
% 242.26/48.85  
% 242.26/48.85  Sub-proof #726 shows that the following formulas are inconsistent:
% 242.26/48.85  ----------------------------------------------------------------
% 242.26/48.85    (1)   ~ (all_52_3 = e0)
% 242.26/48.85    (2)   ~ (all_52_1 = all_52_3)
% 242.26/48.85    (3)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 242.26/48.85    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.26/48.85    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.85         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.85    (6)   ~ (all_52_3 = e1)
% 242.26/48.85    (7)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.26/48.85    (8)   ~ (all_52_11 = e2)
% 242.26/48.85    (9)  all_54_13 = all_52_7
% 242.26/48.85    (10)   ~ (all_52_11 = e1)
% 242.26/48.85    (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.85          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.85    (12)   ~ (all_52_7 = all_52_11)
% 242.26/48.85    (13)   ~ (all_52_1 = all_52_2)
% 242.26/48.85    (14)  op(e0, e1) = all_34_1
% 242.26/48.85    (15)   ~ (all_52_7 = e3)
% 242.26/48.85    (16)  op(e1, e0) = e1
% 242.26/48.85    (17)   ~ (all_52_2 = all_52_3)
% 242.26/48.85    (18)  all_58_3 = e3
% 242.26/48.85    (19)  op(e0, e1) = e1
% 242.26/48.85    (20)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.85          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.85    (21)   ~ (all_52_2 = e1)
% 242.26/48.85    (22)  op(e3, e3) = e1
% 242.26/48.85    (23)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.85    (24)  all_54_4 = all_52_1
% 242.26/48.85    (25)  op(e1, e0) = e3
% 242.26/48.85    (26)   ~ (all_52_7 = e1)
% 242.26/48.85    (27)  all_54_12 = all_52_3
% 242.26/48.85    (28)  op(e0, e1) = e0
% 242.26/48.85    (29)   ~ (all_52_3 = e2)
% 242.26/48.85    (30)  op(e0, e2) = all_52_7
% 242.26/48.85    (31)  op(e0, e1) = all_20_1
% 242.26/48.85    (32)   ~ (all_52_4 = e3)
% 242.26/48.85    (33)  op(e3, e2) = all_52_4
% 242.26/48.85    (34)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.85    (35)  all_58_7 = e1
% 242.26/48.85    (36)   ~ (all_52_2 = e2)
% 242.26/48.85    (37)  all_54_8 = all_52_2
% 242.26/48.85    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.85    (39)  all_58_4 = e3
% 242.26/48.85    (40)  all_54_14 = all_52_11
% 242.26/48.85    (41)   ~ (all_52_1 = e1)
% 242.26/48.85  
% 242.26/48.85  Begin of proof
% 242.26/48.85  | 
% 242.26/48.85  | BETA: splitting (4) gives:
% 242.26/48.85  | 
% 242.26/48.85  | Case 1:
% 242.26/48.85  | | 
% 242.26/48.85  | |   (42)  all_54_12 = e3
% 242.26/48.85  | | 
% 242.26/48.85  | | COMBINE_EQS: (27), (42) imply:
% 242.26/48.85  | |   (43)  all_52_3 = e3
% 242.26/48.85  | | 
% 242.26/48.85  | | REDUCE: (2), (43) imply:
% 242.26/48.85  | |   (44)   ~ (all_52_1 = e3)
% 242.26/48.85  | | 
% 242.26/48.85  | | REDUCE: (17), (43) imply:
% 242.26/48.85  | |   (45)   ~ (all_52_2 = e3)
% 242.26/48.85  | | 
% 242.26/48.85  | | REDUCE: (6), (43) imply:
% 242.26/48.85  | |   (46)   ~ (e3 = e1)
% 242.26/48.85  | | 
% 242.26/48.85  | | BETA: splitting (7) gives:
% 242.26/48.85  | | 
% 242.26/48.85  | | Case 1:
% 242.26/48.85  | | | 
% 242.26/48.85  | | |   (47)  all_54_8 = e3
% 242.26/48.85  | | | 
% 242.26/48.85  | | | COMBINE_EQS: (37), (47) imply:
% 242.26/48.85  | | |   (48)  all_52_2 = e3
% 242.26/48.85  | | | 
% 242.26/48.85  | | | REDUCE: (45), (48) imply:
% 242.26/48.85  | | |   (49)  $false
% 242.26/48.85  | | | 
% 242.26/48.85  | | | CLOSE: (49) is inconsistent.
% 242.26/48.85  | | | 
% 242.26/48.85  | | Case 2:
% 242.26/48.85  | | | 
% 242.26/48.85  | | |   (50)   ~ (all_54_8 = e3)
% 242.26/48.85  | | |   (51)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.26/48.85  | | | 
% 242.26/48.85  | | | BETA: splitting (51) gives:
% 242.26/48.85  | | | 
% 242.26/48.85  | | | Case 1:
% 242.26/48.85  | | | | 
% 242.26/48.85  | | | |   (52)  all_54_8 = e2
% 242.26/48.85  | | | | 
% 242.26/48.85  | | | | COMBINE_EQS: (37), (52) imply:
% 242.26/48.85  | | | |   (53)  all_52_2 = e2
% 242.26/48.85  | | | | 
% 242.26/48.85  | | | | REDUCE: (36), (53) imply:
% 242.26/48.85  | | | |   (54)  $false
% 242.26/48.85  | | | | 
% 242.26/48.85  | | | | CLOSE: (54) is inconsistent.
% 242.26/48.85  | | | | 
% 242.26/48.85  | | | Case 2:
% 242.26/48.85  | | | | 
% 242.26/48.85  | | | |   (55)  all_54_8 = e1 | all_54_8 = e0
% 242.26/48.85  | | | | 
% 242.26/48.85  | | | | BETA: splitting (55) gives:
% 242.26/48.85  | | | | 
% 242.26/48.85  | | | | Case 1:
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | |   (56)  all_54_8 = e1
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | | REF_CLOSE: (21), (37), (56) are inconsistent by sub-proof #1951.
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | Case 2:
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | |   (57)  all_54_8 = e0
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | | COMBINE_EQS: (37), (57) imply:
% 242.26/48.85  | | | | |   (58)  all_52_2 = e0
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | | SIMP: (58) implies:
% 242.26/48.85  | | | | |   (59)  all_52_2 = e0
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | | REDUCE: (13), (59) imply:
% 242.26/48.85  | | | | |   (60)   ~ (all_52_1 = e0)
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | | REDUCE: (45), (59) imply:
% 242.26/48.85  | | | | |   (61)   ~ (e3 = e0)
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | | SIMP: (61) implies:
% 242.26/48.85  | | | | |   (62)   ~ (e3 = e0)
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | | REDUCE: (21), (59) imply:
% 242.26/48.85  | | | | |   (63)   ~ (e1 = e0)
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | | SIMP: (63) implies:
% 242.26/48.85  | | | | |   (64)   ~ (e1 = e0)
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | | BETA: splitting (3) gives:
% 242.26/48.85  | | | | | 
% 242.26/48.85  | | | | | Case 1:
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | |   (65)  all_54_4 = e2
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | COMBINE_EQS: (24), (65) imply:
% 242.26/48.85  | | | | | |   (66)  all_52_1 = e2
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | SIMP: (66) implies:
% 242.26/48.85  | | | | | |   (67)  all_52_1 = e2
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | REDUCE: (44), (67) imply:
% 242.26/48.85  | | | | | |   (68)   ~ (e3 = e2)
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | SIMP: (68) implies:
% 242.26/48.85  | | | | | |   (69)   ~ (e3 = e2)
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | REDUCE: (41), (67) imply:
% 242.26/48.85  | | | | | |   (70)   ~ (e2 = e1)
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | REDUCE: (60), (67) imply:
% 242.26/48.85  | | | | | |   (71)   ~ (e2 = e0)
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | GROUND_INST: instantiating (38) with e0, all_20_1, e1, e0,
% 242.26/48.85  | | | | | |              simplifying with (28), (31) gives:
% 242.26/48.85  | | | | | |   (72)  all_20_1 = e0
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | GROUND_INST: instantiating (38) with all_20_1, all_34_1, e1, e0,
% 242.26/48.85  | | | | | |              simplifying with (14), (31) gives:
% 242.26/48.85  | | | | | |   (73)  all_34_1 = all_20_1
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | GROUND_INST: instantiating (38) with e1, all_34_1, e1, e0,
% 242.26/48.85  | | | | | |              simplifying with (14), (19) gives:
% 242.26/48.85  | | | | | |   (74)  all_34_1 = e1
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | GROUND_INST: instantiating (38) with e1, e3, e0, e1, simplifying
% 242.26/48.85  | | | | | |              with (16), (25) gives:
% 242.26/48.85  | | | | | |   (75)  e3 = e1
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | COMBINE_EQS: (73), (74) imply:
% 242.26/48.85  | | | | | |   (76)  all_20_1 = e1
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | SIMP: (76) implies:
% 242.26/48.85  | | | | | |   (77)  all_20_1 = e1
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | COMBINE_EQS: (72), (77) imply:
% 242.26/48.85  | | | | | |   (78)  e1 = e0
% 242.26/48.85  | | | | | | 
% 242.26/48.85  | | | | | | SIMP: (78) implies:
% 242.26/48.86  | | | | | |   (79)  e1 = e0
% 242.26/48.86  | | | | | | 
% 242.26/48.86  | | | | | | COMBINE_EQS: (75), (79) imply:
% 242.26/48.86  | | | | | |   (80)  e3 = e0
% 242.26/48.86  | | | | | | 
% 242.26/48.86  | | | | | | COMBINE_EQS: (39), (80) imply:
% 242.26/48.86  | | | | | |   (81)  all_58_4 = e0
% 242.26/48.86  | | | | | | 
% 242.26/48.86  | | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (12), (15), (18), (20), (22),
% 242.26/48.86  | | | | | |            (23), (26), (30), (32), (33), (34), (35), (38), (40),
% 242.26/48.86  | | | | | |            (46), (62), (64), (69), (70), (71), (81) are inconsistent
% 242.26/48.86  | | | | | |            by sub-proof #731.
% 242.26/48.86  | | | | | | 
% 242.26/48.86  | | | | | Case 2:
% 242.26/48.86  | | | | | | 
% 242.26/48.86  | | | | | |   (82)  all_54_4 = e1 | all_54_4 = e0
% 242.26/48.86  | | | | | | 
% 242.26/48.86  | | | | | | BETA: splitting (82) gives:
% 242.26/48.86  | | | | | | 
% 242.26/48.86  | | | | | | Case 1:
% 242.26/48.86  | | | | | | | 
% 242.26/48.86  | | | | | | |   (83)  all_54_4 = e1
% 242.26/48.86  | | | | | | | 
% 242.26/48.86  | | | | | | | REF_CLOSE: (24), (41), (83) are inconsistent by sub-proof #2086.
% 242.26/48.86  | | | | | | | 
% 242.26/48.86  | | | | | | Case 2:
% 242.26/48.86  | | | | | | | 
% 242.26/48.86  | | | | | | |   (84)  all_54_4 = e0
% 242.26/48.86  | | | | | | | 
% 242.26/48.86  | | | | | | | REF_CLOSE: (24), (60), (84) are inconsistent by sub-proof #1923.
% 242.26/48.86  | | | | | | | 
% 242.26/48.86  | | | | | | End of split
% 242.26/48.86  | | | | | | 
% 242.26/48.86  | | | | | End of split
% 242.26/48.86  | | | | | 
% 242.26/48.86  | | | | End of split
% 242.26/48.86  | | | | 
% 242.26/48.86  | | | End of split
% 242.26/48.86  | | | 
% 242.26/48.86  | | End of split
% 242.26/48.86  | | 
% 242.26/48.86  | Case 2:
% 242.26/48.86  | | 
% 242.26/48.86  | |   (85)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.26/48.86  | | 
% 242.26/48.86  | | REF_CLOSE: (1), (6), (27), (29), (85) are inconsistent by sub-proof #2066.
% 242.26/48.86  | | 
% 242.26/48.86  | End of split
% 242.26/48.86  | 
% 242.26/48.86  End of proof
% 242.26/48.86  
% 242.26/48.86  Sub-proof #727 shows that the following formulas are inconsistent:
% 242.26/48.86  ----------------------------------------------------------------
% 242.26/48.86    (1)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.26/48.86             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.26/48.86           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 242.26/48.86           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.86           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 242.26/48.86           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.86           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.26/48.86    (2)   ~ (e3 = e2)
% 242.26/48.86    (3)  op(e3, e0) = e2
% 242.26/48.86    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.86    (5)  all_56_11 = e3
% 242.26/48.86  
% 242.26/48.86  Begin of proof
% 242.26/48.86  | 
% 242.26/48.86  | BETA: splitting (1) gives:
% 242.26/48.86  | 
% 242.26/48.86  | Case 1:
% 242.26/48.86  | | 
% 242.26/48.86  | |   (6)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.26/48.86  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.26/48.86  | |        op(e1, e3) = e1
% 242.26/48.86  | | 
% 242.26/48.86  | | ALPHA: (6) implies:
% 242.26/48.86  | |   (7)   ~ (all_56_11 = e3)
% 242.26/48.86  | | 
% 242.26/48.86  | | REDUCE: (5), (7) imply:
% 242.26/48.86  | |   (8)  $false
% 242.26/48.86  | | 
% 242.26/48.86  | | CLOSE: (8) is inconsistent.
% 242.26/48.86  | | 
% 242.26/48.86  | Case 2:
% 242.26/48.86  | | 
% 242.26/48.86  | |   (9)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 242.26/48.86  | |            = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 242.26/48.86  | |          e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.86  | |          (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.86  | |          (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.26/48.86  | | 
% 242.26/48.86  | | BETA: splitting (9) gives:
% 242.26/48.86  | | 
% 242.26/48.86  | | Case 1:
% 242.26/48.86  | | | 
% 242.26/48.86  | | |   (10)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.86  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.86  | | |         op(e3, e0) = e3 & op(e0, e3) = e3
% 242.26/48.86  | | | 
% 242.26/48.86  | | | ALPHA: (10) implies:
% 242.26/48.86  | | |   (11)  op(e3, e0) = e3
% 242.26/48.86  | | | 
% 242.26/48.86  | | | REF_CLOSE: (2), (3), (4), (11) are inconsistent by sub-proof #2125.
% 242.26/48.86  | | | 
% 242.26/48.86  | | Case 2:
% 242.26/48.86  | | | 
% 242.26/48.86  | | |   (12)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 242.26/48.86  | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.86  | | |         op(e3, e0) = e0 & op(e0, e3) = e0
% 242.26/48.86  | | | 
% 242.26/48.86  | | | ALPHA: (12) implies:
% 242.26/48.86  | | |   (13)   ~ (all_56_11 = e3)
% 242.26/48.86  | | | 
% 242.26/48.86  | | | REDUCE: (5), (13) imply:
% 242.26/48.86  | | |   (14)  $false
% 242.26/48.86  | | | 
% 242.26/48.86  | | | CLOSE: (14) is inconsistent.
% 242.26/48.86  | | | 
% 242.26/48.86  | | End of split
% 242.26/48.86  | | 
% 242.26/48.86  | End of split
% 242.26/48.86  | 
% 242.26/48.86  End of proof
% 242.26/48.86  
% 242.26/48.86  Sub-proof #728 shows that the following formulas are inconsistent:
% 242.26/48.86  ----------------------------------------------------------------
% 242.26/48.86    (1)  all_58_8 = e0 & op(e1, e1) = e0
% 242.26/48.86    (2)  all_58_8 = e2
% 242.26/48.86    (3)   ~ (e2 = e0)
% 242.26/48.86  
% 242.26/48.86  Begin of proof
% 242.26/48.86  | 
% 242.26/48.86  | ALPHA: (1) implies:
% 242.26/48.86  |   (4)  all_58_8 = e0
% 242.26/48.86  | 
% 242.26/48.86  | COMBINE_EQS: (2), (4) imply:
% 242.26/48.86  |   (5)  e2 = e0
% 242.26/48.86  | 
% 242.26/48.86  | REDUCE: (3), (5) imply:
% 242.26/48.86  |   (6)  $false
% 242.26/48.86  | 
% 242.26/48.86  | CLOSE: (6) is inconsistent.
% 242.26/48.86  | 
% 242.26/48.86  End of proof
% 242.26/48.86  
% 242.26/48.86  Sub-proof #729 shows that the following formulas are inconsistent:
% 242.26/48.86  ----------------------------------------------------------------
% 242.26/48.86    (1)  all_58_8 = e3 & op(e1, e1) = e3
% 242.26/48.86    (2)  all_58_8 = e2
% 242.26/48.86    (3)   ~ (e3 = e2)
% 242.26/48.86  
% 242.26/48.86  Begin of proof
% 242.26/48.86  | 
% 242.26/48.86  | ALPHA: (1) implies:
% 242.26/48.86  |   (4)  all_58_8 = e3
% 242.26/48.86  | 
% 242.26/48.86  | COMBINE_EQS: (2), (4) imply:
% 242.26/48.86  |   (5)  e3 = e2
% 242.26/48.86  | 
% 242.26/48.86  | SIMP: (5) implies:
% 242.26/48.86  |   (6)  e3 = e2
% 242.26/48.86  | 
% 242.26/48.86  | REDUCE: (3), (6) imply:
% 242.26/48.86  |   (7)  $false
% 242.26/48.86  | 
% 242.26/48.86  | CLOSE: (7) is inconsistent.
% 242.26/48.86  | 
% 242.26/48.86  End of proof
% 242.26/48.86  
% 242.26/48.86  Sub-proof #730 shows that the following formulas are inconsistent:
% 242.26/48.86  ----------------------------------------------------------------
% 242.26/48.86    (1)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 242.26/48.86    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.86         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.86    (3)   ~ (e3 = e0)
% 242.26/48.86    (4)   ~ (e2 = e0)
% 242.26/48.86    (5)   ~ (all_52_11 = e2)
% 242.26/48.86    (6)  all_54_13 = all_52_7
% 242.26/48.86    (7)   ~ (all_52_11 = e1)
% 242.26/48.86    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.86         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.86    (9)   ~ (all_52_7 = all_52_11)
% 242.26/48.86    (10)   ~ (all_52_7 = e3)
% 242.26/48.86    (11)   ~ (e3 = e1)
% 242.26/48.86    (12)  all_58_3 = e3
% 242.26/48.86    (13)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.86          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.86    (14)  op(e3, e3) = e1
% 242.26/48.86    (15)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.86    (16)   ~ (e3 = e2)
% 242.26/48.86    (17)   ~ (all_52_7 = e1)
% 242.26/48.86    (18)  op(e2, e3) = e2
% 242.26/48.86    (19)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.26/48.86            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.26/48.86              e3) = all_42_1 & $i(all_42_1))
% 242.26/48.86    (20)  op(e0, e2) = all_52_7
% 242.26/48.86    (21)   ~ (all_52_4 = e3)
% 242.26/48.86    (22)  op(e3, e2) = all_52_4
% 242.26/48.86    (23)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.86    (24)  all_58_7 = e1
% 242.26/48.86    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.86    (26)   ~ (e1 = e0)
% 242.26/48.86    (27)  all_58_4 = e3
% 242.26/48.86    (28)  all_54_14 = all_52_11
% 242.26/48.86    (29)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.86            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.86            & $i(all_8_1))
% 242.26/48.86    (30)   ~ (e2 = e1)
% 242.26/48.86  
% 242.26/48.86  Begin of proof
% 242.26/48.86  | 
% 242.26/48.86  | BETA: splitting (1) gives:
% 242.26/48.86  | 
% 242.26/48.86  | Case 1:
% 242.26/48.86  | | 
% 242.26/48.86  | |   (31)  all_58_2 = e0 & op(e2, e3) = e0
% 242.26/48.86  | | 
% 242.26/48.86  | | ALPHA: (31) implies:
% 242.26/48.86  | |   (32)  op(e2, e3) = e0
% 242.26/48.86  | | 
% 242.26/48.86  | | REF_CLOSE: (4), (18), (19), (25), (29), (32) are inconsistent by sub-proof
% 242.26/48.86  | |            #733.
% 242.26/48.86  | | 
% 242.26/48.86  | Case 2:
% 242.26/48.86  | | 
% 242.26/48.86  | |   (33)  all_58_3 = e0 & op(e2, e2) = e0
% 242.26/48.86  | | 
% 242.26/48.86  | | ALPHA: (33) implies:
% 242.26/48.86  | |   (34)  all_58_3 = e0
% 242.26/48.86  | | 
% 242.26/48.86  | | COMBINE_EQS: (12), (34) imply:
% 242.26/48.86  | |   (35)  e3 = e0
% 242.26/48.86  | | 
% 242.26/48.86  | | COMBINE_EQS: (27), (35) imply:
% 242.26/48.86  | |   (36)  all_58_4 = e0
% 242.26/48.86  | | 
% 242.26/48.86  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 242.26/48.86  | |            (14), (15), (16), (17), (20), (21), (22), (23), (24), (25), (26),
% 242.26/48.86  | |            (28), (30), (36) are inconsistent by sub-proof #731.
% 242.26/48.86  | | 
% 242.26/48.86  | End of split
% 242.26/48.86  | 
% 242.26/48.86  End of proof
% 242.26/48.86  
% 242.26/48.86  Sub-proof #731 shows that the following formulas are inconsistent:
% 242.26/48.86  ----------------------------------------------------------------
% 242.26/48.86    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.86         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.86    (2)   ~ (e3 = e0)
% 242.26/48.86    (3)   ~ (e2 = e0)
% 242.26/48.86    (4)   ~ (all_52_11 = e2)
% 242.26/48.86    (5)  all_54_13 = all_52_7
% 242.26/48.86    (6)   ~ (all_52_11 = e1)
% 242.26/48.86    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.86         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.86    (8)   ~ (all_52_7 = all_52_11)
% 242.26/48.86    (9)   ~ (all_52_7 = e3)
% 242.26/48.86    (10)   ~ (e3 = e1)
% 242.26/48.86    (11)  all_58_3 = e3
% 242.26/48.86    (12)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.86          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.86    (13)  op(e3, e3) = e1
% 242.26/48.86    (14)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.86    (15)   ~ (e3 = e2)
% 242.26/48.86    (16)   ~ (all_52_7 = e1)
% 242.26/48.86    (17)  op(e0, e2) = all_52_7
% 242.26/48.86    (18)   ~ (all_52_4 = e3)
% 242.26/48.86    (19)  op(e3, e2) = all_52_4
% 242.26/48.86    (20)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.86    (21)  all_58_7 = e1
% 242.26/48.86    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.86    (23)   ~ (e1 = e0)
% 242.26/48.86    (24)  all_54_14 = all_52_11
% 242.26/48.86    (25)  all_58_4 = e0
% 242.26/48.86    (26)   ~ (e2 = e1)
% 242.26/48.86  
% 242.26/48.86  Begin of proof
% 242.26/48.86  | 
% 242.26/48.86  | BETA: splitting (12) gives:
% 242.26/48.86  | 
% 242.26/48.86  | Case 1:
% 242.26/48.86  | | 
% 242.26/48.86  | |   (27)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 242.26/48.86  | |           e3)
% 242.26/48.86  | | 
% 242.26/48.86  | | REF_CLOSE: (10), (13), (18), (19), (22), (27) are inconsistent by sub-proof
% 242.26/48.86  | |            #1401.
% 242.26/48.86  | | 
% 242.26/48.86  | Case 2:
% 242.26/48.86  | | 
% 242.26/48.86  | |   (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 242.26/48.86  | |           e3)
% 242.26/48.86  | | 
% 242.26/48.86  | | BETA: splitting (28) gives:
% 242.26/48.86  | | 
% 242.26/48.86  | | Case 1:
% 242.26/48.86  | | | 
% 242.26/48.86  | | |   (29)  all_58_4 = e3 & op(e3, e1) = e3
% 242.26/48.86  | | | 
% 242.26/48.86  | | | ALPHA: (29) implies:
% 242.26/48.86  | | |   (30)  all_58_4 = e3
% 242.26/48.86  | | | 
% 242.26/48.86  | | | REF_CLOSE: (2), (25), (30) are inconsistent by sub-proof #2186.
% 242.26/48.86  | | | 
% 242.26/48.86  | | Case 2:
% 242.26/48.86  | | | 
% 242.26/48.86  | | |   (31)  all_58_9 = e3 & op(e3, e0) = e3
% 242.26/48.86  | | | 
% 242.26/48.86  | | | ALPHA: (31) implies:
% 242.26/48.86  | | |   (32)  all_58_9 = e3
% 242.26/48.86  | | | 
% 242.26/48.86  | | | BETA: splitting (1) gives:
% 242.26/48.86  | | | 
% 242.26/48.86  | | | Case 1:
% 242.26/48.86  | | | | 
% 242.26/48.86  | | | |   (33)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 242.26/48.86  | | | |           = e2)
% 242.26/48.86  | | | | 
% 242.26/48.86  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14),
% 242.26/48.86  | | | |            (16), (17), (20), (21), (22), (23), (24), (26), (33) are
% 242.26/48.86  | | | |            inconsistent by sub-proof #734.
% 242.26/48.86  | | | | 
% 242.26/48.86  | | | Case 2:
% 242.26/48.86  | | | | 
% 242.26/48.86  | | | |   (34)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 242.26/48.86  | | | |           = e2)
% 242.26/48.86  | | | | 
% 242.26/48.86  | | | | BETA: splitting (34) gives:
% 242.26/48.86  | | | | 
% 242.26/48.86  | | | | Case 1:
% 242.26/48.86  | | | | | 
% 242.26/48.86  | | | | |   (35)  all_58_4 = e2 & op(e3, e1) = e2
% 242.26/48.86  | | | | | 
% 242.26/48.86  | | | | | ALPHA: (35) implies:
% 242.26/48.86  | | | | |   (36)  all_58_4 = e2
% 242.26/48.86  | | | | | 
% 242.26/48.86  | | | | | REF_CLOSE: (3), (25), (36) are inconsistent by sub-proof #1666.
% 242.26/48.86  | | | | | 
% 242.26/48.86  | | | | Case 2:
% 242.26/48.86  | | | | | 
% 242.26/48.86  | | | | |   (37)  all_58_9 = e2 & op(e3, e0) = e2
% 242.26/48.86  | | | | | 
% 242.26/48.86  | | | | | REF_CLOSE: (15), (32), (37) are inconsistent by sub-proof #732.
% 242.26/48.86  | | | | | 
% 242.26/48.86  | | | | End of split
% 242.26/48.86  | | | | 
% 242.26/48.86  | | | End of split
% 242.26/48.86  | | | 
% 242.26/48.86  | | End of split
% 242.26/48.86  | | 
% 242.26/48.86  | End of split
% 242.26/48.86  | 
% 242.26/48.86  End of proof
% 242.26/48.86  
% 242.26/48.86  Sub-proof #732 shows that the following formulas are inconsistent:
% 242.26/48.86  ----------------------------------------------------------------
% 242.26/48.86    (1)  all_58_9 = e2 & op(e3, e0) = e2
% 242.26/48.86    (2)  all_58_9 = e3
% 242.26/48.86    (3)   ~ (e3 = e2)
% 242.26/48.86  
% 242.26/48.86  Begin of proof
% 242.26/48.86  | 
% 242.26/48.86  | ALPHA: (1) implies:
% 242.26/48.86  |   (4)  all_58_9 = e2
% 242.26/48.86  | 
% 242.26/48.86  | COMBINE_EQS: (2), (4) imply:
% 242.26/48.86  |   (5)  e3 = e2
% 242.26/48.86  | 
% 242.26/48.86  | SIMP: (5) implies:
% 242.26/48.86  |   (6)  e3 = e2
% 242.26/48.86  | 
% 242.26/48.86  | REDUCE: (3), (6) imply:
% 242.26/48.86  |   (7)  $false
% 242.26/48.86  | 
% 242.26/48.86  | CLOSE: (7) is inconsistent.
% 242.26/48.86  | 
% 242.26/48.86  End of proof
% 242.26/48.86  
% 242.26/48.86  Sub-proof #733 shows that the following formulas are inconsistent:
% 242.26/48.86  ----------------------------------------------------------------
% 242.26/48.86    (1)  op(e2, e3) = e0
% 242.26/48.86    (2)   ~ (e2 = e0)
% 242.26/48.86    (3)  op(e2, e3) = e2
% 242.26/48.86    (4)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 242.26/48.86           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 242.26/48.86           all_42_1 & $i(all_42_1))
% 242.26/48.86    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.86    (6)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.86           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.86           & $i(all_8_1))
% 242.26/48.86  
% 242.26/48.86  Begin of proof
% 242.26/48.86  | 
% 242.26/48.86  | BETA: splitting (4) gives:
% 242.26/48.86  | 
% 242.26/48.86  | Case 1:
% 242.26/48.86  | | 
% 242.26/48.86  | |   (7)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.26/48.86  | |        all_42_1 & $i(all_42_0) & $i(all_42_1)
% 242.26/48.86  | | 
% 242.26/48.86  | | ALPHA: (7) implies:
% 242.26/48.86  | |   (8)  op(e2, e3) = all_42_1
% 242.26/48.86  | | 
% 242.26/48.86  | | REF_CLOSE: (1), (2), (3), (5), (6), (8) are inconsistent by sub-proof #889.
% 242.26/48.86  | | 
% 242.26/48.86  | Case 2:
% 242.26/48.86  | | 
% 242.26/48.86  | |   (9)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 242.26/48.86  | | 
% 242.26/48.86  | | ALPHA: (9) implies:
% 242.26/48.86  | |   (10)  op(e2, e3) = all_42_1
% 242.26/48.86  | | 
% 242.26/48.86  | | REF_CLOSE: (1), (2), (3), (5), (6), (10) are inconsistent by sub-proof #889.
% 242.26/48.86  | | 
% 242.26/48.86  | End of split
% 242.26/48.86  | 
% 242.26/48.86  End of proof
% 242.26/48.86  
% 242.26/48.86  Sub-proof #734 shows that the following formulas are inconsistent:
% 242.26/48.86  ----------------------------------------------------------------
% 242.26/48.86    (1)   ~ (e3 = e0)
% 242.26/48.86    (2)   ~ (e2 = e0)
% 242.26/48.86    (3)   ~ (all_52_11 = e2)
% 242.26/48.86    (4)  all_54_13 = all_52_7
% 242.26/48.86    (5)   ~ (all_52_11 = e1)
% 242.26/48.86    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.86         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.86    (7)   ~ (all_52_7 = all_52_11)
% 242.26/48.86    (8)   ~ (all_52_7 = e3)
% 242.26/48.86    (9)  all_58_3 = e3
% 242.26/48.86    (10)  op(e3, e3) = e1
% 242.26/48.86    (11)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.26/48.86    (12)   ~ (all_52_7 = e1)
% 242.26/48.86    (13)  op(e0, e2) = all_52_7
% 242.26/48.86    (14)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.26/48.86    (15)  all_58_7 = e1
% 242.26/48.86    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.86    (17)   ~ (e1 = e0)
% 242.26/48.86    (18)  all_54_14 = all_52_11
% 242.26/48.86    (19)   ~ (e2 = e1)
% 242.26/48.86    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 242.26/48.86  
% 242.26/48.86  Begin of proof
% 242.26/48.86  | 
% 242.26/48.86  | BETA: splitting (20) gives:
% 242.26/48.86  | 
% 242.26/48.86  | Case 1:
% 242.26/48.86  | | 
% 242.26/48.86  | |   (21)  all_58_0 = e2 & op(e3, e3) = e2
% 242.26/48.86  | | 
% 242.26/48.86  | | ALPHA: (21) implies:
% 242.26/48.86  | |   (22)  op(e3, e3) = e2
% 242.26/48.86  | | 
% 242.26/48.87  | | REF_CLOSE: (10), (16), (19), (22) are inconsistent by sub-proof #2267.
% 242.26/48.87  | | 
% 242.26/48.87  | Case 2:
% 242.26/48.87  | | 
% 242.26/48.87  | |   (23)  all_58_1 = e2 & op(e3, e2) = e2
% 242.26/48.87  | | 
% 242.26/48.87  | | ALPHA: (23) implies:
% 242.26/48.87  | |   (24)  all_58_1 = e2
% 242.26/48.87  | | 
% 242.26/48.87  | | BETA: splitting (6) gives:
% 242.26/48.87  | | 
% 242.26/48.87  | | Case 1:
% 242.26/48.87  | | | 
% 242.26/48.87  | | |   (25)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 242.26/48.87  | | |           e0)
% 242.26/48.87  | | | 
% 242.26/48.87  | | | BETA: splitting (25) gives:
% 242.26/48.87  | | | 
% 242.26/48.87  | | | Case 1:
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | |   (26)  all_58_1 = e0 & op(e3, e2) = e0
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | | REF_CLOSE: (2), (24), (26) are inconsistent by sub-proof #2187.
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | Case 2:
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | |   (27)  all_58_3 = e0 & op(e2, e2) = e0
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | | REF_CLOSE: (1), (9), (27) are inconsistent by sub-proof #1719.
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | End of split
% 242.26/48.87  | | | 
% 242.26/48.87  | | Case 2:
% 242.26/48.87  | | | 
% 242.26/48.87  | | |   (28)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.26/48.87  | | |           e0)
% 242.26/48.87  | | | 
% 242.26/48.87  | | | BETA: splitting (28) gives:
% 242.26/48.87  | | | 
% 242.26/48.87  | | | Case 1:
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | |   (29)  all_58_7 = e0 & op(e1, e2) = e0
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | | REF_CLOSE: (15), (17), (29) are inconsistent by sub-proof #1558.
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | Case 2:
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | |   (30)  all_58_13 = e0 & op(e0, e2) = e0
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | | ALPHA: (30) implies:
% 242.26/48.87  | | | |   (31)  op(e0, e2) = e0
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | | REF_CLOSE: (3), (4), (5), (7), (8), (11), (12), (13), (14), (16), (18),
% 242.26/48.87  | | | |            (31) are inconsistent by sub-proof #904.
% 242.26/48.87  | | | | 
% 242.26/48.87  | | | End of split
% 242.26/48.87  | | | 
% 242.26/48.87  | | End of split
% 242.26/48.87  | | 
% 242.26/48.87  | End of split
% 242.26/48.87  | 
% 242.26/48.87  End of proof
% 242.26/48.87  
% 242.26/48.87  Sub-proof #735 shows that the following formulas are inconsistent:
% 242.26/48.87  ----------------------------------------------------------------
% 242.26/48.87    (1)   ~ (e3 = e0)
% 242.26/48.87    (2)   ~ (e2 = e0)
% 242.26/48.87    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.87         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.87    (4)  all_58_3 = e3
% 242.26/48.87    (5)   ~ (e3 = e2)
% 242.26/48.87    (6)  all_58_15 = e1
% 242.26/48.87    (7)  all_58_12 = e3
% 242.26/48.87    (8)  all_58_14 = e0
% 242.26/48.87    (9)  all_58_7 = e1
% 242.26/48.87    (10)  all_58_1 = e2
% 242.26/48.87    (11)   ~ (e1 = e0)
% 242.26/48.87    (12)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.87          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.87            e2)
% 242.26/48.87    (13)   ~ (e2 = e1)
% 242.26/48.87  
% 242.26/48.87  Begin of proof
% 242.26/48.87  | 
% 242.26/48.87  | BETA: splitting (12) gives:
% 242.26/48.87  | 
% 242.26/48.87  | Case 1:
% 242.26/48.87  | | 
% 242.26/48.87  | |   (14)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 242.26/48.87  | |           e2)
% 242.26/48.87  | | 
% 242.26/48.87  | | BETA: splitting (14) gives:
% 242.26/48.87  | | 
% 242.26/48.87  | | Case 1:
% 242.26/48.87  | | | 
% 242.26/48.87  | | |   (15)  all_58_12 = e2 & op(e0, e3) = e2
% 242.26/48.87  | | | 
% 242.26/48.87  | | | ALPHA: (15) implies:
% 242.26/48.87  | | |   (16)  all_58_12 = e2
% 242.26/48.87  | | | 
% 242.26/48.87  | | | REF_CLOSE: (5), (7), (16) are inconsistent by sub-proof #1552.
% 242.26/48.87  | | | 
% 242.26/48.87  | | Case 2:
% 242.26/48.87  | | | 
% 242.26/48.87  | | |   (17)  all_58_13 = e2 & op(e0, e2) = e2
% 242.26/48.87  | | | 
% 242.26/48.87  | | | ALPHA: (17) implies:
% 242.26/48.87  | | |   (18)  all_58_13 = e2
% 242.26/48.87  | | | 
% 242.26/48.87  | | | REF_CLOSE: (1), (2), (3), (4), (9), (10), (11), (18) are inconsistent by
% 242.26/48.87  | | |            sub-proof #969.
% 242.26/48.87  | | | 
% 242.26/48.87  | | End of split
% 242.26/48.87  | | 
% 242.26/48.87  | Case 2:
% 242.26/48.87  | | 
% 242.26/48.87  | |   (19)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.87  | |           e2)
% 242.26/48.87  | | 
% 242.26/48.87  | | BETA: splitting (19) gives:
% 242.26/48.87  | | 
% 242.26/48.87  | | Case 1:
% 242.26/48.87  | | | 
% 242.26/48.87  | | |   (20)  all_58_14 = e2 & op(e0, e1) = e2
% 242.26/48.87  | | | 
% 242.26/48.87  | | | REF_CLOSE: (2), (8), (20) are inconsistent by sub-proof #2077.
% 242.26/48.87  | | | 
% 242.26/48.87  | | Case 2:
% 242.26/48.87  | | | 
% 242.26/48.87  | | |   (21)  all_58_15 = e2 & op(e0, e0) = e2
% 242.26/48.87  | | | 
% 242.26/48.87  | | | REF_CLOSE: (6), (13), (21) are inconsistent by sub-proof #1917.
% 242.26/48.87  | | | 
% 242.26/48.87  | | End of split
% 242.26/48.87  | | 
% 242.26/48.87  | End of split
% 242.26/48.87  | 
% 242.26/48.87  End of proof
% 242.26/48.87  
% 242.26/48.87  Sub-proof #736 shows that the following formulas are inconsistent:
% 242.26/48.87  ----------------------------------------------------------------
% 242.26/48.87    (1)   ~ (e2 = e0)
% 242.26/48.87    (2)  all_58_6 = e2
% 242.26/48.87    (3)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 242.26/48.87    (4)  all_58_7 = e1
% 242.26/48.87    (5)   ~ (e1 = e0)
% 242.26/48.87  
% 242.26/48.87  Begin of proof
% 242.26/48.87  | 
% 242.26/48.87  | BETA: splitting (3) gives:
% 242.26/48.87  | 
% 242.26/48.87  | Case 1:
% 242.26/48.87  | | 
% 242.26/48.87  | |   (6)  all_58_6 = e0 & op(e1, e3) = e0
% 242.26/48.87  | | 
% 242.26/48.87  | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #1678.
% 242.26/48.87  | | 
% 242.26/48.87  | Case 2:
% 242.26/48.87  | | 
% 242.26/48.87  | |   (7)  all_58_7 = e0 & op(e1, e2) = e0
% 242.26/48.87  | | 
% 242.26/48.87  | | ALPHA: (7) implies:
% 242.26/48.87  | |   (8)  all_58_7 = e0
% 242.26/48.87  | | 
% 242.26/48.87  | | COMBINE_EQS: (4), (8) imply:
% 242.26/48.87  | |   (9)  e1 = e0
% 242.26/48.87  | | 
% 242.26/48.87  | | SIMP: (9) implies:
% 242.26/48.87  | |   (10)  e1 = e0
% 242.26/48.87  | | 
% 242.26/48.87  | | REDUCE: (5), (10) imply:
% 242.26/48.87  | |   (11)  $false
% 242.26/48.87  | | 
% 242.26/48.87  | | CLOSE: (11) is inconsistent.
% 242.26/48.87  | | 
% 242.26/48.87  | End of split
% 242.26/48.87  | 
% 242.26/48.87  End of proof
% 242.26/48.87  
% 242.26/48.87  Sub-proof #737 shows that the following formulas are inconsistent:
% 242.26/48.87  ----------------------------------------------------------------
% 242.26/48.87    (1)   ~ (e3 = e0)
% 242.26/48.87    (2)   ~ (e2 = e0)
% 242.26/48.87    (3)   ~ (e3 = e1)
% 242.26/48.87    (4)  all_58_9 = e1 & op(e3, e0) = e1
% 242.26/48.87    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.26/48.87         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.26/48.87    (6)  op(e3, e3) = e1
% 242.26/48.87    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.87         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.87    (8)   ~ (e3 = e2)
% 242.26/48.87    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.26/48.87         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.26/48.87    (10)  all_58_9 = e3
% 242.26/48.87    (11)  op(e2, e3) = all_52_1
% 242.26/48.87    (12)  all_58_12 = e3
% 242.26/48.87    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.87    (14)   ~ (e1 = e0)
% 242.26/48.87    (15)   ~ (all_52_1 = e3)
% 242.26/48.87    (16)   ~ (e2 = e1)
% 242.26/48.87  
% 242.26/48.87  Begin of proof
% 242.26/48.87  | 
% 242.26/48.87  | ALPHA: (4) implies:
% 242.26/48.87  |   (17)  all_58_9 = e1
% 242.26/48.87  | 
% 242.26/48.87  | COMBINE_EQS: (10), (17) imply:
% 242.26/48.87  |   (18)  e3 = e1
% 242.26/48.87  | 
% 242.26/48.87  | COMBINE_EQS: (12), (18) imply:
% 242.26/48.87  |   (19)  all_58_12 = e1
% 242.26/48.87  | 
% 242.26/48.87  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (13), (14), (15),
% 242.26/48.87  |            (16), (19) are inconsistent by sub-proof #1204.
% 242.26/48.87  | 
% 242.26/48.87  End of proof
% 242.26/48.87  
% 242.26/48.87  Sub-proof #738 shows that the following formulas are inconsistent:
% 242.26/48.87  ----------------------------------------------------------------
% 242.26/48.87    (1)   ~ (e3 = e0)
% 242.26/48.87    (2)   ~ (e2 = e0)
% 242.26/48.87    (3)   ~ (e3 = e1)
% 242.26/48.87    (4)  all_58_3 = e3
% 242.26/48.87    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.26/48.87         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.26/48.87    (6)  op(e3, e3) = e1
% 242.26/48.87    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.87         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.87    (8)   ~ (e3 = e2)
% 242.26/48.87    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.26/48.87         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.26/48.87    (10)  op(e2, e3) = all_52_1
% 242.26/48.87    (11)  all_58_12 = e3
% 242.26/48.87    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.87    (13)  all_58_3 = e1 & op(e2, e2) = e1
% 242.26/48.87    (14)   ~ (e1 = e0)
% 242.26/48.87    (15)   ~ (all_52_1 = e3)
% 242.26/48.87    (16)   ~ (e2 = e1)
% 242.26/48.87  
% 242.26/48.87  Begin of proof
% 242.26/48.87  | 
% 242.26/48.87  | ALPHA: (13) implies:
% 242.26/48.87  |   (17)  all_58_3 = e1
% 242.26/48.87  | 
% 242.26/48.87  | COMBINE_EQS: (4), (17) imply:
% 242.26/48.87  |   (18)  e3 = e1
% 242.26/48.87  | 
% 242.26/48.87  | COMBINE_EQS: (11), (18) imply:
% 242.26/48.87  |   (19)  all_58_12 = e1
% 242.26/48.87  | 
% 242.26/48.87  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (14), (15),
% 242.26/48.87  |            (16), (19) are inconsistent by sub-proof #1204.
% 242.26/48.87  | 
% 242.26/48.87  End of proof
% 242.26/48.87  
% 242.26/48.87  Sub-proof #739 shows that the following formulas are inconsistent:
% 242.26/48.87  ----------------------------------------------------------------
% 242.26/48.87    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 242.26/48.87    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.87         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.87    (3)   ~ (e3 = e0)
% 242.26/48.87    (4)   ~ (e2 = e0)
% 242.26/48.87    (5)   ~ (all_52_13 = e1)
% 242.26/48.87    (6)   ~ (e3 = e1)
% 242.26/48.87    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.87         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.87    (8)  all_58_3 = e3
% 242.26/48.87    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.26/48.87         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.26/48.87    (10)  op(e3, e3) = e1
% 242.26/48.87    (11)  op(e2, e1) = all_52_9
% 242.26/48.87    (12)   ~ (e3 = e2)
% 242.26/48.87    (13)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.26/48.87          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.26/48.87    (14)  op(e2, e3) = all_52_1
% 242.26/48.87    (15)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.26/48.87          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.87    (16)   ~ (all_52_4 = e3)
% 242.26/48.87    (17)  op(e3, e2) = all_52_4
% 242.26/48.87    (18)   ~ (all_52_9 = e3)
% 242.26/48.87    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.87    (20)   ~ (e1 = e0)
% 242.26/48.87    (21)  op(e2, e0) = all_52_13
% 242.26/48.87    (22)  all_58_14 = e1
% 242.26/48.87    (23)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.26/48.87          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.26/48.87    (24)   ~ (e2 = e1)
% 242.26/48.87    (25)   ~ (all_52_1 = e1)
% 242.26/48.87  
% 242.26/48.87  Begin of proof
% 242.26/48.87  | 
% 242.26/48.87  | BETA: splitting (1) gives:
% 242.26/48.87  | 
% 242.26/48.87  | Case 1:
% 242.26/48.87  | | 
% 242.26/48.87  | |   (26)  all_58_4 = e3 & op(e3, e1) = e3
% 242.26/48.87  | | 
% 242.26/48.87  | | ALPHA: (26) implies:
% 242.26/48.87  | |   (27)  all_58_4 = e3
% 242.26/48.87  | | 
% 242.26/48.87  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 242.26/48.87  | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (27)
% 242.26/48.87  | |            are inconsistent by sub-proof #1029.
% 242.26/48.87  | | 
% 242.26/48.87  | Case 2:
% 242.26/48.87  | | 
% 242.26/48.87  | |   (28)  all_58_5 = e3 & op(e2, e1) = e3
% 242.26/48.87  | | 
% 242.26/48.87  | | REF_CLOSE: (11), (18), (19), (28) are inconsistent by sub-proof #1822.
% 242.26/48.87  | | 
% 242.26/48.87  | End of split
% 242.26/48.87  | 
% 242.26/48.87  End of proof
% 242.26/48.87  
% 242.26/48.87  Sub-proof #740 shows that the following formulas are inconsistent:
% 242.26/48.87  ----------------------------------------------------------------
% 242.26/48.87    (1)   ~ (e3 = e0)
% 242.26/48.87    (2)   ~ (e2 = e0)
% 242.26/48.87    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.26/48.87         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.87    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.87         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.87    (5)   ~ (e3 = e1)
% 242.26/48.87    (6)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.26/48.87    (7)  all_58_3 = e3
% 242.26/48.87    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.26/48.87         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.26/48.87    (9)  op(e3, e3) = e1
% 242.26/48.87    (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.87          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.87    (11)   ~ (e3 = e2)
% 242.26/48.87    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.26/48.87          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.26/48.87    (13)  op(e2, e3) = all_52_1
% 242.26/48.87    (14)  all_58_7 = e1
% 242.26/48.87    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.87    (16)   ~ (e1 = e0)
% 242.26/48.87    (17)   ~ (all_52_1 = e3)
% 242.26/48.87    (18)   ~ (e2 = e1)
% 242.26/48.87  
% 242.26/48.87  Begin of proof
% 242.26/48.87  | 
% 242.26/48.87  | BETA: splitting (6) gives:
% 242.26/48.87  | 
% 242.26/48.87  | Case 1:
% 242.26/48.87  | | 
% 242.26/48.87  | |   (19)  all_58_12 = e1 & op(e0, e3) = e1
% 242.26/48.87  | | 
% 242.26/48.87  | | ALPHA: (19) implies:
% 242.26/48.87  | |   (20)  all_58_12 = e1
% 242.26/48.87  | | 
% 242.26/48.87  | | REF_CLOSE: (1), (2), (5), (8), (9), (10), (11), (12), (13), (15), (16),
% 242.26/48.87  | |            (17), (18), (20) are inconsistent by sub-proof #1204.
% 242.26/48.87  | | 
% 242.26/48.87  | Case 2:
% 242.26/48.87  | | 
% 242.26/48.87  | |   (21)  all_58_13 = e1 & op(e0, e2) = e1
% 242.26/48.87  | | 
% 242.26/48.87  | | ALPHA: (21) implies:
% 242.26/48.87  | |   (22)  all_58_13 = e1
% 242.26/48.87  | | 
% 242.26/48.87  | | REF_CLOSE: (1), (2), (3), (4), (7), (11), (14), (16), (18), (22) are
% 242.26/48.87  | |            inconsistent by sub-proof #1457.
% 242.26/48.87  | | 
% 242.26/48.87  | End of split
% 242.26/48.87  | 
% 242.26/48.87  End of proof
% 242.26/48.87  
% 242.26/48.87  Sub-proof #741 shows that the following formulas are inconsistent:
% 242.26/48.87  ----------------------------------------------------------------
% 242.26/48.87    (1)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 242.26/48.87    (2)   ~ (e3 = e1)
% 242.26/48.87    (3)  all_58_3 = e3
% 242.26/48.87    (4)  op(e3, e2) = all_52_4
% 242.26/48.87    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.87    (6)   ~ (all_52_4 = e1)
% 242.26/48.87  
% 242.26/48.87  Begin of proof
% 242.26/48.87  | 
% 242.26/48.87  | BETA: splitting (1) gives:
% 242.26/48.87  | 
% 242.26/48.87  | Case 1:
% 242.26/48.87  | | 
% 242.26/48.87  | |   (7)  all_58_1 = e1 & op(e3, e2) = e1
% 242.26/48.87  | | 
% 242.26/48.87  | | ALPHA: (7) implies:
% 242.26/48.87  | |   (8)  op(e3, e2) = e1
% 242.26/48.87  | | 
% 242.26/48.87  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2228.
% 242.26/48.87  | | 
% 242.26/48.87  | Case 2:
% 242.26/48.87  | | 
% 242.26/48.87  | |   (9)  all_58_3 = e1 & op(e2, e2) = e1
% 242.26/48.87  | | 
% 242.26/48.87  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #2197.
% 242.26/48.87  | | 
% 242.26/48.87  | End of split
% 242.26/48.87  | 
% 242.26/48.87  End of proof
% 242.26/48.87  
% 242.26/48.87  Sub-proof #742 shows that the following formulas are inconsistent:
% 242.26/48.87  ----------------------------------------------------------------
% 242.26/48.87    (1)   ~ (all_52_9 = all_6_2)
% 242.26/48.88    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 242.26/48.88           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 242.26/48.88             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.26/48.88           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.26/48.88             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 242.26/48.88           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.88           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.26/48.88           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.88           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 242.26/48.88           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.88           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.26/48.88             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.88           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.88           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 242.26/48.88           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.88           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 242.26/48.88           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.88           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.26/48.88             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.26/48.88           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.88           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 242.26/48.88           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.88           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 242.26/48.88           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.88           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.26/48.88             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.26/48.88           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.88           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.88    (3)  all_58_3 = e3
% 242.26/48.88    (4)  all_54_10 = all_6_2
% 242.26/48.88    (5)   ~ (all_6_2 = e3)
% 242.26/48.88    (6)  op(e2, e1) = all_52_9
% 242.26/48.88    (7)   ~ (all_6_2 = e0)
% 242.26/48.88    (8)  all_56_31 = e0
% 242.26/48.88    (9)  op(e2, e3) = all_52_1
% 242.26/48.88    (10)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 242.26/48.88    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.88    (12)  all_56_11 = e3
% 242.26/48.88    (13)  all_56_21 = all_6_2
% 242.26/48.88    (14)  op(e2, e0) = all_52_13
% 242.26/48.88    (15)   ~ (all_52_1 = e3)
% 242.26/48.88    (16)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.26/48.88          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.26/48.88    (17)  all_56_1 = e1
% 242.26/48.88    (18)   ~ (all_52_1 = e1)
% 242.26/48.88  
% 242.26/48.88  Begin of proof
% 242.26/48.88  | 
% 242.26/48.88  | BETA: splitting (2) gives:
% 242.26/48.88  | 
% 242.26/48.88  | Case 1:
% 242.26/48.88  | | 
% 242.26/48.88  | |   (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 242.26/48.88  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 242.26/48.88  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 242.26/48.88  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.88  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 242.26/48.88  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 242.26/48.88  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 242.26/48.88  | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 242.26/48.88  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.88  | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 242.26/48.88  | |           = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &
% 242.26/48.88  | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 242.26/48.88  | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 242.26/48.88  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.88  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.26/48.88  | | 
% 242.26/48.88  | | REF_CLOSE: (8), (9), (11), (12), (15), (17), (19) are inconsistent by
% 242.26/48.88  | |            sub-proof #744.
% 242.26/48.88  | | 
% 242.26/48.88  | Case 2:
% 242.26/48.88  | | 
% 242.26/48.88  | |   (20)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 242.26/48.88  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.26/48.88  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 242.26/48.88  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.26/48.88  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 242.26/48.88  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.88  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.88  | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 242.26/48.88  | |           e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.26/48.88  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 242.26/48.88  | |         (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.88  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.88  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 242.26/48.88  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 242.26/48.88  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.88  | | 
% 242.26/48.88  | | BETA: splitting (20) gives:
% 242.26/48.88  | | 
% 242.26/48.88  | | Case 1:
% 242.26/48.88  | | | 
% 242.26/48.88  | | |   (21)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 242.26/48.88  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.26/48.88  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 242.26/48.88  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 242.26/48.88  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 242.26/48.88  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.88  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.88  | | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.26/48.88  | | | 
% 242.26/48.88  | | | BETA: splitting (21) gives:
% 242.26/48.88  | | | 
% 242.26/48.88  | | | Case 1:
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | |   (22)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 242.26/48.88  | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.26/48.88  | | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | ALPHA: (22) implies:
% 242.26/48.88  | | | |   (23)   ~ (all_56_1 = e1)
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | REDUCE: (17), (23) imply:
% 242.26/48.88  | | | |   (24)  $false
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | CLOSE: (24) is inconsistent.
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | Case 2:
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | |   (25)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.88  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.26/48.88  | | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 242.26/48.88  | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 242.26/48.88  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 &
% 242.26/48.88  | | | |           op(e0, e2) = e2)
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | BETA: splitting (25) gives:
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | Case 1:
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | |   (26)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.88  | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.26/48.88  | | | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | | ALPHA: (26) implies:
% 242.26/48.88  | | | | |   (27)   ~ (all_56_21 = e2)
% 242.26/48.88  | | | | |   (28)  op(e2, e1) = e1
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | | REDUCE: (13), (27) imply:
% 242.26/48.88  | | | | |   (29)   ~ (all_6_2 = e2)
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | | BETA: splitting (10) gives:
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | | Case 1:
% 242.26/48.88  | | | | | | 
% 242.26/48.88  | | | | | |   (30)  all_54_10 = e3
% 242.26/48.88  | | | | | | 
% 242.26/48.88  | | | | | | REF_CLOSE: (4), (5), (30) are inconsistent by sub-proof #2313.
% 242.26/48.88  | | | | | | 
% 242.26/48.88  | | | | | Case 2:
% 242.26/48.88  | | | | | | 
% 242.26/48.88  | | | | | |   (31)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 242.26/48.88  | | | | | | 
% 242.26/48.88  | | | | | | REF_CLOSE: (1), (4), (6), (7), (11), (28), (29), (31) are
% 242.26/48.88  | | | | | |            inconsistent by sub-proof #1730.
% 242.26/48.88  | | | | | | 
% 242.26/48.88  | | | | | End of split
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | Case 2:
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | |   (32)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.88  | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.88  | | | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | | ALPHA: (32) implies:
% 242.26/48.88  | | | | |   (33)   ~ (all_56_31 = e0)
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | | REDUCE: (8), (33) imply:
% 242.26/48.88  | | | | |   (34)  $false
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | | CLOSE: (34) is inconsistent.
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | End of split
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | End of split
% 242.26/48.88  | | | 
% 242.26/48.88  | | Case 2:
% 242.26/48.88  | | | 
% 242.26/48.88  | | |   (35)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.88  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.26/48.88  | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29
% 242.26/48.88  | | |           = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 242.26/48.88  | | |             = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 242.26/48.88  | | |           e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 242.26/48.88  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.26/48.88  | | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.88  | | | 
% 242.26/48.88  | | | BETA: splitting (35) gives:
% 242.26/48.88  | | | 
% 242.26/48.88  | | | Case 1:
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | |   (36)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.88  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.26/48.88  | | | |         op(e2, e0) = e0 & op(e0, e2) = e0
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | ALPHA: (36) implies:
% 242.26/48.88  | | | |   (37)   ~ (all_56_21 = e2)
% 242.26/48.88  | | | |   (38)  op(e2, e0) = e0
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | REDUCE: (13), (37) imply:
% 242.26/48.88  | | | |   (39)   ~ (all_6_2 = e2)
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | BETA: splitting (10) gives:
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | Case 1:
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | |   (40)  all_54_10 = e3
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | | REF_CLOSE: (4), (5), (40) are inconsistent by sub-proof #2313.
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | Case 2:
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | |   (41)   ~ (all_54_10 = e3)
% 242.26/48.88  | | | | |   (42)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (11), (14), (16), (18),
% 242.26/48.88  | | | | |            (38), (39), (42) are inconsistent by sub-proof #790.
% 242.26/48.88  | | | | | 
% 242.26/48.88  | | | | End of split
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | Case 2:
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | |   (43)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.88  | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.88  | | | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 242.26/48.88  | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.88  | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 &
% 242.26/48.88  | | | |           op(e0, e1) = e0)
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | REF_CLOSE: (8), (17), (43) are inconsistent by sub-proof #743.
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | End of split
% 242.26/48.88  | | | 
% 242.26/48.88  | | End of split
% 242.26/48.88  | | 
% 242.26/48.88  | End of split
% 242.26/48.88  | 
% 242.26/48.88  End of proof
% 242.26/48.88  
% 242.26/48.88  Sub-proof #743 shows that the following formulas are inconsistent:
% 242.26/48.88  ----------------------------------------------------------------
% 242.26/48.88    (1)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 242.26/48.88             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 242.26/48.88           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 242.26/48.88             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 242.26/48.88           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.88    (2)  all_56_31 = e0
% 242.26/48.88    (3)  all_56_1 = e1
% 242.26/48.88  
% 242.26/48.88  Begin of proof
% 242.26/48.88  | 
% 242.26/48.88  | BETA: splitting (1) gives:
% 242.26/48.88  | 
% 242.26/48.88  | Case 1:
% 242.26/48.88  | | 
% 242.26/48.88  | |   (4)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 242.26/48.88  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 242.26/48.88  | |        & op(e0, e1) = e1
% 242.26/48.88  | | 
% 242.26/48.88  | | ALPHA: (4) implies:
% 242.26/48.88  | |   (5)   ~ (all_56_31 = e0)
% 242.26/48.88  | | 
% 242.26/48.88  | | REDUCE: (2), (5) imply:
% 242.26/48.88  | |   (6)  $false
% 242.26/48.88  | | 
% 242.26/48.88  | | CLOSE: (6) is inconsistent.
% 242.26/48.88  | | 
% 242.26/48.88  | Case 2:
% 242.26/48.88  | | 
% 242.26/48.88  | |   (7)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 242.26/48.88  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 242.26/48.88  | |        & op(e0, e1) = e0
% 242.26/48.88  | | 
% 242.26/48.88  | | ALPHA: (7) implies:
% 242.26/48.88  | |   (8)   ~ (all_56_1 = e1)
% 242.26/48.88  | | 
% 242.26/48.88  | | REDUCE: (3), (8) imply:
% 242.26/48.88  | |   (9)  $false
% 242.26/48.88  | | 
% 242.26/48.88  | | CLOSE: (9) is inconsistent.
% 242.26/48.88  | | 
% 242.26/48.88  | End of split
% 242.26/48.88  | 
% 242.26/48.88  End of proof
% 242.26/48.88  
% 242.26/48.88  Sub-proof #744 shows that the following formulas are inconsistent:
% 242.26/48.88  ----------------------------------------------------------------
% 242.26/48.88    (1)  all_56_31 = e0
% 242.26/48.88    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 242.26/48.88           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 242.26/48.88             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.26/48.88           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.26/48.88             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 242.26/48.88           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.88           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.26/48.88           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.88           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 242.26/48.88           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.88           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.26/48.88             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.88           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.88           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.26/48.88    (3)  op(e2, e3) = all_52_1
% 242.26/48.88    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.88    (5)  all_56_11 = e3
% 242.26/48.88    (6)   ~ (all_52_1 = e3)
% 242.26/48.88    (7)  all_56_1 = e1
% 242.26/48.88  
% 242.26/48.88  Begin of proof
% 242.26/48.88  | 
% 242.26/48.88  | BETA: splitting (2) gives:
% 242.26/48.88  | 
% 242.26/48.88  | Case 1:
% 242.26/48.88  | | 
% 242.26/48.88  | |   (8)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.26/48.88  | |            e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3
% 242.26/48.88  | |          & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 242.26/48.88  | |            = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 242.26/48.88  | |            = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 242.26/48.88  | |          all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.88  | |          (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 242.26/48.88  | |            e3) = e3)
% 242.26/48.88  | | 
% 242.26/48.88  | | REF_CLOSE: (3), (4), (5), (6), (7), (8) are inconsistent by sub-proof #745.
% 242.26/48.88  | | 
% 242.26/48.88  | Case 2:
% 242.26/48.88  | | 
% 242.26/48.88  | |   (9)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 242.26/48.88  | |            = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 242.26/48.88  | |          e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 242.26/48.88  | |          (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.88  | |          (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 242.26/48.88  | |          e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.88  | |          (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 242.26/48.88  | |            e3) = e0)
% 242.26/48.88  | | 
% 242.26/48.88  | | BETA: splitting (9) gives:
% 242.26/48.88  | | 
% 242.26/48.88  | | Case 1:
% 242.26/48.88  | | | 
% 242.26/48.88  | | |   (10)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 242.26/48.88  | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.88  | | |         op(e3, e1) = e1 & op(e1, e3) = e1
% 242.26/48.88  | | | 
% 242.26/48.88  | | | ALPHA: (10) implies:
% 242.26/48.88  | | |   (11)   ~ (all_56_11 = e3)
% 242.26/48.88  | | | 
% 242.26/48.88  | | | REDUCE: (5), (11) imply:
% 242.26/48.88  | | |   (12)  $false
% 242.26/48.88  | | | 
% 242.26/48.88  | | | CLOSE: (12) is inconsistent.
% 242.26/48.88  | | | 
% 242.26/48.88  | | Case 2:
% 242.26/48.88  | | | 
% 242.26/48.88  | | |   (13)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.88  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.88  | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 242.26/48.88  | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 242.26/48.88  | | |             = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 242.26/48.88  | | |           e0)
% 242.26/48.88  | | | 
% 242.26/48.88  | | | BETA: splitting (13) gives:
% 242.26/48.88  | | | 
% 242.26/48.88  | | | Case 1:
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | |   (14)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.88  | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.26/48.88  | | | |         op(e3, e0) = e3 & op(e0, e3) = e3
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | ALPHA: (14) implies:
% 242.26/48.88  | | | |   (15)   ~ (all_56_31 = e0)
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | REDUCE: (1), (15) imply:
% 242.26/48.88  | | | |   (16)  $false
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | CLOSE: (16) is inconsistent.
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | Case 2:
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | |   (17)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 242.26/48.88  | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.88  | | | |         op(e3, e0) = e0 & op(e0, e3) = e0
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | ALPHA: (17) implies:
% 242.26/48.88  | | | |   (18)   ~ (all_56_11 = e3)
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | REDUCE: (5), (18) imply:
% 242.26/48.88  | | | |   (19)  $false
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | | CLOSE: (19) is inconsistent.
% 242.26/48.88  | | | | 
% 242.26/48.88  | | | End of split
% 242.26/48.88  | | | 
% 242.26/48.88  | | End of split
% 242.26/48.88  | | 
% 242.26/48.88  | End of split
% 242.26/48.88  | 
% 242.26/48.88  End of proof
% 242.26/48.88  
% 242.26/48.88  Sub-proof #745 shows that the following formulas are inconsistent:
% 242.26/48.88  ----------------------------------------------------------------
% 242.26/48.88    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 242.26/48.88           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 242.26/48.88             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.26/48.88           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.26/48.88             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 242.26/48.88           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.88           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.26/48.88    (2)  op(e2, e3) = all_52_1
% 242.26/48.89    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.89    (4)  all_56_11 = e3
% 242.26/48.89    (5)   ~ (all_52_1 = e3)
% 242.26/48.89    (6)  all_56_1 = e1
% 242.26/48.89  
% 242.26/48.89  Begin of proof
% 242.26/48.89  | 
% 242.26/48.89  | BETA: splitting (1) gives:
% 242.26/48.89  | 
% 242.26/48.89  | Case 1:
% 242.26/48.89  | | 
% 242.26/48.89  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.26/48.89  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.26/48.89  | |        op(e2, e3) = e3
% 242.26/48.89  | | 
% 242.26/48.89  | | ALPHA: (7) implies:
% 242.26/48.89  | |   (8)  op(e2, e3) = e3
% 242.26/48.89  | | 
% 242.26/48.89  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #2337.
% 242.26/48.89  | | 
% 242.26/48.89  | Case 2:
% 242.26/48.89  | | 
% 242.26/48.89  | |   (9)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.26/48.89  | |            e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2
% 242.26/48.89  | |          & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1
% 242.26/48.89  | |            = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 242.26/48.89  | |            = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.26/48.89  | | 
% 242.26/48.89  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #746.
% 242.26/48.89  | | 
% 242.26/48.89  | End of split
% 242.26/48.89  | 
% 242.26/48.89  End of proof
% 242.26/48.89  
% 242.26/48.89  Sub-proof #746 shows that the following formulas are inconsistent:
% 242.26/48.89  ----------------------------------------------------------------
% 242.26/48.89    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 242.26/48.89           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 242.26/48.89             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.26/48.89           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 242.26/48.89             e1) = e3 & op(e1, e3) = e3)
% 242.26/48.89    (2)  all_56_11 = e3
% 242.26/48.89    (3)  all_56_1 = e1
% 242.26/48.89  
% 242.26/48.89  Begin of proof
% 242.26/48.89  | 
% 242.26/48.89  | BETA: splitting (1) gives:
% 242.26/48.89  | 
% 242.26/48.89  | Case 1:
% 242.26/48.89  | | 
% 242.26/48.89  | |   (4)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.26/48.89  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 242.26/48.89  | |        op(e2, e3) = e2
% 242.26/48.89  | | 
% 242.26/48.89  | | ALPHA: (4) implies:
% 242.26/48.89  | |   (5)   ~ (all_56_11 = e3)
% 242.26/48.89  | | 
% 242.26/48.89  | | REDUCE: (2), (5) imply:
% 242.26/48.89  | |   (6)  $false
% 242.26/48.89  | | 
% 242.26/48.89  | | CLOSE: (6) is inconsistent.
% 242.26/48.89  | | 
% 242.26/48.89  | Case 2:
% 242.26/48.89  | | 
% 242.26/48.89  | |   (7)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 242.26/48.89  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 242.26/48.89  | |        op(e1, e3) = e3
% 242.26/48.89  | | 
% 242.26/48.89  | | ALPHA: (7) implies:
% 242.26/48.89  | |   (8)   ~ (all_56_1 = e1)
% 242.26/48.89  | | 
% 242.26/48.89  | | REDUCE: (3), (8) imply:
% 242.26/48.89  | |   (9)  $false
% 242.26/48.89  | | 
% 242.26/48.89  | | CLOSE: (9) is inconsistent.
% 242.26/48.89  | | 
% 242.26/48.89  | End of split
% 242.26/48.89  | 
% 242.26/48.89  End of proof
% 242.26/48.89  
% 242.26/48.89  Sub-proof #747 shows that the following formulas are inconsistent:
% 242.26/48.89  ----------------------------------------------------------------
% 242.26/48.89    (1)   ~ (e3 = e0)
% 242.26/48.89    (2)  op(e0, e1) = all_52_11
% 242.26/48.89    (3)  all_58_6 = e3
% 242.26/48.89    (4)   ~ (e2 = e0)
% 242.26/48.89    (5)  all_58_15 = e3
% 242.26/48.89    (6)  op(e0, e3) = all_52_3
% 242.26/48.89    (7)   ~ (e3 = e1)
% 242.26/48.89    (8)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.89         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.89    (9)  all_58_2 = e2
% 242.26/48.89    (10)  op(e0, all_52_3) = e0
% 242.26/48.89    (11)  all_58_3 = e3
% 242.26/48.89    (12)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.26/48.89            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.26/48.89              e3) = all_26_1 & $i(all_26_1))
% 242.26/48.89    (13)   ~ (all_52_11 = e3)
% 242.26/48.89    (14)  op(e2, e1) = all_52_9
% 242.26/48.89    (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.89          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.89    (16)   ~ (e3 = e2)
% 242.26/48.89    (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.26/48.89          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.26/48.89    (18)  all_58_2 = e2 & op(e2, e3) = e2
% 242.26/48.89    (19)  op(e2, e0) = e0
% 242.26/48.89    (20)  op(e0, e2) = e0
% 242.26/48.89    (21)   ~ (all_52_11 = e0)
% 242.26/48.89    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.89    (23)  op(e1, e1) = e0
% 242.26/48.89    (24)   ~ (e1 = e0)
% 242.26/48.89    (25)  op(e3, e3) = e0
% 242.26/48.89    (26)  all_58_4 = e3
% 242.26/48.89    (27)  op(e2, e0) = all_52_13
% 242.26/48.89    (28)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.26/48.89          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.26/48.89            e1)
% 242.26/48.89    (29)   ~ (all_52_9 = all_52_11)
% 242.26/48.89    (30)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.26/48.89          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.26/48.89    (31)   ~ (e2 = e1)
% 242.26/48.89  
% 242.26/48.89  Begin of proof
% 242.26/48.89  | 
% 242.26/48.89  | BETA: splitting (30) gives:
% 242.26/48.89  | 
% 242.26/48.89  | Case 1:
% 242.26/48.89  | | 
% 242.26/48.89  | |   (32)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 242.26/48.89  | |           e1)
% 242.26/48.89  | | 
% 242.26/48.89  | | BETA: splitting (32) gives:
% 242.26/48.89  | | 
% 242.26/48.89  | | Case 1:
% 242.26/48.89  | | | 
% 242.26/48.89  | | |   (33)  all_58_2 = e1 & op(e2, e3) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | REF_CLOSE: (9), (31), (33) are inconsistent by sub-proof #852.
% 242.26/48.89  | | | 
% 242.26/48.89  | | Case 2:
% 242.26/48.89  | | | 
% 242.26/48.89  | | |   (34)  all_58_3 = e1 & op(e2, e2) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | REF_CLOSE: (7), (11), (34) are inconsistent by sub-proof #2197.
% 242.26/48.89  | | | 
% 242.26/48.89  | | End of split
% 242.26/48.89  | | 
% 242.26/48.89  | Case 2:
% 242.26/48.89  | | 
% 242.26/48.89  | |   (35)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 242.26/48.89  | |           e1)
% 242.26/48.89  | | 
% 242.26/48.89  | | BETA: splitting (35) gives:
% 242.26/48.89  | | 
% 242.26/48.89  | | Case 1:
% 242.26/48.89  | | | 
% 242.26/48.89  | | |   (36)  all_58_5 = e1 & op(e2, e1) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | ALPHA: (36) implies:
% 242.26/48.89  | | |   (37)  all_58_5 = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | BETA: splitting (17) gives:
% 242.26/48.89  | | | 
% 242.26/48.89  | | | Case 1:
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | |   (38)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 242.26/48.89  | | | |           = e2)
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | | REF_CLOSE: (16), (26), (31), (37), (38) are inconsistent by sub-proof
% 242.26/48.89  | | | |            #762.
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | Case 2:
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | |   (39)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 242.26/48.89  | | | |           = e2)
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | | BETA: splitting (39) gives:
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | | Case 1:
% 242.26/48.89  | | | | | 
% 242.26/48.89  | | | | |   (40)  all_58_8 = e2 & op(e1, e1) = e2
% 242.26/48.89  | | | | | 
% 242.26/48.89  | | | | | ALPHA: (40) implies:
% 242.26/48.89  | | | | |   (41)  op(e1, e1) = e2
% 242.26/48.89  | | | | | 
% 242.26/48.89  | | | | | REF_CLOSE: (4), (22), (23), (41) are inconsistent by sub-proof #2211.
% 242.26/48.89  | | | | | 
% 242.26/48.89  | | | | Case 2:
% 242.26/48.89  | | | | | 
% 242.26/48.89  | | | | |   (42)  all_58_14 = e2 & op(e0, e1) = e2
% 242.26/48.89  | | | | | 
% 242.26/48.89  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (13),
% 242.26/48.89  | | | | |            (14), (15), (16), (17), (18), (20), (21), (22), (24), (25),
% 242.26/48.89  | | | | |            (26), (28), (29), (31), (36), (37), (42) are inconsistent
% 242.26/48.89  | | | | |            by sub-proof #748.
% 242.26/48.89  | | | | | 
% 242.26/48.89  | | | | End of split
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | End of split
% 242.26/48.89  | | | 
% 242.26/48.89  | | Case 2:
% 242.26/48.89  | | | 
% 242.26/48.89  | | |   (43)  all_58_10 = e1 & op(e2, e0) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | ALPHA: (43) implies:
% 242.26/48.89  | | |   (44)  op(e2, e0) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | REF_CLOSE: (19), (22), (24), (27), (44) are inconsistent by sub-proof
% 242.26/48.89  | | |            #1778.
% 242.26/48.89  | | | 
% 242.26/48.89  | | End of split
% 242.26/48.89  | | 
% 242.26/48.89  | End of split
% 242.26/48.89  | 
% 242.26/48.89  End of proof
% 242.26/48.89  
% 242.26/48.89  Sub-proof #748 shows that the following formulas are inconsistent:
% 242.26/48.89  ----------------------------------------------------------------
% 242.26/48.89    (1)   ~ (e3 = e0)
% 242.26/48.89    (2)  op(e0, e1) = all_52_11
% 242.26/48.89    (3)  all_58_6 = e3
% 242.26/48.89    (4)   ~ (e2 = e0)
% 242.26/48.89    (5)  all_58_5 = e1 & op(e2, e1) = e1
% 242.26/48.89    (6)  all_58_14 = e2 & op(e0, e1) = e2
% 242.26/48.89    (7)  all_58_15 = e3
% 242.26/48.89    (8)  op(e0, e3) = all_52_3
% 242.26/48.89    (9)   ~ (e3 = e1)
% 242.26/48.89    (10)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.89          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.89    (11)  op(e0, all_52_3) = e0
% 242.26/48.89    (12)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.26/48.89            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.26/48.89              e3) = all_26_1 & $i(all_26_1))
% 242.26/48.89    (13)   ~ (all_52_11 = e3)
% 242.26/48.89    (14)  op(e2, e1) = all_52_9
% 242.26/48.89    (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.89          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.89    (16)   ~ (e3 = e2)
% 242.26/48.89    (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.26/48.89          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.26/48.89    (18)  all_58_2 = e2 & op(e2, e3) = e2
% 242.26/48.89    (19)  op(e0, e2) = e0
% 242.26/48.89    (20)   ~ (all_52_11 = e0)
% 242.26/48.89    (21)  all_58_5 = e1
% 242.26/48.89    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.89    (23)   ~ (e1 = e0)
% 242.26/48.89    (24)  op(e3, e3) = e0
% 242.26/48.89    (25)  all_58_4 = e3
% 242.26/48.89    (26)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.26/48.89          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.26/48.89            e1)
% 242.26/48.89    (27)   ~ (all_52_9 = all_52_11)
% 242.26/48.89    (28)   ~ (e2 = e1)
% 242.26/48.89  
% 242.26/48.89  Begin of proof
% 242.26/48.89  | 
% 242.26/48.89  | BETA: splitting (26) gives:
% 242.26/48.89  | 
% 242.26/48.89  | Case 1:
% 242.26/48.89  | | 
% 242.26/48.89  | |   (29)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 242.26/48.89  | |           e1)
% 242.26/48.89  | | 
% 242.26/48.89  | | BETA: splitting (29) gives:
% 242.26/48.89  | | 
% 242.26/48.89  | | Case 1:
% 242.26/48.89  | | | 
% 242.26/48.89  | | |   (30)  all_58_12 = e1 & op(e0, e3) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | ALPHA: (30) implies:
% 242.26/48.89  | | |   (31)  all_58_12 = e1
% 242.26/48.89  | | |   (32)  op(e0, e3) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | ALPHA: (18) implies:
% 242.26/48.89  | | |   (33)  all_58_2 = e2
% 242.26/48.89  | | | 
% 242.26/48.89  | | | ALPHA: (6) implies:
% 242.26/48.89  | | |   (34)  op(e0, e1) = e2
% 242.26/48.89  | | | 
% 242.26/48.89  | | | ALPHA: (5) implies:
% 242.26/48.89  | | |   (35)  op(e2, e1) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | GROUND_INST: instantiating (22) with all_52_11, e2, e1, e0, simplifying
% 242.26/48.89  | | |              with (2), (34) gives:
% 242.26/48.89  | | |   (36)  all_52_11 = e2
% 242.26/48.89  | | | 
% 242.26/48.89  | | | GROUND_INST: instantiating (22) with all_52_3, e1, e3, e0, simplifying
% 242.26/48.89  | | |              with (8), (32) gives:
% 242.26/48.89  | | |   (37)  all_52_3 = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | GROUND_INST: instantiating (22) with all_52_9, e1, e1, e2, simplifying
% 242.26/48.89  | | |              with (14), (35) gives:
% 242.26/48.89  | | |   (38)  all_52_9 = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | REDUCE: (27), (36), (38) imply:
% 242.26/48.89  | | |   (39)   ~ (e2 = e1)
% 242.26/48.89  | | | 
% 242.26/48.89  | | | REDUCE: (13), (36) imply:
% 242.26/48.89  | | |   (40)   ~ (e3 = e2)
% 242.26/48.89  | | | 
% 242.26/48.89  | | | REDUCE: (11), (37) imply:
% 242.26/48.89  | | |   (41)  op(e0, e1) = e0
% 242.26/48.89  | | | 
% 242.26/48.89  | | | BETA: splitting (12) gives:
% 242.26/48.89  | | | 
% 242.26/48.89  | | | Case 1:
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | | GROUND_INST: instantiating (22) with e2, e0, e1, e0, simplifying with
% 242.26/48.89  | | | |              (34), (41) gives:
% 242.26/48.89  | | | |   (42)  e2 = e0
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | | COMBINE_EQS: (33), (42) imply:
% 242.26/48.89  | | | |   (43)  all_58_2 = e0
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | | REF_CLOSE: (3), (4), (15), (16), (22), (24), (28), (31), (43) are
% 242.26/48.89  | | | |            inconsistent by sub-proof #1267.
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | Case 2:
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | |   (44)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | | REF_CLOSE: (22), (32), (44) are inconsistent by sub-proof #1386.
% 242.26/48.89  | | | | 
% 242.26/48.89  | | | End of split
% 242.26/48.89  | | | 
% 242.26/48.89  | | Case 2:
% 242.26/48.89  | | | 
% 242.26/48.89  | | |   (45)  all_58_13 = e1 & op(e0, e2) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | ALPHA: (45) implies:
% 242.26/48.89  | | |   (46)  op(e0, e2) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | REF_CLOSE: (19), (22), (23), (46) are inconsistent by sub-proof #1872.
% 242.26/48.89  | | | 
% 242.26/48.89  | | End of split
% 242.26/48.89  | | 
% 242.26/48.89  | Case 2:
% 242.26/48.89  | | 
% 242.26/48.89  | |   (47)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.26/48.89  | |           e1)
% 242.26/48.89  | | 
% 242.26/48.89  | | BETA: splitting (47) gives:
% 242.26/48.89  | | 
% 242.26/48.89  | | Case 1:
% 242.26/48.89  | | | 
% 242.26/48.89  | | |   (48)  all_58_14 = e1 & op(e0, e1) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | ALPHA: (48) implies:
% 242.26/48.89  | | |   (49)  all_58_14 = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | REF_CLOSE: (1), (4), (10), (16), (17), (21), (23), (25), (28), (49) are
% 242.26/48.89  | | |            inconsistent by sub-proof #1481.
% 242.26/48.89  | | | 
% 242.26/48.89  | | Case 2:
% 242.26/48.89  | | | 
% 242.26/48.89  | | |   (50)  all_58_15 = e1 & op(e0, e0) = e1
% 242.26/48.89  | | | 
% 242.26/48.89  | | | REF_CLOSE: (7), (9), (50) are inconsistent by sub-proof #1393.
% 242.26/48.89  | | | 
% 242.26/48.89  | | End of split
% 242.26/48.89  | | 
% 242.26/48.89  | End of split
% 242.26/48.89  | 
% 242.26/48.89  End of proof
% 242.26/48.89  
% 242.26/48.89  Sub-proof #749 shows that the following formulas are inconsistent:
% 242.26/48.89  ----------------------------------------------------------------
% 242.26/48.89    (1)  op(e2, e2) = e3
% 242.26/48.89    (2)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.26/48.89           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.26/48.89           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.26/48.89           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.26/48.89           & $i(all_56_23))
% 242.26/48.89    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.26/48.89         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.89    (4)   ~ (e3 = e0)
% 242.26/48.89    (5)  all_58_6 = e3
% 242.26/48.89    (6)   ~ (e2 = e0)
% 242.26/48.89    (7)  op(e1, e0) = all_52_14
% 242.26/48.89    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.89    (9)   ~ (all_52_7 = e3)
% 242.26/48.89    (10)  all_58_15 = e3
% 242.26/48.89    (11)   ~ (e3 = e1)
% 242.26/48.89    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.89          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.89    (13)  op(e0, e1) = e1
% 242.26/48.89    (14)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.26/48.89            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.26/48.89              e3) = all_26_1 & $i(all_26_1))
% 242.26/48.89    (15)  op(e2, e1) = e2
% 242.26/48.89    (16)  all_56_21 = e0
% 242.26/48.89    (17)   ~ (e3 = e2)
% 242.26/48.89    (18)   ~ (all_52_14 = e0)
% 242.26/48.89    (19)  op(e2, e3) = e1
% 242.26/48.89    (20)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.26/48.89            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.26/48.89              e3) = all_42_1 & $i(all_42_1))
% 242.26/48.89    (21)  op(e0, e2) = e0
% 242.26/48.89    (22)  op(e0, e2) = all_52_7
% 242.26/48.89    (23)  op(e0, e0) = e3
% 242.26/48.90    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.90    (25)  op(e3, e1) = e3
% 242.26/48.90    (26)  op(e3, e3) = e0
% 242.26/48.90    (27)  op(e1, all_52_14) = e1
% 242.26/48.90    (28)  all_58_4 = e3
% 242.26/48.90    (29)  all_58_14 = e1
% 242.26/48.90    (30)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.90          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.90            e2)
% 242.26/48.90    (31)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.90            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.90            & $i(all_8_1))
% 242.26/48.90    (32)   ~ (e2 = e1)
% 242.26/48.90  
% 242.26/48.90  Begin of proof
% 242.26/48.90  | 
% 242.26/48.90  | BETA: splitting (8) gives:
% 242.26/48.90  | 
% 242.26/48.90  | Case 1:
% 242.26/48.90  | | 
% 242.26/48.90  | |   (33)  all_58_6 = e2 & op(e1, e3) = e2
% 242.26/48.90  | | 
% 242.26/48.90  | | REF_CLOSE: (5), (17), (33) are inconsistent by sub-proof #2219.
% 242.26/48.90  | | 
% 242.26/48.90  | Case 2:
% 242.26/48.90  | | 
% 242.26/48.90  | |   (34)  all_58_12 = e2 & op(e0, e3) = e2
% 242.26/48.90  | | 
% 242.26/48.90  | | ALPHA: (34) implies:
% 242.26/48.90  | |   (35)  op(e0, e3) = e2
% 242.26/48.90  | | 
% 242.26/48.90  | | BETA: splitting (2) gives:
% 242.26/48.90  | | 
% 242.26/48.90  | | Case 1:
% 242.26/48.90  | | | 
% 242.26/48.90  | | |   (36)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17
% 242.26/48.90  | | |           & $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 &
% 242.26/48.90  | | |           op(e2, e1) = all_56_19 & $i(all_56_19))
% 242.26/48.90  | | | 
% 242.26/48.90  | | | BETA: splitting (36) gives:
% 242.26/48.90  | | | 
% 242.26/48.90  | | | Case 1:
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | |   (37)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17
% 242.26/48.90  | | | |         & $i(all_56_17)
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | | ALPHA: (37) implies:
% 242.26/48.90  | | | |   (38)  op(e3, e1) = all_56_17
% 242.26/48.90  | | | |   (39)  op(e3, all_56_17) = e3
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | | BETA: splitting (31) gives:
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | | Case 1:
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | |   (40)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) =
% 242.26/48.90  | | | | |         all_8_1 & $i(all_8_0) & $i(all_8_1)
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | ALPHA: (40) implies:
% 242.26/48.90  | | | | |   (41)  op(e2, e3) = all_8_1
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | REF_CLOSE: (3), (4), (6), (9), (10), (11), (14), (17), (19), (20),
% 242.26/48.90  | | | | |            (21), (22), (24), (25), (26), (29), (30), (32), (35), (38),
% 242.26/48.90  | | | | |            (39), (41) are inconsistent by sub-proof #751.
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | Case 2:
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | |   (42)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | ALPHA: (42) implies:
% 242.26/48.90  | | | | |   (43)  op(e2, e3) = all_8_1
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | REF_CLOSE: (3), (4), (6), (9), (10), (11), (14), (17), (19), (20),
% 242.26/48.90  | | | | |            (21), (22), (24), (25), (26), (29), (30), (32), (35), (38),
% 242.26/48.90  | | | | |            (39), (43) are inconsistent by sub-proof #751.
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | End of split
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | Case 2:
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | |   (44)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19
% 242.26/48.90  | | | |         & $i(all_56_19)
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | | ALPHA: (44) implies:
% 242.26/48.90  | | | |   (45)  op(e2, e1) = all_56_19
% 242.26/48.90  | | | |   (46)  op(e2, all_56_19) = e2
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | | REF_CLOSE: (1), (15), (17), (19), (20), (24), (31), (45), (46) are
% 242.26/48.90  | | | |            inconsistent by sub-proof #750.
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | End of split
% 242.26/48.90  | | | 
% 242.26/48.90  | | Case 2:
% 242.26/48.90  | | | 
% 242.26/48.90  | | |   (47)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 = e0 &
% 242.26/48.90  | | |           op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 & $i(all_56_23))
% 242.26/48.90  | | | 
% 242.26/48.90  | | | BETA: splitting (47) gives:
% 242.26/48.90  | | | 
% 242.26/48.90  | | | Case 1:
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | |   (48)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | | ALPHA: (48) implies:
% 242.26/48.90  | | | |   (49)  op(e1, all_56_21) = e1
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | | REDUCE: (16), (49) imply:
% 242.26/48.90  | | | |   (50)  op(e1, e0) = e1
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | | BETA: splitting (31) gives:
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | | Case 1:
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | GROUND_INST: instantiating (24) with all_52_14, e1, e0, e1,
% 242.26/48.90  | | | | |              simplifying with (7), (50) gives:
% 242.26/48.90  | | | | |   (51)  all_52_14 = e1
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | REDUCE: (18), (51) imply:
% 242.26/48.90  | | | | |   (52)   ~ (e1 = e0)
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | REDUCE: (27), (51) imply:
% 242.26/48.90  | | | | |   (53)  op(e1, e1) = e1
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | REF_CLOSE: (4), (6), (12), (13), (15), (24), (28), (52), (53) are
% 242.26/48.90  | | | | |            inconsistent by sub-proof #1503.
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | Case 2:
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | |   (54)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | ALPHA: (54) implies:
% 242.26/48.90  | | | | |   (55)   ~ (all_8_1 = e0)
% 242.26/48.90  | | | | |   (56)  op(e2, e3) = all_8_1
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | BETA: splitting (20) gives:
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | | Case 1:
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | |   (57)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2,
% 242.26/48.90  | | | | | |           e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | | ALPHA: (57) implies:
% 242.26/48.90  | | | | | |   (58)  op(e2, e3) = all_42_1
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | | GROUND_INST: instantiating (24) with all_52_14, e1, e0, e1,
% 242.26/48.90  | | | | | |              simplifying with (7), (50) gives:
% 242.26/48.90  | | | | | |   (59)  all_52_14 = e1
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | | GROUND_INST: instantiating (24) with e1, all_42_1, e3, e2,
% 242.26/48.90  | | | | | |              simplifying with (19), (58) gives:
% 242.26/48.90  | | | | | |   (60)  all_42_1 = e1
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | | GROUND_INST: instantiating (24) with all_8_1, all_42_1, e3, e2,
% 242.26/48.90  | | | | | |              simplifying with (56), (58) gives:
% 242.26/48.90  | | | | | |   (61)  all_42_1 = all_8_1
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | | COMBINE_EQS: (60), (61) imply:
% 242.26/48.90  | | | | | |   (62)  all_8_1 = e1
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | | REDUCE: (55), (62) imply:
% 242.26/48.90  | | | | | |   (63)   ~ (e1 = e0)
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | | REDUCE: (27), (59) imply:
% 242.26/48.90  | | | | | |   (64)  op(e1, e1) = e1
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | | REF_CLOSE: (4), (6), (12), (13), (15), (24), (28), (63), (64) are
% 242.26/48.90  | | | | | |            inconsistent by sub-proof #1503.
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | Case 2:
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | |   (65)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | | ALPHA: (65) implies:
% 242.26/48.90  | | | | | |   (66)   ~ (all_42_1 = e1)
% 242.26/48.90  | | | | | |   (67)  op(e2, e3) = all_42_1
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | | REF_CLOSE: (19), (24), (56), (66), (67) are inconsistent by
% 242.26/48.90  | | | | | |            sub-proof #935.
% 242.26/48.90  | | | | | | 
% 242.26/48.90  | | | | | End of split
% 242.26/48.90  | | | | | 
% 242.26/48.90  | | | | End of split
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | Case 2:
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | |   (68)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.26/48.90  | | | |         & $i(all_56_23)
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | | ALPHA: (68) implies:
% 242.26/48.90  | | | |   (69)  op(e0, e1) = all_56_23
% 242.26/48.90  | | | |   (70)  op(e0, all_56_23) = e0
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | | REF_CLOSE: (4), (13), (19), (20), (23), (24), (31), (69), (70) are
% 242.26/48.90  | | | |            inconsistent by sub-proof #755.
% 242.26/48.90  | | | | 
% 242.26/48.90  | | | End of split
% 242.26/48.90  | | | 
% 242.26/48.90  | | End of split
% 242.26/48.90  | | 
% 242.26/48.90  | End of split
% 242.26/48.90  | 
% 242.26/48.90  End of proof
% 242.26/48.90  
% 242.26/48.90  Sub-proof #750 shows that the following formulas are inconsistent:
% 242.26/48.90  ----------------------------------------------------------------
% 242.26/48.90    (1)  op(e2, e2) = e3
% 242.26/48.90    (2)  op(e2, e1) = e2
% 242.26/48.90    (3)   ~ (e3 = e2)
% 242.26/48.90    (4)  op(e2, e3) = e1
% 242.26/48.90    (5)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 242.26/48.90           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 242.26/48.90           all_42_1 & $i(all_42_1))
% 242.26/48.90    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.90    (7)  op(e2, e1) = all_56_19
% 242.26/48.90    (8)  op(e2, all_56_19) = e2
% 242.26/48.90    (9)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.90           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.90           & $i(all_8_1))
% 242.26/48.90  
% 242.26/48.90  Begin of proof
% 242.26/48.90  | 
% 242.26/48.90  | BETA: splitting (9) gives:
% 242.26/48.90  | 
% 242.26/48.90  | Case 1:
% 242.26/48.90  | | 
% 242.26/48.90  | |   (10)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1
% 242.26/48.90  | |         & $i(all_8_0) & $i(all_8_1)
% 242.26/48.90  | | 
% 242.26/48.90  | | ALPHA: (10) implies:
% 242.26/48.90  | |   (11)  op(e2, e3) = all_8_1
% 242.26/48.90  | | 
% 242.26/48.90  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11) are inconsistent by
% 242.26/48.90  | |            sub-proof #854.
% 242.26/48.90  | | 
% 242.26/48.90  | Case 2:
% 242.26/48.90  | | 
% 242.26/48.90  | |   (12)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 242.26/48.90  | | 
% 242.26/48.90  | | ALPHA: (12) implies:
% 242.26/48.90  | |   (13)  op(e2, e3) = all_8_1
% 242.26/48.90  | | 
% 242.26/48.90  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (13) are inconsistent by
% 242.26/48.90  | |            sub-proof #854.
% 242.26/48.90  | | 
% 242.26/48.90  | End of split
% 242.26/48.90  | 
% 242.26/48.90  End of proof
% 242.26/48.90  
% 242.26/48.90  Sub-proof #751 shows that the following formulas are inconsistent:
% 242.26/48.90  ----------------------------------------------------------------
% 242.26/48.90    (1)  op(e3, e1) = all_56_17
% 242.26/48.90    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.26/48.90         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.90    (3)   ~ (e3 = e0)
% 242.26/48.90    (4)   ~ (e2 = e0)
% 242.26/48.90    (5)   ~ (all_52_7 = e3)
% 242.26/48.90    (6)  all_58_15 = e3
% 242.26/48.90    (7)   ~ (e3 = e1)
% 242.26/48.90    (8)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 242.26/48.90           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 242.26/48.90           all_26_1 & $i(all_26_1))
% 242.26/48.90    (9)   ~ (e3 = e2)
% 242.26/48.90    (10)  op(e2, e3) = e1
% 242.26/48.90    (11)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.26/48.90            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.26/48.90              e3) = all_42_1 & $i(all_42_1))
% 242.26/48.90    (12)  op(e0, e3) = e2
% 242.26/48.90    (13)  op(e0, e2) = e0
% 242.26/48.90    (14)  op(e0, e2) = all_52_7
% 242.26/48.90    (15)  op(e3, all_56_17) = e3
% 242.26/48.90    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.90    (17)  op(e2, e3) = all_8_1
% 242.26/48.90    (18)  op(e3, e1) = e3
% 242.26/48.90    (19)  op(e3, e3) = e0
% 242.26/48.90    (20)  all_58_14 = e1
% 242.26/48.90    (21)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.90          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.90            e2)
% 242.26/48.90    (22)   ~ (e2 = e1)
% 242.26/48.90  
% 242.26/48.90  Begin of proof
% 242.26/48.90  | 
% 242.26/48.90  | BETA: splitting (8) gives:
% 242.26/48.90  | 
% 242.26/48.90  | Case 1:
% 242.26/48.90  | | 
% 242.26/48.90  | | 
% 242.26/48.90  | | GROUND_INST: instantiating (16) with e3, all_56_17, e1, e3, simplifying with
% 242.26/48.90  | |              (1), (18) gives:
% 242.26/48.90  | |   (23)  all_56_17 = e3
% 242.26/48.90  | | 
% 242.26/48.90  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (13), (14), (15), (16), (19),
% 242.26/48.90  | |            (20), (21), (22), (23) are inconsistent by sub-proof #759.
% 242.26/48.90  | | 
% 242.26/48.90  | Case 2:
% 242.26/48.90  | | 
% 242.26/48.90  | |   (24)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 242.26/48.90  | | 
% 242.26/48.90  | | ALPHA: (24) implies:
% 242.26/48.90  | |   (25)   ~ (all_26_1 = e1)
% 242.26/48.90  | |   (26)  op(e0, e3) = all_26_1
% 242.26/48.90  | | 
% 242.26/48.90  | | BETA: splitting (11) gives:
% 242.26/48.90  | | 
% 242.26/48.90  | | Case 1:
% 242.26/48.90  | | | 
% 242.26/48.90  | | | 
% 242.26/48.90  | | | GROUND_INST: instantiating (16) with e2, all_26_1, e3, e0, simplifying
% 242.26/48.90  | | |              with (12), (26) gives:
% 242.26/48.90  | | |   (27)  all_26_1 = e2
% 242.26/48.90  | | | 
% 242.26/48.90  | | | GROUND_INST: instantiating (16) with e3, all_56_17, e1, e3, simplifying
% 242.26/48.90  | | |              with (1), (18) gives:
% 242.26/48.90  | | |   (28)  all_56_17 = e3
% 242.26/48.90  | | | 
% 242.26/48.90  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (13), (14), (15), (16),
% 242.26/48.90  | | |            (19), (20), (21), (22), (28) are inconsistent by sub-proof
% 242.26/48.90  | | |            #759.
% 242.26/48.90  | | | 
% 242.26/48.90  | | Case 2:
% 242.26/48.90  | | | 
% 242.26/48.90  | | |   (29)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 242.26/48.90  | | | 
% 242.26/48.90  | | | ALPHA: (29) implies:
% 242.26/48.90  | | |   (30)   ~ (all_42_1 = e1)
% 242.26/48.90  | | |   (31)  op(e2, e3) = all_42_1
% 242.26/48.90  | | | 
% 242.26/48.90  | | | REF_CLOSE: (10), (16), (17), (30), (31) are inconsistent by sub-proof
% 242.26/48.90  | | |            #935.
% 242.26/48.90  | | | 
% 242.26/48.90  | | End of split
% 242.26/48.90  | | 
% 242.26/48.90  | End of split
% 242.26/48.90  | 
% 242.26/48.90  End of proof
% 242.26/48.90  
% 242.26/48.90  Sub-proof #752 shows that the following formulas are inconsistent:
% 242.26/48.90  ----------------------------------------------------------------
% 242.26/48.90    (1)  op(e2, e2) = e3
% 242.26/48.90    (2)   ~ (e3 = e2)
% 242.26/48.90    (3)  op(e2, e0) = e0
% 242.26/48.90    (4)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 242.26/48.90         $i(all_56_27)
% 242.26/48.90    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.90  
% 242.26/48.90  Begin of proof
% 242.26/48.90  | 
% 242.26/48.90  | ALPHA: (4) implies:
% 242.26/48.90  |   (6)  op(e2, e0) = all_56_27
% 242.26/48.90  |   (7)  op(e2, all_56_27) = e2
% 242.26/48.90  | 
% 242.26/48.90  | GROUND_INST: instantiating (5) with e0, all_56_27, e0, e2, simplifying with
% 242.26/48.90  |              (3), (6) gives:
% 242.26/48.90  |   (8)  all_56_27 = e0
% 242.26/48.90  | 
% 242.26/48.90  | REDUCE: (7), (8) imply:
% 242.26/48.90  |   (9)  op(e2, e0) = e2
% 242.26/48.90  | 
% 242.26/48.90  | REF_CLOSE: (1), (2), (5), (6), (7), (9) are inconsistent by sub-proof #954.
% 242.26/48.90  | 
% 242.26/48.90  End of proof
% 242.26/48.90  
% 242.26/48.90  Sub-proof #753 shows that the following formulas are inconsistent:
% 242.26/48.90  ----------------------------------------------------------------
% 242.26/48.90    (1)  op(e2, e2) = e3
% 242.26/48.90    (2)  op(e3, all_52_12) = e3
% 242.26/48.90    (3)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.26/48.90           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.26/48.90           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.26/48.90           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.26/48.90           & $i(all_56_23))
% 242.26/48.90    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.26/48.90         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.90    (5)   ~ (e3 = e0)
% 242.26/48.90    (6)   ~ (e2 = e0)
% 242.26/48.90    (7)   ~ (all_52_12 = e0)
% 242.26/48.90    (8)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.26/48.90         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.26/48.90    (9)  op(e1, e0) = all_52_14
% 242.26/48.90    (10)   ~ (all_52_7 = e3)
% 242.26/48.90    (11)  all_58_15 = e3
% 242.26/48.90    (12)   ~ (e3 = e1)
% 242.26/48.90    (13)   ~ (all_52_12 = all_52_14)
% 242.26/48.90    (14)  all_58_3 = e3
% 242.26/48.90    (15)  op(e2, e1) = e2
% 242.26/48.90    (16)  all_56_21 = e0
% 242.26/48.90    (17)   ~ (e3 = e2)
% 242.26/48.90    (18)  op(e2, e0) = e0
% 242.26/48.90    (19)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.26/48.91            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.26/48.91              e3) = all_42_1 & $i(all_42_1))
% 242.26/48.91    (20)  op(e0, e2) = e0
% 242.26/48.91    (21)  all_58_5 = e2
% 242.26/48.91    (22)  op(e0, e2) = all_52_7
% 242.26/48.91    (23)   ~ (all_52_4 = e3)
% 242.26/48.91    (24)  op(e3, e2) = all_52_4
% 242.26/48.91    (25)  op(e0, e0) = e3
% 242.26/48.91    (26)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 242.26/48.91    (27)  all_54_3 = all_52_12
% 242.26/48.91    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.91    (29)  op(e3, e1) = e3
% 242.26/48.91    (30)  op(e1, e1) = e0
% 242.26/48.91    (31)   ~ (e1 = e0)
% 242.26/48.91    (32)  op(e3, e3) = e0
% 242.26/48.91    (33)  all_58_4 = e3
% 242.26/48.91    (34)  op(e2, e0) = all_52_13
% 242.26/48.91    (35)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.91          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.91            e2)
% 242.26/48.91    (36)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.91            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.91            & $i(all_8_1))
% 242.26/48.91    (37)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.26/48.91          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.26/48.91    (38)   ~ (e2 = e1)
% 242.26/48.91  
% 242.26/48.91  Begin of proof
% 242.26/48.91  | 
% 242.26/48.91  | BETA: splitting (37) gives:
% 242.26/48.91  | 
% 242.26/48.91  | Case 1:
% 242.26/48.91  | | 
% 242.26/48.91  | |   (39)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 242.26/48.91  | |           e1)
% 242.26/48.91  | | 
% 242.26/48.91  | | BETA: splitting (39) gives:
% 242.26/48.91  | | 
% 242.26/48.91  | | Case 1:
% 242.26/48.91  | | | 
% 242.26/48.91  | | |   (40)  all_58_2 = e1 & op(e2, e3) = e1
% 242.26/48.91  | | | 
% 242.26/48.91  | | | ALPHA: (40) implies:
% 242.26/48.91  | | |   (41)  op(e2, e3) = e1
% 242.26/48.91  | | | 
% 242.26/48.91  | | | BETA: splitting (8) gives:
% 242.26/48.91  | | | 
% 242.26/48.91  | | | Case 1:
% 242.26/48.91  | | | | 
% 242.26/48.91  | | | |   (42)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 242.26/48.91  | | | |           = e1)
% 242.26/48.91  | | | | 
% 242.26/48.91  | | | | BETA: splitting (42) gives:
% 242.26/48.91  | | | | 
% 242.26/48.91  | | | | Case 1:
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | |   (43)  all_58_4 = e1 & op(e3, e1) = e1
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | | REF_CLOSE: (12), (33), (43) are inconsistent by sub-proof #2042.
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | Case 2:
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | |   (44)  all_58_5 = e1 & op(e2, e1) = e1
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | | REF_CLOSE: (21), (38), (44) are inconsistent by sub-proof #1548.
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | End of split
% 242.26/48.91  | | | | 
% 242.26/48.91  | | | Case 2:
% 242.26/48.91  | | | | 
% 242.26/48.91  | | | |   (45)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 242.26/48.91  | | | |           = e1)
% 242.26/48.91  | | | | 
% 242.26/48.91  | | | | BETA: splitting (45) gives:
% 242.26/48.91  | | | | 
% 242.26/48.91  | | | | Case 1:
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | |   (46)  all_58_8 = e1 & op(e1, e1) = e1
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | | ALPHA: (46) implies:
% 242.26/48.91  | | | | |   (47)  op(e1, e1) = e1
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | | REF_CLOSE: (28), (30), (31), (47) are inconsistent by sub-proof #2220.
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | Case 2:
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | |   (48)  all_58_14 = e1 & op(e0, e1) = e1
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | | ALPHA: (48) implies:
% 242.26/48.91  | | | | |   (49)  all_58_14 = e1
% 242.26/48.91  | | | | |   (50)  op(e0, e1) = e1
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | | BETA: splitting (3) gives:
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | | Case 1:
% 242.26/48.91  | | | | | | 
% 242.26/48.91  | | | | | |   (51)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 242.26/48.91  | | | | | |           all_56_17 & $i(all_56_17)) | (all_56_18 = e2 & op(e2,
% 242.26/48.91  | | | | | |             all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 242.26/48.91  | | | | | |           $i(all_56_19))
% 242.26/48.91  | | | | | | 
% 242.26/48.91  | | | | | | BETA: splitting (51) gives:
% 242.26/48.91  | | | | | | 
% 242.26/48.91  | | | | | | Case 1:
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | |   (52)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 242.26/48.91  | | | | | | |         all_56_17 & $i(all_56_17)
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | | ALPHA: (52) implies:
% 242.26/48.91  | | | | | | |   (53)  op(e3, e1) = all_56_17
% 242.26/48.91  | | | | | | |   (54)  op(e3, all_56_17) = e3
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | | GROUND_INST: instantiating (28) with e3, all_56_17, e1, e3,
% 242.26/48.91  | | | | | | |              simplifying with (29), (53) gives:
% 242.26/48.91  | | | | | | |   (55)  all_56_17 = e3
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (17), (20), (22),
% 242.26/48.91  | | | | | | |            (28), (32), (35), (38), (49), (54), (55) are
% 242.26/48.91  | | | | | | |            inconsistent by sub-proof #759.
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | Case 2:
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | |   (56)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 242.26/48.91  | | | | | | |         all_56_19 & $i(all_56_19)
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | | REF_CLOSE: (1), (15), (17), (28), (56) are inconsistent by
% 242.26/48.91  | | | | | | |            sub-proof #758.
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | End of split
% 242.26/48.91  | | | | | | 
% 242.26/48.91  | | | | | Case 2:
% 242.26/48.91  | | | | | | 
% 242.26/48.91  | | | | | |   (57)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 = e0
% 242.26/48.91  | | | | | |           & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 242.26/48.91  | | | | | |           $i(all_56_23))
% 242.26/48.91  | | | | | | 
% 242.26/48.91  | | | | | | BETA: splitting (57) gives:
% 242.26/48.91  | | | | | | 
% 242.26/48.91  | | | | | | Case 1:
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | |   (58)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | | ALPHA: (58) implies:
% 242.26/48.91  | | | | | | |   (59)  op(e1, all_56_21) = e1
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | | REDUCE: (16), (59) imply:
% 242.26/48.91  | | | | | | |   (60)  op(e1, e0) = e1
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | | BETA: splitting (36) gives:
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | | Case 1:
% 242.26/48.91  | | | | | | | | 
% 242.26/48.91  | | | | | | | |   (61)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2,
% 242.26/48.91  | | | | | | | |           e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 242.26/48.91  | | | | | | | | 
% 242.26/48.91  | | | | | | | | ALPHA: (61) implies:
% 242.26/48.91  | | | | | | | |   (62)  op(e2, e3) = all_8_1
% 242.26/48.91  | | | | | | | | 
% 242.26/48.91  | | | | | | | | REF_CLOSE: (2), (7), (9), (13), (19), (23), (24), (26), (27),
% 242.26/48.91  | | | | | | | |            (28), (41), (60), (62) are inconsistent by sub-proof
% 242.26/48.91  | | | | | | | |            #757.
% 242.26/48.91  | | | | | | | | 
% 242.26/48.91  | | | | | | | Case 2:
% 242.26/48.91  | | | | | | | | 
% 242.26/48.91  | | | | | | | |   (63)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 242.26/48.91  | | | | | | | | 
% 242.26/48.91  | | | | | | | | ALPHA: (63) implies:
% 242.26/48.91  | | | | | | | |   (64)  op(e2, e3) = all_8_1
% 242.26/48.91  | | | | | | | | 
% 242.26/48.91  | | | | | | | | REF_CLOSE: (2), (7), (9), (13), (19), (23), (24), (26), (27),
% 242.26/48.91  | | | | | | | |            (28), (41), (60), (64) are inconsistent by sub-proof
% 242.26/48.91  | | | | | | | |            #757.
% 242.26/48.91  | | | | | | | | 
% 242.26/48.91  | | | | | | | End of split
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | Case 2:
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | |   (65)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 242.26/48.91  | | | | | | |         all_56_23 & $i(all_56_23)
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | | ALPHA: (65) implies:
% 242.26/48.91  | | | | | | |   (66)  op(e0, e1) = all_56_23
% 242.26/48.91  | | | | | | |   (67)  op(e0, all_56_23) = e0
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | | REF_CLOSE: (5), (19), (25), (28), (36), (41), (50), (66), (67) are
% 242.26/48.91  | | | | | | |            inconsistent by sub-proof #755.
% 242.26/48.91  | | | | | | | 
% 242.26/48.91  | | | | | | End of split
% 242.26/48.91  | | | | | | 
% 242.26/48.91  | | | | | End of split
% 242.26/48.91  | | | | | 
% 242.26/48.91  | | | | End of split
% 242.26/48.91  | | | | 
% 242.26/48.91  | | | End of split
% 242.26/48.91  | | | 
% 242.26/48.91  | | Case 2:
% 242.26/48.91  | | | 
% 242.26/48.91  | | |   (68)  all_58_3 = e1 & op(e2, e2) = e1
% 242.26/48.91  | | | 
% 242.26/48.91  | | | REF_CLOSE: (12), (14), (68) are inconsistent by sub-proof #2197.
% 242.26/48.91  | | | 
% 242.26/48.91  | | End of split
% 242.26/48.91  | | 
% 242.26/48.91  | Case 2:
% 242.26/48.91  | | 
% 242.26/48.91  | |   (69)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 242.26/48.91  | |           e1)
% 242.26/48.91  | | 
% 242.26/48.91  | | REF_CLOSE: (18), (21), (28), (31), (34), (38), (69) are inconsistent by
% 242.26/48.91  | |            sub-proof #754.
% 242.26/48.91  | | 
% 242.26/48.91  | End of split
% 242.26/48.91  | 
% 242.26/48.91  End of proof
% 242.26/48.91  
% 242.26/48.91  Sub-proof #754 shows that the following formulas are inconsistent:
% 242.26/48.91  ----------------------------------------------------------------
% 242.26/48.91    (1)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.26/48.91    (2)  op(e2, e0) = e0
% 242.26/48.91    (3)  all_58_5 = e2
% 242.26/48.91    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.91    (5)   ~ (e1 = e0)
% 242.26/48.91    (6)  op(e2, e0) = all_52_13
% 242.26/48.91    (7)   ~ (e2 = e1)
% 242.26/48.91  
% 242.26/48.91  Begin of proof
% 242.26/48.91  | 
% 242.26/48.91  | BETA: splitting (1) gives:
% 242.26/48.91  | 
% 242.26/48.91  | Case 1:
% 242.26/48.91  | | 
% 242.26/48.91  | |   (8)  all_58_5 = e1 & op(e2, e1) = e1
% 242.26/48.91  | | 
% 242.26/48.91  | | REF_CLOSE: (3), (7), (8) are inconsistent by sub-proof #1548.
% 242.26/48.91  | | 
% 242.26/48.91  | Case 2:
% 242.26/48.91  | | 
% 242.26/48.91  | |   (9)  all_58_10 = e1 & op(e2, e0) = e1
% 242.26/48.91  | | 
% 242.26/48.91  | | ALPHA: (9) implies:
% 242.26/48.91  | |   (10)  op(e2, e0) = e1
% 242.26/48.91  | | 
% 242.26/48.91  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #1778.
% 242.26/48.91  | | 
% 242.26/48.91  | End of split
% 242.26/48.91  | 
% 242.26/48.91  End of proof
% 242.26/48.91  
% 242.26/48.91  Sub-proof #755 shows that the following formulas are inconsistent:
% 242.26/48.91  ----------------------------------------------------------------
% 242.26/48.91    (1)   ~ (e3 = e0)
% 242.26/48.91    (2)  op(e0, e1) = all_56_23
% 242.26/48.91    (3)  op(e0, e1) = e1
% 242.26/48.91    (4)  op(e2, e3) = e1
% 242.26/48.91    (5)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 242.26/48.91           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 242.26/48.91           all_42_1 & $i(all_42_1))
% 242.26/48.91    (6)  op(e0, e0) = e3
% 242.26/48.91    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.91    (8)  op(e0, all_56_23) = e0
% 242.26/48.91    (9)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.91           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.91           & $i(all_8_1))
% 242.26/48.91  
% 242.26/48.91  Begin of proof
% 242.26/48.91  | 
% 242.26/48.91  | BETA: splitting (9) gives:
% 242.26/48.91  | 
% 242.26/48.91  | Case 1:
% 242.26/48.91  | | 
% 242.26/48.91  | |   (10)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1
% 242.26/48.91  | |         & $i(all_8_0) & $i(all_8_1)
% 242.26/48.91  | | 
% 242.26/48.91  | | ALPHA: (10) implies:
% 242.26/48.91  | |   (11)  op(e2, e3) = all_8_1
% 242.26/48.91  | | 
% 242.26/48.91  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11) are inconsistent by
% 242.26/48.91  | |            sub-proof #756.
% 242.26/48.91  | | 
% 242.26/48.91  | Case 2:
% 242.26/48.91  | | 
% 242.26/48.91  | |   (12)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 242.26/48.91  | | 
% 242.26/48.91  | | ALPHA: (12) implies:
% 242.26/48.91  | |   (13)  op(e2, e3) = all_8_1
% 242.26/48.91  | | 
% 242.26/48.91  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (13) are inconsistent by
% 242.26/48.91  | |            sub-proof #756.
% 242.26/48.91  | | 
% 242.26/48.91  | End of split
% 242.26/48.91  | 
% 242.26/48.91  End of proof
% 242.26/48.91  
% 242.26/48.91  Sub-proof #756 shows that the following formulas are inconsistent:
% 242.26/48.91  ----------------------------------------------------------------
% 242.26/48.91    (1)   ~ (e3 = e0)
% 242.26/48.91    (2)  op(e0, e1) = all_56_23
% 242.26/48.91    (3)  op(e0, e1) = e1
% 242.26/48.91    (4)  op(e2, e3) = e1
% 242.26/48.91    (5)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 242.26/48.91           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 242.26/48.91           all_42_1 & $i(all_42_1))
% 242.26/48.91    (6)  op(e0, e0) = e3
% 242.26/48.91    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.91    (8)  op(e2, e3) = all_8_1
% 242.26/48.91    (9)  op(e0, all_56_23) = e0
% 242.26/48.91  
% 242.26/48.91  Begin of proof
% 242.26/48.91  | 
% 242.26/48.91  | BETA: splitting (5) gives:
% 242.26/48.91  | 
% 242.26/48.91  | Case 1:
% 242.26/48.91  | | 
% 242.26/48.91  | | 
% 242.26/48.91  | | GROUND_INST: instantiating (7) with e1, all_56_23, e1, e0, simplifying with
% 242.26/48.91  | |              (2), (3) gives:
% 242.26/48.91  | |   (10)  all_56_23 = e1
% 242.26/48.91  | | 
% 242.26/48.91  | | REDUCE: (9), (10) imply:
% 242.26/48.91  | |   (11)  op(e0, e1) = e0
% 242.26/48.91  | | 
% 242.26/48.91  | | REF_CLOSE: (1), (2), (6), (7), (9), (11) are inconsistent by sub-proof
% 242.26/48.91  | |            #1395.
% 242.26/48.91  | | 
% 242.26/48.91  | Case 2:
% 242.26/48.91  | | 
% 242.26/48.91  | |   (12)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 242.26/48.91  | | 
% 242.26/48.91  | | ALPHA: (12) implies:
% 242.26/48.91  | |   (13)   ~ (all_42_1 = e1)
% 242.26/48.91  | |   (14)  op(e2, e3) = all_42_1
% 242.26/48.91  | | 
% 242.26/48.91  | | REF_CLOSE: (4), (7), (8), (13), (14) are inconsistent by sub-proof #935.
% 242.26/48.91  | | 
% 242.26/48.91  | End of split
% 242.26/48.91  | 
% 242.26/48.91  End of proof
% 242.26/48.91  
% 242.26/48.91  Sub-proof #757 shows that the following formulas are inconsistent:
% 242.26/48.91  ----------------------------------------------------------------
% 242.26/48.91    (1)  op(e3, all_52_12) = e3
% 242.26/48.91    (2)   ~ (all_52_12 = e0)
% 242.26/48.91    (3)  op(e1, e0) = all_52_14
% 242.26/48.91    (4)  op(e1, e0) = e1
% 242.26/48.91    (5)   ~ (all_52_12 = all_52_14)
% 242.26/48.91    (6)  op(e2, e3) = e1
% 242.26/48.91    (7)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 242.26/48.91           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 242.26/48.91           all_42_1 & $i(all_42_1))
% 242.26/48.91    (8)   ~ (all_52_4 = e3)
% 242.26/48.91    (9)  op(e3, e2) = all_52_4
% 242.26/48.91    (10)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 242.26/48.91    (11)  all_54_3 = all_52_12
% 242.26/48.91    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.91    (13)  op(e2, e3) = all_8_1
% 242.26/48.91  
% 242.26/48.91  Begin of proof
% 242.26/48.91  | 
% 242.26/48.91  | BETA: splitting (7) gives:
% 242.26/48.91  | 
% 242.26/48.91  | Case 1:
% 242.26/48.91  | | 
% 242.26/48.91  | | 
% 242.26/48.91  | | GROUND_INST: instantiating (12) with all_52_14, e1, e0, e1, simplifying with
% 242.26/48.91  | |              (3), (4) gives:
% 242.26/48.91  | |   (14)  all_52_14 = e1
% 242.26/48.91  | | 
% 242.26/48.91  | | REDUCE: (5), (14) imply:
% 242.26/48.91  | |   (15)   ~ (all_52_12 = e1)
% 242.26/48.91  | | 
% 242.26/48.91  | | BETA: splitting (10) gives:
% 242.26/48.91  | | 
% 242.26/48.91  | | Case 1:
% 242.26/48.91  | | | 
% 242.26/48.91  | | |   (16)  all_54_3 = e2
% 242.26/48.91  | | | 
% 242.26/48.91  | | | COMBINE_EQS: (11), (16) imply:
% 242.26/48.91  | | |   (17)  all_52_12 = e2
% 242.26/48.91  | | | 
% 242.26/48.91  | | | SIMP: (17) implies:
% 242.26/48.91  | | |   (18)  all_52_12 = e2
% 242.26/48.91  | | | 
% 242.26/48.91  | | | REDUCE: (1), (18) imply:
% 242.26/48.91  | | |   (19)  op(e3, e2) = e3
% 242.26/48.91  | | | 
% 242.26/48.91  | | | REF_CLOSE: (8), (9), (12), (19) are inconsistent by sub-proof #2192.
% 242.26/48.91  | | | 
% 242.26/48.91  | | Case 2:
% 242.26/48.91  | | | 
% 242.26/48.91  | | |   (20)  all_54_3 = e1 | all_54_3 = e0
% 242.26/48.91  | | | 
% 242.26/48.91  | | | REF_CLOSE: (2), (11), (15), (20) are inconsistent by sub-proof #2287.
% 242.26/48.91  | | | 
% 242.26/48.91  | | End of split
% 242.26/48.91  | | 
% 242.26/48.91  | Case 2:
% 242.26/48.91  | | 
% 242.26/48.91  | |   (21)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 242.26/48.91  | | 
% 242.26/48.91  | | ALPHA: (21) implies:
% 242.26/48.91  | |   (22)   ~ (all_42_1 = e1)
% 242.26/48.91  | |   (23)  op(e2, e3) = all_42_1
% 242.26/48.91  | | 
% 242.26/48.91  | | REF_CLOSE: (6), (12), (13), (22), (23) are inconsistent by sub-proof #935.
% 242.26/48.91  | | 
% 242.26/48.91  | End of split
% 242.26/48.91  | 
% 242.26/48.91  End of proof
% 242.26/48.91  
% 242.26/48.91  Sub-proof #758 shows that the following formulas are inconsistent:
% 242.26/48.91  ----------------------------------------------------------------
% 242.26/48.91    (1)  op(e2, e2) = e3
% 242.26/48.91    (2)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 242.26/48.91         $i(all_56_19)
% 242.26/48.91    (3)  op(e2, e1) = e2
% 242.26/48.91    (4)   ~ (e3 = e2)
% 242.26/48.91    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.91  
% 242.26/48.91  Begin of proof
% 242.26/48.91  | 
% 242.26/48.91  | ALPHA: (2) implies:
% 242.26/48.91  |   (6)  op(e2, e1) = all_56_19
% 242.26/48.91  |   (7)  op(e2, all_56_19) = e2
% 242.26/48.91  | 
% 242.26/48.91  | GROUND_INST: instantiating (5) with e2, all_56_19, e1, e2, simplifying with
% 242.26/48.91  |              (3), (6) gives:
% 242.26/48.91  |   (8)  all_56_19 = e2
% 242.26/48.91  | 
% 242.26/48.91  | REDUCE: (7), (8) imply:
% 242.26/48.91  |   (9)  op(e2, e2) = e2
% 242.26/48.91  | 
% 242.26/48.91  | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2140.
% 242.26/48.91  | 
% 242.26/48.91  End of proof
% 242.26/48.91  
% 242.26/48.91  Sub-proof #759 shows that the following formulas are inconsistent:
% 242.26/48.91  ----------------------------------------------------------------
% 242.26/48.91    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.26/48.91         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.91    (2)   ~ (e3 = e0)
% 242.26/48.91    (3)   ~ (e2 = e0)
% 242.26/48.91    (4)   ~ (all_52_7 = e3)
% 242.26/48.91    (5)  all_58_15 = e3
% 242.26/48.91    (6)   ~ (e3 = e1)
% 242.26/48.91    (7)   ~ (e3 = e2)
% 242.26/48.91    (8)  all_56_17 = e3
% 242.26/48.92    (9)  op(e0, e2) = e0
% 242.26/48.92    (10)  op(e0, e2) = all_52_7
% 242.26/48.92    (11)  op(e3, all_56_17) = e3
% 242.26/48.92    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.92    (13)  op(e3, e3) = e0
% 242.26/48.92    (14)  all_58_14 = e1
% 242.26/48.92    (15)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.92          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.92            e2)
% 242.26/48.92    (16)   ~ (e2 = e1)
% 242.26/48.92  
% 242.26/48.92  Begin of proof
% 242.26/48.92  | 
% 242.26/48.92  | REDUCE: (8), (11) imply:
% 242.26/48.92  |   (17)  op(e3, e3) = e3
% 242.26/48.92  | 
% 242.26/48.92  | GROUND_INST: instantiating (12) with e0, e3, e3, e3, simplifying with (13),
% 242.26/48.92  |              (17) gives:
% 242.26/48.92  |   (18)  e3 = e0
% 242.26/48.92  | 
% 242.26/48.92  | COMBINE_EQS: (5), (18) imply:
% 242.26/48.92  |   (19)  all_58_15 = e0
% 242.26/48.92  | 
% 242.26/48.92  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (12), (14), (15), (16),
% 242.26/48.92  |            (19) are inconsistent by sub-proof #760.
% 242.26/48.92  | 
% 242.26/48.92  End of proof
% 242.26/48.92  
% 242.26/48.92  Sub-proof #760 shows that the following formulas are inconsistent:
% 242.26/48.92  ----------------------------------------------------------------
% 242.26/48.92    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.26/48.92         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.26/48.92    (2)   ~ (e3 = e0)
% 242.26/48.92    (3)   ~ (e2 = e0)
% 242.26/48.92    (4)   ~ (all_52_7 = e3)
% 242.26/48.92    (5)   ~ (e3 = e1)
% 242.26/48.92    (6)   ~ (e3 = e2)
% 242.26/48.92    (7)  op(e0, e2) = e0
% 242.26/48.92    (8)  op(e0, e2) = all_52_7
% 242.26/48.92    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.92    (10)  all_58_15 = e0
% 242.26/48.92    (11)  all_58_14 = e1
% 242.26/48.92    (12)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.92          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.92            e2)
% 242.26/48.92    (13)   ~ (e2 = e1)
% 242.26/48.92  
% 242.26/48.92  Begin of proof
% 242.26/48.92  | 
% 242.26/48.92  | BETA: splitting (1) gives:
% 242.26/48.92  | 
% 242.26/48.92  | Case 1:
% 242.26/48.92  | | 
% 242.26/48.92  | |   (14)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 242.26/48.92  | |           e3)
% 242.26/48.92  | | 
% 242.26/48.92  | | BETA: splitting (14) gives:
% 242.26/48.92  | | 
% 242.26/48.92  | | Case 1:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (15)  all_58_12 = e3 & op(e0, e3) = e3
% 242.26/48.92  | | | 
% 242.26/48.92  | | | ALPHA: (15) implies:
% 242.26/48.92  | | |   (16)  all_58_12 = e3
% 242.26/48.92  | | | 
% 242.26/48.92  | | | BETA: splitting (12) gives:
% 242.26/48.92  | | | 
% 242.26/48.92  | | | Case 1:
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | |   (17)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 242.26/48.92  | | | |             e2) = e2)
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | | BETA: splitting (17) gives:
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | | Case 1:
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | |   (18)  all_58_12 = e2 & op(e0, e3) = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | ALPHA: (18) implies:
% 242.26/48.92  | | | | |   (19)  all_58_12 = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | REF_CLOSE: (6), (16), (19) are inconsistent by sub-proof #1552.
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | Case 2:
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | |   (20)  all_58_13 = e2 & op(e0, e2) = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | ALPHA: (20) implies:
% 242.26/48.92  | | | | |   (21)  op(e0, e2) = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | REF_CLOSE: (3), (7), (9), (21) are inconsistent by sub-proof #2132.
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | End of split
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | Case 2:
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | |   (22)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 242.26/48.92  | | | |             e0) = e2)
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | | BETA: splitting (22) gives:
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | | Case 1:
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | |   (23)  all_58_14 = e2 & op(e0, e1) = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | REF_CLOSE: (11), (13), (23) are inconsistent by sub-proof #1771.
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | Case 2:
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | |   (24)  all_58_15 = e2 & op(e0, e0) = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | REF_CLOSE: (3), (10), (24) are inconsistent by sub-proof #1654.
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | End of split
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | End of split
% 242.26/48.92  | | | 
% 242.26/48.92  | | Case 2:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (25)  all_58_13 = e3 & op(e0, e2) = e3
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (4), (8), (9), (25) are inconsistent by sub-proof #1919.
% 242.26/48.92  | | | 
% 242.26/48.92  | | End of split
% 242.26/48.92  | | 
% 242.26/48.92  | Case 2:
% 242.26/48.92  | | 
% 242.26/48.92  | |   (26)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 242.26/48.92  | |           e3)
% 242.26/48.92  | | 
% 242.26/48.92  | | BETA: splitting (26) gives:
% 242.26/48.92  | | 
% 242.26/48.92  | | Case 1:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (27)  all_58_14 = e3 & op(e0, e1) = e3
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (5), (11), (27) are inconsistent by sub-proof #1773.
% 242.26/48.92  | | | 
% 242.26/48.92  | | Case 2:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (28)  all_58_15 = e3 & op(e0, e0) = e3
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (2), (10), (28) are inconsistent by sub-proof #1496.
% 242.26/48.92  | | | 
% 242.26/48.92  | | End of split
% 242.26/48.92  | | 
% 242.26/48.92  | End of split
% 242.26/48.92  | 
% 242.26/48.92  End of proof
% 242.26/48.92  
% 242.26/48.92  Sub-proof #761 shows that the following formulas are inconsistent:
% 242.26/48.92  ----------------------------------------------------------------
% 242.26/48.92    (1)  op(e2, e2) = e3
% 242.26/48.92    (2)  op(e2, all_52_1) = e2
% 242.26/48.92    (3)  op(e0, e1) = all_52_11
% 242.26/48.92    (4)   ~ (e2 = e0)
% 242.26/48.92    (5)   ~ (e3 = e1)
% 242.26/48.92    (6)  all_58_2 = e2
% 242.26/48.92    (7)  all_58_3 = e3
% 242.26/48.92    (8)   ~ (all_52_11 = e3)
% 242.26/48.92    (9)   ~ (e3 = e2)
% 242.26/48.92    (10)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.26/48.92          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.26/48.92    (11)  all_58_2 = e2 & op(e2, e3) = e2
% 242.26/48.92    (12)  op(e2, e0) = e0
% 242.26/48.92    (13)  op(e2, e3) = all_52_1
% 242.26/48.92    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.92    (15)  op(e1, e1) = e0
% 242.26/48.92    (16)   ~ (e1 = e0)
% 242.26/48.92    (17)  all_58_4 = e3
% 242.26/48.92    (18)  op(e2, e0) = all_52_13
% 242.26/48.92    (19)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.26/48.92          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.26/48.92    (20)   ~ (e2 = e1)
% 242.26/48.92  
% 242.26/48.92  Begin of proof
% 242.26/48.92  | 
% 242.26/48.92  | BETA: splitting (19) gives:
% 242.26/48.92  | 
% 242.26/48.92  | Case 1:
% 242.26/48.92  | | 
% 242.26/48.92  | |   (21)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 242.26/48.92  | |           e1)
% 242.26/48.92  | | 
% 242.26/48.92  | | BETA: splitting (21) gives:
% 242.26/48.92  | | 
% 242.26/48.92  | | Case 1:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (22)  all_58_2 = e1 & op(e2, e3) = e1
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (6), (20), (22) are inconsistent by sub-proof #852.
% 242.26/48.92  | | | 
% 242.26/48.92  | | Case 2:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (23)  all_58_3 = e1 & op(e2, e2) = e1
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (5), (7), (23) are inconsistent by sub-proof #2197.
% 242.26/48.92  | | | 
% 242.26/48.92  | | End of split
% 242.26/48.92  | | 
% 242.26/48.92  | Case 2:
% 242.26/48.92  | | 
% 242.26/48.92  | |   (24)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 242.26/48.92  | |           e1)
% 242.26/48.92  | | 
% 242.26/48.92  | | BETA: splitting (24) gives:
% 242.26/48.92  | | 
% 242.26/48.92  | | Case 1:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (25)  all_58_5 = e1 & op(e2, e1) = e1
% 242.26/48.92  | | | 
% 242.26/48.92  | | | ALPHA: (25) implies:
% 242.26/48.92  | | |   (26)  all_58_5 = e1
% 242.26/48.92  | | | 
% 242.26/48.92  | | | BETA: splitting (10) gives:
% 242.26/48.92  | | | 
% 242.26/48.92  | | | Case 1:
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | |   (27)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 242.26/48.92  | | | |           = e2)
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | | REF_CLOSE: (9), (17), (20), (26), (27) are inconsistent by sub-proof
% 242.26/48.92  | | | |            #762.
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | Case 2:
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | |   (28)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 242.26/48.92  | | | |           = e2)
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | | BETA: splitting (28) gives:
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | | Case 1:
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | |   (29)  all_58_8 = e2 & op(e1, e1) = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | ALPHA: (29) implies:
% 242.26/48.92  | | | | |   (30)  op(e1, e1) = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | REF_CLOSE: (4), (14), (15), (30) are inconsistent by sub-proof #2211.
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | Case 2:
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | |   (31)  all_58_14 = e2 & op(e0, e1) = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | ALPHA: (11) implies:
% 242.26/48.92  | | | | |   (32)  op(e2, e3) = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | ALPHA: (31) implies:
% 242.26/48.92  | | | | |   (33)  op(e0, e1) = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | GROUND_INST: instantiating (14) with all_52_11, e2, e1, e0,
% 242.26/48.92  | | | | |              simplifying with (3), (33) gives:
% 242.26/48.92  | | | | |   (34)  all_52_11 = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | GROUND_INST: instantiating (14) with all_52_1, e2, e3, e2, simplifying
% 242.26/48.92  | | | | |              with (13), (32) gives:
% 242.26/48.92  | | | | |   (35)  all_52_1 = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | REDUCE: (8), (34) imply:
% 242.26/48.92  | | | | |   (36)   ~ (e3 = e2)
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | REDUCE: (2), (35) imply:
% 242.26/48.92  | | | | |   (37)  op(e2, e2) = e2
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | | REF_CLOSE: (1), (9), (14), (37) are inconsistent by sub-proof #2140.
% 242.26/48.92  | | | | | 
% 242.26/48.92  | | | | End of split
% 242.26/48.92  | | | | 
% 242.26/48.92  | | | End of split
% 242.26/48.92  | | | 
% 242.26/48.92  | | Case 2:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (38)  all_58_10 = e1 & op(e2, e0) = e1
% 242.26/48.92  | | | 
% 242.26/48.92  | | | ALPHA: (38) implies:
% 242.26/48.92  | | |   (39)  op(e2, e0) = e1
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (12), (14), (16), (18), (39) are inconsistent by sub-proof
% 242.26/48.92  | | |            #1778.
% 242.26/48.92  | | | 
% 242.26/48.92  | | End of split
% 242.26/48.92  | | 
% 242.26/48.92  | End of split
% 242.26/48.92  | 
% 242.26/48.92  End of proof
% 242.26/48.92  
% 242.26/48.92  Sub-proof #762 shows that the following formulas are inconsistent:
% 242.26/48.92  ----------------------------------------------------------------
% 242.26/48.92    (1)   ~ (e3 = e2)
% 242.26/48.92    (2)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2)
% 242.26/48.92    (3)  all_58_5 = e1
% 242.26/48.92    (4)  all_58_4 = e3
% 242.26/48.92    (5)   ~ (e2 = e1)
% 242.26/48.92  
% 242.26/48.92  Begin of proof
% 242.26/48.92  | 
% 242.26/48.92  | BETA: splitting (2) gives:
% 242.26/48.92  | 
% 242.26/48.92  | Case 1:
% 242.26/48.92  | | 
% 242.26/48.92  | |   (6)  all_58_4 = e2 & op(e3, e1) = e2
% 242.26/48.92  | | 
% 242.26/48.92  | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #1476.
% 242.26/48.92  | | 
% 242.26/48.92  | Case 2:
% 242.26/48.92  | | 
% 242.26/48.92  | |   (7)  all_58_5 = e2 & op(e2, e1) = e2
% 242.26/48.92  | | 
% 242.26/48.92  | | ALPHA: (7) implies:
% 242.26/48.92  | |   (8)  all_58_5 = e2
% 242.26/48.92  | | 
% 242.26/48.92  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #1665.
% 242.26/48.92  | | 
% 242.26/48.92  | End of split
% 242.26/48.92  | 
% 242.26/48.92  End of proof
% 242.26/48.92  
% 242.26/48.92  Sub-proof #763 shows that the following formulas are inconsistent:
% 242.26/48.92  ----------------------------------------------------------------
% 242.26/48.92    (1)   ~ (e3 = e0)
% 242.26/48.92    (2)  all_58_6 = e3
% 242.26/48.92    (3)  op(e1, e2) = all_52_6
% 242.26/48.92    (4)  all_58_3 = e3
% 242.26/48.92    (5)  all_58_3 = e0 & op(e2, e2) = e0
% 242.26/48.92    (6)   ~ (e3 = e2)
% 242.26/48.92    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.26/48.92         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.26/48.92    (8)   ~ (all_52_6 = e3)
% 242.26/48.92    (9)  op(e1, e1) = e2
% 242.26/48.92    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.92    (11)  all_58_11 = e0
% 242.26/48.92  
% 242.26/48.92  Begin of proof
% 242.26/48.92  | 
% 242.26/48.92  | ALPHA: (5) implies:
% 242.26/48.92  |   (12)  all_58_3 = e0
% 242.26/48.92  | 
% 242.26/48.92  | COMBINE_EQS: (4), (12) imply:
% 242.26/48.92  |   (13)  e3 = e0
% 242.26/48.92  | 
% 242.26/48.92  | COMBINE_EQS: (2), (13) imply:
% 242.26/48.92  |   (14)  all_58_6 = e0
% 242.26/48.92  | 
% 242.26/48.92  | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (14) are inconsistent by
% 242.26/48.92  |            sub-proof #1686.
% 242.26/48.92  | 
% 242.26/48.92  End of proof
% 242.26/48.92  
% 242.26/48.92  Sub-proof #764 shows that the following formulas are inconsistent:
% 242.26/48.92  ----------------------------------------------------------------
% 242.26/48.92    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.92         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.92    (2)   ~ (e2 = e0)
% 242.26/48.92    (3)  all_58_1 = e0
% 242.26/48.92    (4)   ~ (e3 = e1)
% 242.26/48.92    (5)   ~ (e3 = e2)
% 242.26/48.92    (6)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.26/48.92         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.26/48.92    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.92    (8)   ~ (e1 = e0)
% 242.26/48.92    (9)  op(e3, e3) = e0
% 242.26/48.92    (10)  all_58_4 = e3
% 242.26/48.92    (11)   ~ (e2 = e1)
% 242.26/48.92  
% 242.26/48.92  Begin of proof
% 242.26/48.92  | 
% 242.26/48.92  | BETA: splitting (1) gives:
% 242.26/48.92  | 
% 242.26/48.92  | Case 1:
% 242.26/48.92  | | 
% 242.26/48.92  | |   (12)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 242.26/48.92  | |           e2)
% 242.26/48.92  | | 
% 242.26/48.92  | | BETA: splitting (12) gives:
% 242.26/48.92  | | 
% 242.26/48.92  | | Case 1:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (13)  all_58_0 = e2 & op(e3, e3) = e2
% 242.26/48.92  | | | 
% 242.26/48.92  | | | ALPHA: (13) implies:
% 242.26/48.92  | | |   (14)  op(e3, e3) = e2
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (2), (7), (9), (14) are inconsistent by sub-proof #2188.
% 242.26/48.92  | | | 
% 242.26/48.92  | | Case 2:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (15)  all_58_1 = e2 & op(e3, e2) = e2
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (2), (3), (15) are inconsistent by sub-proof #1478.
% 242.26/48.92  | | | 
% 242.26/48.92  | | End of split
% 242.26/48.92  | | 
% 242.26/48.92  | Case 2:
% 242.26/48.92  | | 
% 242.26/48.92  | |   (16)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 242.26/48.92  | |           e2)
% 242.26/48.92  | | 
% 242.26/48.92  | | BETA: splitting (16) gives:
% 242.26/48.92  | | 
% 242.26/48.92  | | Case 1:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (17)  all_58_4 = e2 & op(e3, e1) = e2
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (5), (10), (17) are inconsistent by sub-proof #1476.
% 242.26/48.92  | | | 
% 242.26/48.92  | | Case 2:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (18)  all_58_9 = e2 & op(e3, e0) = e2
% 242.26/48.92  | | | 
% 242.26/48.92  | | | ALPHA: (18) implies:
% 242.26/48.92  | | |   (19)  all_58_9 = e2
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (19) are inconsistent
% 242.26/48.92  | | |            by sub-proof #1016.
% 242.26/48.92  | | | 
% 242.26/48.92  | | End of split
% 242.26/48.92  | | 
% 242.26/48.92  | End of split
% 242.26/48.92  | 
% 242.26/48.92  End of proof
% 242.26/48.92  
% 242.26/48.92  Sub-proof #765 shows that the following formulas are inconsistent:
% 242.26/48.92  ----------------------------------------------------------------
% 242.26/48.92    (1)   ~ (e2 = e0)
% 242.26/48.92    (2)  all_58_15 = e3
% 242.26/48.92    (3)  op(e0, e1) = e1
% 242.26/48.92    (4)   ~ (e3 = e2)
% 242.26/48.92    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.92    (6)   ~ (e1 = e0)
% 242.26/48.92    (7)  all_58_13 = e1
% 242.26/48.92    (8)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 242.26/48.92         (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.92    (9)  op(e0, e2) = e1
% 242.26/48.92    (10)  all_58_14 = e1
% 242.26/48.92    (11)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.92          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.26/48.92            e2)
% 242.26/48.92    (12)   ~ (e2 = e1)
% 242.26/48.92  
% 242.26/48.92  Begin of proof
% 242.26/48.92  | 
% 242.26/48.92  | BETA: splitting (8) gives:
% 242.26/48.92  | 
% 242.26/48.92  | Case 1:
% 242.26/48.92  | | 
% 242.26/48.92  | |   (13)  all_58_12 = e0 & op(e0, e3) = e0
% 242.26/48.92  | | 
% 242.26/48.92  | | ALPHA: (13) implies:
% 242.26/48.92  | |   (14)  all_58_12 = e0
% 242.26/48.92  | | 
% 242.26/48.92  | | REF_CLOSE: (1), (2), (4), (7), (10), (11), (12), (14) are inconsistent by
% 242.26/48.92  | |            sub-proof #1230.
% 242.26/48.92  | | 
% 242.26/48.92  | Case 2:
% 242.26/48.92  | | 
% 242.26/48.92  | |   (15)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 242.26/48.92  | |           e0)
% 242.26/48.92  | | 
% 242.26/48.92  | | BETA: splitting (15) gives:
% 242.26/48.92  | | 
% 242.26/48.92  | | Case 1:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (16)  all_58_13 = e0 & op(e0, e2) = e0
% 242.26/48.92  | | | 
% 242.26/48.92  | | | ALPHA: (16) implies:
% 242.26/48.92  | | |   (17)  op(e0, e2) = e0
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (5), (6), (9), (17) are inconsistent by sub-proof #1872.
% 242.26/48.92  | | | 
% 242.26/48.92  | | Case 2:
% 242.26/48.92  | | | 
% 242.26/48.92  | | |   (18)  all_58_14 = e0 & op(e0, e1) = e0
% 242.26/48.92  | | | 
% 242.26/48.92  | | | ALPHA: (18) implies:
% 242.26/48.92  | | |   (19)  op(e0, e1) = e0
% 242.26/48.92  | | | 
% 242.26/48.92  | | | REF_CLOSE: (3), (5), (6), (19) are inconsistent by sub-proof #2158.
% 242.26/48.92  | | | 
% 242.26/48.92  | | End of split
% 242.26/48.92  | | 
% 242.26/48.92  | End of split
% 242.26/48.92  | 
% 242.26/48.92  End of proof
% 242.26/48.92  
% 242.26/48.92  Sub-proof #766 shows that the following formulas are inconsistent:
% 242.26/48.92  ----------------------------------------------------------------
% 242.26/48.92    (1)  op(e1, e0) = e0
% 242.26/48.92    (2)  op(e1, all_56_29) = e1
% 242.26/48.92    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.92    (4)   ~ (e1 = e0)
% 242.26/48.93    (5)  op(e1, e0) = all_56_29
% 242.26/48.93  
% 242.26/48.93  Begin of proof
% 242.26/48.93  | 
% 242.26/48.93  | GROUND_INST: instantiating (3) with e0, all_56_29, e0, e1, simplifying with
% 242.26/48.93  |              (1), (5) gives:
% 242.26/48.93  |   (6)  all_56_29 = e0
% 242.26/48.93  | 
% 242.26/48.93  | REDUCE: (2), (6) imply:
% 242.26/48.93  |   (7)  op(e1, e0) = e1
% 242.26/48.93  | 
% 242.26/48.93  | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #2284.
% 242.26/48.93  | 
% 242.26/48.93  End of proof
% 242.26/48.93  
% 242.26/48.93  Sub-proof #767 shows that the following formulas are inconsistent:
% 242.26/48.93  ----------------------------------------------------------------
% 242.26/48.93    (1)  op(e2, e2) = e3
% 242.26/48.93    (2)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.26/48.93           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.26/48.93           all_12_1 & $i(all_12_1))
% 242.26/48.93    (3)  all_56_21 = e2
% 242.26/48.93    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.26/48.93         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.26/48.93    (5)  op(e1, e2) = all_56_13
% 242.26/48.93    (6)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.26/48.93           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.26/48.93           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.26/48.93           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.26/48.93           & $i(all_56_23))
% 242.26/48.93    (7)   ~ (e3 = e0)
% 242.26/48.93    (8)  op(e0, e1) = all_52_11
% 242.26/48.93    (9)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.26/48.93         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.26/48.93    (10)  all_58_6 = e3
% 242.26/48.93    (11)  op(e1, e2) = e1
% 242.26/48.93    (12)   ~ (e2 = e0)
% 242.26/48.93    (13)  op(e1, e2) = all_52_6
% 242.26/48.93    (14)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.26/48.93          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.26/48.93    (15)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.26/48.93              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.26/48.93            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.26/48.93            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.26/48.93            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.26/48.93             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.93            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.26/48.93            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.26/48.93            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.26/48.93            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.93            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.26/48.93              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.26/48.93            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.26/48.93            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.26/48.93            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.26/48.93            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.26/48.93            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.26/48.93            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.26/48.93              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.26/48.93            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.26/48.93            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.26/48.93            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.26/48.93            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.26/48.93            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.26/48.93            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.26/48.93              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.26/48.93            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.26/48.93            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.26/48.93    (16)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.93          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.26/48.93    (17)   ~ (all_52_12 = e0)
% 242.26/48.93    (18)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1)
% 242.26/48.93    (19)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.26/48.93          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.26/48.93    (20)  op(e1, e0) = all_52_14
% 242.26/48.93    (21)  all_58_15 = e3
% 242.26/48.93    (22)  op(e0, e3) = all_52_3
% 242.26/48.93    (23)   ~ (e3 = e1)
% 242.26/48.93    (24)  all_58_8 = e2
% 242.26/48.93    (25)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.26/48.93          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.26/48.93    (26)  op(e0, all_52_3) = e0
% 242.26/48.93    (27)  all_58_3 = e3
% 242.26/48.93    (28)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.26/48.93            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.26/48.93              e3) = all_26_1 & $i(all_26_1))
% 242.26/48.93    (29)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.93              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.26/48.93                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.26/48.93                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.26/48.93    (30)   ~ (all_52_14 = e2)
% 242.26/48.93    (31)  op(e2, e1) = all_52_9
% 242.26/48.93    (32)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.26/48.93          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.26/48.93    (33)   ~ (e3 = e2)
% 242.26/48.93    (34)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.26/48.93            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.26/48.93            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.26/48.93            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.26/48.93            op(e0, all_56_31) = e0)
% 242.26/48.93    (35)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 242.26/48.93            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 242.26/48.93              e0) = all_16_1 & $i(all_16_1))
% 242.26/48.93    (36)  op(e3, e0) = all_52_12
% 242.26/48.93    (37)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.26/48.93            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.26/48.93              e3) = all_42_1 & $i(all_42_1))
% 242.26/48.93    (38)  op(e2, e3) = all_52_1
% 242.26/48.93    (39)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.26/48.93          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.26/48.93    (40)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 242.26/48.93            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 242.26/48.93              e0) = all_50_1 & $i(all_50_1))
% 242.26/48.93    (41)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 242.26/48.93            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 242.26/48.93              e2) = all_40_1 & $i(all_40_1))
% 242.26/48.93    (42)  op(e1, e1) = e2
% 242.26/48.93    (43)  op(e0, e2) = all_52_7
% 242.26/48.93    (44)   ~ (all_52_13 = all_52_14)
% 242.26/48.93    (45)   ~ (all_52_4 = e3)
% 242.26/48.93    (46)  op(e3, e2) = all_52_4
% 242.26/48.93    (47)  all_58_1 = e2
% 242.26/48.93    (48)   ~ (all_52_9 = e3)
% 242.26/48.93    (49)  all_56_31 = e3
% 242.26/48.93    (50)  op(e0, e0) = e3
% 242.26/48.93    (51)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.26/48.93          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.26/48.93    (52)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.26/48.93          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.26/48.93    (53)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.26/48.93          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.26/48.93    (54)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.26/48.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.26/48.93    (55)   ~ (all_52_12 = e3)
% 242.26/48.93    (56)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.26/48.93            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.26/48.93              e2) = all_36_1 & $i(all_36_1))
% 242.26/48.93    (57)  op(e1, all_56_13) = e1
% 242.26/48.93    (58)  op(e3, e3) = e0
% 242.26/48.93    (59)  all_58_4 = e3
% 242.26/48.93    (60)   ~ (all_52_13 = e3)
% 242.26/48.93    (61)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.26/48.93          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.26/48.93    (62)  all_56_1 = e0
% 242.26/48.93    (63)  op(e2, e0) = all_52_13
% 242.26/48.93    (64)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.26/48.93          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.26/48.93            e1)
% 242.26/48.93    (65)   ~ (all_52_1 = e3)
% 242.26/48.93    (66)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.26/48.93            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.26/48.93            & $i(all_8_1))
% 242.26/48.93    (67)   ~ (e2 = e1)
% 242.26/48.93  
% 242.26/48.93  Begin of proof
% 242.26/48.93  | 
% 242.26/48.93  | ALPHA: (18) implies:
% 242.26/48.93  |   (68)   ~ (all_36_1 = e0)
% 242.26/48.93  |   (69)  op(e1, e2) = all_36_1
% 242.26/48.93  | 
% 242.26/48.93  | BETA: splitting (41) gives:
% 242.26/48.93  | 
% 242.26/48.93  | Case 1:
% 242.26/48.93  | | 
% 242.26/48.93  | |   (70)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 242.26/48.93  | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 242.26/48.93  | | 
% 242.26/48.93  | | ALPHA: (70) implies:
% 242.26/48.93  | |   (71)  op(e1, e2) = all_40_1
% 242.26/48.93  | |   (72)  op(all_40_1, e1) = all_40_0
% 242.26/48.93  | | 
% 242.26/48.93  | | GROUND_INST: instantiating (54) with all_36_1, all_40_1, e2, e1, simplifying
% 242.26/48.93  | |              with (69), (71) gives:
% 242.26/48.93  | |   (73)  all_40_1 = all_36_1
% 242.26/48.93  | | 
% 242.26/48.93  | | GROUND_INST: instantiating (54) with e1, all_56_13, e2, e1, simplifying with
% 242.26/48.93  | |              (5), (11) gives:
% 242.26/48.93  | |   (74)  all_56_13 = e1
% 242.26/48.93  | | 
% 242.26/48.93  | | GROUND_INST: instantiating (54) with all_40_1, all_56_13, e2, e1,
% 242.26/48.93  | |              simplifying with (5), (71) gives:
% 242.38/48.93  | |   (75)  all_56_13 = all_40_1
% 242.38/48.93  | | 
% 242.38/48.93  | | COMBINE_EQS: (74), (75) imply:
% 242.38/48.93  | |   (76)  all_40_1 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | SIMP: (76) implies:
% 242.38/48.93  | |   (77)  all_40_1 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | COMBINE_EQS: (73), (77) imply:
% 242.38/48.93  | |   (78)  all_36_1 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | SIMP: (78) implies:
% 242.38/48.93  | |   (79)  all_36_1 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | REDUCE: (68), (79) imply:
% 242.38/48.93  | |   (80)   ~ (e1 = e0)
% 242.38/48.93  | | 
% 242.38/48.93  | | REDUCE: (72), (77) imply:
% 242.38/48.93  | |   (81)  op(e1, e1) = all_40_0
% 242.38/48.93  | | 
% 242.38/48.93  | | REDUCE: (57), (74) imply:
% 242.38/48.93  | |   (82)  op(e1, e1) = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | GROUND_INST: instantiating (54) with e2, all_40_0, e1, e1, simplifying with
% 242.38/48.93  | |              (42), (81) gives:
% 242.38/48.93  | |   (83)  all_40_0 = e2
% 242.38/48.93  | | 
% 242.38/48.93  | | GROUND_INST: instantiating (54) with e1, all_40_0, e1, e1, simplifying with
% 242.38/48.93  | |              (81), (82) gives:
% 242.38/48.93  | |   (84)  all_40_0 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | COMBINE_EQS: (83), (84) imply:
% 242.38/48.93  | |   (85)  e2 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | COMBINE_EQS: (47), (85) imply:
% 242.38/48.93  | |   (86)  all_58_1 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14),
% 242.38/48.93  | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 242.38/48.93  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 242.38/48.93  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (48), (49),
% 242.38/48.93  | |            (50), (51), (52), (53), (54), (55), (56), (58), (59), (60), (61),
% 242.38/48.93  | |            (62), (63), (64), (65), (66), (67), (80), (86) are inconsistent
% 242.38/48.93  | |            by sub-proof #774.
% 242.38/48.93  | | 
% 242.38/48.93  | Case 2:
% 242.38/48.93  | | 
% 242.38/48.93  | |   (87)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 242.38/48.93  | | 
% 242.38/48.93  | | ALPHA: (87) implies:
% 242.38/48.93  | |   (88)   ~ (all_40_1 = e3)
% 242.38/48.93  | |   (89)  op(e1, e2) = all_40_1
% 242.38/48.93  | | 
% 242.38/48.93  | | GROUND_INST: instantiating (54) with all_36_1, all_40_1, e2, e1, simplifying
% 242.38/48.93  | |              with (69), (89) gives:
% 242.38/48.93  | |   (90)  all_40_1 = all_36_1
% 242.38/48.93  | | 
% 242.38/48.93  | | GROUND_INST: instantiating (54) with e1, all_56_13, e2, e1, simplifying with
% 242.38/48.93  | |              (5), (11) gives:
% 242.38/48.93  | |   (91)  all_56_13 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | GROUND_INST: instantiating (54) with all_40_1, all_56_13, e2, e1,
% 242.38/48.93  | |              simplifying with (5), (89) gives:
% 242.38/48.93  | |   (92)  all_56_13 = all_40_1
% 242.38/48.93  | | 
% 242.38/48.93  | | COMBINE_EQS: (91), (92) imply:
% 242.38/48.93  | |   (93)  all_40_1 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | SIMP: (93) implies:
% 242.38/48.93  | |   (94)  all_40_1 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | COMBINE_EQS: (90), (94) imply:
% 242.38/48.93  | |   (95)  all_36_1 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | SIMP: (95) implies:
% 242.38/48.93  | |   (96)  all_36_1 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | REDUCE: (88), (94) imply:
% 242.38/48.93  | |   (97)   ~ (e3 = e1)
% 242.38/48.93  | | 
% 242.38/48.93  | | REDUCE: (68), (96) imply:
% 242.38/48.93  | |   (98)   ~ (e1 = e0)
% 242.38/48.93  | | 
% 242.38/48.93  | | REDUCE: (57), (91) imply:
% 242.38/48.93  | |   (99)  op(e1, e1) = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | GROUND_INST: instantiating (54) with e2, e1, e1, e1, simplifying with (42),
% 242.38/48.93  | |              (99) gives:
% 242.38/48.93  | |   (100)  e2 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | COMBINE_EQS: (47), (100) imply:
% 242.38/48.93  | |   (101)  all_58_1 = e1
% 242.38/48.93  | | 
% 242.38/48.93  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14),
% 242.38/48.93  | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 242.38/48.94  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 242.38/48.94  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (48), (49),
% 242.38/48.94  | |            (50), (51), (52), (53), (54), (55), (56), (58), (59), (60), (61),
% 242.38/48.94  | |            (62), (63), (64), (65), (66), (67), (98), (101) are inconsistent
% 242.38/48.94  | |            by sub-proof #774.
% 242.38/48.94  | | 
% 242.38/48.94  | End of split
% 242.38/48.94  | 
% 242.38/48.94  End of proof
% 242.38/48.94  
% 242.38/48.94  Sub-proof #768 shows that the following formulas are inconsistent:
% 242.38/48.94  ----------------------------------------------------------------
% 242.38/48.94    (1)  op(e2, e2) = e3
% 242.38/48.94    (2)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.38/48.94           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.38/48.94           all_12_1 & $i(all_12_1))
% 242.38/48.94    (3)  all_56_21 = e2
% 242.38/48.94    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.38/48.94         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.38/48.94    (5)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.38/48.94           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.38/48.94           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.38/48.94           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.38/48.94           & $i(all_56_23))
% 242.38/48.94    (6)   ~ (e3 = e0)
% 242.38/48.94    (7)  op(e0, e1) = all_52_11
% 242.38/48.94    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.38/48.94         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.38/48.94    (9)  all_58_6 = e3
% 242.38/48.94    (10)   ~ (e2 = e0)
% 242.38/48.94    (11)  op(e1, e2) = all_52_6
% 242.38/48.94    (12)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.38/48.94          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.38/48.94    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.38/48.94              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.38/48.94            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.38/48.94            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.38/48.94            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.38/48.94             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.38/48.94            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.38/48.94            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.38/48.94            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.38/48.94            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.38/48.94            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.38/48.94              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.38/48.94            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.38/48.94            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.38/48.94            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.38/48.94            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.38/48.94            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.38/48.94            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.38/48.94              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.38/48.94            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.38/48.94            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.38/48.94            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.38/48.94            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.38/48.94            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.38/48.94            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.38/48.94              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.38/48.94            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.38/48.94            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.38/48.94    (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.38/48.94          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.38/48.94    (15)   ~ (all_52_12 = e0)
% 242.38/48.94    (16)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.38/48.94          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.38/48.94    (17)  op(e1, e0) = all_52_14
% 242.38/48.94    (18)  all_36_0 = e1
% 242.38/48.94    (19)  all_58_15 = e3
% 242.38/48.94    (20)  op(e0, e3) = all_52_3
% 242.38/48.94    (21)   ~ (e3 = e1)
% 242.38/48.94    (22)  all_58_8 = e2
% 242.38/48.94    (23)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.38/48.94          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.38/48.94    (24)  op(e0, all_52_3) = e0
% 242.38/48.94    (25)  all_58_3 = e3
% 242.38/48.94    (26)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.38/48.94            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.38/48.94              e3) = all_26_1 & $i(all_26_1))
% 242.38/48.94    (27)  all_36_0 = e2
% 242.38/48.94    (28)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.38/48.94              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.38/48.94                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.38/48.94                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.38/48.94    (29)   ~ (all_52_14 = e2)
% 242.38/48.94    (30)  op(e2, e1) = all_52_9
% 242.38/48.94    (31)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.38/48.94          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.38/48.94    (32)   ~ (e3 = e2)
% 242.38/48.94    (33)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.38/48.94            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.38/48.94            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.38/48.94            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.38/48.94            op(e0, all_56_31) = e0)
% 242.38/48.94    (34)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 242.38/48.94            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 242.38/48.94              e0) = all_16_1 & $i(all_16_1))
% 242.38/48.94    (35)  op(e3, e0) = all_52_12
% 242.38/48.94    (36)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.38/48.94            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.38/48.94              e3) = all_42_1 & $i(all_42_1))
% 242.38/48.94    (37)  op(e2, e3) = all_52_1
% 242.38/48.94    (38)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.38/48.94          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.38/48.94    (39)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 242.38/48.94            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 242.38/48.94              e0) = all_50_1 & $i(all_50_1))
% 242.38/48.94    (40)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 242.38/48.94            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 242.38/48.94              e2) = all_40_1 & $i(all_40_1))
% 242.38/48.94    (41)  op(e1, e1) = e2
% 242.38/48.94    (42)  op(e0, e2) = all_52_7
% 242.38/48.94    (43)   ~ (all_52_13 = all_52_14)
% 242.38/48.94    (44)   ~ (all_52_4 = e3)
% 242.38/48.94    (45)  op(e3, e2) = all_52_4
% 242.38/48.94    (46)  all_58_1 = e2
% 242.38/48.94    (47)   ~ (all_52_9 = e3)
% 242.38/48.94    (48)  all_56_31 = e3
% 242.38/48.94    (49)  op(e0, e0) = e3
% 242.38/48.94    (50)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.38/48.94          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.38/48.94    (51)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.38/48.94          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.38/48.94    (52)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.38/48.94          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.38/48.94    (53)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.38/48.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.38/48.94    (54)   ~ (all_52_12 = e3)
% 242.38/48.94    (55)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.38/48.94            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.38/48.94              e2) = all_36_1 & $i(all_36_1))
% 242.38/48.94    (56)   ~ (e1 = e0)
% 242.38/48.94    (57)  op(e3, e3) = e0
% 242.38/48.94    (58)  all_58_4 = e3
% 242.38/48.94    (59)   ~ (all_52_13 = e3)
% 242.38/48.94    (60)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.38/48.94          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.38/48.94    (61)  all_56_1 = e0
% 242.38/48.94    (62)  op(e2, e0) = all_52_13
% 242.38/48.94    (63)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.38/48.94          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.38/48.94            e1)
% 242.38/48.94    (64)   ~ (all_52_1 = e3)
% 242.38/48.94    (65)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.38/48.94            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.38/48.94            & $i(all_8_1))
% 242.38/48.94    (66)   ~ (e2 = e1)
% 242.38/48.94  
% 242.38/48.94  Begin of proof
% 242.38/48.94  | 
% 242.38/48.94  | COMBINE_EQS: (18), (27) imply:
% 242.38/48.94  |   (67)  e2 = e1
% 242.38/48.94  | 
% 242.38/48.94  | COMBINE_EQS: (46), (67) imply:
% 242.38/48.94  |   (68)  all_58_1 = e1
% 242.38/48.94  | 
% 242.38/48.94  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.38/48.94  |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 242.38/48.94  |            (25), (26), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 242.38/48.94  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (47), (48),
% 242.38/48.94  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 242.38/48.94  |            (60), (61), (62), (63), (64), (65), (66), (68) are inconsistent by
% 242.38/48.94  |            sub-proof #774.
% 242.38/48.94  | 
% 242.38/48.94  End of proof
% 242.38/48.94  
% 242.38/48.94  Sub-proof #769 shows that the following formulas are inconsistent:
% 242.38/48.94  ----------------------------------------------------------------
% 242.38/48.94    (1)  op(e2, e2) = e3
% 242.38/48.94    (2)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.38/48.94           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.38/48.94           all_12_1 & $i(all_12_1))
% 242.38/48.94    (3)  all_56_21 = e2
% 242.38/48.94    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.38/48.94         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.38/48.94    (5)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.38/48.94           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.38/48.94           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.38/48.94           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.38/48.94           & $i(all_56_23))
% 242.38/48.94    (6)   ~ (e3 = e0)
% 242.38/48.94    (7)  op(e0, e1) = all_52_11
% 242.38/48.94    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.38/48.94         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.38/48.94    (9)  all_58_6 = e3
% 242.38/48.94    (10)   ~ (e2 = e0)
% 242.38/48.94    (11)  op(e1, e2) = all_52_6
% 242.38/48.94    (12)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.38/48.94          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.38/48.94    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.38/48.94              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.38/48.94            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.38/48.94            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.38/48.94            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.38/48.94             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.38/48.94            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.38/48.94            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.38/48.94            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.38/48.94            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.38/48.94            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.38/48.94              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.38/48.94            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.38/48.94            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.38/48.94            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.38/48.94            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.38/48.94            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.38/48.94            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.38/48.94              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.38/48.94            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.38/48.94            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.38/48.94            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.38/48.94            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.38/48.94            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.38/48.94            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.38/48.94              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.38/48.94            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.38/48.94            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.38/48.94    (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.38/48.94          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.38/48.94    (15)   ~ (all_52_12 = e0)
% 242.38/48.94    (16)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.38/48.94          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.38/48.94    (17)  op(e1, e0) = all_52_14
% 242.38/48.94    (18)  all_58_15 = e3
% 242.38/48.94    (19)  op(e0, e3) = all_52_3
% 242.38/48.94    (20)   ~ (e3 = e1)
% 242.38/48.94    (21)  all_58_8 = e2
% 242.38/48.94    (22)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.38/48.94          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.38/48.94    (23)  op(e0, all_52_3) = e0
% 242.38/48.94    (24)  all_58_3 = e3
% 242.38/48.94    (25)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.38/48.94            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.38/48.94              e3) = all_26_1 & $i(all_26_1))
% 242.38/48.95    (26)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.38/48.95              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.38/48.95                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.38/48.95                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.38/48.95    (27)   ~ (all_52_14 = e2)
% 242.38/48.95    (28)  op(e2, e1) = all_52_9
% 242.38/48.95    (29)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.38/48.95          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.38/48.95    (30)   ~ (e3 = e2)
% 242.38/48.95    (31)  op(e2, e3) = e2
% 242.38/48.95    (32)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.38/48.95            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.38/48.95            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.38/48.95            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.38/48.95            op(e0, all_56_31) = e0)
% 242.38/48.95    (33)  op(e2, e3) = e1
% 242.38/48.95    (34)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 242.38/48.95            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 242.38/48.95              e0) = all_16_1 & $i(all_16_1))
% 242.38/48.95    (35)  op(e3, e0) = all_52_12
% 242.38/48.95    (36)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.38/48.95            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.38/48.95              e3) = all_42_1 & $i(all_42_1))
% 242.38/48.95    (37)  op(e2, e3) = all_52_1
% 242.38/48.95    (38)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.38/48.95          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.38/48.95    (39)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 242.38/48.95            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 242.38/48.95              e0) = all_50_1 & $i(all_50_1))
% 242.38/48.95    (40)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 242.38/48.95            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 242.38/48.95              e2) = all_40_1 & $i(all_40_1))
% 242.38/48.95    (41)  op(e1, e1) = e2
% 242.38/48.95    (42)  op(e0, e2) = all_52_7
% 242.38/48.95    (43)   ~ (all_52_13 = all_52_14)
% 242.38/48.95    (44)   ~ (all_52_4 = e3)
% 242.38/48.95    (45)  op(e3, e2) = all_52_4
% 242.38/48.95    (46)  all_58_1 = e2
% 242.38/48.95    (47)   ~ (all_52_9 = e3)
% 242.38/48.95    (48)  all_56_31 = e3
% 242.38/48.95    (49)  op(e0, e0) = e3
% 242.38/48.95    (50)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.38/48.95          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.38/48.95    (51)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.38/48.95          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.38/48.95    (52)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.38/48.95          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.38/48.95    (53)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.38/48.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.38/48.95    (54)   ~ (all_52_12 = e3)
% 242.38/48.95    (55)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.38/48.95            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.38/48.95              e2) = all_36_1 & $i(all_36_1))
% 242.38/48.95    (56)   ~ (e1 = e0)
% 242.38/48.95    (57)  op(e3, e3) = e0
% 242.38/48.95    (58)  all_58_4 = e3
% 242.38/48.95    (59)   ~ (all_52_13 = e3)
% 242.38/48.95    (60)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.38/48.95          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.38/48.95    (61)  all_56_1 = e0
% 242.38/48.95    (62)  op(e2, e0) = all_52_13
% 242.38/48.95    (63)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.38/48.95          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.38/48.95            e1)
% 242.38/48.95    (64)   ~ (all_52_1 = e3)
% 242.38/48.95    (65)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.38/48.95            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.38/48.95            & $i(all_8_1))
% 242.38/48.95    (66)   ~ (e2 = e1)
% 242.38/48.95  
% 242.38/48.95  Begin of proof
% 242.38/48.95  | 
% 242.38/48.95  | BETA: splitting (65) gives:
% 242.38/48.95  | 
% 242.38/48.95  | Case 1:
% 242.38/48.95  | | 
% 242.38/48.95  | |   (67)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1
% 242.38/48.95  | |         & $i(all_8_0) & $i(all_8_1)
% 242.38/48.95  | | 
% 242.38/48.95  | | ALPHA: (67) implies:
% 242.38/48.95  | |   (68)  op(e2, e3) = all_8_1
% 242.38/48.95  | | 
% 242.38/48.95  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.38/48.95  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 242.38/48.95  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 242.38/48.95  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 242.38/48.95  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 242.38/48.95  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (68)
% 242.38/48.95  | |            are inconsistent by sub-proof #770.
% 242.38/48.95  | | 
% 242.38/48.95  | Case 2:
% 242.38/48.95  | | 
% 242.38/48.95  | |   (69)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 242.38/48.95  | | 
% 242.38/48.95  | | ALPHA: (69) implies:
% 242.38/48.95  | |   (70)  op(e2, e3) = all_8_1
% 242.38/48.95  | | 
% 242.38/48.95  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.38/48.95  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 242.38/48.95  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 242.38/48.95  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 242.38/48.95  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 242.38/48.95  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (70)
% 242.38/48.95  | |            are inconsistent by sub-proof #770.
% 242.38/48.95  | | 
% 242.38/48.95  | End of split
% 242.38/48.95  | 
% 242.38/48.95  End of proof
% 242.38/48.95  
% 242.38/48.95  Sub-proof #770 shows that the following formulas are inconsistent:
% 242.38/48.95  ----------------------------------------------------------------
% 242.38/48.95    (1)  op(e2, e2) = e3
% 242.38/48.95    (2)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.38/48.95           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.38/48.95           all_12_1 & $i(all_12_1))
% 242.38/48.95    (3)  all_56_21 = e2
% 242.38/48.95    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.38/48.95         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.38/48.95    (5)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.38/48.95           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.38/48.95           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.38/48.95           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.38/48.95           & $i(all_56_23))
% 242.38/48.95    (6)   ~ (e3 = e0)
% 242.38/48.95    (7)  op(e0, e1) = all_52_11
% 242.38/48.95    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.38/48.95         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.38/48.95    (9)  all_58_6 = e3
% 242.38/48.95    (10)   ~ (e2 = e0)
% 242.38/48.95    (11)  op(e1, e2) = all_52_6
% 242.38/48.95    (12)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.38/48.95          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.38/48.95    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.38/48.95              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.38/48.95            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.38/48.95            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.38/48.95            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.38/48.95             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.38/48.95            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.38/48.95            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.38/48.95            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.38/48.95            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.38/48.95            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.38/48.95              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.38/48.95            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.38/48.95            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.38/48.95            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.38/48.95            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.38/48.95            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.38/48.95            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.38/48.95              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.38/48.95            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.38/48.95            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.38/48.95            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.38/48.95            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.38/48.95            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.38/48.95            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.38/48.95              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.38/48.95            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.38/48.95            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.38/48.95    (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.38/48.95          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.38/48.95    (15)   ~ (all_52_12 = e0)
% 242.38/48.95    (16)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.38/48.95          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.38/48.95    (17)  op(e1, e0) = all_52_14
% 242.38/48.95    (18)  all_58_15 = e3
% 242.38/48.95    (19)  op(e0, e3) = all_52_3
% 242.38/48.95    (20)   ~ (e3 = e1)
% 242.38/48.95    (21)  all_58_8 = e2
% 242.38/48.95    (22)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.38/48.95          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.38/48.95    (23)  op(e0, all_52_3) = e0
% 242.38/48.95    (24)  all_58_3 = e3
% 242.38/48.95    (25)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.38/48.95            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.38/48.95              e3) = all_26_1 & $i(all_26_1))
% 242.38/48.95    (26)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.38/48.95              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.38/48.95                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.38/48.95                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.38/48.95    (27)   ~ (all_52_14 = e2)
% 242.38/48.95    (28)  op(e2, e1) = all_52_9
% 242.38/48.95    (29)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.38/48.95          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.38/48.95    (30)   ~ (e3 = e2)
% 242.38/48.95    (31)  op(e2, e3) = e2
% 242.38/48.95    (32)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.38/48.95            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.38/48.95            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.38/48.95            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.38/48.95            op(e0, all_56_31) = e0)
% 242.38/48.95    (33)  op(e2, e3) = e1
% 242.38/48.95    (34)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 242.38/48.95            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 242.38/48.95              e0) = all_16_1 & $i(all_16_1))
% 242.38/48.95    (35)  op(e3, e0) = all_52_12
% 242.38/48.95    (36)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.38/48.95            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.38/48.95              e3) = all_42_1 & $i(all_42_1))
% 242.38/48.95    (37)  op(e2, e3) = all_52_1
% 242.38/48.95    (38)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.38/48.95          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.38/48.95    (39)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 242.38/48.95            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 242.38/48.95              e0) = all_50_1 & $i(all_50_1))
% 242.38/48.95    (40)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 242.38/48.95            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 242.38/48.95              e2) = all_40_1 & $i(all_40_1))
% 242.38/48.95    (41)  op(e1, e1) = e2
% 242.38/48.95    (42)  op(e0, e2) = all_52_7
% 242.38/48.95    (43)   ~ (all_52_13 = all_52_14)
% 242.38/48.95    (44)   ~ (all_52_4 = e3)
% 242.38/48.95    (45)  op(e3, e2) = all_52_4
% 242.38/48.95    (46)  all_58_1 = e2
% 242.38/48.95    (47)   ~ (all_52_9 = e3)
% 242.38/48.95    (48)  all_56_31 = e3
% 242.38/48.95    (49)  op(e0, e0) = e3
% 242.38/48.95    (50)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.38/48.95          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.38/48.95    (51)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.38/48.95          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.38/48.95    (52)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.38/48.95          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.38/48.95    (53)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.38/48.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.38/48.95    (54)  op(e2, e3) = all_8_1
% 242.38/48.95    (55)   ~ (all_52_12 = e3)
% 242.38/48.95    (56)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.38/48.95            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.38/48.95              e2) = all_36_1 & $i(all_36_1))
% 242.38/48.95    (57)   ~ (e1 = e0)
% 242.38/48.95    (58)  op(e3, e3) = e0
% 242.38/48.95    (59)  all_58_4 = e3
% 242.38/48.95    (60)   ~ (all_52_13 = e3)
% 242.38/48.96    (61)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.38/48.96          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.38/48.96    (62)  all_56_1 = e0
% 242.38/48.96    (63)  op(e2, e0) = all_52_13
% 242.38/48.96    (64)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.38/48.96          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.38/48.96            e1)
% 242.38/48.96    (65)   ~ (all_52_1 = e3)
% 242.38/48.96    (66)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.38/48.96            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.38/48.96            & $i(all_8_1))
% 242.38/48.96    (67)   ~ (e2 = e1)
% 242.38/48.96  
% 242.38/48.96  Begin of proof
% 242.38/48.96  | 
% 242.38/48.96  | BETA: splitting (36) gives:
% 242.38/48.96  | 
% 242.38/48.96  | Case 1:
% 242.38/48.96  | | 
% 242.38/48.96  | |   (68)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.38/48.96  | |         all_42_1 & $i(all_42_0) & $i(all_42_1)
% 242.38/48.96  | | 
% 242.38/48.96  | | ALPHA: (68) implies:
% 242.38/48.96  | |   (69)  op(e2, e3) = all_42_1
% 242.38/48.96  | | 
% 242.38/48.96  | | GROUND_INST: instantiating (53) with e1, all_42_1, e3, e2, simplifying with
% 242.38/48.96  | |              (33), (69) gives:
% 242.38/48.96  | |   (70)  all_42_1 = e1
% 242.38/48.96  | | 
% 242.38/48.96  | | GROUND_INST: instantiating (53) with all_8_1, all_42_1, e3, e2, simplifying
% 242.38/48.96  | |              with (54), (69) gives:
% 242.38/48.96  | |   (71)  all_42_1 = all_8_1
% 242.38/48.96  | | 
% 242.38/48.96  | | GROUND_INST: instantiating (53) with e2, all_42_1, e3, e2, simplifying with
% 242.38/48.96  | |              (31), (69) gives:
% 242.38/48.96  | |   (72)  all_42_1 = e2
% 242.38/48.96  | | 
% 242.38/48.96  | | COMBINE_EQS: (71), (72) imply:
% 242.38/48.96  | |   (73)  all_8_1 = e2
% 242.38/48.96  | | 
% 242.38/48.96  | | COMBINE_EQS: (70), (71) imply:
% 242.38/48.96  | |   (74)  all_8_1 = e1
% 242.38/48.96  | | 
% 242.38/48.96  | | COMBINE_EQS: (73), (74) imply:
% 242.38/48.96  | |   (75)  e2 = e1
% 242.38/48.96  | | 
% 242.38/48.96  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.38/48.96  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 242.38/48.96  | |            (24), (25), (26), (27), (28), (29), (30), (32), (34), (35), (36),
% 242.38/48.96  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 242.38/48.96  | |            (48), (49), (50), (51), (52), (53), (55), (56), (57), (58), (59),
% 242.38/48.96  | |            (60), (61), (62), (63), (64), (65), (66), (67), (75) are
% 242.38/48.96  | |            inconsistent by sub-proof #773.
% 242.38/48.96  | | 
% 242.38/48.96  | Case 2:
% 242.38/48.96  | | 
% 242.38/48.96  | |   (76)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 242.38/48.96  | | 
% 242.38/48.96  | | ALPHA: (76) implies:
% 242.38/48.96  | |   (77)   ~ (all_42_1 = e1)
% 242.38/48.96  | |   (78)  op(e2, e3) = all_42_1
% 242.38/48.96  | | 
% 242.38/48.96  | | REF_CLOSE: (33), (53), (54), (77), (78) are inconsistent by sub-proof #935.
% 242.38/48.96  | | 
% 242.38/48.96  | End of split
% 242.38/48.96  | 
% 242.38/48.96  End of proof
% 242.38/48.96  
% 242.38/48.96  Sub-proof #771 shows that the following formulas are inconsistent:
% 242.38/48.96  ----------------------------------------------------------------
% 242.38/48.96    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.38/48.96           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.38/48.96           all_12_1 & $i(all_12_1))
% 242.38/48.96    (2)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 242.38/48.96         $i(all_56_9)
% 242.38/48.96    (3)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 242.38/48.96           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 242.38/48.96           all_26_1 & $i(all_26_1))
% 242.38/48.96    (4)  op(e3, e2) = e2
% 242.38/48.96    (5)  op(e0, e3) = e2
% 242.38/48.96    (6)   ~ (all_52_4 = e3)
% 242.38/48.96    (7)  op(e3, e2) = all_52_4
% 242.38/48.96    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.38/48.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.38/48.96  
% 242.38/48.96  Begin of proof
% 242.38/48.96  | 
% 242.38/48.96  | ALPHA: (2) implies:
% 242.38/48.96  |   (9)  op(e3, e2) = all_56_9
% 242.38/48.96  |   (10)  op(e3, all_56_9) = e3
% 242.38/48.96  | 
% 242.38/48.96  | BETA: splitting (1) gives:
% 242.38/48.96  | 
% 242.38/48.96  | Case 1:
% 242.38/48.96  | | 
% 242.38/48.96  | | 
% 242.38/48.96  | | GROUND_INST: instantiating (8) with e2, all_56_9, e2, e3, simplifying with
% 242.38/48.96  | |              (4), (9) gives:
% 242.38/48.96  | |   (11)  all_56_9 = e2
% 242.38/48.96  | | 
% 242.38/48.96  | | REDUCE: (10), (11) imply:
% 242.38/48.96  | |   (12)  op(e3, e2) = e3
% 242.38/48.96  | | 
% 242.38/48.96  | | REF_CLOSE: (6), (7), (8), (12) are inconsistent by sub-proof #2192.
% 242.38/48.96  | | 
% 242.38/48.96  | Case 2:
% 242.38/48.96  | | 
% 242.38/48.96  | |   (13)   ~ (all_12_1 = e2) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 242.38/48.96  | | 
% 242.38/48.96  | | ALPHA: (13) implies:
% 242.38/48.96  | |   (14)   ~ (all_12_1 = e2)
% 242.38/48.96  | |   (15)  op(e0, e3) = all_12_1
% 242.38/48.96  | | 
% 242.38/48.96  | | REF_CLOSE: (3), (5), (8), (14), (15) are inconsistent by sub-proof #1300.
% 242.38/48.96  | | 
% 242.38/48.96  | End of split
% 242.38/48.96  | 
% 242.38/48.96  End of proof
% 242.38/48.96  
% 242.38/48.96  Sub-proof #772 shows that the following formulas are inconsistent:
% 242.38/48.96  ----------------------------------------------------------------
% 242.38/48.96    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.38/48.96         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.38/48.96    (2)  all_58_12 = e2
% 242.38/48.96    (3)   ~ (all_52_7 = e3)
% 242.38/48.96    (4)  all_58_15 = e3
% 242.38/48.96    (5)   ~ (e3 = e1)
% 242.38/48.96    (6)  all_58_3 = e3
% 242.38/48.96    (7)   ~ (e3 = e2)
% 242.38/48.96    (8)  op(e0, e2) = all_52_7
% 242.38/48.96    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.38/48.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.38/48.96    (10)  all_58_3 = e1 & op(e2, e2) = e1
% 242.38/48.96    (11)  all_58_14 = e1
% 242.38/48.96  
% 242.38/48.96  Begin of proof
% 242.38/48.96  | 
% 242.38/48.96  | ALPHA: (10) implies:
% 242.38/48.96  |   (12)  all_58_3 = e1
% 242.38/48.96  | 
% 242.38/48.96  | COMBINE_EQS: (6), (12) imply:
% 242.38/48.96  |   (13)  e3 = e1
% 242.38/48.96  | 
% 242.38/48.96  | COMBINE_EQS: (4), (13) imply:
% 242.38/48.96  |   (14)  all_58_15 = e1
% 242.38/48.96  | 
% 242.38/48.96  | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (14) are inconsistent by
% 242.38/48.96  |            sub-proof #1814.
% 242.38/48.96  | 
% 242.38/48.96  End of proof
% 242.38/48.96  
% 242.38/48.96  Sub-proof #773 shows that the following formulas are inconsistent:
% 242.38/48.96  ----------------------------------------------------------------
% 242.38/48.96    (1)  op(e2, e2) = e3
% 242.38/48.96    (2)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.38/48.96           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.38/48.96           all_12_1 & $i(all_12_1))
% 242.38/48.96    (3)  all_56_21 = e2
% 242.38/48.96    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.38/48.96         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.38/48.96    (5)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.38/48.96           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.38/48.96           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.38/48.96           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.38/48.96           & $i(all_56_23))
% 242.38/48.96    (6)   ~ (e3 = e0)
% 242.38/48.96    (7)  op(e0, e1) = all_52_11
% 242.38/48.96    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.38/48.96         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.38/48.96    (9)  all_58_6 = e3
% 242.38/48.96    (10)   ~ (e2 = e0)
% 242.38/48.96    (11)  op(e1, e2) = all_52_6
% 242.38/48.96    (12)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.38/48.96          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.38/48.96    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.38/48.96              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.38/48.96            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.38/48.96            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.38/48.96            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.38/48.96             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.38/48.96            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.38/48.96            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.38/48.96            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.38/48.96            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.38/48.96            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.38/48.96              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.38/48.96            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.38/48.96            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.38/48.96            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.38/48.96            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.38/48.96            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.38/48.96            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.38/48.96              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.38/48.96            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.38/48.96            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.38/48.96            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.38/48.96            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.38/48.96            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.38/48.96            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.38/48.96              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.38/48.96            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.38/48.96            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.38/48.96    (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.38/48.96          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.38/48.96    (15)   ~ (all_52_12 = e0)
% 242.38/48.96    (16)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.38/48.96          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.38/48.96    (17)  op(e1, e0) = all_52_14
% 242.38/48.96    (18)  all_58_15 = e3
% 242.38/48.96    (19)  op(e0, e3) = all_52_3
% 242.38/48.96    (20)   ~ (e3 = e1)
% 242.38/48.96    (21)  all_58_8 = e2
% 242.38/48.96    (22)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.38/48.96          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.38/48.96    (23)  op(e0, all_52_3) = e0
% 242.38/48.96    (24)  all_58_3 = e3
% 242.38/48.96    (25)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.38/48.96            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.38/48.96              e3) = all_26_1 & $i(all_26_1))
% 242.38/48.96    (26)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.38/48.96              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.38/48.96                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.38/48.96                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.38/48.96    (27)   ~ (all_52_14 = e2)
% 242.38/48.96    (28)  op(e2, e1) = all_52_9
% 242.38/48.96    (29)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.38/48.96          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.38/48.96    (30)   ~ (e3 = e2)
% 242.38/48.96    (31)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.38/48.96            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.38/48.96            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.38/48.96            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.38/48.96            op(e0, all_56_31) = e0)
% 242.38/48.96    (32)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 242.38/48.96            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 242.38/48.96              e0) = all_16_1 & $i(all_16_1))
% 242.38/48.96    (33)  op(e3, e0) = all_52_12
% 242.38/48.96    (34)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.38/48.96            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.38/48.96              e3) = all_42_1 & $i(all_42_1))
% 242.38/48.96    (35)  op(e2, e3) = all_52_1
% 242.38/48.96    (36)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.38/48.96          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.38/48.96    (37)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 242.38/48.96            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 242.38/48.96              e0) = all_50_1 & $i(all_50_1))
% 242.38/48.96    (38)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 242.38/48.96            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 242.38/48.96              e2) = all_40_1 & $i(all_40_1))
% 242.38/48.96    (39)  op(e1, e1) = e2
% 242.38/48.96    (40)  op(e0, e2) = all_52_7
% 242.38/48.96    (41)   ~ (all_52_13 = all_52_14)
% 242.38/48.96    (42)   ~ (all_52_4 = e3)
% 242.38/48.96    (43)  op(e3, e2) = all_52_4
% 242.38/48.96    (44)  all_58_1 = e2
% 242.38/48.96    (45)   ~ (all_52_9 = e3)
% 242.38/48.96    (46)  all_56_31 = e3
% 242.38/48.96    (47)  op(e0, e0) = e3
% 242.38/48.96    (48)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.38/48.96          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.38/48.96    (49)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.38/48.96          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.38/48.96    (50)  e2 = e1
% 242.38/48.96    (51)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.38/48.96          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.38/48.96    (52)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.38/48.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.38/48.96    (53)   ~ (all_52_12 = e3)
% 242.38/48.96    (54)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.38/48.96            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.38/48.96              e2) = all_36_1 & $i(all_36_1))
% 242.38/48.96    (55)   ~ (e1 = e0)
% 242.38/48.96    (56)  op(e3, e3) = e0
% 242.38/48.96    (57)  all_58_4 = e3
% 242.38/48.96    (58)   ~ (all_52_13 = e3)
% 242.38/48.96    (59)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.38/48.96          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.38/48.96    (60)  all_56_1 = e0
% 242.38/48.96    (61)  op(e2, e0) = all_52_13
% 242.38/48.97    (62)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.38/48.97          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.38/48.97            e1)
% 242.38/48.97    (63)   ~ (all_52_1 = e3)
% 242.38/48.97    (64)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.38/48.97            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.38/48.97            & $i(all_8_1))
% 242.38/48.97    (65)   ~ (e2 = e1)
% 242.38/48.97  
% 242.38/48.97  Begin of proof
% 242.38/48.97  | 
% 242.38/48.97  | SIMP: (50) implies:
% 242.38/48.97  |   (66)  e2 = e1
% 242.38/48.97  | 
% 242.38/48.97  | COMBINE_EQS: (44), (66) imply:
% 242.38/48.97  |   (67)  all_58_1 = e1
% 242.38/48.97  | 
% 242.38/48.97  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.38/48.97  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 242.38/48.97  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 242.38/48.97  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (45), (46),
% 242.38/48.97  |            (47), (48), (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 242.38/48.97  |            (59), (60), (61), (62), (63), (64), (65), (67) are inconsistent by
% 242.38/48.97  |            sub-proof #774.
% 242.38/48.97  | 
% 242.38/48.97  End of proof
% 242.38/48.97  
% 242.38/48.97  Sub-proof #774 shows that the following formulas are inconsistent:
% 242.38/48.97  ----------------------------------------------------------------
% 242.38/48.97    (1)  op(e2, e2) = e3
% 242.38/48.97    (2)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.38/48.97           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.38/48.97           all_12_1 & $i(all_12_1))
% 242.38/48.97    (3)  all_56_21 = e2
% 242.38/48.97    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.38/48.97         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.38/48.97    (5)  all_58_1 = e1
% 242.38/48.97    (6)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.38/48.97           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.38/48.97           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.38/48.97           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.38/48.97           & $i(all_56_23))
% 242.38/48.97    (7)   ~ (e3 = e0)
% 242.38/48.97    (8)  op(e0, e1) = all_52_11
% 242.38/48.97    (9)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.38/48.97         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.38/48.97    (10)  all_58_6 = e3
% 242.38/48.97    (11)   ~ (e2 = e0)
% 242.38/48.97    (12)  op(e1, e2) = all_52_6
% 242.38/48.97    (13)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.38/48.97          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.38/48.97    (14)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.38/48.97              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.38/48.97            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.38/48.97            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.38/48.97            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.38/48.97             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.38/48.97            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.38/48.97            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.38/48.97            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.38/48.97            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.38/48.97            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.38/48.97              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.38/48.97            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.38/48.97            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.38/48.97            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.38/48.97            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.38/48.97            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.38/48.97            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.38/48.97              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.38/48.97            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.38/48.97            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.38/48.97            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.38/48.97            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.38/48.97            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.38/48.97            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.38/48.97              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.38/48.97            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.38/48.97            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.38/48.97    (15)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.38/48.97          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.38/48.97    (16)   ~ (all_52_12 = e0)
% 242.38/48.97    (17)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.38/48.97          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.38/48.97    (18)  op(e1, e0) = all_52_14
% 242.38/48.97    (19)  all_58_15 = e3
% 242.38/48.97    (20)  op(e0, e3) = all_52_3
% 242.38/48.97    (21)   ~ (e3 = e1)
% 242.38/48.97    (22)  all_58_8 = e2
% 242.38/48.97    (23)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.38/48.97          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.38/48.97    (24)  op(e0, all_52_3) = e0
% 242.38/48.97    (25)  all_58_3 = e3
% 242.38/48.97    (26)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.38/48.97            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.38/48.97              e3) = all_26_1 & $i(all_26_1))
% 242.38/48.97    (27)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.38/48.97              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.38/48.97                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.38/48.97                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.38/48.97    (28)   ~ (all_52_14 = e2)
% 242.38/48.97    (29)  op(e2, e1) = all_52_9
% 242.38/48.97    (30)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.38/48.97          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.38/48.97    (31)   ~ (e3 = e2)
% 242.38/48.97    (32)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.38/48.97            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.38/48.97            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.38/48.97            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.38/48.97            op(e0, all_56_31) = e0)
% 242.38/48.97    (33)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 242.38/48.97            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 242.38/48.97              e0) = all_16_1 & $i(all_16_1))
% 242.38/48.97    (34)  op(e3, e0) = all_52_12
% 242.38/48.97    (35)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.38/48.97            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.38/48.97              e3) = all_42_1 & $i(all_42_1))
% 242.38/48.97    (36)  op(e2, e3) = all_52_1
% 242.38/48.97    (37)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.38/48.97          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.38/48.97    (38)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 242.38/48.97            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 242.38/48.97              e0) = all_50_1 & $i(all_50_1))
% 242.38/48.97    (39)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 242.38/48.97            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 242.38/48.97              e2) = all_40_1 & $i(all_40_1))
% 242.38/48.97    (40)  op(e1, e1) = e2
% 242.38/48.97    (41)  op(e0, e2) = all_52_7
% 242.38/48.97    (42)   ~ (all_52_13 = all_52_14)
% 242.38/48.97    (43)   ~ (all_52_4 = e3)
% 242.38/48.97    (44)  op(e3, e2) = all_52_4
% 242.38/48.97    (45)   ~ (all_52_9 = e3)
% 242.38/48.97    (46)  all_56_31 = e3
% 242.38/48.97    (47)  op(e0, e0) = e3
% 242.38/48.97    (48)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.38/48.97          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.38/48.97    (49)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.38/48.97          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.38/48.97    (50)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.38/48.97          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.38/48.97    (51)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.38/48.97            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.38/48.97    (52)   ~ (all_52_12 = e3)
% 242.38/48.97    (53)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.38/48.97            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.38/48.97              e2) = all_36_1 & $i(all_36_1))
% 242.38/48.97    (54)   ~ (e1 = e0)
% 242.38/48.97    (55)  op(e3, e3) = e0
% 242.38/48.97    (56)  all_58_4 = e3
% 242.38/48.97    (57)   ~ (all_52_13 = e3)
% 242.38/48.97    (58)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.38/48.97          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.38/48.97    (59)  all_56_1 = e0
% 242.38/48.97    (60)  op(e2, e0) = all_52_13
% 242.38/48.97    (61)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.38/48.97          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.38/48.97            e1)
% 242.38/48.97    (62)   ~ (all_52_1 = e3)
% 242.38/48.97    (63)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.38/48.97            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.38/48.97            & $i(all_8_1))
% 242.38/48.97    (64)   ~ (e2 = e1)
% 242.38/48.97  
% 242.38/48.97  Begin of proof
% 242.38/48.97  | 
% 242.38/48.97  | BETA: splitting (13) gives:
% 242.38/48.97  | 
% 242.38/48.97  | Case 1:
% 242.38/48.97  | | 
% 242.38/48.97  | |   (65)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 242.38/48.97  | |           e2)
% 242.38/48.97  | | 
% 242.38/48.97  | | REF_CLOSE: (1), (5), (31), (51), (64), (65) are inconsistent by sub-proof
% 242.38/48.97  | |            #1721.
% 242.38/48.97  | | 
% 242.38/48.97  | Case 2:
% 242.38/48.97  | | 
% 242.38/48.97  | |   (66)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 242.38/48.97  | |           e2)
% 242.38/48.97  | | 
% 242.38/48.97  | | BETA: splitting (66) gives:
% 242.38/48.97  | | 
% 242.38/48.97  | | Case 1:
% 242.38/48.97  | | | 
% 242.38/48.97  | | |   (67)  all_58_7 = e2 & op(e1, e2) = e2
% 242.38/48.97  | | | 
% 242.38/48.97  | | | ALPHA: (67) implies:
% 242.38/48.97  | | |   (68)  all_58_7 = e2
% 242.38/48.97  | | | 
% 242.38/48.97  | | | REF_CLOSE: (7), (9), (10), (11), (21), (22), (40), (51), (54), (58), (64),
% 242.38/48.97  | | |            (68) are inconsistent by sub-proof #1801.
% 242.38/48.97  | | | 
% 242.38/48.97  | | Case 2:
% 242.38/48.97  | | | 
% 242.38/48.97  | | |   (69)  all_58_13 = e2 & op(e0, e2) = e2
% 242.38/48.97  | | | 
% 242.38/48.97  | | | ALPHA: (69) implies:
% 242.38/48.97  | | |   (70)  all_58_13 = e2
% 242.38/48.97  | | |   (71)  op(e0, e2) = e2
% 242.38/48.97  | | | 
% 242.38/48.97  | | | BETA: splitting (4) gives:
% 242.38/48.97  | | | 
% 242.38/48.97  | | | Case 1:
% 242.38/48.97  | | | | 
% 242.38/48.97  | | | |   (72)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 242.38/48.97  | | | |           = e2)
% 242.38/48.97  | | | | 
% 242.38/48.97  | | | | REF_CLOSE: (5), (11), (51), (55), (64), (72) are inconsistent by
% 242.38/48.97  | | | |            sub-proof #785.
% 242.38/48.97  | | | | 
% 242.38/48.97  | | | Case 2:
% 242.38/48.97  | | | | 
% 242.38/48.97  | | | |   (73)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 242.38/48.97  | | | |           = e2)
% 242.38/48.97  | | | | 
% 242.38/48.97  | | | | BETA: splitting (73) gives:
% 242.38/48.97  | | | | 
% 242.38/48.97  | | | | Case 1:
% 242.38/48.97  | | | | | 
% 242.38/48.97  | | | | |   (74)  all_58_4 = e2 & op(e3, e1) = e2
% 242.38/48.97  | | | | | 
% 242.38/48.97  | | | | | REF_CLOSE: (31), (56), (74) are inconsistent by sub-proof #1476.
% 242.38/48.97  | | | | | 
% 242.38/48.97  | | | | Case 2:
% 242.38/48.97  | | | | | 
% 242.38/48.97  | | | | |   (75)  all_58_9 = e2 & op(e3, e0) = e2
% 242.38/48.97  | | | | | 
% 242.38/48.97  | | | | | ALPHA: (75) implies:
% 242.38/48.97  | | | | |   (76)  all_58_9 = e2
% 242.38/48.97  | | | | |   (77)  op(e3, e0) = e2
% 242.38/48.97  | | | | | 
% 242.38/48.97  | | | | | BETA: splitting (27) gives:
% 242.38/48.97  | | | | | 
% 242.38/48.97  | | | | | Case 1:
% 242.38/48.97  | | | | | | 
% 242.38/48.97  | | | | | |   (78)  all_58_15 = e0 & op(e0, e0) = e0
% 242.38/48.97  | | | | | | 
% 242.38/48.97  | | | | | | ALPHA: (78) implies:
% 242.38/48.97  | | | | | |   (79)  op(e0, e0) = e0
% 242.38/48.97  | | | | | | 
% 242.38/48.97  | | | | | | REF_CLOSE: (7), (47), (51), (79) are inconsistent by sub-proof
% 242.38/48.97  | | | | | |            #2079.
% 242.38/48.97  | | | | | | 
% 242.38/48.97  | | | | | Case 2:
% 242.38/48.97  | | | | | | 
% 242.38/48.97  | | | | | |   (80)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 242.38/48.97  | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 242.38/48.97  | | | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.38/48.97  | | | | | |             op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.38/48.97  | | | | | | 
% 242.38/48.97  | | | | | | ALPHA: (80) implies:
% 242.38/48.97  | | | | | |   (81)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.38/48.97  | | | | | |           op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.38/48.97  | | | | | |   (82)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 242.38/48.97  | | | | | |             e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.38/48.97  | | | | | | 
% 242.38/48.97  | | | | | | BETA: splitting (15) gives:
% 242.38/48.97  | | | | | | 
% 242.38/48.97  | | | | | | Case 1:
% 242.38/48.97  | | | | | | | 
% 242.38/48.97  | | | | | | |   (83)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 242.38/48.97  | | | | | | |           op(e2, e2) = e0)
% 242.38/48.97  | | | | | | | 
% 242.38/48.97  | | | | | | | REF_CLOSE: (7), (21), (25), (48), (51), (54), (55), (56), (64),
% 242.38/48.97  | | | | | | |            (76), (83) are inconsistent by sub-proof #784.
% 242.38/48.97  | | | | | | | 
% 242.38/48.97  | | | | | | Case 2:
% 242.38/48.97  | | | | | | | 
% 242.38/48.97  | | | | | | |   (84)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 242.38/48.97  | | | | | | |           op(e0, e2) = e0)
% 242.38/48.97  | | | | | | | 
% 242.38/48.97  | | | | | | | BETA: splitting (84) gives:
% 242.38/48.97  | | | | | | | 
% 242.38/48.97  | | | | | | | Case 1:
% 242.38/48.97  | | | | | | | | 
% 242.38/48.97  | | | | | | | |   (85)  all_58_7 = e0 & op(e1, e2) = e0
% 242.38/48.97  | | | | | | | | 
% 242.38/48.97  | | | | | | | | ALPHA: (85) implies:
% 242.38/48.97  | | | | | | | |   (86)  all_58_7 = e0
% 242.38/48.97  | | | | | | | |   (87)  op(e1, e2) = e0
% 242.38/48.97  | | | | | | | | 
% 242.38/48.97  | | | | | | | | BETA: splitting (9) gives:
% 242.38/48.97  | | | | | | | | 
% 242.38/48.97  | | | | | | | | Case 1:
% 242.38/48.97  | | | | | | | | | 
% 242.38/48.97  | | | | | | | | |   (88)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 242.38/48.97  | | | | | | | | |           op(e1, e2) = e1)
% 242.38/48.97  | | | | | | | | | 
% 242.38/48.97  | | | | | | | | | REF_CLOSE: (10), (12), (21), (51), (54), (87), (88) are
% 242.38/48.97  | | | | | | | | |            inconsistent by sub-proof #1019.
% 242.38/48.97  | | | | | | | | | 
% 242.38/48.97  | | | | | | | | Case 2:
% 242.38/48.97  | | | | | | | | | 
% 242.38/48.97  | | | | | | | | |   (89)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 242.38/48.97  | | | | | | | | |           op(e1, e0) = e1)
% 242.38/48.97  | | | | | | | | | 
% 242.38/48.97  | | | | | | | | | BETA: splitting (89) gives:
% 242.38/48.97  | | | | | | | | | 
% 242.38/48.97  | | | | | | | | | Case 1:
% 242.38/48.97  | | | | | | | | | | 
% 242.38/48.97  | | | | | | | | | |   (90)  all_58_8 = e1 & op(e1, e1) = e1
% 242.38/48.97  | | | | | | | | | | 
% 242.38/48.97  | | | | | | | | | | ALPHA: (90) implies:
% 242.38/48.98  | | | | | | | | | |   (91)  all_58_8 = e1
% 242.38/48.98  | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | REF_CLOSE: (22), (64), (91) are inconsistent by sub-proof
% 242.38/48.98  | | | | | | | | | |            #1802.
% 242.38/48.98  | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | Case 2:
% 242.38/48.98  | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | |   (92)  all_58_11 = e1 & op(e1, e0) = e1
% 242.38/48.98  | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | ALPHA: (92) implies:
% 242.38/48.98  | | | | | | | | | |   (93)  all_58_11 = e1
% 242.38/48.98  | | | | | | | | | |   (94)  op(e1, e0) = e1
% 242.38/48.98  | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | BETA: splitting (81) gives:
% 242.38/48.98  | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | Case 1:
% 242.38/48.98  | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | |   (95)  all_58_12 = e0 & op(e0, e3) = e0
% 242.38/48.98  | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | ALPHA: (95) implies:
% 242.38/48.98  | | | | | | | | | | |   (96)  all_58_12 = e0
% 242.38/48.98  | | | | | | | | | | |   (97)  op(e0, e3) = e0
% 242.38/48.98  | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | REF_CLOSE: (7), (11), (19), (20), (21), (23), (24), (27),
% 242.38/48.98  | | | | | | | | | | |            (29), (40), (45), (47), (51), (54), (56), (61),
% 242.38/48.98  | | | | | | | | | | |            (64), (70), (96), (97) are inconsistent by
% 242.38/48.98  | | | | | | | | | | |            sub-proof #811.
% 242.38/48.98  | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | Case 2:
% 242.38/48.98  | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | |   (98)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 242.38/48.98  | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 242.38/48.98  | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | BETA: splitting (98) gives:
% 242.38/48.98  | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | Case 1:
% 242.38/48.98  | | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | |   (99)  all_58_13 = e0 & op(e0, e2) = e0
% 242.38/48.98  | | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | | ALPHA: (99) implies:
% 242.38/48.98  | | | | | | | | | | | |   (100)  op(e0, e2) = e0
% 242.38/48.98  | | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | | REF_CLOSE: (11), (51), (71), (100) are inconsistent by
% 242.38/48.98  | | | | | | | | | | | |            sub-proof #2132.
% 242.38/48.98  | | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | Case 2:
% 242.38/48.98  | | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | |   (101)  all_58_14 = e0 & op(e0, e1) = e0
% 242.38/48.98  | | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | | ALPHA: (101) implies:
% 242.38/48.98  | | | | | | | | | | | |   (102)  op(e0, e1) = e0
% 242.38/48.98  | | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (11), (12),
% 242.38/48.98  | | | | | | | | | | | |            (14), (16), (17), (18), (19), (20), (21), (22),
% 242.38/48.98  | | | | | | | | | | | |            (25), (26), (28), (29), (30), (31), (32), (33),
% 242.38/48.98  | | | | | | | | | | | |            (34), (35), (36), (37), (38), (39), (41), (42),
% 242.38/48.98  | | | | | | | | | | | |            (43), (44), (46), (47), (48), (49), (50), (51),
% 242.38/48.98  | | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 242.38/48.98  | | | | | | | | | | | |            (60), (61), (62), (63), (64), (70), (71), (76),
% 242.38/48.98  | | | | | | | | | | | |            (77), (82), (86), (87), (93), (94), (102) are
% 242.38/48.98  | | | | | | | | | | | |            inconsistent by sub-proof #777.
% 242.38/48.98  | | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | | End of split
% 242.38/48.98  | | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | | End of split
% 242.38/48.98  | | | | | | | | | | 
% 242.38/48.98  | | | | | | | | | End of split
% 242.38/48.98  | | | | | | | | | 
% 242.38/48.98  | | | | | | | | End of split
% 242.38/48.98  | | | | | | | | 
% 242.38/48.98  | | | | | | | Case 2:
% 242.38/48.98  | | | | | | | | 
% 242.38/48.98  | | | | | | | |   (103)  all_58_13 = e0 & op(e0, e2) = e0
% 242.38/48.98  | | | | | | | | 
% 242.38/48.98  | | | | | | | | ALPHA: (103) implies:
% 242.38/48.98  | | | | | | | |   (104)  op(e0, e2) = e0
% 242.38/48.98  | | | | | | | | 
% 242.38/48.98  | | | | | | | | REF_CLOSE: (11), (51), (71), (104) are inconsistent by sub-proof
% 242.38/48.98  | | | | | | | |            #2132.
% 242.38/48.98  | | | | | | | | 
% 242.38/48.98  | | | | | | | End of split
% 242.38/48.98  | | | | | | | 
% 242.38/48.98  | | | | | | End of split
% 242.38/48.98  | | | | | | 
% 242.38/48.98  | | | | | End of split
% 242.38/48.98  | | | | | 
% 242.38/48.98  | | | | End of split
% 242.38/48.98  | | | | 
% 242.38/48.98  | | | End of split
% 242.38/48.98  | | | 
% 242.38/48.98  | | End of split
% 242.38/48.98  | | 
% 242.38/48.98  | End of split
% 242.38/48.98  | 
% 242.38/48.98  End of proof
% 242.38/48.98  
% 242.38/48.98  Sub-proof #775 shows that the following formulas are inconsistent:
% 242.38/48.98  ----------------------------------------------------------------
% 242.38/48.98    (1)   ~ (e3 = e0)
% 242.38/48.98    (2)   ~ (e2 = e0)
% 242.38/48.98    (3)  all_58_8 = e2
% 242.38/48.98    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.38/48.98         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.38/48.98    (5)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.38/48.98    (6)  op(e2, e0) = e2
% 242.38/48.98    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.38/48.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.38/48.98    (8)   ~ (e1 = e0)
% 242.38/48.98    (9)  all_58_4 = e3
% 242.38/48.98    (10)  all_58_14 = e1
% 242.38/48.98    (11)   ~ (e2 = e1)
% 242.38/48.98  
% 242.38/48.98  Begin of proof
% 242.38/48.98  | 
% 242.38/48.98  | BETA: splitting (5) gives:
% 242.38/48.98  | 
% 242.38/48.98  | Case 1:
% 242.38/48.98  | | 
% 242.38/48.98  | |   (12)  all_58_5 = e1 & op(e2, e1) = e1
% 242.38/48.98  | | 
% 242.38/48.98  | | ALPHA: (12) implies:
% 242.38/48.98  | |   (13)  all_58_5 = e1
% 242.38/48.98  | | 
% 242.38/48.98  | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (13) are inconsistent by
% 242.38/48.98  | |            sub-proof #1482.
% 242.38/48.98  | | 
% 242.38/48.98  | Case 2:
% 242.38/48.98  | | 
% 242.38/48.98  | |   (14)  all_58_10 = e1 & op(e2, e0) = e1
% 242.38/48.98  | | 
% 242.38/48.98  | | ALPHA: (14) implies:
% 242.38/48.98  | |   (15)  op(e2, e0) = e1
% 242.38/48.98  | | 
% 242.38/48.98  | | REF_CLOSE: (6), (7), (11), (15) are inconsistent by sub-proof #1659.
% 242.38/48.98  | | 
% 242.38/48.98  | End of split
% 242.38/48.98  | 
% 242.38/48.98  End of proof
% 242.38/48.98  
% 242.38/48.98  Sub-proof #776 shows that the following formulas are inconsistent:
% 242.38/48.98  ----------------------------------------------------------------
% 242.38/48.98    (1)   ~ (all_52_3 = e0)
% 242.38/48.98    (2)  op(e2, e2) = e3
% 242.38/48.98    (3)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.38/48.98           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.38/48.98           all_12_1 & $i(all_12_1))
% 242.38/48.98    (4)  all_56_21 = e2
% 242.38/48.98    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.38/48.98         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.38/48.98    (6)  all_58_1 = e1
% 242.38/48.98    (7)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.38/48.98           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.38/48.98           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.38/48.98           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.38/48.98           & $i(all_56_23))
% 242.38/48.98    (8)   ~ (e3 = e0)
% 242.38/48.98    (9)  op(e0, e1) = all_52_11
% 242.38/48.98    (10)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.38/48.98          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.38/48.98    (11)  all_58_6 = e3
% 242.38/48.98    (12)   ~ (e2 = e0)
% 242.38/48.98    (13)  op(e1, e2) = all_52_6
% 242.38/48.98    (14)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.38/48.98          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.38/48.98    (15)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.38/48.98              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.38/48.98            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.38/48.98            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.38/48.98            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.38/48.98             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.38/48.98            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.49/48.98            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.49/48.98            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.49/48.98            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.49/48.98            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.49/48.98              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.49/48.98            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.49/48.98            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.49/48.98            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.49/48.98            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.49/48.98            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.49/48.98            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.49/48.98              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.49/48.98            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.49/48.98            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.49/48.98            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.49/48.98            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.49/48.98            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.49/48.98            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.49/48.98              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.49/48.98            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.49/48.98            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.49/48.98    (16)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.49/48.98          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.49/48.98    (17)   ~ (all_52_12 = e0)
% 242.49/48.98    (18)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.49/48.98          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.49/48.98    (19)  op(e1, e0) = all_52_14
% 242.49/48.98    (20)  all_58_15 = e3
% 242.49/48.98    (21)  op(e0, e3) = all_52_3
% 242.49/48.98    (22)   ~ (e3 = e1)
% 242.49/48.98    (23)  all_58_8 = e2
% 242.49/48.98    (24)  all_58_3 = e3
% 242.49/48.98    (25)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.49/48.98            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.49/48.98              e3) = all_26_1 & $i(all_26_1))
% 242.49/48.98    (26)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.49/48.98              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.49/48.98                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.49/48.98                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.49/48.98    (27)   ~ (all_52_14 = e2)
% 242.49/48.98    (28)  op(e2, e1) = all_52_9
% 242.49/48.98    (29)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.49/48.98          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.49/48.98    (30)   ~ (e3 = e2)
% 242.49/48.98    (31)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.49/48.98            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.49/48.98            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.49/48.98            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.49/48.98            op(e0, all_56_31) = e0)
% 242.49/48.98    (32)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 242.49/48.98            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 242.49/48.98              e0) = all_16_1 & $i(all_16_1))
% 242.49/48.98    (33)  op(e3, e0) = all_52_12
% 242.49/48.98    (34)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.49/48.98            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.49/48.98              e3) = all_42_1 & $i(all_42_1))
% 242.49/48.98    (35)  op(e2, e3) = all_52_1
% 242.49/48.98    (36)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.49/48.98          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.49/48.98    (37)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 242.49/48.98            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 242.49/48.98              e0) = all_50_1 & $i(all_50_1))
% 242.49/48.98    (38)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 242.49/48.98            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 242.49/48.98              e2) = all_40_1 & $i(all_40_1))
% 242.49/48.98    (39)  op(e1, e1) = e2
% 242.49/48.98    (40)  op(e0, e2) = all_52_7
% 242.49/48.98    (41)   ~ (all_52_13 = all_52_14)
% 242.49/48.98    (42)   ~ (all_52_4 = e3)
% 242.49/48.98    (43)  op(e3, e2) = all_52_4
% 242.49/48.98    (44)  all_56_31 = e3
% 242.49/48.98    (45)  op(e0, e0) = e3
% 242.49/48.98    (46)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.49/48.98          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.49/48.98    (47)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.49/48.98          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.49/48.98    (48)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.49/48.98          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.49/48.98    (49)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.49/48.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.49/48.98    (50)   ~ (all_52_12 = e3)
% 242.49/48.98    (51)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.49/48.98            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.49/48.98              e2) = all_36_1 & $i(all_36_1))
% 242.49/48.98    (52)   ~ (e1 = e0)
% 242.49/48.98    (53)  op(e3, e3) = e0
% 242.49/48.98    (54)  all_58_4 = e3
% 242.49/48.98    (55)   ~ (all_52_13 = e3)
% 242.49/48.98    (56)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.49/48.98          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.49/48.98    (57)  all_56_1 = e0
% 242.49/48.98    (58)  op(e2, e0) = all_52_13
% 242.49/48.98    (59)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.49/48.98          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.49/48.98            e1)
% 242.49/48.98    (60)   ~ (all_52_1 = e3)
% 242.49/48.98    (61)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.49/48.98            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.49/48.98            & $i(all_8_1))
% 242.49/48.98    (62)   ~ (e2 = e1)
% 242.49/48.98  
% 242.49/48.98  Begin of proof
% 242.49/48.98  | 
% 242.49/48.98  | BETA: splitting (14) gives:
% 242.49/48.98  | 
% 242.49/48.98  | Case 1:
% 242.49/48.98  | | 
% 242.49/48.98  | |   (63)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 242.49/48.98  | |           e2)
% 242.49/48.98  | | 
% 242.49/48.98  | | REF_CLOSE: (2), (6), (30), (49), (62), (63) are inconsistent by sub-proof
% 242.49/48.98  | |            #1721.
% 242.49/48.98  | | 
% 242.49/48.98  | Case 2:
% 242.49/48.98  | | 
% 242.49/48.98  | |   (64)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 242.49/48.98  | |           e2)
% 242.49/48.98  | | 
% 242.49/48.98  | | BETA: splitting (64) gives:
% 242.49/48.98  | | 
% 242.49/48.98  | | Case 1:
% 242.49/48.98  | | | 
% 242.49/48.98  | | |   (65)  all_58_7 = e2 & op(e1, e2) = e2
% 242.49/48.98  | | | 
% 242.49/48.98  | | | ALPHA: (65) implies:
% 242.49/48.98  | | |   (66)  all_58_7 = e2
% 242.49/48.98  | | | 
% 242.49/48.98  | | | REF_CLOSE: (8), (10), (11), (12), (22), (23), (39), (49), (52), (56),
% 242.49/48.98  | | |            (62), (66) are inconsistent by sub-proof #1801.
% 242.49/48.98  | | | 
% 242.49/48.98  | | Case 2:
% 242.49/48.98  | | | 
% 242.49/48.98  | | |   (67)  all_58_13 = e2 & op(e0, e2) = e2
% 242.49/48.98  | | | 
% 242.49/48.98  | | | ALPHA: (67) implies:
% 242.49/48.98  | | |   (68)  all_58_13 = e2
% 242.49/48.98  | | |   (69)  op(e0, e2) = e2
% 242.49/48.98  | | | 
% 242.49/48.98  | | | BETA: splitting (5) gives:
% 242.49/48.98  | | | 
% 242.49/48.98  | | | Case 1:
% 242.49/48.98  | | | | 
% 242.49/48.98  | | | |   (70)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 242.49/48.98  | | | |           = e2)
% 242.49/48.98  | | | | 
% 242.49/48.98  | | | | REF_CLOSE: (6), (12), (49), (53), (62), (70) are inconsistent by
% 242.49/48.98  | | | |            sub-proof #785.
% 242.49/48.98  | | | | 
% 242.49/48.98  | | | Case 2:
% 242.49/48.98  | | | | 
% 242.49/48.99  | | | |   (71)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 242.49/48.99  | | | |           = e2)
% 242.49/48.99  | | | | 
% 242.49/48.99  | | | | BETA: splitting (71) gives:
% 242.49/48.99  | | | | 
% 242.49/48.99  | | | | Case 1:
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | |   (72)  all_58_4 = e2 & op(e3, e1) = e2
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | | REF_CLOSE: (30), (54), (72) are inconsistent by sub-proof #1476.
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | Case 2:
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | |   (73)  all_58_9 = e2 & op(e3, e0) = e2
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | | ALPHA: (73) implies:
% 242.49/48.99  | | | | |   (74)  all_58_9 = e2
% 242.49/48.99  | | | | |   (75)  op(e3, e0) = e2
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | | BETA: splitting (26) gives:
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | | Case 1:
% 242.49/48.99  | | | | | | 
% 242.49/48.99  | | | | | |   (76)  all_58_15 = e0 & op(e0, e0) = e0
% 242.49/48.99  | | | | | | 
% 242.49/48.99  | | | | | | ALPHA: (76) implies:
% 242.49/48.99  | | | | | |   (77)  op(e0, e0) = e0
% 242.49/48.99  | | | | | | 
% 242.49/48.99  | | | | | | REF_CLOSE: (8), (45), (49), (77) are inconsistent by sub-proof
% 242.49/48.99  | | | | | |            #2079.
% 242.49/48.99  | | | | | | 
% 242.49/48.99  | | | | | Case 2:
% 242.49/48.99  | | | | | | 
% 242.49/48.99  | | | | | |   (78)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 242.49/48.99  | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 242.49/48.99  | | | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.49/48.99  | | | | | |             op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.49/48.99  | | | | | | 
% 242.49/48.99  | | | | | | ALPHA: (78) implies:
% 242.49/48.99  | | | | | |   (79)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.49/48.99  | | | | | |           op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.49/48.99  | | | | | |   (80)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 242.49/48.99  | | | | | |             e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.49/48.99  | | | | | | 
% 242.49/48.99  | | | | | | BETA: splitting (16) gives:
% 242.49/48.99  | | | | | | 
% 242.49/48.99  | | | | | | Case 1:
% 242.49/48.99  | | | | | | | 
% 242.49/48.99  | | | | | | |   (81)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 242.49/48.99  | | | | | | |           op(e2, e2) = e0)
% 242.49/48.99  | | | | | | | 
% 242.49/48.99  | | | | | | | REF_CLOSE: (8), (22), (24), (46), (49), (52), (53), (54), (62),
% 242.49/48.99  | | | | | | |            (74), (81) are inconsistent by sub-proof #784.
% 242.49/48.99  | | | | | | | 
% 242.49/48.99  | | | | | | Case 2:
% 242.49/48.99  | | | | | | | 
% 242.49/48.99  | | | | | | |   (82)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 242.49/48.99  | | | | | | |           op(e0, e2) = e0)
% 242.49/48.99  | | | | | | | 
% 242.49/48.99  | | | | | | | BETA: splitting (82) gives:
% 242.49/48.99  | | | | | | | 
% 242.49/48.99  | | | | | | | Case 1:
% 242.49/48.99  | | | | | | | | 
% 242.49/48.99  | | | | | | | |   (83)  all_58_7 = e0 & op(e1, e2) = e0
% 242.49/48.99  | | | | | | | | 
% 242.49/48.99  | | | | | | | | ALPHA: (83) implies:
% 242.49/48.99  | | | | | | | |   (84)  all_58_7 = e0
% 242.49/48.99  | | | | | | | |   (85)  op(e1, e2) = e0
% 242.49/48.99  | | | | | | | | 
% 242.49/48.99  | | | | | | | | BETA: splitting (10) gives:
% 242.49/48.99  | | | | | | | | 
% 242.49/48.99  | | | | | | | | Case 1:
% 242.49/48.99  | | | | | | | | | 
% 242.49/48.99  | | | | | | | | |   (86)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 242.49/48.99  | | | | | | | | |           op(e1, e2) = e1)
% 242.49/48.99  | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | REF_CLOSE: (11), (13), (22), (49), (52), (85), (86) are
% 242.49/48.99  | | | | | | | | |            inconsistent by sub-proof #1019.
% 242.49/48.99  | | | | | | | | | 
% 242.49/48.99  | | | | | | | | Case 2:
% 242.49/48.99  | | | | | | | | | 
% 242.49/48.99  | | | | | | | | |   (87)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 242.49/48.99  | | | | | | | | |           op(e1, e0) = e1)
% 242.49/48.99  | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | BETA: splitting (87) gives:
% 242.49/48.99  | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | Case 1:
% 242.49/48.99  | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | |   (88)  all_58_8 = e1 & op(e1, e1) = e1
% 242.49/48.99  | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | ALPHA: (88) implies:
% 242.49/48.99  | | | | | | | | | |   (89)  all_58_8 = e1
% 242.49/48.99  | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | REF_CLOSE: (23), (62), (89) are inconsistent by sub-proof
% 242.49/48.99  | | | | | | | | | |            #1802.
% 242.49/48.99  | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | Case 2:
% 242.49/48.99  | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | |   (90)  all_58_11 = e1 & op(e1, e0) = e1
% 242.49/48.99  | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | ALPHA: (90) implies:
% 242.49/48.99  | | | | | | | | | |   (91)  all_58_11 = e1
% 242.49/48.99  | | | | | | | | | |   (92)  op(e1, e0) = e1
% 242.49/48.99  | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | BETA: splitting (79) gives:
% 242.49/48.99  | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | Case 1:
% 242.49/48.99  | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | |   (93)  all_58_12 = e0 & op(e0, e3) = e0
% 242.49/48.99  | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | ALPHA: (93) implies:
% 242.49/48.99  | | | | | | | | | | |   (94)  op(e0, e3) = e0
% 242.49/48.99  | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | REF_CLOSE: (1), (21), (49), (94) are inconsistent by
% 242.49/48.99  | | | | | | | | | | |            sub-proof #2331.
% 242.49/48.99  | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | Case 2:
% 242.49/48.99  | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | |   (95)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 242.49/48.99  | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 242.49/48.99  | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | BETA: splitting (95) gives:
% 242.49/48.99  | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | Case 1:
% 242.49/48.99  | | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | |   (96)  all_58_13 = e0 & op(e0, e2) = e0
% 242.49/48.99  | | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | | ALPHA: (96) implies:
% 242.49/48.99  | | | | | | | | | | | |   (97)  op(e0, e2) = e0
% 242.49/48.99  | | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | | REF_CLOSE: (12), (49), (69), (97) are inconsistent by
% 242.49/48.99  | | | | | | | | | | | |            sub-proof #2132.
% 242.49/48.99  | | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | Case 2:
% 242.49/48.99  | | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | |   (98)  all_58_14 = e0 & op(e0, e1) = e0
% 242.49/48.99  | | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | | ALPHA: (98) implies:
% 242.49/48.99  | | | | | | | | | | | |   (99)  op(e0, e1) = e0
% 242.49/48.99  | | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (11), (12), (13),
% 242.49/48.99  | | | | | | | | | | | |            (15), (17), (18), (19), (20), (21), (22), (23),
% 242.49/48.99  | | | | | | | | | | | |            (24), (25), (27), (28), (29), (30), (31), (32),
% 242.49/48.99  | | | | | | | | | | | |            (33), (34), (35), (36), (37), (38), (40), (41),
% 242.49/48.99  | | | | | | | | | | | |            (42), (43), (44), (45), (46), (47), (48), (49),
% 242.49/48.99  | | | | | | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57),
% 242.49/48.99  | | | | | | | | | | | |            (58), (59), (60), (61), (62), (68), (69), (74),
% 242.49/48.99  | | | | | | | | | | | |            (75), (80), (84), (85), (91), (92), (99) are
% 242.49/48.99  | | | | | | | | | | | |            inconsistent by sub-proof #777.
% 242.49/48.99  | | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | | End of split
% 242.49/48.99  | | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | | End of split
% 242.49/48.99  | | | | | | | | | | 
% 242.49/48.99  | | | | | | | | | End of split
% 242.49/48.99  | | | | | | | | | 
% 242.49/48.99  | | | | | | | | End of split
% 242.49/48.99  | | | | | | | | 
% 242.49/48.99  | | | | | | | Case 2:
% 242.49/48.99  | | | | | | | | 
% 242.49/48.99  | | | | | | | |   (100)  all_58_13 = e0 & op(e0, e2) = e0
% 242.49/48.99  | | | | | | | | 
% 242.49/48.99  | | | | | | | | ALPHA: (100) implies:
% 242.49/48.99  | | | | | | | |   (101)  op(e0, e2) = e0
% 242.49/48.99  | | | | | | | | 
% 242.49/48.99  | | | | | | | | REF_CLOSE: (12), (49), (69), (101) are inconsistent by sub-proof
% 242.49/48.99  | | | | | | | |            #2132.
% 242.49/48.99  | | | | | | | | 
% 242.49/48.99  | | | | | | | End of split
% 242.49/48.99  | | | | | | | 
% 242.49/48.99  | | | | | | End of split
% 242.49/48.99  | | | | | | 
% 242.49/48.99  | | | | | End of split
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | End of split
% 242.49/48.99  | | | | 
% 242.49/48.99  | | | End of split
% 242.49/48.99  | | | 
% 242.49/48.99  | | End of split
% 242.49/48.99  | | 
% 242.49/48.99  | End of split
% 242.49/48.99  | 
% 242.49/48.99  End of proof
% 242.49/48.99  
% 242.49/48.99  Sub-proof #777 shows that the following formulas are inconsistent:
% 242.49/48.99  ----------------------------------------------------------------
% 242.49/48.99    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.49/48.99           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.49/48.99           all_12_1 & $i(all_12_1))
% 242.49/48.99    (2)  all_56_21 = e2
% 242.49/48.99    (3)  all_58_1 = e1
% 242.49/48.99    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.49/48.99           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.49/48.99           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.49/48.99           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.49/48.99           & $i(all_56_23))
% 242.49/48.99    (5)   ~ (e3 = e0)
% 242.49/48.99    (6)  op(e0, e1) = all_52_11
% 242.49/48.99    (7)  all_58_6 = e3
% 242.49/48.99    (8)   ~ (e2 = e0)
% 242.49/48.99    (9)  all_58_7 = e0
% 242.49/48.99    (10)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.49/48.99          (all_58_11 = e0 & op(e1, e0) = e0)
% 242.49/48.99    (11)  op(e1, e2) = all_52_6
% 242.49/48.99    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.49/48.99              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.49/48.99            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.49/48.99            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.49/48.99            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.49/48.99             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.49/48.99            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.49/48.99            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.49/48.99            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.49/48.99            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.49/48.99            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.49/48.99              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.49/48.99            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.49/48.99            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.49/48.99            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.49/48.99            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.49/48.99            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.49/48.99            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.49/48.99              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.49/48.99            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.49/48.99            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.49/48.99            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.49/48.99            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.49/48.99            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.49/48.99            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.49/48.99              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.49/48.99            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.49/48.99            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.49/48.99    (13)   ~ (all_52_12 = e0)
% 242.49/48.99    (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.49/48.99          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.49/48.99    (15)  all_58_11 = e1
% 242.49/48.99    (16)  op(e1, e0) = all_52_14
% 242.49/48.99    (17)  all_58_15 = e3
% 242.49/48.99    (18)  op(e0, e3) = all_52_3
% 242.49/48.99    (19)  op(e0, e2) = e2
% 242.49/48.99    (20)   ~ (e3 = e1)
% 242.49/48.99    (21)  all_58_8 = e2
% 242.49/48.99    (22)  op(e1, e0) = e1
% 242.49/48.99    (23)  all_58_3 = e3
% 242.49/48.99    (24)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.49/48.99            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.49/48.99              e3) = all_26_1 & $i(all_26_1))
% 242.49/48.99    (25)   ~ (all_52_14 = e2)
% 242.49/48.99    (26)  op(e2, e1) = all_52_9
% 242.49/48.99    (27)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.49/48.99          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.49/48.99    (28)  op(e1, e2) = e0
% 242.49/48.99    (29)   ~ (e3 = e2)
% 242.49/48.99    (30)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.49/48.99            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.49/48.99            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.49/48.99            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.49/48.99            op(e0, all_56_31) = e0)
% 242.49/48.99    (31)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 242.49/48.99            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 242.49/48.99              e0) = all_16_1 & $i(all_16_1))
% 242.49/48.99    (32)  op(e3, e0) = all_52_12
% 242.49/48.99    (33)  op(e0, e1) = e0
% 242.49/48.99    (34)  all_58_13 = e2
% 242.49/48.99    (35)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.49/48.99            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.49/48.99              e3) = all_42_1 & $i(all_42_1))
% 242.49/48.99    (36)  op(e2, e3) = all_52_1
% 242.49/48.99    (37)  op(e3, e0) = e2
% 242.49/48.99    (38)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.49/48.99          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.49/48.99    (39)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 242.49/48.99            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 242.49/48.99              e0) = all_50_1 & $i(all_50_1))
% 242.49/48.99    (40)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 242.49/48.99            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 242.49/48.99              e2) = all_40_1 & $i(all_40_1))
% 242.49/48.99    (41)  op(e0, e2) = all_52_7
% 242.49/48.99    (42)   ~ (all_52_13 = all_52_14)
% 242.49/48.99    (43)   ~ (all_52_4 = e3)
% 242.49/48.99    (44)  op(e3, e2) = all_52_4
% 242.49/48.99    (45)  all_56_31 = e3
% 242.49/48.99    (46)  op(e0, e0) = e3
% 242.49/48.99    (47)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.49/48.99          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.49/48.99    (48)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.49/48.99          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.49/48.99    (49)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.49/48.99          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.49/48.99    (50)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.49/48.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.49/48.99    (51)   ~ (all_52_12 = e3)
% 242.49/48.99    (52)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 242.49/48.99            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 242.49/48.99              e2) = all_36_1 & $i(all_36_1))
% 242.49/48.99    (53)   ~ (e1 = e0)
% 242.49/48.99    (54)  op(e3, e3) = e0
% 242.49/48.99    (55)  all_58_4 = e3
% 242.49/48.99    (56)   ~ (all_52_13 = e3)
% 242.49/48.99    (57)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.49/48.99          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.49/48.99    (58)  all_56_1 = e0
% 242.49/48.99    (59)  op(e2, e0) = all_52_13
% 242.49/48.99    (60)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.49/48.99          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.49/48.99            e1)
% 242.49/48.99    (61)  all_58_9 = e2
% 242.49/48.99    (62)   ~ (all_52_1 = e3)
% 242.49/48.99    (63)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.49/48.99            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.49/48.99            & $i(all_8_1))
% 242.49/48.99    (64)   ~ (e2 = e1)
% 242.49/48.99  
% 242.49/48.99  Begin of proof
% 242.49/48.99  | 
% 242.49/48.99  | BETA: splitting (60) gives:
% 242.49/48.99  | 
% 242.49/48.99  | Case 1:
% 242.49/48.99  | | 
% 242.49/48.99  | |   (65)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 242.49/48.99  | |           e1)
% 242.49/48.99  | | 
% 242.49/48.99  | | BETA: splitting (65) gives:
% 242.49/48.99  | | 
% 242.49/48.99  | | Case 1:
% 242.49/48.99  | | | 
% 242.49/48.99  | | |   (66)  all_58_12 = e1 & op(e0, e3) = e1
% 242.49/48.99  | | | 
% 242.49/48.99  | | | ALPHA: (66) implies:
% 242.49/48.99  | | |   (67)  all_58_12 = e1
% 242.49/48.99  | | |   (68)  op(e0, e3) = e1
% 242.49/48.99  | | | 
% 242.49/48.99  | | | BETA: splitting (14) gives:
% 242.49/48.99  | | | 
% 242.49/48.99  | | | Case 1:
% 242.49/48.99  | | | | 
% 242.49/48.99  | | | |   (69)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 242.49/48.99  | | | |           = e1)
% 242.49/48.99  | | | | 
% 242.49/48.99  | | | | BETA: splitting (69) gives:
% 242.49/48.99  | | | | 
% 242.49/48.99  | | | | Case 1:
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | |   (70)  all_58_4 = e1 & op(e3, e1) = e1
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | | REF_CLOSE: (20), (55), (70) are inconsistent by sub-proof #2042.
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | Case 2:
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | |   (71)  all_58_5 = e1 & op(e2, e1) = e1
% 242.49/48.99  | | | | | 
% 242.49/48.99  | | | | | ALPHA: (71) implies:
% 242.49/49.00  | | | | |   (72)  all_58_5 = e1
% 242.49/49.00  | | | | |   (73)  op(e2, e1) = e1
% 242.49/49.00  | | | | | 
% 242.49/49.00  | | | | | BETA: splitting (27) gives:
% 242.49/49.00  | | | | | 
% 242.49/49.00  | | | | | Case 1:
% 242.49/49.00  | | | | | | 
% 242.49/49.00  | | | | | |   (74)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2,
% 242.49/49.00  | | | | | |             e3) = e2)
% 242.49/49.00  | | | | | | 
% 242.49/49.00  | | | | | | BETA: splitting (74) gives:
% 242.49/49.00  | | | | | | 
% 242.49/49.00  | | | | | | Case 1:
% 242.49/49.00  | | | | | | | 
% 242.49/49.00  | | | | | | |   (75)  all_58_0 = e2 & op(e3, e3) = e2
% 242.49/49.00  | | | | | | | 
% 242.49/49.00  | | | | | | | ALPHA: (75) implies:
% 242.49/49.00  | | | | | | |   (76)  op(e3, e3) = e2
% 242.49/49.00  | | | | | | | 
% 242.49/49.00  | | | | | | | REF_CLOSE: (5), (8), (20), (38), (47), (50), (53), (55), (61),
% 242.49/49.00  | | | | | | |            (64), (76) are inconsistent by sub-proof #1562.
% 242.49/49.00  | | | | | | | 
% 242.49/49.00  | | | | | | Case 2:
% 242.49/49.00  | | | | | | | 
% 242.49/49.00  | | | | | | |   (77)  all_58_2 = e2 & op(e2, e3) = e2
% 242.49/49.00  | | | | | | | 
% 242.49/49.00  | | | | | | | ALPHA: (77) implies:
% 242.49/49.00  | | | | | | |   (78)  all_58_2 = e2
% 242.49/49.00  | | | | | | |   (79)  op(e2, e3) = e2
% 242.49/49.00  | | | | | | | 
% 242.49/49.00  | | | | | | | BETA: splitting (10) gives:
% 242.49/49.00  | | | | | | | 
% 242.49/49.00  | | | | | | | Case 1:
% 242.49/49.00  | | | | | | | | 
% 242.49/49.00  | | | | | | | |   (80)  all_58_9 = e0 & op(e3, e0) = e0
% 242.49/49.00  | | | | | | | | 
% 242.49/49.00  | | | | | | | | ALPHA: (80) implies:
% 242.49/49.00  | | | | | | | |   (81)  all_58_9 = e0
% 242.49/49.00  | | | | | | | | 
% 242.49/49.00  | | | | | | | | COMBINE_EQS: (61), (81) imply:
% 242.49/49.00  | | | | | | | |   (82)  e2 = e0
% 242.49/49.00  | | | | | | | | 
% 242.49/49.00  | | | | | | | | COMBINE_EQS: (78), (82) imply:
% 242.49/49.00  | | | | | | | |   (83)  all_58_2 = e0
% 242.49/49.00  | | | | | | | | 
% 242.49/49.00  | | | | | | | | REF_CLOSE: (7), (8), (27), (29), (50), (54), (64), (67), (83)
% 242.49/49.00  | | | | | | | |            are inconsistent by sub-proof #1267.
% 242.49/49.00  | | | | | | | | 
% 242.49/49.00  | | | | | | | Case 2:
% 242.49/49.00  | | | | | | | | 
% 242.49/49.00  | | | | | | | |   (84)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.49/49.00  | | | | | | | |           op(e1, e0) = e0)
% 242.49/49.00  | | | | | | | | 
% 242.49/49.00  | | | | | | | | BETA: splitting (84) gives:
% 242.49/49.00  | | | | | | | | 
% 242.49/49.00  | | | | | | | | Case 1:
% 242.49/49.00  | | | | | | | | | 
% 242.49/49.00  | | | | | | | | |   (85)  all_58_10 = e0 & op(e2, e0) = e0
% 242.49/49.00  | | | | | | | | | 
% 242.49/49.00  | | | | | | | | | ALPHA: (85) implies:
% 242.49/49.00  | | | | | | | | |   (86)  op(e2, e0) = e0
% 242.49/49.00  | | | | | | | | | 
% 242.49/49.00  | | | | | | | | | GROUND_INST: instantiating (50) with all_52_11, e0, e1, e0,
% 242.49/49.00  | | | | | | | | |              simplifying with (6), (33) gives:
% 242.49/49.00  | | | | | | | | |   (87)  all_52_11 = e0
% 242.49/49.00  | | | | | | | | | 
% 242.49/49.00  | | | | | | | | | GROUND_INST: instantiating (50) with all_52_7, e2, e2, e0,
% 242.49/49.00  | | | | | | | | |              simplifying with (19), (41) gives:
% 242.49/49.00  | | | | | | | | |   (88)  all_52_7 = e2
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | GROUND_INST: instantiating (50) with all_52_3, e1, e3, e0,
% 242.51/49.00  | | | | | | | | |              simplifying with (18), (68) gives:
% 242.51/49.00  | | | | | | | | |   (89)  all_52_3 = e1
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | GROUND_INST: instantiating (50) with all_52_14, e1, e0, e1,
% 242.51/49.00  | | | | | | | | |              simplifying with (16), (22) gives:
% 242.51/49.00  | | | | | | | | |   (90)  all_52_14 = e1
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | GROUND_INST: instantiating (50) with all_52_6, e0, e2, e1,
% 242.51/49.00  | | | | | | | | |              simplifying with (11), (28) gives:
% 242.51/49.00  | | | | | | | | |   (91)  all_52_6 = e0
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | GROUND_INST: instantiating (50) with all_52_13, e0, e0, e2,
% 242.51/49.00  | | | | | | | | |              simplifying with (59), (86) gives:
% 242.51/49.00  | | | | | | | | |   (92)  all_52_13 = e0
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | GROUND_INST: instantiating (50) with all_52_9, e1, e1, e2,
% 242.51/49.00  | | | | | | | | |              simplifying with (26), (73) gives:
% 242.51/49.00  | | | | | | | | |   (93)  all_52_9 = e1
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | GROUND_INST: instantiating (50) with all_52_1, e2, e3, e2,
% 242.51/49.00  | | | | | | | | |              simplifying with (36), (79) gives:
% 242.51/49.00  | | | | | | | | |   (94)  all_52_1 = e2
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | GROUND_INST: instantiating (50) with all_52_12, e2, e0, e3,
% 242.51/49.00  | | | | | | | | |              simplifying with (32), (37) gives:
% 242.51/49.00  | | | | | | | | |   (95)  all_52_12 = e2
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | REDUCE: (51), (95) imply:
% 242.51/49.00  | | | | | | | | |   (96)   ~ (e3 = e2)
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | REDUCE: (42), (90), (92) imply:
% 242.51/49.00  | | | | | | | | |   (97)   ~ (e1 = e0)
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | REDUCE: (56), (92) imply:
% 242.51/49.00  | | | | | | | | |   (98)   ~ (e3 = e0)
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | REDUCE: (25), (90) imply:
% 242.51/49.00  | | | | | | | | |   (99)   ~ (e2 = e1)
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | BETA: splitting (4) gives:
% 242.51/49.00  | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | |   (100)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 242.51/49.00  | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)) | (all_56_18 =
% 242.51/49.00  | | | | | | | | | |            e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 242.51/49.00  | | | | | | | | | |            all_56_19 & $i(all_56_19))
% 242.51/49.00  | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | BETA: splitting (100) gives:
% 242.51/49.00  | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | |   (101)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 242.51/49.00  | | | | | | | | | | |            e1) = all_56_17 & $i(all_56_17)
% 242.51/49.00  | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | ALPHA: (101) implies:
% 242.51/49.00  | | | | | | | | | | |   (102)  op(e3, all_56_17) = e3
% 242.51/49.00  | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | BETA: splitting (12) gives:
% 242.51/49.00  | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | |   (103)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.51/49.00  | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.51/49.00  | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 242.51/49.00  | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 242.51/49.00  | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.51/49.00  | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 242.51/49.00  | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 242.51/49.00  | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.51/49.00  | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 242.51/49.00  | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 242.51/49.00  | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.51/49.00  | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 242.51/49.00  | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | BETA: splitting (103) gives:
% 242.51/49.00  | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | |   (104)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.51/49.00  | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.51/49.00  | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 242.51/49.00  | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 242.51/49.00  | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.51/49.00  | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 242.51/49.00  | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.51/49.00  | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.51/49.00  | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 242.51/49.00  | | | | | | | | | | | | |            = e3)
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | BETA: splitting (104) gives:
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | |   (105)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 242.51/49.00  | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 242.51/49.00  | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 242.51/49.00  | | | | | | | | | | | | | |          e3
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | ALPHA: (105) implies:
% 242.51/49.00  | | | | | | | | | | | | | |   (106)  op(e2, e3) = e3
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | REF_CLOSE: (36), (50), (62), (106) are inconsistent by
% 242.51/49.00  | | | | | | | | | | | | | |            sub-proof #2337.
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | Case 2:
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | |   (107)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 242.51/49.00  | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 242.51/49.00  | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 242.51/49.00  | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 242.51/49.00  | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.51/49.00  | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | |   (108)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.51/49.00  | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.51/49.00  | | | | | | | | | | | | | | |          (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 242.51/49.00  | | | | | | | | | | | | | | |          e2
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 242.51/49.00  | | | | | | | | | | | | | | |   (109)   ~ (all_56_31 = e3)
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | REDUCE: (45), (109) imply:
% 242.51/49.00  | | | | | | | | | | | | | | |   (110)  $false
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | CLOSE: (110) is inconsistent.
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | Case 2:
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | |   (111)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 242.51/49.00  | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 242.51/49.00  | | | | | | | | | | | | | | |            e3) = e3
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 242.51/49.00  | | | | | | | | | | | | | | |   (112)  all_56_17 = e3
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | REDUCE: (102), (112) imply:
% 242.51/49.00  | | | | | | | | | | | | | | |   (113)  op(e3, e3) = e3
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | REF_CLOSE: (5), (50), (54), (113) are inconsistent by
% 242.51/49.00  | | | | | | | | | | | | | | |            sub-proof #1940.
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | End of split
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | End of split
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | Case 2:
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | |   (114)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 242.51/49.00  | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.51/49.00  | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 242.51/49.00  | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 242.51/49.00  | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.51/49.00  | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 242.51/49.00  | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 242.51/49.00  | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.51/49.00  | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 242.51/49.00  | | | | | | | | | | | | |            = e0)
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | BETA: splitting (114) gives:
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | |   (115)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 242.51/49.00  | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 242.51/49.00  | | | | | | | | | | | | | |            e3) = e1
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | ALPHA: (115) implies:
% 242.51/49.00  | | | | | | | | | | | | | |   (116)   ~ (all_56_31 = e3)
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | REDUCE: (45), (116) imply:
% 242.51/49.00  | | | | | | | | | | | | | |   (117)  $false
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | CLOSE: (117) is inconsistent.
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | Case 2:
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | |   (118)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 242.51/49.00  | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 242.51/49.00  | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 242.51/49.00  | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 242.51/49.00  | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.51/49.00  | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | |   (119)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 242.51/49.00  | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 242.51/49.00  | | | | | | | | | | | | | | |            e3) = e3
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 242.51/49.00  | | | | | | | | | | | | | | |   (120)  op(e3, e0) = e3
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | REF_CLOSE: (29), (37), (50), (120) are inconsistent by
% 242.51/49.00  | | | | | | | | | | | | | | |            sub-proof #2125.
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | Case 2:
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | |   (121)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 242.51/49.00  | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 242.51/49.00  | | | | | | | | | | | | | | |            e3) = e0
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 242.51/49.00  | | | | | | | | | | | | | | |   (122)  op(e0, e3) = e0
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | REF_CLOSE: (1), (24), (50), (53), (68), (122) are
% 242.51/49.00  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1384.
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | End of split
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | End of split
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | End of split
% 242.51/49.00  | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | Case 2:
% 242.51/49.00  | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | |   (123)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 242.51/49.00  | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 242.51/49.00  | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 242.51/49.00  | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 242.51/49.00  | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.51/49.00  | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 242.51/49.00  | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 242.51/49.00  | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.51/49.00  | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 242.51/49.00  | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 242.51/49.00  | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.51/49.00  | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 242.51/49.00  | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 242.51/49.00  | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | BETA: splitting (123) gives:
% 242.51/49.00  | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | |   (124)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 242.51/49.00  | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 242.51/49.00  | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 242.51/49.00  | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 242.51/49.00  | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.51/49.00  | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 242.51/49.00  | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.51/49.00  | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.51/49.00  | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 242.51/49.00  | | | | | | | | | | | | |            = e2)
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | BETA: splitting (124) gives:
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | |   (125)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 242.51/49.00  | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 242.51/49.00  | | | | | | | | | | | | | |            e2) = e2
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | ALPHA: (125) implies:
% 242.51/49.00  | | | | | | | | | | | | | |   (126)   ~ (all_56_31 = e1)
% 242.51/49.00  | | | | | | | | | | | | | |   (127)   ~ (all_56_21 = e1)
% 242.51/49.00  | | | | | | | | | | | | | |   (128)   ~ (all_56_1 = e1)
% 242.51/49.00  | | | | | | | | | | | | | |   (129)  op(e1, e2) = e2
% 242.51/49.00  | | | | | | | | | | | | | |   (130)  op(e2, e1) = e2
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | |   (131)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 242.51/49.00  | | | | | | | | | | | | | | |          op(e1, e2) = all_36_1 & $i(all_36_0) &
% 242.51/49.00  | | | | | | | | | | | | | | |          $i(all_36_1)
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 242.51/49.00  | | | | | | | | | | | | | | |   (132)  op(e1, e2) = all_36_1
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | Case 1:
% 242.51/49.00  | | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | |   (133)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 242.51/49.00  | | | | | | | | | | | | | | | |          op(e1, e2) = all_40_1 & $i(all_40_0) &
% 242.51/49.00  | | | | | | | | | | | | | | | |          $i(all_40_1)
% 242.51/49.00  | | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 242.51/49.00  | | | | | | | | | | | | | | | |   (134)  op(e1, e2) = all_40_1
% 242.51/49.00  | | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (20), (28), (37), (39), (47), (50), (53),
% 242.51/49.00  | | | | | | | | | | | | | | | |            (54), (55), (61), (64), (73), (129), (130), (132),
% 242.51/49.00  | | | | | | | | | | | | | | | |            (134) are inconsistent by sub-proof #783.
% 242.51/49.00  | | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | Case 2:
% 242.51/49.00  | | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | |   (135)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 242.51/49.00  | | | | | | | | | | | | | | | |          $i(all_40_1)
% 242.51/49.00  | | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 242.51/49.00  | | | | | | | | | | | | | | | |   (136)  op(e1, e2) = all_40_1
% 242.51/49.00  | | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (20), (28), (37), (39), (47), (50), (53),
% 242.51/49.00  | | | | | | | | | | | | | | | |            (54), (55), (61), (64), (73), (129), (130), (132),
% 242.51/49.00  | | | | | | | | | | | | | | | |            (136) are inconsistent by sub-proof #783.
% 242.51/49.00  | | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | End of split
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | Case 2:
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | |   (137)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 242.51/49.00  | | | | | | | | | | | | | | |          $i(all_36_1)
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 242.51/49.00  | | | | | | | | | | | | | | |   (138)   ~ (all_36_1 = e0)
% 242.51/49.00  | | | | | | | | | | | | | | |   (139)  op(e1, e2) = all_36_1
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | | REF_CLOSE: (28), (40), (50), (138), (139) are inconsistent by
% 242.51/49.00  | | | | | | | | | | | | | | |            sub-proof #782.
% 242.51/49.00  | | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | End of split
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | Case 2:
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | |   (140)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 242.51/49.00  | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.51/49.00  | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 242.51/49.00  | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 242.51/49.00  | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 242.51/49.00  | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.51/49.00  | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (28), (50), (53), (86), (140) are
% 242.51/49.00  | | | | | | | | | | | | | |            inconsistent by sub-proof #781.
% 242.51/49.00  | | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | | End of split
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.00  | | | | | | | | | | | | Case 2:
% 242.51/49.00  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | |   (141)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 242.51/49.01  | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.51/49.01  | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 242.51/49.01  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 242.51/49.01  | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 242.51/49.01  | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.51/49.01  | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 242.51/49.01  | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 242.51/49.01  | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.51/49.01  | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 242.51/49.01  | | | | | | | | | | | | |            = e0)
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | BETA: splitting (141) gives:
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | Case 1:
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | |   (142)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 242.51/49.01  | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 242.51/49.01  | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 242.51/49.01  | | | | | | | | | | | | | |            e2) = e0
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | ALPHA: (142) implies:
% 242.51/49.01  | | | | | | | | | | | | | |   (143)  op(e0, e2) = e0
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | REF_CLOSE: (8), (19), (50), (143) are inconsistent by
% 242.51/49.01  | | | | | | | | | | | | | |            sub-proof #2132.
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | Case 2:
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | |   (144)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 242.51/49.01  | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 242.51/49.01  | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 242.51/49.01  | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 242.51/49.01  | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 242.51/49.01  | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.51/49.01  | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | REF_CLOSE: (22), (33), (50), (53), (144) are inconsistent by
% 242.51/49.01  | | | | | | | | | | | | | |            sub-proof #1240.
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | End of split
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | End of split
% 242.51/49.01  | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | End of split
% 242.51/49.01  | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | Case 2:
% 242.51/49.01  | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | |   (145)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 242.51/49.01  | | | | | | | | | | |            e1) = all_56_19 & $i(all_56_19)
% 242.51/49.01  | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | ALPHA: (145) implies:
% 242.51/49.01  | | | | | | | | | | |   (146)  op(e2, e1) = all_56_19
% 242.51/49.01  | | | | | | | | | | |   (147)  op(e2, all_56_19) = e2
% 242.51/49.01  | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | BETA: splitting (30) gives:
% 242.51/49.01  | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | Case 1:
% 242.51/49.01  | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | |   (148)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 242.51/49.01  | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 242.51/49.01  | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 242.51/49.01  | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 242.51/49.01  | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | BETA: splitting (148) gives:
% 242.51/49.01  | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | Case 1:
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | |   (149)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 242.51/49.01  | | | | | | | | | | | | |            e0) = all_56_25 & $i(all_56_25)
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | ALPHA: (149) implies:
% 242.51/49.01  | | | | | | | | | | | | |   (150)  op(e3, e0) = all_56_25
% 242.51/49.01  | | | | | | | | | | | | |   (151)  op(e3, all_56_25) = e3
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | BETA: splitting (31) gives:
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | Case 1:
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | |   (152)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 &
% 242.51/49.01  | | | | | | | | | | | | | |          op(e3, e0) = all_16_1 & $i(all_16_0) &
% 242.51/49.01  | | | | | | | | | | | | | |          $i(all_16_1)
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | ALPHA: (152) implies:
% 242.51/49.01  | | | | | | | | | | | | | |   (153)  op(e3, e0) = all_16_1
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | REF_CLOSE: (37), (39), (43), (44), (50), (150), (151), (153)
% 242.51/49.01  | | | | | | | | | | | | | |            are inconsistent by sub-proof #780.
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | Case 2:
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | |   (154)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 242.51/49.01  | | | | | | | | | | | | | |          $i(all_16_1)
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | ALPHA: (154) implies:
% 242.51/49.01  | | | | | | | | | | | | | |   (155)  op(e3, e0) = all_16_1
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | REF_CLOSE: (37), (39), (43), (44), (50), (150), (151), (155)
% 242.51/49.01  | | | | | | | | | | | | | |            are inconsistent by sub-proof #780.
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | End of split
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | Case 2:
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | |   (156)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 242.51/49.01  | | | | | | | | | | | | |            e0) = all_56_27 & $i(all_56_27)
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | REF_CLOSE: (5), (8), (23), (35), (49), (50), (53), (63),
% 242.51/49.01  | | | | | | | | | | | | |            (72), (78), (79), (86), (156) are inconsistent by
% 242.51/49.01  | | | | | | | | | | | | |            sub-proof #778.
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | End of split
% 242.51/49.01  | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | Case 2:
% 242.51/49.01  | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | |   (157)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 242.51/49.01  | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 242.51/49.01  | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 242.51/49.01  | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | BETA: splitting (157) gives:
% 242.51/49.01  | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | Case 1:
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | |   (158)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 242.51/49.01  | | | | | | | | | | | | |            e0) = all_56_29 & $i(all_56_29)
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | ALPHA: (158) implies:
% 242.51/49.01  | | | | | | | | | | | | |   (159)  op(e1, e0) = all_56_29
% 242.51/49.01  | | | | | | | | | | | | |   (160)  op(e1, all_56_29) = e1
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | BETA: splitting (39) gives:
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | Case 1:
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | GROUND_INST: instantiating (50) with e1, all_56_29, e0, e1,
% 242.51/49.01  | | | | | | | | | | | | | |              simplifying with (22), (159) gives:
% 242.51/49.01  | | | | | | | | | | | | | |   (161)  all_56_29 = e1
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | GROUND_INST: instantiating (50) with e1, all_56_19, e1, e2,
% 242.51/49.01  | | | | | | | | | | | | | |              simplifying with (73), (146) gives:
% 242.51/49.01  | | | | | | | | | | | | | |   (162)  all_56_19 = e1
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | REDUCE: (147), (162) imply:
% 242.51/49.01  | | | | | | | | | | | | | |   (163)  op(e2, e1) = e2
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | REDUCE: (160), (161) imply:
% 242.51/49.01  | | | | | | | | | | | | | |   (164)  op(e1, e1) = e1
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | GROUND_INST: instantiating (50) with e1, e2, e1, e2,
% 242.51/49.01  | | | | | | | | | | | | | |              simplifying with (73), (163) gives:
% 242.51/49.01  | | | | | | | | | | | | | |   (165)  e2 = e1
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | COMBINE_EQS: (21), (165) imply:
% 242.51/49.01  | | | | | | | | | | | | | |   (166)  all_58_8 = e1
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (15), (22), (29), (48), (50), (53),
% 242.51/49.01  | | | | | | | | | | | | | |            (57), (64), (164), (166) are inconsistent by
% 242.51/49.01  | | | | | | | | | | | | | |            sub-proof #804.
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | Case 2:
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | |   (167)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 &
% 242.51/49.01  | | | | | | | | | | | | | |          $i(all_50_1)
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | ALPHA: (167) implies:
% 242.51/49.01  | | | | | | | | | | | | | |   (168)   ~ (all_50_1 = e2)
% 242.51/49.01  | | | | | | | | | | | | | |   (169)  op(e3, e0) = all_50_1
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | | REF_CLOSE: (37), (50), (168), (169) are inconsistent by
% 242.51/49.01  | | | | | | | | | | | | | |            sub-proof #1884.
% 242.51/49.01  | | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | End of split
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | Case 2:
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | |   (170)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | ALPHA: (170) implies:
% 242.51/49.01  | | | | | | | | | | | | |   (171)  op(e0, all_56_31) = e0
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | REDUCE: (45), (171) imply:
% 242.51/49.01  | | | | | | | | | | | | |   (172)  op(e0, e3) = e0
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | | REF_CLOSE: (1), (24), (50), (53), (68), (172) are
% 242.51/49.01  | | | | | | | | | | | | |            inconsistent by sub-proof #1384.
% 242.51/49.01  | | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | | End of split
% 242.51/49.01  | | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | | End of split
% 242.51/49.01  | | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | End of split
% 242.51/49.01  | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | Case 2:
% 242.51/49.01  | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | |   (173)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 242.51/49.01  | | | | | | | | | |          (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 242.51/49.01  | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23))
% 242.51/49.01  | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | | REF_CLOSE: (2), (5), (11), (28), (33), (46), (50), (53),
% 242.51/49.01  | | | | | | | | | |            (173) are inconsistent by sub-proof #1324.
% 242.51/49.01  | | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | End of split
% 242.51/49.01  | | | | | | | | | 
% 242.51/49.01  | | | | | | | | Case 2:
% 242.51/49.01  | | | | | | | | | 
% 242.51/49.01  | | | | | | | | |   (174)  all_58_11 = e0 & op(e1, e0) = e0
% 242.51/49.01  | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | ALPHA: (174) implies:
% 242.51/49.01  | | | | | | | | |   (175)  op(e1, e0) = e0
% 242.51/49.01  | | | | | | | | | 
% 242.51/49.01  | | | | | | | | | REF_CLOSE: (22), (50), (53), (175) are inconsistent by
% 242.51/49.01  | | | | | | | | |            sub-proof #2284.
% 242.51/49.01  | | | | | | | | | 
% 242.51/49.01  | | | | | | | | End of split
% 242.51/49.01  | | | | | | | | 
% 242.51/49.01  | | | | | | | End of split
% 242.51/49.01  | | | | | | | 
% 242.51/49.01  | | | | | | End of split
% 242.51/49.01  | | | | | | 
% 242.51/49.01  | | | | | Case 2:
% 242.51/49.01  | | | | | | 
% 242.51/49.01  | | | | | |   (176)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 &
% 242.51/49.01  | | | | | |            op(e0, e3) = e2)
% 242.51/49.01  | | | | | | 
% 242.51/49.01  | | | | | | BETA: splitting (176) gives:
% 242.51/49.01  | | | | | | 
% 242.51/49.01  | | | | | | Case 1:
% 242.51/49.01  | | | | | | | 
% 242.51/49.01  | | | | | | |   (177)  all_58_6 = e2 & op(e1, e3) = e2
% 242.51/49.01  | | | | | | | 
% 242.51/49.01  | | | | | | | REF_CLOSE: (7), (29), (177) are inconsistent by sub-proof #2219.
% 242.51/49.01  | | | | | | | 
% 242.51/49.01  | | | | | | Case 2:
% 242.51/49.01  | | | | | | | 
% 242.51/49.01  | | | | | | |   (178)  all_58_12 = e2 & op(e0, e3) = e2
% 242.51/49.01  | | | | | | | 
% 242.51/49.01  | | | | | | | ALPHA: (178) implies:
% 242.51/49.01  | | | | | | |   (179)  all_58_12 = e2
% 242.51/49.01  | | | | | | | 
% 242.51/49.01  | | | | | | | COMBINE_EQS: (67), (179) imply:
% 242.51/49.01  | | | | | | |   (180)  e2 = e1
% 242.51/49.01  | | | | | | | 
% 242.51/49.01  | | | | | | | SIMP: (180) implies:
% 242.51/49.01  | | | | | | |   (181)  e2 = e1
% 242.51/49.01  | | | | | | | 
% 242.51/49.01  | | | | | | | COMBINE_EQS: (21), (181) imply:
% 242.51/49.01  | | | | | | |   (182)  all_58_8 = e1
% 242.51/49.01  | | | | | | | 
% 242.51/49.01  | | | | | | | REF_CLOSE: (7), (8), (9), (15), (29), (48), (64), (182) are
% 242.51/49.01  | | | | | | |            inconsistent by sub-proof #988.
% 242.51/49.01  | | | | | | | 
% 242.51/49.01  | | | | | | End of split
% 242.51/49.01  | | | | | | 
% 242.51/49.01  | | | | | End of split
% 242.51/49.01  | | | | | 
% 242.51/49.01  | | | | End of split
% 242.51/49.01  | | | | 
% 242.51/49.01  | | | Case 2:
% 242.51/49.01  | | | | 
% 242.51/49.01  | | | |   (183)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0,
% 242.51/49.01  | | | |              e1) = e1)
% 242.51/49.01  | | | | 
% 242.51/49.01  | | | | BETA: splitting (183) gives:
% 242.51/49.01  | | | | 
% 242.51/49.01  | | | | Case 1:
% 242.51/49.01  | | | | | 
% 242.51/49.01  | | | | |   (184)  all_58_8 = e1 & op(e1, e1) = e1
% 242.51/49.01  | | | | | 
% 242.51/49.01  | | | | | ALPHA: (184) implies:
% 242.51/49.01  | | | | |   (185)  all_58_8 = e1
% 242.51/49.01  | | | | | 
% 242.51/49.01  | | | | | REF_CLOSE: (7), (8), (9), (15), (29), (48), (64), (185) are
% 242.51/49.01  | | | | |            inconsistent by sub-proof #988.
% 242.51/49.01  | | | | | 
% 242.51/49.01  | | | | Case 2:
% 242.51/49.01  | | | | | 
% 242.51/49.01  | | | | |   (186)  all_58_14 = e1 & op(e0, e1) = e1
% 242.51/49.01  | | | | | 
% 242.51/49.01  | | | | | ALPHA: (186) implies:
% 242.51/49.01  | | | | |   (187)  op(e0, e1) = e1
% 242.51/49.01  | | | | | 
% 242.51/49.01  | | | | | REF_CLOSE: (33), (50), (53), (187) are inconsistent by sub-proof
% 242.51/49.01  | | | | |            #2158.
% 242.51/49.01  | | | | | 
% 242.51/49.01  | | | | End of split
% 242.51/49.01  | | | | 
% 242.51/49.01  | | | End of split
% 242.51/49.01  | | | 
% 242.51/49.01  | | Case 2:
% 242.51/49.01  | | | 
% 242.51/49.01  | | |   (188)  all_58_13 = e1 & op(e0, e2) = e1
% 242.51/49.01  | | | 
% 242.51/49.01  | | | ALPHA: (188) implies:
% 242.51/49.01  | | |   (189)  all_58_13 = e1
% 242.51/49.01  | | | 
% 242.51/49.01  | | | COMBINE_EQS: (34), (189) imply:
% 242.51/49.01  | | |   (190)  e2 = e1
% 242.51/49.01  | | | 
% 242.51/49.01  | | | COMBINE_EQS: (21), (190) imply:
% 242.51/49.01  | | |   (191)  all_58_8 = e1
% 242.51/49.01  | | | 
% 242.51/49.01  | | | REF_CLOSE: (7), (8), (9), (15), (29), (48), (64), (191) are inconsistent
% 242.51/49.01  | | |            by sub-proof #988.
% 242.51/49.01  | | | 
% 242.51/49.01  | | End of split
% 242.51/49.01  | | 
% 242.51/49.01  | Case 2:
% 242.51/49.01  | | 
% 242.51/49.01  | |   (192)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.51/49.01  | |            e1)
% 242.51/49.01  | | 
% 242.51/49.01  | | REF_CLOSE: (17), (20), (33), (50), (53), (192) are inconsistent by sub-proof
% 242.51/49.01  | |            #1255.
% 242.51/49.01  | | 
% 242.51/49.01  | End of split
% 242.51/49.01  | 
% 242.51/49.01  End of proof
% 242.51/49.01  
% 242.51/49.01  Sub-proof #778 shows that the following formulas are inconsistent:
% 242.51/49.01  ----------------------------------------------------------------
% 242.51/49.01    (1)   ~ (e3 = e0)
% 242.51/49.01    (2)   ~ (e2 = e0)
% 242.51/49.01    (3)  all_58_2 = e2
% 242.51/49.01    (4)  all_58_3 = e3
% 242.51/49.01    (5)  op(e2, e3) = e2
% 242.51/49.01    (6)  op(e2, e0) = e0
% 242.51/49.01    (7)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 242.51/49.01           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 242.51/49.01           all_42_1 & $i(all_42_1))
% 242.51/49.01    (8)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 242.51/49.01         $i(all_56_27)
% 242.51/49.01    (9)  all_58_5 = e1
% 242.51/49.01    (10)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.51/49.01          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.51/49.01    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.51/49.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.51/49.01    (12)   ~ (e1 = e0)
% 242.51/49.01    (13)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.51/49.01            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.51/49.01            & $i(all_8_1))
% 242.51/49.01  
% 242.51/49.01  Begin of proof
% 242.51/49.01  | 
% 242.51/49.01  | ALPHA: (8) implies:
% 242.51/49.01  |   (14)  op(e2, e0) = all_56_27
% 242.51/49.01  |   (15)  op(e2, all_56_27) = e2
% 242.51/49.01  | 
% 242.51/49.01  | BETA: splitting (13) gives:
% 242.51/49.01  | 
% 242.51/49.01  | Case 1:
% 242.51/49.01  | | 
% 242.51/49.01  | | 
% 242.51/49.01  | | GROUND_INST: instantiating (11) with e0, all_56_27, e0, e2, simplifying with
% 242.51/49.01  | |              (6), (14) gives:
% 242.51/49.01  | |   (16)  all_56_27 = e0
% 242.51/49.01  | | 
% 242.51/49.01  | | REDUCE: (15), (16) imply:
% 242.51/49.01  | |   (17)  op(e2, e0) = e2
% 242.51/49.01  | | 
% 242.51/49.01  | | REF_CLOSE: (1), (2), (3), (4), (9), (10), (11), (12), (17) are inconsistent
% 242.51/49.01  | |            by sub-proof #840.
% 242.51/49.01  | | 
% 242.51/49.01  | Case 2:
% 242.51/49.01  | | 
% 242.51/49.01  | |   (18)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 242.51/49.01  | | 
% 242.51/49.01  | | ALPHA: (18) implies:
% 242.51/49.01  | |   (19)   ~ (all_8_1 = e0)
% 242.51/49.01  | |   (20)  op(e2, e3) = all_8_1
% 242.51/49.01  | | 
% 242.51/49.01  | | BETA: splitting (7) gives:
% 242.51/49.01  | | 
% 242.51/49.01  | | Case 1:
% 242.51/49.01  | | | 
% 242.51/49.01  | | |   (21)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.51/49.01  | | |         all_42_1 & $i(all_42_0) & $i(all_42_1)
% 242.51/49.01  | | | 
% 242.51/49.01  | | | ALPHA: (21) implies:
% 242.51/49.01  | | |   (22)  op(e2, e3) = all_42_1
% 242.51/49.01  | | | 
% 242.51/49.01  | | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (11), (12), (14), (15),
% 242.51/49.01  | | |            (19), (20), (22) are inconsistent by sub-proof #779.
% 242.51/49.01  | | | 
% 242.51/49.01  | | Case 2:
% 242.51/49.01  | | | 
% 242.51/49.01  | | |   (23)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 242.51/49.01  | | | 
% 242.51/49.01  | | | ALPHA: (23) implies:
% 242.51/49.01  | | |   (24)  op(e2, e3) = all_42_1
% 242.51/49.01  | | | 
% 242.51/49.01  | | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (11), (12), (14), (15),
% 242.51/49.01  | | |            (19), (20), (24) are inconsistent by sub-proof #779.
% 242.51/49.01  | | | 
% 242.51/49.01  | | End of split
% 242.51/49.01  | | 
% 242.51/49.01  | End of split
% 242.51/49.01  | 
% 242.51/49.01  End of proof
% 242.51/49.01  
% 242.51/49.01  Sub-proof #779 shows that the following formulas are inconsistent:
% 242.51/49.01  ----------------------------------------------------------------
% 242.51/49.01    (1)  op(e2, e0) = all_56_27
% 242.51/49.01    (2)   ~ (e3 = e0)
% 242.51/49.01    (3)  op(e2, all_56_27) = e2
% 242.51/49.01    (4)  op(e2, e3) = all_42_1
% 242.51/49.01    (5)  all_58_2 = e2
% 242.51/49.01    (6)  all_58_3 = e3
% 242.51/49.01    (7)   ~ (all_8_1 = e0)
% 242.51/49.01    (8)  op(e2, e3) = e2
% 242.51/49.01    (9)  op(e2, e0) = e0
% 242.51/49.01    (10)  all_58_5 = e1
% 242.51/49.01    (11)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.51/49.01          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.51/49.01    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.51/49.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.51/49.01    (13)  op(e2, e3) = all_8_1
% 242.51/49.01    (14)   ~ (e1 = e0)
% 242.51/49.01  
% 242.51/49.01  Begin of proof
% 242.51/49.01  | 
% 242.51/49.01  | GROUND_INST: instantiating (12) with e0, all_56_27, e0, e2, simplifying with
% 242.51/49.01  |              (1), (9) gives:
% 242.51/49.01  |   (15)  all_56_27 = e0
% 242.51/49.01  | 
% 242.51/49.01  | GROUND_INST: instantiating (12) with all_8_1, all_42_1, e3, e2, simplifying
% 242.51/49.01  |              with (4), (13) gives:
% 242.51/49.01  |   (16)  all_42_1 = all_8_1
% 242.51/49.01  | 
% 242.51/49.01  | GROUND_INST: instantiating (12) with e2, all_42_1, e3, e2, simplifying with
% 242.51/49.01  |              (4), (8) gives:
% 242.51/49.01  |   (17)  all_42_1 = e2
% 242.51/49.01  | 
% 242.51/49.01  | COMBINE_EQS: (16), (17) imply:
% 242.51/49.01  |   (18)  all_8_1 = e2
% 242.51/49.01  | 
% 242.51/49.01  | REDUCE: (7), (18) imply:
% 242.51/49.01  |   (19)   ~ (e2 = e0)
% 242.51/49.01  | 
% 242.51/49.01  | REDUCE: (3), (15) imply:
% 242.51/49.01  |   (20)  op(e2, e0) = e2
% 242.51/49.01  | 
% 242.51/49.01  | REF_CLOSE: (2), (5), (6), (10), (11), (12), (14), (19), (20) are inconsistent
% 242.51/49.01  |            by sub-proof #840.
% 242.51/49.01  | 
% 242.51/49.01  End of proof
% 242.51/49.01  
% 242.51/49.01  Sub-proof #780 shows that the following formulas are inconsistent:
% 242.51/49.01  ----------------------------------------------------------------
% 242.51/49.01    (1)  op(e3, e0) = all_16_1
% 242.52/49.01    (2)  op(e3, all_56_25) = e3
% 242.52/49.01    (3)  op(e3, e0) = e2
% 242.52/49.01    (4)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) = all_50_1
% 242.52/49.01           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0) =
% 242.52/49.01           all_50_1 & $i(all_50_1))
% 242.52/49.01    (5)  op(e3, e0) = all_56_25
% 242.52/49.01    (6)   ~ (all_52_4 = e3)
% 242.52/49.01    (7)  op(e3, e2) = all_52_4
% 242.52/49.02    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.02  
% 242.52/49.02  Begin of proof
% 242.52/49.02  | 
% 242.52/49.02  | BETA: splitting (4) gives:
% 242.52/49.02  | 
% 242.52/49.02  | Case 1:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (9)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 242.52/49.02  | |        all_50_1 & $i(all_50_0) & $i(all_50_1)
% 242.52/49.02  | | 
% 242.52/49.02  | | ALPHA: (9) implies:
% 242.52/49.02  | |   (10)  op(e3, e0) = all_50_1
% 242.52/49.02  | | 
% 242.52/49.02  | | GROUND_INST: instantiating (8) with e2, all_50_1, e0, e3, simplifying with
% 242.52/49.02  | |              (3), (10) gives:
% 242.52/49.02  | |   (11)  all_50_1 = e2
% 242.52/49.02  | | 
% 242.52/49.02  | | GROUND_INST: instantiating (8) with all_50_1, all_56_25, e0, e3, simplifying
% 242.52/49.02  | |              with (5), (10) gives:
% 242.52/49.02  | |   (12)  all_56_25 = all_50_1
% 242.52/49.02  | | 
% 242.52/49.02  | | GROUND_INST: instantiating (8) with all_16_1, all_56_25, e0, e3, simplifying
% 242.52/49.02  | |              with (1), (5) gives:
% 242.52/49.02  | |   (13)  all_56_25 = all_16_1
% 242.52/49.02  | | 
% 242.52/49.02  | | COMBINE_EQS: (12), (13) imply:
% 242.52/49.02  | |   (14)  all_50_1 = all_16_1
% 242.52/49.02  | | 
% 242.52/49.02  | | SIMP: (14) implies:
% 242.52/49.02  | |   (15)  all_50_1 = all_16_1
% 242.52/49.02  | | 
% 242.52/49.02  | | COMBINE_EQS: (11), (15) imply:
% 242.52/49.02  | |   (16)  all_16_1 = e2
% 242.52/49.02  | | 
% 242.52/49.02  | | SIMP: (16) implies:
% 242.52/49.02  | |   (17)  all_16_1 = e2
% 242.52/49.02  | | 
% 242.52/49.02  | | COMBINE_EQS: (13), (17) imply:
% 242.52/49.02  | |   (18)  all_56_25 = e2
% 242.52/49.02  | | 
% 242.52/49.02  | | REDUCE: (2), (18) imply:
% 242.52/49.02  | |   (19)  op(e3, e2) = e3
% 242.52/49.02  | | 
% 242.52/49.02  | | REF_CLOSE: (6), (7), (8), (19) are inconsistent by sub-proof #2192.
% 242.52/49.02  | | 
% 242.52/49.02  | Case 2:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (20)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 & $i(all_50_1)
% 242.52/49.02  | | 
% 242.52/49.02  | | ALPHA: (20) implies:
% 242.52/49.02  | |   (21)   ~ (all_50_1 = e2)
% 242.52/49.02  | |   (22)  op(e3, e0) = all_50_1
% 242.52/49.02  | | 
% 242.52/49.02  | | GROUND_INST: instantiating (8) with e2, all_50_1, e0, e3, simplifying with
% 242.52/49.02  | |              (3), (22) gives:
% 242.52/49.02  | |   (23)  all_50_1 = e2
% 242.52/49.02  | | 
% 242.52/49.02  | | REDUCE: (21), (23) imply:
% 242.52/49.02  | |   (24)  $false
% 242.52/49.02  | | 
% 242.52/49.02  | | CLOSE: (24) is inconsistent.
% 242.52/49.02  | | 
% 242.52/49.02  | End of split
% 242.52/49.02  | 
% 242.52/49.02  End of proof
% 242.52/49.02  
% 242.52/49.02  Sub-proof #781 shows that the following formulas are inconsistent:
% 242.52/49.02  ----------------------------------------------------------------
% 242.52/49.02    (1)   ~ (e2 = e0)
% 242.52/49.02    (2)  op(e1, e2) = all_52_6
% 242.52/49.02    (3)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.52/49.02             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 242.52/49.02           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 242.52/49.02             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 242.52/49.02           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.52/49.02    (4)  op(e1, e2) = e0
% 242.52/49.02    (5)  op(e2, e0) = e0
% 242.52/49.02    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.02    (7)   ~ (e1 = e0)
% 242.52/49.02  
% 242.52/49.02  Begin of proof
% 242.52/49.02  | 
% 242.52/49.02  | BETA: splitting (3) gives:
% 242.52/49.02  | 
% 242.52/49.02  | Case 1:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (8)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 242.52/49.02  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 242.52/49.02  | |        & op(e1, e2) = e1
% 242.52/49.02  | | 
% 242.52/49.02  | | ALPHA: (8) implies:
% 242.52/49.02  | |   (9)  op(e1, e2) = e1
% 242.52/49.02  | | 
% 242.52/49.02  | | REF_CLOSE: (2), (4), (6), (7), (9) are inconsistent by sub-proof #2136.
% 242.52/49.02  | | 
% 242.52/49.02  | Case 2:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (10)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 242.52/49.02  | |           = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) =
% 242.52/49.02  | |         e2 & op(e0, e2) = e2
% 242.52/49.02  | | 
% 242.52/49.02  | | ALPHA: (10) implies:
% 242.52/49.02  | |   (11)  op(e2, e0) = e2
% 242.52/49.02  | | 
% 242.52/49.02  | | REF_CLOSE: (1), (5), (6), (11) are inconsistent by sub-proof #2121.
% 242.52/49.02  | | 
% 242.52/49.02  | End of split
% 242.52/49.02  | 
% 242.52/49.02  End of proof
% 242.52/49.02  
% 242.52/49.02  Sub-proof #782 shows that the following formulas are inconsistent:
% 242.52/49.02  ----------------------------------------------------------------
% 242.52/49.02    (1)  op(e1, e2) = e0
% 242.52/49.02    (2)  op(e1, e2) = all_36_1
% 242.52/49.02    (3)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) = all_40_1
% 242.52/49.02           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2) =
% 242.52/49.02           all_40_1 & $i(all_40_1))
% 242.52/49.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.02    (5)   ~ (all_36_1 = e0)
% 242.52/49.02  
% 242.52/49.02  Begin of proof
% 242.52/49.02  | 
% 242.52/49.02  | BETA: splitting (3) gives:
% 242.52/49.02  | 
% 242.52/49.02  | Case 1:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (6)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 242.52/49.02  | |        all_40_1 & $i(all_40_0) & $i(all_40_1)
% 242.52/49.02  | | 
% 242.52/49.02  | | ALPHA: (6) implies:
% 242.52/49.02  | |   (7)  op(e1, e2) = all_40_1
% 242.52/49.02  | | 
% 242.52/49.02  | | REF_CLOSE: (1), (2), (4), (5), (7) are inconsistent by sub-proof #1883.
% 242.52/49.02  | | 
% 242.52/49.02  | Case 2:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (8)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 242.52/49.02  | | 
% 242.52/49.02  | | ALPHA: (8) implies:
% 242.52/49.02  | |   (9)  op(e1, e2) = all_40_1
% 242.52/49.02  | | 
% 242.52/49.02  | | REF_CLOSE: (1), (2), (4), (5), (9) are inconsistent by sub-proof #1883.
% 242.52/49.02  | | 
% 242.52/49.02  | End of split
% 242.52/49.02  | 
% 242.52/49.02  End of proof
% 242.52/49.02  
% 242.52/49.02  Sub-proof #783 shows that the following formulas are inconsistent:
% 242.52/49.02  ----------------------------------------------------------------
% 242.52/49.02    (1)  all_58_1 = e1
% 242.52/49.02    (2)  op(e2, e1) = e1
% 242.52/49.02    (3)   ~ (e3 = e1)
% 242.52/49.02    (4)  op(e2, e1) = e2
% 242.52/49.02    (5)  op(e1, e2) = e0
% 242.52/49.02    (6)  op(e3, e0) = e2
% 242.52/49.02    (7)  op(e1, e2) = all_36_1
% 242.52/49.02    (8)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) = all_50_1
% 242.52/49.02           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0) =
% 242.52/49.02           all_50_1 & $i(all_50_1))
% 242.52/49.02    (9)  op(e1, e2) = e2
% 242.52/49.02    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.52/49.02          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.52/49.02    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.02    (12)  op(e1, e2) = all_40_1
% 242.52/49.02    (13)   ~ (e1 = e0)
% 242.52/49.02    (14)  op(e3, e3) = e0
% 242.52/49.02    (15)  all_58_4 = e3
% 242.52/49.02    (16)  all_58_9 = e2
% 242.52/49.02    (17)   ~ (e2 = e1)
% 242.52/49.02  
% 242.52/49.02  Begin of proof
% 242.52/49.02  | 
% 242.52/49.02  | BETA: splitting (8) gives:
% 242.52/49.02  | 
% 242.52/49.02  | Case 1:
% 242.52/49.02  | | 
% 242.52/49.02  | | 
% 242.52/49.02  | | GROUND_INST: instantiating (11) with e2, all_36_1, e2, e1, simplifying with
% 242.52/49.02  | |              (7), (9) gives:
% 242.52/49.02  | |   (18)  all_36_1 = e2
% 242.52/49.02  | | 
% 242.52/49.02  | | GROUND_INST: instantiating (11) with e0, all_40_1, e2, e1, simplifying with
% 242.52/49.02  | |              (5), (12) gives:
% 242.52/49.02  | |   (19)  all_40_1 = e0
% 242.52/49.02  | | 
% 242.52/49.02  | | GROUND_INST: instantiating (11) with all_36_1, all_40_1, e2, e1, simplifying
% 242.52/49.02  | |              with (7), (12) gives:
% 242.52/49.02  | |   (20)  all_40_1 = all_36_1
% 242.52/49.02  | | 
% 242.52/49.02  | | GROUND_INST: instantiating (11) with e1, e2, e1, e2, simplifying with (2),
% 242.52/49.02  | |              (4) gives:
% 242.52/49.02  | |   (21)  e2 = e1
% 242.52/49.02  | | 
% 242.52/49.02  | | COMBINE_EQS: (19), (20) imply:
% 242.52/49.02  | |   (22)  all_36_1 = e0
% 242.52/49.02  | | 
% 242.52/49.02  | | SIMP: (22) implies:
% 242.52/49.02  | |   (23)  all_36_1 = e0
% 242.52/49.02  | | 
% 242.52/49.02  | | COMBINE_EQS: (18), (23) imply:
% 242.52/49.02  | |   (24)  e2 = e0
% 242.52/49.02  | | 
% 242.52/49.02  | | SIMP: (24) implies:
% 242.52/49.02  | |   (25)  e2 = e0
% 242.52/49.02  | | 
% 242.52/49.02  | | COMBINE_EQS: (21), (25) imply:
% 242.52/49.02  | |   (26)  e1 = e0
% 242.52/49.02  | | 
% 242.52/49.02  | | SIMP: (26) implies:
% 242.52/49.02  | |   (27)  e1 = e0
% 242.52/49.02  | | 
% 242.52/49.02  | | COMBINE_EQS: (1), (27) imply:
% 242.52/49.02  | |   (28)  all_58_1 = e0
% 242.52/49.02  | | 
% 242.52/49.02  | | REF_CLOSE: (3), (10), (11), (13), (14), (15), (16), (17), (28) are
% 242.52/49.02  | |            inconsistent by sub-proof #1016.
% 242.52/49.02  | | 
% 242.52/49.02  | Case 2:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (29)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 & $i(all_50_1)
% 242.52/49.02  | | 
% 242.52/49.02  | | ALPHA: (29) implies:
% 242.52/49.02  | |   (30)   ~ (all_50_1 = e2)
% 242.52/49.02  | |   (31)  op(e3, e0) = all_50_1
% 242.52/49.02  | | 
% 242.52/49.02  | | REF_CLOSE: (6), (11), (30), (31) are inconsistent by sub-proof #1884.
% 242.52/49.02  | | 
% 242.52/49.02  | End of split
% 242.52/49.02  | 
% 242.52/49.02  End of proof
% 242.52/49.02  
% 242.52/49.02  Sub-proof #784 shows that the following formulas are inconsistent:
% 242.52/49.02  ----------------------------------------------------------------
% 242.52/49.02    (1)   ~ (e3 = e0)
% 242.52/49.02    (2)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 242.52/49.02    (3)   ~ (e3 = e1)
% 242.52/49.02    (4)  all_58_3 = e3
% 242.52/49.02    (5)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.52/49.02         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.52/49.02    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.02    (7)   ~ (e1 = e0)
% 242.52/49.02    (8)  op(e3, e3) = e0
% 242.52/49.02    (9)  all_58_4 = e3
% 242.52/49.02    (10)  all_58_9 = e2
% 242.52/49.02    (11)   ~ (e2 = e1)
% 242.52/49.02  
% 242.52/49.02  Begin of proof
% 242.52/49.02  | 
% 242.52/49.02  | BETA: splitting (2) gives:
% 242.52/49.02  | 
% 242.52/49.02  | Case 1:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (12)  all_58_1 = e0 & op(e3, e2) = e0
% 242.52/49.02  | | 
% 242.52/49.02  | | ALPHA: (12) implies:
% 242.52/49.02  | |   (13)  all_58_1 = e0
% 242.52/49.02  | | 
% 242.52/49.02  | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (10), (11), (13) are inconsistent
% 242.52/49.02  | |            by sub-proof #1016.
% 242.52/49.02  | | 
% 242.52/49.02  | Case 2:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (14)  all_58_3 = e0 & op(e2, e2) = e0
% 242.52/49.02  | | 
% 242.52/49.02  | | REF_CLOSE: (1), (4), (14) are inconsistent by sub-proof #1719.
% 242.52/49.02  | | 
% 242.52/49.02  | End of split
% 242.52/49.02  | 
% 242.52/49.02  End of proof
% 242.52/49.02  
% 242.52/49.02  Sub-proof #785 shows that the following formulas are inconsistent:
% 242.52/49.02  ----------------------------------------------------------------
% 242.52/49.02    (1)  all_58_1 = e1
% 242.52/49.02    (2)   ~ (e2 = e0)
% 242.52/49.02    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.02    (4)  op(e3, e3) = e0
% 242.52/49.02    (5)   ~ (e2 = e1)
% 242.52/49.02    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 242.52/49.02  
% 242.52/49.02  Begin of proof
% 242.52/49.02  | 
% 242.52/49.02  | BETA: splitting (6) gives:
% 242.52/49.02  | 
% 242.52/49.02  | Case 1:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 242.52/49.02  | | 
% 242.52/49.02  | | ALPHA: (7) implies:
% 242.52/49.02  | |   (8)  op(e3, e3) = e2
% 242.52/49.02  | | 
% 242.52/49.02  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2188.
% 242.52/49.02  | | 
% 242.52/49.02  | Case 2:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (9)  all_58_1 = e2 & op(e3, e2) = e2
% 242.52/49.02  | | 
% 242.52/49.02  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #1722.
% 242.52/49.02  | | 
% 242.52/49.02  | End of split
% 242.52/49.02  | 
% 242.52/49.02  End of proof
% 242.52/49.02  
% 242.52/49.02  Sub-proof #786 shows that the following formulas are inconsistent:
% 242.52/49.02  ----------------------------------------------------------------
% 242.52/49.02    (1)   ~ (e3 = e0)
% 242.52/49.02    (2)  all_58_6 = e3
% 242.52/49.02    (3)  op(e1, e2) = all_52_6
% 242.52/49.02    (4)   ~ (e3 = e2)
% 242.52/49.02    (5)  all_58_4 = e0 & op(e3, e1) = e0
% 242.52/49.02    (6)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.52/49.02         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.52/49.02    (7)  all_58_11 = e2
% 242.52/49.02    (8)   ~ (all_52_6 = e3)
% 242.52/49.02    (9)  op(e1, e1) = e2
% 242.52/49.02    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.02    (11)  all_58_4 = e3
% 242.52/49.02  
% 242.52/49.02  Begin of proof
% 242.52/49.02  | 
% 242.52/49.02  | ALPHA: (5) implies:
% 242.52/49.02  |   (12)  all_58_4 = e0
% 242.52/49.02  | 
% 242.52/49.02  | COMBINE_EQS: (11), (12) imply:
% 242.52/49.02  |   (13)  e3 = e0
% 242.52/49.02  | 
% 242.52/49.02  | COMBINE_EQS: (2), (13) imply:
% 242.52/49.02  |   (14)  all_58_6 = e0
% 242.52/49.02  | 
% 242.52/49.02  | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (14) are inconsistent by
% 242.52/49.02  |            sub-proof #997.
% 242.52/49.02  | 
% 242.52/49.02  End of proof
% 242.52/49.02  
% 242.52/49.02  Sub-proof #787 shows that the following formulas are inconsistent:
% 242.52/49.02  ----------------------------------------------------------------
% 242.52/49.02    (1)   ~ (e3 = e0)
% 242.52/49.02    (2)  op(e1, e1) = e1
% 242.52/49.02    (3)   ~ (e2 = e0)
% 242.52/49.02    (4)  op(e1, e2) = all_52_6
% 242.52/49.02    (5)  all_58_11 = e1
% 242.52/49.02    (6)  all_58_8 = e1
% 242.52/49.02    (7)   ~ (e3 = e1)
% 242.52/49.02    (8)  op(e1, e0) = e1
% 242.52/49.02    (9)   ~ (e3 = e2)
% 242.52/49.02    (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.52/49.02          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.52/49.02    (11)   ~ (all_52_6 = e3)
% 242.52/49.02    (12)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.52/49.02          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.52/49.02    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.02    (14)   ~ (e1 = e0)
% 242.52/49.02    (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.52/49.02          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.52/49.02    (16)   ~ (e2 = e1)
% 242.52/49.02  
% 242.52/49.02  Begin of proof
% 242.52/49.02  | 
% 242.52/49.02  | BETA: splitting (10) gives:
% 242.52/49.02  | 
% 242.52/49.02  | Case 1:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (17)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 242.52/49.02  | |           e3)
% 242.52/49.02  | | 
% 242.52/49.02  | | BETA: splitting (17) gives:
% 242.52/49.02  | | 
% 242.52/49.02  | | Case 1:
% 242.52/49.02  | | | 
% 242.52/49.02  | | |   (18)  all_58_6 = e3 & op(e1, e3) = e3
% 242.52/49.02  | | | 
% 242.52/49.02  | | | ALPHA: (18) implies:
% 242.52/49.02  | | |   (19)  all_58_6 = e3
% 242.52/49.02  | | | 
% 242.52/49.02  | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (12), (13), (14), (15),
% 242.52/49.02  | | |            (16), (19) are inconsistent by sub-proof #804.
% 242.52/49.02  | | | 
% 242.52/49.02  | | Case 2:
% 242.52/49.02  | | | 
% 242.52/49.02  | | |   (20)  all_58_7 = e3 & op(e1, e2) = e3
% 242.52/49.02  | | | 
% 242.52/49.02  | | | ALPHA: (20) implies:
% 242.52/49.02  | | |   (21)  op(e1, e2) = e3
% 242.52/49.02  | | | 
% 242.52/49.02  | | | REF_CLOSE: (4), (11), (13), (21) are inconsistent by sub-proof #2191.
% 242.52/49.02  | | | 
% 242.52/49.02  | | End of split
% 242.52/49.02  | | 
% 242.52/49.02  | Case 2:
% 242.52/49.02  | | 
% 242.52/49.02  | |   (22)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 242.52/49.02  | |           e3)
% 242.52/49.02  | | 
% 242.52/49.02  | | BETA: splitting (22) gives:
% 242.52/49.02  | | 
% 242.52/49.02  | | Case 1:
% 242.52/49.02  | | | 
% 242.52/49.02  | | |   (23)  all_58_8 = e3 & op(e1, e1) = e3
% 242.52/49.02  | | | 
% 242.52/49.02  | | | ALPHA: (23) implies:
% 242.52/49.02  | | |   (24)  all_58_8 = e3
% 242.52/49.02  | | | 
% 242.52/49.02  | | | COMBINE_EQS: (6), (24) imply:
% 242.52/49.02  | | |   (25)  e3 = e1
% 242.52/49.02  | | | 
% 242.52/49.02  | | | REDUCE: (7), (25) imply:
% 242.52/49.02  | | |   (26)  $false
% 242.52/49.02  | | | 
% 242.52/49.02  | | | CLOSE: (26) is inconsistent.
% 242.52/49.02  | | | 
% 242.52/49.02  | | Case 2:
% 242.52/49.02  | | | 
% 242.52/49.02  | | |   (27)  all_58_11 = e3 & op(e1, e0) = e3
% 242.52/49.02  | | | 
% 242.52/49.02  | | | REF_CLOSE: (5), (7), (27) are inconsistent by sub-proof #788.
% 242.52/49.02  | | | 
% 242.52/49.02  | | End of split
% 242.52/49.02  | | 
% 242.52/49.02  | End of split
% 242.52/49.02  | 
% 242.52/49.02  End of proof
% 242.52/49.02  
% 242.52/49.02  Sub-proof #788 shows that the following formulas are inconsistent:
% 242.52/49.02  ----------------------------------------------------------------
% 242.52/49.02    (1)  all_58_11 = e3 & op(e1, e0) = e3
% 242.52/49.02    (2)  all_58_11 = e1
% 242.52/49.02    (3)   ~ (e3 = e1)
% 242.52/49.02  
% 242.52/49.02  Begin of proof
% 242.52/49.02  | 
% 242.52/49.02  | ALPHA: (1) implies:
% 242.52/49.02  |   (4)  all_58_11 = e3
% 242.52/49.02  | 
% 242.52/49.02  | COMBINE_EQS: (2), (4) imply:
% 242.52/49.02  |   (5)  e3 = e1
% 242.52/49.02  | 
% 242.52/49.02  | REDUCE: (3), (5) imply:
% 242.52/49.02  |   (6)  $false
% 242.52/49.02  | 
% 242.52/49.02  | CLOSE: (6) is inconsistent.
% 242.52/49.02  | 
% 242.52/49.02  End of proof
% 242.52/49.02  
% 242.52/49.02  Sub-proof #789 shows that the following formulas are inconsistent:
% 242.52/49.02  ----------------------------------------------------------------
% 242.52/49.02    (1)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 242.52/49.02    (2)   ~ (e3 = e0)
% 242.52/49.02    (3)  all_58_6 = e3
% 242.52/49.02    (4)   ~ (e2 = e0)
% 242.52/49.03    (5)   ~ (e3 = e1)
% 242.52/49.03    (6)  all_58_3 = e3
% 242.52/49.03    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.52/49.03         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.52/49.03    (8)   ~ (e3 = e2)
% 242.52/49.03    (9)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.52/49.03         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.52/49.03    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.03    (11)   ~ (e1 = e0)
% 242.52/49.03    (12)  op(e3, e3) = e0
% 242.52/49.03    (13)   ~ (e2 = e1)
% 242.52/49.03  
% 242.52/49.03  Begin of proof
% 242.52/49.03  | 
% 242.52/49.03  | BETA: splitting (1) gives:
% 242.52/49.03  | 
% 242.52/49.03  | Case 1:
% 242.52/49.03  | | 
% 242.52/49.03  | |   (14)  all_58_2 = e0 & op(e2, e3) = e0
% 242.52/49.03  | | 
% 242.52/49.03  | | ALPHA: (14) implies:
% 242.52/49.03  | |   (15)  all_58_2 = e0
% 242.52/49.03  | | 
% 242.52/49.03  | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (15) are
% 242.52/49.03  | |            inconsistent by sub-proof #1266.
% 242.52/49.03  | | 
% 242.52/49.03  | Case 2:
% 242.52/49.03  | | 
% 242.52/49.03  | |   (16)  all_58_3 = e0 & op(e2, e2) = e0
% 242.52/49.03  | | 
% 242.52/49.03  | | REF_CLOSE: (2), (6), (16) are inconsistent by sub-proof #1719.
% 242.52/49.03  | | 
% 242.52/49.03  | End of split
% 242.52/49.03  | 
% 242.52/49.03  End of proof
% 242.52/49.03  
% 242.52/49.03  Sub-proof #790 shows that the following formulas are inconsistent:
% 242.52/49.03  ----------------------------------------------------------------
% 242.52/49.03    (1)   ~ (all_52_9 = all_6_2)
% 242.52/49.03    (2)   ~ (all_6_2 = e2)
% 242.52/49.03    (3)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 242.52/49.03    (4)  all_58_3 = e3
% 242.52/49.03    (5)  all_54_10 = all_6_2
% 242.52/49.03    (6)   ~ (all_6_2 = e3)
% 242.52/49.03    (7)  op(e2, e1) = all_52_9
% 242.52/49.03    (8)   ~ (all_6_2 = e0)
% 242.52/49.03    (9)  op(e2, e0) = e0
% 242.52/49.03    (10)  op(e2, e3) = all_52_1
% 242.52/49.03    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.03    (12)  op(e2, e0) = all_52_13
% 242.52/49.03    (13)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.52/49.03          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.52/49.03    (14)   ~ (all_52_1 = e1)
% 242.52/49.03  
% 242.52/49.03  Begin of proof
% 242.52/49.03  | 
% 242.52/49.03  | BETA: splitting (3) gives:
% 242.52/49.03  | 
% 242.52/49.03  | Case 1:
% 242.52/49.03  | | 
% 242.52/49.03  | |   (15)  all_54_10 = e2
% 242.52/49.03  | | 
% 242.52/49.03  | | REF_CLOSE: (2), (5), (15) are inconsistent by sub-proof #2312.
% 242.52/49.03  | | 
% 242.52/49.03  | Case 2:
% 242.52/49.03  | | 
% 242.52/49.03  | |   (16)  all_54_10 = e1 | all_54_10 = e0
% 242.52/49.03  | | 
% 242.52/49.03  | | BETA: splitting (16) gives:
% 242.52/49.03  | | 
% 242.52/49.03  | | Case 1:
% 242.52/49.03  | | | 
% 242.52/49.03  | | |   (17)  all_54_10 = e1
% 242.52/49.03  | | | 
% 242.52/49.03  | | | COMBINE_EQS: (5), (17) imply:
% 242.52/49.03  | | |   (18)  all_6_2 = e1
% 242.52/49.03  | | | 
% 242.52/49.03  | | | SIMP: (18) implies:
% 242.52/49.03  | | |   (19)  all_6_2 = e1
% 242.52/49.03  | | | 
% 242.52/49.03  | | | REDUCE: (1), (19) imply:
% 242.52/49.03  | | |   (20)   ~ (all_52_9 = e1)
% 242.52/49.03  | | | 
% 242.52/49.03  | | | REDUCE: (6), (19) imply:
% 242.52/49.03  | | |   (21)   ~ (e3 = e1)
% 242.52/49.03  | | | 
% 242.52/49.03  | | | SIMP: (21) implies:
% 242.52/49.03  | | |   (22)   ~ (e3 = e1)
% 242.52/49.03  | | | 
% 242.52/49.03  | | | REDUCE: (8), (19) imply:
% 242.52/49.03  | | |   (23)   ~ (e1 = e0)
% 242.52/49.03  | | | 
% 242.52/49.03  | | | REF_CLOSE: (4), (7), (9), (10), (11), (12), (13), (14), (20), (22), (23)
% 242.52/49.03  | | |            are inconsistent by sub-proof #1777.
% 242.52/49.03  | | | 
% 242.52/49.03  | | Case 2:
% 242.52/49.03  | | | 
% 242.52/49.03  | | |   (24)  all_54_10 = e0
% 242.52/49.03  | | | 
% 242.52/49.03  | | | REF_CLOSE: (5), (8), (24) are inconsistent by sub-proof #2303.
% 242.52/49.03  | | | 
% 242.52/49.03  | | End of split
% 242.52/49.03  | | 
% 242.52/49.03  | End of split
% 242.52/49.03  | 
% 242.52/49.03  End of proof
% 242.52/49.03  
% 242.52/49.03  Sub-proof #791 shows that the following formulas are inconsistent:
% 242.52/49.03  ----------------------------------------------------------------
% 242.52/49.03    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 242.52/49.03           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 242.52/49.03             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.52/49.03           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.52/49.03             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 242.52/49.03           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.52/49.03           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.52/49.03    (2)  op(e2, e3) = all_52_1
% 242.52/49.03    (3)  all_56_21 = e1
% 242.52/49.03    (4)  all_56_31 = e3
% 242.52/49.03    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.03    (6)   ~ (all_52_1 = e3)
% 242.52/49.03  
% 242.52/49.03  Begin of proof
% 242.52/49.03  | 
% 242.52/49.03  | BETA: splitting (1) gives:
% 242.52/49.03  | 
% 242.52/49.03  | Case 1:
% 242.52/49.03  | | 
% 242.52/49.03  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.52/49.03  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.52/49.03  | |        op(e2, e3) = e3
% 242.52/49.03  | | 
% 242.52/49.03  | | ALPHA: (7) implies:
% 242.52/49.03  | |   (8)  op(e2, e3) = e3
% 242.52/49.03  | | 
% 242.52/49.03  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2337.
% 242.52/49.03  | | 
% 242.52/49.03  | Case 2:
% 242.52/49.03  | | 
% 242.52/49.03  | |   (9)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.52/49.03  | |            e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2
% 242.52/49.03  | |          & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1
% 242.52/49.03  | |            = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 242.52/49.03  | |            = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.52/49.03  | | 
% 242.52/49.03  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #1280.
% 242.52/49.03  | | 
% 242.52/49.03  | End of split
% 242.52/49.03  | 
% 242.52/49.03  End of proof
% 242.52/49.03  
% 242.52/49.03  Sub-proof #792 shows that the following formulas are inconsistent:
% 242.52/49.03  ----------------------------------------------------------------
% 242.52/49.03    (1)  op(e2, e2) = e3
% 242.52/49.03    (2)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.52/49.03           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.52/49.03           all_12_1 & $i(all_12_1))
% 242.52/49.03    (3)   ~ (e3 = e0)
% 242.52/49.03    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.52/49.03         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.52/49.03    (5)  all_58_6 = e3
% 242.52/49.03    (6)   ~ (e2 = e0)
% 242.52/49.03    (7)  op(e1, e2) = all_52_6
% 242.52/49.03    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.52/49.03         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.52/49.03    (9)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 242.52/49.03         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 242.52/49.03    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.52/49.03          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.52/49.03    (11)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.52/49.03          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.52/49.03    (12)  all_58_14 = e2
% 242.52/49.03    (13)  all_58_15 = e3
% 242.52/49.03    (14)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.52/49.03          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.52/49.03    (15)   ~ (e3 = e1)
% 242.52/49.03    (16)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.52/49.03          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.52/49.03    (17)  all_58_3 = e3
% 242.52/49.03    (18)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.52/49.03            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.52/49.03              e3) = all_26_1 & $i(all_26_1))
% 242.52/49.03    (19)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.52/49.03              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.52/49.03                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.52/49.03                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.52/49.03    (20)  op(e2, e1) = all_52_9
% 242.52/49.03    (21)   ~ (e3 = e2)
% 242.52/49.03    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.52/49.03          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.52/49.03    (23)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.52/49.03            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.52/49.03            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.52/49.03            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.52/49.03            op(e0, all_56_31) = e0)
% 242.52/49.03    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.52/49.03          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.52/49.03    (25)  op(e3, e0) = all_52_12
% 242.52/49.03    (26)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.52/49.03            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.52/49.03              e3) = all_42_1 & $i(all_42_1))
% 242.52/49.03    (27)  op(e2, e3) = all_52_1
% 242.52/49.03    (28)  op(e3, e3) = e2
% 242.52/49.03    (29)  all_56_31 = e3
% 242.52/49.03    (30)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.52/49.03          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.52/49.03    (31)  op(e0, e0) = e3
% 242.52/49.03    (32)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.52/49.03          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.52/49.03    (33)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.52/49.03          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.52/49.03    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.52/49.03          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.52/49.03    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.03    (36)   ~ (all_52_12 = e3)
% 242.52/49.03    (37)  op(e1, e1) = e0
% 242.52/49.03    (38)   ~ (e1 = e0)
% 242.52/49.03    (39)  all_58_4 = e3
% 242.52/49.03    (40)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.52/49.03          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.52/49.03            e1)
% 242.52/49.03    (41)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.52/49.03          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.52/49.03            e2)
% 242.52/49.03    (42)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.52/49.03          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.52/49.03    (43)   ~ (all_52_1 = e2)
% 242.52/49.03    (44)   ~ (e2 = e1)
% 242.52/49.03  
% 242.52/49.03  Begin of proof
% 242.52/49.03  | 
% 242.52/49.03  | BETA: splitting (11) gives:
% 242.52/49.03  | 
% 242.52/49.03  | Case 1:
% 242.52/49.03  | | 
% 242.52/49.03  | |   (45)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 242.52/49.03  | |           e1)
% 242.52/49.03  | | 
% 242.52/49.03  | | BETA: splitting (45) gives:
% 242.52/49.03  | | 
% 242.52/49.03  | | Case 1:
% 242.52/49.03  | | | 
% 242.52/49.03  | | |   (46)  all_58_4 = e1 & op(e3, e1) = e1
% 242.52/49.03  | | | 
% 242.52/49.03  | | | ALPHA: (46) implies:
% 242.52/49.03  | | |   (47)  all_58_4 = e1
% 242.52/49.03  | | | 
% 242.52/49.03  | | | REF_CLOSE: (15), (39), (47) are inconsistent by sub-proof #2184.
% 242.52/49.03  | | | 
% 242.52/49.03  | | Case 2:
% 242.52/49.03  | | | 
% 242.52/49.03  | | |   (48)  all_58_5 = e1 & op(e2, e1) = e1
% 242.52/49.03  | | | 
% 242.52/49.03  | | | ALPHA: (48) implies:
% 242.52/49.03  | | |   (49)  all_58_5 = e1
% 242.52/49.03  | | | 
% 242.52/49.03  | | | BETA: splitting (14) gives:
% 242.52/49.03  | | | 
% 242.52/49.03  | | | Case 1:
% 242.52/49.03  | | | | 
% 242.52/49.03  | | | |   (50)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2)
% 242.52/49.03  | | | |           = e2)
% 242.52/49.03  | | | | 
% 242.52/49.03  | | | | REF_CLOSE: (17), (21), (27), (35), (43), (50) are inconsistent by
% 242.52/49.03  | | | |            sub-proof #825.
% 242.52/49.03  | | | | 
% 242.52/49.03  | | | Case 2:
% 242.52/49.03  | | | | 
% 242.52/49.03  | | | |   (51)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0)
% 242.52/49.03  | | | |           = e2)
% 242.52/49.03  | | | | 
% 242.52/49.03  | | | | BETA: splitting (51) gives:
% 242.52/49.03  | | | | 
% 242.52/49.03  | | | | Case 1:
% 242.52/49.03  | | | | | 
% 242.52/49.03  | | | | |   (52)  all_58_5 = e2 & op(e2, e1) = e2
% 242.52/49.03  | | | | | 
% 242.52/49.03  | | | | | ALPHA: (52) implies:
% 242.52/49.03  | | | | |   (53)  all_58_5 = e2
% 242.52/49.03  | | | | | 
% 242.52/49.03  | | | | | COMBINE_EQS: (49), (53) imply:
% 242.52/49.03  | | | | |   (54)  e2 = e1
% 242.52/49.03  | | | | | 
% 242.52/49.03  | | | | | REF_CLOSE: (3), (6), (12), (16), (21), (22), (38), (39), (44), (49),
% 242.52/49.03  | | | | |            (54) are inconsistent by sub-proof #839.
% 242.52/49.03  | | | | | 
% 242.52/49.03  | | | | Case 2:
% 242.52/49.03  | | | | | 
% 242.52/49.03  | | | | |   (55)  all_58_10 = e2 & op(e2, e0) = e2
% 242.52/49.03  | | | | | 
% 242.52/49.03  | | | | | ALPHA: (55) implies:
% 242.52/49.03  | | | | |   (56)  all_58_10 = e2
% 242.52/49.03  | | | | |   (57)  op(e2, e0) = e2
% 242.52/49.03  | | | | | 
% 242.52/49.03  | | | | | BETA: splitting (19) gives:
% 242.52/49.03  | | | | | 
% 242.52/49.03  | | | | | Case 1:
% 242.52/49.03  | | | | | | 
% 242.52/49.03  | | | | | |   (58)  all_58_15 = e0 & op(e0, e0) = e0
% 242.52/49.03  | | | | | | 
% 242.52/49.03  | | | | | | ALPHA: (58) implies:
% 242.52/49.03  | | | | | |   (59)  op(e0, e0) = e0
% 242.52/49.03  | | | | | | 
% 242.52/49.03  | | | | | | REF_CLOSE: (3), (31), (35), (59) are inconsistent by sub-proof
% 242.52/49.03  | | | | | |            #2079.
% 242.52/49.03  | | | | | | 
% 242.52/49.03  | | | | | Case 2:
% 242.52/49.03  | | | | | | 
% 242.52/49.03  | | | | | |   (60)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 242.52/49.03  | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 242.52/49.03  | | | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.52/49.03  | | | | | |             op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.52/49.03  | | | | | | 
% 242.52/49.03  | | | | | | ALPHA: (60) implies:
% 242.52/49.03  | | | | | |   (61)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 242.52/49.03  | | | | | |             e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.52/49.03  | | | | | | 
% 242.52/49.03  | | | | | | BETA: splitting (34) gives:
% 242.52/49.03  | | | | | | 
% 242.52/49.03  | | | | | | Case 1:
% 242.52/49.03  | | | | | | | 
% 242.52/49.03  | | | | | | |   (62)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 242.52/49.03  | | | | | | |           op(e2, e2) = e0)
% 242.52/49.03  | | | | | | | 
% 242.52/49.03  | | | | | | | BETA: splitting (62) gives:
% 242.52/49.03  | | | | | | | 
% 242.52/49.03  | | | | | | | Case 1:
% 242.52/49.03  | | | | | | | | 
% 242.52/49.03  | | | | | | | |   (63)  all_58_2 = e0 & op(e2, e3) = e0
% 242.52/49.03  | | | | | | | | 
% 242.52/49.03  | | | | | | | | ALPHA: (63) implies:
% 242.52/49.03  | | | | | | | |   (64)  all_58_2 = e0
% 242.52/49.03  | | | | | | | |   (65)  op(e2, e3) = e0
% 242.52/49.03  | | | | | | | | 
% 242.52/49.03  | | | | | | | | BETA: splitting (61) gives:
% 242.52/49.03  | | | | | | | | 
% 242.52/49.03  | | | | | | | | Case 1:
% 242.52/49.03  | | | | | | | | | 
% 242.52/49.03  | | | | | | | | |   (66)  all_58_9 = e0 & op(e3, e0) = e0
% 242.52/49.03  | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | ALPHA: (66) implies:
% 242.52/49.03  | | | | | | | | |   (67)  all_58_9 = e0
% 242.52/49.03  | | | | | | | | |   (68)  op(e3, e0) = e0
% 242.52/49.03  | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | BETA: splitting (32) gives:
% 242.52/49.03  | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | Case 1:
% 242.52/49.03  | | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | |   (69)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 &
% 242.52/49.03  | | | | | | | | | |           op(e3, e2) = e1)
% 242.52/49.03  | | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | | BETA: splitting (69) gives:
% 242.52/49.03  | | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | | Case 1:
% 242.52/49.03  | | | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | | |   (70)  all_58_0 = e1 & op(e3, e3) = e1
% 242.52/49.03  | | | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | | | ALPHA: (70) implies:
% 242.52/49.03  | | | | | | | | | | |   (71)  op(e3, e3) = e1
% 242.52/49.03  | | | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | | | REF_CLOSE: (28), (35), (44), (71) are inconsistent by
% 242.52/49.03  | | | | | | | | | | |            sub-proof #2267.
% 242.52/49.03  | | | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | | Case 2:
% 242.52/49.03  | | | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | | |   (72)  all_58_1 = e1 & op(e3, e2) = e1
% 242.52/49.03  | | | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | | | ALPHA: (72) implies:
% 242.52/49.03  | | | | | | | | | | |   (73)  all_58_1 = e1
% 242.52/49.03  | | | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | | | BETA: splitting (10) gives:
% 242.52/49.03  | | | | | | | | | | | 
% 242.52/49.03  | | | | | | | | | | | Case 1:
% 242.52/49.03  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | |   (74)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 242.52/49.04  | | | | | | | | | | | |           & op(e2, e2) = e0)
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | BETA: splitting (74) gives:
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | |   (75)  all_58_1 = e0 & op(e3, e2) = e0
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | REF_CLOSE: (38), (73), (75) are inconsistent by sub-proof
% 242.52/49.04  | | | | | | | | | | | | |            #1720.
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | |   (76)  all_58_3 = e0 & op(e2, e2) = e0
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | REF_CLOSE: (3), (17), (76) are inconsistent by sub-proof
% 242.52/49.04  | | | | | | | | | | | | |            #1719.
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | |   (77)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 242.52/49.04  | | | | | | | | | | | |           e0 & op(e0, e2) = e0)
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | BETA: splitting (77) gives:
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | |   (78)  all_58_7 = e0 & op(e1, e2) = e0
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | ALPHA: (78) implies:
% 242.52/49.04  | | | | | | | | | | | | |   (79)  all_58_7 = e0
% 242.52/49.04  | | | | | | | | | | | | |   (80)  op(e1, e2) = e0
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (15), (21), (33), (35), (37),
% 242.52/49.04  | | | | | | | | | | | | |            (38), (44), (79), (80) are inconsistent by
% 242.52/49.04  | | | | | | | | | | | | |            sub-proof #1018.
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | |   (81)  all_58_13 = e0 & op(e0, e2) = e0
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | ALPHA: (81) implies:
% 242.52/49.04  | | | | | | | | | | | | |   (82)  op(e0, e2) = e0
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | BETA: splitting (8) gives:
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | |   (83)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 242.52/49.04  | | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | |   (84)  all_58_1 = e2 & op(e3, e2) = e2
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 242.52/49.04  | | | | | | | | | | | | | | |   (85)  all_58_1 = e2
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | REF_CLOSE: (15), (28), (32), (35), (38), (39), (44), (67),
% 242.52/49.04  | | | | | | | | | | | | | | |            (85) are inconsistent by sub-proof #2181.
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | |   (86)  all_58_3 = e2 & op(e2, e2) = e2
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | REF_CLOSE: (17), (21), (86) are inconsistent by sub-proof
% 242.52/49.04  | | | | | | | | | | | | | | |            #1458.
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | |   (87)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 242.52/49.04  | | | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | |   (88)  all_58_7 = e2 & op(e1, e2) = e2
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | ALPHA: (88) implies:
% 242.52/49.04  | | | | | | | | | | | | | | |   (89)  all_58_7 = e2
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | |   (90)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 242.52/49.04  | | | | | | | | | | | | | | | |           & op(e1, e2) = e1)
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | |   (91)  all_58_6 = e1 & op(e1, e3) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (91) are inconsistent by sub-proof
% 242.52/49.04  | | | | | | | | | | | | | | | | |            #1803.
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | |   (92)  all_58_7 = e1 & op(e1, e2) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | |   (93)  all_58_7 = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (93) imply:
% 242.52/49.04  | | | | | | | | | | | | | | | | |   (94)  e2 = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (94) imply:
% 242.52/49.04  | | | | | | | | | | | | | | | | |   (95)  all_58_10 = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (14), (17), (21), (34), (38), (44),
% 242.52/49.04  | | | | | | | | | | | | | | | | |            (49), (95) are inconsistent by sub-proof #992.
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | |   (96)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 242.52/49.04  | | | | | | | | | | | | | | | |           e1 & op(e1, e0) = e1)
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | |   (97)  all_58_8 = e1 & op(e1, e1) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | |   (98)  op(e1, e1) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (37), (38), (98) are inconsistent by
% 242.52/49.04  | | | | | | | | | | | | | | | | |            sub-proof #2220.
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | |   (99)  all_58_11 = e1 & op(e1, e0) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | |   (100)  op(e1, e0) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | |   (101)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (35), (38), (44), (64), (101) are
% 242.52/49.04  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #796.
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | |   (102)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 242.52/49.04  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | |   (103)  all_58_6 = e1 & op(e1, e3) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (103) are inconsistent by sub-proof
% 242.52/49.04  | | | | | | | | | | | | | | | | | | |            #1803.
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | |   (104)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | |   (105)  op(e0, e3) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |   (106)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (107)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_25 & $i(all_56_25)
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (108)  op(e3, e0) = all_56_25
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (109)  op(e3, all_56_25) = e3
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with e0, all_56_25, e0, e3,
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |              simplifying with (68), (108) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (110)  all_56_25 = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (110) imply:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (111)  op(e3, e0) = e3
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (35), (36), (111) are inconsistent by
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2179.
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (112)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 &
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |          $i(all_26_1)
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (105), (112) are inconsistent by sub-proof
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |            #1386.
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (113)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_27 & $i(all_56_27)
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (114)  op(e2, e0) = all_56_27
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (115)  op(e2, all_56_27) = e2
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (21), (35), (57), (114), (115) are
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #954.
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |   (116)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (117)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |            e0) = all_56_29 & $i(all_56_29)
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (118)  op(e1, e0) = all_56_29
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (119)  op(e1, all_56_29) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with e1, all_56_29, e0, e1,
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |              simplifying with (100), (118) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (120)  all_56_29 = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (120) imply:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (121)  op(e1, e1) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (37), (38), (121) are inconsistent by
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2220.
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (122)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 &
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |          $i(all_42_1)
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (123)   ~ (all_42_1 = e1)
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (124)  op(e2, e3) = all_42_1
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with e1, all_56_29, e0, e1,
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |              simplifying with (100), (118) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (125)  all_56_29 = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with e0, all_42_1, e3, e2,
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |              simplifying with (65), (124) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (126)  all_42_1 = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (126) imply:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (127)   ~ (e1 = e0)
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (125) imply:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |   (128)  op(e1, e1) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (37), (38), (128) are inconsistent by
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2220.
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (129)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (130)  op(e0, all_56_31) = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | REDUCE: (29), (130) imply:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |   (131)  op(e0, e3) = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (18), (35), (38), (105), (131) are
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1384.
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | |   (132)  all_58_13 = e2 & op(e0, e2) = e2
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 242.52/49.04  | | | | | | | | | | | | | | |   (133)  op(e0, e2) = e2
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | REF_CLOSE: (6), (35), (82), (133) are inconsistent by
% 242.52/49.04  | | | | | | | | | | | | | | |            sub-proof #2132.
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | |   (134)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 242.52/49.04  | | | | | | | | | |            & op(e3, e0) = e1)
% 242.52/49.04  | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | REF_CLOSE: (15), (38), (39), (67), (134) are inconsistent by
% 242.52/49.04  | | | | | | | | | |            sub-proof #1216.
% 242.52/49.04  | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | 
% 242.52/49.04  | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | 
% 242.52/49.04  | | | | | | | | |   (135)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0
% 242.52/49.04  | | | | | | | | |            & op(e1, e0) = e0)
% 242.52/49.04  | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | REF_CLOSE: (4), (5), (6), (15), (21), (33), (35), (37), (38),
% 242.52/49.04  | | | | | | | | |            (44), (57), (135) are inconsistent by sub-proof
% 242.52/49.04  | | | | | | | | |            #793.
% 242.52/49.04  | | | | | | | | | 
% 242.52/49.04  | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | 
% 242.52/49.04  | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | 
% 242.52/49.04  | | | | | | | |   (136)  all_58_3 = e0 & op(e2, e2) = e0
% 242.52/49.04  | | | | | | | | 
% 242.52/49.04  | | | | | | | | REF_CLOSE: (3), (17), (136) are inconsistent by sub-proof #1719.
% 242.52/49.04  | | | | | | | | 
% 242.52/49.04  | | | | | | | End of split
% 242.52/49.04  | | | | | | | 
% 242.52/49.04  | | | | | | Case 2:
% 242.52/49.04  | | | | | | | 
% 242.52/49.04  | | | | | | |   (137)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 242.52/49.04  | | | | | | |            op(e2, e0) = e0)
% 242.52/49.04  | | | | | | | 
% 242.52/49.04  | | | | | | | BETA: splitting (137) gives:
% 242.52/49.04  | | | | | | | 
% 242.52/49.04  | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | 
% 242.52/49.04  | | | | | | | |   (138)  all_58_5 = e0 & op(e2, e1) = e0
% 242.52/49.04  | | | | | | | | 
% 242.52/49.04  | | | | | | | | ALPHA: (138) implies:
% 242.52/49.04  | | | | | | | |   (139)  op(e2, e1) = e0
% 242.52/49.04  | | | | | | | | 
% 242.52/49.04  | | | | | | | | BETA: splitting (19) gives:
% 242.52/49.04  | | | | | | | | 
% 242.52/49.04  | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | 
% 242.52/49.04  | | | | | | | | |   (140)  all_58_15 = e0 & op(e0, e0) = e0
% 242.52/49.04  | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | ALPHA: (140) implies:
% 242.52/49.04  | | | | | | | | |   (141)  op(e0, e0) = e0
% 242.52/49.04  | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | REF_CLOSE: (3), (31), (35), (141) are inconsistent by
% 242.52/49.04  | | | | | | | | |            sub-proof #2079.
% 242.52/49.04  | | | | | | | | | 
% 242.52/49.04  | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | BETA: splitting (61) gives:
% 242.52/49.04  | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | |   (142)  all_58_9 = e0 & op(e3, e0) = e0
% 242.52/49.04  | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | ALPHA: (142) implies:
% 242.52/49.04  | | | | | | | | | |   (143)  all_58_9 = e0
% 242.52/49.04  | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | BETA: splitting (32) gives:
% 242.52/49.04  | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | |   (144)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 242.52/49.04  | | | | | | | | | | |            & op(e3, e2) = e1)
% 242.52/49.04  | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | BETA: splitting (144) gives:
% 242.52/49.04  | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | |   (145)  all_58_0 = e1 & op(e3, e3) = e1
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | ALPHA: (145) implies:
% 242.52/49.04  | | | | | | | | | | | |   (146)  op(e3, e3) = e1
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | REF_CLOSE: (28), (35), (44), (146) are inconsistent by
% 242.52/49.04  | | | | | | | | | | | |            sub-proof #2267.
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | |   (147)  all_58_1 = e1 & op(e3, e2) = e1
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | ALPHA: (147) implies:
% 242.52/49.04  | | | | | | | | | | | |   (148)  all_58_1 = e1
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | BETA: splitting (9) gives:
% 242.52/49.04  | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | |   (149)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 242.52/49.04  | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | REF_CLOSE: (35), (38), (44), (57), (143), (149) are
% 242.52/49.04  | | | | | | | | | | | | |            inconsistent by sub-proof #1658.
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | |   (150)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 242.52/49.04  | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | BETA: splitting (150) gives:
% 242.52/49.04  | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | |   (151)  all_58_11 = e1 & op(e1, e0) = e1
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | ALPHA: (151) implies:
% 242.52/49.04  | | | | | | | | | | | | | |   (152)  all_58_11 = e1
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 242.52/49.04  | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | |   (153)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 242.52/49.04  | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | |   (154)  all_58_1 = e0 & op(e3, e2) = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | REF_CLOSE: (38), (148), (154) are inconsistent by sub-proof
% 242.52/49.04  | | | | | | | | | | | | | | | |            #1720.
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | |   (155)  all_58_3 = e0 & op(e2, e2) = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | |   (156)  all_58_3 = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (17), (156) are inconsistent by sub-proof
% 242.52/49.04  | | | | | | | | | | | | | | | |            #1460.
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | |   (157)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 242.52/49.04  | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | |   (158)  all_58_7 = e0 & op(e1, e2) = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | |   (159)  all_58_7 = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (21), (33), (35), (37), (44), (152),
% 242.52/49.04  | | | | | | | | | | | | | | | |            (159) are inconsistent by sub-proof #1325.
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | |   (160)  all_58_13 = e0 & op(e0, e2) = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | |   (161)  op(e0, e2) = e0
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | |   (162)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 242.52/49.04  | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | |   (163)  all_58_12 = e2 & op(e0, e3) = e2
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | | |   (164)  all_58_12 = e2
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (15), (24), (28), (30), (35), (38),
% 242.52/49.04  | | | | | | | | | | | | | | | | | |            (44), (164) are inconsistent by sub-proof #1756.
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | |   (165)  all_58_13 = e2 & op(e0, e2) = e2
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | | |   (166)  op(e0, e2) = e2
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (35), (161), (166) are inconsistent by
% 242.52/49.04  | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | End of split
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | |   (167)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 242.52/49.04  | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | |   (168)  all_58_14 = e2 & op(e0, e1) = e2
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | |   (169)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 242.52/49.04  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |   (170)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |   (171)  all_58_12 = e1
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (15), (17), (20), (24), (28), (35),
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |            (38), (42), (44), (57), (139), (171) are
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #973.
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.04  | | | | | | | | | | | | | | | | | | | |   (172)  all_58_13 = e1 & op(e0, e2) = e1
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | |   (173)  op(e0, e2) = e1
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (38), (161), (173) are inconsistent by
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | |            sub-proof #1872.
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | |   (174)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 242.52/49.05  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | |   (175)  all_58_14 = e1 & op(e0, e1) = e1
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | |   (176)  all_58_14 = e1
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (44), (176) are inconsistent by sub-proof
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | |            #2044.
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | |   (177)  all_58_15 = e1 & op(e0, e0) = e1
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | |   (178)  all_58_15 = e1
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (178) are inconsistent by sub-proof
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | |            #2249.
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.05  | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | |   (179)  all_58_15 = e2 & op(e0, e0) = e2
% 242.52/49.05  | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 242.52/49.05  | | | | | | | | | | | | | | | | | |   (180)  op(e0, e0) = e2
% 242.52/49.05  | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (31), (35), (180) are inconsistent by
% 242.52/49.05  | | | | | | | | | | | | | | | | | |            sub-proof #1388.
% 242.52/49.05  | | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | Case 2:
% 242.52/49.05  | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | |   (181)  all_58_15 = e1 & op(e0, e0) = e1
% 242.52/49.05  | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | ALPHA: (181) implies:
% 242.52/49.05  | | | | | | | | | | | | | |   (182)  all_58_15 = e1
% 242.52/49.05  | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (182) are inconsistent by sub-proof
% 242.52/49.05  | | | | | | | | | | | | | |            #2249.
% 242.52/49.05  | | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | Case 2:
% 242.52/49.05  | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | |   (183)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 242.52/49.05  | | | | | | | | | | |            & op(e3, e0) = e1)
% 242.52/49.05  | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | | REF_CLOSE: (15), (38), (39), (143), (183) are inconsistent by
% 242.52/49.05  | | | | | | | | | | |            sub-proof #2182.
% 242.52/49.05  | | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | Case 2:
% 242.52/49.05  | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | |   (184)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 242.52/49.05  | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 242.52/49.05  | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (15), (21), (33), (35), (37), (38),
% 242.52/49.05  | | | | | | | | | |            (44), (57), (184) are inconsistent by sub-proof
% 242.52/49.05  | | | | | | | | | |            #793.
% 242.52/49.05  | | | | | | | | | | 
% 242.52/49.05  | | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | | 
% 242.52/49.05  | | | | | | | | End of split
% 242.52/49.05  | | | | | | | | 
% 242.52/49.05  | | | | | | | Case 2:
% 242.52/49.05  | | | | | | | | 
% 242.52/49.05  | | | | | | | |   (185)  all_58_10 = e0 & op(e2, e0) = e0
% 242.52/49.05  | | | | | | | | 
% 242.52/49.05  | | | | | | | | ALPHA: (185) implies:
% 242.52/49.05  | | | | | | | |   (186)  op(e2, e0) = e0
% 242.52/49.05  | | | | | | | | 
% 242.52/49.05  | | | | | | | | REF_CLOSE: (6), (35), (57), (186) are inconsistent by sub-proof
% 242.52/49.05  | | | | | | | |            #2121.
% 242.52/49.05  | | | | | | | | 
% 242.52/49.05  | | | | | | | End of split
% 242.52/49.05  | | | | | | | 
% 242.52/49.05  | | | | | | End of split
% 242.52/49.05  | | | | | | 
% 242.52/49.05  | | | | | End of split
% 242.52/49.05  | | | | | 
% 242.52/49.05  | | | | End of split
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | End of split
% 242.52/49.05  | | | 
% 242.52/49.05  | | End of split
% 242.52/49.05  | | 
% 242.52/49.05  | Case 2:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (187)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 242.52/49.05  | |            e1)
% 242.52/49.05  | | 
% 242.52/49.05  | | REF_CLOSE: (12), (35), (37), (38), (44), (187) are inconsistent by sub-proof
% 242.52/49.05  | |            #1435.
% 242.52/49.05  | | 
% 242.52/49.05  | End of split
% 242.52/49.05  | 
% 242.52/49.05  End of proof
% 242.52/49.05  
% 242.52/49.05  Sub-proof #793 shows that the following formulas are inconsistent:
% 242.52/49.05  ----------------------------------------------------------------
% 242.52/49.05    (1)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.52/49.05         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.52/49.05    (2)  all_58_6 = e3
% 242.52/49.05    (3)   ~ (e2 = e0)
% 242.52/49.05    (4)   ~ (e3 = e1)
% 242.52/49.05    (5)   ~ (e3 = e2)
% 242.52/49.05    (6)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.52/49.05    (7)  op(e2, e0) = e2
% 242.52/49.05    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.52/49.05         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.52/49.05    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.05    (10)  op(e1, e1) = e0
% 242.52/49.05    (11)   ~ (e1 = e0)
% 242.52/49.05    (12)   ~ (e2 = e1)
% 242.52/49.05  
% 242.52/49.05  Begin of proof
% 242.52/49.05  | 
% 242.52/49.05  | BETA: splitting (6) gives:
% 242.52/49.05  | 
% 242.52/49.05  | Case 1:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (13)  all_58_10 = e0 & op(e2, e0) = e0
% 242.52/49.05  | | 
% 242.52/49.05  | | ALPHA: (13) implies:
% 242.52/49.05  | |   (14)  op(e2, e0) = e0
% 242.52/49.05  | | 
% 242.52/49.05  | | REF_CLOSE: (3), (7), (9), (14) are inconsistent by sub-proof #2121.
% 242.52/49.05  | | 
% 242.52/49.05  | Case 2:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (15)  all_58_11 = e0 & op(e1, e0) = e0
% 242.52/49.05  | | 
% 242.52/49.05  | | ALPHA: (15) implies:
% 242.52/49.05  | |   (16)  all_58_11 = e0
% 242.52/49.05  | |   (17)  op(e1, e0) = e0
% 242.52/49.05  | | 
% 242.52/49.05  | | BETA: splitting (8) gives:
% 242.52/49.05  | | 
% 242.52/49.05  | | Case 1:
% 242.52/49.05  | | | 
% 242.52/49.05  | | |   (18)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 242.52/49.05  | | |           e2)
% 242.52/49.05  | | | 
% 242.52/49.05  | | | BETA: splitting (18) gives:
% 242.52/49.05  | | | 
% 242.52/49.05  | | | Case 1:
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | |   (19)  all_58_6 = e2 & op(e1, e3) = e2
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | | ALPHA: (19) implies:
% 242.52/49.05  | | | |   (20)  all_58_6 = e2
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | | REF_CLOSE: (2), (5), (20) are inconsistent by sub-proof #2024.
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | Case 2:
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | |   (21)  all_58_7 = e2 & op(e1, e2) = e2
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | | ALPHA: (21) implies:
% 242.52/49.05  | | | |   (22)  all_58_7 = e2
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | | REF_CLOSE: (1), (2), (4), (9), (10), (11), (12), (17), (22) are
% 242.52/49.05  | | | |            inconsistent by sub-proof #794.
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | End of split
% 242.52/49.05  | | | 
% 242.52/49.05  | | Case 2:
% 242.52/49.05  | | | 
% 242.52/49.05  | | |   (23)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 242.52/49.05  | | |           e2)
% 242.52/49.05  | | | 
% 242.52/49.05  | | | BETA: splitting (23) gives:
% 242.52/49.05  | | | 
% 242.52/49.05  | | | Case 1:
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | |   (24)  all_58_8 = e2 & op(e1, e1) = e2
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | | ALPHA: (24) implies:
% 242.52/49.05  | | | |   (25)  op(e1, e1) = e2
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | | REF_CLOSE: (3), (9), (10), (25) are inconsistent by sub-proof #2211.
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | Case 2:
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | |   (26)  all_58_11 = e2 & op(e1, e0) = e2
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | | REF_CLOSE: (3), (16), (26) are inconsistent by sub-proof #2216.
% 242.52/49.05  | | | | 
% 242.52/49.05  | | | End of split
% 242.52/49.05  | | | 
% 242.52/49.05  | | End of split
% 242.52/49.05  | | 
% 242.52/49.05  | End of split
% 242.52/49.05  | 
% 242.52/49.05  End of proof
% 242.52/49.05  
% 242.52/49.05  Sub-proof #794 shows that the following formulas are inconsistent:
% 242.52/49.05  ----------------------------------------------------------------
% 242.52/49.05    (1)  op(e1, e0) = e0
% 242.52/49.05    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.52/49.05         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.52/49.05    (3)  all_58_6 = e3
% 242.52/49.05    (4)   ~ (e3 = e1)
% 242.52/49.05    (5)  all_58_7 = e2
% 242.52/49.05    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.05    (7)  op(e1, e1) = e0
% 242.52/49.05    (8)   ~ (e1 = e0)
% 242.52/49.05    (9)   ~ (e2 = e1)
% 242.52/49.05  
% 242.52/49.05  Begin of proof
% 242.52/49.05  | 
% 242.52/49.05  | BETA: splitting (2) gives:
% 242.52/49.05  | 
% 242.52/49.05  | Case 1:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (10)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 242.52/49.05  | |           e1)
% 242.52/49.05  | | 
% 242.52/49.05  | | BETA: splitting (10) gives:
% 242.52/49.05  | | 
% 242.52/49.05  | | Case 1:
% 242.52/49.05  | | | 
% 242.52/49.05  | | |   (11)  all_58_6 = e1 & op(e1, e3) = e1
% 242.52/49.05  | | | 
% 242.52/49.05  | | | ALPHA: (11) implies:
% 242.52/49.05  | | |   (12)  all_58_6 = e1
% 242.52/49.05  | | | 
% 242.52/49.05  | | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #1758.
% 242.52/49.05  | | | 
% 242.52/49.05  | | Case 2:
% 242.52/49.05  | | | 
% 242.52/49.05  | | |   (13)  all_58_7 = e1 & op(e1, e2) = e1
% 242.52/49.05  | | | 
% 242.52/49.05  | | | ALPHA: (13) implies:
% 242.52/49.05  | | |   (14)  all_58_7 = e1
% 242.52/49.05  | | | 
% 242.52/49.05  | | | REF_CLOSE: (5), (9), (14) are inconsistent by sub-proof #2134.
% 242.52/49.05  | | | 
% 242.52/49.05  | | End of split
% 242.52/49.05  | | 
% 242.52/49.05  | Case 2:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (15)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 242.52/49.05  | |           e1)
% 242.52/49.05  | | 
% 242.52/49.05  | | REF_CLOSE: (1), (6), (7), (8), (15) are inconsistent by sub-proof #795.
% 242.52/49.05  | | 
% 242.52/49.05  | End of split
% 242.52/49.05  | 
% 242.52/49.05  End of proof
% 242.52/49.05  
% 242.52/49.05  Sub-proof #795 shows that the following formulas are inconsistent:
% 242.52/49.05  ----------------------------------------------------------------
% 242.52/49.05    (1)  op(e1, e0) = e0
% 242.52/49.05    (2)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.52/49.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.05    (4)  op(e1, e1) = e0
% 242.52/49.05    (5)   ~ (e1 = e0)
% 242.52/49.05  
% 242.52/49.05  Begin of proof
% 242.52/49.05  | 
% 242.52/49.05  | BETA: splitting (2) gives:
% 242.52/49.05  | 
% 242.52/49.05  | Case 1:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (6)  all_58_8 = e1 & op(e1, e1) = e1
% 242.52/49.05  | | 
% 242.52/49.05  | | ALPHA: (6) implies:
% 242.52/49.05  | |   (7)  op(e1, e1) = e1
% 242.52/49.05  | | 
% 242.52/49.05  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #2220.
% 242.52/49.05  | | 
% 242.52/49.05  | Case 2:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (8)  all_58_11 = e1 & op(e1, e0) = e1
% 242.52/49.05  | | 
% 242.52/49.05  | | ALPHA: (8) implies:
% 242.52/49.05  | |   (9)  op(e1, e0) = e1
% 242.52/49.05  | | 
% 242.52/49.05  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #2284.
% 242.52/49.05  | | 
% 242.52/49.05  | End of split
% 242.52/49.05  | 
% 242.52/49.05  End of proof
% 242.52/49.05  
% 242.52/49.05  Sub-proof #796 shows that the following formulas are inconsistent:
% 242.52/49.05  ----------------------------------------------------------------
% 242.52/49.05    (1)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 242.52/49.05    (2)  op(e3, e3) = e2
% 242.52/49.05    (3)  all_58_2 = e0
% 242.52/49.05    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.05    (5)   ~ (e1 = e0)
% 242.52/49.05    (6)   ~ (e2 = e1)
% 242.52/49.05  
% 242.52/49.05  Begin of proof
% 242.52/49.05  | 
% 242.52/49.05  | BETA: splitting (1) gives:
% 242.52/49.05  | 
% 242.52/49.05  | Case 1:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 242.52/49.05  | | 
% 242.52/49.05  | | ALPHA: (7) implies:
% 242.52/49.05  | |   (8)  op(e3, e3) = e1
% 242.52/49.05  | | 
% 242.52/49.05  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2267.
% 242.52/49.05  | | 
% 242.52/49.05  | Case 2:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (9)  all_58_2 = e1 & op(e2, e3) = e1
% 242.52/49.05  | | 
% 242.52/49.05  | | ALPHA: (9) implies:
% 242.52/49.05  | |   (10)  all_58_2 = e1
% 242.52/49.05  | | 
% 242.52/49.05  | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #1268.
% 242.52/49.05  | | 
% 242.52/49.05  | End of split
% 242.52/49.05  | 
% 242.52/49.05  End of proof
% 242.52/49.05  
% 242.52/49.05  Sub-proof #797 shows that the following formulas are inconsistent:
% 242.52/49.05  ----------------------------------------------------------------
% 242.52/49.05    (1)   ~ (e3 = e0)
% 242.52/49.05    (2)  op(e0, e1) = all_56_23
% 242.52/49.05    (3)  op(e0, e1) = e1
% 242.52/49.05    (4)  op(e3, e2) = all_24_1
% 242.52/49.05    (5)  op(e3, e2) = e0
% 242.52/49.05    (6)  op(e0, e0) = e3
% 242.52/49.05    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.05    (8)  op(e0, all_56_23) = e0
% 242.52/49.05    (9)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) = all_32_1
% 242.52/49.05           & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2) =
% 242.52/49.05           all_32_1 & $i(all_32_1))
% 242.52/49.05  
% 242.52/49.05  Begin of proof
% 242.52/49.05  | 
% 242.52/49.05  | BETA: splitting (9) gives:
% 242.52/49.05  | 
% 242.52/49.05  | Case 1:
% 242.52/49.05  | | 
% 242.52/49.05  | | 
% 242.52/49.05  | | GROUND_INST: instantiating (7) with e1, all_56_23, e1, e0, simplifying with
% 242.52/49.05  | |              (2), (3) gives:
% 242.52/49.05  | |   (10)  all_56_23 = e1
% 242.52/49.05  | | 
% 242.52/49.05  | | REDUCE: (8), (10) imply:
% 242.52/49.05  | |   (11)  op(e0, e1) = e0
% 242.52/49.05  | | 
% 242.52/49.05  | | REF_CLOSE: (1), (2), (6), (7), (8), (11) are inconsistent by sub-proof
% 242.52/49.05  | |            #1395.
% 242.52/49.05  | | 
% 242.52/49.05  | Case 2:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (12)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 & $i(all_32_1)
% 242.52/49.05  | | 
% 242.52/49.05  | | ALPHA: (12) implies:
% 242.52/49.05  | |   (13)   ~ (all_32_1 = e0)
% 242.52/49.05  | |   (14)  op(e3, e2) = all_32_1
% 242.52/49.05  | | 
% 242.52/49.05  | | REF_CLOSE: (4), (5), (7), (13), (14) are inconsistent by sub-proof #2065.
% 242.52/49.05  | | 
% 242.52/49.05  | End of split
% 242.52/49.05  | 
% 242.52/49.05  End of proof
% 242.52/49.05  
% 242.52/49.05  Sub-proof #798 shows that the following formulas are inconsistent:
% 242.52/49.05  ----------------------------------------------------------------
% 242.52/49.05    (1)   ~ (e3 = e0)
% 242.52/49.05    (2)   ~ (e2 = e0)
% 242.52/49.05    (3)  op(e1, e0) = e1
% 242.52/49.05    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.52/49.05         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.52/49.05    (5)   ~ (e3 = e2)
% 242.52/49.05    (6)  op(e3, e2) = all_24_1
% 242.52/49.05    (7)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.52/49.05         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.52/49.05    (8)  op(e1, e0) = all_28_1
% 242.52/49.05    (9)  op(e3, e2) = e0
% 242.52/49.05    (10)  all_58_5 = e2
% 242.52/49.05    (11)  ( ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 & op(e1, e0) =
% 242.52/49.05            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e1,
% 242.52/49.05              e0) = all_18_1 & $i(all_18_1))
% 242.52/49.05    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.05    (13)  op(e1, e0) = e2
% 242.52/49.05    (14)   ~ (e1 = e0)
% 242.52/49.05    (15)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 242.52/49.05            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3,
% 242.52/49.05              e2) = all_32_1 & $i(all_32_1))
% 242.52/49.05    (16)  all_58_4 = e3
% 242.52/49.05    (17)  all_58_14 = e1
% 242.52/49.05    (18)   ~ (e2 = e1)
% 242.52/49.05  
% 242.52/49.05  Begin of proof
% 242.52/49.05  | 
% 242.52/49.05  | BETA: splitting (11) gives:
% 242.52/49.05  | 
% 242.52/49.05  | Case 1:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (19)   ~ (all_18_0 = e2) & op(all_18_1, e1) = all_18_0 & op(e1, e0) =
% 242.52/49.05  | |         all_18_1 & $i(all_18_0) & $i(all_18_1)
% 242.52/49.05  | | 
% 242.52/49.05  | | ALPHA: (19) implies:
% 242.52/49.05  | |   (20)  op(e1, e0) = all_18_1
% 242.52/49.05  | | 
% 242.52/49.05  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 242.52/49.05  | |            (14), (15), (16), (17), (18), (20) are inconsistent by sub-proof
% 242.52/49.05  | |            #799.
% 242.52/49.05  | | 
% 242.52/49.05  | Case 2:
% 242.52/49.05  | | 
% 242.52/49.05  | |   (21)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 & $i(all_18_1)
% 242.52/49.05  | | 
% 242.52/49.05  | | ALPHA: (21) implies:
% 242.52/49.05  | |   (22)  op(e1, e0) = all_18_1
% 242.52/49.05  | | 
% 242.52/49.05  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 242.52/49.05  | |            (14), (15), (16), (17), (18), (22) are inconsistent by sub-proof
% 242.52/49.05  | |            #799.
% 242.52/49.05  | | 
% 242.52/49.05  | End of split
% 242.52/49.05  | 
% 242.52/49.05  End of proof
% 242.52/49.05  
% 242.52/49.05  Sub-proof #799 shows that the following formulas are inconsistent:
% 242.52/49.05  ----------------------------------------------------------------
% 242.52/49.05    (1)   ~ (e3 = e0)
% 242.52/49.05    (2)   ~ (e2 = e0)
% 242.52/49.05    (3)  op(e1, e0) = e1
% 242.52/49.05    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.52/49.05         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.52/49.05    (5)  op(e1, e0) = all_18_1
% 242.52/49.05    (6)   ~ (e3 = e2)
% 242.52/49.05    (7)  op(e3, e2) = all_24_1
% 242.52/49.05    (8)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.52/49.05         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.52/49.05    (9)  op(e1, e0) = all_28_1
% 242.52/49.05    (10)  op(e3, e2) = e0
% 242.52/49.05    (11)  all_58_5 = e2
% 242.52/49.05    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.05    (13)  op(e1, e0) = e2
% 242.52/49.05    (14)   ~ (e1 = e0)
% 242.52/49.05    (15)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 242.52/49.05            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3,
% 242.52/49.05              e2) = all_32_1 & $i(all_32_1))
% 242.52/49.05    (16)  all_58_4 = e3
% 242.52/49.05    (17)  all_58_14 = e1
% 242.52/49.06    (18)   ~ (e2 = e1)
% 242.52/49.06  
% 242.52/49.06  Begin of proof
% 242.52/49.06  | 
% 242.52/49.06  | BETA: splitting (15) gives:
% 242.52/49.06  | 
% 242.52/49.06  | Case 1:
% 242.52/49.06  | | 
% 242.52/49.06  | | 
% 242.52/49.06  | | GROUND_INST: instantiating (12) with e1, all_18_1, e0, e1, simplifying with
% 242.52/49.06  | |              (3), (5) gives:
% 242.52/49.06  | |   (19)  all_18_1 = e1
% 242.52/49.06  | | 
% 242.52/49.06  | | GROUND_INST: instantiating (12) with e2, all_28_1, e0, e1, simplifying with
% 242.52/49.06  | |              (9), (13) gives:
% 242.52/49.06  | |   (20)  all_28_1 = e2
% 242.52/49.06  | | 
% 242.52/49.06  | | GROUND_INST: instantiating (12) with all_18_1, all_28_1, e0, e1, simplifying
% 242.52/49.06  | |              with (5), (9) gives:
% 242.52/49.06  | |   (21)  all_28_1 = all_18_1
% 242.52/49.06  | | 
% 242.52/49.06  | | COMBINE_EQS: (20), (21) imply:
% 242.52/49.06  | |   (22)  all_18_1 = e2
% 242.52/49.06  | | 
% 242.52/49.06  | | SIMP: (22) implies:
% 242.52/49.06  | |   (23)  all_18_1 = e2
% 242.52/49.06  | | 
% 242.52/49.06  | | COMBINE_EQS: (19), (23) imply:
% 242.52/49.06  | |   (24)  e2 = e1
% 242.52/49.06  | | 
% 242.52/49.06  | | COMBINE_EQS: (11), (24) imply:
% 242.52/49.06  | |   (25)  all_58_5 = e1
% 242.52/49.06  | | 
% 242.52/49.06  | | REF_CLOSE: (1), (2), (4), (6), (8), (14), (16), (17), (18), (25) are
% 242.52/49.06  | |            inconsistent by sub-proof #1481.
% 242.52/49.06  | | 
% 242.52/49.06  | Case 2:
% 242.52/49.06  | | 
% 242.52/49.06  | |   (26)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 & $i(all_32_1)
% 242.52/49.06  | | 
% 242.52/49.06  | | ALPHA: (26) implies:
% 242.52/49.06  | |   (27)   ~ (all_32_1 = e0)
% 242.52/49.06  | |   (28)  op(e3, e2) = all_32_1
% 242.52/49.06  | | 
% 242.52/49.06  | | REF_CLOSE: (7), (10), (12), (27), (28) are inconsistent by sub-proof #2065.
% 242.52/49.06  | | 
% 242.52/49.06  | End of split
% 242.52/49.06  | 
% 242.52/49.06  End of proof
% 242.52/49.06  
% 242.52/49.06  Sub-proof #800 shows that the following formulas are inconsistent:
% 242.52/49.06  ----------------------------------------------------------------
% 242.52/49.06    (1)   ~ (e2 = e0)
% 242.52/49.06    (2)  all_58_15 = e3
% 242.52/49.06    (3)  op(e0, e2) = e2
% 242.52/49.06    (4)   ~ (e3 = e2)
% 242.52/49.06    (5)  op(e3, e2) = all_24_1
% 242.52/49.06    (6)  op(e3, e2) = e0
% 242.52/49.06    (7)  op(e0, e2) = all_56_15
% 242.52/49.06    (8)  all_58_12 = e0
% 242.52/49.06    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.06    (10)  op(e0, all_56_15) = e0
% 242.52/49.06    (11)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 242.52/49.06            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3,
% 242.52/49.06              e2) = all_32_1 & $i(all_32_1))
% 242.52/49.06    (12)  all_58_14 = e1
% 242.52/49.06    (13)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.52/49.06          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.52/49.06            e2)
% 242.52/49.06    (14)   ~ (e2 = e1)
% 242.52/49.06  
% 242.52/49.06  Begin of proof
% 242.52/49.06  | 
% 242.52/49.06  | BETA: splitting (11) gives:
% 242.52/49.06  | 
% 242.52/49.06  | Case 1:
% 242.52/49.06  | | 
% 242.52/49.06  | | 
% 242.52/49.06  | | GROUND_INST: instantiating (9) with e2, all_56_15, e2, e0, simplifying with
% 242.52/49.06  | |              (3), (7) gives:
% 242.52/49.06  | |   (15)  all_56_15 = e2
% 242.52/49.06  | | 
% 242.52/49.06  | | REDUCE: (10), (15) imply:
% 242.52/49.06  | |   (16)  op(e0, e2) = e0
% 242.52/49.06  | | 
% 242.52/49.06  | | REF_CLOSE: (1), (2), (4), (8), (9), (12), (13), (14), (16) are inconsistent
% 242.52/49.06  | |            by sub-proof #1012.
% 242.52/49.06  | | 
% 242.52/49.06  | Case 2:
% 242.52/49.06  | | 
% 242.52/49.06  | |   (17)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 & $i(all_32_1)
% 242.52/49.06  | | 
% 242.52/49.06  | | ALPHA: (17) implies:
% 242.52/49.06  | |   (18)   ~ (all_32_1 = e0)
% 242.52/49.06  | |   (19)  op(e3, e2) = all_32_1
% 242.52/49.06  | | 
% 242.52/49.06  | | REF_CLOSE: (5), (6), (9), (18), (19) are inconsistent by sub-proof #2065.
% 242.52/49.06  | | 
% 242.52/49.06  | End of split
% 242.52/49.06  | 
% 242.52/49.06  End of proof
% 242.52/49.06  
% 242.52/49.06  Sub-proof #801 shows that the following formulas are inconsistent:
% 242.52/49.06  ----------------------------------------------------------------
% 242.52/49.06    (1)  op(e3, e2) = all_56_9
% 242.52/49.06    (2)  op(e3, all_56_9) = e3
% 242.52/49.06    (3)  op(e3, e2) = all_24_1
% 242.52/49.06    (4)  op(e3, e0) = all_52_12
% 242.52/49.06    (5)  op(e3, e2) = e0
% 242.52/49.06    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.06    (7)   ~ (all_52_12 = e3)
% 242.52/49.06    (8)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) = all_32_1
% 242.52/49.06           & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2) =
% 242.52/49.06           all_32_1 & $i(all_32_1))
% 242.52/49.06  
% 242.52/49.06  Begin of proof
% 242.52/49.06  | 
% 242.52/49.06  | BETA: splitting (8) gives:
% 242.52/49.06  | 
% 242.52/49.06  | Case 1:
% 242.52/49.06  | | 
% 242.52/49.06  | |   (9)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 242.52/49.06  | |        all_32_1 & $i(all_32_0) & $i(all_32_1)
% 242.52/49.06  | | 
% 242.52/49.06  | | ALPHA: (9) implies:
% 242.52/49.06  | |   (10)  op(e3, e2) = all_32_1
% 242.52/49.06  | | 
% 242.52/49.06  | | GROUND_INST: instantiating (6) with e0, all_32_1, e2, e3, simplifying with
% 242.52/49.06  | |              (5), (10) gives:
% 242.52/49.06  | |   (11)  all_32_1 = e0
% 242.52/49.06  | | 
% 242.52/49.06  | | GROUND_INST: instantiating (6) with all_32_1, all_56_9, e2, e3, simplifying
% 242.52/49.06  | |              with (1), (10) gives:
% 242.52/49.06  | |   (12)  all_56_9 = all_32_1
% 242.52/49.06  | | 
% 242.52/49.06  | | GROUND_INST: instantiating (6) with all_24_1, all_56_9, e2, e3, simplifying
% 242.52/49.06  | |              with (1), (3) gives:
% 242.52/49.06  | |   (13)  all_56_9 = all_24_1
% 242.52/49.06  | | 
% 242.52/49.06  | | COMBINE_EQS: (12), (13) imply:
% 242.52/49.06  | |   (14)  all_32_1 = all_24_1
% 242.52/49.06  | | 
% 242.52/49.06  | | SIMP: (14) implies:
% 242.52/49.06  | |   (15)  all_32_1 = all_24_1
% 242.52/49.06  | | 
% 242.52/49.06  | | COMBINE_EQS: (11), (15) imply:
% 242.52/49.06  | |   (16)  all_24_1 = e0
% 242.52/49.06  | | 
% 242.52/49.06  | | COMBINE_EQS: (13), (16) imply:
% 242.52/49.06  | |   (17)  all_56_9 = e0
% 242.52/49.06  | | 
% 242.52/49.06  | | REDUCE: (2), (17) imply:
% 242.52/49.06  | |   (18)  op(e3, e0) = e3
% 242.52/49.06  | | 
% 242.52/49.06  | | REF_CLOSE: (4), (6), (7), (18) are inconsistent by sub-proof #2179.
% 242.52/49.06  | | 
% 242.52/49.06  | Case 2:
% 242.52/49.06  | | 
% 242.52/49.06  | |   (19)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 & $i(all_32_1)
% 242.52/49.06  | | 
% 242.52/49.06  | | ALPHA: (19) implies:
% 242.52/49.06  | |   (20)   ~ (all_32_1 = e0)
% 242.52/49.06  | |   (21)  op(e3, e2) = all_32_1
% 242.52/49.06  | | 
% 242.52/49.06  | | REF_CLOSE: (3), (5), (6), (20), (21) are inconsistent by sub-proof #2065.
% 242.52/49.06  | | 
% 242.52/49.06  | End of split
% 242.52/49.06  | 
% 242.52/49.06  End of proof
% 242.52/49.06  
% 242.52/49.06  Sub-proof #802 shows that the following formulas are inconsistent:
% 242.52/49.06  ----------------------------------------------------------------
% 242.52/49.06    (1)   ~ (e3 = e0)
% 242.52/49.06    (2)   ~ (e2 = e0)
% 242.52/49.06    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.52/49.06         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.52/49.06    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.52/49.06         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.52/49.06    (5)  all_58_3 = e3
% 242.52/49.06    (6)   ~ (e3 = e2)
% 242.52/49.06    (7)  all_58_13 = e2
% 242.52/49.06    (8)  all_58_7 = e1
% 242.52/49.06    (9)   ~ (e1 = e0)
% 242.52/49.06    (10)  all_58_7 = e2 & op(e1, e2) = e2
% 242.52/49.06    (11)   ~ (e2 = e1)
% 242.52/49.06  
% 242.52/49.06  Begin of proof
% 242.52/49.06  | 
% 242.52/49.06  | ALPHA: (10) implies:
% 242.52/49.06  |   (12)  all_58_7 = e2
% 242.52/49.06  | 
% 242.52/49.06  | COMBINE_EQS: (8), (12) imply:
% 242.52/49.06  |   (13)  e2 = e1
% 242.52/49.06  | 
% 242.52/49.06  | SIMP: (13) implies:
% 242.52/49.06  |   (14)  e2 = e1
% 242.52/49.06  | 
% 242.52/49.06  | COMBINE_EQS: (7), (14) imply:
% 242.52/49.06  |   (15)  all_58_13 = e1
% 242.52/49.06  | 
% 242.52/49.06  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (15) are inconsistent
% 242.52/49.06  |            by sub-proof #1457.
% 242.52/49.06  | 
% 242.52/49.06  End of proof
% 242.52/49.06  
% 242.52/49.06  Sub-proof #803 shows that the following formulas are inconsistent:
% 242.52/49.06  ----------------------------------------------------------------
% 242.52/49.06    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.52/49.06         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.52/49.06    (2)   ~ (e3 = e0)
% 242.52/49.06    (3)  op(e1, e1) = e1
% 242.52/49.06    (4)  all_58_6 = e3
% 242.52/49.06    (5)   ~ (e2 = e0)
% 242.52/49.06    (6)  op(e1, e2) = all_52_6
% 242.52/49.06    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.52/49.06         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.52/49.06    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 242.52/49.06         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 242.52/49.06    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.52/49.06         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.52/49.06    (10)  all_58_8 = e1
% 242.52/49.06    (11)  all_58_15 = e3
% 242.52/49.06    (12)   ~ (e3 = e1)
% 242.52/49.06    (13)  all_58_7 = e2
% 242.52/49.06    (14)  all_58_3 = e3
% 242.52/49.06    (15)  op(e2, e1) = all_52_9
% 242.52/49.06    (16)   ~ (e3 = e2)
% 242.52/49.06    (17)  all_58_8 = e1 & op(e1, e1) = e1
% 242.52/49.06    (18)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.52/49.06          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.52/49.06    (19)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.52/49.06          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.52/49.06    (20)  op(e3, e3) = e2
% 242.52/49.06    (21)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.52/49.06          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.52/49.06    (22)   ~ (all_52_6 = e3)
% 242.52/49.06    (23)  op(e1, e1) = e2
% 242.52/49.06    (24)  op(e2, e1) = e0
% 242.52/49.06    (25)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.52/49.06          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.52/49.06    (26)  op(e0, e0) = e3
% 242.52/49.06    (27)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.52/49.06          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.52/49.06    (28)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.52/49.06          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.52/49.06    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.06    (30)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.52/49.06          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.52/49.06    (31)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.52/49.06          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.52/49.06    (32)  all_58_11 = e0
% 242.52/49.06    (33)   ~ (e1 = e0)
% 242.52/49.06    (34)  all_58_4 = e3
% 242.52/49.06    (35)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.52/49.06          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.52/49.06    (36)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.52/49.06          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.52/49.06    (37)   ~ (e2 = e1)
% 242.52/49.06  
% 242.52/49.06  Begin of proof
% 242.52/49.06  | 
% 242.52/49.06  | BETA: splitting (30) gives:
% 242.52/49.06  | 
% 242.52/49.06  | Case 1:
% 242.52/49.06  | | 
% 242.52/49.06  | |   (38)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 242.52/49.06  | |           e2)
% 242.52/49.06  | | 
% 242.52/49.06  | | BETA: splitting (38) gives:
% 242.52/49.06  | | 
% 242.52/49.06  | | Case 1:
% 242.52/49.06  | | | 
% 242.52/49.06  | | |   (39)  all_58_9 = e2 & op(e3, e0) = e2
% 242.52/49.06  | | | 
% 242.52/49.06  | | | ALPHA: (39) implies:
% 242.52/49.06  | | |   (40)  all_58_9 = e2
% 242.52/49.06  | | | 
% 242.52/49.06  | | | REF_CLOSE: (2), (5), (12), (20), (21), (27), (29), (33), (34), (37), (40)
% 242.52/49.06  | | |            are inconsistent by sub-proof #1562.
% 242.52/49.06  | | | 
% 242.52/49.06  | | Case 2:
% 242.52/49.06  | | | 
% 242.52/49.06  | | |   (41)  all_58_10 = e2 & op(e2, e0) = e2
% 242.52/49.06  | | | 
% 242.52/49.06  | | | ALPHA: (41) implies:
% 242.52/49.06  | | |   (42)  op(e2, e0) = e2
% 242.52/49.06  | | | 
% 242.52/49.06  | | | BETA: splitting (8) gives:
% 242.52/49.06  | | | 
% 242.52/49.06  | | | Case 1:
% 242.52/49.06  | | | | 
% 242.52/49.06  | | | |   (43)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 242.52/49.06  | | | |           = e1)
% 242.52/49.06  | | | | 
% 242.52/49.06  | | | | BETA: splitting (43) gives:
% 242.52/49.06  | | | | 
% 242.52/49.06  | | | | Case 1:
% 242.52/49.06  | | | | | 
% 242.52/49.06  | | | | |   (44)  all_58_9 = e1 & op(e3, e0) = e1
% 242.52/49.06  | | | | | 
% 242.52/49.06  | | | | | ALPHA: (44) implies:
% 242.52/49.06  | | | | |   (45)  all_58_9 = e1
% 242.52/49.06  | | | | | 
% 242.52/49.06  | | | | | BETA: splitting (21) gives:
% 242.52/49.06  | | | | | 
% 242.52/49.06  | | | | | Case 1:
% 242.52/49.06  | | | | | | 
% 242.52/49.06  | | | | | |   (46)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 242.52/49.06  | | | | | |             e2) = e0)
% 242.52/49.06  | | | | | | 
% 242.52/49.06  | | | | | | BETA: splitting (46) gives:
% 242.52/49.06  | | | | | | 
% 242.52/49.06  | | | | | | Case 1:
% 242.52/49.06  | | | | | | | 
% 242.52/49.06  | | | | | | |   (47)  all_58_0 = e0 & op(e3, e3) = e0
% 242.52/49.06  | | | | | | | 
% 242.52/49.06  | | | | | | | ALPHA: (47) implies:
% 242.52/49.06  | | | | | | |   (48)  op(e3, e3) = e0
% 242.52/49.06  | | | | | | | 
% 242.52/49.06  | | | | | | | REF_CLOSE: (5), (20), (29), (48) are inconsistent by sub-proof
% 242.52/49.06  | | | | | | |            #2188.
% 242.52/49.06  | | | | | | | 
% 242.52/49.06  | | | | | | Case 2:
% 242.52/49.06  | | | | | | | 
% 242.52/49.06  | | | | | | |   (49)  all_58_1 = e0 & op(e3, e2) = e0
% 242.52/49.06  | | | | | | | 
% 242.52/49.06  | | | | | | | ALPHA: (49) implies:
% 242.52/49.06  | | | | | | |   (50)  all_58_1 = e0
% 242.52/49.06  | | | | | | | 
% 242.52/49.06  | | | | | | | BETA: splitting (36) gives:
% 242.52/49.06  | | | | | | | 
% 242.52/49.06  | | | | | | | Case 1:
% 242.52/49.06  | | | | | | | | 
% 242.52/49.06  | | | | | | | |   (51)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 242.52/49.06  | | | | | | | |           op(e2, e2) = e1)
% 242.52/49.06  | | | | | | | | 
% 242.52/49.06  | | | | | | | | BETA: splitting (51) gives:
% 242.52/49.06  | | | | | | | | 
% 242.52/49.06  | | | | | | | | Case 1:
% 242.52/49.06  | | | | | | | | | 
% 242.52/49.06  | | | | | | | | |   (52)  all_58_2 = e1 & op(e2, e3) = e1
% 242.52/49.06  | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | ALPHA: (52) implies:
% 242.52/49.06  | | | | | | | | |   (53)  all_58_2 = e1
% 242.52/49.06  | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | BETA: splitting (31) gives:
% 242.52/49.06  | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | Case 1:
% 242.52/49.06  | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | |   (54)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 242.52/49.06  | | | | | | | | | |           op(e2, e2) = e1)
% 242.52/49.06  | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | BETA: splitting (54) gives:
% 242.52/49.06  | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | Case 1:
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | |   (55)  all_58_1 = e1 & op(e3, e2) = e1
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | REF_CLOSE: (33), (50), (55) are inconsistent by sub-proof
% 242.52/49.06  | | | | | | | | | | |            #2015.
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | Case 2:
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | |   (56)  all_58_3 = e1 & op(e2, e2) = e1
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | REF_CLOSE: (12), (14), (56) are inconsistent by sub-proof
% 242.52/49.06  | | | | | | | | | | |            #2197.
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | End of split
% 242.52/49.06  | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | Case 2:
% 242.52/49.06  | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | |   (57)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1
% 242.52/49.06  | | | | | | | | | |           & op(e0, e2) = e1)
% 242.52/49.06  | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | BETA: splitting (57) gives:
% 242.52/49.06  | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | Case 1:
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | |   (58)  all_58_7 = e1 & op(e1, e2) = e1
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | ALPHA: (58) implies:
% 242.52/49.06  | | | | | | | | | | |   (59)  all_58_7 = e1
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | REF_CLOSE: (4), (5), (10), (16), (28), (32), (37), (59) are
% 242.52/49.06  | | | | | | | | | | |            inconsistent by sub-proof #2215.
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | Case 2:
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | |   (60)  all_58_13 = e1 & op(e0, e2) = e1
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | BETA: splitting (18) gives:
% 242.52/49.06  | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | Case 1:
% 242.52/49.06  | | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | |   (61)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 242.52/49.06  | | | | | | | | | | | |           & op(e2, e3) = e0)
% 242.52/49.06  | | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | | REF_CLOSE: (5), (20), (29), (33), (53), (61) are inconsistent
% 242.52/49.06  | | | | | | | | | | | |            by sub-proof #806.
% 242.52/49.06  | | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | Case 2:
% 242.52/49.06  | | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | |   (62)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 242.52/49.06  | | | | | | | | | | | |           e0 & op(e0, e3) = e0)
% 242.52/49.06  | | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | | BETA: splitting (62) gives:
% 242.52/49.06  | | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | | Case 1:
% 242.52/49.06  | | | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | | |   (63)  all_58_6 = e0 & op(e1, e3) = e0
% 242.52/49.06  | | | | | | | | | | | | | 
% 242.52/49.06  | | | | | | | | | | | | | ALPHA: (63) implies:
% 242.52/49.06  | | | | | | | | | | | | |   (64)  all_58_6 = e0
% 242.52/49.06  | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | REF_CLOSE: (2), (6), (16), (19), (22), (23), (29), (32), (64)
% 242.52/49.07  | | | | | | | | | | | | |            are inconsistent by sub-proof #1686.
% 242.52/49.07  | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | Case 2:
% 242.52/49.07  | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | |   (65)  all_58_12 = e0 & op(e0, e3) = e0
% 242.52/49.07  | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | ALPHA: (65) implies:
% 242.52/49.07  | | | | | | | | | | | | |   (66)  all_58_12 = e0
% 242.52/49.07  | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | BETA: splitting (25) gives:
% 242.52/49.07  | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | Case 1:
% 242.52/49.07  | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | |   (67)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 242.52/49.07  | | | | | | | | | | | | | |           & op(e2, e3) = e1)
% 242.52/49.07  | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 242.52/49.07  | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | Case 1:
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | |   (68)  all_58_0 = e1 & op(e3, e3) = e1
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | | ALPHA: (68) implies:
% 242.52/49.07  | | | | | | | | | | | | | | |   (69)  op(e3, e3) = e1
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (16), (29), (34), (37), (45), (50), (69)
% 242.52/49.07  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1338.
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | Case 2:
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | | ALPHA: (60) implies:
% 242.52/49.07  | | | | | | | | | | | | | | |   (70)  all_58_13 = e1
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with e1, e2, e1, e1,
% 242.52/49.07  | | | | | | | | | | | | | | |              simplifying with (3), (23) gives:
% 242.52/49.07  | | | | | | | | | | | | | | |   (71)  e2 = e1
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | | COMBINE_EQS: (13), (71) imply:
% 242.52/49.07  | | | | | | | | | | | | | | |   (72)  all_58_7 = e1
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (9), (14), (16), (33), (37), (70),
% 242.52/49.07  | | | | | | | | | | | | | | |            (72) are inconsistent by sub-proof #1457.
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | End of split
% 242.52/49.07  | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | Case 2:
% 242.52/49.07  | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | |   (73)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 242.52/49.07  | | | | | | | | | | | | | |           e1 & op(e0, e3) = e1)
% 242.52/49.07  | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 242.52/49.07  | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | Case 1:
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | |   (74)  all_58_6 = e1 & op(e1, e3) = e1
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | | ALPHA: (74) implies:
% 242.52/49.07  | | | | | | | | | | | | | | |   (75)  all_58_6 = e1
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (75) are inconsistent by sub-proof
% 242.52/49.07  | | | | | | | | | | | | | | |            #1758.
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | Case 2:
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | |   (76)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | | REF_CLOSE: (33), (66), (76) are inconsistent by sub-proof
% 242.52/49.07  | | | | | | | | | | | | | | |            #805.
% 242.52/49.07  | | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | | End of split
% 242.52/49.07  | | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | | End of split
% 242.52/49.07  | | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | | End of split
% 242.52/49.07  | | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | | End of split
% 242.52/49.07  | | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | | End of split
% 242.52/49.07  | | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | End of split
% 242.52/49.07  | | | | | | | | | 
% 242.52/49.07  | | | | | | | | Case 2:
% 242.52/49.07  | | | | | | | | | 
% 242.52/49.07  | | | | | | | | |   (77)  all_58_3 = e1 & op(e2, e2) = e1
% 242.52/49.07  | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | ALPHA: (77) implies:
% 242.52/49.07  | | | | | | | | |   (78)  all_58_3 = e1
% 242.52/49.07  | | | | | | | | | 
% 242.52/49.07  | | | | | | | | | REF_CLOSE: (12), (14), (78) are inconsistent by sub-proof
% 242.52/49.07  | | | | | | | | |            #1999.
% 242.52/49.07  | | | | | | | | | 
% 242.52/49.07  | | | | | | | | End of split
% 242.52/49.07  | | | | | | | | 
% 242.52/49.07  | | | | | | | Case 2:
% 242.52/49.07  | | | | | | | | 
% 242.52/49.07  | | | | | | | |   (79)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 242.52/49.07  | | | | | | | |           op(e2, e0) = e1)
% 242.52/49.07  | | | | | | | | 
% 242.52/49.07  | | | | | | | | REF_CLOSE: (15), (24), (29), (33), (37), (42), (79) are
% 242.52/49.07  | | | | | | | |            inconsistent by sub-proof #975.
% 242.52/49.07  | | | | | | | | 
% 242.52/49.07  | | | | | | | End of split
% 242.52/49.07  | | | | | | | 
% 242.52/49.07  | | | | | | End of split
% 242.52/49.07  | | | | | | 
% 242.52/49.07  | | | | | Case 2:
% 242.52/49.07  | | | | | | 
% 242.52/49.07  | | | | | |   (80)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 242.52/49.07  | | | | | |             e0) = e0)
% 242.52/49.07  | | | | | | 
% 242.52/49.07  | | | | | | BETA: splitting (80) gives:
% 242.52/49.07  | | | | | | 
% 242.52/49.07  | | | | | | Case 1:
% 242.52/49.07  | | | | | | | 
% 242.52/49.07  | | | | | | |   (81)  all_58_4 = e0 & op(e3, e1) = e0
% 242.52/49.07  | | | | | | | 
% 242.52/49.07  | | | | | | | ALPHA: (81) implies:
% 242.52/49.07  | | | | | | |   (82)  all_58_4 = e0
% 242.52/49.07  | | | | | | | 
% 242.52/49.07  | | | | | | | COMBINE_EQS: (34), (82) imply:
% 242.52/49.07  | | | | | | |   (83)  e3 = e0
% 242.52/49.07  | | | | | | | 
% 242.52/49.07  | | | | | | | SIMP: (83) implies:
% 242.52/49.07  | | | | | | |   (84)  e3 = e0
% 242.52/49.07  | | | | | | | 
% 242.52/49.07  | | | | | | | COMBINE_EQS: (4), (84) imply:
% 242.52/49.07  | | | | | | |   (85)  all_58_6 = e0
% 242.52/49.07  | | | | | | | 
% 242.52/49.07  | | | | | | | REF_CLOSE: (2), (6), (16), (19), (22), (23), (29), (32), (85) are
% 242.52/49.07  | | | | | | |            inconsistent by sub-proof #1686.
% 242.52/49.07  | | | | | | | 
% 242.52/49.07  | | | | | | Case 2:
% 242.52/49.07  | | | | | | | 
% 242.52/49.07  | | | | | | |   (86)  all_58_9 = e0 & op(e3, e0) = e0
% 242.52/49.07  | | | | | | | 
% 242.52/49.07  | | | | | | | REF_CLOSE: (33), (45), (86) are inconsistent by sub-proof #1696.
% 242.52/49.07  | | | | | | | 
% 242.52/49.07  | | | | | | End of split
% 242.52/49.07  | | | | | | 
% 242.52/49.07  | | | | | End of split
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | Case 2:
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | |   (87)  all_58_10 = e1 & op(e2, e0) = e1
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | | ALPHA: (87) implies:
% 242.52/49.07  | | | | |   (88)  op(e2, e0) = e1
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | | REF_CLOSE: (29), (37), (42), (88) are inconsistent by sub-proof #1659.
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | End of split
% 242.52/49.07  | | | | 
% 242.52/49.07  | | | Case 2:
% 242.52/49.07  | | | | 
% 242.52/49.07  | | | |   (89)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 242.52/49.07  | | | |             e0) = e1)
% 242.52/49.07  | | | | 
% 242.52/49.07  | | | | BETA: splitting (89) gives:
% 242.52/49.07  | | | | 
% 242.52/49.07  | | | | Case 1:
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | |   (90)  all_58_11 = e1 & op(e1, e0) = e1
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | | ALPHA: (90) implies:
% 242.52/49.07  | | | | |   (91)  all_58_11 = e1
% 242.52/49.07  | | | | |   (92)  op(e1, e0) = e1
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | | REF_CLOSE: (2), (3), (4), (5), (10), (16), (28), (29), (33), (35),
% 242.52/49.07  | | | | |            (37), (91), (92) are inconsistent by sub-proof #804.
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | Case 2:
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | |   (93)  all_58_15 = e1 & op(e0, e0) = e1
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | | REF_CLOSE: (11), (12), (93) are inconsistent by sub-proof #1393.
% 242.52/49.07  | | | | | 
% 242.52/49.07  | | | | End of split
% 242.52/49.07  | | | | 
% 242.52/49.07  | | | End of split
% 242.52/49.07  | | | 
% 242.52/49.07  | | End of split
% 242.52/49.07  | | 
% 242.52/49.07  | Case 2:
% 242.52/49.07  | | 
% 242.52/49.07  | |   (94)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.52/49.07  | |           e2)
% 242.52/49.07  | | 
% 242.52/49.07  | | REF_CLOSE: (2), (3), (5), (6), (13), (16), (19), (22), (23), (26), (29),
% 242.52/49.07  | |            (33), (35), (94) are inconsistent by sub-proof #834.
% 242.52/49.07  | | 
% 242.52/49.07  | End of split
% 242.52/49.07  | 
% 242.52/49.07  End of proof
% 242.52/49.07  
% 242.52/49.07  Sub-proof #804 shows that the following formulas are inconsistent:
% 242.52/49.07  ----------------------------------------------------------------
% 242.52/49.07    (1)   ~ (e3 = e0)
% 242.52/49.07    (2)  op(e1, e1) = e1
% 242.52/49.07    (3)  all_58_6 = e3
% 242.52/49.07    (4)   ~ (e2 = e0)
% 242.52/49.07    (5)  all_58_11 = e1
% 242.52/49.07    (6)  all_58_8 = e1
% 242.52/49.07    (7)  op(e1, e0) = e1
% 242.52/49.07    (8)   ~ (e3 = e2)
% 242.52/49.07    (9)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.52/49.07         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.52/49.07    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.07            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.07    (11)   ~ (e1 = e0)
% 242.52/49.07    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.52/49.07          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.52/49.07    (13)   ~ (e2 = e1)
% 242.52/49.07  
% 242.52/49.07  Begin of proof
% 242.52/49.07  | 
% 242.52/49.07  | BETA: splitting (12) gives:
% 242.52/49.07  | 
% 242.52/49.07  | Case 1:
% 242.52/49.07  | | 
% 242.52/49.07  | |   (14)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 242.52/49.07  | |           e0)
% 242.52/49.07  | | 
% 242.52/49.07  | | BETA: splitting (14) gives:
% 242.52/49.07  | | 
% 242.52/49.07  | | Case 1:
% 242.52/49.07  | | | 
% 242.52/49.07  | | |   (15)  all_58_6 = e0 & op(e1, e3) = e0
% 242.52/49.07  | | | 
% 242.52/49.07  | | | ALPHA: (15) implies:
% 242.52/49.07  | | |   (16)  all_58_6 = e0
% 242.52/49.07  | | | 
% 242.52/49.07  | | | REF_CLOSE: (1), (3), (16) are inconsistent by sub-proof #2222.
% 242.52/49.07  | | | 
% 242.52/49.07  | | Case 2:
% 242.52/49.07  | | | 
% 242.52/49.07  | | |   (17)  all_58_7 = e0 & op(e1, e2) = e0
% 242.52/49.07  | | | 
% 242.52/49.07  | | | ALPHA: (17) implies:
% 242.52/49.07  | | |   (18)  all_58_7 = e0
% 242.52/49.07  | | | 
% 242.52/49.07  | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (13), (18) are inconsistent by
% 242.52/49.07  | | |            sub-proof #988.
% 242.52/49.07  | | | 
% 242.52/49.07  | | End of split
% 242.52/49.07  | | 
% 242.52/49.07  | Case 2:
% 242.52/49.07  | | 
% 242.52/49.07  | |   (19)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.52/49.07  | |           e0)
% 242.52/49.07  | | 
% 242.52/49.07  | | BETA: splitting (19) gives:
% 242.52/49.07  | | 
% 242.52/49.07  | | Case 1:
% 242.52/49.07  | | | 
% 242.52/49.07  | | |   (20)  all_58_8 = e0 & op(e1, e1) = e0
% 242.52/49.07  | | | 
% 242.52/49.07  | | | ALPHA: (20) implies:
% 242.52/49.07  | | |   (21)  op(e1, e1) = e0
% 242.52/49.07  | | | 
% 242.52/49.07  | | | REF_CLOSE: (2), (10), (11), (21) are inconsistent by sub-proof #2220.
% 242.52/49.07  | | | 
% 242.52/49.07  | | Case 2:
% 242.52/49.07  | | | 
% 242.52/49.07  | | |   (22)  all_58_11 = e0 & op(e1, e0) = e0
% 242.52/49.07  | | | 
% 242.52/49.07  | | | ALPHA: (22) implies:
% 242.52/49.07  | | |   (23)  op(e1, e0) = e0
% 242.52/49.07  | | | 
% 242.52/49.07  | | | REF_CLOSE: (7), (10), (11), (23) are inconsistent by sub-proof #2284.
% 242.52/49.07  | | | 
% 242.52/49.07  | | End of split
% 242.52/49.07  | | 
% 242.52/49.07  | End of split
% 242.52/49.07  | 
% 242.52/49.07  End of proof
% 242.52/49.07  
% 242.52/49.07  Sub-proof #805 shows that the following formulas are inconsistent:
% 242.52/49.07  ----------------------------------------------------------------
% 242.52/49.07    (1)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.07    (2)  all_58_12 = e0
% 242.52/49.07    (3)   ~ (e1 = e0)
% 242.52/49.07  
% 242.52/49.07  Begin of proof
% 242.52/49.07  | 
% 242.52/49.07  | ALPHA: (1) implies:
% 242.52/49.07  |   (4)  all_58_12 = e1
% 242.52/49.07  | 
% 242.52/49.07  | COMBINE_EQS: (2), (4) imply:
% 242.52/49.07  |   (5)  e1 = e0
% 242.52/49.07  | 
% 242.52/49.07  | REDUCE: (3), (5) imply:
% 242.52/49.07  |   (6)  $false
% 242.52/49.07  | 
% 242.52/49.07  | CLOSE: (6) is inconsistent.
% 242.52/49.07  | 
% 242.52/49.07  End of proof
% 242.52/49.07  
% 242.52/49.07  Sub-proof #806 shows that the following formulas are inconsistent:
% 242.52/49.07  ----------------------------------------------------------------
% 242.52/49.07    (1)   ~ (e2 = e0)
% 242.52/49.07    (2)  op(e3, e3) = e2
% 242.52/49.07    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.07    (4)   ~ (e1 = e0)
% 242.52/49.07    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 242.52/49.07    (6)  all_58_2 = e1
% 242.52/49.07  
% 242.52/49.07  Begin of proof
% 242.52/49.07  | 
% 242.52/49.07  | BETA: splitting (5) gives:
% 242.52/49.07  | 
% 242.52/49.07  | Case 1:
% 242.52/49.07  | | 
% 242.52/49.07  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 242.52/49.07  | | 
% 242.52/49.07  | | ALPHA: (7) implies:
% 242.52/49.07  | |   (8)  op(e3, e3) = e0
% 242.52/49.07  | | 
% 242.52/49.07  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2188.
% 242.52/49.07  | | 
% 242.52/49.07  | Case 2:
% 242.52/49.07  | | 
% 242.52/49.07  | |   (9)  all_58_2 = e0 & op(e2, e3) = e0
% 242.52/49.07  | | 
% 242.52/49.07  | | ALPHA: (9) implies:
% 242.52/49.07  | |   (10)  all_58_2 = e0
% 242.52/49.07  | | 
% 242.52/49.07  | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #1268.
% 242.52/49.07  | | 
% 242.52/49.07  | End of split
% 242.52/49.07  | 
% 242.52/49.07  End of proof
% 242.52/49.07  
% 242.52/49.07  Sub-proof #807 shows that the following formulas are inconsistent:
% 242.52/49.07  ----------------------------------------------------------------
% 242.52/49.07    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.52/49.07           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.52/49.07           all_12_1 & $i(all_12_1))
% 242.52/49.07    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 242.52/49.07             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 242.52/49.07           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 242.52/49.07         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 242.52/49.07           $i(all_56_7))
% 242.52/49.07    (3)  all_56_21 = e2
% 242.52/49.07    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.52/49.07         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.52/49.07    (5)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.52/49.07           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.52/49.07           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.52/49.07           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.52/49.07           & $i(all_56_23))
% 242.52/49.07    (6)   ~ (e3 = e0)
% 242.52/49.07    (7)  all_58_13 = e2 & op(e0, e2) = e2
% 242.52/49.07    (8)  op(e0, e1) = all_52_11
% 242.52/49.07    (9)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.52/49.07         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.52/49.07    (10)  all_42_2 = e3
% 242.52/49.07    (11)  all_58_6 = e3
% 242.52/49.07    (12)   ~ (e2 = e0)
% 242.52/49.07    (13)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 242.52/49.07            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 242.52/49.07            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 242.52/49.07            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 242.52/49.07            = all_56_15 & $i(all_56_15))
% 242.52/49.07    (14)   ~ (all_52_11 = e2)
% 242.52/49.07    (15)  op(e1, e2) = all_52_6
% 242.52/49.07    (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.52/49.07          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.52/49.07    (17)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.52/49.07          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.52/49.07    (18)   ~ (all_52_6 = e2)
% 242.52/49.07    (19)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 &
% 242.52/49.07            op(e2, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 242.52/49.07              e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.52/49.07    (20)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.52/49.07          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.52/49.07    (21)  op(e1, e3) = e3
% 242.52/49.07    (22)  op(e1, e0) = all_52_14
% 242.52/49.07    (23)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.52/49.07    (24)  all_58_15 = e3
% 242.52/49.07    (25)  op(e0, e3) = all_52_3
% 242.52/49.07    (26)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.52/49.07          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.52/49.07    (27)   ~ (e3 = e1)
% 242.52/49.07    (28)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.52/49.07          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.52/49.07    (29)  all_58_3 = e3
% 242.52/49.07    (30)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.52/49.07          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.52/49.07    (31)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.52/49.07            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.52/49.07              e3) = all_26_1 & $i(all_26_1))
% 242.52/49.07    (32)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.52/49.07          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.52/49.07    (33)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.52/49.07              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.52/49.07                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.52/49.07                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.52/49.07    (34)   ~ (all_52_11 = e3)
% 242.52/49.07    (35)  op(e2, e1) = all_52_9
% 242.52/49.07    (36)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.52/49.07          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.52/49.07    (37)   ~ (e3 = e2)
% 242.52/49.07    (38)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.52/49.07          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.52/49.07    (39)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.52/49.07          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.52/49.07    (40)  op(e3, e0) = all_52_12
% 242.52/49.07    (41)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.52/49.07          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.52/49.07    (42)   ~ (all_52_6 = all_52_14)
% 242.52/49.07    (43)  op(e2, e3) = all_52_1
% 242.52/49.07    (44)  op(e3, e3) = e2
% 242.52/49.07    (45)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.52/49.07          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.52/49.07    (46)   ~ (all_52_6 = e3)
% 242.52/49.07    (47)  op(e1, e1) = e2
% 242.52/49.08    (48)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.52/49.08          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.52/49.08    (49)  all_56_1 = e2
% 242.52/49.08    (50)  all_54_1 = all_52_4
% 242.52/49.08    (51)   ~ (all_52_4 = e3)
% 242.52/49.08    (52)  op(e3, e2) = all_52_4
% 242.52/49.08    (53)   ~ (all_52_9 = e3)
% 242.52/49.08    (54)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.52/49.08          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.52/49.08    (55)  op(e0, e0) = e3
% 242.52/49.08    (56)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.52/49.08          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.52/49.08    (57)   ~ (all_52_4 = e2)
% 242.52/49.08    (58)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.52/49.08          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.52/49.08    (59)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.52/49.08          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.52/49.08    (60)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.52/49.08          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.52/49.08    (61)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.08            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.08    (62)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.52/49.08          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.52/49.08    (63)  op(e3, e1) = e3
% 242.52/49.08    (64)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.52/49.08          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.52/49.08    (65)   ~ (all_52_12 = e3)
% 242.52/49.08    (66)  all_56_11 = e3
% 242.52/49.08    (67)   ~ (e1 = e0)
% 242.52/49.08    (68)  all_58_4 = e3
% 242.52/49.08    (69)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.52/49.08          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.52/49.08    (70)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.52/49.08          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.52/49.08            e1)
% 242.52/49.08    (71)   ~ (all_52_1 = e3)
% 242.52/49.08    (72)   ~ (all_52_9 = all_52_11)
% 242.52/49.08    (73)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.52/49.08            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.52/49.08            & $i(all_8_1))
% 242.52/49.08    (74)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.52/49.08          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.52/49.08    (75)   ~ (all_52_1 = e2)
% 242.52/49.08    (76)   ~ (all_52_4 = all_52_6)
% 242.52/49.08    (77)   ~ (e2 = e1)
% 242.52/49.08    (78)   ~ (all_52_9 = e2)
% 242.52/49.08  
% 242.52/49.08  Begin of proof
% 242.52/49.08  | 
% 242.52/49.08  | ALPHA: (7) implies:
% 242.52/49.08  |   (79)  all_58_13 = e2
% 242.52/49.08  |   (80)  op(e0, e2) = e2
% 242.52/49.08  | 
% 242.52/49.08  | BETA: splitting (38) gives:
% 242.52/49.08  | 
% 242.52/49.08  | Case 1:
% 242.52/49.08  | | 
% 242.52/49.08  | |   (81)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 242.52/49.08  | |           e2)
% 242.52/49.08  | | 
% 242.52/49.08  | | BETA: splitting (81) gives:
% 242.52/49.08  | | 
% 242.52/49.08  | | Case 1:
% 242.52/49.08  | | | 
% 242.52/49.08  | | |   (82)  all_58_4 = e2 & op(e3, e1) = e2
% 242.52/49.08  | | | 
% 242.52/49.08  | | | REF_CLOSE: (37), (68), (82) are inconsistent by sub-proof #1476.
% 242.52/49.08  | | | 
% 242.52/49.08  | | Case 2:
% 242.52/49.08  | | | 
% 242.52/49.08  | | |   (83)  all_58_5 = e2 & op(e2, e1) = e2
% 242.52/49.08  | | | 
% 242.52/49.08  | | | ALPHA: (83) implies:
% 242.52/49.08  | | |   (84)  all_58_5 = e2
% 242.52/49.08  | | | 
% 242.52/49.08  | | | REF_CLOSE: (4), (6), (11), (12), (15), (16), (20), (24), (26), (27), (28),
% 242.52/49.08  | | |            (29), (30), (32), (33), (35), (36), (37), (39), (41), (43),
% 242.52/49.08  | | |            (44), (45), (46), (47), (48), (51), (52), (53), (55), (56),
% 242.52/49.08  | | |            (58), (59), (60), (61), (62), (64), (67), (68), (69), (70),
% 242.52/49.08  | | |            (71), (74), (77), (79), (84) are inconsistent by sub-proof
% 242.52/49.08  | | |            #826.
% 242.52/49.08  | | | 
% 242.52/49.08  | | End of split
% 242.52/49.08  | | 
% 242.52/49.08  | Case 2:
% 242.52/49.08  | | 
% 242.52/49.08  | |   (85)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 242.52/49.08  | |           e2)
% 242.52/49.08  | | 
% 242.52/49.08  | | BETA: splitting (85) gives:
% 242.52/49.08  | | 
% 242.52/49.08  | | Case 1:
% 242.52/49.08  | | | 
% 242.52/49.08  | | |   (86)  all_58_8 = e2 & op(e1, e1) = e2
% 242.52/49.08  | | | 
% 242.52/49.08  | | | ALPHA: (86) implies:
% 242.52/49.08  | | |   (87)  all_58_8 = e2
% 242.52/49.08  | | | 
% 242.52/49.08  | | | BETA: splitting (26) gives:
% 242.52/49.08  | | | 
% 242.52/49.08  | | | Case 1:
% 242.52/49.08  | | | | 
% 242.52/49.08  | | | |   (88)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2)
% 242.52/49.08  | | | |           = e2)
% 242.52/49.08  | | | | 
% 242.52/49.08  | | | | REF_CLOSE: (29), (37), (43), (61), (75), (88) are inconsistent by
% 242.52/49.08  | | | |            sub-proof #825.
% 242.52/49.08  | | | | 
% 242.52/49.08  | | | Case 2:
% 242.52/49.08  | | | | 
% 242.52/49.08  | | | |   (89)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0)
% 242.52/49.08  | | | |           = e2)
% 242.52/49.08  | | | | 
% 242.52/49.08  | | | | BETA: splitting (89) gives:
% 242.52/49.08  | | | | 
% 242.52/49.08  | | | | Case 1:
% 242.52/49.08  | | | | | 
% 242.52/49.08  | | | | |   (90)  all_58_5 = e2 & op(e2, e1) = e2
% 242.52/49.08  | | | | | 
% 242.52/49.08  | | | | | ALPHA: (90) implies:
% 242.52/49.08  | | | | |   (91)  all_58_5 = e2
% 242.52/49.08  | | | | | 
% 242.52/49.08  | | | | | REF_CLOSE: (4), (6), (11), (12), (15), (16), (20), (24), (26), (27),
% 242.52/49.08  | | | | |            (28), (29), (30), (32), (33), (35), (36), (37), (39), (41),
% 242.52/49.08  | | | | |            (43), (44), (45), (46), (47), (48), (51), (52), (53), (55),
% 242.52/49.08  | | | | |            (56), (58), (59), (60), (61), (62), (64), (67), (68), (69),
% 242.52/49.08  | | | | |            (70), (71), (74), (77), (79), (91) are inconsistent by
% 242.52/49.08  | | | | |            sub-proof #826.
% 242.52/49.08  | | | | | 
% 242.52/49.08  | | | | Case 2:
% 242.52/49.08  | | | | | 
% 242.52/49.08  | | | | |   (92)  all_58_10 = e2 & op(e2, e0) = e2
% 242.52/49.08  | | | | | 
% 242.52/49.08  | | | | | ALPHA: (92) implies:
% 242.52/49.08  | | | | |   (93)  all_58_10 = e2
% 242.52/49.08  | | | | |   (94)  op(e2, e0) = e2
% 242.52/49.08  | | | | | 
% 242.52/49.08  | | | | | BETA: splitting (19) gives:
% 242.52/49.08  | | | | | 
% 242.52/49.08  | | | | | Case 1:
% 242.52/49.08  | | | | | | 
% 242.52/49.08  | | | | | |   (95)   ~ (all_42_2 = e3)
% 242.52/49.08  | | | | | | 
% 242.52/49.08  | | | | | | REDUCE: (10), (95) imply:
% 242.52/49.08  | | | | | |   (96)  $false
% 242.52/49.08  | | | | | | 
% 242.52/49.08  | | | | | | CLOSE: (96) is inconsistent.
% 242.52/49.08  | | | | | | 
% 242.52/49.08  | | | | | Case 2:
% 242.52/49.08  | | | | | | 
% 242.52/49.08  | | | | | |   (97)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2,
% 242.52/49.08  | | | | | |             e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 242.52/49.08  | | | | | |           (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1))
% 242.52/49.08  | | | | | | 
% 242.52/49.08  | | | | | | BETA: splitting (23) gives:
% 242.52/49.08  | | | | | | 
% 242.52/49.08  | | | | | | Case 1:
% 242.52/49.08  | | | | | | | 
% 242.52/49.08  | | | | | | |   (98)  all_54_1 = e3
% 242.52/49.08  | | | | | | | 
% 242.52/49.08  | | | | | | | REF_CLOSE: (50), (51), (98) are inconsistent by sub-proof #1930.
% 242.52/49.08  | | | | | | | 
% 242.52/49.08  | | | | | | Case 2:
% 242.52/49.08  | | | | | | | 
% 242.52/49.08  | | | | | | |   (99)   ~ (all_54_1 = e3)
% 242.52/49.08  | | | | | | |   (100)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.52/49.08  | | | | | | | 
% 242.52/49.08  | | | | | | | BETA: splitting (2) gives:
% 242.52/49.08  | | | | | | | 
% 242.52/49.08  | | | | | | | Case 1:
% 242.52/49.08  | | | | | | | | 
% 242.52/49.08  | | | | | | | |   (101)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 =
% 242.52/49.08  | | | | | | | |            e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 242.52/49.08  | | | | | | | |            $i(all_56_3))
% 242.52/49.08  | | | | | | | | 
% 242.52/49.08  | | | | | | | | BETA: splitting (101) gives:
% 242.52/49.08  | | | | | | | | 
% 242.52/49.08  | | | | | | | | Case 1:
% 242.52/49.08  | | | | | | | | | 
% 242.52/49.08  | | | | | | | | |   (102)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 242.52/49.08  | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | ALPHA: (102) implies:
% 242.52/49.08  | | | | | | | | |   (103)  op(e3, all_56_1) = e3
% 242.52/49.08  | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | REDUCE: (49), (103) imply:
% 242.52/49.08  | | | | | | | | |   (104)  op(e3, e2) = e3
% 242.52/49.08  | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | REF_CLOSE: (51), (52), (61), (104) are inconsistent by
% 242.52/49.08  | | | | | | | | |            sub-proof #2192.
% 242.52/49.08  | | | | | | | | | 
% 242.52/49.08  | | | | | | | | Case 2:
% 242.52/49.08  | | | | | | | | | 
% 242.52/49.08  | | | | | | | | |   (105)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 242.52/49.08  | | | | | | | | |          all_56_3 & $i(all_56_3)
% 242.52/49.08  | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | ALPHA: (105) implies:
% 242.52/49.08  | | | | | | | | |   (106)  op(e2, e3) = all_56_3
% 242.52/49.08  | | | | | | | | |   (107)  op(e2, all_56_3) = e2
% 242.52/49.08  | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | GROUND_INST: instantiating (61) with all_52_1, all_56_3, e3,
% 242.52/49.08  | | | | | | | | |              e2, simplifying with (43), (106) gives:
% 242.52/49.08  | | | | | | | | |   (108)  all_56_3 = all_52_1
% 242.52/49.08  | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | REDUCE: (107), (108) imply:
% 242.52/49.08  | | | | | | | | |   (109)  op(e2, all_52_1) = e2
% 242.52/49.08  | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | BETA: splitting (13) gives:
% 242.52/49.08  | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | Case 1:
% 242.52/49.08  | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | |   (110)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 242.52/49.08  | | | | | | | | | |            = all_56_9 & $i(all_56_9)) | (all_56_10 = e2 &
% 242.52/49.08  | | | | | | | | | |            op(e2, all_56_11) = e2)
% 242.52/49.08  | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | BETA: splitting (110) gives:
% 242.52/49.08  | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | Case 1:
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | |   (111)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 242.52/49.08  | | | | | | | | | | |          = all_56_9 & $i(all_56_9)
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | ALPHA: (111) implies:
% 242.52/49.08  | | | | | | | | | | |   (112)  op(e3, e2) = all_56_9
% 242.52/49.08  | | | | | | | | | | |   (113)  op(e3, all_56_9) = e3
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_4, all_56_9, e2,
% 242.52/49.08  | | | | | | | | | | |              e3, simplifying with (52), (112) gives:
% 242.52/49.08  | | | | | | | | | | |   (114)  all_56_9 = all_52_4
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | REDUCE: (113), (114) imply:
% 242.52/49.08  | | | | | | | | | | |   (115)  op(e3, all_52_4) = e3
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | BETA: splitting (54) gives:
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | Case 1:
% 242.52/49.08  | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | |   (116)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 242.52/49.08  | | | | | | | | | | | |            & op(e2, e3) = e1)
% 242.52/49.08  | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | BETA: splitting (116) gives:
% 242.52/49.08  | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | Case 1:
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | |   (117)  all_58_0 = e1 & op(e3, e3) = e1
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | ALPHA: (117) implies:
% 242.52/49.08  | | | | | | | | | | | | |   (118)  op(e3, e3) = e1
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | REF_CLOSE: (44), (61), (77), (118) are inconsistent by
% 242.52/49.08  | | | | | | | | | | | | |            sub-proof #2267.
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | Case 2:
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | |   (119)  all_58_2 = e1 & op(e2, e3) = e1
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | ALPHA: (119) implies:
% 242.52/49.08  | | | | | | | | | | | | |   (120)  op(e2, e3) = e1
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | BETA: splitting (70) gives:
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | Case 1:
% 242.52/49.08  | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | |   (121)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 242.52/49.08  | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 242.52/49.08  | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 242.52/49.08  | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | Case 1:
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | |   (122)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 242.52/49.08  | | | | | | | | | | | | | | |   (123)  all_58_12 = e1
% 242.52/49.08  | | | | | | | | | | | | | | |   (124)  op(e0, e3) = e1
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (11), (12), (14), (15),
% 242.52/49.08  | | | | | | | | | | | | | | |            (25), (26), (27), (28), (29), (31), (34), (35),
% 242.52/49.08  | | | | | | | | | | | | | | |            (37), (39), (40), (43), (44), (47), (50), (55),
% 242.52/49.08  | | | | | | | | | | | | | | |            (57), (60), (61), (63), (65), (67), (68), (72),
% 242.52/49.08  | | | | | | | | | | | | | | |            (73), (74), (76), (77), (78), (93), (94), (97),
% 242.52/49.08  | | | | | | | | | | | | | | |            (100), (115), (123), (124) are inconsistent by
% 242.52/49.08  | | | | | | | | | | | | | | |            sub-proof #817.
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | Case 2:
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | |   (125)  all_58_13 = e1 & op(e0, e2) = e1
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | | REF_CLOSE: (77), (79), (125) are inconsistent by sub-proof
% 242.52/49.08  | | | | | | | | | | | | | | |            #1751.
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | End of split
% 242.52/49.08  | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | Case 2:
% 242.52/49.08  | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | |   (126)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 242.52/49.08  | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 242.52/49.08  | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 242.52/49.08  | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | Case 1:
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | |   (127)  all_58_14 = e1 & op(e0, e1) = e1
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 242.52/49.08  | | | | | | | | | | | | | | |   (128)  op(e0, e1) = e1
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (28), (33), (35), (43), (47), (55),
% 242.52/49.08  | | | | | | | | | | | | | | |            (61), (67), (68), (78), (109), (120), (128) are
% 242.52/49.08  | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | Case 2:
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | |   (129)  all_58_15 = e1 & op(e0, e0) = e1
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (129) are inconsistent by sub-proof
% 242.52/49.08  | | | | | | | | | | | | | | |            #1393.
% 242.52/49.08  | | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | | End of split
% 242.52/49.08  | | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | End of split
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | End of split
% 242.52/49.08  | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | Case 2:
% 242.52/49.08  | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | |   (130)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 242.52/49.08  | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 242.52/49.08  | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | BETA: splitting (130) gives:
% 242.52/49.08  | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | Case 1:
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | |   (131)  all_58_6 = e1 & op(e1, e3) = e1
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | REF_CLOSE: (11), (27), (131) are inconsistent by sub-proof
% 242.52/49.08  | | | | | | | | | | | | |            #1803.
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | Case 2:
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | |   (132)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | ALPHA: (132) implies:
% 242.52/49.08  | | | | | | | | | | | | |   (133)  all_58_12 = e1
% 242.52/49.08  | | | | | | | | | | | | |   (134)  op(e0, e3) = e1
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (11), (12), (14), (15),
% 242.52/49.08  | | | | | | | | | | | | |            (25), (26), (27), (28), (29), (31), (34), (35),
% 242.52/49.08  | | | | | | | | | | | | |            (37), (39), (40), (43), (44), (47), (50), (55),
% 242.52/49.08  | | | | | | | | | | | | |            (57), (60), (61), (63), (65), (67), (68), (72),
% 242.52/49.08  | | | | | | | | | | | | |            (73), (74), (76), (77), (78), (93), (94), (97),
% 242.52/49.08  | | | | | | | | | | | | |            (100), (115), (133), (134) are inconsistent by
% 242.52/49.08  | | | | | | | | | | | | |            sub-proof #817.
% 242.52/49.08  | | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | | End of split
% 242.52/49.08  | | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | End of split
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | Case 2:
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | |   (135)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | ALPHA: (135) implies:
% 242.52/49.08  | | | | | | | | | | |   (136)  op(e2, all_56_11) = e2
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | REDUCE: (66), (136) imply:
% 242.52/49.08  | | | | | | | | | | |   (137)  op(e2, e3) = e2
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | REF_CLOSE: (43), (61), (75), (137) are inconsistent by
% 242.52/49.08  | | | | | | | | | | |            sub-proof #2336.
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | End of split
% 242.52/49.08  | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | Case 2:
% 242.52/49.08  | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | |   (138)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 242.52/49.08  | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)) | (all_56_14 =
% 242.52/49.08  | | | | | | | | | |            e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 242.52/49.08  | | | | | | | | | |            all_56_15 & $i(all_56_15))
% 242.52/49.08  | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | BETA: splitting (138) gives:
% 242.52/49.08  | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | Case 1:
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | |   (139)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 242.52/49.08  | | | | | | | | | | |            e2) = all_56_13 & $i(all_56_13)
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | ALPHA: (139) implies:
% 242.52/49.08  | | | | | | | | | | |   (140)  op(e1, e2) = all_56_13
% 242.52/49.08  | | | | | | | | | | |   (141)  op(e1, all_56_13) = e1
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_6, all_56_13, e2,
% 242.52/49.08  | | | | | | | | | | |              e1, simplifying with (15), (140) gives:
% 242.52/49.08  | | | | | | | | | | |   (142)  all_56_13 = all_52_6
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | REDUCE: (141), (142) imply:
% 242.52/49.08  | | | | | | | | | | |   (143)  op(e1, all_52_6) = e1
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.08  | | | | | | | | | | | BETA: splitting (54) gives:
% 242.52/49.08  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | |   (144)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 242.52/49.09  | | | | | | | | | | | |            & op(e2, e3) = e1)
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | BETA: splitting (144) gives:
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | |   (145)  all_58_0 = e1 & op(e3, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | ALPHA: (145) implies:
% 242.52/49.09  | | | | | | | | | | | | |   (146)  op(e3, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | REF_CLOSE: (44), (61), (77), (146) are inconsistent by
% 242.52/49.09  | | | | | | | | | | | | |            sub-proof #2267.
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | |   (147)  all_58_2 = e1 & op(e2, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | ALPHA: (147) implies:
% 242.52/49.09  | | | | | | | | | | | | |   (148)  op(e2, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | BETA: splitting (70) gives:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | |   (149)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 242.52/49.09  | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (12), (14),
% 242.52/49.09  | | | | | | | | | | | | | |            (15), (16), (17), (18), (22), (25), (26), (27),
% 242.52/49.09  | | | | | | | | | | | | | |            (28), (29), (31), (34), (35), (37), (39), (41),
% 242.52/49.09  | | | | | | | | | | | | | |            (42), (43), (44), (46), (47), (55), (59), (60),
% 242.52/49.09  | | | | | | | | | | | | | |            (61), (63), (67), (68), (69), (72), (73), (74),
% 242.52/49.09  | | | | | | | | | | | | | |            (77), (78), (79), (87), (93), (94), (97), (143),
% 242.52/49.09  | | | | | | | | | | | | | |            (149) are inconsistent by sub-proof #814.
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | |   (150)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 242.52/49.09  | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | |   (151)  all_58_14 = e1 & op(e0, e1) = e1
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 242.52/49.09  | | | | | | | | | | | | | | |   (152)  op(e0, e1) = e1
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (28), (33), (35), (43), (47), (55),
% 242.52/49.09  | | | | | | | | | | | | | | |            (61), (67), (68), (78), (109), (148), (152) are
% 242.52/49.09  | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | |   (153)  all_58_15 = e1 & op(e0, e0) = e1
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (153) are inconsistent by sub-proof
% 242.52/49.09  | | | | | | | | | | | | | | |            #1393.
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | |   (154)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 242.52/49.09  | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | BETA: splitting (154) gives:
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | |   (155)  all_58_6 = e1 & op(e1, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | REF_CLOSE: (11), (27), (155) are inconsistent by sub-proof
% 242.52/49.09  | | | | | | | | | | | | |            #1803.
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | |   (156)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | ALPHA: (156) implies:
% 242.52/49.09  | | | | | | | | | | | | |   (157)  all_58_12 = e1
% 242.52/49.09  | | | | | | | | | | | | |   (158)  op(e0, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (12), (14),
% 242.52/49.09  | | | | | | | | | | | | |            (15), (16), (17), (18), (22), (25), (26), (27),
% 242.52/49.09  | | | | | | | | | | | | |            (28), (29), (31), (34), (35), (37), (39), (41),
% 242.52/49.09  | | | | | | | | | | | | |            (42), (43), (44), (46), (47), (55), (59), (60),
% 242.52/49.09  | | | | | | | | | | | | |            (61), (63), (67), (68), (69), (72), (73), (74),
% 242.52/49.09  | | | | | | | | | | | | |            (77), (78), (79), (87), (93), (94), (97), (143),
% 242.52/49.09  | | | | | | | | | | | | |            (157), (158) are inconsistent by sub-proof #815.
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | |   (159)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 242.52/49.09  | | | | | | | | | | |            e2) = all_56_15 & $i(all_56_15)
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | ALPHA: (159) implies:
% 242.52/49.09  | | | | | | | | | | |   (160)  op(e0, e2) = all_56_15
% 242.52/49.09  | | | | | | | | | | |   (161)  op(e0, all_56_15) = e0
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | REF_CLOSE: (12), (61), (80), (160), (161) are inconsistent by
% 242.52/49.09  | | | | | | | | | | |            sub-proof #2053.
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | 
% 242.52/49.09  | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | 
% 242.52/49.09  | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | 
% 242.52/49.09  | | | | | | | |   (162)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 242.52/49.09  | | | | | | | |            all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 242.52/49.09  | | | | | | | |              all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 242.52/49.09  | | | | | | | |            $i(all_56_7))
% 242.52/49.09  | | | | | | | | 
% 242.52/49.09  | | | | | | | | BETA: splitting (162) gives:
% 242.52/49.09  | | | | | | | | 
% 242.52/49.09  | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | 
% 242.52/49.09  | | | | | | | | |   (163)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 242.52/49.09  | | | | | | | | |          all_56_5 & $i(all_56_5)
% 242.52/49.09  | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | ALPHA: (163) implies:
% 242.52/49.09  | | | | | | | | |   (164)  op(e1, e3) = all_56_5
% 242.52/49.09  | | | | | | | | |   (165)  op(e1, all_56_5) = e1
% 242.52/49.09  | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | REF_CLOSE: (21), (27), (61), (164), (165) are inconsistent by
% 242.52/49.09  | | | | | | | | |            sub-proof #2243.
% 242.52/49.09  | | | | | | | | | 
% 242.52/49.09  | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | 
% 242.52/49.09  | | | | | | | | |   (166)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 242.52/49.09  | | | | | | | | |          all_56_7 & $i(all_56_7)
% 242.52/49.09  | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | ALPHA: (166) implies:
% 242.52/49.09  | | | | | | | | |   (167)  op(e0, e3) = all_56_7
% 242.52/49.09  | | | | | | | | |   (168)  op(e0, all_56_7) = e0
% 242.52/49.09  | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | GROUND_INST: instantiating (61) with all_52_3, all_56_7, e3,
% 242.52/49.09  | | | | | | | | |              e0, simplifying with (25), (167) gives:
% 242.52/49.09  | | | | | | | | |   (169)  all_56_7 = all_52_3
% 242.52/49.09  | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | REDUCE: (168), (169) imply:
% 242.52/49.09  | | | | | | | | |   (170)  op(e0, all_52_3) = e0
% 242.52/49.09  | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | BETA: splitting (13) gives:
% 242.52/49.09  | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | |   (171)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 242.52/49.09  | | | | | | | | | |            = all_56_9 & $i(all_56_9)) | (all_56_10 = e2 &
% 242.52/49.09  | | | | | | | | | |            op(e2, all_56_11) = e2)
% 242.52/49.09  | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | BETA: splitting (171) gives:
% 242.52/49.09  | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | |   (172)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 242.52/49.09  | | | | | | | | | | |          = all_56_9 & $i(all_56_9)
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | ALPHA: (172) implies:
% 242.52/49.09  | | | | | | | | | | |   (173)  op(e3, e2) = all_56_9
% 242.52/49.09  | | | | | | | | | | |   (174)  op(e3, all_56_9) = e3
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_4, all_56_9, e2,
% 242.52/49.09  | | | | | | | | | | |              e3, simplifying with (52), (173) gives:
% 242.52/49.09  | | | | | | | | | | |   (175)  all_56_9 = all_52_4
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | REDUCE: (174), (175) imply:
% 242.52/49.09  | | | | | | | | | | |   (176)  op(e3, all_52_4) = e3
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | BETA: splitting (54) gives:
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | |   (177)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 242.52/49.09  | | | | | | | | | | | |            & op(e2, e3) = e1)
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | BETA: splitting (177) gives:
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | |   (178)  all_58_0 = e1 & op(e3, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | ALPHA: (178) implies:
% 242.52/49.09  | | | | | | | | | | | | |   (179)  op(e3, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | REF_CLOSE: (44), (61), (77), (179) are inconsistent by
% 242.52/49.09  | | | | | | | | | | | | |            sub-proof #2267.
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | |   (180)  all_58_2 = e1 & op(e2, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | ALPHA: (180) implies:
% 242.52/49.09  | | | | | | | | | | | | |   (181)  all_58_2 = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (24), (25), (27), (28), (33),
% 242.52/49.09  | | | | | | | | | | | | |            (35), (39), (44), (47), (53), (55), (61), (67),
% 242.52/49.09  | | | | | | | | | | | | |            (68), (70), (77), (79), (170), (181) are
% 242.52/49.09  | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | |   (182)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 242.52/49.09  | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | BETA: splitting (182) gives:
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | |   (183)  all_58_6 = e1 & op(e1, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | REF_CLOSE: (11), (27), (183) are inconsistent by sub-proof
% 242.52/49.09  | | | | | | | | | | | | |            #1803.
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | |   (184)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | ALPHA: (184) implies:
% 242.52/49.09  | | | | | | | | | | | | |   (185)  op(e0, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | BETA: splitting (39) gives:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | |   (186)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 242.52/49.09  | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | |   (187)  all_58_0 = e0 & op(e3, e3) = e0
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 242.52/49.09  | | | | | | | | | | | | | | |   (188)  op(e3, e3) = e0
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | REF_CLOSE: (12), (44), (61), (188) are inconsistent by
% 242.52/49.09  | | | | | | | | | | | | | | |            sub-proof #2188.
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | |   (189)  all_58_2 = e0 & op(e2, e3) = e0
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 242.52/49.09  | | | | | | | | | | | | | | |   (190)  op(e2, e3) = e0
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | |   (191)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 242.52/49.09  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 242.52/49.09  | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 242.52/49.09  | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | |   (192)  all_58_2 = e1 & op(e2, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 242.52/49.09  | | | | | | | | | | | | | | | | |   (193)  all_58_2 = e1
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (24), (25), (27), (28), (33),
% 242.52/49.09  | | | | | | | | | | | | | | | | |            (35), (39), (44), (47), (53), (55), (61), (67),
% 242.52/49.09  | | | | | | | | | | | | | | | | |            (68), (70), (77), (79), (170), (193) are
% 242.52/49.09  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | |   (194)  all_58_3 = e1 & op(e2, e2) = e1
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (29), (194) are inconsistent by sub-proof
% 242.52/49.09  | | | | | | | | | | | | | | | | |            #2197.
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | |   (195)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 242.52/49.09  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 242.52/49.09  | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 242.52/49.09  | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | |   (196)  all_58_5 = e1 & op(e2, e1) = e1
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 242.52/49.09  | | | | | | | | | | | | | | | | |   (197)  all_58_5 = e1
% 242.52/49.09  | | | | | | | | | | | | | | | | |   (198)  op(e2, e1) = e1
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (12), (14), (15), (25),
% 242.52/49.09  | | | | | | | | | | | | | | | | |            (26), (28), (29), (31), (34), (35), (37), (40),
% 242.52/49.09  | | | | | | | | | | | | | | | | |            (43), (44), (47), (50), (55), (57), (60), (61),
% 242.52/49.09  | | | | | | | | | | | | | | | | |            (63), (65), (67), (68), (72), (73), (76), (78),
% 242.52/49.09  | | | | | | | | | | | | | | | | |            (93), (97), (100), (176), (185), (190), (197),
% 242.52/49.09  | | | | | | | | | | | | | | | | |            (198) are inconsistent by sub-proof #819.
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | |   (199)  all_58_10 = e1 & op(e2, e0) = e1
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 242.52/49.09  | | | | | | | | | | | | | | | | |   (200)  op(e2, e0) = e1
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (77), (94), (200) are inconsistent by
% 242.52/49.09  | | | | | | | | | | | | | | | | |            sub-proof #1659.
% 242.52/49.09  | | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | |   (201)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 242.52/49.09  | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | |   (202)  all_58_6 = e0 & op(e1, e3) = e0
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (202) are inconsistent by sub-proof
% 242.52/49.09  | | | | | | | | | | | | | | |            #2213.
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | |   (203)  all_58_12 = e0 & op(e0, e3) = e0
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 242.52/49.09  | | | | | | | | | | | | | | |   (204)  all_58_12 = e0
% 242.52/49.09  | | | | | | | | | | | | | | |   (205)  op(e0, e3) = e0
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (24), (25), (27), (28), (33), (35),
% 242.52/49.09  | | | | | | | | | | | | | | |            (47), (53), (55), (61), (67), (68), (70), (77),
% 242.52/49.09  | | | | | | | | | | | | | | |            (79), (170), (204), (205) are inconsistent by
% 242.52/49.09  | | | | | | | | | | | | | | |            sub-proof #811.
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | |   (206)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | ALPHA: (206) implies:
% 242.52/49.09  | | | | | | | | | | |   (207)  op(e2, all_56_11) = e2
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | REDUCE: (66), (207) imply:
% 242.52/49.09  | | | | | | | | | | |   (208)  op(e2, e3) = e2
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_1, e2, e3, e2,
% 242.52/49.09  | | | | | | | | | | |              simplifying with (43), (208) gives:
% 242.52/49.09  | | | | | | | | | | |   (209)  all_52_1 = e2
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | REDUCE: (75), (209) imply:
% 242.52/49.09  | | | | | | | | | | |   (210)  $false
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | CLOSE: (210) is inconsistent.
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | End of split
% 242.52/49.09  | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | |   (211)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 242.52/49.09  | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)) | (all_56_14 =
% 242.52/49.09  | | | | | | | | | |            e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 242.52/49.09  | | | | | | | | | |            all_56_15 & $i(all_56_15))
% 242.52/49.09  | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | BETA: splitting (211) gives:
% 242.52/49.09  | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | |   (212)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 242.52/49.09  | | | | | | | | | | |            e2) = all_56_13 & $i(all_56_13)
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | ALPHA: (212) implies:
% 242.52/49.09  | | | | | | | | | | |   (213)  op(e1, e2) = all_56_13
% 242.52/49.09  | | | | | | | | | | |   (214)  op(e1, all_56_13) = e1
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | GROUND_INST: instantiating (61) with all_52_6, all_56_13, e2,
% 242.52/49.09  | | | | | | | | | | |              e1, simplifying with (15), (213) gives:
% 242.52/49.09  | | | | | | | | | | |   (215)  all_56_13 = all_52_6
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | REDUCE: (214), (215) imply:
% 242.52/49.09  | | | | | | | | | | |   (216)  op(e1, all_52_6) = e1
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | BETA: splitting (54) gives:
% 242.52/49.09  | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | |   (217)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 242.52/49.09  | | | | | | | | | | | |            & op(e2, e3) = e1)
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | BETA: splitting (217) gives:
% 242.52/49.09  | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | |   (218)  all_58_0 = e1 & op(e3, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | ALPHA: (218) implies:
% 242.52/49.09  | | | | | | | | | | | | |   (219)  op(e3, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | REF_CLOSE: (44), (61), (77), (219) are inconsistent by
% 242.52/49.09  | | | | | | | | | | | | |            sub-proof #2267.
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | |   (220)  all_58_2 = e1 & op(e2, e3) = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | ALPHA: (220) implies:
% 242.52/49.09  | | | | | | | | | | | | |   (221)  all_58_2 = e1
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | BETA: splitting (39) gives:
% 242.52/49.09  | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | |   (222)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 242.52/49.09  | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | REF_CLOSE: (12), (44), (61), (67), (221), (222) are
% 242.52/49.09  | | | | | | | | | | | | | |            inconsistent by sub-proof #1761.
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | |   (223)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 242.52/49.09  | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 242.52/49.09  | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | |   (224)  all_58_6 = e0 & op(e1, e3) = e0
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (224) are inconsistent by sub-proof
% 242.52/49.09  | | | | | | | | | | | | | | |            #2213.
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | Case 2:
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | |   (225)  all_58_12 = e0 & op(e0, e3) = e0
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 242.52/49.09  | | | | | | | | | | | | | | |   (226)  op(e0, e3) = e0
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 242.52/49.09  | | | | | | | | | | | | | | | 
% 242.52/49.09  | | | | | | | | | | | | | | | Case 1:
% 242.52/49.09  | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | |   (227)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 242.52/49.10  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 242.52/49.10  | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (12), (14),
% 242.52/49.10  | | | | | | | | | | | | | | | |            (15), (16), (17), (18), (22), (25), (26), (27),
% 242.52/49.10  | | | | | | | | | | | | | | | |            (28), (29), (31), (34), (35), (37), (39), (41),
% 242.52/49.10  | | | | | | | | | | | | | | | |            (42), (43), (44), (46), (47), (55), (59), (60),
% 242.52/49.10  | | | | | | | | | | | | | | | |            (61), (63), (67), (68), (69), (72), (73), (74),
% 242.52/49.10  | | | | | | | | | | | | | | | |            (77), (78), (79), (87), (93), (94), (97), (216),
% 242.52/49.10  | | | | | | | | | | | | | | | |            (227) are inconsistent by sub-proof #814.
% 242.52/49.10  | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | Case 2:
% 242.52/49.10  | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | |   (228)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 242.52/49.10  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 242.52/49.10  | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 242.52/49.10  | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | | Case 1:
% 242.52/49.10  | | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | | |   (229)  all_58_14 = e1 & op(e0, e1) = e1
% 242.52/49.10  | | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 242.52/49.10  | | | | | | | | | | | | | | | | |   (230)  op(e0, e1) = e1
% 242.52/49.10  | | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (24), (25), (28), (33), (35), (47),
% 242.52/49.10  | | | | | | | | | | | | | | | | |            (53), (55), (61), (67), (68), (170), (226), (230)
% 242.52/49.10  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #812.
% 242.52/49.10  | | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | | Case 2:
% 242.52/49.10  | | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | | |   (231)  all_58_15 = e1 & op(e0, e0) = e1
% 242.52/49.10  | | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (231) are inconsistent by sub-proof
% 242.52/49.10  | | | | | | | | | | | | | | | | |            #1393.
% 242.52/49.10  | | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | | End of split
% 242.52/49.10  | | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | | End of split
% 242.52/49.10  | | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | | End of split
% 242.52/49.10  | | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | End of split
% 242.52/49.10  | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | End of split
% 242.52/49.10  | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | Case 2:
% 242.52/49.10  | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | |   (232)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 242.52/49.10  | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 242.52/49.10  | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | BETA: splitting (232) gives:
% 242.52/49.10  | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | Case 1:
% 242.52/49.10  | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | |   (233)  all_58_6 = e1 & op(e1, e3) = e1
% 242.52/49.10  | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | REF_CLOSE: (11), (27), (233) are inconsistent by sub-proof
% 242.52/49.10  | | | | | | | | | | | | |            #1803.
% 242.52/49.10  | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | Case 2:
% 242.52/49.10  | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | |   (234)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.10  | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | ALPHA: (234) implies:
% 242.52/49.10  | | | | | | | | | | | | |   (235)  all_58_12 = e1
% 242.52/49.10  | | | | | | | | | | | | |   (236)  op(e0, e3) = e1
% 242.52/49.10  | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (12), (14),
% 242.52/49.10  | | | | | | | | | | | | |            (15), (16), (17), (18), (22), (25), (26), (27),
% 242.52/49.10  | | | | | | | | | | | | |            (28), (29), (31), (34), (35), (37), (39), (41),
% 242.52/49.10  | | | | | | | | | | | | |            (42), (43), (44), (46), (47), (55), (59), (60),
% 242.52/49.10  | | | | | | | | | | | | |            (61), (63), (67), (68), (69), (72), (73), (74),
% 242.52/49.10  | | | | | | | | | | | | |            (77), (78), (79), (87), (93), (94), (97), (216),
% 242.52/49.10  | | | | | | | | | | | | |            (235), (236) are inconsistent by sub-proof #815.
% 242.52/49.10  | | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | | End of split
% 242.52/49.10  | | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | End of split
% 242.52/49.10  | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | Case 2:
% 242.52/49.10  | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | |   (237)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 242.52/49.10  | | | | | | | | | | |            e2) = all_56_15 & $i(all_56_15)
% 242.52/49.10  | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | ALPHA: (237) implies:
% 242.52/49.10  | | | | | | | | | | |   (238)  op(e0, e2) = all_56_15
% 242.52/49.10  | | | | | | | | | | |   (239)  op(e0, all_56_15) = e0
% 242.52/49.10  | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | | REF_CLOSE: (12), (61), (80), (238), (239) are inconsistent by
% 242.52/49.10  | | | | | | | | | | |            sub-proof #2053.
% 242.52/49.10  | | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | | End of split
% 242.52/49.10  | | | | | | | | | | 
% 242.52/49.10  | | | | | | | | | End of split
% 242.52/49.10  | | | | | | | | | 
% 242.52/49.10  | | | | | | | | End of split
% 242.52/49.10  | | | | | | | | 
% 242.52/49.10  | | | | | | | End of split
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | End of split
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | End of split
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | End of split
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | End of split
% 242.52/49.10  | | | 
% 242.52/49.10  | | Case 2:
% 242.52/49.10  | | | 
% 242.52/49.10  | | |   (240)  all_58_14 = e2 & op(e0, e1) = e2
% 242.52/49.10  | | | 
% 242.52/49.10  | | | ALPHA: (240) implies:
% 242.52/49.10  | | |   (241)  all_58_14 = e2
% 242.52/49.10  | | | 
% 242.52/49.10  | | | BETA: splitting (28) gives:
% 242.52/49.10  | | | 
% 242.52/49.10  | | | Case 1:
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | |   (242)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1)
% 242.52/49.10  | | | |            = e0)
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | BETA: splitting (242) gives:
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | Case 1:
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | |   (243)  all_58_4 = e0 & op(e3, e1) = e0
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | | REF_CLOSE: (6), (68), (243) are inconsistent by sub-proof #1697.
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | Case 2:
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | |   (244)  all_58_5 = e0 & op(e2, e1) = e0
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | | ALPHA: (244) implies:
% 242.52/49.10  | | | | |   (245)  op(e2, e1) = e0
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | | BETA: splitting (59) gives:
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | | Case 1:
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | |   (246)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 242.52/49.10  | | | | | |              e2) = e2)
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | | REF_CLOSE: (6), (11), (12), (16), (17), (24), (27), (29), (33),
% 242.52/49.10  | | | | | |            (37), (61), (67), (70), (77), (79), (80), (241), (246)
% 242.52/49.10  | | | | | |            are inconsistent by sub-proof #809.
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | Case 2:
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | |   (247)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 242.52/49.10  | | | | | |            op(e1, e0) = e2)
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | | BETA: splitting (247) gives:
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | | Case 1:
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | |   (248)  all_58_8 = e2 & op(e1, e1) = e2
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | | ALPHA: (248) implies:
% 242.52/49.10  | | | | | | |   (249)  all_58_8 = e2
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | | REF_CLOSE: (20), (27), (35), (61), (67), (68), (77), (241), (245),
% 242.52/49.10  | | | | | | |            (249) are inconsistent by sub-proof #2039.
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | Case 2:
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | |   (250)  all_58_11 = e2 & op(e1, e0) = e2
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | | REF_CLOSE: (6), (11), (12), (15), (24), (27), (33), (37), (41),
% 242.52/49.10  | | | | | | |            (46), (47), (61), (67), (70), (77), (79), (80), (241),
% 242.52/49.10  | | | | | | |            (250) are inconsistent by sub-proof #808.
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | End of split
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | End of split
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | End of split
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | Case 2:
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | |   (251)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 242.52/49.10  | | | |              e1) = e0)
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | BETA: splitting (251) gives:
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | Case 1:
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | |   (252)  all_58_8 = e0 & op(e1, e1) = e0
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | | ALPHA: (252) implies:
% 242.52/49.10  | | | | |   (253)  all_58_8 = e0
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | | BETA: splitting (59) gives:
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | | Case 1:
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | |   (254)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 242.52/49.10  | | | | | |              e2) = e2)
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | | REF_CLOSE: (6), (11), (12), (16), (17), (24), (27), (29), (33),
% 242.52/49.10  | | | | | |            (37), (61), (67), (70), (77), (79), (80), (241), (254)
% 242.52/49.10  | | | | | |            are inconsistent by sub-proof #809.
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | Case 2:
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | |   (255)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 242.52/49.10  | | | | | |            op(e1, e0) = e2)
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | | BETA: splitting (255) gives:
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | | Case 1:
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | |   (256)  all_58_8 = e2 & op(e1, e1) = e2
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | | ALPHA: (256) implies:
% 242.52/49.10  | | | | | | |   (257)  all_58_8 = e2
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | | REF_CLOSE: (12), (253), (257) are inconsistent by sub-proof #1556.
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | Case 2:
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | |   (258)  all_58_11 = e2 & op(e1, e0) = e2
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | | REF_CLOSE: (6), (11), (12), (15), (24), (27), (33), (37), (41),
% 242.52/49.10  | | | | | | |            (46), (47), (61), (67), (70), (77), (79), (80), (241),
% 242.52/49.10  | | | | | | |            (258) are inconsistent by sub-proof #808.
% 242.52/49.10  | | | | | | | 
% 242.52/49.10  | | | | | | End of split
% 242.52/49.10  | | | | | | 
% 242.52/49.10  | | | | | End of split
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | Case 2:
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | |   (259)  all_58_14 = e0 & op(e0, e1) = e0
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | | REF_CLOSE: (12), (241), (259) are inconsistent by sub-proof #2036.
% 242.52/49.10  | | | | | 
% 242.52/49.10  | | | | End of split
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | End of split
% 242.52/49.10  | | | 
% 242.52/49.10  | | End of split
% 242.52/49.10  | | 
% 242.52/49.10  | End of split
% 242.52/49.10  | 
% 242.52/49.10  End of proof
% 242.52/49.10  
% 242.52/49.10  Sub-proof #808 shows that the following formulas are inconsistent:
% 242.52/49.10  ----------------------------------------------------------------
% 242.52/49.10    (1)   ~ (e3 = e0)
% 242.52/49.10    (2)  all_58_6 = e3
% 242.52/49.10    (3)   ~ (e2 = e0)
% 242.52/49.10    (4)  op(e1, e2) = all_52_6
% 242.52/49.10    (5)  all_58_14 = e2
% 242.52/49.10    (6)  all_58_15 = e3
% 242.52/49.10    (7)  op(e0, e2) = e2
% 242.52/49.10    (8)   ~ (e3 = e1)
% 242.52/49.10    (9)  all_58_11 = e2 & op(e1, e0) = e2
% 242.52/49.10    (10)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.52/49.10              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.52/49.10                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.52/49.10                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.52/49.10    (11)   ~ (e3 = e2)
% 242.52/49.10    (12)  all_58_13 = e2
% 242.52/49.10    (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.52/49.10          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.52/49.10    (14)   ~ (all_52_6 = e3)
% 242.52/49.10    (15)  op(e1, e1) = e2
% 242.52/49.10    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.10            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.10    (17)   ~ (e1 = e0)
% 242.52/49.10    (18)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.52/49.10          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.52/49.10            e1)
% 242.52/49.10    (19)   ~ (e2 = e1)
% 242.52/49.10  
% 242.52/49.10  Begin of proof
% 242.52/49.10  | 
% 242.52/49.10  | ALPHA: (9) implies:
% 242.52/49.10  |   (20)  all_58_11 = e2
% 242.52/49.10  | 
% 242.52/49.10  | BETA: splitting (18) gives:
% 242.52/49.10  | 
% 242.52/49.10  | Case 1:
% 242.52/49.10  | | 
% 242.52/49.10  | |   (21)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 242.52/49.10  | |           e1)
% 242.52/49.10  | | 
% 242.52/49.10  | | BETA: splitting (21) gives:
% 242.52/49.10  | | 
% 242.52/49.10  | | Case 1:
% 242.52/49.10  | | | 
% 242.52/49.10  | | |   (22)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.10  | | | 
% 242.52/49.10  | | | ALPHA: (22) implies:
% 242.52/49.10  | | |   (23)  all_58_12 = e1
% 242.52/49.10  | | | 
% 242.52/49.10  | | | BETA: splitting (10) gives:
% 242.52/49.10  | | | 
% 242.52/49.10  | | | Case 1:
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | |   (24)  all_58_15 = e0 & op(e0, e0) = e0
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | REF_CLOSE: (1), (2), (4), (6), (11), (13), (14), (15), (16), (20), (24)
% 242.52/49.10  | | | |            are inconsistent by sub-proof #832.
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | Case 2:
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | |   (25)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 242.52/49.10  | | | |               e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 242.52/49.10  | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 242.52/49.10  | | | |               e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | ALPHA: (25) implies:
% 242.52/49.10  | | | |   (26)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 242.52/49.10  | | | |             e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | REF_CLOSE: (3), (5), (7), (16), (17), (23), (26) are inconsistent by
% 242.52/49.10  | | | |            sub-proof #1538.
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | End of split
% 242.52/49.10  | | | 
% 242.52/49.10  | | Case 2:
% 242.52/49.10  | | | 
% 242.52/49.10  | | |   (27)  all_58_13 = e1 & op(e0, e2) = e1
% 242.52/49.10  | | | 
% 242.52/49.10  | | | REF_CLOSE: (12), (19), (27) are inconsistent by sub-proof #1751.
% 242.52/49.10  | | | 
% 242.52/49.10  | | End of split
% 242.52/49.10  | | 
% 242.52/49.10  | Case 2:
% 242.52/49.10  | | 
% 242.52/49.10  | |   (28)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.52/49.10  | |           e1)
% 242.52/49.10  | | 
% 242.52/49.10  | | BETA: splitting (28) gives:
% 242.52/49.10  | | 
% 242.52/49.10  | | Case 1:
% 242.52/49.10  | | | 
% 242.52/49.10  | | |   (29)  all_58_14 = e1 & op(e0, e1) = e1
% 242.52/49.10  | | | 
% 242.52/49.10  | | | REF_CLOSE: (5), (19), (29) are inconsistent by sub-proof #2040.
% 242.52/49.10  | | | 
% 242.52/49.10  | | Case 2:
% 242.52/49.10  | | | 
% 242.52/49.10  | | |   (30)  all_58_15 = e1 & op(e0, e0) = e1
% 242.52/49.10  | | | 
% 242.52/49.10  | | | REF_CLOSE: (6), (8), (30) are inconsistent by sub-proof #1393.
% 242.52/49.10  | | | 
% 242.52/49.10  | | End of split
% 242.52/49.10  | | 
% 242.52/49.10  | End of split
% 242.52/49.10  | 
% 242.52/49.10  End of proof
% 242.52/49.10  
% 242.52/49.10  Sub-proof #809 shows that the following formulas are inconsistent:
% 242.52/49.10  ----------------------------------------------------------------
% 242.52/49.10    (1)   ~ (e3 = e0)
% 242.52/49.10    (2)  all_58_6 = e3
% 242.52/49.10    (3)   ~ (e2 = e0)
% 242.52/49.10    (4)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.52/49.10         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.52/49.10    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.52/49.10         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.52/49.10    (6)  all_58_14 = e2
% 242.52/49.10    (7)  all_58_15 = e3
% 242.52/49.10    (8)  op(e0, e2) = e2
% 242.52/49.10    (9)   ~ (e3 = e1)
% 242.52/49.10    (10)  all_58_3 = e3
% 242.52/49.10    (11)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.52/49.10              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.52/49.10                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.52/49.10                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.52/49.10    (12)   ~ (e3 = e2)
% 242.52/49.10    (13)  all_58_13 = e2
% 242.52/49.10    (14)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 242.52/49.10    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.10            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.10    (16)   ~ (e1 = e0)
% 242.52/49.10    (17)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.52/49.10          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.52/49.10            e1)
% 242.52/49.10    (18)   ~ (e2 = e1)
% 242.52/49.10  
% 242.52/49.10  Begin of proof
% 242.52/49.10  | 
% 242.52/49.10  | BETA: splitting (14) gives:
% 242.52/49.10  | 
% 242.52/49.10  | Case 1:
% 242.52/49.10  | | 
% 242.52/49.10  | |   (19)  all_58_6 = e2 & op(e1, e3) = e2
% 242.52/49.10  | | 
% 242.52/49.10  | | REF_CLOSE: (2), (12), (19) are inconsistent by sub-proof #2219.
% 242.52/49.10  | | 
% 242.52/49.10  | Case 2:
% 242.52/49.10  | | 
% 242.52/49.10  | |   (20)  all_58_7 = e2 & op(e1, e2) = e2
% 242.52/49.10  | | 
% 242.52/49.10  | | ALPHA: (20) implies:
% 242.52/49.10  | |   (21)  all_58_7 = e2
% 242.52/49.10  | | 
% 242.52/49.10  | | BETA: splitting (17) gives:
% 242.52/49.10  | | 
% 242.52/49.10  | | Case 1:
% 242.52/49.10  | | | 
% 242.52/49.10  | | |   (22)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2)
% 242.52/49.10  | | |           = e1)
% 242.52/49.10  | | | 
% 242.52/49.10  | | | BETA: splitting (22) gives:
% 242.52/49.10  | | | 
% 242.52/49.10  | | | Case 1:
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | |   (23)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | ALPHA: (23) implies:
% 242.52/49.10  | | | |   (24)  all_58_12 = e1
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | REF_CLOSE: (1), (3), (6), (7), (8), (11), (15), (16), (24) are
% 242.52/49.10  | | | |            inconsistent by sub-proof #1537.
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | Case 2:
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | |   (25)  all_58_13 = e1 & op(e0, e2) = e1
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | REF_CLOSE: (1), (3), (4), (5), (10), (12), (13), (16), (18), (21), (25)
% 242.52/49.10  | | | |            are inconsistent by sub-proof #1455.
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | End of split
% 242.52/49.10  | | | 
% 242.52/49.10  | | Case 2:
% 242.52/49.10  | | | 
% 242.52/49.10  | | |   (26)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0)
% 242.52/49.10  | | |           = e1)
% 242.52/49.10  | | | 
% 242.52/49.10  | | | BETA: splitting (26) gives:
% 242.52/49.10  | | | 
% 242.52/49.10  | | | Case 1:
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | |   (27)  all_58_14 = e1 & op(e0, e1) = e1
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | ALPHA: (27) implies:
% 242.52/49.10  | | | |   (28)  all_58_14 = e1
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | COMBINE_EQS: (6), (28) imply:
% 242.52/49.10  | | | |   (29)  e2 = e1
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | SIMP: (29) implies:
% 242.52/49.10  | | | |   (30)  e2 = e1
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | COMBINE_EQS: (13), (30) imply:
% 242.52/49.10  | | | |   (31)  all_58_13 = e1
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | COMBINE_EQS: (21), (30) imply:
% 242.52/49.10  | | | |   (32)  all_58_7 = e1
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | REF_CLOSE: (1), (3), (4), (5), (10), (12), (16), (18), (31), (32) are
% 242.52/49.10  | | | |            inconsistent by sub-proof #1457.
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | Case 2:
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | |   (33)  all_58_15 = e1 & op(e0, e0) = e1
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | ALPHA: (33) implies:
% 242.52/49.10  | | | |   (34)  all_58_15 = e1
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | | REF_CLOSE: (7), (9), (34) are inconsistent by sub-proof #2249.
% 242.52/49.10  | | | | 
% 242.52/49.10  | | | End of split
% 242.52/49.10  | | | 
% 242.52/49.10  | | End of split
% 242.52/49.10  | | 
% 242.52/49.10  | End of split
% 242.52/49.10  | 
% 242.52/49.10  End of proof
% 242.52/49.10  
% 242.52/49.10  Sub-proof #810 shows that the following formulas are inconsistent:
% 242.52/49.10  ----------------------------------------------------------------
% 242.52/49.11    (1)   ~ (e3 = e0)
% 242.52/49.11    (2)  all_58_6 = e3
% 242.52/49.11    (3)   ~ (e2 = e0)
% 242.52/49.11    (4)  all_58_15 = e3
% 242.52/49.11    (5)  op(e0, e3) = all_52_3
% 242.52/49.11    (6)   ~ (e3 = e1)
% 242.52/49.11    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.52/49.11         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.52/49.11    (8)  op(e0, all_52_3) = e0
% 242.52/49.11    (9)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.52/49.11             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.52/49.11               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.52/49.11               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.52/49.11    (10)  op(e2, e1) = all_52_9
% 242.52/49.11    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.52/49.11          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.52/49.11    (12)  all_58_13 = e2
% 242.52/49.11    (13)  op(e3, e3) = e2
% 242.52/49.11    (14)  op(e1, e1) = e2
% 242.52/49.11    (15)   ~ (all_52_9 = e3)
% 242.52/49.11    (16)  op(e0, e0) = e3
% 242.52/49.11    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.11    (18)   ~ (e1 = e0)
% 242.52/49.11    (19)  all_58_4 = e3
% 242.52/49.11    (20)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.52/49.11          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.52/49.11            e1)
% 242.52/49.11    (21)  all_58_2 = e1
% 242.52/49.11    (22)   ~ (e2 = e1)
% 242.52/49.11  
% 242.52/49.11  Begin of proof
% 242.52/49.11  | 
% 242.52/49.11  | BETA: splitting (11) gives:
% 242.52/49.11  | 
% 242.52/49.11  | Case 1:
% 242.52/49.11  | | 
% 242.52/49.11  | |   (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 242.52/49.11  | |           e0)
% 242.52/49.11  | | 
% 242.52/49.11  | | REF_CLOSE: (3), (13), (17), (18), (21), (23) are inconsistent by sub-proof
% 242.52/49.11  | |            #1761.
% 242.52/49.11  | | 
% 242.52/49.11  | Case 2:
% 242.52/49.11  | | 
% 242.52/49.11  | |   (24)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 242.52/49.11  | |           e0)
% 242.52/49.11  | | 
% 242.52/49.11  | | BETA: splitting (24) gives:
% 242.52/49.11  | | 
% 242.52/49.11  | | Case 1:
% 242.52/49.11  | | | 
% 242.52/49.11  | | |   (25)  all_58_6 = e0 & op(e1, e3) = e0
% 242.52/49.11  | | | 
% 242.52/49.11  | | | REF_CLOSE: (1), (2), (25) are inconsistent by sub-proof #2213.
% 242.52/49.11  | | | 
% 242.52/49.11  | | Case 2:
% 242.52/49.11  | | | 
% 242.52/49.11  | | |   (26)  all_58_12 = e0 & op(e0, e3) = e0
% 242.52/49.11  | | | 
% 242.52/49.11  | | | ALPHA: (26) implies:
% 242.52/49.11  | | |   (27)  all_58_12 = e0
% 242.52/49.11  | | |   (28)  op(e0, e3) = e0
% 242.52/49.11  | | | 
% 242.52/49.11  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14), (15),
% 242.52/49.11  | | |            (16), (17), (18), (19), (20), (22), (27), (28) are inconsistent
% 242.52/49.11  | | |            by sub-proof #811.
% 242.52/49.11  | | | 
% 242.52/49.11  | | End of split
% 242.52/49.11  | | 
% 242.52/49.11  | End of split
% 242.52/49.11  | 
% 242.52/49.11  End of proof
% 242.52/49.11  
% 242.52/49.11  Sub-proof #811 shows that the following formulas are inconsistent:
% 242.52/49.11  ----------------------------------------------------------------
% 242.52/49.11    (1)   ~ (e3 = e0)
% 242.52/49.11    (2)   ~ (e2 = e0)
% 242.52/49.11    (3)  all_58_15 = e3
% 242.52/49.11    (4)  op(e0, e3) = all_52_3
% 242.52/49.11    (5)   ~ (e3 = e1)
% 242.52/49.11    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.52/49.11         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.52/49.11    (7)  op(e0, all_52_3) = e0
% 242.52/49.11    (8)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.52/49.11             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.52/49.11               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.52/49.11               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.52/49.11    (9)  op(e2, e1) = all_52_9
% 242.52/49.11    (10)  op(e0, e3) = e0
% 242.52/49.11    (11)  all_58_13 = e2
% 242.52/49.11    (12)  all_58_12 = e0
% 242.52/49.11    (13)  op(e1, e1) = e2
% 242.52/49.11    (14)   ~ (all_52_9 = e3)
% 242.52/49.11    (15)  op(e0, e0) = e3
% 242.52/49.11    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.11    (17)   ~ (e1 = e0)
% 242.52/49.11    (18)  all_58_4 = e3
% 242.52/49.11    (19)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.52/49.11          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.52/49.11            e1)
% 242.52/49.11    (20)   ~ (e2 = e1)
% 242.52/49.11  
% 242.52/49.11  Begin of proof
% 242.52/49.11  | 
% 242.52/49.11  | BETA: splitting (19) gives:
% 242.52/49.11  | 
% 242.52/49.11  | Case 1:
% 242.52/49.11  | | 
% 242.52/49.11  | |   (21)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 242.52/49.11  | |           e1)
% 242.52/49.11  | | 
% 242.52/49.11  | | BETA: splitting (21) gives:
% 242.52/49.11  | | 
% 242.52/49.11  | | Case 1:
% 242.52/49.11  | | | 
% 242.52/49.11  | | |   (22)  all_58_12 = e1 & op(e0, e3) = e1
% 242.52/49.11  | | | 
% 242.52/49.11  | | | ALPHA: (22) implies:
% 242.52/49.11  | | |   (23)  all_58_12 = e1
% 242.52/49.11  | | | 
% 242.52/49.11  | | | REF_CLOSE: (12), (17), (23) are inconsistent by sub-proof #1539.
% 242.52/49.11  | | | 
% 242.52/49.11  | | Case 2:
% 242.52/49.11  | | | 
% 242.52/49.11  | | |   (24)  all_58_13 = e1 & op(e0, e2) = e1
% 242.52/49.11  | | | 
% 242.52/49.11  | | | REF_CLOSE: (11), (20), (24) are inconsistent by sub-proof #1751.
% 242.52/49.11  | | | 
% 242.52/49.11  | | End of split
% 242.52/49.11  | | 
% 242.52/49.11  | Case 2:
% 242.52/49.11  | | 
% 242.52/49.11  | |   (25)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.52/49.11  | |           e1)
% 242.52/49.11  | | 
% 242.52/49.11  | | BETA: splitting (25) gives:
% 242.52/49.11  | | 
% 242.52/49.11  | | Case 1:
% 242.52/49.11  | | | 
% 242.52/49.11  | | |   (26)  all_58_14 = e1 & op(e0, e1) = e1
% 242.52/49.11  | | | 
% 242.52/49.11  | | | ALPHA: (26) implies:
% 242.52/49.11  | | |   (27)  op(e0, e1) = e1
% 242.52/49.11  | | | 
% 242.52/49.11  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (13), (14), (15),
% 242.52/49.11  | | |            (16), (17), (18), (27) are inconsistent by sub-proof #812.
% 242.52/49.11  | | | 
% 242.52/49.11  | | Case 2:
% 242.52/49.11  | | | 
% 242.52/49.11  | | |   (28)  all_58_15 = e1 & op(e0, e0) = e1
% 242.52/49.11  | | | 
% 242.52/49.11  | | | REF_CLOSE: (3), (5), (28) are inconsistent by sub-proof #1393.
% 242.52/49.11  | | | 
% 242.52/49.11  | | End of split
% 242.52/49.11  | | 
% 242.52/49.11  | End of split
% 242.52/49.11  | 
% 242.52/49.11  End of proof
% 242.52/49.11  
% 242.52/49.11  Sub-proof #812 shows that the following formulas are inconsistent:
% 242.52/49.11  ----------------------------------------------------------------
% 242.52/49.11    (1)   ~ (e3 = e0)
% 242.52/49.11    (2)   ~ (e2 = e0)
% 242.52/49.11    (3)  all_58_15 = e3
% 242.52/49.11    (4)  op(e0, e3) = all_52_3
% 242.52/49.11    (5)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.52/49.11         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.52/49.11    (6)  op(e0, all_52_3) = e0
% 242.52/49.11    (7)  op(e0, e1) = e1
% 242.52/49.11    (8)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.52/49.11             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.52/49.11               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.52/49.11               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.52/49.11    (9)  op(e2, e1) = all_52_9
% 242.52/49.11    (10)  op(e0, e3) = e0
% 242.52/49.11    (11)  op(e1, e1) = e2
% 242.52/49.11    (12)   ~ (all_52_9 = e3)
% 242.52/49.11    (13)  op(e0, e0) = e3
% 242.52/49.11    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.11    (15)   ~ (e1 = e0)
% 242.52/49.11    (16)  all_58_4 = e3
% 242.52/49.11  
% 242.52/49.11  Begin of proof
% 242.52/49.11  | 
% 242.52/49.11  | BETA: splitting (5) gives:
% 242.52/49.11  | 
% 242.52/49.11  | Case 1:
% 242.52/49.11  | | 
% 242.52/49.11  | |   (17)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 242.52/49.11  | |           e0)
% 242.52/49.11  | | 
% 242.52/49.11  | | BETA: splitting (17) gives:
% 242.52/49.11  | | 
% 242.52/49.11  | | Case 1:
% 242.52/49.11  | | | 
% 242.52/49.11  | | |   (18)  all_58_4 = e0 & op(e3, e1) = e0
% 242.52/49.11  | | | 
% 242.52/49.11  | | | REF_CLOSE: (1), (16), (18) are inconsistent by sub-proof #1697.
% 242.52/49.11  | | | 
% 242.52/49.11  | | Case 2:
% 242.52/49.11  | | | 
% 242.52/49.11  | | |   (19)  all_58_5 = e0 & op(e2, e1) = e0
% 242.52/49.11  | | | 
% 242.52/49.11  | | | ALPHA: (19) implies:
% 242.52/49.11  | | |   (20)  op(e2, e1) = e0
% 242.52/49.11  | | | 
% 242.52/49.11  | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (12), (13), (14), (20) are
% 242.52/49.11  | | |            inconsistent by sub-proof #813.
% 242.52/49.11  | | | 
% 242.52/49.11  | | End of split
% 242.52/49.11  | | 
% 242.52/49.11  | Case 2:
% 242.52/49.11  | | 
% 242.52/49.11  | |   (21)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 242.52/49.11  | |           e0)
% 242.52/49.11  | | 
% 242.52/49.11  | | REF_CLOSE: (2), (7), (11), (14), (15), (21) are inconsistent by sub-proof
% 242.52/49.11  | |            #1036.
% 242.52/49.11  | | 
% 242.52/49.11  | End of split
% 242.52/49.11  | 
% 242.52/49.11  End of proof
% 242.52/49.11  
% 242.52/49.11  Sub-proof #813 shows that the following formulas are inconsistent:
% 242.52/49.11  ----------------------------------------------------------------
% 242.52/49.11    (1)   ~ (e3 = e0)
% 242.52/49.11    (2)  all_58_15 = e3
% 242.52/49.11    (3)  op(e0, e3) = all_52_3
% 242.52/49.11    (4)  op(e0, all_52_3) = e0
% 242.52/49.11    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.52/49.11             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.52/49.11               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.52/49.11               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.52/49.11    (6)  op(e2, e1) = all_52_9
% 242.52/49.11    (7)  op(e0, e3) = e0
% 242.52/49.11    (8)  op(e2, e1) = e0
% 242.52/49.11    (9)   ~ (all_52_9 = e3)
% 242.52/49.11    (10)  op(e0, e0) = e3
% 242.52/49.11    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.11  
% 242.52/49.11  Begin of proof
% 242.52/49.11  | 
% 242.52/49.11  | BETA: splitting (5) gives:
% 242.52/49.11  | 
% 242.52/49.11  | Case 1:
% 242.52/49.11  | | 
% 242.52/49.11  | |   (12)  all_58_15 = e0 & op(e0, e0) = e0
% 242.52/49.11  | | 
% 242.52/49.11  | | ALPHA: (12) implies:
% 242.52/49.11  | |   (13)  all_58_15 = e0
% 242.52/49.11  | | 
% 242.52/49.11  | | COMBINE_EQS: (2), (13) imply:
% 242.52/49.11  | |   (14)  e3 = e0
% 242.52/49.11  | | 
% 242.52/49.11  | | REDUCE: (1), (14) imply:
% 242.52/49.11  | |   (15)  $false
% 242.52/49.11  | | 
% 242.52/49.11  | | CLOSE: (15) is inconsistent.
% 242.52/49.11  | | 
% 242.52/49.11  | Case 2:
% 242.52/49.11  | | 
% 242.52/49.11  | | 
% 242.52/49.11  | | GROUND_INST: instantiating (11) with all_52_3, e0, e3, e0, simplifying with
% 242.52/49.11  | |              (3), (7) gives:
% 242.52/49.11  | |   (16)  all_52_3 = e0
% 242.52/49.11  | | 
% 242.52/49.11  | | GROUND_INST: instantiating (11) with all_52_9, e0, e1, e2, simplifying with
% 242.52/49.11  | |              (6), (8) gives:
% 242.52/49.11  | |   (17)  all_52_9 = e0
% 242.52/49.11  | | 
% 242.52/49.11  | | REDUCE: (9), (17) imply:
% 242.52/49.11  | |   (18)   ~ (e3 = e0)
% 242.52/49.11  | | 
% 242.52/49.11  | | REDUCE: (4), (16) imply:
% 242.52/49.11  | |   (19)  op(e0, e0) = e0
% 242.52/49.11  | | 
% 242.52/49.11  | | REF_CLOSE: (1), (10), (11), (19) are inconsistent by sub-proof #2079.
% 242.52/49.11  | | 
% 242.52/49.11  | End of split
% 242.52/49.11  | 
% 242.52/49.11  End of proof
% 242.52/49.11  
% 242.52/49.11  Sub-proof #814 shows that the following formulas are inconsistent:
% 242.52/49.11  ----------------------------------------------------------------
% 242.52/49.11    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.52/49.11           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.52/49.11           all_12_1 & $i(all_12_1))
% 242.52/49.11    (2)  all_56_21 = e2
% 242.52/49.11    (3)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.52/49.11           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.52/49.11           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.52/49.11           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.52/49.11           & $i(all_56_23))
% 242.52/49.11    (4)   ~ (e3 = e0)
% 242.52/49.11    (5)  op(e0, e1) = all_52_11
% 242.52/49.11    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.52/49.11         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.52/49.11    (7)  all_58_6 = e3
% 242.52/49.11    (8)   ~ (e2 = e0)
% 242.52/49.11    (9)   ~ (all_52_11 = e2)
% 242.52/49.11    (10)  op(e1, e2) = all_52_6
% 242.52/49.11    (11)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.52/49.11          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.52/49.11    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.52/49.11          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.52/49.11    (13)   ~ (all_52_6 = e2)
% 242.52/49.11    (14)  op(e1, e0) = all_52_14
% 242.52/49.11    (15)  op(e0, e3) = all_52_3
% 242.52/49.11    (16)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.52/49.11          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.52/49.11    (17)   ~ (e3 = e1)
% 242.52/49.11    (18)  all_58_8 = e2
% 242.52/49.11    (19)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.52/49.11          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.52/49.11    (20)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.52/49.11    (21)  all_58_3 = e3
% 242.52/49.11    (22)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.52/49.11            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.52/49.11              e3) = all_26_1 & $i(all_26_1))
% 242.52/49.11    (23)   ~ (all_52_11 = e3)
% 242.52/49.11    (24)  op(e2, e1) = all_52_9
% 242.52/49.11    (25)   ~ (e3 = e2)
% 242.52/49.11    (26)  all_58_10 = e2
% 242.52/49.11    (27)  op(e2, e0) = e2
% 242.52/49.11    (28)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.52/49.11          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.52/49.11    (29)  all_58_13 = e2
% 242.52/49.11    (30)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.52/49.11          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.52/49.11    (31)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.52/49.11            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.52/49.11              e3) = all_42_1 & $i(all_42_1))
% 242.52/49.11    (32)   ~ (all_52_6 = all_52_14)
% 242.52/49.11    (33)  op(e2, e3) = all_52_1
% 242.52/49.11    (34)  op(e3, e3) = e2
% 242.52/49.11    (35)   ~ (all_52_6 = e3)
% 242.52/49.11    (36)  op(e1, e1) = e2
% 242.52/49.11    (37)  op(e0, e0) = e3
% 242.52/49.11    (38)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.52/49.11          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.52/49.11    (39)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.52/49.11          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.52/49.11    (40)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.52/49.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.52/49.11    (41)  op(e3, e1) = e3
% 242.52/49.12    (42)   ~ (e1 = e0)
% 242.52/49.12    (43)  all_58_4 = e3
% 242.62/49.12    (44)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.62/49.12          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.62/49.12    (45)   ~ (all_52_9 = all_52_11)
% 242.62/49.12    (46)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.62/49.12            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.62/49.12            & $i(all_8_1))
% 242.62/49.12    (47)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.62/49.12          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.62/49.12    (48)   ~ (e2 = e1)
% 242.62/49.12    (49)  op(e1, all_52_6) = e1
% 242.62/49.12    (50)   ~ (all_52_9 = e2)
% 242.62/49.12  
% 242.62/49.12  Begin of proof
% 242.62/49.12  | 
% 242.62/49.12  | BETA: splitting (20) gives:
% 242.62/49.12  | 
% 242.62/49.12  | Case 1:
% 242.62/49.12  | | 
% 242.62/49.12  | |   (51)  all_58_12 = e1 & op(e0, e3) = e1
% 242.62/49.12  | | 
% 242.62/49.12  | | ALPHA: (51) implies:
% 242.62/49.12  | |   (52)  all_58_12 = e1
% 242.62/49.12  | |   (53)  op(e0, e3) = e1
% 242.62/49.12  | | 
% 242.62/49.12  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.62/49.12  | |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 242.62/49.12  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 242.62/49.12  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 242.62/49.12  | |            (47), (48), (49), (50), (52), (53) are inconsistent by sub-proof
% 242.62/49.12  | |            #815.
% 242.62/49.12  | | 
% 242.62/49.12  | Case 2:
% 242.62/49.12  | | 
% 242.62/49.12  | |   (54)  all_58_13 = e1 & op(e0, e2) = e1
% 242.62/49.12  | | 
% 242.62/49.12  | | REF_CLOSE: (29), (48), (54) are inconsistent by sub-proof #1751.
% 242.62/49.12  | | 
% 242.62/49.12  | End of split
% 242.62/49.12  | 
% 242.62/49.12  End of proof
% 242.62/49.12  
% 242.62/49.12  Sub-proof #815 shows that the following formulas are inconsistent:
% 242.62/49.12  ----------------------------------------------------------------
% 242.62/49.12    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.62/49.12           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.62/49.12           all_12_1 & $i(all_12_1))
% 242.62/49.12    (2)  all_56_21 = e2
% 242.62/49.12    (3)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.62/49.12           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.62/49.12           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.62/49.12           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.62/49.12           & $i(all_56_23))
% 242.62/49.12    (4)   ~ (e3 = e0)
% 242.62/49.12    (5)  op(e0, e1) = all_52_11
% 242.62/49.12    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.62/49.12         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.62/49.12    (7)  all_58_6 = e3
% 242.62/49.12    (8)   ~ (e2 = e0)
% 242.62/49.12    (9)   ~ (all_52_11 = e2)
% 242.62/49.12    (10)  op(e1, e2) = all_52_6
% 242.62/49.12    (11)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.12          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.62/49.12    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.12          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.62/49.12    (13)   ~ (all_52_6 = e2)
% 242.62/49.12    (14)  op(e1, e0) = all_52_14
% 242.62/49.12    (15)  op(e0, e3) = all_52_3
% 242.62/49.12    (16)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.12          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.12    (17)   ~ (e3 = e1)
% 242.62/49.12    (18)  all_58_8 = e2
% 242.62/49.12    (19)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.62/49.12          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.62/49.12    (20)  all_58_3 = e3
% 242.62/49.12    (21)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.62/49.12            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.62/49.12              e3) = all_26_1 & $i(all_26_1))
% 242.62/49.12    (22)  all_58_12 = e1
% 242.62/49.12    (23)   ~ (all_52_11 = e3)
% 242.62/49.12    (24)  op(e2, e1) = all_52_9
% 242.62/49.12    (25)   ~ (e3 = e2)
% 242.62/49.12    (26)  all_58_10 = e2
% 242.62/49.12    (27)  op(e0, e3) = e1
% 242.62/49.12    (28)  op(e2, e0) = e2
% 242.62/49.12    (29)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.62/49.12          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.62/49.12    (30)  all_58_13 = e2
% 242.62/49.12    (31)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.62/49.12          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.62/49.12    (32)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.62/49.12            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.62/49.12              e3) = all_42_1 & $i(all_42_1))
% 242.62/49.12    (33)   ~ (all_52_6 = all_52_14)
% 242.62/49.12    (34)  op(e2, e3) = all_52_1
% 242.62/49.12    (35)  op(e3, e3) = e2
% 242.62/49.12    (36)   ~ (all_52_6 = e3)
% 242.62/49.12    (37)  op(e1, e1) = e2
% 242.62/49.12    (38)  op(e0, e0) = e3
% 242.62/49.12    (39)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.62/49.12          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.62/49.12    (40)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.12          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.12    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.12    (42)  op(e3, e1) = e3
% 242.62/49.12    (43)   ~ (e1 = e0)
% 242.62/49.12    (44)  all_58_4 = e3
% 242.62/49.12    (45)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.62/49.12          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.62/49.12    (46)   ~ (all_52_9 = all_52_11)
% 242.62/49.12    (47)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.62/49.12            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.62/49.12            & $i(all_8_1))
% 242.62/49.12    (48)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.62/49.12          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.62/49.12    (49)   ~ (e2 = e1)
% 242.62/49.12    (50)  op(e1, all_52_6) = e1
% 242.62/49.12    (51)   ~ (all_52_9 = e2)
% 242.62/49.12  
% 242.62/49.12  Begin of proof
% 242.62/49.12  | 
% 242.62/49.12  | BETA: splitting (29) gives:
% 242.62/49.12  | 
% 242.62/49.12  | Case 1:
% 242.62/49.12  | | 
% 242.62/49.12  | |   (52)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 242.62/49.12  | |           e0)
% 242.62/49.12  | | 
% 242.62/49.12  | | BETA: splitting (52) gives:
% 242.62/49.12  | | 
% 242.62/49.12  | | Case 1:
% 242.62/49.12  | | | 
% 242.62/49.12  | | |   (53)  all_58_0 = e0 & op(e3, e3) = e0
% 242.62/49.12  | | | 
% 242.62/49.12  | | | ALPHA: (53) implies:
% 242.62/49.12  | | |   (54)  op(e3, e3) = e0
% 242.62/49.12  | | | 
% 242.62/49.12  | | | REF_CLOSE: (8), (35), (41), (54) are inconsistent by sub-proof #2188.
% 242.62/49.12  | | | 
% 242.62/49.12  | | Case 2:
% 242.62/49.12  | | | 
% 242.62/49.12  | | |   (55)  all_58_2 = e0 & op(e2, e3) = e0
% 242.62/49.12  | | | 
% 242.62/49.12  | | | ALPHA: (55) implies:
% 242.62/49.12  | | |   (56)  all_58_2 = e0
% 242.62/49.12  | | |   (57)  op(e2, e3) = e0
% 242.62/49.12  | | | 
% 242.62/49.12  | | | BETA: splitting (48) gives:
% 242.62/49.12  | | | 
% 242.62/49.12  | | | Case 1:
% 242.62/49.12  | | | | 
% 242.62/49.12  | | | |   (58)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 242.62/49.12  | | | |           = e1)
% 242.62/49.12  | | | | 
% 242.62/49.12  | | | | REF_CLOSE: (17), (20), (43), (56), (58) are inconsistent by sub-proof
% 242.62/49.12  | | | |            #824.
% 242.62/49.12  | | | | 
% 242.62/49.12  | | | Case 2:
% 242.62/49.12  | | | | 
% 242.62/49.12  | | | |   (59)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 242.62/49.12  | | | |           = e1)
% 242.62/49.12  | | | | 
% 242.62/49.12  | | | | BETA: splitting (59) gives:
% 242.62/49.12  | | | | 
% 242.62/49.12  | | | | Case 1:
% 242.62/49.12  | | | | | 
% 242.62/49.12  | | | | |   (60)  all_58_5 = e1 & op(e2, e1) = e1
% 242.62/49.12  | | | | | 
% 242.62/49.12  | | | | | ALPHA: (60) implies:
% 242.62/49.12  | | | | |   (61)  all_58_5 = e1
% 242.62/49.12  | | | | |   (62)  op(e2, e1) = e1
% 242.62/49.12  | | | | | 
% 242.62/49.12  | | | | | BETA: splitting (19) gives:
% 242.62/49.12  | | | | | 
% 242.62/49.12  | | | | | Case 1:
% 242.62/49.12  | | | | | | 
% 242.62/49.12  | | | | | |   (63)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 242.62/49.12  | | | | | |             e1) = e0)
% 242.62/49.12  | | | | | | 
% 242.62/49.12  | | | | | | REF_CLOSE: (4), (24), (41), (43), (44), (62), (63) are inconsistent
% 242.62/49.12  | | | | | |            by sub-proof #823.
% 242.62/49.12  | | | | | | 
% 242.62/49.12  | | | | | Case 2:
% 242.62/49.12  | | | | | | 
% 242.62/49.12  | | | | | |   (64)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 242.62/49.12  | | | | | |             e1) = e0)
% 242.62/49.12  | | | | | | 
% 242.62/49.12  | | | | | | BETA: splitting (64) gives:
% 242.62/49.12  | | | | | | 
% 242.62/49.12  | | | | | | Case 1:
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | |   (65)  all_58_8 = e0 & op(e1, e1) = e0
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | ALPHA: (65) implies:
% 242.62/49.12  | | | | | | |   (66)  op(e1, e1) = e0
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | REF_CLOSE: (8), (37), (41), (66) are inconsistent by sub-proof
% 242.62/49.12  | | | | | | |            #2211.
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | Case 2:
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | |   (67)  all_58_14 = e0 & op(e0, e1) = e0
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | ALPHA: (67) implies:
% 242.62/49.12  | | | | | | |   (68)  op(e0, e1) = e0
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | GROUND_INST: instantiating (41) with all_52_11, e0, e1, e0,
% 242.62/49.12  | | | | | | |              simplifying with (5), (68) gives:
% 242.62/49.12  | | | | | | |   (69)  all_52_11 = e0
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | GROUND_INST: instantiating (41) with all_52_3, e1, e3, e0,
% 242.62/49.12  | | | | | | |              simplifying with (15), (27) gives:
% 242.62/49.12  | | | | | | |   (70)  all_52_3 = e1
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | GROUND_INST: instantiating (41) with all_52_9, e1, e1, e2,
% 242.62/49.12  | | | | | | |              simplifying with (24), (62) gives:
% 242.62/49.12  | | | | | | |   (71)  all_52_9 = e1
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | GROUND_INST: instantiating (41) with all_52_1, e0, e3, e2,
% 242.62/49.12  | | | | | | |              simplifying with (34), (57) gives:
% 242.62/49.12  | | | | | | |   (72)  all_52_1 = e0
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | REDUCE: (51), (71) imply:
% 242.62/49.12  | | | | | | |   (73)   ~ (e2 = e1)
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | REDUCE: (23), (69) imply:
% 242.62/49.12  | | | | | | |   (74)   ~ (e3 = e0)
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | REDUCE: (9), (69) imply:
% 242.62/49.12  | | | | | | |   (75)   ~ (e2 = e0)
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | BETA: splitting (47) gives:
% 242.62/49.12  | | | | | | | 
% 242.62/49.12  | | | | | | | Case 1:
% 242.62/49.12  | | | | | | | | 
% 242.62/49.12  | | | | | | | |   (76)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2,
% 242.62/49.12  | | | | | | | |           e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 242.62/49.12  | | | | | | | | 
% 242.62/49.12  | | | | | | | | ALPHA: (76) implies:
% 242.62/49.12  | | | | | | | |   (77)  op(e2, e3) = all_8_1
% 242.62/49.12  | | | | | | | | 
% 242.62/49.12  | | | | | | | | BETA: splitting (3) gives:
% 242.62/49.12  | | | | | | | | 
% 242.62/49.12  | | | | | | | | Case 1:
% 242.62/49.12  | | | | | | | | | 
% 242.62/49.12  | | | | | | | | |   (78)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1)
% 242.62/49.12  | | | | | | | | |           = all_56_17 & $i(all_56_17)) | (all_56_18 = e2 &
% 242.62/49.12  | | | | | | | | |           op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 242.62/49.12  | | | | | | | | |           $i(all_56_19))
% 242.62/49.12  | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | BETA: splitting (78) gives:
% 242.62/49.12  | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | Case 1:
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | |   (79)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1)
% 242.62/49.12  | | | | | | | | | |         = all_56_17 & $i(all_56_17)
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | ALPHA: (79) implies:
% 242.62/49.12  | | | | | | | | | |   (80)  op(e3, e1) = all_56_17
% 242.62/49.12  | | | | | | | | | |   (81)  op(e3, all_56_17) = e3
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | REF_CLOSE: (25), (35), (41), (42), (80), (81) are
% 242.62/49.12  | | | | | | | | | |            inconsistent by sub-proof #2098.
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | Case 2:
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | |   (82)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.62/49.12  | | | | | | | | | |         = all_56_19 & $i(all_56_19)
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | ALPHA: (82) implies:
% 242.62/49.12  | | | | | | | | | |   (83)  op(e2, e1) = all_56_19
% 242.62/49.12  | | | | | | | | | |   (84)  op(e2, all_56_19) = e2
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | REF_CLOSE: (1), (4), (8), (16), (20), (21), (25), (26), (27),
% 242.62/49.12  | | | | | | | | | |            (32), (40), (41), (43), (49), (57), (61), (62),
% 242.62/49.12  | | | | | | | | | |            (77), (83), (84) are inconsistent by sub-proof
% 242.62/49.12  | | | | | | | | | |            #820.
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | End of split
% 242.62/49.12  | | | | | | | | | 
% 242.62/49.12  | | | | | | | | Case 2:
% 242.62/49.12  | | | | | | | | | 
% 242.62/49.12  | | | | | | | | |   (85)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22
% 242.62/49.12  | | | | | | | | |           = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 242.62/49.12  | | | | | | | | |           all_56_23 & $i(all_56_23))
% 242.62/49.12  | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | BETA: splitting (85) gives:
% 242.62/49.12  | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | Case 1:
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | |   (86)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | ALPHA: (86) implies:
% 242.62/49.12  | | | | | | | | | |   (87)  op(e1, all_56_21) = e1
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | REDUCE: (2), (87) imply:
% 242.62/49.12  | | | | | | | | | |   (88)  op(e1, e2) = e1
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | GROUND_INST: instantiating (41) with all_52_6, e1, e2, e1,
% 242.62/49.12  | | | | | | | | | |              simplifying with (10), (88) gives:
% 242.62/49.12  | | | | | | | | | |   (89)  all_52_6 = e1
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | REDUCE: (33), (89) imply:
% 242.62/49.12  | | | | | | | | | |   (90)   ~ (all_52_14 = e1)
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | SIMP: (90) implies:
% 242.62/49.12  | | | | | | | | | |   (91)   ~ (all_52_14 = e1)
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | REDUCE: (36), (89) imply:
% 242.62/49.12  | | | | | | | | | |   (92)   ~ (e3 = e1)
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | REDUCE: (50), (89) imply:
% 242.62/49.12  | | | | | | | | | |   (93)  op(e1, e1) = e1
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | BETA: splitting (6) gives:
% 242.62/49.12  | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | Case 1:
% 242.62/49.12  | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | |   (94)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 242.62/49.12  | | | | | | | | | | |           & op(e1, e2) = e1)
% 242.62/49.12  | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | BETA: splitting (94) gives:
% 242.62/49.12  | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | Case 1:
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | |   (95)  all_58_6 = e1 & op(e1, e3) = e1
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | | ALPHA: (95) implies:
% 242.62/49.12  | | | | | | | | | | | |   (96)  all_58_6 = e1
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | | REF_CLOSE: (7), (17), (96) are inconsistent by sub-proof
% 242.62/49.12  | | | | | | | | | | | |            #1758.
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | Case 2:
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | |   (97)  all_58_7 = e1 & op(e1, e2) = e1
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | | ALPHA: (97) implies:
% 242.62/49.12  | | | | | | | | | | | |   (98)  all_58_7 = e1
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (10), (11), (12), (18), (20), (25),
% 242.62/49.12  | | | | | | | | | | | |            (30), (31), (36), (37), (39), (41), (43), (45),
% 242.62/49.12  | | | | | | | | | | | |            (49), (88), (93), (98) are inconsistent by
% 242.62/49.12  | | | | | | | | | | | |            sub-proof #963.
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | End of split
% 242.62/49.12  | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | Case 2:
% 242.62/49.12  | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | |   (99)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 242.62/49.12  | | | | | | | | | | |           e1 & op(e1, e0) = e1)
% 242.62/49.12  | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | BETA: splitting (99) gives:
% 242.62/49.12  | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | Case 1:
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | |   (100)  all_58_8 = e1 & op(e1, e1) = e1
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | | ALPHA: (100) implies:
% 242.62/49.12  | | | | | | | | | | | |   (101)  all_58_8 = e1
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | | COMBINE_EQS: (18), (101) imply:
% 242.62/49.12  | | | | | | | | | | | |   (102)  e2 = e1
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | | SIMP: (102) implies:
% 242.62/49.12  | | | | | | | | | | | |   (103)  e2 = e1
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.12  | | | | | | | | | | | | COMBINE_EQS: (26), (103) imply:
% 242.62/49.12  | | | | | | | | | | | |   (104)  all_58_10 = e1
% 242.62/49.12  | | | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | | | | REF_CLOSE: (4), (8), (16), (20), (25), (40), (43), (49),
% 242.62/49.13  | | | | | | | | | | | |            (61), (104) are inconsistent by sub-proof #992.
% 242.62/49.13  | | | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | | | Case 2:
% 242.62/49.13  | | | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | | | |   (105)  all_58_11 = e1 & op(e1, e0) = e1
% 242.62/49.13  | | | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | | | | ALPHA: (105) implies:
% 242.62/49.13  | | | | | | | | | | | |   (106)  op(e1, e0) = e1
% 242.62/49.13  | | | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | | | | REF_CLOSE: (14), (41), (91), (106) are inconsistent by
% 242.62/49.13  | | | | | | | | | | | |            sub-proof #2304.
% 242.62/49.13  | | | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | | | End of split
% 242.62/49.13  | | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | | End of split
% 242.62/49.13  | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | Case 2:
% 242.62/49.13  | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | |   (107)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 242.62/49.13  | | | | | | | | | |            e1) = all_56_23 & $i(all_56_23)
% 242.62/49.13  | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | | ALPHA: (107) implies:
% 242.62/49.13  | | | | | | | | | |   (108)  op(e0, e1) = all_56_23
% 242.62/49.13  | | | | | | | | | |   (109)  op(e0, all_56_23) = e0
% 242.62/49.13  | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | | REF_CLOSE: (4), (38), (41), (68), (108), (109) are
% 242.62/49.13  | | | | | | | | | |            inconsistent by sub-proof #1395.
% 242.62/49.13  | | | | | | | | | | 
% 242.62/49.13  | | | | | | | | | End of split
% 242.62/49.13  | | | | | | | | | 
% 242.62/49.13  | | | | | | | | End of split
% 242.62/49.13  | | | | | | | | 
% 242.62/49.13  | | | | | | | Case 2:
% 242.62/49.13  | | | | | | | | 
% 242.62/49.13  | | | | | | | |   (110)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 242.62/49.13  | | | | | | | | 
% 242.62/49.13  | | | | | | | | ALPHA: (110) implies:
% 242.62/49.13  | | | | | | | |   (111)   ~ (all_8_1 = e0)
% 242.62/49.13  | | | | | | | |   (112)  op(e2, e3) = all_8_1
% 242.62/49.13  | | | | | | | | 
% 242.62/49.13  | | | | | | | | REF_CLOSE: (32), (41), (57), (111), (112) are inconsistent by
% 242.62/49.13  | | | | | | | |            sub-proof #897.
% 242.62/49.13  | | | | | | | | 
% 242.62/49.13  | | | | | | | End of split
% 242.62/49.13  | | | | | | | 
% 242.62/49.13  | | | | | | End of split
% 242.62/49.13  | | | | | | 
% 242.62/49.13  | | | | | End of split
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | Case 2:
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | |   (113)  all_58_10 = e1 & op(e2, e0) = e1
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | | ALPHA: (113) implies:
% 242.62/49.13  | | | | |   (114)  op(e2, e0) = e1
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | | REF_CLOSE: (28), (41), (49), (114) are inconsistent by sub-proof
% 242.62/49.13  | | | | |            #1659.
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | End of split
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | End of split
% 242.62/49.13  | | | 
% 242.62/49.13  | | End of split
% 242.62/49.13  | | 
% 242.62/49.13  | Case 2:
% 242.62/49.13  | | 
% 242.62/49.13  | |   (115)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 242.62/49.13  | |            e0)
% 242.62/49.13  | | 
% 242.62/49.13  | | REF_CLOSE: (4), (7), (22), (43), (115) are inconsistent by sub-proof #818.
% 242.62/49.13  | | 
% 242.62/49.13  | End of split
% 242.62/49.13  | 
% 242.62/49.13  End of proof
% 242.62/49.13  
% 242.62/49.13  Sub-proof #816 shows that the following formulas are inconsistent:
% 242.62/49.13  ----------------------------------------------------------------
% 242.62/49.13    (1)   ~ (e3 = e0)
% 242.62/49.13    (2)  op(e2, all_52_1) = e2
% 242.62/49.13    (3)   ~ (e2 = e0)
% 242.62/49.13    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.62/49.13         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.62/49.13    (5)  op(e0, e1) = e1
% 242.62/49.13    (6)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.62/49.13             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.62/49.13               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.62/49.13               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.62/49.13    (7)  op(e2, e1) = all_52_9
% 242.62/49.13    (8)  op(e2, e3) = e1
% 242.62/49.13    (9)  op(e2, e3) = all_52_1
% 242.62/49.13    (10)  op(e1, e1) = e2
% 242.62/49.13    (11)  op(e0, e0) = e3
% 242.62/49.13    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.13    (13)   ~ (e1 = e0)
% 242.62/49.13    (14)  all_58_4 = e3
% 242.62/49.13    (15)   ~ (all_52_9 = e2)
% 242.62/49.13  
% 242.62/49.13  Begin of proof
% 242.62/49.13  | 
% 242.62/49.13  | BETA: splitting (4) gives:
% 242.62/49.13  | 
% 242.62/49.13  | Case 1:
% 242.62/49.13  | | 
% 242.62/49.13  | |   (16)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 242.62/49.13  | |           e0)
% 242.62/49.13  | | 
% 242.62/49.13  | | BETA: splitting (16) gives:
% 242.62/49.13  | | 
% 242.62/49.13  | | Case 1:
% 242.62/49.13  | | | 
% 242.62/49.13  | | |   (17)  all_58_4 = e0 & op(e3, e1) = e0
% 242.62/49.13  | | | 
% 242.62/49.13  | | | REF_CLOSE: (1), (14), (17) are inconsistent by sub-proof #1697.
% 242.62/49.13  | | | 
% 242.62/49.13  | | Case 2:
% 242.62/49.13  | | | 
% 242.62/49.13  | | |   (18)  all_58_5 = e0 & op(e2, e1) = e0
% 242.62/49.13  | | | 
% 242.62/49.13  | | | ALPHA: (18) implies:
% 242.62/49.13  | | |   (19)  op(e2, e1) = e0
% 242.62/49.13  | | | 
% 242.62/49.13  | | | BETA: splitting (6) gives:
% 242.62/49.13  | | | 
% 242.62/49.13  | | | Case 1:
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | |   (20)  all_58_15 = e0 & op(e0, e0) = e0
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | | ALPHA: (20) implies:
% 242.62/49.13  | | | |   (21)  op(e0, e0) = e0
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | | REF_CLOSE: (1), (11), (12), (21) are inconsistent by sub-proof #2079.
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | Case 2:
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | | GROUND_INST: instantiating (12) with all_52_9, e0, e1, e2, simplifying
% 242.62/49.13  | | | |              with (7), (19) gives:
% 242.62/49.13  | | | |   (22)  all_52_9 = e0
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | | GROUND_INST: instantiating (12) with all_52_1, e1, e3, e2, simplifying
% 242.62/49.13  | | | |              with (8), (9) gives:
% 242.62/49.13  | | | |   (23)  all_52_1 = e1
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | | REDUCE: (15), (22) imply:
% 242.62/49.13  | | | |   (24)   ~ (e2 = e0)
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | | REDUCE: (2), (23) imply:
% 242.62/49.13  | | | |   (25)  op(e2, e1) = e2
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | | REF_CLOSE: (3), (12), (19), (25) are inconsistent by sub-proof #1906.
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | End of split
% 242.62/49.13  | | | 
% 242.62/49.13  | | End of split
% 242.62/49.13  | | 
% 242.62/49.13  | Case 2:
% 242.62/49.13  | | 
% 242.62/49.13  | |   (26)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 242.62/49.13  | |           e0)
% 242.62/49.13  | | 
% 242.62/49.13  | | REF_CLOSE: (3), (5), (10), (12), (13), (26) are inconsistent by sub-proof
% 242.62/49.13  | |            #1036.
% 242.62/49.13  | | 
% 242.62/49.13  | End of split
% 242.62/49.13  | 
% 242.62/49.13  End of proof
% 242.62/49.13  
% 242.62/49.13  Sub-proof #817 shows that the following formulas are inconsistent:
% 242.62/49.13  ----------------------------------------------------------------
% 242.62/49.13    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.62/49.13           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.62/49.13           all_12_1 & $i(all_12_1))
% 242.62/49.13    (2)  all_56_21 = e2
% 242.62/49.13    (3)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.62/49.13    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.62/49.13           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.62/49.13           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.62/49.13           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.62/49.13           & $i(all_56_23))
% 242.62/49.13    (5)   ~ (e3 = e0)
% 242.62/49.13    (6)  op(e0, e1) = all_52_11
% 242.62/49.13    (7)  all_58_6 = e3
% 242.62/49.13    (8)   ~ (e2 = e0)
% 242.62/49.13    (9)   ~ (all_52_11 = e2)
% 242.62/49.13    (10)  op(e1, e2) = all_52_6
% 242.62/49.13    (11)  op(e0, e3) = all_52_3
% 242.62/49.13    (12)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.13          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.13    (13)   ~ (e3 = e1)
% 242.62/49.13    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.62/49.13          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.62/49.13    (15)  all_58_3 = e3
% 242.62/49.13    (16)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.62/49.13            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.62/49.13              e3) = all_26_1 & $i(all_26_1))
% 242.62/49.13    (17)  all_58_12 = e1
% 242.62/49.13    (18)   ~ (all_52_11 = e3)
% 242.62/49.13    (19)  op(e2, e1) = all_52_9
% 242.62/49.13    (20)   ~ (e3 = e2)
% 242.62/49.13    (21)  all_58_10 = e2
% 242.62/49.13    (22)  op(e0, e3) = e1
% 242.62/49.13    (23)  op(e2, e0) = e2
% 242.62/49.13    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.62/49.13          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.62/49.13    (25)  op(e3, e0) = all_52_12
% 242.62/49.13    (26)  op(e3, all_52_4) = e3
% 242.62/49.13    (27)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.62/49.13            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.62/49.13              e3) = all_42_1 & $i(all_42_1))
% 242.62/49.13    (28)  op(e2, e3) = all_52_1
% 242.62/49.13    (29)  op(e3, e3) = e2
% 242.62/49.13    (30)  op(e1, e1) = e2
% 242.62/49.13    (31)  all_54_1 = all_52_4
% 242.62/49.13    (32)  op(e0, e0) = e3
% 242.62/49.13    (33)   ~ (all_52_4 = e2)
% 242.62/49.13    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.13          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.13    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.13    (36)  op(e3, e1) = e3
% 242.62/49.13    (37)   ~ (all_52_12 = e3)
% 242.62/49.13    (38)   ~ (e1 = e0)
% 242.62/49.13    (39)  all_58_4 = e3
% 242.62/49.13    (40)   ~ (all_52_9 = all_52_11)
% 242.62/49.13    (41)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.62/49.13            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.62/49.13            & $i(all_8_1))
% 242.62/49.13    (42)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.62/49.13          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.62/49.13    (43)   ~ (all_52_4 = all_52_6)
% 242.62/49.13    (44)   ~ (e2 = e1)
% 242.62/49.13    (45)   ~ (all_52_9 = e2)
% 242.62/49.13  
% 242.62/49.13  Begin of proof
% 242.62/49.13  | 
% 242.62/49.13  | BETA: splitting (24) gives:
% 242.62/49.13  | 
% 242.62/49.13  | Case 1:
% 242.62/49.13  | | 
% 242.62/49.13  | |   (46)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 242.62/49.13  | |           e0)
% 242.62/49.13  | | 
% 242.62/49.13  | | BETA: splitting (46) gives:
% 242.62/49.13  | | 
% 242.62/49.13  | | Case 1:
% 242.62/49.13  | | | 
% 242.62/49.13  | | |   (47)  all_58_0 = e0 & op(e3, e3) = e0
% 242.62/49.13  | | | 
% 242.62/49.13  | | | ALPHA: (47) implies:
% 242.62/49.13  | | |   (48)  op(e3, e3) = e0
% 242.62/49.13  | | | 
% 242.62/49.13  | | | REF_CLOSE: (8), (29), (35), (48) are inconsistent by sub-proof #2188.
% 242.62/49.13  | | | 
% 242.62/49.13  | | Case 2:
% 242.62/49.13  | | | 
% 242.62/49.13  | | |   (49)  all_58_2 = e0 & op(e2, e3) = e0
% 242.62/49.13  | | | 
% 242.62/49.13  | | | ALPHA: (49) implies:
% 242.62/49.13  | | |   (50)  all_58_2 = e0
% 242.62/49.13  | | |   (51)  op(e2, e3) = e0
% 242.62/49.13  | | | 
% 242.62/49.13  | | | BETA: splitting (42) gives:
% 242.62/49.13  | | | 
% 242.62/49.13  | | | Case 1:
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | |   (52)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 242.62/49.13  | | | |           = e1)
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | | REF_CLOSE: (13), (15), (38), (50), (52) are inconsistent by sub-proof
% 242.62/49.13  | | | |            #824.
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | Case 2:
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | |   (53)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 242.62/49.13  | | | |           = e1)
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | | BETA: splitting (53) gives:
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | | Case 1:
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | |   (54)  all_58_5 = e1 & op(e2, e1) = e1
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | | ALPHA: (54) implies:
% 242.62/49.13  | | | | |   (55)  all_58_5 = e1
% 242.62/49.13  | | | | |   (56)  op(e2, e1) = e1
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 242.62/49.13  | | | | |            (14), (15), (16), (18), (19), (20), (21), (22), (25), (26),
% 242.62/49.13  | | | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 242.62/49.13  | | | | |            (37), (38), (39), (40), (41), (43), (45), (51), (55), (56)
% 242.62/49.13  | | | | |            are inconsistent by sub-proof #819.
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | Case 2:
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | |   (57)  all_58_10 = e1 & op(e2, e0) = e1
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | | ALPHA: (57) implies:
% 242.62/49.13  | | | | |   (58)  op(e2, e0) = e1
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | | REF_CLOSE: (23), (35), (44), (58) are inconsistent by sub-proof #1659.
% 242.62/49.13  | | | | | 
% 242.62/49.13  | | | | End of split
% 242.62/49.13  | | | | 
% 242.62/49.13  | | | End of split
% 242.62/49.13  | | | 
% 242.62/49.13  | | End of split
% 242.62/49.13  | | 
% 242.62/49.13  | Case 2:
% 242.62/49.13  | | 
% 242.62/49.13  | |   (59)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 242.62/49.13  | |           e0)
% 242.62/49.13  | | 
% 242.62/49.13  | | REF_CLOSE: (5), (7), (17), (38), (59) are inconsistent by sub-proof #818.
% 242.62/49.13  | | 
% 242.62/49.13  | End of split
% 242.62/49.13  | 
% 242.62/49.13  End of proof
% 242.62/49.13  
% 242.62/49.13  Sub-proof #818 shows that the following formulas are inconsistent:
% 242.62/49.13  ----------------------------------------------------------------
% 242.62/49.13    (1)   ~ (e3 = e0)
% 242.62/49.13    (2)  all_58_6 = e3
% 242.62/49.13    (3)  all_58_12 = e1
% 242.62/49.13    (4)   ~ (e1 = e0)
% 242.62/49.13    (5)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.62/49.13  
% 242.62/49.13  Begin of proof
% 242.62/49.13  | 
% 242.62/49.13  | BETA: splitting (5) gives:
% 242.62/49.13  | 
% 242.62/49.13  | Case 1:
% 242.62/49.13  | | 
% 242.62/49.13  | |   (6)  all_58_6 = e0 & op(e1, e3) = e0
% 242.62/49.13  | | 
% 242.62/49.13  | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #2213.
% 242.62/49.13  | | 
% 242.62/49.13  | Case 2:
% 242.62/49.13  | | 
% 242.62/49.13  | |   (7)  all_58_12 = e0 & op(e0, e3) = e0
% 242.62/49.13  | | 
% 242.62/49.13  | | ALPHA: (7) implies:
% 242.62/49.13  | |   (8)  all_58_12 = e0
% 242.62/49.13  | | 
% 242.62/49.13  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #1539.
% 242.62/49.13  | | 
% 242.62/49.13  | End of split
% 242.62/49.13  | 
% 242.62/49.13  End of proof
% 242.62/49.13  
% 242.62/49.13  Sub-proof #819 shows that the following formulas are inconsistent:
% 242.62/49.13  ----------------------------------------------------------------
% 242.62/49.13    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.62/49.13           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.62/49.13           all_12_1 & $i(all_12_1))
% 242.62/49.13    (2)  all_56_21 = e2
% 242.62/49.13    (3)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.62/49.13    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.62/49.13           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.62/49.13           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.62/49.13           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.62/49.13           & $i(all_56_23))
% 242.62/49.13    (5)   ~ (e3 = e0)
% 242.62/49.13    (6)  op(e2, e3) = e0
% 242.62/49.13    (7)  op(e0, e1) = all_52_11
% 242.62/49.13    (8)  op(e2, e1) = e1
% 242.62/49.13    (9)   ~ (e2 = e0)
% 242.62/49.13    (10)   ~ (all_52_11 = e2)
% 242.62/49.13    (11)  op(e1, e2) = all_52_6
% 242.62/49.13    (12)  op(e0, e3) = all_52_3
% 242.62/49.13    (13)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.13          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.13    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.62/49.13          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.62/49.13    (15)  all_58_3 = e3
% 242.62/49.13    (16)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.62/49.13            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 242.62/49.13              e3) = all_26_1 & $i(all_26_1))
% 242.62/49.13    (17)   ~ (all_52_11 = e3)
% 242.62/49.13    (18)  op(e2, e1) = all_52_9
% 242.62/49.13    (19)   ~ (e3 = e2)
% 242.62/49.13    (20)  all_58_10 = e2
% 242.62/49.13    (21)  op(e0, e3) = e1
% 242.62/49.13    (22)  op(e3, e0) = all_52_12
% 242.62/49.13    (23)  op(e3, all_52_4) = e3
% 242.62/49.13    (24)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.62/49.13            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.62/49.13              e3) = all_42_1 & $i(all_42_1))
% 242.62/49.13    (25)  op(e2, e3) = all_52_1
% 242.62/49.13    (26)  op(e3, e3) = e2
% 242.62/49.13    (27)  op(e1, e1) = e2
% 242.62/49.13    (28)  all_54_1 = all_52_4
% 242.62/49.13    (29)  all_58_5 = e1
% 242.62/49.13    (30)  op(e0, e0) = e3
% 242.62/49.13    (31)   ~ (all_52_4 = e2)
% 242.62/49.14    (32)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.14          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.14    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.14    (34)  op(e3, e1) = e3
% 242.62/49.14    (35)   ~ (all_52_12 = e3)
% 242.62/49.14    (36)   ~ (e1 = e0)
% 242.62/49.14    (37)  all_58_4 = e3
% 242.62/49.14    (38)   ~ (all_52_9 = all_52_11)
% 242.62/49.14    (39)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.62/49.14            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.62/49.14            & $i(all_8_1))
% 242.62/49.14    (40)   ~ (all_52_4 = all_52_6)
% 242.62/49.14    (41)   ~ (all_52_9 = e2)
% 242.62/49.14  
% 242.62/49.14  Begin of proof
% 242.62/49.14  | 
% 242.62/49.14  | BETA: splitting (14) gives:
% 242.62/49.14  | 
% 242.62/49.14  | Case 1:
% 242.62/49.14  | | 
% 242.62/49.14  | |   (42)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 242.62/49.14  | |           e0)
% 242.62/49.14  | | 
% 242.62/49.14  | | REF_CLOSE: (5), (8), (18), (33), (36), (37), (42) are inconsistent by
% 242.62/49.14  | |            sub-proof #823.
% 242.62/49.14  | | 
% 242.62/49.14  | Case 2:
% 242.62/49.14  | | 
% 242.62/49.14  | |   (43)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 242.62/49.14  | |           e0)
% 242.62/49.14  | | 
% 242.62/49.14  | | BETA: splitting (43) gives:
% 242.62/49.14  | | 
% 242.62/49.14  | | Case 1:
% 242.62/49.14  | | | 
% 242.62/49.14  | | |   (44)  all_58_8 = e0 & op(e1, e1) = e0
% 242.62/49.14  | | | 
% 242.62/49.14  | | | ALPHA: (44) implies:
% 242.62/49.14  | | |   (45)  op(e1, e1) = e0
% 242.62/49.14  | | | 
% 242.62/49.14  | | | REF_CLOSE: (9), (27), (33), (45) are inconsistent by sub-proof #2211.
% 242.62/49.14  | | | 
% 242.62/49.14  | | Case 2:
% 242.62/49.14  | | | 
% 242.62/49.14  | | |   (46)  all_58_14 = e0 & op(e0, e1) = e0
% 242.62/49.14  | | | 
% 242.62/49.14  | | | ALPHA: (46) implies:
% 242.62/49.14  | | |   (47)  op(e0, e1) = e0
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (33) with all_52_11, e0, e1, e0, simplifying
% 242.62/49.14  | | |              with (7), (47) gives:
% 242.62/49.14  | | |   (48)  all_52_11 = e0
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (33) with all_52_3, e1, e3, e0, simplifying
% 242.62/49.14  | | |              with (12), (21) gives:
% 242.62/49.14  | | |   (49)  all_52_3 = e1
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (33) with all_52_9, e1, e1, e2, simplifying
% 242.62/49.14  | | |              with (8), (18) gives:
% 242.62/49.14  | | |   (50)  all_52_9 = e1
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (33) with all_52_1, e0, e3, e2, simplifying
% 242.62/49.14  | | |              with (6), (25) gives:
% 242.62/49.14  | | |   (51)  all_52_1 = e0
% 242.62/49.14  | | | 
% 242.62/49.14  | | | REDUCE: (41), (50) imply:
% 242.62/49.14  | | |   (52)   ~ (e2 = e1)
% 242.62/49.14  | | | 
% 242.62/49.14  | | | SIMP: (52) implies:
% 242.62/49.14  | | |   (53)   ~ (e2 = e1)
% 242.62/49.14  | | | 
% 242.62/49.14  | | | REDUCE: (17), (48) imply:
% 242.62/49.14  | | |   (54)   ~ (e3 = e0)
% 242.62/49.14  | | | 
% 242.62/49.14  | | | REDUCE: (10), (48) imply:
% 242.62/49.14  | | |   (55)   ~ (e2 = e0)
% 242.62/49.14  | | | 
% 242.62/49.14  | | | BETA: splitting (39) gives:
% 242.62/49.14  | | | 
% 242.62/49.14  | | | Case 1:
% 242.62/49.14  | | | | 
% 242.62/49.14  | | | |   (56)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) =
% 242.62/49.14  | | | |         all_8_1 & $i(all_8_0) & $i(all_8_1)
% 242.62/49.14  | | | | 
% 242.62/49.14  | | | | ALPHA: (56) implies:
% 242.62/49.14  | | | |   (57)  op(e2, e3) = all_8_1
% 242.62/49.14  | | | | 
% 242.62/49.14  | | | | BETA: splitting (4) gives:
% 242.62/49.14  | | | | 
% 242.62/49.14  | | | | Case 1:
% 242.62/49.14  | | | | | 
% 242.62/49.14  | | | | |   (58)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 242.62/49.14  | | | | |           all_56_17 & $i(all_56_17)) | (all_56_18 = e2 & op(e2,
% 242.62/49.14  | | | | |             all_56_19) = e2 & op(e2, e1) = all_56_19 & $i(all_56_19))
% 242.62/49.14  | | | | | 
% 242.62/49.14  | | | | | BETA: splitting (58) gives:
% 242.62/49.14  | | | | | 
% 242.62/49.14  | | | | | Case 1:
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | |   (59)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 242.62/49.14  | | | | | |         all_56_17 & $i(all_56_17)
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | ALPHA: (59) implies:
% 242.62/49.14  | | | | | |   (60)  op(e3, e1) = all_56_17
% 242.62/49.14  | | | | | |   (61)  op(e3, all_56_17) = e3
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | REF_CLOSE: (19), (26), (33), (34), (60), (61) are inconsistent by
% 242.62/49.14  | | | | | |            sub-proof #2098.
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | Case 2:
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | |   (62)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 242.62/49.14  | | | | | |         all_56_19 & $i(all_56_19)
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | ALPHA: (62) implies:
% 242.62/49.14  | | | | | |   (63)  op(e2, e1) = all_56_19
% 242.62/49.14  | | | | | |   (64)  op(e2, all_56_19) = e2
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | REF_CLOSE: (1), (5), (6), (8), (9), (13), (15), (16), (19), (20),
% 242.62/49.14  | | | | | |            (21), (24), (29), (32), (33), (36), (53), (57), (63),
% 242.62/49.14  | | | | | |            (64) are inconsistent by sub-proof #820.
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | End of split
% 242.62/49.14  | | | | | 
% 242.62/49.14  | | | | Case 2:
% 242.62/49.14  | | | | | 
% 242.62/49.14  | | | | |   (65)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 = e0 &
% 242.62/49.14  | | | | |           op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 242.62/49.14  | | | | |           $i(all_56_23))
% 242.62/49.14  | | | | | 
% 242.62/49.14  | | | | | BETA: splitting (65) gives:
% 242.62/49.14  | | | | | 
% 242.62/49.14  | | | | | Case 1:
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | |   (66)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | ALPHA: (66) implies:
% 242.62/49.14  | | | | | |   (67)  op(e1, all_56_21) = e1
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | REDUCE: (2), (67) imply:
% 242.62/49.14  | | | | | |   (68)  op(e1, e2) = e1
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | GROUND_INST: instantiating (33) with all_52_6, e1, e2, e1,
% 242.62/49.14  | | | | | |              simplifying with (11), (68) gives:
% 242.62/49.14  | | | | | |   (69)  all_52_6 = e1
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | REDUCE: (40), (69) imply:
% 242.62/49.14  | | | | | |   (70)   ~ (all_52_4 = e1)
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | BETA: splitting (3) gives:
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | Case 1:
% 242.62/49.14  | | | | | | | 
% 242.62/49.14  | | | | | | |   (71)  all_54_1 = e2
% 242.62/49.14  | | | | | | | 
% 242.62/49.14  | | | | | | | REF_CLOSE: (28), (31), (71) are inconsistent by sub-proof #1928.
% 242.62/49.14  | | | | | | | 
% 242.62/49.14  | | | | | | Case 2:
% 242.62/49.14  | | | | | | | 
% 242.62/49.14  | | | | | | |   (72)  all_54_1 = e1 | all_54_1 = e0
% 242.62/49.14  | | | | | | | 
% 242.62/49.14  | | | | | | | BETA: splitting (72) gives:
% 242.62/49.14  | | | | | | | 
% 242.62/49.14  | | | | | | | Case 1:
% 242.62/49.14  | | | | | | | | 
% 242.62/49.14  | | | | | | | |   (73)  all_54_1 = e1
% 242.62/49.14  | | | | | | | | 
% 242.62/49.14  | | | | | | | | REF_CLOSE: (28), (70), (73) are inconsistent by sub-proof #2051.
% 242.62/49.14  | | | | | | | | 
% 242.62/49.14  | | | | | | | Case 2:
% 242.62/49.14  | | | | | | | | 
% 242.62/49.14  | | | | | | | |   (74)  all_54_1 = e0
% 242.62/49.14  | | | | | | | | 
% 242.62/49.14  | | | | | | | | COMBINE_EQS: (28), (74) imply:
% 242.62/49.14  | | | | | | | |   (75)  all_52_4 = e0
% 242.62/49.14  | | | | | | | | 
% 242.62/49.14  | | | | | | | | SIMP: (75) implies:
% 242.62/49.14  | | | | | | | |   (76)  all_52_4 = e0
% 242.62/49.14  | | | | | | | | 
% 242.62/49.14  | | | | | | | | REDUCE: (23), (76) imply:
% 242.62/49.14  | | | | | | | |   (77)  op(e3, e0) = e3
% 242.62/49.14  | | | | | | | | 
% 242.62/49.14  | | | | | | | | REF_CLOSE: (22), (33), (35), (77) are inconsistent by sub-proof
% 242.62/49.14  | | | | | | | |            #2179.
% 242.62/49.14  | | | | | | | | 
% 242.62/49.14  | | | | | | | End of split
% 242.62/49.14  | | | | | | | 
% 242.62/49.14  | | | | | | End of split
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | Case 2:
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | |   (78)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 242.62/49.14  | | | | | |         all_56_23 & $i(all_56_23)
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | ALPHA: (78) implies:
% 242.62/49.14  | | | | | |   (79)  op(e0, e1) = all_56_23
% 242.62/49.14  | | | | | |   (80)  op(e0, all_56_23) = e0
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | | REF_CLOSE: (5), (30), (33), (47), (79), (80) are inconsistent by
% 242.62/49.14  | | | | | |            sub-proof #1395.
% 242.62/49.14  | | | | | | 
% 242.62/49.14  | | | | | End of split
% 242.62/49.14  | | | | | 
% 242.62/49.14  | | | | End of split
% 242.62/49.14  | | | | 
% 242.62/49.14  | | | Case 2:
% 242.62/49.14  | | | | 
% 242.62/49.14  | | | |   (81)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 242.62/49.14  | | | | 
% 242.62/49.14  | | | | ALPHA: (81) implies:
% 242.62/49.14  | | | |   (82)   ~ (all_8_1 = e0)
% 242.62/49.14  | | | |   (83)  op(e2, e3) = all_8_1
% 242.62/49.14  | | | | 
% 242.62/49.14  | | | | REF_CLOSE: (6), (24), (33), (82), (83) are inconsistent by sub-proof
% 242.62/49.14  | | | |            #897.
% 242.62/49.14  | | | | 
% 242.62/49.14  | | | End of split
% 242.62/49.14  | | | 
% 242.62/49.14  | | End of split
% 242.62/49.14  | | 
% 242.62/49.14  | End of split
% 242.62/49.14  | 
% 242.62/49.14  End of proof
% 242.62/49.14  
% 242.62/49.14  Sub-proof #820 shows that the following formulas are inconsistent:
% 242.62/49.14  ----------------------------------------------------------------
% 242.62/49.14    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.62/49.14           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.62/49.14           all_12_1 & $i(all_12_1))
% 242.62/49.14    (2)   ~ (e3 = e0)
% 242.62/49.14    (3)  op(e2, e3) = e0
% 242.62/49.14    (4)  op(e2, e1) = e1
% 242.62/49.14    (5)   ~ (e2 = e0)
% 242.62/49.14    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.14         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.14    (7)  all_58_3 = e3
% 242.62/49.14    (8)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 242.62/49.14           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 242.62/49.14           all_26_1 & $i(all_26_1))
% 242.62/49.14    (9)   ~ (e3 = e2)
% 242.62/49.14    (10)  all_58_10 = e2
% 242.62/49.14    (11)  op(e0, e3) = e1
% 242.62/49.14    (12)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.62/49.14            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.62/49.14              e3) = all_42_1 & $i(all_42_1))
% 242.62/49.14    (13)  all_58_5 = e1
% 242.62/49.14    (14)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.14          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.14    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.14    (16)  op(e2, e3) = all_8_1
% 242.62/49.14    (17)  op(e2, e1) = all_56_19
% 242.62/49.14    (18)   ~ (e1 = e0)
% 242.62/49.14    (19)  op(e2, all_56_19) = e2
% 242.62/49.14    (20)   ~ (e2 = e1)
% 242.62/49.14  
% 242.62/49.14  Begin of proof
% 242.62/49.14  | 
% 242.62/49.14  | BETA: splitting (8) gives:
% 242.62/49.14  | 
% 242.62/49.14  | Case 1:
% 242.62/49.14  | | 
% 242.62/49.14  | |   (21)   ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 242.62/49.14  | |         all_26_1 & $i(all_26_0) & $i(all_26_1)
% 242.62/49.14  | | 
% 242.62/49.14  | | ALPHA: (21) implies:
% 242.62/49.14  | |   (22)  op(e0, e3) = all_26_1
% 242.62/49.14  | | 
% 242.62/49.14  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 242.62/49.14  | |            (14), (15), (16), (17), (18), (19), (20), (22) are inconsistent
% 242.62/49.14  | |            by sub-proof #821.
% 242.62/49.14  | | 
% 242.62/49.14  | Case 2:
% 242.62/49.14  | | 
% 242.62/49.14  | |   (23)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 242.62/49.14  | | 
% 242.62/49.14  | | ALPHA: (23) implies:
% 242.62/49.14  | |   (24)  op(e0, e3) = all_26_1
% 242.62/49.14  | | 
% 242.62/49.14  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 242.62/49.14  | |            (14), (15), (16), (17), (18), (19), (20), (24) are inconsistent
% 242.62/49.14  | |            by sub-proof #821.
% 242.62/49.14  | | 
% 242.62/49.14  | End of split
% 242.62/49.14  | 
% 242.62/49.14  End of proof
% 242.62/49.14  
% 242.62/49.14  Sub-proof #821 shows that the following formulas are inconsistent:
% 242.62/49.14  ----------------------------------------------------------------
% 242.62/49.14    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 242.62/49.14           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 242.62/49.14           all_12_1 & $i(all_12_1))
% 242.62/49.14    (2)   ~ (e3 = e0)
% 242.62/49.14    (3)  op(e2, e3) = e0
% 242.62/49.14    (4)  op(e2, e1) = e1
% 242.62/49.14    (5)   ~ (e2 = e0)
% 242.62/49.14    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.14         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.14    (7)  all_58_3 = e3
% 242.62/49.14    (8)   ~ (e3 = e2)
% 242.62/49.14    (9)  all_58_10 = e2
% 242.62/49.14    (10)  op(e0, e3) = e1
% 242.62/49.14    (11)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.62/49.14            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.62/49.14              e3) = all_42_1 & $i(all_42_1))
% 242.62/49.14    (12)  op(e0, e3) = all_26_1
% 242.62/49.14    (13)  all_58_5 = e1
% 242.62/49.14    (14)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.14          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.14    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.14    (16)  op(e2, e3) = all_8_1
% 242.62/49.14    (17)  op(e2, e1) = all_56_19
% 242.62/49.14    (18)   ~ (e1 = e0)
% 242.62/49.14    (19)  op(e2, all_56_19) = e2
% 242.62/49.14    (20)   ~ (e2 = e1)
% 242.62/49.14  
% 242.62/49.14  Begin of proof
% 242.62/49.14  | 
% 242.62/49.14  | BETA: splitting (11) gives:
% 242.62/49.14  | 
% 242.62/49.14  | Case 1:
% 242.62/49.14  | | 
% 242.62/49.14  | | 
% 242.62/49.14  | | GROUND_INST: instantiating (15) with e1, all_56_19, e1, e2, simplifying with
% 242.62/49.14  | |              (4), (17) gives:
% 242.62/49.14  | |   (21)  all_56_19 = e1
% 242.62/49.14  | | 
% 242.62/49.14  | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (13), (14), (15), (17), (18), (19),
% 242.62/49.14  | |            (20), (21) are inconsistent by sub-proof #822.
% 242.62/49.14  | | 
% 242.62/49.14  | Case 2:
% 242.62/49.14  | | 
% 242.62/49.14  | |   (22)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 242.62/49.14  | | 
% 242.62/49.14  | | ALPHA: (22) implies:
% 242.62/49.14  | |   (23)   ~ (all_42_1 = e1)
% 242.62/49.14  | |   (24)  op(e2, e3) = all_42_1
% 242.62/49.14  | | 
% 242.62/49.14  | | BETA: splitting (1) gives:
% 242.62/49.14  | | 
% 242.62/49.14  | | Case 1:
% 242.62/49.14  | | | 
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (15) with e1, all_56_19, e1, e2, simplifying
% 242.62/49.14  | | |              with (4), (17) gives:
% 242.62/49.14  | | |   (25)  all_56_19 = e1
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (15) with e0, all_42_1, e3, e2, simplifying
% 242.62/49.14  | | |              with (3), (24) gives:
% 242.62/49.14  | | |   (26)  all_42_1 = e0
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (15) with all_8_1, all_42_1, e3, e2,
% 242.62/49.14  | | |              simplifying with (16), (24) gives:
% 242.62/49.14  | | |   (27)  all_42_1 = all_8_1
% 242.62/49.14  | | | 
% 242.62/49.14  | | | COMBINE_EQS: (26), (27) imply:
% 242.62/49.14  | | |   (28)  all_8_1 = e0
% 242.62/49.14  | | | 
% 242.62/49.14  | | | REDUCE: (23), (26) imply:
% 242.62/49.14  | | |   (29)   ~ (e1 = e0)
% 242.62/49.14  | | | 
% 242.62/49.14  | | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (13), (14), (15), (17), (18),
% 242.62/49.14  | | |            (19), (20), (25) are inconsistent by sub-proof #822.
% 242.62/49.14  | | | 
% 242.62/49.14  | | Case 2:
% 242.62/49.14  | | | 
% 242.62/49.14  | | |   (30)   ~ (all_12_1 = e2) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 242.62/49.14  | | | 
% 242.62/49.14  | | | ALPHA: (30) implies:
% 242.62/49.14  | | |   (31)   ~ (all_12_1 = e2)
% 242.62/49.14  | | |   (32)  op(e0, e3) = all_12_1
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (15) with e1, all_26_1, e3, e0, simplifying
% 242.62/49.14  | | |              with (10), (12) gives:
% 242.62/49.14  | | |   (33)  all_26_1 = e1
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (15) with all_12_1, all_26_1, e3, e0,
% 242.62/49.14  | | |              simplifying with (12), (32) gives:
% 242.62/49.14  | | |   (34)  all_26_1 = all_12_1
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (15) with e1, all_56_19, e1, e2, simplifying
% 242.62/49.14  | | |              with (4), (17) gives:
% 242.62/49.14  | | |   (35)  all_56_19 = e1
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (15) with e0, all_42_1, e3, e2, simplifying
% 242.62/49.14  | | |              with (3), (24) gives:
% 242.62/49.14  | | |   (36)  all_42_1 = e0
% 242.62/49.14  | | | 
% 242.62/49.14  | | | GROUND_INST: instantiating (15) with all_8_1, all_42_1, e3, e2,
% 242.62/49.14  | | |              simplifying with (16), (24) gives:
% 242.62/49.14  | | |   (37)  all_42_1 = all_8_1
% 242.62/49.14  | | | 
% 242.62/49.14  | | | COMBINE_EQS: (36), (37) imply:
% 242.62/49.14  | | |   (38)  all_8_1 = e0
% 242.62/49.14  | | | 
% 242.62/49.14  | | | COMBINE_EQS: (33), (34) imply:
% 242.62/49.14  | | |   (39)  all_12_1 = e1
% 242.62/49.14  | | | 
% 242.62/49.14  | | | REDUCE: (23), (36) imply:
% 242.62/49.14  | | |   (40)   ~ (e1 = e0)
% 242.62/49.14  | | | 
% 242.62/49.14  | | | REDUCE: (31), (39) imply:
% 242.62/49.14  | | |   (41)   ~ (e2 = e1)
% 242.62/49.14  | | | 
% 242.62/49.14  | | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (13), (14), (15), (17), (18),
% 242.62/49.14  | | |            (19), (20), (35) are inconsistent by sub-proof #822.
% 242.62/49.14  | | | 
% 242.62/49.14  | | End of split
% 242.62/49.14  | | 
% 242.62/49.14  | End of split
% 242.62/49.14  | 
% 242.62/49.14  End of proof
% 242.62/49.14  
% 242.62/49.14  Sub-proof #822 shows that the following formulas are inconsistent:
% 242.62/49.14  ----------------------------------------------------------------
% 242.62/49.14    (1)   ~ (e3 = e0)
% 242.62/49.14    (2)   ~ (e2 = e0)
% 242.62/49.15    (3)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.15         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.15    (4)  all_58_3 = e3
% 242.62/49.15    (5)   ~ (e3 = e2)
% 242.62/49.15    (6)  all_58_10 = e2
% 242.62/49.15    (7)  all_56_19 = e1
% 242.62/49.15    (8)  all_58_5 = e1
% 242.62/49.15    (9)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.15         (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.15    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.15    (11)  op(e2, e1) = all_56_19
% 242.62/49.15    (12)   ~ (e1 = e0)
% 242.62/49.15    (13)  op(e2, all_56_19) = e2
% 242.62/49.15    (14)   ~ (e2 = e1)
% 242.62/49.15  
% 242.62/49.15  Begin of proof
% 242.62/49.15  | 
% 242.62/49.15  | REDUCE: (7), (13) imply:
% 242.62/49.15  |   (15)  op(e2, e1) = e2
% 242.62/49.15  | 
% 242.62/49.15  | REDUCE: (7), (11) imply:
% 242.62/49.15  |   (16)  op(e2, e1) = e1
% 242.62/49.15  | 
% 242.62/49.15  | GROUND_INST: instantiating (10) with e1, e2, e1, e2, simplifying with (15),
% 242.62/49.15  |              (16) gives:
% 242.62/49.15  |   (17)  e2 = e1
% 242.62/49.15  | 
% 242.62/49.15  | COMBINE_EQS: (6), (17) imply:
% 242.62/49.15  |   (18)  all_58_10 = e1
% 242.62/49.15  | 
% 242.62/49.15  | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (12), (14), (18) are
% 242.62/49.15  |            inconsistent by sub-proof #992.
% 242.62/49.15  | 
% 242.62/49.15  End of proof
% 242.62/49.15  
% 242.62/49.15  Sub-proof #823 shows that the following formulas are inconsistent:
% 242.62/49.15  ----------------------------------------------------------------
% 242.62/49.15    (1)   ~ (e3 = e0)
% 242.62/49.15    (2)  op(e2, e1) = e1
% 242.62/49.15    (3)  op(e2, e1) = all_52_9
% 242.62/49.15    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 242.62/49.15    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.15    (6)   ~ (e1 = e0)
% 242.62/49.15    (7)  all_58_4 = e3
% 242.62/49.15  
% 242.62/49.15  Begin of proof
% 242.62/49.15  | 
% 242.62/49.15  | BETA: splitting (4) gives:
% 242.62/49.15  | 
% 242.62/49.15  | Case 1:
% 242.62/49.15  | | 
% 242.62/49.15  | |   (8)  all_58_4 = e0 & op(e3, e1) = e0
% 242.62/49.15  | | 
% 242.62/49.15  | | REF_CLOSE: (1), (7), (8) are inconsistent by sub-proof #1697.
% 242.62/49.15  | | 
% 242.62/49.15  | Case 2:
% 242.62/49.15  | | 
% 242.62/49.15  | |   (9)  all_58_5 = e0 & op(e2, e1) = e0
% 242.62/49.15  | | 
% 242.62/49.15  | | ALPHA: (9) implies:
% 242.62/49.15  | |   (10)  op(e2, e1) = e0
% 242.62/49.15  | | 
% 242.62/49.15  | | REF_CLOSE: (2), (3), (5), (6), (10) are inconsistent by sub-proof #2165.
% 242.62/49.15  | | 
% 242.62/49.15  | End of split
% 242.62/49.15  | 
% 242.62/49.15  End of proof
% 242.62/49.15  
% 242.62/49.15  Sub-proof #824 shows that the following formulas are inconsistent:
% 242.62/49.15  ----------------------------------------------------------------
% 242.62/49.15    (1)   ~ (e3 = e1)
% 242.62/49.15    (2)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 242.62/49.15    (3)  all_58_3 = e3
% 242.62/49.15    (4)  all_58_2 = e0
% 242.62/49.15    (5)   ~ (e1 = e0)
% 242.62/49.15  
% 242.62/49.15  Begin of proof
% 242.62/49.15  | 
% 242.62/49.15  | BETA: splitting (2) gives:
% 242.62/49.15  | 
% 242.62/49.15  | Case 1:
% 242.62/49.15  | | 
% 242.62/49.15  | |   (6)  all_58_2 = e1 & op(e2, e3) = e1
% 242.62/49.15  | | 
% 242.62/49.15  | | ALPHA: (6) implies:
% 242.62/49.15  | |   (7)  all_58_2 = e1
% 242.62/49.15  | | 
% 242.62/49.15  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #1268.
% 242.62/49.15  | | 
% 242.62/49.15  | Case 2:
% 242.62/49.15  | | 
% 242.62/49.15  | |   (8)  all_58_3 = e1 & op(e2, e2) = e1
% 242.62/49.15  | | 
% 242.62/49.15  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #2197.
% 242.62/49.15  | | 
% 242.62/49.15  | End of split
% 242.62/49.15  | 
% 242.62/49.15  End of proof
% 242.62/49.15  
% 242.62/49.15  Sub-proof #825 shows that the following formulas are inconsistent:
% 242.62/49.15  ----------------------------------------------------------------
% 242.62/49.15    (1)  all_58_3 = e3
% 242.62/49.15    (2)   ~ (e3 = e2)
% 242.62/49.15    (3)  op(e2, e3) = all_52_1
% 242.62/49.15    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 242.62/49.15    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.15    (6)   ~ (all_52_1 = e2)
% 242.62/49.15  
% 242.62/49.15  Begin of proof
% 242.62/49.15  | 
% 242.62/49.15  | BETA: splitting (4) gives:
% 242.62/49.15  | 
% 242.62/49.15  | Case 1:
% 242.62/49.15  | | 
% 242.62/49.15  | |   (7)  all_58_2 = e2 & op(e2, e3) = e2
% 242.62/49.15  | | 
% 242.62/49.15  | | ALPHA: (7) implies:
% 242.62/49.15  | |   (8)  op(e2, e3) = e2
% 242.62/49.15  | | 
% 242.62/49.15  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2336.
% 242.62/49.15  | | 
% 242.62/49.15  | Case 2:
% 242.62/49.15  | | 
% 242.62/49.15  | |   (9)  all_58_3 = e2 & op(e2, e2) = e2
% 242.62/49.15  | | 
% 242.62/49.15  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #1458.
% 242.62/49.15  | | 
% 242.62/49.15  | End of split
% 242.62/49.15  | 
% 242.62/49.15  End of proof
% 242.62/49.15  
% 242.62/49.15  Sub-proof #826 shows that the following formulas are inconsistent:
% 242.62/49.15  ----------------------------------------------------------------
% 242.62/49.15    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.62/49.15         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.62/49.15    (2)   ~ (e3 = e0)
% 242.62/49.15    (3)  all_58_6 = e3
% 242.62/49.15    (4)   ~ (e2 = e0)
% 242.62/49.15    (5)  op(e1, e2) = all_52_6
% 242.62/49.15    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.15         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.62/49.15    (7)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.62/49.15         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.62/49.15    (8)  all_58_15 = e3
% 242.62/49.15    (9)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.15         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.15    (10)   ~ (e3 = e1)
% 242.62/49.15    (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.62/49.15          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.62/49.15    (12)  all_58_3 = e3
% 242.62/49.15    (13)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.62/49.15          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.62/49.15    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.62/49.15          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.62/49.15    (15)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.62/49.15              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.62/49.15                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.62/49.15                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.62/49.15    (16)  op(e2, e1) = all_52_9
% 242.62/49.15    (17)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.62/49.15          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.62/49.15    (18)   ~ (e3 = e2)
% 242.62/49.15    (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.62/49.15          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.62/49.15    (20)  all_58_13 = e2
% 242.62/49.15    (21)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.62/49.15          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.62/49.15    (22)  op(e2, e3) = all_52_1
% 242.62/49.15    (23)  op(e3, e3) = e2
% 242.62/49.15    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.62/49.15          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.62/49.15    (25)   ~ (all_52_6 = e3)
% 242.62/49.15    (26)  op(e1, e1) = e2
% 242.62/49.15    (27)  all_58_5 = e2
% 242.62/49.15    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.62/49.15          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.62/49.15    (29)   ~ (all_52_4 = e3)
% 242.62/49.15    (30)  op(e3, e2) = all_52_4
% 242.62/49.15    (31)   ~ (all_52_9 = e3)
% 242.62/49.15    (32)  op(e0, e0) = e3
% 242.62/49.15    (33)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.62/49.15          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.62/49.15    (34)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.62/49.15          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.62/49.15    (35)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.62/49.15          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.62/49.15    (36)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.15          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.15    (37)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.15    (38)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.62/49.15          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.62/49.15    (39)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.62/49.15          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.62/49.15    (40)   ~ (e1 = e0)
% 242.62/49.15    (41)  all_58_4 = e3
% 242.62/49.15    (42)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.62/49.15          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.62/49.15    (43)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.62/49.15          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.62/49.15            e1)
% 242.62/49.15    (44)   ~ (all_52_1 = e3)
% 242.62/49.15    (45)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.62/49.15          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.62/49.15    (46)   ~ (e2 = e1)
% 242.62/49.15  
% 242.62/49.15  Begin of proof
% 242.62/49.15  | 
% 242.62/49.15  | BETA: splitting (11) gives:
% 242.62/49.15  | 
% 242.62/49.15  | Case 1:
% 242.62/49.15  | | 
% 242.62/49.15  | |   (47)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 242.62/49.15  | |           e0)
% 242.62/49.15  | | 
% 242.62/49.15  | | BETA: splitting (47) gives:
% 242.62/49.15  | | 
% 242.62/49.15  | | Case 1:
% 242.62/49.15  | | | 
% 242.62/49.15  | | |   (48)  all_58_4 = e0 & op(e3, e1) = e0
% 242.62/49.15  | | | 
% 242.62/49.15  | | | REF_CLOSE: (2), (41), (48) are inconsistent by sub-proof #1697.
% 242.62/49.15  | | | 
% 242.62/49.15  | | Case 2:
% 242.62/49.15  | | | 
% 242.62/49.15  | | |   (49)  all_58_5 = e0 & op(e2, e1) = e0
% 242.62/49.15  | | | 
% 242.62/49.15  | | | REF_CLOSE: (4), (27), (49) are inconsistent by sub-proof #836.
% 242.62/49.15  | | | 
% 242.62/49.15  | | End of split
% 242.62/49.15  | | 
% 242.62/49.15  | Case 2:
% 242.62/49.15  | | 
% 242.62/49.15  | |   (50)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 242.62/49.15  | |           e0)
% 242.62/49.15  | | 
% 242.62/49.15  | | BETA: splitting (50) gives:
% 242.62/49.15  | | 
% 242.62/49.15  | | Case 1:
% 242.62/49.15  | | | 
% 242.62/49.15  | | |   (51)  all_58_8 = e0 & op(e1, e1) = e0
% 242.62/49.15  | | | 
% 242.62/49.15  | | | ALPHA: (51) implies:
% 242.62/49.15  | | |   (52)  op(e1, e1) = e0
% 242.62/49.15  | | | 
% 242.62/49.15  | | | REF_CLOSE: (4), (26), (37), (52) are inconsistent by sub-proof #2211.
% 242.62/49.15  | | | 
% 242.62/49.15  | | Case 2:
% 242.62/49.15  | | | 
% 242.62/49.15  | | |   (53)  all_58_14 = e0 & op(e0, e1) = e0
% 242.62/49.15  | | | 
% 242.62/49.15  | | | ALPHA: (53) implies:
% 242.62/49.15  | | |   (54)  all_58_14 = e0
% 242.62/49.15  | | |   (55)  op(e0, e1) = e0
% 242.62/49.15  | | | 
% 242.62/49.15  | | | BETA: splitting (7) gives:
% 242.62/49.15  | | | 
% 242.62/49.15  | | | Case 1:
% 242.62/49.15  | | | | 
% 242.62/49.15  | | | |   (56)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 242.62/49.15  | | | |           = e1)
% 242.62/49.15  | | | | 
% 242.62/49.15  | | | | BETA: splitting (56) gives:
% 242.62/49.15  | | | | 
% 242.62/49.15  | | | | Case 1:
% 242.62/49.15  | | | | | 
% 242.62/49.15  | | | | |   (57)  all_58_4 = e1 & op(e3, e1) = e1
% 242.62/49.15  | | | | | 
% 242.62/49.15  | | | | | REF_CLOSE: (10), (41), (57) are inconsistent by sub-proof #2042.
% 242.62/49.15  | | | | | 
% 242.62/49.15  | | | | Case 2:
% 242.62/49.15  | | | | | 
% 242.62/49.15  | | | | |   (58)  all_58_5 = e1 & op(e2, e1) = e1
% 242.62/49.15  | | | | | 
% 242.62/49.15  | | | | | REF_CLOSE: (27), (46), (58) are inconsistent by sub-proof #1548.
% 242.62/49.15  | | | | | 
% 242.62/49.15  | | | | End of split
% 242.62/49.15  | | | | 
% 242.62/49.15  | | | Case 2:
% 242.62/49.15  | | | | 
% 242.62/49.15  | | | |   (59)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 242.62/49.15  | | | |           = e1)
% 242.62/49.15  | | | | 
% 242.62/49.15  | | | | BETA: splitting (59) gives:
% 242.62/49.15  | | | | 
% 242.62/49.15  | | | | Case 1:
% 242.62/49.15  | | | | | 
% 242.62/49.15  | | | | |   (60)  all_58_8 = e1 & op(e1, e1) = e1
% 242.62/49.15  | | | | | 
% 242.62/49.15  | | | | | ALPHA: (60) implies:
% 242.62/49.15  | | | | |   (61)  all_58_8 = e1
% 242.62/49.15  | | | | |   (62)  op(e1, e1) = e1
% 242.62/49.15  | | | | | 
% 242.62/49.15  | | | | | BETA: splitting (35) gives:
% 242.62/49.15  | | | | | 
% 242.62/49.15  | | | | | Case 1:
% 242.62/49.15  | | | | | | 
% 242.62/49.15  | | | | | |   (63)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 242.62/49.15  | | | | | |             e2) = e2)
% 242.62/49.15  | | | | | | 
% 242.62/49.15  | | | | | | BETA: splitting (63) gives:
% 242.62/49.15  | | | | | | 
% 242.62/49.15  | | | | | | Case 1:
% 242.62/49.15  | | | | | | | 
% 242.62/49.15  | | | | | | |   (64)  all_58_6 = e2 & op(e1, e3) = e2
% 242.62/49.15  | | | | | | | 
% 242.62/49.15  | | | | | | | REF_CLOSE: (3), (18), (64) are inconsistent by sub-proof #2219.
% 242.62/49.15  | | | | | | | 
% 242.62/49.15  | | | | | | Case 2:
% 242.62/49.15  | | | | | | | 
% 242.62/49.15  | | | | | | |   (65)  all_58_7 = e2 & op(e1, e2) = e2
% 242.62/49.15  | | | | | | | 
% 242.62/49.15  | | | | | | | ALPHA: (65) implies:
% 242.62/49.15  | | | | | | |   (66)  all_58_7 = e2
% 242.62/49.15  | | | | | | | 
% 242.62/49.15  | | | | | | | BETA: splitting (38) gives:
% 242.62/49.15  | | | | | | | 
% 242.62/49.15  | | | | | | | Case 1:
% 242.62/49.15  | | | | | | | | 
% 242.62/49.15  | | | | | | | |   (67)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 242.62/49.15  | | | | | | | |           op(e2, e0) = e2)
% 242.62/49.15  | | | | | | | | 
% 242.62/49.15  | | | | | | | | BETA: splitting (67) gives:
% 242.62/49.15  | | | | | | | | 
% 242.62/49.15  | | | | | | | | Case 1:
% 242.62/49.15  | | | | | | | | | 
% 242.62/49.15  | | | | | | | | |   (68)  all_58_9 = e2 & op(e3, e0) = e2
% 242.62/49.15  | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | ALPHA: (68) implies:
% 242.62/49.15  | | | | | | | | |   (69)  all_58_9 = e2
% 242.62/49.15  | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | REF_CLOSE: (2), (4), (10), (23), (24), (34), (37), (40), (41),
% 242.62/49.15  | | | | | | | | |            (46), (69) are inconsistent by sub-proof #1562.
% 242.62/49.15  | | | | | | | | | 
% 242.62/49.15  | | | | | | | | Case 2:
% 242.62/49.15  | | | | | | | | | 
% 242.62/49.15  | | | | | | | | |   (70)  all_58_10 = e2 & op(e2, e0) = e2
% 242.62/49.15  | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | ALPHA: (70) implies:
% 242.62/49.15  | | | | | | | | |   (71)  op(e2, e0) = e2
% 242.62/49.15  | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | BETA: splitting (42) gives:
% 242.62/49.15  | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | Case 1:
% 242.62/49.15  | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | |   (72)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 242.62/49.15  | | | | | | | | | |           op(e1, e2) = e0)
% 242.62/49.15  | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | BETA: splitting (72) gives:
% 242.62/49.15  | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | Case 1:
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | |   (73)  all_58_6 = e0 & op(e1, e3) = e0
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | ALPHA: (73) implies:
% 242.62/49.15  | | | | | | | | | | |   (74)  all_58_6 = e0
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | REF_CLOSE: (2), (3), (74) are inconsistent by sub-proof
% 242.62/49.15  | | | | | | | | | | |            #2222.
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | Case 2:
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | |   (75)  all_58_7 = e0 & op(e1, e2) = e0
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | ALPHA: (75) implies:
% 242.62/49.15  | | | | | | | | | | |   (76)  all_58_7 = e0
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | REF_CLOSE: (4), (66), (76) are inconsistent by sub-proof
% 242.62/49.15  | | | | | | | | | | |            #1587.
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | End of split
% 242.62/49.15  | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | Case 2:
% 242.62/49.15  | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | |   (77)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0
% 242.62/49.15  | | | | | | | | | |           & op(e1, e0) = e0)
% 242.62/49.15  | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | BETA: splitting (77) gives:
% 242.62/49.15  | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | Case 1:
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | |   (78)  all_58_8 = e0 & op(e1, e1) = e0
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | ALPHA: (78) implies:
% 242.62/49.15  | | | | | | | | | | |   (79)  op(e1, e1) = e0
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | REF_CLOSE: (37), (40), (62), (79) are inconsistent by
% 242.62/49.15  | | | | | | | | | | |            sub-proof #2220.
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | Case 2:
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | |   (80)  all_58_11 = e0 & op(e1, e0) = e0
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | ALPHA: (80) implies:
% 242.62/49.15  | | | | | | | | | | |   (81)  all_58_11 = e0
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | BETA: splitting (36) gives:
% 242.62/49.15  | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | Case 1:
% 242.62/49.15  | | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | |   (82)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 242.62/49.15  | | | | | | | | | | | |           & op(e2, e2) = e0)
% 242.62/49.15  | | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | | BETA: splitting (82) gives:
% 242.62/49.15  | | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | | Case 1:
% 242.62/49.15  | | | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | | |   (83)  all_58_2 = e0 & op(e2, e3) = e0
% 242.62/49.15  | | | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | | | ALPHA: (83) implies:
% 242.62/49.15  | | | | | | | | | | | | |   (84)  all_58_2 = e0
% 242.62/49.15  | | | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | | | BETA: splitting (45) gives:
% 242.62/49.15  | | | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | | | Case 1:
% 242.62/49.15  | | | | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | | | |   (85)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 242.62/49.15  | | | | | | | | | | | | | |           & op(e2, e2) = e1)
% 242.62/49.15  | | | | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (40), (84), (85) are inconsistent by
% 242.62/49.15  | | | | | | | | | | | | | |            sub-proof #976.
% 242.62/49.15  | | | | | | | | | | | | | | 
% 242.62/49.15  | | | | | | | | | | | | | Case 2:
% 242.62/49.15  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | |   (86)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 242.62/49.16  | | | | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 242.62/49.16  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 242.62/49.16  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | |   (87)  all_58_5 = e1 & op(e2, e1) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 242.62/49.16  | | | | | | | | | | | | | | |   (88)  all_58_5 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | COMBINE_EQS: (27), (88) imply:
% 242.62/49.16  | | | | | | | | | | | | | | |   (89)  e2 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | SIMP: (89) implies:
% 242.62/49.16  | | | | | | | | | | | | | | |   (90)  e2 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | COMBINE_EQS: (66), (90) imply:
% 242.62/49.16  | | | | | | | | | | | | | | |   (91)  all_58_7 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (18), (35), (46), (61), (81), (91) are
% 242.62/49.16  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2215.
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | |   (92)  all_58_10 = e1 & op(e2, e0) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 242.62/49.16  | | | | | | | | | | | | | | |   (93)  op(e2, e0) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | REF_CLOSE: (37), (46), (71), (93) are inconsistent by
% 242.62/49.16  | | | | | | | | | | | | | | |            sub-proof #1659.
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | |   (94)  all_58_3 = e0 & op(e2, e2) = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | ALPHA: (94) implies:
% 242.62/49.16  | | | | | | | | | | | | |   (95)  all_58_3 = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | COMBINE_EQS: (12), (95) imply:
% 242.62/49.16  | | | | | | | | | | | | |   (96)  e3 = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | SIMP: (96) implies:
% 242.62/49.16  | | | | | | | | | | | | |   (97)  e3 = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | COMBINE_EQS: (3), (97) imply:
% 242.62/49.16  | | | | | | | | | | | | |   (98)  all_58_6 = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | REF_CLOSE: (2), (5), (18), (21), (25), (26), (37), (81), (98)
% 242.62/49.16  | | | | | | | | | | | | |            are inconsistent by sub-proof #1686.
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | |   (99)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 242.62/49.16  | | | | | | | | | | | |           e0 & op(e2, e0) = e0)
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | BETA: splitting (99) gives:
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | |   (100)  all_58_5 = e0 & op(e2, e1) = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | ALPHA: (100) implies:
% 242.62/49.16  | | | | | | | | | | | | |   (101)  all_58_5 = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | REF_CLOSE: (4), (27), (101) are inconsistent by sub-proof
% 242.62/49.16  | | | | | | | | | | | | |            #835.
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | |   (102)  all_58_10 = e0 & op(e2, e0) = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | ALPHA: (102) implies:
% 242.62/49.16  | | | | | | | | | | | | |   (103)  op(e2, e0) = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | REF_CLOSE: (4), (37), (71), (103) are inconsistent by
% 242.62/49.16  | | | | | | | | | | | | |            sub-proof #2121.
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | 
% 242.62/49.16  | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | 
% 242.62/49.16  | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | 
% 242.62/49.16  | | | | | | | |   (104)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 242.62/49.16  | | | | | | | |            op(e0, e0) = e2)
% 242.62/49.16  | | | | | | | | 
% 242.62/49.16  | | | | | | | | REF_CLOSE: (2), (4), (5), (18), (21), (25), (26), (32), (37),
% 242.62/49.16  | | | | | | | |            (40), (42), (62), (66), (104) are inconsistent by
% 242.62/49.16  | | | | | | | |            sub-proof #834.
% 242.62/49.16  | | | | | | | | 
% 242.62/49.16  | | | | | | | End of split
% 242.62/49.16  | | | | | | | 
% 242.62/49.16  | | | | | | End of split
% 242.62/49.16  | | | | | | 
% 242.62/49.16  | | | | | Case 2:
% 242.62/49.16  | | | | | | 
% 242.62/49.16  | | | | | |   (105)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 242.62/49.16  | | | | | |            op(e1, e0) = e2)
% 242.62/49.16  | | | | | | 
% 242.62/49.16  | | | | | | BETA: splitting (105) gives:
% 242.62/49.16  | | | | | | 
% 242.62/49.16  | | | | | | Case 1:
% 242.62/49.16  | | | | | | | 
% 242.62/49.16  | | | | | | |   (106)  all_58_8 = e2 & op(e1, e1) = e2
% 242.62/49.16  | | | | | | | 
% 242.62/49.16  | | | | | | | ALPHA: (106) implies:
% 242.62/49.16  | | | | | | |   (107)  all_58_8 = e2
% 242.62/49.16  | | | | | | | 
% 242.62/49.16  | | | | | | | REF_CLOSE: (46), (61), (107) are inconsistent by sub-proof #1802.
% 242.62/49.16  | | | | | | | 
% 242.62/49.16  | | | | | | Case 2:
% 242.62/49.16  | | | | | | | 
% 242.62/49.16  | | | | | | |   (108)  all_58_11 = e2 & op(e1, e0) = e2
% 242.62/49.16  | | | | | | | 
% 242.62/49.16  | | | | | | | ALPHA: (108) implies:
% 242.62/49.16  | | | | | | |   (109)  all_58_11 = e2
% 242.62/49.16  | | | | | | | 
% 242.62/49.16  | | | | | | | BETA: splitting (43) gives:
% 242.62/49.16  | | | | | | | 
% 242.62/49.16  | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | 
% 242.62/49.16  | | | | | | | |   (110)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 242.62/49.16  | | | | | | | |            op(e0, e2) = e1)
% 242.62/49.16  | | | | | | | | 
% 242.62/49.16  | | | | | | | | BETA: splitting (110) gives:
% 242.62/49.16  | | | | | | | | 
% 242.62/49.16  | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | 
% 242.62/49.16  | | | | | | | | |   (111)  all_58_12 = e1 & op(e0, e3) = e1
% 242.62/49.16  | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | ALPHA: (111) implies:
% 242.62/49.16  | | | | | | | | |   (112)  all_58_12 = e1
% 242.62/49.16  | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | BETA: splitting (42) gives:
% 242.62/49.16  | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | |   (113)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 242.62/49.16  | | | | | | | | | |            & op(e1, e2) = e0)
% 242.62/49.16  | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | BETA: splitting (113) gives:
% 242.62/49.16  | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | |   (114)  all_58_6 = e0 & op(e1, e3) = e0
% 242.62/49.16  | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | ALPHA: (114) implies:
% 242.62/49.16  | | | | | | | | | | |   (115)  all_58_6 = e0
% 242.62/49.16  | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | REF_CLOSE: (2), (5), (18), (21), (25), (26), (37), (109),
% 242.62/49.16  | | | | | | | | | | |            (115) are inconsistent by sub-proof #997.
% 242.62/49.16  | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | |   (116)  all_58_7 = e0 & op(e1, e2) = e0
% 242.62/49.16  | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | ALPHA: (116) implies:
% 242.62/49.16  | | | | | | | | | | |   (117)  all_58_7 = e0
% 242.62/49.16  | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | BETA: splitting (19) gives:
% 242.62/49.16  | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | |   (118)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 242.62/49.16  | | | | | | | | | | | |            & op(e2, e3) = e0)
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | BETA: splitting (118) gives:
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | |   (119)  all_58_0 = e0 & op(e3, e3) = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | ALPHA: (119) implies:
% 242.62/49.16  | | | | | | | | | | | | |   (120)  op(e3, e3) = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | REF_CLOSE: (4), (23), (37), (120) are inconsistent by
% 242.62/49.16  | | | | | | | | | | | | |            sub-proof #2188.
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | |   (121)  all_58_2 = e0 & op(e2, e3) = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | ALPHA: (121) implies:
% 242.62/49.16  | | | | | | | | | | | | |   (122)  all_58_2 = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | BETA: splitting (39) gives:
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | |   (123)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 242.62/49.16  | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 242.62/49.16  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 242.62/49.16  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | |   (124)  all_58_1 = e1 & op(e3, e2) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 242.62/49.16  | | | | | | | | | | | | | | |   (125)  all_58_1 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | |   (126)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (40), (122), (126) are inconsistent by
% 242.62/49.16  | | | | | | | | | | | | | | | |            sub-proof #976.
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | |   (127)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 242.62/49.16  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | |   (128)  all_58_5 = e1 & op(e2, e1) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 242.62/49.16  | | | | | | | | | | | | | | | | |   (129)  all_58_5 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (129) imply:
% 242.62/49.16  | | | | | | | | | | | | | | | | |   (130)  e2 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | SIMP: (130) implies:
% 242.62/49.16  | | | | | | | | | | | | | | | | |   (131)  e2 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (131) imply:
% 242.62/49.16  | | | | | | | | | | | | | | | | |   (132)  all_58_11 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (18), (35), (46), (61), (117), (132) are
% 242.62/49.16  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #988.
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | |   (133)  all_58_10 = e1 & op(e2, e0) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 242.62/49.16  | | | | | | | | | | | | | | | | |   (134)  all_58_10 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | |   (135)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 242.62/49.16  | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 242.62/49.16  | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23), (37), (40), (125), (135) are
% 242.62/49.16  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1698.
% 242.62/49.16  | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | |   (136)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 242.62/49.16  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 242.62/49.16  | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | |   (137)  all_58_4 = e0 & op(e3, e1) = e0
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | |   (138)  all_58_4 = e0
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (18), (21), (25), (26), (37), (41),
% 242.62/49.16  | | | | | | | | | | | | | | | | | | |            (109), (138) are inconsistent by sub-proof #990.
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | |   (139)  all_58_9 = e0 & op(e3, e0) = e0
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | |   (140)  all_58_9 = e0
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | |   (141)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |   (142)  all_58_0 = e1 & op(e3, e3) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |   (143)  op(e3, e3) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10),
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |            (21), (22), (24), (25), (26), (27), (28), (29),
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |            (30), (31), (33), (36), (37), (38), (40), (41),
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |            (43), (44), (46), (54), (62), (109), (117), (122),
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |            (134), (143) are inconsistent by sub-proof #827.
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (37) with e1, e2, e1, e1,
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |              simplifying with (26), (62) gives:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |   (144)  e2 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (144) imply:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |   (145)  all_58_5 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (9), (12), (18), (36), (40), (46),
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |            (134), (145) are inconsistent by sub-proof #992.
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | |   (146)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |   (147)  all_58_4 = e1 & op(e3, e1) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |   (148)  all_58_4 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (148) imply:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |   (149)  e3 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | SIMP: (149) implies:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |   (150)  e3 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (150) imply:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |   (151)  all_58_15 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (10), (18), (33), (109), (134), (140), (151)
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1619.
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |   (152)  all_58_9 = e1 & op(e3, e0) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | |   (153)  all_58_9 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | |   (154)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23), (37), (40), (125), (154) are
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1698.
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | |   (155)  all_58_4 = e0 & op(e3, e1) = e0
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | |   (156)  all_58_4 = e0
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (18), (21), (25), (26), (37), (41),
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | |            (109), (156) are inconsistent by sub-proof #990.
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (140), (153) are inconsistent by sub-proof
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | |            #1744.
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | |   (157)  all_58_3 = e1 & op(e2, e2) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 242.62/49.16  | | | | | | | | | | | | | | |   (158)  all_58_3 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (158) are inconsistent by sub-proof
% 242.62/49.16  | | | | | | | | | | | | | | |            #1999.
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | |   (159)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 242.62/49.16  | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 242.62/49.16  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 242.62/49.16  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | |   (160)  all_58_7 = e1 & op(e1, e2) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 242.62/49.16  | | | | | | | | | | | | | | |   (161)  all_58_7 = e1
% 242.62/49.16  | | | | | | | | | | | | | | |   (162)  op(e1, e2) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (18), (21), (25), (26), (37), (40),
% 242.62/49.16  | | | | | | | | | | | | | | | |            (109), (113), (162) are inconsistent by sub-proof
% 242.62/49.16  | | | | | | | | | | | | | | | |            #989.
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | |   (163)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 242.62/49.16  | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (18), (35), (37), (40), (46), (61),
% 242.62/49.16  | | | | | | | | | | | | | | | |            (62), (161), (163) are inconsistent by sub-proof
% 242.62/49.16  | | | | | | | | | | | | | | | |            #1270.
% 242.62/49.16  | | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | |   (164)  all_58_13 = e1 & op(e0, e2) = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 242.62/49.16  | | | | | | | | | | | | | | |   (165)  all_58_13 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | COMBINE_EQS: (20), (165) imply:
% 242.62/49.16  | | | | | | | | | | | | | | |   (166)  e2 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | SIMP: (166) implies:
% 242.62/49.16  | | | | | | | | | | | | | | |   (167)  e2 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | COMBINE_EQS: (109), (167) imply:
% 242.62/49.16  | | | | | | | | | | | | | | |   (168)  all_58_11 = e1
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (18), (35), (46), (61), (117), (168) are
% 242.62/49.16  | | | | | | | | | | | | | | |            inconsistent by sub-proof #988.
% 242.62/49.16  | | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | |   (169)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 242.62/49.16  | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | BETA: splitting (169) gives:
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | Case 1:
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | |   (170)  all_58_6 = e0 & op(e1, e3) = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | ALPHA: (170) implies:
% 242.62/49.16  | | | | | | | | | | | | |   (171)  all_58_6 = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | REF_CLOSE: (2), (5), (18), (21), (25), (26), (37), (109),
% 242.62/49.16  | | | | | | | | | | | | |            (171) are inconsistent by sub-proof #997.
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | |   (172)  all_58_12 = e0 & op(e0, e3) = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | ALPHA: (172) implies:
% 242.62/49.16  | | | | | | | | | | | | |   (173)  all_58_12 = e0
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | | REF_CLOSE: (40), (112), (173) are inconsistent by sub-proof
% 242.62/49.16  | | | | | | | | | | | | |            #1539.
% 242.62/49.16  | | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | |   (174)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0
% 242.62/49.16  | | | | | | | | | |            & op(e1, e0) = e0)
% 242.62/49.16  | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | | REF_CLOSE: (4), (37), (40), (62), (109), (174) are
% 242.62/49.16  | | | | | | | | | |            inconsistent by sub-proof #986.
% 242.62/49.16  | | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | | 
% 242.62/49.16  | | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | | 
% 242.62/49.16  | | | | | | | | |   (175)  all_58_13 = e1 & op(e0, e2) = e1
% 242.62/49.16  | | | | | | | | | 
% 242.62/49.16  | | | | | | | | | REF_CLOSE: (20), (46), (175) are inconsistent by sub-proof
% 242.62/49.16  | | | | | | | | |            #1751.
% 242.62/49.16  | | | | | | | | | 
% 242.62/49.16  | | | | | | | | End of split
% 242.62/49.16  | | | | | | | | 
% 242.62/49.16  | | | | | | | Case 2:
% 242.62/49.16  | | | | | | | | 
% 242.62/49.16  | | | | | | | |   (176)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 242.62/49.16  | | | | | | | |            op(e0, e0) = e1)
% 242.62/49.16  | | | | | | | | 
% 242.62/49.16  | | | | | | | | REF_CLOSE: (8), (10), (37), (40), (55), (176) are inconsistent
% 242.62/49.16  | | | | | | | |            by sub-proof #1255.
% 242.62/49.16  | | | | | | | | 
% 242.62/49.16  | | | | | | | End of split
% 242.62/49.16  | | | | | | | 
% 242.62/49.16  | | | | | | End of split
% 242.62/49.16  | | | | | | 
% 242.62/49.16  | | | | | End of split
% 242.62/49.16  | | | | | 
% 242.62/49.16  | | | | Case 2:
% 242.62/49.16  | | | | | 
% 242.62/49.16  | | | | |   (177)  all_58_14 = e1 & op(e0, e1) = e1
% 242.62/49.16  | | | | | 
% 242.62/49.16  | | | | | ALPHA: (177) implies:
% 242.62/49.16  | | | | |   (178)  op(e0, e1) = e1
% 242.62/49.16  | | | | | 
% 242.62/49.16  | | | | | REF_CLOSE: (37), (40), (55), (178) are inconsistent by sub-proof
% 242.62/49.16  | | | | |            #2158.
% 242.62/49.16  | | | | | 
% 242.62/49.16  | | | | End of split
% 242.62/49.16  | | | | 
% 242.62/49.16  | | | End of split
% 242.62/49.16  | | | 
% 242.62/49.16  | | End of split
% 242.62/49.16  | | 
% 242.62/49.16  | End of split
% 242.62/49.16  | 
% 242.62/49.16  End of proof
% 242.62/49.16  
% 242.62/49.16  Sub-proof #827 shows that the following formulas are inconsistent:
% 242.62/49.16  ----------------------------------------------------------------
% 242.62/49.16    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.62/49.16         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.62/49.16    (2)   ~ (e3 = e0)
% 242.62/49.16    (3)  op(e1, e1) = e1
% 242.62/49.16    (4)  all_58_6 = e3
% 242.62/49.16    (5)   ~ (e2 = e0)
% 242.62/49.16    (6)  all_58_7 = e0
% 242.62/49.16    (7)  op(e1, e2) = all_52_6
% 242.62/49.16    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.16         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.62/49.16    (9)  all_58_15 = e3
% 242.62/49.16    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.16          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.17    (11)   ~ (e3 = e1)
% 242.62/49.17    (12)  all_58_3 = e3
% 242.62/49.17    (13)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.62/49.17          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.62/49.17    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.62/49.17          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.62/49.17    (15)  op(e3, e3) = e1
% 242.62/49.17    (16)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.62/49.17              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.62/49.17                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.62/49.17                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.62/49.17    (17)  op(e2, e1) = all_52_9
% 242.62/49.17    (18)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.62/49.17          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.62/49.17    (19)   ~ (e3 = e2)
% 242.62/49.17    (20)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.62/49.17          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.62/49.17    (21)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.62/49.17          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.62/49.17    (22)  all_58_11 = e2
% 242.62/49.17    (23)  op(e2, e3) = all_52_1
% 242.62/49.17    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.62/49.17          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.62/49.17    (25)   ~ (all_52_6 = e3)
% 242.62/49.17    (26)  op(e1, e1) = e2
% 242.62/49.17    (27)  all_58_5 = e2
% 242.62/49.17    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.62/49.17          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.62/49.17    (29)  all_58_2 = e0
% 242.62/49.17    (30)   ~ (all_52_4 = e3)
% 242.62/49.17    (31)  op(e3, e2) = all_52_4
% 242.62/49.17    (32)  all_58_14 = e0
% 242.62/49.17    (33)   ~ (all_52_9 = e3)
% 242.62/49.17    (34)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.62/49.17          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.62/49.17    (35)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.17          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.17    (36)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.17    (37)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.62/49.17          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.62/49.17    (38)   ~ (e1 = e0)
% 242.62/49.17    (39)  all_58_4 = e3
% 242.62/49.17    (40)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.62/49.17          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.62/49.17            e1)
% 242.62/49.17    (41)   ~ (all_52_1 = e3)
% 242.62/49.17    (42)  all_58_10 = e1
% 242.62/49.17    (43)   ~ (e2 = e1)
% 242.62/49.17  
% 242.62/49.17  Begin of proof
% 242.62/49.17  | 
% 242.62/49.17  | BETA: splitting (18) gives:
% 242.62/49.17  | 
% 242.62/49.17  | Case 1:
% 242.62/49.17  | | 
% 242.62/49.17  | |   (44)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 242.62/49.17  | |           e2)
% 242.62/49.17  | | 
% 242.62/49.17  | | REF_CLOSE: (5), (15), (29), (36), (43), (44) are inconsistent by sub-proof
% 242.62/49.17  | |            #1329.
% 242.62/49.17  | | 
% 242.62/49.17  | Case 2:
% 242.62/49.17  | | 
% 242.62/49.17  | |   (45)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 242.62/49.17  | |           e2)
% 242.62/49.17  | | 
% 242.62/49.17  | | BETA: splitting (45) gives:
% 242.62/49.17  | | 
% 242.62/49.17  | | Case 1:
% 242.62/49.17  | | | 
% 242.62/49.17  | | |   (46)  all_58_6 = e2 & op(e1, e3) = e2
% 242.62/49.17  | | | 
% 242.62/49.17  | | | ALPHA: (46) implies:
% 242.62/49.17  | | |   (47)  all_58_6 = e2
% 242.62/49.17  | | | 
% 242.62/49.17  | | | COMBINE_EQS: (4), (47) imply:
% 242.62/49.17  | | |   (48)  e3 = e2
% 242.62/49.17  | | | 
% 242.62/49.17  | | | SIMP: (48) implies:
% 242.62/49.17  | | |   (49)  e3 = e2
% 242.62/49.17  | | | 
% 242.62/49.17  | | | COMBINE_EQS: (39), (49) imply:
% 242.62/49.17  | | |   (50)  all_58_4 = e2
% 242.62/49.17  | | | 
% 242.62/49.17  | | | REF_CLOSE: (2), (4), (7), (17), (19), (21), (22), (25), (26), (28), (32),
% 242.62/49.17  | | |            (33), (36), (50) are inconsistent by sub-proof #833.
% 242.62/49.17  | | | 
% 242.62/49.17  | | Case 2:
% 242.62/49.17  | | | 
% 242.62/49.17  | | |   (51)  all_58_12 = e2 & op(e0, e3) = e2
% 242.62/49.17  | | | 
% 242.62/49.17  | | | ALPHA: (51) implies:
% 242.62/49.17  | | |   (52)  all_58_12 = e2
% 242.62/49.17  | | | 
% 242.62/49.17  | | | BETA: splitting (40) gives:
% 242.62/49.17  | | | 
% 242.62/49.17  | | | Case 1:
% 242.62/49.17  | | | | 
% 242.62/49.17  | | | |   (53)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0,
% 242.62/49.17  | | | |             e2) = e1)
% 242.62/49.17  | | | | 
% 242.62/49.17  | | | | BETA: splitting (53) gives:
% 242.62/49.17  | | | | 
% 242.62/49.17  | | | | Case 1:
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | |   (54)  all_58_12 = e1 & op(e0, e3) = e1
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | | ALPHA: (54) implies:
% 242.62/49.17  | | | | |   (55)  all_58_12 = e1
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | | REF_CLOSE: (4), (5), (15), (18), (19), (29), (36), (43), (55) are
% 242.62/49.17  | | | | |            inconsistent by sub-proof #1328.
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | Case 2:
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | |   (56)  all_58_13 = e1 & op(e0, e2) = e1
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | | ALPHA: (56) implies:
% 242.62/49.17  | | | | |   (57)  all_58_13 = e1
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | | BETA: splitting (8) gives:
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | | Case 1:
% 242.62/49.17  | | | | | | 
% 242.62/49.17  | | | | | |   (58)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2,
% 242.62/49.17  | | | | | |             e2) = e2)
% 242.62/49.17  | | | | | | 
% 242.62/49.17  | | | | | | BETA: splitting (58) gives:
% 242.62/49.17  | | | | | | 
% 242.62/49.17  | | | | | | Case 1:
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | |   (59)  all_58_1 = e2 & op(e3, e2) = e2
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | ALPHA: (59) implies:
% 242.62/49.17  | | | | | | |   (60)  all_58_1 = e2
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | BETA: splitting (16) gives:
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | Case 1:
% 242.62/49.17  | | | | | | | | 
% 242.62/49.17  | | | | | | | |   (61)  all_58_15 = e0 & op(e0, e0) = e0
% 242.62/49.17  | | | | | | | | 
% 242.62/49.17  | | | | | | | | REF_CLOSE: (2), (4), (7), (9), (19), (21), (22), (25), (26),
% 242.62/49.17  | | | | | | | |            (36), (61) are inconsistent by sub-proof #832.
% 242.62/49.17  | | | | | | | | 
% 242.62/49.17  | | | | | | | Case 2:
% 242.62/49.17  | | | | | | | | 
% 242.62/49.17  | | | | | | | |   (62)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 242.62/49.17  | | | | | | | |             op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.62/49.17  | | | | | | | |             e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 242.62/49.17  | | | | | | | |           (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 242.62/49.17  | | | | | | | |             op(e0, e1) = e0))
% 242.62/49.17  | | | | | | | | 
% 242.62/49.17  | | | | | | | | ALPHA: (62) implies:
% 242.62/49.17  | | | | | | | |   (63)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 242.62/49.17  | | | | | | | |           op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.62/49.17  | | | | | | | | 
% 242.62/49.17  | | | | | | | | BETA: splitting (24) gives:
% 242.62/49.17  | | | | | | | | 
% 242.62/49.17  | | | | | | | | Case 1:
% 242.62/49.17  | | | | | | | | | 
% 242.62/49.17  | | | | | | | | |   (64)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 242.62/49.17  | | | | | | | | |           op(e3, e2) = e0)
% 242.62/49.17  | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | BETA: splitting (64) gives:
% 242.62/49.17  | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | Case 1:
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | |   (65)  all_58_0 = e0 & op(e3, e3) = e0
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | ALPHA: (65) implies:
% 242.62/49.17  | | | | | | | | | |   (66)  op(e3, e3) = e0
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | REF_CLOSE: (15), (36), (38), (66) are inconsistent by
% 242.62/49.17  | | | | | | | | | |            sub-proof #1828.
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | Case 2:
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | |   (67)  all_58_1 = e0 & op(e3, e2) = e0
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | ALPHA: (67) implies:
% 242.62/49.17  | | | | | | | | | |   (68)  all_58_1 = e0
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | COMBINE_EQS: (60), (68) imply:
% 242.62/49.17  | | | | | | | | | |   (69)  e2 = e0
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | COMBINE_EQS: (52), (69) imply:
% 242.62/49.17  | | | | | | | | | |   (70)  all_58_12 = e0
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | REF_CLOSE: (2), (5), (11), (14), (15), (18), (19), (23),
% 242.62/49.17  | | | | | | | | | |            (29), (36), (41), (43), (70) are inconsistent by
% 242.62/49.17  | | | | | | | | | |            sub-proof #1149.
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | End of split
% 242.62/49.17  | | | | | | | | | 
% 242.62/49.17  | | | | | | | | Case 2:
% 242.62/49.17  | | | | | | | | | 
% 242.62/49.17  | | | | | | | | |   (71)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 242.62/49.17  | | | | | | | | |           op(e3, e0) = e0)
% 242.62/49.17  | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | BETA: splitting (71) gives:
% 242.62/49.17  | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | Case 1:
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | |   (72)  all_58_4 = e0 & op(e3, e1) = e0
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | ALPHA: (72) implies:
% 242.62/49.17  | | | | | | | | | |   (73)  all_58_4 = e0
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | REF_CLOSE: (2), (4), (7), (19), (21), (22), (25), (26), (36),
% 242.62/49.17  | | | | | | | | | |            (39), (73) are inconsistent by sub-proof #990.
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | Case 2:
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | |   (74)  all_58_9 = e0 & op(e3, e0) = e0
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | ALPHA: (74) implies:
% 242.62/49.17  | | | | | | | | | |   (75)  all_58_9 = e0
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | BETA: splitting (1) gives:
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | Case 1:
% 242.62/49.17  | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | |   (76)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 242.62/49.17  | | | | | | | | | | |           & op(e3, e2) = e2)
% 242.62/49.17  | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | BETA: splitting (76) gives:
% 242.62/49.17  | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | Case 1:
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | |   (77)  all_58_0 = e2 & op(e3, e3) = e2
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | ALPHA: (77) implies:
% 242.62/49.17  | | | | | | | | | | | |   (78)  op(e3, e3) = e2
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | REF_CLOSE: (15), (36), (43), (78) are inconsistent by
% 242.62/49.17  | | | | | | | | | | | |            sub-proof #2267.
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | Case 2:
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | GROUND_INST: instantiating (36) with e1, e2, e1, e1,
% 242.62/49.17  | | | | | | | | | | | |              simplifying with (3), (26) gives:
% 242.62/49.17  | | | | | | | | | | | |   (79)  e2 = e1
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | COMBINE_EQS: (27), (79) imply:
% 242.62/49.17  | | | | | | | | | | | |   (80)  all_58_5 = e1
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | BETA: splitting (10) gives:
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | Case 1:
% 242.62/49.17  | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | |   (81)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 242.62/49.17  | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 242.62/49.17  | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | REF_CLOSE: (2), (5), (9), (10), (11), (12), (19), (34), (35),
% 242.62/49.17  | | | | | | | | | | | | |            (36), (37), (38), (42), (43), (63), (80), (81) are
% 242.62/49.17  | | | | | | | | | | | | |            inconsistent by sub-proof #830.
% 242.62/49.17  | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | Case 2:
% 242.62/49.17  | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | |   (82)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 242.62/49.17  | | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 242.62/49.17  | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | BETA: splitting (82) gives:
% 242.62/49.17  | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | Case 1:
% 242.62/49.17  | | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | |   (83)  all_58_5 = e2 & op(e2, e1) = e2
% 242.62/49.17  | | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | | COMBINE_EQS: (27), (80) imply:
% 242.62/49.17  | | | | | | | | | | | | | |   (84)  e2 = e1
% 242.62/49.17  | | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | | COMBINE_EQS: (52), (79) imply:
% 242.62/49.17  | | | | | | | | | | | | | |   (85)  all_58_12 = e1
% 242.62/49.17  | | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (11), (14), (15), (18), (19), (20),
% 242.62/49.17  | | | | | | | | | | | | | |            (23), (36), (38), (41), (43), (85) are
% 242.62/49.17  | | | | | | | | | | | | | |            inconsistent by sub-proof #1204.
% 242.62/49.17  | | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | Case 2:
% 242.62/49.17  | | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | |   (86)  all_58_10 = e2 & op(e2, e0) = e2
% 242.62/49.17  | | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | | ALPHA: (86) implies:
% 242.62/49.17  | | | | | | | | | | | | | |   (87)  all_58_10 = e2
% 242.62/49.17  | | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | | COMBINE_EQS: (52), (79) imply:
% 242.62/49.17  | | | | | | | | | | | | | |   (88)  all_58_12 = e1
% 242.62/49.17  | | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (11), (14), (15), (18), (19), (20),
% 242.62/49.17  | | | | | | | | | | | | | |            (23), (36), (38), (41), (43), (88) are
% 242.62/49.17  | | | | | | | | | | | | | |            inconsistent by sub-proof #1204.
% 242.62/49.17  | | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | | End of split
% 242.62/49.17  | | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | End of split
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | End of split
% 242.62/49.17  | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | Case 2:
% 242.62/49.17  | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | |   (89)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 242.62/49.17  | | | | | | | | | | |           & op(e3, e0) = e2)
% 242.62/49.17  | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | BETA: splitting (89) gives:
% 242.62/49.17  | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | Case 1:
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | |   (90)  all_58_4 = e2 & op(e3, e1) = e2
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | ALPHA: (90) implies:
% 242.62/49.17  | | | | | | | | | | | |   (91)  all_58_4 = e2
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (17), (19), (21), (22), (25), (26),
% 242.62/49.17  | | | | | | | | | | | |            (28), (32), (33), (36), (91) are inconsistent by
% 242.62/49.17  | | | | | | | | | | | |            sub-proof #833.
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | Case 2:
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | |   (92)  all_58_9 = e2 & op(e3, e0) = e2
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | ALPHA: (92) implies:
% 242.62/49.17  | | | | | | | | | | | |   (93)  all_58_9 = e2
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | | REF_CLOSE: (1), (5), (15), (19), (36), (39), (43), (60),
% 242.62/49.17  | | | | | | | | | | | |            (75), (93) are inconsistent by sub-proof #829.
% 242.62/49.17  | | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | | End of split
% 242.62/49.17  | | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | | End of split
% 242.62/49.17  | | | | | | | | | | 
% 242.62/49.17  | | | | | | | | | End of split
% 242.62/49.17  | | | | | | | | | 
% 242.62/49.17  | | | | | | | | End of split
% 242.62/49.17  | | | | | | | | 
% 242.62/49.17  | | | | | | | End of split
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | Case 2:
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | |   (94)  all_58_3 = e2 & op(e2, e2) = e2
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | ALPHA: (94) implies:
% 242.62/49.17  | | | | | | |   (95)  all_58_3 = e2
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | COMBINE_EQS: (12), (95) imply:
% 242.62/49.17  | | | | | | |   (96)  e3 = e2
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | SIMP: (96) implies:
% 242.62/49.17  | | | | | | |   (97)  e3 = e2
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | COMBINE_EQS: (39), (97) imply:
% 242.62/49.17  | | | | | | |   (98)  all_58_4 = e2
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | REF_CLOSE: (2), (4), (7), (17), (19), (21), (22), (25), (26),
% 242.62/49.17  | | | | | | |            (28), (32), (33), (36), (98) are inconsistent by
% 242.62/49.17  | | | | | | |            sub-proof #833.
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | End of split
% 242.62/49.17  | | | | | | 
% 242.62/49.17  | | | | | Case 2:
% 242.62/49.17  | | | | | | 
% 242.62/49.17  | | | | | |   (99)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0,
% 242.62/49.17  | | | | | |             e2) = e2)
% 242.62/49.17  | | | | | | 
% 242.62/49.17  | | | | | | BETA: splitting (99) gives:
% 242.62/49.17  | | | | | | 
% 242.62/49.17  | | | | | | Case 1:
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | |   (100)  all_58_7 = e2 & op(e1, e2) = e2
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | ALPHA: (100) implies:
% 242.62/49.17  | | | | | | |   (101)  all_58_7 = e2
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | COMBINE_EQS: (6), (101) imply:
% 242.62/49.17  | | | | | | |   (102)  e2 = e0
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | COMBINE_EQS: (52), (102) imply:
% 242.62/49.17  | | | | | | |   (103)  all_58_12 = e0
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | REF_CLOSE: (2), (5), (11), (14), (15), (18), (19), (23), (29),
% 242.62/49.17  | | | | | | |            (36), (41), (43), (103) are inconsistent by sub-proof
% 242.62/49.17  | | | | | | |            #1149.
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | Case 2:
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | |   (104)  all_58_13 = e2 & op(e0, e2) = e2
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | ALPHA: (104) implies:
% 242.62/49.17  | | | | | | |   (105)  all_58_13 = e2
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | COMBINE_EQS: (57), (105) imply:
% 242.62/49.17  | | | | | | |   (106)  e2 = e1
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | COMBINE_EQS: (27), (106) imply:
% 242.62/49.17  | | | | | | |   (107)  all_58_5 = e1
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | | REF_CLOSE: (2), (5), (10), (12), (19), (35), (38), (42), (43),
% 242.62/49.17  | | | | | | |            (107) are inconsistent by sub-proof #992.
% 242.62/49.17  | | | | | | | 
% 242.62/49.17  | | | | | | End of split
% 242.62/49.17  | | | | | | 
% 242.62/49.17  | | | | | End of split
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | End of split
% 242.62/49.17  | | | | 
% 242.62/49.17  | | | Case 2:
% 242.62/49.17  | | | | 
% 242.62/49.17  | | | |   (108)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 242.62/49.17  | | | |              e0) = e1)
% 242.62/49.17  | | | | 
% 242.62/49.17  | | | | BETA: splitting (108) gives:
% 242.62/49.17  | | | | 
% 242.62/49.17  | | | | Case 1:
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | |   (109)  all_58_14 = e1 & op(e0, e1) = e1
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | | REF_CLOSE: (32), (38), (109) are inconsistent by sub-proof #828.
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | Case 2:
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | |   (110)  all_58_15 = e1 & op(e0, e0) = e1
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | | ALPHA: (110) implies:
% 242.62/49.17  | | | | |   (111)  all_58_15 = e1
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | | REF_CLOSE: (1), (2), (5), (9), (11), (13), (15), (19), (24), (30),
% 242.62/49.17  | | | | |            (31), (36), (38), (39), (43), (111) are inconsistent by
% 242.62/49.17  | | | | |            sub-proof #1093.
% 242.62/49.17  | | | | | 
% 242.62/49.17  | | | | End of split
% 242.62/49.17  | | | | 
% 242.62/49.17  | | | End of split
% 242.62/49.17  | | | 
% 242.62/49.17  | | End of split
% 242.62/49.17  | | 
% 242.62/49.17  | End of split
% 242.62/49.17  | 
% 242.62/49.17  End of proof
% 242.62/49.17  
% 242.62/49.17  Sub-proof #828 shows that the following formulas are inconsistent:
% 242.62/49.17  ----------------------------------------------------------------
% 242.62/49.17    (1)  all_58_14 = e1 & op(e0, e1) = e1
% 242.62/49.17    (2)  all_58_14 = e0
% 242.62/49.17    (3)   ~ (e1 = e0)
% 242.62/49.17  
% 242.62/49.17  Begin of proof
% 242.62/49.17  | 
% 242.62/49.17  | ALPHA: (1) implies:
% 242.62/49.17  |   (4)  all_58_14 = e1
% 242.62/49.17  | 
% 242.62/49.17  | COMBINE_EQS: (2), (4) imply:
% 242.62/49.17  |   (5)  e1 = e0
% 242.62/49.17  | 
% 242.62/49.17  | REDUCE: (3), (5) imply:
% 242.62/49.17  |   (6)  $false
% 242.62/49.17  | 
% 242.62/49.17  | CLOSE: (6) is inconsistent.
% 242.62/49.17  | 
% 242.62/49.17  End of proof
% 242.62/49.17  
% 242.62/49.17  Sub-proof #829 shows that the following formulas are inconsistent:
% 242.62/49.17  ----------------------------------------------------------------
% 242.62/49.17    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.62/49.17         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.62/49.17    (2)   ~ (e2 = e0)
% 242.62/49.17    (3)  all_58_9 = e0
% 242.62/49.17    (4)  op(e3, e3) = e1
% 242.62/49.17    (5)   ~ (e3 = e2)
% 242.62/49.17    (6)  all_58_1 = e2
% 242.62/49.18    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.18    (8)  all_58_4 = e3
% 242.62/49.18    (9)  all_58_9 = e2
% 242.62/49.18    (10)   ~ (e2 = e1)
% 242.62/49.18  
% 242.62/49.18  Begin of proof
% 242.62/49.18  | 
% 242.62/49.18  | COMBINE_EQS: (3), (9) imply:
% 242.62/49.18  |   (11)  e2 = e0
% 242.62/49.18  | 
% 242.62/49.18  | COMBINE_EQS: (6), (11) imply:
% 242.62/49.18  |   (12)  all_58_1 = e0
% 242.62/49.18  | 
% 242.62/49.18  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (12) are inconsistent by
% 242.62/49.18  |            sub-proof #1097.
% 242.62/49.18  | 
% 242.62/49.18  End of proof
% 242.62/49.18  
% 242.62/49.18  Sub-proof #830 shows that the following formulas are inconsistent:
% 242.62/49.18  ----------------------------------------------------------------
% 242.62/49.18    (1)   ~ (e3 = e0)
% 242.62/49.18    (2)   ~ (e2 = e0)
% 242.62/49.18    (3)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.62/49.18         (all_58_11 = e0 & op(e1, e0) = e0)
% 242.62/49.18    (4)  all_58_15 = e3
% 242.62/49.18    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.18         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.18    (6)   ~ (e3 = e1)
% 242.62/49.18    (7)  all_58_3 = e3
% 242.62/49.18    (8)   ~ (e3 = e2)
% 242.62/49.18    (9)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 242.62/49.18    (10)  all_58_5 = e1
% 242.62/49.18    (11)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.62/49.18          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.62/49.18    (12)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.18          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.18    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.18    (14)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.62/49.18          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.62/49.18    (15)   ~ (e1 = e0)
% 242.62/49.18    (16)  all_58_10 = e1
% 242.62/49.18    (17)   ~ (e2 = e1)
% 242.62/49.18  
% 242.62/49.18  Begin of proof
% 242.62/49.18  | 
% 242.62/49.18  | BETA: splitting (9) gives:
% 242.62/49.18  | 
% 242.62/49.18  | Case 1:
% 242.62/49.18  | | 
% 242.62/49.18  | |   (18)  all_58_2 = e2 & op(e2, e3) = e2
% 242.62/49.18  | | 
% 242.62/49.18  | | ALPHA: (18) implies:
% 242.62/49.18  | |   (19)  all_58_2 = e2
% 242.62/49.18  | | 
% 242.62/49.18  | | REF_CLOSE: (1), (2), (7), (10), (12), (15), (16), (19) are inconsistent by
% 242.62/49.18  | |            sub-proof #994.
% 242.62/49.18  | | 
% 242.62/49.18  | Case 2:
% 242.62/49.18  | | 
% 242.62/49.18  | |   (20)  all_58_3 = e2 & op(e2, e2) = e2
% 242.62/49.18  | | 
% 242.62/49.18  | | ALPHA: (20) implies:
% 242.62/49.18  | |   (21)  all_58_3 = e2
% 242.62/49.18  | | 
% 242.62/49.18  | | COMBINE_EQS: (7), (21) imply:
% 242.62/49.18  | |   (22)  e3 = e2
% 242.62/49.18  | | 
% 242.62/49.18  | | SIMP: (22) implies:
% 242.62/49.18  | |   (23)  e3 = e2
% 242.62/49.18  | | 
% 242.62/49.18  | | COMBINE_EQS: (4), (23) imply:
% 242.62/49.18  | |   (24)  all_58_15 = e2
% 242.62/49.18  | | 
% 242.62/49.18  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 242.62/49.18  | |            (15), (16), (17), (24) are inconsistent by sub-proof #831.
% 242.62/49.18  | | 
% 242.62/49.18  | End of split
% 242.62/49.18  | 
% 242.62/49.18  End of proof
% 242.62/49.18  
% 242.62/49.18  Sub-proof #831 shows that the following formulas are inconsistent:
% 242.62/49.18  ----------------------------------------------------------------
% 242.62/49.18    (1)   ~ (e3 = e0)
% 242.62/49.18    (2)   ~ (e2 = e0)
% 242.62/49.18    (3)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.62/49.18         (all_58_11 = e0 & op(e1, e0) = e0)
% 242.62/49.18    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.18         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.18    (5)   ~ (e3 = e1)
% 242.62/49.18    (6)  all_58_3 = e3
% 242.62/49.18    (7)  all_58_15 = e2
% 242.62/49.18    (8)   ~ (e3 = e2)
% 242.62/49.18    (9)  all_58_5 = e1
% 242.62/49.18    (10)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.62/49.18          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.62/49.18    (11)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.18          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.18    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.18    (13)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.62/49.18          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.62/49.18    (14)   ~ (e1 = e0)
% 242.62/49.18    (15)  all_58_10 = e1
% 242.62/49.18    (16)   ~ (e2 = e1)
% 242.62/49.18  
% 242.62/49.18  Begin of proof
% 242.62/49.18  | 
% 242.62/49.18  | BETA: splitting (4) gives:
% 242.62/49.18  | 
% 242.62/49.18  | Case 1:
% 242.62/49.18  | | 
% 242.62/49.18  | |   (17)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 242.62/49.18  | |           e2)
% 242.62/49.18  | | 
% 242.62/49.18  | | REF_CLOSE: (1), (2), (6), (8), (9), (11), (14), (15), (17) are inconsistent
% 242.62/49.18  | |            by sub-proof #993.
% 242.62/49.18  | | 
% 242.62/49.18  | Case 2:
% 242.62/49.18  | | 
% 242.62/49.18  | |   (18)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 242.62/49.18  | |           e2)
% 242.62/49.18  | | 
% 242.62/49.18  | | BETA: splitting (18) gives:
% 242.62/49.18  | | 
% 242.62/49.18  | | Case 1:
% 242.62/49.18  | | | 
% 242.62/49.18  | | |   (19)  all_58_5 = e2 & op(e2, e1) = e2
% 242.62/49.18  | | | 
% 242.62/49.18  | | | ALPHA: (19) implies:
% 242.62/49.18  | | |   (20)  all_58_5 = e2
% 242.62/49.18  | | | 
% 242.62/49.18  | | | COMBINE_EQS: (9), (20) imply:
% 242.62/49.18  | | |   (21)  e2 = e1
% 242.62/49.18  | | | 
% 242.62/49.18  | | | SIMP: (21) implies:
% 242.62/49.18  | | |   (22)  e2 = e1
% 242.62/49.18  | | | 
% 242.62/49.18  | | | COMBINE_EQS: (7), (22) imply:
% 242.62/49.18  | | |   (23)  all_58_15 = e1
% 242.62/49.18  | | | 
% 242.62/49.18  | | | REF_CLOSE: (1), (2), (3), (5), (8), (10), (12), (13), (14), (15), (16),
% 242.62/49.18  | | |            (23) are inconsistent by sub-proof #910.
% 242.62/49.18  | | | 
% 242.62/49.18  | | Case 2:
% 242.62/49.18  | | | 
% 242.62/49.18  | | |   (24)  all_58_10 = e2 & op(e2, e0) = e2
% 242.62/49.18  | | | 
% 242.62/49.18  | | | ALPHA: (24) implies:
% 242.62/49.18  | | |   (25)  all_58_10 = e2
% 242.62/49.18  | | | 
% 242.62/49.18  | | | COMBINE_EQS: (15), (25) imply:
% 242.62/49.18  | | |   (26)  e2 = e1
% 242.62/49.18  | | | 
% 242.62/49.18  | | | COMBINE_EQS: (7), (26) imply:
% 242.62/49.18  | | |   (27)  all_58_15 = e1
% 242.62/49.18  | | | 
% 242.62/49.18  | | | REF_CLOSE: (1), (2), (3), (5), (8), (10), (12), (13), (14), (15), (16),
% 242.62/49.18  | | |            (27) are inconsistent by sub-proof #910.
% 242.62/49.18  | | | 
% 242.62/49.18  | | End of split
% 242.62/49.18  | | 
% 242.62/49.18  | End of split
% 242.62/49.18  | 
% 242.62/49.18  End of proof
% 242.62/49.18  
% 242.62/49.18  Sub-proof #832 shows that the following formulas are inconsistent:
% 242.62/49.18  ----------------------------------------------------------------
% 242.62/49.18    (1)   ~ (e3 = e0)
% 242.62/49.18    (2)  all_58_6 = e3
% 242.62/49.18    (3)  op(e1, e2) = all_52_6
% 242.62/49.18    (4)  all_58_15 = e3
% 242.62/49.18    (5)  all_58_15 = e0 & op(e0, e0) = e0
% 242.62/49.18    (6)   ~ (e3 = e2)
% 242.62/49.18    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.62/49.18         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.62/49.18    (8)  all_58_11 = e2
% 242.62/49.18    (9)   ~ (all_52_6 = e3)
% 242.62/49.18    (10)  op(e1, e1) = e2
% 242.62/49.18    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.18  
% 242.62/49.18  Begin of proof
% 242.62/49.18  | 
% 242.62/49.18  | ALPHA: (5) implies:
% 242.62/49.18  |   (12)  all_58_15 = e0
% 242.62/49.18  | 
% 242.62/49.18  | COMBINE_EQS: (4), (12) imply:
% 242.62/49.18  |   (13)  e3 = e0
% 242.62/49.18  | 
% 242.62/49.18  | SIMP: (13) implies:
% 242.62/49.18  |   (14)  e3 = e0
% 242.62/49.18  | 
% 242.62/49.18  | COMBINE_EQS: (2), (14) imply:
% 242.62/49.18  |   (15)  all_58_6 = e0
% 242.62/49.18  | 
% 242.62/49.18  | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (15) are inconsistent by
% 242.62/49.18  |            sub-proof #997.
% 242.62/49.18  | 
% 242.62/49.18  End of proof
% 242.62/49.18  
% 242.62/49.18  Sub-proof #833 shows that the following formulas are inconsistent:
% 242.62/49.18  ----------------------------------------------------------------
% 242.62/49.18    (1)   ~ (e3 = e0)
% 242.62/49.18    (2)  all_58_6 = e3
% 242.62/49.18    (3)  op(e1, e2) = all_52_6
% 242.62/49.18    (4)  all_58_4 = e2
% 242.62/49.18    (5)  op(e2, e1) = all_52_9
% 242.62/49.18    (6)   ~ (e3 = e2)
% 242.62/49.18    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.62/49.18         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.62/49.18    (8)  all_58_11 = e2
% 242.62/49.18    (9)   ~ (all_52_6 = e3)
% 242.62/49.18    (10)  op(e1, e1) = e2
% 242.62/49.18    (11)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.62/49.18          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.62/49.18    (12)  all_58_14 = e0
% 242.62/49.18    (13)   ~ (all_52_9 = e3)
% 242.62/49.18    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.18  
% 242.62/49.18  Begin of proof
% 242.62/49.18  | 
% 242.62/49.18  | BETA: splitting (11) gives:
% 242.62/49.18  | 
% 242.62/49.18  | Case 1:
% 242.62/49.18  | | 
% 242.62/49.18  | |   (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 242.62/49.18  | |           e3)
% 242.62/49.18  | | 
% 242.62/49.18  | | BETA: splitting (15) gives:
% 242.62/49.18  | | 
% 242.62/49.18  | | Case 1:
% 242.62/49.18  | | | 
% 242.62/49.18  | | |   (16)  all_58_4 = e3 & op(e3, e1) = e3
% 242.62/49.18  | | | 
% 242.62/49.18  | | | REF_CLOSE: (4), (6), (16) are inconsistent by sub-proof #2167.
% 242.62/49.18  | | | 
% 242.62/49.18  | | Case 2:
% 242.62/49.18  | | | 
% 242.62/49.18  | | |   (17)  all_58_5 = e3 & op(e2, e1) = e3
% 242.62/49.18  | | | 
% 242.62/49.18  | | | REF_CLOSE: (5), (13), (14), (17) are inconsistent by sub-proof #1822.
% 242.62/49.18  | | | 
% 242.62/49.18  | | End of split
% 242.62/49.18  | | 
% 242.62/49.18  | Case 2:
% 242.62/49.18  | | 
% 242.62/49.18  | |   (18)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 242.62/49.18  | |           e3)
% 242.62/49.18  | | 
% 242.62/49.18  | | BETA: splitting (18) gives:
% 242.62/49.18  | | 
% 242.62/49.18  | | Case 1:
% 242.62/49.18  | | | 
% 242.62/49.18  | | |   (19)  all_58_8 = e3 & op(e1, e1) = e3
% 242.62/49.18  | | | 
% 242.62/49.18  | | | ALPHA: (19) implies:
% 242.62/49.18  | | |   (20)  op(e1, e1) = e3
% 242.62/49.18  | | | 
% 242.62/49.18  | | | REF_CLOSE: (6), (10), (14), (20) are inconsistent by sub-proof #2206.
% 242.62/49.18  | | | 
% 242.62/49.18  | | Case 2:
% 242.62/49.18  | | | 
% 242.62/49.18  | | |   (21)  all_58_14 = e3 & op(e0, e1) = e3
% 242.62/49.18  | | | 
% 242.62/49.18  | | | ALPHA: (21) implies:
% 242.62/49.18  | | |   (22)  all_58_14 = e3
% 242.62/49.18  | | | 
% 242.62/49.18  | | | COMBINE_EQS: (12), (22) imply:
% 242.62/49.18  | | |   (23)  e3 = e0
% 242.62/49.18  | | | 
% 242.62/49.18  | | | SIMP: (23) implies:
% 242.62/49.18  | | |   (24)  e3 = e0
% 242.62/49.18  | | | 
% 242.62/49.18  | | | COMBINE_EQS: (2), (24) imply:
% 242.62/49.18  | | |   (25)  all_58_6 = e0
% 242.62/49.18  | | | 
% 242.62/49.18  | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (14), (25) are inconsistent
% 242.62/49.18  | | |            by sub-proof #997.
% 242.62/49.18  | | | 
% 242.62/49.18  | | End of split
% 242.62/49.18  | | 
% 242.62/49.18  | End of split
% 242.62/49.18  | 
% 242.62/49.18  End of proof
% 242.62/49.18  
% 242.62/49.18  Sub-proof #834 shows that the following formulas are inconsistent:
% 242.62/49.18  ----------------------------------------------------------------
% 242.62/49.18    (1)   ~ (e3 = e0)
% 242.62/49.18    (2)  op(e1, e1) = e1
% 242.62/49.18    (3)   ~ (e2 = e0)
% 242.62/49.18    (4)  op(e1, e2) = all_52_6
% 242.62/49.18    (5)  all_58_7 = e2
% 242.62/49.18    (6)   ~ (e3 = e2)
% 242.62/49.18    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.62/49.18         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.62/49.18    (8)   ~ (all_52_6 = e3)
% 242.62/49.18    (9)  op(e1, e1) = e2
% 242.62/49.18    (10)  op(e0, e0) = e3
% 242.62/49.18    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.18    (12)   ~ (e1 = e0)
% 242.62/49.18    (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.62/49.18          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.62/49.18    (14)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.62/49.18  
% 242.62/49.18  Begin of proof
% 242.62/49.18  | 
% 242.62/49.18  | BETA: splitting (14) gives:
% 242.62/49.18  | 
% 242.62/49.18  | Case 1:
% 242.62/49.18  | | 
% 242.62/49.18  | |   (15)  all_58_11 = e2 & op(e1, e0) = e2
% 242.62/49.18  | | 
% 242.62/49.18  | | ALPHA: (15) implies:
% 242.62/49.18  | |   (16)  all_58_11 = e2
% 242.62/49.18  | | 
% 242.62/49.18  | | BETA: splitting (13) gives:
% 242.62/49.18  | | 
% 242.62/49.18  | | Case 1:
% 242.62/49.18  | | | 
% 242.62/49.18  | | |   (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 242.62/49.18  | | |           e0)
% 242.62/49.18  | | | 
% 242.62/49.18  | | | BETA: splitting (17) gives:
% 242.62/49.18  | | | 
% 242.62/49.18  | | | Case 1:
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | |   (18)  all_58_6 = e0 & op(e1, e3) = e0
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | | ALPHA: (18) implies:
% 242.62/49.18  | | | |   (19)  all_58_6 = e0
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (11), (16), (19) are
% 242.62/49.18  | | | |            inconsistent by sub-proof #997.
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | Case 2:
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | |   (20)  all_58_7 = e0 & op(e1, e2) = e0
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | | REF_CLOSE: (3), (5), (20) are inconsistent by sub-proof #2212.
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | End of split
% 242.62/49.18  | | | 
% 242.62/49.18  | | Case 2:
% 242.62/49.18  | | | 
% 242.62/49.18  | | |   (21)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.62/49.18  | | |           e0)
% 242.62/49.18  | | | 
% 242.62/49.18  | | | BETA: splitting (21) gives:
% 242.62/49.18  | | | 
% 242.62/49.18  | | | Case 1:
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | |   (22)  all_58_8 = e0 & op(e1, e1) = e0
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | | ALPHA: (22) implies:
% 242.62/49.18  | | | |   (23)  op(e1, e1) = e0
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | | REF_CLOSE: (2), (11), (12), (23) are inconsistent by sub-proof #2220.
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | Case 2:
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | |   (24)  all_58_11 = e0 & op(e1, e0) = e0
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | | ALPHA: (24) implies:
% 242.62/49.18  | | | |   (25)  all_58_11 = e0
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | | REF_CLOSE: (3), (16), (25) are inconsistent by sub-proof #2110.
% 242.62/49.18  | | | | 
% 242.62/49.18  | | | End of split
% 242.62/49.18  | | | 
% 242.62/49.18  | | End of split
% 242.62/49.18  | | 
% 242.62/49.18  | Case 2:
% 242.62/49.18  | | 
% 242.62/49.18  | |   (26)  all_58_15 = e2 & op(e0, e0) = e2
% 242.62/49.18  | | 
% 242.62/49.18  | | ALPHA: (26) implies:
% 242.62/49.18  | |   (27)  op(e0, e0) = e2
% 242.62/49.18  | | 
% 242.62/49.18  | | REF_CLOSE: (6), (10), (11), (27) are inconsistent by sub-proof #1388.
% 242.62/49.18  | | 
% 242.62/49.18  | End of split
% 242.62/49.18  | 
% 242.62/49.18  End of proof
% 242.62/49.18  
% 242.62/49.18  Sub-proof #835 shows that the following formulas are inconsistent:
% 242.62/49.18  ----------------------------------------------------------------
% 242.62/49.18    (1)  all_58_5 = e2
% 242.62/49.18    (2)  all_58_5 = e0
% 242.62/49.18    (3)   ~ (e2 = e0)
% 242.62/49.18  
% 242.62/49.18  Begin of proof
% 242.62/49.18  | 
% 242.62/49.18  | COMBINE_EQS: (1), (2) imply:
% 242.62/49.18  |   (4)  e2 = e0
% 242.62/49.18  | 
% 242.62/49.18  | SIMP: (4) implies:
% 242.62/49.18  |   (5)  e2 = e0
% 242.62/49.18  | 
% 242.62/49.18  | REDUCE: (3), (5) imply:
% 242.62/49.18  |   (6)  $false
% 242.62/49.18  | 
% 242.62/49.18  | CLOSE: (6) is inconsistent.
% 242.62/49.18  | 
% 242.62/49.18  End of proof
% 242.62/49.18  
% 242.62/49.18  Sub-proof #836 shows that the following formulas are inconsistent:
% 242.62/49.18  ----------------------------------------------------------------
% 242.62/49.18    (1)  all_58_5 = e0 & op(e2, e1) = e0
% 242.62/49.18    (2)  all_58_5 = e2
% 242.62/49.18    (3)   ~ (e2 = e0)
% 242.62/49.18  
% 242.62/49.18  Begin of proof
% 242.62/49.18  | 
% 242.62/49.18  | ALPHA: (1) implies:
% 242.62/49.18  |   (4)  all_58_5 = e0
% 242.62/49.18  | 
% 242.62/49.18  | COMBINE_EQS: (2), (4) imply:
% 242.62/49.18  |   (5)  e2 = e0
% 242.62/49.18  | 
% 242.62/49.18  | REDUCE: (3), (5) imply:
% 242.62/49.18  |   (6)  $false
% 242.62/49.18  | 
% 242.62/49.18  | CLOSE: (6) is inconsistent.
% 242.62/49.18  | 
% 242.62/49.18  End of proof
% 242.62/49.18  
% 242.62/49.18  Sub-proof #837 shows that the following formulas are inconsistent:
% 242.62/49.18  ----------------------------------------------------------------
% 242.62/49.18    (1)   ~ (all_52_6 = e1)
% 242.62/49.18    (2)   ~ (all_52_6 = e2)
% 242.62/49.18    (3)  all_54_11 = all_52_14
% 242.62/49.18    (4)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 242.62/49.18    (5)   ~ (all_52_14 = e2)
% 242.62/49.18    (6)  all_54_9 = all_52_6
% 242.62/49.18    (7)   ~ (all_52_14 = e1)
% 242.62/49.18    (8)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.62/49.18    (9)   ~ (all_52_6 = all_52_14)
% 242.62/49.18    (10)   ~ (all_52_14 = e3)
% 242.62/49.18    (11)   ~ (all_52_6 = e3)
% 242.62/49.18  
% 242.62/49.18  Begin of proof
% 242.62/49.18  | 
% 242.62/49.18  | BETA: splitting (8) gives:
% 242.62/49.18  | 
% 242.62/49.18  | Case 1:
% 242.62/49.18  | | 
% 242.62/49.18  | |   (12)  all_54_9 = e3
% 242.62/49.18  | | 
% 242.62/49.18  | | REF_CLOSE: (6), (11), (12) are inconsistent by sub-proof #1955.
% 242.62/49.18  | | 
% 242.62/49.18  | Case 2:
% 242.62/49.18  | | 
% 242.62/49.18  | |   (13)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.62/49.18  | | 
% 242.62/49.18  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (13) are
% 242.62/49.18  | |            inconsistent by sub-proof #1693.
% 242.62/49.18  | | 
% 242.62/49.18  | End of split
% 242.62/49.18  | 
% 242.62/49.18  End of proof
% 242.62/49.18  
% 242.62/49.18  Sub-proof #838 shows that the following formulas are inconsistent:
% 242.62/49.18  ----------------------------------------------------------------
% 242.62/49.19    (1)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.62/49.19             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.62/49.19           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 242.62/49.19           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.62/49.19           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 242.62/49.19           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.62/49.19           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.62/49.19    (2)  op(e3, e0) = all_52_12
% 242.62/49.19    (3)  all_56_31 = e3
% 242.62/49.19    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.19    (5)   ~ (all_52_12 = e3)
% 242.62/49.19  
% 242.62/49.19  Begin of proof
% 242.62/49.19  | 
% 242.62/49.19  | BETA: splitting (1) gives:
% 242.62/49.19  | 
% 242.62/49.19  | Case 1:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (6)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.62/49.19  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.62/49.19  | |        op(e1, e3) = e1
% 242.62/49.19  | | 
% 242.62/49.19  | | ALPHA: (6) implies:
% 242.62/49.19  | |   (7)   ~ (all_56_31 = e3)
% 242.62/49.19  | | 
% 242.62/49.19  | | REDUCE: (3), (7) imply:
% 242.62/49.19  | |   (8)  $false
% 242.62/49.19  | | 
% 242.62/49.19  | | CLOSE: (8) is inconsistent.
% 242.62/49.19  | | 
% 242.62/49.19  | Case 2:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (9)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 242.62/49.19  | |            = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 242.62/49.19  | |          e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.62/49.19  | |          (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.62/49.19  | |          (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.62/49.19  | | 
% 242.62/49.19  | | BETA: splitting (9) gives:
% 242.62/49.19  | | 
% 242.62/49.19  | | Case 1:
% 242.62/49.19  | | | 
% 242.62/49.19  | | |   (10)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.62/49.19  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.62/49.19  | | |         op(e3, e0) = e3 & op(e0, e3) = e3
% 242.62/49.19  | | | 
% 242.62/49.19  | | | ALPHA: (10) implies:
% 242.62/49.19  | | |   (11)  op(e3, e0) = e3
% 242.62/49.19  | | | 
% 242.62/49.19  | | | REF_CLOSE: (2), (4), (5), (11) are inconsistent by sub-proof #2179.
% 242.62/49.19  | | | 
% 242.62/49.19  | | Case 2:
% 242.62/49.19  | | | 
% 242.62/49.19  | | |   (12)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 242.62/49.19  | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.62/49.19  | | |         op(e3, e0) = e0 & op(e0, e3) = e0
% 242.62/49.19  | | | 
% 242.62/49.19  | | | ALPHA: (12) implies:
% 242.62/49.19  | | |   (13)   ~ (all_56_31 = e3)
% 242.62/49.19  | | | 
% 242.62/49.19  | | | REDUCE: (3), (13) imply:
% 242.62/49.19  | | |   (14)  $false
% 242.62/49.19  | | | 
% 242.62/49.19  | | | CLOSE: (14) is inconsistent.
% 242.62/49.19  | | | 
% 242.62/49.19  | | End of split
% 242.62/49.19  | | 
% 242.62/49.19  | End of split
% 242.62/49.19  | 
% 242.62/49.19  End of proof
% 242.62/49.19  
% 242.62/49.19  Sub-proof #839 shows that the following formulas are inconsistent:
% 242.62/49.19  ----------------------------------------------------------------
% 242.62/49.19    (1)   ~ (e3 = e0)
% 242.62/49.19    (2)   ~ (e2 = e0)
% 242.62/49.19    (3)  all_58_14 = e2
% 242.62/49.19    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.62/49.19         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.62/49.19    (5)   ~ (e3 = e2)
% 242.62/49.19    (6)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.62/49.19         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.62/49.19    (7)  all_58_5 = e1
% 242.62/49.19    (8)  e2 = e1
% 242.62/49.19    (9)   ~ (e1 = e0)
% 242.62/49.19    (10)  all_58_4 = e3
% 242.62/49.19    (11)   ~ (e2 = e1)
% 242.62/49.19  
% 242.62/49.19  Begin of proof
% 242.62/49.19  | 
% 242.62/49.19  | SIMP: (8) implies:
% 242.62/49.19  |   (12)  e2 = e1
% 242.62/49.19  | 
% 242.62/49.19  | COMBINE_EQS: (3), (12) imply:
% 242.62/49.19  |   (13)  all_58_14 = e1
% 242.62/49.19  | 
% 242.62/49.19  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (13) are
% 242.62/49.19  |            inconsistent by sub-proof #1481.
% 242.62/49.19  | 
% 242.62/49.19  End of proof
% 242.62/49.19  
% 242.62/49.19  Sub-proof #840 shows that the following formulas are inconsistent:
% 242.62/49.19  ----------------------------------------------------------------
% 242.62/49.19    (1)   ~ (e3 = e0)
% 242.62/49.19    (2)   ~ (e2 = e0)
% 242.62/49.19    (3)  all_58_2 = e2
% 242.62/49.19    (4)  all_58_3 = e3
% 242.62/49.19    (5)  op(e2, e0) = e2
% 242.62/49.19    (6)  all_58_5 = e1
% 242.62/49.19    (7)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.19         (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.19    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.19    (9)   ~ (e1 = e0)
% 242.62/49.19  
% 242.62/49.19  Begin of proof
% 242.62/49.19  | 
% 242.62/49.19  | BETA: splitting (7) gives:
% 242.62/49.19  | 
% 242.62/49.19  | Case 1:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (10)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 242.62/49.19  | |           e0)
% 242.62/49.19  | | 
% 242.62/49.19  | | REF_CLOSE: (1), (2), (3), (4), (10) are inconsistent by sub-proof #996.
% 242.62/49.19  | | 
% 242.62/49.19  | Case 2:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (11)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 242.62/49.19  | |           e0)
% 242.62/49.19  | | 
% 242.62/49.19  | | BETA: splitting (11) gives:
% 242.62/49.19  | | 
% 242.62/49.19  | | Case 1:
% 242.62/49.19  | | | 
% 242.62/49.19  | | |   (12)  all_58_5 = e0 & op(e2, e1) = e0
% 242.62/49.19  | | | 
% 242.62/49.19  | | | REF_CLOSE: (6), (9), (12) are inconsistent by sub-proof #1485.
% 242.62/49.19  | | | 
% 242.62/49.19  | | Case 2:
% 242.62/49.19  | | | 
% 242.62/49.19  | | |   (13)  all_58_10 = e0 & op(e2, e0) = e0
% 242.62/49.19  | | | 
% 242.62/49.19  | | | ALPHA: (13) implies:
% 242.62/49.19  | | |   (14)  op(e2, e0) = e0
% 242.62/49.19  | | | 
% 242.62/49.19  | | | REF_CLOSE: (2), (5), (8), (14) are inconsistent by sub-proof #2121.
% 242.62/49.19  | | | 
% 242.62/49.19  | | End of split
% 242.62/49.19  | | 
% 242.62/49.19  | End of split
% 242.62/49.19  | 
% 242.62/49.19  End of proof
% 242.62/49.19  
% 242.62/49.19  Sub-proof #841 shows that the following formulas are inconsistent:
% 242.62/49.19  ----------------------------------------------------------------
% 242.62/49.19    (1)   ~ (e3 = e0)
% 242.62/49.19    (2)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.62/49.19    (3)  op(e0, e1) = all_52_11
% 242.62/49.19    (4)   ~ (e2 = e0)
% 242.62/49.19    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.62/49.19         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.19    (6)   ~ (e3 = e1)
% 242.62/49.19    (7)  all_58_3 = e3
% 242.62/49.19    (8)  all_58_11 = e3
% 242.62/49.19    (9)   ~ (all_52_11 = e3)
% 242.62/49.19    (10)   ~ (e3 = e2)
% 242.62/49.19    (11)  all_58_15 = e1
% 242.62/49.19    (12)  op(e3, e0) = e2
% 242.62/49.19    (13)  all_58_5 = e1
% 242.62/49.19    (14)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.62/49.19          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.62/49.19    (15)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.62/49.19          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.62/49.19    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.19    (17)   ~ (e1 = e0)
% 242.62/49.19    (18)   ~ (e2 = e1)
% 242.62/49.19  
% 242.62/49.19  Begin of proof
% 242.62/49.19  | 
% 242.62/49.19  | BETA: splitting (2) gives:
% 242.62/49.19  | 
% 242.62/49.19  | Case 1:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (19)  all_58_14 = e3 & op(e0, e1) = e3
% 242.62/49.19  | | 
% 242.62/49.19  | | REF_CLOSE: (3), (9), (16), (19) are inconsistent by sub-proof #1647.
% 242.62/49.19  | | 
% 242.62/49.19  | Case 2:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (20)  all_58_15 = e3 & op(e0, e0) = e3
% 242.62/49.19  | | 
% 242.62/49.19  | | ALPHA: (20) implies:
% 242.62/49.19  | |   (21)  all_58_15 = e3
% 242.62/49.19  | | 
% 242.62/49.19  | | COMBINE_EQS: (11), (21) imply:
% 242.62/49.19  | |   (22)  e3 = e1
% 242.62/49.19  | | 
% 242.62/49.19  | | SIMP: (22) implies:
% 242.62/49.19  | |   (23)  e3 = e1
% 242.62/49.19  | | 
% 242.62/49.19  | | COMBINE_EQS: (8), (23) imply:
% 242.62/49.19  | |   (24)  all_58_11 = e1
% 242.62/49.19  | | 
% 242.62/49.19  | | REF_CLOSE: (1), (4), (5), (6), (7), (10), (11), (12), (13), (14), (15),
% 242.62/49.19  | |            (16), (17), (18), (24) are inconsistent by sub-proof #914.
% 242.62/49.19  | | 
% 242.62/49.19  | End of split
% 242.62/49.19  | 
% 242.62/49.19  End of proof
% 242.62/49.19  
% 242.62/49.19  Sub-proof #842 shows that the following formulas are inconsistent:
% 242.62/49.19  ----------------------------------------------------------------
% 242.62/49.19    (1)   ~ (e3 = e0)
% 242.62/49.19    (2)   ~ (e2 = e0)
% 242.62/49.19    (3)  all_58_11 = e3
% 242.62/49.19    (4)  all_58_11 = e2 & op(e1, e0) = e2
% 242.62/49.19    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.62/49.19             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.62/49.19               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.62/49.19               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.62/49.19    (6)  op(e2, e1) = all_52_9
% 242.62/49.19    (7)   ~ (e3 = e2)
% 242.62/49.19    (8)  all_58_15 = e1
% 242.62/49.19    (9)  all_58_12 = e3
% 242.62/49.19    (10)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.62/49.19          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.62/49.19    (11)   ~ (all_52_9 = e3)
% 242.62/49.19    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.19    (13)  op(e1, e1) = e0
% 242.62/49.19    (14)   ~ (e1 = e0)
% 242.62/49.19    (15)  all_58_4 = e3
% 242.62/49.19    (16)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.62/49.19          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.62/49.19            e2)
% 242.62/49.19    (17)   ~ (e2 = e1)
% 242.62/49.19  
% 242.62/49.19  Begin of proof
% 242.62/49.19  | 
% 242.62/49.19  | ALPHA: (4) implies:
% 242.62/49.19  |   (18)  all_58_11 = e2
% 242.62/49.19  | 
% 242.62/49.19  | COMBINE_EQS: (3), (18) imply:
% 242.62/49.19  |   (19)  e3 = e2
% 242.62/49.19  | 
% 242.62/49.19  | COMBINE_EQS: (15), (19) imply:
% 242.62/49.19  |   (20)  all_58_4 = e2
% 242.62/49.19  | 
% 242.62/49.19  | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 242.62/49.19  |            (16), (17), (20) are inconsistent by sub-proof #843.
% 242.62/49.19  | 
% 242.62/49.19  End of proof
% 242.62/49.19  
% 242.62/49.19  Sub-proof #843 shows that the following formulas are inconsistent:
% 242.62/49.19  ----------------------------------------------------------------
% 242.62/49.19    (1)   ~ (e3 = e0)
% 242.62/49.19    (2)   ~ (e2 = e0)
% 242.62/49.19    (3)  all_58_4 = e2
% 242.62/49.19    (4)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.62/49.19             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.62/49.19               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.62/49.19               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.62/49.19    (5)  op(e2, e1) = all_52_9
% 242.62/49.19    (6)   ~ (e3 = e2)
% 242.62/49.19    (7)  all_58_15 = e1
% 242.62/49.19    (8)  all_58_12 = e3
% 242.62/49.19    (9)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.62/49.19         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.62/49.19    (10)   ~ (all_52_9 = e3)
% 242.62/49.19    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.19    (12)  op(e1, e1) = e0
% 242.62/49.19    (13)   ~ (e1 = e0)
% 242.62/49.19    (14)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.62/49.19          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.62/49.19            e2)
% 242.62/49.19    (15)   ~ (e2 = e1)
% 242.62/49.19  
% 242.62/49.19  Begin of proof
% 242.62/49.19  | 
% 242.62/49.19  | BETA: splitting (9) gives:
% 242.62/49.19  | 
% 242.62/49.19  | Case 1:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (16)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 242.62/49.19  | |           e3)
% 242.62/49.19  | | 
% 242.62/49.19  | | REF_CLOSE: (3), (5), (6), (10), (11), (16) are inconsistent by sub-proof
% 242.62/49.19  | |            #1494.
% 242.62/49.19  | | 
% 242.62/49.19  | Case 2:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (17)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 242.62/49.19  | |           e3)
% 242.62/49.19  | | 
% 242.62/49.19  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (11), (12), (13), (14), (15), (17)
% 242.62/49.19  | |            are inconsistent by sub-proof #844.
% 242.62/49.19  | | 
% 242.62/49.19  | End of split
% 242.62/49.19  | 
% 242.62/49.19  End of proof
% 242.62/49.19  
% 242.62/49.19  Sub-proof #844 shows that the following formulas are inconsistent:
% 242.62/49.19  ----------------------------------------------------------------
% 242.62/49.19    (1)   ~ (e3 = e0)
% 242.62/49.19    (2)   ~ (e2 = e0)
% 242.62/49.19    (3)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.62/49.19    (4)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.62/49.19             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.62/49.19               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.62/49.19               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.62/49.19    (5)   ~ (e3 = e2)
% 242.62/49.19    (6)  all_58_15 = e1
% 242.62/49.19    (7)  all_58_12 = e3
% 242.62/49.19    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.19    (9)  op(e1, e1) = e0
% 242.62/49.19    (10)   ~ (e1 = e0)
% 242.62/49.19    (11)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.62/49.19          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.62/49.19            e2)
% 242.62/49.19    (12)   ~ (e2 = e1)
% 242.62/49.19  
% 242.62/49.19  Begin of proof
% 242.62/49.19  | 
% 242.62/49.19  | BETA: splitting (3) gives:
% 242.62/49.19  | 
% 242.62/49.19  | Case 1:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (13)  all_58_8 = e3 & op(e1, e1) = e3
% 242.62/49.19  | | 
% 242.62/49.19  | | REF_CLOSE: (1), (8), (9), (13) are inconsistent by sub-proof #2018.
% 242.62/49.19  | | 
% 242.62/49.19  | Case 2:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (14)  all_58_14 = e3 & op(e0, e1) = e3
% 242.62/49.19  | | 
% 242.62/49.19  | | ALPHA: (14) implies:
% 242.62/49.19  | |   (15)  all_58_14 = e3
% 242.62/49.19  | | 
% 242.62/49.19  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (11), (12), (15) are
% 242.62/49.19  | |            inconsistent by sub-proof #1863.
% 242.62/49.19  | | 
% 242.62/49.19  | End of split
% 242.62/49.19  | 
% 242.62/49.19  End of proof
% 242.62/49.19  
% 242.62/49.19  Sub-proof #845 shows that the following formulas are inconsistent:
% 242.62/49.19  ----------------------------------------------------------------
% 242.62/49.19    (1)   ~ (e2 = e0)
% 242.62/49.19    (2)  op(e2, e1) = all_52_9
% 242.62/49.19    (3)  op(e2, e0) = e0
% 242.62/49.19    (4)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.62/49.19    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.19    (6)   ~ (all_52_9 = e2)
% 242.62/49.19  
% 242.62/49.19  Begin of proof
% 242.62/49.19  | 
% 242.62/49.19  | BETA: splitting (4) gives:
% 242.62/49.19  | 
% 242.62/49.19  | Case 1:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (7)  all_58_5 = e2 & op(e2, e1) = e2
% 242.62/49.19  | | 
% 242.62/49.19  | | ALPHA: (7) implies:
% 242.62/49.19  | |   (8)  op(e2, e1) = e2
% 242.62/49.19  | | 
% 242.62/49.19  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2328.
% 242.62/49.19  | | 
% 242.62/49.19  | Case 2:
% 242.62/49.19  | | 
% 242.62/49.19  | |   (9)  all_58_10 = e2 & op(e2, e0) = e2
% 242.62/49.19  | | 
% 242.62/49.19  | | ALPHA: (9) implies:
% 242.62/49.19  | |   (10)  op(e2, e0) = e2
% 242.62/49.19  | | 
% 242.62/49.19  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2121.
% 242.62/49.19  | | 
% 242.62/49.19  | End of split
% 242.62/49.19  | 
% 242.62/49.19  End of proof
% 242.62/49.19  
% 242.62/49.19  Sub-proof #846 shows that the following formulas are inconsistent:
% 242.62/49.19  ----------------------------------------------------------------
% 242.62/49.19    (1)   ~ (e3 = e0)
% 242.62/49.19    (2)  op(e0, e1) = all_52_11
% 242.62/49.19    (3)   ~ (e2 = e0)
% 242.62/49.19    (4)  all_58_4 = e2
% 242.62/49.19    (5)   ~ (e3 = e1)
% 242.62/49.19    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.62/49.19         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.62/49.19    (7)  all_58_2 = e2
% 242.62/49.19    (8)  all_58_3 = e3
% 242.62/49.19    (9)  all_58_12 = e1
% 242.62/49.19    (10)   ~ (all_52_11 = e3)
% 242.62/49.19    (11)  op(e2, e1) = all_52_9
% 242.62/49.19    (12)   ~ (e3 = e2)
% 242.62/49.19    (13)  op(e2, e0) = e0
% 242.62/49.19    (14)  all_58_15 = e1
% 242.62/49.19    (15)  op(e0, e2) = e0
% 242.62/49.19    (16)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.62/49.19          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.62/49.19    (17)   ~ (all_52_9 = e3)
% 242.62/49.20    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.20    (19)   ~ (e1 = e0)
% 242.62/49.20    (20)  op(e2, e0) = all_52_13
% 242.62/49.20    (21)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.62/49.20          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.62/49.20            e2)
% 242.62/49.20    (22)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.62/49.20          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.62/49.20    (23)   ~ (e2 = e1)
% 242.62/49.20  
% 242.62/49.20  Begin of proof
% 242.62/49.20  | 
% 242.62/49.20  | BETA: splitting (21) gives:
% 242.62/49.20  | 
% 242.62/49.20  | Case 1:
% 242.62/49.20  | | 
% 242.62/49.20  | |   (24)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 242.62/49.20  | |           e2)
% 242.62/49.20  | | 
% 242.62/49.20  | | REF_CLOSE: (3), (9), (15), (18), (23), (24) are inconsistent by sub-proof
% 242.62/49.20  | |            #849.
% 242.62/49.20  | | 
% 242.62/49.20  | Case 2:
% 242.62/49.20  | | 
% 242.62/49.20  | |   (25)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.62/49.20  | |           e2)
% 242.62/49.20  | | 
% 242.62/49.20  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 242.62/49.20  | |            (14), (16), (17), (18), (19), (20), (22), (23), (25) are
% 242.62/49.20  | |            inconsistent by sub-proof #847.
% 242.62/49.20  | | 
% 242.62/49.20  | End of split
% 242.62/49.20  | 
% 242.62/49.20  End of proof
% 242.62/49.20  
% 242.62/49.20  Sub-proof #847 shows that the following formulas are inconsistent:
% 242.62/49.20  ----------------------------------------------------------------
% 242.62/49.20    (1)   ~ (e3 = e0)
% 242.62/49.20    (2)  op(e0, e1) = all_52_11
% 242.62/49.20    (3)   ~ (e2 = e0)
% 242.62/49.20    (4)  all_58_4 = e2
% 242.62/49.20    (5)   ~ (e3 = e1)
% 242.62/49.20    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.62/49.20         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.62/49.20    (7)  all_58_2 = e2
% 242.62/49.20    (8)  all_58_3 = e3
% 242.62/49.20    (9)   ~ (all_52_11 = e3)
% 242.62/49.20    (10)  op(e2, e1) = all_52_9
% 242.62/49.20    (11)   ~ (e3 = e2)
% 242.62/49.20    (12)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.62/49.20    (13)  op(e2, e0) = e0
% 242.62/49.20    (14)  all_58_15 = e1
% 242.62/49.20    (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.62/49.20          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.62/49.20    (16)   ~ (all_52_9 = e3)
% 242.62/49.20    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.62/49.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.62/49.20    (18)   ~ (e1 = e0)
% 242.62/49.20    (19)  op(e2, e0) = all_52_13
% 242.62/49.20    (20)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.62/49.20          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.62/49.20    (21)   ~ (e2 = e1)
% 242.62/49.20  
% 242.62/49.20  Begin of proof
% 242.62/49.20  | 
% 242.62/49.20  | BETA: splitting (12) gives:
% 242.70/49.20  | 
% 242.70/49.20  | Case 1:
% 242.70/49.20  | | 
% 242.70/49.20  | |   (22)  all_58_14 = e2 & op(e0, e1) = e2
% 242.70/49.20  | | 
% 242.70/49.20  | | ALPHA: (22) implies:
% 242.70/49.20  | |   (23)  all_58_14 = e2
% 242.70/49.20  | | 
% 242.70/49.20  | | BETA: splitting (20) gives:
% 242.70/49.20  | | 
% 242.70/49.20  | | Case 1:
% 242.70/49.20  | | | 
% 242.70/49.20  | | |   (24)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 242.70/49.20  | | |           e1)
% 242.70/49.20  | | | 
% 242.70/49.20  | | | BETA: splitting (24) gives:
% 242.70/49.20  | | | 
% 242.70/49.20  | | | Case 1:
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | |   (25)  all_58_2 = e1 & op(e2, e3) = e1
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | | REF_CLOSE: (7), (21), (25) are inconsistent by sub-proof #852.
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | Case 2:
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | |   (26)  all_58_3 = e1 & op(e2, e2) = e1
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | | REF_CLOSE: (5), (8), (26) are inconsistent by sub-proof #2197.
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | End of split
% 242.70/49.20  | | | 
% 242.70/49.20  | | Case 2:
% 242.70/49.20  | | | 
% 242.70/49.20  | | |   (27)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 242.70/49.20  | | |           e1)
% 242.70/49.20  | | | 
% 242.70/49.20  | | | BETA: splitting (27) gives:
% 242.70/49.20  | | | 
% 242.70/49.20  | | | Case 1:
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | |   (28)  all_58_5 = e1 & op(e2, e1) = e1
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | | ALPHA: (28) implies:
% 242.70/49.20  | | | |   (29)  all_58_5 = e1
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | | BETA: splitting (15) gives:
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | | Case 1:
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | |   (30)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2,
% 242.70/49.20  | | | | |             e1) = e3)
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | | REF_CLOSE: (4), (10), (11), (16), (17), (30) are inconsistent by
% 242.70/49.20  | | | | |            sub-proof #1494.
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | Case 2:
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | |   (31)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0,
% 242.70/49.20  | | | | |             e1) = e3)
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | | BETA: splitting (31) gives:
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | | Case 1:
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | |   (32)  all_58_8 = e3 & op(e1, e1) = e3
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | | ALPHA: (32) implies:
% 242.70/49.20  | | | | | |   (33)  all_58_8 = e3
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | | REF_CLOSE: (1), (3), (4), (6), (18), (23), (29), (33) are
% 242.70/49.20  | | | | | |            inconsistent by sub-proof #848.
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | Case 2:
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | |   (34)  all_58_14 = e3 & op(e0, e1) = e3
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | | REF_CLOSE: (2), (9), (17), (34) are inconsistent by sub-proof #1647.
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | End of split
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | End of split
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | Case 2:
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | |   (35)  all_58_10 = e1 & op(e2, e0) = e1
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | | ALPHA: (35) implies:
% 242.70/49.20  | | | |   (36)  op(e2, e0) = e1
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | | REF_CLOSE: (13), (17), (18), (19), (36) are inconsistent by sub-proof
% 242.70/49.20  | | | |            #1778.
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | End of split
% 242.70/49.20  | | | 
% 242.70/49.20  | | End of split
% 242.70/49.20  | | 
% 242.70/49.20  | Case 2:
% 242.70/49.20  | | 
% 242.70/49.20  | |   (37)  all_58_15 = e2 & op(e0, e0) = e2
% 242.70/49.20  | | 
% 242.70/49.20  | | ALPHA: (37) implies:
% 242.70/49.20  | |   (38)  all_58_15 = e2
% 242.70/49.20  | | 
% 242.70/49.20  | | REF_CLOSE: (14), (21), (38) are inconsistent by sub-proof #2231.
% 242.70/49.20  | | 
% 242.70/49.20  | End of split
% 242.70/49.20  | 
% 242.70/49.20  End of proof
% 242.70/49.20  
% 242.70/49.20  Sub-proof #848 shows that the following formulas are inconsistent:
% 242.70/49.20  ----------------------------------------------------------------
% 242.70/49.20    (1)   ~ (e3 = e0)
% 242.70/49.20    (2)   ~ (e2 = e0)
% 242.70/49.20    (3)  all_58_4 = e2
% 242.70/49.20    (4)  all_58_14 = e2
% 242.70/49.20    (5)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.70/49.20         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.70/49.20    (6)  all_58_5 = e1
% 242.70/49.20    (7)  all_58_8 = e3
% 242.70/49.20    (8)   ~ (e1 = e0)
% 242.70/49.20  
% 242.70/49.20  Begin of proof
% 242.70/49.20  | 
% 242.70/49.20  | BETA: splitting (5) gives:
% 242.70/49.20  | 
% 242.70/49.20  | Case 1:
% 242.70/49.20  | | 
% 242.70/49.20  | |   (9)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 242.70/49.20  | | 
% 242.70/49.20  | | BETA: splitting (9) gives:
% 242.70/49.20  | | 
% 242.70/49.20  | | Case 1:
% 242.70/49.20  | | | 
% 242.70/49.20  | | |   (10)  all_58_4 = e0 & op(e3, e1) = e0
% 242.70/49.20  | | | 
% 242.70/49.20  | | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #2170.
% 242.70/49.20  | | | 
% 242.70/49.20  | | Case 2:
% 242.70/49.20  | | | 
% 242.70/49.20  | | |   (11)  all_58_5 = e0 & op(e2, e1) = e0
% 242.70/49.20  | | | 
% 242.70/49.20  | | | REF_CLOSE: (6), (8), (11) are inconsistent by sub-proof #1485.
% 242.70/49.20  | | | 
% 242.70/49.20  | | End of split
% 242.70/49.20  | | 
% 242.70/49.20  | Case 2:
% 242.70/49.20  | | 
% 242.70/49.20  | |   (12)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 242.70/49.20  | |           e0)
% 242.70/49.20  | | 
% 242.70/49.20  | | BETA: splitting (12) gives:
% 242.70/49.20  | | 
% 242.70/49.20  | | Case 1:
% 242.70/49.20  | | | 
% 242.70/49.20  | | |   (13)  all_58_8 = e0 & op(e1, e1) = e0
% 242.70/49.20  | | | 
% 242.70/49.20  | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #1421.
% 242.70/49.20  | | | 
% 242.70/49.20  | | Case 2:
% 242.70/49.20  | | | 
% 242.70/49.20  | | |   (14)  all_58_14 = e0 & op(e0, e1) = e0
% 242.70/49.20  | | | 
% 242.70/49.20  | | | ALPHA: (14) implies:
% 242.70/49.20  | | |   (15)  all_58_14 = e0
% 242.70/49.20  | | | 
% 242.70/49.20  | | | REF_CLOSE: (2), (4), (15) are inconsistent by sub-proof #2114.
% 242.70/49.20  | | | 
% 242.70/49.20  | | End of split
% 242.70/49.20  | | 
% 242.70/49.20  | End of split
% 242.70/49.20  | 
% 242.70/49.20  End of proof
% 242.70/49.20  
% 242.70/49.20  Sub-proof #849 shows that the following formulas are inconsistent:
% 242.70/49.20  ----------------------------------------------------------------
% 242.70/49.20    (1)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.20    (2)   ~ (e2 = e0)
% 242.70/49.20    (3)  all_58_12 = e1
% 242.70/49.20    (4)  op(e0, e2) = e0
% 242.70/49.20    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.20    (6)   ~ (e2 = e1)
% 242.70/49.20  
% 242.70/49.20  Begin of proof
% 242.70/49.20  | 
% 242.70/49.20  | BETA: splitting (1) gives:
% 242.70/49.20  | 
% 242.70/49.20  | Case 1:
% 242.70/49.20  | | 
% 242.70/49.20  | |   (7)  all_58_12 = e2 & op(e0, e3) = e2
% 242.70/49.20  | | 
% 242.70/49.20  | | REF_CLOSE: (3), (6), (7) are inconsistent by sub-proof #1302.
% 242.70/49.20  | | 
% 242.70/49.20  | Case 2:
% 242.70/49.20  | | 
% 242.70/49.20  | |   (8)  all_58_13 = e2 & op(e0, e2) = e2
% 242.70/49.20  | | 
% 242.70/49.20  | | ALPHA: (8) implies:
% 242.70/49.20  | |   (9)  op(e0, e2) = e2
% 242.70/49.20  | | 
% 242.70/49.20  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2132.
% 242.70/49.20  | | 
% 242.70/49.20  | End of split
% 242.70/49.20  | 
% 242.70/49.20  End of proof
% 242.70/49.20  
% 242.70/49.20  Sub-proof #850 shows that the following formulas are inconsistent:
% 242.70/49.20  ----------------------------------------------------------------
% 242.70/49.20    (1)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 242.70/49.20    (2)  op(e1, e2) = all_52_6
% 242.70/49.20    (3)   ~ (e3 = e1)
% 242.70/49.20    (4)  all_58_6 = e1
% 242.70/49.20    (5)   ~ (all_52_6 = e3)
% 242.70/49.20    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.20  
% 242.70/49.20  Begin of proof
% 242.70/49.20  | 
% 242.70/49.20  | BETA: splitting (1) gives:
% 242.70/49.20  | 
% 242.70/49.20  | Case 1:
% 242.70/49.20  | | 
% 242.70/49.20  | |   (7)  all_58_6 = e3 & op(e1, e3) = e3
% 242.70/49.20  | | 
% 242.70/49.20  | | ALPHA: (7) implies:
% 242.70/49.20  | |   (8)  all_58_6 = e3
% 242.70/49.20  | | 
% 242.70/49.20  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #1758.
% 242.70/49.20  | | 
% 242.70/49.20  | Case 2:
% 242.70/49.20  | | 
% 242.70/49.20  | |   (9)  all_58_7 = e3 & op(e1, e2) = e3
% 242.70/49.20  | | 
% 242.70/49.20  | | ALPHA: (9) implies:
% 242.70/49.20  | |   (10)  op(e1, e2) = e3
% 242.70/49.20  | | 
% 242.70/49.20  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #2191.
% 242.70/49.20  | | 
% 242.70/49.20  | End of split
% 242.70/49.20  | 
% 242.70/49.20  End of proof
% 242.70/49.20  
% 242.70/49.20  Sub-proof #851 shows that the following formulas are inconsistent:
% 242.70/49.20  ----------------------------------------------------------------
% 242.70/49.20    (1)  all_58_2 = e2
% 242.70/49.20    (2)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 242.70/49.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.20    (4)   ~ (e1 = e0)
% 242.70/49.20    (5)  op(e3, e3) = e0
% 242.70/49.20    (6)   ~ (e2 = e1)
% 242.70/49.20  
% 242.70/49.20  Begin of proof
% 242.70/49.20  | 
% 242.70/49.20  | BETA: splitting (2) gives:
% 242.70/49.20  | 
% 242.70/49.20  | Case 1:
% 242.70/49.20  | | 
% 242.70/49.20  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 242.70/49.20  | | 
% 242.70/49.20  | | ALPHA: (7) implies:
% 242.70/49.20  | |   (8)  op(e3, e3) = e1
% 242.70/49.20  | | 
% 242.70/49.20  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1828.
% 242.70/49.20  | | 
% 242.70/49.20  | Case 2:
% 242.70/49.20  | | 
% 242.70/49.20  | |   (9)  all_58_2 = e1 & op(e2, e3) = e1
% 242.70/49.20  | | 
% 242.70/49.20  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #852.
% 242.70/49.20  | | 
% 242.70/49.20  | End of split
% 242.70/49.20  | 
% 242.70/49.20  End of proof
% 242.70/49.20  
% 242.70/49.20  Sub-proof #852 shows that the following formulas are inconsistent:
% 242.70/49.20  ----------------------------------------------------------------
% 242.70/49.20    (1)  all_58_2 = e1 & op(e2, e3) = e1
% 242.70/49.20    (2)  all_58_2 = e2
% 242.70/49.20    (3)   ~ (e2 = e1)
% 242.70/49.20  
% 242.70/49.20  Begin of proof
% 242.70/49.20  | 
% 242.70/49.20  | ALPHA: (1) implies:
% 242.70/49.20  |   (4)  all_58_2 = e1
% 242.70/49.20  | 
% 242.70/49.20  | COMBINE_EQS: (2), (4) imply:
% 242.70/49.20  |   (5)  e2 = e1
% 242.70/49.20  | 
% 242.70/49.20  | REDUCE: (3), (5) imply:
% 242.70/49.20  |   (6)  $false
% 242.70/49.20  | 
% 242.70/49.20  | CLOSE: (6) is inconsistent.
% 242.70/49.20  | 
% 242.70/49.20  End of proof
% 242.70/49.20  
% 242.70/49.20  Sub-proof #853 shows that the following formulas are inconsistent:
% 242.70/49.20  ----------------------------------------------------------------
% 242.70/49.20    (1)   ~ (all_52_3 = e0)
% 242.70/49.20    (2)  op(e2, e2) = e3
% 242.70/49.20    (3)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 242.70/49.20           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.70/49.20           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 242.70/49.20           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 242.70/49.20           & $i(all_56_23))
% 242.70/49.20    (4)  op(e0, e1) = e3
% 242.70/49.20    (5)  op(e1, e0) = all_52_14
% 242.70/49.20    (6)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.70/49.20    (7)   ~ (all_52_8 = e0)
% 242.70/49.20    (8)  op(e0, e3) = all_52_3
% 242.70/49.20    (9)   ~ (all_52_6 = e0)
% 242.70/49.20    (10)  all_54_11 = all_52_14
% 242.70/49.20    (11)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 242.70/49.20    (12)  op(e2, e1) = e2
% 242.70/49.20    (13)  all_54_2 = all_52_8
% 242.70/49.20    (14)  all_56_21 = e0
% 242.70/49.20    (15)  op(e3, e1) = all_52_8
% 242.70/49.20    (16)  all_54_9 = all_52_6
% 242.70/49.20    (17)   ~ (all_52_14 = e1)
% 242.70/49.20    (18)   ~ (all_52_14 = e0)
% 242.70/49.20    (19)  op(e2, e3) = e1
% 242.70/49.20    (20)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.70/49.20    (21)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.70/49.20    (22)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.70/49.20            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.70/49.20              e3) = all_42_1 & $i(all_42_1))
% 242.70/49.20    (23)   ~ (all_52_6 = all_52_14)
% 242.70/49.20    (24)   ~ (all_52_6 = e3)
% 242.70/49.20    (25)  all_54_1 = all_52_4
% 242.70/49.20    (26)   ~ (all_52_4 = e3)
% 242.70/49.20    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.20    (28)  op(e2, e3) = all_8_1
% 242.70/49.20    (29)   ~ (all_52_4 = all_52_8)
% 242.70/49.20    (30)   ~ (all_52_4 = all_52_6)
% 242.70/49.20    (31)   ~ (all_52_4 = e0)
% 242.70/49.20    (32)   ~ (all_52_8 = e3)
% 242.70/49.20  
% 242.70/49.20  Begin of proof
% 242.70/49.20  | 
% 242.70/49.20  | BETA: splitting (11) gives:
% 242.70/49.20  | 
% 242.70/49.20  | Case 1:
% 242.70/49.20  | | 
% 242.70/49.20  | |   (33)  all_54_11 = e2
% 242.70/49.20  | | 
% 242.70/49.20  | | COMBINE_EQS: (10), (33) imply:
% 242.70/49.20  | |   (34)  all_52_14 = e2
% 242.70/49.20  | | 
% 242.70/49.20  | | SIMP: (34) implies:
% 242.70/49.20  | |   (35)  all_52_14 = e2
% 242.70/49.20  | | 
% 242.70/49.20  | | REDUCE: (23), (35) imply:
% 242.70/49.20  | |   (36)   ~ (all_52_6 = e2)
% 242.70/49.20  | | 
% 242.70/49.20  | | BETA: splitting (20) gives:
% 242.70/49.20  | | 
% 242.70/49.20  | | Case 1:
% 242.70/49.20  | | | 
% 242.70/49.20  | | |   (37)  all_54_9 = e3
% 242.70/49.20  | | | 
% 242.70/49.20  | | | COMBINE_EQS: (16), (37) imply:
% 242.70/49.20  | | |   (38)  all_52_6 = e3
% 242.70/49.20  | | | 
% 242.70/49.20  | | | REDUCE: (24), (38) imply:
% 242.70/49.20  | | |   (39)  $false
% 242.70/49.20  | | | 
% 242.70/49.20  | | | CLOSE: (39) is inconsistent.
% 242.70/49.20  | | | 
% 242.70/49.20  | | Case 2:
% 242.70/49.20  | | | 
% 242.70/49.20  | | |   (40)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.70/49.20  | | | 
% 242.70/49.20  | | | BETA: splitting (40) gives:
% 242.70/49.20  | | | 
% 242.70/49.20  | | | Case 1:
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | |   (41)  all_54_9 = e2
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | | REF_CLOSE: (16), (36), (41) are inconsistent by sub-proof #1954.
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | Case 2:
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | |   (42)  all_54_9 = e1 | all_54_9 = e0
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | | BETA: splitting (42) gives:
% 242.70/49.20  | | | | 
% 242.70/49.20  | | | | Case 1:
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | |   (43)  all_54_9 = e1
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | | COMBINE_EQS: (16), (43) imply:
% 242.70/49.20  | | | | |   (44)  all_52_6 = e1
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | | SIMP: (44) implies:
% 242.70/49.20  | | | | |   (45)  all_52_6 = e1
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | | REDUCE: (30), (45) imply:
% 242.70/49.20  | | | | |   (46)   ~ (all_52_4 = e1)
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | | BETA: splitting (6) gives:
% 242.70/49.20  | | | | | 
% 242.70/49.20  | | | | | Case 1:
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | |   (47)  all_54_1 = e3
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | | REF_CLOSE: (25), (26), (47) are inconsistent by sub-proof #1930.
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | Case 2:
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | |   (48)   ~ (all_54_1 = e3)
% 242.70/49.20  | | | | | |   (49)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | | BETA: splitting (49) gives:
% 242.70/49.20  | | | | | | 
% 242.70/49.20  | | | | | | Case 1:
% 242.70/49.20  | | | | | | | 
% 242.70/49.20  | | | | | | |   (50)  all_54_1 = e2
% 242.70/49.20  | | | | | | | 
% 242.70/49.20  | | | | | | | COMBINE_EQS: (25), (50) imply:
% 242.70/49.20  | | | | | | |   (51)  all_52_4 = e2
% 242.70/49.20  | | | | | | | 
% 242.70/49.20  | | | | | | | SIMP: (51) implies:
% 242.70/49.20  | | | | | | |   (52)  all_52_4 = e2
% 242.70/49.20  | | | | | | | 
% 242.70/49.20  | | | | | | | REDUCE: (29), (52) imply:
% 242.70/49.20  | | | | | | |   (53)   ~ (all_52_8 = e2)
% 242.70/49.20  | | | | | | | 
% 242.70/49.20  | | | | | | | SIMP: (53) implies:
% 242.70/49.20  | | | | | | |   (54)   ~ (all_52_8 = e2)
% 242.70/49.20  | | | | | | | 
% 242.70/49.20  | | | | | | | REDUCE: (26), (52) imply:
% 242.70/49.20  | | | | | | |   (55)   ~ (e3 = e2)
% 242.70/49.20  | | | | | | | 
% 242.70/49.20  | | | | | | | SIMP: (55) implies:
% 242.70/49.20  | | | | | | |   (56)   ~ (e3 = e2)
% 242.70/49.20  | | | | | | | 
% 242.70/49.20  | | | | | | | BETA: splitting (21) gives:
% 242.70/49.20  | | | | | | | 
% 242.70/49.20  | | | | | | | Case 1:
% 242.70/49.20  | | | | | | | | 
% 242.70/49.20  | | | | | | | |   (57)  all_54_2 = e3
% 242.70/49.20  | | | | | | | | 
% 242.70/49.20  | | | | | | | | REF_CLOSE: (13), (32), (57) are inconsistent by sub-proof #1987.
% 242.70/49.20  | | | | | | | | 
% 242.70/49.20  | | | | | | | Case 2:
% 242.70/49.20  | | | | | | | | 
% 242.70/49.21  | | | | | | | |   (58)   ~ (all_54_2 = e3)
% 242.70/49.21  | | | | | | | |   (59)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.70/49.21  | | | | | | | | 
% 242.70/49.21  | | | | | | | | BETA: splitting (3) gives:
% 242.70/49.21  | | | | | | | | 
% 242.70/49.21  | | | | | | | | Case 1:
% 242.70/49.21  | | | | | | | | | 
% 242.70/49.21  | | | | | | | | |   (60)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1)
% 242.70/49.21  | | | | | | | | |           = all_56_17 & $i(all_56_17)) | (all_56_18 = e2 &
% 242.70/49.21  | | | | | | | | |           op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 242.70/49.21  | | | | | | | | |           $i(all_56_19))
% 242.70/49.21  | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | BETA: splitting (60) gives:
% 242.70/49.21  | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | Case 1:
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | |   (61)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1)
% 242.70/49.21  | | | | | | | | | |         = all_56_17 & $i(all_56_17)
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | ALPHA: (61) implies:
% 242.70/49.21  | | | | | | | | | |   (62)  op(e3, e1) = all_56_17
% 242.70/49.21  | | | | | | | | | |   (63)  op(e3, all_56_17) = e3
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | BETA: splitting (59) gives:
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | Case 1:
% 242.70/49.21  | | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | |   (64)  all_54_2 = e2
% 242.70/49.21  | | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | | REF_CLOSE: (13), (54), (64) are inconsistent by sub-proof
% 242.70/49.21  | | | | | | | | | | |            #1986.
% 242.70/49.21  | | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | Case 2:
% 242.70/49.21  | | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | |   (65)  all_54_2 = e1 | all_54_2 = e0
% 242.70/49.21  | | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | | REF_CLOSE: (7), (13), (15), (27), (32), (62), (63), (65) are
% 242.70/49.21  | | | | | | | | | | |            inconsistent by sub-proof #1522.
% 242.70/49.21  | | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | End of split
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | Case 2:
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | |   (66)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 242.70/49.21  | | | | | | | | | |         = all_56_19 & $i(all_56_19)
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | ALPHA: (66) implies:
% 242.70/49.21  | | | | | | | | | |   (67)  op(e2, e1) = all_56_19
% 242.70/49.21  | | | | | | | | | |   (68)  op(e2, all_56_19) = e2
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | REF_CLOSE: (2), (12), (19), (22), (27), (28), (56), (67),
% 242.70/49.21  | | | | | | | | | |            (68) are inconsistent by sub-proof #854.
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | End of split
% 242.70/49.21  | | | | | | | | | 
% 242.70/49.21  | | | | | | | | Case 2:
% 242.70/49.21  | | | | | | | | | 
% 242.70/49.21  | | | | | | | | |   (69)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22
% 242.70/49.21  | | | | | | | | |           = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 242.70/49.21  | | | | | | | | |           all_56_23 & $i(all_56_23))
% 242.70/49.21  | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | BETA: splitting (69) gives:
% 242.70/49.21  | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | Case 1:
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | |   (70)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | ALPHA: (70) implies:
% 242.70/49.21  | | | | | | | | | |   (71)  op(e1, all_56_21) = e1
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | REDUCE: (14), (71) imply:
% 242.70/49.21  | | | | | | | | | |   (72)  op(e1, e0) = e1
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | REF_CLOSE: (5), (17), (27), (72) are inconsistent by
% 242.70/49.21  | | | | | | | | | |            sub-proof #2304.
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | Case 2:
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | |   (73)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1)
% 242.70/49.21  | | | | | | | | | |         = all_56_23 & $i(all_56_23)
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | ALPHA: (73) implies:
% 242.70/49.21  | | | | | | | | | |   (74)  op(e0, e1) = all_56_23
% 242.70/49.21  | | | | | | | | | |   (75)  op(e0, all_56_23) = e0
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | GROUND_INST: instantiating (27) with e3, all_56_23, e1, e0,
% 242.70/49.21  | | | | | | | | | |              simplifying with (4), (74) gives:
% 242.70/49.21  | | | | | | | | | |   (76)  all_56_23 = e3
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | REDUCE: (75), (76) imply:
% 242.70/49.21  | | | | | | | | | |   (77)  op(e0, e3) = e0
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | | REF_CLOSE: (1), (8), (27), (77) are inconsistent by sub-proof
% 242.70/49.21  | | | | | | | | | |            #2331.
% 242.70/49.21  | | | | | | | | | | 
% 242.70/49.21  | | | | | | | | | End of split
% 242.70/49.21  | | | | | | | | | 
% 242.70/49.21  | | | | | | | | End of split
% 242.70/49.21  | | | | | | | | 
% 242.70/49.21  | | | | | | | End of split
% 242.70/49.21  | | | | | | | 
% 242.70/49.21  | | | | | | Case 2:
% 242.70/49.21  | | | | | | | 
% 242.70/49.21  | | | | | | |   (78)  all_54_1 = e1 | all_54_1 = e0
% 242.70/49.21  | | | | | | | 
% 242.70/49.21  | | | | | | | REF_CLOSE: (25), (31), (46), (78) are inconsistent by sub-proof
% 242.70/49.21  | | | | | | |            #2049.
% 242.70/49.21  | | | | | | | 
% 242.70/49.21  | | | | | | End of split
% 242.70/49.21  | | | | | | 
% 242.70/49.21  | | | | | End of split
% 242.70/49.21  | | | | | 
% 242.70/49.21  | | | | Case 2:
% 242.70/49.21  | | | | | 
% 242.70/49.21  | | | | |   (79)  all_54_9 = e0
% 242.70/49.21  | | | | | 
% 242.70/49.21  | | | | | REF_CLOSE: (9), (16), (79) are inconsistent by sub-proof #1953.
% 242.70/49.21  | | | | | 
% 242.70/49.21  | | | | End of split
% 242.70/49.21  | | | | 
% 242.70/49.21  | | | End of split
% 242.70/49.21  | | | 
% 242.70/49.21  | | End of split
% 242.70/49.21  | | 
% 242.70/49.21  | Case 2:
% 242.70/49.21  | | 
% 242.70/49.21  | |   (80)  all_54_11 = e1 | all_54_11 = e0
% 242.70/49.21  | | 
% 242.70/49.21  | | REF_CLOSE: (10), (17), (18), (80) are inconsistent by sub-proof #2174.
% 242.70/49.21  | | 
% 242.70/49.21  | End of split
% 242.70/49.21  | 
% 242.70/49.21  End of proof
% 242.70/49.21  
% 242.70/49.21  Sub-proof #854 shows that the following formulas are inconsistent:
% 242.70/49.21  ----------------------------------------------------------------
% 242.70/49.21    (1)  op(e2, e2) = e3
% 242.70/49.21    (2)  op(e2, e1) = e2
% 242.70/49.21    (3)   ~ (e3 = e2)
% 242.70/49.21    (4)  op(e2, e3) = e1
% 242.70/49.21    (5)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 242.70/49.21           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 242.70/49.21           all_42_1 & $i(all_42_1))
% 242.70/49.21    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.21    (7)  op(e2, e3) = all_8_1
% 242.70/49.21    (8)  op(e2, e1) = all_56_19
% 242.70/49.21    (9)  op(e2, all_56_19) = e2
% 242.70/49.21  
% 242.70/49.21  Begin of proof
% 242.70/49.21  | 
% 242.70/49.21  | BETA: splitting (5) gives:
% 242.70/49.21  | 
% 242.70/49.21  | Case 1:
% 242.70/49.21  | | 
% 242.70/49.21  | | 
% 242.70/49.21  | | GROUND_INST: instantiating (6) with e2, all_56_19, e1, e2, simplifying with
% 242.70/49.21  | |              (2), (8) gives:
% 242.70/49.21  | |   (10)  all_56_19 = e2
% 242.70/49.21  | | 
% 242.70/49.21  | | REDUCE: (9), (10) imply:
% 242.70/49.21  | |   (11)  op(e2, e2) = e2
% 242.70/49.21  | | 
% 242.70/49.21  | | REF_CLOSE: (1), (3), (6), (11) are inconsistent by sub-proof #2140.
% 242.70/49.21  | | 
% 242.70/49.21  | Case 2:
% 242.70/49.21  | | 
% 242.70/49.21  | |   (12)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 242.70/49.21  | | 
% 242.70/49.21  | | ALPHA: (12) implies:
% 242.70/49.21  | |   (13)   ~ (all_42_1 = e1)
% 242.70/49.21  | |   (14)  op(e2, e3) = all_42_1
% 242.70/49.21  | | 
% 242.70/49.21  | | REF_CLOSE: (4), (6), (7), (13), (14) are inconsistent by sub-proof #935.
% 242.70/49.21  | | 
% 242.70/49.21  | End of split
% 242.70/49.21  | 
% 242.70/49.21  End of proof
% 242.70/49.21  
% 242.70/49.21  Sub-proof #855 shows that the following formulas are inconsistent:
% 242.70/49.21  ----------------------------------------------------------------
% 242.70/49.21    (1)  op(e2, e1) = all_52_9
% 242.70/49.21    (2)  all_56_31 = e1
% 242.70/49.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.21    (4)  all_56_1 = e0
% 242.70/49.21    (5)   ~ (all_52_9 = e1)
% 242.70/49.21    (6)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 242.70/49.21             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 242.70/49.21           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 242.70/49.21             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 242.70/49.21           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 242.70/49.21           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.70/49.21           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.70/49.21  
% 242.70/49.21  Begin of proof
% 242.70/49.21  | 
% 242.70/49.21  | BETA: splitting (6) gives:
% 242.70/49.21  | 
% 242.70/49.21  | Case 1:
% 242.70/49.21  | | 
% 242.70/49.21  | |   (7)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 242.70/49.21  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 242.70/49.21  | |        & op(e1, e2) = e2
% 242.70/49.21  | | 
% 242.70/49.21  | | ALPHA: (7) implies:
% 242.70/49.21  | |   (8)   ~ (all_56_31 = e1)
% 242.70/49.21  | | 
% 242.70/49.21  | | REDUCE: (2), (8) imply:
% 242.70/49.21  | |   (9)  $false
% 242.70/49.21  | | 
% 242.70/49.21  | | CLOSE: (9) is inconsistent.
% 242.70/49.21  | | 
% 242.70/49.21  | Case 2:
% 242.70/49.21  | | 
% 242.70/49.21  | |   (10)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.70/49.21  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.70/49.21  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 242.70/49.21  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 242.70/49.21  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.70/49.21  | | 
% 242.70/49.21  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #1295.
% 242.70/49.21  | | 
% 242.70/49.21  | End of split
% 242.70/49.21  | 
% 242.70/49.21  End of proof
% 242.70/49.21  
% 242.70/49.21  Sub-proof #856 shows that the following formulas are inconsistent:
% 242.70/49.21  ----------------------------------------------------------------
% 242.70/49.21    (1)   ~ (all_52_3 = e0)
% 242.70/49.21    (2)  op(e0, e3) = all_52_3
% 242.70/49.21    (3)   ~ (all_52_2 = e1)
% 242.70/49.21    (4)  all_56_31 = e1
% 242.70/49.21    (5)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 242.70/49.21           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 242.70/49.21             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.70/49.21           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.70/49.21             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 242.70/49.21           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.70/49.21           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.70/49.21           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.70/49.21           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 242.70/49.21           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.21           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.70/49.21             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.70/49.21           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.70/49.21           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.70/49.21    (6)  op(e2, e3) = all_52_1
% 242.70/49.21    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.21    (8)  op(e1, e3) = all_52_2
% 242.70/49.21    (9)  all_56_11 = e3
% 242.70/49.21    (10)  all_56_1 = e0
% 242.70/49.21    (11)   ~ (all_52_1 = e3)
% 242.70/49.21  
% 242.70/49.21  Begin of proof
% 242.70/49.21  | 
% 242.70/49.21  | BETA: splitting (5) gives:
% 242.70/49.21  | 
% 242.70/49.21  | Case 1:
% 242.70/49.21  | | 
% 242.70/49.21  | |   (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 242.70/49.21  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 242.70/49.21  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 242.70/49.21  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.70/49.21  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 242.70/49.21  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 242.70/49.21  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 242.70/49.21  | |           op(e1, e3) = e3)
% 242.70/49.21  | | 
% 242.70/49.21  | | REF_CLOSE: (4), (6), (7), (9), (11), (12) are inconsistent by sub-proof
% 242.70/49.21  | |            #857.
% 242.70/49.21  | | 
% 242.70/49.21  | Case 2:
% 242.70/49.21  | | 
% 242.70/49.21  | |   (13)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 242.70/49.21  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 242.70/49.21  | |           e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 242.70/49.21  | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.70/49.21  | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7
% 242.70/49.21  | |           = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &
% 242.70/49.21  | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 242.70/49.21  | |           op(e0, e3) = e0)
% 242.70/49.21  | | 
% 242.70/49.21  | | BETA: splitting (13) gives:
% 242.70/49.21  | | 
% 242.70/49.21  | | Case 1:
% 242.70/49.21  | | | 
% 242.70/49.21  | | |   (14)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 242.70/49.21  | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.70/49.21  | | |         op(e3, e1) = e1 & op(e1, e3) = e1
% 242.70/49.21  | | | 
% 242.70/49.21  | | | ALPHA: (14) implies:
% 242.70/49.21  | | |   (15)  op(e1, e3) = e1
% 242.70/49.21  | | | 
% 242.70/49.21  | | | REF_CLOSE: (3), (7), (8), (15) are inconsistent by sub-proof #1948.
% 242.70/49.21  | | | 
% 242.70/49.21  | | Case 2:
% 242.70/49.21  | | | 
% 242.70/49.21  | | |   (16)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.21  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.70/49.21  | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 242.70/49.21  | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 242.70/49.21  | | |             = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 242.70/49.21  | | |           e0)
% 242.70/49.21  | | | 
% 242.70/49.21  | | | REF_CLOSE: (1), (2), (7), (10), (16) are inconsistent by sub-proof #1829.
% 242.70/49.21  | | | 
% 242.70/49.21  | | End of split
% 242.70/49.21  | | 
% 242.70/49.21  | End of split
% 242.70/49.21  | 
% 242.70/49.21  End of proof
% 242.70/49.21  
% 242.70/49.21  Sub-proof #857 shows that the following formulas are inconsistent:
% 242.70/49.21  ----------------------------------------------------------------
% 242.70/49.21    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 242.70/49.21           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 242.70/49.21             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.70/49.21           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.70/49.21             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 242.70/49.21           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.70/49.21           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.70/49.21    (2)  all_56_31 = e1
% 242.70/49.21    (3)  op(e2, e3) = all_52_1
% 242.70/49.21    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.21    (5)  all_56_11 = e3
% 242.70/49.21    (6)   ~ (all_52_1 = e3)
% 242.70/49.21  
% 242.70/49.21  Begin of proof
% 242.70/49.21  | 
% 242.70/49.21  | BETA: splitting (1) gives:
% 242.70/49.21  | 
% 242.70/49.21  | Case 1:
% 242.70/49.21  | | 
% 242.70/49.21  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.70/49.21  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.70/49.21  | |        op(e2, e3) = e3
% 242.70/49.21  | | 
% 242.70/49.21  | | ALPHA: (7) implies:
% 242.70/49.21  | |   (8)  op(e2, e3) = e3
% 242.70/49.21  | | 
% 242.70/49.21  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #2337.
% 242.70/49.21  | | 
% 242.70/49.21  | Case 2:
% 242.70/49.21  | | 
% 242.70/49.21  | |   (9)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.70/49.21  | |            e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2
% 242.70/49.21  | |          & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1
% 242.70/49.21  | |            = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 242.70/49.21  | |            = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.70/49.21  | | 
% 242.70/49.21  | | BETA: splitting (9) gives:
% 242.70/49.21  | | 
% 242.70/49.21  | | Case 1:
% 242.70/49.21  | | | 
% 242.70/49.21  | | |   (10)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 242.70/49.21  | | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 242.70/49.21  | | |         e2 & op(e2, e3) = e2
% 242.70/49.21  | | | 
% 242.70/49.21  | | | ALPHA: (10) implies:
% 242.70/49.21  | | |   (11)   ~ (all_56_11 = e3)
% 242.70/49.21  | | | 
% 242.70/49.21  | | | REDUCE: (5), (11) imply:
% 242.70/49.21  | | |   (12)  $false
% 242.70/49.21  | | | 
% 242.70/49.21  | | | CLOSE: (12) is inconsistent.
% 242.70/49.21  | | | 
% 242.70/49.21  | | Case 2:
% 242.70/49.21  | | | 
% 242.70/49.21  | | |   (13)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.70/49.21  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.70/49.21  | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 242.70/49.21  | | | 
% 242.70/49.21  | | | ALPHA: (13) implies:
% 242.70/49.21  | | |   (14)   ~ (all_56_31 = e1)
% 242.70/49.21  | | | 
% 242.70/49.21  | | | REDUCE: (2), (14) imply:
% 242.70/49.21  | | |   (15)  $false
% 242.70/49.21  | | | 
% 242.70/49.21  | | | CLOSE: (15) is inconsistent.
% 242.70/49.21  | | | 
% 242.70/49.21  | | End of split
% 242.70/49.21  | | 
% 242.70/49.21  | End of split
% 242.70/49.21  | 
% 242.70/49.21  End of proof
% 242.70/49.21  
% 242.70/49.21  Sub-proof #858 shows that the following formulas are inconsistent:
% 242.70/49.21  ----------------------------------------------------------------
% 242.70/49.21    (1)   ~ (e2 = e0)
% 242.70/49.21    (2)  op(e1, e0) = all_52_14
% 242.70/49.21    (3)  op(e2, e1) = all_52_9
% 242.70/49.21    (4)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 242.70/49.21             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 242.70/49.21           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 242.70/49.21             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 242.70/49.21           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 242.70/49.21           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.70/49.21           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 242.70/49.21           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.70/49.21           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 242.70/49.21           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.21           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.70/49.21             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.70/49.21           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.70/49.21           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.70/49.21    (5)   ~ (all_52_14 = e0)
% 242.70/49.21    (6)  all_56_31 = e0
% 242.70/49.21    (7)  op(e2, e1) = e0
% 242.70/49.21    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.21    (9)   ~ (e1 = e0)
% 242.70/49.21    (10)  op(e2, e0) = all_52_13
% 242.70/49.21    (11)   ~ (all_52_13 = e0)
% 242.70/49.21  
% 242.70/49.21  Begin of proof
% 242.70/49.21  | 
% 242.70/49.21  | BETA: splitting (4) gives:
% 242.70/49.21  | 
% 242.70/49.21  | Case 1:
% 242.70/49.21  | | 
% 242.70/49.22  | |   (12)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 242.70/49.22  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.70/49.22  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 242.70/49.22  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.70/49.22  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 242.70/49.22  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.22  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.70/49.22  | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.70/49.22  | | 
% 242.70/49.22  | | BETA: splitting (12) gives:
% 242.70/49.22  | | 
% 242.70/49.22  | | Case 1:
% 242.70/49.22  | | | 
% 242.70/49.22  | | |   (13)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 242.70/49.22  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.70/49.22  | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | ALPHA: (13) implies:
% 242.70/49.22  | | |   (14)  op(e2, e1) = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | REF_CLOSE: (1), (7), (8), (14) are inconsistent by sub-proof #1906.
% 242.70/49.22  | | | 
% 242.70/49.22  | | Case 2:
% 242.70/49.22  | | | 
% 242.70/49.22  | | |   (15)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.70/49.22  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.70/49.22  | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27
% 242.70/49.22  | | |           = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 242.70/49.22  | | |             = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 242.70/49.22  | | |           e2)
% 242.70/49.22  | | | 
% 242.70/49.22  | | | BETA: splitting (15) gives:
% 242.70/49.22  | | | 
% 242.70/49.22  | | | Case 1:
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | |   (16)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.70/49.22  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.70/49.22  | | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | | ALPHA: (16) implies:
% 242.70/49.22  | | | |   (17)  op(e2, e1) = e1
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | | REF_CLOSE: (3), (7), (8), (9), (17) are inconsistent by sub-proof #2165.
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | Case 2:
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | |   (18)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.22  | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.70/49.22  | | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | | ALPHA: (18) implies:
% 242.70/49.22  | | | |   (19)   ~ (all_56_31 = e0)
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | | REDUCE: (6), (19) imply:
% 242.70/49.22  | | | |   (20)  $false
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | | CLOSE: (20) is inconsistent.
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | End of split
% 242.70/49.22  | | | 
% 242.70/49.22  | | End of split
% 242.70/49.22  | | 
% 242.70/49.22  | Case 2:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (21)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 242.70/49.22  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.70/49.22  | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 242.70/49.22  | |           e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 242.70/49.22  | |             e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 242.70/49.22  | |         (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 242.70/49.22  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.70/49.22  | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.70/49.22  | | 
% 242.70/49.22  | | REF_CLOSE: (2), (5), (6), (8), (10), (11), (21) are inconsistent by
% 242.70/49.22  | |            sub-proof #2321.
% 242.70/49.22  | | 
% 242.70/49.22  | End of split
% 242.70/49.22  | 
% 242.70/49.22  End of proof
% 242.70/49.22  
% 242.70/49.22  Sub-proof #859 shows that the following formulas are inconsistent:
% 242.70/49.22  ----------------------------------------------------------------
% 242.70/49.22    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.70/49.22         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.70/49.22    (2)   ~ (e3 = e0)
% 242.70/49.22    (3)   ~ (e2 = e0)
% 242.70/49.22    (4)   ~ (all_52_7 = e3)
% 242.70/49.22    (5)   ~ (e3 = e1)
% 242.70/49.22    (6)   ~ (e3 = e2)
% 242.70/49.22    (7)  op(e0, e1) = e0
% 242.70/49.22    (8)  all_58_12 = e3
% 242.70/49.22    (9)  op(e0, e2) = all_52_7
% 242.70/49.22    (10)  all_58_14 = e0
% 242.70/49.22    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.22    (12)  op(e0, e0) = e0
% 242.70/49.22    (13)   ~ (e1 = e0)
% 242.70/49.22    (14)  all_58_15 = e0
% 242.70/49.22    (15)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.70/49.22          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.70/49.22            e1)
% 242.70/49.22    (16)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.22          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.70/49.22            e2)
% 242.70/49.22    (17)   ~ (e2 = e1)
% 242.70/49.22  
% 242.70/49.22  Begin of proof
% 242.70/49.22  | 
% 242.70/49.22  | BETA: splitting (16) gives:
% 242.70/49.22  | 
% 242.70/49.22  | Case 1:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (18)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 242.70/49.22  | |           e2)
% 242.70/49.22  | | 
% 242.70/49.22  | | BETA: splitting (18) gives:
% 242.70/49.22  | | 
% 242.70/49.22  | | Case 1:
% 242.70/49.22  | | | 
% 242.70/49.22  | | |   (19)  all_58_12 = e2 & op(e0, e3) = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | ALPHA: (19) implies:
% 242.70/49.22  | | |   (20)  all_58_12 = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | REF_CLOSE: (6), (8), (20) are inconsistent by sub-proof #1552.
% 242.70/49.22  | | | 
% 242.70/49.22  | | Case 2:
% 242.70/49.22  | | | 
% 242.70/49.22  | | |   (21)  all_58_13 = e2 & op(e0, e2) = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | ALPHA: (21) implies:
% 242.70/49.22  | | |   (22)  all_58_13 = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (11), (12), (13), (15), (17),
% 242.70/49.22  | | |            (22) are inconsistent by sub-proof #860.
% 242.70/49.22  | | | 
% 242.70/49.22  | | End of split
% 242.70/49.22  | | 
% 242.70/49.22  | Case 2:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (23)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.70/49.22  | |           e2)
% 242.70/49.22  | | 
% 242.70/49.22  | | BETA: splitting (23) gives:
% 242.70/49.22  | | 
% 242.70/49.22  | | Case 1:
% 242.70/49.22  | | | 
% 242.70/49.22  | | |   (24)  all_58_14 = e2 & op(e0, e1) = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | REF_CLOSE: (3), (10), (24) are inconsistent by sub-proof #2077.
% 242.70/49.22  | | | 
% 242.70/49.22  | | Case 2:
% 242.70/49.22  | | | 
% 242.70/49.22  | | |   (25)  all_58_15 = e2 & op(e0, e0) = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | ALPHA: (25) implies:
% 242.70/49.22  | | |   (26)  all_58_15 = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | REF_CLOSE: (3), (14), (26) are inconsistent by sub-proof #1507.
% 242.70/49.22  | | | 
% 242.70/49.22  | | End of split
% 242.70/49.22  | | 
% 242.70/49.22  | End of split
% 242.70/49.22  | 
% 242.70/49.22  End of proof
% 242.70/49.22  
% 242.70/49.22  Sub-proof #860 shows that the following formulas are inconsistent:
% 242.70/49.22  ----------------------------------------------------------------
% 242.70/49.22    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.70/49.22         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.70/49.22    (2)   ~ (e3 = e0)
% 242.70/49.22    (3)   ~ (all_52_7 = e3)
% 242.70/49.22    (4)   ~ (e3 = e1)
% 242.70/49.22    (5)  op(e0, e1) = e0
% 242.70/49.22    (6)  all_58_13 = e2
% 242.70/49.22    (7)  op(e0, e2) = all_52_7
% 242.70/49.22    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.22    (9)  op(e0, e0) = e0
% 242.70/49.22    (10)   ~ (e1 = e0)
% 242.70/49.22    (11)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.70/49.22          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.70/49.22            e1)
% 242.70/49.22    (12)   ~ (e2 = e1)
% 242.70/49.22  
% 242.70/49.22  Begin of proof
% 242.70/49.22  | 
% 242.70/49.22  | BETA: splitting (11) gives:
% 242.70/49.22  | 
% 242.70/49.22  | Case 1:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (13)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 242.70/49.22  | |           e1)
% 242.70/49.22  | | 
% 242.70/49.22  | | BETA: splitting (13) gives:
% 242.70/49.22  | | 
% 242.70/49.22  | | Case 1:
% 242.70/49.22  | | | 
% 242.70/49.22  | | |   (14)  all_58_12 = e1 & op(e0, e3) = e1
% 242.70/49.22  | | | 
% 242.70/49.22  | | | ALPHA: (14) implies:
% 242.70/49.22  | | |   (15)  all_58_12 = e1
% 242.70/49.22  | | | 
% 242.70/49.22  | | | BETA: splitting (1) gives:
% 242.70/49.22  | | | 
% 242.70/49.22  | | | Case 1:
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | |   (16)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 242.70/49.22  | | | |             e2) = e3)
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | | BETA: splitting (16) gives:
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | | Case 1:
% 242.70/49.22  | | | | | 
% 242.70/49.22  | | | | |   (17)  all_58_12 = e3 & op(e0, e3) = e3
% 242.70/49.22  | | | | | 
% 242.70/49.22  | | | | | REF_CLOSE: (4), (15), (17) are inconsistent by sub-proof #1205.
% 242.70/49.22  | | | | | 
% 242.70/49.22  | | | | Case 2:
% 242.70/49.22  | | | | | 
% 242.70/49.22  | | | | |   (18)  all_58_13 = e3 & op(e0, e2) = e3
% 242.70/49.22  | | | | | 
% 242.70/49.22  | | | | | REF_CLOSE: (3), (7), (8), (18) are inconsistent by sub-proof #1919.
% 242.70/49.22  | | | | | 
% 242.70/49.22  | | | | End of split
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | Case 2:
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | |   (19)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 242.70/49.22  | | | |             e0) = e3)
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | | REF_CLOSE: (2), (5), (8), (9), (19) are inconsistent by sub-proof #1085.
% 242.70/49.22  | | | | 
% 242.70/49.22  | | | End of split
% 242.70/49.22  | | | 
% 242.70/49.22  | | Case 2:
% 242.70/49.22  | | | 
% 242.70/49.22  | | |   (20)  all_58_13 = e1 & op(e0, e2) = e1
% 242.70/49.22  | | | 
% 242.70/49.22  | | | ALPHA: (20) implies:
% 242.70/49.22  | | |   (21)  all_58_13 = e1
% 242.70/49.22  | | | 
% 242.70/49.22  | | | REF_CLOSE: (6), (12), (21) are inconsistent by sub-proof #1544.
% 242.70/49.22  | | | 
% 242.70/49.22  | | End of split
% 242.70/49.22  | | 
% 242.70/49.22  | Case 2:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (22)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.70/49.22  | |           e1)
% 242.70/49.22  | | 
% 242.70/49.22  | | REF_CLOSE: (5), (8), (9), (10), (22) are inconsistent by sub-proof #2074.
% 242.70/49.22  | | 
% 242.70/49.22  | End of split
% 242.70/49.22  | 
% 242.70/49.22  End of proof
% 242.70/49.22  
% 242.70/49.22  Sub-proof #861 shows that the following formulas are inconsistent:
% 242.70/49.22  ----------------------------------------------------------------
% 242.70/49.22    (1)  op(e2, e2) = e3
% 242.70/49.22    (2)   ~ (e2 = e0)
% 242.70/49.22    (3)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.22         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.70/49.22    (4)   ~ (e3 = e1)
% 242.70/49.22    (5)  all_58_3 = e3
% 242.70/49.22    (6)  op(e2, e1) = all_52_9
% 242.70/49.22    (7)   ~ (e3 = e2)
% 242.70/49.22    (8)  op(e2, e1) = e0
% 242.70/49.22    (9)  all_58_2 = e0
% 242.70/49.22    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.22    (11)   ~ (e1 = e0)
% 242.70/49.22    (12)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.70/49.22          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.70/49.22    (13)   ~ (e2 = e1)
% 242.70/49.22  
% 242.70/49.22  Begin of proof
% 242.70/49.22  | 
% 242.70/49.22  | BETA: splitting (3) gives:
% 242.70/49.22  | 
% 242.70/49.22  | Case 1:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (14)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 242.70/49.22  | |           e2)
% 242.70/49.22  | | 
% 242.70/49.22  | | BETA: splitting (14) gives:
% 242.70/49.22  | | 
% 242.70/49.22  | | Case 1:
% 242.70/49.22  | | | 
% 242.70/49.22  | | |   (15)  all_58_2 = e2 & op(e2, e3) = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | REF_CLOSE: (2), (9), (15) are inconsistent by sub-proof #1575.
% 242.70/49.22  | | | 
% 242.70/49.22  | | Case 2:
% 242.70/49.22  | | | 
% 242.70/49.22  | | |   (16)  all_58_3 = e2 & op(e2, e2) = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | ALPHA: (16) implies:
% 242.70/49.22  | | |   (17)  op(e2, e2) = e2
% 242.70/49.22  | | | 
% 242.70/49.22  | | | REF_CLOSE: (1), (7), (10), (17) are inconsistent by sub-proof #2140.
% 242.70/49.22  | | | 
% 242.70/49.22  | | End of split
% 242.70/49.22  | | 
% 242.70/49.22  | Case 2:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (18)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 242.70/49.22  | |           e2)
% 242.70/49.22  | | 
% 242.70/49.22  | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (18) are
% 242.70/49.22  | |            inconsistent by sub-proof #862.
% 242.70/49.22  | | 
% 242.70/49.22  | End of split
% 242.70/49.22  | 
% 242.70/49.22  End of proof
% 242.70/49.22  
% 242.70/49.22  Sub-proof #862 shows that the following formulas are inconsistent:
% 242.70/49.22  ----------------------------------------------------------------
% 242.70/49.22    (1)   ~ (e2 = e0)
% 242.70/49.22    (2)   ~ (e3 = e1)
% 242.70/49.22    (3)  all_58_3 = e3
% 242.70/49.22    (4)  op(e2, e1) = all_52_9
% 242.70/49.22    (5)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.70/49.22    (6)  op(e2, e1) = e0
% 242.70/49.22    (7)  all_58_2 = e0
% 242.70/49.22    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.22    (9)   ~ (e1 = e0)
% 242.70/49.22    (10)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.70/49.22          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.70/49.22    (11)   ~ (e2 = e1)
% 242.70/49.22  
% 242.70/49.22  Begin of proof
% 242.70/49.22  | 
% 242.70/49.22  | BETA: splitting (5) gives:
% 242.70/49.22  | 
% 242.70/49.22  | Case 1:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (12)  all_58_5 = e2 & op(e2, e1) = e2
% 242.70/49.22  | | 
% 242.70/49.22  | | ALPHA: (12) implies:
% 242.70/49.22  | |   (13)  op(e2, e1) = e2
% 242.70/49.22  | | 
% 242.70/49.22  | | REF_CLOSE: (1), (6), (8), (13) are inconsistent by sub-proof #1906.
% 242.70/49.22  | | 
% 242.70/49.22  | Case 2:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (14)  all_58_10 = e2 & op(e2, e0) = e2
% 242.70/49.22  | | 
% 242.70/49.22  | | ALPHA: (14) implies:
% 242.70/49.22  | |   (15)  op(e2, e0) = e2
% 242.70/49.22  | | 
% 242.70/49.22  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (15) are
% 242.70/49.22  | |            inconsistent by sub-proof #974.
% 242.70/49.22  | | 
% 242.70/49.22  | End of split
% 242.70/49.22  | 
% 242.70/49.22  End of proof
% 242.70/49.22  
% 242.70/49.22  Sub-proof #863 shows that the following formulas are inconsistent:
% 242.70/49.22  ----------------------------------------------------------------
% 242.70/49.22    (1)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.70/49.22             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.70/49.22           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 242.70/49.22           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.70/49.22           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 242.70/49.22           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.70/49.22           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.70/49.22    (2)  all_56_11 = e3
% 242.70/49.22    (3)  all_56_21 = e0
% 242.70/49.22  
% 242.70/49.22  Begin of proof
% 242.70/49.22  | 
% 242.70/49.22  | BETA: splitting (1) gives:
% 242.70/49.22  | 
% 242.70/49.22  | Case 1:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (4)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.70/49.22  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.70/49.22  | |        op(e1, e3) = e1
% 242.70/49.22  | | 
% 242.70/49.22  | | ALPHA: (4) implies:
% 242.70/49.22  | |   (5)   ~ (all_56_11 = e3)
% 242.70/49.22  | | 
% 242.70/49.22  | | REDUCE: (2), (5) imply:
% 242.70/49.22  | |   (6)  $false
% 242.70/49.22  | | 
% 242.70/49.22  | | CLOSE: (6) is inconsistent.
% 242.70/49.22  | | 
% 242.70/49.22  | Case 2:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (7)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 242.70/49.22  | |            = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 242.70/49.22  | |          e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.70/49.22  | |          (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.70/49.22  | |          (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.70/49.22  | | 
% 242.70/49.22  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #864.
% 242.70/49.22  | | 
% 242.70/49.22  | End of split
% 242.70/49.22  | 
% 242.70/49.22  End of proof
% 242.70/49.22  
% 242.70/49.22  Sub-proof #864 shows that the following formulas are inconsistent:
% 242.70/49.22  ----------------------------------------------------------------
% 242.70/49.22    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 242.70/49.22             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 242.70/49.22           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 242.70/49.22           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.70/49.22           op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.70/49.22    (2)  all_56_21 = e0
% 242.70/49.22    (3)  all_56_11 = e3
% 242.70/49.22  
% 242.70/49.22  Begin of proof
% 242.70/49.22  | 
% 242.70/49.22  | BETA: splitting (1) gives:
% 242.70/49.22  | 
% 242.70/49.22  | Case 1:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (4)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 242.70/49.22  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 242.70/49.22  | |        op(e0, e3) = e3
% 242.70/49.22  | | 
% 242.70/49.22  | | ALPHA: (4) implies:
% 242.70/49.22  | |   (5)   ~ (all_56_21 = e0)
% 242.70/49.22  | | 
% 242.70/49.22  | | REDUCE: (2), (5) imply:
% 242.70/49.22  | |   (6)  $false
% 242.70/49.22  | | 
% 242.70/49.22  | | CLOSE: (6) is inconsistent.
% 242.70/49.22  | | 
% 242.70/49.22  | Case 2:
% 242.70/49.22  | | 
% 242.70/49.22  | |   (7)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.70/49.22  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 242.70/49.22  | |        op(e0, e3) = e0
% 242.70/49.22  | | 
% 242.70/49.22  | | ALPHA: (7) implies:
% 242.70/49.22  | |   (8)   ~ (all_56_11 = e3)
% 242.70/49.22  | | 
% 242.70/49.22  | | REDUCE: (3), (8) imply:
% 242.70/49.22  | |   (9)  $false
% 242.70/49.22  | | 
% 242.70/49.22  | | CLOSE: (9) is inconsistent.
% 242.70/49.22  | | 
% 242.70/49.22  | End of split
% 242.70/49.22  | 
% 242.70/49.22  End of proof
% 242.70/49.22  
% 242.70/49.22  Sub-proof #865 shows that the following formulas are inconsistent:
% 242.70/49.22  ----------------------------------------------------------------
% 242.70/49.22    (1)  op(e2, e2) = e3
% 242.70/49.22    (2)   ~ (all_34_1 = e2)
% 242.70/49.22    (3)   ~ (e3 = e0)
% 242.70/49.22    (4)  op(e1, e2) = e1
% 242.70/49.22    (5)   ~ (e2 = e0)
% 242.70/49.22    (6)  op(e1, e2) = all_52_6
% 242.70/49.22    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.22         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.22    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.22         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.70/49.22    (9)  op(e0, e1) = all_34_1
% 242.70/49.22    (10)  all_58_3 = e3
% 242.70/49.22    (11)   ~ (e3 = e2)
% 242.70/49.22    (12)  all_58_15 = e1
% 242.70/49.22    (13)  op(e0, e1) = all_20_1
% 242.70/49.23    (14)  all_58_7 = e1
% 242.70/49.23    (15)  all_58_1 = e2
% 242.70/49.23    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.23    (17)   ~ (e1 = e0)
% 242.70/49.23    (18)  all_58_12 = e1 & op(e0, e3) = e1
% 242.70/49.23    (19)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.23          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.70/49.23            e2)
% 242.70/49.23    (20)   ~ (e2 = e1)
% 242.70/49.23  
% 242.70/49.23  Begin of proof
% 242.70/49.23  | 
% 242.70/49.23  | ALPHA: (18) implies:
% 242.70/49.23  |   (21)  all_58_12 = e1
% 242.70/49.23  | 
% 242.70/49.23  | BETA: splitting (19) gives:
% 242.70/49.23  | 
% 242.70/49.23  | Case 1:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (22)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 242.70/49.23  | |           e2)
% 242.70/49.23  | | 
% 242.70/49.23  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (14), (15), (16),
% 242.70/49.23  | |            (17), (20), (21), (22) are inconsistent by sub-proof #872.
% 242.70/49.23  | | 
% 242.70/49.23  | Case 2:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (23)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.70/49.23  | |           e2)
% 242.70/49.23  | | 
% 242.70/49.23  | | BETA: splitting (23) gives:
% 242.70/49.23  | | 
% 242.70/49.23  | | Case 1:
% 242.70/49.23  | | | 
% 242.70/49.23  | | |   (24)  all_58_14 = e2 & op(e0, e1) = e2
% 242.70/49.23  | | | 
% 242.70/49.23  | | | ALPHA: (24) implies:
% 242.70/49.23  | | |   (25)  op(e0, e1) = e2
% 242.70/49.23  | | | 
% 242.70/49.23  | | | REF_CLOSE: (2), (9), (13), (16), (25) are inconsistent by sub-proof #2237.
% 242.70/49.23  | | | 
% 242.70/49.23  | | Case 2:
% 242.70/49.23  | | | 
% 242.70/49.23  | | |   (26)  all_58_15 = e2 & op(e0, e0) = e2
% 242.70/49.23  | | | 
% 242.70/49.23  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14),
% 242.70/49.23  | | |            (15), (16), (17), (20), (26) are inconsistent by sub-proof
% 242.70/49.23  | | |            #871.
% 242.70/49.23  | | | 
% 242.70/49.23  | | End of split
% 242.70/49.23  | | 
% 242.70/49.23  | End of split
% 242.70/49.23  | 
% 242.70/49.23  End of proof
% 242.70/49.23  
% 242.70/49.23  Sub-proof #866 shows that the following formulas are inconsistent:
% 242.70/49.23  ----------------------------------------------------------------
% 242.70/49.23    (1)  op(e1, e0) = all_28_1
% 242.70/49.23    (2)  all_58_15 = e1
% 242.70/49.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.23    (4)   ~ (all_28_1 = e2)
% 242.70/49.23    (5)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.70/49.23    (6)   ~ (e2 = e1)
% 242.70/49.23  
% 242.70/49.23  Begin of proof
% 242.70/49.23  | 
% 242.70/49.23  | BETA: splitting (5) gives:
% 242.70/49.23  | 
% 242.70/49.23  | Case 1:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (7)  all_58_11 = e2 & op(e1, e0) = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | ALPHA: (7) implies:
% 242.70/49.23  | |   (8)  op(e1, e0) = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1944.
% 242.70/49.23  | | 
% 242.70/49.23  | Case 2:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (9)  all_58_15 = e2 & op(e0, e0) = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #1917.
% 242.70/49.23  | | 
% 242.70/49.23  | End of split
% 242.70/49.23  | 
% 242.70/49.23  End of proof
% 242.70/49.23  
% 242.70/49.23  Sub-proof #867 shows that the following formulas are inconsistent:
% 242.70/49.23  ----------------------------------------------------------------
% 242.70/49.23    (1)  op(e0, e0) = e1
% 242.70/49.23    (2)  all_54_3 = all_20_0
% 242.70/49.23    (3)   ~ (e3 = e0)
% 242.70/49.23    (4)  all_54_2 = all_18_0
% 242.70/49.23    (5)   ~ (e2 = e0)
% 242.70/49.23    (6)  op(e1, e0) = all_52_14
% 242.70/49.23    (7)   ~ (all_52_8 = e0)
% 242.70/49.23    (8)   ~ (all_52_13 = all_20_0)
% 242.70/49.23    (9)   ~ (e3 = e1)
% 242.70/49.23    (10)   ~ (all_20_0 = e1)
% 242.70/49.23    (11)  all_58_11 = e3
% 242.70/49.23    (12)  all_54_2 = all_52_8
% 242.70/49.23    (13)   ~ (all_20_0 = e2)
% 242.70/49.23    (14)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.70/49.23              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.70/49.23                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.70/49.23                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.70/49.23    (15)   ~ (e3 = e2)
% 242.70/49.23    (16)   ~ (all_52_14 = e0)
% 242.70/49.23    (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.70/49.23    (18)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.70/49.23    (19)   ~ (all_18_0 = e2)
% 242.70/49.23    (20)  all_58_15 = e1
% 242.70/49.23    (21)  op(e3, e2) = all_52_4
% 242.70/49.23    (22)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 242.70/49.23    (23)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.70/49.23          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.70/49.23    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.23    (25)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.70/49.23          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.70/49.23    (26)   ~ (e1 = e0)
% 242.70/49.23    (27)  op(e3, e3) = e3
% 242.70/49.23    (28)  op(e2, e0) = all_52_13
% 242.70/49.23    (29)   ~ (all_52_4 = all_52_8)
% 242.70/49.23    (30)   ~ (e2 = e1)
% 242.70/49.23  
% 242.70/49.23  Begin of proof
% 242.70/49.23  | 
% 242.70/49.23  | BETA: splitting (17) gives:
% 242.70/49.23  | 
% 242.70/49.23  | Case 1:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (31)  all_58_4 = e2 & op(e3, e1) = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | ALPHA: (31) implies:
% 242.70/49.23  | |   (32)  all_58_4 = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | REF_CLOSE: (1), (3), (4), (5), (7), (9), (11), (12), (14), (15), (18), (19),
% 242.70/49.23  | |            (20), (21), (23), (24), (25), (26), (27), (29), (30), (32) are
% 242.70/49.23  | |            inconsistent by sub-proof #868.
% 242.70/49.23  | | 
% 242.70/49.23  | Case 2:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (33)  all_58_9 = e2 & op(e3, e0) = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | REF_CLOSE: (1), (2), (5), (6), (8), (10), (13), (14), (16), (22), (24),
% 242.70/49.23  | |            (26), (28), (33) are inconsistent by sub-proof #1122.
% 242.70/49.23  | | 
% 242.70/49.23  | End of split
% 242.70/49.23  | 
% 242.70/49.23  End of proof
% 242.70/49.23  
% 242.70/49.23  Sub-proof #868 shows that the following formulas are inconsistent:
% 242.70/49.23  ----------------------------------------------------------------
% 242.70/49.23    (1)  op(e0, e0) = e1
% 242.70/49.23    (2)   ~ (e3 = e0)
% 242.70/49.23    (3)  all_54_2 = all_18_0
% 242.70/49.23    (4)   ~ (e2 = e0)
% 242.70/49.23    (5)  all_58_4 = e2
% 242.70/49.23    (6)   ~ (all_52_8 = e0)
% 242.70/49.23    (7)   ~ (e3 = e1)
% 242.70/49.23    (8)  all_58_11 = e3
% 242.70/49.23    (9)  all_54_2 = all_52_8
% 242.70/49.23    (10)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.70/49.23              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.70/49.23                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.70/49.23                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.70/49.23    (11)   ~ (e3 = e2)
% 242.70/49.23    (12)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.70/49.23    (13)   ~ (all_18_0 = e2)
% 242.70/49.23    (14)  all_58_15 = e1
% 242.70/49.23    (15)  op(e3, e2) = all_52_4
% 242.70/49.23    (16)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.70/49.23          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.70/49.23    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.23    (18)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.70/49.23          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.70/49.23    (19)   ~ (e1 = e0)
% 242.70/49.23    (20)  op(e3, e3) = e3
% 242.70/49.23    (21)   ~ (all_52_4 = all_52_8)
% 242.70/49.23    (22)   ~ (e2 = e1)
% 242.70/49.23  
% 242.70/49.23  Begin of proof
% 242.70/49.23  | 
% 242.70/49.23  | BETA: splitting (12) gives:
% 242.70/49.23  | 
% 242.70/49.23  | Case 1:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (23)  all_54_2 = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | REF_CLOSE: (3), (13), (23) are inconsistent by sub-proof #1527.
% 242.70/49.23  | | 
% 242.70/49.23  | Case 2:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (24)  all_54_2 = e1 | all_54_2 = e0
% 242.70/49.23  | | 
% 242.70/49.23  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (14), (15),
% 242.70/49.23  | |            (16), (17), (18), (19), (20), (21), (22), (24) are inconsistent
% 242.70/49.23  | |            by sub-proof #869.
% 242.70/49.23  | | 
% 242.70/49.23  | End of split
% 242.70/49.23  | 
% 242.70/49.23  End of proof
% 242.70/49.23  
% 242.70/49.23  Sub-proof #869 shows that the following formulas are inconsistent:
% 242.70/49.23  ----------------------------------------------------------------
% 242.70/49.23    (1)  op(e0, e0) = e1
% 242.70/49.23    (2)   ~ (e3 = e0)
% 242.70/49.23    (3)  all_54_2 = e1 | all_54_2 = e0
% 242.70/49.23    (4)   ~ (e2 = e0)
% 242.70/49.23    (5)  all_58_4 = e2
% 242.70/49.23    (6)   ~ (all_52_8 = e0)
% 242.70/49.23    (7)   ~ (e3 = e1)
% 242.70/49.23    (8)  all_58_11 = e3
% 242.70/49.23    (9)  all_54_2 = all_52_8
% 242.70/49.23    (10)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.70/49.23              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.70/49.23                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.70/49.23                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.70/49.23    (11)   ~ (e3 = e2)
% 242.70/49.23    (12)  all_58_15 = e1
% 242.70/49.23    (13)  op(e3, e2) = all_52_4
% 242.70/49.23    (14)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.70/49.23          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.70/49.23    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.23    (16)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.70/49.23          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.70/49.23    (17)   ~ (e1 = e0)
% 242.70/49.23    (18)  op(e3, e3) = e3
% 242.70/49.23    (19)   ~ (all_52_4 = all_52_8)
% 242.70/49.23    (20)   ~ (e2 = e1)
% 242.70/49.23  
% 242.70/49.23  Begin of proof
% 242.70/49.23  | 
% 242.70/49.23  | BETA: splitting (14) gives:
% 242.70/49.23  | 
% 242.70/49.23  | Case 1:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (21)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 242.70/49.23  | |           e1)
% 242.70/49.23  | | 
% 242.70/49.23  | | BETA: splitting (21) gives:
% 242.70/49.23  | | 
% 242.70/49.23  | | Case 1:
% 242.70/49.23  | | | 
% 242.70/49.23  | | |   (22)  all_58_0 = e1 & op(e3, e3) = e1
% 242.70/49.23  | | | 
% 242.70/49.23  | | | ALPHA: (22) implies:
% 242.70/49.23  | | |   (23)  op(e3, e3) = e1
% 242.70/49.23  | | | 
% 242.70/49.23  | | | REF_CLOSE: (7), (15), (18), (23) are inconsistent by sub-proof #1578.
% 242.70/49.23  | | | 
% 242.70/49.23  | | Case 2:
% 242.70/49.23  | | | 
% 242.70/49.23  | | |   (24)  all_58_1 = e1 & op(e3, e2) = e1
% 242.70/49.23  | | | 
% 242.70/49.23  | | | ALPHA: (24) implies:
% 242.70/49.23  | | |   (25)  op(e3, e2) = e1
% 242.70/49.23  | | | 
% 242.70/49.23  | | | REF_CLOSE: (3), (6), (9), (13), (15), (19), (25) are inconsistent by
% 242.70/49.23  | | |            sub-proof #1642.
% 242.70/49.23  | | | 
% 242.70/49.23  | | End of split
% 242.70/49.23  | | 
% 242.70/49.23  | Case 2:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (26)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 242.70/49.23  | |           e1)
% 242.70/49.23  | | 
% 242.70/49.23  | | BETA: splitting (26) gives:
% 242.70/49.23  | | 
% 242.70/49.23  | | Case 1:
% 242.70/49.23  | | | 
% 242.70/49.23  | | |   (27)  all_58_4 = e1 & op(e3, e1) = e1
% 242.70/49.23  | | | 
% 242.70/49.23  | | | ALPHA: (27) implies:
% 242.70/49.23  | | |   (28)  all_58_4 = e1
% 242.70/49.23  | | | 
% 242.70/49.23  | | | REF_CLOSE: (5), (20), (28) are inconsistent by sub-proof #1786.
% 242.70/49.23  | | | 
% 242.70/49.23  | | Case 2:
% 242.70/49.23  | | | 
% 242.70/49.23  | | |   (29)  all_58_9 = e1 & op(e3, e0) = e1
% 242.70/49.23  | | | 
% 242.70/49.23  | | | ALPHA: (29) implies:
% 242.70/49.23  | | |   (30)  all_58_9 = e1
% 242.70/49.23  | | | 
% 242.70/49.23  | | | REF_CLOSE: (1), (2), (4), (8), (10), (11), (12), (15), (16), (17), (20),
% 242.70/49.23  | | |            (30) are inconsistent by sub-proof #1740.
% 242.70/49.23  | | | 
% 242.70/49.23  | | End of split
% 242.70/49.23  | | 
% 242.70/49.23  | End of split
% 242.70/49.23  | 
% 242.70/49.23  End of proof
% 242.70/49.23  
% 242.70/49.23  Sub-proof #870 shows that the following formulas are inconsistent:
% 242.70/49.23  ----------------------------------------------------------------
% 242.70/49.23    (1)  op(e2, e2) = e3
% 242.70/49.23    (2)   ~ (e3 = e0)
% 242.70/49.23    (3)  op(e1, e2) = e1
% 242.70/49.23    (4)   ~ (e2 = e0)
% 242.70/49.23    (5)  op(e1, e2) = all_52_6
% 242.70/49.23    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.23         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.23    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.23         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.70/49.23    (8)  all_58_3 = e3
% 242.70/49.23    (9)   ~ (e3 = e2)
% 242.70/49.23    (10)  all_58_15 = e1
% 242.70/49.23    (11)  all_58_7 = e1
% 242.70/49.23    (12)  all_58_1 = e2
% 242.70/49.23    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.23    (14)  all_58_14 = e3
% 242.70/49.23    (15)   ~ (e1 = e0)
% 242.70/49.23    (16)  all_58_12 = e1 & op(e0, e3) = e1
% 242.70/49.23    (17)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.23          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.70/49.23            e2)
% 242.70/49.23    (18)   ~ (e2 = e1)
% 242.70/49.23  
% 242.70/49.23  Begin of proof
% 242.70/49.23  | 
% 242.70/49.23  | ALPHA: (16) implies:
% 242.70/49.23  |   (19)  all_58_12 = e1
% 242.70/49.23  | 
% 242.70/49.23  | BETA: splitting (17) gives:
% 242.70/49.23  | 
% 242.70/49.23  | Case 1:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (20)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 242.70/49.23  | |           e2)
% 242.70/49.23  | | 
% 242.70/49.23  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 242.70/49.23  | |            (15), (18), (19), (20) are inconsistent by sub-proof #872.
% 242.70/49.23  | | 
% 242.70/49.23  | Case 2:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (21)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.70/49.23  | |           e2)
% 242.70/49.23  | | 
% 242.70/49.23  | | BETA: splitting (21) gives:
% 242.70/49.23  | | 
% 242.70/49.23  | | Case 1:
% 242.70/49.23  | | | 
% 242.70/49.23  | | |   (22)  all_58_14 = e2 & op(e0, e1) = e2
% 242.70/49.23  | | | 
% 242.70/49.23  | | | ALPHA: (22) implies:
% 242.70/49.23  | | |   (23)  all_58_14 = e2
% 242.70/49.23  | | | 
% 242.70/49.23  | | | REF_CLOSE: (9), (14), (23) are inconsistent by sub-proof #2117.
% 242.70/49.23  | | | 
% 242.70/49.23  | | Case 2:
% 242.70/49.23  | | | 
% 242.70/49.23  | | |   (24)  all_58_15 = e2 & op(e0, e0) = e2
% 242.70/49.23  | | | 
% 242.70/49.23  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.70/49.23  | | |            (13), (15), (18), (24) are inconsistent by sub-proof #871.
% 242.70/49.23  | | | 
% 242.70/49.23  | | End of split
% 242.70/49.23  | | 
% 242.70/49.23  | End of split
% 242.70/49.23  | 
% 242.70/49.23  End of proof
% 242.70/49.23  
% 242.70/49.23  Sub-proof #871 shows that the following formulas are inconsistent:
% 242.70/49.23  ----------------------------------------------------------------
% 242.70/49.23    (1)  op(e2, e2) = e3
% 242.70/49.23    (2)   ~ (e3 = e0)
% 242.70/49.23    (3)  op(e1, e2) = e1
% 242.70/49.23    (4)   ~ (e2 = e0)
% 242.70/49.23    (5)  op(e1, e2) = all_52_6
% 242.70/49.23    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.23         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.23    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.23         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.70/49.23    (8)  all_58_15 = e2 & op(e0, e0) = e2
% 242.70/49.23    (9)  all_58_3 = e3
% 242.70/49.23    (10)   ~ (e3 = e2)
% 242.70/49.23    (11)  all_58_15 = e1
% 242.70/49.23    (12)  all_58_7 = e1
% 242.70/49.23    (13)  all_58_1 = e2
% 242.70/49.23    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.23    (15)   ~ (e1 = e0)
% 242.70/49.23    (16)   ~ (e2 = e1)
% 242.70/49.23  
% 242.70/49.23  Begin of proof
% 242.70/49.23  | 
% 242.70/49.23  | ALPHA: (8) implies:
% 242.70/49.23  |   (17)  all_58_15 = e2
% 242.70/49.23  | 
% 242.70/49.23  | COMBINE_EQS: (11), (17) imply:
% 242.70/49.23  |   (18)  e2 = e1
% 242.70/49.23  | 
% 242.70/49.23  | COMBINE_EQS: (13), (18) imply:
% 242.70/49.23  |   (19)  all_58_1 = e1
% 242.70/49.23  | 
% 242.70/49.23  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (14), (15),
% 242.70/49.23  |            (16), (19) are inconsistent by sub-proof #1717.
% 242.70/49.23  | 
% 242.70/49.23  End of proof
% 242.70/49.23  
% 242.70/49.23  Sub-proof #872 shows that the following formulas are inconsistent:
% 242.70/49.23  ----------------------------------------------------------------
% 242.70/49.23    (1)  op(e2, e2) = e3
% 242.70/49.23    (2)   ~ (e3 = e0)
% 242.70/49.23    (3)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.23    (4)  op(e1, e2) = e1
% 242.70/49.23    (5)   ~ (e2 = e0)
% 242.70/49.23    (6)  op(e1, e2) = all_52_6
% 242.70/49.23    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.23         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.23    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.23         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.70/49.23    (9)  all_58_3 = e3
% 242.70/49.23    (10)  all_58_12 = e1
% 242.70/49.23    (11)   ~ (e3 = e2)
% 242.70/49.23    (12)  all_58_7 = e1
% 242.70/49.23    (13)  all_58_1 = e2
% 242.70/49.23    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.23    (15)   ~ (e1 = e0)
% 242.70/49.23    (16)   ~ (e2 = e1)
% 242.70/49.23  
% 242.70/49.23  Begin of proof
% 242.70/49.23  | 
% 242.70/49.23  | BETA: splitting (3) gives:
% 242.70/49.23  | 
% 242.70/49.23  | Case 1:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (17)  all_58_12 = e2 & op(e0, e3) = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | ALPHA: (17) implies:
% 242.70/49.23  | |   (18)  all_58_12 = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | COMBINE_EQS: (10), (18) imply:
% 242.70/49.23  | |   (19)  e2 = e1
% 242.70/49.23  | | 
% 242.70/49.23  | | SIMP: (19) implies:
% 242.70/49.23  | |   (20)  e2 = e1
% 242.70/49.23  | | 
% 242.70/49.23  | | COMBINE_EQS: (13), (20) imply:
% 242.70/49.23  | |   (21)  all_58_1 = e1
% 242.70/49.23  | | 
% 242.70/49.23  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15),
% 242.70/49.23  | |            (16), (21) are inconsistent by sub-proof #1717.
% 242.70/49.23  | | 
% 242.70/49.23  | Case 2:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (22)  all_58_13 = e2 & op(e0, e2) = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | ALPHA: (22) implies:
% 242.70/49.23  | |   (23)  all_58_13 = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | REF_CLOSE: (2), (5), (8), (9), (12), (13), (15), (23) are inconsistent by
% 242.70/49.23  | |            sub-proof #969.
% 242.70/49.23  | | 
% 242.70/49.23  | End of split
% 242.70/49.23  | 
% 242.70/49.23  End of proof
% 242.70/49.23  
% 242.70/49.23  Sub-proof #873 shows that the following formulas are inconsistent:
% 242.70/49.23  ----------------------------------------------------------------
% 242.70/49.23    (1)  op(e2, e2) = e3
% 242.70/49.23    (2)   ~ (e3 = e0)
% 242.70/49.23    (3)  op(e1, e2) = e1
% 242.70/49.23    (4)   ~ (e2 = e0)
% 242.70/49.23    (5)  op(e1, e2) = all_52_6
% 242.70/49.23    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.23         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.23    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.23         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.70/49.23    (8)  all_58_3 = e3
% 242.70/49.23    (9)   ~ (e3 = e2)
% 242.70/49.23    (10)  all_58_6 = e1
% 242.70/49.23    (11)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 242.70/49.23    (12)  all_58_7 = e1
% 242.70/49.23    (13)  all_58_1 = e2
% 242.70/49.23    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.23    (15)   ~ (e1 = e0)
% 242.70/49.23    (16)   ~ (e2 = e1)
% 242.70/49.23  
% 242.70/49.23  Begin of proof
% 242.70/49.23  | 
% 242.70/49.23  | BETA: splitting (11) gives:
% 242.70/49.23  | 
% 242.70/49.23  | Case 1:
% 242.70/49.23  | | 
% 242.70/49.23  | |   (17)  all_58_6 = e2 & op(e1, e3) = e2
% 242.70/49.23  | | 
% 242.70/49.23  | | ALPHA: (17) implies:
% 242.70/49.24  | |   (18)  all_58_6 = e2
% 242.70/49.24  | | 
% 242.70/49.24  | | COMBINE_EQS: (10), (18) imply:
% 242.70/49.24  | |   (19)  e2 = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | COMBINE_EQS: (13), (19) imply:
% 242.70/49.24  | |   (20)  all_58_1 = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (14), (15),
% 242.70/49.24  | |            (16), (20) are inconsistent by sub-proof #1717.
% 242.70/49.24  | | 
% 242.70/49.24  | Case 2:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (21)  all_58_7 = e2 & op(e1, e2) = e2
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 242.70/49.24  | |            (15), (16), (21) are inconsistent by sub-proof #874.
% 242.70/49.24  | | 
% 242.70/49.24  | End of split
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #874 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)  op(e2, e2) = e3
% 242.70/49.24    (2)   ~ (e3 = e0)
% 242.70/49.24    (3)  op(e1, e2) = e1
% 242.70/49.24    (4)   ~ (e2 = e0)
% 242.70/49.24    (5)  op(e1, e2) = all_52_6
% 242.70/49.24    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.24         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.24    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.24         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.70/49.24    (8)  all_58_3 = e3
% 242.70/49.24    (9)   ~ (e3 = e2)
% 242.70/49.24    (10)  all_58_7 = e1
% 242.70/49.24    (11)  all_58_1 = e2
% 242.70/49.24    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.24    (13)   ~ (e1 = e0)
% 242.70/49.24    (14)  all_58_7 = e2 & op(e1, e2) = e2
% 242.70/49.24    (15)   ~ (e2 = e1)
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | ALPHA: (14) implies:
% 242.70/49.24  |   (16)  all_58_7 = e2
% 242.70/49.24  | 
% 242.70/49.24  | COMBINE_EQS: (10), (16) imply:
% 242.70/49.24  |   (17)  e2 = e1
% 242.70/49.24  | 
% 242.70/49.24  | COMBINE_EQS: (11), (17) imply:
% 242.70/49.24  |   (18)  all_58_1 = e1
% 242.70/49.24  | 
% 242.70/49.24  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 242.70/49.24  |            (15), (18) are inconsistent by sub-proof #1717.
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #875 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)  op(e0, e0) = e1
% 242.70/49.24    (2)  op(e2, e2) = e3
% 242.70/49.24    (3)   ~ (e3 = e0)
% 242.70/49.24    (4)   ~ (e2 = e0)
% 242.70/49.24    (5)  op(e0, e1) = e3
% 242.70/49.24    (6)   ~ (all_52_1 = all_52_2)
% 242.70/49.24    (7)   ~ (e3 = e1)
% 242.70/49.24    (8)  all_58_11 = e3
% 242.70/49.24    (9)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.70/49.24             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.70/49.24               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.70/49.24               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.70/49.24    (10)   ~ (e3 = e2)
% 242.70/49.24    (11)  op(e1, e0) = e3
% 242.70/49.24    (12)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 242.70/49.24    (13)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.70/49.24            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.70/49.24            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.70/49.24            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.70/49.24            op(e0, all_56_31) = e0)
% 242.70/49.24    (14)  op(e2, e0) = e2
% 242.70/49.24    (15)  all_56_31 = e1
% 242.70/49.24    (16)  op(e3, e0) = all_52_12
% 242.70/49.24    (17)  op(e2, e3) = all_52_1
% 242.70/49.24    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.24    (19)  op(e1, e3) = all_52_2
% 242.70/49.24    (20)   ~ (all_52_12 = e3)
% 242.70/49.24    (21)   ~ (e1 = e0)
% 242.70/49.24    (22)  op(e3, e3) = e3
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | BETA: splitting (12) gives:
% 242.70/49.24  | 
% 242.70/49.24  | Case 1:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (23)  all_58_0 = e1 & op(e3, e3) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | ALPHA: (23) implies:
% 242.70/49.24  | |   (24)  op(e3, e3) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (7), (18), (22), (24) are inconsistent by sub-proof #1578.
% 242.70/49.24  | | 
% 242.70/49.24  | Case 2:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (25)  all_58_2 = e1 & op(e2, e3) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 242.70/49.24  | |            (15), (16), (17), (18), (19), (20), (21), (25) are inconsistent
% 242.70/49.24  | |            by sub-proof #953.
% 242.70/49.24  | | 
% 242.70/49.24  | End of split
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #876 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)  all_54_2 = e1 | all_54_2 = e0
% 242.70/49.24    (2)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 242.70/49.24    (3)   ~ (all_52_8 = e0)
% 242.70/49.24    (4)   ~ (e3 = e1)
% 242.70/49.24    (5)  all_58_3 = e3
% 242.70/49.24    (6)  all_54_2 = all_52_8
% 242.70/49.24    (7)  op(e3, e2) = all_52_4
% 242.70/49.24    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.24    (9)   ~ (all_52_4 = all_52_8)
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | BETA: splitting (2) gives:
% 242.70/49.24  | 
% 242.70/49.24  | Case 1:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (10)  all_58_1 = e1 & op(e3, e2) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | ALPHA: (10) implies:
% 242.70/49.24  | |   (11)  op(e3, e2) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (11) are inconsistent by sub-proof
% 242.70/49.24  | |            #1642.
% 242.70/49.24  | | 
% 242.70/49.24  | Case 2:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (12)  all_58_3 = e1 & op(e2, e2) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | ALPHA: (12) implies:
% 242.70/49.24  | |   (13)  all_58_3 = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #1999.
% 242.70/49.24  | | 
% 242.70/49.24  | End of split
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #877 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)  all_54_2 = all_18_0
% 242.70/49.24    (2)  all_54_2 = e3
% 242.70/49.24    (3)   ~ (all_18_0 = e3)
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | COMBINE_EQS: (1), (2) imply:
% 242.70/49.24  |   (4)  all_18_0 = e3
% 242.70/49.24  | 
% 242.70/49.24  | SIMP: (4) implies:
% 242.70/49.24  |   (5)  all_18_0 = e3
% 242.70/49.24  | 
% 242.70/49.24  | REDUCE: (3), (5) imply:
% 242.70/49.24  |   (6)  $false
% 242.70/49.24  | 
% 242.70/49.24  | CLOSE: (6) is inconsistent.
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #878 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)  op(e0, e0) = e1
% 242.70/49.24    (2)   ~ (e3 = e0)
% 242.70/49.24    (3)   ~ (e2 = e0)
% 242.70/49.24    (4)   ~ (all_52_13 = e1)
% 242.70/49.24    (5)   ~ (e3 = e1)
% 242.70/49.24    (6)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.70/49.24             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.70/49.24               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.70/49.24               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.70/49.24    (7)   ~ (e3 = e2)
% 242.70/49.24    (8)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.70/49.24         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.70/49.24    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.24    (10)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.70/49.24          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.70/49.24    (11)   ~ (e1 = e0)
% 242.70/49.24    (12)   ~ (all_52_13 = e3)
% 242.70/49.24    (13)  op(e2, e0) = all_52_13
% 242.70/49.24    (14)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.70/49.24    (15)   ~ (e2 = e1)
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | BETA: splitting (14) gives:
% 242.70/49.24  | 
% 242.70/49.24  | Case 1:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (16)  all_58_9 = e1 & op(e3, e0) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | ALPHA: (16) implies:
% 242.70/49.24  | |   (17)  all_58_9 = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 242.70/49.24  | |            (15), (17) are inconsistent by sub-proof #1600.
% 242.70/49.24  | | 
% 242.70/49.24  | Case 2:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (18)  all_58_10 = e1 & op(e2, e0) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (4), (9), (13), (18) are inconsistent by sub-proof #2277.
% 242.70/49.24  | | 
% 242.70/49.24  | End of split
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #879 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)   ~ (all_10_2 = e1)
% 242.70/49.24    (2)   ~ (all_42_1 = e1)
% 242.70/49.24    (3)  op(e2, e3) = all_42_1
% 242.70/49.24    (4)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 242.70/49.24    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.24    (6)  op(e3, e3) = all_10_2
% 242.70/49.24    (7)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.70/49.24           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.70/49.24           & $i(all_8_1))
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | BETA: splitting (4) gives:
% 242.70/49.24  | 
% 242.70/49.24  | Case 1:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (8)  all_58_0 = e1 & op(e3, e3) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2230.
% 242.70/49.24  | | 
% 242.70/49.24  | Case 2:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (9)  all_58_2 = e1 & op(e2, e3) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | ALPHA: (9) implies:
% 242.70/49.24  | |   (10)  op(e2, e3) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (2), (3), (5), (7), (10) are inconsistent by sub-proof #934.
% 242.70/49.24  | | 
% 242.70/49.24  | End of split
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #880 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)  all_54_13 = e1 | all_54_13 = e0
% 242.70/49.24    (2)  all_54_13 = all_8_0
% 242.70/49.24    (3)   ~ (all_8_0 = e1)
% 242.70/49.24    (4)   ~ (all_8_0 = e0)
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | BETA: splitting (1) gives:
% 242.70/49.24  | 
% 242.70/49.24  | Case 1:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (5)  all_54_13 = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | COMBINE_EQS: (2), (5) imply:
% 242.70/49.24  | |   (6)  all_8_0 = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | SIMP: (6) implies:
% 242.70/49.24  | |   (7)  all_8_0 = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | REDUCE: (3), (7) imply:
% 242.70/49.24  | |   (8)  $false
% 242.70/49.24  | | 
% 242.70/49.24  | | CLOSE: (8) is inconsistent.
% 242.70/49.24  | | 
% 242.70/49.24  | Case 2:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (9)  all_54_13 = e0
% 242.70/49.24  | | 
% 242.70/49.24  | | COMBINE_EQS: (2), (9) imply:
% 242.70/49.24  | |   (10)  all_8_0 = e0
% 242.70/49.24  | | 
% 242.70/49.24  | | SIMP: (10) implies:
% 242.70/49.24  | |   (11)  all_8_0 = e0
% 242.70/49.24  | | 
% 242.70/49.24  | | REDUCE: (4), (11) imply:
% 242.70/49.24  | |   (12)  $false
% 242.70/49.24  | | 
% 242.70/49.24  | | CLOSE: (12) is inconsistent.
% 242.70/49.24  | | 
% 242.70/49.24  | End of split
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #881 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)   ~ (e3 = e0)
% 242.70/49.24    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.70/49.24         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.70/49.24    (3)   ~ (e2 = e0)
% 242.70/49.24    (4)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.24         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.24    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.24         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.70/49.24    (6)   ~ (all_52_6 = e2)
% 242.70/49.24    (7)  op(e1, e0) = all_52_14
% 242.70/49.24    (8)   ~ (all_52_6 = e0)
% 242.70/49.24    (9)  all_58_3 = e3
% 242.70/49.24    (10)  all_54_9 = all_52_6
% 242.70/49.24    (11)   ~ (e3 = e2)
% 242.70/49.24    (12)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.70/49.24    (13)   ~ (all_52_6 = all_52_14)
% 242.70/49.24    (14)   ~ (all_52_6 = e3)
% 242.70/49.24    (15)   ~ (all_52_2 = all_52_6)
% 242.70/49.24    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.24    (17)  op(e1, e3) = all_52_2
% 242.70/49.24    (18)  op(e1, e1) = e0
% 242.70/49.24    (19)  all_58_13 = e1
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | BETA: splitting (12) gives:
% 242.70/49.24  | 
% 242.70/49.24  | Case 1:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (20)  all_54_9 = e3
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (10), (14), (20) are inconsistent by sub-proof #1955.
% 242.70/49.24  | | 
% 242.70/49.24  | Case 2:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (21)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.70/49.24  | | 
% 242.70/49.24  | | BETA: splitting (21) gives:
% 242.70/49.24  | | 
% 242.70/49.24  | | Case 1:
% 242.70/49.24  | | | 
% 242.70/49.24  | | |   (22)  all_54_9 = e2
% 242.70/49.24  | | | 
% 242.70/49.24  | | | REF_CLOSE: (6), (10), (22) are inconsistent by sub-proof #1954.
% 242.70/49.24  | | | 
% 242.70/49.24  | | Case 2:
% 242.70/49.24  | | | 
% 242.70/49.24  | | |   (23)   ~ (all_54_9 = e2)
% 242.70/49.24  | | |   (24)  all_54_9 = e1 | all_54_9 = e0
% 242.70/49.24  | | | 
% 242.70/49.24  | | | BETA: splitting (24) gives:
% 242.70/49.24  | | | 
% 242.70/49.24  | | | Case 1:
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | |   (25)  all_54_9 = e1
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | | COMBINE_EQS: (10), (25) imply:
% 242.70/49.24  | | | |   (26)  all_52_6 = e1
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | | SIMP: (26) implies:
% 242.70/49.24  | | | |   (27)  all_52_6 = e1
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | | REDUCE: (15), (27) imply:
% 242.70/49.24  | | | |   (28)   ~ (all_52_2 = e1)
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | | REDUCE: (13), (27) imply:
% 242.70/49.24  | | | |   (29)   ~ (all_52_14 = e1)
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | | SIMP: (29) implies:
% 242.70/49.24  | | | |   (30)   ~ (all_52_14 = e1)
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | | REDUCE: (6), (27) imply:
% 242.70/49.24  | | | |   (31)   ~ (e2 = e1)
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | | SIMP: (31) implies:
% 242.70/49.24  | | | |   (32)   ~ (e2 = e1)
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | | REDUCE: (8), (27) imply:
% 242.70/49.24  | | | |   (33)   ~ (e1 = e0)
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (11), (16), (17), (18),
% 242.70/49.24  | | | |            (19), (28), (30), (32), (33) are inconsistent by sub-proof
% 242.70/49.24  | | | |            #887.
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | Case 2:
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | |   (34)  all_54_9 = e0
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | | REF_CLOSE: (8), (10), (34) are inconsistent by sub-proof #1953.
% 242.70/49.24  | | | | 
% 242.70/49.24  | | | End of split
% 242.70/49.24  | | | 
% 242.70/49.24  | | End of split
% 242.70/49.24  | | 
% 242.70/49.24  | End of split
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #882 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)  op(e2, e2) = e3
% 242.70/49.24    (2)   ~ (e2 = e0)
% 242.70/49.24    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.24         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.24    (4)  all_58_1 = e0
% 242.70/49.24    (5)   ~ (e3 = e2)
% 242.70/49.24    (6)  op(e0, e2) = e0
% 242.70/49.24    (7)  all_58_7 = e1
% 242.70/49.24    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.24    (9)   ~ (e2 = e1)
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | BETA: splitting (3) gives:
% 242.70/49.24  | 
% 242.70/49.24  | Case 1:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 242.70/49.24  | |           e2)
% 242.70/49.24  | | 
% 242.70/49.24  | | BETA: splitting (10) gives:
% 242.70/49.24  | | 
% 242.70/49.24  | | Case 1:
% 242.70/49.24  | | | 
% 242.70/49.24  | | |   (11)  all_58_1 = e2 & op(e3, e2) = e2
% 242.70/49.24  | | | 
% 242.70/49.24  | | | REF_CLOSE: (2), (4), (11) are inconsistent by sub-proof #1478.
% 242.70/49.24  | | | 
% 242.70/49.24  | | Case 2:
% 242.70/49.24  | | | 
% 242.70/49.24  | | |   (12)  all_58_3 = e2 & op(e2, e2) = e2
% 242.70/49.24  | | | 
% 242.70/49.24  | | | ALPHA: (12) implies:
% 242.70/49.24  | | |   (13)  op(e2, e2) = e2
% 242.70/49.24  | | | 
% 242.70/49.24  | | | REF_CLOSE: (1), (5), (8), (13) are inconsistent by sub-proof #2140.
% 242.70/49.24  | | | 
% 242.70/49.24  | | End of split
% 242.70/49.24  | | 
% 242.70/49.24  | Case 2:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (14)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 242.70/49.24  | |           e2)
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (2), (6), (7), (8), (9), (14) are inconsistent by sub-proof
% 242.70/49.24  | |            #1376.
% 242.70/49.24  | | 
% 242.70/49.24  | End of split
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #883 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)   ~ (all_52_3 = e0)
% 242.70/49.24    (2)  op(e1, e2) = all_56_13
% 242.70/49.24    (3)  op(e1, e2) = e1
% 242.70/49.24    (4)   ~ (all_10_2 = e1)
% 242.70/49.24    (5)  op(e0, e3) = all_52_3
% 242.70/49.24    (6)   ~ (all_52_2 = e1)
% 242.70/49.24    (7)  all_58_2 = e0
% 242.70/49.24    (8)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.70/49.24         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.70/49.24    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.24    (10)  op(e1, e3) = all_52_2
% 242.70/49.24    (11)  op(e3, e3) = all_10_2
% 242.70/49.24    (12)  op(e1, e1) = e0
% 242.70/49.24    (13)  op(e1, all_56_13) = e1
% 242.70/49.24    (14)   ~ (e1 = e0)
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | BETA: splitting (8) gives:
% 242.70/49.24  | 
% 242.70/49.24  | Case 1:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (15)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 242.70/49.24  | |           e1)
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (4), (7), (9), (11), (14), (15) are inconsistent by sub-proof
% 242.70/49.24  | |            #890.
% 242.70/49.24  | | 
% 242.70/49.24  | Case 2:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (16)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 242.70/49.24  | |           e1)
% 242.70/49.24  | | 
% 242.70/49.24  | | BETA: splitting (16) gives:
% 242.70/49.24  | | 
% 242.70/49.24  | | Case 1:
% 242.70/49.24  | | | 
% 242.70/49.24  | | |   (17)  all_58_6 = e1 & op(e1, e3) = e1
% 242.70/49.24  | | | 
% 242.70/49.24  | | | ALPHA: (17) implies:
% 242.70/49.24  | | |   (18)  op(e1, e3) = e1
% 242.70/49.24  | | | 
% 242.70/49.24  | | | REF_CLOSE: (6), (9), (10), (18) are inconsistent by sub-proof #1948.
% 242.70/49.24  | | | 
% 242.70/49.24  | | Case 2:
% 242.70/49.24  | | | 
% 242.70/49.24  | | |   (19)  all_58_12 = e1 & op(e0, e3) = e1
% 242.70/49.24  | | | 
% 242.70/49.24  | | | ALPHA: (19) implies:
% 242.70/49.24  | | |   (20)  op(e0, e3) = e1
% 242.70/49.24  | | | 
% 242.70/49.24  | | | GROUND_INST: instantiating (9) with all_52_3, e1, e3, e0, simplifying with
% 242.70/49.24  | | |              (5), (20) gives:
% 242.70/49.24  | | |   (21)  all_52_3 = e1
% 242.70/49.24  | | | 
% 242.70/49.24  | | | GROUND_INST: instantiating (9) with e1, all_56_13, e2, e1, simplifying
% 242.70/49.24  | | |              with (2), (3) gives:
% 242.70/49.24  | | |   (22)  all_56_13 = e1
% 242.70/49.24  | | | 
% 242.70/49.24  | | | REDUCE: (13), (22) imply:
% 242.70/49.24  | | |   (23)  op(e1, e1) = e1
% 242.70/49.24  | | | 
% 242.70/49.24  | | | REF_CLOSE: (9), (12), (14), (23) are inconsistent by sub-proof #2220.
% 242.70/49.24  | | | 
% 242.70/49.24  | | End of split
% 242.70/49.24  | | 
% 242.70/49.24  | End of split
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #884 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)  op(e2, e3) = e0
% 242.70/49.24    (2)   ~ (e2 = e0)
% 242.70/49.24    (3)  op(e2, e3) = all_42_1
% 242.70/49.24    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.24    (5)  all_56_11 = e3
% 242.70/49.24    (6)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 242.70/49.24    (7)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.70/49.24           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.70/49.24           & $i(all_8_1))
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | ALPHA: (6) implies:
% 242.70/49.24  |   (8)  op(e2, all_56_11) = e2
% 242.70/49.24  | 
% 242.70/49.24  | REDUCE: (5), (8) imply:
% 242.70/49.24  |   (9)  op(e2, e3) = e2
% 242.70/49.24  | 
% 242.70/49.24  | REF_CLOSE: (1), (2), (3), (4), (7), (9) are inconsistent by sub-proof #889.
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #885 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 242.70/49.24    (2)   ~ (all_10_2 = e0)
% 242.70/49.24    (3)   ~ (all_10_2 = e1)
% 242.70/49.24    (4)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.70/49.24             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 242.70/49.24           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 242.70/49.24             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 242.70/49.24           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.70/49.24    (5)   ~ (all_52_12 = all_10_2)
% 242.70/49.24    (6)  all_56_31 = e0
% 242.70/49.24    (7)  op(e3, e0) = all_52_12
% 242.70/49.24    (8)  op(e3, e0) = e3
% 242.70/49.24    (9)  all_56_1 = all_10_2
% 242.70/49.24    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.24    (11)  all_54_0 = all_10_2
% 242.70/49.24  
% 242.70/49.24  Begin of proof
% 242.70/49.24  | 
% 242.70/49.24  | BETA: splitting (4) gives:
% 242.70/49.24  | 
% 242.70/49.24  | Case 1:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (12)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 242.70/49.24  | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) =
% 242.70/49.24  | |         e1 & op(e1, e2) = e1
% 242.70/49.24  | | 
% 242.70/49.24  | | ALPHA: (12) implies:
% 242.70/49.24  | |   (13)   ~ (all_56_1 = e2)
% 242.70/49.24  | | 
% 242.70/49.24  | | REDUCE: (9), (13) imply:
% 242.70/49.24  | |   (14)   ~ (all_10_2 = e2)
% 242.70/49.24  | | 
% 242.70/49.24  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (14) are inconsistent
% 242.70/49.24  | |            by sub-proof #1669.
% 242.70/49.24  | | 
% 242.70/49.24  | Case 2:
% 242.70/49.24  | | 
% 242.70/49.24  | |   (15)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 242.70/49.24  | |           = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) =
% 242.70/49.24  | |         e2 & op(e0, e2) = e2
% 242.70/49.24  | | 
% 242.70/49.24  | | ALPHA: (15) implies:
% 242.70/49.24  | |   (16)   ~ (all_56_31 = e0)
% 242.70/49.24  | | 
% 242.70/49.24  | | REDUCE: (6), (16) imply:
% 242.70/49.24  | |   (17)  $false
% 242.70/49.24  | | 
% 242.70/49.24  | | CLOSE: (17) is inconsistent.
% 242.70/49.24  | | 
% 242.70/49.24  | End of split
% 242.70/49.24  | 
% 242.70/49.24  End of proof
% 242.70/49.24  
% 242.70/49.24  Sub-proof #886 shows that the following formulas are inconsistent:
% 242.70/49.24  ----------------------------------------------------------------
% 242.70/49.24    (1)  all_28_2 = e0
% 242.70/49.24    (2)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 242.70/49.24    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.70/49.24         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.70/49.24    (4)   ~ (e3 = e0)
% 242.70/49.24    (5)   ~ (all_32_2 = e2) | ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 242.70/49.24           op(e3, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 242.70/49.24             e0) & op(e3, e2) = all_32_1 & $i(all_32_1))
% 242.70/49.24    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.70/49.24         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.70/49.24    (7)   ~ (all_52_8 = all_52_9)
% 242.70/49.24    (8)  op(e1, e2) = e1
% 242.70/49.24    (9)  op(e1, e2) = all_52_6
% 242.70/49.24    (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.24          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.24    (11)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 242.70/49.24          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 242.70/49.24    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.24          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.70/49.24    (13)   ~ (all_10_2 = e0)
% 242.70/49.24    (14)  op(e1, e0) = all_52_14
% 242.70/49.24    (15)   ~ (all_52_7 = e3)
% 242.70/49.24    (16)   ~ (all_10_2 = e1)
% 242.70/49.24    (17)   ~ (all_52_8 = all_10_2)
% 242.70/49.24    (18)   ~ (all_52_8 = e0)
% 242.70/49.24    (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.24          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.70/49.24    (20)  op(e0, e2) = e2
% 242.70/49.24    (21)   ~ (e3 = e1)
% 242.70/49.24    (22)  all_58_3 = e3
% 242.70/49.24    (23)   ~ (all_52_2 = e1)
% 242.70/49.24    (24)  all_54_2 = all_52_8
% 242.70/49.24    (25)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.70/49.24          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.70/49.24    (26)  all_58_12 = e1
% 242.70/49.24    (27)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.70/49.24              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.70/49.24                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.70/49.24                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.70/49.24    (28)  op(e2, e1) = all_52_9
% 242.70/49.24    (29)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.70/49.24          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.70/49.24    (30)   ~ (e3 = e2)
% 242.70/49.24    (31)   ~ (all_52_12 = all_10_2)
% 242.70/49.25    (32)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.70/49.25          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.70/49.25    (33)   ~ (all_52_14 = e1)
% 242.70/49.25    (34)   ~ (all_28_2 = e0) | ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 &
% 242.70/49.25            op(e1, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 242.70/49.25              e2) & op(e1, e0) = all_28_1 & $i(all_28_1))
% 242.70/49.25    (35)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.70/49.25    (36)  op(e3, e0) = all_52_12
% 242.70/49.25    (37)  all_58_13 = e2
% 242.70/49.25    (38)  all_32_2 = all_10_2
% 242.70/49.25    (39)  op(e3, e0) = e3
% 242.70/49.25    (40)  op(e2, e3) = all_52_1
% 242.70/49.25    (41)  op(e1, e2) = e2
% 242.70/49.25    (42)  op(e0, e2) = all_52_7
% 242.70/49.25    (43)  all_58_2 = e0
% 242.70/49.25    (44)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.70/49.25          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.70/49.25    (45)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.70/49.25          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.70/49.25    (46)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.70/49.25          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.70/49.25    (47)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.25          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.70/49.25    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.25    (49)  op(e0, e0) = e0
% 242.70/49.25    (50)  all_58_14 = e3
% 242.70/49.25    (51)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.70/49.25          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.70/49.25    (52)  op(e1, e3) = all_52_2
% 242.70/49.25    (53)  op(e3, e3) = all_10_2
% 242.70/49.25    (54)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.70/49.25          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.70/49.25    (55)  op(e1, e1) = e0
% 242.70/49.25    (56)   ~ (e1 = e0)
% 242.70/49.25    (57)   ~ (all_52_13 = e3)
% 242.70/49.25    (58)  all_58_15 = e0
% 242.70/49.25    (59)  op(e2, e0) = all_52_13
% 242.70/49.25    (60)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.70/49.25          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 242.70/49.25            e1)
% 242.70/49.25    (61)  all_54_0 = all_10_2
% 242.70/49.25    (62)   ~ (all_52_1 = e3)
% 242.70/49.25    (63)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.25          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.70/49.25            e2)
% 242.70/49.25    (64)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.70/49.25          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.70/49.25    (65)   ~ (all_52_8 = e3)
% 242.70/49.25  
% 242.70/49.25  Begin of proof
% 242.70/49.25  | 
% 242.70/49.25  | BETA: splitting (5) gives:
% 242.70/49.25  | 
% 242.70/49.25  | Case 1:
% 242.70/49.25  | | 
% 242.70/49.25  | |   (66)   ~ (all_32_2 = e2)
% 242.70/49.25  | | 
% 242.70/49.25  | | REDUCE: (38), (66) imply:
% 242.70/49.25  | |   (67)   ~ (all_10_2 = e2)
% 242.70/49.25  | | 
% 242.70/49.25  | | REF_CLOSE: (2), (13), (16), (31), (36), (39), (48), (61), (67) are
% 242.70/49.25  | |            inconsistent by sub-proof #1669.
% 242.70/49.25  | | 
% 242.70/49.25  | Case 2:
% 242.70/49.25  | | 
% 242.70/49.25  | |   (68)  all_32_2 = e2
% 242.70/49.25  | | 
% 242.70/49.25  | | COMBINE_EQS: (38), (68) imply:
% 242.70/49.25  | |   (69)  all_10_2 = e2
% 242.70/49.25  | | 
% 242.70/49.25  | | REDUCE: (17), (69) imply:
% 242.70/49.25  | |   (70)   ~ (all_52_8 = e2)
% 242.70/49.25  | | 
% 242.70/49.25  | | REDUCE: (16), (69) imply:
% 242.70/49.25  | |   (71)   ~ (e2 = e1)
% 242.70/49.25  | | 
% 242.70/49.25  | | REDUCE: (13), (69) imply:
% 242.70/49.25  | |   (72)   ~ (e2 = e0)
% 242.70/49.25  | | 
% 242.70/49.25  | | REDUCE: (53), (69) imply:
% 242.70/49.25  | |   (73)  op(e3, e3) = e2
% 242.70/49.25  | | 
% 242.70/49.25  | | BETA: splitting (25) gives:
% 242.70/49.25  | | 
% 242.70/49.25  | | Case 1:
% 242.70/49.25  | | | 
% 242.70/49.25  | | |   (74)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 242.70/49.25  | | |           e3)
% 242.70/49.25  | | | 
% 242.70/49.25  | | | REF_CLOSE: (30), (40), (48), (62), (73), (74) are inconsistent by
% 242.70/49.25  | | |            sub-proof #1404.
% 242.70/49.25  | | | 
% 242.70/49.25  | | Case 2:
% 242.70/49.25  | | | 
% 242.70/49.25  | | |   (75)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 242.70/49.25  | | |           e3)
% 242.70/49.25  | | | 
% 242.70/49.25  | | | BETA: splitting (75) gives:
% 242.70/49.25  | | | 
% 242.70/49.25  | | | Case 1:
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | |   (76)  all_58_6 = e3 & op(e1, e3) = e3
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | | ALPHA: (76) implies:
% 242.70/49.25  | | | |   (77)  all_58_6 = e3
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | | BETA: splitting (35) gives:
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | | Case 1:
% 242.70/49.25  | | | | | 
% 242.70/49.25  | | | | |   (78)  all_54_2 = e3
% 242.70/49.25  | | | | | 
% 242.70/49.25  | | | | | COMBINE_EQS: (24), (78) imply:
% 242.70/49.25  | | | | |   (79)  all_52_8 = e3
% 242.70/49.25  | | | | | 
% 242.70/49.25  | | | | | REDUCE: (65), (79) imply:
% 242.70/49.25  | | | | |   (80)  $false
% 242.70/49.25  | | | | | 
% 242.70/49.25  | | | | | CLOSE: (80) is inconsistent.
% 242.70/49.25  | | | | | 
% 242.70/49.25  | | | | Case 2:
% 242.70/49.25  | | | | | 
% 242.70/49.25  | | | | |   (81)   ~ (all_54_2 = e3)
% 242.70/49.25  | | | | |   (82)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 242.70/49.25  | | | | | 
% 242.70/49.25  | | | | | BETA: splitting (82) gives:
% 242.70/49.25  | | | | | 
% 242.70/49.25  | | | | | Case 1:
% 242.70/49.25  | | | | | | 
% 242.70/49.25  | | | | | |   (83)  all_54_2 = e2
% 242.70/49.25  | | | | | | 
% 242.70/49.25  | | | | | | COMBINE_EQS: (24), (83) imply:
% 242.70/49.25  | | | | | |   (84)  all_52_8 = e2
% 242.70/49.25  | | | | | | 
% 242.70/49.25  | | | | | | REDUCE: (70), (84) imply:
% 242.70/49.25  | | | | | |   (85)  $false
% 242.70/49.25  | | | | | | 
% 242.70/49.25  | | | | | | CLOSE: (85) is inconsistent.
% 242.70/49.25  | | | | | | 
% 242.70/49.25  | | | | | Case 2:
% 242.70/49.25  | | | | | | 
% 242.70/49.25  | | | | | |   (86)   ~ (all_54_2 = e2)
% 242.70/49.25  | | | | | |   (87)  all_54_2 = e1 | all_54_2 = e0
% 242.70/49.25  | | | | | | 
% 242.70/49.25  | | | | | | BETA: splitting (46) gives:
% 242.70/49.25  | | | | | | 
% 242.70/49.25  | | | | | | Case 1:
% 242.70/49.25  | | | | | | | 
% 242.70/49.25  | | | | | | |   (88)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 242.70/49.25  | | | | | | |           op(e1, e2) = e2)
% 242.70/49.25  | | | | | | | 
% 242.70/49.25  | | | | | | | BETA: splitting (88) gives:
% 242.70/49.25  | | | | | | | 
% 242.70/49.25  | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | |   (89)  all_58_6 = e2 & op(e1, e3) = e2
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | | ALPHA: (89) implies:
% 242.70/49.25  | | | | | | | |   (90)  all_58_6 = e2
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | | COMBINE_EQS: (77), (90) imply:
% 242.70/49.25  | | | | | | | |   (91)  e3 = e2
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | | COMBINE_EQS: (50), (91) imply:
% 242.70/49.25  | | | | | | | |   (92)  all_58_14 = e2
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | | REF_CLOSE: (3), (4), (15), (20), (21), (26), (27), (30), (42),
% 242.70/49.25  | | | | | | | |            (48), (56), (72), (92) are inconsistent by sub-proof
% 242.70/49.25  | | | | | | | |            #1536.
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | |   (93)  all_58_7 = e2 & op(e1, e2) = e2
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | | ALPHA: (93) implies:
% 242.70/49.25  | | | | | | | |   (94)  all_58_7 = e2
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | | REF_CLOSE: (4), (10), (12), (20), (21), (22), (30), (37), (48),
% 242.70/49.25  | | | | | | | |            (54), (56), (71), (72), (94) are inconsistent by
% 242.70/49.25  | | | | | | | |            sub-proof #1454.
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | End of split
% 242.70/49.25  | | | | | | | 
% 242.70/49.25  | | | | | | Case 2:
% 242.70/49.25  | | | | | | | 
% 242.70/49.25  | | | | | | |   (95)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 242.70/49.25  | | | | | | |           op(e1, e0) = e2)
% 242.70/49.25  | | | | | | | 
% 242.70/49.25  | | | | | | | BETA: splitting (95) gives:
% 242.70/49.25  | | | | | | | 
% 242.70/49.25  | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | |   (96)  all_58_8 = e2 & op(e1, e1) = e2
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | | ALPHA: (96) implies:
% 242.70/49.25  | | | | | | | |   (97)  op(e1, e1) = e2
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | | REF_CLOSE: (48), (55), (72), (97) are inconsistent by sub-proof
% 242.70/49.25  | | | | | | | |            #2211.
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | |   (98)  all_58_11 = e2 & op(e1, e0) = e2
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | | ALPHA: (98) implies:
% 242.70/49.25  | | | | | | | |   (99)  op(e1, e0) = e2
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | | BETA: splitting (87) gives:
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | |   (100)  all_54_2 = e1
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | COMBINE_EQS: (24), (100) imply:
% 242.70/49.25  | | | | | | | | |   (101)  all_52_8 = e1
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | REDUCE: (7), (101) imply:
% 242.70/49.25  | | | | | | | | |   (102)   ~ (all_52_9 = e1)
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | SIMP: (102) implies:
% 242.70/49.25  | | | | | | | | |   (103)   ~ (all_52_9 = e1)
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | REDUCE: (65), (101) imply:
% 242.70/49.25  | | | | | | | | |   (104)   ~ (e3 = e1)
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | REDUCE: (70), (101) imply:
% 242.70/49.25  | | | | | | | | |   (105)   ~ (e2 = e1)
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | BETA: splitting (11) gives:
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | |   (106)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1
% 242.70/49.25  | | | | | | | | | |            & op(e2, e0) = e1)
% 242.70/49.25  | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | BETA: splitting (106) gives:
% 242.70/49.25  | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | |   (107)  all_58_9 = e1 & op(e3, e0) = e1
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | ALPHA: (107) implies:
% 242.70/49.25  | | | | | | | | | | |   (108)  all_58_9 = e1
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | BETA: splitting (64) gives:
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | |   (109)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 242.70/49.25  | | | | | | | | | | | |            & op(e2, e2) = e1)
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | BETA: splitting (109) gives:
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | |   (110)  all_58_2 = e1 & op(e2, e3) = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | ALPHA: (110) implies:
% 242.70/49.25  | | | | | | | | | | | | |   (111)  all_58_2 = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | COMBINE_EQS: (43), (111) imply:
% 242.70/49.25  | | | | | | | | | | | | |   (112)  e1 = e0
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | SIMP: (112) implies:
% 242.70/49.25  | | | | | | | | | | | | |   (113)  e1 = e0
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | COMBINE_EQS: (108), (113) imply:
% 242.70/49.25  | | | | | | | | | | | | |   (114)  all_58_9 = e0
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | REF_CLOSE: (4), (11), (21), (30), (44), (48), (49), (51),
% 242.70/49.25  | | | | | | | | | | | | |            (56), (57), (58), (59), (71), (72), (114) are
% 242.70/49.25  | | | | | | | | | | | | |            inconsistent by sub-proof #1652.
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | |   (115)  all_58_3 = e1 & op(e2, e2) = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | REF_CLOSE: (21), (22), (115) are inconsistent by sub-proof
% 242.70/49.25  | | | | | | | | | | | | |            #2197.
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | |   (116)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 242.70/49.25  | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | BETA: splitting (116) gives:
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | |   (117)  all_58_5 = e1 & op(e2, e1) = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | ALPHA: (117) implies:
% 242.70/49.25  | | | | | | | | | | | | |   (118)  op(e2, e1) = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | REF_CLOSE: (28), (48), (103), (118) are inconsistent by
% 242.70/49.25  | | | | | | | | | | | | |            sub-proof #2306.
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | |   (119)  all_58_10 = e1 & op(e2, e0) = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | ALPHA: (119) implies:
% 242.70/49.25  | | | | | | | | | | | | |   (120)  all_58_10 = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | REF_CLOSE: (4), (21), (30), (44), (51), (58), (71), (72),
% 242.70/49.25  | | | | | | | | | | | | |            (108), (120) are inconsistent by sub-proof #1495.
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | |   (121)  all_58_10 = e1 & op(e2, e0) = e1
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | ALPHA: (121) implies:
% 242.70/49.25  | | | | | | | | | | |   (122)  all_58_10 = e1
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | BETA: splitting (45) gives:
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | |   (123)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 242.70/49.25  | | | | | | | | | | | |            & op(e3, e2) = e1)
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | BETA: splitting (123) gives:
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | |   (124)  all_58_0 = e1 & op(e3, e3) = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | ALPHA: (124) implies:
% 242.70/49.25  | | | | | | | | | | | | |   (125)  op(e3, e3) = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | REF_CLOSE: (26), (29), (30), (43), (48), (71), (72), (77),
% 242.70/49.25  | | | | | | | | | | | | |            (125) are inconsistent by sub-proof #1328.
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | |   (126)  all_58_1 = e1 & op(e3, e2) = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | ALPHA: (126) implies:
% 242.70/49.25  | | | | | | | | | | | | |   (127)  all_58_1 = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (12), (20), (22), (48), (56), (72),
% 242.70/49.25  | | | | | | | | | | | | |            (127) are inconsistent by sub-proof #1718.
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | |   (128)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 242.70/49.25  | | | | | | | | | | | |            & op(e3, e0) = e1)
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | BETA: splitting (128) gives:
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | |   (129)  all_58_4 = e1 & op(e3, e1) = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | ALPHA: (129) implies:
% 242.70/49.25  | | | | | | | | | | | | |   (130)  all_58_4 = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | BETA: splitting (32) gives:
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | |   (131)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 242.70/49.25  | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 242.70/49.25  | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 242.70/49.25  | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | |   (132)  all_58_4 = e2 & op(e3, e1) = e2
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 242.70/49.25  | | | | | | | | | | | | | | |   (133)  all_58_4 = e2
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | COMBINE_EQS: (130), (133) imply:
% 242.70/49.25  | | | | | | | | | | | | | | |   (134)  e2 = e1
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | SIMP: (134) implies:
% 242.70/49.25  | | | | | | | | | | | | | | |   (135)  e2 = e1
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | COMBINE_EQS: (37), (135) imply:
% 242.70/49.25  | | | | | | | | | | | | | | |   (136)  all_58_13 = e1
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (10), (12), (14), (22), (23), (30),
% 242.70/49.25  | | | | | | | | | | | | | | |            (33), (48), (52), (55), (56), (71), (72), (136)
% 242.70/49.25  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #887.
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | |   (137)  all_58_5 = e2 & op(e2, e1) = e2
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 242.70/49.25  | | | | | | | | | | | | | | |   (138)  all_58_5 = e2
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | |   (139)   ~ (all_28_2 = e0)
% 242.70/49.25  | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | REDUCE: (1), (139) imply:
% 242.70/49.25  | | | | | | | | | | | | | | | |   (140)  $false
% 242.70/49.25  | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 242.70/49.25  | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | |   (141)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0
% 242.70/49.25  | | | | | | | | | | | | | | | |            & op(e1, e0) = all_28_1 & $i(all_28_0) &
% 242.70/49.25  | | | | | | | | | | | | | | | |            $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0)
% 242.70/49.25  | | | | | | | | | | | | | | | |            = all_28_1 & $i(all_28_1))
% 242.70/49.25  | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 242.70/49.25  | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (48) with e1, e2, e2, e1,
% 242.70/49.25  | | | | | | | | | | | | | | | | |              simplifying with (8), (41) gives:
% 242.70/49.25  | | | | | | | | | | | | | | | | |   (142)  e2 = e1
% 242.70/49.25  | | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (142) imply:
% 242.70/49.25  | | | | | | | | | | | | | | | | |   (143)  all_58_5 = e1
% 242.70/49.25  | | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19), (22), (30), (47), (56), (71), (72),
% 242.70/49.25  | | | | | | | | | | | | | | | | |            (122), (143) are inconsistent by sub-proof #992.
% 242.70/49.25  | | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | |   (144)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 &
% 242.70/49.25  | | | | | | | | | | | | | | | | |          $i(all_28_1)
% 242.70/49.25  | | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 242.70/49.25  | | | | | | | | | | | | | | | | |   (145)   ~ (all_28_1 = e2)
% 242.70/49.25  | | | | | | | | | | | | | | | | |   (146)  op(e1, e0) = all_28_1
% 242.70/49.25  | | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (99), (145), (146) are inconsistent by
% 242.70/49.25  | | | | | | | | | | | | | | | | |            sub-proof #1944.
% 242.70/49.25  | | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | |   (147)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 242.70/49.25  | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 242.70/49.25  | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 242.70/49.25  | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | |   (148)  all_58_8 = e2 & op(e1, e1) = e2
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 242.70/49.25  | | | | | | | | | | | | | | |   (149)  op(e1, e1) = e2
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | REF_CLOSE: (48), (55), (72), (149) are inconsistent by
% 242.70/49.25  | | | | | | | | | | | | | | |            sub-proof #2211.
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | |   (150)  all_58_14 = e2 & op(e0, e1) = e2
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 242.70/49.25  | | | | | | | | | | | | | | |   (151)  all_58_14 = e2
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (15), (20), (21), (26), (27), (30),
% 242.70/49.25  | | | | | | | | | | | | | | |            (42), (48), (56), (72), (151) are inconsistent by
% 242.70/49.25  | | | | | | | | | | | | | | |            sub-proof #1536.
% 242.70/49.25  | | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | |   (152)  all_58_9 = e1 & op(e3, e0) = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | ALPHA: (152) implies:
% 242.70/49.25  | | | | | | | | | | | | |   (153)  all_58_9 = e1
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | | REF_CLOSE: (4), (21), (30), (44), (51), (58), (71), (72),
% 242.70/49.25  | | | | | | | | | | | | |            (122), (153) are inconsistent by sub-proof #1495.
% 242.70/49.25  | | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | |   (154)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 242.70/49.25  | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 242.70/49.25  | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | BETA: splitting (154) gives:
% 242.70/49.25  | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | Case 1:
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | |   (155)  all_58_11 = e1 & op(e1, e0) = e1
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | ALPHA: (155) implies:
% 242.70/49.25  | | | | | | | | | | |   (156)  op(e1, e0) = e1
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | REF_CLOSE: (14), (33), (48), (156) are inconsistent by
% 242.70/49.25  | | | | | | | | | | |            sub-proof #2304.
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | |   (157)  all_58_15 = e1 & op(e0, e0) = e1
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | ALPHA: (157) implies:
% 242.70/49.25  | | | | | | | | | | |   (158)  op(e0, e0) = e1
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | | REF_CLOSE: (48), (49), (56), (158) are inconsistent by
% 242.70/49.25  | | | | | | | | | | |            sub-proof #2274.
% 242.70/49.25  | | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | Case 2:
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | |   (159)  all_54_2 = e0
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | COMBINE_EQS: (24), (159) imply:
% 242.70/49.25  | | | | | | | | |   (160)  all_52_8 = e0
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | REDUCE: (18), (160) imply:
% 242.70/49.25  | | | | | | | | |   (161)  $false
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | | CLOSE: (161) is inconsistent.
% 242.70/49.25  | | | | | | | | | 
% 242.70/49.25  | | | | | | | | End of split
% 242.70/49.25  | | | | | | | | 
% 242.70/49.25  | | | | | | | End of split
% 242.70/49.25  | | | | | | | 
% 242.70/49.25  | | | | | | End of split
% 242.70/49.25  | | | | | | 
% 242.70/49.25  | | | | | End of split
% 242.70/49.25  | | | | | 
% 242.70/49.25  | | | | End of split
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | Case 2:
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | |   (162)  all_58_12 = e3 & op(e0, e3) = e3
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | | ALPHA: (162) implies:
% 242.70/49.25  | | | |   (163)  all_58_12 = e3
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | | REF_CLOSE: (4), (21), (27), (30), (48), (50), (56), (60), (63), (71),
% 242.70/49.25  | | | |            (72), (163) are inconsistent by sub-proof #1862.
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | End of split
% 242.70/49.25  | | | 
% 242.70/49.25  | | End of split
% 242.70/49.25  | | 
% 242.70/49.25  | End of split
% 242.70/49.25  | 
% 242.70/49.25  End of proof
% 242.70/49.25  
% 242.70/49.25  Sub-proof #887 shows that the following formulas are inconsistent:
% 242.70/49.25  ----------------------------------------------------------------
% 242.70/49.25    (1)   ~ (e3 = e0)
% 242.70/49.25    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.70/49.25         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.70/49.25    (3)   ~ (e2 = e0)
% 242.70/49.25    (4)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.25         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.70/49.25    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.25         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.70/49.25    (6)  op(e1, e0) = all_52_14
% 242.70/49.25    (7)  all_58_3 = e3
% 242.70/49.25    (8)   ~ (all_52_2 = e1)
% 242.70/49.25    (9)   ~ (e3 = e2)
% 242.70/49.25    (10)   ~ (all_52_14 = e1)
% 242.70/49.25    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.25    (12)  op(e1, e3) = all_52_2
% 242.70/49.25    (13)  op(e1, e1) = e0
% 242.70/49.25    (14)   ~ (e1 = e0)
% 242.70/49.25    (15)  all_58_13 = e1
% 242.70/49.25    (16)   ~ (e2 = e1)
% 242.70/49.25  
% 242.70/49.25  Begin of proof
% 242.70/49.25  | 
% 242.70/49.25  | BETA: splitting (2) gives:
% 242.70/49.25  | 
% 242.70/49.25  | Case 1:
% 242.70/49.25  | | 
% 242.70/49.25  | |   (17)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 242.70/49.25  | |           e1)
% 242.70/49.25  | | 
% 242.70/49.25  | | BETA: splitting (17) gives:
% 242.70/49.25  | | 
% 242.70/49.25  | | Case 1:
% 242.70/49.25  | | | 
% 242.70/49.25  | | |   (18)  all_58_6 = e1 & op(e1, e3) = e1
% 242.70/49.25  | | | 
% 242.70/49.25  | | | ALPHA: (18) implies:
% 242.70/49.25  | | |   (19)  op(e1, e3) = e1
% 242.70/49.25  | | | 
% 242.70/49.25  | | | REF_CLOSE: (8), (11), (12), (19) are inconsistent by sub-proof #1948.
% 242.70/49.25  | | | 
% 242.70/49.25  | | Case 2:
% 242.70/49.25  | | | 
% 242.70/49.25  | | |   (20)  all_58_7 = e1 & op(e1, e2) = e1
% 242.70/49.25  | | | 
% 242.70/49.25  | | | ALPHA: (20) implies:
% 242.70/49.25  | | |   (21)  all_58_7 = e1
% 242.70/49.25  | | | 
% 242.70/49.25  | | | REF_CLOSE: (1), (3), (4), (5), (7), (9), (14), (15), (16), (21) are
% 242.70/49.25  | | |            inconsistent by sub-proof #1457.
% 242.70/49.25  | | | 
% 242.70/49.25  | | End of split
% 242.70/49.25  | | 
% 242.70/49.25  | Case 2:
% 242.70/49.25  | | 
% 242.70/49.25  | |   (22)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 242.70/49.25  | |           e1)
% 242.70/49.25  | | 
% 242.70/49.25  | | REF_CLOSE: (6), (10), (11), (13), (14), (22) are inconsistent by sub-proof
% 242.70/49.25  | |            #1086.
% 242.70/49.25  | | 
% 242.70/49.25  | End of split
% 242.70/49.25  | 
% 242.70/49.25  End of proof
% 242.70/49.25  
% 242.70/49.25  Sub-proof #888 shows that the following formulas are inconsistent:
% 242.70/49.25  ----------------------------------------------------------------
% 242.70/49.25    (1)   ~ (all_52_3 = e0)
% 242.70/49.25    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.70/49.25    (3)  op(e2, e3) = e0
% 242.70/49.25    (4)   ~ (e2 = e0)
% 242.70/49.25    (5)   ~ (all_52_7 = all_52_11)
% 242.70/49.25    (6)  op(e0, e3) = all_52_3
% 242.70/49.25    (7)  op(e0, e2) = e2
% 242.70/49.25    (8)  op(e2, e3) = all_42_1
% 242.70/49.25    (9)   ~ (all_52_2 = all_52_3)
% 242.70/49.25    (10)   ~ (all_52_2 = e1)
% 242.70/49.25    (11)   ~ (all_52_3 = all_52_7)
% 242.70/49.25    (12)  op(e3, e1) = all_52_8
% 242.70/49.25    (13)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.70/49.25    (14)   ~ (all_52_3 = all_52_11)
% 242.70/49.25    (15)  all_56_31 = e0
% 242.70/49.25    (16)  all_54_12 = all_52_3
% 242.70/49.25    (17)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.70/49.25              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.70/49.25            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.70/49.25            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.70/49.25            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.70/49.25             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.70/49.25            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.70/49.25            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.70/49.25            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.70/49.25            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.25            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.70/49.25              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.70/49.25            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.70/49.25            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.70/49.25    (18)  op(e2, e3) = all_52_1
% 242.70/49.25    (19)   ~ (all_52_11 = e0)
% 242.70/49.25    (20)  op(e0, e2) = all_52_7
% 242.70/49.25    (21)   ~ (all_52_8 = all_52_11)
% 242.70/49.25    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.25    (23)  op(e1, e3) = all_52_2
% 242.70/49.25    (24)   ~ (all_52_1 = e3)
% 242.70/49.25    (25)  all_54_14 = all_52_11
% 242.70/49.25    (26)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.70/49.25            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.70/49.25            & $i(all_8_1))
% 242.70/49.25  
% 242.70/49.25  Begin of proof
% 242.70/49.25  | 
% 242.70/49.25  | BETA: splitting (17) gives:
% 242.70/49.25  | 
% 242.70/49.25  | Case 1:
% 242.70/49.25  | | 
% 242.70/49.25  | |   (27)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 242.70/49.25  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 242.70/49.25  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 242.70/49.25  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.70/49.25  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 242.70/49.25  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 242.70/49.25  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 242.70/49.25  | |           op(e1, e3) = e3)
% 242.70/49.25  | | 
% 242.70/49.25  | | BETA: splitting (27) gives:
% 242.70/49.25  | | 
% 242.70/49.25  | | Case 1:
% 242.70/49.25  | | | 
% 242.70/49.25  | | |   (28)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 242.70/49.25  | | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 242.70/49.25  | | |         e3 & op(e2, e3) = e3
% 242.70/49.25  | | | 
% 242.70/49.25  | | | ALPHA: (28) implies:
% 242.70/49.25  | | |   (29)  op(e2, e3) = e3
% 242.70/49.25  | | | 
% 242.70/49.25  | | | REF_CLOSE: (18), (22), (24), (29) are inconsistent by sub-proof #2337.
% 242.70/49.25  | | | 
% 242.70/49.25  | | Case 2:
% 242.70/49.25  | | | 
% 242.70/49.25  | | |   (30)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.70/49.25  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.70/49.25  | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17
% 242.70/49.25  | | |           = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 242.70/49.25  | | |             = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 242.70/49.25  | | |           e3)
% 242.70/49.25  | | | 
% 242.70/49.25  | | | BETA: splitting (30) gives:
% 242.70/49.25  | | | 
% 242.70/49.25  | | | Case 1:
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | |   (31)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.70/49.25  | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.70/49.25  | | | |         op(e3, e2) = e2 & op(e2, e3) = e2
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | | ALPHA: (31) implies:
% 242.70/49.25  | | | |   (32)  op(e2, e3) = e2
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | | REF_CLOSE: (3), (4), (8), (22), (26), (32) are inconsistent by sub-proof
% 242.70/49.25  | | | |            #889.
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | Case 2:
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | |   (33)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.70/49.25  | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.70/49.25  | | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | | REF_CLOSE: (1), (2), (5), (7), (9), (11), (12), (13), (14), (16), (19),
% 242.70/49.25  | | | |            (20), (21), (22), (23), (25), (33) are inconsistent by
% 242.70/49.25  | | | |            sub-proof #1854.
% 242.70/49.25  | | | | 
% 242.70/49.25  | | | End of split
% 242.70/49.25  | | | 
% 242.70/49.25  | | End of split
% 242.70/49.25  | | 
% 242.70/49.25  | Case 2:
% 242.70/49.25  | | 
% 242.70/49.25  | |   (34)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 242.70/49.25  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 242.70/49.25  | |           e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 242.70/49.25  | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.70/49.25  | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7
% 242.70/49.25  | |           = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &
% 242.70/49.25  | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 242.70/49.25  | |           op(e0, e3) = e0)
% 242.70/49.25  | | 
% 242.70/49.25  | | REF_CLOSE: (1), (6), (10), (15), (22), (23), (34) are inconsistent by
% 242.70/49.25  | |            sub-proof #1002.
% 242.70/49.25  | | 
% 242.70/49.25  | End of split
% 242.70/49.25  | 
% 242.70/49.25  End of proof
% 242.70/49.25  
% 242.70/49.25  Sub-proof #889 shows that the following formulas are inconsistent:
% 242.70/49.25  ----------------------------------------------------------------
% 242.70/49.25    (1)  op(e2, e3) = e0
% 242.70/49.25    (2)   ~ (e2 = e0)
% 242.70/49.25    (3)  op(e2, e3) = all_42_1
% 242.70/49.25    (4)  op(e2, e3) = e2
% 242.70/49.26    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.26    (6)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.70/49.26           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.70/49.26           & $i(all_8_1))
% 242.70/49.26  
% 242.70/49.26  Begin of proof
% 242.70/49.26  | 
% 242.70/49.26  | BETA: splitting (6) gives:
% 242.70/49.26  | 
% 242.70/49.26  | Case 1:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (7)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1
% 242.70/49.26  | |        & $i(all_8_0) & $i(all_8_1)
% 242.70/49.26  | | 
% 242.70/49.26  | | ALPHA: (7) implies:
% 242.70/49.26  | |   (8)  op(e2, e3) = all_8_1
% 242.70/49.26  | | 
% 242.70/49.26  | | REF_CLOSE: (1), (2), (3), (4), (5), (8) are inconsistent by sub-proof #903.
% 242.70/49.26  | | 
% 242.70/49.26  | Case 2:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (9)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 242.70/49.26  | | 
% 242.70/49.26  | | ALPHA: (9) implies:
% 242.70/49.26  | |   (10)  op(e2, e3) = all_8_1
% 242.70/49.26  | | 
% 242.70/49.26  | | REF_CLOSE: (1), (2), (3), (4), (5), (10) are inconsistent by sub-proof #903.
% 242.70/49.26  | | 
% 242.70/49.26  | End of split
% 242.70/49.26  | 
% 242.70/49.26  End of proof
% 242.70/49.26  
% 242.70/49.26  Sub-proof #890 shows that the following formulas are inconsistent:
% 242.70/49.26  ----------------------------------------------------------------
% 242.70/49.26    (1)   ~ (all_10_2 = e1)
% 242.70/49.26    (2)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 242.70/49.26    (3)  all_58_2 = e0
% 242.70/49.26    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.26    (5)  op(e3, e3) = all_10_2
% 242.70/49.26    (6)   ~ (e1 = e0)
% 242.70/49.26  
% 242.70/49.26  Begin of proof
% 242.70/49.26  | 
% 242.70/49.26  | BETA: splitting (2) gives:
% 242.70/49.26  | 
% 242.70/49.26  | Case 1:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 242.70/49.26  | | 
% 242.70/49.26  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #2230.
% 242.70/49.26  | | 
% 242.70/49.26  | Case 2:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (8)  all_58_2 = e1 & op(e2, e3) = e1
% 242.70/49.26  | | 
% 242.70/49.26  | | ALPHA: (8) implies:
% 242.70/49.26  | |   (9)  all_58_2 = e1
% 242.70/49.26  | | 
% 242.70/49.26  | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #1268.
% 242.70/49.26  | | 
% 242.70/49.26  | End of split
% 242.70/49.26  | 
% 242.70/49.26  End of proof
% 242.70/49.26  
% 242.70/49.26  Sub-proof #891 shows that the following formulas are inconsistent:
% 242.70/49.26  ----------------------------------------------------------------
% 242.70/49.26    (1)  op(e2, e2) = e3
% 242.70/49.26    (2)   ~ (e3 = e0)
% 242.70/49.26    (3)   ~ (e2 = e0)
% 242.70/49.26    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.26         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.70/49.26    (5)  op(e0, e2) = e2
% 242.70/49.26    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 242.70/49.26    (7)  all_58_3 = e3
% 242.70/49.26    (8)   ~ (e3 = e2)
% 242.70/49.26    (9)  all_58_7 = e1
% 242.70/49.26    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.26    (11)   ~ (e1 = e0)
% 242.70/49.26  
% 242.70/49.26  Begin of proof
% 242.70/49.26  | 
% 242.70/49.26  | BETA: splitting (6) gives:
% 242.70/49.26  | 
% 242.70/49.26  | Case 1:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (12)  all_58_1 = e2 & op(e3, e2) = e2
% 242.70/49.26  | | 
% 242.70/49.26  | | ALPHA: (12) implies:
% 242.70/49.26  | |   (13)  all_58_1 = e2
% 242.70/49.26  | | 
% 242.70/49.26  | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (13) are inconsistent
% 242.70/49.26  | |            by sub-proof #1353.
% 242.70/49.26  | | 
% 242.70/49.26  | Case 2:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (14)  all_58_3 = e2 & op(e2, e2) = e2
% 242.70/49.26  | | 
% 242.70/49.26  | | ALPHA: (14) implies:
% 242.70/49.26  | |   (15)  op(e2, e2) = e2
% 242.70/49.26  | | 
% 242.70/49.26  | | REF_CLOSE: (1), (8), (10), (15) are inconsistent by sub-proof #2140.
% 242.70/49.26  | | 
% 242.70/49.26  | End of split
% 242.70/49.26  | 
% 242.70/49.26  End of proof
% 242.70/49.26  
% 242.70/49.26  Sub-proof #892 shows that the following formulas are inconsistent:
% 242.70/49.26  ----------------------------------------------------------------
% 242.70/49.26    (1)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 242.70/49.26    (2)  all_58_1 = e0
% 242.70/49.26    (3)   ~ (e3 = e1)
% 242.70/49.26    (4)  all_58_3 = e3
% 242.70/49.26    (5)   ~ (e1 = e0)
% 242.70/49.26  
% 242.70/49.26  Begin of proof
% 242.70/49.26  | 
% 242.70/49.26  | BETA: splitting (1) gives:
% 242.70/49.26  | 
% 242.70/49.26  | Case 1:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (6)  all_58_1 = e1 & op(e3, e2) = e1
% 242.70/49.26  | | 
% 242.70/49.26  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #2015.
% 242.70/49.26  | | 
% 242.70/49.26  | Case 2:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (7)  all_58_3 = e1 & op(e2, e2) = e1
% 242.70/49.26  | | 
% 242.70/49.26  | | ALPHA: (7) implies:
% 242.70/49.26  | |   (8)  all_58_3 = e1
% 242.70/49.26  | | 
% 242.70/49.26  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #1999.
% 242.70/49.26  | | 
% 242.70/49.26  | End of split
% 242.70/49.26  | 
% 242.70/49.26  End of proof
% 242.70/49.26  
% 242.70/49.26  Sub-proof #893 shows that the following formulas are inconsistent:
% 242.70/49.26  ----------------------------------------------------------------
% 242.70/49.26    (1)  all_54_13 = all_8_0
% 242.70/49.26    (2)  all_54_13 = e3
% 242.70/49.26    (3)   ~ (all_8_0 = e3)
% 242.70/49.26  
% 242.70/49.26  Begin of proof
% 242.70/49.26  | 
% 242.70/49.26  | COMBINE_EQS: (1), (2) imply:
% 242.70/49.26  |   (4)  all_8_0 = e3
% 242.70/49.26  | 
% 242.70/49.26  | SIMP: (4) implies:
% 242.70/49.26  |   (5)  all_8_0 = e3
% 242.70/49.26  | 
% 242.70/49.26  | REDUCE: (3), (5) imply:
% 242.70/49.26  |   (6)  $false
% 242.70/49.26  | 
% 242.70/49.26  | CLOSE: (6) is inconsistent.
% 242.70/49.26  | 
% 242.70/49.26  End of proof
% 242.70/49.26  
% 242.70/49.26  Sub-proof #894 shows that the following formulas are inconsistent:
% 242.70/49.26  ----------------------------------------------------------------
% 242.70/49.26    (1)  op(e0, e0) = e1
% 242.70/49.26    (2)  op(e2, e2) = e3
% 242.70/49.26    (3)   ~ (e3 = e0)
% 242.70/49.26    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.70/49.26         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.70/49.26    (5)   ~ (e2 = e0)
% 242.70/49.26    (6)  op(e1, e2) = all_52_6
% 242.70/49.26    (7)  op(e1, e0) = all_52_14
% 242.70/49.26    (8)   ~ (all_52_13 = e1)
% 242.70/49.26    (9)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.70/49.26         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.70/49.26    (10)   ~ (e3 = e1)
% 242.70/49.26    (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.70/49.26          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.70/49.26    (12)  all_58_3 = e3
% 242.70/49.26    (13)  all_58_11 = e2 & op(e1, e0) = e2
% 242.70/49.26    (14)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.70/49.26              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.70/49.26                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.70/49.26                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.70/49.26    (15)  op(e2, e1) = all_52_9
% 242.70/49.26    (16)   ~ (e3 = e2)
% 242.70/49.26    (17)   ~ (all_52_14 = e1)
% 242.70/49.26    (18)   ~ (all_52_7 = e1)
% 242.70/49.26    (19)  all_58_15 = e1
% 242.70/49.26    (20)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.70/49.26          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.70/49.26    (21)  op(e2, e3) = all_52_1
% 242.70/49.26    (22)  op(e3, e3) = e2
% 242.70/49.26    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.70/49.26          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.70/49.26    (24)   ~ (all_52_6 = e3)
% 242.70/49.26    (25)  op(e1, e1) = e2
% 242.70/49.26    (26)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.70/49.26          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.70/49.26    (27)  op(e0, e2) = all_52_7
% 242.70/49.26    (28)   ~ (all_52_9 = e3)
% 242.70/49.26    (29)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.70/49.26          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.70/49.26    (30)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.70/49.26          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.70/49.26    (31)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.70/49.26          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.70/49.26    (32)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.26    (33)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.70/49.26          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.70/49.26    (34)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.70/49.26          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.70/49.26    (35)   ~ (e1 = e0)
% 242.70/49.26    (36)   ~ (all_52_13 = e3)
% 242.70/49.26    (37)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.70/49.26          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.70/49.26    (38)  op(e2, e0) = all_52_13
% 242.70/49.26    (39)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.70/49.26          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.70/49.26    (40)   ~ (all_52_1 = e2)
% 242.70/49.26    (41)   ~ (e2 = e1)
% 242.70/49.26  
% 242.70/49.26  Begin of proof
% 242.70/49.26  | 
% 242.70/49.26  | ALPHA: (13) implies:
% 242.70/49.26  |   (42)  all_58_11 = e2
% 242.70/49.26  | 
% 242.70/49.26  | BETA: splitting (20) gives:
% 242.70/49.26  | 
% 242.70/49.26  | Case 1:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (43)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 242.70/49.26  | |           e3)
% 242.70/49.26  | | 
% 242.70/49.26  | | BETA: splitting (43) gives:
% 242.70/49.26  | | 
% 242.70/49.26  | | Case 1:
% 242.70/49.26  | | | 
% 242.70/49.26  | | |   (44)  all_58_6 = e3 & op(e1, e3) = e3
% 242.70/49.26  | | | 
% 242.70/49.26  | | | ALPHA: (44) implies:
% 242.70/49.26  | | |   (45)  all_58_6 = e3
% 242.70/49.26  | | | 
% 242.70/49.26  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.70/49.26  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 242.70/49.26  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 242.70/49.26  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (45) are
% 242.70/49.26  | | |            inconsistent by sub-proof #911.
% 242.70/49.26  | | | 
% 242.70/49.26  | | Case 2:
% 242.70/49.26  | | | 
% 242.70/49.26  | | |   (46)  all_58_7 = e3 & op(e1, e2) = e3
% 242.70/49.26  | | | 
% 242.70/49.26  | | | ALPHA: (46) implies:
% 242.70/49.26  | | |   (47)  op(e1, e2) = e3
% 242.70/49.26  | | | 
% 242.70/49.26  | | | REF_CLOSE: (6), (24), (32), (47) are inconsistent by sub-proof #2191.
% 242.70/49.26  | | | 
% 242.70/49.26  | | End of split
% 242.70/49.26  | | 
% 242.70/49.26  | Case 2:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (48)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 242.70/49.26  | |           e3)
% 242.70/49.26  | | 
% 242.70/49.26  | | REF_CLOSE: (16), (25), (32), (42), (48) are inconsistent by sub-proof #2029.
% 242.70/49.26  | | 
% 242.70/49.26  | End of split
% 242.70/49.26  | 
% 242.70/49.26  End of proof
% 242.70/49.26  
% 242.70/49.26  Sub-proof #895 shows that the following formulas are inconsistent:
% 242.70/49.26  ----------------------------------------------------------------
% 242.70/49.26    (1)  op(e2, e3) = all_56_3
% 242.70/49.26    (2)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.70/49.26    (3)   ~ (all_52_6 = e2)
% 242.70/49.26    (4)  all_54_11 = all_52_14
% 242.70/49.26    (5)   ~ (all_52_2 = e1)
% 242.70/49.26    (6)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 242.70/49.26    (7)   ~ (all_52_2 = all_52_14)
% 242.70/49.26    (8)   ~ (all_52_14 = e2)
% 242.70/49.26    (9)  all_54_9 = all_52_6
% 242.70/49.26    (10)   ~ (all_52_14 = e1)
% 242.70/49.26    (11)  op(e2, e3) = e1
% 242.70/49.26    (12)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.70/49.26    (13)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.70/49.26            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2,
% 242.70/49.26              e3) = all_42_1 & $i(all_42_1))
% 242.70/49.26    (14)   ~ (all_52_6 = all_52_14)
% 242.70/49.26    (15)  op(e2, all_56_3) = e2
% 242.70/49.26    (16)   ~ (all_52_2 = e0)
% 242.70/49.26    (17)  op(e2, e1) = e0
% 242.70/49.26    (18)   ~ (all_52_2 = e2)
% 242.70/49.26    (19)  all_54_8 = all_52_2
% 242.70/49.26    (20)   ~ (all_52_2 = all_52_6)
% 242.70/49.26    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.26    (22)  op(e2, e3) = all_8_1
% 242.70/49.26  
% 242.70/49.26  Begin of proof
% 242.70/49.26  | 
% 242.70/49.26  | BETA: splitting (2) gives:
% 242.70/49.26  | 
% 242.70/49.26  | Case 1:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (23)  all_54_8 = e3
% 242.70/49.26  | | 
% 242.70/49.26  | | COMBINE_EQS: (19), (23) imply:
% 242.70/49.26  | |   (24)  all_52_2 = e3
% 242.70/49.26  | | 
% 242.70/49.26  | | SIMP: (24) implies:
% 242.70/49.26  | |   (25)  all_52_2 = e3
% 242.70/49.26  | | 
% 242.70/49.26  | | REDUCE: (20), (25) imply:
% 242.70/49.26  | |   (26)   ~ (all_52_6 = e3)
% 242.70/49.26  | | 
% 242.70/49.26  | | SIMP: (26) implies:
% 242.70/49.26  | |   (27)   ~ (all_52_6 = e3)
% 242.70/49.26  | | 
% 242.70/49.26  | | REDUCE: (7), (25) imply:
% 242.70/49.26  | |   (28)   ~ (all_52_14 = e3)
% 242.70/49.26  | | 
% 242.70/49.26  | | SIMP: (28) implies:
% 242.70/49.26  | |   (29)   ~ (all_52_14 = e3)
% 242.70/49.26  | | 
% 242.70/49.26  | | BETA: splitting (6) gives:
% 242.70/49.26  | | 
% 242.70/49.26  | | Case 1:
% 242.70/49.26  | | | 
% 242.70/49.26  | | |   (30)  all_54_11 = e3
% 242.70/49.26  | | | 
% 242.70/49.26  | | | COMBINE_EQS: (4), (30) imply:
% 242.70/49.26  | | |   (31)  all_52_14 = e3
% 242.70/49.26  | | | 
% 242.70/49.26  | | | REDUCE: (29), (31) imply:
% 242.70/49.26  | | |   (32)  $false
% 242.70/49.26  | | | 
% 242.70/49.26  | | | CLOSE: (32) is inconsistent.
% 242.70/49.26  | | | 
% 242.70/49.26  | | Case 2:
% 242.70/49.26  | | | 
% 242.70/49.26  | | |   (33)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 242.70/49.26  | | | 
% 242.70/49.26  | | | BETA: splitting (33) gives:
% 242.70/49.26  | | | 
% 242.70/49.26  | | | Case 1:
% 242.70/49.26  | | | | 
% 242.70/49.26  | | | |   (34)  all_54_11 = e2
% 242.70/49.26  | | | | 
% 242.70/49.26  | | | | REF_CLOSE: (4), (8), (34) are inconsistent by sub-proof #2177.
% 242.70/49.26  | | | | 
% 242.70/49.26  | | | Case 2:
% 242.70/49.26  | | | | 
% 242.70/49.26  | | | |   (35)   ~ (all_54_11 = e2)
% 242.70/49.26  | | | |   (36)  all_54_11 = e1 | all_54_11 = e0
% 242.70/49.26  | | | | 
% 242.70/49.26  | | | | BETA: splitting (13) gives:
% 242.70/49.26  | | | | 
% 242.70/49.26  | | | | Case 1:
% 242.70/49.26  | | | | | 
% 242.70/49.26  | | | | |   (37)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3)
% 242.70/49.26  | | | | |         = all_42_1 & $i(all_42_0) & $i(all_42_1)
% 242.70/49.26  | | | | | 
% 242.70/49.26  | | | | | ALPHA: (37) implies:
% 242.70/49.26  | | | | |   (38)  op(e2, e3) = all_42_1
% 242.70/49.26  | | | | | 
% 242.70/49.26  | | | | | BETA: splitting (36) gives:
% 242.70/49.26  | | | | | 
% 242.70/49.26  | | | | | Case 1:
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | |   (39)  all_54_11 = e1
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | | COMBINE_EQS: (4), (39) imply:
% 242.70/49.26  | | | | | |   (40)  all_52_14 = e1
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | | REDUCE: (10), (40) imply:
% 242.70/49.26  | | | | | |   (41)  $false
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | | CLOSE: (41) is inconsistent.
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | Case 2:
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | |   (42)  all_54_11 = e0
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | | COMBINE_EQS: (4), (42) imply:
% 242.70/49.26  | | | | | |   (43)  all_52_14 = e0
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | | REDUCE: (14), (43) imply:
% 242.70/49.26  | | | | | |   (44)   ~ (all_52_6 = e0)
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | | REDUCE: (8), (43) imply:
% 242.70/49.26  | | | | | |   (45)   ~ (e2 = e0)
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | | SIMP: (45) implies:
% 242.70/49.26  | | | | | |   (46)   ~ (e2 = e0)
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | | BETA: splitting (12) gives:
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | | Case 1:
% 242.70/49.26  | | | | | | | 
% 242.70/49.26  | | | | | | |   (47)  all_54_9 = e3
% 242.70/49.26  | | | | | | | 
% 242.70/49.26  | | | | | | | REF_CLOSE: (9), (27), (47) are inconsistent by sub-proof #1955.
% 242.70/49.26  | | | | | | | 
% 242.70/49.26  | | | | | | Case 2:
% 242.70/49.26  | | | | | | | 
% 242.70/49.26  | | | | | | |   (48)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.70/49.26  | | | | | | | 
% 242.70/49.26  | | | | | | | BETA: splitting (48) gives:
% 242.70/49.26  | | | | | | | 
% 242.70/49.26  | | | | | | | Case 1:
% 242.70/49.26  | | | | | | | | 
% 242.70/49.26  | | | | | | | |   (49)  all_54_9 = e2
% 242.70/49.26  | | | | | | | | 
% 242.70/49.26  | | | | | | | | REF_CLOSE: (3), (9), (49) are inconsistent by sub-proof #1954.
% 242.70/49.26  | | | | | | | | 
% 242.70/49.26  | | | | | | | Case 2:
% 242.70/49.26  | | | | | | | | 
% 242.70/49.26  | | | | | | | |   (50)  all_54_9 = e1 | all_54_9 = e0
% 242.70/49.26  | | | | | | | | 
% 242.70/49.26  | | | | | | | | BETA: splitting (50) gives:
% 242.70/49.26  | | | | | | | | 
% 242.70/49.26  | | | | | | | | Case 1:
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | | GROUND_INST: instantiating (21) with all_42_1, all_56_3, e3,
% 242.70/49.26  | | | | | | | | |              e2, simplifying with (1), (38) gives:
% 242.70/49.26  | | | | | | | | |   (51)  all_56_3 = all_42_1
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | | GROUND_INST: instantiating (21) with all_8_1, all_56_3, e3, e2,
% 242.70/49.26  | | | | | | | | |              simplifying with (1), (22) gives:
% 242.70/49.26  | | | | | | | | |   (52)  all_56_3 = all_8_1
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | | GROUND_INST: instantiating (21) with e1, all_56_3, e3, e2,
% 242.70/49.26  | | | | | | | | |              simplifying with (1), (11) gives:
% 242.70/49.26  | | | | | | | | |   (53)  all_56_3 = e1
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | | COMBINE_EQS: (51), (53) imply:
% 242.70/49.26  | | | | | | | | |   (54)  all_42_1 = e1
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | | COMBINE_EQS: (51), (52) imply:
% 242.70/49.26  | | | | | | | | |   (55)  all_42_1 = all_8_1
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | | COMBINE_EQS: (54), (55) imply:
% 242.70/49.26  | | | | | | | | |   (56)  all_8_1 = e1
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | | REDUCE: (15), (53) imply:
% 242.70/49.26  | | | | | | | | |   (57)  op(e2, e1) = e2
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | | REF_CLOSE: (17), (21), (46), (57) are inconsistent by
% 242.70/49.26  | | | | | | | | |            sub-proof #1906.
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | Case 2:
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | |   (58)  all_54_9 = e0
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | | REF_CLOSE: (9), (44), (58) are inconsistent by sub-proof
% 242.70/49.26  | | | | | | | | |            #1953.
% 242.70/49.26  | | | | | | | | | 
% 242.70/49.26  | | | | | | | | End of split
% 242.70/49.26  | | | | | | | | 
% 242.70/49.26  | | | | | | | End of split
% 242.70/49.26  | | | | | | | 
% 242.70/49.26  | | | | | | End of split
% 242.70/49.26  | | | | | | 
% 242.70/49.26  | | | | | End of split
% 242.70/49.26  | | | | | 
% 242.70/49.26  | | | | Case 2:
% 242.70/49.26  | | | | | 
% 242.70/49.26  | | | | |   (59)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 242.70/49.26  | | | | | 
% 242.70/49.26  | | | | | ALPHA: (59) implies:
% 242.70/49.26  | | | | |   (60)   ~ (all_42_1 = e1)
% 242.70/49.26  | | | | |   (61)  op(e2, e3) = all_42_1
% 242.70/49.26  | | | | | 
% 242.70/49.26  | | | | | REF_CLOSE: (11), (21), (22), (60), (61) are inconsistent by sub-proof
% 242.70/49.26  | | | | |            #935.
% 242.70/49.26  | | | | | 
% 242.70/49.26  | | | | End of split
% 242.70/49.26  | | | | 
% 242.70/49.26  | | | End of split
% 242.70/49.26  | | | 
% 242.70/49.26  | | End of split
% 242.70/49.26  | | 
% 242.70/49.26  | Case 2:
% 242.70/49.26  | | 
% 242.70/49.26  | |   (62)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.70/49.26  | | 
% 242.70/49.26  | | REF_CLOSE: (5), (16), (18), (19), (62) are inconsistent by sub-proof #1949.
% 242.70/49.26  | | 
% 242.70/49.26  | End of split
% 242.70/49.26  | 
% 242.70/49.26  End of proof
% 242.70/49.26  
% 242.70/49.26  Sub-proof #896 shows that the following formulas are inconsistent:
% 242.70/49.26  ----------------------------------------------------------------
% 242.70/49.26    (1)   ~ (e3 = e0)
% 242.70/49.26    (2)   ~ (e2 = e0)
% 242.70/49.26    (3)  op(e0, e1) = e3
% 242.70/49.26    (4)  op(e0, e2) = e2
% 242.70/49.26    (5)  all_58_12 = e1
% 242.70/49.26    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.26    (7)   ~ (e1 = e0)
% 242.70/49.26    (8)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 242.70/49.26         (all_58_14 = e0 & op(e0, e1) = e0)
% 242.70/49.26  
% 242.70/49.26  Begin of proof
% 242.70/49.26  | 
% 242.70/49.26  | BETA: splitting (8) gives:
% 242.70/49.26  | 
% 242.70/49.26  | Case 1:
% 242.70/49.26  | | 
% 242.70/49.27  | |   (9)  all_58_12 = e0 & op(e0, e3) = e0
% 242.70/49.27  | | 
% 242.70/49.27  | | ALPHA: (9) implies:
% 242.70/49.27  | |   (10)  all_58_12 = e0
% 242.70/49.27  | | 
% 242.70/49.27  | | REF_CLOSE: (5), (7), (10) are inconsistent by sub-proof #1539.
% 242.70/49.27  | | 
% 242.70/49.27  | Case 2:
% 242.70/49.27  | | 
% 242.70/49.27  | |   (11)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 242.70/49.27  | |           e0)
% 242.70/49.27  | | 
% 242.70/49.27  | | REF_CLOSE: (1), (2), (3), (4), (6), (11) are inconsistent by sub-proof
% 242.70/49.27  | |            #1635.
% 242.70/49.27  | | 
% 242.70/49.27  | End of split
% 242.70/49.27  | 
% 242.70/49.27  End of proof
% 242.70/49.27  
% 242.70/49.27  Sub-proof #897 shows that the following formulas are inconsistent:
% 242.70/49.27  ----------------------------------------------------------------
% 242.70/49.27    (1)  op(e2, e3) = e0
% 242.70/49.27    (2)   ~ (all_8_1 = e0)
% 242.70/49.27    (3)  ( ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) = all_42_1
% 242.70/49.27           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e2, e3) =
% 242.70/49.27           all_42_1 & $i(all_42_1))
% 242.70/49.27    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.27    (5)  op(e2, e3) = all_8_1
% 242.70/49.27  
% 242.70/49.27  Begin of proof
% 242.70/49.27  | 
% 242.70/49.27  | BETA: splitting (3) gives:
% 242.70/49.27  | 
% 242.70/49.27  | Case 1:
% 242.70/49.27  | | 
% 242.70/49.27  | |   (6)   ~ (all_42_0 = e0) & op(all_42_1, e2) = all_42_0 & op(e2, e3) =
% 242.70/49.27  | |        all_42_1 & $i(all_42_0) & $i(all_42_1)
% 242.70/49.27  | | 
% 242.70/49.27  | | ALPHA: (6) implies:
% 242.70/49.27  | |   (7)  op(e2, e3) = all_42_1
% 242.70/49.27  | | 
% 242.70/49.27  | | REF_CLOSE: (1), (2), (4), (5), (7) are inconsistent by sub-proof #898.
% 242.70/49.27  | | 
% 242.70/49.27  | Case 2:
% 242.70/49.27  | | 
% 242.70/49.27  | |   (8)   ~ (all_42_1 = e1) & op(e2, e3) = all_42_1 & $i(all_42_1)
% 242.70/49.27  | | 
% 242.70/49.27  | | ALPHA: (8) implies:
% 242.70/49.27  | |   (9)  op(e2, e3) = all_42_1
% 242.70/49.27  | | 
% 242.70/49.27  | | REF_CLOSE: (1), (2), (4), (5), (9) are inconsistent by sub-proof #898.
% 242.70/49.27  | | 
% 242.70/49.27  | End of split
% 242.70/49.27  | 
% 242.70/49.27  End of proof
% 242.70/49.27  
% 242.70/49.27  Sub-proof #898 shows that the following formulas are inconsistent:
% 242.70/49.27  ----------------------------------------------------------------
% 242.70/49.27    (1)  op(e2, e3) = e0
% 242.70/49.27    (2)  op(e2, e3) = all_42_1
% 242.70/49.27    (3)   ~ (all_8_1 = e0)
% 242.70/49.27    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.27    (5)  op(e2, e3) = all_8_1
% 242.70/49.27  
% 242.70/49.27  Begin of proof
% 242.70/49.27  | 
% 242.70/49.27  | GROUND_INST: instantiating (4) with all_8_1, all_42_1, e3, e2, simplifying
% 242.70/49.27  |              with (2), (5) gives:
% 242.70/49.27  |   (6)  all_42_1 = all_8_1
% 242.70/49.27  | 
% 242.70/49.27  | GROUND_INST: instantiating (4) with e0, all_42_1, e3, e2, simplifying with
% 242.70/49.27  |              (1), (2) gives:
% 242.70/49.27  |   (7)  all_42_1 = e0
% 242.70/49.27  | 
% 242.70/49.27  | COMBINE_EQS: (6), (7) imply:
% 242.70/49.27  |   (8)  all_8_1 = e0
% 242.70/49.27  | 
% 242.70/49.27  | REDUCE: (3), (8) imply:
% 242.70/49.27  |   (9)  $false
% 242.70/49.27  | 
% 242.70/49.27  | CLOSE: (9) is inconsistent.
% 242.70/49.27  | 
% 242.70/49.27  End of proof
% 242.70/49.27  
% 242.70/49.27  Sub-proof #899 shows that the following formulas are inconsistent:
% 242.70/49.27  ----------------------------------------------------------------
% 242.70/49.27    (1)  op(e0, e0) = e1
% 242.70/49.27    (2)  all_56_21 = e2
% 242.70/49.27    (3)  op(e3, e2) = e1
% 242.70/49.27    (4)  op(e0, e1) = all_56_23
% 242.70/49.27    (5)  op(e2, e3) = e0
% 242.70/49.27    (6)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 242.70/49.27           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 242.70/49.27           all_24_1 & $i(all_24_1))
% 242.70/49.27    (7)   ~ (e2 = e0)
% 242.70/49.27    (8)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 242.70/49.27           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 242.70/49.27           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 242.70/49.27         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 242.70/49.27           $i(all_56_15))
% 242.70/49.27    (9)  all_54_13 = all_52_7
% 242.70/49.27    (10)  op(e1, e2) = all_52_6
% 242.70/49.27    (11)   ~ (all_52_11 = e1)
% 242.70/49.27    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.70/49.27              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.70/49.27            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.70/49.27            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.70/49.27            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.70/49.27             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.70/49.27            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.70/49.27            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.70/49.27            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.70/49.27            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.27            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.70/49.27              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.70/49.27            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.70/49.27            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.70/49.27            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.70/49.27            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.70/49.27            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.70/49.27            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.70/49.27              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.70/49.27            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.70/49.27            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.70/49.27            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.70/49.27            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.70/49.27            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.27            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.70/49.27              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.70/49.27            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.70/49.27            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.70/49.27    (13)   ~ (all_52_7 = all_52_11)
% 242.70/49.27    (14)  op(e1, e0) = all_52_14
% 242.70/49.27    (15)   ~ (all_52_7 = e3)
% 242.70/49.27    (16)  op(e2, e3) = all_42_1
% 242.70/49.27    (17)  op(e1, e2) = e0
% 242.70/49.27    (18)   ~ (all_52_14 = e1)
% 242.70/49.27    (19)   ~ (all_52_7 = e1)
% 242.70/49.27    (20)  op(e2, e0) = e2
% 242.70/49.27    (21)  all_56_31 = e1
% 242.70/49.27    (22)  op(e3, e0) = all_52_12
% 242.70/49.27    (23)  op(e0, e1) = e0
% 242.70/49.27    (24)  op(e2, e3) = all_52_1
% 242.70/49.27    (25)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 242.70/49.27            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 242.70/49.27              e2) = all_40_1 & $i(all_40_1))
% 242.70/49.27    (26)  op(e0, e2) = all_52_7
% 242.70/49.27    (27)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.70/49.27    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.70/49.27            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.70/49.27    (29)  op(e2, e3) = all_8_1
% 242.70/49.27    (30)   ~ (all_52_12 = e3)
% 242.70/49.27    (31)  all_56_11 = e3
% 242.70/49.27    (32)  op(e0, all_56_23) = e0
% 242.70/49.27    (33)   ~ (e1 = e0)
% 242.70/49.27    (34)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 242.70/49.27            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3,
% 242.70/49.27              e2) = all_32_1 & $i(all_32_1))
% 242.70/49.27    (35)   ~ (all_52_1 = e3)
% 242.70/49.27    (36)  all_54_14 = all_52_11
% 242.70/49.27    (37)  all_54_14 = e1 | all_54_14 = e0
% 242.70/49.27  
% 242.70/49.27  Begin of proof
% 242.70/49.27  | 
% 242.70/49.27  | BETA: splitting (12) gives:
% 242.70/49.27  | 
% 242.70/49.27  | Case 1:
% 242.70/49.27  | | 
% 242.70/49.27  | |   (38)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 242.70/49.27  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 242.70/49.27  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 242.70/49.27  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.70/49.27  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 242.70/49.27  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 242.70/49.27  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 242.70/49.27  | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 242.70/49.27  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.70/49.27  | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 242.70/49.27  | |           = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &
% 242.70/49.27  | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 242.70/49.27  | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 242.70/49.27  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.70/49.27  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.70/49.27  | | 
% 242.70/49.27  | | BETA: splitting (38) gives:
% 242.70/49.27  | | 
% 242.70/49.27  | | Case 1:
% 242.70/49.27  | | | 
% 242.70/49.27  | | |   (39)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 242.70/49.27  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.70/49.27  | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 242.70/49.27  | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 242.70/49.27  | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 242.70/49.27  | | |         | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.70/49.27  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.70/49.27  | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.70/49.27  | | | 
% 242.70/49.27  | | | BETA: splitting (39) gives:
% 242.70/49.27  | | | 
% 242.70/49.27  | | | Case 1:
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | |   (40)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 242.70/49.27  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.70/49.27  | | | |         op(e3, e2) = e3 & op(e2, e3) = e3
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | ALPHA: (40) implies:
% 242.70/49.27  | | | |   (41)  op(e2, e3) = e3
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | REF_CLOSE: (24), (28), (35), (41) are inconsistent by sub-proof #2337.
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | Case 2:
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | |   (42)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.70/49.27  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.70/49.27  | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 242.70/49.27  | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.70/49.27  | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 242.70/49.27  | | | |           op(e1, e3) = e3)
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | BETA: splitting (42) gives:
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | Case 1:
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | |   (43)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.70/49.27  | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.70/49.27  | | | | |         op(e3, e2) = e2 & op(e2, e3) = e2
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | | ALPHA: (43) implies:
% 242.70/49.27  | | | | |   (44)  op(e2, e3) = e2
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | | REF_CLOSE: (5), (7), (16), (28), (29), (44) are inconsistent by
% 242.70/49.27  | | | | |            sub-proof #903.
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | Case 2:
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | |   (45)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.70/49.27  | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.70/49.27  | | | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | | ALPHA: (45) implies:
% 242.70/49.27  | | | | |   (46)   ~ (all_56_31 = e1)
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | | REDUCE: (21), (46) imply:
% 242.70/49.27  | | | | |   (47)  $false
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | | CLOSE: (47) is inconsistent.
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | End of split
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | End of split
% 242.70/49.27  | | | 
% 242.70/49.27  | | Case 2:
% 242.70/49.27  | | | 
% 242.70/49.27  | | |   (48)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 242.70/49.27  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.70/49.27  | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 242.70/49.27  | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 242.70/49.27  | | |             = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 242.70/49.27  | | |           e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 242.70/49.27  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.70/49.27  | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.70/49.27  | | | 
% 242.70/49.27  | | | BETA: splitting (48) gives:
% 242.70/49.27  | | | 
% 242.70/49.27  | | | Case 1:
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | |   (49)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 242.70/49.27  | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.70/49.27  | | | |         op(e3, e1) = e1 & op(e1, e3) = e1
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | ALPHA: (49) implies:
% 242.70/49.27  | | | |   (50)   ~ (all_56_11 = e3)
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | REDUCE: (31), (50) imply:
% 242.70/49.27  | | | |   (51)  $false
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | CLOSE: (51) is inconsistent.
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | Case 2:
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | |   (52)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.27  | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.70/49.27  | | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 242.70/49.27  | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.70/49.27  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 242.70/49.27  | | | |           op(e0, e3) = e0)
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | REF_CLOSE: (22), (28), (30), (31), (52) are inconsistent by sub-proof
% 242.70/49.27  | | | |            #902.
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | End of split
% 242.70/49.27  | | | 
% 242.70/49.27  | | End of split
% 242.70/49.27  | | 
% 242.70/49.27  | Case 2:
% 242.70/49.27  | | 
% 242.70/49.27  | |   (53)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 242.70/49.27  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.70/49.27  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 242.70/49.27  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.70/49.27  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 242.70/49.27  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.27  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.70/49.27  | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 242.70/49.27  | |           e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.70/49.27  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 242.70/49.27  | |         (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.27  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.70/49.27  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 242.70/49.27  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 242.70/49.27  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.70/49.27  | | 
% 242.70/49.27  | | BETA: splitting (53) gives:
% 242.70/49.27  | | 
% 242.70/49.27  | | Case 1:
% 242.70/49.27  | | | 
% 242.70/49.27  | | |   (54)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 242.70/49.27  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.70/49.27  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 242.70/49.27  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 242.70/49.27  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 242.70/49.27  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.27  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.70/49.27  | | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.70/49.27  | | | 
% 242.70/49.27  | | | BETA: splitting (54) gives:
% 242.70/49.27  | | | 
% 242.70/49.27  | | | Case 1:
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | |   (55)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 242.70/49.27  | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.70/49.27  | | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | ALPHA: (55) implies:
% 242.70/49.27  | | | |   (56)   ~ (all_56_31 = e1)
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | REDUCE: (21), (56) imply:
% 242.70/49.27  | | | |   (57)  $false
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | CLOSE: (57) is inconsistent.
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | Case 2:
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | |   (58)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.70/49.27  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.70/49.27  | | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 242.70/49.27  | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 242.70/49.27  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 &
% 242.70/49.27  | | | |           op(e0, e2) = e2)
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | BETA: splitting (58) gives:
% 242.70/49.27  | | | | 
% 242.70/49.27  | | | | Case 1:
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | |   (59)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.70/49.27  | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.70/49.27  | | | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | | ALPHA: (59) implies:
% 242.70/49.27  | | | | |   (60)  op(e1, e2) = e1
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | | REF_CLOSE: (10), (17), (28), (33), (60) are inconsistent by sub-proof
% 242.70/49.27  | | | | |            #2136.
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | Case 2:
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | |   (61)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.70/49.27  | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.70/49.27  | | | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | | ALPHA: (61) implies:
% 242.70/49.27  | | | | |   (62)  all_56_15 = e2
% 242.70/49.27  | | | | |   (63)   ~ (all_56_31 = e0)
% 242.70/49.27  | | | | |   (64)   ~ (all_56_21 = e0)
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | | BETA: splitting (8) gives:
% 242.70/49.27  | | | | | 
% 242.70/49.27  | | | | | Case 1:
% 242.70/49.27  | | | | | | 
% 242.70/49.27  | | | | | |   (65)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) =
% 242.70/49.27  | | | | | |           all_56_9 & $i(all_56_9)) | (all_56_10 = e2 & op(e2,
% 242.70/49.27  | | | | | |             all_56_11) = e2)
% 242.70/49.28  | | | | | | 
% 242.70/49.28  | | | | | | BETA: splitting (65) gives:
% 242.70/49.28  | | | | | | 
% 242.70/49.28  | | | | | | Case 1:
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | |   (66)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) =
% 242.70/49.28  | | | | | | |         all_56_9 & $i(all_56_9)
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | | ALPHA: (66) implies:
% 242.70/49.28  | | | | | | |   (67)  op(e3, e2) = all_56_9
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | | BETA: splitting (34) gives:
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | | Case 1:
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | |   (68)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 242.70/49.28  | | | | | | | |         op(e3, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | | ALPHA: (68) implies:
% 242.70/49.28  | | | | | | | |   (69)  op(e3, e2) = all_32_1
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | | BETA: splitting (6) gives:
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | | Case 1:
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | GROUND_INST: instantiating (28) with e0, all_56_23, e1, e0,
% 242.70/49.28  | | | | | | | | |              simplifying with (4), (23) gives:
% 242.70/49.28  | | | | | | | | |   (70)  all_56_23 = e0
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | REDUCE: (32), (70) imply:
% 242.70/49.28  | | | | | | | | |   (71)  op(e0, e0) = e0
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | REF_CLOSE: (1), (28), (33), (71) are inconsistent by sub-proof
% 242.70/49.28  | | | | | | | | |            #2274.
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | Case 2:
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | |   (72)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 242.70/49.28  | | | | | | | | |         $i(all_24_1)
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | ALPHA: (72) implies:
% 242.70/49.28  | | | | | | | | |   (73)   ~ (all_24_1 = e1)
% 242.70/49.28  | | | | | | | | |   (74)  op(e3, e2) = all_24_1
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | REF_CLOSE: (3), (28), (69), (73), (74) are inconsistent by
% 242.70/49.28  | | | | | | | | |            sub-proof #2239.
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | End of split
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | Case 2:
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | |   (75)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 242.70/49.28  | | | | | | | |         $i(all_32_1)
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | | ALPHA: (75) implies:
% 242.70/49.28  | | | | | | | |   (76)   ~ (all_32_1 = e0)
% 242.70/49.28  | | | | | | | |   (77)  op(e3, e2) = all_32_1
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | | BETA: splitting (6) gives:
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | | Case 1:
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | GROUND_INST: instantiating (28) with e0, all_56_23, e1, e0,
% 242.70/49.28  | | | | | | | | |              simplifying with (4), (23) gives:
% 242.70/49.28  | | | | | | | | |   (78)  all_56_23 = e0
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | GROUND_INST: instantiating (28) with all_32_1, all_56_9, e2,
% 242.70/49.28  | | | | | | | | |              e3, simplifying with (67), (77) gives:
% 242.70/49.28  | | | | | | | | |   (79)  all_56_9 = all_32_1
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | GROUND_INST: instantiating (28) with e1, all_56_9, e2, e3,
% 242.70/49.28  | | | | | | | | |              simplifying with (3), (67) gives:
% 242.70/49.28  | | | | | | | | |   (80)  all_56_9 = e1
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | COMBINE_EQS: (79), (80) imply:
% 242.70/49.28  | | | | | | | | |   (81)  all_32_1 = e1
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | SIMP: (81) implies:
% 242.70/49.28  | | | | | | | | |   (82)  all_32_1 = e1
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | REDUCE: (32), (78) imply:
% 242.70/49.28  | | | | | | | | |   (83)  op(e0, e0) = e0
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | REF_CLOSE: (1), (28), (33), (83) are inconsistent by sub-proof
% 242.70/49.28  | | | | | | | | |            #2274.
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | Case 2:
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | |   (84)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 242.70/49.28  | | | | | | | | |         $i(all_24_1)
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | ALPHA: (84) implies:
% 242.70/49.28  | | | | | | | | |   (85)   ~ (all_24_1 = e1)
% 242.70/49.28  | | | | | | | | |   (86)  op(e3, e2) = all_24_1
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | | REF_CLOSE: (3), (28), (77), (85), (86) are inconsistent by
% 242.70/49.28  | | | | | | | | |            sub-proof #2239.
% 242.70/49.28  | | | | | | | | | 
% 242.70/49.28  | | | | | | | | End of split
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | End of split
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | Case 2:
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | |   (87)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | | ALPHA: (87) implies:
% 242.70/49.28  | | | | | | |   (88)  op(e2, all_56_11) = e2
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | | REDUCE: (31), (88) imply:
% 242.70/49.28  | | | | | | |   (89)  op(e2, e3) = e2
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | | REF_CLOSE: (5), (7), (16), (28), (29), (89) are inconsistent by
% 242.70/49.28  | | | | | | |            sub-proof #903.
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | End of split
% 242.70/49.28  | | | | | | 
% 242.70/49.28  | | | | | Case 2:
% 242.70/49.28  | | | | | | 
% 242.70/49.28  | | | | | |   (90)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 242.70/49.28  | | | | | |           all_56_13 & $i(all_56_13)) | (all_56_14 = e0 & op(e0,
% 242.70/49.28  | | | | | |             all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 242.70/49.28  | | | | | |           $i(all_56_15))
% 242.70/49.28  | | | | | | 
% 242.70/49.28  | | | | | | BETA: splitting (90) gives:
% 242.70/49.28  | | | | | | 
% 242.70/49.28  | | | | | | Case 1:
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | |   (91)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 242.70/49.28  | | | | | | |         all_56_13 & $i(all_56_13)
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | | ALPHA: (91) implies:
% 242.70/49.28  | | | | | | |   (92)  op(e1, e2) = all_56_13
% 242.70/49.28  | | | | | | |   (93)  op(e1, all_56_13) = e1
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | | BETA: splitting (25) gives:
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | | Case 1:
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | |   (94)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 242.70/49.28  | | | | | | | |         op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | | ALPHA: (94) implies:
% 242.70/49.28  | | | | | | | |   (95)  op(e1, e2) = all_40_1
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | | REF_CLOSE: (3), (6), (14), (17), (18), (28), (34), (92), (93),
% 242.70/49.28  | | | | | | | |            (95) are inconsistent by sub-proof #900.
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | Case 2:
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | |   (96)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 242.70/49.28  | | | | | | | |         $i(all_40_1)
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | | ALPHA: (96) implies:
% 242.70/49.28  | | | | | | | |   (97)  op(e1, e2) = all_40_1
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | | REF_CLOSE: (3), (6), (14), (17), (18), (28), (34), (92), (93),
% 242.70/49.28  | | | | | | | |            (97) are inconsistent by sub-proof #900.
% 242.70/49.28  | | | | | | | | 
% 242.70/49.28  | | | | | | | End of split
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | Case 2:
% 242.70/49.28  | | | | | | | 
% 242.70/49.28  | | | | | | |   (98)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 242.78/49.28  | | | | | | |         all_56_15 & $i(all_56_15)
% 242.78/49.28  | | | | | | | 
% 242.78/49.28  | | | | | | | ALPHA: (98) implies:
% 242.78/49.28  | | | | | | |   (99)  op(e0, all_56_15) = e0
% 242.78/49.28  | | | | | | | 
% 242.78/49.28  | | | | | | | REDUCE: (62), (99) imply:
% 242.78/49.28  | | | | | | |   (100)  op(e0, e2) = e0
% 242.78/49.28  | | | | | | | 
% 242.78/49.28  | | | | | | | REF_CLOSE: (9), (11), (13), (15), (19), (26), (27), (28), (36),
% 242.78/49.28  | | | | | | |            (37), (100) are inconsistent by sub-proof #905.
% 242.78/49.28  | | | | | | | 
% 242.78/49.28  | | | | | | End of split
% 242.78/49.28  | | | | | | 
% 242.78/49.28  | | | | | End of split
% 242.78/49.28  | | | | | 
% 242.78/49.28  | | | | End of split
% 242.78/49.28  | | | | 
% 242.78/49.28  | | | End of split
% 242.78/49.28  | | | 
% 242.78/49.28  | | Case 2:
% 242.78/49.28  | | | 
% 242.78/49.28  | | |   (101)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 242.78/49.28  | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.78/49.28  | | |            op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 242.78/49.28  | | |            all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 242.78/49.28  | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 242.78/49.28  | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.78/49.28  | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 242.78/49.28  | | |            ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.78/49.28  | | | 
% 242.78/49.28  | | | REF_CLOSE: (7), (14), (18), (20), (21), (28), (101) are inconsistent by
% 242.78/49.28  | | |            sub-proof #1076.
% 242.78/49.28  | | | 
% 242.78/49.28  | | End of split
% 242.78/49.28  | | 
% 242.78/49.28  | End of split
% 242.78/49.28  | 
% 242.78/49.28  End of proof
% 242.78/49.28  
% 242.78/49.28  Sub-proof #900 shows that the following formulas are inconsistent:
% 242.78/49.28  ----------------------------------------------------------------
% 242.78/49.28    (1)  op(e3, e2) = e1
% 242.78/49.28    (2)  op(e1, e2) = all_56_13
% 242.78/49.28    (3)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 242.78/49.28           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 242.78/49.28           all_24_1 & $i(all_24_1))
% 242.78/49.28    (4)  op(e1, e0) = all_52_14
% 242.78/49.28    (5)  op(e1, e2) = e0
% 242.78/49.28    (6)   ~ (all_52_14 = e1)
% 242.78/49.28    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.28    (8)  op(e1, e2) = all_40_1
% 242.78/49.28    (9)  op(e1, all_56_13) = e1
% 242.78/49.28    (10)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 242.78/49.28            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3,
% 242.78/49.28              e2) = all_32_1 & $i(all_32_1))
% 242.78/49.28  
% 242.78/49.28  Begin of proof
% 242.78/49.28  | 
% 242.78/49.28  | BETA: splitting (10) gives:
% 242.78/49.28  | 
% 242.78/49.28  | Case 1:
% 242.78/49.28  | | 
% 242.78/49.28  | |   (11)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 242.78/49.28  | |         all_32_1 & $i(all_32_0) & $i(all_32_1)
% 242.78/49.28  | | 
% 242.78/49.28  | | ALPHA: (11) implies:
% 242.78/49.28  | |   (12)  op(e3, e2) = all_32_1
% 242.78/49.28  | | 
% 242.78/49.28  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12) are
% 242.78/49.28  | |            inconsistent by sub-proof #901.
% 242.78/49.28  | | 
% 242.78/49.28  | Case 2:
% 242.78/49.28  | | 
% 242.78/49.28  | |   (13)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 & $i(all_32_1)
% 242.78/49.28  | | 
% 242.78/49.28  | | ALPHA: (13) implies:
% 242.78/49.28  | |   (14)  op(e3, e2) = all_32_1
% 242.78/49.28  | | 
% 242.78/49.28  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (14) are
% 242.78/49.28  | |            inconsistent by sub-proof #901.
% 242.78/49.28  | | 
% 242.78/49.28  | End of split
% 242.78/49.28  | 
% 242.78/49.28  End of proof
% 242.78/49.28  
% 242.78/49.28  Sub-proof #901 shows that the following formulas are inconsistent:
% 242.78/49.28  ----------------------------------------------------------------
% 242.78/49.28    (1)  op(e3, e2) = e1
% 242.78/49.28    (2)  op(e1, e2) = all_56_13
% 242.78/49.28    (3)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 242.78/49.28           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 242.78/49.28           all_24_1 & $i(all_24_1))
% 242.78/49.28    (4)  op(e3, e2) = all_32_1
% 242.78/49.28    (5)  op(e1, e0) = all_52_14
% 242.78/49.28    (6)  op(e1, e2) = e0
% 242.78/49.28    (7)   ~ (all_52_14 = e1)
% 242.78/49.28    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.28    (9)  op(e1, e2) = all_40_1
% 242.78/49.28    (10)  op(e1, all_56_13) = e1
% 242.78/49.28  
% 242.78/49.28  Begin of proof
% 242.78/49.28  | 
% 242.78/49.28  | BETA: splitting (3) gives:
% 242.78/49.28  | 
% 242.78/49.28  | Case 1:
% 242.78/49.28  | | 
% 242.78/49.28  | | 
% 242.78/49.28  | | GROUND_INST: instantiating (8) with all_40_1, all_56_13, e2, e1, simplifying
% 242.78/49.28  | |              with (2), (9) gives:
% 242.78/49.28  | |   (11)  all_56_13 = all_40_1
% 242.78/49.28  | | 
% 242.78/49.28  | | GROUND_INST: instantiating (8) with e0, all_56_13, e2, e1, simplifying with
% 242.78/49.28  | |              (2), (6) gives:
% 242.78/49.28  | |   (12)  all_56_13 = e0
% 242.78/49.28  | | 
% 242.78/49.28  | | COMBINE_EQS: (11), (12) imply:
% 242.78/49.28  | |   (13)  all_40_1 = e0
% 242.78/49.28  | | 
% 242.78/49.28  | | REDUCE: (10), (12) imply:
% 242.78/49.28  | |   (14)  op(e1, e0) = e1
% 242.78/49.28  | | 
% 242.78/49.28  | | REF_CLOSE: (5), (7), (8), (14) are inconsistent by sub-proof #2304.
% 242.78/49.28  | | 
% 242.78/49.28  | Case 2:
% 242.78/49.28  | | 
% 242.78/49.28  | |   (15)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 & $i(all_24_1)
% 242.78/49.28  | | 
% 242.78/49.28  | | ALPHA: (15) implies:
% 242.78/49.28  | |   (16)   ~ (all_24_1 = e1)
% 242.78/49.28  | |   (17)  op(e3, e2) = all_24_1
% 242.78/49.28  | | 
% 242.78/49.28  | | REF_CLOSE: (1), (4), (8), (16), (17) are inconsistent by sub-proof #2239.
% 242.78/49.28  | | 
% 242.78/49.28  | End of split
% 242.78/49.28  | 
% 242.78/49.28  End of proof
% 242.78/49.28  
% 242.78/49.28  Sub-proof #902 shows that the following formulas are inconsistent:
% 242.78/49.28  ----------------------------------------------------------------
% 242.78/49.28    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 242.78/49.28             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 242.78/49.28           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 242.78/49.28           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.78/49.28           op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.78/49.28    (2)  op(e3, e0) = all_52_12
% 242.78/49.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.28    (4)   ~ (all_52_12 = e3)
% 242.78/49.28    (5)  all_56_11 = e3
% 242.78/49.28  
% 242.78/49.28  Begin of proof
% 242.78/49.28  | 
% 242.78/49.28  | BETA: splitting (1) gives:
% 242.78/49.28  | 
% 242.78/49.28  | Case 1:
% 242.78/49.28  | | 
% 242.78/49.28  | |   (6)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 242.78/49.28  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 242.78/49.28  | |        op(e0, e3) = e3
% 242.78/49.28  | | 
% 242.78/49.28  | | ALPHA: (6) implies:
% 242.78/49.28  | |   (7)  op(e3, e0) = e3
% 242.78/49.28  | | 
% 242.78/49.28  | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #2179.
% 242.78/49.28  | | 
% 242.78/49.28  | Case 2:
% 242.78/49.28  | | 
% 242.78/49.28  | |   (8)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.78/49.28  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 242.78/49.28  | |        op(e0, e3) = e0
% 242.78/49.28  | | 
% 242.78/49.28  | | ALPHA: (8) implies:
% 242.78/49.28  | |   (9)   ~ (all_56_11 = e3)
% 242.78/49.28  | | 
% 242.78/49.28  | | REDUCE: (5), (9) imply:
% 242.78/49.28  | |   (10)  $false
% 242.78/49.28  | | 
% 242.78/49.28  | | CLOSE: (10) is inconsistent.
% 242.78/49.28  | | 
% 242.78/49.28  | End of split
% 242.78/49.28  | 
% 242.78/49.28  End of proof
% 242.78/49.28  
% 242.78/49.28  Sub-proof #903 shows that the following formulas are inconsistent:
% 242.78/49.28  ----------------------------------------------------------------
% 242.78/49.28    (1)  op(e2, e3) = e0
% 242.78/49.28    (2)   ~ (e2 = e0)
% 242.78/49.28    (3)  op(e2, e3) = all_42_1
% 242.78/49.28    (4)  op(e2, e3) = e2
% 242.78/49.28    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.28    (6)  op(e2, e3) = all_8_1
% 242.78/49.28  
% 242.78/49.28  Begin of proof
% 242.78/49.28  | 
% 242.78/49.28  | GROUND_INST: instantiating (5) with all_8_1, all_42_1, e3, e2, simplifying
% 242.78/49.28  |              with (3), (6) gives:
% 242.78/49.28  |   (7)  all_42_1 = all_8_1
% 242.78/49.28  | 
% 242.78/49.28  | GROUND_INST: instantiating (5) with e2, all_42_1, e3, e2, simplifying with
% 242.78/49.28  |              (3), (4) gives:
% 242.78/49.28  |   (8)  all_42_1 = e2
% 242.78/49.28  | 
% 242.78/49.28  | GROUND_INST: instantiating (5) with e0, all_42_1, e3, e2, simplifying with
% 242.78/49.28  |              (1), (3) gives:
% 242.78/49.28  |   (9)  all_42_1 = e0
% 242.78/49.28  | 
% 242.78/49.28  | COMBINE_EQS: (7), (8) imply:
% 242.78/49.28  |   (10)  all_8_1 = e2
% 242.78/49.28  | 
% 242.78/49.28  | COMBINE_EQS: (7), (9) imply:
% 242.78/49.28  |   (11)  all_8_1 = e0
% 242.78/49.28  | 
% 242.78/49.28  | COMBINE_EQS: (10), (11) imply:
% 242.78/49.28  |   (12)  e2 = e0
% 242.78/49.28  | 
% 242.78/49.28  | SIMP: (12) implies:
% 242.78/49.28  |   (13)  e2 = e0
% 242.78/49.28  | 
% 242.78/49.28  | REDUCE: (2), (13) imply:
% 242.78/49.28  |   (14)  $false
% 242.78/49.28  | 
% 242.78/49.28  | CLOSE: (14) is inconsistent.
% 242.78/49.28  | 
% 242.78/49.28  End of proof
% 242.78/49.28  
% 242.78/49.28  Sub-proof #904 shows that the following formulas are inconsistent:
% 242.78/49.28  ----------------------------------------------------------------
% 242.78/49.28    (1)   ~ (all_52_11 = e2)
% 242.78/49.28    (2)  all_54_13 = all_52_7
% 242.78/49.28    (3)   ~ (all_52_11 = e1)
% 242.78/49.28    (4)   ~ (all_52_7 = all_52_11)
% 242.78/49.28    (5)   ~ (all_52_7 = e3)
% 242.78/49.28    (6)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.78/49.28    (7)   ~ (all_52_7 = e1)
% 242.78/49.28    (8)  op(e0, e2) = e0
% 242.78/49.28    (9)  op(e0, e2) = all_52_7
% 242.78/49.28    (10)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.78/49.28    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.28    (12)  all_54_14 = all_52_11
% 242.78/49.28  
% 242.78/49.28  Begin of proof
% 242.78/49.28  | 
% 242.78/49.28  | BETA: splitting (6) gives:
% 242.78/49.28  | 
% 242.78/49.28  | Case 1:
% 242.78/49.28  | | 
% 242.78/49.28  | |   (13)  all_54_14 = e2
% 242.78/49.28  | | 
% 242.78/49.28  | | COMBINE_EQS: (12), (13) imply:
% 242.78/49.28  | |   (14)  all_52_11 = e2
% 242.78/49.28  | | 
% 242.78/49.28  | | REDUCE: (1), (14) imply:
% 242.78/49.28  | |   (15)  $false
% 242.78/49.28  | | 
% 242.78/49.28  | | CLOSE: (15) is inconsistent.
% 242.78/49.28  | | 
% 242.78/49.28  | Case 2:
% 242.78/49.28  | | 
% 242.78/49.28  | |   (16)  all_54_14 = e1 | all_54_14 = e0
% 242.78/49.28  | | 
% 242.78/49.28  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (16) are
% 242.78/49.28  | |            inconsistent by sub-proof #905.
% 242.78/49.28  | | 
% 242.78/49.28  | End of split
% 242.78/49.28  | 
% 242.78/49.28  End of proof
% 242.78/49.28  
% 242.78/49.28  Sub-proof #905 shows that the following formulas are inconsistent:
% 242.78/49.28  ----------------------------------------------------------------
% 242.78/49.28    (1)  all_54_13 = all_52_7
% 242.78/49.28    (2)   ~ (all_52_11 = e1)
% 242.78/49.28    (3)   ~ (all_52_7 = all_52_11)
% 242.78/49.28    (4)   ~ (all_52_7 = e3)
% 242.78/49.28    (5)   ~ (all_52_7 = e1)
% 242.78/49.28    (6)  op(e0, e2) = e0
% 242.78/49.28    (7)  op(e0, e2) = all_52_7
% 242.78/49.28    (8)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.78/49.28    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.28    (10)  all_54_14 = all_52_11
% 242.78/49.28    (11)  all_54_14 = e1 | all_54_14 = e0
% 242.78/49.28  
% 242.78/49.28  Begin of proof
% 242.78/49.28  | 
% 242.78/49.28  | BETA: splitting (11) gives:
% 242.78/49.28  | 
% 242.78/49.28  | Case 1:
% 242.78/49.28  | | 
% 242.78/49.28  | |   (12)  all_54_14 = e1
% 242.78/49.28  | | 
% 242.78/49.28  | | COMBINE_EQS: (10), (12) imply:
% 242.78/49.28  | |   (13)  all_52_11 = e1
% 242.78/49.28  | | 
% 242.78/49.28  | | REDUCE: (2), (13) imply:
% 242.78/49.28  | |   (14)  $false
% 242.78/49.28  | | 
% 242.78/49.28  | | CLOSE: (14) is inconsistent.
% 242.78/49.28  | | 
% 242.78/49.28  | Case 2:
% 242.78/49.28  | | 
% 242.78/49.28  | |   (15)  all_54_14 = e0
% 242.78/49.28  | | 
% 242.78/49.28  | | COMBINE_EQS: (10), (15) imply:
% 242.78/49.28  | |   (16)  all_52_11 = e0
% 242.78/49.28  | | 
% 242.78/49.28  | | REDUCE: (3), (16) imply:
% 242.78/49.28  | |   (17)   ~ (all_52_7 = e0)
% 242.78/49.28  | | 
% 242.78/49.28  | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (17) are inconsistent by
% 242.78/49.28  | |            sub-proof #1964.
% 242.78/49.28  | | 
% 242.78/49.28  | End of split
% 242.78/49.28  | 
% 242.78/49.28  End of proof
% 242.78/49.28  
% 242.78/49.28  Sub-proof #906 shows that the following formulas are inconsistent:
% 242.78/49.28  ----------------------------------------------------------------
% 242.78/49.29    (1)  op(e0, e0) = e1
% 242.78/49.29    (2)  op(e2, e2) = e3
% 242.78/49.29    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.78/49.29         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.78/49.29    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.78/49.29         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.29    (5)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.78/49.29           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.78/49.29             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.78/49.29    (6)   ~ (e3 = e0)
% 242.78/49.29    (7)  op(e0, e1) = all_52_11
% 242.78/49.29    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.78/49.29         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.78/49.29    (9)  all_58_6 = e3
% 242.78/49.29    (10)   ~ (e2 = e0)
% 242.78/49.29    (11)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.78/49.29          (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.29    (12)  op(e1, e1) = all_6_2
% 242.78/49.29    (13)   ~ (all_52_1 = all_52_2)
% 242.78/49.29    (14)  op(e1, e0) = all_52_14
% 242.78/49.29    (15)   ~ (all_52_13 = e1)
% 242.78/49.29    (16)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.78/49.29            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.78/49.29              e1) = all_20_1 & $i(all_20_1))
% 242.78/49.29    (17)   ~ (all_52_7 = e3)
% 242.78/49.29    (18)   ~ (e3 = e1)
% 242.78/49.29    (19)  all_58_8 = e2
% 242.78/49.29    (20)   ~ (all_52_12 = e1)
% 242.78/49.29    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.78/49.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.78/49.29    (22)   ~ (all_52_12 = all_52_14)
% 242.78/49.29    (23)  all_58_3 = e3
% 242.78/49.29    (24)   ~ (all_52_12 = all_52_13)
% 242.78/49.29    (25)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.78/49.29          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.78/49.29    (26)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 242.78/49.29    (27)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.29              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.78/49.29                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.78/49.29                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.78/49.29    (28)  op(e2, e1) = all_52_9
% 242.78/49.29    (29)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.78/49.29          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.78/49.29    (30)   ~ (e3 = e2)
% 242.78/49.29    (31)   ~ (all_52_14 = e1)
% 242.78/49.29    (32)  all_58_10 = e2
% 242.78/49.29    (33)   ~ (all_6_2 = e0)
% 242.78/49.29    (34)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.78/49.29            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.78/49.29            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.78/49.29            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.78/49.29            op(e0, all_56_31) = e0)
% 242.78/49.29    (35)  op(e2, e0) = e2
% 242.78/49.29    (36)  all_56_31 = e1
% 242.78/49.29    (37)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 242.78/49.29    (38)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.78/49.29          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.78/49.29    (39)  all_58_15 = e1
% 242.78/49.29    (40)  op(e3, e0) = all_52_12
% 242.78/49.29    (41)  op(e2, e3) = all_52_1
% 242.78/49.29    (42)  op(e3, e3) = e2
% 242.78/49.29    (43)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.78/49.29          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.29    (44)  all_34_2 = e1
% 242.78/49.29    (45)  op(e1, e1) = e2
% 242.78/49.29    (46)  all_54_7 = all_52_13
% 242.78/49.29    (47)  op(e0, e2) = all_52_7
% 242.78/49.29    (48)   ~ (all_52_13 = all_52_14)
% 242.78/49.29    (49)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.78/49.29          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.29    (50)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.78/49.29          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.78/49.29    (51)  all_54_3 = all_52_12
% 242.78/49.29    (52)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.29    (53)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.78/49.29          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.78/49.29    (54)  op(e1, e3) = all_52_2
% 242.78/49.29    (55)   ~ (e1 = e0)
% 242.78/49.29    (56)  all_58_4 = e3
% 242.78/49.29    (57)   ~ (all_52_13 = e3)
% 242.78/49.29    (58)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.78/49.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.29    (59)  op(e2, e0) = all_52_13
% 242.78/49.29    (60)   ~ (all_52_1 = e3)
% 242.78/49.29    (61)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.29          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.78/49.29            e2)
% 242.78/49.29    (62)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.78/49.29          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.78/49.29    (63)  all_58_2 = e1
% 242.78/49.29    (64)   ~ (e2 = e1)
% 242.78/49.29  
% 242.78/49.29  Begin of proof
% 242.78/49.29  | 
% 242.78/49.29  | BETA: splitting (50) gives:
% 242.78/49.29  | 
% 242.78/49.29  | Case 1:
% 242.78/49.29  | | 
% 242.78/49.29  | |   (65)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 242.78/49.29  | |           e1)
% 242.78/49.29  | | 
% 242.78/49.29  | | BETA: splitting (65) gives:
% 242.78/49.29  | | 
% 242.78/49.29  | | Case 1:
% 242.78/49.29  | | | 
% 242.78/49.29  | | |   (66)  all_58_0 = e1 & op(e3, e3) = e1
% 242.78/49.29  | | | 
% 242.78/49.29  | | | ALPHA: (66) implies:
% 242.78/49.29  | | |   (67)  op(e3, e3) = e1
% 242.78/49.29  | | | 
% 242.78/49.29  | | | REF_CLOSE: (42), (52), (64), (67) are inconsistent by sub-proof #2267.
% 242.78/49.29  | | | 
% 242.78/49.29  | | Case 2:
% 242.78/49.29  | | | 
% 242.78/49.29  | | |   (68)  all_58_1 = e1 & op(e3, e2) = e1
% 242.78/49.29  | | | 
% 242.78/49.29  | | | ALPHA: (68) implies:
% 242.78/49.29  | | |   (69)  all_58_1 = e1
% 242.78/49.29  | | | 
% 242.78/49.29  | | | BETA: splitting (43) gives:
% 242.78/49.29  | | | 
% 242.78/49.29  | | | Case 1:
% 242.78/49.29  | | | | 
% 242.78/49.29  | | | |   (70)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 242.78/49.29  | | | |           = e0)
% 242.78/49.29  | | | | 
% 242.78/49.29  | | | | REF_CLOSE: (10), (42), (52), (55), (69), (70) are inconsistent by
% 242.78/49.29  | | | |            sub-proof #1698.
% 242.78/49.29  | | | | 
% 242.78/49.29  | | | Case 2:
% 242.78/49.29  | | | | 
% 242.78/49.29  | | | |   (71)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 242.78/49.29  | | | |           = e0)
% 242.78/49.29  | | | | 
% 242.78/49.29  | | | | BETA: splitting (71) gives:
% 242.78/49.29  | | | | 
% 242.78/49.29  | | | | Case 1:
% 242.78/49.29  | | | | | 
% 242.78/49.29  | | | | |   (72)  all_58_4 = e0 & op(e3, e1) = e0
% 242.78/49.29  | | | | | 
% 242.78/49.29  | | | | | REF_CLOSE: (6), (56), (72) are inconsistent by sub-proof #1697.
% 242.78/49.29  | | | | | 
% 242.78/49.29  | | | | Case 2:
% 242.78/49.29  | | | | | 
% 242.78/49.29  | | | | |   (73)  all_58_9 = e0 & op(e3, e0) = e0
% 242.78/49.29  | | | | | 
% 242.78/49.29  | | | | | ALPHA: (73) implies:
% 242.78/49.29  | | | | |   (74)  all_58_9 = e0
% 242.78/49.29  | | | | | 
% 242.78/49.29  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 242.78/49.29  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 242.78/49.29  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 242.78/49.29  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 242.78/49.29  | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 242.78/49.29  | | | | |            (54), (55), (57), (58), (59), (60), (61), (62), (63), (64),
% 242.78/49.29  | | | | |            (74) are inconsistent by sub-proof #908.
% 242.78/49.29  | | | | | 
% 242.78/49.29  | | | | End of split
% 242.78/49.29  | | | | 
% 242.78/49.29  | | | End of split
% 242.78/49.29  | | | 
% 242.78/49.29  | | End of split
% 242.78/49.29  | | 
% 242.78/49.29  | Case 2:
% 242.78/49.29  | | 
% 242.78/49.29  | |   (75)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 242.78/49.29  | |           e1)
% 242.78/49.29  | | 
% 242.78/49.29  | | REF_CLOSE: (1), (6), (10), (18), (27), (35), (39), (49), (52), (55), (56),
% 242.78/49.29  | |            (57), (59), (75) are inconsistent by sub-proof #907.
% 242.78/49.29  | | 
% 242.78/49.29  | End of split
% 242.78/49.29  | 
% 242.78/49.29  End of proof
% 242.78/49.29  
% 242.78/49.29  Sub-proof #907 shows that the following formulas are inconsistent:
% 242.78/49.29  ----------------------------------------------------------------
% 242.78/49.29    (1)  op(e0, e0) = e1
% 242.78/49.29    (2)   ~ (e3 = e0)
% 242.78/49.29    (3)   ~ (e2 = e0)
% 242.78/49.29    (4)   ~ (e3 = e1)
% 242.78/49.29    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.29             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.29               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.78/49.29               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.78/49.29    (6)  op(e2, e0) = e2
% 242.78/49.29    (7)  all_58_15 = e1
% 242.78/49.29    (8)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.78/49.29         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.29    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.29    (10)   ~ (e1 = e0)
% 242.78/49.29    (11)  all_58_4 = e3
% 242.78/49.29    (12)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.78/49.29    (13)   ~ (all_52_13 = e3)
% 242.78/49.29    (14)  op(e2, e0) = all_52_13
% 242.78/49.29  
% 242.78/49.29  Begin of proof
% 242.78/49.29  | 
% 242.78/49.29  | BETA: splitting (12) gives:
% 242.78/49.29  | 
% 242.78/49.29  | Case 1:
% 242.78/49.29  | | 
% 242.78/49.29  | |   (15)  all_58_4 = e1 & op(e3, e1) = e1
% 242.78/49.29  | | 
% 242.78/49.29  | | REF_CLOSE: (4), (11), (15) are inconsistent by sub-proof #2042.
% 242.78/49.29  | | 
% 242.78/49.29  | Case 2:
% 242.78/49.29  | | 
% 242.78/49.29  | |   (16)  all_58_9 = e1 & op(e3, e0) = e1
% 242.78/49.29  | | 
% 242.78/49.29  | | ALPHA: (16) implies:
% 242.78/49.29  | |   (17)  all_58_9 = e1
% 242.78/49.29  | | 
% 242.78/49.29  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 242.78/49.29  | |            (17) are inconsistent by sub-proof #971.
% 242.78/49.29  | | 
% 242.78/49.29  | End of split
% 242.78/49.29  | 
% 242.78/49.29  End of proof
% 242.78/49.29  
% 242.78/49.29  Sub-proof #908 shows that the following formulas are inconsistent:
% 242.78/49.29  ----------------------------------------------------------------
% 242.78/49.29    (1)  op(e0, e0) = e1
% 242.78/49.29    (2)  op(e2, e2) = e3
% 242.78/49.29    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.78/49.29         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.78/49.29    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.78/49.29         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.29    (5)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.78/49.29           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.78/49.29             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.78/49.29    (6)   ~ (e3 = e0)
% 242.78/49.29    (7)  op(e0, e1) = all_52_11
% 242.78/49.29    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.78/49.29         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.78/49.29    (9)  all_58_6 = e3
% 242.78/49.29    (10)   ~ (e2 = e0)
% 242.78/49.29    (11)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.78/49.29          (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.29    (12)  all_58_9 = e0
% 242.78/49.29    (13)  op(e1, e1) = all_6_2
% 242.78/49.29    (14)   ~ (all_52_1 = all_52_2)
% 242.78/49.29    (15)  op(e1, e0) = all_52_14
% 242.78/49.29    (16)   ~ (all_52_13 = e1)
% 242.78/49.29    (17)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.78/49.29            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.78/49.29              e1) = all_20_1 & $i(all_20_1))
% 242.78/49.29    (18)   ~ (all_52_7 = e3)
% 242.78/49.29    (19)   ~ (e3 = e1)
% 242.78/49.29    (20)  all_58_8 = e2
% 242.78/49.29    (21)   ~ (all_52_12 = e1)
% 242.78/49.29    (22)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.78/49.29          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.78/49.29    (23)   ~ (all_52_12 = all_52_14)
% 242.78/49.29    (24)  all_58_3 = e3
% 242.78/49.29    (25)   ~ (all_52_12 = all_52_13)
% 242.78/49.29    (26)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.78/49.29          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.78/49.29    (27)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 242.78/49.29    (28)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.29              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.78/49.29                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.78/49.29                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.78/49.29    (29)  op(e2, e1) = all_52_9
% 242.78/49.29    (30)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.78/49.29          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.78/49.29    (31)   ~ (e3 = e2)
% 242.78/49.29    (32)   ~ (all_52_14 = e1)
% 242.78/49.29    (33)  all_58_10 = e2
% 242.78/49.29    (34)   ~ (all_6_2 = e0)
% 242.78/49.29    (35)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.78/49.29            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.78/49.29            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.78/49.29            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.78/49.29            op(e0, all_56_31) = e0)
% 242.78/49.29    (36)  op(e2, e0) = e2
% 242.78/49.29    (37)  all_56_31 = e1
% 242.78/49.29    (38)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 242.78/49.29    (39)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.78/49.29          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.78/49.29    (40)  all_58_15 = e1
% 242.78/49.29    (41)  op(e3, e0) = all_52_12
% 242.78/49.29    (42)  op(e2, e3) = all_52_1
% 242.78/49.29    (43)  all_34_2 = e1
% 242.78/49.29    (44)  op(e1, e1) = e2
% 242.78/49.29    (45)  all_54_7 = all_52_13
% 242.78/49.29    (46)  op(e0, e2) = all_52_7
% 242.78/49.29    (47)   ~ (all_52_13 = all_52_14)
% 242.78/49.29    (48)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.78/49.29          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.29    (49)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.78/49.29          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.78/49.29    (50)  all_54_3 = all_52_12
% 242.78/49.30    (51)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.30            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.30    (52)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.78/49.30          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.78/49.30    (53)  op(e1, e3) = all_52_2
% 242.78/49.30    (54)   ~ (e1 = e0)
% 242.78/49.30    (55)   ~ (all_52_13 = e3)
% 242.78/49.30    (56)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.78/49.30          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.30    (57)  op(e2, e0) = all_52_13
% 242.78/49.30    (58)   ~ (all_52_1 = e3)
% 242.78/49.30    (59)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.30          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.78/49.30            e2)
% 242.78/49.30    (60)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.78/49.30          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.78/49.30    (61)  all_58_2 = e1
% 242.78/49.30    (62)   ~ (e2 = e1)
% 242.78/49.30  
% 242.78/49.30  Begin of proof
% 242.78/49.30  | 
% 242.78/49.30  | BETA: splitting (48) gives:
% 242.78/49.30  | 
% 242.78/49.30  | Case 1:
% 242.78/49.30  | | 
% 242.78/49.30  | |   (63)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 242.78/49.30  | |           e3)
% 242.78/49.30  | | 
% 242.78/49.30  | | REF_CLOSE: (6), (12), (51), (55), (57), (63) are inconsistent by sub-proof
% 242.78/49.30  | |            #1062.
% 242.78/49.30  | | 
% 242.78/49.30  | Case 2:
% 242.78/49.30  | | 
% 242.78/49.30  | |   (64)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 242.78/49.30  | |           e3)
% 242.78/49.30  | | 
% 242.78/49.30  | | BETA: splitting (64) gives:
% 242.78/49.30  | | 
% 242.78/49.30  | | Case 1:
% 242.78/49.30  | | | 
% 242.78/49.30  | | |   (65)  all_58_11 = e3 & op(e1, e0) = e3
% 242.78/49.30  | | | 
% 242.78/49.30  | | | ALPHA: (65) implies:
% 242.78/49.30  | | |   (66)  all_58_11 = e3
% 242.78/49.30  | | |   (67)  op(e1, e0) = e3
% 242.78/49.30  | | | 
% 242.78/49.30  | | | BETA: splitting (4) gives:
% 242.78/49.30  | | | 
% 242.78/49.30  | | | Case 1:
% 242.78/49.30  | | | | 
% 242.78/49.30  | | | |   (68)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 242.78/49.30  | | | |             e2) = e3)
% 242.78/49.30  | | | | 
% 242.78/49.30  | | | | BETA: splitting (68) gives:
% 242.78/49.30  | | | | 
% 242.78/49.30  | | | | Case 1:
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | |   (69)  all_58_12 = e3 & op(e0, e3) = e3
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | | ALPHA: (69) implies:
% 242.78/49.30  | | | | |   (70)  all_58_12 = e3
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | | REF_CLOSE: (6), (9), (10), (30), (31), (39), (51), (54), (61), (62),
% 242.78/49.30  | | | | |            (70) are inconsistent by sub-proof #1970.
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | Case 2:
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | |   (71)  all_58_13 = e3 & op(e0, e2) = e3
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | | REF_CLOSE: (18), (46), (51), (71) are inconsistent by sub-proof #1919.
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | End of split
% 242.78/49.30  | | | | 
% 242.78/49.30  | | | Case 2:
% 242.78/49.30  | | | | 
% 242.78/49.30  | | | |   (72)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 242.78/49.30  | | | |             e0) = e3)
% 242.78/49.30  | | | | 
% 242.78/49.30  | | | | BETA: splitting (72) gives:
% 242.78/49.30  | | | | 
% 242.78/49.30  | | | | Case 1:
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | |   (73)  all_58_14 = e3 & op(e0, e1) = e3
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | | ALPHA: (73) implies:
% 242.78/49.30  | | | | |   (74)  all_58_14 = e3
% 242.78/49.30  | | | | |   (75)  op(e0, e1) = e3
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | | BETA: splitting (8) gives:
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | | Case 1:
% 242.78/49.30  | | | | | | 
% 242.78/49.30  | | | | | |   (76)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1,
% 242.78/49.30  | | | | | |             e2) = e1)
% 242.78/49.30  | | | | | | 
% 242.78/49.30  | | | | | | BETA: splitting (76) gives:
% 242.78/49.30  | | | | | | 
% 242.78/49.30  | | | | | | Case 1:
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | |   (77)  all_58_6 = e1 & op(e1, e3) = e1
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | | ALPHA: (77) implies:
% 242.78/49.30  | | | | | | |   (78)  all_58_6 = e1
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | | REF_CLOSE: (9), (19), (78) are inconsistent by sub-proof #1758.
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | Case 2:
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | |   (79)  all_58_7 = e1 & op(e1, e2) = e1
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | | ALPHA: (79) implies:
% 242.78/49.30  | | | | | | |   (80)  all_58_7 = e1
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | | BETA: splitting (26) gives:
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | | Case 1:
% 242.78/49.30  | | | | | | | | 
% 242.78/49.30  | | | | | | | |   (81)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 242.78/49.30  | | | | | | | |           op(e2, e3) = e3)
% 242.78/49.30  | | | | | | | | 
% 242.78/49.30  | | | | | | | | BETA: splitting (81) gives:
% 242.78/49.30  | | | | | | | | 
% 242.78/49.30  | | | | | | | | Case 1:
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | |   (82)  all_58_0 = e3 & op(e3, e3) = e3
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | | ALPHA: (82) implies:
% 242.78/49.30  | | | | | | | | |   (83)  op(e3, e3) = e3
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (7), (13), (14), (15), (16),
% 242.78/49.30  | | | | | | | | |            (17), (21), (22), (23), (24), (25), (27), (28),
% 242.78/49.30  | | | | | | | | |            (29), (32), (34), (35), (37), (38), (41), (42),
% 242.78/49.30  | | | | | | | | |            (43), (45), (47), (49), (50), (51), (53), (57),
% 242.78/49.30  | | | | | | | | |            (60), (66), (67), (74), (75), (83) are inconsistent
% 242.78/49.30  | | | | | | | | |            by sub-proof #951.
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | Case 2:
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | |   (84)  all_58_2 = e3 & op(e2, e3) = e3
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | | ALPHA: (84) implies:
% 242.78/49.30  | | | | | | | | |   (85)  op(e2, e3) = e3
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | | REF_CLOSE: (42), (51), (58), (85) are inconsistent by
% 242.78/49.30  | | | | | | | | |            sub-proof #2337.
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | End of split
% 242.78/49.30  | | | | | | | | 
% 242.78/49.30  | | | | | | | Case 2:
% 242.78/49.30  | | | | | | | | 
% 242.78/49.30  | | | | | | | |   (86)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 242.78/49.30  | | | | | | | |           op(e0, e3) = e3)
% 242.78/49.30  | | | | | | | | 
% 242.78/49.30  | | | | | | | | BETA: splitting (86) gives:
% 242.78/49.30  | | | | | | | | 
% 242.78/49.30  | | | | | | | | Case 1:
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | |   (87)  all_58_6 = e3 & op(e1, e3) = e3
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | | REF_CLOSE: (6), (9), (10), (20), (54), (56), (66), (80) are
% 242.78/49.30  | | | | | | | | |            inconsistent by sub-proof #909.
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | Case 2:
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | |   (88)  all_58_12 = e3 & op(e0, e3) = e3
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | | ALPHA: (88) implies:
% 242.78/49.30  | | | | | | | | |   (89)  all_58_12 = e3
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | | REF_CLOSE: (6), (10), (28), (31), (40), (54), (59), (62),
% 242.78/49.30  | | | | | | | | |            (74), (89) are inconsistent by sub-proof #1863.
% 242.78/49.30  | | | | | | | | | 
% 242.78/49.30  | | | | | | | | End of split
% 242.78/49.30  | | | | | | | | 
% 242.78/49.30  | | | | | | | End of split
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | End of split
% 242.78/49.30  | | | | | | 
% 242.78/49.30  | | | | | Case 2:
% 242.78/49.30  | | | | | | 
% 242.78/49.30  | | | | | |   (90)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1,
% 242.78/49.30  | | | | | |             e0) = e1)
% 242.78/49.30  | | | | | | 
% 242.78/49.30  | | | | | | BETA: splitting (90) gives:
% 242.78/49.30  | | | | | | 
% 242.78/49.30  | | | | | | Case 1:
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | |   (91)  all_58_8 = e1 & op(e1, e1) = e1
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | | ALPHA: (91) implies:
% 242.78/49.30  | | | | | | |   (92)  op(e1, e1) = e1
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | | REF_CLOSE: (6), (10), (11), (12), (19), (31), (33), (36), (40),
% 242.78/49.30  | | | | | | |            (44), (48), (51), (52), (55), (57), (62), (66), (92)
% 242.78/49.30  | | | | | | |            are inconsistent by sub-proof #919.
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | Case 2:
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | |   (93)  all_58_11 = e1 & op(e1, e0) = e1
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | | ALPHA: (93) implies:
% 242.78/49.30  | | | | | | |   (94)  op(e1, e0) = e1
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | | REF_CLOSE: (15), (32), (51), (94) are inconsistent by sub-proof
% 242.78/49.30  | | | | | | |            #2304.
% 242.78/49.30  | | | | | | | 
% 242.78/49.30  | | | | | | End of split
% 242.78/49.30  | | | | | | 
% 242.78/49.30  | | | | | End of split
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | Case 2:
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | |   (95)  all_58_15 = e3 & op(e0, e0) = e3
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | | REF_CLOSE: (19), (40), (95) are inconsistent by sub-proof #1915.
% 242.78/49.30  | | | | | 
% 242.78/49.30  | | | | End of split
% 242.78/49.30  | | | | 
% 242.78/49.30  | | | End of split
% 242.78/49.30  | | | 
% 242.78/49.30  | | Case 2:
% 242.78/49.30  | | | 
% 242.78/49.30  | | |   (96)  all_58_15 = e3 & op(e0, e0) = e3
% 242.78/49.30  | | | 
% 242.78/49.30  | | | REF_CLOSE: (19), (40), (96) are inconsistent by sub-proof #1915.
% 242.78/49.30  | | | 
% 242.78/49.30  | | End of split
% 242.78/49.30  | | 
% 242.78/49.30  | End of split
% 242.78/49.30  | 
% 242.78/49.30  End of proof
% 242.78/49.30  
% 242.78/49.30  Sub-proof #909 shows that the following formulas are inconsistent:
% 242.78/49.30  ----------------------------------------------------------------
% 242.78/49.30    (1)   ~ (e3 = e0)
% 242.78/49.30    (2)  all_58_6 = e3
% 242.78/49.30    (3)   ~ (e2 = e0)
% 242.78/49.30    (4)  all_58_8 = e2
% 242.78/49.30    (5)  all_58_11 = e3
% 242.78/49.30    (6)  all_58_7 = e1
% 242.78/49.30    (7)   ~ (e1 = e0)
% 242.78/49.30    (8)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.78/49.30         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.30  
% 242.78/49.30  Begin of proof
% 242.78/49.30  | 
% 242.78/49.30  | BETA: splitting (8) gives:
% 242.78/49.30  | 
% 242.78/49.30  | Case 1:
% 242.78/49.30  | | 
% 242.78/49.30  | |   (9)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 242.78/49.30  | | 
% 242.78/49.30  | | REF_CLOSE: (1), (2), (6), (7), (9) are inconsistent by sub-proof #1557.
% 242.78/49.30  | | 
% 242.78/49.30  | Case 2:
% 242.78/49.30  | | 
% 242.78/49.30  | |   (10)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.30  | |           e0)
% 242.78/49.30  | | 
% 242.78/49.30  | | BETA: splitting (10) gives:
% 242.78/49.30  | | 
% 242.78/49.30  | | Case 1:
% 242.78/49.30  | | | 
% 242.78/49.30  | | |   (11)  all_58_8 = e0 & op(e1, e1) = e0
% 242.78/49.30  | | | 
% 242.78/49.30  | | | ALPHA: (11) implies:
% 242.78/49.30  | | |   (12)  all_58_8 = e0
% 242.78/49.30  | | | 
% 242.78/49.30  | | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #1556.
% 242.78/49.30  | | | 
% 242.78/49.30  | | Case 2:
% 242.78/49.30  | | | 
% 242.78/49.30  | | |   (13)  all_58_11 = e0 & op(e1, e0) = e0
% 242.78/49.30  | | | 
% 242.78/49.30  | | | ALPHA: (13) implies:
% 242.78/49.30  | | |   (14)  all_58_11 = e0
% 242.78/49.30  | | | 
% 242.78/49.30  | | | REF_CLOSE: (1), (5), (14) are inconsistent by sub-proof #1688.
% 242.78/49.30  | | | 
% 242.78/49.30  | | End of split
% 242.78/49.30  | | 
% 242.78/49.30  | End of split
% 242.78/49.30  | 
% 242.78/49.30  End of proof
% 242.78/49.30  
% 242.78/49.30  Sub-proof #910 shows that the following formulas are inconsistent:
% 242.78/49.30  ----------------------------------------------------------------
% 242.78/49.30    (1)   ~ (e3 = e0)
% 242.78/49.30    (2)   ~ (e2 = e0)
% 242.78/49.30    (3)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.78/49.30         (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.30    (4)   ~ (e3 = e1)
% 242.78/49.30    (5)   ~ (e3 = e2)
% 242.78/49.30    (6)  all_58_15 = e1
% 242.78/49.30    (7)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.78/49.30         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.30    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.30    (9)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.78/49.30         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.78/49.30    (10)   ~ (e1 = e0)
% 242.78/49.30    (11)  all_58_10 = e1
% 242.78/49.30    (12)   ~ (e2 = e1)
% 242.78/49.30  
% 242.78/49.30  Begin of proof
% 242.78/49.30  | 
% 242.78/49.30  | BETA: splitting (3) gives:
% 242.78/49.30  | 
% 242.78/49.30  | Case 1:
% 242.78/49.30  | | 
% 242.78/49.30  | |   (13)  all_58_9 = e0 & op(e3, e0) = e0
% 242.78/49.30  | | 
% 242.78/49.30  | | ALPHA: (13) implies:
% 242.78/49.30  | |   (14)  all_58_9 = e0
% 242.78/49.30  | | 
% 242.78/49.30  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11), (12), (14) are
% 242.78/49.30  | |            inconsistent by sub-proof #1618.
% 242.78/49.30  | | 
% 242.78/49.30  | Case 2:
% 242.78/49.30  | | 
% 242.78/49.30  | |   (15)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.30  | |           e0)
% 242.78/49.30  | | 
% 242.78/49.30  | | BETA: splitting (15) gives:
% 242.78/49.30  | | 
% 242.78/49.30  | | Case 1:
% 242.78/49.30  | | | 
% 242.78/49.30  | | |   (16)  all_58_10 = e0 & op(e2, e0) = e0
% 242.78/49.30  | | | 
% 242.78/49.30  | | | REF_CLOSE: (10), (11), (16) are inconsistent by sub-proof #995.
% 242.78/49.30  | | | 
% 242.78/49.30  | | Case 2:
% 242.78/49.30  | | | 
% 242.78/49.30  | | |   (17)  all_58_11 = e0 & op(e1, e0) = e0
% 242.78/49.30  | | | 
% 242.78/49.30  | | | ALPHA: (17) implies:
% 242.78/49.30  | | |   (18)  all_58_11 = e0
% 242.78/49.30  | | | 
% 242.78/49.30  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (18) are
% 242.78/49.30  | | |            inconsistent by sub-proof #1597.
% 242.78/49.30  | | | 
% 242.78/49.30  | | End of split
% 242.78/49.30  | | 
% 242.78/49.30  | End of split
% 242.78/49.30  | 
% 242.78/49.30  End of proof
% 242.78/49.30  
% 242.78/49.30  Sub-proof #911 shows that the following formulas are inconsistent:
% 242.78/49.30  ----------------------------------------------------------------
% 242.78/49.30    (1)  op(e0, e0) = e1
% 242.78/49.30    (2)  op(e2, e2) = e3
% 242.78/49.30    (3)   ~ (e3 = e0)
% 242.78/49.30    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.78/49.30         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.78/49.30    (5)  all_58_6 = e3
% 242.78/49.30    (6)   ~ (e2 = e0)
% 242.78/49.30    (7)  op(e1, e2) = all_52_6
% 242.78/49.30    (8)  op(e1, e0) = all_52_14
% 242.78/49.30    (9)   ~ (all_52_13 = e1)
% 242.78/49.30    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.78/49.30          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.78/49.30    (11)   ~ (e3 = e1)
% 242.78/49.30    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.78/49.30          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.78/49.30    (13)  all_58_3 = e3
% 242.78/49.30    (14)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.30              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.78/49.30                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.78/49.30                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.78/49.30    (15)  op(e2, e1) = all_52_9
% 242.78/49.30    (16)   ~ (e3 = e2)
% 242.78/49.30    (17)   ~ (all_52_14 = e1)
% 242.78/49.30    (18)   ~ (all_52_7 = e1)
% 242.78/49.30    (19)  all_58_15 = e1
% 242.78/49.30    (20)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.78/49.30          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.78/49.30    (21)  all_58_11 = e2
% 242.78/49.30    (22)  op(e2, e3) = all_52_1
% 242.78/49.30    (23)  op(e3, e3) = e2
% 242.78/49.30    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.78/49.30          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.30    (25)   ~ (all_52_6 = e3)
% 242.78/49.30    (26)  op(e1, e1) = e2
% 242.78/49.30    (27)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.78/49.30          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.78/49.30    (28)  op(e0, e2) = all_52_7
% 242.78/49.30    (29)   ~ (all_52_9 = e3)
% 242.78/49.31    (30)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.78/49.31          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.31    (31)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.78/49.31          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.78/49.31    (32)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.78/49.31          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.78/49.31    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.31    (34)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.78/49.31          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.78/49.31    (35)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.78/49.31          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.78/49.31    (36)   ~ (e1 = e0)
% 242.78/49.31    (37)   ~ (all_52_13 = e3)
% 242.78/49.31    (38)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.78/49.31          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.31    (39)  op(e2, e0) = all_52_13
% 242.78/49.31    (40)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.78/49.31          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.78/49.31    (41)   ~ (all_52_1 = e2)
% 242.78/49.31    (42)   ~ (e2 = e1)
% 242.78/49.31  
% 242.78/49.31  Begin of proof
% 242.78/49.31  | 
% 242.78/49.31  | BETA: splitting (38) gives:
% 242.78/49.31  | 
% 242.78/49.31  | Case 1:
% 242.78/49.31  | | 
% 242.78/49.31  | |   (43)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 242.78/49.31  | |           e0)
% 242.78/49.31  | | 
% 242.78/49.31  | | BETA: splitting (43) gives:
% 242.78/49.31  | | 
% 242.78/49.31  | | Case 1:
% 242.78/49.31  | | | 
% 242.78/49.31  | | |   (44)  all_58_6 = e0 & op(e1, e3) = e0
% 242.78/49.31  | | | 
% 242.78/49.31  | | | ALPHA: (44) implies:
% 242.78/49.31  | | |   (45)  all_58_6 = e0
% 242.78/49.31  | | | 
% 242.78/49.31  | | | REF_CLOSE: (3), (7), (16), (20), (21), (25), (26), (33), (45) are
% 242.78/49.31  | | |            inconsistent by sub-proof #997.
% 242.78/49.31  | | | 
% 242.78/49.31  | | Case 2:
% 242.78/49.31  | | | 
% 242.78/49.31  | | |   (46)  all_58_7 = e0 & op(e1, e2) = e0
% 242.78/49.31  | | | 
% 242.78/49.31  | | | ALPHA: (46) implies:
% 242.78/49.31  | | |   (47)  all_58_7 = e0
% 242.78/49.31  | | |   (48)  op(e1, e2) = e0
% 242.78/49.31  | | | 
% 242.78/49.31  | | | BETA: splitting (30) gives:
% 242.78/49.31  | | | 
% 242.78/49.31  | | | Case 1:
% 242.78/49.31  | | | | 
% 242.78/49.31  | | | |   (49)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0)
% 242.78/49.31  | | | |           = e3)
% 242.78/49.31  | | | | 
% 242.78/49.31  | | | | BETA: splitting (49) gives:
% 242.78/49.31  | | | | 
% 242.78/49.31  | | | | Case 1:
% 242.78/49.31  | | | | | 
% 242.78/49.31  | | | | |   (50)  all_58_9 = e3 & op(e3, e0) = e3
% 242.78/49.31  | | | | | 
% 242.78/49.31  | | | | | ALPHA: (50) implies:
% 242.78/49.31  | | | | |   (51)  all_58_9 = e3
% 242.78/49.31  | | | | | 
% 242.78/49.31  | | | | | BETA: splitting (35) gives:
% 242.78/49.31  | | | | | 
% 242.78/49.31  | | | | | Case 1:
% 242.78/49.31  | | | | | | 
% 242.78/49.31  | | | | | |   (52)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 242.78/49.31  | | | | | |             e2) = e1)
% 242.78/49.31  | | | | | | 
% 242.78/49.31  | | | | | | BETA: splitting (52) gives:
% 242.78/49.31  | | | | | | 
% 242.78/49.31  | | | | | | Case 1:
% 242.78/49.31  | | | | | | | 
% 242.78/49.31  | | | | | | |   (53)  all_58_1 = e1 & op(e3, e2) = e1
% 242.78/49.31  | | | | | | | 
% 242.78/49.31  | | | | | | | ALPHA: (53) implies:
% 242.78/49.31  | | | | | | |   (54)  all_58_1 = e1
% 242.78/49.31  | | | | | | | 
% 242.78/49.31  | | | | | | | BETA: splitting (10) gives:
% 242.78/49.31  | | | | | | | 
% 242.78/49.31  | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | 
% 242.78/49.31  | | | | | | | |   (55)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 242.78/49.31  | | | | | | | |           op(e2, e2) = e2)
% 242.78/49.31  | | | | | | | | 
% 242.78/49.31  | | | | | | | | REF_CLOSE: (2), (16), (22), (33), (41), (55) are inconsistent by
% 242.78/49.31  | | | | | | | |            sub-proof #998.
% 242.78/49.31  | | | | | | | | 
% 242.78/49.31  | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | 
% 242.78/49.31  | | | | | | | |   (56)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 242.78/49.31  | | | | | | | |           op(e2, e0) = e2)
% 242.78/49.31  | | | | | | | | 
% 242.78/49.31  | | | | | | | | BETA: splitting (56) gives:
% 242.78/49.31  | | | | | | | | 
% 242.78/49.31  | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | 
% 242.78/49.31  | | | | | | | | |   (57)  all_58_5 = e2 & op(e2, e1) = e2
% 242.78/49.31  | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | ALPHA: (57) implies:
% 242.78/49.31  | | | | | | | | |   (58)  all_58_5 = e2
% 242.78/49.31  | | | | | | | | |   (59)  op(e2, e1) = e2
% 242.78/49.31  | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | BETA: splitting (40) gives:
% 242.78/49.31  | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | |   (60)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 242.78/49.31  | | | | | | | | | |           op(e2, e2) = e1)
% 242.78/49.31  | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | BETA: splitting (60) gives:
% 242.78/49.31  | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | |   (61)  all_58_2 = e1 & op(e2, e3) = e1
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | ALPHA: (61) implies:
% 242.78/49.31  | | | | | | | | | | |   (62)  all_58_2 = e1
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | BETA: splitting (32) gives:
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | |   (63)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 242.78/49.31  | | | | | | | | | | | |           & op(e2, e2) = e0)
% 242.78/49.31  | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | BETA: splitting (63) gives:
% 242.78/49.31  | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | |   (64)  all_58_2 = e0 & op(e2, e3) = e0
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | ALPHA: (64) implies:
% 242.78/49.31  | | | | | | | | | | | | |   (65)  all_58_2 = e0
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | REF_CLOSE: (36), (62), (65) are inconsistent by sub-proof
% 242.78/49.31  | | | | | | | | | | | | |            #1268.
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | |   (66)  all_58_3 = e0 & op(e2, e2) = e0
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (13), (16), (20), (21), (25), (26),
% 242.78/49.31  | | | | | | | | | | | | |            (33), (66) are inconsistent by sub-proof #916.
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | |   (67)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 242.78/49.31  | | | | | | | | | | | |           e0 & op(e2, e0) = e0)
% 242.78/49.31  | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | BETA: splitting (67) gives:
% 242.78/49.31  | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | |   (68)  all_58_5 = e0 & op(e2, e1) = e0
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | ALPHA: (68) implies:
% 242.78/49.31  | | | | | | | | | | | | |   (69)  op(e2, e1) = e0
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | REF_CLOSE: (6), (33), (59), (69) are inconsistent by
% 242.78/49.31  | | | | | | | | | | | | |            sub-proof #1906.
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | |   (70)  all_58_10 = e0 & op(e2, e0) = e0
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | ALPHA: (70) implies:
% 242.78/49.31  | | | | | | | | | | | | |   (71)  op(e2, e0) = e0
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | BETA: splitting (24) gives:
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | |   (72)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 242.78/49.31  | | | | | | | | | | | | | |           & op(e3, e2) = e0)
% 242.78/49.31  | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | REF_CLOSE: (6), (23), (33), (36), (54), (72) are inconsistent
% 242.78/49.31  | | | | | | | | | | | | | |            by sub-proof #1698.
% 242.78/49.31  | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | |   (73)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 242.78/49.31  | | | | | | | | | | | | | |           & op(e3, e0) = e0)
% 242.78/49.31  | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 242.78/49.31  | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | |   (74)  all_58_4 = e0 & op(e3, e1) = e0
% 242.78/49.31  | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | ALPHA: (74) implies:
% 242.78/49.31  | | | | | | | | | | | | | | |   (75)  all_58_4 = e0
% 242.78/49.31  | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 242.78/49.31  | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | |   (76)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 242.78/49.31  | | | | | | | | | | | | | | | |           & op(e2, e1) = e3)
% 242.78/49.31  | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 242.78/49.31  | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | |   (77)  all_58_4 = e3 & op(e3, e1) = e3
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | ALPHA: (77) implies:
% 242.78/49.31  | | | | | | | | | | | | | | | | |   (78)  all_58_4 = e3
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (78) imply:
% 242.78/49.31  | | | | | | | | | | | | | | | | |   (79)  e3 = e0
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (79) imply:
% 242.78/49.31  | | | | | | | | | | | | | | | | |   (80)  all_58_6 = e0
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (16), (20), (21), (25), (26), (33), (80)
% 242.78/49.31  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #997.
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | |   (81)  all_58_5 = e3 & op(e2, e1) = e3
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (29), (33), (81) are inconsistent by
% 242.78/49.31  | | | | | | | | | | | | | | | | |            sub-proof #1822.
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | |   (82)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 242.78/49.31  | | | | | | | | | | | | | | | |           e3 & op(e0, e1) = e3)
% 242.78/49.31  | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 242.78/49.31  | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | |   (83)  all_58_8 = e3 & op(e1, e1) = e3
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | ALPHA: (83) implies:
% 242.78/49.31  | | | | | | | | | | | | | | | | |   (84)  op(e1, e1) = e3
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (26), (33), (84) are inconsistent by
% 242.78/49.31  | | | | | | | | | | | | | | | | |            sub-proof #2206.
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | |   (85)  all_58_14 = e3 & op(e0, e1) = e3
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | ALPHA: (85) implies:
% 242.78/49.31  | | | | | | | | | | | | | | | | |   (86)  op(e0, e1) = e3
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | |   (87)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 242.78/49.31  | | | | | | | | | | | | | | | | | |           & op(e1, e2) = e1)
% 242.78/49.31  | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | |   (88)  all_58_6 = e1 & op(e1, e3) = e1
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | ALPHA: (88) implies:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | |   (89)  all_58_6 = e1
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (89) are inconsistent by sub-proof
% 242.78/49.31  | | | | | | | | | | | | | | | | | | |            #1758.
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | |   (90)  all_58_7 = e1 & op(e1, e2) = e1
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (16), (20), (21), (25), (26), (33),
% 242.78/49.31  | | | | | | | | | | | | | | | | | | |            (36), (38), (90) are inconsistent by sub-proof
% 242.78/49.31  | | | | | | | | | | | | | | | | | | |            #915.
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | |   (91)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 242.78/49.31  | | | | | | | | | | | | | | | | | |           e1 & op(e1, e0) = e1)
% 242.78/49.31  | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | |   (92)  all_58_8 = e1 & op(e1, e1) = e1
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | |   (93)  op(e1, e1) = e1
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | |   (94)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | |           & op(e2, e1) = e0)
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with e1, e2, e1, e1,
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |              simplifying with (26), (93) gives:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |   (95)  e2 = e1
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (95) imply:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |   (96)  all_58_11 = e1
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (95) imply:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |   (97)  all_58_5 = e1
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (10), (11), (13), (16), (19), (30),
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |            (32), (33), (34), (36), (42), (71), (96), (97) are
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #913.
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |   (98)  all_58_5 = e0 & op(e2, e1) = e0
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |   (99)  op(e2, e1) = e0
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (33), (59), (99) are inconsistent by
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1906.
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | |   (100)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |   (101)  all_58_8 = e0 & op(e1, e1) = e0
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |   (102)  op(e1, e1) = e0
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (11), (16), (31), (33), (36),
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |            (42), (47), (48), (102) are inconsistent by
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1018.
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |   (103)  all_58_14 = e0 & op(e0, e1) = e0
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |   (104)  op(e0, e1) = e0
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (33), (86), (104) are inconsistent by
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2164.
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | |   (105)  all_58_11 = e1 & op(e1, e0) = e1
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 242.78/49.31  | | | | | | | | | | | | | | | | | | |   (106)  op(e1, e0) = e1
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (33), (106) are inconsistent by
% 242.78/49.31  | | | | | | | | | | | | | | | | | | |            sub-proof #2304.
% 242.78/49.31  | | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | |   (107)  all_58_9 = e0 & op(e3, e0) = e0
% 242.78/49.31  | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (16), (20), (21), (25), (26), (33),
% 242.78/49.31  | | | | | | | | | | | | | | |            (51), (107) are inconsistent by sub-proof #912.
% 242.78/49.31  | | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | |   (108)  all_58_3 = e1 & op(e2, e2) = e1
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | ALPHA: (108) implies:
% 242.78/49.31  | | | | | | | | | | |   (109)  all_58_3 = e1
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | REF_CLOSE: (11), (13), (109) are inconsistent by sub-proof
% 242.78/49.31  | | | | | | | | | | |            #1999.
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | |   (110)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1
% 242.78/49.31  | | | | | | | | | |            & op(e2, e0) = e1)
% 242.78/49.31  | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | BETA: splitting (110) gives:
% 242.78/49.31  | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | |   (111)  all_58_5 = e1 & op(e2, e1) = e1
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | REF_CLOSE: (42), (58), (111) are inconsistent by sub-proof
% 242.78/49.31  | | | | | | | | | | |            #1548.
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | |   (112)  all_58_10 = e1 & op(e2, e0) = e1
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | | REF_CLOSE: (9), (33), (39), (112) are inconsistent by
% 242.78/49.31  | | | | | | | | | | |            sub-proof #2277.
% 242.78/49.31  | | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | End of split
% 242.78/49.31  | | | | | | | | | 
% 242.78/49.31  | | | | | | | | Case 2:
% 242.78/49.31  | | | | | | | | | 
% 242.78/49.31  | | | | | | | | |   (113)  all_58_10 = e2 & op(e2, e0) = e2
% 242.78/49.31  | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | ALPHA: (113) implies:
% 242.78/49.31  | | | | | | | | |   (114)  op(e2, e0) = e2
% 242.78/49.31  | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | BETA: splitting (14) gives:
% 242.78/49.31  | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | Case 1:
% 242.78/49.31  | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | |   (115)  all_58_15 = e0 & op(e0, e0) = e0
% 242.78/49.31  | | | | | | | | | | 
% 242.78/49.31  | | | | | | | | | | ALPHA: (115) implies:
% 242.78/49.31  | | | | | | | | | |   (116)  op(e0, e0) = e0
% 242.78/49.32  | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | REF_CLOSE: (1), (33), (36), (116) are inconsistent by
% 242.78/49.32  | | | | | | | | | |            sub-proof #2274.
% 242.78/49.32  | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | Case 2:
% 242.78/49.32  | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | |   (117)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.78/49.32  | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.78/49.32  | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 242.78/49.32  | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.78/49.32  | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.78/49.32  | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | ALPHA: (117) implies:
% 242.78/49.32  | | | | | | | | | |   (118)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 242.78/49.32  | | | | | | | | | |            & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.78/49.32  | | | | | | | | | |            = e0)
% 242.78/49.32  | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | BETA: splitting (118) gives:
% 242.78/49.32  | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | Case 1:
% 242.78/49.32  | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | |   (119)  all_58_9 = e0 & op(e3, e0) = e0
% 242.78/49.32  | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | ALPHA: (119) implies:
% 242.78/49.32  | | | | | | | | | | |   (120)  all_58_9 = e0
% 242.78/49.32  | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | COMBINE_EQS: (51), (120) imply:
% 242.78/49.32  | | | | | | | | | | |   (121)  e3 = e0
% 242.78/49.32  | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | SIMP: (121) implies:
% 242.78/49.32  | | | | | | | | | | |   (122)  e3 = e0
% 242.78/49.32  | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | COMBINE_EQS: (5), (122) imply:
% 242.78/49.32  | | | | | | | | | | |   (123)  all_58_6 = e0
% 242.78/49.32  | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | REF_CLOSE: (3), (7), (16), (20), (21), (25), (26), (33),
% 242.78/49.32  | | | | | | | | | | |            (123) are inconsistent by sub-proof #997.
% 242.78/49.32  | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | Case 2:
% 242.78/49.32  | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | |   (124)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 242.78/49.32  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 242.78/49.32  | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | BETA: splitting (124) gives:
% 242.78/49.32  | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | Case 1:
% 242.78/49.32  | | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | |   (125)  all_58_10 = e0 & op(e2, e0) = e0
% 242.78/49.32  | | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | | ALPHA: (125) implies:
% 242.78/49.32  | | | | | | | | | | | |   (126)  op(e2, e0) = e0
% 242.78/49.32  | | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | | REF_CLOSE: (6), (33), (114), (126) are inconsistent by
% 242.78/49.32  | | | | | | | | | | | |            sub-proof #2121.
% 242.78/49.32  | | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | Case 2:
% 242.78/49.32  | | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | |   (127)  all_58_11 = e0 & op(e1, e0) = e0
% 242.78/49.32  | | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | | ALPHA: (127) implies:
% 242.78/49.32  | | | | | | | | | | | |   (128)  all_58_11 = e0
% 242.78/49.32  | | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | | REF_CLOSE: (6), (21), (128) are inconsistent by sub-proof
% 242.78/49.32  | | | | | | | | | | | |            #2110.
% 242.78/49.32  | | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | | End of split
% 242.78/49.32  | | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | | End of split
% 242.78/49.32  | | | | | | | | | | 
% 242.78/49.32  | | | | | | | | | End of split
% 242.78/49.32  | | | | | | | | | 
% 242.78/49.32  | | | | | | | | End of split
% 242.78/49.32  | | | | | | | | 
% 242.78/49.32  | | | | | | | End of split
% 242.78/49.32  | | | | | | | 
% 242.78/49.32  | | | | | | Case 2:
% 242.78/49.32  | | | | | | | 
% 242.78/49.32  | | | | | | |   (129)  all_58_3 = e1 & op(e2, e2) = e1
% 242.78/49.32  | | | | | | | 
% 242.78/49.32  | | | | | | | REF_CLOSE: (11), (13), (129) are inconsistent by sub-proof #2197.
% 242.78/49.32  | | | | | | | 
% 242.78/49.32  | | | | | | End of split
% 242.78/49.32  | | | | | | 
% 242.78/49.32  | | | | | Case 2:
% 242.78/49.32  | | | | | | 
% 242.78/49.32  | | | | | |   (130)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 242.78/49.32  | | | | | |            op(e0, e2) = e1)
% 242.78/49.32  | | | | | | 
% 242.78/49.32  | | | | | | BETA: splitting (130) gives:
% 242.78/49.32  | | | | | | 
% 242.78/49.32  | | | | | | Case 1:
% 242.78/49.32  | | | | | | | 
% 242.78/49.32  | | | | | | |   (131)  all_58_7 = e1 & op(e1, e2) = e1
% 242.78/49.32  | | | | | | | 
% 242.78/49.32  | | | | | | | REF_CLOSE: (3), (6), (7), (16), (20), (21), (25), (26), (33),
% 242.78/49.32  | | | | | | |            (36), (38), (131) are inconsistent by sub-proof #915.
% 242.78/49.32  | | | | | | | 
% 242.78/49.32  | | | | | | Case 2:
% 242.78/49.32  | | | | | | | 
% 242.78/49.32  | | | | | | |   (132)  all_58_13 = e1 & op(e0, e2) = e1
% 242.78/49.32  | | | | | | | 
% 242.78/49.32  | | | | | | | REF_CLOSE: (18), (28), (33), (132) are inconsistent by sub-proof
% 242.78/49.32  | | | | | | |            #2275.
% 242.78/49.32  | | | | | | | 
% 242.78/49.32  | | | | | | End of split
% 242.78/49.32  | | | | | | 
% 242.78/49.32  | | | | | End of split
% 242.78/49.32  | | | | | 
% 242.78/49.32  | | | | Case 2:
% 242.78/49.32  | | | | | 
% 242.78/49.32  | | | | |   (133)  all_58_10 = e3 & op(e2, e0) = e3
% 242.78/49.32  | | | | | 
% 242.78/49.32  | | | | | ALPHA: (133) implies:
% 242.78/49.32  | | | | |   (134)  op(e2, e0) = e3
% 242.78/49.32  | | | | | 
% 242.78/49.32  | | | | | REF_CLOSE: (33), (37), (39), (134) are inconsistent by sub-proof
% 242.78/49.32  | | | | |            #1994.
% 242.78/49.32  | | | | | 
% 242.78/49.32  | | | | End of split
% 242.78/49.32  | | | | 
% 242.78/49.32  | | | Case 2:
% 242.78/49.32  | | | | 
% 242.78/49.32  | | | |   (135)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 242.78/49.32  | | | |              e0) = e3)
% 242.78/49.32  | | | | 
% 242.78/49.32  | | | | REF_CLOSE: (3), (4), (5), (6), (7), (11), (14), (16), (20), (21), (25),
% 242.78/49.32  | | | |            (26), (31), (33), (36), (38), (42), (135) are inconsistent by
% 242.78/49.32  | | | |            sub-proof #981.
% 242.78/49.32  | | | | 
% 242.78/49.32  | | | End of split
% 242.78/49.32  | | | 
% 242.78/49.32  | | End of split
% 242.78/49.32  | | 
% 242.78/49.32  | Case 2:
% 242.78/49.32  | | 
% 242.78/49.32  | |   (136)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.32  | |            e0)
% 242.78/49.32  | | 
% 242.78/49.32  | | REF_CLOSE: (6), (21), (26), (33), (136) are inconsistent by sub-proof #2032.
% 242.78/49.32  | | 
% 242.78/49.32  | End of split
% 242.78/49.32  | 
% 242.78/49.32  End of proof
% 242.78/49.32  
% 242.78/49.32  Sub-proof #912 shows that the following formulas are inconsistent:
% 242.78/49.32  ----------------------------------------------------------------
% 242.78/49.32    (1)   ~ (e3 = e0)
% 242.78/49.32    (2)  all_58_6 = e3
% 242.78/49.32    (3)  op(e1, e2) = all_52_6
% 242.78/49.32    (4)  all_58_9 = e0 & op(e3, e0) = e0
% 242.78/49.32    (5)   ~ (e3 = e2)
% 242.78/49.32    (6)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.78/49.32         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.78/49.32    (7)  all_58_9 = e3
% 242.78/49.32    (8)  all_58_11 = e2
% 242.78/49.32    (9)   ~ (all_52_6 = e3)
% 242.78/49.32    (10)  op(e1, e1) = e2
% 242.78/49.32    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.32  
% 242.78/49.32  Begin of proof
% 242.78/49.32  | 
% 242.78/49.32  | ALPHA: (4) implies:
% 242.78/49.32  |   (12)  all_58_9 = e0
% 242.78/49.32  | 
% 242.78/49.32  | COMBINE_EQS: (7), (12) imply:
% 242.78/49.32  |   (13)  e3 = e0
% 242.78/49.32  | 
% 242.78/49.32  | COMBINE_EQS: (2), (13) imply:
% 242.78/49.32  |   (14)  all_58_6 = e0
% 242.78/49.32  | 
% 242.78/49.32  | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (14) are inconsistent by
% 242.78/49.32  |            sub-proof #997.
% 242.78/49.32  | 
% 242.78/49.32  End of proof
% 242.78/49.32  
% 242.78/49.32  Sub-proof #913 shows that the following formulas are inconsistent:
% 242.78/49.32  ----------------------------------------------------------------
% 242.78/49.32    (1)   ~ (e3 = e0)
% 242.78/49.32    (2)   ~ (e2 = e0)
% 242.78/49.32    (3)  all_58_11 = e1
% 242.78/49.32    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.78/49.32         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.78/49.32    (5)   ~ (e3 = e1)
% 242.78/49.32    (6)  all_58_3 = e3
% 242.78/49.32    (7)   ~ (e3 = e2)
% 242.78/49.32    (8)  op(e2, e0) = e0
% 242.78/49.32    (9)  all_58_15 = e1
% 242.78/49.32    (10)  all_58_5 = e1
% 242.78/49.32    (11)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.78/49.32          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.32    (12)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.78/49.32          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.78/49.32    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.32    (14)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.78/49.32          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.78/49.32    (15)   ~ (e1 = e0)
% 242.78/49.32    (16)   ~ (e2 = e1)
% 242.78/49.32  
% 242.78/49.32  Begin of proof
% 242.78/49.32  | 
% 242.78/49.32  | BETA: splitting (14) gives:
% 242.78/49.32  | 
% 242.78/49.32  | Case 1:
% 242.78/49.32  | | 
% 242.78/49.32  | |   (17)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 242.78/49.32  | |           e2)
% 242.78/49.32  | | 
% 242.78/49.32  | | BETA: splitting (17) gives:
% 242.78/49.32  | | 
% 242.78/49.32  | | Case 1:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (18)  all_58_9 = e2 & op(e3, e0) = e2
% 242.78/49.32  | | | 
% 242.78/49.32  | | | ALPHA: (18) implies:
% 242.78/49.32  | | |   (19)  op(e3, e0) = e2
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 242.78/49.32  | | |            (15), (16), (19) are inconsistent by sub-proof #914.
% 242.78/49.32  | | | 
% 242.78/49.32  | | Case 2:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (20)  all_58_10 = e2 & op(e2, e0) = e2
% 242.78/49.32  | | | 
% 242.78/49.32  | | | ALPHA: (20) implies:
% 242.78/49.32  | | |   (21)  op(e2, e0) = e2
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (2), (8), (13), (21) are inconsistent by sub-proof #2121.
% 242.78/49.32  | | | 
% 242.78/49.32  | | End of split
% 242.78/49.32  | | 
% 242.78/49.32  | Case 2:
% 242.78/49.32  | | 
% 242.78/49.32  | |   (22)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.78/49.32  | |           e2)
% 242.78/49.32  | | 
% 242.78/49.32  | | BETA: splitting (22) gives:
% 242.78/49.32  | | 
% 242.78/49.32  | | Case 1:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (23)  all_58_11 = e2 & op(e1, e0) = e2
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (3), (16), (23) are inconsistent by sub-proof #1554.
% 242.78/49.32  | | | 
% 242.78/49.32  | | Case 2:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (24)  all_58_15 = e2 & op(e0, e0) = e2
% 242.78/49.32  | | | 
% 242.78/49.32  | | | ALPHA: (24) implies:
% 242.78/49.32  | | |   (25)  all_58_15 = e2
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (9), (16), (25) are inconsistent by sub-proof #2231.
% 242.78/49.32  | | | 
% 242.78/49.32  | | End of split
% 242.78/49.32  | | 
% 242.78/49.32  | End of split
% 242.78/49.32  | 
% 242.78/49.32  End of proof
% 242.78/49.32  
% 242.78/49.32  Sub-proof #914 shows that the following formulas are inconsistent:
% 242.78/49.32  ----------------------------------------------------------------
% 242.78/49.32    (1)   ~ (e3 = e0)
% 242.78/49.32    (2)   ~ (e2 = e0)
% 242.78/49.32    (3)  all_58_11 = e1
% 242.78/49.32    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.78/49.32         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.78/49.32    (5)   ~ (e3 = e1)
% 242.78/49.32    (6)  all_58_3 = e3
% 242.78/49.32    (7)   ~ (e3 = e2)
% 242.78/49.32    (8)  all_58_15 = e1
% 242.78/49.32    (9)  op(e3, e0) = e2
% 242.78/49.32    (10)  all_58_5 = e1
% 242.78/49.32    (11)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.78/49.32          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.32    (12)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.78/49.32          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.78/49.32    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.32    (14)   ~ (e1 = e0)
% 242.78/49.32    (15)   ~ (e2 = e1)
% 242.78/49.32  
% 242.78/49.32  Begin of proof
% 242.78/49.32  | 
% 242.78/49.32  | BETA: splitting (11) gives:
% 242.78/49.32  | 
% 242.78/49.32  | Case 1:
% 242.78/49.32  | | 
% 242.78/49.32  | |   (16)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 242.78/49.32  | |           e3)
% 242.78/49.32  | | 
% 242.78/49.32  | | BETA: splitting (16) gives:
% 242.78/49.32  | | 
% 242.78/49.32  | | Case 1:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (17)  all_58_9 = e3 & op(e3, e0) = e3
% 242.78/49.32  | | | 
% 242.78/49.32  | | | ALPHA: (17) implies:
% 242.78/49.32  | | |   (18)  op(e3, e0) = e3
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (7), (9), (13), (18) are inconsistent by sub-proof #2125.
% 242.78/49.32  | | | 
% 242.78/49.32  | | Case 2:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (19)  all_58_10 = e3 & op(e2, e0) = e3
% 242.78/49.32  | | | 
% 242.78/49.32  | | | ALPHA: (19) implies:
% 242.78/49.32  | | |   (20)  all_58_10 = e3
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (1), (2), (4), (6), (7), (10), (12), (14), (15), (20) are
% 242.78/49.32  | | |            inconsistent by sub-proof #1101.
% 242.78/49.32  | | | 
% 242.78/49.32  | | End of split
% 242.78/49.32  | | 
% 242.78/49.32  | Case 2:
% 242.78/49.32  | | 
% 242.78/49.32  | |   (21)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 242.78/49.32  | |           e3)
% 242.78/49.32  | | 
% 242.78/49.32  | | BETA: splitting (21) gives:
% 242.78/49.32  | | 
% 242.78/49.32  | | Case 1:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (22)  all_58_11 = e3 & op(e1, e0) = e3
% 242.78/49.32  | | | 
% 242.78/49.32  | | | ALPHA: (22) implies:
% 242.78/49.32  | | |   (23)  all_58_11 = e3
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (3), (5), (23) are inconsistent by sub-proof #1980.
% 242.78/49.32  | | | 
% 242.78/49.32  | | Case 2:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (24)  all_58_15 = e3 & op(e0, e0) = e3
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (5), (8), (24) are inconsistent by sub-proof #1915.
% 242.78/49.32  | | | 
% 242.78/49.32  | | End of split
% 242.78/49.32  | | 
% 242.78/49.32  | End of split
% 242.78/49.32  | 
% 242.78/49.32  End of proof
% 242.78/49.32  
% 242.78/49.32  Sub-proof #915 shows that the following formulas are inconsistent:
% 242.78/49.32  ----------------------------------------------------------------
% 242.78/49.32    (1)   ~ (e3 = e0)
% 242.78/49.32    (2)   ~ (e2 = e0)
% 242.78/49.32    (3)  op(e1, e2) = all_52_6
% 242.78/49.32    (4)   ~ (e3 = e2)
% 242.78/49.32    (5)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.78/49.32         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.78/49.32    (6)  all_58_11 = e2
% 242.78/49.32    (7)   ~ (all_52_6 = e3)
% 242.78/49.32    (8)  op(e1, e1) = e2
% 242.78/49.32    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.32    (10)  all_58_7 = e1 & op(e1, e2) = e1
% 242.78/49.32    (11)   ~ (e1 = e0)
% 242.78/49.32    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.78/49.32          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.32  
% 242.78/49.32  Begin of proof
% 242.78/49.32  | 
% 242.78/49.32  | ALPHA: (10) implies:
% 242.78/49.32  |   (13)  op(e1, e2) = e1
% 242.78/49.32  | 
% 242.78/49.32  | BETA: splitting (12) gives:
% 242.78/49.32  | 
% 242.78/49.32  | Case 1:
% 242.78/49.32  | | 
% 242.78/49.32  | |   (14)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 242.78/49.32  | |           e0)
% 242.78/49.32  | | 
% 242.78/49.32  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14) are
% 242.78/49.32  | |            inconsistent by sub-proof #989.
% 242.78/49.32  | | 
% 242.78/49.32  | Case 2:
% 242.78/49.32  | | 
% 242.78/49.32  | |   (15)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.32  | |           e0)
% 242.78/49.32  | | 
% 242.78/49.32  | | REF_CLOSE: (2), (6), (8), (9), (15) are inconsistent by sub-proof #2032.
% 242.78/49.32  | | 
% 242.78/49.32  | End of split
% 242.78/49.32  | 
% 242.78/49.32  End of proof
% 242.78/49.32  
% 242.78/49.32  Sub-proof #916 shows that the following formulas are inconsistent:
% 242.78/49.32  ----------------------------------------------------------------
% 242.78/49.32    (1)   ~ (e3 = e0)
% 242.78/49.32    (2)  all_58_6 = e3
% 242.78/49.32    (3)  op(e1, e2) = all_52_6
% 242.78/49.32    (4)  all_58_3 = e3
% 242.78/49.32    (5)  all_58_3 = e0 & op(e2, e2) = e0
% 242.78/49.32    (6)   ~ (e3 = e2)
% 242.78/49.32    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.78/49.32         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.78/49.32    (8)  all_58_11 = e2
% 242.78/49.32    (9)   ~ (all_52_6 = e3)
% 242.78/49.32    (10)  op(e1, e1) = e2
% 242.78/49.32    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.32  
% 242.78/49.32  Begin of proof
% 242.78/49.32  | 
% 242.78/49.32  | ALPHA: (5) implies:
% 242.78/49.32  |   (12)  all_58_3 = e0
% 242.78/49.32  | 
% 242.78/49.32  | COMBINE_EQS: (4), (12) imply:
% 242.78/49.32  |   (13)  e3 = e0
% 242.78/49.32  | 
% 242.78/49.32  | COMBINE_EQS: (2), (13) imply:
% 242.78/49.32  |   (14)  all_58_6 = e0
% 242.78/49.32  | 
% 242.78/49.32  | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (14) are inconsistent by
% 242.78/49.32  |            sub-proof #997.
% 242.78/49.32  | 
% 242.78/49.32  End of proof
% 242.78/49.32  
% 242.78/49.32  Sub-proof #917 shows that the following formulas are inconsistent:
% 242.78/49.32  ----------------------------------------------------------------
% 242.78/49.32    (1)   ~ (e3 = e0)
% 242.78/49.32    (2)  op(e1, e2) = e1
% 242.78/49.32    (3)   ~ (e2 = e0)
% 242.78/49.32    (4)  op(e1, e2) = all_52_6
% 242.78/49.32    (5)  all_58_6 = e2
% 242.78/49.32    (6)   ~ (e3 = e2)
% 242.78/49.32    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.78/49.32         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.78/49.32    (8)   ~ (all_52_6 = e3)
% 242.78/49.32    (9)  op(e1, e1) = e2
% 242.78/49.32    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.32    (11)   ~ (e1 = e0)
% 242.78/49.32    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.78/49.32          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.32  
% 242.78/49.32  Begin of proof
% 242.78/49.32  | 
% 242.78/49.32  | BETA: splitting (12) gives:
% 242.78/49.32  | 
% 242.78/49.32  | Case 1:
% 242.78/49.32  | | 
% 242.78/49.32  | |   (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 242.78/49.32  | |           e0)
% 242.78/49.32  | | 
% 242.78/49.32  | | BETA: splitting (13) gives:
% 242.78/49.32  | | 
% 242.78/49.32  | | Case 1:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (14)  all_58_6 = e0 & op(e1, e3) = e0
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (3), (5), (14) are inconsistent by sub-proof #1678.
% 242.78/49.32  | | | 
% 242.78/49.32  | | Case 2:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (15)  all_58_7 = e0 & op(e1, e2) = e0
% 242.78/49.32  | | | 
% 242.78/49.32  | | | ALPHA: (15) implies:
% 242.78/49.32  | | |   (16)  op(e1, e2) = e0
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (2), (4), (10), (11), (16) are inconsistent by sub-proof #2136.
% 242.78/49.32  | | | 
% 242.78/49.32  | | End of split
% 242.78/49.32  | | 
% 242.78/49.32  | Case 2:
% 242.78/49.32  | | 
% 242.78/49.32  | |   (17)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.32  | |           e0)
% 242.78/49.32  | | 
% 242.78/49.32  | | BETA: splitting (17) gives:
% 242.78/49.32  | | 
% 242.78/49.32  | | Case 1:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (18)  all_58_8 = e0 & op(e1, e1) = e0
% 242.78/49.32  | | | 
% 242.78/49.32  | | | ALPHA: (18) implies:
% 242.78/49.32  | | |   (19)  op(e1, e1) = e0
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (3), (9), (10), (19) are inconsistent by sub-proof #2211.
% 242.78/49.32  | | | 
% 242.78/49.32  | | Case 2:
% 242.78/49.32  | | | 
% 242.78/49.32  | | |   (20)  all_58_11 = e0 & op(e1, e0) = e0
% 242.78/49.32  | | | 
% 242.78/49.32  | | | ALPHA: (20) implies:
% 242.78/49.32  | | |   (21)  all_58_11 = e0
% 242.78/49.32  | | | 
% 242.78/49.32  | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (21) are inconsistent
% 242.78/49.32  | | |            by sub-proof #967.
% 242.78/49.33  | | | 
% 242.78/49.33  | | End of split
% 242.78/49.33  | | 
% 242.78/49.33  | End of split
% 242.78/49.33  | 
% 242.78/49.33  End of proof
% 242.78/49.33  
% 242.78/49.33  Sub-proof #918 shows that the following formulas are inconsistent:
% 242.78/49.33  ----------------------------------------------------------------
% 242.78/49.33    (1)  all_58_1 = e1
% 242.78/49.33    (2)   ~ (e3 = e0)
% 242.78/49.33    (3)  op(e1, e1) = e1
% 242.78/49.33    (4)   ~ (e2 = e0)
% 242.78/49.33    (5)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.78/49.33         (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.33    (6)  op(e1, e2) = all_52_6
% 242.78/49.33    (7)   ~ (e3 = e1)
% 242.78/49.33    (8)  all_58_3 = e3
% 242.78/49.33    (9)  op(e2, e1) = all_52_9
% 242.78/49.33    (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.78/49.33          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.78/49.33    (11)   ~ (e3 = e2)
% 242.78/49.33    (12)  all_58_10 = e2
% 242.78/49.33    (13)  op(e2, e0) = e2
% 242.78/49.33    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.78/49.33          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.78/49.33    (15)  all_58_15 = e1
% 242.78/49.33    (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.78/49.33          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.78/49.33    (17)  op(e3, e3) = e2
% 242.78/49.33    (18)  all_58_12 = e3
% 242.78/49.33    (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.78/49.33          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.33    (20)   ~ (all_52_6 = e3)
% 242.78/49.33    (21)  op(e1, e1) = e2
% 242.78/49.33    (22)  op(e2, e1) = e0
% 242.78/49.33    (23)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.78/49.33          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.33    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.33    (25)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.78/49.33          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.78/49.33    (26)   ~ (e1 = e0)
% 242.78/49.33    (27)  all_58_4 = e3
% 242.78/49.33    (28)   ~ (all_52_13 = e3)
% 242.78/49.33    (29)  op(e2, e0) = all_52_13
% 242.78/49.33    (30)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.78/49.33          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.78/49.33    (31)   ~ (e2 = e1)
% 242.78/49.33  
% 242.78/49.33  Begin of proof
% 242.78/49.33  | 
% 242.78/49.33  | BETA: splitting (19) gives:
% 242.78/49.33  | 
% 242.78/49.33  | Case 1:
% 242.78/49.33  | | 
% 242.78/49.33  | |   (32)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 242.78/49.33  | |           e0)
% 242.78/49.33  | | 
% 242.78/49.33  | | REF_CLOSE: (1), (4), (17), (24), (26), (32) are inconsistent by sub-proof
% 242.78/49.33  | |            #1698.
% 242.78/49.33  | | 
% 242.78/49.33  | Case 2:
% 242.78/49.33  | | 
% 242.78/49.33  | |   (33)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 242.78/49.33  | |           e0)
% 242.78/49.33  | | 
% 242.78/49.33  | | BETA: splitting (33) gives:
% 242.78/49.33  | | 
% 242.78/49.33  | | Case 1:
% 242.78/49.33  | | | 
% 242.78/49.33  | | |   (34)  all_58_4 = e0 & op(e3, e1) = e0
% 242.78/49.33  | | | 
% 242.78/49.33  | | | REF_CLOSE: (2), (27), (34) are inconsistent by sub-proof #1697.
% 242.78/49.33  | | | 
% 242.78/49.33  | | Case 2:
% 242.78/49.33  | | | 
% 242.78/49.33  | | |   (35)  all_58_9 = e0 & op(e3, e0) = e0
% 242.78/49.33  | | | 
% 242.78/49.33  | | | ALPHA: (35) implies:
% 242.78/49.33  | | |   (36)  all_58_9 = e0
% 242.78/49.33  | | | 
% 242.78/49.33  | | | BETA: splitting (30) gives:
% 242.78/49.33  | | | 
% 242.78/49.33  | | | Case 1:
% 242.78/49.33  | | | | 
% 242.78/49.33  | | | |   (37)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 242.78/49.33  | | | |           = e1)
% 242.78/49.33  | | | | 
% 242.78/49.33  | | | | BETA: splitting (37) gives:
% 242.78/49.33  | | | | 
% 242.78/49.33  | | | | Case 1:
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | |   (38)  all_58_2 = e1 & op(e2, e3) = e1
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | | ALPHA: (38) implies:
% 242.78/49.33  | | | | |   (39)  all_58_2 = e1
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | | BETA: splitting (16) gives:
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | | Case 1:
% 242.78/49.33  | | | | | | 
% 242.78/49.33  | | | | | |   (40)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 242.78/49.33  | | | | | |             e2) = e3)
% 242.78/49.33  | | | | | | 
% 242.78/49.33  | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (14), (18), (20), (24), (26),
% 242.78/49.33  | | | | | |            (31), (39), (40) are inconsistent by sub-proof #977.
% 242.78/49.33  | | | | | | 
% 242.78/49.33  | | | | | Case 2:
% 242.78/49.33  | | | | | | 
% 242.78/49.33  | | | | | |   (41)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 242.78/49.33  | | | | | |             e0) = e3)
% 242.78/49.33  | | | | | | 
% 242.78/49.33  | | | | | | BETA: splitting (41) gives:
% 242.78/49.33  | | | | | | 
% 242.78/49.33  | | | | | | Case 1:
% 242.78/49.33  | | | | | | | 
% 242.78/49.33  | | | | | | |   (42)  all_58_8 = e3 & op(e1, e1) = e3
% 242.78/49.33  | | | | | | | 
% 242.78/49.33  | | | | | | | ALPHA: (42) implies:
% 242.78/49.33  | | | | | | |   (43)  op(e1, e1) = e3
% 242.78/49.33  | | | | | | | 
% 242.78/49.33  | | | | | | | REF_CLOSE: (11), (21), (24), (43) are inconsistent by sub-proof
% 242.78/49.33  | | | | | | |            #2206.
% 242.78/49.33  | | | | | | | 
% 242.78/49.33  | | | | | | Case 2:
% 242.78/49.33  | | | | | | | 
% 242.78/49.33  | | | | | | |   (44)  all_58_11 = e3 & op(e1, e0) = e3
% 242.78/49.33  | | | | | | | 
% 242.78/49.33  | | | | | | | ALPHA: (44) implies:
% 242.78/49.33  | | | | | | |   (45)  all_58_11 = e3
% 242.78/49.33  | | | | | | | 
% 242.78/49.33  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (11), (12), (13), (15), (21),
% 242.78/49.33  | | | | | | |            (23), (24), (25), (28), (29), (31), (36), (45) are
% 242.78/49.33  | | | | | | |            inconsistent by sub-proof #919.
% 242.78/49.33  | | | | | | | 
% 242.78/49.33  | | | | | | End of split
% 242.78/49.33  | | | | | | 
% 242.78/49.33  | | | | | End of split
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | Case 2:
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | |   (46)  all_58_3 = e1 & op(e2, e2) = e1
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | | ALPHA: (46) implies:
% 242.78/49.33  | | | | |   (47)  all_58_3 = e1
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | | REF_CLOSE: (7), (8), (47) are inconsistent by sub-proof #1999.
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | End of split
% 242.78/49.33  | | | | 
% 242.78/49.33  | | | Case 2:
% 242.78/49.33  | | | | 
% 242.78/49.33  | | | |   (48)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 242.78/49.33  | | | |           = e1)
% 242.78/49.33  | | | | 
% 242.78/49.33  | | | | BETA: splitting (48) gives:
% 242.78/49.33  | | | | 
% 242.78/49.33  | | | | Case 1:
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | |   (49)  all_58_5 = e1 & op(e2, e1) = e1
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | | ALPHA: (49) implies:
% 242.78/49.33  | | | | |   (50)  op(e2, e1) = e1
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | | REF_CLOSE: (9), (22), (24), (26), (50) are inconsistent by sub-proof
% 242.78/49.33  | | | | |            #2165.
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | Case 2:
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | |   (51)  all_58_10 = e1 & op(e2, e0) = e1
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | | ALPHA: (51) implies:
% 242.78/49.33  | | | | |   (52)  all_58_10 = e1
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | | REF_CLOSE: (2), (4), (7), (11), (15), (23), (25), (31), (36), (52) are
% 242.78/49.33  | | | | |            inconsistent by sub-proof #1618.
% 242.78/49.33  | | | | | 
% 242.78/49.33  | | | | End of split
% 242.78/49.33  | | | | 
% 242.78/49.33  | | | End of split
% 242.78/49.33  | | | 
% 242.78/49.33  | | End of split
% 242.78/49.33  | | 
% 242.78/49.33  | End of split
% 242.78/49.33  | 
% 242.78/49.33  End of proof
% 242.78/49.33  
% 242.78/49.33  Sub-proof #919 shows that the following formulas are inconsistent:
% 242.78/49.33  ----------------------------------------------------------------
% 242.78/49.33    (1)   ~ (e3 = e0)
% 242.78/49.33    (2)  op(e1, e1) = e1
% 242.78/49.33    (3)   ~ (e2 = e0)
% 242.78/49.33    (4)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.78/49.33         (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.33    (5)  all_58_9 = e0
% 242.78/49.33    (6)   ~ (e3 = e1)
% 242.78/49.33    (7)  all_58_11 = e3
% 242.78/49.33    (8)   ~ (e3 = e2)
% 242.78/49.33    (9)  all_58_10 = e2
% 242.78/49.33    (10)  op(e2, e0) = e2
% 242.78/49.33    (11)  all_58_15 = e1
% 242.78/49.33    (12)  op(e1, e1) = e2
% 242.78/49.33    (13)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.78/49.33          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.33    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.33    (15)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.78/49.33          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.78/49.33    (16)   ~ (all_52_13 = e3)
% 242.78/49.33    (17)  op(e2, e0) = all_52_13
% 242.78/49.33    (18)   ~ (e2 = e1)
% 242.78/49.33  
% 242.78/49.33  Begin of proof
% 242.78/49.33  | 
% 242.78/49.33  | BETA: splitting (13) gives:
% 242.78/49.33  | 
% 242.78/49.33  | Case 1:
% 242.78/49.33  | | 
% 242.78/49.33  | |   (19)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 242.78/49.33  | |           e3)
% 242.78/49.33  | | 
% 242.78/49.33  | | BETA: splitting (19) gives:
% 242.78/49.33  | | 
% 242.78/49.33  | | Case 1:
% 242.78/49.33  | | | 
% 242.78/49.33  | | |   (20)  all_58_9 = e3 & op(e3, e0) = e3
% 242.78/49.33  | | | 
% 242.78/49.33  | | | REF_CLOSE: (1), (3), (4), (7), (10), (14), (20) are inconsistent by
% 242.78/49.33  | | |            sub-proof #920.
% 242.78/49.33  | | | 
% 242.78/49.33  | | Case 2:
% 242.78/49.33  | | | 
% 242.78/49.33  | | |   (21)  all_58_10 = e3 & op(e2, e0) = e3
% 242.78/49.33  | | | 
% 242.78/49.33  | | | ALPHA: (21) implies:
% 242.78/49.33  | | |   (22)  op(e2, e0) = e3
% 242.78/49.33  | | | 
% 242.78/49.33  | | | REF_CLOSE: (14), (16), (17), (22) are inconsistent by sub-proof #1994.
% 242.78/49.33  | | | 
% 242.78/49.33  | | End of split
% 242.78/49.33  | | 
% 242.78/49.33  | Case 2:
% 242.78/49.33  | | 
% 242.78/49.33  | |   (23)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 242.78/49.33  | |           e3)
% 242.78/49.33  | | 
% 242.78/49.33  | | BETA: splitting (23) gives:
% 242.78/49.33  | | 
% 242.78/49.33  | | Case 1:
% 242.78/49.33  | | | 
% 242.78/49.33  | | | 
% 242.78/49.33  | | | GROUND_INST: instantiating (14) with e1, e2, e1, e1, simplifying with (2),
% 242.78/49.33  | | |              (12) gives:
% 242.78/49.33  | | |   (24)  e2 = e1
% 242.78/49.33  | | | 
% 242.78/49.33  | | | COMBINE_EQS: (9), (24) imply:
% 242.78/49.33  | | |   (25)  all_58_10 = e1
% 242.78/49.33  | | | 
% 242.78/49.33  | | | REF_CLOSE: (1), (3), (5), (6), (8), (11), (13), (15), (18), (25) are
% 242.78/49.33  | | |            inconsistent by sub-proof #1618.
% 242.78/49.33  | | | 
% 242.78/49.33  | | Case 2:
% 242.78/49.33  | | | 
% 242.78/49.33  | | |   (26)  all_58_15 = e3 & op(e0, e0) = e3
% 242.78/49.33  | | | 
% 242.78/49.33  | | | ALPHA: (26) implies:
% 242.78/49.33  | | |   (27)  all_58_15 = e3
% 242.78/49.33  | | | 
% 242.78/49.33  | | | REF_CLOSE: (6), (11), (27) are inconsistent by sub-proof #2249.
% 242.78/49.33  | | | 
% 242.78/49.33  | | End of split
% 242.78/49.33  | | 
% 242.78/49.33  | End of split
% 242.78/49.33  | 
% 242.78/49.33  End of proof
% 242.78/49.33  
% 242.78/49.33  Sub-proof #920 shows that the following formulas are inconsistent:
% 242.78/49.33  ----------------------------------------------------------------
% 242.78/49.33    (1)   ~ (e3 = e0)
% 242.78/49.33    (2)   ~ (e2 = e0)
% 242.78/49.33    (3)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 242.78/49.33         (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.33    (4)  all_58_11 = e3
% 242.78/49.33    (5)  all_58_9 = e3 & op(e3, e0) = e3
% 242.78/49.33    (6)  op(e2, e0) = e2
% 242.78/49.33    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.33  
% 242.78/49.33  Begin of proof
% 242.78/49.33  | 
% 242.78/49.33  | ALPHA: (5) implies:
% 242.78/49.33  |   (8)  all_58_9 = e3
% 242.78/49.33  | 
% 242.78/49.33  | BETA: splitting (3) gives:
% 242.78/49.33  | 
% 242.78/49.33  | Case 1:
% 242.78/49.33  | | 
% 242.78/49.33  | |   (9)  all_58_9 = e0 & op(e3, e0) = e0
% 242.78/49.33  | | 
% 242.78/49.33  | | REF_CLOSE: (1), (8), (9) are inconsistent by sub-proof #2103.
% 242.78/49.33  | | 
% 242.78/49.33  | Case 2:
% 242.78/49.33  | | 
% 242.78/49.33  | |   (10)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.33  | |           e0)
% 242.78/49.33  | | 
% 242.78/49.33  | | REF_CLOSE: (1), (2), (4), (6), (7), (10) are inconsistent by sub-proof #955.
% 242.78/49.33  | | 
% 242.78/49.33  | End of split
% 242.78/49.33  | 
% 242.78/49.33  End of proof
% 242.78/49.33  
% 242.78/49.33  Sub-proof #921 shows that the following formulas are inconsistent:
% 242.78/49.33  ----------------------------------------------------------------
% 242.78/49.33    (1)   ~ (e3 = e0)
% 242.78/49.33    (2)   ~ (e2 = e0)
% 242.78/49.33    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.78/49.33         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.33    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.78/49.33         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.78/49.33    (5)  op(e0, e2) = e2
% 242.78/49.33    (6)   ~ (e3 = e1)
% 242.78/49.33    (7)  all_58_7 = e2
% 242.78/49.33    (8)  all_58_3 = e3
% 242.78/49.33    (9)   ~ (e3 = e2)
% 242.78/49.33    (10)   ~ (all_52_7 = e1)
% 242.78/49.33    (11)  all_58_13 = e2
% 242.78/49.33    (12)  op(e0, e2) = all_52_7
% 242.78/49.33    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.33    (14)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.78/49.33          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.78/49.33    (15)   ~ (e1 = e0)
% 242.78/49.33    (16)   ~ (e2 = e1)
% 242.78/49.33  
% 242.78/49.33  Begin of proof
% 242.78/49.33  | 
% 242.78/49.33  | BETA: splitting (14) gives:
% 242.78/49.33  | 
% 242.78/49.33  | Case 1:
% 242.78/49.33  | | 
% 242.78/49.33  | |   (17)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 242.78/49.33  | |           e1)
% 242.78/49.33  | | 
% 242.78/49.33  | | BETA: splitting (17) gives:
% 242.78/49.33  | | 
% 242.78/49.33  | | Case 1:
% 242.78/49.33  | | | 
% 242.78/49.33  | | |   (18)  all_58_1 = e1 & op(e3, e2) = e1
% 242.78/49.33  | | | 
% 242.78/49.33  | | | ALPHA: (18) implies:
% 242.78/49.33  | | |   (19)  all_58_1 = e1
% 242.78/49.33  | | | 
% 242.78/49.33  | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (13), (15), (19) are inconsistent
% 242.78/49.33  | | |            by sub-proof #1461.
% 242.78/49.33  | | | 
% 242.78/49.33  | | Case 2:
% 242.78/49.33  | | | 
% 242.78/49.33  | | |   (20)  all_58_3 = e1 & op(e2, e2) = e1
% 242.78/49.33  | | | 
% 242.78/49.33  | | | REF_CLOSE: (6), (8), (20) are inconsistent by sub-proof #2197.
% 242.78/49.33  | | | 
% 242.78/49.33  | | End of split
% 242.78/49.33  | | 
% 242.78/49.33  | Case 2:
% 242.78/49.33  | | 
% 242.78/49.33  | |   (21)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 242.78/49.33  | |           e1)
% 242.78/49.33  | | 
% 242.78/49.33  | | BETA: splitting (21) gives:
% 242.78/49.33  | | 
% 242.78/49.33  | | Case 1:
% 242.78/49.33  | | | 
% 242.78/49.33  | | |   (22)  all_58_7 = e1 & op(e1, e2) = e1
% 242.78/49.33  | | | 
% 242.78/49.33  | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (11), (15), (16), (22) are
% 242.78/49.33  | | |            inconsistent by sub-proof #1456.
% 242.78/49.33  | | | 
% 242.78/49.33  | | Case 2:
% 242.78/49.33  | | | 
% 242.78/49.33  | | |   (23)  all_58_13 = e1 & op(e0, e2) = e1
% 242.78/49.33  | | | 
% 242.78/49.33  | | | REF_CLOSE: (10), (12), (13), (23) are inconsistent by sub-proof #2275.
% 242.78/49.33  | | | 
% 242.78/49.33  | | End of split
% 242.78/49.33  | | 
% 242.78/49.33  | End of split
% 242.78/49.33  | 
% 242.78/49.33  End of proof
% 242.78/49.33  
% 242.78/49.33  Sub-proof #922 shows that the following formulas are inconsistent:
% 242.78/49.33  ----------------------------------------------------------------
% 242.78/49.33    (1)   ~ (e3 = e0)
% 242.78/49.33    (2)   ~ (e2 = e0)
% 242.78/49.33    (3)  all_58_12 = e3 & op(e0, e3) = e3
% 242.78/49.33    (4)   ~ (e3 = e1)
% 242.78/49.33    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.33             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.33               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.78/49.33               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.78/49.33    (6)  op(e2, e1) = all_52_9
% 242.78/49.33    (7)   ~ (e3 = e2)
% 242.78/49.33    (8)  all_58_15 = e1
% 242.78/49.33    (9)  op(e3, e3) = e2
% 242.78/49.33    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.78/49.33          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.33    (11)  op(e1, e1) = e2
% 242.78/49.33    (12)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.78/49.33          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.78/49.33    (13)   ~ (all_52_9 = e3)
% 242.78/49.33    (14)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.78/49.33          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.78/49.33    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.33    (16)   ~ (e1 = e0)
% 242.78/49.33    (17)  all_58_9 = e2
% 242.78/49.33    (18)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.33          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.78/49.33            e2)
% 242.78/49.33    (19)   ~ (e2 = e1)
% 242.78/49.33  
% 242.78/49.33  Begin of proof
% 242.78/49.33  | 
% 242.78/49.33  | ALPHA: (3) implies:
% 242.78/49.33  |   (20)  all_58_12 = e3
% 242.78/49.33  | 
% 242.78/49.33  | BETA: splitting (12) gives:
% 242.78/49.33  | 
% 242.78/49.33  | Case 1:
% 242.78/49.33  | | 
% 242.78/49.33  | |   (21)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 242.78/49.33  | |           e3)
% 242.78/49.33  | | 
% 242.78/49.33  | | REF_CLOSE: (1), (2), (4), (6), (9), (10), (13), (14), (15), (16), (17),
% 242.78/49.33  | |            (19), (21) are inconsistent by sub-proof #923.
% 242.78/49.33  | | 
% 242.78/49.33  | Case 2:
% 242.78/49.33  | | 
% 242.78/49.33  | |   (22)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 242.78/49.33  | |           e3)
% 242.78/49.33  | | 
% 242.78/49.33  | | REF_CLOSE: (1), (2), (5), (7), (8), (11), (15), (16), (18), (19), (20), (22)
% 242.78/49.33  | |            are inconsistent by sub-proof #930.
% 242.78/49.33  | | 
% 242.78/49.33  | End of split
% 242.78/49.33  | 
% 242.78/49.33  End of proof
% 242.78/49.33  
% 242.78/49.33  Sub-proof #923 shows that the following formulas are inconsistent:
% 242.78/49.33  ----------------------------------------------------------------
% 242.78/49.34    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 242.78/49.34    (2)   ~ (e3 = e0)
% 242.78/49.34    (3)   ~ (e2 = e0)
% 242.78/49.34    (4)   ~ (e3 = e1)
% 242.78/49.34    (5)  op(e2, e1) = all_52_9
% 242.78/49.34    (6)  op(e3, e3) = e2
% 242.78/49.34    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.78/49.34         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.34    (8)   ~ (all_52_9 = e3)
% 242.78/49.34    (9)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.78/49.34         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.78/49.34    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.34    (11)   ~ (e1 = e0)
% 242.78/49.34    (12)  all_58_9 = e2
% 242.78/49.34    (13)   ~ (e2 = e1)
% 242.78/49.34  
% 242.78/49.34  Begin of proof
% 242.78/49.34  | 
% 242.78/49.34  | BETA: splitting (1) gives:
% 242.78/49.34  | 
% 242.78/49.34  | Case 1:
% 242.78/49.34  | | 
% 242.78/49.34  | |   (14)  all_58_4 = e3 & op(e3, e1) = e3
% 242.78/49.34  | | 
% 242.78/49.34  | | ALPHA: (14) implies:
% 242.78/49.34  | |   (15)  all_58_4 = e3
% 242.78/49.34  | | 
% 242.78/49.34  | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (15) are
% 242.78/49.34  | |            inconsistent by sub-proof #1562.
% 242.78/49.34  | | 
% 242.78/49.34  | Case 2:
% 242.78/49.34  | | 
% 242.78/49.34  | |   (16)  all_58_5 = e3 & op(e2, e1) = e3
% 242.78/49.34  | | 
% 242.78/49.34  | | REF_CLOSE: (5), (8), (10), (16) are inconsistent by sub-proof #1822.
% 242.78/49.34  | | 
% 242.78/49.34  | End of split
% 242.78/49.34  | 
% 242.78/49.34  End of proof
% 242.78/49.34  
% 242.78/49.34  Sub-proof #924 shows that the following formulas are inconsistent:
% 242.78/49.34  ----------------------------------------------------------------
% 242.78/49.34    (1)  op(e0, e0) = e1
% 242.78/49.34    (2)  op(e2, e2) = e3
% 242.78/49.34    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.78/49.34         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.78/49.34    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.78/49.34         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.34    (5)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.78/49.34           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.78/49.34             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.78/49.34    (6)   ~ (e3 = e0)
% 242.78/49.34    (7)  op(e0, e1) = all_52_11
% 242.78/49.34    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 242.78/49.34    (9)   ~ (e2 = e0)
% 242.78/49.34    (10)  op(e1, e1) = all_6_2
% 242.78/49.34    (11)   ~ (all_52_1 = all_52_2)
% 242.78/49.34    (12)  op(e1, e0) = all_52_14
% 242.78/49.34    (13)   ~ (all_52_13 = e1)
% 242.78/49.34    (14)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.78/49.34            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.78/49.34              e1) = all_20_1 & $i(all_20_1))
% 242.78/49.34    (15)   ~ (all_52_7 = e3)
% 242.78/49.34    (16)   ~ (e3 = e1)
% 242.78/49.34    (17)   ~ (all_52_12 = e1)
% 242.78/49.34    (18)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.78/49.34          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.78/49.34    (19)   ~ (all_52_12 = all_52_14)
% 242.78/49.34    (20)  all_58_3 = e3
% 242.78/49.34    (21)   ~ (all_52_12 = all_52_13)
% 242.78/49.34    (22)  all_58_11 = e3
% 242.78/49.34    (23)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 242.78/49.34    (24)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.34              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.78/49.34                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.78/49.34                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.78/49.34    (25)   ~ (all_6_2 = e3)
% 242.78/49.34    (26)  op(e2, e1) = all_52_9
% 242.78/49.34    (27)   ~ (e3 = e2)
% 242.78/49.34    (28)  op(e1, e0) = e3
% 242.78/49.34    (29)   ~ (all_52_14 = e1)
% 242.78/49.34    (30)   ~ (all_6_2 = e0)
% 242.78/49.34    (31)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.78/49.34            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.78/49.34            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.78/49.34            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.78/49.34            op(e0, all_56_31) = e0)
% 242.78/49.34    (32)  all_56_31 = e1
% 242.78/49.34    (33)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 242.78/49.34    (34)  all_58_15 = e1
% 242.78/49.34    (35)  op(e3, e0) = all_52_12
% 242.78/49.34    (36)  op(e2, e3) = all_52_1
% 242.78/49.34    (37)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.78/49.34          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.34    (38)  all_34_2 = e1
% 242.78/49.34    (39)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.78/49.34          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.78/49.34    (40)  all_54_7 = all_52_13
% 242.78/49.34    (41)  op(e0, e2) = all_52_7
% 242.78/49.34    (42)   ~ (all_52_13 = all_52_14)
% 242.78/49.34    (43)   ~ (all_52_9 = e3)
% 242.78/49.34    (44)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.78/49.34          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.34    (45)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.78/49.34          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.78/49.34    (46)  all_54_3 = all_52_12
% 242.78/49.34    (47)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.34    (48)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.78/49.34          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.78/49.34    (49)  op(e1, e3) = all_52_2
% 242.78/49.34    (50)   ~ (e1 = e0)
% 242.78/49.34    (51)  op(e2, e0) = all_52_13
% 242.78/49.34    (52)   ~ (all_52_1 = e3)
% 242.78/49.34    (53)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.34          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.78/49.34            e2)
% 242.78/49.34    (54)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.78/49.34          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.78/49.34    (55)   ~ (e2 = e1)
% 242.78/49.34  
% 242.78/49.34  Begin of proof
% 242.78/49.34  | 
% 242.78/49.34  | BETA: splitting (8) gives:
% 242.78/49.34  | 
% 242.78/49.34  | Case 1:
% 242.78/49.34  | | 
% 242.78/49.34  | |   (56)  all_58_0 = e3 & op(e3, e3) = e3
% 242.78/49.34  | | 
% 242.78/49.34  | | ALPHA: (56) implies:
% 242.78/49.34  | |   (57)  op(e3, e3) = e3
% 242.78/49.34  | | 
% 242.78/49.34  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 242.78/49.34  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 242.78/49.34  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 242.78/49.34  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 242.78/49.34  | |            (47), (48), (49), (50), (51), (53), (54), (55), (57) are
% 242.78/49.34  | |            inconsistent by sub-proof #950.
% 242.78/49.34  | | 
% 242.78/49.34  | Case 2:
% 242.78/49.34  | | 
% 242.78/49.34  | |   (58)  all_58_2 = e3 & op(e2, e3) = e3
% 242.78/49.34  | | 
% 242.78/49.34  | | ALPHA: (58) implies:
% 242.78/49.34  | |   (59)  op(e2, e3) = e3
% 242.78/49.34  | | 
% 242.78/49.34  | | REF_CLOSE: (36), (47), (52), (59) are inconsistent by sub-proof #2337.
% 242.78/49.34  | | 
% 242.78/49.34  | End of split
% 242.78/49.34  | 
% 242.78/49.34  End of proof
% 242.78/49.34  
% 242.78/49.34  Sub-proof #925 shows that the following formulas are inconsistent:
% 242.78/49.34  ----------------------------------------------------------------
% 242.78/49.34    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.78/49.34         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.34    (2)   ~ (e3 = e0)
% 242.78/49.34    (3)  op(e1, e2) = e1
% 242.78/49.34    (4)   ~ (e2 = e0)
% 242.78/49.34    (5)  op(e1, e2) = all_52_6
% 242.78/49.34    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.78/49.34         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.78/49.34    (7)   ~ (all_52_7 = e3)
% 242.78/49.34    (8)   ~ (e3 = e1)
% 242.78/49.34    (9)  all_58_3 = e3
% 242.78/49.34    (10)   ~ (e3 = e2)
% 242.78/49.34    (11)  all_58_15 = e1
% 242.78/49.34    (12)  all_58_12 = e0
% 242.78/49.34    (13)  op(e0, e2) = all_52_7
% 242.78/49.34    (14)  all_58_1 = e2
% 242.78/49.34    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.34    (16)   ~ (e1 = e0)
% 242.78/49.34    (17)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.34          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.78/49.34            e2)
% 242.78/49.34    (18)   ~ (e2 = e1)
% 242.78/49.34  
% 242.78/49.34  Begin of proof
% 242.78/49.34  | 
% 242.78/49.34  | BETA: splitting (6) gives:
% 242.78/49.34  | 
% 242.78/49.34  | Case 1:
% 242.78/49.34  | | 
% 242.78/49.34  | |   (19)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 242.78/49.34  | |           e0)
% 242.78/49.34  | | 
% 242.78/49.34  | | BETA: splitting (19) gives:
% 242.78/49.34  | | 
% 242.78/49.34  | | Case 1:
% 242.78/49.34  | | | 
% 242.78/49.34  | | |   (20)  all_58_1 = e0 & op(e3, e2) = e0
% 242.78/49.34  | | | 
% 242.78/49.34  | | | REF_CLOSE: (4), (14), (20) are inconsistent by sub-proof #2187.
% 242.78/49.34  | | | 
% 242.78/49.34  | | Case 2:
% 242.78/49.34  | | | 
% 242.78/49.34  | | |   (21)  all_58_3 = e0 & op(e2, e2) = e0
% 242.78/49.34  | | | 
% 242.78/49.34  | | | REF_CLOSE: (2), (9), (21) are inconsistent by sub-proof #1719.
% 242.78/49.34  | | | 
% 242.78/49.34  | | End of split
% 242.78/49.34  | | 
% 242.78/49.34  | Case 2:
% 242.78/49.34  | | 
% 242.78/49.34  | |   (22)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.78/49.34  | |           e0)
% 242.78/49.34  | | 
% 242.78/49.34  | | BETA: splitting (22) gives:
% 242.78/49.34  | | 
% 242.78/49.34  | | Case 1:
% 242.78/49.34  | | | 
% 242.78/49.34  | | |   (23)  all_58_7 = e0 & op(e1, e2) = e0
% 242.78/49.34  | | | 
% 242.78/49.34  | | | ALPHA: (23) implies:
% 242.78/49.34  | | |   (24)  op(e1, e2) = e0
% 242.78/49.34  | | | 
% 242.78/49.34  | | | REF_CLOSE: (3), (5), (15), (16), (24) are inconsistent by sub-proof #2136.
% 242.78/49.34  | | | 
% 242.78/49.34  | | Case 2:
% 242.78/49.34  | | | 
% 242.78/49.34  | | |   (25)  all_58_13 = e0 & op(e0, e2) = e0
% 242.78/49.34  | | | 
% 242.78/49.34  | | | ALPHA: (25) implies:
% 242.78/49.34  | | |   (26)  op(e0, e2) = e0
% 242.78/49.34  | | | 
% 242.78/49.34  | | | REF_CLOSE: (1), (2), (4), (7), (8), (10), (11), (12), (13), (15), (17),
% 242.78/49.34  | | |            (18), (26) are inconsistent by sub-proof #1914.
% 242.78/49.34  | | | 
% 242.78/49.34  | | End of split
% 242.78/49.34  | | 
% 242.78/49.34  | End of split
% 242.78/49.34  | 
% 242.78/49.34  End of proof
% 242.78/49.34  
% 242.78/49.34  Sub-proof #926 shows that the following formulas are inconsistent:
% 242.78/49.34  ----------------------------------------------------------------
% 242.78/49.34    (1)   ~ (e3 = e0)
% 242.78/49.34    (2)  all_54_10 = e1 | all_54_10 = e0
% 242.78/49.34    (3)  op(e0, e1) = e3
% 242.78/49.34    (4)  op(e1, e1) = all_6_2
% 242.78/49.34    (5)  all_54_10 = all_6_2
% 242.78/49.34    (6)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.78/49.34    (7)   ~ (all_6_2 = e0)
% 242.78/49.34    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.34  
% 242.78/49.34  Begin of proof
% 242.78/49.34  | 
% 242.78/49.34  | BETA: splitting (6) gives:
% 242.78/49.34  | 
% 242.78/49.34  | Case 1:
% 242.78/49.34  | | 
% 242.78/49.34  | |   (9)  all_58_8 = e0 & op(e1, e1) = e0
% 242.78/49.34  | | 
% 242.78/49.34  | | REF_CLOSE: (2), (4), (5), (7), (8), (9) are inconsistent by sub-proof #942.
% 242.78/49.34  | | 
% 242.78/49.34  | Case 2:
% 242.78/49.34  | | 
% 242.78/49.34  | |   (10)  all_58_14 = e0 & op(e0, e1) = e0
% 242.78/49.34  | | 
% 242.78/49.34  | | ALPHA: (10) implies:
% 242.78/49.34  | |   (11)  op(e0, e1) = e0
% 242.78/49.34  | | 
% 242.78/49.34  | | REF_CLOSE: (1), (3), (8), (11) are inconsistent by sub-proof #2164.
% 242.78/49.34  | | 
% 242.78/49.34  | End of split
% 242.78/49.34  | 
% 242.78/49.34  End of proof
% 242.78/49.34  
% 242.78/49.34  Sub-proof #927 shows that the following formulas are inconsistent:
% 242.78/49.34  ----------------------------------------------------------------
% 242.78/49.34    (1)  op(e0, e0) = e1
% 242.78/49.34    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.78/49.34         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.34    (3)   ~ (e3 = e0)
% 242.78/49.34    (4)  op(e1, e1) = e1
% 242.78/49.34    (5)  all_58_6 = e3
% 242.78/49.34    (6)  op(e1, e2) = e1
% 242.78/49.34    (7)   ~ (e2 = e0)
% 242.78/49.34    (8)  op(e1, e2) = all_52_6
% 242.78/49.34    (9)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.78/49.34         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.34    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.78/49.34          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.78/49.34    (11)   ~ (all_52_7 = e3)
% 242.78/49.34    (12)  op(e0, e2) = e2
% 242.78/49.34    (13)   ~ (e3 = e1)
% 242.78/49.34    (14)  all_58_3 = e3
% 242.78/49.34    (15)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.34              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.78/49.34                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.78/49.34                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.78/49.34    (16)   ~ (e3 = e2)
% 242.78/49.34    (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 242.78/49.34          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 242.78/49.34    (18)  all_58_15 = e1
% 242.78/49.34    (19)  all_58_13 = e2
% 242.78/49.34    (20)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.78/49.34          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.78/49.34    (21)  all_58_4 = e1
% 242.78/49.34    (22)   ~ (all_52_6 = e3)
% 242.78/49.34    (23)  op(e0, e2) = all_52_7
% 242.78/49.34    (24)  op(e2, e1) = e0
% 242.78/49.34    (25)  all_58_7 = e1
% 242.78/49.34    (26)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.78/49.34          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.78/49.34    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.34    (28)   ~ (e1 = e0)
% 242.78/49.34    (29)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.78/49.34          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.34    (30)   ~ (e2 = e1)
% 242.78/49.34  
% 242.78/49.34  Begin of proof
% 242.78/49.34  | 
% 242.78/49.34  | BETA: splitting (17) gives:
% 242.78/49.34  | 
% 242.78/49.34  | Case 1:
% 242.78/49.34  | | 
% 242.78/49.34  | |   (31)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 242.78/49.34  | |           e2)
% 242.78/49.34  | | 
% 242.78/49.34  | | BETA: splitting (31) gives:
% 242.78/49.34  | | 
% 242.78/49.34  | | Case 1:
% 242.78/49.34  | | | 
% 242.78/49.34  | | |   (32)  all_58_4 = e2 & op(e3, e1) = e2
% 242.78/49.34  | | | 
% 242.78/49.34  | | | ALPHA: (32) implies:
% 242.78/49.34  | | |   (33)  all_58_4 = e2
% 242.78/49.34  | | | 
% 242.78/49.34  | | | COMBINE_EQS: (21), (33) imply:
% 242.78/49.34  | | |   (34)  e2 = e1
% 242.78/49.34  | | | 
% 242.78/49.34  | | | COMBINE_EQS: (19), (34) imply:
% 242.78/49.34  | | |   (35)  all_58_13 = e1
% 242.78/49.34  | | | 
% 242.78/49.34  | | | REF_CLOSE: (3), (7), (9), (10), (14), (16), (25), (28), (30), (35) are
% 242.78/49.34  | | |            inconsistent by sub-proof #1457.
% 242.78/49.34  | | | 
% 242.78/49.34  | | Case 2:
% 242.78/49.34  | | | 
% 242.78/49.34  | | |   (36)  all_58_5 = e2 & op(e2, e1) = e2
% 242.78/49.34  | | | 
% 242.78/49.34  | | | ALPHA: (36) implies:
% 242.78/49.34  | | |   (37)  op(e2, e1) = e2
% 242.78/49.34  | | | 
% 242.78/49.34  | | | REF_CLOSE: (7), (24), (27), (37) are inconsistent by sub-proof #1906.
% 242.78/49.34  | | | 
% 242.78/49.34  | | End of split
% 242.78/49.34  | | 
% 242.78/49.34  | Case 2:
% 242.78/49.34  | | 
% 242.78/49.35  | |   (38)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 242.78/49.35  | |           e2)
% 242.78/49.35  | | 
% 242.78/49.35  | | BETA: splitting (38) gives:
% 242.78/49.35  | | 
% 242.78/49.35  | | Case 1:
% 242.78/49.35  | | | 
% 242.78/49.35  | | |   (39)  all_58_8 = e2 & op(e1, e1) = e2
% 242.78/49.35  | | | 
% 242.78/49.35  | | | ALPHA: (39) implies:
% 242.78/49.35  | | |   (40)  all_58_8 = e2
% 242.78/49.35  | | |   (41)  op(e1, e1) = e2
% 242.78/49.35  | | | 
% 242.78/49.35  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (14), (16), (19),
% 242.78/49.35  | | |            (20), (22), (25), (26), (27), (28), (29), (30), (40), (41) are
% 242.78/49.35  | | |            inconsistent by sub-proof #963.
% 242.78/49.35  | | | 
% 242.78/49.35  | | Case 2:
% 242.78/49.35  | | | 
% 242.78/49.35  | | |   (42)  all_58_14 = e2 & op(e0, e1) = e2
% 242.78/49.35  | | | 
% 242.78/49.35  | | | ALPHA: (42) implies:
% 242.78/49.35  | | |   (43)  all_58_14 = e2
% 242.78/49.35  | | | 
% 242.78/49.35  | | | REF_CLOSE: (1), (2), (3), (7), (11), (12), (13), (15), (16), (18), (23),
% 242.78/49.35  | | |            (27), (28), (43) are inconsistent by sub-proof #1636.
% 242.78/49.35  | | | 
% 242.78/49.35  | | End of split
% 242.78/49.35  | | 
% 242.78/49.35  | End of split
% 242.78/49.35  | 
% 242.78/49.35  End of proof
% 242.78/49.35  
% 242.78/49.35  Sub-proof #928 shows that the following formulas are inconsistent:
% 242.78/49.35  ----------------------------------------------------------------
% 242.78/49.35    (1)   ~ (e3 = e0)
% 242.78/49.35    (2)  op(e1, e2) = e1
% 242.78/49.35    (3)   ~ (e2 = e0)
% 242.78/49.35    (4)  op(e1, e2) = all_52_6
% 242.78/49.35    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.78/49.35         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.78/49.35    (6)  op(e0, e2) = e2
% 242.78/49.35    (7)  all_58_3 = e3
% 242.78/49.35    (8)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 242.78/49.35    (9)  op(e3, e3) = e2
% 242.78/49.35    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.35    (11)   ~ (e1 = e0)
% 242.78/49.35    (12)   ~ (e2 = e1)
% 242.78/49.35  
% 242.78/49.35  Begin of proof
% 242.78/49.35  | 
% 242.78/49.35  | BETA: splitting (8) gives:
% 242.78/49.35  | 
% 242.78/49.35  | Case 1:
% 242.78/49.35  | | 
% 242.78/49.35  | |   (13)  all_58_0 = e1 & op(e3, e3) = e1
% 242.78/49.35  | | 
% 242.78/49.35  | | ALPHA: (13) implies:
% 242.78/49.35  | |   (14)  op(e3, e3) = e1
% 242.78/49.35  | | 
% 242.78/49.35  | | REF_CLOSE: (9), (10), (12), (14) are inconsistent by sub-proof #2267.
% 242.78/49.35  | | 
% 242.78/49.35  | Case 2:
% 242.78/49.35  | | 
% 242.78/49.35  | |   (15)  all_58_1 = e1 & op(e3, e2) = e1
% 242.78/49.35  | | 
% 242.78/49.35  | | ALPHA: (15) implies:
% 242.78/49.35  | |   (16)  all_58_1 = e1
% 242.78/49.35  | | 
% 242.78/49.35  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (16) are
% 242.78/49.35  | |            inconsistent by sub-proof #1718.
% 242.78/49.35  | | 
% 242.78/49.35  | End of split
% 242.78/49.35  | 
% 242.78/49.35  End of proof
% 242.78/49.35  
% 242.78/49.35  Sub-proof #929 shows that the following formulas are inconsistent:
% 242.78/49.35  ----------------------------------------------------------------
% 242.78/49.35    (1)  op(e2, e2) = e3
% 242.78/49.35    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.78/49.35         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.35    (3)   ~ (e3 = e0)
% 242.78/49.35    (4)   ~ (e2 = e0)
% 242.78/49.35    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.78/49.35         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.78/49.35    (6)   ~ (all_52_7 = e3)
% 242.78/49.35    (7)   ~ (e3 = e1)
% 242.78/49.35    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 242.78/49.35    (9)  all_58_3 = e3
% 242.78/49.35    (10)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.78/49.35          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.78/49.35    (11)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.35              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.78/49.35                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.78/49.35                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.78/49.35    (12)  op(e2, e1) = all_52_9
% 242.78/49.35    (13)   ~ (e3 = e2)
% 242.78/49.35    (14)   ~ (all_52_7 = e1)
% 242.78/49.35    (15)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.78/49.35          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.78/49.35    (16)  all_58_15 = e1
% 242.78/49.35    (17)  op(e2, e3) = all_52_1
% 242.78/49.35    (18)  op(e3, e3) = e2
% 242.78/49.35    (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.78/49.35          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.35    (20)  op(e1, e1) = e2
% 242.78/49.35    (21)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.78/49.35          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.78/49.35    (22)  op(e0, e2) = all_52_7
% 242.78/49.35    (23)   ~ (all_52_9 = e3)
% 242.78/49.35    (24)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.78/49.35          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.78/49.35    (25)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.78/49.35          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.78/49.35    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.35    (27)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.78/49.35          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.78/49.35    (28)   ~ (e1 = e0)
% 242.78/49.35    (29)   ~ (all_52_1 = e3)
% 242.78/49.35    (30)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.35          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.78/49.35            e2)
% 242.78/49.35    (31)   ~ (e2 = e1)
% 242.78/49.35  
% 242.78/49.35  Begin of proof
% 242.78/49.35  | 
% 242.78/49.35  | BETA: splitting (8) gives:
% 242.78/49.35  | 
% 242.78/49.35  | Case 1:
% 242.78/49.35  | | 
% 242.78/49.35  | |   (32)  all_58_1 = e2 & op(e3, e2) = e2
% 242.78/49.35  | | 
% 242.78/49.35  | | ALPHA: (32) implies:
% 242.78/49.35  | |   (33)  all_58_1 = e2
% 242.78/49.35  | | 
% 242.78/49.35  | | BETA: splitting (30) gives:
% 242.78/49.35  | | 
% 242.78/49.35  | | Case 1:
% 242.78/49.35  | | | 
% 242.78/49.35  | | |   (34)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2)
% 242.78/49.35  | | |           = e2)
% 242.78/49.35  | | | 
% 242.78/49.35  | | | BETA: splitting (34) gives:
% 242.78/49.35  | | | 
% 242.78/49.35  | | | Case 1:
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | |   (35)  all_58_12 = e2 & op(e0, e3) = e2
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | | REF_CLOSE: (2), (3), (4), (6), (7), (10), (11), (13), (15), (16), (17),
% 242.78/49.35  | | | |            (18), (22), (24), (26), (28), (29), (30), (31), (35) are
% 242.78/49.35  | | | |            inconsistent by sub-proof #931.
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | Case 2:
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | |   (36)  all_58_13 = e2 & op(e0, e2) = e2
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | | ALPHA: (36) implies:
% 242.78/49.35  | | | |   (37)  op(e0, e2) = e2
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | | REF_CLOSE: (3), (4), (5), (7), (9), (14), (22), (26), (27), (28), (31),
% 242.78/49.35  | | | |            (33), (37) are inconsistent by sub-proof #1352.
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | End of split
% 242.78/49.35  | | | 
% 242.78/49.35  | | Case 2:
% 242.78/49.35  | | | 
% 242.78/49.35  | | |   (38)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0)
% 242.78/49.35  | | |           = e2)
% 242.78/49.35  | | | 
% 242.78/49.35  | | | BETA: splitting (38) gives:
% 242.78/49.35  | | | 
% 242.78/49.35  | | | Case 1:
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | |   (39)  all_58_14 = e2 & op(e0, e1) = e2
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | | ALPHA: (39) implies:
% 242.78/49.35  | | | |   (40)  all_58_14 = e2
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | | BETA: splitting (2) gives:
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | | Case 1:
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | |   (41)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 242.78/49.35  | | | | |             e2) = e3)
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | | BETA: splitting (41) gives:
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | | Case 1:
% 242.78/49.35  | | | | | | 
% 242.78/49.35  | | | | | |   (42)  all_58_12 = e3 & op(e0, e3) = e3
% 242.78/49.35  | | | | | | 
% 242.78/49.35  | | | | | | ALPHA: (42) implies:
% 242.78/49.35  | | | | | |   (43)  all_58_12 = e3
% 242.78/49.35  | | | | | | 
% 242.78/49.35  | | | | | | BETA: splitting (21) gives:
% 242.78/49.35  | | | | | | 
% 242.78/49.35  | | | | | | Case 1:
% 242.78/49.35  | | | | | | | 
% 242.78/49.35  | | | | | | |   (44)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 242.78/49.35  | | | | | | |           op(e2, e1) = e3)
% 242.78/49.35  | | | | | | | 
% 242.78/49.35  | | | | | | | REF_CLOSE: (3), (4), (7), (12), (18), (19), (23), (25), (26),
% 242.78/49.35  | | | | | | |            (28), (31), (33), (44) are inconsistent by sub-proof
% 242.78/49.35  | | | | | | |            #978.
% 242.78/49.35  | | | | | | | 
% 242.78/49.35  | | | | | | Case 2:
% 242.78/49.35  | | | | | | | 
% 242.78/49.35  | | | | | | |   (45)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 242.78/49.35  | | | | | | |           op(e0, e1) = e3)
% 242.78/49.35  | | | | | | | 
% 242.78/49.35  | | | | | | | REF_CLOSE: (3), (4), (11), (13), (16), (20), (26), (28), (30),
% 242.78/49.35  | | | | | | |            (31), (43), (45) are inconsistent by sub-proof #930.
% 242.78/49.35  | | | | | | | 
% 242.78/49.35  | | | | | | End of split
% 242.78/49.35  | | | | | | 
% 242.78/49.35  | | | | | Case 2:
% 242.78/49.35  | | | | | | 
% 242.78/49.35  | | | | | |   (46)  all_58_13 = e3 & op(e0, e2) = e3
% 242.78/49.35  | | | | | | 
% 242.78/49.35  | | | | | | REF_CLOSE: (6), (22), (26), (46) are inconsistent by sub-proof
% 242.78/49.35  | | | | | |            #1919.
% 242.78/49.35  | | | | | | 
% 242.78/49.35  | | | | | End of split
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | Case 2:
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | |   (47)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 242.78/49.35  | | | | |             e0) = e3)
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | | REF_CLOSE: (7), (13), (16), (40), (47) are inconsistent by sub-proof
% 242.78/49.35  | | | | |            #1638.
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | End of split
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | Case 2:
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | |   (48)  all_58_15 = e2 & op(e0, e0) = e2
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | | ALPHA: (48) implies:
% 242.78/49.35  | | | |   (49)  all_58_15 = e2
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | | REF_CLOSE: (16), (31), (49) are inconsistent by sub-proof #2231.
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | End of split
% 242.78/49.35  | | | 
% 242.78/49.35  | | End of split
% 242.78/49.35  | | 
% 242.78/49.35  | Case 2:
% 242.78/49.35  | | 
% 242.78/49.35  | |   (50)  all_58_3 = e2 & op(e2, e2) = e2
% 242.78/49.35  | | 
% 242.78/49.35  | | ALPHA: (50) implies:
% 242.78/49.35  | |   (51)  op(e2, e2) = e2
% 242.78/49.35  | | 
% 242.78/49.35  | | REF_CLOSE: (1), (13), (26), (51) are inconsistent by sub-proof #2140.
% 242.78/49.35  | | 
% 242.78/49.35  | End of split
% 242.78/49.35  | 
% 242.78/49.35  End of proof
% 242.78/49.35  
% 242.78/49.35  Sub-proof #930 shows that the following formulas are inconsistent:
% 242.78/49.35  ----------------------------------------------------------------
% 242.78/49.35    (1)   ~ (e3 = e0)
% 242.78/49.35    (2)   ~ (e2 = e0)
% 242.78/49.35    (3)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.78/49.35    (4)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.35             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.35               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.78/49.35               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.78/49.35    (5)   ~ (e3 = e2)
% 242.78/49.35    (6)  all_58_15 = e1
% 242.78/49.35    (7)  all_58_12 = e3
% 242.78/49.35    (8)  op(e1, e1) = e2
% 242.78/49.35    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.35    (10)   ~ (e1 = e0)
% 242.78/49.35    (11)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.35          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.78/49.35            e2)
% 242.78/49.35    (12)   ~ (e2 = e1)
% 242.78/49.35  
% 242.78/49.35  Begin of proof
% 242.78/49.35  | 
% 242.78/49.35  | BETA: splitting (3) gives:
% 242.78/49.35  | 
% 242.78/49.35  | Case 1:
% 242.78/49.35  | | 
% 242.78/49.35  | |   (13)  all_58_8 = e3 & op(e1, e1) = e3
% 242.78/49.35  | | 
% 242.78/49.35  | | ALPHA: (13) implies:
% 242.78/49.35  | |   (14)  op(e1, e1) = e3
% 242.78/49.35  | | 
% 242.78/49.35  | | REF_CLOSE: (5), (8), (9), (14) are inconsistent by sub-proof #2206.
% 242.78/49.35  | | 
% 242.78/49.35  | Case 2:
% 242.78/49.35  | | 
% 242.78/49.35  | |   (15)  all_58_14 = e3 & op(e0, e1) = e3
% 242.78/49.35  | | 
% 242.78/49.35  | | ALPHA: (15) implies:
% 242.78/49.35  | |   (16)  all_58_14 = e3
% 242.78/49.35  | | 
% 242.78/49.35  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (11), (12), (16) are
% 242.78/49.35  | |            inconsistent by sub-proof #1863.
% 242.78/49.35  | | 
% 242.78/49.35  | End of split
% 242.78/49.35  | 
% 242.78/49.35  End of proof
% 242.78/49.35  
% 242.78/49.35  Sub-proof #931 shows that the following formulas are inconsistent:
% 242.78/49.35  ----------------------------------------------------------------
% 242.78/49.35    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.78/49.35         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.35    (2)   ~ (e3 = e0)
% 242.78/49.35    (3)   ~ (e2 = e0)
% 242.78/49.35    (4)   ~ (all_52_7 = e3)
% 242.78/49.35    (5)   ~ (e3 = e1)
% 242.78/49.35    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.78/49.35         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.78/49.35    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.78/49.35             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.35               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.78/49.35               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.78/49.35    (8)   ~ (e3 = e2)
% 242.78/49.35    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.78/49.35         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.78/49.35    (10)  all_58_15 = e1
% 242.78/49.35    (11)  op(e2, e3) = all_52_1
% 242.78/49.35    (12)  op(e3, e3) = e2
% 242.78/49.35    (13)  op(e0, e2) = all_52_7
% 242.78/49.35    (14)  all_58_12 = e2 & op(e0, e3) = e2
% 242.78/49.35    (15)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.78/49.35          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.78/49.35    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.35    (17)   ~ (e1 = e0)
% 242.78/49.35    (18)   ~ (all_52_1 = e3)
% 242.78/49.35    (19)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.35          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.78/49.35            e2)
% 242.78/49.35    (20)   ~ (e2 = e1)
% 242.78/49.35  
% 242.78/49.35  Begin of proof
% 242.78/49.35  | 
% 242.78/49.35  | ALPHA: (14) implies:
% 242.78/49.35  |   (21)  all_58_12 = e2
% 242.78/49.35  | 
% 242.78/49.35  | BETA: splitting (1) gives:
% 242.78/49.35  | 
% 242.78/49.35  | Case 1:
% 242.78/49.35  | | 
% 242.78/49.35  | |   (22)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 242.78/49.35  | |           e3)
% 242.78/49.35  | | 
% 242.78/49.35  | | REF_CLOSE: (4), (8), (13), (16), (21), (22) are inconsistent by sub-proof
% 242.78/49.35  | |            #1551.
% 242.78/49.35  | | 
% 242.78/49.35  | Case 2:
% 242.78/49.35  | | 
% 242.78/49.35  | |   (23)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 242.78/49.35  | |           e3)
% 242.78/49.35  | | 
% 242.78/49.35  | | BETA: splitting (23) gives:
% 242.78/49.35  | | 
% 242.78/49.35  | | Case 1:
% 242.78/49.35  | | | 
% 242.78/49.35  | | |   (24)  all_58_14 = e3 & op(e0, e1) = e3
% 242.78/49.35  | | | 
% 242.78/49.35  | | | ALPHA: (24) implies:
% 242.78/49.35  | | |   (25)  all_58_14 = e3
% 242.78/49.35  | | | 
% 242.78/49.35  | | | BETA: splitting (6) gives:
% 242.78/49.35  | | | 
% 242.78/49.35  | | | Case 1:
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | |   (26)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 242.78/49.35  | | | |           = e3)
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | | REF_CLOSE: (8), (11), (12), (16), (18), (26) are inconsistent by
% 242.78/49.35  | | | |            sub-proof #1404.
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | Case 2:
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | |   (27)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 242.78/49.35  | | | |           = e3)
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | | BETA: splitting (27) gives:
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | | Case 1:
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | |   (28)  all_58_6 = e3 & op(e1, e3) = e3
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | | ALPHA: (28) implies:
% 242.78/49.35  | | | | |   (29)  all_58_6 = e3
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | | REF_CLOSE: (2), (3), (5), (9), (12), (15), (16), (17), (20), (21),
% 242.78/49.35  | | | | |            (29) are inconsistent by sub-proof #1756.
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | Case 2:
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | |   (30)  all_58_12 = e3 & op(e0, e3) = e3
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | | ALPHA: (30) implies:
% 242.78/49.35  | | | | |   (31)  all_58_12 = e3
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | | REF_CLOSE: (2), (3), (7), (8), (10), (17), (19), (20), (25), (31) are
% 242.78/49.35  | | | | |            inconsistent by sub-proof #1863.
% 242.78/49.35  | | | | | 
% 242.78/49.35  | | | | End of split
% 242.78/49.35  | | | | 
% 242.78/49.35  | | | End of split
% 242.78/49.35  | | | 
% 242.78/49.35  | | Case 2:
% 242.78/49.35  | | | 
% 242.78/49.35  | | |   (32)  all_58_15 = e3 & op(e0, e0) = e3
% 242.78/49.35  | | | 
% 242.78/49.35  | | | ALPHA: (32) implies:
% 242.78/49.35  | | |   (33)  all_58_15 = e3
% 242.78/49.35  | | | 
% 242.78/49.35  | | | REF_CLOSE: (5), (10), (33) are inconsistent by sub-proof #2249.
% 242.78/49.35  | | | 
% 242.78/49.35  | | End of split
% 242.78/49.35  | | 
% 242.78/49.35  | End of split
% 242.78/49.35  | 
% 242.78/49.35  End of proof
% 242.78/49.35  
% 242.78/49.35  Sub-proof #932 shows that the following formulas are inconsistent:
% 242.78/49.35  ----------------------------------------------------------------
% 242.78/49.36    (1)   ~ (e3 = e0)
% 242.78/49.36    (2)  all_54_10 = e1 | all_54_10 = e0
% 242.78/49.36    (3)  op(e1, e2) = e1
% 242.78/49.36    (4)   ~ (e2 = e0)
% 242.78/49.36    (5)  op(e1, e2) = all_52_6
% 242.78/49.36    (6)  all_58_6 = e2
% 242.78/49.36    (7)  op(e1, e1) = all_6_2
% 242.78/49.36    (8)  all_58_11 = e3
% 242.78/49.36    (9)  all_54_10 = all_6_2
% 242.78/49.36    (10)   ~ (all_6_2 = e0)
% 242.78/49.36    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.36    (12)   ~ (e1 = e0)
% 242.78/49.36    (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.78/49.36          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.36  
% 242.78/49.36  Begin of proof
% 242.78/49.36  | 
% 242.78/49.36  | BETA: splitting (13) gives:
% 242.78/49.36  | 
% 242.78/49.36  | Case 1:
% 242.78/49.36  | | 
% 242.78/49.36  | |   (14)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 242.78/49.36  | |           e0)
% 242.78/49.36  | | 
% 242.78/49.36  | | BETA: splitting (14) gives:
% 242.78/49.36  | | 
% 242.78/49.36  | | Case 1:
% 242.78/49.36  | | | 
% 242.78/49.36  | | |   (15)  all_58_6 = e0 & op(e1, e3) = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | ALPHA: (15) implies:
% 242.78/49.36  | | |   (16)  all_58_6 = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | REF_CLOSE: (4), (6), (16) are inconsistent by sub-proof #1982.
% 242.78/49.36  | | | 
% 242.78/49.36  | | Case 2:
% 242.78/49.36  | | | 
% 242.78/49.36  | | |   (17)  all_58_7 = e0 & op(e1, e2) = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | ALPHA: (17) implies:
% 242.78/49.36  | | |   (18)  op(e1, e2) = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | REF_CLOSE: (3), (5), (11), (12), (18) are inconsistent by sub-proof #2136.
% 242.78/49.36  | | | 
% 242.78/49.36  | | End of split
% 242.78/49.36  | | 
% 242.78/49.36  | Case 2:
% 242.78/49.36  | | 
% 242.78/49.36  | |   (19)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.36  | |           e0)
% 242.78/49.36  | | 
% 242.78/49.36  | | BETA: splitting (19) gives:
% 242.78/49.36  | | 
% 242.78/49.36  | | Case 1:
% 242.78/49.36  | | | 
% 242.78/49.36  | | |   (20)  all_58_8 = e0 & op(e1, e1) = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | REF_CLOSE: (2), (7), (9), (10), (11), (20) are inconsistent by sub-proof
% 242.78/49.36  | | |            #942.
% 242.78/49.36  | | | 
% 242.78/49.36  | | Case 2:
% 242.78/49.36  | | | 
% 242.78/49.36  | | |   (21)  all_58_11 = e0 & op(e1, e0) = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | ALPHA: (21) implies:
% 242.78/49.36  | | |   (22)  all_58_11 = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | REF_CLOSE: (1), (8), (22) are inconsistent by sub-proof #1688.
% 242.78/49.36  | | | 
% 242.78/49.36  | | End of split
% 242.78/49.36  | | 
% 242.78/49.36  | End of split
% 242.78/49.36  | 
% 242.78/49.36  End of proof
% 242.78/49.36  
% 242.78/49.36  Sub-proof #933 shows that the following formulas are inconsistent:
% 242.78/49.36  ----------------------------------------------------------------
% 242.78/49.36    (1)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 242.78/49.36    (2)  op(e1, e2) = all_52_6
% 242.78/49.36    (3)  all_58_6 = e2
% 242.78/49.36    (4)   ~ (e3 = e2)
% 242.78/49.36    (5)   ~ (all_52_6 = e3)
% 242.78/49.36    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.36  
% 242.78/49.36  Begin of proof
% 242.78/49.36  | 
% 242.78/49.36  | BETA: splitting (1) gives:
% 242.78/49.36  | 
% 242.78/49.36  | Case 1:
% 242.78/49.36  | | 
% 242.78/49.36  | |   (7)  all_58_6 = e3 & op(e1, e3) = e3
% 242.78/49.36  | | 
% 242.78/49.36  | | ALPHA: (7) implies:
% 242.78/49.36  | |   (8)  all_58_6 = e3
% 242.78/49.36  | | 
% 242.78/49.36  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #2024.
% 242.78/49.36  | | 
% 242.78/49.36  | Case 2:
% 242.78/49.36  | | 
% 242.78/49.36  | |   (9)  all_58_7 = e3 & op(e1, e2) = e3
% 242.78/49.36  | | 
% 242.78/49.36  | | ALPHA: (9) implies:
% 242.78/49.36  | |   (10)  op(e1, e2) = e3
% 242.78/49.36  | | 
% 242.78/49.36  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #2191.
% 242.78/49.36  | | 
% 242.78/49.36  | End of split
% 242.78/49.36  | 
% 242.78/49.36  End of proof
% 242.78/49.36  
% 242.78/49.36  Sub-proof #934 shows that the following formulas are inconsistent:
% 242.78/49.36  ----------------------------------------------------------------
% 242.78/49.36    (1)   ~ (all_42_1 = e1)
% 242.78/49.36    (2)  op(e2, e3) = all_42_1
% 242.78/49.36    (3)  op(e2, e3) = e1
% 242.78/49.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.36    (5)  ( ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 242.78/49.36           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e2, e3) = all_8_1
% 242.78/49.36           & $i(all_8_1))
% 242.78/49.36  
% 242.78/49.36  Begin of proof
% 242.78/49.36  | 
% 242.78/49.36  | BETA: splitting (5) gives:
% 242.78/49.36  | 
% 242.78/49.36  | Case 1:
% 242.78/49.36  | | 
% 242.78/49.36  | |   (6)   ~ (all_8_0 = e1) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1
% 242.78/49.36  | |        & $i(all_8_0) & $i(all_8_1)
% 242.78/49.36  | | 
% 242.78/49.36  | | ALPHA: (6) implies:
% 242.78/49.36  | |   (7)  op(e2, e3) = all_8_1
% 242.78/49.36  | | 
% 242.78/49.36  | | REF_CLOSE: (1), (2), (3), (4), (7) are inconsistent by sub-proof #935.
% 242.78/49.36  | | 
% 242.78/49.36  | Case 2:
% 242.78/49.36  | | 
% 242.78/49.36  | |   (8)   ~ (all_8_1 = e0) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 242.78/49.36  | | 
% 242.78/49.36  | | ALPHA: (8) implies:
% 242.78/49.36  | |   (9)  op(e2, e3) = all_8_1
% 242.78/49.36  | | 
% 242.78/49.36  | | REF_CLOSE: (1), (2), (3), (4), (9) are inconsistent by sub-proof #935.
% 242.78/49.36  | | 
% 242.78/49.36  | End of split
% 242.78/49.36  | 
% 242.78/49.36  End of proof
% 242.78/49.36  
% 242.78/49.36  Sub-proof #935 shows that the following formulas are inconsistent:
% 242.78/49.36  ----------------------------------------------------------------
% 242.78/49.36    (1)   ~ (all_42_1 = e1)
% 242.78/49.36    (2)  op(e2, e3) = all_42_1
% 242.78/49.36    (3)  op(e2, e3) = e1
% 242.78/49.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.36    (5)  op(e2, e3) = all_8_1
% 242.78/49.36  
% 242.78/49.36  Begin of proof
% 242.78/49.36  | 
% 242.78/49.36  | GROUND_INST: instantiating (4) with e1, all_42_1, e3, e2, simplifying with
% 242.78/49.36  |              (2), (3) gives:
% 242.78/49.36  |   (6)  all_42_1 = e1
% 242.78/49.36  | 
% 242.78/49.36  | GROUND_INST: instantiating (4) with all_8_1, all_42_1, e3, e2, simplifying
% 242.78/49.36  |              with (2), (5) gives:
% 242.78/49.36  |   (7)  all_42_1 = all_8_1
% 242.78/49.36  | 
% 242.78/49.36  | COMBINE_EQS: (6), (7) imply:
% 242.78/49.36  |   (8)  all_8_1 = e1
% 242.78/49.36  | 
% 242.78/49.36  | REDUCE: (1), (6) imply:
% 242.78/49.36  |   (9)  $false
% 242.78/49.36  | 
% 242.78/49.36  | CLOSE: (9) is inconsistent.
% 242.78/49.36  | 
% 242.78/49.36  End of proof
% 242.78/49.36  
% 242.78/49.36  Sub-proof #936 shows that the following formulas are inconsistent:
% 242.78/49.36  ----------------------------------------------------------------
% 242.78/49.36    (1)  op(e2, e2) = e3
% 242.78/49.36    (2)   ~ (all_52_6 = e1)
% 242.78/49.36    (3)  op(e3, e2) = e1
% 242.78/49.36    (4)  all_58_1 = e1
% 242.78/49.36    (5)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.78/49.36    (6)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.78/49.36         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.36    (7)   ~ (e3 = e0)
% 242.78/49.36    (8)  all_54_10 = e1 | all_54_10 = e0
% 242.78/49.36    (9)   ~ (e2 = e0)
% 242.78/49.36    (10)  all_54_13 = all_52_7
% 242.78/49.36    (11)  op(e3, e2) = all_32_1
% 242.78/49.36    (12)  op(e1, e2) = all_52_6
% 242.78/49.36    (13)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.78/49.36          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.36    (14)  op(e1, e1) = all_6_2
% 242.78/49.36    (15)  all_58_8 = e1
% 242.78/49.36    (16)  op(e1, e0) = all_52_14
% 242.78/49.36    (17)   ~ (all_52_7 = e3)
% 242.78/49.36    (18)  op(all_42_1, e2) = all_42_0
% 242.78/49.36    (19)  op(all_24_1, e3) = all_24_0
% 242.78/49.36    (20)  op(e2, e3) = all_42_1
% 242.78/49.36    (21)   ~ (all_52_2 = e1)
% 242.78/49.36    (22)   ~ (all_42_0 = e0)
% 242.78/49.36    (23)  all_54_10 = all_6_2
% 242.78/49.36    (24)   ~ (all_24_0 = e0)
% 242.78/49.36    (25)   ~ (all_52_2 = all_52_14)
% 242.78/49.36    (26)   ~ (all_6_2 = e3)
% 242.78/49.36    (27)  all_54_9 = all_52_6
% 242.78/49.36    (28)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.78/49.36          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.78/49.36    (29)   ~ (e3 = e2)
% 242.78/49.36    (30)  op(e3, e2) = all_24_1
% 242.78/49.36    (31)   ~ (all_8_1 = e0)
% 242.78/49.36    (32)   ~ (all_52_7 = e1)
% 242.78/49.36    (33)   ~ (all_6_2 = e0)
% 242.78/49.36    (34)  op(e2, e3) = e1
% 242.78/49.36    (35)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.78/49.36    (36)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.78/49.36          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.78/49.36    (37)  all_58_15 = e1
% 242.78/49.36    (38)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.78/49.36          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.78/49.36    (39)  op(e3, e3) = e2
% 242.78/49.36    (40)   ~ (all_52_6 = e3)
% 242.78/49.36    (41)  op(e0, e2) = all_52_7
% 242.78/49.36    (42)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.78/49.36    (43)   ~ (all_52_2 = e2)
% 242.78/49.36    (44)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.78/49.36          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.78/49.36    (45)  all_54_8 = all_52_2
% 242.78/49.36    (46)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.78/49.36          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.78/49.36    (47)   ~ (all_52_2 = all_52_6)
% 242.78/49.36    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.36    (49)  op(e2, e3) = all_8_1
% 242.78/49.36    (50)  op(e1, e3) = all_52_2
% 242.78/49.36    (51)   ~ (all_52_6 = all_52_7)
% 242.78/49.36    (52)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.78/49.36          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.78/49.36    (53)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.36          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.78/49.36            e2)
% 242.78/49.36    (54)  all_58_2 = e1
% 242.78/49.36    (55)   ~ (e2 = e1)
% 242.78/49.36  
% 242.78/49.36  Begin of proof
% 242.78/49.36  | 
% 242.78/49.36  | GROUND_INST: instantiating (48) with e1, all_42_1, e3, e2, simplifying with
% 242.78/49.36  |              (20), (34) gives:
% 242.78/49.36  |   (56)  all_42_1 = e1
% 242.78/49.36  | 
% 242.78/49.36  | GROUND_INST: instantiating (48) with all_8_1, all_42_1, e3, e2, simplifying
% 242.78/49.36  |              with (20), (49) gives:
% 242.78/49.36  |   (57)  all_42_1 = all_8_1
% 242.78/49.36  | 
% 242.78/49.36  | GROUND_INST: instantiating (48) with e1, all_32_1, e2, e3, simplifying with
% 242.78/49.36  |              (3), (11) gives:
% 242.78/49.36  |   (58)  all_32_1 = e1
% 242.78/49.36  | 
% 242.78/49.36  | GROUND_INST: instantiating (48) with all_24_1, all_32_1, e2, e3, simplifying
% 242.78/49.36  |              with (11), (30) gives:
% 242.78/49.36  |   (59)  all_32_1 = all_24_1
% 242.78/49.36  | 
% 242.78/49.36  | COMBINE_EQS: (56), (57) imply:
% 242.78/49.36  |   (60)  all_8_1 = e1
% 242.78/49.36  | 
% 242.78/49.36  | COMBINE_EQS: (58), (59) imply:
% 242.78/49.36  |   (61)  all_24_1 = e1
% 242.78/49.36  | 
% 242.78/49.36  | SIMP: (61) implies:
% 242.78/49.36  |   (62)  all_24_1 = e1
% 242.78/49.36  | 
% 242.78/49.36  | REDUCE: (31), (60) imply:
% 242.78/49.36  |   (63)   ~ (e1 = e0)
% 242.78/49.36  | 
% 242.78/49.36  | REDUCE: (18), (56) imply:
% 242.78/49.36  |   (64)  op(e1, e2) = all_42_0
% 242.78/49.36  | 
% 242.78/49.36  | REDUCE: (19), (62) imply:
% 242.78/49.36  |   (65)  op(e1, e3) = all_24_0
% 242.78/49.36  | 
% 242.78/49.36  | GROUND_INST: instantiating (48) with all_52_6, all_42_0, e2, e1, simplifying
% 242.78/49.36  |              with (12), (64) gives:
% 242.78/49.36  |   (66)  all_52_6 = all_42_0
% 242.78/49.36  | 
% 242.78/49.36  | GROUND_INST: instantiating (48) with all_52_2, all_24_0, e3, e1, simplifying
% 242.78/49.36  |              with (50), (65) gives:
% 242.78/49.36  |   (67)  all_52_2 = all_24_0
% 242.78/49.36  | 
% 242.78/49.36  | COMBINE_EQS: (27), (66) imply:
% 242.78/49.36  |   (68)  all_54_9 = all_42_0
% 242.78/49.36  | 
% 242.78/49.36  | COMBINE_EQS: (45), (67) imply:
% 242.78/49.36  |   (69)  all_54_8 = all_24_0
% 242.78/49.36  | 
% 242.78/49.36  | REDUCE: (47), (66), (67) imply:
% 242.78/49.36  |   (70)   ~ (all_42_0 = all_24_0)
% 242.78/49.36  | 
% 242.78/49.36  | SIMP: (70) implies:
% 242.78/49.36  |   (71)   ~ (all_42_0 = all_24_0)
% 242.78/49.36  | 
% 242.78/49.36  | REDUCE: (25), (67) imply:
% 242.78/49.36  |   (72)   ~ (all_52_14 = all_24_0)
% 242.78/49.36  | 
% 242.78/49.36  | SIMP: (72) implies:
% 242.78/49.36  |   (73)   ~ (all_52_14 = all_24_0)
% 242.78/49.36  | 
% 242.78/49.36  | REDUCE: (43), (67) imply:
% 242.78/49.36  |   (74)   ~ (all_24_0 = e2)
% 242.78/49.36  | 
% 242.78/49.36  | REDUCE: (21), (67) imply:
% 242.78/49.36  |   (75)   ~ (all_24_0 = e1)
% 242.78/49.36  | 
% 242.78/49.36  | REDUCE: (51), (66) imply:
% 242.78/49.36  |   (76)   ~ (all_52_7 = all_42_0)
% 242.78/49.36  | 
% 242.78/49.36  | SIMP: (76) implies:
% 242.78/49.36  |   (77)   ~ (all_52_7 = all_42_0)
% 242.78/49.36  | 
% 242.78/49.36  | REDUCE: (40), (66) imply:
% 242.78/49.36  |   (78)   ~ (all_42_0 = e3)
% 242.78/49.36  | 
% 242.78/49.36  | REDUCE: (2), (66) imply:
% 242.78/49.36  |   (79)   ~ (all_42_0 = e1)
% 242.78/49.36  | 
% 242.78/49.36  | BETA: splitting (52) gives:
% 242.78/49.36  | 
% 242.78/49.36  | Case 1:
% 242.78/49.36  | | 
% 242.78/49.36  | |   (80)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 242.78/49.36  | |           e0)
% 242.78/49.36  | | 
% 242.78/49.36  | | BETA: splitting (80) gives:
% 242.78/49.36  | | 
% 242.78/49.36  | | Case 1:
% 242.78/49.36  | | | 
% 242.78/49.36  | | |   (81)  all_58_6 = e0 & op(e1, e3) = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | ALPHA: (81) implies:
% 242.78/49.36  | | |   (82)  all_58_6 = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | BETA: splitting (38) gives:
% 242.78/49.36  | | | 
% 242.78/49.36  | | | Case 1:
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | |   (83)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 242.78/49.36  | | | |           = e3)
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | | REF_CLOSE: (7), (12), (40), (48), (82), (83) are inconsistent by
% 242.78/49.36  | | | |            sub-proof #1689.
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | Case 2:
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | |   (84)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 242.78/49.36  | | | |           = e3)
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | | REF_CLOSE: (5), (14), (16), (24), (26), (48), (69), (73), (74), (75),
% 242.78/49.36  | | | |            (84) are inconsistent by sub-proof #948.
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | End of split
% 242.78/49.36  | | | 
% 242.78/49.36  | | Case 2:
% 242.78/49.36  | | | 
% 242.78/49.36  | | |   (85)  all_58_7 = e0 & op(e1, e2) = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | ALPHA: (85) implies:
% 242.78/49.36  | | |   (86)  all_58_7 = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | BETA: splitting (13) gives:
% 242.78/49.36  | | | 
% 242.78/49.36  | | | Case 1:
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | |   (87)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2)
% 242.78/49.36  | | | |           = e2)
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | | REF_CLOSE: (1), (4), (29), (48), (55), (87) are inconsistent by
% 242.78/49.36  | | | |            sub-proof #1721.
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | Case 2:
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | |   (88)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2)
% 242.78/49.36  | | | |           = e2)
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | | BETA: splitting (88) gives:
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | | Case 1:
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | |   (89)  all_58_7 = e2 & op(e1, e2) = e2
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | | REF_CLOSE: (9), (86), (89) are inconsistent by sub-proof #1326.
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | Case 2:
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | |   (90)  all_58_13 = e2 & op(e0, e2) = e2
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | | ALPHA: (90) implies:
% 242.78/49.36  | | | | |   (91)  op(e0, e2) = e2
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | | BETA: splitting (35) gives:
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | | Case 1:
% 242.78/49.36  | | | | | | 
% 242.78/49.36  | | | | | |   (92)  all_54_9 = e3
% 242.78/49.36  | | | | | | 
% 242.78/49.36  | | | | | | REF_CLOSE: (68), (78), (92) are inconsistent by sub-proof #938.
% 242.78/49.36  | | | | | | 
% 242.78/49.36  | | | | | Case 2:
% 242.78/49.36  | | | | | | 
% 242.78/49.36  | | | | | |   (93)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.78/49.36  | | | | | | 
% 242.78/49.36  | | | | | | REF_CLOSE: (10), (17), (22), (32), (41), (42), (48), (68), (77),
% 242.78/49.36  | | | | | |            (79), (91), (93) are inconsistent by sub-proof #937.
% 242.78/49.36  | | | | | | 
% 242.78/49.36  | | | | | End of split
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | End of split
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | End of split
% 242.78/49.36  | | | 
% 242.78/49.36  | | End of split
% 242.78/49.36  | | 
% 242.78/49.36  | Case 2:
% 242.78/49.36  | | 
% 242.78/49.36  | |   (94)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.78/49.36  | |           e0)
% 242.78/49.36  | | 
% 242.78/49.36  | | BETA: splitting (94) gives:
% 242.78/49.36  | | 
% 242.78/49.36  | | Case 1:
% 242.78/49.36  | | | 
% 242.78/49.36  | | |   (95)  all_58_8 = e0 & op(e1, e1) = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | REF_CLOSE: (8), (14), (23), (33), (48), (95) are inconsistent by sub-proof
% 242.78/49.36  | | |            #942.
% 242.78/49.36  | | | 
% 242.78/49.36  | | Case 2:
% 242.78/49.36  | | | 
% 242.78/49.36  | | |   (96)  all_58_11 = e0 & op(e1, e0) = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | ALPHA: (96) implies:
% 242.78/49.36  | | |   (97)  all_58_11 = e0
% 242.78/49.36  | | | 
% 242.78/49.36  | | | BETA: splitting (38) gives:
% 242.78/49.36  | | | 
% 242.78/49.36  | | | Case 1:
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | |   (98)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 242.78/49.36  | | | |           = e3)
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | | BETA: splitting (98) gives:
% 242.78/49.36  | | | | 
% 242.78/49.36  | | | | Case 1:
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | |   (99)  all_58_6 = e3 & op(e1, e3) = e3
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | | ALPHA: (99) implies:
% 242.78/49.36  | | | | |   (100)  all_58_6 = e3
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | | BETA: splitting (46) gives:
% 242.78/49.36  | | | | | 
% 242.78/49.36  | | | | | Case 1:
% 242.78/49.36  | | | | | | 
% 242.78/49.37  | | | | | |   (101)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 242.78/49.37  | | | | | |              e2) = e2)
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | BETA: splitting (101) gives:
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | Case 1:
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | |   (102)  all_58_6 = e2 & op(e1, e3) = e2
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | | ALPHA: (102) implies:
% 242.78/49.37  | | | | | | |   (103)  all_58_6 = e2
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | | REF_CLOSE: (5), (12), (14), (16), (24), (26), (29), (38), (40),
% 242.78/49.37  | | | | | | |            (48), (69), (73), (74), (75), (103) are inconsistent by
% 242.78/49.37  | | | | | | |            sub-proof #941.
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | Case 2:
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | |   (104)  all_58_7 = e2 & op(e1, e2) = e2
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | | ALPHA: (104) implies:
% 242.78/49.37  | | | | | | |   (105)  all_58_7 = e2
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | | BETA: splitting (5) gives:
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | |   (106)  all_54_8 = e3
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | COMBINE_EQS: (69), (106) imply:
% 242.78/49.37  | | | | | | | |   (107)  all_24_0 = e3
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | SIMP: (107) implies:
% 242.78/49.37  | | | | | | | |   (108)  all_24_0 = e3
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | REDUCE: (73), (108) imply:
% 242.78/49.37  | | | | | | | |   (109)   ~ (all_52_14 = e3)
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | REDUCE: (75), (108) imply:
% 242.78/49.37  | | | | | | | |   (110)   ~ (e3 = e1)
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | BETA: splitting (6) gives:
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | |   (111)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3
% 242.78/49.37  | | | | | | | | |            & op(e0, e2) = e3)
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | BETA: splitting (111) gives:
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | |   (112)  all_58_12 = e3 & op(e0, e3) = e3
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | REF_CLOSE: (7), (9), (12), (14), (16), (26), (28), (29),
% 242.78/49.37  | | | | | | | | | |            (36), (38), (40), (44), (48), (55), (63), (109),
% 242.78/49.37  | | | | | | | | | |            (110), (112) are inconsistent by sub-proof #1528.
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | |   (113)  all_58_13 = e3 & op(e0, e2) = e3
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | REF_CLOSE: (17), (41), (48), (113) are inconsistent by
% 242.78/49.37  | | | | | | | | | |            sub-proof #1919.
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | End of split
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | |   (114)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3
% 242.78/49.37  | | | | | | | | |            & op(e0, e0) = e3)
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | BETA: splitting (114) gives:
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | |   (115)  all_58_14 = e3 & op(e0, e1) = e3
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | ALPHA: (115) implies:
% 242.78/49.37  | | | | | | | | | |   (116)  all_58_14 = e3
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | BETA: splitting (35) gives:
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | |   (117)  all_54_9 = e3
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | REF_CLOSE: (68), (78), (117) are inconsistent by sub-proof
% 242.78/49.37  | | | | | | | | | | |            #938.
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | |   (118)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | BETA: splitting (53) gives:
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | |   (119)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 242.78/49.37  | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 242.78/49.37  | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | BETA: splitting (119) gives:
% 242.78/49.37  | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | |   (120)  all_58_12 = e2 & op(e0, e3) = e2
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | | ALPHA: (120) implies:
% 242.78/49.37  | | | | | | | | | | | | |   (121)  all_58_12 = e2
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (39), (48), (54), (63), (100),
% 242.78/49.37  | | | | | | | | | | | | |            (121) are inconsistent by sub-proof #1759.
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | |   (122)  all_58_13 = e2 & op(e0, e2) = e2
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | | ALPHA: (122) implies:
% 242.78/49.37  | | | | | | | | | | | | |   (123)  op(e0, e2) = e2
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | | REF_CLOSE: (10), (17), (22), (32), (41), (42), (48), (68),
% 242.78/49.37  | | | | | | | | | | | | |            (77), (79), (118), (123) are inconsistent by
% 242.78/49.37  | | | | | | | | | | | | |            sub-proof #937.
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | End of split
% 242.78/49.37  | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | |   (124)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 242.78/49.37  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 242.78/49.37  | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | BETA: splitting (124) gives:
% 242.78/49.37  | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | |   (125)  all_58_14 = e2 & op(e0, e1) = e2
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | | ALPHA: (125) implies:
% 242.78/49.37  | | | | | | | | | | | | |   (126)  all_58_14 = e2
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | | COMBINE_EQS: (116), (126) imply:
% 242.78/49.37  | | | | | | | | | | | | |   (127)  e3 = e2
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | | SIMP: (127) implies:
% 242.78/49.37  | | | | | | | | | | | | |   (128)  e3 = e2
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | | COMBINE_EQS: (100), (128) imply:
% 242.78/49.37  | | | | | | | | | | | | |   (129)  all_58_6 = e2
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | | REF_CLOSE: (5), (12), (14), (16), (24), (26), (29), (38),
% 242.78/49.37  | | | | | | | | | | | | |            (40), (48), (69), (73), (74), (75), (129) are
% 242.78/49.37  | | | | | | | | | | | | |            inconsistent by sub-proof #941.
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | |   (130)  all_58_15 = e2 & op(e0, e0) = e2
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | | REF_CLOSE: (9), (15), (29), (37), (46), (55), (97), (100),
% 242.78/49.37  | | | | | | | | | | | | |            (105), (130) are inconsistent by sub-proof #940.
% 242.78/49.37  | | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | | End of split
% 242.78/49.37  | | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | End of split
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | End of split
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | |   (131)  all_58_15 = e3 & op(e0, e0) = e3
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | ALPHA: (131) implies:
% 242.78/49.37  | | | | | | | | | |   (132)  all_58_15 = e3
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | REF_CLOSE: (37), (110), (132) are inconsistent by sub-proof
% 242.78/49.37  | | | | | | | | | |            #2249.
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | End of split
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | End of split
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | |   (133)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | REF_CLOSE: (24), (69), (74), (75), (133) are inconsistent by
% 242.78/49.37  | | | | | | | |            sub-proof #2241.
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | End of split
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | End of split
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | Case 2:
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | |   (134)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 242.78/49.37  | | | | | |            op(e1, e0) = e2)
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | BETA: splitting (134) gives:
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | Case 1:
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | |   (135)  all_58_8 = e2 & op(e1, e1) = e2
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | | REF_CLOSE: (15), (55), (135) are inconsistent by sub-proof #2217.
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | Case 2:
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | |   (136)  all_58_11 = e2 & op(e1, e0) = e2
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | | REF_CLOSE: (9), (97), (136) are inconsistent by sub-proof #2216.
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | End of split
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | End of split
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | Case 2:
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | |   (137)  all_58_7 = e3 & op(e1, e2) = e3
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | | ALPHA: (137) implies:
% 242.78/49.37  | | | | |   (138)  op(e1, e2) = e3
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | | REF_CLOSE: (12), (40), (48), (138) are inconsistent by sub-proof
% 242.78/49.37  | | | | |            #2191.
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | End of split
% 242.78/49.37  | | | | 
% 242.78/49.37  | | | Case 2:
% 242.78/49.37  | | | | 
% 242.78/49.37  | | | |   (139)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 242.78/49.37  | | | |              e0) = e3)
% 242.78/49.37  | | | | 
% 242.78/49.37  | | | | REF_CLOSE: (5), (14), (16), (24), (26), (48), (69), (73), (74), (75),
% 242.78/49.37  | | | |            (139) are inconsistent by sub-proof #948.
% 242.78/49.37  | | | | 
% 242.78/49.37  | | | End of split
% 242.78/49.37  | | | 
% 242.78/49.37  | | End of split
% 242.78/49.37  | | 
% 242.78/49.37  | End of split
% 242.78/49.37  | 
% 242.78/49.37  End of proof
% 242.78/49.37  
% 242.78/49.37  Sub-proof #937 shows that the following formulas are inconsistent:
% 242.78/49.37  ----------------------------------------------------------------
% 242.78/49.37    (1)   ~ (all_42_0 = e1)
% 242.78/49.37    (2)  all_54_13 = all_52_7
% 242.78/49.37    (3)   ~ (all_52_7 = e3)
% 242.78/49.37    (4)  op(e0, e2) = e2
% 242.78/49.37    (5)   ~ (all_42_0 = e0)
% 242.78/49.37    (6)  all_54_9 = all_42_0
% 242.78/49.37    (7)   ~ (all_52_7 = e1)
% 242.78/49.37    (8)  op(e0, e2) = all_52_7
% 242.78/49.37    (9)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.78/49.37    (10)   ~ (all_52_7 = all_42_0)
% 242.78/49.37    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.37    (12)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.78/49.37  
% 242.78/49.37  Begin of proof
% 242.78/49.37  | 
% 242.78/49.37  | BETA: splitting (12) gives:
% 242.78/49.37  | 
% 242.78/49.37  | Case 1:
% 242.78/49.37  | | 
% 242.78/49.37  | |   (13)  all_54_9 = e2
% 242.78/49.37  | | 
% 242.78/49.37  | | COMBINE_EQS: (6), (13) imply:
% 242.78/49.37  | |   (14)  all_42_0 = e2
% 242.78/49.37  | | 
% 242.78/49.37  | | SIMP: (14) implies:
% 242.78/49.37  | |   (15)  all_42_0 = e2
% 242.78/49.37  | | 
% 242.78/49.37  | | REDUCE: (10), (15) imply:
% 242.78/49.37  | |   (16)   ~ (all_52_7 = e2)
% 242.78/49.37  | | 
% 242.78/49.37  | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (11), (16) are inconsistent by
% 242.78/49.37  | |            sub-proof #1816.
% 242.78/49.37  | | 
% 242.78/49.37  | Case 2:
% 242.78/49.37  | | 
% 242.78/49.37  | |   (17)  all_54_9 = e1 | all_54_9 = e0
% 242.78/49.37  | | 
% 242.78/49.37  | | BETA: splitting (17) gives:
% 242.78/49.37  | | 
% 242.78/49.37  | | Case 1:
% 242.78/49.37  | | | 
% 242.78/49.37  | | |   (18)  all_54_9 = e1
% 242.78/49.37  | | | 
% 242.78/49.37  | | | COMBINE_EQS: (6), (18) imply:
% 242.78/49.37  | | |   (19)  all_42_0 = e1
% 242.78/49.37  | | | 
% 242.78/49.37  | | | SIMP: (19) implies:
% 242.78/49.37  | | |   (20)  all_42_0 = e1
% 242.78/49.37  | | | 
% 242.78/49.37  | | | REDUCE: (1), (20) imply:
% 242.78/49.37  | | |   (21)  $false
% 242.78/49.37  | | | 
% 242.78/49.37  | | | CLOSE: (21) is inconsistent.
% 242.78/49.37  | | | 
% 242.78/49.37  | | Case 2:
% 242.78/49.37  | | | 
% 242.78/49.37  | | |   (22)  all_54_9 = e0
% 242.78/49.37  | | | 
% 242.78/49.37  | | | COMBINE_EQS: (6), (22) imply:
% 242.78/49.37  | | |   (23)  all_42_0 = e0
% 242.78/49.37  | | | 
% 242.78/49.37  | | | SIMP: (23) implies:
% 242.78/49.37  | | |   (24)  all_42_0 = e0
% 242.78/49.37  | | | 
% 242.78/49.37  | | | REDUCE: (5), (24) imply:
% 242.78/49.37  | | |   (25)  $false
% 242.78/49.37  | | | 
% 242.78/49.37  | | | CLOSE: (25) is inconsistent.
% 242.78/49.37  | | | 
% 242.78/49.37  | | End of split
% 242.78/49.37  | | 
% 242.78/49.37  | End of split
% 242.78/49.37  | 
% 242.78/49.37  End of proof
% 242.78/49.37  
% 242.78/49.37  Sub-proof #938 shows that the following formulas are inconsistent:
% 242.78/49.37  ----------------------------------------------------------------
% 242.78/49.37    (1)  all_54_9 = all_42_0
% 242.78/49.37    (2)  all_54_9 = e3
% 242.78/49.37    (3)   ~ (all_42_0 = e3)
% 242.78/49.37  
% 242.78/49.37  Begin of proof
% 242.78/49.37  | 
% 242.78/49.37  | COMBINE_EQS: (1), (2) imply:
% 242.78/49.37  |   (4)  all_42_0 = e3
% 242.78/49.37  | 
% 242.78/49.37  | SIMP: (4) implies:
% 242.78/49.37  |   (5)  all_42_0 = e3
% 242.78/49.37  | 
% 242.78/49.37  | REDUCE: (3), (5) imply:
% 242.78/49.37  |   (6)  $false
% 242.78/49.37  | 
% 242.78/49.37  | CLOSE: (6) is inconsistent.
% 242.78/49.37  | 
% 242.78/49.37  End of proof
% 242.78/49.37  
% 242.78/49.37  Sub-proof #939 shows that the following formulas are inconsistent:
% 242.78/49.37  ----------------------------------------------------------------
% 242.78/49.37    (1)   ~ (all_24_0 = all_8_0)
% 242.78/49.37    (2)   ~ (all_52_14 = all_24_0)
% 242.78/49.37    (3)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.78/49.37    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.78/49.37         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.78/49.37    (5)   ~ (e2 = e0)
% 242.78/49.37    (6)  all_54_13 = all_52_7
% 242.78/49.37    (7)  op(e1, e2) = all_52_6
% 242.78/49.37    (8)  op(e1, e1) = all_6_2
% 242.78/49.37    (9)  all_58_8 = e1
% 242.78/49.37    (10)  op(e1, e0) = all_52_14
% 242.78/49.37    (11)   ~ (all_52_7 = e3)
% 242.78/49.37    (12)  all_54_9 = all_8_0
% 242.78/49.37    (13)   ~ (all_24_0 = e0)
% 242.78/49.37    (14)   ~ (all_6_2 = e3)
% 242.78/49.37    (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.78/49.37          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.78/49.37    (16)   ~ (e3 = e2)
% 242.78/49.37    (17)   ~ (all_52_7 = e1)
% 242.78/49.37    (18)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.78/49.37    (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.78/49.37          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.78/49.37    (20)  all_58_15 = e1
% 242.78/49.37    (21)   ~ (all_52_7 = all_8_0)
% 242.78/49.37    (22)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.78/49.37          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.78/49.37    (23)  op(e3, e3) = e2
% 242.78/49.37    (24)   ~ (all_52_6 = e3)
% 242.78/49.37    (25)  op(e0, e2) = all_52_7
% 242.78/49.37    (26)   ~ (all_8_0 = e0)
% 242.78/49.37    (27)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.78/49.37    (28)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.78/49.37          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.78/49.37    (29)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.78/49.37          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.78/49.37    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.78/49.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.78/49.37    (31)  all_58_11 = e0
% 242.78/49.37    (32)   ~ (all_8_0 = e1)
% 242.78/49.37    (33)   ~ (e1 = e0)
% 242.78/49.37    (34)   ~ (all_24_0 = e1)
% 242.78/49.37    (35)  all_54_8 = all_24_0
% 242.78/49.37    (36)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.78/49.37          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.78/49.37            e2)
% 242.78/49.37    (37)  all_58_2 = e1
% 242.78/49.37    (38)   ~ (all_24_0 = e2)
% 242.78/49.37    (39)   ~ (e2 = e1)
% 242.78/49.37  
% 242.78/49.37  Begin of proof
% 242.78/49.37  | 
% 242.78/49.37  | BETA: splitting (22) gives:
% 242.78/49.37  | 
% 242.78/49.37  | Case 1:
% 242.78/49.37  | | 
% 242.78/49.37  | |   (40)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 242.78/49.37  | |           e3)
% 242.78/49.37  | | 
% 242.78/49.37  | | BETA: splitting (40) gives:
% 242.78/49.37  | | 
% 242.78/49.37  | | Case 1:
% 242.78/49.37  | | | 
% 242.78/49.37  | | |   (41)  all_58_6 = e3 & op(e1, e3) = e3
% 242.78/49.37  | | | 
% 242.78/49.37  | | | ALPHA: (41) implies:
% 242.78/49.37  | | |   (42)  all_58_6 = e3
% 242.78/49.37  | | | 
% 242.78/49.37  | | | BETA: splitting (29) gives:
% 242.78/49.37  | | | 
% 242.78/49.37  | | | Case 1:
% 242.78/49.37  | | | | 
% 242.78/49.37  | | | |   (43)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 242.78/49.37  | | | |           = e2)
% 242.78/49.37  | | | | 
% 242.78/49.37  | | | | BETA: splitting (43) gives:
% 242.78/49.37  | | | | 
% 242.78/49.37  | | | | Case 1:
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | |   (44)  all_58_6 = e2 & op(e1, e3) = e2
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | | ALPHA: (44) implies:
% 242.78/49.37  | | | | |   (45)  all_58_6 = e2
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | | REF_CLOSE: (2), (3), (7), (8), (10), (13), (14), (16), (22), (24),
% 242.78/49.37  | | | | |            (30), (34), (35), (38), (45) are inconsistent by sub-proof
% 242.78/49.37  | | | | |            #941.
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | Case 2:
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | |   (46)  all_58_7 = e2 & op(e1, e2) = e2
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | | ALPHA: (46) implies:
% 242.78/49.37  | | | | |   (47)  all_58_7 = e2
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | | BETA: splitting (3) gives:
% 242.78/49.37  | | | | | 
% 242.78/49.37  | | | | | Case 1:
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | |   (48)  all_54_8 = e3
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | COMBINE_EQS: (35), (48) imply:
% 242.78/49.37  | | | | | |   (49)  all_24_0 = e3
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | SIMP: (49) implies:
% 242.78/49.37  | | | | | |   (50)  all_24_0 = e3
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | REDUCE: (2), (50) imply:
% 242.78/49.37  | | | | | |   (51)   ~ (all_52_14 = e3)
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | REDUCE: (1), (50) imply:
% 242.78/49.37  | | | | | |   (52)   ~ (all_8_0 = e3)
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | SIMP: (52) implies:
% 242.78/49.37  | | | | | |   (53)   ~ (all_8_0 = e3)
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | REDUCE: (34), (50) imply:
% 242.78/49.37  | | | | | |   (54)   ~ (e3 = e1)
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | REDUCE: (13), (50) imply:
% 242.78/49.37  | | | | | |   (55)   ~ (e3 = e0)
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | BETA: splitting (4) gives:
% 242.78/49.37  | | | | | | 
% 242.78/49.37  | | | | | | Case 1:
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | |   (56)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 242.78/49.37  | | | | | | |           op(e0, e2) = e3)
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | | BETA: splitting (56) gives:
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | |   (57)  all_58_12 = e3 & op(e0, e3) = e3
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | REF_CLOSE: (5), (7), (8), (10), (14), (15), (16), (19), (22),
% 242.78/49.37  | | | | | | | |            (24), (28), (30), (33), (39), (51), (54), (55), (57)
% 242.78/49.37  | | | | | | | |            are inconsistent by sub-proof #1528.
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | |   (58)  all_58_13 = e3 & op(e0, e2) = e3
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | REF_CLOSE: (11), (25), (30), (58) are inconsistent by sub-proof
% 242.78/49.37  | | | | | | | |            #1919.
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | End of split
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | Case 2:
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | |   (59)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 242.78/49.37  | | | | | | |           op(e0, e0) = e3)
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | | BETA: splitting (59) gives:
% 242.78/49.37  | | | | | | | 
% 242.78/49.37  | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | |   (60)  all_58_14 = e3 & op(e0, e1) = e3
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | ALPHA: (60) implies:
% 242.78/49.37  | | | | | | | |   (61)  all_58_14 = e3
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | BETA: splitting (18) gives:
% 242.78/49.37  | | | | | | | | 
% 242.78/49.37  | | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | |   (62)  all_54_9 = e3
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | REF_CLOSE: (12), (53), (62) are inconsistent by sub-proof
% 242.78/49.37  | | | | | | | | |            #946.
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | |   (63)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | BETA: splitting (36) gives:
% 242.78/49.37  | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | |   (64)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2
% 242.78/49.37  | | | | | | | | | |           & op(e0, e2) = e2)
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | BETA: splitting (64) gives:
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | |   (65)  all_58_12 = e2 & op(e0, e3) = e2
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | ALPHA: (65) implies:
% 242.78/49.37  | | | | | | | | | | |   (66)  all_58_12 = e2
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | REF_CLOSE: (5), (19), (23), (30), (33), (37), (42), (55),
% 242.78/49.37  | | | | | | | | | | |            (66) are inconsistent by sub-proof #1759.
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | |   (67)  all_58_13 = e2 & op(e0, e2) = e2
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | ALPHA: (67) implies:
% 242.78/49.37  | | | | | | | | | | |   (68)  op(e0, e2) = e2
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (17), (21), (25), (26), (27),
% 242.78/49.37  | | | | | | | | | | |            (30), (32), (63), (68) are inconsistent by
% 242.78/49.37  | | | | | | | | | | |            sub-proof #944.
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | End of split
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | Case 2:
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | |   (69)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2
% 242.78/49.37  | | | | | | | | | |           & op(e0, e0) = e2)
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | BETA: splitting (69) gives:
% 242.78/49.37  | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | Case 1:
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | |   (70)  all_58_14 = e2 & op(e0, e1) = e2
% 242.78/49.37  | | | | | | | | | | | 
% 242.78/49.37  | | | | | | | | | | | ALPHA: (70) implies:
% 242.78/49.38  | | | | | | | | | | |   (71)  all_58_14 = e2
% 242.78/49.38  | | | | | | | | | | | 
% 242.78/49.38  | | | | | | | | | | | COMBINE_EQS: (61), (71) imply:
% 242.78/49.38  | | | | | | | | | | |   (72)  e3 = e2
% 242.78/49.38  | | | | | | | | | | | 
% 242.78/49.38  | | | | | | | | | | | COMBINE_EQS: (42), (72) imply:
% 242.78/49.38  | | | | | | | | | | |   (73)  all_58_6 = e2
% 242.78/49.38  | | | | | | | | | | | 
% 242.78/49.38  | | | | | | | | | | | REF_CLOSE: (2), (3), (7), (8), (10), (13), (14), (16), (22),
% 242.78/49.38  | | | | | | | | | | |            (24), (30), (34), (35), (38), (73) are
% 242.78/49.38  | | | | | | | | | | |            inconsistent by sub-proof #941.
% 242.78/49.38  | | | | | | | | | | | 
% 242.78/49.38  | | | | | | | | | | Case 2:
% 242.78/49.38  | | | | | | | | | | | 
% 242.78/49.38  | | | | | | | | | | |   (74)  all_58_15 = e2 & op(e0, e0) = e2
% 242.78/49.38  | | | | | | | | | | | 
% 242.78/49.38  | | | | | | | | | | | REF_CLOSE: (5), (9), (16), (20), (29), (31), (39), (42),
% 242.78/49.38  | | | | | | | | | | |            (47), (74) are inconsistent by sub-proof #940.
% 242.78/49.38  | | | | | | | | | | | 
% 242.78/49.38  | | | | | | | | | | End of split
% 242.78/49.38  | | | | | | | | | | 
% 242.78/49.38  | | | | | | | | | End of split
% 242.78/49.38  | | | | | | | | | 
% 242.78/49.38  | | | | | | | | End of split
% 242.78/49.38  | | | | | | | | 
% 242.78/49.38  | | | | | | | Case 2:
% 242.78/49.38  | | | | | | | | 
% 242.78/49.38  | | | | | | | |   (75)  all_58_15 = e3 & op(e0, e0) = e3
% 242.78/49.38  | | | | | | | | 
% 242.78/49.38  | | | | | | | | ALPHA: (75) implies:
% 242.78/49.38  | | | | | | | |   (76)  all_58_15 = e3
% 242.78/49.38  | | | | | | | | 
% 242.78/49.38  | | | | | | | | REF_CLOSE: (20), (54), (76) are inconsistent by sub-proof #2249.
% 242.78/49.38  | | | | | | | | 
% 242.78/49.38  | | | | | | | End of split
% 242.78/49.38  | | | | | | | 
% 242.78/49.38  | | | | | | End of split
% 242.78/49.38  | | | | | | 
% 242.78/49.38  | | | | | Case 2:
% 242.78/49.38  | | | | | | 
% 242.78/49.38  | | | | | |   (77)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.78/49.38  | | | | | | 
% 242.78/49.38  | | | | | | REF_CLOSE: (13), (34), (35), (38), (77) are inconsistent by
% 242.78/49.38  | | | | | |            sub-proof #2241.
% 242.78/49.38  | | | | | | 
% 242.78/49.38  | | | | | End of split
% 242.78/49.38  | | | | | 
% 242.78/49.38  | | | | End of split
% 242.78/49.38  | | | | 
% 242.78/49.38  | | | Case 2:
% 242.78/49.38  | | | | 
% 242.78/49.38  | | | |   (78)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0)
% 242.78/49.38  | | | |           = e2)
% 242.78/49.38  | | | | 
% 242.78/49.38  | | | | BETA: splitting (78) gives:
% 242.78/49.38  | | | | 
% 242.78/49.38  | | | | Case 1:
% 242.78/49.38  | | | | | 
% 242.78/49.38  | | | | |   (79)  all_58_8 = e2 & op(e1, e1) = e2
% 242.78/49.38  | | | | | 
% 242.78/49.38  | | | | | REF_CLOSE: (9), (39), (79) are inconsistent by sub-proof #2217.
% 242.78/49.38  | | | | | 
% 242.78/49.38  | | | | Case 2:
% 242.78/49.38  | | | | | 
% 242.78/49.38  | | | | |   (80)  all_58_11 = e2 & op(e1, e0) = e2
% 242.78/49.38  | | | | | 
% 242.78/49.38  | | | | | REF_CLOSE: (5), (31), (80) are inconsistent by sub-proof #2216.
% 242.78/49.38  | | | | | 
% 242.78/49.38  | | | | End of split
% 242.78/49.38  | | | | 
% 242.78/49.38  | | | End of split
% 242.78/49.38  | | | 
% 242.78/49.38  | | Case 2:
% 242.78/49.38  | | | 
% 242.78/49.38  | | |   (81)  all_58_7 = e3 & op(e1, e2) = e3
% 242.78/49.38  | | | 
% 242.78/49.38  | | | ALPHA: (81) implies:
% 242.78/49.38  | | |   (82)  op(e1, e2) = e3
% 242.78/49.38  | | | 
% 242.78/49.38  | | | REF_CLOSE: (7), (24), (30), (82) are inconsistent by sub-proof #2191.
% 242.78/49.38  | | | 
% 242.78/49.38  | | End of split
% 242.78/49.38  | | 
% 242.78/49.38  | Case 2:
% 242.78/49.38  | | 
% 242.78/49.38  | |   (83)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 242.78/49.38  | |           e3)
% 242.78/49.38  | | 
% 242.78/49.38  | | REF_CLOSE: (2), (3), (8), (10), (13), (14), (30), (34), (35), (38), (83) are
% 242.78/49.38  | |            inconsistent by sub-proof #948.
% 242.78/49.38  | | 
% 242.78/49.38  | End of split
% 242.78/49.38  | 
% 242.78/49.38  End of proof
% 242.78/49.38  
% 242.78/49.38  Sub-proof #940 shows that the following formulas are inconsistent:
% 242.78/49.38  ----------------------------------------------------------------
% 242.78/49.38    (1)  all_58_6 = e3
% 242.78/49.38    (2)   ~ (e2 = e0)
% 242.78/49.38    (3)  all_58_8 = e1
% 242.78/49.38    (4)  all_58_15 = e2 & op(e0, e0) = e2
% 242.78/49.38    (5)  all_58_7 = e2
% 242.78/49.38    (6)   ~ (e3 = e2)
% 242.78/49.38    (7)  all_58_15 = e1
% 242.78/49.38    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.78/49.38         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.78/49.38    (9)  all_58_11 = e0
% 242.78/49.38    (10)   ~ (e2 = e1)
% 242.78/49.38  
% 242.78/49.38  Begin of proof
% 242.78/49.38  | 
% 242.78/49.38  | ALPHA: (4) implies:
% 242.78/49.38  |   (11)  all_58_15 = e2
% 242.78/49.38  | 
% 242.78/49.38  | COMBINE_EQS: (7), (11) imply:
% 242.78/49.38  |   (12)  e2 = e1
% 242.78/49.38  | 
% 242.78/49.38  | COMBINE_EQS: (5), (12) imply:
% 242.78/49.38  |   (13)  all_58_7 = e1
% 242.78/49.38  | 
% 242.78/49.38  | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (13) are inconsistent by
% 242.78/49.38  |            sub-proof #2215.
% 242.78/49.38  | 
% 242.78/49.38  End of proof
% 242.78/49.38  
% 242.78/49.38  Sub-proof #941 shows that the following formulas are inconsistent:
% 242.78/49.38  ----------------------------------------------------------------
% 242.78/49.38    (1)   ~ (all_52_14 = all_24_0)
% 242.89/49.38    (2)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.89/49.38    (3)  op(e1, e2) = all_52_6
% 242.89/49.38    (4)  all_58_6 = e2
% 242.89/49.38    (5)  op(e1, e1) = all_6_2
% 242.89/49.38    (6)  op(e1, e0) = all_52_14
% 242.89/49.38    (7)   ~ (all_24_0 = e0)
% 242.89/49.38    (8)   ~ (all_6_2 = e3)
% 242.89/49.38    (9)   ~ (e3 = e2)
% 242.89/49.38    (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.89/49.38          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.89/49.38    (11)   ~ (all_52_6 = e3)
% 242.89/49.38    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.89/49.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.89/49.38    (13)   ~ (all_24_0 = e1)
% 242.89/49.38    (14)  all_54_8 = all_24_0
% 242.89/49.38    (15)   ~ (all_24_0 = e2)
% 242.89/49.38  
% 242.89/49.38  Begin of proof
% 242.89/49.38  | 
% 242.89/49.38  | BETA: splitting (10) gives:
% 242.89/49.38  | 
% 242.89/49.38  | Case 1:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 242.89/49.38  | |           e3)
% 242.89/49.38  | | 
% 242.89/49.38  | | REF_CLOSE: (3), (4), (9), (11), (12), (16) are inconsistent by sub-proof
% 242.89/49.38  | |            #968.
% 242.89/49.38  | | 
% 242.89/49.38  | Case 2:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (17)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 242.89/49.38  | |           e3)
% 242.89/49.38  | | 
% 242.89/49.38  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (12), (13), (14), (15), (17) are
% 242.89/49.38  | |            inconsistent by sub-proof #948.
% 242.89/49.38  | | 
% 242.89/49.38  | End of split
% 242.89/49.38  | 
% 242.89/49.38  End of proof
% 242.89/49.38  
% 242.89/49.38  Sub-proof #942 shows that the following formulas are inconsistent:
% 242.89/49.38  ----------------------------------------------------------------
% 242.89/49.38    (1)  all_54_10 = e1 | all_54_10 = e0
% 242.89/49.38    (2)  op(e1, e1) = all_6_2
% 242.89/49.38    (3)  all_54_10 = all_6_2
% 242.89/49.38    (4)   ~ (all_6_2 = e0)
% 242.89/49.38    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.89/49.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.89/49.38    (6)  all_58_8 = e0 & op(e1, e1) = e0
% 242.89/49.38  
% 242.89/49.38  Begin of proof
% 242.89/49.38  | 
% 242.89/49.38  | ALPHA: (6) implies:
% 242.89/49.38  |   (7)  op(e1, e1) = e0
% 242.89/49.38  | 
% 242.89/49.38  | BETA: splitting (1) gives:
% 242.89/49.38  | 
% 242.89/49.38  | Case 1:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (8)  all_54_10 = e1
% 242.89/49.38  | | 
% 242.89/49.38  | | COMBINE_EQS: (3), (8) imply:
% 242.89/49.38  | |   (9)  all_6_2 = e1
% 242.89/49.38  | | 
% 242.89/49.38  | | SIMP: (9) implies:
% 242.89/49.38  | |   (10)  all_6_2 = e1
% 242.89/49.38  | | 
% 242.89/49.38  | | REDUCE: (4), (10) imply:
% 242.89/49.38  | |   (11)   ~ (e1 = e0)
% 242.89/49.38  | | 
% 242.89/49.38  | | REDUCE: (2), (10) imply:
% 242.89/49.38  | |   (12)  op(e1, e1) = e1
% 242.89/49.38  | | 
% 242.89/49.38  | | REF_CLOSE: (5), (7), (11), (12) are inconsistent by sub-proof #2220.
% 242.89/49.38  | | 
% 242.89/49.38  | Case 2:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (13)  all_54_10 = e0
% 242.89/49.38  | | 
% 242.89/49.38  | | REF_CLOSE: (3), (4), (13) are inconsistent by sub-proof #2303.
% 242.89/49.38  | | 
% 242.89/49.38  | End of split
% 242.89/49.38  | 
% 242.89/49.38  End of proof
% 242.89/49.38  
% 242.89/49.38  Sub-proof #943 shows that the following formulas are inconsistent:
% 242.89/49.38  ----------------------------------------------------------------
% 242.89/49.38    (1)  op(e2, e2) = e3
% 242.89/49.38    (2)  all_58_1 = e1
% 242.89/49.38    (3)   ~ (e2 = e0)
% 242.89/49.38    (4)  all_58_7 = e0
% 242.89/49.38    (5)  all_54_13 = all_52_7
% 242.89/49.38    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.89/49.38         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.89/49.38    (7)   ~ (all_52_7 = e3)
% 242.89/49.38    (8)  all_54_9 = all_8_0
% 242.89/49.38    (9)   ~ (e3 = e2)
% 242.89/49.38    (10)   ~ (all_52_7 = e1)
% 242.89/49.38    (11)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.89/49.38    (12)   ~ (all_8_0 = e3)
% 242.89/49.38    (13)   ~ (all_52_7 = all_8_0)
% 242.89/49.38    (14)  op(e0, e2) = all_52_7
% 242.89/49.38    (15)   ~ (all_8_0 = e0)
% 242.89/49.38    (16)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.89/49.38    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.89/49.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.89/49.38    (18)   ~ (all_8_0 = e1)
% 242.89/49.38    (19)   ~ (e2 = e1)
% 242.89/49.38  
% 242.89/49.38  Begin of proof
% 242.89/49.38  | 
% 242.89/49.38  | BETA: splitting (6) gives:
% 242.89/49.38  | 
% 242.89/49.38  | Case 1:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (20)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 242.89/49.38  | |           e2)
% 242.89/49.38  | | 
% 242.89/49.38  | | REF_CLOSE: (1), (2), (9), (17), (19), (20) are inconsistent by sub-proof
% 242.89/49.38  | |            #1721.
% 242.89/49.38  | | 
% 242.89/49.38  | Case 2:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (21)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 242.89/49.38  | |           e2)
% 242.89/49.38  | | 
% 242.89/49.38  | | BETA: splitting (21) gives:
% 242.89/49.38  | | 
% 242.89/49.38  | | Case 1:
% 242.89/49.38  | | | 
% 242.89/49.38  | | |   (22)  all_58_7 = e2 & op(e1, e2) = e2
% 242.89/49.38  | | | 
% 242.89/49.38  | | | REF_CLOSE: (3), (4), (22) are inconsistent by sub-proof #1326.
% 242.89/49.38  | | | 
% 242.89/49.38  | | Case 2:
% 242.89/49.38  | | | 
% 242.89/49.38  | | |   (23)  all_58_13 = e2 & op(e0, e2) = e2
% 242.89/49.38  | | | 
% 242.89/49.38  | | | ALPHA: (23) implies:
% 242.89/49.38  | | |   (24)  op(e0, e2) = e2
% 242.89/49.38  | | | 
% 242.89/49.38  | | | BETA: splitting (11) gives:
% 242.89/49.38  | | | 
% 242.89/49.38  | | | Case 1:
% 242.89/49.38  | | | | 
% 242.89/49.38  | | | |   (25)  all_54_9 = e3
% 242.89/49.38  | | | | 
% 242.89/49.38  | | | | REF_CLOSE: (8), (12), (25) are inconsistent by sub-proof #946.
% 242.89/49.38  | | | | 
% 242.89/49.38  | | | Case 2:
% 242.89/49.38  | | | | 
% 242.89/49.38  | | | |   (26)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.89/49.38  | | | | 
% 242.89/49.38  | | | | REF_CLOSE: (5), (7), (8), (10), (13), (14), (15), (16), (17), (18),
% 242.89/49.38  | | | |            (24), (26) are inconsistent by sub-proof #944.
% 242.89/49.38  | | | | 
% 242.89/49.38  | | | End of split
% 242.89/49.38  | | | 
% 242.89/49.38  | | End of split
% 242.89/49.38  | | 
% 242.89/49.38  | End of split
% 242.89/49.38  | 
% 242.89/49.38  End of proof
% 242.89/49.38  
% 242.89/49.38  Sub-proof #944 shows that the following formulas are inconsistent:
% 242.89/49.38  ----------------------------------------------------------------
% 242.89/49.38    (1)  all_54_13 = all_52_7
% 242.89/49.38    (2)   ~ (all_52_7 = e3)
% 242.89/49.38    (3)  all_54_9 = all_8_0
% 242.89/49.38    (4)  op(e0, e2) = e2
% 242.89/49.38    (5)   ~ (all_52_7 = e1)
% 242.89/49.38    (6)   ~ (all_52_7 = all_8_0)
% 242.89/49.38    (7)  op(e0, e2) = all_52_7
% 242.89/49.38    (8)   ~ (all_8_0 = e0)
% 242.89/49.38    (9)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 242.89/49.38    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.89/49.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.89/49.38    (11)   ~ (all_8_0 = e1)
% 242.89/49.38    (12)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 242.89/49.38  
% 242.89/49.38  Begin of proof
% 242.89/49.38  | 
% 242.89/49.38  | BETA: splitting (12) gives:
% 242.89/49.38  | 
% 242.89/49.38  | Case 1:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (13)  all_54_9 = e2
% 242.89/49.38  | | 
% 242.89/49.38  | | COMBINE_EQS: (3), (13) imply:
% 242.89/49.38  | |   (14)  all_8_0 = e2
% 242.89/49.38  | | 
% 242.89/49.38  | | SIMP: (14) implies:
% 242.89/49.38  | |   (15)  all_8_0 = e2
% 242.89/49.38  | | 
% 242.89/49.38  | | REDUCE: (6), (15) imply:
% 242.89/49.38  | |   (16)   ~ (all_52_7 = e2)
% 242.89/49.38  | | 
% 242.89/49.38  | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (16) are inconsistent by
% 242.89/49.38  | |            sub-proof #1816.
% 242.89/49.38  | | 
% 242.89/49.38  | Case 2:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (17)  all_54_9 = e1 | all_54_9 = e0
% 242.89/49.38  | | 
% 242.89/49.38  | | REF_CLOSE: (3), (8), (11), (17) are inconsistent by sub-proof #945.
% 242.89/49.38  | | 
% 242.89/49.38  | End of split
% 242.89/49.38  | 
% 242.89/49.38  End of proof
% 242.89/49.38  
% 242.89/49.38  Sub-proof #945 shows that the following formulas are inconsistent:
% 242.89/49.38  ----------------------------------------------------------------
% 242.89/49.38    (1)  all_54_9 = e1 | all_54_9 = e0
% 242.89/49.38    (2)  all_54_9 = all_8_0
% 242.89/49.38    (3)   ~ (all_8_0 = e1)
% 242.89/49.38    (4)   ~ (all_8_0 = e0)
% 242.89/49.38  
% 242.89/49.38  Begin of proof
% 242.89/49.38  | 
% 242.89/49.38  | BETA: splitting (1) gives:
% 242.89/49.38  | 
% 242.89/49.38  | Case 1:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (5)  all_54_9 = e1
% 242.89/49.38  | | 
% 242.89/49.38  | | COMBINE_EQS: (2), (5) imply:
% 242.89/49.38  | |   (6)  all_8_0 = e1
% 242.89/49.38  | | 
% 242.89/49.38  | | SIMP: (6) implies:
% 242.89/49.38  | |   (7)  all_8_0 = e1
% 242.89/49.38  | | 
% 242.89/49.38  | | REDUCE: (3), (7) imply:
% 242.89/49.38  | |   (8)  $false
% 242.89/49.38  | | 
% 242.89/49.38  | | CLOSE: (8) is inconsistent.
% 242.89/49.38  | | 
% 242.89/49.38  | Case 2:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (9)  all_54_9 = e0
% 242.89/49.38  | | 
% 242.89/49.38  | | COMBINE_EQS: (2), (9) imply:
% 242.89/49.38  | |   (10)  all_8_0 = e0
% 242.89/49.38  | | 
% 242.89/49.38  | | SIMP: (10) implies:
% 242.89/49.38  | |   (11)  all_8_0 = e0
% 242.89/49.38  | | 
% 242.89/49.38  | | REDUCE: (4), (11) imply:
% 242.89/49.38  | |   (12)  $false
% 242.89/49.38  | | 
% 242.89/49.38  | | CLOSE: (12) is inconsistent.
% 242.89/49.38  | | 
% 242.89/49.38  | End of split
% 242.89/49.38  | 
% 242.89/49.38  End of proof
% 242.89/49.38  
% 242.89/49.38  Sub-proof #946 shows that the following formulas are inconsistent:
% 242.89/49.38  ----------------------------------------------------------------
% 242.89/49.38    (1)  all_54_9 = all_8_0
% 242.89/49.38    (2)  all_54_9 = e3
% 242.89/49.38    (3)   ~ (all_8_0 = e3)
% 242.89/49.38  
% 242.89/49.38  Begin of proof
% 242.89/49.38  | 
% 242.89/49.38  | COMBINE_EQS: (1), (2) imply:
% 242.89/49.38  |   (4)  all_8_0 = e3
% 242.89/49.38  | 
% 242.89/49.38  | SIMP: (4) implies:
% 242.89/49.38  |   (5)  all_8_0 = e3
% 242.89/49.38  | 
% 242.89/49.38  | REDUCE: (3), (5) imply:
% 242.89/49.38  |   (6)  $false
% 242.89/49.38  | 
% 242.89/49.38  | CLOSE: (6) is inconsistent.
% 242.89/49.38  | 
% 242.89/49.38  End of proof
% 242.89/49.38  
% 242.89/49.38  Sub-proof #947 shows that the following formulas are inconsistent:
% 242.89/49.38  ----------------------------------------------------------------
% 242.89/49.38    (1)   ~ (all_52_14 = all_24_0)
% 242.89/49.38    (2)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.89/49.38    (3)   ~ (e3 = e0)
% 242.89/49.38    (4)  op(e1, e2) = all_52_6
% 242.89/49.38    (5)  op(e1, e1) = all_6_2
% 242.89/49.38    (6)  op(e1, e0) = all_52_14
% 242.89/49.38    (7)   ~ (all_24_0 = e0)
% 242.89/49.38    (8)   ~ (all_6_2 = e3)
% 242.89/49.38    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.89/49.38         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.89/49.38    (10)   ~ (all_52_6 = e3)
% 242.89/49.38    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.89/49.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.89/49.38    (12)  all_58_6 = e0 & op(e1, e3) = e0
% 242.89/49.38    (13)   ~ (all_24_0 = e1)
% 242.89/49.38    (14)  all_54_8 = all_24_0
% 242.89/49.38    (15)   ~ (all_24_0 = e2)
% 242.89/49.38  
% 242.89/49.38  Begin of proof
% 242.89/49.38  | 
% 242.89/49.38  | ALPHA: (12) implies:
% 242.89/49.38  |   (16)  all_58_6 = e0
% 242.89/49.38  | 
% 242.89/49.38  | BETA: splitting (9) gives:
% 242.89/49.38  | 
% 242.89/49.38  | Case 1:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (17)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 242.89/49.38  | |           e3)
% 242.89/49.38  | | 
% 242.89/49.38  | | REF_CLOSE: (3), (4), (10), (11), (16), (17) are inconsistent by sub-proof
% 242.89/49.38  | |            #1689.
% 242.89/49.38  | | 
% 242.89/49.38  | Case 2:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (18)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 242.89/49.38  | |           e3)
% 242.89/49.38  | | 
% 242.89/49.38  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (11), (13), (14), (15), (18) are
% 242.89/49.38  | |            inconsistent by sub-proof #948.
% 242.89/49.38  | | 
% 242.89/49.38  | End of split
% 242.89/49.38  | 
% 242.89/49.38  End of proof
% 242.89/49.38  
% 242.89/49.38  Sub-proof #948 shows that the following formulas are inconsistent:
% 242.89/49.38  ----------------------------------------------------------------
% 242.89/49.38    (1)   ~ (all_52_14 = all_24_0)
% 242.89/49.38    (2)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.89/49.38    (3)  op(e1, e1) = all_6_2
% 242.89/49.38    (4)  op(e1, e0) = all_52_14
% 242.89/49.38    (5)   ~ (all_24_0 = e0)
% 242.89/49.38    (6)   ~ (all_6_2 = e3)
% 242.89/49.38    (7)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.89/49.38    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.89/49.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.89/49.38    (9)   ~ (all_24_0 = e1)
% 242.89/49.38    (10)  all_54_8 = all_24_0
% 242.89/49.38    (11)   ~ (all_24_0 = e2)
% 242.89/49.38  
% 242.89/49.38  Begin of proof
% 242.89/49.38  | 
% 242.89/49.38  | BETA: splitting (7) gives:
% 242.89/49.38  | 
% 242.89/49.38  | Case 1:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (12)  all_58_8 = e3 & op(e1, e1) = e3
% 242.89/49.38  | | 
% 242.89/49.38  | | REF_CLOSE: (3), (6), (8), (12) are inconsistent by sub-proof #2092.
% 242.89/49.38  | | 
% 242.89/49.38  | Case 2:
% 242.89/49.38  | | 
% 242.89/49.38  | |   (13)  all_58_11 = e3 & op(e1, e0) = e3
% 242.89/49.38  | | 
% 242.89/49.38  | | ALPHA: (13) implies:
% 242.89/49.38  | |   (14)  op(e1, e0) = e3
% 242.89/49.38  | | 
% 242.89/49.38  | | BETA: splitting (2) gives:
% 242.89/49.38  | | 
% 242.89/49.38  | | Case 1:
% 242.89/49.38  | | | 
% 242.89/49.38  | | |   (15)  all_54_8 = e3
% 242.89/49.38  | | | 
% 242.89/49.38  | | | COMBINE_EQS: (10), (15) imply:
% 242.89/49.38  | | |   (16)  all_24_0 = e3
% 242.89/49.38  | | | 
% 242.89/49.38  | | | SIMP: (16) implies:
% 242.89/49.38  | | |   (17)  all_24_0 = e3
% 242.89/49.38  | | | 
% 242.89/49.38  | | | REDUCE: (1), (17) imply:
% 242.89/49.38  | | |   (18)   ~ (all_52_14 = e3)
% 242.89/49.38  | | | 
% 242.89/49.38  | | | REF_CLOSE: (4), (8), (14), (18) are inconsistent by sub-proof #2149.
% 242.89/49.38  | | | 
% 242.89/49.38  | | Case 2:
% 242.89/49.38  | | | 
% 242.89/49.38  | | |   (19)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 242.89/49.38  | | | 
% 242.89/49.38  | | | REF_CLOSE: (5), (9), (10), (11), (19) are inconsistent by sub-proof #2241.
% 242.89/49.38  | | | 
% 242.89/49.38  | | End of split
% 242.89/49.38  | | 
% 242.89/49.38  | End of split
% 242.89/49.38  | 
% 242.89/49.38  End of proof
% 242.89/49.38  
% 242.89/49.38  Sub-proof #949 shows that the following formulas are inconsistent:
% 242.89/49.38  ----------------------------------------------------------------
% 242.89/49.38    (1)  op(e2, e2) = e3
% 242.89/49.38    (2)  all_58_1 = e1
% 242.89/49.38    (3)   ~ (e3 = e0)
% 242.89/49.38    (4)   ~ (e2 = e0)
% 242.89/49.38    (5)  op(e1, e2) = all_52_6
% 242.89/49.38    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.89/49.38         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.89/49.38    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.89/49.38         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.89/49.38    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 242.89/49.38    (9)  all_58_3 = e3
% 242.89/49.38    (10)   ~ (all_52_2 = e1)
% 242.89/49.38    (11)   ~ (e3 = e2)
% 242.89/49.38    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.89/49.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.89/49.38    (13)  op(e1, e3) = all_52_2
% 242.89/49.38    (14)   ~ (e1 = e0)
% 242.89/49.38    (15)   ~ (e2 = e1)
% 242.89/49.38  
% 242.89/49.38  Begin of proof
% 242.89/49.38  | 
% 242.89/49.38  | BETA: splitting (8) gives:
% 242.89/49.38  | 
% 242.89/49.38  | Case 1:
% 242.89/49.38  | | 
% 242.89/49.39  | |   (16)  all_58_6 = e1 & op(e1, e3) = e1
% 242.89/49.39  | | 
% 242.89/49.39  | | ALPHA: (16) implies:
% 242.89/49.39  | |   (17)  op(e1, e3) = e1
% 242.89/49.39  | | 
% 242.89/49.39  | | REF_CLOSE: (10), (12), (13), (17) are inconsistent by sub-proof #1948.
% 242.89/49.39  | | 
% 242.89/49.39  | Case 2:
% 242.89/49.39  | | 
% 242.89/49.39  | |   (18)  all_58_7 = e1 & op(e1, e2) = e1
% 242.89/49.39  | | 
% 242.89/49.39  | | ALPHA: (18) implies:
% 242.89/49.39  | |   (19)  all_58_7 = e1
% 242.89/49.39  | |   (20)  op(e1, e2) = e1
% 242.89/49.39  | | 
% 242.89/49.39  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (14), (15),
% 242.89/49.39  | |            (19), (20) are inconsistent by sub-proof #1717.
% 242.89/49.39  | | 
% 242.89/49.39  | End of split
% 242.89/49.39  | 
% 242.89/49.39  End of proof
% 242.89/49.39  
% 242.89/49.39  Sub-proof #950 shows that the following formulas are inconsistent:
% 242.89/49.39  ----------------------------------------------------------------
% 242.89/49.39    (1)  op(e0, e0) = e1
% 242.89/49.39    (2)  op(e2, e2) = e3
% 242.89/49.39    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.89/49.39         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.89/49.39    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.89/49.39         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.89/49.39    (5)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.89/49.39           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.89/49.39             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.89/49.39    (6)   ~ (e3 = e0)
% 242.89/49.39    (7)  op(e0, e1) = all_52_11
% 242.89/49.39    (8)   ~ (e2 = e0)
% 242.89/49.39    (9)  op(e1, e1) = all_6_2
% 242.89/49.39    (10)   ~ (all_52_1 = all_52_2)
% 242.89/49.39    (11)  op(e1, e0) = all_52_14
% 242.89/49.39    (12)   ~ (all_52_13 = e1)
% 242.89/49.39    (13)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.89/49.39            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.89/49.39              e1) = all_20_1 & $i(all_20_1))
% 242.89/49.39    (14)   ~ (all_52_7 = e3)
% 242.89/49.39    (15)   ~ (e3 = e1)
% 242.89/49.39    (16)   ~ (all_52_12 = e1)
% 242.89/49.39    (17)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.89/49.39          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.89/49.39    (18)   ~ (all_52_12 = all_52_14)
% 242.89/49.39    (19)  all_58_3 = e3
% 242.89/49.39    (20)   ~ (all_52_12 = all_52_13)
% 242.89/49.39    (21)  all_58_11 = e3
% 242.89/49.39    (22)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 242.89/49.39    (23)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.89/49.39              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.89/49.39                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.89/49.39                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.89/49.39    (24)   ~ (all_6_2 = e3)
% 242.89/49.39    (25)  op(e2, e1) = all_52_9
% 242.89/49.39    (26)   ~ (e3 = e2)
% 242.89/49.39    (27)  op(e1, e0) = e3
% 242.89/49.39    (28)   ~ (all_52_14 = e1)
% 242.89/49.39    (29)   ~ (all_6_2 = e0)
% 242.89/49.39    (30)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.89/49.39            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.89/49.39            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.89/49.39            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.89/49.39            op(e0, all_56_31) = e0)
% 242.89/49.39    (31)  all_56_31 = e1
% 242.89/49.39    (32)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 242.89/49.39    (33)  all_58_15 = e1
% 242.89/49.39    (34)  op(e3, e0) = all_52_12
% 242.89/49.39    (35)  op(e2, e3) = all_52_1
% 242.89/49.39    (36)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.89/49.39          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.89/49.39    (37)  all_34_2 = e1
% 242.89/49.39    (38)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.89/49.39          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.89/49.39    (39)  all_54_7 = all_52_13
% 242.89/49.39    (40)  op(e0, e2) = all_52_7
% 242.89/49.39    (41)   ~ (all_52_13 = all_52_14)
% 242.89/49.39    (42)   ~ (all_52_9 = e3)
% 242.89/49.39    (43)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.89/49.39          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.89/49.39    (44)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.89/49.39          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.89/49.39    (45)  all_54_3 = all_52_12
% 242.89/49.39    (46)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.89/49.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.89/49.39    (47)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.89/49.39          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.89/49.39    (48)  op(e1, e3) = all_52_2
% 242.89/49.39    (49)   ~ (e1 = e0)
% 242.89/49.39    (50)  op(e3, e3) = e3
% 242.89/49.39    (51)  op(e2, e0) = all_52_13
% 242.89/49.39    (52)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.89/49.39          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.89/49.39            e2)
% 242.89/49.39    (53)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.89/49.39          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.89/49.39    (54)   ~ (e2 = e1)
% 242.89/49.39  
% 242.89/49.39  Begin of proof
% 242.89/49.39  | 
% 242.89/49.39  | BETA: splitting (4) gives:
% 242.89/49.39  | 
% 242.89/49.39  | Case 1:
% 242.89/49.39  | | 
% 242.89/49.39  | |   (55)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 242.89/49.39  | |           e3)
% 242.89/49.39  | | 
% 242.89/49.39  | | BETA: splitting (55) gives:
% 242.89/49.39  | | 
% 242.89/49.39  | | Case 1:
% 242.89/49.39  | | | 
% 242.89/49.39  | | |   (56)  all_58_12 = e3 & op(e0, e3) = e3
% 242.89/49.39  | | | 
% 242.89/49.39  | | | ALPHA: (56) implies:
% 242.89/49.39  | | |   (57)  all_58_12 = e3
% 242.89/49.39  | | | 
% 242.89/49.39  | | | BETA: splitting (38) gives:
% 242.89/49.39  | | | 
% 242.89/49.39  | | | Case 1:
% 242.89/49.39  | | | | 
% 242.89/49.39  | | | |   (58)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 242.89/49.39  | | | |           = e3)
% 242.89/49.39  | | | | 
% 242.89/49.39  | | | | BETA: splitting (58) gives:
% 242.89/49.39  | | | | 
% 242.89/49.39  | | | | Case 1:
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | |   (59)  all_58_4 = e3 & op(e3, e1) = e3
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | | ALPHA: (59) implies:
% 242.89/49.39  | | | | |   (60)  all_58_4 = e3
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | | BETA: splitting (44) gives:
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | | Case 1:
% 242.89/49.39  | | | | | | 
% 242.89/49.39  | | | | | |   (61)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3,
% 242.89/49.39  | | | | | |             e2) = e1)
% 242.89/49.39  | | | | | | 
% 242.89/49.39  | | | | | | BETA: splitting (61) gives:
% 242.89/49.39  | | | | | | 
% 242.89/49.39  | | | | | | Case 1:
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | |   (62)  all_58_0 = e1 & op(e3, e3) = e1
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | | ALPHA: (62) implies:
% 242.89/49.39  | | | | | | |   (63)  op(e3, e3) = e1
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | | REF_CLOSE: (15), (46), (50), (63) are inconsistent by sub-proof
% 242.89/49.39  | | | | | | |            #1578.
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | Case 2:
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | |   (64)  all_58_1 = e1 & op(e3, e2) = e1
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | | ALPHA: (64) implies:
% 242.89/49.39  | | | | | | |   (65)  all_58_1 = e1
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | | BETA: splitting (36) gives:
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | | Case 1:
% 242.89/49.39  | | | | | | | | 
% 242.89/49.39  | | | | | | | |   (66)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 242.89/49.39  | | | | | | | |           op(e3, e2) = e0)
% 242.89/49.39  | | | | | | | | 
% 242.89/49.39  | | | | | | | | BETA: splitting (66) gives:
% 242.89/49.39  | | | | | | | | 
% 242.89/49.39  | | | | | | | | Case 1:
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | |   (67)  all_58_0 = e0 & op(e3, e3) = e0
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | ALPHA: (67) implies:
% 242.89/49.39  | | | | | | | | |   (68)  op(e3, e3) = e0
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | REF_CLOSE: (6), (46), (50), (68) are inconsistent by sub-proof
% 242.89/49.39  | | | | | | | | |            #1940.
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | Case 2:
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | |   (69)  all_58_1 = e0 & op(e3, e2) = e0
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | REF_CLOSE: (49), (65), (69) are inconsistent by sub-proof
% 242.89/49.39  | | | | | | | | |            #1720.
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | End of split
% 242.89/49.39  | | | | | | | | 
% 242.89/49.39  | | | | | | | Case 2:
% 242.89/49.39  | | | | | | | | 
% 242.89/49.39  | | | | | | | |   (70)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 242.89/49.39  | | | | | | | |           op(e3, e0) = e0)
% 242.89/49.39  | | | | | | | | 
% 242.89/49.39  | | | | | | | | BETA: splitting (70) gives:
% 242.89/49.39  | | | | | | | | 
% 242.89/49.39  | | | | | | | | Case 1:
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | |   (71)  all_58_4 = e0 & op(e3, e1) = e0
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | ALPHA: (71) implies:
% 242.89/49.39  | | | | | | | | |   (72)  all_58_4 = e0
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | REF_CLOSE: (6), (60), (72) are inconsistent by sub-proof
% 242.89/49.39  | | | | | | | | |            #2186.
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | Case 2:
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | |   (73)  all_58_9 = e0 & op(e3, e0) = e0
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | ALPHA: (73) implies:
% 242.89/49.39  | | | | | | | | |   (74)  all_58_9 = e0
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | BETA: splitting (47) gives:
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | Case 1:
% 242.89/49.39  | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | |   (75)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2
% 242.89/49.39  | | | | | | | | | |           & op(e2, e0) = e2)
% 242.89/49.39  | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | BETA: splitting (75) gives:
% 242.89/49.39  | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | Case 1:
% 242.89/49.39  | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | |   (76)  all_58_9 = e2 & op(e3, e0) = e2
% 242.89/49.39  | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | ALPHA: (76) implies:
% 242.89/49.39  | | | | | | | | | | |   (77)  all_58_9 = e2
% 242.89/49.39  | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | REF_CLOSE: (8), (74), (77) are inconsistent by sub-proof
% 242.89/49.39  | | | | | | | | | | |            #1660.
% 242.89/49.39  | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | Case 2:
% 242.89/49.39  | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | |   (78)  all_58_10 = e2 & op(e2, e0) = e2
% 242.89/49.39  | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | ALPHA: (78) implies:
% 242.89/49.39  | | | | | | | | | | |   (79)  all_58_10 = e2
% 242.89/49.39  | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | BETA: splitting (3) gives:
% 242.89/49.39  | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | Case 1:
% 242.89/49.39  | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | |   (80)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 242.89/49.39  | | | | | | | | | | | |           & op(e3, e2) = e2)
% 242.89/49.39  | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | BETA: splitting (80) gives:
% 242.89/49.39  | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | Case 1:
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | |   (81)  all_58_0 = e2 & op(e3, e3) = e2
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | ALPHA: (81) implies:
% 242.89/49.39  | | | | | | | | | | | | |   (82)  op(e3, e3) = e2
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | GROUND_INST: instantiating (46) with e2, e3, e3, e3,
% 242.89/49.39  | | | | | | | | | | | | |              simplifying with (50), (82) gives:
% 242.89/49.39  | | | | | | | | | | | | |   (83)  e3 = e2
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | REDUCE: (26), (83) imply:
% 242.89/49.39  | | | | | | | | | | | | |   (84)  $false
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | CLOSE: (84) is inconsistent.
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | Case 2:
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | |   (85)  all_58_1 = e2 & op(e3, e2) = e2
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | ALPHA: (85) implies:
% 242.89/49.39  | | | | | | | | | | | | |   (86)  all_58_1 = e2
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | COMBINE_EQS: (65), (86) imply:
% 242.89/49.39  | | | | | | | | | | | | |   (87)  e2 = e1
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | SIMP: (87) implies:
% 242.89/49.39  | | | | | | | | | | | | |   (88)  e2 = e1
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | COMBINE_EQS: (79), (88) imply:
% 242.89/49.39  | | | | | | | | | | | | |   (89)  all_58_10 = e1
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (15), (26), (33), (43), (47), (54),
% 242.89/49.39  | | | | | | | | | | | | |            (74), (89) are inconsistent by sub-proof #1618.
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | End of split
% 242.89/49.39  | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | Case 2:
% 242.89/49.39  | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | |   (90)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 242.89/49.39  | | | | | | | | | | | |           & op(e3, e0) = e2)
% 242.89/49.39  | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | BETA: splitting (90) gives:
% 242.89/49.39  | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | Case 1:
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | |   (91)  all_58_4 = e2 & op(e3, e1) = e2
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | ALPHA: (91) implies:
% 242.89/49.39  | | | | | | | | | | | | |   (92)  all_58_4 = e2
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | REF_CLOSE: (26), (60), (92) are inconsistent by sub-proof
% 242.89/49.39  | | | | | | | | | | | | |            #1902.
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | Case 2:
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | |   (93)  all_58_9 = e2 & op(e3, e0) = e2
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | ALPHA: (93) implies:
% 242.89/49.39  | | | | | | | | | | | | |   (94)  all_58_9 = e2
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | | REF_CLOSE: (8), (74), (94) are inconsistent by sub-proof
% 242.89/49.39  | | | | | | | | | | | | |            #1660.
% 242.89/49.39  | | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | | End of split
% 242.89/49.39  | | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | | End of split
% 242.89/49.39  | | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | End of split
% 242.89/49.39  | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | Case 2:
% 242.89/49.39  | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | |   (95)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2
% 242.89/49.39  | | | | | | | | | |           & op(e0, e0) = e2)
% 242.89/49.39  | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | | REF_CLOSE: (21), (26), (33), (54), (95) are inconsistent by
% 242.89/49.39  | | | | | | | | | |            sub-proof #958.
% 242.89/49.39  | | | | | | | | | | 
% 242.89/49.39  | | | | | | | | | End of split
% 242.89/49.39  | | | | | | | | | 
% 242.89/49.39  | | | | | | | | End of split
% 242.89/49.39  | | | | | | | | 
% 242.89/49.39  | | | | | | | End of split
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | End of split
% 242.89/49.39  | | | | | | 
% 242.89/49.39  | | | | | Case 2:
% 242.89/49.39  | | | | | | 
% 242.89/49.39  | | | | | |   (96)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3,
% 242.89/49.39  | | | | | |             e0) = e1)
% 242.89/49.39  | | | | | | 
% 242.89/49.39  | | | | | | BETA: splitting (96) gives:
% 242.89/49.39  | | | | | | 
% 242.89/49.39  | | | | | | Case 1:
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | |   (97)  all_58_4 = e1 & op(e3, e1) = e1
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | | REF_CLOSE: (15), (60), (97) are inconsistent by sub-proof #2042.
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | Case 2:
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | |   (98)  all_58_9 = e1 & op(e3, e0) = e1
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | | ALPHA: (98) implies:
% 242.89/49.39  | | | | | | |   (99)  all_58_9 = e1
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | | REF_CLOSE: (1), (6), (8), (21), (23), (26), (33), (46), (47),
% 242.89/49.39  | | | | | | |            (49), (54), (99) are inconsistent by sub-proof #1740.
% 242.89/49.39  | | | | | | | 
% 242.89/49.39  | | | | | | End of split
% 242.89/49.39  | | | | | | 
% 242.89/49.39  | | | | | End of split
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | Case 2:
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | |   (100)  all_58_5 = e3 & op(e2, e1) = e3
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | | REF_CLOSE: (25), (42), (46), (100) are inconsistent by sub-proof
% 242.89/49.39  | | | | |            #1822.
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | End of split
% 242.89/49.39  | | | | 
% 242.89/49.39  | | | Case 2:
% 242.89/49.39  | | | | 
% 242.89/49.39  | | | |   (101)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0,
% 242.89/49.39  | | | |              e1) = e3)
% 242.89/49.39  | | | | 
% 242.89/49.39  | | | | BETA: splitting (101) gives:
% 242.89/49.39  | | | | 
% 242.89/49.39  | | | | Case 1:
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | |   (102)  all_58_8 = e3 & op(e1, e1) = e3
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | | REF_CLOSE: (9), (24), (46), (102) are inconsistent by sub-proof #2092.
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | Case 2:
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | |   (103)  all_58_14 = e3 & op(e0, e1) = e3
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | | ALPHA: (103) implies:
% 242.89/49.39  | | | | |   (104)  all_58_14 = e3
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | | REF_CLOSE: (6), (8), (23), (26), (33), (49), (52), (54), (57), (104)
% 242.89/49.39  | | | | |            are inconsistent by sub-proof #1863.
% 242.89/49.39  | | | | | 
% 242.89/49.39  | | | | End of split
% 242.89/49.39  | | | | 
% 242.89/49.39  | | | End of split
% 242.89/49.39  | | | 
% 242.89/49.39  | | Case 2:
% 242.89/49.39  | | | 
% 242.89/49.39  | | |   (105)  all_58_13 = e3 & op(e0, e2) = e3
% 242.89/49.39  | | | 
% 242.89/49.39  | | | REF_CLOSE: (14), (40), (46), (105) are inconsistent by sub-proof #1919.
% 242.89/49.39  | | | 
% 242.89/49.39  | | End of split
% 242.89/49.39  | | 
% 242.89/49.39  | Case 2:
% 242.89/49.39  | | 
% 242.89/49.39  | |   (106)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 242.89/49.39  | |            e3)
% 242.89/49.39  | | 
% 242.89/49.39  | | BETA: splitting (106) gives:
% 242.89/49.39  | | 
% 242.89/49.39  | | Case 1:
% 242.89/49.39  | | | 
% 242.89/49.39  | | |   (107)  all_58_14 = e3 & op(e0, e1) = e3
% 242.89/49.39  | | | 
% 242.89/49.39  | | | ALPHA: (107) implies:
% 242.89/49.39  | | |   (108)  all_58_14 = e3
% 242.89/49.39  | | |   (109)  op(e0, e1) = e3
% 242.89/49.39  | | | 
% 242.89/49.39  | | | REF_CLOSE: (1), (2), (3), (5), (7), (9), (10), (11), (12), (13), (16),
% 242.89/49.39  | | |            (17), (18), (19), (20), (21), (22), (23), (25), (27), (28),
% 242.89/49.39  | | |            (29), (30), (31), (32), (34), (35), (37), (39), (41), (44),
% 242.89/49.39  | | |            (45), (46), (48), (50), (51), (53), (108), (109) are
% 242.89/49.39  | | |            inconsistent by sub-proof #951.
% 242.89/49.39  | | | 
% 242.89/49.39  | | Case 2:
% 242.89/49.39  | | | 
% 242.89/49.39  | | |   (110)  all_58_15 = e3 & op(e0, e0) = e3
% 242.89/49.39  | | | 
% 242.89/49.39  | | | ALPHA: (110) implies:
% 242.89/49.39  | | |   (111)  all_58_15 = e3
% 242.89/49.39  | | | 
% 242.89/49.39  | | | REF_CLOSE: (15), (33), (111) are inconsistent by sub-proof #2249.
% 242.89/49.39  | | | 
% 242.89/49.39  | | End of split
% 242.89/49.39  | | 
% 242.89/49.39  | End of split
% 242.89/49.39  | 
% 242.89/49.39  End of proof
% 242.89/49.39  
% 242.89/49.39  Sub-proof #951 shows that the following formulas are inconsistent:
% 242.89/49.39  ----------------------------------------------------------------
% 242.89/49.39    (1)  op(e0, e0) = e1
% 242.89/49.39    (2)  op(e2, e2) = e3
% 242.89/49.39    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.89/49.39         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.89/49.39    (4)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 242.89/49.39           op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 242.89/49.39             e2) & op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.89/49.39    (5)  op(e0, e1) = all_52_11
% 242.89/49.39    (6)  op(e0, e1) = e3
% 242.89/49.39    (7)  op(e1, e1) = all_6_2
% 242.89/49.39    (8)   ~ (all_52_1 = all_52_2)
% 242.89/49.39    (9)  op(e1, e0) = all_52_14
% 242.89/49.39    (10)   ~ (all_52_13 = e1)
% 242.89/49.39    (11)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.89/49.39            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 242.89/49.39              e1) = all_20_1 & $i(all_20_1))
% 242.89/49.39    (12)   ~ (all_52_12 = e1)
% 242.89/49.39    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.89/49.39          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.89/49.39    (14)   ~ (all_52_12 = all_52_14)
% 242.89/49.39    (15)  all_58_3 = e3
% 242.89/49.39    (16)   ~ (all_52_12 = all_52_13)
% 242.89/49.39    (17)  all_58_11 = e3
% 242.89/49.40    (18)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 242.89/49.40    (19)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.89/49.40              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.89/49.40                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.89/49.40                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.89/49.40    (20)  op(e2, e1) = all_52_9
% 242.89/49.40    (21)  op(e1, e0) = e3
% 242.89/49.40    (22)   ~ (all_52_14 = e1)
% 242.89/49.40    (23)   ~ (all_6_2 = e0)
% 242.89/49.40    (24)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.89/49.40            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.89/49.40            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.89/49.40            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.89/49.40            op(e0, all_56_31) = e0)
% 242.89/49.40    (25)  all_56_31 = e1
% 242.89/49.40    (26)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 242.89/49.40    (27)  op(e3, e0) = all_52_12
% 242.89/49.40    (28)  op(e2, e3) = all_52_1
% 242.89/49.40    (29)  all_34_2 = e1
% 242.89/49.40    (30)  all_54_7 = all_52_13
% 242.89/49.40    (31)   ~ (all_52_13 = all_52_14)
% 242.91/49.40    (32)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.91/49.40          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.91/49.40    (33)  all_54_3 = all_52_12
% 242.91/49.40    (34)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.91/49.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.91/49.40    (35)  all_58_14 = e3
% 242.91/49.40    (36)  op(e1, e3) = all_52_2
% 242.91/49.40    (37)  op(e3, e3) = e3
% 242.91/49.40    (38)  op(e2, e0) = all_52_13
% 242.91/49.40    (39)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.91/49.40          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.91/49.40  
% 242.91/49.40  Begin of proof
% 242.91/49.40  | 
% 242.91/49.40  | GROUND_INST: instantiating (34) with all_52_11, e3, e1, e0, simplifying with
% 242.91/49.40  |              (5), (6) gives:
% 242.91/49.40  |   (40)  all_52_11 = e3
% 242.91/49.40  | 
% 242.91/49.40  | GROUND_INST: instantiating (34) with all_52_14, e3, e0, e1, simplifying with
% 242.91/49.40  |              (9), (21) gives:
% 242.91/49.40  |   (41)  all_52_14 = e3
% 242.91/49.40  | 
% 242.91/49.40  | REDUCE: (14), (41) imply:
% 242.91/49.40  |   (42)   ~ (all_52_12 = e3)
% 242.91/49.40  | 
% 242.91/49.40  | REDUCE: (31), (41) imply:
% 242.91/49.40  |   (43)   ~ (all_52_13 = e3)
% 242.91/49.40  | 
% 242.91/49.40  | REDUCE: (22), (41) imply:
% 242.91/49.40  |   (44)   ~ (e3 = e1)
% 242.91/49.40  | 
% 242.91/49.40  | BETA: splitting (4) gives:
% 242.91/49.40  | 
% 242.91/49.40  | Case 1:
% 242.91/49.40  | | 
% 242.91/49.40  | |   (45)   ~ (all_34_2 = e1)
% 242.91/49.40  | | 
% 242.91/49.40  | | REDUCE: (29), (45) imply:
% 242.91/49.40  | |   (46)  $false
% 242.91/49.40  | | 
% 242.91/49.40  | | CLOSE: (46) is inconsistent.
% 242.91/49.40  | | 
% 242.91/49.40  | Case 2:
% 242.91/49.40  | | 
% 242.91/49.40  | |   (47)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 242.91/49.40  | |           all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) &
% 242.91/49.40  | |           op(e0, e1) = all_34_1 & $i(all_34_1))
% 242.91/49.40  | | 
% 242.91/49.40  | | BETA: splitting (47) gives:
% 242.91/49.40  | | 
% 242.91/49.40  | | Case 1:
% 242.91/49.40  | | | 
% 242.91/49.40  | | |   (48)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 242.91/49.40  | | |         all_34_1 & $i(all_34_0) & $i(all_34_1)
% 242.91/49.40  | | | 
% 242.91/49.40  | | | ALPHA: (48) implies:
% 242.91/49.40  | | |   (49)  op(e0, e1) = all_34_1
% 242.91/49.40  | | | 
% 242.91/49.40  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (11), (12), (13), (15),
% 242.91/49.40  | | |            (16), (17), (18), (19), (20), (21), (23), (24), (25), (26),
% 242.91/49.40  | | |            (27), (28), (30), (32), (33), (34), (35), (36), (37), (38),
% 242.91/49.40  | | |            (39), (42), (43), (44), (49) are inconsistent by sub-proof
% 242.91/49.40  | | |            #952.
% 242.91/49.40  | | | 
% 242.91/49.40  | | Case 2:
% 242.91/49.40  | | | 
% 242.91/49.40  | | |   (50)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 242.91/49.40  | | | 
% 242.91/49.40  | | | ALPHA: (50) implies:
% 242.91/49.40  | | |   (51)  op(e0, e1) = all_34_1
% 242.91/49.40  | | | 
% 242.91/49.40  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (11), (12), (13), (15),
% 242.91/49.40  | | |            (16), (17), (18), (19), (20), (21), (23), (24), (25), (26),
% 242.91/49.40  | | |            (27), (28), (30), (32), (33), (34), (35), (36), (37), (38),
% 242.91/49.40  | | |            (39), (42), (43), (44), (51) are inconsistent by sub-proof
% 242.91/49.40  | | |            #952.
% 242.91/49.40  | | | 
% 242.91/49.40  | | End of split
% 242.91/49.40  | | 
% 242.91/49.40  | End of split
% 242.91/49.40  | 
% 242.91/49.40  End of proof
% 242.91/49.40  
% 242.91/49.40  Sub-proof #952 shows that the following formulas are inconsistent:
% 242.91/49.40  ----------------------------------------------------------------
% 242.91/49.40    (1)  op(e0, e0) = e1
% 242.91/49.40    (2)  op(e2, e2) = e3
% 242.91/49.40    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.91/49.40         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.91/49.40    (4)  op(e0, e1) = e3
% 242.91/49.40    (5)  op(e1, e1) = all_6_2
% 242.91/49.40    (6)   ~ (all_52_1 = all_52_2)
% 242.91/49.40    (7)  op(e0, e1) = all_34_1
% 242.91/49.40    (8)   ~ (all_52_13 = e1)
% 242.91/49.40    (9)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) = all_20_1
% 242.91/49.40           & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1) =
% 242.91/49.40           all_20_1 & $i(all_20_1))
% 242.91/49.40    (10)   ~ (e3 = e1)
% 242.91/49.40    (11)   ~ (all_52_12 = e1)
% 242.91/49.40    (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.91/49.40          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.91/49.40    (13)  all_58_3 = e3
% 242.91/49.40    (14)   ~ (all_52_12 = all_52_13)
% 242.91/49.40    (15)  all_58_11 = e3
% 242.91/49.40    (16)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 242.91/49.40    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.91/49.40              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.91/49.40                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.91/49.40                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.91/49.40    (18)  op(e2, e1) = all_52_9
% 242.91/49.40    (19)  op(e1, e0) = e3
% 242.91/49.40    (20)   ~ (all_6_2 = e0)
% 242.91/49.40    (21)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.91/49.40            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.91/49.40            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.91/49.40            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.91/49.40            op(e0, all_56_31) = e0)
% 242.91/49.40    (22)  all_56_31 = e1
% 242.91/49.40    (23)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 242.91/49.40    (24)  op(e3, e0) = all_52_12
% 242.91/49.40    (25)  op(e2, e3) = all_52_1
% 242.91/49.40    (26)  all_54_7 = all_52_13
% 242.91/49.40    (27)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.91/49.40          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.91/49.40    (28)  all_54_3 = all_52_12
% 242.91/49.40    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.91/49.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.91/49.40    (30)  all_58_14 = e3
% 242.91/49.40    (31)  op(e1, e3) = all_52_2
% 242.91/49.40    (32)   ~ (all_52_12 = e3)
% 242.91/49.40    (33)  op(e3, e3) = e3
% 242.91/49.40    (34)   ~ (all_52_13 = e3)
% 242.91/49.40    (35)  op(e2, e0) = all_52_13
% 242.91/49.40    (36)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.91/49.40          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.91/49.40  
% 242.91/49.40  Begin of proof
% 242.91/49.40  | 
% 242.91/49.40  | BETA: splitting (9) gives:
% 242.91/49.40  | 
% 242.91/49.40  | Case 1:
% 242.91/49.40  | | 
% 242.91/49.40  | |   (37)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 242.91/49.40  | |         all_20_1 & $i(all_20_0) & $i(all_20_1)
% 242.91/49.40  | | 
% 242.91/49.40  | | ALPHA: (37) implies:
% 242.91/49.40  | |   (38)   ~ (all_20_0 = e2)
% 242.91/49.40  | |   (39)  op(e0, e1) = all_20_1
% 242.91/49.40  | |   (40)  op(all_20_1, e0) = all_20_0
% 242.91/49.40  | | 
% 242.91/49.40  | | GROUND_INST: instantiating (29) with e3, all_34_1, e1, e0, simplifying with
% 242.91/49.40  | |              (4), (7) gives:
% 242.91/49.40  | |   (41)  all_34_1 = e3
% 242.91/49.40  | | 
% 242.91/49.40  | | GROUND_INST: instantiating (29) with all_20_1, all_34_1, e1, e0, simplifying
% 242.91/49.40  | |              with (7), (39) gives:
% 242.91/49.40  | |   (42)  all_34_1 = all_20_1
% 242.91/49.40  | | 
% 242.91/49.40  | | COMBINE_EQS: (41), (42) imply:
% 242.91/49.40  | |   (43)  all_20_1 = e3
% 242.91/49.40  | | 
% 242.91/49.40  | | SIMP: (43) implies:
% 242.91/49.40  | |   (44)  all_20_1 = e3
% 242.91/49.40  | | 
% 242.91/49.40  | | REDUCE: (40), (44) imply:
% 242.91/49.40  | |   (45)  op(e3, e0) = all_20_0
% 242.91/49.40  | | 
% 242.91/49.40  | | GROUND_INST: instantiating (29) with all_52_12, all_20_0, e0, e3,
% 242.91/49.40  | |              simplifying with (24), (45) gives:
% 242.91/49.40  | |   (46)  all_52_12 = all_20_0
% 242.91/49.40  | | 
% 242.91/49.40  | | COMBINE_EQS: (28), (46) imply:
% 242.91/49.40  | |   (47)  all_54_3 = all_20_0
% 242.91/49.40  | | 
% 242.91/49.40  | | REDUCE: (14), (46) imply:
% 242.91/49.40  | |   (48)   ~ (all_52_13 = all_20_0)
% 242.91/49.40  | | 
% 242.91/49.40  | | SIMP: (48) implies:
% 242.91/49.40  | |   (49)   ~ (all_52_13 = all_20_0)
% 242.91/49.40  | | 
% 242.91/49.40  | | REDUCE: (32), (46) imply:
% 242.91/49.40  | |   (50)   ~ (all_20_0 = e3)
% 242.91/49.40  | | 
% 242.91/49.40  | | REDUCE: (11), (46) imply:
% 242.91/49.40  | |   (51)   ~ (all_20_0 = e1)
% 242.91/49.40  | | 
% 242.91/49.40  | | BETA: splitting (16) gives:
% 242.91/49.40  | | 
% 242.91/49.40  | | Case 1:
% 242.91/49.40  | | | 
% 242.91/49.40  | | |   (52)  all_54_3 = e3
% 242.91/49.40  | | | 
% 242.91/49.40  | | | REF_CLOSE: (47), (50), (52) are inconsistent by sub-proof #957.
% 242.91/49.40  | | | 
% 242.91/49.40  | | Case 2:
% 242.91/49.40  | | | 
% 242.91/49.40  | | |   (53)   ~ (all_54_3 = e3)
% 242.91/49.40  | | |   (54)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 242.91/49.40  | | | 
% 242.91/49.40  | | | BETA: splitting (54) gives:
% 242.91/49.40  | | | 
% 242.91/49.40  | | | Case 1:
% 242.91/49.40  | | | | 
% 242.91/49.40  | | | |   (55)  all_54_3 = e2
% 242.91/49.40  | | | | 
% 242.91/49.40  | | | | COMBINE_EQS: (47), (55) imply:
% 242.91/49.40  | | | |   (56)  all_20_0 = e2
% 242.91/49.40  | | | | 
% 242.91/49.40  | | | | SIMP: (56) implies:
% 242.91/49.40  | | | |   (57)  all_20_0 = e2
% 242.91/49.40  | | | | 
% 242.91/49.40  | | | | REDUCE: (38), (57) imply:
% 242.91/49.40  | | | |   (58)  $false
% 242.91/49.40  | | | | 
% 242.91/49.40  | | | | CLOSE: (58) is inconsistent.
% 242.91/49.40  | | | | 
% 242.91/49.40  | | | Case 2:
% 242.91/49.40  | | | | 
% 242.91/49.40  | | | |   (59)  all_54_3 = e1 | all_54_3 = e0
% 242.91/49.40  | | | | 
% 242.91/49.40  | | | | BETA: splitting (59) gives:
% 242.91/49.40  | | | | 
% 242.91/49.40  | | | | Case 1:
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | |   (60)  all_54_3 = e1
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | | COMBINE_EQS: (47), (60) imply:
% 242.91/49.40  | | | | |   (61)  all_20_0 = e1
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | | SIMP: (61) implies:
% 242.91/49.40  | | | | |   (62)  all_20_0 = e1
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | | REDUCE: (51), (62) imply:
% 242.91/49.40  | | | | |   (63)  $false
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | | CLOSE: (63) is inconsistent.
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | Case 2:
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | |   (64)  all_54_3 = e0
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | | COMBINE_EQS: (47), (64) imply:
% 242.91/49.40  | | | | |   (65)  all_20_0 = e0
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | | SIMP: (65) implies:
% 242.91/49.40  | | | | |   (66)  all_20_0 = e0
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | | REDUCE: (49), (66) imply:
% 242.91/49.40  | | | | |   (67)   ~ (all_52_13 = e0)
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | | REDUCE: (50), (66) imply:
% 242.91/49.40  | | | | |   (68)   ~ (e3 = e0)
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | | SIMP: (68) implies:
% 242.91/49.40  | | | | |   (69)   ~ (e3 = e0)
% 242.91/49.40  | | | | | 
% 242.91/49.40  | | | | | REDUCE: (51), (66) imply:
% 242.91/49.41  | | | | |   (70)   ~ (e1 = e0)
% 242.91/49.41  | | | | | 
% 242.91/49.41  | | | | | SIMP: (70) implies:
% 242.91/49.41  | | | | |   (71)   ~ (e1 = e0)
% 242.91/49.41  | | | | | 
% 242.91/49.41  | | | | | BETA: splitting (23) gives:
% 242.91/49.41  | | | | | 
% 242.91/49.41  | | | | | Case 1:
% 242.91/49.41  | | | | | | 
% 242.91/49.41  | | | | | |   (72)  all_54_7 = e3
% 242.91/49.41  | | | | | | 
% 242.91/49.41  | | | | | | COMBINE_EQS: (26), (72) imply:
% 242.91/49.41  | | | | | |   (73)  all_52_13 = e3
% 242.91/49.41  | | | | | | 
% 242.91/49.41  | | | | | | REDUCE: (34), (73) imply:
% 242.91/49.41  | | | | | |   (74)  $false
% 242.91/49.41  | | | | | | 
% 242.91/49.41  | | | | | | CLOSE: (74) is inconsistent.
% 242.91/49.41  | | | | | | 
% 242.91/49.41  | | | | | Case 2:
% 242.91/49.41  | | | | | | 
% 242.91/49.41  | | | | | |   (75)   ~ (all_54_7 = e3)
% 242.91/49.41  | | | | | |   (76)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 242.91/49.41  | | | | | | 
% 242.91/49.41  | | | | | | BETA: splitting (76) gives:
% 242.91/49.41  | | | | | | 
% 242.91/49.41  | | | | | | Case 1:
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | |   (77)  all_54_7 = e2
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | | COMBINE_EQS: (26), (77) imply:
% 242.91/49.41  | | | | | | |   (78)  all_52_13 = e2
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | | REDUCE: (34), (78) imply:
% 242.91/49.41  | | | | | | |   (79)   ~ (e3 = e2)
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | | SIMP: (79) implies:
% 242.91/49.41  | | | | | | |   (80)   ~ (e3 = e2)
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | | REDUCE: (8), (78) imply:
% 242.91/49.41  | | | | | | |   (81)   ~ (e2 = e1)
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | | REDUCE: (67), (78) imply:
% 242.91/49.41  | | | | | | |   (82)   ~ (e2 = e0)
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | | REDUCE: (35), (78) imply:
% 242.91/49.41  | | | | | | |   (83)  op(e2, e0) = e2
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | | BETA: splitting (12) gives:
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | | Case 1:
% 242.91/49.41  | | | | | | | | 
% 242.91/49.41  | | | | | | | |   (84)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 242.91/49.41  | | | | | | | |           op(e2, e1) = e0)
% 242.91/49.41  | | | | | | | | 
% 242.91/49.41  | | | | | | | | BETA: splitting (84) gives:
% 242.91/49.41  | | | | | | | | 
% 242.91/49.41  | | | | | | | | Case 1:
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | |   (85)  all_58_4 = e0 & op(e3, e1) = e0
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | ALPHA: (85) implies:
% 242.91/49.41  | | | | | | | | |   (86)  all_58_4 = e0
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | BETA: splitting (27) gives:
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | Case 1:
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | |   (87)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 &
% 242.91/49.41  | | | | | | | | | |           op(e3, e2) = e1)
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | BETA: splitting (87) gives:
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | Case 1:
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | |   (88)  all_58_0 = e1 & op(e3, e3) = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | ALPHA: (88) implies:
% 242.91/49.41  | | | | | | | | | | |   (89)  op(e3, e3) = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | REF_CLOSE: (10), (29), (33), (89) are inconsistent by
% 242.91/49.41  | | | | | | | | | | |            sub-proof #1578.
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | Case 2:
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | |   (90)  all_58_1 = e1 & op(e3, e2) = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | ALPHA: (90) implies:
% 242.91/49.41  | | | | | | | | | | |   (91)  all_58_1 = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | BETA: splitting (17) gives:
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | Case 1:
% 242.91/49.41  | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | |   (92)  all_58_15 = e0 & op(e0, e0) = e0
% 242.91/49.41  | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | ALPHA: (92) implies:
% 242.91/49.41  | | | | | | | | | | | |   (93)  op(e0, e0) = e0
% 242.91/49.41  | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | REF_CLOSE: (1), (29), (71), (93) are inconsistent by
% 242.91/49.41  | | | | | | | | | | | |            sub-proof #2274.
% 242.91/49.41  | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | Case 2:
% 242.91/49.41  | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | |   (94)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.91/49.41  | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.91/49.41  | | | | | | | | | | | |             op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 242.91/49.41  | | | | | | | | | | | |               e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.91/49.41  | | | | | | | | | | | |             e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.91/49.41  | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | ALPHA: (94) implies:
% 242.91/49.41  | | | | | | | | | | | |   (95)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.91/49.41  | | | | | | | | | | | |           e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 242.91/49.41  | | | | | | | | | | | |             e0) = e0)
% 242.91/49.41  | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | BETA: splitting (95) gives:
% 242.91/49.41  | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | Case 1:
% 242.91/49.41  | | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | |   (96)  all_58_9 = e0 & op(e3, e0) = e0
% 242.91/49.41  | | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | | ALPHA: (96) implies:
% 242.91/49.41  | | | | | | | | | | | | |   (97)  all_58_9 = e0
% 242.91/49.41  | | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | | REF_CLOSE: (3), (29), (33), (80), (81), (82), (86), (91),
% 242.91/49.41  | | | | | | | | | | | | |            (97) are inconsistent by sub-proof #956.
% 242.91/49.41  | | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | Case 2:
% 242.91/49.41  | | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | |   (98)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 242.91/49.41  | | | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 242.91/49.41  | | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | | REF_CLOSE: (15), (29), (69), (82), (83), (98) are
% 242.91/49.41  | | | | | | | | | | | | |            inconsistent by sub-proof #955.
% 242.91/49.41  | | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | | End of split
% 242.91/49.41  | | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | End of split
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | End of split
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | Case 2:
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | |   (99)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 &
% 242.91/49.41  | | | | | | | | | |           op(e3, e0) = e1)
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | BETA: splitting (99) gives:
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | Case 1:
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | |   (100)  all_58_4 = e1 & op(e3, e1) = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | REF_CLOSE: (71), (86), (100) are inconsistent by sub-proof
% 242.91/49.41  | | | | | | | | | | |            #2047.
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | Case 2:
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | |   (101)  all_58_9 = e1 & op(e3, e0) = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | ALPHA: (101) implies:
% 242.91/49.41  | | | | | | | | | | |   (102)  all_58_9 = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | REF_CLOSE: (1), (15), (17), (29), (69), (71), (82), (83),
% 242.91/49.41  | | | | | | | | | | |            (102) are inconsistent by sub-proof #1742.
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | End of split
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | End of split
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | Case 2:
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | |   (103)  all_58_5 = e0 & op(e2, e1) = e0
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | ALPHA: (103) implies:
% 242.91/49.41  | | | | | | | | |   (104)  op(e2, e1) = e0
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | BETA: splitting (36) gives:
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | Case 1:
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | |   (105)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 242.91/49.41  | | | | | | | | | |            & op(e2, e2) = e1)
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | BETA: splitting (105) gives:
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | Case 1:
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | |   (106)  all_58_2 = e1 & op(e2, e3) = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (15), (17), (19), (21), (22),
% 242.91/49.41  | | | | | | | | | | |            (24), (25), (29), (31), (32), (69), (71), (80),
% 242.91/49.41  | | | | | | | | | | |            (82), (83), (106) are inconsistent by sub-proof
% 242.91/49.41  | | | | | | | | | | |            #953.
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | Case 2:
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | |   (107)  all_58_3 = e1 & op(e2, e2) = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | REF_CLOSE: (10), (13), (107) are inconsistent by sub-proof
% 242.91/49.41  | | | | | | | | | | |            #2197.
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | End of split
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | Case 2:
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | |   (108)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1
% 242.91/49.41  | | | | | | | | | |            & op(e2, e0) = e1)
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | BETA: splitting (108) gives:
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | Case 1:
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | |   (109)  all_58_5 = e1 & op(e2, e1) = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | ALPHA: (109) implies:
% 242.91/49.41  | | | | | | | | | | |   (110)  op(e2, e1) = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | REF_CLOSE: (18), (29), (71), (104), (110) are inconsistent by
% 242.91/49.41  | | | | | | | | | | |            sub-proof #2165.
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | Case 2:
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | |   (111)  all_58_10 = e1 & op(e2, e0) = e1
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | | REF_CLOSE: (8), (29), (35), (111) are inconsistent by
% 242.91/49.41  | | | | | | | | | | |            sub-proof #2277.
% 242.91/49.41  | | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | | End of split
% 242.91/49.41  | | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | End of split
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | End of split
% 242.91/49.41  | | | | | | | | 
% 242.91/49.41  | | | | | | | Case 2:
% 242.91/49.41  | | | | | | | | 
% 242.91/49.41  | | | | | | | |   (112)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 242.91/49.41  | | | | | | | |            op(e0, e1) = e0)
% 242.91/49.41  | | | | | | | | 
% 242.91/49.41  | | | | | | | | BETA: splitting (112) gives:
% 242.91/49.41  | | | | | | | | 
% 242.91/49.41  | | | | | | | | Case 1:
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | |   (113)  all_58_8 = e0 & op(e1, e1) = e0
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | REF_CLOSE: (5), (20), (29), (113) are inconsistent by
% 242.91/49.41  | | | | | | | | |            sub-proof #1833.
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | Case 2:
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | |   (114)  all_58_14 = e0 & op(e0, e1) = e0
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | | REF_CLOSE: (30), (69), (114) are inconsistent by sub-proof
% 242.91/49.41  | | | | | | | | |            #2081.
% 242.91/49.41  | | | | | | | | | 
% 242.91/49.41  | | | | | | | | End of split
% 242.91/49.41  | | | | | | | | 
% 242.91/49.41  | | | | | | | End of split
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | Case 2:
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | |   (115)  all_54_7 = e1 | all_54_7 = e0
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | | REF_CLOSE: (8), (26), (67), (115) are inconsistent by sub-proof
% 242.91/49.41  | | | | | | |            #2293.
% 242.91/49.41  | | | | | | | 
% 242.91/49.41  | | | | | | End of split
% 242.91/49.41  | | | | | | 
% 242.91/49.41  | | | | | End of split
% 242.91/49.41  | | | | | 
% 242.91/49.41  | | | | End of split
% 242.91/49.41  | | | | 
% 242.91/49.41  | | | End of split
% 242.91/49.41  | | | 
% 242.91/49.41  | | End of split
% 242.91/49.41  | | 
% 242.91/49.41  | Case 2:
% 242.91/49.41  | | 
% 242.91/49.41  | |   (116)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 & $i(all_20_1)
% 242.91/49.41  | | 
% 242.91/49.41  | | ALPHA: (116) implies:
% 242.91/49.41  | |   (117)   ~ (all_20_1 = e3)
% 242.91/49.41  | |   (118)  op(e0, e1) = all_20_1
% 242.91/49.41  | | 
% 242.91/49.41  | | REF_CLOSE: (4), (7), (29), (117), (118) are inconsistent by sub-proof #1806.
% 242.91/49.41  | | 
% 242.91/49.41  | End of split
% 242.91/49.41  | 
% 242.91/49.41  End of proof
% 242.91/49.41  
% 242.91/49.41  Sub-proof #953 shows that the following formulas are inconsistent:
% 242.91/49.41  ----------------------------------------------------------------
% 242.91/49.41    (1)  op(e0, e0) = e1
% 242.91/49.41    (2)  op(e2, e2) = e3
% 242.91/49.41    (3)   ~ (e3 = e0)
% 242.91/49.41    (4)   ~ (e2 = e0)
% 242.91/49.41    (5)  op(e0, e1) = e3
% 242.91/49.41    (6)   ~ (all_52_1 = all_52_2)
% 242.91/49.41    (7)  all_58_2 = e1 & op(e2, e3) = e1
% 242.91/49.41    (8)  all_58_11 = e3
% 242.91/49.41    (9)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.91/49.41             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.91/49.41               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.91/49.41               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.91/49.41    (10)   ~ (e3 = e2)
% 242.91/49.41    (11)  op(e1, e0) = e3
% 242.91/49.41    (12)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.91/49.41            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 242.91/49.41            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 242.91/49.41            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 242.91/49.41            op(e0, all_56_31) = e0)
% 242.91/49.41    (13)  op(e2, e0) = e2
% 242.91/49.41    (14)  all_56_31 = e1
% 242.91/49.41    (15)  op(e3, e0) = all_52_12
% 242.91/49.41    (16)  op(e2, e3) = all_52_1
% 242.91/49.41    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.91/49.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.91/49.41    (18)  op(e1, e3) = all_52_2
% 242.91/49.41    (19)   ~ (all_52_12 = e3)
% 242.91/49.41    (20)   ~ (e1 = e0)
% 242.91/49.41  
% 242.91/49.41  Begin of proof
% 242.91/49.41  | 
% 242.91/49.41  | ALPHA: (7) implies:
% 242.91/49.41  |   (21)  op(e2, e3) = e1
% 242.91/49.41  | 
% 242.91/49.41  | BETA: splitting (12) gives:
% 242.91/49.41  | 
% 242.91/49.41  | Case 1:
% 242.91/49.41  | | 
% 242.91/49.41  | |   (22)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.91/49.41  | |           $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 242.91/49.41  | |             e0) = all_56_27 & $i(all_56_27))
% 242.91/49.41  | | 
% 242.91/49.41  | | BETA: splitting (22) gives:
% 242.91/49.41  | | 
% 242.91/49.41  | | Case 1:
% 242.91/49.41  | | | 
% 242.91/49.41  | | |   (23)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 242.91/49.41  | | |         $i(all_56_25)
% 242.91/49.41  | | | 
% 242.91/49.41  | | | ALPHA: (23) implies:
% 242.91/49.41  | | |   (24)  op(e3, e0) = all_56_25
% 242.91/49.41  | | |   (25)  op(e3, all_56_25) = e3
% 242.91/49.41  | | | 
% 242.91/49.41  | | | REF_CLOSE: (1), (3), (4), (8), (9), (13), (15), (17), (19), (20), (24),
% 242.91/49.41  | | |            (25) are inconsistent by sub-proof #1121.
% 242.91/49.41  | | | 
% 242.91/49.41  | | Case 2:
% 242.91/49.41  | | | 
% 242.91/49.41  | | |   (26)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 242.91/49.41  | | |         $i(all_56_27)
% 242.91/49.41  | | | 
% 242.91/49.41  | | | ALPHA: (26) implies:
% 242.91/49.41  | | |   (27)  op(e2, e0) = all_56_27
% 242.91/49.41  | | |   (28)  op(e2, all_56_27) = e2
% 242.91/49.41  | | | 
% 242.91/49.41  | | | REF_CLOSE: (2), (10), (13), (17), (27), (28) are inconsistent by sub-proof
% 242.91/49.41  | | |            #954.
% 242.91/49.41  | | | 
% 242.91/49.41  | | End of split
% 242.91/49.41  | | 
% 242.91/49.41  | Case 2:
% 242.91/49.41  | | 
% 242.91/49.41  | |   (29)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 242.91/49.41  | |           $i(all_56_29)) | (all_56_30 = e0 & op(e0, all_56_31) = e0)
% 242.91/49.41  | | 
% 242.91/49.41  | | BETA: splitting (29) gives:
% 242.91/49.41  | | 
% 242.91/49.41  | | Case 1:
% 242.91/49.41  | | | 
% 242.91/49.41  | | |   (30)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 242.91/49.41  | | |         $i(all_56_29)
% 242.91/49.41  | | | 
% 242.91/49.41  | | | ALPHA: (30) implies:
% 242.91/49.41  | | |   (31)  op(e1, e0) = all_56_29
% 242.91/49.41  | | |   (32)  op(e1, all_56_29) = e1
% 242.91/49.41  | | | 
% 242.91/49.41  | | | GROUND_INST: instantiating (17) with e3, all_56_29, e0, e1, simplifying
% 242.91/49.41  | | |              with (11), (31) gives:
% 242.91/49.41  | | |   (33)  all_56_29 = e3
% 242.91/49.41  | | | 
% 242.91/49.41  | | | GROUND_INST: instantiating (17) with all_52_1, e1, e3, e2, simplifying
% 242.91/49.41  | | |              with (16), (21) gives:
% 242.91/49.41  | | |   (34)  all_52_1 = e1
% 242.91/49.41  | | | 
% 242.91/49.41  | | | REDUCE: (6), (34) imply:
% 242.91/49.41  | | |   (35)   ~ (all_52_2 = e1)
% 242.91/49.41  | | | 
% 242.91/49.41  | | | SIMP: (35) implies:
% 242.91/49.41  | | |   (36)   ~ (all_52_2 = e1)
% 242.91/49.41  | | | 
% 242.91/49.41  | | | REDUCE: (32), (33) imply:
% 242.91/49.41  | | |   (37)  op(e1, e3) = e1
% 242.91/49.41  | | | 
% 242.91/49.41  | | | REF_CLOSE: (17), (18), (36), (37) are inconsistent by sub-proof #1948.
% 242.91/49.41  | | | 
% 242.91/49.41  | | Case 2:
% 242.91/49.41  | | | 
% 242.91/49.41  | | |   (38)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 242.91/49.41  | | | 
% 242.91/49.41  | | | ALPHA: (38) implies:
% 242.91/49.41  | | |   (39)  op(e0, all_56_31) = e0
% 242.91/49.41  | | | 
% 242.91/49.41  | | | REDUCE: (14), (39) imply:
% 242.91/49.41  | | |   (40)  op(e0, e1) = e0
% 242.91/49.41  | | | 
% 242.91/49.41  | | | REF_CLOSE: (3), (5), (17), (40) are inconsistent by sub-proof #2164.
% 242.91/49.41  | | | 
% 242.91/49.41  | | End of split
% 242.91/49.41  | | 
% 242.91/49.41  | End of split
% 242.91/49.41  | 
% 242.91/49.41  End of proof
% 242.91/49.41  
% 242.91/49.41  Sub-proof #954 shows that the following formulas are inconsistent:
% 242.91/49.41  ----------------------------------------------------------------
% 242.91/49.41    (1)  op(e2, e0) = all_56_27
% 242.91/49.41    (2)  op(e2, e2) = e3
% 242.91/49.41    (3)  op(e2, all_56_27) = e2
% 242.91/49.41    (4)   ~ (e3 = e2)
% 242.91/49.41    (5)  op(e2, e0) = e2
% 242.91/49.41    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.91/49.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.91/49.41  
% 242.91/49.41  Begin of proof
% 242.91/49.41  | 
% 242.91/49.41  | GROUND_INST: instantiating (6) with e2, all_56_27, e0, e2, simplifying with
% 242.91/49.41  |              (1), (5) gives:
% 242.91/49.41  |   (7)  all_56_27 = e2
% 242.91/49.41  | 
% 242.91/49.41  | REDUCE: (3), (7) imply:
% 242.91/49.41  |   (8)  op(e2, e2) = e2
% 242.91/49.41  | 
% 242.91/49.41  | GROUND_INST: instantiating (6) with e3, e2, e2, e2, simplifying with (2), (8)
% 242.91/49.41  |              gives:
% 242.91/49.41  |   (9)  e3 = e2
% 242.91/49.41  | 
% 242.91/49.41  | REDUCE: (4), (9) imply:
% 242.91/49.41  |   (10)  $false
% 242.91/49.41  | 
% 242.91/49.41  | CLOSE: (10) is inconsistent.
% 242.91/49.41  | 
% 242.91/49.41  End of proof
% 242.91/49.41  
% 242.91/49.41  Sub-proof #955 shows that the following formulas are inconsistent:
% 242.91/49.41  ----------------------------------------------------------------
% 242.91/49.41    (1)   ~ (e3 = e0)
% 242.91/49.41    (2)   ~ (e2 = e0)
% 242.91/49.41    (3)  all_58_11 = e3
% 242.91/49.41    (4)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.91/49.41    (5)  op(e2, e0) = e2
% 242.91/49.41    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.91/49.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.91/49.41  
% 242.91/49.41  Begin of proof
% 242.91/49.41  | 
% 242.91/49.41  | BETA: splitting (4) gives:
% 242.91/49.41  | 
% 242.91/49.41  | Case 1:
% 242.91/49.41  | | 
% 242.91/49.41  | |   (7)  all_58_10 = e0 & op(e2, e0) = e0
% 242.91/49.41  | | 
% 242.91/49.41  | | ALPHA: (7) implies:
% 242.91/49.41  | |   (8)  op(e2, e0) = e0
% 242.91/49.41  | | 
% 242.91/49.41  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2121.
% 242.91/49.41  | | 
% 242.91/49.41  | Case 2:
% 242.91/49.41  | | 
% 242.91/49.41  | |   (9)  all_58_11 = e0 & op(e1, e0) = e0
% 242.91/49.41  | | 
% 242.91/49.41  | | ALPHA: (9) implies:
% 242.91/49.41  | |   (10)  all_58_11 = e0
% 242.91/49.41  | | 
% 242.91/49.41  | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #1688.
% 242.91/49.41  | | 
% 242.91/49.41  | End of split
% 242.91/49.41  | 
% 242.91/49.41  End of proof
% 242.91/49.41  
% 242.91/49.41  Sub-proof #956 shows that the following formulas are inconsistent:
% 242.91/49.41  ----------------------------------------------------------------
% 242.91/49.41    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 242.91/49.41         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 242.91/49.41    (2)  all_58_1 = e1
% 242.91/49.41    (3)   ~ (e2 = e0)
% 242.91/49.41    (4)  all_58_9 = e0
% 242.91/49.41    (5)   ~ (e3 = e2)
% 242.91/49.41    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.91/49.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.91/49.41    (7)  op(e3, e3) = e3
% 242.91/49.41    (8)  all_58_4 = e0
% 242.91/49.41    (9)   ~ (e2 = e1)
% 242.91/49.41  
% 242.91/49.41  Begin of proof
% 242.91/49.41  | 
% 242.91/49.41  | BETA: splitting (1) gives:
% 242.91/49.41  | 
% 242.91/49.41  | Case 1:
% 242.91/49.41  | | 
% 242.91/49.41  | |   (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 242.91/49.41  | |           e2)
% 242.91/49.41  | | 
% 242.91/49.41  | | BETA: splitting (10) gives:
% 242.91/49.41  | | 
% 242.91/49.41  | | Case 1:
% 242.91/49.41  | | | 
% 242.94/49.41  | | |   (11)  all_58_0 = e2 & op(e3, e3) = e2
% 242.94/49.41  | | | 
% 242.94/49.41  | | | ALPHA: (11) implies:
% 242.94/49.41  | | |   (12)  op(e3, e3) = e2
% 242.94/49.41  | | | 
% 242.94/49.41  | | | REF_CLOSE: (5), (6), (7), (12) are inconsistent by sub-proof #2194.
% 242.94/49.41  | | | 
% 242.94/49.41  | | Case 2:
% 242.94/49.41  | | | 
% 242.94/49.41  | | |   (13)  all_58_1 = e2 & op(e3, e2) = e2
% 242.94/49.41  | | | 
% 242.94/49.41  | | | REF_CLOSE: (2), (9), (13) are inconsistent by sub-proof #1722.
% 242.94/49.41  | | | 
% 242.94/49.41  | | End of split
% 242.94/49.41  | | 
% 242.94/49.41  | Case 2:
% 242.94/49.41  | | 
% 242.94/49.41  | |   (14)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 242.94/49.41  | |           e2)
% 242.94/49.41  | | 
% 242.94/49.41  | | BETA: splitting (14) gives:
% 242.94/49.41  | | 
% 242.94/49.41  | | Case 1:
% 242.94/49.41  | | | 
% 242.94/49.42  | | |   (15)  all_58_4 = e2 & op(e3, e1) = e2
% 242.94/49.42  | | | 
% 242.94/49.42  | | | ALPHA: (15) implies:
% 242.94/49.42  | | |   (16)  all_58_4 = e2
% 242.94/49.42  | | | 
% 242.94/49.42  | | | REF_CLOSE: (3), (8), (16) are inconsistent by sub-proof #1666.
% 242.94/49.42  | | | 
% 242.94/49.42  | | Case 2:
% 242.94/49.42  | | | 
% 242.94/49.42  | | |   (17)  all_58_9 = e2 & op(e3, e0) = e2
% 242.94/49.42  | | | 
% 242.94/49.42  | | | REF_CLOSE: (3), (4), (17) are inconsistent by sub-proof #1655.
% 242.94/49.42  | | | 
% 242.94/49.42  | | End of split
% 242.94/49.42  | | 
% 242.94/49.42  | End of split
% 242.94/49.42  | 
% 242.94/49.42  End of proof
% 242.94/49.42  
% 242.94/49.42  Sub-proof #957 shows that the following formulas are inconsistent:
% 242.94/49.42  ----------------------------------------------------------------
% 242.94/49.42    (1)  all_54_3 = all_20_0
% 242.94/49.42    (2)  all_54_3 = e3
% 242.94/49.42    (3)   ~ (all_20_0 = e3)
% 242.94/49.42  
% 242.94/49.42  Begin of proof
% 242.94/49.42  | 
% 242.94/49.42  | COMBINE_EQS: (1), (2) imply:
% 242.94/49.42  |   (4)  all_20_0 = e3
% 242.94/49.42  | 
% 242.94/49.42  | SIMP: (4) implies:
% 242.94/49.42  |   (5)  all_20_0 = e3
% 242.94/49.42  | 
% 242.94/49.42  | REDUCE: (3), (5) imply:
% 242.94/49.42  |   (6)  $false
% 242.94/49.42  | 
% 242.94/49.42  | CLOSE: (6) is inconsistent.
% 242.94/49.42  | 
% 242.94/49.42  End of proof
% 242.94/49.42  
% 242.94/49.42  Sub-proof #958 shows that the following formulas are inconsistent:
% 242.94/49.42  ----------------------------------------------------------------
% 242.94/49.42    (1)  all_58_11 = e3
% 242.94/49.42    (2)   ~ (e3 = e2)
% 242.94/49.42    (3)  all_58_15 = e1
% 242.94/49.42    (4)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.94/49.42    (5)   ~ (e2 = e1)
% 242.94/49.42  
% 242.94/49.42  Begin of proof
% 242.94/49.42  | 
% 242.94/49.42  | BETA: splitting (4) gives:
% 242.94/49.42  | 
% 242.94/49.42  | Case 1:
% 242.94/49.42  | | 
% 242.94/49.42  | |   (6)  all_58_11 = e2 & op(e1, e0) = e2
% 242.94/49.42  | | 
% 242.94/49.42  | | ALPHA: (6) implies:
% 242.94/49.42  | |   (7)  all_58_11 = e2
% 242.94/49.42  | | 
% 242.94/49.42  | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #2030.
% 242.94/49.42  | | 
% 242.94/49.42  | Case 2:
% 242.94/49.42  | | 
% 242.94/49.42  | |   (8)  all_58_15 = e2 & op(e0, e0) = e2
% 242.94/49.42  | | 
% 242.94/49.42  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #1917.
% 242.94/49.42  | | 
% 242.94/49.42  | End of split
% 242.94/49.42  | 
% 242.94/49.42  End of proof
% 242.94/49.42  
% 242.94/49.42  Sub-proof #959 shows that the following formulas are inconsistent:
% 242.94/49.42  ----------------------------------------------------------------
% 242.94/49.42    (1)  op(e0, e0) = e1
% 242.94/49.42    (2)   ~ (e3 = e0)
% 242.94/49.42    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.94/49.42         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.94/49.42    (4)  all_58_6 = e3
% 242.94/49.42    (5)   ~ (e2 = e0)
% 242.94/49.42    (6)  op(e1, e2) = all_52_6
% 242.94/49.42    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.94/49.42         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.94/49.42    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.42         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.94/49.42    (9)  op(e1, e0) = all_52_14
% 242.94/49.42    (10)   ~ (e3 = e1)
% 242.94/49.42    (11)  all_58_3 = e3
% 242.94/49.42    (12)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.42              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.94/49.42                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.94/49.42                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.94/49.42    (13)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.94/49.42          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.94/49.42    (14)   ~ (e3 = e2)
% 242.94/49.42    (15)   ~ (all_52_14 = e1)
% 242.94/49.42    (16)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.94/49.42          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.94/49.42    (17)  all_58_15 = e1
% 242.94/49.42    (18)  op(e3, e0) = all_52_12
% 242.94/49.42    (19)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.42          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.42    (20)   ~ (all_52_6 = e3)
% 242.94/49.42    (21)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.94/49.42          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.94/49.42    (22)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.94/49.42          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.94/49.42    (23)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.42          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.42    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.42    (25)  all_58_14 = e3
% 242.94/49.42    (26)   ~ (all_52_12 = e3)
% 242.94/49.42    (27)   ~ (e1 = e0)
% 242.94/49.42    (28)  op(e3, e3) = e3
% 242.94/49.42    (29)   ~ (all_52_13 = e3)
% 242.94/49.42    (30)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.94/49.42          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.94/49.42    (31)  op(e2, e0) = all_52_13
% 242.94/49.42    (32)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.94/49.42          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.94/49.42            e2)
% 242.94/49.42    (33)   ~ (e2 = e1)
% 242.94/49.42  
% 242.94/49.42  Begin of proof
% 242.94/49.42  | 
% 242.94/49.42  | BETA: splitting (22) gives:
% 242.94/49.42  | 
% 242.94/49.42  | Case 1:
% 242.94/49.42  | | 
% 242.94/49.42  | |   (34)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 242.94/49.42  | |           e3)
% 242.94/49.42  | | 
% 242.94/49.42  | | REF_CLOSE: (18), (24), (26), (29), (31), (34) are inconsistent by sub-proof
% 242.94/49.42  | |            #1592.
% 242.94/49.42  | | 
% 242.94/49.42  | Case 2:
% 242.94/49.42  | | 
% 242.94/49.42  | |   (35)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 242.94/49.42  | |           e3)
% 242.94/49.42  | | 
% 242.94/49.42  | | BETA: splitting (35) gives:
% 242.94/49.42  | | 
% 242.94/49.42  | | Case 1:
% 242.94/49.42  | | | 
% 242.94/49.42  | | |   (36)  all_58_11 = e3 & op(e1, e0) = e3
% 242.94/49.42  | | | 
% 242.94/49.42  | | | ALPHA: (36) implies:
% 242.94/49.42  | | |   (37)  all_58_11 = e3
% 242.94/49.42  | | | 
% 242.94/49.42  | | | BETA: splitting (30) gives:
% 242.94/49.42  | | | 
% 242.94/49.42  | | | Case 1:
% 242.94/49.42  | | | | 
% 242.94/49.42  | | | |   (38)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2)
% 242.94/49.42  | | | |           = e0)
% 242.94/49.42  | | | | 
% 242.94/49.42  | | | | BETA: splitting (38) gives:
% 242.94/49.42  | | | | 
% 242.94/49.42  | | | | Case 1:
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | |   (39)  all_58_6 = e0 & op(e1, e3) = e0
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | | REF_CLOSE: (2), (4), (39) are inconsistent by sub-proof #2213.
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | Case 2:
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | |   (40)  all_58_7 = e0 & op(e1, e2) = e0
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | | ALPHA: (40) implies:
% 242.94/49.42  | | | | |   (41)  all_58_7 = e0
% 242.94/49.42  | | | | |   (42)  op(e1, e2) = e0
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | | BETA: splitting (21) gives:
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | | Case 1:
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | |   (43)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 242.94/49.42  | | | | | |             e3) = e1)
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | | BETA: splitting (43) gives:
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | | Case 1:
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | |   (44)  all_58_0 = e1 & op(e3, e3) = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | ALPHA: (44) implies:
% 242.94/49.42  | | | | | | |   (45)  op(e3, e3) = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | REF_CLOSE: (10), (24), (28), (45) are inconsistent by sub-proof
% 242.94/49.42  | | | | | | |            #1578.
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | Case 2:
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | |   (46)  all_58_2 = e1 & op(e2, e3) = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | ALPHA: (46) implies:
% 242.94/49.42  | | | | | | |   (47)  all_58_2 = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | REF_CLOSE: (2), (4), (5), (13), (14), (16), (24), (27), (28),
% 242.94/49.42  | | | | | | |            (33), (47) are inconsistent by sub-proof #1577.
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | End of split
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | Case 2:
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | |   (48)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 242.94/49.42  | | | | | |             e3) = e1)
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | | BETA: splitting (48) gives:
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | | Case 1:
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | |   (49)  all_58_6 = e1 & op(e1, e3) = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | ALPHA: (49) implies:
% 242.94/49.42  | | | | | | |   (50)  all_58_6 = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | REF_CLOSE: (4), (10), (50) are inconsistent by sub-proof #1758.
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | Case 2:
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | |   (51)  all_58_12 = e1 & op(e0, e3) = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | ALPHA: (51) implies:
% 242.94/49.42  | | | | | | |   (52)  all_58_12 = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | BETA: splitting (32) gives:
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | 
% 242.94/49.42  | | | | | | | |   (53)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 242.94/49.42  | | | | | | | |           op(e0, e2) = e2)
% 242.94/49.42  | | | | | | | | 
% 242.94/49.42  | | | | | | | | BETA: splitting (53) gives:
% 242.94/49.42  | | | | | | | | 
% 242.94/49.42  | | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | |   (54)  all_58_12 = e2 & op(e0, e3) = e2
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | REF_CLOSE: (33), (52), (54) are inconsistent by sub-proof
% 242.94/49.42  | | | | | | | | |            #1302.
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | |   (55)  all_58_13 = e2 & op(e0, e2) = e2
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | ALPHA: (55) implies:
% 242.94/49.42  | | | | | | | | |   (56)  all_58_13 = e2
% 242.94/49.42  | | | | | | | | |   (57)  op(e0, e2) = e2
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 242.94/49.42  | | | | | | | | |            (11), (12), (14), (15), (19), (20), (23), (24),
% 242.94/49.42  | | | | | | | | |            (25), (27), (30), (33), (37), (41), (42), (52),
% 242.94/49.42  | | | | | | | | |            (56), (57) are inconsistent by sub-proof #962.
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | End of split
% 242.94/49.42  | | | | | | | | 
% 242.94/49.42  | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | 
% 242.94/49.42  | | | | | | | |   (58)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 242.94/49.42  | | | | | | | |           op(e0, e0) = e2)
% 242.94/49.42  | | | | | | | | 
% 242.94/49.42  | | | | | | | | REF_CLOSE: (14), (17), (25), (33), (58) are inconsistent by
% 242.94/49.42  | | | | | | | |            sub-proof #961.
% 242.94/49.42  | | | | | | | | 
% 242.94/49.42  | | | | | | | End of split
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | End of split
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | End of split
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | End of split
% 242.94/49.42  | | | | 
% 242.94/49.42  | | | Case 2:
% 242.94/49.42  | | | | 
% 242.94/49.42  | | | |   (59)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.94/49.42  | | | |           = e0)
% 242.94/49.42  | | | | 
% 242.94/49.42  | | | | BETA: splitting (59) gives:
% 242.94/49.42  | | | | 
% 242.94/49.42  | | | | Case 1:
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | |   (60)  all_58_8 = e0 & op(e1, e1) = e0
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | | ALPHA: (60) implies:
% 242.94/49.42  | | | | |   (61)  op(e1, e1) = e0
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | | BETA: splitting (21) gives:
% 242.94/49.42  | | | | | 
% 242.94/49.42  | | | | | Case 1:
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | |   (62)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 242.94/49.42  | | | | | |             e3) = e1)
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | | REF_CLOSE: (2), (4), (5), (10), (13), (14), (16), (24), (27), (28),
% 242.94/49.42  | | | | | |            (33), (62) are inconsistent by sub-proof #1576.
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | Case 2:
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | |   (63)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 242.94/49.42  | | | | | |             e3) = e1)
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | | BETA: splitting (63) gives:
% 242.94/49.42  | | | | | | 
% 242.94/49.42  | | | | | | Case 1:
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | |   (64)  all_58_6 = e1 & op(e1, e3) = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | ALPHA: (64) implies:
% 242.94/49.42  | | | | | | |   (65)  all_58_6 = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | REF_CLOSE: (4), (10), (65) are inconsistent by sub-proof #1758.
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | Case 2:
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | |   (66)  all_58_12 = e1 & op(e0, e3) = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | ALPHA: (66) implies:
% 242.94/49.42  | | | | | | |   (67)  all_58_12 = e1
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | BETA: splitting (32) gives:
% 242.94/49.42  | | | | | | | 
% 242.94/49.42  | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | 
% 242.94/49.42  | | | | | | | |   (68)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 242.94/49.42  | | | | | | | |           op(e0, e2) = e2)
% 242.94/49.42  | | | | | | | | 
% 242.94/49.42  | | | | | | | | BETA: splitting (68) gives:
% 242.94/49.42  | | | | | | | | 
% 242.94/49.42  | | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | |   (69)  all_58_12 = e2 & op(e0, e3) = e2
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | REF_CLOSE: (33), (67), (69) are inconsistent by sub-proof
% 242.94/49.42  | | | | | | | | |            #1302.
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | |   (70)  all_58_13 = e2 & op(e0, e2) = e2
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | ALPHA: (70) implies:
% 242.94/49.42  | | | | | | | | |   (71)  all_58_13 = e2
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | BETA: splitting (3) gives:
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | |   (72)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 242.94/49.42  | | | | | | | | | |           op(e1, e2) = e1)
% 242.94/49.42  | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | BETA: splitting (72) gives:
% 242.94/49.42  | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | |   (73)  all_58_6 = e1 & op(e1, e3) = e1
% 242.94/49.42  | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | ALPHA: (73) implies:
% 242.94/49.42  | | | | | | | | | | |   (74)  all_58_6 = e1
% 242.94/49.42  | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | REF_CLOSE: (4), (10), (74) are inconsistent by sub-proof
% 242.94/49.42  | | | | | | | | | | |            #1758.
% 242.94/49.42  | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | |   (75)  all_58_7 = e1 & op(e1, e2) = e1
% 242.94/49.42  | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | ALPHA: (75) implies:
% 242.94/49.42  | | | | | | | | | | |   (76)  all_58_7 = e1
% 242.94/49.42  | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | BETA: splitting (13) gives:
% 242.94/49.42  | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | |   (77)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 242.94/49.42  | | | | | | | | | | | |           & op(e2, e3) = e2)
% 242.94/49.42  | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | BETA: splitting (77) gives:
% 242.94/49.42  | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | |   (78)  all_58_0 = e2 & op(e3, e3) = e2
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | ALPHA: (78) implies:
% 242.94/49.42  | | | | | | | | | | | | |   (79)  op(e3, e3) = e2
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | REF_CLOSE: (14), (24), (28), (79) are inconsistent by
% 242.94/49.42  | | | | | | | | | | | | |            sub-proof #2194.
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | |   (80)  all_58_2 = e2 & op(e2, e3) = e2
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | ALPHA: (80) implies:
% 242.94/49.42  | | | | | | | | | | | | |   (81)  all_58_2 = e2
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | BETA: splitting (16) gives:
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | |   (82)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 242.94/49.42  | | | | | | | | | | | | | |           & op(e2, e3) = e0)
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | |   (83)  all_58_0 = e0 & op(e3, e3) = e0
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | | ALPHA: (83) implies:
% 242.94/49.42  | | | | | | | | | | | | | | |   (84)  op(e3, e3) = e0
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | | REF_CLOSE: (2), (24), (28), (84) are inconsistent by
% 242.94/49.42  | | | | | | | | | | | | | | |            sub-proof #1940.
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | |   (85)  all_58_2 = e0 & op(e2, e3) = e0
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | | REF_CLOSE: (5), (81), (85) are inconsistent by sub-proof
% 242.94/49.42  | | | | | | | | | | | | | | |            #1535.
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | End of split
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | |   (86)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 242.94/49.42  | | | | | | | | | | | | | |           e0 & op(e0, e3) = e0)
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | |   (87)  all_58_6 = e0 & op(e1, e3) = e0
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 242.94/49.42  | | | | | | | | | | | | | | |   (88)  all_58_6 = e0
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | | COMBINE_EQS: (4), (88) imply:
% 242.94/49.42  | | | | | | | | | | | | | | |   (89)  e3 = e0
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | | COMBINE_EQS: (37), (89) imply:
% 242.94/49.42  | | | | | | | | | | | | | | |   (90)  all_58_11 = e0
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (14), (19), (20), (23), (24), (33),
% 242.94/49.42  | | | | | | | | | | | | | | |            (76), (88), (90) are inconsistent by sub-proof
% 242.94/49.42  | | | | | | | | | | | | | | |            #960.
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | |   (91)  all_58_12 = e0 & op(e0, e3) = e0
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | | REF_CLOSE: (27), (67), (91) are inconsistent by sub-proof
% 242.94/49.42  | | | | | | | | | | | | | | |            #1207.
% 242.94/49.42  | | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | End of split
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | End of split
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | End of split
% 242.94/49.42  | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | |   (92)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 242.94/49.42  | | | | | | | | | | | |           e2 & op(e0, e3) = e2)
% 242.94/49.42  | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | BETA: splitting (92) gives:
% 242.94/49.42  | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | |   (93)  all_58_6 = e2 & op(e1, e3) = e2
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | ALPHA: (93) implies:
% 242.94/49.42  | | | | | | | | | | | | |   (94)  all_58_6 = e2
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | REF_CLOSE: (4), (14), (94) are inconsistent by sub-proof
% 242.94/49.42  | | | | | | | | | | | | |            #2024.
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | |   (95)  all_58_12 = e2 & op(e0, e3) = e2
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | ALPHA: (95) implies:
% 242.94/49.42  | | | | | | | | | | | | |   (96)  all_58_12 = e2
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | COMBINE_EQS: (67), (96) imply:
% 242.94/49.42  | | | | | | | | | | | | |   (97)  e2 = e1
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | COMBINE_EQS: (71), (97) imply:
% 242.94/49.42  | | | | | | | | | | | | |   (98)  all_58_13 = e1
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | BETA: splitting (12) gives:
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | Case 1:
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | |   (99)  all_58_15 = e0 & op(e0, e0) = e0
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | ALPHA: (99) implies:
% 242.94/49.42  | | | | | | | | | | | | | |   (100)  op(e0, e0) = e0
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | REF_CLOSE: (1), (24), (27), (100) are inconsistent by
% 242.94/49.42  | | | | | | | | | | | | | |            sub-proof #2274.
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | |   (101)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 242.94/49.42  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 242.94/49.42  | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 242.94/49.42  | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.94/49.42  | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | ALPHA: (101) implies:
% 242.94/49.42  | | | | | | | | | | | | | |   (102)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 242.94/49.42  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 242.94/49.42  | | | | | | | | | | | | | |              e1) = e0)
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (25), (27), (96), (98), (102) are
% 242.94/49.42  | | | | | | | | | | | | | |            inconsistent by sub-proof #2080.
% 242.94/49.42  | | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | | End of split
% 242.94/49.42  | | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | | End of split
% 242.94/49.42  | | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | | End of split
% 242.94/49.42  | | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | End of split
% 242.94/49.42  | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | |   (103)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1
% 242.94/49.42  | | | | | | | | | |            & op(e1, e0) = e1)
% 242.94/49.42  | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | | REF_CLOSE: (9), (15), (24), (27), (61), (103) are
% 242.94/49.42  | | | | | | | | | |            inconsistent by sub-proof #1086.
% 242.94/49.42  | | | | | | | | | | 
% 242.94/49.42  | | | | | | | | | End of split
% 242.94/49.42  | | | | | | | | | 
% 242.94/49.42  | | | | | | | | End of split
% 242.94/49.42  | | | | | | | | 
% 242.94/49.42  | | | | | | | Case 2:
% 242.94/49.42  | | | | | | | | 
% 242.94/49.43  | | | | | | | |   (104)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 242.94/49.43  | | | | | | | |            op(e0, e0) = e2)
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | | REF_CLOSE: (14), (17), (25), (33), (104) are inconsistent by
% 242.94/49.43  | | | | | | | |            sub-proof #961.
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | End of split
% 242.94/49.43  | | | | | | | 
% 242.94/49.43  | | | | | | End of split
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | End of split
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | Case 2:
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | |   (105)  all_58_11 = e0 & op(e1, e0) = e0
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | | REF_CLOSE: (2), (37), (105) are inconsistent by sub-proof #2204.
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | End of split
% 242.94/49.43  | | | | 
% 242.94/49.43  | | | End of split
% 242.94/49.43  | | | 
% 242.94/49.43  | | Case 2:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (106)  all_58_15 = e3 & op(e0, e0) = e3
% 242.94/49.43  | | | 
% 242.94/49.43  | | | ALPHA: (106) implies:
% 242.94/49.43  | | |   (107)  all_58_15 = e3
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (10), (17), (107) are inconsistent by sub-proof #2249.
% 242.94/49.43  | | | 
% 242.94/49.43  | | End of split
% 242.94/49.43  | | 
% 242.94/49.43  | End of split
% 242.94/49.43  | 
% 242.94/49.43  End of proof
% 242.94/49.43  
% 242.94/49.43  Sub-proof #960 shows that the following formulas are inconsistent:
% 242.94/49.43  ----------------------------------------------------------------
% 242.94/49.43    (1)   ~ (e3 = e0)
% 242.94/49.43    (2)   ~ (e2 = e0)
% 242.94/49.43    (3)  op(e1, e2) = all_52_6
% 242.94/49.43    (4)   ~ (e3 = e2)
% 242.94/49.43    (5)  all_58_6 = e0
% 242.94/49.43    (6)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.43         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.43    (7)   ~ (all_52_6 = e3)
% 242.94/49.43    (8)  all_58_7 = e1
% 242.94/49.43    (9)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.43         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.43    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.43    (11)  all_58_11 = e0
% 242.94/49.43    (12)   ~ (e2 = e1)
% 242.94/49.43  
% 242.94/49.43  Begin of proof
% 242.94/49.43  | 
% 242.94/49.43  | BETA: splitting (9) gives:
% 242.94/49.43  | 
% 242.94/49.43  | Case 1:
% 242.94/49.43  | | 
% 242.94/49.43  | |   (13)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 242.94/49.43  | |           e2)
% 242.94/49.43  | | 
% 242.94/49.43  | | BETA: splitting (13) gives:
% 242.94/49.43  | | 
% 242.94/49.43  | | Case 1:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (14)  all_58_6 = e2 & op(e1, e3) = e2
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (2), (5), (14) are inconsistent by sub-proof #1444.
% 242.94/49.43  | | | 
% 242.94/49.43  | | Case 2:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (15)  all_58_7 = e2 & op(e1, e2) = e2
% 242.94/49.43  | | | 
% 242.94/49.43  | | | ALPHA: (15) implies:
% 242.94/49.43  | | |   (16)  all_58_7 = e2
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (8), (12), (16) are inconsistent by sub-proof #2134.
% 242.94/49.43  | | | 
% 242.94/49.43  | | End of split
% 242.94/49.43  | | 
% 242.94/49.43  | Case 2:
% 242.94/49.43  | | 
% 242.94/49.43  | |   (17)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 242.94/49.43  | |           e2)
% 242.94/49.43  | | 
% 242.94/49.43  | | BETA: splitting (17) gives:
% 242.94/49.43  | | 
% 242.94/49.43  | | Case 1:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (18)  all_58_8 = e2 & op(e1, e1) = e2
% 242.94/49.43  | | | 
% 242.94/49.43  | | | ALPHA: (18) implies:
% 242.94/49.43  | | |   (19)  op(e1, e1) = e2
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (19) are inconsistent
% 242.94/49.43  | | |            by sub-proof #1686.
% 242.94/49.43  | | | 
% 242.94/49.43  | | Case 2:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (20)  all_58_11 = e2 & op(e1, e0) = e2
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (2), (11), (20) are inconsistent by sub-proof #2216.
% 242.94/49.43  | | | 
% 242.94/49.43  | | End of split
% 242.94/49.43  | | 
% 242.94/49.43  | End of split
% 242.94/49.43  | 
% 242.94/49.43  End of proof
% 242.94/49.43  
% 242.94/49.43  Sub-proof #961 shows that the following formulas are inconsistent:
% 242.94/49.43  ----------------------------------------------------------------
% 242.94/49.43    (1)   ~ (e3 = e2)
% 242.94/49.43    (2)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.94/49.43    (3)  all_58_15 = e1
% 242.94/49.43    (4)  all_58_14 = e3
% 242.94/49.43    (5)   ~ (e2 = e1)
% 242.94/49.43  
% 242.94/49.43  Begin of proof
% 242.94/49.43  | 
% 242.94/49.43  | BETA: splitting (2) gives:
% 242.94/49.43  | 
% 242.94/49.43  | Case 1:
% 242.94/49.43  | | 
% 242.94/49.43  | |   (6)  all_58_14 = e2 & op(e0, e1) = e2
% 242.94/49.43  | | 
% 242.94/49.43  | | ALPHA: (6) implies:
% 242.94/49.43  | |   (7)  all_58_14 = e2
% 242.94/49.43  | | 
% 242.94/49.43  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #2117.
% 242.94/49.43  | | 
% 242.94/49.43  | Case 2:
% 242.94/49.43  | | 
% 242.94/49.43  | |   (8)  all_58_15 = e2 & op(e0, e0) = e2
% 242.94/49.43  | | 
% 242.94/49.43  | | ALPHA: (8) implies:
% 242.94/49.43  | |   (9)  all_58_15 = e2
% 242.94/49.43  | | 
% 242.94/49.43  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #2231.
% 242.94/49.43  | | 
% 242.94/49.43  | End of split
% 242.94/49.43  | 
% 242.94/49.43  End of proof
% 242.94/49.43  
% 242.94/49.43  Sub-proof #962 shows that the following formulas are inconsistent:
% 242.94/49.43  ----------------------------------------------------------------
% 242.94/49.43    (1)  op(e0, e0) = e1
% 242.94/49.43    (2)   ~ (e3 = e0)
% 242.94/49.43    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.94/49.43         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.94/49.43    (4)  all_58_6 = e3
% 242.94/49.43    (5)   ~ (e2 = e0)
% 242.94/49.43    (6)  all_58_7 = e0
% 242.94/49.43    (7)  op(e1, e2) = all_52_6
% 242.94/49.43    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.94/49.43         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.94/49.43    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.43         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.94/49.43    (10)  op(e1, e0) = all_52_14
% 242.94/49.43    (11)  op(e0, e2) = e2
% 242.94/49.43    (12)   ~ (e3 = e1)
% 242.94/49.43    (13)  all_58_3 = e3
% 242.94/49.43    (14)  all_58_11 = e3
% 242.94/49.43    (15)  all_58_12 = e1
% 242.94/49.43    (16)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.43              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.94/49.43                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.94/49.43                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.94/49.43    (17)  op(e1, e2) = e0
% 242.94/49.43    (18)   ~ (e3 = e2)
% 242.94/49.43    (19)   ~ (all_52_14 = e1)
% 242.94/49.43    (20)  all_58_13 = e2
% 242.94/49.43    (21)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.43          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.43    (22)   ~ (all_52_6 = e3)
% 242.94/49.43    (23)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.43          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.43    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.43    (25)  all_58_14 = e3
% 242.94/49.43    (26)   ~ (e1 = e0)
% 242.94/49.43    (27)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.94/49.43          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.94/49.43    (28)   ~ (e2 = e1)
% 242.94/49.43  
% 242.94/49.43  Begin of proof
% 242.94/49.43  | 
% 242.94/49.43  | BETA: splitting (3) gives:
% 242.94/49.43  | 
% 242.94/49.43  | Case 1:
% 242.94/49.43  | | 
% 242.94/49.43  | |   (29)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 242.94/49.43  | |           e1)
% 242.94/49.43  | | 
% 242.94/49.43  | | BETA: splitting (29) gives:
% 242.94/49.43  | | 
% 242.94/49.43  | | Case 1:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (30)  all_58_6 = e1 & op(e1, e3) = e1
% 242.94/49.43  | | | 
% 242.94/49.43  | | | ALPHA: (30) implies:
% 242.94/49.43  | | |   (31)  all_58_6 = e1
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (4), (12), (31) are inconsistent by sub-proof #1758.
% 242.94/49.43  | | | 
% 242.94/49.43  | | Case 2:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (32)  all_58_7 = e1 & op(e1, e2) = e1
% 242.94/49.43  | | | 
% 242.94/49.43  | | | ALPHA: (32) implies:
% 242.94/49.43  | | |   (33)  op(e1, e2) = e1
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (7), (17), (24), (26), (33) are inconsistent by sub-proof
% 242.94/49.43  | | |            #2136.
% 242.94/49.43  | | | 
% 242.94/49.43  | | End of split
% 242.94/49.43  | | 
% 242.94/49.43  | Case 2:
% 242.94/49.43  | | 
% 242.94/49.43  | |   (34)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 242.94/49.43  | |           e1)
% 242.94/49.43  | | 
% 242.94/49.43  | | BETA: splitting (34) gives:
% 242.94/49.43  | | 
% 242.94/49.43  | | Case 1:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (35)  all_58_8 = e1 & op(e1, e1) = e1
% 242.94/49.43  | | | 
% 242.94/49.43  | | | ALPHA: (35) implies:
% 242.94/49.43  | | |   (36)  op(e1, e1) = e1
% 242.94/49.43  | | | 
% 242.94/49.43  | | | BETA: splitting (16) gives:
% 242.94/49.43  | | | 
% 242.94/49.43  | | | Case 1:
% 242.94/49.43  | | | | 
% 242.94/49.43  | | | |   (37)  all_58_15 = e0 & op(e0, e0) = e0
% 242.94/49.43  | | | | 
% 242.94/49.43  | | | | ALPHA: (37) implies:
% 242.94/49.43  | | | |   (38)  op(e0, e0) = e0
% 242.94/49.43  | | | | 
% 242.94/49.43  | | | | REF_CLOSE: (1), (24), (26), (38) are inconsistent by sub-proof #2274.
% 242.94/49.43  | | | | 
% 242.94/49.43  | | | Case 2:
% 242.94/49.43  | | | | 
% 242.94/49.43  | | | |   (39)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 242.94/49.43  | | | |               e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 242.94/49.43  | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 242.94/49.43  | | | |               e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 242.94/49.43  | | | | 
% 242.94/49.43  | | | | ALPHA: (39) implies:
% 242.94/49.43  | | | |   (40)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 242.94/49.43  | | | |             e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.94/49.43  | | | | 
% 242.94/49.43  | | | | BETA: splitting (23) gives:
% 242.94/49.43  | | | | 
% 242.94/49.43  | | | | Case 1:
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | |   (41)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 242.94/49.43  | | | | |             e2) = e2)
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | | BETA: splitting (41) gives:
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | | Case 1:
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | |   (42)  all_58_6 = e2 & op(e1, e3) = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | ALPHA: (42) implies:
% 242.94/49.43  | | | | | |   (43)  all_58_6 = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | COMBINE_EQS: (4), (43) imply:
% 242.94/49.43  | | | | | |   (44)  e3 = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | SIMP: (44) implies:
% 242.94/49.43  | | | | | |   (45)  e3 = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | COMBINE_EQS: (25), (45) imply:
% 242.94/49.43  | | | | | |   (46)  all_58_14 = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | REF_CLOSE: (5), (11), (15), (24), (26), (40), (46) are inconsistent
% 242.94/49.43  | | | | | |            by sub-proof #1538.
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | Case 2:
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | |   (47)  all_58_7 = e2 & op(e1, e2) = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | REF_CLOSE: (5), (6), (47) are inconsistent by sub-proof #1326.
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | End of split
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | Case 2:
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | |   (48)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 242.94/49.43  | | | | |             e0) = e2)
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | | BETA: splitting (48) gives:
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | | Case 1:
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | |   (49)  all_58_8 = e2 & op(e1, e1) = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | ALPHA: (49) implies:
% 242.94/49.43  | | | | | |   (50)  all_58_8 = e2
% 242.94/49.43  | | | | | |   (51)  op(e1, e1) = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | BETA: splitting (3) gives:
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | Case 1:
% 242.94/49.43  | | | | | | | 
% 242.94/49.43  | | | | | | |   (52)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 242.94/49.43  | | | | | | |           op(e1, e2) = e1)
% 242.94/49.43  | | | | | | | 
% 242.94/49.43  | | | | | | | BETA: splitting (52) gives:
% 242.94/49.43  | | | | | | | 
% 242.94/49.43  | | | | | | | Case 1:
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | |   (53)  all_58_6 = e1 & op(e1, e3) = e1
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | | REF_CLOSE: (4), (12), (53) are inconsistent by sub-proof #1803.
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | Case 2:
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | |   (54)  all_58_7 = e1 & op(e1, e2) = e1
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | | ALPHA: (54) implies:
% 242.94/49.43  | | | | | | | |   (55)  all_58_7 = e1
% 242.94/49.43  | | | | | | | |   (56)  op(e1, e2) = e1
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (13), (18), (20), (21),
% 242.94/49.43  | | | | | | | |            (22), (23), (24), (26), (27), (28), (36), (50), (51),
% 242.94/49.43  | | | | | | | |            (55), (56) are inconsistent by sub-proof #963.
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | End of split
% 242.94/49.43  | | | | | | | 
% 242.94/49.43  | | | | | | Case 2:
% 242.94/49.43  | | | | | | | 
% 242.94/49.43  | | | | | | | 
% 242.94/49.43  | | | | | | | BETA: splitting (34) gives:
% 242.94/49.43  | | | | | | | 
% 242.94/49.43  | | | | | | | Case 1:
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | | REF_CLOSE: (28), (35), (50) are inconsistent by sub-proof #2045.
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | Case 2:
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | |   (57)  all_58_11 = e1 & op(e1, e0) = e1
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | | ALPHA: (57) implies:
% 242.94/49.43  | | | | | | | |   (58)  op(e1, e0) = e1
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | | REF_CLOSE: (10), (19), (24), (58) are inconsistent by sub-proof
% 242.94/49.43  | | | | | | | |            #2304.
% 242.94/49.43  | | | | | | | | 
% 242.94/49.43  | | | | | | | End of split
% 242.94/49.43  | | | | | | | 
% 242.94/49.43  | | | | | | End of split
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | Case 2:
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | |   (59)  all_58_11 = e2 & op(e1, e0) = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | ALPHA: (59) implies:
% 242.94/49.43  | | | | | |   (60)  all_58_11 = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | COMBINE_EQS: (14), (60) imply:
% 242.94/49.43  | | | | | |   (61)  e3 = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | COMBINE_EQS: (25), (61) imply:
% 242.94/49.43  | | | | | |   (62)  all_58_14 = e2
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | | REF_CLOSE: (5), (11), (15), (24), (26), (40), (62) are inconsistent
% 242.94/49.43  | | | | | |            by sub-proof #1538.
% 242.94/49.43  | | | | | | 
% 242.94/49.43  | | | | | End of split
% 242.94/49.43  | | | | | 
% 242.94/49.43  | | | | End of split
% 242.94/49.43  | | | | 
% 242.94/49.43  | | | End of split
% 242.94/49.43  | | | 
% 242.94/49.43  | | Case 2:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (63)  all_58_11 = e1 & op(e1, e0) = e1
% 242.94/49.43  | | | 
% 242.94/49.43  | | | ALPHA: (63) implies:
% 242.94/49.43  | | |   (64)  op(e1, e0) = e1
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (10), (19), (24), (64) are inconsistent by sub-proof #2304.
% 242.94/49.43  | | | 
% 242.94/49.43  | | End of split
% 242.94/49.43  | | 
% 242.94/49.43  | End of split
% 242.94/49.43  | 
% 242.94/49.43  End of proof
% 242.94/49.43  
% 242.94/49.43  Sub-proof #963 shows that the following formulas are inconsistent:
% 242.94/49.43  ----------------------------------------------------------------
% 242.94/49.43    (1)   ~ (e3 = e0)
% 242.94/49.43    (2)  op(e1, e1) = e1
% 242.94/49.43    (3)  all_58_6 = e3
% 242.94/49.43    (4)  op(e1, e2) = e1
% 242.94/49.43    (5)   ~ (e2 = e0)
% 242.94/49.43    (6)  op(e1, e2) = all_52_6
% 242.94/49.43    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.94/49.43         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.94/49.43    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.43         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.94/49.43    (9)  all_58_8 = e2
% 242.94/49.43    (10)  all_58_3 = e3
% 242.94/49.43    (11)   ~ (e3 = e2)
% 242.94/49.43    (12)  all_58_13 = e2
% 242.94/49.43    (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.43          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.43    (14)   ~ (all_52_6 = e3)
% 242.94/49.43    (15)  op(e1, e1) = e2
% 242.94/49.43    (16)  all_58_7 = e1
% 242.94/49.43    (17)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.43          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.43    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.43    (19)   ~ (e1 = e0)
% 242.94/49.43    (20)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.94/49.43          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.94/49.43    (21)   ~ (e2 = e1)
% 242.94/49.43  
% 242.94/49.43  Begin of proof
% 242.94/49.43  | 
% 242.94/49.43  | BETA: splitting (20) gives:
% 242.94/49.43  | 
% 242.94/49.43  | Case 1:
% 242.94/49.43  | | 
% 242.94/49.43  | |   (22)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 242.94/49.43  | |           e0)
% 242.94/49.43  | | 
% 242.94/49.43  | | BETA: splitting (22) gives:
% 242.94/49.43  | | 
% 242.94/49.43  | | Case 1:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (23)  all_58_6 = e0 & op(e1, e3) = e0
% 242.94/49.43  | | | 
% 242.94/49.43  | | | ALPHA: (23) implies:
% 242.94/49.43  | | |   (24)  all_58_6 = e0
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (1), (3), (24) are inconsistent by sub-proof #2222.
% 242.94/49.43  | | | 
% 242.94/49.43  | | Case 2:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (25)  all_58_7 = e0 & op(e1, e2) = e0
% 242.94/49.43  | | | 
% 242.94/49.43  | | | ALPHA: (25) implies:
% 242.94/49.43  | | |   (26)  op(e1, e2) = e0
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (4), (6), (18), (19), (26) are inconsistent by sub-proof #2136.
% 242.94/49.43  | | | 
% 242.94/49.43  | | End of split
% 242.94/49.43  | | 
% 242.94/49.43  | Case 2:
% 242.94/49.43  | | 
% 242.94/49.43  | |   (27)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.94/49.43  | |           e0)
% 242.94/49.43  | | 
% 242.94/49.43  | | BETA: splitting (27) gives:
% 242.94/49.43  | | 
% 242.94/49.43  | | Case 1:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (28)  all_58_8 = e0 & op(e1, e1) = e0
% 242.94/49.43  | | | 
% 242.94/49.43  | | | ALPHA: (28) implies:
% 242.94/49.43  | | |   (29)  op(e1, e1) = e0
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (2), (18), (19), (29) are inconsistent by sub-proof #2220.
% 242.94/49.43  | | | 
% 242.94/49.43  | | Case 2:
% 242.94/49.43  | | | 
% 242.94/49.43  | | |   (30)  all_58_11 = e0 & op(e1, e0) = e0
% 242.94/49.43  | | | 
% 242.94/49.43  | | | ALPHA: (30) implies:
% 242.94/49.43  | | |   (31)  all_58_11 = e0
% 242.94/49.43  | | | 
% 242.94/49.43  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 242.94/49.43  | | |            (14), (15), (16), (17), (18), (19), (21), (31) are inconsistent
% 242.94/49.43  | | |            by sub-proof #964.
% 242.94/49.43  | | | 
% 242.94/49.43  | | End of split
% 242.94/49.43  | | 
% 242.94/49.43  | End of split
% 242.94/49.43  | 
% 242.94/49.43  End of proof
% 242.94/49.43  
% 242.94/49.43  Sub-proof #964 shows that the following formulas are inconsistent:
% 242.94/49.43  ----------------------------------------------------------------
% 242.94/49.43    (1)   ~ (e3 = e0)
% 242.94/49.43    (2)  op(e1, e1) = e1
% 242.94/49.43    (3)  all_58_6 = e3
% 242.94/49.43    (4)   ~ (e2 = e0)
% 242.94/49.43    (5)  op(e1, e2) = all_52_6
% 242.94/49.43    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.94/49.43         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.94/49.43    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.43         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.94/49.43    (8)  all_58_8 = e2
% 242.94/49.43    (9)  all_58_3 = e3
% 242.94/49.43    (10)   ~ (e3 = e2)
% 242.94/49.43    (11)  all_58_13 = e2
% 242.94/49.44    (12)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.44          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.44    (13)   ~ (all_52_6 = e3)
% 242.94/49.44    (14)  op(e1, e1) = e2
% 242.94/49.44    (15)  all_58_7 = e1
% 242.94/49.44    (16)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.44          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.44    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.44    (18)  all_58_11 = e0
% 242.94/49.44    (19)   ~ (e1 = e0)
% 242.94/49.44    (20)   ~ (e2 = e1)
% 242.94/49.44  
% 242.94/49.44  Begin of proof
% 242.94/49.44  | 
% 242.94/49.44  | BETA: splitting (6) gives:
% 242.94/49.44  | 
% 242.94/49.44  | Case 1:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (21)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 242.94/49.44  | |           e2)
% 242.94/49.44  | | 
% 242.94/49.44  | | BETA: splitting (21) gives:
% 242.94/49.44  | | 
% 242.94/49.44  | | Case 1:
% 242.94/49.44  | | | 
% 242.94/49.44  | | |   (22)  all_58_1 = e2 & op(e3, e2) = e2
% 242.94/49.44  | | | 
% 242.94/49.44  | | | ALPHA: (22) implies:
% 242.94/49.44  | | |   (23)  all_58_1 = e2
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (1), (4), (7), (9), (11), (15), (19), (23) are inconsistent by
% 242.94/49.44  | | |            sub-proof #969.
% 242.94/49.44  | | | 
% 242.94/49.44  | | Case 2:
% 242.94/49.44  | | | 
% 242.94/49.44  | | |   (24)  all_58_3 = e2 & op(e2, e2) = e2
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (1), (3), (5), (9), (10), (12), (13), (14), (17), (18), (24)
% 242.94/49.44  | | |            are inconsistent by sub-proof #966.
% 242.94/49.44  | | | 
% 242.94/49.44  | | End of split
% 242.94/49.44  | | 
% 242.94/49.44  | Case 2:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (25)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 242.94/49.44  | |           e2)
% 242.94/49.44  | | 
% 242.94/49.44  | | BETA: splitting (25) gives:
% 242.94/49.44  | | 
% 242.94/49.44  | | Case 1:
% 242.94/49.44  | | | 
% 242.94/49.44  | | |   (26)  all_58_7 = e2 & op(e1, e2) = e2
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (3), (4), (8), (10), (15), (16), (18), (20), (26) are
% 242.94/49.44  | | |            inconsistent by sub-proof #965.
% 242.94/49.44  | | | 
% 242.94/49.44  | | Case 2:
% 242.94/49.44  | | | 
% 242.94/49.44  | | | 
% 242.94/49.44  | | | GROUND_INST: instantiating (17) with e1, e2, e1, e1, simplifying with (2),
% 242.94/49.44  | | |              (14) gives:
% 242.94/49.44  | | |   (27)  e2 = e1
% 242.94/49.44  | | | 
% 242.94/49.44  | | | COMBINE_EQS: (8), (27) imply:
% 242.94/49.44  | | |   (28)  all_58_8 = e1
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (3), (4), (10), (15), (16), (18), (20), (28) are inconsistent
% 242.94/49.44  | | |            by sub-proof #2215.
% 242.94/49.44  | | | 
% 242.94/49.44  | | End of split
% 242.94/49.44  | | 
% 242.94/49.44  | End of split
% 242.94/49.44  | 
% 242.94/49.44  End of proof
% 242.94/49.44  
% 242.94/49.44  Sub-proof #965 shows that the following formulas are inconsistent:
% 242.94/49.44  ----------------------------------------------------------------
% 242.94/49.44    (1)  all_58_6 = e3
% 242.94/49.44    (2)   ~ (e2 = e0)
% 242.94/49.44    (3)  all_58_8 = e2
% 242.94/49.44    (4)   ~ (e3 = e2)
% 242.94/49.44    (5)  all_58_7 = e1
% 242.94/49.44    (6)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.44         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.44    (7)  all_58_11 = e0
% 242.94/49.44    (8)  all_58_7 = e2 & op(e1, e2) = e2
% 242.94/49.44    (9)   ~ (e2 = e1)
% 242.94/49.44  
% 242.94/49.44  Begin of proof
% 242.94/49.44  | 
% 242.94/49.44  | ALPHA: (8) implies:
% 242.94/49.44  |   (10)  all_58_7 = e2
% 242.94/49.44  | 
% 242.94/49.44  | COMBINE_EQS: (5), (10) imply:
% 242.94/49.44  |   (11)  e2 = e1
% 242.94/49.44  | 
% 242.94/49.44  | SIMP: (11) implies:
% 242.94/49.44  |   (12)  e2 = e1
% 242.94/49.44  | 
% 242.94/49.44  | COMBINE_EQS: (3), (12) imply:
% 242.94/49.44  |   (13)  all_58_8 = e1
% 242.94/49.44  | 
% 242.94/49.44  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (13) are inconsistent by
% 242.94/49.44  |            sub-proof #2215.
% 242.94/49.44  | 
% 242.94/49.44  End of proof
% 242.94/49.44  
% 242.94/49.44  Sub-proof #966 shows that the following formulas are inconsistent:
% 242.94/49.44  ----------------------------------------------------------------
% 242.94/49.44    (1)   ~ (e3 = e0)
% 242.94/49.44    (2)  all_58_6 = e3
% 242.94/49.44    (3)  op(e1, e2) = all_52_6
% 242.94/49.44    (4)  all_58_3 = e3
% 242.94/49.44    (5)   ~ (e3 = e2)
% 242.94/49.44    (6)  all_58_3 = e2 & op(e2, e2) = e2
% 242.94/49.44    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.44         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.44    (8)   ~ (all_52_6 = e3)
% 242.94/49.44    (9)  op(e1, e1) = e2
% 242.94/49.44    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.44    (11)  all_58_11 = e0
% 242.94/49.44  
% 242.94/49.44  Begin of proof
% 242.94/49.44  | 
% 242.94/49.44  | ALPHA: (6) implies:
% 242.94/49.44  |   (12)  all_58_3 = e2
% 242.94/49.44  | 
% 242.94/49.44  | COMBINE_EQS: (4), (12) imply:
% 242.94/49.44  |   (13)  e3 = e2
% 242.94/49.44  | 
% 242.94/49.44  | COMBINE_EQS: (2), (13) imply:
% 242.94/49.44  |   (14)  all_58_6 = e2
% 242.94/49.44  | 
% 242.94/49.44  | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (14) are inconsistent by
% 242.94/49.44  |            sub-proof #967.
% 242.94/49.44  | 
% 242.94/49.44  End of proof
% 242.94/49.44  
% 242.94/49.44  Sub-proof #967 shows that the following formulas are inconsistent:
% 242.94/49.44  ----------------------------------------------------------------
% 242.94/49.44    (1)   ~ (e3 = e0)
% 242.94/49.44    (2)  op(e1, e2) = all_52_6
% 242.94/49.44    (3)  all_58_6 = e2
% 242.94/49.44    (4)   ~ (e3 = e2)
% 242.94/49.44    (5)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.44         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.44    (6)   ~ (all_52_6 = e3)
% 242.94/49.44    (7)  op(e1, e1) = e2
% 242.94/49.44    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.44    (9)  all_58_11 = e0
% 242.94/49.44  
% 242.94/49.44  Begin of proof
% 242.94/49.44  | 
% 242.94/49.44  | BETA: splitting (5) gives:
% 242.94/49.44  | 
% 242.94/49.44  | Case 1:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 242.94/49.44  | |           e3)
% 242.94/49.44  | | 
% 242.94/49.44  | | REF_CLOSE: (2), (3), (4), (6), (8), (10) are inconsistent by sub-proof #968.
% 242.94/49.44  | | 
% 242.94/49.44  | Case 2:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (11)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 242.94/49.44  | |           e3)
% 242.94/49.44  | | 
% 242.94/49.44  | | REF_CLOSE: (1), (4), (7), (8), (9), (11) are inconsistent by sub-proof
% 242.94/49.44  | |            #1687.
% 242.94/49.44  | | 
% 242.94/49.44  | End of split
% 242.94/49.44  | 
% 242.94/49.44  End of proof
% 242.94/49.44  
% 242.94/49.44  Sub-proof #968 shows that the following formulas are inconsistent:
% 242.94/49.44  ----------------------------------------------------------------
% 242.94/49.44    (1)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 242.94/49.44    (2)  op(e1, e2) = all_52_6
% 242.94/49.44    (3)  all_58_6 = e2
% 242.94/49.44    (4)   ~ (e3 = e2)
% 242.94/49.44    (5)   ~ (all_52_6 = e3)
% 242.94/49.44    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.44  
% 242.94/49.44  Begin of proof
% 242.94/49.44  | 
% 242.94/49.44  | BETA: splitting (1) gives:
% 242.94/49.44  | 
% 242.94/49.44  | Case 1:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (7)  all_58_6 = e3 & op(e1, e3) = e3
% 242.94/49.44  | | 
% 242.94/49.44  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1838.
% 242.94/49.44  | | 
% 242.94/49.44  | Case 2:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (8)  all_58_7 = e3 & op(e1, e2) = e3
% 242.94/49.44  | | 
% 242.94/49.44  | | ALPHA: (8) implies:
% 242.94/49.44  | |   (9)  op(e1, e2) = e3
% 242.94/49.44  | | 
% 242.94/49.44  | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #2191.
% 242.94/49.44  | | 
% 242.94/49.44  | End of split
% 242.94/49.44  | 
% 242.94/49.44  End of proof
% 242.94/49.44  
% 242.94/49.44  Sub-proof #969 shows that the following formulas are inconsistent:
% 242.94/49.44  ----------------------------------------------------------------
% 242.94/49.44    (1)   ~ (e3 = e0)
% 242.94/49.44    (2)   ~ (e2 = e0)
% 242.94/49.44    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.44         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.94/49.44    (4)  all_58_3 = e3
% 242.94/49.44    (5)  all_58_13 = e2
% 242.94/49.44    (6)  all_58_7 = e1
% 242.94/49.44    (7)  all_58_1 = e2
% 242.94/49.44    (8)   ~ (e1 = e0)
% 242.94/49.44  
% 242.94/49.44  Begin of proof
% 242.94/49.44  | 
% 242.94/49.44  | BETA: splitting (3) gives:
% 242.94/49.44  | 
% 242.94/49.44  | Case 1:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 242.94/49.44  | | 
% 242.94/49.44  | | BETA: splitting (9) gives:
% 242.94/49.44  | | 
% 242.94/49.44  | | Case 1:
% 242.94/49.44  | | | 
% 242.94/49.44  | | |   (10)  all_58_1 = e0 & op(e3, e2) = e0
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (2), (7), (10) are inconsistent by sub-proof #2187.
% 242.94/49.44  | | | 
% 242.94/49.44  | | Case 2:
% 242.94/49.44  | | | 
% 242.94/49.44  | | |   (11)  all_58_3 = e0 & op(e2, e2) = e0
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #1719.
% 242.94/49.44  | | | 
% 242.94/49.44  | | End of split
% 242.94/49.44  | | 
% 242.94/49.44  | Case 2:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (12)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 242.94/49.44  | |           e0)
% 242.94/49.44  | | 
% 242.94/49.44  | | BETA: splitting (12) gives:
% 242.94/49.44  | | 
% 242.94/49.44  | | Case 1:
% 242.94/49.44  | | | 
% 242.94/49.44  | | |   (13)  all_58_7 = e0 & op(e1, e2) = e0
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #1558.
% 242.94/49.44  | | | 
% 242.94/49.44  | | Case 2:
% 242.94/49.44  | | | 
% 242.94/49.44  | | |   (14)  all_58_13 = e0 & op(e0, e2) = e0
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (2), (5), (14) are inconsistent by sub-proof #1866.
% 242.94/49.44  | | | 
% 242.94/49.44  | | End of split
% 242.94/49.44  | | 
% 242.94/49.44  | End of split
% 242.94/49.44  | 
% 242.94/49.44  End of proof
% 242.94/49.44  
% 242.94/49.44  Sub-proof #970 shows that the following formulas are inconsistent:
% 242.94/49.44  ----------------------------------------------------------------
% 242.94/49.44    (1)   ~ (e3 = e0)
% 242.94/49.44    (2)   ~ (e2 = e0)
% 242.94/49.44    (3)  op(e1, e2) = all_52_6
% 242.94/49.44    (4)   ~ (e3 = e1)
% 242.94/49.44    (5)  all_58_7 = e2
% 242.94/49.44    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.94/49.44         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.94/49.44    (7)   ~ (e3 = e2)
% 242.94/49.44    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.94/49.44         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.94/49.44    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.44         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.44    (10)  all_58_6 = e1
% 242.94/49.44    (11)  all_58_12 = e3
% 242.94/49.44    (12)   ~ (all_52_6 = e3)
% 242.94/49.44    (13)  op(e1, e1) = e2
% 242.94/49.44    (14)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.94/49.44          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.94/49.44    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.44    (16)   ~ (e1 = e0)
% 242.94/49.44    (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.94/49.44          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.94/49.44    (18)   ~ (e2 = e1)
% 242.94/49.44  
% 242.94/49.44  Begin of proof
% 242.94/49.44  | 
% 242.94/49.44  | BETA: splitting (9) gives:
% 242.94/49.44  | 
% 242.94/49.44  | Case 1:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (19)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 242.94/49.44  | |           e3)
% 242.94/49.44  | | 
% 242.94/49.44  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (11), (12), (14), (15), (16),
% 242.94/49.44  | |            (18), (19) are inconsistent by sub-proof #1530.
% 242.94/49.44  | | 
% 242.94/49.44  | Case 2:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (20)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 242.94/49.44  | |           e3)
% 242.94/49.44  | | 
% 242.94/49.44  | | REF_CLOSE: (1), (2), (5), (7), (10), (13), (15), (16), (17), (20) are
% 242.94/49.44  | |            inconsistent by sub-proof #2201.
% 242.94/49.44  | | 
% 242.94/49.44  | End of split
% 242.94/49.44  | 
% 242.94/49.44  End of proof
% 242.94/49.44  
% 242.94/49.44  Sub-proof #971 shows that the following formulas are inconsistent:
% 242.94/49.44  ----------------------------------------------------------------
% 242.94/49.44    (1)  op(e0, e0) = e1
% 242.94/49.44    (2)   ~ (e3 = e0)
% 242.94/49.44    (3)   ~ (e2 = e0)
% 242.94/49.44    (4)   ~ (e3 = e1)
% 242.94/49.44    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.44             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.94/49.44               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.94/49.44               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.94/49.44    (6)  op(e2, e0) = e2
% 242.94/49.44    (7)  all_58_15 = e1
% 242.94/49.44    (8)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.94/49.44         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.94/49.44    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.44    (10)   ~ (e1 = e0)
% 242.94/49.44    (11)  all_58_9 = e1
% 242.94/49.44    (12)   ~ (all_52_13 = e3)
% 242.94/49.44    (13)  op(e2, e0) = all_52_13
% 242.94/49.44  
% 242.94/49.44  Begin of proof
% 242.94/49.44  | 
% 242.94/49.44  | BETA: splitting (8) gives:
% 242.94/49.44  | 
% 242.94/49.44  | Case 1:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (14)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 242.94/49.44  | |           e3)
% 242.94/49.44  | | 
% 242.94/49.44  | | REF_CLOSE: (4), (9), (11), (12), (13), (14) are inconsistent by sub-proof
% 242.94/49.44  | |            #1602.
% 242.94/49.44  | | 
% 242.94/49.44  | Case 2:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (15)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 242.94/49.44  | |           e3)
% 242.94/49.44  | | 
% 242.94/49.44  | | BETA: splitting (15) gives:
% 242.94/49.44  | | 
% 242.94/49.44  | | Case 1:
% 242.94/49.44  | | | 
% 242.94/49.44  | | |   (16)  all_58_11 = e3 & op(e1, e0) = e3
% 242.94/49.44  | | | 
% 242.94/49.44  | | | ALPHA: (16) implies:
% 242.94/49.44  | | |   (17)  all_58_11 = e3
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (11), (17) are inconsistent
% 242.94/49.44  | | |            by sub-proof #1742.
% 242.94/49.44  | | | 
% 242.94/49.44  | | Case 2:
% 242.94/49.44  | | | 
% 242.94/49.44  | | |   (18)  all_58_15 = e3 & op(e0, e0) = e3
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (4), (7), (18) are inconsistent by sub-proof #1915.
% 242.94/49.44  | | | 
% 242.94/49.44  | | End of split
% 242.94/49.44  | | 
% 242.94/49.44  | End of split
% 242.94/49.44  | 
% 242.94/49.44  End of proof
% 242.94/49.44  
% 242.94/49.44  Sub-proof #972 shows that the following formulas are inconsistent:
% 242.94/49.44  ----------------------------------------------------------------
% 242.94/49.44    (1)   ~ (e3 = e0)
% 242.94/49.44    (2)   ~ (e2 = e0)
% 242.94/49.44    (3)   ~ (e3 = e1)
% 242.94/49.44    (4)  all_58_3 = e3
% 242.94/49.44    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.94/49.44         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.94/49.44    (6)  all_58_12 = e1
% 242.94/49.44    (7)  op(e2, e1) = all_52_9
% 242.94/49.44    (8)   ~ (e3 = e2)
% 242.94/49.44    (9)  op(e2, e0) = e2
% 242.94/49.44    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.94/49.44          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.94/49.44    (11)  op(e2, e3) = all_52_1
% 242.94/49.44    (12)  op(e3, e3) = e2
% 242.94/49.44    (13)  op(e2, e1) = e0
% 242.94/49.44    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.44    (15)   ~ (e1 = e0)
% 242.94/49.44    (16)   ~ (all_52_1 = e3)
% 242.94/49.44    (17)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.94/49.44          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.94/49.44    (18)   ~ (e2 = e1)
% 242.94/49.44  
% 242.94/49.44  Begin of proof
% 242.94/49.44  | 
% 242.94/49.44  | BETA: splitting (5) gives:
% 242.94/49.44  | 
% 242.94/49.44  | Case 1:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (19)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 242.94/49.44  | |           e3)
% 242.94/49.44  | | 
% 242.94/49.44  | | REF_CLOSE: (8), (11), (12), (14), (16), (19) are inconsistent by sub-proof
% 242.94/49.44  | |            #1404.
% 242.94/49.44  | | 
% 242.94/49.44  | Case 2:
% 242.94/49.44  | | 
% 242.94/49.44  | |   (20)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 242.94/49.44  | |           e3)
% 242.94/49.44  | | 
% 242.94/49.44  | | BETA: splitting (20) gives:
% 242.94/49.44  | | 
% 242.94/49.44  | | Case 1:
% 242.94/49.44  | | | 
% 242.94/49.44  | | |   (21)  all_58_6 = e3 & op(e1, e3) = e3
% 242.94/49.44  | | | 
% 242.94/49.44  | | | ALPHA: (21) implies:
% 242.94/49.44  | | |   (22)  all_58_6 = e3
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (12), (13), (14),
% 242.94/49.44  | | |            (15), (17), (18), (22) are inconsistent by sub-proof #973.
% 242.94/49.44  | | | 
% 242.94/49.44  | | Case 2:
% 242.94/49.44  | | | 
% 242.94/49.44  | | |   (23)  all_58_12 = e3 & op(e0, e3) = e3
% 242.94/49.44  | | | 
% 242.94/49.44  | | | ALPHA: (23) implies:
% 242.94/49.44  | | |   (24)  all_58_12 = e3
% 242.94/49.44  | | | 
% 242.94/49.44  | | | REF_CLOSE: (3), (6), (24) are inconsistent by sub-proof #1542.
% 242.94/49.44  | | | 
% 242.94/49.44  | | End of split
% 242.94/49.44  | | 
% 242.94/49.44  | End of split
% 242.94/49.44  | 
% 242.94/49.44  End of proof
% 242.94/49.44  
% 242.94/49.44  Sub-proof #973 shows that the following formulas are inconsistent:
% 242.94/49.44  ----------------------------------------------------------------
% 242.94/49.44    (1)   ~ (e3 = e0)
% 242.94/49.44    (2)  all_58_6 = e3
% 242.94/49.44    (3)   ~ (e2 = e0)
% 242.94/49.44    (4)   ~ (e3 = e1)
% 242.94/49.44    (5)  all_58_3 = e3
% 242.94/49.44    (6)  all_58_12 = e1
% 242.94/49.44    (7)  op(e2, e1) = all_52_9
% 242.94/49.44    (8)  op(e2, e0) = e2
% 242.94/49.45    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.94/49.45         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.94/49.45    (10)  op(e3, e3) = e2
% 242.94/49.45    (11)  op(e2, e1) = e0
% 242.94/49.45    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.45    (13)   ~ (e1 = e0)
% 242.94/49.45    (14)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.94/49.45          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.94/49.45    (15)   ~ (e2 = e1)
% 242.94/49.45  
% 242.94/49.45  Begin of proof
% 242.94/49.45  | 
% 242.94/49.45  | BETA: splitting (9) gives:
% 242.94/49.45  | 
% 242.94/49.45  | Case 1:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (16)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 242.94/49.45  | |           e0)
% 242.94/49.45  | | 
% 242.94/49.45  | | BETA: splitting (16) gives:
% 242.94/49.45  | | 
% 242.94/49.45  | | Case 1:
% 242.94/49.45  | | | 
% 242.94/49.45  | | |   (17)  all_58_0 = e0 & op(e3, e3) = e0
% 242.94/49.45  | | | 
% 242.94/49.45  | | | ALPHA: (17) implies:
% 242.94/49.45  | | |   (18)  op(e3, e3) = e0
% 242.94/49.45  | | | 
% 242.94/49.45  | | | REF_CLOSE: (3), (10), (12), (18) are inconsistent by sub-proof #2188.
% 242.94/49.45  | | | 
% 242.94/49.45  | | Case 2:
% 242.94/49.45  | | | 
% 242.94/49.45  | | |   (19)  all_58_2 = e0 & op(e2, e3) = e0
% 242.94/49.45  | | | 
% 242.94/49.45  | | | ALPHA: (19) implies:
% 242.94/49.45  | | |   (20)  all_58_2 = e0
% 242.94/49.45  | | | 
% 242.94/49.45  | | | REF_CLOSE: (4), (5), (7), (8), (11), (12), (13), (14), (15), (20) are
% 242.94/49.45  | | |            inconsistent by sub-proof #974.
% 242.94/49.45  | | | 
% 242.94/49.45  | | End of split
% 242.94/49.45  | | 
% 242.94/49.45  | Case 2:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (21)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 242.94/49.45  | |           e0)
% 242.94/49.45  | | 
% 242.94/49.45  | | BETA: splitting (21) gives:
% 242.94/49.45  | | 
% 242.94/49.45  | | Case 1:
% 242.94/49.45  | | | 
% 242.94/49.45  | | |   (22)  all_58_6 = e0 & op(e1, e3) = e0
% 242.94/49.45  | | | 
% 242.94/49.45  | | | ALPHA: (22) implies:
% 242.94/49.45  | | |   (23)  all_58_6 = e0
% 242.94/49.45  | | | 
% 242.94/49.45  | | | REF_CLOSE: (1), (2), (23) are inconsistent by sub-proof #2222.
% 242.94/49.45  | | | 
% 242.94/49.45  | | Case 2:
% 242.94/49.45  | | | 
% 242.94/49.45  | | |   (24)  all_58_12 = e0 & op(e0, e3) = e0
% 242.94/49.45  | | | 
% 242.94/49.45  | | | ALPHA: (24) implies:
% 242.94/49.45  | | |   (25)  all_58_12 = e0
% 242.94/49.45  | | | 
% 242.94/49.45  | | | REF_CLOSE: (6), (13), (25) are inconsistent by sub-proof #1539.
% 242.94/49.45  | | | 
% 242.94/49.45  | | End of split
% 242.94/49.45  | | 
% 242.94/49.45  | End of split
% 242.94/49.45  | 
% 242.94/49.45  End of proof
% 242.94/49.45  
% 242.94/49.45  Sub-proof #974 shows that the following formulas are inconsistent:
% 242.94/49.45  ----------------------------------------------------------------
% 242.94/49.45    (1)   ~ (e3 = e1)
% 242.94/49.45    (2)  all_58_3 = e3
% 242.94/49.45    (3)  op(e2, e1) = all_52_9
% 242.94/49.45    (4)  op(e2, e0) = e2
% 242.94/49.45    (5)  op(e2, e1) = e0
% 242.94/49.45    (6)  all_58_2 = e0
% 242.94/49.45    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.45    (8)   ~ (e1 = e0)
% 242.94/49.45    (9)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.94/49.45         (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.94/49.45    (10)   ~ (e2 = e1)
% 242.94/49.45  
% 242.94/49.45  Begin of proof
% 242.94/49.45  | 
% 242.94/49.45  | BETA: splitting (9) gives:
% 242.94/49.45  | 
% 242.94/49.45  | Case 1:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (11)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 242.94/49.45  | |           e1)
% 242.94/49.45  | | 
% 242.94/49.45  | | REF_CLOSE: (1), (2), (6), (8), (11) are inconsistent by sub-proof #976.
% 242.94/49.45  | | 
% 242.94/49.45  | Case 2:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (12)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 242.94/49.45  | |           e1)
% 242.94/49.45  | | 
% 242.94/49.45  | | REF_CLOSE: (3), (4), (5), (7), (8), (10), (12) are inconsistent by sub-proof
% 242.94/49.45  | |            #975.
% 242.94/49.45  | | 
% 242.94/49.45  | End of split
% 242.94/49.45  | 
% 242.94/49.45  End of proof
% 242.94/49.45  
% 242.94/49.45  Sub-proof #975 shows that the following formulas are inconsistent:
% 242.94/49.45  ----------------------------------------------------------------
% 242.94/49.45    (1)  op(e2, e1) = all_52_9
% 242.94/49.45    (2)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 242.94/49.45    (3)  op(e2, e0) = e2
% 242.94/49.45    (4)  op(e2, e1) = e0
% 242.94/49.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.45    (6)   ~ (e1 = e0)
% 242.94/49.45    (7)   ~ (e2 = e1)
% 242.94/49.45  
% 242.94/49.45  Begin of proof
% 242.94/49.45  | 
% 242.94/49.45  | BETA: splitting (2) gives:
% 242.94/49.45  | 
% 242.94/49.45  | Case 1:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (8)  all_58_5 = e1 & op(e2, e1) = e1
% 242.94/49.45  | | 
% 242.94/49.45  | | ALPHA: (8) implies:
% 242.94/49.45  | |   (9)  op(e2, e1) = e1
% 242.94/49.45  | | 
% 242.94/49.45  | | REF_CLOSE: (1), (4), (5), (6), (9) are inconsistent by sub-proof #2165.
% 242.94/49.45  | | 
% 242.94/49.45  | Case 2:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (10)  all_58_10 = e1 & op(e2, e0) = e1
% 242.94/49.45  | | 
% 242.94/49.45  | | ALPHA: (10) implies:
% 242.94/49.45  | |   (11)  op(e2, e0) = e1
% 242.94/49.45  | | 
% 242.94/49.45  | | REF_CLOSE: (3), (5), (7), (11) are inconsistent by sub-proof #1659.
% 242.94/49.45  | | 
% 242.94/49.45  | End of split
% 242.94/49.45  | 
% 242.94/49.45  End of proof
% 242.94/49.45  
% 242.94/49.45  Sub-proof #976 shows that the following formulas are inconsistent:
% 242.94/49.45  ----------------------------------------------------------------
% 242.94/49.45    (1)   ~ (e3 = e1)
% 242.94/49.45    (2)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 242.94/49.45    (3)  all_58_3 = e3
% 242.94/49.45    (4)  all_58_2 = e0
% 242.94/49.45    (5)   ~ (e1 = e0)
% 242.94/49.45  
% 242.94/49.45  Begin of proof
% 242.94/49.45  | 
% 242.94/49.45  | BETA: splitting (2) gives:
% 242.94/49.45  | 
% 242.94/49.45  | Case 1:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (6)  all_58_2 = e1 & op(e2, e3) = e1
% 242.94/49.45  | | 
% 242.94/49.45  | | ALPHA: (6) implies:
% 242.94/49.45  | |   (7)  all_58_2 = e1
% 242.94/49.45  | | 
% 242.94/49.45  | | COMBINE_EQS: (4), (7) imply:
% 242.94/49.45  | |   (8)  e1 = e0
% 242.94/49.45  | | 
% 242.94/49.45  | | REDUCE: (5), (8) imply:
% 242.94/49.45  | |   (9)  $false
% 242.94/49.45  | | 
% 242.94/49.45  | | CLOSE: (9) is inconsistent.
% 242.94/49.45  | | 
% 242.94/49.45  | Case 2:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (10)  all_58_3 = e1 & op(e2, e2) = e1
% 242.94/49.45  | | 
% 242.94/49.45  | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #2197.
% 242.94/49.45  | | 
% 242.94/49.45  | End of split
% 242.94/49.45  | 
% 242.94/49.45  End of proof
% 242.94/49.45  
% 242.94/49.45  Sub-proof #977 shows that the following formulas are inconsistent:
% 242.94/49.45  ----------------------------------------------------------------
% 242.94/49.45    (1)   ~ (e3 = e0)
% 242.94/49.45    (2)   ~ (e2 = e0)
% 242.94/49.45    (3)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 242.94/49.45    (4)  op(e1, e2) = all_52_6
% 242.94/49.45    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.94/49.45         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.94/49.45    (6)   ~ (e3 = e2)
% 242.94/49.45    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.94/49.45         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.94/49.45    (8)  all_58_12 = e3
% 242.94/49.45    (9)   ~ (all_52_6 = e3)
% 242.94/49.45    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.45    (11)   ~ (e1 = e0)
% 242.94/49.45    (12)  all_58_2 = e1
% 242.94/49.45    (13)   ~ (e2 = e1)
% 242.94/49.45  
% 242.94/49.45  Begin of proof
% 242.94/49.45  | 
% 242.94/49.45  | BETA: splitting (3) gives:
% 242.94/49.45  | 
% 242.94/49.45  | Case 1:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (14)  all_58_6 = e3 & op(e1, e3) = e3
% 242.94/49.45  | | 
% 242.94/49.45  | | ALPHA: (14) implies:
% 242.94/49.45  | |   (15)  all_58_6 = e3
% 242.94/49.45  | | 
% 242.94/49.45  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (13), (15) are
% 242.94/49.45  | |            inconsistent by sub-proof #1970.
% 242.94/49.45  | | 
% 242.94/49.45  | Case 2:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (16)  all_58_7 = e3 & op(e1, e2) = e3
% 242.94/49.45  | | 
% 242.94/49.45  | | ALPHA: (16) implies:
% 242.94/49.45  | |   (17)  op(e1, e2) = e3
% 242.94/49.45  | | 
% 242.94/49.45  | | REF_CLOSE: (4), (9), (10), (17) are inconsistent by sub-proof #2191.
% 242.94/49.45  | | 
% 242.94/49.45  | End of split
% 242.94/49.45  | 
% 242.94/49.45  End of proof
% 242.94/49.45  
% 242.94/49.45  Sub-proof #978 shows that the following formulas are inconsistent:
% 242.94/49.45  ----------------------------------------------------------------
% 242.94/49.45    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 242.94/49.45    (2)   ~ (e3 = e0)
% 242.94/49.45    (3)   ~ (e2 = e0)
% 242.94/49.45    (4)   ~ (e3 = e1)
% 242.94/49.45    (5)  op(e2, e1) = all_52_9
% 242.94/49.45    (6)  op(e3, e3) = e2
% 242.94/49.45    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.94/49.45         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.45    (8)  all_58_1 = e2
% 242.94/49.45    (9)   ~ (all_52_9 = e3)
% 242.94/49.45    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.94/49.45          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.94/49.45    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.45    (12)   ~ (e1 = e0)
% 242.94/49.45    (13)   ~ (e2 = e1)
% 242.94/49.45  
% 242.94/49.45  Begin of proof
% 242.94/49.45  | 
% 242.94/49.45  | BETA: splitting (1) gives:
% 242.94/49.45  | 
% 242.94/49.45  | Case 1:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (14)  all_58_4 = e3 & op(e3, e1) = e3
% 242.94/49.45  | | 
% 242.94/49.45  | | ALPHA: (14) implies:
% 242.94/49.45  | |   (15)  all_58_4 = e3
% 242.94/49.45  | | 
% 242.94/49.45  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (12), (13), (15) are
% 242.94/49.45  | |            inconsistent by sub-proof #2180.
% 242.94/49.45  | | 
% 242.94/49.45  | Case 2:
% 242.94/49.45  | | 
% 242.94/49.45  | |   (16)  all_58_5 = e3 & op(e2, e1) = e3
% 242.94/49.45  | | 
% 242.94/49.45  | | REF_CLOSE: (5), (9), (11), (16) are inconsistent by sub-proof #1822.
% 242.94/49.45  | | 
% 242.94/49.45  | End of split
% 242.94/49.45  | 
% 242.94/49.45  End of proof
% 242.94/49.45  
% 242.94/49.45  Sub-proof #979 shows that the following formulas are inconsistent:
% 242.94/49.45  ----------------------------------------------------------------
% 242.94/49.45    (1)   ~ (all_52_3 = e0)
% 242.94/49.45    (2)  op(e2, e2) = e3
% 242.94/49.45    (3)  all_56_21 = e2
% 242.94/49.45    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.94/49.45    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.94/49.45         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.94/49.45    (6)   ~ (e3 = e0)
% 242.94/49.45    (7)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.94/49.45         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.94/49.45    (8)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 242.94/49.45    (9)   ~ (e2 = e0)
% 242.94/49.45    (10)  op(e1, e2) = all_52_6
% 242.94/49.45    (11)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 242.94/49.45          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 242.94/49.45    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.94/49.45              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.94/49.45            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.94/49.45            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.94/49.45            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.94/49.45             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.45            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.94/49.45            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.94/49.45            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.94/49.45            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.45            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.94/49.45              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.94/49.45            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.45            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.94/49.45            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.94/49.45            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.94/49.45            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.94/49.45            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.94/49.45              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.94/49.45            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.94/49.45            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.94/49.45            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.94/49.45            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.94/49.45            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.45            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.94/49.45              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.94/49.45            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.45            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.94/49.45    (13)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.45          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.94/49.45    (14)   ~ (all_52_7 = all_52_11)
% 242.94/49.45    (15)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.94/49.45          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.94/49.45    (16)  op(e1, e0) = all_52_14
% 242.94/49.45    (17)   ~ (all_52_7 = e3)
% 242.94/49.45    (18)  op(e0, e3) = all_52_3
% 242.94/49.45    (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.94/49.45          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.94/49.45    (20)   ~ (e3 = e1)
% 242.94/49.45    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.94/49.45          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.94/49.45    (22)   ~ (all_52_2 = all_52_3)
% 242.94/49.45    (23)  all_58_3 = e3
% 242.94/49.45    (24)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.94/49.45          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.94/49.45    (25)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 242.94/49.45          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 242.94/49.45    (26)   ~ (all_52_3 = all_52_7)
% 242.94/49.45    (27)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.45              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.94/49.45                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.94/49.45                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.94/49.45    (28)  op(e3, e1) = all_52_8
% 242.94/49.45    (29)  op(e2, e1) = all_52_9
% 242.94/49.45    (30)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.94/49.45          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.94/49.45    (31)   ~ (e3 = e2)
% 242.94/49.45    (32)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.94/49.45    (33)   ~ (all_52_3 = all_52_11)
% 242.94/49.45    (34)   ~ (all_52_14 = e0)
% 242.94/49.45    (35)  all_56_31 = e0
% 242.94/49.45    (36)  all_54_12 = all_52_3
% 242.94/49.45    (37)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.94/49.45          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.94/49.45    (38)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.45          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.45    (39)  op(e2, e3) = all_52_1
% 242.94/49.45    (40)  op(e3, e3) = e2
% 242.94/49.45    (41)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.94/49.45          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.45    (42)   ~ (all_52_6 = e3)
% 242.94/49.45    (43)  op(e1, e1) = e2
% 242.94/49.45    (44)   ~ (all_52_11 = e0)
% 242.94/49.45    (45)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.94/49.45          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.94/49.45    (46)  op(e0, e2) = all_52_7
% 242.94/49.45    (47)   ~ (all_52_4 = e3)
% 242.94/49.45    (48)  op(e3, e2) = all_52_4
% 242.94/49.45    (49)   ~ (all_52_8 = all_52_11)
% 242.94/49.45    (50)   ~ (all_52_9 = e3)
% 242.94/49.45    (51)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.94/49.45          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.94/49.46    (52)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.94/49.46          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.94/49.46    (53)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.94/49.46          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.94/49.46    (54)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.46          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.46    (55)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.46          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.94/49.46    (56)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.46    (57)  op(e0, e0) = e0
% 242.94/49.46    (58)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.94/49.46          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.94/49.46    (59)  op(e1, e3) = all_52_2
% 242.94/49.46    (60)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.94/49.46          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.94/49.46    (61)  all_56_11 = e3
% 242.94/49.46    (62)   ~ (e1 = e0)
% 242.94/49.46    (63)   ~ (all_52_13 = e3)
% 242.94/49.46    (64)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.94/49.46          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.94/49.46    (65)  all_58_15 = e0
% 242.94/49.46    (66)  op(e2, e0) = all_52_13
% 242.94/49.46    (67)   ~ (all_52_1 = e3)
% 242.94/49.46    (68)  all_54_14 = all_52_11
% 242.94/49.46    (69)   ~ (all_52_1 = e2)
% 242.94/49.46    (70)   ~ (e2 = e1)
% 242.94/49.46    (71)   ~ (all_52_9 = e2)
% 242.94/49.46  
% 242.94/49.46  Begin of proof
% 242.94/49.46  | 
% 242.94/49.46  | BETA: splitting (8) gives:
% 242.94/49.46  | 
% 242.94/49.46  | Case 1:
% 242.94/49.46  | | 
% 242.94/49.46  | |   (72)  all_58_12 = e2 & op(e0, e3) = e2
% 242.94/49.46  | | 
% 242.94/49.46  | | ALPHA: (72) implies:
% 242.94/49.46  | |   (73)  all_58_12 = e2
% 242.94/49.46  | | 
% 242.94/49.46  | | REF_CLOSE: (6), (9), (20), (25), (31), (37), (39), (40), (51), (56), (62),
% 242.94/49.46  | |            (67), (70), (73) are inconsistent by sub-proof #1403.
% 242.94/49.46  | | 
% 242.94/49.46  | Case 2:
% 242.94/49.46  | | 
% 242.94/49.46  | |   (74)  all_58_13 = e2 & op(e0, e2) = e2
% 242.94/49.46  | | 
% 242.94/49.46  | | ALPHA: (74) implies:
% 242.94/49.46  | |   (75)  all_58_13 = e2
% 242.94/49.46  | |   (76)  op(e0, e2) = e2
% 242.94/49.46  | | 
% 242.94/49.46  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 242.94/49.46  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 242.94/49.46  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 242.94/49.46  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 242.94/49.46  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 242.94/49.46  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 242.94/49.46  | |            (70), (71), (75), (76) are inconsistent by sub-proof #980.
% 242.94/49.46  | | 
% 242.94/49.46  | End of split
% 242.94/49.46  | 
% 242.94/49.46  End of proof
% 242.94/49.46  
% 242.94/49.46  Sub-proof #980 shows that the following formulas are inconsistent:
% 242.94/49.46  ----------------------------------------------------------------
% 242.94/49.46    (1)   ~ (all_52_3 = e0)
% 242.94/49.46    (2)  op(e2, e2) = e3
% 242.94/49.46    (3)  all_56_21 = e2
% 242.94/49.46    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.94/49.46    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 242.94/49.46         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.94/49.46    (6)   ~ (e3 = e0)
% 242.94/49.46    (7)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.94/49.46         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.94/49.46    (8)   ~ (e2 = e0)
% 242.94/49.46    (9)  op(e1, e2) = all_52_6
% 242.94/49.46    (10)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 242.94/49.46          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 242.94/49.46    (11)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.94/49.46              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.94/49.46            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.94/49.46            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.94/49.46            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 242.94/49.46             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.46            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.94/49.46            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.94/49.46            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 242.94/49.46            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.46            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.94/49.46              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.94/49.46            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.46            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 242.94/49.46            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.94/49.46            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 242.94/49.46            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.94/49.46            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.94/49.46              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.94/49.46            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.94/49.46            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 242.94/49.46            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.94/49.46            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 242.94/49.46            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.46            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.94/49.46              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.94/49.46            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.46            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.94/49.46    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.46          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 242.94/49.46    (13)   ~ (all_52_7 = all_52_11)
% 242.94/49.46    (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 242.94/49.46          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 242.94/49.46    (15)  op(e1, e0) = all_52_14
% 242.94/49.46    (16)   ~ (all_52_7 = e3)
% 242.94/49.46    (17)  op(e0, e3) = all_52_3
% 242.94/49.46    (18)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.94/49.46          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.94/49.46    (19)  op(e0, e2) = e2
% 242.94/49.46    (20)   ~ (e3 = e1)
% 242.94/49.46    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 242.94/49.46          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 242.94/49.46    (22)   ~ (all_52_2 = all_52_3)
% 242.94/49.46    (23)  all_58_3 = e3
% 242.94/49.46    (24)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 242.94/49.46          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 242.94/49.46    (25)   ~ (all_52_3 = all_52_7)
% 242.94/49.46    (26)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.46              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.94/49.46                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.94/49.46                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.94/49.46    (27)  op(e3, e1) = all_52_8
% 242.94/49.46    (28)  op(e2, e1) = all_52_9
% 242.94/49.46    (29)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 242.94/49.46          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 242.94/49.46    (30)   ~ (e3 = e2)
% 242.94/49.46    (31)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.94/49.46    (32)   ~ (all_52_3 = all_52_11)
% 242.94/49.46    (33)   ~ (all_52_14 = e0)
% 242.94/49.46    (34)  all_56_31 = e0
% 242.94/49.46    (35)  all_54_12 = all_52_3
% 242.94/49.46    (36)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 242.94/49.46          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 242.94/49.46    (37)  all_58_13 = e2
% 242.94/49.46    (38)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.46          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.46    (39)  op(e2, e3) = all_52_1
% 242.94/49.46    (40)  op(e3, e3) = e2
% 242.94/49.46    (41)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.94/49.46          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.46    (42)   ~ (all_52_6 = e3)
% 242.94/49.46    (43)  op(e1, e1) = e2
% 242.94/49.46    (44)   ~ (all_52_11 = e0)
% 242.94/49.46    (45)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 242.94/49.46          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 242.94/49.46    (46)  op(e0, e2) = all_52_7
% 242.94/49.46    (47)   ~ (all_52_4 = e3)
% 242.94/49.46    (48)  op(e3, e2) = all_52_4
% 242.94/49.46    (49)   ~ (all_52_8 = all_52_11)
% 242.94/49.46    (50)   ~ (all_52_9 = e3)
% 242.94/49.46    (51)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 242.94/49.46          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 242.94/49.46    (52)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.94/49.46          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.94/49.46    (53)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 242.94/49.46          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 242.94/49.46    (54)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.46          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.46    (55)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.46          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.94/49.46    (56)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.46    (57)  op(e0, e0) = e0
% 242.94/49.46    (58)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.94/49.46          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.94/49.46    (59)  op(e1, e3) = all_52_2
% 242.94/49.46    (60)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 242.94/49.46          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.94/49.46    (61)  all_56_11 = e3
% 242.94/49.46    (62)   ~ (e1 = e0)
% 242.94/49.46    (63)   ~ (all_52_13 = e3)
% 242.94/49.46    (64)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.94/49.46          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.94/49.46    (65)  all_58_15 = e0
% 242.94/49.46    (66)  op(e2, e0) = all_52_13
% 242.94/49.46    (67)   ~ (all_52_1 = e3)
% 242.94/49.46    (68)  all_54_14 = all_52_11
% 242.94/49.46    (69)   ~ (all_52_1 = e2)
% 242.94/49.46    (70)   ~ (e2 = e1)
% 242.94/49.46    (71)   ~ (all_52_9 = e2)
% 242.94/49.46  
% 242.94/49.46  Begin of proof
% 242.94/49.46  | 
% 242.94/49.46  | BETA: splitting (58) gives:
% 242.94/49.46  | 
% 242.94/49.46  | Case 1:
% 242.94/49.46  | | 
% 242.94/49.46  | |   (72)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 242.94/49.46  | |           e2)
% 242.94/49.46  | | 
% 242.94/49.46  | | BETA: splitting (72) gives:
% 242.94/49.46  | | 
% 242.94/49.46  | | Case 1:
% 242.94/49.46  | | | 
% 242.94/49.46  | | |   (73)  all_58_9 = e2 & op(e3, e0) = e2
% 242.94/49.46  | | | 
% 242.94/49.46  | | | ALPHA: (73) implies:
% 242.94/49.46  | | |   (74)  all_58_9 = e2
% 242.94/49.46  | | |   (75)  op(e3, e0) = e2
% 242.94/49.46  | | | 
% 242.94/49.46  | | | REF_CLOSE: (6), (8), (20), (24), (30), (40), (41), (47), (48), (53), (56),
% 242.94/49.46  | | |            (62), (70), (74), (75) are inconsistent by sub-proof #1069.
% 242.94/49.46  | | | 
% 242.94/49.46  | | Case 2:
% 242.94/49.46  | | | 
% 242.94/49.46  | | |   (76)  all_58_10 = e2 & op(e2, e0) = e2
% 242.94/49.46  | | | 
% 242.94/49.46  | | | ALPHA: (76) implies:
% 242.94/49.46  | | |   (77)  op(e2, e0) = e2
% 242.94/49.46  | | | 
% 242.94/49.46  | | | REF_CLOSE: (1), (3), (4), (8), (11), (13), (15), (17), (19), (22), (25),
% 242.94/49.46  | | |            (27), (28), (31), (32), (33), (34), (35), (39), (44), (46),
% 242.94/49.46  | | |            (49), (56), (59), (61), (67), (68), (69), (71), (77) are
% 242.94/49.46  | | |            inconsistent by sub-proof #999.
% 242.94/49.46  | | | 
% 242.94/49.46  | | End of split
% 242.94/49.46  | | 
% 242.94/49.46  | Case 2:
% 242.94/49.46  | | 
% 242.94/49.46  | |   (78)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 242.94/49.46  | |           e2)
% 242.94/49.46  | | 
% 242.94/49.46  | | BETA: splitting (78) gives:
% 242.94/49.46  | | 
% 242.94/49.46  | | Case 1:
% 242.94/49.46  | | | 
% 242.94/49.46  | | |   (79)  all_58_11 = e2 & op(e1, e0) = e2
% 242.94/49.46  | | | 
% 242.94/49.46  | | | ALPHA: (79) implies:
% 242.94/49.46  | | |   (80)  all_58_11 = e2
% 242.94/49.46  | | | 
% 242.94/49.46  | | | BETA: splitting (38) gives:
% 242.94/49.46  | | | 
% 242.94/49.46  | | | Case 1:
% 242.94/49.46  | | | | 
% 242.94/49.46  | | | |   (81)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 242.94/49.46  | | | |           = e3)
% 242.94/49.46  | | | | 
% 242.94/49.46  | | | | BETA: splitting (81) gives:
% 242.94/49.46  | | | | 
% 242.94/49.46  | | | | Case 1:
% 242.94/49.46  | | | | | 
% 242.94/49.46  | | | | |   (82)  all_58_6 = e3 & op(e1, e3) = e3
% 242.94/49.46  | | | | | 
% 242.94/49.46  | | | | | ALPHA: (82) implies:
% 242.94/49.46  | | | | |   (83)  all_58_6 = e3
% 242.94/49.46  | | | | | 
% 242.94/49.46  | | | | | BETA: splitting (52) gives:
% 242.94/49.46  | | | | | 
% 242.94/49.46  | | | | | Case 1:
% 242.94/49.46  | | | | | | 
% 242.94/49.46  | | | | | |   (84)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2,
% 242.94/49.46  | | | | | |             e0) = e3)
% 242.94/49.46  | | | | | | 
% 242.94/49.46  | | | | | | BETA: splitting (84) gives:
% 242.94/49.46  | | | | | | 
% 242.94/49.46  | | | | | | Case 1:
% 242.94/49.46  | | | | | | | 
% 242.94/49.46  | | | | | | |   (85)  all_58_9 = e3 & op(e3, e0) = e3
% 242.94/49.46  | | | | | | | 
% 242.94/49.46  | | | | | | | ALPHA: (85) implies:
% 242.94/49.46  | | | | | | |   (86)  all_58_9 = e3
% 242.94/49.46  | | | | | | | 
% 242.94/49.46  | | | | | | | BETA: splitting (10) gives:
% 242.94/49.46  | | | | | | | 
% 242.94/49.46  | | | | | | | Case 1:
% 242.94/49.46  | | | | | | | | 
% 242.94/49.46  | | | | | | | |   (87)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 &
% 242.94/49.46  | | | | | | | |           op(e2, e0) = e1)
% 242.94/49.46  | | | | | | | | 
% 242.94/49.46  | | | | | | | | BETA: splitting (87) gives:
% 242.94/49.46  | | | | | | | | 
% 242.94/49.46  | | | | | | | | Case 1:
% 242.94/49.46  | | | | | | | | | 
% 242.94/49.46  | | | | | | | | |   (88)  all_58_9 = e1 & op(e3, e0) = e1
% 242.94/49.46  | | | | | | | | | 
% 242.94/49.46  | | | | | | | | | ALPHA: (88) implies:
% 242.94/49.46  | | | | | | | | |   (89)  all_58_9 = e1
% 242.94/49.46  | | | | | | | | | 
% 242.94/49.46  | | | | | | | | | COMBINE_EQS: (86), (89) imply:
% 242.94/49.46  | | | | | | | | |   (90)  e3 = e1
% 242.94/49.46  | | | | | | | | | 
% 242.94/49.46  | | | | | | | | | REDUCE: (20), (90) imply:
% 242.94/49.46  | | | | | | | | |   (91)  $false
% 242.94/49.46  | | | | | | | | | 
% 242.94/49.46  | | | | | | | | | CLOSE: (91) is inconsistent.
% 242.94/49.46  | | | | | | | | | 
% 242.94/49.46  | | | | | | | | Case 2:
% 242.94/49.46  | | | | | | | | | 
% 242.94/49.46  | | | | | | | | |   (92)  all_58_10 = e1 & op(e2, e0) = e1
% 242.94/49.46  | | | | | | | | | 
% 242.94/49.46  | | | | | | | | | ALPHA: (92) implies:
% 242.94/49.46  | | | | | | | | |   (93)  all_58_10 = e1
% 242.94/49.46  | | | | | | | | |   (94)  op(e2, e0) = e1
% 242.94/49.46  | | | | | | | | | 
% 242.94/49.46  | | | | | | | | | BETA: splitting (18) gives:
% 242.94/49.46  | | | | | | | | | 
% 242.94/49.46  | | | | | | | | | Case 1:
% 242.94/49.46  | | | | | | | | | | 
% 242.94/49.46  | | | | | | | | | |   (95)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 242.94/49.46  | | | | | | | | | |           op(e2, e2) = e2)
% 242.94/49.46  | | | | | | | | | | 
% 242.94/49.46  | | | | | | | | | | REF_CLOSE: (2), (30), (39), (56), (69), (95) are inconsistent
% 242.94/49.46  | | | | | | | | | |            by sub-proof #998.
% 242.94/49.46  | | | | | | | | | | 
% 242.94/49.46  | | | | | | | | | Case 2:
% 242.94/49.46  | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | |   (96)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2
% 242.94/49.47  | | | | | | | | | |           & op(e2, e0) = e2)
% 242.94/49.47  | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | BETA: splitting (96) gives:
% 242.94/49.47  | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | |   (97)  all_58_5 = e2 & op(e2, e1) = e2
% 242.94/49.47  | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | ALPHA: (97) implies:
% 242.94/49.47  | | | | | | | | | | |   (98)  all_58_5 = e2
% 242.94/49.47  | | | | | | | | | | |   (99)  op(e2, e1) = e2
% 242.94/49.47  | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | BETA: splitting (21) gives:
% 242.94/49.47  | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | |   (100)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 242.94/49.47  | | | | | | | | | | | |            & op(e2, e1) = e0)
% 242.94/49.47  | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | BETA: splitting (100) gives:
% 242.94/49.47  | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | |   (101)  all_58_4 = e0 & op(e3, e1) = e0
% 242.94/49.47  | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | ALPHA: (101) implies:
% 242.94/49.47  | | | | | | | | | | | | |   (102)  all_58_4 = e0
% 242.94/49.47  | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 242.94/49.47  | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | |   (103)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 242.94/49.47  | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 242.94/49.47  | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 242.94/49.47  | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | |   (104)  all_58_6 = e0 & op(e1, e3) = e0
% 242.94/49.47  | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 242.94/49.47  | | | | | | | | | | | | | | |   (105)  all_58_6 = e0
% 242.94/49.47  | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (30), (38), (42), (43), (56), (80),
% 242.94/49.47  | | | | | | | | | | | | | | |            (105) are inconsistent by sub-proof #997.
% 242.94/49.47  | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | |   (106)  all_58_7 = e0 & op(e1, e2) = e0
% 242.94/49.47  | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 242.94/49.47  | | | | | | | | | | | | | | |   (107)  op(e1, e2) = e0
% 242.94/49.47  | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | |   (108)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 242.94/49.47  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 242.94/49.47  | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | |   (109)  all_58_1 = e1 & op(e3, e2) = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | |   (110)  all_58_1 = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | |   (111)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (18), (23), (30), (40), (41), (55),
% 242.94/49.47  | | | | | | | | | | | | | | | | | |            (56), (62), (70), (86), (93), (110), (111) are
% 242.94/49.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | |   (112)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | |   (113)  all_58_8 = e1 & op(e1, e1) = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | |   (114)  op(e1, e1) = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | |   (115)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |   (116)  all_58_4 = e3 & op(e3, e1) = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |   (117)  all_58_4 = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (30), (38), (42), (43), (56), (80),
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |            (83), (102), (117) are inconsistent by sub-proof
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |            #990.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |   (118)  all_58_5 = e3 & op(e2, e1) = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (50), (56), (118) are inconsistent by
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1822.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | |   (119)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |   (120)  all_58_8 = e3 & op(e1, e1) = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |   (121)  op(e1, e1) = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (43), (56), (121) are inconsistent by
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2206.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |   (122)  all_58_14 = e3 & op(e0, e1) = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |   (123)  op(e0, e1) = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |   (124)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |   (125)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |   (126)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |          e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |   (127)  op(e2, e3) = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (56), (67), (127) are inconsistent by
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2337.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |   (128)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (129)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |          e2
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (130)  op(e2, e3) = e2
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (56), (69), (130) are inconsistent by
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2336.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (131)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (132)   ~ (all_56_31 = e1)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (133)   ~ (all_56_21 = e1)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (132) imply:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (134)   ~ (e1 = e0)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (56) with e1, e2, e1, e1,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (43), (114) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (135)  e2 = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (135) imply:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (136)  all_58_5 = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (18), (23), (30), (55), (62), (70),
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (136) are inconsistent by sub-proof #992.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |   (137)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (34), (56), (61), (137) are
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1001.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |   (138)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |   (139)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |   (140)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |   (141)   ~ (all_56_31 = e1)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |   (142)  op(e1, e2) = e2
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (141) imply:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |   (143)   ~ (e1 = e0)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (43), (56), (62), (107), (114), (142) are
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2221.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |   (144)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (145)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (146)  op(e1, e2) = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (12), (19), (23), (56), (62),
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            (110), (146) are inconsistent by sub-proof #1718.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (147)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (148)  op(e2, e0) = e2
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (70), (94), (148) are inconsistent by
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1659.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |   (149)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |   (150)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |   (151)  op(e2, e0) = e0
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (62), (66), (94), (151) are inconsistent by
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1778.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |   (152)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (153)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (154)   ~ (all_56_31 = e0)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (154) imply:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (155)  $false
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (156)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = e0
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (157)  op(e0, e1) = e0
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (56), (123), (157) are inconsistent by
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2164.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | |   (158)  all_58_14 = e1 & op(e0, e1) = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | |   (159)  all_58_14 = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | |   (160)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (20), (29), (30), (36), (46),
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | |            (51), (56), (62), (70), (83), (160) are
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1138.
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | |   (161)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |   (162)  all_58_14 = e3 & op(e0, e1) = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |   (163)  all_58_14 = e3
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (163) imply:
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | |   (164)  e3 = e1
% 242.94/49.47  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (164) imply:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |   (165)  all_58_9 = e1
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (20), (24), (30), (40), (41), (47),
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |            (48), (56), (62), (110), (165) are inconsistent by
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1694.
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |   (166)  all_58_15 = e3 & op(e0, e0) = e3
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |   (167)  op(e0, e0) = e3
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (20), (26), (30), (38), (42),
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |            (43), (54), (56), (62), (64), (70), (80), (83),
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |            (167) are inconsistent by sub-proof #984.
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | |   (168)  all_58_3 = e1 & op(e2, e2) = e1
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (20), (23), (30), (52), (58), (65),
% 242.94/49.48  | | | | | | | | | | | | | | | | |            (70), (86), (93), (168) are inconsistent by
% 242.94/49.48  | | | | | | | | | | | | | | | | |            sub-proof #983.
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | |   (169)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 242.94/49.48  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 242.94/49.48  | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (18), (23), (30), (37), (55), (56),
% 242.94/49.48  | | | | | | | | | | | | | | | |            (62), (70), (93), (98), (107), (169) are
% 242.94/49.48  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 242.94/49.48  | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | |   (170)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 242.94/49.48  | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 242.94/49.48  | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | REF_CLOSE: (8), (43), (56), (80), (170) are inconsistent by
% 242.94/49.48  | | | | | | | | | | | | | |            sub-proof #2032.
% 242.94/49.48  | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | |   (171)  all_58_5 = e0 & op(e2, e1) = e0
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | ALPHA: (171) implies:
% 242.94/49.48  | | | | | | | | | | | | |   (172)  op(e2, e1) = e0
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | REF_CLOSE: (8), (56), (99), (172) are inconsistent by
% 242.94/49.48  | | | | | | | | | | | | |            sub-proof #1906.
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | |   (173)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 242.94/49.48  | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 242.94/49.48  | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | BETA: splitting (173) gives:
% 242.94/49.48  | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | Case 1:
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | |   (174)  all_58_8 = e0 & op(e1, e1) = e0
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | ALPHA: (174) implies:
% 242.94/49.48  | | | | | | | | | | | | |   (175)  op(e1, e1) = e0
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | REF_CLOSE: (8), (43), (56), (175) are inconsistent by
% 242.94/49.48  | | | | | | | | | | | | |            sub-proof #2211.
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | |   (176)  all_58_14 = e0 & op(e0, e1) = e0
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | ALPHA: (176) implies:
% 242.94/49.48  | | | | | | | | | | | | |   (177)  op(e0, e1) = e0
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | Case 1:
% 242.94/49.48  | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | |   (178)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 242.94/49.48  | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 242.94/49.48  | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 242.94/49.48  | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | Case 1:
% 242.94/49.48  | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | |   (179)  all_58_6 = e0 & op(e1, e3) = e0
% 242.94/49.48  | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 242.94/49.48  | | | | | | | | | | | | | | |   (180)  all_58_6 = e0
% 242.94/49.48  | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (30), (38), (42), (43), (56), (80),
% 242.94/49.48  | | | | | | | | | | | | | | |            (180) are inconsistent by sub-proof #997.
% 242.94/49.48  | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | |   (181)  all_58_7 = e0 & op(e1, e2) = e0
% 242.94/49.48  | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 242.94/49.48  | | | | | | | | | | | | | | |   (182)  all_58_7 = e0
% 242.94/49.48  | | | | | | | | | | | | | | |   (183)  op(e1, e2) = e0
% 242.94/49.48  | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 242.94/49.48  | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | Case 1:
% 242.94/49.48  | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | |   (184)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 242.94/49.48  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 242.94/49.48  | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 242.94/49.48  | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | |   (185)  all_58_1 = e1 & op(e3, e2) = e1
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 242.94/49.48  | | | | | | | | | | | | | | | | |   (186)  all_58_1 = e1
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | |   (187)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 242.94/49.48  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 242.94/49.48  | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (18), (23), (30), (40), (41), (55),
% 242.94/49.48  | | | | | | | | | | | | | | | | | |            (56), (62), (70), (86), (93), (186), (187) are
% 242.94/49.48  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #991.
% 242.94/49.48  | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | |   (188)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 242.94/49.48  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 242.94/49.48  | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | |   (189)  all_58_8 = e1 & op(e1, e1) = e1
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | |   (190)  all_58_8 = e1
% 242.94/49.48  | | | | | | | | | | | | | | | | | | |   (191)  op(e1, e1) = e1
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | |   (192)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (20), (29), (30), (36), (46),
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | |            (51), (56), (62), (70), (83), (192) are
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1138.
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | |   (193)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |   (194)  all_58_14 = e3 & op(e0, e1) = e3
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |   (195)  op(e0, e1) = e3
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (56), (177), (195) are inconsistent by
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2164.
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |   (196)  all_58_15 = e3 & op(e0, e0) = e3
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |   (197)  op(e0, e0) = e3
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (26), (30), (43), (54), (56), (70),
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |            (80), (83), (182), (190), (191), (197) are
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #987.
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | |   (198)  all_58_14 = e1 & op(e0, e1) = e1
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | ALPHA: (198) implies:
% 242.94/49.48  | | | | | | | | | | | | | | | | | | |   (199)  op(e0, e1) = e1
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (62), (177), (199) are inconsistent by
% 242.94/49.48  | | | | | | | | | | | | | | | | | | |            sub-proof #2158.
% 242.94/49.48  | | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | |   (200)  all_58_3 = e1 & op(e2, e2) = e1
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (20), (23), (30), (52), (58), (65),
% 242.94/49.48  | | | | | | | | | | | | | | | | |            (70), (86), (93), (200) are inconsistent by
% 242.94/49.48  | | | | | | | | | | | | | | | | |            sub-proof #983.
% 242.94/49.48  | | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | |   (201)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 242.94/49.48  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 242.94/49.48  | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (18), (23), (30), (37), (55), (56),
% 242.94/49.48  | | | | | | | | | | | | | | | |            (62), (70), (93), (98), (183), (201) are
% 242.94/49.48  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 242.94/49.48  | | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | |   (202)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 242.94/49.48  | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 242.94/49.48  | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | | REF_CLOSE: (8), (43), (56), (80), (202) are inconsistent by
% 242.94/49.48  | | | | | | | | | | | | | |            sub-proof #2109.
% 242.94/49.48  | | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | |   (203)  all_58_10 = e2 & op(e2, e0) = e2
% 242.94/49.48  | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | ALPHA: (203) implies:
% 242.94/49.48  | | | | | | | | | | |   (204)  op(e2, e0) = e2
% 242.94/49.48  | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | | REF_CLOSE: (56), (70), (94), (204) are inconsistent by
% 242.94/49.48  | | | | | | | | | | |            sub-proof #1659.
% 242.94/49.48  | | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | | 
% 242.94/49.48  | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | 
% 242.94/49.48  | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | 
% 242.94/49.48  | | | | | | | |   (205)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 242.94/49.48  | | | | | | | |            op(e0, e0) = e1)
% 242.94/49.48  | | | | | | | | 
% 242.94/49.48  | | | | | | | | BETA: splitting (205) gives:
% 242.94/49.48  | | | | | | | | 
% 242.94/49.48  | | | | | | | | Case 1:
% 242.94/49.48  | | | | | | | | | 
% 242.94/49.48  | | | | | | | | |   (206)  all_58_11 = e1 & op(e1, e0) = e1
% 242.94/49.48  | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | REF_CLOSE: (70), (80), (206) are inconsistent by sub-proof
% 242.94/49.48  | | | | | | | | |            #1346.
% 242.94/49.48  | | | | | | | | | 
% 242.94/49.48  | | | | | | | | Case 2:
% 242.94/49.48  | | | | | | | | | 
% 242.94/49.48  | | | | | | | | |   (207)  all_58_15 = e1 & op(e0, e0) = e1
% 242.94/49.48  | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | ALPHA: (207) implies:
% 242.94/49.48  | | | | | | | | |   (208)  op(e0, e0) = e1
% 242.94/49.48  | | | | | | | | | 
% 242.94/49.48  | | | | | | | | | REF_CLOSE: (56), (57), (62), (208) are inconsistent by
% 242.94/49.48  | | | | | | | | |            sub-proof #2274.
% 242.94/49.48  | | | | | | | | | 
% 242.94/49.48  | | | | | | | | End of split
% 242.94/49.48  | | | | | | | | 
% 242.94/49.48  | | | | | | | End of split
% 242.94/49.48  | | | | | | | 
% 242.94/49.48  | | | | | | Case 2:
% 242.94/49.48  | | | | | | | 
% 242.94/49.48  | | | | | | |   (209)  all_58_10 = e3 & op(e2, e0) = e3
% 242.94/49.48  | | | | | | | 
% 242.94/49.48  | | | | | | | ALPHA: (209) implies:
% 242.94/49.48  | | | | | | |   (210)  op(e2, e0) = e3
% 242.94/49.48  | | | | | | | 
% 242.94/49.48  | | | | | | | REF_CLOSE: (56), (63), (66), (210) are inconsistent by sub-proof
% 242.94/49.48  | | | | | | |            #1994.
% 242.94/49.48  | | | | | | | 
% 242.94/49.48  | | | | | | End of split
% 242.94/49.48  | | | | | | 
% 242.94/49.48  | | | | | Case 2:
% 242.94/49.48  | | | | | | 
% 242.94/49.48  | | | | | |   (211)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 242.94/49.48  | | | | | |            op(e0, e0) = e3)
% 242.94/49.48  | | | | | | 
% 242.94/49.48  | | | | | | REF_CLOSE: (6), (7), (8), (9), (20), (26), (30), (38), (42), (43),
% 242.94/49.48  | | | | | |            (54), (56), (62), (64), (70), (80), (83), (211) are
% 242.94/49.48  | | | | | |            inconsistent by sub-proof #981.
% 242.94/49.48  | | | | | | 
% 242.94/49.48  | | | | | End of split
% 242.94/49.48  | | | | | 
% 242.94/49.48  | | | | Case 2:
% 242.94/49.48  | | | | | 
% 242.94/49.48  | | | | |   (212)  all_58_7 = e3 & op(e1, e2) = e3
% 242.94/49.48  | | | | | 
% 242.94/49.48  | | | | | ALPHA: (212) implies:
% 242.94/49.48  | | | | |   (213)  op(e1, e2) = e3
% 242.94/49.48  | | | | | 
% 242.94/49.48  | | | | | REF_CLOSE: (9), (42), (56), (213) are inconsistent by sub-proof #2191.
% 242.94/49.48  | | | | | 
% 242.94/49.48  | | | | End of split
% 242.94/49.48  | | | | 
% 242.94/49.48  | | | Case 2:
% 242.94/49.48  | | | | 
% 242.94/49.48  | | | |   (214)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 242.94/49.48  | | | |              e0) = e3)
% 242.94/49.48  | | | | 
% 242.94/49.48  | | | | REF_CLOSE: (30), (43), (56), (80), (214) are inconsistent by sub-proof
% 242.94/49.48  | | | |            #2029.
% 242.94/49.48  | | | | 
% 242.94/49.48  | | | End of split
% 242.94/49.48  | | | 
% 242.94/49.48  | | Case 2:
% 242.94/49.48  | | | 
% 242.94/49.48  | | |   (215)  all_58_15 = e2 & op(e0, e0) = e2
% 242.94/49.48  | | | 
% 242.94/49.48  | | | ALPHA: (215) implies:
% 242.94/49.48  | | |   (216)  all_58_15 = e2
% 242.94/49.48  | | | 
% 242.94/49.48  | | | REF_CLOSE: (8), (65), (216) are inconsistent by sub-proof #1507.
% 242.94/49.48  | | | 
% 242.94/49.48  | | End of split
% 242.94/49.48  | | 
% 242.94/49.48  | End of split
% 242.94/49.48  | 
% 242.94/49.48  End of proof
% 242.94/49.48  
% 242.94/49.48  Sub-proof #981 shows that the following formulas are inconsistent:
% 242.94/49.48  ----------------------------------------------------------------
% 242.94/49.48    (1)   ~ (e3 = e0)
% 242.94/49.48    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.94/49.48         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.94/49.48    (3)  all_58_6 = e3
% 242.94/49.48    (4)   ~ (e2 = e0)
% 242.94/49.48    (5)  op(e1, e2) = all_52_6
% 242.94/49.48    (6)   ~ (e3 = e1)
% 242.94/49.48    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.48             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.94/49.48               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.94/49.48               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.94/49.48    (8)   ~ (e3 = e2)
% 242.94/49.48    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.48         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.48    (10)  all_58_11 = e2
% 242.94/49.48    (11)   ~ (all_52_6 = e3)
% 242.94/49.48    (12)  op(e1, e1) = e2
% 242.94/49.48    (13)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.48          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.48    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.48    (15)   ~ (e1 = e0)
% 242.94/49.48    (16)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.94/49.48    (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.94/49.48          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.94/49.48    (18)   ~ (e2 = e1)
% 242.94/49.48  
% 242.94/49.48  Begin of proof
% 242.94/49.48  | 
% 242.94/49.48  | BETA: splitting (16) gives:
% 242.94/49.48  | 
% 242.94/49.48  | Case 1:
% 242.94/49.48  | | 
% 242.94/49.48  | |   (19)  all_58_11 = e3 & op(e1, e0) = e3
% 242.94/49.48  | | 
% 242.94/49.48  | | ALPHA: (19) implies:
% 242.94/49.48  | |   (20)  all_58_11 = e3
% 242.94/49.48  | | 
% 242.94/49.48  | | REF_CLOSE: (8), (10), (20) are inconsistent by sub-proof #2030.
% 242.94/49.48  | | 
% 242.94/49.48  | Case 2:
% 242.94/49.48  | | 
% 242.94/49.48  | |   (21)  all_58_15 = e3 & op(e0, e0) = e3
% 242.94/49.48  | | 
% 242.94/49.48  | | ALPHA: (21) implies:
% 242.94/49.48  | |   (22)  op(e0, e0) = e3
% 242.94/49.48  | | 
% 242.94/49.48  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 242.94/49.48  | |            (13), (14), (15), (17), (18), (22) are inconsistent by sub-proof
% 242.94/49.48  | |            #984.
% 242.94/49.48  | | 
% 242.94/49.48  | End of split
% 242.94/49.48  | 
% 242.94/49.48  End of proof
% 242.94/49.48  
% 242.94/49.48  Sub-proof #982 shows that the following formulas are inconsistent:
% 242.94/49.48  ----------------------------------------------------------------
% 242.94/49.48    (1)   ~ (e3 = e0)
% 242.94/49.48    (2)   ~ (e2 = e0)
% 242.94/49.48    (3)  op(e1, e2) = all_52_6
% 242.94/49.48    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.94/49.48         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.94/49.48    (5)  all_58_3 = e3
% 242.94/49.48    (6)  op(e1, e2) = e0
% 242.94/49.48    (7)   ~ (e3 = e2)
% 242.94/49.48    (8)  all_58_13 = e2
% 242.94/49.48    (9)  all_58_5 = e2
% 242.94/49.48    (10)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.48          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.94/49.48    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.48    (12)   ~ (e1 = e0)
% 242.94/49.48    (13)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 242.94/49.48    (14)  all_58_10 = e1
% 242.94/49.48    (15)   ~ (e2 = e1)
% 242.94/49.48  
% 242.94/49.48  Begin of proof
% 242.94/49.48  | 
% 242.94/49.48  | BETA: splitting (13) gives:
% 242.94/49.48  | 
% 242.94/49.48  | Case 1:
% 242.94/49.48  | | 
% 242.94/49.48  | |   (16)  all_58_7 = e1 & op(e1, e2) = e1
% 242.94/49.48  | | 
% 242.94/49.48  | | ALPHA: (16) implies:
% 242.94/49.48  | |   (17)  op(e1, e2) = e1
% 242.94/49.48  | | 
% 242.94/49.48  | | REF_CLOSE: (3), (6), (11), (12), (17) are inconsistent by sub-proof #2136.
% 242.94/49.48  | | 
% 242.94/49.48  | Case 2:
% 242.94/49.48  | | 
% 242.94/49.48  | |   (18)  all_58_13 = e1 & op(e0, e2) = e1
% 242.94/49.48  | | 
% 242.94/49.48  | | ALPHA: (18) implies:
% 242.94/49.48  | |   (19)  all_58_13 = e1
% 242.94/49.48  | | 
% 242.94/49.48  | | COMBINE_EQS: (8), (19) imply:
% 242.94/49.48  | |   (20)  e2 = e1
% 242.94/49.48  | | 
% 242.94/49.48  | | SIMP: (20) implies:
% 242.94/49.48  | |   (21)  e2 = e1
% 242.94/49.48  | | 
% 242.94/49.48  | | COMBINE_EQS: (9), (21) imply:
% 242.94/49.48  | |   (22)  all_58_5 = e1
% 242.94/49.48  | | 
% 242.94/49.48  | | REF_CLOSE: (1), (2), (4), (5), (7), (10), (12), (14), (15), (22) are
% 242.94/49.48  | |            inconsistent by sub-proof #992.
% 242.94/49.48  | | 
% 242.94/49.48  | End of split
% 242.94/49.48  | 
% 242.94/49.48  End of proof
% 242.94/49.48  
% 242.94/49.48  Sub-proof #983 shows that the following formulas are inconsistent:
% 242.94/49.48  ----------------------------------------------------------------
% 242.94/49.48    (1)   ~ (e3 = e0)
% 242.94/49.48    (2)   ~ (e2 = e0)
% 242.94/49.48    (3)   ~ (e3 = e1)
% 242.94/49.48    (4)  all_58_3 = e3
% 242.94/49.48    (5)   ~ (e3 = e2)
% 242.94/49.48    (6)  all_58_9 = e3
% 242.94/49.48    (7)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 242.94/49.48         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 242.94/49.48    (8)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 242.94/49.48         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 242.94/49.48    (9)  all_58_3 = e1 & op(e2, e2) = e1
% 242.94/49.48    (10)  all_58_15 = e0
% 242.94/49.48    (11)  all_58_10 = e1
% 242.94/49.48    (12)   ~ (e2 = e1)
% 242.94/49.48  
% 242.94/49.48  Begin of proof
% 242.94/49.48  | 
% 242.94/49.48  | ALPHA: (9) implies:
% 242.94/49.48  |   (13)  all_58_3 = e1
% 242.94/49.48  | 
% 242.94/49.48  | COMBINE_EQS: (4), (13) imply:
% 242.94/49.48  |   (14)  e3 = e1
% 242.94/49.48  | 
% 242.94/49.48  | COMBINE_EQS: (6), (14) imply:
% 242.94/49.48  |   (15)  all_58_9 = e1
% 242.94/49.48  | 
% 242.94/49.48  | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (12), (15) are
% 242.94/49.48  |            inconsistent by sub-proof #1495.
% 242.94/49.48  | 
% 242.94/49.48  End of proof
% 242.94/49.48  
% 242.94/49.48  Sub-proof #984 shows that the following formulas are inconsistent:
% 242.94/49.48  ----------------------------------------------------------------
% 242.94/49.48    (1)   ~ (e3 = e0)
% 242.94/49.48    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 242.94/49.48         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 242.94/49.48    (3)  all_58_6 = e3
% 242.94/49.49    (4)   ~ (e2 = e0)
% 242.94/49.49    (5)  op(e1, e2) = all_52_6
% 242.94/49.49    (6)   ~ (e3 = e1)
% 242.94/49.49    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.49             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.94/49.49               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.94/49.49               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.94/49.49    (8)   ~ (e3 = e2)
% 242.94/49.49    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.49         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.49    (10)  all_58_11 = e2
% 242.94/49.49    (11)   ~ (all_52_6 = e3)
% 242.94/49.49    (12)  op(e1, e1) = e2
% 242.94/49.49    (13)  op(e0, e0) = e3
% 242.94/49.49    (14)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.49          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.49    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.49    (16)   ~ (e1 = e0)
% 242.94/49.49    (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.94/49.49          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.94/49.49    (18)   ~ (e2 = e1)
% 242.94/49.49  
% 242.94/49.49  Begin of proof
% 242.94/49.49  | 
% 242.94/49.49  | BETA: splitting (2) gives:
% 242.94/49.49  | 
% 242.94/49.49  | Case 1:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (19)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 242.94/49.49  | |           e1)
% 242.94/49.49  | | 
% 242.94/49.49  | | BETA: splitting (19) gives:
% 242.94/49.49  | | 
% 242.94/49.49  | | Case 1:
% 242.94/49.49  | | | 
% 242.94/49.49  | | |   (20)  all_58_6 = e1 & op(e1, e3) = e1
% 242.94/49.49  | | | 
% 242.94/49.49  | | | REF_CLOSE: (3), (6), (20) are inconsistent by sub-proof #1803.
% 242.94/49.49  | | | 
% 242.94/49.49  | | Case 2:
% 242.94/49.49  | | | 
% 242.94/49.49  | | |   (21)  all_58_7 = e1 & op(e1, e2) = e1
% 242.94/49.49  | | | 
% 242.94/49.49  | | | ALPHA: (21) implies:
% 242.94/49.49  | | |   (22)  op(e1, e2) = e1
% 242.94/49.49  | | | 
% 242.94/49.49  | | | BETA: splitting (17) gives:
% 242.94/49.49  | | | 
% 242.94/49.49  | | | Case 1:
% 242.94/49.49  | | | | 
% 242.94/49.49  | | | |   (23)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2)
% 242.94/49.49  | | | |           = e0)
% 242.94/49.49  | | | | 
% 242.94/49.49  | | | | REF_CLOSE: (1), (5), (8), (9), (10), (11), (12), (15), (16), (22), (23)
% 242.94/49.49  | | | |            are inconsistent by sub-proof #989.
% 242.94/49.49  | | | | 
% 242.94/49.49  | | | Case 2:
% 242.94/49.49  | | | | 
% 242.94/49.49  | | | |   (24)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0)
% 242.94/49.49  | | | |           = e0)
% 242.94/49.49  | | | | 
% 242.94/49.49  | | | | REF_CLOSE: (4), (10), (12), (15), (24) are inconsistent by sub-proof
% 242.94/49.49  | | | |            #2032.
% 242.94/49.49  | | | | 
% 242.94/49.49  | | | End of split
% 242.94/49.49  | | | 
% 242.94/49.49  | | End of split
% 242.94/49.49  | | 
% 242.94/49.49  | Case 2:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (25)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 242.94/49.49  | |           e1)
% 242.94/49.49  | | 
% 242.94/49.49  | | BETA: splitting (25) gives:
% 242.94/49.49  | | 
% 242.94/49.49  | | Case 1:
% 242.94/49.49  | | | 
% 242.94/49.49  | | |   (26)  all_58_8 = e1 & op(e1, e1) = e1
% 242.94/49.49  | | | 
% 242.94/49.49  | | | ALPHA: (26) implies:
% 242.94/49.49  | | |   (27)  all_58_8 = e1
% 242.94/49.49  | | |   (28)  op(e1, e1) = e1
% 242.94/49.49  | | | 
% 242.94/49.49  | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 242.94/49.49  | | |            (14), (15), (16), (17), (18), (27), (28) are inconsistent by
% 242.94/49.49  | | |            sub-proof #985.
% 242.94/49.49  | | | 
% 242.94/49.49  | | Case 2:
% 242.94/49.49  | | | 
% 242.94/49.49  | | |   (29)  all_58_11 = e1 & op(e1, e0) = e1
% 242.94/49.49  | | | 
% 242.94/49.49  | | | ALPHA: (29) implies:
% 242.94/49.49  | | |   (30)  all_58_11 = e1
% 242.94/49.49  | | | 
% 242.94/49.49  | | | REF_CLOSE: (10), (18), (30) are inconsistent by sub-proof #1020.
% 242.94/49.49  | | | 
% 242.94/49.49  | | End of split
% 242.94/49.49  | | 
% 242.94/49.49  | End of split
% 242.94/49.49  | 
% 242.94/49.49  End of proof
% 242.94/49.49  
% 242.94/49.49  Sub-proof #985 shows that the following formulas are inconsistent:
% 242.94/49.49  ----------------------------------------------------------------
% 242.94/49.49    (1)   ~ (e3 = e0)
% 242.94/49.49    (2)  op(e1, e1) = e1
% 242.94/49.49    (3)  all_58_6 = e3
% 242.94/49.49    (4)   ~ (e2 = e0)
% 242.94/49.49    (5)  op(e1, e2) = all_52_6
% 242.94/49.49    (6)  all_58_8 = e1
% 242.94/49.49    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.49             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.94/49.49               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.94/49.49               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.94/49.49    (8)   ~ (e3 = e2)
% 242.94/49.49    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.49         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.49    (10)  all_58_11 = e2
% 242.94/49.49    (11)   ~ (all_52_6 = e3)
% 242.94/49.49    (12)  op(e1, e1) = e2
% 242.94/49.49    (13)  op(e0, e0) = e3
% 242.94/49.49    (14)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.49          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.49    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.49    (16)   ~ (e1 = e0)
% 242.94/49.49    (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 242.94/49.49          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.94/49.49    (18)   ~ (e2 = e1)
% 242.94/49.49  
% 242.94/49.49  Begin of proof
% 242.94/49.49  | 
% 242.94/49.49  | BETA: splitting (17) gives:
% 242.94/49.49  | 
% 242.94/49.49  | Case 1:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (19)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 242.94/49.49  | |           e0)
% 242.94/49.49  | | 
% 242.94/49.49  | | BETA: splitting (19) gives:
% 242.94/49.49  | | 
% 242.94/49.49  | | Case 1:
% 242.94/49.49  | | | 
% 242.94/49.49  | | |   (20)  all_58_6 = e0 & op(e1, e3) = e0
% 242.94/49.49  | | | 
% 242.94/49.49  | | | ALPHA: (20) implies:
% 242.94/49.49  | | |   (21)  all_58_6 = e0
% 242.94/49.49  | | | 
% 242.94/49.49  | | | REF_CLOSE: (1), (5), (8), (9), (10), (11), (12), (15), (21) are
% 242.94/49.49  | | |            inconsistent by sub-proof #997.
% 242.94/49.49  | | | 
% 242.94/49.49  | | Case 2:
% 242.94/49.49  | | | 
% 242.94/49.49  | | |   (22)  all_58_7 = e0 & op(e1, e2) = e0
% 242.94/49.49  | | | 
% 242.94/49.49  | | | ALPHA: (22) implies:
% 242.94/49.49  | | |   (23)  all_58_7 = e0
% 242.94/49.49  | | | 
% 242.94/49.49  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (12), (13), (14),
% 242.94/49.49  | | |            (15), (18), (23) are inconsistent by sub-proof #987.
% 242.94/49.49  | | | 
% 242.94/49.49  | | End of split
% 242.94/49.49  | | 
% 242.94/49.49  | Case 2:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (24)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.94/49.49  | |           e0)
% 242.94/49.49  | | 
% 242.94/49.49  | | REF_CLOSE: (2), (4), (10), (15), (16), (24) are inconsistent by sub-proof
% 242.94/49.49  | |            #986.
% 242.94/49.49  | | 
% 242.94/49.49  | End of split
% 242.94/49.49  | 
% 242.94/49.49  End of proof
% 242.94/49.49  
% 242.94/49.49  Sub-proof #986 shows that the following formulas are inconsistent:
% 242.94/49.49  ----------------------------------------------------------------
% 242.94/49.49    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 242.94/49.49    (2)  op(e1, e1) = e1
% 242.94/49.49    (3)   ~ (e2 = e0)
% 242.94/49.49    (4)  all_58_11 = e2
% 242.94/49.49    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.49    (6)   ~ (e1 = e0)
% 242.94/49.49  
% 242.94/49.49  Begin of proof
% 242.94/49.49  | 
% 242.94/49.49  | BETA: splitting (1) gives:
% 242.94/49.49  | 
% 242.94/49.49  | Case 1:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 242.94/49.49  | | 
% 242.94/49.49  | | ALPHA: (7) implies:
% 242.94/49.49  | |   (8)  op(e1, e1) = e0
% 242.94/49.49  | | 
% 242.94/49.49  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2220.
% 242.94/49.49  | | 
% 242.94/49.49  | Case 2:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (9)  all_58_11 = e0 & op(e1, e0) = e0
% 242.94/49.49  | | 
% 242.94/49.49  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #2033.
% 242.94/49.49  | | 
% 242.94/49.49  | End of split
% 242.94/49.49  | 
% 242.94/49.49  End of proof
% 242.94/49.49  
% 242.94/49.49  Sub-proof #987 shows that the following formulas are inconsistent:
% 242.94/49.49  ----------------------------------------------------------------
% 242.94/49.49    (1)   ~ (e3 = e0)
% 242.94/49.49    (2)  op(e1, e1) = e1
% 242.94/49.49    (3)  all_58_6 = e3
% 242.94/49.49    (4)   ~ (e2 = e0)
% 242.94/49.49    (5)  all_58_7 = e0
% 242.94/49.49    (6)  all_58_8 = e1
% 242.94/49.49    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.49             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 242.94/49.49               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 242.94/49.49               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 242.94/49.49    (8)   ~ (e3 = e2)
% 242.94/49.49    (9)  all_58_11 = e2
% 242.94/49.49    (10)  op(e1, e1) = e2
% 242.94/49.49    (11)  op(e0, e0) = e3
% 242.94/49.49    (12)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.49          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.49    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.49    (14)   ~ (e2 = e1)
% 242.94/49.49  
% 242.94/49.49  Begin of proof
% 242.94/49.49  | 
% 242.94/49.49  | BETA: splitting (7) gives:
% 242.94/49.49  | 
% 242.94/49.49  | Case 1:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (15)  all_58_15 = e0 & op(e0, e0) = e0
% 242.94/49.49  | | 
% 242.94/49.49  | | ALPHA: (15) implies:
% 242.94/49.49  | |   (16)  op(e0, e0) = e0
% 242.94/49.49  | | 
% 242.94/49.49  | | REF_CLOSE: (1), (11), (13), (16) are inconsistent by sub-proof #2079.
% 242.94/49.49  | | 
% 242.94/49.49  | Case 2:
% 242.94/49.49  | | 
% 242.94/49.49  | | 
% 242.94/49.49  | | GROUND_INST: instantiating (13) with e1, e2, e1, e1, simplifying with (2),
% 242.94/49.49  | |              (10) gives:
% 242.94/49.49  | |   (17)  e2 = e1
% 242.94/49.49  | | 
% 242.94/49.49  | | COMBINE_EQS: (9), (17) imply:
% 242.94/49.49  | |   (18)  all_58_11 = e1
% 242.94/49.49  | | 
% 242.94/49.49  | | REF_CLOSE: (3), (4), (5), (6), (8), (12), (14), (18) are inconsistent by
% 242.94/49.49  | |            sub-proof #988.
% 242.94/49.49  | | 
% 242.94/49.49  | End of split
% 242.94/49.49  | 
% 242.94/49.49  End of proof
% 242.94/49.49  
% 242.94/49.49  Sub-proof #988 shows that the following formulas are inconsistent:
% 242.94/49.49  ----------------------------------------------------------------
% 242.94/49.49    (1)  all_58_6 = e3
% 242.94/49.49    (2)   ~ (e2 = e0)
% 242.94/49.49    (3)  all_58_7 = e0
% 242.94/49.49    (4)  all_58_11 = e1
% 242.94/49.49    (5)  all_58_8 = e1
% 242.94/49.49    (6)   ~ (e3 = e2)
% 242.94/49.49    (7)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 242.94/49.49         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 242.94/49.49    (8)   ~ (e2 = e1)
% 242.94/49.49  
% 242.94/49.49  Begin of proof
% 242.94/49.49  | 
% 242.94/49.49  | BETA: splitting (7) gives:
% 242.94/49.49  | 
% 242.94/49.49  | Case 1:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (9)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 242.94/49.49  | | 
% 242.94/49.49  | | BETA: splitting (9) gives:
% 242.94/49.49  | | 
% 242.94/49.49  | | Case 1:
% 242.94/49.49  | | | 
% 242.94/49.49  | | |   (10)  all_58_6 = e2 & op(e1, e3) = e2
% 242.94/49.49  | | | 
% 242.94/49.49  | | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #2219.
% 242.94/49.49  | | | 
% 242.94/49.49  | | Case 2:
% 242.94/49.49  | | | 
% 242.94/49.49  | | |   (11)  all_58_7 = e2 & op(e1, e2) = e2
% 242.94/49.49  | | | 
% 242.94/49.49  | | | REF_CLOSE: (2), (3), (11) are inconsistent by sub-proof #1326.
% 242.94/49.49  | | | 
% 242.94/49.49  | | End of split
% 242.94/49.49  | | 
% 242.94/49.49  | Case 2:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (12)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 242.94/49.49  | |           e2)
% 242.94/49.49  | | 
% 242.94/49.49  | | BETA: splitting (12) gives:
% 242.94/49.49  | | 
% 242.94/49.49  | | Case 1:
% 242.94/49.49  | | | 
% 242.94/49.49  | | |   (13)  all_58_8 = e2 & op(e1, e1) = e2
% 242.94/49.49  | | | 
% 242.94/49.49  | | | REF_CLOSE: (5), (8), (13) are inconsistent by sub-proof #2217.
% 242.94/49.49  | | | 
% 242.94/49.49  | | Case 2:
% 242.94/49.49  | | | 
% 242.94/49.49  | | |   (14)  all_58_11 = e2 & op(e1, e0) = e2
% 242.94/49.49  | | | 
% 242.94/49.49  | | | ALPHA: (14) implies:
% 242.94/49.49  | | |   (15)  all_58_11 = e2
% 242.94/49.49  | | | 
% 242.94/49.49  | | | REF_CLOSE: (4), (8), (15) are inconsistent by sub-proof #1020.
% 242.94/49.49  | | | 
% 242.94/49.49  | | End of split
% 242.94/49.49  | | 
% 242.94/49.49  | End of split
% 242.94/49.49  | 
% 242.94/49.49  End of proof
% 242.94/49.49  
% 242.94/49.49  Sub-proof #989 shows that the following formulas are inconsistent:
% 242.94/49.49  ----------------------------------------------------------------
% 242.94/49.49    (1)   ~ (e3 = e0)
% 242.94/49.49    (2)  op(e1, e2) = e1
% 242.94/49.49    (3)  op(e1, e2) = all_52_6
% 242.94/49.49    (4)   ~ (e3 = e2)
% 242.94/49.49    (5)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.49         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.49    (6)  all_58_11 = e2
% 242.94/49.49    (7)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 242.94/49.49    (8)   ~ (all_52_6 = e3)
% 242.94/49.49    (9)  op(e1, e1) = e2
% 242.94/49.49    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.49    (11)   ~ (e1 = e0)
% 242.94/49.49  
% 242.94/49.49  Begin of proof
% 242.94/49.49  | 
% 242.94/49.49  | BETA: splitting (7) gives:
% 242.94/49.49  | 
% 242.94/49.49  | Case 1:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (12)  all_58_6 = e0 & op(e1, e3) = e0
% 242.94/49.49  | | 
% 242.94/49.49  | | ALPHA: (12) implies:
% 242.94/49.49  | |   (13)  all_58_6 = e0
% 242.94/49.49  | | 
% 242.94/49.49  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (13) are inconsistent by
% 242.94/49.49  | |            sub-proof #997.
% 242.94/49.49  | | 
% 242.94/49.49  | Case 2:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (14)  all_58_7 = e0 & op(e1, e2) = e0
% 242.94/49.49  | | 
% 242.94/49.49  | | ALPHA: (14) implies:
% 242.94/49.49  | |   (15)  op(e1, e2) = e0
% 242.94/49.49  | | 
% 242.94/49.49  | | REF_CLOSE: (2), (3), (10), (11), (15) are inconsistent by sub-proof #2136.
% 242.94/49.49  | | 
% 242.94/49.49  | End of split
% 242.94/49.49  | 
% 242.94/49.49  End of proof
% 242.94/49.49  
% 242.94/49.49  Sub-proof #990 shows that the following formulas are inconsistent:
% 242.94/49.49  ----------------------------------------------------------------
% 242.94/49.49    (1)   ~ (e3 = e0)
% 242.94/49.49    (2)  all_58_6 = e3
% 242.94/49.49    (3)  op(e1, e2) = all_52_6
% 242.94/49.49    (4)   ~ (e3 = e2)
% 242.94/49.49    (5)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.49         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.49    (6)  all_58_11 = e2
% 242.94/49.49    (7)   ~ (all_52_6 = e3)
% 242.94/49.49    (8)  op(e1, e1) = e2
% 242.94/49.49    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.49    (10)  all_58_4 = e3
% 242.94/49.49    (11)  all_58_4 = e0
% 242.94/49.49  
% 242.94/49.49  Begin of proof
% 242.94/49.49  | 
% 242.94/49.49  | COMBINE_EQS: (10), (11) imply:
% 242.94/49.49  |   (12)  e3 = e0
% 242.94/49.49  | 
% 242.94/49.49  | SIMP: (12) implies:
% 242.94/49.49  |   (13)  e3 = e0
% 242.94/49.49  | 
% 242.94/49.49  | COMBINE_EQS: (2), (13) imply:
% 242.94/49.49  |   (14)  all_58_6 = e0
% 242.94/49.49  | 
% 242.94/49.49  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (14) are inconsistent by
% 242.94/49.49  |            sub-proof #997.
% 242.94/49.49  | 
% 242.94/49.49  End of proof
% 242.94/49.49  
% 242.94/49.49  Sub-proof #991 shows that the following formulas are inconsistent:
% 242.94/49.49  ----------------------------------------------------------------
% 242.94/49.49    (1)  all_58_1 = e1
% 242.94/49.49    (2)   ~ (e3 = e0)
% 242.94/49.49    (3)   ~ (e2 = e0)
% 242.94/49.49    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 242.94/49.49    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.94/49.49         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.94/49.49    (6)  all_58_3 = e3
% 242.94/49.49    (7)   ~ (e3 = e2)
% 242.94/49.49    (8)  all_58_9 = e3
% 242.94/49.49    (9)  op(e3, e3) = e2
% 242.94/49.49    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 242.94/49.49          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 242.94/49.49    (11)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.49          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.94/49.49    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.49    (13)   ~ (e1 = e0)
% 242.94/49.49    (14)  all_58_10 = e1
% 242.94/49.49    (15)   ~ (e2 = e1)
% 242.94/49.49  
% 242.94/49.49  Begin of proof
% 242.94/49.49  | 
% 242.94/49.49  | BETA: splitting (4) gives:
% 242.94/49.49  | 
% 242.94/49.49  | Case 1:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (16)  all_58_4 = e1 & op(e3, e1) = e1
% 242.94/49.49  | | 
% 242.94/49.49  | | ALPHA: (16) implies:
% 242.94/49.49  | |   (17)  all_58_4 = e1
% 242.94/49.49  | | 
% 242.94/49.49  | | REF_CLOSE: (1), (2), (3), (8), (9), (10), (12), (13), (17) are inconsistent
% 242.94/49.49  | |            by sub-proof #1646.
% 242.94/49.49  | | 
% 242.94/49.49  | Case 2:
% 242.94/49.49  | | 
% 242.94/49.49  | |   (18)  all_58_5 = e1 & op(e2, e1) = e1
% 242.94/49.49  | | 
% 242.94/49.49  | | ALPHA: (18) implies:
% 242.94/49.49  | |   (19)  all_58_5 = e1
% 242.94/49.49  | | 
% 242.94/49.49  | | REF_CLOSE: (2), (3), (5), (6), (7), (11), (13), (14), (15), (19) are
% 242.94/49.49  | |            inconsistent by sub-proof #992.
% 242.94/49.49  | | 
% 242.94/49.49  | End of split
% 242.94/49.49  | 
% 242.94/49.49  End of proof
% 242.94/49.49  
% 242.94/49.49  Sub-proof #992 shows that the following formulas are inconsistent:
% 242.94/49.49  ----------------------------------------------------------------
% 242.94/49.49    (1)   ~ (e3 = e0)
% 242.94/49.49    (2)   ~ (e2 = e0)
% 242.94/49.50    (3)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 242.94/49.50         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 242.94/49.50    (4)  all_58_3 = e3
% 242.94/49.50    (5)   ~ (e3 = e2)
% 242.94/49.50    (6)  all_58_5 = e1
% 242.94/49.50    (7)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.50         (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.94/49.50    (8)   ~ (e1 = e0)
% 242.94/49.50    (9)  all_58_10 = e1
% 242.94/49.50    (10)   ~ (e2 = e1)
% 242.94/49.50  
% 242.94/49.50  Begin of proof
% 242.94/49.50  | 
% 242.94/49.50  | BETA: splitting (3) gives:
% 242.94/49.50  | 
% 242.94/49.50  | Case 1:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (11)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 242.94/49.50  | |           e2)
% 242.94/49.50  | | 
% 242.94/49.50  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11) are inconsistent by
% 242.94/49.50  | |            sub-proof #993.
% 242.94/49.50  | | 
% 242.94/49.50  | Case 2:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (12)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 242.94/49.50  | |           e2)
% 242.94/49.50  | | 
% 242.94/49.50  | | BETA: splitting (12) gives:
% 242.94/49.50  | | 
% 242.94/49.50  | | Case 1:
% 242.94/49.50  | | | 
% 242.94/49.50  | | |   (13)  all_58_5 = e2 & op(e2, e1) = e2
% 242.94/49.50  | | | 
% 242.94/49.50  | | | ALPHA: (13) implies:
% 242.94/49.50  | | |   (14)  all_58_5 = e2
% 242.94/49.50  | | | 
% 242.94/49.50  | | | REF_CLOSE: (6), (10), (14) are inconsistent by sub-proof #1665.
% 242.94/49.50  | | | 
% 242.94/49.50  | | Case 2:
% 242.94/49.50  | | | 
% 242.94/49.50  | | |   (15)  all_58_10 = e2 & op(e2, e0) = e2
% 242.94/49.50  | | | 
% 242.94/49.50  | | | REF_CLOSE: (9), (10), (15) are inconsistent by sub-proof #1622.
% 242.94/49.50  | | | 
% 242.94/49.50  | | End of split
% 242.94/49.50  | | 
% 242.94/49.50  | End of split
% 242.94/49.50  | 
% 242.94/49.50  End of proof
% 242.94/49.50  
% 242.94/49.50  Sub-proof #993 shows that the following formulas are inconsistent:
% 242.94/49.50  ----------------------------------------------------------------
% 242.94/49.50    (1)   ~ (e3 = e0)
% 242.94/49.50    (2)   ~ (e2 = e0)
% 242.94/49.50    (3)  all_58_3 = e3
% 242.94/49.50    (4)   ~ (e3 = e2)
% 242.94/49.50    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 242.94/49.50    (6)  all_58_5 = e1
% 242.94/49.50    (7)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.50         (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.94/49.50    (8)   ~ (e1 = e0)
% 242.94/49.50    (9)  all_58_10 = e1
% 242.94/49.50  
% 242.94/49.50  Begin of proof
% 242.94/49.50  | 
% 242.94/49.50  | BETA: splitting (5) gives:
% 242.94/49.50  | 
% 242.94/49.50  | Case 1:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (10)  all_58_2 = e2 & op(e2, e3) = e2
% 242.94/49.50  | | 
% 242.94/49.50  | | ALPHA: (10) implies:
% 242.94/49.50  | |   (11)  all_58_2 = e2
% 242.94/49.50  | | 
% 242.94/49.50  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (11) are inconsistent by
% 242.94/49.50  | |            sub-proof #994.
% 242.94/49.50  | | 
% 242.94/49.50  | Case 2:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (12)  all_58_3 = e2 & op(e2, e2) = e2
% 242.94/49.50  | | 
% 242.94/49.50  | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #1106.
% 242.94/49.50  | | 
% 242.94/49.50  | End of split
% 242.94/49.50  | 
% 242.94/49.50  End of proof
% 242.94/49.50  
% 242.94/49.50  Sub-proof #994 shows that the following formulas are inconsistent:
% 242.94/49.50  ----------------------------------------------------------------
% 242.94/49.50    (1)   ~ (e3 = e0)
% 242.94/49.50    (2)   ~ (e2 = e0)
% 242.94/49.50    (3)  all_58_2 = e2
% 242.94/49.50    (4)  all_58_3 = e3
% 242.94/49.50    (5)  all_58_5 = e1
% 242.94/49.50    (6)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 242.94/49.50         (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 242.94/49.50    (7)   ~ (e1 = e0)
% 242.94/49.50    (8)  all_58_10 = e1
% 242.94/49.50  
% 242.94/49.50  Begin of proof
% 242.94/49.50  | 
% 242.94/49.50  | BETA: splitting (6) gives:
% 242.94/49.50  | 
% 242.94/49.50  | Case 1:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (9)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 242.94/49.50  | | 
% 242.94/49.50  | | REF_CLOSE: (1), (2), (3), (4), (9) are inconsistent by sub-proof #996.
% 242.94/49.50  | | 
% 242.94/49.50  | Case 2:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (10)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 242.94/49.50  | |           e0)
% 242.94/49.50  | | 
% 242.94/49.50  | | BETA: splitting (10) gives:
% 242.94/49.50  | | 
% 242.94/49.50  | | Case 1:
% 242.94/49.50  | | | 
% 242.94/49.50  | | |   (11)  all_58_5 = e0 & op(e2, e1) = e0
% 242.94/49.50  | | | 
% 242.94/49.50  | | | REF_CLOSE: (5), (7), (11) are inconsistent by sub-proof #1485.
% 242.94/49.50  | | | 
% 242.94/49.50  | | Case 2:
% 242.94/49.50  | | | 
% 242.94/49.50  | | |   (12)  all_58_10 = e0 & op(e2, e0) = e0
% 242.94/49.50  | | | 
% 242.94/49.50  | | | REF_CLOSE: (7), (8), (12) are inconsistent by sub-proof #995.
% 242.94/49.50  | | | 
% 242.94/49.50  | | End of split
% 242.94/49.50  | | 
% 242.94/49.50  | End of split
% 242.94/49.50  | 
% 242.94/49.50  End of proof
% 242.94/49.50  
% 242.94/49.50  Sub-proof #995 shows that the following formulas are inconsistent:
% 242.94/49.50  ----------------------------------------------------------------
% 242.94/49.50    (1)  all_58_10 = e0 & op(e2, e0) = e0
% 242.94/49.50    (2)  all_58_10 = e1
% 242.94/49.50    (3)   ~ (e1 = e0)
% 242.94/49.50  
% 242.94/49.50  Begin of proof
% 242.94/49.50  | 
% 242.94/49.50  | ALPHA: (1) implies:
% 242.94/49.50  |   (4)  all_58_10 = e0
% 242.94/49.50  | 
% 242.94/49.50  | COMBINE_EQS: (2), (4) imply:
% 242.94/49.50  |   (5)  e1 = e0
% 242.94/49.50  | 
% 242.94/49.50  | REDUCE: (3), (5) imply:
% 242.94/49.50  |   (6)  $false
% 242.94/49.50  | 
% 242.94/49.50  | CLOSE: (6) is inconsistent.
% 242.94/49.50  | 
% 242.94/49.50  End of proof
% 242.94/49.50  
% 242.94/49.50  Sub-proof #996 shows that the following formulas are inconsistent:
% 242.94/49.50  ----------------------------------------------------------------
% 242.94/49.50    (1)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 242.94/49.50    (2)   ~ (e3 = e0)
% 242.94/49.50    (3)   ~ (e2 = e0)
% 242.94/49.50    (4)  all_58_2 = e2
% 242.94/49.50    (5)  all_58_3 = e3
% 242.94/49.50  
% 242.94/49.50  Begin of proof
% 242.94/49.50  | 
% 242.94/49.50  | BETA: splitting (1) gives:
% 242.94/49.50  | 
% 242.94/49.50  | Case 1:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (6)  all_58_2 = e0 & op(e2, e3) = e0
% 242.94/49.50  | | 
% 242.94/49.50  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #1535.
% 242.94/49.50  | | 
% 242.94/49.50  | Case 2:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (7)  all_58_3 = e0 & op(e2, e2) = e0
% 242.94/49.50  | | 
% 242.94/49.50  | | ALPHA: (7) implies:
% 242.94/49.50  | |   (8)  all_58_3 = e0
% 242.94/49.50  | | 
% 242.94/49.50  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #1460.
% 242.94/49.50  | | 
% 242.94/49.50  | End of split
% 242.94/49.50  | 
% 242.94/49.50  End of proof
% 242.94/49.50  
% 242.94/49.50  Sub-proof #997 shows that the following formulas are inconsistent:
% 242.94/49.50  ----------------------------------------------------------------
% 242.94/49.50    (1)   ~ (e3 = e0)
% 242.94/49.50    (2)  op(e1, e2) = all_52_6
% 242.94/49.50    (3)   ~ (e3 = e2)
% 242.94/49.50    (4)  all_58_6 = e0
% 242.94/49.50    (5)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 242.94/49.50         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 242.94/49.50    (6)  all_58_11 = e2
% 242.94/49.50    (7)   ~ (all_52_6 = e3)
% 242.94/49.50    (8)  op(e1, e1) = e2
% 242.94/49.50    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.50  
% 242.94/49.50  Begin of proof
% 242.94/49.50  | 
% 242.94/49.50  | BETA: splitting (5) gives:
% 242.94/49.50  | 
% 242.94/49.50  | Case 1:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 242.94/49.50  | |           e3)
% 242.94/49.50  | | 
% 242.94/49.50  | | REF_CLOSE: (1), (2), (4), (7), (9), (10) are inconsistent by sub-proof
% 242.94/49.50  | |            #1983.
% 242.94/49.50  | | 
% 242.94/49.50  | Case 2:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (11)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 242.94/49.50  | |           e3)
% 242.94/49.50  | | 
% 242.94/49.50  | | REF_CLOSE: (3), (6), (8), (9), (11) are inconsistent by sub-proof #2107.
% 242.94/49.50  | | 
% 242.94/49.50  | End of split
% 242.94/49.50  | 
% 242.94/49.50  End of proof
% 242.94/49.50  
% 242.94/49.50  Sub-proof #998 shows that the following formulas are inconsistent:
% 242.94/49.50  ----------------------------------------------------------------
% 242.94/49.50    (1)  op(e2, e2) = e3
% 242.94/49.50    (2)   ~ (e3 = e2)
% 242.94/49.50    (3)  op(e2, e3) = all_52_1
% 242.94/49.50    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 242.94/49.50    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.50    (6)   ~ (all_52_1 = e2)
% 242.94/49.50  
% 242.94/49.50  Begin of proof
% 242.94/49.50  | 
% 242.94/49.50  | BETA: splitting (4) gives:
% 242.94/49.50  | 
% 242.94/49.50  | Case 1:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (7)  all_58_2 = e2 & op(e2, e3) = e2
% 242.94/49.50  | | 
% 242.94/49.50  | | ALPHA: (7) implies:
% 242.94/49.50  | |   (8)  op(e2, e3) = e2
% 242.94/49.50  | | 
% 242.94/49.50  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2336.
% 242.94/49.50  | | 
% 242.94/49.50  | Case 2:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (9)  all_58_3 = e2 & op(e2, e2) = e2
% 242.94/49.50  | | 
% 242.94/49.50  | | ALPHA: (9) implies:
% 242.94/49.50  | |   (10)  op(e2, e2) = e2
% 242.94/49.50  | | 
% 242.94/49.50  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #2140.
% 242.94/49.50  | | 
% 242.94/49.50  | End of split
% 242.94/49.50  | 
% 242.94/49.50  End of proof
% 242.94/49.50  
% 242.94/49.50  Sub-proof #999 shows that the following formulas are inconsistent:
% 242.94/49.50  ----------------------------------------------------------------
% 242.94/49.50    (1)   ~ (all_52_3 = e0)
% 242.94/49.50    (2)  all_56_21 = e2
% 242.94/49.50    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 242.94/49.50    (4)   ~ (e2 = e0)
% 242.94/49.50    (5)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 242.94/49.50           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 242.94/49.50             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.94/49.50           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.94/49.50             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 242.94/49.50           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.50           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 242.94/49.50           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 242.94/49.50           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 242.94/49.50           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.50           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 242.94/49.50             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.94/49.50           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.50           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 242.94/49.50           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.94/49.50           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 242.94/49.50           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 242.94/49.50           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 242.94/49.50             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 242.94/49.50           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 242.94/49.50           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 242.94/49.50           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 242.94/49.50           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 242.94/49.50           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.50           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 242.94/49.50             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 242.94/49.50           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.50           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.94/49.50    (6)   ~ (all_52_7 = all_52_11)
% 242.94/49.50    (7)  op(e1, e0) = all_52_14
% 242.94/49.50    (8)  op(e0, e3) = all_52_3
% 242.94/49.50    (9)  op(e0, e2) = e2
% 242.94/49.50    (10)   ~ (all_52_2 = all_52_3)
% 242.94/49.50    (11)   ~ (all_52_3 = all_52_7)
% 242.94/49.50    (12)  op(e3, e1) = all_52_8
% 242.94/49.50    (13)  op(e2, e1) = all_52_9
% 242.94/49.50    (14)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 242.94/49.50    (15)   ~ (all_52_3 = all_52_11)
% 242.94/49.50    (16)   ~ (all_52_14 = e0)
% 242.94/49.50    (17)  op(e2, e0) = e2
% 242.94/49.50    (18)  all_56_31 = e0
% 242.94/49.50    (19)  all_54_12 = all_52_3
% 242.94/49.50    (20)  op(e2, e3) = all_52_1
% 242.94/49.50    (21)   ~ (all_52_11 = e0)
% 242.94/49.50    (22)  op(e0, e2) = all_52_7
% 242.94/49.50    (23)   ~ (all_52_8 = all_52_11)
% 242.94/49.50    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.50    (25)  op(e1, e3) = all_52_2
% 242.94/49.50    (26)  all_56_11 = e3
% 242.94/49.50    (27)   ~ (all_52_1 = e3)
% 242.94/49.50    (28)  all_54_14 = all_52_11
% 242.94/49.50    (29)   ~ (all_52_1 = e2)
% 242.94/49.50    (30)   ~ (all_52_9 = e2)
% 242.94/49.50  
% 242.94/49.50  Begin of proof
% 242.94/49.50  | 
% 242.94/49.50  | BETA: splitting (5) gives:
% 242.94/49.50  | 
% 242.94/49.50  | Case 1:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (31)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 242.94/49.50  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 242.94/49.50  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 242.94/49.50  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.50  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 242.94/49.50  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 242.94/49.50  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 242.94/49.50  | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 242.94/49.50  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.50  | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 242.94/49.50  | |           = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &
% 242.94/49.50  | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 242.94/49.50  | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 242.94/49.50  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.50  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.94/49.50  | | 
% 242.94/49.50  | | BETA: splitting (31) gives:
% 242.94/49.50  | | 
% 242.94/49.50  | | Case 1:
% 242.94/49.50  | | | 
% 242.94/49.50  | | |   (32)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 242.94/49.50  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.94/49.50  | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 242.94/49.50  | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 242.94/49.50  | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 242.94/49.50  | | |         | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.94/49.50  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.94/49.50  | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.94/49.50  | | | 
% 242.94/49.50  | | | BETA: splitting (32) gives:
% 242.94/49.50  | | | 
% 242.94/49.50  | | | Case 1:
% 242.94/49.50  | | | | 
% 242.94/49.50  | | | |   (33)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 242.94/49.50  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.94/49.50  | | | |         op(e3, e2) = e3 & op(e2, e3) = e3
% 242.94/49.50  | | | | 
% 242.94/49.50  | | | | ALPHA: (33) implies:
% 242.94/49.50  | | | |   (34)  op(e2, e3) = e3
% 242.94/49.50  | | | | 
% 242.94/49.50  | | | | REF_CLOSE: (20), (24), (27), (34) are inconsistent by sub-proof #2337.
% 242.94/49.50  | | | | 
% 242.94/49.50  | | | Case 2:
% 242.94/49.50  | | | | 
% 242.94/49.50  | | | |   (35)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.94/49.50  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.94/49.50  | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 242.94/49.50  | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 242.94/49.50  | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 242.94/49.50  | | | |           op(e1, e3) = e3)
% 242.94/49.50  | | | | 
% 242.94/49.50  | | | | BETA: splitting (35) gives:
% 242.94/49.50  | | | | 
% 242.94/49.50  | | | | Case 1:
% 242.94/49.50  | | | | | 
% 242.94/49.50  | | | | |   (36)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.94/49.50  | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.94/49.50  | | | | |         op(e3, e2) = e2 & op(e2, e3) = e2
% 242.94/49.50  | | | | | 
% 242.94/49.50  | | | | | ALPHA: (36) implies:
% 242.94/49.50  | | | | |   (37)  op(e2, e3) = e2
% 242.94/49.50  | | | | | 
% 242.94/49.50  | | | | | REF_CLOSE: (20), (24), (29), (37) are inconsistent by sub-proof #2336.
% 242.94/49.50  | | | | | 
% 242.94/49.50  | | | | Case 2:
% 242.94/49.50  | | | | | 
% 242.94/49.50  | | | | |   (38)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.94/49.50  | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.94/49.50  | | | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 242.94/49.50  | | | | | 
% 242.94/49.50  | | | | | REF_CLOSE: (1), (3), (6), (9), (10), (11), (12), (14), (15), (19),
% 242.94/49.50  | | | | |            (21), (22), (23), (24), (25), (28), (38) are inconsistent
% 242.94/49.50  | | | | |            by sub-proof #1854.
% 242.94/49.50  | | | | | 
% 242.94/49.50  | | | | End of split
% 242.94/49.50  | | | | 
% 242.94/49.50  | | | End of split
% 242.94/49.50  | | | 
% 242.94/49.50  | | Case 2:
% 242.94/49.50  | | | 
% 242.94/49.50  | | |   (39)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 242.94/49.50  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.94/49.50  | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 242.94/49.50  | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 242.94/49.50  | | |             = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 242.94/49.50  | | |           e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 242.94/49.50  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 242.94/49.50  | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.94/49.50  | | | 
% 242.94/49.50  | | | REF_CLOSE: (1), (8), (18), (24), (26), (39) are inconsistent by sub-proof
% 242.94/49.50  | | |            #1001.
% 242.94/49.50  | | | 
% 242.94/49.50  | | End of split
% 242.94/49.50  | | 
% 242.94/49.50  | Case 2:
% 242.94/49.50  | | 
% 242.94/49.50  | |   (40)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 242.94/49.50  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.94/49.50  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 242.94/49.50  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.94/49.50  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 242.94/49.50  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.50  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.94/49.50  | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 242.94/49.50  | |           e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 242.94/49.50  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 242.94/49.50  | |         (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.50  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.94/49.50  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 242.94/49.50  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 242.94/49.50  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.94/49.50  | | 
% 242.94/49.50  | | BETA: splitting (40) gives:
% 242.94/49.50  | | 
% 242.94/49.50  | | Case 1:
% 242.94/49.50  | | | 
% 242.94/49.51  | | |   (41)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 242.94/49.51  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.94/49.51  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 242.94/49.51  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 242.94/49.51  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 242.94/49.51  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.51  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.94/49.51  | | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 242.94/49.51  | | | 
% 242.94/49.51  | | | REF_CLOSE: (2), (13), (18), (24), (30), (41) are inconsistent by sub-proof
% 242.94/49.51  | | |            #1732.
% 242.94/49.51  | | | 
% 242.94/49.51  | | Case 2:
% 242.94/49.51  | | | 
% 242.94/49.51  | | |   (42)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 242.94/49.51  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 242.94/49.51  | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29
% 242.94/49.51  | | |           = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 242.94/49.51  | | |             = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 242.94/49.51  | | |           e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 242.94/49.51  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 242.94/49.51  | | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.94/49.51  | | | 
% 242.94/49.51  | | | REF_CLOSE: (4), (7), (16), (17), (18), (24), (42) are inconsistent by
% 242.94/49.51  | | |            sub-proof #1000.
% 242.94/49.51  | | | 
% 242.94/49.51  | | End of split
% 242.94/49.51  | | 
% 242.94/49.51  | End of split
% 242.94/49.51  | 
% 242.94/49.51  End of proof
% 242.94/49.51  
% 242.94/49.51  Sub-proof #1000 shows that the following formulas are inconsistent:
% 242.94/49.51  ----------------------------------------------------------------
% 242.94/49.51    (1)   ~ (e2 = e0)
% 242.94/49.51    (2)  op(e1, e0) = all_52_14
% 242.94/49.51    (3)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.94/49.51             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 242.94/49.51           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 242.94/49.51             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 242.94/49.51           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 242.94/49.51           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.51           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.94/49.51    (4)   ~ (all_52_14 = e0)
% 242.94/49.51    (5)  op(e2, e0) = e2
% 242.94/49.51    (6)  all_56_31 = e0
% 242.94/49.51    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.51  
% 242.94/49.51  Begin of proof
% 242.94/49.51  | 
% 242.94/49.51  | BETA: splitting (3) gives:
% 242.94/49.51  | 
% 242.94/49.51  | Case 1:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 242.94/49.51  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 242.94/49.51  | |        & op(e0, e2) = e0
% 242.94/49.51  | | 
% 242.94/49.51  | | ALPHA: (8) implies:
% 242.94/49.51  | |   (9)  op(e2, e0) = e0
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (1), (5), (7), (9) are inconsistent by sub-proof #2121.
% 242.94/49.51  | | 
% 242.94/49.51  | Case 2:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 242.94/49.51  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.94/49.51  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 242.94/49.51  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 242.94/49.51  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (2), (4), (6), (7), (10) are inconsistent by sub-proof #2322.
% 242.94/49.51  | | 
% 242.94/49.51  | End of split
% 242.94/49.51  | 
% 242.94/49.51  End of proof
% 242.94/49.51  
% 242.94/49.51  Sub-proof #1001 shows that the following formulas are inconsistent:
% 242.94/49.51  ----------------------------------------------------------------
% 242.94/49.51    (1)   ~ (all_52_3 = e0)
% 242.94/49.51    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.94/49.51             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.94/49.51           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 242.94/49.51           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.94/49.51           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 242.94/49.51           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.51           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.94/49.51    (3)  op(e0, e3) = all_52_3
% 242.94/49.51    (4)  all_56_31 = e0
% 242.94/49.51    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.51    (6)  all_56_11 = e3
% 242.94/49.51  
% 242.94/49.51  Begin of proof
% 242.94/49.51  | 
% 242.94/49.51  | BETA: splitting (2) gives:
% 242.94/49.51  | 
% 242.94/49.51  | Case 1:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (7)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.94/49.51  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.94/49.51  | |        op(e1, e3) = e1
% 242.94/49.51  | | 
% 242.94/49.51  | | ALPHA: (7) implies:
% 242.94/49.51  | |   (8)   ~ (all_56_11 = e3)
% 242.94/49.51  | | 
% 242.94/49.51  | | REDUCE: (6), (8) imply:
% 242.94/49.51  | |   (9)  $false
% 242.94/49.51  | | 
% 242.94/49.51  | | CLOSE: (9) is inconsistent.
% 242.94/49.51  | | 
% 242.94/49.51  | Case 2:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 242.94/49.51  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 242.94/49.51  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.94/49.51  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.51  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #2308.
% 242.94/49.51  | | 
% 242.94/49.51  | End of split
% 242.94/49.51  | 
% 242.94/49.51  End of proof
% 242.94/49.51  
% 242.94/49.51  Sub-proof #1002 shows that the following formulas are inconsistent:
% 242.94/49.51  ----------------------------------------------------------------
% 242.94/49.51    (1)   ~ (all_52_3 = e0)
% 242.94/49.51    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.94/49.51             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.94/49.51           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 242.94/49.51           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.94/49.51           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 242.94/49.51           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.51           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.94/49.51    (3)  op(e0, e3) = all_52_3
% 242.94/49.51    (4)   ~ (all_52_2 = e1)
% 242.94/49.51    (5)  all_56_31 = e0
% 242.94/49.51    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.51    (7)  op(e1, e3) = all_52_2
% 242.94/49.51  
% 242.94/49.51  Begin of proof
% 242.94/49.51  | 
% 242.94/49.51  | BETA: splitting (2) gives:
% 242.94/49.51  | 
% 242.94/49.51  | Case 1:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (8)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.94/49.51  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.94/49.51  | |        op(e1, e3) = e1
% 242.94/49.51  | | 
% 242.94/49.51  | | ALPHA: (8) implies:
% 242.94/49.51  | |   (9)  op(e1, e3) = e1
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (4), (6), (7), (9) are inconsistent by sub-proof #1948.
% 242.94/49.51  | | 
% 242.94/49.51  | Case 2:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 242.94/49.51  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 242.94/49.51  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.94/49.51  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.51  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #2308.
% 242.94/49.51  | | 
% 242.94/49.51  | End of split
% 242.94/49.51  | 
% 242.94/49.51  End of proof
% 242.94/49.51  
% 242.94/49.51  Sub-proof #1003 shows that the following formulas are inconsistent:
% 242.94/49.51  ----------------------------------------------------------------
% 242.94/49.51    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 242.94/49.51           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 242.94/49.51             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.94/49.51           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.94/49.51             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 242.94/49.51           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.51           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.94/49.51    (2)  op(e2, e3) = all_52_1
% 242.94/49.51    (3)  all_56_21 = e1
% 242.94/49.51    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.51    (5)   ~ (all_52_1 = e3)
% 242.94/49.51    (6)   ~ (all_52_1 = e2)
% 242.94/49.51  
% 242.94/49.51  Begin of proof
% 242.94/49.51  | 
% 242.94/49.51  | BETA: splitting (1) gives:
% 242.94/49.51  | 
% 242.94/49.51  | Case 1:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.94/49.51  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.94/49.51  | |        op(e2, e3) = e3
% 242.94/49.51  | | 
% 242.94/49.51  | | ALPHA: (7) implies:
% 242.94/49.51  | |   (8)  op(e2, e3) = e3
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2337.
% 242.94/49.51  | | 
% 242.94/49.51  | Case 2:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (9)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.94/49.51  | |            e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2
% 242.94/49.51  | |          & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1
% 242.94/49.51  | |            = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 242.94/49.51  | |            = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (2), (3), (4), (6), (9) are inconsistent by sub-proof #2311.
% 242.94/49.51  | | 
% 242.94/49.51  | End of split
% 242.94/49.51  | 
% 242.94/49.51  End of proof
% 242.94/49.51  
% 242.94/49.51  Sub-proof #1004 shows that the following formulas are inconsistent:
% 242.94/49.51  ----------------------------------------------------------------
% 242.94/49.51    (1)   ~ (all_52_3 = e0)
% 242.94/49.51    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.94/49.51             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.94/49.51           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 242.94/49.51           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.94/49.51           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 242.94/49.51           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.51           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.94/49.51    (3)  op(e0, e3) = all_52_3
% 242.94/49.51    (4)  op(e3, e0) = all_52_12
% 242.94/49.51    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.51    (6)   ~ (all_52_12 = e3)
% 242.94/49.51    (7)  all_56_11 = e3
% 242.94/49.51  
% 242.94/49.51  Begin of proof
% 242.94/49.51  | 
% 242.94/49.51  | BETA: splitting (2) gives:
% 242.94/49.51  | 
% 242.94/49.51  | Case 1:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (8)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.94/49.51  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.94/49.51  | |        op(e1, e3) = e1
% 242.94/49.51  | | 
% 242.94/49.51  | | ALPHA: (8) implies:
% 242.94/49.51  | |   (9)   ~ (all_56_11 = e3)
% 242.94/49.51  | | 
% 242.94/49.51  | | REDUCE: (7), (9) imply:
% 242.94/49.51  | |   (10)  $false
% 242.94/49.51  | | 
% 242.94/49.51  | | CLOSE: (10) is inconsistent.
% 242.94/49.51  | | 
% 242.94/49.51  | Case 2:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (11)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 242.94/49.51  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 242.94/49.51  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.94/49.51  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.51  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (1), (3), (4), (5), (6), (11) are inconsistent by sub-proof
% 242.94/49.51  | |            #1794.
% 242.94/49.51  | | 
% 242.94/49.51  | End of split
% 242.94/49.51  | 
% 242.94/49.51  End of proof
% 242.94/49.51  
% 242.94/49.51  Sub-proof #1005 shows that the following formulas are inconsistent:
% 242.94/49.51  ----------------------------------------------------------------
% 242.94/49.51    (1)   ~ (all_52_3 = e0)
% 242.94/49.51    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.94/49.51             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.94/49.51           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 242.94/49.51           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 242.94/49.51           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 242.94/49.51           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.51           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.94/49.51    (3)  op(e0, e3) = all_52_3
% 242.94/49.51    (4)   ~ (all_52_2 = e1)
% 242.94/49.51    (5)  op(e3, e0) = all_52_12
% 242.94/49.51    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.51    (7)  op(e1, e3) = all_52_2
% 242.94/49.51    (8)   ~ (all_52_12 = e3)
% 242.94/49.51  
% 242.94/49.51  Begin of proof
% 242.94/49.51  | 
% 242.94/49.51  | BETA: splitting (2) gives:
% 242.94/49.51  | 
% 242.94/49.51  | Case 1:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (9)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.94/49.51  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 242.94/49.51  | |        op(e1, e3) = e1
% 242.94/49.51  | | 
% 242.94/49.51  | | ALPHA: (9) implies:
% 242.94/49.51  | |   (10)  op(e1, e3) = e1
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (4), (6), (7), (10) are inconsistent by sub-proof #1948.
% 242.94/49.51  | | 
% 242.94/49.51  | Case 2:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (11)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 242.94/49.51  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 242.94/49.51  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 242.94/49.51  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 242.94/49.51  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (1), (3), (5), (6), (8), (11) are inconsistent by sub-proof
% 242.94/49.51  | |            #1794.
% 242.94/49.51  | | 
% 242.94/49.51  | End of split
% 242.94/49.51  | 
% 242.94/49.51  End of proof
% 242.94/49.51  
% 242.94/49.51  Sub-proof #1006 shows that the following formulas are inconsistent:
% 242.94/49.51  ----------------------------------------------------------------
% 242.94/49.51    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 242.94/49.51           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 242.94/49.51             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 242.94/49.51           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 242.94/49.51             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 242.94/49.51           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.51           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.94/49.51    (2)  op(e3, e1) = all_52_8
% 242.94/49.51    (3)  op(e2, e3) = all_52_1
% 242.94/49.51    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.51    (5)  all_56_11 = e3
% 242.94/49.51    (6)   ~ (all_52_1 = e3)
% 242.94/49.51    (7)   ~ (all_52_8 = e3)
% 242.94/49.51  
% 242.94/49.51  Begin of proof
% 242.94/49.51  | 
% 242.94/49.51  | BETA: splitting (1) gives:
% 242.94/49.51  | 
% 242.94/49.51  | Case 1:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 242.94/49.51  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 242.94/49.51  | |        op(e2, e3) = e3
% 242.94/49.51  | | 
% 242.94/49.51  | | ALPHA: (8) implies:
% 242.94/49.51  | |   (9)  op(e2, e3) = e3
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #2337.
% 242.94/49.51  | | 
% 242.94/49.51  | Case 2:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 242.94/49.51  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 242.94/49.51  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 242.94/49.51  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 242.94/49.51  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (2), (4), (5), (7), (10) are inconsistent by sub-proof #1007.
% 242.94/49.51  | | 
% 242.94/49.51  | End of split
% 242.94/49.51  | 
% 242.94/49.51  End of proof
% 242.94/49.51  
% 242.94/49.51  Sub-proof #1007 shows that the following formulas are inconsistent:
% 242.94/49.51  ----------------------------------------------------------------
% 242.94/49.51    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 242.94/49.51           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 242.94/49.51             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 242.94/49.51           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 242.94/49.51             e1) = e3 & op(e1, e3) = e3)
% 242.94/49.51    (2)  op(e3, e1) = all_52_8
% 242.94/49.51    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 242.94/49.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 242.94/49.51    (4)  all_56_11 = e3
% 242.94/49.51    (5)   ~ (all_52_8 = e3)
% 242.94/49.51  
% 242.94/49.51  Begin of proof
% 242.94/49.51  | 
% 242.94/49.51  | BETA: splitting (1) gives:
% 242.94/49.51  | 
% 242.94/49.51  | Case 1:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (6)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 242.94/49.51  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 242.94/49.51  | |        op(e2, e3) = e2
% 242.94/49.51  | | 
% 242.94/49.51  | | ALPHA: (6) implies:
% 242.94/49.51  | |   (7)   ~ (all_56_11 = e3)
% 242.94/49.51  | | 
% 242.94/49.51  | | REDUCE: (4), (7) imply:
% 242.94/49.51  | |   (8)  $false
% 242.94/49.51  | | 
% 242.94/49.51  | | CLOSE: (8) is inconsistent.
% 242.94/49.51  | | 
% 242.94/49.51  | Case 2:
% 242.94/49.51  | | 
% 242.94/49.51  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 242.94/49.51  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 242.94/49.51  | |        op(e1, e3) = e3
% 242.94/49.51  | | 
% 242.94/49.51  | | ALPHA: (9) implies:
% 242.94/49.51  | |   (10)  op(e3, e1) = e3
% 242.94/49.51  | | 
% 242.94/49.51  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #2260.
% 242.94/49.51  | | 
% 242.94/49.51  | End of split
% 242.94/49.51  | 
% 242.94/49.51  End of proof
% 242.94/49.51  
% 242.94/49.51  Sub-proof #1008 shows that the following formulas are inconsistent:
% 242.94/49.51  ----------------------------------------------------------------
% 242.94/49.51    (1)   ~ (e3 = e0)
% 242.94/49.51    (2)   ~ (e2 = e0)
% 242.94/49.51    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 242.94/49.51         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 242.94/49.51    (4)  op(e1, e2) = all_52_6
% 242.94/49.52    (5)  op(e1, e1) = all_6_2
% 242.94/49.52    (6)  op(e1, e0) = all_52_14
% 242.94/49.52    (7)   ~ (e3 = e1)
% 242.94/49.52    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.04/49.52         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.04/49.52    (9)  op(e3, e3) = e1
% 243.04/49.52    (10)   ~ (all_6_2 = e3)
% 243.04/49.52    (11)  op(e2, e1) = all_52_9
% 243.04/49.52    (12)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.04/49.52          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.04/49.52    (13)   ~ (e3 = e2)
% 243.04/49.52    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.04/49.52          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.04/49.52    (15)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.04/49.52          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.04/49.52    (16)   ~ (all_52_14 = e3)
% 243.04/49.52    (17)   ~ (all_52_6 = e3)
% 243.04/49.52    (18)   ~ (all_52_9 = e3)
% 243.04/49.52    (19)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.04/49.52          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.04/49.52    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.52    (21)   ~ (e1 = e0)
% 243.04/49.52    (22)   ~ (all_52_13 = e3)
% 243.04/49.52    (23)  op(e2, e0) = all_52_13
% 243.04/49.52    (24)  all_58_3 = e0
% 243.04/49.52    (25)   ~ (e2 = e1)
% 243.04/49.52  
% 243.04/49.52  Begin of proof
% 243.04/49.52  | 
% 243.04/49.52  | BETA: splitting (8) gives:
% 243.04/49.52  | 
% 243.04/49.52  | Case 1:
% 243.04/49.52  | | 
% 243.04/49.52  | |   (26)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 243.04/49.52  | |           e3)
% 243.04/49.52  | | 
% 243.04/49.52  | | BETA: splitting (26) gives:
% 243.04/49.52  | | 
% 243.04/49.52  | | Case 1:
% 243.04/49.52  | | | 
% 243.04/49.52  | | |   (27)  all_58_0 = e3 & op(e3, e3) = e3
% 243.04/49.52  | | | 
% 243.04/49.52  | | | ALPHA: (27) implies:
% 243.04/49.52  | | |   (28)  op(e3, e3) = e3
% 243.04/49.52  | | | 
% 243.04/49.52  | | | REF_CLOSE: (7), (9), (20), (28) are inconsistent by sub-proof #1578.
% 243.04/49.52  | | | 
% 243.04/49.52  | | Case 2:
% 243.04/49.52  | | | 
% 243.04/49.52  | | |   (29)  all_58_2 = e3 & op(e2, e3) = e3
% 243.04/49.52  | | | 
% 243.04/49.52  | | | ALPHA: (29) implies:
% 243.04/49.52  | | |   (30)  all_58_2 = e3
% 243.04/49.52  | | | 
% 243.04/49.52  | | | BETA: splitting (15) gives:
% 243.04/49.52  | | | 
% 243.04/49.52  | | | Case 1:
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | |   (31)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 243.04/49.52  | | | |           = e3)
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | | BETA: splitting (31) gives:
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | | Case 1:
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | |   (32)  all_58_6 = e3 & op(e1, e3) = e3
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | | ALPHA: (32) implies:
% 243.04/49.52  | | | | |   (33)  all_58_6 = e3
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | | REF_CLOSE: (1), (2), (9), (12), (13), (14), (20), (21), (25), (30),
% 243.04/49.52  | | | | |            (33) are inconsistent by sub-proof #1221.
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | Case 2:
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | |   (34)  all_58_7 = e3 & op(e1, e2) = e3
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | | ALPHA: (34) implies:
% 243.04/49.52  | | | | |   (35)  op(e1, e2) = e3
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | | REF_CLOSE: (4), (17), (20), (35) are inconsistent by sub-proof #2191.
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | End of split
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | Case 2:
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | |   (36)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 243.04/49.52  | | | |           = e3)
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | | REF_CLOSE: (5), (6), (10), (16), (20), (36) are inconsistent by
% 243.04/49.52  | | | |            sub-proof #1529.
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | End of split
% 243.04/49.52  | | | 
% 243.04/49.52  | | End of split
% 243.04/49.52  | | 
% 243.04/49.52  | Case 2:
% 243.04/49.52  | | 
% 243.04/49.52  | |   (37)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 243.04/49.52  | |           e3)
% 243.04/49.52  | | 
% 243.04/49.52  | | BETA: splitting (37) gives:
% 243.04/49.52  | | 
% 243.04/49.52  | | Case 1:
% 243.04/49.52  | | | 
% 243.04/49.52  | | |   (38)  all_58_6 = e3 & op(e1, e3) = e3
% 243.04/49.52  | | | 
% 243.04/49.52  | | | ALPHA: (38) implies:
% 243.04/49.52  | | |   (39)  all_58_6 = e3
% 243.04/49.52  | | | 
% 243.04/49.52  | | | REF_CLOSE: (1), (2), (3), (9), (11), (12), (13), (14), (18), (20), (21),
% 243.04/49.52  | | |            (22), (23), (24), (25), (39) are inconsistent by sub-proof
% 243.04/49.52  | | |            #1220.
% 243.04/49.52  | | | 
% 243.04/49.52  | | Case 2:
% 243.04/49.52  | | | 
% 243.04/49.52  | | |   (40)  all_58_12 = e3 & op(e0, e3) = e3
% 243.04/49.52  | | | 
% 243.04/49.52  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (12), (13), (14), (15),
% 243.04/49.52  | | |            (16), (17), (19), (20), (21), (25), (40) are inconsistent by
% 243.04/49.52  | | |            sub-proof #1528.
% 243.04/49.52  | | | 
% 243.04/49.52  | | End of split
% 243.04/49.52  | | 
% 243.04/49.52  | End of split
% 243.04/49.52  | 
% 243.04/49.52  End of proof
% 243.04/49.52  
% 243.04/49.52  Sub-proof #1009 shows that the following formulas are inconsistent:
% 243.04/49.52  ----------------------------------------------------------------
% 243.04/49.52    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.52         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.52    (2)   ~ (all_8_2 = e0)
% 243.04/49.52    (3)   ~ (e3 = e0)
% 243.04/49.52    (4)  all_56_11 = e1
% 243.04/49.52    (5)  op(e0, e1) = all_52_11
% 243.04/49.52    (6)   ~ (all_52_8 = all_52_9)
% 243.04/49.52    (7)   ~ (e2 = e0)
% 243.04/49.52    (8)  op(e1, e2) = all_52_6
% 243.04/49.52    (9)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.52         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.52    (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.04/49.52              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.04/49.52            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.04/49.52            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.04/49.52            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.04/49.52             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.52            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.04/49.52            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.04/49.52            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.04/49.52            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.52            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.04/49.52              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.04/49.52            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.04/49.52            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.04/49.52            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.04/49.52            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.04/49.52            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.04/49.52            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.04/49.52              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.04/49.52            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.52            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.04/49.52            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.04/49.52            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.04/49.52            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.52            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.04/49.52              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.04/49.52            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.52            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.52    (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.04/49.52          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.04/49.52    (12)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.04/49.52          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.04/49.52    (13)  all_58_11 = e1
% 243.04/49.52    (14)  op(e1, e0) = all_52_14
% 243.04/49.52    (15)   ~ (all_52_13 = e1)
% 243.04/49.52    (16)   ~ (all_52_7 = e3)
% 243.04/49.52    (17)   ~ (all_52_8 = e0)
% 243.04/49.52    (18)  all_58_15 = e3
% 243.04/49.52    (19)  op(e0, e3) = all_52_3
% 243.04/49.52    (20)   ~ (all_52_6 = e0)
% 243.04/49.52    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.04/49.52          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.52    (22)  all_54_6 = all_52_9
% 243.04/49.52    (23)   ~ (all_52_8 = e1)
% 243.04/49.52    (24)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.52          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.52    (25)  all_54_2 = all_52_8
% 243.04/49.52    (26)  op(e3, e3) = e1
% 243.04/49.52    (27)   ~ (all_52_9 = e0)
% 243.04/49.52    (28)   ~ (all_52_1 = all_52_9)
% 243.04/49.52    (29)  all_56_21 = e0
% 243.04/49.52    (30)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.52              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.04/49.52                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.52                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.52    (31)   ~ (all_52_11 = e3)
% 243.04/49.52    (32)  op(e3, e1) = all_52_8
% 243.04/49.52    (33)  op(e2, e1) = all_52_9
% 243.04/49.52    (34)   ~ (e3 = e2)
% 243.04/49.52    (35)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.04/49.52          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.04/49.52    (36)   ~ (all_52_14 = e0)
% 243.04/49.52    (37)  op(e2, e2) = e1
% 243.04/49.52    (38)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.04/49.52    (39)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.04/49.52    (40)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.04/49.52          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.04/49.52    (41)  op(e3, e0) = all_52_12
% 243.04/49.52    (42)   ~ (all_52_9 = all_52_13)
% 243.04/49.52    (43)   ~ (all_52_3 = e3)
% 243.04/49.52    (44)  op(e2, e2) = all_8_2
% 243.04/49.52    (45)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.04/49.52    (46)  op(e2, e3) = all_52_1
% 243.04/49.52    (47)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.52          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.52    (48)   ~ (all_52_1 = all_52_13)
% 243.04/49.52    (49)   ~ (all_52_2 = e0)
% 243.04/49.52    (50)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.04/49.52          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.04/49.52    (51)  all_54_7 = all_52_13
% 243.04/49.52    (52)  op(e0, e2) = all_52_7
% 243.04/49.52    (53)  op(e3, e2) = all_52_4
% 243.04/49.52    (54)  all_56_31 = e3
% 243.04/49.52    (55)  op(e0, e0) = e3
% 243.04/49.52    (56)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.04/49.52          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.04/49.52    (57)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.52    (58)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.04/49.52          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.04/49.52    (59)  op(e1, e3) = all_52_2
% 243.04/49.52    (60)   ~ (all_52_12 = e3)
% 243.04/49.52    (61)  op(e1, e1) = e0
% 243.04/49.52    (62)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.04/49.52          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.04/49.52    (63)   ~ (e1 = e0)
% 243.04/49.52    (64)   ~ (all_52_13 = e3)
% 243.04/49.52    (65)  op(e2, e0) = all_52_13
% 243.04/49.52    (66)   ~ (all_52_9 = e1)
% 243.04/49.52    (67)  all_58_14 = e1
% 243.04/49.52    (68)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.52          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.04/49.52            e2)
% 243.04/49.52    (69)   ~ (all_52_4 = all_52_8)
% 243.04/49.52    (70)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.04/49.52          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.04/49.52    (71)   ~ (e2 = e1)
% 243.04/49.52    (72)   ~ (all_52_1 = e1)
% 243.04/49.52  
% 243.04/49.52  Begin of proof
% 243.04/49.52  | 
% 243.04/49.52  | BETA: splitting (39) gives:
% 243.04/49.52  | 
% 243.04/49.52  | Case 1:
% 243.04/49.52  | | 
% 243.04/49.52  | |   (73)  all_54_2 = e3
% 243.04/49.52  | | 
% 243.04/49.52  | | COMBINE_EQS: (25), (73) imply:
% 243.04/49.52  | |   (74)  all_52_8 = e3
% 243.04/49.52  | | 
% 243.04/49.52  | | SIMP: (74) implies:
% 243.04/49.52  | |   (75)  all_52_8 = e3
% 243.04/49.52  | | 
% 243.04/49.52  | | REDUCE: (69), (75) imply:
% 243.04/49.52  | |   (76)   ~ (all_52_4 = e3)
% 243.04/49.52  | | 
% 243.04/49.52  | | REDUCE: (6), (75) imply:
% 243.04/49.52  | |   (77)   ~ (all_52_9 = e3)
% 243.04/49.52  | | 
% 243.04/49.52  | | SIMP: (77) implies:
% 243.04/49.52  | |   (78)   ~ (all_52_9 = e3)
% 243.04/49.52  | | 
% 243.04/49.52  | | REDUCE: (23), (75) imply:
% 243.04/49.52  | |   (79)   ~ (e3 = e1)
% 243.04/49.52  | | 
% 243.04/49.52  | | BETA: splitting (35) gives:
% 243.04/49.52  | | 
% 243.04/49.52  | | Case 1:
% 243.04/49.52  | | | 
% 243.04/49.52  | | |   (80)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 243.04/49.52  | | |           e2)
% 243.04/49.52  | | | 
% 243.04/49.52  | | | BETA: splitting (80) gives:
% 243.04/49.52  | | | 
% 243.04/49.52  | | | Case 1:
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | |   (81)  all_58_4 = e2 & op(e3, e1) = e2
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | | ALPHA: (81) implies:
% 243.04/49.52  | | | |   (82)  all_58_4 = e2
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | | REF_CLOSE: (3), (5), (31), (33), (34), (50), (57), (61), (78), (82) are
% 243.04/49.52  | | | |            inconsistent by sub-proof #1493.
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | Case 2:
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | |   (83)  all_58_5 = e2 & op(e2, e1) = e2
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | | ALPHA: (83) implies:
% 243.04/49.52  | | | |   (84)  all_58_5 = e2
% 243.04/49.52  | | | |   (85)  op(e2, e1) = e2
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | | BETA: splitting (45) gives:
% 243.04/49.52  | | | | 
% 243.04/49.52  | | | | Case 1:
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | |   (86)  all_54_6 = e3
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | | REF_CLOSE: (22), (78), (86) are inconsistent by sub-proof #1825.
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | Case 2:
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | |   (87)   ~ (all_54_6 = e3)
% 243.04/49.52  | | | | |   (88)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | | BETA: splitting (88) gives:
% 243.04/49.52  | | | | | 
% 243.04/49.52  | | | | | Case 1:
% 243.04/49.52  | | | | | | 
% 243.04/49.52  | | | | | |   (89)  all_54_6 = e2
% 243.04/49.52  | | | | | | 
% 243.04/49.52  | | | | | | COMBINE_EQS: (22), (89) imply:
% 243.04/49.52  | | | | | |   (90)  all_52_9 = e2
% 243.04/49.52  | | | | | | 
% 243.04/49.52  | | | | | | SIMP: (90) implies:
% 243.04/49.52  | | | | | |   (91)  all_52_9 = e2
% 243.04/49.52  | | | | | | 
% 243.04/49.52  | | | | | | REDUCE: (42), (91) imply:
% 243.04/49.52  | | | | | |   (92)   ~ (all_52_13 = e2)
% 243.04/49.52  | | | | | | 
% 243.04/49.52  | | | | | | SIMP: (92) implies:
% 243.04/49.52  | | | | | |   (93)   ~ (all_52_13 = e2)
% 243.04/49.52  | | | | | | 
% 243.04/49.52  | | | | | | REDUCE: (78), (91) imply:
% 243.04/49.52  | | | | | |   (94)   ~ (e3 = e2)
% 243.04/49.52  | | | | | | 
% 243.04/49.52  | | | | | | BETA: splitting (38) gives:
% 243.04/49.52  | | | | | | 
% 243.04/49.52  | | | | | | Case 1:
% 243.04/49.52  | | | | | | | 
% 243.04/49.52  | | | | | | |   (95)  all_54_7 = e3
% 243.04/49.52  | | | | | | | 
% 243.04/49.52  | | | | | | | REF_CLOSE: (51), (64), (95) are inconsistent by sub-proof #2296.
% 243.04/49.52  | | | | | | | 
% 243.04/49.52  | | | | | | Case 2:
% 243.04/49.52  | | | | | | | 
% 243.04/49.52  | | | | | | |   (96)   ~ (all_54_7 = e3)
% 243.04/49.52  | | | | | | |   (97)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.04/49.52  | | | | | | | 
% 243.04/49.52  | | | | | | | BETA: splitting (50) gives:
% 243.04/49.52  | | | | | | | 
% 243.04/49.52  | | | | | | | Case 1:
% 243.04/49.52  | | | | | | | | 
% 243.04/49.52  | | | | | | | |   (98)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 243.04/49.52  | | | | | | | |           op(e2, e1) = e3)
% 243.04/49.52  | | | | | | | | 
% 243.04/49.52  | | | | | | | | BETA: splitting (98) gives:
% 243.04/49.53  | | | | | | | | 
% 243.04/49.53  | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | 
% 243.04/49.53  | | | | | | | | |   (99)  all_58_4 = e3 & op(e3, e1) = e3
% 243.04/49.53  | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | ALPHA: (99) implies:
% 243.04/49.53  | | | | | | | | |   (100)  all_58_4 = e3
% 243.04/49.53  | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | BETA: splitting (62) gives:
% 243.04/49.53  | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | |   (101)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 243.04/49.53  | | | | | | | | | |            & op(e2, e2) = e3)
% 243.04/49.53  | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | REF_CLOSE: (1), (3), (7), (15), (21), (24), (26), (34), (35),
% 243.04/49.53  | | | | | | | | | |            (46), (47), (53), (57), (63), (65), (67), (70),
% 243.04/49.53  | | | | | | | | | |            (71), (72), (76), (79), (100), (101) are
% 243.04/49.53  | | | | | | | | | |            inconsistent by sub-proof #1028.
% 243.04/49.53  | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | |   (102)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3
% 243.04/49.53  | | | | | | | | | |            & op(e0, e2) = e3)
% 243.04/49.53  | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | BETA: splitting (102) gives:
% 243.04/49.53  | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | |   (103)  all_58_7 = e3 & op(e1, e2) = e3
% 243.04/49.53  | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | ALPHA: (103) implies:
% 243.04/49.53  | | | | | | | | | | |   (104)  all_58_7 = e3
% 243.04/49.53  | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | BETA: splitting (97) gives:
% 243.04/49.53  | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | |   (105)  all_54_7 = e2
% 243.04/49.53  | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | REF_CLOSE: (51), (93), (105) are inconsistent by sub-proof
% 243.04/49.53  | | | | | | | | | | | |            #1997.
% 243.04/49.53  | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | |   (106)   ~ (all_54_7 = e2)
% 243.04/49.53  | | | | | | | | | | | |   (107)  all_54_7 = e1 | all_54_7 = e0
% 243.04/49.53  | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | BETA: splitting (107) gives:
% 243.04/49.53  | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | |   (108)  all_54_7 = e1
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | REF_CLOSE: (15), (51), (108) are inconsistent by sub-proof
% 243.04/49.53  | | | | | | | | | | | | |            #2295.
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | |   (109)  all_54_7 = e0
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | COMBINE_EQS: (51), (109) imply:
% 243.04/49.53  | | | | | | | | | | | | |   (110)  all_52_13 = e0
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | SIMP: (110) implies:
% 243.04/49.53  | | | | | | | | | | | | |   (111)  all_52_13 = e0
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | REDUCE: (48), (111) imply:
% 243.04/49.53  | | | | | | | | | | | | |   (112)   ~ (all_52_1 = e0)
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | REDUCE: (64), (111) imply:
% 243.04/49.53  | | | | | | | | | | | | |   (113)   ~ (e3 = e0)
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | REDUCE: (93), (111) imply:
% 243.04/49.53  | | | | | | | | | | | | |   (114)   ~ (e2 = e0)
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | REDUCE: (15), (111) imply:
% 243.04/49.53  | | | | | | | | | | | | |   (115)   ~ (e1 = e0)
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | REDUCE: (65), (111) imply:
% 243.04/49.53  | | | | | | | | | | | | |   (116)  op(e2, e0) = e0
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | BETA: splitting (68) gives:
% 243.04/49.53  | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | |   (117)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 243.04/49.53  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 243.04/49.53  | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 243.04/49.53  | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | |   (118)  all_58_12 = e2 & op(e0, e3) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 243.04/49.53  | | | | | | | | | | | | | | |   (119)  all_58_12 = e2
% 243.04/49.53  | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | |   (120)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 243.04/49.53  | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 243.04/49.53  | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | |   (121)  all_58_9 = e2 & op(e3, e0) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | |   (122)  all_58_9 = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | |   (123)  op(e3, e0) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | |   (124)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |   (125)  all_58_1 = e2 & op(e3, e2) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |   (126)  op(e3, e2) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |   (127)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (26), (57), (63), (126), (127) are
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1017.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |   (128)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (24), (26), (34), (53), (57), (76),
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |            (79), (123), (128) are inconsistent by sub-proof
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |            #1096.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |   (129)  all_58_3 = e2 & op(e2, e2) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |   (130)  op(e2, e2) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (57), (71), (130) are inconsistent by
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |            sub-proof #2235.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | |   (131)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |   (132)  all_58_7 = e2 & op(e1, e2) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (31), (33), (34), (50), (57), (61),
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |            (78), (100), (104), (132) are inconsistent by
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |            sub-proof #1219.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |   (133)  all_58_13 = e2 & op(e0, e2) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |   (134)  op(e0, e2) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |   (135)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | |   (136)  all_58_1 = e0 & op(e3, e2) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | |   (137)  all_58_1 = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |   (138)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (139)  all_58_0 = e0 & op(e3, e3) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (140)  op(e3, e3) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (57), (63), (71), (79), (100), (122), (137),
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            (140) are inconsistent by sub-proof #1016.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (141)  all_58_2 = e0 & op(e2, e3) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (57), (112), (141) are inconsistent by
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1985.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |   (142)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (143)  all_58_6 = e0 & op(e1, e3) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (144)  op(e1, e3) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (57), (59), (144) are inconsistent by
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2023.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (145)  all_58_12 = e0 & op(e0, e3) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (146)  all_58_12 = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (146) imply:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (147)  e2 = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (147) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (148)  e2 = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (148) imply:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (149)  all_58_9 = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (7), (24), (26), (34), (57), (71), (79),
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            (137), (149) are inconsistent by sub-proof #1089.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | |   (150)  all_58_3 = e0 & op(e2, e2) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (44), (57), (150) are inconsistent by
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1992.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |   (151)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (20), (57), (134), (151) are
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1015.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | |   (152)  all_58_10 = e2 & op(e2, e0) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | |   (153)  op(e2, e0) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (57), (116), (153) are inconsistent by
% 243.04/49.53  | | | | | | | | | | | | | | | | |            sub-proof #2121.
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | |   (154)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 243.04/49.53  | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 243.04/49.53  | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (13), (21), (34), (35), (55), (57),
% 243.04/49.53  | | | | | | | | | | | | | | | |            (63), (67), (71), (84), (100), (154) are
% 243.04/49.53  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 243.04/49.53  | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | |   (155)  all_58_13 = e2 & op(e0, e2) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 243.04/49.53  | | | | | | | | | | | | | | |   (156)  op(e0, e2) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | |   (157)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 243.04/49.53  | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | |   (158)  all_58_1 = e0 & op(e3, e2) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | |   (159)  op(e3, e2) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | |   (160)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |   (161)  all_58_9 = e2 & op(e3, e0) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | |   (162)  op(e3, e0) = e2
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |   (163)  all_58_15 = e0 & op(e0, e0) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |   (164)  op(e0, e0) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (55), (57), (164) are inconsistent by
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |            sub-proof #2079.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |   (165)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |              e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |   (166)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | |   (167)  all_58_12 = e0 & op(e0, e3) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | |   (168)  all_58_12 = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |   (169)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (170)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (57), (159), (170) are inconsistent
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2000.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |   (171)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |   (172)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |   (173)  op(e3, e1) = e1
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (32), (57), (173) are inconsistent by
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2309.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |   (174)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (175)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (176)  op(e0, e3) = e3
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (43), (57), (176) are inconsistent by
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2332.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (177)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (178)  op(e3, e0) = e0
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (57), (162), (178) are inconsistent by
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2154.
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |   (179)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 243.04/49.53  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |   (180)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |   (181)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |   (182)   ~ (all_56_11 = e1)
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (182) imply:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |   (183)  $false
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (183) is inconsistent.
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |   (184)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (33), (57), (66), (116), (184) are
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1920.
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |   (185)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |   (187)  op(e0, e2) = e0
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18), (34), (57), (67), (68), (71), (168),
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            (187) are inconsistent by sub-proof #1012.
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |   (188)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (29), (36), (57), (188) are inconsistent by
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1320.
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | |   (189)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (34), (35), (57), (61), (63), (71),
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | |            (79), (100), (156), (189) are inconsistent by
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1011.
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | |   (190)  all_58_10 = e2 & op(e2, e0) = e2
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | |   (191)  op(e2, e0) = e2
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (57), (116), (191) are inconsistent by
% 243.04/49.54  | | | | | | | | | | | | | | | | | | |            sub-proof #2121.
% 243.04/49.54  | | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | |   (192)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 243.04/49.54  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 243.04/49.54  | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (13), (21), (34), (35), (55), (57),
% 243.04/49.54  | | | | | | | | | | | | | | | | | |            (63), (67), (71), (84), (100), (192) are
% 243.04/49.54  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 243.04/49.54  | | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | |   (193)  all_58_3 = e0 & op(e2, e2) = e0
% 243.04/49.54  | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (44), (57), (193) are inconsistent by
% 243.04/49.54  | | | | | | | | | | | | | | | | |            sub-proof #1992.
% 243.04/49.54  | | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | |   (194)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 243.04/49.54  | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 243.04/49.54  | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (20), (57), (156), (194) are
% 243.04/49.54  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1015.
% 243.04/49.54  | | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | |   (195)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 243.04/49.54  | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 243.04/49.54  | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 243.04/49.54  | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | Case 1:
% 243.04/49.54  | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | |   (196)  all_58_14 = e2 & op(e0, e1) = e2
% 243.04/49.54  | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 243.04/49.54  | | | | | | | | | | | | | | |   (197)  all_58_14 = e2
% 243.04/49.54  | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | COMBINE_EQS: (67), (197) imply:
% 243.04/49.54  | | | | | | | | | | | | | | |   (198)  e2 = e1
% 243.04/49.54  | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | COMBINE_EQS: (84), (198) imply:
% 243.04/49.54  | | | | | | | | | | | | | | |   (199)  all_58_5 = e1
% 243.04/49.54  | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (21), (34), (35), (63), (67), (71),
% 243.04/49.54  | | | | | | | | | | | | | | |            (100), (199) are inconsistent by sub-proof #1481.
% 243.04/49.54  | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | |   (200)  all_58_15 = e2 & op(e0, e0) = e2
% 243.04/49.54  | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 243.04/49.54  | | | | | | | | | | | | | | |   (201)  op(e0, e0) = e2
% 243.04/49.54  | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | | REF_CLOSE: (34), (55), (57), (201) are inconsistent by
% 243.04/49.54  | | | | | | | | | | | | | | |            sub-proof #1388.
% 243.04/49.54  | | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | |   (202)  all_58_13 = e3 & op(e0, e2) = e3
% 243.04/49.54  | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | REF_CLOSE: (16), (52), (57), (202) are inconsistent by
% 243.04/49.54  | | | | | | | | | | |            sub-proof #1919.
% 243.04/49.54  | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | |   (203)  all_58_5 = e3 & op(e2, e1) = e3
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | ALPHA: (203) implies:
% 243.04/49.54  | | | | | | | | |   (204)  op(e2, e1) = e3
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | REF_CLOSE: (34), (57), (85), (204) are inconsistent by
% 243.04/49.54  | | | | | | | | |            sub-proof #2256.
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | |   (205)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 243.04/49.54  | | | | | | | |            op(e0, e1) = e3)
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | | BETA: splitting (205) gives:
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | | Case 1:
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | |   (206)  all_58_8 = e3 & op(e1, e1) = e3
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | REF_CLOSE: (3), (57), (61), (206) are inconsistent by
% 243.04/49.54  | | | | | | | | |            sub-proof #2018.
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | |   (207)  all_58_14 = e3 & op(e0, e1) = e3
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | REF_CLOSE: (5), (31), (57), (207) are inconsistent by
% 243.04/49.54  | | | | | | | | |            sub-proof #1647.
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | End of split
% 243.04/49.54  | | | | | | | 
% 243.04/49.54  | | | | | | End of split
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | Case 2:
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | |   (208)   ~ (all_54_6 = e2)
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | | REDUCE: (22), (208) imply:
% 243.04/49.54  | | | | | |   (209)   ~ (all_52_9 = e2)
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | | REF_CLOSE: (33), (57), (85), (209) are inconsistent by sub-proof
% 243.04/49.54  | | | | | |            #2328.
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | End of split
% 243.04/49.54  | | | | | 
% 243.04/49.54  | | | | End of split
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | End of split
% 243.04/49.54  | | | 
% 243.04/49.54  | | Case 2:
% 243.04/49.54  | | | 
% 243.04/49.54  | | |   (210)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 243.04/49.54  | | |            = e2)
% 243.04/49.54  | | | 
% 243.04/49.54  | | | BETA: splitting (210) gives:
% 243.04/49.54  | | | 
% 243.04/49.54  | | | Case 1:
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | |   (211)  all_58_8 = e2 & op(e1, e1) = e2
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | | ALPHA: (211) implies:
% 243.04/49.54  | | | |   (212)  op(e1, e1) = e2
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | | REF_CLOSE: (7), (57), (61), (212) are inconsistent by sub-proof #2211.
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | Case 2:
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | |   (213)  all_58_14 = e2 & op(e0, e1) = e2
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | | REF_CLOSE: (67), (71), (213) are inconsistent by sub-proof #1771.
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | End of split
% 243.04/49.54  | | | 
% 243.04/49.54  | | End of split
% 243.04/49.54  | | 
% 243.04/49.54  | Case 2:
% 243.04/49.54  | | 
% 243.04/49.54  | |   (214)   ~ (all_54_2 = e3)
% 243.04/49.54  | |   (215)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.04/49.54  | | 
% 243.04/49.54  | | REDUCE: (25), (214) imply:
% 243.04/49.54  | |   (216)   ~ (all_52_8 = e3)
% 243.04/49.54  | | 
% 243.04/49.54  | | BETA: splitting (215) gives:
% 243.04/49.54  | | 
% 243.04/49.54  | | Case 1:
% 243.04/49.54  | | | 
% 243.04/49.54  | | |   (217)  all_54_2 = e2
% 243.04/49.54  | | | 
% 243.04/49.54  | | | COMBINE_EQS: (25), (217) imply:
% 243.04/49.54  | | |   (218)  all_52_8 = e2
% 243.04/49.54  | | | 
% 243.04/49.54  | | | SIMP: (218) implies:
% 243.04/49.54  | | |   (219)  all_52_8 = e2
% 243.04/49.54  | | | 
% 243.04/49.54  | | | REDUCE: (6), (219) imply:
% 243.04/49.54  | | |   (220)   ~ (all_52_9 = e2)
% 243.04/49.54  | | | 
% 243.04/49.54  | | | SIMP: (220) implies:
% 243.04/49.54  | | |   (221)   ~ (all_52_9 = e2)
% 243.04/49.54  | | | 
% 243.04/49.54  | | | BETA: splitting (45) gives:
% 243.04/49.54  | | | 
% 243.04/49.54  | | | Case 1:
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | |   (222)  all_54_6 = e3
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | | COMBINE_EQS: (22), (222) imply:
% 243.04/49.54  | | | |   (223)  all_52_9 = e3
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | | SIMP: (223) implies:
% 243.04/49.54  | | | |   (224)  all_52_9 = e3
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | | REDUCE: (28), (224) imply:
% 243.04/49.54  | | | |   (225)   ~ (all_52_1 = e3)
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | | REDUCE: (66), (224) imply:
% 243.04/49.54  | | | |   (226)   ~ (e3 = e1)
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | | REDUCE: (33), (224) imply:
% 243.04/49.54  | | | |   (227)  op(e2, e1) = e3
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | | BETA: splitting (24) gives:
% 243.04/49.54  | | | | 
% 243.04/49.54  | | | | Case 1:
% 243.04/49.54  | | | | | 
% 243.04/49.54  | | | | |   (228)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3,
% 243.04/49.54  | | | | |              e2) = e3)
% 243.04/49.54  | | | | | 
% 243.04/49.54  | | | | | BETA: splitting (228) gives:
% 243.04/49.54  | | | | | 
% 243.04/49.54  | | | | | Case 1:
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | |   (229)  all_58_0 = e3 & op(e3, e3) = e3
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | | ALPHA: (229) implies:
% 243.04/49.54  | | | | | |   (230)  op(e3, e3) = e3
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | | REF_CLOSE: (26), (57), (226), (230) are inconsistent by sub-proof
% 243.04/49.54  | | | | | |            #1578.
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | Case 2:
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | |   (231)  all_58_1 = e3 & op(e3, e2) = e3
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | | ALPHA: (231) implies:
% 243.04/49.54  | | | | | |   (232)  op(e3, e2) = e3
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | | BETA: splitting (58) gives:
% 243.04/49.54  | | | | | | 
% 243.04/49.54  | | | | | | Case 1:
% 243.04/49.54  | | | | | | | 
% 243.04/49.54  | | | | | | |   (233)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 243.04/49.54  | | | | | | |            op(e2, e0) = e2)
% 243.04/49.54  | | | | | | | 
% 243.04/49.54  | | | | | | | BETA: splitting (233) gives:
% 243.04/49.54  | | | | | | | 
% 243.04/49.54  | | | | | | | Case 1:
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | |   (234)  all_58_9 = e2 & op(e3, e0) = e2
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | | ALPHA: (234) implies:
% 243.04/49.54  | | | | | | | |   (235)  op(e3, e0) = e2
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | | REF_CLOSE: (3), (7), (17), (26), (32), (47), (57), (63), (232),
% 243.04/49.54  | | | | | | | |            (235) are inconsistent by sub-proof #1523.
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | |   (236)  all_58_10 = e2 & op(e2, e0) = e2
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | | ALPHA: (236) implies:
% 243.04/49.54  | | | | | | | |   (237)  op(e2, e0) = e2
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | | BETA: splitting (10) gives:
% 243.04/49.54  | | | | | | | | 
% 243.04/49.54  | | | | | | | | Case 1:
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | |   (238)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &
% 243.04/49.54  | | | | | | | | |             ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.04/49.54  | | | | | | | | |            e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 243.04/49.54  | | | | | | | | |              = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.04/49.54  | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 243.04/49.54  | | | | | | | | |              e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 243.04/49.54  | | | | | | | | |            = e3 & op(e1, e3) = e3) | (all_56_5 = e1 &
% 243.04/49.54  | | | | | | | | |            all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 243.04/49.54  | | | | | | | | |              = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 243.04/49.54  | | | | | | | | |            & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 =
% 243.04/49.54  | | | | | | | | |            e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 243.04/49.54  | | | | | | | | |            e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 243.04/49.54  | | | | | | | | |            = e0 & op(e0, e3) = e0)
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | BETA: splitting (238) gives:
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | Case 1:
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | |   (239)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 243.04/49.54  | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.04/49.54  | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.04/49.54  | | | | | | | | | |            e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 243.04/49.54  | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.04/49.54  | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.04/49.54  | | | | | | | | | |              e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 243.04/49.54  | | | | | | | | | |            all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.04/49.54  | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.54  | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 243.04/49.54  | | | | | | | | | |            e3)
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | REF_CLOSE: (32), (46), (54), (57), (216), (225), (239) are
% 243.04/49.54  | | | | | | | | | |            inconsistent by sub-proof #1316.
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | |   (240)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 243.04/49.54  | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.04/49.54  | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 243.04/49.54  | | | | | | | | | |              e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 & 
% 243.04/49.54  | | | | | | | | | |            ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.04/49.54  | | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.04/49.54  | | | | | | | | | |              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 243.04/49.54  | | | | | | | | | |            all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.04/49.54  | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.04/49.54  | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 243.04/49.54  | | | | | | | | | |            e0)
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | REF_CLOSE: (19), (23), (32), (43), (54), (57), (240) are
% 243.04/49.54  | | | | | | | | | |            inconsistent by sub-proof #1411.
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | |   (241)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 243.04/49.54  | | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.04/49.54  | | | | | | | | |            e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1)
% 243.04/49.54  | | | | | | | | |            = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 243.04/49.54  | | | | | | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.04/49.54  | | | | | | | | |              = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.04/49.54  | | | | | | | | |            & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.04/49.54  | | | | | | | | |            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.04/49.54  | | | | | | | | |            e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.04/49.54  | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0)
% 243.04/49.54  | | | | | | | | |            = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 243.04/49.54  | | | | | | | | |            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 243.04/49.54  | | | | | | | | |              = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.04/49.54  | | | | | | | | |            & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | BETA: splitting (241) gives:
% 243.04/49.54  | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | Case 1:
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | |   (242)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.04/49.54  | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.04/49.54  | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 243.04/49.54  | | | | | | | | | |              e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 & 
% 243.04/49.54  | | | | | | | | | |            ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.04/49.54  | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.04/49.54  | | | | | | | | | |              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 243.04/49.54  | | | | | | | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.54  | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.54  | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 243.04/49.54  | | | | | | | | | |            e2)
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | BETA: splitting (242) gives:
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | Case 1:
% 243.04/49.54  | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | |   (243)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.04/49.54  | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.04/49.54  | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 243.04/49.54  | | | | | | | | | | |            e2) = e2
% 243.04/49.54  | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | ALPHA: (243) implies:
% 243.04/49.54  | | | | | | | | | | |   (244)  op(e2, e1) = e2
% 243.04/49.54  | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | REF_CLOSE: (34), (57), (227), (244) are inconsistent by
% 243.04/49.54  | | | | | | | | | | |            sub-proof #2256.
% 243.04/49.54  | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | |   (245)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.04/49.54  | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.04/49.54  | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.04/49.54  | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 243.04/49.54  | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.04/49.54  | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.04/49.54  | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.04/49.54  | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | | REF_CLOSE: (29), (33), (57), (66), (245) are inconsistent by
% 243.04/49.54  | | | | | | | | | | |            sub-proof #1941.
% 243.04/49.54  | | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | | End of split
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.54  | | | | | | | | | Case 2:
% 243.04/49.54  | | | | | | | | | | 
% 243.04/49.55  | | | | | | | | | |   (246)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.04/49.55  | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.04/49.55  | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.04/49.55  | | | | | | | | | |              e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 & 
% 243.04/49.55  | | | | | | | | | |            ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.04/49.55  | | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.04/49.55  | | | | | | | | | |              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 243.04/49.55  | | | | | | | | | |            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.04/49.55  | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.55  | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 243.04/49.55  | | | | | | | | | |            e0)
% 243.04/49.55  | | | | | | | | | | 
% 243.04/49.55  | | | | | | | | | | BETA: splitting (246) gives:
% 243.04/49.55  | | | | | | | | | | 
% 243.04/49.55  | | | | | | | | | | Case 1:
% 243.04/49.55  | | | | | | | | | | | 
% 243.04/49.55  | | | | | | | | | | |   (247)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.04/49.55  | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.04/49.55  | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.04/49.55  | | | | | | | | | | |            e2) = e0
% 243.04/49.55  | | | | | | | | | | | 
% 243.04/49.55  | | | | | | | | | | | ALPHA: (247) implies:
% 243.04/49.55  | | | | | | | | | | |   (248)  op(e2, e0) = e0
% 243.04/49.55  | | | | | | | | | | | 
% 243.04/49.55  | | | | | | | | | | | REF_CLOSE: (7), (57), (237), (248) are inconsistent by
% 243.04/49.55  | | | | | | | | | | |            sub-proof #2121.
% 243.04/49.55  | | | | | | | | | | | 
% 243.04/49.55  | | | | | | | | | | Case 2:
% 243.04/49.55  | | | | | | | | | | | 
% 243.04/49.55  | | | | | | | | | | |   (249)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.04/49.55  | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.04/49.55  | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.04/49.55  | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.04/49.55  | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.04/49.55  | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.04/49.55  | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.55  | | | | | | | | | | | 
% 243.04/49.55  | | | | | | | | | | | REF_CLOSE: (14), (29), (36), (57), (249) are inconsistent by
% 243.04/49.55  | | | | | | | | | | |            sub-proof #1320.
% 243.04/49.55  | | | | | | | | | | | 
% 243.04/49.55  | | | | | | | | | | End of split
% 243.04/49.55  | | | | | | | | | | 
% 243.04/49.55  | | | | | | | | | End of split
% 243.04/49.55  | | | | | | | | | 
% 243.04/49.55  | | | | | | | | End of split
% 243.04/49.55  | | | | | | | | 
% 243.04/49.55  | | | | | | | End of split
% 243.04/49.55  | | | | | | | 
% 243.04/49.55  | | | | | | Case 2:
% 243.04/49.55  | | | | | | | 
% 243.04/49.55  | | | | | | |   (250)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 243.04/49.55  | | | | | | |            op(e0, e0) = e2)
% 243.04/49.55  | | | | | | | 
% 243.04/49.55  | | | | | | | BETA: splitting (250) gives:
% 243.04/49.55  | | | | | | | 
% 243.04/49.55  | | | | | | | Case 1:
% 243.04/49.55  | | | | | | | | 
% 243.04/49.55  | | | | | | | |   (251)  all_58_11 = e2 & op(e1, e0) = e2
% 243.04/49.55  | | | | | | | | 
% 243.04/49.55  | | | | | | | | ALPHA: (251) implies:
% 243.04/49.55  | | | | | | | |   (252)  all_58_11 = e2
% 243.04/49.55  | | | | | | | | 
% 243.04/49.55  | | | | | | | | REF_CLOSE: (13), (71), (252) are inconsistent by sub-proof
% 243.04/49.55  | | | | | | | |            #1020.
% 243.04/49.55  | | | | | | | | 
% 243.04/49.55  | | | | | | | Case 2:
% 243.04/49.55  | | | | | | | | 
% 243.04/49.55  | | | | | | | |   (253)  all_58_15 = e2 & op(e0, e0) = e2
% 243.04/49.55  | | | | | | | | 
% 243.04/49.55  | | | | | | | | ALPHA: (253) implies:
% 243.04/49.55  | | | | | | | |   (254)  op(e0, e0) = e2
% 243.04/49.55  | | | | | | | | 
% 243.04/49.55  | | | | | | | | REF_CLOSE: (34), (55), (57), (254) are inconsistent by sub-proof
% 243.04/49.55  | | | | | | | |            #1388.
% 243.04/49.55  | | | | | | | | 
% 243.04/49.55  | | | | | | | End of split
% 243.04/49.55  | | | | | | | 
% 243.04/49.55  | | | | | | End of split
% 243.04/49.55  | | | | | | 
% 243.04/49.55  | | | | | End of split
% 243.04/49.55  | | | | | 
% 243.04/49.55  | | | | Case 2:
% 243.04/49.55  | | | | | 
% 243.04/49.55  | | | | |   (255)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 243.04/49.55  | | | | |              e0) = e3)
% 243.04/49.55  | | | | | 
% 243.04/49.55  | | | | | REF_CLOSE: (32), (41), (57), (60), (216), (255) are inconsistent by
% 243.04/49.55  | | | | |            sub-proof #1515.
% 243.04/49.55  | | | | | 
% 243.04/49.55  | | | | End of split
% 243.04/49.55  | | | | 
% 243.04/49.55  | | | Case 2:
% 243.04/49.55  | | | | 
% 243.04/49.55  | | | |   (256)   ~ (all_54_6 = e3)
% 243.04/49.55  | | | | 
% 243.04/49.55  | | | | REDUCE: (22), (256) imply:
% 243.04/49.55  | | | |   (257)   ~ (all_52_9 = e3)
% 243.04/49.55  | | | | 
% 243.04/49.55  | | | | REF_CLOSE: (3), (5), (31), (32), (33), (50), (57), (61), (216), (257)
% 243.04/49.55  | | | |            are inconsistent by sub-proof #1010.
% 243.04/49.55  | | | | 
% 243.04/49.55  | | | End of split
% 243.04/49.55  | | | 
% 243.04/49.55  | | Case 2:
% 243.04/49.55  | | | 
% 243.04/49.55  | | |   (258)  all_54_2 = e1 | all_54_2 = e0
% 243.04/49.55  | | | 
% 243.04/49.55  | | | REF_CLOSE: (17), (23), (25), (258) are inconsistent by sub-proof #1336.
% 243.04/49.55  | | | 
% 243.04/49.55  | | End of split
% 243.04/49.55  | | 
% 243.04/49.55  | End of split
% 243.04/49.55  | 
% 243.04/49.55  End of proof
% 243.04/49.55  
% 243.04/49.55  Sub-proof #1010 shows that the following formulas are inconsistent:
% 243.04/49.55  ----------------------------------------------------------------
% 243.04/49.55    (1)   ~ (e3 = e0)
% 243.04/49.55    (2)  op(e0, e1) = all_52_11
% 243.04/49.55    (3)   ~ (all_52_11 = e3)
% 243.04/49.55    (4)  op(e3, e1) = all_52_8
% 243.04/49.55    (5)  op(e2, e1) = all_52_9
% 243.04/49.55    (6)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.04/49.55         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.04/49.55    (7)   ~ (all_52_9 = e3)
% 243.04/49.55    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.55    (9)  op(e1, e1) = e0
% 243.04/49.55    (10)   ~ (all_52_8 = e3)
% 243.04/49.55  
% 243.04/49.55  Begin of proof
% 243.04/49.55  | 
% 243.04/49.55  | BETA: splitting (6) gives:
% 243.04/49.55  | 
% 243.04/49.55  | Case 1:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (11)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 243.04/49.55  | |           e3)
% 243.04/49.55  | | 
% 243.04/49.55  | | REF_CLOSE: (4), (5), (7), (8), (10), (11) are inconsistent by sub-proof
% 243.04/49.55  | |            #1628.
% 243.04/49.55  | | 
% 243.04/49.55  | Case 2:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (12)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 243.04/49.55  | |           e3)
% 243.04/49.55  | | 
% 243.04/49.55  | | BETA: splitting (12) gives:
% 243.04/49.55  | | 
% 243.04/49.55  | | Case 1:
% 243.04/49.55  | | | 
% 243.04/49.55  | | |   (13)  all_58_8 = e3 & op(e1, e1) = e3
% 243.04/49.55  | | | 
% 243.04/49.55  | | | REF_CLOSE: (1), (8), (9), (13) are inconsistent by sub-proof #2018.
% 243.04/49.55  | | | 
% 243.04/49.55  | | Case 2:
% 243.04/49.55  | | | 
% 243.04/49.55  | | |   (14)  all_58_14 = e3 & op(e0, e1) = e3
% 243.04/49.55  | | | 
% 243.04/49.55  | | | REF_CLOSE: (2), (3), (8), (14) are inconsistent by sub-proof #1647.
% 243.04/49.55  | | | 
% 243.04/49.55  | | End of split
% 243.04/49.55  | | 
% 243.04/49.55  | End of split
% 243.04/49.55  | 
% 243.04/49.55  End of proof
% 243.04/49.55  
% 243.04/49.55  Sub-proof #1011 shows that the following formulas are inconsistent:
% 243.04/49.55  ----------------------------------------------------------------
% 243.04/49.55    (1)   ~ (e2 = e0)
% 243.04/49.55    (2)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.04/49.55         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.04/49.55    (3)  op(e0, e2) = e2
% 243.04/49.55    (4)   ~ (e3 = e1)
% 243.04/49.55    (5)   ~ (e3 = e2)
% 243.04/49.55    (6)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.04/49.55         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.04/49.55    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.55    (8)  op(e1, e1) = e0
% 243.04/49.55    (9)   ~ (e1 = e0)
% 243.04/49.55    (10)  all_58_4 = e3
% 243.04/49.55    (11)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.55    (12)   ~ (e2 = e1)
% 243.04/49.55  
% 243.04/49.55  Begin of proof
% 243.04/49.55  | 
% 243.04/49.55  | BETA: splitting (11) gives:
% 243.04/49.55  | 
% 243.04/49.55  | Case 1:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (13)  all_58_13 = e0 & op(e0, e2) = e0
% 243.04/49.55  | | 
% 243.04/49.55  | | ALPHA: (13) implies:
% 243.04/49.55  | |   (14)  op(e0, e2) = e0
% 243.04/49.55  | | 
% 243.04/49.55  | | REF_CLOSE: (1), (3), (7), (14) are inconsistent by sub-proof #2132.
% 243.04/49.55  | | 
% 243.04/49.55  | Case 2:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (15)  all_58_14 = e0 & op(e0, e1) = e0
% 243.04/49.55  | | 
% 243.04/49.55  | | ALPHA: (15) implies:
% 243.04/49.55  | |   (16)  all_58_14 = e0
% 243.04/49.55  | |   (17)  op(e0, e1) = e0
% 243.04/49.55  | | 
% 243.04/49.55  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (16), (17)
% 243.04/49.55  | |            are inconsistent by sub-proof #1241.
% 243.04/49.55  | | 
% 243.04/49.55  | End of split
% 243.04/49.55  | 
% 243.04/49.55  End of proof
% 243.04/49.55  
% 243.04/49.55  Sub-proof #1012 shows that the following formulas are inconsistent:
% 243.04/49.55  ----------------------------------------------------------------
% 243.04/49.55    (1)   ~ (e2 = e0)
% 243.04/49.55    (2)  all_58_15 = e3
% 243.04/49.55    (3)   ~ (e3 = e2)
% 243.04/49.55    (4)  all_58_12 = e0
% 243.04/49.55    (5)  op(e0, e2) = e0
% 243.04/49.55    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.55    (7)  all_58_14 = e1
% 243.04/49.55    (8)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 243.04/49.55         (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.04/49.55    (9)   ~ (e2 = e1)
% 243.04/49.55  
% 243.04/49.55  Begin of proof
% 243.04/49.55  | 
% 243.04/49.55  | BETA: splitting (8) gives:
% 243.04/49.55  | 
% 243.04/49.55  | Case 1:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (10)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 243.04/49.55  | |           e2)
% 243.04/49.55  | | 
% 243.04/49.55  | | BETA: splitting (10) gives:
% 243.04/49.55  | | 
% 243.04/49.55  | | Case 1:
% 243.04/49.55  | | | 
% 243.04/49.55  | | |   (11)  all_58_12 = e2 & op(e0, e3) = e2
% 243.04/49.55  | | | 
% 243.04/49.55  | | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #1013.
% 243.04/49.55  | | | 
% 243.04/49.55  | | Case 2:
% 243.04/49.55  | | | 
% 243.04/49.55  | | |   (12)  all_58_13 = e2 & op(e0, e2) = e2
% 243.04/49.55  | | | 
% 243.04/49.55  | | | ALPHA: (12) implies:
% 243.04/49.55  | | |   (13)  op(e0, e2) = e2
% 243.04/49.55  | | | 
% 243.04/49.55  | | | REF_CLOSE: (1), (5), (6), (13) are inconsistent by sub-proof #2132.
% 243.04/49.55  | | | 
% 243.04/49.55  | | End of split
% 243.04/49.55  | | 
% 243.04/49.55  | Case 2:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (14)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.04/49.55  | |           e2)
% 243.04/49.55  | | 
% 243.04/49.55  | | BETA: splitting (14) gives:
% 243.04/49.55  | | 
% 243.04/49.55  | | Case 1:
% 243.04/49.55  | | | 
% 243.04/49.55  | | |   (15)  all_58_14 = e2 & op(e0, e1) = e2
% 243.04/49.55  | | | 
% 243.04/49.55  | | | REF_CLOSE: (7), (9), (15) are inconsistent by sub-proof #1771.
% 243.04/49.55  | | | 
% 243.04/49.55  | | Case 2:
% 243.04/49.55  | | | 
% 243.04/49.55  | | |   (16)  all_58_15 = e2 & op(e0, e0) = e2
% 243.04/49.55  | | | 
% 243.04/49.55  | | | REF_CLOSE: (2), (3), (16) are inconsistent by sub-proof #1231.
% 243.04/49.55  | | | 
% 243.04/49.55  | | End of split
% 243.04/49.55  | | 
% 243.04/49.55  | End of split
% 243.04/49.55  | 
% 243.04/49.55  End of proof
% 243.04/49.55  
% 243.04/49.55  Sub-proof #1013 shows that the following formulas are inconsistent:
% 243.04/49.55  ----------------------------------------------------------------
% 243.04/49.55    (1)  all_58_12 = e2 & op(e0, e3) = e2
% 243.04/49.55    (2)  all_58_12 = e0
% 243.04/49.55    (3)   ~ (e2 = e0)
% 243.04/49.55  
% 243.04/49.55  Begin of proof
% 243.04/49.55  | 
% 243.04/49.55  | ALPHA: (1) implies:
% 243.04/49.55  |   (4)  all_58_12 = e2
% 243.04/49.55  | 
% 243.04/49.55  | COMBINE_EQS: (2), (4) imply:
% 243.04/49.55  |   (5)  e2 = e0
% 243.04/49.55  | 
% 243.04/49.55  | REDUCE: (3), (5) imply:
% 243.04/49.55  |   (6)  $false
% 243.04/49.55  | 
% 243.04/49.55  | CLOSE: (6) is inconsistent.
% 243.04/49.55  | 
% 243.04/49.55  End of proof
% 243.04/49.55  
% 243.04/49.55  Sub-proof #1014 shows that the following formulas are inconsistent:
% 243.04/49.55  ----------------------------------------------------------------
% 243.04/49.55    (1)   ~ (e3 = e0)
% 243.04/49.55    (2)   ~ (e2 = e0)
% 243.04/49.55    (3)  all_58_11 = e1
% 243.04/49.55    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.04/49.55         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.55    (5)   ~ (e3 = e2)
% 243.04/49.55    (6)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.04/49.55         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.04/49.55    (7)  all_58_5 = e2
% 243.04/49.55    (8)  op(e0, e0) = e3
% 243.04/49.55    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.55    (10)   ~ (e1 = e0)
% 243.04/49.55    (11)  all_58_4 = e3
% 243.04/49.55    (12)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.04/49.55    (13)  all_58_14 = e1
% 243.04/49.55    (14)   ~ (e2 = e1)
% 243.04/49.55  
% 243.04/49.55  Begin of proof
% 243.04/49.55  | 
% 243.04/49.55  | BETA: splitting (12) gives:
% 243.04/49.55  | 
% 243.04/49.55  | Case 1:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (15)  all_58_11 = e2 & op(e1, e0) = e2
% 243.04/49.55  | | 
% 243.04/49.55  | | ALPHA: (15) implies:
% 243.04/49.55  | |   (16)  all_58_11 = e2
% 243.04/49.55  | | 
% 243.04/49.55  | | COMBINE_EQS: (3), (16) imply:
% 243.04/49.55  | |   (17)  e2 = e1
% 243.04/49.55  | | 
% 243.04/49.55  | | COMBINE_EQS: (7), (17) imply:
% 243.04/49.55  | |   (18)  all_58_5 = e1
% 243.04/49.55  | | 
% 243.04/49.55  | | REF_CLOSE: (1), (2), (4), (5), (6), (10), (11), (13), (14), (18) are
% 243.04/49.55  | |            inconsistent by sub-proof #1481.
% 243.04/49.55  | | 
% 243.04/49.55  | Case 2:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (19)  all_58_15 = e2 & op(e0, e0) = e2
% 243.04/49.55  | | 
% 243.04/49.55  | | ALPHA: (19) implies:
% 243.04/49.55  | |   (20)  op(e0, e0) = e2
% 243.04/49.55  | | 
% 243.04/49.55  | | REF_CLOSE: (5), (8), (9), (20) are inconsistent by sub-proof #1388.
% 243.04/49.55  | | 
% 243.04/49.55  | End of split
% 243.04/49.55  | 
% 243.04/49.55  End of proof
% 243.04/49.55  
% 243.04/49.55  Sub-proof #1015 shows that the following formulas are inconsistent:
% 243.04/49.55  ----------------------------------------------------------------
% 243.04/49.55    (1)   ~ (e2 = e0)
% 243.04/49.55    (2)  op(e1, e2) = all_52_6
% 243.04/49.55    (3)  op(e0, e2) = e2
% 243.04/49.55    (4)   ~ (all_52_6 = e0)
% 243.04/49.55    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.55    (6)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.04/49.55  
% 243.04/49.55  Begin of proof
% 243.04/49.55  | 
% 243.04/49.55  | BETA: splitting (6) gives:
% 243.04/49.55  | 
% 243.04/49.55  | Case 1:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (7)  all_58_7 = e0 & op(e1, e2) = e0
% 243.04/49.55  | | 
% 243.04/49.55  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #2022.
% 243.04/49.55  | | 
% 243.04/49.55  | Case 2:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (8)  all_58_13 = e0 & op(e0, e2) = e0
% 243.04/49.55  | | 
% 243.04/49.55  | | ALPHA: (8) implies:
% 243.04/49.55  | |   (9)  op(e0, e2) = e0
% 243.04/49.55  | | 
% 243.04/49.55  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #2132.
% 243.04/49.55  | | 
% 243.04/49.55  | End of split
% 243.04/49.55  | 
% 243.04/49.55  End of proof
% 243.04/49.55  
% 243.04/49.55  Sub-proof #1016 shows that the following formulas are inconsistent:
% 243.04/49.55  ----------------------------------------------------------------
% 243.04/49.55    (1)  all_58_1 = e0
% 243.04/49.55    (2)   ~ (e3 = e1)
% 243.04/49.55    (3)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.04/49.55         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.04/49.55    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.55    (5)   ~ (e1 = e0)
% 243.04/49.55    (6)  op(e3, e3) = e0
% 243.04/49.55    (7)  all_58_4 = e3
% 243.04/49.55    (8)  all_58_9 = e2
% 243.04/49.55    (9)   ~ (e2 = e1)
% 243.04/49.55  
% 243.04/49.55  Begin of proof
% 243.04/49.55  | 
% 243.04/49.55  | BETA: splitting (3) gives:
% 243.04/49.55  | 
% 243.04/49.55  | Case 1:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 243.04/49.55  | |           e1)
% 243.04/49.55  | | 
% 243.04/49.55  | | BETA: splitting (10) gives:
% 243.04/49.55  | | 
% 243.04/49.55  | | Case 1:
% 243.04/49.55  | | | 
% 243.04/49.55  | | |   (11)  all_58_0 = e1 & op(e3, e3) = e1
% 243.04/49.55  | | | 
% 243.04/49.55  | | | ALPHA: (11) implies:
% 243.04/49.55  | | |   (12)  op(e3, e3) = e1
% 243.04/49.55  | | | 
% 243.04/49.55  | | | REF_CLOSE: (4), (5), (6), (12) are inconsistent by sub-proof #1828.
% 243.04/49.55  | | | 
% 243.04/49.55  | | Case 2:
% 243.04/49.55  | | | 
% 243.04/49.55  | | |   (13)  all_58_1 = e1 & op(e3, e2) = e1
% 243.04/49.55  | | | 
% 243.04/49.55  | | | REF_CLOSE: (1), (5), (13) are inconsistent by sub-proof #2015.
% 243.04/49.55  | | | 
% 243.04/49.55  | | End of split
% 243.04/49.55  | | 
% 243.04/49.55  | Case 2:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 243.04/49.55  | |           e1)
% 243.04/49.55  | | 
% 243.04/49.55  | | BETA: splitting (14) gives:
% 243.04/49.55  | | 
% 243.04/49.55  | | Case 1:
% 243.04/49.55  | | | 
% 243.04/49.55  | | |   (15)  all_58_4 = e1 & op(e3, e1) = e1
% 243.04/49.55  | | | 
% 243.04/49.55  | | | REF_CLOSE: (2), (7), (15) are inconsistent by sub-proof #2042.
% 243.04/49.55  | | | 
% 243.04/49.55  | | Case 2:
% 243.04/49.55  | | | 
% 243.04/49.55  | | |   (16)  all_58_9 = e1 & op(e3, e0) = e1
% 243.04/49.55  | | | 
% 243.04/49.55  | | | ALPHA: (16) implies:
% 243.04/49.55  | | |   (17)  all_58_9 = e1
% 243.04/49.55  | | | 
% 243.04/49.55  | | | REF_CLOSE: (8), (9), (17) are inconsistent by sub-proof #1605.
% 243.04/49.55  | | | 
% 243.04/49.55  | | End of split
% 243.04/49.55  | | 
% 243.04/49.55  | End of split
% 243.04/49.55  | 
% 243.04/49.55  End of proof
% 243.04/49.55  
% 243.04/49.55  Sub-proof #1017 shows that the following formulas are inconsistent:
% 243.04/49.55  ----------------------------------------------------------------
% 243.04/49.55    (1)   ~ (e2 = e0)
% 243.04/49.55    (2)  op(e3, e2) = e2
% 243.04/49.55    (3)  op(e3, e3) = e1
% 243.04/49.55    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.55    (5)   ~ (e1 = e0)
% 243.04/49.55    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 243.04/49.55  
% 243.04/49.55  Begin of proof
% 243.04/49.55  | 
% 243.04/49.55  | BETA: splitting (6) gives:
% 243.04/49.55  | 
% 243.04/49.55  | Case 1:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 243.04/49.55  | | 
% 243.04/49.55  | | ALPHA: (7) implies:
% 243.04/49.55  | |   (8)  op(e3, e3) = e0
% 243.04/49.55  | | 
% 243.04/49.55  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1828.
% 243.04/49.55  | | 
% 243.04/49.55  | Case 2:
% 243.04/49.55  | | 
% 243.04/49.55  | |   (9)  all_58_1 = e0 & op(e3, e2) = e0
% 243.04/49.55  | | 
% 243.04/49.55  | | ALPHA: (9) implies:
% 243.04/49.55  | |   (10)  op(e3, e2) = e0
% 243.04/49.55  | | 
% 243.04/49.55  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #2026.
% 243.04/49.55  | | 
% 243.04/49.55  | End of split
% 243.04/49.55  | 
% 243.04/49.55  End of proof
% 243.04/49.55  
% 243.04/49.55  Sub-proof #1018 shows that the following formulas are inconsistent:
% 243.04/49.55  ----------------------------------------------------------------
% 243.04/49.55    (1)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.04/49.55         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.04/49.55    (2)  all_58_6 = e3
% 243.04/49.55    (3)   ~ (e2 = e0)
% 243.04/49.55    (4)  all_58_7 = e0
% 243.04/49.55    (5)  op(e1, e2) = all_52_6
% 243.04/49.55    (6)   ~ (e3 = e1)
% 243.04/49.55    (7)  op(e1, e2) = e0
% 243.04/49.55    (8)   ~ (e3 = e2)
% 243.04/49.55    (9)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.04/49.55         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.04/49.55    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.55    (11)  op(e1, e1) = e0
% 243.04/49.55    (12)   ~ (e1 = e0)
% 243.04/49.55    (13)   ~ (e2 = e1)
% 243.04/49.55  
% 243.04/49.56  Begin of proof
% 243.04/49.56  | 
% 243.04/49.56  | BETA: splitting (1) gives:
% 243.04/49.56  | 
% 243.04/49.56  | Case 1:
% 243.04/49.56  | | 
% 243.04/49.56  | |   (14)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 243.04/49.56  | |           e1)
% 243.04/49.56  | | 
% 243.04/49.56  | | REF_CLOSE: (2), (5), (6), (7), (10), (12), (14) are inconsistent by
% 243.04/49.56  | |            sub-proof #1019.
% 243.04/49.56  | | 
% 243.04/49.56  | Case 2:
% 243.04/49.56  | | 
% 243.04/49.56  | |   (15)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 243.04/49.56  | |           e1)
% 243.04/49.56  | | 
% 243.04/49.56  | | BETA: splitting (15) gives:
% 243.04/49.56  | | 
% 243.04/49.56  | | Case 1:
% 243.04/49.56  | | | 
% 243.04/49.56  | | |   (16)  all_58_8 = e1 & op(e1, e1) = e1
% 243.04/49.56  | | | 
% 243.04/49.56  | | | ALPHA: (16) implies:
% 243.04/49.56  | | |   (17)  op(e1, e1) = e1
% 243.04/49.56  | | | 
% 243.04/49.56  | | | REF_CLOSE: (10), (11), (12), (17) are inconsistent by sub-proof #2220.
% 243.04/49.56  | | | 
% 243.04/49.56  | | Case 2:
% 243.04/49.56  | | | 
% 243.04/49.56  | | |   (18)  all_58_11 = e1 & op(e1, e0) = e1
% 243.04/49.56  | | | 
% 243.04/49.56  | | | ALPHA: (18) implies:
% 243.04/49.56  | | |   (19)  all_58_11 = e1
% 243.04/49.56  | | | 
% 243.04/49.56  | | | REF_CLOSE: (2), (3), (4), (8), (9), (10), (11), (13), (19) are
% 243.04/49.56  | | |            inconsistent by sub-proof #1325.
% 243.04/49.56  | | | 
% 243.04/49.56  | | End of split
% 243.04/49.56  | | 
% 243.04/49.56  | End of split
% 243.04/49.56  | 
% 243.04/49.56  End of proof
% 243.04/49.56  
% 243.04/49.56  Sub-proof #1019 shows that the following formulas are inconsistent:
% 243.04/49.56  ----------------------------------------------------------------
% 243.04/49.56    (1)  all_58_6 = e3
% 243.04/49.56    (2)  op(e1, e2) = all_52_6
% 243.04/49.56    (3)   ~ (e3 = e1)
% 243.04/49.56    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 243.04/49.56    (5)  op(e1, e2) = e0
% 243.04/49.56    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.56    (7)   ~ (e1 = e0)
% 243.04/49.56  
% 243.04/49.56  Begin of proof
% 243.04/49.56  | 
% 243.04/49.56  | BETA: splitting (4) gives:
% 243.04/49.56  | 
% 243.04/49.56  | Case 1:
% 243.04/49.56  | | 
% 243.04/49.56  | |   (8)  all_58_6 = e1 & op(e1, e3) = e1
% 243.04/49.56  | | 
% 243.04/49.56  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #1803.
% 243.04/49.56  | | 
% 243.04/49.56  | Case 2:
% 243.04/49.56  | | 
% 243.04/49.56  | |   (9)  all_58_7 = e1 & op(e1, e2) = e1
% 243.04/49.56  | | 
% 243.04/49.56  | | ALPHA: (9) implies:
% 243.04/49.56  | |   (10)  op(e1, e2) = e1
% 243.04/49.56  | | 
% 243.04/49.56  | | REF_CLOSE: (2), (5), (6), (7), (10) are inconsistent by sub-proof #2136.
% 243.04/49.56  | | 
% 243.04/49.56  | End of split
% 243.04/49.56  | 
% 243.04/49.56  End of proof
% 243.04/49.56  
% 243.04/49.56  Sub-proof #1020 shows that the following formulas are inconsistent:
% 243.04/49.56  ----------------------------------------------------------------
% 243.04/49.56    (1)  all_58_11 = e2
% 243.04/49.56    (2)  all_58_11 = e1
% 243.04/49.56    (3)   ~ (e2 = e1)
% 243.04/49.56  
% 243.04/49.56  Begin of proof
% 243.04/49.56  | 
% 243.04/49.56  | COMBINE_EQS: (1), (2) imply:
% 243.04/49.56  |   (4)  e2 = e1
% 243.04/49.56  | 
% 243.04/49.56  | SIMP: (4) implies:
% 243.04/49.56  |   (5)  e2 = e1
% 243.04/49.56  | 
% 243.04/49.56  | REDUCE: (3), (5) imply:
% 243.04/49.56  |   (6)  $false
% 243.04/49.56  | 
% 243.04/49.56  | CLOSE: (6) is inconsistent.
% 243.04/49.56  | 
% 243.04/49.56  End of proof
% 243.04/49.56  
% 243.04/49.56  Sub-proof #1021 shows that the following formulas are inconsistent:
% 243.04/49.56  ----------------------------------------------------------------
% 243.04/49.56    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 243.04/49.56           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 243.04/49.56           all_12_1 & $i(all_12_1))
% 243.04/49.56    (2)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.04/49.56    (3)   ~ (e3 = e0)
% 243.04/49.56    (4)  all_56_11 = e1
% 243.04/49.56    (5)   ~ (e2 = e0)
% 243.04/49.56    (6)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.04/49.56           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.04/49.56           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 243.04/49.56         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 243.04/49.56           $i(all_56_15))
% 243.04/49.56    (7)   ~ (all_52_13 = e1)
% 243.04/49.56    (8)  op(e1, e2) = e3
% 243.04/49.56    (9)   ~ (all_52_2 = e1)
% 243.04/49.56    (10)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.04/49.56            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 243.04/49.56              e3) = all_26_1 & $i(all_26_1))
% 243.04/49.56    (11)  op(e3, e2) = e2
% 243.04/49.56    (12)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.04/49.56    (13)  op(e0, e3) = e2
% 243.04/49.56    (14)  op(e0, e2) = e0
% 243.04/49.56    (15)  op(e1, e2) = all_36_1
% 243.04/49.56    (16)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 243.04/49.56            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 243.04/49.56              e2) = all_40_1 & $i(all_40_1))
% 243.04/49.56    (17)  all_54_7 = all_52_13
% 243.04/49.56    (18)  op(e2, e1) = e0
% 243.04/49.56    (19)  all_54_1 = all_52_4
% 243.04/49.56    (20)   ~ (all_52_4 = e3)
% 243.04/49.56    (21)  op(e3, e2) = all_52_4
% 243.04/49.56    (22)  op(e0, e0) = e3
% 243.04/49.56    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.56    (24)  op(e1, e3) = all_52_2
% 243.04/49.56    (25)   ~ (all_52_4 = e1)
% 243.04/49.56    (26)   ~ (all_52_13 = e3)
% 243.04/49.56    (27)   ~ (all_52_13 = e0)
% 243.04/49.56    (28)   ~ (all_52_4 = e0)
% 243.04/49.56  
% 243.04/49.56  Begin of proof
% 243.04/49.56  | 
% 243.04/49.56  | BETA: splitting (16) gives:
% 243.04/49.56  | 
% 243.04/49.56  | Case 1:
% 243.04/49.56  | | 
% 243.04/49.56  | |   (29)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 243.04/49.56  | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 243.04/49.56  | | 
% 243.04/49.56  | | ALPHA: (29) implies:
% 243.04/49.56  | |   (30)  op(e1, e2) = all_40_1
% 243.04/49.56  | | 
% 243.04/49.56  | | BETA: splitting (6) gives:
% 243.04/49.56  | | 
% 243.04/49.56  | | Case 1:
% 243.04/49.56  | | | 
% 243.04/49.56  | | |   (31)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.04/49.56  | | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 243.04/49.56  | | | 
% 243.04/49.56  | | | REF_CLOSE: (4), (5), (7), (11), (12), (17), (18), (20), (21), (23), (26),
% 243.04/49.56  | | |            (27), (31) are inconsistent by sub-proof #1023.
% 243.04/49.56  | | | 
% 243.04/49.56  | | Case 2:
% 243.04/49.56  | | | 
% 243.04/49.56  | | |   (32)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13
% 243.04/49.56  | | |           & $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 &
% 243.04/49.56  | | |           op(e0, e2) = all_56_15 & $i(all_56_15))
% 243.04/49.56  | | | 
% 243.04/49.56  | | | BETA: splitting (32) gives:
% 243.04/49.56  | | | 
% 243.04/49.56  | | | Case 1:
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | |   (33)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13
% 243.04/49.56  | | | |         & $i(all_56_13)
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | ALPHA: (33) implies:
% 243.04/49.56  | | | |   (34)  op(e1, e2) = all_56_13
% 243.04/49.56  | | | |   (35)  op(e1, all_56_13) = e1
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | BETA: splitting (2) gives:
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | Case 1:
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | | GROUND_INST: instantiating (23) with e3, all_40_1, e2, e1, simplifying
% 243.04/49.56  | | | | |              with (8), (30) gives:
% 243.04/49.56  | | | | |   (36)  all_40_1 = e3
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | | GROUND_INST: instantiating (23) with all_40_1, all_56_13, e2, e1,
% 243.04/49.56  | | | | |              simplifying with (30), (34) gives:
% 243.04/49.56  | | | | |   (37)  all_56_13 = all_40_1
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | | GROUND_INST: instantiating (23) with all_36_1, all_56_13, e2, e1,
% 243.04/49.56  | | | | |              simplifying with (15), (34) gives:
% 243.04/49.56  | | | | |   (38)  all_56_13 = all_36_1
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | | COMBINE_EQS: (37), (38) imply:
% 243.04/49.56  | | | | |   (39)  all_40_1 = all_36_1
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | | SIMP: (39) implies:
% 243.04/49.56  | | | | |   (40)  all_40_1 = all_36_1
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | | COMBINE_EQS: (36), (40) imply:
% 243.04/49.56  | | | | |   (41)  all_36_1 = e3
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | | COMBINE_EQS: (38), (41) imply:
% 243.04/49.56  | | | | |   (42)  all_56_13 = e3
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | | REDUCE: (35), (42) imply:
% 243.04/49.56  | | | | |   (43)  op(e1, e3) = e1
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | | REF_CLOSE: (9), (23), (24), (43) are inconsistent by sub-proof #1948.
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | Case 2:
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | |   (44)  all_54_1 = e1 | all_54_1 = e0
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | | REF_CLOSE: (19), (25), (28), (44) are inconsistent by sub-proof #2049.
% 243.04/49.56  | | | | | 
% 243.04/49.56  | | | | End of split
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | Case 2:
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | |   (45)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15
% 243.04/49.56  | | | |         & $i(all_56_15)
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | REF_CLOSE: (1), (3), (10), (13), (14), (22), (23), (45) are inconsistent
% 243.04/49.56  | | | |            by sub-proof #1022.
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | End of split
% 243.04/49.56  | | | 
% 243.04/49.56  | | End of split
% 243.04/49.56  | | 
% 243.04/49.56  | Case 2:
% 243.04/49.56  | | 
% 243.04/49.56  | |   (46)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 243.04/49.56  | | 
% 243.04/49.56  | | ALPHA: (46) implies:
% 243.04/49.56  | |   (47)   ~ (all_40_1 = e3)
% 243.04/49.56  | |   (48)  op(e1, e2) = all_40_1
% 243.04/49.56  | | 
% 243.04/49.56  | | BETA: splitting (6) gives:
% 243.04/49.56  | | 
% 243.04/49.56  | | Case 1:
% 243.04/49.56  | | | 
% 243.04/49.56  | | |   (49)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.04/49.56  | | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 243.04/49.56  | | | 
% 243.04/49.56  | | | REF_CLOSE: (4), (5), (7), (11), (12), (17), (18), (20), (21), (23), (26),
% 243.04/49.56  | | |            (27), (49) are inconsistent by sub-proof #1023.
% 243.04/49.56  | | | 
% 243.04/49.56  | | Case 2:
% 243.04/49.56  | | | 
% 243.04/49.56  | | |   (50)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13
% 243.04/49.56  | | |           & $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 &
% 243.04/49.56  | | |           op(e0, e2) = all_56_15 & $i(all_56_15))
% 243.04/49.56  | | | 
% 243.04/49.56  | | | BETA: splitting (50) gives:
% 243.04/49.56  | | | 
% 243.04/49.56  | | | Case 1:
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | |   (51)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13
% 243.04/49.56  | | | |         & $i(all_56_13)
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | ALPHA: (51) implies:
% 243.04/49.56  | | | |   (52)  op(e1, e2) = all_56_13
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | GROUND_INST: instantiating (23) with e3, all_40_1, e2, e1, simplifying
% 243.04/49.56  | | | |              with (8), (48) gives:
% 243.04/49.56  | | | |   (53)  all_40_1 = e3
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | GROUND_INST: instantiating (23) with all_40_1, all_56_13, e2, e1,
% 243.04/49.56  | | | |              simplifying with (48), (52) gives:
% 243.04/49.56  | | | |   (54)  all_56_13 = all_40_1
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | GROUND_INST: instantiating (23) with all_36_1, all_56_13, e2, e1,
% 243.04/49.56  | | | |              simplifying with (15), (52) gives:
% 243.04/49.56  | | | |   (55)  all_56_13 = all_36_1
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | COMBINE_EQS: (54), (55) imply:
% 243.04/49.56  | | | |   (56)  all_40_1 = all_36_1
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | SIMP: (56) implies:
% 243.04/49.56  | | | |   (57)  all_40_1 = all_36_1
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | REF_CLOSE: (47), (53), (57) are inconsistent by sub-proof #2146.
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | Case 2:
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | |   (58)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15
% 243.04/49.56  | | | |         & $i(all_56_15)
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | | REF_CLOSE: (1), (3), (10), (13), (14), (22), (23), (58) are inconsistent
% 243.04/49.56  | | | |            by sub-proof #1022.
% 243.04/49.56  | | | | 
% 243.04/49.56  | | | End of split
% 243.04/49.56  | | | 
% 243.04/49.56  | | End of split
% 243.04/49.56  | | 
% 243.04/49.56  | End of split
% 243.04/49.56  | 
% 243.04/49.56  End of proof
% 243.04/49.56  
% 243.04/49.56  Sub-proof #1022 shows that the following formulas are inconsistent:
% 243.04/49.56  ----------------------------------------------------------------
% 243.04/49.56    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 243.04/49.56           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 243.04/49.56           all_12_1 & $i(all_12_1))
% 243.04/49.56    (2)   ~ (e3 = e0)
% 243.04/49.56    (3)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 243.04/49.56         $i(all_56_15)
% 243.04/49.56    (4)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 243.04/49.56           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 243.04/49.56           all_26_1 & $i(all_26_1))
% 243.04/49.56    (5)  op(e0, e3) = e2
% 243.04/49.56    (6)  op(e0, e2) = e0
% 243.04/49.56    (7)  op(e0, e0) = e3
% 243.04/49.56    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.56  
% 243.04/49.56  Begin of proof
% 243.04/49.56  | 
% 243.04/49.56  | ALPHA: (3) implies:
% 243.04/49.56  |   (9)  op(e0, e2) = all_56_15
% 243.04/49.56  |   (10)  op(e0, all_56_15) = e0
% 243.04/49.56  | 
% 243.04/49.56  | BETA: splitting (1) gives:
% 243.04/49.56  | 
% 243.04/49.56  | Case 1:
% 243.04/49.56  | | 
% 243.04/49.56  | | 
% 243.04/49.56  | | GROUND_INST: instantiating (8) with e0, all_56_15, e2, e0, simplifying with
% 243.04/49.56  | |              (6), (9) gives:
% 243.04/49.56  | |   (11)  all_56_15 = e0
% 243.04/49.56  | | 
% 243.04/49.56  | | REDUCE: (10), (11) imply:
% 243.04/49.56  | |   (12)  op(e0, e0) = e0
% 243.04/49.56  | | 
% 243.04/49.56  | | REF_CLOSE: (2), (7), (8), (12) are inconsistent by sub-proof #2079.
% 243.04/49.56  | | 
% 243.04/49.56  | Case 2:
% 243.04/49.56  | | 
% 243.04/49.56  | |   (13)   ~ (all_12_1 = e2) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 243.04/49.56  | | 
% 243.04/49.56  | | ALPHA: (13) implies:
% 243.04/49.56  | |   (14)   ~ (all_12_1 = e2)
% 243.04/49.56  | |   (15)  op(e0, e3) = all_12_1
% 243.04/49.56  | | 
% 243.04/49.56  | | REF_CLOSE: (4), (5), (8), (14), (15) are inconsistent by sub-proof #1300.
% 243.04/49.56  | | 
% 243.04/49.56  | End of split
% 243.04/49.56  | 
% 243.04/49.56  End of proof
% 243.04/49.56  
% 243.04/49.56  Sub-proof #1023 shows that the following formulas are inconsistent:
% 243.04/49.56  ----------------------------------------------------------------
% 243.04/49.56    (1)  all_56_11 = e1
% 243.04/49.56    (2)   ~ (e2 = e0)
% 243.04/49.56    (3)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.04/49.56           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 243.04/49.56    (4)   ~ (all_52_13 = e1)
% 243.04/49.56    (5)  op(e3, e2) = e2
% 243.04/49.56    (6)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.04/49.56    (7)  all_54_7 = all_52_13
% 243.04/49.56    (8)  op(e2, e1) = e0
% 243.04/49.56    (9)   ~ (all_52_4 = e3)
% 243.04/49.56    (10)  op(e3, e2) = all_52_4
% 243.04/49.56    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.56    (12)   ~ (all_52_13 = e3)
% 243.04/49.56    (13)   ~ (all_52_13 = e0)
% 243.04/49.56  
% 243.04/49.56  Begin of proof
% 243.04/49.56  | 
% 243.04/49.56  | BETA: splitting (3) gives:
% 243.04/49.56  | 
% 243.04/49.56  | Case 1:
% 243.04/49.56  | | 
% 243.04/49.56  | |   (14)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.04/49.56  | |         $i(all_56_9)
% 243.04/49.56  | | 
% 243.04/49.56  | | ALPHA: (14) implies:
% 243.04/49.56  | |   (15)  op(e3, e2) = all_56_9
% 243.04/49.56  | |   (16)  op(e3, all_56_9) = e3
% 243.04/49.56  | | 
% 243.04/49.56  | | BETA: splitting (6) gives:
% 243.04/49.56  | | 
% 243.04/49.56  | | Case 1:
% 243.04/49.56  | | | 
% 243.04/49.56  | | |   (17)  all_54_7 = e3
% 243.04/49.56  | | | 
% 243.04/49.56  | | | REF_CLOSE: (7), (12), (17) are inconsistent by sub-proof #2296.
% 243.04/49.56  | | | 
% 243.04/49.56  | | Case 2:
% 243.04/49.56  | | | 
% 243.04/49.56  | | |   (18)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.04/49.56  | | | 
% 243.04/49.56  | | | REF_CLOSE: (4), (5), (7), (9), (10), (11), (13), (15), (16), (18) are
% 243.04/49.56  | | |            inconsistent by sub-proof #1024.
% 243.04/49.56  | | | 
% 243.04/49.56  | | End of split
% 243.04/49.56  | | 
% 243.04/49.56  | Case 2:
% 243.04/49.56  | | 
% 243.04/49.56  | |   (19)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 243.04/49.56  | | 
% 243.04/49.56  | | ALPHA: (19) implies:
% 243.04/49.56  | |   (20)  op(e2, all_56_11) = e2
% 243.04/49.56  | | 
% 243.04/49.56  | | REDUCE: (1), (20) imply:
% 243.04/49.56  | |   (21)  op(e2, e1) = e2
% 243.04/49.56  | | 
% 243.04/49.56  | | REF_CLOSE: (2), (8), (11), (21) are inconsistent by sub-proof #1906.
% 243.04/49.56  | | 
% 243.04/49.56  | End of split
% 243.04/49.56  | 
% 243.04/49.56  End of proof
% 243.04/49.56  
% 243.04/49.56  Sub-proof #1024 shows that the following formulas are inconsistent:
% 243.04/49.56  ----------------------------------------------------------------
% 243.04/49.56    (1)  op(e3, e2) = all_56_9
% 243.04/49.56    (2)  op(e3, all_56_9) = e3
% 243.04/49.56    (3)   ~ (all_52_13 = e1)
% 243.04/49.56    (4)  op(e3, e2) = e2
% 243.04/49.56    (5)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.04/49.56    (6)  all_54_7 = all_52_13
% 243.04/49.56    (7)   ~ (all_52_4 = e3)
% 243.04/49.56    (8)  op(e3, e2) = all_52_4
% 243.04/49.56    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.56    (10)   ~ (all_52_13 = e0)
% 243.04/49.56  
% 243.04/49.56  Begin of proof
% 243.04/49.56  | 
% 243.04/49.56  | BETA: splitting (5) gives:
% 243.04/49.56  | 
% 243.04/49.56  | Case 1:
% 243.04/49.56  | | 
% 243.04/49.56  | | 
% 243.04/49.56  | | GROUND_INST: instantiating (9) with e2, all_56_9, e2, e3, simplifying with
% 243.04/49.56  | |              (1), (4) gives:
% 243.04/49.56  | |   (11)  all_56_9 = e2
% 243.04/49.56  | | 
% 243.04/49.56  | | REDUCE: (2), (11) imply:
% 243.04/49.56  | |   (12)  op(e3, e2) = e3
% 243.04/49.56  | | 
% 243.04/49.56  | | REF_CLOSE: (7), (8), (9), (12) are inconsistent by sub-proof #2192.
% 243.04/49.56  | | 
% 243.04/49.56  | Case 2:
% 243.04/49.56  | | 
% 243.04/49.56  | |   (13)  all_54_7 = e1 | all_54_7 = e0
% 243.04/49.56  | | 
% 243.04/49.56  | | REF_CLOSE: (3), (6), (10), (13) are inconsistent by sub-proof #2293.
% 243.04/49.56  | | 
% 243.04/49.56  | End of split
% 243.04/49.56  | 
% 243.04/49.56  End of proof
% 243.04/49.56  
% 243.04/49.56  Sub-proof #1025 shows that the following formulas are inconsistent:
% 243.04/49.56  ----------------------------------------------------------------
% 243.04/49.56    (1)   ~ (e2 = e0)
% 243.04/49.57    (2)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.04/49.57         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.04/49.57    (3)   ~ (e3 = e1)
% 243.04/49.57    (4)  op(e2, e1) = all_52_9
% 243.04/49.57    (5)   ~ (e3 = e2)
% 243.04/49.57    (6)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.04/49.57         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.04/49.57    (7)  op(e2, e1) = e0
% 243.04/49.57    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.57    (9)  op(e1, e1) = e0
% 243.04/49.57    (10)   ~ (e1 = e0)
% 243.04/49.57    (11)  all_58_4 = e3
% 243.04/49.57    (12)   ~ (e2 = e1)
% 243.04/49.57  
% 243.04/49.57  Begin of proof
% 243.04/49.57  | 
% 243.04/49.57  | BETA: splitting (6) gives:
% 243.04/49.57  | 
% 243.04/49.57  | Case 1:
% 243.04/49.57  | | 
% 243.04/49.57  | |   (13)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 243.04/49.57  | |           e2)
% 243.04/49.57  | | 
% 243.04/49.57  | | BETA: splitting (13) gives:
% 243.04/49.57  | | 
% 243.04/49.57  | | Case 1:
% 243.04/49.57  | | | 
% 243.04/49.57  | | |   (14)  all_58_4 = e2 & op(e3, e1) = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | ALPHA: (14) implies:
% 243.04/49.57  | | |   (15)  all_58_4 = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | REF_CLOSE: (5), (11), (15) are inconsistent by sub-proof #1902.
% 243.04/49.57  | | | 
% 243.04/49.57  | | Case 2:
% 243.04/49.57  | | | 
% 243.04/49.57  | | |   (16)  all_58_5 = e2 & op(e2, e1) = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | ALPHA: (16) implies:
% 243.04/49.57  | | |   (17)  op(e2, e1) = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | REF_CLOSE: (1), (7), (8), (17) are inconsistent by sub-proof #1906.
% 243.04/49.57  | | | 
% 243.04/49.57  | | End of split
% 243.04/49.57  | | 
% 243.04/49.57  | Case 2:
% 243.04/49.57  | | 
% 243.04/49.57  | |   (18)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 243.04/49.57  | |           e2)
% 243.04/49.57  | | 
% 243.04/49.57  | | BETA: splitting (18) gives:
% 243.04/49.57  | | 
% 243.04/49.57  | | Case 1:
% 243.04/49.57  | | | 
% 243.04/49.57  | | |   (19)  all_58_8 = e2 & op(e1, e1) = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | ALPHA: (19) implies:
% 243.04/49.57  | | |   (20)  op(e1, e1) = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | REF_CLOSE: (1), (8), (9), (20) are inconsistent by sub-proof #2211.
% 243.04/49.57  | | | 
% 243.04/49.57  | | Case 2:
% 243.04/49.57  | | | 
% 243.04/49.57  | | |   (21)  all_58_14 = e2 & op(e0, e1) = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | ALPHA: (21) implies:
% 243.04/49.57  | | |   (22)  all_58_14 = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (12), (22) are
% 243.04/49.57  | | |            inconsistent by sub-proof #1026.
% 243.04/49.57  | | | 
% 243.04/49.57  | | End of split
% 243.04/49.57  | | 
% 243.04/49.57  | End of split
% 243.04/49.57  | 
% 243.04/49.57  End of proof
% 243.04/49.57  
% 243.04/49.57  Sub-proof #1026 shows that the following formulas are inconsistent:
% 243.04/49.57  ----------------------------------------------------------------
% 243.04/49.57    (1)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.04/49.57         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.04/49.57    (2)  all_58_14 = e2
% 243.04/49.57    (3)   ~ (e3 = e1)
% 243.04/49.57    (4)  op(e2, e1) = all_52_9
% 243.04/49.57    (5)  op(e2, e1) = e0
% 243.04/49.57    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.57    (7)  op(e1, e1) = e0
% 243.04/49.57    (8)   ~ (e1 = e0)
% 243.04/49.57    (9)  all_58_4 = e3
% 243.04/49.57    (10)   ~ (e2 = e1)
% 243.04/49.57  
% 243.04/49.57  Begin of proof
% 243.04/49.57  | 
% 243.04/49.57  | BETA: splitting (1) gives:
% 243.04/49.57  | 
% 243.04/49.57  | Case 1:
% 243.04/49.57  | | 
% 243.04/49.57  | |   (11)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 243.04/49.57  | |           e1)
% 243.04/49.57  | | 
% 243.04/49.57  | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (11) are inconsistent by sub-proof
% 243.04/49.57  | |            #1879.
% 243.04/49.57  | | 
% 243.04/49.57  | Case 2:
% 243.04/49.57  | | 
% 243.04/49.57  | |   (12)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 243.04/49.57  | |           e1)
% 243.04/49.57  | | 
% 243.04/49.57  | | REF_CLOSE: (2), (6), (7), (8), (10), (12) are inconsistent by sub-proof
% 243.04/49.57  | |            #1435.
% 243.04/49.57  | | 
% 243.04/49.57  | End of split
% 243.04/49.57  | 
% 243.04/49.57  End of proof
% 243.04/49.57  
% 243.04/49.57  Sub-proof #1027 shows that the following formulas are inconsistent:
% 243.04/49.57  ----------------------------------------------------------------
% 243.04/49.57    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.57         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.57    (2)   ~ (e3 = e0)
% 243.04/49.57    (3)  all_58_7 = e0 & op(e1, e2) = e0
% 243.04/49.57    (4)   ~ (e2 = e0)
% 243.04/49.57    (5)  all_58_9 = e0
% 243.04/49.57    (6)   ~ (e3 = e1)
% 243.04/49.57    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.57         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.57    (8)  op(e3, e3) = e1
% 243.04/49.57    (9)   ~ (e3 = e2)
% 243.04/49.57    (10)  all_58_7 = e3
% 243.04/49.57    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.57    (12)  all_58_4 = e3
% 243.04/49.57    (13)   ~ (e2 = e1)
% 243.04/49.57  
% 243.04/49.57  Begin of proof
% 243.04/49.57  | 
% 243.04/49.57  | ALPHA: (3) implies:
% 243.04/49.57  |   (14)  all_58_7 = e0
% 243.04/49.57  | 
% 243.04/49.57  | COMBINE_EQS: (10), (14) imply:
% 243.04/49.57  |   (15)  e3 = e0
% 243.04/49.57  | 
% 243.04/49.57  | COMBINE_EQS: (12), (15) imply:
% 243.04/49.57  |   (16)  all_58_4 = e0
% 243.04/49.57  | 
% 243.04/49.57  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (13), (16) are
% 243.04/49.57  |            inconsistent by sub-proof #1190.
% 243.04/49.57  | 
% 243.04/49.57  End of proof
% 243.04/49.57  
% 243.04/49.57  Sub-proof #1028 shows that the following formulas are inconsistent:
% 243.04/49.57  ----------------------------------------------------------------
% 243.04/49.57    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.57         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.57    (2)   ~ (e3 = e0)
% 243.04/49.57    (3)   ~ (e2 = e0)
% 243.04/49.57    (4)   ~ (all_52_13 = e1)
% 243.04/49.57    (5)   ~ (e3 = e1)
% 243.04/49.57    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.04/49.57         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.57    (7)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 243.04/49.57    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.57         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.57    (9)  op(e3, e3) = e1
% 243.04/49.57    (10)   ~ (e3 = e2)
% 243.04/49.57    (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.04/49.57          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.04/49.57    (12)  op(e2, e3) = all_52_1
% 243.04/49.57    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.57          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.57    (14)   ~ (all_52_4 = e3)
% 243.04/49.57    (15)  op(e3, e2) = all_52_4
% 243.04/49.57    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.57    (17)   ~ (e1 = e0)
% 243.04/49.57    (18)  all_58_4 = e3
% 243.04/49.57    (19)  op(e2, e0) = all_52_13
% 243.04/49.57    (20)  all_58_14 = e1
% 243.04/49.57    (21)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.04/49.57          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.04/49.57    (22)   ~ (e2 = e1)
% 243.04/49.57    (23)   ~ (all_52_1 = e1)
% 243.04/49.57  
% 243.04/49.57  Begin of proof
% 243.04/49.57  | 
% 243.04/49.57  | BETA: splitting (7) gives:
% 243.04/49.57  | 
% 243.04/49.57  | Case 1:
% 243.04/49.57  | | 
% 243.04/49.57  | |   (24)  all_58_1 = e3 & op(e3, e2) = e3
% 243.04/49.57  | | 
% 243.04/49.57  | | ALPHA: (24) implies:
% 243.04/49.57  | |   (25)  op(e3, e2) = e3
% 243.04/49.57  | | 
% 243.04/49.57  | | REF_CLOSE: (14), (15), (16), (25) are inconsistent by sub-proof #2192.
% 243.04/49.57  | | 
% 243.04/49.57  | Case 2:
% 243.04/49.57  | | 
% 243.04/49.57  | |   (26)  all_58_3 = e3 & op(e2, e2) = e3
% 243.04/49.57  | | 
% 243.04/49.57  | | ALPHA: (26) implies:
% 243.04/49.57  | |   (27)  all_58_3 = e3
% 243.04/49.57  | | 
% 243.04/49.57  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 243.04/49.57  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (27)
% 243.04/49.57  | |            are inconsistent by sub-proof #1029.
% 243.04/49.57  | | 
% 243.04/49.57  | End of split
% 243.04/49.57  | 
% 243.04/49.57  End of proof
% 243.04/49.57  
% 243.04/49.57  Sub-proof #1029 shows that the following formulas are inconsistent:
% 243.04/49.57  ----------------------------------------------------------------
% 243.04/49.57    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.57         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.57    (2)   ~ (e3 = e0)
% 243.04/49.57    (3)   ~ (e2 = e0)
% 243.04/49.57    (4)   ~ (all_52_13 = e1)
% 243.04/49.57    (5)   ~ (e3 = e1)
% 243.04/49.57    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.04/49.57         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.57    (7)  all_58_3 = e3
% 243.04/49.57    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.57         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.57    (9)  op(e3, e3) = e1
% 243.04/49.57    (10)   ~ (e3 = e2)
% 243.04/49.57    (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.04/49.57          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.04/49.57    (12)  op(e2, e3) = all_52_1
% 243.04/49.57    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.57          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.57    (14)   ~ (all_52_4 = e3)
% 243.04/49.57    (15)  op(e3, e2) = all_52_4
% 243.04/49.57    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.57    (17)   ~ (e1 = e0)
% 243.04/49.57    (18)  all_58_4 = e3
% 243.04/49.57    (19)  op(e2, e0) = all_52_13
% 243.04/49.57    (20)  all_58_14 = e1
% 243.04/49.57    (21)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.04/49.57          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.04/49.57    (22)   ~ (e2 = e1)
% 243.04/49.57    (23)   ~ (all_52_1 = e1)
% 243.04/49.57  
% 243.04/49.57  Begin of proof
% 243.04/49.57  | 
% 243.04/49.57  | BETA: splitting (21) gives:
% 243.04/49.57  | 
% 243.04/49.57  | Case 1:
% 243.04/49.57  | | 
% 243.04/49.57  | |   (24)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 243.04/49.57  | |           e1)
% 243.04/49.57  | | 
% 243.04/49.57  | | BETA: splitting (24) gives:
% 243.04/49.57  | | 
% 243.04/49.57  | | Case 1:
% 243.04/49.57  | | | 
% 243.04/49.57  | | |   (25)  all_58_2 = e1 & op(e2, e3) = e1
% 243.04/49.57  | | | 
% 243.04/49.57  | | | REF_CLOSE: (12), (16), (23), (25) are inconsistent by sub-proof #2229.
% 243.04/49.57  | | | 
% 243.04/49.57  | | Case 2:
% 243.04/49.57  | | | 
% 243.04/49.57  | | |   (26)  all_58_3 = e1 & op(e2, e2) = e1
% 243.04/49.57  | | | 
% 243.04/49.57  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (13), (14), (15),
% 243.04/49.57  | | |            (16), (17), (18), (22), (26) are inconsistent by sub-proof
% 243.04/49.57  | | |            #1030.
% 243.04/49.57  | | | 
% 243.04/49.57  | | End of split
% 243.04/49.57  | | 
% 243.04/49.57  | Case 2:
% 243.04/49.57  | | 
% 243.04/49.57  | |   (27)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 243.04/49.57  | |           e1)
% 243.04/49.57  | | 
% 243.04/49.57  | | BETA: splitting (27) gives:
% 243.04/49.57  | | 
% 243.04/49.57  | | Case 1:
% 243.04/49.57  | | | 
% 243.04/49.57  | | |   (28)  all_58_5 = e1 & op(e2, e1) = e1
% 243.04/49.57  | | | 
% 243.04/49.57  | | | ALPHA: (28) implies:
% 243.04/49.57  | | |   (29)  all_58_5 = e1
% 243.04/49.57  | | | 
% 243.04/49.57  | | | REF_CLOSE: (2), (3), (6), (10), (11), (17), (18), (20), (22), (29) are
% 243.04/49.57  | | |            inconsistent by sub-proof #1481.
% 243.04/49.57  | | | 
% 243.04/49.57  | | Case 2:
% 243.04/49.57  | | | 
% 243.04/49.57  | | |   (30)  all_58_10 = e1 & op(e2, e0) = e1
% 243.04/49.57  | | | 
% 243.04/49.57  | | | REF_CLOSE: (4), (16), (19), (30) are inconsistent by sub-proof #2277.
% 243.04/49.57  | | | 
% 243.04/49.57  | | End of split
% 243.04/49.57  | | 
% 243.04/49.57  | End of split
% 243.04/49.57  | 
% 243.04/49.57  End of proof
% 243.04/49.57  
% 243.04/49.57  Sub-proof #1030 shows that the following formulas are inconsistent:
% 243.04/49.57  ----------------------------------------------------------------
% 243.04/49.57    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.57         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.57    (2)   ~ (e3 = e0)
% 243.04/49.57    (3)   ~ (e2 = e0)
% 243.04/49.57    (4)   ~ (e3 = e1)
% 243.04/49.57    (5)  all_58_3 = e3
% 243.04/49.57    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.57         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.57    (7)  op(e3, e3) = e1
% 243.04/49.57    (8)   ~ (e3 = e2)
% 243.04/49.57    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.57         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.57    (10)   ~ (all_52_4 = e3)
% 243.04/49.57    (11)  op(e3, e2) = all_52_4
% 243.04/49.57    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.57    (13)  all_58_3 = e1 & op(e2, e2) = e1
% 243.04/49.57    (14)   ~ (e1 = e0)
% 243.04/49.57    (15)  all_58_4 = e3
% 243.04/49.57    (16)   ~ (e2 = e1)
% 243.04/49.57  
% 243.04/49.57  Begin of proof
% 243.04/49.57  | 
% 243.04/49.57  | ALPHA: (13) implies:
% 243.04/49.57  |   (17)  all_58_3 = e1
% 243.04/49.57  | 
% 243.04/49.57  | COMBINE_EQS: (5), (17) imply:
% 243.04/49.57  |   (18)  e3 = e1
% 243.04/49.57  | 
% 243.04/49.57  | COMBINE_EQS: (15), (18) imply:
% 243.04/49.57  |   (19)  all_58_4 = e1
% 243.04/49.57  | 
% 243.04/49.57  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 243.04/49.57  |            (16), (19) are inconsistent by sub-proof #1468.
% 243.04/49.57  | 
% 243.04/49.57  End of proof
% 243.04/49.57  
% 243.04/49.57  Sub-proof #1031 shows that the following formulas are inconsistent:
% 243.04/49.57  ----------------------------------------------------------------
% 243.04/49.57    (1)   ~ (e3 = e0)
% 243.04/49.57    (2)   ~ (e2 = e0)
% 243.04/49.57    (3)  all_58_15 = e3
% 243.04/49.57    (4)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.57             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.04/49.57               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.57               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.57    (5)   ~ (e3 = e2)
% 243.04/49.57    (6)  all_58_12 = e3
% 243.04/49.57    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.57    (8)   ~ (e1 = e0)
% 243.04/49.57    (9)  all_58_14 = e1
% 243.04/49.57    (10)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.57          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.04/49.57            e2)
% 243.04/49.57    (11)   ~ (e2 = e1)
% 243.04/49.57  
% 243.04/49.57  Begin of proof
% 243.04/49.57  | 
% 243.04/49.57  | BETA: splitting (10) gives:
% 243.04/49.57  | 
% 243.04/49.57  | Case 1:
% 243.04/49.57  | | 
% 243.04/49.57  | |   (12)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 243.04/49.57  | |           e2)
% 243.04/49.57  | | 
% 243.04/49.57  | | BETA: splitting (12) gives:
% 243.04/49.57  | | 
% 243.04/49.57  | | Case 1:
% 243.04/49.57  | | | 
% 243.04/49.57  | | |   (13)  all_58_12 = e2 & op(e0, e3) = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | ALPHA: (13) implies:
% 243.04/49.57  | | |   (14)  all_58_12 = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | REF_CLOSE: (5), (6), (14) are inconsistent by sub-proof #1552.
% 243.04/49.57  | | | 
% 243.04/49.57  | | Case 2:
% 243.04/49.57  | | | 
% 243.04/49.57  | | |   (15)  all_58_13 = e2 & op(e0, e2) = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | ALPHA: (15) implies:
% 243.04/49.57  | | |   (16)  op(e0, e2) = e2
% 243.04/49.57  | | | 
% 243.04/49.57  | | | BETA: splitting (4) gives:
% 243.04/49.57  | | | 
% 243.04/49.57  | | | Case 1:
% 243.04/49.57  | | | | 
% 243.04/49.57  | | | |   (17)  all_58_15 = e0 & op(e0, e0) = e0
% 243.04/49.57  | | | | 
% 243.04/49.57  | | | | ALPHA: (17) implies:
% 243.04/49.57  | | | |   (18)  all_58_15 = e0
% 243.04/49.57  | | | | 
% 243.04/49.57  | | | | REF_CLOSE: (1), (3), (18) are inconsistent by sub-proof #1540.
% 243.04/49.57  | | | | 
% 243.04/49.57  | | | Case 2:
% 243.04/49.57  | | | | 
% 243.04/49.57  | | | |   (19)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 243.04/49.57  | | | |               e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 243.04/49.57  | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 243.04/49.57  | | | |               e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 243.04/49.57  | | | | 
% 243.04/49.57  | | | | ALPHA: (19) implies:
% 243.04/49.58  | | | |   (20)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 243.04/49.58  | | | |             e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.58  | | | | 
% 243.04/49.58  | | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (16), (20) are inconsistent by
% 243.04/49.58  | | | |            sub-proof #1032.
% 243.04/49.58  | | | | 
% 243.04/49.58  | | | End of split
% 243.04/49.58  | | | 
% 243.04/49.58  | | End of split
% 243.04/49.58  | | 
% 243.04/49.58  | Case 2:
% 243.04/49.58  | | 
% 243.04/49.58  | |   (21)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.04/49.58  | |           e2)
% 243.04/49.58  | | 
% 243.04/49.58  | | BETA: splitting (21) gives:
% 243.04/49.58  | | 
% 243.04/49.58  | | Case 1:
% 243.04/49.58  | | | 
% 243.04/49.58  | | |   (22)  all_58_14 = e2 & op(e0, e1) = e2
% 243.04/49.58  | | | 
% 243.04/49.58  | | | REF_CLOSE: (9), (11), (22) are inconsistent by sub-proof #1771.
% 243.04/49.58  | | | 
% 243.04/49.58  | | Case 2:
% 243.04/49.58  | | | 
% 243.04/49.58  | | |   (23)  all_58_15 = e2 & op(e0, e0) = e2
% 243.04/49.58  | | | 
% 243.04/49.58  | | | REF_CLOSE: (3), (5), (23) are inconsistent by sub-proof #1231.
% 243.04/49.58  | | | 
% 243.04/49.58  | | End of split
% 243.04/49.58  | | 
% 243.04/49.58  | End of split
% 243.04/49.58  | 
% 243.04/49.58  End of proof
% 243.04/49.58  
% 243.04/49.58  Sub-proof #1032 shows that the following formulas are inconsistent:
% 243.04/49.58  ----------------------------------------------------------------
% 243.04/49.58    (1)   ~ (e3 = e0)
% 243.04/49.58    (2)   ~ (e2 = e0)
% 243.04/49.58    (3)  op(e0, e2) = e2
% 243.04/49.58    (4)  all_58_12 = e3
% 243.04/49.58    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.58    (6)   ~ (e1 = e0)
% 243.04/49.58    (7)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.04/49.58         (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.58    (8)  all_58_14 = e1
% 243.04/49.58  
% 243.04/49.58  Begin of proof
% 243.04/49.58  | 
% 243.04/49.58  | BETA: splitting (7) gives:
% 243.04/49.58  | 
% 243.04/49.58  | Case 1:
% 243.04/49.58  | | 
% 243.04/49.58  | |   (9)  all_58_12 = e0 & op(e0, e3) = e0
% 243.04/49.58  | | 
% 243.04/49.58  | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #1641.
% 243.04/49.58  | | 
% 243.04/49.58  | Case 2:
% 243.04/49.58  | | 
% 243.04/49.58  | |   (10)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 243.04/49.58  | |           e0)
% 243.04/49.58  | | 
% 243.04/49.58  | | BETA: splitting (10) gives:
% 243.04/49.58  | | 
% 243.04/49.58  | | Case 1:
% 243.04/49.58  | | | 
% 243.04/49.58  | | |   (11)  all_58_13 = e0 & op(e0, e2) = e0
% 243.04/49.58  | | | 
% 243.04/49.58  | | | ALPHA: (11) implies:
% 243.04/49.58  | | |   (12)  op(e0, e2) = e0
% 243.04/49.58  | | | 
% 243.04/49.58  | | | REF_CLOSE: (2), (3), (5), (12) are inconsistent by sub-proof #2132.
% 243.04/49.58  | | | 
% 243.04/49.58  | | Case 2:
% 243.04/49.58  | | | 
% 243.04/49.58  | | |   (13)  all_58_14 = e0 & op(e0, e1) = e0
% 243.04/49.58  | | | 
% 243.04/49.58  | | | ALPHA: (13) implies:
% 243.04/49.58  | | |   (14)  all_58_14 = e0
% 243.04/49.58  | | | 
% 243.04/49.58  | | | REF_CLOSE: (6), (8), (14) are inconsistent by sub-proof #1033.
% 243.04/49.58  | | | 
% 243.04/49.58  | | End of split
% 243.04/49.58  | | 
% 243.04/49.58  | End of split
% 243.04/49.58  | 
% 243.04/49.58  End of proof
% 243.04/49.58  
% 243.04/49.58  Sub-proof #1033 shows that the following formulas are inconsistent:
% 243.04/49.58  ----------------------------------------------------------------
% 243.04/49.58    (1)  all_58_14 = e1
% 243.04/49.58    (2)  all_58_14 = e0
% 243.04/49.58    (3)   ~ (e1 = e0)
% 243.04/49.58  
% 243.04/49.58  Begin of proof
% 243.04/49.58  | 
% 243.04/49.58  | COMBINE_EQS: (1), (2) imply:
% 243.04/49.58  |   (4)  e1 = e0
% 243.04/49.58  | 
% 243.04/49.58  | SIMP: (4) implies:
% 243.04/49.58  |   (5)  e1 = e0
% 243.04/49.58  | 
% 243.04/49.58  | REDUCE: (3), (5) imply:
% 243.04/49.58  |   (6)  $false
% 243.04/49.58  | 
% 243.04/49.58  | CLOSE: (6) is inconsistent.
% 243.04/49.58  | 
% 243.04/49.58  End of proof
% 243.04/49.58  
% 243.04/49.58  Sub-proof #1034 shows that the following formulas are inconsistent:
% 243.04/49.58  ----------------------------------------------------------------
% 243.04/49.58    (1)   ~ (all_12_1 = e2)
% 243.04/49.58    (2)  all_56_7 = e0
% 243.04/49.58    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.04/49.58         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.58    (4)  op(e0, e1) = all_52_11
% 243.04/49.58    (5)  op(e1, e2) = all_52_6
% 243.04/49.58    (6)  op(e1, e1) = all_6_2
% 243.04/49.58    (7)  op(e1, e0) = all_52_14
% 243.04/49.58    (8)   ~ (all_52_7 = e3)
% 243.04/49.58    (9)  all_12_1 = e0
% 243.04/49.58    (10)   ~ (e3 = e1)
% 243.04/49.58    (11)   ~ (all_22_1 = e0)
% 243.04/49.58    (12)  all_22_1 = e3
% 243.04/49.58    (13)   ~ (all_52_11 = e3)
% 243.04/49.58    (14)   ~ (all_6_2 = e3)
% 243.04/49.58    (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.04/49.58          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.04/49.58    (16)   ~ (e3 = e2)
% 243.04/49.58    (17)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.04/49.58          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.04/49.58    (18)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.04/49.58          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.04/49.58    (19)   ~ (all_52_14 = e3)
% 243.04/49.58    (20)   ~ (all_52_6 = e3)
% 243.04/49.58    (21)  op(e0, e2) = all_52_7
% 243.04/49.58    (22)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.04/49.58          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.04/49.58    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.58    (24)  op(e0, all_56_7) = e0
% 243.04/49.58    (25)   ~ (e1 = e0)
% 243.04/49.58    (26)   ~ (e2 = e1)
% 243.04/49.58  
% 243.04/49.58  Begin of proof
% 243.04/49.58  | 
% 243.04/49.58  | REDUCE: (11), (12) imply:
% 243.04/49.58  |   (27)   ~ (e3 = e0)
% 243.04/49.58  | 
% 243.04/49.58  | REDUCE: (1), (9) imply:
% 243.04/49.58  |   (28)   ~ (e2 = e0)
% 243.04/49.58  | 
% 243.04/49.58  | SIMP: (28) implies:
% 243.04/49.58  |   (29)   ~ (e2 = e0)
% 243.04/49.58  | 
% 243.04/49.58  | REDUCE: (2), (24) imply:
% 243.04/49.58  |   (30)  op(e0, e0) = e0
% 243.04/49.58  | 
% 243.04/49.58  | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (13), (14), (15), (16), (17),
% 243.04/49.58  |            (18), (19), (20), (21), (22), (23), (25), (26), (27), (29), (30)
% 243.04/49.58  |            are inconsistent by sub-proof #1035.
% 243.04/49.58  | 
% 243.04/49.58  End of proof
% 243.04/49.58  
% 243.04/49.58  Sub-proof #1035 shows that the following formulas are inconsistent:
% 243.04/49.58  ----------------------------------------------------------------
% 243.04/49.58    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.04/49.58         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.58    (2)   ~ (e3 = e0)
% 243.04/49.58    (3)  op(e0, e1) = all_52_11
% 243.04/49.58    (4)   ~ (e2 = e0)
% 243.04/49.58    (5)  op(e1, e2) = all_52_6
% 243.04/49.58    (6)  op(e1, e1) = all_6_2
% 243.04/49.58    (7)  op(e1, e0) = all_52_14
% 243.04/49.58    (8)   ~ (all_52_7 = e3)
% 243.04/49.58    (9)   ~ (e3 = e1)
% 243.04/49.58    (10)   ~ (all_52_11 = e3)
% 243.04/49.58    (11)   ~ (all_6_2 = e3)
% 243.04/49.58    (12)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.04/49.58          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.04/49.58    (13)   ~ (e3 = e2)
% 243.04/49.58    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.04/49.58          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.04/49.58    (15)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.04/49.58          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.04/49.58    (16)   ~ (all_52_14 = e3)
% 243.04/49.58    (17)   ~ (all_52_6 = e3)
% 243.04/49.58    (18)  op(e0, e2) = all_52_7
% 243.04/49.58    (19)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.04/49.58          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.04/49.58    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.58    (21)  op(e0, e0) = e0
% 243.04/49.58    (22)   ~ (e1 = e0)
% 243.04/49.58    (23)   ~ (e2 = e1)
% 243.04/49.58  
% 243.04/49.58  Begin of proof
% 243.04/49.58  | 
% 243.04/49.58  | BETA: splitting (1) gives:
% 243.04/49.58  | 
% 243.04/49.58  | Case 1:
% 243.04/49.58  | | 
% 243.04/49.58  | |   (24)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 243.04/49.58  | |           e3)
% 243.04/49.58  | | 
% 243.04/49.58  | | BETA: splitting (24) gives:
% 243.04/49.58  | | 
% 243.04/49.58  | | Case 1:
% 243.04/49.58  | | | 
% 243.04/49.58  | | |   (25)  all_58_12 = e3 & op(e0, e3) = e3
% 243.04/49.58  | | | 
% 243.04/49.58  | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (11), (12), (13), (14), (15),
% 243.04/49.58  | | |            (16), (17), (19), (20), (22), (23), (25) are inconsistent by
% 243.04/49.58  | | |            sub-proof #1528.
% 243.04/49.58  | | | 
% 243.04/49.58  | | Case 2:
% 243.04/49.58  | | | 
% 243.04/49.58  | | |   (26)  all_58_13 = e3 & op(e0, e2) = e3
% 243.04/49.58  | | | 
% 243.04/49.58  | | | REF_CLOSE: (8), (18), (20), (26) are inconsistent by sub-proof #1919.
% 243.04/49.58  | | | 
% 243.04/49.58  | | End of split
% 243.04/49.58  | | 
% 243.04/49.58  | Case 2:
% 243.04/49.58  | | 
% 243.04/49.58  | |   (27)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 243.04/49.58  | |           e3)
% 243.04/49.58  | | 
% 243.04/49.58  | | REF_CLOSE: (2), (3), (10), (20), (21), (27) are inconsistent by sub-proof
% 243.04/49.58  | |            #1580.
% 243.04/49.58  | | 
% 243.04/49.58  | End of split
% 243.04/49.58  | 
% 243.04/49.58  End of proof
% 243.04/49.58  
% 243.04/49.58  Sub-proof #1036 shows that the following formulas are inconsistent:
% 243.04/49.58  ----------------------------------------------------------------
% 243.04/49.58    (1)   ~ (e2 = e0)
% 243.04/49.58    (2)  op(e0, e1) = e1
% 243.04/49.58    (3)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.58    (4)  op(e1, e1) = e2
% 243.04/49.58    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.58    (6)   ~ (e1 = e0)
% 243.04/49.58  
% 243.04/49.58  Begin of proof
% 243.04/49.58  | 
% 243.04/49.58  | BETA: splitting (3) gives:
% 243.04/49.58  | 
% 243.04/49.58  | Case 1:
% 243.04/49.58  | | 
% 243.04/49.58  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 243.04/49.58  | | 
% 243.04/49.58  | | ALPHA: (7) implies:
% 243.04/49.58  | |   (8)  op(e1, e1) = e0
% 243.04/49.58  | | 
% 243.04/49.58  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2211.
% 243.04/49.58  | | 
% 243.04/49.58  | Case 2:
% 243.04/49.58  | | 
% 243.04/49.58  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 243.04/49.58  | | 
% 243.04/49.58  | | ALPHA: (9) implies:
% 243.04/49.58  | |   (10)  op(e0, e1) = e0
% 243.04/49.58  | | 
% 243.04/49.58  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #2158.
% 243.04/49.58  | | 
% 243.04/49.58  | End of split
% 243.04/49.58  | 
% 243.04/49.58  End of proof
% 243.04/49.58  
% 243.04/49.58  Sub-proof #1037 shows that the following formulas are inconsistent:
% 243.04/49.58  ----------------------------------------------------------------
% 243.04/49.58    (1)   ~ (e3 = e2)
% 243.04/49.58    (2)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.04/49.58    (3)  op(e0, e0) = e3
% 243.04/49.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.58    (5)  all_58_14 = e1
% 243.04/49.58    (6)   ~ (e2 = e1)
% 243.04/49.58  
% 243.04/49.58  Begin of proof
% 243.04/49.58  | 
% 243.04/49.58  | BETA: splitting (2) gives:
% 243.04/49.58  | 
% 243.04/49.58  | Case 1:
% 243.04/49.58  | | 
% 243.04/49.58  | |   (7)  all_58_14 = e2 & op(e0, e1) = e2
% 243.04/49.58  | | 
% 243.04/49.58  | | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #1771.
% 243.04/49.58  | | 
% 243.04/49.58  | Case 2:
% 243.04/49.58  | | 
% 243.04/49.58  | |   (8)  all_58_15 = e2 & op(e0, e0) = e2
% 243.04/49.58  | | 
% 243.04/49.58  | | ALPHA: (8) implies:
% 243.04/49.58  | |   (9)  op(e0, e0) = e2
% 243.04/49.58  | | 
% 243.04/49.58  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #1388.
% 243.04/49.58  | | 
% 243.04/49.58  | End of split
% 243.04/49.58  | 
% 243.04/49.58  End of proof
% 243.04/49.58  
% 243.04/49.58  Sub-proof #1038 shows that the following formulas are inconsistent:
% 243.04/49.58  ----------------------------------------------------------------
% 243.04/49.58    (1)   ~ (e3 = e0)
% 243.04/49.58    (2)  op(e0, e1) = all_56_23
% 243.04/49.58    (3)  op(e0, e1) = e2
% 243.04/49.58    (4)  op(e2, e1) = e1
% 243.04/49.58    (5)  all_58_9 = e0
% 243.04/49.58    (6)  op(e0, e2) = e3
% 243.04/49.58    (7)   ~ (all_28_0 = e3)
% 243.04/49.58    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.58         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.58    (9)  op(e2, e1) = all_28_0
% 243.04/49.58    (10)  op(e3, e3) = e1
% 243.04/49.58    (11)   ~ (e3 = e2)
% 243.04/49.58    (12)  op(e0, e1) = all_20_1
% 243.04/49.58    (13)  all_58_1 = e2
% 243.04/49.58    (14)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 243.04/49.58            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 243.04/49.58              e1) = all_34_1 & $i(all_34_1))
% 243.04/49.58    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.58    (16)  op(e0, all_56_23) = e0
% 243.04/49.58    (17)  all_58_4 = e3
% 243.04/49.58  
% 243.04/49.58  Begin of proof
% 243.04/49.58  | 
% 243.04/49.58  | BETA: splitting (14) gives:
% 243.04/49.58  | 
% 243.04/49.58  | Case 1:
% 243.04/49.58  | | 
% 243.04/49.58  | |   (18)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 243.04/49.58  | |         all_34_1 & $i(all_34_0) & $i(all_34_1)
% 243.04/49.58  | | 
% 243.04/49.58  | | ALPHA: (18) implies:
% 243.04/49.58  | |   (19)  op(e0, e1) = all_34_1
% 243.04/49.58  | | 
% 243.04/49.58  | | GROUND_INST: instantiating (15) with all_34_1, all_56_23, e1, e0,
% 243.04/49.58  | |              simplifying with (2), (19) gives:
% 243.04/49.58  | |   (20)  all_56_23 = all_34_1
% 243.04/49.58  | | 
% 243.04/49.58  | | GROUND_INST: instantiating (15) with all_20_1, all_56_23, e1, e0,
% 243.04/49.58  | |              simplifying with (2), (12) gives:
% 243.04/49.58  | |   (21)  all_56_23 = all_20_1
% 243.04/49.58  | | 
% 243.04/49.58  | | GROUND_INST: instantiating (15) with e2, all_56_23, e1, e0, simplifying with
% 243.04/49.58  | |              (2), (3) gives:
% 243.04/49.58  | |   (22)  all_56_23 = e2
% 243.04/49.58  | | 
% 243.04/49.58  | | GROUND_INST: instantiating (15) with e1, all_28_0, e1, e2, simplifying with
% 243.04/49.58  | |              (4), (9) gives:
% 243.04/49.58  | |   (23)  all_28_0 = e1
% 243.04/49.58  | | 
% 243.04/49.58  | | COMBINE_EQS: (20), (22) imply:
% 243.04/49.58  | |   (24)  all_34_1 = e2
% 243.04/49.58  | | 
% 243.04/49.58  | | COMBINE_EQS: (20), (21) imply:
% 243.04/49.58  | |   (25)  all_34_1 = all_20_1
% 243.04/49.58  | | 
% 243.04/49.58  | | COMBINE_EQS: (24), (25) imply:
% 243.04/49.58  | |   (26)  all_20_1 = e2
% 243.04/49.58  | | 
% 243.04/49.58  | | REDUCE: (7), (23) imply:
% 243.04/49.58  | |   (27)   ~ (e3 = e1)
% 243.04/49.58  | | 
% 243.04/49.58  | | SIMP: (27) implies:
% 243.04/49.58  | |   (28)   ~ (e3 = e1)
% 243.04/49.58  | | 
% 243.04/49.58  | | REDUCE: (16), (22) imply:
% 243.04/49.58  | |   (29)  op(e0, e2) = e0
% 243.04/49.58  | | 
% 243.04/49.58  | | REF_CLOSE: (1), (5), (6), (8), (10), (11), (13), (15), (17), (28), (29) are
% 243.04/49.58  | |            inconsistent by sub-proof #1042.
% 243.04/49.58  | | 
% 243.04/49.58  | Case 2:
% 243.04/49.58  | | 
% 243.04/49.58  | |   (30)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 243.04/49.58  | | 
% 243.04/49.58  | | ALPHA: (30) implies:
% 243.04/49.58  | |   (31)   ~ (all_34_1 = e2)
% 243.04/49.58  | |   (32)  op(e0, e1) = all_34_1
% 243.04/49.58  | | 
% 243.04/49.58  | | REF_CLOSE: (3), (12), (15), (31), (32) are inconsistent by sub-proof #2237.
% 243.04/49.58  | | 
% 243.04/49.58  | End of split
% 243.04/49.58  | 
% 243.04/49.58  End of proof
% 243.04/49.58  
% 243.04/49.58  Sub-proof #1039 shows that the following formulas are inconsistent:
% 243.04/49.58  ----------------------------------------------------------------
% 243.04/49.58    (1)  all_58_10 = e3
% 243.04/49.58    (2)   ~ (e3 = e0)
% 243.04/49.58    (3)  all_58_9 = e0
% 243.04/49.58    (4)   ~ (e3 = e1)
% 243.04/49.58    (5)   ~ (e3 = e2)
% 243.04/49.58    (6)  all_58_15 = e1
% 243.04/49.58    (7)  all_58_7 = e3 & op(e1, e2) = e3
% 243.04/49.58    (8)  all_58_11 = e2
% 243.04/49.58    (9)  all_58_7 = e1
% 243.04/49.58    (10)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.04/49.58          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.58  
% 243.04/49.58  Begin of proof
% 243.04/49.58  | 
% 243.04/49.58  | ALPHA: (7) implies:
% 243.04/49.58  |   (11)  all_58_7 = e3
% 243.04/49.58  | 
% 243.04/49.58  | COMBINE_EQS: (9), (11) imply:
% 243.04/49.58  |   (12)  e3 = e1
% 243.04/49.58  | 
% 243.04/49.58  | SIMP: (12) implies:
% 243.04/49.58  |   (13)  e3 = e1
% 243.04/49.58  | 
% 243.04/49.58  | COMBINE_EQS: (1), (13) imply:
% 243.04/49.58  |   (14)  all_58_10 = e1
% 243.04/49.58  | 
% 243.04/49.58  | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (14) are inconsistent by
% 243.04/49.58  |            sub-proof #1619.
% 243.04/49.58  | 
% 243.04/49.58  End of proof
% 243.04/49.58  
% 243.04/49.58  Sub-proof #1040 shows that the following formulas are inconsistent:
% 243.04/49.58  ----------------------------------------------------------------
% 243.04/49.58    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.04/49.58    (2)   ~ (e3 = e0)
% 243.04/49.58    (3)  all_58_6 = e3
% 243.04/49.58    (4)   ~ (e2 = e0)
% 243.04/49.58    (5)   ~ (e3 = e1)
% 243.04/49.58    (6)  op(e2, e2) = e0
% 243.04/49.58    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.04/49.58         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.04/49.58    (8)  op(e3, e3) = e1
% 243.04/49.58    (9)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 243.04/49.58         $i(all_56_3)
% 243.04/49.58    (10)  all_54_4 = all_52_1
% 243.04/49.59    (11)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.04/49.59          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.04/49.59    (12)   ~ (e3 = e2)
% 243.04/49.59    (13)   ~ (all_52_1 = e0)
% 243.04/49.59    (14)  all_58_12 = e0
% 243.04/49.59    (15)  op(e2, e3) = all_52_1
% 243.04/49.59    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.59    (17)   ~ (all_52_1 = e3)
% 243.04/49.59    (18)   ~ (e2 = e1)
% 243.04/49.59    (19)   ~ (all_52_1 = e1)
% 243.04/49.59  
% 243.04/49.59  Begin of proof
% 243.04/49.59  | 
% 243.04/49.59  | ALPHA: (9) implies:
% 243.04/49.59  |   (20)  op(e2, e3) = all_56_3
% 243.04/49.59  |   (21)  op(e2, all_56_3) = e2
% 243.04/49.59  | 
% 243.04/49.59  | BETA: splitting (11) gives:
% 243.04/49.59  | 
% 243.04/49.59  | Case 1:
% 243.04/49.59  | | 
% 243.04/49.59  | |   (22)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 243.04/49.59  | |           e2)
% 243.04/49.59  | | 
% 243.04/49.59  | | BETA: splitting (22) gives:
% 243.04/49.59  | | 
% 243.04/49.59  | | Case 1:
% 243.04/49.59  | | | 
% 243.04/49.59  | | |   (23)  all_58_0 = e2 & op(e3, e3) = e2
% 243.04/49.59  | | | 
% 243.04/49.59  | | | ALPHA: (23) implies:
% 243.04/49.59  | | |   (24)  op(e3, e3) = e2
% 243.04/49.59  | | | 
% 243.04/49.59  | | | REF_CLOSE: (8), (16), (18), (24) are inconsistent by sub-proof #2267.
% 243.04/49.59  | | | 
% 243.04/49.59  | | Case 2:
% 243.04/49.59  | | | 
% 243.04/49.59  | | |   (25)  all_58_2 = e2 & op(e2, e3) = e2
% 243.04/49.59  | | | 
% 243.04/49.59  | | | ALPHA: (25) implies:
% 243.04/49.59  | | |   (26)  all_58_2 = e2
% 243.04/49.59  | | |   (27)  op(e2, e3) = e2
% 243.04/49.59  | | | 
% 243.04/49.59  | | | GROUND_INST: instantiating (16) with e2, all_56_3, e3, e2, simplifying
% 243.04/49.59  | | |              with (20), (27) gives:
% 243.04/49.59  | | |   (28)  all_56_3 = e2
% 243.04/49.59  | | | 
% 243.04/49.59  | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (13), (14), (15),
% 243.04/49.59  | | |            (16), (17), (19), (21), (26), (28) are inconsistent by
% 243.04/49.59  | | |            sub-proof #1080.
% 243.04/49.59  | | | 
% 243.04/49.59  | | End of split
% 243.04/49.59  | | 
% 243.04/49.59  | Case 2:
% 243.04/49.59  | | 
% 243.04/49.59  | |   (29)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 243.04/49.59  | |           e2)
% 243.04/49.59  | | 
% 243.04/49.59  | | REF_CLOSE: (3), (4), (12), (14), (29) are inconsistent by sub-proof #1151.
% 243.04/49.59  | | 
% 243.04/49.59  | End of split
% 243.04/49.59  | 
% 243.04/49.59  End of proof
% 243.04/49.59  
% 243.04/49.59  Sub-proof #1041 shows that the following formulas are inconsistent:
% 243.04/49.59  ----------------------------------------------------------------
% 243.04/49.59    (1)  op(e3, e2) = all_14_0
% 243.04/49.59    (2)   ~ (e3 = e0)
% 243.04/49.59    (3)  op(e0, e1) = all_56_23
% 243.04/49.59    (4)  op(e0, e1) = e2
% 243.04/49.59    (5)  op(e2, e1) = e1
% 243.04/49.59    (6)  all_58_9 = e0
% 243.04/49.59    (7)  op(e0, e2) = e3
% 243.04/49.59    (8)   ~ (all_28_0 = e3)
% 243.04/49.59    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.59         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.59    (10)  op(e2, e1) = all_28_0
% 243.04/49.59    (11)  op(e3, e2) = e2
% 243.04/49.59    (12)  op(e3, e3) = e1
% 243.04/49.59    (13)  op(e0, e2) = all_56_15
% 243.04/49.59    (14)  op(e0, e1) = all_20_1
% 243.04/49.59    (15)  all_58_1 = e2
% 243.04/49.59    (16)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 243.04/49.59            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 243.04/49.59              e1) = all_34_1 & $i(all_34_1))
% 243.04/49.59    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.59    (18)  op(e3, e2) = all_48_0
% 243.04/49.59    (19)  op(e0, all_56_23) = e0
% 243.04/49.59    (20)   ~ (all_14_0 = e3)
% 243.04/49.59    (21)  all_58_4 = e3
% 243.04/49.59  
% 243.04/49.59  Begin of proof
% 243.04/49.59  | 
% 243.04/49.59  | BETA: splitting (16) gives:
% 243.04/49.59  | 
% 243.04/49.59  | Case 1:
% 243.04/49.59  | | 
% 243.04/49.59  | | 
% 243.04/49.59  | | GROUND_INST: instantiating (17) with e2, all_56_23, e1, e0, simplifying with
% 243.04/49.59  | |              (3), (4) gives:
% 243.04/49.59  | |   (22)  all_56_23 = e2
% 243.04/49.59  | | 
% 243.04/49.59  | | GROUND_INST: instantiating (17) with e3, all_56_15, e2, e0, simplifying with
% 243.04/49.59  | |              (7), (13) gives:
% 243.04/49.59  | |   (23)  all_56_15 = e3
% 243.04/49.59  | | 
% 243.04/49.59  | | GROUND_INST: instantiating (17) with e1, all_28_0, e1, e2, simplifying with
% 243.04/49.59  | |              (5), (10) gives:
% 243.04/49.59  | |   (24)  all_28_0 = e1
% 243.04/49.59  | | 
% 243.04/49.59  | | GROUND_INST: instantiating (17) with all_14_0, all_48_0, e2, e3, simplifying
% 243.04/49.59  | |              with (1), (18) gives:
% 243.04/49.59  | |   (25)  all_48_0 = all_14_0
% 243.04/49.59  | | 
% 243.04/49.59  | | GROUND_INST: instantiating (17) with e2, all_48_0, e2, e3, simplifying with
% 243.04/49.59  | |              (11), (18) gives:
% 243.04/49.59  | |   (26)  all_48_0 = e2
% 243.04/49.59  | | 
% 243.04/49.59  | | COMBINE_EQS: (25), (26) imply:
% 243.04/49.59  | |   (27)  all_14_0 = e2
% 243.04/49.59  | | 
% 243.04/49.59  | | REDUCE: (8), (24) imply:
% 243.04/49.59  | |   (28)   ~ (e3 = e1)
% 243.04/49.59  | | 
% 243.04/49.59  | | SIMP: (28) implies:
% 243.04/49.59  | |   (29)   ~ (e3 = e1)
% 243.04/49.59  | | 
% 243.04/49.59  | | REDUCE: (20), (27) imply:
% 243.04/49.59  | |   (30)   ~ (e3 = e2)
% 243.04/49.59  | | 
% 243.04/49.59  | | SIMP: (30) implies:
% 243.04/49.59  | |   (31)   ~ (e3 = e2)
% 243.04/49.59  | | 
% 243.04/49.59  | | REDUCE: (19), (22) imply:
% 243.04/49.59  | |   (32)  op(e0, e2) = e0
% 243.04/49.59  | | 
% 243.04/49.59  | | REF_CLOSE: (2), (6), (7), (9), (12), (15), (17), (21), (29), (31), (32) are
% 243.04/49.59  | |            inconsistent by sub-proof #1042.
% 243.04/49.59  | | 
% 243.04/49.59  | Case 2:
% 243.04/49.59  | | 
% 243.04/49.59  | |   (33)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 243.04/49.59  | | 
% 243.04/49.59  | | ALPHA: (33) implies:
% 243.04/49.59  | |   (34)   ~ (all_34_1 = e2)
% 243.04/49.59  | |   (35)  op(e0, e1) = all_34_1
% 243.04/49.59  | | 
% 243.04/49.59  | | REF_CLOSE: (4), (14), (17), (34), (35) are inconsistent by sub-proof #2237.
% 243.04/49.59  | | 
% 243.04/49.59  | End of split
% 243.04/49.59  | 
% 243.04/49.59  End of proof
% 243.04/49.59  
% 243.04/49.59  Sub-proof #1042 shows that the following formulas are inconsistent:
% 243.04/49.59  ----------------------------------------------------------------
% 243.04/49.59    (1)   ~ (e3 = e0)
% 243.04/49.59    (2)  all_58_9 = e0
% 243.04/49.59    (3)   ~ (e3 = e1)
% 243.04/49.59    (4)  op(e0, e2) = e3
% 243.04/49.59    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.59         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.59    (6)  op(e3, e3) = e1
% 243.04/49.59    (7)   ~ (e3 = e2)
% 243.04/49.59    (8)  op(e0, e2) = e0
% 243.04/49.59    (9)  all_58_1 = e2
% 243.04/49.59    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.59    (11)  all_58_4 = e3
% 243.04/49.59  
% 243.04/49.59  Begin of proof
% 243.04/49.59  | 
% 243.04/49.59  | GROUND_INST: instantiating (10) with e3, e0, e2, e0, simplifying with (4), (8)
% 243.04/49.59  |              gives:
% 243.04/49.59  |   (12)  e3 = e0
% 243.04/49.59  | 
% 243.04/49.59  | COMBINE_EQS: (11), (12) imply:
% 243.04/49.59  |   (13)  all_58_4 = e0
% 243.04/49.59  | 
% 243.04/49.59  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (13) are inconsistent by
% 243.04/49.59  |            sub-proof #1191.
% 243.04/49.59  | 
% 243.04/49.59  End of proof
% 243.04/49.59  
% 243.04/49.59  Sub-proof #1043 shows that the following formulas are inconsistent:
% 243.04/49.59  ----------------------------------------------------------------
% 243.04/49.59    (1)   ~ (e3 = e0)
% 243.04/49.59    (2)   ~ (e2 = e0)
% 243.04/49.59    (3)  all_58_9 = e0
% 243.04/49.59    (4)  all_58_14 = e2
% 243.04/49.59    (5)   ~ (e3 = e1)
% 243.04/49.59    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.04/49.59         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.59    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.59         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.59    (8)  op(e2, e1) = all_28_0
% 243.04/49.59    (9)  op(e3, e3) = e1
% 243.04/49.59    (10)   ~ (e3 = e2)
% 243.04/49.59    (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.04/49.59          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.04/49.59    (12)  all_28_0 = e1
% 243.04/49.59    (13)  all_56_19 = e1
% 243.04/49.59    (14)   ~ (all_52_4 = e3)
% 243.04/49.59    (15)  op(e3, e2) = all_52_4
% 243.04/49.59    (16)  all_58_5 = e1
% 243.04/49.59    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.59    (18)   ~ (e1 = e0)
% 243.04/49.59    (19)  op(e2, all_56_19) = e2
% 243.04/49.59    (20)   ~ (e2 = e1)
% 243.04/49.59  
% 243.04/49.59  Begin of proof
% 243.04/49.59  | 
% 243.04/49.59  | REDUCE: (13), (19) imply:
% 243.04/49.59  |   (21)  op(e2, e1) = e2
% 243.04/49.59  | 
% 243.04/49.59  | REDUCE: (8), (12) imply:
% 243.04/49.59  |   (22)  op(e2, e1) = e1
% 243.04/49.59  | 
% 243.04/49.59  | GROUND_INST: instantiating (17) with e1, e2, e1, e2, simplifying with (21),
% 243.04/49.59  |              (22) gives:
% 243.04/49.59  |   (23)  e2 = e1
% 243.04/49.59  | 
% 243.04/49.59  | COMBINE_EQS: (4), (23) imply:
% 243.04/49.59  |   (24)  all_58_14 = e1
% 243.04/49.59  | 
% 243.04/49.59  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (14), (15), (16),
% 243.04/49.59  |            (17), (18), (20), (24) are inconsistent by sub-proof #1044.
% 243.04/49.59  | 
% 243.04/49.59  End of proof
% 243.04/49.59  
% 243.04/49.59  Sub-proof #1044 shows that the following formulas are inconsistent:
% 243.04/49.59  ----------------------------------------------------------------
% 243.04/49.59    (1)   ~ (e3 = e0)
% 243.04/49.59    (2)   ~ (e2 = e0)
% 243.04/49.59    (3)  all_58_9 = e0
% 243.04/49.59    (4)   ~ (e3 = e1)
% 243.04/49.59    (5)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.04/49.59         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.59    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.59         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.59    (7)  op(e3, e3) = e1
% 243.04/49.59    (8)   ~ (e3 = e2)
% 243.04/49.59    (9)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.04/49.59         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.04/49.59    (10)   ~ (all_52_4 = e3)
% 243.04/49.59    (11)  op(e3, e2) = all_52_4
% 243.04/49.59    (12)  all_58_5 = e1
% 243.04/49.59    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.59    (14)   ~ (e1 = e0)
% 243.04/49.59    (15)  all_58_14 = e1
% 243.04/49.59    (16)   ~ (e2 = e1)
% 243.04/49.59  
% 243.04/49.59  Begin of proof
% 243.04/49.59  | 
% 243.04/49.59  | BETA: splitting (6) gives:
% 243.04/49.59  | 
% 243.04/49.59  | Case 1:
% 243.04/49.59  | | 
% 243.04/49.59  | |   (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 243.04/49.59  | |           e3)
% 243.04/49.59  | | 
% 243.04/49.59  | | REF_CLOSE: (4), (7), (10), (11), (13), (17) are inconsistent by sub-proof
% 243.04/49.59  | |            #1401.
% 243.04/49.59  | | 
% 243.04/49.59  | Case 2:
% 243.04/49.59  | | 
% 243.04/49.59  | |   (18)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 243.04/49.59  | |           e3)
% 243.04/49.59  | | 
% 243.04/49.59  | | BETA: splitting (18) gives:
% 243.04/49.59  | | 
% 243.04/49.59  | | Case 1:
% 243.04/49.59  | | | 
% 243.04/49.59  | | |   (19)  all_58_4 = e3 & op(e3, e1) = e3
% 243.04/49.59  | | | 
% 243.04/49.59  | | | ALPHA: (19) implies:
% 243.04/49.59  | | |   (20)  all_58_4 = e3
% 243.04/49.59  | | | 
% 243.04/49.59  | | | REF_CLOSE: (1), (2), (5), (8), (9), (12), (14), (15), (16), (20) are
% 243.04/49.59  | | |            inconsistent by sub-proof #1481.
% 243.04/49.59  | | | 
% 243.04/49.59  | | Case 2:
% 243.04/49.59  | | | 
% 243.04/49.59  | | |   (21)  all_58_9 = e3 & op(e3, e0) = e3
% 243.04/49.59  | | | 
% 243.04/49.59  | | | REF_CLOSE: (1), (3), (21) are inconsistent by sub-proof #1621.
% 243.04/49.59  | | | 
% 243.04/49.59  | | End of split
% 243.04/49.59  | | 
% 243.04/49.59  | End of split
% 243.04/49.59  | 
% 243.04/49.59  End of proof
% 243.04/49.59  
% 243.04/49.59  Sub-proof #1045 shows that the following formulas are inconsistent:
% 243.04/49.59  ----------------------------------------------------------------
% 243.04/49.59    (1)  op(e1, e2) = all_56_13
% 243.04/49.59    (2)  op(e0, e1) = e2
% 243.04/49.59    (3)  op(e1, e2) = e1
% 243.04/49.59    (4)  op(e0, e1) = all_20_1
% 243.04/49.59    (5)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) = all_34_1
% 243.04/49.59           & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1) =
% 243.04/49.59           all_34_1 & $i(all_34_1))
% 243.04/49.59    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.59    (7)  op(e1, e1) = e0
% 243.04/49.59    (8)  op(e1, all_56_13) = e1
% 243.04/49.59    (9)   ~ (e1 = e0)
% 243.04/49.59  
% 243.04/49.59  Begin of proof
% 243.04/49.59  | 
% 243.04/49.59  | BETA: splitting (5) gives:
% 243.04/49.59  | 
% 243.04/49.59  | Case 1:
% 243.04/49.59  | | 
% 243.04/49.59  | | 
% 243.04/49.59  | | GROUND_INST: instantiating (6) with e1, all_56_13, e2, e1, simplifying with
% 243.04/49.59  | |              (1), (3) gives:
% 243.04/49.59  | |   (10)  all_56_13 = e1
% 243.04/49.59  | | 
% 243.04/49.59  | | REDUCE: (8), (10) imply:
% 243.04/49.59  | |   (11)  op(e1, e1) = e1
% 243.04/49.59  | | 
% 243.04/49.59  | | REF_CLOSE: (6), (7), (9), (11) are inconsistent by sub-proof #2220.
% 243.04/49.59  | | 
% 243.04/49.59  | Case 2:
% 243.04/49.59  | | 
% 243.04/49.59  | |   (12)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 243.04/49.59  | | 
% 243.04/49.59  | | ALPHA: (12) implies:
% 243.04/49.59  | |   (13)   ~ (all_34_1 = e2)
% 243.04/49.59  | |   (14)  op(e0, e1) = all_34_1
% 243.04/49.59  | | 
% 243.04/49.59  | | REF_CLOSE: (2), (4), (6), (13), (14) are inconsistent by sub-proof #2237.
% 243.04/49.59  | | 
% 243.04/49.59  | End of split
% 243.04/49.59  | 
% 243.04/49.59  End of proof
% 243.04/49.59  
% 243.04/49.59  Sub-proof #1046 shows that the following formulas are inconsistent:
% 243.04/49.59  ----------------------------------------------------------------
% 243.04/49.59    (1)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.04/49.59           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 243.04/49.59    (2)  op(e2, e0) = e3
% 243.04/49.59    (3)  op(e3, e2) = e2
% 243.04/49.59    (4)   ~ (e3 = e2)
% 243.04/49.59    (5)  all_56_11 = e0
% 243.04/49.59    (6)   ~ (all_52_4 = e3)
% 243.04/49.59    (7)  op(e3, e2) = all_52_4
% 243.04/49.59    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.59  
% 243.04/49.59  Begin of proof
% 243.04/49.59  | 
% 243.04/49.59  | BETA: splitting (1) gives:
% 243.04/49.59  | 
% 243.04/49.59  | Case 1:
% 243.04/49.59  | | 
% 243.04/49.59  | |   (9)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.04/49.59  | |        $i(all_56_9)
% 243.04/49.59  | | 
% 243.04/49.59  | | REF_CLOSE: (3), (6), (7), (8), (9) are inconsistent by sub-proof #1358.
% 243.04/49.59  | | 
% 243.04/49.59  | Case 2:
% 243.04/49.59  | | 
% 243.04/49.59  | |   (10)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 243.04/49.59  | | 
% 243.04/49.59  | | ALPHA: (10) implies:
% 243.04/49.59  | |   (11)  op(e2, all_56_11) = e2
% 243.04/49.59  | | 
% 243.04/49.59  | | REDUCE: (5), (11) imply:
% 243.04/49.59  | |   (12)  op(e2, e0) = e2
% 243.04/49.59  | | 
% 243.04/49.59  | | REF_CLOSE: (2), (4), (8), (12) are inconsistent by sub-proof #2152.
% 243.04/49.59  | | 
% 243.04/49.59  | End of split
% 243.04/49.59  | 
% 243.04/49.59  End of proof
% 243.04/49.59  
% 243.04/49.59  Sub-proof #1047 shows that the following formulas are inconsistent:
% 243.04/49.59  ----------------------------------------------------------------
% 243.04/49.59    (1)  op(e3, e1) = all_56_17
% 243.04/49.59    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.59         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.59    (3)   ~ (e3 = e0)
% 243.04/49.59    (4)  all_58_6 = e3
% 243.04/49.59    (5)  op(e2, e1) = e1
% 243.04/49.59    (6)   ~ (e2 = e0)
% 243.04/49.59    (7)  all_58_9 = e0
% 243.04/49.59    (8)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) = all_38_1
% 243.04/49.59           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 243.04/49.59           all_38_1 & $i(all_38_1))
% 243.04/49.59    (9)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) = all_20_1
% 243.04/49.59           & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1) =
% 243.04/49.59           all_20_1 & $i(all_20_1))
% 243.04/49.59    (10)   ~ (e3 = e1)
% 243.04/49.59    (11)  all_58_2 = e2
% 243.04/49.59    (12)   ~ (all_28_0 = e3)
% 243.04/49.60    (13)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.04/49.60            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 243.04/49.60              e1) = all_10_1 & $i(all_10_1))
% 243.04/49.60    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.60          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.60    (15)  op(e2, e1) = all_28_0
% 243.04/49.60    (16)  op(e3, e3) = e1
% 243.04/49.60    (17)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.04/49.60          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.04/49.60    (18)   ~ (e3 = e2)
% 243.04/49.60    (19)  all_58_15 = e1
% 243.04/49.60    (20)  all_58_12 = e0
% 243.04/49.60    (21)   ~ (all_52_4 = e3)
% 243.04/49.60    (22)  op(e3, e2) = all_52_4
% 243.04/49.60    (23)  op(e3, all_56_17) = e3
% 243.04/49.60    (24)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 243.04/49.60            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 243.04/49.60              e1) = all_34_1 & $i(all_34_1))
% 243.04/49.60    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.60            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.60    (26)  op(e3, e1) = e3
% 243.04/49.60    (27)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.60          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.04/49.60            e2)
% 243.04/49.60    (28)  all_58_13 = e3
% 243.04/49.60    (29)   ~ (e2 = e1)
% 243.04/49.60  
% 243.04/49.60  Begin of proof
% 243.04/49.60  | 
% 243.04/49.60  | BETA: splitting (2) gives:
% 243.04/49.60  | 
% 243.04/49.60  | Case 1:
% 243.04/49.60  | | 
% 243.04/49.60  | |   (30)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 243.04/49.60  | |           e2)
% 243.04/49.60  | | 
% 243.04/49.60  | | BETA: splitting (30) gives:
% 243.04/49.60  | | 
% 243.04/49.60  | | Case 1:
% 243.04/49.60  | | | 
% 243.04/49.60  | | |   (31)  all_58_0 = e2 & op(e3, e3) = e2
% 243.04/49.60  | | | 
% 243.04/49.60  | | | ALPHA: (31) implies:
% 243.04/49.60  | | |   (32)  op(e3, e3) = e2
% 243.04/49.60  | | | 
% 243.04/49.60  | | | REF_CLOSE: (1), (18), (23), (25), (26), (32) are inconsistent by sub-proof
% 243.04/49.60  | | |            #2098.
% 243.04/49.60  | | | 
% 243.04/49.60  | | Case 2:
% 243.04/49.60  | | | 
% 243.04/49.60  | | |   (33)  all_58_1 = e2 & op(e3, e2) = e2
% 243.04/49.60  | | | 
% 243.04/49.60  | | | ALPHA: (33) implies:
% 243.04/49.60  | | |   (34)  all_58_1 = e2
% 243.04/49.60  | | | 
% 243.04/49.60  | | | BETA: splitting (14) gives:
% 243.04/49.60  | | | 
% 243.04/49.60  | | | Case 1:
% 243.04/49.60  | | | | 
% 243.04/49.60  | | | |   (35)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 243.04/49.60  | | | |           = e3)
% 243.04/49.60  | | | | 
% 243.04/49.60  | | | | REF_CLOSE: (10), (16), (21), (22), (25), (35) are inconsistent by
% 243.04/49.60  | | | |            sub-proof #1401.
% 243.04/49.60  | | | | 
% 243.04/49.60  | | | Case 2:
% 243.04/49.60  | | | | 
% 243.04/49.60  | | | |   (36)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 243.04/49.60  | | | |           = e3)
% 243.04/49.60  | | | | 
% 243.04/49.60  | | | | BETA: splitting (36) gives:
% 243.04/49.60  | | | | 
% 243.04/49.60  | | | | Case 1:
% 243.04/49.60  | | | | | 
% 243.04/49.60  | | | | |   (37)  all_58_4 = e3 & op(e3, e1) = e3
% 243.04/49.60  | | | | | 
% 243.04/49.60  | | | | | ALPHA: (37) implies:
% 243.04/49.60  | | | | |   (38)  all_58_4 = e3
% 243.04/49.60  | | | | | 
% 243.04/49.60  | | | | | BETA: splitting (27) gives:
% 243.04/49.60  | | | | | 
% 243.04/49.60  | | | | | Case 1:
% 243.04/49.60  | | | | | | 
% 243.04/49.60  | | | | | |   (39)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 243.04/49.60  | | | | | |           op(e0, e2) = e2)
% 243.04/49.60  | | | | | | 
% 243.04/49.60  | | | | | | REF_CLOSE: (2), (3), (6), (7), (10), (14), (16), (18), (20), (21),
% 243.04/49.60  | | | | | |            (22), (25), (28), (29), (34), (38), (39) are inconsistent
% 243.04/49.60  | | | | | |            by sub-proof #1053.
% 243.04/49.60  | | | | | | 
% 243.04/49.60  | | | | | Case 2:
% 243.04/49.60  | | | | | | 
% 243.04/49.60  | | | | | |   (40)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 243.04/49.60  | | | | | |           op(e0, e0) = e2)
% 243.04/49.60  | | | | | | 
% 243.04/49.60  | | | | | | BETA: splitting (40) gives:
% 243.04/49.60  | | | | | | 
% 243.04/49.60  | | | | | | Case 1:
% 243.04/49.60  | | | | | | | 
% 243.04/49.60  | | | | | | |   (41)  all_58_14 = e2 & op(e0, e1) = e2
% 243.04/49.60  | | | | | | | 
% 243.04/49.60  | | | | | | | ALPHA: (41) implies:
% 243.04/49.60  | | | | | | |   (42)  op(e0, e1) = e2
% 243.04/49.60  | | | | | | | 
% 243.04/49.60  | | | | | | | BETA: splitting (13) gives:
% 243.04/49.60  | | | | | | | 
% 243.04/49.60  | | | | | | | Case 1:
% 243.04/49.60  | | | | | | | | 
% 243.04/49.60  | | | | | | | |   (43)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 &
% 243.04/49.60  | | | | | | | |         op(e3, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)
% 243.04/49.60  | | | | | | | | 
% 243.04/49.60  | | | | | | | | ALPHA: (43) implies:
% 243.04/49.60  | | | | | | | |   (44)  op(e3, e1) = all_10_1
% 243.04/49.60  | | | | | | | | 
% 243.04/49.60  | | | | | | | | REF_CLOSE: (1), (5), (8), (9), (12), (15), (16), (23), (24),
% 243.04/49.60  | | | | | | | |            (25), (26), (42), (44) are inconsistent by sub-proof
% 243.04/49.60  | | | | | | | |            #1050.
% 243.04/49.60  | | | | | | | | 
% 243.04/49.60  | | | | | | | Case 2:
% 243.04/49.60  | | | | | | | | 
% 243.04/49.60  | | | | | | | |   (45)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 &
% 243.04/49.60  | | | | | | | |         $i(all_10_1)
% 243.04/49.60  | | | | | | | | 
% 243.04/49.60  | | | | | | | | ALPHA: (45) implies:
% 243.04/49.60  | | | | | | | |   (46)  op(e3, e1) = all_10_1
% 243.04/49.60  | | | | | | | | 
% 243.04/49.60  | | | | | | | | REF_CLOSE: (1), (5), (8), (9), (12), (15), (16), (23), (24),
% 243.04/49.60  | | | | | | | |            (25), (26), (42), (46) are inconsistent by sub-proof
% 243.04/49.60  | | | | | | | |            #1050.
% 243.04/49.60  | | | | | | | | 
% 243.04/49.60  | | | | | | | End of split
% 243.04/49.60  | | | | | | | 
% 243.04/49.60  | | | | | | Case 2:
% 243.04/49.60  | | | | | | | 
% 243.04/49.60  | | | | | | |   (47)  all_58_15 = e2 & op(e0, e0) = e2
% 243.04/49.60  | | | | | | | 
% 243.04/49.60  | | | | | | | REF_CLOSE: (19), (29), (47) are inconsistent by sub-proof #1917.
% 243.04/49.60  | | | | | | | 
% 243.04/49.60  | | | | | | End of split
% 243.04/49.60  | | | | | | 
% 243.04/49.60  | | | | | End of split
% 243.04/49.60  | | | | | 
% 243.04/49.60  | | | | Case 2:
% 243.04/49.60  | | | | | 
% 243.04/49.60  | | | | |   (48)  all_58_9 = e3 & op(e3, e0) = e3
% 243.04/49.60  | | | | | 
% 243.04/49.60  | | | | | ALPHA: (48) implies:
% 243.04/49.60  | | | | |   (49)  all_58_9 = e3
% 243.04/49.60  | | | | | 
% 243.04/49.60  | | | | | REF_CLOSE: (3), (7), (49) are inconsistent by sub-proof #1958.
% 243.04/49.60  | | | | | 
% 243.04/49.60  | | | | End of split
% 243.04/49.60  | | | | 
% 243.04/49.60  | | | End of split
% 243.04/49.60  | | | 
% 243.04/49.60  | | End of split
% 243.04/49.60  | | 
% 243.04/49.60  | Case 2:
% 243.04/49.60  | | 
% 243.04/49.60  | |   (50)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 243.04/49.60  | |           e2)
% 243.04/49.60  | | 
% 243.04/49.60  | | REF_CLOSE: (3), (4), (6), (7), (10), (11), (14), (16), (17), (18), (20),
% 243.04/49.60  | |            (21), (22), (25), (29), (50) are inconsistent by sub-proof #1048.
% 243.04/49.60  | | 
% 243.04/49.60  | End of split
% 243.04/49.60  | 
% 243.04/49.60  End of proof
% 243.04/49.60  
% 243.04/49.60  Sub-proof #1048 shows that the following formulas are inconsistent:
% 243.04/49.60  ----------------------------------------------------------------
% 243.04/49.60    (1)   ~ (e3 = e0)
% 243.04/49.60    (2)  all_58_6 = e3
% 243.04/49.60    (3)   ~ (e2 = e0)
% 243.04/49.60    (4)  all_58_9 = e0
% 243.04/49.60    (5)   ~ (e3 = e1)
% 243.04/49.60    (6)  all_58_2 = e2
% 243.04/49.60    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.60         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.60    (8)  op(e3, e3) = e1
% 243.04/49.60    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.04/49.60         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.04/49.60    (10)   ~ (e3 = e2)
% 243.04/49.60    (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.60    (12)  all_58_12 = e0
% 243.04/49.60    (13)   ~ (all_52_4 = e3)
% 243.04/49.60    (14)  op(e3, e2) = all_52_4
% 243.04/49.60    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.60            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.60    (16)   ~ (e2 = e1)
% 243.04/49.60  
% 243.04/49.60  Begin of proof
% 243.04/49.60  | 
% 243.04/49.60  | BETA: splitting (11) gives:
% 243.04/49.60  | 
% 243.04/49.60  | Case 1:
% 243.04/49.60  | | 
% 243.04/49.60  | |   (17)  all_58_4 = e2 & op(e3, e1) = e2
% 243.04/49.60  | | 
% 243.04/49.60  | | ALPHA: (17) implies:
% 243.04/49.60  | |   (18)  all_58_4 = e2
% 243.04/49.60  | | 
% 243.04/49.60  | | REF_CLOSE: (1), (4), (5), (7), (8), (10), (13), (14), (15), (18) are
% 243.04/49.60  | |            inconsistent by sub-proof #1143.
% 243.04/49.60  | | 
% 243.04/49.60  | Case 2:
% 243.04/49.60  | | 
% 243.04/49.60  | |   (19)  all_58_9 = e2 & op(e3, e0) = e2
% 243.04/49.60  | | 
% 243.04/49.60  | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (12), (15), (16), (19) are
% 243.04/49.60  | |            inconsistent by sub-proof #1049.
% 243.04/49.60  | | 
% 243.04/49.60  | End of split
% 243.04/49.60  | 
% 243.04/49.60  End of proof
% 243.04/49.60  
% 243.04/49.60  Sub-proof #1049 shows that the following formulas are inconsistent:
% 243.04/49.60  ----------------------------------------------------------------
% 243.04/49.60    (1)  all_58_6 = e3
% 243.04/49.60    (2)   ~ (e2 = e0)
% 243.04/49.60    (3)  all_58_9 = e0
% 243.04/49.60    (4)  all_58_2 = e2
% 243.04/49.60    (5)  op(e3, e3) = e1
% 243.04/49.60    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.04/49.60         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.04/49.60    (7)   ~ (e3 = e2)
% 243.04/49.60    (8)  all_58_12 = e0
% 243.04/49.60    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.60    (10)  all_58_9 = e2 & op(e3, e0) = e2
% 243.04/49.60    (11)   ~ (e2 = e1)
% 243.04/49.60  
% 243.04/49.60  Begin of proof
% 243.04/49.60  | 
% 243.04/49.60  | ALPHA: (10) implies:
% 243.04/49.60  |   (12)  all_58_9 = e2
% 243.04/49.60  | 
% 243.04/49.60  | COMBINE_EQS: (3), (12) imply:
% 243.04/49.60  |   (13)  e2 = e0
% 243.04/49.60  | 
% 243.04/49.60  | SIMP: (13) implies:
% 243.04/49.60  |   (14)  e2 = e0
% 243.04/49.60  | 
% 243.04/49.60  | COMBINE_EQS: (4), (14) imply:
% 243.04/49.60  |   (15)  all_58_2 = e0
% 243.04/49.60  | 
% 243.04/49.60  | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (15) are inconsistent by
% 243.04/49.60  |            sub-proof #1150.
% 243.04/49.60  | 
% 243.04/49.60  End of proof
% 243.04/49.60  
% 243.04/49.60  Sub-proof #1050 shows that the following formulas are inconsistent:
% 243.04/49.60  ----------------------------------------------------------------
% 243.04/49.60    (1)  op(e3, e1) = all_56_17
% 243.04/49.60    (2)  op(e0, e1) = e2
% 243.04/49.60    (3)  op(e2, e1) = e1
% 243.04/49.60    (4)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) = all_38_1
% 243.04/49.60           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 243.04/49.60           all_38_1 & $i(all_38_1))
% 243.04/49.60    (5)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) = all_20_1
% 243.04/49.60           & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1) =
% 243.04/49.60           all_20_1 & $i(all_20_1))
% 243.04/49.60    (6)   ~ (all_28_0 = e3)
% 243.04/49.60    (7)  op(e2, e1) = all_28_0
% 243.04/49.60    (8)  op(e3, e3) = e1
% 243.04/49.60    (9)  op(e3, all_56_17) = e3
% 243.04/49.60    (10)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 243.04/49.60            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 243.04/49.60              e1) = all_34_1 & $i(all_34_1))
% 243.04/49.60    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.60            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.60    (12)  op(e3, e1) = all_10_1
% 243.04/49.60    (13)  op(e3, e1) = e3
% 243.04/49.60  
% 243.04/49.60  Begin of proof
% 243.04/49.60  | 
% 243.04/49.60  | BETA: splitting (4) gives:
% 243.04/49.60  | 
% 243.04/49.60  | Case 1:
% 243.04/49.60  | | 
% 243.04/49.60  | |   (14)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 243.04/49.60  | |         all_38_1 & $i(all_38_0) & $i(all_38_1)
% 243.04/49.60  | | 
% 243.04/49.60  | | ALPHA: (14) implies:
% 243.04/49.60  | |   (15)  op(e3, e1) = all_38_1
% 243.04/49.60  | | 
% 243.04/49.60  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 243.04/49.60  | |            (15) are inconsistent by sub-proof #1051.
% 243.04/49.60  | | 
% 243.04/49.60  | Case 2:
% 243.04/49.60  | | 
% 243.04/49.60  | |   (16)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1)
% 243.04/49.60  | | 
% 243.04/49.60  | | ALPHA: (16) implies:
% 243.04/49.60  | |   (17)  op(e3, e1) = all_38_1
% 243.04/49.60  | | 
% 243.04/49.60  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 243.04/49.60  | |            (17) are inconsistent by sub-proof #1051.
% 243.04/49.60  | | 
% 243.04/49.60  | End of split
% 243.04/49.60  | 
% 243.04/49.60  End of proof
% 243.04/49.60  
% 243.04/49.60  Sub-proof #1051 shows that the following formulas are inconsistent:
% 243.04/49.60  ----------------------------------------------------------------
% 243.04/49.60    (1)  op(e3, e1) = all_56_17
% 243.04/49.60    (2)  op(e0, e1) = e2
% 243.04/49.60    (3)  op(e2, e1) = e1
% 243.04/49.60    (4)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) = all_20_1
% 243.04/49.60           & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1) =
% 243.04/49.60           all_20_1 & $i(all_20_1))
% 243.04/49.60    (5)   ~ (all_28_0 = e3)
% 243.04/49.60    (6)  op(e2, e1) = all_28_0
% 243.04/49.60    (7)  op(e3, e3) = e1
% 243.04/49.60    (8)  op(e3, e1) = all_38_1
% 243.04/49.60    (9)  op(e3, all_56_17) = e3
% 243.04/49.60    (10)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 243.04/49.60            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 243.04/49.60              e1) = all_34_1 & $i(all_34_1))
% 243.04/49.60    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.60            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.60    (12)  op(e3, e1) = all_10_1
% 243.04/49.60    (13)  op(e3, e1) = e3
% 243.04/49.60  
% 243.04/49.60  Begin of proof
% 243.04/49.60  | 
% 243.04/49.60  | BETA: splitting (4) gives:
% 243.04/49.60  | 
% 243.04/49.60  | Case 1:
% 243.04/49.60  | | 
% 243.04/49.60  | |   (14)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 243.04/49.60  | |         all_20_1 & $i(all_20_0) & $i(all_20_1)
% 243.04/49.60  | | 
% 243.04/49.60  | | ALPHA: (14) implies:
% 243.04/49.60  | |   (15)  op(e0, e1) = all_20_1
% 243.04/49.60  | | 
% 243.04/49.60  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 243.04/49.60  | |            (15) are inconsistent by sub-proof #1052.
% 243.04/49.60  | | 
% 243.04/49.60  | Case 2:
% 243.04/49.60  | | 
% 243.04/49.60  | |   (16)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 & $i(all_20_1)
% 243.04/49.60  | | 
% 243.04/49.60  | | ALPHA: (16) implies:
% 243.04/49.60  | |   (17)  op(e0, e1) = all_20_1
% 243.04/49.60  | | 
% 243.04/49.60  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 243.04/49.60  | |            (17) are inconsistent by sub-proof #1052.
% 243.04/49.60  | | 
% 243.04/49.60  | End of split
% 243.04/49.60  | 
% 243.04/49.60  End of proof
% 243.04/49.60  
% 243.04/49.60  Sub-proof #1052 shows that the following formulas are inconsistent:
% 243.04/49.60  ----------------------------------------------------------------
% 243.04/49.60    (1)  op(e3, e1) = all_56_17
% 243.04/49.60    (2)  op(e0, e1) = e2
% 243.04/49.60    (3)  op(e2, e1) = e1
% 243.04/49.60    (4)   ~ (all_28_0 = e3)
% 243.04/49.60    (5)  op(e2, e1) = all_28_0
% 243.04/49.60    (6)  op(e3, e3) = e1
% 243.04/49.60    (7)  op(e3, e1) = all_38_1
% 243.04/49.60    (8)  op(e0, e1) = all_20_1
% 243.04/49.60    (9)  op(e3, all_56_17) = e3
% 243.04/49.60    (10)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 243.04/49.60            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 243.04/49.60              e1) = all_34_1 & $i(all_34_1))
% 243.04/49.60    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.60            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.60    (12)  op(e3, e1) = all_10_1
% 243.04/49.60    (13)  op(e3, e1) = e3
% 243.04/49.60  
% 243.04/49.60  Begin of proof
% 243.04/49.60  | 
% 243.04/49.60  | BETA: splitting (10) gives:
% 243.04/49.60  | 
% 243.04/49.60  | Case 1:
% 243.04/49.60  | | 
% 243.04/49.60  | | 
% 243.04/49.60  | | GROUND_INST: instantiating (11) with e1, all_28_0, e1, e2, simplifying with
% 243.04/49.60  | |              (3), (5) gives:
% 243.04/49.60  | |   (14)  all_28_0 = e1
% 243.04/49.60  | | 
% 243.04/49.60  | | GROUND_INST: instantiating (11) with e3, all_38_1, e1, e3, simplifying with
% 243.04/49.60  | |              (7), (13) gives:
% 243.04/49.60  | |   (15)  all_38_1 = e3
% 243.04/49.60  | | 
% 243.04/49.60  | | GROUND_INST: instantiating (11) with all_38_1, all_56_17, e1, e3,
% 243.04/49.60  | |              simplifying with (1), (7) gives:
% 243.04/49.60  | |   (16)  all_56_17 = all_38_1
% 243.04/49.60  | | 
% 243.04/49.60  | | GROUND_INST: instantiating (11) with all_10_1, all_56_17, e1, e3,
% 243.04/49.60  | |              simplifying with (1), (12) gives:
% 243.04/49.60  | |   (17)  all_56_17 = all_10_1
% 243.04/49.60  | | 
% 243.04/49.60  | | COMBINE_EQS: (16), (17) imply:
% 243.04/49.60  | |   (18)  all_38_1 = all_10_1
% 243.04/49.60  | | 
% 243.04/49.60  | | SIMP: (18) implies:
% 243.04/49.60  | |   (19)  all_38_1 = all_10_1
% 243.04/49.60  | | 
% 243.04/49.60  | | COMBINE_EQS: (15), (19) imply:
% 243.04/49.60  | |   (20)  all_10_1 = e3
% 243.04/49.60  | | 
% 243.04/49.60  | | SIMP: (20) implies:
% 243.04/49.60  | |   (21)  all_10_1 = e3
% 243.04/49.60  | | 
% 243.04/49.60  | | COMBINE_EQS: (17), (21) imply:
% 243.04/49.60  | |   (22)  all_56_17 = e3
% 243.04/49.60  | | 
% 243.04/49.60  | | REDUCE: (4), (14) imply:
% 243.04/49.60  | |   (23)   ~ (e3 = e1)
% 243.04/49.60  | | 
% 243.04/49.60  | | SIMP: (23) implies:
% 243.04/49.60  | |   (24)   ~ (e3 = e1)
% 243.04/49.60  | | 
% 243.04/49.60  | | REDUCE: (9), (22) imply:
% 243.04/49.60  | |   (25)  op(e3, e3) = e3
% 243.04/49.60  | | 
% 243.04/49.60  | | REF_CLOSE: (6), (11), (24), (25) are inconsistent by sub-proof #1578.
% 243.04/49.60  | | 
% 243.04/49.60  | Case 2:
% 243.04/49.60  | | 
% 243.04/49.60  | |   (26)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 243.04/49.60  | | 
% 243.04/49.60  | | ALPHA: (26) implies:
% 243.04/49.60  | |   (27)   ~ (all_34_1 = e2)
% 243.04/49.60  | |   (28)  op(e0, e1) = all_34_1
% 243.04/49.60  | | 
% 243.04/49.60  | | REF_CLOSE: (2), (8), (11), (27), (28) are inconsistent by sub-proof #2237.
% 243.04/49.60  | | 
% 243.04/49.60  | End of split
% 243.04/49.60  | 
% 243.04/49.60  End of proof
% 243.04/49.60  
% 243.04/49.60  Sub-proof #1053 shows that the following formulas are inconsistent:
% 243.04/49.60  ----------------------------------------------------------------
% 243.04/49.61    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.61         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.61    (2)   ~ (e3 = e0)
% 243.04/49.61    (3)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.61    (4)   ~ (e2 = e0)
% 243.04/49.61    (5)  all_58_9 = e0
% 243.04/49.61    (6)   ~ (e3 = e1)
% 243.04/49.61    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.61         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.61    (8)  op(e3, e3) = e1
% 243.04/49.61    (9)   ~ (e3 = e2)
% 243.04/49.61    (10)  all_58_12 = e0
% 243.04/49.61    (11)   ~ (all_52_4 = e3)
% 243.04/49.61    (12)  op(e3, e2) = all_52_4
% 243.04/49.61    (13)  all_58_1 = e2
% 243.04/49.61    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.61    (15)  all_58_4 = e3
% 243.04/49.61    (16)  all_58_13 = e3
% 243.04/49.61    (17)   ~ (e2 = e1)
% 243.04/49.61  
% 243.04/49.61  Begin of proof
% 243.04/49.61  | 
% 243.04/49.61  | BETA: splitting (3) gives:
% 243.04/49.61  | 
% 243.04/49.61  | Case 1:
% 243.04/49.61  | | 
% 243.04/49.61  | |   (18)  all_58_12 = e2 & op(e0, e3) = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | REF_CLOSE: (1), (4), (5), (8), (9), (10), (13), (14), (15), (17), (18) are
% 243.04/49.61  | |            inconsistent by sub-proof #1054.
% 243.04/49.61  | | 
% 243.04/49.61  | Case 2:
% 243.04/49.61  | | 
% 243.04/49.61  | |   (19)  all_58_13 = e2 & op(e0, e2) = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | ALPHA: (19) implies:
% 243.04/49.61  | |   (20)  all_58_13 = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | COMBINE_EQS: (16), (20) imply:
% 243.04/49.61  | |   (21)  e3 = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | SIMP: (21) implies:
% 243.04/49.61  | |   (22)  e3 = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | COMBINE_EQS: (15), (22) imply:
% 243.04/49.61  | |   (23)  all_58_4 = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (11), (12), (14), (23) are
% 243.04/49.61  | |            inconsistent by sub-proof #1143.
% 243.04/49.61  | | 
% 243.04/49.61  | End of split
% 243.04/49.61  | 
% 243.04/49.61  End of proof
% 243.04/49.61  
% 243.04/49.61  Sub-proof #1054 shows that the following formulas are inconsistent:
% 243.04/49.61  ----------------------------------------------------------------
% 243.04/49.61    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.61         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.61    (2)   ~ (e2 = e0)
% 243.04/49.61    (3)  all_58_9 = e0
% 243.04/49.61    (4)  op(e3, e3) = e1
% 243.04/49.61    (5)   ~ (e3 = e2)
% 243.04/49.61    (6)  all_58_12 = e0
% 243.04/49.61    (7)  all_58_12 = e2 & op(e0, e3) = e2
% 243.04/49.61    (8)  all_58_1 = e2
% 243.04/49.61    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.61    (10)  all_58_4 = e3
% 243.04/49.61    (11)   ~ (e2 = e1)
% 243.04/49.61  
% 243.04/49.61  Begin of proof
% 243.04/49.61  | 
% 243.04/49.61  | ALPHA: (7) implies:
% 243.04/49.61  |   (12)  all_58_12 = e2
% 243.04/49.61  | 
% 243.04/49.61  | COMBINE_EQS: (6), (12) imply:
% 243.04/49.61  |   (13)  e2 = e0
% 243.04/49.61  | 
% 243.04/49.61  | COMBINE_EQS: (8), (13) imply:
% 243.04/49.61  |   (14)  all_58_1 = e0
% 243.04/49.61  | 
% 243.04/49.61  | REF_CLOSE: (1), (2), (3), (4), (5), (9), (10), (11), (14) are inconsistent by
% 243.04/49.61  |            sub-proof #1097.
% 243.04/49.61  | 
% 243.04/49.61  End of proof
% 243.04/49.61  
% 243.04/49.61  Sub-proof #1055 shows that the following formulas are inconsistent:
% 243.04/49.61  ----------------------------------------------------------------
% 243.04/49.61    (1)   ~ (e3 = e0)
% 243.04/49.61    (2)  op(e0, e1) = all_52_11
% 243.04/49.61    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.04/49.61         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.04/49.61    (4)   ~ (e2 = e0)
% 243.04/49.61    (5)  all_58_9 = e0
% 243.04/49.61    (6)   ~ (e3 = e1)
% 243.04/49.61    (7)  op(e2, e2) = e0
% 243.04/49.61    (8)   ~ (all_52_2 = e1)
% 243.04/49.61    (9)   ~ (e3 = e2)
% 243.04/49.61    (10)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 243.04/49.61            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 243.04/49.61              e0) = all_48_1 & $i(all_48_1))
% 243.04/49.61    (11)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 243.04/49.61            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 243.04/49.61            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 243.04/49.61            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 243.04/49.61            op(e0, all_56_31) = e0)
% 243.04/49.61    (12)  all_56_31 = e1
% 243.04/49.61    (13)  all_58_15 = e1
% 243.04/49.61    (14)   ~ (all_52_11 = e0)
% 243.04/49.61    (15)  all_58_7 = e1
% 243.04/49.61    (16)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.04/49.61          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.04/49.61    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.61    (18)  op(e3, e0) = e0
% 243.04/49.61    (19)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.04/49.61          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.04/49.61    (20)  op(e1, e3) = all_52_2
% 243.04/49.61    (21)  op(e1, e1) = e0
% 243.04/49.61    (22)   ~ (e1 = e0)
% 243.04/49.61    (23)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.61    (24)   ~ (e2 = e1)
% 243.04/49.61  
% 243.04/49.61  Begin of proof
% 243.04/49.61  | 
% 243.04/49.61  | BETA: splitting (23) gives:
% 243.04/49.61  | 
% 243.04/49.61  | Case 1:
% 243.04/49.61  | | 
% 243.04/49.61  | |   (25)  all_58_11 = e3 & op(e1, e0) = e3
% 243.04/49.61  | | 
% 243.04/49.61  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 243.04/49.61  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 243.04/49.61  | |            (25) are inconsistent by sub-proof #1056.
% 243.04/49.61  | | 
% 243.04/49.61  | Case 2:
% 243.04/49.61  | | 
% 243.04/49.61  | |   (26)  all_58_15 = e3 & op(e0, e0) = e3
% 243.04/49.61  | | 
% 243.04/49.61  | | ALPHA: (26) implies:
% 243.04/49.61  | |   (27)  all_58_15 = e3
% 243.04/49.61  | | 
% 243.04/49.61  | | REF_CLOSE: (6), (13), (27) are inconsistent by sub-proof #2249.
% 243.04/49.61  | | 
% 243.04/49.61  | End of split
% 243.04/49.61  | 
% 243.04/49.61  End of proof
% 243.04/49.61  
% 243.04/49.61  Sub-proof #1056 shows that the following formulas are inconsistent:
% 243.04/49.61  ----------------------------------------------------------------
% 243.04/49.61    (1)   ~ (e3 = e0)
% 243.04/49.61    (2)  op(e0, e1) = all_52_11
% 243.04/49.61    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.04/49.61         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.04/49.61    (4)   ~ (e2 = e0)
% 243.04/49.61    (5)  all_58_9 = e0
% 243.04/49.61    (6)   ~ (e3 = e1)
% 243.04/49.61    (7)  op(e2, e2) = e0
% 243.04/49.61    (8)   ~ (all_52_2 = e1)
% 243.04/49.61    (9)   ~ (e3 = e2)
% 243.04/49.61    (10)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 243.04/49.61            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 243.04/49.61              e0) = all_48_1 & $i(all_48_1))
% 243.04/49.61    (11)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 243.04/49.61            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 243.04/49.61            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 243.04/49.61            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 243.04/49.61            op(e0, all_56_31) = e0)
% 243.04/49.61    (12)  all_56_31 = e1
% 243.04/49.61    (13)  all_58_15 = e1
% 243.04/49.61    (14)   ~ (all_52_11 = e0)
% 243.04/49.61    (15)  all_58_11 = e3 & op(e1, e0) = e3
% 243.04/49.61    (16)  all_58_7 = e1
% 243.04/49.61    (17)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.04/49.61          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.04/49.61    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.61    (19)  op(e3, e0) = e0
% 243.04/49.61    (20)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.04/49.61          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.04/49.61    (21)  op(e1, e3) = all_52_2
% 243.04/49.61    (22)  op(e1, e1) = e0
% 243.04/49.61    (23)   ~ (e1 = e0)
% 243.04/49.61    (24)   ~ (e2 = e1)
% 243.04/49.61  
% 243.04/49.61  Begin of proof
% 243.04/49.61  | 
% 243.04/49.61  | ALPHA: (15) implies:
% 243.04/49.61  |   (25)  all_58_11 = e3
% 243.04/49.61  |   (26)  op(e1, e0) = e3
% 243.04/49.61  | 
% 243.04/49.61  | BETA: splitting (17) gives:
% 243.04/49.61  | 
% 243.04/49.61  | Case 1:
% 243.04/49.61  | | 
% 243.04/49.61  | |   (27)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 243.04/49.61  | |           e2)
% 243.04/49.61  | | 
% 243.04/49.61  | | BETA: splitting (27) gives:
% 243.04/49.61  | | 
% 243.04/49.61  | | Case 1:
% 243.04/49.61  | | | 
% 243.04/49.61  | | |   (28)  all_58_6 = e2 & op(e1, e3) = e2
% 243.04/49.61  | | | 
% 243.04/49.61  | | | ALPHA: (28) implies:
% 243.04/49.61  | | |   (29)  all_58_6 = e2
% 243.04/49.61  | | | 
% 243.04/49.61  | | | BETA: splitting (11) gives:
% 243.04/49.61  | | | 
% 243.04/49.61  | | | Case 1:
% 243.04/49.61  | | | | 
% 243.04/49.61  | | | |   (30)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 243.04/49.61  | | | |           all_56_25 & $i(all_56_25)) | (all_56_26 = e2 & op(e2,
% 243.04/49.61  | | | |             all_56_27) = e2 & op(e2, e0) = all_56_27 & $i(all_56_27))
% 243.04/49.61  | | | | 
% 243.04/49.61  | | | | BETA: splitting (30) gives:
% 243.04/49.61  | | | | 
% 243.04/49.61  | | | | Case 1:
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | |   (31)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 243.04/49.61  | | | | |         all_56_25 & $i(all_56_25)
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | | ALPHA: (31) implies:
% 243.04/49.61  | | | | |   (32)  op(e3, e0) = all_56_25
% 243.04/49.61  | | | | |   (33)  op(e3, all_56_25) = e3
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | | REF_CLOSE: (1), (18), (19), (32), (33) are inconsistent by sub-proof
% 243.04/49.61  | | | | |            #1926.
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | Case 2:
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | |   (34)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 243.04/49.61  | | | | |         all_56_27 & $i(all_56_27)
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | | ALPHA: (34) implies:
% 243.04/49.61  | | | | |   (35)  op(e2, e0) = all_56_27
% 243.04/49.61  | | | | |   (36)  op(e2, all_56_27) = e2
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | | BETA: splitting (20) gives:
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | | Case 1:
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | |   (37)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 243.04/49.61  | | | | | |             e0) = e2)
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | | BETA: splitting (37) gives:
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | | Case 1:
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | |   (38)  all_58_9 = e2 & op(e3, e0) = e2
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | | REF_CLOSE: (3), (4), (5), (6), (9), (17), (18), (22), (23), (24),
% 243.04/49.61  | | | | | | |            (25), (29), (38) are inconsistent by sub-proof #1061.
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | Case 2:
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | |   (39)  all_58_10 = e2 & op(e2, e0) = e2
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | | ALPHA: (39) implies:
% 243.04/49.61  | | | | | | |   (40)  op(e2, e0) = e2
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | | REF_CLOSE: (4), (7), (10), (18), (35), (36), (40) are inconsistent
% 243.04/49.61  | | | | | | |            by sub-proof #1059.
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | End of split
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | Case 2:
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | |   (41)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 243.04/49.61  | | | | | |           op(e0, e0) = e2)
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | | REF_CLOSE: (9), (13), (24), (25), (41) are inconsistent by sub-proof
% 243.04/49.61  | | | | | |            #1058.
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | End of split
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | End of split
% 243.04/49.61  | | | | 
% 243.04/49.61  | | | Case 2:
% 243.04/49.61  | | | | 
% 243.04/49.61  | | | |   (42)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 243.04/49.61  | | | |           all_56_29 & $i(all_56_29)) | (all_56_30 = e0 & op(e0,
% 243.04/49.61  | | | |             all_56_31) = e0)
% 243.04/49.61  | | | | 
% 243.04/49.61  | | | | BETA: splitting (42) gives:
% 243.04/49.61  | | | | 
% 243.04/49.61  | | | | Case 1:
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | |   (43)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 243.04/49.61  | | | | |         all_56_29 & $i(all_56_29)
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | | ALPHA: (43) implies:
% 243.04/49.61  | | | | |   (44)  op(e1, e0) = all_56_29
% 243.04/49.61  | | | | |   (45)  op(e1, all_56_29) = e1
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | | BETA: splitting (20) gives:
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | | Case 1:
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | |   (46)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 243.04/49.61  | | | | | |             e0) = e2)
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | | BETA: splitting (46) gives:
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | | Case 1:
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | |   (47)  all_58_9 = e2 & op(e3, e0) = e2
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | | REF_CLOSE: (3), (4), (5), (6), (9), (17), (18), (22), (23), (24),
% 243.04/49.61  | | | | | | |            (25), (29), (47) are inconsistent by sub-proof #1061.
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | Case 2:
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | | GROUND_INST: instantiating (18) with e3, all_56_29, e0, e1,
% 243.04/49.61  | | | | | | |              simplifying with (26), (44) gives:
% 243.04/49.61  | | | | | | |   (48)  all_56_29 = e3
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | | REDUCE: (45), (48) imply:
% 243.04/49.61  | | | | | | |   (49)  op(e1, e3) = e1
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | | REF_CLOSE: (8), (18), (21), (49) are inconsistent by sub-proof
% 243.04/49.61  | | | | | | |            #1948.
% 243.04/49.61  | | | | | | | 
% 243.04/49.61  | | | | | | End of split
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | Case 2:
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | |   (50)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 243.04/49.61  | | | | | |           op(e0, e0) = e2)
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | | REF_CLOSE: (9), (13), (24), (25), (50) are inconsistent by sub-proof
% 243.04/49.61  | | | | | |            #1058.
% 243.04/49.61  | | | | | | 
% 243.04/49.61  | | | | | End of split
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | Case 2:
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | |   (51)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | | ALPHA: (51) implies:
% 243.04/49.61  | | | | |   (52)  op(e0, all_56_31) = e0
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | | REDUCE: (12), (52) imply:
% 243.04/49.61  | | | | |   (53)  op(e0, e1) = e0
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | | REF_CLOSE: (2), (14), (18), (53) are inconsistent by sub-proof #1911.
% 243.04/49.61  | | | | | 
% 243.04/49.61  | | | | End of split
% 243.04/49.61  | | | | 
% 243.04/49.61  | | | End of split
% 243.04/49.61  | | | 
% 243.04/49.61  | | Case 2:
% 243.04/49.61  | | | 
% 243.04/49.61  | | |   (54)  all_58_7 = e2 & op(e1, e2) = e2
% 243.04/49.61  | | | 
% 243.04/49.61  | | | ALPHA: (54) implies:
% 243.04/49.61  | | |   (55)  all_58_7 = e2
% 243.04/49.61  | | | 
% 243.04/49.61  | | | REF_CLOSE: (16), (24), (55) are inconsistent by sub-proof #2134.
% 243.04/49.61  | | | 
% 243.04/49.61  | | End of split
% 243.04/49.61  | | 
% 243.04/49.61  | Case 2:
% 243.04/49.61  | | 
% 243.04/49.61  | |   (56)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 243.04/49.61  | |           e2)
% 243.04/49.61  | | 
% 243.04/49.61  | | REF_CLOSE: (4), (9), (18), (22), (25), (56) are inconsistent by sub-proof
% 243.04/49.61  | |            #1057.
% 243.04/49.61  | | 
% 243.04/49.61  | End of split
% 243.04/49.61  | 
% 243.04/49.61  End of proof
% 243.04/49.61  
% 243.04/49.61  Sub-proof #1057 shows that the following formulas are inconsistent:
% 243.04/49.61  ----------------------------------------------------------------
% 243.04/49.61    (1)   ~ (e2 = e0)
% 243.04/49.61    (2)  all_58_11 = e3
% 243.04/49.61    (3)   ~ (e3 = e2)
% 243.04/49.61    (4)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.04/49.61    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.61    (6)  op(e1, e1) = e0
% 243.04/49.61  
% 243.04/49.61  Begin of proof
% 243.04/49.61  | 
% 243.04/49.61  | BETA: splitting (4) gives:
% 243.04/49.61  | 
% 243.04/49.61  | Case 1:
% 243.04/49.61  | | 
% 243.04/49.61  | |   (7)  all_58_8 = e2 & op(e1, e1) = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | ALPHA: (7) implies:
% 243.04/49.61  | |   (8)  op(e1, e1) = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2211.
% 243.04/49.61  | | 
% 243.04/49.61  | Case 2:
% 243.04/49.61  | | 
% 243.04/49.61  | |   (9)  all_58_11 = e2 & op(e1, e0) = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #1741.
% 243.04/49.61  | | 
% 243.04/49.61  | End of split
% 243.04/49.61  | 
% 243.04/49.61  End of proof
% 243.04/49.61  
% 243.04/49.61  Sub-proof #1058 shows that the following formulas are inconsistent:
% 243.04/49.61  ----------------------------------------------------------------
% 243.04/49.61    (1)  all_58_11 = e3
% 243.04/49.61    (2)   ~ (e3 = e2)
% 243.04/49.61    (3)  all_58_15 = e1
% 243.04/49.61    (4)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.04/49.61    (5)   ~ (e2 = e1)
% 243.04/49.61  
% 243.04/49.61  Begin of proof
% 243.04/49.61  | 
% 243.04/49.61  | BETA: splitting (4) gives:
% 243.04/49.61  | 
% 243.04/49.61  | Case 1:
% 243.04/49.61  | | 
% 243.04/49.61  | |   (6)  all_58_11 = e2 & op(e1, e0) = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #1741.
% 243.04/49.61  | | 
% 243.04/49.61  | Case 2:
% 243.04/49.61  | | 
% 243.04/49.61  | |   (7)  all_58_15 = e2 & op(e0, e0) = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | ALPHA: (7) implies:
% 243.04/49.61  | |   (8)  all_58_15 = e2
% 243.04/49.61  | | 
% 243.04/49.61  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #2231.
% 243.04/49.61  | | 
% 243.04/49.61  | End of split
% 243.04/49.61  | 
% 243.04/49.61  End of proof
% 243.04/49.61  
% 243.04/49.61  Sub-proof #1059 shows that the following formulas are inconsistent:
% 243.04/49.61  ----------------------------------------------------------------
% 243.04/49.61    (1)  op(e2, e0) = all_56_27
% 243.04/49.61    (2)   ~ (e2 = e0)
% 243.04/49.61    (3)  op(e2, all_56_27) = e2
% 243.04/49.61    (4)  op(e2, e2) = e0
% 243.04/49.62    (5)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) = all_48_1
% 243.04/49.62           & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0) =
% 243.04/49.62           all_48_1 & $i(all_48_1))
% 243.04/49.62    (6)  op(e2, e0) = e2
% 243.04/49.62    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.62  
% 243.04/49.62  Begin of proof
% 243.04/49.62  | 
% 243.04/49.62  | BETA: splitting (5) gives:
% 243.04/49.62  | 
% 243.04/49.62  | Case 1:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (8)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 243.04/49.62  | |        all_48_1 & $i(all_48_0) & $i(all_48_1)
% 243.04/49.62  | | 
% 243.04/49.62  | | ALPHA: (8) implies:
% 243.04/49.62  | |   (9)  op(e2, e0) = all_48_1
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9) are inconsistent by sub-proof
% 243.04/49.62  | |            #1060.
% 243.04/49.62  | | 
% 243.04/49.62  | Case 2:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (10)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 & $i(all_48_1)
% 243.04/49.62  | | 
% 243.04/49.62  | | ALPHA: (10) implies:
% 243.04/49.62  | |   (11)  op(e2, e0) = all_48_1
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (11) are inconsistent by sub-proof
% 243.04/49.62  | |            #1060.
% 243.04/49.62  | | 
% 243.04/49.62  | End of split
% 243.04/49.62  | 
% 243.04/49.62  End of proof
% 243.04/49.62  
% 243.04/49.62  Sub-proof #1060 shows that the following formulas are inconsistent:
% 243.04/49.62  ----------------------------------------------------------------
% 243.04/49.62    (1)  op(e2, e0) = all_56_27
% 243.04/49.62    (2)   ~ (e2 = e0)
% 243.04/49.62    (3)  op(e2, all_56_27) = e2
% 243.04/49.62    (4)  op(e2, e2) = e0
% 243.04/49.62    (5)  op(e2, e0) = e2
% 243.04/49.62    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.62    (7)  op(e2, e0) = all_48_1
% 243.04/49.62  
% 243.04/49.62  Begin of proof
% 243.04/49.62  | 
% 243.04/49.62  | GROUND_INST: instantiating (6) with all_48_1, all_56_27, e0, e2, simplifying
% 243.04/49.62  |              with (1), (7) gives:
% 243.04/49.62  |   (8)  all_56_27 = all_48_1
% 243.04/49.62  | 
% 243.04/49.62  | GROUND_INST: instantiating (6) with e2, all_56_27, e0, e2, simplifying with
% 243.04/49.62  |              (1), (5) gives:
% 243.04/49.62  |   (9)  all_56_27 = e2
% 243.04/49.62  | 
% 243.04/49.62  | COMBINE_EQS: (8), (9) imply:
% 243.04/49.62  |   (10)  all_48_1 = e2
% 243.04/49.62  | 
% 243.04/49.62  | REDUCE: (3), (9) imply:
% 243.04/49.62  |   (11)  op(e2, e2) = e2
% 243.04/49.62  | 
% 243.04/49.62  | REF_CLOSE: (2), (4), (6), (11) are inconsistent by sub-proof #2137.
% 243.04/49.62  | 
% 243.04/49.62  End of proof
% 243.04/49.62  
% 243.04/49.62  Sub-proof #1061 shows that the following formulas are inconsistent:
% 243.04/49.62  ----------------------------------------------------------------
% 243.04/49.62    (1)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.04/49.62         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.04/49.62    (2)   ~ (e2 = e0)
% 243.04/49.62    (3)  all_58_6 = e2
% 243.04/49.62    (4)  all_58_9 = e0
% 243.04/49.62    (5)   ~ (e3 = e1)
% 243.04/49.62    (6)  all_58_11 = e3
% 243.04/49.62    (7)   ~ (e3 = e2)
% 243.04/49.62    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.04/49.62         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.04/49.62    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.62    (10)  op(e1, e1) = e0
% 243.04/49.62    (11)   ~ (e1 = e0)
% 243.04/49.62    (12)  all_58_9 = e2 & op(e3, e0) = e2
% 243.04/49.62    (13)   ~ (e2 = e1)
% 243.04/49.62  
% 243.04/49.62  Begin of proof
% 243.04/49.62  | 
% 243.04/49.62  | ALPHA: (12) implies:
% 243.04/49.62  |   (14)  all_58_9 = e2
% 243.04/49.62  | 
% 243.04/49.62  | COMBINE_EQS: (4), (14) imply:
% 243.04/49.62  |   (15)  e2 = e0
% 243.04/49.62  | 
% 243.04/49.62  | SIMP: (15) implies:
% 243.04/49.62  |   (16)  e2 = e0
% 243.04/49.62  | 
% 243.04/49.62  | COMBINE_EQS: (3), (16) imply:
% 243.04/49.62  |   (17)  all_58_6 = e0
% 243.04/49.62  | 
% 243.04/49.62  | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (13), (17) are
% 243.04/49.62  |            inconsistent by sub-proof #1978.
% 243.04/49.62  | 
% 243.04/49.62  End of proof
% 243.04/49.62  
% 243.04/49.62  Sub-proof #1062 shows that the following formulas are inconsistent:
% 243.04/49.62  ----------------------------------------------------------------
% 243.04/49.62    (1)   ~ (e3 = e0)
% 243.04/49.62    (2)  all_58_9 = e0
% 243.04/49.62    (3)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.04/49.62    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.62    (5)   ~ (all_52_13 = e3)
% 243.04/49.62    (6)  op(e2, e0) = all_52_13
% 243.04/49.62  
% 243.04/49.62  Begin of proof
% 243.04/49.62  | 
% 243.04/49.62  | BETA: splitting (3) gives:
% 243.04/49.62  | 
% 243.04/49.62  | Case 1:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (7)  all_58_9 = e3 & op(e3, e0) = e3
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #1621.
% 243.04/49.62  | | 
% 243.04/49.62  | Case 2:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (8)  all_58_10 = e3 & op(e2, e0) = e3
% 243.04/49.62  | | 
% 243.04/49.62  | | ALPHA: (8) implies:
% 243.04/49.62  | |   (9)  op(e2, e0) = e3
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #1994.
% 243.04/49.62  | | 
% 243.04/49.62  | End of split
% 243.04/49.62  | 
% 243.04/49.62  End of proof
% 243.04/49.62  
% 243.04/49.62  Sub-proof #1063 shows that the following formulas are inconsistent:
% 243.04/49.62  ----------------------------------------------------------------
% 243.04/49.62    (1)   ~ (e3 = e0)
% 243.04/49.62    (2)   ~ (e2 = e0)
% 243.04/49.62    (3)  op(e1, e2) = all_52_6
% 243.04/49.62    (4)   ~ (all_52_6 = e0)
% 243.04/49.62    (5)   ~ (e3 = e1)
% 243.04/49.62    (6)  all_58_11 = e2 & op(e1, e0) = e2
% 243.04/49.62    (7)   ~ (e3 = e2)
% 243.04/49.62    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.04/49.62         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.04/49.62    (9)  op(e1, e1) = e2
% 243.04/49.62    (10)  all_58_7 = e1
% 243.04/49.62    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.62    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.04/49.62          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.04/49.62  
% 243.04/49.62  Begin of proof
% 243.04/49.62  | 
% 243.04/49.62  | ALPHA: (6) implies:
% 243.04/49.62  |   (13)  all_58_11 = e2
% 243.04/49.62  | 
% 243.04/49.62  | BETA: splitting (8) gives:
% 243.04/49.62  | 
% 243.04/49.62  | Case 1:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (14)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 243.04/49.62  | |           e3)
% 243.04/49.62  | | 
% 243.04/49.62  | | BETA: splitting (14) gives:
% 243.04/49.62  | | 
% 243.04/49.62  | | Case 1:
% 243.04/49.62  | | | 
% 243.04/49.62  | | |   (15)  all_58_6 = e3 & op(e1, e3) = e3
% 243.04/49.62  | | | 
% 243.04/49.62  | | | REF_CLOSE: (1), (2), (3), (4), (9), (11), (12), (13), (15) are
% 243.04/49.62  | | |            inconsistent by sub-proof #1672.
% 243.04/49.62  | | | 
% 243.04/49.62  | | Case 2:
% 243.04/49.62  | | | 
% 243.04/49.62  | | |   (16)  all_58_7 = e3 & op(e1, e2) = e3
% 243.04/49.62  | | | 
% 243.04/49.62  | | | REF_CLOSE: (5), (10), (16) are inconsistent by sub-proof #2138.
% 243.04/49.62  | | | 
% 243.04/49.62  | | End of split
% 243.04/49.62  | | 
% 243.04/49.62  | Case 2:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (17)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 243.04/49.62  | |           e3)
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (7), (9), (11), (13), (17) are inconsistent by sub-proof #2107.
% 243.04/49.62  | | 
% 243.04/49.62  | End of split
% 243.04/49.62  | 
% 243.04/49.62  End of proof
% 243.04/49.62  
% 243.04/49.62  Sub-proof #1064 shows that the following formulas are inconsistent:
% 243.04/49.62  ----------------------------------------------------------------
% 243.04/49.62    (1)   ~ (e3 = e0)
% 243.04/49.62    (2)   ~ (e3 = e1)
% 243.04/49.62    (3)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.62         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.62    (4)  op(e3, e3) = e1
% 243.04/49.62    (5)   ~ (e3 = e2)
% 243.04/49.62    (6)  op(e3, e0) = e2
% 243.04/49.62    (7)  all_58_11 = e3 & op(e1, e0) = e3
% 243.04/49.62    (8)   ~ (all_52_4 = e3)
% 243.04/49.62    (9)  op(e3, e2) = all_52_4
% 243.04/49.62    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.62    (11)  all_58_11 = e0
% 243.04/49.62    (12)  all_58_4 = e3
% 243.04/49.62  
% 243.04/49.62  Begin of proof
% 243.04/49.62  | 
% 243.04/49.62  | ALPHA: (7) implies:
% 243.04/49.62  |   (13)  all_58_11 = e3
% 243.04/49.62  | 
% 243.04/49.62  | COMBINE_EQS: (11), (13) imply:
% 243.04/49.62  |   (14)  e3 = e0
% 243.04/49.62  | 
% 243.04/49.62  | SIMP: (14) implies:
% 243.04/49.62  |   (15)  e3 = e0
% 243.04/49.62  | 
% 243.04/49.62  | COMBINE_EQS: (12), (15) imply:
% 243.04/49.62  |   (16)  all_58_4 = e0
% 243.04/49.62  | 
% 243.04/49.62  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (16) are inconsistent
% 243.04/49.62  |            by sub-proof #1400.
% 243.04/49.62  | 
% 243.04/49.62  End of proof
% 243.04/49.62  
% 243.04/49.62  Sub-proof #1065 shows that the following formulas are inconsistent:
% 243.04/49.62  ----------------------------------------------------------------
% 243.04/49.62    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.62         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.62    (2)   ~ (e2 = e0)
% 243.04/49.62    (3)  all_58_9 = e0
% 243.04/49.62    (4)  op(e3, e3) = e1
% 243.04/49.62    (5)   ~ (e3 = e2)
% 243.04/49.62    (6)  all_58_1 = e2
% 243.04/49.62    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.62    (8)  all_58_4 = e3
% 243.04/49.62    (9)  all_58_9 = e2
% 243.04/49.62    (10)   ~ (e2 = e1)
% 243.04/49.62  
% 243.04/49.62  Begin of proof
% 243.04/49.62  | 
% 243.04/49.62  | COMBINE_EQS: (3), (9) imply:
% 243.04/49.62  |   (11)  e2 = e0
% 243.04/49.62  | 
% 243.04/49.62  | SIMP: (11) implies:
% 243.04/49.62  |   (12)  e2 = e0
% 243.04/49.62  | 
% 243.04/49.62  | COMBINE_EQS: (6), (12) imply:
% 243.04/49.62  |   (13)  all_58_1 = e0
% 243.04/49.62  | 
% 243.04/49.62  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (13) are inconsistent by
% 243.04/49.62  |            sub-proof #1097.
% 243.04/49.62  | 
% 243.04/49.62  End of proof
% 243.04/49.62  
% 243.04/49.62  Sub-proof #1066 shows that the following formulas are inconsistent:
% 243.04/49.62  ----------------------------------------------------------------
% 243.04/49.62    (1)  op(e3, e3) = e1
% 243.04/49.62    (2)  op(e3, e2) = all_52_4
% 243.04/49.62    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.62    (4)   ~ (e1 = e0)
% 243.04/49.62    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 243.04/49.62    (6)   ~ (all_52_4 = e0)
% 243.04/49.62  
% 243.04/49.62  Begin of proof
% 243.04/49.62  | 
% 243.04/49.62  | BETA: splitting (5) gives:
% 243.04/49.62  | 
% 243.04/49.62  | Case 1:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 243.04/49.62  | | 
% 243.04/49.62  | | ALPHA: (7) implies:
% 243.04/49.62  | |   (8)  op(e3, e3) = e0
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1828.
% 243.04/49.62  | | 
% 243.04/49.62  | Case 2:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (9)  all_58_1 = e0 & op(e3, e2) = e0
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #1968.
% 243.04/49.62  | | 
% 243.04/49.62  | End of split
% 243.04/49.62  | 
% 243.04/49.62  End of proof
% 243.04/49.62  
% 243.04/49.62  Sub-proof #1067 shows that the following formulas are inconsistent:
% 243.04/49.62  ----------------------------------------------------------------
% 243.04/49.62    (1)   ~ (e3 = e0)
% 243.04/49.62    (2)   ~ (e2 = e0)
% 243.04/49.62    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.62         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.62    (4)  all_58_14 = e2
% 243.04/49.62    (5)   ~ (e3 = e1)
% 243.04/49.62    (6)   ~ (e3 = e2)
% 243.04/49.62    (7)  all_58_12 = e3
% 243.04/49.62    (8)  all_58_7 = e1
% 243.04/49.62    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.62    (10)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.04/49.62          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.04/49.62    (11)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.04/49.62          | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.62    (12)  all_58_3 = e0
% 243.04/49.62    (13)   ~ (e2 = e1)
% 243.04/49.62  
% 243.04/49.62  Begin of proof
% 243.04/49.62  | 
% 243.04/49.62  | BETA: splitting (11) gives:
% 243.04/49.62  | 
% 243.04/49.62  | Case 1:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (14)  all_58_12 = e0 & op(e0, e3) = e0
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (1), (7), (14) are inconsistent by sub-proof #1641.
% 243.04/49.62  | | 
% 243.04/49.62  | Case 2:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (15)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 243.04/49.62  | |           e0)
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (15)
% 243.04/49.62  | |            are inconsistent by sub-proof #1068.
% 243.04/49.62  | | 
% 243.04/49.62  | End of split
% 243.04/49.62  | 
% 243.04/49.62  End of proof
% 243.04/49.62  
% 243.04/49.62  Sub-proof #1068 shows that the following formulas are inconsistent:
% 243.04/49.62  ----------------------------------------------------------------
% 243.04/49.62    (1)   ~ (e3 = e0)
% 243.04/49.62    (2)   ~ (e2 = e0)
% 243.04/49.62    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.62         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.62    (4)  all_58_14 = e2
% 243.04/49.62    (5)   ~ (e3 = e1)
% 243.04/49.62    (6)   ~ (e3 = e2)
% 243.04/49.62    (7)  all_58_7 = e1
% 243.04/49.62    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.62    (9)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.04/49.62         (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.04/49.62    (10)  all_58_3 = e0
% 243.04/49.62    (11)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.62    (12)   ~ (e2 = e1)
% 243.04/49.62  
% 243.04/49.62  Begin of proof
% 243.04/49.62  | 
% 243.04/49.62  | BETA: splitting (11) gives:
% 243.04/49.62  | 
% 243.04/49.62  | Case 1:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (13)  all_58_13 = e0 & op(e0, e2) = e0
% 243.04/49.62  | | 
% 243.04/49.62  | | ALPHA: (13) implies:
% 243.04/49.62  | |   (14)  all_58_13 = e0
% 243.04/49.62  | |   (15)  op(e0, e2) = e0
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (14), (15)
% 243.04/49.62  | |            are inconsistent by sub-proof #1375.
% 243.04/49.62  | | 
% 243.04/49.62  | Case 2:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (16)  all_58_14 = e0 & op(e0, e1) = e0
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (2), (4), (16) are inconsistent by sub-proof #2036.
% 243.04/49.62  | | 
% 243.04/49.62  | End of split
% 243.04/49.62  | 
% 243.04/49.62  End of proof
% 243.04/49.62  
% 243.04/49.62  Sub-proof #1069 shows that the following formulas are inconsistent:
% 243.04/49.62  ----------------------------------------------------------------
% 243.04/49.62    (1)   ~ (e3 = e0)
% 243.04/49.62    (2)   ~ (e2 = e0)
% 243.04/49.62    (3)   ~ (e3 = e1)
% 243.04/49.62    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.62         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.62    (5)   ~ (e3 = e2)
% 243.04/49.62    (6)  op(e3, e3) = e2
% 243.04/49.62    (7)  op(e3, e0) = e2
% 243.04/49.62    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.62         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.62    (9)   ~ (all_52_4 = e3)
% 243.04/49.62    (10)  op(e3, e2) = all_52_4
% 243.04/49.62    (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.04/49.62          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.04/49.62    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.62    (13)   ~ (e1 = e0)
% 243.04/49.62    (14)  all_58_9 = e2
% 243.04/49.62    (15)   ~ (e2 = e1)
% 243.04/49.62  
% 243.04/49.62  Begin of proof
% 243.04/49.62  | 
% 243.04/49.62  | BETA: splitting (4) gives:
% 243.04/49.62  | 
% 243.04/49.62  | Case 1:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 243.04/49.62  | |           e3)
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (5), (6), (9), (10), (12), (16) are inconsistent by sub-proof
% 243.04/49.62  | |            #1959.
% 243.04/49.62  | | 
% 243.04/49.62  | Case 2:
% 243.04/49.62  | | 
% 243.04/49.62  | |   (17)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 243.04/49.62  | |           e3)
% 243.04/49.62  | | 
% 243.04/49.62  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (11), (12), (13), (14), (15),
% 243.04/49.62  | |            (17) are inconsistent by sub-proof #1561.
% 243.04/49.62  | | 
% 243.04/49.62  | End of split
% 243.04/49.62  | 
% 243.04/49.62  End of proof
% 243.04/49.62  
% 243.04/49.62  Sub-proof #1070 shows that the following formulas are inconsistent:
% 243.04/49.62  ----------------------------------------------------------------
% 243.04/49.62    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.62         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.63    (2)   ~ (e3 = e0)
% 243.04/49.63    (3)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.63    (4)  op(e0, e1) = all_52_11
% 243.04/49.63    (5)   ~ (e2 = e0)
% 243.04/49.63    (6)   ~ (e3 = e1)
% 243.04/49.63    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.63         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.63    (8)  op(e3, e3) = e1
% 243.04/49.63    (9)   ~ (all_52_11 = e3)
% 243.04/49.63    (10)   ~ (e3 = e2)
% 243.04/49.63    (11)  all_58_15 = e1
% 243.04/49.63    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.63          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.63    (13)   ~ (all_52_4 = e3)
% 243.04/49.63    (14)  op(e3, e2) = all_52_4
% 243.04/49.63    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.63            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.63    (16)   ~ (e1 = e0)
% 243.04/49.63    (17)  all_58_4 = e3
% 243.04/49.63    (18)   ~ (e2 = e1)
% 243.04/49.63  
% 243.04/49.63  Begin of proof
% 243.04/49.63  | 
% 243.04/49.63  | BETA: splitting (3) gives:
% 243.04/49.63  | 
% 243.04/49.63  | Case 1:
% 243.04/49.63  | | 
% 243.04/49.63  | |   (19)  all_58_14 = e3 & op(e0, e1) = e3
% 243.04/49.63  | | 
% 243.04/49.63  | | REF_CLOSE: (4), (9), (15), (19) are inconsistent by sub-proof #1647.
% 243.04/49.63  | | 
% 243.04/49.63  | Case 2:
% 243.04/49.63  | | 
% 243.04/49.63  | |   (20)  all_58_15 = e3 & op(e0, e0) = e3
% 243.04/49.63  | | 
% 243.04/49.63  | | ALPHA: (20) implies:
% 243.04/49.63  | |   (21)  all_58_15 = e3
% 243.04/49.63  | | 
% 243.04/49.63  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 243.04/49.63  | |            (16), (17), (18), (21) are inconsistent by sub-proof #1093.
% 243.04/49.63  | | 
% 243.04/49.63  | End of split
% 243.04/49.63  | 
% 243.04/49.63  End of proof
% 243.04/49.63  
% 243.04/49.63  Sub-proof #1071 shows that the following formulas are inconsistent:
% 243.04/49.63  ----------------------------------------------------------------
% 243.04/49.63    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.63         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.63    (2)   ~ (e3 = e0)
% 243.04/49.63    (3)   ~ (e2 = e0)
% 243.04/49.63    (4)   ~ (e3 = e1)
% 243.04/49.63    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.63         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.63    (6)  op(e3, e3) = e1
% 243.04/49.63    (7)   ~ (e3 = e2)
% 243.04/49.63    (8)  all_58_7 = e3 & op(e1, e2) = e3
% 243.04/49.63    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.63         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.63    (10)   ~ (all_52_4 = e3)
% 243.04/49.63    (11)  op(e3, e2) = all_52_4
% 243.04/49.63    (12)  all_58_7 = e1
% 243.04/49.63    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.63            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.63    (14)   ~ (e1 = e0)
% 243.04/49.63    (15)  all_58_4 = e3
% 243.04/49.63    (16)   ~ (e2 = e1)
% 243.04/49.63  
% 243.04/49.63  Begin of proof
% 243.04/49.63  | 
% 243.04/49.63  | ALPHA: (8) implies:
% 243.04/49.63  |   (17)  all_58_7 = e3
% 243.04/49.63  | 
% 243.04/49.63  | COMBINE_EQS: (12), (17) imply:
% 243.04/49.63  |   (18)  e3 = e1
% 243.04/49.63  | 
% 243.04/49.63  | SIMP: (18) implies:
% 243.04/49.63  |   (19)  e3 = e1
% 243.04/49.63  | 
% 243.04/49.63  | COMBINE_EQS: (15), (19) imply:
% 243.04/49.63  |   (20)  all_58_4 = e1
% 243.04/49.63  | 
% 243.04/49.63  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 243.04/49.63  |            (16), (20) are inconsistent by sub-proof #1468.
% 243.04/49.63  | 
% 243.04/49.63  End of proof
% 243.04/49.63  
% 243.04/49.63  Sub-proof #1072 shows that the following formulas are inconsistent:
% 243.04/49.63  ----------------------------------------------------------------
% 243.04/49.63    (1)  all_56_21 = e2
% 243.04/49.63    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.63         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.63    (3)   ~ (e3 = e0)
% 243.04/49.63    (4)   ~ (all_52_7 = e2)
% 243.04/49.63    (5)   ~ (e2 = e0)
% 243.04/49.63    (6)   ~ (all_52_11 = e2)
% 243.04/49.63    (7)  all_54_13 = all_52_7
% 243.04/49.63    (8)   ~ (all_52_11 = e1)
% 243.04/49.63    (9)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.04/49.63           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.04/49.63             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.04/49.63           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.04/49.63             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.04/49.63           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.63           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.04/49.63           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.04/49.63           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.04/49.63           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.63           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.04/49.63             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.04/49.63           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.04/49.63           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 243.04/49.63           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.04/49.63           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.04/49.63           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.04/49.63           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.04/49.63             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.04/49.63           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.63           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 243.04/49.63           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.04/49.63           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.04/49.63           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.63           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.04/49.63             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.04/49.63           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.63           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.63    (10)   ~ (all_52_7 = all_52_11)
% 243.04/49.63    (11)  op(e1, e0) = all_52_14
% 243.04/49.63    (12)   ~ (all_52_13 = e1)
% 243.04/49.63    (13)  op(e0, e3) = all_52_3
% 243.04/49.63    (14)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.63          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.04/49.63    (15)   ~ (e3 = e1)
% 243.04/49.63    (16)  all_54_11 = all_52_14
% 243.04/49.63    (17)   ~ (all_52_12 = e1)
% 243.04/49.63    (18)   ~ (all_52_12 = all_52_14)
% 243.04/49.63    (19)   ~ (all_52_8 = e1)
% 243.04/49.63    (20)   ~ (all_52_12 = all_52_13)
% 243.04/49.63    (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.63          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.63    (22)  all_54_2 = all_52_8
% 243.04/49.63    (23)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.04/49.63    (24)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.04/49.63          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.04/49.63    (25)  op(e3, e3) = e1
% 243.04/49.63    (26)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.04/49.63    (27)   ~ (all_52_14 = e2)
% 243.04/49.63    (28)   ~ (all_52_8 = all_52_12)
% 243.04/49.63    (29)  op(e3, e1) = all_52_8
% 243.04/49.63    (30)   ~ (e3 = e2)
% 243.04/49.63    (31)   ~ (all_52_14 = e1)
% 243.04/49.63    (32)   ~ (all_52_7 = e1)
% 243.04/49.63    (33)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.04/49.63    (34)   ~ (all_52_3 = all_52_11)
% 243.04/49.63    (35)  all_56_31 = e1
% 243.04/49.63    (36)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.04/49.63    (37)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.04/49.63    (38)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.04/49.63          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.04/49.63    (39)  op(e3, e0) = all_52_12
% 243.04/49.63    (40)   ~ (all_52_1 = e0)
% 243.04/49.63    (41)  all_56_11 = e0
% 243.04/49.63    (42)  op(e2, e3) = all_52_1
% 243.04/49.63    (43)  op(e3, e0) = e2
% 243.04/49.63    (44)   ~ (all_52_12 = e2)
% 243.04/49.63    (45)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.63          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.63    (46)   ~ (all_52_1 = all_52_13)
% 243.04/49.63    (47)  all_54_7 = all_52_13
% 243.04/49.63    (48)   ~ (all_52_13 = all_52_14)
% 243.04/49.63    (49)   ~ (all_52_4 = e3)
% 243.04/49.63    (50)  op(e3, e2) = all_52_4
% 243.04/49.63    (51)   ~ (all_52_8 = all_52_11)
% 243.04/49.63    (52)   ~ (all_52_7 = e0)
% 243.04/49.63    (53)  all_58_12 = e2 & op(e0, e3) = e2
% 243.04/49.63    (54)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.04/49.63    (55)  all_58_5 = e1
% 243.04/49.63    (56)  all_54_3 = all_52_12
% 243.04/49.63    (57)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.63            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.63    (58)   ~ (e1 = e0)
% 243.04/49.63    (59)   ~ (all_52_8 = e2)
% 243.04/49.63    (60)  all_58_9 = e2
% 243.04/49.63    (61)  all_58_3 = e0
% 243.04/49.63    (62)  all_54_14 = all_52_11
% 243.04/49.63    (63)   ~ (e2 = e1)
% 243.04/49.63  
% 243.04/49.63  Begin of proof
% 243.04/49.63  | 
% 243.04/49.63  | ALPHA: (53) implies:
% 243.04/49.63  |   (64)  all_58_12 = e2
% 243.04/49.63  | 
% 243.04/49.63  | BETA: splitting (38) gives:
% 243.04/49.63  | 
% 243.04/49.63  | Case 1:
% 243.04/49.63  | | 
% 243.04/49.63  | |   (65)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 243.04/49.63  | |           e0)
% 243.04/49.63  | | 
% 243.04/49.63  | | REF_CLOSE: (25), (40), (42), (57), (58), (65) are inconsistent by sub-proof
% 243.04/49.63  | |            #1272.
% 243.04/49.63  | | 
% 243.04/49.63  | Case 2:
% 243.04/49.63  | | 
% 243.04/49.63  | |   (66)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 243.04/49.63  | |           e0)
% 243.04/49.63  | | 
% 243.04/49.63  | | BETA: splitting (66) gives:
% 243.04/49.63  | | 
% 243.04/49.63  | | Case 1:
% 243.04/49.63  | | | 
% 243.04/49.63  | | |   (67)  all_58_6 = e0 & op(e1, e3) = e0
% 243.04/49.63  | | | 
% 243.04/49.63  | | | ALPHA: (67) implies:
% 243.04/49.63  | | |   (68)  all_58_6 = e0
% 243.04/49.63  | | | 
% 243.04/49.63  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 243.04/49.63  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 243.04/49.63  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 243.04/49.63  | | |            (33), (34), (35), (36), (37), (39), (41), (42), (43), (44),
% 243.04/49.63  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (54), (55),
% 243.04/49.63  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (68) are
% 243.04/49.63  | | |            inconsistent by sub-proof #1073.
% 243.04/49.63  | | | 
% 243.04/49.63  | | Case 2:
% 243.04/49.63  | | | 
% 243.04/49.63  | | |   (69)  all_58_12 = e0 & op(e0, e3) = e0
% 243.04/49.63  | | | 
% 243.04/49.63  | | | ALPHA: (69) implies:
% 243.04/49.63  | | |   (70)  all_58_12 = e0
% 243.04/49.63  | | | 
% 243.04/49.63  | | | REF_CLOSE: (5), (64), (70) are inconsistent by sub-proof #2083.
% 243.04/49.63  | | | 
% 243.04/49.63  | | End of split
% 243.04/49.63  | | 
% 243.04/49.63  | End of split
% 243.04/49.63  | 
% 243.04/49.63  End of proof
% 243.04/49.63  
% 243.04/49.63  Sub-proof #1073 shows that the following formulas are inconsistent:
% 243.04/49.63  ----------------------------------------------------------------
% 243.04/49.63    (1)  all_56_21 = e2
% 243.04/49.63    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.63         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.63    (3)   ~ (e3 = e0)
% 243.04/49.63    (4)   ~ (all_52_7 = e2)
% 243.04/49.63    (5)   ~ (e2 = e0)
% 243.04/49.63    (6)   ~ (all_52_11 = e2)
% 243.04/49.63    (7)  all_54_13 = all_52_7
% 243.04/49.63    (8)  all_58_12 = e2
% 243.04/49.63    (9)   ~ (all_52_11 = e1)
% 243.04/49.63    (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.04/49.63              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.04/49.63            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.04/49.63            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.04/49.63            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.04/49.63             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.63            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.04/49.63            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.04/49.63            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.04/49.63            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.63            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.04/49.63              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.04/49.63            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.04/49.63            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.04/49.63            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.04/49.63            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.04/49.63            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.04/49.63            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.04/49.63              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.04/49.63            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.63            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.04/49.63            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.04/49.63            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.04/49.63            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.63            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.04/49.63              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.04/49.63            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.63            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.63    (11)   ~ (all_52_7 = all_52_11)
% 243.04/49.63    (12)  op(e1, e0) = all_52_14
% 243.04/49.63    (13)   ~ (all_52_13 = e1)
% 243.04/49.63    (14)  op(e0, e3) = all_52_3
% 243.04/49.63    (15)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.63          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.04/49.63    (16)   ~ (e3 = e1)
% 243.04/49.63    (17)  all_54_11 = all_52_14
% 243.04/49.63    (18)   ~ (all_52_12 = e1)
% 243.04/49.63    (19)   ~ (all_52_12 = all_52_14)
% 243.04/49.63    (20)   ~ (all_52_8 = e1)
% 243.04/49.63    (21)   ~ (all_52_12 = all_52_13)
% 243.04/49.63    (22)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.63          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.63    (23)  all_54_2 = all_52_8
% 243.04/49.63    (24)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.04/49.63    (25)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.04/49.63          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.04/49.63    (26)  op(e3, e3) = e1
% 243.04/49.63    (27)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.04/49.63    (28)   ~ (all_52_14 = e2)
% 243.04/49.63    (29)   ~ (all_52_8 = all_52_12)
% 243.04/49.63    (30)  op(e3, e1) = all_52_8
% 243.04/49.63    (31)   ~ (e3 = e2)
% 243.04/49.63    (32)  all_58_6 = e0
% 243.04/49.63    (33)   ~ (all_52_14 = e1)
% 243.04/49.63    (34)   ~ (all_52_7 = e1)
% 243.04/49.63    (35)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.04/49.63    (36)   ~ (all_52_3 = all_52_11)
% 243.04/49.63    (37)  all_56_31 = e1
% 243.04/49.64    (38)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.04/49.64    (39)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.04/49.64    (40)  op(e3, e0) = all_52_12
% 243.04/49.64    (41)  all_56_11 = e0
% 243.04/49.64    (42)  op(e2, e3) = all_52_1
% 243.04/49.64    (43)  op(e3, e0) = e2
% 243.04/49.64    (44)   ~ (all_52_12 = e2)
% 243.04/49.64    (45)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.64          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.64    (46)   ~ (all_52_1 = all_52_13)
% 243.04/49.64    (47)  all_54_7 = all_52_13
% 243.04/49.64    (48)   ~ (all_52_13 = all_52_14)
% 243.04/49.64    (49)   ~ (all_52_4 = e3)
% 243.04/49.64    (50)  op(e3, e2) = all_52_4
% 243.04/49.64    (51)   ~ (all_52_8 = all_52_11)
% 243.04/49.64    (52)   ~ (all_52_7 = e0)
% 243.04/49.64    (53)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.04/49.64    (54)  all_58_5 = e1
% 243.04/49.64    (55)  all_54_3 = all_52_12
% 243.04/49.64    (56)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.64    (57)   ~ (e1 = e0)
% 243.04/49.64    (58)   ~ (all_52_8 = e2)
% 243.04/49.64    (59)  all_58_9 = e2
% 243.04/49.64    (60)  all_58_3 = e0
% 243.04/49.64    (61)  all_54_14 = all_52_11
% 243.04/49.64    (62)   ~ (e2 = e1)
% 243.04/49.64  
% 243.04/49.64  Begin of proof
% 243.04/49.64  | 
% 243.04/49.64  | BETA: splitting (22) gives:
% 243.04/49.64  | 
% 243.04/49.64  | Case 1:
% 243.04/49.64  | | 
% 243.04/49.64  | |   (63)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 243.04/49.64  | |           e3)
% 243.04/49.64  | | 
% 243.04/49.64  | | REF_CLOSE: (16), (26), (49), (50), (56), (63) are inconsistent by sub-proof
% 243.04/49.64  | |            #1401.
% 243.04/49.64  | | 
% 243.04/49.64  | Case 2:
% 243.04/49.64  | | 
% 243.04/49.64  | |   (64)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 243.04/49.64  | |           e3)
% 243.04/49.64  | | 
% 243.04/49.64  | | BETA: splitting (64) gives:
% 243.04/49.64  | | 
% 243.04/49.64  | | Case 1:
% 243.04/49.64  | | | 
% 243.04/49.64  | | |   (65)  all_58_4 = e3 & op(e3, e1) = e3
% 243.04/49.64  | | | 
% 243.04/49.64  | | | ALPHA: (65) implies:
% 243.04/49.64  | | |   (66)  all_58_4 = e3
% 243.04/49.64  | | | 
% 243.04/49.64  | | | BETA: splitting (25) gives:
% 243.04/49.64  | | | 
% 243.04/49.64  | | | Case 1:
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | |   (67)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 243.04/49.64  | | | |           = e3)
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | | BETA: splitting (67) gives:
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | | Case 1:
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | |   (68)  all_58_0 = e3 & op(e3, e3) = e3
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | ALPHA: (68) implies:
% 243.04/49.64  | | | | |   (69)  op(e3, e3) = e3
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | REF_CLOSE: (16), (26), (56), (69) are inconsistent by sub-proof #1578.
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | Case 2:
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | |   (70)  all_58_2 = e3 & op(e2, e3) = e3
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | ALPHA: (70) implies:
% 243.04/49.64  | | | | |   (71)  all_58_2 = e3
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | BETA: splitting (15) gives:
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | Case 1:
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | |   (72)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2,
% 243.04/49.64  | | | | | |             e2) = e2)
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | | BETA: splitting (72) gives:
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | | Case 1:
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | |   (73)  all_58_2 = e2 & op(e2, e3) = e2
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | | REF_CLOSE: (31), (71), (73) are inconsistent by sub-proof #1224.
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | Case 2:
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | |   (74)  all_58_3 = e2 & op(e2, e2) = e2
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | | REF_CLOSE: (5), (60), (74) are inconsistent by sub-proof #1082.
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | End of split
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | Case 2:
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | |   (75)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2,
% 243.04/49.64  | | | | | |             e0) = e2)
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | | BETA: splitting (75) gives:
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | | Case 1:
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | |   (76)  all_58_5 = e2 & op(e2, e1) = e2
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | | ALPHA: (76) implies:
% 243.04/49.64  | | | | | | |   (77)  all_58_5 = e2
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | | COMBINE_EQS: (54), (77) imply:
% 243.04/49.64  | | | | | | |   (78)  e2 = e1
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | | SIMP: (78) implies:
% 243.04/49.64  | | | | | | |   (79)  e2 = e1
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | | COMBINE_EQS: (59), (79) imply:
% 243.04/49.64  | | | | | | |   (80)  all_58_9 = e1
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | | REF_CLOSE: (2), (3), (5), (26), (31), (45), (56), (57), (62),
% 243.04/49.64  | | | | | | |            (66), (80) are inconsistent by sub-proof #1292.
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | Case 2:
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | |   (81)  all_58_10 = e2 & op(e2, e0) = e2
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | | REF_CLOSE: (1), (4), (6), (7), (9), (10), (11), (12), (13), (14),
% 243.04/49.64  | | | | | | |            (17), (18), (19), (20), (21), (23), (24), (27), (28),
% 243.04/49.64  | | | | | | |            (29), (30), (33), (34), (35), (36), (37), (38), (39),
% 243.04/49.64  | | | | | | |            (40), (41), (42), (44), (46), (47), (48), (49), (50),
% 243.04/49.64  | | | | | | |            (51), (52), (53), (55), (56), (58), (61), (81) are
% 243.04/49.64  | | | | | | |            inconsistent by sub-proof #1075.
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | End of split
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | End of split
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | End of split
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | Case 2:
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | |   (82)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 243.04/49.64  | | | |           = e3)
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | | BETA: splitting (82) gives:
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | | Case 1:
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | |   (83)  all_58_6 = e3 & op(e1, e3) = e3
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | ALPHA: (83) implies:
% 243.04/49.64  | | | | |   (84)  all_58_6 = e3
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | REF_CLOSE: (3), (16), (22), (26), (31), (32), (43), (49), (50), (56),
% 243.04/49.64  | | | | |            (66), (84) are inconsistent by sub-proof #1074.
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | Case 2:
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | |   (85)  all_58_12 = e3 & op(e0, e3) = e3
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | ALPHA: (85) implies:
% 243.04/49.64  | | | | |   (86)  all_58_12 = e3
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | REF_CLOSE: (8), (31), (86) are inconsistent by sub-proof #1552.
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | End of split
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | End of split
% 243.04/49.64  | | | 
% 243.04/49.64  | | Case 2:
% 243.04/49.64  | | | 
% 243.04/49.64  | | |   (87)  all_58_9 = e3 & op(e3, e0) = e3
% 243.04/49.64  | | | 
% 243.04/49.64  | | | ALPHA: (87) implies:
% 243.04/49.64  | | |   (88)  op(e3, e0) = e3
% 243.04/49.64  | | | 
% 243.04/49.64  | | | REF_CLOSE: (31), (43), (56), (88) are inconsistent by sub-proof #2125.
% 243.04/49.64  | | | 
% 243.04/49.64  | | End of split
% 243.04/49.64  | | 
% 243.04/49.64  | End of split
% 243.04/49.64  | 
% 243.04/49.64  End of proof
% 243.04/49.64  
% 243.04/49.64  Sub-proof #1074 shows that the following formulas are inconsistent:
% 243.04/49.64  ----------------------------------------------------------------
% 243.04/49.64    (1)   ~ (e3 = e0)
% 243.04/49.64    (2)  all_58_6 = e3
% 243.04/49.64    (3)   ~ (e3 = e1)
% 243.04/49.64    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.64         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.64    (5)  op(e3, e3) = e1
% 243.04/49.64    (6)   ~ (e3 = e2)
% 243.04/49.64    (7)  all_58_6 = e0
% 243.04/49.64    (8)  op(e3, e0) = e2
% 243.04/49.64    (9)   ~ (all_52_4 = e3)
% 243.04/49.64    (10)  op(e3, e2) = all_52_4
% 243.04/49.64    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.64    (12)  all_58_4 = e3
% 243.04/49.64  
% 243.04/49.64  Begin of proof
% 243.04/49.64  | 
% 243.04/49.64  | COMBINE_EQS: (2), (7) imply:
% 243.04/49.64  |   (13)  e3 = e0
% 243.04/49.64  | 
% 243.04/49.64  | SIMP: (13) implies:
% 243.04/49.64  |   (14)  e3 = e0
% 243.04/49.64  | 
% 243.04/49.64  | COMBINE_EQS: (12), (14) imply:
% 243.04/49.64  |   (15)  all_58_4 = e0
% 243.04/49.64  | 
% 243.04/49.64  | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (15) are
% 243.04/49.64  |            inconsistent by sub-proof #1400.
% 243.04/49.64  | 
% 243.04/49.64  End of proof
% 243.04/49.64  
% 243.04/49.64  Sub-proof #1075 shows that the following formulas are inconsistent:
% 243.04/49.64  ----------------------------------------------------------------
% 243.04/49.64    (1)  all_56_21 = e2
% 243.04/49.64    (2)   ~ (all_52_7 = e2)
% 243.04/49.64    (3)   ~ (all_52_11 = e2)
% 243.04/49.64    (4)  all_54_13 = all_52_7
% 243.04/49.64    (5)   ~ (all_52_11 = e1)
% 243.04/49.64    (6)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.04/49.64           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.04/49.64             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.04/49.64           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.04/49.64             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.04/49.64           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.64           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.04/49.64           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.04/49.64           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.04/49.64           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.64           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.04/49.64             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.04/49.64           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.04/49.64           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 243.04/49.64           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.04/49.64           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.04/49.64           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.04/49.64           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.04/49.64             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.04/49.64           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.64           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 243.04/49.64           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.04/49.64           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.04/49.64           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.64           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.04/49.64             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.04/49.64           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.64           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.64    (7)   ~ (all_52_7 = all_52_11)
% 243.04/49.64    (8)  op(e1, e0) = all_52_14
% 243.04/49.64    (9)   ~ (all_52_13 = e1)
% 243.04/49.64    (10)  all_58_10 = e2 & op(e2, e0) = e2
% 243.04/49.64    (11)  op(e0, e3) = all_52_3
% 243.04/49.64    (12)  all_54_11 = all_52_14
% 243.04/49.64    (13)   ~ (all_52_12 = e1)
% 243.04/49.64    (14)   ~ (all_52_12 = all_52_14)
% 243.04/49.64    (15)   ~ (all_52_8 = e1)
% 243.04/49.64    (16)   ~ (all_52_12 = all_52_13)
% 243.04/49.64    (17)  all_54_2 = all_52_8
% 243.04/49.64    (18)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.04/49.64    (19)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.04/49.64    (20)   ~ (all_52_14 = e2)
% 243.04/49.64    (21)   ~ (all_52_8 = all_52_12)
% 243.04/49.64    (22)  op(e3, e1) = all_52_8
% 243.04/49.64    (23)   ~ (all_52_14 = e1)
% 243.04/49.64    (24)   ~ (all_52_7 = e1)
% 243.04/49.64    (25)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.04/49.64    (26)   ~ (all_52_3 = all_52_11)
% 243.04/49.64    (27)  all_56_31 = e1
% 243.04/49.64    (28)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.04/49.64    (29)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.04/49.64    (30)  op(e3, e0) = all_52_12
% 243.04/49.64    (31)  all_56_11 = e0
% 243.04/49.64    (32)  op(e2, e3) = all_52_1
% 243.04/49.64    (33)   ~ (all_52_12 = e2)
% 243.04/49.64    (34)   ~ (all_52_1 = all_52_13)
% 243.04/49.64    (35)  all_54_7 = all_52_13
% 243.04/49.64    (36)   ~ (all_52_13 = all_52_14)
% 243.04/49.64    (37)   ~ (all_52_4 = e3)
% 243.04/49.64    (38)  op(e3, e2) = all_52_4
% 243.04/49.64    (39)   ~ (all_52_8 = all_52_11)
% 243.04/49.64    (40)   ~ (all_52_7 = e0)
% 243.04/49.64    (41)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.04/49.64    (42)  all_54_3 = all_52_12
% 243.04/49.64    (43)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.64    (44)   ~ (all_52_8 = e2)
% 243.04/49.64    (45)  all_54_14 = all_52_11
% 243.04/49.64  
% 243.04/49.64  Begin of proof
% 243.04/49.64  | 
% 243.04/49.64  | ALPHA: (10) implies:
% 243.04/49.64  |   (46)  op(e2, e0) = e2
% 243.04/49.64  | 
% 243.04/49.64  | BETA: splitting (41) gives:
% 243.04/49.64  | 
% 243.04/49.64  | Case 1:
% 243.04/49.64  | | 
% 243.04/49.64  | |   (47)  all_54_13 = e3
% 243.04/49.64  | | 
% 243.04/49.64  | | COMBINE_EQS: (4), (47) imply:
% 243.04/49.64  | |   (48)  all_52_7 = e3
% 243.04/49.64  | | 
% 243.04/49.64  | | REDUCE: (7), (48) imply:
% 243.04/49.64  | |   (49)   ~ (all_52_11 = e3)
% 243.04/49.64  | | 
% 243.04/49.64  | | SIMP: (49) implies:
% 243.04/49.64  | |   (50)   ~ (all_52_11 = e3)
% 243.04/49.64  | | 
% 243.04/49.64  | | BETA: splitting (25) gives:
% 243.04/49.64  | | 
% 243.04/49.64  | | Case 1:
% 243.04/49.64  | | | 
% 243.04/49.64  | | |   (51)  all_54_14 = e3
% 243.04/49.64  | | | 
% 243.04/49.64  | | | COMBINE_EQS: (45), (51) imply:
% 243.04/49.64  | | |   (52)  all_52_11 = e3
% 243.04/49.64  | | | 
% 243.04/49.64  | | | REDUCE: (50), (52) imply:
% 243.04/49.64  | | |   (53)  $false
% 243.04/49.64  | | | 
% 243.04/49.64  | | | CLOSE: (53) is inconsistent.
% 243.04/49.64  | | | 
% 243.04/49.64  | | Case 2:
% 243.04/49.64  | | | 
% 243.04/49.64  | | |   (54)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.04/49.64  | | | 
% 243.04/49.64  | | | BETA: splitting (54) gives:
% 243.04/49.64  | | | 
% 243.04/49.64  | | | Case 1:
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | |   (55)  all_54_14 = e2
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | | COMBINE_EQS: (45), (55) imply:
% 243.04/49.64  | | | |   (56)  all_52_11 = e2
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | | REDUCE: (3), (56) imply:
% 243.04/49.64  | | | |   (57)  $false
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | | CLOSE: (57) is inconsistent.
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | Case 2:
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | |   (58)   ~ (all_54_14 = e2)
% 243.04/49.64  | | | |   (59)  all_54_14 = e1 | all_54_14 = e0
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | | BETA: splitting (59) gives:
% 243.04/49.64  | | | | 
% 243.04/49.64  | | | | Case 1:
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | |   (60)  all_54_14 = e1
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | REF_CLOSE: (5), (45), (60) are inconsistent by sub-proof #1937.
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | Case 2:
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | |   (61)  all_54_14 = e0
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | COMBINE_EQS: (45), (61) imply:
% 243.04/49.64  | | | | |   (62)  all_52_11 = e0
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | SIMP: (62) implies:
% 243.04/49.64  | | | | |   (63)  all_52_11 = e0
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | REDUCE: (26), (63) imply:
% 243.04/49.64  | | | | |   (64)   ~ (all_52_3 = e0)
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | REDUCE: (39), (63) imply:
% 243.04/49.64  | | | | |   (65)   ~ (all_52_8 = e0)
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | REDUCE: (3), (63) imply:
% 243.04/49.64  | | | | |   (66)   ~ (e2 = e0)
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | SIMP: (66) implies:
% 243.04/49.64  | | | | |   (67)   ~ (e2 = e0)
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | BETA: splitting (29) gives:
% 243.04/49.64  | | | | | 
% 243.04/49.64  | | | | | Case 1:
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | |   (68)  all_54_2 = e3
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | | COMBINE_EQS: (17), (68) imply:
% 243.04/49.64  | | | | | |   (69)  all_52_8 = e3
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | | SIMP: (69) implies:
% 243.04/49.64  | | | | | |   (70)  all_52_8 = e3
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | | REDUCE: (21), (70) imply:
% 243.04/49.64  | | | | | |   (71)   ~ (all_52_12 = e3)
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | | SIMP: (71) implies:
% 243.04/49.64  | | | | | |   (72)   ~ (all_52_12 = e3)
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | | BETA: splitting (19) gives:
% 243.04/49.64  | | | | | | 
% 243.04/49.64  | | | | | | Case 1:
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | |   (73)  all_54_3 = e3
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | | REF_CLOSE: (42), (72), (73) are inconsistent by sub-proof #2057.
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | Case 2:
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | |   (74)   ~ (all_54_3 = e3)
% 243.04/49.64  | | | | | | |   (75)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | | BETA: splitting (75) gives:
% 243.04/49.64  | | | | | | | 
% 243.04/49.64  | | | | | | | Case 1:
% 243.04/49.64  | | | | | | | | 
% 243.04/49.64  | | | | | | | |   (76)  all_54_3 = e2
% 243.04/49.64  | | | | | | | | 
% 243.04/49.64  | | | | | | | | REF_CLOSE: (33), (42), (76) are inconsistent by sub-proof #2290.
% 243.04/49.64  | | | | | | | | 
% 243.04/49.64  | | | | | | | Case 2:
% 243.04/49.64  | | | | | | | | 
% 243.04/49.64  | | | | | | | |   (77)  all_54_3 = e1 | all_54_3 = e0
% 243.04/49.64  | | | | | | | | 
% 243.04/49.64  | | | | | | | | BETA: splitting (6) gives:
% 243.04/49.64  | | | | | | | | 
% 243.04/49.64  | | | | | | | | Case 1:
% 243.04/49.64  | | | | | | | | | 
% 243.04/49.64  | | | | | | | | |   (78)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 243.04/49.64  | | | | | | | | |           ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.04/49.64  | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.04/49.64  | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 243.04/49.64  | | | | | | | | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.04/49.64  | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3)
% 243.04/49.64  | | | | | | | | |           = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.04/49.64  | | | | | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.04/49.64  | | | | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 243.04/49.64  | | | | | | | | |           = e3 & op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17
% 243.04/49.64  | | | | | | | | |           = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.04/49.64  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1)
% 243.04/49.64  | | | | | | | | |           = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 243.04/49.64  | | | | | | | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.04/49.64  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0)
% 243.04/49.64  | | | | | | | | |           = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 243.04/49.64  | | | | | | | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.04/49.64  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 243.04/49.64  | | | | | | | | |           = e0 & op(e0, e3) = e0)
% 243.04/49.64  | | | | | | | | | 
% 243.04/49.64  | | | | | | | | | BETA: splitting (78) gives:
% 243.04/49.64  | | | | | | | | | 
% 243.04/49.64  | | | | | | | | | Case 1:
% 243.04/49.64  | | | | | | | | | | 
% 243.04/49.64  | | | | | | | | | |   (79)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 243.04/49.64  | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.04/49.64  | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.04/49.64  | | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 243.04/49.64  | | | | | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.04/49.64  | | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.04/49.64  | | | | | | | | | |             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 243.04/49.64  | | | | | | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.04/49.64  | | | | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.64  | | | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 243.04/49.64  | | | | | | | | | |           e3)
% 243.04/49.64  | | | | | | | | | | 
% 243.04/49.64  | | | | | | | | | | BETA: splitting (79) gives:
% 243.04/49.64  | | | | | | | | | | 
% 243.04/49.64  | | | | | | | | | | Case 1:
% 243.04/49.64  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | |   (80)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 243.04/49.65  | | | | | | | | | | |         &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.04/49.65  | | | | | | | | | | |         (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.04/49.65  | | | | | | | | | | |         e3
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | ALPHA: (80) implies:
% 243.04/49.65  | | | | | | | | | | |   (81)  op(e3, e2) = e3
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | REF_CLOSE: (37), (38), (43), (81) are inconsistent by
% 243.04/49.65  | | | | | | | | | | |            sub-proof #2192.
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | Case 2:
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | |   (82)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 243.04/49.65  | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.04/49.65  | | | | | | | | | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.04/49.65  | | | | | | | | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 243.04/49.65  | | | | | | | | | | |           e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.04/49.65  | | | | | | | | | | |           ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.04/49.65  | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | BETA: splitting (82) gives:
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | Case 1:
% 243.04/49.65  | | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | |   (83)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.04/49.65  | | | | | | | | | | | |         &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.04/49.65  | | | | | | | | | | | |         (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 243.04/49.65  | | | | | | | | | | | |         e2
% 243.04/49.65  | | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | | ALPHA: (83) implies:
% 243.04/49.65  | | | | | | | | | | | |   (84)  op(e2, e3) = e2
% 243.04/49.65  | | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | | REF_CLOSE: (9), (12), (13), (14), (16), (18), (20), (23),
% 243.04/49.65  | | | | | | | | | | | |            (28), (32), (34), (35), (36), (42), (43), (77),
% 243.04/49.65  | | | | | | | | | | | |            (84) are inconsistent by sub-proof #2172.
% 243.04/49.65  | | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | Case 2:
% 243.04/49.65  | | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | |   (85)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 243.04/49.65  | | | | | | | | | | | |           e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.04/49.65  | | | | | | | | | | | |         &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 243.04/49.65  | | | | | | | | | | | |           e3) = e3
% 243.04/49.65  | | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | | ALPHA: (85) implies:
% 243.04/49.65  | | | | | | | | | | | |   (86)   ~ (all_56_31 = e1)
% 243.04/49.65  | | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | | REDUCE: (27), (86) imply:
% 243.04/49.65  | | | | | | | | | | | |   (87)  $false
% 243.04/49.65  | | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | | CLOSE: (87) is inconsistent.
% 243.04/49.65  | | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | End of split
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | End of split
% 243.04/49.65  | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | Case 2:
% 243.04/49.65  | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | |   (88)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3)
% 243.04/49.65  | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.04/49.65  | | | | | | | | | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.04/49.65  | | | | | | | | | |           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 243.04/49.65  | | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.04/49.65  | | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.04/49.65  | | | | | | | | | |             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 243.04/49.65  | | | | | | | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.04/49.65  | | | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.04/49.65  | | | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 243.04/49.65  | | | | | | | | | |           e0)
% 243.04/49.65  | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | BETA: splitting (88) gives:
% 243.04/49.65  | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | Case 1:
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | |   (89)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 243.04/49.65  | | | | | | | | | | |           e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.04/49.65  | | | | | | | | | | |         &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 243.04/49.65  | | | | | | | | | | |           e3) = e1
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | ALPHA: (89) implies:
% 243.04/49.65  | | | | | | | | | | |   (90)  op(e3, e1) = e1
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | REF_CLOSE: (15), (22), (43), (90) are inconsistent by
% 243.04/49.65  | | | | | | | | | | |            sub-proof #2309.
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | Case 2:
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | |   (91)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 243.04/49.65  | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.04/49.65  | | | | | | | | | | |             e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.04/49.65  | | | | | | | | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 243.04/49.65  | | | | | | | | | | |           e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.04/49.65  | | | | | | | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.04/49.65  | | | | | | | | | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | | REF_CLOSE: (11), (30), (43), (64), (72), (91) are
% 243.04/49.65  | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 243.04/49.65  | | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | End of split
% 243.04/49.65  | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | End of split
% 243.04/49.65  | | | | | | | | | 
% 243.04/49.65  | | | | | | | | Case 2:
% 243.04/49.65  | | | | | | | | | 
% 243.04/49.65  | | | | | | | | |   (92)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 243.04/49.65  | | | | | | | | |           &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.65  | | | | | | | | |           (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.04/49.65  | | | | | | | | |           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~
% 243.04/49.65  | | | | | | | | |           (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.04/49.65  | | | | | | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1)
% 243.04/49.65  | | | | | | | | |           = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 243.04/49.65  | | | | | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.04/49.65  | | | | | | | | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.04/49.65  | | | | | | | | |           & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.04/49.65  | | | | | | | | |           e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.04/49.65  | | | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.04/49.65  | | | | | | | | |           (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.04/49.65  | | | | | | | | |           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 243.04/49.65  | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.04/49.65  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0)
% 243.04/49.65  | | | | | | | | |           = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 243.04/49.65  | | | | | | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 243.04/49.65  | | | | | | | | |             = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.04/49.65  | | | | | | | | |           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.65  | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | BETA: splitting (92) gives:
% 243.04/49.65  | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | Case 1:
% 243.04/49.65  | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | |   (93)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.04/49.65  | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.04/49.65  | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 243.04/49.65  | | | | | | | | | |             e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 & 
% 243.04/49.65  | | | | | | | | | |           ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.04/49.65  | | | | | | | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.04/49.65  | | | | | | | | | |             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 243.04/49.65  | | | | | | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.65  | | | | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.65  | | | | | | | | | |           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 243.04/49.65  | | | | | | | | | |           e2)
% 243.04/49.65  | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | REF_CLOSE: (1), (27), (31), (93) are inconsistent by
% 243.04/49.65  | | | | | | | | | |            sub-proof #1077.
% 243.04/49.65  | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | Case 2:
% 243.04/49.65  | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | |   (94)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.04/49.65  | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.04/49.65  | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.04/49.65  | | | | | | | | | |             e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 & 
% 243.04/49.65  | | | | | | | | | |           ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.04/49.65  | | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.04/49.65  | | | | | | | | | |             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 243.04/49.65  | | | | | | | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.04/49.65  | | | | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.65  | | | | | | | | | |           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 243.04/49.65  | | | | | | | | | |           e0)
% 243.04/49.65  | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | | REF_CLOSE: (8), (23), (27), (43), (46), (67), (94) are
% 243.04/49.65  | | | | | | | | | |            inconsistent by sub-proof #1076.
% 243.04/49.65  | | | | | | | | | | 
% 243.04/49.65  | | | | | | | | | End of split
% 243.04/49.65  | | | | | | | | | 
% 243.04/49.65  | | | | | | | | End of split
% 243.04/49.65  | | | | | | | | 
% 243.04/49.65  | | | | | | | End of split
% 243.04/49.65  | | | | | | | 
% 243.04/49.65  | | | | | | End of split
% 243.04/49.65  | | | | | | 
% 243.04/49.65  | | | | | Case 2:
% 243.04/49.65  | | | | | | 
% 243.04/49.65  | | | | | |   (95)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.04/49.65  | | | | | | 
% 243.04/49.65  | | | | | | REF_CLOSE: (15), (17), (44), (65), (95) are inconsistent by
% 243.04/49.65  | | | | | |            sub-proof #1335.
% 243.04/49.65  | | | | | | 
% 243.04/49.65  | | | | | End of split
% 243.04/49.65  | | | | | 
% 243.04/49.65  | | | | End of split
% 243.04/49.65  | | | | 
% 243.04/49.65  | | | End of split
% 243.04/49.65  | | | 
% 243.04/49.65  | | End of split
% 243.04/49.65  | | 
% 243.04/49.65  | Case 2:
% 243.04/49.65  | | 
% 243.04/49.65  | |   (96)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.04/49.65  | | 
% 243.04/49.65  | | REF_CLOSE: (2), (4), (24), (40), (96) are inconsistent by sub-proof #1648.
% 243.04/49.65  | | 
% 243.04/49.65  | End of split
% 243.04/49.65  | 
% 243.04/49.65  End of proof
% 243.04/49.65  
% 243.04/49.65  Sub-proof #1076 shows that the following formulas are inconsistent:
% 243.04/49.65  ----------------------------------------------------------------
% 243.04/49.65    (1)   ~ (e2 = e0)
% 243.04/49.65    (2)  op(e1, e0) = all_52_14
% 243.04/49.65    (3)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.04/49.65             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 243.04/49.65           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.04/49.65             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.04/49.65           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 243.04/49.65           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.65           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.65    (4)   ~ (all_52_14 = e1)
% 243.04/49.65    (5)  op(e2, e0) = e2
% 243.04/49.65    (6)  all_56_31 = e1
% 243.04/49.65    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.65  
% 243.04/49.65  Begin of proof
% 243.04/49.65  | 
% 243.04/49.65  | BETA: splitting (3) gives:
% 243.04/49.65  | 
% 243.04/49.65  | Case 1:
% 243.04/49.65  | | 
% 243.04/49.65  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.04/49.65  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 243.04/49.65  | |        & op(e0, e2) = e0
% 243.04/49.65  | | 
% 243.04/49.65  | | ALPHA: (8) implies:
% 243.04/49.65  | |   (9)  op(e2, e0) = e0
% 243.04/49.65  | | 
% 243.04/49.65  | | REF_CLOSE: (1), (5), (7), (9) are inconsistent by sub-proof #2121.
% 243.04/49.65  | | 
% 243.04/49.65  | Case 2:
% 243.04/49.65  | | 
% 243.04/49.65  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.65  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.04/49.65  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.04/49.65  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.04/49.65  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.65  | | 
% 243.04/49.65  | | REF_CLOSE: (2), (4), (6), (7), (10) are inconsistent by sub-proof #2269.
% 243.04/49.65  | | 
% 243.04/49.65  | End of split
% 243.04/49.65  | 
% 243.04/49.65  End of proof
% 243.04/49.65  
% 243.04/49.65  Sub-proof #1077 shows that the following formulas are inconsistent:
% 243.04/49.65  ----------------------------------------------------------------
% 243.04/49.65    (1)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 243.04/49.65             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.04/49.65           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.04/49.65             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.04/49.65           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 243.04/49.65           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.65           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.04/49.65    (2)  all_56_31 = e1
% 243.04/49.65    (3)  all_56_21 = e2
% 243.04/49.65    (4)  all_56_11 = e0
% 243.04/49.65  
% 243.04/49.65  Begin of proof
% 243.04/49.65  | 
% 243.04/49.65  | BETA: splitting (1) gives:
% 243.04/49.65  | 
% 243.04/49.65  | Case 1:
% 243.04/49.65  | | 
% 243.04/49.65  | |   (5)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 243.04/49.65  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 243.04/49.65  | |        & op(e1, e2) = e2
% 243.04/49.65  | | 
% 243.04/49.65  | | ALPHA: (5) implies:
% 243.04/49.65  | |   (6)   ~ (all_56_31 = e1)
% 243.04/49.65  | | 
% 243.04/49.65  | | REDUCE: (2), (6) imply:
% 243.04/49.65  | |   (7)  $false
% 243.04/49.65  | | 
% 243.04/49.65  | | CLOSE: (7) is inconsistent.
% 243.04/49.65  | | 
% 243.04/49.65  | Case 2:
% 243.04/49.65  | | 
% 243.04/49.65  | |   (8)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.04/49.65  | |            = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) =
% 243.04/49.65  | |          e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.04/49.65  | |          (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.65  | |          (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.04/49.65  | | 
% 243.04/49.65  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #1245.
% 243.04/49.65  | | 
% 243.04/49.65  | End of split
% 243.04/49.65  | 
% 243.04/49.65  End of proof
% 243.04/49.65  
% 243.04/49.65  Sub-proof #1078 shows that the following formulas are inconsistent:
% 243.04/49.65  ----------------------------------------------------------------
% 243.04/49.65    (1)  op(e0, e0) = e1
% 243.04/49.65    (2)  op(e0, e1) = all_52_11
% 243.04/49.65    (3)   ~ (e2 = e0)
% 243.04/49.65    (4)   ~ (all_52_11 = e2)
% 243.04/49.65    (5)   ~ (all_52_11 = e1)
% 243.04/49.65    (6)  op(e0, e2) = e2
% 243.04/49.65    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.65             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.04/49.65               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.65               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.65    (8)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.04/49.65    (9)  all_58_12 = e3
% 243.04/49.65    (10)   ~ (all_52_11 = e0)
% 243.04/49.65    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.65            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.65    (12)   ~ (e1 = e0)
% 243.04/49.65    (13)  all_54_14 = all_52_11
% 243.04/49.65  
% 243.04/49.65  Begin of proof
% 243.04/49.65  | 
% 243.04/49.65  | BETA: splitting (8) gives:
% 243.04/49.65  | 
% 243.04/49.65  | Case 1:
% 243.04/49.65  | | 
% 243.04/49.65  | |   (14)  all_54_14 = e3
% 243.04/49.65  | | 
% 243.04/49.65  | | COMBINE_EQS: (13), (14) imply:
% 243.04/49.65  | |   (15)  all_52_11 = e3
% 243.04/49.65  | | 
% 243.04/49.65  | | REDUCE: (10), (15) imply:
% 243.04/49.65  | |   (16)   ~ (e3 = e0)
% 243.04/49.65  | | 
% 243.04/49.65  | | REDUCE: (2), (15) imply:
% 243.04/49.65  | |   (17)  op(e0, e1) = e3
% 243.04/49.65  | | 
% 243.04/49.65  | | REF_CLOSE: (1), (3), (6), (7), (9), (11), (12), (16), (17) are inconsistent
% 243.04/49.65  | |            by sub-proof #1634.
% 243.04/49.65  | | 
% 243.04/49.65  | Case 2:
% 243.04/49.65  | | 
% 243.04/49.65  | |   (18)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.04/49.65  | | 
% 243.04/49.65  | | REF_CLOSE: (4), (5), (10), (13), (18) are inconsistent by sub-proof #1798.
% 243.04/49.65  | | 
% 243.04/49.65  | End of split
% 243.04/49.65  | 
% 243.04/49.65  End of proof
% 243.04/49.65  
% 243.04/49.65  Sub-proof #1079 shows that the following formulas are inconsistent:
% 243.04/49.65  ----------------------------------------------------------------
% 243.04/49.65    (1)  op(e0, e0) = e1
% 243.04/49.65    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.04/49.65    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.04/49.65             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.04/49.65           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.04/49.65         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.04/49.65           $i(all_56_7))
% 243.04/49.65    (4)   ~ (e3 = e0)
% 243.04/49.65    (5)   ~ (e2 = e0)
% 243.04/49.65    (6)  all_56_3 = e2
% 243.04/49.65    (7)  op(e1, e3) = e3
% 243.04/49.65    (8)   ~ (e3 = e1)
% 243.04/49.65    (9)  op(e2, e2) = e0
% 243.04/49.65    (10)  all_58_2 = e2
% 243.04/49.65    (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.04/49.65          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.04/49.65    (12)  op(e3, e3) = e1
% 243.04/49.65    (13)  all_54_4 = all_52_1
% 243.04/49.65    (14)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.65              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.04/49.65                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.65                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.65    (15)  op(e3, e1) = all_52_8
% 243.04/49.65    (16)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.04/49.65          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.04/49.65    (17)   ~ (e3 = e2)
% 243.04/49.65    (18)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.04/49.65          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.04/49.65    (19)   ~ (all_52_1 = e0)
% 243.04/49.65    (20)  op(e2, e3) = all_52_1
% 243.04/49.65    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.65            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.65    (22)  all_58_14 = e3
% 243.04/49.65    (23)   ~ (e1 = e0)
% 243.04/49.65    (24)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.04/49.65          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.04/49.65            e1)
% 243.04/49.65    (25)   ~ (all_52_1 = e3)
% 243.04/49.65    (26)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.65          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.04/49.65            e2)
% 243.04/49.65    (27)  all_56_1 = e1
% 243.04/49.65    (28)   ~ (e2 = e1)
% 243.04/49.65    (29)   ~ (all_52_1 = e1)
% 243.04/49.65    (30)   ~ (all_52_8 = e3)
% 243.04/49.65  
% 243.04/49.65  Begin of proof
% 243.04/49.65  | 
% 243.04/49.65  | BETA: splitting (18) gives:
% 243.04/49.65  | 
% 243.04/49.65  | Case 1:
% 243.04/49.65  | | 
% 243.04/49.65  | |   (31)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 243.04/49.65  | |           e0)
% 243.04/49.65  | | 
% 243.04/49.65  | | REF_CLOSE: (12), (19), (20), (21), (23), (31) are inconsistent by sub-proof
% 243.04/49.65  | |            #1272.
% 243.04/49.65  | | 
% 243.04/49.65  | Case 2:
% 243.04/49.65  | | 
% 243.04/49.65  | |   (32)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 243.04/49.65  | |           e0)
% 243.04/49.65  | | 
% 243.04/49.65  | | BETA: splitting (32) gives:
% 243.04/49.65  | | 
% 243.04/49.65  | | Case 1:
% 243.04/49.65  | | | 
% 243.04/49.65  | | |   (33)  all_58_6 = e0 & op(e1, e3) = e0
% 243.04/49.65  | | | 
% 243.04/49.65  | | | ALPHA: (33) implies:
% 243.04/49.65  | | |   (34)  all_58_6 = e0
% 243.04/49.65  | | | 
% 243.04/49.65  | | | REF_CLOSE: (4), (5), (8), (11), (12), (14), (16), (17), (18), (20), (21),
% 243.04/49.65  | | |            (22), (23), (24), (25), (26), (28), (34) are inconsistent by
% 243.04/49.65  | | |            sub-proof #1199.
% 243.04/49.65  | | | 
% 243.04/49.65  | | Case 2:
% 243.04/49.65  | | | 
% 243.04/49.65  | | |   (35)  all_58_12 = e0 & op(e0, e3) = e0
% 243.04/49.65  | | | 
% 243.04/49.65  | | | ALPHA: (35) implies:
% 243.04/49.65  | | |   (36)  all_58_12 = e0
% 243.04/49.65  | | |   (37)  op(e0, e3) = e0
% 243.04/49.65  | | | 
% 243.04/49.65  | | | BETA: splitting (3) gives:
% 243.04/49.65  | | | 
% 243.04/49.65  | | | Case 1:
% 243.04/49.65  | | | | 
% 243.04/49.66  | | | |   (38)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 243.04/49.66  | | | |           op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 243.04/49.66  | | | | 
% 243.04/49.66  | | | | BETA: splitting (38) gives:
% 243.04/49.66  | | | | 
% 243.04/49.66  | | | | Case 1:
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | |   (39)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | | ALPHA: (39) implies:
% 243.04/49.66  | | | | |   (40)  op(e3, all_56_1) = e3
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | | REDUCE: (27), (40) imply:
% 243.04/49.66  | | | | |   (41)  op(e3, e1) = e3
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | | REF_CLOSE: (15), (21), (30), (41) are inconsistent by sub-proof #2260.
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | Case 2:
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | |   (42)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3
% 243.04/49.66  | | | | |         & $i(all_56_3)
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | | ALPHA: (42) implies:
% 243.04/49.66  | | | | |   (43)  op(e2, all_56_3) = e2
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | | REF_CLOSE: (2), (4), (6), (8), (9), (10), (11), (12), (13), (16),
% 243.04/49.66  | | | | |            (19), (20), (21), (25), (29), (36), (43) are inconsistent
% 243.04/49.66  | | | | |            by sub-proof #1080.
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | End of split
% 243.04/49.66  | | | | 
% 243.04/49.66  | | | Case 2:
% 243.04/49.66  | | | | 
% 243.04/49.66  | | | |   (44)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 243.04/49.66  | | | |           $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 &
% 243.04/49.66  | | | |           op(e0, e3) = all_56_7 & $i(all_56_7))
% 243.04/49.66  | | | | 
% 243.04/49.66  | | | | REF_CLOSE: (1), (2), (7), (8), (13), (19), (21), (23), (29), (37), (44)
% 243.04/49.66  | | | |            are inconsistent by sub-proof #1152.
% 243.04/49.66  | | | | 
% 243.04/49.66  | | | End of split
% 243.04/49.66  | | | 
% 243.04/49.66  | | End of split
% 243.04/49.66  | | 
% 243.04/49.66  | End of split
% 243.04/49.66  | 
% 243.04/49.66  End of proof
% 243.04/49.66  
% 243.04/49.66  Sub-proof #1080 shows that the following formulas are inconsistent:
% 243.04/49.66  ----------------------------------------------------------------
% 243.04/49.66    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.04/49.66    (2)   ~ (e3 = e0)
% 243.04/49.66    (3)  all_56_3 = e2
% 243.04/49.66    (4)   ~ (e3 = e1)
% 243.04/49.66    (5)  op(e2, e2) = e0
% 243.04/49.66    (6)  all_58_2 = e2
% 243.04/49.66    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.04/49.66         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.04/49.66    (8)  op(e3, e3) = e1
% 243.04/49.66    (9)  all_54_4 = all_52_1
% 243.04/49.66    (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.04/49.66          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.04/49.66    (11)   ~ (all_52_1 = e0)
% 243.04/49.66    (12)  all_58_12 = e0
% 243.04/49.66    (13)  op(e2, e3) = all_52_1
% 243.04/49.66    (14)  op(e2, all_56_3) = e2
% 243.04/49.66    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.66    (16)   ~ (all_52_1 = e3)
% 243.04/49.66    (17)   ~ (all_52_1 = e1)
% 243.04/49.66  
% 243.04/49.66  Begin of proof
% 243.04/49.66  | 
% 243.04/49.66  | REDUCE: (3), (14) imply:
% 243.04/49.66  |   (18)  op(e2, e2) = e2
% 243.04/49.66  | 
% 243.04/49.66  | BETA: splitting (1) gives:
% 243.04/49.66  | 
% 243.04/49.66  | Case 1:
% 243.04/49.66  | | 
% 243.04/49.66  | |   (19)  all_54_4 = e2
% 243.04/49.66  | | 
% 243.04/49.66  | | COMBINE_EQS: (9), (19) imply:
% 243.04/49.66  | |   (20)  all_52_1 = e2
% 243.04/49.66  | | 
% 243.04/49.66  | | SIMP: (20) implies:
% 243.04/49.66  | |   (21)  all_52_1 = e2
% 243.04/49.66  | | 
% 243.04/49.66  | | REDUCE: (16), (21) imply:
% 243.04/49.66  | |   (22)   ~ (e3 = e2)
% 243.04/49.66  | | 
% 243.04/49.66  | | SIMP: (22) implies:
% 243.04/49.66  | |   (23)   ~ (e3 = e2)
% 243.04/49.66  | | 
% 243.04/49.66  | | REDUCE: (17), (21) imply:
% 243.04/49.66  | |   (24)   ~ (e2 = e1)
% 243.04/49.66  | | 
% 243.04/49.66  | | REDUCE: (11), (21) imply:
% 243.04/49.66  | |   (25)   ~ (e2 = e0)
% 243.04/49.66  | | 
% 243.04/49.66  | | GROUND_INST: instantiating (15) with e0, e2, e2, e2, simplifying with (5),
% 243.04/49.66  | |              (18) gives:
% 243.04/49.66  | |   (26)  e2 = e0
% 243.04/49.66  | | 
% 243.04/49.66  | | COMBINE_EQS: (6), (26) imply:
% 243.04/49.66  | |   (27)  all_58_2 = e0
% 243.04/49.66  | | 
% 243.04/49.66  | | REF_CLOSE: (2), (4), (7), (8), (10), (12), (13), (15), (16), (23), (24),
% 243.04/49.66  | |            (25), (27) are inconsistent by sub-proof #1149.
% 243.04/49.66  | | 
% 243.04/49.66  | Case 2:
% 243.04/49.66  | | 
% 243.04/49.66  | |   (28)  all_54_4 = e1 | all_54_4 = e0
% 243.04/49.66  | | 
% 243.04/49.66  | | REF_CLOSE: (9), (11), (17), (28) are inconsistent by sub-proof #1922.
% 243.04/49.66  | | 
% 243.04/49.66  | End of split
% 243.04/49.66  | 
% 243.04/49.66  End of proof
% 243.04/49.66  
% 243.04/49.66  Sub-proof #1081 shows that the following formulas are inconsistent:
% 243.04/49.66  ----------------------------------------------------------------
% 243.04/49.66    (1)  op(e0, e0) = e1
% 243.04/49.66    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.04/49.66         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.66    (3)   ~ (e3 = e0)
% 243.04/49.66    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 243.04/49.66    (5)   ~ (e2 = e0)
% 243.04/49.66    (6)   ~ (all_52_7 = e3)
% 243.04/49.66    (7)  op(e0, e2) = e2
% 243.04/49.66    (8)   ~ (e3 = e1)
% 243.04/49.66    (9)  all_58_2 = e2
% 243.04/49.66    (10)  op(e3, e3) = e1
% 243.04/49.66    (11)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.66              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.04/49.66                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.66                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.66    (12)   ~ (e3 = e2)
% 243.04/49.66    (13)  all_58_15 = e1
% 243.04/49.66    (14)  op(e0, e2) = all_52_7
% 243.04/49.66    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.66    (16)  all_58_14 = e3
% 243.04/49.66    (17)   ~ (e1 = e0)
% 243.04/49.66  
% 243.04/49.66  Begin of proof
% 243.04/49.66  | 
% 243.04/49.66  | BETA: splitting (4) gives:
% 243.04/49.66  | 
% 243.04/49.66  | Case 1:
% 243.04/49.66  | | 
% 243.04/49.66  | |   (18)  all_58_0 = e3 & op(e3, e3) = e3
% 243.04/49.66  | | 
% 243.04/49.66  | | ALPHA: (18) implies:
% 243.04/49.66  | |   (19)  op(e3, e3) = e3
% 243.04/49.66  | | 
% 243.04/49.66  | | REF_CLOSE: (8), (10), (15), (19) are inconsistent by sub-proof #1578.
% 243.04/49.66  | | 
% 243.04/49.66  | Case 2:
% 243.04/49.66  | | 
% 243.04/49.66  | |   (20)  all_58_2 = e3 & op(e2, e3) = e3
% 243.04/49.66  | | 
% 243.04/49.66  | | ALPHA: (20) implies:
% 243.04/49.66  | |   (21)  all_58_2 = e3
% 243.04/49.66  | | 
% 243.04/49.66  | | COMBINE_EQS: (9), (21) imply:
% 243.04/49.66  | |   (22)  e3 = e2
% 243.04/49.66  | | 
% 243.04/49.66  | | COMBINE_EQS: (16), (22) imply:
% 243.04/49.66  | |   (23)  all_58_14 = e2
% 243.04/49.66  | | 
% 243.04/49.66  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (11), (12), (13), (14), (15),
% 243.04/49.66  | |            (17), (23) are inconsistent by sub-proof #1636.
% 243.04/49.66  | | 
% 243.04/49.66  | End of split
% 243.04/49.66  | 
% 243.04/49.66  End of proof
% 243.04/49.66  
% 243.04/49.66  Sub-proof #1082 shows that the following formulas are inconsistent:
% 243.04/49.66  ----------------------------------------------------------------
% 243.04/49.66    (1)  all_58_3 = e2 & op(e2, e2) = e2
% 243.04/49.66    (2)  all_58_3 = e0
% 243.04/49.66    (3)   ~ (e2 = e0)
% 243.04/49.66  
% 243.04/49.66  Begin of proof
% 243.04/49.66  | 
% 243.04/49.66  | ALPHA: (1) implies:
% 243.04/49.66  |   (4)  all_58_3 = e2
% 243.04/49.66  | 
% 243.04/49.66  | COMBINE_EQS: (2), (4) imply:
% 243.04/49.66  |   (5)  e2 = e0
% 243.04/49.66  | 
% 243.04/49.66  | SIMP: (5) implies:
% 243.04/49.66  |   (6)  e2 = e0
% 243.04/49.66  | 
% 243.04/49.66  | REDUCE: (3), (6) imply:
% 243.04/49.66  |   (7)  $false
% 243.04/49.66  | 
% 243.04/49.66  | CLOSE: (7) is inconsistent.
% 243.04/49.66  | 
% 243.04/49.66  End of proof
% 243.04/49.66  
% 243.04/49.66  Sub-proof #1083 shows that the following formulas are inconsistent:
% 243.04/49.66  ----------------------------------------------------------------
% 243.04/49.66    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.04/49.66    (2)  op(e1, e1) = all_6_2
% 243.04/49.66    (3)  op(e1, e0) = all_52_14
% 243.04/49.66    (4)   ~ (all_6_2 = e0)
% 243.04/49.66    (5)   ~ (all_52_14 = e0)
% 243.04/49.66    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.66  
% 243.04/49.66  Begin of proof
% 243.04/49.66  | 
% 243.04/49.66  | BETA: splitting (1) gives:
% 243.04/49.66  | 
% 243.04/49.66  | Case 1:
% 243.04/49.66  | | 
% 243.04/49.66  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 243.04/49.66  | | 
% 243.04/49.66  | | REF_CLOSE: (2), (4), (6), (7) are inconsistent by sub-proof #1833.
% 243.04/49.66  | | 
% 243.04/49.66  | Case 2:
% 243.04/49.66  | | 
% 243.04/49.66  | |   (8)  all_58_11 = e0 & op(e1, e0) = e0
% 243.04/49.66  | | 
% 243.04/49.66  | | ALPHA: (8) implies:
% 243.04/49.66  | |   (9)  op(e1, e0) = e0
% 243.04/49.66  | | 
% 243.04/49.66  | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #2323.
% 243.04/49.66  | | 
% 243.04/49.66  | End of split
% 243.04/49.66  | 
% 243.04/49.66  End of proof
% 243.04/49.66  
% 243.04/49.66  Sub-proof #1084 shows that the following formulas are inconsistent:
% 243.04/49.66  ----------------------------------------------------------------
% 243.04/49.66    (1)   ~ (all_52_1 = all_52_3)
% 243.04/49.66    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.04/49.66             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.04/49.66           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.04/49.66         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.04/49.66           $i(all_56_7))
% 243.04/49.66    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.04/49.66    (4)   ~ (all_52_3 = e1)
% 243.04/49.66    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.04/49.66         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.66    (6)   ~ (e3 = e0)
% 243.04/49.66    (7)   ~ (e2 = e0)
% 243.04/49.66    (8)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.04/49.66         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.04/49.66    (9)  op(e1, e1) = all_6_2
% 243.04/49.66    (10)   ~ (all_52_1 = all_52_2)
% 243.04/49.66    (11)  op(e1, e0) = all_52_14
% 243.04/49.66    (12)  op(e0, e3) = all_52_3
% 243.04/49.66    (13)   ~ (e3 = e1)
% 243.04/49.66    (14)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.04/49.66          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.66    (15)   ~ (all_52_2 = all_52_3)
% 243.04/49.66    (16)  op(e2, e2) = e0
% 243.04/49.66    (17)   ~ (all_52_8 = e1)
% 243.04/49.66    (18)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.04/49.66            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 243.04/49.66              e1) = all_10_1 & $i(all_10_1))
% 243.04/49.66    (19)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.04/49.66          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.04/49.66    (20)  op(e3, e3) = e1
% 243.04/49.66    (21)   ~ (all_52_9 = e0)
% 243.04/49.66    (22)  all_54_4 = all_52_1
% 243.04/49.66    (23)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.66              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.04/49.66                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.66                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.66    (24)   ~ (all_6_2 = e3)
% 243.04/49.66    (25)  op(e3, e1) = all_52_8
% 243.04/49.66    (26)  op(e2, e1) = all_52_9
% 243.04/49.66    (27)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.04/49.66          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.04/49.66    (28)   ~ (e3 = e2)
% 243.04/49.66    (29)  all_58_6 = e0
% 243.04/49.66    (30)   ~ (all_6_2 = e0)
% 243.04/49.66    (31)  all_54_12 = all_52_3
% 243.04/49.66    (32)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.04/49.66          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.04/49.66    (33)  all_38_2 = e1
% 243.04/49.66    (34)  op(e2, e3) = all_52_1
% 243.04/49.66    (35)  op(e1, e3) = e0
% 243.04/49.66    (36)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.04/49.66    (37)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.04/49.66          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.04/49.66    (38)   ~ (all_52_13 = all_52_14)
% 243.04/49.66    (39)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.66    (40)  op(e0, e0) = e0
% 243.04/49.66    (41)  op(e1, e3) = all_52_2
% 243.04/49.66    (42)   ~ (e1 = e0)
% 243.04/49.66    (43)  op(e2, e0) = all_52_13
% 243.04/49.66    (44)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.04/49.66          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.04/49.66            e1)
% 243.04/49.66    (45)  all_58_3 = e0
% 243.04/49.66    (46)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.66          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.04/49.66            e2)
% 243.04/49.66    (47)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.04/49.66          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.04/49.66    (48)  all_56_1 = e1
% 243.04/49.66    (49)   ~ (e2 = e1)
% 243.04/49.66    (50)   ~ (all_52_1 = e1)
% 243.04/49.66    (51)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 243.04/49.66            op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 243.04/49.66              e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 243.04/49.66  
% 243.04/49.66  Begin of proof
% 243.04/49.66  | 
% 243.04/49.66  | BETA: splitting (14) gives:
% 243.04/49.66  | 
% 243.04/49.66  | Case 1:
% 243.04/49.66  | | 
% 243.04/49.66  | |   (52)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 243.04/49.66  | |           e0)
% 243.04/49.66  | | 
% 243.04/49.66  | | BETA: splitting (52) gives:
% 243.04/49.66  | | 
% 243.04/49.66  | | Case 1:
% 243.04/49.66  | | | 
% 243.04/49.66  | | |   (53)  all_58_4 = e0 & op(e3, e1) = e0
% 243.04/49.66  | | | 
% 243.04/49.66  | | | ALPHA: (53) implies:
% 243.04/49.66  | | |   (54)  all_58_4 = e0
% 243.04/49.66  | | |   (55)  op(e3, e1) = e0
% 243.04/49.66  | | | 
% 243.04/49.66  | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (12), (15), (16),
% 243.04/49.66  | | |            (17), (18), (19), (20), (22), (23), (24), (25), (27), (29),
% 243.04/49.66  | | |            (31), (32), (33), (34), (35), (36), (37), (38), (39), (41),
% 243.04/49.66  | | |            (43), (44), (45), (46), (47), (48), (50), (51), (54), (55) are
% 243.04/49.66  | | |            inconsistent by sub-proof #1193.
% 243.04/49.66  | | | 
% 243.04/49.66  | | Case 2:
% 243.04/49.66  | | | 
% 243.04/49.66  | | |   (56)  all_58_5 = e0 & op(e2, e1) = e0
% 243.04/49.66  | | | 
% 243.04/49.66  | | | REF_CLOSE: (21), (26), (39), (56) are inconsistent by sub-proof #2088.
% 243.04/49.66  | | | 
% 243.04/49.66  | | End of split
% 243.04/49.66  | | 
% 243.04/49.66  | Case 2:
% 243.04/49.66  | | 
% 243.04/49.66  | |   (57)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 243.04/49.66  | |           e0)
% 243.04/49.66  | | 
% 243.04/49.66  | | BETA: splitting (57) gives:
% 243.04/49.66  | | 
% 243.04/49.66  | | Case 1:
% 243.04/49.66  | | | 
% 243.04/49.66  | | |   (58)  all_58_8 = e0 & op(e1, e1) = e0
% 243.04/49.66  | | | 
% 243.04/49.66  | | | REF_CLOSE: (9), (30), (39), (58) are inconsistent by sub-proof #1833.
% 243.04/49.66  | | | 
% 243.04/49.66  | | Case 2:
% 243.04/49.66  | | | 
% 243.04/49.66  | | |   (59)  all_58_14 = e0 & op(e0, e1) = e0
% 243.04/49.66  | | | 
% 243.04/49.66  | | | ALPHA: (59) implies:
% 243.04/49.66  | | |   (60)  all_58_14 = e0
% 243.04/49.66  | | |   (61)  op(e0, e1) = e0
% 243.04/49.66  | | | 
% 243.04/49.66  | | | BETA: splitting (44) gives:
% 243.04/49.66  | | | 
% 243.04/49.66  | | | Case 1:
% 243.04/49.66  | | | | 
% 243.04/49.66  | | | |   (62)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0,
% 243.04/49.66  | | | |             e2) = e1)
% 243.04/49.66  | | | | 
% 243.04/49.66  | | | | BETA: splitting (62) gives:
% 243.04/49.66  | | | | 
% 243.04/49.66  | | | | Case 1:
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | |   (63)  all_58_12 = e1 & op(e0, e3) = e1
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | | REF_CLOSE: (4), (12), (39), (63) are inconsistent by sub-proof #2276.
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | Case 2:
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | |   (64)  all_58_13 = e1 & op(e0, e2) = e1
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | | ALPHA: (64) implies:
% 243.04/49.66  | | | | |   (65)  all_58_13 = e1
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | | BETA: splitting (46) gives:
% 243.04/49.66  | | | | | 
% 243.04/49.66  | | | | | Case 1:
% 243.04/49.66  | | | | | | 
% 243.04/49.66  | | | | | |   (66)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 243.04/49.66  | | | | | |           op(e0, e2) = e2)
% 243.04/49.66  | | | | | | 
% 243.04/49.66  | | | | | | BETA: splitting (66) gives:
% 243.04/49.66  | | | | | | 
% 243.04/49.66  | | | | | | Case 1:
% 243.04/49.66  | | | | | | | 
% 243.04/49.67  | | | | | | |   (67)  all_58_12 = e2 & op(e0, e3) = e2
% 243.04/49.67  | | | | | | | 
% 243.04/49.67  | | | | | | | ALPHA: (67) implies:
% 243.04/49.67  | | | | | | |   (68)  all_58_12 = e2
% 243.04/49.67  | | | | | | | 
% 243.04/49.67  | | | | | | | BETA: splitting (5) gives:
% 243.04/49.67  | | | | | | | 
% 243.04/49.67  | | | | | | | Case 1:
% 243.04/49.67  | | | | | | | | 
% 243.04/49.67  | | | | | | | |   (69)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 243.04/49.67  | | | | | | | |           op(e0, e2) = e3)
% 243.04/49.67  | | | | | | | | 
% 243.04/49.67  | | | | | | | | BETA: splitting (69) gives:
% 243.04/49.67  | | | | | | | | 
% 243.04/49.67  | | | | | | | | Case 1:
% 243.04/49.67  | | | | | | | | | 
% 243.04/49.67  | | | | | | | | |   (70)  all_58_12 = e3 & op(e0, e3) = e3
% 243.04/49.67  | | | | | | | | | 
% 243.04/49.67  | | | | | | | | | REF_CLOSE: (28), (68), (70) are inconsistent by sub-proof
% 243.04/49.67  | | | | | | | | |            #2085.
% 243.04/49.67  | | | | | | | | | 
% 243.04/49.67  | | | | | | | | Case 2:
% 243.04/49.67  | | | | | | | | | 
% 243.04/49.67  | | | | | | | | |   (71)  all_58_13 = e3 & op(e0, e2) = e3
% 243.04/49.67  | | | | | | | | | 
% 243.04/49.67  | | | | | | | | | REF_CLOSE: (13), (65), (71) are inconsistent by sub-proof
% 243.04/49.67  | | | | | | | | |            #2084.
% 243.04/49.67  | | | | | | | | | 
% 243.04/49.67  | | | | | | | | End of split
% 243.04/49.67  | | | | | | | | 
% 243.04/49.67  | | | | | | | Case 2:
% 243.04/49.67  | | | | | | | | 
% 243.04/49.67  | | | | | | | |   (72)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 243.04/49.67  | | | | | | | |           op(e0, e0) = e3)
% 243.04/49.67  | | | | | | | | 
% 243.04/49.67  | | | | | | | | REF_CLOSE: (6), (39), (40), (61), (72) are inconsistent by
% 243.04/49.67  | | | | | | | |            sub-proof #1085.
% 243.04/49.67  | | | | | | | | 
% 243.04/49.67  | | | | | | | End of split
% 243.04/49.67  | | | | | | | 
% 243.04/49.67  | | | | | | Case 2:
% 243.04/49.67  | | | | | | | 
% 243.04/49.67  | | | | | | |   (73)  all_58_13 = e2 & op(e0, e2) = e2
% 243.04/49.67  | | | | | | | 
% 243.04/49.67  | | | | | | | REF_CLOSE: (49), (65), (73) are inconsistent by sub-proof #2078.
% 243.04/49.67  | | | | | | | 
% 243.04/49.67  | | | | | | End of split
% 243.04/49.67  | | | | | | 
% 243.04/49.67  | | | | | Case 2:
% 243.04/49.67  | | | | | | 
% 243.04/49.67  | | | | | |   (74)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 243.04/49.67  | | | | | |           op(e0, e0) = e2)
% 243.04/49.67  | | | | | | 
% 243.04/49.67  | | | | | | REF_CLOSE: (7), (39), (40), (60), (74) are inconsistent by sub-proof
% 243.04/49.67  | | | | | |            #2076.
% 243.04/49.67  | | | | | | 
% 243.04/49.67  | | | | | End of split
% 243.04/49.67  | | | | | 
% 243.04/49.67  | | | | End of split
% 243.04/49.67  | | | | 
% 243.04/49.67  | | | Case 2:
% 243.04/49.67  | | | | 
% 243.04/49.67  | | | |   (75)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 243.04/49.67  | | | |             e0) = e1)
% 243.04/49.67  | | | | 
% 243.04/49.67  | | | | REF_CLOSE: (39), (40), (42), (61), (75) are inconsistent by sub-proof
% 243.04/49.67  | | | |            #2074.
% 243.04/49.67  | | | | 
% 243.04/49.67  | | | End of split
% 243.04/49.67  | | | 
% 243.04/49.67  | | End of split
% 243.04/49.67  | | 
% 243.04/49.67  | End of split
% 243.04/49.67  | 
% 243.04/49.67  End of proof
% 243.04/49.67  
% 243.04/49.67  Sub-proof #1085 shows that the following formulas are inconsistent:
% 243.04/49.67  ----------------------------------------------------------------
% 243.04/49.67    (1)   ~ (e3 = e0)
% 243.04/49.67    (2)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.67    (3)  op(e0, e1) = e0
% 243.04/49.67    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.67    (5)  op(e0, e0) = e0
% 243.04/49.67  
% 243.04/49.67  Begin of proof
% 243.04/49.67  | 
% 243.04/49.67  | BETA: splitting (2) gives:
% 243.04/49.67  | 
% 243.04/49.67  | Case 1:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (6)  all_58_14 = e3 & op(e0, e1) = e3
% 243.04/49.67  | | 
% 243.04/49.67  | | ALPHA: (6) implies:
% 243.04/49.67  | |   (7)  op(e0, e1) = e3
% 243.04/49.67  | | 
% 243.04/49.67  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #2164.
% 243.04/49.67  | | 
% 243.04/49.67  | Case 2:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (8)  all_58_15 = e3 & op(e0, e0) = e3
% 243.04/49.67  | | 
% 243.04/49.67  | | ALPHA: (8) implies:
% 243.04/49.67  | |   (9)  op(e0, e0) = e3
% 243.04/49.67  | | 
% 243.04/49.67  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2079.
% 243.04/49.67  | | 
% 243.04/49.67  | End of split
% 243.04/49.67  | 
% 243.04/49.67  End of proof
% 243.04/49.67  
% 243.04/49.67  Sub-proof #1086 shows that the following formulas are inconsistent:
% 243.04/49.67  ----------------------------------------------------------------
% 243.04/49.67    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.04/49.67    (2)  op(e1, e0) = all_52_14
% 243.04/49.67    (3)   ~ (all_52_14 = e1)
% 243.04/49.67    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.67    (5)  op(e1, e1) = e0
% 243.04/49.67    (6)   ~ (e1 = e0)
% 243.04/49.67  
% 243.04/49.67  Begin of proof
% 243.04/49.67  | 
% 243.04/49.67  | BETA: splitting (1) gives:
% 243.04/49.67  | 
% 243.04/49.67  | Case 1:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (7)  all_58_8 = e1 & op(e1, e1) = e1
% 243.04/49.67  | | 
% 243.04/49.67  | | ALPHA: (7) implies:
% 243.04/49.67  | |   (8)  op(e1, e1) = e1
% 243.04/49.67  | | 
% 243.04/49.67  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2220.
% 243.04/49.67  | | 
% 243.04/49.67  | Case 2:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (9)  all_58_11 = e1 & op(e1, e0) = e1
% 243.04/49.67  | | 
% 243.04/49.67  | | ALPHA: (9) implies:
% 243.04/49.67  | |   (10)  op(e1, e0) = e1
% 243.04/49.67  | | 
% 243.04/49.67  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #2304.
% 243.04/49.67  | | 
% 243.04/49.67  | End of split
% 243.04/49.67  | 
% 243.04/49.67  End of proof
% 243.04/49.67  
% 243.04/49.67  Sub-proof #1087 shows that the following formulas are inconsistent:
% 243.04/49.67  ----------------------------------------------------------------
% 243.04/49.67    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.67         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.67    (2)   ~ (all_8_2 = e0)
% 243.04/49.67    (3)   ~ (all_52_3 = e1)
% 243.04/49.67    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.04/49.67         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.67    (5)   ~ (e3 = e0)
% 243.04/49.67    (6)   ~ (e2 = e0)
% 243.04/49.67    (7)  op(e1, e2) = all_52_6
% 243.04/49.67    (8)  all_58_9 = e0
% 243.04/49.67    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.04/49.67         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.04/49.67    (10)  op(e0, e3) = all_52_3
% 243.04/49.67    (11)   ~ (all_52_6 = e0)
% 243.04/49.67    (12)   ~ (e3 = e1)
% 243.04/49.67    (13)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.67          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.67    (14)  op(e3, e3) = e1
% 243.04/49.67    (15)   ~ (e3 = e2)
% 243.04/49.67    (16)  op(e2, e2) = all_8_2
% 243.04/49.67    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.67    (18)  op(e0, e0) = e0
% 243.04/49.67    (19)   ~ (e1 = e0)
% 243.04/49.67    (20)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.04/49.67          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.04/49.67            e1)
% 243.04/49.67    (21)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.67          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.04/49.67            e2)
% 243.04/49.67    (22)   ~ (e2 = e1)
% 243.04/49.67  
% 243.04/49.67  Begin of proof
% 243.04/49.67  | 
% 243.04/49.67  | BETA: splitting (9) gives:
% 243.04/49.67  | 
% 243.04/49.67  | Case 1:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (23)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 243.04/49.67  | |           e0)
% 243.04/49.67  | | 
% 243.04/49.67  | | REF_CLOSE: (1), (2), (5), (6), (8), (12), (13), (14), (15), (16), (17),
% 243.04/49.67  | |            (22), (23) are inconsistent by sub-proof #1088.
% 243.04/49.67  | | 
% 243.04/49.67  | Case 2:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (24)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 243.04/49.67  | |           e0)
% 243.04/49.67  | | 
% 243.04/49.67  | | BETA: splitting (24) gives:
% 243.04/49.67  | | 
% 243.04/49.67  | | Case 1:
% 243.04/49.67  | | | 
% 243.04/49.67  | | |   (25)  all_58_7 = e0 & op(e1, e2) = e0
% 243.04/49.67  | | | 
% 243.04/49.67  | | | REF_CLOSE: (7), (11), (17), (25) are inconsistent by sub-proof #2022.
% 243.04/49.67  | | | 
% 243.04/49.67  | | Case 2:
% 243.04/49.67  | | | 
% 243.04/49.67  | | |   (26)  all_58_13 = e0 & op(e0, e2) = e0
% 243.04/49.67  | | | 
% 243.04/49.67  | | | ALPHA: (26) implies:
% 243.04/49.67  | | |   (27)  op(e0, e2) = e0
% 243.04/49.67  | | | 
% 243.04/49.67  | | | REF_CLOSE: (3), (4), (5), (6), (10), (12), (15), (17), (18), (19), (20),
% 243.04/49.67  | | |            (21), (22), (27) are inconsistent by sub-proof #1770.
% 243.04/49.67  | | | 
% 243.04/49.67  | | End of split
% 243.04/49.67  | | 
% 243.04/49.67  | End of split
% 243.04/49.67  | 
% 243.04/49.67  End of proof
% 243.04/49.67  
% 243.04/49.67  Sub-proof #1088 shows that the following formulas are inconsistent:
% 243.04/49.67  ----------------------------------------------------------------
% 243.04/49.67    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.67         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.67    (2)   ~ (all_8_2 = e0)
% 243.04/49.67    (3)   ~ (e3 = e0)
% 243.04/49.67    (4)   ~ (e2 = e0)
% 243.04/49.67    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 243.04/49.67    (6)  all_58_9 = e0
% 243.04/49.67    (7)   ~ (e3 = e1)
% 243.04/49.67    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.67         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.67    (9)  op(e3, e3) = e1
% 243.04/49.67    (10)   ~ (e3 = e2)
% 243.04/49.67    (11)  op(e2, e2) = all_8_2
% 243.04/49.67    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.67    (13)   ~ (e2 = e1)
% 243.04/49.67  
% 243.04/49.67  Begin of proof
% 243.04/49.67  | 
% 243.04/49.67  | BETA: splitting (5) gives:
% 243.04/49.67  | 
% 243.04/49.67  | Case 1:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (14)  all_58_1 = e0 & op(e3, e2) = e0
% 243.04/49.67  | | 
% 243.04/49.67  | | ALPHA: (14) implies:
% 243.04/49.67  | |   (15)  all_58_1 = e0
% 243.04/49.67  | | 
% 243.04/49.67  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12), (13), (15) are
% 243.04/49.67  | |            inconsistent by sub-proof #1089.
% 243.04/49.67  | | 
% 243.04/49.67  | Case 2:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (16)  all_58_3 = e0 & op(e2, e2) = e0
% 243.04/49.67  | | 
% 243.04/49.67  | | REF_CLOSE: (2), (11), (12), (16) are inconsistent by sub-proof #1992.
% 243.04/49.67  | | 
% 243.04/49.67  | End of split
% 243.04/49.67  | 
% 243.04/49.67  End of proof
% 243.04/49.67  
% 243.04/49.67  Sub-proof #1089 shows that the following formulas are inconsistent:
% 243.04/49.67  ----------------------------------------------------------------
% 243.04/49.67    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.67         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.67    (2)   ~ (e3 = e0)
% 243.04/49.67    (3)   ~ (e2 = e0)
% 243.04/49.67    (4)  all_58_9 = e0
% 243.04/49.67    (5)  all_58_1 = e0
% 243.04/49.67    (6)   ~ (e3 = e1)
% 243.04/49.67    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.67         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.67    (8)  op(e3, e3) = e1
% 243.04/49.67    (9)   ~ (e3 = e2)
% 243.04/49.67    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.67    (11)   ~ (e2 = e1)
% 243.04/49.67  
% 243.04/49.67  Begin of proof
% 243.04/49.67  | 
% 243.04/49.67  | BETA: splitting (7) gives:
% 243.04/49.67  | 
% 243.04/49.67  | Case 1:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (12)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 243.04/49.67  | |           e3)
% 243.04/49.67  | | 
% 243.04/49.67  | | BETA: splitting (12) gives:
% 243.04/49.67  | | 
% 243.04/49.67  | | Case 1:
% 243.04/49.67  | | | 
% 243.04/49.67  | | |   (13)  all_58_0 = e3 & op(e3, e3) = e3
% 243.04/49.67  | | | 
% 243.04/49.67  | | | ALPHA: (13) implies:
% 243.04/49.67  | | |   (14)  op(e3, e3) = e3
% 243.04/49.67  | | | 
% 243.04/49.67  | | | REF_CLOSE: (6), (8), (10), (14) are inconsistent by sub-proof #1578.
% 243.04/49.67  | | | 
% 243.04/49.67  | | Case 2:
% 243.04/49.67  | | | 
% 243.04/49.67  | | |   (15)  all_58_1 = e3 & op(e3, e2) = e3
% 243.04/49.67  | | | 
% 243.04/49.67  | | | ALPHA: (15) implies:
% 243.04/49.67  | | |   (16)  all_58_1 = e3
% 243.04/49.67  | | | 
% 243.04/49.67  | | | COMBINE_EQS: (5), (16) imply:
% 243.04/49.67  | | |   (17)  e3 = e0
% 243.04/49.67  | | | 
% 243.04/49.67  | | | SIMP: (17) implies:
% 243.04/49.67  | | |   (18)  e3 = e0
% 243.04/49.67  | | | 
% 243.04/49.67  | | | REDUCE: (2), (18) imply:
% 243.04/49.67  | | |   (19)  $false
% 243.04/49.67  | | | 
% 243.04/49.67  | | | CLOSE: (19) is inconsistent.
% 243.04/49.67  | | | 
% 243.04/49.67  | | End of split
% 243.04/49.67  | | 
% 243.04/49.67  | Case 2:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (20)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 243.04/49.67  | |           e3)
% 243.04/49.67  | | 
% 243.04/49.67  | | BETA: splitting (20) gives:
% 243.04/49.67  | | 
% 243.04/49.67  | | Case 1:
% 243.04/49.67  | | | 
% 243.04/49.67  | | |   (21)  all_58_4 = e3 & op(e3, e1) = e3
% 243.04/49.67  | | | 
% 243.04/49.67  | | | ALPHA: (21) implies:
% 243.04/49.67  | | |   (22)  all_58_4 = e3
% 243.04/49.67  | | | 
% 243.04/49.67  | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (11), (22) are inconsistent
% 243.04/49.67  | | |            by sub-proof #1097.
% 243.04/49.67  | | | 
% 243.04/49.67  | | Case 2:
% 243.04/49.67  | | | 
% 243.04/49.67  | | |   (23)  all_58_9 = e3 & op(e3, e0) = e3
% 243.04/49.67  | | | 
% 243.04/49.67  | | | REF_CLOSE: (2), (4), (23) are inconsistent by sub-proof #1621.
% 243.04/49.67  | | | 
% 243.04/49.67  | | End of split
% 243.04/49.67  | | 
% 243.04/49.67  | End of split
% 243.04/49.67  | 
% 243.04/49.67  End of proof
% 243.04/49.67  
% 243.04/49.67  Sub-proof #1090 shows that the following formulas are inconsistent:
% 243.04/49.67  ----------------------------------------------------------------
% 243.04/49.67    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.67         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.67    (2)   ~ (e3 = e0)
% 243.04/49.67    (3)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.67    (4)   ~ (e2 = e0)
% 243.04/49.67    (5)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.04/49.67         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.04/49.67    (6)  op(e1, e1) = all_6_2
% 243.04/49.67    (7)   ~ (e3 = e1)
% 243.04/49.67    (8)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.04/49.67         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.67    (9)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.67         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.67    (10)  op(e3, e3) = e1
% 243.04/49.67    (11)  op(e2, e1) = all_52_9
% 243.04/49.67    (12)   ~ (e3 = e2)
% 243.04/49.67    (13)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.04/49.67          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.04/49.67    (14)   ~ (all_6_2 = e0)
% 243.04/49.67    (15)  all_58_15 = e1
% 243.04/49.67    (16)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.67          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.67    (17)   ~ (all_52_4 = e3)
% 243.04/49.67    (18)  op(e3, e2) = all_52_4
% 243.04/49.67    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.67    (20)   ~ (e1 = e0)
% 243.04/49.67    (21)  all_58_4 = e3
% 243.04/49.67    (22)   ~ (e2 = e1)
% 243.04/49.67  
% 243.04/49.67  Begin of proof
% 243.04/49.67  | 
% 243.04/49.67  | BETA: splitting (3) gives:
% 243.04/49.67  | 
% 243.04/49.67  | Case 1:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (23)  all_58_14 = e3 & op(e0, e1) = e3
% 243.04/49.67  | | 
% 243.04/49.67  | | ALPHA: (23) implies:
% 243.04/49.67  | |   (24)  all_58_14 = e3
% 243.04/49.67  | |   (25)  op(e0, e1) = e3
% 243.04/49.67  | | 
% 243.04/49.67  | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (11), (12), (13), (14), (19), (20),
% 243.04/49.67  | |            (21), (22), (24), (25) are inconsistent by sub-proof #1094.
% 243.04/49.67  | | 
% 243.04/49.67  | Case 2:
% 243.04/49.67  | | 
% 243.04/49.67  | |   (26)  all_58_15 = e3 & op(e0, e0) = e3
% 243.04/49.67  | | 
% 243.04/49.67  | | REF_CLOSE: (1), (2), (4), (7), (9), (10), (12), (15), (16), (17), (18),
% 243.04/49.67  | |            (19), (20), (21), (22), (26) are inconsistent by sub-proof #1091.
% 243.04/49.67  | | 
% 243.04/49.67  | End of split
% 243.04/49.67  | 
% 243.04/49.67  End of proof
% 243.04/49.67  
% 243.04/49.67  Sub-proof #1091 shows that the following formulas are inconsistent:
% 243.04/49.67  ----------------------------------------------------------------
% 243.04/49.67    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.67         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.67    (2)   ~ (e3 = e0)
% 243.04/49.67    (3)   ~ (e2 = e0)
% 243.04/49.67    (4)   ~ (e3 = e1)
% 243.04/49.67    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.67         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.67    (6)  op(e3, e3) = e1
% 243.04/49.67    (7)  all_58_15 = e3 & op(e0, e0) = e3
% 243.04/49.67    (8)   ~ (e3 = e2)
% 243.04/49.67    (9)  all_58_15 = e1
% 243.04/49.67    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.67          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.67    (11)   ~ (all_52_4 = e3)
% 243.04/49.67    (12)  op(e3, e2) = all_52_4
% 243.04/49.67    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.67    (14)   ~ (e1 = e0)
% 243.04/49.67    (15)  all_58_4 = e3
% 243.04/49.67    (16)   ~ (e2 = e1)
% 243.04/49.67  
% 243.04/49.67  Begin of proof
% 243.04/49.67  | 
% 243.04/49.67  | ALPHA: (7) implies:
% 243.04/49.67  |   (17)  all_58_15 = e3
% 243.04/49.67  | 
% 243.04/49.68  | COMBINE_EQS: (9), (17) imply:
% 243.04/49.68  |   (18)  e3 = e1
% 243.04/49.68  | 
% 243.04/49.68  | COMBINE_EQS: (15), (18) imply:
% 243.04/49.68  |   (19)  all_58_4 = e1
% 243.04/49.68  | 
% 243.04/49.68  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14),
% 243.04/49.68  |            (16), (19) are inconsistent by sub-proof #1468.
% 243.04/49.68  | 
% 243.04/49.68  End of proof
% 243.04/49.68  
% 243.04/49.68  Sub-proof #1092 shows that the following formulas are inconsistent:
% 243.04/49.68  ----------------------------------------------------------------
% 243.04/49.68    (1)  op(e2, e0) = e3
% 243.04/49.68    (2)  op(e2, e1) = all_52_9
% 243.04/49.68    (3)   ~ (e3 = e2)
% 243.04/49.68    (4)  all_56_31 = e1
% 243.04/49.68    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.68    (6)   ~ (all_52_9 = e1)
% 243.04/49.68    (7)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 243.04/49.68             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.04/49.68           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.04/49.68             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.04/49.68           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 243.04/49.68           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.68           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.04/49.68  
% 243.04/49.68  Begin of proof
% 243.04/49.68  | 
% 243.04/49.68  | BETA: splitting (7) gives:
% 243.04/49.68  | 
% 243.04/49.68  | Case 1:
% 243.04/49.68  | | 
% 243.04/49.68  | |   (8)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 243.04/49.68  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 243.04/49.68  | |        & op(e1, e2) = e2
% 243.04/49.68  | | 
% 243.04/49.68  | | ALPHA: (8) implies:
% 243.04/49.68  | |   (9)   ~ (all_56_31 = e1)
% 243.04/49.68  | | 
% 243.04/49.68  | | REDUCE: (4), (9) imply:
% 243.04/49.68  | |   (10)  $false
% 243.04/49.68  | | 
% 243.04/49.68  | | CLOSE: (10) is inconsistent.
% 243.04/49.68  | | 
% 243.04/49.68  | Case 2:
% 243.04/49.68  | | 
% 243.04/49.68  | |   (11)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.04/49.68  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.04/49.68  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 243.04/49.68  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.04/49.68  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.04/49.68  | | 
% 243.04/49.68  | | BETA: splitting (11) gives:
% 243.04/49.68  | | 
% 243.04/49.68  | | Case 1:
% 243.04/49.68  | | | 
% 243.04/49.68  | | |   (12)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.04/49.68  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.04/49.68  | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 243.04/49.68  | | | 
% 243.04/49.68  | | | ALPHA: (12) implies:
% 243.04/49.68  | | |   (13)  op(e2, e1) = e1
% 243.04/49.68  | | | 
% 243.04/49.68  | | | REF_CLOSE: (2), (5), (6), (13) are inconsistent by sub-proof #2306.
% 243.04/49.68  | | | 
% 243.04/49.68  | | Case 2:
% 243.04/49.68  | | | 
% 243.04/49.68  | | |   (14)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.68  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.04/49.68  | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 243.04/49.68  | | | 
% 243.04/49.68  | | | ALPHA: (14) implies:
% 243.04/49.68  | | |   (15)  op(e2, e0) = e2
% 243.04/49.68  | | | 
% 243.04/49.68  | | | REF_CLOSE: (1), (3), (5), (15) are inconsistent by sub-proof #2152.
% 243.04/49.68  | | | 
% 243.04/49.68  | | End of split
% 243.04/49.68  | | 
% 243.04/49.68  | End of split
% 243.04/49.68  | 
% 243.04/49.68  End of proof
% 243.04/49.68  
% 243.04/49.68  Sub-proof #1093 shows that the following formulas are inconsistent:
% 243.04/49.68  ----------------------------------------------------------------
% 243.04/49.68    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.68         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.68    (2)   ~ (e3 = e0)
% 243.04/49.68    (3)   ~ (e2 = e0)
% 243.04/49.68    (4)  all_58_15 = e3
% 243.04/49.68    (5)   ~ (e3 = e1)
% 243.04/49.68    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.68         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.68    (7)  op(e3, e3) = e1
% 243.04/49.68    (8)   ~ (e3 = e2)
% 243.04/49.68    (9)  all_58_15 = e1
% 243.04/49.68    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.68          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.68    (11)   ~ (all_52_4 = e3)
% 243.04/49.68    (12)  op(e3, e2) = all_52_4
% 243.04/49.68    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.68    (14)   ~ (e1 = e0)
% 243.04/49.68    (15)  all_58_4 = e3
% 243.04/49.68    (16)   ~ (e2 = e1)
% 243.04/49.68  
% 243.04/49.68  Begin of proof
% 243.04/49.68  | 
% 243.04/49.68  | COMBINE_EQS: (4), (9) imply:
% 243.04/49.68  |   (17)  e3 = e1
% 243.04/49.68  | 
% 243.04/49.68  | SIMP: (17) implies:
% 243.04/49.68  |   (18)  e3 = e1
% 243.04/49.68  | 
% 243.04/49.68  | COMBINE_EQS: (15), (18) imply:
% 243.04/49.68  |   (19)  all_58_4 = e1
% 243.04/49.68  | 
% 243.04/49.68  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 243.04/49.68  |            (16), (19) are inconsistent by sub-proof #1468.
% 243.04/49.68  | 
% 243.04/49.68  End of proof
% 243.04/49.68  
% 243.04/49.68  Sub-proof #1094 shows that the following formulas are inconsistent:
% 243.04/49.68  ----------------------------------------------------------------
% 243.04/49.68    (1)   ~ (e3 = e0)
% 243.04/49.68    (2)   ~ (e2 = e0)
% 243.04/49.68    (3)  op(e0, e1) = e3
% 243.04/49.68    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.04/49.68         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.04/49.68    (5)  op(e1, e1) = all_6_2
% 243.04/49.68    (6)   ~ (e3 = e1)
% 243.04/49.68    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.04/49.68         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.68    (8)  op(e2, e1) = all_52_9
% 243.04/49.68    (9)   ~ (e3 = e2)
% 243.04/49.68    (10)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.04/49.68          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.04/49.68    (11)   ~ (all_6_2 = e0)
% 243.04/49.68    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.68    (13)  all_58_14 = e3
% 243.04/49.68    (14)   ~ (e1 = e0)
% 243.04/49.68    (15)  all_58_4 = e3
% 243.04/49.68    (16)   ~ (e2 = e1)
% 243.04/49.68  
% 243.04/49.68  Begin of proof
% 243.04/49.68  | 
% 243.04/49.68  | BETA: splitting (7) gives:
% 243.04/49.68  | 
% 243.04/49.68  | Case 1:
% 243.04/49.68  | | 
% 243.04/49.68  | |   (17)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 243.04/49.68  | |           e0)
% 243.04/49.68  | | 
% 243.04/49.68  | | BETA: splitting (17) gives:
% 243.04/49.68  | | 
% 243.04/49.68  | | Case 1:
% 243.04/49.68  | | | 
% 243.04/49.68  | | |   (18)  all_58_4 = e0 & op(e3, e1) = e0
% 243.04/49.68  | | | 
% 243.04/49.68  | | | REF_CLOSE: (1), (15), (18) are inconsistent by sub-proof #1697.
% 243.04/49.68  | | | 
% 243.04/49.68  | | Case 2:
% 243.04/49.68  | | | 
% 243.04/49.68  | | |   (19)  all_58_5 = e0 & op(e2, e1) = e0
% 243.04/49.68  | | | 
% 243.04/49.68  | | | ALPHA: (19) implies:
% 243.04/49.68  | | |   (20)  op(e2, e1) = e0
% 243.04/49.68  | | | 
% 243.04/49.68  | | | BETA: splitting (10) gives:
% 243.04/49.68  | | | 
% 243.04/49.68  | | | Case 1:
% 243.04/49.68  | | | | 
% 243.04/49.68  | | | |   (21)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 243.04/49.68  | | | |           = e2)
% 243.04/49.68  | | | | 
% 243.04/49.68  | | | | BETA: splitting (21) gives:
% 243.04/49.68  | | | | 
% 243.04/49.68  | | | | Case 1:
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | |   (22)  all_58_4 = e2 & op(e3, e1) = e2
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | | REF_CLOSE: (9), (15), (22) are inconsistent by sub-proof #1476.
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | Case 2:
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | |   (23)  all_58_5 = e2 & op(e2, e1) = e2
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | | ALPHA: (23) implies:
% 243.04/49.68  | | | | |   (24)  op(e2, e1) = e2
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | | REF_CLOSE: (2), (12), (20), (24) are inconsistent by sub-proof #1906.
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | End of split
% 243.04/49.68  | | | | 
% 243.04/49.68  | | | Case 2:
% 243.04/49.68  | | | | 
% 243.04/49.68  | | | |   (25)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 243.04/49.68  | | | |           = e2)
% 243.04/49.68  | | | | 
% 243.04/49.68  | | | | BETA: splitting (25) gives:
% 243.04/49.68  | | | | 
% 243.04/49.68  | | | | Case 1:
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | |   (26)  all_58_8 = e2 & op(e1, e1) = e2
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | | ALPHA: (26) implies:
% 243.04/49.68  | | | | |   (27)  all_58_8 = e2
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | | BETA: splitting (4) gives:
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | | Case 1:
% 243.04/49.68  | | | | | | 
% 243.04/49.68  | | | | | |   (28)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 243.04/49.68  | | | | | |             e1) = e1)
% 243.04/49.68  | | | | | | 
% 243.04/49.68  | | | | | | REF_CLOSE: (6), (8), (12), (14), (15), (20), (28) are inconsistent
% 243.04/49.68  | | | | | |            by sub-proof #2041.
% 243.04/49.68  | | | | | | 
% 243.04/49.68  | | | | | Case 2:
% 243.04/49.68  | | | | | | 
% 243.04/49.68  | | | | | |   (29)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0,
% 243.04/49.68  | | | | | |             e1) = e1)
% 243.04/49.68  | | | | | | 
% 243.04/49.68  | | | | | | BETA: splitting (29) gives:
% 243.04/49.68  | | | | | | 
% 243.04/49.68  | | | | | | Case 1:
% 243.04/49.68  | | | | | | | 
% 243.04/49.68  | | | | | | |   (30)  all_58_8 = e1 & op(e1, e1) = e1
% 243.04/49.68  | | | | | | | 
% 243.04/49.68  | | | | | | | ALPHA: (30) implies:
% 243.04/49.68  | | | | | | |   (31)  all_58_8 = e1
% 243.04/49.68  | | | | | | | 
% 243.04/49.68  | | | | | | | REF_CLOSE: (16), (27), (31) are inconsistent by sub-proof #1802.
% 243.04/49.68  | | | | | | | 
% 243.04/49.68  | | | | | | Case 2:
% 243.04/49.68  | | | | | | | 
% 243.04/49.68  | | | | | | |   (32)  all_58_14 = e1 & op(e0, e1) = e1
% 243.04/49.68  | | | | | | | 
% 243.04/49.68  | | | | | | | ALPHA: (32) implies:
% 243.04/49.68  | | | | | | |   (33)  all_58_14 = e1
% 243.04/49.68  | | | | | | | 
% 243.04/49.68  | | | | | | | REF_CLOSE: (6), (13), (33) are inconsistent by sub-proof #1844.
% 243.04/49.68  | | | | | | | 
% 243.04/49.68  | | | | | | End of split
% 243.04/49.68  | | | | | | 
% 243.04/49.68  | | | | | End of split
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | Case 2:
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | |   (34)  all_58_14 = e2 & op(e0, e1) = e2
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | | REF_CLOSE: (9), (13), (34) are inconsistent by sub-proof #1864.
% 243.04/49.68  | | | | | 
% 243.04/49.68  | | | | End of split
% 243.04/49.68  | | | | 
% 243.04/49.68  | | | End of split
% 243.04/49.68  | | | 
% 243.04/49.68  | | End of split
% 243.04/49.68  | | 
% 243.04/49.68  | Case 2:
% 243.04/49.68  | | 
% 243.04/49.68  | |   (35)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 243.04/49.68  | |           e0)
% 243.04/49.68  | | 
% 243.04/49.68  | | BETA: splitting (35) gives:
% 243.04/49.68  | | 
% 243.04/49.68  | | Case 1:
% 243.04/49.68  | | | 
% 243.04/49.68  | | |   (36)  all_58_8 = e0 & op(e1, e1) = e0
% 243.04/49.68  | | | 
% 243.04/49.68  | | | REF_CLOSE: (5), (11), (12), (36) are inconsistent by sub-proof #1833.
% 243.04/49.68  | | | 
% 243.04/49.68  | | Case 2:
% 243.04/49.68  | | | 
% 243.04/49.68  | | |   (37)  all_58_14 = e0 & op(e0, e1) = e0
% 243.04/49.68  | | | 
% 243.04/49.68  | | | ALPHA: (37) implies:
% 243.04/49.68  | | |   (38)  op(e0, e1) = e0
% 243.04/49.68  | | | 
% 243.04/49.68  | | | REF_CLOSE: (1), (3), (12), (38) are inconsistent by sub-proof #2164.
% 243.04/49.68  | | | 
% 243.04/49.68  | | End of split
% 243.04/49.68  | | 
% 243.04/49.68  | End of split
% 243.04/49.68  | 
% 243.04/49.68  End of proof
% 243.04/49.68  
% 243.04/49.68  Sub-proof #1095 shows that the following formulas are inconsistent:
% 243.04/49.68  ----------------------------------------------------------------
% 243.04/49.68    (1)  op(e1, e2) = all_56_13
% 243.04/49.68    (2)  op(e0, e1) = e2
% 243.04/49.68    (3)  op(e1, e2) = e3
% 243.04/49.68    (4)   ~ (all_52_2 = e1)
% 243.04/49.68    (5)  op(e0, e1) = all_20_1
% 243.04/49.68    (6)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) = all_34_1
% 243.04/49.68           & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1) =
% 243.04/49.68           all_34_1 & $i(all_34_1))
% 243.04/49.68    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.68    (8)  op(e1, e3) = all_52_2
% 243.04/49.68    (9)  op(e1, all_56_13) = e1
% 243.04/49.68  
% 243.04/49.68  Begin of proof
% 243.04/49.68  | 
% 243.04/49.68  | BETA: splitting (6) gives:
% 243.04/49.68  | 
% 243.04/49.68  | Case 1:
% 243.04/49.68  | | 
% 243.04/49.68  | | 
% 243.04/49.68  | | GROUND_INST: instantiating (7) with e3, all_56_13, e2, e1, simplifying with
% 243.04/49.68  | |              (1), (3) gives:
% 243.04/49.68  | |   (10)  all_56_13 = e3
% 243.04/49.68  | | 
% 243.04/49.68  | | REDUCE: (9), (10) imply:
% 243.04/49.68  | |   (11)  op(e1, e3) = e1
% 243.04/49.68  | | 
% 243.04/49.68  | | REF_CLOSE: (4), (7), (8), (11) are inconsistent by sub-proof #1948.
% 243.04/49.68  | | 
% 243.04/49.68  | Case 2:
% 243.04/49.68  | | 
% 243.04/49.68  | |   (12)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 243.04/49.68  | | 
% 243.04/49.68  | | ALPHA: (12) implies:
% 243.04/49.68  | |   (13)   ~ (all_34_1 = e2)
% 243.04/49.68  | |   (14)  op(e0, e1) = all_34_1
% 243.04/49.68  | | 
% 243.04/49.68  | | REF_CLOSE: (2), (5), (7), (13), (14) are inconsistent by sub-proof #2237.
% 243.04/49.68  | | 
% 243.04/49.68  | End of split
% 243.04/49.68  | 
% 243.04/49.68  End of proof
% 243.04/49.68  
% 243.04/49.68  Sub-proof #1096 shows that the following formulas are inconsistent:
% 243.04/49.68  ----------------------------------------------------------------
% 243.04/49.68    (1)   ~ (e3 = e0)
% 243.04/49.68    (2)   ~ (e2 = e0)
% 243.04/49.69    (3)   ~ (e3 = e1)
% 243.04/49.69    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.69         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.69    (5)  op(e3, e3) = e1
% 243.04/49.69    (6)   ~ (e3 = e2)
% 243.04/49.69    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.69    (8)  op(e3, e0) = e2
% 243.04/49.69    (9)   ~ (all_52_4 = e3)
% 243.04/49.69    (10)  op(e3, e2) = all_52_4
% 243.04/49.69    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.69  
% 243.04/49.69  Begin of proof
% 243.04/49.69  | 
% 243.04/49.69  | BETA: splitting (7) gives:
% 243.04/49.69  | 
% 243.04/49.69  | Case 1:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (12)  all_58_4 = e0 & op(e3, e1) = e0
% 243.04/49.69  | | 
% 243.04/49.69  | | ALPHA: (12) implies:
% 243.04/49.69  | |   (13)  all_58_4 = e0
% 243.04/49.69  | | 
% 243.04/49.69  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (13) are
% 243.04/49.69  | |            inconsistent by sub-proof #1400.
% 243.04/49.69  | | 
% 243.04/49.69  | Case 2:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (14)  all_58_9 = e0 & op(e3, e0) = e0
% 243.04/49.69  | | 
% 243.04/49.69  | | ALPHA: (14) implies:
% 243.04/49.69  | |   (15)  op(e3, e0) = e0
% 243.04/49.69  | | 
% 243.04/49.69  | | REF_CLOSE: (2), (8), (11), (15) are inconsistent by sub-proof #2154.
% 243.04/49.69  | | 
% 243.04/49.69  | End of split
% 243.04/49.69  | 
% 243.04/49.69  End of proof
% 243.04/49.69  
% 243.04/49.69  Sub-proof #1097 shows that the following formulas are inconsistent:
% 243.04/49.69  ----------------------------------------------------------------
% 243.04/49.69    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.69         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.69    (2)   ~ (e2 = e0)
% 243.04/49.69    (3)  all_58_9 = e0
% 243.04/49.69    (4)  all_58_1 = e0
% 243.04/49.69    (5)  op(e3, e3) = e1
% 243.04/49.69    (6)   ~ (e3 = e2)
% 243.04/49.69    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.69    (8)  all_58_4 = e3
% 243.04/49.69    (9)   ~ (e2 = e1)
% 243.04/49.69  
% 243.04/49.69  Begin of proof
% 243.04/49.69  | 
% 243.04/49.69  | BETA: splitting (1) gives:
% 243.04/49.69  | 
% 243.04/49.69  | Case 1:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 243.04/49.69  | |           e2)
% 243.04/49.69  | | 
% 243.04/49.69  | | REF_CLOSE: (2), (4), (5), (7), (9), (10) are inconsistent by sub-proof
% 243.04/49.69  | |            #1477.
% 243.04/49.69  | | 
% 243.04/49.69  | Case 2:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 243.04/49.69  | |           e2)
% 243.04/49.69  | | 
% 243.04/49.69  | | BETA: splitting (11) gives:
% 243.04/49.69  | | 
% 243.04/49.69  | | Case 1:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (12)  all_58_4 = e2 & op(e3, e1) = e2
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (6), (8), (12) are inconsistent by sub-proof #1476.
% 243.04/49.69  | | | 
% 243.04/49.69  | | Case 2:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (13)  all_58_9 = e2 & op(e3, e0) = e2
% 243.04/49.69  | | | 
% 243.04/49.69  | | | ALPHA: (13) implies:
% 243.04/49.69  | | |   (14)  all_58_9 = e2
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (2), (3), (14) are inconsistent by sub-proof #1660.
% 243.04/49.69  | | | 
% 243.04/49.69  | | End of split
% 243.04/49.69  | | 
% 243.04/49.69  | End of split
% 243.04/49.69  | 
% 243.04/49.69  End of proof
% 243.04/49.69  
% 243.04/49.69  Sub-proof #1098 shows that the following formulas are inconsistent:
% 243.04/49.69  ----------------------------------------------------------------
% 243.04/49.69    (1)  all_58_10 = e3
% 243.04/49.69    (2)   ~ (e3 = e0)
% 243.04/49.69    (3)   ~ (e2 = e0)
% 243.04/49.69    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.69         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.04/49.69    (5)   ~ (e3 = e1)
% 243.04/49.69    (6)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 243.04/49.69    (7)   ~ (e3 = e2)
% 243.04/49.69    (8)  op(e2, e3) = all_52_1
% 243.04/49.69    (9)   ~ (all_52_4 = e3)
% 243.04/49.69    (10)  op(e3, e2) = all_52_4
% 243.04/49.69    (11)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.04/49.69          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 243.04/49.69    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.69    (13)   ~ (e1 = e0)
% 243.04/49.69    (14)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.04/49.69          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.04/49.69    (15)   ~ (e2 = e1)
% 243.04/49.69    (16)   ~ (all_52_1 = e1)
% 243.04/49.69  
% 243.04/49.69  Begin of proof
% 243.04/49.69  | 
% 243.04/49.69  | BETA: splitting (6) gives:
% 243.04/49.69  | 
% 243.04/49.69  | Case 1:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (17)  all_58_1 = e3 & op(e3, e2) = e3
% 243.04/49.69  | | 
% 243.04/49.69  | | ALPHA: (17) implies:
% 243.04/49.69  | |   (18)  op(e3, e2) = e3
% 243.04/49.69  | | 
% 243.04/49.69  | | REF_CLOSE: (9), (10), (12), (18) are inconsistent by sub-proof #2192.
% 243.04/49.69  | | 
% 243.04/49.69  | Case 2:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (19)  all_58_3 = e3 & op(e2, e2) = e3
% 243.04/49.69  | | 
% 243.04/49.69  | | ALPHA: (19) implies:
% 243.04/49.69  | |   (20)  all_58_3 = e3
% 243.04/49.69  | | 
% 243.04/49.69  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (12), (13), (14), (15),
% 243.04/49.69  | |            (16), (20) are inconsistent by sub-proof #1099.
% 243.04/49.69  | | 
% 243.04/49.69  | End of split
% 243.04/49.69  | 
% 243.04/49.69  End of proof
% 243.04/49.69  
% 243.04/49.69  Sub-proof #1099 shows that the following formulas are inconsistent:
% 243.04/49.69  ----------------------------------------------------------------
% 243.04/49.69    (1)  all_58_10 = e3
% 243.04/49.69    (2)   ~ (e3 = e0)
% 243.04/49.69    (3)   ~ (e2 = e0)
% 243.04/49.69    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.69         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.04/49.69    (5)   ~ (e3 = e1)
% 243.04/49.69    (6)  all_58_3 = e3
% 243.04/49.69    (7)   ~ (e3 = e2)
% 243.04/49.69    (8)  op(e2, e3) = all_52_1
% 243.04/49.69    (9)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.04/49.69         (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 243.04/49.69    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.69    (11)   ~ (e1 = e0)
% 243.04/49.69    (12)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.04/49.69          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.04/49.69    (13)   ~ (e2 = e1)
% 243.04/49.69    (14)   ~ (all_52_1 = e1)
% 243.04/49.69  
% 243.04/49.69  Begin of proof
% 243.04/49.69  | 
% 243.04/49.69  | BETA: splitting (12) gives:
% 243.04/49.69  | 
% 243.04/49.69  | Case 1:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (15)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 243.04/49.69  | |           e1)
% 243.04/49.69  | | 
% 243.04/49.69  | | BETA: splitting (15) gives:
% 243.04/49.69  | | 
% 243.04/49.69  | | Case 1:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (16)  all_58_2 = e1 & op(e2, e3) = e1
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (8), (10), (14), (16) are inconsistent by sub-proof #2229.
% 243.04/49.69  | | | 
% 243.04/49.69  | | Case 2:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (17)  all_58_3 = e1 & op(e2, e2) = e1
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (5), (6), (17) are inconsistent by sub-proof #2197.
% 243.04/49.69  | | | 
% 243.04/49.69  | | End of split
% 243.04/49.69  | | 
% 243.04/49.69  | Case 2:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (18)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 243.04/49.69  | |           e1)
% 243.04/49.69  | | 
% 243.04/49.69  | | BETA: splitting (18) gives:
% 243.04/49.69  | | 
% 243.04/49.69  | | Case 1:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (19)  all_58_5 = e1 & op(e2, e1) = e1
% 243.04/49.69  | | | 
% 243.04/49.69  | | | ALPHA: (19) implies:
% 243.04/49.69  | | |   (20)  all_58_5 = e1
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (11), (13), (20) are
% 243.04/49.69  | | |            inconsistent by sub-proof #1101.
% 243.04/49.69  | | | 
% 243.04/49.69  | | Case 2:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (21)  all_58_10 = e1 & op(e2, e0) = e1
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (1), (5), (21) are inconsistent by sub-proof #1100.
% 243.04/49.69  | | | 
% 243.04/49.69  | | End of split
% 243.04/49.69  | | 
% 243.04/49.69  | End of split
% 243.04/49.69  | 
% 243.04/49.69  End of proof
% 243.04/49.69  
% 243.04/49.69  Sub-proof #1100 shows that the following formulas are inconsistent:
% 243.04/49.69  ----------------------------------------------------------------
% 243.04/49.69    (1)  all_58_10 = e1 & op(e2, e0) = e1
% 243.04/49.69    (2)  all_58_10 = e3
% 243.04/49.69    (3)   ~ (e3 = e1)
% 243.04/49.69  
% 243.04/49.69  Begin of proof
% 243.04/49.69  | 
% 243.04/49.69  | ALPHA: (1) implies:
% 243.04/49.69  |   (4)  all_58_10 = e1
% 243.04/49.69  | 
% 243.04/49.69  | COMBINE_EQS: (2), (4) imply:
% 243.04/49.69  |   (5)  e3 = e1
% 243.04/49.69  | 
% 243.04/49.69  | SIMP: (5) implies:
% 243.04/49.69  |   (6)  e3 = e1
% 243.04/49.69  | 
% 243.04/49.69  | REDUCE: (3), (6) imply:
% 243.04/49.69  |   (7)  $false
% 243.04/49.69  | 
% 243.04/49.69  | CLOSE: (7) is inconsistent.
% 243.04/49.69  | 
% 243.04/49.69  End of proof
% 243.04/49.69  
% 243.04/49.69  Sub-proof #1101 shows that the following formulas are inconsistent:
% 243.04/49.69  ----------------------------------------------------------------
% 243.04/49.69    (1)  all_58_10 = e3
% 243.04/49.69    (2)   ~ (e3 = e0)
% 243.04/49.69    (3)   ~ (e2 = e0)
% 243.04/49.69    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.69         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.04/49.69    (5)  all_58_3 = e3
% 243.04/49.69    (6)   ~ (e3 = e2)
% 243.04/49.69    (7)  all_58_5 = e1
% 243.04/49.69    (8)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.04/49.69         (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 243.04/49.69    (9)   ~ (e1 = e0)
% 243.04/49.69    (10)   ~ (e2 = e1)
% 243.04/49.69  
% 243.04/49.69  Begin of proof
% 243.04/49.69  | 
% 243.04/49.69  | BETA: splitting (8) gives:
% 243.04/49.69  | 
% 243.04/49.69  | Case 1:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (11)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 243.04/49.69  | |           e0)
% 243.04/49.69  | | 
% 243.04/49.69  | | BETA: splitting (11) gives:
% 243.04/49.69  | | 
% 243.04/49.69  | | Case 1:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (12)  all_58_2 = e0 & op(e2, e3) = e0
% 243.04/49.69  | | | 
% 243.04/49.69  | | | ALPHA: (12) implies:
% 243.04/49.69  | | |   (13)  all_58_2 = e0
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (13) are inconsistent by
% 243.04/49.69  | | |            sub-proof #1104.
% 243.04/49.69  | | | 
% 243.04/49.69  | | Case 2:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (14)  all_58_3 = e0 & op(e2, e2) = e0
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (2), (5), (14) are inconsistent by sub-proof #1719.
% 243.04/49.69  | | | 
% 243.04/49.69  | | End of split
% 243.04/49.69  | | 
% 243.04/49.69  | Case 2:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (15)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.04/49.69  | |           e0)
% 243.04/49.69  | | 
% 243.04/49.69  | | BETA: splitting (15) gives:
% 243.04/49.69  | | 
% 243.04/49.69  | | Case 1:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (16)  all_58_5 = e0 & op(e2, e1) = e0
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (7), (9), (16) are inconsistent by sub-proof #1103.
% 243.04/49.69  | | | 
% 243.04/49.69  | | Case 2:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (17)  all_58_10 = e0 & op(e2, e0) = e0
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (1), (2), (17) are inconsistent by sub-proof #1102.
% 243.04/49.69  | | | 
% 243.04/49.69  | | End of split
% 243.04/49.69  | | 
% 243.04/49.69  | End of split
% 243.04/49.69  | 
% 243.04/49.69  End of proof
% 243.04/49.69  
% 243.04/49.69  Sub-proof #1102 shows that the following formulas are inconsistent:
% 243.04/49.69  ----------------------------------------------------------------
% 243.04/49.69    (1)  all_58_10 = e0 & op(e2, e0) = e0
% 243.04/49.69    (2)  all_58_10 = e3
% 243.04/49.69    (3)   ~ (e3 = e0)
% 243.04/49.69  
% 243.04/49.69  Begin of proof
% 243.04/49.69  | 
% 243.04/49.69  | ALPHA: (1) implies:
% 243.04/49.69  |   (4)  all_58_10 = e0
% 243.04/49.69  | 
% 243.04/49.69  | COMBINE_EQS: (2), (4) imply:
% 243.04/49.69  |   (5)  e3 = e0
% 243.04/49.69  | 
% 243.04/49.69  | SIMP: (5) implies:
% 243.04/49.69  |   (6)  e3 = e0
% 243.04/49.69  | 
% 243.04/49.69  | REDUCE: (3), (6) imply:
% 243.04/49.69  |   (7)  $false
% 243.04/49.69  | 
% 243.04/49.69  | CLOSE: (7) is inconsistent.
% 243.04/49.69  | 
% 243.04/49.69  End of proof
% 243.04/49.69  
% 243.04/49.69  Sub-proof #1103 shows that the following formulas are inconsistent:
% 243.04/49.69  ----------------------------------------------------------------
% 243.04/49.69    (1)  all_58_5 = e0 & op(e2, e1) = e0
% 243.04/49.69    (2)  all_58_5 = e1
% 243.04/49.69    (3)   ~ (e1 = e0)
% 243.04/49.69  
% 243.04/49.69  Begin of proof
% 243.04/49.69  | 
% 243.04/49.69  | ALPHA: (1) implies:
% 243.04/49.69  |   (4)  all_58_5 = e0
% 243.04/49.69  | 
% 243.04/49.69  | COMBINE_EQS: (2), (4) imply:
% 243.04/49.69  |   (5)  e1 = e0
% 243.04/49.69  | 
% 243.04/49.69  | SIMP: (5) implies:
% 243.04/49.69  |   (6)  e1 = e0
% 243.04/49.69  | 
% 243.04/49.69  | REDUCE: (3), (6) imply:
% 243.04/49.69  |   (7)  $false
% 243.04/49.69  | 
% 243.04/49.69  | CLOSE: (7) is inconsistent.
% 243.04/49.69  | 
% 243.04/49.69  End of proof
% 243.04/49.69  
% 243.04/49.69  Sub-proof #1104 shows that the following formulas are inconsistent:
% 243.04/49.69  ----------------------------------------------------------------
% 243.04/49.69    (1)  all_58_10 = e3
% 243.04/49.69    (2)   ~ (e2 = e0)
% 243.04/49.69    (3)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.69         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.04/49.69    (4)  all_58_3 = e3
% 243.04/49.69    (5)   ~ (e3 = e2)
% 243.04/49.69    (6)  all_58_2 = e0
% 243.04/49.69    (7)  all_58_5 = e1
% 243.04/49.69    (8)   ~ (e2 = e1)
% 243.04/49.69  
% 243.04/49.69  Begin of proof
% 243.04/49.69  | 
% 243.04/49.69  | BETA: splitting (3) gives:
% 243.04/49.69  | 
% 243.04/49.69  | Case 1:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (9)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 243.04/49.69  | | 
% 243.04/49.69  | | BETA: splitting (9) gives:
% 243.04/49.69  | | 
% 243.04/49.69  | | Case 1:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (10)  all_58_2 = e2 & op(e2, e3) = e2
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #1575.
% 243.04/49.69  | | | 
% 243.04/49.69  | | Case 2:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (11)  all_58_3 = e2 & op(e2, e2) = e2
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #1106.
% 243.04/49.69  | | | 
% 243.04/49.69  | | End of split
% 243.04/49.69  | | 
% 243.04/49.69  | Case 2:
% 243.04/49.69  | | 
% 243.04/49.69  | |   (12)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 243.04/49.69  | |           e2)
% 243.04/49.69  | | 
% 243.04/49.69  | | BETA: splitting (12) gives:
% 243.04/49.69  | | 
% 243.04/49.69  | | Case 1:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (13)  all_58_5 = e2 & op(e2, e1) = e2
% 243.04/49.69  | | | 
% 243.04/49.69  | | | ALPHA: (13) implies:
% 243.04/49.69  | | |   (14)  all_58_5 = e2
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (7), (8), (14) are inconsistent by sub-proof #1665.
% 243.04/49.69  | | | 
% 243.04/49.69  | | Case 2:
% 243.04/49.69  | | | 
% 243.04/49.69  | | |   (15)  all_58_10 = e2 & op(e2, e0) = e2
% 243.04/49.69  | | | 
% 243.04/49.69  | | | REF_CLOSE: (1), (5), (15) are inconsistent by sub-proof #1105.
% 243.04/49.69  | | | 
% 243.04/49.69  | | End of split
% 243.04/49.69  | | 
% 243.04/49.69  | End of split
% 243.04/49.69  | 
% 243.04/49.69  End of proof
% 243.04/49.69  
% 243.04/49.69  Sub-proof #1105 shows that the following formulas are inconsistent:
% 243.04/49.69  ----------------------------------------------------------------
% 243.04/49.69    (1)  all_58_10 = e2 & op(e2, e0) = e2
% 243.04/49.69    (2)  all_58_10 = e3
% 243.04/49.69    (3)   ~ (e3 = e2)
% 243.04/49.69  
% 243.04/49.69  Begin of proof
% 243.04/49.69  | 
% 243.04/49.69  | ALPHA: (1) implies:
% 243.04/49.69  |   (4)  all_58_10 = e2
% 243.04/49.69  | 
% 243.04/49.69  | COMBINE_EQS: (2), (4) imply:
% 243.04/49.69  |   (5)  e3 = e2
% 243.04/49.69  | 
% 243.04/49.69  | SIMP: (5) implies:
% 243.04/49.69  |   (6)  e3 = e2
% 243.04/49.69  | 
% 243.04/49.69  | REDUCE: (3), (6) imply:
% 243.04/49.69  |   (7)  $false
% 243.04/49.69  | 
% 243.04/49.69  | CLOSE: (7) is inconsistent.
% 243.04/49.69  | 
% 243.04/49.69  End of proof
% 243.04/49.69  
% 243.04/49.69  Sub-proof #1106 shows that the following formulas are inconsistent:
% 243.04/49.69  ----------------------------------------------------------------
% 243.04/49.69    (1)  all_58_3 = e2 & op(e2, e2) = e2
% 243.04/49.69    (2)  all_58_3 = e3
% 243.04/49.70    (3)   ~ (e3 = e2)
% 243.04/49.70  
% 243.04/49.70  Begin of proof
% 243.04/49.70  | 
% 243.04/49.70  | ALPHA: (1) implies:
% 243.04/49.70  |   (4)  all_58_3 = e2
% 243.04/49.70  | 
% 243.04/49.70  | COMBINE_EQS: (2), (4) imply:
% 243.04/49.70  |   (5)  e3 = e2
% 243.04/49.70  | 
% 243.04/49.70  | SIMP: (5) implies:
% 243.04/49.70  |   (6)  e3 = e2
% 243.04/49.70  | 
% 243.04/49.70  | REDUCE: (3), (6) imply:
% 243.04/49.70  |   (7)  $false
% 243.04/49.70  | 
% 243.04/49.70  | CLOSE: (7) is inconsistent.
% 243.04/49.70  | 
% 243.04/49.70  End of proof
% 243.04/49.70  
% 243.04/49.70  Sub-proof #1107 shows that the following formulas are inconsistent:
% 243.04/49.70  ----------------------------------------------------------------
% 243.04/49.70    (1)   ~ (e3 = e0)
% 243.04/49.70    (2)  op(e1, e0) = all_52_14
% 243.04/49.70    (3)  op(e0, e2) = e3
% 243.04/49.70    (4)  op(e2, e1) = all_52_9
% 243.04/49.70    (5)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 243.04/49.70             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.04/49.70           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.04/49.70             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.04/49.70           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 243.04/49.70           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.04/49.70           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 243.04/49.70           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.04/49.70           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.04/49.70           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.70           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.04/49.70             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.04/49.70           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.04/49.70           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.70    (6)   ~ (e3 = e2)
% 243.04/49.70    (7)   ~ (all_52_14 = e1)
% 243.04/49.70    (8)  all_56_31 = e1
% 243.04/49.70    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.70    (10)   ~ (all_52_9 = e1)
% 243.04/49.70  
% 243.04/49.70  Begin of proof
% 243.04/49.70  | 
% 243.04/49.70  | BETA: splitting (5) gives:
% 243.04/49.70  | 
% 243.04/49.70  | Case 1:
% 243.04/49.70  | | 
% 243.04/49.70  | |   (11)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.04/49.70  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.04/49.70  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.04/49.70  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.04/49.70  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 243.04/49.70  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.70  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.04/49.70  | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.04/49.70  | | 
% 243.04/49.70  | | BETA: splitting (11) gives:
% 243.04/49.70  | | 
% 243.04/49.70  | | Case 1:
% 243.04/49.70  | | | 
% 243.04/49.70  | | |   (12)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.04/49.70  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.04/49.70  | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 243.04/49.70  | | | 
% 243.04/49.70  | | | ALPHA: (12) implies:
% 243.04/49.70  | | |   (13)   ~ (all_56_31 = e1)
% 243.04/49.70  | | | 
% 243.04/49.70  | | | REDUCE: (8), (13) imply:
% 243.04/49.70  | | |   (14)  $false
% 243.04/49.70  | | | 
% 243.04/49.70  | | | CLOSE: (14) is inconsistent.
% 243.04/49.70  | | | 
% 243.04/49.70  | | Case 2:
% 243.04/49.70  | | | 
% 243.04/49.70  | | |   (15)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.04/49.70  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.04/49.70  | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27
% 243.04/49.70  | | |           = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 243.04/49.70  | | |             = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 243.04/49.70  | | |           e2)
% 243.04/49.70  | | | 
% 243.04/49.70  | | | REF_CLOSE: (3), (4), (6), (9), (10), (15) are inconsistent by sub-proof
% 243.04/49.70  | | |            #1108.
% 243.04/49.70  | | | 
% 243.04/49.70  | | End of split
% 243.04/49.70  | | 
% 243.04/49.70  | Case 2:
% 243.04/49.70  | | 
% 243.04/49.70  | |   (16)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.04/49.70  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.04/49.70  | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 243.04/49.70  | |           e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.04/49.70  | |             e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 243.04/49.70  | |         (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.04/49.70  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.04/49.70  | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.04/49.70  | | 
% 243.04/49.70  | | BETA: splitting (16) gives:
% 243.04/49.70  | | 
% 243.04/49.70  | | Case 1:
% 243.04/49.70  | | | 
% 243.04/49.70  | | |   (17)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.04/49.70  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.04/49.70  | | |         op(e2, e0) = e0 & op(e0, e2) = e0
% 243.04/49.70  | | | 
% 243.04/49.70  | | | ALPHA: (17) implies:
% 243.04/49.70  | | |   (18)  op(e0, e2) = e0
% 243.04/49.70  | | | 
% 243.04/49.70  | | | REF_CLOSE: (1), (3), (9), (18) are inconsistent by sub-proof #1961.
% 243.04/49.70  | | | 
% 243.04/49.70  | | Case 2:
% 243.04/49.70  | | | 
% 243.04/49.70  | | |   (19)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.04/49.70  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.04/49.70  | | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29
% 243.04/49.70  | | |           = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 243.04/49.70  | | |             = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 243.04/49.70  | | |           e0)
% 243.04/49.70  | | | 
% 243.04/49.70  | | | REF_CLOSE: (2), (7), (8), (9), (19) are inconsistent by sub-proof #2269.
% 243.04/49.70  | | | 
% 243.04/49.70  | | End of split
% 243.04/49.70  | | 
% 243.04/49.70  | End of split
% 243.04/49.70  | 
% 243.04/49.70  End of proof
% 243.04/49.70  
% 243.04/49.70  Sub-proof #1108 shows that the following formulas are inconsistent:
% 243.04/49.70  ----------------------------------------------------------------
% 243.04/49.70    (1)  op(e0, e2) = e3
% 243.04/49.70    (2)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.04/49.70             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.04/49.70           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 243.04/49.70             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.04/49.70           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.04/49.70    (3)  op(e2, e1) = all_52_9
% 243.04/49.70    (4)   ~ (e3 = e2)
% 243.04/49.70    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.70    (6)   ~ (all_52_9 = e1)
% 243.04/49.70  
% 243.04/49.70  Begin of proof
% 243.04/49.70  | 
% 243.04/49.70  | BETA: splitting (2) gives:
% 243.04/49.70  | 
% 243.04/49.70  | Case 1:
% 243.04/49.70  | | 
% 243.04/49.70  | |   (7)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.04/49.70  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 243.04/49.70  | |        & op(e1, e2) = e1
% 243.04/49.70  | | 
% 243.04/49.70  | | ALPHA: (7) implies:
% 243.04/49.70  | |   (8)  op(e2, e1) = e1
% 243.04/49.70  | | 
% 243.04/49.70  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2306.
% 243.04/49.70  | | 
% 243.04/49.70  | Case 2:
% 243.04/49.70  | | 
% 243.04/49.70  | |   (9)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.04/49.70  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 243.04/49.70  | |        & op(e0, e2) = e2
% 243.04/49.70  | | 
% 243.04/49.70  | | ALPHA: (9) implies:
% 243.04/49.70  | |   (10)  op(e0, e2) = e2
% 243.04/49.70  | | 
% 243.04/49.70  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2254.
% 243.04/49.70  | | 
% 243.04/49.70  | End of split
% 243.04/49.70  | 
% 243.04/49.70  End of proof
% 243.04/49.70  
% 243.04/49.70  Sub-proof #1109 shows that the following formulas are inconsistent:
% 243.04/49.70  ----------------------------------------------------------------
% 243.04/49.70    (1)   ~ (e3 = e0)
% 243.04/49.70    (2)  op(e0, e2) = e3
% 243.04/49.70    (3)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) = all_22_1
% 243.04/49.70           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1) =
% 243.04/49.70           all_22_1 & $i(all_22_1))
% 243.04/49.70    (4)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 243.04/49.70           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 243.04/49.70           all_30_1 & $i(all_30_1))
% 243.04/49.70    (5)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 243.04/49.71    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.71    (7)  op(e3, e1) = e3
% 243.04/49.71  
% 243.04/49.71  Begin of proof
% 243.04/49.71  | 
% 243.04/49.71  | BETA: splitting (5) gives:
% 243.04/49.71  | 
% 243.04/49.71  | Case 1:
% 243.04/49.71  | | 
% 243.04/49.71  | |   (8)  all_58_4 = e0 & op(e3, e1) = e0
% 243.04/49.71  | | 
% 243.04/49.71  | | ALPHA: (8) implies:
% 243.04/49.71  | |   (9)  op(e3, e1) = e0
% 243.04/49.71  | | 
% 243.04/49.71  | | REF_CLOSE: (1), (6), (7), (9) are inconsistent by sub-proof #2118.
% 243.04/49.71  | | 
% 243.04/49.71  | Case 2:
% 243.04/49.71  | | 
% 243.04/49.71  | |   (10)  all_58_5 = e0 & op(e2, e1) = e0
% 243.04/49.71  | | 
% 243.04/49.71  | | ALPHA: (10) implies:
% 243.04/49.71  | |   (11)  op(e2, e1) = e0
% 243.04/49.71  | | 
% 243.04/49.71  | | REF_CLOSE: (2), (3), (4), (6), (11) are inconsistent by sub-proof #1110.
% 243.04/49.71  | | 
% 243.04/49.71  | End of split
% 243.04/49.71  | 
% 243.04/49.71  End of proof
% 243.04/49.71  
% 243.04/49.71  Sub-proof #1110 shows that the following formulas are inconsistent:
% 243.04/49.71  ----------------------------------------------------------------
% 243.04/49.71    (1)  op(e0, e2) = e3
% 243.04/49.71    (2)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) = all_22_1
% 243.04/49.71           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2, e1) =
% 243.04/49.71           all_22_1 & $i(all_22_1))
% 243.04/49.71    (3)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 243.04/49.71           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 243.04/49.71           all_30_1 & $i(all_30_1))
% 243.04/49.71    (4)  op(e2, e1) = e0
% 243.04/49.71    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.71  
% 243.04/49.71  Begin of proof
% 243.04/49.71  | 
% 243.04/49.71  | BETA: splitting (2) gives:
% 243.04/49.71  | 
% 243.04/49.71  | Case 1:
% 243.04/49.71  | | 
% 243.04/49.71  | |   (6)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) =
% 243.04/49.71  | |        all_22_1 & $i(all_22_0) & $i(all_22_1)
% 243.04/49.71  | | 
% 243.04/49.71  | | ALPHA: (6) implies:
% 243.04/49.71  | |   (7)   ~ (all_22_0 = e3)
% 243.04/49.71  | |   (8)  op(e2, e1) = all_22_1
% 243.04/49.71  | |   (9)  op(all_22_1, e2) = all_22_0
% 243.04/49.71  | | 
% 243.04/49.71  | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9) are inconsistent by sub-proof
% 243.04/49.71  | |            #1860.
% 243.04/49.71  | | 
% 243.04/49.71  | Case 2:
% 243.04/49.71  | | 
% 243.04/49.71  | |   (10)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 & $i(all_22_1)
% 243.04/49.71  | | 
% 243.04/49.71  | | ALPHA: (10) implies:
% 243.04/49.71  | |   (11)   ~ (all_22_1 = e0)
% 243.04/49.71  | |   (12)  op(e2, e1) = all_22_1
% 243.04/49.71  | | 
% 243.04/49.71  | | REF_CLOSE: (3), (4), (5), (11), (12) are inconsistent by sub-proof #1356.
% 243.04/49.71  | | 
% 243.04/49.71  | End of split
% 243.04/49.71  | 
% 243.04/49.71  End of proof
% 243.04/49.71  
% 243.04/49.71  Sub-proof #1111 shows that the following formulas are inconsistent:
% 243.04/49.71  ----------------------------------------------------------------
% 243.04/49.71    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.71         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.71    (2)   ~ (e3 = e0)
% 243.04/49.71    (3)   ~ (e2 = e0)
% 243.04/49.71    (4)   ~ (e3 = e1)
% 243.04/49.71    (5)  all_58_3 = e3
% 243.04/49.71    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.71         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.71    (7)  all_58_3 = e1
% 243.04/49.71    (8)  op(e3, e3) = e1
% 243.04/49.71    (9)   ~ (e3 = e2)
% 243.04/49.71    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.04/49.71          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.71    (11)   ~ (all_52_4 = e3)
% 243.04/49.71    (12)  op(e3, e2) = all_52_4
% 243.04/49.71    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.71    (14)   ~ (e1 = e0)
% 243.04/49.71    (15)  all_58_4 = e3
% 243.04/49.71    (16)   ~ (e2 = e1)
% 243.04/49.71  
% 243.04/49.71  Begin of proof
% 243.04/49.71  | 
% 243.04/49.71  | COMBINE_EQS: (5), (7) imply:
% 243.04/49.71  |   (17)  e3 = e1
% 243.04/49.71  | 
% 243.04/49.71  | SIMP: (17) implies:
% 243.04/49.71  |   (18)  e3 = e1
% 243.04/49.71  | 
% 243.04/49.71  | COMBINE_EQS: (15), (18) imply:
% 243.04/49.71  |   (19)  all_58_4 = e1
% 243.04/49.71  | 
% 243.04/49.71  | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (14),
% 243.04/49.71  |            (16), (19) are inconsistent by sub-proof #1468.
% 243.04/49.71  | 
% 243.04/49.71  End of proof
% 243.04/49.71  
% 243.04/49.71  Sub-proof #1112 shows that the following formulas are inconsistent:
% 243.04/49.71  ----------------------------------------------------------------
% 243.04/49.71    (1)  op(e0, e0) = e1
% 243.04/49.71    (2)  all_54_3 = all_20_0
% 243.04/49.71    (3)   ~ (e3 = e0)
% 243.04/49.71    (4)   ~ (e2 = e0)
% 243.04/49.71    (5)  op(e0, e1) = e3
% 243.04/49.71    (6)  op(e1, e0) = all_52_14
% 243.04/49.71    (7)   ~ (all_52_13 = all_20_0)
% 243.04/49.71    (8)   ~ (e3 = e1)
% 243.04/49.71    (9)   ~ (all_20_0 = e1)
% 243.04/49.71    (10)   ~ (all_52_2 = e1)
% 243.04/49.71    (11)   ~ (all_20_0 = e2)
% 243.04/49.71    (12)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.71              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.04/49.71                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.71                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.71    (13)   ~ (e3 = e2)
% 243.04/49.71    (14)   ~ (all_52_14 = e0)
% 243.04/49.71    (15)  op(e2, e2) = e1
% 243.04/49.71    (16)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 243.04/49.71            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 243.04/49.71            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 243.04/49.71            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 243.04/49.71            op(e0, all_56_31) = e0)
% 243.04/49.71    (17)  all_56_31 = e1
% 243.04/49.71    (18)  all_58_15 = e1
% 243.04/49.71    (19)  op(e3, e0) = all_52_12
% 243.04/49.71    (20)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.04/49.71          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.71    (21)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.04/49.71    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.71    (23)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.04/49.71          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.04/49.71    (24)  op(e1, e3) = all_52_2
% 243.04/49.71    (25)   ~ (all_52_12 = e3)
% 243.04/49.71    (26)   ~ (e1 = e0)
% 243.04/49.71    (27)   ~ (all_52_13 = e3)
% 243.04/49.71    (28)  op(e2, e0) = all_52_13
% 243.04/49.71    (29)   ~ (e2 = e1)
% 243.04/49.71  
% 243.04/49.71  Begin of proof
% 243.04/49.71  | 
% 243.04/49.71  | BETA: splitting (20) gives:
% 243.04/49.71  | 
% 243.04/49.71  | Case 1:
% 243.04/49.71  | | 
% 243.04/49.71  | |   (30)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 243.04/49.71  | |           e3)
% 243.04/49.71  | | 
% 243.04/49.71  | | REF_CLOSE: (19), (22), (25), (27), (28), (30) are inconsistent by sub-proof
% 243.04/49.71  | |            #1592.
% 243.04/49.71  | | 
% 243.04/49.71  | Case 2:
% 243.04/49.71  | | 
% 243.04/49.71  | |   (31)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 243.04/49.71  | |           e3)
% 243.04/49.71  | | 
% 243.04/49.71  | | BETA: splitting (31) gives:
% 243.04/49.71  | | 
% 243.04/49.71  | | Case 1:
% 243.04/49.71  | | | 
% 243.04/49.71  | | |   (32)  all_58_11 = e3 & op(e1, e0) = e3
% 243.04/49.71  | | | 
% 243.04/49.71  | | | ALPHA: (32) implies:
% 243.04/49.71  | | |   (33)  all_58_11 = e3
% 243.04/49.71  | | |   (34)  op(e1, e0) = e3
% 243.04/49.71  | | | 
% 243.04/49.71  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 243.04/49.71  | | |            (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 243.04/49.71  | | |            (25), (26), (28), (29), (33), (34) are inconsistent by
% 243.04/49.71  | | |            sub-proof #1120.
% 243.04/49.71  | | | 
% 243.04/49.71  | | Case 2:
% 243.04/49.71  | | | 
% 243.04/49.71  | | |   (35)  all_58_15 = e3 & op(e0, e0) = e3
% 243.04/49.71  | | | 
% 243.04/49.71  | | | ALPHA: (35) implies:
% 243.04/49.71  | | |   (36)  all_58_15 = e3
% 243.04/49.71  | | | 
% 243.04/49.71  | | | REF_CLOSE: (8), (18), (36) are inconsistent by sub-proof #2249.
% 243.04/49.71  | | | 
% 243.04/49.71  | | End of split
% 243.04/49.71  | | 
% 243.04/49.71  | End of split
% 243.04/49.71  | 
% 243.04/49.71  End of proof
% 243.04/49.71  
% 243.04/49.71  Sub-proof #1113 shows that the following formulas are inconsistent:
% 243.04/49.71  ----------------------------------------------------------------
% 243.04/49.71    (1)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 & $i(all_10_1)
% 243.04/49.71    (2)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) = all_38_1
% 243.04/49.71           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 243.04/49.71           all_38_1 & $i(all_38_1))
% 243.04/49.71    (3)  op(e3, e1) = e2
% 243.04/49.71    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.71  
% 243.04/49.71  Begin of proof
% 243.04/49.71  | 
% 243.04/49.71  | ALPHA: (1) implies:
% 243.04/49.71  |   (5)   ~ (all_10_1 = e2)
% 243.04/49.71  |   (6)  op(e3, e1) = all_10_1
% 243.04/49.71  | 
% 243.04/49.71  | BETA: splitting (2) gives:
% 243.04/49.71  | 
% 243.04/49.71  | Case 1:
% 243.04/49.71  | | 
% 243.04/49.71  | |   (7)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 243.04/49.71  | |        all_38_1 & $i(all_38_0) & $i(all_38_1)
% 243.04/49.71  | | 
% 243.04/49.71  | | ALPHA: (7) implies:
% 243.04/49.71  | |   (8)  op(e3, e1) = all_38_1
% 243.04/49.71  | | 
% 243.04/49.71  | | REF_CLOSE: (3), (4), (5), (6), (8) are inconsistent by sub-proof #1114.
% 243.04/49.71  | | 
% 243.04/49.71  | Case 2:
% 243.04/49.71  | | 
% 243.04/49.71  | |   (9)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1)
% 243.04/49.71  | | 
% 243.04/49.71  | | ALPHA: (9) implies:
% 243.04/49.71  | |   (10)  op(e3, e1) = all_38_1
% 243.04/49.71  | | 
% 243.04/49.71  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #1114.
% 243.04/49.71  | | 
% 243.04/49.71  | End of split
% 243.04/49.71  | 
% 243.04/49.71  End of proof
% 243.04/49.71  
% 243.04/49.71  Sub-proof #1114 shows that the following formulas are inconsistent:
% 243.04/49.71  ----------------------------------------------------------------
% 243.04/49.71    (1)   ~ (all_10_1 = e2)
% 243.04/49.71    (2)  op(e3, e1) = all_38_1
% 243.04/49.71    (3)  op(e3, e1) = e2
% 243.04/49.71    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.71    (5)  op(e3, e1) = all_10_1
% 243.04/49.71  
% 243.04/49.71  Begin of proof
% 243.04/49.71  | 
% 243.04/49.71  | GROUND_INST: instantiating (4) with all_10_1, all_38_1, e1, e3, simplifying
% 243.04/49.71  |              with (2), (5) gives:
% 243.04/49.71  |   (6)  all_38_1 = all_10_1
% 243.04/49.71  | 
% 243.04/49.71  | GROUND_INST: instantiating (4) with e2, all_38_1, e1, e3, simplifying with
% 243.04/49.71  |              (2), (3) gives:
% 243.04/49.72  |   (7)  all_38_1 = e2
% 243.04/49.72  | 
% 243.04/49.72  | COMBINE_EQS: (6), (7) imply:
% 243.04/49.72  |   (8)  all_10_1 = e2
% 243.04/49.72  | 
% 243.04/49.72  | SIMP: (8) implies:
% 243.04/49.72  |   (9)  all_10_1 = e2
% 243.04/49.72  | 
% 243.04/49.72  | REDUCE: (1), (9) imply:
% 243.04/49.72  |   (10)  $false
% 243.04/49.72  | 
% 243.04/49.72  | CLOSE: (10) is inconsistent.
% 243.04/49.72  | 
% 243.04/49.72  End of proof
% 243.04/49.72  
% 243.04/49.72  Sub-proof #1115 shows that the following formulas are inconsistent:
% 243.04/49.72  ----------------------------------------------------------------
% 243.04/49.72    (1)  op(e0, e0) = e1
% 243.04/49.72    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.04/49.72             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.04/49.72           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.04/49.72         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.04/49.72           $i(all_56_7))
% 243.04/49.72    (3)   ~ (all_52_6 = e1)
% 243.04/49.72    (4)   ~ (e3 = e0)
% 243.04/49.72    (5)   ~ (e2 = e0)
% 243.04/49.72    (6)  op(e1, e2) = all_52_6
% 243.04/49.72    (7)  op(e1, e1) = all_6_2
% 243.04/49.72    (8)  op(e1, e0) = all_52_14
% 243.04/49.72    (9)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.72         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.04/49.72    (10)   ~ (e3 = e1)
% 243.04/49.72    (11)  all_54_11 = all_52_14
% 243.04/49.72    (12)  op(e2, e0) = e3
% 243.04/49.72    (13)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.04/49.72    (14)  op(e3, e3) = e1
% 243.04/49.72    (15)  all_54_4 = all_52_1
% 243.04/49.72    (16)   ~ (all_6_2 = e3)
% 243.04/49.72    (17)  op(e3, e1) = all_52_8
% 243.04/49.72    (18)  all_54_9 = all_52_6
% 243.04/49.72    (19)   ~ (e3 = e2)
% 243.04/49.72    (20)   ~ (all_52_14 = e1)
% 243.04/49.72    (21)   ~ (all_52_14 = e0)
% 243.04/49.72    (22)  op(e2, e2) = e1
% 243.04/49.72    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.04/49.72          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.04/49.72    (24)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.04/49.72          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.04/49.72    (25)   ~ (all_52_1 = e0)
% 243.04/49.72    (26)   ~ (all_52_6 = all_52_14)
% 243.04/49.72    (27)  op(e2, e3) = all_52_1
% 243.04/49.72    (28)   ~ (all_52_14 = e3)
% 243.04/49.72    (29)   ~ (all_52_6 = e3)
% 243.04/49.72    (30)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.04/49.72    (31)  op(e2, e1) = e0
% 243.04/49.72    (32)   ~ (all_10_0 = e3)
% 243.04/49.72    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.72    (34)   ~ (e1 = e0)
% 243.04/49.72    (35)  all_54_4 = all_10_0
% 243.04/49.72    (36)  all_56_1 = e1
% 243.04/49.72    (37)   ~ (e2 = e1)
% 243.04/49.72    (38)   ~ (all_52_1 = e1)
% 243.04/49.72    (39)   ~ (all_52_8 = e3)
% 243.04/49.72    (40)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.04/49.72  
% 243.04/49.72  Begin of proof
% 243.04/49.72  | 
% 243.04/49.72  | BETA: splitting (13) gives:
% 243.04/49.72  | 
% 243.04/49.72  | Case 1:
% 243.04/49.72  | | 
% 243.04/49.72  | |   (41)  all_54_11 = e3
% 243.04/49.72  | | 
% 243.04/49.72  | | REF_CLOSE: (11), (28), (41) are inconsistent by sub-proof #1998.
% 243.04/49.72  | | 
% 243.04/49.72  | Case 2:
% 243.04/49.72  | | 
% 243.04/49.72  | |   (42)   ~ (all_54_11 = e3)
% 243.04/49.72  | |   (43)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.04/49.72  | | 
% 243.04/49.72  | | BETA: splitting (30) gives:
% 243.04/49.72  | | 
% 243.04/49.72  | | Case 1:
% 243.04/49.72  | | | 
% 243.04/49.72  | | |   (44)  all_54_4 = e3
% 243.04/49.72  | | | 
% 243.04/49.72  | | | COMBINE_EQS: (35), (44) imply:
% 243.04/49.72  | | |   (45)  all_10_0 = e3
% 243.04/49.72  | | | 
% 243.04/49.72  | | | SIMP: (45) implies:
% 243.04/49.72  | | |   (46)  all_10_0 = e3
% 243.04/49.72  | | | 
% 243.04/49.72  | | | REDUCE: (32), (46) imply:
% 243.04/49.72  | | |   (47)  $false
% 243.04/49.72  | | | 
% 243.04/49.72  | | | CLOSE: (47) is inconsistent.
% 243.04/49.72  | | | 
% 243.04/49.72  | | Case 2:
% 243.04/49.72  | | | 
% 243.04/49.72  | | |   (48)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.04/49.72  | | | 
% 243.04/49.72  | | | BETA: splitting (24) gives:
% 243.04/49.72  | | | 
% 243.04/49.72  | | | Case 1:
% 243.04/49.72  | | | | 
% 243.04/49.72  | | | |   (49)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 243.04/49.72  | | | |           = e3)
% 243.04/49.72  | | | | 
% 243.04/49.72  | | | | BETA: splitting (49) gives:
% 243.04/49.72  | | | | 
% 243.04/49.72  | | | | Case 1:
% 243.04/49.72  | | | | | 
% 243.04/49.72  | | | | |   (50)  all_58_6 = e3 & op(e1, e3) = e3
% 243.04/49.72  | | | | | 
% 243.04/49.72  | | | | | ALPHA: (50) implies:
% 243.04/49.72  | | | | |   (51)  all_58_6 = e3
% 243.04/49.72  | | | | |   (52)  op(e1, e3) = e3
% 243.04/49.72  | | | | | 
% 243.04/49.72  | | | | | BETA: splitting (9) gives:
% 243.04/49.72  | | | | | 
% 243.04/49.72  | | | | | Case 1:
% 243.04/49.72  | | | | | | 
% 243.04/49.72  | | | | | |   (53)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2,
% 243.04/49.72  | | | | | |             e2) = e2)
% 243.04/49.72  | | | | | | 
% 243.04/49.72  | | | | | | BETA: splitting (53) gives:
% 243.04/49.72  | | | | | | 
% 243.04/49.72  | | | | | | Case 1:
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | |   (54)  all_58_2 = e2 & op(e2, e3) = e2
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | | ALPHA: (54) implies:
% 243.04/49.72  | | | | | | |   (55)  op(e2, e3) = e2
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | | BETA: splitting (23) gives:
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | | Case 1:
% 243.04/49.72  | | | | | | | | 
% 243.04/49.72  | | | | | | | |   (56)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 243.04/49.72  | | | | | | | |           op(e2, e3) = e0)
% 243.04/49.72  | | | | | | | | 
% 243.04/49.72  | | | | | | | | REF_CLOSE: (14), (25), (27), (33), (34), (56) are inconsistent
% 243.04/49.72  | | | | | | | |            by sub-proof #1272.
% 243.04/49.72  | | | | | | | | 
% 243.04/49.72  | | | | | | | Case 2:
% 243.04/49.72  | | | | | | | | 
% 243.04/49.72  | | | | | | | |   (57)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 243.04/49.72  | | | | | | | |           op(e0, e3) = e0)
% 243.04/49.72  | | | | | | | | 
% 243.04/49.72  | | | | | | | | BETA: splitting (57) gives:
% 243.04/49.72  | | | | | | | | 
% 243.04/49.72  | | | | | | | | Case 1:
% 243.04/49.72  | | | | | | | | | 
% 243.04/49.72  | | | | | | | | |   (58)  all_58_6 = e0 & op(e1, e3) = e0
% 243.04/49.72  | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | REF_CLOSE: (4), (51), (58) are inconsistent by sub-proof
% 243.04/49.72  | | | | | | | | |            #2213.
% 243.04/49.72  | | | | | | | | | 
% 243.04/49.72  | | | | | | | | Case 2:
% 243.04/49.72  | | | | | | | | | 
% 243.04/49.72  | | | | | | | | |   (59)  all_58_12 = e0 & op(e0, e3) = e0
% 243.04/49.72  | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | ALPHA: (59) implies:
% 243.04/49.72  | | | | | | | | |   (60)  op(e0, e3) = e0
% 243.04/49.72  | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | BETA: splitting (2) gives:
% 243.04/49.72  | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | Case 1:
% 243.04/49.72  | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | |   (61)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2
% 243.04/49.72  | | | | | | | | | |           = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 243.04/49.72  | | | | | | | | | |           all_56_3 & $i(all_56_3))
% 243.04/49.72  | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | BETA: splitting (61) gives:
% 243.04/49.72  | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | Case 1:
% 243.04/49.72  | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | |   (62)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 243.04/49.72  | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | ALPHA: (62) implies:
% 243.04/49.72  | | | | | | | | | | |   (63)  op(e3, all_56_1) = e3
% 243.04/49.72  | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | REDUCE: (36), (63) imply:
% 243.04/49.72  | | | | | | | | | | |   (64)  op(e3, e1) = e3
% 243.04/49.72  | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | REF_CLOSE: (17), (33), (39), (64) are inconsistent by
% 243.04/49.72  | | | | | | | | | | |            sub-proof #2260.
% 243.04/49.72  | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | Case 2:
% 243.04/49.72  | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | |   (65)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 243.04/49.72  | | | | | | | | | | |         = all_56_3 & $i(all_56_3)
% 243.04/49.72  | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | ALPHA: (65) implies:
% 243.04/49.72  | | | | | | | | | | |   (66)  op(e2, e3) = all_56_3
% 243.04/49.72  | | | | | | | | | | |   (67)  op(e2, all_56_3) = e2
% 243.04/49.72  | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | BETA: splitting (43) gives:
% 243.04/49.72  | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | Case 1:
% 243.04/49.72  | | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | |   (68)  all_54_11 = e2
% 243.04/49.72  | | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | | COMBINE_EQS: (11), (68) imply:
% 243.04/49.72  | | | | | | | | | | | |   (69)  all_52_14 = e2
% 243.04/49.72  | | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | | REDUCE: (26), (69) imply:
% 243.04/49.72  | | | | | | | | | | | |   (70)   ~ (all_52_6 = e2)
% 243.04/49.72  | | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | | REF_CLOSE: (3), (18), (22), (33), (37), (40), (55), (66),
% 243.04/49.72  | | | | | | | | | | | |            (67), (70) are inconsistent by sub-proof #1116.
% 243.04/49.72  | | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | Case 2:
% 243.04/49.72  | | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | |   (71)  all_54_11 = e1 | all_54_11 = e0
% 243.04/49.72  | | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | | REF_CLOSE: (11), (20), (21), (71) are inconsistent by
% 243.04/49.72  | | | | | | | | | | | |            sub-proof #2174.
% 243.04/49.72  | | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | | End of split
% 243.04/49.72  | | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | End of split
% 243.04/49.72  | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | Case 2:
% 243.04/49.72  | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | |   (72)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 243.04/49.72  | | | | | | | | | |           = all_56_5 & $i(all_56_5)) | (all_56_6 = e0 &
% 243.04/49.72  | | | | | | | | | |           op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.04/49.72  | | | | | | | | | |           $i(all_56_7))
% 243.04/49.72  | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | | REF_CLOSE: (1), (10), (15), (25), (33), (34), (38), (48),
% 243.04/49.72  | | | | | | | | | |            (52), (60), (72) are inconsistent by sub-proof
% 243.04/49.72  | | | | | | | | | |            #1152.
% 243.04/49.72  | | | | | | | | | | 
% 243.04/49.72  | | | | | | | | | End of split
% 243.04/49.72  | | | | | | | | | 
% 243.04/49.72  | | | | | | | | End of split
% 243.04/49.72  | | | | | | | | 
% 243.04/49.72  | | | | | | | End of split
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | Case 2:
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | |   (73)  all_58_3 = e2 & op(e2, e2) = e2
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | | ALPHA: (73) implies:
% 243.04/49.72  | | | | | | |   (74)  op(e2, e2) = e2
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | | REF_CLOSE: (22), (33), (37), (74) are inconsistent by sub-proof
% 243.04/49.72  | | | | | | |            #2235.
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | End of split
% 243.04/49.72  | | | | | | 
% 243.04/49.72  | | | | | Case 2:
% 243.04/49.72  | | | | | | 
% 243.04/49.72  | | | | | |   (75)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2,
% 243.04/49.72  | | | | | |             e0) = e2)
% 243.04/49.72  | | | | | | 
% 243.04/49.72  | | | | | | BETA: splitting (75) gives:
% 243.04/49.72  | | | | | | 
% 243.04/49.72  | | | | | | Case 1:
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | |   (76)  all_58_5 = e2 & op(e2, e1) = e2
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | | ALPHA: (76) implies:
% 243.04/49.72  | | | | | | |   (77)  op(e2, e1) = e2
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | | REF_CLOSE: (5), (31), (33), (77) are inconsistent by sub-proof
% 243.04/49.72  | | | | | | |            #1906.
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | Case 2:
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | |   (78)  all_58_10 = e2 & op(e2, e0) = e2
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | | ALPHA: (78) implies:
% 243.04/49.72  | | | | | | |   (79)  op(e2, e0) = e2
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | | REF_CLOSE: (12), (19), (33), (79) are inconsistent by sub-proof
% 243.04/49.72  | | | | | | |            #2152.
% 243.04/49.72  | | | | | | | 
% 243.04/49.72  | | | | | | End of split
% 243.04/49.72  | | | | | | 
% 243.04/49.72  | | | | | End of split
% 243.04/49.72  | | | | | 
% 243.04/49.72  | | | | Case 2:
% 243.04/49.72  | | | | | 
% 243.04/49.72  | | | | |   (80)  all_58_7 = e3 & op(e1, e2) = e3
% 243.04/49.72  | | | | | 
% 243.04/49.72  | | | | | ALPHA: (80) implies:
% 243.04/49.72  | | | | |   (81)  op(e1, e2) = e3
% 243.04/49.72  | | | | | 
% 243.04/49.72  | | | | | REF_CLOSE: (6), (29), (33), (81) are inconsistent by sub-proof #2191.
% 243.04/49.72  | | | | | 
% 243.04/49.72  | | | | End of split
% 243.04/49.72  | | | | 
% 243.04/49.72  | | | Case 2:
% 243.04/49.72  | | | | 
% 243.04/49.72  | | | |   (82)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 243.04/49.72  | | | |           = e3)
% 243.04/49.72  | | | | 
% 243.04/49.72  | | | | REF_CLOSE: (7), (8), (16), (28), (33), (82) are inconsistent by
% 243.04/49.72  | | | |            sub-proof #1529.
% 243.04/49.72  | | | | 
% 243.04/49.72  | | | End of split
% 243.04/49.72  | | | 
% 243.04/49.72  | | End of split
% 243.04/49.72  | | 
% 243.04/49.72  | End of split
% 243.04/49.72  | 
% 243.04/49.72  End of proof
% 243.04/49.72  
% 243.04/49.72  Sub-proof #1116 shows that the following formulas are inconsistent:
% 243.04/49.72  ----------------------------------------------------------------
% 243.04/49.72    (1)  op(e2, e3) = all_56_3
% 243.04/49.72    (2)   ~ (all_52_6 = e1)
% 243.04/49.72    (3)   ~ (all_52_6 = e2)
% 243.04/49.72    (4)  all_54_9 = all_52_6
% 243.04/49.72    (5)  op(e2, e3) = e2
% 243.04/49.72    (6)  op(e2, e2) = e1
% 243.04/49.72    (7)  op(e2, all_56_3) = e2
% 243.04/49.72    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.72    (9)   ~ (e2 = e1)
% 243.04/49.72    (10)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.04/49.72  
% 243.04/49.72  Begin of proof
% 243.04/49.72  | 
% 243.04/49.72  | BETA: splitting (10) gives:
% 243.04/49.72  | 
% 243.04/49.72  | Case 1:
% 243.04/49.72  | | 
% 243.04/49.72  | |   (11)  all_54_9 = e2
% 243.04/49.72  | | 
% 243.04/49.72  | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #1954.
% 243.04/49.72  | | 
% 243.04/49.72  | Case 2:
% 243.04/49.72  | | 
% 243.04/49.72  | |   (12)  all_54_9 = e1 | all_54_9 = e0
% 243.04/49.72  | | 
% 243.04/49.72  | | BETA: splitting (12) gives:
% 243.04/49.72  | | 
% 243.04/49.72  | | Case 1:
% 243.04/49.72  | | | 
% 243.04/49.72  | | |   (13)  all_54_9 = e1
% 243.04/49.72  | | | 
% 243.04/49.72  | | | REF_CLOSE: (2), (4), (13) are inconsistent by sub-proof #2055.
% 243.04/49.72  | | | 
% 243.04/49.72  | | Case 2:
% 243.04/49.72  | | | 
% 243.04/49.72  | | | 
% 243.04/49.72  | | | GROUND_INST: instantiating (8) with e2, all_56_3, e3, e2, simplifying with
% 243.04/49.72  | | |              (1), (5) gives:
% 243.04/49.72  | | |   (14)  all_56_3 = e2
% 243.04/49.72  | | | 
% 243.04/49.72  | | | REDUCE: (7), (14) imply:
% 243.04/49.72  | | |   (15)  op(e2, e2) = e2
% 243.04/49.72  | | | 
% 243.04/49.72  | | | REF_CLOSE: (6), (8), (9), (15) are inconsistent by sub-proof #2235.
% 243.04/49.72  | | | 
% 243.04/49.72  | | End of split
% 243.04/49.72  | | 
% 243.04/49.72  | End of split
% 243.04/49.72  | 
% 243.04/49.72  End of proof
% 243.04/49.72  
% 243.04/49.72  Sub-proof #1117 shows that the following formulas are inconsistent:
% 243.04/49.72  ----------------------------------------------------------------
% 243.04/49.72    (1)  op(e0, e0) = e1
% 243.04/49.72    (2)   ~ (all_52_6 = e1)
% 243.04/49.72    (3)   ~ (all_52_3 = e1)
% 243.04/49.72    (4)   ~ (e3 = e0)
% 243.04/49.72    (5)  all_56_11 = e1
% 243.04/49.72    (6)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.04/49.72           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.04/49.72           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 243.04/49.72         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 243.04/49.72           $i(all_56_15))
% 243.04/49.72    (7)  op(e0, e1) = e3
% 243.04/49.72    (8)  all_54_13 = all_52_7
% 243.04/49.72    (9)  op(e1, e2) = all_52_6
% 243.04/49.72    (10)  op(e1, e0) = all_52_14
% 243.04/49.72    (11)   ~ (all_52_7 = e3)
% 243.04/49.72    (12)   ~ (e3 = e1)
% 243.04/49.72    (13)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) =
% 243.04/49.72            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2,
% 243.04/49.72              e1) = all_22_1 & $i(all_22_1))
% 243.04/49.72    (14)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.04/49.72    (15)  op(e3, e3) = e1
% 243.04/49.72    (16)   ~ (all_52_3 = all_52_7)
% 243.04/49.72    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.72              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.04/49.72                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.72                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.72    (18)  all_54_9 = all_52_6
% 243.04/49.72    (19)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) =
% 243.04/49.72            all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2,
% 243.04/49.72              e1) = all_30_1 & $i(all_30_1))
% 243.04/49.72    (20)   ~ (all_52_14 = e1)
% 243.04/49.72    (21)   ~ (all_52_7 = e1)
% 243.04/49.72    (22)   ~ (all_30_0 = e0)
% 243.04/49.72    (23)  all_54_12 = all_52_3
% 243.04/49.72    (24)  all_58_15 = e1
% 243.04/49.72    (25)  op(e0, e2) = all_52_7
% 243.04/49.72    (26)  op(e2, e1) = e0
% 243.04/49.72    (27)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.04/49.72    (28)  op(all_30_1, e2) = all_30_0
% 243.04/49.72    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.72    (30)  all_58_14 = e3
% 243.04/49.72    (31)   ~ (all_52_6 = all_52_7)
% 243.04/49.72    (32)   ~ (e1 = e0)
% 243.04/49.72    (33)  op(e3, e2) = e3
% 243.04/49.72    (34)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.72          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.04/49.72            e2)
% 243.04/49.72    (35)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.04/49.72    (36)  op(e2, e1) = all_30_1
% 243.04/49.72  
% 243.04/49.72  Begin of proof
% 243.04/49.72  | 
% 243.04/49.72  | BETA: splitting (13) gives:
% 243.04/49.72  | 
% 243.04/49.72  | Case 1:
% 243.04/49.72  | | 
% 243.04/49.72  | |   (37)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) =
% 243.04/49.72  | |         all_22_1 & $i(all_22_0) & $i(all_22_1)
% 243.04/49.72  | | 
% 243.04/49.72  | | ALPHA: (37) implies:
% 243.04/49.72  | |   (38)  op(e2, e1) = all_22_1
% 243.04/49.72  | |   (39)  op(all_22_1, e2) = all_22_0
% 243.04/49.72  | | 
% 243.04/49.72  | | GROUND_INST: instantiating (29) with all_22_1, all_30_1, e1, e2, simplifying
% 243.04/49.72  | |              with (36), (38) gives:
% 243.04/49.72  | |   (40)  all_30_1 = all_22_1
% 243.04/49.72  | | 
% 243.04/49.72  | | GROUND_INST: instantiating (29) with e0, all_30_1, e1, e2, simplifying with
% 243.04/49.72  | |              (26), (36) gives:
% 243.04/49.72  | |   (41)  all_30_1 = e0
% 243.04/49.72  | | 
% 243.04/49.72  | | COMBINE_EQS: (40), (41) imply:
% 243.04/49.72  | |   (42)  all_22_1 = e0
% 243.04/49.72  | | 
% 243.04/49.72  | | REDUCE: (28), (41) imply:
% 243.04/49.72  | |   (43)  op(e0, e2) = all_30_0
% 243.04/49.72  | | 
% 243.04/49.72  | | REDUCE: (39), (42) imply:
% 243.04/49.72  | |   (44)  op(e0, e2) = all_22_0
% 243.04/49.72  | | 
% 243.04/49.72  | | GROUND_INST: instantiating (29) with all_52_7, all_22_0, e2, e0, simplifying
% 243.04/49.72  | |              with (25), (44) gives:
% 243.04/49.72  | |   (45)  all_52_7 = all_22_0
% 243.04/49.72  | | 
% 243.04/49.72  | | GROUND_INST: instantiating (29) with all_52_7, all_30_0, e2, e0, simplifying
% 243.04/49.72  | |              with (25), (43) gives:
% 243.04/49.72  | |   (46)  all_52_7 = all_30_0
% 243.04/49.72  | | 
% 243.04/49.72  | | COMBINE_EQS: (45), (46) imply:
% 243.04/49.72  | |   (47)  all_30_0 = all_22_0
% 243.04/49.72  | | 
% 243.04/49.72  | | SIMP: (47) implies:
% 243.04/49.72  | |   (48)  all_30_0 = all_22_0
% 243.04/49.72  | | 
% 243.04/49.72  | | COMBINE_EQS: (8), (45) imply:
% 243.04/49.72  | |   (49)  all_54_13 = all_22_0
% 243.04/49.72  | | 
% 243.04/49.72  | | REDUCE: (16), (45) imply:
% 243.04/49.72  | |   (50)   ~ (all_52_3 = all_22_0)
% 243.04/49.72  | | 
% 243.04/49.72  | | REDUCE: (31), (45) imply:
% 243.04/49.72  | |   (51)   ~ (all_52_6 = all_22_0)
% 243.04/49.72  | | 
% 243.04/49.72  | | REDUCE: (11), (45) imply:
% 243.04/49.73  | |   (52)   ~ (all_22_0 = e3)
% 243.04/49.73  | | 
% 243.04/49.73  | | REDUCE: (21), (45) imply:
% 243.04/49.73  | |   (53)   ~ (all_22_0 = e1)
% 243.04/49.73  | | 
% 243.04/49.73  | | REDUCE: (22), (48) imply:
% 243.04/49.73  | |   (54)   ~ (all_22_0 = e0)
% 243.04/49.73  | | 
% 243.04/49.73  | | BETA: splitting (17) gives:
% 243.04/49.73  | | 
% 243.04/49.73  | | Case 1:
% 243.04/49.73  | | | 
% 243.04/49.73  | | |   (55)  all_58_15 = e0 & op(e0, e0) = e0
% 243.04/49.73  | | | 
% 243.04/49.73  | | | ALPHA: (55) implies:
% 243.04/49.73  | | |   (56)  op(e0, e0) = e0
% 243.04/49.73  | | | 
% 243.04/49.73  | | | REF_CLOSE: (1), (29), (32), (56) are inconsistent by sub-proof #2274.
% 243.04/49.73  | | | 
% 243.04/49.73  | | Case 2:
% 243.04/49.73  | | | 
% 243.04/49.73  | | |   (57)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 243.04/49.73  | | |             = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0
% 243.04/49.73  | | |             & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.04/49.73  | | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 243.04/49.73  | | | 
% 243.04/49.73  | | | ALPHA: (57) implies:
% 243.04/49.73  | | |   (58)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2)
% 243.04/49.73  | | |           = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.73  | | | 
% 243.04/49.73  | | | BETA: splitting (14) gives:
% 243.04/49.73  | | | 
% 243.04/49.73  | | | Case 1:
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | |   (59)  all_54_13 = e2
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | COMBINE_EQS: (49), (59) imply:
% 243.04/49.73  | | | |   (60)  all_22_0 = e2
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | SIMP: (60) implies:
% 243.04/49.73  | | | |   (61)  all_22_0 = e2
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | REDUCE: (50), (61) imply:
% 243.04/49.73  | | | |   (62)   ~ (all_52_3 = e2)
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | REDUCE: (51), (61) imply:
% 243.04/49.73  | | | |   (63)   ~ (all_52_6 = e2)
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | REDUCE: (52), (61) imply:
% 243.04/49.73  | | | |   (64)   ~ (e3 = e2)
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | SIMP: (64) implies:
% 243.04/49.73  | | | |   (65)   ~ (e3 = e2)
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | REDUCE: (53), (61) imply:
% 243.04/49.73  | | | |   (66)   ~ (e2 = e1)
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | REDUCE: (54), (61) imply:
% 243.04/49.73  | | | |   (67)   ~ (e2 = e0)
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | REDUCE: (44), (61) imply:
% 243.04/49.73  | | | |   (68)  op(e0, e2) = e2
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | BETA: splitting (35) gives:
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | Case 1:
% 243.04/49.73  | | | | | 
% 243.04/49.73  | | | | |   (69)  all_54_9 = e2
% 243.04/49.73  | | | | | 
% 243.04/49.73  | | | | | REF_CLOSE: (18), (63), (69) are inconsistent by sub-proof #1954.
% 243.04/49.73  | | | | | 
% 243.04/49.73  | | | | Case 2:
% 243.04/49.73  | | | | | 
% 243.04/49.73  | | | | |   (70)   ~ (all_54_9 = e2)
% 243.04/49.73  | | | | |   (71)  all_54_9 = e1 | all_54_9 = e0
% 243.04/49.73  | | | | | 
% 243.04/49.73  | | | | | BETA: splitting (6) gives:
% 243.04/49.73  | | | | | 
% 243.04/49.73  | | | | | Case 1:
% 243.04/49.73  | | | | | | 
% 243.04/49.73  | | | | | |   (72)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) =
% 243.04/49.73  | | | | | |           all_56_9 & $i(all_56_9)) | (all_56_10 = e2 & op(e2,
% 243.04/49.73  | | | | | |             all_56_11) = e2)
% 243.04/49.73  | | | | | | 
% 243.04/49.73  | | | | | | BETA: splitting (72) gives:
% 243.04/49.73  | | | | | | 
% 243.04/49.73  | | | | | | Case 1:
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | |   (73)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) =
% 243.04/49.73  | | | | | | |         all_56_9 & $i(all_56_9)
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | | ALPHA: (73) implies:
% 243.04/49.73  | | | | | | |   (74)  op(e3, e2) = all_56_9
% 243.04/49.73  | | | | | | |   (75)  op(e3, all_56_9) = e3
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | | BETA: splitting (27) gives:
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | | Case 1:
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | |   (76)  all_54_12 = e2
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | | REF_CLOSE: (23), (62), (76) are inconsistent by sub-proof #2264.
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | Case 2:
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | |   (77)  all_54_12 = e1 | all_54_12 = e0
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | | BETA: splitting (77) gives:
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | | Case 1:
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | |   (78)  all_54_12 = e1
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | REF_CLOSE: (3), (23), (78) are inconsistent by sub-proof
% 243.04/49.73  | | | | | | | | |            #2263.
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | Case 2:
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | GROUND_INST: instantiating (29) with e3, all_56_9, e2, e3,
% 243.04/49.73  | | | | | | | | |              simplifying with (33), (74) gives:
% 243.04/49.73  | | | | | | | | |   (79)  all_56_9 = e3
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | REDUCE: (75), (79) imply:
% 243.04/49.73  | | | | | | | | |   (80)  op(e3, e3) = e3
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | REF_CLOSE: (12), (15), (29), (80) are inconsistent by
% 243.04/49.73  | | | | | | | | |            sub-proof #1578.
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | End of split
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | End of split
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | Case 2:
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | |   (81)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | | ALPHA: (81) implies:
% 243.04/49.73  | | | | | | |   (82)  op(e2, all_56_11) = e2
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | | REDUCE: (5), (82) imply:
% 243.04/49.73  | | | | | | |   (83)  op(e2, e1) = e2
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | | REF_CLOSE: (26), (29), (67), (83) are inconsistent by sub-proof
% 243.04/49.73  | | | | | | |            #1906.
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | End of split
% 243.04/49.73  | | | | | | 
% 243.04/49.73  | | | | | Case 2:
% 243.04/49.73  | | | | | | 
% 243.04/49.73  | | | | | |   (84)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 243.04/49.73  | | | | | |           all_56_13 & $i(all_56_13)) | (all_56_14 = e0 & op(e0,
% 243.04/49.73  | | | | | |             all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 243.04/49.73  | | | | | |           $i(all_56_15))
% 243.04/49.73  | | | | | | 
% 243.04/49.73  | | | | | | BETA: splitting (84) gives:
% 243.04/49.73  | | | | | | 
% 243.04/49.73  | | | | | | Case 1:
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | |   (85)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 243.04/49.73  | | | | | | |         all_56_13 & $i(all_56_13)
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | | REF_CLOSE: (2), (9), (10), (18), (20), (29), (71), (85) are
% 243.04/49.73  | | | | | | |            inconsistent by sub-proof #2054.
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | Case 2:
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | |   (86)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 243.04/49.73  | | | | | | |         all_56_15 & $i(all_56_15)
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | | ALPHA: (86) implies:
% 243.04/49.73  | | | | | | |   (87)  op(e0, e2) = all_56_15
% 243.04/49.73  | | | | | | |   (88)  op(e0, all_56_15) = e0
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | | BETA: splitting (58) gives:
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | | Case 1:
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | |   (89)  all_58_12 = e0 & op(e0, e3) = e0
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | | ALPHA: (89) implies:
% 243.04/49.73  | | | | | | | |   (90)  all_58_12 = e0
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | | BETA: splitting (71) gives:
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | | Case 1:
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | |   (91)  all_54_9 = e1
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | REF_CLOSE: (2), (18), (91) are inconsistent by sub-proof
% 243.04/49.73  | | | | | | | | |            #2055.
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | Case 2:
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | |   (92)  all_54_9 = e0
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | COMBINE_EQS: (18), (92) imply:
% 243.04/49.73  | | | | | | | | |   (93)  all_52_6 = e0
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | SIMP: (93) implies:
% 243.04/49.73  | | | | | | | | |   (94)  all_52_6 = e0
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | REDUCE: (63), (94) imply:
% 243.04/49.73  | | | | | | | | |   (95)   ~ (e2 = e0)
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | GROUND_INST: instantiating (29) with e2, all_56_15, e2, e0,
% 243.04/49.73  | | | | | | | | |              simplifying with (68), (87) gives:
% 243.04/49.73  | | | | | | | | |   (96)  all_56_15 = e2
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | REDUCE: (88), (96) imply:
% 243.04/49.73  | | | | | | | | |   (97)  op(e0, e2) = e0
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | | REF_CLOSE: (24), (29), (30), (34), (65), (66), (67), (90),
% 243.04/49.73  | | | | | | | | |            (97) are inconsistent by sub-proof #1916.
% 243.04/49.73  | | | | | | | | | 
% 243.04/49.73  | | | | | | | | End of split
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | Case 2:
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | |   (98)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 243.04/49.73  | | | | | | | |           op(e0, e1) = e0)
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | | REF_CLOSE: (4), (7), (29), (67), (68), (98) are inconsistent by
% 243.04/49.73  | | | | | | | |            sub-proof #1635.
% 243.04/49.73  | | | | | | | | 
% 243.04/49.73  | | | | | | | End of split
% 243.04/49.73  | | | | | | | 
% 243.04/49.73  | | | | | | End of split
% 243.04/49.73  | | | | | | 
% 243.04/49.73  | | | | | End of split
% 243.04/49.73  | | | | | 
% 243.04/49.73  | | | | End of split
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | Case 2:
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | |   (99)  all_54_13 = e1 | all_54_13 = e0
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | REF_CLOSE: (49), (53), (54), (99) are inconsistent by sub-proof #1842.
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | End of split
% 243.04/49.73  | | | 
% 243.04/49.73  | | End of split
% 243.04/49.73  | | 
% 243.04/49.73  | Case 2:
% 243.04/49.73  | | 
% 243.04/49.73  | |   (100)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 & $i(all_22_1)
% 243.04/49.73  | | 
% 243.04/49.73  | | ALPHA: (100) implies:
% 243.04/49.73  | |   (101)   ~ (all_22_1 = e0)
% 243.04/49.73  | |   (102)  op(e2, e1) = all_22_1
% 243.04/49.73  | | 
% 243.04/49.73  | | REF_CLOSE: (19), (26), (29), (101), (102) are inconsistent by sub-proof
% 243.04/49.73  | |            #1356.
% 243.04/49.73  | | 
% 243.04/49.73  | End of split
% 243.04/49.73  | 
% 243.04/49.73  End of proof
% 243.04/49.73  
% 243.04/49.73  Sub-proof #1118 shows that the following formulas are inconsistent:
% 243.04/49.73  ----------------------------------------------------------------
% 243.04/49.73    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.04/49.73    (2)   ~ (all_10_0 = e2)
% 243.04/49.73    (3)  all_54_4 = all_52_1
% 243.04/49.73    (4)   ~ (all_52_1 = e0)
% 243.04/49.73    (5)  all_54_4 = all_10_0
% 243.04/49.73    (6)   ~ (all_52_1 = e1)
% 243.04/49.73  
% 243.04/49.73  Begin of proof
% 243.04/49.73  | 
% 243.04/49.73  | BETA: splitting (1) gives:
% 243.04/49.73  | 
% 243.04/49.73  | Case 1:
% 243.04/49.73  | | 
% 243.04/49.73  | |   (7)  all_54_4 = e2
% 243.04/49.73  | | 
% 243.04/49.73  | | COMBINE_EQS: (5), (7) imply:
% 243.04/49.73  | |   (8)  all_10_0 = e2
% 243.04/49.73  | | 
% 243.04/49.73  | | REDUCE: (2), (8) imply:
% 243.04/49.73  | |   (9)  $false
% 243.04/49.73  | | 
% 243.04/49.73  | | CLOSE: (9) is inconsistent.
% 243.04/49.73  | | 
% 243.04/49.73  | Case 2:
% 243.04/49.73  | | 
% 243.04/49.73  | |   (10)  all_54_4 = e1 | all_54_4 = e0
% 243.04/49.73  | | 
% 243.04/49.73  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #1922.
% 243.04/49.73  | | 
% 243.04/49.73  | End of split
% 243.04/49.73  | 
% 243.04/49.73  End of proof
% 243.04/49.73  
% 243.04/49.73  Sub-proof #1119 shows that the following formulas are inconsistent:
% 243.04/49.73  ----------------------------------------------------------------
% 243.04/49.73    (1)  op(e0, e0) = e1
% 243.04/49.73    (2)  all_54_3 = all_20_0
% 243.04/49.73    (3)   ~ (e3 = e0)
% 243.04/49.73    (4)   ~ (e2 = e0)
% 243.04/49.73    (5)  op(e0, e1) = e3
% 243.04/49.73    (6)  op(e0, e1) = all_34_1
% 243.04/49.73    (7)  op(e1, e0) = all_52_14
% 243.04/49.73    (8)   ~ (all_52_13 = all_20_0)
% 243.04/49.73    (9)   ~ (e3 = e1)
% 243.04/49.73    (10)   ~ (all_20_0 = e1)
% 243.04/49.73    (11)  op(all_34_1, e0) = all_34_0
% 243.04/49.73    (12)   ~ (all_52_2 = e1)
% 243.04/49.73    (13)   ~ (all_20_0 = e2)
% 243.04/49.73    (14)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.73              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.04/49.73                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.73                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.73    (15)   ~ (e3 = e2)
% 243.04/49.73    (16)   ~ (all_52_14 = e0)
% 243.04/49.73    (17)  op(e2, e2) = e1
% 243.04/49.73    (18)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 243.04/49.73            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 243.04/49.73            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 243.04/49.73            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 243.04/49.73            op(e0, all_56_31) = e0)
% 243.04/49.73    (19)  all_56_31 = e1
% 243.04/49.73    (20)  all_58_15 = e1
% 243.04/49.73    (21)  op(e3, e0) = all_52_12
% 243.04/49.73    (22)   ~ (all_34_0 = e3)
% 243.04/49.73    (23)  op(e0, e1) = all_20_1
% 243.04/49.73    (24)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.04/49.73          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.73    (25)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.04/49.73    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.73    (27)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.04/49.73          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.04/49.73    (28)  op(e1, e3) = all_52_2
% 243.04/49.73    (29)   ~ (all_52_12 = e3)
% 243.04/49.73    (30)   ~ (e1 = e0)
% 243.04/49.73    (31)   ~ (all_52_13 = e3)
% 243.04/49.73    (32)  op(e2, e0) = all_52_13
% 243.04/49.73    (33)   ~ (e2 = e1)
% 243.04/49.73  
% 243.04/49.73  Begin of proof
% 243.04/49.73  | 
% 243.04/49.73  | BETA: splitting (24) gives:
% 243.04/49.73  | 
% 243.04/49.73  | Case 1:
% 243.04/49.73  | | 
% 243.04/49.73  | |   (34)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 243.04/49.73  | |           e3)
% 243.04/49.73  | | 
% 243.04/49.73  | | BETA: splitting (34) gives:
% 243.04/49.73  | | 
% 243.04/49.73  | | Case 1:
% 243.04/49.73  | | | 
% 243.04/49.73  | | |   (35)  all_58_9 = e3 & op(e3, e0) = e3
% 243.04/49.73  | | | 
% 243.04/49.73  | | | ALPHA: (35) implies:
% 243.04/49.73  | | |   (36)  op(e3, e0) = e3
% 243.04/49.73  | | | 
% 243.04/49.73  | | | REF_CLOSE: (5), (6), (11), (22), (23), (26), (36) are inconsistent by
% 243.04/49.73  | | |            sub-proof #2250.
% 243.04/49.73  | | | 
% 243.04/49.73  | | Case 2:
% 243.04/49.73  | | | 
% 243.04/49.73  | | |   (37)  all_58_10 = e3 & op(e2, e0) = e3
% 243.04/49.73  | | | 
% 243.04/49.73  | | | ALPHA: (37) implies:
% 243.04/49.73  | | |   (38)  op(e2, e0) = e3
% 243.04/49.73  | | | 
% 243.04/49.73  | | | REF_CLOSE: (26), (31), (32), (38) are inconsistent by sub-proof #1994.
% 243.04/49.73  | | | 
% 243.04/49.73  | | End of split
% 243.04/49.73  | | 
% 243.04/49.73  | Case 2:
% 243.04/49.73  | | 
% 243.04/49.73  | |   (39)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 243.04/49.73  | |           e3)
% 243.04/49.73  | | 
% 243.04/49.73  | | BETA: splitting (39) gives:
% 243.04/49.73  | | 
% 243.04/49.73  | | Case 1:
% 243.04/49.73  | | | 
% 243.04/49.73  | | |   (40)  all_58_11 = e3 & op(e1, e0) = e3
% 243.04/49.73  | | | 
% 243.04/49.73  | | | ALPHA: (40) implies:
% 243.04/49.73  | | |   (41)  all_58_11 = e3
% 243.04/49.73  | | |   (42)  op(e1, e0) = e3
% 243.04/49.73  | | | 
% 243.04/49.73  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (12), (13), (14),
% 243.04/49.73  | | |            (15), (16), (17), (18), (19), (20), (21), (25), (26), (27),
% 243.04/49.73  | | |            (28), (29), (30), (32), (33), (41), (42) are inconsistent by
% 243.04/49.73  | | |            sub-proof #1120.
% 243.04/49.73  | | | 
% 243.04/49.73  | | Case 2:
% 243.04/49.73  | | | 
% 243.04/49.73  | | |   (43)  all_58_15 = e3 & op(e0, e0) = e3
% 243.04/49.73  | | | 
% 243.04/49.73  | | | ALPHA: (43) implies:
% 243.04/49.73  | | |   (44)  all_58_15 = e3
% 243.04/49.73  | | | 
% 243.04/49.73  | | | REF_CLOSE: (9), (20), (44) are inconsistent by sub-proof #2249.
% 243.04/49.73  | | | 
% 243.04/49.73  | | End of split
% 243.04/49.73  | | 
% 243.04/49.73  | End of split
% 243.04/49.73  | 
% 243.04/49.73  End of proof
% 243.04/49.73  
% 243.04/49.73  Sub-proof #1120 shows that the following formulas are inconsistent:
% 243.04/49.73  ----------------------------------------------------------------
% 243.04/49.73    (1)  op(e0, e0) = e1
% 243.04/49.73    (2)  all_54_3 = all_20_0
% 243.04/49.73    (3)   ~ (e3 = e0)
% 243.04/49.73    (4)   ~ (e2 = e0)
% 243.04/49.73    (5)  op(e0, e1) = e3
% 243.04/49.73    (6)  op(e1, e0) = all_52_14
% 243.04/49.73    (7)   ~ (all_52_13 = all_20_0)
% 243.04/49.73    (8)   ~ (all_20_0 = e1)
% 243.04/49.73    (9)  all_58_11 = e3
% 243.04/49.73    (10)   ~ (all_52_2 = e1)
% 243.04/49.73    (11)   ~ (all_20_0 = e2)
% 243.04/49.73    (12)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.73              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.04/49.73                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.73                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.73    (13)   ~ (e3 = e2)
% 243.04/49.73    (14)  op(e1, e0) = e3
% 243.04/49.73    (15)   ~ (all_52_14 = e0)
% 243.04/49.73    (16)  op(e2, e2) = e1
% 243.04/49.73    (17)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 243.04/49.73            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 243.04/49.73            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 243.04/49.73            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 243.04/49.73            op(e0, all_56_31) = e0)
% 243.04/49.73    (18)  all_56_31 = e1
% 243.04/49.73    (19)  all_58_15 = e1
% 243.04/49.73    (20)  op(e3, e0) = all_52_12
% 243.04/49.73    (21)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.04/49.73    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.73    (23)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.04/49.73          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.04/49.73    (24)  op(e1, e3) = all_52_2
% 243.04/49.73    (25)   ~ (all_52_12 = e3)
% 243.04/49.73    (26)   ~ (e1 = e0)
% 243.04/49.73    (27)  op(e2, e0) = all_52_13
% 243.04/49.73    (28)   ~ (e2 = e1)
% 243.04/49.73  
% 243.04/49.73  Begin of proof
% 243.04/49.73  | 
% 243.04/49.73  | BETA: splitting (23) gives:
% 243.04/49.73  | 
% 243.04/49.73  | Case 1:
% 243.04/49.73  | | 
% 243.04/49.73  | |   (29)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 243.04/49.73  | |           e2)
% 243.04/49.73  | | 
% 243.04/49.73  | | BETA: splitting (29) gives:
% 243.04/49.73  | | 
% 243.04/49.73  | | Case 1:
% 243.04/49.73  | | | 
% 243.04/49.73  | | |   (30)  all_58_9 = e2 & op(e3, e0) = e2
% 243.04/49.73  | | | 
% 243.04/49.73  | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (11), (12), (15), (21), (22),
% 243.04/49.73  | | |            (26), (27), (30) are inconsistent by sub-proof #1122.
% 243.04/49.73  | | | 
% 243.04/49.73  | | Case 2:
% 243.04/49.73  | | | 
% 243.04/49.73  | | |   (31)  all_58_10 = e2 & op(e2, e0) = e2
% 243.04/49.73  | | | 
% 243.04/49.73  | | | ALPHA: (31) implies:
% 243.04/49.73  | | |   (32)  op(e2, e0) = e2
% 243.04/49.73  | | | 
% 243.04/49.73  | | | BETA: splitting (17) gives:
% 243.04/49.73  | | | 
% 243.04/49.73  | | | Case 1:
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | |   (33)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 243.04/49.73  | | | |           all_56_25 & $i(all_56_25)) | (all_56_26 = e2 & op(e2,
% 243.04/49.73  | | | |             all_56_27) = e2 & op(e2, e0) = all_56_27 & $i(all_56_27))
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | BETA: splitting (33) gives:
% 243.04/49.73  | | | | 
% 243.04/49.73  | | | | Case 1:
% 243.04/49.73  | | | | | 
% 243.04/49.73  | | | | |   (34)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 243.04/49.73  | | | | |         all_56_25 & $i(all_56_25)
% 243.04/49.73  | | | | | 
% 243.04/49.73  | | | | | ALPHA: (34) implies:
% 243.04/49.74  | | | | |   (35)  op(e3, e0) = all_56_25
% 243.04/49.74  | | | | |   (36)  op(e3, all_56_25) = e3
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | REF_CLOSE: (1), (3), (4), (9), (12), (20), (22), (25), (26), (32),
% 243.04/49.74  | | | | |            (35), (36) are inconsistent by sub-proof #1121.
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | Case 2:
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | |   (37)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 243.04/49.74  | | | | |         all_56_27 & $i(all_56_27)
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | ALPHA: (37) implies:
% 243.04/49.74  | | | | |   (38)  op(e2, e0) = all_56_27
% 243.04/49.74  | | | | |   (39)  op(e2, all_56_27) = e2
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | GROUND_INST: instantiating (22) with e2, all_56_27, e0, e2,
% 243.04/49.74  | | | | |              simplifying with (32), (38) gives:
% 243.04/49.74  | | | | |   (40)  all_56_27 = e2
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | REDUCE: (39), (40) imply:
% 243.04/49.74  | | | | |   (41)  op(e2, e2) = e2
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | REF_CLOSE: (16), (22), (28), (41) are inconsistent by sub-proof #2235.
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | End of split
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | Case 2:
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | |   (42)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 243.04/49.74  | | | |           all_56_29 & $i(all_56_29)) | (all_56_30 = e0 & op(e0,
% 243.04/49.74  | | | |             all_56_31) = e0)
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | | BETA: splitting (42) gives:
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | | Case 1:
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | |   (43)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 243.04/49.74  | | | | |         all_56_29 & $i(all_56_29)
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | ALPHA: (43) implies:
% 243.04/49.74  | | | | |   (44)  op(e1, e0) = all_56_29
% 243.04/49.74  | | | | |   (45)  op(e1, all_56_29) = e1
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | GROUND_INST: instantiating (22) with e3, all_56_29, e0, e1,
% 243.04/49.74  | | | | |              simplifying with (14), (44) gives:
% 243.04/49.74  | | | | |   (46)  all_56_29 = e3
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | REDUCE: (45), (46) imply:
% 243.04/49.74  | | | | |   (47)  op(e1, e3) = e1
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | REF_CLOSE: (10), (22), (24), (47) are inconsistent by sub-proof #1948.
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | Case 2:
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | |   (48)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | ALPHA: (48) implies:
% 243.04/49.74  | | | | |   (49)  op(e0, all_56_31) = e0
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | REDUCE: (18), (49) imply:
% 243.04/49.74  | | | | |   (50)  op(e0, e1) = e0
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | REF_CLOSE: (3), (5), (22), (50) are inconsistent by sub-proof #2164.
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | End of split
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | End of split
% 243.04/49.74  | | | 
% 243.04/49.74  | | End of split
% 243.04/49.74  | | 
% 243.04/49.74  | Case 2:
% 243.04/49.74  | | 
% 243.04/49.74  | |   (51)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.04/49.74  | |           e2)
% 243.04/49.74  | | 
% 243.04/49.74  | | BETA: splitting (51) gives:
% 243.04/49.74  | | 
% 243.04/49.74  | | Case 1:
% 243.04/49.74  | | | 
% 243.04/49.74  | | |   (52)  all_58_11 = e2 & op(e1, e0) = e2
% 243.04/49.74  | | | 
% 243.04/49.74  | | | ALPHA: (52) implies:
% 243.04/49.74  | | |   (53)  all_58_11 = e2
% 243.04/49.74  | | | 
% 243.04/49.74  | | | REF_CLOSE: (9), (13), (53) are inconsistent by sub-proof #2030.
% 243.04/49.74  | | | 
% 243.04/49.74  | | Case 2:
% 243.04/49.74  | | | 
% 243.04/49.74  | | |   (54)  all_58_15 = e2 & op(e0, e0) = e2
% 243.04/49.74  | | | 
% 243.04/49.74  | | | ALPHA: (54) implies:
% 243.04/49.74  | | |   (55)  all_58_15 = e2
% 243.04/49.74  | | | 
% 243.04/49.74  | | | REF_CLOSE: (19), (28), (55) are inconsistent by sub-proof #2231.
% 243.04/49.74  | | | 
% 243.04/49.74  | | End of split
% 243.04/49.74  | | 
% 243.04/49.74  | End of split
% 243.04/49.74  | 
% 243.04/49.74  End of proof
% 243.04/49.74  
% 243.04/49.74  Sub-proof #1121 shows that the following formulas are inconsistent:
% 243.04/49.74  ----------------------------------------------------------------
% 243.04/49.74    (1)  op(e0, e0) = e1
% 243.04/49.74    (2)   ~ (e3 = e0)
% 243.04/49.74    (3)   ~ (e2 = e0)
% 243.04/49.74    (4)  op(e3, all_56_25) = e3
% 243.04/49.74    (5)  all_58_11 = e3
% 243.04/49.74    (6)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.74             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.04/49.74               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.74               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.74    (7)  op(e2, e0) = e2
% 243.04/49.74    (8)  op(e3, e0) = all_52_12
% 243.04/49.74    (9)  op(e3, e0) = all_56_25
% 243.04/49.74    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.74            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.74    (11)   ~ (all_52_12 = e3)
% 243.04/49.74    (12)   ~ (e1 = e0)
% 243.04/49.74  
% 243.04/49.74  Begin of proof
% 243.04/49.74  | 
% 243.04/49.74  | BETA: splitting (6) gives:
% 243.04/49.74  | 
% 243.04/49.74  | Case 1:
% 243.04/49.74  | | 
% 243.04/49.74  | |   (13)  all_58_15 = e0 & op(e0, e0) = e0
% 243.04/49.74  | | 
% 243.04/49.74  | | ALPHA: (13) implies:
% 243.04/49.74  | |   (14)  op(e0, e0) = e0
% 243.04/49.74  | | 
% 243.04/49.74  | | REF_CLOSE: (1), (10), (12), (14) are inconsistent by sub-proof #2274.
% 243.04/49.74  | | 
% 243.04/49.74  | Case 2:
% 243.04/49.74  | | 
% 243.04/49.74  | |   (15)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.04/49.74  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 243.04/49.74  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.04/49.74  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 243.04/49.74  | | 
% 243.04/49.74  | | ALPHA: (15) implies:
% 243.04/49.74  | |   (16)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.04/49.74  | |           e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.04/49.74  | | 
% 243.04/49.74  | | BETA: splitting (16) gives:
% 243.04/49.74  | | 
% 243.04/49.74  | | Case 1:
% 243.04/49.74  | | | 
% 243.04/49.74  | | |   (17)  all_58_9 = e0 & op(e3, e0) = e0
% 243.04/49.74  | | | 
% 243.04/49.74  | | | ALPHA: (17) implies:
% 243.04/49.74  | | |   (18)  op(e3, e0) = e0
% 243.04/49.74  | | | 
% 243.04/49.74  | | | GROUND_INST: instantiating (10) with e0, all_56_25, e0, e3, simplifying
% 243.04/49.74  | | |              with (9), (18) gives:
% 243.04/49.74  | | |   (19)  all_56_25 = e0
% 243.04/49.74  | | | 
% 243.04/49.74  | | | REDUCE: (4), (19) imply:
% 243.04/49.74  | | |   (20)  op(e3, e0) = e3
% 243.04/49.74  | | | 
% 243.04/49.74  | | | REF_CLOSE: (8), (10), (11), (20) are inconsistent by sub-proof #2179.
% 243.04/49.74  | | | 
% 243.04/49.74  | | Case 2:
% 243.04/49.74  | | | 
% 243.04/49.74  | | |   (21)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.04/49.74  | | |           = e0)
% 243.04/49.74  | | | 
% 243.04/49.74  | | | REF_CLOSE: (2), (3), (5), (7), (10), (21) are inconsistent by sub-proof
% 243.04/49.74  | | |            #1743.
% 243.04/49.74  | | | 
% 243.04/49.74  | | End of split
% 243.04/49.74  | | 
% 243.04/49.74  | End of split
% 243.04/49.74  | 
% 243.04/49.74  End of proof
% 243.04/49.74  
% 243.04/49.74  Sub-proof #1122 shows that the following formulas are inconsistent:
% 243.04/49.74  ----------------------------------------------------------------
% 243.04/49.74    (1)  op(e0, e0) = e1
% 243.04/49.74    (2)  all_54_3 = all_20_0
% 243.04/49.74    (3)   ~ (e2 = e0)
% 243.04/49.74    (4)  op(e1, e0) = all_52_14
% 243.04/49.74    (5)   ~ (all_52_13 = all_20_0)
% 243.04/49.74    (6)   ~ (all_20_0 = e1)
% 243.04/49.74    (7)   ~ (all_20_0 = e2)
% 243.04/49.74    (8)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.74             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.04/49.74               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.74               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.74    (9)   ~ (all_52_14 = e0)
% 243.04/49.74    (10)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.04/49.74    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.74            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.74    (12)   ~ (e1 = e0)
% 243.04/49.74    (13)  op(e2, e0) = all_52_13
% 243.04/49.74    (14)  all_58_9 = e2 & op(e3, e0) = e2
% 243.04/49.74  
% 243.04/49.74  Begin of proof
% 243.04/49.74  | 
% 243.04/49.74  | ALPHA: (14) implies:
% 243.04/49.74  |   (15)  all_58_9 = e2
% 243.04/49.74  | 
% 243.04/49.74  | BETA: splitting (8) gives:
% 243.04/49.74  | 
% 243.04/49.74  | Case 1:
% 243.04/49.74  | | 
% 243.04/49.74  | |   (16)  all_58_15 = e0 & op(e0, e0) = e0
% 243.04/49.74  | | 
% 243.04/49.74  | | ALPHA: (16) implies:
% 243.04/49.74  | |   (17)  op(e0, e0) = e0
% 243.04/49.74  | | 
% 243.04/49.74  | | REF_CLOSE: (1), (11), (12), (17) are inconsistent by sub-proof #2274.
% 243.04/49.74  | | 
% 243.04/49.74  | Case 2:
% 243.04/49.74  | | 
% 243.04/49.74  | |   (18)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.04/49.74  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 243.04/49.74  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.04/49.74  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 243.04/49.74  | | 
% 243.04/49.74  | | ALPHA: (18) implies:
% 243.04/49.74  | |   (19)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.04/49.74  | |           e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.04/49.74  | | 
% 243.04/49.74  | | BETA: splitting (19) gives:
% 243.04/49.74  | | 
% 243.04/49.74  | | Case 1:
% 243.04/49.74  | | | 
% 243.04/49.74  | | |   (20)  all_58_9 = e0 & op(e3, e0) = e0
% 243.04/49.74  | | | 
% 243.04/49.74  | | | REF_CLOSE: (3), (15), (20) are inconsistent by sub-proof #1563.
% 243.04/49.74  | | | 
% 243.04/49.74  | | Case 2:
% 243.04/49.74  | | | 
% 243.04/49.74  | | |   (21)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.04/49.74  | | |           = e0)
% 243.04/49.74  | | | 
% 243.04/49.74  | | | BETA: splitting (21) gives:
% 243.04/49.74  | | | 
% 243.04/49.74  | | | Case 1:
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | |   (22)  all_58_10 = e0 & op(e2, e0) = e0
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | | ALPHA: (22) implies:
% 243.04/49.74  | | | |   (23)  op(e2, e0) = e0
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | | BETA: splitting (10) gives:
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | | Case 1:
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | |   (24)  all_54_3 = e2
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | COMBINE_EQS: (2), (24) imply:
% 243.04/49.74  | | | | |   (25)  all_20_0 = e2
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | REDUCE: (7), (25) imply:
% 243.04/49.74  | | | | |   (26)  $false
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | CLOSE: (26) is inconsistent.
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | Case 2:
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | |   (27)  all_54_3 = e1 | all_54_3 = e0
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | BETA: splitting (27) gives:
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | | Case 1:
% 243.04/49.74  | | | | | | 
% 243.04/49.74  | | | | | |   (28)  all_54_3 = e1
% 243.04/49.74  | | | | | | 
% 243.04/49.74  | | | | | | COMBINE_EQS: (2), (28) imply:
% 243.04/49.74  | | | | | |   (29)  all_20_0 = e1
% 243.04/49.74  | | | | | | 
% 243.04/49.74  | | | | | | REDUCE: (6), (29) imply:
% 243.04/49.74  | | | | | |   (30)  $false
% 243.04/49.74  | | | | | | 
% 243.04/49.74  | | | | | | CLOSE: (30) is inconsistent.
% 243.04/49.74  | | | | | | 
% 243.04/49.74  | | | | | Case 2:
% 243.04/49.74  | | | | | | 
% 243.04/49.74  | | | | | |   (31)  all_54_3 = e0
% 243.04/49.74  | | | | | | 
% 243.04/49.74  | | | | | | COMBINE_EQS: (2), (31) imply:
% 243.04/49.74  | | | | | |   (32)  all_20_0 = e0
% 243.04/49.74  | | | | | | 
% 243.04/49.74  | | | | | | REDUCE: (5), (32) imply:
% 243.04/49.74  | | | | | |   (33)   ~ (all_52_13 = e0)
% 243.04/49.74  | | | | | | 
% 243.04/49.74  | | | | | | REF_CLOSE: (11), (13), (23), (33) are inconsistent by sub-proof
% 243.04/49.74  | | | | | |            #2324.
% 243.04/49.74  | | | | | | 
% 243.04/49.74  | | | | | End of split
% 243.04/49.74  | | | | | 
% 243.04/49.74  | | | | End of split
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | Case 2:
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | |   (34)  all_58_11 = e0 & op(e1, e0) = e0
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | | ALPHA: (34) implies:
% 243.04/49.74  | | | |   (35)  op(e1, e0) = e0
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | | REF_CLOSE: (4), (9), (11), (35) are inconsistent by sub-proof #2323.
% 243.04/49.74  | | | | 
% 243.04/49.74  | | | End of split
% 243.04/49.74  | | | 
% 243.04/49.74  | | End of split
% 243.04/49.74  | | 
% 243.04/49.74  | End of split
% 243.04/49.74  | 
% 243.04/49.74  End of proof
% 243.04/49.74  
% 243.04/49.74  Sub-proof #1123 shows that the following formulas are inconsistent:
% 243.04/49.74  ----------------------------------------------------------------
% 243.04/49.74    (1)   ~ (all_52_7 = e3)
% 243.04/49.74    (2)  op(e0, e3) = all_52_3
% 243.04/49.74    (3)   ~ (all_52_3 = e3)
% 243.04/49.74    (4)  op(e0, e2) = all_52_7
% 243.04/49.74    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.74    (6)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.04/49.74  
% 243.04/49.74  Begin of proof
% 243.04/49.74  | 
% 243.04/49.74  | BETA: splitting (6) gives:
% 243.04/49.74  | 
% 243.04/49.74  | Case 1:
% 243.04/49.74  | | 
% 243.04/49.74  | |   (7)  all_58_12 = e3 & op(e0, e3) = e3
% 243.04/49.74  | | 
% 243.04/49.74  | | ALPHA: (7) implies:
% 243.04/49.74  | |   (8)  op(e0, e3) = e3
% 243.04/49.74  | | 
% 243.04/49.74  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #2332.
% 243.04/49.74  | | 
% 243.04/49.74  | Case 2:
% 243.04/49.74  | | 
% 243.04/49.74  | |   (9)  all_58_13 = e3 & op(e0, e2) = e3
% 243.04/49.74  | | 
% 243.04/49.74  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1919.
% 243.04/49.74  | | 
% 243.04/49.74  | End of split
% 243.04/49.74  | 
% 243.04/49.74  End of proof
% 243.04/49.74  
% 243.04/49.74  Sub-proof #1124 shows that the following formulas are inconsistent:
% 243.04/49.74  ----------------------------------------------------------------
% 243.04/49.74    (1)  op(e0, e0) = e1
% 243.04/49.74    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.04/49.74         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.04/49.74    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.04/49.74         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.04/49.74    (4)   ~ (e3 = e0)
% 243.04/49.74    (5)  all_58_1 = e3
% 243.04/49.74    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.04/49.74         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.04/49.74    (7)  op(e1, e1) = e1
% 243.04/49.74    (8)   ~ (e2 = e0)
% 243.04/49.74    (9)  all_58_5 = e3
% 243.04/49.74    (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.74          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.74    (11)  all_58_8 = e1
% 243.04/49.74    (12)  op(e1, e0) = all_52_14
% 243.04/49.74    (13)  all_58_14 = e2
% 243.04/49.74    (14)   ~ (all_52_7 = e3)
% 243.04/49.74    (15)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.04/49.74          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.04/49.74    (16)   ~ (e3 = e1)
% 243.04/49.74    (17)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.04/49.74          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.74    (18)  all_58_11 = e3
% 243.04/49.74    (19)   ~ (all_22_1 = e0)
% 243.04/49.74    (20)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.04/49.74          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.04/49.74    (21)  op(e3, e3) = e1
% 243.04/49.74    (22)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.04/49.74              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.04/49.74                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.04/49.74                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.04/49.74    (23)  op(e1, all_52_2) = e1
% 243.04/49.74    (24)   ~ (e3 = e2)
% 243.04/49.74    (25)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.04/49.74          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.04/49.74    (26)   ~ (all_52_14 = e1)
% 243.04/49.74    (27)  op(e2, e2) = e1
% 243.04/49.74    (28)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.04/49.74          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.04/49.74    (29)  all_58_15 = e1
% 243.04/49.74    (30)  all_58_12 = e3
% 243.04/49.74    (31)  op(e0, e2) = all_52_7
% 243.04/49.74    (32)  op(e2, e1) = e3
% 243.04/49.74    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.04/49.74            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.04/49.74    (34)  op(e1, e3) = all_52_2
% 243.04/49.74    (35)   ~ (e1 = e0)
% 243.04/49.74    (36)  op(e2, e1) = all_22_1
% 243.04/49.74    (37)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.04/49.74          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.04/49.74    (38)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.04/49.74          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.04/49.74            e2)
% 243.04/49.74    (39)   ~ (e2 = e1)
% 243.04/49.74    (40)  op(e2, e1) = all_30_1
% 243.04/49.74  
% 243.04/49.74  Begin of proof
% 243.04/49.74  | 
% 243.04/49.74  | BETA: splitting (22) gives:
% 243.04/49.74  | 
% 243.04/49.74  | Case 1:
% 243.04/49.74  | | 
% 243.04/49.74  | |   (41)  all_58_15 = e0 & op(e0, e0) = e0
% 243.04/49.74  | | 
% 243.04/49.74  | | ALPHA: (41) implies:
% 243.04/49.74  | |   (42)  op(e0, e0) = e0
% 243.04/49.74  | | 
% 243.04/49.74  | | REF_CLOSE: (1), (33), (35), (42) are inconsistent by sub-proof #2274.
% 243.04/49.74  | | 
% 243.04/49.74  | Case 2:
% 243.04/49.74  | | 
% 243.04/49.74  | |   (43)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.04/49.74  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 243.04/49.74  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.04/49.74  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 243.04/49.74  | | 
% 243.04/49.74  | | ALPHA: (43) implies:
% 243.04/49.75  | |   (44)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 243.04/49.75  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.04/49.75  | |   (45)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.04/49.75  | |           e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.04/49.75  | | 
% 243.04/49.75  | | BETA: splitting (44) gives:
% 243.04/49.75  | | 
% 243.04/49.75  | | Case 1:
% 243.04/49.75  | | | 
% 243.04/49.75  | | |   (46)  all_58_12 = e0 & op(e0, e3) = e0
% 243.04/49.75  | | | 
% 243.04/49.75  | | | ALPHA: (46) implies:
% 243.04/49.75  | | |   (47)  all_58_12 = e0
% 243.04/49.75  | | | 
% 243.04/49.75  | | | REF_CLOSE: (4), (30), (47) are inconsistent by sub-proof #1971.
% 243.04/49.75  | | | 
% 243.04/49.75  | | Case 2:
% 243.04/49.75  | | | 
% 243.04/49.75  | | |   (48)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 243.04/49.75  | | |           = e0)
% 243.04/49.75  | | | 
% 243.04/49.75  | | | BETA: splitting (48) gives:
% 243.04/49.75  | | | 
% 243.04/49.75  | | | Case 1:
% 243.04/49.75  | | | | 
% 243.04/49.75  | | | |   (49)  all_58_13 = e0 & op(e0, e2) = e0
% 243.04/49.75  | | | | 
% 243.04/49.75  | | | | ALPHA: (49) implies:
% 243.04/49.75  | | | |   (50)  op(e0, e2) = e0
% 243.04/49.75  | | | | 
% 243.04/49.75  | | | | BETA: splitting (10) gives:
% 243.04/49.75  | | | | 
% 243.04/49.75  | | | | Case 1:
% 243.04/49.75  | | | | | 
% 243.04/49.75  | | | | |   (51)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2,
% 243.04/49.75  | | | | |             e2) = e2)
% 243.04/49.75  | | | | | 
% 243.04/49.75  | | | | | REF_CLOSE: (5), (24), (27), (33), (39), (51) are inconsistent by
% 243.04/49.75  | | | | |            sub-proof #1322.
% 243.04/49.75  | | | | | 
% 243.04/49.75  | | | | Case 2:
% 243.04/49.75  | | | | | 
% 243.04/49.75  | | | | |   (52)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0,
% 243.04/49.75  | | | | |             e2) = e2)
% 243.04/49.75  | | | | | 
% 243.04/49.75  | | | | | BETA: splitting (52) gives:
% 243.04/49.75  | | | | | 
% 243.04/49.75  | | | | | Case 1:
% 243.04/49.75  | | | | | | 
% 243.04/49.75  | | | | | |   (53)  all_58_7 = e2 & op(e1, e2) = e2
% 243.04/49.75  | | | | | | 
% 243.04/49.75  | | | | | | ALPHA: (53) implies:
% 243.04/49.75  | | | | | |   (54)  all_58_7 = e2
% 243.04/49.75  | | | | | | 
% 243.04/49.75  | | | | | | BETA: splitting (17) gives:
% 243.04/49.75  | | | | | | 
% 243.04/49.75  | | | | | | Case 1:
% 243.04/49.75  | | | | | | | 
% 243.04/49.75  | | | | | | |   (55)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 243.04/49.75  | | | | | | |           op(e2, e1) = e0)
% 243.04/49.75  | | | | | | | 
% 243.04/49.75  | | | | | | | BETA: splitting (55) gives:
% 243.04/49.75  | | | | | | | 
% 243.04/49.75  | | | | | | | Case 1:
% 243.04/49.75  | | | | | | | | 
% 243.04/49.75  | | | | | | | |   (56)  all_58_4 = e0 & op(e3, e1) = e0
% 243.04/49.75  | | | | | | | | 
% 243.04/49.75  | | | | | | | | ALPHA: (56) implies:
% 243.04/49.75  | | | | | | | |   (57)  all_58_4 = e0
% 243.04/49.75  | | | | | | | | 
% 243.04/49.75  | | | | | | | | BETA: splitting (2) gives:
% 243.04/49.75  | | | | | | | | 
% 243.04/49.75  | | | | | | | | Case 1:
% 243.04/49.75  | | | | | | | | | 
% 243.04/49.75  | | | | | | | | |   (58)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 &
% 243.04/49.75  | | | | | | | | |           op(e3, e2) = e2)
% 243.04/49.75  | | | | | | | | | 
% 243.04/49.75  | | | | | | | | | REF_CLOSE: (5), (21), (24), (33), (39), (58) are inconsistent
% 243.04/49.75  | | | | | | | | |            by sub-proof #1132.
% 243.04/49.75  | | | | | | | | | 
% 243.04/49.75  | | | | | | | | Case 2:
% 243.04/49.75  | | | | | | | | | 
% 243.04/49.75  | | | | | | | | |   (59)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 &
% 243.04/49.75  | | | | | | | | |           op(e3, e0) = e2)
% 243.04/49.75  | | | | | | | | | 
% 243.04/49.75  | | | | | | | | | BETA: splitting (59) gives:
% 243.04/49.75  | | | | | | | | | 
% 243.04/49.75  | | | | | | | | | Case 1:
% 243.04/49.75  | | | | | | | | | | 
% 243.04/49.75  | | | | | | | | | |   (60)  all_58_4 = e2 & op(e3, e1) = e2
% 243.04/49.75  | | | | | | | | | | 
% 243.04/49.75  | | | | | | | | | | REF_CLOSE: (8), (9), (11), (13), (24), (25), (39), (57), (60)
% 243.04/49.75  | | | | | | | | | |            are inconsistent by sub-proof #1156.
% 243.04/49.75  | | | | | | | | | | 
% 243.04/49.75  | | | | | | | | | Case 2:
% 243.04/49.75  | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | |   (61)  all_58_9 = e2 & op(e3, e0) = e2
% 243.21/49.75  | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | ALPHA: (61) implies:
% 243.21/49.75  | | | | | | | | | |   (62)  all_58_9 = e2
% 243.21/49.75  | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | BETA: splitting (45) gives:
% 243.21/49.75  | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | Case 1:
% 243.21/49.75  | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | |   (63)  all_58_9 = e0 & op(e3, e0) = e0
% 243.21/49.75  | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | ALPHA: (63) implies:
% 243.21/49.75  | | | | | | | | | | |   (64)  all_58_9 = e0
% 243.21/49.75  | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (16), (20), (21), (24), (33), (39),
% 243.21/49.75  | | | | | | | | | | |            (57), (64) are inconsistent by sub-proof #1190.
% 243.21/49.75  | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | Case 2:
% 243.21/49.75  | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | |   (65)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 243.21/49.75  | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 243.21/49.75  | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | BETA: splitting (65) gives:
% 243.21/49.75  | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | Case 1:
% 243.21/49.75  | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | |   (66)  all_58_10 = e0 & op(e2, e0) = e0
% 243.21/49.75  | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | ALPHA: (66) implies:
% 243.21/49.75  | | | | | | | | | | | |   (67)  op(e2, e0) = e0
% 243.21/49.75  | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | BETA: splitting (15) gives:
% 243.21/49.75  | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | Case 1:
% 243.21/49.75  | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | |   (68)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 243.21/49.75  | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 243.21/49.75  | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | BETA: splitting (68) gives:
% 243.21/49.75  | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | Case 1:
% 243.21/49.75  | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | |   (69)  all_58_2 = e2 & op(e2, e3) = e2
% 243.21/49.75  | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | ALPHA: (69) implies:
% 243.21/49.75  | | | | | | | | | | | | | |   (70)  all_58_2 = e2
% 243.21/49.75  | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 243.21/49.75  | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | Case 1:
% 243.21/49.75  | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | |   (71)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 243.21/49.75  | | | | | | | | | | | | | | |           & op(e2, e3) = e0)
% 243.21/49.75  | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (16), (20), (21), (24), (33), (35),
% 243.21/49.75  | | | | | | | | | | | | | | |            (39), (57), (62), (70), (71) are inconsistent by
% 243.21/49.75  | | | | | | | | | | | | | | |            sub-proof #1130.
% 243.21/49.75  | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | Case 2:
% 243.21/49.75  | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | |   (72)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 243.21/49.75  | | | | | | | | | | | | | | |           e0 & op(e0, e3) = e0)
% 243.21/49.75  | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 243.21/49.75  | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | Case 1:
% 243.21/49.75  | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | |   (73)  all_58_6 = e0 & op(e1, e3) = e0
% 243.21/49.75  | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | ALPHA: (73) implies:
% 243.21/49.75  | | | | | | | | | | | | | | | |   (74)  all_58_6 = e0
% 243.21/49.75  | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 243.21/49.75  | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | Case 1:
% 243.21/49.75  | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | |   (75)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 243.21/49.75  | | | | | | | | | | | | | | | | |           & op(e1, e2) = e0)
% 243.21/49.75  | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 243.21/49.75  | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | Case 1:
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (23), (26), (33), (34), (73) are
% 243.21/49.75  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1188.
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | Case 2:
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | |   (76)  all_58_7 = e0 & op(e1, e2) = e0
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (8), (16), (20), (21), (24), (33), (39),
% 243.21/49.75  | | | | | | | | | | | | | | | | | |            (54), (57), (62), (76) are inconsistent by
% 243.21/49.75  | | | | | | | | | | | | | | | | | |            sub-proof #1125.
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | End of split
% 243.21/49.75  | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | Case 2:
% 243.21/49.75  | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | |   (77)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 243.21/49.75  | | | | | | | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 243.21/49.75  | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 243.21/49.75  | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | Case 1:
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | |   (78)  all_58_8 = e0 & op(e1, e1) = e0
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | | ALPHA: (78) implies:
% 243.21/49.75  | | | | | | | | | | | | | | | | | |   (79)  op(e1, e1) = e0
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (18), (33), (35), (39), (54), (74),
% 243.21/49.75  | | | | | | | | | | | | | | | | | |            (79) are inconsistent by sub-proof #1979.
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | Case 2:
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | |   (80)  all_58_11 = e0 & op(e1, e0) = e0
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (8), (14), (16), (18), (24), (29), (30),
% 243.21/49.75  | | | | | | | | | | | | | | | | | |            (31), (33), (38), (39), (50), (80) are
% 243.21/49.75  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1128.
% 243.21/49.75  | | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | | End of split
% 243.21/49.75  | | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | End of split
% 243.21/49.75  | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | Case 2:
% 243.21/49.75  | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | |   (81)  all_58_12 = e0 & op(e0, e3) = e0
% 243.21/49.75  | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | ALPHA: (81) implies:
% 243.21/49.75  | | | | | | | | | | | | | | | |   (82)  all_58_12 = e0
% 243.21/49.75  | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (8), (14), (16), (24), (29), (31), (33),
% 243.21/49.75  | | | | | | | | | | | | | | | |            (38), (39), (50), (82) are inconsistent by
% 243.21/49.75  | | | | | | | | | | | | | | | |            sub-proof #1914.
% 243.21/49.75  | | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | | End of split
% 243.21/49.75  | | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | End of split
% 243.21/49.75  | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | Case 2:
% 243.21/49.75  | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | |   (83)  all_58_3 = e2 & op(e2, e2) = e2
% 243.21/49.75  | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | ALPHA: (83) implies:
% 243.21/49.75  | | | | | | | | | | | | | |   (84)  op(e2, e2) = e2
% 243.21/49.75  | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | | REF_CLOSE: (27), (33), (39), (84) are inconsistent by
% 243.21/49.75  | | | | | | | | | | | | | |            sub-proof #2235.
% 243.21/49.75  | | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | End of split
% 243.21/49.75  | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | Case 2:
% 243.21/49.75  | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | |   (85)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 243.21/49.75  | | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 243.21/49.75  | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | | REF_CLOSE: (8), (24), (32), (33), (67), (85) are inconsistent
% 243.21/49.75  | | | | | | | | | | | | |            by sub-proof #1129.
% 243.21/49.75  | | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | End of split
% 243.21/49.75  | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | Case 2:
% 243.21/49.75  | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | |   (86)  all_58_11 = e0 & op(e1, e0) = e0
% 243.21/49.75  | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | | REF_CLOSE: (3), (4), (8), (14), (16), (18), (24), (29), (30),
% 243.21/49.75  | | | | | | | | | | | |            (31), (33), (38), (39), (50), (86) are
% 243.21/49.75  | | | | | | | | | | | |            inconsistent by sub-proof #1128.
% 243.21/49.75  | | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | | End of split
% 243.21/49.75  | | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | | End of split
% 243.21/49.75  | | | | | | | | | | 
% 243.21/49.75  | | | | | | | | | End of split
% 243.21/49.75  | | | | | | | | | 
% 243.21/49.75  | | | | | | | | End of split
% 243.21/49.75  | | | | | | | | 
% 243.21/49.75  | | | | | | | Case 2:
% 243.21/49.75  | | | | | | | | 
% 243.21/49.75  | | | | | | | |   (87)  all_58_5 = e0 & op(e2, e1) = e0
% 243.21/49.75  | | | | | | | | 
% 243.21/49.75  | | | | | | | | ALPHA: (87) implies:
% 243.21/49.75  | | | | | | | |   (88)  op(e2, e1) = e0
% 243.21/49.75  | | | | | | | | 
% 243.21/49.75  | | | | | | | | REF_CLOSE: (19), (33), (36), (40), (88) are inconsistent by
% 243.21/49.75  | | | | | | | |            sub-proof #1841.
% 243.21/49.75  | | | | | | | | 
% 243.21/49.75  | | | | | | | End of split
% 243.21/49.75  | | | | | | | 
% 243.21/49.75  | | | | | | Case 2:
% 243.21/49.75  | | | | | | | 
% 243.21/49.75  | | | | | | |   (89)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 243.21/49.75  | | | | | | |           op(e0, e1) = e0)
% 243.21/49.75  | | | | | | | 
% 243.21/49.75  | | | | | | | REF_CLOSE: (7), (8), (13), (33), (35), (89) are inconsistent by
% 243.21/49.75  | | | | | | |            sub-proof #1127.
% 243.21/49.75  | | | | | | | 
% 243.21/49.75  | | | | | | End of split
% 243.21/49.75  | | | | | | 
% 243.21/49.75  | | | | | Case 2:
% 243.21/49.75  | | | | | | 
% 243.21/49.75  | | | | | |   (90)  all_58_13 = e2 & op(e0, e2) = e2
% 243.21/49.75  | | | | | | 
% 243.21/49.75  | | | | | | ALPHA: (90) implies:
% 243.21/49.75  | | | | | |   (91)  op(e0, e2) = e2
% 243.21/49.75  | | | | | | 
% 243.21/49.75  | | | | | | REF_CLOSE: (8), (33), (50), (91) are inconsistent by sub-proof
% 243.21/49.75  | | | | | |            #2132.
% 243.21/49.75  | | | | | | 
% 243.21/49.75  | | | | | End of split
% 243.21/49.75  | | | | | 
% 243.21/49.75  | | | | End of split
% 243.21/49.75  | | | | 
% 243.21/49.75  | | | Case 2:
% 243.21/49.75  | | | | 
% 243.21/49.75  | | | |   (92)  all_58_14 = e0 & op(e0, e1) = e0
% 243.21/49.75  | | | | 
% 243.21/49.75  | | | | REF_CLOSE: (8), (13), (92) are inconsistent by sub-proof #2036.
% 243.21/49.75  | | | | 
% 243.21/49.75  | | | End of split
% 243.21/49.75  | | | 
% 243.21/49.75  | | End of split
% 243.21/49.75  | | 
% 243.21/49.75  | End of split
% 243.21/49.75  | 
% 243.21/49.75  End of proof
% 243.21/49.75  
% 243.21/49.75  Sub-proof #1125 shows that the following formulas are inconsistent:
% 243.21/49.75  ----------------------------------------------------------------
% 243.21/49.75    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.21/49.75         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.21/49.75    (2)   ~ (e3 = e0)
% 243.21/49.75    (3)  all_58_7 = e0 & op(e1, e2) = e0
% 243.21/49.75    (4)   ~ (e2 = e0)
% 243.21/49.75    (5)   ~ (e3 = e1)
% 243.21/49.75    (6)  all_58_7 = e2
% 243.21/49.75    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.21/49.75         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.21/49.75    (8)  op(e3, e3) = e1
% 243.21/49.75    (9)   ~ (e3 = e2)
% 243.21/49.75    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.75    (11)  all_58_9 = e2
% 243.21/49.75    (12)  all_58_4 = e0
% 243.21/49.75    (13)   ~ (e2 = e1)
% 243.21/49.75  
% 243.21/49.75  Begin of proof
% 243.21/49.75  | 
% 243.21/49.75  | ALPHA: (3) implies:
% 243.21/49.75  |   (14)  all_58_7 = e0
% 243.21/49.75  | 
% 243.21/49.75  | COMBINE_EQS: (6), (14) imply:
% 243.21/49.75  |   (15)  e2 = e0
% 243.21/49.75  | 
% 243.21/49.75  | COMBINE_EQS: (11), (15) imply:
% 243.21/49.75  |   (16)  all_58_9 = e0
% 243.21/49.75  | 
% 243.21/49.75  | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (12), (13), (16) are
% 243.21/49.75  |            inconsistent by sub-proof #1190.
% 243.21/49.75  | 
% 243.21/49.75  End of proof
% 243.21/49.75  
% 243.21/49.75  Sub-proof #1126 shows that the following formulas are inconsistent:
% 243.21/49.75  ----------------------------------------------------------------
% 243.21/49.75    (1)  op(e0, e0) = e1
% 243.21/49.75    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.21/49.75         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.21/49.75    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.21/49.75         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.21/49.75    (4)   ~ (e3 = e0)
% 243.21/49.75    (5)  all_58_1 = e3
% 243.21/49.75    (6)  op(e1, e1) = e1
% 243.21/49.75    (7)   ~ (e2 = e0)
% 243.21/49.75    (8)  all_58_5 = e3
% 243.21/49.75    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.21/49.75         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.21/49.75    (10)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.21/49.75          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.21/49.75    (11)  all_58_8 = e1
% 243.21/49.75    (12)   ~ (all_52_7 = e3)
% 243.21/49.75    (13)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.21/49.75          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.21/49.75    (14)  op(e0, e2) = e2
% 243.21/49.75    (15)   ~ (e3 = e1)
% 243.21/49.75    (16)   ~ (all_52_8 = e1)
% 243.21/49.75    (17)   ~ (all_52_12 = all_52_13)
% 243.21/49.75    (18)  all_58_11 = e3
% 243.21/49.75    (19)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.21/49.75          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.21/49.75    (20)  all_58_3 = e1
% 243.21/49.75    (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.21/49.75          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.21/49.75    (22)  op(e3, e3) = e1
% 243.21/49.75    (23)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.21/49.75              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.21/49.75                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.21/49.75                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.21/49.75    (24)  op(e3, e1) = all_52_8
% 243.21/49.75    (25)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.21/49.75          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.21/49.75    (26)   ~ (e3 = e2)
% 243.21/49.75    (27)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.21/49.75          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.21/49.75    (28)  op(e2, e2) = e1
% 243.21/49.75    (29)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.21/49.75          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.21/49.75    (30)  all_58_15 = e1
% 243.21/49.75    (31)  op(e3, e0) = all_52_12
% 243.21/49.75    (32)  op(e2, e3) = all_52_1
% 243.21/49.75    (33)  all_58_12 = e3
% 243.21/49.75    (34)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.21/49.75          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.21/49.75    (35)  op(e0, e2) = all_52_7
% 243.21/49.75    (36)  op(e2, e1) = e3
% 243.21/49.75    (37)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.21/49.75          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.21/49.75    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.75    (39)   ~ (e1 = e0)
% 243.21/49.75    (40)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.21/49.75          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.21/49.75    (41)  op(e0, all_52_7) = e0
% 243.21/49.75    (42)  op(e2, e0) = all_52_13
% 243.21/49.75    (43)   ~ (all_52_1 = e3)
% 243.21/49.75    (44)   ~ (e2 = e1)
% 243.21/49.75  
% 243.21/49.75  Begin of proof
% 243.21/49.75  | 
% 243.21/49.75  | BETA: splitting (9) gives:
% 243.21/49.75  | 
% 243.21/49.75  | Case 1:
% 243.21/49.75  | | 
% 243.21/49.75  | |   (45)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 243.21/49.75  | |           e0)
% 243.21/49.75  | | 
% 243.21/49.75  | | BETA: splitting (45) gives:
% 243.21/49.75  | | 
% 243.21/49.75  | | Case 1:
% 243.21/49.75  | | | 
% 243.21/49.75  | | |   (46)  all_58_1 = e0 & op(e3, e2) = e0
% 243.21/49.75  | | | 
% 243.21/49.75  | | | REF_CLOSE: (4), (5), (46) are inconsistent by sub-proof #2133.
% 243.21/49.75  | | | 
% 243.21/49.75  | | Case 2:
% 243.21/49.75  | | | 
% 243.21/49.75  | | |   (47)  all_58_3 = e0 & op(e2, e2) = e0
% 243.21/49.75  | | | 
% 243.21/49.75  | | | REF_CLOSE: (20), (39), (47) are inconsistent by sub-proof #1180.
% 243.21/49.75  | | | 
% 243.21/49.75  | | End of split
% 243.21/49.75  | | 
% 243.21/49.75  | Case 2:
% 243.21/49.75  | | 
% 243.21/49.75  | |   (48)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 243.21/49.75  | |           e0)
% 243.21/49.75  | | 
% 243.21/49.75  | | BETA: splitting (48) gives:
% 243.21/49.75  | | 
% 243.21/49.75  | | Case 1:
% 243.21/49.75  | | | 
% 243.21/49.75  | | |   (49)  all_58_7 = e0 & op(e1, e2) = e0
% 243.21/49.75  | | | 
% 243.21/49.75  | | | ALPHA: (49) implies:
% 243.21/49.75  | | |   (50)  all_58_7 = e0
% 243.21/49.75  | | | 
% 243.21/49.75  | | | BETA: splitting (23) gives:
% 243.21/49.75  | | | 
% 243.21/49.75  | | | Case 1:
% 243.21/49.75  | | | | 
% 243.21/49.75  | | | |   (51)  all_58_15 = e0 & op(e0, e0) = e0
% 243.21/49.75  | | | | 
% 243.21/49.75  | | | | ALPHA: (51) implies:
% 243.21/49.75  | | | |   (52)  op(e0, e0) = e0
% 243.21/49.75  | | | | 
% 243.21/49.75  | | | | REF_CLOSE: (1), (38), (39), (52) are inconsistent by sub-proof #2274.
% 243.21/49.75  | | | | 
% 243.21/49.75  | | | Case 2:
% 243.21/49.75  | | | | 
% 243.21/49.76  | | | |   (53)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 243.21/49.76  | | | |               e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 243.21/49.76  | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 243.21/49.76  | | | |               e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 243.21/49.76  | | | | 
% 243.21/49.76  | | | | ALPHA: (53) implies:
% 243.21/49.76  | | | |   (54)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 243.21/49.76  | | | |             e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.21/49.76  | | | | 
% 243.21/49.76  | | | | BETA: splitting (37) gives:
% 243.21/49.76  | | | | 
% 243.21/49.76  | | | | Case 1:
% 243.21/49.76  | | | | | 
% 243.21/49.76  | | | | |   (55)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 243.21/49.76  | | | | |             e2) = e2)
% 243.21/49.76  | | | | | 
% 243.21/49.76  | | | | | BETA: splitting (55) gives:
% 243.21/49.76  | | | | | 
% 243.21/49.76  | | | | | Case 1:
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | |   (56)  all_58_6 = e2 & op(e1, e3) = e2
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | | ALPHA: (56) implies:
% 243.21/49.76  | | | | | |   (57)  all_58_6 = e2
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | | BETA: splitting (29) gives:
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | | Case 1:
% 243.21/49.76  | | | | | | | 
% 243.21/49.76  | | | | | | |   (58)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 243.21/49.76  | | | | | | |           op(e2, e3) = e0)
% 243.21/49.76  | | | | | | | 
% 243.21/49.76  | | | | | | | BETA: splitting (58) gives:
% 243.21/49.76  | | | | | | | 
% 243.21/49.76  | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | |   (59)  all_58_0 = e0 & op(e3, e3) = e0
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | | ALPHA: (59) implies:
% 243.21/49.76  | | | | | | | |   (60)  op(e3, e3) = e0
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | | REF_CLOSE: (22), (38), (39), (60) are inconsistent by sub-proof
% 243.21/49.76  | | | | | | | |            #1828.
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | |   (61)  all_58_2 = e0 & op(e2, e3) = e0
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | | ALPHA: (61) implies:
% 243.21/49.76  | | | | | | | |   (62)  all_58_2 = e0
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | | BETA: splitting (13) gives:
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | 
% 243.21/49.76  | | | | | | | | |   (63)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 243.21/49.76  | | | | | | | | |           op(e2, e2) = e2)
% 243.21/49.76  | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | BETA: splitting (63) gives:
% 243.21/49.76  | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | |   (64)  all_58_2 = e2 & op(e2, e3) = e2
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | REF_CLOSE: (7), (62), (64) are inconsistent by sub-proof
% 243.21/49.76  | | | | | | | | | |            #1575.
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | |   (65)  all_58_3 = e2 & op(e2, e2) = e2
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | ALPHA: (65) implies:
% 243.21/49.76  | | | | | | | | | |   (66)  op(e2, e2) = e2
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | REF_CLOSE: (28), (38), (44), (66) are inconsistent by
% 243.21/49.76  | | | | | | | | | |            sub-proof #2235.
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | 
% 243.21/49.76  | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | 
% 243.21/49.76  | | | | | | | | |   (67)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 243.21/49.76  | | | | | | | | |           op(e2, e0) = e2)
% 243.21/49.76  | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | BETA: splitting (67) gives:
% 243.21/49.76  | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | |   (68)  all_58_5 = e2 & op(e2, e1) = e2
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | ALPHA: (68) implies:
% 243.21/49.76  | | | | | | | | | |   (69)  op(e2, e1) = e2
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | REF_CLOSE: (26), (36), (38), (69) are inconsistent by
% 243.21/49.76  | | | | | | | | | |            sub-proof #2256.
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | |   (70)  all_58_10 = e2 & op(e2, e0) = e2
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | ALPHA: (70) implies:
% 243.21/49.76  | | | | | | | | | |   (71)  op(e2, e0) = e2
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | BETA: splitting (54) gives:
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | |   (72)  all_58_12 = e0 & op(e0, e3) = e0
% 243.21/49.76  | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | ALPHA: (72) implies:
% 243.21/49.76  | | | | | | | | | | |   (73)  all_58_12 = e0
% 243.21/49.76  | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | REF_CLOSE: (4), (7), (15), (21), (22), (25), (26), (32),
% 243.21/49.76  | | | | | | | | | | |            (38), (43), (44), (62), (73) are inconsistent by
% 243.21/49.76  | | | | | | | | | | |            sub-proof #1149.
% 243.21/49.76  | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | |   (74)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 243.21/49.76  | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 243.21/49.76  | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | BETA: splitting (74) gives:
% 243.21/49.76  | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | |   (75)  all_58_13 = e0 & op(e0, e2) = e0
% 243.21/49.76  | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | ALPHA: (75) implies:
% 243.21/49.76  | | | | | | | | | | | |   (76)  op(e0, e2) = e0
% 243.21/49.76  | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | REF_CLOSE: (7), (14), (38), (76) are inconsistent by
% 243.21/49.76  | | | | | | | | | | | |            sub-proof #2132.
% 243.21/49.76  | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | |   (77)  all_58_14 = e0 & op(e0, e1) = e0
% 243.21/49.76  | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | ALPHA: (77) implies:
% 243.21/49.76  | | | | | | | | | | | |   (78)  all_58_14 = e0
% 243.21/49.76  | | | | | | | | | | | |   (79)  op(e0, e1) = e0
% 243.21/49.76  | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | BETA: splitting (27) gives:
% 243.21/49.76  | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | |   (80)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 243.21/49.76  | | | | | | | | | | | | |           & op(e2, e1) = e2)
% 243.21/49.76  | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | BETA: splitting (80) gives:
% 243.21/49.76  | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | |   (81)  all_58_4 = e2 & op(e3, e1) = e2
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | ALPHA: (81) implies:
% 243.21/49.76  | | | | | | | | | | | | | |   (82)  all_58_4 = e2
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | |   (83)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 243.21/49.76  | | | | | | | | | | | | | | |           & op(e3, e2) = e0)
% 243.21/49.76  | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 243.21/49.76  | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | |   (84)  all_58_0 = e0 & op(e3, e3) = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 243.21/49.76  | | | | | | | | | | | | | | | |   (85)  op(e3, e3) = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | REF_CLOSE: (22), (38), (39), (85) are inconsistent by
% 243.21/49.76  | | | | | | | | | | | | | | | |            sub-proof #1828.
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | |   (86)  all_58_1 = e0 & op(e3, e2) = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | ALPHA: (86) implies:
% 243.21/49.76  | | | | | | | | | | | | | | | |   (87)  all_58_1 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (87) imply:
% 243.21/49.76  | | | | | | | | | | | | | | | |   (88)  e3 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (88) imply:
% 243.21/49.76  | | | | | | | | | | | | | | | |   (89)  all_58_12 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (15), (21), (22), (25), (26), (32),
% 243.21/49.76  | | | | | | | | | | | | | | | |            (38), (43), (44), (62), (89) are inconsistent by
% 243.21/49.76  | | | | | | | | | | | | | | | |            sub-proof #1149.
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | |   (90)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 243.21/49.76  | | | | | | | | | | | | | | |           & op(e3, e0) = e0)
% 243.21/49.76  | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 243.21/49.76  | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | |   (91)  all_58_4 = e0 & op(e3, e1) = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | ALPHA: (91) implies:
% 243.21/49.76  | | | | | | | | | | | | | | | |   (92)  all_58_4 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10), (15), (16), (24), (26), (27),
% 243.21/49.76  | | | | | | | | | | | | | | | |            (38), (39), (44), (78), (79), (92) are
% 243.21/49.76  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1243.
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | |   (93)  all_58_9 = e0 & op(e3, e0) = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 243.21/49.76  | | | | | | | | | | | | | | | |   (94)  all_58_9 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | |   (95)  op(e3, e0) = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | |   (96)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | |           & op(e1, e2) = e0)
% 243.21/49.76  | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 243.21/49.76  | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (97)  all_58_6 = e0 & op(e1, e3) = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (98)  all_58_6 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (98) imply:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (99)  e2 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (99) imply:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (100)  all_58_4 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (15), (19), (22), (26), (38), (44),
% 243.21/49.76  | | | | | | | | | | | | | | | | | |            (94), (100) are inconsistent by sub-proof #1190.
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_52_7, e2, e2, e0,
% 243.21/49.76  | | | | | | | | | | | | | | | | | |              simplifying with (14), (35) gives:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (101)  all_52_7 = e2
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_52_13, e2, e0, e2,
% 243.21/49.76  | | | | | | | | | | | | | | | | | |              simplifying with (42), (71) gives:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (102)  all_52_13 = e2
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_52_12, e0, e0, e3,
% 243.21/49.76  | | | | | | | | | | | | | | | | | |              simplifying with (31), (95) gives:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (103)  all_52_12 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | REDUCE: (17), (102), (103) imply:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (104)   ~ (e2 = e0)
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | REDUCE: (41), (101) imply:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (105)  op(e0, e2) = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14), (38), (105) are inconsistent by
% 243.21/49.76  | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | |   (106)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 243.21/49.76  | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 243.21/49.76  | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 243.21/49.76  | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (107)  all_58_8 = e0 & op(e1, e1) = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (108)  op(e1, e1) = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (38), (39), (108) are inconsistent by
% 243.21/49.76  | | | | | | | | | | | | | | | | | |            sub-proof #2220.
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (109)  all_58_11 = e0 & op(e1, e0) = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (110)  all_58_11 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (110) imply:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (111)  e3 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (111) imply:
% 243.21/49.76  | | | | | | | | | | | | | | | | | |   (112)  all_58_12 = e0
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (15), (21), (22), (25), (26), (32),
% 243.21/49.76  | | | | | | | | | | | | | | | | | |            (38), (43), (44), (62), (112) are inconsistent by
% 243.21/49.76  | | | | | | | | | | | | | | | | | |            sub-proof #1149.
% 243.21/49.76  | | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | |   (113)  all_58_5 = e2 & op(e2, e1) = e2
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | ALPHA: (113) implies:
% 243.21/49.76  | | | | | | | | | | | | | |   (114)  op(e2, e1) = e2
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | REF_CLOSE: (26), (36), (38), (114) are inconsistent by
% 243.21/49.76  | | | | | | | | | | | | | |            sub-proof #2256.
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | |   (115)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 243.21/49.76  | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 243.21/49.76  | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | BETA: splitting (115) gives:
% 243.21/49.76  | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | |   (116)  all_58_8 = e2 & op(e1, e1) = e2
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | ALPHA: (116) implies:
% 243.21/49.76  | | | | | | | | | | | | | |   (117)  all_58_8 = e2
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | COMBINE_EQS: (11), (117) imply:
% 243.21/49.76  | | | | | | | | | | | | | |   (118)  e2 = e1
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | SIMP: (118) implies:
% 243.21/49.76  | | | | | | | | | | | | | |   (119)  e2 = e1
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | COMBINE_EQS: (57), (119) imply:
% 243.21/49.76  | | | | | | | | | | | | | |   (120)  all_58_6 = e1
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (15), (21), (22), (25), (26), (29),
% 243.21/49.76  | | | | | | | | | | | | | |            (32), (38), (39), (43), (44), (120) are
% 243.21/49.76  | | | | | | | | | | | | | |            inconsistent by sub-proof #1161.
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | |   (121)  all_58_14 = e2 & op(e0, e1) = e2
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | ALPHA: (121) implies:
% 243.21/49.76  | | | | | | | | | | | | | |   (122)  all_58_14 = e2
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (7), (12), (14), (15), (26), (30), (35),
% 243.21/49.76  | | | | | | | | | | | | | |            (38), (54), (122) are inconsistent by sub-proof
% 243.21/49.76  | | | | | | | | | | | | | |            #1637.
% 243.21/49.76  | | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | | 
% 243.21/49.76  | | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | | 
% 243.21/49.76  | | | | | | | | End of split
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | End of split
% 243.21/49.76  | | | | | | | 
% 243.21/49.76  | | | | | | Case 2:
% 243.21/49.76  | | | | | | | 
% 243.21/49.76  | | | | | | |   (123)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 243.21/49.76  | | | | | | |            op(e0, e3) = e0)
% 243.21/49.76  | | | | | | | 
% 243.21/49.76  | | | | | | | BETA: splitting (123) gives:
% 243.21/49.76  | | | | | | | 
% 243.21/49.76  | | | | | | | Case 1:
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | |   (124)  all_58_6 = e0 & op(e1, e3) = e0
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | | REF_CLOSE: (7), (57), (124) are inconsistent by sub-proof #1678.
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | Case 2:
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | |   (125)  all_58_12 = e0 & op(e0, e3) = e0
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | | REF_CLOSE: (4), (33), (125) are inconsistent by sub-proof #1641.
% 243.21/49.76  | | | | | | | | 
% 243.21/49.76  | | | | | | | End of split
% 243.21/49.76  | | | | | | | 
% 243.21/49.76  | | | | | | End of split
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | Case 2:
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | |   (126)  all_58_7 = e2 & op(e1, e2) = e2
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | | ALPHA: (126) implies:
% 243.21/49.76  | | | | | |   (127)  all_58_7 = e2
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | | REF_CLOSE: (7), (50), (127) are inconsistent by sub-proof #1587.
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | End of split
% 243.21/49.76  | | | | | 
% 243.21/49.76  | | | | Case 2:
% 243.21/49.76  | | | | | 
% 243.21/49.76  | | | | |   (128)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 243.21/49.76  | | | | |              e0) = e2)
% 243.21/49.76  | | | | | 
% 243.21/49.76  | | | | | BETA: splitting (128) gives:
% 243.21/49.76  | | | | | 
% 243.21/49.76  | | | | | Case 1:
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | |   (129)  all_58_8 = e2 & op(e1, e1) = e2
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | | ALPHA: (129) implies:
% 243.21/49.76  | | | | | |   (130)  all_58_8 = e2
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | | REF_CLOSE: (11), (44), (130) are inconsistent by sub-proof #1802.
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | Case 2:
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | |   (131)  all_58_11 = e2 & op(e1, e0) = e2
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | | ALPHA: (131) implies:
% 243.21/49.76  | | | | | |   (132)  all_58_11 = e2
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | | REF_CLOSE: (18), (26), (132) are inconsistent by sub-proof #2030.
% 243.21/49.76  | | | | | | 
% 243.21/49.76  | | | | | End of split
% 243.21/49.76  | | | | | 
% 243.21/49.76  | | | | End of split
% 243.21/49.76  | | | | 
% 243.21/49.76  | | | End of split
% 243.21/49.76  | | | 
% 243.21/49.76  | | Case 2:
% 243.21/49.76  | | | 
% 243.21/49.76  | | |   (133)  all_58_13 = e0 & op(e0, e2) = e0
% 243.21/49.76  | | | 
% 243.21/49.76  | | | ALPHA: (133) implies:
% 243.21/49.76  | | |   (134)  op(e0, e2) = e0
% 243.21/49.76  | | | 
% 243.21/49.76  | | | REF_CLOSE: (7), (14), (38), (134) are inconsistent by sub-proof #2132.
% 243.21/49.76  | | | 
% 243.21/49.76  | | End of split
% 243.21/49.76  | | 
% 243.21/49.76  | End of split
% 243.21/49.76  | 
% 243.21/49.76  End of proof
% 243.21/49.76  
% 243.21/49.76  Sub-proof #1127 shows that the following formulas are inconsistent:
% 243.21/49.76  ----------------------------------------------------------------
% 243.21/49.76    (1)  op(e1, e1) = e1
% 243.21/49.76    (2)   ~ (e2 = e0)
% 243.21/49.76    (3)  all_58_14 = e2
% 243.21/49.76    (4)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.21/49.76    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.76    (6)   ~ (e1 = e0)
% 243.21/49.76  
% 243.21/49.76  Begin of proof
% 243.21/49.76  | 
% 243.21/49.76  | BETA: splitting (4) gives:
% 243.21/49.76  | 
% 243.21/49.76  | Case 1:
% 243.21/49.76  | | 
% 243.21/49.76  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 243.21/49.76  | | 
% 243.21/49.76  | | ALPHA: (7) implies:
% 243.21/49.76  | |   (8)  op(e1, e1) = e0
% 243.21/49.76  | | 
% 243.21/49.76  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2220.
% 243.21/49.76  | | 
% 243.21/49.76  | Case 2:
% 243.21/49.76  | | 
% 243.21/49.76  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 243.21/49.76  | | 
% 243.21/49.76  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #2036.
% 243.21/49.76  | | 
% 243.21/49.76  | End of split
% 243.21/49.76  | 
% 243.21/49.76  End of proof
% 243.21/49.76  
% 243.21/49.76  Sub-proof #1128 shows that the following formulas are inconsistent:
% 243.21/49.76  ----------------------------------------------------------------
% 243.21/49.76    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.21/49.76         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.21/49.76    (2)   ~ (e3 = e0)
% 243.21/49.76    (3)   ~ (e2 = e0)
% 243.21/49.76    (4)   ~ (all_52_7 = e3)
% 243.21/49.76    (5)   ~ (e3 = e1)
% 243.21/49.76    (6)  all_58_11 = e3
% 243.21/49.76    (7)   ~ (e3 = e2)
% 243.21/49.76    (8)  all_58_11 = e0 & op(e1, e0) = e0
% 243.21/49.76    (9)  all_58_15 = e1
% 243.21/49.76    (10)  all_58_12 = e3
% 243.21/49.76    (11)  op(e0, e2) = e0
% 243.21/49.76    (12)  op(e0, e2) = all_52_7
% 243.21/49.76    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.76            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.76    (14)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.21/49.76          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.21/49.76            e2)
% 243.21/49.76    (15)   ~ (e2 = e1)
% 243.21/49.76  
% 243.21/49.76  Begin of proof
% 243.21/49.76  | 
% 243.21/49.76  | ALPHA: (8) implies:
% 243.21/49.76  |   (16)  all_58_11 = e0
% 243.21/49.76  | 
% 243.21/49.76  | COMBINE_EQS: (6), (16) imply:
% 243.21/49.76  |   (17)  e3 = e0
% 243.21/49.76  | 
% 243.21/49.76  | COMBINE_EQS: (10), (17) imply:
% 243.21/49.76  |   (18)  all_58_12 = e0
% 243.21/49.76  | 
% 243.21/49.76  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (11), (12), (13), (14), (15),
% 243.21/49.76  |            (18) are inconsistent by sub-proof #1914.
% 243.21/49.76  | 
% 243.21/49.76  End of proof
% 243.21/49.76  
% 243.21/49.76  Sub-proof #1129 shows that the following formulas are inconsistent:
% 243.21/49.76  ----------------------------------------------------------------
% 243.21/49.76    (1)   ~ (e2 = e0)
% 243.21/49.76    (2)   ~ (e3 = e2)
% 243.21/49.76    (3)  op(e2, e0) = e0
% 243.21/49.76    (4)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.21/49.76    (5)  op(e2, e1) = e3
% 243.21/49.76    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.76  
% 243.21/49.76  Begin of proof
% 243.21/49.76  | 
% 243.21/49.76  | BETA: splitting (4) gives:
% 243.21/49.76  | 
% 243.21/49.76  | Case 1:
% 243.21/49.76  | | 
% 243.21/49.76  | |   (7)  all_58_5 = e2 & op(e2, e1) = e2
% 243.21/49.76  | | 
% 243.21/49.76  | | ALPHA: (7) implies:
% 243.21/49.76  | |   (8)  op(e2, e1) = e2
% 243.21/49.76  | | 
% 243.21/49.76  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2256.
% 243.21/49.76  | | 
% 243.21/49.76  | Case 2:
% 243.21/49.76  | | 
% 243.21/49.76  | |   (9)  all_58_10 = e2 & op(e2, e0) = e2
% 243.21/49.76  | | 
% 243.21/49.76  | | ALPHA: (9) implies:
% 243.21/49.76  | |   (10)  op(e2, e0) = e2
% 243.21/49.76  | | 
% 243.21/49.76  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #2121.
% 243.21/49.76  | | 
% 243.21/49.76  | End of split
% 243.21/49.76  | 
% 243.21/49.76  End of proof
% 243.21/49.76  
% 243.21/49.76  Sub-proof #1130 shows that the following formulas are inconsistent:
% 243.21/49.76  ----------------------------------------------------------------
% 243.21/49.77    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.21/49.77         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.21/49.77    (2)   ~ (e3 = e0)
% 243.21/49.77    (3)   ~ (e2 = e0)
% 243.21/49.77    (4)   ~ (e3 = e1)
% 243.21/49.77    (5)  all_58_2 = e2
% 243.21/49.77    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.21/49.77         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.21/49.77    (7)  op(e3, e3) = e1
% 243.21/49.77    (8)   ~ (e3 = e2)
% 243.21/49.77    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.77    (10)   ~ (e1 = e0)
% 243.21/49.77    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 243.21/49.77    (12)  all_58_9 = e2
% 243.21/49.77    (13)  all_58_4 = e0
% 243.21/49.77    (14)   ~ (e2 = e1)
% 243.21/49.77  
% 243.21/49.77  Begin of proof
% 243.21/49.77  | 
% 243.21/49.77  | BETA: splitting (11) gives:
% 243.21/49.77  | 
% 243.21/49.77  | Case 1:
% 243.21/49.77  | | 
% 243.21/49.77  | |   (15)  all_58_0 = e0 & op(e3, e3) = e0
% 243.21/49.77  | | 
% 243.21/49.77  | | ALPHA: (15) implies:
% 243.21/49.77  | |   (16)  op(e3, e3) = e0
% 243.21/49.77  | | 
% 243.21/49.77  | | REF_CLOSE: (7), (9), (10), (16) are inconsistent by sub-proof #1828.
% 243.21/49.77  | | 
% 243.21/49.77  | Case 2:
% 243.21/49.77  | | 
% 243.21/49.77  | |   (17)  all_58_2 = e0 & op(e2, e3) = e0
% 243.21/49.77  | | 
% 243.21/49.77  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 243.21/49.77  | |            (17) are inconsistent by sub-proof #1131.
% 243.21/49.77  | | 
% 243.21/49.77  | End of split
% 243.21/49.77  | 
% 243.21/49.77  End of proof
% 243.21/49.77  
% 243.21/49.77  Sub-proof #1131 shows that the following formulas are inconsistent:
% 243.21/49.77  ----------------------------------------------------------------
% 243.21/49.77    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.21/49.77         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.21/49.77    (2)   ~ (e3 = e0)
% 243.21/49.77    (3)   ~ (e2 = e0)
% 243.21/49.77    (4)   ~ (e3 = e1)
% 243.21/49.77    (5)  all_58_2 = e2
% 243.21/49.77    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.21/49.77         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.21/49.77    (7)  op(e3, e3) = e1
% 243.21/49.77    (8)   ~ (e3 = e2)
% 243.21/49.77    (9)  all_58_2 = e0 & op(e2, e3) = e0
% 243.21/49.77    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.77    (11)  all_58_9 = e2
% 243.21/49.77    (12)  all_58_4 = e0
% 243.21/49.77    (13)   ~ (e2 = e1)
% 243.21/49.77  
% 243.21/49.77  Begin of proof
% 243.21/49.77  | 
% 243.21/49.77  | ALPHA: (9) implies:
% 243.21/49.77  |   (14)  all_58_2 = e0
% 243.21/49.77  | 
% 243.21/49.77  | COMBINE_EQS: (5), (14) imply:
% 243.21/49.77  |   (15)  e2 = e0
% 243.21/49.77  | 
% 243.21/49.77  | COMBINE_EQS: (11), (15) imply:
% 243.21/49.77  |   (16)  all_58_9 = e0
% 243.21/49.77  | 
% 243.21/49.77  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (12), (13), (16) are
% 243.21/49.77  |            inconsistent by sub-proof #1190.
% 243.21/49.77  | 
% 243.21/49.77  End of proof
% 243.21/49.77  
% 243.21/49.77  Sub-proof #1132 shows that the following formulas are inconsistent:
% 243.21/49.77  ----------------------------------------------------------------
% 243.21/49.77    (1)  all_58_1 = e3
% 243.21/49.77    (2)  op(e3, e3) = e1
% 243.21/49.77    (3)   ~ (e3 = e2)
% 243.21/49.77    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.77    (5)   ~ (e2 = e1)
% 243.21/49.77    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 243.21/49.77  
% 243.21/49.77  Begin of proof
% 243.21/49.77  | 
% 243.21/49.77  | BETA: splitting (6) gives:
% 243.21/49.77  | 
% 243.21/49.77  | Case 1:
% 243.21/49.77  | | 
% 243.21/49.77  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 243.21/49.77  | | 
% 243.21/49.77  | | ALPHA: (7) implies:
% 243.21/49.77  | |   (8)  op(e3, e3) = e2
% 243.21/49.77  | | 
% 243.21/49.77  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2267.
% 243.21/49.77  | | 
% 243.21/49.77  | Case 2:
% 243.21/49.77  | | 
% 243.21/49.77  | |   (9)  all_58_1 = e2 & op(e3, e2) = e2
% 243.21/49.77  | | 
% 243.21/49.77  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1590.
% 243.21/49.77  | | 
% 243.21/49.77  | End of split
% 243.21/49.77  | 
% 243.21/49.77  End of proof
% 243.21/49.77  
% 243.21/49.77  Sub-proof #1133 shows that the following formulas are inconsistent:
% 243.21/49.77  ----------------------------------------------------------------
% 243.21/49.77    (1)  op(e0, e0) = e1
% 243.21/49.77    (2)   ~ (e3 = e0)
% 243.21/49.77    (3)  all_58_1 = e3
% 243.21/49.77    (4)   ~ (e2 = e0)
% 243.21/49.77    (5)  op(e1, e2) = all_52_6
% 243.21/49.77    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.21/49.77         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.21/49.77    (7)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.21/49.77         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.21/49.77    (8)  op(e1, e1) = all_6_2
% 243.21/49.77    (9)  all_58_8 = e1
% 243.21/49.77    (10)  op(e1, e0) = all_52_14
% 243.21/49.77    (11)  op(e0, e2) = e2
% 243.21/49.77    (12)   ~ (e3 = e1)
% 243.21/49.77    (13)   ~ (all_52_8 = e1)
% 243.21/49.77    (14)  all_58_11 = e3
% 243.21/49.77    (15)  all_58_3 = e1
% 243.21/49.77    (16)  op(e3, e3) = e1
% 243.21/49.77    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.21/49.77              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.21/49.77                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.21/49.77                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.21/49.77    (18)   ~ (all_6_2 = e3)
% 243.21/49.77    (19)  op(e3, e1) = all_52_8
% 243.21/49.77    (20)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.21/49.77          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.21/49.77    (21)   ~ (e3 = e2)
% 243.21/49.77    (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.21/49.77          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.21/49.77    (23)   ~ (all_52_14 = e1)
% 243.21/49.77    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.21/49.77          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.21/49.77    (25)  all_58_12 = e3
% 243.21/49.77    (26)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.21/49.77          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.21/49.77    (27)  op(e2, e1) = e3
% 243.21/49.77    (28)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.21/49.77          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.21/49.77    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.77    (30)   ~ (e1 = e0)
% 243.21/49.77    (31)   ~ (e2 = e1)
% 243.21/49.77    (32)  op(e1, all_52_6) = e1
% 243.21/49.77  
% 243.21/49.77  Begin of proof
% 243.21/49.77  | 
% 243.21/49.77  | BETA: splitting (17) gives:
% 243.21/49.77  | 
% 243.21/49.77  | Case 1:
% 243.21/49.77  | | 
% 243.21/49.77  | |   (33)  all_58_15 = e0 & op(e0, e0) = e0
% 243.21/49.77  | | 
% 243.21/49.77  | | ALPHA: (33) implies:
% 243.21/49.77  | |   (34)  op(e0, e0) = e0
% 243.21/49.77  | | 
% 243.21/49.77  | | REF_CLOSE: (1), (29), (30), (34) are inconsistent by sub-proof #2274.
% 243.21/49.77  | | 
% 243.21/49.77  | Case 2:
% 243.21/49.77  | | 
% 243.21/49.77  | |   (35)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.21/49.77  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 243.21/49.77  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.21/49.77  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 243.21/49.77  | | 
% 243.21/49.77  | | ALPHA: (35) implies:
% 243.21/49.77  | |   (36)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 243.21/49.77  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.21/49.77  | | 
% 243.21/49.77  | | BETA: splitting (36) gives:
% 243.21/49.77  | | 
% 243.21/49.77  | | Case 1:
% 243.21/49.77  | | | 
% 243.21/49.77  | | |   (37)  all_58_12 = e0 & op(e0, e3) = e0
% 243.21/49.77  | | | 
% 243.21/49.77  | | | ALPHA: (37) implies:
% 243.21/49.77  | | |   (38)  all_58_12 = e0
% 243.21/49.77  | | | 
% 243.21/49.77  | | | REF_CLOSE: (2), (25), (38) are inconsistent by sub-proof #1971.
% 243.21/49.77  | | | 
% 243.21/49.77  | | Case 2:
% 243.21/49.77  | | | 
% 243.21/49.77  | | |   (39)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 243.21/49.77  | | |           = e0)
% 243.21/49.77  | | | 
% 243.21/49.77  | | | BETA: splitting (39) gives:
% 243.21/49.77  | | | 
% 243.21/49.77  | | | Case 1:
% 243.21/49.77  | | | | 
% 243.21/49.77  | | | |   (40)  all_58_13 = e0 & op(e0, e2) = e0
% 243.21/49.77  | | | | 
% 243.21/49.77  | | | | ALPHA: (40) implies:
% 243.21/49.77  | | | |   (41)  op(e0, e2) = e0
% 243.21/49.77  | | | | 
% 243.21/49.77  | | | | REF_CLOSE: (4), (11), (29), (41) are inconsistent by sub-proof #2132.
% 243.21/49.77  | | | | 
% 243.21/49.77  | | | Case 2:
% 243.21/49.77  | | | | 
% 243.21/49.77  | | | |   (42)  all_58_14 = e0 & op(e0, e1) = e0
% 243.21/49.77  | | | | 
% 243.21/49.77  | | | | ALPHA: (42) implies:
% 243.21/49.77  | | | |   (43)  all_58_14 = e0
% 243.21/49.77  | | | |   (44)  op(e0, e1) = e0
% 243.21/49.77  | | | | 
% 243.21/49.77  | | | | BETA: splitting (22) gives:
% 243.21/49.77  | | | | 
% 243.21/49.77  | | | | Case 1:
% 243.21/49.77  | | | | | 
% 243.21/49.77  | | | | |   (45)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 243.21/49.77  | | | | |             e1) = e2)
% 243.21/49.77  | | | | | 
% 243.21/49.77  | | | | | BETA: splitting (45) gives:
% 243.21/49.77  | | | | | 
% 243.21/49.77  | | | | | Case 1:
% 243.21/49.77  | | | | | | 
% 243.21/49.77  | | | | | |   (46)  all_58_4 = e2 & op(e3, e1) = e2
% 243.21/49.77  | | | | | | 
% 243.21/49.77  | | | | | | ALPHA: (46) implies:
% 243.21/49.77  | | | | | |   (47)  all_58_4 = e2
% 243.21/49.77  | | | | | | 
% 243.21/49.77  | | | | | | BETA: splitting (6) gives:
% 243.21/49.77  | | | | | | 
% 243.21/49.77  | | | | | | Case 1:
% 243.21/49.77  | | | | | | | 
% 243.21/49.77  | | | | | | |   (48)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 243.21/49.77  | | | | | | |           op(e2, e2) = e0)
% 243.21/49.77  | | | | | | | 
% 243.21/49.77  | | | | | | | BETA: splitting (48) gives:
% 243.21/49.77  | | | | | | | 
% 243.21/49.77  | | | | | | | Case 1:
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | |   (49)  all_58_1 = e0 & op(e3, e2) = e0
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | | REF_CLOSE: (2), (3), (49) are inconsistent by sub-proof #2133.
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | Case 2:
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | |   (50)  all_58_3 = e0 & op(e2, e2) = e0
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | | REF_CLOSE: (15), (30), (50) are inconsistent by sub-proof #1180.
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | End of split
% 243.21/49.77  | | | | | | | 
% 243.21/49.77  | | | | | | Case 2:
% 243.21/49.77  | | | | | | | 
% 243.21/49.77  | | | | | | |   (51)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 243.21/49.77  | | | | | | |           op(e0, e2) = e0)
% 243.21/49.77  | | | | | | | 
% 243.21/49.77  | | | | | | | BETA: splitting (51) gives:
% 243.21/49.77  | | | | | | | 
% 243.21/49.77  | | | | | | | Case 1:
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | |   (52)  all_58_7 = e0 & op(e1, e2) = e0
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | | ALPHA: (52) implies:
% 243.21/49.77  | | | | | | | |   (53)  all_58_7 = e0
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | | BETA: splitting (28) gives:
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | | Case 1:
% 243.21/49.77  | | | | | | | | | 
% 243.21/49.77  | | | | | | | | |   (54)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 243.21/49.77  | | | | | | | | |           op(e1, e2) = e2)
% 243.21/49.77  | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | BETA: splitting (54) gives:
% 243.21/49.77  | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | Case 1:
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | |   (55)  all_58_6 = e2 & op(e1, e3) = e2
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | ALPHA: (55) implies:
% 243.21/49.77  | | | | | | | | | |   (56)  all_58_6 = e2
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | BETA: splitting (24) gives:
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | Case 1:
% 243.21/49.77  | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | |   (57)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 243.21/49.77  | | | | | | | | | | |           & op(e2, e3) = e0)
% 243.21/49.77  | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | BETA: splitting (57) gives:
% 243.21/49.77  | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | Case 1:
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | |   (58)  all_58_0 = e0 & op(e3, e3) = e0
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | ALPHA: (58) implies:
% 243.21/49.77  | | | | | | | | | | | |   (59)  op(e3, e3) = e0
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | REF_CLOSE: (16), (29), (30), (59) are inconsistent by
% 243.21/49.77  | | | | | | | | | | | |            sub-proof #1828.
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | Case 2:
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | |   (60)  all_58_2 = e0 & op(e2, e3) = e0
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | ALPHA: (60) implies:
% 243.21/49.77  | | | | | | | | | | | |   (61)  all_58_2 = e0
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | BETA: splitting (20) gives:
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | Case 1:
% 243.21/49.77  | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | |   (62)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 243.21/49.77  | | | | | | | | | | | | |           & op(e2, e3) = e2)
% 243.21/49.77  | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | BETA: splitting (62) gives:
% 243.21/49.77  | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | Case 1:
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | |   (63)  all_58_0 = e2 & op(e3, e3) = e2
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | ALPHA: (63) implies:
% 243.21/49.77  | | | | | | | | | | | | | |   (64)  op(e3, e3) = e2
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | REF_CLOSE: (16), (29), (31), (64) are inconsistent by
% 243.21/49.77  | | | | | | | | | | | | | |            sub-proof #2267.
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | Case 2:
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | |   (65)  all_58_2 = e2 & op(e2, e3) = e2
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | ALPHA: (65) implies:
% 243.21/49.77  | | | | | | | | | | | | | |   (66)  all_58_2 = e2
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | COMBINE_EQS: (61), (66) imply:
% 243.21/49.77  | | | | | | | | | | | | | |   (67)  e2 = e0
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | SIMP: (67) implies:
% 243.21/49.77  | | | | | | | | | | | | | |   (68)  e2 = e0
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | COMBINE_EQS: (47), (68) imply:
% 243.21/49.77  | | | | | | | | | | | | | |   (69)  all_58_4 = e0
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (8), (12), (13), (18), (19), (21),
% 243.21/49.77  | | | | | | | | | | | | | |            (22), (26), (29), (30), (31), (43), (44), (69) are
% 243.21/49.77  | | | | | | | | | | | | | |            inconsistent by sub-proof #1242.
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | End of split
% 243.21/49.77  | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | Case 2:
% 243.21/49.77  | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | |   (70)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 243.21/49.77  | | | | | | | | | | | | |           e2 & op(e0, e3) = e2)
% 243.21/49.77  | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | BETA: splitting (70) gives:
% 243.21/49.77  | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | Case 1:
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | ALPHA: (52) implies:
% 243.21/49.77  | | | | | | | | | | | | | |   (71)  op(e1, e2) = e0
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_52_6, e0, e2, e1,
% 243.21/49.77  | | | | | | | | | | | | | |              simplifying with (5), (71) gives:
% 243.21/49.77  | | | | | | | | | | | | | |   (72)  all_52_6 = e0
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | REDUCE: (32), (72) imply:
% 243.21/49.77  | | | | | | | | | | | | | |   (73)  op(e1, e0) = e1
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | REF_CLOSE: (10), (23), (29), (73) are inconsistent by
% 243.21/49.77  | | | | | | | | | | | | | |            sub-proof #2304.
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | Case 2:
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | |   (74)  all_58_12 = e2 & op(e0, e3) = e2
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | | REF_CLOSE: (21), (25), (74) are inconsistent by sub-proof
% 243.21/49.77  | | | | | | | | | | | | | |            #1974.
% 243.21/49.77  | | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | | End of split
% 243.21/49.77  | | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | End of split
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | End of split
% 243.21/49.77  | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | Case 2:
% 243.21/49.77  | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | |   (75)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 243.21/49.77  | | | | | | | | | | |           e0 & op(e0, e3) = e0)
% 243.21/49.77  | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | BETA: splitting (75) gives:
% 243.21/49.77  | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | Case 1:
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | |   (76)  all_58_6 = e0 & op(e1, e3) = e0
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | ALPHA: (76) implies:
% 243.21/49.77  | | | | | | | | | | | |   (77)  all_58_6 = e0
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | COMBINE_EQS: (56), (77) imply:
% 243.21/49.77  | | | | | | | | | | | |   (78)  e2 = e0
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | COMBINE_EQS: (47), (78) imply:
% 243.21/49.77  | | | | | | | | | | | |   (79)  all_58_4 = e0
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (8), (12), (13), (18), (19), (21),
% 243.21/49.77  | | | | | | | | | | | |            (22), (26), (29), (30), (31), (43), (44), (79) are
% 243.21/49.77  | | | | | | | | | | | |            inconsistent by sub-proof #1242.
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | Case 2:
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | |   (80)  all_58_12 = e0 & op(e0, e3) = e0
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | | REF_CLOSE: (2), (25), (80) are inconsistent by sub-proof
% 243.21/49.77  | | | | | | | | | | | |            #1641.
% 243.21/49.77  | | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | | End of split
% 243.21/49.77  | | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | End of split
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | Case 2:
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | |   (81)  all_58_7 = e2 & op(e1, e2) = e2
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | ALPHA: (81) implies:
% 243.21/49.77  | | | | | | | | | |   (82)  all_58_7 = e2
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | COMBINE_EQS: (53), (82) imply:
% 243.21/49.77  | | | | | | | | | |   (83)  e2 = e0
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | SIMP: (83) implies:
% 243.21/49.77  | | | | | | | | | |   (84)  e2 = e0
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | COMBINE_EQS: (47), (84) imply:
% 243.21/49.77  | | | | | | | | | |   (85)  all_58_4 = e0
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | REF_CLOSE: (2), (4), (7), (8), (12), (13), (18), (19), (21),
% 243.21/49.77  | | | | | | | | | |            (22), (26), (29), (30), (31), (43), (44), (85) are
% 243.21/49.77  | | | | | | | | | |            inconsistent by sub-proof #1242.
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | End of split
% 243.21/49.77  | | | | | | | | | 
% 243.21/49.77  | | | | | | | | Case 2:
% 243.21/49.77  | | | | | | | | | 
% 243.21/49.77  | | | | | | | | |   (86)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 243.21/49.77  | | | | | | | | |           op(e1, e0) = e2)
% 243.21/49.77  | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | BETA: splitting (86) gives:
% 243.21/49.77  | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | Case 1:
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | |   (87)  all_58_8 = e2 & op(e1, e1) = e2
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | REF_CLOSE: (9), (31), (87) are inconsistent by sub-proof
% 243.21/49.77  | | | | | | | | | |            #2217.
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | Case 2:
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | |   (88)  all_58_11 = e2 & op(e1, e0) = e2
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | | REF_CLOSE: (14), (21), (88) are inconsistent by sub-proof
% 243.21/49.77  | | | | | | | | | |            #1741.
% 243.21/49.77  | | | | | | | | | | 
% 243.21/49.77  | | | | | | | | | End of split
% 243.21/49.77  | | | | | | | | | 
% 243.21/49.77  | | | | | | | | End of split
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | Case 2:
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | |   (89)  all_58_13 = e0 & op(e0, e2) = e0
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | | ALPHA: (89) implies:
% 243.21/49.77  | | | | | | | |   (90)  op(e0, e2) = e0
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | | REF_CLOSE: (4), (11), (29), (90) are inconsistent by sub-proof
% 243.21/49.77  | | | | | | | |            #2132.
% 243.21/49.77  | | | | | | | | 
% 243.21/49.77  | | | | | | | End of split
% 243.21/49.77  | | | | | | | 
% 243.21/49.77  | | | | | | End of split
% 243.21/49.77  | | | | | | 
% 243.21/49.77  | | | | | Case 2:
% 243.21/49.77  | | | | | | 
% 243.21/49.77  | | | | | |   (91)  all_58_5 = e2 & op(e2, e1) = e2
% 243.21/49.77  | | | | | | 
% 243.21/49.77  | | | | | | ALPHA: (91) implies:
% 243.21/49.78  | | | | | |   (92)  op(e2, e1) = e2
% 243.21/49.78  | | | | | | 
% 243.21/49.78  | | | | | | REF_CLOSE: (21), (27), (29), (92) are inconsistent by sub-proof
% 243.21/49.78  | | | | | |            #2256.
% 243.21/49.78  | | | | | | 
% 243.21/49.78  | | | | | End of split
% 243.21/49.78  | | | | | 
% 243.21/49.78  | | | | Case 2:
% 243.21/49.78  | | | | | 
% 243.21/49.78  | | | | |   (93)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 243.21/49.78  | | | | |             e1) = e2)
% 243.21/49.78  | | | | | 
% 243.21/49.78  | | | | | BETA: splitting (93) gives:
% 243.21/49.78  | | | | | 
% 243.21/49.78  | | | | | Case 1:
% 243.21/49.78  | | | | | | 
% 243.21/49.78  | | | | | |   (94)  all_58_8 = e2 & op(e1, e1) = e2
% 243.21/49.78  | | | | | | 
% 243.21/49.78  | | | | | | ALPHA: (94) implies:
% 243.21/49.78  | | | | | |   (95)  all_58_8 = e2
% 243.21/49.78  | | | | | | 
% 243.21/49.78  | | | | | | REF_CLOSE: (9), (31), (95) are inconsistent by sub-proof #1802.
% 243.21/49.78  | | | | | | 
% 243.21/49.78  | | | | | Case 2:
% 243.21/49.78  | | | | | | 
% 243.21/49.78  | | | | | |   (96)  all_58_14 = e2 & op(e0, e1) = e2
% 243.21/49.78  | | | | | | 
% 243.21/49.78  | | | | | | ALPHA: (96) implies:
% 243.21/49.78  | | | | | |   (97)  all_58_14 = e2
% 243.21/49.78  | | | | | | 
% 243.21/49.78  | | | | | | REF_CLOSE: (2), (4), (11), (25), (29), (36), (97) are inconsistent
% 243.21/49.78  | | | | | |            by sub-proof #1639.
% 243.21/49.78  | | | | | | 
% 243.21/49.78  | | | | | End of split
% 243.21/49.78  | | | | | 
% 243.21/49.78  | | | | End of split
% 243.21/49.78  | | | | 
% 243.21/49.78  | | | End of split
% 243.21/49.78  | | | 
% 243.21/49.78  | | End of split
% 243.21/49.78  | | 
% 243.21/49.78  | End of split
% 243.21/49.78  | 
% 243.21/49.78  End of proof
% 243.21/49.78  
% 243.21/49.78  Sub-proof #1134 shows that the following formulas are inconsistent:
% 243.21/49.78  ----------------------------------------------------------------
% 243.21/49.78    (1)  all_56_11 = e1
% 243.21/49.78    (2)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.21/49.78           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 243.21/49.78    (3)   ~ (e3 = e1)
% 243.21/49.78    (4)  op(e3, e3) = e1
% 243.21/49.78    (5)   ~ (e3 = e2)
% 243.21/49.78    (6)  op(e2, e1) = e3
% 243.21/49.78    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.78    (8)  op(e3, e2) = e3
% 243.21/49.78  
% 243.21/49.78  Begin of proof
% 243.21/49.78  | 
% 243.21/49.78  | BETA: splitting (2) gives:
% 243.21/49.78  | 
% 243.21/49.78  | Case 1:
% 243.21/49.78  | | 
% 243.21/49.78  | |   (9)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.21/49.78  | |        $i(all_56_9)
% 243.21/49.78  | | 
% 243.21/49.78  | | REF_CLOSE: (3), (4), (7), (8), (9) are inconsistent by sub-proof #1135.
% 243.21/49.78  | | 
% 243.21/49.78  | Case 2:
% 243.21/49.78  | | 
% 243.21/49.78  | |   (10)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 243.21/49.78  | | 
% 243.21/49.78  | | ALPHA: (10) implies:
% 243.21/49.78  | |   (11)  op(e2, all_56_11) = e2
% 243.21/49.78  | | 
% 243.21/49.78  | | REDUCE: (1), (11) imply:
% 243.21/49.78  | |   (12)  op(e2, e1) = e2
% 243.21/49.78  | | 
% 243.21/49.78  | | REF_CLOSE: (5), (6), (7), (12) are inconsistent by sub-proof #2256.
% 243.21/49.78  | | 
% 243.21/49.78  | End of split
% 243.21/49.78  | 
% 243.21/49.78  End of proof
% 243.21/49.78  
% 243.21/49.78  Sub-proof #1135 shows that the following formulas are inconsistent:
% 243.21/49.78  ----------------------------------------------------------------
% 243.21/49.78    (1)   ~ (e3 = e1)
% 243.21/49.78    (2)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.21/49.78         $i(all_56_9)
% 243.21/49.78    (3)  op(e3, e3) = e1
% 243.21/49.78    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.78    (5)  op(e3, e2) = e3
% 243.21/49.78  
% 243.21/49.78  Begin of proof
% 243.21/49.78  | 
% 243.21/49.78  | ALPHA: (2) implies:
% 243.21/49.78  |   (6)  op(e3, e2) = all_56_9
% 243.21/49.78  |   (7)  op(e3, all_56_9) = e3
% 243.21/49.78  | 
% 243.21/49.78  | GROUND_INST: instantiating (4) with e3, all_56_9, e2, e3, simplifying with
% 243.21/49.78  |              (5), (6) gives:
% 243.21/49.78  |   (8)  all_56_9 = e3
% 243.21/49.78  | 
% 243.21/49.78  | REDUCE: (7), (8) imply:
% 243.21/49.78  |   (9)  op(e3, e3) = e3
% 243.21/49.78  | 
% 243.21/49.78  | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #1578.
% 243.21/49.78  | 
% 243.21/49.78  End of proof
% 243.21/49.78  
% 243.21/49.78  Sub-proof #1136 shows that the following formulas are inconsistent:
% 243.21/49.78  ----------------------------------------------------------------
% 243.21/49.78    (1)   ~ (e3 = e0)
% 243.21/49.78    (2)   ~ (e2 = e0)
% 243.21/49.78    (3)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 243.21/49.78    (4)  op(e1, e2) = all_52_6
% 243.21/49.78    (5)  op(e3, e3) = e1
% 243.21/49.78    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.21/49.78         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.21/49.78    (7)   ~ (e3 = e2)
% 243.21/49.78    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.21/49.78         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.21/49.78    (9)  all_58_12 = e3
% 243.21/49.78    (10)   ~ (all_52_6 = e3)
% 243.21/49.78    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.78            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.78    (12)   ~ (e1 = e0)
% 243.21/49.78    (13)   ~ (e2 = e1)
% 243.21/49.78  
% 243.21/49.78  Begin of proof
% 243.21/49.78  | 
% 243.21/49.78  | BETA: splitting (3) gives:
% 243.21/49.78  | 
% 243.21/49.78  | Case 1:
% 243.21/49.78  | | 
% 243.21/49.78  | |   (14)  all_58_6 = e3 & op(e1, e3) = e3
% 243.21/49.78  | | 
% 243.21/49.78  | | ALPHA: (14) implies:
% 243.21/49.78  | |   (15)  all_58_6 = e3
% 243.21/49.78  | | 
% 243.21/49.78  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (13), (15) are
% 243.21/49.78  | |            inconsistent by sub-proof #1532.
% 243.21/49.78  | | 
% 243.21/49.78  | Case 2:
% 243.21/49.78  | | 
% 243.21/49.78  | |   (16)  all_58_7 = e3 & op(e1, e2) = e3
% 243.21/49.78  | | 
% 243.21/49.78  | | ALPHA: (16) implies:
% 243.21/49.78  | |   (17)  op(e1, e2) = e3
% 243.21/49.78  | | 
% 243.21/49.78  | | REF_CLOSE: (4), (10), (11), (17) are inconsistent by sub-proof #2191.
% 243.21/49.78  | | 
% 243.21/49.78  | End of split
% 243.21/49.78  | 
% 243.21/49.78  End of proof
% 243.21/49.78  
% 243.21/49.78  Sub-proof #1137 shows that the following formulas are inconsistent:
% 243.21/49.78  ----------------------------------------------------------------
% 243.21/49.78    (1)   ~ (e3 = e0)
% 243.21/49.78    (2)  all_58_6 = e3
% 243.21/49.78    (3)   ~ (e2 = e0)
% 243.21/49.78    (4)   ~ (e3 = e1)
% 243.21/49.78    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.21/49.78         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.21/49.78    (6)  op(e3, e3) = e1
% 243.21/49.78    (7)  all_58_15 = e3 & op(e0, e0) = e3
% 243.21/49.78    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.21/49.78         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.21/49.78    (9)   ~ (e3 = e2)
% 243.21/49.78    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.21/49.78          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.21/49.78    (11)  all_58_15 = e1
% 243.21/49.78    (12)  op(e2, e3) = all_52_1
% 243.21/49.78    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.78            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.78    (14)   ~ (e1 = e0)
% 243.21/49.78    (15)   ~ (all_52_1 = e3)
% 243.21/49.78    (16)   ~ (e2 = e1)
% 243.21/49.78  
% 243.21/49.78  Begin of proof
% 243.21/49.78  | 
% 243.21/49.78  | ALPHA: (7) implies:
% 243.21/49.78  |   (17)  all_58_15 = e3
% 243.21/49.78  | 
% 243.21/49.78  | COMBINE_EQS: (11), (17) imply:
% 243.21/49.78  |   (18)  e3 = e1
% 243.21/49.78  | 
% 243.21/49.78  | COMBINE_EQS: (2), (18) imply:
% 243.21/49.78  |   (19)  all_58_6 = e1
% 243.21/49.78  | 
% 243.21/49.78  | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14), (15),
% 243.21/49.78  |            (16), (19) are inconsistent by sub-proof #1161.
% 243.21/49.78  | 
% 243.21/49.78  End of proof
% 243.21/49.78  
% 243.21/49.78  Sub-proof #1138 shows that the following formulas are inconsistent:
% 243.21/49.78  ----------------------------------------------------------------
% 243.21/49.78    (1)   ~ (e3 = e0)
% 243.21/49.78    (2)  all_58_6 = e3
% 243.21/49.78    (3)   ~ (e2 = e0)
% 243.21/49.78    (4)   ~ (all_52_7 = e3)
% 243.21/49.78    (5)   ~ (e3 = e1)
% 243.21/49.78    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.21/49.78         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.21/49.78    (7)   ~ (e3 = e2)
% 243.21/49.78    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.21/49.78         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.21/49.78    (9)  op(e0, e2) = all_52_7
% 243.21/49.78    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.21/49.78          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.21/49.78    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.78            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.78    (12)   ~ (e1 = e0)
% 243.21/49.78    (13)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.21/49.78    (14)   ~ (e2 = e1)
% 243.21/49.78  
% 243.21/49.78  Begin of proof
% 243.21/49.78  | 
% 243.21/49.78  | BETA: splitting (13) gives:
% 243.21/49.78  | 
% 243.21/49.78  | Case 1:
% 243.21/49.78  | | 
% 243.21/49.78  | |   (15)  all_58_12 = e3 & op(e0, e3) = e3
% 243.21/49.78  | | 
% 243.21/49.78  | | ALPHA: (15) implies:
% 243.21/49.78  | |   (16)  all_58_12 = e3
% 243.21/49.78  | | 
% 243.21/49.78  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (14), (16)
% 243.21/49.78  | |            are inconsistent by sub-proof #1531.
% 243.21/49.78  | | 
% 243.21/49.78  | Case 2:
% 243.21/49.78  | | 
% 243.21/49.78  | |   (17)  all_58_13 = e3 & op(e0, e2) = e3
% 243.21/49.78  | | 
% 243.21/49.78  | | REF_CLOSE: (4), (9), (11), (17) are inconsistent by sub-proof #1919.
% 243.21/49.78  | | 
% 243.21/49.78  | End of split
% 243.21/49.78  | 
% 243.21/49.78  End of proof
% 243.21/49.78  
% 243.21/49.78  Sub-proof #1139 shows that the following formulas are inconsistent:
% 243.21/49.78  ----------------------------------------------------------------
% 243.21/49.78    (1)  op(e0, e0) = e1
% 243.21/49.78    (2)   ~ (all_52_1 = all_52_3)
% 243.21/49.78    (3)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.21/49.78    (4)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.21/49.78             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.21/49.78           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.21/49.78         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.21/49.78           $i(all_56_7))
% 243.21/49.78    (5)   ~ (all_52_6 = e1)
% 243.21/49.78    (6)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.21/49.78    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.21/49.78         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.21/49.78    (8)   ~ (all_52_3 = e1)
% 243.21/49.78    (9)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.21/49.78         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.21/49.78    (10)   ~ (all_52_7 = e2)
% 243.21/49.78    (11)  all_56_11 = e1
% 243.21/49.78    (12)  op(e0, e1) = all_52_11
% 243.21/49.78    (13)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.21/49.78            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.21/49.78            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 243.21/49.78            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 243.21/49.78            = all_56_15 & $i(all_56_15))
% 243.21/49.78    (14)  all_54_13 = all_52_7
% 243.21/49.78    (15)  all_58_5 = e3
% 243.21/49.78    (16)  op(e1, e2) = all_52_6
% 243.21/49.78    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.21/49.78          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.21/49.78    (18)   ~ (all_52_11 = e1)
% 243.21/49.78    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.21/49.78              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.21/49.78            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.21/49.78            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.21/49.78            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.21/49.78             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.21/49.78            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.21/49.78            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.21/49.78            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.21/49.78            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.21/49.78            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.21/49.78              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.21/49.78            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.21/49.78            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.21/49.78            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.21/49.78            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.21/49.78            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.21/49.78            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.21/49.78              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.21/49.78            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.21/49.78            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.21/49.78            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.21/49.78            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.21/49.78            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.21/49.78            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.21/49.78              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.21/49.78            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.21/49.78            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.21/49.78    (20)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 243.21/49.78            all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3,
% 243.21/49.78              e1) = all_38_1 & $i(all_38_1))
% 243.21/49.78    (21)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.21/49.78          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.21/49.78    (22)   ~ (all_52_6 = e2)
% 243.21/49.78    (23)   ~ (all_52_7 = all_52_11)
% 243.21/49.78    (24)  op(e1, e1) = all_6_2
% 243.21/49.78    (25)  all_58_8 = e1
% 243.21/49.78    (26)  op(e1, e0) = all_52_14
% 243.21/49.78    (27)   ~ (all_52_13 = e1)
% 243.21/49.78    (28)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 243.21/49.78            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 243.21/49.78              e1) = all_20_1 & $i(all_20_1))
% 243.21/49.78    (29)  op(e0, e3) = all_52_3
% 243.21/49.78    (30)   ~ (e3 = e1)
% 243.21/49.78    (31)  all_54_11 = all_52_14
% 243.21/49.78    (32)   ~ (all_52_8 = e1)
% 243.21/49.78    (33)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.21/49.78    (34)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.21/49.78            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 243.21/49.78              e1) = all_10_1 & $i(all_10_1))
% 243.21/49.78    (35)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.21/49.78          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.21/49.78    (36)  all_58_3 = e1
% 243.21/49.78    (37)   ~ (all_52_2 = e1)
% 243.21/49.78    (38)  all_54_2 = all_52_8
% 243.21/49.78    (39)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.21/49.78          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.21/49.78    (40)  op(e3, e3) = e1
% 243.21/49.78    (41)   ~ (all_52_3 = all_52_7)
% 243.21/49.78    (42)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.21/49.78    (43)  all_54_4 = all_52_1
% 243.21/49.78    (44)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.21/49.78              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.21/49.78                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.21/49.78                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.21/49.78    (45)   ~ (all_52_11 = e3)
% 243.21/49.78    (46)   ~ (all_6_2 = e3)
% 243.21/49.78    (47)  op(e3, e1) = all_52_8
% 243.21/49.79    (48)  op(e2, e1) = all_52_9
% 243.21/49.79    (49)  all_54_9 = all_52_6
% 243.21/49.79    (50)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.21/49.79          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.21/49.79    (51)   ~ (e3 = e2)
% 243.21/49.79    (52)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.21/49.79          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.21/49.79    (53)   ~ (all_52_14 = e1)
% 243.21/49.79    (54)   ~ (all_52_7 = e1)
% 243.21/49.79    (55)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.21/49.79    (56)   ~ (all_52_3 = all_52_11)
% 243.21/49.79    (57)  op(e2, e2) = e1
% 243.21/49.79    (58)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 243.21/49.79            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 243.21/49.79            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 243.21/49.79            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 243.21/49.79            op(e0, all_56_31) = e0)
% 243.21/49.79    (59)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.21/49.79    (60)  all_56_31 = e1
% 243.21/49.79    (61)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.21/49.79    (62)  all_54_12 = all_52_3
% 243.21/49.79    (63)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.21/49.79          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.21/49.79    (64)  all_58_15 = e1
% 243.21/49.79    (65)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.21/49.79          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.21/49.79    (66)  all_58_9 = e3
% 243.21/49.79    (67)   ~ (all_52_6 = all_52_14)
% 243.21/49.79    (68)  op(e3, e0) = e3
% 243.21/49.79    (69)  op(e2, e3) = all_52_1
% 243.21/49.79    (70)   ~ (all_52_14 = e3)
% 243.21/49.79    (71)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.21/49.79          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.21/49.79    (72)  all_54_7 = all_52_13
% 243.21/49.79    (73)  op(e0, e2) = all_52_7
% 243.21/49.79    (74)   ~ (all_52_13 = all_52_14)
% 243.21/49.79    (75)   ~ (all_52_4 = e3)
% 243.21/49.79    (76)  op(e3, e2) = all_52_4
% 243.21/49.79    (77)   ~ (all_52_8 = all_52_11)
% 243.21/49.79    (78)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.21/49.79    (79)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.21/49.79          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.21/49.79    (80)  op(e2, e1) = e3
% 243.21/49.79    (81)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 243.21/49.79            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 243.21/49.79              e1) = all_34_1 & $i(all_34_1))
% 243.21/49.79    (82)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.21/49.79          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.21/49.79    (83)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.21/49.79          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.21/49.79    (84)   ~ (all_52_2 = all_52_6)
% 243.21/49.79    (85)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.21/49.79          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 243.21/49.79    (86)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.79    (87)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.21/49.79          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.21/49.79    (88)  op(e1, e3) = all_52_2
% 243.21/49.79    (89)   ~ (all_52_6 = all_52_7)
% 243.21/49.79    (90)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.21/49.79          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.21/49.79    (91)   ~ (all_52_4 = e1)
% 243.21/49.79    (92)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.21/49.79          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.21/49.79    (93)   ~ (all_52_8 = e2)
% 243.21/49.79    (94)  op(e2, e0) = all_52_13
% 243.21/49.79    (95)   ~ (all_52_1 = e3)
% 243.21/49.79    (96)   ~ (all_52_9 = e1)
% 243.21/49.79    (97)  all_54_14 = all_52_11
% 243.21/49.79    (98)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.21/49.79          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.21/49.79            e2)
% 243.21/49.79    (99)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.21/49.79          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.21/49.79    (100)  all_56_1 = e1
% 243.21/49.79    (101)  all_58_4 = e0
% 243.21/49.79    (102)   ~ (e2 = e1)
% 243.21/49.79    (103)   ~ (all_52_1 = e1)
% 243.21/49.79    (104)   ~ (all_52_8 = e3)
% 243.21/49.79  
% 243.21/49.79  Begin of proof
% 243.21/49.79  | 
% 243.21/49.79  | BETA: splitting (61) gives:
% 243.21/49.79  | 
% 243.21/49.79  | Case 1:
% 243.21/49.79  | | 
% 243.21/49.79  | |   (105)  all_54_2 = e2
% 243.21/49.79  | | 
% 243.21/49.79  | | COMBINE_EQS: (38), (105) imply:
% 243.21/49.79  | |   (106)  all_52_8 = e2
% 243.21/49.79  | | 
% 243.21/49.79  | | REDUCE: (93), (106) imply:
% 243.21/49.79  | |   (107)  $false
% 243.21/49.79  | | 
% 243.21/49.79  | | CLOSE: (107) is inconsistent.
% 243.21/49.79  | | 
% 243.21/49.79  | Case 2:
% 243.21/49.79  | | 
% 243.21/49.79  | |   (108)   ~ (all_54_2 = e2)
% 243.21/49.79  | |   (109)  all_54_2 = e1 | all_54_2 = e0
% 243.21/49.79  | | 
% 243.21/49.79  | | BETA: splitting (109) gives:
% 243.21/49.79  | | 
% 243.21/49.79  | | Case 1:
% 243.21/49.79  | | | 
% 243.21/49.79  | | |   (110)  all_54_2 = e1
% 243.21/49.79  | | | 
% 243.21/49.79  | | | COMBINE_EQS: (38), (110) imply:
% 243.21/49.79  | | |   (111)  all_52_8 = e1
% 243.21/49.79  | | | 
% 243.21/49.79  | | | REDUCE: (32), (111) imply:
% 243.21/49.79  | | |   (112)  $false
% 243.21/49.79  | | | 
% 243.21/49.79  | | | CLOSE: (112) is inconsistent.
% 243.21/49.79  | | | 
% 243.21/49.79  | | Case 2:
% 243.21/49.79  | | | 
% 243.21/49.79  | | |   (113)  all_54_2 = e0
% 243.21/49.79  | | | 
% 243.21/49.79  | | | COMBINE_EQS: (38), (113) imply:
% 243.21/49.79  | | |   (114)  all_52_8 = e0
% 243.21/49.79  | | | 
% 243.21/49.79  | | | REDUCE: (77), (114) imply:
% 243.21/49.79  | | |   (115)   ~ (all_52_11 = e0)
% 243.21/49.79  | | | 
% 243.21/49.79  | | | SIMP: (115) implies:
% 243.21/49.79  | | |   (116)   ~ (all_52_11 = e0)
% 243.21/49.79  | | | 
% 243.21/49.79  | | | REDUCE: (104), (114) imply:
% 243.21/49.79  | | |   (117)   ~ (e3 = e0)
% 243.21/49.79  | | | 
% 243.21/49.79  | | | SIMP: (117) implies:
% 243.21/49.79  | | |   (118)   ~ (e3 = e0)
% 243.21/49.79  | | | 
% 243.21/49.79  | | | REDUCE: (93), (114) imply:
% 243.21/49.79  | | |   (119)   ~ (e2 = e0)
% 243.21/49.79  | | | 
% 243.21/49.79  | | | SIMP: (119) implies:
% 243.21/49.79  | | |   (120)   ~ (e2 = e0)
% 243.21/49.79  | | | 
% 243.21/49.79  | | | REDUCE: (32), (114) imply:
% 243.21/49.79  | | |   (121)   ~ (e1 = e0)
% 243.21/49.79  | | | 
% 243.21/49.79  | | | SIMP: (121) implies:
% 243.21/49.79  | | |   (122)   ~ (e1 = e0)
% 243.21/49.79  | | | 
% 243.21/49.79  | | | REDUCE: (47), (114) imply:
% 243.21/49.79  | | |   (123)  op(e3, e1) = e0
% 243.21/49.79  | | | 
% 243.21/49.79  | | | BETA: splitting (55) gives:
% 243.21/49.79  | | | 
% 243.21/49.79  | | | Case 1:
% 243.21/49.79  | | | | 
% 243.21/49.79  | | | |   (124)  all_54_14 = e3
% 243.21/49.79  | | | | 
% 243.21/49.79  | | | | REF_CLOSE: (45), (97), (124) are inconsistent by sub-proof #1796.
% 243.21/49.79  | | | | 
% 243.21/49.79  | | | Case 2:
% 243.21/49.79  | | | | 
% 243.21/49.79  | | | |   (125)   ~ (all_54_14 = e3)
% 243.21/49.79  | | | |   (126)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.21/49.79  | | | | 
% 243.21/49.79  | | | | BETA: splitting (20) gives:
% 243.21/49.79  | | | | 
% 243.21/49.79  | | | | Case 1:
% 243.21/49.79  | | | | | 
% 243.21/49.79  | | | | |   (127)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1)
% 243.21/49.79  | | | | |          = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 243.21/49.79  | | | | | 
% 243.21/49.79  | | | | | ALPHA: (127) implies:
% 243.21/49.79  | | | | |   (128)   ~ (all_38_0 = e2)
% 243.21/49.79  | | | | |   (129)  op(e3, e1) = all_38_1
% 243.21/49.79  | | | | |   (130)  op(all_38_1, e3) = all_38_0
% 243.21/49.79  | | | | | 
% 243.21/49.79  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 243.21/49.79  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (21), (22),
% 243.21/49.79  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 243.21/49.79  | | | | |            (33), (34), (35), (36), (37), (39), (40), (41), (42), (43),
% 243.21/49.79  | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 243.21/49.79  | | | | |            (54), (56), (57), (58), (59), (60), (62), (63), (64), (65),
% 243.21/49.79  | | | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 243.21/49.79  | | | | |            (76), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 243.21/49.79  | | | | |            (87), (88), (89), (90), (91), (92), (94), (95), (96), (97),
% 243.21/49.79  | | | | |            (98), (99), (100), (101), (102), (103), (104), (116),
% 243.21/49.79  | | | | |            (118), (120), (122), (123), (126), (128), (129), (130) are
% 243.21/49.79  | | | | |            inconsistent by sub-proof #1144.
% 243.21/49.79  | | | | | 
% 243.21/49.79  | | | | Case 2:
% 243.21/49.79  | | | | | 
% 243.21/49.79  | | | | |   (131)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1)
% 243.21/49.79  | | | | | 
% 243.21/49.79  | | | | | ALPHA: (131) implies:
% 243.21/49.79  | | | | |   (132)   ~ (all_38_1 = e0)
% 243.21/49.79  | | | | |   (133)  op(e3, e1) = all_38_1
% 243.21/49.79  | | | | | 
% 243.21/49.79  | | | | | REF_CLOSE: (34), (86), (123), (132), (133) are inconsistent by
% 243.21/49.79  | | | | |            sub-proof #1194.
% 243.21/49.79  | | | | | 
% 243.21/49.79  | | | | End of split
% 243.21/49.79  | | | | 
% 243.21/49.79  | | | End of split
% 243.21/49.79  | | | 
% 243.21/49.79  | | End of split
% 243.21/49.79  | | 
% 243.21/49.79  | End of split
% 243.21/49.79  | 
% 243.21/49.79  End of proof
% 243.21/49.79  
% 243.21/49.79  Sub-proof #1140 shows that the following formulas are inconsistent:
% 243.21/49.79  ----------------------------------------------------------------
% 243.21/49.79    (1)  op(e0, e0) = e1
% 243.21/49.79    (2)   ~ (all_52_1 = all_52_3)
% 243.21/49.79    (3)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.21/49.79    (4)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.21/49.79             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.21/49.79           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.21/49.79         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.21/49.79           $i(all_56_7))
% 243.21/49.79    (5)   ~ (all_52_6 = e1)
% 243.21/49.79    (6)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.21/49.79    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.21/49.79         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.21/49.79    (8)   ~ (all_52_3 = e1)
% 243.21/49.79    (9)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.21/49.79         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.21/49.79    (10)   ~ (all_52_7 = e2)
% 243.21/49.79    (11)  all_56_11 = e1
% 243.21/49.79    (12)  op(e0, e1) = all_52_11
% 243.21/49.79    (13)  op(e1, e1) = e1
% 243.21/49.79    (14)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.21/49.79            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.21/49.79            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 243.21/49.79            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 243.21/49.79            = all_56_15 & $i(all_56_15))
% 243.21/49.79    (15)  all_54_13 = all_52_7
% 243.21/49.79    (16)  all_58_5 = e3
% 243.21/49.79    (17)  op(e1, e2) = all_52_6
% 243.21/49.79    (18)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.21/49.79          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.21/49.79    (19)   ~ (all_52_11 = e1)
% 243.21/49.79    (20)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.21/49.79              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.21/49.79            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.21/49.79            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.21/49.79            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.21/49.79             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.21/49.79            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.21/49.79            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.21/49.79            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.21/49.79            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.21/49.79            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.21/49.79              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.21/49.79            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.21/49.79            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.21/49.79            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.21/49.79            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.21/49.79            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.21/49.79            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.21/49.79              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.21/49.79            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.21/49.79            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.21/49.79            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.21/49.79            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.21/49.79            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.21/49.79            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.21/49.79              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.21/49.79            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.21/49.79            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.21/49.79    (21)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 243.21/49.79            all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3,
% 243.21/49.79              e1) = all_38_1 & $i(all_38_1))
% 243.21/49.79    (22)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.21/49.79          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.21/49.79    (23)   ~ (all_52_6 = e2)
% 243.21/49.79    (24)   ~ (all_52_7 = all_52_11)
% 243.21/49.79    (25)  op(e1, e1) = all_6_2
% 243.21/49.79    (26)  all_58_1 = e0
% 243.21/49.79    (27)  all_58_8 = e1
% 243.21/49.79    (28)  op(e1, e0) = all_52_14
% 243.21/49.79    (29)   ~ (all_52_13 = e1)
% 243.21/49.79    (30)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 243.21/49.79            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 243.21/49.79              e1) = all_20_1 & $i(all_20_1))
% 243.21/49.79    (31)  op(e0, e3) = all_52_3
% 243.21/49.79    (32)   ~ (e3 = e1)
% 243.21/49.79    (33)  all_54_11 = all_52_14
% 243.21/49.79    (34)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.21/49.79          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.21/49.79    (35)   ~ (all_52_8 = e1)
% 243.21/49.79    (36)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.21/49.80    (37)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.21/49.80            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 243.21/49.80              e1) = all_10_1 & $i(all_10_1))
% 243.21/49.80    (38)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.21/49.80          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.21/49.80    (39)  all_58_3 = e1
% 243.21/49.80    (40)   ~ (all_52_2 = e1)
% 243.21/49.80    (41)  all_54_2 = all_52_8
% 243.21/49.80    (42)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.21/49.80          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.21/49.80    (43)  op(e3, e3) = e1
% 243.21/49.80    (44)   ~ (all_52_3 = all_52_7)
% 243.21/49.80    (45)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.21/49.80    (46)  all_54_4 = all_52_1
% 243.21/49.80    (47)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.21/49.80              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.21/49.80                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.21/49.80                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.21/49.80    (48)   ~ (all_52_11 = e3)
% 243.21/49.80    (49)   ~ (all_6_2 = e3)
% 243.21/49.80    (50)  op(e3, e1) = all_52_8
% 243.21/49.80    (51)  op(e2, e1) = all_52_9
% 243.21/49.80    (52)  all_54_9 = all_52_6
% 243.21/49.80    (53)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.21/49.80          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.21/49.80    (54)   ~ (e3 = e2)
% 243.21/49.80    (55)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.21/49.80          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.21/49.80    (56)   ~ (all_52_14 = e1)
% 243.21/49.80    (57)   ~ (all_52_7 = e1)
% 243.21/49.80    (58)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.21/49.80    (59)   ~ (all_52_3 = all_52_11)
% 243.21/49.80    (60)  op(e2, e2) = e1
% 243.21/49.80    (61)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 243.21/49.80            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 243.21/49.80            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 243.21/49.80            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 243.21/49.80            op(e0, all_56_31) = e0)
% 243.21/49.80    (62)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.21/49.80    (63)  all_56_31 = e1
% 243.21/49.80    (64)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.21/49.80    (65)  all_54_12 = all_52_3
% 243.21/49.80    (66)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.21/49.80          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.21/49.80    (67)  all_58_15 = e1
% 243.21/49.80    (68)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.21/49.80          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.21/49.80    (69)  all_58_9 = e3
% 243.21/49.80    (70)   ~ (all_52_6 = all_52_14)
% 243.21/49.80    (71)  op(e3, e0) = e3
% 243.21/49.80    (72)  op(e2, e3) = all_52_1
% 243.21/49.80    (73)   ~ (all_52_14 = e3)
% 243.21/49.80    (74)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.21/49.80          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.21/49.80    (75)  all_54_7 = all_52_13
% 243.21/49.80    (76)  op(e0, e2) = all_52_7
% 243.21/49.80    (77)   ~ (all_52_13 = all_52_14)
% 243.21/49.80    (78)   ~ (all_52_4 = e3)
% 243.21/49.80    (79)  op(e3, e2) = all_52_4
% 243.21/49.80    (80)   ~ (all_52_8 = all_52_11)
% 243.21/49.80    (81)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.21/49.80    (82)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.21/49.80          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.21/49.80    (83)  op(e2, e1) = e3
% 243.21/49.80    (84)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 243.21/49.80            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 243.21/49.80              e1) = all_34_1 & $i(all_34_1))
% 243.21/49.80    (85)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.21/49.80          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.21/49.80    (86)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.21/49.80          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.21/49.80    (87)   ~ (all_52_2 = all_52_6)
% 243.21/49.80    (88)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.21/49.80          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 243.21/49.80    (89)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.80            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.80    (90)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.21/49.80          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.21/49.80    (91)  op(e1, e3) = all_52_2
% 243.21/49.80    (92)   ~ (all_52_6 = all_52_7)
% 243.21/49.80    (93)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.21/49.80          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.21/49.80    (94)   ~ (all_52_4 = e1)
% 243.21/49.80    (95)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.21/49.80          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.21/49.80    (96)   ~ (all_52_8 = e2)
% 243.21/49.80    (97)  op(e2, e0) = all_52_13
% 243.21/49.80    (98)   ~ (all_52_1 = e3)
% 243.21/49.80    (99)   ~ (all_52_9 = e1)
% 243.21/49.80    (100)  all_54_14 = all_52_11
% 243.21/49.80    (101)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.21/49.80           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.21/49.80             e2)
% 243.21/49.80    (102)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.21/49.80           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.21/49.80    (103)  all_56_1 = e1
% 243.21/49.80    (104)   ~ (e2 = e1)
% 243.21/49.80    (105)   ~ (all_52_1 = e1)
% 243.21/49.80    (106)   ~ (all_52_8 = e3)
% 243.21/49.80  
% 243.21/49.80  Begin of proof
% 243.21/49.80  | 
% 243.21/49.80  | BETA: splitting (64) gives:
% 243.21/49.80  | 
% 243.21/49.80  | Case 1:
% 243.21/49.80  | | 
% 243.21/49.80  | |   (107)  all_54_2 = e2
% 243.21/49.80  | | 
% 243.21/49.80  | | COMBINE_EQS: (41), (107) imply:
% 243.21/49.80  | |   (108)  all_52_8 = e2
% 243.21/49.80  | | 
% 243.21/49.80  | | REDUCE: (96), (108) imply:
% 243.21/49.80  | |   (109)  $false
% 243.21/49.80  | | 
% 243.21/49.80  | | CLOSE: (109) is inconsistent.
% 243.21/49.80  | | 
% 243.21/49.80  | Case 2:
% 243.21/49.80  | | 
% 243.21/49.80  | |   (110)   ~ (all_54_2 = e2)
% 243.21/49.80  | |   (111)  all_54_2 = e1 | all_54_2 = e0
% 243.21/49.80  | | 
% 243.21/49.80  | | BETA: splitting (111) gives:
% 243.21/49.80  | | 
% 243.21/49.80  | | Case 1:
% 243.21/49.80  | | | 
% 243.21/49.80  | | |   (112)  all_54_2 = e1
% 243.21/49.80  | | | 
% 243.21/49.80  | | | COMBINE_EQS: (41), (112) imply:
% 243.21/49.80  | | |   (113)  all_52_8 = e1
% 243.21/49.80  | | | 
% 243.21/49.80  | | | REDUCE: (35), (113) imply:
% 243.21/49.80  | | |   (114)  $false
% 243.21/49.80  | | | 
% 243.21/49.80  | | | CLOSE: (114) is inconsistent.
% 243.21/49.80  | | | 
% 243.21/49.80  | | Case 2:
% 243.21/49.80  | | | 
% 243.21/49.80  | | |   (115)  all_54_2 = e0
% 243.21/49.80  | | | 
% 243.21/49.80  | | | COMBINE_EQS: (41), (115) imply:
% 243.21/49.80  | | |   (116)  all_52_8 = e0
% 243.21/49.80  | | | 
% 243.21/49.80  | | | REDUCE: (80), (116) imply:
% 243.21/49.80  | | |   (117)   ~ (all_52_11 = e0)
% 243.21/49.80  | | | 
% 243.21/49.80  | | | SIMP: (117) implies:
% 243.21/49.80  | | |   (118)   ~ (all_52_11 = e0)
% 243.21/49.80  | | | 
% 243.21/49.80  | | | REDUCE: (106), (116) imply:
% 243.21/49.80  | | |   (119)   ~ (e3 = e0)
% 243.21/49.80  | | | 
% 243.21/49.80  | | | SIMP: (119) implies:
% 243.21/49.80  | | |   (120)   ~ (e3 = e0)
% 243.21/49.80  | | | 
% 243.21/49.80  | | | REDUCE: (96), (116) imply:
% 243.21/49.80  | | |   (121)   ~ (e2 = e0)
% 243.21/49.80  | | | 
% 243.21/49.80  | | | SIMP: (121) implies:
% 243.21/49.80  | | |   (122)   ~ (e2 = e0)
% 243.21/49.80  | | | 
% 243.21/49.80  | | | REDUCE: (35), (116) imply:
% 243.21/49.80  | | |   (123)   ~ (e1 = e0)
% 243.21/49.80  | | | 
% 243.21/49.80  | | | SIMP: (123) implies:
% 243.21/49.80  | | |   (124)   ~ (e1 = e0)
% 243.21/49.80  | | | 
% 243.21/49.80  | | | REDUCE: (50), (116) imply:
% 243.21/49.80  | | |   (125)  op(e3, e1) = e0
% 243.21/49.80  | | | 
% 243.21/49.80  | | | BETA: splitting (58) gives:
% 243.21/49.80  | | | 
% 243.21/49.80  | | | Case 1:
% 243.21/49.80  | | | | 
% 243.21/49.80  | | | |   (126)  all_54_14 = e3
% 243.21/49.80  | | | | 
% 243.21/49.80  | | | | REF_CLOSE: (48), (100), (126) are inconsistent by sub-proof #1796.
% 243.21/49.80  | | | | 
% 243.21/49.80  | | | Case 2:
% 243.21/49.80  | | | | 
% 243.21/49.80  | | | |   (127)   ~ (all_54_14 = e3)
% 243.21/49.80  | | | |   (128)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.21/49.80  | | | | 
% 243.21/49.80  | | | | BETA: splitting (55) gives:
% 243.21/49.80  | | | | 
% 243.21/49.80  | | | | Case 1:
% 243.21/49.80  | | | | | 
% 243.21/49.80  | | | | |   (129)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 243.21/49.80  | | | | |              e1) = e2)
% 243.21/49.80  | | | | | 
% 243.21/49.80  | | | | | BETA: splitting (129) gives:
% 243.21/49.80  | | | | | 
% 243.21/49.80  | | | | | Case 1:
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | |   (130)  all_58_4 = e2 & op(e3, e1) = e2
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | | ALPHA: (130) implies:
% 243.21/49.80  | | | | | |   (131)  all_58_4 = e2
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | | BETA: splitting (21) gives:
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | | Case 1:
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | |   (132)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3,
% 243.21/49.80  | | | | | | |            e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | | ALPHA: (132) implies:
% 243.21/49.80  | | | | | | |   (133)   ~ (all_38_0 = e2)
% 243.21/49.80  | | | | | | |   (134)  op(e3, e1) = all_38_1
% 243.21/49.80  | | | | | | |   (135)  op(all_38_1, e3) = all_38_0
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | | BETA: splitting (34) gives:
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | | Case 1:
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | |   (136)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 243.21/49.80  | | | | | | | |            op(e2, e1) = e0)
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | | BETA: splitting (136) gives:
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | | Case 1:
% 243.21/49.80  | | | | | | | | | 
% 243.21/49.80  | | | | | | | | |   (137)  all_58_4 = e0 & op(e3, e1) = e0
% 243.21/49.80  | | | | | | | | | 
% 243.21/49.80  | | | | | | | | | ALPHA: (137) implies:
% 243.21/49.80  | | | | | | | | |   (138)  all_58_4 = e0
% 243.21/49.80  | | | | | | | | | 
% 243.21/49.80  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 243.21/49.80  | | | | | | | | |            (11), (12), (14), (15), (16), (17), (18), (19),
% 243.21/49.80  | | | | | | | | |            (20), (22), (23), (24), (25), (27), (28), (29),
% 243.21/49.80  | | | | | | | | |            (30), (31), (32), (33), (35), (36), (37), (38),
% 243.21/49.80  | | | | | | | | |            (39), (40), (42), (43), (44), (45), (46), (47),
% 243.21/49.80  | | | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55),
% 243.21/49.80  | | | | | | | | |            (56), (57), (59), (60), (61), (62), (63), (65),
% 243.21/49.80  | | | | | | | | |            (66), (67), (68), (69), (70), (71), (72), (73),
% 243.21/49.80  | | | | | | | | |            (74), (75), (76), (77), (78), (79), (81), (82),
% 243.21/49.80  | | | | | | | | |            (83), (84), (85), (86), (87), (88), (89), (90),
% 243.21/49.80  | | | | | | | | |            (91), (92), (93), (94), (95), (97), (98), (99),
% 243.21/49.80  | | | | | | | | |            (100), (101), (102), (103), (104), (105), (106),
% 243.21/49.80  | | | | | | | | |            (118), (120), (122), (124), (125), (128), (133),
% 243.21/49.80  | | | | | | | | |            (134), (135), (138) are inconsistent by sub-proof
% 243.21/49.80  | | | | | | | | |            #1144.
% 243.21/49.80  | | | | | | | | | 
% 243.21/49.80  | | | | | | | | Case 2:
% 243.21/49.80  | | | | | | | | | 
% 243.21/49.80  | | | | | | | | |   (139)  all_58_5 = e0 & op(e2, e1) = e0
% 243.21/49.80  | | | | | | | | | 
% 243.21/49.80  | | | | | | | | | REF_CLOSE: (16), (32), (38), (43), (54), (69), (78), (79),
% 243.21/49.80  | | | | | | | | |            (89), (120), (131), (139) are inconsistent by
% 243.21/49.80  | | | | | | | | |            sub-proof #1142.
% 243.21/49.80  | | | | | | | | | 
% 243.21/49.80  | | | | | | | | End of split
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | Case 2:
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | |   (140)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 243.21/49.80  | | | | | | | |            op(e0, e1) = e0)
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | | REF_CLOSE: (12), (13), (89), (118), (124), (140) are
% 243.21/49.80  | | | | | | | |            inconsistent by sub-proof #1141.
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | End of split
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | Case 2:
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | |   (141)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1)
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | | ALPHA: (141) implies:
% 243.21/49.80  | | | | | | |   (142)   ~ (all_38_1 = e0)
% 243.21/49.80  | | | | | | |   (143)  op(e3, e1) = all_38_1
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | | REF_CLOSE: (37), (89), (125), (142), (143) are inconsistent by
% 243.21/49.80  | | | | | | |            sub-proof #1194.
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | End of split
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | Case 2:
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | |   (144)  all_58_5 = e2 & op(e2, e1) = e2
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | | ALPHA: (144) implies:
% 243.21/49.80  | | | | | |   (145)  op(e2, e1) = e2
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | | REF_CLOSE: (54), (83), (89), (145) are inconsistent by sub-proof
% 243.21/49.80  | | | | | |            #2256.
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | End of split
% 243.21/49.80  | | | | | 
% 243.21/49.80  | | | | Case 2:
% 243.21/49.80  | | | | | 
% 243.21/49.80  | | | | |   (146)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 243.21/49.80  | | | | |              e1) = e2)
% 243.21/49.80  | | | | | 
% 243.21/49.80  | | | | | BETA: splitting (146) gives:
% 243.21/49.80  | | | | | 
% 243.21/49.80  | | | | | Case 1:
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | |   (147)  all_58_8 = e2 & op(e1, e1) = e2
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | | ALPHA: (147) implies:
% 243.21/49.80  | | | | | |   (148)  all_58_8 = e2
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | | REF_CLOSE: (27), (104), (148) are inconsistent by sub-proof #1802.
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | Case 2:
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | |   (149)  all_58_14 = e2 & op(e0, e1) = e2
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | | ALPHA: (149) implies:
% 243.21/49.80  | | | | | |   (150)  all_58_14 = e2
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | | BETA: splitting (21) gives:
% 243.21/49.80  | | | | | | 
% 243.21/49.80  | | | | | | Case 1:
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | |   (151)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3,
% 243.21/49.80  | | | | | | |            e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | | ALPHA: (151) implies:
% 243.21/49.80  | | | | | | |   (152)   ~ (all_38_0 = e2)
% 243.21/49.80  | | | | | | |   (153)  op(e3, e1) = all_38_1
% 243.21/49.80  | | | | | | |   (154)  op(all_38_1, e3) = all_38_0
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | | BETA: splitting (7) gives:
% 243.21/49.80  | | | | | | | 
% 243.21/49.80  | | | | | | | Case 1:
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | |   (155)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 &
% 243.21/49.80  | | | | | | | |            op(e3, e2) = e2)
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | | REF_CLOSE: (26), (43), (89), (104), (122), (155) are
% 243.21/49.80  | | | | | | | |            inconsistent by sub-proof #1477.
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | Case 2:
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | |   (156)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 &
% 243.21/49.80  | | | | | | | |            op(e3, e0) = e2)
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | | BETA: splitting (156) gives:
% 243.21/49.80  | | | | | | | | 
% 243.21/49.80  | | | | | | | | Case 1:
% 243.21/49.80  | | | | | | | | | 
% 243.21/49.80  | | | | | | | | |   (157)  all_58_4 = e2 & op(e3, e1) = e2
% 243.21/49.80  | | | | | | | | | 
% 243.21/49.80  | | | | | | | | | ALPHA: (157) implies:
% 243.21/49.80  | | | | | | | | |   (158)  all_58_4 = e2
% 243.21/49.80  | | | | | | | | | 
% 243.21/49.80  | | | | | | | | | BETA: splitting (34) gives:
% 243.21/49.80  | | | | | | | | | 
% 243.21/49.80  | | | | | | | | | Case 1:
% 243.21/49.80  | | | | | | | | | | 
% 243.21/49.80  | | | | | | | | | |   (159)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 243.21/49.80  | | | | | | | | | |            & op(e2, e1) = e0)
% 243.21/49.80  | | | | | | | | | | 
% 243.21/49.80  | | | | | | | | | | BETA: splitting (159) gives:
% 243.21/49.80  | | | | | | | | | | 
% 243.21/49.80  | | | | | | | | | | Case 1:
% 243.21/49.80  | | | | | | | | | | | 
% 243.21/49.80  | | | | | | | | | | |   (160)  all_58_4 = e0 & op(e3, e1) = e0
% 243.21/49.80  | | | | | | | | | | | 
% 243.21/49.80  | | | | | | | | | | | ALPHA: (160) implies:
% 243.21/49.80  | | | | | | | | | | |   (161)  all_58_4 = e0
% 243.21/49.80  | | | | | | | | | | | 
% 243.21/49.81  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 243.21/49.81  | | | | | | | | | | |            (11), (12), (14), (15), (16), (17), (18), (19),
% 243.21/49.81  | | | | | | | | | | |            (20), (22), (23), (24), (25), (27), (28), (29),
% 243.21/49.81  | | | | | | | | | | |            (30), (31), (32), (33), (35), (36), (37), (38),
% 243.21/49.81  | | | | | | | | | | |            (39), (40), (42), (43), (44), (45), (46), (47),
% 243.21/49.81  | | | | | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55),
% 243.21/49.81  | | | | | | | | | | |            (56), (57), (59), (60), (61), (62), (63), (65),
% 243.21/49.81  | | | | | | | | | | |            (66), (67), (68), (69), (70), (71), (72), (73),
% 243.21/49.81  | | | | | | | | | | |            (74), (75), (76), (77), (78), (79), (81), (82),
% 243.21/49.81  | | | | | | | | | | |            (83), (84), (85), (86), (87), (88), (89), (90),
% 243.21/49.81  | | | | | | | | | | |            (91), (92), (93), (94), (95), (97), (98), (99),
% 243.21/49.81  | | | | | | | | | | |            (100), (101), (102), (103), (104), (105), (106),
% 243.21/49.81  | | | | | | | | | | |            (118), (120), (122), (124), (125), (128), (150),
% 243.21/49.81  | | | | | | | | | | |            (152), (153), (154), (161) are inconsistent by
% 243.21/49.81  | | | | | | | | | | |            sub-proof #1145.
% 243.21/49.81  | | | | | | | | | | | 
% 243.21/49.81  | | | | | | | | | | Case 2:
% 243.21/49.81  | | | | | | | | | | | 
% 243.21/49.81  | | | | | | | | | | |   (162)  all_58_5 = e0 & op(e2, e1) = e0
% 243.21/49.81  | | | | | | | | | | | 
% 243.21/49.81  | | | | | | | | | | | REF_CLOSE: (16), (32), (38), (43), (54), (69), (78), (79),
% 243.21/49.81  | | | | | | | | | | |            (89), (120), (158), (162) are inconsistent by
% 243.21/49.81  | | | | | | | | | | |            sub-proof #1142.
% 243.21/49.81  | | | | | | | | | | | 
% 243.21/49.81  | | | | | | | | | | End of split
% 243.21/49.81  | | | | | | | | | | 
% 243.21/49.81  | | | | | | | | | Case 2:
% 243.21/49.81  | | | | | | | | | | 
% 243.21/49.81  | | | | | | | | | |   (163)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0
% 243.21/49.81  | | | | | | | | | |            & op(e0, e1) = e0)
% 243.21/49.81  | | | | | | | | | | 
% 243.21/49.81  | | | | | | | | | | REF_CLOSE: (12), (13), (89), (118), (124), (163) are
% 243.21/49.81  | | | | | | | | | |            inconsistent by sub-proof #1141.
% 243.21/49.81  | | | | | | | | | | 
% 243.21/49.81  | | | | | | | | | End of split
% 243.21/49.81  | | | | | | | | | 
% 243.21/49.81  | | | | | | | | Case 2:
% 243.21/49.81  | | | | | | | | | 
% 243.21/49.81  | | | | | | | | |   (164)  all_58_9 = e2 & op(e3, e0) = e2
% 243.21/49.81  | | | | | | | | | 
% 243.21/49.81  | | | | | | | | | ALPHA: (164) implies:
% 243.21/49.81  | | | | | | | | |   (165)  op(e3, e0) = e2
% 243.21/49.81  | | | | | | | | | 
% 243.21/49.81  | | | | | | | | | REF_CLOSE: (54), (71), (89), (165) are inconsistent by
% 243.21/49.81  | | | | | | | | |            sub-proof #2125.
% 243.21/49.81  | | | | | | | | | 
% 243.21/49.81  | | | | | | | | End of split
% 243.21/49.81  | | | | | | | | 
% 243.21/49.81  | | | | | | | End of split
% 243.21/49.81  | | | | | | | 
% 243.21/49.81  | | | | | | Case 2:
% 243.21/49.81  | | | | | | | 
% 243.21/49.81  | | | | | | |   (166)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1)
% 243.21/49.81  | | | | | | | 
% 243.21/49.81  | | | | | | | ALPHA: (166) implies:
% 243.21/49.81  | | | | | | |   (167)   ~ (all_38_1 = e0)
% 243.21/49.81  | | | | | | |   (168)  op(e3, e1) = all_38_1
% 243.21/49.81  | | | | | | | 
% 243.21/49.81  | | | | | | | REF_CLOSE: (37), (89), (125), (167), (168) are inconsistent by
% 243.21/49.81  | | | | | | |            sub-proof #1194.
% 243.21/49.81  | | | | | | | 
% 243.21/49.81  | | | | | | End of split
% 243.21/49.81  | | | | | | 
% 243.21/49.81  | | | | | End of split
% 243.21/49.81  | | | | | 
% 243.21/49.81  | | | | End of split
% 243.21/49.81  | | | | 
% 243.21/49.81  | | | End of split
% 243.21/49.81  | | | 
% 243.21/49.81  | | End of split
% 243.21/49.81  | | 
% 243.21/49.81  | End of split
% 243.21/49.81  | 
% 243.21/49.81  End of proof
% 243.21/49.81  
% 243.21/49.81  Sub-proof #1141 shows that the following formulas are inconsistent:
% 243.21/49.81  ----------------------------------------------------------------
% 243.21/49.81    (1)  op(e0, e1) = all_52_11
% 243.21/49.81    (2)  op(e1, e1) = e1
% 243.21/49.81    (3)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.21/49.81    (4)   ~ (all_52_11 = e0)
% 243.21/49.81    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.81    (6)   ~ (e1 = e0)
% 243.21/49.81  
% 243.21/49.81  Begin of proof
% 243.21/49.81  | 
% 243.21/49.81  | BETA: splitting (3) gives:
% 243.21/49.81  | 
% 243.21/49.81  | Case 1:
% 243.21/49.81  | | 
% 243.21/49.81  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 243.21/49.81  | | 
% 243.21/49.81  | | ALPHA: (7) implies:
% 243.21/49.81  | |   (8)  op(e1, e1) = e0
% 243.21/49.81  | | 
% 243.21/49.81  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2220.
% 243.21/49.81  | | 
% 243.21/49.81  | Case 2:
% 243.21/49.81  | | 
% 243.21/49.81  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 243.21/49.81  | | 
% 243.21/49.81  | | ALPHA: (9) implies:
% 243.21/49.81  | |   (10)  op(e0, e1) = e0
% 243.21/49.81  | | 
% 243.21/49.81  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #1911.
% 243.21/49.81  | | 
% 243.21/49.81  | End of split
% 243.21/49.81  | 
% 243.21/49.81  End of proof
% 243.21/49.81  
% 243.21/49.81  Sub-proof #1142 shows that the following formulas are inconsistent:
% 243.21/49.81  ----------------------------------------------------------------
% 243.21/49.81    (1)   ~ (e3 = e0)
% 243.21/49.81    (2)  all_58_5 = e3
% 243.21/49.81    (3)  all_58_4 = e2
% 243.21/49.81    (4)   ~ (e3 = e1)
% 243.21/49.81    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.21/49.81         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.21/49.81    (6)  op(e3, e3) = e1
% 243.21/49.81    (7)   ~ (e3 = e2)
% 243.21/49.81    (8)  all_58_9 = e3
% 243.21/49.81    (9)   ~ (all_52_4 = e3)
% 243.21/49.81    (10)  op(e3, e2) = all_52_4
% 243.21/49.81    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.81    (12)  all_58_5 = e0 & op(e2, e1) = e0
% 243.21/49.81  
% 243.21/49.81  Begin of proof
% 243.21/49.81  | 
% 243.21/49.81  | ALPHA: (12) implies:
% 243.21/49.81  |   (13)  all_58_5 = e0
% 243.21/49.81  | 
% 243.21/49.81  | COMBINE_EQS: (2), (13) imply:
% 243.21/49.81  |   (14)  e3 = e0
% 243.21/49.81  | 
% 243.21/49.81  | COMBINE_EQS: (8), (14) imply:
% 243.21/49.81  |   (15)  all_58_9 = e0
% 243.21/49.81  | 
% 243.21/49.81  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (15) are
% 243.21/49.81  |            inconsistent by sub-proof #1143.
% 243.21/49.81  | 
% 243.21/49.81  End of proof
% 243.21/49.81  
% 243.21/49.81  Sub-proof #1143 shows that the following formulas are inconsistent:
% 243.21/49.81  ----------------------------------------------------------------
% 243.21/49.81    (1)   ~ (e3 = e0)
% 243.21/49.81    (2)  all_58_9 = e0
% 243.21/49.81    (3)  all_58_4 = e2
% 243.21/49.81    (4)   ~ (e3 = e1)
% 243.21/49.81    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.21/49.81         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.21/49.81    (6)  op(e3, e3) = e1
% 243.21/49.81    (7)   ~ (e3 = e2)
% 243.21/49.81    (8)   ~ (all_52_4 = e3)
% 243.21/49.81    (9)  op(e3, e2) = all_52_4
% 243.21/49.81    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.81  
% 243.21/49.81  Begin of proof
% 243.21/49.81  | 
% 243.21/49.81  | BETA: splitting (5) gives:
% 243.21/49.81  | 
% 243.21/49.81  | Case 1:
% 243.21/49.81  | | 
% 243.21/49.81  | |   (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 243.21/49.81  | |           e3)
% 243.21/49.81  | | 
% 243.21/49.81  | | REF_CLOSE: (4), (6), (8), (9), (10), (11) are inconsistent by sub-proof
% 243.21/49.81  | |            #1401.
% 243.21/49.81  | | 
% 243.21/49.81  | Case 2:
% 243.21/49.81  | | 
% 243.21/49.81  | |   (12)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 243.21/49.81  | |           e3)
% 243.21/49.81  | | 
% 243.21/49.81  | | BETA: splitting (12) gives:
% 243.21/49.81  | | 
% 243.21/49.81  | | Case 1:
% 243.21/49.81  | | | 
% 243.21/49.81  | | |   (13)  all_58_4 = e3 & op(e3, e1) = e3
% 243.21/49.81  | | | 
% 243.21/49.81  | | | ALPHA: (13) implies:
% 243.21/49.81  | | |   (14)  all_58_4 = e3
% 243.21/49.81  | | | 
% 243.21/49.81  | | | REF_CLOSE: (3), (7), (14) are inconsistent by sub-proof #1902.
% 243.21/49.81  | | | 
% 243.21/49.81  | | Case 2:
% 243.21/49.81  | | | 
% 243.21/49.81  | | |   (15)  all_58_9 = e3 & op(e3, e0) = e3
% 243.21/49.81  | | | 
% 243.21/49.81  | | | ALPHA: (15) implies:
% 243.21/49.81  | | |   (16)  all_58_9 = e3
% 243.21/49.81  | | | 
% 243.21/49.81  | | | REF_CLOSE: (1), (2), (16) are inconsistent by sub-proof #1958.
% 243.21/49.81  | | | 
% 243.21/49.81  | | End of split
% 243.21/49.81  | | 
% 243.21/49.81  | End of split
% 243.21/49.81  | 
% 243.21/49.81  End of proof
% 243.21/49.81  
% 243.21/49.81  Sub-proof #1144 shows that the following formulas are inconsistent:
% 243.21/49.81  ----------------------------------------------------------------
% 243.21/49.81    (1)  op(e0, e0) = e1
% 243.21/49.81    (2)   ~ (all_52_1 = all_52_3)
% 243.21/49.81    (3)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.21/49.81    (4)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.21/49.81             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.21/49.81           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.21/49.81         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.21/49.81           $i(all_56_7))
% 243.21/49.81    (5)   ~ (all_52_6 = e1)
% 243.21/49.81    (6)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.21/49.81    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.21/49.81         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.21/49.81    (8)   ~ (all_52_3 = e1)
% 243.21/49.81    (9)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.21/49.81         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.21/49.81    (10)   ~ (all_38_0 = e2)
% 243.21/49.81    (11)   ~ (e3 = e0)
% 243.21/49.81    (12)   ~ (all_52_7 = e2)
% 243.21/49.81    (13)  all_56_11 = e1
% 243.21/49.81    (14)  op(e0, e1) = all_52_11
% 243.21/49.81    (15)   ~ (e2 = e0)
% 243.21/49.81    (16)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.21/49.81            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.21/49.81            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 243.21/49.81            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 243.21/49.81            = all_56_15 & $i(all_56_15))
% 243.21/49.81    (17)  all_54_13 = all_52_7
% 243.21/49.81    (18)  all_58_5 = e3
% 243.21/49.81    (19)  op(e1, e2) = all_52_6
% 243.21/49.81    (20)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.21/49.81          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.21/49.81    (21)   ~ (all_52_11 = e1)
% 243.21/49.81    (22)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.21/49.81              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.21/49.81            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.21/49.81            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.21/49.81            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.21/49.81             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.21/49.81            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.21/49.81            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.21/49.81            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.21/49.81            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.21/49.81            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.21/49.81              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.21/49.81            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.21/49.81            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.21/49.81            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.21/49.81            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.21/49.81            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.21/49.81            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.21/49.81              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.21/49.81            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.21/49.81            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.21/49.81            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.21/49.81            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.21/49.81            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.21/49.81            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.21/49.81              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.21/49.81            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.21/49.81            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.21/49.81    (23)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.21/49.81          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.21/49.81    (24)   ~ (all_52_6 = e2)
% 243.21/49.81    (25)   ~ (all_52_7 = all_52_11)
% 243.21/49.81    (26)  op(all_38_1, e3) = all_38_0
% 243.21/49.81    (27)  op(e1, e1) = all_6_2
% 243.21/49.81    (28)  all_58_8 = e1
% 243.21/49.81    (29)  op(e1, e0) = all_52_14
% 243.21/49.81    (30)   ~ (all_52_13 = e1)
% 243.21/49.81    (31)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 243.21/49.81            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 243.21/49.81              e1) = all_20_1 & $i(all_20_1))
% 243.21/49.81    (32)  op(e0, e3) = all_52_3
% 243.21/49.81    (33)   ~ (e3 = e1)
% 243.21/49.81    (34)  all_54_11 = all_52_14
% 243.21/49.81    (35)  op(e3, e1) = e0
% 243.21/49.81    (36)   ~ (all_52_8 = e1)
% 243.21/49.81    (37)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.21/49.81    (38)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.21/49.81            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 243.21/49.81              e1) = all_10_1 & $i(all_10_1))
% 243.21/49.81    (39)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.21/49.81          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.21/49.81    (40)  all_58_3 = e1
% 243.21/49.81    (41)   ~ (all_52_2 = e1)
% 243.21/49.81    (42)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.21/49.81          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.21/49.81    (43)  op(e3, e3) = e1
% 243.21/49.81    (44)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.21/49.81    (45)   ~ (all_52_3 = all_52_7)
% 243.21/49.81    (46)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.21/49.81    (47)  all_54_4 = all_52_1
% 243.21/49.81    (48)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.21/49.81              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.21/49.81                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.21/49.81                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.21/49.81    (49)   ~ (all_52_11 = e3)
% 243.21/49.81    (50)   ~ (all_6_2 = e3)
% 243.21/49.81    (51)  op(e3, e1) = all_52_8
% 243.21/49.81    (52)  op(e2, e1) = all_52_9
% 243.21/49.81    (53)  all_54_9 = all_52_6
% 243.21/49.81    (54)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.21/49.81          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.21/49.81    (55)   ~ (e3 = e2)
% 243.21/49.81    (56)  op(e3, e1) = all_38_1
% 243.21/49.81    (57)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.21/49.81          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.21/49.81    (58)   ~ (all_52_14 = e1)
% 243.21/49.81    (59)   ~ (all_52_7 = e1)
% 243.21/49.81    (60)   ~ (all_52_3 = all_52_11)
% 243.21/49.81    (61)  op(e2, e2) = e1
% 243.21/49.81    (62)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 243.21/49.81            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 243.21/49.81            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 243.21/49.81            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 243.21/49.81            op(e0, all_56_31) = e0)
% 243.21/49.81    (63)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.21/49.81    (64)  all_56_31 = e1
% 243.21/49.81    (65)  all_54_12 = all_52_3
% 243.21/49.81    (66)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.21/49.81          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.21/49.81    (67)  all_58_15 = e1
% 243.21/49.81    (68)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.21/49.81          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.21/49.81    (69)  all_58_9 = e3
% 243.21/49.81    (70)   ~ (all_52_6 = all_52_14)
% 243.21/49.81    (71)  op(e3, e0) = e3
% 243.21/49.81    (72)  op(e2, e3) = all_52_1
% 243.21/49.81    (73)   ~ (all_52_14 = e3)
% 243.21/49.82    (74)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.21/49.82          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.21/49.82    (75)   ~ (all_52_11 = e0)
% 243.21/49.82    (76)  all_54_7 = all_52_13
% 243.21/49.82    (77)  op(e0, e2) = all_52_7
% 243.21/49.82    (78)   ~ (all_52_13 = all_52_14)
% 243.21/49.82    (79)   ~ (all_52_4 = e3)
% 243.21/49.82    (80)  op(e3, e2) = all_52_4
% 243.21/49.82    (81)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.21/49.82    (82)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.21/49.82          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.21/49.82    (83)  op(e2, e1) = e3
% 243.21/49.82    (84)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 243.21/49.82            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 243.21/49.82              e1) = all_34_1 & $i(all_34_1))
% 243.21/49.82    (85)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.21/49.82          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.21/49.82    (86)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.21/49.82          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.21/49.82    (87)   ~ (all_52_2 = all_52_6)
% 243.21/49.82    (88)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.21/49.82          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 243.21/49.82    (89)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.82    (90)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.21/49.82          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.21/49.82    (91)  op(e1, e3) = all_52_2
% 243.21/49.82    (92)   ~ (all_52_6 = all_52_7)
% 243.21/49.82    (93)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.21/49.82          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.21/49.82    (94)   ~ (all_52_4 = e1)
% 243.21/49.82    (95)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.21/49.82          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.21/49.82    (96)   ~ (e1 = e0)
% 243.21/49.82    (97)  op(e2, e0) = all_52_13
% 243.21/49.82    (98)   ~ (all_52_1 = e3)
% 243.21/49.82    (99)   ~ (all_52_9 = e1)
% 243.21/49.82    (100)  all_54_14 = all_52_11
% 243.21/49.82    (101)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.21/49.82           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.21/49.82             e2)
% 243.21/49.82    (102)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.21/49.82           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.21/49.82    (103)  all_56_1 = e1
% 243.21/49.82    (104)  all_58_4 = e0
% 243.21/49.82    (105)   ~ (e2 = e1)
% 243.21/49.82    (106)   ~ (all_52_1 = e1)
% 243.21/49.82    (107)   ~ (all_52_8 = e3)
% 243.21/49.82  
% 243.21/49.82  Begin of proof
% 243.21/49.82  | 
% 243.21/49.82  | BETA: splitting (57) gives:
% 243.21/49.82  | 
% 243.21/49.82  | Case 1:
% 243.21/49.82  | | 
% 243.21/49.82  | |   (108)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 243.21/49.82  | |            e2)
% 243.21/49.82  | | 
% 243.21/49.82  | | BETA: splitting (108) gives:
% 243.21/49.82  | | 
% 243.21/49.82  | | Case 1:
% 243.21/49.82  | | | 
% 243.21/49.82  | | |   (109)  all_58_4 = e2 & op(e3, e1) = e2
% 243.21/49.82  | | | 
% 243.21/49.82  | | | ALPHA: (109) implies:
% 243.21/49.82  | | |   (110)  all_58_4 = e2
% 243.21/49.82  | | | 
% 243.21/49.82  | | | REF_CLOSE: (15), (104), (110) are inconsistent by sub-proof #1666.
% 243.21/49.82  | | | 
% 243.21/49.82  | | Case 2:
% 243.21/49.82  | | | 
% 243.21/49.82  | | |   (111)  all_58_5 = e2 & op(e2, e1) = e2
% 243.21/49.82  | | | 
% 243.21/49.82  | | | ALPHA: (111) implies:
% 243.21/49.82  | | |   (112)  op(e2, e1) = e2
% 243.21/49.82  | | | 
% 243.21/49.82  | | | REF_CLOSE: (55), (83), (89), (112) are inconsistent by sub-proof #2256.
% 243.21/49.82  | | | 
% 243.21/49.82  | | End of split
% 243.21/49.82  | | 
% 243.21/49.82  | Case 2:
% 243.21/49.82  | | 
% 243.21/49.82  | |   (113)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 243.21/49.82  | |            e2)
% 243.21/49.82  | | 
% 243.21/49.82  | | BETA: splitting (113) gives:
% 243.21/49.82  | | 
% 243.21/49.82  | | Case 1:
% 243.21/49.82  | | | 
% 243.21/49.82  | | |   (114)  all_58_8 = e2 & op(e1, e1) = e2
% 243.21/49.82  | | | 
% 243.21/49.82  | | | ALPHA: (114) implies:
% 243.21/49.82  | | |   (115)  all_58_8 = e2
% 243.21/49.82  | | | 
% 243.21/49.82  | | | REF_CLOSE: (28), (105), (115) are inconsistent by sub-proof #1802.
% 243.21/49.82  | | | 
% 243.21/49.82  | | Case 2:
% 243.21/49.82  | | | 
% 243.21/49.82  | | |   (116)  all_58_14 = e2 & op(e0, e1) = e2
% 243.21/49.82  | | | 
% 243.21/49.82  | | | ALPHA: (116) implies:
% 243.21/49.82  | | |   (117)  all_58_14 = e2
% 243.21/49.82  | | | 
% 243.21/49.82  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 243.21/49.82  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 243.21/49.82  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 243.21/49.82  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 243.21/49.82  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 243.21/49.82  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 243.21/49.82  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 243.21/49.82  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 243.21/49.82  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 243.21/49.82  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 243.21/49.82  | | |            (103), (104), (105), (106), (107), (117) are inconsistent by
% 243.21/49.82  | | |            sub-proof #1145.
% 243.21/49.82  | | | 
% 243.21/49.82  | | End of split
% 243.21/49.82  | | 
% 243.21/49.82  | End of split
% 243.21/49.82  | 
% 243.21/49.82  End of proof
% 243.21/49.82  
% 243.21/49.82  Sub-proof #1145 shows that the following formulas are inconsistent:
% 243.21/49.82  ----------------------------------------------------------------
% 243.21/49.82    (1)  op(e0, e0) = e1
% 243.21/49.82    (2)   ~ (all_52_1 = all_52_3)
% 243.21/49.82    (3)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.21/49.82    (4)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.21/49.82             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.21/49.82           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.21/49.82         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.21/49.82           $i(all_56_7))
% 243.21/49.82    (5)   ~ (all_52_6 = e1)
% 243.21/49.82    (6)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.21/49.82    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.21/49.82         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.21/49.82    (8)   ~ (all_52_3 = e1)
% 243.21/49.82    (9)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.21/49.82         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.21/49.82    (10)   ~ (all_38_0 = e2)
% 243.21/49.82    (11)   ~ (e3 = e0)
% 243.21/49.82    (12)   ~ (all_52_7 = e2)
% 243.21/49.82    (13)  all_56_11 = e1
% 243.21/49.82    (14)  op(e0, e1) = all_52_11
% 243.21/49.82    (15)   ~ (e2 = e0)
% 243.21/49.82    (16)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.21/49.82            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.21/49.82            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 243.21/49.82            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 243.21/49.82            = all_56_15 & $i(all_56_15))
% 243.21/49.82    (17)  all_54_13 = all_52_7
% 243.21/49.82    (18)  all_58_5 = e3
% 243.21/49.82    (19)  op(e1, e2) = all_52_6
% 243.21/49.82    (20)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.21/49.82          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.21/49.82    (21)   ~ (all_52_11 = e1)
% 243.21/49.82    (22)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.21/49.82              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.21/49.82            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.21/49.82            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.21/49.82            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.21/49.82             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.21/49.82            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.21/49.82            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.21/49.82            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.21/49.82            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.21/49.82            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.21/49.82              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.21/49.82            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.21/49.82            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.21/49.82            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.21/49.82            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.21/49.82            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.21/49.82            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.21/49.82              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.21/49.82            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.21/49.82            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.21/49.82            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.21/49.82            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.21/49.82            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.21/49.82            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.21/49.82              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.21/49.82            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.21/49.82            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.21/49.82    (23)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.21/49.82          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.21/49.82    (24)   ~ (all_52_6 = e2)
% 243.21/49.82    (25)   ~ (all_52_7 = all_52_11)
% 243.21/49.82    (26)  op(all_38_1, e3) = all_38_0
% 243.21/49.82    (27)  op(e1, e1) = all_6_2
% 243.21/49.82    (28)  all_58_8 = e1
% 243.21/49.82    (29)  op(e1, e0) = all_52_14
% 243.21/49.82    (30)   ~ (all_52_13 = e1)
% 243.21/49.82    (31)  all_58_14 = e2
% 243.21/49.82    (32)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 243.21/49.82            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 243.21/49.82              e1) = all_20_1 & $i(all_20_1))
% 243.21/49.82    (33)  op(e0, e3) = all_52_3
% 243.21/49.82    (34)   ~ (e3 = e1)
% 243.21/49.82    (35)  all_54_11 = all_52_14
% 243.21/49.82    (36)  op(e3, e1) = e0
% 243.21/49.82    (37)   ~ (all_52_8 = e1)
% 243.21/49.82    (38)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.21/49.82    (39)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.21/49.82            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 243.21/49.82              e1) = all_10_1 & $i(all_10_1))
% 243.21/49.82    (40)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.21/49.82          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.21/49.82    (41)  all_58_3 = e1
% 243.21/49.82    (42)   ~ (all_52_2 = e1)
% 243.21/49.82    (43)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.21/49.82          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.21/49.82    (44)  op(e3, e3) = e1
% 243.21/49.82    (45)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.21/49.82    (46)   ~ (all_52_3 = all_52_7)
% 243.21/49.82    (47)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.21/49.82    (48)  all_54_4 = all_52_1
% 243.21/49.82    (49)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.21/49.82              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.21/49.82                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.21/49.82                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.21/49.82    (50)   ~ (all_52_11 = e3)
% 243.21/49.82    (51)   ~ (all_6_2 = e3)
% 243.21/49.82    (52)  op(e3, e1) = all_52_8
% 243.21/49.82    (53)  op(e2, e1) = all_52_9
% 243.21/49.82    (54)  all_54_9 = all_52_6
% 243.21/49.82    (55)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.21/49.82          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.21/49.82    (56)   ~ (e3 = e2)
% 243.21/49.82    (57)  op(e3, e1) = all_38_1
% 243.21/49.82    (58)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.21/49.82          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.21/49.82    (59)   ~ (all_52_14 = e1)
% 243.21/49.82    (60)   ~ (all_52_7 = e1)
% 243.21/49.82    (61)   ~ (all_52_3 = all_52_11)
% 243.21/49.82    (62)  op(e2, e2) = e1
% 243.21/49.82    (63)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 243.21/49.82            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 243.21/49.82            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 243.21/49.82            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 243.21/49.82            op(e0, all_56_31) = e0)
% 243.21/49.82    (64)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.21/49.82    (65)  all_56_31 = e1
% 243.21/49.82    (66)  all_54_12 = all_52_3
% 243.21/49.82    (67)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.21/49.82          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.21/49.82    (68)  all_58_15 = e1
% 243.21/49.82    (69)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.21/49.82          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.21/49.82    (70)  all_58_9 = e3
% 243.21/49.82    (71)   ~ (all_52_6 = all_52_14)
% 243.21/49.82    (72)  op(e3, e0) = e3
% 243.21/49.82    (73)  op(e2, e3) = all_52_1
% 243.21/49.82    (74)   ~ (all_52_14 = e3)
% 243.21/49.82    (75)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.21/49.82          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.21/49.82    (76)   ~ (all_52_11 = e0)
% 243.21/49.82    (77)  all_54_7 = all_52_13
% 243.21/49.82    (78)  op(e0, e2) = all_52_7
% 243.21/49.82    (79)   ~ (all_52_13 = all_52_14)
% 243.21/49.82    (80)   ~ (all_52_4 = e3)
% 243.21/49.82    (81)  op(e3, e2) = all_52_4
% 243.21/49.82    (82)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.21/49.82    (83)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.21/49.82          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.21/49.82    (84)  op(e2, e1) = e3
% 243.21/49.82    (85)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 243.21/49.82            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 243.21/49.82              e1) = all_34_1 & $i(all_34_1))
% 243.21/49.82    (86)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.21/49.82          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.21/49.82    (87)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.21/49.82          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.21/49.82    (88)   ~ (all_52_2 = all_52_6)
% 243.21/49.83    (89)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.21/49.83          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 243.21/49.83    (90)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.21/49.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.21/49.83    (91)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.21/49.83          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.21/49.83    (92)  op(e1, e3) = all_52_2
% 243.21/49.83    (93)   ~ (all_52_6 = all_52_7)
% 243.21/49.83    (94)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.21/49.83          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.21/49.83    (95)   ~ (all_52_4 = e1)
% 243.21/49.83    (96)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.21/49.83          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.21/49.83    (97)   ~ (e1 = e0)
% 243.21/49.83    (98)  op(e2, e0) = all_52_13
% 243.21/49.83    (99)   ~ (all_52_1 = e3)
% 243.21/49.83    (100)   ~ (all_52_9 = e1)
% 243.21/49.83    (101)  all_54_14 = all_52_11
% 243.21/49.83    (102)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.21/49.83           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.21/49.83             e2)
% 243.21/49.83    (103)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.21/49.83           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.21/49.83    (104)  all_56_1 = e1
% 243.21/49.83    (105)  all_58_4 = e0
% 243.21/49.83    (106)   ~ (e2 = e1)
% 243.21/49.83    (107)   ~ (all_52_1 = e1)
% 243.21/49.83    (108)   ~ (all_52_8 = e3)
% 243.21/49.83  
% 243.21/49.83  Begin of proof
% 243.21/49.83  | 
% 243.21/49.83  | BETA: splitting (39) gives:
% 243.21/49.83  | 
% 243.21/49.83  | Case 1:
% 243.21/49.83  | | 
% 243.21/49.83  | |   (109)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.21/49.83  | |          all_10_1 & $i(all_10_0) & $i(all_10_1)
% 243.21/49.83  | | 
% 243.21/49.83  | | ALPHA: (109) implies:
% 243.21/49.83  | |   (110)   ~ (all_10_0 = e0)
% 243.21/49.83  | |   (111)  op(e3, e1) = all_10_1
% 243.21/49.83  | |   (112)  op(all_10_1, e3) = all_10_0
% 243.21/49.83  | | 
% 243.21/49.83  | | BETA: splitting (7) gives:
% 243.21/49.83  | | 
% 243.21/49.83  | | Case 1:
% 243.21/49.83  | | | 
% 243.21/49.83  | | |   (113)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 243.21/49.83  | | |            e2)
% 243.21/49.83  | | | 
% 243.21/49.83  | | | BETA: splitting (113) gives:
% 243.21/49.83  | | | 
% 243.21/49.83  | | | Case 1:
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | |   (114)  all_58_0 = e2 & op(e3, e3) = e2
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | ALPHA: (114) implies:
% 243.21/49.83  | | | |   (115)  op(e3, e3) = e2
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | REF_CLOSE: (44), (90), (106), (115) are inconsistent by sub-proof #2267.
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | Case 2:
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | |   (116)  all_58_1 = e2 & op(e3, e2) = e2
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | ALPHA: (116) implies:
% 243.21/49.83  | | | |   (117)  all_58_1 = e2
% 243.21/49.83  | | | |   (118)  op(e3, e2) = e2
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | GROUND_INST: instantiating (90) with all_10_1, all_38_1, e1, e3,
% 243.21/49.83  | | | |              simplifying with (57), (111) gives:
% 243.21/49.83  | | | |   (119)  all_38_1 = all_10_1
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | GROUND_INST: instantiating (90) with e0, all_38_1, e1, e3, simplifying
% 243.21/49.83  | | | |              with (36), (57) gives:
% 243.21/49.83  | | | |   (120)  all_38_1 = e0
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | COMBINE_EQS: (119), (120) imply:
% 243.21/49.83  | | | |   (121)  all_10_1 = e0
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | SIMP: (121) implies:
% 243.21/49.83  | | | |   (122)  all_10_1 = e0
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | REDUCE: (26), (120) imply:
% 243.21/49.83  | | | |   (123)  op(e0, e3) = all_38_0
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | REDUCE: (112), (122) imply:
% 243.21/49.83  | | | |   (124)  op(e0, e3) = all_10_0
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | GROUND_INST: instantiating (90) with all_52_3, all_10_0, e3, e0,
% 243.21/49.83  | | | |              simplifying with (33), (124) gives:
% 243.21/49.83  | | | |   (125)  all_52_3 = all_10_0
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | GROUND_INST: instantiating (90) with all_52_3, all_38_0, e3, e0,
% 243.21/49.83  | | | |              simplifying with (33), (123) gives:
% 243.21/49.83  | | | |   (126)  all_52_3 = all_38_0
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | COMBINE_EQS: (125), (126) imply:
% 243.21/49.83  | | | |   (127)  all_38_0 = all_10_0
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | SIMP: (127) implies:
% 243.21/49.83  | | | |   (128)  all_38_0 = all_10_0
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | COMBINE_EQS: (66), (125) imply:
% 243.21/49.83  | | | |   (129)  all_54_12 = all_10_0
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | REDUCE: (2), (125) imply:
% 243.21/49.83  | | | |   (130)   ~ (all_52_1 = all_10_0)
% 243.21/49.83  | | | | 
% 243.21/49.83  | | | | REDUCE: (46), (125) imply:
% 243.35/49.83  | | | |   (131)   ~ (all_52_7 = all_10_0)
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | | SIMP: (131) implies:
% 243.35/49.83  | | | |   (132)   ~ (all_52_7 = all_10_0)
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | | REDUCE: (8), (125) imply:
% 243.35/49.83  | | | |   (133)   ~ (all_10_0 = e1)
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | | REDUCE: (10), (128) imply:
% 243.35/49.83  | | | |   (134)   ~ (all_10_0 = e2)
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | | BETA: splitting (49) gives:
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | | Case 1:
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | |   (135)  all_58_15 = e0 & op(e0, e0) = e0
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | | ALPHA: (135) implies:
% 243.35/49.83  | | | | |   (136)  op(e0, e0) = e0
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | | REF_CLOSE: (1), (90), (97), (136) are inconsistent by sub-proof #2274.
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | Case 2:
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | |   (137)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 243.35/49.83  | | | | |                e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 243.35/49.83  | | | | |          ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.83  | | | | |              op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | | ALPHA: (137) implies:
% 243.35/49.83  | | | | |   (138)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 243.35/49.83  | | | | |              e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | | BETA: splitting (6) gives:
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | | Case 1:
% 243.35/49.83  | | | | | | 
% 243.35/49.83  | | | | | |   (139)  all_54_12 = e3
% 243.35/49.83  | | | | | | 
% 243.35/49.83  | | | | | | COMBINE_EQS: (129), (139) imply:
% 243.35/49.83  | | | | | |   (140)  all_10_0 = e3
% 243.35/49.83  | | | | | | 
% 243.35/49.83  | | | | | | SIMP: (140) implies:
% 243.35/49.83  | | | | | |   (141)  all_10_0 = e3
% 243.35/49.83  | | | | | | 
% 243.35/49.83  | | | | | | REDUCE: (132), (141) imply:
% 243.35/49.83  | | | | | |   (142)   ~ (all_52_7 = e3)
% 243.35/49.83  | | | | | | 
% 243.35/49.83  | | | | | | BETA: splitting (82) gives:
% 243.35/49.83  | | | | | | 
% 243.35/49.83  | | | | | | Case 1:
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | |   (143)  all_54_13 = e3
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | | REF_CLOSE: (17), (142), (143) are inconsistent by sub-proof #2010.
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | Case 2:
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | |   (144)   ~ (all_54_13 = e3)
% 243.35/49.83  | | | | | | |   (145)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | | BETA: splitting (145) gives:
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | | Case 1:
% 243.35/49.83  | | | | | | | | 
% 243.35/49.83  | | | | | | | |   (146)  all_54_13 = e2
% 243.35/49.83  | | | | | | | | 
% 243.35/49.83  | | | | | | | | REF_CLOSE: (12), (17), (146) are inconsistent by sub-proof
% 243.35/49.83  | | | | | | | |            #2009.
% 243.35/49.83  | | | | | | | | 
% 243.35/49.83  | | | | | | | Case 2:
% 243.35/49.83  | | | | | | | | 
% 243.35/49.83  | | | | | | | |   (147)  all_54_13 = e1 | all_54_13 = e0
% 243.35/49.83  | | | | | | | | 
% 243.35/49.83  | | | | | | | | BETA: splitting (96) gives:
% 243.35/49.83  | | | | | | | | 
% 243.35/49.83  | | | | | | | | Case 1:
% 243.35/49.83  | | | | | | | | | 
% 243.35/49.83  | | | | | | | | |   (148)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 &
% 243.35/49.83  | | | | | | | | |            op(e2, e2) = e3)
% 243.35/49.83  | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | BETA: splitting (148) gives:
% 243.35/49.83  | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | Case 1:
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | |   (149)  all_58_1 = e3 & op(e3, e2) = e3
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | ALPHA: (149) implies:
% 243.35/49.83  | | | | | | | | | |   (150)  op(e3, e2) = e3
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | REF_CLOSE: (80), (81), (90), (150) are inconsistent by
% 243.35/49.83  | | | | | | | | | |            sub-proof #2192.
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | Case 2:
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | |   (151)  all_58_3 = e3 & op(e2, e2) = e3
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | ALPHA: (151) implies:
% 243.35/49.83  | | | | | | | | | |   (152)  all_58_3 = e3
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | COMBINE_EQS: (41), (152) imply:
% 243.35/49.83  | | | | | | | | | |   (153)  e3 = e1
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | COMBINE_EQS: (70), (153) imply:
% 243.35/49.83  | | | | | | | | | |   (154)  all_58_9 = e1
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | BETA: splitting (103) gives:
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | Case 1:
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | |   (155)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 243.35/49.83  | | | | | | | | | | |            & op(e2, e2) = e1)
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | BETA: splitting (155) gives:
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | Case 1:
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | |   (156)  all_58_2 = e1 & op(e2, e3) = e1
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | REF_CLOSE: (73), (90), (107), (156) are inconsistent by
% 243.35/49.83  | | | | | | | | | | | |            sub-proof #2229.
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | Case 2:
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | |   (157)  all_58_3 = e1 & op(e2, e2) = e1
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | REF_CLOSE: (34), (152), (157) are inconsistent by sub-proof
% 243.35/49.83  | | | | | | | | | | | |            #2197.
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | End of split
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | Case 2:
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | |   (158)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 243.35/49.83  | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | BETA: splitting (158) gives:
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | Case 1:
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | |   (159)  all_58_5 = e1 & op(e2, e1) = e1
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | ALPHA: (159) implies:
% 243.35/49.83  | | | | | | | | | | | |   (160)  op(e2, e1) = e1
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | REF_CLOSE: (53), (90), (100), (160) are inconsistent by
% 243.35/49.83  | | | | | | | | | | | |            sub-proof #2306.
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | Case 2:
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | |   (161)  all_58_10 = e1 & op(e2, e0) = e1
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | ALPHA: (161) implies:
% 243.35/49.83  | | | | | | | | | | | |   (162)  all_58_10 = e1
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | REF_CLOSE: (7), (11), (15), (34), (40), (44), (56), (75),
% 243.35/49.83  | | | | | | | | | | | |            (80), (81), (86), (90), (91), (97), (106), (138),
% 243.35/49.83  | | | | | | | | | | | |            (154), (162) are inconsistent by sub-proof #1168.
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | End of split
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | End of split
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | End of split
% 243.35/49.83  | | | | | | | | | 
% 243.35/49.83  | | | | | | | | Case 2:
% 243.35/49.83  | | | | | | | | | 
% 243.35/49.83  | | | | | | | | |   (163)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 &
% 243.35/49.83  | | | | | | | | |            op(e0, e2) = e3)
% 243.35/49.83  | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | BETA: splitting (163) gives:
% 243.35/49.83  | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | Case 1:
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | |   (164)  all_58_7 = e3 & op(e1, e2) = e3
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | ALPHA: (164) implies:
% 243.35/49.83  | | | | | | | | | |   (165)  all_58_7 = e3
% 243.35/49.83  | | | | | | | | | |   (166)  op(e1, e2) = e3
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | BETA: splitting (16) gives:
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | Case 1:
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | |   (167)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 243.35/49.83  | | | | | | | | | | |              e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 243.35/49.83  | | | | | | | | | | |            e2 & op(e2, all_56_11) = e2)
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | BETA: splitting (167) gives:
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | Case 1:
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | |   (168)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2)
% 243.35/49.83  | | | | | | | | | | | |          = all_56_9 & $i(all_56_9)
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | ALPHA: (168) implies:
% 243.35/49.83  | | | | | | | | | | | |   (169)  op(e3, e2) = all_56_9
% 243.35/49.83  | | | | | | | | | | | |   (170)  op(e3, all_56_9) = e3
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | REF_CLOSE: (1), (9), (11), (15), (18), (20), (23), (28),
% 243.35/49.83  | | | | | | | | | | | |            (31), (34), (40), (43), (44), (49), (55), (56),
% 243.35/49.83  | | | | | | | | | | | |            (58), (67), (68), (70), (73), (78), (80), (81),
% 243.35/49.83  | | | | | | | | | | | |            (90), (94), (95), (96), (97), (99), (102), (105),
% 243.35/49.83  | | | | | | | | | | | |            (106), (117), (118), (142), (165), (169), (170)
% 243.35/49.83  | | | | | | | | | | | |            are inconsistent by sub-proof #1158.
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | Case 2:
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | |   (171)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | ALPHA: (171) implies:
% 243.35/49.83  | | | | | | | | | | | |   (172)  op(e2, all_56_11) = e2
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | REDUCE: (13), (172) imply:
% 243.35/49.83  | | | | | | | | | | | |   (173)  op(e2, e1) = e2
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | REF_CLOSE: (56), (84), (90), (173) are inconsistent by
% 243.35/49.83  | | | | | | | | | | | |            sub-proof #2256.
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | End of split
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | Case 2:
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | |   (174)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 243.35/49.83  | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 243.35/49.83  | | | | | | | | | | |            = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 243.35/49.83  | | | | | | | | | | |            all_56_15 & $i(all_56_15))
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | BETA: splitting (174) gives:
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | Case 1:
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | |   (175)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 243.35/49.83  | | | | | | | | | | | |            e2) = all_56_13 & $i(all_56_13)
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | ALPHA: (175) implies:
% 243.35/49.83  | | | | | | | | | | | |   (176)  op(e1, e2) = all_56_13
% 243.35/49.83  | | | | | | | | | | | |   (177)  op(e1, all_56_13) = e1
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | GROUND_INST: instantiating (90) with e3, all_56_13, e2, e1,
% 243.35/49.83  | | | | | | | | | | | |              simplifying with (166), (176) gives:
% 243.35/49.83  | | | | | | | | | | | |   (178)  all_56_13 = e3
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | REDUCE: (177), (178) imply:
% 243.35/49.83  | | | | | | | | | | | |   (179)  op(e1, e3) = e1
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | REF_CLOSE: (42), (90), (92), (179) are inconsistent by
% 243.35/49.83  | | | | | | | | | | | |            sub-proof #1948.
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | Case 2:
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | |   (180)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 243.35/49.83  | | | | | | | | | | | |            e2) = all_56_15 & $i(all_56_15)
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | ALPHA: (180) implies:
% 243.35/49.83  | | | | | | | | | | | |   (181)  op(e0, e2) = all_56_15
% 243.35/49.83  | | | | | | | | | | | |   (182)  op(e0, all_56_15) = e0
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | | REF_CLOSE: (1), (17), (60), (78), (90), (147), (181), (182)
% 243.35/49.83  | | | | | | | | | | | |            are inconsistent by sub-proof #1933.
% 243.35/49.83  | | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | | End of split
% 243.35/49.83  | | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | End of split
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | Case 2:
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | |   (183)  all_58_13 = e3 & op(e0, e2) = e3
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | | REF_CLOSE: (78), (90), (142), (183) are inconsistent by
% 243.35/49.83  | | | | | | | | | |            sub-proof #1919.
% 243.35/49.83  | | | | | | | | | | 
% 243.35/49.83  | | | | | | | | | End of split
% 243.35/49.83  | | | | | | | | | 
% 243.35/49.83  | | | | | | | | End of split
% 243.35/49.83  | | | | | | | | 
% 243.35/49.83  | | | | | | | End of split
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | End of split
% 243.35/49.83  | | | | | | 
% 243.35/49.83  | | | | | Case 2:
% 243.35/49.83  | | | | | | 
% 243.35/49.83  | | | | | |   (184)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.35/49.83  | | | | | | 
% 243.35/49.83  | | | | | | BETA: splitting (184) gives:
% 243.35/49.83  | | | | | | 
% 243.35/49.83  | | | | | | Case 1:
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | |   (185)  all_54_12 = e2
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | | COMBINE_EQS: (129), (185) imply:
% 243.35/49.83  | | | | | | |   (186)  all_10_0 = e2
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | | SIMP: (186) implies:
% 243.35/49.83  | | | | | | |   (187)  all_10_0 = e2
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | | REDUCE: (134), (187) imply:
% 243.35/49.83  | | | | | | |   (188)  $false
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | | CLOSE: (188) is inconsistent.
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | Case 2:
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | |   (189)  all_54_12 = e1 | all_54_12 = e0
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | | REF_CLOSE: (110), (129), (133), (189) are inconsistent by
% 243.35/49.83  | | | | | | |            sub-proof #1157.
% 243.35/49.83  | | | | | | | 
% 243.35/49.83  | | | | | | End of split
% 243.35/49.83  | | | | | | 
% 243.35/49.83  | | | | | End of split
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | End of split
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | End of split
% 243.35/49.83  | | | 
% 243.35/49.83  | | Case 2:
% 243.35/49.83  | | | 
% 243.35/49.83  | | |   (190)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 243.35/49.83  | | |            e2)
% 243.35/49.83  | | | 
% 243.35/49.83  | | | REF_CLOSE: (11), (15), (18), (28), (31), (34), (40), (44), (56), (58),
% 243.35/49.83  | | |            (80), (81), (90), (105), (106), (190) are inconsistent by
% 243.35/49.83  | | |            sub-proof #1155.
% 243.35/49.83  | | | 
% 243.35/49.83  | | End of split
% 243.35/49.83  | | 
% 243.35/49.83  | Case 2:
% 243.35/49.83  | | 
% 243.35/49.83  | |   (191)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 & $i(all_10_1)
% 243.35/49.83  | | 
% 243.35/49.83  | | ALPHA: (191) implies:
% 243.35/49.83  | |   (192)   ~ (all_10_1 = e2)
% 243.35/49.83  | |   (193)  op(e3, e1) = all_10_1
% 243.35/49.83  | | 
% 243.35/49.83  | | BETA: splitting (7) gives:
% 243.35/49.83  | | 
% 243.35/49.83  | | Case 1:
% 243.35/49.83  | | | 
% 243.35/49.83  | | |   (194)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 243.35/49.83  | | |            e2)
% 243.35/49.83  | | | 
% 243.35/49.83  | | | BETA: splitting (194) gives:
% 243.35/49.83  | | | 
% 243.35/49.83  | | | Case 1:
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | |   (195)  all_58_0 = e2 & op(e3, e3) = e2
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | | ALPHA: (195) implies:
% 243.35/49.83  | | | |   (196)  op(e3, e3) = e2
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | | REF_CLOSE: (44), (90), (106), (196) are inconsistent by sub-proof #2267.
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | Case 2:
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | |   (197)  all_58_1 = e2 & op(e3, e2) = e2
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | | ALPHA: (197) implies:
% 243.35/49.83  | | | |   (198)  all_58_1 = e2
% 243.35/49.83  | | | |   (199)  op(e3, e2) = e2
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | | BETA: splitting (45) gives:
% 243.35/49.83  | | | | 
% 243.35/49.83  | | | | Case 1:
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | |   (200)  all_54_14 = e2
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | | COMBINE_EQS: (101), (200) imply:
% 243.35/49.83  | | | | |   (201)  all_52_11 = e2
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | | SIMP: (201) implies:
% 243.35/49.83  | | | | |   (202)  all_52_11 = e2
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | | REDUCE: (61), (202) imply:
% 243.35/49.83  | | | | |   (203)   ~ (all_52_3 = e2)
% 243.35/49.83  | | | | | 
% 243.35/49.83  | | | | | REDUCE: (50), (202) imply:
% 243.35/49.84  | | | | |   (204)   ~ (e3 = e2)
% 243.35/49.84  | | | | | 
% 243.35/49.84  | | | | | REDUCE: (14), (202) imply:
% 243.35/49.84  | | | | |   (205)  op(e0, e1) = e2
% 243.35/49.84  | | | | | 
% 243.35/49.84  | | | | | BETA: splitting (85) gives:
% 243.35/49.84  | | | | | 
% 243.35/49.84  | | | | | Case 1:
% 243.35/49.84  | | | | | | 
% 243.35/49.84  | | | | | |   (206)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0,
% 243.35/49.84  | | | | | |            e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)
% 243.35/49.84  | | | | | | 
% 243.35/49.84  | | | | | | ALPHA: (206) implies:
% 243.35/49.84  | | | | | |   (207)  op(e0, e1) = all_34_1
% 243.35/49.84  | | | | | |   (208)  op(all_34_1, e0) = all_34_0
% 243.35/49.84  | | | | | | 
% 243.35/49.84  | | | | | | BETA: splitting (32) gives:
% 243.35/49.84  | | | | | | 
% 243.35/49.84  | | | | | | Case 1:
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | |   (209)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0,
% 243.35/49.84  | | | | | | |            e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | ALPHA: (209) implies:
% 243.35/49.84  | | | | | | |   (210)   ~ (all_20_0 = e2)
% 243.35/49.84  | | | | | | |   (211)  op(e0, e1) = all_20_1
% 243.35/49.84  | | | | | | |   (212)  op(all_20_1, e0) = all_20_0
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | GROUND_INST: instantiating (90) with all_20_1, all_34_1, e1, e0,
% 243.35/49.84  | | | | | | |              simplifying with (207), (211) gives:
% 243.35/49.84  | | | | | | |   (213)  all_34_1 = all_20_1
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | GROUND_INST: instantiating (90) with e2, all_34_1, e1, e0,
% 243.35/49.84  | | | | | | |              simplifying with (205), (207) gives:
% 243.35/49.84  | | | | | | |   (214)  all_34_1 = e2
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | COMBINE_EQS: (213), (214) imply:
% 243.35/49.84  | | | | | | |   (215)  all_20_1 = e2
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | SIMP: (215) implies:
% 243.35/49.84  | | | | | | |   (216)  all_20_1 = e2
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | REDUCE: (208), (214) imply:
% 243.35/49.84  | | | | | | |   (217)  op(e2, e0) = all_34_0
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | REDUCE: (212), (216) imply:
% 243.35/49.84  | | | | | | |   (218)  op(e2, e0) = all_20_0
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | GROUND_INST: instantiating (90) with all_52_13, all_20_0, e0, e2,
% 243.35/49.84  | | | | | | |              simplifying with (98), (218) gives:
% 243.35/49.84  | | | | | | |   (219)  all_52_13 = all_20_0
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | GROUND_INST: instantiating (90) with all_52_13, all_34_0, e0, e2,
% 243.35/49.84  | | | | | | |              simplifying with (98), (217) gives:
% 243.35/49.84  | | | | | | |   (220)  all_52_13 = all_34_0
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | COMBINE_EQS: (219), (220) imply:
% 243.35/49.84  | | | | | | |   (221)  all_34_0 = all_20_0
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | COMBINE_EQS: (77), (219) imply:
% 243.35/49.84  | | | | | | |   (222)  all_54_7 = all_20_0
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | REDUCE: (79), (219) imply:
% 243.35/49.84  | | | | | | |   (223)   ~ (all_52_14 = all_20_0)
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | SIMP: (223) implies:
% 243.35/49.84  | | | | | | |   (224)   ~ (all_52_14 = all_20_0)
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | REDUCE: (30), (219) imply:
% 243.35/49.84  | | | | | | |   (225)   ~ (all_20_0 = e1)
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | BETA: splitting (91) gives:
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | Case 1:
% 243.35/49.84  | | | | | | | | 
% 243.35/49.84  | | | | | | | |   (226)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 243.35/49.84  | | | | | | | |            op(e2, e0) = e2)
% 243.35/49.84  | | | | | | | | 
% 243.35/49.84  | | | | | | | | BETA: splitting (226) gives:
% 243.35/49.84  | | | | | | | | 
% 243.35/49.84  | | | | | | | | Case 1:
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | |   (227)  all_58_9 = e2 & op(e3, e0) = e2
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | ALPHA: (227) implies:
% 243.35/49.84  | | | | | | | | |   (228)  op(e3, e0) = e2
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | REF_CLOSE: (11), (34), (40), (44), (56), (80), (81), (90),
% 243.35/49.84  | | | | | | | | |            (105), (228) are inconsistent by sub-proof #1400.
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | Case 2:
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | |   (229)  all_58_10 = e2 & op(e2, e0) = e2
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | ALPHA: (229) implies:
% 243.35/49.84  | | | | | | | | |   (230)  op(e2, e0) = e2
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | BETA: splitting (47) gives:
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | Case 1:
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | |   (231)  all_54_7 = e2
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | COMBINE_EQS: (222), (231) imply:
% 243.35/49.84  | | | | | | | | | |   (232)  all_20_0 = e2
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | REDUCE: (210), (232) imply:
% 243.35/49.84  | | | | | | | | | |   (233)  $false
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | CLOSE: (233) is inconsistent.
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | Case 2:
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | |   (234)   ~ (all_54_7 = e2)
% 243.35/49.84  | | | | | | | | | |   (235)  all_54_7 = e1 | all_54_7 = e0
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | BETA: splitting (235) gives:
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | Case 1:
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | |   (236)  all_54_7 = e1
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | COMBINE_EQS: (222), (236) imply:
% 243.35/49.84  | | | | | | | | | | |   (237)  all_20_0 = e1
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | REDUCE: (225), (237) imply:
% 243.35/49.84  | | | | | | | | | | |   (238)  $false
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | CLOSE: (238) is inconsistent.
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | Case 2:
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | |   (239)  all_54_7 = e0
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | COMBINE_EQS: (222), (239) imply:
% 243.35/49.84  | | | | | | | | | | |   (240)  all_20_0 = e0
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | REDUCE: (210), (240) imply:
% 243.35/49.84  | | | | | | | | | | |   (241)   ~ (e2 = e0)
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | REDUCE: (218), (240) imply:
% 243.35/49.84  | | | | | | | | | | |   (242)  op(e2, e0) = e0
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | REF_CLOSE: (15), (90), (230), (242) are inconsistent by
% 243.35/49.84  | | | | | | | | | | |            sub-proof #2121.
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | End of split
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | End of split
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | End of split
% 243.35/49.84  | | | | | | | | 
% 243.35/49.84  | | | | | | | Case 2:
% 243.35/49.84  | | | | | | | | 
% 243.35/49.84  | | | | | | | |   (243)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 243.35/49.84  | | | | | | | |            op(e0, e0) = e2)
% 243.35/49.84  | | | | | | | | 
% 243.35/49.84  | | | | | | | | BETA: splitting (243) gives:
% 243.35/49.84  | | | | | | | | 
% 243.35/49.84  | | | | | | | | Case 1:
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | |   (244)  all_58_11 = e2 & op(e1, e0) = e2
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | ALPHA: (244) implies:
% 243.35/49.84  | | | | | | | | |   (245)  op(e1, e0) = e2
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | BETA: splitting (47) gives:
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | Case 1:
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | |   (246)  all_54_7 = e2
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | COMBINE_EQS: (222), (246) imply:
% 243.35/49.84  | | | | | | | | | |   (247)  all_20_0 = e2
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | REDUCE: (210), (247) imply:
% 243.35/49.84  | | | | | | | | | |   (248)  $false
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | CLOSE: (248) is inconsistent.
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | Case 2:
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | |   (249)  all_54_7 = e1 | all_54_7 = e0
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | BETA: splitting (249) gives:
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | Case 1:
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | |   (250)  all_54_7 = e1
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | COMBINE_EQS: (222), (250) imply:
% 243.35/49.84  | | | | | | | | | | |   (251)  all_20_0 = e1
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | REDUCE: (225), (251) imply:
% 243.35/49.84  | | | | | | | | | | |   (252)  $false
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | CLOSE: (252) is inconsistent.
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | Case 2:
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | |   (253)  all_54_7 = e0
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | COMBINE_EQS: (222), (253) imply:
% 243.35/49.84  | | | | | | | | | | |   (254)  all_20_0 = e0
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | REDUCE: (224), (254) imply:
% 243.35/49.84  | | | | | | | | | | |   (255)   ~ (all_52_14 = e0)
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | REDUCE: (218), (254) imply:
% 243.35/49.84  | | | | | | | | | | |   (256)  op(e2, e0) = e0
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | BETA: splitting (63) gives:
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | Case 1:
% 243.35/49.84  | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | |   (257)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 243.35/49.84  | | | | | | | | | | | |              e0) = all_56_25 & $i(all_56_25)) | (all_56_26
% 243.35/49.84  | | | | | | | | | | | |            = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 243.35/49.84  | | | | | | | | | | | |            all_56_27 & $i(all_56_27))
% 243.35/49.84  | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | BETA: splitting (257) gives:
% 243.35/49.84  | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | Case 1:
% 243.35/49.84  | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | |   (258)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3,
% 243.35/49.84  | | | | | | | | | | | | |            e0) = all_56_25 & $i(all_56_25)
% 243.35/49.84  | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | ALPHA: (258) implies:
% 243.35/49.84  | | | | | | | | | | | | |   (259)  op(e3, e0) = all_56_25
% 243.35/49.84  | | | | | | | | | | | | |   (260)  op(e3, all_56_25) = e3
% 243.35/49.84  | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | BETA: splitting (38) gives:
% 243.35/49.84  | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | Case 1:
% 243.35/49.84  | | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | | GROUND_INST: instantiating (90) with e3, all_56_25, e0, e3,
% 243.35/49.84  | | | | | | | | | | | | | |              simplifying with (72), (259) gives:
% 243.35/49.84  | | | | | | | | | | | | | |   (261)  all_56_25 = e3
% 243.35/49.84  | | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | | REDUCE: (260), (261) imply:
% 243.35/49.84  | | | | | | | | | | | | | |   (262)  op(e3, e3) = e3
% 243.35/49.84  | | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | | REF_CLOSE: (34), (44), (90), (262) are inconsistent by
% 243.35/49.84  | | | | | | | | | | | | | |            sub-proof #1578.
% 243.35/49.84  | | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | Case 2:
% 243.35/49.84  | | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | |   (263)  all_54_11 = e1 | all_54_11 = e0
% 243.35/49.84  | | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | | REF_CLOSE: (35), (59), (255), (263) are inconsistent by
% 243.35/49.84  | | | | | | | | | | | | | |            sub-proof #2174.
% 243.35/49.84  | | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | End of split
% 243.35/49.84  | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | Case 2:
% 243.35/49.84  | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | |   (264)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 243.35/49.84  | | | | | | | | | | | | |            e0) = all_56_27 & $i(all_56_27)
% 243.35/49.84  | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | ALPHA: (264) implies:
% 243.35/49.84  | | | | | | | | | | | | |   (265)  op(e2, e0) = all_56_27
% 243.35/49.84  | | | | | | | | | | | | |   (266)  op(e2, all_56_27) = e2
% 243.35/49.84  | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | | REF_CLOSE: (35), (38), (59), (90), (255), (256), (265), (266)
% 243.35/49.84  | | | | | | | | | | | | |            are inconsistent by sub-proof #1912.
% 243.35/49.84  | | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | End of split
% 243.35/49.84  | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | Case 2:
% 243.35/49.84  | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | |   (267)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1,
% 243.35/49.84  | | | | | | | | | | | |              e0) = all_56_29 & $i(all_56_29)) | (all_56_30
% 243.35/49.84  | | | | | | | | | | | |            = e0 & op(e0, all_56_31) = e0)
% 243.35/49.84  | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | | REF_CLOSE: (5), (14), (19), (65), (76), (90), (245), (267)
% 243.35/49.84  | | | | | | | | | | | |            are inconsistent by sub-proof #1910.
% 243.35/49.84  | | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | | End of split
% 243.35/49.84  | | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | | End of split
% 243.35/49.84  | | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | End of split
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | Case 2:
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | |   (268)  all_58_15 = e2 & op(e0, e0) = e2
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | ALPHA: (268) implies:
% 243.35/49.84  | | | | | | | | |   (269)  all_58_15 = e2
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | | REF_CLOSE: (68), (106), (269) are inconsistent by sub-proof
% 243.35/49.84  | | | | | | | | |            #2231.
% 243.35/49.84  | | | | | | | | | 
% 243.35/49.84  | | | | | | | | End of split
% 243.35/49.84  | | | | | | | | 
% 243.35/49.84  | | | | | | | End of split
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | Case 2:
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | |   (270)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 & $i(all_20_1)
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | ALPHA: (270) implies:
% 243.35/49.84  | | | | | | |   (271)   ~ (all_20_1 = e3)
% 243.35/49.84  | | | | | | |   (272)  op(e0, e1) = all_20_1
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 243.35/49.84  | | | | | | |            (12), (13), (16), (17), (18), (19), (20), (22), (23),
% 243.35/49.84  | | | | | | |            (24), (26), (27), (28), (29), (31), (33), (34), (36),
% 243.35/49.84  | | | | | | |            (37), (40), (41), (42), (43), (44), (46), (48), (49),
% 243.35/49.84  | | | | | | |            (51), (52), (53), (54), (55), (57), (58), (59), (60),
% 243.35/49.84  | | | | | | |            (62), (64), (65), (66), (67), (68), (69), (70), (71),
% 243.35/49.84  | | | | | | |            (72), (73), (74), (75), (78), (80), (81), (82), (83),
% 243.35/49.84  | | | | | | |            (84), (87), (88), (89), (90), (92), (93), (94), (95),
% 243.35/49.84  | | | | | | |            (96), (97), (99), (100), (102), (104), (105), (106),
% 243.35/49.84  | | | | | | |            (107), (108), (192), (193), (198), (199), (203), (205),
% 243.35/49.84  | | | | | | |            (207), (271), (272) are inconsistent by sub-proof
% 243.35/49.84  | | | | | | |            #1146.
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | End of split
% 243.35/49.84  | | | | | | 
% 243.35/49.84  | | | | | Case 2:
% 243.35/49.84  | | | | | | 
% 243.35/49.84  | | | | | |   (273)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 243.35/49.84  | | | | | | 
% 243.35/49.84  | | | | | | ALPHA: (273) implies:
% 243.35/49.84  | | | | | |   (274)   ~ (all_34_1 = e2)
% 243.35/49.84  | | | | | |   (275)  op(e0, e1) = all_34_1
% 243.35/49.84  | | | | | | 
% 243.35/49.84  | | | | | | BETA: splitting (32) gives:
% 243.35/49.84  | | | | | | 
% 243.35/49.84  | | | | | | Case 1:
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | |   (276)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0,
% 243.35/49.84  | | | | | | |            e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | ALPHA: (276) implies:
% 243.35/49.84  | | | | | | |   (277)  op(e0, e1) = all_20_1
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | REF_CLOSE: (90), (205), (274), (275), (277) are inconsistent by
% 243.35/49.84  | | | | | | |            sub-proof #2237.
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | Case 2:
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | |   (278)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 & $i(all_20_1)
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | ALPHA: (278) implies:
% 243.35/49.84  | | | | | | |   (279)   ~ (all_20_1 = e3)
% 243.35/49.84  | | | | | | |   (280)  op(e0, e1) = all_20_1
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 243.35/49.84  | | | | | | |            (12), (13), (16), (17), (18), (19), (20), (22), (23),
% 243.35/49.84  | | | | | | |            (24), (26), (27), (28), (29), (31), (33), (34), (36),
% 243.35/49.84  | | | | | | |            (37), (40), (41), (42), (43), (44), (46), (48), (49),
% 243.35/49.84  | | | | | | |            (51), (52), (53), (54), (55), (57), (58), (59), (60),
% 243.35/49.84  | | | | | | |            (62), (64), (65), (66), (67), (68), (69), (70), (71),
% 243.35/49.84  | | | | | | |            (72), (73), (74), (75), (78), (80), (81), (82), (83),
% 243.35/49.84  | | | | | | |            (84), (87), (88), (89), (90), (92), (93), (94), (95),
% 243.35/49.84  | | | | | | |            (96), (97), (99), (100), (102), (104), (105), (106),
% 243.35/49.84  | | | | | | |            (107), (108), (192), (193), (198), (199), (203), (205),
% 243.35/49.84  | | | | | | |            (275), (279), (280) are inconsistent by sub-proof
% 243.35/49.84  | | | | | | |            #1146.
% 243.35/49.84  | | | | | | | 
% 243.35/49.84  | | | | | | End of split
% 243.35/49.84  | | | | | | 
% 243.35/49.84  | | | | | End of split
% 243.35/49.84  | | | | | 
% 243.35/49.84  | | | | Case 2:
% 243.35/49.84  | | | | | 
% 243.35/49.84  | | | | |   (281)  all_54_14 = e1 | all_54_14 = e0
% 243.35/49.84  | | | | | 
% 243.35/49.84  | | | | | REF_CLOSE: (21), (76), (101), (281) are inconsistent by sub-proof
% 243.35/49.84  | | | | |            #1935.
% 243.35/49.84  | | | | | 
% 243.35/49.84  | | | | End of split
% 243.35/49.84  | | | | 
% 243.35/49.84  | | | End of split
% 243.35/49.84  | | | 
% 243.35/49.84  | | Case 2:
% 243.35/49.84  | | | 
% 243.35/49.84  | | |   (282)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 243.35/49.84  | | |            e2)
% 243.35/49.84  | | | 
% 243.35/49.84  | | | REF_CLOSE: (11), (15), (18), (28), (31), (34), (40), (44), (56), (58),
% 243.35/49.84  | | |            (80), (81), (90), (105), (106), (282) are inconsistent by
% 243.35/49.84  | | |            sub-proof #1155.
% 243.35/49.84  | | | 
% 243.35/49.84  | | End of split
% 243.35/49.84  | | 
% 243.35/49.84  | End of split
% 243.35/49.84  | 
% 243.35/49.84  End of proof
% 243.35/49.84  
% 243.35/49.84  Sub-proof #1146 shows that the following formulas are inconsistent:
% 243.35/49.84  ----------------------------------------------------------------
% 243.35/49.84    (1)  op(e0, e0) = e1
% 243.35/49.84    (2)   ~ (all_52_1 = all_52_3)
% 243.35/49.84    (3)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.35/49.84    (4)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.35/49.84             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.35/49.84           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.35/49.84         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.35/49.84           $i(all_56_7))
% 243.35/49.84    (5)   ~ (all_52_6 = e1)
% 243.35/49.84    (6)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.35/49.84    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.35/49.84         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.35/49.84    (8)   ~ (all_52_3 = e1)
% 243.35/49.84    (9)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.35/49.84         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.35/49.84    (10)   ~ (e3 = e0)
% 243.35/49.84    (11)   ~ (all_52_7 = e2)
% 243.35/49.84    (12)  all_56_11 = e1
% 243.35/49.84    (13)  op(e0, e1) = e2
% 243.35/49.84    (14)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.35/49.84            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.35/49.84            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 243.35/49.84            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 243.35/49.84            = all_56_15 & $i(all_56_15))
% 243.35/49.84    (15)  all_54_13 = all_52_7
% 243.35/49.84    (16)  all_58_5 = e3
% 243.35/49.84    (17)  op(e1, e2) = all_52_6
% 243.35/49.84    (18)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.35/49.84          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.35/49.85    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.35/49.85              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.35/49.85            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.35/49.85            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.35/49.85            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.35/49.85             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.35/49.85            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.35/49.85            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.35/49.85            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.35/49.85            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.35/49.85            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.35/49.85              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.35/49.85            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.35/49.85            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.35/49.85            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.35/49.85            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.35/49.85            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.35/49.85            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.35/49.85              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.35/49.85            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.35/49.85            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.35/49.85            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.35/49.85            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.35/49.85            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.35/49.85            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.35/49.85              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.35/49.85            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.35/49.85            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.35/49.85    (20)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.35/49.85          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.35/49.85    (21)   ~ (all_52_6 = e2)
% 243.35/49.85    (22)  op(all_38_1, e3) = all_38_0
% 243.35/49.85    (23)  op(e1, e1) = all_6_2
% 243.35/49.85    (24)  op(e0, e1) = all_34_1
% 243.35/49.85    (25)  all_58_8 = e1
% 243.35/49.85    (26)  op(e1, e0) = all_52_14
% 243.35/49.85    (27)  all_58_14 = e2
% 243.35/49.85    (28)  op(e0, e3) = all_52_3
% 243.35/49.85    (29)   ~ (e3 = e1)
% 243.35/49.85    (30)  op(e3, e1) = e0
% 243.35/49.85    (31)   ~ (all_52_8 = e1)
% 243.35/49.85    (32)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.35/49.85          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.35/49.85    (33)  all_58_3 = e1
% 243.35/49.85    (34)   ~ (all_52_2 = e1)
% 243.35/49.85    (35)  op(e3, e2) = e2
% 243.35/49.85    (36)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.35/49.85          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.35/49.85    (37)  op(e3, e3) = e1
% 243.35/49.85    (38)   ~ (all_10_1 = e2)
% 243.35/49.85    (39)   ~ (all_52_3 = all_52_7)
% 243.35/49.85    (40)  all_54_4 = all_52_1
% 243.35/49.85    (41)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.85              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.35/49.85                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.85                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.35/49.85    (42)   ~ (all_6_2 = e3)
% 243.35/49.85    (43)  op(e3, e1) = all_52_8
% 243.35/49.85    (44)  op(e2, e1) = all_52_9
% 243.35/49.85    (45)  all_54_9 = all_52_6
% 243.35/49.85    (46)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.35/49.85          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.85    (47)  op(e3, e1) = all_38_1
% 243.35/49.85    (48)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.35/49.85          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.35/49.85    (49)   ~ (all_52_14 = e1)
% 243.35/49.85    (50)   ~ (all_52_7 = e1)
% 243.35/49.85    (51)  op(e2, e2) = e1
% 243.35/49.85    (52)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.35/49.85    (53)  all_56_31 = e1
% 243.35/49.85    (54)  all_54_12 = all_52_3
% 243.35/49.85    (55)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.85          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.85    (56)  all_58_15 = e1
% 243.35/49.85    (57)   ~ (all_52_3 = e2)
% 243.35/49.85    (58)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.35/49.85          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.35/49.85    (59)  all_58_9 = e3
% 243.35/49.85    (60)   ~ (all_52_6 = all_52_14)
% 243.35/49.85    (61)  op(e3, e0) = e3
% 243.35/49.85    (62)  op(e2, e3) = all_52_1
% 243.35/49.85    (63)   ~ (all_52_14 = e3)
% 243.35/49.85    (64)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.35/49.85          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.85    (65)  op(e0, e2) = all_52_7
% 243.35/49.85    (66)  op(e0, e1) = all_20_1
% 243.35/49.85    (67)   ~ (all_52_4 = e3)
% 243.35/49.85    (68)  op(e3, e2) = all_52_4
% 243.35/49.85    (69)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.35/49.85    (70)  all_58_1 = e2
% 243.35/49.85    (71)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.35/49.85          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.35/49.85    (72)  op(e2, e1) = e3
% 243.35/49.85    (73)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.35/49.85          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.35/49.85    (74)   ~ (all_52_2 = all_52_6)
% 243.35/49.85    (75)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.35/49.85          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 243.35/49.85    (76)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.85    (77)  op(e3, e1) = all_10_1
% 243.35/49.85    (78)  op(e1, e3) = all_52_2
% 243.35/49.85    (79)   ~ (all_52_6 = all_52_7)
% 243.35/49.85    (80)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.35/49.85          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.35/49.85    (81)   ~ (all_52_4 = e1)
% 243.35/49.85    (82)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.35/49.85          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.35/49.85    (83)   ~ (e1 = e0)
% 243.35/49.85    (84)   ~ (all_20_1 = e3)
% 243.35/49.85    (85)   ~ (all_52_1 = e3)
% 243.35/49.85    (86)   ~ (all_52_9 = e1)
% 243.35/49.85    (87)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.35/49.85          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.35/49.85            e2)
% 243.35/49.85    (88)  all_56_1 = e1
% 243.35/49.85    (89)  all_58_4 = e0
% 243.35/49.85    (90)   ~ (e2 = e1)
% 243.35/49.85    (91)   ~ (all_52_1 = e1)
% 243.35/49.85    (92)   ~ (all_52_8 = e3)
% 243.35/49.85  
% 243.35/49.85  Begin of proof
% 243.35/49.85  | 
% 243.35/49.85  | GROUND_INST: instantiating (76) with all_20_1, all_34_1, e1, e0, simplifying
% 243.35/49.85  |              with (24), (66) gives:
% 243.35/49.85  |   (93)  all_34_1 = all_20_1
% 243.35/49.85  | 
% 243.35/49.85  | GROUND_INST: instantiating (76) with e2, all_34_1, e1, e0, simplifying with
% 243.35/49.85  |              (13), (24) gives:
% 243.35/49.85  |   (94)  all_34_1 = e2
% 243.35/49.85  | 
% 243.35/49.85  | GROUND_INST: instantiating (76) with all_10_1, all_38_1, e1, e3, simplifying
% 243.35/49.85  |              with (47), (77) gives:
% 243.35/49.85  |   (95)  all_38_1 = all_10_1
% 243.35/49.85  | 
% 243.35/49.85  | GROUND_INST: instantiating (76) with e0, all_38_1, e1, e3, simplifying with
% 243.35/49.85  |              (30), (47) gives:
% 243.35/49.85  |   (96)  all_38_1 = e0
% 243.35/49.85  | 
% 243.35/49.85  | COMBINE_EQS: (95), (96) imply:
% 243.35/49.85  |   (97)  all_10_1 = e0
% 243.35/49.85  | 
% 243.35/49.85  | SIMP: (97) implies:
% 243.35/49.85  |   (98)  all_10_1 = e0
% 243.35/49.85  | 
% 243.35/49.85  | COMBINE_EQS: (93), (94) imply:
% 243.35/49.85  |   (99)  all_20_1 = e2
% 243.35/49.85  | 
% 243.35/49.85  | SIMP: (99) implies:
% 243.35/49.85  |   (100)  all_20_1 = e2
% 243.35/49.85  | 
% 243.35/49.85  | REDUCE: (84), (100) imply:
% 243.35/49.85  |   (101)   ~ (e3 = e2)
% 243.35/49.85  | 
% 243.35/49.85  | SIMP: (101) implies:
% 243.35/49.85  |   (102)   ~ (e3 = e2)
% 243.35/49.85  | 
% 243.35/49.85  | REDUCE: (38), (98) imply:
% 243.35/49.85  |   (103)   ~ (e2 = e0)
% 243.35/49.85  | 
% 243.35/49.85  | SIMP: (103) implies:
% 243.35/49.85  |   (104)   ~ (e2 = e0)
% 243.35/49.85  | 
% 243.35/49.85  | REDUCE: (22), (96) imply:
% 243.35/49.85  |   (105)  op(e0, e3) = all_38_0
% 243.35/49.85  | 
% 243.35/49.85  | GROUND_INST: instantiating (76) with all_52_3, all_38_0, e3, e0, simplifying
% 243.35/49.85  |              with (28), (105) gives:
% 243.35/49.85  |   (106)  all_52_3 = all_38_0
% 243.35/49.85  | 
% 243.35/49.85  | COMBINE_EQS: (54), (106) imply:
% 243.35/49.85  |   (107)  all_54_12 = all_38_0
% 243.35/49.85  | 
% 243.35/49.85  | REDUCE: (2), (106) imply:
% 243.35/49.85  |   (108)   ~ (all_52_1 = all_38_0)
% 243.35/49.85  | 
% 243.35/49.85  | REDUCE: (39), (106) imply:
% 243.35/49.85  |   (109)   ~ (all_52_7 = all_38_0)
% 243.35/49.85  | 
% 243.35/49.85  | SIMP: (109) implies:
% 243.35/49.85  |   (110)   ~ (all_52_7 = all_38_0)
% 243.35/49.85  | 
% 243.35/49.85  | REDUCE: (57), (106) imply:
% 243.35/49.85  |   (111)   ~ (all_38_0 = e2)
% 243.35/49.85  | 
% 243.35/49.85  | REDUCE: (8), (106) imply:
% 243.35/49.85  |   (112)   ~ (all_38_0 = e1)
% 243.35/49.85  | 
% 243.35/49.85  | BETA: splitting (52) gives:
% 243.35/49.85  | 
% 243.35/49.85  | Case 1:
% 243.35/49.85  | | 
% 243.35/49.85  | |   (113)  all_54_9 = e3
% 243.35/49.85  | | 
% 243.35/49.85  | | COMBINE_EQS: (45), (113) imply:
% 243.35/49.85  | |   (114)  all_52_6 = e3
% 243.35/49.85  | | 
% 243.35/49.85  | | REDUCE: (79), (114) imply:
% 243.35/49.85  | |   (115)   ~ (all_52_7 = e3)
% 243.35/49.85  | | 
% 243.35/49.85  | | SIMP: (115) implies:
% 243.35/49.85  | |   (116)   ~ (all_52_7 = e3)
% 243.35/49.85  | | 
% 243.35/49.85  | | REDUCE: (60), (114) imply:
% 243.35/49.85  | |   (117)   ~ (all_52_14 = e3)
% 243.35/49.85  | | 
% 243.35/49.85  | | REDUCE: (17), (114) imply:
% 243.35/49.85  | |   (118)  op(e1, e2) = e3
% 243.35/49.85  | | 
% 243.35/49.85  | | BETA: splitting (69) gives:
% 243.35/49.85  | | 
% 243.35/49.85  | | Case 1:
% 243.35/49.85  | | | 
% 243.35/49.85  | | |   (119)  all_54_13 = e3
% 243.35/49.85  | | | 
% 243.35/49.85  | | | REF_CLOSE: (15), (116), (119) are inconsistent by sub-proof #2010.
% 243.35/49.85  | | | 
% 243.35/49.85  | | Case 2:
% 243.35/49.85  | | | 
% 243.35/49.85  | | |   (120)   ~ (all_54_13 = e3)
% 243.35/49.85  | | |   (121)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.35/49.85  | | | 
% 243.35/49.85  | | | BETA: splitting (14) gives:
% 243.35/49.85  | | | 
% 243.35/49.85  | | | Case 1:
% 243.35/49.85  | | | | 
% 243.35/49.85  | | | |   (122)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9
% 243.35/49.85  | | | |            & $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 243.35/49.85  | | | | 
% 243.35/49.85  | | | | BETA: splitting (122) gives:
% 243.35/49.85  | | | | 
% 243.35/49.85  | | | | Case 1:
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | |   (123)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9
% 243.35/49.85  | | | | |          & $i(all_56_9)
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | | ALPHA: (123) implies:
% 243.35/49.85  | | | | |   (124)  op(e3, e2) = all_56_9
% 243.35/49.85  | | | | |   (125)  op(e3, all_56_9) = e3
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | | BETA: splitting (58) gives:
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | | Case 1:
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | |   (126)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 243.35/49.85  | | | | | |              e2) = e3)
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | | BETA: splitting (126) gives:
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | | Case 1:
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | |   (127)  all_58_6 = e3 & op(e1, e3) = e3
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | | ALPHA: (127) implies:
% 243.35/49.85  | | | | | | |   (128)  all_58_6 = e3
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | | REF_CLOSE: (9), (10), (27), (29), (36), (37), (41), (46), (55),
% 243.35/49.85  | | | | | | |            (56), (62), (65), (76), (83), (85), (87), (90), (102),
% 243.35/49.85  | | | | | | |            (104), (116), (128) are inconsistent by sub-proof
% 243.35/49.85  | | | | | | |            #1159.
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | Case 2:
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | |   (129)  all_58_7 = e3 & op(e1, e2) = e3
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | | ALPHA: (129) implies:
% 243.35/49.85  | | | | | | |   (130)  all_58_7 = e3
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | | REF_CLOSE: (1), (9), (10), (16), (18), (20), (25), (27), (29),
% 243.35/49.85  | | | | | | |            (32), (35), (36), (37), (41), (46), (48), (55), (56),
% 243.35/49.85  | | | | | | |            (59), (62), (65), (67), (68), (70), (76), (80), (81),
% 243.35/49.85  | | | | | | |            (82), (83), (85), (87), (89), (90), (102), (104),
% 243.35/49.85  | | | | | | |            (116), (124), (125), (130) are inconsistent by
% 243.35/49.85  | | | | | | |            sub-proof #1158.
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | End of split
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | Case 2:
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | |   (131)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 &
% 243.35/49.85  | | | | | |            op(e1, e0) = e3)
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | | REF_CLOSE: (23), (26), (42), (63), (76), (131) are inconsistent by
% 243.35/49.85  | | | | | |            sub-proof #1529.
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | End of split
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | Case 2:
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | |   (132)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | | ALPHA: (132) implies:
% 243.35/49.85  | | | | |   (133)  op(e2, all_56_11) = e2
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | | REDUCE: (12), (133) imply:
% 243.35/49.85  | | | | |   (134)  op(e2, e1) = e2
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | | REF_CLOSE: (72), (76), (102), (134) are inconsistent by sub-proof
% 243.35/49.85  | | | | |            #2256.
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | End of split
% 243.35/49.85  | | | | 
% 243.35/49.85  | | | Case 2:
% 243.35/49.85  | | | | 
% 243.35/49.85  | | | |   (135)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 243.35/49.85  | | | |            all_56_13 & $i(all_56_13)) | (all_56_14 = e0 & op(e0,
% 243.35/49.85  | | | |              all_56_15) = e0 & op(e0, e2) = all_56_15 & $i(all_56_15))
% 243.35/49.85  | | | | 
% 243.35/49.85  | | | | BETA: splitting (135) gives:
% 243.35/49.85  | | | | 
% 243.35/49.85  | | | | Case 1:
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | |   (136)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) =
% 243.35/49.85  | | | | |          all_56_13 & $i(all_56_13)
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | | ALPHA: (136) implies:
% 243.35/49.85  | | | | |   (137)  op(e1, e2) = all_56_13
% 243.35/49.85  | | | | |   (138)  op(e1, all_56_13) = e1
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | | BETA: splitting (121) gives:
% 243.35/49.85  | | | | | 
% 243.35/49.85  | | | | | Case 1:
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | |   (139)  all_54_13 = e2
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | | REF_CLOSE: (11), (15), (139) are inconsistent by sub-proof #2009.
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | Case 2:
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | |   (140)  all_54_13 = e1 | all_54_13 = e0
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | | BETA: splitting (140) gives:
% 243.35/49.85  | | | | | | 
% 243.35/49.85  | | | | | | Case 1:
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | |   (141)  all_54_13 = e1
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | | REF_CLOSE: (15), (50), (141) are inconsistent by sub-proof #1966.
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | Case 2:
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | |   (142)  all_54_13 = e0
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | | COMBINE_EQS: (15), (142) imply:
% 243.35/49.85  | | | | | | |   (143)  all_52_7 = e0
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | | SIMP: (143) implies:
% 243.35/49.85  | | | | | | |   (144)  all_52_7 = e0
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | | REDUCE: (110), (144) imply:
% 243.35/49.85  | | | | | | |   (145)   ~ (all_38_0 = e0)
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | | SIMP: (145) implies:
% 243.35/49.85  | | | | | | |   (146)   ~ (all_38_0 = e0)
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | | BETA: splitting (6) gives:
% 243.35/49.85  | | | | | | | 
% 243.35/49.85  | | | | | | | Case 1:
% 243.35/49.85  | | | | | | | | 
% 243.35/49.85  | | | | | | | | 
% 243.35/49.85  | | | | | | | | GROUND_INST: instantiating (76) with e3, all_56_13, e2, e1,
% 243.35/49.85  | | | | | | | |              simplifying with (118), (137) gives:
% 243.35/49.85  | | | | | | | |   (147)  all_56_13 = e3
% 243.35/49.85  | | | | | | | | 
% 243.35/49.85  | | | | | | | | REDUCE: (138), (147) imply:
% 243.35/49.85  | | | | | | | |   (148)  op(e1, e3) = e1
% 243.35/49.85  | | | | | | | | 
% 243.35/49.85  | | | | | | | | REF_CLOSE: (34), (76), (78), (148) are inconsistent by sub-proof
% 243.35/49.85  | | | | | | | |            #1948.
% 243.35/49.85  | | | | | | | | 
% 243.35/49.85  | | | | | | | Case 2:
% 243.35/49.85  | | | | | | | | 
% 243.35/49.85  | | | | | | | |   (149)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.35/49.85  | | | | | | | | 
% 243.35/49.85  | | | | | | | | BETA: splitting (149) gives:
% 243.35/49.85  | | | | | | | | 
% 243.35/49.85  | | | | | | | | Case 1:
% 243.35/49.85  | | | | | | | | | 
% 243.35/49.85  | | | | | | | | |   (150)  all_54_12 = e2
% 243.35/49.85  | | | | | | | | | 
% 243.35/49.85  | | | | | | | | | REF_CLOSE: (107), (111), (150) are inconsistent by sub-proof
% 243.35/49.85  | | | | | | | | |            #1197.
% 243.35/49.85  | | | | | | | | | 
% 243.35/49.85  | | | | | | | | Case 2:
% 243.35/49.85  | | | | | | | | | 
% 243.35/49.85  | | | | | | | | |   (151)  all_54_12 = e1 | all_54_12 = e0
% 243.35/49.85  | | | | | | | | | 
% 243.35/49.85  | | | | | | | | | BETA: splitting (151) gives:
% 243.35/49.85  | | | | | | | | | 
% 243.35/49.85  | | | | | | | | | Case 1:
% 243.35/49.85  | | | | | | | | | | 
% 243.35/49.85  | | | | | | | | | |   (152)  all_54_12 = e1
% 243.35/49.85  | | | | | | | | | | 
% 243.35/49.85  | | | | | | | | | | REF_CLOSE: (107), (112), (152) are inconsistent by sub-proof
% 243.35/49.85  | | | | | | | | | |            #1154.
% 243.35/49.85  | | | | | | | | | | 
% 243.35/49.85  | | | | | | | | | Case 2:
% 243.35/49.85  | | | | | | | | | | 
% 243.35/49.85  | | | | | | | | | |   (153)  all_54_12 = e0
% 243.35/49.85  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | COMBINE_EQS: (107), (153) imply:
% 243.35/49.86  | | | | | | | | | |   (154)  all_38_0 = e0
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | SIMP: (154) implies:
% 243.35/49.86  | | | | | | | | | |   (155)  all_38_0 = e0
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | REDUCE: (146), (155) imply:
% 243.35/49.86  | | | | | | | | | |   (156)  $false
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | CLOSE: (156) is inconsistent.
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | End of split
% 243.35/49.86  | | | | | | | | | 
% 243.35/49.86  | | | | | | | | End of split
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | End of split
% 243.35/49.86  | | | | | | | 
% 243.35/49.86  | | | | | | End of split
% 243.35/49.86  | | | | | | 
% 243.35/49.86  | | | | | End of split
% 243.35/49.86  | | | | | 
% 243.35/49.86  | | | | Case 2:
% 243.35/49.86  | | | | | 
% 243.35/49.86  | | | | |   (157)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 243.35/49.86  | | | | |          all_56_15 & $i(all_56_15)
% 243.35/49.86  | | | | | 
% 243.35/49.86  | | | | | REF_CLOSE: (1), (11), (15), (50), (65), (76), (121), (157) are
% 243.35/49.86  | | | | |            inconsistent by sub-proof #1932.
% 243.35/49.86  | | | | | 
% 243.35/49.86  | | | | End of split
% 243.35/49.86  | | | | 
% 243.35/49.86  | | | End of split
% 243.35/49.86  | | | 
% 243.35/49.86  | | End of split
% 243.35/49.86  | | 
% 243.35/49.86  | Case 2:
% 243.35/49.86  | | 
% 243.35/49.86  | |   (158)   ~ (all_54_9 = e3)
% 243.35/49.86  | |   (159)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.35/49.86  | | 
% 243.35/49.86  | | REDUCE: (45), (158) imply:
% 243.35/49.86  | |   (160)   ~ (all_52_6 = e3)
% 243.35/49.86  | | 
% 243.35/49.86  | | BETA: splitting (58) gives:
% 243.35/49.86  | | 
% 243.35/49.86  | | Case 1:
% 243.35/49.86  | | | 
% 243.35/49.86  | | |   (161)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 243.35/49.86  | | |            e3)
% 243.35/49.86  | | | 
% 243.35/49.86  | | | BETA: splitting (161) gives:
% 243.35/49.86  | | | 
% 243.35/49.86  | | | Case 1:
% 243.35/49.86  | | | | 
% 243.35/49.86  | | | |   (162)  all_58_6 = e3 & op(e1, e3) = e3
% 243.35/49.86  | | | | 
% 243.35/49.86  | | | | ALPHA: (162) implies:
% 243.35/49.86  | | | |   (163)  all_58_6 = e3
% 243.35/49.86  | | | |   (164)  op(e1, e3) = e3
% 243.35/49.86  | | | | 
% 243.35/49.86  | | | | BETA: splitting (46) gives:
% 243.35/49.86  | | | | 
% 243.35/49.86  | | | | Case 1:
% 243.35/49.86  | | | | | 
% 243.35/49.86  | | | | |   (165)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2,
% 243.35/49.86  | | | | |              e3) = e2)
% 243.35/49.86  | | | | | 
% 243.35/49.86  | | | | | BETA: splitting (165) gives:
% 243.35/49.86  | | | | | 
% 243.35/49.86  | | | | | Case 1:
% 243.35/49.86  | | | | | | 
% 243.35/49.86  | | | | | |   (166)  all_58_0 = e2 & op(e3, e3) = e2
% 243.35/49.86  | | | | | | 
% 243.35/49.86  | | | | | | ALPHA: (166) implies:
% 243.35/49.86  | | | | | |   (167)  op(e3, e3) = e2
% 243.35/49.86  | | | | | | 
% 243.35/49.86  | | | | | | REF_CLOSE: (37), (76), (90), (167) are inconsistent by sub-proof
% 243.35/49.86  | | | | | |            #2267.
% 243.35/49.86  | | | | | | 
% 243.35/49.86  | | | | | Case 2:
% 243.35/49.86  | | | | | | 
% 243.35/49.86  | | | | | |   (168)  all_58_2 = e2 & op(e2, e3) = e2
% 243.35/49.86  | | | | | | 
% 243.35/49.86  | | | | | | ALPHA: (168) implies:
% 243.35/49.86  | | | | | |   (169)  all_58_2 = e2
% 243.35/49.86  | | | | | | 
% 243.35/49.86  | | | | | | BETA: splitting (75) gives:
% 243.35/49.86  | | | | | | 
% 243.35/49.86  | | | | | | Case 1:
% 243.35/49.86  | | | | | | | 
% 243.35/49.86  | | | | | | |   (170)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 243.35/49.86  | | | | | | |            op(e2, e2) = e0)
% 243.35/49.86  | | | | | | | 
% 243.35/49.86  | | | | | | | BETA: splitting (170) gives:
% 243.35/49.86  | | | | | | | 
% 243.35/49.86  | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | |   (171)  all_58_2 = e0 & op(e2, e3) = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | ALPHA: (171) implies:
% 243.35/49.86  | | | | | | | |   (172)  all_58_2 = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | COMBINE_EQS: (169), (172) imply:
% 243.35/49.86  | | | | | | | |   (173)  e2 = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | SIMP: (173) implies:
% 243.35/49.86  | | | | | | | |   (174)  e2 = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | COMBINE_EQS: (27), (174) imply:
% 243.35/49.86  | | | | | | | |   (175)  all_58_14 = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | REF_CLOSE: (16), (25), (48), (89), (90), (102), (104), (175) are
% 243.35/49.86  | | | | | | | |            inconsistent by sub-proof #1265.
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | |   (176)  all_58_3 = e0 & op(e2, e2) = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | REF_CLOSE: (33), (83), (176) are inconsistent by sub-proof
% 243.35/49.86  | | | | | | | |            #1180.
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | End of split
% 243.35/49.86  | | | | | | | 
% 243.35/49.86  | | | | | | Case 2:
% 243.35/49.86  | | | | | | | 
% 243.35/49.86  | | | | | | |   (177)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 243.35/49.86  | | | | | | |            op(e2, e0) = e0)
% 243.35/49.86  | | | | | | | 
% 243.35/49.86  | | | | | | | BETA: splitting (177) gives:
% 243.35/49.86  | | | | | | | 
% 243.35/49.86  | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | |   (178)  all_58_5 = e0 & op(e2, e1) = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | ALPHA: (178) implies:
% 243.35/49.86  | | | | | | | |   (179)  all_58_5 = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | COMBINE_EQS: (16), (179) imply:
% 243.35/49.86  | | | | | | | |   (180)  e3 = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | COMBINE_EQS: (59), (180) imply:
% 243.35/49.86  | | | | | | | |   (181)  all_58_9 = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | REF_CLOSE: (10), (29), (32), (37), (70), (76), (89), (102),
% 243.35/49.86  | | | | | | | |            (181) are inconsistent by sub-proof #1191.
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | |   (182)  all_58_10 = e0 & op(e2, e0) = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | ALPHA: (182) implies:
% 243.35/49.86  | | | | | | | |   (183)  op(e2, e0) = e0
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | BETA: splitting (159) gives:
% 243.35/49.86  | | | | | | | | 
% 243.35/49.86  | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | 
% 243.35/49.86  | | | | | | | | |   (184)  all_54_9 = e2
% 243.35/49.86  | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | REF_CLOSE: (21), (45), (184) are inconsistent by sub-proof
% 243.35/49.86  | | | | | | | | |            #1954.
% 243.35/49.86  | | | | | | | | | 
% 243.35/49.86  | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | 
% 243.35/49.86  | | | | | | | | |   (185)  all_54_9 = e1 | all_54_9 = e0
% 243.35/49.86  | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | BETA: splitting (185) gives:
% 243.35/49.86  | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | |   (186)  all_54_9 = e1
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | COMBINE_EQS: (45), (186) imply:
% 243.35/49.86  | | | | | | | | | |   (187)  all_52_6 = e1
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | REDUCE: (5), (187) imply:
% 243.35/49.86  | | | | | | | | | |   (188)  $false
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | CLOSE: (188) is inconsistent.
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | |   (189)  all_54_9 = e0
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | COMBINE_EQS: (45), (189) imply:
% 243.35/49.86  | | | | | | | | | |   (190)  all_52_6 = e0
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | REDUCE: (79), (190) imply:
% 243.35/49.86  | | | | | | | | | |   (191)   ~ (all_52_7 = e0)
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | SIMP: (191) implies:
% 243.35/49.86  | | | | | | | | | |   (192)   ~ (all_52_7 = e0)
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | REDUCE: (60), (190) imply:
% 243.35/49.86  | | | | | | | | | |   (193)   ~ (all_52_14 = e0)
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | SIMP: (193) implies:
% 243.35/49.86  | | | | | | | | | |   (194)   ~ (all_52_14 = e0)
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | BETA: splitting (69) gives:
% 243.35/49.86  | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | |   (195)  all_54_13 = e3
% 243.35/49.86  | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | COMBINE_EQS: (15), (195) imply:
% 243.35/49.86  | | | | | | | | | | |   (196)  all_52_7 = e3
% 243.35/49.86  | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | REDUCE: (110), (196) imply:
% 243.35/49.86  | | | | | | | | | | |   (197)   ~ (all_38_0 = e3)
% 243.35/49.86  | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | SIMP: (197) implies:
% 243.35/49.86  | | | | | | | | | | |   (198)   ~ (all_38_0 = e3)
% 243.35/49.86  | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | REDUCE: (65), (196) imply:
% 243.35/49.86  | | | | | | | | | | |   (199)  op(e0, e2) = e3
% 243.35/49.86  | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | BETA: splitting (6) gives:
% 243.35/49.86  | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | |   (200)  all_54_12 = e3
% 243.35/49.86  | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | COMBINE_EQS: (107), (200) imply:
% 243.35/49.86  | | | | | | | | | | | |   (201)  all_38_0 = e3
% 243.35/49.86  | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | SIMP: (201) implies:
% 243.35/49.86  | | | | | | | | | | | |   (202)  all_38_0 = e3
% 243.35/49.86  | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | REDUCE: (198), (202) imply:
% 243.35/49.86  | | | | | | | | | | | |   (203)  $false
% 243.35/49.86  | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | CLOSE: (203) is inconsistent.
% 243.35/49.86  | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | |   (204)   ~ (all_54_12 = e3)
% 243.35/49.86  | | | | | | | | | | | |   (205)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.35/49.86  | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | BETA: splitting (205) gives:
% 243.35/49.86  | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | |   (206)  all_54_12 = e2
% 243.35/49.86  | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | REF_CLOSE: (107), (111), (206) are inconsistent by sub-proof
% 243.35/49.86  | | | | | | | | | | | | |            #1197.
% 243.35/49.86  | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | |   (207)   ~ (all_54_12 = e2)
% 243.35/49.86  | | | | | | | | | | | | |   (208)  all_54_12 = e1 | all_54_12 = e0
% 243.35/49.86  | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | BETA: splitting (208) gives:
% 243.35/49.86  | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | |   (209)  all_54_12 = e1
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | REF_CLOSE: (107), (112), (209) are inconsistent by sub-proof
% 243.35/49.86  | | | | | | | | | | | | | |            #1154.
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | |   (210)  all_54_12 = e0
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | COMBINE_EQS: (107), (210) imply:
% 243.35/49.86  | | | | | | | | | | | | | |   (211)  all_38_0 = e0
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | SIMP: (211) implies:
% 243.35/49.86  | | | | | | | | | | | | | |   (212)  all_38_0 = e0
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | REDUCE: (108), (212) imply:
% 243.35/49.86  | | | | | | | | | | | | | |   (213)   ~ (all_52_1 = e0)
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | REDUCE: (198), (212) imply:
% 243.35/49.86  | | | | | | | | | | | | | |   (214)   ~ (e3 = e0)
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | REDUCE: (112), (212) imply:
% 243.35/49.86  | | | | | | | | | | | | | |   (215)   ~ (e1 = e0)
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | REDUCE: (105), (212) imply:
% 243.35/49.86  | | | | | | | | | | | | | |   (216)  op(e0, e3) = e0
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 243.35/49.86  | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | |   (217)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 243.35/49.86  | | | | | | | | | | | | | | |          (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 243.35/49.86  | | | | | | | | | | | | | | |              e3) = all_56_3 & $i(all_56_3))
% 243.35/49.86  | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 243.35/49.86  | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | |   (218)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 243.35/49.86  | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 243.35/49.86  | | | | | | | | | | | | | | | |   (219)  op(e3, all_56_1) = e3
% 243.35/49.86  | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | REDUCE: (88), (219) imply:
% 243.35/49.86  | | | | | | | | | | | | | | | |   (220)  op(e3, e1) = e3
% 243.35/49.86  | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | REF_CLOSE: (43), (76), (92), (220) are inconsistent by
% 243.35/49.86  | | | | | | | | | | | | | | | |            sub-proof #2260.
% 243.35/49.86  | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | |   (221)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 243.35/49.86  | | | | | | | | | | | | | | | |          = all_56_3 & $i(all_56_3)
% 243.35/49.86  | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 243.35/49.86  | | | | | | | | | | | | | | | |   (222)  op(e2, e3) = all_56_3
% 243.35/49.86  | | | | | | | | | | | | | | | |   (223)  op(e2, all_56_3) = e2
% 243.35/49.86  | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 243.35/49.86  | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | |   (224)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 243.35/49.86  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.35/49.86  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.35/49.86  | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.35/49.86  | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.35/49.86  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.35/49.86  | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 243.35/49.86  | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 243.35/49.86  | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.35/49.86  | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 243.35/49.86  | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 243.35/49.86  | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.35/49.86  | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 243.35/49.86  | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 243.35/49.86  | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | |   (225)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            = e3)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |   (226)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |          e3
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |   (227)  op(e2, e3) = e3
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (102), (222), (223), (227) are inconsistent
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            by sub-proof #2262.
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |   (228)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (229)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |          e2
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (230)  all_56_3 = e2
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | REDUCE: (223), (230) imply:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (231)  op(e2, e2) = e2
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (76), (90), (231) are inconsistent by
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |            sub-proof #2235.
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (232)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (233)  op(e3, e1) = e3
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (76), (92), (233) are inconsistent by
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |            sub-proof #2260.
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | End of split
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | End of split
% 243.35/49.86  | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | |   (234)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 243.35/49.86  | | | | | | | | | | | | | | | | | |            = e0)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |   (235)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            e3) = e1
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |   (236)  op(e3, e1) = e1
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (43), (76), (236) are inconsistent by
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            sub-proof #2309.
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |   (237)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.35/49.86  | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (238)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (239)  op(e0, e3) = e3
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (76) with e0, e3, e3, e0,
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |              simplifying with (216), (239) gives:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (240)  e3 = e0
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (240) imply:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (241)  all_58_9 = e0
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (29), (32), (37), (70), (76), (89), (102),
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |            (241) are inconsistent by sub-proof #1191.
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (242)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |            e3) = e0
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (243)   ~ (all_56_31 = e3)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (244)  op(e3, e0) = e0
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (243) imply:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (245)   ~ (e3 = e1)
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (76) with e3, e0, e0, e3,
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |              simplifying with (61), (244) gives:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (246)  e3 = e0
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (246) imply:
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |   (247)  all_58_9 = e0
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (29), (32), (37), (70), (76), (89), (102),
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | |            (247) are inconsistent by sub-proof #1191.
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | End of split
% 243.35/49.86  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | | End of split
% 243.35/49.86  | | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | | End of split
% 243.35/49.86  | | | | | | | | | | | | | | | | | 
% 243.35/49.86  | | | | | | | | | | | | | | | | Case 2:
% 243.35/49.86  | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | |   (248)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.35/49.87  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.35/49.87  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.35/49.87  | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.35/49.87  | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.35/49.87  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.35/49.87  | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 243.35/49.87  | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 243.35/49.87  | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.35/49.87  | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 243.35/49.87  | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 243.35/49.87  | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 243.35/49.87  | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 243.35/49.87  | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 243.35/49.87  | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | |   (249)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            = e2)
% 243.35/49.87  | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |   (250)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            e2) = e2
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |   (251)   ~ (all_56_31 = e1)
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | REDUCE: (53), (251) imply:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |   (252)  $false
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | CLOSE: (252) is inconsistent.
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |   (253)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (76), (86), (104), (183), (253) are
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1920.
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | |   (254)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 243.35/49.87  | | | | | | | | | | | | | | | | | |            = e0)
% 243.35/49.87  | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |   (255)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            e2) = e0
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |   (256)  op(e0, e2) = e0
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (76) with e0, e3, e2, e0,
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |              simplifying with (199), (256) gives:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |   (257)  e3 = e0
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (257) imply:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |   (258)  all_58_9 = e0
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (29), (32), (37), (70), (76), (89), (102),
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            (258) are inconsistent by sub-proof #1191.
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |   (259)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (49), (76), (194), (259) are inconsistent by
% 243.35/49.87  | | | | | | | | | | | | | | | | | | |            sub-proof #1989.
% 243.35/49.87  | | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | |   (260)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 243.35/49.87  | | | | | | | | | | | | | | |              e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 243.35/49.87  | | | | | | | | | | | | | | |            e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 243.35/49.87  | | | | | | | | | | | | | | |            all_56_7 & $i(all_56_7))
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (29), (40), (76), (83), (91), (164),
% 243.35/49.87  | | | | | | | | | | | | | | |            (213), (216), (260) are inconsistent by sub-proof
% 243.35/49.87  | | | | | | | | | | | | | | |            #1152.
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | |   (261)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | REF_CLOSE: (11), (15), (50), (192), (261) are inconsistent by
% 243.35/49.87  | | | | | | | | | | |            sub-proof #1648.
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | 
% 243.35/49.87  | | | | | | | End of split
% 243.35/49.87  | | | | | | | 
% 243.35/49.87  | | | | | | End of split
% 243.35/49.87  | | | | | | 
% 243.35/49.87  | | | | | End of split
% 243.35/49.87  | | | | | 
% 243.35/49.87  | | | | Case 2:
% 243.35/49.87  | | | | | 
% 243.35/49.87  | | | | |   (262)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0,
% 243.35/49.87  | | | | |              e3) = e2)
% 243.35/49.87  | | | | | 
% 243.35/49.87  | | | | | BETA: splitting (262) gives:
% 243.35/49.87  | | | | | 
% 243.35/49.87  | | | | | Case 1:
% 243.35/49.87  | | | | | | 
% 243.35/49.87  | | | | | |   (263)  all_58_6 = e2 & op(e1, e3) = e2
% 243.35/49.87  | | | | | | 
% 243.35/49.87  | | | | | | REF_CLOSE: (102), (163), (263) are inconsistent by sub-proof #2219.
% 243.35/49.87  | | | | | | 
% 243.35/49.87  | | | | | Case 2:
% 243.35/49.87  | | | | | | 
% 243.35/49.87  | | | | | |   (264)  all_58_12 = e2 & op(e0, e3) = e2
% 243.35/49.87  | | | | | | 
% 243.35/49.87  | | | | | | ALPHA: (264) implies:
% 243.35/49.87  | | | | | |   (265)  all_58_12 = e2
% 243.35/49.87  | | | | | | 
% 243.35/49.87  | | | | | | BETA: splitting (41) gives:
% 243.35/49.87  | | | | | | 
% 243.35/49.87  | | | | | | Case 1:
% 243.35/49.87  | | | | | | | 
% 243.35/49.87  | | | | | | |   (266)  all_58_15 = e0 & op(e0, e0) = e0
% 243.35/49.87  | | | | | | | 
% 243.35/49.87  | | | | | | | ALPHA: (266) implies:
% 243.35/49.87  | | | | | | |   (267)  op(e0, e0) = e0
% 243.35/49.87  | | | | | | | 
% 243.35/49.87  | | | | | | | REF_CLOSE: (1), (76), (83), (267) are inconsistent by sub-proof
% 243.35/49.87  | | | | | | |            #2274.
% 243.35/49.87  | | | | | | | 
% 243.35/49.87  | | | | | | Case 2:
% 243.35/49.87  | | | | | | | 
% 243.35/49.87  | | | | | | |   (268)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 243.35/49.87  | | | | | | |              op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.35/49.87  | | | | | | |              e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 243.35/49.87  | | | | | | |            (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 243.35/49.87  | | | | | | |              op(e0, e1) = e0))
% 243.35/49.87  | | | | | | | 
% 243.35/49.87  | | | | | | | ALPHA: (268) implies:
% 243.35/49.87  | | | | | | |   (269)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.87  | | | | | | |            op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.35/49.87  | | | | | | | 
% 243.35/49.87  | | | | | | | BETA: splitting (9) gives:
% 243.35/49.87  | | | | | | | 
% 243.35/49.87  | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | 
% 243.35/49.87  | | | | | | | |   (270)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 243.35/49.87  | | | | | | | |            op(e0, e2) = e3)
% 243.35/49.87  | | | | | | | | 
% 243.35/49.87  | | | | | | | | BETA: splitting (270) gives:
% 243.35/49.87  | | | | | | | | 
% 243.35/49.87  | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | |   (271)  all_58_12 = e3 & op(e0, e3) = e3
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | REF_CLOSE: (10), (17), (23), (26), (29), (42), (46), (55),
% 243.35/49.87  | | | | | | | | |            (58), (63), (71), (76), (83), (90), (102), (104),
% 243.35/49.87  | | | | | | | | |            (160), (271) are inconsistent by sub-proof #1528.
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | |   (272)  all_58_13 = e3 & op(e0, e2) = e3
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | ALPHA: (272) implies:
% 243.35/49.87  | | | | | | | | |   (273)  all_58_13 = e3
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | BETA: splitting (159) gives:
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | |   (274)  all_54_9 = e2
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | REF_CLOSE: (21), (45), (274) are inconsistent by sub-proof
% 243.35/49.87  | | | | | | | | | |            #1954.
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | |   (275)   ~ (all_54_9 = e2)
% 243.35/49.87  | | | | | | | | | |   (276)  all_54_9 = e1 | all_54_9 = e0
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | BETA: splitting (276) gives:
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | |   (277)  all_54_9 = e1
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | REF_CLOSE: (5), (45), (277) are inconsistent by sub-proof
% 243.35/49.87  | | | | | | | | | | |            #2055.
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | |   (278)  all_54_9 = e0
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | COMBINE_EQS: (45), (278) imply:
% 243.35/49.87  | | | | | | | | | | |   (279)  all_52_6 = e0
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | SIMP: (279) implies:
% 243.35/49.87  | | | | | | | | | | |   (280)  all_52_6 = e0
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | REDUCE: (74), (280) imply:
% 243.35/49.87  | | | | | | | | | | |   (281)   ~ (all_52_2 = e0)
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | REDUCE: (160), (280) imply:
% 243.35/49.87  | | | | | | | | | | |   (282)   ~ (e3 = e0)
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | REDUCE: (5), (280) imply:
% 243.35/49.87  | | | | | | | | | | |   (283)   ~ (e1 = e0)
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | BETA: splitting (55) gives:
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | |   (284)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 243.35/49.87  | | | | | | | | | | | |            & op(e2, e3) = e0)
% 243.35/49.87  | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | BETA: splitting (284) gives:
% 243.35/49.87  | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | |   (285)  all_58_0 = e0 & op(e3, e3) = e0
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | ALPHA: (285) implies:
% 243.35/49.87  | | | | | | | | | | | | |   (286)  op(e3, e3) = e0
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | REF_CLOSE: (29), (59), (70), (73), (76), (83), (89), (90),
% 243.35/49.87  | | | | | | | | | | | | |            (286) are inconsistent by sub-proof #1708.
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | |   (287)  all_58_2 = e0 & op(e2, e3) = e0
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | ALPHA: (287) implies:
% 243.35/49.87  | | | | | | | | | | | | |   (288)  all_58_2 = e0
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | BETA: splitting (269) gives:
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | |   (289)  all_58_12 = e0 & op(e0, e3) = e0
% 243.35/49.87  | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | ALPHA: (289) implies:
% 243.35/49.87  | | | | | | | | | | | | | |   (290)  all_58_12 = e0
% 243.35/49.87  | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | REF_CLOSE: (10), (29), (36), (37), (46), (62), (76), (85),
% 243.35/49.87  | | | | | | | | | | | | | |            (90), (102), (104), (288), (290) are inconsistent
% 243.35/49.87  | | | | | | | | | | | | | |            by sub-proof #1149.
% 243.35/49.87  | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | |   (291)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 243.35/49.87  | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 243.35/49.87  | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | BETA: splitting (291) gives:
% 243.35/49.87  | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | |   (292)  all_58_13 = e0 & op(e0, e2) = e0
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | ALPHA: (292) implies:
% 243.35/49.87  | | | | | | | | | | | | | | |   (293)  all_58_13 = e0
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | COMBINE_EQS: (273), (293) imply:
% 243.35/49.87  | | | | | | | | | | | | | | |   (294)  e3 = e0
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | SIMP: (294) implies:
% 243.35/49.87  | | | | | | | | | | | | | | |   (295)  e3 = e0
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | COMBINE_EQS: (59), (295) imply:
% 243.35/49.87  | | | | | | | | | | | | | | |   (296)  all_58_9 = e0
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | REF_CLOSE: (10), (29), (32), (37), (70), (76), (89), (102),
% 243.35/49.87  | | | | | | | | | | | | | | |            (296) are inconsistent by sub-proof #1191.
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | |   (297)  all_58_14 = e0 & op(e0, e1) = e0
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 243.35/49.87  | | | | | | | | | | | | | | |   (298)  all_58_14 = e0
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | | REF_CLOSE: (16), (25), (48), (89), (90), (102), (104), (298)
% 243.35/49.87  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1265.
% 243.35/49.87  | | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | |   (299)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 243.35/49.87  | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 243.35/49.87  | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | BETA: splitting (299) gives:
% 243.35/49.87  | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | |   (300)  all_58_6 = e0 & op(e1, e3) = e0
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | ALPHA: (300) implies:
% 243.35/49.87  | | | | | | | | | | | | |   (301)  op(e1, e3) = e0
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | REF_CLOSE: (76), (78), (281), (301) are inconsistent by
% 243.35/49.87  | | | | | | | | | | | | |            sub-proof #2023.
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | |   (302)  all_58_12 = e0 & op(e0, e3) = e0
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | ALPHA: (302) implies:
% 243.35/49.87  | | | | | | | | | | | | |   (303)  all_58_12 = e0
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | COMBINE_EQS: (265), (303) imply:
% 243.35/49.87  | | | | | | | | | | | | |   (304)  e2 = e0
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | COMBINE_EQS: (27), (304) imply:
% 243.35/49.87  | | | | | | | | | | | | |   (305)  all_58_14 = e0
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | | REF_CLOSE: (16), (25), (48), (89), (90), (102), (104), (305)
% 243.35/49.87  | | | | | | | | | | | | |            are inconsistent by sub-proof #1265.
% 243.35/49.87  | | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | 
% 243.35/49.87  | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | 
% 243.35/49.87  | | | | | | | |   (306)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 243.35/49.87  | | | | | | | |            op(e0, e0) = e3)
% 243.35/49.87  | | | | | | | | 
% 243.35/49.87  | | | | | | | | BETA: splitting (306) gives:
% 243.35/49.87  | | | | | | | | 
% 243.35/49.87  | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | |   (307)  all_58_14 = e3 & op(e0, e1) = e3
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | ALPHA: (307) implies:
% 243.35/49.87  | | | | | | | | |   (308)  op(e0, e1) = e3
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | REF_CLOSE: (24), (66), (76), (84), (308) are inconsistent by
% 243.35/49.87  | | | | | | | | |            sub-proof #1806.
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | |   (309)  all_58_15 = e3 & op(e0, e0) = e3
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | ALPHA: (309) implies:
% 243.35/49.87  | | | | | | | | |   (310)  all_58_15 = e3
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | COMBINE_EQS: (56), (310) imply:
% 243.35/49.87  | | | | | | | | |   (311)  e3 = e1
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | COMBINE_EQS: (163), (311) imply:
% 243.35/49.87  | | | | | | | | |   (312)  all_58_6 = e1
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | BETA: splitting (36) gives:
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | |   (313)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 243.35/49.87  | | | | | | | | | |            & op(e2, e3) = e3)
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | REF_CLOSE: (29), (37), (62), (76), (85), (313) are
% 243.35/49.87  | | | | | | | | | |            inconsistent by sub-proof #1208.
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | |   (314)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3
% 243.35/49.87  | | | | | | | | | |            & op(e0, e3) = e3)
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | BETA: splitting (314) gives:
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | Case 1:
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | COMBINE_EQS: (163), (312) imply:
% 243.35/49.87  | | | | | | | | | | |   (315)  e3 = e1
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | COMBINE_EQS: (59), (311) imply:
% 243.35/49.87  | | | | | | | | | | |   (316)  all_58_9 = e1
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | REF_CLOSE: (7), (10), (29), (32), (37), (46), (55), (64),
% 243.35/49.87  | | | | | | | | | | |            (67), (68), (76), (83), (90), (102), (104), (163),
% 243.35/49.87  | | | | | | | | | | |            (265), (316) are inconsistent by sub-proof #1147.
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | Case 2:
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | |   (317)  all_58_12 = e3 & op(e0, e3) = e3
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | ALPHA: (317) implies:
% 243.35/49.87  | | | | | | | | | | |   (318)  all_58_12 = e3
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | | REF_CLOSE: (102), (265), (318) are inconsistent by sub-proof
% 243.35/49.87  | | | | | | | | | | |            #1552.
% 243.35/49.87  | | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | | 
% 243.35/49.87  | | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | | 
% 243.35/49.87  | | | | | | | | End of split
% 243.35/49.87  | | | | | | | | 
% 243.35/49.87  | | | | | | | End of split
% 243.35/49.87  | | | | | | | 
% 243.35/49.87  | | | | | | End of split
% 243.35/49.87  | | | | | | 
% 243.35/49.87  | | | | | End of split
% 243.35/49.87  | | | | | 
% 243.35/49.87  | | | | End of split
% 243.35/49.87  | | | | 
% 243.35/49.87  | | | Case 2:
% 243.35/49.87  | | | | 
% 243.35/49.87  | | | |   (319)  all_58_7 = e3 & op(e1, e2) = e3
% 243.35/49.87  | | | | 
% 243.35/49.87  | | | | ALPHA: (319) implies:
% 243.35/49.87  | | | |   (320)  op(e1, e2) = e3
% 243.35/49.87  | | | | 
% 243.35/49.87  | | | | REF_CLOSE: (17), (76), (160), (320) are inconsistent by sub-proof #2191.
% 243.35/49.87  | | | | 
% 243.35/49.87  | | | End of split
% 243.35/49.87  | | | 
% 243.35/49.87  | | Case 2:
% 243.35/49.87  | | | 
% 243.35/49.87  | | |   (321)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 243.35/49.87  | | |            = e3)
% 243.35/49.87  | | | 
% 243.35/49.87  | | | REF_CLOSE: (23), (26), (42), (63), (76), (321) are inconsistent by
% 243.35/49.87  | | |            sub-proof #1529.
% 243.35/49.87  | | | 
% 243.35/49.87  | | End of split
% 243.35/49.87  | | 
% 243.35/49.87  | End of split
% 243.35/49.87  | 
% 243.35/49.87  End of proof
% 243.35/49.87  
% 243.35/49.87  Sub-proof #1147 shows that the following formulas are inconsistent:
% 243.35/49.87  ----------------------------------------------------------------
% 243.35/49.87    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.35/49.87         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.35/49.87    (2)   ~ (e3 = e0)
% 243.35/49.87    (3)  all_58_6 = e3
% 243.35/49.87    (4)   ~ (e2 = e0)
% 243.35/49.87    (5)  all_58_12 = e2
% 243.35/49.87    (6)   ~ (e3 = e1)
% 243.35/49.87    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.35/49.87         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.35/49.87    (8)  op(e3, e3) = e1
% 243.35/49.87    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.35/49.87         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.87    (10)   ~ (e3 = e2)
% 243.35/49.87    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.87          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.87    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.35/49.87          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.87    (13)   ~ (all_52_4 = e3)
% 243.35/49.87    (14)  op(e3, e2) = all_52_4
% 243.35/49.87    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.87    (16)   ~ (e1 = e0)
% 243.35/49.87    (17)  all_58_9 = e1
% 243.35/49.87    (18)   ~ (e2 = e1)
% 243.35/49.87  
% 243.35/49.87  Begin of proof
% 243.35/49.87  | 
% 243.35/49.87  | BETA: splitting (7) gives:
% 243.35/49.87  | 
% 243.35/49.88  | Case 1:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (19)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 243.35/49.88  | |           e3)
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (6), (8), (13), (14), (15), (19) are inconsistent by sub-proof
% 243.35/49.88  | |            #1401.
% 243.35/49.88  | | 
% 243.35/49.88  | Case 2:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (20)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 243.35/49.88  | |           e3)
% 243.35/49.88  | | 
% 243.35/49.88  | | BETA: splitting (20) gives:
% 243.35/49.88  | | 
% 243.35/49.88  | | Case 1:
% 243.35/49.88  | | | 
% 243.35/49.88  | | |   (21)  all_58_4 = e3 & op(e3, e1) = e3
% 243.35/49.88  | | | 
% 243.35/49.88  | | | ALPHA: (21) implies:
% 243.35/49.88  | | |   (22)  all_58_4 = e3
% 243.35/49.88  | | | 
% 243.35/49.88  | | | BETA: splitting (12) gives:
% 243.35/49.88  | | | 
% 243.35/49.88  | | | Case 1:
% 243.35/49.88  | | | | 
% 243.35/49.88  | | | |   (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 243.35/49.88  | | | |           = e0)
% 243.35/49.88  | | | | 
% 243.35/49.88  | | | | BETA: splitting (23) gives:
% 243.35/49.88  | | | | 
% 243.35/49.88  | | | | Case 1:
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | |   (24)  all_58_0 = e0 & op(e3, e3) = e0
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | | ALPHA: (24) implies:
% 243.35/49.88  | | | | |   (25)  op(e3, e3) = e0
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | | REF_CLOSE: (8), (15), (16), (25) are inconsistent by sub-proof #1828.
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | Case 2:
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | |   (26)  all_58_1 = e0 & op(e3, e2) = e0
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | | ALPHA: (26) implies:
% 243.35/49.88  | | | | |   (27)  all_58_1 = e0
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (15), (16),
% 243.35/49.88  | | | | |            (17), (18), (22), (27) are inconsistent by sub-proof #1148.
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | End of split
% 243.35/49.88  | | | | 
% 243.35/49.88  | | | Case 2:
% 243.35/49.88  | | | | 
% 243.35/49.88  | | | |   (28)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 243.35/49.88  | | | |           = e0)
% 243.35/49.88  | | | | 
% 243.35/49.88  | | | | BETA: splitting (28) gives:
% 243.35/49.88  | | | | 
% 243.35/49.88  | | | | Case 1:
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | |   (29)  all_58_4 = e0 & op(e3, e1) = e0
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | | ALPHA: (29) implies:
% 243.35/49.88  | | | | |   (30)  all_58_4 = e0
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | | REF_CLOSE: (2), (22), (30) are inconsistent by sub-proof #2186.
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | Case 2:
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | |   (31)  all_58_9 = e0 & op(e3, e0) = e0
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | | ALPHA: (31) implies:
% 243.35/49.88  | | | | |   (32)  all_58_9 = e0
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | | REF_CLOSE: (16), (17), (32) are inconsistent by sub-proof #1744.
% 243.35/49.88  | | | | | 
% 243.35/49.88  | | | | End of split
% 243.35/49.88  | | | | 
% 243.35/49.88  | | | End of split
% 243.35/49.88  | | | 
% 243.35/49.88  | | Case 2:
% 243.35/49.88  | | | 
% 243.35/49.88  | | |   (33)  all_58_9 = e3 & op(e3, e0) = e3
% 243.35/49.88  | | | 
% 243.35/49.88  | | | REF_CLOSE: (6), (17), (33) are inconsistent by sub-proof #1603.
% 243.35/49.88  | | | 
% 243.35/49.88  | | End of split
% 243.35/49.88  | | 
% 243.35/49.88  | End of split
% 243.35/49.88  | 
% 243.35/49.88  End of proof
% 243.35/49.88  
% 243.35/49.88  Sub-proof #1148 shows that the following formulas are inconsistent:
% 243.35/49.88  ----------------------------------------------------------------
% 243.35/49.88    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.35/49.88         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.35/49.88    (2)   ~ (e3 = e0)
% 243.35/49.88    (3)  all_58_6 = e3
% 243.35/49.88    (4)   ~ (e2 = e0)
% 243.35/49.88    (5)  all_58_12 = e2
% 243.35/49.88    (6)  all_58_1 = e0
% 243.35/49.88    (7)  op(e3, e3) = e1
% 243.35/49.88    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.35/49.88         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.88    (9)   ~ (e3 = e2)
% 243.35/49.88    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.88          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.88    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.88    (12)   ~ (e1 = e0)
% 243.35/49.88    (13)  all_58_4 = e3
% 243.35/49.88    (14)  all_58_9 = e1
% 243.35/49.88    (15)   ~ (e2 = e1)
% 243.35/49.88  
% 243.35/49.88  Begin of proof
% 243.35/49.88  | 
% 243.35/49.88  | BETA: splitting (1) gives:
% 243.35/49.88  | 
% 243.35/49.88  | Case 1:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (16)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 243.35/49.88  | |           e2)
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (4), (6), (7), (11), (15), (16) are inconsistent by sub-proof
% 243.35/49.88  | |            #1477.
% 243.35/49.88  | | 
% 243.35/49.88  | Case 2:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 243.35/49.88  | |           e2)
% 243.35/49.88  | | 
% 243.35/49.88  | | BETA: splitting (17) gives:
% 243.35/49.88  | | 
% 243.35/49.88  | | Case 1:
% 243.35/49.88  | | | 
% 243.35/49.88  | | |   (18)  all_58_4 = e2 & op(e3, e1) = e2
% 243.35/49.88  | | | 
% 243.35/49.88  | | | REF_CLOSE: (9), (13), (18) are inconsistent by sub-proof #1476.
% 243.35/49.88  | | | 
% 243.35/49.88  | | Case 2:
% 243.35/49.88  | | | 
% 243.35/49.88  | | |   (19)  all_58_9 = e2 & op(e3, e0) = e2
% 243.35/49.88  | | | 
% 243.35/49.88  | | | ALPHA: (19) implies:
% 243.35/49.88  | | |   (20)  all_58_9 = e2
% 243.35/49.88  | | | 
% 243.35/49.88  | | | COMBINE_EQS: (14), (20) imply:
% 243.35/49.88  | | |   (21)  e2 = e1
% 243.35/49.88  | | | 
% 243.35/49.88  | | | COMBINE_EQS: (5), (21) imply:
% 243.35/49.88  | | |   (22)  all_58_12 = e1
% 243.35/49.88  | | | 
% 243.35/49.88  | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (12), (15), (22) are
% 243.35/49.88  | | |            inconsistent by sub-proof #1206.
% 243.35/49.88  | | | 
% 243.35/49.88  | | End of split
% 243.35/49.88  | | 
% 243.35/49.88  | End of split
% 243.35/49.88  | 
% 243.35/49.88  End of proof
% 243.35/49.88  
% 243.35/49.88  Sub-proof #1149 shows that the following formulas are inconsistent:
% 243.35/49.88  ----------------------------------------------------------------
% 243.35/49.88    (1)   ~ (e3 = e0)
% 243.35/49.88    (2)   ~ (e2 = e0)
% 243.35/49.88    (3)   ~ (e3 = e1)
% 243.35/49.88    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.35/49.88         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.35/49.88    (5)  op(e3, e3) = e1
% 243.35/49.88    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.35/49.88         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.88    (7)   ~ (e3 = e2)
% 243.35/49.88    (8)  all_58_12 = e0
% 243.35/49.88    (9)  op(e2, e3) = all_52_1
% 243.35/49.88    (10)  all_58_2 = e0
% 243.35/49.88    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.88    (12)   ~ (all_52_1 = e3)
% 243.35/49.88    (13)   ~ (e2 = e1)
% 243.35/49.88  
% 243.35/49.88  Begin of proof
% 243.35/49.88  | 
% 243.35/49.88  | BETA: splitting (4) gives:
% 243.35/49.88  | 
% 243.35/49.88  | Case 1:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 243.35/49.88  | |           e3)
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (3), (5), (9), (11), (12), (14) are inconsistent by sub-proof
% 243.35/49.88  | |            #1208.
% 243.35/49.88  | | 
% 243.35/49.88  | Case 2:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (15)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 243.35/49.88  | |           e3)
% 243.35/49.88  | | 
% 243.35/49.88  | | BETA: splitting (15) gives:
% 243.35/49.88  | | 
% 243.35/49.88  | | Case 1:
% 243.35/49.88  | | | 
% 243.35/49.88  | | |   (16)  all_58_6 = e3 & op(e1, e3) = e3
% 243.35/49.88  | | | 
% 243.35/49.88  | | | ALPHA: (16) implies:
% 243.35/49.88  | | |   (17)  all_58_6 = e3
% 243.35/49.88  | | | 
% 243.35/49.88  | | | REF_CLOSE: (2), (5), (6), (7), (8), (10), (11), (13), (17) are
% 243.35/49.88  | | |            inconsistent by sub-proof #1150.
% 243.35/49.88  | | | 
% 243.35/49.88  | | Case 2:
% 243.35/49.88  | | | 
% 243.35/49.88  | | |   (18)  all_58_12 = e3 & op(e0, e3) = e3
% 243.35/49.88  | | | 
% 243.35/49.88  | | | ALPHA: (18) implies:
% 243.35/49.88  | | |   (19)  all_58_12 = e3
% 243.35/49.88  | | | 
% 243.35/49.88  | | | REF_CLOSE: (1), (8), (19) are inconsistent by sub-proof #1971.
% 243.35/49.88  | | | 
% 243.35/49.88  | | End of split
% 243.35/49.88  | | 
% 243.35/49.88  | End of split
% 243.35/49.88  | 
% 243.35/49.88  End of proof
% 243.35/49.88  
% 243.35/49.88  Sub-proof #1150 shows that the following formulas are inconsistent:
% 243.35/49.88  ----------------------------------------------------------------
% 243.35/49.88    (1)  all_58_6 = e3
% 243.35/49.88    (2)   ~ (e2 = e0)
% 243.35/49.88    (3)  op(e3, e3) = e1
% 243.35/49.88    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.35/49.88         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.88    (5)   ~ (e3 = e2)
% 243.35/49.88    (6)  all_58_12 = e0
% 243.35/49.88    (7)  all_58_2 = e0
% 243.35/49.88    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.88    (9)   ~ (e2 = e1)
% 243.35/49.88  
% 243.35/49.88  Begin of proof
% 243.35/49.88  | 
% 243.35/49.88  | BETA: splitting (4) gives:
% 243.35/49.88  | 
% 243.35/49.88  | Case 1:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 243.35/49.88  | |           e2)
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (2), (3), (7), (8), (9), (10) are inconsistent by sub-proof
% 243.35/49.88  | |            #1329.
% 243.35/49.88  | | 
% 243.35/49.88  | Case 2:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (11)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 243.35/49.88  | |           e2)
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (1), (2), (5), (6), (11) are inconsistent by sub-proof #1151.
% 243.35/49.88  | | 
% 243.35/49.88  | End of split
% 243.35/49.88  | 
% 243.35/49.88  End of proof
% 243.35/49.88  
% 243.35/49.88  Sub-proof #1151 shows that the following formulas are inconsistent:
% 243.35/49.88  ----------------------------------------------------------------
% 243.35/49.88    (1)  all_58_6 = e3
% 243.35/49.88    (2)   ~ (e2 = e0)
% 243.35/49.88    (3)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.88    (4)   ~ (e3 = e2)
% 243.35/49.88    (5)  all_58_12 = e0
% 243.35/49.88  
% 243.35/49.88  Begin of proof
% 243.35/49.88  | 
% 243.35/49.88  | BETA: splitting (3) gives:
% 243.35/49.88  | 
% 243.35/49.88  | Case 1:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (6)  all_58_6 = e2 & op(e1, e3) = e2
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #2219.
% 243.35/49.88  | | 
% 243.35/49.88  | Case 2:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (7)  all_58_12 = e2 & op(e0, e3) = e2
% 243.35/49.88  | | 
% 243.35/49.88  | | ALPHA: (7) implies:
% 243.35/49.88  | |   (8)  all_58_12 = e2
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #2083.
% 243.35/49.88  | | 
% 243.35/49.88  | End of split
% 243.35/49.88  | 
% 243.35/49.88  End of proof
% 243.35/49.88  
% 243.35/49.88  Sub-proof #1152 shows that the following formulas are inconsistent:
% 243.35/49.88  ----------------------------------------------------------------
% 243.35/49.88    (1)  op(e0, e0) = e1
% 243.35/49.88    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.35/49.88    (3)  op(e1, e3) = e3
% 243.35/49.88    (4)   ~ (e3 = e1)
% 243.35/49.88    (5)  all_54_4 = all_52_1
% 243.35/49.88    (6)  op(e0, e3) = e0
% 243.35/49.88    (7)   ~ (all_52_1 = e0)
% 243.35/49.88    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.88    (9)   ~ (e1 = e0)
% 243.35/49.88    (10)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 243.35/49.88            $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 243.35/49.88            all_56_7 & $i(all_56_7))
% 243.35/49.88    (11)   ~ (all_52_1 = e1)
% 243.35/49.88  
% 243.35/49.88  Begin of proof
% 243.35/49.88  | 
% 243.35/49.88  | BETA: splitting (10) gives:
% 243.35/49.88  | 
% 243.35/49.88  | Case 1:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (12)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 243.35/49.88  | |         $i(all_56_5)
% 243.35/49.88  | | 
% 243.35/49.88  | | ALPHA: (12) implies:
% 243.35/49.88  | |   (13)  op(e1, e3) = all_56_5
% 243.35/49.88  | |   (14)  op(e1, all_56_5) = e1
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (3), (4), (8), (13), (14) are inconsistent by sub-proof #2243.
% 243.35/49.88  | | 
% 243.35/49.88  | Case 2:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (15)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.35/49.88  | |         $i(all_56_7)
% 243.35/49.88  | | 
% 243.35/49.88  | | ALPHA: (15) implies:
% 243.35/49.88  | |   (16)  op(e0, e3) = all_56_7
% 243.35/49.88  | |   (17)  op(e0, all_56_7) = e0
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (16), (17) are
% 243.35/49.88  | |            inconsistent by sub-proof #1153.
% 243.35/49.88  | | 
% 243.35/49.88  | End of split
% 243.35/49.88  | 
% 243.35/49.88  End of proof
% 243.35/49.88  
% 243.35/49.88  Sub-proof #1153 shows that the following formulas are inconsistent:
% 243.35/49.88  ----------------------------------------------------------------
% 243.35/49.88    (1)  op(e0, e0) = e1
% 243.35/49.88    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.35/49.88    (3)  op(e0, e3) = all_56_7
% 243.35/49.88    (4)  all_54_4 = all_52_1
% 243.35/49.88    (5)  op(e0, e3) = e0
% 243.35/49.88    (6)   ~ (all_52_1 = e0)
% 243.35/49.88    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.88    (8)  op(e0, all_56_7) = e0
% 243.35/49.88    (9)   ~ (e1 = e0)
% 243.35/49.88    (10)   ~ (all_52_1 = e1)
% 243.35/49.88  
% 243.35/49.88  Begin of proof
% 243.35/49.88  | 
% 243.35/49.88  | BETA: splitting (2) gives:
% 243.35/49.88  | 
% 243.35/49.88  | Case 1:
% 243.35/49.88  | | 
% 243.35/49.88  | | 
% 243.35/49.88  | | GROUND_INST: instantiating (7) with e0, all_56_7, e3, e0, simplifying with
% 243.35/49.88  | |              (3), (5) gives:
% 243.35/49.88  | |   (11)  all_56_7 = e0
% 243.35/49.88  | | 
% 243.35/49.88  | | REDUCE: (8), (11) imply:
% 243.35/49.88  | |   (12)  op(e0, e0) = e0
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (1), (7), (9), (12) are inconsistent by sub-proof #2274.
% 243.35/49.88  | | 
% 243.35/49.88  | Case 2:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (13)  all_54_4 = e1 | all_54_4 = e0
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (4), (6), (10), (13) are inconsistent by sub-proof #1922.
% 243.35/49.88  | | 
% 243.35/49.88  | End of split
% 243.35/49.88  | 
% 243.35/49.88  End of proof
% 243.35/49.88  
% 243.35/49.88  Sub-proof #1154 shows that the following formulas are inconsistent:
% 243.35/49.88  ----------------------------------------------------------------
% 243.35/49.88    (1)  all_54_12 = all_38_0
% 243.35/49.88    (2)  all_54_12 = e1
% 243.35/49.88    (3)   ~ (all_38_0 = e1)
% 243.35/49.88  
% 243.35/49.88  Begin of proof
% 243.35/49.88  | 
% 243.35/49.88  | COMBINE_EQS: (1), (2) imply:
% 243.35/49.88  |   (4)  all_38_0 = e1
% 243.35/49.88  | 
% 243.35/49.88  | SIMP: (4) implies:
% 243.35/49.88  |   (5)  all_38_0 = e1
% 243.35/49.88  | 
% 243.35/49.88  | REDUCE: (3), (5) imply:
% 243.35/49.88  |   (6)  $false
% 243.35/49.88  | 
% 243.35/49.88  | CLOSE: (6) is inconsistent.
% 243.35/49.88  | 
% 243.35/49.88  End of proof
% 243.35/49.88  
% 243.35/49.88  Sub-proof #1155 shows that the following formulas are inconsistent:
% 243.35/49.88  ----------------------------------------------------------------
% 243.35/49.88    (1)   ~ (e3 = e0)
% 243.35/49.88    (2)   ~ (e2 = e0)
% 243.35/49.88    (3)  all_58_5 = e3
% 243.35/49.88    (4)  all_58_8 = e1
% 243.35/49.88    (5)  all_58_14 = e2
% 243.35/49.88    (6)   ~ (e3 = e1)
% 243.35/49.88    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.35/49.88         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.35/49.88    (8)  op(e3, e3) = e1
% 243.35/49.88    (9)   ~ (e3 = e2)
% 243.35/49.88    (10)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.35/49.88          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.35/49.88    (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.35/49.88    (12)   ~ (all_52_4 = e3)
% 243.35/49.88    (13)  op(e3, e2) = all_52_4
% 243.35/49.88    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.88    (15)  all_58_4 = e0
% 243.35/49.88    (16)   ~ (e2 = e1)
% 243.35/49.88  
% 243.35/49.88  Begin of proof
% 243.35/49.88  | 
% 243.35/49.88  | BETA: splitting (11) gives:
% 243.35/49.88  | 
% 243.35/49.88  | Case 1:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (17)  all_58_4 = e2 & op(e3, e1) = e2
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (2), (3), (4), (5), (9), (10), (15), (16), (17) are inconsistent
% 243.35/49.88  | |            by sub-proof #1156.
% 243.35/49.88  | | 
% 243.35/49.88  | Case 2:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (18)  all_58_9 = e2 & op(e3, e0) = e2
% 243.35/49.88  | | 
% 243.35/49.88  | | ALPHA: (18) implies:
% 243.35/49.88  | |   (19)  op(e3, e0) = e2
% 243.35/49.88  | | 
% 243.35/49.88  | | REF_CLOSE: (1), (6), (7), (8), (9), (12), (13), (14), (15), (19) are
% 243.35/49.88  | |            inconsistent by sub-proof #1400.
% 243.35/49.88  | | 
% 243.35/49.88  | End of split
% 243.35/49.88  | 
% 243.35/49.88  End of proof
% 243.35/49.88  
% 243.35/49.88  Sub-proof #1156 shows that the following formulas are inconsistent:
% 243.35/49.88  ----------------------------------------------------------------
% 243.35/49.88    (1)   ~ (e2 = e0)
% 243.35/49.88    (2)  all_58_5 = e3
% 243.35/49.88    (3)  all_58_8 = e1
% 243.35/49.88    (4)  all_58_14 = e2
% 243.35/49.88    (5)   ~ (e3 = e2)
% 243.35/49.88    (6)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.35/49.88         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.35/49.88    (7)  all_58_4 = e2 & op(e3, e1) = e2
% 243.35/49.88    (8)  all_58_4 = e0
% 243.35/49.88    (9)   ~ (e2 = e1)
% 243.35/49.88  
% 243.35/49.88  Begin of proof
% 243.35/49.88  | 
% 243.35/49.88  | ALPHA: (7) implies:
% 243.35/49.88  |   (10)  all_58_4 = e2
% 243.35/49.88  | 
% 243.35/49.88  | COMBINE_EQS: (8), (10) imply:
% 243.35/49.88  |   (11)  e2 = e0
% 243.35/49.88  | 
% 243.35/49.88  | SIMP: (11) implies:
% 243.35/49.88  |   (12)  e2 = e0
% 243.35/49.88  | 
% 243.35/49.88  | COMBINE_EQS: (4), (12) imply:
% 243.35/49.88  |   (13)  all_58_14 = e0
% 243.35/49.88  | 
% 243.35/49.88  | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (13) are inconsistent by
% 243.35/49.88  |            sub-proof #1265.
% 243.35/49.88  | 
% 243.35/49.88  End of proof
% 243.35/49.88  
% 243.35/49.88  Sub-proof #1157 shows that the following formulas are inconsistent:
% 243.35/49.88  ----------------------------------------------------------------
% 243.35/49.88    (1)  all_54_12 = e1 | all_54_12 = e0
% 243.35/49.88    (2)  all_54_12 = all_10_0
% 243.35/49.88    (3)   ~ (all_10_0 = e1)
% 243.35/49.88    (4)   ~ (all_10_0 = e0)
% 243.35/49.88  
% 243.35/49.88  Begin of proof
% 243.35/49.88  | 
% 243.35/49.88  | BETA: splitting (1) gives:
% 243.35/49.88  | 
% 243.35/49.88  | Case 1:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (5)  all_54_12 = e1
% 243.35/49.88  | | 
% 243.35/49.88  | | COMBINE_EQS: (2), (5) imply:
% 243.35/49.88  | |   (6)  all_10_0 = e1
% 243.35/49.88  | | 
% 243.35/49.88  | | SIMP: (6) implies:
% 243.35/49.88  | |   (7)  all_10_0 = e1
% 243.35/49.88  | | 
% 243.35/49.88  | | REDUCE: (3), (7) imply:
% 243.35/49.88  | |   (8)  $false
% 243.35/49.88  | | 
% 243.35/49.88  | | CLOSE: (8) is inconsistent.
% 243.35/49.88  | | 
% 243.35/49.88  | Case 2:
% 243.35/49.88  | | 
% 243.35/49.88  | |   (9)  all_54_12 = e0
% 243.35/49.89  | | 
% 243.35/49.89  | | COMBINE_EQS: (2), (9) imply:
% 243.35/49.89  | |   (10)  all_10_0 = e0
% 243.35/49.89  | | 
% 243.35/49.89  | | SIMP: (10) implies:
% 243.35/49.89  | |   (11)  all_10_0 = e0
% 243.35/49.89  | | 
% 243.35/49.89  | | REDUCE: (4), (11) imply:
% 243.35/49.89  | |   (12)  $false
% 243.35/49.89  | | 
% 243.35/49.89  | | CLOSE: (12) is inconsistent.
% 243.35/49.89  | | 
% 243.35/49.89  | End of split
% 243.35/49.89  | 
% 243.35/49.89  End of proof
% 243.35/49.89  
% 243.35/49.89  Sub-proof #1158 shows that the following formulas are inconsistent:
% 243.35/49.89  ----------------------------------------------------------------
% 243.35/49.89    (1)  op(e0, e0) = e1
% 243.35/49.89    (2)  op(e3, e2) = all_56_9
% 243.35/49.89    (3)  op(e3, all_56_9) = e3
% 243.35/49.89    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.35/49.89         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.35/49.89    (5)   ~ (e3 = e0)
% 243.35/49.89    (6)   ~ (e2 = e0)
% 243.35/49.89    (7)  all_58_5 = e3
% 243.35/49.89    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.35/49.89         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.35/49.89    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.35/49.89         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.35/49.89    (10)  all_58_8 = e1
% 243.35/49.89    (11)  all_58_14 = e2
% 243.35/49.89    (12)   ~ (all_52_7 = e3)
% 243.35/49.89    (13)   ~ (e3 = e1)
% 243.35/49.89    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.35/49.89          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.35/49.89    (15)  op(e3, e2) = e2
% 243.35/49.89    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.35/49.89          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.35/49.89    (17)  op(e3, e3) = e1
% 243.35/49.89    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.89              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.35/49.89                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.89                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.35/49.89    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.35/49.89          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.89    (20)   ~ (e3 = e2)
% 243.35/49.89    (21)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.35/49.89          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.35/49.89    (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.89          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.89    (23)  all_58_15 = e1
% 243.35/49.89    (24)  all_58_7 = e3
% 243.35/49.89    (25)  all_58_9 = e3
% 243.35/49.89    (26)  op(e2, e3) = all_52_1
% 243.35/49.89    (27)  op(e0, e2) = all_52_7
% 243.35/49.89    (28)   ~ (all_52_4 = e3)
% 243.35/49.89    (29)  op(e3, e2) = all_52_4
% 243.35/49.89    (30)  all_58_1 = e2
% 243.35/49.89    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.89    (32)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.35/49.89          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.35/49.89    (33)   ~ (all_52_4 = e1)
% 243.35/49.89    (34)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.35/49.89          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.35/49.89    (35)   ~ (e1 = e0)
% 243.35/49.89    (36)   ~ (all_52_1 = e3)
% 243.35/49.89    (37)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.35/49.89          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.35/49.89            e2)
% 243.35/49.89    (38)  all_58_4 = e0
% 243.35/49.89    (39)   ~ (e2 = e1)
% 243.35/49.89  
% 243.35/49.89  Begin of proof
% 243.35/49.89  | 
% 243.35/49.89  | BETA: splitting (16) gives:
% 243.35/49.89  | 
% 243.35/49.89  | Case 1:
% 243.35/49.89  | | 
% 243.35/49.89  | |   (40)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 243.35/49.89  | |           e3)
% 243.35/49.89  | | 
% 243.35/49.89  | | REF_CLOSE: (13), (17), (26), (31), (36), (40) are inconsistent by sub-proof
% 243.35/49.89  | |            #1208.
% 243.35/49.89  | | 
% 243.35/49.89  | Case 2:
% 243.35/49.89  | | 
% 243.35/49.89  | |   (41)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 243.35/49.89  | |           e3)
% 243.35/49.89  | | 
% 243.35/49.89  | | BETA: splitting (41) gives:
% 243.35/49.89  | | 
% 243.35/49.89  | | Case 1:
% 243.35/49.89  | | | 
% 243.35/49.89  | | |   (42)  all_58_6 = e3 & op(e1, e3) = e3
% 243.35/49.89  | | | 
% 243.35/49.89  | | | ALPHA: (42) implies:
% 243.35/49.89  | | |   (43)  all_58_6 = e3
% 243.35/49.89  | | | 
% 243.35/49.89  | | | REF_CLOSE: (4), (5), (6), (11), (12), (13), (16), (17), (18), (19), (20),
% 243.35/49.89  | | |            (22), (23), (26), (27), (31), (35), (36), (37), (39), (43) are
% 243.35/49.89  | | |            inconsistent by sub-proof #1159.
% 243.35/49.89  | | | 
% 243.35/49.89  | | Case 2:
% 243.35/49.89  | | | 
% 243.35/49.89  | | |   (44)  all_58_12 = e3 & op(e0, e3) = e3
% 243.35/49.89  | | | 
% 243.35/49.89  | | | ALPHA: (44) implies:
% 243.35/49.89  | | |   (45)  all_58_12 = e3
% 243.35/49.89  | | | 
% 243.35/49.89  | | | BETA: splitting (18) gives:
% 243.35/49.89  | | | 
% 243.35/49.89  | | | Case 1:
% 243.35/49.89  | | | | 
% 243.35/49.89  | | | |   (46)  all_58_15 = e0 & op(e0, e0) = e0
% 243.35/49.89  | | | | 
% 243.35/49.89  | | | | ALPHA: (46) implies:
% 243.35/49.89  | | | |   (47)  op(e0, e0) = e0
% 243.35/49.89  | | | | 
% 243.35/49.89  | | | | REF_CLOSE: (1), (31), (35), (47) are inconsistent by sub-proof #2274.
% 243.35/49.89  | | | | 
% 243.35/49.89  | | | Case 2:
% 243.35/49.89  | | | | 
% 243.35/49.89  | | | |   (48)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 243.35/49.89  | | | |               e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 243.35/49.89  | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 243.35/49.89  | | | |               e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 243.35/49.89  | | | | 
% 243.35/49.89  | | | | ALPHA: (48) implies:
% 243.35/49.89  | | | |   (49)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 243.35/49.89  | | | |             e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.35/49.89  | | | | 
% 243.35/49.89  | | | | BETA: splitting (49) gives:
% 243.35/49.89  | | | | 
% 243.35/49.89  | | | | Case 1:
% 243.35/49.89  | | | | | 
% 243.35/49.89  | | | | |   (50)  all_58_12 = e0 & op(e0, e3) = e0
% 243.35/49.89  | | | | | 
% 243.35/49.89  | | | | | ALPHA: (50) implies:
% 243.35/49.89  | | | | |   (51)  all_58_12 = e0
% 243.35/49.89  | | | | | 
% 243.35/49.89  | | | | | COMBINE_EQS: (45), (51) imply:
% 243.35/49.89  | | | | |   (52)  e3 = e0
% 243.35/49.89  | | | | | 
% 243.35/49.89  | | | | | COMBINE_EQS: (25), (52) imply:
% 243.35/49.89  | | | | |   (53)  all_58_9 = e0
% 243.35/49.89  | | | | | 
% 243.35/49.89  | | | | | REF_CLOSE: (5), (13), (14), (17), (20), (30), (31), (38), (53) are
% 243.35/49.89  | | | | |            inconsistent by sub-proof #1191.
% 243.35/49.89  | | | | | 
% 243.35/49.89  | | | | Case 2:
% 243.35/49.89  | | | | | 
% 243.35/49.89  | | | | |   (54)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 243.35/49.89  | | | | |             e1) = e0)
% 243.35/49.89  | | | | | 
% 243.35/49.89  | | | | | BETA: splitting (54) gives:
% 243.35/49.89  | | | | | 
% 243.35/49.89  | | | | | Case 1:
% 243.35/49.89  | | | | | | 
% 243.35/49.89  | | | | | |   (55)  all_58_13 = e0 & op(e0, e2) = e0
% 243.35/49.89  | | | | | | 
% 243.35/49.89  | | | | | | ALPHA: (55) implies:
% 243.35/49.89  | | | | | |   (56)  all_58_13 = e0
% 243.35/49.89  | | | | | |   (57)  op(e0, e2) = e0
% 243.35/49.89  | | | | | | 
% 243.35/49.89  | | | | | | BETA: splitting (9) gives:
% 243.35/49.89  | | | | | | 
% 243.35/49.89  | | | | | | Case 1:
% 243.35/49.89  | | | | | | | 
% 243.35/49.89  | | | | | | |   (58)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 243.35/49.89  | | | | | | |           op(e2, e2) = e0)
% 243.35/49.89  | | | | | | | 
% 243.35/49.89  | | | | | | | BETA: splitting (58) gives:
% 243.35/49.89  | | | | | | | 
% 243.35/49.89  | | | | | | | Case 1:
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | |   (59)  all_58_1 = e0 & op(e3, e2) = e0
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | | ALPHA: (59) implies:
% 243.35/49.89  | | | | | | | |   (60)  all_58_1 = e0
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | | COMBINE_EQS: (30), (60) imply:
% 243.35/49.89  | | | | | | | |   (61)  e2 = e0
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | | COMBINE_EQS: (11), (61) imply:
% 243.35/49.89  | | | | | | | |   (62)  all_58_14 = e0
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | | REF_CLOSE: (6), (7), (10), (20), (21), (38), (39), (62) are
% 243.35/49.89  | | | | | | | |            inconsistent by sub-proof #1265.
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | Case 2:
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | |   (63)  all_58_3 = e0 & op(e2, e2) = e0
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | | ALPHA: (63) implies:
% 243.35/49.89  | | | | | | | |   (64)  all_58_3 = e0
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | | REF_CLOSE: (5), (6), (8), (13), (20), (29), (31), (32), (33),
% 243.35/49.89  | | | | | | | |            (34), (35), (39), (56), (57), (64) are inconsistent
% 243.35/49.89  | | | | | | | |            by sub-proof #1374.
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | End of split
% 243.35/49.89  | | | | | | | 
% 243.35/49.89  | | | | | | Case 2:
% 243.35/49.89  | | | | | | | 
% 243.35/49.89  | | | | | | |   (65)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 243.35/49.89  | | | | | | |           op(e0, e2) = e0)
% 243.35/49.89  | | | | | | | 
% 243.35/49.89  | | | | | | | BETA: splitting (65) gives:
% 243.35/49.89  | | | | | | | 
% 243.35/49.89  | | | | | | | Case 1:
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | |   (66)  all_58_7 = e0 & op(e1, e2) = e0
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | | REF_CLOSE: (5), (13), (14), (17), (20), (24), (25), (30), (31),
% 243.35/49.89  | | | | | | | |            (38), (66) are inconsistent by sub-proof #1176.
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | Case 2:
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | | GROUND_INST: instantiating (31) with e2, all_56_9, e2, e3,
% 243.35/49.89  | | | | | | | |              simplifying with (2), (15) gives:
% 243.35/49.89  | | | | | | | |   (67)  all_56_9 = e2
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | | REDUCE: (3), (67) imply:
% 243.35/49.89  | | | | | | | |   (68)  op(e3, e2) = e3
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | | REF_CLOSE: (28), (29), (31), (68) are inconsistent by sub-proof
% 243.35/49.89  | | | | | | | |            #2192.
% 243.35/49.89  | | | | | | | | 
% 243.35/49.89  | | | | | | | End of split
% 243.35/49.89  | | | | | | | 
% 243.35/49.89  | | | | | | End of split
% 243.35/49.89  | | | | | | 
% 243.35/49.89  | | | | | Case 2:
% 243.35/49.89  | | | | | | 
% 243.35/49.89  | | | | | |   (69)  all_58_14 = e0 & op(e0, e1) = e0
% 243.35/49.89  | | | | | | 
% 243.35/49.89  | | | | | | ALPHA: (69) implies:
% 243.35/49.89  | | | | | |   (70)  all_58_14 = e0
% 243.35/49.89  | | | | | | 
% 243.35/49.89  | | | | | | REF_CLOSE: (6), (7), (10), (20), (21), (38), (39), (70) are
% 243.35/49.89  | | | | | |            inconsistent by sub-proof #1265.
% 243.35/49.89  | | | | | | 
% 243.35/49.89  | | | | | End of split
% 243.35/49.89  | | | | | 
% 243.35/49.89  | | | | End of split
% 243.35/49.89  | | | | 
% 243.35/49.89  | | | End of split
% 243.35/49.89  | | | 
% 243.35/49.89  | | End of split
% 243.35/49.89  | | 
% 243.35/49.89  | End of split
% 243.35/49.89  | 
% 243.35/49.89  End of proof
% 243.35/49.89  
% 243.35/49.89  Sub-proof #1159 shows that the following formulas are inconsistent:
% 243.35/49.89  ----------------------------------------------------------------
% 243.35/49.89    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 243.35/49.89         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.35/49.89    (2)   ~ (e3 = e0)
% 243.35/49.89    (3)  all_58_6 = e3
% 243.35/49.89    (4)   ~ (e2 = e0)
% 243.35/49.89    (5)  all_58_14 = e2
% 243.35/49.89    (6)   ~ (all_52_7 = e3)
% 243.35/49.89    (7)   ~ (e3 = e1)
% 243.35/49.89    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.35/49.89         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.35/49.89    (9)  op(e3, e3) = e1
% 243.35/49.89    (10)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.89              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.35/49.89                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.89                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.35/49.89    (11)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.35/49.89          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.89    (12)   ~ (e3 = e2)
% 243.35/49.89    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.89          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.89    (14)  all_58_15 = e1
% 243.35/49.89    (15)  op(e2, e3) = all_52_1
% 243.35/49.89    (16)  op(e0, e2) = all_52_7
% 243.35/49.89    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.89    (18)   ~ (e1 = e0)
% 243.35/49.89    (19)   ~ (all_52_1 = e3)
% 243.35/49.89    (20)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.35/49.89          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.35/49.89            e2)
% 243.35/49.89    (21)   ~ (e2 = e1)
% 243.35/49.89  
% 243.35/49.89  Begin of proof
% 243.35/49.89  | 
% 243.35/49.89  | BETA: splitting (1) gives:
% 243.35/49.89  | 
% 243.35/49.89  | Case 1:
% 243.35/49.89  | | 
% 243.35/49.89  | |   (22)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 243.35/49.89  | |           e3)
% 243.35/49.89  | | 
% 243.35/49.89  | | REF_CLOSE: (2), (3), (4), (6), (9), (11), (12), (13), (16), (17), (18),
% 243.35/49.89  | |            (21), (22) are inconsistent by sub-proof #1167.
% 243.35/49.89  | | 
% 243.35/49.89  | Case 2:
% 243.35/49.89  | | 
% 243.35/49.89  | |   (23)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 243.35/49.89  | |           e3)
% 243.35/49.89  | | 
% 243.35/49.89  | | BETA: splitting (23) gives:
% 243.35/49.89  | | 
% 243.35/49.89  | | Case 1:
% 243.35/49.89  | | | 
% 243.35/49.89  | | |   (24)  all_58_14 = e3 & op(e0, e1) = e3
% 243.35/49.89  | | | 
% 243.35/49.89  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (14), (15),
% 243.35/49.89  | | |            (17), (18), (19), (20), (21), (24) are inconsistent by
% 243.35/49.89  | | |            sub-proof #1165.
% 243.35/49.89  | | | 
% 243.35/49.89  | | Case 2:
% 243.35/49.89  | | | 
% 243.35/49.89  | | |   (25)  all_58_15 = e3 & op(e0, e0) = e3
% 243.35/49.89  | | | 
% 243.35/49.89  | | | ALPHA: (25) implies:
% 243.35/49.89  | | |   (26)  all_58_15 = e3
% 243.35/49.89  | | | 
% 243.35/49.89  | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (11), (12), (13), (14), (15),
% 243.35/49.89  | | |            (17), (18), (19), (21), (26) are inconsistent by sub-proof
% 243.35/49.89  | | |            #1160.
% 243.35/49.89  | | | 
% 243.35/49.89  | | End of split
% 243.35/49.89  | | 
% 243.35/49.89  | End of split
% 243.35/49.89  | 
% 243.35/49.89  End of proof
% 243.35/49.89  
% 243.35/49.89  Sub-proof #1160 shows that the following formulas are inconsistent:
% 243.35/49.89  ----------------------------------------------------------------
% 243.35/49.89    (1)   ~ (e3 = e0)
% 243.35/49.89    (2)  all_58_6 = e3
% 243.35/49.89    (3)   ~ (e2 = e0)
% 243.35/49.89    (4)  all_58_15 = e3
% 243.35/49.89    (5)   ~ (e3 = e1)
% 243.35/49.89    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.35/49.89         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.35/49.89    (7)  op(e3, e3) = e1
% 243.35/49.89    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.35/49.89         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.89    (9)   ~ (e3 = e2)
% 243.35/49.89    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.89          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.89    (11)  all_58_15 = e1
% 243.35/49.89    (12)  op(e2, e3) = all_52_1
% 243.35/49.89    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.89    (14)   ~ (e1 = e0)
% 243.35/49.89    (15)   ~ (all_52_1 = e3)
% 243.35/49.89    (16)   ~ (e2 = e1)
% 243.35/49.89  
% 243.35/49.89  Begin of proof
% 243.35/49.89  | 
% 243.35/49.89  | COMBINE_EQS: (4), (11) imply:
% 243.35/49.89  |   (17)  e3 = e1
% 243.35/49.89  | 
% 243.35/49.89  | SIMP: (17) implies:
% 243.35/49.89  |   (18)  e3 = e1
% 243.35/49.89  | 
% 243.35/49.89  | COMBINE_EQS: (2), (18) imply:
% 243.35/49.89  |   (19)  all_58_6 = e1
% 243.35/49.89  | 
% 243.35/49.89  | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14), (15),
% 243.35/49.89  |            (16), (19) are inconsistent by sub-proof #1161.
% 243.35/49.89  | 
% 243.35/49.89  End of proof
% 243.35/49.89  
% 243.35/49.89  Sub-proof #1161 shows that the following formulas are inconsistent:
% 243.35/49.89  ----------------------------------------------------------------
% 243.35/49.89    (1)   ~ (e3 = e0)
% 243.35/49.89    (2)   ~ (e2 = e0)
% 243.35/49.89    (3)   ~ (e3 = e1)
% 243.35/49.89    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.35/49.89         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.35/49.89    (5)  op(e3, e3) = e1
% 243.35/49.89    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.35/49.89         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.89    (7)   ~ (e3 = e2)
% 243.35/49.90    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.90         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.90    (9)  all_58_6 = e1
% 243.35/49.90    (10)  op(e2, e3) = all_52_1
% 243.35/49.90    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.90    (12)   ~ (e1 = e0)
% 243.35/49.90    (13)   ~ (all_52_1 = e3)
% 243.35/49.90    (14)   ~ (e2 = e1)
% 243.35/49.90  
% 243.35/49.90  Begin of proof
% 243.35/49.90  | 
% 243.35/49.90  | BETA: splitting (4) gives:
% 243.35/49.90  | 
% 243.35/49.90  | Case 1:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 243.35/49.90  | |           e3)
% 243.35/49.90  | | 
% 243.35/49.90  | | REF_CLOSE: (3), (5), (10), (11), (13), (15) are inconsistent by sub-proof
% 243.35/49.90  | |            #1208.
% 243.35/49.90  | | 
% 243.35/49.90  | Case 2:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 243.35/49.90  | |           e3)
% 243.35/49.90  | | 
% 243.35/49.90  | | BETA: splitting (16) gives:
% 243.35/49.90  | | 
% 243.35/49.90  | | Case 1:
% 243.35/49.90  | | | 
% 243.35/49.90  | | |   (17)  all_58_6 = e3 & op(e1, e3) = e3
% 243.35/49.90  | | | 
% 243.35/49.90  | | | ALPHA: (17) implies:
% 243.35/49.90  | | |   (18)  all_58_6 = e3
% 243.35/49.90  | | | 
% 243.35/49.90  | | | COMBINE_EQS: (9), (18) imply:
% 243.35/49.90  | | |   (19)  e3 = e1
% 243.35/49.90  | | | 
% 243.35/49.90  | | | REDUCE: (3), (19) imply:
% 243.35/49.90  | | |   (20)  $false
% 243.35/49.90  | | | 
% 243.35/49.90  | | | CLOSE: (20) is inconsistent.
% 243.35/49.90  | | | 
% 243.35/49.90  | | Case 2:
% 243.35/49.90  | | | 
% 243.35/49.90  | | |   (21)  all_58_12 = e3 & op(e0, e3) = e3
% 243.35/49.90  | | | 
% 243.35/49.90  | | | ALPHA: (21) implies:
% 243.35/49.90  | | |   (22)  all_58_12 = e3
% 243.35/49.90  | | | 
% 243.35/49.90  | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (14), (22) are
% 243.35/49.90  | | |            inconsistent by sub-proof #1162.
% 243.35/49.90  | | | 
% 243.35/49.90  | | End of split
% 243.35/49.90  | | 
% 243.35/49.90  | End of split
% 243.35/49.90  | 
% 243.35/49.90  End of proof
% 243.35/49.90  
% 243.35/49.90  Sub-proof #1162 shows that the following formulas are inconsistent:
% 243.35/49.90  ----------------------------------------------------------------
% 243.35/49.90    (1)   ~ (e3 = e0)
% 243.35/49.90    (2)   ~ (e2 = e0)
% 243.35/49.90    (3)  op(e3, e3) = e1
% 243.35/49.90    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.35/49.90         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.90    (5)   ~ (e3 = e2)
% 243.35/49.90    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.90         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.90    (7)  all_58_6 = e1
% 243.35/49.90    (8)  all_58_12 = e3
% 243.35/49.90    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.90    (10)   ~ (e1 = e0)
% 243.35/49.90    (11)   ~ (e2 = e1)
% 243.35/49.90  
% 243.35/49.90  Begin of proof
% 243.35/49.90  | 
% 243.35/49.90  | BETA: splitting (4) gives:
% 243.35/49.90  | 
% 243.35/49.90  | Case 1:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (12)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 243.35/49.90  | |           e2)
% 243.35/49.90  | | 
% 243.35/49.90  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12) are
% 243.35/49.90  | |            inconsistent by sub-proof #1163.
% 243.35/49.90  | | 
% 243.35/49.90  | Case 2:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (13)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 243.35/49.90  | |           e2)
% 243.35/49.90  | | 
% 243.35/49.90  | | BETA: splitting (13) gives:
% 243.35/49.90  | | 
% 243.35/49.90  | | Case 1:
% 243.35/49.90  | | | 
% 243.35/49.90  | | |   (14)  all_58_6 = e2 & op(e1, e3) = e2
% 243.35/49.90  | | | 
% 243.35/49.90  | | | ALPHA: (14) implies:
% 243.35/49.90  | | |   (15)  all_58_6 = e2
% 243.35/49.90  | | | 
% 243.35/49.90  | | | COMBINE_EQS: (7), (15) imply:
% 243.35/49.90  | | |   (16)  e2 = e1
% 243.35/49.90  | | | 
% 243.35/49.90  | | | REDUCE: (11), (16) imply:
% 243.35/49.90  | | |   (17)  $false
% 243.35/49.90  | | | 
% 243.35/49.90  | | | CLOSE: (17) is inconsistent.
% 243.35/49.90  | | | 
% 243.35/49.90  | | Case 2:
% 243.35/49.90  | | | 
% 243.35/49.90  | | |   (18)  all_58_12 = e2 & op(e0, e3) = e2
% 243.35/49.90  | | | 
% 243.35/49.90  | | | ALPHA: (18) implies:
% 243.35/49.90  | | |   (19)  all_58_12 = e2
% 243.35/49.90  | | | 
% 243.35/49.90  | | | REF_CLOSE: (5), (8), (19) are inconsistent by sub-proof #1552.
% 243.35/49.90  | | | 
% 243.35/49.90  | | End of split
% 243.35/49.90  | | 
% 243.35/49.90  | End of split
% 243.35/49.90  | 
% 243.35/49.90  End of proof
% 243.35/49.90  
% 243.35/49.90  Sub-proof #1163 shows that the following formulas are inconsistent:
% 243.35/49.90  ----------------------------------------------------------------
% 243.35/49.90    (1)   ~ (e3 = e0)
% 243.35/49.90    (2)   ~ (e2 = e0)
% 243.35/49.90    (3)  op(e3, e3) = e1
% 243.35/49.90    (4)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.90         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.90    (5)  all_58_6 = e1
% 243.35/49.90    (6)  all_58_12 = e3
% 243.35/49.90    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 243.35/49.90    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.90    (9)   ~ (e1 = e0)
% 243.35/49.90    (10)   ~ (e2 = e1)
% 243.35/49.90  
% 243.35/49.90  Begin of proof
% 243.35/49.90  | 
% 243.35/49.90  | BETA: splitting (7) gives:
% 243.35/49.90  | 
% 243.35/49.90  | Case 1:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (11)  all_58_0 = e2 & op(e3, e3) = e2
% 243.35/49.90  | | 
% 243.35/49.90  | | ALPHA: (11) implies:
% 243.35/49.90  | |   (12)  op(e3, e3) = e2
% 243.35/49.90  | | 
% 243.35/49.90  | | REF_CLOSE: (3), (8), (10), (12) are inconsistent by sub-proof #2267.
% 243.35/49.90  | | 
% 243.35/49.90  | Case 2:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (13)  all_58_2 = e2 & op(e2, e3) = e2
% 243.35/49.90  | | 
% 243.35/49.90  | | ALPHA: (13) implies:
% 243.35/49.90  | |   (14)  all_58_2 = e2
% 243.35/49.90  | | 
% 243.35/49.90  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (14) are inconsistent by
% 243.35/49.90  | |            sub-proof #1164.
% 243.35/49.90  | | 
% 243.35/49.90  | End of split
% 243.35/49.90  | 
% 243.35/49.90  End of proof
% 243.35/49.90  
% 243.35/49.90  Sub-proof #1164 shows that the following formulas are inconsistent:
% 243.35/49.90  ----------------------------------------------------------------
% 243.35/49.90    (1)   ~ (e3 = e0)
% 243.35/49.90    (2)   ~ (e2 = e0)
% 243.35/49.90    (3)  all_58_2 = e2
% 243.35/49.90    (4)  op(e3, e3) = e1
% 243.35/49.90    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.90         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.90    (6)  all_58_6 = e1
% 243.35/49.90    (7)  all_58_12 = e3
% 243.35/49.90    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.90    (9)   ~ (e1 = e0)
% 243.35/49.90  
% 243.35/49.90  Begin of proof
% 243.35/49.90  | 
% 243.35/49.90  | BETA: splitting (5) gives:
% 243.35/49.90  | 
% 243.35/49.90  | Case 1:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 243.35/49.90  | |           e0)
% 243.35/49.90  | | 
% 243.35/49.90  | | REF_CLOSE: (2), (3), (4), (8), (9), (10) are inconsistent by sub-proof
% 243.35/49.90  | |            #1534.
% 243.35/49.90  | | 
% 243.35/49.90  | Case 2:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (11)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 243.35/49.90  | |           e0)
% 243.35/49.90  | | 
% 243.35/49.90  | | BETA: splitting (11) gives:
% 243.35/49.90  | | 
% 243.35/49.90  | | Case 1:
% 243.35/49.90  | | | 
% 243.35/49.90  | | |   (12)  all_58_6 = e0 & op(e1, e3) = e0
% 243.35/49.90  | | | 
% 243.35/49.90  | | | ALPHA: (12) implies:
% 243.35/49.90  | | |   (13)  all_58_6 = e0
% 243.35/49.90  | | | 
% 243.35/49.90  | | | REF_CLOSE: (6), (9), (13) are inconsistent by sub-proof #1981.
% 243.35/49.90  | | | 
% 243.35/49.90  | | Case 2:
% 243.35/49.90  | | | 
% 243.35/49.90  | | |   (14)  all_58_12 = e0 & op(e0, e3) = e0
% 243.35/49.90  | | | 
% 243.35/49.90  | | | ALPHA: (14) implies:
% 243.35/49.90  | | |   (15)  all_58_12 = e0
% 243.35/49.90  | | | 
% 243.35/49.90  | | | REF_CLOSE: (1), (7), (15) are inconsistent by sub-proof #1971.
% 243.35/49.90  | | | 
% 243.35/49.90  | | End of split
% 243.35/49.90  | | 
% 243.35/49.90  | End of split
% 243.35/49.90  | 
% 243.35/49.90  End of proof
% 243.35/49.90  
% 243.35/49.90  Sub-proof #1165 shows that the following formulas are inconsistent:
% 243.35/49.90  ----------------------------------------------------------------
% 243.35/49.90    (1)   ~ (e3 = e0)
% 243.35/49.90    (2)  all_58_14 = e3 & op(e0, e1) = e3
% 243.35/49.90    (3)  all_58_6 = e3
% 243.35/49.90    (4)   ~ (e2 = e0)
% 243.35/49.90    (5)  all_58_14 = e2
% 243.35/49.90    (6)   ~ (e3 = e1)
% 243.35/49.90    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.35/49.90         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.35/49.90    (8)  op(e3, e3) = e1
% 243.35/49.90    (9)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.90             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.35/49.90               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.90               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.35/49.90    (10)   ~ (e3 = e2)
% 243.35/49.90    (11)  all_58_15 = e1
% 243.35/49.90    (12)  op(e2, e3) = all_52_1
% 243.35/49.90    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.90    (14)   ~ (e1 = e0)
% 243.35/49.90    (15)   ~ (all_52_1 = e3)
% 243.35/49.90    (16)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.35/49.90          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.35/49.90            e2)
% 243.35/49.90    (17)   ~ (e2 = e1)
% 243.35/49.90  
% 243.35/49.90  Begin of proof
% 243.35/49.90  | 
% 243.35/49.90  | ALPHA: (2) implies:
% 243.35/49.90  |   (18)  all_58_14 = e3
% 243.35/49.90  | 
% 243.35/49.90  | COMBINE_EQS: (5), (18) imply:
% 243.35/49.90  |   (19)  e3 = e2
% 243.35/49.90  | 
% 243.35/49.90  | COMBINE_EQS: (3), (19) imply:
% 243.35/49.90  |   (20)  all_58_6 = e2
% 243.35/49.90  | 
% 243.35/49.90  | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 243.35/49.90  |            (16), (17), (18), (20) are inconsistent by sub-proof #1166.
% 243.35/49.90  | 
% 243.35/49.90  End of proof
% 243.35/49.90  
% 243.35/49.90  Sub-proof #1166 shows that the following formulas are inconsistent:
% 243.35/49.90  ----------------------------------------------------------------
% 243.35/49.90    (1)   ~ (e3 = e0)
% 243.35/49.90    (2)   ~ (e2 = e0)
% 243.35/49.90    (3)  all_58_6 = e2
% 243.35/49.90    (4)   ~ (e3 = e1)
% 243.35/49.90    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.35/49.90         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.35/49.90    (6)  op(e3, e3) = e1
% 243.35/49.90    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.90             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.35/49.90               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.90               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.35/49.90    (8)   ~ (e3 = e2)
% 243.35/49.90    (9)  all_58_15 = e1
% 243.35/49.90    (10)  op(e2, e3) = all_52_1
% 243.35/49.90    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.90    (12)  all_58_14 = e3
% 243.35/49.90    (13)   ~ (e1 = e0)
% 243.35/49.90    (14)   ~ (all_52_1 = e3)
% 243.35/49.90    (15)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.35/49.90          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.35/49.90            e2)
% 243.35/49.90    (16)   ~ (e2 = e1)
% 243.35/49.90  
% 243.35/49.90  Begin of proof
% 243.35/49.90  | 
% 243.35/49.90  | BETA: splitting (5) gives:
% 243.35/49.90  | 
% 243.35/49.90  | Case 1:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (17)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 243.35/49.90  | |           e3)
% 243.35/49.90  | | 
% 243.35/49.90  | | REF_CLOSE: (4), (6), (10), (11), (14), (17) are inconsistent by sub-proof
% 243.35/49.90  | |            #1208.
% 243.35/49.90  | | 
% 243.35/49.90  | Case 2:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (18)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 243.35/49.90  | |           e3)
% 243.35/49.90  | | 
% 243.35/49.90  | | BETA: splitting (18) gives:
% 243.35/49.90  | | 
% 243.35/49.90  | | Case 1:
% 243.35/49.90  | | | 
% 243.35/49.90  | | |   (19)  all_58_6 = e3 & op(e1, e3) = e3
% 243.35/49.90  | | | 
% 243.35/49.90  | | | ALPHA: (19) implies:
% 243.35/49.90  | | |   (20)  all_58_6 = e3
% 243.35/49.90  | | | 
% 243.35/49.90  | | | REF_CLOSE: (3), (8), (20) are inconsistent by sub-proof #2024.
% 243.35/49.90  | | | 
% 243.35/49.90  | | Case 2:
% 243.35/49.90  | | | 
% 243.35/49.90  | | |   (21)  all_58_12 = e3 & op(e0, e3) = e3
% 243.35/49.90  | | | 
% 243.35/49.90  | | | ALPHA: (21) implies:
% 243.35/49.90  | | |   (22)  all_58_12 = e3
% 243.35/49.90  | | | 
% 243.35/49.90  | | | REF_CLOSE: (1), (2), (7), (8), (9), (12), (13), (15), (16), (22) are
% 243.35/49.90  | | |            inconsistent by sub-proof #1863.
% 243.35/49.90  | | | 
% 243.35/49.90  | | End of split
% 243.35/49.90  | | 
% 243.35/49.90  | End of split
% 243.35/49.90  | 
% 243.35/49.90  End of proof
% 243.35/49.90  
% 243.35/49.90  Sub-proof #1167 shows that the following formulas are inconsistent:
% 243.35/49.90  ----------------------------------------------------------------
% 243.35/49.90    (1)   ~ (e3 = e0)
% 243.35/49.90    (2)  all_58_6 = e3
% 243.35/49.90    (3)   ~ (e2 = e0)
% 243.35/49.90    (4)   ~ (all_52_7 = e3)
% 243.35/49.90    (5)  op(e3, e3) = e1
% 243.35/49.90    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.35/49.90         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.35/49.90    (7)   ~ (e3 = e2)
% 243.35/49.90    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.90         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.90    (9)  op(e0, e2) = all_52_7
% 243.35/49.90    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.90    (11)   ~ (e1 = e0)
% 243.35/49.90    (12)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.35/49.90    (13)   ~ (e2 = e1)
% 243.35/49.90  
% 243.35/49.90  Begin of proof
% 243.35/49.90  | 
% 243.35/49.90  | BETA: splitting (12) gives:
% 243.35/49.90  | 
% 243.35/49.90  | Case 1:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (14)  all_58_12 = e3 & op(e0, e3) = e3
% 243.35/49.90  | | 
% 243.35/49.90  | | ALPHA: (14) implies:
% 243.35/49.90  | |   (15)  all_58_12 = e3
% 243.35/49.90  | | 
% 243.35/49.90  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (13), (15) are
% 243.35/49.90  | |            inconsistent by sub-proof #1532.
% 243.35/49.90  | | 
% 243.35/49.90  | Case 2:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (16)  all_58_13 = e3 & op(e0, e2) = e3
% 243.35/49.90  | | 
% 243.35/49.90  | | REF_CLOSE: (4), (9), (10), (16) are inconsistent by sub-proof #1919.
% 243.35/49.90  | | 
% 243.35/49.90  | End of split
% 243.35/49.90  | 
% 243.35/49.90  End of proof
% 243.35/49.90  
% 243.35/49.90  Sub-proof #1168 shows that the following formulas are inconsistent:
% 243.35/49.90  ----------------------------------------------------------------
% 243.35/49.90    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.35/49.90         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.35/49.90    (2)   ~ (e3 = e0)
% 243.35/49.90    (3)   ~ (e2 = e0)
% 243.35/49.90    (4)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 243.35/49.90         (all_58_11 = e0 & op(e1, e0) = e0)
% 243.35/49.90    (5)   ~ (e3 = e1)
% 243.35/49.90    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.35/49.90         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.35/49.90    (7)  op(e3, e3) = e1
% 243.35/49.90    (8)   ~ (e3 = e2)
% 243.35/49.90    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.35/49.90         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.90    (10)   ~ (all_52_4 = e3)
% 243.35/49.90    (11)  op(e3, e2) = all_52_4
% 243.35/49.90    (12)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.35/49.90          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.35/49.90    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.90    (14)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.35/49.90          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.35/49.90    (15)   ~ (e1 = e0)
% 243.35/49.90    (16)  all_58_9 = e1
% 243.35/49.90    (17)  all_58_10 = e1
% 243.35/49.90    (18)   ~ (e2 = e1)
% 243.35/49.90  
% 243.35/49.90  Begin of proof
% 243.35/49.90  | 
% 243.35/49.90  | BETA: splitting (4) gives:
% 243.35/49.90  | 
% 243.35/49.90  | Case 1:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (19)  all_58_9 = e0 & op(e3, e0) = e0
% 243.35/49.90  | | 
% 243.35/49.90  | | REF_CLOSE: (15), (16), (19) are inconsistent by sub-proof #1696.
% 243.35/49.90  | | 
% 243.35/49.90  | Case 2:
% 243.35/49.90  | | 
% 243.35/49.90  | |   (20)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.35/49.90  | |           e0)
% 243.35/49.90  | | 
% 243.35/49.90  | | BETA: splitting (20) gives:
% 243.35/49.90  | | 
% 243.35/49.90  | | Case 1:
% 243.35/49.90  | | | 
% 243.35/49.90  | | |   (21)  all_58_10 = e0 & op(e2, e0) = e0
% 243.35/49.90  | | | 
% 243.35/49.90  | | | ALPHA: (21) implies:
% 243.35/49.90  | | |   (22)  all_58_10 = e0
% 243.35/49.90  | | | 
% 243.35/49.90  | | | REF_CLOSE: (15), (17), (22) are inconsistent by sub-proof #1173.
% 243.35/49.90  | | | 
% 243.35/49.90  | | Case 2:
% 243.35/49.90  | | | 
% 243.35/49.90  | | |   (23)  all_58_11 = e0 & op(e1, e0) = e0
% 243.35/49.90  | | | 
% 243.35/49.90  | | | ALPHA: (23) implies:
% 243.35/49.90  | | |   (24)  all_58_11 = e0
% 243.35/49.90  | | | 
% 243.35/49.90  | | | BETA: splitting (14) gives:
% 243.35/49.90  | | | 
% 243.35/49.90  | | | Case 1:
% 243.35/49.90  | | | | 
% 243.35/49.91  | | | |   (25)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 243.35/49.91  | | | |           = e2)
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | | REF_CLOSE: (16), (17), (18), (25) are inconsistent by sub-proof #1508.
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | Case 2:
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | |   (26)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 243.35/49.91  | | | |             e0) = e2)
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | | BETA: splitting (26) gives:
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | | Case 1:
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | |   (27)  all_58_11 = e2 & op(e1, e0) = e2
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | | REF_CLOSE: (3), (24), (27) are inconsistent by sub-proof #2216.
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | Case 2:
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | |   (28)  all_58_15 = e2 & op(e0, e0) = e2
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | | ALPHA: (28) implies:
% 243.35/49.91  | | | | |   (29)  all_58_15 = e2
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 243.35/49.91  | | | | |            (13), (15), (16), (17), (18), (24), (29) are inconsistent
% 243.35/49.91  | | | | |            by sub-proof #1169.
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | End of split
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | End of split
% 243.35/49.91  | | | 
% 243.35/49.91  | | End of split
% 243.35/49.91  | | 
% 243.35/49.91  | End of split
% 243.35/49.91  | 
% 243.35/49.91  End of proof
% 243.35/49.91  
% 243.35/49.91  Sub-proof #1169 shows that the following formulas are inconsistent:
% 243.35/49.91  ----------------------------------------------------------------
% 243.35/49.91    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.35/49.91         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.35/49.91    (2)   ~ (e3 = e0)
% 243.35/49.91    (3)   ~ (e2 = e0)
% 243.35/49.91    (4)   ~ (e3 = e1)
% 243.35/49.91    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.35/49.91         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.35/49.91    (6)  op(e3, e3) = e1
% 243.35/49.91    (7)  all_58_15 = e2
% 243.35/49.91    (8)   ~ (e3 = e2)
% 243.35/49.91    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.35/49.91         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.91    (10)   ~ (all_52_4 = e3)
% 243.35/49.91    (11)  op(e3, e2) = all_52_4
% 243.35/49.91    (12)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.35/49.91          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.35/49.91    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.91    (14)  all_58_11 = e0
% 243.35/49.91    (15)   ~ (e1 = e0)
% 243.35/49.91    (16)  all_58_9 = e1
% 243.35/49.91    (17)  all_58_10 = e1
% 243.35/49.91    (18)   ~ (e2 = e1)
% 243.35/49.91  
% 243.35/49.91  Begin of proof
% 243.35/49.91  | 
% 243.35/49.91  | BETA: splitting (5) gives:
% 243.35/49.91  | 
% 243.35/49.91  | Case 1:
% 243.35/49.91  | | 
% 243.35/49.91  | |   (19)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 243.35/49.91  | |           e3)
% 243.35/49.91  | | 
% 243.35/49.91  | | REF_CLOSE: (4), (6), (10), (11), (13), (19) are inconsistent by sub-proof
% 243.35/49.91  | |            #1401.
% 243.35/49.91  | | 
% 243.35/49.91  | Case 2:
% 243.35/49.91  | | 
% 243.35/49.91  | |   (20)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 243.35/49.91  | |           e3)
% 243.35/49.91  | | 
% 243.35/49.91  | | BETA: splitting (20) gives:
% 243.35/49.91  | | 
% 243.35/49.91  | | Case 1:
% 243.35/49.91  | | | 
% 243.35/49.91  | | |   (21)  all_58_4 = e3 & op(e3, e1) = e3
% 243.35/49.91  | | | 
% 243.35/49.91  | | | ALPHA: (21) implies:
% 243.35/49.91  | | |   (22)  all_58_4 = e3
% 243.35/49.91  | | | 
% 243.35/49.91  | | | BETA: splitting (12) gives:
% 243.35/49.91  | | | 
% 243.35/49.91  | | | Case 1:
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | |   (23)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0)
% 243.35/49.91  | | | |           = e3)
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | | BETA: splitting (23) gives:
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | | Case 1:
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | |   (24)  all_58_9 = e3 & op(e3, e0) = e3
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (13), (15), (16), (18), (22),
% 243.35/49.91  | | | | |            (24) are inconsistent by sub-proof #1172.
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | Case 2:
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | |   (25)  all_58_10 = e3 & op(e2, e0) = e3
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13),
% 243.35/49.91  | | | | |            (15), (17), (18), (22), (25) are inconsistent by sub-proof
% 243.35/49.91  | | | | |            #1171.
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | End of split
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | Case 2:
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | |   (26)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 243.35/49.91  | | | |             e0) = e3)
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | | BETA: splitting (26) gives:
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | | Case 1:
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | |   (27)  all_58_11 = e3 & op(e1, e0) = e3
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | | REF_CLOSE: (2), (14), (27) are inconsistent by sub-proof #2091.
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | Case 2:
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | |   (28)  all_58_15 = e3 & op(e0, e0) = e3
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | | REF_CLOSE: (7), (8), (28) are inconsistent by sub-proof #1170.
% 243.35/49.91  | | | | | 
% 243.35/49.91  | | | | End of split
% 243.35/49.91  | | | | 
% 243.35/49.91  | | | End of split
% 243.35/49.91  | | | 
% 243.35/49.91  | | Case 2:
% 243.35/49.91  | | | 
% 243.35/49.91  | | |   (29)  all_58_9 = e3 & op(e3, e0) = e3
% 243.35/49.91  | | | 
% 243.35/49.91  | | | ALPHA: (29) implies:
% 243.35/49.91  | | |   (30)  all_58_9 = e3
% 243.35/49.91  | | | 
% 243.35/49.91  | | | REF_CLOSE: (4), (16), (30) are inconsistent by sub-proof #1709.
% 243.35/49.91  | | | 
% 243.35/49.91  | | End of split
% 243.35/49.91  | | 
% 243.35/49.91  | End of split
% 243.35/49.91  | 
% 243.35/49.91  End of proof
% 243.35/49.91  
% 243.35/49.91  Sub-proof #1170 shows that the following formulas are inconsistent:
% 243.35/49.91  ----------------------------------------------------------------
% 243.35/49.91    (1)  all_58_15 = e3 & op(e0, e0) = e3
% 243.35/49.91    (2)  all_58_15 = e2
% 243.35/49.91    (3)   ~ (e3 = e2)
% 243.35/49.91  
% 243.35/49.91  Begin of proof
% 243.35/49.91  | 
% 243.35/49.91  | ALPHA: (1) implies:
% 243.35/49.91  |   (4)  all_58_15 = e3
% 243.35/49.91  | 
% 243.35/49.91  | COMBINE_EQS: (2), (4) imply:
% 243.35/49.91  |   (5)  e3 = e2
% 243.35/49.91  | 
% 243.35/49.91  | REDUCE: (3), (5) imply:
% 243.35/49.91  |   (6)  $false
% 243.35/49.91  | 
% 243.35/49.91  | CLOSE: (6) is inconsistent.
% 243.35/49.91  | 
% 243.35/49.91  End of proof
% 243.35/49.91  
% 243.35/49.91  Sub-proof #1171 shows that the following formulas are inconsistent:
% 243.35/49.91  ----------------------------------------------------------------
% 243.35/49.91    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.35/49.91         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.35/49.91    (2)   ~ (e3 = e0)
% 243.35/49.91    (3)   ~ (e2 = e0)
% 243.35/49.91    (4)   ~ (e3 = e1)
% 243.35/49.91    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.35/49.91         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.35/49.91    (6)  all_58_10 = e3 & op(e2, e0) = e3
% 243.35/49.91    (7)  op(e3, e3) = e1
% 243.35/49.91    (8)   ~ (e3 = e2)
% 243.35/49.91    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.35/49.91         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.91    (10)   ~ (all_52_4 = e3)
% 243.35/49.91    (11)  op(e3, e2) = all_52_4
% 243.35/49.91    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.91    (13)   ~ (e1 = e0)
% 243.35/49.91    (14)  all_58_4 = e3
% 243.35/49.91    (15)  all_58_10 = e1
% 243.35/49.91    (16)   ~ (e2 = e1)
% 243.35/49.91  
% 243.35/49.91  Begin of proof
% 243.35/49.91  | 
% 243.35/49.91  | ALPHA: (6) implies:
% 243.35/49.91  |   (17)  all_58_10 = e3
% 243.35/49.91  | 
% 243.35/49.91  | COMBINE_EQS: (15), (17) imply:
% 243.35/49.91  |   (18)  e3 = e1
% 243.35/49.91  | 
% 243.35/49.91  | COMBINE_EQS: (14), (18) imply:
% 243.35/49.91  |   (19)  all_58_4 = e1
% 243.35/49.91  | 
% 243.35/49.91  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 243.35/49.91  |            (16), (19) are inconsistent by sub-proof #1468.
% 243.35/49.91  | 
% 243.35/49.91  End of proof
% 243.35/49.91  
% 243.35/49.91  Sub-proof #1172 shows that the following formulas are inconsistent:
% 243.35/49.91  ----------------------------------------------------------------
% 243.35/49.91    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.35/49.91         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.35/49.91    (2)   ~ (e3 = e0)
% 243.35/49.91    (3)   ~ (e2 = e0)
% 243.35/49.91    (4)  all_58_9 = e3 & op(e3, e0) = e3
% 243.35/49.91    (5)  op(e3, e3) = e1
% 243.35/49.91    (6)   ~ (e3 = e2)
% 243.35/49.91    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.35/49.91         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.91    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.91    (9)   ~ (e1 = e0)
% 243.35/49.91    (10)  all_58_4 = e3
% 243.35/49.91    (11)  all_58_9 = e1
% 243.35/49.91    (12)   ~ (e2 = e1)
% 243.35/49.91  
% 243.35/49.91  Begin of proof
% 243.35/49.91  | 
% 243.35/49.91  | ALPHA: (4) implies:
% 243.35/49.91  |   (13)  all_58_9 = e3
% 243.35/49.91  | 
% 243.35/49.91  | COMBINE_EQS: (11), (13) imply:
% 243.35/49.91  |   (14)  e3 = e1
% 243.35/49.91  | 
% 243.35/49.91  | COMBINE_EQS: (10), (14) imply:
% 243.35/49.91  |   (15)  all_58_4 = e1
% 243.35/49.91  | 
% 243.35/49.91  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (12), (13), (15) are
% 243.35/49.91  |            inconsistent by sub-proof #1469.
% 243.35/49.91  | 
% 243.35/49.91  End of proof
% 243.35/49.91  
% 243.35/49.91  Sub-proof #1173 shows that the following formulas are inconsistent:
% 243.35/49.91  ----------------------------------------------------------------
% 243.35/49.91    (1)  all_58_10 = e1
% 243.35/49.91    (2)  all_58_10 = e0
% 243.35/49.91    (3)   ~ (e1 = e0)
% 243.35/49.91  
% 243.35/49.91  Begin of proof
% 243.35/49.91  | 
% 243.35/49.91  | COMBINE_EQS: (1), (2) imply:
% 243.35/49.91  |   (4)  e1 = e0
% 243.35/49.91  | 
% 243.35/49.91  | SIMP: (4) implies:
% 243.35/49.91  |   (5)  e1 = e0
% 243.35/49.91  | 
% 243.35/49.91  | REDUCE: (3), (5) imply:
% 243.35/49.91  |   (6)  $false
% 243.35/49.91  | 
% 243.35/49.91  | CLOSE: (6) is inconsistent.
% 243.35/49.91  | 
% 243.35/49.91  End of proof
% 243.35/49.91  
% 243.35/49.91  Sub-proof #1174 shows that the following formulas are inconsistent:
% 243.35/49.91  ----------------------------------------------------------------
% 243.35/49.91    (1)  op(e0, e0) = e1
% 243.35/49.91    (2)  all_58_3 = e3 & op(e2, e2) = e3
% 243.35/49.91    (3)   ~ (e3 = e0)
% 243.35/49.91    (4)   ~ (e2 = e0)
% 243.35/49.91    (5)   ~ (e3 = e1)
% 243.35/49.91    (6)  all_58_3 = e1
% 243.35/49.91    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.91             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.35/49.91               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.91               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.35/49.91    (8)   ~ (e3 = e2)
% 243.35/49.91    (9)  all_58_15 = e1
% 243.35/49.91    (10)  all_58_9 = e3
% 243.35/49.91    (11)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.35/49.91          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.35/49.91    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.91    (13)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.35/49.91          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.35/49.91    (14)   ~ (e1 = e0)
% 243.35/49.91    (15)   ~ (all_52_13 = e3)
% 243.35/49.91    (16)  op(e2, e0) = all_52_13
% 243.35/49.91    (17)   ~ (e2 = e1)
% 243.35/49.91  
% 243.35/49.91  Begin of proof
% 243.35/49.91  | 
% 243.35/49.91  | ALPHA: (2) implies:
% 243.35/49.91  |   (18)  all_58_3 = e3
% 243.35/49.91  | 
% 243.35/49.91  | COMBINE_EQS: (6), (18) imply:
% 243.35/49.91  |   (19)  e3 = e1
% 243.35/49.91  | 
% 243.35/49.91  | SIMP: (19) implies:
% 243.35/49.91  |   (20)  e3 = e1
% 243.35/49.91  | 
% 243.35/49.91  | COMBINE_EQS: (10), (20) imply:
% 243.35/49.91  |   (21)  all_58_9 = e1
% 243.35/49.91  | 
% 243.35/49.91  | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14), (15),
% 243.35/49.91  |            (16), (17), (21) are inconsistent by sub-proof #1601.
% 243.35/49.91  | 
% 243.35/49.91  End of proof
% 243.35/49.91  
% 243.35/49.91  Sub-proof #1175 shows that the following formulas are inconsistent:
% 243.35/49.91  ----------------------------------------------------------------
% 243.35/49.91    (1)  op(e0, e0) = e1
% 243.35/49.91    (2)   ~ (e3 = e0)
% 243.35/49.91    (3)  op(e1, e2) = e1
% 243.35/49.91    (4)   ~ (e2 = e0)
% 243.35/49.91    (5)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) = all_38_1
% 243.35/49.91           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e3, e1) =
% 243.35/49.91           all_38_1 & $i(all_38_1))
% 243.35/49.91    (6)   ~ (e3 = e1)
% 243.35/49.91    (7)  op(e3, e1) = e0
% 243.35/49.91    (8)  op(e1, e2) = e3
% 243.35/49.91    (9)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.91             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.35/49.91               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.91               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.35/49.91    (10)   ~ (e3 = e2)
% 243.35/49.91    (11)  all_58_15 = e1
% 243.35/49.91    (12)  all_58_9 = e3
% 243.35/49.91    (13)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.35/49.91          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.35/49.91    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.91    (15)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.35/49.91          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.35/49.91    (16)  op(e3, e1) = all_10_1
% 243.35/49.91    (17)   ~ (e1 = e0)
% 243.35/49.91    (18)   ~ (all_52_13 = e3)
% 243.35/49.91    (19)  op(e2, e0) = all_52_13
% 243.35/49.91    (20)   ~ (e2 = e1)
% 243.35/49.91  
% 243.35/49.91  Begin of proof
% 243.35/49.91  | 
% 243.35/49.91  | BETA: splitting (5) gives:
% 243.35/49.91  | 
% 243.35/49.91  | Case 1:
% 243.35/49.91  | | 
% 243.35/49.91  | | 
% 243.35/49.91  | | GROUND_INST: instantiating (14) with e3, e1, e2, e1, simplifying with (3),
% 243.35/49.91  | |              (8) gives:
% 243.35/49.91  | |   (21)  e3 = e1
% 243.35/49.91  | | 
% 243.35/49.91  | | COMBINE_EQS: (12), (21) imply:
% 243.35/49.91  | |   (22)  all_58_9 = e1
% 243.35/49.91  | | 
% 243.35/49.91  | | REF_CLOSE: (1), (2), (4), (6), (9), (10), (11), (13), (14), (15), (17),
% 243.35/49.91  | |            (18), (19), (20), (22) are inconsistent by sub-proof #1601.
% 243.35/49.91  | | 
% 243.35/49.91  | Case 2:
% 243.35/49.91  | | 
% 243.35/49.91  | |   (23)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1)
% 243.35/49.91  | | 
% 243.35/49.91  | | ALPHA: (23) implies:
% 243.35/49.91  | |   (24)   ~ (all_38_1 = e0)
% 243.35/49.91  | |   (25)  op(e3, e1) = all_38_1
% 243.35/49.91  | | 
% 243.35/49.91  | | REF_CLOSE: (7), (14), (16), (24), (25) are inconsistent by sub-proof #1195.
% 243.35/49.91  | | 
% 243.35/49.91  | End of split
% 243.35/49.91  | 
% 243.35/49.91  End of proof
% 243.35/49.91  
% 243.35/49.91  Sub-proof #1176 shows that the following formulas are inconsistent:
% 243.35/49.91  ----------------------------------------------------------------
% 243.35/49.91    (1)   ~ (e3 = e0)
% 243.35/49.91    (2)  all_58_7 = e0 & op(e1, e2) = e0
% 243.35/49.91    (3)   ~ (e3 = e1)
% 243.35/49.91    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.35/49.91         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.35/49.91    (5)  op(e3, e3) = e1
% 243.35/49.91    (6)   ~ (e3 = e2)
% 243.35/49.91    (7)  all_58_7 = e3
% 243.35/49.91    (8)  all_58_9 = e3
% 243.35/49.91    (9)  all_58_1 = e2
% 243.35/49.91    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.91    (11)  all_58_4 = e0
% 243.35/49.91  
% 243.35/49.91  Begin of proof
% 243.35/49.91  | 
% 243.35/49.91  | ALPHA: (2) implies:
% 243.35/49.91  |   (12)  all_58_7 = e0
% 243.35/49.91  | 
% 243.35/49.91  | COMBINE_EQS: (7), (12) imply:
% 243.35/49.91  |   (13)  e3 = e0
% 243.35/49.91  | 
% 243.35/49.91  | COMBINE_EQS: (8), (13) imply:
% 243.35/49.91  |   (14)  all_58_9 = e0
% 243.35/49.91  | 
% 243.35/49.91  | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (11), (14) are inconsistent by
% 243.35/49.91  |            sub-proof #1191.
% 243.35/49.91  | 
% 243.35/49.91  End of proof
% 243.35/49.91  
% 243.35/49.91  Sub-proof #1177 shows that the following formulas are inconsistent:
% 243.35/49.91  ----------------------------------------------------------------
% 243.35/49.91    (1)  op(e0, e0) = e1
% 243.35/49.91    (2)   ~ (e3 = e0)
% 243.35/49.91    (3)  op(e1, e0) = e0
% 243.35/49.91    (4)   ~ (e2 = e0)
% 243.35/49.91    (5)  op(e1, e0) = all_52_14
% 243.35/49.91    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.35/49.91         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.35/49.91    (7)  all_58_3 = e1
% 243.35/49.92    (8)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.92             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.35/49.92               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.92               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.35/49.92    (9)   ~ (e3 = e2)
% 243.35/49.92    (10)   ~ (all_52_14 = e1)
% 243.35/49.92    (11)  op(e2, e2) = e1
% 243.35/49.92    (12)  all_58_15 = e1
% 243.35/49.92    (13)  all_58_9 = e3
% 243.35/49.92    (14)  op(e3, e0) = e3
% 243.35/49.92    (15)   ~ (all_52_14 = e3)
% 243.35/49.92    (16)   ~ (all_52_13 = all_52_14)
% 243.35/49.92    (17)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.35/49.92          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 243.35/49.92    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.92    (19)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.35/49.92          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.35/49.92    (20)  all_58_11 = e0
% 243.35/49.92    (21)   ~ (e1 = e0)
% 243.35/49.92    (22)  op(e1, all_52_14) = e1
% 243.35/49.92    (23)  all_58_2 = e3
% 243.35/49.92    (24)  op(e2, e0) = all_52_13
% 243.35/49.92    (25)   ~ (e2 = e1)
% 243.35/49.92  
% 243.35/49.92  Begin of proof
% 243.35/49.92  | 
% 243.35/49.92  | BETA: splitting (19) gives:
% 243.35/49.92  | 
% 243.35/49.92  | Case 1:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (26)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 243.35/49.92  | |           e2)
% 243.35/49.92  | | 
% 243.35/49.92  | | BETA: splitting (26) gives:
% 243.35/49.92  | | 
% 243.35/49.92  | | Case 1:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (27)  all_58_9 = e2 & op(e3, e0) = e2
% 243.35/49.92  | | | 
% 243.35/49.92  | | | ALPHA: (27) implies:
% 243.35/49.92  | | |   (28)  op(e3, e0) = e2
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REF_CLOSE: (9), (14), (18), (28) are inconsistent by sub-proof #2125.
% 243.35/49.92  | | | 
% 243.35/49.92  | | Case 2:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (29)  all_58_10 = e2 & op(e2, e0) = e2
% 243.35/49.92  | | | 
% 243.35/49.92  | | | ALPHA: (29) implies:
% 243.35/49.92  | | |   (30)  op(e2, e0) = e2
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 243.35/49.92  | | |            (15), (16), (17), (18), (21), (22), (23), (24), (25), (30) are
% 243.35/49.92  | | |            inconsistent by sub-proof #1179.
% 243.35/49.92  | | | 
% 243.35/49.92  | | End of split
% 243.35/49.92  | | 
% 243.35/49.92  | Case 2:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (31)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.35/49.92  | |           e2)
% 243.35/49.92  | | 
% 243.35/49.92  | | REF_CLOSE: (4), (12), (20), (25), (31) are inconsistent by sub-proof #1178.
% 243.35/49.92  | | 
% 243.35/49.92  | End of split
% 243.35/49.92  | 
% 243.35/49.92  End of proof
% 243.35/49.92  
% 243.35/49.92  Sub-proof #1178 shows that the following formulas are inconsistent:
% 243.35/49.92  ----------------------------------------------------------------
% 243.35/49.92    (1)   ~ (e2 = e0)
% 243.35/49.92    (2)  all_58_15 = e1
% 243.35/49.92    (3)  all_58_11 = e0
% 243.35/49.92    (4)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.35/49.92    (5)   ~ (e2 = e1)
% 243.35/49.92  
% 243.35/49.92  Begin of proof
% 243.35/49.92  | 
% 243.35/49.92  | BETA: splitting (4) gives:
% 243.35/49.92  | 
% 243.35/49.92  | Case 1:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (6)  all_58_11 = e2 & op(e1, e0) = e2
% 243.35/49.92  | | 
% 243.35/49.92  | | ALPHA: (6) implies:
% 243.35/49.92  | |   (7)  all_58_11 = e2
% 243.35/49.92  | | 
% 243.35/49.92  | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #2110.
% 243.35/49.92  | | 
% 243.35/49.92  | Case 2:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (8)  all_58_15 = e2 & op(e0, e0) = e2
% 243.35/49.92  | | 
% 243.35/49.92  | | ALPHA: (8) implies:
% 243.35/49.92  | |   (9)  all_58_15 = e2
% 243.35/49.92  | | 
% 243.35/49.92  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #2231.
% 243.35/49.92  | | 
% 243.35/49.92  | End of split
% 243.35/49.92  | 
% 243.35/49.92  End of proof
% 243.35/49.92  
% 243.35/49.92  Sub-proof #1179 shows that the following formulas are inconsistent:
% 243.35/49.92  ----------------------------------------------------------------
% 243.35/49.92    (1)  op(e0, e0) = e1
% 243.35/49.92    (2)   ~ (e3 = e0)
% 243.35/49.92    (3)  op(e1, e0) = e0
% 243.35/49.92    (4)   ~ (e2 = e0)
% 243.35/49.92    (5)  op(e1, e0) = all_52_14
% 243.35/49.92    (6)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.35/49.92         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.35/49.92    (7)  all_58_3 = e1
% 243.35/49.92    (8)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.92             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.35/49.92               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.92               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.35/49.92    (9)   ~ (e3 = e2)
% 243.35/49.92    (10)   ~ (all_52_14 = e1)
% 243.35/49.92    (11)  op(e2, e2) = e1
% 243.35/49.92    (12)  op(e2, e0) = e2
% 243.35/49.92    (13)  all_58_9 = e3
% 243.35/49.92    (14)   ~ (all_52_14 = e3)
% 243.35/49.92    (15)   ~ (all_52_13 = all_52_14)
% 243.35/49.92    (16)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.35/49.92          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 243.35/49.92    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.92    (18)   ~ (e1 = e0)
% 243.35/49.92    (19)  op(e1, all_52_14) = e1
% 243.35/49.92    (20)  all_58_2 = e3
% 243.35/49.92    (21)  op(e2, e0) = all_52_13
% 243.35/49.92    (22)   ~ (e2 = e1)
% 243.35/49.92  
% 243.35/49.92  Begin of proof
% 243.35/49.92  | 
% 243.35/49.92  | BETA: splitting (16) gives:
% 243.35/49.92  | 
% 243.35/49.92  | Case 1:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (23)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 243.35/49.92  | |           e0)
% 243.35/49.92  | | 
% 243.35/49.92  | | BETA: splitting (23) gives:
% 243.35/49.92  | | 
% 243.35/49.92  | | Case 1:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (24)  all_58_2 = e0 & op(e2, e3) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REF_CLOSE: (2), (20), (24) are inconsistent by sub-proof #1351.
% 243.35/49.92  | | | 
% 243.35/49.92  | | Case 2:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (25)  all_58_3 = e0 & op(e2, e2) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REF_CLOSE: (7), (18), (25) are inconsistent by sub-proof #1180.
% 243.35/49.92  | | | 
% 243.35/49.92  | | End of split
% 243.35/49.92  | | 
% 243.35/49.92  | Case 2:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (26)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.35/49.92  | |           e0)
% 243.35/49.92  | | 
% 243.35/49.92  | | BETA: splitting (26) gives:
% 243.35/49.92  | | 
% 243.35/49.92  | | Case 1:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (27)  all_58_5 = e0 & op(e2, e1) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | ALPHA: (27) implies:
% 243.35/49.92  | | |   (28)  op(e2, e1) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | BETA: splitting (8) gives:
% 243.35/49.92  | | | 
% 243.35/49.92  | | | Case 1:
% 243.35/49.92  | | | | 
% 243.35/49.92  | | | |   (29)  all_58_15 = e0 & op(e0, e0) = e0
% 243.35/49.92  | | | | 
% 243.35/49.92  | | | | ALPHA: (29) implies:
% 243.35/49.92  | | | |   (30)  op(e0, e0) = e0
% 243.35/49.92  | | | | 
% 243.35/49.92  | | | | REF_CLOSE: (1), (17), (18), (30) are inconsistent by sub-proof #2274.
% 243.35/49.92  | | | | 
% 243.35/49.92  | | | Case 2:
% 243.35/49.92  | | | | 
% 243.35/49.92  | | | |   (31)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 243.35/49.92  | | | |               e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 243.35/49.92  | | | |         ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 243.35/49.92  | | | |               e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 243.35/49.92  | | | | 
% 243.35/49.92  | | | | ALPHA: (31) implies:
% 243.35/49.92  | | | |   (32)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 243.35/49.92  | | | |           = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.35/49.92  | | | | 
% 243.35/49.92  | | | | BETA: splitting (6) gives:
% 243.35/49.92  | | | | 
% 243.35/49.92  | | | | Case 1:
% 243.35/49.92  | | | | | 
% 243.35/49.92  | | | | |   (33)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2,
% 243.35/49.92  | | | | |             e2) = e2)
% 243.35/49.92  | | | | | 
% 243.35/49.92  | | | | | REF_CLOSE: (9), (11), (17), (20), (22), (33) are inconsistent by
% 243.35/49.92  | | | | |            sub-proof #1209.
% 243.35/49.92  | | | | | 
% 243.35/49.92  | | | | Case 2:
% 243.35/49.92  | | | | | 
% 243.35/49.92  | | | | |   (34)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2,
% 243.35/49.92  | | | | |             e0) = e2)
% 243.35/49.92  | | | | | 
% 243.35/49.92  | | | | | BETA: splitting (34) gives:
% 243.35/49.92  | | | | | 
% 243.35/49.92  | | | | | Case 1:
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | |   (35)  all_58_5 = e2 & op(e2, e1) = e2
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | | ALPHA: (35) implies:
% 243.35/49.92  | | | | | |   (36)  op(e2, e1) = e2
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | | REF_CLOSE: (4), (17), (28), (36) are inconsistent by sub-proof
% 243.35/49.92  | | | | | |            #1906.
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | Case 2:
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | |   (37)  all_58_10 = e2 & op(e2, e0) = e2
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | | GROUND_INST: instantiating (17) with all_52_14, e0, e0, e1,
% 243.35/49.92  | | | | | |              simplifying with (3), (5) gives:
% 243.35/49.92  | | | | | |   (38)  all_52_14 = e0
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | | GROUND_INST: instantiating (17) with all_52_13, e2, e0, e2,
% 243.35/49.92  | | | | | |              simplifying with (12), (21) gives:
% 243.35/49.92  | | | | | |   (39)  all_52_13 = e2
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | | REDUCE: (14), (38) imply:
% 243.35/49.92  | | | | | |   (40)   ~ (e3 = e0)
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | | REDUCE: (10), (38) imply:
% 243.35/49.92  | | | | | |   (41)   ~ (e1 = e0)
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | | REDUCE: (19), (38) imply:
% 243.35/49.92  | | | | | |   (42)  op(e1, e0) = e1
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | | REF_CLOSE: (2), (4), (12), (13), (17), (18), (32), (42) are
% 243.35/49.92  | | | | | |            inconsistent by sub-proof #2101.
% 243.35/49.92  | | | | | | 
% 243.35/49.92  | | | | | End of split
% 243.35/49.92  | | | | | 
% 243.35/49.92  | | | | End of split
% 243.35/49.92  | | | | 
% 243.35/49.92  | | | End of split
% 243.35/49.92  | | | 
% 243.35/49.92  | | Case 2:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (43)  all_58_10 = e0 & op(e2, e0) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | ALPHA: (43) implies:
% 243.35/49.92  | | |   (44)  op(e2, e0) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REF_CLOSE: (4), (12), (17), (44) are inconsistent by sub-proof #2121.
% 243.35/49.92  | | | 
% 243.35/49.92  | | End of split
% 243.35/49.92  | | 
% 243.35/49.92  | End of split
% 243.35/49.92  | 
% 243.35/49.92  End of proof
% 243.35/49.92  
% 243.35/49.92  Sub-proof #1180 shows that the following formulas are inconsistent:
% 243.35/49.92  ----------------------------------------------------------------
% 243.35/49.92    (1)  all_58_3 = e0 & op(e2, e2) = e0
% 243.35/49.92    (2)  all_58_3 = e1
% 243.35/49.92    (3)   ~ (e1 = e0)
% 243.35/49.92  
% 243.35/49.92  Begin of proof
% 243.35/49.92  | 
% 243.35/49.92  | ALPHA: (1) implies:
% 243.35/49.92  |   (4)  all_58_3 = e0
% 243.35/49.92  | 
% 243.35/49.92  | COMBINE_EQS: (2), (4) imply:
% 243.35/49.92  |   (5)  e1 = e0
% 243.35/49.92  | 
% 243.35/49.92  | REDUCE: (3), (5) imply:
% 243.35/49.92  |   (6)  $false
% 243.35/49.92  | 
% 243.35/49.92  | CLOSE: (6) is inconsistent.
% 243.35/49.92  | 
% 243.35/49.92  End of proof
% 243.35/49.92  
% 243.35/49.92  Sub-proof #1181 shows that the following formulas are inconsistent:
% 243.35/49.92  ----------------------------------------------------------------
% 243.35/49.92    (1)  op(e2, all_52_13) = e2
% 243.35/49.92    (2)   ~ (e2 = e0)
% 243.35/49.92    (3)  all_58_10 = e0 & op(e2, e0) = e0
% 243.35/49.92    (4)  op(e1, e0) = all_52_14
% 243.35/49.92    (5)   ~ (e3 = e2)
% 243.35/49.92    (6)  op(e2, e0) = e0
% 243.35/49.92    (7)  all_58_15 = e1
% 243.35/49.92    (8)  op(e3, e0) = e3
% 243.35/49.92    (9)   ~ (all_52_13 = all_52_14)
% 243.35/49.92    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.92    (11)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.35/49.92          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.35/49.92    (12)  op(e2, e0) = all_52_13
% 243.35/49.92    (13)   ~ (e2 = e1)
% 243.35/49.92  
% 243.35/49.92  Begin of proof
% 243.35/49.92  | 
% 243.35/49.92  | BETA: splitting (11) gives:
% 243.35/49.92  | 
% 243.35/49.92  | Case 1:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (14)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 243.35/49.92  | |           e2)
% 243.35/49.92  | | 
% 243.35/49.92  | | REF_CLOSE: (2), (5), (6), (8), (10), (14) are inconsistent by sub-proof
% 243.35/49.92  | |            #1182.
% 243.35/49.92  | | 
% 243.35/49.92  | Case 2:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (15)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.35/49.92  | |           e2)
% 243.35/49.92  | | 
% 243.35/49.92  | | BETA: splitting (15) gives:
% 243.35/49.92  | | 
% 243.35/49.92  | | Case 1:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (16)  all_58_11 = e2 & op(e1, e0) = e2
% 243.35/49.92  | | | 
% 243.35/49.92  | | | ALPHA: (16) implies:
% 243.35/49.92  | | |   (17)  op(e1, e0) = e2
% 243.35/49.92  | | | 
% 243.35/49.92  | | | GROUND_INST: instantiating (10) with all_52_14, e2, e0, e1, simplifying
% 243.35/49.92  | | |              with (4), (17) gives:
% 243.35/49.92  | | |   (18)  all_52_14 = e2
% 243.35/49.92  | | | 
% 243.35/49.92  | | | GROUND_INST: instantiating (10) with all_52_13, e0, e0, e2, simplifying
% 243.35/49.92  | | |              with (6), (12) gives:
% 243.35/49.92  | | |   (19)  all_52_13 = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REDUCE: (9), (18), (19) imply:
% 243.35/49.92  | | |   (20)   ~ (e2 = e0)
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REDUCE: (1), (19) imply:
% 243.35/49.92  | | |   (21)  op(e2, e0) = e2
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REF_CLOSE: (2), (6), (10), (21) are inconsistent by sub-proof #2121.
% 243.35/49.92  | | | 
% 243.35/49.92  | | Case 2:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (22)  all_58_15 = e2 & op(e0, e0) = e2
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REF_CLOSE: (7), (13), (22) are inconsistent by sub-proof #1917.
% 243.35/49.92  | | | 
% 243.35/49.92  | | End of split
% 243.35/49.92  | | 
% 243.35/49.92  | End of split
% 243.35/49.92  | 
% 243.35/49.92  End of proof
% 243.35/49.92  
% 243.35/49.92  Sub-proof #1182 shows that the following formulas are inconsistent:
% 243.35/49.92  ----------------------------------------------------------------
% 243.35/49.92    (1)   ~ (e2 = e0)
% 243.35/49.92    (2)   ~ (e3 = e2)
% 243.35/49.92    (3)  op(e2, e0) = e0
% 243.35/49.92    (4)  op(e3, e0) = e3
% 243.35/49.92    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.92    (6)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.35/49.92  
% 243.35/49.92  Begin of proof
% 243.35/49.92  | 
% 243.35/49.92  | BETA: splitting (6) gives:
% 243.35/49.92  | 
% 243.35/49.92  | Case 1:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (7)  all_58_9 = e2 & op(e3, e0) = e2
% 243.35/49.92  | | 
% 243.35/49.92  | | ALPHA: (7) implies:
% 243.35/49.92  | |   (8)  op(e3, e0) = e2
% 243.35/49.92  | | 
% 243.35/49.92  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2125.
% 243.35/49.92  | | 
% 243.35/49.92  | Case 2:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (9)  all_58_10 = e2 & op(e2, e0) = e2
% 243.35/49.92  | | 
% 243.35/49.92  | | ALPHA: (9) implies:
% 243.35/49.92  | |   (10)  op(e2, e0) = e2
% 243.35/49.92  | | 
% 243.35/49.92  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2121.
% 243.35/49.92  | | 
% 243.35/49.92  | End of split
% 243.35/49.92  | 
% 243.35/49.92  End of proof
% 243.35/49.92  
% 243.35/49.92  Sub-proof #1183 shows that the following formulas are inconsistent:
% 243.35/49.92  ----------------------------------------------------------------
% 243.35/49.92    (1)  op(e0, e0) = e1
% 243.35/49.92    (2)   ~ (e3 = e0)
% 243.35/49.92    (3)  op(e1, e1) = e1
% 243.35/49.92    (4)   ~ (e2 = e0)
% 243.35/49.92    (5)  all_58_6 = e2
% 243.35/49.92    (6)  op(e1, e0) = all_52_14
% 243.35/49.92    (7)  op(e0, e3) = all_52_3
% 243.35/49.92    (8)  op(e0, all_52_3) = e0
% 243.35/49.92    (9)  op(e3, e3) = e1
% 243.35/49.92    (10)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.35/49.92              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.35/49.92                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.35/49.92                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.35/49.92    (11)   ~ (all_52_14 = e1)
% 243.35/49.92    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.35/49.92          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.35/49.92    (13)  all_58_7 = e3
% 243.35/49.92    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.35/49.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.35/49.92    (15)   ~ (e1 = e0)
% 243.35/49.92    (16)  all_58_2 = e3
% 243.35/49.92    (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.35/49.92          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.35/49.92  
% 243.35/49.92  Begin of proof
% 243.35/49.92  | 
% 243.35/49.92  | BETA: splitting (17) gives:
% 243.35/49.92  | 
% 243.35/49.92  | Case 1:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (18)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 243.35/49.92  | |           e0)
% 243.35/49.92  | | 
% 243.35/49.92  | | BETA: splitting (18) gives:
% 243.35/49.92  | | 
% 243.35/49.92  | | Case 1:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (19)  all_58_6 = e0 & op(e1, e3) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REF_CLOSE: (4), (5), (19) are inconsistent by sub-proof #1678.
% 243.35/49.92  | | | 
% 243.35/49.92  | | Case 2:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (20)  all_58_7 = e0 & op(e1, e2) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REF_CLOSE: (2), (13), (20) are inconsistent by sub-proof #2034.
% 243.35/49.92  | | | 
% 243.35/49.92  | | End of split
% 243.35/49.92  | | 
% 243.35/49.92  | Case 2:
% 243.35/49.92  | | 
% 243.35/49.92  | |   (21)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.35/49.92  | |           e0)
% 243.35/49.92  | | 
% 243.35/49.92  | | BETA: splitting (21) gives:
% 243.35/49.92  | | 
% 243.35/49.92  | | Case 1:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (22)  all_58_8 = e0 & op(e1, e1) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | ALPHA: (22) implies:
% 243.35/49.92  | | |   (23)  op(e1, e1) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | REF_CLOSE: (3), (14), (15), (23) are inconsistent by sub-proof #2220.
% 243.35/49.92  | | | 
% 243.35/49.92  | | Case 2:
% 243.35/49.92  | | | 
% 243.35/49.92  | | |   (24)  all_58_11 = e0 & op(e1, e0) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | ALPHA: (24) implies:
% 243.35/49.92  | | |   (25)  op(e1, e0) = e0
% 243.35/49.92  | | | 
% 243.35/49.92  | | | BETA: splitting (12) gives:
% 243.35/49.92  | | | 
% 243.35/49.92  | | | Case 1:
% 243.35/49.92  | | | | 
% 243.35/49.93  | | | |   (26)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 243.35/49.93  | | | |           = e0)
% 243.35/49.93  | | | | 
% 243.35/49.93  | | | | REF_CLOSE: (2), (9), (14), (15), (16), (26) are inconsistent by
% 243.35/49.93  | | | |            sub-proof #1222.
% 243.35/49.93  | | | | 
% 243.35/49.93  | | | Case 2:
% 243.35/49.93  | | | | 
% 243.35/49.93  | | | |   (27)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 243.35/49.93  | | | |           = e0)
% 243.35/49.93  | | | | 
% 243.35/49.93  | | | | BETA: splitting (27) gives:
% 243.35/49.93  | | | | 
% 243.35/49.93  | | | | Case 1:
% 243.35/49.93  | | | | | 
% 243.35/49.93  | | | | |   (28)  all_58_6 = e0 & op(e1, e3) = e0
% 243.35/49.93  | | | | | 
% 243.35/49.93  | | | | | REF_CLOSE: (4), (5), (28) are inconsistent by sub-proof #1678.
% 243.35/49.93  | | | | | 
% 243.35/49.93  | | | | Case 2:
% 243.35/49.93  | | | | | 
% 243.35/49.93  | | | | |   (29)  all_58_12 = e0 & op(e0, e3) = e0
% 243.35/49.93  | | | | | 
% 243.35/49.93  | | | | | ALPHA: (29) implies:
% 243.35/49.93  | | | | |   (30)  op(e0, e3) = e0
% 243.35/49.93  | | | | | 
% 243.35/49.93  | | | | | BETA: splitting (10) gives:
% 243.35/49.93  | | | | | 
% 243.35/49.93  | | | | | Case 1:
% 243.35/49.93  | | | | | | 
% 243.35/49.93  | | | | | |   (31)  all_58_15 = e0 & op(e0, e0) = e0
% 243.35/49.93  | | | | | | 
% 243.35/49.93  | | | | | | ALPHA: (31) implies:
% 243.35/49.93  | | | | | |   (32)  op(e0, e0) = e0
% 243.35/49.93  | | | | | | 
% 243.35/49.93  | | | | | | REF_CLOSE: (1), (14), (15), (32) are inconsistent by sub-proof
% 243.35/49.93  | | | | | |            #2274.
% 243.35/49.93  | | | | | | 
% 243.35/49.93  | | | | | Case 2:
% 243.35/49.93  | | | | | | 
% 243.35/49.93  | | | | | | 
% 243.35/49.93  | | | | | | GROUND_INST: instantiating (14) with all_52_3, e0, e3, e0,
% 243.35/49.93  | | | | | |              simplifying with (7), (30) gives:
% 243.35/49.93  | | | | | |   (33)  all_52_3 = e0
% 243.35/49.93  | | | | | | 
% 243.35/49.93  | | | | | | GROUND_INST: instantiating (14) with all_52_14, e0, e0, e1,
% 243.35/49.93  | | | | | |              simplifying with (6), (25) gives:
% 243.35/49.93  | | | | | |   (34)  all_52_14 = e0
% 243.35/49.93  | | | | | | 
% 243.35/49.93  | | | | | | REDUCE: (11), (34) imply:
% 243.35/49.93  | | | | | |   (35)   ~ (e1 = e0)
% 243.35/49.93  | | | | | | 
% 243.35/49.93  | | | | | | REDUCE: (8), (33) imply:
% 243.35/49.93  | | | | | |   (36)  op(e0, e0) = e0
% 243.35/49.93  | | | | | | 
% 243.35/49.93  | | | | | | REF_CLOSE: (1), (14), (15), (36) are inconsistent by sub-proof
% 243.35/49.93  | | | | | |            #2274.
% 243.35/49.93  | | | | | | 
% 243.35/49.93  | | | | | End of split
% 243.35/49.93  | | | | | 
% 243.35/49.93  | | | | End of split
% 243.35/49.93  | | | | 
% 243.35/49.93  | | | End of split
% 243.35/49.93  | | | 
% 243.35/49.93  | | End of split
% 243.35/49.93  | | 
% 243.35/49.93  | End of split
% 243.35/49.93  | 
% 243.35/49.93  End of proof
% 243.35/49.93  
% 243.35/49.93  Sub-proof #1184 shows that the following formulas are inconsistent:
% 243.35/49.93  ----------------------------------------------------------------
% 243.35/49.93    (1)  op(e0, e0) = e1
% 243.35/49.93    (2)   ~ (all_52_1 = all_52_3)
% 243.35/49.93    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.35/49.93             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.35/49.93           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.35/49.93         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.35/49.93           $i(all_56_7))
% 243.35/49.93    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.35/49.93    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.35/49.93         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.35/49.93    (6)   ~ (all_52_3 = e1)
% 243.35/49.93    (7)   ~ (e3 = e0)
% 243.35/49.93    (8)  op(e1, e1) = e1
% 243.35/49.93    (9)   ~ (e2 = e0)
% 243.35/49.93    (10)  op(e0, e1) = e3
% 243.35/49.93    (11)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.35/49.93          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.35/49.93    (12)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.35/49.93          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.35/49.93    (13)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.35/49.93          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.35/49.93    (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.35/49.93          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.45/49.93    (15)  op(e1, e1) = all_6_2
% 243.45/49.93    (16)   ~ (all_52_1 = all_52_2)
% 243.45/49.93    (17)  op(e1, e0) = all_52_14
% 243.45/49.93    (18)  op(e0, e3) = all_52_3
% 243.45/49.93    (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.45/49.93          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.45/49.93    (20)   ~ (e3 = e1)
% 243.45/49.93    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.45/49.93          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.45/49.93    (22)   ~ (all_52_2 = all_52_3)
% 243.45/49.93    (23)   ~ (all_52_8 = e1)
% 243.45/49.93    (24)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.45/49.93            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 243.45/49.93              e1) = all_10_1 & $i(all_10_1))
% 243.45/49.93    (25)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.45/49.93          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.45/49.93    (26)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.93          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.93    (27)  op(e3, e3) = e1
% 243.45/49.93    (28)  all_54_4 = all_52_1
% 243.45/49.93    (29)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.45/49.93              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.45/49.93                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.45/49.93                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.45/49.93    (30)   ~ (all_6_2 = e3)
% 243.45/49.93    (31)  op(e3, e1) = all_52_8
% 243.45/49.93    (32)  op(e1, all_52_2) = e1
% 243.45/49.93    (33)  op(e2, e1) = all_52_9
% 243.45/49.93    (34)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.93          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.93    (35)   ~ (e3 = e2)
% 243.45/49.93    (36)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.45/49.93          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.45/49.93    (37)   ~ (all_52_14 = e1)
% 243.45/49.93    (38)  op(e2, e2) = e1
% 243.45/49.93    (39)  all_54_12 = all_52_3
% 243.45/49.93    (40)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.93          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.93    (41)  all_58_15 = e1
% 243.45/49.93    (42)  all_58_7 = e3
% 243.45/49.93    (43)  all_58_9 = e3
% 243.45/49.93    (44)  all_38_2 = e1
% 243.45/49.93    (45)  op(e2, e3) = all_52_1
% 243.45/49.93    (46)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.45/49.93    (47)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.45/49.93          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.45/49.93    (48)   ~ (all_52_13 = all_52_14)
% 243.45/49.93    (49)   ~ (all_52_4 = e3)
% 243.45/49.93    (50)  op(e3, e2) = all_52_4
% 243.45/49.93    (51)   ~ (all_52_9 = e3)
% 243.45/49.93    (52)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.93    (53)  op(e1, e3) = all_52_2
% 243.45/49.93    (54)   ~ (e1 = e0)
% 243.45/49.93    (55)  all_58_2 = e3
% 243.45/49.93    (56)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.45/49.93          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.45/49.93    (57)  op(e2, e0) = all_52_13
% 243.45/49.93    (58)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.45/49.93          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.45/49.93            e1)
% 243.45/49.93    (59)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.45/49.93    (60)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.45/49.93          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.45/49.93            e2)
% 243.45/49.93    (61)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.45/49.93          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.45/49.93    (62)  all_56_1 = e1
% 243.45/49.93    (63)   ~ (e2 = e1)
% 243.45/49.93    (64)   ~ (all_52_1 = e1)
% 243.45/49.93    (65)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 243.45/49.93            op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 243.45/49.93              e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 243.45/49.93  
% 243.45/49.93  Begin of proof
% 243.45/49.93  | 
% 243.45/49.93  | BETA: splitting (59) gives:
% 243.45/49.93  | 
% 243.45/49.93  | Case 1:
% 243.45/49.93  | | 
% 243.45/49.93  | |   (66)  all_58_11 = e2 & op(e1, e0) = e2
% 243.45/49.93  | | 
% 243.45/49.93  | | ALPHA: (66) implies:
% 243.45/49.93  | |   (67)  all_58_11 = e2
% 243.45/49.93  | | 
% 243.45/49.93  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 243.45/49.93  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 243.45/49.93  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 243.45/49.93  | |            (35), (36), (37), (38), (39), (40), (42), (43), (44), (45), (46),
% 243.45/49.93  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 243.45/49.93  | |            (58), (60), (61), (62), (63), (64), (65), (67) are inconsistent
% 243.45/49.93  | |            by sub-proof #1185.
% 243.45/49.93  | | 
% 243.45/49.93  | Case 2:
% 243.45/49.93  | | 
% 243.45/49.93  | |   (68)  all_58_15 = e2 & op(e0, e0) = e2
% 243.45/49.93  | | 
% 243.45/49.93  | | ALPHA: (68) implies:
% 243.45/49.93  | |   (69)  all_58_15 = e2
% 243.45/49.93  | | 
% 243.45/49.93  | | REF_CLOSE: (41), (63), (69) are inconsistent by sub-proof #2231.
% 243.45/49.93  | | 
% 243.45/49.93  | End of split
% 243.45/49.93  | 
% 243.45/49.93  End of proof
% 243.45/49.93  
% 243.45/49.93  Sub-proof #1185 shows that the following formulas are inconsistent:
% 243.45/49.93  ----------------------------------------------------------------
% 243.45/49.93    (1)  op(e0, e0) = e1
% 243.45/49.93    (2)   ~ (all_52_1 = all_52_3)
% 243.45/49.93    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.45/49.93             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.45/49.93           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.45/49.93         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.45/49.93           $i(all_56_7))
% 243.45/49.93    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.45/49.93    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.45/49.93         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.45/49.93    (6)   ~ (all_52_3 = e1)
% 243.45/49.93    (7)   ~ (e3 = e0)
% 243.45/49.93    (8)  op(e1, e1) = e1
% 243.45/49.93    (9)   ~ (e2 = e0)
% 243.45/49.93    (10)  op(e0, e1) = e3
% 243.45/49.93    (11)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.45/49.93          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.45/49.93    (12)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.45/49.93          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.45/49.93    (13)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.45/49.93          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.45/49.93    (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.45/49.93          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.45/49.93    (15)  op(e1, e1) = all_6_2
% 243.45/49.93    (16)   ~ (all_52_1 = all_52_2)
% 243.45/49.93    (17)  op(e1, e0) = all_52_14
% 243.45/49.93    (18)  op(e0, e3) = all_52_3
% 243.45/49.93    (19)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.45/49.93          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.45/49.93    (20)   ~ (e3 = e1)
% 243.45/49.93    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.45/49.93          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.45/49.93    (22)   ~ (all_52_2 = all_52_3)
% 243.45/49.93    (23)   ~ (all_52_8 = e1)
% 243.45/49.93    (24)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.45/49.93            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 243.45/49.93              e1) = all_10_1 & $i(all_10_1))
% 243.45/49.93    (25)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.45/49.93          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.45/49.93    (26)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.93          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.93    (27)  op(e3, e3) = e1
% 243.45/49.93    (28)  all_54_4 = all_52_1
% 243.45/49.93    (29)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.45/49.93              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.45/49.93                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.45/49.93                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.45/49.93    (30)   ~ (all_6_2 = e3)
% 243.45/49.93    (31)  op(e3, e1) = all_52_8
% 243.45/49.93    (32)  op(e1, all_52_2) = e1
% 243.45/49.93    (33)  op(e2, e1) = all_52_9
% 243.45/49.93    (34)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.93          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.93    (35)   ~ (e3 = e2)
% 243.45/49.93    (36)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.45/49.93          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.45/49.93    (37)   ~ (all_52_14 = e1)
% 243.45/49.93    (38)  op(e2, e2) = e1
% 243.45/49.93    (39)  all_54_12 = all_52_3
% 243.45/49.93    (40)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.93          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.93    (41)  all_58_7 = e3
% 243.45/49.93    (42)  all_58_9 = e3
% 243.45/49.93    (43)  all_38_2 = e1
% 243.45/49.93    (44)  all_58_11 = e2
% 243.45/49.93    (45)  op(e2, e3) = all_52_1
% 243.45/49.93    (46)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.45/49.93    (47)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.45/49.93          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.45/49.93    (48)   ~ (all_52_13 = all_52_14)
% 243.45/49.93    (49)   ~ (all_52_4 = e3)
% 243.45/49.93    (50)  op(e3, e2) = all_52_4
% 243.45/49.93    (51)   ~ (all_52_9 = e3)
% 243.45/49.93    (52)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.93    (53)  op(e1, e3) = all_52_2
% 243.45/49.93    (54)   ~ (e1 = e0)
% 243.45/49.93    (55)  all_58_2 = e3
% 243.45/49.93    (56)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.45/49.93          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.45/49.94    (57)  op(e2, e0) = all_52_13
% 243.45/49.94    (58)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.45/49.94          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.45/49.94            e1)
% 243.45/49.94    (59)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.45/49.94          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.45/49.94            e2)
% 243.45/49.94    (60)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.45/49.94          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.45/49.94    (61)  all_56_1 = e1
% 243.45/49.94    (62)   ~ (e2 = e1)
% 243.45/49.94    (63)   ~ (all_52_1 = e1)
% 243.45/49.94    (64)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 243.45/49.94            op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 243.45/49.94              e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 243.45/49.94  
% 243.45/49.94  Begin of proof
% 243.45/49.94  | 
% 243.45/49.94  | BETA: splitting (29) gives:
% 243.45/49.94  | 
% 243.45/49.94  | Case 1:
% 243.45/49.94  | | 
% 243.45/49.94  | |   (65)  all_58_15 = e0 & op(e0, e0) = e0
% 243.45/49.94  | | 
% 243.45/49.94  | | ALPHA: (65) implies:
% 243.45/49.94  | |   (66)  op(e0, e0) = e0
% 243.45/49.94  | | 
% 243.45/49.94  | | REF_CLOSE: (1), (52), (54), (66) are inconsistent by sub-proof #2274.
% 243.45/49.94  | | 
% 243.45/49.94  | Case 2:
% 243.45/49.94  | | 
% 243.45/49.94  | |   (67)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.45/49.94  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 243.45/49.94  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.45/49.94  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 243.45/49.94  | | 
% 243.45/49.94  | | ALPHA: (67) implies:
% 243.45/49.94  | |   (68)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.45/49.94  | |           e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.45/49.94  | | 
% 243.45/49.94  | | BETA: splitting (68) gives:
% 243.45/49.94  | | 
% 243.45/49.94  | | Case 1:
% 243.45/49.94  | | | 
% 243.45/49.94  | | |   (69)  all_58_9 = e0 & op(e3, e0) = e0
% 243.45/49.94  | | | 
% 243.45/49.94  | | | REF_CLOSE: (7), (42), (69) are inconsistent by sub-proof #2103.
% 243.45/49.94  | | | 
% 243.45/49.94  | | Case 2:
% 243.45/49.94  | | | 
% 243.45/49.94  | | |   (70)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.45/49.94  | | |           = e0)
% 243.45/49.94  | | | 
% 243.45/49.94  | | | BETA: splitting (70) gives:
% 243.45/49.94  | | | 
% 243.45/49.94  | | | Case 1:
% 243.45/49.94  | | | | 
% 243.45/49.94  | | | |   (71)  all_58_10 = e0 & op(e2, e0) = e0
% 243.45/49.94  | | | | 
% 243.45/49.94  | | | | ALPHA: (71) implies:
% 243.45/49.94  | | | |   (72)  op(e2, e0) = e0
% 243.45/49.94  | | | | 
% 243.45/49.94  | | | | BETA: splitting (19) gives:
% 243.45/49.94  | | | | 
% 243.45/49.94  | | | | Case 1:
% 243.45/49.94  | | | | | 
% 243.45/49.94  | | | | |   (73)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2,
% 243.45/49.94  | | | | |             e2) = e2)
% 243.45/49.94  | | | | | 
% 243.45/49.94  | | | | | REF_CLOSE: (35), (38), (52), (55), (62), (73) are inconsistent by
% 243.45/49.94  | | | | |            sub-proof #1209.
% 243.45/49.94  | | | | | 
% 243.45/49.94  | | | | Case 2:
% 243.45/49.94  | | | | | 
% 243.45/49.94  | | | | |   (74)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2,
% 243.45/49.94  | | | | |             e0) = e2)
% 243.45/49.94  | | | | | 
% 243.45/49.94  | | | | | BETA: splitting (74) gives:
% 243.45/49.94  | | | | | 
% 243.45/49.94  | | | | | Case 1:
% 243.45/49.94  | | | | | | 
% 243.45/49.94  | | | | | |   (75)  all_58_5 = e2 & op(e2, e1) = e2
% 243.45/49.94  | | | | | | 
% 243.45/49.94  | | | | | | ALPHA: (75) implies:
% 243.45/49.94  | | | | | |   (76)  op(e2, e1) = e2
% 243.45/49.94  | | | | | | 
% 243.45/49.94  | | | | | | BETA: splitting (21) gives:
% 243.45/49.94  | | | | | | 
% 243.45/49.94  | | | | | | Case 1:
% 243.45/49.94  | | | | | | | 
% 243.45/49.94  | | | | | | |   (77)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 243.45/49.94  | | | | | | |           op(e2, e1) = e0)
% 243.45/49.94  | | | | | | | 
% 243.45/49.94  | | | | | | | BETA: splitting (77) gives:
% 243.45/49.94  | | | | | | | 
% 243.45/49.94  | | | | | | | Case 1:
% 243.45/49.94  | | | | | | | | 
% 243.45/49.94  | | | | | | | |   (78)  all_58_4 = e0 & op(e3, e1) = e0
% 243.45/49.94  | | | | | | | | 
% 243.45/49.94  | | | | | | | | ALPHA: (78) implies:
% 243.45/49.94  | | | | | | | |   (79)  all_58_4 = e0
% 243.45/49.94  | | | | | | | |   (80)  op(e3, e1) = e0
% 243.45/49.94  | | | | | | | | 
% 243.45/49.94  | | | | | | | | BETA: splitting (56) gives:
% 243.45/49.94  | | | | | | | | 
% 243.45/49.94  | | | | | | | | Case 1:
% 243.45/49.94  | | | | | | | | | 
% 243.45/49.94  | | | | | | | | |   (81)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 243.45/49.94  | | | | | | | | |           op(e1, e2) = e0)
% 243.45/49.94  | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | BETA: splitting (81) gives:
% 243.45/49.94  | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | Case 1:
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | |   (82)  all_58_6 = e0 & op(e1, e3) = e0
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | ALPHA: (82) implies:
% 243.45/49.94  | | | | | | | | | |   (83)  all_58_6 = e0
% 243.45/49.94  | | | | | | | | | |   (84)  op(e1, e3) = e0
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | BETA: splitting (5) gives:
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | Case 1:
% 243.45/49.94  | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | |   (85)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 243.45/49.94  | | | | | | | | | | |           & op(e3, e2) = e2)
% 243.45/49.94  | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | BETA: splitting (85) gives:
% 243.45/49.94  | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | Case 1:
% 243.45/49.94  | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | |   (86)  all_58_0 = e2 & op(e3, e3) = e2
% 243.45/49.94  | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | ALPHA: (86) implies:
% 243.45/49.94  | | | | | | | | | | | |   (87)  op(e3, e3) = e2
% 243.45/49.94  | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | REF_CLOSE: (27), (52), (62), (87) are inconsistent by
% 243.45/49.94  | | | | | | | | | | | |            sub-proof #2267.
% 243.45/49.94  | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | Case 2:
% 243.45/49.94  | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | |   (88)  all_58_1 = e2 & op(e3, e2) = e2
% 243.45/49.94  | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | ALPHA: (88) implies:
% 243.45/49.94  | | | | | | | | | | | |   (89)  all_58_1 = e2
% 243.45/49.94  | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | BETA: splitting (13) gives:
% 243.45/49.94  | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | Case 1:
% 243.45/49.94  | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | |   (90)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 243.45/49.94  | | | | | | | | | | | | |           & op(e2, e2) = e0)
% 243.45/49.94  | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (9), (11), (15), (16), (17),
% 243.45/49.94  | | | | | | | | | | | | |            (18), (22), (23), (24), (26), (27), (28), (29),
% 243.45/49.94  | | | | | | | | | | | | |            (30), (31), (34), (39), (40), (43), (45), (46),
% 243.45/49.94  | | | | | | | | | | | | |            (47), (48), (52), (53), (57), (58), (59), (60),
% 243.45/49.94  | | | | | | | | | | | | |            (61), (63), (64), (79), (80), (83), (84), (89),
% 243.45/49.94  | | | | | | | | | | | | |            (90) are inconsistent by sub-proof #1192.
% 243.45/49.94  | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | Case 2:
% 243.45/49.94  | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | |   (91)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 243.45/49.94  | | | | | | | | | | | | |           e0 & op(e0, e2) = e0)
% 243.45/49.94  | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | BETA: splitting (91) gives:
% 243.45/49.94  | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | Case 1:
% 243.45/49.94  | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | |   (92)  all_58_7 = e0 & op(e1, e2) = e0
% 243.45/49.94  | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (20), (25), (27), (35), (41), (42),
% 243.45/49.94  | | | | | | | | | | | | | |            (52), (62), (79), (92) are inconsistent by
% 243.45/49.94  | | | | | | | | | | | | | |            sub-proof #1189.
% 243.45/49.94  | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | Case 2:
% 243.45/49.94  | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | |   (93)  all_58_13 = e0 & op(e0, e2) = e0
% 243.45/49.94  | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | ALPHA: (93) implies:
% 243.45/49.94  | | | | | | | | | | | | | |   (94)  op(e0, e2) = e0
% 243.45/49.94  | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 243.45/49.94  | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | Case 1:
% 243.45/49.94  | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | |   (95)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 243.45/49.94  | | | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 243.45/49.94  | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 243.45/49.94  | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | Case 1:
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | | REF_CLOSE: (17), (32), (37), (52), (53), (82) are
% 243.45/49.94  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1188.
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | Case 2:
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | |   (96)  all_58_3 = e2 & op(e2, e2) = e2
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 243.45/49.94  | | | | | | | | | | | | | | | |   (97)  op(e2, e2) = e2
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | | REF_CLOSE: (38), (52), (62), (97) are inconsistent by
% 243.45/49.94  | | | | | | | | | | | | | | | |            sub-proof #2235.
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | End of split
% 243.45/49.94  | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | Case 2:
% 243.45/49.94  | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | |   (98)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 243.45/49.94  | | | | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 243.45/49.94  | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 243.45/49.94  | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | Case 1:
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | |   (99)  all_58_7 = e2 & op(e1, e2) = e2
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | | REF_CLOSE: (35), (41), (99) are inconsistent by sub-proof
% 243.45/49.94  | | | | | | | | | | | | | | | |            #1416.
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | Case 2:
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | |   (100)  all_58_13 = e2 & op(e0, e2) = e2
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 243.45/49.94  | | | | | | | | | | | | | | | |   (101)  op(e0, e2) = e2
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (52), (94), (101) are inconsistent by
% 243.45/49.94  | | | | | | | | | | | | | | | |            sub-proof #2132.
% 243.45/49.94  | | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | | End of split
% 243.45/49.94  | | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | | End of split
% 243.45/49.94  | | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | | End of split
% 243.45/49.94  | | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | | End of split
% 243.45/49.94  | | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | End of split
% 243.45/49.94  | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | Case 2:
% 243.45/49.94  | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | |   (102)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 243.45/49.94  | | | | | | | | | | |            & op(e3, e0) = e2)
% 243.45/49.94  | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | | REF_CLOSE: (7), (9), (20), (25), (27), (35), (49), (50),
% 243.45/49.94  | | | | | | | | | | |            (52), (79), (102) are inconsistent by sub-proof
% 243.45/49.94  | | | | | | | | | | |            #1187.
% 243.45/49.94  | | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | End of split
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | Case 2:
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | |   (103)  all_58_7 = e0 & op(e1, e2) = e0
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | REF_CLOSE: (5), (7), (9), (20), (25), (27), (35), (41), (42),
% 243.45/49.94  | | | | | | | | | |            (52), (62), (79), (103) are inconsistent by
% 243.45/49.94  | | | | | | | | | |            sub-proof #1189.
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | End of split
% 243.45/49.94  | | | | | | | | | 
% 243.45/49.94  | | | | | | | | Case 2:
% 243.45/49.94  | | | | | | | | | 
% 243.45/49.94  | | | | | | | | |   (104)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 243.45/49.94  | | | | | | | | |            op(e1, e0) = e0)
% 243.45/49.94  | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | BETA: splitting (104) gives:
% 243.45/49.94  | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | Case 1:
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | |   (105)  all_58_8 = e0 & op(e1, e1) = e0
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | ALPHA: (105) implies:
% 243.45/49.94  | | | | | | | | | |   (106)  op(e1, e1) = e0
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | REF_CLOSE: (7), (9), (14), (20), (33), (35), (36), (47),
% 243.45/49.94  | | | | | | | | | |            (51), (52), (54), (62), (79), (106) are
% 243.45/49.94  | | | | | | | | | |            inconsistent by sub-proof #1662.
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | Case 2:
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | |   (107)  all_58_11 = e0 & op(e1, e0) = e0
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | | REF_CLOSE: (9), (44), (107) are inconsistent by sub-proof
% 243.45/49.94  | | | | | | | | | |            #2033.
% 243.45/49.94  | | | | | | | | | | 
% 243.45/49.94  | | | | | | | | | End of split
% 243.45/49.94  | | | | | | | | | 
% 243.45/49.94  | | | | | | | | End of split
% 243.45/49.94  | | | | | | | | 
% 243.45/49.94  | | | | | | | Case 2:
% 243.45/49.94  | | | | | | | | 
% 243.45/49.94  | | | | | | | |   (108)  all_58_5 = e0 & op(e2, e1) = e0
% 243.45/49.94  | | | | | | | | 
% 243.45/49.94  | | | | | | | | ALPHA: (108) implies:
% 243.45/49.94  | | | | | | | |   (109)  op(e2, e1) = e0
% 243.45/49.94  | | | | | | | | 
% 243.45/49.94  | | | | | | | | REF_CLOSE: (9), (52), (76), (109) are inconsistent by sub-proof
% 243.45/49.94  | | | | | | | |            #1906.
% 243.45/49.94  | | | | | | | | 
% 243.45/49.94  | | | | | | | End of split
% 243.45/49.94  | | | | | | | 
% 243.45/49.94  | | | | | | Case 2:
% 243.45/49.94  | | | | | | | 
% 243.45/49.94  | | | | | | |   (110)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 243.45/49.94  | | | | | | |            op(e0, e1) = e0)
% 243.45/49.94  | | | | | | | 
% 243.45/49.94  | | | | | | | REF_CLOSE: (7), (8), (10), (52), (54), (110) are inconsistent by
% 243.45/49.94  | | | | | | |            sub-proof #1186.
% 243.45/49.94  | | | | | | | 
% 243.45/49.94  | | | | | | End of split
% 243.45/49.94  | | | | | | 
% 243.45/49.94  | | | | | Case 2:
% 243.45/49.94  | | | | | | 
% 243.45/49.94  | | | | | |   (111)  all_58_10 = e2 & op(e2, e0) = e2
% 243.45/49.94  | | | | | | 
% 243.45/49.94  | | | | | | ALPHA: (111) implies:
% 243.45/49.94  | | | | | |   (112)  op(e2, e0) = e2
% 243.45/49.94  | | | | | | 
% 243.45/49.94  | | | | | | REF_CLOSE: (9), (52), (72), (112) are inconsistent by sub-proof
% 243.45/49.94  | | | | | |            #2121.
% 243.45/49.94  | | | | | | 
% 243.45/49.94  | | | | | End of split
% 243.45/49.94  | | | | | 
% 243.45/49.94  | | | | End of split
% 243.45/49.94  | | | | 
% 243.45/49.94  | | | Case 2:
% 243.45/49.94  | | | | 
% 243.45/49.94  | | | |   (113)  all_58_11 = e0 & op(e1, e0) = e0
% 243.45/49.94  | | | | 
% 243.45/49.94  | | | | ALPHA: (113) implies:
% 243.45/49.94  | | | |   (114)  all_58_11 = e0
% 243.45/49.94  | | | | 
% 243.45/49.94  | | | | REF_CLOSE: (9), (44), (114) are inconsistent by sub-proof #2110.
% 243.45/49.94  | | | | 
% 243.45/49.94  | | | End of split
% 243.45/49.94  | | | 
% 243.45/49.94  | | End of split
% 243.45/49.94  | | 
% 243.45/49.94  | End of split
% 243.45/49.94  | 
% 243.45/49.94  End of proof
% 243.45/49.94  
% 243.45/49.94  Sub-proof #1186 shows that the following formulas are inconsistent:
% 243.45/49.94  ----------------------------------------------------------------
% 243.45/49.94    (1)   ~ (e3 = e0)
% 243.45/49.94    (2)  op(e1, e1) = e1
% 243.45/49.94    (3)  op(e0, e1) = e3
% 243.45/49.94    (4)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.45/49.94    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.94    (6)   ~ (e1 = e0)
% 243.45/49.94  
% 243.45/49.94  Begin of proof
% 243.45/49.94  | 
% 243.45/49.94  | BETA: splitting (4) gives:
% 243.45/49.94  | 
% 243.45/49.94  | Case 1:
% 243.45/49.94  | | 
% 243.45/49.94  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 243.45/49.94  | | 
% 243.45/49.94  | | ALPHA: (7) implies:
% 243.45/49.94  | |   (8)  op(e1, e1) = e0
% 243.45/49.94  | | 
% 243.45/49.94  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2220.
% 243.45/49.94  | | 
% 243.45/49.94  | Case 2:
% 243.45/49.94  | | 
% 243.45/49.94  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 243.45/49.94  | | 
% 243.45/49.94  | | ALPHA: (9) implies:
% 243.45/49.94  | |   (10)  op(e0, e1) = e0
% 243.45/49.94  | | 
% 243.45/49.94  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2164.
% 243.45/49.94  | | 
% 243.45/49.94  | End of split
% 243.45/49.94  | 
% 243.45/49.94  End of proof
% 243.45/49.94  
% 243.45/49.94  Sub-proof #1187 shows that the following formulas are inconsistent:
% 243.45/49.94  ----------------------------------------------------------------
% 243.45/49.94    (1)   ~ (e3 = e0)
% 243.45/49.94    (2)   ~ (e2 = e0)
% 243.45/49.94    (3)   ~ (e3 = e1)
% 243.45/49.94    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.45/49.94         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.45/49.94    (5)  op(e3, e3) = e1
% 243.45/49.94    (6)   ~ (e3 = e2)
% 243.45/49.94    (7)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.45/49.94    (8)   ~ (all_52_4 = e3)
% 243.45/49.94    (9)  op(e3, e2) = all_52_4
% 243.45/49.94    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.94    (11)  all_58_4 = e0
% 243.45/49.94  
% 243.45/49.94  Begin of proof
% 243.45/49.94  | 
% 243.45/49.94  | BETA: splitting (7) gives:
% 243.45/49.94  | 
% 243.45/49.94  | Case 1:
% 243.45/49.94  | | 
% 243.45/49.94  | |   (12)  all_58_4 = e2 & op(e3, e1) = e2
% 243.45/49.94  | | 
% 243.45/49.94  | | ALPHA: (12) implies:
% 243.45/49.94  | |   (13)  all_58_4 = e2
% 243.45/49.94  | | 
% 243.45/49.94  | | REF_CLOSE: (2), (11), (13) are inconsistent by sub-proof #1666.
% 243.45/49.94  | | 
% 243.45/49.94  | Case 2:
% 243.45/49.94  | | 
% 243.45/49.94  | |   (14)  all_58_9 = e2 & op(e3, e0) = e2
% 243.45/49.94  | | 
% 243.45/49.94  | | ALPHA: (14) implies:
% 243.45/49.94  | |   (15)  op(e3, e0) = e2
% 243.45/49.94  | | 
% 243.45/49.94  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (15) are
% 243.45/49.94  | |            inconsistent by sub-proof #1400.
% 243.45/49.94  | | 
% 243.45/49.94  | End of split
% 243.45/49.94  | 
% 243.45/49.94  End of proof
% 243.45/49.94  
% 243.45/49.94  Sub-proof #1188 shows that the following formulas are inconsistent:
% 243.45/49.94  ----------------------------------------------------------------
% 243.45/49.94    (1)  op(e1, e0) = all_52_14
% 243.45/49.94    (2)  op(e1, all_52_2) = e1
% 243.45/49.94    (3)   ~ (all_52_14 = e1)
% 243.45/49.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.94    (5)  op(e1, e3) = all_52_2
% 243.45/49.94    (6)  all_58_6 = e0 & op(e1, e3) = e0
% 243.45/49.94  
% 243.45/49.94  Begin of proof
% 243.45/49.94  | 
% 243.45/49.94  | ALPHA: (6) implies:
% 243.45/49.94  |   (7)  op(e1, e3) = e0
% 243.45/49.94  | 
% 243.45/49.94  | GROUND_INST: instantiating (4) with all_52_2, e0, e3, e1, simplifying with
% 243.45/49.94  |              (5), (7) gives:
% 243.45/49.94  |   (8)  all_52_2 = e0
% 243.45/49.94  | 
% 243.45/49.94  | REDUCE: (2), (8) imply:
% 243.45/49.94  |   (9)  op(e1, e0) = e1
% 243.45/49.94  | 
% 243.45/49.94  | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #2304.
% 243.45/49.94  | 
% 243.45/49.94  End of proof
% 243.45/49.94  
% 243.45/49.94  Sub-proof #1189 shows that the following formulas are inconsistent:
% 243.45/49.94  ----------------------------------------------------------------
% 243.45/49.94    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.45/49.94         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.45/49.94    (2)   ~ (e3 = e0)
% 243.45/49.94    (3)  all_58_7 = e0 & op(e1, e2) = e0
% 243.45/49.94    (4)   ~ (e2 = e0)
% 243.45/49.94    (5)   ~ (e3 = e1)
% 243.45/49.94    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.45/49.94         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.45/49.94    (7)  op(e3, e3) = e1
% 243.45/49.94    (8)   ~ (e3 = e2)
% 243.45/49.94    (9)  all_58_7 = e3
% 243.45/49.94    (10)  all_58_9 = e3
% 243.45/49.94    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.94    (12)  all_58_4 = e0
% 243.45/49.94    (13)   ~ (e2 = e1)
% 243.45/49.94  
% 243.45/49.94  Begin of proof
% 243.45/49.94  | 
% 243.45/49.94  | ALPHA: (3) implies:
% 243.45/49.94  |   (14)  all_58_7 = e0
% 243.45/49.94  | 
% 243.45/49.94  | COMBINE_EQS: (9), (14) imply:
% 243.45/49.94  |   (15)  e3 = e0
% 243.45/49.94  | 
% 243.45/49.94  | COMBINE_EQS: (10), (15) imply:
% 243.45/49.94  |   (16)  all_58_9 = e0
% 243.45/49.94  | 
% 243.45/49.94  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (11), (12), (13), (16) are
% 243.45/49.94  |            inconsistent by sub-proof #1190.
% 243.45/49.94  | 
% 243.45/49.94  End of proof
% 243.45/49.94  
% 243.45/49.94  Sub-proof #1190 shows that the following formulas are inconsistent:
% 243.45/49.94  ----------------------------------------------------------------
% 243.45/49.94    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.45/49.94         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.45/49.94    (2)   ~ (e3 = e0)
% 243.45/49.94    (3)   ~ (e2 = e0)
% 243.45/49.94    (4)  all_58_9 = e0
% 243.45/49.94    (5)   ~ (e3 = e1)
% 243.45/49.95    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.45/49.95         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.45/49.95    (7)  op(e3, e3) = e1
% 243.45/49.95    (8)   ~ (e3 = e2)
% 243.45/49.95    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.95    (10)  all_58_4 = e0
% 243.45/49.95    (11)   ~ (e2 = e1)
% 243.45/49.95  
% 243.45/49.95  Begin of proof
% 243.45/49.95  | 
% 243.45/49.95  | BETA: splitting (1) gives:
% 243.45/49.95  | 
% 243.45/49.95  | Case 1:
% 243.45/49.95  | | 
% 243.45/49.95  | |   (12)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 243.45/49.95  | |           e2)
% 243.45/49.95  | | 
% 243.45/49.95  | | BETA: splitting (12) gives:
% 243.45/49.95  | | 
% 243.45/49.95  | | Case 1:
% 243.45/49.95  | | | 
% 243.45/49.95  | | |   (13)  all_58_0 = e2 & op(e3, e3) = e2
% 243.45/49.95  | | | 
% 243.45/49.95  | | | ALPHA: (13) implies:
% 243.45/49.95  | | |   (14)  op(e3, e3) = e2
% 243.45/49.95  | | | 
% 243.45/49.95  | | | REF_CLOSE: (7), (9), (11), (14) are inconsistent by sub-proof #2267.
% 243.45/49.95  | | | 
% 243.45/49.95  | | Case 2:
% 243.45/49.95  | | | 
% 243.45/49.95  | | |   (15)  all_58_1 = e2 & op(e3, e2) = e2
% 243.45/49.95  | | | 
% 243.45/49.95  | | | ALPHA: (15) implies:
% 243.45/49.95  | | |   (16)  all_58_1 = e2
% 243.45/49.95  | | | 
% 243.45/49.95  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (16) are inconsistent
% 243.45/49.95  | | |            by sub-proof #1191.
% 243.45/49.95  | | | 
% 243.45/49.95  | | End of split
% 243.45/49.95  | | 
% 243.45/49.95  | Case 2:
% 243.45/49.95  | | 
% 243.45/49.95  | |   (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 243.45/49.95  | |           e2)
% 243.45/49.95  | | 
% 243.45/49.95  | | BETA: splitting (17) gives:
% 243.45/49.95  | | 
% 243.45/49.95  | | Case 1:
% 243.45/49.95  | | | 
% 243.45/49.95  | | |   (18)  all_58_4 = e2 & op(e3, e1) = e2
% 243.45/49.95  | | | 
% 243.45/49.95  | | | REF_CLOSE: (3), (10), (18) are inconsistent by sub-proof #1707.
% 243.45/49.95  | | | 
% 243.45/49.95  | | Case 2:
% 243.45/49.95  | | | 
% 243.45/49.95  | | |   (19)  all_58_9 = e2 & op(e3, e0) = e2
% 243.45/49.95  | | | 
% 243.45/49.95  | | | REF_CLOSE: (3), (4), (19) are inconsistent by sub-proof #1655.
% 243.45/49.95  | | | 
% 243.45/49.95  | | End of split
% 243.45/49.95  | | 
% 243.45/49.95  | End of split
% 243.45/49.95  | 
% 243.45/49.95  End of proof
% 243.45/49.95  
% 243.45/49.95  Sub-proof #1191 shows that the following formulas are inconsistent:
% 243.45/49.95  ----------------------------------------------------------------
% 243.45/49.95    (1)   ~ (e3 = e0)
% 243.45/49.95    (2)  all_58_9 = e0
% 243.45/49.95    (3)   ~ (e3 = e1)
% 243.45/49.95    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.45/49.95         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.45/49.95    (5)  op(e3, e3) = e1
% 243.45/49.95    (6)   ~ (e3 = e2)
% 243.45/49.95    (7)  all_58_1 = e2
% 243.45/49.95    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.95    (9)  all_58_4 = e0
% 243.45/49.95  
% 243.45/49.95  Begin of proof
% 243.45/49.95  | 
% 243.45/49.95  | BETA: splitting (4) gives:
% 243.45/49.95  | 
% 243.45/49.95  | Case 1:
% 243.45/49.95  | | 
% 243.45/49.95  | |   (10)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 243.45/49.95  | |           e3)
% 243.45/49.95  | | 
% 243.45/49.95  | | BETA: splitting (10) gives:
% 243.45/49.95  | | 
% 243.45/49.95  | | Case 1:
% 243.45/49.95  | | | 
% 243.45/49.95  | | |   (11)  all_58_0 = e3 & op(e3, e3) = e3
% 243.45/49.95  | | | 
% 243.45/49.95  | | | ALPHA: (11) implies:
% 243.45/49.95  | | |   (12)  op(e3, e3) = e3
% 243.45/49.95  | | | 
% 243.45/49.95  | | | REF_CLOSE: (3), (5), (8), (12) are inconsistent by sub-proof #1578.
% 243.45/49.95  | | | 
% 243.45/49.95  | | Case 2:
% 243.45/49.95  | | | 
% 243.45/49.95  | | |   (13)  all_58_1 = e3 & op(e3, e2) = e3
% 243.45/49.95  | | | 
% 243.45/49.95  | | | REF_CLOSE: (6), (7), (13) are inconsistent by sub-proof #2141.
% 243.45/49.95  | | | 
% 243.45/49.95  | | End of split
% 243.45/49.95  | | 
% 243.45/49.95  | Case 2:
% 243.45/49.95  | | 
% 243.45/49.95  | |   (14)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 243.45/49.95  | |           e3)
% 243.45/49.95  | | 
% 243.45/49.95  | | BETA: splitting (14) gives:
% 243.45/49.95  | | 
% 243.45/49.95  | | Case 1:
% 243.45/49.95  | | | 
% 243.45/49.95  | | |   (15)  all_58_4 = e3 & op(e3, e1) = e3
% 243.45/49.95  | | | 
% 243.45/49.95  | | | ALPHA: (15) implies:
% 243.45/49.95  | | |   (16)  all_58_4 = e3
% 243.45/49.95  | | | 
% 243.45/49.95  | | | REF_CLOSE: (1), (9), (16) are inconsistent by sub-proof #2186.
% 243.45/49.95  | | | 
% 243.45/49.95  | | Case 2:
% 243.45/49.95  | | | 
% 243.45/49.95  | | |   (17)  all_58_9 = e3 & op(e3, e0) = e3
% 243.45/49.95  | | | 
% 243.45/49.95  | | | REF_CLOSE: (1), (2), (17) are inconsistent by sub-proof #1621.
% 243.45/49.95  | | | 
% 243.45/49.95  | | End of split
% 243.45/49.95  | | 
% 243.45/49.95  | End of split
% 243.45/49.95  | 
% 243.45/49.95  End of proof
% 243.45/49.95  
% 243.45/49.95  Sub-proof #1192 shows that the following formulas are inconsistent:
% 243.45/49.95  ----------------------------------------------------------------
% 243.45/49.95    (1)   ~ (all_52_1 = all_52_3)
% 243.45/49.95    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.45/49.95             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.45/49.95           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.45/49.95         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.45/49.95           $i(all_56_7))
% 243.45/49.95    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.45/49.95    (4)   ~ (all_52_3 = e1)
% 243.45/49.95    (5)   ~ (e2 = e0)
% 243.45/49.95    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 243.45/49.95    (7)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.45/49.95         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.45/49.95    (8)  op(e1, e1) = all_6_2
% 243.45/49.95    (9)   ~ (all_52_1 = all_52_2)
% 243.45/49.95    (10)  op(e1, e0) = all_52_14
% 243.45/49.95    (11)  op(e0, e3) = all_52_3
% 243.45/49.95    (12)   ~ (all_52_2 = all_52_3)
% 243.45/49.95    (13)  op(e3, e1) = e0
% 243.45/49.95    (14)   ~ (all_52_8 = e1)
% 243.45/49.95    (15)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.45/49.95            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 243.45/49.95              e1) = all_10_1 & $i(all_10_1))
% 243.45/49.95    (16)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.95          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.95    (17)  op(e3, e3) = e1
% 243.45/49.95    (18)  all_54_4 = all_52_1
% 243.45/49.95    (19)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.45/49.95              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.45/49.95                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.45/49.95                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.45/49.95    (20)   ~ (all_6_2 = e3)
% 243.45/49.95    (21)  op(e3, e1) = all_52_8
% 243.45/49.95    (22)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.95          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.95    (23)  all_58_6 = e0
% 243.45/49.95    (24)  all_54_12 = all_52_3
% 243.45/49.95    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.95          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.95    (26)  all_38_2 = e1
% 243.45/49.95    (27)  op(e2, e3) = all_52_1
% 243.45/49.95    (28)  op(e1, e3) = e0
% 243.45/49.95    (29)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.45/49.95    (30)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.45/49.95          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.45/49.95    (31)   ~ (all_52_13 = all_52_14)
% 243.45/49.95    (32)  all_58_1 = e2
% 243.45/49.95    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.95    (34)  op(e1, e3) = all_52_2
% 243.45/49.95    (35)  op(e2, e0) = all_52_13
% 243.45/49.95    (36)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.45/49.95          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.45/49.95            e1)
% 243.45/49.95    (37)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.45/49.95          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.45/49.95            e2)
% 243.45/49.95    (38)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.45/49.95          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.45/49.95    (39)  all_56_1 = e1
% 243.45/49.95    (40)  all_58_4 = e0
% 243.45/49.95    (41)   ~ (all_52_1 = e1)
% 243.45/49.95    (42)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 243.45/49.95            op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 243.45/49.95              e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 243.45/49.95  
% 243.45/49.95  Begin of proof
% 243.45/49.95  | 
% 243.45/49.95  | BETA: splitting (6) gives:
% 243.45/49.95  | 
% 243.45/49.95  | Case 1:
% 243.45/49.95  | | 
% 243.45/49.95  | |   (43)  all_58_1 = e0 & op(e3, e2) = e0
% 243.45/49.95  | | 
% 243.45/49.95  | | REF_CLOSE: (5), (32), (43) are inconsistent by sub-proof #2187.
% 243.45/49.95  | | 
% 243.45/49.95  | Case 2:
% 243.45/49.95  | | 
% 243.45/49.95  | |   (44)  all_58_3 = e0 & op(e2, e2) = e0
% 243.45/49.95  | | 
% 243.45/49.95  | | ALPHA: (44) implies:
% 243.45/49.95  | |   (45)  all_58_3 = e0
% 243.45/49.95  | |   (46)  op(e2, e2) = e0
% 243.45/49.95  | | 
% 243.45/49.95  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14),
% 243.45/49.95  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 243.45/49.95  | |            (26), (27), (28), (29), (30), (31), (33), (34), (35), (36), (37),
% 243.45/49.95  | |            (38), (39), (40), (41), (42), (45), (46) are inconsistent by
% 243.45/49.95  | |            sub-proof #1193.
% 243.45/49.95  | | 
% 243.45/49.95  | End of split
% 243.45/49.95  | 
% 243.45/49.95  End of proof
% 243.45/49.95  
% 243.45/49.95  Sub-proof #1193 shows that the following formulas are inconsistent:
% 243.45/49.95  ----------------------------------------------------------------
% 243.45/49.95    (1)   ~ (all_52_1 = all_52_3)
% 243.45/49.95    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.45/49.95             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.45/49.95           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.45/49.95         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.45/49.95           $i(all_56_7))
% 243.45/49.95    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.45/49.95    (4)   ~ (all_52_3 = e1)
% 243.45/49.95    (5)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.45/49.95         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.45/49.95    (6)  op(e1, e1) = all_6_2
% 243.45/49.95    (7)   ~ (all_52_1 = all_52_2)
% 243.45/49.95    (8)  op(e1, e0) = all_52_14
% 243.45/49.95    (9)  op(e0, e3) = all_52_3
% 243.45/49.95    (10)   ~ (all_52_2 = all_52_3)
% 243.45/49.95    (11)  op(e2, e2) = e0
% 243.45/49.95    (12)  op(e3, e1) = e0
% 243.45/49.95    (13)   ~ (all_52_8 = e1)
% 243.45/49.95    (14)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.45/49.95            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3,
% 243.45/49.95              e1) = all_10_1 & $i(all_10_1))
% 243.45/49.95    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.95          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.95    (16)  op(e3, e3) = e1
% 243.45/49.95    (17)  all_54_4 = all_52_1
% 243.45/49.95    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.45/49.95              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.45/49.95                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.45/49.95                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.45/49.95    (19)   ~ (all_6_2 = e3)
% 243.45/49.95    (20)  op(e3, e1) = all_52_8
% 243.45/49.95    (21)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.95          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.95    (22)  all_58_6 = e0
% 243.45/49.95    (23)  all_54_12 = all_52_3
% 243.45/49.95    (24)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.95          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.95    (25)  all_38_2 = e1
% 243.45/49.95    (26)  op(e2, e3) = all_52_1
% 243.45/49.95    (27)  op(e1, e3) = e0
% 243.45/49.95    (28)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.45/49.95    (29)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.45/49.95          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.45/49.95    (30)   ~ (all_52_13 = all_52_14)
% 243.45/49.95    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.95    (32)  op(e1, e3) = all_52_2
% 243.45/49.95    (33)  op(e2, e0) = all_52_13
% 243.45/49.95    (34)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.45/49.95          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.45/49.95            e1)
% 243.45/49.95    (35)  all_58_3 = e0
% 243.45/49.95    (36)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.45/49.95          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.45/49.95            e2)
% 243.45/49.95    (37)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.45/49.95          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.45/49.95    (38)  all_56_1 = e1
% 243.45/49.95    (39)  all_58_4 = e0
% 243.45/49.95    (40)   ~ (all_52_1 = e1)
% 243.45/49.95    (41)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 &
% 243.45/49.95            op(e3, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 243.45/49.95              e0) & op(e3, e1) = all_38_1 & $i(all_38_1))
% 243.45/49.95  
% 243.45/49.95  Begin of proof
% 243.45/49.95  | 
% 243.45/49.95  | GROUND_INST: instantiating (31) with all_52_2, e0, e3, e1, simplifying with
% 243.45/49.95  |              (27), (32) gives:
% 243.45/49.95  |   (42)  all_52_2 = e0
% 243.45/49.95  | 
% 243.45/49.95  | GROUND_INST: instantiating (31) with all_52_8, e0, e1, e3, simplifying with
% 243.45/49.95  |              (12), (20) gives:
% 243.45/49.95  |   (43)  all_52_8 = e0
% 243.45/49.95  | 
% 243.45/49.95  | REDUCE: (7), (42) imply:
% 243.45/49.95  |   (44)   ~ (all_52_1 = e0)
% 243.45/49.95  | 
% 243.45/49.95  | REDUCE: (10), (42) imply:
% 243.45/49.95  |   (45)   ~ (all_52_3 = e0)
% 243.45/49.95  | 
% 243.45/49.95  | SIMP: (45) implies:
% 243.45/49.95  |   (46)   ~ (all_52_3 = e0)
% 243.45/49.95  | 
% 243.45/49.95  | REDUCE: (13), (43) imply:
% 243.45/49.95  |   (47)   ~ (e1 = e0)
% 243.45/49.95  | 
% 243.45/49.95  | SIMP: (47) implies:
% 243.45/49.95  |   (48)   ~ (e1 = e0)
% 243.45/49.95  | 
% 243.45/49.95  | BETA: splitting (41) gives:
% 243.45/49.95  | 
% 243.45/49.95  | Case 1:
% 243.45/49.95  | | 
% 243.45/49.95  | |   (49)   ~ (all_38_2 = e1)
% 243.45/49.95  | | 
% 243.45/49.95  | | REDUCE: (25), (49) imply:
% 243.45/49.95  | |   (50)  $false
% 243.45/49.95  | | 
% 243.45/49.95  | | CLOSE: (50) is inconsistent.
% 243.45/49.95  | | 
% 243.45/49.95  | Case 2:
% 243.45/49.95  | | 
% 243.45/49.95  | |   (51)  ( ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 243.45/49.95  | |           all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) &
% 243.45/49.95  | |           op(e3, e1) = all_38_1 & $i(all_38_1))
% 243.45/49.95  | | 
% 243.45/49.95  | | BETA: splitting (51) gives:
% 243.45/49.95  | | 
% 243.45/49.95  | | Case 1:
% 243.45/49.95  | | | 
% 243.45/49.95  | | |   (52)   ~ (all_38_0 = e2) & op(all_38_1, e3) = all_38_0 & op(e3, e1) =
% 243.45/49.95  | | |         all_38_1 & $i(all_38_0) & $i(all_38_1)
% 243.45/49.95  | | | 
% 243.45/49.95  | | | ALPHA: (52) implies:
% 243.45/49.95  | | |   (53)   ~ (all_38_0 = e2)
% 243.45/49.95  | | |   (54)  op(e3, e1) = all_38_1
% 243.45/49.95  | | |   (55)  op(all_38_1, e3) = all_38_0
% 243.45/49.95  | | | 
% 243.45/49.95  | | | BETA: splitting (14) gives:
% 243.45/49.95  | | | 
% 243.45/49.95  | | | Case 1:
% 243.45/49.95  | | | | 
% 243.45/49.95  | | | |   (56)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.45/49.95  | | | |         all_10_1 & $i(all_10_0) & $i(all_10_1)
% 243.45/49.95  | | | | 
% 243.45/49.95  | | | | ALPHA: (56) implies:
% 243.45/49.95  | | | |   (57)  op(e3, e1) = all_10_1
% 243.45/49.95  | | | | 
% 243.45/49.96  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (15),
% 243.45/49.96  | | | |            (16), (17), (18), (19), (21), (22), (23), (24), (26), (27),
% 243.45/49.96  | | | |            (28), (29), (30), (31), (33), (34), (35), (36), (37), (38),
% 243.45/49.96  | | | |            (39), (40), (44), (46), (48), (53), (54), (55), (57) are
% 243.45/49.96  | | | |            inconsistent by sub-proof #1196.
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | Case 2:
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | |   (58)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 & $i(all_10_1)
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | | ALPHA: (58) implies:
% 243.45/49.96  | | | |   (59)  op(e3, e1) = all_10_1
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (15),
% 243.45/49.96  | | | |            (16), (17), (18), (19), (21), (22), (23), (24), (26), (27),
% 243.45/49.96  | | | |            (28), (29), (30), (31), (33), (34), (35), (36), (37), (38),
% 243.45/49.96  | | | |            (39), (40), (44), (46), (48), (53), (54), (55), (59) are
% 243.45/49.96  | | | |            inconsistent by sub-proof #1196.
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | End of split
% 243.45/49.96  | | | 
% 243.45/49.96  | | Case 2:
% 243.45/49.96  | | | 
% 243.45/49.96  | | |   (60)   ~ (all_38_1 = e0) & op(e3, e1) = all_38_1 & $i(all_38_1)
% 243.45/49.96  | | | 
% 243.45/49.96  | | | ALPHA: (60) implies:
% 243.45/49.96  | | |   (61)   ~ (all_38_1 = e0)
% 243.45/49.96  | | |   (62)  op(e3, e1) = all_38_1
% 243.45/49.96  | | | 
% 243.45/49.96  | | | REF_CLOSE: (12), (14), (31), (61), (62) are inconsistent by sub-proof
% 243.45/49.96  | | |            #1194.
% 243.45/49.96  | | | 
% 243.45/49.96  | | End of split
% 243.45/49.96  | | 
% 243.45/49.96  | End of split
% 243.45/49.96  | 
% 243.45/49.96  End of proof
% 243.45/49.96  
% 243.45/49.96  Sub-proof #1194 shows that the following formulas are inconsistent:
% 243.45/49.96  ----------------------------------------------------------------
% 243.45/49.96    (1)   ~ (all_38_1 = e0)
% 243.45/49.96    (2)  op(e3, e1) = e0
% 243.45/49.96    (3)  ( ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) = all_10_1
% 243.45/49.96           & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e3, e1) =
% 243.45/49.96           all_10_1 & $i(all_10_1))
% 243.45/49.96    (4)  op(e3, e1) = all_38_1
% 243.45/49.96    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.96  
% 243.45/49.96  Begin of proof
% 243.45/49.96  | 
% 243.45/49.96  | BETA: splitting (3) gives:
% 243.45/49.96  | 
% 243.45/49.96  | Case 1:
% 243.45/49.96  | | 
% 243.45/49.96  | |   (6)   ~ (all_10_0 = e0) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 243.45/49.96  | |        all_10_1 & $i(all_10_0) & $i(all_10_1)
% 243.45/49.96  | | 
% 243.45/49.96  | | ALPHA: (6) implies:
% 243.45/49.96  | |   (7)  op(e3, e1) = all_10_1
% 243.45/49.96  | | 
% 243.45/49.96  | | REF_CLOSE: (1), (2), (4), (5), (7) are inconsistent by sub-proof #1195.
% 243.45/49.96  | | 
% 243.45/49.96  | Case 2:
% 243.45/49.96  | | 
% 243.45/49.96  | |   (8)   ~ (all_10_1 = e2) & op(e3, e1) = all_10_1 & $i(all_10_1)
% 243.45/49.96  | | 
% 243.45/49.96  | | ALPHA: (8) implies:
% 243.45/49.96  | |   (9)  op(e3, e1) = all_10_1
% 243.45/49.96  | | 
% 243.45/49.96  | | REF_CLOSE: (1), (2), (4), (5), (9) are inconsistent by sub-proof #1195.
% 243.45/49.96  | | 
% 243.45/49.96  | End of split
% 243.45/49.96  | 
% 243.45/49.96  End of proof
% 243.45/49.96  
% 243.45/49.96  Sub-proof #1195 shows that the following formulas are inconsistent:
% 243.45/49.96  ----------------------------------------------------------------
% 243.45/49.96    (1)   ~ (all_38_1 = e0)
% 243.45/49.96    (2)  op(e3, e1) = e0
% 243.45/49.96    (3)  op(e3, e1) = all_38_1
% 243.45/49.96    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.96    (5)  op(e3, e1) = all_10_1
% 243.45/49.96  
% 243.45/49.96  Begin of proof
% 243.45/49.96  | 
% 243.45/49.96  | GROUND_INST: instantiating (4) with e0, all_38_1, e1, e3, simplifying with
% 243.45/49.96  |              (2), (3) gives:
% 243.45/49.96  |   (6)  all_38_1 = e0
% 243.45/49.96  | 
% 243.45/49.96  | GROUND_INST: instantiating (4) with all_10_1, all_38_1, e1, e3, simplifying
% 243.45/49.96  |              with (3), (5) gives:
% 243.45/49.96  |   (7)  all_38_1 = all_10_1
% 243.45/49.96  | 
% 243.45/49.96  | COMBINE_EQS: (6), (7) imply:
% 243.45/49.96  |   (8)  all_10_1 = e0
% 243.45/49.96  | 
% 243.45/49.96  | REDUCE: (1), (6) imply:
% 243.45/49.96  |   (9)  $false
% 243.45/49.96  | 
% 243.45/49.96  | CLOSE: (9) is inconsistent.
% 243.45/49.96  | 
% 243.45/49.96  End of proof
% 243.45/49.96  
% 243.45/49.96  Sub-proof #1196 shows that the following formulas are inconsistent:
% 243.45/49.96  ----------------------------------------------------------------
% 243.45/49.96    (1)   ~ (all_52_3 = e0)
% 243.45/49.96    (2)   ~ (all_52_1 = all_52_3)
% 243.45/49.96    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.45/49.96             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.45/49.96           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.45/49.96         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.45/49.96           $i(all_56_7))
% 243.45/49.96    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.45/49.96    (5)   ~ (all_52_3 = e1)
% 243.45/49.96    (6)   ~ (all_38_0 = e2)
% 243.45/49.96    (7)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.45/49.96         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.45/49.96    (8)  op(all_38_1, e3) = all_38_0
% 243.45/49.96    (9)  op(e1, e1) = all_6_2
% 243.45/49.96    (10)  op(e1, e0) = all_52_14
% 243.45/49.96    (11)  op(e0, e3) = all_52_3
% 243.45/49.96    (12)  op(e2, e2) = e0
% 243.45/49.96    (13)  op(e3, e1) = e0
% 243.45/49.96    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.96          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.96    (15)  op(e3, e3) = e1
% 243.45/49.96    (16)  all_54_4 = all_52_1
% 243.45/49.96    (17)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.45/49.96              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.45/49.96                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.45/49.96                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.45/49.96    (18)   ~ (all_6_2 = e3)
% 243.45/49.96    (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.96          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.96    (20)  op(e3, e1) = all_38_1
% 243.45/49.96    (21)  all_58_6 = e0
% 243.45/49.96    (22)  all_54_12 = all_52_3
% 243.45/49.96    (23)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.96          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.96    (24)   ~ (all_52_1 = e0)
% 243.45/49.96    (25)  op(e2, e3) = all_52_1
% 243.45/49.96    (26)  op(e1, e3) = e0
% 243.45/49.96    (27)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.45/49.96    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.45/49.96          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.45/49.96    (29)   ~ (all_52_13 = all_52_14)
% 243.45/49.96    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.96    (31)  op(e3, e1) = all_10_1
% 243.45/49.96    (32)   ~ (e1 = e0)
% 243.45/49.96    (33)  op(e2, e0) = all_52_13
% 243.45/49.96    (34)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.45/49.96          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.45/49.96            e1)
% 243.45/49.96    (35)  all_58_3 = e0
% 243.45/49.96    (36)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.45/49.96          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.45/49.96            e2)
% 243.45/49.96    (37)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.45/49.96          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.45/49.96    (38)  all_56_1 = e1
% 243.45/49.96    (39)  all_58_4 = e0
% 243.45/49.96    (40)   ~ (all_52_1 = e1)
% 243.45/49.96  
% 243.45/49.96  Begin of proof
% 243.45/49.96  | 
% 243.45/49.96  | GROUND_INST: instantiating (30) with e0, all_38_1, e1, e3, simplifying with
% 243.45/49.96  |              (13), (20) gives:
% 243.45/49.96  |   (41)  all_38_1 = e0
% 243.45/49.96  | 
% 243.45/49.96  | GROUND_INST: instantiating (30) with all_10_1, all_38_1, e1, e3, simplifying
% 243.45/49.96  |              with (20), (31) gives:
% 243.45/49.96  |   (42)  all_38_1 = all_10_1
% 243.45/49.96  | 
% 243.45/49.96  | COMBINE_EQS: (41), (42) imply:
% 243.45/49.96  |   (43)  all_10_1 = e0
% 243.45/49.96  | 
% 243.45/49.96  | REDUCE: (8), (41) imply:
% 243.45/49.96  |   (44)  op(e0, e3) = all_38_0
% 243.45/49.96  | 
% 243.45/49.96  | GROUND_INST: instantiating (30) with all_52_3, all_38_0, e3, e0, simplifying
% 243.45/49.96  |              with (11), (44) gives:
% 243.45/49.96  |   (45)  all_52_3 = all_38_0
% 243.45/49.96  | 
% 243.45/49.96  | COMBINE_EQS: (22), (45) imply:
% 243.45/49.96  |   (46)  all_54_12 = all_38_0
% 243.45/49.96  | 
% 243.45/49.96  | REDUCE: (2), (45) imply:
% 243.45/49.96  |   (47)   ~ (all_52_1 = all_38_0)
% 243.45/49.96  | 
% 243.45/49.96  | REDUCE: (5), (45) imply:
% 243.45/49.96  |   (48)   ~ (all_38_0 = e1)
% 243.45/49.96  | 
% 243.45/49.96  | REDUCE: (1), (45) imply:
% 243.45/49.96  |   (49)   ~ (all_38_0 = e0)
% 243.45/49.96  | 
% 243.45/49.96  | BETA: splitting (4) gives:
% 243.45/49.96  | 
% 243.45/49.96  | Case 1:
% 243.45/49.96  | | 
% 243.45/49.96  | |   (50)  all_54_12 = e3
% 243.45/49.96  | | 
% 243.45/49.96  | | COMBINE_EQS: (46), (50) imply:
% 243.45/49.96  | |   (51)  all_38_0 = e3
% 243.45/49.96  | | 
% 243.45/49.96  | | SIMP: (51) implies:
% 243.45/49.96  | |   (52)  all_38_0 = e3
% 243.45/49.96  | | 
% 243.45/49.96  | | REDUCE: (47), (52) imply:
% 243.45/49.96  | |   (53)   ~ (all_52_1 = e3)
% 243.45/49.96  | | 
% 243.45/49.96  | | REDUCE: (48), (52) imply:
% 243.45/49.96  | |   (54)   ~ (e3 = e1)
% 243.45/49.96  | | 
% 243.45/49.96  | | REDUCE: (49), (52) imply:
% 243.45/49.96  | |   (55)   ~ (e3 = e0)
% 243.45/49.96  | | 
% 243.45/49.96  | | BETA: splitting (27) gives:
% 243.45/49.96  | | 
% 243.45/49.96  | | Case 1:
% 243.45/49.96  | | | 
% 243.45/49.96  | | |   (56)  all_54_4 = e3
% 243.45/49.96  | | | 
% 243.45/49.96  | | | REF_CLOSE: (16), (53), (56) are inconsistent by sub-proof #2100.
% 243.45/49.96  | | | 
% 243.45/49.96  | | Case 2:
% 243.45/49.96  | | | 
% 243.45/49.96  | | |   (57)   ~ (all_54_4 = e3)
% 243.45/49.96  | | |   (58)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.45/49.96  | | | 
% 243.45/49.96  | | | BETA: splitting (58) gives:
% 243.45/49.96  | | | 
% 243.45/49.96  | | | Case 1:
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | |   (59)  all_54_4 = e2
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | | COMBINE_EQS: (16), (59) imply:
% 243.45/49.96  | | | |   (60)  all_52_1 = e2
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | | SIMP: (60) implies:
% 243.45/49.96  | | | |   (61)  all_52_1 = e2
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | | REDUCE: (53), (61) imply:
% 243.45/49.96  | | | |   (62)   ~ (e3 = e2)
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | | SIMP: (62) implies:
% 243.45/49.96  | | | |   (63)   ~ (e3 = e2)
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | | REDUCE: (40), (61) imply:
% 243.45/49.96  | | | |   (64)   ~ (e2 = e1)
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | | REDUCE: (24), (61) imply:
% 243.45/49.96  | | | |   (65)   ~ (e2 = e0)
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | | REDUCE: (25), (61) imply:
% 243.45/49.96  | | | |   (66)  op(e2, e3) = e2
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | | BETA: splitting (3) gives:
% 243.45/49.96  | | | | 
% 243.45/49.96  | | | | Case 1:
% 243.45/49.96  | | | | | 
% 243.45/49.96  | | | | |   (67)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 243.45/49.96  | | | | |           op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 243.45/49.96  | | | | |           $i(all_56_3))
% 243.45/49.96  | | | | | 
% 243.45/49.96  | | | | | BETA: splitting (67) gives:
% 243.45/49.96  | | | | | 
% 243.45/49.96  | | | | | Case 1:
% 243.45/49.96  | | | | | | 
% 243.45/49.96  | | | | | |   (68)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 243.45/49.96  | | | | | | 
% 243.45/49.96  | | | | | | ALPHA: (68) implies:
% 243.45/49.96  | | | | | |   (69)  op(e3, all_56_1) = e3
% 243.45/49.96  | | | | | | 
% 243.45/49.96  | | | | | | REDUCE: (38), (69) imply:
% 243.45/49.96  | | | | | |   (70)  op(e3, e1) = e3
% 243.45/49.96  | | | | | | 
% 243.45/49.96  | | | | | | REF_CLOSE: (13), (30), (55), (70) are inconsistent by sub-proof
% 243.45/49.96  | | | | | |            #2118.
% 243.45/49.96  | | | | | | 
% 243.45/49.96  | | | | | Case 2:
% 243.45/49.96  | | | | | | 
% 243.45/49.96  | | | | | |   (71)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 243.45/49.96  | | | | | |         all_56_3 & $i(all_56_3)
% 243.45/49.96  | | | | | | 
% 243.45/49.96  | | | | | | ALPHA: (71) implies:
% 243.45/49.96  | | | | | |   (72)  op(e2, e3) = all_56_3
% 243.45/49.96  | | | | | |   (73)  op(e2, all_56_3) = e2
% 243.45/49.96  | | | | | | 
% 243.45/49.96  | | | | | | BETA: splitting (28) gives:
% 243.45/49.96  | | | | | | 
% 243.45/49.96  | | | | | | Case 1:
% 243.45/49.96  | | | | | | | 
% 243.45/49.96  | | | | | | |   (74)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 243.45/49.96  | | | | | | |           op(e2, e1) = e3)
% 243.45/49.96  | | | | | | | 
% 243.45/49.96  | | | | | | | BETA: splitting (74) gives:
% 243.45/49.96  | | | | | | | 
% 243.45/49.96  | | | | | | | Case 1:
% 243.45/49.96  | | | | | | | | 
% 243.45/49.96  | | | | | | | |   (75)  all_58_4 = e3 & op(e3, e1) = e3
% 243.45/49.96  | | | | | | | | 
% 243.45/49.96  | | | | | | | | REF_CLOSE: (39), (55), (75) are inconsistent by sub-proof #1244.
% 243.45/49.96  | | | | | | | | 
% 243.45/49.96  | | | | | | | Case 2:
% 243.45/49.96  | | | | | | | | 
% 243.45/49.96  | | | | | | | |   (76)  all_58_5 = e3 & op(e2, e1) = e3
% 243.45/49.96  | | | | | | | | 
% 243.45/49.96  | | | | | | | | ALPHA: (76) implies:
% 243.45/49.96  | | | | | | | |   (77)  all_58_5 = e3
% 243.45/49.96  | | | | | | | | 
% 243.45/49.96  | | | | | | | | BETA: splitting (14) gives:
% 243.45/49.96  | | | | | | | | 
% 243.45/49.96  | | | | | | | | Case 1:
% 243.45/49.96  | | | | | | | | | 
% 243.45/49.96  | | | | | | | | |   (78)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 243.45/49.96  | | | | | | | | |           op(e2, e3) = e3)
% 243.45/49.96  | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | REF_CLOSE: (15), (25), (30), (53), (54), (78) are inconsistent
% 243.45/49.96  | | | | | | | | |            by sub-proof #1208.
% 243.45/49.96  | | | | | | | | | 
% 243.45/49.96  | | | | | | | | Case 2:
% 243.45/49.96  | | | | | | | | | 
% 243.45/49.96  | | | | | | | | |   (79)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 243.45/49.96  | | | | | | | | |           op(e0, e3) = e3)
% 243.45/49.96  | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | BETA: splitting (79) gives:
% 243.45/49.96  | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | Case 1:
% 243.45/49.96  | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | |   (80)  all_58_6 = e3 & op(e1, e3) = e3
% 243.45/49.96  | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | ALPHA: (80) implies:
% 243.45/49.96  | | | | | | | | | |   (81)  all_58_6 = e3
% 243.45/49.96  | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | REF_CLOSE: (21), (55), (81) are inconsistent by sub-proof
% 243.45/49.96  | | | | | | | | | |            #2222.
% 243.45/49.96  | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | Case 2:
% 243.45/49.96  | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | |   (82)  all_58_12 = e3 & op(e0, e3) = e3
% 243.45/49.96  | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | ALPHA: (82) implies:
% 243.45/49.96  | | | | | | | | | |   (83)  all_58_12 = e3
% 243.45/49.96  | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | BETA: splitting (37) gives:
% 243.45/49.96  | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | Case 1:
% 243.45/49.96  | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | |   (84)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 243.45/49.96  | | | | | | | | | | |           & op(e2, e2) = e1)
% 243.45/49.96  | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | BETA: splitting (84) gives:
% 243.45/49.96  | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | Case 1:
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | |   (85)  all_58_2 = e1 & op(e2, e3) = e1
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | REF_CLOSE: (25), (30), (40), (85) are inconsistent by
% 243.45/49.96  | | | | | | | | | | | |            sub-proof #2229.
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | Case 2:
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | |   (86)  all_58_3 = e1 & op(e2, e2) = e1
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | REF_CLOSE: (32), (35), (86) are inconsistent by sub-proof
% 243.45/49.96  | | | | | | | | | | | |            #1591.
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | End of split
% 243.45/49.96  | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | Case 2:
% 243.45/49.96  | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | |   (87)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 243.45/49.96  | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 243.45/49.96  | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | BETA: splitting (87) gives:
% 243.45/49.96  | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | Case 1:
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | |   (88)  all_58_5 = e1 & op(e2, e1) = e1
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | REF_CLOSE: (14), (15), (19), (23), (25), (30), (32), (53),
% 243.45/49.96  | | | | | | | | | | | |            (54), (55), (63), (64), (65), (77), (83), (88) are
% 243.45/49.96  | | | | | | | | | | | |            inconsistent by sub-proof #1203.
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | Case 2:
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | |   (89)  all_58_10 = e1 & op(e2, e0) = e1
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | ALPHA: (89) implies:
% 243.45/49.96  | | | | | | | | | | | |   (90)  all_58_10 = e1
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | BETA: splitting (7) gives:
% 243.45/49.96  | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | Case 1:
% 243.45/49.96  | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | |   (91)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 243.45/49.96  | | | | | | | | | | | | |           & op(e2, e2) = e3)
% 243.45/49.96  | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | BETA: splitting (91) gives:
% 243.45/49.96  | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | Case 1:
% 243.45/49.96  | | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | |   (92)  all_58_2 = e3 & op(e2, e3) = e3
% 243.45/49.96  | | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | | ALPHA: (92) implies:
% 243.45/49.96  | | | | | | | | | | | | | |   (93)  op(e2, e3) = e3
% 243.45/49.96  | | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | | REF_CLOSE: (25), (30), (53), (93) are inconsistent by
% 243.45/49.96  | | | | | | | | | | | | | |            sub-proof #2337.
% 243.45/49.96  | | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | Case 2:
% 243.45/49.96  | | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | |   (94)  all_58_3 = e3 & op(e2, e2) = e3
% 243.45/49.96  | | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | | REF_CLOSE: (35), (55), (94) are inconsistent by sub-proof
% 243.45/49.96  | | | | | | | | | | | | | |            #1516.
% 243.45/49.96  | | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | End of split
% 243.45/49.96  | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | Case 2:
% 243.45/49.96  | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | |   (95)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 243.45/49.96  | | | | | | | | | | | | |           e3 & op(e2, e0) = e3)
% 243.45/49.96  | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | BETA: splitting (95) gives:
% 243.45/49.96  | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | Case 1:
% 243.45/49.96  | | | | | | | | | | | | | | 
% 243.45/49.96  | | | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with e2, all_56_3, e3, e2,
% 243.45/49.97  | | | | | | | | | | | | | |              simplifying with (66), (72) gives:
% 243.45/49.97  | | | | | | | | | | | | | |   (96)  all_56_3 = e2
% 243.45/49.97  | | | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | | | REDUCE: (73), (96) imply:
% 243.45/49.97  | | | | | | | | | | | | | |   (97)  op(e2, e2) = e2
% 243.45/49.97  | | | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | | | REF_CLOSE: (12), (30), (65), (97) are inconsistent by
% 243.45/49.97  | | | | | | | | | | | | | |            sub-proof #2137.
% 243.45/49.97  | | | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | | |   (98)  all_58_10 = e3 & op(e2, e0) = e3
% 243.45/49.97  | | | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (19), (23), (25), (30), (32), (53),
% 243.45/49.97  | | | | | | | | | | | | | |            (54), (55), (63), (64), (65), (83), (90), (98) are
% 243.45/49.97  | | | | | | | | | | | | | |            inconsistent by sub-proof #1202.
% 243.45/49.97  | | | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | End of split
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | Case 2:
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | |   (99)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 243.45/49.97  | | | | | | |           op(e0, e1) = e3)
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | | REF_CLOSE: (9), (14), (15), (17), (18), (19), (21), (23), (25),
% 243.45/49.97  | | | | | | |            (30), (32), (34), (36), (53), (54), (55), (63), (64),
% 243.45/49.97  | | | | | | |            (65), (99) are inconsistent by sub-proof #1198.
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | End of split
% 243.45/49.97  | | | | | | 
% 243.45/49.97  | | | | | End of split
% 243.45/49.97  | | | | | 
% 243.45/49.97  | | | | Case 2:
% 243.45/49.97  | | | | | 
% 243.45/49.97  | | | | |   (100)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 243.45/49.97  | | | | |            all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 243.45/49.97  | | | | |              all_56_7) = e0 & op(e0, e3) = all_56_7 & $i(all_56_7))
% 243.45/49.97  | | | | | 
% 243.45/49.97  | | | | | BETA: splitting (100) gives:
% 243.45/49.97  | | | | | 
% 243.45/49.97  | | | | | Case 1:
% 243.45/49.97  | | | | | | 
% 243.45/49.97  | | | | | |   (101)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 243.45/49.97  | | | | | |          all_56_5 & $i(all_56_5)
% 243.45/49.97  | | | | | | 
% 243.45/49.97  | | | | | | ALPHA: (101) implies:
% 243.45/49.97  | | | | | |   (102)  op(e1, e3) = all_56_5
% 243.45/49.97  | | | | | |   (103)  op(e1, all_56_5) = e1
% 243.45/49.97  | | | | | | 
% 243.45/49.97  | | | | | | BETA: splitting (28) gives:
% 243.45/49.97  | | | | | | 
% 243.45/49.97  | | | | | | Case 1:
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | |   (104)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 243.45/49.97  | | | | | | |            op(e2, e1) = e3)
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | | BETA: splitting (104) gives:
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | |   (105)  all_58_4 = e3 & op(e3, e1) = e3
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | | REF_CLOSE: (39), (55), (105) are inconsistent by sub-proof
% 243.45/49.97  | | | | | | | |            #1244.
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | |   (106)  all_58_5 = e3 & op(e2, e1) = e3
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | | ALPHA: (106) implies:
% 243.45/49.97  | | | | | | | |   (107)  all_58_5 = e3
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | | BETA: splitting (14) gives:
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | |   (108)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 243.45/49.97  | | | | | | | | |            op(e2, e3) = e3)
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | REF_CLOSE: (15), (25), (30), (53), (54), (108) are
% 243.45/49.97  | | | | | | | | |            inconsistent by sub-proof #1208.
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | |   (109)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 243.45/49.97  | | | | | | | | |            op(e0, e3) = e3)
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | BETA: splitting (109) gives:
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | |   (110)  all_58_6 = e3 & op(e1, e3) = e3
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | ALPHA: (110) implies:
% 243.45/49.97  | | | | | | | | | |   (111)  op(e1, e3) = e3
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | REF_CLOSE: (30), (54), (102), (103), (111) are inconsistent
% 243.45/49.97  | | | | | | | | | |            by sub-proof #2243.
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | |   (112)  all_58_12 = e3 & op(e0, e3) = e3
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | ALPHA: (112) implies:
% 243.45/49.97  | | | | | | | | | |   (113)  all_58_12 = e3
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | BETA: splitting (37) gives:
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | |   (114)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 243.45/49.97  | | | | | | | | | | |            & op(e2, e2) = e1)
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | BETA: splitting (114) gives:
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | |   (115)  all_58_2 = e1 & op(e2, e3) = e1
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | REF_CLOSE: (25), (30), (40), (115) are inconsistent by
% 243.45/49.97  | | | | | | | | | | | |            sub-proof #2229.
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | |   (116)  all_58_3 = e1 & op(e2, e2) = e1
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | REF_CLOSE: (32), (35), (116) are inconsistent by sub-proof
% 243.45/49.97  | | | | | | | | | | | |            #1591.
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | |   (117)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 243.45/49.97  | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | BETA: splitting (117) gives:
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | |   (118)  all_58_5 = e1 & op(e2, e1) = e1
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | REF_CLOSE: (14), (15), (19), (23), (25), (30), (32), (53),
% 243.45/49.97  | | | | | | | | | | | |            (54), (55), (63), (64), (65), (107), (113), (118)
% 243.45/49.97  | | | | | | | | | | | |            are inconsistent by sub-proof #1203.
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | |   (119)  all_58_10 = e1 & op(e2, e0) = e1
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | ALPHA: (119) implies:
% 243.45/49.97  | | | | | | | | | | | |   (120)  op(e2, e0) = e1
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | GROUND_INST: instantiating (30) with e0, all_56_5, e3, e1,
% 243.45/49.97  | | | | | | | | | | | |              simplifying with (26), (102) gives:
% 243.45/49.97  | | | | | | | | | | | |   (121)  all_56_5 = e0
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_52_13, e1, e0, e2,
% 243.45/49.97  | | | | | | | | | | | |              simplifying with (33), (120) gives:
% 243.45/49.97  | | | | | | | | | | | |   (122)  all_52_13 = e1
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | REDUCE: (29), (122) imply:
% 243.45/49.97  | | | | | | | | | | | |   (123)   ~ (all_52_14 = e1)
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | SIMP: (123) implies:
% 243.45/49.97  | | | | | | | | | | | |   (124)   ~ (all_52_14 = e1)
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | REDUCE: (103), (121) imply:
% 243.45/49.97  | | | | | | | | | | | |   (125)  op(e1, e0) = e1
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | REF_CLOSE: (10), (30), (124), (125) are inconsistent by
% 243.45/49.97  | | | | | | | | | | | |            sub-proof #2304.
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | End of split
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | Case 2:
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | |   (126)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 243.45/49.97  | | | | | | |            op(e0, e1) = e3)
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | | REF_CLOSE: (9), (14), (15), (17), (18), (19), (21), (23), (25),
% 243.45/49.97  | | | | | | |            (30), (32), (34), (36), (53), (54), (55), (63), (64),
% 243.45/49.97  | | | | | | |            (65), (126) are inconsistent by sub-proof #1198.
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | End of split
% 243.45/49.97  | | | | | | 
% 243.45/49.97  | | | | | Case 2:
% 243.45/49.97  | | | | | | 
% 243.45/49.97  | | | | | |   (127)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 243.45/49.97  | | | | | |          all_56_7 & $i(all_56_7)
% 243.45/49.97  | | | | | | 
% 243.45/49.97  | | | | | | ALPHA: (127) implies:
% 243.45/49.97  | | | | | |   (128)  op(e0, e3) = all_56_7
% 243.45/49.97  | | | | | |   (129)  op(e0, all_56_7) = e0
% 243.45/49.97  | | | | | | 
% 243.45/49.97  | | | | | | BETA: splitting (28) gives:
% 243.45/49.97  | | | | | | 
% 243.45/49.97  | | | | | | Case 1:
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | |   (130)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 243.45/49.97  | | | | | | |            op(e2, e1) = e3)
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | | BETA: splitting (130) gives:
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | |   (131)  all_58_4 = e3 & op(e3, e1) = e3
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | | REF_CLOSE: (39), (55), (131) are inconsistent by sub-proof
% 243.45/49.97  | | | | | | | |            #1244.
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | |   (132)  all_58_5 = e3 & op(e2, e1) = e3
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | | ALPHA: (132) implies:
% 243.45/49.97  | | | | | | | |   (133)  all_58_5 = e3
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | | BETA: splitting (14) gives:
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | |   (134)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 243.45/49.97  | | | | | | | | |            op(e2, e3) = e3)
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | REF_CLOSE: (15), (25), (30), (53), (54), (134) are
% 243.45/49.97  | | | | | | | | |            inconsistent by sub-proof #1208.
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | |   (135)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 243.45/49.97  | | | | | | | | |            op(e0, e3) = e3)
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | BETA: splitting (135) gives:
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | |   (136)  all_58_6 = e3 & op(e1, e3) = e3
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | ALPHA: (136) implies:
% 243.45/49.97  | | | | | | | | | |   (137)  all_58_6 = e3
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | REF_CLOSE: (21), (55), (137) are inconsistent by sub-proof
% 243.45/49.97  | | | | | | | | | |            #2222.
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | |   (138)  all_58_12 = e3 & op(e0, e3) = e3
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | ALPHA: (138) implies:
% 243.45/49.97  | | | | | | | | | |   (139)  all_58_12 = e3
% 243.45/49.97  | | | | | | | | | |   (140)  op(e0, e3) = e3
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | BETA: splitting (37) gives:
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | |   (141)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 243.45/49.97  | | | | | | | | | | |            & op(e2, e2) = e1)
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | BETA: splitting (141) gives:
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | |   (142)  all_58_2 = e1 & op(e2, e3) = e1
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | REF_CLOSE: (25), (30), (40), (142) are inconsistent by
% 243.45/49.97  | | | | | | | | | | | |            sub-proof #2229.
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | |   (143)  all_58_3 = e1 & op(e2, e2) = e1
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | REF_CLOSE: (32), (35), (143) are inconsistent by sub-proof
% 243.45/49.97  | | | | | | | | | | | |            #1591.
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | |   (144)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 243.45/49.97  | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | BETA: splitting (144) gives:
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | Case 1:
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | |   (145)  all_58_5 = e1 & op(e2, e1) = e1
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | REF_CLOSE: (14), (15), (19), (23), (25), (30), (32), (53),
% 243.45/49.97  | | | | | | | | | | | |            (54), (55), (63), (64), (65), (133), (139), (145)
% 243.45/49.97  | | | | | | | | | | | |            are inconsistent by sub-proof #1203.
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | Case 2:
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | GROUND_INST: instantiating (30) with e3, all_56_7, e3, e0,
% 243.45/49.97  | | | | | | | | | | | |              simplifying with (128), (140) gives:
% 243.45/49.97  | | | | | | | | | | | |   (146)  all_56_7 = e3
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | REDUCE: (129), (146) imply:
% 243.45/49.97  | | | | | | | | | | | |   (147)  op(e0, e3) = e0
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | | REF_CLOSE: (1), (11), (30), (147) are inconsistent by
% 243.45/49.97  | | | | | | | | | | | |            sub-proof #2331.
% 243.45/49.97  | | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | | 
% 243.45/49.97  | | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | | 
% 243.45/49.97  | | | | | | | | End of split
% 243.45/49.97  | | | | | | | | 
% 243.45/49.97  | | | | | | | End of split
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | Case 2:
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | |   (148)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 243.45/49.97  | | | | | | |            op(e0, e1) = e3)
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | | REF_CLOSE: (9), (14), (15), (17), (18), (19), (21), (23), (25),
% 243.45/49.97  | | | | | | |            (30), (32), (34), (36), (53), (54), (55), (63), (64),
% 243.45/49.97  | | | | | | |            (65), (148) are inconsistent by sub-proof #1198.
% 243.45/49.97  | | | | | | | 
% 243.45/49.97  | | | | | | End of split
% 243.45/49.97  | | | | | | 
% 243.45/49.97  | | | | | End of split
% 243.45/49.97  | | | | | 
% 243.45/49.97  | | | | End of split
% 243.45/49.97  | | | | 
% 243.45/49.97  | | | Case 2:
% 243.45/49.97  | | | | 
% 243.45/49.97  | | | |   (149)  all_54_4 = e1 | all_54_4 = e0
% 243.45/49.97  | | | | 
% 243.45/49.97  | | | | REF_CLOSE: (16), (24), (40), (149) are inconsistent by sub-proof #1922.
% 243.45/49.97  | | | | 
% 243.45/49.97  | | | End of split
% 243.45/49.97  | | | 
% 243.45/49.97  | | End of split
% 243.45/49.97  | | 
% 243.45/49.97  | Case 2:
% 243.45/49.97  | | 
% 243.45/49.97  | |   (150)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.45/49.97  | | 
% 243.45/49.97  | | BETA: splitting (150) gives:
% 243.45/49.97  | | 
% 243.45/49.97  | | Case 1:
% 243.45/49.97  | | | 
% 243.45/49.97  | | |   (151)  all_54_12 = e2
% 243.45/49.97  | | | 
% 243.45/49.97  | | | REF_CLOSE: (6), (46), (151) are inconsistent by sub-proof #1197.
% 243.45/49.97  | | | 
% 243.45/49.97  | | Case 2:
% 243.45/49.97  | | | 
% 243.45/49.97  | | |   (152)  all_54_12 = e1 | all_54_12 = e0
% 243.45/49.97  | | | 
% 243.45/49.97  | | | REF_CLOSE: (1), (5), (22), (152) are inconsistent by sub-proof #2067.
% 243.45/49.97  | | | 
% 243.45/49.97  | | End of split
% 243.45/49.97  | | 
% 243.45/49.97  | End of split
% 243.45/49.97  | 
% 243.45/49.97  End of proof
% 243.45/49.97  
% 243.45/49.97  Sub-proof #1197 shows that the following formulas are inconsistent:
% 243.45/49.97  ----------------------------------------------------------------
% 243.45/49.97    (1)  all_54_12 = all_38_0
% 243.45/49.97    (2)  all_54_12 = e2
% 243.45/49.97    (3)   ~ (all_38_0 = e2)
% 243.45/49.97  
% 243.45/49.97  Begin of proof
% 243.45/49.97  | 
% 243.45/49.97  | COMBINE_EQS: (1), (2) imply:
% 243.45/49.97  |   (4)  all_38_0 = e2
% 243.45/49.97  | 
% 243.45/49.97  | SIMP: (4) implies:
% 243.45/49.97  |   (5)  all_38_0 = e2
% 243.45/49.97  | 
% 243.45/49.97  | REDUCE: (3), (5) imply:
% 243.45/49.97  |   (6)  $false
% 243.45/49.97  | 
% 243.45/49.97  | CLOSE: (6) is inconsistent.
% 243.45/49.97  | 
% 243.45/49.97  End of proof
% 243.45/49.97  
% 243.45/49.97  Sub-proof #1198 shows that the following formulas are inconsistent:
% 243.45/49.97  ----------------------------------------------------------------
% 243.45/49.97    (1)   ~ (e3 = e0)
% 243.45/49.97    (2)   ~ (e2 = e0)
% 243.45/49.97    (3)  op(e1, e1) = all_6_2
% 243.45/49.97    (4)   ~ (e3 = e1)
% 243.45/49.97    (5)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.45/49.97    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.97         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.97    (7)  op(e3, e3) = e1
% 243.45/49.97    (8)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.45/49.97             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.45/49.97               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.45/49.97               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.45/49.97    (9)   ~ (all_6_2 = e3)
% 243.45/49.97    (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.97          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.97    (11)   ~ (e3 = e2)
% 243.45/49.97    (12)  all_58_6 = e0
% 243.45/49.97    (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.97          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.97    (14)  op(e2, e3) = all_52_1
% 243.45/49.97    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.97            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.97    (16)   ~ (e1 = e0)
% 243.45/49.97    (17)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.45/49.97          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.45/49.97            e1)
% 243.45/49.97    (18)   ~ (all_52_1 = e3)
% 243.45/49.97    (19)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.45/49.97          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.45/49.97            e2)
% 243.45/49.97    (20)   ~ (e2 = e1)
% 243.45/49.97  
% 243.45/49.97  Begin of proof
% 243.45/49.97  | 
% 243.45/49.97  | BETA: splitting (5) gives:
% 243.45/49.97  | 
% 243.45/49.97  | Case 1:
% 243.45/49.97  | | 
% 243.45/49.97  | |   (21)  all_58_8 = e3 & op(e1, e1) = e3
% 243.45/49.97  | | 
% 243.45/49.97  | | REF_CLOSE: (3), (9), (15), (21) are inconsistent by sub-proof #2092.
% 243.45/49.97  | | 
% 243.45/49.97  | Case 2:
% 243.45/49.97  | | 
% 243.45/49.97  | |   (22)  all_58_14 = e3 & op(e0, e1) = e3
% 243.45/49.97  | | 
% 243.45/49.97  | | ALPHA: (22) implies:
% 243.45/49.97  | |   (23)  all_58_14 = e3
% 243.45/49.97  | | 
% 243.45/49.97  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 243.45/49.97  | |            (16), (17), (18), (19), (20), (23) are inconsistent by sub-proof
% 243.45/49.97  | |            #1199.
% 243.45/49.97  | | 
% 243.45/49.97  | End of split
% 243.45/49.97  | 
% 243.45/49.97  End of proof
% 243.45/49.97  
% 243.45/49.97  Sub-proof #1199 shows that the following formulas are inconsistent:
% 243.45/49.97  ----------------------------------------------------------------
% 243.45/49.97    (1)   ~ (e3 = e0)
% 243.45/49.97    (2)   ~ (e2 = e0)
% 243.45/49.97    (3)   ~ (e3 = e1)
% 243.45/49.97    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.97         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.97    (5)  op(e3, e3) = e1
% 243.45/49.97    (6)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.45/49.97             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.45/49.97               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.45/49.97               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.45/49.97    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.97         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.97    (8)   ~ (e3 = e2)
% 243.45/49.97    (9)  all_58_6 = e0
% 243.45/49.97    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.98          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.98    (11)  op(e2, e3) = all_52_1
% 243.45/49.98    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.98    (13)  all_58_14 = e3
% 243.45/49.98    (14)   ~ (e1 = e0)
% 243.45/49.98    (15)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.45/49.98          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.45/49.98            e1)
% 243.45/49.98    (16)   ~ (all_52_1 = e3)
% 243.45/49.98    (17)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.45/49.98          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.45/49.98            e2)
% 243.45/49.98    (18)   ~ (e2 = e1)
% 243.45/49.98  
% 243.45/49.98  Begin of proof
% 243.45/49.98  | 
% 243.45/49.98  | BETA: splitting (4) gives:
% 243.45/49.98  | 
% 243.45/49.98  | Case 1:
% 243.45/49.98  | | 
% 243.45/49.98  | |   (19)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 243.45/49.98  | |           e3)
% 243.45/49.98  | | 
% 243.45/49.98  | | REF_CLOSE: (3), (5), (11), (12), (16), (19) are inconsistent by sub-proof
% 243.45/49.98  | |            #1208.
% 243.45/49.98  | | 
% 243.45/49.98  | Case 2:
% 243.45/49.98  | | 
% 243.45/49.98  | |   (20)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 243.45/49.98  | |           e3)
% 243.45/49.98  | | 
% 243.45/49.98  | | BETA: splitting (20) gives:
% 243.45/49.98  | | 
% 243.45/49.98  | | Case 1:
% 243.45/49.98  | | | 
% 243.45/49.98  | | |   (21)  all_58_6 = e3 & op(e1, e3) = e3
% 243.45/49.98  | | | 
% 243.45/49.98  | | | REF_CLOSE: (1), (9), (21) are inconsistent by sub-proof #1690.
% 243.45/49.98  | | | 
% 243.45/49.98  | | Case 2:
% 243.45/49.98  | | | 
% 243.45/49.98  | | |   (22)  all_58_12 = e3 & op(e0, e3) = e3
% 243.45/49.98  | | | 
% 243.45/49.98  | | | ALPHA: (22) implies:
% 243.45/49.98  | | |   (23)  all_58_12 = e3
% 243.45/49.98  | | | 
% 243.45/49.98  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 243.45/49.98  | | |            (14), (15), (16), (17), (18), (23) are inconsistent by
% 243.45/49.98  | | |            sub-proof #1200.
% 243.45/49.98  | | | 
% 243.45/49.98  | | End of split
% 243.45/49.98  | | 
% 243.45/49.98  | End of split
% 243.45/49.98  | 
% 243.45/49.98  End of proof
% 243.45/49.98  
% 243.45/49.98  Sub-proof #1200 shows that the following formulas are inconsistent:
% 243.45/49.98  ----------------------------------------------------------------
% 243.45/49.98    (1)   ~ (e3 = e0)
% 243.45/49.98    (2)   ~ (e2 = e0)
% 243.45/49.98    (3)   ~ (e3 = e1)
% 243.45/49.98    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.98         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.98    (5)  op(e3, e3) = e1
% 243.45/49.98    (6)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.45/49.98             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.45/49.98               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.45/49.98               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.45/49.98    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.98         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.98    (8)   ~ (e3 = e2)
% 243.45/49.98    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.98         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.98    (10)  op(e2, e3) = all_52_1
% 243.45/49.98    (11)  all_58_12 = e3
% 243.45/49.98    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.98    (13)  all_58_14 = e3
% 243.45/49.98    (14)   ~ (e1 = e0)
% 243.45/49.98    (15)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.45/49.98          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.45/49.98            e1)
% 243.45/49.98    (16)   ~ (all_52_1 = e3)
% 243.45/49.98    (17)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.45/49.98          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.45/49.98            e2)
% 243.45/49.98    (18)   ~ (e2 = e1)
% 243.45/49.98  
% 243.45/49.98  Begin of proof
% 243.45/49.98  | 
% 243.45/49.98  | BETA: splitting (15) gives:
% 243.45/49.98  | 
% 243.45/49.98  | Case 1:
% 243.45/49.98  | | 
% 243.45/49.98  | |   (19)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 243.45/49.98  | |           e1)
% 243.45/49.98  | | 
% 243.45/49.98  | | BETA: splitting (19) gives:
% 243.45/49.98  | | 
% 243.45/49.98  | | Case 1:
% 243.45/49.98  | | | 
% 243.45/49.98  | | |   (20)  all_58_12 = e1 & op(e0, e3) = e1
% 243.45/49.98  | | | 
% 243.45/49.98  | | | ALPHA: (20) implies:
% 243.45/49.98  | | |   (21)  all_58_12 = e1
% 243.45/49.98  | | | 
% 243.45/49.98  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (14), (16),
% 243.45/49.98  | | |            (18), (21) are inconsistent by sub-proof #1204.
% 243.45/49.98  | | | 
% 243.45/49.98  | | Case 2:
% 243.45/49.98  | | | 
% 243.45/49.98  | | |   (22)  all_58_13 = e1 & op(e0, e2) = e1
% 243.45/49.98  | | | 
% 243.45/49.98  | | | ALPHA: (22) implies:
% 243.45/49.98  | | |   (23)  all_58_13 = e1
% 243.45/49.98  | | |   (24)  op(e0, e2) = e1
% 243.45/49.98  | | | 
% 243.45/49.98  | | | REF_CLOSE: (1), (2), (6), (8), (11), (12), (13), (14), (17), (18), (23),
% 243.45/49.98  | | |            (24) are inconsistent by sub-proof #1868.
% 243.45/49.98  | | | 
% 243.45/49.98  | | End of split
% 243.45/49.98  | | 
% 243.45/49.98  | Case 2:
% 243.45/49.98  | | 
% 243.45/49.98  | |   (25)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.45/49.98  | |           e1)
% 243.45/49.98  | | 
% 243.45/49.98  | | BETA: splitting (25) gives:
% 243.45/49.98  | | 
% 243.45/49.98  | | Case 1:
% 243.45/49.98  | | | 
% 243.45/49.98  | | |   (26)  all_58_14 = e1 & op(e0, e1) = e1
% 243.45/49.98  | | | 
% 243.45/49.98  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 243.45/49.98  | | |            (14), (16), (18), (26) are inconsistent by sub-proof #1201.
% 243.45/49.98  | | | 
% 243.45/49.98  | | Case 2:
% 243.45/49.98  | | | 
% 243.45/49.98  | | |   (27)  all_58_15 = e1 & op(e0, e0) = e1
% 243.45/49.98  | | | 
% 243.45/49.98  | | | ALPHA: (27) implies:
% 243.45/49.98  | | |   (28)  all_58_15 = e1
% 243.45/49.98  | | | 
% 243.45/49.98  | | | REF_CLOSE: (1), (2), (6), (8), (11), (13), (14), (17), (18), (28) are
% 243.45/49.98  | | |            inconsistent by sub-proof #1863.
% 243.45/49.98  | | | 
% 243.45/49.98  | | End of split
% 243.45/49.98  | | 
% 243.45/49.98  | End of split
% 243.45/49.98  | 
% 243.45/49.98  End of proof
% 243.45/49.98  
% 243.45/49.98  Sub-proof #1201 shows that the following formulas are inconsistent:
% 243.45/49.98  ----------------------------------------------------------------
% 243.45/49.98    (1)  all_58_14 = e1 & op(e0, e1) = e1
% 243.45/49.98    (2)   ~ (e3 = e0)
% 243.45/49.98    (3)   ~ (e2 = e0)
% 243.45/49.98    (4)   ~ (e3 = e1)
% 243.45/49.98    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.98         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.98    (6)  op(e3, e3) = e1
% 243.45/49.98    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.98         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.98    (8)   ~ (e3 = e2)
% 243.45/49.98    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.98         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.98    (10)  op(e2, e3) = all_52_1
% 243.45/49.98    (11)  all_58_12 = e3
% 243.45/49.98    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.98    (13)  all_58_14 = e3
% 243.45/49.98    (14)   ~ (e1 = e0)
% 243.45/49.98    (15)   ~ (all_52_1 = e3)
% 243.45/49.98    (16)   ~ (e2 = e1)
% 243.45/49.98  
% 243.45/49.98  Begin of proof
% 243.45/49.98  | 
% 243.45/49.98  | ALPHA: (1) implies:
% 243.45/49.98  |   (17)  all_58_14 = e1
% 243.45/49.98  | 
% 243.45/49.98  | COMBINE_EQS: (13), (17) imply:
% 243.45/49.98  |   (18)  e3 = e1
% 243.45/49.98  | 
% 243.45/49.98  | SIMP: (18) implies:
% 243.45/49.98  |   (19)  e3 = e1
% 243.45/49.98  | 
% 243.45/49.98  | COMBINE_EQS: (11), (19) imply:
% 243.45/49.98  |   (20)  all_58_12 = e1
% 243.45/49.98  | 
% 243.45/49.98  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14), (15),
% 243.45/49.98  |            (16), (20) are inconsistent by sub-proof #1204.
% 243.45/49.98  | 
% 243.45/49.98  End of proof
% 243.45/49.98  
% 243.45/49.98  Sub-proof #1202 shows that the following formulas are inconsistent:
% 243.45/49.98  ----------------------------------------------------------------
% 243.45/49.98    (1)   ~ (e3 = e0)
% 243.45/49.98    (2)   ~ (e2 = e0)
% 243.45/49.98    (3)   ~ (e3 = e1)
% 243.45/49.98    (4)  all_58_10 = e3 & op(e2, e0) = e3
% 243.45/49.98    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.98         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.98    (6)  op(e3, e3) = e1
% 243.45/49.98    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.98         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.98    (8)   ~ (e3 = e2)
% 243.45/49.98    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.98         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.98    (10)  op(e2, e3) = all_52_1
% 243.45/49.98    (11)  all_58_12 = e3
% 243.45/49.98    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.98    (13)   ~ (e1 = e0)
% 243.45/49.98    (14)   ~ (all_52_1 = e3)
% 243.45/49.98    (15)  all_58_10 = e1
% 243.45/49.98    (16)   ~ (e2 = e1)
% 243.45/49.98  
% 243.45/49.98  Begin of proof
% 243.45/49.98  | 
% 243.45/49.98  | ALPHA: (4) implies:
% 243.45/49.98  |   (17)  all_58_10 = e3
% 243.45/49.98  | 
% 243.45/49.98  | COMBINE_EQS: (15), (17) imply:
% 243.45/49.98  |   (18)  e3 = e1
% 243.45/49.98  | 
% 243.45/49.98  | COMBINE_EQS: (11), (18) imply:
% 243.45/49.98  |   (19)  all_58_12 = e1
% 243.45/49.98  | 
% 243.45/49.98  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 243.45/49.98  |            (16), (19) are inconsistent by sub-proof #1204.
% 243.45/49.98  | 
% 243.45/49.98  End of proof
% 243.45/49.98  
% 243.45/49.98  Sub-proof #1203 shows that the following formulas are inconsistent:
% 243.45/49.98  ----------------------------------------------------------------
% 243.45/49.98    (1)   ~ (e3 = e0)
% 243.45/49.98    (2)   ~ (e2 = e0)
% 243.45/49.98    (3)  all_58_5 = e3
% 243.45/49.98    (4)  all_58_5 = e1 & op(e2, e1) = e1
% 243.45/49.98    (5)   ~ (e3 = e1)
% 243.45/49.98    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.98         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.98    (7)  op(e3, e3) = e1
% 243.45/49.98    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.98         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.98    (9)   ~ (e3 = e2)
% 243.45/49.98    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.98          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.98    (11)  op(e2, e3) = all_52_1
% 243.45/49.98    (12)  all_58_12 = e3
% 243.45/49.98    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.98    (14)   ~ (e1 = e0)
% 243.45/49.98    (15)   ~ (all_52_1 = e3)
% 243.45/49.98    (16)   ~ (e2 = e1)
% 243.45/49.98  
% 243.45/49.98  Begin of proof
% 243.45/49.98  | 
% 243.45/49.98  | ALPHA: (4) implies:
% 243.45/49.98  |   (17)  all_58_5 = e1
% 243.45/49.98  | 
% 243.45/49.98  | COMBINE_EQS: (3), (17) imply:
% 243.45/49.98  |   (18)  e3 = e1
% 243.45/49.98  | 
% 243.45/49.98  | COMBINE_EQS: (12), (18) imply:
% 243.45/49.98  |   (19)  all_58_12 = e1
% 243.45/49.98  | 
% 243.45/49.98  | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (13), (14), (15),
% 243.45/49.98  |            (16), (19) are inconsistent by sub-proof #1204.
% 243.45/49.98  | 
% 243.45/49.98  End of proof
% 243.45/49.98  
% 243.45/49.98  Sub-proof #1204 shows that the following formulas are inconsistent:
% 243.45/49.98  ----------------------------------------------------------------
% 243.45/49.98    (1)   ~ (e3 = e0)
% 243.45/49.98    (2)   ~ (e2 = e0)
% 243.45/49.98    (3)   ~ (e3 = e1)
% 243.45/49.98    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.45/49.98         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.45/49.98    (5)  all_58_12 = e1
% 243.45/49.98    (6)  op(e3, e3) = e1
% 243.45/49.98    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.98         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.98    (8)   ~ (e3 = e2)
% 243.45/49.98    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.98         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.98    (10)  op(e2, e3) = all_52_1
% 243.45/49.98    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.98    (12)   ~ (e1 = e0)
% 243.45/49.98    (13)   ~ (all_52_1 = e3)
% 243.45/49.98    (14)   ~ (e2 = e1)
% 243.45/49.98  
% 243.45/49.98  Begin of proof
% 243.45/49.98  | 
% 243.45/49.98  | BETA: splitting (4) gives:
% 243.45/49.98  | 
% 243.45/49.98  | Case 1:
% 243.45/49.98  | | 
% 243.45/49.98  | |   (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 243.45/49.98  | |           e3)
% 243.45/49.98  | | 
% 243.45/49.98  | | REF_CLOSE: (3), (6), (10), (11), (13), (15) are inconsistent by sub-proof
% 243.45/49.98  | |            #1208.
% 243.45/49.98  | | 
% 243.45/49.98  | Case 2:
% 243.45/49.98  | | 
% 243.45/49.98  | |   (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 243.45/49.98  | |           e3)
% 243.45/49.98  | | 
% 243.45/49.98  | | BETA: splitting (16) gives:
% 243.45/49.98  | | 
% 243.45/49.98  | | Case 1:
% 243.45/49.98  | | | 
% 243.45/49.98  | | |   (17)  all_58_6 = e3 & op(e1, e3) = e3
% 243.45/49.98  | | | 
% 243.45/49.98  | | | ALPHA: (17) implies:
% 243.45/49.98  | | |   (18)  all_58_6 = e3
% 243.45/49.98  | | | 
% 243.45/49.98  | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (14), (18) are
% 243.45/49.98  | | |            inconsistent by sub-proof #1206.
% 243.45/49.98  | | | 
% 243.45/49.98  | | Case 2:
% 243.45/49.98  | | | 
% 243.45/49.98  | | |   (19)  all_58_12 = e3 & op(e0, e3) = e3
% 243.45/49.98  | | | 
% 243.45/49.98  | | | REF_CLOSE: (3), (5), (19) are inconsistent by sub-proof #1205.
% 243.45/49.98  | | | 
% 243.45/49.98  | | End of split
% 243.45/49.98  | | 
% 243.45/49.98  | End of split
% 243.45/49.98  | 
% 243.45/49.98  End of proof
% 243.45/49.98  
% 243.45/49.98  Sub-proof #1205 shows that the following formulas are inconsistent:
% 243.45/49.98  ----------------------------------------------------------------
% 243.45/49.98    (1)  all_58_12 = e3 & op(e0, e3) = e3
% 243.45/49.98    (2)  all_58_12 = e1
% 243.45/49.98    (3)   ~ (e3 = e1)
% 243.45/49.98  
% 243.45/49.98  Begin of proof
% 243.45/49.98  | 
% 243.45/49.98  | ALPHA: (1) implies:
% 243.45/49.98  |   (4)  all_58_12 = e3
% 243.45/49.98  | 
% 243.45/49.98  | COMBINE_EQS: (2), (4) imply:
% 243.45/49.98  |   (5)  e3 = e1
% 243.45/49.98  | 
% 243.45/49.98  | REDUCE: (3), (5) imply:
% 243.45/49.98  |   (6)  $false
% 243.45/49.98  | 
% 243.45/49.98  | CLOSE: (6) is inconsistent.
% 243.45/49.98  | 
% 243.45/49.98  End of proof
% 243.45/49.98  
% 243.45/49.98  Sub-proof #1206 shows that the following formulas are inconsistent:
% 243.45/49.98  ----------------------------------------------------------------
% 243.45/49.98    (1)   ~ (e3 = e0)
% 243.45/49.98    (2)  all_58_6 = e3
% 243.45/49.98    (3)   ~ (e2 = e0)
% 243.45/49.98    (4)  all_58_12 = e1
% 243.45/49.98    (5)  op(e3, e3) = e1
% 243.45/49.98    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.45/49.98         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.45/49.98    (7)   ~ (e3 = e2)
% 243.45/49.98    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.45/49.98         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.45/49.98    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.98    (10)   ~ (e1 = e0)
% 243.45/49.98    (11)   ~ (e2 = e1)
% 243.45/49.98  
% 243.45/49.98  Begin of proof
% 243.45/49.98  | 
% 243.45/49.98  | BETA: splitting (8) gives:
% 243.45/49.98  | 
% 243.45/49.98  | Case 1:
% 243.45/49.98  | | 
% 243.45/49.98  | |   (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 243.45/49.98  | |           e0)
% 243.45/49.98  | | 
% 243.45/49.98  | | BETA: splitting (12) gives:
% 243.45/49.98  | | 
% 243.45/49.98  | | Case 1:
% 243.45/49.98  | | | 
% 243.45/49.98  | | |   (13)  all_58_0 = e0 & op(e3, e3) = e0
% 243.45/49.98  | | | 
% 243.45/49.98  | | | ALPHA: (13) implies:
% 243.45/49.98  | | |   (14)  op(e3, e3) = e0
% 243.45/49.98  | | | 
% 243.45/49.98  | | | REF_CLOSE: (5), (9), (10), (14) are inconsistent by sub-proof #1828.
% 243.45/49.98  | | | 
% 243.45/49.98  | | Case 2:
% 243.45/49.98  | | | 
% 243.45/49.99  | | |   (15)  all_58_2 = e0 & op(e2, e3) = e0
% 243.45/49.99  | | | 
% 243.45/49.99  | | | ALPHA: (15) implies:
% 243.45/49.99  | | |   (16)  all_58_2 = e0
% 243.45/49.99  | | | 
% 243.45/49.99  | | | BETA: splitting (6) gives:
% 243.45/49.99  | | | 
% 243.45/49.99  | | | Case 1:
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | |   (17)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3)
% 243.45/49.99  | | | |           = e2)
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | | REF_CLOSE: (3), (5), (9), (11), (16), (17) are inconsistent by sub-proof
% 243.45/49.99  | | | |            #1329.
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | Case 2:
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | |   (18)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3)
% 243.45/49.99  | | | |           = e2)
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | | REF_CLOSE: (2), (4), (7), (11), (18) are inconsistent by sub-proof
% 243.45/49.99  | | | |            #1574.
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | End of split
% 243.45/49.99  | | | 
% 243.45/49.99  | | End of split
% 243.45/49.99  | | 
% 243.45/49.99  | Case 2:
% 243.45/49.99  | | 
% 243.45/49.99  | |   (19)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 243.45/49.99  | |           e0)
% 243.45/49.99  | | 
% 243.45/49.99  | | BETA: splitting (19) gives:
% 243.45/49.99  | | 
% 243.45/49.99  | | Case 1:
% 243.45/49.99  | | | 
% 243.45/49.99  | | |   (20)  all_58_6 = e0 & op(e1, e3) = e0
% 243.45/49.99  | | | 
% 243.45/49.99  | | | ALPHA: (20) implies:
% 243.45/49.99  | | |   (21)  all_58_6 = e0
% 243.45/49.99  | | | 
% 243.45/49.99  | | | REF_CLOSE: (1), (2), (21) are inconsistent by sub-proof #2222.
% 243.45/49.99  | | | 
% 243.45/49.99  | | Case 2:
% 243.45/49.99  | | | 
% 243.45/49.99  | | |   (22)  all_58_12 = e0 & op(e0, e3) = e0
% 243.45/49.99  | | | 
% 243.45/49.99  | | | REF_CLOSE: (4), (10), (22) are inconsistent by sub-proof #1207.
% 243.45/49.99  | | | 
% 243.45/49.99  | | End of split
% 243.45/49.99  | | 
% 243.45/49.99  | End of split
% 243.45/49.99  | 
% 243.45/49.99  End of proof
% 243.45/49.99  
% 243.45/49.99  Sub-proof #1207 shows that the following formulas are inconsistent:
% 243.45/49.99  ----------------------------------------------------------------
% 243.45/49.99    (1)  all_58_12 = e0 & op(e0, e3) = e0
% 243.45/49.99    (2)  all_58_12 = e1
% 243.45/49.99    (3)   ~ (e1 = e0)
% 243.45/49.99  
% 243.45/49.99  Begin of proof
% 243.45/49.99  | 
% 243.45/49.99  | ALPHA: (1) implies:
% 243.45/49.99  |   (4)  all_58_12 = e0
% 243.45/49.99  | 
% 243.45/49.99  | COMBINE_EQS: (2), (4) imply:
% 243.45/49.99  |   (5)  e1 = e0
% 243.45/49.99  | 
% 243.45/49.99  | REDUCE: (3), (5) imply:
% 243.45/49.99  |   (6)  $false
% 243.45/49.99  | 
% 243.45/49.99  | CLOSE: (6) is inconsistent.
% 243.45/49.99  | 
% 243.45/49.99  End of proof
% 243.45/49.99  
% 243.45/49.99  Sub-proof #1208 shows that the following formulas are inconsistent:
% 243.45/49.99  ----------------------------------------------------------------
% 243.45/49.99    (1)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 243.45/49.99    (2)   ~ (e3 = e1)
% 243.45/49.99    (3)  op(e3, e3) = e1
% 243.45/49.99    (4)  op(e2, e3) = all_52_1
% 243.45/49.99    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.99    (6)   ~ (all_52_1 = e3)
% 243.45/49.99  
% 243.45/49.99  Begin of proof
% 243.45/49.99  | 
% 243.45/49.99  | BETA: splitting (1) gives:
% 243.45/49.99  | 
% 243.45/49.99  | Case 1:
% 243.45/49.99  | | 
% 243.45/49.99  | |   (7)  all_58_0 = e3 & op(e3, e3) = e3
% 243.45/49.99  | | 
% 243.45/49.99  | | ALPHA: (7) implies:
% 243.45/49.99  | |   (8)  op(e3, e3) = e3
% 243.45/49.99  | | 
% 243.45/49.99  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1578.
% 243.45/49.99  | | 
% 243.45/49.99  | Case 2:
% 243.45/49.99  | | 
% 243.45/49.99  | |   (9)  all_58_2 = e3 & op(e2, e3) = e3
% 243.45/49.99  | | 
% 243.45/49.99  | | ALPHA: (9) implies:
% 243.45/49.99  | |   (10)  op(e2, e3) = e3
% 243.45/49.99  | | 
% 243.45/49.99  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #2337.
% 243.45/49.99  | | 
% 243.45/49.99  | End of split
% 243.45/49.99  | 
% 243.45/49.99  End of proof
% 243.45/49.99  
% 243.45/49.99  Sub-proof #1209 shows that the following formulas are inconsistent:
% 243.45/49.99  ----------------------------------------------------------------
% 243.45/49.99    (1)   ~ (e3 = e2)
% 243.45/49.99    (2)  op(e2, e2) = e1
% 243.45/49.99    (3)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 243.45/49.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.99    (5)  all_58_2 = e3
% 243.45/49.99    (6)   ~ (e2 = e1)
% 243.45/49.99  
% 243.45/49.99  Begin of proof
% 243.45/49.99  | 
% 243.45/49.99  | BETA: splitting (3) gives:
% 243.45/49.99  | 
% 243.45/49.99  | Case 1:
% 243.45/49.99  | | 
% 243.45/49.99  | |   (7)  all_58_2 = e2 & op(e2, e3) = e2
% 243.45/49.99  | | 
% 243.45/49.99  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #1224.
% 243.45/49.99  | | 
% 243.45/49.99  | Case 2:
% 243.45/49.99  | | 
% 243.45/49.99  | |   (8)  all_58_3 = e2 & op(e2, e2) = e2
% 243.45/49.99  | | 
% 243.45/49.99  | | ALPHA: (8) implies:
% 243.45/49.99  | |   (9)  op(e2, e2) = e2
% 243.45/49.99  | | 
% 243.45/49.99  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #2235.
% 243.45/49.99  | | 
% 243.45/49.99  | End of split
% 243.45/49.99  | 
% 243.45/49.99  End of proof
% 243.45/49.99  
% 243.45/49.99  Sub-proof #1210 shows that the following formulas are inconsistent:
% 243.45/49.99  ----------------------------------------------------------------
% 243.45/49.99    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.45/49.99             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 243.45/49.99    (2)  op(e2, e3) = e3
% 243.45/49.99    (3)  op(e3, e1) = all_52_8
% 243.45/49.99    (4)   ~ (e3 = e2)
% 243.45/49.99    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.99    (6)  all_56_1 = e1
% 243.45/49.99    (7)   ~ (all_52_8 = e3)
% 243.45/49.99  
% 243.45/49.99  Begin of proof
% 243.45/49.99  | 
% 243.45/49.99  | BETA: splitting (1) gives:
% 243.45/49.99  | 
% 243.45/49.99  | Case 1:
% 243.45/49.99  | | 
% 243.45/49.99  | |   (8)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 243.45/49.99  | | 
% 243.45/49.99  | | ALPHA: (8) implies:
% 243.45/49.99  | |   (9)  op(e3, all_56_1) = e3
% 243.45/49.99  | | 
% 243.45/49.99  | | REDUCE: (6), (9) imply:
% 243.45/49.99  | |   (10)  op(e3, e1) = e3
% 243.45/49.99  | | 
% 243.45/49.99  | | REF_CLOSE: (3), (5), (7), (10) are inconsistent by sub-proof #2260.
% 243.45/49.99  | | 
% 243.45/49.99  | Case 2:
% 243.45/49.99  | | 
% 243.45/49.99  | |   (11)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 243.45/49.99  | |         $i(all_56_3)
% 243.45/49.99  | | 
% 243.45/49.99  | | ALPHA: (11) implies:
% 243.45/49.99  | |   (12)  op(e2, e3) = all_56_3
% 243.45/49.99  | |   (13)  op(e2, all_56_3) = e2
% 243.45/49.99  | | 
% 243.45/49.99  | | REF_CLOSE: (2), (4), (5), (12), (13) are inconsistent by sub-proof #2262.
% 243.45/49.99  | | 
% 243.45/49.99  | End of split
% 243.45/49.99  | 
% 243.45/49.99  End of proof
% 243.45/49.99  
% 243.45/49.99  Sub-proof #1211 shows that the following formulas are inconsistent:
% 243.45/49.99  ----------------------------------------------------------------
% 243.45/49.99    (1)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 243.45/49.99    (2)   ~ (all_52_8 = e1)
% 243.45/49.99    (3)  op(e3, e1) = all_52_8
% 243.45/49.99    (4)  op(e2, e1) = all_52_9
% 243.45/49.99    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.99    (6)   ~ (all_52_9 = e1)
% 243.45/49.99  
% 243.45/49.99  Begin of proof
% 243.45/49.99  | 
% 243.45/49.99  | BETA: splitting (1) gives:
% 243.45/49.99  | 
% 243.45/49.99  | Case 1:
% 243.45/49.99  | | 
% 243.45/49.99  | |   (7)  all_58_4 = e1 & op(e3, e1) = e1
% 243.45/49.99  | | 
% 243.45/49.99  | | ALPHA: (7) implies:
% 243.45/49.99  | |   (8)  op(e3, e1) = e1
% 243.45/49.99  | | 
% 243.45/49.99  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #2309.
% 243.45/49.99  | | 
% 243.45/49.99  | Case 2:
% 243.45/49.99  | | 
% 243.45/49.99  | |   (9)  all_58_5 = e1 & op(e2, e1) = e1
% 243.45/49.99  | | 
% 243.45/49.99  | | ALPHA: (9) implies:
% 243.45/49.99  | |   (10)  op(e2, e1) = e1
% 243.45/49.99  | | 
% 243.45/49.99  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #2306.
% 243.45/49.99  | | 
% 243.45/49.99  | End of split
% 243.45/49.99  | 
% 243.45/49.99  End of proof
% 243.45/49.99  
% 243.45/49.99  Sub-proof #1212 shows that the following formulas are inconsistent:
% 243.45/49.99  ----------------------------------------------------------------
% 243.45/49.99    (1)   ~ (all_8_2 = e1)
% 243.45/49.99    (2)   ~ (all_52_3 = e0)
% 243.45/49.99    (3)   ~ (all_52_9 = all_8_2)
% 243.45/49.99    (4)   ~ (all_8_2 = e0)
% 243.45/49.99    (5)   ~ (all_52_1 = all_8_2)
% 243.45/49.99    (6)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.45/49.99           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.45/49.99             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.45/49.99           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.45/49.99             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.45/49.99           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.45/49.99           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.45/49.99           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.45/49.99           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.45/49.99           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.45/49.99           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.45/49.99             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.45/49.99           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.45/49.99           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 243.45/49.99           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.45/49.99           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.45/49.99           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.45/49.99           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.45/49.99             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.45/49.99           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.45/49.99           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 243.45/49.99           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.45/49.99           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.45/49.99           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.45/49.99           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.45/49.99             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.45/49.99           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.45/49.99           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.45/49.99    (7)  op(e1, e0) = all_52_14
% 243.45/49.99    (8)  op(e0, e3) = all_52_3
% 243.45/49.99    (9)   ~ (all_52_8 = e1)
% 243.45/49.99    (10)  op(e3, e1) = all_52_8
% 243.45/49.99    (11)  op(e2, e1) = all_52_9
% 243.45/49.99    (12)   ~ (all_52_14 = e0)
% 243.45/49.99    (13)  all_56_31 = e0
% 243.45/49.99    (14)  all_54_5 = all_8_2
% 243.45/49.99    (15)  op(e2, e3) = all_52_1
% 243.45/49.99    (16)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 243.45/49.99    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.45/49.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.45/49.99    (18)   ~ (all_8_2 = e3)
% 243.45/49.99    (19)  all_56_11 = all_8_2
% 243.45/49.99    (20)  op(e2, e0) = all_52_13
% 243.45/49.99    (21)   ~ (all_52_13 = e0)
% 243.45/49.99    (22)  all_56_1 = e1
% 243.45/49.99  
% 243.45/49.99  Begin of proof
% 243.45/49.99  | 
% 243.45/49.99  | BETA: splitting (16) gives:
% 243.45/49.99  | 
% 243.45/49.99  | Case 1:
% 243.45/49.99  | | 
% 243.45/49.99  | |   (23)  all_54_5 = e3
% 243.45/49.99  | | 
% 243.45/49.99  | | COMBINE_EQS: (14), (23) imply:
% 243.45/49.99  | |   (24)  all_8_2 = e3
% 243.45/49.99  | | 
% 243.45/49.99  | | REDUCE: (18), (24) imply:
% 243.45/49.99  | |   (25)  $false
% 243.45/49.99  | | 
% 243.45/49.99  | | CLOSE: (25) is inconsistent.
% 243.45/49.99  | | 
% 243.45/49.99  | Case 2:
% 243.45/49.99  | | 
% 243.45/49.99  | |   (26)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 243.45/49.99  | | 
% 243.45/49.99  | | BETA: splitting (26) gives:
% 243.45/49.99  | | 
% 243.45/49.99  | | Case 1:
% 243.45/49.99  | | | 
% 243.45/49.99  | | |   (27)  all_54_5 = e2
% 243.45/49.99  | | | 
% 243.45/49.99  | | | COMBINE_EQS: (14), (27) imply:
% 243.45/49.99  | | |   (28)  all_8_2 = e2
% 243.45/49.99  | | | 
% 243.45/49.99  | | | COMBINE_EQS: (19), (28) imply:
% 243.45/49.99  | | |   (29)  all_56_11 = e2
% 243.45/49.99  | | | 
% 243.45/49.99  | | | REDUCE: (5), (28) imply:
% 243.45/49.99  | | |   (30)   ~ (all_52_1 = e2)
% 243.45/49.99  | | | 
% 243.45/49.99  | | | REDUCE: (3), (28) imply:
% 243.45/49.99  | | |   (31)   ~ (all_52_9 = e2)
% 243.45/49.99  | | | 
% 243.45/49.99  | | | BETA: splitting (6) gives:
% 243.45/49.99  | | | 
% 243.45/49.99  | | | Case 1:
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | |   (32)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 243.45/49.99  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.45/49.99  | | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9
% 243.45/49.99  | | | |           = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.45/49.99  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.45/49.99  | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.45/49.99  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 243.45/49.99  | | | |           ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 243.45/49.99  | | | |         (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 243.45/49.99  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.45/49.99  | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 243.45/49.99  | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.45/49.99  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.45/49.99  | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.45/49.99  | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) & 
% 243.45/49.99  | | | |           ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | | BETA: splitting (32) gives:
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | | Case 1:
% 243.45/49.99  | | | | | 
% 243.45/49.99  | | | | |   (33)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 243.45/49.99  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.45/49.99  | | | | |           & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 &
% 243.45/49.99  | | | | |           all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.45/49.99  | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.45/49.99  | | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.45/49.99  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.45/49.99  | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.45/49.99  | | | | | 
% 243.45/49.99  | | | | | REF_CLOSE: (15), (17), (22), (29), (30), (33) are inconsistent by
% 243.45/49.99  | | | | |            sub-proof #1213.
% 243.45/49.99  | | | | | 
% 243.45/49.99  | | | | Case 2:
% 243.45/49.99  | | | | | 
% 243.45/49.99  | | | | |   (34)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 243.45/49.99  | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 243.45/49.99  | | | | |           & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 243.45/49.99  | | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.45/49.99  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.45/49.99  | | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.45/49.99  | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.45/49.99  | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.45/49.99  | | | | | 
% 243.45/49.99  | | | | | REF_CLOSE: (2), (8), (9), (10), (13), (17), (34) are inconsistent by
% 243.45/49.99  | | | | |            sub-proof #2307.
% 243.45/49.99  | | | | | 
% 243.45/49.99  | | | | End of split
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | Case 2:
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | |   (35)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.45/49.99  | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.45/49.99  | | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 243.45/49.99  | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.45/49.99  | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.45/49.99  | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.45/49.99  | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) & 
% 243.45/49.99  | | | |           ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 243.45/49.99  | | | |         (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.45/49.99  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.45/49.99  | | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 243.45/49.99  | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.45/49.99  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.45/49.99  | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.45/49.99  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 243.45/49.99  | | | |           ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | | BETA: splitting (35) gives:
% 243.45/49.99  | | | | 
% 243.45/49.99  | | | | Case 1:
% 243.45/49.99  | | | | | 
% 243.45/49.99  | | | | |   (36)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.45/49.99  | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.45/49.99  | | | | |           & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 243.45/49.99  | | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.45/49.99  | | | | |           ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.45/49.99  | | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.45/49.99  | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 243.45/49.99  | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.45/49.99  | | | | | 
% 243.45/49.99  | | | | | BETA: splitting (36) gives:
% 243.45/49.99  | | | | | 
% 243.45/49.99  | | | | | Case 1:
% 243.45/49.99  | | | | | | 
% 243.45/49.99  | | | | | |   (37)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.45/49.99  | | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.45/49.99  | | | | | |         & op(e2, e1) = e2 & op(e1, e2) = e2
% 243.45/49.99  | | | | | | 
% 243.45/49.99  | | | | | | ALPHA: (37) implies:
% 243.45/49.99  | | | | | |   (38)  op(e2, e1) = e2
% 243.45/49.99  | | | | | | 
% 243.45/49.99  | | | | | | REF_CLOSE: (11), (17), (31), (38) are inconsistent by sub-proof
% 243.45/49.99  | | | | | |            #2328.
% 243.45/49.99  | | | | | | 
% 243.45/49.99  | | | | | Case 2:
% 243.45/49.99  | | | | | | 
% 243.45/49.99  | | | | | |   (39)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.45/49.99  | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 243.45/49.99  | | | | | |             e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 =
% 243.45/49.99  | | | | | |           e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 243.45/49.99  | | | | | |             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2,
% 243.45/49.99  | | | | | |             e0) = e2 & op(e0, e2) = e2)
% 243.45/49.99  | | | | | | 
% 243.45/49.99  | | | | | | BETA: splitting (39) gives:
% 243.45/49.99  | | | | | | 
% 243.45/49.99  | | | | | | Case 1:
% 243.45/49.99  | | | | | | | 
% 243.45/49.99  | | | | | | |   (40)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.45/49.99  | | | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 243.45/49.99  | | | | | | |           e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 243.45/49.99  | | | | | | | 
% 243.45/49.99  | | | | | | | ALPHA: (40) implies:
% 243.45/49.99  | | | | | | |   (41)   ~ (all_56_11 = e2)
% 243.45/49.99  | | | | | | | 
% 243.45/49.99  | | | | | | | REDUCE: (29), (41) imply:
% 243.45/49.99  | | | | | | |   (42)  $false
% 243.45/49.99  | | | | | | | 
% 243.45/49.99  | | | | | | | CLOSE: (42) is inconsistent.
% 243.45/49.99  | | | | | | | 
% 243.45/49.99  | | | | | | Case 2:
% 243.45/49.99  | | | | | | | 
% 243.45/49.99  | | | | | | |   (43)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.45/49.99  | | | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 243.45/49.99  | | | | | | |           e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 243.45/49.99  | | | | | | | 
% 243.45/49.99  | | | | | | | ALPHA: (43) implies:
% 243.45/49.99  | | | | | | |   (44)   ~ (all_56_31 = e0)
% 243.45/49.99  | | | | | | | 
% 243.45/49.99  | | | | | | | REDUCE: (13), (44) imply:
% 243.45/49.99  | | | | | | |   (45)  $false
% 243.45/49.99  | | | | | | | 
% 243.45/49.99  | | | | | | | CLOSE: (45) is inconsistent.
% 243.45/49.99  | | | | | | | 
% 243.45/49.99  | | | | | | End of split
% 243.45/50.00  | | | | | | 
% 243.45/50.00  | | | | | End of split
% 243.45/50.00  | | | | | 
% 243.45/50.00  | | | | Case 2:
% 243.45/50.00  | | | | | 
% 243.45/50.00  | | | | |   (46)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.45/50.00  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.45/50.00  | | | | |           & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 243.45/50.00  | | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.45/50.00  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.45/50.00  | | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.45/50.00  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.45/50.00  | | | | |           &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.45/50.00  | | | | | 
% 243.45/50.00  | | | | | REF_CLOSE: (7), (12), (13), (17), (20), (21), (46) are inconsistent by
% 243.45/50.00  | | | | |            sub-proof #2321.
% 243.45/50.00  | | | | | 
% 243.45/50.00  | | | | End of split
% 243.45/50.00  | | | | 
% 243.45/50.00  | | | End of split
% 243.45/50.00  | | | 
% 243.45/50.00  | | Case 2:
% 243.45/50.00  | | | 
% 243.45/50.00  | | |   (47)  all_54_5 = e1 | all_54_5 = e0
% 243.45/50.00  | | | 
% 243.45/50.00  | | | REF_CLOSE: (1), (4), (14), (47) are inconsistent by sub-proof #2300.
% 243.45/50.00  | | | 
% 243.45/50.00  | | End of split
% 243.45/50.00  | | 
% 243.45/50.00  | End of split
% 243.45/50.00  | 
% 243.45/50.00  End of proof
% 243.45/50.00  
% 243.45/50.00  Sub-proof #1213 shows that the following formulas are inconsistent:
% 243.45/50.00  ----------------------------------------------------------------
% 243.52/50.00    (1)  all_56_11 = e2
% 243.52/50.00    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.52/50.00           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.52/50.00             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.52/50.00           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.52/50.00             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.52/50.00           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.00           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.52/50.00    (3)  op(e2, e3) = all_52_1
% 243.52/50.00    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.00    (5)   ~ (all_52_1 = e2)
% 243.52/50.00    (6)  all_56_1 = e1
% 243.52/50.00  
% 243.52/50.00  Begin of proof
% 243.52/50.00  | 
% 243.52/50.00  | BETA: splitting (2) gives:
% 243.52/50.00  | 
% 243.52/50.00  | Case 1:
% 243.52/50.00  | | 
% 243.52/50.00  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.52/50.00  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.52/50.00  | |        op(e2, e3) = e3
% 243.52/50.00  | | 
% 243.52/50.00  | | ALPHA: (7) implies:
% 243.52/50.00  | |   (8)   ~ (all_56_11 = e2)
% 243.52/50.00  | | 
% 243.52/50.00  | | REDUCE: (1), (8) imply:
% 243.52/50.00  | |   (9)  $false
% 243.52/50.00  | | 
% 243.52/50.00  | | CLOSE: (9) is inconsistent.
% 243.52/50.00  | | 
% 243.52/50.00  | Case 2:
% 243.52/50.00  | | 
% 243.52/50.00  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 243.52/50.00  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 243.52/50.00  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.52/50.00  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.00  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.52/50.00  | | 
% 243.52/50.00  | | BETA: splitting (10) gives:
% 243.52/50.00  | | 
% 243.52/50.00  | | Case 1:
% 243.52/50.00  | | | 
% 243.52/50.00  | | |   (11)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 243.52/50.00  | | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 243.52/50.00  | | |         e2 & op(e2, e3) = e2
% 243.52/50.00  | | | 
% 243.52/50.00  | | | ALPHA: (11) implies:
% 243.52/50.00  | | |   (12)  op(e2, e3) = e2
% 243.52/50.00  | | | 
% 243.52/50.00  | | | REF_CLOSE: (3), (4), (5), (12) are inconsistent by sub-proof #2336.
% 243.52/50.00  | | | 
% 243.52/50.00  | | Case 2:
% 243.52/50.00  | | | 
% 243.52/50.00  | | |   (13)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.52/50.00  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.52/50.00  | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 243.52/50.00  | | | 
% 243.52/50.00  | | | ALPHA: (13) implies:
% 243.52/50.00  | | |   (14)   ~ (all_56_1 = e1)
% 243.52/50.00  | | | 
% 243.52/50.00  | | | REDUCE: (6), (14) imply:
% 243.52/50.00  | | |   (15)  $false
% 243.52/50.00  | | | 
% 243.52/50.00  | | | CLOSE: (15) is inconsistent.
% 243.52/50.00  | | | 
% 243.52/50.00  | | End of split
% 243.52/50.00  | | 
% 243.52/50.00  | End of split
% 243.52/50.00  | 
% 243.52/50.00  End of proof
% 243.52/50.00  
% 243.52/50.00  Sub-proof #1214 shows that the following formulas are inconsistent:
% 243.52/50.00  ----------------------------------------------------------------
% 243.52/50.00    (1)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 243.52/50.00    (2)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.52/50.00    (3)   ~ (e3 = e0)
% 243.52/50.00    (4)  op(e0, e1) = all_52_11
% 243.52/50.00    (5)   ~ (all_52_8 = all_52_9)
% 243.52/50.00    (6)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.52/50.00         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.52/50.00    (7)  op(e1, e2) = all_52_6
% 243.52/50.00    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.52/50.00         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.52/50.00    (9)  all_58_9 = e0
% 243.52/50.00    (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.52/50.00              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.52/50.00            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.52/50.00            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.52/50.00            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.52/50.00             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.00            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.52/50.00            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.52/50.00            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.52/50.00            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.00            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.52/50.00              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.52/50.00            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.52/50.00            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.52/50.00            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.52/50.00            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.52/50.00            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.00            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.52/50.00              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.52/50.00            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.52/50.00            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.52/50.00            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.52/50.00            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.52/50.00            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.00            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.52/50.00              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.52/50.00            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.00            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.52/50.00    (11)   ~ (all_10_2 = e0)
% 243.52/50.00    (12)   ~ (all_52_1 = all_52_2)
% 243.52/50.00    (13)  op(e1, e0) = all_52_14
% 243.52/50.00    (14)   ~ (all_10_2 = e1)
% 243.52/50.00    (15)  all_58_15 = e3
% 243.52/50.00    (16)  op(e0, e3) = all_52_3
% 243.52/50.00    (17)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.52/50.00          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.52/50.00    (18)   ~ (all_52_1 = all_10_2)
% 243.52/50.00    (19)   ~ (e3 = e1)
% 243.52/50.00    (20)  op(e2, e2) = e0
% 243.52/50.00    (21)  all_54_6 = all_52_9
% 243.52/50.00    (22)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.52/50.00          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.52/50.00    (23)   ~ (all_52_2 = all_52_14)
% 243.52/50.00    (24)   ~ (all_52_1 = all_52_9)
% 243.52/50.00    (25)  all_56_21 = e0
% 243.52/50.00    (26)  all_54_4 = all_52_1
% 243.52/50.00    (27)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.52/50.00              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.52/50.00                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.52/50.00                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.52/50.00    (28)   ~ (all_52_11 = e3)
% 243.52/50.00    (29)  op(e3, e1) = all_52_8
% 243.52/50.00    (30)  op(e2, e1) = all_52_9
% 243.52/50.00    (31)  all_54_9 = all_52_6
% 243.52/50.00    (32)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.52/50.00          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.52/50.00    (33)   ~ (e3 = e2)
% 243.52/50.00    (34)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 243.52/50.00            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 243.52/50.00              e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 243.52/50.00    (35)   ~ (all_52_14 = e0)
% 243.52/50.00    (36)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.52/50.00    (37)  op(e0, e3) = e0
% 243.52/50.00    (38)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.52/50.00          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.52/50.00    (39)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.52/50.00          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.52/50.00    (40)   ~ (all_52_3 = e3)
% 243.52/50.00    (41)   ~ (all_52_1 = e0)
% 243.52/50.00    (42)   ~ (all_52_2 = all_10_2)
% 243.52/50.00    (43)  all_24_2 = all_10_2
% 243.52/50.00    (44)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.52/50.00    (45)  op(e0, e3) = all_12_1
% 243.52/50.00    (46)  op(e2, e3) = all_52_1
% 243.52/50.00    (47)   ~ (all_52_14 = e3)
% 243.52/50.00    (48)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.52/50.00          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.52/50.00    (49)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.52/50.00    (50)   ~ (all_52_1 = all_52_13)
% 243.52/50.00    (51)   ~ (all_52_2 = e0)
% 243.52/50.00    (52)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.52/50.00          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.52/50.00    (53)  op(e3, e2) = all_52_4
% 243.52/50.00    (54)  all_56_31 = e3
% 243.52/50.00    (55)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.52/50.00          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.52/50.00    (56)  op(e0, e0) = e3
% 243.52/50.00    (57)  all_26_2 = e3
% 243.52/50.00    (58)  all_54_8 = all_52_2
% 243.52/50.00    (59)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.52/50.00          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.52/50.00    (60)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.52/50.00          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.52/50.00    (61)  all_56_1 = all_10_2
% 243.52/50.00    (62)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.00    (63)  op(e1, e3) = all_52_2
% 243.52/50.00    (64)  op(e3, e3) = all_10_2
% 243.52/50.00    (65)  op(e1, e1) = e0
% 243.52/50.00    (66)   ~ (e1 = e0)
% 243.52/50.00    (67)   ~ (all_52_13 = e3)
% 243.52/50.00    (68)  op(e2, e0) = all_52_13
% 243.52/50.00    (69)  all_54_0 = all_10_2
% 243.52/50.00    (70)  all_58_3 = e0
% 243.52/50.00    (71)   ~ (all_24_2 = e2) | ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 243.52/50.00            op(e3, e2) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 243.52/50.00              e1) & op(e3, e2) = all_24_1 & $i(all_24_1))
% 243.52/50.00    (72)   ~ (all_52_13 = e0)
% 243.52/50.00    (73)   ~ (all_52_4 = all_52_6)
% 243.52/50.00  
% 243.52/50.00  Begin of proof
% 243.52/50.00  | 
% 243.52/50.00  | BETA: splitting (34) gives:
% 243.52/50.00  | 
% 243.52/50.00  | Case 1:
% 243.52/50.00  | | 
% 243.52/50.00  | |   (74)   ~ (all_26_2 = e3)
% 243.52/50.00  | | 
% 243.52/50.00  | | REDUCE: (57), (74) imply:
% 243.52/50.00  | |   (75)  $false
% 243.52/50.00  | | 
% 243.52/50.00  | | CLOSE: (75) is inconsistent.
% 243.52/50.00  | | 
% 243.52/50.00  | Case 2:
% 243.52/50.00  | | 
% 243.52/50.00  | |   (76)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.52/50.00  | |           all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) &
% 243.52/50.00  | |           op(e0, e3) = all_26_1 & $i(all_26_1))
% 243.52/50.00  | | 
% 243.52/50.00  | | GROUND_INST: instantiating (62) with e0, all_12_1, e3, e0, simplifying with
% 243.52/50.00  | |              (37), (45) gives:
% 243.52/50.00  | |   (77)  all_12_1 = e0
% 243.52/50.00  | | 
% 243.52/50.00  | | BETA: splitting (76) gives:
% 243.52/50.00  | | 
% 243.52/50.00  | | Case 1:
% 243.52/50.00  | | | 
% 243.52/50.00  | | |   (78)   ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.52/50.00  | | |         all_26_1 & $i(all_26_0) & $i(all_26_1)
% 243.52/50.00  | | | 
% 243.52/50.00  | | | ALPHA: (78) implies:
% 243.52/50.00  | | |   (79)   ~ (all_26_0 = e2)
% 243.52/50.00  | | |   (80)  op(e0, e3) = all_26_1
% 243.52/50.00  | | |   (81)  op(all_26_1, e0) = all_26_0
% 243.52/50.00  | | | 
% 243.52/50.00  | | | GROUND_INST: instantiating (62) with e0, all_26_1, e3, e0, simplifying
% 243.52/50.00  | | |              with (37), (80) gives:
% 243.52/50.00  | | |   (82)  all_26_1 = e0
% 243.52/50.00  | | | 
% 243.52/50.00  | | | REDUCE: (81), (82) imply:
% 243.52/50.00  | | |   (83)  op(e0, e0) = all_26_0
% 243.52/50.00  | | | 
% 243.52/50.00  | | | GROUND_INST: instantiating (62) with e3, all_26_0, e0, e0, simplifying
% 243.52/50.00  | | |              with (56), (83) gives:
% 243.52/50.00  | | |   (84)  all_26_0 = e3
% 243.52/50.00  | | | 
% 243.52/50.00  | | | BETA: splitting (71) gives:
% 243.52/50.00  | | | 
% 243.52/50.00  | | | Case 1:
% 243.52/50.00  | | | | 
% 243.52/50.00  | | | |   (85)   ~ (all_24_2 = e2)
% 243.52/50.00  | | | | 
% 243.52/50.00  | | | | REDUCE: (43), (85) imply:
% 243.52/50.00  | | | |   (86)   ~ (all_10_2 = e2)
% 243.52/50.00  | | | | 
% 243.52/50.00  | | | | REF_CLOSE: (1), (5), (6), (10), (11), (13), (14), (16), (18), (24),
% 243.52/50.00  | | | |            (25), (29), (30), (35), (40), (46), (54), (62), (67), (68),
% 243.52/50.00  | | | |            (69), (70), (72), (86) are inconsistent by sub-proof #1225.
% 243.52/50.00  | | | | 
% 243.52/50.00  | | | Case 2:
% 243.52/50.00  | | | | 
% 243.52/50.00  | | | |   (87)  all_24_2 = e2
% 243.52/50.00  | | | | 
% 243.52/50.00  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 243.52/50.00  | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 243.52/50.00  | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 243.52/50.00  | | | |            (33), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 243.52/50.00  | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 243.52/50.00  | | | |            (54), (55), (56), (58), (59), (60), (61), (62), (63), (64),
% 243.52/50.00  | | | |            (65), (66), (67), (68), (70), (72), (73), (80), (87) are
% 243.52/50.00  | | | |            inconsistent by sub-proof #1215.
% 243.52/50.00  | | | | 
% 243.52/50.00  | | | End of split
% 243.52/50.00  | | | 
% 243.52/50.00  | | Case 2:
% 243.52/50.00  | | | 
% 243.52/50.00  | | |   (88)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 243.52/50.00  | | | 
% 243.52/50.00  | | | ALPHA: (88) implies:
% 243.52/50.00  | | |   (89)   ~ (all_26_1 = e1)
% 243.52/50.00  | | |   (90)  op(e0, e3) = all_26_1
% 243.52/50.00  | | | 
% 243.52/50.00  | | | GROUND_INST: instantiating (62) with e0, all_26_1, e3, e0, simplifying
% 243.52/50.00  | | |              with (37), (90) gives:
% 243.52/50.00  | | |   (91)  all_26_1 = e0
% 243.52/50.00  | | | 
% 243.52/50.00  | | | REDUCE: (89), (91) imply:
% 243.52/50.00  | | |   (92)   ~ (e1 = e0)
% 243.52/50.00  | | | 
% 243.52/50.00  | | | BETA: splitting (71) gives:
% 243.52/50.00  | | | 
% 243.52/50.00  | | | Case 1:
% 243.52/50.00  | | | | 
% 243.52/50.00  | | | |   (93)   ~ (all_24_2 = e2)
% 243.52/50.00  | | | | 
% 243.52/50.00  | | | | REDUCE: (43), (93) imply:
% 243.52/50.00  | | | |   (94)   ~ (all_10_2 = e2)
% 243.52/50.00  | | | | 
% 243.52/50.01  | | | | REF_CLOSE: (1), (5), (6), (10), (11), (13), (14), (16), (18), (24),
% 243.52/50.01  | | | |            (25), (29), (30), (35), (40), (46), (54), (62), (67), (68),
% 243.52/50.01  | | | |            (69), (70), (72), (94) are inconsistent by sub-proof #1225.
% 243.52/50.01  | | | | 
% 243.52/50.01  | | | Case 2:
% 243.52/50.01  | | | | 
% 243.52/50.01  | | | |   (95)  all_24_2 = e2
% 243.52/50.01  | | | | 
% 243.52/50.01  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 243.52/50.01  | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 243.52/50.01  | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 243.52/50.01  | | | |            (33), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 243.52/50.01  | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 243.52/50.01  | | | |            (54), (55), (56), (58), (59), (60), (61), (62), (63), (64),
% 243.52/50.01  | | | |            (65), (66), (67), (68), (70), (72), (73), (90), (95) are
% 243.52/50.01  | | | |            inconsistent by sub-proof #1215.
% 243.52/50.01  | | | | 
% 243.52/50.01  | | | End of split
% 243.52/50.01  | | | 
% 243.52/50.01  | | End of split
% 243.52/50.01  | | 
% 243.52/50.01  | End of split
% 243.52/50.01  | 
% 243.52/50.01  End of proof
% 243.52/50.01  
% 243.52/50.01  Sub-proof #1215 shows that the following formulas are inconsistent:
% 243.52/50.01  ----------------------------------------------------------------
% 243.52/50.01    (1)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.52/50.01    (2)   ~ (e3 = e0)
% 243.52/50.01    (3)  op(e0, e1) = all_52_11
% 243.52/50.01    (4)   ~ (all_52_8 = all_52_9)
% 243.52/50.01    (5)  all_24_2 = e2
% 243.52/50.01    (6)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.52/50.01         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.52/50.01    (7)  op(e1, e2) = all_52_6
% 243.52/50.01    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.52/50.01         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.52/50.01    (9)  all_58_9 = e0
% 243.52/50.01    (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.52/50.01              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.52/50.01            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.52/50.01            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.52/50.01            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.52/50.01             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.01            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.52/50.01            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.52/50.01            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.52/50.01            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.01            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.52/50.01              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.52/50.01            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.52/50.01            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.52/50.01            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.52/50.01            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.52/50.01            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.01            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.52/50.01              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.52/50.01            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.52/50.01            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.52/50.01            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.52/50.01            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.52/50.01            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.01            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.52/50.01              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.52/50.01            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.01            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.52/50.01    (11)   ~ (all_10_2 = e0)
% 243.52/50.01    (12)   ~ (all_52_1 = all_52_2)
% 243.52/50.01    (13)  op(e1, e0) = all_52_14
% 243.52/50.01    (14)   ~ (all_10_2 = e1)
% 243.52/50.01    (15)  all_58_15 = e3
% 243.52/50.01    (16)  op(e0, e3) = all_52_3
% 243.52/50.01    (17)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.52/50.01          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.52/50.01    (18)   ~ (all_52_1 = all_10_2)
% 243.52/50.01    (19)   ~ (e3 = e1)
% 243.52/50.01    (20)  op(e2, e2) = e0
% 243.52/50.01    (21)  all_54_6 = all_52_9
% 243.52/50.01    (22)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.52/50.01          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.52/50.01    (23)   ~ (all_52_2 = all_52_14)
% 243.52/50.01    (24)   ~ (all_52_1 = all_52_9)
% 243.52/50.01    (25)  all_56_21 = e0
% 243.52/50.01    (26)  all_54_4 = all_52_1
% 243.52/50.01    (27)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.52/50.01              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.52/50.01                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.52/50.01                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.52/50.01    (28)   ~ (all_52_11 = e3)
% 243.52/50.01    (29)  op(e3, e1) = all_52_8
% 243.52/50.01    (30)  op(e2, e1) = all_52_9
% 243.52/50.01    (31)  all_54_9 = all_52_6
% 243.52/50.01    (32)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.52/50.01          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.52/50.01    (33)   ~ (e3 = e2)
% 243.52/50.01    (34)   ~ (all_52_14 = e0)
% 243.52/50.01    (35)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.52/50.01    (36)  op(e0, e3) = e0
% 243.52/50.01    (37)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.52/50.01          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.52/50.01    (38)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.52/50.01          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.52/50.01    (39)   ~ (all_52_3 = e3)
% 243.52/50.01    (40)   ~ (all_52_1 = e0)
% 243.52/50.01    (41)   ~ (all_52_2 = all_10_2)
% 243.52/50.01    (42)  all_24_2 = all_10_2
% 243.52/50.01    (43)  op(e0, e3) = all_26_1
% 243.52/50.01    (44)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.52/50.01    (45)  op(e0, e3) = all_12_1
% 243.52/50.01    (46)  op(e2, e3) = all_52_1
% 243.52/50.01    (47)   ~ (all_52_14 = e3)
% 243.52/50.01    (48)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.52/50.01          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.52/50.01    (49)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.52/50.01    (50)   ~ (all_52_1 = all_52_13)
% 243.52/50.01    (51)   ~ (all_52_2 = e0)
% 243.52/50.01    (52)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.52/50.01          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.52/50.01    (53)  op(e3, e2) = all_52_4
% 243.52/50.01    (54)  all_56_31 = e3
% 243.52/50.01    (55)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.52/50.01          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.52/50.01    (56)  op(e0, e0) = e3
% 243.52/50.01    (57)  all_54_8 = all_52_2
% 243.52/50.01    (58)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.52/50.01          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.52/50.01    (59)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.52/50.01          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.52/50.01    (60)  all_56_1 = all_10_2
% 243.52/50.01    (61)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.01    (62)  op(e1, e3) = all_52_2
% 243.52/50.01    (63)  op(e3, e3) = all_10_2
% 243.52/50.01    (64)  op(e1, e1) = e0
% 243.52/50.01    (65)   ~ (e1 = e0)
% 243.52/50.01    (66)   ~ (all_52_13 = e3)
% 243.52/50.01    (67)  op(e2, e0) = all_52_13
% 243.52/50.01    (68)  all_58_3 = e0
% 243.52/50.01    (69)   ~ (all_52_13 = e0)
% 243.52/50.01    (70)   ~ (all_52_4 = all_52_6)
% 243.52/50.01  
% 243.52/50.01  Begin of proof
% 243.52/50.01  | 
% 243.52/50.01  | COMBINE_EQS: (5), (42) imply:
% 243.52/50.01  |   (71)  all_10_2 = e2
% 243.52/50.01  | 
% 243.52/50.01  | SIMP: (71) implies:
% 243.52/50.01  |   (72)  all_10_2 = e2
% 243.52/50.01  | 
% 243.52/50.01  | COMBINE_EQS: (60), (72) imply:
% 243.52/50.01  |   (73)  all_56_1 = e2
% 243.52/50.01  | 
% 243.52/50.01  | REDUCE: (18), (72) imply:
% 243.52/50.01  |   (74)   ~ (all_52_1 = e2)
% 243.52/50.01  | 
% 243.52/50.01  | REDUCE: (41), (72) imply:
% 243.52/50.01  |   (75)   ~ (all_52_2 = e2)
% 243.52/50.01  | 
% 243.52/50.01  | REDUCE: (14), (72) imply:
% 243.52/50.01  |   (76)   ~ (e2 = e1)
% 243.52/50.01  | 
% 243.52/50.01  | REDUCE: (11), (72) imply:
% 243.52/50.01  |   (77)   ~ (e2 = e0)
% 243.52/50.01  | 
% 243.52/50.01  | REDUCE: (63), (72) imply:
% 243.52/50.01  |   (78)  op(e3, e3) = e2
% 243.52/50.01  | 
% 243.52/50.01  | BETA: splitting (49) gives:
% 243.52/50.01  | 
% 243.52/50.01  | Case 1:
% 243.52/50.01  | | 
% 243.52/50.01  | |   (79)  all_54_4 = e3
% 243.52/50.01  | | 
% 243.52/50.01  | | COMBINE_EQS: (26), (79) imply:
% 243.52/50.01  | |   (80)  all_52_1 = e3
% 243.52/50.01  | | 
% 243.52/50.01  | | SIMP: (80) implies:
% 243.52/50.01  | |   (81)  all_52_1 = e3
% 243.52/50.01  | | 
% 243.52/50.01  | | REDUCE: (12), (81) imply:
% 243.52/50.01  | |   (82)   ~ (all_52_2 = e3)
% 243.52/50.01  | | 
% 243.52/50.01  | | SIMP: (82) implies:
% 243.52/50.01  | |   (83)   ~ (all_52_2 = e3)
% 243.52/50.01  | | 
% 243.52/50.01  | | REDUCE: (24), (81) imply:
% 243.52/50.01  | |   (84)   ~ (all_52_9 = e3)
% 243.52/50.01  | | 
% 243.52/50.01  | | SIMP: (84) implies:
% 243.52/50.01  | |   (85)   ~ (all_52_9 = e3)
% 243.52/50.01  | | 
% 243.52/50.01  | | REDUCE: (50), (81) imply:
% 243.52/50.01  | |   (86)   ~ (all_52_13 = e3)
% 243.52/50.01  | | 
% 243.52/50.01  | | BETA: splitting (6) gives:
% 243.52/50.01  | | 
% 243.52/50.01  | | Case 1:
% 243.52/50.01  | | | 
% 243.52/50.01  | | |   (87)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 243.52/50.01  | | |           e3)
% 243.52/50.01  | | | 
% 243.52/50.01  | | | BETA: splitting (87) gives:
% 243.52/50.01  | | | 
% 243.52/50.01  | | | Case 1:
% 243.52/50.01  | | | | 
% 243.52/50.01  | | | |   (88)  all_58_2 = e3 & op(e2, e3) = e3
% 243.52/50.01  | | | | 
% 243.52/50.01  | | | | ALPHA: (88) implies:
% 243.52/50.01  | | | |   (89)  all_58_2 = e3
% 243.52/50.01  | | | |   (90)  op(e2, e3) = e3
% 243.52/50.01  | | | | 
% 243.52/50.01  | | | | BETA: splitting (1) gives:
% 243.52/50.01  | | | | 
% 243.52/50.01  | | | | Case 1:
% 243.52/50.01  | | | | | 
% 243.52/50.01  | | | | |   (91)  all_54_8 = e3
% 243.52/50.01  | | | | | 
% 243.52/50.01  | | | | | COMBINE_EQS: (57), (91) imply:
% 243.52/50.01  | | | | |   (92)  all_52_2 = e3
% 243.52/50.01  | | | | | 
% 243.52/50.01  | | | | | REDUCE: (83), (92) imply:
% 243.52/50.01  | | | | |   (93)  $false
% 243.52/50.01  | | | | | 
% 243.52/50.01  | | | | | CLOSE: (93) is inconsistent.
% 243.52/50.01  | | | | | 
% 243.52/50.01  | | | | Case 2:
% 243.52/50.01  | | | | | 
% 243.52/50.01  | | | | |   (94)   ~ (all_54_8 = e3)
% 243.52/50.01  | | | | |   (95)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.52/50.01  | | | | | 
% 243.52/50.01  | | | | | BETA: splitting (52) gives:
% 243.52/50.01  | | | | | 
% 243.52/50.01  | | | | | Case 1:
% 243.52/50.01  | | | | | | 
% 243.52/50.01  | | | | | |   (96)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2,
% 243.52/50.01  | | | | | |             e1) = e3)
% 243.52/50.01  | | | | | | 
% 243.52/50.01  | | | | | | BETA: splitting (96) gives:
% 243.52/50.01  | | | | | | 
% 243.52/50.01  | | | | | | Case 1:
% 243.52/50.01  | | | | | | | 
% 243.52/50.01  | | | | | | |   (97)  all_58_4 = e3 & op(e3, e1) = e3
% 243.52/50.01  | | | | | | | 
% 243.52/50.01  | | | | | | | ALPHA: (97) implies:
% 243.52/50.01  | | | | | | |   (98)  all_58_4 = e3
% 243.52/50.01  | | | | | | | 
% 243.52/50.01  | | | | | | | BETA: splitting (38) gives:
% 243.52/50.01  | | | | | | | 
% 243.52/50.01  | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | 
% 243.52/50.01  | | | | | | | |   (99)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 &
% 243.52/50.01  | | | | | | | |           op(e1, e2) = e3)
% 243.52/50.01  | | | | | | | | 
% 243.52/50.01  | | | | | | | | BETA: splitting (99) gives:
% 243.52/50.01  | | | | | | | | 
% 243.52/50.01  | | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | | 
% 243.52/50.01  | | | | | | | | |   (100)  all_58_6 = e3 & op(e1, e3) = e3
% 243.52/50.01  | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | ALPHA: (100) implies:
% 243.52/50.01  | | | | | | | | |   (101)  all_58_6 = e3
% 243.52/50.01  | | | | | | | | |   (102)  op(e1, e3) = e3
% 243.52/50.01  | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | BETA: splitting (55) gives:
% 243.52/50.01  | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | |   (103)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 243.52/50.01  | | | | | | | | | |            & op(e2, e3) = e1)
% 243.52/50.01  | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | BETA: splitting (103) gives:
% 243.52/50.01  | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | |   (104)  all_58_0 = e1 & op(e3, e3) = e1
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | ALPHA: (104) implies:
% 243.52/50.01  | | | | | | | | | | |   (105)  op(e3, e3) = e1
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | REF_CLOSE: (2), (6), (30), (32), (33), (37), (61), (65),
% 243.52/50.01  | | | | | | | | | | |            (66), (67), (68), (76), (77), (85), (101), (105)
% 243.52/50.01  | | | | | | | | | | |            are inconsistent by sub-proof #1220.
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | Case 2:
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | |   (106)  all_58_2 = e1 & op(e2, e3) = e1
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | REF_CLOSE: (19), (89), (106) are inconsistent by sub-proof
% 243.52/50.01  | | | | | | | | | | |            #1765.
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | End of split
% 243.52/50.01  | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | Case 2:
% 243.52/50.01  | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | |   (107)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 243.52/50.01  | | | | | | | | | |            & op(e0, e3) = e1)
% 243.52/50.01  | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | BETA: splitting (107) gives:
% 243.52/50.01  | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | |   (108)  all_58_6 = e1 & op(e1, e3) = e1
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | ALPHA: (108) implies:
% 243.52/50.01  | | | | | | | | | | |   (109)  op(e1, e3) = e1
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | REF_CLOSE: (19), (61), (102), (109) are inconsistent by
% 243.52/50.01  | | | | | | | | | | |            sub-proof #2225.
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | Case 2:
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | |   (110)  all_58_12 = e1 & op(e0, e3) = e1
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | ALPHA: (110) implies:
% 243.52/50.01  | | | | | | | | | | |   (111)  op(e0, e3) = e1
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | REF_CLOSE: (36), (43), (45), (61), (65), (111) are
% 243.52/50.01  | | | | | | | | | | |            inconsistent by sub-proof #1387.
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | End of split
% 243.52/50.01  | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | End of split
% 243.52/50.01  | | | | | | | | | 
% 243.52/50.01  | | | | | | | | Case 2:
% 243.52/50.01  | | | | | | | | | 
% 243.52/50.01  | | | | | | | | |   (112)  all_58_7 = e3 & op(e1, e2) = e3
% 243.52/50.01  | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | ALPHA: (112) implies:
% 243.52/50.01  | | | | | | | | |   (113)  all_58_7 = e3
% 243.52/50.01  | | | | | | | | |   (114)  op(e1, e2) = e3
% 243.52/50.01  | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | BETA: splitting (58) gives:
% 243.52/50.01  | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | |   (115)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 243.52/50.01  | | | | | | | | | |            & op(e3, e2) = e1)
% 243.52/50.01  | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | BETA: splitting (115) gives:
% 243.52/50.01  | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | |   (116)  all_58_0 = e1 & op(e3, e3) = e1
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | ALPHA: (116) implies:
% 243.52/50.01  | | | | | | | | | | |   (117)  op(e3, e3) = e1
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | REF_CLOSE: (61), (76), (78), (117) are inconsistent by
% 243.52/50.01  | | | | | | | | | | |            sub-proof #2267.
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | Case 2:
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | |   (118)  all_58_1 = e1 & op(e3, e2) = e1
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | ALPHA: (118) implies:
% 243.52/50.01  | | | | | | | | | | |   (119)  all_58_1 = e1
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | BETA: splitting (59) gives:
% 243.52/50.01  | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | |   (120)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 243.52/50.01  | | | | | | | | | | | |            & op(e1, e2) = e2)
% 243.52/50.01  | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | BETA: splitting (120) gives:
% 243.52/50.01  | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | |   (121)  all_58_6 = e2 & op(e1, e3) = e2
% 243.52/50.01  | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | ALPHA: (121) implies:
% 243.52/50.01  | | | | | | | | | | | | |   (122)  all_58_6 = e2
% 243.52/50.01  | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | BETA: splitting (55) gives:
% 243.52/50.01  | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | |   (123)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 243.52/50.01  | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 243.52/50.01  | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 243.52/50.01  | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | |   (124)  all_58_0 = e1 & op(e3, e3) = e1
% 243.52/50.01  | | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 243.52/50.01  | | | | | | | | | | | | | | |   (125)  op(e3, e3) = e1
% 243.52/50.01  | | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | | REF_CLOSE: (61), (76), (78), (125) are inconsistent by
% 243.52/50.01  | | | | | | | | | | | | | | |            sub-proof #2267.
% 243.52/50.01  | | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | Case 2:
% 243.52/50.01  | | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | |   (126)  all_58_2 = e1 & op(e2, e3) = e1
% 243.52/50.01  | | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 243.52/50.01  | | | | | | | | | | | | | | |   (127)  all_58_2 = e1
% 243.52/50.01  | | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (22), (33), (39), (61), (78), (122),
% 243.52/50.01  | | | | | | | | | | | | | | |            (127) are inconsistent by sub-proof #1342.
% 243.52/50.01  | | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | End of split
% 243.52/50.01  | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | Case 2:
% 243.52/50.01  | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | |   (128)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 243.52/50.01  | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 243.52/50.01  | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 243.52/50.01  | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | Case 1:
% 243.52/50.01  | | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | |   (129)  all_58_6 = e1 & op(e1, e3) = e1
% 243.52/50.01  | | | | | | | | | | | | | | | 
% 243.52/50.01  | | | | | | | | | | | | | | | REF_CLOSE: (76), (122), (129) are inconsistent by sub-proof
% 243.52/50.01  | | | | | | | | | | | | | | |            #1423.
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | |   (130)  all_58_12 = e1 & op(e0, e3) = e1
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 243.52/50.02  | | | | | | | | | | | | | | |   (131)  op(e0, e3) = e1
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | REF_CLOSE: (36), (43), (45), (61), (65), (131) are
% 243.52/50.02  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1387.
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | |   (132)  all_58_7 = e2 & op(e1, e2) = e2
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (28), (30), (33), (52), (61), (64),
% 243.52/50.02  | | | | | | | | | | | | |            (85), (98), (113), (132) are inconsistent by
% 243.52/50.02  | | | | | | | | | | | | |            sub-proof #1219.
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | |   (133)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 243.52/50.02  | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 243.52/50.02  | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | BETA: splitting (133) gives:
% 243.52/50.02  | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | |   (134)  all_58_8 = e2 & op(e1, e1) = e2
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | ALPHA: (134) implies:
% 243.52/50.02  | | | | | | | | | | | | |   (135)  op(e1, e1) = e2
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | REF_CLOSE: (61), (64), (77), (135) are inconsistent by
% 243.52/50.02  | | | | | | | | | | | | |            sub-proof #2211.
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | |   (136)  all_58_11 = e2 & op(e1, e0) = e2
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | ALPHA: (136) implies:
% 243.52/50.02  | | | | | | | | | | | | |   (137)  all_58_11 = e2
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | BETA: splitting (95) gives:
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | |   (138)  all_54_8 = e2
% 243.52/50.02  | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | COMBINE_EQS: (57), (138) imply:
% 243.52/50.02  | | | | | | | | | | | | | |   (139)  all_52_2 = e2
% 243.52/50.02  | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | REDUCE: (75), (139) imply:
% 243.52/50.02  | | | | | | | | | | | | | |   (140)  $false
% 243.52/50.02  | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 243.52/50.02  | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | |   (141)   ~ (all_54_8 = e2)
% 243.52/50.02  | | | | | | | | | | | | | |   (142)  all_54_8 = e1 | all_54_8 = e0
% 243.52/50.02  | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 243.52/50.02  | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | |   (143)  all_54_8 = e1
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | COMBINE_EQS: (57), (143) imply:
% 243.52/50.02  | | | | | | | | | | | | | | |   (144)  all_52_2 = e1
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | REDUCE: (23), (144) imply:
% 243.52/50.02  | | | | | | | | | | | | | | |   (145)   ~ (all_52_14 = e1)
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | SIMP: (145) implies:
% 243.52/50.02  | | | | | | | | | | | | | | |   (146)   ~ (all_52_14 = e1)
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | REDUCE: (83), (144) imply:
% 243.52/50.02  | | | | | | | | | | | | | | |   (147)   ~ (e3 = e1)
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | REDUCE: (75), (144) imply:
% 243.52/50.02  | | | | | | | | | | | | | | |   (148)   ~ (e2 = e1)
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | REDUCE: (62), (144) imply:
% 243.52/50.02  | | | | | | | | | | | | | | |   (149)  op(e1, e3) = e1
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | |   (150)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 243.52/50.02  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 243.52/50.02  | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 243.52/50.02  | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | |   (151)  all_58_9 = e1 & op(e3, e0) = e1
% 243.52/50.02  | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 243.52/50.02  | | | | | | | | | | | | | | | | |   (152)  all_58_9 = e1
% 243.52/50.02  | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (48), (61), (65), (77), (78), (98), (119),
% 243.52/50.02  | | | | | | | | | | | | | | | | |            (152) are inconsistent by sub-proof #1695.
% 243.52/50.02  | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | |   (153)  all_58_10 = e1 & op(e2, e0) = e1
% 243.52/50.02  | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 243.52/50.02  | | | | | | | | | | | | | | | | |   (154)  op(e2, e0) = e1
% 243.52/50.02  | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 243.52/50.02  | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | |   (155)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.52/50.02  | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.52/50.02  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |   (156)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            = e3)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (157)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |          e3
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (158)  op(e3, e2) = e3
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (31), (35), (53), (61), (70), (114), (158)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2190.
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (159)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (33), (61), (90), (149), (159) are
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1218.
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |   (160)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            = e0)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (39), (54), (61), (160) are inconsistent by
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            sub-proof #1389.
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | |   (161)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.52/50.02  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 243.52/50.02  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |   (162)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            = e2)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (163)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (164)   ~ (all_56_31 = e1)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (165)   ~ (all_56_21 = e1)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (166)   ~ (all_56_1 = e1)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (167)  op(e1, e2) = e2
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (165) imply:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (168)   ~ (e1 = e0)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | |   (169)  all_54_6 = e3
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (85), (169) are inconsistent by sub-proof
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | |            #1825.
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | |   (170)   ~ (all_54_6 = e3)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | |   (171)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |   (172)  all_54_6 = e2
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (172) imply:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |   (173)  all_52_9 = e2
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | SIMP: (173) implies:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |   (174)  all_52_9 = e2
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (174) imply:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |   (175)   ~ (e3 = e2)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (61) with e2, e3, e2, e1,
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |              simplifying with (114), (167) gives:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |   (176)  e3 = e2
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (176) imply:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |   (177)  all_58_4 = e2
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (28), (30), (33), (52), (61), (64),
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |            (85), (177) are inconsistent by sub-proof #1493.
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |   (178)   ~ (all_54_6 = e2)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (178) imply:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |   (179)   ~ (all_52_9 = e2)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (15), (17), (19), (20), (27), (30),
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |            (46), (56), (61), (65), (74), (76), (77), (137),
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | |            (179) are inconsistent by sub-proof #1233.
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (180)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (73), (76), (154), (180) are inconsistent by
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            sub-proof #1217.
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |   (181)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | |            = e0)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (182)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (183)  op(e2, e0) = e0
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (65), (67), (154), (183) are inconsistent by
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            sub-proof #1778.
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |   (184)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (34), (61), (146), (184) are inconsistent by
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | |            sub-proof #1989.
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | |   (185)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 243.52/50.02  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 243.52/50.02  | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (19), (61), (146), (185) are
% 243.52/50.02  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1297.
% 243.52/50.02  | | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | |   (186)  all_54_8 = e0
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | COMBINE_EQS: (57), (186) imply:
% 243.52/50.02  | | | | | | | | | | | | | | |   (187)  all_52_2 = e0
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | REDUCE: (51), (187) imply:
% 243.52/50.02  | | | | | | | | | | | | | | |   (188)  $false
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent.
% 243.52/50.02  | | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | |   (189)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 243.52/50.02  | | | | | | | | | |            & op(e3, e0) = e1)
% 243.52/50.02  | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | | REF_CLOSE: (9), (19), (65), (98), (189) are inconsistent by
% 243.52/50.02  | | | | | | | | | |            sub-proof #1216.
% 243.52/50.02  | | | | | | | | | | 
% 243.52/50.02  | | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | | 
% 243.52/50.02  | | | | | | | | End of split
% 243.52/50.02  | | | | | | | | 
% 243.52/50.02  | | | | | | | Case 2:
% 243.52/50.02  | | | | | | | | 
% 243.52/50.02  | | | | | | | |   (190)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 &
% 243.52/50.02  | | | | | | | |            op(e1, e0) = e3)
% 243.52/50.02  | | | | | | | | 
% 243.52/50.02  | | | | | | | | REF_CLOSE: (2), (13), (47), (61), (64), (190) are inconsistent
% 243.52/50.02  | | | | | | | |            by sub-proof #1909.
% 243.52/50.02  | | | | | | | | 
% 243.52/50.02  | | | | | | | End of split
% 243.52/50.02  | | | | | | | 
% 243.52/50.02  | | | | | | Case 2:
% 243.52/50.02  | | | | | | | 
% 243.52/50.02  | | | | | | |   (191)  all_58_5 = e3 & op(e2, e1) = e3
% 243.52/50.02  | | | | | | | 
% 243.52/50.02  | | | | | | | REF_CLOSE: (30), (61), (85), (191) are inconsistent by sub-proof
% 243.52/50.02  | | | | | | |            #1822.
% 243.52/50.02  | | | | | | | 
% 243.52/50.02  | | | | | | End of split
% 243.52/50.02  | | | | | | 
% 243.52/50.02  | | | | | Case 2:
% 243.52/50.02  | | | | | | 
% 243.52/50.02  | | | | | |   (192)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 243.52/50.02  | | | | | |            op(e0, e1) = e3)
% 243.52/50.02  | | | | | | 
% 243.52/50.02  | | | | | | BETA: splitting (192) gives:
% 243.52/50.02  | | | | | | 
% 243.52/50.02  | | | | | | Case 1:
% 243.52/50.02  | | | | | | | 
% 243.52/50.02  | | | | | | |   (193)  all_58_8 = e3 & op(e1, e1) = e3
% 243.52/50.02  | | | | | | | 
% 243.52/50.02  | | | | | | | REF_CLOSE: (2), (61), (64), (193) are inconsistent by sub-proof
% 243.52/50.02  | | | | | | |            #2018.
% 243.52/50.02  | | | | | | | 
% 243.52/50.02  | | | | | | Case 2:
% 243.52/50.02  | | | | | | | 
% 243.52/50.02  | | | | | | |   (194)  all_58_14 = e3 & op(e0, e1) = e3
% 243.52/50.02  | | | | | | | 
% 243.52/50.02  | | | | | | | REF_CLOSE: (3), (28), (61), (194) are inconsistent by sub-proof
% 243.52/50.02  | | | | | | |            #1647.
% 243.52/50.02  | | | | | | | 
% 243.52/50.02  | | | | | | End of split
% 243.52/50.02  | | | | | | 
% 243.52/50.02  | | | | | End of split
% 243.52/50.02  | | | | | 
% 243.52/50.02  | | | | End of split
% 243.52/50.02  | | | | 
% 243.52/50.02  | | | Case 2:
% 243.52/50.02  | | | | 
% 243.52/50.02  | | | |   (195)  all_58_3 = e3 & op(e2, e2) = e3
% 243.52/50.02  | | | | 
% 243.52/50.02  | | | | ALPHA: (195) implies:
% 243.52/50.02  | | | |   (196)  all_58_3 = e3
% 243.52/50.02  | | | | 
% 243.52/50.02  | | | | REF_CLOSE: (2), (68), (196) are inconsistent by sub-proof #1460.
% 243.52/50.02  | | | | 
% 243.52/50.02  | | | End of split
% 243.52/50.02  | | | 
% 243.52/50.02  | | Case 2:
% 243.52/50.02  | | | 
% 243.52/50.02  | | |   (197)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0)
% 243.52/50.02  | | |            = e3)
% 243.52/50.02  | | | 
% 243.52/50.02  | | | REF_CLOSE: (30), (61), (66), (67), (85), (197) are inconsistent by
% 243.52/50.02  | | |            sub-proof #1649.
% 243.52/50.02  | | | 
% 243.52/50.02  | | End of split
% 243.52/50.02  | | 
% 243.52/50.02  | Case 2:
% 243.52/50.02  | | 
% 243.52/50.02  | |   (198)   ~ (all_54_4 = e3)
% 243.52/50.02  | | 
% 243.52/50.02  | | REDUCE: (26), (198) imply:
% 243.52/50.02  | |   (199)   ~ (all_52_1 = e3)
% 243.52/50.02  | | 
% 243.52/50.02  | | REF_CLOSE: (2), (4), (6), (10), (13), (16), (19), (24), (25), (29), (30),
% 243.52/50.02  | |            (33), (34), (39), (46), (54), (61), (66), (67), (68), (69), (199)
% 243.52/50.02  | |            are inconsistent by sub-proof #1226.
% 243.52/50.02  | | 
% 243.52/50.02  | End of split
% 243.52/50.02  | 
% 243.52/50.02  End of proof
% 243.52/50.02  
% 243.52/50.02  Sub-proof #1216 shows that the following formulas are inconsistent:
% 243.52/50.02  ----------------------------------------------------------------
% 243.52/50.02    (1)  all_58_9 = e0
% 243.52/50.02    (2)   ~ (e3 = e1)
% 243.52/50.02    (3)   ~ (e1 = e0)
% 243.52/50.02    (4)  all_58_4 = e3
% 243.52/50.02    (5)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.52/50.02  
% 243.52/50.02  Begin of proof
% 243.52/50.02  | 
% 243.52/50.02  | BETA: splitting (5) gives:
% 243.52/50.02  | 
% 243.52/50.02  | Case 1:
% 243.52/50.02  | | 
% 243.52/50.02  | |   (6)  all_58_4 = e1 & op(e3, e1) = e1
% 243.52/50.02  | | 
% 243.52/50.02  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2042.
% 243.52/50.02  | | 
% 243.52/50.02  | Case 2:
% 243.52/50.02  | | 
% 243.52/50.02  | |   (7)  all_58_9 = e1 & op(e3, e0) = e1
% 243.52/50.02  | | 
% 243.52/50.02  | | ALPHA: (7) implies:
% 243.52/50.02  | |   (8)  all_58_9 = e1
% 243.52/50.02  | | 
% 243.52/50.02  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #1744.
% 243.52/50.02  | | 
% 243.52/50.02  | End of split
% 243.52/50.02  | 
% 243.52/50.02  End of proof
% 243.52/50.02  
% 243.52/50.02  Sub-proof #1217 shows that the following formulas are inconsistent:
% 243.52/50.02  ----------------------------------------------------------------
% 243.52/50.02    (1)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.52/50.02             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.52/50.02           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 243.52/50.02             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.52/50.02           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.52/50.02    (2)  all_56_1 = e2
% 243.52/50.02    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.02    (4)  op(e2, e0) = e1
% 243.52/50.02    (5)   ~ (e2 = e1)
% 243.52/50.02  
% 243.52/50.02  Begin of proof
% 243.52/50.02  | 
% 243.52/50.02  | BETA: splitting (1) gives:
% 243.52/50.02  | 
% 243.52/50.02  | Case 1:
% 243.52/50.02  | | 
% 243.52/50.02  | |   (6)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.52/50.02  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 243.52/50.02  | |        & op(e1, e2) = e1
% 243.52/50.02  | | 
% 243.52/50.02  | | ALPHA: (6) implies:
% 243.52/50.02  | |   (7)   ~ (all_56_1 = e2)
% 243.52/50.02  | | 
% 243.52/50.02  | | REDUCE: (2), (7) imply:
% 243.52/50.02  | |   (8)  $false
% 243.52/50.02  | | 
% 243.52/50.02  | | CLOSE: (8) is inconsistent.
% 243.52/50.03  | | 
% 243.52/50.03  | Case 2:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (9)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.52/50.03  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 243.52/50.03  | |        & op(e0, e2) = e2
% 243.52/50.03  | | 
% 243.52/50.03  | | ALPHA: (9) implies:
% 243.52/50.03  | |   (10)  op(e2, e0) = e2
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #1659.
% 243.52/50.03  | | 
% 243.52/50.03  | End of split
% 243.52/50.03  | 
% 243.52/50.03  End of proof
% 243.52/50.03  
% 243.52/50.03  Sub-proof #1218 shows that the following formulas are inconsistent:
% 243.52/50.03  ----------------------------------------------------------------
% 243.52/50.03    (1)  op(e2, e3) = e3
% 243.52/50.03    (2)   ~ (e3 = e1)
% 243.52/50.03    (3)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 243.52/50.03           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 243.52/50.03             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.52/50.03           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 243.52/50.03             e1) = e3 & op(e1, e3) = e3)
% 243.52/50.03    (4)   ~ (e3 = e2)
% 243.52/50.03    (5)  op(e1, e3) = e1
% 243.52/50.03    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.03  
% 243.52/50.03  Begin of proof
% 243.52/50.03  | 
% 243.52/50.03  | BETA: splitting (3) gives:
% 243.52/50.03  | 
% 243.52/50.03  | Case 1:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 243.52/50.03  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.52/50.03  | |        op(e2, e3) = e2
% 243.52/50.03  | | 
% 243.52/50.03  | | ALPHA: (7) implies:
% 243.52/50.03  | |   (8)  op(e2, e3) = e2
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #1897.
% 243.52/50.03  | | 
% 243.52/50.03  | Case 2:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 243.52/50.03  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 243.52/50.03  | |        op(e1, e3) = e3
% 243.52/50.03  | | 
% 243.52/50.03  | | ALPHA: (9) implies:
% 243.52/50.03  | |   (10)  op(e1, e3) = e3
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #2225.
% 243.52/50.03  | | 
% 243.52/50.03  | End of split
% 243.52/50.03  | 
% 243.52/50.03  End of proof
% 243.52/50.03  
% 243.52/50.03  Sub-proof #1219 shows that the following formulas are inconsistent:
% 243.52/50.03  ----------------------------------------------------------------
% 243.52/50.03    (1)   ~ (e3 = e0)
% 243.52/50.03    (2)  op(e0, e1) = all_52_11
% 243.52/50.03    (3)   ~ (all_52_11 = e3)
% 243.52/50.03    (4)  op(e2, e1) = all_52_9
% 243.52/50.03    (5)   ~ (e3 = e2)
% 243.52/50.03    (6)  all_58_7 = e3
% 243.52/50.03    (7)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.52/50.03         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.52/50.03    (8)   ~ (all_52_9 = e3)
% 243.52/50.03    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.03    (10)  op(e1, e1) = e0
% 243.52/50.03    (11)  all_58_7 = e2 & op(e1, e2) = e2
% 243.52/50.03    (12)  all_58_4 = e3
% 243.52/50.03  
% 243.52/50.03  Begin of proof
% 243.52/50.03  | 
% 243.52/50.03  | ALPHA: (11) implies:
% 243.52/50.03  |   (13)  all_58_7 = e2
% 243.52/50.03  | 
% 243.52/50.03  | COMBINE_EQS: (6), (13) imply:
% 243.52/50.03  |   (14)  e3 = e2
% 243.52/50.03  | 
% 243.52/50.03  | SIMP: (14) implies:
% 243.52/50.03  |   (15)  e3 = e2
% 243.52/50.03  | 
% 243.52/50.03  | COMBINE_EQS: (12), (15) imply:
% 243.52/50.03  |   (16)  all_58_4 = e2
% 243.52/50.03  | 
% 243.52/50.03  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (16) are inconsistent
% 243.52/50.03  |            by sub-proof #1493.
% 243.52/50.03  | 
% 243.52/50.03  End of proof
% 243.52/50.03  
% 243.52/50.03  Sub-proof #1220 shows that the following formulas are inconsistent:
% 243.52/50.03  ----------------------------------------------------------------
% 243.52/50.03    (1)   ~ (e3 = e0)
% 243.52/50.03    (2)  all_58_6 = e3
% 243.52/50.03    (3)   ~ (e2 = e0)
% 243.52/50.03    (4)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.52/50.03         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.52/50.03    (5)  op(e3, e3) = e1
% 243.52/50.03    (6)  op(e2, e1) = all_52_9
% 243.52/50.03    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.52/50.03         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.52/50.03    (8)   ~ (e3 = e2)
% 243.52/50.03    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.52/50.03         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.52/50.03    (10)   ~ (all_52_9 = e3)
% 243.52/50.03    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.03    (12)   ~ (e1 = e0)
% 243.52/50.03    (13)   ~ (all_52_13 = e3)
% 243.52/50.03    (14)  op(e2, e0) = all_52_13
% 243.52/50.03    (15)  all_58_3 = e0
% 243.52/50.03    (16)   ~ (e2 = e1)
% 243.52/50.03  
% 243.52/50.03  Begin of proof
% 243.52/50.03  | 
% 243.52/50.03  | BETA: splitting (4) gives:
% 243.52/50.03  | 
% 243.52/50.03  | Case 1:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (17)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 243.52/50.03  | |           e3)
% 243.52/50.03  | | 
% 243.52/50.03  | | BETA: splitting (17) gives:
% 243.52/50.03  | | 
% 243.52/50.03  | | Case 1:
% 243.52/50.03  | | | 
% 243.52/50.03  | | |   (18)  all_58_2 = e3 & op(e2, e3) = e3
% 243.52/50.03  | | | 
% 243.52/50.03  | | | ALPHA: (18) implies:
% 243.52/50.03  | | |   (19)  all_58_2 = e3
% 243.52/50.03  | | | 
% 243.52/50.03  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (12), (16), (19) are
% 243.52/50.03  | | |            inconsistent by sub-proof #1221.
% 243.52/50.03  | | | 
% 243.52/50.03  | | Case 2:
% 243.52/50.03  | | | 
% 243.52/50.03  | | |   (20)  all_58_3 = e3 & op(e2, e2) = e3
% 243.52/50.03  | | | 
% 243.52/50.03  | | | REF_CLOSE: (1), (15), (20) are inconsistent by sub-proof #1516.
% 243.52/50.03  | | | 
% 243.52/50.03  | | End of split
% 243.52/50.03  | | 
% 243.52/50.03  | Case 2:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (21)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 243.52/50.03  | |           e3)
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (6), (10), (11), (13), (14), (21) are inconsistent by sub-proof
% 243.52/50.03  | |            #1649.
% 243.52/50.03  | | 
% 243.52/50.03  | End of split
% 243.52/50.03  | 
% 243.52/50.03  End of proof
% 243.52/50.03  
% 243.52/50.03  Sub-proof #1221 shows that the following formulas are inconsistent:
% 243.52/50.03  ----------------------------------------------------------------
% 243.52/50.03    (1)   ~ (e3 = e0)
% 243.52/50.03    (2)  all_58_6 = e3
% 243.52/50.03    (3)   ~ (e2 = e0)
% 243.52/50.03    (4)  op(e3, e3) = e1
% 243.52/50.03    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.52/50.03         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.52/50.03    (6)   ~ (e3 = e2)
% 243.52/50.03    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.52/50.03         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.52/50.03    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.03    (9)   ~ (e1 = e0)
% 243.52/50.03    (10)  all_58_2 = e3
% 243.52/50.03    (11)   ~ (e2 = e1)
% 243.52/50.03  
% 243.52/50.03  Begin of proof
% 243.52/50.03  | 
% 243.52/50.03  | BETA: splitting (5) gives:
% 243.52/50.03  | 
% 243.52/50.03  | Case 1:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (12)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 243.52/50.03  | |           e2)
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (4), (6), (8), (10), (11), (12) are inconsistent by sub-proof
% 243.52/50.03  | |            #1223.
% 243.52/50.03  | | 
% 243.52/50.03  | Case 2:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (13)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 243.52/50.03  | |           e2)
% 243.52/50.03  | | 
% 243.52/50.03  | | BETA: splitting (13) gives:
% 243.52/50.03  | | 
% 243.52/50.03  | | Case 1:
% 243.52/50.03  | | | 
% 243.52/50.03  | | |   (14)  all_58_6 = e2 & op(e1, e3) = e2
% 243.52/50.03  | | | 
% 243.52/50.03  | | | REF_CLOSE: (2), (6), (14) are inconsistent by sub-proof #2219.
% 243.52/50.03  | | | 
% 243.52/50.03  | | Case 2:
% 243.52/50.03  | | | 
% 243.52/50.03  | | |   (15)  all_58_12 = e2 & op(e0, e3) = e2
% 243.52/50.03  | | | 
% 243.52/50.03  | | | ALPHA: (15) implies:
% 243.52/50.03  | | |   (16)  all_58_12 = e2
% 243.52/50.03  | | | 
% 243.52/50.03  | | | BETA: splitting (7) gives:
% 243.52/50.03  | | | 
% 243.52/50.03  | | | Case 1:
% 243.52/50.03  | | | | 
% 243.52/50.03  | | | |   (17)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 243.52/50.03  | | | |           = e0)
% 243.52/50.03  | | | | 
% 243.52/50.03  | | | | REF_CLOSE: (1), (4), (8), (9), (10), (17) are inconsistent by sub-proof
% 243.52/50.03  | | | |            #1222.
% 243.52/50.03  | | | | 
% 243.52/50.03  | | | Case 2:
% 243.52/50.03  | | | | 
% 243.52/50.03  | | | |   (18)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 243.52/50.03  | | | |           = e0)
% 243.52/50.03  | | | | 
% 243.52/50.03  | | | | BETA: splitting (18) gives:
% 243.52/50.03  | | | | 
% 243.52/50.03  | | | | Case 1:
% 243.52/50.03  | | | | | 
% 243.52/50.03  | | | | |   (19)  all_58_6 = e0 & op(e1, e3) = e0
% 243.52/50.03  | | | | | 
% 243.52/50.03  | | | | | REF_CLOSE: (1), (2), (19) are inconsistent by sub-proof #2213.
% 243.52/50.03  | | | | | 
% 243.52/50.03  | | | | Case 2:
% 243.52/50.03  | | | | | 
% 243.52/50.03  | | | | |   (20)  all_58_12 = e0 & op(e0, e3) = e0
% 243.52/50.03  | | | | | 
% 243.52/50.03  | | | | | ALPHA: (20) implies:
% 243.52/50.03  | | | | |   (21)  all_58_12 = e0
% 243.52/50.03  | | | | | 
% 243.52/50.03  | | | | | REF_CLOSE: (3), (16), (21) are inconsistent by sub-proof #2083.
% 243.52/50.03  | | | | | 
% 243.52/50.03  | | | | End of split
% 243.52/50.03  | | | | 
% 243.52/50.03  | | | End of split
% 243.52/50.03  | | | 
% 243.52/50.03  | | End of split
% 243.52/50.03  | | 
% 243.52/50.03  | End of split
% 243.52/50.03  | 
% 243.52/50.03  End of proof
% 243.52/50.03  
% 243.52/50.03  Sub-proof #1222 shows that the following formulas are inconsistent:
% 243.52/50.03  ----------------------------------------------------------------
% 243.52/50.03    (1)   ~ (e3 = e0)
% 243.52/50.03    (2)  op(e3, e3) = e1
% 243.52/50.03    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.03    (4)   ~ (e1 = e0)
% 243.52/50.03    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 243.52/50.03    (6)  all_58_2 = e3
% 243.52/50.03  
% 243.52/50.03  Begin of proof
% 243.52/50.03  | 
% 243.52/50.03  | BETA: splitting (5) gives:
% 243.52/50.03  | 
% 243.52/50.03  | Case 1:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 243.52/50.03  | | 
% 243.52/50.03  | | ALPHA: (7) implies:
% 243.52/50.03  | |   (8)  op(e3, e3) = e0
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1828.
% 243.52/50.03  | | 
% 243.52/50.03  | Case 2:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (9)  all_58_2 = e0 & op(e2, e3) = e0
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #1351.
% 243.52/50.03  | | 
% 243.52/50.03  | End of split
% 243.52/50.03  | 
% 243.52/50.03  End of proof
% 243.52/50.03  
% 243.52/50.03  Sub-proof #1223 shows that the following formulas are inconsistent:
% 243.52/50.03  ----------------------------------------------------------------
% 243.52/50.03    (1)  op(e3, e3) = e1
% 243.52/50.03    (2)   ~ (e3 = e2)
% 243.52/50.03    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 243.52/50.03    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.03    (5)  all_58_2 = e3
% 243.52/50.03    (6)   ~ (e2 = e1)
% 243.52/50.03  
% 243.52/50.03  Begin of proof
% 243.52/50.03  | 
% 243.52/50.03  | BETA: splitting (3) gives:
% 243.52/50.03  | 
% 243.52/50.03  | Case 1:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 243.52/50.03  | | 
% 243.52/50.03  | | ALPHA: (7) implies:
% 243.52/50.03  | |   (8)  op(e3, e3) = e2
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #2267.
% 243.52/50.03  | | 
% 243.52/50.03  | Case 2:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (9)  all_58_2 = e2 & op(e2, e3) = e2
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #1224.
% 243.52/50.03  | | 
% 243.52/50.03  | End of split
% 243.52/50.03  | 
% 243.52/50.03  End of proof
% 243.52/50.03  
% 243.52/50.03  Sub-proof #1224 shows that the following formulas are inconsistent:
% 243.52/50.03  ----------------------------------------------------------------
% 243.52/50.03    (1)  all_58_2 = e2 & op(e2, e3) = e2
% 243.52/50.03    (2)  all_58_2 = e3
% 243.52/50.03    (3)   ~ (e3 = e2)
% 243.52/50.03  
% 243.52/50.03  Begin of proof
% 243.52/50.03  | 
% 243.52/50.03  | ALPHA: (1) implies:
% 243.52/50.03  |   (4)  all_58_2 = e2
% 243.52/50.03  | 
% 243.52/50.03  | COMBINE_EQS: (2), (4) imply:
% 243.52/50.03  |   (5)  e3 = e2
% 243.52/50.03  | 
% 243.52/50.03  | REDUCE: (3), (5) imply:
% 243.52/50.03  |   (6)  $false
% 243.52/50.03  | 
% 243.52/50.03  | CLOSE: (6) is inconsistent.
% 243.52/50.03  | 
% 243.52/50.03  End of proof
% 243.52/50.03  
% 243.52/50.03  Sub-proof #1225 shows that the following formulas are inconsistent:
% 243.52/50.03  ----------------------------------------------------------------
% 243.52/50.03    (1)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 243.52/50.03    (2)   ~ (all_52_8 = all_52_9)
% 243.52/50.03    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.52/50.03         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.52/50.03    (4)   ~ (all_10_2 = e2)
% 243.52/50.03    (5)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.52/50.03           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.52/50.03             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.52/50.03           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.52/50.03             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.52/50.03           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.03           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.52/50.03           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.52/50.03           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.52/50.03           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.03           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.52/50.03             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.52/50.03           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.52/50.03           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 243.52/50.03           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.52/50.03           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.52/50.03           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.03           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.52/50.03             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.52/50.03           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.52/50.03           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 243.52/50.03           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.52/50.03           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.52/50.03           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.03           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.52/50.03             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.52/50.03           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.03           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.52/50.03    (6)   ~ (all_10_2 = e0)
% 243.52/50.03    (7)  op(e1, e0) = all_52_14
% 243.52/50.03    (8)   ~ (all_10_2 = e1)
% 243.52/50.03    (9)  op(e0, e3) = all_52_3
% 243.52/50.03    (10)   ~ (all_52_1 = all_10_2)
% 243.52/50.03    (11)   ~ (all_52_1 = all_52_9)
% 243.52/50.03    (12)  all_56_21 = e0
% 243.52/50.03    (13)  op(e3, e1) = all_52_8
% 243.52/50.03    (14)  op(e2, e1) = all_52_9
% 243.52/50.03    (15)   ~ (all_52_14 = e0)
% 243.52/50.03    (16)   ~ (all_52_3 = e3)
% 243.52/50.03    (17)  op(e2, e3) = all_52_1
% 243.52/50.03    (18)  all_56_31 = e3
% 243.52/50.03    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.03    (20)   ~ (all_52_13 = e3)
% 243.52/50.03    (21)  op(e2, e0) = all_52_13
% 243.52/50.03    (22)  all_54_0 = all_10_2
% 243.52/50.03    (23)  all_58_3 = e0
% 243.52/50.03    (24)   ~ (all_52_13 = e0)
% 243.52/50.03  
% 243.52/50.03  Begin of proof
% 243.52/50.03  | 
% 243.52/50.03  | BETA: splitting (1) gives:
% 243.52/50.03  | 
% 243.52/50.03  | Case 1:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (25)  all_54_0 = e3
% 243.52/50.03  | | 
% 243.52/50.03  | | COMBINE_EQS: (22), (25) imply:
% 243.52/50.03  | |   (26)  all_10_2 = e3
% 243.52/50.03  | | 
% 243.52/50.03  | | REDUCE: (10), (26) imply:
% 243.52/50.03  | |   (27)   ~ (all_52_1 = e3)
% 243.52/50.03  | | 
% 243.52/50.03  | | REDUCE: (4), (26) imply:
% 243.52/50.03  | |   (28)   ~ (e3 = e2)
% 243.52/50.03  | | 
% 243.52/50.03  | | REDUCE: (8), (26) imply:
% 243.52/50.03  | |   (29)   ~ (e3 = e1)
% 243.52/50.03  | | 
% 243.52/50.03  | | REDUCE: (6), (26) imply:
% 243.52/50.03  | |   (30)   ~ (e3 = e0)
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (2), (3), (5), (7), (9), (11), (12), (13), (14), (15), (16),
% 243.52/50.03  | |            (17), (18), (19), (20), (21), (23), (24), (27), (28), (29), (30)
% 243.52/50.03  | |            are inconsistent by sub-proof #1226.
% 243.52/50.03  | | 
% 243.52/50.03  | Case 2:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (31)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (4), (6), (8), (22), (31) are inconsistent by sub-proof #2319.
% 243.52/50.03  | | 
% 243.52/50.03  | End of split
% 243.52/50.03  | 
% 243.52/50.03  End of proof
% 243.52/50.03  
% 243.52/50.03  Sub-proof #1226 shows that the following formulas are inconsistent:
% 243.52/50.03  ----------------------------------------------------------------
% 243.52/50.03    (1)   ~ (e3 = e0)
% 243.52/50.03    (2)   ~ (all_52_8 = all_52_9)
% 243.52/50.03    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.52/50.03         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.52/50.03    (4)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.52/50.03           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.52/50.03             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.52/50.03           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.52/50.03             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.52/50.03           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.03           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.52/50.03           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.52/50.03           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.52/50.03           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.03           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.52/50.03             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.52/50.03           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.52/50.03           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 243.52/50.03           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.52/50.03           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.52/50.03           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.03           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.52/50.03             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.52/50.03           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.52/50.03           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 243.52/50.03           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.52/50.03           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.52/50.03           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.03           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.52/50.03             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.52/50.03           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.03           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.52/50.03    (5)  op(e1, e0) = all_52_14
% 243.52/50.03    (6)  op(e0, e3) = all_52_3
% 243.52/50.03    (7)   ~ (e3 = e1)
% 243.52/50.03    (8)   ~ (all_52_1 = all_52_9)
% 243.52/50.03    (9)  all_56_21 = e0
% 243.52/50.03    (10)  op(e3, e1) = all_52_8
% 243.52/50.03    (11)  op(e2, e1) = all_52_9
% 243.52/50.03    (12)   ~ (e3 = e2)
% 243.52/50.03    (13)   ~ (all_52_14 = e0)
% 243.52/50.03    (14)   ~ (all_52_3 = e3)
% 243.52/50.03    (15)  op(e2, e3) = all_52_1
% 243.52/50.03    (16)  all_56_31 = e3
% 243.52/50.03    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.03    (18)   ~ (all_52_13 = e3)
% 243.52/50.03    (19)  op(e2, e0) = all_52_13
% 243.52/50.03    (20)  all_58_3 = e0
% 243.52/50.03    (21)   ~ (all_52_1 = e3)
% 243.52/50.03    (22)   ~ (all_52_13 = e0)
% 243.52/50.03  
% 243.52/50.03  Begin of proof
% 243.52/50.03  | 
% 243.52/50.03  | BETA: splitting (3) gives:
% 243.52/50.03  | 
% 243.52/50.03  | Case 1:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (23)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 243.52/50.03  | |           e3)
% 243.52/50.03  | | 
% 243.52/50.03  | | REF_CLOSE: (1), (15), (17), (20), (21), (23) are inconsistent by sub-proof
% 243.52/50.03  | |            #1424.
% 243.52/50.03  | | 
% 243.52/50.03  | Case 2:
% 243.52/50.03  | | 
% 243.52/50.03  | |   (24)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 243.52/50.03  | |           e3)
% 243.52/50.03  | | 
% 243.52/50.03  | | BETA: splitting (24) gives:
% 243.52/50.03  | | 
% 243.52/50.03  | | Case 1:
% 243.52/50.03  | | | 
% 243.52/50.03  | | |   (25)  all_58_5 = e3 & op(e2, e1) = e3
% 243.52/50.03  | | | 
% 243.52/50.03  | | | ALPHA: (25) implies:
% 243.52/50.03  | | |   (26)  op(e2, e1) = e3
% 243.52/50.03  | | | 
% 243.52/50.03  | | | GROUND_INST: instantiating (17) with all_52_9, e3, e1, e2, simplifying
% 243.52/50.03  | | |              with (11), (26) gives:
% 243.52/50.03  | | |   (27)  all_52_9 = e3
% 243.52/50.03  | | | 
% 243.52/50.03  | | | REDUCE: (2), (27) imply:
% 243.52/50.03  | | |   (28)   ~ (all_52_8 = e3)
% 243.52/50.03  | | | 
% 243.52/50.03  | | | BETA: splitting (4) gives:
% 243.52/50.03  | | | 
% 243.52/50.03  | | | Case 1:
% 243.52/50.03  | | | | 
% 243.52/50.04  | | | |   (29)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.04  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.52/50.04  | | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9
% 243.52/50.04  | | | |           = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.52/50.04  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.52/50.04  | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.52/50.04  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 243.52/50.04  | | | |           ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 243.52/50.04  | | | |         (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 243.52/50.04  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.52/50.04  | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 243.52/50.04  | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.52/50.04  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.52/50.04  | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.52/50.04  | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) & 
% 243.52/50.04  | | | |           ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.52/50.04  | | | | 
% 243.52/50.04  | | | | BETA: splitting (29) gives:
% 243.52/50.04  | | | | 
% 243.52/50.04  | | | | Case 1:
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | |   (30)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.04  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.52/50.04  | | | | |           & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 &
% 243.52/50.04  | | | | |           all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.52/50.04  | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.52/50.04  | | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.52/50.04  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.52/50.04  | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | | REF_CLOSE: (10), (15), (16), (17), (21), (28), (30) are inconsistent
% 243.52/50.04  | | | | |            by sub-proof #1316.
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | Case 2:
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | |   (31)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 243.52/50.04  | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 243.52/50.04  | | | | |           & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 243.52/50.04  | | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.52/50.04  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.52/50.04  | | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.52/50.04  | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.52/50.04  | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | | REF_CLOSE: (6), (14), (16), (17), (31) are inconsistent by sub-proof
% 243.52/50.04  | | | | |            #1389.
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | End of split
% 243.52/50.04  | | | | 
% 243.52/50.04  | | | Case 2:
% 243.52/50.04  | | | | 
% 243.52/50.04  | | | |   (32)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.52/50.04  | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.52/50.04  | | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 243.52/50.04  | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.52/50.04  | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.52/50.04  | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.52/50.04  | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) & 
% 243.52/50.04  | | | |           ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 243.52/50.04  | | | |         (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.04  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.52/50.04  | | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 243.52/50.04  | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.52/50.04  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.52/50.04  | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.52/50.04  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 243.52/50.04  | | | |           ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.52/50.04  | | | | 
% 243.52/50.04  | | | | BETA: splitting (32) gives:
% 243.52/50.04  | | | | 
% 243.52/50.04  | | | | Case 1:
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | |   (33)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.52/50.04  | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.52/50.04  | | | | |           & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 243.52/50.04  | | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.52/50.04  | | | | |           ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.52/50.04  | | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.52/50.04  | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 243.52/50.04  | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | | BETA: splitting (33) gives:
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | | Case 1:
% 243.52/50.04  | | | | | | 
% 243.52/50.04  | | | | | |   (34)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.52/50.04  | | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.52/50.04  | | | | | |         & op(e2, e1) = e2 & op(e1, e2) = e2
% 243.52/50.04  | | | | | | 
% 243.52/50.04  | | | | | | ALPHA: (34) implies:
% 243.52/50.04  | | | | | |   (35)  op(e2, e1) = e2
% 243.52/50.04  | | | | | | 
% 243.52/50.04  | | | | | | REF_CLOSE: (12), (17), (26), (35) are inconsistent by sub-proof
% 243.52/50.04  | | | | | |            #2256.
% 243.52/50.04  | | | | | | 
% 243.52/50.04  | | | | | Case 2:
% 243.52/50.04  | | | | | | 
% 243.52/50.04  | | | | | |   (36)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.04  | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 243.52/50.04  | | | | | |             e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 =
% 243.52/50.04  | | | | | |           e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 243.52/50.04  | | | | | |             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2,
% 243.52/50.04  | | | | | |             e0) = e2 & op(e0, e2) = e2)
% 243.52/50.04  | | | | | | 
% 243.52/50.04  | | | | | | BETA: splitting (36) gives:
% 243.52/50.04  | | | | | | 
% 243.52/50.04  | | | | | | Case 1:
% 243.52/50.04  | | | | | | | 
% 243.52/50.04  | | | | | | |   (37)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.04  | | | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 243.52/50.04  | | | | | | |           e2) & op(e2, e1) = e1 & op(e1, e2) = e1
% 243.52/50.04  | | | | | | | 
% 243.52/50.04  | | | | | | | ALPHA: (37) implies:
% 243.52/50.04  | | | | | | |   (38)  op(e2, e1) = e1
% 243.52/50.04  | | | | | | | 
% 243.52/50.04  | | | | | | | GROUND_INST: instantiating (17) with e3, e1, e1, e2, simplifying
% 243.52/50.04  | | | | | | |              with (26), (38) gives:
% 243.52/50.04  | | | | | | |   (39)  e3 = e1
% 243.52/50.04  | | | | | | | 
% 243.52/50.04  | | | | | | | REDUCE: (7), (39) imply:
% 243.52/50.04  | | | | | | |   (40)  $false
% 243.52/50.04  | | | | | | | 
% 243.52/50.04  | | | | | | | CLOSE: (40) is inconsistent.
% 243.52/50.04  | | | | | | | 
% 243.52/50.04  | | | | | | Case 2:
% 243.52/50.04  | | | | | | | 
% 243.52/50.04  | | | | | | |   (41)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.04  | | | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 243.52/50.04  | | | | | | |           e0) & op(e2, e0) = e2 & op(e0, e2) = e2
% 243.52/50.04  | | | | | | | 
% 243.52/50.04  | | | | | | | ALPHA: (41) implies:
% 243.52/50.04  | | | | | | |   (42)   ~ (all_56_21 = e0)
% 243.52/50.04  | | | | | | | 
% 243.52/50.04  | | | | | | | REDUCE: (9), (42) imply:
% 243.52/50.04  | | | | | | |   (43)  $false
% 243.52/50.04  | | | | | | | 
% 243.52/50.04  | | | | | | | CLOSE: (43) is inconsistent.
% 243.52/50.04  | | | | | | | 
% 243.52/50.04  | | | | | | End of split
% 243.52/50.04  | | | | | | 
% 243.52/50.04  | | | | | End of split
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | Case 2:
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | |   (44)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.04  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.52/50.04  | | | | |           & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 243.52/50.04  | | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.52/50.04  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.52/50.04  | | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.52/50.04  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.52/50.04  | | | | |           &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | | REF_CLOSE: (5), (9), (13), (17), (19), (22), (44) are inconsistent by
% 243.52/50.04  | | | | |            sub-proof #1227.
% 243.52/50.04  | | | | | 
% 243.52/50.04  | | | | End of split
% 243.52/50.04  | | | | 
% 243.52/50.04  | | | End of split
% 243.52/50.04  | | | 
% 243.52/50.04  | | Case 2:
% 243.52/50.04  | | | 
% 243.52/50.04  | | |   (45)  all_58_10 = e3 & op(e2, e0) = e3
% 243.52/50.04  | | | 
% 243.52/50.04  | | | ALPHA: (45) implies:
% 243.52/50.04  | | |   (46)  op(e2, e0) = e3
% 243.52/50.04  | | | 
% 243.52/50.04  | | | REF_CLOSE: (17), (18), (19), (46) are inconsistent by sub-proof #1994.
% 243.52/50.04  | | | 
% 243.52/50.04  | | End of split
% 243.52/50.04  | | 
% 243.52/50.04  | End of split
% 243.52/50.04  | 
% 243.52/50.04  End of proof
% 243.52/50.04  
% 243.52/50.04  Sub-proof #1227 shows that the following formulas are inconsistent:
% 243.52/50.04  ----------------------------------------------------------------
% 243.52/50.04    (1)  op(e1, e0) = all_52_14
% 243.52/50.04    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.52/50.04             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 243.52/50.04           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.52/50.04             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.52/50.04           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 243.52/50.04           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.04           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.52/50.04    (3)  all_56_21 = e0
% 243.52/50.04    (4)   ~ (all_52_14 = e0)
% 243.52/50.04    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.04    (6)  op(e2, e0) = all_52_13
% 243.52/50.04    (7)   ~ (all_52_13 = e0)
% 243.52/50.04  
% 243.52/50.04  Begin of proof
% 243.52/50.04  | 
% 243.52/50.04  | BETA: splitting (2) gives:
% 243.52/50.04  | 
% 243.52/50.04  | Case 1:
% 243.52/50.04  | | 
% 243.52/50.04  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.52/50.04  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 243.52/50.04  | |        & op(e0, e2) = e0
% 243.52/50.04  | | 
% 243.52/50.04  | | ALPHA: (8) implies:
% 243.52/50.04  | |   (9)  op(e2, e0) = e0
% 243.52/50.04  | | 
% 243.52/50.04  | | REF_CLOSE: (5), (6), (7), (9) are inconsistent by sub-proof #2324.
% 243.52/50.04  | | 
% 243.52/50.04  | Case 2:
% 243.52/50.04  | | 
% 243.52/50.04  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.04  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.52/50.04  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.52/50.04  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.52/50.04  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.52/50.04  | | 
% 243.52/50.04  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #1320.
% 243.52/50.04  | | 
% 243.52/50.04  | End of split
% 243.52/50.04  | 
% 243.52/50.04  End of proof
% 243.52/50.04  
% 243.52/50.04  Sub-proof #1228 shows that the following formulas are inconsistent:
% 243.52/50.04  ----------------------------------------------------------------
% 243.52/50.04    (1)   ~ (e2 = e0)
% 243.52/50.04    (2)  all_58_14 = e2
% 243.52/50.04    (3)  op(e0, e2) = all_52_7
% 243.52/50.04    (4)   ~ (all_52_7 = e0)
% 243.52/50.04    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.04    (6)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.52/50.04  
% 243.52/50.04  Begin of proof
% 243.52/50.04  | 
% 243.52/50.04  | BETA: splitting (6) gives:
% 243.52/50.04  | 
% 243.52/50.04  | Case 1:
% 243.52/50.04  | | 
% 243.52/50.04  | |   (7)  all_58_13 = e0 & op(e0, e2) = e0
% 243.52/50.04  | | 
% 243.52/50.04  | | ALPHA: (7) implies:
% 243.52/50.04  | |   (8)  op(e0, e2) = e0
% 243.52/50.04  | | 
% 243.52/50.04  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2252.
% 243.52/50.04  | | 
% 243.52/50.04  | Case 2:
% 243.52/50.04  | | 
% 243.52/50.04  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 243.52/50.04  | | 
% 243.52/50.04  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #2036.
% 243.52/50.04  | | 
% 243.52/50.04  | End of split
% 243.52/50.04  | 
% 243.52/50.04  End of proof
% 243.52/50.04  
% 243.52/50.04  Sub-proof #1229 shows that the following formulas are inconsistent:
% 243.52/50.04  ----------------------------------------------------------------
% 243.52/50.04    (1)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.52/50.04    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.52/50.04         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.52/50.04    (3)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 243.52/50.04           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 243.52/50.04           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 243.52/50.04           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 243.52/50.04           & $i(all_56_23))
% 243.52/50.04    (4)   ~ (all_52_9 = all_6_2)
% 243.52/50.04    (5)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.52/50.04    (6)   ~ (e3 = e0)
% 243.52/50.04    (7)  op(e0, e1) = all_52_11
% 243.52/50.04    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.52/50.04         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.52/50.04    (9)   ~ (all_52_8 = all_52_9)
% 243.52/50.04    (10)   ~ (e2 = e0)
% 243.52/50.04    (11)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.52/50.04            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.52/50.04            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 243.52/50.04            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 243.52/50.04            = all_56_15 & $i(all_56_15))
% 243.52/50.04    (12)  all_54_13 = all_52_7
% 243.52/50.04    (13)   ~ (all_52_8 = all_6_2)
% 243.52/50.04    (14)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.52/50.04          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.52/50.04    (15)  op(e1, e2) = all_52_6
% 243.52/50.04    (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.52/50.04          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.52/50.04    (17)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.52/50.04          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.52/50.04    (18)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.52/50.04              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.52/50.04            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.52/50.04            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.52/50.04            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.52/50.04             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.04            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.52/50.04            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.52/50.04            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.52/50.04            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.04            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.52/50.04              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.52/50.04            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.52/50.04            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.52/50.04            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.52/50.04            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.52/50.04            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.04            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.52/50.04              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.52/50.04            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.52/50.04            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.52/50.04            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.52/50.04            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.52/50.04            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.04            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.52/50.04              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.52/50.04            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.04            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.52/50.04    (19)   ~ (all_52_7 = all_52_11)
% 243.52/50.04    (20)  all_40_2 = all_6_2
% 243.52/50.04    (21)  op(e1, e1) = all_6_2
% 243.52/50.04    (22)   ~ (all_52_1 = all_52_2)
% 243.52/50.04    (23)  op(e1, e0) = all_52_14
% 243.52/50.04    (24)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.52/50.04    (25)  all_58_15 = e3
% 243.52/50.04    (26)  op(e0, e3) = all_52_3
% 243.52/50.04    (27)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.52/50.04          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.52/50.04    (28)   ~ (all_52_6 = e0)
% 243.52/50.04    (29)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.52/50.04          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.52/50.04    (30)   ~ (all_52_2 = all_52_3)
% 243.52/50.04    (31)  op(e2, e2) = e0
% 243.52/50.04    (32)   ~ (all_52_12 = all_52_14)
% 243.52/50.04    (33)  all_54_6 = all_52_9
% 243.52/50.04    (34)  op(e3, e1) = e0
% 243.52/50.04    (35)   ~ (all_52_12 = all_52_13)
% 243.52/50.04    (36)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.52/50.04          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.52/50.04    (37)  all_54_10 = all_6_2
% 243.52/50.04    (38)  all_54_2 = all_52_8
% 243.52/50.04    (39)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.52/50.04          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.52/50.04    (40)   ~ (all_52_2 = all_52_14)
% 243.52/50.04    (41)   ~ (all_52_1 = all_52_9)
% 243.52/50.04    (42)   ~ (all_52_3 = all_52_7)
% 243.52/50.04    (43)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.52/50.04    (44)  all_54_4 = all_52_1
% 243.52/50.05    (45)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.52/50.05              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.52/50.05                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.52/50.05                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.52/50.05    (46)   ~ (all_52_11 = e3)
% 243.52/50.05    (47)   ~ (all_52_8 = all_52_12)
% 243.52/50.05    (48)  op(e3, e1) = all_52_8
% 243.52/50.05    (49)  op(e2, e1) = all_52_9
% 243.52/50.05    (50)  all_54_9 = all_52_6
% 243.52/50.05    (51)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.52/50.05          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.52/50.05    (52)   ~ (e3 = e2)
% 243.52/50.05    (53)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.52/50.05          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.52/50.05    (54)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 243.52/50.05            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 243.52/50.05              e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 243.52/50.05    (55)   ~ (all_52_3 = all_52_11)
% 243.52/50.05    (56)   ~ (all_52_14 = all_6_2)
% 243.52/50.05    (57)   ~ (all_6_2 = e0)
% 243.52/50.05    (58)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.52/50.05    (59)   ~ (all_52_6 = all_6_2)
% 243.52/50.05    (60)  all_54_12 = all_52_3
% 243.52/50.05    (61)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.52/50.05    (62)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.52/50.05          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.52/50.05    (63)  op(e3, e0) = all_52_12
% 243.52/50.05    (64)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.52/50.05          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.52/50.05    (65)   ~ (all_52_9 = all_52_13)
% 243.52/50.05    (66)   ~ (all_52_3 = e3)
% 243.52/50.05    (67)   ~ (all_52_1 = e0)
% 243.52/50.05    (68)  all_56_11 = e0
% 243.52/50.05    (69)   ~ (all_52_4 = all_52_12)
% 243.52/50.05    (70)   ~ (all_52_2 = all_6_2)
% 243.52/50.05    (71)   ~ (all_52_6 = all_52_14)
% 243.52/50.05    (72)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.52/50.05    (73)  all_58_11 = e2
% 243.52/50.05    (74)  op(e2, e3) = all_52_1
% 243.52/50.05    (75)   ~ (all_52_14 = e3)
% 243.52/50.05    (76)  all_36_2 = all_6_2
% 243.52/50.05    (77)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.52/50.05    (78)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.52/50.05    (79)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 243.52/50.05            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 243.52/50.05              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 243.52/50.05    (80)  op(e1, e1) = e2
% 243.52/50.05    (81)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.52/50.05          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.52/50.05    (82)  op(e0, e2) = all_52_7
% 243.52/50.05    (83)   ~ (all_52_13 = all_52_14)
% 243.52/50.05    (84)  all_54_1 = all_52_4
% 243.52/50.05    (85)  op(e3, e2) = all_52_4
% 243.52/50.05    (86)   ~ (all_52_8 = all_52_11)
% 243.52/50.05    (87)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.52/50.05    (88)  all_56_31 = e3
% 243.52/50.05    (89)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.52/50.05          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.52/50.05    (90)  op(e0, e0) = e3
% 243.52/50.05    (91)  all_26_2 = e3
% 243.52/50.05    (92)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.52/50.05          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.52/50.05    (93)  all_54_8 = all_52_2
% 243.52/50.05    (94)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.52/50.05          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.52/50.05    (95)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.52/50.05          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.52/50.05    (96)  all_54_3 = all_52_12
% 243.52/50.05    (97)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.05    (98)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.52/50.05          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.52/50.05    (99)  op(e1, e3) = all_52_2
% 243.52/50.05    (100)   ~ (all_52_6 = all_52_7)
% 243.52/50.05    (101)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.52/50.05           (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.52/50.05    (102)   ~ (all_52_12 = e3)
% 243.52/50.05    (103)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.52/50.05           (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.52/50.05    (104)  all_56_21 = all_6_2
% 243.52/50.05    (105)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.52/50.05           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.52/50.05    (106)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 243.52/50.05             & op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 243.52/50.05             (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 243.52/50.05    (107)  op(e2, e0) = all_52_13
% 243.52/50.05    (108)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.52/50.05           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.52/50.05             e1)
% 243.52/50.05    (109)  all_58_3 = e0
% 243.52/50.05    (110)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.52/50.05           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.52/50.05             e2)
% 243.52/50.05    (111)   ~ (all_52_9 = all_52_11)
% 243.52/50.05    (112)   ~ (all_52_4 = all_52_8)
% 243.52/50.05    (113)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.52/50.05           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.52/50.05    (114)   ~ (all_52_13 = e0)
% 243.52/50.05    (115)   ~ (all_52_4 = all_52_6)
% 243.52/50.05    (116)   ~ (all_52_4 = e0)
% 243.52/50.05    (117)   ~ (all_52_4 = all_52_7)
% 243.52/50.05  
% 243.52/50.05  Begin of proof
% 243.52/50.05  | 
% 243.52/50.05  | BETA: splitting (64) gives:
% 243.52/50.05  | 
% 243.52/50.05  | Case 1:
% 243.52/50.05  | | 
% 243.52/50.05  | |   (118)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 243.52/50.05  | |            e3)
% 243.52/50.05  | | 
% 243.52/50.05  | | BETA: splitting (118) gives:
% 243.52/50.05  | | 
% 243.52/50.05  | | Case 1:
% 243.52/50.05  | | | 
% 243.52/50.05  | | |   (119)  all_58_6 = e3 & op(e1, e3) = e3
% 243.52/50.05  | | | 
% 243.52/50.05  | | | REF_CLOSE: (6), (10), (15), (28), (73), (80), (97), (105), (119) are
% 243.52/50.05  | | |            inconsistent by sub-proof #1672.
% 243.52/50.05  | | | 
% 243.52/50.05  | | Case 2:
% 243.52/50.05  | | | 
% 243.52/50.05  | | |   (120)  all_58_7 = e3 & op(e1, e2) = e3
% 243.52/50.05  | | | 
% 243.52/50.05  | | | ALPHA: (120) implies:
% 243.52/50.05  | | |   (121)  op(e1, e2) = e3
% 243.52/50.05  | | | 
% 243.52/50.05  | | | BETA: splitting (81) gives:
% 243.52/50.05  | | | 
% 243.52/50.05  | | | Case 1:
% 243.52/50.05  | | | | 
% 243.52/50.05  | | | |   (122)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 243.52/50.05  | | | |            = e3)
% 243.52/50.05  | | | | 
% 243.52/50.05  | | | | BETA: splitting (122) gives:
% 243.52/50.05  | | | | 
% 243.52/50.05  | | | | Case 1:
% 243.52/50.05  | | | | | 
% 243.52/50.05  | | | | |   (123)  all_58_4 = e3 & op(e3, e1) = e3
% 243.52/50.05  | | | | | 
% 243.52/50.05  | | | | | ALPHA: (123) implies:
% 243.52/50.05  | | | | |   (124)  op(e3, e1) = e3
% 243.52/50.05  | | | | | 
% 243.52/50.05  | | | | | REF_CLOSE: (6), (34), (97), (124) are inconsistent by sub-proof #2118.
% 243.52/50.05  | | | | | 
% 243.52/50.05  | | | | Case 2:
% 243.52/50.05  | | | | | 
% 243.52/50.05  | | | | |   (125)  all_58_5 = e3 & op(e2, e1) = e3
% 243.52/50.05  | | | | | 
% 243.52/50.05  | | | | | ALPHA: (125) implies:
% 243.52/50.05  | | | | |   (126)  op(e2, e1) = e3
% 243.52/50.05  | | | | | 
% 243.52/50.05  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13),
% 243.52/50.05  | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 243.52/50.05  | | | | |            (24), (25), (26), (27), (29), (30), (31), (32), (33), (35),
% 243.52/50.05  | | | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 243.52/50.05  | | | | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 243.52/50.05  | | | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 243.52/50.05  | | | | |            (67), (68), (69), (70), (71), (72), (74), (76), (77), (78),
% 243.52/50.05  | | | | |            (79), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 243.52/50.05  | | | | |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 243.52/50.05  | | | | |            (100), (101), (102), (103), (104), (105), (106), (107),
% 243.52/50.05  | | | | |            (108), (109), (110), (111), (112), (113), (114), (115),
% 243.52/50.05  | | | | |            (116), (117), (121), (126) are inconsistent by sub-proof
% 243.52/50.05  | | | | |            #1252.
% 243.52/50.05  | | | | | 
% 243.52/50.05  | | | | End of split
% 243.52/50.05  | | | | 
% 243.52/50.05  | | | Case 2:
% 243.52/50.05  | | | | 
% 243.52/50.05  | | | |   (127)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0,
% 243.52/50.05  | | | |              e1) = e3)
% 243.52/50.05  | | | | 
% 243.52/50.05  | | | | REF_CLOSE: (7), (46), (52), (80), (97), (127) are inconsistent by
% 243.52/50.05  | | | |            sub-proof #1307.
% 243.52/50.05  | | | | 
% 243.52/50.05  | | | End of split
% 243.52/50.05  | | | 
% 243.52/50.05  | | End of split
% 243.52/50.05  | | 
% 243.52/50.05  | Case 2:
% 243.52/50.05  | | 
% 243.52/50.05  | |   (128)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 243.52/50.05  | |            e3)
% 243.52/50.05  | | 
% 243.52/50.05  | | REF_CLOSE: (23), (52), (75), (80), (97), (128) are inconsistent by sub-proof
% 243.52/50.05  | |            #2148.
% 243.52/50.05  | | 
% 243.52/50.05  | End of split
% 243.52/50.05  | 
% 243.52/50.05  End of proof
% 243.52/50.05  
% 243.52/50.05  Sub-proof #1230 shows that the following formulas are inconsistent:
% 243.52/50.05  ----------------------------------------------------------------
% 243.52/50.05    (1)   ~ (e2 = e0)
% 243.52/50.05    (2)  all_58_15 = e3
% 243.52/50.05    (3)   ~ (e3 = e2)
% 243.52/50.05    (4)  all_58_12 = e0
% 243.52/50.05    (5)  all_58_13 = e1
% 243.52/50.05    (6)  all_58_14 = e1
% 243.52/50.05    (7)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 243.52/50.05         (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.52/50.05    (8)   ~ (e2 = e1)
% 243.52/50.05  
% 243.52/50.05  Begin of proof
% 243.52/50.05  | 
% 243.52/50.05  | BETA: splitting (7) gives:
% 243.52/50.05  | 
% 243.52/50.05  | Case 1:
% 243.52/50.05  | | 
% 243.52/50.05  | |   (9)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 243.52/50.05  | |          e2)
% 243.52/50.05  | | 
% 243.52/50.05  | | BETA: splitting (9) gives:
% 243.52/50.05  | | 
% 243.52/50.05  | | Case 1:
% 243.52/50.05  | | | 
% 243.52/50.05  | | |   (10)  all_58_12 = e2 & op(e0, e3) = e2
% 243.52/50.05  | | | 
% 243.52/50.05  | | | ALPHA: (10) implies:
% 243.52/50.05  | | |   (11)  all_58_12 = e2
% 243.52/50.05  | | | 
% 243.52/50.05  | | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #2083.
% 243.52/50.05  | | | 
% 243.52/50.05  | | Case 2:
% 243.52/50.05  | | | 
% 243.52/50.05  | | |   (12)  all_58_13 = e2 & op(e0, e2) = e2
% 243.52/50.05  | | | 
% 243.52/50.05  | | | ALPHA: (12) implies:
% 243.52/50.05  | | |   (13)  all_58_13 = e2
% 243.52/50.05  | | | 
% 243.52/50.05  | | | REF_CLOSE: (5), (8), (13) are inconsistent by sub-proof #1544.
% 243.52/50.05  | | | 
% 243.52/50.05  | | End of split
% 243.52/50.05  | | 
% 243.52/50.05  | Case 2:
% 243.52/50.05  | | 
% 243.52/50.05  | |   (14)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.52/50.05  | |           e2)
% 243.52/50.05  | | 
% 243.52/50.05  | | BETA: splitting (14) gives:
% 243.52/50.05  | | 
% 243.52/50.05  | | Case 1:
% 243.52/50.05  | | | 
% 243.52/50.05  | | |   (15)  all_58_14 = e2 & op(e0, e1) = e2
% 243.52/50.05  | | | 
% 243.52/50.05  | | | ALPHA: (15) implies:
% 243.52/50.05  | | |   (16)  all_58_14 = e2
% 243.52/50.05  | | | 
% 243.52/50.05  | | | REF_CLOSE: (6), (8), (16) are inconsistent by sub-proof #2044.
% 243.52/50.05  | | | 
% 243.52/50.05  | | Case 2:
% 243.52/50.05  | | | 
% 243.52/50.05  | | |   (17)  all_58_15 = e2 & op(e0, e0) = e2
% 243.52/50.05  | | | 
% 243.52/50.05  | | | REF_CLOSE: (2), (3), (17) are inconsistent by sub-proof #1231.
% 243.52/50.05  | | | 
% 243.52/50.05  | | End of split
% 243.52/50.05  | | 
% 243.52/50.05  | End of split
% 243.52/50.05  | 
% 243.52/50.05  End of proof
% 243.52/50.05  
% 243.52/50.05  Sub-proof #1231 shows that the following formulas are inconsistent:
% 243.52/50.05  ----------------------------------------------------------------
% 243.52/50.05    (1)  all_58_15 = e2 & op(e0, e0) = e2
% 243.52/50.05    (2)  all_58_15 = e3
% 243.52/50.05    (3)   ~ (e3 = e2)
% 243.52/50.05  
% 243.52/50.05  Begin of proof
% 243.52/50.05  | 
% 243.52/50.05  | ALPHA: (1) implies:
% 243.52/50.05  |   (4)  all_58_15 = e2
% 243.52/50.05  | 
% 243.52/50.05  | COMBINE_EQS: (2), (4) imply:
% 243.52/50.05  |   (5)  e3 = e2
% 243.52/50.05  | 
% 243.52/50.05  | REDUCE: (3), (5) imply:
% 243.52/50.05  |   (6)  $false
% 243.52/50.05  | 
% 243.52/50.05  | CLOSE: (6) is inconsistent.
% 243.52/50.05  | 
% 243.52/50.05  End of proof
% 243.52/50.05  
% 243.52/50.05  Sub-proof #1232 shows that the following formulas are inconsistent:
% 243.52/50.05  ----------------------------------------------------------------
% 243.52/50.05    (1)   ~ (e3 = e0)
% 243.52/50.05    (2)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 243.52/50.05    (3)  all_58_5 = e3
% 243.52/50.05    (4)  all_58_14 = e2
% 243.52/50.05    (5)   ~ (e3 = e1)
% 243.52/50.05    (6)  op(e3, e1) = e0
% 243.52/50.05    (7)   ~ (e3 = e2)
% 243.52/50.05    (8)  op(e3, e3) = e2
% 243.52/50.05    (9)  op(e1, e1) = e2
% 243.52/50.05    (10)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.52/50.05          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.52/50.05    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.05    (12)  all_58_2 = e1
% 243.52/50.05  
% 243.52/50.05  Begin of proof
% 243.52/50.05  | 
% 243.52/50.05  | BETA: splitting (2) gives:
% 243.52/50.05  | 
% 243.52/50.05  | Case 1:
% 243.52/50.05  | | 
% 243.52/50.05  | |   (13)  all_58_0 = e3 & op(e3, e3) = e3
% 243.52/50.05  | | 
% 243.52/50.05  | | ALPHA: (13) implies:
% 243.52/50.05  | |   (14)  op(e3, e3) = e3
% 243.52/50.05  | | 
% 243.52/50.05  | | REF_CLOSE: (7), (8), (11), (14) are inconsistent by sub-proof #2194.
% 243.52/50.05  | | 
% 243.52/50.05  | Case 2:
% 243.52/50.05  | | 
% 243.52/50.05  | |   (15)  all_58_2 = e3 & op(e2, e3) = e3
% 243.52/50.05  | | 
% 243.52/50.05  | | ALPHA: (15) implies:
% 243.52/50.05  | |   (16)  all_58_2 = e3
% 243.52/50.05  | | 
% 243.52/50.05  | | COMBINE_EQS: (12), (16) imply:
% 243.52/50.05  | |   (17)  e3 = e1
% 243.52/50.05  | | 
% 243.52/50.05  | | COMBINE_EQS: (3), (17) imply:
% 243.52/50.05  | |   (18)  all_58_5 = e1
% 243.52/50.05  | | 
% 243.52/50.05  | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (18) are inconsistent
% 243.52/50.05  | |            by sub-proof #2115.
% 243.52/50.05  | | 
% 243.52/50.05  | End of split
% 243.52/50.05  | 
% 243.52/50.05  End of proof
% 243.52/50.05  
% 243.52/50.05  Sub-proof #1233 shows that the following formulas are inconsistent:
% 243.52/50.05  ----------------------------------------------------------------
% 243.52/50.05    (1)   ~ (e3 = e0)
% 243.52/50.05    (2)   ~ (e2 = e0)
% 243.52/50.05    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.52/50.05         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.52/50.05    (4)  all_58_15 = e3
% 243.52/50.05    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.52/50.05         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.52/50.05    (6)   ~ (e3 = e1)
% 243.52/50.05    (7)  op(e2, e2) = e0
% 243.52/50.05    (8)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.52/50.05             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.52/50.05               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.52/50.05               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.52/50.05    (9)  op(e2, e1) = all_52_9
% 243.52/50.05    (10)  all_58_11 = e2
% 243.52/50.05    (11)  op(e2, e3) = all_52_1
% 243.52/50.05    (12)  op(e0, e0) = e3
% 243.52/50.05    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.05    (14)   ~ (e1 = e0)
% 243.52/50.06    (15)   ~ (all_52_1 = e2)
% 243.52/50.06    (16)   ~ (e2 = e1)
% 243.52/50.06    (17)   ~ (all_52_9 = e2)
% 243.52/50.06  
% 243.52/50.06  Begin of proof
% 243.52/50.06  | 
% 243.52/50.06  | BETA: splitting (8) gives:
% 243.52/50.06  | 
% 243.52/50.06  | Case 1:
% 243.52/50.06  | | 
% 243.52/50.06  | |   (18)  all_58_15 = e0 & op(e0, e0) = e0
% 243.52/50.06  | | 
% 243.52/50.06  | | ALPHA: (18) implies:
% 243.52/50.06  | |   (19)  op(e0, e0) = e0
% 243.52/50.06  | | 
% 243.52/50.06  | | REF_CLOSE: (1), (12), (13), (19) are inconsistent by sub-proof #2079.
% 243.52/50.06  | | 
% 243.52/50.06  | Case 2:
% 243.52/50.06  | | 
% 243.52/50.06  | |   (20)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.52/50.06  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 243.52/50.06  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.52/50.06  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 243.52/50.06  | | 
% 243.52/50.06  | | ALPHA: (20) implies:
% 243.52/50.06  | |   (21)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.52/50.06  | |           e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.52/50.06  | | 
% 243.52/50.06  | | BETA: splitting (5) gives:
% 243.52/50.06  | | 
% 243.52/50.06  | | Case 1:
% 243.52/50.06  | | | 
% 243.52/50.06  | | |   (22)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 243.52/50.06  | | |           e2)
% 243.52/50.06  | | | 
% 243.52/50.06  | | | REF_CLOSE: (2), (7), (11), (13), (15), (22) are inconsistent by sub-proof
% 243.52/50.06  | | |            #1234.
% 243.52/50.06  | | | 
% 243.52/50.06  | | Case 2:
% 243.52/50.06  | | | 
% 243.52/50.06  | | |   (23)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 243.52/50.06  | | |           e2)
% 243.52/50.06  | | | 
% 243.52/50.06  | | | BETA: splitting (23) gives:
% 243.52/50.06  | | | 
% 243.52/50.06  | | | Case 1:
% 243.52/50.06  | | | | 
% 243.52/50.06  | | | |   (24)  all_58_5 = e2 & op(e2, e1) = e2
% 243.52/50.06  | | | | 
% 243.52/50.06  | | | | ALPHA: (24) implies:
% 243.52/50.06  | | | |   (25)  op(e2, e1) = e2
% 243.52/50.06  | | | | 
% 243.52/50.06  | | | | REF_CLOSE: (9), (13), (17), (25) are inconsistent by sub-proof #2328.
% 243.52/50.06  | | | | 
% 243.52/50.06  | | | Case 2:
% 243.52/50.06  | | | | 
% 243.52/50.06  | | | |   (26)  all_58_10 = e2 & op(e2, e0) = e2
% 243.52/50.06  | | | | 
% 243.52/50.06  | | | | ALPHA: (26) implies:
% 243.52/50.06  | | | |   (27)  op(e2, e0) = e2
% 243.52/50.06  | | | | 
% 243.52/50.06  | | | | REF_CLOSE: (2), (3), (4), (6), (10), (13), (14), (16), (21), (27) are
% 243.52/50.06  | | | |            inconsistent by sub-proof #1345.
% 243.52/50.06  | | | | 
% 243.52/50.06  | | | End of split
% 243.52/50.06  | | | 
% 243.52/50.06  | | End of split
% 243.52/50.06  | | 
% 243.52/50.06  | End of split
% 243.52/50.06  | 
% 243.52/50.06  End of proof
% 243.52/50.06  
% 243.52/50.06  Sub-proof #1234 shows that the following formulas are inconsistent:
% 243.52/50.06  ----------------------------------------------------------------
% 243.52/50.06    (1)   ~ (e2 = e0)
% 243.52/50.06    (2)  op(e2, e2) = e0
% 243.52/50.06    (3)  op(e2, e3) = all_52_1
% 243.52/50.06    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 243.52/50.06    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.52/50.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.52/50.06    (6)   ~ (all_52_1 = e2)
% 243.52/50.06  
% 243.52/50.06  Begin of proof
% 243.52/50.06  | 
% 243.52/50.06  | BETA: splitting (4) gives:
% 243.52/50.06  | 
% 243.52/50.06  | Case 1:
% 243.52/50.06  | | 
% 243.52/50.06  | |   (7)  all_58_2 = e2 & op(e2, e3) = e2
% 243.52/50.06  | | 
% 243.52/50.06  | | ALPHA: (7) implies:
% 243.52/50.06  | |   (8)  op(e2, e3) = e2
% 243.52/50.06  | | 
% 243.52/50.06  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2336.
% 243.52/50.06  | | 
% 243.52/50.06  | Case 2:
% 243.52/50.06  | | 
% 243.52/50.06  | |   (9)  all_58_3 = e2 & op(e2, e2) = e2
% 243.52/50.06  | | 
% 243.52/50.06  | | ALPHA: (9) implies:
% 243.52/50.06  | |   (10)  op(e2, e2) = e2
% 243.52/50.06  | | 
% 243.52/50.06  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #2137.
% 243.52/50.06  | | 
% 243.52/50.06  | End of split
% 243.52/50.06  | 
% 243.52/50.06  End of proof
% 243.52/50.06  
% 243.52/50.06  Sub-proof #1235 shows that the following formulas are inconsistent:
% 243.52/50.06  ----------------------------------------------------------------
% 243.52/50.06    (1)  all_56_21 = e2
% 243.52/50.06    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.52/50.06    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.52/50.06         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.52/50.06    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 243.52/50.06           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 243.52/50.06           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 243.52/50.06           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 243.52/50.06           & $i(all_56_23))
% 243.52/50.06    (5)   ~ (all_52_9 = all_6_2)
% 243.52/50.06    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.52/50.06    (7)   ~ (e3 = e0)
% 243.52/50.06    (8)  op(e0, e1) = all_52_11
% 243.52/50.06    (9)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.52/50.06         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.52/50.06    (10)   ~ (all_52_8 = all_52_9)
% 243.52/50.06    (11)   ~ (e2 = e0)
% 243.52/50.06    (12)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.52/50.06            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.52/50.06            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 243.52/50.06            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 243.52/50.06            = all_56_15 & $i(all_56_15))
% 243.52/50.06    (13)  all_54_13 = all_52_7
% 243.52/50.06    (14)   ~ (all_52_8 = all_6_2)
% 243.52/50.06    (15)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.52/50.06          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.52/50.06    (16)  op(e1, e2) = all_52_6
% 243.52/50.06    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.52/50.06          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.52/50.06    (18)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.52/50.06          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.52/50.06    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.52/50.06              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.52/50.06            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.52/50.06            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.52/50.06            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.52/50.06             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.06            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.52/50.06            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.52/50.06            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.52/50.06            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.06            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.52/50.06              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.52/50.06            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.52/50.06            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.52/50.06            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.52/50.06            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.52/50.06            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.52/50.06            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.52/50.06              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.52/50.06            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.52/50.06            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.52/50.06            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.52/50.06            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.52/50.06            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.52/50.06            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.52/50.06              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.52/50.06            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.52/50.06            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.52/50.06    (20)   ~ (all_52_7 = all_52_11)
% 243.52/50.06    (21)  all_40_2 = all_6_2
% 243.52/50.06    (22)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.52/50.06          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.52/50.06    (23)  op(e1, e1) = all_6_2
% 243.52/50.06    (24)   ~ (all_52_1 = all_52_2)
% 243.52/50.06    (25)  op(e1, e0) = all_52_14
% 243.52/50.06    (26)   ~ (all_52_7 = e3)
% 243.52/50.06    (27)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.52/50.06    (28)  all_58_15 = e3
% 243.52/50.06    (29)  op(e0, e3) = all_52_3
% 243.52/50.06    (30)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.52/50.06          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.52/50.06    (31)  op(e0, e2) = e2
% 243.52/50.06    (32)   ~ (all_52_6 = e0)
% 243.52/50.06    (33)   ~ (e3 = e1)
% 243.52/50.06    (34)  all_58_8 = e2
% 243.52/50.06    (35)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.52/50.06          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.52/50.06    (36)   ~ (all_52_2 = all_52_3)
% 243.52/50.06    (37)  op(e2, e2) = e0
% 243.52/50.06    (38)   ~ (all_52_12 = all_52_14)
% 243.52/50.06    (39)  all_54_6 = all_52_9
% 243.52/50.06    (40)   ~ (all_52_12 = all_52_13)
% 243.52/50.06    (41)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.52/50.06          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.52/50.06    (42)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.52/50.06            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 243.52/50.06              e3) = all_26_1 & $i(all_26_1))
% 243.52/50.06    (43)  all_36_2 = e2
% 243.52/50.06    (44)  all_54_10 = all_6_2
% 243.52/50.06    (45)  all_54_2 = all_52_8
% 243.52/50.06    (46)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.52/50.06          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.52/50.06    (47)   ~ (all_52_2 = all_52_14)
% 243.52/50.06    (48)   ~ (all_52_9 = e0)
% 243.52/50.06    (49)   ~ (all_52_1 = all_52_9)
% 243.52/50.06    (50)   ~ (all_52_3 = all_52_7)
% 243.52/50.06    (51)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.52/50.06    (52)  all_54_4 = all_52_1
% 243.52/50.06    (53)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.52/50.06              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.52/50.06                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.52/50.06                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.52/50.06    (54)   ~ (all_52_11 = e3)
% 243.52/50.06    (55)   ~ (all_6_2 = e3)
% 243.52/50.06    (56)   ~ (all_52_8 = all_52_12)
% 243.52/50.06    (57)  op(e3, e1) = all_52_8
% 243.52/50.06    (58)  op(e2, e1) = all_52_9
% 243.52/50.06    (59)  all_54_9 = all_52_6
% 243.52/50.06    (60)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.52/50.06          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.52/50.06    (61)   ~ (e3 = e2)
% 243.52/50.06    (62)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.52/50.06          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.52/50.06    (63)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 243.52/50.06            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 243.52/50.06              e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 243.52/50.06    (64)   ~ (all_52_3 = all_52_11)
% 243.52/50.06    (65)   ~ (all_52_14 = all_6_2)
% 243.52/50.06    (66)   ~ (all_6_2 = e0)
% 243.52/50.06    (67)  op(e2, e0) = e2
% 243.52/50.06    (68)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.52/50.06    (69)   ~ (all_52_6 = all_6_2)
% 243.52/50.06    (70)  all_54_12 = all_52_3
% 243.52/50.06    (71)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.52/50.06    (72)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.52/50.06          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.52/50.06    (73)  op(e3, e0) = all_52_12
% 243.52/50.06    (74)  all_58_13 = e2
% 243.52/50.06    (75)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.52/50.06          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.52/50.06    (76)   ~ (all_52_9 = all_52_13)
% 243.52/50.06    (77)   ~ (all_52_3 = e3)
% 243.52/50.06    (78)   ~ (all_52_1 = e0)
% 243.52/50.06    (79)  all_56_11 = e0
% 243.52/50.06    (80)   ~ (all_52_4 = all_52_12)
% 243.52/50.06    (81)   ~ (all_52_2 = all_6_2)
% 243.52/50.06    (82)   ~ (all_52_6 = all_52_14)
% 243.52/50.06    (83)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.52/50.06    (84)  op(e2, e3) = all_52_1
% 243.52/50.06    (85)  op(e3, e3) = e2
% 243.52/50.06    (86)   ~ (all_52_14 = e3)
% 243.52/50.06    (87)  all_36_2 = all_6_2
% 243.52/50.06    (88)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.52/50.06    (89)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.52/50.06          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.52/50.06    (90)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.52/50.06    (91)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 243.52/50.06            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 243.52/50.06              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 243.52/50.06    (92)  op(e1, e1) = e2
% 243.52/50.06    (93)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.52/50.06          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.52/50.06    (94)  op(e0, e2) = all_52_7
% 243.52/50.06    (95)   ~ (all_52_13 = all_52_14)
% 243.52/50.06    (96)  all_56_1 = e2
% 243.52/50.06    (97)  all_54_1 = all_52_4
% 243.52/50.06    (98)  op(e3, e2) = all_52_4
% 243.52/50.06    (99)   ~ (all_52_8 = all_52_11)
% 243.52/50.06    (100)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.52/50.06    (101)  all_56_31 = e3
% 243.52/50.06    (102)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.52/50.06           (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.52/50.06    (103)  op(e0, e0) = e3
% 243.52/50.06    (104)  all_26_2 = e3
% 243.52/50.06    (105)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.52/50.06           | (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 243.52/50.06             e3)
% 243.52/50.06    (106)   ~ (all_52_4 = e2)
% 243.52/50.06    (107)  all_54_8 = all_52_2
% 243.52/50.06    (108)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.52/50.06           (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.52/50.06    (109)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.52/50.06           (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.52/50.06    (110)  all_54_3 = all_52_12
% 243.52/50.06    (111)  all_40_2 = e2
% 243.59/50.06    (112)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.06             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.06    (113)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.59/50.06           | (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.59/50.06             e2)
% 243.59/50.07    (114)  op(e1, e3) = all_52_2
% 243.59/50.07    (115)   ~ (all_52_6 = all_52_7)
% 243.59/50.07    (116)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.59/50.07           (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.59/50.07    (117)   ~ (all_52_12 = e3)
% 243.59/50.07    (118)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 243.59/50.07             all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) &
% 243.59/50.07             op(e1, e2) = all_36_1 & $i(all_36_1))
% 243.59/50.07    (119)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.59/50.07           (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.59/50.07    (120)   ~ (e1 = e0)
% 243.59/50.07    (121)  all_56_21 = all_6_2
% 243.59/50.07    (122)   ~ (all_52_13 = e3)
% 243.59/50.07    (123)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.59/50.07           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.59/50.07    (124)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 243.59/50.07             & op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 243.59/50.07             (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 243.59/50.07    (125)  op(e2, e0) = all_52_13
% 243.59/50.07    (126)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.59/50.07           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.59/50.07             e1)
% 243.59/50.07    (127)  all_58_3 = e0
% 243.59/50.07    (128)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.59/50.07           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.59/50.07             e2)
% 243.59/50.07    (129)   ~ (all_52_9 = all_52_11)
% 243.59/50.07    (130)   ~ (all_52_4 = all_52_8)
% 243.59/50.07    (131)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.59/50.07           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.59/50.07    (132)   ~ (all_52_13 = e0)
% 243.59/50.07    (133)   ~ (all_52_1 = e2)
% 243.59/50.07    (134)   ~ (all_52_4 = all_52_6)
% 243.59/50.07    (135)   ~ (all_52_4 = e0)
% 243.59/50.07    (136)   ~ (e2 = e1)
% 243.59/50.07    (137)   ~ (all_52_4 = all_52_7)
% 243.59/50.07    (138)   ~ (all_52_9 = e2)
% 243.59/50.07  
% 243.59/50.07  Begin of proof
% 243.59/50.07  | 
% 243.59/50.07  | BETA: splitting (124) gives:
% 243.59/50.07  | 
% 243.59/50.07  | Case 1:
% 243.59/50.07  | | 
% 243.59/50.07  | |   (139)   ~ (all_40_2 = e2)
% 243.59/50.07  | | 
% 243.59/50.07  | | REDUCE: (111), (139) imply:
% 243.59/50.07  | |   (140)  $false
% 243.59/50.07  | | 
% 243.59/50.07  | | CLOSE: (140) is inconsistent.
% 243.59/50.07  | | 
% 243.59/50.07  | Case 2:
% 243.59/50.07  | | 
% 243.59/50.07  | |   (141)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 243.59/50.07  | |            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) &
% 243.59/50.07  | |            op(e1, e2) = all_40_1 & $i(all_40_1))
% 243.59/50.07  | | 
% 243.59/50.07  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 243.59/50.07  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 243.59/50.07  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 243.59/50.07  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 243.59/50.07  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 243.59/50.07  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 243.59/50.07  | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 243.59/50.07  | |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 243.59/50.07  | |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 243.59/50.07  | |            (100), (101), (102), (103), (104), (105), (106), (107), (108),
% 243.59/50.07  | |            (109), (110), (112), (113), (114), (115), (116), (117), (118),
% 243.59/50.07  | |            (119), (120), (121), (122), (123), (124), (125), (126), (127),
% 243.59/50.07  | |            (128), (129), (130), (131), (132), (133), (134), (135), (136),
% 243.59/50.07  | |            (137), (138), (141) are inconsistent by sub-proof #1236.
% 243.59/50.07  | | 
% 243.59/50.07  | End of split
% 243.59/50.07  | 
% 243.59/50.07  End of proof
% 243.59/50.07  
% 243.59/50.07  Sub-proof #1236 shows that the following formulas are inconsistent:
% 243.59/50.07  ----------------------------------------------------------------
% 243.59/50.07    (1)  all_56_21 = e2
% 243.59/50.07    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.59/50.07    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.59/50.07         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.59/50.07    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 243.59/50.07           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 243.59/50.07           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 243.59/50.07           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 243.59/50.07           & $i(all_56_23))
% 243.59/50.07    (5)   ~ (all_52_9 = all_6_2)
% 243.59/50.07    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.59/50.07    (7)   ~ (e3 = e0)
% 243.59/50.07    (8)  op(e0, e1) = all_52_11
% 243.59/50.07    (9)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.59/50.07         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.59/50.07    (10)   ~ (all_52_8 = all_52_9)
% 243.59/50.07    (11)   ~ (e2 = e0)
% 243.59/50.07    (12)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.59/50.07            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.59/50.07            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 243.59/50.07            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 243.59/50.07            = all_56_15 & $i(all_56_15))
% 243.59/50.07    (13)  all_54_13 = all_52_7
% 243.59/50.07    (14)   ~ (all_52_8 = all_6_2)
% 243.59/50.07    (15)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.59/50.07          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.59/50.07    (16)  op(e1, e2) = all_52_6
% 243.59/50.07    (17)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.59/50.07          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.59/50.07    (18)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.59/50.07          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.59/50.07    (19)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.59/50.07              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.59/50.07            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.59/50.07            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.07            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.59/50.07             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.07            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.59/50.07            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.59/50.07            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.59/50.07            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.07            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.59/50.07              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.59/50.07            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.07            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.59/50.07            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.59/50.07            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.59/50.07            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.07            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.59/50.07              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.59/50.07            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.59/50.07            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.59/50.07            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.59/50.07            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.59/50.07            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.07            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.59/50.07              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.59/50.07            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.07            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.07    (20)   ~ (all_52_7 = all_52_11)
% 243.59/50.07    (21)  all_40_2 = all_6_2
% 243.59/50.07    (22)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.59/50.07          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.59/50.07    (23)  op(e1, e1) = all_6_2
% 243.59/50.07    (24)   ~ (all_52_1 = all_52_2)
% 243.59/50.07    (25)  op(e1, e0) = all_52_14
% 243.59/50.07    (26)   ~ (all_52_7 = e3)
% 243.59/50.07    (27)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.59/50.07    (28)  all_58_15 = e3
% 243.59/50.07    (29)  op(e0, e3) = all_52_3
% 243.59/50.07    (30)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.59/50.07          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.59/50.07    (31)  op(e0, e2) = e2
% 243.59/50.07    (32)   ~ (all_52_6 = e0)
% 243.59/50.07    (33)   ~ (e3 = e1)
% 243.59/50.07    (34)  all_58_8 = e2
% 243.59/50.07    (35)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.59/50.07          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.59/50.07    (36)   ~ (all_52_2 = all_52_3)
% 243.59/50.07    (37)  op(e2, e2) = e0
% 243.59/50.07    (38)   ~ (all_52_12 = all_52_14)
% 243.59/50.07    (39)  all_54_6 = all_52_9
% 243.59/50.07    (40)   ~ (all_52_12 = all_52_13)
% 243.59/50.07    (41)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.59/50.07          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.59/50.07    (42)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.59/50.07            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 243.59/50.07              e3) = all_26_1 & $i(all_26_1))
% 243.59/50.07    (43)  all_36_2 = e2
% 243.59/50.07    (44)  all_54_10 = all_6_2
% 243.59/50.07    (45)  all_54_2 = all_52_8
% 243.59/50.07    (46)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.59/50.07          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.59/50.07    (47)   ~ (all_52_2 = all_52_14)
% 243.59/50.07    (48)   ~ (all_52_9 = e0)
% 243.59/50.07    (49)   ~ (all_52_1 = all_52_9)
% 243.59/50.07    (50)   ~ (all_52_3 = all_52_7)
% 243.59/50.07    (51)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.59/50.07    (52)  all_54_4 = all_52_1
% 243.59/50.07    (53)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.59/50.07              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.59/50.07                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.59/50.07                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.59/50.07    (54)   ~ (all_52_11 = e3)
% 243.59/50.07    (55)   ~ (all_6_2 = e3)
% 243.59/50.07    (56)   ~ (all_52_8 = all_52_12)
% 243.59/50.07    (57)  op(e3, e1) = all_52_8
% 243.59/50.07    (58)  op(e2, e1) = all_52_9
% 243.59/50.07    (59)  all_54_9 = all_52_6
% 243.59/50.07    (60)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.59/50.07          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.59/50.07    (61)   ~ (e3 = e2)
% 243.59/50.07    (62)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.59/50.07          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.59/50.07    (63)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 243.59/50.07            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 243.59/50.07              e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 243.59/50.07    (64)   ~ (all_52_3 = all_52_11)
% 243.59/50.07    (65)   ~ (all_52_14 = all_6_2)
% 243.59/50.07    (66)   ~ (all_6_2 = e0)
% 243.59/50.07    (67)  op(e2, e0) = e2
% 243.59/50.07    (68)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.59/50.07    (69)   ~ (all_52_6 = all_6_2)
% 243.59/50.07    (70)  all_54_12 = all_52_3
% 243.59/50.07    (71)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.59/50.07    (72)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.59/50.07          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.59/50.07    (73)  op(e3, e0) = all_52_12
% 243.59/50.07    (74)  all_58_13 = e2
% 243.59/50.07    (75)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.59/50.07          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.59/50.07    (76)   ~ (all_52_9 = all_52_13)
% 243.59/50.07    (77)   ~ (all_52_3 = e3)
% 243.59/50.07    (78)   ~ (all_52_1 = e0)
% 243.59/50.07    (79)  all_56_11 = e0
% 243.59/50.07    (80)   ~ (all_52_4 = all_52_12)
% 243.59/50.07    (81)   ~ (all_52_2 = all_6_2)
% 243.59/50.07    (82)   ~ (all_52_6 = all_52_14)
% 243.59/50.07    (83)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.59/50.07    (84)  op(e2, e3) = all_52_1
% 243.59/50.07    (85)  op(e3, e3) = e2
% 243.59/50.07    (86)   ~ (all_52_14 = e3)
% 243.59/50.07    (87)  all_36_2 = all_6_2
% 243.59/50.07    (88)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.59/50.07    (89)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.59/50.07          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.59/50.07    (90)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 243.59/50.07            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 243.59/50.07              e2) = all_40_1 & $i(all_40_1))
% 243.59/50.07    (91)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.59/50.07    (92)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 243.59/50.07            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 243.59/50.07              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 243.59/50.07    (93)  op(e1, e1) = e2
% 243.59/50.07    (94)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.59/50.07          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.59/50.07    (95)  op(e0, e2) = all_52_7
% 243.59/50.07    (96)   ~ (all_52_13 = all_52_14)
% 243.59/50.07    (97)  all_56_1 = e2
% 243.59/50.07    (98)  all_54_1 = all_52_4
% 243.59/50.07    (99)  op(e3, e2) = all_52_4
% 243.59/50.07    (100)   ~ (all_52_8 = all_52_11)
% 243.59/50.07    (101)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.59/50.07    (102)  all_56_31 = e3
% 243.59/50.07    (103)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.59/50.07           (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.59/50.07    (104)  op(e0, e0) = e3
% 243.59/50.07    (105)  all_26_2 = e3
% 243.59/50.07    (106)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.59/50.07           | (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 243.59/50.07             e3)
% 243.59/50.08    (107)   ~ (all_52_4 = e2)
% 243.59/50.08    (108)  all_54_8 = all_52_2
% 243.59/50.08    (109)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.59/50.08           (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.59/50.08    (110)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.59/50.08           (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.59/50.08    (111)  all_54_3 = all_52_12
% 243.59/50.08    (112)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.08             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.08    (113)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.59/50.08           | (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.59/50.08             e2)
% 243.59/50.08    (114)  op(e1, e3) = all_52_2
% 243.59/50.08    (115)   ~ (all_52_6 = all_52_7)
% 243.59/50.08    (116)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.59/50.08           (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.59/50.08    (117)   ~ (all_52_12 = e3)
% 243.59/50.08    (118)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 243.59/50.08             all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) &
% 243.59/50.08             op(e1, e2) = all_36_1 & $i(all_36_1))
% 243.59/50.08    (119)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.59/50.08           (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.59/50.08    (120)   ~ (e1 = e0)
% 243.59/50.08    (121)  all_56_21 = all_6_2
% 243.59/50.08    (122)   ~ (all_52_13 = e3)
% 243.59/50.08    (123)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.59/50.08           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.59/50.08    (124)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 243.59/50.08             & op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 243.59/50.08             (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 243.59/50.08    (125)  op(e2, e0) = all_52_13
% 243.59/50.08    (126)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.59/50.08           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.59/50.08             e1)
% 243.59/50.08    (127)  all_58_3 = e0
% 243.59/50.08    (128)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.59/50.08           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.59/50.08             e2)
% 243.59/50.08    (129)   ~ (all_52_9 = all_52_11)
% 243.59/50.08    (130)   ~ (all_52_4 = all_52_8)
% 243.59/50.08    (131)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.59/50.08           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.59/50.08    (132)   ~ (all_52_13 = e0)
% 243.59/50.08    (133)   ~ (all_52_1 = e2)
% 243.59/50.08    (134)   ~ (all_52_4 = all_52_6)
% 243.59/50.08    (135)   ~ (all_52_4 = e0)
% 243.59/50.08    (136)   ~ (e2 = e1)
% 243.59/50.08    (137)   ~ (all_52_4 = all_52_7)
% 243.59/50.08    (138)   ~ (all_52_9 = e2)
% 243.59/50.08  
% 243.59/50.08  Begin of proof
% 243.59/50.08  | 
% 243.59/50.08  | BETA: splitting (27) gives:
% 243.59/50.08  | 
% 243.59/50.08  | Case 1:
% 243.59/50.08  | | 
% 243.59/50.08  | |   (139)  all_54_1 = e3
% 243.59/50.08  | | 
% 243.59/50.08  | | COMBINE_EQS: (98), (139) imply:
% 243.59/50.08  | |   (140)  all_52_4 = e3
% 243.59/50.08  | | 
% 243.59/50.08  | | SIMP: (140) implies:
% 243.59/50.08  | |   (141)  all_52_4 = e3
% 243.59/50.08  | | 
% 243.59/50.08  | | REDUCE: (134), (141) imply:
% 243.59/50.08  | |   (142)   ~ (all_52_6 = e3)
% 243.59/50.08  | | 
% 243.59/50.08  | | SIMP: (142) implies:
% 243.59/50.08  | |   (143)   ~ (all_52_6 = e3)
% 243.59/50.08  | | 
% 243.59/50.08  | | REDUCE: (130), (141) imply:
% 243.59/50.08  | |   (144)   ~ (all_52_8 = e3)
% 243.59/50.08  | | 
% 243.59/50.08  | | SIMP: (144) implies:
% 243.59/50.08  | |   (145)   ~ (all_52_8 = e3)
% 243.59/50.08  | | 
% 243.59/50.08  | | REDUCE: (80), (141) imply:
% 243.59/50.08  | |   (146)   ~ (all_52_12 = e3)
% 243.59/50.08  | | 
% 243.59/50.08  | | BETA: splitting (75) gives:
% 243.59/50.08  | | 
% 243.59/50.08  | | Case 1:
% 243.59/50.08  | | | 
% 243.59/50.08  | | |   (147)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 243.59/50.08  | | |            e3)
% 243.59/50.08  | | | 
% 243.59/50.08  | | | BETA: splitting (147) gives:
% 243.59/50.08  | | | 
% 243.59/50.08  | | | Case 1:
% 243.59/50.08  | | | | 
% 243.59/50.08  | | | |   (148)  all_58_6 = e3 & op(e1, e3) = e3
% 243.59/50.08  | | | | 
% 243.59/50.08  | | | | ALPHA: (148) implies:
% 243.59/50.08  | | | |   (149)  all_58_6 = e3
% 243.59/50.08  | | | |   (150)  op(e1, e3) = e3
% 243.59/50.08  | | | | 
% 243.59/50.08  | | | | BETA: splitting (116) gives:
% 243.59/50.08  | | | | 
% 243.59/50.08  | | | | Case 1:
% 243.59/50.08  | | | | | 
% 243.59/50.08  | | | | |   (151)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 243.59/50.08  | | | | |              e2) = e1)
% 243.59/50.08  | | | | | 
% 243.59/50.08  | | | | | BETA: splitting (151) gives:
% 243.59/50.08  | | | | | 
% 243.59/50.08  | | | | | Case 1:
% 243.59/50.08  | | | | | | 
% 243.59/50.08  | | | | | |   (152)  all_58_1 = e1 & op(e3, e2) = e1
% 243.59/50.08  | | | | | | 
% 243.59/50.08  | | | | | | ALPHA: (152) implies:
% 243.59/50.08  | | | | | |   (153)  all_58_1 = e1
% 243.59/50.08  | | | | | | 
% 243.59/50.08  | | | | | | REF_CLOSE: (33), (41), (57), (61), (73), (85), (112), (117), (145),
% 243.59/50.08  | | | | | |            (153) are inconsistent by sub-proof #1327.
% 243.59/50.08  | | | | | | 
% 243.59/50.08  | | | | | Case 2:
% 243.59/50.08  | | | | | | 
% 243.59/50.08  | | | | | |   (154)  all_58_3 = e1 & op(e2, e2) = e1
% 243.59/50.08  | | | | | | 
% 243.59/50.08  | | | | | | REF_CLOSE: (120), (127), (154) are inconsistent by sub-proof #1752.
% 243.59/50.08  | | | | | | 
% 243.59/50.08  | | | | | End of split
% 243.59/50.08  | | | | | 
% 243.59/50.08  | | | | Case 2:
% 243.59/50.08  | | | | | 
% 243.59/50.08  | | | | |   (155)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 243.59/50.08  | | | | |              e2) = e1)
% 243.59/50.08  | | | | | 
% 243.59/50.08  | | | | | BETA: splitting (155) gives:
% 243.59/50.08  | | | | | 
% 243.59/50.08  | | | | | Case 1:
% 243.59/50.08  | | | | | | 
% 243.59/50.08  | | | | | |   (156)  all_58_7 = e1 & op(e1, e2) = e1
% 243.59/50.08  | | | | | | 
% 243.59/50.08  | | | | | | ALPHA: (156) implies:
% 243.59/50.08  | | | | | |   (157)  all_58_7 = e1
% 243.59/50.08  | | | | | | 
% 243.59/50.08  | | | | | | BETA: splitting (94) gives:
% 243.59/50.08  | | | | | | 
% 243.59/50.08  | | | | | | Case 1:
% 243.59/50.08  | | | | | | | 
% 243.59/50.08  | | | | | | |   (158)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 243.59/50.08  | | | | | | |            op(e2, e1) = e3)
% 243.59/50.08  | | | | | | | 
% 243.59/50.08  | | | | | | | BETA: splitting (158) gives:
% 243.59/50.08  | | | | | | | 
% 243.59/50.08  | | | | | | | Case 1:
% 243.59/50.08  | | | | | | | | 
% 243.59/50.08  | | | | | | | |   (159)  all_58_4 = e3 & op(e3, e1) = e3
% 243.59/50.08  | | | | | | | | 
% 243.59/50.08  | | | | | | | | ALPHA: (159) implies:
% 243.59/50.08  | | | | | | | |   (160)  op(e3, e1) = e3
% 243.59/50.08  | | | | | | | | 
% 243.59/50.08  | | | | | | | | REF_CLOSE: (57), (112), (145), (160) are inconsistent by
% 243.59/50.08  | | | | | | | |            sub-proof #2260.
% 243.59/50.08  | | | | | | | | 
% 243.59/50.08  | | | | | | | Case 2:
% 243.59/50.08  | | | | | | | | 
% 243.59/50.08  | | | | | | | |   (161)  all_58_5 = e3 & op(e2, e1) = e3
% 243.59/50.08  | | | | | | | | 
% 243.59/50.08  | | | | | | | | ALPHA: (161) implies:
% 243.59/50.08  | | | | | | | |   (162)  op(e2, e1) = e3
% 243.59/50.08  | | | | | | | | 
% 243.59/50.08  | | | | | | | | BETA: splitting (19) gives:
% 243.59/50.08  | | | | | | | | 
% 243.59/50.08  | | | | | | | | Case 1:
% 243.59/50.08  | | | | | | | | | 
% 243.59/50.08  | | | | | | | | |   (163)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &
% 243.59/50.08  | | | | | | | | |             ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.59/50.08  | | | | | | | | |            e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 243.59/50.08  | | | | | | | | |              = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.59/50.08  | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 243.59/50.08  | | | | | | | | |              e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 243.59/50.08  | | | | | | | | |            = e3 & op(e1, e3) = e3) | (all_56_5 = e1 &
% 243.59/50.08  | | | | | | | | |            all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 243.59/50.08  | | | | | | | | |              = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 243.59/50.08  | | | | | | | | |            & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 =
% 243.59/50.08  | | | | | | | | |            e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 243.59/50.08  | | | | | | | | |            e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 243.59/50.08  | | | | | | | | |            = e0 & op(e0, e3) = e0)
% 243.59/50.08  | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | BETA: splitting (163) gives:
% 243.59/50.08  | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | Case 1:
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | |   (164)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 243.59/50.08  | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.59/50.08  | | | | | | | | | |            e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.59/50.08  | | | | | | | | | |              e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 243.59/50.08  | | | | | | | | | |            all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 243.59/50.08  | | | | | | | | | |            e3)
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | BETA: splitting (164) gives:
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | Case 1:
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | |   (165)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 243.59/50.08  | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.59/50.08  | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.59/50.08  | | | | | | | | | | |          e3
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | ALPHA: (165) implies:
% 243.59/50.08  | | | | | | | | | | |   (166)   ~ (all_56_21 = e2)
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | REDUCE: (1), (166) imply:
% 243.59/50.08  | | | | | | | | | | |   (167)  $false
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | Case 2:
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | |   (168)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 243.59/50.08  | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.59/50.08  | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.59/50.08  | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 243.59/50.08  | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.59/50.08  | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.08  | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | REF_CLOSE: (57), (84), (112), (133), (145), (168) are
% 243.59/50.08  | | | | | | | | | | |            inconsistent by sub-proof #1608.
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | End of split
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | Case 2:
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | |   (169)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 243.59/50.08  | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.59/50.08  | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 243.59/50.08  | | | | | | | | | |              e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 & 
% 243.59/50.08  | | | | | | | | | |            ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.59/50.08  | | | | | | | | | |              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 243.59/50.08  | | | | | | | | | |            all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 243.59/50.08  | | | | | | | | | |            e0)
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | BETA: splitting (169) gives:
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | Case 1:
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | |   (170)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 243.59/50.08  | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.59/50.08  | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 243.59/50.08  | | | | | | | | | | |            e3) = e1
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | ALPHA: (170) implies:
% 243.59/50.08  | | | | | | | | | | |   (171)  op(e1, e3) = e1
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | REF_CLOSE: (33), (112), (150), (171) are inconsistent by
% 243.59/50.08  | | | | | | | | | | |            sub-proof #2225.
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | Case 2:
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | |   (172)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 243.59/50.08  | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.59/50.08  | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.59/50.08  | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 243.59/50.08  | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.59/50.08  | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.08  | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | REF_CLOSE: (29), (77), (102), (112), (172) are inconsistent
% 243.59/50.08  | | | | | | | | | | |            by sub-proof #1412.
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | End of split
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | End of split
% 243.59/50.08  | | | | | | | | | 
% 243.59/50.08  | | | | | | | | Case 2:
% 243.59/50.08  | | | | | | | | | 
% 243.59/50.08  | | | | | | | | |   (173)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 243.59/50.08  | | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.59/50.08  | | | | | | | | |            e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1)
% 243.59/50.08  | | | | | | | | |            = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 243.59/50.08  | | | | | | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.59/50.08  | | | | | | | | |              = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.59/50.08  | | | | | | | | |            & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.59/50.08  | | | | | | | | |            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.59/50.08  | | | | | | | | |            e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.59/50.08  | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0)
% 243.59/50.08  | | | | | | | | |            = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 243.59/50.08  | | | | | | | | |            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 243.59/50.08  | | | | | | | | |              = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.59/50.08  | | | | | | | | |            & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.08  | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | BETA: splitting (173) gives:
% 243.59/50.08  | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | Case 1:
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | |   (174)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.59/50.08  | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.59/50.08  | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 243.59/50.08  | | | | | | | | | |              e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 & 
% 243.59/50.08  | | | | | | | | | |            ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.59/50.08  | | | | | | | | | |              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 243.59/50.08  | | | | | | | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 243.59/50.08  | | | | | | | | | |            e2)
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | BETA: splitting (174) gives:
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | Case 1:
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | |   (175)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.59/50.08  | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.59/50.08  | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 243.59/50.08  | | | | | | | | | | |            e2) = e2
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | ALPHA: (175) implies:
% 243.59/50.08  | | | | | | | | | | |   (176)  op(e2, e1) = e2
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | REF_CLOSE: (61), (112), (162), (176) are inconsistent by
% 243.59/50.08  | | | | | | | | | | |            sub-proof #2256.
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | Case 2:
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | |   (177)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.59/50.08  | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.59/50.08  | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.59/50.08  | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 243.59/50.08  | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.59/50.08  | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.59/50.08  | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | REF_CLOSE: (1), (79), (177) are inconsistent by sub-proof
% 243.59/50.08  | | | | | | | | | | |            #1245.
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | End of split
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | Case 2:
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | |   (178)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.59/50.08  | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.59/50.08  | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.59/50.08  | | | | | | | | | |              e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 & 
% 243.59/50.08  | | | | | | | | | |            ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.59/50.08  | | | | | | | | | |              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 243.59/50.08  | | | | | | | | | |            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.08  | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 243.59/50.08  | | | | | | | | | |            e0)
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | BETA: splitting (178) gives:
% 243.59/50.08  | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | Case 1:
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | |   (179)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.59/50.08  | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.59/50.08  | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.59/50.08  | | | | | | | | | | |            e2) = e0
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | ALPHA: (179) implies:
% 243.59/50.08  | | | | | | | | | | |   (180)  op(e2, e0) = e0
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | REF_CLOSE: (11), (67), (112), (180) are inconsistent by
% 243.59/50.08  | | | | | | | | | | |            sub-proof #2121.
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | Case 2:
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | |   (181)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.59/50.08  | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.59/50.08  | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.59/50.08  | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.59/50.08  | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.59/50.08  | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.08  | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | BETA: splitting (181) gives:
% 243.59/50.08  | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | Case 1:
% 243.59/50.08  | | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | |   (182)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.59/50.08  | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 243.59/50.08  | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 243.59/50.08  | | | | | | | | | | | |            e1) = e1
% 243.59/50.08  | | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | | ALPHA: (182) implies:
% 243.59/50.08  | | | | | | | | | | | |   (183)  op(e1, e0) = e1
% 243.59/50.08  | | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | | REF_CLOSE: (7), (11), (34), (112), (120), (123), (149),
% 243.59/50.08  | | | | | | | | | | | |            (157), (183) are inconsistent by sub-proof #1555.
% 243.59/50.08  | | | | | | | | | | | | 
% 243.59/50.08  | | | | | | | | | | | Case 2:
% 243.59/50.08  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | |   (184)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 243.59/50.09  | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.59/50.09  | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 243.59/50.09  | | | | | | | | | | | |            e1) = e0
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | ALPHA: (184) implies:
% 243.59/50.09  | | | | | | | | | | | |   (185)  op(e0, e1) = e0
% 243.59/50.09  | | | | | | | | | | | |   (186)  op(e1, e0) = e0
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (12),
% 243.59/50.09  | | | | | | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20),
% 243.59/50.09  | | | | | | | | | | | |            (21), (23), (24), (25), (26), (27), (28), (29),
% 243.59/50.09  | | | | | | | | | | | |            (30), (33), (35), (36), (37), (38), (39), (40),
% 243.59/50.09  | | | | | | | | | | | |            (41), (43), (44), (45), (46), (47), (49), (50),
% 243.59/50.09  | | | | | | | | | | | |            (51), (52), (53), (55), (56), (57), (58), (59),
% 243.59/50.09  | | | | | | | | | | | |            (60), (62), (63), (64), (65), (68), (69), (70),
% 243.59/50.09  | | | | | | | | | | | |            (71), (72), (73), (75), (77), (78), (79), (80),
% 243.59/50.09  | | | | | | | | | | | |            (81), (82), (83), (84), (86), (87), (88), (91),
% 243.59/50.09  | | | | | | | | | | | |            (92), (94), (95), (96), (98), (99), (100), (101),
% 243.59/50.09  | | | | | | | | | | | |            (102), (103), (104), (105), (106), (108), (109),
% 243.59/50.09  | | | | | | | | | | | |            (110), (111), (112), (113), (114), (115), (116),
% 243.59/50.09  | | | | | | | | | | | |            (117), (119), (120), (121), (122), (123), (124),
% 243.59/50.09  | | | | | | | | | | | |            (125), (126), (127), (128), (129), (130), (131),
% 243.59/50.09  | | | | | | | | | | | |            (134), (135), (136), (137), (185), (186) are
% 243.59/50.09  | | | | | | | | | | | |            inconsistent by sub-proof #1253.
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | End of split
% 243.59/50.09  | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | End of split
% 243.59/50.09  | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | End of split
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | End of split
% 243.59/50.09  | | | | | | | | 
% 243.59/50.09  | | | | | | | End of split
% 243.59/50.09  | | | | | | | 
% 243.59/50.09  | | | | | | Case 2:
% 243.59/50.09  | | | | | | | 
% 243.59/50.09  | | | | | | |   (187)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 243.59/50.09  | | | | | | |            op(e0, e1) = e3)
% 243.59/50.09  | | | | | | | 
% 243.59/50.09  | | | | | | | REF_CLOSE: (8), (54), (61), (93), (112), (187) are inconsistent by
% 243.59/50.09  | | | | | | |            sub-proof #1307.
% 243.59/50.09  | | | | | | | 
% 243.59/50.09  | | | | | | End of split
% 243.59/50.09  | | | | | | 
% 243.59/50.09  | | | | | Case 2:
% 243.59/50.09  | | | | | | 
% 243.59/50.09  | | | | | |   (188)  all_58_13 = e1 & op(e0, e2) = e1
% 243.59/50.09  | | | | | | 
% 243.59/50.09  | | | | | | ALPHA: (188) implies:
% 243.59/50.09  | | | | | |   (189)  all_58_13 = e1
% 243.59/50.09  | | | | | | 
% 243.59/50.09  | | | | | | REF_CLOSE: (74), (136), (189) are inconsistent by sub-proof #1544.
% 243.59/50.09  | | | | | | 
% 243.59/50.09  | | | | | End of split
% 243.59/50.09  | | | | | 
% 243.59/50.09  | | | | End of split
% 243.59/50.09  | | | | 
% 243.59/50.09  | | | Case 2:
% 243.59/50.09  | | | | 
% 243.59/50.09  | | | |   (190)  all_58_7 = e3 & op(e1, e2) = e3
% 243.59/50.09  | | | | 
% 243.59/50.09  | | | | ALPHA: (190) implies:
% 243.59/50.09  | | | |   (191)  op(e1, e2) = e3
% 243.59/50.09  | | | | 
% 243.59/50.09  | | | | REF_CLOSE: (16), (112), (143), (191) are inconsistent by sub-proof
% 243.59/50.09  | | | |            #2191.
% 243.59/50.09  | | | | 
% 243.59/50.09  | | | End of split
% 243.59/50.09  | | | 
% 243.59/50.09  | | Case 2:
% 243.59/50.09  | | | 
% 243.59/50.09  | | |   (192)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 243.59/50.09  | | |            = e3)
% 243.59/50.09  | | | 
% 243.59/50.09  | | | REF_CLOSE: (25), (61), (86), (93), (112), (192) are inconsistent by
% 243.59/50.09  | | |            sub-proof #2148.
% 243.59/50.09  | | | 
% 243.59/50.09  | | End of split
% 243.59/50.09  | | 
% 243.59/50.09  | Case 2:
% 243.59/50.09  | | 
% 243.59/50.09  | |   (193)   ~ (all_54_1 = e3)
% 243.59/50.09  | |   (194)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.59/50.09  | | 
% 243.59/50.09  | | REDUCE: (98), (193) imply:
% 243.59/50.09  | |   (195)   ~ (all_52_4 = e3)
% 243.59/50.09  | | 
% 243.59/50.09  | | BETA: splitting (194) gives:
% 243.59/50.09  | | 
% 243.59/50.09  | | Case 1:
% 243.59/50.09  | | | 
% 243.59/50.09  | | |   (196)  all_54_1 = e2
% 243.59/50.09  | | | 
% 243.59/50.09  | | | REF_CLOSE: (98), (107), (196) are inconsistent by sub-proof #1928.
% 243.59/50.09  | | | 
% 243.59/50.09  | | Case 2:
% 243.59/50.09  | | | 
% 243.59/50.09  | | |   (197)   ~ (all_54_1 = e2)
% 243.59/50.09  | | |   (198)  all_54_1 = e1 | all_54_1 = e0
% 243.59/50.09  | | | 
% 243.59/50.09  | | | BETA: splitting (41) gives:
% 243.59/50.09  | | | 
% 243.59/50.09  | | | Case 1:
% 243.59/50.09  | | | | 
% 243.59/50.09  | | | |   (199)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 243.59/50.09  | | | |            = e3)
% 243.59/50.09  | | | | 
% 243.59/50.09  | | | | REF_CLOSE: (61), (85), (99), (112), (195), (199) are inconsistent by
% 243.59/50.09  | | | |            sub-proof #1959.
% 243.59/50.09  | | | | 
% 243.59/50.09  | | | Case 2:
% 243.59/50.09  | | | | 
% 243.59/50.09  | | | |   (200)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 243.59/50.09  | | | |            = e3)
% 243.59/50.09  | | | | 
% 243.59/50.09  | | | | BETA: splitting (200) gives:
% 243.59/50.09  | | | | 
% 243.59/50.09  | | | | Case 1:
% 243.59/50.09  | | | | | 
% 243.59/50.09  | | | | |   (201)  all_58_4 = e3 & op(e3, e1) = e3
% 243.59/50.09  | | | | | 
% 243.59/50.09  | | | | | ALPHA: (201) implies:
% 243.59/50.09  | | | | |   (202)  all_58_4 = e3
% 243.59/50.09  | | | | |   (203)  op(e3, e1) = e3
% 243.59/50.09  | | | | | 
% 243.59/50.09  | | | | | BETA: splitting (119) gives:
% 243.59/50.09  | | | | | 
% 243.59/50.09  | | | | | Case 1:
% 243.59/50.09  | | | | | | 
% 243.59/50.09  | | | | | |   (204)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2,
% 243.59/50.09  | | | | | |              e2) = e3)
% 243.59/50.09  | | | | | | 
% 243.59/50.09  | | | | | | REF_CLOSE: (7), (99), (112), (127), (195), (204) are inconsistent by
% 243.59/50.09  | | | | | |            sub-proof #1430.
% 243.59/50.09  | | | | | | 
% 243.59/50.09  | | | | | Case 2:
% 243.59/50.09  | | | | | | 
% 243.59/50.09  | | | | | |   (205)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 &
% 243.59/50.09  | | | | | |            op(e0, e2) = e3)
% 243.59/50.09  | | | | | | 
% 243.59/50.09  | | | | | | BETA: splitting (205) gives:
% 243.59/50.09  | | | | | | 
% 243.59/50.09  | | | | | | Case 1:
% 243.59/50.09  | | | | | | | 
% 243.59/50.09  | | | | | | |   (206)  all_58_7 = e3 & op(e1, e2) = e3
% 243.59/50.09  | | | | | | | 
% 243.59/50.09  | | | | | | | ALPHA: (206) implies:
% 243.59/50.09  | | | | | | |   (207)  op(e1, e2) = e3
% 243.59/50.09  | | | | | | | 
% 243.59/50.09  | | | | | | | BETA: splitting (35) gives:
% 243.59/50.09  | | | | | | | 
% 243.59/50.09  | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | 
% 243.59/50.09  | | | | | | | |   (208)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 243.59/50.09  | | | | | | | |            op(e2, e1) = e0)
% 243.59/50.09  | | | | | | | | 
% 243.59/50.09  | | | | | | | | BETA: splitting (208) gives:
% 243.59/50.09  | | | | | | | | 
% 243.59/50.09  | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | |   (209)  all_58_4 = e0 & op(e3, e1) = e0
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | ALPHA: (209) implies:
% 243.59/50.09  | | | | | | | | |   (210)  op(e3, e1) = e0
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | REF_CLOSE: (7), (112), (203), (210) are inconsistent by
% 243.59/50.09  | | | | | | | | |            sub-proof #2118.
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | Case 2:
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | |   (211)  all_58_5 = e0 & op(e2, e1) = e0
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | REF_CLOSE: (48), (58), (112), (211) are inconsistent by
% 243.59/50.09  | | | | | | | | |            sub-proof #2088.
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | End of split
% 243.59/50.09  | | | | | | | | 
% 243.59/50.09  | | | | | | | Case 2:
% 243.59/50.09  | | | | | | | | 
% 243.59/50.09  | | | | | | | |   (212)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 243.59/50.09  | | | | | | | |            op(e0, e1) = e0)
% 243.59/50.09  | | | | | | | | 
% 243.59/50.09  | | | | | | | | BETA: splitting (212) gives:
% 243.59/50.09  | | | | | | | | 
% 243.59/50.09  | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | |   (213)  all_58_8 = e0 & op(e1, e1) = e0
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | ALPHA: (213) implies:
% 243.59/50.09  | | | | | | | | |   (214)  op(e1, e1) = e0
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | REF_CLOSE: (11), (93), (112), (214) are inconsistent by
% 243.59/50.09  | | | | | | | | |            sub-proof #2211.
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | Case 2:
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | |   (215)  all_58_14 = e0 & op(e0, e1) = e0
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | ALPHA: (215) implies:
% 243.59/50.09  | | | | | | | | |   (216)  all_58_14 = e0
% 243.59/50.09  | | | | | | | | |   (217)  op(e0, e1) = e0
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | BETA: splitting (116) gives:
% 243.59/50.09  | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | |   (218)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 243.59/50.09  | | | | | | | | | |            & op(e2, e2) = e1)
% 243.59/50.09  | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | BETA: splitting (218) gives:
% 243.59/50.09  | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | |   (219)  all_58_1 = e1 & op(e3, e2) = e1
% 243.59/50.09  | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | ALPHA: (219) implies:
% 243.59/50.09  | | | | | | | | | | |   (220)  all_58_1 = e1
% 243.59/50.09  | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | BETA: splitting (198) gives:
% 243.59/50.09  | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | |   (221)  all_54_1 = e1
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | COMBINE_EQS: (98), (221) imply:
% 243.59/50.09  | | | | | | | | | | | |   (222)  all_52_4 = e1
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | SIMP: (222) implies:
% 243.59/50.09  | | | | | | | | | | | |   (223)  all_52_4 = e1
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | REDUCE: (130), (223) imply:
% 243.59/50.09  | | | | | | | | | | | |   (224)   ~ (all_52_8 = e1)
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | SIMP: (224) implies:
% 243.59/50.09  | | | | | | | | | | | |   (225)   ~ (all_52_8 = e1)
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | REDUCE: (195), (223) imply:
% 243.59/50.09  | | | | | | | | | | | |   (226)   ~ (e3 = e1)
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | REDUCE: (107), (223) imply:
% 243.59/50.09  | | | | | | | | | | | |   (227)   ~ (e2 = e1)
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | BETA: splitting (22) gives:
% 243.59/50.09  | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | |   (228)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 243.59/50.09  | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 243.59/50.09  | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | BETA: splitting (228) gives:
% 243.59/50.09  | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | |   (229)  all_58_4 = e1 & op(e3, e1) = e1
% 243.59/50.09  | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | ALPHA: (229) implies:
% 243.59/50.09  | | | | | | | | | | | | | |   (230)  all_58_4 = e1
% 243.59/50.09  | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (33), (41), (61), (85), (89), (99),
% 243.59/50.09  | | | | | | | | | | | | | |            (112), (120), (195), (220), (230) are inconsistent
% 243.59/50.09  | | | | | | | | | | | | | |            by sub-proof #1645.
% 243.59/50.09  | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | Case 2:
% 243.59/50.09  | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | |   (231)  all_58_5 = e1 & op(e2, e1) = e1
% 243.59/50.09  | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | ALPHA: (231) implies:
% 243.59/50.09  | | | | | | | | | | | | | |   (232)  all_58_5 = e1
% 243.59/50.09  | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 243.59/50.09  | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | |   (233)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 243.59/50.09  | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 243.59/50.09  | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | |   (234)  all_58_9 = e1 & op(e3, e0) = e1
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 243.59/50.09  | | | | | | | | | | | | | | | |   (235)  all_58_9 = e1
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (85), (89), (112), (120), (202), (220),
% 243.59/50.09  | | | | | | | | | | | | | | | |            (235) are inconsistent by sub-proof #1695.
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | Case 2:
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | |   (236)  all_58_10 = e1 & op(e2, e0) = e1
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 243.59/50.09  | | | | | | | | | | | | | | | |   (237)  op(e2, e0) = e1
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | REF_CLOSE: (67), (112), (136), (237) are inconsistent by
% 243.59/50.09  | | | | | | | | | | | | | | | |            sub-proof #1659.
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | End of split
% 243.59/50.09  | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | Case 2:
% 243.59/50.09  | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | |   (238)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 243.59/50.09  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 243.59/50.09  | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | |   (239)  all_58_11 = e1 & op(e1, e0) = e1
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 243.59/50.09  | | | | | | | | | | | | | | | |   (240)  op(e1, e0) = e1
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | |   (241)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 243.59/50.09  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 243.59/50.09  | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | |   (242)  all_58_2 = e3 & op(e2, e3) = e3
% 243.59/50.09  | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 243.59/50.09  | | | | | | | | | | | | | | | | | |   (243)  all_58_2 = e3
% 243.59/50.09  | | | | | | | | | | | | | | | | | |   (244)  op(e2, e3) = e3
% 243.59/50.09  | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |   (245)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.59/50.09  | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | |   (246)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | |            = e3)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |   (247)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |          e3
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |   (248)  op(e3, e2) = e3
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (112), (195), (248) are inconsistent by
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2192.
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |   (249)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |   (250)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |          e2
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |   (251)  op(e2, e3) = e2
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (112), (133), (251) are inconsistent by
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2336.
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |   (252)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |   (253)   ~ (all_56_31 = e1)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |   (254)   ~ (all_56_21 = e1)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |   (255)   ~ (all_56_11 = e1)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |   (256)  op(e1, e3) = e3
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (79), (255) imply:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | |   (257)   ~ (e1 = e0)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | |   (258)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | |   (259)  all_58_12 = e1 & op(e0, e3) = e1
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | |   (260)  op(e0, e3) = e1
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_58_6 = e0 & op(e1, e3) = e0
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  op(e1, e3) = e0
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (112) with e0, e3, e3, e1,
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (256), (263) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  e3 = e0
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (264) imply:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_58_4 = e0
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (22), (23), (33), (55), (57), (61),
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (62), (94), (112), (120), (136), (216), (217),
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (265) are inconsistent by sub-proof #1242.
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 &
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_26_1)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (260), (266) are inconsistent by sub-proof
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1386.
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_58_7 = e0 & op(e1, e2) = e0
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (32), (112), (267) are inconsistent by
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2022.
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_58_8 = e0 & op(e1, e1) = e0
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  op(e1, e1) = e0
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (22), (33), (61), (62), (112), (120), (136),
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (216), (217), (270) are inconsistent by
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1241.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_58_11 = e0 & op(e1, e0) = e0
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  op(e1, e0) = e0
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (120), (240), (272) are inconsistent by
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |   (273)  all_58_13 = e1 & op(e0, e2) = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_58_13 = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (274) imply:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |   (275)  e2 = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (30), (33), (34), (35), (37), (58),
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |            (61), (62), (93), (94), (112), (120), (127),
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |            (131), (136), (138), (216), (243), (244), (275)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1257.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | |   (276)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |   (277)  all_58_14 = e1 & op(e0, e1) = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_58_14 = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (35), (61), (62), (120), (136), (202),
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |            (232), (278) are inconsistent by sub-proof #1481.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_58_15 = e1 & op(e0, e0) = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_58_15 = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (28), (33), (41), (61), (85), (89),
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |            (99), (112), (120), (195), (202), (220), (280) are
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1644.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |   (281)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            = e0)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (57), (77), (102), (112), (225), (281) are
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1411.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |   (282)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 243.59/50.10  | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |   (283)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            = e2)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |   (284)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |   (285)  op(e2, e1) = e2
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (112), (138), (285) are inconsistent by
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2328.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |   (286)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |   (287)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |   (288)  op(e1, e2) = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (90), (112), (118), (207), (288) are
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1332.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |   (289)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (289) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |   (290)   ~ (all_56_11 = e0)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (79), (290) imply:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | |   (291)  $false
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |   (292)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | |            = e0)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |   (293)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |   (294)  op(e2, e0) = e0
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (67), (112), (294) are inconsistent by
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2121.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |   (295)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (120), (217), (240), (295) are inconsistent
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1240.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | |   (296)  all_58_3 = e3 & op(e2, e2) = e3
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | |   (297)  all_58_3 = e3
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (297) imply:
% 243.59/50.10  | | | | | | | | | | | | | | | | | |   (298)  e3 = e0
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | SIMP: (298) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | |   (299)  e3 = e0
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (299) imply:
% 243.59/50.10  | | | | | | | | | | | | | | | | | |   (300)  all_58_4 = e0
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (22), (23), (33), (55), (57), (61),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (62), (94), (112), (120), (136), (216), (217),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (225), (300) are inconsistent by sub-proof #1242.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | |   (301)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 243.59/50.10  | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 243.59/50.10  | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 243.59/50.10  | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | Case 1:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | |   (302)  all_58_5 = e3 & op(e2, e1) = e3
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | |   (303)  op(e2, e1) = e3
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (20), (21), (23), (24), (25), (26), (27), (28),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (29), (30), (35), (36), (37), (38), (39), (40),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (41), (44), (45), (46), (47), (49), (50), (51),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (52), (53), (56), (57), (58), (59), (60), (61),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (62), (63), (64), (65), (66), (68), (69), (70),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (71), (72), (73), (75), (76), (77), (78), (79),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (80), (81), (82), (83), (84), (87), (88), (91),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (92), (94), (95), (96), (98), (99), (100), (101),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (102), (103), (104), (105), (106), (108), (109),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (110), (111), (112), (113), (114), (115), (116),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (117), (119), (121), (123), (124), (125), (126),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (127), (128), (129), (130), (131), (132), (134),
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            (135), (137), (195), (303) are inconsistent by
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            sub-proof #1251.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | |   (304)  all_58_10 = e3 & op(e2, e0) = e3
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | ALPHA: (304) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | | | |   (305)  op(e2, e0) = e3
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (67), (112), (305) are inconsistent by
% 243.59/50.10  | | | | | | | | | | | | | | | | | |            sub-proof #2152.
% 243.59/50.10  | | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | |   (306)  all_58_15 = e1 & op(e0, e0) = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 243.59/50.10  | | | | | | | | | | | | | | | |   (307)  all_58_15 = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (307) imply:
% 243.59/50.10  | | | | | | | | | | | | | | | |   (308)  e3 = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (308) imply:
% 243.59/50.10  | | | | | | | | | | | | | | | |   (309)  all_58_4 = e1
% 243.59/50.10  | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (33), (41), (61), (85), (89), (99),
% 243.59/50.10  | | | | | | | | | | | | | | | |            (112), (120), (195), (220), (309) are inconsistent
% 243.59/50.10  | | | | | | | | | | | | | | | |            by sub-proof #1645.
% 243.59/50.10  | | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | |   (310)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 243.59/50.10  | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 243.59/50.10  | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | BETA: splitting (310) gives:
% 243.59/50.10  | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | Case 1:
% 243.59/50.10  | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | |   (311)  all_58_8 = e1 & op(e1, e1) = e1
% 243.59/50.10  | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | ALPHA: (311) implies:
% 243.59/50.10  | | | | | | | | | | | | | |   (312)  all_58_8 = e1
% 243.59/50.10  | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | COMBINE_EQS: (34), (312) imply:
% 243.59/50.10  | | | | | | | | | | | | | |   (313)  e2 = e1
% 243.59/50.10  | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | COMBINE_EQS: (97), (313) imply:
% 243.59/50.10  | | | | | | | | | | | | | |   (314)  all_56_1 = e1
% 243.59/50.10  | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | REF_CLOSE: (1), (19), (29), (57), (58), (77), (79), (102),
% 243.59/50.10  | | | | | | | | | | | | | |            (112), (125), (132), (138), (225), (314) are
% 243.59/50.10  | | | | | | | | | | | | | |            inconsistent by sub-proof #1237.
% 243.59/50.10  | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | |   (315)  all_58_14 = e1 & op(e0, e1) = e1
% 243.59/50.10  | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | ALPHA: (315) implies:
% 243.59/50.10  | | | | | | | | | | | | | |   (316)  op(e0, e1) = e1
% 243.59/50.10  | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | | REF_CLOSE: (112), (120), (217), (316) are inconsistent by
% 243.59/50.10  | | | | | | | | | | | | | |            sub-proof #2158.
% 243.59/50.10  | | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | |   (317)  all_54_1 = e0
% 243.59/50.10  | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | | REF_CLOSE: (98), (135), (317) are inconsistent by sub-proof
% 243.59/50.10  | | | | | | | | | | | |            #2050.
% 243.59/50.10  | | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | |   (318)  all_58_3 = e1 & op(e2, e2) = e1
% 243.59/50.10  | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | REF_CLOSE: (120), (127), (318) are inconsistent by sub-proof
% 243.59/50.10  | | | | | | | | | | |            #1752.
% 243.59/50.10  | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | |   (319)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1
% 243.59/50.10  | | | | | | | | | |            & op(e0, e2) = e1)
% 243.59/50.10  | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | BETA: splitting (319) gives:
% 243.59/50.10  | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | Case 1:
% 243.59/50.10  | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | |   (320)  all_58_7 = e1 & op(e1, e2) = e1
% 243.59/50.10  | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | ALPHA: (320) implies:
% 243.59/50.10  | | | | | | | | | | |   (321)  op(e1, e2) = e1
% 243.59/50.10  | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | REF_CLOSE: (33), (90), (112), (118), (207), (321) are
% 243.59/50.10  | | | | | | | | | | |            inconsistent by sub-proof #1332.
% 243.59/50.10  | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | Case 2:
% 243.59/50.10  | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | |   (322)  all_58_13 = e1 & op(e0, e2) = e1
% 243.59/50.10  | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | | REF_CLOSE: (74), (136), (322) are inconsistent by sub-proof
% 243.59/50.10  | | | | | | | | | | |            #1751.
% 243.59/50.10  | | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | | 
% 243.59/50.10  | | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | | 
% 243.59/50.10  | | | | | | | | End of split
% 243.59/50.10  | | | | | | | | 
% 243.59/50.10  | | | | | | | End of split
% 243.59/50.10  | | | | | | | 
% 243.59/50.10  | | | | | | Case 2:
% 243.59/50.10  | | | | | | | 
% 243.59/50.10  | | | | | | |   (323)  all_58_13 = e3 & op(e0, e2) = e3
% 243.59/50.10  | | | | | | | 
% 243.59/50.10  | | | | | | | ALPHA: (323) implies:
% 243.59/50.10  | | | | | | |   (324)  op(e0, e2) = e3
% 243.59/50.10  | | | | | | | 
% 243.59/50.10  | | | | | | | REF_CLOSE: (31), (61), (112), (324) are inconsistent by sub-proof
% 243.59/50.10  | | | | | | |            #2254.
% 243.59/50.10  | | | | | | | 
% 243.59/50.10  | | | | | | End of split
% 243.59/50.10  | | | | | | 
% 243.59/50.10  | | | | | End of split
% 243.59/50.10  | | | | | 
% 243.59/50.10  | | | | Case 2:
% 243.59/50.10  | | | | | 
% 243.59/50.10  | | | | |   (325)  all_58_9 = e3 & op(e3, e0) = e3
% 243.59/50.10  | | | | | 
% 243.59/50.10  | | | | | ALPHA: (325) implies:
% 243.59/50.10  | | | | |   (326)  op(e3, e0) = e3
% 243.59/50.10  | | | | | 
% 243.59/50.10  | | | | | REF_CLOSE: (73), (112), (117), (326) are inconsistent by sub-proof
% 243.59/50.10  | | | | |            #2179.
% 243.59/50.10  | | | | | 
% 243.59/50.10  | | | | End of split
% 243.59/50.10  | | | | 
% 243.59/50.10  | | | End of split
% 243.59/50.10  | | | 
% 243.59/50.10  | | End of split
% 243.59/50.10  | | 
% 243.59/50.10  | End of split
% 243.59/50.10  | 
% 243.59/50.10  End of proof
% 243.59/50.10  
% 243.59/50.10  Sub-proof #1237 shows that the following formulas are inconsistent:
% 243.59/50.10  ----------------------------------------------------------------
% 243.59/50.10    (1)  all_56_21 = e2
% 243.59/50.11    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.59/50.11           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.59/50.11             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.59/50.11           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.59/50.11             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.59/50.11           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.11           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.59/50.11           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.59/50.11           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.59/50.11           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.11           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.59/50.11             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.59/50.11           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.11           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 243.59/50.11           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.59/50.11           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.59/50.11           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.11           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.59/50.11             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.59/50.11           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.59/50.11           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 243.59/50.11           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.59/50.11           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.59/50.11           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.11           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.59/50.11             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.59/50.11           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.11           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.11    (3)  op(e0, e3) = all_52_3
% 243.59/50.11    (4)   ~ (all_52_8 = e1)
% 243.59/50.11    (5)  op(e3, e1) = all_52_8
% 243.59/50.11    (6)  op(e2, e1) = all_52_9
% 243.59/50.11    (7)   ~ (all_52_3 = e3)
% 243.59/50.11    (8)  all_56_11 = e0
% 243.59/50.11    (9)  all_56_31 = e3
% 243.59/50.11    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.11    (11)  op(e2, e0) = all_52_13
% 243.59/50.11    (12)   ~ (all_52_13 = e0)
% 243.59/50.11    (13)  all_56_1 = e1
% 243.59/50.11    (14)   ~ (all_52_9 = e2)
% 243.59/50.11  
% 243.59/50.11  Begin of proof
% 243.59/50.11  | 
% 243.59/50.11  | BETA: splitting (2) gives:
% 243.59/50.11  | 
% 243.59/50.11  | Case 1:
% 243.59/50.11  | | 
% 243.59/50.11  | |   (15)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.59/50.11  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 243.59/50.11  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 243.59/50.11  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.11  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 243.59/50.11  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 243.59/50.11  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 243.59/50.11  | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 243.59/50.11  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.11  | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 243.59/50.11  | |           = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &
% 243.59/50.11  | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.59/50.11  | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 243.59/50.11  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.11  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.59/50.11  | | 
% 243.59/50.11  | | BETA: splitting (15) gives:
% 243.59/50.11  | | 
% 243.59/50.11  | | Case 1:
% 243.59/50.11  | | | 
% 243.59/50.11  | | |   (16)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.11  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.59/50.11  | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.59/50.11  | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.59/50.11  | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 243.59/50.11  | | |         | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.11  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.11  | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.59/50.11  | | | 
% 243.59/50.11  | | | BETA: splitting (16) gives:
% 243.59/50.11  | | | 
% 243.59/50.11  | | | Case 1:
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | |   (17)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.11  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.59/50.11  | | | |         op(e3, e2) = e3 & op(e2, e3) = e3
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | | ALPHA: (17) implies:
% 243.59/50.11  | | | |   (18)   ~ (all_56_21 = e2)
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | | REDUCE: (1), (18) imply:
% 243.59/50.11  | | | |   (19)  $false
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | | CLOSE: (19) is inconsistent.
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | Case 2:
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | |   (20)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.59/50.11  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.11  | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 243.59/50.11  | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.59/50.11  | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 243.59/50.11  | | | |           op(e1, e3) = e3)
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | | REF_CLOSE: (9), (13), (20) are inconsistent by sub-proof #1239.
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | End of split
% 243.59/50.11  | | | 
% 243.59/50.11  | | Case 2:
% 243.59/50.11  | | | 
% 243.59/50.11  | | |   (21)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 243.59/50.11  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.11  | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 243.59/50.11  | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 243.59/50.11  | | |             = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 243.59/50.11  | | |           e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.59/50.11  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.11  | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.59/50.11  | | | 
% 243.59/50.11  | | | REF_CLOSE: (3), (4), (5), (7), (9), (10), (21) are inconsistent by
% 243.59/50.11  | | |            sub-proof #1411.
% 243.59/50.11  | | | 
% 243.59/50.11  | | End of split
% 243.59/50.11  | | 
% 243.59/50.11  | Case 2:
% 243.59/50.11  | | 
% 243.59/50.11  | |   (22)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.11  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.11  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.59/50.11  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.59/50.11  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 243.59/50.11  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.11  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.59/50.11  | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 243.59/50.11  | |           e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.59/50.11  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 243.59/50.11  | |         (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.11  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.59/50.11  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.59/50.11  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.59/50.11  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.11  | | 
% 243.59/50.11  | | BETA: splitting (22) gives:
% 243.59/50.11  | | 
% 243.59/50.11  | | Case 1:
% 243.59/50.11  | | | 
% 243.59/50.11  | | |   (23)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.11  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.11  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 243.59/50.11  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 243.59/50.11  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 243.59/50.11  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.11  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.59/50.11  | | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.59/50.11  | | | 
% 243.59/50.11  | | | BETA: splitting (23) gives:
% 243.59/50.11  | | | 
% 243.59/50.11  | | | Case 1:
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | |   (24)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.11  | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.11  | | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | | ALPHA: (24) implies:
% 243.59/50.11  | | | |   (25)  op(e2, e1) = e2
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | | REF_CLOSE: (6), (10), (14), (25) are inconsistent by sub-proof #2328.
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | Case 2:
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | |   (26)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.11  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.59/50.11  | | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 243.59/50.11  | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.59/50.11  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 &
% 243.59/50.11  | | | |           op(e0, e2) = e2)
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | | REF_CLOSE: (1), (8), (26) are inconsistent by sub-proof #1245.
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | End of split
% 243.59/50.11  | | | 
% 243.59/50.11  | | Case 2:
% 243.59/50.11  | | | 
% 243.59/50.11  | | |   (27)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.11  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.59/50.11  | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29
% 243.59/50.11  | | |           = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 243.59/50.11  | | |             = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 243.59/50.11  | | |           e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.11  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.11  | | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.11  | | | 
% 243.59/50.11  | | | REF_CLOSE: (8), (10), (11), (12), (13), (27) are inconsistent by sub-proof
% 243.59/50.11  | | |            #1238.
% 243.59/50.11  | | | 
% 243.59/50.11  | | End of split
% 243.59/50.11  | | 
% 243.59/50.11  | End of split
% 243.59/50.11  | 
% 243.59/50.11  End of proof
% 243.59/50.11  
% 243.59/50.11  Sub-proof #1238 shows that the following formulas are inconsistent:
% 243.59/50.11  ----------------------------------------------------------------
% 243.59/50.11    (1)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.59/50.11             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 243.59/50.11           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.59/50.11             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.59/50.11           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 243.59/50.11           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.11           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.11    (2)  all_56_11 = e0
% 243.59/50.11    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.11    (4)  op(e2, e0) = all_52_13
% 243.59/50.11    (5)   ~ (all_52_13 = e0)
% 243.59/50.11    (6)  all_56_1 = e1
% 243.59/50.11  
% 243.59/50.11  Begin of proof
% 243.59/50.11  | 
% 243.59/50.11  | BETA: splitting (1) gives:
% 243.59/50.11  | 
% 243.59/50.11  | Case 1:
% 243.59/50.11  | | 
% 243.59/50.11  | |   (7)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.59/50.11  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 243.59/50.11  | |        & op(e0, e2) = e0
% 243.59/50.11  | | 
% 243.59/50.11  | | ALPHA: (7) implies:
% 243.59/50.11  | |   (8)  op(e2, e0) = e0
% 243.59/50.11  | | 
% 243.59/50.11  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2324.
% 243.59/50.11  | | 
% 243.59/50.11  | Case 2:
% 243.59/50.11  | | 
% 243.59/50.11  | |   (9)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.59/50.11  | |            = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) =
% 243.59/50.11  | |          e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.59/50.11  | |          (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.11  | |          (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.11  | | 
% 243.59/50.11  | | BETA: splitting (9) gives:
% 243.59/50.11  | | 
% 243.59/50.11  | | Case 1:
% 243.59/50.11  | | | 
% 243.59/50.11  | | |   (10)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.11  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.59/50.11  | | |         op(e1, e0) = e1 & op(e0, e1) = e1
% 243.59/50.11  | | | 
% 243.59/50.11  | | | ALPHA: (10) implies:
% 243.59/50.11  | | |   (11)   ~ (all_56_11 = e0)
% 243.59/50.11  | | | 
% 243.59/50.11  | | | REDUCE: (2), (11) imply:
% 243.59/50.11  | | |   (12)  $false
% 243.59/50.11  | | | 
% 243.59/50.11  | | | CLOSE: (12) is inconsistent.
% 243.59/50.11  | | | 
% 243.59/50.11  | | Case 2:
% 243.59/50.11  | | | 
% 243.59/50.11  | | |   (13)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.11  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.11  | | |         op(e1, e0) = e0 & op(e0, e1) = e0
% 243.59/50.11  | | | 
% 243.59/50.11  | | | ALPHA: (13) implies:
% 243.59/50.11  | | |   (14)   ~ (all_56_1 = e1)
% 243.59/50.11  | | | 
% 243.59/50.11  | | | REDUCE: (6), (14) imply:
% 243.59/50.11  | | |   (15)  $false
% 243.59/50.11  | | | 
% 243.59/50.11  | | | CLOSE: (15) is inconsistent.
% 243.59/50.11  | | | 
% 243.59/50.11  | | End of split
% 243.59/50.11  | | 
% 243.59/50.11  | End of split
% 243.59/50.11  | 
% 243.59/50.11  End of proof
% 243.59/50.11  
% 243.59/50.11  Sub-proof #1239 shows that the following formulas are inconsistent:
% 243.59/50.11  ----------------------------------------------------------------
% 243.59/50.11    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 243.59/50.11           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 243.59/50.11             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.11           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 243.59/50.11             e1) = e3 & op(e1, e3) = e3)
% 243.59/50.11    (2)  all_56_31 = e3
% 243.59/50.11    (3)  all_56_1 = e1
% 243.59/50.11  
% 243.59/50.11  Begin of proof
% 243.59/50.11  | 
% 243.59/50.11  | BETA: splitting (1) gives:
% 243.59/50.11  | 
% 243.59/50.11  | Case 1:
% 243.59/50.11  | | 
% 243.59/50.11  | |   (4)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 243.59/50.11  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.59/50.11  | |        op(e2, e3) = e2
% 243.59/50.11  | | 
% 243.59/50.11  | | ALPHA: (4) implies:
% 243.59/50.11  | |   (5)   ~ (all_56_31 = e3)
% 243.59/50.11  | | 
% 243.59/50.11  | | REDUCE: (2), (5) imply:
% 243.59/50.11  | |   (6)  $false
% 243.59/50.11  | | 
% 243.59/50.11  | | CLOSE: (6) is inconsistent.
% 243.59/50.11  | | 
% 243.59/50.11  | Case 2:
% 243.59/50.11  | | 
% 243.59/50.11  | |   (7)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 243.59/50.11  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 243.59/50.11  | |        op(e1, e3) = e3
% 243.59/50.11  | | 
% 243.59/50.11  | | ALPHA: (7) implies:
% 243.59/50.11  | |   (8)   ~ (all_56_1 = e1)
% 243.59/50.11  | | 
% 243.59/50.11  | | REDUCE: (3), (8) imply:
% 243.59/50.11  | |   (9)  $false
% 243.59/50.11  | | 
% 243.59/50.11  | | CLOSE: (9) is inconsistent.
% 243.59/50.11  | | 
% 243.59/50.11  | End of split
% 243.59/50.11  | 
% 243.59/50.11  End of proof
% 243.59/50.11  
% 243.59/50.11  Sub-proof #1240 shows that the following formulas are inconsistent:
% 243.59/50.11  ----------------------------------------------------------------
% 243.59/50.11    (1)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 243.59/50.11             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.59/50.11           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 243.59/50.11             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.59/50.11           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.11    (2)  op(e1, e0) = e1
% 243.59/50.11    (3)  op(e0, e1) = e0
% 243.59/50.11    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.11    (5)   ~ (e1 = e0)
% 243.59/50.11  
% 243.59/50.11  Begin of proof
% 243.59/50.11  | 
% 243.59/50.11  | BETA: splitting (1) gives:
% 243.59/50.11  | 
% 243.59/50.11  | Case 1:
% 243.59/50.11  | | 
% 243.59/50.11  | |   (6)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.59/50.11  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 243.59/50.11  | |        & op(e0, e1) = e1
% 243.59/50.11  | | 
% 243.59/50.11  | | ALPHA: (6) implies:
% 243.59/50.11  | |   (7)  op(e0, e1) = e1
% 243.59/50.11  | | 
% 243.59/50.11  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #2158.
% 243.59/50.11  | | 
% 243.59/50.11  | Case 2:
% 243.59/50.11  | | 
% 243.59/50.11  | |   (8)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 243.59/50.11  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 243.59/50.11  | |        & op(e0, e1) = e0
% 243.59/50.11  | | 
% 243.59/50.11  | | ALPHA: (8) implies:
% 243.59/50.11  | |   (9)  op(e1, e0) = e0
% 243.59/50.11  | | 
% 243.59/50.11  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2284.
% 243.59/50.11  | | 
% 243.59/50.11  | End of split
% 243.59/50.11  | 
% 243.59/50.11  End of proof
% 243.59/50.11  
% 243.59/50.11  Sub-proof #1241 shows that the following formulas are inconsistent:
% 243.59/50.11  ----------------------------------------------------------------
% 243.59/50.11    (1)   ~ (e2 = e0)
% 243.59/50.11    (2)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.59/50.11         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.59/50.11    (3)   ~ (e3 = e1)
% 243.59/50.11    (4)   ~ (e3 = e2)
% 243.59/50.11    (5)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.59/50.11         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.59/50.11    (6)  op(e0, e1) = e0
% 243.59/50.11    (7)  all_58_14 = e0
% 243.59/50.11    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.11    (9)  op(e1, e1) = e0
% 243.59/50.11    (10)   ~ (e1 = e0)
% 243.59/50.11    (11)  all_58_4 = e3
% 243.59/50.11    (12)   ~ (e2 = e1)
% 243.59/50.11  
% 243.59/50.11  Begin of proof
% 243.59/50.11  | 
% 243.59/50.11  | BETA: splitting (5) gives:
% 243.59/50.11  | 
% 243.59/50.11  | Case 1:
% 243.59/50.11  | | 
% 243.59/50.11  | |   (13)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 243.59/50.11  | |           e2)
% 243.59/50.11  | | 
% 243.59/50.11  | | BETA: splitting (13) gives:
% 243.59/50.11  | | 
% 243.59/50.11  | | Case 1:
% 243.59/50.11  | | | 
% 243.59/50.11  | | |   (14)  all_58_4 = e2 & op(e3, e1) = e2
% 243.59/50.11  | | | 
% 243.59/50.11  | | | ALPHA: (14) implies:
% 243.59/50.11  | | |   (15)  all_58_4 = e2
% 243.59/50.11  | | | 
% 243.59/50.11  | | | REF_CLOSE: (4), (11), (15) are inconsistent by sub-proof #1902.
% 243.59/50.11  | | | 
% 243.59/50.11  | | Case 2:
% 243.59/50.11  | | | 
% 243.59/50.11  | | |   (16)  all_58_5 = e2 & op(e2, e1) = e2
% 243.59/50.11  | | | 
% 243.59/50.11  | | | ALPHA: (16) implies:
% 243.59/50.11  | | |   (17)  all_58_5 = e2
% 243.59/50.11  | | | 
% 243.59/50.11  | | | BETA: splitting (2) gives:
% 243.59/50.11  | | | 
% 243.59/50.11  | | | Case 1:
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | |   (18)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 243.59/50.11  | | | |           = e1)
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | | BETA: splitting (18) gives:
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | | Case 1:
% 243.59/50.11  | | | | | 
% 243.59/50.11  | | | | |   (19)  all_58_4 = e1 & op(e3, e1) = e1
% 243.59/50.11  | | | | | 
% 243.59/50.11  | | | | | ALPHA: (19) implies:
% 243.59/50.11  | | | | |   (20)  all_58_4 = e1
% 243.59/50.11  | | | | | 
% 243.59/50.11  | | | | | REF_CLOSE: (3), (11), (20) are inconsistent by sub-proof #2184.
% 243.59/50.11  | | | | | 
% 243.59/50.11  | | | | Case 2:
% 243.59/50.11  | | | | | 
% 243.59/50.11  | | | | |   (21)  all_58_5 = e1 & op(e2, e1) = e1
% 243.59/50.11  | | | | | 
% 243.59/50.11  | | | | | REF_CLOSE: (12), (17), (21) are inconsistent by sub-proof #1548.
% 243.59/50.11  | | | | | 
% 243.59/50.11  | | | | End of split
% 243.59/50.11  | | | | 
% 243.59/50.11  | | | Case 2:
% 243.59/50.11  | | | | 
% 243.59/50.12  | | | |   (22)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 243.59/50.12  | | | |           = e1)
% 243.59/50.12  | | | | 
% 243.59/50.12  | | | | BETA: splitting (22) gives:
% 243.59/50.12  | | | | 
% 243.59/50.12  | | | | Case 1:
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | |   (23)  all_58_8 = e1 & op(e1, e1) = e1
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | | ALPHA: (23) implies:
% 243.59/50.12  | | | | |   (24)  op(e1, e1) = e1
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | | REF_CLOSE: (8), (9), (10), (24) are inconsistent by sub-proof #2220.
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | Case 2:
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | |   (25)  all_58_14 = e1 & op(e0, e1) = e1
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | | ALPHA: (25) implies:
% 243.59/50.12  | | | | |   (26)  op(e0, e1) = e1
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | | REF_CLOSE: (6), (8), (10), (26) are inconsistent by sub-proof #2158.
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | End of split
% 243.59/50.12  | | | | 
% 243.59/50.12  | | | End of split
% 243.59/50.12  | | | 
% 243.59/50.12  | | End of split
% 243.59/50.12  | | 
% 243.59/50.12  | Case 2:
% 243.59/50.12  | | 
% 243.59/50.12  | |   (27)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 243.59/50.12  | |           e2)
% 243.59/50.12  | | 
% 243.59/50.12  | | BETA: splitting (27) gives:
% 243.59/50.12  | | 
% 243.59/50.12  | | Case 1:
% 243.59/50.12  | | | 
% 243.59/50.12  | | |   (28)  all_58_8 = e2 & op(e1, e1) = e2
% 243.59/50.12  | | | 
% 243.59/50.12  | | | ALPHA: (28) implies:
% 243.59/50.12  | | |   (29)  op(e1, e1) = e2
% 243.59/50.12  | | | 
% 243.59/50.12  | | | REF_CLOSE: (1), (8), (9), (29) are inconsistent by sub-proof #2211.
% 243.59/50.12  | | | 
% 243.59/50.12  | | Case 2:
% 243.59/50.12  | | | 
% 243.59/50.12  | | |   (30)  all_58_14 = e2 & op(e0, e1) = e2
% 243.59/50.12  | | | 
% 243.59/50.12  | | | REF_CLOSE: (1), (7), (30) are inconsistent by sub-proof #2077.
% 243.59/50.12  | | | 
% 243.59/50.12  | | End of split
% 243.59/50.12  | | 
% 243.59/50.12  | End of split
% 243.59/50.12  | 
% 243.59/50.12  End of proof
% 243.59/50.12  
% 243.59/50.12  Sub-proof #1242 shows that the following formulas are inconsistent:
% 243.59/50.12  ----------------------------------------------------------------
% 243.59/50.12    (1)   ~ (e3 = e0)
% 243.59/50.12    (2)   ~ (e2 = e0)
% 243.59/50.12    (3)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.59/50.12         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.59/50.12    (4)  op(e1, e1) = all_6_2
% 243.59/50.12    (5)   ~ (e3 = e1)
% 243.59/50.12    (6)   ~ (all_52_8 = e1)
% 243.59/50.12    (7)   ~ (all_6_2 = e3)
% 243.59/50.12    (8)  op(e3, e1) = all_52_8
% 243.59/50.12    (9)   ~ (e3 = e2)
% 243.59/50.12    (10)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.59/50.12          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.59/50.12    (11)  op(e0, e1) = e0
% 243.59/50.12    (12)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.59/50.12          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.59/50.12    (13)  all_58_14 = e0
% 243.59/50.12    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.12    (15)   ~ (e1 = e0)
% 243.59/50.12    (16)  all_58_4 = e0
% 243.59/50.12    (17)   ~ (e2 = e1)
% 243.59/50.12  
% 243.59/50.12  Begin of proof
% 243.59/50.12  | 
% 243.59/50.12  | BETA: splitting (12) gives:
% 243.59/50.12  | 
% 243.59/50.12  | Case 1:
% 243.59/50.12  | | 
% 243.59/50.12  | |   (18)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 243.59/50.12  | |           e3)
% 243.59/50.12  | | 
% 243.59/50.12  | | BETA: splitting (18) gives:
% 243.59/50.12  | | 
% 243.59/50.12  | | Case 1:
% 243.59/50.12  | | | 
% 243.59/50.12  | | |   (19)  all_58_4 = e3 & op(e3, e1) = e3
% 243.59/50.12  | | | 
% 243.59/50.12  | | | REF_CLOSE: (1), (16), (19) are inconsistent by sub-proof #1244.
% 243.59/50.12  | | | 
% 243.59/50.12  | | Case 2:
% 243.59/50.12  | | | 
% 243.59/50.12  | | |   (20)  all_58_5 = e3 & op(e2, e1) = e3
% 243.59/50.12  | | | 
% 243.59/50.12  | | | ALPHA: (20) implies:
% 243.59/50.12  | | |   (21)  all_58_5 = e3
% 243.59/50.12  | | | 
% 243.59/50.12  | | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (13), (14), (15),
% 243.59/50.12  | | |            (16), (17), (21) are inconsistent by sub-proof #1243.
% 243.59/50.12  | | | 
% 243.59/50.12  | | End of split
% 243.59/50.12  | | 
% 243.59/50.12  | Case 2:
% 243.59/50.12  | | 
% 243.59/50.12  | |   (22)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 243.59/50.12  | |           e3)
% 243.59/50.12  | | 
% 243.59/50.12  | | REF_CLOSE: (1), (4), (7), (11), (14), (22) are inconsistent by sub-proof
% 243.59/50.12  | |            #1627.
% 243.59/50.12  | | 
% 243.59/50.12  | End of split
% 243.59/50.12  | 
% 243.59/50.12  End of proof
% 243.59/50.12  
% 243.59/50.12  Sub-proof #1243 shows that the following formulas are inconsistent:
% 243.59/50.12  ----------------------------------------------------------------
% 243.59/50.12    (1)   ~ (e2 = e0)
% 243.59/50.12    (2)  all_58_5 = e3
% 243.59/50.12    (3)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.59/50.12         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.59/50.12    (4)   ~ (e3 = e1)
% 243.59/50.12    (5)   ~ (all_52_8 = e1)
% 243.59/50.12    (6)  op(e3, e1) = all_52_8
% 243.59/50.12    (7)   ~ (e3 = e2)
% 243.59/50.12    (8)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.59/50.12         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.59/50.12    (9)  op(e0, e1) = e0
% 243.59/50.12    (10)  all_58_14 = e0
% 243.59/50.12    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.12    (12)   ~ (e1 = e0)
% 243.59/50.12    (13)  all_58_4 = e0
% 243.59/50.12    (14)   ~ (e2 = e1)
% 243.59/50.12  
% 243.59/50.12  Begin of proof
% 243.59/50.12  | 
% 243.59/50.12  | BETA: splitting (3) gives:
% 243.59/50.12  | 
% 243.59/50.12  | Case 1:
% 243.59/50.12  | | 
% 243.59/50.12  | |   (15)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 243.59/50.12  | |           e1)
% 243.59/50.12  | | 
% 243.59/50.12  | | BETA: splitting (15) gives:
% 243.59/50.12  | | 
% 243.59/50.12  | | Case 1:
% 243.59/50.12  | | | 
% 243.59/50.12  | | |   (16)  all_58_4 = e1 & op(e3, e1) = e1
% 243.59/50.12  | | | 
% 243.59/50.12  | | | ALPHA: (16) implies:
% 243.59/50.12  | | |   (17)  op(e3, e1) = e1
% 243.59/50.12  | | | 
% 243.59/50.12  | | | REF_CLOSE: (5), (6), (11), (17) are inconsistent by sub-proof #2309.
% 243.59/50.12  | | | 
% 243.59/50.12  | | Case 2:
% 243.59/50.12  | | | 
% 243.59/50.12  | | |   (18)  all_58_5 = e1 & op(e2, e1) = e1
% 243.59/50.12  | | | 
% 243.59/50.12  | | | ALPHA: (18) implies:
% 243.59/50.12  | | |   (19)  all_58_5 = e1
% 243.59/50.12  | | | 
% 243.59/50.12  | | | COMBINE_EQS: (2), (19) imply:
% 243.59/50.12  | | |   (20)  e3 = e1
% 243.59/50.12  | | | 
% 243.59/50.12  | | | REDUCE: (4), (20) imply:
% 243.59/50.12  | | |   (21)  $false
% 243.59/50.12  | | | 
% 243.59/50.12  | | | CLOSE: (21) is inconsistent.
% 243.59/50.12  | | | 
% 243.59/50.12  | | End of split
% 243.59/50.12  | | 
% 243.59/50.12  | Case 2:
% 243.59/50.12  | | 
% 243.59/50.12  | |   (22)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 243.59/50.12  | |           e1)
% 243.59/50.12  | | 
% 243.59/50.12  | | BETA: splitting (22) gives:
% 243.59/50.12  | | 
% 243.59/50.12  | | Case 1:
% 243.59/50.12  | | | 
% 243.59/50.12  | | |   (23)  all_58_8 = e1 & op(e1, e1) = e1
% 243.59/50.12  | | | 
% 243.59/50.12  | | | ALPHA: (23) implies:
% 243.59/50.12  | | |   (24)  all_58_8 = e1
% 243.59/50.12  | | | 
% 243.59/50.12  | | | REF_CLOSE: (1), (2), (7), (8), (10), (13), (14), (24) are inconsistent by
% 243.59/50.12  | | |            sub-proof #1265.
% 243.59/50.12  | | | 
% 243.59/50.12  | | Case 2:
% 243.59/50.12  | | | 
% 243.59/50.12  | | |   (25)  all_58_14 = e1 & op(e0, e1) = e1
% 243.59/50.12  | | | 
% 243.59/50.12  | | | ALPHA: (25) implies:
% 243.59/50.12  | | |   (26)  op(e0, e1) = e1
% 243.59/50.12  | | | 
% 243.59/50.12  | | | REF_CLOSE: (9), (11), (12), (26) are inconsistent by sub-proof #2158.
% 243.59/50.12  | | | 
% 243.59/50.12  | | End of split
% 243.59/50.12  | | 
% 243.59/50.12  | End of split
% 243.59/50.12  | 
% 243.59/50.12  End of proof
% 243.59/50.12  
% 243.59/50.12  Sub-proof #1244 shows that the following formulas are inconsistent:
% 243.59/50.12  ----------------------------------------------------------------
% 243.59/50.12    (1)  all_58_4 = e3 & op(e3, e1) = e3
% 243.59/50.12    (2)  all_58_4 = e0
% 243.59/50.12    (3)   ~ (e3 = e0)
% 243.59/50.12  
% 243.59/50.12  Begin of proof
% 243.59/50.12  | 
% 243.59/50.12  | ALPHA: (1) implies:
% 243.59/50.12  |   (4)  all_58_4 = e3
% 243.59/50.12  | 
% 243.59/50.12  | COMBINE_EQS: (2), (4) imply:
% 243.59/50.12  |   (5)  e3 = e0
% 243.59/50.12  | 
% 243.59/50.12  | REDUCE: (3), (5) imply:
% 243.59/50.12  |   (6)  $false
% 243.59/50.12  | 
% 243.59/50.12  | CLOSE: (6) is inconsistent.
% 243.59/50.12  | 
% 243.59/50.12  End of proof
% 243.59/50.12  
% 243.59/50.12  Sub-proof #1245 shows that the following formulas are inconsistent:
% 243.59/50.12  ----------------------------------------------------------------
% 243.59/50.12    (1)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.59/50.12             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.59/50.12           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 243.59/50.12             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.59/50.12           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.59/50.12    (2)  all_56_21 = e2
% 243.59/50.12    (3)  all_56_11 = e0
% 243.59/50.12  
% 243.59/50.12  Begin of proof
% 243.59/50.12  | 
% 243.59/50.12  | BETA: splitting (1) gives:
% 243.59/50.12  | 
% 243.59/50.12  | Case 1:
% 243.59/50.12  | | 
% 243.59/50.12  | |   (4)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.59/50.12  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 243.59/50.12  | |        & op(e1, e2) = e1
% 243.59/50.12  | | 
% 243.59/50.12  | | ALPHA: (4) implies:
% 243.59/50.12  | |   (5)   ~ (all_56_21 = e2)
% 243.59/50.12  | | 
% 243.59/50.12  | | REDUCE: (2), (5) imply:
% 243.59/50.12  | |   (6)  $false
% 243.59/50.12  | | 
% 243.59/50.12  | | CLOSE: (6) is inconsistent.
% 243.59/50.12  | | 
% 243.59/50.12  | Case 2:
% 243.59/50.12  | | 
% 243.59/50.12  | |   (7)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.59/50.12  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 243.59/50.12  | |        & op(e0, e2) = e2
% 243.59/50.12  | | 
% 243.59/50.12  | | ALPHA: (7) implies:
% 243.59/50.12  | |   (8)   ~ (all_56_11 = e0)
% 243.59/50.12  | | 
% 243.59/50.12  | | REDUCE: (3), (8) imply:
% 243.59/50.12  | |   (9)  $false
% 243.59/50.12  | | 
% 243.59/50.12  | | CLOSE: (9) is inconsistent.
% 243.59/50.12  | | 
% 243.59/50.12  | End of split
% 243.59/50.12  | 
% 243.59/50.12  End of proof
% 243.59/50.12  
% 243.59/50.12  Sub-proof #1246 shows that the following formulas are inconsistent:
% 243.59/50.12  ----------------------------------------------------------------
% 243.59/50.12    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 243.59/50.12           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 243.59/50.12           all_12_1 & $i(all_12_1))
% 243.59/50.12    (2)   ~ (e3 = e0)
% 243.59/50.12    (3)   ~ (e2 = e0)
% 243.59/50.12    (4)  op(e1, e2) = all_52_6
% 243.59/50.12    (5)  all_58_6 = e2
% 243.59/50.12    (6)  op(e1, e1) = all_6_2
% 243.59/50.12    (7)  all_58_15 = e3
% 243.59/50.12    (8)  op(e0, e3) = all_52_3
% 243.59/50.12    (9)   ~ (all_52_6 = e0)
% 243.59/50.12    (10)   ~ (e3 = e1)
% 243.59/50.12    (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.59/50.12          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.59/50.12    (12)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.59/50.12            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 243.59/50.12              e3) = all_26_1 & $i(all_26_1))
% 243.59/50.12    (13)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.59/50.12          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.59/50.12    (14)  op(e2, e1) = all_52_9
% 243.59/50.12    (15)   ~ (e3 = e2)
% 243.59/50.12    (16)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.59/50.12          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.59/50.12    (17)   ~ (all_6_2 = e0)
% 243.59/50.12    (18)  op(e2, e0) = e2
% 243.59/50.12    (19)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.59/50.12          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.59/50.12    (20)  all_58_7 = e3
% 243.59/50.12    (21)  all_58_13 = e2
% 243.59/50.12    (22)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.59/50.12          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.59/50.12    (23)   ~ (all_52_3 = e3)
% 243.59/50.12    (24)   ~ (all_52_1 = e0)
% 243.59/50.12    (25)  op(e2, e3) = all_52_1
% 243.59/50.12    (26)  op(e3, e3) = e2
% 243.59/50.12    (27)  op(e1, e1) = e2
% 243.59/50.12    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.59/50.12          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.59/50.12    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.12    (30)   ~ (e1 = e0)
% 243.59/50.12    (31)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.59/50.12          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.59/50.12    (32)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.59/50.12          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.59/50.12            e1)
% 243.59/50.12    (33)  all_58_3 = e0
% 243.59/50.12    (34)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.59/50.12          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.59/50.12    (35)   ~ (e2 = e1)
% 243.59/50.12  
% 243.59/50.12  Begin of proof
% 243.59/50.12  | 
% 243.59/50.12  | BETA: splitting (13) gives:
% 243.59/50.12  | 
% 243.59/50.12  | Case 1:
% 243.59/50.12  | | 
% 243.59/50.12  | |   (36)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 243.59/50.12  | |           e3)
% 243.59/50.12  | | 
% 243.59/50.12  | | BETA: splitting (36) gives:
% 243.59/50.12  | | 
% 243.59/50.12  | | Case 1:
% 243.59/50.12  | | | 
% 243.59/50.12  | | |   (37)  all_58_0 = e3 & op(e3, e3) = e3
% 243.59/50.12  | | | 
% 243.59/50.12  | | | ALPHA: (37) implies:
% 243.59/50.12  | | |   (38)  op(e3, e3) = e3
% 243.59/50.12  | | | 
% 243.59/50.12  | | | REF_CLOSE: (15), (26), (29), (38) are inconsistent by sub-proof #2194.
% 243.59/50.12  | | | 
% 243.59/50.12  | | Case 2:
% 243.59/50.12  | | | 
% 243.59/50.12  | | |   (39)  all_58_2 = e3 & op(e2, e3) = e3
% 243.59/50.12  | | | 
% 243.59/50.12  | | | ALPHA: (39) implies:
% 243.59/50.12  | | |   (40)  all_58_2 = e3
% 243.59/50.12  | | | 
% 243.59/50.12  | | | BETA: splitting (19) gives:
% 243.59/50.12  | | | 
% 243.59/50.12  | | | Case 1:
% 243.59/50.12  | | | | 
% 243.59/50.12  | | | |   (41)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 243.59/50.12  | | | |           = e0)
% 243.59/50.12  | | | | 
% 243.59/50.12  | | | | REF_CLOSE: (3), (24), (25), (26), (29), (41) are inconsistent by
% 243.59/50.12  | | | |            sub-proof #1984.
% 243.59/50.12  | | | | 
% 243.59/50.12  | | | Case 2:
% 243.59/50.12  | | | | 
% 243.59/50.12  | | | |   (42)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 243.59/50.12  | | | |           = e0)
% 243.59/50.12  | | | | 
% 243.59/50.12  | | | | BETA: splitting (42) gives:
% 243.59/50.12  | | | | 
% 243.59/50.12  | | | | Case 1:
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | |   (43)  all_58_6 = e0 & op(e1, e3) = e0
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | | REF_CLOSE: (3), (5), (43) are inconsistent by sub-proof #1678.
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | Case 2:
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | |   (44)  all_58_12 = e0 & op(e0, e3) = e0
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | | ALPHA: (44) implies:
% 243.59/50.12  | | | | |   (45)  op(e0, e3) = e0
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | | BETA: splitting (32) gives:
% 243.59/50.12  | | | | | 
% 243.59/50.12  | | | | | Case 1:
% 243.59/50.12  | | | | | | 
% 243.59/50.12  | | | | | |   (46)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 243.59/50.12  | | | | | |           op(e0, e2) = e1)
% 243.59/50.12  | | | | | | 
% 243.59/50.12  | | | | | | BETA: splitting (46) gives:
% 243.59/50.12  | | | | | | 
% 243.59/50.12  | | | | | | Case 1:
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | |   (47)  all_58_12 = e1 & op(e0, e3) = e1
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | | ALPHA: (47) implies:
% 243.59/50.12  | | | | | | |   (48)  op(e0, e3) = e1
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | | REF_CLOSE: (1), (12), (29), (30), (45), (48) are inconsistent by
% 243.59/50.12  | | | | | | |            sub-proof #1384.
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | Case 2:
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | |   (49)  all_58_13 = e1 & op(e0, e2) = e1
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | | ALPHA: (49) implies:
% 243.59/50.12  | | | | | | |   (50)  all_58_13 = e1
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | | REF_CLOSE: (21), (35), (50) are inconsistent by sub-proof #1544.
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | End of split
% 243.59/50.12  | | | | | | 
% 243.59/50.12  | | | | | Case 2:
% 243.59/50.12  | | | | | | 
% 243.59/50.12  | | | | | |   (51)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 243.59/50.12  | | | | | |           op(e0, e0) = e1)
% 243.59/50.12  | | | | | | 
% 243.59/50.12  | | | | | | BETA: splitting (51) gives:
% 243.59/50.12  | | | | | | 
% 243.59/50.12  | | | | | | Case 1:
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | |   (52)  all_58_14 = e1 & op(e0, e1) = e1
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | | ALPHA: (52) implies:
% 243.59/50.12  | | | | | | |   (53)  all_58_14 = e1
% 243.59/50.12  | | | | | | |   (54)  op(e0, e1) = e1
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | | BETA: splitting (34) gives:
% 243.59/50.12  | | | | | | | 
% 243.59/50.12  | | | | | | | Case 1:
% 243.59/50.12  | | | | | | | | 
% 243.59/50.12  | | | | | | | |   (55)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 243.59/50.12  | | | | | | | |           op(e2, e2) = e1)
% 243.59/50.12  | | | | | | | | 
% 243.59/50.12  | | | | | | | | BETA: splitting (55) gives:
% 243.59/50.12  | | | | | | | | 
% 243.59/50.12  | | | | | | | | Case 1:
% 243.59/50.12  | | | | | | | | | 
% 243.59/50.12  | | | | | | | | |   (56)  all_58_2 = e1 & op(e2, e3) = e1
% 243.59/50.12  | | | | | | | | | 
% 243.59/50.12  | | | | | | | | | ALPHA: (56) implies:
% 243.59/50.12  | | | | | | | | |   (57)  all_58_2 = e1
% 243.59/50.12  | | | | | | | | | 
% 243.59/50.12  | | | | | | | | | COMBINE_EQS: (40), (57) imply:
% 243.59/50.12  | | | | | | | | |   (58)  e3 = e1
% 243.59/50.12  | | | | | | | | | 
% 243.59/50.12  | | | | | | | | | SIMP: (58) implies:
% 243.59/50.12  | | | | | | | | |   (59)  e3 = e1
% 243.59/50.12  | | | | | | | | | 
% 243.59/50.12  | | | | | | | | | COMBINE_EQS: (20), (59) imply:
% 243.59/50.12  | | | | | | | | |   (60)  all_58_7 = e1
% 243.59/50.12  | | | | | | | | | 
% 243.59/50.12  | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (9), (10), (15), (22), (27),
% 243.59/50.12  | | | | | | | | |            (29), (31), (60) are inconsistent by sub-proof
% 243.59/50.12  | | | | | | | | |            #1676.
% 243.59/50.12  | | | | | | | | | 
% 243.59/50.12  | | | | | | | | Case 2:
% 243.59/50.12  | | | | | | | | | 
% 243.59/50.12  | | | | | | | | |   (61)  all_58_3 = e1 & op(e2, e2) = e1
% 243.59/50.12  | | | | | | | | | 
% 243.59/50.12  | | | | | | | | | REF_CLOSE: (30), (33), (61) are inconsistent by sub-proof
% 243.59/50.12  | | | | | | | | |            #1752.
% 243.59/50.12  | | | | | | | | | 
% 243.59/50.12  | | | | | | | | End of split
% 243.59/50.12  | | | | | | | | 
% 243.59/50.12  | | | | | | | Case 2:
% 243.59/50.12  | | | | | | | | 
% 243.59/50.13  | | | | | | | |   (62)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 243.59/50.13  | | | | | | | |           op(e2, e0) = e1)
% 243.59/50.13  | | | | | | | | 
% 243.59/50.13  | | | | | | | | BETA: splitting (62) gives:
% 243.59/50.13  | | | | | | | | 
% 243.59/50.13  | | | | | | | | Case 1:
% 243.59/50.13  | | | | | | | | | 
% 243.59/50.13  | | | | | | | | |   (63)  all_58_5 = e1 & op(e2, e1) = e1
% 243.59/50.13  | | | | | | | | | 
% 243.59/50.13  | | | | | | | | | ALPHA: (63) implies:
% 243.59/50.13  | | | | | | | | |   (64)  all_58_5 = e1
% 243.59/50.13  | | | | | | | | |   (65)  op(e2, e1) = e1
% 243.59/50.13  | | | | | | | | | 
% 243.59/50.13  | | | | | | | | | REF_CLOSE: (2), (3), (6), (10), (11), (14), (15), (16), (17),
% 243.59/50.13  | | | | | | | | |            (28), (29), (30), (35), (53), (54), (64), (65) are
% 243.59/50.13  | | | | | | | | |            inconsistent by sub-proof #1247.
% 243.59/50.13  | | | | | | | | | 
% 243.59/50.13  | | | | | | | | Case 2:
% 243.59/50.13  | | | | | | | | | 
% 243.59/50.13  | | | | | | | | |   (66)  all_58_10 = e1 & op(e2, e0) = e1
% 243.59/50.13  | | | | | | | | | 
% 243.59/50.13  | | | | | | | | | ALPHA: (66) implies:
% 243.59/50.13  | | | | | | | | |   (67)  op(e2, e0) = e1
% 243.59/50.13  | | | | | | | | | 
% 243.59/50.13  | | | | | | | | | REF_CLOSE: (18), (29), (35), (67) are inconsistent by
% 243.59/50.13  | | | | | | | | |            sub-proof #1659.
% 243.59/50.13  | | | | | | | | | 
% 243.59/50.13  | | | | | | | | End of split
% 243.59/50.13  | | | | | | | | 
% 243.59/50.13  | | | | | | | End of split
% 243.59/50.13  | | | | | | | 
% 243.59/50.13  | | | | | | Case 2:
% 243.59/50.13  | | | | | | | 
% 243.59/50.13  | | | | | | |   (68)  all_58_15 = e1 & op(e0, e0) = e1
% 243.59/50.13  | | | | | | | 
% 243.59/50.13  | | | | | | | ALPHA: (68) implies:
% 243.59/50.13  | | | | | | |   (69)  all_58_15 = e1
% 243.59/50.13  | | | | | | | 
% 243.59/50.13  | | | | | | | COMBINE_EQS: (7), (69) imply:
% 243.59/50.13  | | | | | | |   (70)  e3 = e1
% 243.59/50.13  | | | | | | | 
% 243.59/50.13  | | | | | | | SIMP: (70) implies:
% 243.59/50.13  | | | | | | |   (71)  e3 = e1
% 243.59/50.13  | | | | | | | 
% 243.59/50.13  | | | | | | | COMBINE_EQS: (20), (71) imply:
% 243.59/50.13  | | | | | | |   (72)  all_58_7 = e1
% 243.59/50.13  | | | | | | | 
% 243.59/50.13  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (9), (10), (15), (22), (27), (29),
% 243.59/50.13  | | | | | | |            (31), (72) are inconsistent by sub-proof #1676.
% 243.59/50.13  | | | | | | | 
% 243.59/50.13  | | | | | | End of split
% 243.59/50.13  | | | | | | 
% 243.59/50.13  | | | | | End of split
% 243.59/50.13  | | | | | 
% 243.59/50.13  | | | | End of split
% 243.59/50.13  | | | | 
% 243.59/50.13  | | | End of split
% 243.59/50.13  | | | 
% 243.59/50.13  | | End of split
% 243.59/50.13  | | 
% 243.59/50.13  | Case 2:
% 243.59/50.13  | | 
% 243.59/50.13  | |   (73)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 243.59/50.13  | |           e3)
% 243.59/50.13  | | 
% 243.59/50.13  | | REF_CLOSE: (5), (8), (15), (23), (29), (73) are inconsistent by sub-proof
% 243.59/50.13  | |            #1349.
% 243.59/50.13  | | 
% 243.59/50.13  | End of split
% 243.59/50.13  | 
% 243.59/50.13  End of proof
% 243.59/50.13  
% 243.59/50.13  Sub-proof #1247 shows that the following formulas are inconsistent:
% 243.59/50.13  ----------------------------------------------------------------
% 243.59/50.13    (1)   ~ (e3 = e0)
% 243.59/50.13    (2)  op(e2, e1) = e1
% 243.59/50.13    (3)   ~ (e2 = e0)
% 243.59/50.13    (4)  op(e1, e1) = all_6_2
% 243.59/50.13    (5)   ~ (e3 = e1)
% 243.59/50.13    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.59/50.13         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.59/50.13    (7)  op(e0, e1) = e1
% 243.59/50.13    (8)  op(e2, e1) = all_52_9
% 243.59/50.13    (9)   ~ (e3 = e2)
% 243.59/50.13    (10)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.59/50.13          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.59/50.13    (11)   ~ (all_6_2 = e0)
% 243.59/50.13    (12)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.59/50.13          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.59/50.13    (13)  all_58_5 = e1
% 243.59/50.13    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.13    (15)   ~ (e1 = e0)
% 243.59/50.13    (16)  all_58_14 = e1
% 243.59/50.13    (17)   ~ (e2 = e1)
% 243.59/50.13  
% 243.59/50.13  Begin of proof
% 243.59/50.13  | 
% 243.59/50.13  | BETA: splitting (6) gives:
% 243.59/50.13  | 
% 243.59/50.13  | Case 1:
% 243.59/50.13  | | 
% 243.59/50.13  | |   (18)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 243.59/50.13  | |           e0)
% 243.59/50.13  | | 
% 243.59/50.13  | | BETA: splitting (18) gives:
% 243.59/50.13  | | 
% 243.59/50.13  | | Case 1:
% 243.59/50.13  | | | 
% 243.59/50.13  | | |   (19)  all_58_4 = e0 & op(e3, e1) = e0
% 243.59/50.13  | | | 
% 243.59/50.13  | | | ALPHA: (19) implies:
% 243.59/50.13  | | |   (20)  all_58_4 = e0
% 243.59/50.13  | | | 
% 243.59/50.13  | | | REF_CLOSE: (1), (3), (5), (6), (9), (10), (12), (13), (14), (15), (16),
% 243.59/50.13  | | |            (17), (20) are inconsistent by sub-proof #1248.
% 243.59/50.13  | | | 
% 243.59/50.13  | | Case 2:
% 243.59/50.13  | | | 
% 243.59/50.13  | | |   (21)  all_58_5 = e0 & op(e2, e1) = e0
% 243.59/50.13  | | | 
% 243.59/50.13  | | | ALPHA: (21) implies:
% 243.59/50.13  | | |   (22)  op(e2, e1) = e0
% 243.59/50.13  | | | 
% 243.59/50.13  | | | REF_CLOSE: (2), (8), (14), (15), (22) are inconsistent by sub-proof #2165.
% 243.59/50.13  | | | 
% 243.59/50.13  | | End of split
% 243.59/50.13  | | 
% 243.59/50.13  | Case 2:
% 243.59/50.13  | | 
% 243.59/50.13  | |   (23)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 243.59/50.13  | |           e0)
% 243.59/50.13  | | 
% 243.59/50.13  | | BETA: splitting (23) gives:
% 243.59/50.13  | | 
% 243.59/50.13  | | Case 1:
% 243.59/50.13  | | | 
% 243.59/50.13  | | |   (24)  all_58_8 = e0 & op(e1, e1) = e0
% 243.59/50.13  | | | 
% 243.59/50.13  | | | REF_CLOSE: (4), (11), (14), (24) are inconsistent by sub-proof #1833.
% 243.59/50.13  | | | 
% 243.59/50.13  | | Case 2:
% 243.59/50.13  | | | 
% 243.59/50.13  | | |   (25)  all_58_14 = e0 & op(e0, e1) = e0
% 243.59/50.13  | | | 
% 243.59/50.13  | | | ALPHA: (25) implies:
% 243.59/50.13  | | |   (26)  op(e0, e1) = e0
% 243.59/50.13  | | | 
% 243.59/50.13  | | | REF_CLOSE: (7), (14), (15), (26) are inconsistent by sub-proof #2158.
% 243.59/50.13  | | | 
% 243.59/50.13  | | End of split
% 243.59/50.13  | | 
% 243.59/50.13  | End of split
% 243.59/50.13  | 
% 243.59/50.13  End of proof
% 243.59/50.13  
% 243.59/50.13  Sub-proof #1248 shows that the following formulas are inconsistent:
% 243.59/50.13  ----------------------------------------------------------------
% 243.59/50.13    (1)   ~ (e3 = e0)
% 243.59/50.13    (2)   ~ (e2 = e0)
% 243.59/50.13    (3)   ~ (e3 = e1)
% 243.59/50.13    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.59/50.13         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.59/50.13    (5)   ~ (e3 = e2)
% 243.59/50.13    (6)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.59/50.13         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.59/50.13    (7)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.59/50.13         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.59/50.13    (8)  all_58_5 = e1
% 243.59/50.13    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.13    (10)   ~ (e1 = e0)
% 243.59/50.13    (11)  all_58_14 = e1
% 243.59/50.13    (12)  all_58_4 = e0
% 243.59/50.13    (13)   ~ (e2 = e1)
% 243.59/50.13  
% 243.59/50.13  Begin of proof
% 243.59/50.13  | 
% 243.59/50.13  | BETA: splitting (6) gives:
% 243.59/50.13  | 
% 243.59/50.13  | Case 1:
% 243.59/50.13  | | 
% 243.59/50.13  | |   (14)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 243.59/50.13  | |           e2)
% 243.59/50.13  | | 
% 243.59/50.13  | | BETA: splitting (14) gives:
% 243.59/50.13  | | 
% 243.59/50.13  | | Case 1:
% 243.59/50.13  | | | 
% 243.59/50.13  | | |   (15)  all_58_4 = e2 & op(e3, e1) = e2
% 243.59/50.13  | | | 
% 243.59/50.13  | | | REF_CLOSE: (2), (12), (15) are inconsistent by sub-proof #1707.
% 243.59/50.13  | | | 
% 243.59/50.13  | | Case 2:
% 243.59/50.13  | | | 
% 243.59/50.13  | | |   (16)  all_58_5 = e2 & op(e2, e1) = e2
% 243.59/50.13  | | | 
% 243.59/50.13  | | | ALPHA: (16) implies:
% 243.59/50.13  | | |   (17)  all_58_5 = e2
% 243.59/50.13  | | | 
% 243.59/50.13  | | | REF_CLOSE: (8), (13), (17) are inconsistent by sub-proof #1665.
% 243.59/50.13  | | | 
% 243.59/50.13  | | End of split
% 243.59/50.13  | | 
% 243.59/50.13  | Case 2:
% 243.59/50.13  | | 
% 243.59/50.13  | |   (18)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 243.59/50.13  | |           e2)
% 243.59/50.13  | | 
% 243.59/50.13  | | BETA: splitting (18) gives:
% 243.59/50.13  | | 
% 243.59/50.13  | | Case 1:
% 243.59/50.13  | | | 
% 243.59/50.13  | | |   (19)  all_58_8 = e2 & op(e1, e1) = e2
% 243.59/50.13  | | | 
% 243.59/50.13  | | | ALPHA: (19) implies:
% 243.59/50.13  | | |   (20)  all_58_8 = e2
% 243.59/50.13  | | |   (21)  op(e1, e1) = e2
% 243.59/50.13  | | | 
% 243.59/50.13  | | | BETA: splitting (7) gives:
% 243.59/50.13  | | | 
% 243.59/50.13  | | | Case 1:
% 243.59/50.13  | | | | 
% 243.59/50.13  | | | |   (22)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 243.59/50.13  | | | |           = e3)
% 243.59/50.13  | | | | 
% 243.59/50.13  | | | | BETA: splitting (22) gives:
% 243.59/50.13  | | | | 
% 243.59/50.13  | | | | Case 1:
% 243.59/50.13  | | | | | 
% 243.59/50.13  | | | | |   (23)  all_58_4 = e3 & op(e3, e1) = e3
% 243.59/50.13  | | | | | 
% 243.59/50.13  | | | | | ALPHA: (23) implies:
% 243.59/50.13  | | | | |   (24)  all_58_4 = e3
% 243.59/50.13  | | | | | 
% 243.59/50.13  | | | | | REF_CLOSE: (1), (2), (4), (8), (10), (11), (20), (24) are inconsistent
% 243.59/50.13  | | | | |            by sub-proof #1482.
% 243.59/50.13  | | | | | 
% 243.59/50.13  | | | | Case 2:
% 243.59/50.13  | | | | | 
% 243.59/50.13  | | | | |   (25)  all_58_5 = e3 & op(e2, e1) = e3
% 243.59/50.13  | | | | | 
% 243.59/50.13  | | | | | REF_CLOSE: (3), (8), (25) are inconsistent by sub-proof #2166.
% 243.59/50.13  | | | | | 
% 243.59/50.13  | | | | End of split
% 243.59/50.13  | | | | 
% 243.59/50.13  | | | Case 2:
% 243.59/50.13  | | | | 
% 243.59/50.13  | | | |   (26)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1)
% 243.59/50.13  | | | |           = e3)
% 243.59/50.13  | | | | 
% 243.59/50.13  | | | | REF_CLOSE: (3), (5), (9), (11), (21), (26) are inconsistent by sub-proof
% 243.59/50.13  | | | |            #1249.
% 243.59/50.13  | | | | 
% 243.59/50.13  | | | End of split
% 243.59/50.13  | | | 
% 243.59/50.13  | | Case 2:
% 243.59/50.13  | | | 
% 243.59/50.13  | | |   (27)  all_58_14 = e2 & op(e0, e1) = e2
% 243.59/50.13  | | | 
% 243.59/50.13  | | | REF_CLOSE: (11), (13), (27) are inconsistent by sub-proof #1771.
% 243.59/50.13  | | | 
% 243.59/50.13  | | End of split
% 243.59/50.13  | | 
% 243.59/50.13  | End of split
% 243.59/50.13  | 
% 243.59/50.13  End of proof
% 243.59/50.13  
% 243.59/50.13  Sub-proof #1249 shows that the following formulas are inconsistent:
% 243.59/50.13  ----------------------------------------------------------------
% 243.59/50.13    (1)   ~ (e3 = e1)
% 243.59/50.13    (2)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.59/50.13    (3)   ~ (e3 = e2)
% 243.59/50.13    (4)  op(e1, e1) = e2
% 243.59/50.13    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.13    (6)  all_58_14 = e1
% 243.59/50.13  
% 243.59/50.13  Begin of proof
% 243.59/50.13  | 
% 243.59/50.13  | BETA: splitting (2) gives:
% 243.59/50.13  | 
% 243.59/50.13  | Case 1:
% 243.59/50.13  | | 
% 243.59/50.13  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 243.59/50.13  | | 
% 243.59/50.13  | | ALPHA: (7) implies:
% 243.59/50.13  | |   (8)  op(e1, e1) = e3
% 243.59/50.13  | | 
% 243.59/50.13  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2206.
% 243.59/50.13  | | 
% 243.59/50.13  | Case 2:
% 243.59/50.13  | | 
% 243.59/50.13  | |   (9)  all_58_14 = e3 & op(e0, e1) = e3
% 243.59/50.13  | | 
% 243.59/50.13  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #1773.
% 243.59/50.13  | | 
% 243.59/50.13  | End of split
% 243.59/50.13  | 
% 243.59/50.13  End of proof
% 243.59/50.13  
% 243.59/50.13  Sub-proof #1250 shows that the following formulas are inconsistent:
% 243.59/50.13  ----------------------------------------------------------------
% 243.59/50.13    (1)  op(e1, e0) = all_52_14
% 243.59/50.13    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.59/50.13             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 243.59/50.13           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.59/50.13             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.59/50.13           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 243.59/50.13           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.13           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.13    (3)   ~ (all_52_14 = e1)
% 243.59/50.13    (4)  all_56_21 = e1
% 243.59/50.13    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.13    (6)  op(e2, e0) = all_52_13
% 243.59/50.13    (7)   ~ (all_52_13 = e0)
% 243.59/50.13  
% 243.59/50.13  Begin of proof
% 243.59/50.13  | 
% 243.59/50.13  | BETA: splitting (2) gives:
% 243.59/50.13  | 
% 243.59/50.13  | Case 1:
% 243.59/50.13  | | 
% 243.59/50.13  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.59/50.13  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 243.59/50.13  | |        & op(e0, e2) = e0
% 243.59/50.13  | | 
% 243.59/50.13  | | ALPHA: (8) implies:
% 243.59/50.13  | |   (9)  op(e2, e0) = e0
% 243.59/50.13  | | 
% 243.59/50.13  | | REF_CLOSE: (5), (6), (7), (9) are inconsistent by sub-proof #2324.
% 243.59/50.13  | | 
% 243.59/50.13  | Case 2:
% 243.59/50.13  | | 
% 243.59/50.13  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.13  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.59/50.13  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.59/50.13  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.59/50.13  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.13  | | 
% 243.59/50.13  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #1409.
% 243.59/50.13  | | 
% 243.59/50.13  | End of split
% 243.59/50.13  | 
% 243.59/50.13  End of proof
% 243.59/50.13  
% 243.59/50.13  Sub-proof #1251 shows that the following formulas are inconsistent:
% 243.59/50.13  ----------------------------------------------------------------
% 243.59/50.13    (1)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.59/50.13    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.59/50.13         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.59/50.13    (3)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 243.59/50.13           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 243.59/50.13           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 243.59/50.13           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 243.59/50.13           & $i(all_56_23))
% 243.59/50.13    (4)   ~ (all_52_9 = all_6_2)
% 243.59/50.13    (5)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.59/50.13    (6)   ~ (e3 = e0)
% 243.59/50.13    (7)  op(e0, e1) = all_52_11
% 243.59/50.13    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.59/50.13         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.59/50.13    (9)   ~ (all_52_8 = all_52_9)
% 243.59/50.13    (10)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.59/50.13            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.59/50.13            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 243.59/50.13            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 243.59/50.13            = all_56_15 & $i(all_56_15))
% 243.59/50.13    (11)  all_54_13 = all_52_7
% 243.59/50.13    (12)   ~ (all_52_8 = all_6_2)
% 243.59/50.13    (13)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.59/50.13          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.59/50.13    (14)  op(e1, e2) = all_52_6
% 243.59/50.13    (15)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.59/50.13          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.59/50.13    (16)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.59/50.13          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.59/50.13    (17)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.59/50.13              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.59/50.13            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.59/50.13            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.13            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.59/50.13             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.13            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.59/50.13            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.59/50.13            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.59/50.13            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.13            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.59/50.13              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.59/50.13            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.13            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.59/50.13            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.59/50.13            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.59/50.13            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.13            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.59/50.13              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.59/50.13            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.59/50.13            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.59/50.13            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.59/50.13            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.59/50.13            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.13            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.59/50.13              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.59/50.13            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.13            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.13    (18)   ~ (all_52_7 = all_52_11)
% 243.59/50.13    (19)  all_40_2 = all_6_2
% 243.59/50.13    (20)  op(e1, e1) = all_6_2
% 243.59/50.13    (21)   ~ (all_52_1 = all_52_2)
% 243.59/50.13    (22)  op(e1, e0) = all_52_14
% 243.59/50.13    (23)   ~ (all_52_7 = e3)
% 243.59/50.13    (24)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.59/50.13    (25)  all_58_15 = e3
% 243.59/50.14    (26)  op(e0, e3) = all_52_3
% 243.59/50.14    (27)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.59/50.14          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.59/50.14    (28)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.59/50.14          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.59/50.14    (29)   ~ (all_52_2 = all_52_3)
% 243.59/50.14    (30)  op(e2, e2) = e0
% 243.59/50.14    (31)   ~ (all_52_12 = all_52_14)
% 243.59/50.14    (32)  all_54_6 = all_52_9
% 243.59/50.14    (33)   ~ (all_52_12 = all_52_13)
% 243.59/50.14    (34)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.59/50.14          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.59/50.14    (35)  all_54_10 = all_6_2
% 243.59/50.14    (36)  all_54_2 = all_52_8
% 243.59/50.14    (37)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.59/50.14          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.59/50.14    (38)   ~ (all_52_2 = all_52_14)
% 243.59/50.14    (39)   ~ (all_52_1 = all_52_9)
% 243.59/50.14    (40)   ~ (all_52_3 = all_52_7)
% 243.59/50.14    (41)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.59/50.14    (42)  all_54_4 = all_52_1
% 243.59/50.14    (43)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.59/50.14              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.59/50.14                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.59/50.14                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.59/50.14    (44)   ~ (all_52_8 = all_52_12)
% 243.59/50.14    (45)  op(e3, e1) = all_52_8
% 243.59/50.14    (46)  op(e2, e1) = all_52_9
% 243.59/50.14    (47)  all_54_9 = all_52_6
% 243.59/50.14    (48)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.59/50.14          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.59/50.14    (49)   ~ (e3 = e2)
% 243.59/50.14    (50)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.59/50.14          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.59/50.14    (51)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 243.59/50.14            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 243.59/50.14              e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 243.59/50.14    (52)   ~ (all_52_3 = all_52_11)
% 243.59/50.14    (53)   ~ (all_52_14 = all_6_2)
% 243.59/50.14    (54)   ~ (all_6_2 = e0)
% 243.59/50.14    (55)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.59/50.14    (56)   ~ (all_52_6 = all_6_2)
% 243.59/50.14    (57)  all_54_12 = all_52_3
% 243.59/50.14    (58)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.59/50.14    (59)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.59/50.14          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.59/50.14    (60)  op(e3, e0) = all_52_12
% 243.59/50.14    (61)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.59/50.14          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.59/50.14    (62)   ~ (all_52_9 = all_52_13)
% 243.59/50.14    (63)   ~ (all_52_3 = e3)
% 243.59/50.14    (64)   ~ (all_52_1 = e0)
% 243.59/50.14    (65)  all_56_11 = e0
% 243.59/50.14    (66)   ~ (all_52_4 = all_52_12)
% 243.59/50.14    (67)   ~ (all_52_2 = all_6_2)
% 243.59/50.14    (68)   ~ (all_52_6 = all_52_14)
% 243.59/50.14    (69)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.59/50.14    (70)  op(e2, e3) = all_52_1
% 243.59/50.14    (71)  all_36_2 = all_6_2
% 243.59/50.14    (72)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.59/50.14    (73)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.59/50.14    (74)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 243.59/50.14            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 243.59/50.14              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 243.59/50.14    (75)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.59/50.14          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.59/50.14    (76)  op(e0, e2) = all_52_7
% 243.59/50.14    (77)   ~ (all_52_13 = all_52_14)
% 243.59/50.14    (78)  all_54_1 = all_52_4
% 243.59/50.14    (79)   ~ (all_52_4 = e3)
% 243.59/50.14    (80)  op(e3, e2) = all_52_4
% 243.59/50.14    (81)   ~ (all_52_8 = all_52_11)
% 243.59/50.14    (82)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.59/50.14    (83)  all_56_31 = e3
% 243.59/50.14    (84)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.59/50.14          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.59/50.14    (85)  op(e0, e0) = e3
% 243.59/50.14    (86)  op(e2, e1) = e3
% 243.59/50.14    (87)  all_26_2 = e3
% 243.59/50.14    (88)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.59/50.14          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.59/50.14    (89)  all_54_8 = all_52_2
% 243.59/50.14    (90)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.59/50.14          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.59/50.14    (91)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.59/50.14          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.59/50.14    (92)  all_54_3 = all_52_12
% 243.59/50.14    (93)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.14    (94)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.59/50.14          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.59/50.14    (95)  op(e1, e3) = all_52_2
% 243.59/50.14    (96)   ~ (all_52_6 = all_52_7)
% 243.59/50.14    (97)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.59/50.14          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.59/50.14    (98)   ~ (all_52_12 = e3)
% 243.59/50.14    (99)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.59/50.14          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.59/50.14    (100)  all_56_21 = all_6_2
% 243.59/50.14    (101)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.59/50.14           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.59/50.14    (102)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 243.59/50.14             & op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 243.59/50.14             (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 243.59/50.14    (103)  op(e2, e0) = all_52_13
% 243.59/50.14    (104)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.59/50.14           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.59/50.14             e1)
% 243.59/50.14    (105)  all_58_3 = e0
% 243.59/50.14    (106)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.59/50.14           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.59/50.14             e2)
% 243.59/50.14    (107)   ~ (all_52_9 = all_52_11)
% 243.59/50.14    (108)   ~ (all_52_4 = all_52_8)
% 243.59/50.14    (109)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.59/50.14           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.59/50.14    (110)   ~ (all_52_13 = e0)
% 243.59/50.14    (111)   ~ (all_52_4 = all_52_6)
% 243.59/50.14    (112)   ~ (all_52_4 = e0)
% 243.59/50.14    (113)   ~ (all_52_4 = all_52_7)
% 243.59/50.14  
% 243.59/50.14  Begin of proof
% 243.59/50.14  | 
% 243.59/50.14  | BETA: splitting (99) gives:
% 243.59/50.14  | 
% 243.59/50.14  | Case 1:
% 243.59/50.14  | | 
% 243.59/50.14  | |   (114)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 243.59/50.14  | |            e3)
% 243.59/50.14  | | 
% 243.59/50.14  | | REF_CLOSE: (6), (79), (80), (93), (105), (114) are inconsistent by sub-proof
% 243.59/50.14  | |            #1430.
% 243.59/50.14  | | 
% 243.59/50.14  | Case 2:
% 243.59/50.14  | | 
% 243.59/50.14  | |   (115)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 243.59/50.14  | |            e3)
% 243.59/50.14  | | 
% 243.59/50.14  | | BETA: splitting (115) gives:
% 243.59/50.14  | | 
% 243.59/50.14  | | Case 1:
% 243.59/50.14  | | | 
% 243.59/50.14  | | |   (116)  all_58_7 = e3 & op(e1, e2) = e3
% 243.59/50.14  | | | 
% 243.59/50.14  | | | ALPHA: (116) implies:
% 243.59/50.14  | | |   (117)  op(e1, e2) = e3
% 243.59/50.14  | | | 
% 243.59/50.14  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 243.59/50.14  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 243.59/50.14  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 243.59/50.14  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 243.59/50.14  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 243.59/50.14  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 243.59/50.14  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 243.59/50.14  | | |            (75), (76), (77), (78), (80), (81), (82), (83), (84), (85),
% 243.59/50.14  | | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 243.59/50.14  | | |            (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 243.59/50.14  | | |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 243.59/50.14  | | |            (117) are inconsistent by sub-proof #1252.
% 243.59/50.14  | | | 
% 243.59/50.14  | | Case 2:
% 243.59/50.14  | | | 
% 243.59/50.14  | | |   (118)  all_58_13 = e3 & op(e0, e2) = e3
% 243.59/50.14  | | | 
% 243.59/50.14  | | | REF_CLOSE: (23), (76), (93), (118) are inconsistent by sub-proof #1919.
% 243.59/50.14  | | | 
% 243.59/50.14  | | End of split
% 243.59/50.14  | | 
% 243.59/50.14  | End of split
% 243.59/50.14  | 
% 243.59/50.14  End of proof
% 243.59/50.14  
% 243.59/50.14  Sub-proof #1252 shows that the following formulas are inconsistent:
% 243.59/50.14  ----------------------------------------------------------------
% 243.59/50.14    (1)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.59/50.14    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.59/50.14         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.59/50.14    (3)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 243.59/50.14           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 243.59/50.14           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 243.59/50.14           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 243.59/50.14           & $i(all_56_23))
% 243.59/50.14    (4)   ~ (all_52_9 = all_6_2)
% 243.59/50.14    (5)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.59/50.14    (6)  op(e0, e1) = all_52_11
% 243.59/50.14    (7)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.59/50.14         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.59/50.14    (8)   ~ (all_52_8 = all_52_9)
% 243.59/50.14    (9)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.59/50.14           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.59/50.14           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 243.59/50.14         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 243.59/50.14           $i(all_56_15))
% 243.59/50.14    (10)  all_54_13 = all_52_7
% 243.59/50.14    (11)   ~ (all_52_8 = all_6_2)
% 243.59/50.14    (12)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.59/50.14          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.59/50.14    (13)  op(e1, e2) = all_52_6
% 243.59/50.14    (14)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.59/50.14          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.59/50.14    (15)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.59/50.14          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.59/50.14    (16)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.59/50.14              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.59/50.14            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.59/50.14            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.14            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.59/50.14             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.14            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.59/50.14            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.59/50.14            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.59/50.14            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.14            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.59/50.14              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.59/50.14            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.14            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.59/50.14            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.59/50.14            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.59/50.14            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.14            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.59/50.14              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.59/50.14            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.59/50.14            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.59/50.14            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.59/50.14            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.59/50.14            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.14            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.59/50.14              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.59/50.14            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.14            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.14    (17)   ~ (all_52_7 = all_52_11)
% 243.59/50.14    (18)  all_40_2 = all_6_2
% 243.59/50.14    (19)  op(e1, e1) = all_6_2
% 243.59/50.14    (20)   ~ (all_52_1 = all_52_2)
% 243.59/50.14    (21)  op(e1, e0) = all_52_14
% 243.59/50.14    (22)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.59/50.14    (23)  all_58_15 = e3
% 243.59/50.14    (24)  op(e0, e3) = all_52_3
% 243.59/50.14    (25)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.59/50.14          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.59/50.14    (26)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.59/50.14          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.59/50.14    (27)   ~ (all_52_2 = all_52_3)
% 243.59/50.14    (28)  op(e2, e2) = e0
% 243.59/50.14    (29)   ~ (all_52_12 = all_52_14)
% 243.59/50.14    (30)  all_54_6 = all_52_9
% 243.59/50.14    (31)   ~ (all_52_12 = all_52_13)
% 243.59/50.15    (32)  op(e1, e2) = e3
% 243.59/50.15    (33)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.59/50.15          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.59/50.15    (34)  all_54_10 = all_6_2
% 243.59/50.15    (35)  all_54_2 = all_52_8
% 243.59/50.15    (36)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.59/50.15          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.59/50.15    (37)   ~ (all_52_2 = all_52_14)
% 243.59/50.15    (38)   ~ (all_52_1 = all_52_9)
% 243.59/50.15    (39)   ~ (all_52_3 = all_52_7)
% 243.59/50.15    (40)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.59/50.15    (41)  all_54_4 = all_52_1
% 243.59/50.15    (42)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.59/50.15              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.59/50.15                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.59/50.15                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.59/50.15    (43)   ~ (all_52_8 = all_52_12)
% 243.59/50.15    (44)  op(e3, e1) = all_52_8
% 243.59/50.15    (45)  op(e2, e1) = all_52_9
% 243.59/50.15    (46)  all_54_9 = all_52_6
% 243.59/50.15    (47)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.59/50.15          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.59/50.15    (48)   ~ (e3 = e2)
% 243.59/50.15    (49)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.59/50.15          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.59/50.15    (50)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 243.59/50.15            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 243.59/50.15              e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 243.59/50.15    (51)   ~ (all_52_3 = all_52_11)
% 243.59/50.15    (52)   ~ (all_52_14 = all_6_2)
% 243.59/50.15    (53)   ~ (all_6_2 = e0)
% 243.59/50.15    (54)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.59/50.15    (55)   ~ (all_52_6 = all_6_2)
% 243.59/50.15    (56)  all_54_12 = all_52_3
% 243.59/50.15    (57)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.59/50.15    (58)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.59/50.15          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.59/50.15    (59)  op(e3, e0) = all_52_12
% 243.59/50.15    (60)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.59/50.15          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.59/50.15    (61)   ~ (all_52_9 = all_52_13)
% 243.59/50.15    (62)   ~ (all_52_3 = e3)
% 243.59/50.15    (63)   ~ (all_52_1 = e0)
% 243.59/50.15    (64)  all_56_11 = e0
% 243.59/50.15    (65)   ~ (all_52_4 = all_52_12)
% 243.59/50.15    (66)   ~ (all_52_2 = all_6_2)
% 243.59/50.15    (67)   ~ (all_52_6 = all_52_14)
% 243.59/50.15    (68)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.59/50.15    (69)  op(e2, e3) = all_52_1
% 243.59/50.15    (70)  all_36_2 = all_6_2
% 243.59/50.15    (71)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.59/50.15    (72)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.59/50.15    (73)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 243.59/50.15            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 243.59/50.15              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 243.59/50.15    (74)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.59/50.15          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.59/50.15    (75)  op(e0, e2) = all_52_7
% 243.59/50.15    (76)   ~ (all_52_13 = all_52_14)
% 243.59/50.15    (77)  all_54_1 = all_52_4
% 243.59/50.15    (78)  op(e3, e2) = all_52_4
% 243.59/50.15    (79)   ~ (all_52_8 = all_52_11)
% 243.59/50.15    (80)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.59/50.15    (81)  all_56_31 = e3
% 243.59/50.15    (82)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.59/50.15          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.59/50.15    (83)  op(e0, e0) = e3
% 243.59/50.15    (84)  op(e2, e1) = e3
% 243.59/50.15    (85)  all_26_2 = e3
% 243.59/50.15    (86)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.59/50.15          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.59/50.15    (87)  all_54_8 = all_52_2
% 243.59/50.15    (88)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.59/50.15          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.59/50.15    (89)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.59/50.15          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.59/50.15    (90)  all_54_3 = all_52_12
% 243.59/50.15    (91)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.59/50.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.59/50.15    (92)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.59/50.15          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.59/50.15    (93)  op(e1, e3) = all_52_2
% 243.59/50.15    (94)   ~ (all_52_6 = all_52_7)
% 243.59/50.15    (95)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.59/50.15          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.59/50.15    (96)   ~ (all_52_12 = e3)
% 243.59/50.15    (97)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.59/50.15          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.59/50.15    (98)  all_56_21 = all_6_2
% 243.59/50.15    (99)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.59/50.15          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.59/50.15    (100)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 243.59/50.15             & op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 243.59/50.15             (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 243.59/50.15    (101)  op(e2, e0) = all_52_13
% 243.59/50.15    (102)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.59/50.15           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.59/50.15             e1)
% 243.59/50.15    (103)  all_58_3 = e0
% 243.59/50.15    (104)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.59/50.15           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.59/50.15             e2)
% 243.59/50.15    (105)   ~ (all_52_9 = all_52_11)
% 243.59/50.15    (106)   ~ (all_52_4 = all_52_8)
% 243.59/50.15    (107)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.59/50.15           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.59/50.15    (108)   ~ (all_52_13 = e0)
% 243.59/50.15    (109)   ~ (all_52_4 = all_52_6)
% 243.59/50.15    (110)   ~ (all_52_4 = e0)
% 243.59/50.15    (111)   ~ (all_52_4 = all_52_7)
% 243.59/50.15  
% 243.59/50.15  Begin of proof
% 243.59/50.15  | 
% 243.59/50.15  | GROUND_INST: instantiating (91) with all_52_6, e3, e2, e1, simplifying with
% 243.59/50.15  |              (13), (32) gives:
% 243.59/50.15  |   (112)  all_52_6 = e3
% 243.59/50.15  | 
% 243.59/50.15  | GROUND_INST: instantiating (91) with all_52_9, e3, e1, e2, simplifying with
% 243.59/50.15  |              (45), (84) gives:
% 243.59/50.15  |   (113)  all_52_9 = e3
% 243.59/50.15  | 
% 243.59/50.15  | REDUCE: (38), (113) imply:
% 243.59/50.15  |   (114)   ~ (all_52_1 = e3)
% 243.59/50.15  | 
% 243.59/50.15  | REDUCE: (94), (112) imply:
% 243.59/50.15  |   (115)   ~ (all_52_7 = e3)
% 243.59/50.15  | 
% 243.59/50.15  | SIMP: (115) implies:
% 243.59/50.15  |   (116)   ~ (all_52_7 = e3)
% 243.59/50.15  | 
% 243.59/50.15  | REDUCE: (67), (112) imply:
% 243.59/50.15  |   (117)   ~ (all_52_14 = e3)
% 243.59/50.15  | 
% 243.59/50.15  | SIMP: (117) implies:
% 243.59/50.15  |   (118)   ~ (all_52_14 = e3)
% 243.59/50.15  | 
% 243.59/50.15  | REDUCE: (8), (113) imply:
% 243.59/50.15  |   (119)   ~ (all_52_8 = e3)
% 243.59/50.15  | 
% 243.59/50.15  | REDUCE: (61), (113) imply:
% 243.59/50.15  |   (120)   ~ (all_52_13 = e3)
% 243.59/50.15  | 
% 243.59/50.15  | SIMP: (120) implies:
% 243.59/50.15  |   (121)   ~ (all_52_13 = e3)
% 243.59/50.15  | 
% 243.59/50.15  | REDUCE: (4), (113) imply:
% 243.59/50.15  |   (122)   ~ (all_6_2 = e3)
% 243.59/50.15  | 
% 243.59/50.15  | SIMP: (122) implies:
% 243.59/50.15  |   (123)   ~ (all_6_2 = e3)
% 243.59/50.15  | 
% 243.59/50.15  | BETA: splitting (16) gives:
% 243.59/50.15  | 
% 243.59/50.15  | Case 1:
% 243.59/50.15  | | 
% 243.59/50.15  | |   (124)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.59/50.15  | |              = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2)
% 243.59/50.15  | |            = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 243.59/50.15  | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.15  | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 243.59/50.15  | |            = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1)
% 243.59/50.15  | |            &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 243.59/50.15  | |            op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 243.59/50.15  | |              = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.15  | |            (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 243.59/50.15  | |            = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0)
% 243.59/50.15  | |            &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.59/50.15  | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 243.59/50.15  | |              = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.15  | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.59/50.15  | | 
% 243.59/50.15  | | BETA: splitting (124) gives:
% 243.59/50.15  | | 
% 243.59/50.15  | | Case 1:
% 243.59/50.15  | | | 
% 243.59/50.16  | | |   (125)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.16  | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.59/50.16  | | |            op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9
% 243.59/50.16  | | |            = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 243.59/50.16  | | |              = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 243.59/50.16  | | |            e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.16  | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.16  | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.59/50.16  | | | 
% 243.59/50.16  | | | REF_CLOSE: (44), (69), (81), (91), (114), (119), (125) are inconsistent by
% 243.59/50.16  | | |            sub-proof #1316.
% 243.59/50.16  | | | 
% 243.59/50.16  | | Case 2:
% 243.59/50.16  | | | 
% 243.59/50.16  | | |   (126)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 243.59/50.16  | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.16  | | |            op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 243.59/50.16  | | |            = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 243.59/50.16  | | |              = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 243.59/50.16  | | |            e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.59/50.16  | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.16  | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.59/50.16  | | | 
% 243.59/50.16  | | | REF_CLOSE: (24), (62), (81), (91), (126) are inconsistent by sub-proof
% 243.59/50.16  | | |            #1389.
% 243.59/50.16  | | | 
% 243.59/50.16  | | End of split
% 243.59/50.16  | | 
% 243.59/50.16  | Case 2:
% 243.59/50.16  | | 
% 243.59/50.16  | |   (127)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.16  | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.16  | |            op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 243.59/50.16  | |            = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.59/50.16  | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1)
% 243.59/50.16  | |          | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.16  | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.59/50.16  | |            op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27
% 243.59/50.16  | |            = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.59/50.16  | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0)
% 243.59/50.16  | |          | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.16  | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.59/50.16  | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29
% 243.59/50.16  | |            = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.59/50.16  | |              e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.16  | | 
% 243.59/50.16  | | BETA: splitting (127) gives:
% 243.59/50.16  | | 
% 243.59/50.16  | | Case 1:
% 243.59/50.16  | | | 
% 243.59/50.16  | | |   (128)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.16  | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.16  | | |            op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 243.59/50.16  | | |            all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.59/50.16  | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.59/50.16  | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.59/50.16  | | |            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) & 
% 243.59/50.16  | | |            ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.59/50.16  | | | 
% 243.59/50.16  | | | BETA: splitting (128) gives:
% 243.59/50.16  | | | 
% 243.59/50.16  | | | Case 1:
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | |   (129)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.16  | | | |          (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.59/50.16  | | | |          op(e2, e1) = e2 & op(e1, e2) = e2
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | | ALPHA: (129) implies:
% 243.59/50.16  | | | |   (130)  op(e2, e1) = e2
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | | REF_CLOSE: (48), (84), (91), (130) are inconsistent by sub-proof #2256.
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | Case 2:
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | |   (131)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.16  | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.59/50.16  | | | |            & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 243.59/50.16  | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.59/50.16  | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 &
% 243.59/50.16  | | | |            op(e0, e2) = e2)
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | | REF_CLOSE: (4), (34), (45), (53), (64), (71), (91), (98), (123), (131)
% 243.59/50.16  | | | |            are inconsistent by sub-proof #1728.
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | End of split
% 243.59/50.16  | | | 
% 243.59/50.16  | | Case 2:
% 243.59/50.16  | | | 
% 243.59/50.16  | | |   (132)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.16  | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.59/50.16  | | |            op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 243.59/50.16  | | |            all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.59/50.16  | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.59/50.16  | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.59/50.16  | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 243.59/50.16  | | |            ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.16  | | | 
% 243.59/50.16  | | | BETA: splitting (132) gives:
% 243.59/50.16  | | | 
% 243.59/50.16  | | | Case 1:
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | |   (133)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.16  | | | |          (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.59/50.16  | | | |          op(e2, e0) = e0 & op(e0, e2) = e0
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | | ALPHA: (133) implies:
% 243.59/50.16  | | | |   (134)  op(e2, e0) = e0
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | | REF_CLOSE: (91), (101), (108), (134) are inconsistent by sub-proof
% 243.59/50.16  | | | |            #2324.
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | Case 2:
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | |   (135)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.16  | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.59/50.16  | | | |            & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 243.59/50.16  | | | |            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.59/50.16  | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 &
% 243.59/50.16  | | | |            op(e0, e1) = e0)
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | | BETA: splitting (135) gives:
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | | Case 1:
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | |   (136)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.16  | | | | |          (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.59/50.16  | | | | |          & op(e1, e0) = e1 & op(e0, e1) = e1
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | | ALPHA: (136) implies:
% 243.59/50.16  | | | | |   (137)   ~ (all_56_11 = e0)
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | | REDUCE: (64), (137) imply:
% 243.59/50.16  | | | | |   (138)  $false
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | | CLOSE: (138) is inconsistent.
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | Case 2:
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | |   (139)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.59/50.16  | | | | |          (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.59/50.16  | | | | |          & op(e1, e0) = e0 & op(e0, e1) = e0
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | | ALPHA: (139) implies:
% 243.59/50.16  | | | | |   (140)   ~ (all_56_31 = e1)
% 243.59/50.16  | | | | |   (141)   ~ (all_56_21 = e1)
% 243.59/50.16  | | | | |   (142)   ~ (all_56_11 = e1)
% 243.59/50.16  | | | | |   (143)  op(e0, e1) = e0
% 243.59/50.16  | | | | |   (144)  op(e1, e0) = e0
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | | REDUCE: (64), (142) imply:
% 243.59/50.16  | | | | |   (145)   ~ (e1 = e0)
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | | SIMP: (145) implies:
% 243.59/50.16  | | | | |   (146)   ~ (e1 = e0)
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | | REDUCE: (98), (141) imply:
% 243.59/50.16  | | | | |   (147)   ~ (all_6_2 = e1)
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | | REDUCE: (81), (140) imply:
% 243.59/50.16  | | | | |   (148)   ~ (e3 = e1)
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | | BETA: splitting (71) gives:
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | | Case 1:
% 243.59/50.16  | | | | | | 
% 243.59/50.16  | | | | | |   (149)  all_54_10 = e3
% 243.59/50.16  | | | | | | 
% 243.59/50.16  | | | | | | REF_CLOSE: (34), (123), (149) are inconsistent by sub-proof #2313.
% 243.59/50.16  | | | | | | 
% 243.59/50.16  | | | | | Case 2:
% 243.59/50.16  | | | | | | 
% 243.59/50.16  | | | | | |   (150)   ~ (all_54_10 = e3)
% 243.59/50.16  | | | | | |   (151)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.59/50.16  | | | | | | 
% 243.59/50.16  | | | | | | BETA: splitting (151) gives:
% 243.59/50.16  | | | | | | 
% 243.59/50.16  | | | | | | Case 1:
% 243.59/50.16  | | | | | | | 
% 243.59/50.16  | | | | | | |   (152)  all_54_10 = e2
% 243.59/50.16  | | | | | | | 
% 243.59/50.16  | | | | | | | COMBINE_EQS: (34), (152) imply:
% 243.59/50.16  | | | | | | |   (153)  all_6_2 = e2
% 243.59/50.16  | | | | | | | 
% 243.59/50.16  | | | | | | | SIMP: (153) implies:
% 243.59/50.16  | | | | | | |   (154)  all_6_2 = e2
% 243.59/50.16  | | | | | | | 
% 243.59/50.16  | | | | | | | COMBINE_EQS: (70), (154) imply:
% 243.59/50.16  | | | | | | |   (155)  all_36_2 = e2
% 243.59/50.16  | | | | | | | 
% 243.59/50.16  | | | | | | | REDUCE: (147), (154) imply:
% 243.59/50.16  | | | | | | |   (156)   ~ (e2 = e1)
% 243.59/50.16  | | | | | | | 
% 243.59/50.16  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 243.59/50.16  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 243.59/50.16  | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 243.59/50.16  | | | | | | |            (29), (30), (31), (33), (34), (35), (36), (37), (38),
% 243.59/50.16  | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 243.59/50.16  | | | | | | |            (49), (50), (51), (52), (54), (55), (56), (57), (58),
% 243.59/50.16  | | | | | | |            (59), (60), (62), (63), (64), (65), (66), (67), (68),
% 243.59/50.16  | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 243.59/50.16  | | | | | | |            (78), (79), (80), (81), (82), (83), (85), (86), (87),
% 243.59/50.16  | | | | | | |            (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 243.59/50.16  | | | | | | |            (97), (98), (99), (100), (101), (102), (103), (104),
% 243.59/50.16  | | | | | | |            (105), (106), (107), (109), (110), (111), (116), (118),
% 243.59/50.16  | | | | | | |            (121), (123), (143), (144), (146), (148), (155), (156)
% 243.59/50.16  | | | | | | |            are inconsistent by sub-proof #1253.
% 243.59/50.16  | | | | | | | 
% 243.59/50.16  | | | | | | Case 2:
% 243.59/50.16  | | | | | | | 
% 243.59/50.16  | | | | | | |   (157)  all_54_10 = e1 | all_54_10 = e0
% 243.59/50.16  | | | | | | | 
% 243.59/50.16  | | | | | | | REF_CLOSE: (34), (53), (147), (157) are inconsistent by sub-proof
% 243.59/50.16  | | | | | | |            #2282.
% 243.59/50.16  | | | | | | | 
% 243.59/50.16  | | | | | | End of split
% 243.59/50.16  | | | | | | 
% 243.59/50.16  | | | | | End of split
% 243.59/50.16  | | | | | 
% 243.59/50.16  | | | | End of split
% 243.59/50.16  | | | | 
% 243.59/50.16  | | | End of split
% 243.59/50.16  | | | 
% 243.59/50.16  | | End of split
% 243.59/50.16  | | 
% 243.59/50.16  | End of split
% 243.59/50.16  | 
% 243.59/50.16  End of proof
% 243.59/50.16  
% 243.59/50.16  Sub-proof #1253 shows that the following formulas are inconsistent:
% 243.59/50.16  ----------------------------------------------------------------
% 243.59/50.16    (1)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.59/50.16    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.59/50.16         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.59/50.16    (3)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 243.59/50.16           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 243.59/50.16           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 243.59/50.16           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 243.59/50.16           & $i(all_56_23))
% 243.59/50.16    (4)   ~ (all_52_9 = all_6_2)
% 243.59/50.16    (5)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.59/50.16    (6)  op(e1, e0) = e0
% 243.59/50.16    (7)  op(e0, e1) = all_52_11
% 243.59/50.16    (8)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.59/50.16         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.59/50.16    (9)   ~ (all_52_8 = all_52_9)
% 243.59/50.16    (10)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.59/50.16            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.59/50.16            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 243.59/50.16            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 243.59/50.16            = all_56_15 & $i(all_56_15))
% 243.59/50.16    (11)  all_54_13 = all_52_7
% 243.59/50.16    (12)   ~ (all_52_8 = all_6_2)
% 243.59/50.16    (13)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.59/50.16          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.59/50.16    (14)  op(e1, e2) = all_52_6
% 243.59/50.16    (15)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.59/50.16          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.59/50.16    (16)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.59/50.16          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.59/50.16    (17)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.59/50.16              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.59/50.16            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.59/50.16            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.59/50.16            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.59/50.16             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.16            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.59/50.16            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.59/50.16            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.59/50.16            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.16            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.59/50.16              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.59/50.16            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.59/50.16            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.59/50.16            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.59/50.16            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.59/50.16            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.59/50.16            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.59/50.16              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.59/50.16            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.59/50.16            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.59/50.16            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.59/50.16            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.59/50.16            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.59/50.16            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.59/50.16              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.59/50.16            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.59/50.16            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.59/50.16    (18)   ~ (all_52_7 = all_52_11)
% 243.59/50.16    (19)  all_40_2 = all_6_2
% 243.59/50.16    (20)  op(e1, e1) = all_6_2
% 243.59/50.16    (21)   ~ (all_52_1 = all_52_2)
% 243.59/50.16    (22)  op(e1, e0) = all_52_14
% 243.59/50.16    (23)   ~ (all_52_7 = e3)
% 243.59/50.16    (24)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.59/50.16    (25)  all_58_15 = e3
% 243.59/50.16    (26)  op(e0, e3) = all_52_3
% 243.59/50.16    (27)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.59/50.16          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.59/50.16    (28)   ~ (e3 = e1)
% 243.59/50.17    (29)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.59/50.17          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.59/50.17    (30)   ~ (all_52_2 = all_52_3)
% 243.59/50.17    (31)  op(e2, e2) = e0
% 243.59/50.17    (32)   ~ (all_52_12 = all_52_14)
% 243.59/50.17    (33)  all_54_6 = all_52_9
% 243.59/50.17    (34)   ~ (all_52_12 = all_52_13)
% 243.59/50.17    (35)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.59/50.17          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.59/50.17    (36)  all_36_2 = e2
% 243.59/50.17    (37)  all_54_10 = all_6_2
% 243.59/50.17    (38)  all_54_2 = all_52_8
% 243.70/50.17    (39)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.70/50.17          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.70/50.17    (40)   ~ (all_52_2 = all_52_14)
% 243.70/50.17    (41)   ~ (all_52_1 = all_52_9)
% 243.70/50.17    (42)   ~ (all_52_3 = all_52_7)
% 243.70/50.17    (43)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.70/50.17    (44)  all_54_4 = all_52_1
% 243.70/50.17    (45)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.70/50.17              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.70/50.17                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.70/50.17                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.70/50.17    (46)   ~ (all_6_2 = e3)
% 243.70/50.17    (47)   ~ (all_52_8 = all_52_12)
% 243.70/50.17    (48)  op(e3, e1) = all_52_8
% 243.70/50.17    (49)  op(e2, e1) = all_52_9
% 243.70/50.17    (50)  all_54_9 = all_52_6
% 243.70/50.17    (51)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.70/50.17          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.70/50.17    (52)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.70/50.17          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.70/50.17    (53)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 243.70/50.17            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 243.70/50.17              e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 243.70/50.17    (54)   ~ (all_52_3 = all_52_11)
% 243.70/50.17    (55)   ~ (all_52_14 = all_6_2)
% 243.70/50.17    (56)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.70/50.17    (57)   ~ (all_52_6 = all_6_2)
% 243.70/50.17    (58)  all_54_12 = all_52_3
% 243.70/50.17    (59)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.70/50.17    (60)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.70/50.17          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.70/50.17    (61)  op(e3, e0) = all_52_12
% 243.70/50.17    (62)  op(e0, e1) = e0
% 243.70/50.17    (63)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.70/50.17          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.70/50.17    (64)   ~ (all_52_3 = e3)
% 243.70/50.17    (65)   ~ (all_52_1 = e0)
% 243.70/50.17    (66)  all_56_11 = e0
% 243.70/50.17    (67)   ~ (all_52_4 = all_52_12)
% 243.70/50.17    (68)   ~ (all_52_2 = all_6_2)
% 243.70/50.17    (69)   ~ (all_52_6 = all_52_14)
% 243.70/50.17    (70)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.70/50.17    (71)  op(e2, e3) = all_52_1
% 243.70/50.17    (72)   ~ (all_52_14 = e3)
% 243.70/50.17    (73)  all_36_2 = all_6_2
% 243.70/50.17    (74)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.70/50.17    (75)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.70/50.17    (76)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 243.70/50.17            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 243.70/50.17              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 243.70/50.17    (77)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.70/50.17          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.70/50.17    (78)  op(e0, e2) = all_52_7
% 243.70/50.17    (79)   ~ (all_52_13 = all_52_14)
% 243.70/50.17    (80)  all_54_1 = all_52_4
% 243.70/50.17    (81)  op(e3, e2) = all_52_4
% 243.70/50.17    (82)   ~ (all_52_8 = all_52_11)
% 243.70/50.17    (83)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.70/50.17    (84)  all_56_31 = e3
% 243.70/50.17    (85)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.70/50.17          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.70/50.17    (86)  op(e0, e0) = e3
% 243.70/50.17    (87)  all_26_2 = e3
% 243.70/50.17    (88)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.70/50.17          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.70/50.17    (89)  all_54_8 = all_52_2
% 243.70/50.17    (90)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.70/50.17          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.70/50.17    (91)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.70/50.17          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.70/50.17    (92)  all_54_3 = all_52_12
% 243.70/50.17    (93)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.70/50.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.70/50.17    (94)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.70/50.17          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.70/50.17    (95)  op(e1, e3) = all_52_2
% 243.70/50.17    (96)   ~ (all_52_6 = all_52_7)
% 243.70/50.17    (97)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.70/50.17          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.70/50.17    (98)   ~ (all_52_12 = e3)
% 243.70/50.17    (99)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.70/50.17          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.70/50.17    (100)   ~ (e1 = e0)
% 243.70/50.17    (101)  all_56_21 = all_6_2
% 243.70/50.17    (102)   ~ (all_52_13 = e3)
% 243.70/50.17    (103)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.70/50.17           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.70/50.17    (104)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 243.70/50.17             & op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 243.70/50.17             (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 243.70/50.17    (105)  op(e2, e0) = all_52_13
% 243.70/50.17    (106)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.70/50.17           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.70/50.17             e1)
% 243.70/50.17    (107)  all_58_3 = e0
% 243.70/50.17    (108)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.70/50.17           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.70/50.17             e2)
% 243.70/50.17    (109)   ~ (all_52_9 = all_52_11)
% 243.70/50.17    (110)   ~ (all_52_4 = all_52_8)
% 243.70/50.17    (111)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.70/50.17           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.70/50.17    (112)   ~ (all_52_4 = all_52_6)
% 243.70/50.17    (113)   ~ (all_52_4 = e0)
% 243.70/50.17    (114)   ~ (e2 = e1)
% 243.70/50.17    (115)   ~ (all_52_4 = all_52_7)
% 243.70/50.17  
% 243.70/50.17  Begin of proof
% 243.70/50.17  | 
% 243.70/50.17  | BETA: splitting (76) gives:
% 243.70/50.17  | 
% 243.70/50.17  | Case 1:
% 243.70/50.17  | | 
% 243.70/50.17  | |   (116)   ~ (all_36_2 = e2)
% 243.70/50.17  | | 
% 243.70/50.17  | | REDUCE: (36), (116) imply:
% 243.70/50.17  | |   (117)  $false
% 243.70/50.17  | | 
% 243.70/50.17  | | CLOSE: (117) is inconsistent.
% 243.70/50.17  | | 
% 243.70/50.17  | Case 2:
% 243.70/50.17  | | 
% 243.70/50.17  | | 
% 243.70/50.17  | | GROUND_INST: instantiating (93) with all_52_11, e0, e1, e0, simplifying with
% 243.70/50.17  | |              (7), (62) gives:
% 243.70/50.17  | |   (118)  all_52_11 = e0
% 243.70/50.17  | | 
% 243.70/50.17  | | GROUND_INST: instantiating (93) with all_52_14, e0, e0, e1, simplifying with
% 243.70/50.17  | |              (6), (22) gives:
% 243.70/50.17  | |   (119)  all_52_14 = e0
% 243.70/50.17  | | 
% 243.70/50.17  | | REDUCE: (40), (119) imply:
% 243.70/50.17  | |   (120)   ~ (all_52_2 = e0)
% 243.70/50.17  | | 
% 243.70/50.17  | | REDUCE: (54), (118) imply:
% 243.70/50.17  | |   (121)   ~ (all_52_3 = e0)
% 243.70/50.17  | | 
% 243.70/50.17  | | REDUCE: (18), (118) imply:
% 243.70/50.17  | |   (122)   ~ (all_52_7 = e0)
% 243.70/50.17  | | 
% 243.70/50.17  | | REDUCE: (32), (119) imply:
% 243.70/50.17  | |   (123)   ~ (all_52_12 = e0)
% 243.70/50.17  | | 
% 243.70/50.17  | | REDUCE: (79), (119) imply:
% 243.70/50.17  | |   (124)   ~ (all_52_13 = e0)
% 243.70/50.17  | | 
% 243.70/50.17  | | REDUCE: (72), (119) imply:
% 243.70/50.17  | |   (125)   ~ (e3 = e0)
% 243.70/50.17  | | 
% 243.70/50.17  | | SIMP: (125) implies:
% 243.70/50.17  | |   (126)   ~ (e3 = e0)
% 243.70/50.17  | | 
% 243.70/50.17  | | BETA: splitting (60) gives:
% 243.70/50.17  | | 
% 243.70/50.17  | | Case 1:
% 243.70/50.17  | | | 
% 243.70/50.17  | | |   (127)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 243.70/50.17  | | |            e0)
% 243.70/50.17  | | | 
% 243.70/50.17  | | | BETA: splitting (127) gives:
% 243.70/50.17  | | | 
% 243.70/50.17  | | | Case 1:
% 243.70/50.17  | | | | 
% 243.70/50.17  | | | |   (128)  all_58_0 = e0 & op(e3, e3) = e0
% 243.70/50.17  | | | | 
% 243.70/50.17  | | | | ALPHA: (128) implies:
% 243.70/50.17  | | | |   (129)  op(e3, e3) = e0
% 243.70/50.17  | | | | 
% 243.70/50.17  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 243.70/50.17  | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 243.70/50.17  | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 243.70/50.17  | | | |            (33), (34), (35), (37), (38), (39), (40), (41), (42), (43),
% 243.70/50.17  | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 243.70/50.17  | | | |            (54), (55), (56), (57), (58), (59), (60), (61), (63), (64),
% 243.70/50.17  | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 243.70/50.17  | | | |            (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 243.70/50.17  | | | |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 243.70/50.17  | | | |            (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 243.70/50.17  | | | |            (105), (106), (107), (108), (109), (110), (111), (112),
% 243.70/50.17  | | | |            (113), (114), (115), (121), (122), (123), (124), (126), (129)
% 243.70/50.17  | | | |            are inconsistent by sub-proof #1254.
% 243.70/50.17  | | | | 
% 243.70/50.17  | | | Case 2:
% 243.70/50.17  | | | | 
% 243.70/50.17  | | | |   (130)  all_58_2 = e0 & op(e2, e3) = e0
% 243.70/50.17  | | | | 
% 243.70/50.17  | | | | REF_CLOSE: (65), (71), (93), (130) are inconsistent by sub-proof #1985.
% 243.70/50.17  | | | | 
% 243.70/50.17  | | | End of split
% 243.70/50.17  | | | 
% 243.70/50.17  | | Case 2:
% 243.70/50.17  | | | 
% 243.70/50.17  | | |   (131)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 243.70/50.17  | | |            = e0)
% 243.70/50.17  | | | 
% 243.70/50.17  | | | REF_CLOSE: (26), (93), (95), (120), (121), (131) are inconsistent by
% 243.70/50.17  | | |            sub-proof #1939.
% 243.70/50.17  | | | 
% 243.70/50.17  | | End of split
% 243.70/50.17  | | 
% 243.70/50.17  | End of split
% 243.70/50.17  | 
% 243.70/50.17  End of proof
% 243.70/50.17  
% 243.70/50.17  Sub-proof #1254 shows that the following formulas are inconsistent:
% 243.70/50.17  ----------------------------------------------------------------
% 243.70/50.17    (1)   ~ (all_52_3 = e0)
% 243.70/50.17    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.70/50.17    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.70/50.17         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.70/50.17    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 243.70/50.17           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 243.70/50.17           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 243.70/50.17           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 243.70/50.17           & $i(all_56_23))
% 243.70/50.17    (5)   ~ (all_52_9 = all_6_2)
% 243.70/50.17    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.70/50.17    (7)   ~ (e3 = e0)
% 243.70/50.17    (8)  op(e0, e1) = all_52_11
% 243.70/50.17    (9)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.70/50.17         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.70/50.17    (10)   ~ (all_52_8 = all_52_9)
% 243.70/50.17    (11)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.70/50.17            $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 243.70/50.17            = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 243.70/50.17            $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2)
% 243.70/50.17            = all_56_15 & $i(all_56_15))
% 243.70/50.17    (12)  all_54_13 = all_52_7
% 243.70/50.17    (13)   ~ (all_52_8 = all_6_2)
% 243.70/50.17    (14)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.70/50.17          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.70/50.17    (15)  op(e1, e2) = all_52_6
% 243.70/50.17    (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.70/50.17          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.70/50.17    (17)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.70/50.17          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.70/50.18    (18)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.70/50.18              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.70/50.18            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 243.70/50.18            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.70/50.18            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 243.70/50.18             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.70/50.18            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.70/50.18            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.70/50.18            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 243.70/50.18            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.70/50.18            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.70/50.18              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.70/50.18            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.70/50.18            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 243.70/50.18            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.70/50.18            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 243.70/50.18            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.70/50.18            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.70/50.18              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.70/50.18            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.70/50.18            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.70/50.18            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.70/50.18            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 243.70/50.18            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.70/50.18            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.70/50.18              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.70/50.18            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.70/50.18            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.70/50.18    (19)   ~ (all_52_7 = all_52_11)
% 243.70/50.18    (20)   ~ (all_52_12 = e0)
% 243.70/50.18    (21)  all_40_2 = all_6_2
% 243.70/50.18    (22)  op(e1, e1) = all_6_2
% 243.70/50.18    (23)   ~ (all_52_1 = all_52_2)
% 243.70/50.18    (24)  op(e1, e0) = all_52_14
% 243.70/50.18    (25)   ~ (all_52_7 = e3)
% 243.70/50.18    (26)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.70/50.18    (27)  all_58_15 = e3
% 243.70/50.18    (28)  op(e0, e3) = all_52_3
% 243.70/50.18    (29)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.70/50.18          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.70/50.18    (30)   ~ (e3 = e1)
% 243.70/50.18    (31)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.70/50.18          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.70/50.18    (32)   ~ (all_52_2 = all_52_3)
% 243.70/50.18    (33)  op(e2, e2) = e0
% 243.70/50.18    (34)   ~ (all_52_12 = all_52_14)
% 243.70/50.18    (35)  all_54_6 = all_52_9
% 243.70/50.18    (36)   ~ (all_52_12 = all_52_13)
% 243.70/50.18    (37)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.70/50.18          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.70/50.18    (38)  all_54_10 = all_6_2
% 243.70/50.18    (39)  all_54_2 = all_52_8
% 243.70/50.18    (40)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.70/50.18          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.70/50.18    (41)   ~ (all_52_2 = all_52_14)
% 243.70/50.18    (42)   ~ (all_52_1 = all_52_9)
% 243.70/50.18    (43)   ~ (all_52_3 = all_52_7)
% 243.70/50.18    (44)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.70/50.18    (45)  all_54_4 = all_52_1
% 243.70/50.18    (46)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.70/50.18              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.70/50.18                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.70/50.18                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.70/50.18    (47)   ~ (all_6_2 = e3)
% 243.70/50.18    (48)   ~ (all_52_8 = all_52_12)
% 243.70/50.18    (49)  op(e3, e1) = all_52_8
% 243.70/50.18    (50)  op(e2, e1) = all_52_9
% 243.70/50.18    (51)  all_54_9 = all_52_6
% 243.70/50.18    (52)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.70/50.18          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.70/50.18    (53)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.70/50.18          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.70/50.18    (54)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 243.70/50.18            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 243.70/50.18              e1) & op(e0, e3) = all_26_1 & $i(all_26_1))
% 243.70/50.18    (55)   ~ (all_52_3 = all_52_11)
% 243.70/50.18    (56)   ~ (all_52_14 = all_6_2)
% 243.70/50.18    (57)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.70/50.18    (58)   ~ (all_52_6 = all_6_2)
% 243.70/50.18    (59)  all_54_12 = all_52_3
% 243.70/50.18    (60)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.70/50.18    (61)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.70/50.18          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.70/50.18    (62)  op(e3, e0) = all_52_12
% 243.70/50.18    (63)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.70/50.18          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.70/50.18    (64)   ~ (all_52_3 = e3)
% 243.70/50.18    (65)   ~ (all_52_1 = e0)
% 243.70/50.18    (66)  all_56_11 = e0
% 243.70/50.18    (67)   ~ (all_52_4 = all_52_12)
% 243.70/50.18    (68)   ~ (all_52_2 = all_6_2)
% 243.70/50.18    (69)   ~ (all_52_6 = all_52_14)
% 243.70/50.18    (70)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 243.70/50.18    (71)  op(e2, e3) = all_52_1
% 243.70/50.18    (72)   ~ (all_52_14 = e3)
% 243.70/50.18    (73)  all_36_2 = all_6_2
% 243.70/50.18    (74)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.70/50.18    (75)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.70/50.18    (76)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 243.70/50.18            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 243.70/50.18              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 243.70/50.18    (77)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.70/50.18          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.70/50.18    (78)  op(e0, e2) = all_52_7
% 243.70/50.18    (79)   ~ (all_52_13 = all_52_14)
% 243.70/50.18    (80)  all_54_1 = all_52_4
% 243.70/50.18    (81)  op(e3, e2) = all_52_4
% 243.70/50.18    (82)   ~ (all_52_8 = all_52_11)
% 243.70/50.18    (83)   ~ (all_52_7 = e0)
% 243.70/50.18    (84)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.70/50.18    (85)  all_56_31 = e3
% 243.70/50.18    (86)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.70/50.18          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.70/50.18    (87)  op(e0, e0) = e3
% 243.70/50.18    (88)  all_26_2 = e3
% 243.70/50.18    (89)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.70/50.18          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.70/50.18    (90)  all_54_8 = all_52_2
% 243.70/50.18    (91)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.70/50.18          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.70/50.18    (92)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.70/50.18          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.70/50.18    (93)  all_54_3 = all_52_12
% 243.70/50.18    (94)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.70/50.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.70/50.18    (95)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.70/50.18          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.70/50.18    (96)   ~ (all_52_6 = all_52_7)
% 243.70/50.18    (97)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.70/50.18          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.70/50.18    (98)   ~ (all_52_12 = e3)
% 243.70/50.18    (99)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.70/50.18          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.70/50.18    (100)   ~ (e1 = e0)
% 243.70/50.18    (101)  all_56_21 = all_6_2
% 243.70/50.18    (102)  op(e3, e3) = e0
% 243.70/50.18    (103)   ~ (all_52_13 = e3)
% 243.70/50.18    (104)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.70/50.18           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.70/50.18    (105)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 243.70/50.18             & op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 243.70/50.18             (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 243.70/50.18    (106)  op(e2, e0) = all_52_13
% 243.70/50.18    (107)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.70/50.18           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.70/50.18             e1)
% 243.70/50.18    (108)  all_58_3 = e0
% 243.70/50.18    (109)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.70/50.18           | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.70/50.18             e2)
% 243.70/50.18    (110)   ~ (all_52_9 = all_52_11)
% 243.70/50.18    (111)   ~ (all_52_4 = all_52_8)
% 243.70/50.18    (112)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.70/50.18           (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.70/50.18    (113)   ~ (all_52_13 = e0)
% 243.70/50.18    (114)   ~ (all_52_4 = all_52_6)
% 243.70/50.18    (115)   ~ (all_52_4 = e0)
% 243.70/50.18    (116)   ~ (e2 = e1)
% 243.70/50.18    (117)   ~ (all_52_4 = all_52_7)
% 243.70/50.18  
% 243.70/50.18  Begin of proof
% 243.70/50.18  | 
% 243.70/50.18  | BETA: splitting (46) gives:
% 243.70/50.18  | 
% 243.70/50.18  | Case 1:
% 243.70/50.18  | | 
% 243.70/50.18  | |   (118)  all_58_15 = e0 & op(e0, e0) = e0
% 243.70/50.18  | | 
% 243.70/50.18  | | ALPHA: (118) implies:
% 243.70/50.18  | |   (119)  op(e0, e0) = e0
% 243.70/50.18  | | 
% 243.70/50.18  | | REF_CLOSE: (7), (87), (94), (119) are inconsistent by sub-proof #2079.
% 243.70/50.18  | | 
% 243.70/50.18  | Case 2:
% 243.70/50.18  | | 
% 243.70/50.18  | |   (120)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.70/50.18  | |              e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 243.70/50.18  | |              op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.70/50.18  | |            (all_58_14 = e0 & op(e0, e1) = e0))
% 243.70/50.18  | | 
% 243.70/50.18  | | ALPHA: (120) implies:
% 243.70/50.18  | |   (121)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 243.70/50.18  | |            e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.70/50.18  | |   (122)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.70/50.18  | |            e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.70/50.18  | | 
% 243.70/50.18  | | BETA: splitting (121) gives:
% 243.70/50.18  | | 
% 243.70/50.18  | | Case 1:
% 243.70/50.18  | | | 
% 243.70/50.18  | | |   (123)  all_58_12 = e0 & op(e0, e3) = e0
% 243.70/50.18  | | | 
% 243.70/50.18  | | | ALPHA: (123) implies:
% 243.70/50.18  | | |   (124)  op(e0, e3) = e0
% 243.70/50.18  | | | 
% 243.70/50.18  | | | REF_CLOSE: (1), (28), (94), (124) are inconsistent by sub-proof #2331.
% 243.70/50.18  | | | 
% 243.70/50.18  | | Case 2:
% 243.70/50.18  | | | 
% 243.70/50.18  | | |   (125)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 243.70/50.18  | | |            = e0)
% 243.70/50.18  | | | 
% 243.70/50.18  | | | BETA: splitting (125) gives:
% 243.70/50.18  | | | 
% 243.70/50.18  | | | Case 1:
% 243.70/50.18  | | | | 
% 243.70/50.18  | | | |   (126)  all_58_13 = e0 & op(e0, e2) = e0
% 243.70/50.18  | | | | 
% 243.70/50.18  | | | | ALPHA: (126) implies:
% 243.70/50.18  | | | |   (127)  op(e0, e2) = e0
% 243.70/50.18  | | | | 
% 243.70/50.18  | | | | REF_CLOSE: (78), (83), (94), (127) are inconsistent by sub-proof #2252.
% 243.70/50.18  | | | | 
% 243.70/50.18  | | | Case 2:
% 243.70/50.18  | | | | 
% 243.70/50.18  | | | |   (128)  all_58_14 = e0 & op(e0, e1) = e0
% 243.70/50.18  | | | | 
% 243.70/50.18  | | | | ALPHA: (128) implies:
% 243.70/50.18  | | | |   (129)  all_58_14 = e0
% 243.70/50.18  | | | |   (130)  op(e0, e1) = e0
% 243.70/50.18  | | | | 
% 243.70/50.18  | | | | BETA: splitting (122) gives:
% 243.70/50.18  | | | | 
% 243.70/50.18  | | | | Case 1:
% 243.70/50.18  | | | | | 
% 243.70/50.18  | | | | |   (131)  all_58_9 = e0 & op(e3, e0) = e0
% 243.70/50.18  | | | | | 
% 243.70/50.18  | | | | | ALPHA: (131) implies:
% 243.70/50.18  | | | | |   (132)  op(e3, e0) = e0
% 243.70/50.18  | | | | | 
% 243.70/50.18  | | | | | GROUND_INST: instantiating (94) with all_52_12, e0, e0, e3,
% 243.70/50.18  | | | | |              simplifying with (62), (132) gives:
% 243.70/50.18  | | | | |   (133)  all_52_12 = e0
% 243.70/50.18  | | | | | 
% 243.70/50.18  | | | | | REDUCE: (20), (133) imply:
% 243.70/50.18  | | | | |   (134)  $false
% 243.70/50.18  | | | | | 
% 243.70/50.18  | | | | | CLOSE: (134) is inconsistent.
% 243.70/50.18  | | | | | 
% 243.70/50.18  | | | | Case 2:
% 243.70/50.18  | | | | | 
% 243.70/50.18  | | | | |   (135)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 243.70/50.18  | | | | |              e0) = e0)
% 243.70/50.18  | | | | | 
% 243.70/50.18  | | | | | BETA: splitting (135) gives:
% 243.70/50.18  | | | | | 
% 243.70/50.18  | | | | | Case 1:
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | |   (136)  all_58_10 = e0 & op(e2, e0) = e0
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | ALPHA: (136) implies:
% 243.70/50.18  | | | | | |   (137)  op(e2, e0) = e0
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | REF_CLOSE: (94), (106), (113), (137) are inconsistent by sub-proof
% 243.70/50.18  | | | | | |            #2324.
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | Case 2:
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | |   (138)  all_58_11 = e0 & op(e1, e0) = e0
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | ALPHA: (138) implies:
% 243.70/50.18  | | | | | |   (139)  all_58_11 = e0
% 243.70/50.18  | | | | | |   (140)  op(e1, e0) = e0
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | GROUND_INST: instantiating (94) with all_52_11, e0, e1, e0,
% 243.70/50.18  | | | | | |              simplifying with (8), (130) gives:
% 243.70/50.18  | | | | | |   (141)  all_52_11 = e0
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | GROUND_INST: instantiating (94) with all_52_14, e0, e0, e1,
% 243.70/50.18  | | | | | |              simplifying with (24), (140) gives:
% 243.70/50.18  | | | | | |   (142)  all_52_14 = e0
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | REDUCE: (41), (142) imply:
% 243.70/50.18  | | | | | |   (143)   ~ (all_52_2 = e0)
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | REDUCE: (69), (142) imply:
% 243.70/50.18  | | | | | |   (144)   ~ (all_52_6 = e0)
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | REDUCE: (82), (141) imply:
% 243.70/50.18  | | | | | |   (145)   ~ (all_52_8 = e0)
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | REDUCE: (110), (141) imply:
% 243.70/50.18  | | | | | |   (146)   ~ (all_52_9 = e0)
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | REDUCE: (56), (142) imply:
% 243.70/50.18  | | | | | |   (147)   ~ (all_6_2 = e0)
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | SIMP: (147) implies:
% 243.70/50.18  | | | | | |   (148)   ~ (all_6_2 = e0)
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | REDUCE: (72), (142) imply:
% 243.70/50.18  | | | | | |   (149)   ~ (e3 = e0)
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | BETA: splitting (54) gives:
% 243.70/50.18  | | | | | | 
% 243.70/50.18  | | | | | | Case 1:
% 243.70/50.18  | | | | | | | 
% 243.70/50.18  | | | | | | |   (150)   ~ (all_26_2 = e3)
% 243.70/50.18  | | | | | | | 
% 243.70/50.18  | | | | | | | REDUCE: (88), (150) imply:
% 243.70/50.18  | | | | | | |   (151)  $false
% 243.70/50.18  | | | | | | | 
% 243.70/50.18  | | | | | | | CLOSE: (151) is inconsistent.
% 243.70/50.18  | | | | | | | 
% 243.70/50.18  | | | | | | Case 2:
% 243.70/50.18  | | | | | | | 
% 243.70/50.18  | | | | | | |   (152)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 &
% 243.70/50.18  | | | | | | |            op(e0, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) |
% 243.70/50.18  | | | | | | |          ( ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 &
% 243.70/50.18  | | | | | | |            $i(all_26_1))
% 243.70/50.18  | | | | | | | 
% 243.70/50.18  | | | | | | | BETA: splitting (76) gives:
% 243.70/50.18  | | | | | | | 
% 243.70/50.18  | | | | | | | Case 1:
% 243.70/50.18  | | | | | | | | 
% 243.70/50.18  | | | | | | | |   (153)   ~ (all_36_2 = e2)
% 243.70/50.18  | | | | | | | | 
% 243.70/50.18  | | | | | | | | REDUCE: (73), (153) imply:
% 243.70/50.18  | | | | | | | |   (154)   ~ (all_6_2 = e2)
% 243.70/50.18  | | | | | | | | 
% 243.70/50.18  | | | | | | | | BETA: splitting (74) gives:
% 243.70/50.18  | | | | | | | | 
% 243.70/50.18  | | | | | | | | Case 1:
% 243.70/50.18  | | | | | | | | | 
% 243.70/50.18  | | | | | | | | |   (155)  all_54_10 = e3
% 243.70/50.18  | | | | | | | | | 
% 243.70/50.18  | | | | | | | | | REF_CLOSE: (38), (47), (155) are inconsistent by sub-proof
% 243.70/50.18  | | | | | | | | |            #2313.
% 243.70/50.18  | | | | | | | | | 
% 243.70/50.18  | | | | | | | | Case 2:
% 243.70/50.18  | | | | | | | | | 
% 243.70/50.18  | | | | | | | | |   (156)   ~ (all_54_10 = e3)
% 243.70/50.18  | | | | | | | | |   (157)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.70/50.18  | | | | | | | | | 
% 243.70/50.18  | | | | | | | | | BETA: splitting (157) gives:
% 243.70/50.18  | | | | | | | | | 
% 243.70/50.18  | | | | | | | | | Case 1:
% 243.70/50.18  | | | | | | | | | | 
% 243.70/50.18  | | | | | | | | | |   (158)  all_54_10 = e2
% 243.70/50.18  | | | | | | | | | | 
% 243.70/50.18  | | | | | | | | | | REF_CLOSE: (38), (154), (158) are inconsistent by sub-proof
% 243.70/50.18  | | | | | | | | | |            #2312.
% 243.70/50.18  | | | | | | | | | | 
% 243.70/50.18  | | | | | | | | | Case 2:
% 243.70/50.18  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | |   (159)  all_54_10 = e1 | all_54_10 = e0
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | BETA: splitting (159) gives:
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | |   (160)  all_54_10 = e1
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | COMBINE_EQS: (38), (160) imply:
% 243.70/50.19  | | | | | | | | | | |   (161)  all_6_2 = e1
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | SIMP: (161) implies:
% 243.70/50.19  | | | | | | | | | | |   (162)  all_6_2 = e1
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | COMBINE_EQS: (101), (162) imply:
% 243.70/50.19  | | | | | | | | | | |   (163)  all_56_21 = e1
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | REDUCE: (13), (162) imply:
% 243.70/50.19  | | | | | | | | | | |   (164)   ~ (all_52_8 = e1)
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | BETA: splitting (18) gives:
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | |   (165)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 243.70/50.19  | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.70/50.19  | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.70/50.19  | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.70/50.19  | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.70/50.19  | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.70/50.19  | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 243.70/50.19  | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 243.70/50.19  | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.70/50.19  | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 243.70/50.19  | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 243.70/50.19  | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.70/50.19  | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | BETA: splitting (165) gives:
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | |   (166)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 243.70/50.19  | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.70/50.19  | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.70/50.19  | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.70/50.19  | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.70/50.19  | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.70/50.19  | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 243.70/50.19  | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.70/50.19  | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.70/50.19  | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 243.70/50.19  | | | | | | | | | | | | |            = e3)
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | BETA: splitting (166) gives:
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | |   (167)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 243.70/50.19  | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.70/50.19  | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.70/50.19  | | | | | | | | | | | | | |          e3
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | ALPHA: (167) implies:
% 243.70/50.19  | | | | | | | | | | | | | |   (168)  op(e2, e3) = e3
% 243.70/50.19  | | | | | | | | | | | | | |   (169)  op(e3, e2) = e3
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with all_52_1, e3, e3, e2,
% 243.70/50.19  | | | | | | | | | | | | | |              simplifying with (71), (168) gives:
% 243.70/50.19  | | | | | | | | | | | | | |   (170)  all_52_1 = e3
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with all_52_4, e3, e2, e3,
% 243.70/50.19  | | | | | | | | | | | | | |              simplifying with (81), (169) gives:
% 243.70/50.19  | | | | | | | | | | | | | |   (171)  all_52_4 = e3
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | REDUCE: (42), (170) imply:
% 243.70/50.19  | | | | | | | | | | | | | |   (172)   ~ (all_52_9 = e3)
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | SIMP: (172) implies:
% 243.70/50.19  | | | | | | | | | | | | | |   (173)   ~ (all_52_9 = e3)
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | REDUCE: (111), (171) imply:
% 243.70/50.19  | | | | | | | | | | | | | |   (174)   ~ (all_52_8 = e3)
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | SIMP: (174) implies:
% 243.70/50.19  | | | | | | | | | | | | | |   (175)   ~ (all_52_8 = e3)
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | REF_CLOSE: (7), (22), (47), (49), (50), (77), (94), (130),
% 243.70/50.19  | | | | | | | | | | | | | |            (173), (175) are inconsistent by sub-proof #1626.
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | |   (176)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 243.70/50.19  | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.70/50.19  | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.70/50.19  | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 243.70/50.19  | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.70/50.19  | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.70/50.19  | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | REF_CLOSE: (85), (163), (176) are inconsistent by sub-proof
% 243.70/50.19  | | | | | | | | | | | | | |            #1280.
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | End of split
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | |   (177)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 243.70/50.19  | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.70/50.19  | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 243.70/50.19  | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 243.70/50.19  | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.70/50.19  | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.70/50.19  | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 243.70/50.19  | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.70/50.19  | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.70/50.19  | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 243.70/50.19  | | | | | | | | | | | | |            = e0)
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | REF_CLOSE: (1), (28), (49), (64), (94), (164), (177) are
% 243.70/50.19  | | | | | | | | | | | | |            inconsistent by sub-proof #1313.
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | End of split
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | |   (178)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.70/50.19  | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.70/50.19  | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.70/50.19  | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.70/50.19  | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.70/50.19  | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.70/50.19  | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 243.70/50.19  | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 243.70/50.19  | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.70/50.19  | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 243.70/50.19  | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 243.70/50.19  | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.70/50.19  | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 243.70/50.19  | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | BETA: splitting (178) gives:
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | |   (179)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.70/50.19  | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.70/50.19  | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.70/50.19  | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.70/50.19  | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.70/50.19  | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.70/50.19  | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 243.70/50.19  | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.70/50.19  | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.70/50.19  | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 243.70/50.19  | | | | | | | | | | | | |            = e2)
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | REF_CLOSE: (5), (38), (50), (66), (94), (148), (159), (163),
% 243.70/50.19  | | | | | | | | | | | | |            (179) are inconsistent by sub-proof #1279.
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | |   (180)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.70/50.19  | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.70/50.19  | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 243.70/50.19  | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 243.70/50.19  | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.70/50.19  | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.70/50.19  | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 243.70/50.19  | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.70/50.19  | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.70/50.19  | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 243.70/50.19  | | | | | | | | | | | | |            = e0)
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | BETA: splitting (180) gives:
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | |   (181)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.70/50.19  | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.70/50.19  | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.70/50.19  | | | | | | | | | | | | | |            e2) = e0
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | ALPHA: (181) implies:
% 243.70/50.19  | | | | | | | | | | | | | |   (182)  op(e2, e0) = e0
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | REF_CLOSE: (94), (106), (113), (182) are inconsistent by
% 243.70/50.19  | | | | | | | | | | | | | |            sub-proof #2324.
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | |   (183)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.70/50.19  | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.70/50.19  | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.70/50.19  | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.70/50.19  | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.70/50.19  | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.70/50.19  | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | |   (184)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.70/50.19  | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 243.70/50.19  | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 243.70/50.19  | | | | | | | | | | | | | | |            e1) = e1
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 243.70/50.19  | | | | | | | | | | | | | | |   (185)  op(e1, e0) = e1
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | REF_CLOSE: (94), (100), (140), (185) are inconsistent by
% 243.70/50.19  | | | | | | | | | | | | | | |            sub-proof #2284.
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | |   (186)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 243.70/50.19  | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.70/50.19  | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 243.70/50.19  | | | | | | | | | | | | | | |            e1) = e0
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 243.70/50.19  | | | | | | | | | | | | | | |   (187)   ~ (all_56_21 = e1)
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | REDUCE: (163), (187) imply:
% 243.70/50.19  | | | | | | | | | | | | | | |   (188)  $false
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent.
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | End of split
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | End of split
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | End of split
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | End of split
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | |   (189)  all_54_10 = e0
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | REF_CLOSE: (38), (148), (189) are inconsistent by sub-proof
% 243.70/50.19  | | | | | | | | | | |            #2303.
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | End of split
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | End of split
% 243.70/50.19  | | | | | | | | | 
% 243.70/50.19  | | | | | | | | End of split
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | |   (190)  all_36_2 = e2
% 243.70/50.19  | | | | | | | |   (191)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 243.70/50.19  | | | | | | | |            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1))
% 243.70/50.19  | | | | | | | |          | ( ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 243.70/50.19  | | | | | | | |            $i(all_36_1))
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | COMBINE_EQS: (73), (190) imply:
% 243.70/50.19  | | | | | | | |   (192)  all_6_2 = e2
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | SIMP: (192) implies:
% 243.70/50.19  | | | | | | | |   (193)  all_6_2 = e2
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | COMBINE_EQS: (21), (193) imply:
% 243.70/50.19  | | | | | | | |   (194)  all_40_2 = e2
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | COMBINE_EQS: (101), (193) imply:
% 243.70/50.19  | | | | | | | |   (195)  all_56_21 = e2
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | REDUCE: (68), (193) imply:
% 243.70/50.19  | | | | | | | |   (196)   ~ (all_52_2 = e2)
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | REDUCE: (58), (193) imply:
% 243.70/50.19  | | | | | | | |   (197)   ~ (all_52_6 = e2)
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | REDUCE: (13), (193) imply:
% 243.70/50.19  | | | | | | | |   (198)   ~ (all_52_8 = e2)
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | REDUCE: (5), (193) imply:
% 243.70/50.19  | | | | | | | |   (199)   ~ (all_52_9 = e2)
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | REDUCE: (47), (193) imply:
% 243.70/50.19  | | | | | | | |   (200)   ~ (e3 = e2)
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | SIMP: (200) implies:
% 243.70/50.19  | | | | | | | |   (201)   ~ (e3 = e2)
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | REDUCE: (148), (193) imply:
% 243.70/50.19  | | | | | | | |   (202)   ~ (e2 = e0)
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | REDUCE: (22), (193) imply:
% 243.70/50.19  | | | | | | | |   (203)  op(e1, e1) = e2
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | BETA: splitting (92) gives:
% 243.70/50.19  | | | | | | | | 
% 243.70/50.19  | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | 
% 243.70/50.19  | | | | | | | | |   (204)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 243.70/50.19  | | | | | | | | |            op(e1, e2) = e2)
% 243.70/50.19  | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | BETA: splitting (204) gives:
% 243.70/50.19  | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | |   (205)  all_58_6 = e2 & op(e1, e3) = e2
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | ALPHA: (205) implies:
% 243.70/50.19  | | | | | | | | | |   (206)  all_58_6 = e2
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | REF_CLOSE: (7), (9), (15), (24), (28), (29), (30), (31),
% 243.70/50.19  | | | | | | | | | |            (33), (40), (50), (53), (63), (64), (72), (77),
% 243.70/50.19  | | | | | | | | | |            (94), (100), (102), (104), (108), (112), (116),
% 243.70/50.19  | | | | | | | | | |            (129), (144), (199), (201), (202), (203), (206)
% 243.70/50.19  | | | | | | | | | |            are inconsistent by sub-proof #1274.
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | |   (207)  all_58_7 = e2 & op(e1, e2) = e2
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | ALPHA: (207) implies:
% 243.70/50.19  | | | | | | | | | |   (208)  all_58_7 = e2
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | REF_CLOSE: (3), (7), (9), (15), (24), (25), (27), (28), (29),
% 243.70/50.19  | | | | | | | | | |            (30), (33), (40), (50), (52), (53), (61), (63),
% 243.70/50.19  | | | | | | | | | |            (64), (65), (71), (72), (77), (78), (86), (87),
% 243.70/50.19  | | | | | | | | | |            (89), (91), (92), (94), (95), (97), (99), (100),
% 243.70/50.19  | | | | | | | | | |            (102), (104), (108), (109), (112), (116), (129),
% 243.70/50.19  | | | | | | | | | |            (130), (139), (144), (199), (201), (202), (203),
% 243.70/50.19  | | | | | | | | | |            (208) are inconsistent by sub-proof #1261.
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | End of split
% 243.70/50.19  | | | | | | | | | 
% 243.70/50.19  | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | 
% 243.70/50.19  | | | | | | | | |   (209)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 243.70/50.19  | | | | | | | | |            op(e1, e0) = e2)
% 243.70/50.19  | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | BETA: splitting (209) gives:
% 243.70/50.19  | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | |   (210)  all_58_8 = e2 & op(e1, e1) = e2
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | ALPHA: (210) implies:
% 243.70/50.19  | | | | | | | | | |   (211)  all_58_8 = e2
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | BETA: splitting (105) gives:
% 243.70/50.19  | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | |   (212)   ~ (all_40_2 = e2)
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | REDUCE: (194), (212) imply:
% 243.70/50.19  | | | | | | | | | | |   (213)  $false
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | |   (214)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0
% 243.70/50.19  | | | | | | | | | | |            & op(e1, e2) = all_40_1 & $i(all_40_0) &
% 243.70/50.19  | | | | | | | | | | |            $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2)
% 243.70/50.19  | | | | | | | | | | |            = all_40_1 & $i(all_40_1))
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | BETA: splitting (2) gives:
% 243.70/50.19  | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | |   (215)  all_54_12 = e3
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | REF_CLOSE: (59), (64), (215) are inconsistent by sub-proof
% 243.70/50.19  | | | | | | | | | | | |            #2266.
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | |   (216)   ~ (all_54_12 = e3)
% 243.70/50.19  | | | | | | | | | | | |   (217)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | BETA: splitting (44) gives:
% 243.70/50.19  | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | |   (218)  all_54_3 = e3
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | REF_CLOSE: (93), (98), (218) are inconsistent by sub-proof
% 243.70/50.19  | | | | | | | | | | | | |            #2057.
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | |   (219)   ~ (all_54_3 = e3)
% 243.70/50.19  | | | | | | | | | | | | |   (220)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | BETA: splitting (70) gives:
% 243.70/50.19  | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | |   (221)  all_54_6 = e3
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | COMBINE_EQS: (35), (221) imply:
% 243.70/50.19  | | | | | | | | | | | | | |   (222)  all_52_9 = e3
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | REDUCE: (42), (222) imply:
% 243.70/50.19  | | | | | | | | | | | | | |   (223)   ~ (all_52_1 = e3)
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | REDUCE: (10), (222) imply:
% 243.70/50.19  | | | | | | | | | | | | | |   (224)   ~ (all_52_8 = e3)
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 243.70/50.19  | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | |   (225)  all_54_2 = e3
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | REF_CLOSE: (39), (224), (225) are inconsistent by sub-proof
% 243.70/50.19  | | | | | | | | | | | | | | |            #1987.
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | |   (226)   ~ (all_54_2 = e3)
% 243.70/50.19  | | | | | | | | | | | | | | |   (227)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 243.70/50.19  | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | |   (228)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 243.70/50.19  | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 243.70/50.19  | | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (71), (94), (102), (223), (228) are
% 243.70/50.19  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1445.
% 243.70/50.19  | | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | Case 2:
% 243.70/50.19  | | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | |   (229)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 243.70/50.19  | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 243.70/50.19  | | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 243.70/50.19  | | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | | Case 1:
% 243.70/50.19  | | | | | | | | | | | | | | | | | 
% 243.70/50.19  | | | | | | | | | | | | | | | | |   (230)  all_58_6 = e3 & op(e1, e3) = e3
% 243.70/50.19  | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 243.70/50.20  | | | | | | | | | | | | | | | | |   (231)  all_58_6 = e3
% 243.70/50.20  | | | | | | | | | | | | | | | | |   (232)  op(e1, e3) = e3
% 243.70/50.20  | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 243.70/50.20  | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | Case 1:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | |   (233)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 243.70/50.20  | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 243.70/50.20  | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | Case 1:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | |   (234)  all_58_0 = e3 & op(e3, e3) = e3
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | |   (235)  op(e3, e3) = e3
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (94), (102), (235) are inconsistent by
% 243.70/50.20  | | | | | | | | | | | | | | | | | | |            sub-proof #1940.
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | Case 2:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | |   (236)  all_58_1 = e3 & op(e3, e2) = e3
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | |   (237)  all_58_1 = e3
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | |   (238)  all_54_2 = e2
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (198), (238) are inconsistent by sub-proof
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | |            #1986.
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | |   (239)   ~ (all_54_2 = e2)
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | |   (240)  all_54_2 = e1 | all_54_2 = e0
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | |   (241)  all_54_2 = e1
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (241) imply:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | |   (242)  all_52_8 = e1
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | SIMP: (242) implies:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | |   (243)  all_52_8 = e1
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (243) imply:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | |   (244)   ~ (all_52_4 = e1)
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | REDUCE: (48), (243) imply:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | |   (245)   ~ (all_52_12 = e1)
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | SIMP: (245) implies:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | |   (246)   ~ (all_52_12 = e1)
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | REDUCE: (224), (243) imply:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | |   (247)   ~ (e3 = e1)
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (243) imply:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | |   (248)   ~ (e2 = e1)
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | |   (249)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | |   (250)  all_58_0 = e2 & op(e3, e3) = e2
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | |   (251)  op(e3, e3) = e2
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (102), (202), (251) are inconsistent by
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2188.
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | |   (252)  all_58_1 = e2 & op(e3, e2) = e2
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | |   (253)  all_58_1 = e2
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (237), (253) imply:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | |   (254)  e3 = e2
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (231), (254) imply:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | |   (255)  all_58_6 = e2
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (15), (24), (28), (29), (30), (31),
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | |            (33), (40), (50), (53), (63), (64), (72), (77),
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | |            (94), (100), (102), (104), (108), (112), (116),
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | |            (129), (144), (199), (201), (202), (203), (255)
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1274.
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | |   (256)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | 
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.70/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_58_4 = e2 & op(e3, e1) = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | |   (258)  all_58_4 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (62), (81), (91), (94), (100), (102), (111),
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | |            (116), (145), (240), (246), (258) are inconsistent
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1526.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | |   (259)  all_58_9 = e2 & op(e3, e0) = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_58_9 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | |   (261)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_58_9 = e1 & op(e3, e0) = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (94), (246), (262) are inconsistent by
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2278.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  all_58_10 = e1 & op(e2, e0) = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_58_10 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_58_6 = e1 & op(e1, e3) = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  op(e1, e3) = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (94), (232), (267) are inconsistent by
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2225.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_58_7 = e1 & op(e1, e2) = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_58_7 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_58_1 = e2 & op(e3, e2) = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  all_58_1 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (237), (272) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (273)  e3 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (231), (273) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_58_6 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15), (30), (63), (94), (104), (144), (201),
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (203), (269), (274) are inconsistent by
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1676.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_58_3 = e2 & op(e2, e2) = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (276)  op(e2, e2) = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (94), (202), (276) are inconsistent by
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2137.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (277)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_58_7 = e2 & op(e1, e2) = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_58_7 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (15), (24), (27), (28), (30), (40),
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (50), (53), (61), (63), (64), (65), (71), (72),
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (77), (87), (89), (91), (92), (94), (95), (97),
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (100), (102), (104), (108), (109), (112), (116),
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (129), (130), (139), (144), (199), (201), (202),
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (237), (260), (279) are inconsistent by
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1262.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_58_13 = e2 & op(e0, e2) = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  all_58_13 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  all_54_3 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (282) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  all_52_12 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (283) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  all_52_12 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (284) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (285)   ~ (all_52_4 = e2)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (284) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (286)   ~ (all_52_13 = e2)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (286) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (287)   ~ (all_52_13 = e2)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (288)  all_54_1 = e3
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (288) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_52_4 = e3
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (289) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)  all_52_4 = e3
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (290) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)   ~ (all_52_6 = e3)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (291) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)   ~ (all_52_6 = e3)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (290) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)   ~ (all_52_7 = e3)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (290) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)  op(e3, e2) = e3
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)  all_54_9 = e3
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (295) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_52_6 = e3
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (292), (296) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  $false
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (297) is inconsistent.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_54_9 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (299) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (300)  all_52_6 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (300) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  $false
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (301) is inconsistent.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (302)   ~ (all_54_9 = e2)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  all_54_9 = e1 | all_54_9 = e0
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_58_12 = e1 & op(e0, e3) = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  op(e0, e3) = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  all_54_9 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (307) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_52_6 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (308) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (309)  all_52_6 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (96), (309) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (310)   ~ (all_52_7 = e1)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (310) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (311)   ~ (all_52_7 = e1)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15), (309) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  op(e1, e2) = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_54_13 = e3
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (25), (313) are inconsistent by sub-proof
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e2) = all_36_1 & $i(all_36_0) &
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_36_1)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  op(e1, e2) = all_36_1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  op(all_36_1, e1) = all_36_0
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, all_56_11) = e2)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (12), (43), (59), (66), (83), (94),
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (102), (106), (217), (287), (294), (311), (314),
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (318) are inconsistent by sub-proof #1260.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_15 & $i(all_56_15))
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_13 & $i(all_56_13)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)  op(e1, e2) = all_56_13
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (322)  op(e1, all_56_13) = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (323)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e2) = all_40_1 & $i(all_40_0) &
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_40_1)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  op(e1, e2) = all_40_1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  op(all_40_1, e1) = all_40_0
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with all_36_1, all_40_1, e2,
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (316), (324) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  all_40_1 = all_36_1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with all_40_1, all_56_13, e2,
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (321), (324) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  all_56_13 = all_40_1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with e1, all_56_13, e2, e1,
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (312), (321) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  all_56_13 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (328) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  all_40_1 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (329) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_40_1 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (330) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  all_36_1 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (325), (330) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (332)  op(e1, e1) = all_40_0
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (317), (331) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (333)  op(e1, e1) = all_36_0
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (322), (328) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (334)  op(e1, e1) = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with e1, all_36_0, e1, e1,
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (333), (334) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (335)  all_36_0 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with e2, all_40_0, e1, e1,
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (203), (332) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (336)  all_40_0 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with all_36_0, all_40_0, e1,
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (332), (333) gives:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (337)  all_40_0 = all_36_0
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (337) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (338)  all_36_0 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (338) implies:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (339)  all_36_0 = e2
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (339) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (340)  e2 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (340) imply:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_58_8 = e1
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15), (92), (94), (100), (104), (116), (144),
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (201), (202), (231), (269), (334), (341) are
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1269.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (342)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 &
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_26_1)
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (306), (342) are inconsistent by sub-proof
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1386.
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (343)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_40_1)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (343) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (344)  op(e1, e2) = all_40_1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with all_36_1, all_40_1, e2,
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (316), (344) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (345)  all_40_1 = all_36_1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with all_40_1, all_56_13, e2,
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (321), (344) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (346)  all_56_13 = all_40_1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with e1, all_56_13, e2, e1,
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (312), (321) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (347)  all_56_13 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (347) imply:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (348)  all_40_1 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (348) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (349)  all_40_1 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (345), (349) imply:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (350)  all_36_1 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (317), (350) imply:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (351)  op(e1, e1) = all_36_0
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (322), (347) imply:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (352)  op(e1, e1) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with e2, all_36_0, e1, e1,
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (203), (351) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (353)  all_36_0 = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (94) with e1, all_36_0, e1, e1,
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (351), (352) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (354)  all_36_0 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (353), (354) imply:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (355)  e2 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (355) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (356)  e2 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (356) imply:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (357)  all_58_8 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15), (92), (94), (100), (104), (116), (144),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (201), (202), (231), (269), (352), (357) are
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1269.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (358)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 &
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_26_1)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (306), (358) are inconsistent by sub-proof
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1386.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (359)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_15 & $i(all_56_15)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (43), (59), (78), (83), (94), (217), (311),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (314), (359) are inconsistent by sub-proof #1259.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (360)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 &
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_36_1)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (360) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (361)   ~ (all_36_1 = e0)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (362)  op(e1, e2) = all_36_1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (363)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3,
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_9 & $i(all_56_9)) | (all_56_10 =
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, all_56_11) = e2)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (12), (43), (59), (66), (83), (94),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (102), (106), (217), (287), (294), (311), (314),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (363) are inconsistent by sub-proof #1260.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (364)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_56_13 & $i(all_56_13)) | (all_56_14
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & op(e0, all_56_15) = e0 & op(e0, e2) =
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_15 & $i(all_56_15))
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (364) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (365)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1,
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_13 & $i(all_56_13)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (365) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (366)  op(e1, e2) = all_56_13
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (367)  op(e1, all_56_13) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (368)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e2) = all_40_1 & $i(all_40_0) &
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_40_1)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (369)  op(e1, e2) = all_40_1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15), (92), (94), (104), (116), (144), (152),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (201), (202), (203), (211), (231), (269), (306),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (312), (361), (362), (366), (367), (369) are
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1258.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (370)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_40_1)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (370) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (371)  op(e1, e2) = all_40_1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15), (92), (94), (104), (116), (144), (152),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (201), (202), (203), (211), (231), (269), (306),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (312), (361), (362), (366), (367), (371) are
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1258.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (372)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = all_56_15 & $i(all_56_15)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (43), (59), (78), (83), (94), (217), (311),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (314), (372) are inconsistent by sub-proof #1259.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (373)  all_54_9 = e0
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (144), (373) are inconsistent by sub-proof
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1953.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (374)  all_58_13 = e1 & op(e0, e2) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (374) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (375)  all_58_13 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (375) imply:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (376)  e2 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (376) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (377)  e2 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (377) imply:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (378)  all_58_8 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (92), (116), (139), (201), (202), (231), (269),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (378) are inconsistent by sub-proof #2215.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (379)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (380)  all_58_14 = e1 & op(e0, e1) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (381)  op(e0, e1) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (100), (130), (381) are inconsistent by
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2158.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (382)  all_58_15 = e1 & op(e0, e0) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (382) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (383)  all_58_15 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (30), (89), (94), (95), (116), (139), (201),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (264), (383) are inconsistent by sub-proof
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1597.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (384)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (115), (244), (285), (384) are inconsistent
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2048.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (385)  all_54_3 = e1 | all_54_3 = e0
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (93), (246), (385) are inconsistent by
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2287.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (386)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (386) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (387)  all_58_8 = e1 & op(e1, e1) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (211), (387) are inconsistent by sub-proof
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2045.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (388)  all_58_11 = e1 & op(e1, e0) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (388) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (389)  op(e1, e0) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (100), (140), (389) are inconsistent by
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | |   (390)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (390) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (391)  all_58_11 = e1 & op(e1, e0) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (392)  op(e1, e0) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (100), (140), (392) are inconsistent by
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (393)  all_58_15 = e1 & op(e0, e0) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (30), (393) are inconsistent by sub-proof
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | |            #1393.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | |   (394)  all_54_2 = e0
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (145), (394) are inconsistent by sub-proof
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | |            #1643.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | |   (395)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 243.72/50.21  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (62), (94), (98), (224), (395) are
% 243.72/50.21  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1515.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | |   (396)  all_58_12 = e3 & op(e0, e3) = e3
% 243.72/50.21  | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | ALPHA: (396) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | |   (397)  op(e0, e3) = e3
% 243.72/50.21  | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (64), (94), (397) are inconsistent by
% 243.72/50.21  | | | | | | | | | | | | | | | | |            sub-proof #2332.
% 243.72/50.21  | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | End of split
% 243.72/50.21  | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | |   (398)   ~ (all_54_6 = e3)
% 243.72/50.21  | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | REDUCE: (35), (398) imply:
% 243.72/50.21  | | | | | | | | | | | | | |   (399)   ~ (all_52_9 = e3)
% 243.72/50.21  | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 243.72/50.21  | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | |   (400)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 243.72/50.21  | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 243.72/50.21  | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | BETA: splitting (400) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | |   (401)  all_58_2 = e3 & op(e2, e3) = e3
% 243.72/50.21  | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | ALPHA: (401) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | |   (402)  all_58_2 = e3
% 243.72/50.21  | | | | | | | | | | | | | | | |   (403)  op(e2, e3) = e3
% 243.72/50.21  | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | |   (404)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 243.72/50.21  | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (102), (201), (202), (403), (404) are
% 243.72/50.21  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1824.
% 243.72/50.21  | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | |   (405)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 243.72/50.21  | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 243.72/50.21  | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | BETA: splitting (405) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | |   (406)  all_58_6 = e2 & op(e1, e3) = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | ALPHA: (406) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | |   (407)  all_58_6 = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (15), (24), (28), (29), (30), (31),
% 243.72/50.21  | | | | | | | | | | | | | | | | | |            (33), (40), (50), (53), (63), (64), (72), (77),
% 243.72/50.21  | | | | | | | | | | | | | | | | | |            (94), (100), (102), (104), (108), (112), (116),
% 243.72/50.21  | | | | | | | | | | | | | | | | | |            (129), (144), (199), (201), (202), (203), (407)
% 243.72/50.21  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1274.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | |   (408)  all_58_12 = e2 & op(e0, e3) = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | ALPHA: (408) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | |   (409)  all_58_12 = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | |   (410)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (94), (201), (202), (403), (410) are
% 243.72/50.21  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1509.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | |   (411)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 243.72/50.21  | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | BETA: splitting (411) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | |   (412)  all_58_5 = e2 & op(e2, e1) = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | ALPHA: (412) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | |   (413)  op(e2, e1) = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (94), (199), (413) are inconsistent by
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | |            sub-proof #2328.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | |   (414)  all_58_10 = e2 & op(e2, e0) = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | ALPHA: (414) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | |   (415)  op(e2, e0) = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | |   (416)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (416) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | |   (417)  all_58_12 = e1 & op(e0, e3) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (417) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | |   (418)  all_58_12 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (418) imply:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | |   (419)  e2 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (29), (30), (31), (33), (50), (53), (77),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | |            (94), (100), (108), (112), (116), (129), (199),
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | |            (201), (202), (203), (211), (402), (403), (419)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1257.
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | |   (420)  all_58_13 = e1 & op(e0, e2) = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (420) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | |   (421)  all_58_13 = e1
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | |   (422)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (422) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | |   (423)  all_58_1 = e2 & op(e3, e2) = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (423) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | |   (424)  all_58_1 = e2
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (425)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (425) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (426)  all_58_4 = e3 & op(e3, e1) = e3
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (426) implies:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (427)  all_58_4 = e3
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (428)  op(e3, e1) = e3
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (429)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (429) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (430)  all_58_2 = e1 & op(e2, e3) = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (402), (430) are inconsistent by sub-proof
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1765.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (431)  all_58_3 = e1 & op(e2, e2) = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (108), (431) are inconsistent by sub-proof
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1752.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (432)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (432) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (433)  all_58_5 = e1 & op(e2, e1) = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (433) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (434)  all_58_5 = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (435)  op(e2, e1) = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (436)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (436) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (437)  all_58_1 = e3 & op(e3, e2) = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (437) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (438)  all_58_1 = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (424), (438) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (439)  e3 = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (439) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (440)  e3 = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (427), (440) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (441)  all_58_4 = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (30), (31), (50), (77), (94), (100), (201),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (203), (434), (435), (441) are inconsistent
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2161.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (442)  all_58_3 = e3 & op(e2, e2) = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (442) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (443)  all_58_3 = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (108), (443) are inconsistent by sub-proof
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1460.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (444)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (444) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (445)  all_58_7 = e3 & op(e1, e2) = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (446)  op(e1, e2) = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (447)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_19 & $i(all_56_19))
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (447) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (448)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_56_17 & $i(all_56_17)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (12), (23), (25), (32), (43), (45),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (59), (65), (71), (75), (84), (90), (94), (102),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (143), (196), (217), (403), (428), (448) are
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1291.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (449)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_56_19 & $i(all_56_19)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (449) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (450)  op(e2, e1) = all_56_19
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (451)  op(e2, all_56_19) = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (452)  all_54_4 = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (452) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (453)  all_52_1 = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (453) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (454)  all_52_1 = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (454) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (455)   ~ (all_52_2 = e3)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (455) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (456)   ~ (all_52_2 = e3)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (457)  all_54_8 = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (456), (457) are inconsistent by sub-proof
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2011.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (458)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)  all_54_8 = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (196), (459) are inconsistent by sub-proof
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2007.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (460)  all_54_8 = e1 | all_54_8 = e0
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (460) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (461)  all_54_8 = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (461) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (462)  all_52_2 = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (462) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (463)   ~ (all_52_3 = e1)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (463) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (464)   ~ (all_52_3 = e1)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (465)  all_54_12 = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (465) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (466)  all_52_3 = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (466) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (467)  all_52_3 = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (467) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (468)   ~ (all_52_7 = e2)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (468) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (469)   ~ (all_52_7 = e2)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (25), (50), (84), (94), (199), (435), (450),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (451), (469) are inconsistent by sub-proof #1256.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (470)  all_54_12 = e1 | all_54_12 = e0
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (59), (464), (470) are inconsistent by
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2067.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (471)  all_54_8 = e0
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (471) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (472)  all_52_2 = e0
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (472) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (473)  $false
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (473) is inconsistent.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (474)   ~ (all_54_4 = e3)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (474) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (475)   ~ (all_52_1 = e3)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (94), (403), (475) are inconsistent by
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2337.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (476)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23))
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (476) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (477)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (477) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (478)  op(e1, all_56_21) = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (195), (478) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (479)  op(e1, e2) = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (94), (191), (214), (446), (479) are
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1332.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (480)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_56_23 & $i(all_56_23)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (480) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (481)  op(e0, e1) = all_56_23
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (482)  op(e0, all_56_23) = e0
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (87), (94), (130), (481), (482) are
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1395.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (483)  all_58_13 = e3 & op(e0, e2) = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (78), (94), (483) are inconsistent by
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1919.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (484)  all_58_10 = e1 & op(e2, e0) = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (485)  op(e2, e0) = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (116), (415), (485) are inconsistent by
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1659.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (486)  all_58_5 = e3 & op(e2, e1) = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (94), (399), (486) are inconsistent by
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1822.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (487) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (488)  all_58_8 = e3 & op(e1, e1) = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (488) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  op(e1, e1) = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (201), (203), (489) are inconsistent by
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2206.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (490)  all_58_14 = e3 & op(e0, e1) = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (490) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (491)  all_58_14 = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (100), (121), (202), (409), (421), (491) are
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2080.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |   (492)  all_58_3 = e2 & op(e2, e2) = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (492) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |   (493)  op(e2, e2) = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (94), (202), (493) are inconsistent by
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2137.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | |   (494)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (494) gives:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |   (495)  all_58_7 = e2 & op(e1, e2) = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (495) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |   (496)  all_58_7 = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (15), (24), (25), (27), (28), (29),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |            (30), (33), (40), (50), (52), (53), (61), (63),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |            (64), (65), (71), (72), (77), (78), (86), (87),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |            (89), (91), (92), (94), (95), (97), (99), (100),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |            (102), (104), (108), (109), (112), (116), (129),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |            (130), (139), (144), (199), (201), (202), (203),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |            (496) are inconsistent by sub-proof #1261.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |   (497)  all_58_13 = e2 & op(e0, e2) = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (497) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |   (498)  all_58_13 = e2
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (421), (498) imply:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |   (499)  e2 = e1
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (29), (30), (31), (33), (50), (53), (77),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |            (94), (100), (108), (112), (116), (129), (199),
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |            (201), (202), (203), (211), (402), (403), (499)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1257.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | |   (500)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (30), (94), (100), (130), (500) are
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1255.
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | |   (501)  all_58_3 = e3 & op(e2, e2) = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | ALPHA: (501) implies:
% 243.72/50.22  | | | | | | | | | | | | | | | |   (502)  all_58_3 = e3
% 243.72/50.22  | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (108), (502) are inconsistent by sub-proof
% 243.72/50.22  | | | | | | | | | | | | | | | |            #1460.
% 243.72/50.22  | | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | |   (503)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 243.72/50.22  | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 243.72/50.22  | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | | REF_CLOSE: (50), (94), (103), (106), (399), (503) are
% 243.72/50.22  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1649.
% 243.72/50.22  | | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | Case 2:
% 243.72/50.22  | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | |   (504)  all_58_11 = e2 & op(e1, e0) = e2
% 243.72/50.22  | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | ALPHA: (504) implies:
% 243.72/50.22  | | | | | | | | | |   (505)  all_58_11 = e2
% 243.72/50.22  | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | | REF_CLOSE: (139), (202), (505) are inconsistent by sub-proof
% 243.72/50.22  | | | | | | | | | |            #2110.
% 243.72/50.22  | | | | | | | | | | 
% 243.72/50.22  | | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | | 
% 243.72/50.22  | | | | | | | | End of split
% 243.72/50.22  | | | | | | | | 
% 243.72/50.22  | | | | | | | End of split
% 243.72/50.22  | | | | | | | 
% 243.72/50.22  | | | | | | End of split
% 243.72/50.22  | | | | | | 
% 243.72/50.22  | | | | | End of split
% 243.72/50.22  | | | | | 
% 243.72/50.22  | | | | End of split
% 243.72/50.22  | | | | 
% 243.72/50.22  | | | End of split
% 243.72/50.22  | | | 
% 243.72/50.22  | | End of split
% 243.72/50.22  | | 
% 243.72/50.22  | End of split
% 243.72/50.22  | 
% 243.72/50.22  End of proof
% 243.72/50.22  
% 243.72/50.22  Sub-proof #1255 shows that the following formulas are inconsistent:
% 243.72/50.22  ----------------------------------------------------------------
% 243.72/50.22    (1)  all_58_15 = e3
% 243.72/50.22    (2)   ~ (e3 = e1)
% 243.72/50.22    (3)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.72/50.22    (4)  op(e0, e1) = e0
% 243.72/50.22    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.72/50.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.72/50.22    (6)   ~ (e1 = e0)
% 243.72/50.22  
% 243.72/50.22  Begin of proof
% 243.72/50.22  | 
% 243.72/50.22  | BETA: splitting (3) gives:
% 243.72/50.22  | 
% 243.72/50.22  | Case 1:
% 243.72/50.22  | | 
% 243.72/50.22  | |   (7)  all_58_14 = e1 & op(e0, e1) = e1
% 243.72/50.22  | | 
% 243.72/50.22  | | ALPHA: (7) implies:
% 243.72/50.22  | |   (8)  op(e0, e1) = e1
% 243.72/50.22  | | 
% 243.72/50.22  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2158.
% 243.72/50.22  | | 
% 243.72/50.22  | Case 2:
% 243.72/50.22  | | 
% 243.72/50.22  | |   (9)  all_58_15 = e1 & op(e0, e0) = e1
% 243.72/50.22  | | 
% 243.72/50.22  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #1393.
% 243.72/50.22  | | 
% 243.72/50.22  | End of split
% 243.72/50.22  | 
% 243.72/50.22  End of proof
% 243.72/50.22  
% 243.72/50.22  Sub-proof #1256 shows that the following formulas are inconsistent:
% 243.72/50.22  ----------------------------------------------------------------
% 243.72/50.22    (1)   ~ (all_52_7 = e2)
% 243.72/50.22    (2)  op(e2, e1) = e1
% 243.72/50.22    (3)  all_54_13 = all_52_7
% 243.72/50.22    (4)   ~ (all_52_7 = e3)
% 243.72/50.22    (5)  op(e2, e1) = all_52_9
% 243.72/50.22    (6)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.72/50.22    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.72/50.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.72/50.22    (8)  op(e2, e1) = all_56_19
% 243.72/50.22    (9)  op(e2, all_56_19) = e2
% 243.72/50.22    (10)   ~ (all_52_9 = e2)
% 243.72/50.22  
% 243.72/50.22  Begin of proof
% 243.72/50.22  | 
% 243.72/50.22  | BETA: splitting (6) gives:
% 243.72/50.22  | 
% 243.72/50.22  | Case 1:
% 243.72/50.22  | | 
% 243.72/50.22  | |   (11)  all_54_13 = e3
% 243.72/50.22  | | 
% 243.72/50.22  | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #2010.
% 243.72/50.22  | | 
% 243.72/50.22  | Case 2:
% 243.72/50.22  | | 
% 243.72/50.22  | |   (12)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.72/50.22  | | 
% 243.72/50.22  | | BETA: splitting (12) gives:
% 243.72/50.22  | | 
% 243.72/50.22  | | Case 1:
% 243.72/50.22  | | | 
% 243.72/50.22  | | |   (13)  all_54_13 = e2
% 243.72/50.22  | | | 
% 243.72/50.22  | | | COMBINE_EQS: (3), (13) imply:
% 243.72/50.22  | | |   (14)  all_52_7 = e2
% 243.72/50.22  | | | 
% 243.72/50.22  | | | REDUCE: (1), (14) imply:
% 243.72/50.22  | | |   (15)  $false
% 243.72/50.22  | | | 
% 243.72/50.22  | | | CLOSE: (15) is inconsistent.
% 243.72/50.22  | | | 
% 243.72/50.22  | | Case 2:
% 243.72/50.22  | | | 
% 243.72/50.22  | | | 
% 243.72/50.22  | | | GROUND_INST: instantiating (7) with e1, all_56_19, e1, e2, simplifying
% 243.72/50.22  | | |              with (2), (8) gives:
% 243.72/50.22  | | |   (16)  all_56_19 = e1
% 243.72/50.22  | | | 
% 243.72/50.22  | | | REDUCE: (9), (16) imply:
% 243.72/50.22  | | |   (17)  op(e2, e1) = e2
% 243.72/50.23  | | | 
% 243.72/50.23  | | | REF_CLOSE: (5), (7), (10), (17) are inconsistent by sub-proof #2328.
% 243.72/50.23  | | | 
% 243.72/50.23  | | End of split
% 243.72/50.23  | | 
% 243.72/50.23  | End of split
% 243.72/50.23  | 
% 243.72/50.23  End of proof
% 243.72/50.23  
% 243.72/50.23  Sub-proof #1257 shows that the following formulas are inconsistent:
% 243.72/50.23  ----------------------------------------------------------------
% 243.72/50.23    (1)   ~ (e3 = e0)
% 243.72/50.23    (2)   ~ (e2 = e0)
% 243.72/50.23    (3)  op(e2, e3) = e3
% 243.72/50.23    (4)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.72/50.23         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.72/50.23    (5)   ~ (e3 = e1)
% 243.72/50.23    (6)  all_58_8 = e2
% 243.72/50.23    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.72/50.23         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.72/50.23    (8)  op(e2, e2) = e0
% 243.72/50.23    (9)  op(e2, e1) = all_52_9
% 243.72/50.23    (10)   ~ (e3 = e2)
% 243.72/50.23    (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.72/50.23          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.72/50.23    (12)  op(e1, e1) = e2
% 243.72/50.23    (13)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.72/50.23          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.72/50.23    (14)  all_58_14 = e0
% 243.72/50.23    (15)  e2 = e1
% 243.72/50.23    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.72/50.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.72/50.23    (17)   ~ (e1 = e0)
% 243.72/50.23    (18)  all_58_2 = e3
% 243.72/50.23    (19)  all_58_3 = e0
% 243.72/50.23    (20)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.72/50.23          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.72/50.23    (21)   ~ (e2 = e1)
% 243.72/50.23    (22)   ~ (all_52_9 = e2)
% 243.72/50.23  
% 243.72/50.23  Begin of proof
% 243.72/50.23  | 
% 243.72/50.23  | SIMP: (15) implies:
% 243.72/50.23  |   (23)  e2 = e1
% 243.72/50.23  | 
% 243.72/50.23  | COMBINE_EQS: (6), (23) imply:
% 243.72/50.23  |   (24)  all_58_8 = e1
% 243.72/50.23  | 
% 243.72/50.23  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 243.72/50.23  |            (14), (16), (17), (18), (19), (20), (21), (22), (24) are
% 243.72/50.23  |            inconsistent by sub-proof #1275.
% 243.72/50.23  | 
% 243.72/50.23  End of proof
% 243.72/50.23  
% 243.72/50.23  Sub-proof #1258 shows that the following formulas are inconsistent:
% 243.72/50.23  ----------------------------------------------------------------
% 243.72/50.23    (1)  op(e1, e2) = all_56_13
% 243.72/50.23    (2)   ~ (e3 = e0)
% 243.72/50.23    (3)  all_58_6 = e3
% 243.72/50.23    (4)  op(e1, e2) = e1
% 243.72/50.23    (5)   ~ (e2 = e0)
% 243.72/50.23    (6)  op(e1, e2) = all_52_6
% 243.72/50.23    (7)   ~ (all_52_6 = e0)
% 243.72/50.23    (8)  all_58_8 = e2
% 243.72/50.23    (9)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 243.72/50.23           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 243.72/50.23           all_26_1 & $i(all_26_1))
% 243.72/50.23    (10)   ~ (e3 = e2)
% 243.72/50.23    (11)  op(e0, e3) = e1
% 243.72/50.23    (12)  op(e1, e2) = all_36_1
% 243.72/50.23    (13)  op(e1, e1) = e2
% 243.72/50.23    (14)  all_58_7 = e1
% 243.72/50.23    (15)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.72/50.23          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.72/50.23    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.72/50.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.72/50.23    (17)   ~ (all_36_1 = e0)
% 243.72/50.23    (18)  op(e1, e2) = all_40_1
% 243.72/50.23    (19)  op(e1, all_56_13) = e1
% 243.72/50.23    (20)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.72/50.23          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.72/50.23    (21)   ~ (e2 = e1)
% 243.72/50.23  
% 243.72/50.23  Begin of proof
% 243.72/50.23  | 
% 243.72/50.23  | BETA: splitting (9) gives:
% 243.72/50.23  | 
% 243.72/50.23  | Case 1:
% 243.72/50.23  | | 
% 243.72/50.23  | | 
% 243.78/50.23  | | GROUND_INST: instantiating (16) with all_36_1, all_40_1, e2, e1, simplifying
% 243.78/50.23  | |              with (12), (18) gives:
% 243.78/50.23  | |   (22)  all_40_1 = all_36_1
% 243.78/50.23  | | 
% 243.78/50.23  | | GROUND_INST: instantiating (16) with all_40_1, all_56_13, e2, e1,
% 243.78/50.23  | |              simplifying with (1), (18) gives:
% 243.78/50.23  | |   (23)  all_56_13 = all_40_1
% 243.78/50.23  | | 
% 243.78/50.23  | | GROUND_INST: instantiating (16) with e1, all_56_13, e2, e1, simplifying with
% 243.78/50.23  | |              (1), (4) gives:
% 243.78/50.23  | |   (24)  all_56_13 = e1
% 243.78/50.23  | | 
% 243.78/50.23  | | COMBINE_EQS: (23), (24) imply:
% 243.78/50.23  | |   (25)  all_40_1 = e1
% 243.78/50.23  | | 
% 243.78/50.23  | | SIMP: (25) implies:
% 243.78/50.23  | |   (26)  all_40_1 = e1
% 243.78/50.23  | | 
% 243.78/50.23  | | COMBINE_EQS: (22), (26) imply:
% 243.78/50.23  | |   (27)  all_36_1 = e1
% 243.78/50.23  | | 
% 243.78/50.23  | | REDUCE: (17), (27) imply:
% 243.78/50.23  | |   (28)   ~ (e1 = e0)
% 243.78/50.23  | | 
% 243.78/50.23  | | REDUCE: (19), (24) imply:
% 243.78/50.23  | |   (29)  op(e1, e1) = e1
% 243.78/50.23  | | 
% 243.78/50.23  | | GROUND_INST: instantiating (16) with e2, e1, e1, e1, simplifying with (13),
% 243.78/50.23  | |              (29) gives:
% 243.78/50.23  | |   (30)  e2 = e1
% 243.78/50.23  | | 
% 243.78/50.23  | | COMBINE_EQS: (8), (30) imply:
% 243.78/50.23  | |   (31)  all_58_8 = e1
% 243.78/50.23  | | 
% 243.78/50.23  | | REF_CLOSE: (2), (3), (5), (6), (7), (10), (14), (15), (16), (20), (21),
% 243.78/50.23  | |            (28), (29), (31) are inconsistent by sub-proof #1269.
% 243.78/50.23  | | 
% 243.78/50.23  | Case 2:
% 243.78/50.23  | | 
% 243.78/50.23  | |   (32)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 243.78/50.23  | | 
% 243.78/50.23  | | REF_CLOSE: (11), (16), (32) are inconsistent by sub-proof #1386.
% 243.78/50.23  | | 
% 243.78/50.23  | End of split
% 243.78/50.23  | 
% 243.78/50.23  End of proof
% 243.78/50.23  
% 243.78/50.23  Sub-proof #1259 shows that the following formulas are inconsistent:
% 243.78/50.23  ----------------------------------------------------------------
% 243.78/50.23    (1)  all_54_13 = all_52_7
% 243.78/50.23    (2)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 243.78/50.23         $i(all_56_15)
% 243.78/50.23    (3)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.78/50.23    (4)   ~ (all_52_3 = all_52_7)
% 243.78/50.23    (5)   ~ (all_52_7 = e1)
% 243.78/50.23    (6)  all_54_12 = all_52_3
% 243.78/50.23    (7)  op(e0, e2) = all_52_7
% 243.78/50.23    (8)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.78/50.23    (9)   ~ (all_52_7 = e0)
% 243.78/50.23    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.23  
% 243.78/50.23  Begin of proof
% 243.78/50.23  | 
% 243.78/50.23  | ALPHA: (2) implies:
% 243.78/50.23  |   (11)  op(e0, e2) = all_56_15
% 243.78/50.23  |   (12)  op(e0, all_56_15) = e0
% 243.78/50.23  | 
% 243.78/50.23  | BETA: splitting (3) gives:
% 243.78/50.23  | 
% 243.78/50.23  | Case 1:
% 243.78/50.23  | | 
% 243.78/50.23  | |   (13)  all_54_13 = e2
% 243.78/50.23  | | 
% 243.78/50.23  | | COMBINE_EQS: (1), (13) imply:
% 243.78/50.23  | |   (14)  all_52_7 = e2
% 243.78/50.23  | | 
% 243.78/50.23  | | SIMP: (14) implies:
% 243.78/50.23  | |   (15)  all_52_7 = e2
% 243.78/50.23  | | 
% 243.78/50.23  | | REDUCE: (4), (15) imply:
% 243.78/50.23  | |   (16)   ~ (all_52_3 = e2)
% 243.78/50.23  | | 
% 243.78/50.23  | | REDUCE: (7), (15) imply:
% 243.78/50.23  | |   (17)  op(e0, e2) = e2
% 243.78/50.23  | | 
% 243.78/50.23  | | BETA: splitting (8) gives:
% 243.78/50.23  | | 
% 243.78/50.23  | | Case 1:
% 243.78/50.23  | | | 
% 243.78/50.23  | | |   (18)  all_54_12 = e2
% 243.78/50.23  | | | 
% 243.78/50.23  | | | COMBINE_EQS: (6), (18) imply:
% 243.78/50.23  | | |   (19)  all_52_3 = e2
% 243.78/50.23  | | | 
% 243.78/50.23  | | | REDUCE: (16), (19) imply:
% 243.78/50.23  | | |   (20)  $false
% 243.78/50.23  | | | 
% 243.78/50.23  | | | CLOSE: (20) is inconsistent.
% 243.78/50.23  | | | 
% 243.78/50.23  | | Case 2:
% 243.78/50.23  | | | 
% 243.78/50.23  | | | 
% 243.78/50.23  | | | REF_CLOSE: (1), (3), (5), (7), (9), (10), (11), (12), (17) are
% 243.78/50.23  | | |            inconsistent by sub-proof #1625.
% 243.78/50.23  | | | 
% 243.78/50.23  | | End of split
% 243.78/50.23  | | 
% 243.78/50.23  | Case 2:
% 243.78/50.23  | | 
% 243.78/50.23  | |   (21)  all_54_13 = e1 | all_54_13 = e0
% 243.78/50.23  | | 
% 243.78/50.23  | | REF_CLOSE: (1), (5), (9), (21) are inconsistent by sub-proof #1793.
% 243.78/50.23  | | 
% 243.78/50.23  | End of split
% 243.78/50.23  | 
% 243.78/50.23  End of proof
% 243.78/50.23  
% 243.78/50.23  Sub-proof #1260 shows that the following formulas are inconsistent:
% 243.78/50.23  ----------------------------------------------------------------
% 243.78/50.23    (1)   ~ (all_52_3 = e0)
% 243.78/50.23    (2)   ~ (e3 = e0)
% 243.78/50.23    (3)  all_54_13 = all_52_7
% 243.78/50.23    (4)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.78/50.23           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 243.78/50.23    (5)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.78/50.23    (6)   ~ (all_52_3 = all_52_7)
% 243.78/50.23    (7)   ~ (all_52_7 = e1)
% 243.78/50.23    (8)  all_54_12 = all_52_3
% 243.78/50.23    (9)  all_56_11 = e0
% 243.78/50.23    (10)   ~ (all_52_13 = e2)
% 243.78/50.23    (11)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.78/50.23    (12)   ~ (all_52_7 = e0)
% 243.78/50.24    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.24    (14)  op(e3, e3) = e0
% 243.78/50.24    (15)  op(e3, e2) = e3
% 243.78/50.24    (16)  op(e2, e0) = all_52_13
% 243.78/50.24  
% 243.78/50.24  Begin of proof
% 243.78/50.24  | 
% 243.78/50.24  | BETA: splitting (4) gives:
% 243.78/50.24  | 
% 243.78/50.24  | Case 1:
% 243.78/50.24  | | 
% 243.78/50.24  | |   (17)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.78/50.24  | |         $i(all_56_9)
% 243.78/50.24  | | 
% 243.78/50.24  | | ALPHA: (17) implies:
% 243.78/50.24  | |   (18)  op(e3, e2) = all_56_9
% 243.78/50.24  | |   (19)  op(e3, all_56_9) = e3
% 243.78/50.24  | | 
% 243.78/50.24  | | BETA: splitting (5) gives:
% 243.78/50.24  | | 
% 243.78/50.24  | | Case 1:
% 243.78/50.24  | | | 
% 243.78/50.24  | | |   (20)  all_54_13 = e2
% 243.78/50.24  | | | 
% 243.78/50.24  | | | COMBINE_EQS: (3), (20) imply:
% 243.78/50.24  | | |   (21)  all_52_7 = e2
% 243.78/50.24  | | | 
% 243.78/50.24  | | | SIMP: (21) implies:
% 243.78/50.24  | | |   (22)  all_52_7 = e2
% 243.78/50.24  | | | 
% 243.78/50.24  | | | REDUCE: (6), (22) imply:
% 243.78/50.24  | | |   (23)   ~ (all_52_3 = e2)
% 243.78/50.24  | | | 
% 243.78/50.24  | | | REF_CLOSE: (1), (2), (8), (11), (13), (14), (15), (18), (19), (23) are
% 243.78/50.24  | | |            inconsistent by sub-proof #1439.
% 243.78/50.24  | | | 
% 243.78/50.24  | | Case 2:
% 243.78/50.24  | | | 
% 243.78/50.24  | | |   (24)  all_54_13 = e1 | all_54_13 = e0
% 243.78/50.24  | | | 
% 243.78/50.24  | | | REF_CLOSE: (3), (7), (12), (24) are inconsistent by sub-proof #1793.
% 243.78/50.24  | | | 
% 243.78/50.24  | | End of split
% 243.78/50.24  | | 
% 243.78/50.24  | Case 2:
% 243.78/50.24  | | 
% 243.78/50.24  | |   (25)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 243.78/50.24  | | 
% 243.78/50.24  | | ALPHA: (25) implies:
% 243.78/50.24  | |   (26)  op(e2, all_56_11) = e2
% 243.78/50.24  | | 
% 243.78/50.24  | | REDUCE: (9), (26) imply:
% 243.78/50.24  | |   (27)  op(e2, e0) = e2
% 243.78/50.24  | | 
% 243.78/50.24  | | REF_CLOSE: (10), (13), (16), (27) are inconsistent by sub-proof #2317.
% 243.78/50.24  | | 
% 243.78/50.24  | End of split
% 243.78/50.24  | 
% 243.78/50.24  End of proof
% 243.78/50.24  
% 243.78/50.24  Sub-proof #1261 shows that the following formulas are inconsistent:
% 243.78/50.24  ----------------------------------------------------------------
% 243.78/50.24    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.78/50.24         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.78/50.24    (2)   ~ (e3 = e0)
% 243.78/50.24    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.78/50.24         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.78/50.24    (4)   ~ (e2 = e0)
% 243.78/50.24    (5)  op(e1, e2) = all_52_6
% 243.78/50.24    (6)  op(e1, e0) = all_52_14
% 243.78/50.24    (7)   ~ (all_52_7 = e3)
% 243.78/50.24    (8)  all_58_15 = e3
% 243.78/50.24    (9)  op(e0, e3) = all_52_3
% 243.78/50.24    (10)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.78/50.24          (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.78/50.24    (11)   ~ (all_52_6 = e0)
% 243.78/50.24    (12)   ~ (e3 = e1)
% 243.78/50.24    (13)  all_58_7 = e2
% 243.78/50.24    (14)  op(e2, e2) = e0
% 243.78/50.24    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.78/50.24          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.78/50.24    (16)  op(e2, e1) = all_52_9
% 243.78/50.24    (17)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.78/50.24          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.78/50.24    (18)   ~ (e3 = e2)
% 243.78/50.24    (19)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.78/50.24          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.78/50.24    (20)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.78/50.24          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.78/50.24    (21)  op(e0, e1) = e0
% 243.78/50.24    (22)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.78/50.24          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.78/50.24    (23)   ~ (all_52_3 = e3)
% 243.78/50.24    (24)   ~ (all_52_1 = e0)
% 243.78/50.24    (25)  op(e2, e3) = all_52_1
% 243.78/50.24    (26)   ~ (all_52_14 = e3)
% 243.78/50.24    (27)  op(e1, e1) = e2
% 243.78/50.24    (28)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.78/50.24          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.78/50.24    (29)  op(e0, e2) = all_52_7
% 243.78/50.24    (30)  all_58_14 = e0
% 243.78/50.24    (31)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.78/50.24          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.78/50.24    (32)  op(e0, e0) = e3
% 243.78/50.24    (33)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.78/50.24          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.78/50.24    (34)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.78/50.24          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.78/50.24    (35)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.78/50.24          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.78/50.24    (36)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.24    (37)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.78/50.24          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.78/50.24    (38)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.78/50.24          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.78/50.24    (39)  all_58_11 = e0
% 243.78/50.24    (40)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.78/50.24          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.78/50.24    (41)   ~ (e1 = e0)
% 243.78/50.24    (42)  op(e3, e3) = e0
% 243.78/50.24    (43)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.78/50.24          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.78/50.24    (44)  all_58_3 = e0
% 243.78/50.24    (45)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.78/50.24          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.78/50.24            e2)
% 243.78/50.24    (46)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.78/50.24          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.78/50.24    (47)   ~ (e2 = e1)
% 243.78/50.24    (48)   ~ (all_52_9 = e2)
% 243.78/50.24  
% 243.78/50.24  Begin of proof
% 243.78/50.24  | 
% 243.78/50.24  | BETA: splitting (40) gives:
% 243.78/50.24  | 
% 243.78/50.24  | Case 1:
% 243.78/50.24  | | 
% 243.78/50.24  | |   (49)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 243.78/50.24  | |           e3)
% 243.78/50.24  | | 
% 243.78/50.24  | | BETA: splitting (49) gives:
% 243.78/50.24  | | 
% 243.78/50.24  | | Case 1:
% 243.78/50.24  | | | 
% 243.78/50.24  | | |   (50)  all_58_1 = e3 & op(e3, e2) = e3
% 243.78/50.24  | | | 
% 243.78/50.24  | | | ALPHA: (50) implies:
% 243.78/50.24  | | |   (51)  all_58_1 = e3
% 243.78/50.24  | | | 
% 243.78/50.24  | | | BETA: splitting (1) gives:
% 243.78/50.24  | | | 
% 243.78/50.24  | | | Case 1:
% 243.78/50.24  | | | | 
% 243.78/50.24  | | | |   (52)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 243.78/50.24  | | | |           = e2)
% 243.78/50.24  | | | | 
% 243.78/50.24  | | | | BETA: splitting (52) gives:
% 243.78/50.24  | | | | 
% 243.78/50.24  | | | | Case 1:
% 243.78/50.24  | | | | | 
% 243.78/50.24  | | | | |   (53)  all_58_0 = e2 & op(e3, e3) = e2
% 243.78/50.24  | | | | | 
% 243.78/50.24  | | | | | ALPHA: (53) implies:
% 243.78/50.24  | | | | |   (54)  op(e3, e3) = e2
% 243.78/50.24  | | | | | 
% 243.78/50.24  | | | | | REF_CLOSE: (4), (36), (42), (54) are inconsistent by sub-proof #2188.
% 243.78/50.24  | | | | | 
% 243.78/50.24  | | | | Case 2:
% 243.78/50.24  | | | | | 
% 243.78/50.24  | | | | |   (55)  all_58_1 = e2 & op(e3, e2) = e2
% 243.78/50.24  | | | | | 
% 243.78/50.24  | | | | | REF_CLOSE: (18), (51), (55) are inconsistent by sub-proof #1590.
% 243.78/50.24  | | | | | 
% 243.78/50.24  | | | | End of split
% 243.78/50.24  | | | | 
% 243.78/50.24  | | | Case 2:
% 243.78/50.24  | | | | 
% 243.78/50.24  | | | |   (56)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 243.78/50.24  | | | |           = e2)
% 243.78/50.24  | | | | 
% 243.78/50.24  | | | | BETA: splitting (56) gives:
% 243.78/50.24  | | | | 
% 243.78/50.24  | | | | Case 1:
% 243.78/50.24  | | | | | 
% 243.78/50.24  | | | | |   (57)  all_58_4 = e2 & op(e3, e1) = e2
% 243.78/50.24  | | | | | 
% 243.78/50.24  | | | | | ALPHA: (57) implies:
% 243.78/50.24  | | | | |   (58)  all_58_4 = e2
% 243.78/50.24  | | | | | 
% 243.78/50.24  | | | | | BETA: splitting (3) gives:
% 243.78/50.24  | | | | | 
% 243.78/50.24  | | | | | Case 1:
% 243.78/50.24  | | | | | | 
% 243.78/50.24  | | | | | |   (59)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1,
% 243.78/50.24  | | | | | |             e2) = e1)
% 243.78/50.24  | | | | | | 
% 243.78/50.24  | | | | | | BETA: splitting (59) gives:
% 243.78/50.24  | | | | | | 
% 243.78/50.24  | | | | | | Case 1:
% 243.78/50.24  | | | | | | | 
% 243.78/50.24  | | | | | | |   (60)  all_58_6 = e1 & op(e1, e3) = e1
% 243.78/50.24  | | | | | | | 
% 243.78/50.24  | | | | | | | ALPHA: (60) implies:
% 243.78/50.24  | | | | | | |   (61)  all_58_6 = e1
% 243.78/50.24  | | | | | | | 
% 243.78/50.24  | | | | | | | REF_CLOSE: (2), (3), (4), (8), (9), (12), (13), (15), (16), (18),
% 243.78/50.24  | | | | | | |            (19), (21), (22), (23), (27), (28), (30), (33), (36),
% 243.78/50.24  | | | | | | |            (37), (39), (41), (42), (43), (44), (46), (47), (48),
% 243.78/50.24  | | | | | | |            (61) are inconsistent by sub-proof #1273.
% 243.78/50.24  | | | | | | | 
% 243.78/50.24  | | | | | | Case 2:
% 243.78/50.24  | | | | | | | 
% 243.78/50.24  | | | | | | |   (62)  all_58_7 = e1 & op(e1, e2) = e1
% 243.78/50.24  | | | | | | | 
% 243.78/50.24  | | | | | | | REF_CLOSE: (13), (47), (62) are inconsistent by sub-proof #2224.
% 243.78/50.24  | | | | | | | 
% 243.78/50.24  | | | | | | End of split
% 243.78/50.24  | | | | | | 
% 243.78/50.24  | | | | | Case 2:
% 243.78/50.24  | | | | | | 
% 243.78/50.24  | | | | | |   (63)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1,
% 243.78/50.24  | | | | | |             e0) = e1)
% 243.78/50.24  | | | | | | 
% 243.78/50.24  | | | | | | BETA: splitting (63) gives:
% 243.78/50.24  | | | | | | 
% 243.78/50.24  | | | | | | Case 1:
% 243.78/50.24  | | | | | | | 
% 243.78/50.24  | | | | | | |   (64)  all_58_8 = e1 & op(e1, e1) = e1
% 243.78/50.24  | | | | | | | 
% 243.78/50.24  | | | | | | | ALPHA: (64) implies:
% 243.78/50.24  | | | | | | |   (65)  all_58_8 = e1
% 243.78/50.24  | | | | | | |   (66)  op(e1, e1) = e1
% 243.78/50.24  | | | | | | | 
% 243.78/50.24  | | | | | | | BETA: splitting (38) gives:
% 243.78/50.24  | | | | | | | 
% 243.78/50.24  | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | 
% 243.78/50.24  | | | | | | | |   (67)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 243.78/50.24  | | | | | | | |           op(e2, e2) = e1)
% 243.78/50.24  | | | | | | | | 
% 243.78/50.24  | | | | | | | | BETA: splitting (67) gives:
% 243.78/50.24  | | | | | | | | 
% 243.78/50.24  | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | |   (68)  all_58_1 = e1 & op(e3, e2) = e1
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | REF_CLOSE: (12), (51), (68) are inconsistent by sub-proof
% 243.78/50.24  | | | | | | | | |            #1753.
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | Case 2:
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | |   (69)  all_58_3 = e1 & op(e2, e2) = e1
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | REF_CLOSE: (41), (44), (69) are inconsistent by sub-proof
% 243.78/50.24  | | | | | | | | |            #1752.
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | End of split
% 243.78/50.24  | | | | | | | | 
% 243.78/50.24  | | | | | | | Case 2:
% 243.78/50.24  | | | | | | | | 
% 243.78/50.24  | | | | | | | |   (70)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 243.78/50.24  | | | | | | | |           op(e0, e2) = e1)
% 243.78/50.24  | | | | | | | | 
% 243.78/50.24  | | | | | | | | BETA: splitting (70) gives:
% 243.78/50.24  | | | | | | | | 
% 243.78/50.24  | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | |   (71)  all_58_7 = e1 & op(e1, e2) = e1
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | REF_CLOSE: (13), (47), (71) are inconsistent by sub-proof
% 243.78/50.24  | | | | | | | | |            #2224.
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | Case 2:
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | |   (72)  all_58_13 = e1 & op(e0, e2) = e1
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | ALPHA: (72) implies:
% 243.78/50.24  | | | | | | | | |   (73)  all_58_13 = e1
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | BETA: splitting (28) gives:
% 243.78/50.24  | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | |   (74)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 243.78/50.24  | | | | | | | | | |           op(e2, e1) = e3)
% 243.78/50.24  | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | BETA: splitting (74) gives:
% 243.78/50.24  | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | |   (75)  all_58_4 = e3 & op(e3, e1) = e3
% 243.78/50.24  | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | ALPHA: (75) implies:
% 243.78/50.24  | | | | | | | | | | |   (76)  all_58_4 = e3
% 243.78/50.24  | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | REF_CLOSE: (18), (58), (76) are inconsistent by sub-proof
% 243.78/50.24  | | | | | | | | | | |            #1902.
% 243.78/50.24  | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | Case 2:
% 243.78/50.24  | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | |   (77)  all_58_5 = e3 & op(e2, e1) = e3
% 243.78/50.24  | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | ALPHA: (77) implies:
% 243.78/50.24  | | | | | | | | | | |   (78)  all_58_5 = e3
% 243.78/50.24  | | | | | | | | | | |   (79)  op(e2, e1) = e3
% 243.78/50.24  | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | BETA: splitting (45) gives:
% 243.78/50.24  | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | |   (80)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 243.78/50.24  | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 243.78/50.24  | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | BETA: splitting (80) gives:
% 243.78/50.24  | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | |   (81)  all_58_12 = e2 & op(e0, e3) = e2
% 243.78/50.24  | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | ALPHA: (81) implies:
% 243.78/50.24  | | | | | | | | | | | | |   (82)  all_58_12 = e2
% 243.78/50.24  | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | BETA: splitting (22) gives:
% 243.78/50.24  | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | |   (83)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 243.78/50.24  | | | | | | | | | | | | | |           & op(e1, e2) = e3)
% 243.78/50.24  | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 243.78/50.24  | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | |   (84)  all_58_6 = e3 & op(e1, e3) = e3
% 243.78/50.24  | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 243.78/50.24  | | | | | | | | | | | | | | |   (85)  all_58_6 = e3
% 243.78/50.24  | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 243.78/50.24  | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | |   (86)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 243.78/50.24  | | | | | | | | | | | | | | | |           & op(e2, e3) = e1)
% 243.78/50.24  | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 243.78/50.24  | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | |   (87)  all_58_0 = e1 & op(e3, e3) = e1
% 243.78/50.24  | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 243.78/50.24  | | | | | | | | | | | | | | | | |   (88)  op(e3, e3) = e1
% 243.78/50.24  | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (20), (24), (25), (36), (41), (82),
% 243.78/50.24  | | | | | | | | | | | | | | | | |            (85), (88) are inconsistent by sub-proof #1271.
% 243.78/50.24  | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.24  | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | |   (89)  all_58_2 = e1 & op(e2, e3) = e1
% 243.78/50.24  | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 243.78/50.24  | | | | | | | | | | | | | | | | |   (90)  all_58_2 = e1
% 243.78/50.24  | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 243.78/50.24  | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | |   (91)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 243.78/50.24  | | | | | | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 243.78/50.24  | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |   (92)  all_58_2 = e2 & op(e2, e3) = e2
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |   (93)  all_58_2 = e2
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (93) imply:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |   (94)  e2 = e1
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (94) imply:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |   (95)  all_58_7 = e1
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (11), (18), (35), (36), (41), (43),
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |            (47), (65), (66), (85), (95) are inconsistent by
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |            sub-proof #1269.
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |   (96)  all_58_3 = e2 & op(e2, e2) = e2
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |   (97)  op(e2, e2) = e2
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (36), (97) are inconsistent by
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |            sub-proof #2137.
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.24  | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | |   (98)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 243.78/50.24  | | | | | | | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 243.78/50.24  | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |   (99)  all_58_5 = e2 & op(e2, e1) = e2
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |   (100)  op(e2, e1) = e2
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (36), (79), (100) are inconsistent by
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |            sub-proof #2256.
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |   (101)  all_58_10 = e2 & op(e2, e0) = e2
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | |   (102)  op(e2, e0) = e2
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | |   (103)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 243.78/50.24  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with e1, e2, e1, e1,
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |              simplifying with (27), (66) gives:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (104)  e2 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (104) imply:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (105)  all_58_7 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (11), (18), (35), (36), (41), (43),
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |            (47), (65), (66), (85), (105) are inconsistent by
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1269.
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (106)  all_58_3 = e1 & op(e2, e2) = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (107)  all_58_3 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (107) imply:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (108)  e1 = e0
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | SIMP: (108) implies:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (109)  e1 = e0
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (109) imply:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (110)  all_58_2 = e0
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (17), (18), (31), (36), (41), (42),
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |            (47), (85), (110) are inconsistent by sub-proof
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |            #1266.
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | |   (111)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (112)  all_58_5 = e1 & op(e2, e1) = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (113)  all_58_5 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (113) imply:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (114)  e3 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | SIMP: (114) implies:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (115)  e3 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (115) imply:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (116)  all_58_6 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (9), (12), (13), (15), (16),
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |            (18), (19), (21), (22), (23), (27), (28), (30),
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |            (33), (36), (37), (39), (41), (42), (43), (44),
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (116) are inconsistent by
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1273.
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (117)  all_58_10 = e1 & op(e2, e0) = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |   (118)  op(e2, e0) = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (47), (102), (118) are inconsistent by
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1659.
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | Case 2:
% 243.78/50.25  | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | |   (119)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 243.78/50.25  | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 243.78/50.25  | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 243.78/50.25  | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | |   (120)  all_58_6 = e1 & op(e1, e3) = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 243.78/50.25  | | | | | | | | | | | | | | | | |   (121)  all_58_6 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (9), (12), (13), (15), (16),
% 243.78/50.25  | | | | | | | | | | | | | | | | |            (18), (19), (21), (22), (23), (27), (28), (30),
% 243.78/50.25  | | | | | | | | | | | | | | | | |            (33), (36), (37), (39), (41), (42), (43), (44),
% 243.78/50.25  | | | | | | | | | | | | | | | | |            (46), (47), (48), (121) are inconsistent by
% 243.78/50.25  | | | | | | | | | | | | | | | | |            sub-proof #1273.
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | |   (122)  all_58_12 = e1 & op(e0, e3) = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 243.78/50.25  | | | | | | | | | | | | | | | | |   (123)  all_58_12 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (123) imply:
% 243.78/50.25  | | | | | | | | | | | | | | | | |   (124)  e2 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | SIMP: (124) implies:
% 243.78/50.25  | | | | | | | | | | | | | | | | |   (125)  e2 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (125) imply:
% 243.78/50.25  | | | | | | | | | | | | | | | | |   (126)  all_58_7 = e1
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (11), (18), (35), (36), (41), (43),
% 243.78/50.25  | | | | | | | | | | | | | | | | |            (47), (65), (66), (85), (126) are inconsistent by
% 243.78/50.25  | | | | | | | | | | | | | | | | |            sub-proof #1269.
% 243.78/50.25  | | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | Case 2:
% 243.78/50.25  | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | |   (127)  all_58_7 = e3 & op(e1, e2) = e3
% 243.78/50.25  | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | | REF_CLOSE: (13), (18), (127) are inconsistent by sub-proof
% 243.78/50.25  | | | | | | | | | | | | | | |            #1800.
% 243.78/50.25  | | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | Case 2:
% 243.78/50.25  | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | |   (128)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 243.78/50.25  | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 243.78/50.25  | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | | REF_CLOSE: (6), (18), (26), (27), (36), (128) are
% 243.78/50.25  | | | | | | | | | | | | | |            inconsistent by sub-proof #2148.
% 243.78/50.25  | | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | Case 2:
% 243.78/50.25  | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | |   (129)  all_58_13 = e2 & op(e0, e2) = e2
% 243.78/50.25  | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | | REF_CLOSE: (47), (73), (129) are inconsistent by sub-proof
% 243.78/50.25  | | | | | | | | | | | | |            #2078.
% 243.78/50.25  | | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | Case 2:
% 243.78/50.25  | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | |   (130)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 243.78/50.25  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 243.78/50.25  | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | | REF_CLOSE: (4), (18), (19), (30), (32), (36), (47), (58),
% 243.78/50.25  | | | | | | | | | | | |            (65), (78), (130) are inconsistent by sub-proof
% 243.78/50.25  | | | | | | | | | | | |            #1264.
% 243.78/50.25  | | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | Case 2:
% 243.78/50.25  | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | |   (131)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3
% 243.78/50.25  | | | | | | | | | |            & op(e0, e1) = e3)
% 243.78/50.25  | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | REF_CLOSE: (2), (18), (21), (27), (36), (131) are
% 243.78/50.25  | | | | | | | | | |            inconsistent by sub-proof #1595.
% 243.78/50.25  | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | | 
% 243.78/50.25  | | | | | | | | End of split
% 243.78/50.25  | | | | | | | | 
% 243.78/50.25  | | | | | | | End of split
% 243.78/50.25  | | | | | | | 
% 243.78/50.25  | | | | | | Case 2:
% 243.78/50.25  | | | | | | | 
% 243.78/50.25  | | | | | | |   (132)  all_58_11 = e1 & op(e1, e0) = e1
% 243.78/50.25  | | | | | | | 
% 243.78/50.25  | | | | | | | ALPHA: (132) implies:
% 243.78/50.25  | | | | | | |   (133)  op(e1, e0) = e1
% 243.78/50.25  | | | | | | | 
% 243.78/50.25  | | | | | | | REF_CLOSE: (2), (4), (6), (13), (18), (22), (26), (27), (36),
% 243.78/50.25  | | | | | | |            (41), (43), (133) are inconsistent by sub-proof #1263.
% 243.78/50.25  | | | | | | | 
% 243.78/50.25  | | | | | | End of split
% 243.78/50.25  | | | | | | 
% 243.78/50.25  | | | | | End of split
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | Case 2:
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | |   (134)  all_58_9 = e2 & op(e3, e0) = e2
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | | ALPHA: (134) implies:
% 243.78/50.25  | | | | |   (135)  all_58_9 = e2
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), (15),
% 243.78/50.25  | | | | |            (16), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 243.78/50.25  | | | | |            (27), (28), (30), (32), (33), (34), (35), (36), (37), (38),
% 243.78/50.25  | | | | |            (39), (41), (42), (43), (44), (45), (46), (47), (48), (51),
% 243.78/50.25  | | | | |            (135) are inconsistent by sub-proof #1262.
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | End of split
% 243.78/50.25  | | | | 
% 243.78/50.25  | | | End of split
% 243.78/50.25  | | | 
% 243.78/50.25  | | Case 2:
% 243.78/50.25  | | | 
% 243.78/50.25  | | |   (136)  all_58_3 = e3 & op(e2, e2) = e3
% 243.78/50.25  | | | 
% 243.78/50.25  | | | ALPHA: (136) implies:
% 243.78/50.25  | | |   (137)  all_58_3 = e3
% 243.78/50.25  | | | 
% 243.78/50.25  | | | REF_CLOSE: (2), (44), (137) are inconsistent by sub-proof #1460.
% 243.78/50.25  | | | 
% 243.78/50.25  | | End of split
% 243.78/50.25  | | 
% 243.78/50.25  | Case 2:
% 243.78/50.25  | | 
% 243.78/50.25  | |   (138)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 243.78/50.25  | |            e3)
% 243.78/50.25  | | 
% 243.78/50.25  | | BETA: splitting (138) gives:
% 243.78/50.25  | | 
% 243.78/50.25  | | Case 1:
% 243.78/50.25  | | | 
% 243.78/50.25  | | |   (139)  all_58_7 = e3 & op(e1, e2) = e3
% 243.78/50.25  | | | 
% 243.78/50.25  | | | REF_CLOSE: (13), (18), (139) are inconsistent by sub-proof #1675.
% 243.78/50.25  | | | 
% 243.78/50.25  | | Case 2:
% 243.78/50.25  | | | 
% 243.78/50.25  | | |   (140)  all_58_13 = e3 & op(e0, e2) = e3
% 243.78/50.25  | | | 
% 243.78/50.25  | | | REF_CLOSE: (7), (29), (36), (140) are inconsistent by sub-proof #1919.
% 243.78/50.25  | | | 
% 243.78/50.25  | | End of split
% 243.78/50.25  | | 
% 243.78/50.25  | End of split
% 243.78/50.25  | 
% 243.78/50.25  End of proof
% 243.78/50.25  
% 243.78/50.25  Sub-proof #1262 shows that the following formulas are inconsistent:
% 243.78/50.25  ----------------------------------------------------------------
% 243.78/50.25    (1)   ~ (e3 = e0)
% 243.78/50.25    (2)  all_58_1 = e3
% 243.78/50.25    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.78/50.25         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.78/50.25    (4)   ~ (e2 = e0)
% 243.78/50.25    (5)  op(e1, e2) = all_52_6
% 243.78/50.25    (6)  op(e1, e0) = all_52_14
% 243.78/50.25    (7)  all_58_15 = e3
% 243.78/50.25    (8)  op(e0, e3) = all_52_3
% 243.78/50.25    (9)   ~ (all_52_6 = e0)
% 243.78/50.25    (10)   ~ (e3 = e1)
% 243.78/50.25    (11)  all_58_7 = e2
% 243.78/50.25    (12)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.78/50.25          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.78/50.25    (13)  op(e2, e1) = all_52_9
% 243.78/50.25    (14)   ~ (e3 = e2)
% 243.78/50.25    (15)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.78/50.25          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.78/50.25    (16)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.78/50.25          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.78/50.25    (17)  op(e0, e1) = e0
% 243.78/50.25    (18)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.78/50.25          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.78/50.25    (19)   ~ (all_52_3 = e3)
% 243.78/50.25    (20)   ~ (all_52_1 = e0)
% 243.78/50.25    (21)  op(e2, e3) = all_52_1
% 243.78/50.25    (22)   ~ (all_52_14 = e3)
% 243.78/50.25    (23)  op(e1, e1) = e2
% 243.78/50.25    (24)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.78/50.25          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.78/50.25    (25)  all_58_14 = e0
% 243.78/50.25    (26)  op(e0, e0) = e3
% 243.78/50.25    (27)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.78/50.25          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.78/50.25    (28)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.78/50.25          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.78/50.25    (29)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.78/50.25          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.78/50.25    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.25    (31)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.78/50.25          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.78/50.25    (32)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.78/50.25          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.78/50.25    (33)  all_58_11 = e0
% 243.78/50.25    (34)   ~ (e1 = e0)
% 243.78/50.25    (35)  op(e3, e3) = e0
% 243.78/50.25    (36)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.78/50.25          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.78/50.25    (37)  all_58_9 = e2
% 243.78/50.25    (38)  all_58_3 = e0
% 243.78/50.25    (39)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.78/50.25          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.78/50.25            e2)
% 243.78/50.25    (40)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.78/50.25          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.78/50.25    (41)   ~ (e2 = e1)
% 243.78/50.25    (42)   ~ (all_52_9 = e2)
% 243.78/50.25  
% 243.78/50.25  Begin of proof
% 243.78/50.25  | 
% 243.78/50.25  | BETA: splitting (32) gives:
% 243.78/50.25  | 
% 243.78/50.25  | Case 1:
% 243.78/50.25  | | 
% 243.78/50.25  | |   (43)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 243.78/50.25  | |           e1)
% 243.78/50.25  | | 
% 243.78/50.25  | | BETA: splitting (43) gives:
% 243.78/50.25  | | 
% 243.78/50.25  | | Case 1:
% 243.78/50.25  | | | 
% 243.78/50.25  | | |   (44)  all_58_1 = e1 & op(e3, e2) = e1
% 243.78/50.25  | | | 
% 243.78/50.25  | | | REF_CLOSE: (2), (10), (44) are inconsistent by sub-proof #1753.
% 243.78/50.25  | | | 
% 243.78/50.25  | | Case 2:
% 243.78/50.25  | | | 
% 243.78/50.25  | | |   (45)  all_58_3 = e1 & op(e2, e2) = e1
% 243.78/50.25  | | | 
% 243.78/50.25  | | | REF_CLOSE: (34), (38), (45) are inconsistent by sub-proof #1752.
% 243.78/50.25  | | | 
% 243.78/50.25  | | End of split
% 243.78/50.25  | | 
% 243.78/50.25  | Case 2:
% 243.78/50.25  | | 
% 243.78/50.25  | |   (46)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 243.78/50.25  | |           e1)
% 243.78/50.25  | | 
% 243.78/50.25  | | BETA: splitting (46) gives:
% 243.78/50.25  | | 
% 243.78/50.25  | | Case 1:
% 243.78/50.25  | | | 
% 243.78/50.25  | | |   (47)  all_58_7 = e1 & op(e1, e2) = e1
% 243.78/50.25  | | | 
% 243.78/50.25  | | | REF_CLOSE: (11), (41), (47) are inconsistent by sub-proof #2224.
% 243.78/50.25  | | | 
% 243.78/50.25  | | Case 2:
% 243.78/50.25  | | | 
% 243.78/50.25  | | |   (48)  all_58_13 = e1 & op(e0, e2) = e1
% 243.78/50.25  | | | 
% 243.78/50.25  | | | ALPHA: (48) implies:
% 243.78/50.25  | | |   (49)  all_58_13 = e1
% 243.78/50.25  | | | 
% 243.78/50.25  | | | BETA: splitting (3) gives:
% 243.78/50.25  | | | 
% 243.78/50.25  | | | Case 1:
% 243.78/50.25  | | | | 
% 243.78/50.25  | | | |   (50)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 243.78/50.25  | | | |           = e1)
% 243.78/50.25  | | | | 
% 243.78/50.25  | | | | BETA: splitting (50) gives:
% 243.78/50.25  | | | | 
% 243.78/50.25  | | | | Case 1:
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | |   (51)  all_58_6 = e1 & op(e1, e3) = e1
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | | ALPHA: (51) implies:
% 243.78/50.25  | | | | |   (52)  all_58_6 = e1
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (10), (11), (12), (13), (14),
% 243.78/50.25  | | | | |            (15), (17), (18), (19), (23), (24), (25), (27), (30), (31),
% 243.78/50.25  | | | | |            (33), (34), (35), (36), (38), (40), (41), (42), (52) are
% 243.78/50.25  | | | | |            inconsistent by sub-proof #1273.
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | Case 2:
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | |   (53)  all_58_7 = e1 & op(e1, e2) = e1
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | | REF_CLOSE: (11), (41), (53) are inconsistent by sub-proof #2224.
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | End of split
% 243.78/50.25  | | | | 
% 243.78/50.25  | | | Case 2:
% 243.78/50.25  | | | | 
% 243.78/50.25  | | | |   (54)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0)
% 243.78/50.25  | | | |           = e1)
% 243.78/50.25  | | | | 
% 243.78/50.25  | | | | BETA: splitting (54) gives:
% 243.78/50.25  | | | | 
% 243.78/50.25  | | | | Case 1:
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | |   (55)  all_58_8 = e1 & op(e1, e1) = e1
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | | ALPHA: (55) implies:
% 243.78/50.25  | | | | |   (56)  all_58_8 = e1
% 243.78/50.25  | | | | |   (57)  op(e1, e1) = e1
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | | BETA: splitting (15) gives:
% 243.78/50.25  | | | | | 
% 243.78/50.25  | | | | | Case 1:
% 243.78/50.25  | | | | | | 
% 243.78/50.25  | | | | | |   (58)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 243.78/50.25  | | | | | |             e1) = e2)
% 243.78/50.25  | | | | | | 
% 243.78/50.25  | | | | | | BETA: splitting (58) gives:
% 243.78/50.25  | | | | | | 
% 243.78/50.25  | | | | | | Case 1:
% 243.78/50.25  | | | | | | | 
% 243.78/50.25  | | | | | | |   (59)  all_58_4 = e2 & op(e3, e1) = e2
% 243.78/50.25  | | | | | | | 
% 243.78/50.25  | | | | | | | ALPHA: (59) implies:
% 243.78/50.25  | | | | | | |   (60)  all_58_4 = e2
% 243.78/50.25  | | | | | | | 
% 243.78/50.25  | | | | | | | BETA: splitting (24) gives:
% 243.78/50.25  | | | | | | | 
% 243.78/50.25  | | | | | | | Case 1:
% 243.78/50.25  | | | | | | | | 
% 243.78/50.25  | | | | | | | |   (61)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 243.78/50.25  | | | | | | | |           op(e2, e1) = e3)
% 243.78/50.25  | | | | | | | | 
% 243.78/50.25  | | | | | | | | BETA: splitting (61) gives:
% 243.78/50.25  | | | | | | | | 
% 243.78/50.25  | | | | | | | | Case 1:
% 243.78/50.25  | | | | | | | | | 
% 243.78/50.25  | | | | | | | | |   (62)  all_58_4 = e3 & op(e3, e1) = e3
% 243.78/50.25  | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | ALPHA: (62) implies:
% 243.78/50.25  | | | | | | | | |   (63)  all_58_4 = e3
% 243.78/50.25  | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | REF_CLOSE: (14), (60), (63) are inconsistent by sub-proof
% 243.78/50.25  | | | | | | | | |            #1902.
% 243.78/50.25  | | | | | | | | | 
% 243.78/50.25  | | | | | | | | Case 2:
% 243.78/50.25  | | | | | | | | | 
% 243.78/50.25  | | | | | | | | |   (64)  all_58_5 = e3 & op(e2, e1) = e3
% 243.78/50.25  | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | ALPHA: (64) implies:
% 243.78/50.25  | | | | | | | | |   (65)  all_58_5 = e3
% 243.78/50.25  | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | BETA: splitting (39) gives:
% 243.78/50.25  | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | Case 1:
% 243.78/50.25  | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | |   (66)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2
% 243.78/50.25  | | | | | | | | | |           & op(e0, e2) = e2)
% 243.78/50.25  | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | BETA: splitting (66) gives:
% 243.78/50.25  | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | Case 1:
% 243.78/50.25  | | | | | | | | | | | 
% 243.78/50.25  | | | | | | | | | | |   (67)  all_58_12 = e2 & op(e0, e3) = e2
% 243.78/50.26  | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | ALPHA: (67) implies:
% 243.78/50.26  | | | | | | | | | | |   (68)  all_58_12 = e2
% 243.78/50.26  | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | BETA: splitting (18) gives:
% 243.78/50.26  | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | Case 1:
% 243.78/50.26  | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | |   (69)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 243.78/50.26  | | | | | | | | | | | |           & op(e1, e2) = e3)
% 243.78/50.26  | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | BETA: splitting (69) gives:
% 243.78/50.26  | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | Case 1:
% 243.78/50.26  | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | |   (70)  all_58_6 = e3 & op(e1, e3) = e3
% 243.78/50.26  | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | ALPHA: (70) implies:
% 243.78/50.26  | | | | | | | | | | | | |   (71)  all_58_6 = e3
% 243.78/50.26  | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | BETA: splitting (28) gives:
% 243.78/50.26  | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | Case 1:
% 243.78/50.26  | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | |   (72)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 243.78/50.26  | | | | | | | | | | | | | |           & op(e3, e2) = e1)
% 243.78/50.26  | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 243.78/50.26  | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | Case 1:
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | |   (73)  all_58_0 = e1 & op(e3, e3) = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | ALPHA: (73) implies:
% 243.78/50.26  | | | | | | | | | | | | | | |   (74)  op(e3, e3) = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (16), (20), (21), (30), (34), (68),
% 243.78/50.26  | | | | | | | | | | | | | | |            (71), (74) are inconsistent by sub-proof #1271.
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | Case 2:
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | |   (75)  all_58_1 = e1 & op(e3, e2) = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | ALPHA: (75) implies:
% 243.78/50.26  | | | | | | | | | | | | | | |   (76)  all_58_1 = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | COMBINE_EQS: (2), (76) imply:
% 243.78/50.26  | | | | | | | | | | | | | | |   (77)  e3 = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | COMBINE_EQS: (71), (77) imply:
% 243.78/50.26  | | | | | | | | | | | | | | |   (78)  all_58_6 = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (10), (11), (12), (13),
% 243.78/50.26  | | | | | | | | | | | | | | |            (14), (15), (17), (18), (19), (23), (24), (25),
% 243.78/50.26  | | | | | | | | | | | | | | |            (27), (30), (31), (33), (34), (35), (36), (38),
% 243.78/50.26  | | | | | | | | | | | | | | |            (40), (41), (42), (78) are inconsistent by
% 243.78/50.26  | | | | | | | | | | | | | | |            sub-proof #1273.
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | End of split
% 243.78/50.26  | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | Case 2:
% 243.78/50.26  | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | |   (79)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 243.78/50.26  | | | | | | | | | | | | | |           & op(e3, e0) = e1)
% 243.78/50.26  | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 243.78/50.26  | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | Case 1:
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | |   (80)  all_58_4 = e1 & op(e3, e1) = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | ALPHA: (80) implies:
% 243.78/50.26  | | | | | | | | | | | | | | |   (81)  all_58_4 = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | COMBINE_EQS: (60), (81) imply:
% 243.78/50.26  | | | | | | | | | | | | | | |   (82)  e2 = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | COMBINE_EQS: (11), (82) imply:
% 243.78/50.26  | | | | | | | | | | | | | | |   (83)  all_58_7 = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (9), (14), (29), (30), (34), (36),
% 243.78/50.26  | | | | | | | | | | | | | | |            (41), (56), (57), (71), (83) are inconsistent by
% 243.78/50.26  | | | | | | | | | | | | | | |            sub-proof #1269.
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | Case 2:
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | |   (84)  all_58_9 = e1 & op(e3, e0) = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 243.78/50.26  | | | | | | | | | | | | | | |   (85)  all_58_9 = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | COMBINE_EQS: (37), (85) imply:
% 243.78/50.26  | | | | | | | | | | | | | | |   (86)  e2 = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | SIMP: (86) implies:
% 243.78/50.26  | | | | | | | | | | | | | | |   (87)  e2 = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | COMBINE_EQS: (11), (87) imply:
% 243.78/50.26  | | | | | | | | | | | | | | |   (88)  all_58_7 = e1
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (9), (14), (29), (30), (34), (36),
% 243.78/50.26  | | | | | | | | | | | | | | |            (41), (56), (57), (71), (88) are inconsistent by
% 243.78/50.26  | | | | | | | | | | | | | | |            sub-proof #1269.
% 243.78/50.26  | | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | | End of split
% 243.78/50.26  | | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | End of split
% 243.78/50.26  | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | Case 2:
% 243.78/50.26  | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | |   (89)  all_58_7 = e3 & op(e1, e2) = e3
% 243.78/50.26  | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | | REF_CLOSE: (11), (14), (89) are inconsistent by sub-proof
% 243.78/50.26  | | | | | | | | | | | | |            #1800.
% 243.78/50.26  | | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | End of split
% 243.78/50.26  | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | Case 2:
% 243.78/50.26  | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | |   (90)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 243.78/50.26  | | | | | | | | | | | |           e3 & op(e1, e0) = e3)
% 243.78/50.26  | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | | REF_CLOSE: (6), (14), (22), (23), (30), (90) are inconsistent
% 243.78/50.26  | | | | | | | | | | | |            by sub-proof #2148.
% 243.78/50.26  | | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | End of split
% 243.78/50.26  | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | Case 2:
% 243.78/50.26  | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | |   (91)  all_58_13 = e2 & op(e0, e2) = e2
% 243.78/50.26  | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | | REF_CLOSE: (41), (49), (91) are inconsistent by sub-proof
% 243.78/50.26  | | | | | | | | | | |            #2078.
% 243.78/50.26  | | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | End of split
% 243.78/50.26  | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | Case 2:
% 243.78/50.26  | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | |   (92)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2
% 243.78/50.26  | | | | | | | | | |           & op(e0, e0) = e2)
% 243.78/50.26  | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | | REF_CLOSE: (4), (14), (15), (25), (26), (30), (41), (56),
% 243.78/50.26  | | | | | | | | | |            (60), (65), (92) are inconsistent by sub-proof
% 243.78/50.26  | | | | | | | | | |            #1264.
% 243.78/50.26  | | | | | | | | | | 
% 243.78/50.26  | | | | | | | | | End of split
% 243.78/50.26  | | | | | | | | | 
% 243.78/50.26  | | | | | | | | End of split
% 243.78/50.26  | | | | | | | | 
% 243.78/50.26  | | | | | | | Case 2:
% 243.78/50.26  | | | | | | | | 
% 243.78/50.26  | | | | | | | |   (93)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 243.78/50.26  | | | | | | | |           op(e0, e1) = e3)
% 243.78/50.26  | | | | | | | | 
% 243.78/50.26  | | | | | | | | REF_CLOSE: (1), (14), (17), (23), (30), (93) are inconsistent by
% 243.78/50.26  | | | | | | | |            sub-proof #1595.
% 243.78/50.26  | | | | | | | | 
% 243.78/50.26  | | | | | | | End of split
% 243.78/50.26  | | | | | | | 
% 243.78/50.26  | | | | | | Case 2:
% 243.78/50.26  | | | | | | | 
% 243.78/50.26  | | | | | | |   (94)  all_58_5 = e2 & op(e2, e1) = e2
% 243.78/50.26  | | | | | | | 
% 243.78/50.26  | | | | | | | ALPHA: (94) implies:
% 243.78/50.26  | | | | | | |   (95)  op(e2, e1) = e2
% 243.78/50.26  | | | | | | | 
% 243.78/50.26  | | | | | | | REF_CLOSE: (13), (30), (42), (95) are inconsistent by sub-proof
% 243.78/50.26  | | | | | | |            #2328.
% 243.78/50.26  | | | | | | | 
% 243.78/50.26  | | | | | | End of split
% 243.78/50.26  | | | | | | 
% 243.78/50.26  | | | | | Case 2:
% 243.78/50.26  | | | | | | 
% 243.78/50.26  | | | | | |   (96)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 243.78/50.26  | | | | | |             e1) = e2)
% 243.78/50.26  | | | | | | 
% 243.78/50.26  | | | | | | REF_CLOSE: (4), (25), (41), (56), (96) are inconsistent by sub-proof
% 243.78/50.26  | | | | | |            #1276.
% 243.78/50.26  | | | | | | 
% 243.78/50.26  | | | | | End of split
% 243.78/50.26  | | | | | 
% 243.78/50.26  | | | | Case 2:
% 243.78/50.26  | | | | | 
% 243.78/50.26  | | | | |   (97)  all_58_11 = e1 & op(e1, e0) = e1
% 243.78/50.26  | | | | | 
% 243.78/50.26  | | | | | ALPHA: (97) implies:
% 243.78/50.26  | | | | |   (98)  op(e1, e0) = e1
% 243.78/50.26  | | | | | 
% 243.78/50.26  | | | | | REF_CLOSE: (1), (4), (6), (11), (14), (18), (22), (23), (30), (34),
% 243.78/50.26  | | | | |            (36), (98) are inconsistent by sub-proof #1263.
% 243.78/50.26  | | | | | 
% 243.78/50.26  | | | | End of split
% 243.78/50.26  | | | | 
% 243.78/50.26  | | | End of split
% 243.78/50.26  | | | 
% 243.78/50.26  | | End of split
% 243.78/50.26  | | 
% 243.78/50.26  | End of split
% 243.78/50.26  | 
% 243.78/50.26  End of proof
% 243.78/50.26  
% 243.78/50.26  Sub-proof #1263 shows that the following formulas are inconsistent:
% 243.78/50.26  ----------------------------------------------------------------
% 243.78/50.26    (1)   ~ (e3 = e0)
% 243.78/50.26    (2)   ~ (e2 = e0)
% 243.78/50.26    (3)  op(e1, e0) = all_52_14
% 243.78/50.26    (4)  all_58_7 = e2
% 243.78/50.26    (5)  op(e1, e0) = e1
% 243.78/50.26    (6)   ~ (e3 = e2)
% 243.78/50.26    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.78/50.26         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.78/50.26    (8)   ~ (all_52_14 = e3)
% 243.78/50.26    (9)  op(e1, e1) = e2
% 243.78/50.26    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.26    (11)   ~ (e1 = e0)
% 243.78/50.26    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.78/50.26          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.78/50.26  
% 243.78/50.26  Begin of proof
% 243.78/50.26  | 
% 243.78/50.26  | BETA: splitting (7) gives:
% 243.78/50.26  | 
% 243.78/50.26  | Case 1:
% 243.78/50.26  | | 
% 243.78/50.26  | |   (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 243.78/50.26  | |           e3)
% 243.78/50.26  | | 
% 243.78/50.26  | | BETA: splitting (13) gives:
% 243.78/50.26  | | 
% 243.78/50.26  | | Case 1:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (14)  all_58_6 = e3 & op(e1, e3) = e3
% 243.78/50.26  | | | 
% 243.78/50.26  | | | ALPHA: (14) implies:
% 243.78/50.26  | | |   (15)  all_58_6 = e3
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (1), (2), (4), (5), (9), (10), (11), (12), (15) are
% 243.78/50.26  | | |            inconsistent by sub-proof #2209.
% 243.78/50.26  | | | 
% 243.78/50.26  | | Case 2:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (16)  all_58_7 = e3 & op(e1, e2) = e3
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (4), (6), (16) are inconsistent by sub-proof #1800.
% 243.78/50.26  | | | 
% 243.78/50.26  | | End of split
% 243.78/50.26  | | 
% 243.78/50.26  | Case 2:
% 243.78/50.26  | | 
% 243.78/50.26  | |   (17)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 243.78/50.26  | |           e3)
% 243.78/50.26  | | 
% 243.78/50.26  | | REF_CLOSE: (3), (6), (8), (9), (10), (17) are inconsistent by sub-proof
% 243.78/50.26  | |            #2148.
% 243.78/50.26  | | 
% 243.78/50.26  | End of split
% 243.78/50.26  | 
% 243.78/50.26  End of proof
% 243.78/50.26  
% 243.78/50.26  Sub-proof #1264 shows that the following formulas are inconsistent:
% 243.78/50.26  ----------------------------------------------------------------
% 243.78/50.26    (1)   ~ (e2 = e0)
% 243.78/50.26    (2)  all_58_5 = e3
% 243.78/50.26    (3)  all_58_4 = e2
% 243.78/50.26    (4)  all_58_8 = e1
% 243.78/50.26    (5)   ~ (e3 = e2)
% 243.78/50.26    (6)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.78/50.26         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.78/50.26    (7)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.78/50.26    (8)  all_58_14 = e0
% 243.78/50.26    (9)  op(e0, e0) = e3
% 243.78/50.26    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.26    (11)   ~ (e2 = e1)
% 243.78/50.26  
% 243.78/50.26  Begin of proof
% 243.78/50.26  | 
% 243.78/50.26  | BETA: splitting (7) gives:
% 243.78/50.26  | 
% 243.78/50.26  | Case 1:
% 243.78/50.26  | | 
% 243.78/50.26  | |   (12)  all_58_14 = e2 & op(e0, e1) = e2
% 243.78/50.26  | | 
% 243.78/50.26  | | ALPHA: (12) implies:
% 243.78/50.26  | |   (13)  all_58_14 = e2
% 243.78/50.26  | | 
% 243.78/50.26  | | COMBINE_EQS: (8), (13) imply:
% 243.78/50.26  | |   (14)  e2 = e0
% 243.78/50.26  | | 
% 243.78/50.26  | | COMBINE_EQS: (3), (14) imply:
% 243.78/50.26  | |   (15)  all_58_4 = e0
% 243.78/50.26  | | 
% 243.78/50.26  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (11), (15) are inconsistent by
% 243.78/50.26  | |            sub-proof #1265.
% 243.78/50.26  | | 
% 243.78/50.26  | Case 2:
% 243.78/50.26  | | 
% 243.78/50.26  | |   (16)  all_58_15 = e2 & op(e0, e0) = e2
% 243.78/50.26  | | 
% 243.78/50.26  | | ALPHA: (16) implies:
% 243.78/50.26  | |   (17)  op(e0, e0) = e2
% 243.78/50.26  | | 
% 243.78/50.26  | | REF_CLOSE: (5), (9), (10), (17) are inconsistent by sub-proof #1388.
% 243.78/50.26  | | 
% 243.78/50.26  | End of split
% 243.78/50.26  | 
% 243.78/50.26  End of proof
% 243.78/50.26  
% 243.78/50.26  Sub-proof #1265 shows that the following formulas are inconsistent:
% 243.78/50.26  ----------------------------------------------------------------
% 243.78/50.26    (1)   ~ (e2 = e0)
% 243.78/50.26    (2)  all_58_5 = e3
% 243.78/50.26    (3)  all_58_8 = e1
% 243.78/50.26    (4)   ~ (e3 = e2)
% 243.78/50.26    (5)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.78/50.26         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.78/50.26    (6)  all_58_14 = e0
% 243.78/50.26    (7)  all_58_4 = e0
% 243.78/50.26    (8)   ~ (e2 = e1)
% 243.78/50.26  
% 243.78/50.26  Begin of proof
% 243.78/50.26  | 
% 243.78/50.26  | BETA: splitting (5) gives:
% 243.78/50.26  | 
% 243.78/50.26  | Case 1:
% 243.78/50.26  | | 
% 243.78/50.26  | |   (9)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2)
% 243.78/50.26  | | 
% 243.78/50.26  | | BETA: splitting (9) gives:
% 243.78/50.26  | | 
% 243.78/50.26  | | Case 1:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (10)  all_58_4 = e2 & op(e3, e1) = e2
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (1), (7), (10) are inconsistent by sub-proof #1707.
% 243.78/50.26  | | | 
% 243.78/50.26  | | Case 2:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (11)  all_58_5 = e2 & op(e2, e1) = e2
% 243.78/50.26  | | | 
% 243.78/50.26  | | | ALPHA: (11) implies:
% 243.78/50.26  | | |   (12)  all_58_5 = e2
% 243.78/50.26  | | | 
% 243.78/50.26  | | | COMBINE_EQS: (2), (12) imply:
% 243.78/50.26  | | |   (13)  e3 = e2
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REDUCE: (4), (13) imply:
% 243.78/50.26  | | |   (14)  $false
% 243.78/50.26  | | | 
% 243.78/50.26  | | | CLOSE: (14) is inconsistent.
% 243.78/50.26  | | | 
% 243.78/50.26  | | End of split
% 243.78/50.26  | | 
% 243.78/50.26  | Case 2:
% 243.78/50.26  | | 
% 243.78/50.26  | |   (15)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 243.78/50.26  | |           e2)
% 243.78/50.26  | | 
% 243.78/50.26  | | BETA: splitting (15) gives:
% 243.78/50.26  | | 
% 243.78/50.26  | | Case 1:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (16)  all_58_8 = e2 & op(e1, e1) = e2
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (3), (8), (16) are inconsistent by sub-proof #2217.
% 243.78/50.26  | | | 
% 243.78/50.26  | | Case 2:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (17)  all_58_14 = e2 & op(e0, e1) = e2
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (1), (6), (17) are inconsistent by sub-proof #2077.
% 243.78/50.26  | | | 
% 243.78/50.26  | | End of split
% 243.78/50.26  | | 
% 243.78/50.26  | End of split
% 243.78/50.26  | 
% 243.78/50.26  End of proof
% 243.78/50.26  
% 243.78/50.26  Sub-proof #1266 shows that the following formulas are inconsistent:
% 243.78/50.26  ----------------------------------------------------------------
% 243.78/50.26    (1)  all_58_6 = e3
% 243.78/50.26    (2)   ~ (e2 = e0)
% 243.78/50.26    (3)   ~ (e3 = e1)
% 243.78/50.26    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.78/50.26         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.78/50.26    (5)   ~ (e3 = e2)
% 243.78/50.26    (6)  all_58_2 = e0
% 243.78/50.26    (7)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.78/50.26         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.78/50.26    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.26    (9)   ~ (e1 = e0)
% 243.78/50.26    (10)  op(e3, e3) = e0
% 243.78/50.26    (11)   ~ (e2 = e1)
% 243.78/50.26  
% 243.78/50.26  Begin of proof
% 243.78/50.26  | 
% 243.78/50.26  | BETA: splitting (7) gives:
% 243.78/50.26  | 
% 243.78/50.26  | Case 1:
% 243.78/50.26  | | 
% 243.78/50.26  | |   (12)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 243.78/50.26  | |           e1)
% 243.78/50.26  | | 
% 243.78/50.26  | | BETA: splitting (12) gives:
% 243.78/50.26  | | 
% 243.78/50.26  | | Case 1:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (13)  all_58_0 = e1 & op(e3, e3) = e1
% 243.78/50.26  | | | 
% 243.78/50.26  | | | ALPHA: (13) implies:
% 243.78/50.26  | | |   (14)  op(e3, e3) = e1
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (8), (9), (10), (14) are inconsistent by sub-proof #1828.
% 243.78/50.26  | | | 
% 243.78/50.26  | | Case 2:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (15)  all_58_2 = e1 & op(e2, e3) = e1
% 243.78/50.26  | | | 
% 243.78/50.26  | | | ALPHA: (15) implies:
% 243.78/50.26  | | |   (16)  all_58_2 = e1
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (6), (9), (16) are inconsistent by sub-proof #1268.
% 243.78/50.26  | | | 
% 243.78/50.26  | | End of split
% 243.78/50.26  | | 
% 243.78/50.26  | Case 2:
% 243.78/50.26  | | 
% 243.78/50.26  | |   (17)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 243.78/50.26  | |           e1)
% 243.78/50.26  | | 
% 243.78/50.26  | | BETA: splitting (17) gives:
% 243.78/50.26  | | 
% 243.78/50.26  | | Case 1:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (18)  all_58_6 = e1 & op(e1, e3) = e1
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (1), (3), (18) are inconsistent by sub-proof #1803.
% 243.78/50.26  | | | 
% 243.78/50.26  | | Case 2:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (19)  all_58_12 = e1 & op(e0, e3) = e1
% 243.78/50.26  | | | 
% 243.78/50.26  | | | ALPHA: (19) implies:
% 243.78/50.26  | | |   (20)  all_58_12 = e1
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (11), (20) are inconsistent
% 243.78/50.26  | | |            by sub-proof #1267.
% 243.78/50.26  | | | 
% 243.78/50.26  | | End of split
% 243.78/50.26  | | 
% 243.78/50.26  | End of split
% 243.78/50.26  | 
% 243.78/50.26  End of proof
% 243.78/50.26  
% 243.78/50.26  Sub-proof #1267 shows that the following formulas are inconsistent:
% 243.78/50.26  ----------------------------------------------------------------
% 243.78/50.26    (1)  all_58_6 = e3
% 243.78/50.26    (2)   ~ (e2 = e0)
% 243.78/50.26    (3)  all_58_12 = e1
% 243.78/50.26    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.78/50.26         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.78/50.26    (5)   ~ (e3 = e2)
% 243.78/50.26    (6)  all_58_2 = e0
% 243.78/50.26    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.26    (8)  op(e3, e3) = e0
% 243.78/50.26    (9)   ~ (e2 = e1)
% 243.78/50.26  
% 243.78/50.26  Begin of proof
% 243.78/50.26  | 
% 243.78/50.26  | BETA: splitting (4) gives:
% 243.78/50.26  | 
% 243.78/50.26  | Case 1:
% 243.78/50.26  | | 
% 243.78/50.26  | |   (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 243.78/50.26  | |           e2)
% 243.78/50.26  | | 
% 243.78/50.26  | | BETA: splitting (10) gives:
% 243.78/50.26  | | 
% 243.78/50.26  | | Case 1:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (11)  all_58_0 = e2 & op(e3, e3) = e2
% 243.78/50.26  | | | 
% 243.78/50.26  | | | ALPHA: (11) implies:
% 243.78/50.26  | | |   (12)  op(e3, e3) = e2
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (2), (7), (8), (12) are inconsistent by sub-proof #2188.
% 243.78/50.26  | | | 
% 243.78/50.26  | | Case 2:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (13)  all_58_2 = e2 & op(e2, e3) = e2
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (2), (6), (13) are inconsistent by sub-proof #1575.
% 243.78/50.26  | | | 
% 243.78/50.26  | | End of split
% 243.78/50.26  | | 
% 243.78/50.26  | Case 2:
% 243.78/50.26  | | 
% 243.78/50.26  | |   (14)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 243.78/50.26  | |           e2)
% 243.78/50.26  | | 
% 243.78/50.26  | | BETA: splitting (14) gives:
% 243.78/50.26  | | 
% 243.78/50.26  | | Case 1:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (15)  all_58_6 = e2 & op(e1, e3) = e2
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (1), (5), (15) are inconsistent by sub-proof #2219.
% 243.78/50.26  | | | 
% 243.78/50.26  | | Case 2:
% 243.78/50.26  | | | 
% 243.78/50.26  | | |   (16)  all_58_12 = e2 & op(e0, e3) = e2
% 243.78/50.26  | | | 
% 243.78/50.26  | | | REF_CLOSE: (3), (9), (16) are inconsistent by sub-proof #1302.
% 243.78/50.26  | | | 
% 243.78/50.26  | | End of split
% 243.78/50.26  | | 
% 243.78/50.26  | End of split
% 243.78/50.26  | 
% 243.78/50.26  End of proof
% 243.78/50.26  
% 243.78/50.26  Sub-proof #1268 shows that the following formulas are inconsistent:
% 243.78/50.26  ----------------------------------------------------------------
% 243.78/50.26    (1)  all_58_2 = e1
% 243.78/50.26    (2)  all_58_2 = e0
% 243.78/50.26    (3)   ~ (e1 = e0)
% 243.78/50.26  
% 243.78/50.26  Begin of proof
% 243.78/50.26  | 
% 243.78/50.26  | COMBINE_EQS: (1), (2) imply:
% 243.78/50.26  |   (4)  e1 = e0
% 243.78/50.26  | 
% 243.78/50.26  | SIMP: (4) implies:
% 243.78/50.26  |   (5)  e1 = e0
% 243.78/50.26  | 
% 243.78/50.26  | REDUCE: (3), (5) imply:
% 243.78/50.27  |   (6)  $false
% 243.78/50.27  | 
% 243.78/50.27  | CLOSE: (6) is inconsistent.
% 243.78/50.27  | 
% 243.78/50.27  End of proof
% 243.78/50.27  
% 243.78/50.27  Sub-proof #1269 shows that the following formulas are inconsistent:
% 243.78/50.27  ----------------------------------------------------------------
% 243.78/50.27    (1)   ~ (e3 = e0)
% 243.78/50.27    (2)  op(e1, e1) = e1
% 243.78/50.27    (3)  all_58_6 = e3
% 243.78/50.27    (4)   ~ (e2 = e0)
% 243.78/50.27    (5)  op(e1, e2) = all_52_6
% 243.78/50.27    (6)  all_58_8 = e1
% 243.78/50.27    (7)   ~ (all_52_6 = e0)
% 243.78/50.27    (8)   ~ (e3 = e2)
% 243.78/50.27    (9)  all_58_7 = e1
% 243.78/50.27    (10)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.78/50.27          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.78/50.27    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.27            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.27    (12)   ~ (e1 = e0)
% 243.78/50.27    (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.78/50.27          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.78/50.27    (14)   ~ (e2 = e1)
% 243.78/50.27  
% 243.78/50.27  Begin of proof
% 243.78/50.27  | 
% 243.78/50.27  | BETA: splitting (13) gives:
% 243.78/50.27  | 
% 243.78/50.27  | Case 1:
% 243.78/50.27  | | 
% 243.78/50.27  | |   (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 243.78/50.27  | |           e0)
% 243.78/50.27  | | 
% 243.78/50.27  | | BETA: splitting (15) gives:
% 243.78/50.27  | | 
% 243.78/50.27  | | Case 1:
% 243.78/50.27  | | | 
% 243.78/50.27  | | |   (16)  all_58_6 = e0 & op(e1, e3) = e0
% 243.78/50.27  | | | 
% 243.78/50.27  | | | REF_CLOSE: (1), (3), (16) are inconsistent by sub-proof #2213.
% 243.78/50.27  | | | 
% 243.78/50.27  | | Case 2:
% 243.78/50.27  | | | 
% 243.78/50.27  | | |   (17)  all_58_7 = e0 & op(e1, e2) = e0
% 243.78/50.27  | | | 
% 243.78/50.27  | | | REF_CLOSE: (5), (7), (11), (17) are inconsistent by sub-proof #2022.
% 243.78/50.27  | | | 
% 243.78/50.27  | | End of split
% 243.78/50.27  | | 
% 243.78/50.27  | Case 2:
% 243.78/50.27  | | 
% 243.78/50.27  | |   (18)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.78/50.27  | |           e0)
% 243.78/50.27  | | 
% 243.78/50.27  | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (11), (12), (14), (18) are
% 243.78/50.27  | |            inconsistent by sub-proof #1270.
% 243.78/50.27  | | 
% 243.78/50.27  | End of split
% 243.78/50.27  | 
% 243.78/50.27  End of proof
% 243.78/50.27  
% 243.78/50.27  Sub-proof #1270 shows that the following formulas are inconsistent:
% 243.78/50.27  ----------------------------------------------------------------
% 243.78/50.27    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.78/50.27    (2)  op(e1, e1) = e1
% 243.78/50.27    (3)  all_58_6 = e3
% 243.78/50.27    (4)   ~ (e2 = e0)
% 243.78/50.27    (5)  all_58_8 = e1
% 243.78/50.27    (6)   ~ (e3 = e2)
% 243.78/50.27    (7)  all_58_7 = e1
% 243.78/50.27    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.78/50.27         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.78/50.27    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.27    (10)   ~ (e1 = e0)
% 243.78/50.27    (11)   ~ (e2 = e1)
% 243.78/50.27  
% 243.78/50.27  Begin of proof
% 243.78/50.27  | 
% 243.78/50.27  | BETA: splitting (1) gives:
% 243.78/50.27  | 
% 243.78/50.27  | Case 1:
% 243.78/50.27  | | 
% 243.78/50.27  | |   (12)  all_58_8 = e0 & op(e1, e1) = e0
% 243.78/50.27  | | 
% 243.78/50.27  | | ALPHA: (12) implies:
% 243.78/50.27  | |   (13)  op(e1, e1) = e0
% 243.78/50.27  | | 
% 243.78/50.27  | | REF_CLOSE: (2), (9), (10), (13) are inconsistent by sub-proof #2220.
% 243.78/50.27  | | 
% 243.78/50.27  | Case 2:
% 243.78/50.27  | | 
% 243.78/50.27  | |   (14)  all_58_11 = e0 & op(e1, e0) = e0
% 243.78/50.27  | | 
% 243.78/50.27  | | ALPHA: (14) implies:
% 243.78/50.27  | |   (15)  all_58_11 = e0
% 243.78/50.27  | | 
% 243.78/50.27  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (11), (15) are inconsistent by
% 243.78/50.27  | |            sub-proof #2215.
% 243.78/50.27  | | 
% 243.78/50.27  | End of split
% 243.78/50.27  | 
% 243.78/50.27  End of proof
% 243.78/50.27  
% 243.78/50.27  Sub-proof #1271 shows that the following formulas are inconsistent:
% 243.78/50.27  ----------------------------------------------------------------
% 243.78/50.27    (1)   ~ (e3 = e0)
% 243.78/50.27    (2)  all_58_6 = e3
% 243.78/50.27    (3)   ~ (e2 = e0)
% 243.78/50.27    (4)  all_58_12 = e2
% 243.78/50.27    (5)  op(e3, e3) = e1
% 243.78/50.27    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.78/50.27         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.78/50.27    (7)   ~ (all_52_1 = e0)
% 243.78/50.27    (8)  op(e2, e3) = all_52_1
% 243.78/50.27    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.27    (10)   ~ (e1 = e0)
% 243.78/50.27  
% 243.78/50.27  Begin of proof
% 243.78/50.27  | 
% 243.78/50.27  | BETA: splitting (6) gives:
% 243.78/50.27  | 
% 243.78/50.27  | Case 1:
% 243.78/50.27  | | 
% 243.78/50.27  | |   (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 243.78/50.27  | |           e0)
% 243.78/50.27  | | 
% 243.78/50.27  | | REF_CLOSE: (5), (7), (8), (9), (10), (11) are inconsistent by sub-proof
% 243.78/50.27  | |            #1272.
% 243.78/50.27  | | 
% 243.78/50.27  | Case 2:
% 243.78/50.27  | | 
% 243.78/50.27  | |   (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 243.78/50.27  | |           e0)
% 243.78/50.27  | | 
% 243.78/50.27  | | BETA: splitting (12) gives:
% 243.78/50.27  | | 
% 243.78/50.27  | | Case 1:
% 243.78/50.27  | | | 
% 243.78/50.27  | | |   (13)  all_58_6 = e0 & op(e1, e3) = e0
% 243.78/50.27  | | | 
% 243.78/50.27  | | | ALPHA: (13) implies:
% 243.78/50.27  | | |   (14)  all_58_6 = e0
% 243.78/50.27  | | | 
% 243.78/50.27  | | | REF_CLOSE: (1), (2), (14) are inconsistent by sub-proof #2222.
% 243.78/50.27  | | | 
% 243.78/50.27  | | Case 2:
% 243.78/50.27  | | | 
% 243.78/50.27  | | |   (15)  all_58_12 = e0 & op(e0, e3) = e0
% 243.78/50.27  | | | 
% 243.78/50.27  | | | ALPHA: (15) implies:
% 243.78/50.27  | | |   (16)  all_58_12 = e0
% 243.78/50.27  | | | 
% 243.78/50.27  | | | REF_CLOSE: (3), (4), (16) are inconsistent by sub-proof #2083.
% 243.78/50.27  | | | 
% 243.78/50.27  | | End of split
% 243.78/50.27  | | 
% 243.78/50.27  | End of split
% 243.78/50.27  | 
% 243.78/50.27  End of proof
% 243.78/50.27  
% 243.78/50.27  Sub-proof #1272 shows that the following formulas are inconsistent:
% 243.78/50.27  ----------------------------------------------------------------
% 243.78/50.27    (1)  op(e3, e3) = e1
% 243.78/50.27    (2)   ~ (all_52_1 = e0)
% 243.78/50.27    (3)  op(e2, e3) = all_52_1
% 243.78/50.27    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.27    (5)   ~ (e1 = e0)
% 243.78/50.27    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 243.78/50.27  
% 243.78/50.27  Begin of proof
% 243.78/50.27  | 
% 243.78/50.27  | BETA: splitting (6) gives:
% 243.78/50.27  | 
% 243.78/50.27  | Case 1:
% 243.78/50.27  | | 
% 243.78/50.27  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 243.78/50.27  | | 
% 243.78/50.27  | | ALPHA: (7) implies:
% 243.78/50.27  | |   (8)  op(e3, e3) = e0
% 243.78/50.27  | | 
% 243.78/50.27  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1828.
% 243.78/50.27  | | 
% 243.78/50.27  | Case 2:
% 243.78/50.27  | | 
% 243.78/50.27  | |   (9)  all_58_2 = e0 & op(e2, e3) = e0
% 243.78/50.27  | | 
% 243.78/50.27  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1985.
% 243.78/50.27  | | 
% 243.78/50.27  | End of split
% 243.78/50.27  | 
% 243.78/50.27  End of proof
% 243.78/50.27  
% 243.78/50.27  Sub-proof #1273 shows that the following formulas are inconsistent:
% 243.78/50.27  ----------------------------------------------------------------
% 243.78/50.27    (1)   ~ (e3 = e0)
% 243.78/50.27    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.78/50.27         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.78/50.27    (3)   ~ (e2 = e0)
% 243.78/50.27    (4)  all_58_15 = e3
% 243.78/50.27    (5)  op(e0, e3) = all_52_3
% 243.78/50.27    (6)   ~ (e3 = e1)
% 243.78/50.27    (7)  all_58_7 = e2
% 243.78/50.27    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.78/50.27         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.78/50.27    (9)  op(e2, e1) = all_52_9
% 243.78/50.27    (10)   ~ (e3 = e2)
% 243.78/50.27    (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.78/50.27          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.78/50.27    (12)  op(e0, e1) = e0
% 243.78/50.27    (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.78/50.27          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.78/50.27    (14)   ~ (all_52_3 = e3)
% 243.78/50.27    (15)  all_58_6 = e1
% 243.78/50.27    (16)  op(e1, e1) = e2
% 243.78/50.27    (17)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.78/50.27          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.78/50.27    (18)  all_58_14 = e0
% 243.78/50.27    (19)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.78/50.27          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.78/50.27    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.27            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.27    (21)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.78/50.27          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.78/50.27    (22)  all_58_11 = e0
% 243.78/50.27    (23)   ~ (e1 = e0)
% 243.78/50.27    (24)  op(e3, e3) = e0
% 243.78/50.27    (25)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.78/50.27          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.78/50.27    (26)  all_58_3 = e0
% 243.78/50.27    (27)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.78/50.27          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.78/50.27    (28)   ~ (e2 = e1)
% 243.78/50.27    (29)   ~ (all_52_9 = e2)
% 243.78/50.27  
% 243.78/50.27  Begin of proof
% 243.78/50.27  | 
% 243.78/50.27  | BETA: splitting (8) gives:
% 243.78/50.27  | 
% 243.78/50.27  | Case 1:
% 243.78/50.27  | | 
% 243.78/50.27  | |   (30)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 243.78/50.27  | |           e3)
% 243.78/50.27  | | 
% 243.78/50.27  | | BETA: splitting (30) gives:
% 243.78/50.27  | | 
% 243.78/50.27  | | Case 1:
% 243.78/50.27  | | | 
% 243.78/50.27  | | |   (31)  all_58_0 = e3 & op(e3, e3) = e3
% 243.78/50.27  | | | 
% 243.78/50.27  | | | ALPHA: (31) implies:
% 243.78/50.27  | | |   (32)  op(e3, e3) = e3
% 243.78/50.27  | | | 
% 243.78/50.27  | | | REF_CLOSE: (1), (20), (24), (32) are inconsistent by sub-proof #1940.
% 243.78/50.27  | | | 
% 243.78/50.27  | | Case 2:
% 243.78/50.27  | | | 
% 243.78/50.27  | | |   (33)  all_58_2 = e3 & op(e2, e3) = e3
% 243.78/50.27  | | | 
% 243.78/50.27  | | | ALPHA: (33) implies:
% 243.78/50.27  | | |   (34)  all_58_2 = e3
% 243.78/50.27  | | | 
% 243.78/50.27  | | | BETA: splitting (11) gives:
% 243.78/50.27  | | | 
% 243.78/50.27  | | | Case 1:
% 243.78/50.27  | | | | 
% 243.78/50.27  | | | |   (35)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 243.78/50.27  | | | |           = e2)
% 243.78/50.27  | | | | 
% 243.78/50.27  | | | | BETA: splitting (35) gives:
% 243.78/50.27  | | | | 
% 243.78/50.27  | | | | Case 1:
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | |   (36)  all_58_4 = e2 & op(e3, e1) = e2
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | | ALPHA: (36) implies:
% 243.78/50.27  | | | | |   (37)  all_58_4 = e2
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | | BETA: splitting (17) gives:
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | | Case 1:
% 243.78/50.27  | | | | | | 
% 243.78/50.27  | | | | | |   (38)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2,
% 243.78/50.27  | | | | | |             e1) = e3)
% 243.78/50.27  | | | | | | 
% 243.78/50.27  | | | | | | BETA: splitting (38) gives:
% 243.78/50.27  | | | | | | 
% 243.78/50.27  | | | | | | Case 1:
% 243.78/50.27  | | | | | | | 
% 243.78/50.27  | | | | | | |   (39)  all_58_4 = e3 & op(e3, e1) = e3
% 243.78/50.27  | | | | | | | 
% 243.78/50.27  | | | | | | | REF_CLOSE: (10), (37), (39) are inconsistent by sub-proof #2167.
% 243.78/50.27  | | | | | | | 
% 243.78/50.27  | | | | | | Case 2:
% 243.78/50.27  | | | | | | | 
% 243.78/50.27  | | | | | | |   (40)  all_58_5 = e3 & op(e2, e1) = e3
% 243.78/50.27  | | | | | | | 
% 243.78/50.27  | | | | | | | ALPHA: (40) implies:
% 243.78/50.27  | | | | | | |   (41)  all_58_5 = e3
% 243.78/50.27  | | | | | | | 
% 243.78/50.27  | | | | | | | BETA: splitting (27) gives:
% 243.78/50.27  | | | | | | | 
% 243.78/50.27  | | | | | | | Case 1:
% 243.78/50.27  | | | | | | | | 
% 243.78/50.27  | | | | | | | |   (42)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 243.78/50.27  | | | | | | | |           op(e2, e2) = e1)
% 243.78/50.27  | | | | | | | | 
% 243.78/50.27  | | | | | | | | REF_CLOSE: (6), (23), (26), (34), (42) are inconsistent by
% 243.78/50.27  | | | | | | | |            sub-proof #1277.
% 243.78/50.27  | | | | | | | | 
% 243.78/50.27  | | | | | | | Case 2:
% 243.78/50.27  | | | | | | | | 
% 243.78/50.27  | | | | | | | |   (43)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 243.78/50.27  | | | | | | | |           op(e2, e0) = e1)
% 243.78/50.27  | | | | | | | | 
% 243.78/50.27  | | | | | | | | BETA: splitting (43) gives:
% 243.78/50.27  | | | | | | | | 
% 243.78/50.27  | | | | | | | | Case 1:
% 243.78/50.27  | | | | | | | | | 
% 243.78/50.27  | | | | | | | | |   (44)  all_58_5 = e1 & op(e2, e1) = e1
% 243.78/50.27  | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | ALPHA: (44) implies:
% 243.78/50.27  | | | | | | | | |   (45)  all_58_5 = e1
% 243.78/50.27  | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | REF_CLOSE: (6), (41), (45) are inconsistent by sub-proof
% 243.78/50.27  | | | | | | | | |            #2123.
% 243.78/50.27  | | | | | | | | | 
% 243.78/50.27  | | | | | | | | Case 2:
% 243.78/50.27  | | | | | | | | | 
% 243.78/50.27  | | | | | | | | |   (46)  all_58_10 = e1 & op(e2, e0) = e1
% 243.78/50.27  | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | ALPHA: (46) implies:
% 243.78/50.27  | | | | | | | | |   (47)  all_58_10 = e1
% 243.78/50.27  | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | BETA: splitting (13) gives:
% 243.78/50.27  | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | Case 1:
% 243.78/50.27  | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | |   (48)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 &
% 243.78/50.27  | | | | | | | | | |           op(e1, e2) = e3)
% 243.78/50.27  | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | BETA: splitting (48) gives:
% 243.78/50.27  | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | Case 1:
% 243.78/50.27  | | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | |   (49)  all_58_6 = e3 & op(e1, e3) = e3
% 243.78/50.27  | | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | | ALPHA: (49) implies:
% 243.78/50.27  | | | | | | | | | | |   (50)  all_58_6 = e3
% 243.78/50.27  | | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | | COMBINE_EQS: (15), (50) imply:
% 243.78/50.27  | | | | | | | | | | |   (51)  e3 = e1
% 243.78/50.27  | | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | | COMBINE_EQS: (4), (51) imply:
% 243.78/50.27  | | | | | | | | | | |   (52)  all_58_15 = e1
% 243.78/50.27  | | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (10), (19), (20), (21), (22), (28),
% 243.78/50.27  | | | | | | | | | | |            (47), (52) are inconsistent by sub-proof #1597.
% 243.78/50.27  | | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | Case 2:
% 243.78/50.27  | | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | |   (53)  all_58_7 = e3 & op(e1, e2) = e3
% 243.78/50.27  | | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | | REF_CLOSE: (7), (10), (53) are inconsistent by sub-proof
% 243.78/50.27  | | | | | | | | | | |            #1675.
% 243.78/50.27  | | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | End of split
% 243.78/50.27  | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | Case 2:
% 243.78/50.27  | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | |   (54)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3
% 243.78/50.27  | | | | | | | | | |           & op(e1, e0) = e3)
% 243.78/50.27  | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | | REF_CLOSE: (1), (3), (7), (10), (15), (16), (20), (23), (25),
% 243.78/50.27  | | | | | | | | | |            (54) are inconsistent by sub-proof #2201.
% 243.78/50.27  | | | | | | | | | | 
% 243.78/50.27  | | | | | | | | | End of split
% 243.78/50.27  | | | | | | | | | 
% 243.78/50.27  | | | | | | | | End of split
% 243.78/50.27  | | | | | | | | 
% 243.78/50.27  | | | | | | | End of split
% 243.78/50.27  | | | | | | | 
% 243.78/50.27  | | | | | | End of split
% 243.78/50.27  | | | | | | 
% 243.78/50.27  | | | | | Case 2:
% 243.78/50.27  | | | | | | 
% 243.78/50.27  | | | | | |   (55)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0,
% 243.78/50.27  | | | | | |             e1) = e3)
% 243.78/50.27  | | | | | | 
% 243.78/50.27  | | | | | | REF_CLOSE: (1), (10), (12), (16), (20), (55) are inconsistent by
% 243.78/50.27  | | | | | |            sub-proof #1595.
% 243.78/50.27  | | | | | | 
% 243.78/50.27  | | | | | End of split
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | Case 2:
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | |   (56)  all_58_5 = e2 & op(e2, e1) = e2
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | | ALPHA: (56) implies:
% 243.78/50.27  | | | | |   (57)  op(e2, e1) = e2
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | | REF_CLOSE: (9), (20), (29), (57) are inconsistent by sub-proof #2328.
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | End of split
% 243.78/50.27  | | | | 
% 243.78/50.27  | | | Case 2:
% 243.78/50.27  | | | | 
% 243.78/50.27  | | | |   (58)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 243.78/50.27  | | | |           = e2)
% 243.78/50.27  | | | | 
% 243.78/50.27  | | | | BETA: splitting (58) gives:
% 243.78/50.27  | | | | 
% 243.78/50.27  | | | | Case 1:
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | |   (59)  all_58_8 = e2 & op(e1, e1) = e2
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | | ALPHA: (59) implies:
% 243.78/50.27  | | | | |   (60)  all_58_8 = e2
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (10), (13), (15), (16), (20),
% 243.78/50.27  | | | | |            (23), (25), (28), (60) are inconsistent by sub-proof #1799.
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | Case 2:
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | |   (61)  all_58_14 = e2 & op(e0, e1) = e2
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | | REF_CLOSE: (3), (18), (61) are inconsistent by sub-proof #2077.
% 243.78/50.27  | | | | | 
% 243.78/50.27  | | | | End of split
% 243.78/50.27  | | | | 
% 243.78/50.27  | | | End of split
% 243.78/50.27  | | | 
% 243.78/50.27  | | End of split
% 243.78/50.27  | | 
% 243.78/50.27  | Case 2:
% 243.78/50.27  | | 
% 243.78/50.27  | |   (62)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 243.78/50.27  | |           e3)
% 243.78/50.27  | | 
% 243.78/50.27  | | BETA: splitting (62) gives:
% 243.78/50.27  | | 
% 243.78/50.27  | | Case 1:
% 243.78/50.27  | | | 
% 243.78/50.27  | | |   (63)  all_58_6 = e3 & op(e1, e3) = e3
% 243.78/50.27  | | | 
% 243.78/50.27  | | | ALPHA: (63) implies:
% 243.78/50.27  | | |   (64)  all_58_6 = e3
% 243.78/50.27  | | | 
% 243.78/50.27  | | | REF_CLOSE: (6), (15), (64) are inconsistent by sub-proof #1758.
% 243.78/50.27  | | | 
% 243.78/50.27  | | Case 2:
% 243.78/50.27  | | | 
% 243.78/50.27  | | |   (65)  all_58_12 = e3 & op(e0, e3) = e3
% 243.78/50.27  | | | 
% 243.78/50.27  | | | ALPHA: (65) implies:
% 243.78/50.27  | | |   (66)  op(e0, e3) = e3
% 243.78/50.27  | | | 
% 243.78/50.27  | | | REF_CLOSE: (5), (14), (20), (66) are inconsistent by sub-proof #2332.
% 243.78/50.27  | | | 
% 243.78/50.27  | | End of split
% 243.78/50.27  | | 
% 243.78/50.27  | End of split
% 243.78/50.27  | 
% 243.78/50.27  End of proof
% 243.78/50.27  
% 243.78/50.27  Sub-proof #1274 shows that the following formulas are inconsistent:
% 243.78/50.27  ----------------------------------------------------------------
% 243.78/50.27    (1)   ~ (e3 = e0)
% 243.78/50.27    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.78/50.27         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.78/50.27    (3)   ~ (e2 = e0)
% 243.78/50.27    (4)  op(e1, e2) = all_52_6
% 243.78/50.27    (5)  all_58_6 = e2
% 243.78/50.27    (6)  op(e1, e0) = all_52_14
% 243.78/50.27    (7)  op(e0, e3) = all_52_3
% 243.78/50.27    (8)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.78/50.27         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.78/50.28    (9)   ~ (all_52_6 = e0)
% 243.78/50.28    (10)   ~ (e3 = e1)
% 243.78/50.28    (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.78/50.28          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.78/50.28    (12)  op(e2, e2) = e0
% 243.78/50.28    (13)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.78/50.28          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.78/50.28    (14)  op(e2, e1) = all_52_9
% 243.78/50.28    (15)   ~ (e3 = e2)
% 243.78/50.28    (16)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.78/50.28          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.78/50.28    (17)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.78/50.28          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.78/50.28    (18)   ~ (all_52_3 = e3)
% 243.78/50.28    (19)   ~ (all_52_14 = e3)
% 243.78/50.28    (20)  op(e1, e1) = e2
% 243.78/50.28    (21)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.78/50.28          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.78/50.28    (22)  all_58_14 = e0
% 243.78/50.28    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.28    (24)   ~ (e1 = e0)
% 243.78/50.28    (25)  op(e3, e3) = e0
% 243.78/50.28    (26)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.78/50.28          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.78/50.28    (27)  all_58_3 = e0
% 243.78/50.28    (28)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.78/50.28          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.78/50.28    (29)   ~ (e2 = e1)
% 243.78/50.28    (30)   ~ (all_52_9 = e2)
% 243.78/50.28  
% 243.78/50.28  Begin of proof
% 243.78/50.28  | 
% 243.78/50.28  | BETA: splitting (2) gives:
% 243.78/50.28  | 
% 243.78/50.28  | Case 1:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (31)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 243.78/50.28  | |           e1)
% 243.78/50.28  | | 
% 243.78/50.28  | | REF_CLOSE: (1), (3), (4), (5), (9), (10), (15), (17), (20), (23), (26),
% 243.78/50.28  | |            (29), (31) are inconsistent by sub-proof #1278.
% 243.78/50.28  | | 
% 243.78/50.28  | Case 2:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (32)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 243.78/50.28  | |           e1)
% 243.78/50.28  | | 
% 243.78/50.28  | | BETA: splitting (32) gives:
% 243.78/50.28  | | 
% 243.78/50.28  | | Case 1:
% 243.78/50.28  | | | 
% 243.78/50.28  | | |   (33)  all_58_8 = e1 & op(e1, e1) = e1
% 243.78/50.28  | | | 
% 243.78/50.28  | | | ALPHA: (33) implies:
% 243.78/50.28  | | |   (34)  all_58_8 = e1
% 243.78/50.28  | | | 
% 243.78/50.28  | | | BETA: splitting (13) gives:
% 243.78/50.28  | | | 
% 243.78/50.28  | | | Case 1:
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | |   (35)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 243.78/50.28  | | | |           = e3)
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | | BETA: splitting (35) gives:
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | | Case 1:
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | |   (36)  all_58_0 = e3 & op(e3, e3) = e3
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | | ALPHA: (36) implies:
% 243.78/50.28  | | | | |   (37)  op(e3, e3) = e3
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | | REF_CLOSE: (1), (23), (25), (37) are inconsistent by sub-proof #1940.
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | Case 2:
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | |   (38)  all_58_2 = e3 & op(e2, e3) = e3
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | | ALPHA: (38) implies:
% 243.78/50.28  | | | | |   (39)  all_58_2 = e3
% 243.78/50.28  | | | | |   (40)  op(e2, e3) = e3
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | | REF_CLOSE: (1), (3), (8), (10), (11), (12), (14), (15), (16), (20),
% 243.78/50.28  | | | | |            (21), (22), (23), (24), (27), (28), (29), (30), (34), (39),
% 243.78/50.28  | | | | |            (40) are inconsistent by sub-proof #1275.
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | End of split
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | Case 2:
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | |   (41)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 243.78/50.28  | | | |           = e3)
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | | REF_CLOSE: (5), (7), (15), (18), (23), (41) are inconsistent by
% 243.78/50.28  | | | |            sub-proof #1349.
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | End of split
% 243.78/50.28  | | | 
% 243.78/50.28  | | Case 2:
% 243.78/50.28  | | | 
% 243.78/50.28  | | |   (42)  all_58_11 = e1 & op(e1, e0) = e1
% 243.78/50.28  | | | 
% 243.78/50.28  | | | ALPHA: (42) implies:
% 243.78/50.28  | | |   (43)  op(e1, e0) = e1
% 243.78/50.28  | | | 
% 243.78/50.28  | | | REF_CLOSE: (1), (3), (5), (6), (15), (17), (19), (20), (23), (24), (26),
% 243.78/50.28  | | |            (43) are inconsistent by sub-proof #1406.
% 243.78/50.28  | | | 
% 243.78/50.28  | | End of split
% 243.78/50.28  | | 
% 243.78/50.28  | End of split
% 243.78/50.28  | 
% 243.78/50.28  End of proof
% 243.78/50.28  
% 243.78/50.28  Sub-proof #1275 shows that the following formulas are inconsistent:
% 243.78/50.28  ----------------------------------------------------------------
% 243.78/50.28    (1)   ~ (e3 = e0)
% 243.78/50.28    (2)   ~ (e2 = e0)
% 243.78/50.28    (3)  all_58_8 = e1
% 243.78/50.28    (4)  op(e2, e3) = e3
% 243.78/50.28    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.78/50.28         (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.78/50.28    (6)   ~ (e3 = e1)
% 243.78/50.28    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.78/50.28         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.78/50.28    (8)  op(e2, e2) = e0
% 243.78/50.28    (9)  op(e2, e1) = all_52_9
% 243.78/50.28    (10)   ~ (e3 = e2)
% 243.78/50.28    (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.78/50.28          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.78/50.28    (12)  op(e1, e1) = e2
% 243.78/50.28    (13)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.78/50.28          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.78/50.28    (14)  all_58_14 = e0
% 243.78/50.28    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.28    (16)   ~ (e1 = e0)
% 243.78/50.28    (17)  all_58_2 = e3
% 243.78/50.28    (18)  all_58_3 = e0
% 243.78/50.28    (19)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.78/50.28          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.78/50.28    (20)   ~ (e2 = e1)
% 243.78/50.28    (21)   ~ (all_52_9 = e2)
% 243.78/50.28  
% 243.78/50.28  Begin of proof
% 243.78/50.28  | 
% 243.78/50.28  | BETA: splitting (11) gives:
% 243.78/50.28  | 
% 243.78/50.28  | Case 1:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (22)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 243.78/50.28  | |           e2)
% 243.78/50.28  | | 
% 243.78/50.28  | | BETA: splitting (22) gives:
% 243.78/50.28  | | 
% 243.78/50.28  | | Case 1:
% 243.78/50.28  | | | 
% 243.78/50.28  | | |   (23)  all_58_4 = e2 & op(e3, e1) = e2
% 243.78/50.28  | | | 
% 243.78/50.28  | | | ALPHA: (23) implies:
% 243.78/50.28  | | |   (24)  all_58_4 = e2
% 243.78/50.28  | | | 
% 243.78/50.28  | | | BETA: splitting (5) gives:
% 243.78/50.28  | | | 
% 243.78/50.28  | | | Case 1:
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | |   (25)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2)
% 243.78/50.28  | | | |           = e2)
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | | REF_CLOSE: (2), (4), (8), (10), (15), (25) are inconsistent by sub-proof
% 243.78/50.28  | | | |            #1509.
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | Case 2:
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | |   (26)  (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0)
% 243.78/50.28  | | | |           = e2)
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | | BETA: splitting (26) gives:
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | | Case 1:
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | |   (27)  all_58_5 = e2 & op(e2, e1) = e2
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | | ALPHA: (27) implies:
% 243.78/50.28  | | | | |   (28)  op(e2, e1) = e2
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | | REF_CLOSE: (9), (15), (21), (28) are inconsistent by sub-proof #2328.
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | Case 2:
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | |   (29)  all_58_10 = e2 & op(e2, e0) = e2
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | | ALPHA: (29) implies:
% 243.78/50.28  | | | | |   (30)  op(e2, e0) = e2
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | | BETA: splitting (19) gives:
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | | Case 1:
% 243.78/50.28  | | | | | | 
% 243.78/50.28  | | | | | |   (31)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2,
% 243.78/50.28  | | | | | |             e2) = e1)
% 243.78/50.28  | | | | | | 
% 243.78/50.28  | | | | | | REF_CLOSE: (6), (16), (17), (18), (31) are inconsistent by sub-proof
% 243.78/50.28  | | | | | |            #1277.
% 243.78/50.28  | | | | | | 
% 243.78/50.28  | | | | | Case 2:
% 243.78/50.28  | | | | | | 
% 243.78/50.28  | | | | | |   (32)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2,
% 243.78/50.28  | | | | | |             e0) = e1)
% 243.78/50.28  | | | | | | 
% 243.78/50.28  | | | | | | BETA: splitting (32) gives:
% 243.78/50.28  | | | | | | 
% 243.78/50.28  | | | | | | Case 1:
% 243.78/50.28  | | | | | | | 
% 243.78/50.28  | | | | | | |   (33)  all_58_5 = e1 & op(e2, e1) = e1
% 243.78/50.28  | | | | | | | 
% 243.78/50.28  | | | | | | | ALPHA: (33) implies:
% 243.78/50.28  | | | | | | |   (34)  all_58_5 = e1
% 243.78/50.28  | | | | | | |   (35)  op(e2, e1) = e1
% 243.78/50.28  | | | | | | | 
% 243.78/50.28  | | | | | | | REF_CLOSE: (1), (2), (6), (7), (9), (10), (12), (13), (15), (16),
% 243.78/50.28  | | | | | | |            (24), (34), (35) are inconsistent by sub-proof #2161.
% 243.78/50.28  | | | | | | | 
% 243.78/50.28  | | | | | | Case 2:
% 243.78/50.28  | | | | | | | 
% 243.78/50.28  | | | | | | |   (36)  all_58_10 = e1 & op(e2, e0) = e1
% 243.78/50.28  | | | | | | | 
% 243.78/50.28  | | | | | | | ALPHA: (36) implies:
% 243.78/50.28  | | | | | | |   (37)  op(e2, e0) = e1
% 243.78/50.28  | | | | | | | 
% 243.78/50.28  | | | | | | | REF_CLOSE: (15), (20), (30), (37) are inconsistent by sub-proof
% 243.78/50.28  | | | | | | |            #1659.
% 243.78/50.28  | | | | | | | 
% 243.78/50.28  | | | | | | End of split
% 243.78/50.28  | | | | | | 
% 243.78/50.28  | | | | | End of split
% 243.78/50.28  | | | | | 
% 243.78/50.28  | | | | End of split
% 243.78/50.28  | | | | 
% 243.78/50.28  | | | End of split
% 243.78/50.28  | | | 
% 243.78/50.28  | | Case 2:
% 243.78/50.28  | | | 
% 243.78/50.28  | | |   (38)  all_58_5 = e2 & op(e2, e1) = e2
% 243.78/50.28  | | | 
% 243.78/50.28  | | | ALPHA: (38) implies:
% 243.78/50.28  | | |   (39)  op(e2, e1) = e2
% 243.78/50.28  | | | 
% 243.78/50.28  | | | REF_CLOSE: (9), (15), (21), (39) are inconsistent by sub-proof #2328.
% 243.78/50.28  | | | 
% 243.78/50.28  | | End of split
% 243.78/50.28  | | 
% 243.78/50.28  | Case 2:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (40)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 243.78/50.28  | |           e2)
% 243.78/50.28  | | 
% 243.78/50.28  | | REF_CLOSE: (2), (3), (14), (20), (40) are inconsistent by sub-proof #1276.
% 243.78/50.28  | | 
% 243.78/50.28  | End of split
% 243.78/50.28  | 
% 243.78/50.28  End of proof
% 243.78/50.28  
% 243.78/50.28  Sub-proof #1276 shows that the following formulas are inconsistent:
% 243.78/50.28  ----------------------------------------------------------------
% 243.78/50.28    (1)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.78/50.28    (2)   ~ (e2 = e0)
% 243.78/50.28    (3)  all_58_8 = e1
% 243.78/50.28    (4)  all_58_14 = e0
% 243.78/50.28    (5)   ~ (e2 = e1)
% 243.78/50.28  
% 243.78/50.28  Begin of proof
% 243.78/50.28  | 
% 243.78/50.28  | BETA: splitting (1) gives:
% 243.78/50.28  | 
% 243.78/50.28  | Case 1:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (6)  all_58_8 = e2 & op(e1, e1) = e2
% 243.78/50.28  | | 
% 243.78/50.28  | | ALPHA: (6) implies:
% 243.78/50.28  | |   (7)  all_58_8 = e2
% 243.78/50.28  | | 
% 243.78/50.28  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #1802.
% 243.78/50.28  | | 
% 243.78/50.28  | Case 2:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (8)  all_58_14 = e2 & op(e0, e1) = e2
% 243.78/50.28  | | 
% 243.78/50.28  | | ALPHA: (8) implies:
% 243.78/50.28  | |   (9)  all_58_14 = e2
% 243.78/50.28  | | 
% 243.78/50.28  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #2114.
% 243.78/50.28  | | 
% 243.78/50.28  | End of split
% 243.78/50.28  | 
% 243.78/50.28  End of proof
% 243.78/50.28  
% 243.78/50.28  Sub-proof #1277 shows that the following formulas are inconsistent:
% 243.78/50.28  ----------------------------------------------------------------
% 243.78/50.28    (1)   ~ (e3 = e1)
% 243.78/50.28    (2)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 243.78/50.28    (3)   ~ (e1 = e0)
% 243.78/50.28    (4)  all_58_2 = e3
% 243.78/50.28    (5)  all_58_3 = e0
% 243.78/50.28  
% 243.78/50.28  Begin of proof
% 243.78/50.28  | 
% 243.78/50.28  | BETA: splitting (2) gives:
% 243.78/50.28  | 
% 243.78/50.28  | Case 1:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (6)  all_58_2 = e1 & op(e2, e3) = e1
% 243.78/50.28  | | 
% 243.78/50.28  | | ALPHA: (6) implies:
% 243.78/50.28  | |   (7)  all_58_2 = e1
% 243.78/50.28  | | 
% 243.78/50.28  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #1691.
% 243.78/50.28  | | 
% 243.78/50.28  | Case 2:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (8)  all_58_3 = e1 & op(e2, e2) = e1
% 243.78/50.28  | | 
% 243.78/50.28  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #1752.
% 243.78/50.28  | | 
% 243.78/50.28  | End of split
% 243.78/50.28  | 
% 243.78/50.28  End of proof
% 243.78/50.28  
% 243.78/50.28  Sub-proof #1278 shows that the following formulas are inconsistent:
% 243.78/50.28  ----------------------------------------------------------------
% 243.78/50.28    (1)   ~ (e3 = e0)
% 243.78/50.28    (2)   ~ (e2 = e0)
% 243.78/50.28    (3)  op(e1, e2) = all_52_6
% 243.78/50.28    (4)  all_58_6 = e2
% 243.78/50.28    (5)   ~ (all_52_6 = e0)
% 243.78/50.28    (6)   ~ (e3 = e1)
% 243.78/50.28    (7)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 243.78/50.28    (8)   ~ (e3 = e2)
% 243.78/50.28    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.78/50.28         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.78/50.28    (10)  op(e1, e1) = e2
% 243.78/50.28    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.28    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.78/50.28          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.78/50.28    (13)   ~ (e2 = e1)
% 243.78/50.28  
% 243.78/50.28  Begin of proof
% 243.78/50.28  | 
% 243.78/50.28  | BETA: splitting (7) gives:
% 243.78/50.28  | 
% 243.78/50.28  | Case 1:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (14)  all_58_6 = e1 & op(e1, e3) = e1
% 243.78/50.28  | | 
% 243.78/50.28  | | REF_CLOSE: (4), (13), (14) are inconsistent by sub-proof #1423.
% 243.78/50.28  | | 
% 243.78/50.28  | Case 2:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (15)  all_58_7 = e1 & op(e1, e2) = e1
% 243.78/50.28  | | 
% 243.78/50.28  | | ALPHA: (15) implies:
% 243.78/50.28  | |   (16)  all_58_7 = e1
% 243.78/50.28  | | 
% 243.78/50.28  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (16)
% 243.78/50.28  | |            are inconsistent by sub-proof #1676.
% 243.78/50.28  | | 
% 243.78/50.28  | End of split
% 243.78/50.28  | 
% 243.78/50.28  End of proof
% 243.78/50.28  
% 243.78/50.28  Sub-proof #1279 shows that the following formulas are inconsistent:
% 243.78/50.28  ----------------------------------------------------------------
% 243.78/50.28    (1)   ~ (all_52_9 = all_6_2)
% 243.78/50.28    (2)  all_54_10 = e1 | all_54_10 = e0
% 243.78/50.28    (3)  all_54_10 = all_6_2
% 243.78/50.28    (4)  op(e2, e1) = all_52_9
% 243.78/50.28    (5)   ~ (all_6_2 = e0)
% 243.78/50.28    (6)  all_56_11 = e0
% 243.78/50.28    (7)  all_56_21 = e1
% 243.78/50.28    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.28    (9)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 243.78/50.28             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.78/50.28           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.78/50.28             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.78/50.28           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 243.78/50.28           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.78/50.28           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.78/50.28  
% 243.78/50.28  Begin of proof
% 243.78/50.28  | 
% 243.78/50.28  | BETA: splitting (9) gives:
% 243.78/50.28  | 
% 243.78/50.28  | Case 1:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (10)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 243.78/50.28  | |           = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) =
% 243.78/50.28  | |         e2 & op(e1, e2) = e2
% 243.78/50.28  | | 
% 243.78/50.28  | | ALPHA: (10) implies:
% 243.78/50.28  | |   (11)   ~ (all_56_21 = e1)
% 243.78/50.28  | | 
% 243.78/50.28  | | REDUCE: (7), (11) imply:
% 243.78/50.28  | |   (12)  $false
% 243.78/50.28  | | 
% 243.78/50.28  | | CLOSE: (12) is inconsistent.
% 243.78/50.28  | | 
% 243.78/50.28  | Case 2:
% 243.78/50.28  | | 
% 243.78/50.28  | |   (13)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.78/50.28  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.78/50.28  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 243.78/50.28  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.78/50.28  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.78/50.28  | | 
% 243.78/50.28  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (13) are inconsistent by
% 243.78/50.28  | |            sub-proof #1615.
% 243.78/50.28  | | 
% 243.78/50.28  | End of split
% 243.78/50.28  | 
% 243.78/50.28  End of proof
% 243.78/50.28  
% 243.78/50.28  Sub-proof #1280 shows that the following formulas are inconsistent:
% 243.78/50.28  ----------------------------------------------------------------
% 243.78/50.28    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 243.78/50.28           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 243.78/50.28             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.78/50.28           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 243.78/50.28             e1) = e3 & op(e1, e3) = e3)
% 243.78/50.28    (2)  all_56_31 = e3
% 243.78/50.29    (3)  all_56_21 = e1
% 243.78/50.29  
% 243.78/50.29  Begin of proof
% 243.78/50.29  | 
% 243.78/50.29  | BETA: splitting (1) gives:
% 243.78/50.29  | 
% 243.78/50.29  | Case 1:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (4)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 243.78/50.29  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.78/50.29  | |        op(e2, e3) = e2
% 243.78/50.29  | | 
% 243.78/50.29  | | ALPHA: (4) implies:
% 243.78/50.29  | |   (5)   ~ (all_56_31 = e3)
% 243.78/50.29  | | 
% 243.78/50.29  | | REDUCE: (2), (5) imply:
% 243.78/50.29  | |   (6)  $false
% 243.78/50.29  | | 
% 243.78/50.29  | | CLOSE: (6) is inconsistent.
% 243.78/50.29  | | 
% 243.78/50.29  | Case 2:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (7)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 243.78/50.29  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 243.78/50.29  | |        op(e1, e3) = e3
% 243.78/50.29  | | 
% 243.78/50.29  | | ALPHA: (7) implies:
% 243.78/50.29  | |   (8)   ~ (all_56_21 = e1)
% 243.78/50.29  | | 
% 243.78/50.29  | | REDUCE: (3), (8) imply:
% 243.78/50.29  | |   (9)  $false
% 243.78/50.29  | | 
% 243.78/50.29  | | CLOSE: (9) is inconsistent.
% 243.78/50.29  | | 
% 243.78/50.29  | End of split
% 243.78/50.29  | 
% 243.78/50.29  End of proof
% 243.78/50.29  
% 243.78/50.29  Sub-proof #1281 shows that the following formulas are inconsistent:
% 243.78/50.29  ----------------------------------------------------------------
% 243.78/50.29    (1)  op(e1, e0) = e1
% 243.78/50.29    (2)   ~ (e3 = e2)
% 243.78/50.29    (3)  op(e0, e0) = e3
% 243.78/50.29    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.29    (5)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.78/50.29    (6)   ~ (e2 = e1)
% 243.78/50.29  
% 243.78/50.29  Begin of proof
% 243.78/50.29  | 
% 243.78/50.29  | BETA: splitting (5) gives:
% 243.78/50.29  | 
% 243.78/50.29  | Case 1:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (7)  all_58_11 = e2 & op(e1, e0) = e2
% 243.78/50.29  | | 
% 243.78/50.29  | | ALPHA: (7) implies:
% 243.78/50.29  | |   (8)  op(e1, e0) = e2
% 243.78/50.29  | | 
% 243.78/50.29  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #2019.
% 243.78/50.29  | | 
% 243.78/50.29  | Case 2:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (9)  all_58_15 = e2 & op(e0, e0) = e2
% 243.78/50.29  | | 
% 243.78/50.29  | | ALPHA: (9) implies:
% 243.78/50.29  | |   (10)  op(e0, e0) = e2
% 243.78/50.29  | | 
% 243.78/50.29  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #1388.
% 243.78/50.29  | | 
% 243.78/50.29  | End of split
% 243.78/50.29  | 
% 243.78/50.29  End of proof
% 243.78/50.29  
% 243.78/50.29  Sub-proof #1282 shows that the following formulas are inconsistent:
% 243.78/50.29  ----------------------------------------------------------------
% 243.78/50.29    (1)  op(e0, e1) = e2
% 243.78/50.29    (2)  all_58_6 = e3
% 243.78/50.29    (3)   ~ (all_52_12 = e0)
% 243.78/50.29    (4)  all_58_11 = e1
% 243.78/50.29    (5)   ~ (all_52_8 = e0)
% 243.78/50.29    (6)  op(e0, e3) = all_56_7
% 243.78/50.29    (7)  all_58_7 = e2
% 243.78/50.29    (8)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 243.78/50.29           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 243.78/50.29           all_26_1 & $i(all_26_1))
% 243.78/50.29    (9)  all_54_2 = all_52_8
% 243.78/50.29    (10)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.78/50.29    (11)   ~ (all_52_8 = all_52_12)
% 243.78/50.29    (12)  op(e0, e3) = e1
% 243.78/50.29    (13)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.78/50.29    (14)  op(e0, e3) = all_12_1
% 243.78/50.29    (15)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.78/50.29          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.78/50.29    (16)  all_54_3 = all_52_12
% 243.78/50.29    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.29    (18)   ~ (all_52_12 = e3)
% 243.78/50.29    (19)  op(e0, all_56_7) = e0
% 243.78/50.29    (20)  op(e1, e1) = e0
% 243.78/50.29    (21)   ~ (all_52_8 = e2)
% 243.78/50.29    (22)   ~ (all_52_8 = e3)
% 243.78/50.29  
% 243.78/50.29  Begin of proof
% 243.78/50.29  | 
% 243.78/50.29  | BETA: splitting (13) gives:
% 243.78/50.29  | 
% 243.78/50.29  | Case 1:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (23)  all_54_2 = e3
% 243.78/50.29  | | 
% 243.78/50.29  | | REF_CLOSE: (9), (22), (23) are inconsistent by sub-proof #1987.
% 243.78/50.29  | | 
% 243.78/50.29  | Case 2:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (24)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.78/50.29  | | 
% 243.78/50.29  | | BETA: splitting (24) gives:
% 243.78/50.29  | | 
% 243.78/50.29  | | Case 1:
% 243.78/50.29  | | | 
% 243.78/50.29  | | |   (25)  all_54_2 = e2
% 243.78/50.29  | | | 
% 243.78/50.29  | | | REF_CLOSE: (9), (21), (25) are inconsistent by sub-proof #1986.
% 243.78/50.29  | | | 
% 243.78/50.29  | | Case 2:
% 243.78/50.29  | | | 
% 243.78/50.29  | | |   (26)  all_54_2 = e1 | all_54_2 = e0
% 243.78/50.29  | | | 
% 243.78/50.29  | | | BETA: splitting (26) gives:
% 243.78/50.29  | | | 
% 243.78/50.29  | | | Case 1:
% 243.78/50.29  | | | | 
% 243.78/50.29  | | | |   (27)  all_54_2 = e1
% 243.78/50.29  | | | | 
% 243.78/50.29  | | | | COMBINE_EQS: (9), (27) imply:
% 243.78/50.29  | | | |   (28)  all_52_8 = e1
% 243.78/50.29  | | | | 
% 243.78/50.29  | | | | SIMP: (28) implies:
% 243.78/50.29  | | | |   (29)  all_52_8 = e1
% 243.78/50.29  | | | | 
% 243.78/50.29  | | | | REDUCE: (11), (29) imply:
% 243.78/50.29  | | | |   (30)   ~ (all_52_12 = e1)
% 243.78/50.29  | | | | 
% 243.78/50.29  | | | | SIMP: (30) implies:
% 243.78/50.29  | | | |   (31)   ~ (all_52_12 = e1)
% 243.78/50.29  | | | | 
% 243.78/50.29  | | | | BETA: splitting (10) gives:
% 243.78/50.29  | | | | 
% 243.78/50.29  | | | | Case 1:
% 243.78/50.29  | | | | | 
% 243.78/50.29  | | | | |   (32)  all_54_3 = e3
% 243.78/50.29  | | | | | 
% 243.78/50.29  | | | | | COMBINE_EQS: (16), (32) imply:
% 243.78/50.29  | | | | |   (33)  all_52_12 = e3
% 243.78/50.29  | | | | | 
% 243.78/50.29  | | | | | REDUCE: (18), (33) imply:
% 243.78/50.29  | | | | |   (34)  $false
% 243.78/50.29  | | | | | 
% 243.78/50.29  | | | | | CLOSE: (34) is inconsistent.
% 243.78/50.29  | | | | | 
% 243.78/50.29  | | | | Case 2:
% 243.78/50.29  | | | | | 
% 243.78/50.29  | | | | |   (35)   ~ (all_54_3 = e3)
% 243.78/50.29  | | | | |   (36)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.78/50.29  | | | | | 
% 243.78/50.29  | | | | | BETA: splitting (8) gives:
% 243.78/50.29  | | | | | 
% 243.78/50.29  | | | | | Case 1:
% 243.78/50.29  | | | | | | 
% 243.78/50.29  | | | | | |   (37)   ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0,
% 243.78/50.29  | | | | | |           e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)
% 243.78/50.29  | | | | | | 
% 243.78/50.29  | | | | | | ALPHA: (37) implies:
% 243.78/50.29  | | | | | |   (38)  op(e0, e3) = all_26_1
% 243.78/50.29  | | | | | | 
% 243.78/50.29  | | | | | | BETA: splitting (36) gives:
% 243.78/50.29  | | | | | | 
% 243.78/50.29  | | | | | | Case 1:
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | |   (39)  all_54_3 = e2
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | COMBINE_EQS: (16), (39) imply:
% 243.78/50.29  | | | | | | |   (40)  all_52_12 = e2
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | SIMP: (40) implies:
% 243.78/50.29  | | | | | | |   (41)  all_52_12 = e2
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | REDUCE: (18), (41) imply:
% 243.78/50.29  | | | | | | |   (42)   ~ (e3 = e2)
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | SIMP: (42) implies:
% 243.78/50.29  | | | | | | |   (43)   ~ (e3 = e2)
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | REDUCE: (31), (41) imply:
% 243.78/50.29  | | | | | | |   (44)   ~ (e2 = e1)
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | REDUCE: (3), (41) imply:
% 243.78/50.29  | | | | | | |   (45)   ~ (e2 = e0)
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | GROUND_INST: instantiating (17) with all_12_1, all_26_1, e3, e0,
% 243.78/50.29  | | | | | | |              simplifying with (14), (38) gives:
% 243.78/50.29  | | | | | | |   (46)  all_26_1 = all_12_1
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | GROUND_INST: instantiating (17) with all_26_1, all_56_7, e3, e0,
% 243.78/50.29  | | | | | | |              simplifying with (6), (38) gives:
% 243.78/50.29  | | | | | | |   (47)  all_56_7 = all_26_1
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | GROUND_INST: instantiating (17) with e1, all_56_7, e3, e0,
% 243.78/50.29  | | | | | | |              simplifying with (6), (12) gives:
% 243.78/50.29  | | | | | | |   (48)  all_56_7 = e1
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | COMBINE_EQS: (47), (48) imply:
% 243.78/50.29  | | | | | | |   (49)  all_26_1 = e1
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | SIMP: (49) implies:
% 243.78/50.29  | | | | | | |   (50)  all_26_1 = e1
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | COMBINE_EQS: (46), (50) imply:
% 243.78/50.29  | | | | | | |   (51)  all_12_1 = e1
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | REDUCE: (19), (48) imply:
% 243.78/50.29  | | | | | | |   (52)  op(e0, e1) = e0
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | BETA: splitting (8) gives:
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | Case 1:
% 243.78/50.29  | | | | | | | | 
% 243.78/50.29  | | | | | | | | 
% 243.78/50.29  | | | | | | | | GROUND_INST: instantiating (17) with e2, e0, e1, e0, simplifying
% 243.78/50.29  | | | | | | | |              with (1), (52) gives:
% 243.78/50.29  | | | | | | | |   (53)  e2 = e0
% 243.78/50.29  | | | | | | | | 
% 243.78/50.29  | | | | | | | | COMBINE_EQS: (7), (53) imply:
% 243.78/50.29  | | | | | | | |   (54)  all_58_7 = e0
% 243.78/50.29  | | | | | | | | 
% 243.78/50.29  | | | | | | | | REF_CLOSE: (2), (4), (15), (17), (20), (43), (44), (45), (54)
% 243.78/50.29  | | | | | | | |            are inconsistent by sub-proof #1325.
% 243.78/50.29  | | | | | | | | 
% 243.78/50.29  | | | | | | | Case 2:
% 243.78/50.29  | | | | | | | | 
% 243.78/50.29  | | | | | | | |   (55)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 &
% 243.78/50.29  | | | | | | | |         $i(all_26_1)
% 243.78/50.29  | | | | | | | | 
% 243.78/50.29  | | | | | | | | REF_CLOSE: (12), (17), (55) are inconsistent by sub-proof #1386.
% 243.78/50.29  | | | | | | | | 
% 243.78/50.29  | | | | | | | End of split
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | Case 2:
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | |   (56)  all_54_3 = e1 | all_54_3 = e0
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | | REF_CLOSE: (3), (16), (31), (56) are inconsistent by sub-proof
% 243.78/50.29  | | | | | | |            #2287.
% 243.78/50.29  | | | | | | | 
% 243.78/50.29  | | | | | | End of split
% 243.78/50.29  | | | | | | 
% 243.78/50.29  | | | | | Case 2:
% 243.78/50.29  | | | | | | 
% 243.78/50.29  | | | | | |   (57)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 243.78/50.29  | | | | | | 
% 243.78/50.29  | | | | | | REF_CLOSE: (12), (17), (57) are inconsistent by sub-proof #1386.
% 243.78/50.29  | | | | | | 
% 243.78/50.29  | | | | | End of split
% 243.78/50.29  | | | | | 
% 243.78/50.29  | | | | End of split
% 243.78/50.29  | | | | 
% 243.78/50.29  | | | Case 2:
% 243.78/50.29  | | | | 
% 243.78/50.29  | | | |   (58)  all_54_2 = e0
% 243.78/50.29  | | | | 
% 243.78/50.29  | | | | REF_CLOSE: (5), (9), (58) are inconsistent by sub-proof #1643.
% 243.78/50.29  | | | | 
% 243.78/50.29  | | | End of split
% 243.78/50.29  | | | 
% 243.78/50.29  | | End of split
% 243.78/50.29  | | 
% 243.78/50.29  | End of split
% 243.78/50.29  | 
% 243.78/50.29  End of proof
% 243.78/50.29  
% 243.78/50.29  Sub-proof #1283 shows that the following formulas are inconsistent:
% 243.78/50.29  ----------------------------------------------------------------
% 243.78/50.29    (1)   ~ (e3 = e2)
% 243.78/50.29    (2)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.78/50.29    (3)  op(e0, e0) = e3
% 243.78/50.29    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.29    (5)  all_58_14 = e1
% 243.78/50.29    (6)   ~ (e2 = e1)
% 243.78/50.29  
% 243.78/50.29  Begin of proof
% 243.78/50.29  | 
% 243.78/50.29  | BETA: splitting (2) gives:
% 243.78/50.29  | 
% 243.78/50.29  | Case 1:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (7)  all_58_14 = e2 & op(e0, e1) = e2
% 243.78/50.29  | | 
% 243.78/50.29  | | ALPHA: (7) implies:
% 243.78/50.29  | |   (8)  all_58_14 = e2
% 243.78/50.29  | | 
% 243.78/50.29  | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #2044.
% 243.78/50.29  | | 
% 243.78/50.29  | Case 2:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (9)  all_58_15 = e2 & op(e0, e0) = e2
% 243.78/50.29  | | 
% 243.78/50.29  | | ALPHA: (9) implies:
% 243.78/50.29  | |   (10)  op(e0, e0) = e2
% 243.78/50.29  | | 
% 243.78/50.29  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1388.
% 243.78/50.29  | | 
% 243.78/50.29  | End of split
% 243.78/50.29  | 
% 243.78/50.29  End of proof
% 243.78/50.29  
% 243.78/50.29  Sub-proof #1284 shows that the following formulas are inconsistent:
% 243.78/50.29  ----------------------------------------------------------------
% 243.78/50.29    (1)   ~ (e3 = e0)
% 243.78/50.29    (2)   ~ (e2 = e0)
% 243.78/50.29    (3)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.78/50.29         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.78/50.29    (4)  all_58_14 = e2 & op(e0, e1) = e2
% 243.78/50.29    (5)   ~ (e3 = e1)
% 243.78/50.29    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.78/50.29         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.78/50.29    (7)  op(e2, e1) = e2
% 243.78/50.29    (8)  op(e2, e1) = all_52_9
% 243.78/50.29    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.29    (10)   ~ (e1 = e0)
% 243.78/50.29    (11)  all_58_4 = e3
% 243.78/50.29    (12)   ~ (all_52_9 = e1)
% 243.78/50.29    (13)   ~ (e2 = e1)
% 243.78/50.29  
% 243.78/50.29  Begin of proof
% 243.78/50.29  | 
% 243.78/50.29  | ALPHA: (4) implies:
% 243.78/50.29  |   (14)  all_58_14 = e2
% 243.78/50.29  | 
% 243.78/50.29  | BETA: splitting (3) gives:
% 243.78/50.29  | 
% 243.78/50.29  | Case 1:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (15)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 243.78/50.29  | |           e1)
% 243.78/50.29  | | 
% 243.78/50.29  | | REF_CLOSE: (5), (8), (9), (11), (12), (15) are inconsistent by sub-proof
% 243.78/50.29  | |            #1339.
% 243.78/50.29  | | 
% 243.78/50.29  | Case 2:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (16)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 243.78/50.29  | |           e1)
% 243.78/50.29  | | 
% 243.78/50.29  | | BETA: splitting (16) gives:
% 243.78/50.29  | | 
% 243.78/50.29  | | Case 1:
% 243.78/50.29  | | | 
% 243.78/50.29  | | |   (17)  all_58_8 = e1 & op(e1, e1) = e1
% 243.78/50.29  | | | 
% 243.78/50.29  | | | ALPHA: (17) implies:
% 243.78/50.29  | | |   (18)  op(e1, e1) = e1
% 243.78/50.29  | | | 
% 243.78/50.29  | | | REF_CLOSE: (1), (2), (6), (7), (9), (10), (11), (14), (18) are
% 243.78/50.29  | | |            inconsistent by sub-proof #1285.
% 243.78/50.29  | | | 
% 243.78/50.29  | | Case 2:
% 243.78/50.29  | | | 
% 243.78/50.29  | | |   (19)  all_58_14 = e1 & op(e0, e1) = e1
% 243.78/50.29  | | | 
% 243.78/50.29  | | | REF_CLOSE: (13), (14), (19) are inconsistent by sub-proof #2040.
% 243.78/50.29  | | | 
% 243.78/50.29  | | End of split
% 243.78/50.29  | | 
% 243.78/50.29  | End of split
% 243.78/50.29  | 
% 243.78/50.29  End of proof
% 243.78/50.29  
% 243.78/50.29  Sub-proof #1285 shows that the following formulas are inconsistent:
% 243.78/50.29  ----------------------------------------------------------------
% 243.78/50.29    (1)   ~ (e3 = e0)
% 243.78/50.29    (2)  op(e1, e1) = e1
% 243.78/50.29    (3)   ~ (e2 = e0)
% 243.78/50.29    (4)  all_58_14 = e2
% 243.78/50.29    (5)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.78/50.29         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.78/50.29    (6)  op(e2, e1) = e2
% 243.78/50.29    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.29    (8)   ~ (e1 = e0)
% 243.78/50.29    (9)  all_58_4 = e3
% 243.78/50.29  
% 243.78/50.29  Begin of proof
% 243.78/50.29  | 
% 243.78/50.29  | BETA: splitting (5) gives:
% 243.78/50.29  | 
% 243.78/50.29  | Case 1:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (10)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 243.78/50.29  | |           e0)
% 243.78/50.29  | | 
% 243.78/50.29  | | REF_CLOSE: (1), (3), (6), (7), (9), (10) are inconsistent by sub-proof
% 243.78/50.29  | |            #1504.
% 243.78/50.29  | | 
% 243.78/50.29  | Case 2:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (11)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 243.78/50.29  | |           e0)
% 243.78/50.29  | | 
% 243.78/50.29  | | REF_CLOSE: (2), (3), (4), (7), (8), (11) are inconsistent by sub-proof
% 243.78/50.29  | |            #1286.
% 243.78/50.29  | | 
% 243.78/50.29  | End of split
% 243.78/50.29  | 
% 243.78/50.29  End of proof
% 243.78/50.29  
% 243.78/50.29  Sub-proof #1286 shows that the following formulas are inconsistent:
% 243.78/50.29  ----------------------------------------------------------------
% 243.78/50.29    (1)  op(e1, e1) = e1
% 243.78/50.29    (2)   ~ (e2 = e0)
% 243.78/50.29    (3)  all_58_14 = e2
% 243.78/50.29    (4)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.78/50.29    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.29    (6)   ~ (e1 = e0)
% 243.78/50.29  
% 243.78/50.29  Begin of proof
% 243.78/50.29  | 
% 243.78/50.29  | BETA: splitting (4) gives:
% 243.78/50.29  | 
% 243.78/50.29  | Case 1:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 243.78/50.29  | | 
% 243.78/50.29  | | ALPHA: (7) implies:
% 243.78/50.29  | |   (8)  op(e1, e1) = e0
% 243.78/50.29  | | 
% 243.78/50.29  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2220.
% 243.78/50.29  | | 
% 243.78/50.29  | Case 2:
% 243.78/50.29  | | 
% 243.78/50.29  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 243.78/50.29  | | 
% 243.78/50.29  | | ALPHA: (9) implies:
% 243.78/50.29  | |   (10)  all_58_14 = e0
% 243.78/50.29  | | 
% 243.78/50.29  | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #2114.
% 243.78/50.29  | | 
% 243.78/50.29  | End of split
% 243.78/50.29  | 
% 243.78/50.29  End of proof
% 243.78/50.29  
% 243.78/50.29  Sub-proof #1287 shows that the following formulas are inconsistent:
% 243.78/50.29  ----------------------------------------------------------------
% 243.78/50.29    (1)   ~ (all_52_3 = e0)
% 243.78/50.29    (2)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 243.78/50.29           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 243.78/50.29           all_12_1 & $i(all_12_1))
% 243.78/50.29    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 243.78/50.29             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 243.78/50.29           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 243.78/50.29         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 243.78/50.29           $i(all_56_7))
% 243.78/50.29    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.78/50.29    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.78/50.29         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.78/50.29    (6)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 243.78/50.29           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 243.78/50.29           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 243.78/50.29           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 243.78/50.29           & $i(all_56_23))
% 243.78/50.29    (7)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.78/50.29    (8)   ~ (e3 = e0)
% 243.78/50.29    (9)  op(e0, e1) = all_52_11
% 243.78/50.29    (10)   ~ (e2 = e0)
% 243.78/50.29    (11)   ~ (all_52_11 = e2)
% 243.78/50.29    (12)  all_54_13 = all_52_7
% 243.78/50.29    (13)  op(e1, e2) = all_52_6
% 243.78/50.30    (14)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.78/50.30          (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.78/50.30    (15)  all_58_12 = e2
% 243.78/50.30    (16)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.78/50.30          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.78/50.30    (17)   ~ (all_52_12 = e0)
% 243.78/50.30    (18)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.78/50.30          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.78/50.30    (19)  op(e1, e1) = all_6_2
% 243.78/50.30    (20)   ~ (all_52_1 = all_52_2)
% 243.78/50.30    (21)  op(e1, e0) = all_52_14
% 243.78/50.30    (22)   ~ (all_52_7 = e3)
% 243.78/50.30    (23)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.78/50.30    (24)   ~ (all_52_8 = e0)
% 243.78/50.30    (25)  all_58_15 = e3
% 243.78/50.30    (26)  op(e2, e3) = e3
% 243.78/50.30    (27)  op(e0, e3) = all_52_3
% 243.78/50.30    (28)   ~ (e3 = e1)
% 243.78/50.30    (29)  all_54_11 = all_52_14
% 243.78/50.30    (30)  ( ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 & op(e2, e1) =
% 243.78/50.30            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e2,
% 243.78/50.30              e1) = all_22_1 & $i(all_22_1))
% 243.78/50.30    (31)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.78/50.30          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.78/50.30    (32)   ~ (all_52_2 = all_52_3)
% 243.78/50.30    (33)   ~ (all_52_12 = all_52_14)
% 243.78/50.30    (34)   ~ (all_52_12 = all_52_13)
% 243.78/50.30    (35)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.78/50.30            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 243.78/50.30              e3) = all_26_1 & $i(all_26_1))
% 243.78/50.30    (36)  all_54_2 = all_52_8
% 243.78/50.30    (37)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.78/50.30    (38)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.78/50.30          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.78/50.30    (39)   ~ (all_52_2 = all_52_14)
% 243.78/50.30    (40)   ~ (all_52_3 = all_52_7)
% 243.78/50.30    (41)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.78/50.30    (42)  all_56_21 = e0
% 243.78/50.30    (43)  all_54_4 = all_52_1
% 243.78/50.30    (44)   ~ (all_52_11 = e3)
% 243.78/50.30    (45)   ~ (all_6_2 = e3)
% 243.78/50.30    (46)   ~ (all_52_8 = all_52_12)
% 243.78/50.30    (47)  op(e3, e1) = all_52_8
% 243.78/50.30    (48)  all_50_2 = e0
% 243.78/50.30    (49)  op(e2, e1) = all_52_9
% 243.78/50.30    (50)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.78/50.30          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.78/50.30    (51)   ~ (e3 = e2)
% 243.78/50.30    (52)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 243.78/50.30          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 243.78/50.30    (53)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.78/50.30    (54)   ~ (all_52_3 = all_52_11)
% 243.78/50.30    (55)   ~ (all_52_14 = e0)
% 243.78/50.30    (56)   ~ (all_50_2 = e0) | ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 243.78/50.30            op(e3, e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 243.78/50.30              e2) & op(e3, e0) = all_50_1 & $i(all_50_1))
% 243.78/50.30    (57)  all_54_12 = all_52_3
% 243.78/50.30    (58)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.78/50.30    (59)  op(e2, e0) = e0
% 243.78/50.30    (60)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.78/50.30    (61)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 243.78/50.30            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 243.78/50.30              e0) = all_16_1 & $i(all_16_1))
% 243.78/50.30    (62)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.78/50.30          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.78/50.30    (63)  op(e3, e0) = all_52_12
% 243.78/50.30    (64)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.78/50.30          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.78/50.30    (65)   ~ (all_52_3 = e3)
% 243.78/50.30    (66)   ~ (all_52_1 = e0)
% 243.78/50.30    (67)  op(e2, e3) = all_52_1
% 243.78/50.30    (68)   ~ (all_52_14 = e3)
% 243.78/50.30    (69)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.78/50.30          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.78/50.30    (70)   ~ (all_52_2 = e3)
% 243.78/50.30    (71)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.78/50.30    (72)   ~ (all_52_1 = all_52_13)
% 243.78/50.30    (73)   ~ (all_52_2 = e0)
% 243.78/50.30    (74)   ~ (all_52_11 = e0)
% 243.78/50.30    (75)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.78/50.30          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.78/50.30    (76)  all_54_7 = all_52_13
% 243.78/50.30    (77)   ~ (all_52_13 = all_52_14)
% 243.78/50.30    (78)  all_54_1 = all_52_4
% 243.78/50.30    (79)  op(e3, e2) = all_52_4
% 243.78/50.30    (80)   ~ (all_52_8 = all_52_11)
% 243.78/50.30    (81)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.78/50.30    (82)   ~ (all_52_9 = e3)
% 243.78/50.30    (83)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.78/50.30          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.78/50.30    (84)  op(e0, e0) = e3
% 243.78/50.30    (85)  all_54_8 = all_52_2
% 243.78/50.30    (86)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 243.78/50.30          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 243.78/50.30    (87)   ~ (all_52_2 = all_52_6)
% 243.78/50.30    (88)  all_54_3 = all_52_12
% 243.78/50.30    (89)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.30            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.30    (90)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.78/50.30          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.78/50.30    (91)  op(e1, e3) = all_52_2
% 243.78/50.30    (92)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.78/50.30          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.78/50.30    (93)  op(e1, e1) = e0
% 243.78/50.30    (94)   ~ (all_52_4 = e1)
% 243.78/50.30    (95)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.78/50.30          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.78/50.30    (96)   ~ (e1 = e0)
% 243.78/50.30    (97)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.78/50.30          | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.78/50.30    (98)  op(e3, e3) = e0
% 243.78/50.30    (99)  all_58_4 = e3
% 243.78/50.30    (100)   ~ (all_52_8 = e2)
% 243.78/50.30    (101)   ~ (all_52_13 = e3)
% 243.78/50.30    (102)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.78/50.30           (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.78/50.30    (103)  all_56_1 = e0
% 243.78/50.30    (104)  op(e2, e0) = all_52_13
% 243.78/50.30    (105)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.78/50.30           | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.78/50.30             e1)
% 243.78/50.30    (106)   ~ (all_52_9 = e1)
% 243.78/50.30    (107)  all_54_14 = all_52_11
% 243.78/50.30    (108)   ~ (all_52_4 = all_52_8)
% 243.78/50.30    (109)   ~ (all_52_4 = e0)
% 243.78/50.30    (110)   ~ (e2 = e1)
% 243.78/50.30    (111)   ~ (all_52_1 = e1)
% 243.78/50.30    (112)  op(e2, e1) = all_30_1
% 243.78/50.30  
% 243.78/50.30  Begin of proof
% 243.78/50.30  | 
% 243.78/50.30  | BETA: splitting (86) gives:
% 243.78/50.30  | 
% 243.78/50.30  | Case 1:
% 243.78/50.30  | | 
% 243.78/50.30  | |   (113)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 243.78/50.30  | |            e1)
% 243.78/50.30  | | 
% 243.78/50.30  | | REF_CLOSE: (79), (89), (94), (96), (98), (113) are inconsistent by sub-proof
% 243.78/50.30  | |            #1826.
% 243.78/50.30  | | 
% 243.78/50.30  | Case 2:
% 243.78/50.30  | | 
% 243.78/50.30  | |   (114)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 243.78/50.30  | |            e1)
% 243.78/50.30  | | 
% 243.78/50.30  | | BETA: splitting (114) gives:
% 243.78/50.30  | | 
% 243.78/50.30  | | Case 1:
% 243.78/50.30  | | | 
% 243.78/50.30  | | |   (115)  all_58_4 = e1 & op(e3, e1) = e1
% 243.78/50.30  | | | 
% 243.78/50.30  | | | REF_CLOSE: (28), (99), (115) are inconsistent by sub-proof #2042.
% 243.78/50.30  | | | 
% 243.78/50.30  | | Case 2:
% 243.78/50.30  | | | 
% 243.78/50.30  | | |   (116)  all_58_9 = e1 & op(e3, e0) = e1
% 243.78/50.30  | | | 
% 243.78/50.30  | | | ALPHA: (116) implies:
% 243.78/50.30  | | |   (117)  all_58_9 = e1
% 243.78/50.30  | | |   (118)  op(e3, e0) = e1
% 243.78/50.30  | | | 
% 243.78/50.30  | | | BETA: splitting (18) gives:
% 243.78/50.30  | | | 
% 243.78/50.30  | | | Case 1:
% 243.78/50.30  | | | | 
% 243.78/50.30  | | | |   (119)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 243.78/50.30  | | | |            = e1)
% 243.78/50.30  | | | | 
% 243.78/50.30  | | | | REF_CLOSE: (28), (49), (89), (99), (106), (119) are inconsistent by
% 243.78/50.30  | | | |            sub-proof #1339.
% 243.78/50.30  | | | | 
% 243.78/50.30  | | | Case 2:
% 243.78/50.30  | | | | 
% 243.78/50.30  | | | |   (120)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0,
% 243.78/50.30  | | | |              e1) = e1)
% 243.78/50.30  | | | | 
% 243.78/50.30  | | | | BETA: splitting (120) gives:
% 243.78/50.30  | | | | 
% 243.78/50.30  | | | | Case 1:
% 243.78/50.30  | | | | | 
% 243.78/50.30  | | | | |   (121)  all_58_8 = e1 & op(e1, e1) = e1
% 243.78/50.30  | | | | | 
% 243.78/50.30  | | | | | ALPHA: (121) implies:
% 243.78/50.30  | | | | |   (122)  op(e1, e1) = e1
% 243.78/50.30  | | | | | 
% 243.78/50.30  | | | | | REF_CLOSE: (89), (93), (96), (122) are inconsistent by sub-proof
% 243.78/50.30  | | | | |            #2220.
% 243.78/50.30  | | | | | 
% 243.78/50.30  | | | | Case 2:
% 243.78/50.30  | | | | | 
% 243.78/50.30  | | | | |   (123)  all_58_14 = e1 & op(e0, e1) = e1
% 243.78/50.30  | | | | | 
% 243.78/50.30  | | | | | ALPHA: (123) implies:
% 243.78/50.30  | | | | |   (124)  all_58_14 = e1
% 243.78/50.30  | | | | | 
% 243.78/50.30  | | | | | BETA: splitting (83) gives:
% 243.78/50.30  | | | | | 
% 243.78/50.30  | | | | | Case 1:
% 243.78/50.30  | | | | | | 
% 243.78/50.30  | | | | | |   (125)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 243.78/50.30  | | | | | |              e3) = e1)
% 243.78/50.30  | | | | | | 
% 243.78/50.30  | | | | | | BETA: splitting (125) gives:
% 243.78/50.30  | | | | | | 
% 243.78/50.30  | | | | | | Case 1:
% 243.78/50.30  | | | | | | | 
% 243.78/50.30  | | | | | | |   (126)  all_58_0 = e1 & op(e3, e3) = e1
% 243.78/50.30  | | | | | | | 
% 243.78/50.30  | | | | | | | ALPHA: (126) implies:
% 243.78/50.30  | | | | | | |   (127)  op(e3, e3) = e1
% 243.78/50.30  | | | | | | | 
% 243.78/50.30  | | | | | | | REF_CLOSE: (5), (8), (10), (51), (69), (89), (96), (99), (110),
% 243.78/50.30  | | | | | | |            (117), (127) are inconsistent by sub-proof #1292.
% 243.78/50.30  | | | | | | | 
% 243.78/50.30  | | | | | | Case 2:
% 243.78/50.30  | | | | | | | 
% 243.78/50.30  | | | | | | |   (128)  all_58_2 = e1 & op(e2, e3) = e1
% 243.78/50.30  | | | | | | | 
% 243.78/50.30  | | | | | | | REF_CLOSE: (67), (89), (111), (128) are inconsistent by sub-proof
% 243.78/50.30  | | | | | | |            #2229.
% 243.78/50.30  | | | | | | | 
% 243.78/50.30  | | | | | | End of split
% 243.78/50.30  | | | | | | 
% 243.78/50.30  | | | | | Case 2:
% 243.78/50.30  | | | | | | 
% 243.78/50.30  | | | | | |   (129)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 243.78/50.30  | | | | | |            op(e0, e3) = e1)
% 243.78/50.30  | | | | | | 
% 243.78/50.30  | | | | | | BETA: splitting (129) gives:
% 243.78/50.30  | | | | | | 
% 243.78/50.30  | | | | | | Case 1:
% 243.78/50.30  | | | | | | | 
% 243.78/50.30  | | | | | | |   (130)  all_58_6 = e1 & op(e1, e3) = e1
% 243.78/50.30  | | | | | | | 
% 243.78/50.30  | | | | | | | ALPHA: (130) implies:
% 243.78/50.30  | | | | | | |   (131)  op(e1, e3) = e1
% 243.78/50.30  | | | | | | | 
% 243.78/50.30  | | | | | | | BETA: splitting (52) gives:
% 243.78/50.30  | | | | | | | 
% 243.78/50.30  | | | | | | | Case 1:
% 243.78/50.30  | | | | | | | | 
% 243.78/50.30  | | | | | | | |   (132)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 243.78/50.30  | | | | | | | |            op(e2, e1) = e2)
% 243.78/50.30  | | | | | | | | 
% 243.78/50.30  | | | | | | | | BETA: splitting (132) gives:
% 243.78/50.30  | | | | | | | | 
% 243.78/50.30  | | | | | | | | Case 1:
% 243.78/50.30  | | | | | | | | | 
% 243.78/50.30  | | | | | | | | |   (133)  all_58_4 = e2 & op(e3, e1) = e2
% 243.78/50.30  | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | ALPHA: (133) implies:
% 243.78/50.30  | | | | | | | | |   (134)  all_58_4 = e2
% 243.78/50.30  | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | REF_CLOSE: (8), (9), (44), (49), (51), (75), (82), (89), (93),
% 243.78/50.30  | | | | | | | | |            (134) are inconsistent by sub-proof #1493.
% 243.78/50.30  | | | | | | | | | 
% 243.78/50.30  | | | | | | | | Case 2:
% 243.78/50.30  | | | | | | | | | 
% 243.78/50.30  | | | | | | | | |   (135)  all_58_5 = e2 & op(e2, e1) = e2
% 243.78/50.30  | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | ALPHA: (135) implies:
% 243.78/50.30  | | | | | | | | |   (136)  all_58_5 = e2
% 243.78/50.30  | | | | | | | | |   (137)  op(e2, e1) = e2
% 243.78/50.30  | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | BETA: splitting (90) gives:
% 243.78/50.30  | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | Case 1:
% 243.78/50.30  | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | |   (138)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2
% 243.78/50.30  | | | | | | | | | |            & op(e2, e0) = e2)
% 243.78/50.30  | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | BETA: splitting (138) gives:
% 243.78/50.30  | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | Case 1:
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | |   (139)  all_58_9 = e2 & op(e3, e0) = e2
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | ALPHA: (139) implies:
% 243.78/50.30  | | | | | | | | | | |   (140)  all_58_9 = e2
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | COMBINE_EQS: (117), (140) imply:
% 243.78/50.30  | | | | | | | | | | |   (141)  e2 = e1
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | REF_CLOSE: (8), (10), (31), (51), (52), (96), (99), (110),
% 243.78/50.30  | | | | | | | | | | |            (124), (136), (141) are inconsistent by sub-proof
% 243.78/50.30  | | | | | | | | | | |            #1480.
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | Case 2:
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | |   (142)  all_58_10 = e2 & op(e2, e0) = e2
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | ALPHA: (142) implies:
% 243.78/50.30  | | | | | | | | | | |   (143)  op(e2, e0) = e2
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | REF_CLOSE: (10), (59), (89), (143) are inconsistent by
% 243.78/50.30  | | | | | | | | | | |            sub-proof #2121.
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | End of split
% 243.78/50.30  | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | Case 2:
% 243.78/50.30  | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | |   (144)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 243.78/50.30  | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 243.78/50.30  | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | BETA: splitting (144) gives:
% 243.78/50.30  | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | Case 1:
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | |   (145)  all_58_11 = e2 & op(e1, e0) = e2
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | ALPHA: (145) implies:
% 243.78/50.30  | | | | | | | | | | |   (146)  op(e1, e0) = e2
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | BETA: splitting (53) gives:
% 243.78/50.30  | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | Case 1:
% 243.78/50.30  | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | |   (147)  all_54_14 = e3
% 243.78/50.30  | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | REF_CLOSE: (44), (107), (147) are inconsistent by sub-proof
% 243.78/50.30  | | | | | | | | | | | |            #1796.
% 243.78/50.30  | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | Case 2:
% 243.78/50.30  | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | |   (148)   ~ (all_54_14 = e3)
% 243.78/50.30  | | | | | | | | | | | |   (149)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.78/50.30  | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | BETA: splitting (30) gives:
% 243.78/50.30  | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | Case 1:
% 243.78/50.30  | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | |   (150)   ~ (all_22_0 = e3) & op(all_22_1, e2) = all_22_0 &
% 243.78/50.30  | | | | | | | | | | | | |          op(e2, e1) = all_22_1 & $i(all_22_0) &
% 243.78/50.30  | | | | | | | | | | | | |          $i(all_22_1)
% 243.78/50.30  | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | ALPHA: (150) implies:
% 243.78/50.30  | | | | | | | | | | | | |   (151)  op(e2, e1) = all_22_1
% 243.78/50.30  | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | BETA: splitting (5) gives:
% 243.78/50.30  | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | Case 1:
% 243.78/50.30  | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | |   (152)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 243.78/50.30  | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 243.78/50.30  | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 243.78/50.30  | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | | Case 1:
% 243.78/50.30  | | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | | |   (153)  all_58_0 = e2 & op(e3, e3) = e2
% 243.78/50.30  | | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 243.78/50.30  | | | | | | | | | | | | | | |   (154)  op(e3, e3) = e2
% 243.78/50.30  | | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (15), (27), (28), (38), (51), (62),
% 243.78/50.30  | | | | | | | | | | | | | | |            (65), (66), (67), (83), (89), (96), (110), (154)
% 243.78/50.30  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1755.
% 243.78/50.30  | | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | | Case 2:
% 243.78/50.30  | | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | | |   (155)  all_58_1 = e2 & op(e3, e2) = e2
% 243.78/50.30  | | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 243.78/50.30  | | | | | | | | | | | | | | |   (156)  all_58_1 = e2
% 243.78/50.30  | | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 243.78/50.30  | | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | | | Case 1:
% 243.78/50.30  | | | | | | | | | | | | | | | | 
% 243.78/50.30  | | | | | | | | | | | | | | | |   (157)  all_54_14 = e2
% 243.78/50.30  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | REF_CLOSE: (11), (107), (157) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | |            #1856.
% 243.78/50.31  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | |   (158)  all_54_14 = e1 | all_54_14 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (159)  all_54_14 = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (159) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (160)  all_52_11 = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | SIMP: (160) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (161)  all_52_11 = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | REDUCE: (54), (161) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (162)   ~ (all_52_3 = e1)
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | REDUCE: (80), (161) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (163)   ~ (all_52_8 = e1)
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | REDUCE: (9), (161) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (164)  op(e0, e1) = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | |   (165)  all_54_12 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (65), (165) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | | | |            #2266.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | |   (166)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |   (167)  all_54_12 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (167) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |   (168)  all_52_3 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | SIMP: (168) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |   (169)  all_52_3 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | REDUCE: (32), (169) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |   (170)   ~ (all_52_2 = e2)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | REDUCE: (27), (169) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |   (171)  op(e0, e3) = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (172)  all_54_2 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (172) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (173)  all_52_8 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | SIMP: (173) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (174)  all_52_8 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (174) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (175)   ~ (all_52_4 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (174) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (176)   ~ (all_52_12 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | SIMP: (176) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (177)   ~ (all_52_12 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (174) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (178)  op(e3, e1) = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | |   (179)  all_54_1 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (175), (179) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | |            #1930.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | |   (180)   ~ (all_54_1 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | |   (181)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | |   (182)  all_54_8 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (70), (85), (182) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | |            #2011.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | |   (183)   ~ (all_54_8 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | |   (184)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | |   (185)  all_54_8 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (170), (185) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | |            #2007.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | |   (186)   ~ (all_54_8 = e2)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | |   (187)  all_54_8 = e1 | all_54_8 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_54_8 = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (188) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | |   (189)  all_52_2 = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (189) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | |   (190)  all_52_2 = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (190) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | |   (191)   ~ (all_52_14 = e1)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (191) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | |   (192)   ~ (all_52_14 = e1)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (190) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | |   (193)   ~ (e3 = e1)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (194)  all_54_11 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (194) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  all_52_14 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (195) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  $false
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (197)   ~ (all_54_11 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (198)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (199)  all_54_11 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (199) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_52_14 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (200) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (201)   ~ (all_52_12 = e2)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (200) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (202)   ~ (e3 = e2)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_54_3 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (177), (203) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2057.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (204)   ~ (all_54_3 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (206)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_3 & $i(all_56_3))
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (51), (63), (89), (103), (177), (206) are
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1511.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (207)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_7 & $i(all_56_7))
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (208)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_5 & $i(all_56_5)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  op(e1, e3) = all_56_5
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  op(e1, all_56_5) = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (85), (89), (91), (93), (170), (184), (209),
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210) are inconsistent by sub-proof #2004.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_7 & $i(all_56_7)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  op(e0, e3) = all_56_7
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  op(e0, all_56_7) = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_19 & $i(all_56_19))
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_56_17 & $i(all_56_17)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (12), (20), (22), (26), (32), (40),
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (43), (57), (66), (67), (71), (73), (81), (85),
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (89), (98), (166), (170), (178), (215) are
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1291.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_56_19 & $i(all_56_19)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  op(e2, e1) = all_56_19
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  op(e2, all_56_19) = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  all_54_1 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (219) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)  all_52_4 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (220) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_52_4 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_56_7, e3, e0,
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (171), (212) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  all_56_7 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_30_1, e1, e2,
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (112), (137) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  all_30_1 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with all_30_1, all_56_19, e1,
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (112), (217) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  all_56_19 = all_30_1
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with all_22_1, all_56_19, e1,
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (151), (217) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  all_56_19 = all_22_1
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (225) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  all_30_1 = all_22_1
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (226) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  all_30_1 = all_22_1
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (227) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  all_22_1 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (225), (228) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  all_56_19 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (13), (16), (28), (51), (89), (92),
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (95), (96), (110), (156), (213), (218), (222),
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229) are inconsistent by sub-proof #1290.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  all_54_1 = e1 | all_54_1 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (94), (109), (230) are inconsistent by
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2049.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23))
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (21), (33), (42), (78), (84), (88),
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (89), (94), (109), (164), (181), (201), (205),
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231) are inconsistent by sub-proof #1289.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  all_54_11 = e1 | all_54_11 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (55), (192), (232) are inconsistent by
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2174.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | |   (233)  all_54_8 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (85), (233) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | |            #2006.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (234)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (36), (100), (163), (234) are inconsistent
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |            by sub-proof #1335.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |   (235)  all_54_12 = e1 | all_54_12 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (57), (162), (235) are inconsistent by
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |            sub-proof #2067.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (236)  all_54_14 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (107), (236) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | | |            #1936.
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | |   (237)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 243.78/50.31  | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 243.78/50.31  | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (14), (25), (28), (44), (49), (51),
% 243.78/50.31  | | | | | | | | | | | | | |            (59), (75), (82), (89), (93), (96), (104), (110),
% 243.78/50.31  | | | | | | | | | | | | | |            (146), (237) are inconsistent by sub-proof #1288.
% 243.78/50.31  | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | End of split
% 243.78/50.31  | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | |   (238)   ~ (all_22_1 = e0) & op(e2, e1) = all_22_1 &
% 243.78/50.31  | | | | | | | | | | | | |          $i(all_22_1)
% 243.78/50.31  | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | ALPHA: (238) implies:
% 243.78/50.31  | | | | | | | | | | | | |   (239)   ~ (all_22_1 = e0)
% 243.78/50.31  | | | | | | | | | | | | |   (240)  op(e2, e1) = all_22_1
% 243.78/50.31  | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | BETA: splitting (5) gives:
% 243.78/50.31  | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | |   (241)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 243.78/50.31  | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 243.78/50.31  | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 243.78/50.31  | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | |   (242)  all_58_0 = e2 & op(e3, e3) = e2
% 243.78/50.31  | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 243.78/50.31  | | | | | | | | | | | | | | |   (243)  op(e3, e3) = e2
% 243.78/50.31  | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (15), (27), (28), (38), (51), (62),
% 243.78/50.31  | | | | | | | | | | | | | | |            (65), (66), (67), (83), (89), (96), (110), (243)
% 243.78/50.31  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1755.
% 243.78/50.31  | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | |   (244)  all_58_1 = e2 & op(e3, e2) = e2
% 243.78/50.31  | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 243.78/50.31  | | | | | | | | | | | | | | |   (245)  all_58_1 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | |   (246)  all_54_14 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | REF_CLOSE: (11), (107), (246) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | |            #1856.
% 243.78/50.31  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | |   (247)  all_54_14 = e1 | all_54_14 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (248)  all_54_14 = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (248) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (249)  all_52_11 = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | SIMP: (249) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (250)  all_52_11 = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | REDUCE: (54), (250) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (251)   ~ (all_52_3 = e1)
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | REDUCE: (80), (250) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (252)   ~ (all_52_8 = e1)
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | REDUCE: (9), (250) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | |   (253)  op(e0, e1) = e1
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | |   (254)  all_54_12 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (65), (254) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | | | |            #2266.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | |   (255)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |   (256)  all_54_12 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (256) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |   (257)  all_52_3 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | SIMP: (257) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |   (258)  all_52_3 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | REDUCE: (32), (258) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |   (259)   ~ (all_52_2 = e2)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | REDUCE: (27), (258) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | |   (260)  op(e0, e3) = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (261)  all_54_2 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (261) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (262)  all_52_8 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | SIMP: (262) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (263)  all_52_8 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (263) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (264)   ~ (all_52_4 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (263) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (265)   ~ (all_52_12 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | SIMP: (265) implies:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (266)   ~ (all_52_12 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (263) imply:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | |   (267)  op(e3, e1) = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | |   (268)  all_54_1 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (264), (268) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | |            #1930.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | |   (269)   ~ (all_54_1 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | |   (270)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | |   (271)  all_54_8 = e3
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (70), (85), (271) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | |            #2011.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | |   (272)   ~ (all_54_8 = e3)
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | |   (273)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_54_8 = e2
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (85), (259), (274) are inconsistent by sub-proof
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | |            #2007.
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.31  | | | | | | | | | | | | | | | | | | | | | | |   (275)   ~ (all_54_8 = e2)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | |   (276)  all_54_8 = e1 | all_54_8 = e0
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | |   (277)  all_54_8 = e1
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (277) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_52_2 = e1
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (278) implies:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_52_2 = e1
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (279) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | |   (280)   ~ (all_52_14 = e1)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (280) implies:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | |   (281)   ~ (all_52_14 = e1)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (279) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | |   (282)   ~ (e3 = e1)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  all_54_11 = e3
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (283) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  all_52_14 = e3
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (284) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (285)  $false
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (286)   ~ (all_54_11 = e3)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (288)  all_54_11 = e2
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (288) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_52_14 = e2
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (289) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)   ~ (all_52_12 = e2)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (289) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)   ~ (e3 = e2)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)  all_54_3 = e3
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (266), (292) are inconsistent by sub-proof
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2057.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)   ~ (all_54_3 = e3)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_3 & $i(all_56_3))
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (51), (63), (89), (103), (266), (295) are
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1511.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_7 & $i(all_56_7))
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_5 & $i(all_56_5)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  op(e1, e3) = all_56_5
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  op(e1, all_56_5) = e1
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (85), (89), (91), (93), (259), (273), (298),
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (299) are inconsistent by sub-proof #2004.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (300)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_7 & $i(all_56_7)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  op(e0, e3) = all_56_7
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  op(e0, all_56_7) = e0
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_17 & $i(all_56_17)) | (all_56_18
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_19 & $i(all_56_19))
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_56_17 & $i(all_56_17)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (12), (20), (22), (26), (32), (40),
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (43), (57), (66), (67), (71), (73), (81), (85),
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (89), (98), (255), (259), (267), (304) are
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1291.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_56_19 & $i(all_56_19)
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  op(e2, e1) = all_56_19
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  op(e2, all_56_19) = e2
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_54_1 = e2
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (308) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (309)  all_52_4 = e2
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (309) implies:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  all_52_4 = e2
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_56_7, e3, e0,
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (260), (301) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  all_56_7 = e2
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with e2, all_30_1, e1, e2,
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (112), (137) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_30_1 = e2
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with all_30_1, all_56_19, e1,
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (112), (306) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_56_19 = all_30_1
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (89) with all_22_1, all_56_19, e1,
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (240), (306) gives:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  all_56_19 = all_22_1
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (314) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  all_30_1 = all_22_1
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (315) implies:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  all_30_1 = all_22_1
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (316) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  all_22_1 = e2
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (317) imply:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  all_56_19 = e2
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (13), (16), (28), (51), (89), (92),
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (95), (96), (110), (245), (302), (307), (311),
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (318) are inconsistent by sub-proof #1290.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  all_54_1 = e1 | all_54_1 = e0
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (94), (109), (319) are inconsistent by
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2049.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_56_23 & $i(all_56_23))
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (21), (33), (42), (78), (84), (88),
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (89), (94), (109), (253), (270), (290), (294),
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (320) are inconsistent by sub-proof #1289.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)  all_54_11 = e1 | all_54_11 = e0
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (55), (281), (321) are inconsistent by
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2174.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | |   (322)  all_54_8 = e0
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (85), (322) are inconsistent by sub-proof
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | |            #2006.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | |   (323)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (36), (100), (252), (323) are inconsistent
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | |            by sub-proof #1335.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | |   (324)  all_54_12 = e1 | all_54_12 = e0
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (57), (251), (324) are inconsistent by
% 243.78/50.32  | | | | | | | | | | | | | | | | | | |            sub-proof #2067.
% 243.78/50.32  | | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | |   (325)  all_54_14 = e0
% 243.78/50.32  | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (107), (325) are inconsistent by sub-proof
% 243.78/50.32  | | | | | | | | | | | | | | | | |            #1936.
% 243.78/50.32  | | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | |   (326)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 243.78/50.32  | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 243.78/50.32  | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (14), (25), (28), (44), (49), (51),
% 243.78/50.32  | | | | | | | | | | | | | |            (59), (75), (82), (89), (93), (96), (104), (110),
% 243.78/50.32  | | | | | | | | | | | | | |            (146), (326) are inconsistent by sub-proof #1288.
% 243.78/50.32  | | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | |   (327)  all_58_15 = e2 & op(e0, e0) = e2
% 243.78/50.32  | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | ALPHA: (327) implies:
% 243.78/50.32  | | | | | | | | | | |   (328)  op(e0, e0) = e2
% 243.78/50.32  | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | | REF_CLOSE: (51), (84), (89), (328) are inconsistent by
% 243.78/50.32  | | | | | | | | | | |            sub-proof #1388.
% 243.78/50.32  | | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | | 
% 243.78/50.32  | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | 
% 243.78/50.32  | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | 
% 243.78/50.32  | | | | | | | |   (329)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 243.78/50.32  | | | | | | | |            op(e0, e1) = e2)
% 243.78/50.32  | | | | | | | | 
% 243.78/50.32  | | | | | | | | BETA: splitting (329) gives:
% 243.78/50.32  | | | | | | | | 
% 243.78/50.32  | | | | | | | | Case 1:
% 243.78/50.32  | | | | | | | | | 
% 243.78/50.32  | | | | | | | | |   (330)  all_58_8 = e2 & op(e1, e1) = e2
% 243.78/50.32  | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | ALPHA: (330) implies:
% 243.78/50.32  | | | | | | | | |   (331)  op(e1, e1) = e2
% 243.78/50.32  | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | REF_CLOSE: (8), (10), (21), (28), (51), (55), (64), (68),
% 243.78/50.32  | | | | | | | | |            (73), (89), (91), (102), (131), (331) are
% 243.78/50.32  | | | | | | | | |            inconsistent by sub-proof #1850.
% 243.78/50.32  | | | | | | | | | 
% 243.78/50.32  | | | | | | | | Case 2:
% 243.78/50.32  | | | | | | | | | 
% 243.78/50.32  | | | | | | | | |   (332)  all_58_14 = e2 & op(e0, e1) = e2
% 243.78/50.32  | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | ALPHA: (332) implies:
% 243.78/50.32  | | | | | | | | |   (333)  all_58_14 = e2
% 243.78/50.32  | | | | | | | | | 
% 243.78/50.32  | | | | | | | | | REF_CLOSE: (10), (15), (25), (28), (89), (96), (97), (105),
% 243.78/50.32  | | | | | | | | |            (110), (333) are inconsistent by sub-proof #1392.
% 243.78/50.32  | | | | | | | | | 
% 243.78/50.32  | | | | | | | | End of split
% 243.78/50.32  | | | | | | | | 
% 243.78/50.32  | | | | | | | End of split
% 243.78/50.32  | | | | | | | 
% 243.78/50.32  | | | | | | Case 2:
% 243.78/50.32  | | | | | | | 
% 243.78/50.32  | | | | | | |   (334)  all_58_12 = e1 & op(e0, e3) = e1
% 243.78/50.32  | | | | | | | 
% 243.78/50.32  | | | | | | | ALPHA: (334) implies:
% 243.78/50.32  | | | | | | |   (335)  all_58_12 = e1
% 243.78/50.32  | | | | | | |   (336)  op(e0, e3) = e1
% 243.78/50.32  | | | | | | | 
% 243.78/50.32  | | | | | | | REF_CLOSE: (2), (7), (10), (13), (19), (21), (27), (29), (32),
% 243.78/50.32  | | | | | | |            (33), (34), (35), (37), (45), (48), (50), (51), (56),
% 243.78/50.32  | | | | | | |            (58), (61), (63), (64), (67), (68), (72), (73), (76),
% 243.78/50.32  | | | | | | |            (77), (85), (87), (89), (91), (98), (101), (110),
% 243.78/50.32  | | | | | | |            (118), (335), (336) are inconsistent by sub-proof
% 243.78/50.32  | | | | | | |            #1298.
% 243.78/50.32  | | | | | | | 
% 243.78/50.32  | | | | | | End of split
% 243.78/50.32  | | | | | | 
% 243.78/50.32  | | | | | End of split
% 243.78/50.32  | | | | | 
% 243.78/50.32  | | | | End of split
% 243.78/50.32  | | | | 
% 243.78/50.32  | | | End of split
% 243.78/50.32  | | | 
% 243.78/50.32  | | End of split
% 243.78/50.32  | | 
% 243.78/50.32  | End of split
% 243.78/50.32  | 
% 243.78/50.32  End of proof
% 243.78/50.32  
% 243.78/50.32  Sub-proof #1288 shows that the following formulas are inconsistent:
% 243.78/50.32  ----------------------------------------------------------------
% 243.78/50.32    (1)   ~ (e3 = e0)
% 243.78/50.32    (2)  op(e0, e1) = all_52_11
% 243.78/50.32    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.78/50.32         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.78/50.32    (4)  all_58_15 = e3
% 243.78/50.32    (5)   ~ (e3 = e1)
% 243.78/50.32    (6)   ~ (all_52_11 = e3)
% 243.78/50.32    (7)  op(e2, e1) = all_52_9
% 243.78/50.32    (8)   ~ (e3 = e2)
% 243.78/50.32    (9)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.78/50.32    (10)  op(e2, e0) = e0
% 243.78/50.32    (11)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.78/50.32          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.78/50.32    (12)   ~ (all_52_9 = e3)
% 243.78/50.32    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.32    (14)  op(e1, e1) = e0
% 243.78/50.32    (15)  op(e1, e0) = e2
% 243.78/50.32    (16)   ~ (e1 = e0)
% 243.78/50.32    (17)  op(e2, e0) = all_52_13
% 243.78/50.32    (18)   ~ (e2 = e1)
% 243.78/50.32  
% 243.78/50.32  Begin of proof
% 243.78/50.32  | 
% 243.78/50.32  | BETA: splitting (9) gives:
% 243.78/50.32  | 
% 243.78/50.32  | Case 1:
% 243.78/50.32  | | 
% 243.78/50.32  | |   (19)  all_58_4 = e2 & op(e3, e1) = e2
% 243.78/50.32  | | 
% 243.78/50.32  | | ALPHA: (19) implies:
% 243.78/50.32  | |   (20)  all_58_4 = e2
% 243.78/50.32  | | 
% 243.78/50.32  | | REF_CLOSE: (1), (2), (6), (7), (8), (11), (12), (13), (14), (20) are
% 243.78/50.32  | |            inconsistent by sub-proof #1493.
% 243.78/50.32  | | 
% 243.78/50.32  | Case 2:
% 243.78/50.32  | | 
% 243.78/50.32  | |   (21)  all_58_9 = e2 & op(e3, e0) = e2
% 243.78/50.32  | | 
% 243.78/50.32  | | ALPHA: (21) implies:
% 243.78/50.32  | |   (22)  all_58_9 = e2
% 243.78/50.32  | | 
% 243.78/50.32  | | REF_CLOSE: (3), (4), (5), (10), (13), (15), (16), (17), (18), (22) are
% 243.78/50.32  | |            inconsistent by sub-proof #1305.
% 243.78/50.32  | | 
% 243.78/50.32  | End of split
% 243.78/50.32  | 
% 243.78/50.32  End of proof
% 243.78/50.32  
% 243.78/50.32  Sub-proof #1289 shows that the following formulas are inconsistent:
% 243.78/50.32  ----------------------------------------------------------------
% 243.78/50.32    (1)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 243.78/50.32    (2)   ~ (e3 = e0)
% 243.78/50.32    (3)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 = e0 & op(e0,
% 243.78/50.32             all_56_23) = e0 & op(e0, e1) = all_56_23 & $i(all_56_23))
% 243.78/50.32    (4)   ~ (all_52_12 = e0)
% 243.78/50.32    (5)  op(e1, e0) = all_52_14
% 243.78/50.32    (6)   ~ (all_52_12 = all_52_14)
% 243.78/50.32    (7)  op(e0, e1) = e1
% 243.78/50.32    (8)  all_56_21 = e0
% 243.78/50.32    (9)   ~ (all_52_12 = e2)
% 243.78/50.32    (10)  all_54_1 = all_52_4
% 243.78/50.32    (11)  op(e0, e0) = e3
% 243.78/50.32    (12)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.78/50.32    (13)  all_54_3 = all_52_12
% 243.78/50.32    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.32    (15)   ~ (all_52_4 = e1)
% 243.78/50.32    (16)   ~ (all_52_4 = e0)
% 243.78/50.32  
% 243.78/50.32  Begin of proof
% 243.78/50.32  | 
% 243.78/50.32  | BETA: splitting (3) gives:
% 243.78/50.32  | 
% 243.78/50.32  | Case 1:
% 243.78/50.32  | | 
% 243.78/50.32  | |   (17)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 243.78/50.32  | | 
% 243.78/50.32  | | ALPHA: (17) implies:
% 243.78/50.32  | |   (18)  op(e1, all_56_21) = e1
% 243.78/50.32  | | 
% 243.78/50.32  | | REDUCE: (8), (18) imply:
% 243.78/50.32  | |   (19)  op(e1, e0) = e1
% 243.78/50.32  | | 
% 243.78/50.32  | | REF_CLOSE: (4), (5), (6), (9), (12), (13), (14), (19) are inconsistent by
% 243.78/50.32  | |            sub-proof #1330.
% 243.78/50.32  | | 
% 243.78/50.32  | Case 2:
% 243.78/50.32  | | 
% 243.78/50.32  | |   (20)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 243.78/50.32  | |         $i(all_56_23)
% 243.78/50.32  | | 
% 243.78/50.32  | | ALPHA: (20) implies:
% 243.78/50.32  | |   (21)  op(e0, e1) = all_56_23
% 243.78/50.32  | |   (22)  op(e0, all_56_23) = e0
% 243.78/50.32  | | 
% 243.78/50.32  | | BETA: splitting (1) gives:
% 243.78/50.32  | | 
% 243.78/50.32  | | Case 1:
% 243.78/50.32  | | | 
% 243.78/50.32  | | | 
% 243.78/50.32  | | | GROUND_INST: instantiating (14) with e1, all_56_23, e1, e0, simplifying
% 243.78/50.32  | | |              with (7), (21) gives:
% 243.78/50.32  | | |   (23)  all_56_23 = e1
% 243.78/50.32  | | | 
% 243.78/50.32  | | | REDUCE: (22), (23) imply:
% 243.78/50.32  | | |   (24)  op(e0, e1) = e0
% 243.78/50.32  | | | 
% 243.78/50.32  | | | REF_CLOSE: (2), (11), (14), (21), (22), (24) are inconsistent by sub-proof
% 243.78/50.32  | | |            #1395.
% 243.78/50.32  | | | 
% 243.78/50.32  | | Case 2:
% 243.78/50.32  | | | 
% 243.78/50.32  | | |   (25)  all_54_1 = e1 | all_54_1 = e0
% 243.78/50.32  | | | 
% 243.78/50.32  | | | REF_CLOSE: (10), (15), (16), (25) are inconsistent by sub-proof #2049.
% 243.78/50.32  | | | 
% 243.78/50.32  | | End of split
% 243.78/50.32  | | 
% 243.78/50.32  | End of split
% 243.78/50.32  | 
% 243.78/50.32  End of proof
% 243.78/50.32  
% 243.78/50.32  Sub-proof #1290 shows that the following formulas are inconsistent:
% 243.78/50.32  ----------------------------------------------------------------
% 243.78/50.32    (1)   ~ (e3 = e0)
% 243.78/50.32    (2)   ~ (e2 = e0)
% 243.78/50.32    (3)  op(e1, e2) = all_52_6
% 243.78/50.33    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.78/50.33         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.78/50.33    (5)   ~ (e3 = e1)
% 243.78/50.33    (6)   ~ (e3 = e2)
% 243.78/50.33    (7)  all_56_19 = e2
% 243.78/50.33    (8)  all_58_1 = e2
% 243.78/50.33    (9)  all_56_7 = e2
% 243.78/50.33    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.33    (11)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.78/50.33          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.78/50.33    (12)  op(e0, all_56_7) = e0
% 243.78/50.33    (13)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.78/50.33          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.78/50.33    (14)   ~ (e1 = e0)
% 243.78/50.33    (15)  op(e2, all_56_19) = e2
% 243.78/50.33    (16)   ~ (e2 = e1)
% 243.78/50.33  
% 243.78/50.33  Begin of proof
% 243.78/50.33  | 
% 243.78/50.33  | REDUCE: (7), (15) imply:
% 243.78/50.33  |   (17)  op(e2, e2) = e2
% 243.78/50.33  | 
% 243.78/50.33  | REDUCE: (9), (12) imply:
% 243.78/50.33  |   (18)  op(e0, e2) = e0
% 243.78/50.33  | 
% 243.78/50.33  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (13), (14), (16),
% 243.78/50.33  |            (17), (18) are inconsistent by sub-proof #1811.
% 243.78/50.33  | 
% 243.78/50.33  End of proof
% 243.78/50.33  
% 243.78/50.33  Sub-proof #1291 shows that the following formulas are inconsistent:
% 243.78/50.33  ----------------------------------------------------------------
% 243.78/50.33    (1)   ~ (all_52_3 = e0)
% 243.78/50.33    (2)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.78/50.33    (3)  all_54_13 = all_52_7
% 243.78/50.33    (4)   ~ (all_52_1 = all_52_2)
% 243.78/50.33    (5)   ~ (all_52_7 = e3)
% 243.78/50.33    (6)  op(e2, e3) = e3
% 243.78/50.33    (7)   ~ (all_52_2 = all_52_3)
% 243.78/50.33    (8)   ~ (all_52_3 = all_52_7)
% 243.78/50.33    (9)  all_54_4 = all_52_1
% 243.78/50.33    (10)  all_54_12 = all_52_3
% 243.78/50.33    (11)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 243.78/50.33          $i(all_56_17)
% 243.78/50.33    (12)   ~ (all_52_1 = e0)
% 243.78/50.33    (13)  op(e2, e3) = all_52_1
% 243.78/50.33    (14)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.78/50.33    (15)   ~ (all_52_2 = e0)
% 243.78/50.33    (16)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 243.78/50.33    (17)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.78/50.33    (18)   ~ (all_52_2 = e2)
% 243.78/50.33    (19)  all_54_8 = all_52_2
% 243.78/50.33    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.78/50.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.78/50.33    (21)  op(e3, e1) = e3
% 243.78/50.33    (22)  op(e3, e3) = e0
% 243.78/50.33  
% 243.78/50.33  Begin of proof
% 243.78/50.33  | 
% 243.78/50.33  | ALPHA: (11) implies:
% 243.78/50.33  |   (23)  op(e3, e1) = all_56_17
% 243.78/50.33  |   (24)  op(e3, all_56_17) = e3
% 243.78/50.33  | 
% 243.78/50.33  | BETA: splitting (14) gives:
% 243.78/50.33  | 
% 243.78/50.33  | Case 1:
% 243.78/50.33  | | 
% 243.78/50.33  | |   (25)  all_54_4 = e3
% 243.78/50.33  | | 
% 243.78/50.33  | | COMBINE_EQS: (9), (25) imply:
% 243.78/50.33  | |   (26)  all_52_1 = e3
% 243.78/50.33  | | 
% 243.78/50.33  | | SIMP: (26) implies:
% 243.78/50.33  | |   (27)  all_52_1 = e3
% 243.78/50.33  | | 
% 243.78/50.33  | | REDUCE: (4), (27) imply:
% 243.78/50.33  | |   (28)   ~ (all_52_2 = e3)
% 243.78/50.33  | | 
% 243.78/50.33  | | SIMP: (28) implies:
% 243.78/50.33  | |   (29)   ~ (all_52_2 = e3)
% 243.78/50.33  | | 
% 243.78/50.33  | | REDUCE: (12), (27) imply:
% 243.78/50.33  | |   (30)   ~ (e3 = e0)
% 243.78/50.33  | | 
% 243.78/50.33  | | BETA: splitting (2) gives:
% 243.78/50.33  | | 
% 243.78/50.33  | | Case 1:
% 243.78/50.33  | | | 
% 243.78/50.33  | | |   (31)  all_54_8 = e3
% 243.78/50.33  | | | 
% 243.78/50.33  | | | REF_CLOSE: (19), (29), (31) are inconsistent by sub-proof #2011.
% 243.78/50.33  | | | 
% 243.78/50.33  | | Case 2:
% 243.78/50.33  | | | 
% 243.78/50.33  | | |   (32)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.78/50.33  | | | 
% 243.78/50.33  | | | BETA: splitting (32) gives:
% 243.78/50.33  | | | 
% 243.78/50.33  | | | Case 1:
% 243.78/50.33  | | | | 
% 243.78/50.33  | | | |   (33)  all_54_8 = e2
% 243.78/50.33  | | | | 
% 243.78/50.33  | | | | REF_CLOSE: (18), (19), (33) are inconsistent by sub-proof #2007.
% 243.78/50.33  | | | | 
% 243.91/50.33  | | | Case 2:
% 243.91/50.33  | | | | 
% 243.91/50.33  | | | |   (34)  all_54_8 = e1 | all_54_8 = e0
% 243.91/50.33  | | | | 
% 243.91/50.33  | | | | BETA: splitting (34) gives:
% 243.91/50.33  | | | | 
% 243.91/50.33  | | | | Case 1:
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | |   (35)  all_54_8 = e1
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | | COMBINE_EQS: (19), (35) imply:
% 243.91/50.33  | | | | |   (36)  all_52_2 = e1
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | | REDUCE: (7), (36) imply:
% 243.91/50.33  | | | | |   (37)   ~ (all_52_3 = e1)
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | | SIMP: (37) implies:
% 243.91/50.33  | | | | |   (38)   ~ (all_52_3 = e1)
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | | BETA: splitting (16) gives:
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | | Case 1:
% 243.91/50.33  | | | | | | 
% 243.91/50.33  | | | | | |   (39)  all_54_12 = e2
% 243.91/50.33  | | | | | | 
% 243.91/50.33  | | | | | | COMBINE_EQS: (10), (39) imply:
% 243.91/50.33  | | | | | |   (40)  all_52_3 = e2
% 243.91/50.33  | | | | | | 
% 243.91/50.33  | | | | | | SIMP: (40) implies:
% 243.91/50.33  | | | | | |   (41)  all_52_3 = e2
% 243.91/50.33  | | | | | | 
% 243.91/50.33  | | | | | | REDUCE: (8), (41) imply:
% 243.91/50.33  | | | | | |   (42)   ~ (all_52_7 = e2)
% 243.91/50.33  | | | | | | 
% 243.91/50.33  | | | | | | SIMP: (42) implies:
% 243.91/50.33  | | | | | |   (43)   ~ (all_52_7 = e2)
% 243.91/50.33  | | | | | | 
% 243.91/50.33  | | | | | | REF_CLOSE: (3), (5), (17), (20), (21), (22), (23), (24), (30), (43)
% 243.91/50.33  | | | | | |            are inconsistent by sub-proof #1820.
% 243.91/50.33  | | | | | | 
% 243.91/50.33  | | | | | Case 2:
% 243.91/50.33  | | | | | | 
% 243.91/50.33  | | | | | |   (44)  all_54_12 = e1 | all_54_12 = e0
% 243.91/50.33  | | | | | | 
% 243.91/50.33  | | | | | | REF_CLOSE: (1), (10), (38), (44) are inconsistent by sub-proof
% 243.91/50.33  | | | | | |            #2067.
% 243.91/50.33  | | | | | | 
% 243.91/50.33  | | | | | End of split
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | Case 2:
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | |   (45)  all_54_8 = e0
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | | COMBINE_EQS: (19), (45) imply:
% 243.91/50.33  | | | | |   (46)  all_52_2 = e0
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | | REDUCE: (15), (46) imply:
% 243.91/50.33  | | | | |   (47)  $false
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | | CLOSE: (47) is inconsistent.
% 243.91/50.33  | | | | | 
% 243.91/50.33  | | | | End of split
% 243.91/50.33  | | | | 
% 243.91/50.33  | | | End of split
% 243.91/50.33  | | | 
% 243.91/50.33  | | End of split
% 243.91/50.33  | | 
% 243.91/50.33  | Case 2:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (48)   ~ (all_54_4 = e3)
% 243.91/50.33  | | 
% 243.91/50.33  | | REDUCE: (9), (48) imply:
% 243.91/50.33  | |   (49)   ~ (all_52_1 = e3)
% 243.91/50.33  | | 
% 243.91/50.33  | | REF_CLOSE: (6), (13), (20), (49) are inconsistent by sub-proof #2337.
% 243.91/50.33  | | 
% 243.91/50.33  | End of split
% 243.91/50.33  | 
% 243.91/50.33  End of proof
% 243.91/50.33  
% 243.91/50.33  Sub-proof #1292 shows that the following formulas are inconsistent:
% 243.91/50.33  ----------------------------------------------------------------
% 243.91/50.33    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.91/50.33         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.91/50.33    (2)   ~ (e3 = e0)
% 243.91/50.33    (3)   ~ (e2 = e0)
% 243.91/50.33    (4)  op(e3, e3) = e1
% 243.91/50.33    (5)   ~ (e3 = e2)
% 243.91/50.33    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 243.91/50.33         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.91/50.33    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.33    (8)   ~ (e1 = e0)
% 243.91/50.33    (9)  all_58_4 = e3
% 243.91/50.33    (10)  all_58_9 = e1
% 243.91/50.33    (11)   ~ (e2 = e1)
% 243.91/50.33  
% 243.91/50.33  Begin of proof
% 243.91/50.33  | 
% 243.91/50.33  | BETA: splitting (6) gives:
% 243.91/50.33  | 
% 243.91/50.33  | Case 1:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 243.91/50.33  | |           e0)
% 243.91/50.33  | | 
% 243.91/50.33  | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12) are
% 243.91/50.33  | |            inconsistent by sub-proof #1293.
% 243.91/50.33  | | 
% 243.91/50.33  | Case 2:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 243.91/50.33  | |           e0)
% 243.91/50.33  | | 
% 243.91/50.33  | | BETA: splitting (13) gives:
% 243.91/50.33  | | 
% 243.91/50.33  | | Case 1:
% 243.91/50.33  | | | 
% 243.91/50.33  | | |   (14)  all_58_4 = e0 & op(e3, e1) = e0
% 243.91/50.33  | | | 
% 243.91/50.33  | | | REF_CLOSE: (2), (9), (14) are inconsistent by sub-proof #1697.
% 243.91/50.33  | | | 
% 243.91/50.33  | | Case 2:
% 243.91/50.33  | | | 
% 243.91/50.33  | | |   (15)  all_58_9 = e0 & op(e3, e0) = e0
% 243.91/50.33  | | | 
% 243.91/50.33  | | | ALPHA: (15) implies:
% 243.91/50.33  | | |   (16)  all_58_9 = e0
% 243.91/50.33  | | | 
% 243.91/50.33  | | | REF_CLOSE: (8), (10), (16) are inconsistent by sub-proof #1744.
% 243.91/50.33  | | | 
% 243.91/50.33  | | End of split
% 243.91/50.33  | | 
% 243.91/50.33  | End of split
% 243.91/50.33  | 
% 243.91/50.33  End of proof
% 243.91/50.33  
% 243.91/50.33  Sub-proof #1293 shows that the following formulas are inconsistent:
% 243.91/50.33  ----------------------------------------------------------------
% 243.91/50.33    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.91/50.33         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.91/50.33    (2)   ~ (e2 = e0)
% 243.91/50.33    (3)  op(e3, e3) = e1
% 243.91/50.33    (4)   ~ (e3 = e2)
% 243.91/50.33    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.33    (6)   ~ (e1 = e0)
% 243.91/50.33    (7)  all_58_4 = e3
% 243.91/50.33    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 243.91/50.33    (9)  all_58_9 = e1
% 243.91/50.33    (10)   ~ (e2 = e1)
% 243.91/50.33  
% 243.91/50.33  Begin of proof
% 243.91/50.33  | 
% 243.91/50.33  | BETA: splitting (8) gives:
% 243.91/50.33  | 
% 243.91/50.33  | Case 1:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (11)  all_58_0 = e0 & op(e3, e3) = e0
% 243.91/50.33  | | 
% 243.91/50.33  | | ALPHA: (11) implies:
% 243.91/50.33  | |   (12)  op(e3, e3) = e0
% 243.91/50.33  | | 
% 243.91/50.33  | | REF_CLOSE: (3), (5), (6), (12) are inconsistent by sub-proof #1828.
% 243.91/50.33  | | 
% 243.91/50.33  | Case 2:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (13)  all_58_1 = e0 & op(e3, e2) = e0
% 243.91/50.33  | | 
% 243.91/50.33  | | ALPHA: (13) implies:
% 243.91/50.33  | |   (14)  all_58_1 = e0
% 243.91/50.33  | | 
% 243.91/50.33  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (14) are inconsistent by
% 243.91/50.33  | |            sub-proof #1338.
% 243.91/50.33  | | 
% 243.91/50.33  | End of split
% 243.91/50.33  | 
% 243.91/50.33  End of proof
% 243.91/50.33  
% 243.91/50.33  Sub-proof #1294 shows that the following formulas are inconsistent:
% 243.91/50.33  ----------------------------------------------------------------
% 243.91/50.33    (1)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 243.91/50.33             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.91/50.33           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 243.91/50.33             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.91/50.33           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.91/50.33    (2)  all_56_1 = e0
% 243.91/50.33    (3)  all_56_11 = e1
% 243.91/50.33  
% 243.91/50.33  Begin of proof
% 243.91/50.33  | 
% 243.91/50.33  | BETA: splitting (1) gives:
% 243.91/50.33  | 
% 243.91/50.33  | Case 1:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (4)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.91/50.33  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 243.91/50.33  | |        & op(e0, e1) = e1
% 243.91/50.33  | | 
% 243.91/50.33  | | ALPHA: (4) implies:
% 243.91/50.33  | |   (5)   ~ (all_56_1 = e0)
% 243.91/50.33  | | 
% 243.91/50.33  | | REDUCE: (2), (5) imply:
% 243.91/50.33  | |   (6)  $false
% 243.91/50.33  | | 
% 243.91/50.33  | | CLOSE: (6) is inconsistent.
% 243.91/50.33  | | 
% 243.91/50.33  | Case 2:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (7)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 243.91/50.33  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 243.91/50.33  | |        & op(e0, e1) = e0
% 243.91/50.33  | | 
% 243.91/50.33  | | ALPHA: (7) implies:
% 243.91/50.33  | |   (8)   ~ (all_56_11 = e1)
% 243.91/50.33  | | 
% 243.91/50.33  | | REDUCE: (3), (8) imply:
% 243.91/50.33  | |   (9)  $false
% 243.91/50.33  | | 
% 243.91/50.33  | | CLOSE: (9) is inconsistent.
% 243.91/50.33  | | 
% 243.91/50.33  | End of split
% 243.91/50.33  | 
% 243.91/50.33  End of proof
% 243.91/50.33  
% 243.91/50.33  Sub-proof #1295 shows that the following formulas are inconsistent:
% 243.91/50.33  ----------------------------------------------------------------
% 243.91/50.33    (1)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.91/50.33             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.91/50.33           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 243.91/50.33             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.91/50.33           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.91/50.33    (2)  op(e2, e1) = all_52_9
% 243.91/50.33    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.33    (4)  all_56_1 = e0
% 243.91/50.33    (5)   ~ (all_52_9 = e1)
% 243.91/50.33  
% 243.91/50.33  Begin of proof
% 243.91/50.33  | 
% 243.91/50.33  | BETA: splitting (1) gives:
% 243.91/50.33  | 
% 243.91/50.33  | Case 1:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (6)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.91/50.33  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 243.91/50.33  | |        & op(e1, e2) = e1
% 243.91/50.33  | | 
% 243.91/50.33  | | ALPHA: (6) implies:
% 243.91/50.33  | |   (7)  op(e2, e1) = e1
% 243.91/50.33  | | 
% 243.91/50.33  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #2306.
% 243.91/50.33  | | 
% 243.91/50.33  | Case 2:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (8)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.91/50.33  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 243.91/50.33  | |        & op(e0, e2) = e2
% 243.91/50.33  | | 
% 243.91/50.33  | | ALPHA: (8) implies:
% 243.91/50.33  | |   (9)   ~ (all_56_1 = e0)
% 243.91/50.33  | | 
% 243.91/50.33  | | REDUCE: (4), (9) imply:
% 243.91/50.33  | |   (10)  $false
% 243.91/50.33  | | 
% 243.91/50.33  | | CLOSE: (10) is inconsistent.
% 243.91/50.33  | | 
% 243.91/50.33  | End of split
% 243.91/50.33  | 
% 243.91/50.33  End of proof
% 243.91/50.33  
% 243.91/50.33  Sub-proof #1296 shows that the following formulas are inconsistent:
% 243.91/50.33  ----------------------------------------------------------------
% 243.91/50.33    (1)  op(e0, e1) = all_52_11
% 243.91/50.33    (2)   ~ (all_52_11 = e1)
% 243.91/50.33    (3)  all_58_15 = e3
% 243.91/50.33    (4)   ~ (e3 = e1)
% 243.91/50.33    (5)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.91/50.33    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.33  
% 243.91/50.33  Begin of proof
% 243.91/50.33  | 
% 243.91/50.33  | BETA: splitting (5) gives:
% 243.91/50.33  | 
% 243.91/50.33  | Case 1:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (7)  all_58_14 = e1 & op(e0, e1) = e1
% 243.91/50.33  | | 
% 243.91/50.33  | | ALPHA: (7) implies:
% 243.91/50.33  | |   (8)  op(e0, e1) = e1
% 243.91/50.33  | | 
% 243.91/50.33  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #2272.
% 243.91/50.33  | | 
% 243.91/50.33  | Case 2:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (9)  all_58_15 = e1 & op(e0, e0) = e1
% 243.91/50.33  | | 
% 243.91/50.33  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #1393.
% 243.91/50.33  | | 
% 243.91/50.33  | End of split
% 243.91/50.33  | 
% 243.91/50.33  End of proof
% 243.91/50.33  
% 243.91/50.33  Sub-proof #1297 shows that the following formulas are inconsistent:
% 243.91/50.33  ----------------------------------------------------------------
% 243.91/50.33    (1)  op(e1, e0) = all_52_14
% 243.91/50.33    (2)  all_58_15 = e3
% 243.91/50.33    (3)   ~ (e3 = e1)
% 243.91/50.33    (4)   ~ (all_52_14 = e1)
% 243.91/50.33    (5)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.91/50.33    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.33  
% 243.91/50.33  Begin of proof
% 243.91/50.33  | 
% 243.91/50.33  | BETA: splitting (5) gives:
% 243.91/50.33  | 
% 243.91/50.33  | Case 1:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (7)  all_58_11 = e1 & op(e1, e0) = e1
% 243.91/50.33  | | 
% 243.91/50.33  | | ALPHA: (7) implies:
% 243.91/50.33  | |   (8)  op(e1, e0) = e1
% 243.91/50.33  | | 
% 243.91/50.33  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #2304.
% 243.91/50.33  | | 
% 243.91/50.33  | Case 2:
% 243.91/50.33  | | 
% 243.91/50.33  | |   (9)  all_58_15 = e1 & op(e0, e0) = e1
% 243.91/50.33  | | 
% 243.91/50.33  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #1393.
% 243.91/50.33  | | 
% 243.91/50.33  | End of split
% 243.91/50.33  | 
% 243.91/50.33  End of proof
% 243.91/50.33  
% 243.91/50.33  Sub-proof #1298 shows that the following formulas are inconsistent:
% 243.91/50.33  ----------------------------------------------------------------
% 243.91/50.33    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 243.91/50.33           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 243.91/50.33           all_12_1 & $i(all_12_1))
% 243.91/50.33    (2)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.91/50.33    (3)   ~ (e2 = e0)
% 243.91/50.33    (4)  op(e1, e2) = all_52_6
% 243.91/50.33    (5)  op(e1, e1) = all_6_2
% 243.91/50.33    (6)  op(e3, e0) = e1
% 243.91/50.33    (7)  op(e1, e0) = all_52_14
% 243.91/50.33    (8)  op(e0, e3) = all_52_3
% 243.91/50.33    (9)  all_54_11 = all_52_14
% 243.91/50.33    (10)   ~ (all_52_2 = all_52_3)
% 243.91/50.33    (11)   ~ (all_52_12 = all_52_14)
% 243.91/50.33    (12)   ~ (all_52_12 = all_52_13)
% 243.91/50.33    (13)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.91/50.33            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 243.91/50.33              e3) = all_26_1 & $i(all_26_1))
% 243.91/50.33    (14)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.91/50.33    (15)  all_58_12 = e1
% 243.91/50.33    (16)   ~ (all_6_2 = e3)
% 243.91/50.33    (17)  all_50_2 = e0
% 243.91/50.33    (18)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.91/50.33          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.91/50.33    (19)   ~ (e3 = e2)
% 243.91/50.34    (20)  op(e0, e3) = e1
% 243.91/50.34    (21)   ~ (all_50_2 = e0) | ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 &
% 243.91/50.34            op(e3, e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 243.91/50.34              e2) & op(e3, e0) = all_50_1 & $i(all_50_1))
% 243.91/50.34    (22)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.91/50.34    (23)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 243.91/50.34            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 243.91/50.34              e0) = all_16_1 & $i(all_16_1))
% 243.91/50.34    (24)  op(e3, e0) = all_52_12
% 243.91/50.34    (25)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.91/50.34          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.91/50.34    (26)  op(e2, e3) = all_52_1
% 243.91/50.34    (27)   ~ (all_52_14 = e3)
% 243.91/50.34    (28)   ~ (all_52_1 = all_52_13)
% 243.91/50.34    (29)   ~ (all_52_2 = e0)
% 243.91/50.34    (30)  all_54_7 = all_52_13
% 243.91/50.34    (31)   ~ (all_52_13 = all_52_14)
% 243.91/50.34    (32)  all_54_8 = all_52_2
% 243.91/50.34    (33)   ~ (all_52_2 = all_52_6)
% 243.91/50.34    (34)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.34    (35)  op(e1, e3) = all_52_2
% 243.91/50.34    (36)  op(e3, e3) = e0
% 243.91/50.34    (37)   ~ (all_52_13 = e3)
% 243.91/50.34    (38)   ~ (e2 = e1)
% 243.91/50.34  
% 243.91/50.34  Begin of proof
% 243.91/50.34  | 
% 243.91/50.34  | GROUND_INST: instantiating (34) with all_52_3, e1, e3, e0, simplifying with
% 243.91/50.34  |              (8), (20) gives:
% 243.91/50.34  |   (39)  all_52_3 = e1
% 243.91/50.34  | 
% 243.91/50.34  | GROUND_INST: instantiating (34) with all_52_12, e1, e0, e3, simplifying with
% 243.91/50.34  |              (6), (24) gives:
% 243.91/50.34  |   (40)  all_52_12 = e1
% 243.91/50.34  | 
% 243.91/50.34  | REDUCE: (10), (39) imply:
% 243.91/50.34  |   (41)   ~ (all_52_2 = e1)
% 243.91/50.34  | 
% 243.91/50.34  | REDUCE: (12), (40) imply:
% 243.91/50.34  |   (42)   ~ (all_52_13 = e1)
% 243.91/50.34  | 
% 243.91/50.34  | SIMP: (42) implies:
% 243.91/50.34  |   (43)   ~ (all_52_13 = e1)
% 243.91/50.34  | 
% 243.91/50.34  | REDUCE: (11), (40) imply:
% 243.91/50.34  |   (44)   ~ (all_52_14 = e1)
% 243.91/50.34  | 
% 243.91/50.34  | SIMP: (44) implies:
% 243.91/50.34  |   (45)   ~ (all_52_14 = e1)
% 243.91/50.34  | 
% 243.91/50.34  | BETA: splitting (21) gives:
% 243.91/50.34  | 
% 243.91/50.34  | Case 1:
% 243.91/50.34  | | 
% 243.91/50.34  | |   (46)   ~ (all_50_2 = e0)
% 243.91/50.34  | | 
% 243.91/50.34  | | REDUCE: (17), (46) imply:
% 243.91/50.34  | |   (47)  $false
% 243.91/50.34  | | 
% 243.91/50.34  | | CLOSE: (47) is inconsistent.
% 243.91/50.34  | | 
% 243.91/50.34  | Case 2:
% 243.91/50.34  | | 
% 243.91/50.34  | |   (48)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 243.91/50.34  | |           all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) &
% 243.91/50.34  | |           op(e3, e0) = all_50_1 & $i(all_50_1))
% 243.91/50.34  | | 
% 243.91/50.34  | | BETA: splitting (1) gives:
% 243.91/50.34  | | 
% 243.91/50.34  | | Case 1:
% 243.91/50.34  | | | 
% 243.91/50.34  | | |   (49)   ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 243.91/50.34  | | |         all_12_1 & $i(all_12_0) & $i(all_12_1)
% 243.91/50.34  | | | 
% 243.91/50.34  | | | ALPHA: (49) implies:
% 243.91/50.34  | | |   (50)  op(e0, e3) = all_12_1
% 243.91/50.34  | | |   (51)  op(all_12_1, e0) = all_12_0
% 243.91/50.34  | | | 
% 243.91/50.34  | | | BETA: splitting (13) gives:
% 243.91/50.34  | | | 
% 243.91/50.34  | | | Case 1:
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | |   (52)   ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.91/50.34  | | | |         all_26_1 & $i(all_26_0) & $i(all_26_1)
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | | ALPHA: (52) implies:
% 243.91/50.34  | | | |   (53)   ~ (all_26_0 = e2)
% 243.91/50.34  | | | |   (54)  op(e0, e3) = all_26_1
% 243.91/50.34  | | | |   (55)  op(all_26_1, e0) = all_26_0
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | | BETA: splitting (48) gives:
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | | Case 1:
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | |   (56)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0)
% 243.91/50.34  | | | | |         = all_50_1 & $i(all_50_0) & $i(all_50_1)
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | | ALPHA: (56) implies:
% 243.91/50.34  | | | | |   (57)  op(e3, e0) = all_50_1
% 243.91/50.34  | | | | |   (58)  op(all_50_1, e3) = all_50_0
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | | BETA: splitting (23) gives:
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | | Case 1:
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | |   (59)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3,
% 243.91/50.34  | | | | | |           e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | ALPHA: (59) implies:
% 243.91/50.34  | | | | | |   (60)   ~ (all_16_0 = e2)
% 243.91/50.34  | | | | | |   (61)  op(e3, e0) = all_16_1
% 243.91/50.34  | | | | | |   (62)  op(all_16_1, e3) = all_16_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with e1, all_26_1, e3, e0,
% 243.91/50.34  | | | | | |              simplifying with (20), (54) gives:
% 243.91/50.34  | | | | | |   (63)  all_26_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_12_1, all_26_1, e3, e0,
% 243.91/50.34  | | | | | |              simplifying with (50), (54) gives:
% 243.91/50.34  | | | | | |   (64)  all_26_1 = all_12_1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with e1, all_50_1, e0, e3,
% 243.91/50.34  | | | | | |              simplifying with (6), (57) gives:
% 243.91/50.34  | | | | | |   (65)  all_50_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_16_1, all_50_1, e0, e3,
% 243.91/50.34  | | | | | |              simplifying with (57), (61) gives:
% 243.91/50.34  | | | | | |   (66)  all_50_1 = all_16_1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | COMBINE_EQS: (65), (66) imply:
% 243.91/50.34  | | | | | |   (67)  all_16_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | COMBINE_EQS: (63), (64) imply:
% 243.91/50.34  | | | | | |   (68)  all_12_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | SIMP: (68) implies:
% 243.91/50.34  | | | | | |   (69)  all_12_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REDUCE: (58), (65) imply:
% 243.91/50.34  | | | | | |   (70)  op(e1, e3) = all_50_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REDUCE: (55), (63) imply:
% 243.91/50.34  | | | | | |   (71)  op(e1, e0) = all_26_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REDUCE: (62), (67) imply:
% 243.91/50.34  | | | | | |   (72)  op(e1, e3) = all_16_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REDUCE: (51), (69) imply:
% 243.91/50.34  | | | | | |   (73)  op(e1, e0) = all_12_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_52_14, all_12_0, e0, e1,
% 243.91/50.34  | | | | | |              simplifying with (7), (73) gives:
% 243.91/50.34  | | | | | |   (74)  all_52_14 = all_12_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_52_14, all_26_0, e0, e1,
% 243.91/50.34  | | | | | |              simplifying with (7), (71) gives:
% 243.91/50.34  | | | | | |   (75)  all_52_14 = all_26_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_52_2, all_16_0, e3, e1,
% 243.91/50.34  | | | | | |              simplifying with (35), (72) gives:
% 243.91/50.34  | | | | | |   (76)  all_52_2 = all_16_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_52_2, all_50_0, e3, e1,
% 243.91/50.34  | | | | | |              simplifying with (35), (70) gives:
% 243.91/50.34  | | | | | |   (77)  all_52_2 = all_50_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | COMBINE_EQS: (76), (77) imply:
% 243.91/50.34  | | | | | |   (78)  all_50_0 = all_16_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | COMBINE_EQS: (74), (75) imply:
% 243.91/50.34  | | | | | |   (79)  all_26_0 = all_12_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | SIMP: (79) implies:
% 243.91/50.34  | | | | | |   (80)  all_26_0 = all_12_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (14), (15), (16), (18),
% 243.91/50.34  | | | | | |            (19), (22), (25), (26), (27), (28), (29), (30), (31),
% 243.91/50.34  | | | | | |            (32), (33), (34), (36), (37), (38), (41), (43), (45),
% 243.91/50.34  | | | | | |            (53), (60), (74), (76), (80) are inconsistent by
% 243.91/50.34  | | | | | |            sub-proof #1301.
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | Case 2:
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | |   (81)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 & $i(all_16_1)
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | ALPHA: (81) implies:
% 243.91/50.34  | | | | | |   (82)   ~ (all_16_1 = e1)
% 243.91/50.34  | | | | | |   (83)  op(e3, e0) = all_16_1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REF_CLOSE: (6), (34), (57), (82), (83) are inconsistent by sub-proof
% 243.91/50.34  | | | | | |            #1570.
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | End of split
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | Case 2:
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | |   (84)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 & $i(all_50_1)
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | | ALPHA: (84) implies:
% 243.91/50.34  | | | | |   (85)   ~ (all_50_1 = e2)
% 243.91/50.34  | | | | |   (86)  op(e3, e0) = all_50_1
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | | BETA: splitting (23) gives:
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | | Case 1:
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | |   (87)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3,
% 243.91/50.34  | | | | | |           e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | ALPHA: (87) implies:
% 243.91/50.34  | | | | | |   (88)   ~ (all_16_0 = e2)
% 243.91/50.34  | | | | | |   (89)  op(e3, e0) = all_16_1
% 243.91/50.34  | | | | | |   (90)  op(all_16_1, e3) = all_16_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with e1, all_26_1, e3, e0,
% 243.91/50.34  | | | | | |              simplifying with (20), (54) gives:
% 243.91/50.34  | | | | | |   (91)  all_26_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_12_1, all_26_1, e3, e0,
% 243.91/50.34  | | | | | |              simplifying with (50), (54) gives:
% 243.91/50.34  | | | | | |   (92)  all_26_1 = all_12_1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with e1, all_50_1, e0, e3,
% 243.91/50.34  | | | | | |              simplifying with (6), (86) gives:
% 243.91/50.34  | | | | | |   (93)  all_50_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_16_1, all_50_1, e0, e3,
% 243.91/50.34  | | | | | |              simplifying with (86), (89) gives:
% 243.91/50.34  | | | | | |   (94)  all_50_1 = all_16_1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | COMBINE_EQS: (93), (94) imply:
% 243.91/50.34  | | | | | |   (95)  all_16_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | COMBINE_EQS: (91), (92) imply:
% 243.91/50.34  | | | | | |   (96)  all_12_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | SIMP: (96) implies:
% 243.91/50.34  | | | | | |   (97)  all_12_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REDUCE: (85), (93) imply:
% 243.91/50.34  | | | | | |   (98)   ~ (e2 = e1)
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REDUCE: (55), (91) imply:
% 243.91/50.34  | | | | | |   (99)  op(e1, e0) = all_26_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REDUCE: (90), (95) imply:
% 243.91/50.34  | | | | | |   (100)  op(e1, e3) = all_16_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REDUCE: (51), (97) imply:
% 243.91/50.34  | | | | | |   (101)  op(e1, e0) = all_12_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_52_14, all_12_0, e0, e1,
% 243.91/50.34  | | | | | |              simplifying with (7), (101) gives:
% 243.91/50.34  | | | | | |   (102)  all_52_14 = all_12_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_52_14, all_26_0, e0, e1,
% 243.91/50.34  | | | | | |              simplifying with (7), (99) gives:
% 243.91/50.34  | | | | | |   (103)  all_52_14 = all_26_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_52_2, all_16_0, e3, e1,
% 243.91/50.34  | | | | | |              simplifying with (35), (100) gives:
% 243.91/50.34  | | | | | |   (104)  all_52_2 = all_16_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | COMBINE_EQS: (102), (103) imply:
% 243.91/50.34  | | | | | |   (105)  all_26_0 = all_12_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | SIMP: (105) implies:
% 243.91/50.34  | | | | | |   (106)  all_26_0 = all_12_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (14), (15), (16), (18),
% 243.91/50.34  | | | | | |            (19), (22), (25), (26), (27), (28), (29), (30), (31),
% 243.91/50.34  | | | | | |            (32), (33), (34), (36), (37), (38), (41), (43), (45),
% 243.91/50.34  | | | | | |            (53), (88), (102), (104), (106) are inconsistent by
% 243.91/50.34  | | | | | |            sub-proof #1301.
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | Case 2:
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | |   (107)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 & $i(all_16_1)
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | ALPHA: (107) implies:
% 243.91/50.34  | | | | | |   (108)   ~ (all_16_1 = e1)
% 243.91/50.34  | | | | | |   (109)  op(e3, e0) = all_16_1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REF_CLOSE: (6), (34), (86), (108), (109) are inconsistent by
% 243.91/50.34  | | | | | |            sub-proof #1570.
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | End of split
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | End of split
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | Case 2:
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | |   (110)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | | REF_CLOSE: (20), (34), (110) are inconsistent by sub-proof #1386.
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | End of split
% 243.91/50.34  | | | 
% 243.91/50.34  | | Case 2:
% 243.91/50.34  | | | 
% 243.91/50.34  | | |   (111)   ~ (all_12_1 = e2) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 243.91/50.34  | | | 
% 243.91/50.34  | | | ALPHA: (111) implies:
% 243.91/50.34  | | |   (112)   ~ (all_12_1 = e2)
% 243.91/50.34  | | |   (113)  op(e0, e3) = all_12_1
% 243.91/50.34  | | | 
% 243.91/50.34  | | | BETA: splitting (13) gives:
% 243.91/50.34  | | | 
% 243.91/50.34  | | | Case 1:
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | |   (114)   ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.91/50.34  | | | |          all_26_1 & $i(all_26_0) & $i(all_26_1)
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | | ALPHA: (114) implies:
% 243.91/50.34  | | | |   (115)   ~ (all_26_0 = e2)
% 243.91/50.34  | | | |   (116)  op(e0, e3) = all_26_1
% 243.91/50.34  | | | |   (117)  op(all_26_1, e0) = all_26_0
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | | BETA: splitting (48) gives:
% 243.91/50.34  | | | | 
% 243.91/50.34  | | | | Case 1:
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | |   (118)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0)
% 243.91/50.34  | | | | |          = all_50_1 & $i(all_50_0) & $i(all_50_1)
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | | ALPHA: (118) implies:
% 243.91/50.34  | | | | |   (119)  op(e3, e0) = all_50_1
% 243.91/50.34  | | | | |   (120)  op(all_50_1, e3) = all_50_0
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | | BETA: splitting (23) gives:
% 243.91/50.34  | | | | | 
% 243.91/50.34  | | | | | Case 1:
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | |   (121)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3,
% 243.91/50.34  | | | | | |            e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | ALPHA: (121) implies:
% 243.91/50.34  | | | | | |   (122)   ~ (all_16_0 = e2)
% 243.91/50.34  | | | | | |   (123)  op(e3, e0) = all_16_1
% 243.91/50.34  | | | | | |   (124)  op(all_16_1, e3) = all_16_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with e1, all_26_1, e3, e0,
% 243.91/50.34  | | | | | |              simplifying with (20), (116) gives:
% 243.91/50.34  | | | | | |   (125)  all_26_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with e1, all_50_1, e0, e3,
% 243.91/50.34  | | | | | |              simplifying with (6), (119) gives:
% 243.91/50.34  | | | | | |   (126)  all_50_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_16_1, all_50_1, e0, e3,
% 243.91/50.34  | | | | | |              simplifying with (119), (123) gives:
% 243.91/50.34  | | | | | |   (127)  all_50_1 = all_16_1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | COMBINE_EQS: (126), (127) imply:
% 243.91/50.34  | | | | | |   (128)  all_16_1 = e1
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REDUCE: (120), (126) imply:
% 243.91/50.34  | | | | | |   (129)  op(e1, e3) = all_50_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REDUCE: (117), (125) imply:
% 243.91/50.34  | | | | | |   (130)  op(e1, e0) = all_26_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | REDUCE: (124), (128) imply:
% 243.91/50.34  | | | | | |   (131)  op(e1, e3) = all_16_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_52_14, all_26_0, e0, e1,
% 243.91/50.34  | | | | | |              simplifying with (7), (130) gives:
% 243.91/50.34  | | | | | |   (132)  all_52_14 = all_26_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_52_2, all_16_0, e3, e1,
% 243.91/50.34  | | | | | |              simplifying with (35), (131) gives:
% 243.91/50.34  | | | | | |   (133)  all_52_2 = all_16_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | GROUND_INST: instantiating (34) with all_52_2, all_50_0, e3, e1,
% 243.91/50.34  | | | | | |              simplifying with (35), (129) gives:
% 243.91/50.34  | | | | | |   (134)  all_52_2 = all_50_0
% 243.91/50.34  | | | | | | 
% 243.91/50.34  | | | | | | COMBINE_EQS: (133), (134) imply:
% 243.91/50.34  | | | | | |   (135)  all_50_0 = all_16_0
% 243.91/50.34  | | | | | | 
% 243.91/50.35  | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (13), (14), (16), (18),
% 243.91/50.35  | | | | | |            (19), (22), (25), (26), (27), (28), (29), (30), (31),
% 243.91/50.35  | | | | | |            (32), (33), (34), (36), (37), (41), (43), (45), (112),
% 243.91/50.35  | | | | | |            (113), (115), (122), (132), (133) are inconsistent by
% 243.91/50.35  | | | | | |            sub-proof #1299.
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | Case 2:
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | |   (136)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 & $i(all_16_1)
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | ALPHA: (136) implies:
% 243.91/50.35  | | | | | |   (137)   ~ (all_16_1 = e1)
% 243.91/50.35  | | | | | |   (138)  op(e3, e0) = all_16_1
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | REF_CLOSE: (6), (34), (119), (137), (138) are inconsistent by
% 243.91/50.35  | | | | | |            sub-proof #1570.
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | End of split
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | Case 2:
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | |   (139)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 & $i(all_50_1)
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | ALPHA: (139) implies:
% 243.91/50.35  | | | | |   (140)  op(e3, e0) = all_50_1
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | BETA: splitting (23) gives:
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | Case 1:
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | |   (141)   ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3,
% 243.91/50.35  | | | | | |            e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | ALPHA: (141) implies:
% 243.91/50.35  | | | | | |   (142)   ~ (all_16_0 = e2)
% 243.91/50.35  | | | | | |   (143)  op(e3, e0) = all_16_1
% 243.91/50.35  | | | | | |   (144)  op(all_16_1, e3) = all_16_0
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | GROUND_INST: instantiating (34) with e1, all_26_1, e3, e0,
% 243.91/50.35  | | | | | |              simplifying with (20), (116) gives:
% 243.91/50.35  | | | | | |   (145)  all_26_1 = e1
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | GROUND_INST: instantiating (34) with e1, all_50_1, e0, e3,
% 243.91/50.35  | | | | | |              simplifying with (6), (140) gives:
% 243.91/50.35  | | | | | |   (146)  all_50_1 = e1
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | GROUND_INST: instantiating (34) with all_16_1, all_50_1, e0, e3,
% 243.91/50.35  | | | | | |              simplifying with (140), (143) gives:
% 243.91/50.35  | | | | | |   (147)  all_50_1 = all_16_1
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | COMBINE_EQS: (146), (147) imply:
% 243.91/50.35  | | | | | |   (148)  all_16_1 = e1
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | REDUCE: (117), (145) imply:
% 243.91/50.35  | | | | | |   (149)  op(e1, e0) = all_26_0
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | REDUCE: (144), (148) imply:
% 243.91/50.35  | | | | | |   (150)  op(e1, e3) = all_16_0
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | GROUND_INST: instantiating (34) with all_52_14, all_26_0, e0, e1,
% 243.91/50.35  | | | | | |              simplifying with (7), (149) gives:
% 243.91/50.35  | | | | | |   (151)  all_52_14 = all_26_0
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | GROUND_INST: instantiating (34) with all_52_2, all_16_0, e3, e1,
% 243.91/50.35  | | | | | |              simplifying with (35), (150) gives:
% 243.91/50.35  | | | | | |   (152)  all_52_2 = all_16_0
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (13), (14), (16), (18),
% 243.91/50.35  | | | | | |            (19), (22), (25), (26), (27), (28), (29), (30), (31),
% 243.91/50.35  | | | | | |            (32), (33), (34), (36), (37), (41), (43), (45), (112),
% 243.91/50.35  | | | | | |            (113), (115), (142), (151), (152) are inconsistent by
% 243.91/50.35  | | | | | |            sub-proof #1299.
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | Case 2:
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | |   (153)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 & $i(all_16_1)
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | ALPHA: (153) implies:
% 243.91/50.35  | | | | | |   (154)   ~ (all_16_1 = e1)
% 243.91/50.35  | | | | | |   (155)  op(e3, e0) = all_16_1
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | REF_CLOSE: (6), (34), (140), (154), (155) are inconsistent by
% 243.91/50.35  | | | | | |            sub-proof #1570.
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | End of split
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | End of split
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | Case 2:
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | |   (156)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | | REF_CLOSE: (20), (34), (156) are inconsistent by sub-proof #1386.
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | End of split
% 243.91/50.35  | | | 
% 243.91/50.35  | | End of split
% 243.91/50.35  | | 
% 243.91/50.35  | End of split
% 243.91/50.35  | 
% 243.91/50.35  End of proof
% 243.91/50.35  
% 243.91/50.35  Sub-proof #1299 shows that the following formulas are inconsistent:
% 243.91/50.35  ----------------------------------------------------------------
% 243.91/50.35    (1)   ~ (all_12_1 = e2)
% 243.91/50.35    (2)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.91/50.35    (3)   ~ (e2 = e0)
% 243.91/50.35    (4)  op(e1, e2) = all_52_6
% 243.91/50.35    (5)  all_52_2 = all_16_0
% 243.91/50.35    (6)  op(e1, e1) = all_6_2
% 243.91/50.35    (7)  op(e1, e0) = all_52_14
% 243.91/50.35    (8)   ~ (all_52_13 = e1)
% 243.91/50.35    (9)  all_54_11 = all_52_14
% 243.91/50.35    (10)   ~ (all_52_2 = e1)
% 243.91/50.35    (11)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.91/50.35            all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0,
% 243.91/50.35              e3) = all_26_1 & $i(all_26_1))
% 243.91/50.35    (12)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.91/50.35    (13)   ~ (all_6_2 = e3)
% 243.91/50.35    (14)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.91/50.35          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.91/50.35    (15)   ~ (e3 = e2)
% 243.91/50.35    (16)   ~ (all_52_14 = e1)
% 243.91/50.35    (17)   ~ (all_16_0 = e2)
% 243.91/50.35    (18)   ~ (all_26_0 = e2)
% 243.91/50.35    (19)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.91/50.35    (20)  all_52_14 = all_26_0
% 243.91/50.35    (21)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.91/50.35          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.91/50.35    (22)  op(e0, e3) = all_12_1
% 243.91/50.35    (23)  op(e2, e3) = all_52_1
% 243.91/50.35    (24)   ~ (all_52_14 = e3)
% 243.91/50.35    (25)   ~ (all_52_1 = all_52_13)
% 243.91/50.35    (26)   ~ (all_52_2 = e0)
% 243.91/50.35    (27)  all_54_7 = all_52_13
% 243.91/50.35    (28)   ~ (all_52_13 = all_52_14)
% 243.91/50.35    (29)  all_54_8 = all_52_2
% 243.91/50.35    (30)   ~ (all_52_2 = all_52_6)
% 243.91/50.35    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.35    (32)  op(e3, e3) = e0
% 243.91/50.35    (33)   ~ (all_52_13 = e3)
% 243.91/50.35  
% 243.91/50.35  Begin of proof
% 243.91/50.35  | 
% 243.91/50.35  | COMBINE_EQS: (9), (20) imply:
% 243.91/50.35  |   (34)  all_54_11 = all_26_0
% 243.91/50.35  | 
% 243.91/50.35  | COMBINE_EQS: (5), (29) imply:
% 243.91/50.35  |   (35)  all_54_8 = all_16_0
% 243.91/50.35  | 
% 243.91/50.35  | REDUCE: (5), (30) imply:
% 243.91/50.35  |   (36)   ~ (all_52_6 = all_16_0)
% 243.91/50.35  | 
% 243.91/50.35  | SIMP: (36) implies:
% 243.91/50.35  |   (37)   ~ (all_52_6 = all_16_0)
% 243.91/50.35  | 
% 243.91/50.35  | REDUCE: (20), (28) imply:
% 243.91/50.35  |   (38)   ~ (all_52_13 = all_26_0)
% 243.91/50.35  | 
% 243.91/50.35  | REDUCE: (20), (24) imply:
% 243.91/50.35  |   (39)   ~ (all_26_0 = e3)
% 243.91/50.35  | 
% 243.91/50.35  | REDUCE: (16), (20) imply:
% 243.91/50.35  |   (40)   ~ (all_26_0 = e1)
% 243.91/50.35  | 
% 243.91/50.35  | BETA: splitting (12) gives:
% 243.91/50.35  | 
% 243.91/50.35  | Case 1:
% 243.91/50.35  | | 
% 243.91/50.35  | |   (41)  all_54_11 = e3
% 243.91/50.35  | | 
% 243.91/50.35  | | COMBINE_EQS: (34), (41) imply:
% 243.91/50.35  | |   (42)  all_26_0 = e3
% 243.91/50.35  | | 
% 243.91/50.35  | | SIMP: (42) implies:
% 243.91/50.35  | |   (43)  all_26_0 = e3
% 243.91/50.35  | | 
% 243.91/50.35  | | REDUCE: (39), (43) imply:
% 243.91/50.35  | |   (44)  $false
% 243.91/50.35  | | 
% 243.91/50.35  | | CLOSE: (44) is inconsistent.
% 243.91/50.35  | | 
% 243.91/50.35  | Case 2:
% 243.91/50.35  | | 
% 243.91/50.35  | |   (45)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.91/50.35  | | 
% 243.91/50.35  | | BETA: splitting (45) gives:
% 243.91/50.35  | | 
% 243.91/50.35  | | Case 1:
% 243.91/50.35  | | | 
% 243.91/50.35  | | |   (46)  all_54_11 = e2
% 243.91/50.35  | | | 
% 243.91/50.35  | | | COMBINE_EQS: (34), (46) imply:
% 243.91/50.35  | | |   (47)  all_26_0 = e2
% 243.91/50.35  | | | 
% 243.91/50.35  | | | SIMP: (47) implies:
% 243.91/50.35  | | |   (48)  all_26_0 = e2
% 243.91/50.35  | | | 
% 243.91/50.35  | | | REDUCE: (18), (48) imply:
% 243.91/50.35  | | |   (49)  $false
% 243.91/50.35  | | | 
% 243.91/50.35  | | | CLOSE: (49) is inconsistent.
% 243.91/50.35  | | | 
% 243.91/50.35  | | Case 2:
% 243.91/50.35  | | | 
% 243.91/50.35  | | |   (50)  all_54_11 = e1 | all_54_11 = e0
% 243.91/50.35  | | | 
% 243.91/50.35  | | | BETA: splitting (14) gives:
% 243.91/50.35  | | | 
% 243.91/50.35  | | | Case 1:
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | |   (51)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3)
% 243.91/50.35  | | | |           = e2)
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | | BETA: splitting (51) gives:
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | | Case 1:
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | |   (52)  all_58_0 = e2 & op(e3, e3) = e2
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | ALPHA: (52) implies:
% 243.91/50.35  | | | | |   (53)  op(e3, e3) = e2
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | REF_CLOSE: (3), (31), (32), (53) are inconsistent by sub-proof #2188.
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | Case 2:
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | |   (54)  all_58_2 = e2 & op(e2, e3) = e2
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | ALPHA: (54) implies:
% 243.91/50.35  | | | | |   (55)  op(e2, e3) = e2
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | BETA: splitting (50) gives:
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | Case 1:
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | |   (56)  all_54_11 = e1
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | COMBINE_EQS: (34), (56) imply:
% 243.91/50.35  | | | | | |   (57)  all_26_0 = e1
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | SIMP: (57) implies:
% 243.91/50.35  | | | | | |   (58)  all_26_0 = e1
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | REDUCE: (40), (58) imply:
% 243.91/50.35  | | | | | |   (59)  $false
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | CLOSE: (59) is inconsistent.
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | Case 2:
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | |   (60)  all_54_11 = e0
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | COMBINE_EQS: (34), (60) imply:
% 243.91/50.35  | | | | | |   (61)  all_26_0 = e0
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | SIMP: (61) implies:
% 243.91/50.35  | | | | | |   (62)  all_26_0 = e0
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | REDUCE: (38), (62) imply:
% 243.91/50.35  | | | | | |   (63)   ~ (all_52_13 = e0)
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | | REF_CLOSE: (8), (19), (23), (25), (27), (31), (33), (55), (63) are
% 243.91/50.35  | | | | | |            inconsistent by sub-proof #2291.
% 243.91/50.35  | | | | | | 
% 243.91/50.35  | | | | | End of split
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | End of split
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | Case 2:
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | |   (64)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3)
% 243.91/50.35  | | | |           = e2)
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | | BETA: splitting (64) gives:
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | | Case 1:
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | |   (65)  all_58_6 = e2 & op(e1, e3) = e2
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | REF_CLOSE: (2), (4), (6), (7), (10), (13), (15), (17), (21), (24),
% 243.91/50.35  | | | | |            (26), (29), (31), (35), (37), (65) are inconsistent by
% 243.91/50.35  | | | | |            sub-proof #1303.
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | Case 2:
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | |   (66)  all_58_12 = e2 & op(e0, e3) = e2
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | ALPHA: (66) implies:
% 243.91/50.35  | | | | |   (67)  op(e0, e3) = e2
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | REF_CLOSE: (1), (11), (22), (31), (67) are inconsistent by sub-proof
% 243.91/50.35  | | | | |            #1300.
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | End of split
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | End of split
% 243.91/50.35  | | | 
% 243.91/50.35  | | End of split
% 243.91/50.35  | | 
% 243.91/50.35  | End of split
% 243.91/50.35  | 
% 243.91/50.35  End of proof
% 243.91/50.35  
% 243.91/50.35  Sub-proof #1300 shows that the following formulas are inconsistent:
% 243.91/50.35  ----------------------------------------------------------------
% 243.91/50.35    (1)   ~ (all_12_1 = e2)
% 243.91/50.35    (2)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 243.91/50.35           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 243.91/50.35           all_26_1 & $i(all_26_1))
% 243.91/50.35    (3)  op(e0, e3) = e2
% 243.91/50.35    (4)  op(e0, e3) = all_12_1
% 243.91/50.35    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.35  
% 243.91/50.35  Begin of proof
% 243.91/50.35  | 
% 243.91/50.35  | BETA: splitting (2) gives:
% 243.91/50.35  | 
% 243.91/50.35  | Case 1:
% 243.91/50.35  | | 
% 243.91/50.35  | |   (6)   ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.91/50.35  | |        all_26_1 & $i(all_26_0) & $i(all_26_1)
% 243.91/50.35  | | 
% 243.91/50.35  | | ALPHA: (6) implies:
% 243.91/50.35  | |   (7)  op(e0, e3) = all_26_1
% 243.91/50.35  | | 
% 243.91/50.35  | | REF_CLOSE: (1), (3), (4), (5), (7) are inconsistent by sub-proof #1308.
% 243.91/50.35  | | 
% 243.91/50.35  | Case 2:
% 243.91/50.35  | | 
% 243.91/50.35  | |   (8)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 243.91/50.35  | | 
% 243.91/50.35  | | ALPHA: (8) implies:
% 243.91/50.35  | |   (9)  op(e0, e3) = all_26_1
% 243.91/50.35  | | 
% 243.91/50.35  | | REF_CLOSE: (1), (3), (4), (5), (9) are inconsistent by sub-proof #1308.
% 243.91/50.35  | | 
% 243.91/50.35  | End of split
% 243.91/50.35  | 
% 243.91/50.35  End of proof
% 243.91/50.35  
% 243.91/50.35  Sub-proof #1301 shows that the following formulas are inconsistent:
% 243.91/50.35  ----------------------------------------------------------------
% 243.91/50.35    (1)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.91/50.35    (2)   ~ (e2 = e0)
% 243.91/50.35    (3)  op(e1, e2) = all_52_6
% 243.91/50.35    (4)  all_52_2 = all_16_0
% 243.91/50.35    (5)  op(e1, e1) = all_6_2
% 243.91/50.35    (6)  op(e1, e0) = all_52_14
% 243.91/50.35    (7)   ~ (all_52_13 = e1)
% 243.91/50.35    (8)  all_54_11 = all_52_14
% 243.91/50.35    (9)   ~ (all_52_2 = e1)
% 243.91/50.35    (10)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.91/50.35    (11)  all_58_12 = e1
% 243.91/50.35    (12)   ~ (all_6_2 = e3)
% 243.91/50.35    (13)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.91/50.35          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.91/50.35    (14)   ~ (e3 = e2)
% 243.91/50.35    (15)   ~ (all_52_14 = e1)
% 243.91/50.35    (16)   ~ (all_16_0 = e2)
% 243.91/50.35    (17)   ~ (all_26_0 = e2)
% 243.91/50.35    (18)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.91/50.35    (19)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.91/50.35          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.91/50.35    (20)  op(e2, e3) = all_52_1
% 243.91/50.35    (21)   ~ (all_52_14 = e3)
% 243.91/50.35    (22)   ~ (all_52_1 = all_52_13)
% 243.91/50.35    (23)   ~ (all_52_2 = e0)
% 243.91/50.35    (24)  all_54_7 = all_52_13
% 243.91/50.35    (25)   ~ (all_52_13 = all_52_14)
% 243.91/50.35    (26)  all_26_0 = all_12_0
% 243.91/50.35    (27)  all_54_8 = all_52_2
% 243.91/50.35    (28)   ~ (all_52_2 = all_52_6)
% 243.91/50.35    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.35    (30)  op(e3, e3) = e0
% 243.91/50.35    (31)  all_52_14 = all_12_0
% 243.91/50.35    (32)   ~ (all_52_13 = e3)
% 243.91/50.35    (33)   ~ (e2 = e1)
% 243.91/50.35  
% 243.91/50.35  Begin of proof
% 243.91/50.35  | 
% 243.91/50.35  | COMBINE_EQS: (8), (31) imply:
% 243.91/50.35  |   (34)  all_54_11 = all_12_0
% 243.91/50.35  | 
% 243.91/50.35  | COMBINE_EQS: (4), (27) imply:
% 243.91/50.35  |   (35)  all_54_8 = all_16_0
% 243.91/50.35  | 
% 243.91/50.35  | REDUCE: (4), (28) imply:
% 243.91/50.35  |   (36)   ~ (all_52_6 = all_16_0)
% 243.91/50.35  | 
% 243.91/50.35  | SIMP: (36) implies:
% 243.91/50.35  |   (37)   ~ (all_52_6 = all_16_0)
% 243.91/50.35  | 
% 243.91/50.35  | REDUCE: (25), (31) imply:
% 243.91/50.35  |   (38)   ~ (all_52_13 = all_12_0)
% 243.91/50.35  | 
% 243.91/50.35  | REDUCE: (21), (31) imply:
% 243.91/50.35  |   (39)   ~ (all_12_0 = e3)
% 243.91/50.35  | 
% 243.91/50.35  | REDUCE: (15), (31) imply:
% 243.91/50.35  |   (40)   ~ (all_12_0 = e1)
% 243.91/50.35  | 
% 243.91/50.35  | REDUCE: (17), (26) imply:
% 243.91/50.35  |   (41)   ~ (all_12_0 = e2)
% 243.91/50.35  | 
% 243.91/50.35  | BETA: splitting (10) gives:
% 243.91/50.35  | 
% 243.91/50.35  | Case 1:
% 243.91/50.35  | | 
% 243.91/50.35  | |   (42)  all_54_11 = e3
% 243.91/50.35  | | 
% 243.91/50.35  | | COMBINE_EQS: (34), (42) imply:
% 243.91/50.35  | |   (43)  all_12_0 = e3
% 243.91/50.35  | | 
% 243.91/50.35  | | SIMP: (43) implies:
% 243.91/50.35  | |   (44)  all_12_0 = e3
% 243.91/50.35  | | 
% 243.91/50.35  | | REDUCE: (39), (44) imply:
% 243.91/50.35  | |   (45)  $false
% 243.91/50.35  | | 
% 243.91/50.35  | | CLOSE: (45) is inconsistent.
% 243.91/50.35  | | 
% 243.91/50.35  | Case 2:
% 243.91/50.35  | | 
% 243.91/50.35  | |   (46)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 243.91/50.35  | | 
% 243.91/50.35  | | BETA: splitting (46) gives:
% 243.91/50.35  | | 
% 243.91/50.35  | | Case 1:
% 243.91/50.35  | | | 
% 243.91/50.35  | | |   (47)  all_54_11 = e2
% 243.91/50.35  | | | 
% 243.91/50.35  | | | COMBINE_EQS: (34), (47) imply:
% 243.91/50.35  | | |   (48)  all_12_0 = e2
% 243.91/50.35  | | | 
% 243.91/50.35  | | | SIMP: (48) implies:
% 243.91/50.35  | | |   (49)  all_12_0 = e2
% 243.91/50.35  | | | 
% 243.91/50.35  | | | REDUCE: (41), (49) imply:
% 243.91/50.35  | | |   (50)  $false
% 243.91/50.35  | | | 
% 243.91/50.35  | | | CLOSE: (50) is inconsistent.
% 243.91/50.35  | | | 
% 243.91/50.35  | | Case 2:
% 243.91/50.35  | | | 
% 243.91/50.35  | | |   (51)  all_54_11 = e1 | all_54_11 = e0
% 243.91/50.35  | | | 
% 243.91/50.35  | | | BETA: splitting (13) gives:
% 243.91/50.35  | | | 
% 243.91/50.35  | | | Case 1:
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | |   (52)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3)
% 243.91/50.35  | | | |           = e2)
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | | BETA: splitting (52) gives:
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | | Case 1:
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | |   (53)  all_58_0 = e2 & op(e3, e3) = e2
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | ALPHA: (53) implies:
% 243.91/50.35  | | | | |   (54)  op(e3, e3) = e2
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | REF_CLOSE: (2), (29), (30), (54) are inconsistent by sub-proof #2188.
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | Case 2:
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | |   (55)  all_58_2 = e2 & op(e2, e3) = e2
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | | REF_CLOSE: (7), (18), (20), (22), (24), (29), (32), (34), (38), (40),
% 243.91/50.35  | | | | |            (51), (55) are inconsistent by sub-proof #1304.
% 243.91/50.35  | | | | | 
% 243.91/50.35  | | | | End of split
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | Case 2:
% 243.91/50.35  | | | | 
% 243.91/50.35  | | | |   (56)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3)
% 243.91/50.35  | | | |           = e2)
% 243.91/50.35  | | | | 
% 243.91/50.36  | | | | BETA: splitting (56) gives:
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | | Case 1:
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | |   (57)  all_58_6 = e2 & op(e1, e3) = e2
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | | REF_CLOSE: (1), (3), (5), (6), (9), (12), (14), (16), (19), (21),
% 243.91/50.36  | | | | |            (23), (27), (29), (35), (37), (57) are inconsistent by
% 243.91/50.36  | | | | |            sub-proof #1303.
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | Case 2:
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | |   (58)  all_58_12 = e2 & op(e0, e3) = e2
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | | REF_CLOSE: (11), (33), (58) are inconsistent by sub-proof #1302.
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | End of split
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | End of split
% 243.91/50.36  | | | 
% 243.91/50.36  | | End of split
% 243.91/50.36  | | 
% 243.91/50.36  | End of split
% 243.91/50.36  | 
% 243.91/50.36  End of proof
% 243.91/50.36  
% 243.91/50.36  Sub-proof #1302 shows that the following formulas are inconsistent:
% 243.91/50.36  ----------------------------------------------------------------
% 243.91/50.36    (1)  all_58_12 = e2 & op(e0, e3) = e2
% 243.91/50.36    (2)  all_58_12 = e1
% 243.91/50.36    (3)   ~ (e2 = e1)
% 243.91/50.36  
% 243.91/50.36  Begin of proof
% 243.91/50.36  | 
% 243.91/50.36  | ALPHA: (1) implies:
% 243.91/50.36  |   (4)  all_58_12 = e2
% 243.91/50.36  | 
% 243.91/50.36  | COMBINE_EQS: (2), (4) imply:
% 243.91/50.36  |   (5)  e2 = e1
% 243.91/50.36  | 
% 243.91/50.36  | REDUCE: (3), (5) imply:
% 243.91/50.36  |   (6)  $false
% 243.91/50.36  | 
% 243.91/50.36  | CLOSE: (6) is inconsistent.
% 243.91/50.36  | 
% 243.91/50.36  End of proof
% 243.91/50.36  
% 243.91/50.36  Sub-proof #1303 shows that the following formulas are inconsistent:
% 243.91/50.36  ----------------------------------------------------------------
% 243.91/50.36    (1)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.91/50.36    (2)  op(e1, e2) = all_52_6
% 243.91/50.36    (3)  op(e1, e1) = all_6_2
% 243.91/50.36    (4)  op(e1, e0) = all_52_14
% 243.91/50.36    (5)  all_58_6 = e2 & op(e1, e3) = e2
% 243.91/50.36    (6)   ~ (all_52_2 = e1)
% 243.91/50.36    (7)   ~ (all_52_6 = all_16_0)
% 243.91/50.36    (8)   ~ (all_6_2 = e3)
% 243.91/50.36    (9)   ~ (e3 = e2)
% 243.91/50.36    (10)   ~ (all_16_0 = e2)
% 243.91/50.36    (11)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.91/50.36          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.91/50.36    (12)   ~ (all_52_14 = e3)
% 243.91/50.36    (13)   ~ (all_52_2 = e0)
% 243.91/50.36    (14)  all_54_8 = all_16_0
% 243.91/50.36    (15)  all_54_8 = all_52_2
% 243.91/50.36    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.36  
% 243.91/50.36  Begin of proof
% 243.91/50.36  | 
% 243.91/50.36  | ALPHA: (5) implies:
% 243.91/50.36  |   (17)  all_58_6 = e2
% 243.91/50.36  | 
% 243.91/50.36  | BETA: splitting (11) gives:
% 243.91/50.36  | 
% 243.91/50.36  | Case 1:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (18)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 243.91/50.36  | |           e3)
% 243.91/50.36  | | 
% 243.91/50.36  | | BETA: splitting (18) gives:
% 243.91/50.36  | | 
% 243.91/50.36  | | Case 1:
% 243.91/50.36  | | | 
% 243.91/50.36  | | |   (19)  all_58_6 = e3 & op(e1, e3) = e3
% 243.91/50.36  | | | 
% 243.91/50.36  | | | ALPHA: (19) implies:
% 243.91/50.36  | | |   (20)  all_58_6 = e3
% 243.91/50.36  | | | 
% 243.91/50.36  | | | REF_CLOSE: (9), (17), (20) are inconsistent by sub-proof #2024.
% 243.91/50.36  | | | 
% 243.91/50.36  | | Case 2:
% 243.91/50.36  | | | 
% 243.91/50.36  | | |   (21)  all_58_7 = e3 & op(e1, e2) = e3
% 243.91/50.36  | | | 
% 243.91/50.36  | | | ALPHA: (21) implies:
% 243.91/50.36  | | |   (22)  op(e1, e2) = e3
% 243.91/50.36  | | | 
% 243.91/50.36  | | | BETA: splitting (1) gives:
% 243.91/50.36  | | | 
% 243.91/50.36  | | | Case 1:
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | |   (23)  all_54_8 = e3
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | | COMBINE_EQS: (14), (23) imply:
% 243.91/50.36  | | | |   (24)  all_16_0 = e3
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | | SIMP: (24) implies:
% 243.91/50.36  | | | |   (25)  all_16_0 = e3
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | | REDUCE: (7), (25) imply:
% 243.91/50.36  | | | |   (26)   ~ (all_52_6 = e3)
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | | REF_CLOSE: (2), (16), (22), (26) are inconsistent by sub-proof #2191.
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | Case 2:
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | |   (27)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | | BETA: splitting (27) gives:
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | | Case 1:
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | |   (28)  all_54_8 = e2
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | | COMBINE_EQS: (14), (28) imply:
% 243.91/50.36  | | | | |   (29)  all_16_0 = e2
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | | REDUCE: (10), (29) imply:
% 243.91/50.36  | | | | |   (30)  $false
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | | CLOSE: (30) is inconsistent.
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | Case 2:
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | |   (31)  all_54_8 = e1 | all_54_8 = e0
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | | REF_CLOSE: (6), (13), (15), (31) are inconsistent by sub-proof #1950.
% 243.91/50.36  | | | | | 
% 243.91/50.36  | | | | End of split
% 243.91/50.36  | | | | 
% 243.91/50.36  | | | End of split
% 243.91/50.36  | | | 
% 243.91/50.36  | | End of split
% 243.91/50.36  | | 
% 243.91/50.36  | Case 2:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (32)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 243.91/50.36  | |           e3)
% 243.91/50.36  | | 
% 243.91/50.36  | | REF_CLOSE: (3), (4), (8), (12), (16), (32) are inconsistent by sub-proof
% 243.91/50.36  | |            #1529.
% 243.91/50.36  | | 
% 243.91/50.36  | End of split
% 243.91/50.36  | 
% 243.91/50.36  End of proof
% 243.91/50.36  
% 243.91/50.36  Sub-proof #1304 shows that the following formulas are inconsistent:
% 243.91/50.36  ----------------------------------------------------------------
% 243.91/50.36    (1)   ~ (all_52_13 = e1)
% 243.91/50.36    (2)   ~ (all_12_0 = e1)
% 243.91/50.36    (3)  all_54_11 = all_12_0
% 243.91/50.36    (4)  all_58_2 = e2 & op(e2, e3) = e2
% 243.91/50.36    (5)  all_54_11 = e1 | all_54_11 = e0
% 243.91/50.36    (6)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.91/50.36    (7)   ~ (all_52_13 = all_12_0)
% 243.91/50.36    (8)  op(e2, e3) = all_52_1
% 243.91/50.36    (9)   ~ (all_52_1 = all_52_13)
% 243.91/50.36    (10)  all_54_7 = all_52_13
% 243.91/50.36    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.36    (12)   ~ (all_52_13 = e3)
% 243.91/50.36  
% 243.91/50.36  Begin of proof
% 243.91/50.36  | 
% 243.91/50.36  | ALPHA: (4) implies:
% 243.91/50.36  |   (13)  op(e2, e3) = e2
% 243.91/50.36  | 
% 243.91/50.36  | BETA: splitting (5) gives:
% 243.91/50.36  | 
% 243.91/50.36  | Case 1:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (14)  all_54_11 = e1
% 243.91/50.36  | | 
% 243.91/50.36  | | COMBINE_EQS: (3), (14) imply:
% 243.91/50.36  | |   (15)  all_12_0 = e1
% 243.91/50.36  | | 
% 243.91/50.36  | | SIMP: (15) implies:
% 243.91/50.36  | |   (16)  all_12_0 = e1
% 243.91/50.36  | | 
% 243.91/50.36  | | REDUCE: (2), (16) imply:
% 243.91/50.36  | |   (17)  $false
% 243.91/50.36  | | 
% 243.91/50.36  | | CLOSE: (17) is inconsistent.
% 243.91/50.36  | | 
% 243.91/50.36  | Case 2:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (18)  all_54_11 = e0
% 243.91/50.36  | | 
% 243.91/50.36  | | COMBINE_EQS: (3), (18) imply:
% 243.91/50.36  | |   (19)  all_12_0 = e0
% 243.91/50.36  | | 
% 243.91/50.36  | | SIMP: (19) implies:
% 243.91/50.36  | |   (20)  all_12_0 = e0
% 243.91/50.36  | | 
% 243.91/50.36  | | REDUCE: (7), (20) imply:
% 243.91/50.36  | |   (21)   ~ (all_52_13 = e0)
% 243.91/50.36  | | 
% 243.91/50.36  | | REF_CLOSE: (1), (6), (8), (9), (10), (11), (12), (13), (21) are inconsistent
% 243.91/50.36  | |            by sub-proof #2291.
% 243.91/50.36  | | 
% 243.91/50.36  | End of split
% 243.91/50.36  | 
% 243.91/50.36  End of proof
% 243.91/50.36  
% 243.91/50.36  Sub-proof #1305 shows that the following formulas are inconsistent:
% 243.91/50.36  ----------------------------------------------------------------
% 243.91/50.36    (1)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.91/50.36         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.91/50.36    (2)  all_58_15 = e3
% 243.91/50.36    (3)   ~ (e3 = e1)
% 243.91/50.36    (4)  op(e2, e0) = e0
% 243.91/50.36    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.36    (6)  op(e1, e0) = e2
% 243.91/50.36    (7)   ~ (e1 = e0)
% 243.91/50.36    (8)  op(e2, e0) = all_52_13
% 243.91/50.36    (9)  all_58_9 = e2
% 243.91/50.36    (10)   ~ (e2 = e1)
% 243.91/50.36  
% 243.91/50.36  Begin of proof
% 243.91/50.36  | 
% 243.91/50.36  | BETA: splitting (1) gives:
% 243.91/50.36  | 
% 243.91/50.36  | Case 1:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (11)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 243.91/50.36  | |           e1)
% 243.91/50.36  | | 
% 243.91/50.36  | | BETA: splitting (11) gives:
% 243.91/50.36  | | 
% 243.91/50.36  | | Case 1:
% 243.91/50.36  | | | 
% 243.91/50.36  | | |   (12)  all_58_9 = e1 & op(e3, e0) = e1
% 243.91/50.36  | | | 
% 243.91/50.36  | | | ALPHA: (12) implies:
% 243.91/50.36  | | |   (13)  all_58_9 = e1
% 243.91/50.36  | | | 
% 243.91/50.36  | | | REF_CLOSE: (9), (10), (13) are inconsistent by sub-proof #1605.
% 243.91/50.36  | | | 
% 243.91/50.36  | | Case 2:
% 243.91/50.36  | | | 
% 243.91/50.36  | | |   (14)  all_58_10 = e1 & op(e2, e0) = e1
% 243.91/50.36  | | | 
% 243.91/50.36  | | | ALPHA: (14) implies:
% 243.91/50.36  | | |   (15)  op(e2, e0) = e1
% 243.91/50.36  | | | 
% 243.91/50.36  | | | REF_CLOSE: (4), (5), (7), (8), (15) are inconsistent by sub-proof #1778.
% 243.91/50.36  | | | 
% 243.91/50.36  | | End of split
% 243.91/50.36  | | 
% 243.91/50.36  | Case 2:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (16)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.91/50.36  | |           e1)
% 243.91/50.36  | | 
% 243.91/50.36  | | BETA: splitting (16) gives:
% 243.91/50.36  | | 
% 243.91/50.36  | | Case 1:
% 243.91/50.36  | | | 
% 243.91/50.36  | | |   (17)  all_58_11 = e1 & op(e1, e0) = e1
% 243.91/50.36  | | | 
% 243.91/50.36  | | | ALPHA: (17) implies:
% 243.91/50.36  | | |   (18)  op(e1, e0) = e1
% 243.91/50.36  | | | 
% 243.91/50.36  | | | REF_CLOSE: (5), (6), (10), (18) are inconsistent by sub-proof #2019.
% 243.91/50.36  | | | 
% 243.91/50.36  | | Case 2:
% 243.91/50.36  | | | 
% 243.91/50.36  | | |   (19)  all_58_15 = e1 & op(e0, e0) = e1
% 243.91/50.36  | | | 
% 243.91/50.36  | | | ALPHA: (19) implies:
% 243.91/50.36  | | |   (20)  all_58_15 = e1
% 243.91/50.36  | | | 
% 243.91/50.36  | | | REF_CLOSE: (2), (3), (20) are inconsistent by sub-proof #2249.
% 243.91/50.36  | | | 
% 243.91/50.36  | | End of split
% 243.91/50.36  | | 
% 243.91/50.36  | End of split
% 243.91/50.36  | 
% 243.91/50.36  End of proof
% 243.91/50.36  
% 243.91/50.36  Sub-proof #1306 shows that the following formulas are inconsistent:
% 243.91/50.36  ----------------------------------------------------------------
% 243.91/50.36    (1)   ~ (e3 = e0)
% 243.91/50.36    (2)  op(e0, e1) = all_52_11
% 243.91/50.36    (3)   ~ (e2 = e0)
% 243.91/50.36    (4)  all_58_4 = e2
% 243.91/50.36    (5)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 243.91/50.36         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 243.91/50.36    (6)   ~ (e3 = e1)
% 243.91/50.36    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 243.91/50.36         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.91/50.36    (8)   ~ (all_52_11 = e3)
% 243.91/50.36    (9)  op(e2, e1) = all_52_9
% 243.91/50.36    (10)   ~ (e3 = e2)
% 243.91/50.36    (11)  op(e1, e1) = e2
% 243.91/50.36    (12)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 243.91/50.36          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.91/50.36    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.36    (14)   ~ (e1 = e0)
% 243.91/50.36    (15)   ~ (e2 = e1)
% 243.91/50.36  
% 243.91/50.36  Begin of proof
% 243.91/50.36  | 
% 243.91/50.36  | BETA: splitting (12) gives:
% 243.91/50.36  | 
% 243.91/50.36  | Case 1:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (16)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 243.91/50.36  | |           e3)
% 243.91/50.36  | | 
% 243.91/50.36  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 243.91/50.36  | |            (15), (16) are inconsistent by sub-proof #1901.
% 243.91/50.36  | | 
% 243.91/50.36  | Case 2:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (17)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 243.91/50.36  | |           e3)
% 243.91/50.36  | | 
% 243.91/50.36  | | REF_CLOSE: (2), (8), (10), (11), (13), (17) are inconsistent by sub-proof
% 243.91/50.36  | |            #1307.
% 243.91/50.36  | | 
% 243.91/50.36  | End of split
% 243.91/50.36  | 
% 243.91/50.36  End of proof
% 243.91/50.36  
% 243.91/50.36  Sub-proof #1307 shows that the following formulas are inconsistent:
% 243.91/50.36  ----------------------------------------------------------------
% 243.91/50.36    (1)  op(e0, e1) = all_52_11
% 243.91/50.36    (2)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 243.91/50.36    (3)   ~ (all_52_11 = e3)
% 243.91/50.36    (4)   ~ (e3 = e2)
% 243.91/50.36    (5)  op(e1, e1) = e2
% 243.91/50.36    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.36  
% 243.91/50.36  Begin of proof
% 243.91/50.36  | 
% 243.91/50.36  | BETA: splitting (2) gives:
% 243.91/50.36  | 
% 243.91/50.36  | Case 1:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 243.91/50.36  | | 
% 243.91/50.36  | | ALPHA: (7) implies:
% 243.91/50.36  | |   (8)  op(e1, e1) = e3
% 243.91/50.36  | | 
% 243.91/50.36  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2206.
% 243.91/50.36  | | 
% 243.91/50.36  | Case 2:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (9)  all_58_14 = e3 & op(e0, e1) = e3
% 243.91/50.36  | | 
% 243.91/50.36  | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #1647.
% 243.91/50.36  | | 
% 243.91/50.36  | End of split
% 243.91/50.36  | 
% 243.91/50.36  End of proof
% 243.91/50.36  
% 243.91/50.36  Sub-proof #1308 shows that the following formulas are inconsistent:
% 243.91/50.36  ----------------------------------------------------------------
% 243.91/50.36    (1)   ~ (all_12_1 = e2)
% 243.91/50.36    (2)  op(e0, e3) = e2
% 243.91/50.36    (3)  op(e0, e3) = all_26_1
% 243.91/50.36    (4)  op(e0, e3) = all_12_1
% 243.91/50.36    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.36  
% 243.91/50.36  Begin of proof
% 243.91/50.36  | 
% 243.91/50.36  | GROUND_INST: instantiating (5) with e2, all_26_1, e3, e0, simplifying with
% 243.91/50.36  |              (2), (3) gives:
% 243.91/50.36  |   (6)  all_26_1 = e2
% 243.91/50.36  | 
% 243.91/50.36  | GROUND_INST: instantiating (5) with all_12_1, all_26_1, e3, e0, simplifying
% 243.91/50.36  |              with (3), (4) gives:
% 243.91/50.36  |   (7)  all_26_1 = all_12_1
% 243.91/50.36  | 
% 243.91/50.36  | COMBINE_EQS: (6), (7) imply:
% 243.91/50.36  |   (8)  all_12_1 = e2
% 243.91/50.36  | 
% 243.91/50.36  | REDUCE: (1), (8) imply:
% 243.91/50.36  |   (9)  $false
% 243.91/50.36  | 
% 243.91/50.36  | CLOSE: (9) is inconsistent.
% 243.91/50.36  | 
% 243.91/50.36  End of proof
% 243.91/50.36  
% 243.91/50.36  Sub-proof #1309 shows that the following formulas are inconsistent:
% 243.91/50.36  ----------------------------------------------------------------
% 243.91/50.36    (1)   ~ (all_50_0 = e2)
% 243.91/50.36    (2)   ~ (all_12_0 = e2)
% 243.91/50.36    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.91/50.36         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.91/50.36    (4)  all_58_12 = e2
% 243.91/50.36    (5)  all_54_7 = all_12_0
% 243.91/50.36    (6)  op(e1, e0) = all_52_14
% 243.91/50.36    (7)   ~ (all_50_0 = e1)
% 243.91/50.36    (8)   ~ (all_12_0 = e1)
% 243.91/50.36    (9)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.91/50.36    (10)  op(e2, e1) = all_52_9
% 243.91/50.36    (11)   ~ (all_50_0 = all_12_0)
% 243.91/50.36    (12)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.91/50.36          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.91/50.36    (13)   ~ (all_52_9 = all_50_0)
% 243.91/50.36    (14)   ~ (all_52_14 = e3)
% 243.91/50.36    (15)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.91/50.36    (16)  op(e1, e1) = e2
% 243.91/50.36    (17)   ~ (all_52_2 = e0)
% 243.91/50.36    (18)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.91/50.36          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.91/50.36    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.36    (20)  op(e1, e3) = all_52_2
% 243.91/50.36    (21)  op(e3, e3) = e0
% 243.91/50.36    (22)   ~ (all_52_14 = all_12_0)
% 243.91/50.36    (23)   ~ (all_52_13 = e3)
% 243.91/50.36    (24)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.91/50.36          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.91/50.36    (25)  all_54_4 = all_50_0
% 243.91/50.36    (26)  op(e2, e0) = all_52_13
% 243.91/50.36    (27)  op(e2, e2) = e2
% 243.91/50.36    (28)   ~ (e2 = e1)
% 243.91/50.36  
% 243.91/50.36  Begin of proof
% 243.91/50.36  | 
% 243.91/50.36  | BETA: splitting (9) gives:
% 243.91/50.36  | 
% 243.91/50.36  | Case 1:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (29)  all_54_7 = e2
% 243.91/50.36  | | 
% 243.91/50.36  | | COMBINE_EQS: (5), (29) imply:
% 243.91/50.36  | |   (30)  all_12_0 = e2
% 243.91/50.36  | | 
% 243.91/50.36  | | REDUCE: (2), (30) imply:
% 243.91/50.36  | |   (31)  $false
% 243.91/50.36  | | 
% 243.91/50.36  | | CLOSE: (31) is inconsistent.
% 243.91/50.36  | | 
% 243.91/50.36  | Case 2:
% 243.91/50.36  | | 
% 243.91/50.36  | |   (32)   ~ (all_54_7 = e2)
% 243.91/50.36  | |   (33)  all_54_7 = e1 | all_54_7 = e0
% 243.91/50.36  | | 
% 243.91/50.36  | | BETA: splitting (33) gives:
% 243.91/50.36  | | 
% 243.91/50.36  | | Case 1:
% 243.91/50.36  | | | 
% 243.91/50.36  | | |   (34)  all_54_7 = e1
% 243.91/50.36  | | | 
% 243.91/50.36  | | | COMBINE_EQS: (5), (34) imply:
% 243.91/50.36  | | |   (35)  all_12_0 = e1
% 243.91/50.36  | | | 
% 243.91/50.36  | | | REDUCE: (8), (35) imply:
% 243.91/50.36  | | |   (36)  $false
% 243.91/50.36  | | | 
% 243.91/50.36  | | | CLOSE: (36) is inconsistent.
% 243.91/50.36  | | | 
% 243.91/50.36  | | Case 2:
% 243.91/50.36  | | | 
% 243.91/50.36  | | |   (37)  all_54_7 = e0
% 243.91/50.36  | | | 
% 243.91/50.36  | | | COMBINE_EQS: (5), (37) imply:
% 243.91/50.36  | | |   (38)  all_12_0 = e0
% 243.91/50.36  | | | 
% 243.91/50.36  | | | REDUCE: (22), (38) imply:
% 243.91/50.36  | | |   (39)   ~ (all_52_14 = e0)
% 243.91/50.36  | | | 
% 243.91/50.36  | | | REDUCE: (11), (38) imply:
% 243.91/50.36  | | |   (40)   ~ (all_50_0 = e0)
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REDUCE: (2), (38) imply:
% 243.91/50.37  | | |   (41)   ~ (e2 = e0)
% 243.91/50.37  | | | 
% 243.91/50.37  | | | SIMP: (41) implies:
% 243.91/50.37  | | |   (42)   ~ (e2 = e0)
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REDUCE: (8), (38) imply:
% 243.91/50.37  | | |   (43)   ~ (e1 = e0)
% 243.91/50.37  | | | 
% 243.91/50.37  | | | SIMP: (43) implies:
% 243.91/50.37  | | |   (44)   ~ (e1 = e0)
% 243.91/50.37  | | | 
% 243.91/50.37  | | | BETA: splitting (15) gives:
% 243.91/50.37  | | | 
% 243.91/50.37  | | | Case 1:
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | |   (45)  all_54_4 = e3
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | COMBINE_EQS: (25), (45) imply:
% 243.91/50.37  | | | |   (46)  all_50_0 = e3
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | SIMP: (46) implies:
% 243.91/50.37  | | | |   (47)  all_50_0 = e3
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REDUCE: (13), (47) imply:
% 243.91/50.37  | | | |   (48)   ~ (all_52_9 = e3)
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REDUCE: (1), (47) imply:
% 243.91/50.37  | | | |   (49)   ~ (e3 = e2)
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REDUCE: (7), (47) imply:
% 243.91/50.37  | | | |   (50)   ~ (e3 = e1)
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REDUCE: (40), (47) imply:
% 243.91/50.37  | | | |   (51)   ~ (e3 = e0)
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REF_CLOSE: (3), (4), (6), (10), (12), (14), (16), (17), (18), (19),
% 243.91/50.37  | | | |            (20), (21), (23), (24), (26), (27), (28), (39), (42), (44),
% 243.91/50.37  | | | |            (48), (49), (50), (51) are inconsistent by sub-proof #1311.
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | Case 2:
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | |   (52)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REF_CLOSE: (1), (7), (25), (40), (52) are inconsistent by sub-proof
% 243.91/50.37  | | | |            #1885.
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | End of split
% 243.91/50.37  | | | 
% 243.91/50.37  | | End of split
% 243.91/50.37  | | 
% 243.91/50.37  | End of split
% 243.91/50.37  | 
% 243.91/50.37  End of proof
% 243.91/50.37  
% 243.91/50.37  Sub-proof #1310 shows that the following formulas are inconsistent:
% 243.91/50.37  ----------------------------------------------------------------
% 243.91/50.37    (1)   ~ (all_52_9 = all_16_0)
% 243.91/50.37    (2)   ~ (all_12_0 = e2)
% 243.91/50.37    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.91/50.37         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.91/50.37    (4)  all_58_12 = e2
% 243.91/50.37    (5)  all_54_7 = all_12_0
% 243.91/50.37    (6)  all_54_4 = all_16_0
% 243.91/50.37    (7)  op(e1, e0) = all_52_14
% 243.91/50.37    (8)   ~ (all_16_0 = all_12_0)
% 243.91/50.37    (9)   ~ (all_12_0 = e1)
% 243.91/50.37    (10)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 243.91/50.37    (11)  op(e2, e1) = all_52_9
% 243.91/50.37    (12)   ~ (all_16_0 = e2)
% 243.91/50.37    (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.91/50.37          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.91/50.37    (14)   ~ (all_52_14 = e3)
% 243.91/50.37    (15)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.91/50.37    (16)  op(e1, e1) = e2
% 243.91/50.37    (17)   ~ (all_52_2 = e0)
% 243.91/50.37    (18)   ~ (all_16_0 = e1)
% 243.91/50.37    (19)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.91/50.37          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.91/50.37    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.37    (21)  op(e1, e3) = all_52_2
% 243.91/50.37    (22)  op(e3, e3) = e0
% 243.91/50.37    (23)   ~ (all_52_14 = all_12_0)
% 243.91/50.37    (24)   ~ (all_52_13 = e3)
% 243.91/50.37    (25)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.91/50.37          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.91/50.37    (26)  op(e2, e0) = all_52_13
% 243.91/50.37    (27)  op(e2, e2) = e2
% 243.91/50.37    (28)   ~ (e2 = e1)
% 243.91/50.37  
% 243.91/50.37  Begin of proof
% 243.91/50.37  | 
% 243.91/50.37  | BETA: splitting (10) gives:
% 243.91/50.37  | 
% 243.91/50.37  | Case 1:
% 243.91/50.37  | | 
% 243.91/50.37  | |   (29)  all_54_7 = e2
% 243.91/50.37  | | 
% 243.91/50.37  | | COMBINE_EQS: (5), (29) imply:
% 243.91/50.37  | |   (30)  all_12_0 = e2
% 243.91/50.37  | | 
% 243.91/50.37  | | REDUCE: (2), (30) imply:
% 243.91/50.37  | |   (31)  $false
% 243.91/50.37  | | 
% 243.91/50.37  | | CLOSE: (31) is inconsistent.
% 243.91/50.37  | | 
% 243.91/50.37  | Case 2:
% 243.91/50.37  | | 
% 243.91/50.37  | |   (32)   ~ (all_54_7 = e2)
% 243.91/50.37  | |   (33)  all_54_7 = e1 | all_54_7 = e0
% 243.91/50.37  | | 
% 243.91/50.37  | | BETA: splitting (33) gives:
% 243.91/50.37  | | 
% 243.91/50.37  | | Case 1:
% 243.91/50.37  | | | 
% 243.91/50.37  | | |   (34)  all_54_7 = e1
% 243.91/50.37  | | | 
% 243.91/50.37  | | | COMBINE_EQS: (5), (34) imply:
% 243.91/50.37  | | |   (35)  all_12_0 = e1
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REDUCE: (9), (35) imply:
% 243.91/50.37  | | |   (36)  $false
% 243.91/50.37  | | | 
% 243.91/50.37  | | | CLOSE: (36) is inconsistent.
% 243.91/50.37  | | | 
% 243.91/50.37  | | Case 2:
% 243.91/50.37  | | | 
% 243.91/50.37  | | |   (37)  all_54_7 = e0
% 243.91/50.37  | | | 
% 243.91/50.37  | | | COMBINE_EQS: (5), (37) imply:
% 243.91/50.37  | | |   (38)  all_12_0 = e0
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REDUCE: (23), (38) imply:
% 243.91/50.37  | | |   (39)   ~ (all_52_14 = e0)
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REDUCE: (8), (38) imply:
% 243.91/50.37  | | |   (40)   ~ (all_16_0 = e0)
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REDUCE: (2), (38) imply:
% 243.91/50.37  | | |   (41)   ~ (e2 = e0)
% 243.91/50.37  | | | 
% 243.91/50.37  | | | SIMP: (41) implies:
% 243.91/50.37  | | |   (42)   ~ (e2 = e0)
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REDUCE: (9), (38) imply:
% 243.91/50.37  | | |   (43)   ~ (e1 = e0)
% 243.91/50.37  | | | 
% 243.91/50.37  | | | SIMP: (43) implies:
% 243.91/50.37  | | |   (44)   ~ (e1 = e0)
% 243.91/50.37  | | | 
% 243.91/50.37  | | | BETA: splitting (15) gives:
% 243.91/50.37  | | | 
% 243.91/50.37  | | | Case 1:
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | |   (45)  all_54_4 = e3
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | COMBINE_EQS: (6), (45) imply:
% 243.91/50.37  | | | |   (46)  all_16_0 = e3
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | SIMP: (46) implies:
% 243.91/50.37  | | | |   (47)  all_16_0 = e3
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REDUCE: (1), (47) imply:
% 243.91/50.37  | | | |   (48)   ~ (all_52_9 = e3)
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REDUCE: (12), (47) imply:
% 243.91/50.37  | | | |   (49)   ~ (e3 = e2)
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REDUCE: (18), (47) imply:
% 243.91/50.37  | | | |   (50)   ~ (e3 = e1)
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REDUCE: (40), (47) imply:
% 243.91/50.37  | | | |   (51)   ~ (e3 = e0)
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REF_CLOSE: (3), (4), (7), (11), (13), (14), (16), (17), (19), (20),
% 243.91/50.37  | | | |            (21), (22), (24), (25), (26), (27), (28), (39), (42), (44),
% 243.91/50.37  | | | |            (48), (49), (50), (51) are inconsistent by sub-proof #1311.
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | Case 2:
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | |   (52)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | | REF_CLOSE: (6), (12), (18), (40), (52) are inconsistent by sub-proof
% 243.91/50.37  | | | |            #1886.
% 243.91/50.37  | | | | 
% 243.91/50.37  | | | End of split
% 243.91/50.37  | | | 
% 243.91/50.37  | | End of split
% 243.91/50.37  | | 
% 243.91/50.37  | End of split
% 243.91/50.37  | 
% 243.91/50.37  End of proof
% 243.91/50.37  
% 243.91/50.37  Sub-proof #1311 shows that the following formulas are inconsistent:
% 243.91/50.37  ----------------------------------------------------------------
% 243.91/50.37    (1)   ~ (e3 = e0)
% 243.91/50.37    (2)   ~ (e2 = e0)
% 243.91/50.37    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.91/50.37         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.91/50.37    (4)  all_58_12 = e2
% 243.91/50.37    (5)  op(e1, e0) = all_52_14
% 243.91/50.37    (6)   ~ (e3 = e1)
% 243.91/50.37    (7)  op(e2, e1) = all_52_9
% 243.91/50.37    (8)   ~ (e3 = e2)
% 243.91/50.37    (9)   ~ (all_52_14 = e0)
% 243.91/50.37    (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.91/50.37          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.91/50.37    (11)   ~ (all_52_14 = e3)
% 243.91/50.37    (12)  op(e1, e1) = e2
% 243.91/50.37    (13)   ~ (all_52_2 = e0)
% 243.91/50.37    (14)   ~ (all_52_9 = e3)
% 243.91/50.37    (15)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.91/50.37          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.91/50.37    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.37    (17)  op(e1, e3) = all_52_2
% 243.91/50.37    (18)   ~ (e1 = e0)
% 243.91/50.37    (19)  op(e3, e3) = e0
% 243.91/50.37    (20)   ~ (all_52_13 = e3)
% 243.91/50.37    (21)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.91/50.37          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.91/50.37    (22)  op(e2, e0) = all_52_13
% 243.91/50.37    (23)  op(e2, e2) = e2
% 243.91/50.37    (24)   ~ (e2 = e1)
% 243.91/50.37  
% 243.91/50.37  Begin of proof
% 243.91/50.37  | 
% 243.91/50.37  | BETA: splitting (15) gives:
% 243.91/50.37  | 
% 243.91/50.37  | Case 1:
% 243.91/50.37  | | 
% 243.91/50.37  | |   (25)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 243.91/50.37  | |           e1)
% 243.91/50.37  | | 
% 243.91/50.37  | | BETA: splitting (25) gives:
% 243.91/50.37  | | 
% 243.91/50.37  | | Case 1:
% 243.91/50.37  | | | 
% 243.91/50.37  | | |   (26)  all_58_0 = e1 & op(e3, e3) = e1
% 243.91/50.37  | | | 
% 243.91/50.37  | | | ALPHA: (26) implies:
% 243.91/50.37  | | |   (27)  op(e3, e3) = e1
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REF_CLOSE: (16), (18), (19), (27) are inconsistent by sub-proof #1828.
% 243.91/50.37  | | | 
% 243.91/50.37  | | Case 2:
% 243.91/50.37  | | | 
% 243.91/50.37  | | |   (28)  all_58_2 = e1 & op(e2, e3) = e1
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REF_CLOSE: (3), (6), (7), (8), (14), (16), (20), (22), (23), (28) are
% 243.91/50.37  | | |            inconsistent by sub-proof #1312.
% 243.91/50.37  | | | 
% 243.91/50.37  | | End of split
% 243.91/50.37  | | 
% 243.91/50.37  | Case 2:
% 243.91/50.37  | | 
% 243.91/50.37  | |   (29)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 243.91/50.37  | |           e1)
% 243.91/50.37  | | 
% 243.91/50.37  | | BETA: splitting (29) gives:
% 243.91/50.37  | | 
% 243.91/50.37  | | Case 1:
% 243.91/50.37  | | | 
% 243.91/50.37  | | |   (30)  all_58_6 = e1 & op(e1, e3) = e1
% 243.91/50.37  | | | 
% 243.91/50.37  | | | ALPHA: (30) implies:
% 243.91/50.37  | | |   (31)  op(e1, e3) = e1
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (11), (12), (13), (16),
% 243.91/50.37  | | |            (17), (21), (31) are inconsistent by sub-proof #1850.
% 243.91/50.37  | | | 
% 243.91/50.37  | | Case 2:
% 243.91/50.37  | | | 
% 243.91/50.37  | | |   (32)  all_58_12 = e1 & op(e0, e3) = e1
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REF_CLOSE: (4), (24), (32) are inconsistent by sub-proof #1763.
% 243.91/50.37  | | | 
% 243.91/50.37  | | End of split
% 243.91/50.37  | | 
% 243.91/50.37  | End of split
% 243.91/50.37  | 
% 243.91/50.37  End of proof
% 243.91/50.37  
% 243.91/50.37  Sub-proof #1312 shows that the following formulas are inconsistent:
% 243.91/50.37  ----------------------------------------------------------------
% 243.91/50.37    (1)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.91/50.37         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.91/50.37    (2)   ~ (e3 = e1)
% 243.91/50.37    (3)  all_58_2 = e1 & op(e2, e3) = e1
% 243.91/50.37    (4)  op(e2, e1) = all_52_9
% 243.91/50.37    (5)   ~ (e3 = e2)
% 243.91/50.37    (6)   ~ (all_52_9 = e3)
% 243.91/50.37    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.37    (8)   ~ (all_52_13 = e3)
% 243.91/50.37    (9)  op(e2, e0) = all_52_13
% 243.91/50.37    (10)  op(e2, e2) = e2
% 243.91/50.37  
% 243.91/50.37  Begin of proof
% 243.91/50.37  | 
% 243.91/50.37  | ALPHA: (3) implies:
% 243.91/50.37  |   (11)  all_58_2 = e1
% 243.91/50.37  | 
% 243.91/50.37  | BETA: splitting (1) gives:
% 243.91/50.37  | 
% 243.91/50.37  | Case 1:
% 243.91/50.37  | | 
% 243.91/50.37  | |   (12)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 243.91/50.37  | |           e3)
% 243.91/50.37  | | 
% 243.91/50.37  | | BETA: splitting (12) gives:
% 243.91/50.37  | | 
% 243.91/50.37  | | Case 1:
% 243.91/50.37  | | | 
% 243.91/50.37  | | |   (13)  all_58_2 = e3 & op(e2, e3) = e3
% 243.91/50.37  | | | 
% 243.91/50.37  | | | ALPHA: (13) implies:
% 243.91/50.37  | | |   (14)  all_58_2 = e3
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REF_CLOSE: (2), (11), (14) are inconsistent by sub-proof #1691.
% 243.91/50.37  | | | 
% 243.91/50.37  | | Case 2:
% 243.91/50.37  | | | 
% 243.91/50.37  | | |   (15)  all_58_3 = e3 & op(e2, e2) = e3
% 243.91/50.37  | | | 
% 243.91/50.37  | | | ALPHA: (15) implies:
% 243.91/50.37  | | |   (16)  op(e2, e2) = e3
% 243.91/50.37  | | | 
% 243.91/50.37  | | | REF_CLOSE: (5), (7), (10), (16) are inconsistent by sub-proof #2140.
% 243.91/50.37  | | | 
% 243.91/50.37  | | End of split
% 243.91/50.37  | | 
% 243.91/50.37  | Case 2:
% 243.91/50.37  | | 
% 243.91/50.37  | |   (17)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 243.91/50.37  | |           e3)
% 243.91/50.37  | | 
% 243.91/50.37  | | REF_CLOSE: (4), (6), (7), (8), (9), (17) are inconsistent by sub-proof
% 243.91/50.37  | |            #1649.
% 243.91/50.37  | | 
% 243.91/50.37  | End of split
% 243.91/50.37  | 
% 243.91/50.37  End of proof
% 243.91/50.37  
% 243.91/50.37  Sub-proof #1313 shows that the following formulas are inconsistent:
% 243.91/50.37  ----------------------------------------------------------------
% 243.91/50.37    (1)   ~ (all_52_3 = e0)
% 243.91/50.37    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 243.91/50.37             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 243.91/50.37           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 243.91/50.37           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.91/50.37           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 243.91/50.37           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.91/50.37           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.91/50.37    (3)  op(e0, e3) = all_52_3
% 243.91/50.37    (4)   ~ (all_52_8 = e1)
% 243.91/50.37    (5)  op(e3, e1) = all_52_8
% 243.91/50.37    (6)   ~ (all_52_3 = e3)
% 243.91/50.37    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.37  
% 243.91/50.37  Begin of proof
% 243.91/50.37  | 
% 243.91/50.37  | BETA: splitting (2) gives:
% 243.91/50.37  | 
% 243.91/50.37  | Case 1:
% 243.91/50.37  | | 
% 243.91/50.37  | |   (8)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 243.91/50.37  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 243.91/50.37  | |        op(e1, e3) = e1
% 243.91/50.37  | | 
% 243.91/50.37  | | ALPHA: (8) implies:
% 243.91/50.37  | |   (9)  op(e3, e1) = e1
% 243.91/50.37  | | 
% 243.91/50.37  | | REF_CLOSE: (4), (5), (7), (9) are inconsistent by sub-proof #2309.
% 243.91/50.37  | | 
% 243.91/50.37  | Case 2:
% 243.91/50.37  | | 
% 243.91/50.37  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.91/50.37  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 243.91/50.37  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.91/50.37  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.91/50.37  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.91/50.37  | | 
% 243.91/50.37  | | REF_CLOSE: (1), (3), (6), (7), (10) are inconsistent by sub-proof #2330.
% 243.91/50.37  | | 
% 243.91/50.37  | End of split
% 243.91/50.37  | 
% 243.91/50.37  End of proof
% 243.91/50.37  
% 243.91/50.37  Sub-proof #1314 shows that the following formulas are inconsistent:
% 243.91/50.37  ----------------------------------------------------------------
% 243.91/50.37    (1)  all_56_11 = e1
% 243.91/50.37    (2)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.91/50.37         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.91/50.37    (3)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.91/50.37           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.91/50.37             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.91/50.37           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.91/50.37             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.91/50.37           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.91/50.37           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.91/50.37           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.91/50.37           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.91/50.37           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.91/50.37           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.91/50.37             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.91/50.37           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.91/50.37           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 243.91/50.37           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.91/50.37           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.91/50.37           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.91/50.37           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.91/50.37             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.91/50.37           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.91/50.37           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 243.91/50.37           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.91/50.37           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.91/50.37           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.91/50.37           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.91/50.37             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.91/50.37           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.91/50.37           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.91/50.37    (4)  op(e1, e0) = all_52_14
% 243.91/50.38    (5)  op(e0, e3) = all_52_3
% 243.91/50.38    (6)   ~ (e3 = e1)
% 243.91/50.38    (7)   ~ (all_52_3 = all_52_7)
% 243.91/50.38    (8)  all_56_21 = e0
% 243.91/50.38    (9)  op(e3, e1) = all_52_8
% 243.91/50.38    (10)  op(e2, e1) = all_52_9
% 243.91/50.38    (11)   ~ (all_52_14 = e0)
% 243.91/50.38    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.91/50.38          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.91/50.38    (13)   ~ (all_52_3 = e3)
% 243.91/50.38    (14)  op(e2, e3) = all_52_1
% 243.91/50.38    (15)   ~ (all_52_1 = all_52_13)
% 243.91/50.38    (16)   ~ (all_52_2 = e0)
% 243.91/50.38    (17)  op(e0, e2) = all_52_7
% 243.91/50.38    (18)  all_56_31 = e3
% 243.91/50.38    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.38    (20)  op(e1, e3) = all_52_2
% 243.91/50.38    (21)   ~ (e1 = e0)
% 243.91/50.38    (22)  op(e3, e3) = e3
% 243.91/50.38    (23)   ~ (all_52_13 = e3)
% 243.91/50.38    (24)  op(e2, e0) = all_52_13
% 243.91/50.38    (25)   ~ (all_52_1 = e3)
% 243.91/50.38    (26)   ~ (all_52_9 = e1)
% 243.91/50.38    (27)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.91/50.38          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 243.91/50.38    (28)   ~ (all_52_1 = e1)
% 243.91/50.38    (29)   ~ (all_52_8 = e3)
% 243.91/50.38  
% 243.91/50.38  Begin of proof
% 243.91/50.38  | 
% 243.91/50.38  | BETA: splitting (3) gives:
% 243.91/50.38  | 
% 243.91/50.38  | Case 1:
% 243.91/50.38  | | 
% 243.91/50.38  | |   (30)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.91/50.38  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 243.91/50.38  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 243.91/50.38  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.91/50.38  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 243.91/50.38  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 243.91/50.38  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 243.91/50.38  | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 243.91/50.38  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.91/50.38  | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 243.91/50.38  | |           = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &
% 243.91/50.38  | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.91/50.38  | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 243.91/50.38  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.91/50.38  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.91/50.38  | | 
% 243.91/50.38  | | BETA: splitting (30) gives:
% 243.91/50.38  | | 
% 243.91/50.38  | | Case 1:
% 243.91/50.38  | | | 
% 243.91/50.38  | | |   (31)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 243.91/50.38  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.91/50.38  | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 243.91/50.38  | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.91/50.38  | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 243.91/50.38  | | |         | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.91/50.38  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.91/50.38  | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.91/50.38  | | | 
% 243.91/50.38  | | | REF_CLOSE: (9), (14), (18), (19), (25), (29), (31) are inconsistent by
% 243.91/50.38  | | |            sub-proof #1316.
% 243.91/50.38  | | | 
% 243.91/50.38  | | Case 2:
% 243.91/50.38  | | | 
% 243.91/50.38  | | |   (32)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 243.91/50.38  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.91/50.38  | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 243.91/50.38  | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 243.91/50.38  | | |             = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 243.91/50.38  | | |           e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.91/50.38  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.91/50.38  | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.91/50.38  | | | 
% 243.91/50.38  | | | REF_CLOSE: (5), (13), (18), (19), (32) are inconsistent by sub-proof
% 243.91/50.38  | | |            #1389.
% 243.91/50.38  | | | 
% 243.91/50.38  | | End of split
% 243.91/50.38  | | 
% 243.91/50.38  | Case 2:
% 243.91/50.38  | | 
% 243.91/50.38  | |   (33)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.91/50.38  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.91/50.38  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 243.91/50.38  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.91/50.38  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 243.91/50.38  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.91/50.38  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.91/50.38  | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 243.91/50.38  | |           e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.91/50.38  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 243.91/50.38  | |         (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.91/50.38  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.91/50.38  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.91/50.38  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.91/50.38  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.91/50.38  | | 
% 243.91/50.38  | | BETA: splitting (33) gives:
% 243.91/50.38  | | 
% 243.91/50.38  | | Case 1:
% 243.91/50.38  | | | 
% 243.91/50.38  | | |   (34)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.91/50.38  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.91/50.38  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 243.91/50.38  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 243.91/50.38  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 243.91/50.38  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.91/50.38  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.91/50.38  | | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.91/50.38  | | | 
% 243.91/50.38  | | | REF_CLOSE: (1), (8), (10), (19), (26), (34) are inconsistent by sub-proof
% 243.91/50.38  | | |            #1315.
% 243.91/50.38  | | | 
% 243.91/50.38  | | Case 2:
% 243.91/50.38  | | | 
% 243.91/50.38  | | |   (35)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.91/50.38  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.91/50.38  | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29
% 243.91/50.38  | | |           = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 243.91/50.38  | | |             = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 243.91/50.38  | | |           e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.91/50.38  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.91/50.38  | | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.91/50.38  | | | 
% 243.91/50.38  | | | BETA: splitting (35) gives:
% 243.91/50.38  | | | 
% 243.91/50.38  | | | Case 1:
% 243.91/50.38  | | | | 
% 243.91/50.38  | | | |   (36)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.91/50.38  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.91/50.38  | | | |         op(e2, e0) = e0 & op(e0, e2) = e0
% 243.91/50.38  | | | | 
% 243.91/50.38  | | | | ALPHA: (36) implies:
% 243.91/50.38  | | | |   (37)  op(e0, e2) = e0
% 243.91/50.38  | | | |   (38)  op(e2, e0) = e0
% 243.91/50.38  | | | | 
% 243.91/50.38  | | | | BETA: splitting (2) gives:
% 243.91/50.38  | | | | 
% 243.91/50.38  | | | | Case 1:
% 243.91/50.38  | | | | | 
% 243.91/50.38  | | | | |   (39)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2,
% 243.91/50.38  | | | | |             e2) = e3)
% 243.91/50.38  | | | | | 
% 243.91/50.38  | | | | | BETA: splitting (39) gives:
% 243.91/50.38  | | | | | 
% 243.91/50.38  | | | | | Case 1:
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | |   (40)  all_58_2 = e3 & op(e2, e3) = e3
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | ALPHA: (40) implies:
% 243.91/50.38  | | | | | |   (41)  op(e2, e3) = e3
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | REF_CLOSE: (14), (19), (25), (41) are inconsistent by sub-proof
% 243.91/50.38  | | | | | |            #2337.
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | Case 2:
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | |   (42)  all_58_3 = e3 & op(e2, e2) = e3
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | ALPHA: (42) implies:
% 243.91/50.38  | | | | | |   (43)  all_58_3 = e3
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | REF_CLOSE: (6), (10), (14), (19), (21), (24), (26), (27), (28),
% 243.91/50.38  | | | | | |            (38), (43) are inconsistent by sub-proof #1777.
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | End of split
% 243.91/50.38  | | | | | 
% 243.91/50.38  | | | | Case 2:
% 243.91/50.38  | | | | | 
% 243.91/50.38  | | | | |   (44)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2,
% 243.91/50.38  | | | | |             e0) = e3)
% 243.91/50.38  | | | | | 
% 243.91/50.38  | | | | | BETA: splitting (44) gives:
% 243.91/50.38  | | | | | 
% 243.91/50.38  | | | | | Case 1:
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | GROUND_INST: instantiating (19) with all_52_7, e0, e2, e0,
% 243.91/50.38  | | | | | |              simplifying with (17), (37) gives:
% 243.91/50.38  | | | | | |   (45)  all_52_7 = e0
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | GROUND_INST: instantiating (19) with all_52_13, e0, e0, e2,
% 243.91/50.38  | | | | | |              simplifying with (24), (38) gives:
% 243.91/50.38  | | | | | |   (46)  all_52_13 = e0
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | REDUCE: (15), (46) imply:
% 243.91/50.38  | | | | | |   (47)   ~ (all_52_1 = e0)
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | REDUCE: (7), (45) imply:
% 243.91/50.38  | | | | | |   (48)   ~ (all_52_3 = e0)
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | REDUCE: (23), (46) imply:
% 243.91/50.38  | | | | | |   (49)   ~ (e3 = e0)
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | SIMP: (49) implies:
% 243.91/50.38  | | | | | |   (50)   ~ (e3 = e0)
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | REF_CLOSE: (5), (12), (14), (16), (19), (20), (22), (47), (48), (50)
% 243.91/50.38  | | | | | |            are inconsistent by sub-proof #1938.
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | Case 2:
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | |   (51)  all_58_10 = e3 & op(e2, e0) = e3
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | ALPHA: (51) implies:
% 243.91/50.38  | | | | | |   (52)  op(e2, e0) = e3
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | | REF_CLOSE: (19), (23), (24), (52) are inconsistent by sub-proof
% 243.91/50.38  | | | | | |            #1994.
% 243.91/50.38  | | | | | | 
% 243.91/50.38  | | | | | End of split
% 243.91/50.38  | | | | | 
% 243.91/50.38  | | | | End of split
% 243.91/50.38  | | | | 
% 243.91/50.38  | | | Case 2:
% 243.91/50.38  | | | | 
% 243.91/50.38  | | | |   (53)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.91/50.38  | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.91/50.38  | | | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 243.91/50.38  | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.91/50.38  | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 &
% 243.91/50.38  | | | |           op(e0, e1) = e0)
% 243.91/50.38  | | | | 
% 243.91/50.38  | | | | REF_CLOSE: (4), (8), (11), (19), (53) are inconsistent by sub-proof
% 243.91/50.38  | | | |            #1320.
% 243.91/50.38  | | | | 
% 243.91/50.38  | | | End of split
% 243.91/50.38  | | | 
% 243.91/50.38  | | End of split
% 243.91/50.38  | | 
% 243.91/50.38  | End of split
% 243.91/50.38  | 
% 243.91/50.38  End of proof
% 243.91/50.38  
% 243.91/50.38  Sub-proof #1315 shows that the following formulas are inconsistent:
% 243.91/50.38  ----------------------------------------------------------------
% 243.91/50.38    (1)  all_56_11 = e1
% 243.91/50.38    (2)  all_56_21 = e0
% 243.91/50.38    (3)  op(e2, e1) = all_52_9
% 243.91/50.38    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.38    (5)   ~ (all_52_9 = e1)
% 243.91/50.38    (6)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 243.91/50.38             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 243.91/50.38           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.91/50.38             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.91/50.38           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 243.91/50.38           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.91/50.38           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.91/50.38  
% 243.91/50.38  Begin of proof
% 243.91/50.38  | 
% 243.91/50.38  | BETA: splitting (6) gives:
% 243.91/50.38  | 
% 243.91/50.38  | Case 1:
% 243.91/50.38  | | 
% 243.91/50.38  | |   (7)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 243.91/50.38  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 243.91/50.38  | |        & op(e1, e2) = e2
% 243.91/50.38  | | 
% 243.91/50.38  | | ALPHA: (7) implies:
% 243.91/50.38  | |   (8)   ~ (all_56_11 = e1)
% 243.91/50.38  | | 
% 243.91/50.38  | | REDUCE: (1), (8) imply:
% 243.91/50.38  | |   (9)  $false
% 243.91/50.38  | | 
% 243.91/50.38  | | CLOSE: (9) is inconsistent.
% 243.91/50.38  | | 
% 243.91/50.38  | Case 2:
% 243.91/50.38  | | 
% 243.91/50.38  | |   (10)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.91/50.38  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.91/50.38  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 243.91/50.38  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.91/50.38  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.91/50.38  | | 
% 243.91/50.38  | | REF_CLOSE: (2), (3), (4), (5), (10) are inconsistent by sub-proof #1941.
% 243.91/50.38  | | 
% 243.91/50.38  | End of split
% 243.91/50.38  | 
% 243.91/50.38  End of proof
% 243.91/50.38  
% 243.91/50.38  Sub-proof #1316 shows that the following formulas are inconsistent:
% 243.91/50.38  ----------------------------------------------------------------
% 243.91/50.38    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.91/50.38           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.91/50.38             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.91/50.38           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.91/50.38             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.91/50.38           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.91/50.38           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.91/50.38    (2)  op(e3, e1) = all_52_8
% 243.91/50.38    (3)  op(e2, e3) = all_52_1
% 243.91/50.38    (4)  all_56_31 = e3
% 243.91/50.38    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.38    (6)   ~ (all_52_1 = e3)
% 243.91/50.38    (7)   ~ (all_52_8 = e3)
% 243.91/50.38  
% 243.91/50.38  Begin of proof
% 243.91/50.38  | 
% 243.91/50.38  | BETA: splitting (1) gives:
% 243.91/50.38  | 
% 243.91/50.38  | Case 1:
% 243.91/50.38  | | 
% 243.91/50.38  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.91/50.38  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 243.91/50.38  | |        op(e2, e3) = e3
% 243.91/50.38  | | 
% 243.91/50.38  | | ALPHA: (8) implies:
% 243.91/50.38  | |   (9)  op(e2, e3) = e3
% 243.91/50.38  | | 
% 243.91/50.38  | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #2337.
% 243.91/50.38  | | 
% 243.91/50.38  | Case 2:
% 243.91/50.38  | | 
% 243.91/50.38  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 243.91/50.38  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 243.91/50.38  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.91/50.38  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.91/50.38  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.91/50.38  | | 
% 243.91/50.38  | | REF_CLOSE: (2), (4), (5), (7), (10) are inconsistent by sub-proof #1317.
% 243.91/50.38  | | 
% 243.91/50.38  | End of split
% 243.91/50.38  | 
% 243.91/50.38  End of proof
% 243.91/50.38  
% 243.91/50.38  Sub-proof #1317 shows that the following formulas are inconsistent:
% 243.91/50.38  ----------------------------------------------------------------
% 243.91/50.38    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 243.91/50.38           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 243.91/50.38             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.91/50.38           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 243.91/50.38             e1) = e3 & op(e1, e3) = e3)
% 243.91/50.38    (2)  op(e3, e1) = all_52_8
% 243.91/50.38    (3)  all_56_31 = e3
% 243.91/50.38    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.38    (5)   ~ (all_52_8 = e3)
% 243.91/50.38  
% 243.91/50.38  Begin of proof
% 243.91/50.38  | 
% 243.91/50.38  | BETA: splitting (1) gives:
% 243.91/50.38  | 
% 243.91/50.38  | Case 1:
% 243.91/50.38  | | 
% 243.91/50.38  | |   (6)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 243.91/50.38  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.91/50.38  | |        op(e2, e3) = e2
% 243.91/50.38  | | 
% 243.91/50.38  | | ALPHA: (6) implies:
% 243.91/50.38  | |   (7)   ~ (all_56_31 = e3)
% 243.91/50.38  | | 
% 243.91/50.38  | | REDUCE: (3), (7) imply:
% 243.91/50.38  | |   (8)  $false
% 243.91/50.38  | | 
% 243.91/50.38  | | CLOSE: (8) is inconsistent.
% 243.91/50.38  | | 
% 243.91/50.38  | Case 2:
% 243.91/50.38  | | 
% 243.91/50.38  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 243.91/50.38  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 243.91/50.38  | |        op(e1, e3) = e3
% 243.91/50.38  | | 
% 243.91/50.38  | | ALPHA: (9) implies:
% 243.91/50.38  | |   (10)  op(e3, e1) = e3
% 243.91/50.38  | | 
% 243.91/50.38  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #2260.
% 243.91/50.38  | | 
% 243.91/50.38  | End of split
% 243.91/50.38  | 
% 243.91/50.38  End of proof
% 243.91/50.38  
% 243.91/50.38  Sub-proof #1318 shows that the following formulas are inconsistent:
% 243.91/50.38  ----------------------------------------------------------------
% 243.91/50.38    (1)   ~ (all_8_2 = e1)
% 243.91/50.38    (2)   ~ (all_52_9 = all_8_2)
% 243.91/50.38    (3)   ~ (all_8_2 = e0)
% 243.91/50.38    (4)   ~ (all_52_8 = all_52_9)
% 243.91/50.38    (5)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.91/50.38         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.91/50.38    (6)   ~ (all_52_1 = all_8_2)
% 243.91/50.39    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.91/50.39           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.91/50.39             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.91/50.39           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.91/50.39             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.91/50.39           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.91/50.39           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.91/50.39           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.91/50.39           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.91/50.39           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.91/50.39           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.91/50.39             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.91/50.39           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.91/50.39           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 243.91/50.39           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.91/50.39           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.91/50.39           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.91/50.39           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.91/50.39             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.91/50.39           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.91/50.39           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 243.91/50.39           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.91/50.39           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.91/50.39           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.91/50.39           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.91/50.39             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.91/50.39           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.91/50.39           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.91/50.39    (8)   ~ (all_52_1 = all_52_2)
% 243.91/50.39    (9)  op(e1, e0) = all_52_14
% 243.91/50.39    (10)  op(e0, e3) = all_52_3
% 243.91/50.39    (11)  all_56_21 = e0
% 243.91/50.39    (12)  op(e3, e1) = all_52_8
% 243.91/50.39    (13)  op(e2, e1) = all_52_9
% 243.91/50.39    (14)   ~ (all_52_14 = e0)
% 243.91/50.39    (15)   ~ (all_52_3 = e3)
% 243.91/50.39    (16)  op(e2, e2) = all_8_2
% 243.91/50.39    (17)  all_54_5 = all_8_2
% 243.91/50.39    (18)  op(e2, e3) = all_52_1
% 243.91/50.39    (19)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 243.91/50.39    (20)   ~ (all_52_7 = all_8_2)
% 243.91/50.39    (21)  op(e0, e2) = all_52_7
% 243.91/50.39    (22)  all_56_31 = e3
% 243.91/50.39    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.39    (24)  op(e1, e3) = all_52_2
% 243.91/50.39    (25)   ~ (all_8_2 = e3)
% 243.91/50.39    (26)  all_56_11 = all_8_2
% 243.91/50.39    (27)   ~ (all_52_13 = e3)
% 243.91/50.39    (28)  op(e2, e0) = all_52_13
% 243.91/50.39  
% 243.91/50.39  Begin of proof
% 243.91/50.39  | 
% 243.91/50.39  | BETA: splitting (19) gives:
% 243.91/50.39  | 
% 243.91/50.39  | Case 1:
% 243.91/50.39  | | 
% 243.91/50.39  | |   (29)  all_54_5 = e3
% 243.91/50.39  | | 
% 243.91/50.39  | | COMBINE_EQS: (17), (29) imply:
% 243.91/50.39  | |   (30)  all_8_2 = e3
% 243.91/50.39  | | 
% 243.91/50.39  | | REDUCE: (25), (30) imply:
% 243.91/50.39  | |   (31)  $false
% 243.91/50.39  | | 
% 243.91/50.39  | | CLOSE: (31) is inconsistent.
% 243.91/50.39  | | 
% 243.91/50.39  | Case 2:
% 243.91/50.39  | | 
% 243.91/50.39  | |   (32)   ~ (all_54_5 = e3)
% 243.91/50.39  | |   (33)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 243.91/50.39  | | 
% 243.91/50.39  | | BETA: splitting (33) gives:
% 243.91/50.39  | | 
% 243.91/50.39  | | Case 1:
% 243.91/50.39  | | | 
% 243.91/50.39  | | |   (34)  all_54_5 = e2
% 243.91/50.39  | | | 
% 243.91/50.39  | | | COMBINE_EQS: (17), (34) imply:
% 243.91/50.39  | | |   (35)  all_8_2 = e2
% 243.91/50.39  | | | 
% 243.91/50.39  | | | COMBINE_EQS: (26), (35) imply:
% 243.91/50.39  | | |   (36)  all_56_11 = e2
% 243.91/50.39  | | | 
% 243.91/50.39  | | | REDUCE: (6), (35) imply:
% 243.91/50.39  | | |   (37)   ~ (all_52_1 = e2)
% 243.91/50.39  | | | 
% 243.91/50.39  | | | REDUCE: (20), (35) imply:
% 243.91/50.39  | | |   (38)   ~ (all_52_7 = e2)
% 243.91/50.39  | | | 
% 243.91/50.39  | | | REDUCE: (2), (35) imply:
% 243.91/50.39  | | |   (39)   ~ (all_52_9 = e2)
% 243.91/50.39  | | | 
% 243.91/50.39  | | | REDUCE: (25), (35) imply:
% 243.91/50.39  | | |   (40)   ~ (e3 = e2)
% 243.91/50.39  | | | 
% 243.91/50.39  | | | SIMP: (40) implies:
% 243.91/50.39  | | |   (41)   ~ (e3 = e2)
% 243.91/50.39  | | | 
% 243.91/50.39  | | | REDUCE: (16), (35) imply:
% 243.91/50.39  | | |   (42)  op(e2, e2) = e2
% 243.91/50.39  | | | 
% 243.91/50.39  | | | BETA: splitting (7) gives:
% 243.91/50.39  | | | 
% 243.91/50.39  | | | Case 1:
% 243.91/50.39  | | | | 
% 243.91/50.39  | | | |   (43)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 243.91/50.39  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.91/50.39  | | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9
% 243.91/50.39  | | | |           = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.91/50.39  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.91/50.39  | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.91/50.39  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 243.91/50.39  | | | |           ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 243.91/50.39  | | | |         (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 243.91/50.39  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.91/50.39  | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 243.91/50.39  | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.91/50.39  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.91/50.39  | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.91/50.39  | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) & 
% 243.91/50.39  | | | |           ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.91/50.39  | | | | 
% 243.91/50.39  | | | | BETA: splitting (43) gives:
% 243.91/50.39  | | | | 
% 243.91/50.39  | | | | Case 1:
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | |   (44)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 243.91/50.39  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.91/50.39  | | | | |           & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 &
% 243.91/50.39  | | | | |           all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 243.91/50.39  | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.91/50.39  | | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.91/50.39  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.91/50.39  | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | | BETA: splitting (44) gives:
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | | Case 1:
% 243.91/50.39  | | | | | | 
% 243.91/50.39  | | | | | |   (45)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 243.91/50.39  | | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.91/50.39  | | | | | |         & op(e3, e2) = e3 & op(e2, e3) = e3
% 243.91/50.39  | | | | | | 
% 243.91/50.39  | | | | | | ALPHA: (45) implies:
% 243.91/50.39  | | | | | |   (46)   ~ (all_56_11 = e2)
% 243.91/50.39  | | | | | | 
% 243.91/50.39  | | | | | | REDUCE: (36), (46) imply:
% 243.91/50.39  | | | | | |   (47)  $false
% 243.91/50.39  | | | | | | 
% 243.91/50.39  | | | | | | CLOSE: (47) is inconsistent.
% 243.91/50.39  | | | | | | 
% 243.91/50.39  | | | | | Case 2:
% 243.91/50.39  | | | | | | 
% 243.91/50.39  | | | | | |   (48)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.91/50.39  | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 243.91/50.39  | | | | | |             e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 243.91/50.39  | | | | | |           e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 243.91/50.39  | | | | | |             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 243.91/50.39  | | | | | |             e1) = e3 & op(e1, e3) = e3)
% 243.91/50.39  | | | | | | 
% 243.91/50.39  | | | | | | BETA: splitting (48) gives:
% 243.91/50.39  | | | | | | 
% 243.91/50.39  | | | | | | Case 1:
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | |   (49)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.91/50.39  | | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 243.91/50.39  | | | | | | |           e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | | ALPHA: (49) implies:
% 243.91/50.39  | | | | | | |   (50)  op(e2, e3) = e2
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | | REF_CLOSE: (18), (23), (37), (50) are inconsistent by sub-proof
% 243.91/50.39  | | | | | | |            #2336.
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | Case 2:
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | |   (51)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.91/50.39  | | | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 243.91/50.39  | | | | | | |           e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | | ALPHA: (51) implies:
% 243.91/50.39  | | | | | | |   (52)  op(e1, e3) = e3
% 243.91/50.39  | | | | | | |   (53)  op(e3, e1) = e3
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | | GROUND_INST: instantiating (23) with all_52_2, e3, e3, e1,
% 243.91/50.39  | | | | | | |              simplifying with (24), (52) gives:
% 243.91/50.39  | | | | | | |   (54)  all_52_2 = e3
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | | GROUND_INST: instantiating (23) with all_52_8, e3, e1, e3,
% 243.91/50.39  | | | | | | |              simplifying with (12), (53) gives:
% 243.91/50.39  | | | | | | |   (55)  all_52_8 = e3
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | | REDUCE: (8), (54) imply:
% 243.91/50.39  | | | | | | |   (56)   ~ (all_52_1 = e3)
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | | REDUCE: (4), (55) imply:
% 243.91/50.39  | | | | | | |   (57)   ~ (all_52_9 = e3)
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | | SIMP: (57) implies:
% 243.91/50.39  | | | | | | |   (58)   ~ (all_52_9 = e3)
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | | REF_CLOSE: (5), (13), (18), (23), (27), (28), (41), (42), (56),
% 243.91/50.39  | | | | | | |            (58) are inconsistent by sub-proof #1321.
% 243.91/50.39  | | | | | | | 
% 243.91/50.39  | | | | | | End of split
% 243.91/50.39  | | | | | | 
% 243.91/50.39  | | | | | End of split
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | Case 2:
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | |   (59)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 243.91/50.39  | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 243.91/50.39  | | | | |           & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 243.91/50.39  | | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.91/50.39  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 243.91/50.39  | | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.91/50.39  | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.91/50.39  | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | | REF_CLOSE: (10), (15), (22), (23), (59) are inconsistent by sub-proof
% 243.91/50.39  | | | | |            #1389.
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | End of split
% 243.91/50.39  | | | | 
% 243.91/50.39  | | | Case 2:
% 243.91/50.39  | | | | 
% 243.91/50.39  | | | |   (60)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.91/50.39  | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.91/50.39  | | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 243.91/50.39  | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.91/50.39  | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.91/50.39  | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.91/50.39  | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) & 
% 243.91/50.39  | | | |           ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 243.91/50.39  | | | |         (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.91/50.39  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 243.91/50.39  | | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 243.91/50.39  | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.91/50.39  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.91/50.39  | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.91/50.39  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 243.91/50.39  | | | |           ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.91/50.39  | | | | 
% 243.91/50.39  | | | | BETA: splitting (60) gives:
% 243.91/50.39  | | | | 
% 243.91/50.39  | | | | Case 1:
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | |   (61)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 243.91/50.39  | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.91/50.39  | | | | |           & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 243.91/50.39  | | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 243.91/50.39  | | | | |           ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.91/50.39  | | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.91/50.39  | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 243.91/50.39  | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | | REF_CLOSE: (13), (21), (23), (36), (38), (39), (61) are inconsistent
% 243.91/50.39  | | | | |            by sub-proof #2325.
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | Case 2:
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | |   (62)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.91/50.39  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 243.91/50.39  | | | | |           & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 243.91/50.39  | | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.91/50.39  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.91/50.39  | | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.91/50.39  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.91/50.39  | | | | |           &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | | REF_CLOSE: (9), (11), (14), (23), (36), (62) are inconsistent by
% 243.91/50.39  | | | | |            sub-proof #1319.
% 243.91/50.39  | | | | | 
% 243.91/50.39  | | | | End of split
% 243.91/50.39  | | | | 
% 243.91/50.39  | | | End of split
% 243.91/50.39  | | | 
% 243.91/50.39  | | Case 2:
% 243.91/50.39  | | | 
% 243.91/50.39  | | |   (63)  all_54_5 = e1 | all_54_5 = e0
% 243.91/50.39  | | | 
% 243.91/50.39  | | | REF_CLOSE: (1), (3), (17), (63) are inconsistent by sub-proof #2300.
% 243.91/50.39  | | | 
% 243.91/50.39  | | End of split
% 243.91/50.39  | | 
% 243.91/50.39  | End of split
% 243.91/50.39  | 
% 243.91/50.39  End of proof
% 243.91/50.39  
% 243.91/50.39  Sub-proof #1319 shows that the following formulas are inconsistent:
% 243.91/50.39  ----------------------------------------------------------------
% 243.91/50.39    (1)  all_56_11 = e2
% 243.91/50.39    (2)  op(e1, e0) = all_52_14
% 243.91/50.39    (3)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.91/50.39             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 243.91/50.39           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.91/50.39             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.91/50.39           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 243.91/50.39           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.91/50.39           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.91/50.39    (4)  all_56_21 = e0
% 243.91/50.39    (5)   ~ (all_52_14 = e0)
% 243.91/50.39    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.39  
% 243.91/50.39  Begin of proof
% 243.91/50.39  | 
% 243.91/50.39  | BETA: splitting (3) gives:
% 243.91/50.39  | 
% 243.91/50.39  | Case 1:
% 243.91/50.39  | | 
% 243.91/50.39  | |   (7)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.91/50.39  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 243.91/50.39  | |        & op(e0, e2) = e0
% 243.91/50.39  | | 
% 243.91/50.39  | | ALPHA: (7) implies:
% 243.91/50.39  | |   (8)   ~ (all_56_11 = e2)
% 243.91/50.39  | | 
% 243.91/50.39  | | REDUCE: (1), (8) imply:
% 243.91/50.39  | |   (9)  $false
% 243.91/50.39  | | 
% 243.91/50.39  | | CLOSE: (9) is inconsistent.
% 243.91/50.39  | | 
% 243.91/50.39  | Case 2:
% 243.91/50.39  | | 
% 243.91/50.39  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.91/50.39  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.91/50.39  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.91/50.39  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.91/50.39  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.91/50.39  | | 
% 243.91/50.39  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #1320.
% 243.91/50.39  | | 
% 243.91/50.39  | End of split
% 243.91/50.39  | 
% 243.91/50.39  End of proof
% 243.91/50.39  
% 243.91/50.39  Sub-proof #1320 shows that the following formulas are inconsistent:
% 243.91/50.39  ----------------------------------------------------------------
% 243.91/50.39    (1)  op(e1, e0) = all_52_14
% 243.91/50.39    (2)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 243.91/50.39             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.91/50.39           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 243.91/50.39             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.91/50.39           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.91/50.39    (3)  all_56_21 = e0
% 243.91/50.39    (4)   ~ (all_52_14 = e0)
% 243.91/50.39    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.39  
% 243.91/50.39  Begin of proof
% 243.91/50.39  | 
% 243.91/50.39  | BETA: splitting (2) gives:
% 243.91/50.39  | 
% 243.91/50.39  | Case 1:
% 243.91/50.39  | | 
% 243.91/50.39  | |   (6)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.91/50.39  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 243.91/50.39  | |        & op(e0, e1) = e1
% 243.91/50.39  | | 
% 243.91/50.39  | | ALPHA: (6) implies:
% 243.91/50.39  | |   (7)   ~ (all_56_21 = e0)
% 243.91/50.39  | | 
% 243.91/50.39  | | REDUCE: (3), (7) imply:
% 243.91/50.39  | |   (8)  $false
% 243.91/50.39  | | 
% 243.91/50.39  | | CLOSE: (8) is inconsistent.
% 243.91/50.39  | | 
% 243.91/50.39  | Case 2:
% 243.91/50.39  | | 
% 243.91/50.39  | |   (9)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 243.91/50.39  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 243.91/50.39  | |        & op(e0, e1) = e0
% 243.91/50.39  | | 
% 243.91/50.39  | | ALPHA: (9) implies:
% 243.91/50.39  | |   (10)  op(e1, e0) = e0
% 243.91/50.39  | | 
% 243.91/50.39  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2323.
% 243.91/50.39  | | 
% 243.91/50.39  | End of split
% 243.91/50.39  | 
% 243.91/50.39  End of proof
% 243.91/50.39  
% 243.91/50.39  Sub-proof #1321 shows that the following formulas are inconsistent:
% 243.91/50.39  ----------------------------------------------------------------
% 243.91/50.39    (1)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.91/50.39         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 243.91/50.39    (2)  op(e2, e1) = all_52_9
% 243.91/50.39    (3)   ~ (e3 = e2)
% 243.91/50.39    (4)  op(e2, e3) = all_52_1
% 243.91/50.39    (5)   ~ (all_52_9 = e3)
% 243.91/50.39    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.39    (7)   ~ (all_52_13 = e3)
% 243.91/50.39    (8)  op(e2, e0) = all_52_13
% 243.91/50.39    (9)   ~ (all_52_1 = e3)
% 243.91/50.39    (10)  op(e2, e2) = e2
% 243.91/50.39  
% 243.91/50.39  Begin of proof
% 243.91/50.39  | 
% 243.91/50.39  | BETA: splitting (1) gives:
% 243.91/50.39  | 
% 243.91/50.39  | Case 1:
% 243.91/50.39  | | 
% 243.91/50.39  | |   (11)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 243.91/50.39  | |           e3)
% 243.91/50.39  | | 
% 243.91/50.39  | | REF_CLOSE: (3), (4), (6), (9), (10), (11) are inconsistent by sub-proof
% 243.91/50.39  | |            #1413.
% 243.91/50.39  | | 
% 243.91/50.39  | Case 2:
% 243.91/50.39  | | 
% 243.91/50.39  | |   (12)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 243.91/50.39  | |           e3)
% 243.91/50.39  | | 
% 243.91/50.39  | | REF_CLOSE: (2), (5), (6), (7), (8), (12) are inconsistent by sub-proof
% 243.91/50.39  | |            #1649.
% 243.91/50.39  | | 
% 243.91/50.39  | End of split
% 243.91/50.39  | 
% 243.91/50.39  End of proof
% 243.91/50.39  
% 243.91/50.39  Sub-proof #1322 shows that the following formulas are inconsistent:
% 243.91/50.39  ----------------------------------------------------------------
% 243.91/50.39    (1)  all_58_1 = e3
% 243.91/50.39    (2)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 243.91/50.39    (3)   ~ (e3 = e2)
% 243.91/50.39    (4)  op(e2, e2) = e1
% 243.91/50.40    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.40    (6)   ~ (e2 = e1)
% 243.91/50.40  
% 243.91/50.40  Begin of proof
% 243.91/50.40  | 
% 243.91/50.40  | BETA: splitting (2) gives:
% 243.91/50.40  | 
% 243.91/50.40  | Case 1:
% 243.91/50.40  | | 
% 243.91/50.40  | |   (7)  all_58_1 = e2 & op(e3, e2) = e2
% 243.91/50.40  | | 
% 243.91/50.40  | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #1590.
% 243.91/50.40  | | 
% 243.91/50.40  | Case 2:
% 243.91/50.40  | | 
% 243.91/50.40  | |   (8)  all_58_3 = e2 & op(e2, e2) = e2
% 243.91/50.40  | | 
% 243.91/50.40  | | ALPHA: (8) implies:
% 243.91/50.40  | |   (9)  op(e2, e2) = e2
% 243.91/50.40  | | 
% 243.91/50.40  | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #2235.
% 243.91/50.40  | | 
% 243.91/50.40  | End of split
% 243.91/50.40  | 
% 243.91/50.40  End of proof
% 243.91/50.40  
% 243.91/50.40  Sub-proof #1323 shows that the following formulas are inconsistent:
% 243.91/50.40  ----------------------------------------------------------------
% 243.91/50.40    (1)   ~ (all_8_2 = e0)
% 243.91/50.40    (2)   ~ (e3 = e0)
% 243.91/50.40    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 243.91/50.40    (4)  op(e2, e2) = all_8_2
% 243.91/50.40    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.91/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.91/50.40    (6)  op(e3, e2) = e3
% 243.91/50.40  
% 243.91/50.40  Begin of proof
% 243.91/50.40  | 
% 243.91/50.40  | BETA: splitting (3) gives:
% 243.91/50.40  | 
% 243.91/50.40  | Case 1:
% 243.91/50.40  | | 
% 243.91/50.40  | |   (7)  all_58_1 = e0 & op(e3, e2) = e0
% 243.91/50.40  | | 
% 243.91/50.40  | | ALPHA: (7) implies:
% 243.97/50.40  | |   (8)  op(e3, e2) = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2099.
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (9)  all_58_3 = e0 & op(e2, e2) = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1992.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1324 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)  all_56_21 = e2
% 243.97/50.40    (2)   ~ (e3 = e0)
% 243.97/50.40    (3)  op(e1, e2) = all_52_6
% 243.97/50.40    (4)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 = e0 & op(e0,
% 243.97/50.40             all_56_23) = e0 & op(e0, e1) = all_56_23 & $i(all_56_23))
% 243.97/50.40    (5)  op(e1, e2) = e0
% 243.97/50.40    (6)  op(e0, e1) = e0
% 243.97/50.40    (7)  op(e0, e0) = e3
% 243.97/50.40    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.40    (9)   ~ (e1 = e0)
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (4) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (10)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 243.97/50.40  | | 
% 243.97/50.40  | | ALPHA: (10) implies:
% 243.97/50.40  | |   (11)  op(e1, all_56_21) = e1
% 243.97/50.40  | | 
% 243.97/50.40  | | REDUCE: (1), (11) imply:
% 243.97/50.40  | |   (12)  op(e1, e2) = e1
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (3), (5), (8), (9), (12) are inconsistent by sub-proof #2136.
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (13)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 243.97/50.40  | |         $i(all_56_23)
% 243.97/50.40  | | 
% 243.97/50.40  | | ALPHA: (13) implies:
% 243.97/50.40  | |   (14)  op(e0, e1) = all_56_23
% 243.97/50.40  | |   (15)  op(e0, all_56_23) = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (2), (6), (7), (8), (14), (15) are inconsistent by sub-proof
% 243.97/50.40  | |            #1395.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1325 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)  all_58_6 = e3
% 243.97/50.40    (2)   ~ (e2 = e0)
% 243.97/50.40    (3)  all_58_7 = e0
% 243.97/50.40    (4)  all_58_11 = e1
% 243.97/50.40    (5)   ~ (e3 = e2)
% 243.97/50.40    (6)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 243.97/50.40         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 243.97/50.40    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.40    (8)  op(e1, e1) = e0
% 243.97/50.40    (9)   ~ (e2 = e1)
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (6) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (10)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 243.97/50.40  | |           e2)
% 243.97/50.40  | | 
% 243.97/50.40  | | BETA: splitting (10) gives:
% 243.97/50.40  | | 
% 243.97/50.40  | | Case 1:
% 243.97/50.40  | | | 
% 243.97/50.40  | | |   (11)  all_58_6 = e2 & op(e1, e3) = e2
% 243.97/50.40  | | | 
% 243.97/50.40  | | | ALPHA: (11) implies:
% 243.97/50.40  | | |   (12)  all_58_6 = e2
% 243.97/50.40  | | | 
% 243.97/50.40  | | | REF_CLOSE: (1), (5), (12) are inconsistent by sub-proof #2024.
% 243.97/50.40  | | | 
% 243.97/50.40  | | Case 2:
% 243.97/50.40  | | | 
% 243.97/50.40  | | |   (13)  all_58_7 = e2 & op(e1, e2) = e2
% 243.97/50.40  | | | 
% 243.97/50.40  | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #1326.
% 243.97/50.40  | | | 
% 243.97/50.40  | | End of split
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (14)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 243.97/50.40  | |           e2)
% 243.97/50.40  | | 
% 243.97/50.40  | | BETA: splitting (14) gives:
% 243.97/50.40  | | 
% 243.97/50.40  | | Case 1:
% 243.97/50.40  | | | 
% 243.97/50.40  | | |   (15)  all_58_8 = e2 & op(e1, e1) = e2
% 243.97/50.40  | | | 
% 243.97/50.40  | | | ALPHA: (15) implies:
% 243.97/50.40  | | |   (16)  op(e1, e1) = e2
% 243.97/50.40  | | | 
% 243.97/50.40  | | | REF_CLOSE: (2), (7), (8), (16) are inconsistent by sub-proof #2211.
% 243.97/50.40  | | | 
% 243.97/50.40  | | Case 2:
% 243.97/50.40  | | | 
% 243.97/50.40  | | |   (17)  all_58_11 = e2 & op(e1, e0) = e2
% 243.97/50.40  | | | 
% 243.97/50.40  | | | REF_CLOSE: (4), (9), (17) are inconsistent by sub-proof #1554.
% 243.97/50.40  | | | 
% 243.97/50.40  | | End of split
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1326 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)  all_58_7 = e2 & op(e1, e2) = e2
% 243.97/50.40    (2)  all_58_7 = e0
% 243.97/50.40    (3)   ~ (e2 = e0)
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | ALPHA: (1) implies:
% 243.97/50.40  |   (4)  all_58_7 = e2
% 243.97/50.40  | 
% 243.97/50.40  | COMBINE_EQS: (2), (4) imply:
% 243.97/50.40  |   (5)  e2 = e0
% 243.97/50.40  | 
% 243.97/50.40  | REDUCE: (3), (5) imply:
% 243.97/50.40  |   (6)  $false
% 243.97/50.40  | 
% 243.97/50.40  | CLOSE: (6) is inconsistent.
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1327 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)  all_58_1 = e1
% 243.97/50.40    (2)   ~ (e3 = e1)
% 243.97/50.40    (3)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.97/50.40         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.97/50.40    (4)  op(e3, e1) = all_52_8
% 243.97/50.40    (5)   ~ (e3 = e2)
% 243.97/50.40    (6)  op(e3, e0) = all_52_12
% 243.97/50.40    (7)  op(e3, e3) = e2
% 243.97/50.40    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.40    (9)   ~ (all_52_12 = e3)
% 243.97/50.40    (10)   ~ (all_52_8 = e3)
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (3) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 243.97/50.40  | |           e3)
% 243.97/50.40  | | 
% 243.97/50.40  | | BETA: splitting (11) gives:
% 243.97/50.40  | | 
% 243.97/50.40  | | Case 1:
% 243.97/50.40  | | | 
% 243.97/50.40  | | |   (12)  all_58_0 = e3 & op(e3, e3) = e3
% 243.97/50.40  | | | 
% 243.97/50.40  | | | ALPHA: (12) implies:
% 243.97/50.40  | | |   (13)  op(e3, e3) = e3
% 243.97/50.40  | | | 
% 243.97/50.40  | | | REF_CLOSE: (5), (7), (8), (13) are inconsistent by sub-proof #2194.
% 243.97/50.40  | | | 
% 243.97/50.40  | | Case 2:
% 243.97/50.40  | | | 
% 243.97/50.40  | | |   (14)  all_58_1 = e3 & op(e3, e2) = e3
% 243.97/50.40  | | | 
% 243.97/50.40  | | | REF_CLOSE: (1), (2), (14) are inconsistent by sub-proof #1723.
% 243.97/50.40  | | | 
% 243.97/50.40  | | End of split
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 243.97/50.40  | |           e3)
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (4), (6), (8), (9), (10), (15) are inconsistent by sub-proof
% 243.97/50.40  | |            #1515.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1328 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)  all_58_6 = e3
% 243.97/50.40    (2)   ~ (e2 = e0)
% 243.97/50.40    (3)  all_58_12 = e1
% 243.97/50.40    (4)  op(e3, e3) = e1
% 243.97/50.40    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.97/50.40         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.97/50.40    (6)   ~ (e3 = e2)
% 243.97/50.40    (7)  all_58_2 = e0
% 243.97/50.40    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.40    (9)   ~ (e2 = e1)
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (5) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 243.97/50.40  | |           e2)
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (2), (4), (7), (8), (9), (10) are inconsistent by sub-proof
% 243.97/50.40  | |            #1329.
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (11)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 243.97/50.40  | |           e2)
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (1), (3), (6), (9), (11) are inconsistent by sub-proof #1574.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1329 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)   ~ (e2 = e0)
% 243.97/50.40    (2)  op(e3, e3) = e1
% 243.97/50.40    (3)  all_58_2 = e0
% 243.97/50.40    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 243.97/50.40    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.40    (6)   ~ (e2 = e1)
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (4) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 243.97/50.40  | | 
% 243.97/50.40  | | ALPHA: (7) implies:
% 243.97/50.40  | |   (8)  op(e3, e3) = e2
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2267.
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (9)  all_58_2 = e2 & op(e2, e3) = e2
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1575.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1330 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)   ~ (all_52_12 = e0)
% 243.97/50.40    (2)  op(e1, e0) = all_52_14
% 243.97/50.40    (3)  op(e1, e0) = e1
% 243.97/50.40    (4)   ~ (all_52_12 = all_52_14)
% 243.97/50.40    (5)   ~ (all_52_12 = e2)
% 243.97/50.40    (6)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 243.97/50.40    (7)  all_54_3 = all_52_12
% 243.97/50.40    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (6) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (9)  all_54_3 = e2
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (5), (7), (9) are inconsistent by sub-proof #2290.
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (10)  all_54_3 = e1 | all_54_3 = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10) are inconsistent by sub-proof
% 243.97/50.40  | |            #1331.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1331 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)  all_54_3 = e1 | all_54_3 = e0
% 243.97/50.40    (2)   ~ (all_52_12 = e0)
% 243.97/50.40    (3)  op(e1, e0) = all_52_14
% 243.97/50.40    (4)  op(e1, e0) = e1
% 243.97/50.40    (5)   ~ (all_52_12 = all_52_14)
% 243.97/50.40    (6)  all_54_3 = all_52_12
% 243.97/50.40    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (1) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (8)  all_54_3 = e1
% 243.97/50.40  | | 
% 243.97/50.40  | | COMBINE_EQS: (6), (8) imply:
% 243.97/50.40  | |   (9)  all_52_12 = e1
% 243.97/50.40  | | 
% 243.97/50.40  | | SIMP: (9) implies:
% 243.97/50.40  | |   (10)  all_52_12 = e1
% 243.97/50.40  | | 
% 243.97/50.40  | | REDUCE: (5), (10) imply:
% 243.97/50.40  | |   (11)   ~ (all_52_14 = e1)
% 243.97/50.40  | | 
% 243.97/50.40  | | SIMP: (11) implies:
% 243.97/50.40  | |   (12)   ~ (all_52_14 = e1)
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (3), (4), (7), (12) are inconsistent by sub-proof #2304.
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (13)  all_54_3 = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (2), (6), (13) are inconsistent by sub-proof #2288.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1332 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)  op(e1, e2) = e1
% 243.97/50.40    (2)   ~ (e3 = e1)
% 243.97/50.40    (3)  op(e1, e2) = e3
% 243.97/50.40    (4)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) = all_40_1
% 243.97/50.40           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2) =
% 243.97/50.40           all_40_1 & $i(all_40_1))
% 243.97/50.40    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.40    (6)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) = all_36_1
% 243.97/50.40           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2) =
% 243.97/50.40           all_36_1 & $i(all_36_1))
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (4) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (7)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 243.97/50.40  | |        all_40_1 & $i(all_40_0) & $i(all_40_1)
% 243.97/50.40  | | 
% 243.97/50.40  | | ALPHA: (7) implies:
% 243.97/50.40  | |   (8)  op(e1, e2) = all_40_1
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (1), (2), (3), (5), (6), (8) are inconsistent by sub-proof #1700.
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (9)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #2144.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1333 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)   ~ (e2 = e0)
% 243.97/50.40    (2)  op(e0, e2) = e2
% 243.97/50.40    (3)  op(e0, e1) = e1
% 243.97/50.40    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.40    (5)   ~ (e1 = e0)
% 243.97/50.40    (6)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (6) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (7)  all_58_13 = e0 & op(e0, e2) = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | ALPHA: (7) implies:
% 243.97/50.40  | |   (8)  op(e0, e2) = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2132.
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | ALPHA: (9) implies:
% 243.97/50.40  | |   (10)  op(e0, e1) = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #2158.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1334 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)   ~ (all_52_12 = e0)
% 243.97/50.40    (2)   ~ (all_52_8 = e0)
% 243.97/50.40    (3)  op(e3, e1) = all_52_8
% 243.97/50.40    (4)  op(e3, e0) = all_52_12
% 243.97/50.40    (5)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 243.97/50.40    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (5) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (7)  all_58_4 = e0 & op(e3, e1) = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #1908.
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (8)  all_58_9 = e0 & op(e3, e0) = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | ALPHA: (8) implies:
% 243.97/50.40  | |   (9)  op(e3, e0) = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #2258.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1335 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)   ~ (all_52_8 = e0)
% 243.97/50.40    (2)   ~ (all_52_8 = e1)
% 243.97/50.40    (3)  all_54_2 = all_52_8
% 243.97/50.40    (4)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.97/50.40    (5)   ~ (all_52_8 = e2)
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (4) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (6)  all_54_2 = e2
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #1986.
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (7)  all_54_2 = e1 | all_54_2 = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #1336.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1336 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)  all_54_2 = e1 | all_54_2 = e0
% 243.97/50.40    (2)  all_54_2 = all_52_8
% 243.97/50.40    (3)   ~ (all_52_8 = e1)
% 243.97/50.40    (4)   ~ (all_52_8 = e0)
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | BETA: splitting (1) gives:
% 243.97/50.40  | 
% 243.97/50.40  | Case 1:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (5)  all_54_2 = e1
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1337.
% 243.97/50.40  | | 
% 243.97/50.40  | Case 2:
% 243.97/50.40  | | 
% 243.97/50.40  | |   (6)  all_54_2 = e0
% 243.97/50.40  | | 
% 243.97/50.40  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1643.
% 243.97/50.40  | | 
% 243.97/50.40  | End of split
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1337 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.40    (1)  all_54_2 = all_52_8
% 243.97/50.40    (2)  all_54_2 = e1
% 243.97/50.40    (3)   ~ (all_52_8 = e1)
% 243.97/50.40  
% 243.97/50.40  Begin of proof
% 243.97/50.40  | 
% 243.97/50.40  | COMBINE_EQS: (1), (2) imply:
% 243.97/50.40  |   (4)  all_52_8 = e1
% 243.97/50.40  | 
% 243.97/50.40  | SIMP: (4) implies:
% 243.97/50.40  |   (5)  all_52_8 = e1
% 243.97/50.40  | 
% 243.97/50.40  | REDUCE: (3), (5) imply:
% 243.97/50.40  |   (6)  $false
% 243.97/50.40  | 
% 243.97/50.40  | CLOSE: (6) is inconsistent.
% 243.97/50.40  | 
% 243.97/50.40  End of proof
% 243.97/50.40  
% 243.97/50.40  Sub-proof #1338 shows that the following formulas are inconsistent:
% 243.97/50.40  ----------------------------------------------------------------
% 243.97/50.41    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 243.97/50.41         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 243.97/50.41    (2)   ~ (e2 = e0)
% 243.97/50.41    (3)  all_58_1 = e0
% 243.97/50.41    (4)  op(e3, e3) = e1
% 243.97/50.41    (5)   ~ (e3 = e2)
% 243.97/50.41    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.41    (7)  all_58_4 = e3
% 243.97/50.41    (8)  all_58_9 = e1
% 243.97/50.41    (9)   ~ (e2 = e1)
% 243.97/50.41  
% 243.97/50.41  Begin of proof
% 243.97/50.41  | 
% 243.97/50.41  | BETA: splitting (1) gives:
% 243.97/50.41  | 
% 243.97/50.41  | Case 1:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 243.97/50.41  | |           e2)
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (2), (3), (4), (6), (9), (10) are inconsistent by sub-proof
% 243.97/50.41  | |            #1477.
% 243.97/50.41  | | 
% 243.97/50.41  | Case 2:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 243.97/50.41  | |           e2)
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (5), (7), (8), (9), (11) are inconsistent by sub-proof #1475.
% 243.97/50.41  | | 
% 243.97/50.41  | End of split
% 243.97/50.41  | 
% 243.97/50.41  End of proof
% 243.97/50.41  
% 243.97/50.41  Sub-proof #1339 shows that the following formulas are inconsistent:
% 243.97/50.41  ----------------------------------------------------------------
% 243.97/50.41    (1)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 243.97/50.41    (2)   ~ (e3 = e1)
% 243.97/50.41    (3)  op(e2, e1) = all_52_9
% 243.97/50.41    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.41    (5)  all_58_4 = e3
% 243.97/50.41    (6)   ~ (all_52_9 = e1)
% 243.97/50.41  
% 243.97/50.41  Begin of proof
% 243.97/50.41  | 
% 243.97/50.41  | BETA: splitting (1) gives:
% 243.97/50.41  | 
% 243.97/50.41  | Case 1:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (7)  all_58_4 = e1 & op(e3, e1) = e1
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #2042.
% 243.97/50.41  | | 
% 243.97/50.41  | Case 2:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (8)  all_58_5 = e1 & op(e2, e1) = e1
% 243.97/50.41  | | 
% 243.97/50.41  | | ALPHA: (8) implies:
% 243.97/50.41  | |   (9)  op(e2, e1) = e1
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #2306.
% 243.97/50.41  | | 
% 243.97/50.41  | End of split
% 243.97/50.41  | 
% 243.97/50.41  End of proof
% 243.97/50.41  
% 243.97/50.41  Sub-proof #1340 shows that the following formulas are inconsistent:
% 243.97/50.41  ----------------------------------------------------------------
% 243.97/50.41    (1)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 243.97/50.41    (2)  op(e3, e3) = e2
% 243.97/50.41    (3)  op(e3, e2) = all_52_4
% 243.97/50.41    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.41    (5)   ~ (all_52_4 = e1)
% 243.97/50.41    (6)   ~ (e2 = e1)
% 243.97/50.41  
% 243.97/50.41  Begin of proof
% 243.97/50.41  | 
% 243.97/50.41  | BETA: splitting (1) gives:
% 243.97/50.41  | 
% 243.97/50.41  | Case 1:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 243.97/50.41  | | 
% 243.97/50.41  | | ALPHA: (7) implies:
% 243.97/50.41  | |   (8)  op(e3, e3) = e1
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2267.
% 243.97/50.41  | | 
% 243.97/50.41  | Case 2:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (9)  all_58_1 = e1 & op(e3, e2) = e1
% 243.97/50.41  | | 
% 243.97/50.41  | | ALPHA: (9) implies:
% 243.97/50.41  | |   (10)  op(e3, e2) = e1
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #2228.
% 243.97/50.41  | | 
% 243.97/50.41  | End of split
% 243.97/50.41  | 
% 243.97/50.41  End of proof
% 243.97/50.41  
% 243.97/50.41  Sub-proof #1341 shows that the following formulas are inconsistent:
% 243.97/50.41  ----------------------------------------------------------------
% 243.97/50.41    (1)  all_58_6 = e2
% 243.97/50.41    (2)  op(e0, e3) = all_52_3
% 243.97/50.41    (3)   ~ (e3 = e1)
% 243.97/50.41    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.97/50.41         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.97/50.41    (5)   ~ (e3 = e2)
% 243.97/50.41    (6)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 243.97/50.41    (7)   ~ (all_52_3 = e3)
% 243.97/50.41    (8)  op(e3, e3) = e2
% 243.97/50.41    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.41    (10)   ~ (e2 = e1)
% 243.97/50.41  
% 243.97/50.41  Begin of proof
% 243.97/50.41  | 
% 243.97/50.41  | BETA: splitting (6) gives:
% 243.97/50.41  | 
% 243.97/50.41  | Case 1:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (11)  all_58_0 = e1 & op(e3, e3) = e1
% 243.97/50.41  | | 
% 243.97/50.41  | | ALPHA: (11) implies:
% 243.97/50.41  | |   (12)  op(e3, e3) = e1
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (8), (9), (10), (12) are inconsistent by sub-proof #2267.
% 243.97/50.41  | | 
% 243.97/50.41  | Case 2:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (13)  all_58_2 = e1 & op(e2, e3) = e1
% 243.97/50.41  | | 
% 243.97/50.41  | | ALPHA: (13) implies:
% 243.97/50.41  | |   (14)  all_58_2 = e1
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (14) are inconsistent by
% 243.97/50.41  | |            sub-proof #1342.
% 243.97/50.41  | | 
% 243.97/50.41  | End of split
% 243.97/50.41  | 
% 243.97/50.41  End of proof
% 243.97/50.41  
% 243.97/50.41  Sub-proof #1342 shows that the following formulas are inconsistent:
% 243.97/50.41  ----------------------------------------------------------------
% 243.97/50.41    (1)  all_58_6 = e2
% 243.97/50.41    (2)  op(e0, e3) = all_52_3
% 243.97/50.41    (3)   ~ (e3 = e1)
% 243.97/50.41    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.97/50.41         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.97/50.41    (5)   ~ (e3 = e2)
% 243.97/50.41    (6)   ~ (all_52_3 = e3)
% 243.97/50.41    (7)  op(e3, e3) = e2
% 243.97/50.41    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.41    (9)  all_58_2 = e1
% 243.97/50.41  
% 243.97/50.41  Begin of proof
% 243.97/50.41  | 
% 243.97/50.41  | BETA: splitting (4) gives:
% 243.97/50.41  | 
% 243.97/50.41  | Case 1:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (10)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 243.97/50.41  | |           e3)
% 243.97/50.41  | | 
% 243.97/50.41  | | BETA: splitting (10) gives:
% 243.97/50.41  | | 
% 243.97/50.41  | | Case 1:
% 243.97/50.41  | | | 
% 243.97/50.41  | | |   (11)  all_58_0 = e3 & op(e3, e3) = e3
% 243.97/50.41  | | | 
% 243.97/50.41  | | | ALPHA: (11) implies:
% 243.97/50.41  | | |   (12)  op(e3, e3) = e3
% 243.97/50.41  | | | 
% 243.97/50.41  | | | REF_CLOSE: (5), (7), (8), (12) are inconsistent by sub-proof #2194.
% 243.97/50.41  | | | 
% 243.97/50.41  | | Case 2:
% 243.97/50.41  | | | 
% 243.97/50.41  | | |   (13)  all_58_2 = e3 & op(e2, e3) = e3
% 243.97/50.41  | | | 
% 243.97/50.41  | | | ALPHA: (13) implies:
% 243.97/50.41  | | |   (14)  all_58_2 = e3
% 243.97/50.41  | | | 
% 243.97/50.41  | | | REF_CLOSE: (3), (9), (14) are inconsistent by sub-proof #1691.
% 243.97/50.41  | | | 
% 243.97/50.41  | | End of split
% 243.97/50.41  | | 
% 243.97/50.41  | Case 2:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (15)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 243.97/50.41  | |           e3)
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (1), (2), (5), (6), (8), (15) are inconsistent by sub-proof
% 243.97/50.41  | |            #1349.
% 243.97/50.41  | | 
% 243.97/50.41  | End of split
% 243.97/50.41  | 
% 243.97/50.41  End of proof
% 243.97/50.41  
% 243.97/50.41  Sub-proof #1343 shows that the following formulas are inconsistent:
% 243.97/50.41  ----------------------------------------------------------------
% 243.97/50.41    (1)  op(e1, e0) = all_52_14
% 243.97/50.41    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.97/50.41             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 243.97/50.41           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.97/50.41             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.97/50.41           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 243.97/50.41           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.97/50.41           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.97/50.41    (3)   ~ (all_52_14 = e1)
% 243.97/50.41    (4)  all_56_1 = e2
% 243.97/50.41    (5)  all_56_21 = e1
% 243.97/50.41    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.41  
% 243.97/50.41  Begin of proof
% 243.97/50.41  | 
% 243.97/50.41  | BETA: splitting (2) gives:
% 243.97/50.41  | 
% 243.97/50.41  | Case 1:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (7)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.97/50.41  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 243.97/50.41  | |        & op(e0, e2) = e0
% 243.97/50.41  | | 
% 243.97/50.41  | | ALPHA: (7) implies:
% 243.97/50.41  | |   (8)   ~ (all_56_1 = e2)
% 243.97/50.41  | | 
% 243.97/50.41  | | REDUCE: (4), (8) imply:
% 243.97/50.41  | |   (9)  $false
% 243.97/50.41  | | 
% 243.97/50.41  | | CLOSE: (9) is inconsistent.
% 243.97/50.41  | | 
% 243.97/50.41  | Case 2:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.97/50.41  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.97/50.41  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.97/50.41  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 243.97/50.41  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #1409.
% 243.97/50.41  | | 
% 243.97/50.41  | End of split
% 243.97/50.41  | 
% 243.97/50.41  End of proof
% 243.97/50.41  
% 243.97/50.41  Sub-proof #1344 shows that the following formulas are inconsistent:
% 243.97/50.41  ----------------------------------------------------------------
% 243.97/50.41    (1)   ~ (e3 = e0)
% 243.97/50.41    (2)   ~ (e2 = e0)
% 243.97/50.41    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.97/50.41         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.97/50.41    (4)  all_58_15 = e3
% 243.97/50.41    (5)   ~ (e3 = e1)
% 243.97/50.41    (6)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.97/50.41             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.97/50.41               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.97/50.41               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.97/50.41    (7)  op(e2, e0) = e2
% 243.97/50.41    (8)  all_58_11 = e2
% 243.97/50.41    (9)  op(e0, e0) = e3
% 243.97/50.41    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.41    (11)   ~ (e1 = e0)
% 243.97/50.41    (12)   ~ (e2 = e1)
% 243.97/50.41  
% 243.97/50.41  Begin of proof
% 243.97/50.41  | 
% 243.97/50.41  | BETA: splitting (6) gives:
% 243.97/50.41  | 
% 243.97/50.41  | Case 1:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (13)  all_58_15 = e0 & op(e0, e0) = e0
% 243.97/50.41  | | 
% 243.97/50.41  | | ALPHA: (13) implies:
% 243.97/50.41  | |   (14)  op(e0, e0) = e0
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (1), (9), (10), (14) are inconsistent by sub-proof #2079.
% 243.97/50.41  | | 
% 243.97/50.41  | Case 2:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (15)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.97/50.41  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 243.97/50.41  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.97/50.41  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 243.97/50.41  | | 
% 243.97/50.41  | | ALPHA: (15) implies:
% 243.97/50.41  | |   (16)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.97/50.41  | |           e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (12), (16) are
% 243.97/50.41  | |            inconsistent by sub-proof #1345.
% 243.97/50.41  | | 
% 243.97/50.41  | End of split
% 243.97/50.41  | 
% 243.97/50.41  End of proof
% 243.97/50.41  
% 243.97/50.41  Sub-proof #1345 shows that the following formulas are inconsistent:
% 243.97/50.41  ----------------------------------------------------------------
% 243.97/50.41    (1)   ~ (e2 = e0)
% 243.97/50.41    (2)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 243.97/50.41         (all_58_11 = e0 & op(e1, e0) = e0)
% 243.97/50.41    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 243.97/50.41         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.97/50.41    (4)  all_58_15 = e3
% 243.97/50.41    (5)   ~ (e3 = e1)
% 243.97/50.41    (6)  op(e2, e0) = e2
% 243.97/50.41    (7)  all_58_11 = e2
% 243.97/50.41    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.41    (9)   ~ (e1 = e0)
% 243.97/50.41    (10)   ~ (e2 = e1)
% 243.97/50.41  
% 243.97/50.41  Begin of proof
% 243.97/50.41  | 
% 243.97/50.41  | BETA: splitting (3) gives:
% 243.97/50.41  | 
% 243.97/50.41  | Case 1:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (11)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 243.97/50.41  | |           e1)
% 243.97/50.41  | | 
% 243.97/50.41  | | BETA: splitting (11) gives:
% 243.97/50.41  | | 
% 243.97/50.41  | | Case 1:
% 243.97/50.41  | | | 
% 243.97/50.41  | | |   (12)  all_58_9 = e1 & op(e3, e0) = e1
% 243.97/50.41  | | | 
% 243.97/50.41  | | | ALPHA: (12) implies:
% 243.97/50.41  | | |   (13)  all_58_9 = e1
% 243.97/50.41  | | | 
% 243.97/50.41  | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (13) are inconsistent by
% 243.97/50.41  | | |            sub-proof #1347.
% 243.97/50.41  | | | 
% 243.97/50.41  | | Case 2:
% 243.97/50.41  | | | 
% 243.97/50.41  | | |   (14)  all_58_10 = e1 & op(e2, e0) = e1
% 243.97/50.41  | | | 
% 243.97/50.41  | | | ALPHA: (14) implies:
% 243.97/50.41  | | |   (15)  op(e2, e0) = e1
% 243.97/50.41  | | | 
% 243.97/50.41  | | | REF_CLOSE: (6), (8), (10), (15) are inconsistent by sub-proof #1659.
% 243.97/50.41  | | | 
% 243.97/50.41  | | End of split
% 243.97/50.41  | | 
% 243.97/50.41  | Case 2:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (16)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.97/50.41  | |           e1)
% 243.97/50.41  | | 
% 243.97/50.41  | | BETA: splitting (16) gives:
% 243.97/50.41  | | 
% 243.97/50.41  | | Case 1:
% 243.97/50.41  | | | 
% 243.97/50.41  | | |   (17)  all_58_11 = e1 & op(e1, e0) = e1
% 243.97/50.41  | | | 
% 243.97/50.41  | | | REF_CLOSE: (7), (10), (17) are inconsistent by sub-proof #1346.
% 243.97/50.41  | | | 
% 243.97/50.41  | | Case 2:
% 243.97/50.41  | | | 
% 243.97/50.41  | | |   (18)  all_58_15 = e1 & op(e0, e0) = e1
% 243.97/50.41  | | | 
% 243.97/50.41  | | | REF_CLOSE: (4), (5), (18) are inconsistent by sub-proof #1393.
% 243.97/50.41  | | | 
% 243.97/50.41  | | End of split
% 243.97/50.41  | | 
% 243.97/50.41  | End of split
% 243.97/50.41  | 
% 243.97/50.41  End of proof
% 243.97/50.41  
% 243.97/50.41  Sub-proof #1346 shows that the following formulas are inconsistent:
% 243.97/50.41  ----------------------------------------------------------------
% 243.97/50.41    (1)  all_58_11 = e1 & op(e1, e0) = e1
% 243.97/50.41    (2)  all_58_11 = e2
% 243.97/50.41    (3)   ~ (e2 = e1)
% 243.97/50.41  
% 243.97/50.41  Begin of proof
% 243.97/50.41  | 
% 243.97/50.41  | ALPHA: (1) implies:
% 243.97/50.41  |   (4)  all_58_11 = e1
% 243.97/50.41  | 
% 243.97/50.41  | COMBINE_EQS: (2), (4) imply:
% 243.97/50.41  |   (5)  e2 = e1
% 243.97/50.41  | 
% 243.97/50.41  | REDUCE: (3), (5) imply:
% 243.97/50.41  |   (6)  $false
% 243.97/50.41  | 
% 243.97/50.41  | CLOSE: (6) is inconsistent.
% 243.97/50.41  | 
% 243.97/50.41  End of proof
% 243.97/50.41  
% 243.97/50.41  Sub-proof #1347 shows that the following formulas are inconsistent:
% 243.97/50.41  ----------------------------------------------------------------
% 243.97/50.41    (1)   ~ (e2 = e0)
% 243.97/50.41    (2)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 243.97/50.41         (all_58_11 = e0 & op(e1, e0) = e0)
% 243.97/50.41    (3)  op(e2, e0) = e2
% 243.97/50.41    (4)  all_58_11 = e2
% 243.97/50.41    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.41    (6)   ~ (e1 = e0)
% 243.97/50.41    (7)  all_58_9 = e1
% 243.97/50.41  
% 243.97/50.41  Begin of proof
% 243.97/50.41  | 
% 243.97/50.41  | BETA: splitting (2) gives:
% 243.97/50.41  | 
% 243.97/50.41  | Case 1:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (8)  all_58_9 = e0 & op(e3, e0) = e0
% 243.97/50.41  | | 
% 243.97/50.41  | | REF_CLOSE: (6), (7), (8) are inconsistent by sub-proof #1696.
% 243.97/50.41  | | 
% 243.97/50.41  | Case 2:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (9)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.97/50.41  | |          e0)
% 243.97/50.41  | | 
% 243.97/50.41  | | BETA: splitting (9) gives:
% 243.97/50.41  | | 
% 243.97/50.41  | | Case 1:
% 243.97/50.41  | | | 
% 243.97/50.41  | | |   (10)  all_58_10 = e0 & op(e2, e0) = e0
% 243.97/50.41  | | | 
% 243.97/50.41  | | | ALPHA: (10) implies:
% 243.97/50.41  | | |   (11)  op(e2, e0) = e0
% 243.97/50.41  | | | 
% 243.97/50.41  | | | REF_CLOSE: (1), (3), (5), (11) are inconsistent by sub-proof #2121.
% 243.97/50.41  | | | 
% 243.97/50.41  | | Case 2:
% 243.97/50.41  | | | 
% 243.97/50.41  | | |   (12)  all_58_11 = e0 & op(e1, e0) = e0
% 243.97/50.41  | | | 
% 243.97/50.41  | | | REF_CLOSE: (1), (4), (12) are inconsistent by sub-proof #2033.
% 243.97/50.41  | | | 
% 243.97/50.41  | | End of split
% 243.97/50.41  | | 
% 243.97/50.41  | End of split
% 243.97/50.41  | 
% 243.97/50.41  End of proof
% 243.97/50.41  
% 243.97/50.41  Sub-proof #1348 shows that the following formulas are inconsistent:
% 243.97/50.41  ----------------------------------------------------------------
% 243.97/50.41    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 243.97/50.41           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 243.97/50.41           all_12_1 & $i(all_12_1))
% 243.97/50.41    (2)   ~ (e3 = e0)
% 243.97/50.41    (3)   ~ (e2 = e0)
% 243.97/50.41    (4)  all_58_6 = e2
% 243.97/50.41    (5)  op(e0, e3) = all_52_3
% 243.97/50.41    (6)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 243.97/50.41           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 243.97/50.41           all_26_1 & $i(all_26_1))
% 243.97/50.41    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 243.97/50.41         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.97/50.41    (8)   ~ (e3 = e2)
% 243.97/50.41    (9)  op(e0, e3) = e1
% 243.97/50.41    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.97/50.41          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.97/50.41    (11)   ~ (all_52_3 = e3)
% 243.97/50.41    (12)  op(e3, e3) = e2
% 243.97/50.41    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.41    (14)   ~ (e1 = e0)
% 243.97/50.41  
% 243.97/50.41  Begin of proof
% 243.97/50.41  | 
% 243.97/50.41  | BETA: splitting (7) gives:
% 243.97/50.41  | 
% 243.97/50.41  | Case 1:
% 243.97/50.41  | | 
% 243.97/50.41  | |   (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 243.97/50.41  | |           e3)
% 243.97/50.41  | | 
% 243.97/50.41  | | BETA: splitting (15) gives:
% 243.97/50.41  | | 
% 243.97/50.41  | | Case 1:
% 243.97/50.41  | | | 
% 243.97/50.41  | | |   (16)  all_58_0 = e3 & op(e3, e3) = e3
% 243.97/50.41  | | | 
% 243.97/50.41  | | | ALPHA: (16) implies:
% 243.97/50.41  | | |   (17)  op(e3, e3) = e3
% 243.97/50.41  | | | 
% 243.97/50.41  | | | REF_CLOSE: (8), (12), (13), (17) are inconsistent by sub-proof #2194.
% 243.97/50.41  | | | 
% 243.97/50.41  | | Case 2:
% 243.97/50.41  | | | 
% 243.97/50.41  | | |   (18)  all_58_2 = e3 & op(e2, e3) = e3
% 243.97/50.41  | | | 
% 243.97/50.41  | | | ALPHA: (18) implies:
% 243.97/50.41  | | |   (19)  all_58_2 = e3
% 243.97/50.41  | | | 
% 243.97/50.41  | | | BETA: splitting (10) gives:
% 243.97/50.41  | | | 
% 243.97/50.41  | | | Case 1:
% 243.97/50.41  | | | | 
% 243.97/50.41  | | | |   (20)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 243.97/50.41  | | | |           = e0)
% 243.97/50.41  | | | | 
% 243.97/50.41  | | | | REF_CLOSE: (2), (3), (12), (13), (19), (20) are inconsistent by
% 243.97/50.41  | | | |            sub-proof #1350.
% 243.97/50.41  | | | | 
% 243.97/50.41  | | | Case 2:
% 243.97/50.41  | | | | 
% 243.97/50.42  | | | |   (21)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 243.97/50.42  | | | |           = e0)
% 243.97/50.42  | | | | 
% 243.97/50.42  | | | | BETA: splitting (21) gives:
% 243.97/50.42  | | | | 
% 243.97/50.42  | | | | Case 1:
% 243.97/50.42  | | | | | 
% 243.97/50.42  | | | | |   (22)  all_58_6 = e0 & op(e1, e3) = e0
% 243.97/50.42  | | | | | 
% 243.97/50.42  | | | | | ALPHA: (22) implies:
% 243.97/50.42  | | | | |   (23)  all_58_6 = e0
% 243.97/50.42  | | | | | 
% 243.97/50.42  | | | | | REF_CLOSE: (3), (4), (23) are inconsistent by sub-proof #1982.
% 243.97/50.42  | | | | | 
% 243.97/50.42  | | | | Case 2:
% 243.97/50.42  | | | | | 
% 243.97/50.42  | | | | |   (24)  all_58_12 = e0 & op(e0, e3) = e0
% 243.97/50.42  | | | | | 
% 243.97/50.42  | | | | | ALPHA: (24) implies:
% 243.97/50.42  | | | | |   (25)  op(e0, e3) = e0
% 243.97/50.42  | | | | | 
% 243.97/50.42  | | | | | REF_CLOSE: (1), (6), (9), (13), (14), (25) are inconsistent by
% 243.97/50.42  | | | | |            sub-proof #1384.
% 243.97/50.42  | | | | | 
% 243.97/50.42  | | | | End of split
% 243.97/50.42  | | | | 
% 243.97/50.42  | | | End of split
% 243.97/50.42  | | | 
% 243.97/50.42  | | End of split
% 243.97/50.42  | | 
% 243.97/50.42  | Case 2:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (26)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 243.97/50.42  | |           e3)
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (4), (5), (8), (11), (13), (26) are inconsistent by sub-proof
% 243.97/50.42  | |            #1349.
% 243.97/50.42  | | 
% 243.97/50.42  | End of split
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1349 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)  all_58_6 = e2
% 243.97/50.42    (2)  op(e0, e3) = all_52_3
% 243.97/50.42    (3)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 243.97/50.42    (4)   ~ (e3 = e2)
% 243.97/50.42    (5)   ~ (all_52_3 = e3)
% 243.97/50.42    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | BETA: splitting (3) gives:
% 243.97/50.42  | 
% 243.97/50.42  | Case 1:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (7)  all_58_6 = e3 & op(e1, e3) = e3
% 243.97/50.42  | | 
% 243.97/50.42  | | ALPHA: (7) implies:
% 243.97/50.42  | |   (8)  all_58_6 = e3
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #2024.
% 243.97/50.42  | | 
% 243.97/50.42  | Case 2:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (9)  all_58_12 = e3 & op(e0, e3) = e3
% 243.97/50.42  | | 
% 243.97/50.42  | | ALPHA: (9) implies:
% 243.97/50.42  | |   (10)  op(e0, e3) = e3
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #2332.
% 243.97/50.42  | | 
% 243.97/50.42  | End of split
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1350 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)   ~ (e3 = e0)
% 243.97/50.42    (2)   ~ (e2 = e0)
% 243.97/50.42    (3)  op(e3, e3) = e2
% 243.97/50.42    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.42    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 243.97/50.42    (6)  all_58_2 = e3
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | BETA: splitting (5) gives:
% 243.97/50.42  | 
% 243.97/50.42  | Case 1:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 243.97/50.42  | | 
% 243.97/50.42  | | ALPHA: (7) implies:
% 243.97/50.42  | |   (8)  op(e3, e3) = e0
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2188.
% 243.97/50.42  | | 
% 243.97/50.42  | Case 2:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (9)  all_58_2 = e0 & op(e2, e3) = e0
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #1351.
% 243.97/50.42  | | 
% 243.97/50.42  | End of split
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1351 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)  all_58_2 = e0 & op(e2, e3) = e0
% 243.97/50.42    (2)  all_58_2 = e3
% 243.97/50.42    (3)   ~ (e3 = e0)
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | ALPHA: (1) implies:
% 243.97/50.42  |   (4)  all_58_2 = e0
% 243.97/50.42  | 
% 243.97/50.42  | COMBINE_EQS: (2), (4) imply:
% 243.97/50.42  |   (5)  e3 = e0
% 243.97/50.42  | 
% 243.97/50.42  | REDUCE: (3), (5) imply:
% 243.97/50.42  |   (6)  $false
% 243.97/50.42  | 
% 243.97/50.42  | CLOSE: (6) is inconsistent.
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1352 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)   ~ (e3 = e0)
% 243.97/50.42    (2)   ~ (e2 = e0)
% 243.97/50.42    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.97/50.42         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.97/50.42    (4)  op(e0, e2) = e2
% 243.97/50.42    (5)   ~ (e3 = e1)
% 243.97/50.42    (6)  all_58_3 = e3
% 243.97/50.42    (7)   ~ (all_52_7 = e1)
% 243.97/50.42    (8)  op(e0, e2) = all_52_7
% 243.97/50.42    (9)  all_58_1 = e2
% 243.97/50.42    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.42    (11)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.97/50.42          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.97/50.42    (12)   ~ (e1 = e0)
% 243.97/50.42    (13)   ~ (e2 = e1)
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | BETA: splitting (11) gives:
% 243.97/50.42  | 
% 243.97/50.42  | Case 1:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (14)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 243.97/50.42  | |           e1)
% 243.97/50.42  | | 
% 243.97/50.42  | | BETA: splitting (14) gives:
% 243.97/50.42  | | 
% 243.97/50.42  | | Case 1:
% 243.97/50.42  | | | 
% 243.97/50.42  | | |   (15)  all_58_1 = e1 & op(e3, e2) = e1
% 243.97/50.42  | | | 
% 243.97/50.42  | | | REF_CLOSE: (9), (13), (15) are inconsistent by sub-proof #2185.
% 243.97/50.42  | | | 
% 243.97/50.42  | | Case 2:
% 243.97/50.42  | | | 
% 243.97/50.42  | | |   (16)  all_58_3 = e1 & op(e2, e2) = e1
% 243.97/50.42  | | | 
% 243.97/50.42  | | | REF_CLOSE: (5), (6), (16) are inconsistent by sub-proof #2197.
% 243.97/50.42  | | | 
% 243.97/50.42  | | End of split
% 243.97/50.42  | | 
% 243.97/50.42  | Case 2:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (17)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 243.97/50.42  | |           e1)
% 243.97/50.42  | | 
% 243.97/50.42  | | BETA: splitting (17) gives:
% 243.97/50.42  | | 
% 243.97/50.42  | | Case 1:
% 243.97/50.42  | | | 
% 243.97/50.42  | | |   (18)  all_58_7 = e1 & op(e1, e2) = e1
% 243.97/50.42  | | | 
% 243.97/50.42  | | | ALPHA: (18) implies:
% 243.97/50.42  | | |   (19)  all_58_7 = e1
% 243.97/50.42  | | | 
% 243.97/50.42  | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (12), (19) are inconsistent
% 243.97/50.42  | | |            by sub-proof #1353.
% 243.97/50.42  | | | 
% 243.97/50.42  | | Case 2:
% 243.97/50.42  | | | 
% 243.97/50.42  | | |   (20)  all_58_13 = e1 & op(e0, e2) = e1
% 243.97/50.42  | | | 
% 243.97/50.42  | | | REF_CLOSE: (7), (8), (10), (20) are inconsistent by sub-proof #2275.
% 243.97/50.42  | | | 
% 243.97/50.42  | | End of split
% 243.97/50.42  | | 
% 243.97/50.42  | End of split
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1353 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)   ~ (e3 = e0)
% 243.97/50.42    (2)   ~ (e2 = e0)
% 243.97/50.42    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 243.97/50.42         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 243.97/50.42    (4)  op(e0, e2) = e2
% 243.97/50.42    (5)  all_58_3 = e3
% 243.97/50.42    (6)  all_58_7 = e1
% 243.97/50.42    (7)  all_58_1 = e2
% 243.97/50.42    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.42    (9)   ~ (e1 = e0)
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | BETA: splitting (3) gives:
% 243.97/50.42  | 
% 243.97/50.42  | Case 1:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 243.97/50.42  | |           e0)
% 243.97/50.42  | | 
% 243.97/50.42  | | BETA: splitting (10) gives:
% 243.97/50.42  | | 
% 243.97/50.42  | | Case 1:
% 243.97/50.42  | | | 
% 243.97/50.42  | | |   (11)  all_58_1 = e0 & op(e3, e2) = e0
% 243.97/50.42  | | | 
% 243.97/50.42  | | | REF_CLOSE: (2), (7), (11) are inconsistent by sub-proof #2187.
% 243.97/50.42  | | | 
% 243.97/50.42  | | Case 2:
% 243.97/50.42  | | | 
% 243.97/50.42  | | |   (12)  all_58_3 = e0 & op(e2, e2) = e0
% 243.97/50.42  | | | 
% 243.97/50.42  | | | REF_CLOSE: (1), (5), (12) are inconsistent by sub-proof #1719.
% 243.97/50.42  | | | 
% 243.97/50.42  | | End of split
% 243.97/50.42  | | 
% 243.97/50.42  | Case 2:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (13)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 243.97/50.42  | |           e0)
% 243.97/50.42  | | 
% 243.97/50.42  | | BETA: splitting (13) gives:
% 243.97/50.42  | | 
% 243.97/50.42  | | Case 1:
% 243.97/50.42  | | | 
% 243.97/50.42  | | |   (14)  all_58_7 = e0 & op(e1, e2) = e0
% 243.97/50.42  | | | 
% 243.97/50.42  | | | REF_CLOSE: (6), (9), (14) are inconsistent by sub-proof #1558.
% 243.97/50.42  | | | 
% 243.97/50.42  | | Case 2:
% 243.97/50.42  | | | 
% 243.97/50.42  | | |   (15)  all_58_13 = e0 & op(e0, e2) = e0
% 243.97/50.42  | | | 
% 243.97/50.42  | | | ALPHA: (15) implies:
% 243.97/50.42  | | |   (16)  op(e0, e2) = e0
% 243.97/50.42  | | | 
% 243.97/50.42  | | | REF_CLOSE: (2), (4), (8), (16) are inconsistent by sub-proof #2132.
% 243.97/50.42  | | | 
% 243.97/50.42  | | End of split
% 243.97/50.42  | | 
% 243.97/50.42  | End of split
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1354 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 243.97/50.42    (2)  op(e2, e3) = all_52_1
% 243.97/50.42    (3)  op(e3, e3) = e2
% 243.97/50.42    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.42    (5)   ~ (e2 = e1)
% 243.97/50.42    (6)   ~ (all_52_1 = e1)
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | BETA: splitting (1) gives:
% 243.97/50.42  | 
% 243.97/50.42  | Case 1:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 243.97/50.42  | | 
% 243.97/50.42  | | ALPHA: (7) implies:
% 243.97/50.42  | |   (8)  op(e3, e3) = e1
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2267.
% 243.97/50.42  | | 
% 243.97/50.42  | Case 2:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (9)  all_58_2 = e1 & op(e2, e3) = e1
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #2229.
% 243.97/50.42  | | 
% 243.97/50.42  | End of split
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1355 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)  op(e0, e3) = all_52_3
% 243.97/50.42    (2)   ~ (all_52_8 = e1)
% 243.97/50.42    (3)  op(e3, e1) = all_52_8
% 243.97/50.42    (4)   ~ (all_52_3 = e3)
% 243.97/50.42    (5)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.97/50.42           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.97/50.42             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.97/50.42           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.97/50.42             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.97/50.42           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.97/50.42           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.97/50.42           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.97/50.42           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.97/50.42           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.97/50.42           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.97/50.42             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.97/50.42           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.97/50.42           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.97/50.42    (6)  op(e2, e3) = all_52_1
% 243.97/50.42    (7)  all_56_1 = e2
% 243.97/50.42    (8)  all_56_21 = e1
% 243.97/50.42    (9)  all_56_31 = e3
% 243.97/50.42    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.42    (11)   ~ (all_52_1 = e2)
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | BETA: splitting (5) gives:
% 243.97/50.42  | 
% 243.97/50.42  | Case 1:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.97/50.42  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 243.97/50.42  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 243.97/50.42  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.97/50.42  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 243.97/50.42  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 243.97/50.42  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 243.97/50.42  | |           op(e1, e3) = e3)
% 243.97/50.42  | | 
% 243.97/50.42  | | BETA: splitting (12) gives:
% 243.97/50.42  | | 
% 243.97/50.42  | | Case 1:
% 243.97/50.42  | | | 
% 243.97/50.42  | | |   (13)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.97/50.42  | | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 243.97/50.42  | | |         e3 & op(e2, e3) = e3
% 243.97/50.42  | | | 
% 243.97/50.42  | | | ALPHA: (13) implies:
% 243.97/50.42  | | |   (14)   ~ (all_56_1 = e2)
% 243.97/50.42  | | | 
% 243.97/50.42  | | | REDUCE: (7), (14) imply:
% 243.97/50.42  | | |   (15)  $false
% 243.97/50.42  | | | 
% 243.97/50.42  | | | CLOSE: (15) is inconsistent.
% 243.97/50.42  | | | 
% 243.97/50.42  | | Case 2:
% 243.97/50.42  | | | 
% 243.97/50.42  | | |   (16)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.97/50.42  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 243.97/50.42  | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17
% 243.97/50.42  | | |           = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 243.97/50.42  | | |             = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 243.97/50.42  | | |           e3)
% 243.97/50.42  | | | 
% 243.97/50.42  | | | REF_CLOSE: (6), (8), (10), (11), (16) are inconsistent by sub-proof #2311.
% 243.97/50.42  | | | 
% 243.97/50.42  | | End of split
% 243.97/50.42  | | 
% 243.97/50.42  | Case 2:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (17)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 243.97/50.42  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 243.97/50.42  | |           e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 243.97/50.42  | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.97/50.42  | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7
% 243.97/50.42  | |           = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &
% 243.97/50.42  | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 243.97/50.42  | |           op(e0, e3) = e0)
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (1), (2), (3), (4), (9), (10), (17) are inconsistent by sub-proof
% 243.97/50.42  | |            #1411.
% 243.97/50.42  | | 
% 243.97/50.42  | End of split
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1356 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)   ~ (all_22_1 = e0)
% 243.97/50.42    (2)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 243.97/50.42           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 243.97/50.42           all_30_1 & $i(all_30_1))
% 243.97/50.42    (3)  op(e2, e1) = e0
% 243.97/50.42    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.42    (5)  op(e2, e1) = all_22_1
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | BETA: splitting (2) gives:
% 243.97/50.42  | 
% 243.97/50.42  | Case 1:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (6)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) =
% 243.97/50.42  | |        all_30_1 & $i(all_30_0) & $i(all_30_1)
% 243.97/50.42  | | 
% 243.97/50.42  | | ALPHA: (6) implies:
% 243.97/50.42  | |   (7)  op(e2, e1) = all_30_1
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (1), (3), (4), (5), (7) are inconsistent by sub-proof #1841.
% 243.97/50.42  | | 
% 243.97/50.42  | Case 2:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (8)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 & $i(all_30_1)
% 243.97/50.42  | | 
% 243.97/50.42  | | ALPHA: (8) implies:
% 243.97/50.42  | |   (9)  op(e2, e1) = all_30_1
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (1), (3), (4), (5), (9) are inconsistent by sub-proof #1841.
% 243.97/50.42  | | 
% 243.97/50.42  | End of split
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1357 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)   ~ (e3 = e1)
% 243.97/50.42    (2)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 243.97/50.42    (3)  op(e3, e2) = all_52_4
% 243.97/50.42    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.42    (5)   ~ (all_52_4 = e1)
% 243.97/50.42    (6)  op(e3, e3) = e3
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | BETA: splitting (2) gives:
% 243.97/50.42  | 
% 243.97/50.42  | Case 1:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 243.97/50.42  | | 
% 243.97/50.42  | | ALPHA: (7) implies:
% 243.97/50.42  | |   (8)  op(e3, e3) = e1
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #1578.
% 243.97/50.42  | | 
% 243.97/50.42  | Case 2:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (9)  all_58_1 = e1 & op(e3, e2) = e1
% 243.97/50.42  | | 
% 243.97/50.42  | | ALPHA: (9) implies:
% 243.97/50.42  | |   (10)  op(e3, e2) = e1
% 243.97/50.42  | | 
% 243.97/50.42  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #2228.
% 243.97/50.42  | | 
% 243.97/50.42  | End of split
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1358 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 243.97/50.42         $i(all_56_9)
% 243.97/50.42    (2)  op(e3, e2) = e2
% 243.97/50.42    (3)   ~ (all_52_4 = e3)
% 243.97/50.42    (4)  op(e3, e2) = all_52_4
% 243.97/50.42    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | ALPHA: (1) implies:
% 243.97/50.42  |   (6)  op(e3, e2) = all_56_9
% 243.97/50.42  |   (7)  op(e3, all_56_9) = e3
% 243.97/50.42  | 
% 243.97/50.42  | GROUND_INST: instantiating (5) with e2, all_56_9, e2, e3, simplifying with
% 243.97/50.42  |              (2), (6) gives:
% 243.97/50.42  |   (8)  all_56_9 = e2
% 243.97/50.42  | 
% 243.97/50.42  | REDUCE: (7), (8) imply:
% 243.97/50.42  |   (9)  op(e3, e2) = e3
% 243.97/50.42  | 
% 243.97/50.42  | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #2192.
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1359 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)  all_54_1 = e1 | all_54_1 = e0
% 243.97/50.42    (2)  all_54_1 = all_30_0
% 243.97/50.42    (3)   ~ (all_30_0 = e1)
% 243.97/50.42    (4)   ~ (all_30_0 = e0)
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | BETA: splitting (1) gives:
% 243.97/50.42  | 
% 243.97/50.42  | Case 1:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (5)  all_54_1 = e1
% 243.97/50.42  | | 
% 243.97/50.42  | | COMBINE_EQS: (2), (5) imply:
% 243.97/50.42  | |   (6)  all_30_0 = e1
% 243.97/50.42  | | 
% 243.97/50.42  | | REDUCE: (3), (6) imply:
% 243.97/50.42  | |   (7)  $false
% 243.97/50.42  | | 
% 243.97/50.42  | | CLOSE: (7) is inconsistent.
% 243.97/50.42  | | 
% 243.97/50.42  | Case 2:
% 243.97/50.42  | | 
% 243.97/50.42  | |   (8)  all_54_1 = e0
% 243.97/50.42  | | 
% 243.97/50.42  | | COMBINE_EQS: (2), (8) imply:
% 243.97/50.42  | |   (9)  all_30_0 = e0
% 243.97/50.42  | | 
% 243.97/50.42  | | REDUCE: (4), (9) imply:
% 243.97/50.42  | |   (10)  $false
% 243.97/50.42  | | 
% 243.97/50.42  | | CLOSE: (10) is inconsistent.
% 243.97/50.42  | | 
% 243.97/50.42  | End of split
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1360 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)  all_54_1 = all_30_0
% 243.97/50.42    (2)  all_54_1 = e3
% 243.97/50.42    (3)   ~ (all_30_0 = e3)
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | COMBINE_EQS: (1), (2) imply:
% 243.97/50.42  |   (4)  all_30_0 = e3
% 243.97/50.42  | 
% 243.97/50.42  | SIMP: (4) implies:
% 243.97/50.42  |   (5)  all_30_0 = e3
% 243.97/50.42  | 
% 243.97/50.42  | REDUCE: (3), (5) imply:
% 243.97/50.42  |   (6)  $false
% 243.97/50.42  | 
% 243.97/50.42  | CLOSE: (6) is inconsistent.
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1361 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)  op(e3, e1) = all_52_8
% 243.97/50.42    (2)  all_58_4 = e0 & op(e3, e1) = e0
% 243.97/50.42    (3)  op(e0, e2) = all_56_15
% 243.97/50.42    (4)  op(e0, e2) = e0
% 243.97/50.42    (5)  op(e0, e0) = e3
% 243.97/50.42    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.42    (7)  op(e0, all_56_15) = e0
% 243.97/50.42    (8)   ~ (all_52_8 = e3)
% 243.97/50.42  
% 243.97/50.42  Begin of proof
% 243.97/50.42  | 
% 243.97/50.42  | ALPHA: (2) implies:
% 243.97/50.42  |   (9)  op(e3, e1) = e0
% 243.97/50.42  | 
% 243.97/50.42  | GROUND_INST: instantiating (6) with e0, all_56_15, e2, e0, simplifying with
% 243.97/50.42  |              (3), (4) gives:
% 243.97/50.42  |   (10)  all_56_15 = e0
% 243.97/50.42  | 
% 243.97/50.42  | GROUND_INST: instantiating (6) with all_52_8, e0, e1, e3, simplifying with
% 243.97/50.42  |              (1), (9) gives:
% 243.97/50.42  |   (11)  all_52_8 = e0
% 243.97/50.42  | 
% 243.97/50.42  | REDUCE: (8), (11) imply:
% 243.97/50.42  |   (12)   ~ (e3 = e0)
% 243.97/50.42  | 
% 243.97/50.42  | SIMP: (12) implies:
% 243.97/50.42  |   (13)   ~ (e3 = e0)
% 243.97/50.42  | 
% 243.97/50.42  | REDUCE: (7), (10) imply:
% 243.97/50.42  |   (14)  op(e0, e0) = e0
% 243.97/50.42  | 
% 243.97/50.42  | REF_CLOSE: (5), (6), (13), (14) are inconsistent by sub-proof #2079.
% 243.97/50.42  | 
% 243.97/50.42  End of proof
% 243.97/50.42  
% 243.97/50.42  Sub-proof #1362 shows that the following formulas are inconsistent:
% 243.97/50.42  ----------------------------------------------------------------
% 243.97/50.42    (1)   ~ (e3 = e0)
% 243.97/50.42    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.97/50.42         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.97/50.42    (3)   ~ (e2 = e0)
% 243.97/50.42    (4)  all_58_6 = e2
% 243.97/50.42    (5)  op(e1, e0) = all_52_14
% 243.97/50.42    (6)   ~ (e3 = e1)
% 243.97/50.42    (7)  op(e1, e2) = e3
% 243.97/50.42    (8)   ~ (e3 = e2)
% 243.97/50.42    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.97/50.42         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.97/50.43    (10)   ~ (all_52_14 = e3)
% 243.97/50.43    (11)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 243.97/50.43            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 243.97/50.43              e2) = all_40_1 & $i(all_40_1))
% 243.97/50.43    (12)  op(e1, e1) = e2
% 243.97/50.43    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.43    (14)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 243.97/50.43            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 243.97/50.43              e2) = all_36_1 & $i(all_36_1))
% 243.97/50.43    (15)   ~ (e1 = e0)
% 243.97/50.43    (16)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.97/50.43          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.97/50.43    (17)   ~ (e2 = e1)
% 243.97/50.43  
% 243.97/50.43  Begin of proof
% 243.97/50.43  | 
% 243.97/50.43  | BETA: splitting (11) gives:
% 243.97/50.43  | 
% 243.97/50.43  | Case 1:
% 243.97/50.43  | | 
% 243.97/50.43  | |   (18)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 243.97/50.43  | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 243.97/50.43  | | 
% 243.97/50.43  | | ALPHA: (18) implies:
% 243.97/50.43  | |   (19)  op(e1, e2) = all_40_1
% 243.97/50.43  | | 
% 243.97/50.43  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 243.97/50.43  | |            (14), (15), (16), (17), (19) are inconsistent by sub-proof #1405.
% 243.97/50.43  | | 
% 243.97/50.43  | Case 2:
% 243.97/50.43  | | 
% 243.97/50.43  | |   (20)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 243.97/50.43  | | 
% 243.97/50.43  | | ALPHA: (20) implies:
% 243.97/50.43  | |   (21)  op(e1, e2) = all_40_1
% 243.97/50.43  | | 
% 243.97/50.43  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 243.97/50.43  | |            (14), (15), (16), (17), (21) are inconsistent by sub-proof #1405.
% 243.97/50.43  | | 
% 243.97/50.43  | End of split
% 243.97/50.43  | 
% 243.97/50.43  End of proof
% 243.97/50.43  
% 243.97/50.43  Sub-proof #1363 shows that the following formulas are inconsistent:
% 243.97/50.43  ----------------------------------------------------------------
% 243.97/50.43    (1)   ~ (e3 = e0)
% 243.97/50.43    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 243.97/50.43         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 243.97/50.43    (3)   ~ (e2 = e0)
% 243.97/50.43    (4)  all_58_10 = e0 & op(e2, e0) = e0
% 243.97/50.43    (5)  op(e1, e2) = all_52_6
% 243.97/50.43    (6)   ~ (e3 = e1)
% 243.97/50.43    (7)   ~ (e3 = e2)
% 243.97/50.43    (8)  all_58_7 = e3
% 243.97/50.43    (9)  op(e3, e0) = all_52_12
% 243.97/50.43    (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 243.97/50.43          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 243.97/50.43    (11)   ~ (all_52_12 = e2)
% 243.97/50.43    (12)  op(e1, e1) = e2
% 243.97/50.43    (13)  op(e0, e0) = e3
% 243.97/50.43    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.43    (15)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.97/50.43          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.97/50.43    (16)   ~ (e1 = e0)
% 243.97/50.43    (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.97/50.43          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.97/50.43    (18)   ~ (e2 = e1)
% 243.97/50.43  
% 243.97/50.43  Begin of proof
% 243.97/50.43  | 
% 243.97/50.43  | ALPHA: (4) implies:
% 243.97/50.43  |   (19)  op(e2, e0) = e0
% 243.97/50.43  | 
% 243.97/50.43  | BETA: splitting (15) gives:
% 243.97/50.43  | 
% 243.97/50.43  | Case 1:
% 243.97/50.43  | | 
% 243.97/50.43  | |   (20)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 243.97/50.43  | |           e2)
% 243.97/50.43  | | 
% 243.97/50.43  | | REF_CLOSE: (3), (9), (11), (14), (19), (20) are inconsistent by sub-proof
% 243.97/50.43  | |            #1364.
% 243.97/50.43  | | 
% 243.97/50.43  | Case 2:
% 243.97/50.43  | | 
% 243.97/50.43  | |   (21)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 243.97/50.43  | |           e2)
% 243.97/50.43  | | 
% 243.97/50.43  | | BETA: splitting (21) gives:
% 243.97/50.43  | | 
% 243.97/50.43  | | Case 1:
% 243.97/50.43  | | | 
% 243.97/50.43  | | |   (22)  all_58_11 = e2 & op(e1, e0) = e2
% 243.97/50.43  | | | 
% 243.97/50.43  | | | ALPHA: (22) implies:
% 243.97/50.43  | | |   (23)  all_58_11 = e2
% 243.97/50.43  | | |   (24)  op(e1, e0) = e2
% 243.97/50.43  | | | 
% 243.97/50.43  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (12), (14), (16),
% 243.97/50.43  | | |            (17), (18), (23), (24) are inconsistent by sub-proof #1671.
% 243.97/50.43  | | | 
% 243.97/50.43  | | Case 2:
% 243.97/50.43  | | | 
% 243.97/50.43  | | |   (25)  all_58_15 = e2 & op(e0, e0) = e2
% 243.97/50.43  | | | 
% 243.97/50.43  | | | ALPHA: (25) implies:
% 243.97/50.43  | | |   (26)  op(e0, e0) = e2
% 243.97/50.43  | | | 
% 243.97/50.43  | | | REF_CLOSE: (7), (13), (14), (26) are inconsistent by sub-proof #1388.
% 243.97/50.43  | | | 
% 243.97/50.43  | | End of split
% 243.97/50.43  | | 
% 243.97/50.43  | End of split
% 243.97/50.43  | 
% 243.97/50.43  End of proof
% 243.97/50.43  
% 243.97/50.43  Sub-proof #1364 shows that the following formulas are inconsistent:
% 243.97/50.43  ----------------------------------------------------------------
% 243.97/50.43    (1)   ~ (e2 = e0)
% 243.97/50.43    (2)  op(e2, e0) = e0
% 243.97/50.43    (3)  op(e3, e0) = all_52_12
% 243.97/50.43    (4)   ~ (all_52_12 = e2)
% 243.97/50.43    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.43    (6)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 243.97/50.43  
% 243.97/50.43  Begin of proof
% 243.97/50.43  | 
% 243.97/50.43  | BETA: splitting (6) gives:
% 243.97/50.43  | 
% 243.97/50.43  | Case 1:
% 243.97/50.43  | | 
% 243.97/50.43  | |   (7)  all_58_9 = e2 & op(e3, e0) = e2
% 243.97/50.43  | | 
% 243.97/50.43  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #2318.
% 243.97/50.43  | | 
% 243.97/50.43  | Case 2:
% 243.97/50.43  | | 
% 243.97/50.43  | |   (8)  all_58_10 = e2 & op(e2, e0) = e2
% 243.97/50.43  | | 
% 243.97/50.43  | | ALPHA: (8) implies:
% 243.97/50.43  | |   (9)  op(e2, e0) = e2
% 243.97/50.43  | | 
% 243.97/50.43  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2121.
% 243.97/50.43  | | 
% 243.97/50.43  | End of split
% 243.97/50.43  | 
% 243.97/50.43  End of proof
% 243.97/50.43  
% 243.97/50.43  Sub-proof #1365 shows that the following formulas are inconsistent:
% 243.97/50.43  ----------------------------------------------------------------
% 243.97/50.43    (1)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 243.97/50.43    (2)   ~ (e3 = e0)
% 243.97/50.43    (3)   ~ (e2 = e0)
% 243.97/50.43    (4)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.97/50.43         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.97/50.43    (5)   ~ (e3 = e1)
% 243.97/50.43    (6)  all_58_2 = e2
% 243.97/50.43    (7)   ~ (e3 = e2)
% 243.97/50.43    (8)  all_58_13 = e0
% 243.97/50.43    (9)  op(e0, e2) = e0
% 243.97/50.43    (10)  op(e3, e2) = all_52_4
% 243.97/50.43    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.43    (12)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.97/50.43          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.97/50.43    (13)   ~ (all_52_4 = e1)
% 243.97/50.43    (14)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.97/50.43          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.97/50.43    (15)   ~ (e1 = e0)
% 243.97/50.43    (16)   ~ (e2 = e1)
% 243.97/50.43  
% 243.97/50.43  Begin of proof
% 243.97/50.43  | 
% 243.97/50.43  | BETA: splitting (1) gives:
% 243.97/50.43  | 
% 243.97/50.43  | Case 1:
% 243.97/50.43  | | 
% 243.97/50.43  | |   (17)  all_58_2 = e0 & op(e2, e3) = e0
% 243.97/50.43  | | 
% 243.97/50.43  | | REF_CLOSE: (3), (6), (17) are inconsistent by sub-proof #1535.
% 243.97/50.43  | | 
% 243.97/50.43  | Case 2:
% 243.97/50.43  | | 
% 243.97/50.43  | |   (18)  all_58_3 = e0 & op(e2, e2) = e0
% 243.97/50.43  | | 
% 243.97/50.43  | | ALPHA: (18) implies:
% 243.97/50.43  | |   (19)  all_58_3 = e0
% 243.97/50.43  | | 
% 243.97/50.43  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 243.97/50.43  | |            (15), (16), (19) are inconsistent by sub-proof #1374.
% 243.97/50.43  | | 
% 243.97/50.43  | End of split
% 243.97/50.43  | 
% 243.97/50.43  End of proof
% 243.97/50.43  
% 243.97/50.43  Sub-proof #1366 shows that the following formulas are inconsistent:
% 243.97/50.43  ----------------------------------------------------------------
% 243.97/50.43    (1)   ~ (all_52_3 = e0)
% 243.97/50.43    (2)   ~ (e3 = e0)
% 243.97/50.43    (3)   ~ (all_52_7 = e2)
% 243.97/50.43    (4)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.97/50.43    (5)   ~ (e2 = e0)
% 243.97/50.43    (6)  all_54_13 = all_52_7
% 243.97/50.43    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 243.97/50.43           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 243.97/50.43             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 243.97/50.43           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.97/50.43             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.97/50.43           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.97/50.43           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 243.97/50.43           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.97/50.43           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.97/50.43           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 243.97/50.43           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.97/50.43             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.97/50.43           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.97/50.43           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 243.97/50.43           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.97/50.43           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.97/50.43           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 243.97/50.43           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.97/50.43             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 243.97/50.43           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.97/50.43           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 243.97/50.43           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.97/50.43           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.97/50.43           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 243.97/50.43           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.97/50.43             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 243.97/50.43           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.97/50.43           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.97/50.43    (8)  op(e1, e0) = all_52_14
% 243.97/50.43    (9)  op(e0, e3) = all_52_3
% 243.97/50.43    (10)   ~ (e3 = e1)
% 243.97/50.43    (11)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.97/50.43    (12)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.97/50.43              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 243.97/50.43                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.97/50.43                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.97/50.43    (13)  op(e2, e1) = all_52_9
% 243.97/50.43    (14)   ~ (e3 = e2)
% 243.97/50.43    (15)   ~ (all_52_14 = e1)
% 243.97/50.43    (16)   ~ (all_52_7 = e1)
% 243.97/50.43    (17)  all_58_7 = e3
% 243.97/50.43    (18)  op(e3, e0) = all_52_12
% 243.97/50.43    (19)   ~ (all_52_3 = e3)
% 243.97/50.43    (20)  op(e2, e3) = all_52_1
% 243.97/50.43    (21)   ~ (all_52_12 = e2)
% 243.97/50.43    (22)  op(e0, e2) = e0
% 243.97/50.43    (23)  op(e1, e1) = e2
% 243.97/50.43    (24)  op(e0, e2) = all_52_7
% 243.97/50.43    (25)  all_56_31 = e3
% 243.97/50.43    (26)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.97/50.43          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.97/50.43    (27)  op(e0, e0) = e3
% 243.97/50.43    (28)  op(e2, e1) = e3
% 243.97/50.43    (29)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 243.97/50.43          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 243.97/50.43    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.43    (31)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 243.97/50.43          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 243.97/50.43    (32)   ~ (e1 = e0)
% 243.97/50.43    (33)  op(e3, e3) = e3
% 243.97/50.43    (34)  all_58_9 = e1
% 243.97/50.43    (35)   ~ (all_52_13 = e3)
% 243.97/50.43    (36)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 243.97/50.43          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 243.97/50.43    (37)  op(e2, e0) = all_52_13
% 243.97/50.43    (38)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.97/50.43          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.97/50.43            e1)
% 243.97/50.43    (39)   ~ (all_52_1 = e3)
% 243.97/50.43    (40)   ~ (all_52_9 = e1)
% 243.97/50.43    (41)   ~ (e2 = e1)
% 243.97/50.43    (42)   ~ (all_52_1 = e1)
% 243.97/50.43  
% 243.97/50.43  Begin of proof
% 243.97/50.43  | 
% 243.97/50.43  | BETA: splitting (4) gives:
% 243.97/50.43  | 
% 243.97/50.43  | Case 1:
% 243.97/50.43  | | 
% 243.97/50.43  | |   (43)  all_58_12 = e2 & op(e0, e3) = e2
% 243.97/50.43  | | 
% 243.97/50.43  | | ALPHA: (43) implies:
% 243.97/50.43  | |   (44)  all_58_12 = e2
% 243.97/50.43  | | 
% 243.97/50.43  | | BETA: splitting (26) gives:
% 243.97/50.43  | | 
% 243.97/50.43  | | Case 1:
% 243.97/50.43  | | | 
% 243.97/50.43  | | |   (45)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 243.97/50.43  | | |           e1)
% 243.97/50.43  | | | 
% 243.97/50.43  | | | REF_CLOSE: (10), (20), (30), (33), (42), (45) are inconsistent by
% 243.97/50.43  | | |            sub-proof #1370.
% 243.97/50.43  | | | 
% 243.97/50.43  | | Case 2:
% 243.97/50.43  | | | 
% 243.97/50.43  | | |   (46)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 243.97/50.43  | | |           e1)
% 243.97/50.43  | | | 
% 243.97/50.43  | | | BETA: splitting (46) gives:
% 243.97/50.43  | | | 
% 243.97/50.43  | | | Case 1:
% 243.97/50.43  | | | | 
% 243.97/50.43  | | | |   (47)  all_58_6 = e1 & op(e1, e3) = e1
% 243.97/50.43  | | | | 
% 243.97/50.43  | | | | ALPHA: (47) implies:
% 243.97/50.43  | | | |   (48)  all_58_6 = e1
% 243.97/50.43  | | | |   (49)  op(e1, e3) = e1
% 243.97/50.43  | | | | 
% 243.97/50.43  | | | | BETA: splitting (38) gives:
% 243.97/50.43  | | | | 
% 243.97/50.43  | | | | Case 1:
% 243.97/50.43  | | | | | 
% 243.97/50.43  | | | | |   (50)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0,
% 243.97/50.43  | | | | |             e2) = e1)
% 243.97/50.43  | | | | | 
% 243.97/50.43  | | | | | BETA: splitting (50) gives:
% 243.97/50.43  | | | | | 
% 243.97/50.43  | | | | | Case 1:
% 243.97/50.43  | | | | | | 
% 243.97/50.43  | | | | | |   (51)  all_58_12 = e1 & op(e0, e3) = e1
% 243.97/50.43  | | | | | | 
% 243.97/50.43  | | | | | | REF_CLOSE: (41), (44), (51) are inconsistent by sub-proof #1763.
% 243.97/50.43  | | | | | | 
% 243.97/50.43  | | | | | Case 2:
% 243.97/50.43  | | | | | | 
% 243.97/50.43  | | | | | |   (52)  all_58_13 = e1 & op(e0, e2) = e1
% 243.97/50.43  | | | | | | 
% 243.97/50.43  | | | | | | ALPHA: (52) implies:
% 243.97/50.43  | | | | | |   (53)  op(e0, e2) = e1
% 243.97/50.43  | | | | | | 
% 243.97/50.43  | | | | | | REF_CLOSE: (22), (30), (32), (53) are inconsistent by sub-proof
% 243.97/50.43  | | | | | |            #1872.
% 243.97/50.43  | | | | | | 
% 243.97/50.43  | | | | | End of split
% 243.97/50.43  | | | | | 
% 243.97/50.43  | | | | Case 2:
% 243.97/50.43  | | | | | 
% 243.97/50.43  | | | | |   (54)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 243.97/50.43  | | | | |             e0) = e1)
% 243.97/50.43  | | | | | 
% 243.97/50.43  | | | | | BETA: splitting (54) gives:
% 243.97/50.43  | | | | | 
% 243.97/50.43  | | | | | Case 1:
% 243.97/50.43  | | | | | | 
% 243.97/50.43  | | | | | |   (55)  all_58_14 = e1 & op(e0, e1) = e1
% 243.97/50.43  | | | | | | 
% 243.97/50.43  | | | | | | ALPHA: (55) implies:
% 243.97/50.43  | | | | | |   (56)  op(e0, e1) = e1
% 243.97/50.43  | | | | | | 
% 243.97/50.43  | | | | | | BETA: splitting (31) gives:
% 243.97/50.43  | | | | | | 
% 243.97/50.43  | | | | | | Case 1:
% 243.97/50.43  | | | | | | | 
% 243.97/50.43  | | | | | | |   (57)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 243.97/50.43  | | | | | | |           op(e2, e0) = e2)
% 243.97/50.43  | | | | | | | 
% 243.97/50.43  | | | | | | | BETA: splitting (57) gives:
% 243.97/50.43  | | | | | | | 
% 243.97/50.43  | | | | | | | Case 1:
% 243.97/50.43  | | | | | | | | 
% 243.97/50.43  | | | | | | | |   (58)  all_58_9 = e2 & op(e3, e0) = e2
% 243.97/50.43  | | | | | | | | 
% 243.97/50.43  | | | | | | | | REF_CLOSE: (18), (21), (30), (58) are inconsistent by sub-proof
% 243.97/50.43  | | | | | | | |            #2318.
% 243.97/50.43  | | | | | | | | 
% 243.97/50.43  | | | | | | | Case 2:
% 243.97/50.43  | | | | | | | | 
% 243.97/50.43  | | | | | | | |   (59)  all_58_10 = e2 & op(e2, e0) = e2
% 243.97/50.43  | | | | | | | | 
% 243.97/50.43  | | | | | | | | ALPHA: (59) implies:
% 243.97/50.43  | | | | | | | |   (60)  op(e2, e0) = e2
% 243.97/50.43  | | | | | | | | 
% 243.97/50.43  | | | | | | | | BETA: splitting (7) gives:
% 243.97/50.43  | | | | | | | | 
% 243.97/50.43  | | | | | | | | Case 1:
% 243.97/50.43  | | | | | | | | | 
% 243.97/50.43  | | | | | | | | |   (61)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 243.97/50.43  | | | | | | | | |           ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.97/50.43  | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 243.97/50.43  | | | | | | | | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 243.97/50.43  | | | | | | | | |           &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3)
% 243.97/50.43  | | | | | | | | |           = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 243.97/50.43  | | | | | | | | |           = e3 & op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17
% 243.97/50.43  | | | | | | | | |           = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1)
% 243.97/50.43  | | | | | | | | |           = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 243.97/50.43  | | | | | | | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0)
% 243.97/50.43  | | | | | | | | |           = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 243.97/50.43  | | | | | | | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 243.97/50.43  | | | | | | | | |           = e0 & op(e0, e3) = e0)
% 243.97/50.43  | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | BETA: splitting (61) gives:
% 243.97/50.43  | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | Case 1:
% 243.97/50.43  | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | |   (62)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 243.97/50.43  | | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.97/50.43  | | | | | | | | | |           e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 243.97/50.43  | | | | | | | | | |             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 243.97/50.43  | | | | | | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 243.97/50.43  | | | | | | | | | |           e3)
% 243.97/50.43  | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | | BETA: splitting (62) gives:
% 243.97/50.43  | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | | Case 1:
% 243.97/50.43  | | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | | |   (63)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 243.97/50.43  | | | | | | | | | | |         &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.97/50.43  | | | | | | | | | | |         (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 243.97/50.43  | | | | | | | | | | |         e3
% 243.97/50.43  | | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | | | ALPHA: (63) implies:
% 243.97/50.43  | | | | | | | | | | |   (64)  op(e2, e3) = e3
% 243.97/50.43  | | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | | | REF_CLOSE: (20), (30), (39), (64) are inconsistent by
% 243.97/50.43  | | | | | | | | | | |            sub-proof #2337.
% 243.97/50.43  | | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | | Case 2:
% 243.97/50.43  | | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | | |   (65)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 243.97/50.43  | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 243.97/50.43  | | | | | | | | | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.97/50.43  | | | | | | | | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 243.97/50.43  | | | | | | | | | | |           e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.97/50.43  | | | | | | | | | | |           ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.97/50.43  | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 243.97/50.43  | | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | | | REF_CLOSE: (10), (25), (30), (49), (65) are inconsistent by
% 243.97/50.43  | | | | | | | | | | |            sub-proof #1369.
% 243.97/50.43  | | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | | End of split
% 243.97/50.43  | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | Case 2:
% 243.97/50.43  | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | |   (66)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3)
% 243.97/50.43  | | | | | | | | | |           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 243.97/50.43  | | | | | | | | | |           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 243.97/50.43  | | | | | | | | | |             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 243.97/50.43  | | | | | | | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 243.97/50.43  | | | | | | | | | |           e0)
% 243.97/50.43  | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | | REF_CLOSE: (1), (9), (19), (25), (30), (66) are inconsistent
% 243.97/50.43  | | | | | | | | | |            by sub-proof #1368.
% 243.97/50.43  | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | End of split
% 243.97/50.43  | | | | | | | | | 
% 243.97/50.43  | | | | | | | | Case 2:
% 243.97/50.43  | | | | | | | | | 
% 243.97/50.43  | | | | | | | | |   (67)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 243.97/50.43  | | | | | | | | |           &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 243.97/50.43  | | | | | | | | |           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1)
% 243.97/50.43  | | | | | | | | |           = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 243.97/50.43  | | | | | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.97/50.43  | | | | | | | | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.97/50.43  | | | | | | | | |           & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 243.97/50.43  | | | | | | | | |           e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 243.97/50.43  | | | | | | | | |           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.97/50.43  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0)
% 243.97/50.43  | | | | | | | | |           = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 243.97/50.43  | | | | | | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 243.97/50.43  | | | | | | | | |             = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 243.97/50.43  | | | | | | | | |           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.97/50.43  | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | BETA: splitting (67) gives:
% 243.97/50.43  | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | Case 1:
% 243.97/50.43  | | | | | | | | | | 
% 243.97/50.43  | | | | | | | | | |   (68)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.97/50.43  | | | | | | | | | |             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.97/50.43  | | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 243.97/50.43  | | | | | | | | | |             e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 & 
% 243.97/50.43  | | | | | | | | | |           ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 243.97/50.43  | | | | | | | | | |             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 243.97/50.43  | | | | | | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 243.97/50.43  | | | | | | | | | |           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 243.97/50.44  | | | | | | | | | |           e2)
% 243.97/50.44  | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | BETA: splitting (68) gives:
% 243.97/50.44  | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | Case 1:
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | |   (69)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 243.97/50.44  | | | | | | | | | | |           e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.97/50.44  | | | | | | | | | | |         &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 243.97/50.44  | | | | | | | | | | |           e2) = e2
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | ALPHA: (69) implies:
% 243.97/50.44  | | | | | | | | | | |   (70)  op(e2, e1) = e2
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | REF_CLOSE: (14), (28), (30), (70) are inconsistent by
% 243.97/50.44  | | | | | | | | | | |            sub-proof #2256.
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | Case 2:
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | |   (71)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 243.97/50.44  | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 243.97/50.44  | | | | | | | | | | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.97/50.44  | | | | | | | | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 243.97/50.44  | | | | | | | | | | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 243.97/50.44  | | | | | | | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.97/50.44  | | | | | | | | | | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | REF_CLOSE: (3), (6), (11), (13), (16), (24), (30), (40), (71)
% 243.97/50.44  | | | | | | | | | | |            are inconsistent by sub-proof #1367.
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | End of split
% 243.97/50.44  | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | Case 2:
% 243.97/50.44  | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | |   (72)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.97/50.44  | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.97/50.44  | | | | | | | | | |           &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.97/50.44  | | | | | | | | | |             e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 & 
% 243.97/50.44  | | | | | | | | | |           ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 243.97/50.44  | | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 243.97/50.44  | | | | | | | | | |             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 243.97/50.44  | | | | | | | | | |           all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 243.97/50.44  | | | | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 243.97/50.44  | | | | | | | | | |           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 243.97/50.44  | | | | | | | | | |           e0)
% 243.97/50.44  | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | BETA: splitting (72) gives:
% 243.97/50.44  | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | Case 1:
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | |   (73)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 243.97/50.44  | | | | | | | | | | |           e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 243.97/50.44  | | | | | | | | | | |         &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 243.97/50.44  | | | | | | | | | | |           e2) = e0
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | ALPHA: (73) implies:
% 243.97/50.44  | | | | | | | | | | |   (74)  op(e2, e0) = e0
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | REF_CLOSE: (5), (30), (60), (74) are inconsistent by
% 243.97/50.44  | | | | | | | | | | |            sub-proof #2121.
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | Case 2:
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | |   (75)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.97/50.44  | | | | | | | | | | |             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 243.97/50.44  | | | | | | | | | | |             e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 243.97/50.44  | | | | | | | | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 243.97/50.44  | | | | | | | | | | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 243.97/50.44  | | | | | | | | | | |           ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 243.97/50.44  | | | | | | | | | | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | BETA: splitting (75) gives:
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | Case 1:
% 243.97/50.44  | | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | |   (76)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 243.97/50.44  | | | | | | | | | | | |           e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 243.97/50.44  | | | | | | | | | | | |         &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0,
% 243.97/50.44  | | | | | | | | | | | |           e1) = e1
% 243.97/50.44  | | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | | ALPHA: (76) implies:
% 243.97/50.44  | | | | | | | | | | | |   (77)  op(e1, e0) = e1
% 243.97/50.44  | | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | | REF_CLOSE: (8), (15), (30), (77) are inconsistent by
% 243.97/50.44  | | | | | | | | | | | |            sub-proof #2304.
% 243.97/50.44  | | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | Case 2:
% 243.97/50.44  | | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | |   (78)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 243.97/50.44  | | | | | | | | | | | |           e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 243.97/50.44  | | | | | | | | | | | |         &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0,
% 243.97/50.44  | | | | | | | | | | | |           e1) = e0
% 243.97/50.44  | | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | | ALPHA: (78) implies:
% 243.97/50.44  | | | | | | | | | | | |   (79)  op(e0, e1) = e0
% 243.97/50.44  | | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | | REF_CLOSE: (30), (32), (56), (79) are inconsistent by
% 243.97/50.44  | | | | | | | | | | | |            sub-proof #2158.
% 243.97/50.44  | | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | | End of split
% 243.97/50.44  | | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | | End of split
% 243.97/50.44  | | | | | | | | | | 
% 243.97/50.44  | | | | | | | | | End of split
% 243.97/50.44  | | | | | | | | | 
% 243.97/50.44  | | | | | | | | End of split
% 243.97/50.44  | | | | | | | | 
% 243.97/50.44  | | | | | | | End of split
% 243.97/50.44  | | | | | | | 
% 243.97/50.44  | | | | | | Case 2:
% 243.97/50.44  | | | | | | | 
% 243.97/50.44  | | | | | | |   (80)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 243.97/50.44  | | | | | | |           op(e0, e0) = e2)
% 243.97/50.44  | | | | | | | 
% 243.97/50.44  | | | | | | | BETA: splitting (80) gives:
% 243.97/50.44  | | | | | | | 
% 243.97/50.44  | | | | | | | Case 1:
% 243.97/50.44  | | | | | | | | 
% 243.97/50.44  | | | | | | | |   (81)  all_58_11 = e2 & op(e1, e0) = e2
% 243.97/50.44  | | | | | | | | 
% 243.97/50.44  | | | | | | | | ALPHA: (81) implies:
% 243.97/50.44  | | | | | | | |   (82)  all_58_11 = e2
% 243.97/50.44  | | | | | | | | 
% 243.97/50.44  | | | | | | | | REF_CLOSE: (2), (5), (17), (23), (30), (32), (36), (48), (82)
% 243.97/50.44  | | | | | | | |            are inconsistent by sub-proof #2031.
% 243.97/50.44  | | | | | | | | 
% 243.97/50.44  | | | | | | | Case 2:
% 243.97/50.44  | | | | | | | | 
% 243.97/50.44  | | | | | | | |   (83)  all_58_15 = e2 & op(e0, e0) = e2
% 243.97/50.44  | | | | | | | | 
% 243.97/50.44  | | | | | | | | ALPHA: (83) implies:
% 243.97/50.44  | | | | | | | |   (84)  op(e0, e0) = e2
% 243.97/50.44  | | | | | | | | 
% 243.97/50.44  | | | | | | | | REF_CLOSE: (14), (27), (30), (84) are inconsistent by sub-proof
% 243.97/50.44  | | | | | | | |            #1388.
% 243.97/50.44  | | | | | | | | 
% 243.97/50.44  | | | | | | | End of split
% 243.97/50.44  | | | | | | | 
% 243.97/50.44  | | | | | | End of split
% 243.97/50.44  | | | | | | 
% 243.97/50.44  | | | | | Case 2:
% 243.97/50.44  | | | | | | 
% 243.97/50.44  | | | | | |   (85)  all_58_15 = e1 & op(e0, e0) = e1
% 243.97/50.44  | | | | | | 
% 243.97/50.44  | | | | | | ALPHA: (85) implies:
% 243.97/50.44  | | | | | |   (86)  all_58_15 = e1
% 243.97/50.44  | | | | | |   (87)  op(e0, e0) = e1
% 243.97/50.44  | | | | | | 
% 243.97/50.44  | | | | | | REF_CLOSE: (2), (5), (10), (12), (14), (29), (30), (31), (32), (34),
% 243.97/50.44  | | | | | |            (35), (37), (41), (86), (87) are inconsistent by
% 243.97/50.44  | | | | | |            sub-proof #1601.
% 243.97/50.44  | | | | | | 
% 243.97/50.44  | | | | | End of split
% 243.97/50.44  | | | | | 
% 243.97/50.44  | | | | End of split
% 243.97/50.44  | | | | 
% 243.97/50.44  | | | Case 2:
% 243.97/50.44  | | | | 
% 243.97/50.44  | | | |   (88)  all_58_12 = e1 & op(e0, e3) = e1
% 243.97/50.44  | | | | 
% 243.97/50.44  | | | | REF_CLOSE: (41), (44), (88) are inconsistent by sub-proof #1763.
% 243.97/50.44  | | | | 
% 243.97/50.44  | | | End of split
% 243.97/50.44  | | | 
% 243.97/50.44  | | End of split
% 243.97/50.44  | | 
% 243.97/50.44  | Case 2:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (89)  all_58_13 = e2 & op(e0, e2) = e2
% 243.97/50.44  | | 
% 243.97/50.44  | | ALPHA: (89) implies:
% 243.97/50.44  | |   (90)  op(e0, e2) = e2
% 243.97/50.44  | | 
% 243.97/50.44  | | REF_CLOSE: (3), (6), (11), (16), (24), (30), (90) are inconsistent by
% 243.97/50.44  | |            sub-proof #1817.
% 243.97/50.44  | | 
% 243.97/50.44  | End of split
% 243.97/50.44  | 
% 243.97/50.44  End of proof
% 243.97/50.44  
% 243.97/50.44  Sub-proof #1367 shows that the following formulas are inconsistent:
% 243.97/50.44  ----------------------------------------------------------------
% 243.97/50.44    (1)   ~ (all_52_7 = e2)
% 243.97/50.44    (2)  all_54_13 = all_52_7
% 243.97/50.44    (3)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 243.97/50.44    (4)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 243.97/50.44             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 243.97/50.44           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 243.97/50.44             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 243.97/50.44           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 243.97/50.44    (5)  op(e2, e1) = all_52_9
% 243.97/50.44    (6)   ~ (all_52_7 = e1)
% 243.97/50.44    (7)  op(e0, e2) = all_52_7
% 243.97/50.44    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.44    (9)   ~ (all_52_9 = e1)
% 243.97/50.44  
% 243.97/50.44  Begin of proof
% 243.97/50.44  | 
% 243.97/50.44  | BETA: splitting (4) gives:
% 243.97/50.44  | 
% 243.97/50.44  | Case 1:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (10)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 243.97/50.44  | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) =
% 243.97/50.44  | |         e1 & op(e1, e2) = e1
% 243.97/50.44  | | 
% 243.97/50.44  | | ALPHA: (10) implies:
% 243.97/50.44  | |   (11)  op(e2, e1) = e1
% 243.97/50.44  | | 
% 243.97/50.44  | | REF_CLOSE: (5), (8), (9), (11) are inconsistent by sub-proof #2306.
% 243.97/50.44  | | 
% 243.97/50.44  | Case 2:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (12)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.97/50.44  | |           = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) =
% 243.97/50.44  | |         e2 & op(e0, e2) = e2
% 243.97/50.44  | | 
% 243.97/50.44  | | ALPHA: (12) implies:
% 243.97/50.44  | |   (13)  op(e0, e2) = e2
% 243.97/50.44  | | 
% 243.97/50.44  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (13) are inconsistent by sub-proof
% 243.97/50.44  | |            #1817.
% 243.97/50.44  | | 
% 243.97/50.44  | End of split
% 243.97/50.44  | 
% 243.97/50.44  End of proof
% 243.97/50.44  
% 243.97/50.44  Sub-proof #1368 shows that the following formulas are inconsistent:
% 243.97/50.44  ----------------------------------------------------------------
% 243.97/50.44    (1)   ~ (all_52_3 = e0)
% 243.97/50.44    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 243.97/50.44             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 243.97/50.44           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 243.97/50.44           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.97/50.44           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 243.97/50.44           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.97/50.44           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.97/50.44    (3)  op(e0, e3) = all_52_3
% 243.97/50.44    (4)   ~ (all_52_3 = e3)
% 243.97/50.44    (5)  all_56_31 = e3
% 243.97/50.44    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.44  
% 243.97/50.44  Begin of proof
% 243.97/50.44  | 
% 243.97/50.44  | BETA: splitting (2) gives:
% 243.97/50.44  | 
% 243.97/50.44  | Case 1:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (7)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 243.97/50.44  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 243.97/50.44  | |        op(e1, e3) = e1
% 243.97/50.44  | | 
% 243.97/50.44  | | ALPHA: (7) implies:
% 243.97/50.44  | |   (8)   ~ (all_56_31 = e3)
% 243.97/50.44  | | 
% 243.97/50.44  | | REDUCE: (5), (8) imply:
% 243.97/50.44  | |   (9)  $false
% 243.97/50.44  | | 
% 243.97/50.44  | | CLOSE: (9) is inconsistent.
% 243.97/50.44  | | 
% 243.97/50.44  | Case 2:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.97/50.44  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 243.97/50.44  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.97/50.44  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.97/50.44  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.97/50.44  | | 
% 243.97/50.44  | | REF_CLOSE: (1), (3), (4), (6), (10) are inconsistent by sub-proof #2330.
% 243.97/50.44  | | 
% 243.97/50.44  | End of split
% 243.97/50.44  | 
% 243.97/50.44  End of proof
% 243.97/50.44  
% 243.97/50.44  Sub-proof #1369 shows that the following formulas are inconsistent:
% 243.97/50.44  ----------------------------------------------------------------
% 243.97/50.44    (1)   ~ (e3 = e1)
% 243.97/50.44    (2)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 243.97/50.44           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 243.97/50.44             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 243.97/50.44           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 243.97/50.44             e1) = e3 & op(e1, e3) = e3)
% 243.97/50.44    (3)  op(e1, e3) = e1
% 243.97/50.44    (4)  all_56_31 = e3
% 243.97/50.44    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.44  
% 243.97/50.44  Begin of proof
% 243.97/50.44  | 
% 243.97/50.44  | BETA: splitting (2) gives:
% 243.97/50.44  | 
% 243.97/50.44  | Case 1:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (6)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 243.97/50.44  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 243.97/50.44  | |        op(e2, e3) = e2
% 243.97/50.44  | | 
% 243.97/50.44  | | ALPHA: (6) implies:
% 243.97/50.44  | |   (7)   ~ (all_56_31 = e3)
% 243.97/50.44  | | 
% 243.97/50.44  | | REDUCE: (4), (7) imply:
% 243.97/50.44  | |   (8)  $false
% 243.97/50.44  | | 
% 243.97/50.44  | | CLOSE: (8) is inconsistent.
% 243.97/50.44  | | 
% 243.97/50.44  | Case 2:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 243.97/50.44  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 243.97/50.44  | |        op(e1, e3) = e3
% 243.97/50.44  | | 
% 243.97/50.44  | | ALPHA: (9) implies:
% 243.97/50.44  | |   (10)  op(e1, e3) = e3
% 243.97/50.44  | | 
% 243.97/50.44  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2225.
% 243.97/50.44  | | 
% 243.97/50.44  | End of split
% 243.97/50.44  | 
% 243.97/50.44  End of proof
% 243.97/50.44  
% 243.97/50.44  Sub-proof #1370 shows that the following formulas are inconsistent:
% 243.97/50.44  ----------------------------------------------------------------
% 243.97/50.44    (1)   ~ (e3 = e1)
% 243.97/50.44    (2)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 243.97/50.44    (3)  op(e2, e3) = all_52_1
% 243.97/50.44    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.44    (5)  op(e3, e3) = e3
% 243.97/50.44    (6)   ~ (all_52_1 = e1)
% 243.97/50.44  
% 243.97/50.44  Begin of proof
% 243.97/50.44  | 
% 243.97/50.44  | BETA: splitting (2) gives:
% 243.97/50.44  | 
% 243.97/50.44  | Case 1:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 243.97/50.44  | | 
% 243.97/50.44  | | ALPHA: (7) implies:
% 243.97/50.44  | |   (8)  op(e3, e3) = e1
% 243.97/50.44  | | 
% 243.97/50.44  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1578.
% 243.97/50.44  | | 
% 243.97/50.44  | Case 2:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (9)  all_58_2 = e1 & op(e2, e3) = e1
% 243.97/50.44  | | 
% 243.97/50.44  | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #2229.
% 243.97/50.44  | | 
% 243.97/50.44  | End of split
% 243.97/50.44  | 
% 243.97/50.44  End of proof
% 243.97/50.44  
% 243.97/50.44  Sub-proof #1371 shows that the following formulas are inconsistent:
% 243.97/50.44  ----------------------------------------------------------------
% 243.97/50.44    (1)   ~ (all_6_2 = e2)
% 243.97/50.44    (2)  all_54_10 = all_6_2
% 243.97/50.44    (3)   ~ (all_6_2 = e3)
% 243.97/50.44    (4)   ~ (all_6_2 = e0)
% 243.97/50.44    (5)  op(e1, e3) = e1
% 243.97/50.44    (6)   ~ (all_52_2 = all_6_2)
% 243.97/50.44    (7)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.97/50.44    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.44    (9)  op(e1, e3) = all_52_2
% 243.97/50.44  
% 243.97/50.44  Begin of proof
% 243.97/50.44  | 
% 243.97/50.44  | BETA: splitting (7) gives:
% 243.97/50.44  | 
% 243.97/50.44  | Case 1:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (10)  all_54_10 = e3
% 243.97/50.44  | | 
% 243.97/50.44  | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #2313.
% 243.97/50.44  | | 
% 243.97/50.44  | Case 2:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (11)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.97/50.44  | | 
% 243.97/50.44  | | BETA: splitting (11) gives:
% 243.97/50.44  | | 
% 243.97/50.44  | | Case 1:
% 243.97/50.44  | | | 
% 243.97/50.44  | | |   (12)  all_54_10 = e2
% 243.97/50.44  | | | 
% 243.97/50.44  | | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #2312.
% 243.97/50.44  | | | 
% 243.97/50.44  | | Case 2:
% 243.97/50.44  | | | 
% 243.97/50.44  | | |   (13)  all_54_10 = e1 | all_54_10 = e0
% 243.97/50.44  | | | 
% 243.97/50.44  | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (13) are inconsistent by
% 243.97/50.44  | | |            sub-proof #1372.
% 243.97/50.44  | | | 
% 243.97/50.44  | | End of split
% 243.97/50.44  | | 
% 243.97/50.44  | End of split
% 243.97/50.44  | 
% 243.97/50.44  End of proof
% 243.97/50.44  
% 243.97/50.44  Sub-proof #1372 shows that the following formulas are inconsistent:
% 243.97/50.44  ----------------------------------------------------------------
% 243.97/50.44    (1)  all_54_10 = e1 | all_54_10 = e0
% 243.97/50.44    (2)  all_54_10 = all_6_2
% 243.97/50.44    (3)   ~ (all_6_2 = e0)
% 243.97/50.44    (4)  op(e1, e3) = e1
% 243.97/50.44    (5)   ~ (all_52_2 = all_6_2)
% 243.97/50.44    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.44    (7)  op(e1, e3) = all_52_2
% 243.97/50.44  
% 243.97/50.44  Begin of proof
% 243.97/50.44  | 
% 243.97/50.44  | BETA: splitting (1) gives:
% 243.97/50.44  | 
% 243.97/50.44  | Case 1:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (8)  all_54_10 = e1
% 243.97/50.44  | | 
% 243.97/50.44  | | COMBINE_EQS: (2), (8) imply:
% 243.97/50.44  | |   (9)  all_6_2 = e1
% 243.97/50.44  | | 
% 243.97/50.44  | | SIMP: (9) implies:
% 243.97/50.44  | |   (10)  all_6_2 = e1
% 243.97/50.44  | | 
% 243.97/50.44  | | REDUCE: (5), (10) imply:
% 243.97/50.44  | |   (11)   ~ (all_52_2 = e1)
% 243.97/50.44  | | 
% 243.97/50.44  | | REF_CLOSE: (4), (6), (7), (11) are inconsistent by sub-proof #1948.
% 243.97/50.44  | | 
% 243.97/50.44  | Case 2:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (12)  all_54_10 = e0
% 243.97/50.44  | | 
% 243.97/50.44  | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #2303.
% 243.97/50.44  | | 
% 243.97/50.44  | End of split
% 243.97/50.44  | 
% 243.97/50.44  End of proof
% 243.97/50.44  
% 243.97/50.44  Sub-proof #1373 shows that the following formulas are inconsistent:
% 243.97/50.44  ----------------------------------------------------------------
% 243.97/50.44    (1)   ~ (e3 = e0)
% 243.97/50.44    (2)   ~ (e2 = e0)
% 243.97/50.44    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.97/50.44         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.97/50.44    (4)   ~ (e3 = e1)
% 243.97/50.44    (5)  all_58_3 = e1
% 243.97/50.44    (6)   ~ (e3 = e2)
% 243.97/50.44    (7)  all_58_13 = e0
% 243.97/50.44    (8)  op(e0, e2) = e0
% 243.97/50.44    (9)  op(e3, e2) = all_52_4
% 243.97/50.44    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.44    (11)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.97/50.44          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.97/50.44    (12)   ~ (all_52_4 = e1)
% 243.97/50.44    (13)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.97/50.44          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.97/50.44    (14)   ~ (e1 = e0)
% 243.97/50.44    (15)  all_58_4 = e1 & op(e3, e1) = e1
% 243.97/50.44    (16)  all_58_4 = e0
% 243.97/50.44    (17)   ~ (e2 = e1)
% 243.97/50.44  
% 243.97/50.44  Begin of proof
% 243.97/50.44  | 
% 243.97/50.44  | ALPHA: (15) implies:
% 243.97/50.44  |   (18)  all_58_4 = e1
% 243.97/50.44  | 
% 243.97/50.44  | COMBINE_EQS: (16), (18) imply:
% 243.97/50.44  |   (19)  e1 = e0
% 243.97/50.44  | 
% 243.97/50.44  | SIMP: (19) implies:
% 243.97/50.44  |   (20)  e1 = e0
% 243.97/50.44  | 
% 243.97/50.44  | COMBINE_EQS: (5), (20) imply:
% 243.97/50.44  |   (21)  all_58_3 = e0
% 243.97/50.44  | 
% 243.97/50.44  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 243.97/50.44  |            (14), (17), (21) are inconsistent by sub-proof #1374.
% 243.97/50.44  | 
% 243.97/50.44  End of proof
% 243.97/50.44  
% 243.97/50.44  Sub-proof #1374 shows that the following formulas are inconsistent:
% 243.97/50.44  ----------------------------------------------------------------
% 243.97/50.44    (1)   ~ (e3 = e0)
% 243.97/50.44    (2)   ~ (e2 = e0)
% 243.97/50.44    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.97/50.44         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.97/50.44    (4)   ~ (e3 = e1)
% 243.97/50.44    (5)   ~ (e3 = e2)
% 243.97/50.44    (6)  all_58_13 = e0
% 243.97/50.44    (7)  op(e0, e2) = e0
% 243.97/50.44    (8)  op(e3, e2) = all_52_4
% 243.97/50.44    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.44    (10)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 243.97/50.44          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.97/50.44    (11)   ~ (all_52_4 = e1)
% 243.97/50.44    (12)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.97/50.44          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.97/50.44    (13)   ~ (e1 = e0)
% 243.97/50.44    (14)  all_58_3 = e0
% 243.97/50.44    (15)   ~ (e2 = e1)
% 243.97/50.44  
% 243.97/50.44  Begin of proof
% 243.97/50.44  | 
% 243.97/50.44  | BETA: splitting (10) gives:
% 243.97/50.44  | 
% 243.97/50.44  | Case 1:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (16)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 243.97/50.44  | |           e1)
% 243.97/50.44  | | 
% 243.97/50.44  | | REF_CLOSE: (8), (9), (11), (13), (14), (16) are inconsistent by sub-proof
% 243.97/50.44  | |            #1377.
% 243.97/50.44  | | 
% 243.97/50.44  | Case 2:
% 243.97/50.44  | | 
% 243.97/50.44  | |   (17)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 243.97/50.44  | |           e1)
% 243.97/50.44  | | 
% 243.97/50.44  | | BETA: splitting (17) gives:
% 243.97/50.44  | | 
% 243.97/50.44  | | Case 1:
% 243.97/50.44  | | | 
% 243.97/50.44  | | |   (18)  all_58_7 = e1 & op(e1, e2) = e1
% 243.97/50.44  | | | 
% 243.97/50.44  | | | ALPHA: (18) implies:
% 243.97/50.44  | | |   (19)  all_58_7 = e1
% 243.97/50.44  | | | 
% 243.97/50.44  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (12), (14), (15), (19)
% 243.97/50.44  | | |            are inconsistent by sub-proof #1375.
% 243.97/50.44  | | | 
% 243.97/50.44  | | Case 2:
% 243.97/50.44  | | | 
% 243.97/50.45  | | |   (20)  all_58_13 = e1 & op(e0, e2) = e1
% 243.97/50.45  | | | 
% 243.97/50.45  | | | ALPHA: (20) implies:
% 243.97/50.45  | | |   (21)  op(e0, e2) = e1
% 243.97/50.45  | | | 
% 243.97/50.45  | | | REF_CLOSE: (7), (9), (13), (21) are inconsistent by sub-proof #1872.
% 243.97/50.45  | | | 
% 243.97/50.45  | | End of split
% 243.97/50.45  | | 
% 243.97/50.45  | End of split
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1375 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)   ~ (e3 = e0)
% 243.97/50.45    (2)   ~ (e2 = e0)
% 243.97/50.45    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 243.97/50.45         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.97/50.45    (4)   ~ (e3 = e1)
% 243.97/50.45    (5)   ~ (e3 = e2)
% 243.97/50.45    (6)  all_58_13 = e0
% 243.97/50.45    (7)  op(e0, e2) = e0
% 243.97/50.45    (8)  all_58_7 = e1
% 243.97/50.45    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.45    (10)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 243.97/50.45          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 243.97/50.45    (11)  all_58_3 = e0
% 243.97/50.45    (12)   ~ (e2 = e1)
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | BETA: splitting (10) gives:
% 243.97/50.45  | 
% 243.97/50.45  | Case 1:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (13)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 243.97/50.45  | |           e3)
% 243.97/50.45  | | 
% 243.97/50.45  | | BETA: splitting (13) gives:
% 243.97/50.45  | | 
% 243.97/50.45  | | Case 1:
% 243.97/50.45  | | | 
% 243.97/50.45  | | |   (14)  all_58_1 = e3 & op(e3, e2) = e3
% 243.97/50.45  | | | 
% 243.97/50.45  | | | ALPHA: (14) implies:
% 243.97/50.45  | | |   (15)  all_58_1 = e3
% 243.97/50.45  | | | 
% 243.97/50.45  | | | BETA: splitting (3) gives:
% 243.97/50.45  | | | 
% 243.97/50.45  | | | Case 1:
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | |   (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2)
% 243.97/50.45  | | | |           = e2)
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | | BETA: splitting (16) gives:
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | | Case 1:
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | |   (17)  all_58_1 = e2 & op(e3, e2) = e2
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | | REF_CLOSE: (5), (15), (17) are inconsistent by sub-proof #1590.
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | Case 2:
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | |   (18)  all_58_3 = e2 & op(e2, e2) = e2
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | | ALPHA: (18) implies:
% 243.97/50.45  | | | | |   (19)  all_58_3 = e2
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | | COMBINE_EQS: (11), (19) imply:
% 243.97/50.45  | | | | |   (20)  e2 = e0
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | | REDUCE: (2), (20) imply:
% 243.97/50.45  | | | | |   (21)  $false
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | | CLOSE: (21) is inconsistent.
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | End of split
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | Case 2:
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | |   (22)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2)
% 243.97/50.45  | | | |           = e2)
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | | REF_CLOSE: (2), (7), (8), (9), (12), (22) are inconsistent by sub-proof
% 243.97/50.45  | | | |            #1376.
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | End of split
% 243.97/50.45  | | | 
% 243.97/50.45  | | Case 2:
% 243.97/50.45  | | | 
% 243.97/50.45  | | |   (23)  all_58_3 = e3 & op(e2, e2) = e3
% 243.97/50.45  | | | 
% 243.97/50.45  | | | ALPHA: (23) implies:
% 243.97/50.45  | | |   (24)  all_58_3 = e3
% 243.97/50.45  | | | 
% 243.97/50.45  | | | REF_CLOSE: (1), (11), (24) are inconsistent by sub-proof #1460.
% 243.97/50.45  | | | 
% 243.97/50.45  | | End of split
% 243.97/50.45  | | 
% 243.97/50.45  | Case 2:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (25)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 243.97/50.45  | |           e3)
% 243.97/50.45  | | 
% 243.97/50.45  | | BETA: splitting (25) gives:
% 243.97/50.45  | | 
% 243.97/50.45  | | Case 1:
% 243.97/50.45  | | | 
% 243.97/50.45  | | |   (26)  all_58_7 = e3 & op(e1, e2) = e3
% 243.97/50.45  | | | 
% 243.97/50.45  | | | REF_CLOSE: (4), (8), (26) are inconsistent by sub-proof #1679.
% 243.97/50.45  | | | 
% 243.97/50.45  | | Case 2:
% 243.97/50.45  | | | 
% 243.97/50.45  | | |   (27)  all_58_13 = e3 & op(e0, e2) = e3
% 243.97/50.45  | | | 
% 243.97/50.45  | | | ALPHA: (27) implies:
% 243.97/50.45  | | |   (28)  all_58_13 = e3
% 243.97/50.45  | | | 
% 243.97/50.45  | | | COMBINE_EQS: (6), (28) imply:
% 243.97/50.45  | | |   (29)  e3 = e0
% 243.97/50.45  | | | 
% 243.97/50.45  | | | REDUCE: (1), (29) imply:
% 243.97/50.45  | | |   (30)  $false
% 243.97/50.45  | | | 
% 243.97/50.45  | | | CLOSE: (30) is inconsistent.
% 243.97/50.45  | | | 
% 243.97/50.45  | | End of split
% 243.97/50.45  | | 
% 243.97/50.45  | End of split
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1376 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)   ~ (e2 = e0)
% 243.97/50.45    (2)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 243.97/50.45    (3)  op(e0, e2) = e0
% 243.97/50.45    (4)  all_58_7 = e1
% 243.97/50.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.45    (6)   ~ (e2 = e1)
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | BETA: splitting (2) gives:
% 243.97/50.45  | 
% 243.97/50.45  | Case 1:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (7)  all_58_7 = e2 & op(e1, e2) = e2
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #2218.
% 243.97/50.45  | | 
% 243.97/50.45  | Case 2:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (8)  all_58_13 = e2 & op(e0, e2) = e2
% 243.97/50.45  | | 
% 243.97/50.45  | | ALPHA: (8) implies:
% 243.97/50.45  | |   (9)  op(e0, e2) = e2
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #2132.
% 243.97/50.45  | | 
% 243.97/50.45  | End of split
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1377 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 243.97/50.45    (2)  op(e3, e2) = all_52_4
% 243.97/50.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.45    (4)   ~ (all_52_4 = e1)
% 243.97/50.45    (5)   ~ (e1 = e0)
% 243.97/50.45    (6)  all_58_3 = e0
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | BETA: splitting (1) gives:
% 243.97/50.45  | 
% 243.97/50.45  | Case 1:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (7)  all_58_1 = e1 & op(e3, e2) = e1
% 243.97/50.45  | | 
% 243.97/50.45  | | ALPHA: (7) implies:
% 243.97/50.45  | |   (8)  op(e3, e2) = e1
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2228.
% 243.97/50.45  | | 
% 243.97/50.45  | Case 2:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (9)  all_58_3 = e1 & op(e2, e2) = e1
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #1752.
% 243.97/50.45  | | 
% 243.97/50.45  | End of split
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1378 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)   ~ (e3 = e0)
% 243.97/50.45    (2)   ~ (e3 = e1)
% 243.97/50.45    (3)  op(e3, e1) = e0
% 243.97/50.45    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 243.97/50.45         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.97/50.45    (5)   ~ (all_22_0 = e3)
% 243.97/50.45    (6)  op(e3, e3) = e1
% 243.97/50.45    (7)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 243.97/50.45           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 243.97/50.45           all_30_1 & $i(all_30_1))
% 243.97/50.45    (8)  op(e3, e0) = all_52_12
% 243.97/50.45    (9)  op(all_22_1, e2) = all_22_0
% 243.97/50.45    (10)  op(e2, e1) = e3
% 243.97/50.45    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.45    (12)   ~ (all_52_12 = e3)
% 243.97/50.45    (13)  op(e2, e1) = all_22_1
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | BETA: splitting (4) gives:
% 243.97/50.45  | 
% 243.97/50.45  | Case 1:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 243.97/50.45  | |           e3)
% 243.97/50.45  | | 
% 243.97/50.45  | | BETA: splitting (14) gives:
% 243.97/50.45  | | 
% 243.97/50.45  | | Case 1:
% 243.97/50.45  | | | 
% 243.97/50.45  | | |   (15)  all_58_0 = e3 & op(e3, e3) = e3
% 243.97/50.45  | | | 
% 243.97/50.45  | | | ALPHA: (15) implies:
% 243.97/50.45  | | |   (16)  op(e3, e3) = e3
% 243.97/50.45  | | | 
% 243.97/50.45  | | | REF_CLOSE: (2), (6), (11), (16) are inconsistent by sub-proof #1578.
% 243.97/50.45  | | | 
% 243.97/50.45  | | Case 2:
% 243.97/50.45  | | | 
% 243.97/50.45  | | |   (17)  all_58_1 = e3 & op(e3, e2) = e3
% 243.97/50.45  | | | 
% 243.97/50.45  | | | ALPHA: (17) implies:
% 243.97/50.45  | | |   (18)  op(e3, e2) = e3
% 243.97/50.45  | | | 
% 243.97/50.45  | | | REF_CLOSE: (5), (7), (9), (10), (11), (13), (18) are inconsistent by
% 243.97/50.45  | | |            sub-proof #1380.
% 243.97/50.45  | | | 
% 243.97/50.45  | | End of split
% 243.97/50.45  | | 
% 243.97/50.45  | Case 2:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (19)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 243.97/50.45  | |           e3)
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (1), (3), (8), (11), (12), (19) are inconsistent by sub-proof
% 243.97/50.45  | |            #1379.
% 243.97/50.45  | | 
% 243.97/50.45  | End of split
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1379 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)   ~ (e3 = e0)
% 243.97/50.45    (2)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 243.97/50.45    (3)  op(e3, e1) = e0
% 243.97/50.45    (4)  op(e3, e0) = all_52_12
% 243.97/50.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.45    (6)   ~ (all_52_12 = e3)
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | BETA: splitting (2) gives:
% 243.97/50.45  | 
% 243.97/50.45  | Case 1:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (7)  all_58_4 = e3 & op(e3, e1) = e3
% 243.97/50.45  | | 
% 243.97/50.45  | | ALPHA: (7) implies:
% 243.97/50.45  | |   (8)  op(e3, e1) = e3
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #2118.
% 243.97/50.45  | | 
% 243.97/50.45  | Case 2:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (9)  all_58_9 = e3 & op(e3, e0) = e3
% 243.97/50.45  | | 
% 243.97/50.45  | | ALPHA: (9) implies:
% 243.97/50.45  | |   (10)  op(e3, e0) = e3
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #2179.
% 243.97/50.45  | | 
% 243.97/50.45  | End of split
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1380 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)   ~ (all_22_0 = e3)
% 243.97/50.45    (2)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 243.97/50.45           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 243.97/50.45           all_30_1 & $i(all_30_1))
% 243.97/50.45    (3)  op(all_22_1, e2) = all_22_0
% 243.97/50.45    (4)  op(e2, e1) = e3
% 243.97/50.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.45    (6)  op(e2, e1) = all_22_1
% 243.97/50.45    (7)  op(e3, e2) = e3
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | BETA: splitting (2) gives:
% 243.97/50.45  | 
% 243.97/50.45  | Case 1:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (8)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) =
% 243.97/50.45  | |        all_30_1 & $i(all_30_0) & $i(all_30_1)
% 243.97/50.45  | | 
% 243.97/50.45  | | ALPHA: (8) implies:
% 243.97/50.45  | |   (9)  op(e2, e1) = all_30_1
% 243.97/50.45  | |   (10)  op(all_30_1, e2) = all_30_0
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10) are inconsistent by
% 243.97/50.45  | |            sub-proof #1875.
% 243.97/50.45  | | 
% 243.97/50.45  | Case 2:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (11)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 & $i(all_30_1)
% 243.97/50.45  | | 
% 243.97/50.45  | | ALPHA: (11) implies:
% 243.97/50.45  | |   (12)   ~ (all_30_1 = e3)
% 243.97/50.45  | |   (13)  op(e2, e1) = all_30_1
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (4), (5), (12), (13) are inconsistent by sub-proof #1839.
% 243.97/50.45  | | 
% 243.97/50.45  | End of split
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1381 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)  all_54_1 = e1 | all_54_1 = e0
% 243.97/50.45    (2)  all_54_1 = all_22_0
% 243.97/50.45    (3)   ~ (all_22_0 = e1)
% 243.97/50.45    (4)   ~ (all_22_0 = e0)
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | BETA: splitting (1) gives:
% 243.97/50.45  | 
% 243.97/50.45  | Case 1:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (5)  all_54_1 = e1
% 243.97/50.45  | | 
% 243.97/50.45  | | COMBINE_EQS: (2), (5) imply:
% 243.97/50.45  | |   (6)  all_22_0 = e1
% 243.97/50.45  | | 
% 243.97/50.45  | | REDUCE: (3), (6) imply:
% 243.97/50.45  | |   (7)  $false
% 243.97/50.45  | | 
% 243.97/50.45  | | CLOSE: (7) is inconsistent.
% 243.97/50.45  | | 
% 243.97/50.45  | Case 2:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (8)  all_54_1 = e0
% 243.97/50.45  | | 
% 243.97/50.45  | | COMBINE_EQS: (2), (8) imply:
% 243.97/50.45  | |   (9)  all_22_0 = e0
% 243.97/50.45  | | 
% 243.97/50.45  | | REDUCE: (4), (9) imply:
% 243.97/50.45  | |   (10)  $false
% 243.97/50.45  | | 
% 243.97/50.45  | | CLOSE: (10) is inconsistent.
% 243.97/50.45  | | 
% 243.97/50.45  | End of split
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1382 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)  all_54_1 = all_22_0
% 243.97/50.45    (2)  all_54_1 = e3
% 243.97/50.45    (3)   ~ (all_22_0 = e3)
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | COMBINE_EQS: (1), (2) imply:
% 243.97/50.45  |   (4)  all_22_0 = e3
% 243.97/50.45  | 
% 243.97/50.45  | SIMP: (4) implies:
% 243.97/50.45  |   (5)  all_22_0 = e3
% 243.97/50.45  | 
% 243.97/50.45  | REDUCE: (3), (5) imply:
% 243.97/50.45  |   (6)  $false
% 243.97/50.45  | 
% 243.97/50.45  | CLOSE: (6) is inconsistent.
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1383 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 243.97/50.45           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 243.97/50.45           all_12_1 & $i(all_12_1))
% 243.97/50.45    (2)   ~ (e3 = e0)
% 243.97/50.45    (3)  all_58_6 = e3
% 243.97/50.45    (4)   ~ (e2 = e0)
% 243.97/50.45    (5)  op(e1, e3) = e3
% 243.97/50.45    (6)   ~ (e3 = e1)
% 243.97/50.45    (7)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 243.97/50.45           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 243.97/50.45           all_26_1 & $i(all_26_1))
% 243.97/50.45    (8)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 243.97/50.45         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 243.97/50.45    (9)   ~ (e3 = e2)
% 243.97/50.45    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 243.97/50.45          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 243.97/50.45    (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 243.97/50.45          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 243.97/50.45    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.45    (13)   ~ (e1 = e0)
% 243.97/50.45    (14)  op(e3, e3) = e3
% 243.97/50.45    (15)   ~ (e2 = e1)
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | BETA: splitting (11) gives:
% 243.97/50.45  | 
% 243.97/50.45  | Case 1:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (16)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 243.97/50.45  | |           e1)
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (12), (13), (14), (15), (16)
% 243.97/50.45  | |            are inconsistent by sub-proof #1576.
% 243.97/50.45  | | 
% 243.97/50.45  | Case 2:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (17)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 243.97/50.45  | |           e1)
% 243.97/50.45  | | 
% 243.97/50.45  | | BETA: splitting (17) gives:
% 243.97/50.45  | | 
% 243.97/50.45  | | Case 1:
% 243.97/50.45  | | | 
% 243.97/50.45  | | |   (18)  all_58_6 = e1 & op(e1, e3) = e1
% 243.97/50.45  | | | 
% 243.97/50.45  | | | ALPHA: (18) implies:
% 243.97/50.45  | | |   (19)  op(e1, e3) = e1
% 243.97/50.45  | | | 
% 243.97/50.45  | | | REF_CLOSE: (5), (6), (12), (19) are inconsistent by sub-proof #2225.
% 243.97/50.45  | | | 
% 243.97/50.45  | | Case 2:
% 243.97/50.45  | | | 
% 243.97/50.45  | | |   (20)  all_58_12 = e1 & op(e0, e3) = e1
% 243.97/50.45  | | | 
% 243.97/50.45  | | | ALPHA: (20) implies:
% 243.97/50.45  | | |   (21)  op(e0, e3) = e1
% 243.97/50.45  | | | 
% 243.97/50.45  | | | BETA: splitting (10) gives:
% 243.97/50.45  | | | 
% 243.97/50.45  | | | Case 1:
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | |   (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 243.97/50.45  | | | |           = e0)
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (14),
% 243.97/50.45  | | | |            (15), (22) are inconsistent by sub-proof #1573.
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | Case 2:
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | |   (23)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 243.97/50.45  | | | |           = e0)
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | | BETA: splitting (23) gives:
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | | Case 1:
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | |   (24)  all_58_6 = e0 & op(e1, e3) = e0
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | | REF_CLOSE: (2), (3), (24) are inconsistent by sub-proof #2213.
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | Case 2:
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | |   (25)  all_58_12 = e0 & op(e0, e3) = e0
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | | ALPHA: (25) implies:
% 243.97/50.45  | | | | |   (26)  op(e0, e3) = e0
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | | REF_CLOSE: (1), (7), (12), (13), (21), (26) are inconsistent by
% 243.97/50.45  | | | | |            sub-proof #1384.
% 243.97/50.45  | | | | | 
% 243.97/50.45  | | | | End of split
% 243.97/50.45  | | | | 
% 243.97/50.45  | | | End of split
% 243.97/50.45  | | | 
% 243.97/50.45  | | End of split
% 243.97/50.45  | | 
% 243.97/50.45  | End of split
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1384 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)  ( ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 243.97/50.45           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e0, e3) =
% 243.97/50.45           all_12_1 & $i(all_12_1))
% 243.97/50.45    (2)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 243.97/50.45           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 243.97/50.45           all_26_1 & $i(all_26_1))
% 243.97/50.45    (3)  op(e0, e3) = e1
% 243.97/50.45    (4)  op(e0, e3) = e0
% 243.97/50.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.45    (6)   ~ (e1 = e0)
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | BETA: splitting (1) gives:
% 243.97/50.45  | 
% 243.97/50.45  | Case 1:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (7)   ~ (all_12_0 = e1) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 243.97/50.45  | |        all_12_1 & $i(all_12_0) & $i(all_12_1)
% 243.97/50.45  | | 
% 243.97/50.45  | | ALPHA: (7) implies:
% 243.97/50.45  | |   (8)  op(e0, e3) = all_12_1
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (2), (3), (4), (5), (6), (8) are inconsistent by sub-proof #1385.
% 243.97/50.45  | | 
% 243.97/50.45  | Case 2:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (9)   ~ (all_12_1 = e2) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 243.97/50.45  | | 
% 243.97/50.45  | | ALPHA: (9) implies:
% 243.97/50.45  | |   (10)  op(e0, e3) = all_12_1
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (2), (3), (4), (5), (6), (10) are inconsistent by sub-proof
% 243.97/50.45  | |            #1385.
% 243.97/50.45  | | 
% 243.97/50.45  | End of split
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1385 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)  ( ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) = all_26_1
% 243.97/50.45           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e0, e3) =
% 243.97/50.45           all_26_1 & $i(all_26_1))
% 243.97/50.45    (2)  op(e0, e3) = e1
% 243.97/50.45    (3)  op(e0, e3) = e0
% 243.97/50.45    (4)  op(e0, e3) = all_12_1
% 243.97/50.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.45    (6)   ~ (e1 = e0)
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | BETA: splitting (1) gives:
% 243.97/50.45  | 
% 243.97/50.45  | Case 1:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (7)   ~ (all_26_0 = e2) & op(all_26_1, e0) = all_26_0 & op(e0, e3) =
% 243.97/50.45  | |        all_26_1 & $i(all_26_0) & $i(all_26_1)
% 243.97/50.45  | | 
% 243.97/50.45  | | ALPHA: (7) implies:
% 243.97/50.45  | |   (8)  op(e0, e3) = all_26_1
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (2), (3), (4), (5), (6), (8) are inconsistent by sub-proof #1387.
% 243.97/50.45  | | 
% 243.97/50.45  | Case 2:
% 243.97/50.45  | | 
% 243.97/50.45  | |   (9)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 243.97/50.45  | | 
% 243.97/50.45  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #1386.
% 243.97/50.45  | | 
% 243.97/50.45  | End of split
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1386 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)   ~ (all_26_1 = e1) & op(e0, e3) = all_26_1 & $i(all_26_1)
% 243.97/50.45    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.45    (3)  op(e0, e3) = e1
% 243.97/50.45  
% 243.97/50.45  Begin of proof
% 243.97/50.45  | 
% 243.97/50.45  | ALPHA: (1) implies:
% 243.97/50.45  |   (4)   ~ (all_26_1 = e1)
% 243.97/50.45  |   (5)  op(e0, e3) = all_26_1
% 243.97/50.45  | 
% 243.97/50.45  | GROUND_INST: instantiating (2) with e1, all_26_1, e3, e0, simplifying with
% 243.97/50.45  |              (3), (5) gives:
% 243.97/50.45  |   (6)  all_26_1 = e1
% 243.97/50.45  | 
% 243.97/50.45  | REDUCE: (4), (6) imply:
% 243.97/50.45  |   (7)  $false
% 243.97/50.45  | 
% 243.97/50.45  | CLOSE: (7) is inconsistent.
% 243.97/50.45  | 
% 243.97/50.45  End of proof
% 243.97/50.45  
% 243.97/50.45  Sub-proof #1387 shows that the following formulas are inconsistent:
% 243.97/50.45  ----------------------------------------------------------------
% 243.97/50.45    (1)  op(e0, e3) = e1
% 243.97/50.45    (2)  op(e0, e3) = e0
% 243.97/50.46    (3)  op(e0, e3) = all_26_1
% 243.97/50.46    (4)  op(e0, e3) = all_12_1
% 243.97/50.46    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.46    (6)   ~ (e1 = e0)
% 243.97/50.46  
% 243.97/50.46  Begin of proof
% 243.97/50.46  | 
% 243.97/50.46  | GROUND_INST: instantiating (5) with e1, all_26_1, e3, e0, simplifying with
% 243.97/50.46  |              (1), (3) gives:
% 243.97/50.46  |   (7)  all_26_1 = e1
% 243.97/50.46  | 
% 243.97/50.46  | GROUND_INST: instantiating (5) with all_12_1, all_26_1, e3, e0, simplifying
% 243.97/50.46  |              with (3), (4) gives:
% 243.97/50.46  |   (8)  all_26_1 = all_12_1
% 243.97/50.46  | 
% 243.97/50.46  | GROUND_INST: instantiating (5) with e0, all_26_1, e3, e0, simplifying with
% 243.97/50.46  |              (2), (3) gives:
% 243.97/50.46  |   (9)  all_26_1 = e0
% 243.97/50.46  | 
% 243.97/50.46  | COMBINE_EQS: (7), (8) imply:
% 243.97/50.46  |   (10)  all_12_1 = e1
% 243.97/50.46  | 
% 243.97/50.46  | COMBINE_EQS: (8), (9) imply:
% 243.97/50.46  |   (11)  all_12_1 = e0
% 243.97/50.46  | 
% 243.97/50.46  | COMBINE_EQS: (10), (11) imply:
% 243.97/50.46  |   (12)  e1 = e0
% 243.97/50.46  | 
% 243.97/50.46  | SIMP: (12) implies:
% 243.97/50.46  |   (13)  e1 = e0
% 243.97/50.46  | 
% 243.97/50.46  | REDUCE: (6), (13) imply:
% 243.97/50.46  |   (14)  $false
% 243.97/50.46  | 
% 243.97/50.46  | CLOSE: (14) is inconsistent.
% 243.97/50.46  | 
% 243.97/50.46  End of proof
% 243.97/50.46  
% 243.97/50.46  Sub-proof #1388 shows that the following formulas are inconsistent:
% 243.97/50.46  ----------------------------------------------------------------
% 243.97/50.46    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.46    (2)  op(e0, e0) = e3
% 243.97/50.46    (3)  op(e0, e0) = e2
% 243.97/50.46    (4)   ~ (e3 = e2)
% 243.97/50.46  
% 243.97/50.46  Begin of proof
% 243.97/50.46  | 
% 243.97/50.46  | GROUND_INST: instantiating (1) with e2, e3, e0, e0, simplifying with (2), (3)
% 243.97/50.46  |              gives:
% 243.97/50.46  |   (5)  e3 = e2
% 243.97/50.46  | 
% 243.97/50.46  | REDUCE: (4), (5) imply:
% 243.97/50.46  |   (6)  $false
% 243.97/50.46  | 
% 243.97/50.46  | CLOSE: (6) is inconsistent.
% 243.97/50.46  | 
% 243.97/50.46  End of proof
% 243.97/50.46  
% 243.97/50.46  Sub-proof #1389 shows that the following formulas are inconsistent:
% 243.97/50.46  ----------------------------------------------------------------
% 243.97/50.46    (1)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 243.97/50.46             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 243.97/50.46           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 243.97/50.46           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 243.97/50.46           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 243.97/50.46           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.97/50.46           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.97/50.46    (2)  op(e0, e3) = all_52_3
% 243.97/50.46    (3)   ~ (all_52_3 = e3)
% 243.97/50.46    (4)  all_56_31 = e3
% 243.97/50.46    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.46  
% 243.97/50.46  Begin of proof
% 243.97/50.46  | 
% 243.97/50.46  | BETA: splitting (1) gives:
% 243.97/50.46  | 
% 243.97/50.46  | Case 1:
% 243.97/50.46  | | 
% 243.97/50.46  | |   (6)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 243.97/50.46  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 243.97/50.46  | |        op(e1, e3) = e1
% 243.97/50.46  | | 
% 243.97/50.46  | | ALPHA: (6) implies:
% 243.97/50.46  | |   (7)   ~ (all_56_31 = e3)
% 243.97/50.46  | | 
% 243.97/50.46  | | REDUCE: (4), (7) imply:
% 243.97/50.46  | |   (8)  $false
% 243.97/50.46  | | 
% 243.97/50.46  | | CLOSE: (8) is inconsistent.
% 243.97/50.46  | | 
% 243.97/50.46  | Case 2:
% 243.97/50.46  | | 
% 243.97/50.46  | |   (9)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 243.97/50.46  | |            = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 243.97/50.46  | |          e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 243.97/50.46  | |          (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 243.97/50.46  | |          (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 243.97/50.46  | | 
% 243.97/50.46  | | REF_CLOSE: (2), (3), (4), (5), (9) are inconsistent by sub-proof #1412.
% 243.97/50.46  | | 
% 243.97/50.46  | End of split
% 243.97/50.46  | 
% 243.97/50.46  End of proof
% 243.97/50.46  
% 243.97/50.46  Sub-proof #1390 shows that the following formulas are inconsistent:
% 243.97/50.46  ----------------------------------------------------------------
% 243.97/50.46    (1)   ~ (all_6_2 = e2)
% 243.97/50.46    (2)  all_54_10 = all_6_2
% 243.97/50.46    (3)   ~ (all_6_2 = e3)
% 243.97/50.46    (4)   ~ (all_6_2 = e0)
% 243.97/50.46    (5)   ~ (all_6_2 = e1)
% 243.97/50.46    (6)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.97/50.46  
% 243.97/50.46  Begin of proof
% 243.97/50.46  | 
% 243.97/50.46  | BETA: splitting (6) gives:
% 243.97/50.46  | 
% 243.97/50.46  | Case 1:
% 243.97/50.46  | | 
% 243.97/50.46  | |   (7)  all_54_10 = e3
% 243.97/50.46  | | 
% 243.97/50.46  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #2313.
% 243.97/50.46  | | 
% 243.97/50.46  | Case 2:
% 243.97/50.46  | | 
% 243.97/50.46  | |   (8)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 243.97/50.46  | | 
% 243.97/50.46  | | BETA: splitting (8) gives:
% 243.97/50.46  | | 
% 243.97/50.46  | | Case 1:
% 243.97/50.46  | | | 
% 243.97/50.46  | | |   (9)  all_54_10 = e2
% 243.97/50.46  | | | 
% 243.97/50.46  | | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #2312.
% 243.97/50.46  | | | 
% 243.97/50.46  | | Case 2:
% 243.97/50.46  | | | 
% 243.97/50.46  | | |   (10)  all_54_10 = e1 | all_54_10 = e0
% 243.97/50.46  | | | 
% 243.97/50.46  | | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #2282.
% 243.97/50.46  | | | 
% 243.97/50.46  | | End of split
% 243.97/50.46  | | 
% 243.97/50.46  | End of split
% 243.97/50.46  | 
% 243.97/50.46  End of proof
% 243.97/50.46  
% 243.97/50.46  Sub-proof #1391 shows that the following formulas are inconsistent:
% 243.97/50.46  ----------------------------------------------------------------
% 243.97/50.46    (1)   ~ (e3 = e0)
% 243.97/50.46    (2)   ~ (e2 = e0)
% 243.97/50.46    (3)  all_58_12 = e2
% 243.97/50.46    (4)  all_58_14 = e2
% 243.97/50.46    (5)  all_58_15 = e3
% 243.97/50.46    (6)   ~ (e3 = e1)
% 243.97/50.46    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 243.97/50.46             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 243.97/50.46               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 243.97/50.46               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 243.97/50.46    (8)  op(e0, e0) = e3
% 243.97/50.46    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.46    (10)   ~ (e1 = e0)
% 243.97/50.46    (11)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 243.97/50.46          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.97/50.46            e1)
% 243.97/50.46    (12)   ~ (e2 = e1)
% 243.97/50.46  
% 243.97/50.46  Begin of proof
% 243.97/50.46  | 
% 243.97/50.46  | BETA: splitting (7) gives:
% 243.97/50.46  | 
% 243.97/50.46  | Case 1:
% 243.97/50.46  | | 
% 243.97/50.46  | |   (13)  all_58_15 = e0 & op(e0, e0) = e0
% 243.97/50.46  | | 
% 243.97/50.46  | | ALPHA: (13) implies:
% 243.97/50.46  | |   (14)  op(e0, e0) = e0
% 243.97/50.46  | | 
% 243.97/50.46  | | REF_CLOSE: (1), (8), (9), (14) are inconsistent by sub-proof #2079.
% 243.97/50.46  | | 
% 243.97/50.46  | Case 2:
% 243.97/50.46  | | 
% 243.97/50.46  | |   (15)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 243.97/50.46  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 243.97/50.46  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.97/50.46  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 243.97/50.46  | | 
% 243.97/50.46  | | ALPHA: (15) implies:
% 243.97/50.46  | |   (16)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 243.97/50.46  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.97/50.46  | | 
% 243.97/50.46  | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (12), (16) are
% 243.97/50.46  | |            inconsistent by sub-proof #1392.
% 243.97/50.46  | | 
% 243.97/50.46  | End of split
% 243.97/50.46  | 
% 243.97/50.46  End of proof
% 243.97/50.46  
% 243.97/50.46  Sub-proof #1392 shows that the following formulas are inconsistent:
% 243.97/50.46  ----------------------------------------------------------------
% 243.97/50.46    (1)   ~ (e2 = e0)
% 243.97/50.46    (2)  all_58_12 = e2
% 243.97/50.46    (3)  all_58_14 = e2
% 243.97/50.46    (4)  all_58_15 = e3
% 243.97/50.46    (5)   ~ (e3 = e1)
% 243.97/50.46    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.46    (7)   ~ (e1 = e0)
% 243.97/50.46    (8)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 243.97/50.46         (all_58_14 = e0 & op(e0, e1) = e0)
% 243.97/50.46    (9)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 243.97/50.46         (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 243.97/50.46    (10)   ~ (e2 = e1)
% 243.97/50.46  
% 243.97/50.46  Begin of proof
% 243.97/50.46  | 
% 243.97/50.46  | BETA: splitting (9) gives:
% 243.97/50.46  | 
% 243.97/50.46  | Case 1:
% 243.97/50.46  | | 
% 243.97/50.46  | |   (11)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 243.97/50.46  | |           e1)
% 243.97/50.46  | | 
% 243.97/50.46  | | BETA: splitting (11) gives:
% 243.97/50.46  | | 
% 243.97/50.46  | | Case 1:
% 243.97/50.46  | | | 
% 243.97/50.46  | | |   (12)  all_58_12 = e1 & op(e0, e3) = e1
% 243.97/50.46  | | | 
% 243.97/50.46  | | | REF_CLOSE: (2), (10), (12) are inconsistent by sub-proof #1763.
% 243.97/50.46  | | | 
% 243.97/50.46  | | Case 2:
% 243.97/50.46  | | | 
% 243.97/50.46  | | |   (13)  all_58_13 = e1 & op(e0, e2) = e1
% 243.97/50.46  | | | 
% 243.97/50.46  | | | ALPHA: (13) implies:
% 243.97/50.46  | | |   (14)  op(e0, e2) = e1
% 243.97/50.46  | | | 
% 243.97/50.46  | | | BETA: splitting (8) gives:
% 243.97/50.46  | | | 
% 243.97/50.46  | | | Case 1:
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | |   (15)  all_58_12 = e0 & op(e0, e3) = e0
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | | REF_CLOSE: (1), (2), (15) are inconsistent by sub-proof #1760.
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | Case 2:
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | |   (16)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 243.97/50.46  | | | |             e1) = e0)
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | | BETA: splitting (16) gives:
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | | Case 1:
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | |   (17)  all_58_13 = e0 & op(e0, e2) = e0
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | | ALPHA: (17) implies:
% 243.97/50.46  | | | | |   (18)  op(e0, e2) = e0
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | | REF_CLOSE: (6), (7), (14), (18) are inconsistent by sub-proof #1872.
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | Case 2:
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | |   (19)  all_58_14 = e0 & op(e0, e1) = e0
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | | REF_CLOSE: (1), (3), (19) are inconsistent by sub-proof #2036.
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | End of split
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | End of split
% 243.97/50.46  | | | 
% 243.97/50.46  | | End of split
% 243.97/50.46  | | 
% 243.97/50.46  | Case 2:
% 243.97/50.46  | | 
% 243.97/50.46  | |   (20)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 243.97/50.46  | |           e1)
% 243.97/50.46  | | 
% 243.97/50.46  | | BETA: splitting (20) gives:
% 243.97/50.46  | | 
% 243.97/50.46  | | Case 1:
% 243.97/50.46  | | | 
% 243.97/50.46  | | |   (21)  all_58_14 = e1 & op(e0, e1) = e1
% 243.97/50.46  | | | 
% 243.97/50.46  | | | ALPHA: (21) implies:
% 243.97/50.46  | | |   (22)  all_58_14 = e1
% 243.97/50.46  | | | 
% 243.97/50.46  | | | REF_CLOSE: (3), (10), (22) are inconsistent by sub-proof #2044.
% 243.97/50.46  | | | 
% 243.97/50.46  | | Case 2:
% 243.97/50.46  | | | 
% 243.97/50.46  | | |   (23)  all_58_15 = e1 & op(e0, e0) = e1
% 243.97/50.46  | | | 
% 243.97/50.46  | | | REF_CLOSE: (4), (5), (23) are inconsistent by sub-proof #1393.
% 243.97/50.46  | | | 
% 243.97/50.46  | | End of split
% 243.97/50.46  | | 
% 243.97/50.46  | End of split
% 243.97/50.46  | 
% 243.97/50.46  End of proof
% 243.97/50.46  
% 243.97/50.46  Sub-proof #1393 shows that the following formulas are inconsistent:
% 243.97/50.46  ----------------------------------------------------------------
% 243.97/50.46    (1)  all_58_15 = e1 & op(e0, e0) = e1
% 243.97/50.46    (2)  all_58_15 = e3
% 243.97/50.46    (3)   ~ (e3 = e1)
% 243.97/50.46  
% 243.97/50.46  Begin of proof
% 243.97/50.46  | 
% 243.97/50.46  | ALPHA: (1) implies:
% 243.97/50.46  |   (4)  all_58_15 = e1
% 243.97/50.46  | 
% 243.97/50.46  | COMBINE_EQS: (2), (4) imply:
% 243.97/50.46  |   (5)  e3 = e1
% 243.97/50.46  | 
% 243.97/50.46  | REDUCE: (3), (5) imply:
% 243.97/50.46  |   (6)  $false
% 243.97/50.46  | 
% 243.97/50.46  | CLOSE: (6) is inconsistent.
% 243.97/50.46  | 
% 243.97/50.46  End of proof
% 243.97/50.46  
% 243.97/50.46  Sub-proof #1394 shows that the following formulas are inconsistent:
% 243.97/50.46  ----------------------------------------------------------------
% 243.97/50.46    (1)  all_56_21 = e2
% 243.97/50.46    (2)   ~ (all_52_11 = all_40_0)
% 243.97/50.46    (3)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 243.97/50.46           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 243.97/50.46           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 243.97/50.46           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 243.97/50.46           & $i(all_56_23))
% 243.97/50.46    (4)   ~ (e3 = e0)
% 243.97/50.46    (5)   ~ (e2 = e0)
% 243.97/50.46    (6)   ~ (all_52_11 = e2)
% 243.97/50.46    (7)  op(e1, e2) = e3
% 243.97/50.46    (8)  all_54_2 = all_40_0
% 243.97/50.46    (9)   ~ (all_40_0 = e2)
% 243.97/50.46    (10)   ~ (all_52_11 = e3)
% 243.97/50.46    (11)  op(e3, e1) = all_52_8
% 243.97/50.46    (12)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 243.97/50.46    (13)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.97/50.46    (14)  op(e3, e1) = all_40_0
% 243.97/50.46    (15)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.97/50.46    (16)   ~ (all_40_0 = e3)
% 243.97/50.46    (17)  op(e2, e3) = all_52_1
% 243.97/50.46    (18)  op(e1, e2) = all_36_1
% 243.97/50.46    (19)  op(e1, e1) = e2
% 243.97/50.46    (20)   ~ (all_40_0 = e0)
% 243.97/50.46    (21)  op(e0, e0) = e3
% 243.97/50.46    (22)  op(e2, e1) = e3
% 243.97/50.46    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 243.97/50.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 243.97/50.46    (24)  op(e1, e2) = all_40_1
% 243.97/50.46    (25)  all_54_14 = all_52_11
% 243.97/50.46    (26)   ~ (all_52_1 = e2)
% 243.97/50.46    (27)   ~ (all_52_8 = e3)
% 243.97/50.46  
% 243.97/50.46  Begin of proof
% 243.97/50.46  | 
% 243.97/50.46  | BETA: splitting (12) gives:
% 243.97/50.46  | 
% 243.97/50.46  | Case 1:
% 243.97/50.46  | | 
% 243.97/50.46  | |   (28)  all_58_8 = e0 & op(e1, e1) = e0
% 243.97/50.46  | | 
% 243.97/50.46  | | ALPHA: (28) implies:
% 243.97/50.46  | |   (29)  op(e1, e1) = e0
% 243.97/50.46  | | 
% 243.97/50.46  | | REF_CLOSE: (5), (19), (23), (29) are inconsistent by sub-proof #2211.
% 243.97/50.46  | | 
% 243.97/50.46  | Case 2:
% 243.97/50.46  | | 
% 243.97/50.46  | |   (30)  all_58_14 = e0 & op(e0, e1) = e0
% 243.97/50.46  | | 
% 243.97/50.46  | | ALPHA: (30) implies:
% 243.97/50.46  | |   (31)  op(e0, e1) = e0
% 243.97/50.46  | | 
% 243.97/50.46  | | BETA: splitting (15) gives:
% 243.97/50.46  | | 
% 243.97/50.46  | | Case 1:
% 243.97/50.46  | | | 
% 243.97/50.46  | | |   (32)  all_54_2 = e3
% 243.97/50.46  | | | 
% 243.97/50.46  | | | COMBINE_EQS: (8), (32) imply:
% 243.97/50.46  | | |   (33)  all_40_0 = e3
% 243.97/50.46  | | | 
% 243.97/50.46  | | | REDUCE: (16), (33) imply:
% 243.97/50.46  | | |   (34)  $false
% 243.97/50.46  | | | 
% 243.97/50.46  | | | CLOSE: (34) is inconsistent.
% 243.97/50.46  | | | 
% 243.97/50.46  | | Case 2:
% 243.97/50.46  | | | 
% 243.97/50.46  | | |   (35)   ~ (all_54_2 = e3)
% 243.97/50.46  | | |   (36)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 243.97/50.46  | | | 
% 243.97/50.46  | | | BETA: splitting (36) gives:
% 243.97/50.46  | | | 
% 243.97/50.46  | | | Case 1:
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | |   (37)  all_54_2 = e2
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | | COMBINE_EQS: (8), (37) imply:
% 243.97/50.46  | | | |   (38)  all_40_0 = e2
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | | REDUCE: (9), (38) imply:
% 243.97/50.46  | | | |   (39)  $false
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | | CLOSE: (39) is inconsistent.
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | Case 2:
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | |   (40)  all_54_2 = e1 | all_54_2 = e0
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | | BETA: splitting (40) gives:
% 243.97/50.46  | | | | 
% 243.97/50.46  | | | | Case 1:
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | |   (41)  all_54_2 = e1
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | | COMBINE_EQS: (8), (41) imply:
% 243.97/50.46  | | | | |   (42)  all_40_0 = e1
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | | REDUCE: (2), (42) imply:
% 243.97/50.46  | | | | |   (43)   ~ (all_52_11 = e1)
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | | REDUCE: (16), (42) imply:
% 243.97/50.46  | | | | |   (44)   ~ (e3 = e1)
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | | SIMP: (44) implies:
% 243.97/50.46  | | | | |   (45)   ~ (e3 = e1)
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | | REDUCE: (14), (42) imply:
% 243.97/50.46  | | | | |   (46)  op(e3, e1) = e1
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | | BETA: splitting (13) gives:
% 243.97/50.46  | | | | | 
% 243.97/50.46  | | | | | Case 1:
% 243.97/50.46  | | | | | | 
% 243.97/50.46  | | | | | |   (47)  all_54_14 = e3
% 243.97/50.46  | | | | | | 
% 243.97/50.46  | | | | | | REF_CLOSE: (10), (25), (47) are inconsistent by sub-proof #1796.
% 243.97/50.46  | | | | | | 
% 243.97/50.46  | | | | | Case 2:
% 243.97/50.46  | | | | | | 
% 243.97/50.46  | | | | | |   (48)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 243.97/50.46  | | | | | | 
% 243.97/50.46  | | | | | | BETA: splitting (3) gives:
% 243.97/50.46  | | | | | | 
% 243.97/50.46  | | | | | | Case 1:
% 243.97/50.46  | | | | | | | 
% 243.97/50.46  | | | | | | |   (49)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 243.97/50.46  | | | | | | |           all_56_17 & $i(all_56_17)) | (all_56_18 = e2 & op(e2,
% 243.97/50.46  | | | | | | |             all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 243.97/50.46  | | | | | | |           $i(all_56_19))
% 243.97/50.46  | | | | | | | 
% 243.97/50.46  | | | | | | | BETA: splitting (49) gives:
% 243.97/50.46  | | | | | | | 
% 243.97/50.46  | | | | | | | Case 1:
% 243.97/50.46  | | | | | | | | 
% 243.97/50.46  | | | | | | | |   (50)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 243.97/50.46  | | | | | | | |         all_56_17 & $i(all_56_17)
% 243.97/50.46  | | | | | | | | 
% 243.97/50.46  | | | | | | | | REF_CLOSE: (6), (11), (23), (25), (27), (43), (46), (48), (50)
% 243.97/50.46  | | | | | | | |            are inconsistent by sub-proof #1397.
% 243.97/50.46  | | | | | | | | 
% 243.97/50.46  | | | | | | | Case 2:
% 243.97/50.46  | | | | | | | | 
% 243.97/50.46  | | | | | | | |   (51)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) =
% 243.97/50.46  | | | | | | | |         all_56_19 & $i(all_56_19)
% 243.97/50.46  | | | | | | | | 
% 243.97/50.46  | | | | | | | | REF_CLOSE: (6), (17), (22), (23), (25), (26), (43), (48), (51)
% 243.97/50.46  | | | | | | | |            are inconsistent by sub-proof #1396.
% 243.97/50.46  | | | | | | | | 
% 243.97/50.46  | | | | | | | End of split
% 243.97/50.46  | | | | | | | 
% 243.97/50.46  | | | | | | Case 2:
% 243.97/50.46  | | | | | | | 
% 244.05/50.46  | | | | | | |   (52)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 =
% 244.05/50.46  | | | | | | |           e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 244.05/50.46  | | | | | | |           $i(all_56_23))
% 244.05/50.46  | | | | | | | 
% 244.05/50.46  | | | | | | | BETA: splitting (52) gives:
% 244.05/50.46  | | | | | | | 
% 244.05/50.46  | | | | | | | Case 1:
% 244.05/50.46  | | | | | | | | 
% 244.05/50.46  | | | | | | | |   (53)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 244.05/50.46  | | | | | | | | 
% 244.05/50.46  | | | | | | | | ALPHA: (53) implies:
% 244.05/50.46  | | | | | | | |   (54)  op(e1, all_56_21) = e1
% 244.05/50.46  | | | | | | | | 
% 244.05/50.46  | | | | | | | | REDUCE: (1), (54) imply:
% 244.05/50.46  | | | | | | | |   (55)  op(e1, e2) = e1
% 244.05/50.46  | | | | | | | | 
% 244.05/50.47  | | | | | | | | REF_CLOSE: (7), (18), (23), (24), (45), (55) are inconsistent by
% 244.05/50.47  | | | | | | | |            sub-proof #1701.
% 244.05/50.47  | | | | | | | | 
% 244.05/50.47  | | | | | | | Case 2:
% 244.05/50.47  | | | | | | | | 
% 244.05/50.47  | | | | | | | |   (56)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 244.05/50.47  | | | | | | | |         all_56_23 & $i(all_56_23)
% 244.05/50.47  | | | | | | | | 
% 244.05/50.47  | | | | | | | | ALPHA: (56) implies:
% 244.05/50.47  | | | | | | | |   (57)  op(e0, e1) = all_56_23
% 244.05/50.47  | | | | | | | |   (58)  op(e0, all_56_23) = e0
% 244.05/50.47  | | | | | | | | 
% 244.05/50.47  | | | | | | | | REF_CLOSE: (4), (21), (23), (31), (57), (58) are inconsistent by
% 244.05/50.47  | | | | | | | |            sub-proof #1395.
% 244.05/50.47  | | | | | | | | 
% 244.05/50.47  | | | | | | | End of split
% 244.05/50.47  | | | | | | | 
% 244.05/50.47  | | | | | | End of split
% 244.05/50.47  | | | | | | 
% 244.05/50.47  | | | | | End of split
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | Case 2:
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | |   (59)  all_54_2 = e0
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | COMBINE_EQS: (8), (59) imply:
% 244.05/50.47  | | | | |   (60)  all_40_0 = e0
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | REDUCE: (20), (60) imply:
% 244.05/50.47  | | | | |   (61)  $false
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | CLOSE: (61) is inconsistent.
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | End of split
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | End of split
% 244.05/50.47  | | | 
% 244.05/50.47  | | End of split
% 244.05/50.47  | | 
% 244.05/50.47  | End of split
% 244.05/50.47  | 
% 244.05/50.47  End of proof
% 244.05/50.47  
% 244.05/50.47  Sub-proof #1395 shows that the following formulas are inconsistent:
% 244.05/50.47  ----------------------------------------------------------------
% 244.05/50.47    (1)   ~ (e3 = e0)
% 244.05/50.47    (2)  op(e0, e1) = all_56_23
% 244.05/50.47    (3)  op(e0, e1) = e0
% 244.05/50.47    (4)  op(e0, e0) = e3
% 244.05/50.47    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.47    (6)  op(e0, all_56_23) = e0
% 244.05/50.47  
% 244.05/50.47  Begin of proof
% 244.05/50.47  | 
% 244.05/50.47  | GROUND_INST: instantiating (5) with e0, all_56_23, e1, e0, simplifying with
% 244.05/50.47  |              (2), (3) gives:
% 244.05/50.47  |   (7)  all_56_23 = e0
% 244.05/50.47  | 
% 244.05/50.47  | REDUCE: (6), (7) imply:
% 244.05/50.47  |   (8)  op(e0, e0) = e0
% 244.05/50.47  | 
% 244.05/50.47  | GROUND_INST: instantiating (5) with e3, e0, e0, e0, simplifying with (4), (8)
% 244.05/50.47  |              gives:
% 244.05/50.47  |   (9)  e3 = e0
% 244.05/50.47  | 
% 244.05/50.47  | REDUCE: (1), (9) imply:
% 244.05/50.47  |   (10)  $false
% 244.05/50.47  | 
% 244.05/50.47  | CLOSE: (10) is inconsistent.
% 244.05/50.47  | 
% 244.05/50.47  End of proof
% 244.05/50.47  
% 244.05/50.47  Sub-proof #1396 shows that the following formulas are inconsistent:
% 244.05/50.47  ----------------------------------------------------------------
% 244.05/50.47    (1)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 244.05/50.47         $i(all_56_19)
% 244.05/50.47    (2)   ~ (all_52_11 = e2)
% 244.05/50.47    (3)   ~ (all_52_11 = e1)
% 244.05/50.47    (4)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.05/50.47    (5)  op(e2, e3) = all_52_1
% 244.05/50.47    (6)  op(e2, e1) = e3
% 244.05/50.47    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.47    (8)  all_54_14 = all_52_11
% 244.05/50.47    (9)   ~ (all_52_1 = e2)
% 244.05/50.47  
% 244.05/50.47  Begin of proof
% 244.05/50.47  | 
% 244.05/50.47  | ALPHA: (1) implies:
% 244.05/50.47  |   (10)  op(e2, e1) = all_56_19
% 244.05/50.47  |   (11)  op(e2, all_56_19) = e2
% 244.05/50.47  | 
% 244.05/50.47  | BETA: splitting (4) gives:
% 244.05/50.47  | 
% 244.05/50.47  | Case 1:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (12)  all_54_14 = e2
% 244.05/50.47  | | 
% 244.05/50.47  | | REF_CLOSE: (2), (8), (12) are inconsistent by sub-proof #1856.
% 244.05/50.47  | | 
% 244.05/50.47  | Case 2:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (13)  all_54_14 = e1 | all_54_14 = e0
% 244.05/50.47  | | 
% 244.05/50.47  | | BETA: splitting (13) gives:
% 244.05/50.47  | | 
% 244.05/50.47  | | Case 1:
% 244.05/50.47  | | | 
% 244.05/50.47  | | |   (14)  all_54_14 = e1
% 244.05/50.47  | | | 
% 244.05/50.47  | | | REF_CLOSE: (3), (8), (14) are inconsistent by sub-proof #1937.
% 244.05/50.47  | | | 
% 244.05/50.47  | | Case 2:
% 244.05/50.47  | | | 
% 244.05/50.47  | | | 
% 244.05/50.47  | | | GROUND_INST: instantiating (7) with e3, all_56_19, e1, e2, simplifying
% 244.05/50.47  | | |              with (6), (10) gives:
% 244.05/50.47  | | |   (15)  all_56_19 = e3
% 244.05/50.47  | | | 
% 244.05/50.47  | | | REDUCE: (11), (15) imply:
% 244.05/50.47  | | |   (16)  op(e2, e3) = e2
% 244.05/50.47  | | | 
% 244.05/50.47  | | | REF_CLOSE: (5), (7), (9), (16) are inconsistent by sub-proof #2336.
% 244.05/50.47  | | | 
% 244.05/50.47  | | End of split
% 244.05/50.47  | | 
% 244.05/50.47  | End of split
% 244.05/50.47  | 
% 244.05/50.47  End of proof
% 244.05/50.47  
% 244.05/50.47  Sub-proof #1397 shows that the following formulas are inconsistent:
% 244.05/50.47  ----------------------------------------------------------------
% 244.05/50.47    (1)   ~ (all_52_11 = e2)
% 244.05/50.47    (2)   ~ (all_52_11 = e1)
% 244.05/50.47    (3)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.05/50.47    (4)  op(e3, e1) = all_52_8
% 244.05/50.47    (5)  op(e3, e1) = e1
% 244.05/50.47    (6)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 244.05/50.47         $i(all_56_17)
% 244.05/50.47    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.47    (8)  all_54_14 = all_52_11
% 244.05/50.47    (9)   ~ (all_52_8 = e3)
% 244.05/50.47  
% 244.05/50.47  Begin of proof
% 244.05/50.47  | 
% 244.05/50.47  | ALPHA: (6) implies:
% 244.05/50.47  |   (10)  op(e3, e1) = all_56_17
% 244.05/50.47  |   (11)  op(e3, all_56_17) = e3
% 244.05/50.47  | 
% 244.05/50.47  | BETA: splitting (3) gives:
% 244.05/50.47  | 
% 244.05/50.47  | Case 1:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (12)  all_54_14 = e2
% 244.05/50.47  | | 
% 244.05/50.47  | | REF_CLOSE: (1), (8), (12) are inconsistent by sub-proof #1856.
% 244.05/50.47  | | 
% 244.05/50.47  | Case 2:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (13)  all_54_14 = e1 | all_54_14 = e0
% 244.05/50.47  | | 
% 244.05/50.47  | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (13) are inconsistent
% 244.05/50.47  | |            by sub-proof #1398.
% 244.05/50.47  | | 
% 244.05/50.47  | End of split
% 244.05/50.47  | 
% 244.05/50.47  End of proof
% 244.05/50.47  
% 244.05/50.47  Sub-proof #1398 shows that the following formulas are inconsistent:
% 244.05/50.47  ----------------------------------------------------------------
% 244.05/50.47    (1)  op(e3, e1) = all_56_17
% 244.05/50.47    (2)   ~ (all_52_11 = e1)
% 244.05/50.47    (3)  op(e3, e1) = all_52_8
% 244.05/50.47    (4)  op(e3, e1) = e1
% 244.05/50.47    (5)  op(e3, all_56_17) = e3
% 244.05/50.47    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.47    (7)  all_54_14 = all_52_11
% 244.05/50.47    (8)  all_54_14 = e1 | all_54_14 = e0
% 244.05/50.47    (9)   ~ (all_52_8 = e3)
% 244.05/50.47  
% 244.05/50.47  Begin of proof
% 244.05/50.47  | 
% 244.05/50.47  | BETA: splitting (8) gives:
% 244.05/50.47  | 
% 244.05/50.47  | Case 1:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (10)  all_54_14 = e1
% 244.05/50.47  | | 
% 244.05/50.47  | | REF_CLOSE: (2), (7), (10) are inconsistent by sub-proof #1937.
% 244.05/50.47  | | 
% 244.05/50.47  | Case 2:
% 244.05/50.47  | | 
% 244.05/50.47  | | 
% 244.05/50.47  | | GROUND_INST: instantiating (6) with e1, all_56_17, e1, e3, simplifying with
% 244.05/50.47  | |              (1), (4) gives:
% 244.05/50.47  | |   (11)  all_56_17 = e1
% 244.05/50.47  | | 
% 244.05/50.47  | | REDUCE: (5), (11) imply:
% 244.05/50.47  | |   (12)  op(e3, e1) = e3
% 244.05/50.47  | | 
% 244.05/50.47  | | REF_CLOSE: (3), (6), (9), (12) are inconsistent by sub-proof #2260.
% 244.05/50.47  | | 
% 244.05/50.47  | End of split
% 244.05/50.47  | 
% 244.05/50.47  End of proof
% 244.05/50.47  
% 244.05/50.47  Sub-proof #1399 shows that the following formulas are inconsistent:
% 244.05/50.47  ----------------------------------------------------------------
% 244.05/50.47    (1)   ~ (e3 = e0)
% 244.05/50.47    (2)   ~ (e3 = e1)
% 244.05/50.47    (3)   ~ (all_52_4 = all_40_0)
% 244.05/50.47    (4)  all_54_2 = all_40_0
% 244.05/50.47    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.47         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.47    (6)   ~ (all_40_0 = e2)
% 244.05/50.47    (7)   ~ (e3 = e2)
% 244.05/50.47    (8)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.05/50.47    (9)   ~ (all_40_0 = e3)
% 244.05/50.47    (10)  op(e3, e0) = e2
% 244.05/50.47    (11)   ~ (all_52_4 = e3)
% 244.05/50.47    (12)  op(e3, e2) = all_52_4
% 244.05/50.47    (13)   ~ (all_40_0 = e0)
% 244.05/50.47    (14)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.47          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.47    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.47    (16)   ~ (e1 = e0)
% 244.05/50.47    (17)  all_58_9 = e2
% 244.05/50.47    (18)  all_58_4 = e0
% 244.05/50.47    (19)   ~ (e2 = e1)
% 244.05/50.47  
% 244.05/50.47  Begin of proof
% 244.05/50.47  | 
% 244.05/50.47  | BETA: splitting (14) gives:
% 244.05/50.47  | 
% 244.05/50.47  | Case 1:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (20)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 244.05/50.47  | |           e1)
% 244.05/50.47  | | 
% 244.05/50.47  | | BETA: splitting (20) gives:
% 244.05/50.47  | | 
% 244.05/50.47  | | Case 1:
% 244.05/50.47  | | | 
% 244.05/50.47  | | |   (21)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.47  | | | 
% 244.05/50.47  | | | ALPHA: (21) implies:
% 244.05/50.47  | | |   (22)  op(e3, e3) = e1
% 244.05/50.47  | | | 
% 244.05/50.47  | | | REF_CLOSE: (1), (2), (5), (7), (10), (11), (12), (15), (18), (22) are
% 244.05/50.47  | | |            inconsistent by sub-proof #1400.
% 244.05/50.47  | | | 
% 244.05/50.47  | | Case 2:
% 244.05/50.47  | | | 
% 244.05/50.47  | | |   (23)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.47  | | | 
% 244.05/50.47  | | | ALPHA: (23) implies:
% 244.05/50.47  | | |   (24)  op(e3, e2) = e1
% 244.05/50.47  | | | 
% 244.05/50.47  | | | BETA: splitting (8) gives:
% 244.05/50.47  | | | 
% 244.05/50.47  | | | Case 1:
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | |   (25)  all_54_2 = e3
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | | COMBINE_EQS: (4), (25) imply:
% 244.05/50.47  | | | |   (26)  all_40_0 = e3
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | | REDUCE: (9), (26) imply:
% 244.05/50.47  | | | |   (27)  $false
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | | CLOSE: (27) is inconsistent.
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | Case 2:
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | |   (28)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | | BETA: splitting (28) gives:
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | | Case 1:
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | |   (29)  all_54_2 = e2
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | COMBINE_EQS: (4), (29) imply:
% 244.05/50.47  | | | | |   (30)  all_40_0 = e2
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | REDUCE: (6), (30) imply:
% 244.05/50.47  | | | | |   (31)  $false
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | CLOSE: (31) is inconsistent.
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | Case 2:
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | |   (32)  all_54_2 = e1 | all_54_2 = e0
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | BETA: splitting (32) gives:
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | Case 1:
% 244.05/50.47  | | | | | | 
% 244.05/50.47  | | | | | |   (33)  all_54_2 = e1
% 244.05/50.47  | | | | | | 
% 244.05/50.47  | | | | | | COMBINE_EQS: (4), (33) imply:
% 244.05/50.47  | | | | | |   (34)  all_40_0 = e1
% 244.05/50.47  | | | | | | 
% 244.05/50.47  | | | | | | REDUCE: (3), (34) imply:
% 244.05/50.47  | | | | | |   (35)   ~ (all_52_4 = e1)
% 244.05/50.47  | | | | | | 
% 244.05/50.47  | | | | | | REF_CLOSE: (12), (15), (24), (35) are inconsistent by sub-proof
% 244.05/50.47  | | | | | |            #2228.
% 244.05/50.47  | | | | | | 
% 244.05/50.47  | | | | | Case 2:
% 244.05/50.47  | | | | | | 
% 244.05/50.47  | | | | | |   (36)  all_54_2 = e0
% 244.05/50.47  | | | | | | 
% 244.05/50.47  | | | | | | COMBINE_EQS: (4), (36) imply:
% 244.05/50.47  | | | | | |   (37)  all_40_0 = e0
% 244.05/50.47  | | | | | | 
% 244.05/50.47  | | | | | | REDUCE: (13), (37) imply:
% 244.05/50.47  | | | | | |   (38)  $false
% 244.05/50.47  | | | | | | 
% 244.05/50.47  | | | | | | CLOSE: (38) is inconsistent.
% 244.05/50.47  | | | | | | 
% 244.05/50.47  | | | | | End of split
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | End of split
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | End of split
% 244.05/50.47  | | | 
% 244.05/50.47  | | End of split
% 244.05/50.47  | | 
% 244.05/50.47  | Case 2:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (39)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 244.05/50.47  | |           e1)
% 244.05/50.47  | | 
% 244.05/50.47  | | BETA: splitting (39) gives:
% 244.05/50.47  | | 
% 244.05/50.47  | | Case 1:
% 244.05/50.47  | | | 
% 244.05/50.47  | | |   (40)  all_58_4 = e1 & op(e3, e1) = e1
% 244.05/50.47  | | | 
% 244.05/50.47  | | | REF_CLOSE: (16), (18), (40) are inconsistent by sub-proof #2047.
% 244.05/50.47  | | | 
% 244.05/50.47  | | Case 2:
% 244.05/50.47  | | | 
% 244.05/50.47  | | |   (41)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.47  | | | 
% 244.05/50.47  | | | ALPHA: (41) implies:
% 244.05/50.47  | | |   (42)  all_58_9 = e1
% 244.05/50.47  | | | 
% 244.05/50.47  | | | REF_CLOSE: (17), (19), (42) are inconsistent by sub-proof #1605.
% 244.05/50.47  | | | 
% 244.05/50.47  | | End of split
% 244.05/50.47  | | 
% 244.05/50.47  | End of split
% 244.05/50.47  | 
% 244.05/50.47  End of proof
% 244.05/50.47  
% 244.05/50.47  Sub-proof #1400 shows that the following formulas are inconsistent:
% 244.05/50.47  ----------------------------------------------------------------
% 244.05/50.47    (1)   ~ (e3 = e0)
% 244.05/50.47    (2)   ~ (e3 = e1)
% 244.05/50.47    (3)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.47         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.47    (4)  op(e3, e3) = e1
% 244.05/50.47    (5)   ~ (e3 = e2)
% 244.05/50.47    (6)  op(e3, e0) = e2
% 244.05/50.47    (7)   ~ (all_52_4 = e3)
% 244.05/50.47    (8)  op(e3, e2) = all_52_4
% 244.05/50.47    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.47    (10)  all_58_4 = e0
% 244.05/50.47  
% 244.05/50.47  Begin of proof
% 244.05/50.47  | 
% 244.05/50.47  | BETA: splitting (3) gives:
% 244.05/50.47  | 
% 244.05/50.47  | Case 1:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 244.05/50.47  | |           e3)
% 244.05/50.47  | | 
% 244.05/50.47  | | REF_CLOSE: (2), (4), (7), (8), (9), (11) are inconsistent by sub-proof
% 244.05/50.47  | |            #1401.
% 244.05/50.47  | | 
% 244.05/50.47  | Case 2:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (12)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 244.05/50.47  | |           e3)
% 244.05/50.47  | | 
% 244.05/50.47  | | BETA: splitting (12) gives:
% 244.05/50.47  | | 
% 244.05/50.47  | | Case 1:
% 244.05/50.47  | | | 
% 244.05/50.47  | | |   (13)  all_58_4 = e3 & op(e3, e1) = e3
% 244.05/50.47  | | | 
% 244.05/50.47  | | | ALPHA: (13) implies:
% 244.05/50.47  | | |   (14)  all_58_4 = e3
% 244.05/50.47  | | | 
% 244.05/50.47  | | | REF_CLOSE: (1), (10), (14) are inconsistent by sub-proof #2186.
% 244.05/50.47  | | | 
% 244.05/50.47  | | Case 2:
% 244.05/50.47  | | | 
% 244.05/50.47  | | |   (15)  all_58_9 = e3 & op(e3, e0) = e3
% 244.05/50.47  | | | 
% 244.05/50.47  | | | ALPHA: (15) implies:
% 244.05/50.47  | | |   (16)  op(e3, e0) = e3
% 244.05/50.47  | | | 
% 244.05/50.47  | | | REF_CLOSE: (5), (6), (9), (16) are inconsistent by sub-proof #2125.
% 244.05/50.47  | | | 
% 244.05/50.47  | | End of split
% 244.05/50.47  | | 
% 244.05/50.47  | End of split
% 244.05/50.47  | 
% 244.05/50.47  End of proof
% 244.05/50.47  
% 244.05/50.47  Sub-proof #1401 shows that the following formulas are inconsistent:
% 244.05/50.47  ----------------------------------------------------------------
% 244.05/50.47    (1)   ~ (e3 = e1)
% 244.05/50.47    (2)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 244.05/50.47    (3)  op(e3, e3) = e1
% 244.05/50.47    (4)   ~ (all_52_4 = e3)
% 244.05/50.47    (5)  op(e3, e2) = all_52_4
% 244.05/50.47    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.47  
% 244.05/50.47  Begin of proof
% 244.05/50.47  | 
% 244.05/50.47  | BETA: splitting (2) gives:
% 244.05/50.47  | 
% 244.05/50.47  | Case 1:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (7)  all_58_0 = e3 & op(e3, e3) = e3
% 244.05/50.47  | | 
% 244.05/50.47  | | ALPHA: (7) implies:
% 244.05/50.47  | |   (8)  op(e3, e3) = e3
% 244.05/50.47  | | 
% 244.05/50.47  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #1578.
% 244.05/50.47  | | 
% 244.05/50.47  | Case 2:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (9)  all_58_1 = e3 & op(e3, e2) = e3
% 244.05/50.47  | | 
% 244.05/50.47  | | ALPHA: (9) implies:
% 244.05/50.47  | |   (10)  op(e3, e2) = e3
% 244.05/50.47  | | 
% 244.05/50.47  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #2192.
% 244.05/50.47  | | 
% 244.05/50.47  | End of split
% 244.05/50.47  | 
% 244.05/50.47  End of proof
% 244.05/50.47  
% 244.05/50.47  Sub-proof #1402 shows that the following formulas are inconsistent:
% 244.05/50.47  ----------------------------------------------------------------
% 244.05/50.47    (1)   ~ (e3 = e0)
% 244.05/50.47    (2)   ~ (e2 = e0)
% 244.05/50.47    (3)  all_58_4 = e2
% 244.05/50.47    (4)   ~ (e3 = e1)
% 244.05/50.47    (5)  op(e3, e0) = e2
% 244.05/50.47    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.47         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.47    (7)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.47         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.47    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.47    (9)   ~ (e1 = e0)
% 244.05/50.47    (10)  op(e3, e3) = e3
% 244.05/50.47    (11)  all_58_9 = e2
% 244.05/50.47    (12)   ~ (e2 = e1)
% 244.05/50.47  
% 244.05/50.47  Begin of proof
% 244.05/50.47  | 
% 244.05/50.47  | BETA: splitting (6) gives:
% 244.05/50.47  | 
% 244.05/50.47  | Case 1:
% 244.05/50.47  | | 
% 244.05/50.47  | |   (13)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 244.05/50.47  | |           e0)
% 244.05/50.47  | | 
% 244.05/50.47  | | BETA: splitting (13) gives:
% 244.05/50.47  | | 
% 244.05/50.47  | | Case 1:
% 244.05/50.47  | | | 
% 244.05/50.47  | | |   (14)  all_58_0 = e0 & op(e3, e3) = e0
% 244.05/50.47  | | | 
% 244.05/50.47  | | | ALPHA: (14) implies:
% 244.05/50.47  | | |   (15)  op(e3, e3) = e0
% 244.05/50.47  | | | 
% 244.05/50.47  | | | REF_CLOSE: (1), (8), (10), (15) are inconsistent by sub-proof #1940.
% 244.05/50.47  | | | 
% 244.05/50.47  | | Case 2:
% 244.05/50.47  | | | 
% 244.05/50.47  | | |   (16)  all_58_1 = e0 & op(e3, e2) = e0
% 244.05/50.47  | | | 
% 244.05/50.47  | | | ALPHA: (16) implies:
% 244.05/50.47  | | |   (17)  all_58_1 = e0
% 244.05/50.47  | | | 
% 244.05/50.47  | | | BETA: splitting (7) gives:
% 244.05/50.47  | | | 
% 244.05/50.47  | | | Case 1:
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | |   (18)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 244.05/50.47  | | | |           = e1)
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | | BETA: splitting (18) gives:
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | | Case 1:
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | |   (19)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | ALPHA: (19) implies:
% 244.05/50.47  | | | | |   (20)  op(e3, e3) = e1
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | REF_CLOSE: (4), (8), (10), (20) are inconsistent by sub-proof #1578.
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | Case 2:
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | |   (21)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | REF_CLOSE: (9), (17), (21) are inconsistent by sub-proof #2015.
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | End of split
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | Case 2:
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | |   (22)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 244.05/50.47  | | | |           = e1)
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | | BETA: splitting (22) gives:
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | | Case 1:
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | |   (23)  all_58_4 = e1 & op(e3, e1) = e1
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | REF_CLOSE: (3), (12), (23) are inconsistent by sub-proof #2168.
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | Case 2:
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | |   (24)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | | REF_CLOSE: (11), (12), (24) are inconsistent by sub-proof #1518.
% 244.05/50.47  | | | | | 
% 244.05/50.47  | | | | End of split
% 244.05/50.47  | | | | 
% 244.05/50.47  | | | End of split
% 244.05/50.47  | | | 
% 244.05/50.47  | | End of split
% 244.05/50.47  | | 
% 244.05/50.47  | Case 2:
% 244.05/50.47  | | 
% 244.05/50.48  | |   (25)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 244.05/50.48  | |           e0)
% 244.05/50.48  | | 
% 244.05/50.48  | | BETA: splitting (25) gives:
% 244.05/50.48  | | 
% 244.05/50.48  | | Case 1:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (26)  all_58_4 = e0 & op(e3, e1) = e0
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REF_CLOSE: (2), (3), (26) are inconsistent by sub-proof #2170.
% 244.05/50.48  | | | 
% 244.05/50.48  | | Case 2:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (27)  all_58_9 = e0 & op(e3, e0) = e0
% 244.05/50.48  | | | 
% 244.05/50.48  | | | ALPHA: (27) implies:
% 244.05/50.48  | | |   (28)  op(e3, e0) = e0
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REF_CLOSE: (2), (5), (8), (28) are inconsistent by sub-proof #2154.
% 244.05/50.48  | | | 
% 244.05/50.48  | | End of split
% 244.05/50.48  | | 
% 244.05/50.48  | End of split
% 244.05/50.48  | 
% 244.05/50.48  End of proof
% 244.05/50.48  
% 244.05/50.48  Sub-proof #1403 shows that the following formulas are inconsistent:
% 244.05/50.48  ----------------------------------------------------------------
% 244.05/50.48    (1)   ~ (e3 = e0)
% 244.05/50.48    (2)   ~ (e2 = e0)
% 244.05/50.48    (3)  all_58_12 = e2
% 244.05/50.48    (4)   ~ (e3 = e1)
% 244.05/50.48    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 244.05/50.48         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 244.05/50.48    (6)   ~ (e3 = e2)
% 244.05/50.48    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.05/50.48         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.05/50.48    (8)  op(e2, e3) = all_52_1
% 244.05/50.48    (9)  op(e3, e3) = e2
% 244.05/50.48    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.05/50.48          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.05/50.48    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.48    (12)   ~ (e1 = e0)
% 244.05/50.48    (13)   ~ (all_52_1 = e3)
% 244.05/50.48    (14)   ~ (e2 = e1)
% 244.05/50.48  
% 244.05/50.48  Begin of proof
% 244.05/50.48  | 
% 244.05/50.48  | BETA: splitting (5) gives:
% 244.05/50.48  | 
% 244.05/50.48  | Case 1:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 244.05/50.48  | |           e3)
% 244.05/50.48  | | 
% 244.05/50.48  | | REF_CLOSE: (6), (8), (9), (11), (13), (15) are inconsistent by sub-proof
% 244.05/50.48  | |            #1404.
% 244.05/50.48  | | 
% 244.05/50.48  | Case 2:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 244.05/50.48  | |           e3)
% 244.05/50.48  | | 
% 244.05/50.48  | | BETA: splitting (16) gives:
% 244.05/50.48  | | 
% 244.05/50.48  | | Case 1:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (17)  all_58_6 = e3 & op(e1, e3) = e3
% 244.05/50.48  | | | 
% 244.05/50.48  | | | ALPHA: (17) implies:
% 244.05/50.48  | | |   (18)  all_58_6 = e3
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (12), (14), (18) are
% 244.05/50.48  | | |            inconsistent by sub-proof #1756.
% 244.05/50.48  | | | 
% 244.05/50.48  | | Case 2:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (19)  all_58_12 = e3 & op(e0, e3) = e3
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REF_CLOSE: (3), (6), (19) are inconsistent by sub-proof #2085.
% 244.05/50.48  | | | 
% 244.05/50.48  | | End of split
% 244.05/50.48  | | 
% 244.05/50.48  | End of split
% 244.05/50.48  | 
% 244.05/50.48  End of proof
% 244.05/50.48  
% 244.05/50.48  Sub-proof #1404 shows that the following formulas are inconsistent:
% 244.05/50.48  ----------------------------------------------------------------
% 244.05/50.48    (1)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 244.05/50.48    (2)   ~ (e3 = e2)
% 244.05/50.48    (3)  op(e2, e3) = all_52_1
% 244.05/50.48    (4)  op(e3, e3) = e2
% 244.05/50.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.48    (6)   ~ (all_52_1 = e3)
% 244.05/50.48  
% 244.05/50.48  Begin of proof
% 244.05/50.48  | 
% 244.05/50.48  | BETA: splitting (1) gives:
% 244.05/50.48  | 
% 244.05/50.48  | Case 1:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (7)  all_58_0 = e3 & op(e3, e3) = e3
% 244.05/50.48  | | 
% 244.05/50.48  | | ALPHA: (7) implies:
% 244.05/50.48  | |   (8)  op(e3, e3) = e3
% 244.05/50.48  | | 
% 244.05/50.48  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2194.
% 244.05/50.48  | | 
% 244.05/50.48  | Case 2:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (9)  all_58_2 = e3 & op(e2, e3) = e3
% 244.05/50.48  | | 
% 244.05/50.48  | | ALPHA: (9) implies:
% 244.05/50.48  | |   (10)  op(e2, e3) = e3
% 244.05/50.48  | | 
% 244.05/50.48  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #2337.
% 244.05/50.48  | | 
% 244.05/50.48  | End of split
% 244.05/50.48  | 
% 244.05/50.48  End of proof
% 244.05/50.48  
% 244.05/50.48  Sub-proof #1405 shows that the following formulas are inconsistent:
% 244.05/50.48  ----------------------------------------------------------------
% 244.05/50.48    (1)   ~ (e3 = e0)
% 244.05/50.48    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.05/50.48         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.05/50.48    (3)   ~ (e2 = e0)
% 244.05/50.48    (4)  all_58_6 = e2
% 244.05/50.48    (5)  op(e1, e0) = all_52_14
% 244.05/50.48    (6)   ~ (e3 = e1)
% 244.05/50.48    (7)  op(e1, e2) = e3
% 244.05/50.48    (8)   ~ (e3 = e2)
% 244.05/50.48    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.05/50.48         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.05/50.48    (10)   ~ (all_52_14 = e3)
% 244.05/50.48    (11)  op(e1, e1) = e2
% 244.05/50.48    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.48    (13)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 244.05/50.48            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 244.05/50.48              e2) = all_36_1 & $i(all_36_1))
% 244.05/50.48    (14)  op(e1, e2) = all_40_1
% 244.05/50.48    (15)   ~ (e1 = e0)
% 244.05/50.48    (16)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.05/50.48          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.48    (17)   ~ (e2 = e1)
% 244.05/50.48  
% 244.05/50.48  Begin of proof
% 244.05/50.48  | 
% 244.05/50.48  | BETA: splitting (2) gives:
% 244.05/50.48  | 
% 244.05/50.48  | Case 1:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (18)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 244.05/50.48  | |           e1)
% 244.05/50.48  | | 
% 244.05/50.48  | | BETA: splitting (18) gives:
% 244.05/50.48  | | 
% 244.05/50.48  | | Case 1:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (19)  all_58_6 = e1 & op(e1, e3) = e1
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REF_CLOSE: (4), (17), (19) are inconsistent by sub-proof #1423.
% 244.05/50.48  | | | 
% 244.05/50.48  | | Case 2:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (20)  all_58_7 = e1 & op(e1, e2) = e1
% 244.05/50.48  | | | 
% 244.05/50.48  | | | ALPHA: (20) implies:
% 244.05/50.48  | | |   (21)  op(e1, e2) = e1
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REF_CLOSE: (6), (7), (12), (13), (14), (21) are inconsistent by sub-proof
% 244.05/50.48  | | |            #1700.
% 244.05/50.48  | | | 
% 244.05/50.48  | | End of split
% 244.05/50.48  | | 
% 244.05/50.48  | Case 2:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (22)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 244.05/50.48  | |           e1)
% 244.05/50.48  | | 
% 244.05/50.48  | | BETA: splitting (22) gives:
% 244.05/50.48  | | 
% 244.05/50.48  | | Case 1:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (23)  all_58_8 = e1 & op(e1, e1) = e1
% 244.05/50.48  | | | 
% 244.05/50.48  | | | ALPHA: (23) implies:
% 244.05/50.48  | | |   (24)  op(e1, e1) = e1
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REF_CLOSE: (11), (12), (17), (24) are inconsistent by sub-proof #2159.
% 244.05/50.48  | | | 
% 244.05/50.48  | | Case 2:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (25)  all_58_11 = e1 & op(e1, e0) = e1
% 244.05/50.48  | | | 
% 244.05/50.48  | | | ALPHA: (25) implies:
% 244.05/50.48  | | |   (26)  op(e1, e0) = e1
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (11), (12), (15), (16),
% 244.05/50.48  | | |            (26) are inconsistent by sub-proof #1406.
% 244.05/50.48  | | | 
% 244.05/50.48  | | End of split
% 244.05/50.48  | | 
% 244.05/50.48  | End of split
% 244.05/50.48  | 
% 244.05/50.48  End of proof
% 244.05/50.48  
% 244.05/50.48  Sub-proof #1406 shows that the following formulas are inconsistent:
% 244.05/50.48  ----------------------------------------------------------------
% 244.05/50.48    (1)   ~ (e3 = e0)
% 244.05/50.48    (2)   ~ (e2 = e0)
% 244.05/50.48    (3)  all_58_6 = e2
% 244.05/50.48    (4)  op(e1, e0) = all_52_14
% 244.05/50.48    (5)  op(e1, e0) = e1
% 244.05/50.48    (6)   ~ (e3 = e2)
% 244.05/50.48    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.05/50.48         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.05/50.48    (8)   ~ (all_52_14 = e3)
% 244.05/50.48    (9)  op(e1, e1) = e2
% 244.05/50.48    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.48    (11)   ~ (e1 = e0)
% 244.05/50.48    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.05/50.48          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.48  
% 244.05/50.48  Begin of proof
% 244.05/50.48  | 
% 244.05/50.48  | BETA: splitting (7) gives:
% 244.05/50.48  | 
% 244.05/50.48  | Case 1:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.05/50.48  | |           e3)
% 244.05/50.48  | | 
% 244.05/50.48  | | BETA: splitting (13) gives:
% 244.05/50.48  | | 
% 244.05/50.48  | | Case 1:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (14)  all_58_6 = e3 & op(e1, e3) = e3
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #1838.
% 244.05/50.48  | | | 
% 244.05/50.48  | | Case 2:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (15)  all_58_7 = e3 & op(e1, e2) = e3
% 244.05/50.48  | | | 
% 244.05/50.48  | | | ALPHA: (15) implies:
% 244.05/50.48  | | |   (16)  all_58_7 = e3
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REF_CLOSE: (1), (2), (3), (5), (9), (10), (11), (12), (16) are
% 244.05/50.48  | | |            inconsistent by sub-proof #1836.
% 244.05/50.48  | | | 
% 244.05/50.48  | | End of split
% 244.05/50.48  | | 
% 244.05/50.48  | Case 2:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (17)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.05/50.48  | |           e3)
% 244.05/50.48  | | 
% 244.05/50.48  | | REF_CLOSE: (4), (6), (8), (9), (10), (17) are inconsistent by sub-proof
% 244.05/50.48  | |            #2148.
% 244.05/50.48  | | 
% 244.05/50.48  | End of split
% 244.05/50.48  | 
% 244.05/50.48  End of proof
% 244.05/50.48  
% 244.05/50.48  Sub-proof #1407 shows that the following formulas are inconsistent:
% 244.05/50.48  ----------------------------------------------------------------
% 244.05/50.48    (1)   ~ (e3 = e2)
% 244.05/50.48    (2)  op(e2, e3) = all_52_1
% 244.05/50.48    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 244.05/50.48    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.48    (5)  op(e3, e3) = e3
% 244.05/50.48    (6)   ~ (all_52_1 = e2)
% 244.05/50.48  
% 244.05/50.48  Begin of proof
% 244.05/50.48  | 
% 244.05/50.48  | BETA: splitting (3) gives:
% 244.05/50.48  | 
% 244.05/50.48  | Case 1:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 244.05/50.48  | | 
% 244.05/50.48  | | ALPHA: (7) implies:
% 244.05/50.48  | |   (8)  op(e3, e3) = e2
% 244.05/50.48  | | 
% 244.05/50.48  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2194.
% 244.05/50.48  | | 
% 244.05/50.48  | Case 2:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (9)  all_58_2 = e2 & op(e2, e3) = e2
% 244.05/50.48  | | 
% 244.05/50.48  | | ALPHA: (9) implies:
% 244.05/50.48  | |   (10)  op(e2, e3) = e2
% 244.05/50.48  | | 
% 244.05/50.48  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #2336.
% 244.05/50.48  | | 
% 244.05/50.48  | End of split
% 244.05/50.48  | 
% 244.05/50.48  End of proof
% 244.05/50.48  
% 244.05/50.48  Sub-proof #1408 shows that the following formulas are inconsistent:
% 244.05/50.48  ----------------------------------------------------------------
% 244.05/50.48    (1)  all_56_11 = e2
% 244.05/50.48    (2)   ~ (all_52_9 = all_6_2)
% 244.05/50.48    (3)   ~ (all_52_7 = e2)
% 244.05/50.48    (4)  all_54_10 = e1 | all_54_10 = e0
% 244.05/50.48    (5)  op(e1, e0) = all_52_14
% 244.05/50.48    (6)  all_54_10 = all_6_2
% 244.05/50.48    (7)  op(e2, e1) = all_52_9
% 244.05/50.48    (8)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.05/50.48             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.05/50.48           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.05/50.48             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 244.05/50.48           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 244.05/50.48           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.05/50.48           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.05/50.48           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.05/50.48           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.05/50.48           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.05/50.48           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.05/50.48             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.05/50.48           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.05/50.48           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.05/50.48    (9)   ~ (all_52_14 = e1)
% 244.05/50.48    (10)   ~ (all_6_2 = e0)
% 244.05/50.48    (11)  op(e0, e2) = all_52_7
% 244.05/50.48    (12)  all_56_21 = e1
% 244.05/50.48    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.48    (14)   ~ (all_52_9 = e2)
% 244.05/50.48  
% 244.05/50.48  Begin of proof
% 244.05/50.48  | 
% 244.05/50.48  | BETA: splitting (8) gives:
% 244.05/50.48  | 
% 244.05/50.48  | Case 1:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (15)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 244.05/50.48  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.05/50.48  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.05/50.48  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.05/50.48  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 244.05/50.48  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.05/50.48  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.05/50.48  | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.05/50.48  | | 
% 244.05/50.48  | | REF_CLOSE: (2), (3), (4), (6), (7), (10), (11), (13), (14), (15) are
% 244.05/50.48  | |            inconsistent by sub-proof #1410.
% 244.05/50.48  | | 
% 244.05/50.48  | Case 2:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (16)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 244.05/50.48  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.05/50.48  | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 244.05/50.48  | |           e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.05/50.48  | |             e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 244.05/50.48  | |         (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 244.05/50.48  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.05/50.48  | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.05/50.48  | | 
% 244.05/50.48  | | BETA: splitting (16) gives:
% 244.05/50.48  | | 
% 244.05/50.48  | | Case 1:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (17)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 244.05/50.48  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.05/50.48  | | |         op(e2, e0) = e0 & op(e0, e2) = e0
% 244.05/50.48  | | | 
% 244.05/50.48  | | | ALPHA: (17) implies:
% 244.05/50.48  | | |   (18)   ~ (all_56_11 = e2)
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REDUCE: (1), (18) imply:
% 244.05/50.48  | | |   (19)  $false
% 244.05/50.48  | | | 
% 244.05/50.48  | | | CLOSE: (19) is inconsistent.
% 244.05/50.48  | | | 
% 244.05/50.48  | | Case 2:
% 244.05/50.48  | | | 
% 244.05/50.48  | | |   (20)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.05/50.48  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.05/50.48  | | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29
% 244.05/50.48  | | |           = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 244.05/50.48  | | |             = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 244.05/50.48  | | |           e0)
% 244.05/50.48  | | | 
% 244.05/50.48  | | | REF_CLOSE: (5), (9), (12), (13), (20) are inconsistent by sub-proof #1409.
% 244.05/50.48  | | | 
% 244.05/50.48  | | End of split
% 244.05/50.48  | | 
% 244.05/50.48  | End of split
% 244.05/50.48  | 
% 244.05/50.48  End of proof
% 244.05/50.48  
% 244.05/50.48  Sub-proof #1409 shows that the following formulas are inconsistent:
% 244.05/50.48  ----------------------------------------------------------------
% 244.05/50.48    (1)  op(e1, e0) = all_52_14
% 244.05/50.48    (2)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.05/50.48             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 244.05/50.48           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 244.05/50.48             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 244.05/50.48           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.05/50.48    (3)   ~ (all_52_14 = e1)
% 244.05/50.48    (4)  all_56_21 = e1
% 244.05/50.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.48  
% 244.05/50.48  Begin of proof
% 244.05/50.48  | 
% 244.05/50.48  | BETA: splitting (2) gives:
% 244.05/50.48  | 
% 244.05/50.48  | Case 1:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (6)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.05/50.48  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 244.05/50.48  | |        & op(e0, e1) = e1
% 244.05/50.48  | | 
% 244.05/50.48  | | ALPHA: (6) implies:
% 244.05/50.48  | |   (7)  op(e1, e0) = e1
% 244.05/50.48  | | 
% 244.05/50.48  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #2304.
% 244.05/50.48  | | 
% 244.05/50.48  | Case 2:
% 244.05/50.48  | | 
% 244.05/50.48  | |   (8)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.05/50.48  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 244.05/50.48  | |        & op(e0, e1) = e0
% 244.05/50.48  | | 
% 244.05/50.48  | | ALPHA: (8) implies:
% 244.05/50.48  | |   (9)   ~ (all_56_21 = e1)
% 244.05/50.48  | | 
% 244.05/50.48  | | REDUCE: (4), (9) imply:
% 244.05/50.48  | |   (10)  $false
% 244.05/50.48  | | 
% 244.05/50.48  | | CLOSE: (10) is inconsistent.
% 244.05/50.48  | | 
% 244.05/50.48  | End of split
% 244.05/50.48  | 
% 244.05/50.48  End of proof
% 244.05/50.48  
% 244.05/50.48  Sub-proof #1410 shows that the following formulas are inconsistent:
% 244.05/50.48  ----------------------------------------------------------------
% 244.05/50.48    (1)   ~ (all_52_9 = all_6_2)
% 244.05/50.48    (2)   ~ (all_52_7 = e2)
% 244.05/50.48    (3)  all_54_10 = e1 | all_54_10 = e0
% 244.05/50.48    (4)  all_54_10 = all_6_2
% 244.05/50.48    (5)  op(e2, e1) = all_52_9
% 244.05/50.49    (6)   ~ (all_6_2 = e0)
% 244.05/50.49    (7)  op(e0, e2) = all_52_7
% 244.05/50.49    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.49    (9)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.05/50.49             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.05/50.49           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.05/50.49             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 244.05/50.49           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 244.05/50.49           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.05/50.49           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.05/50.49    (10)   ~ (all_52_9 = e2)
% 244.05/50.49  
% 244.05/50.49  Begin of proof
% 244.05/50.49  | 
% 244.05/50.49  | BETA: splitting (9) gives:
% 244.05/50.49  | 
% 244.05/50.49  | Case 1:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (11)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.05/50.49  | |           = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) =
% 244.05/50.49  | |         e2 & op(e1, e2) = e2
% 244.05/50.49  | | 
% 244.05/50.49  | | ALPHA: (11) implies:
% 244.05/50.49  | |   (12)  op(e2, e1) = e2
% 244.05/50.49  | | 
% 244.05/50.49  | | REF_CLOSE: (5), (8), (10), (12) are inconsistent by sub-proof #2328.
% 244.05/50.49  | | 
% 244.05/50.49  | Case 2:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (13)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.05/50.49  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.05/50.49  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 244.05/50.49  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.05/50.49  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.05/50.49  | | 
% 244.05/50.49  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (13) are inconsistent by
% 244.05/50.49  | |            sub-proof #1904.
% 244.05/50.49  | | 
% 244.05/50.49  | End of split
% 244.05/50.49  | 
% 244.05/50.49  End of proof
% 244.05/50.49  
% 244.05/50.49  Sub-proof #1411 shows that the following formulas are inconsistent:
% 244.05/50.49  ----------------------------------------------------------------
% 244.05/50.49    (1)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.05/50.49             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.05/50.49           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 244.05/50.49           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.05/50.49           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 244.05/50.49           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.05/50.49           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.05/50.49    (2)  op(e0, e3) = all_52_3
% 244.05/50.49    (3)   ~ (all_52_8 = e1)
% 244.05/50.49    (4)  op(e3, e1) = all_52_8
% 244.05/50.49    (5)   ~ (all_52_3 = e3)
% 244.05/50.49    (6)  all_56_31 = e3
% 244.05/50.49    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.49  
% 244.05/50.49  Begin of proof
% 244.05/50.49  | 
% 244.05/50.49  | BETA: splitting (1) gives:
% 244.05/50.49  | 
% 244.05/50.49  | Case 1:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (8)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.05/50.49  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.05/50.49  | |        op(e1, e3) = e1
% 244.05/50.49  | | 
% 244.05/50.49  | | ALPHA: (8) implies:
% 244.05/50.49  | |   (9)  op(e3, e1) = e1
% 244.05/50.49  | | 
% 244.05/50.49  | | REF_CLOSE: (3), (4), (7), (9) are inconsistent by sub-proof #2309.
% 244.05/50.49  | | 
% 244.05/50.49  | Case 2:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.05/50.49  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 244.05/50.49  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.05/50.49  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.05/50.49  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.05/50.49  | | 
% 244.05/50.49  | | REF_CLOSE: (2), (5), (6), (7), (10) are inconsistent by sub-proof #1412.
% 244.05/50.49  | | 
% 244.05/50.49  | End of split
% 244.05/50.49  | 
% 244.05/50.49  End of proof
% 244.05/50.49  
% 244.05/50.49  Sub-proof #1412 shows that the following formulas are inconsistent:
% 244.05/50.49  ----------------------------------------------------------------
% 244.05/50.49    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.05/50.49             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.05/50.49           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 244.05/50.49           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.05/50.49           op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.05/50.49    (2)  op(e0, e3) = all_52_3
% 244.05/50.49    (3)   ~ (all_52_3 = e3)
% 244.05/50.49    (4)  all_56_31 = e3
% 244.05/50.49    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.49  
% 244.05/50.49  Begin of proof
% 244.05/50.49  | 
% 244.05/50.49  | BETA: splitting (1) gives:
% 244.05/50.49  | 
% 244.05/50.49  | Case 1:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (6)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.05/50.49  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.05/50.49  | |        op(e0, e3) = e3
% 244.05/50.49  | | 
% 244.05/50.49  | | ALPHA: (6) implies:
% 244.05/50.49  | |   (7)  op(e0, e3) = e3
% 244.05/50.49  | | 
% 244.05/50.49  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #2332.
% 244.05/50.49  | | 
% 244.05/50.49  | Case 2:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (8)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.05/50.49  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 244.05/50.49  | |        op(e0, e3) = e0
% 244.05/50.49  | | 
% 244.05/50.49  | | ALPHA: (8) implies:
% 244.05/50.49  | |   (9)   ~ (all_56_31 = e3)
% 244.05/50.49  | | 
% 244.05/50.49  | | REDUCE: (4), (9) imply:
% 244.05/50.49  | |   (10)  $false
% 244.05/50.49  | | 
% 244.05/50.49  | | CLOSE: (10) is inconsistent.
% 244.05/50.49  | | 
% 244.05/50.49  | End of split
% 244.05/50.49  | 
% 244.05/50.49  End of proof
% 244.05/50.49  
% 244.05/50.49  Sub-proof #1413 shows that the following formulas are inconsistent:
% 244.05/50.49  ----------------------------------------------------------------
% 244.05/50.49    (1)   ~ (e3 = e2)
% 244.05/50.49    (2)  op(e2, e3) = all_52_1
% 244.05/50.49    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 244.05/50.49    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.49    (5)   ~ (all_52_1 = e3)
% 244.05/50.49    (6)  op(e2, e2) = e2
% 244.05/50.49  
% 244.05/50.49  Begin of proof
% 244.05/50.49  | 
% 244.05/50.49  | BETA: splitting (3) gives:
% 244.05/50.49  | 
% 244.05/50.49  | Case 1:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (7)  all_58_2 = e3 & op(e2, e3) = e3
% 244.05/50.49  | | 
% 244.05/50.49  | | ALPHA: (7) implies:
% 244.05/50.49  | |   (8)  op(e2, e3) = e3
% 244.05/50.49  | | 
% 244.05/50.49  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2337.
% 244.05/50.49  | | 
% 244.05/50.49  | Case 2:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (9)  all_58_3 = e3 & op(e2, e2) = e3
% 244.05/50.49  | | 
% 244.05/50.49  | | ALPHA: (9) implies:
% 244.05/50.49  | |   (10)  op(e2, e2) = e3
% 244.05/50.49  | | 
% 244.05/50.49  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #2140.
% 244.05/50.49  | | 
% 244.05/50.49  | End of split
% 244.05/50.49  | 
% 244.05/50.49  End of proof
% 244.05/50.49  
% 244.05/50.49  Sub-proof #1414 shows that the following formulas are inconsistent:
% 244.05/50.49  ----------------------------------------------------------------
% 244.05/50.49    (1)  op(e0, e1) = all_52_11
% 244.05/50.49    (2)   ~ (all_52_11 = e0)
% 244.05/50.49    (3)  op(e0, e2) = all_52_7
% 244.05/50.49    (4)   ~ (all_52_7 = e0)
% 244.05/50.49    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.49    (6)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.05/50.49  
% 244.05/50.49  Begin of proof
% 244.05/50.49  | 
% 244.05/50.49  | BETA: splitting (6) gives:
% 244.05/50.49  | 
% 244.05/50.49  | Case 1:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (7)  all_58_13 = e0 & op(e0, e2) = e0
% 244.05/50.49  | | 
% 244.05/50.49  | | ALPHA: (7) implies:
% 244.05/50.49  | |   (8)  op(e0, e2) = e0
% 244.05/50.49  | | 
% 244.05/50.49  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2252.
% 244.05/50.49  | | 
% 244.05/50.49  | Case 2:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 244.05/50.49  | | 
% 244.05/50.49  | | ALPHA: (9) implies:
% 244.05/50.49  | |   (10)  op(e0, e1) = e0
% 244.05/50.49  | | 
% 244.05/50.49  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1911.
% 244.05/50.49  | | 
% 244.05/50.49  | End of split
% 244.05/50.49  | 
% 244.05/50.49  End of proof
% 244.05/50.49  
% 244.05/50.49  Sub-proof #1415 shows that the following formulas are inconsistent:
% 244.05/50.49  ----------------------------------------------------------------
% 244.05/50.49    (1)   ~ (e2 = e0)
% 244.05/50.49    (2)   ~ (e3 = e1)
% 244.05/50.49    (3)  op(e1, e2) = e3
% 244.05/50.49    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.05/50.49         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.05/50.49    (5)   ~ (e3 = e2)
% 244.05/50.49    (6)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 244.05/50.49           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0) =
% 244.05/50.49           all_14_1 & $i(all_14_1))
% 244.05/50.49    (7)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) = all_48_1
% 244.05/50.49           & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0) =
% 244.05/50.49           all_48_1 & $i(all_48_1))
% 244.05/50.49    (8)  op(e1, e3) = e1
% 244.05/50.49    (9)  all_58_6 = e1
% 244.05/50.49    (10)  all_58_12 = e3
% 244.05/50.49    (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.05/50.49          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.05/50.49    (12)  op(e2, e1) = e3
% 244.05/50.49    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.49    (14)   ~ (e1 = e0)
% 244.05/50.49    (15)  op(e3, e3) = e0
% 244.05/50.49    (16)  all_58_3 = e0
% 244.05/50.49    (17)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.49          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.05/50.49    (18)   ~ (e2 = e1)
% 244.05/50.49  
% 244.05/50.49  Begin of proof
% 244.05/50.49  | 
% 244.05/50.49  | BETA: splitting (4) gives:
% 244.05/50.49  | 
% 244.05/50.49  | Case 1:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (19)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 244.05/50.49  | |           e2)
% 244.05/50.49  | | 
% 244.05/50.49  | | BETA: splitting (19) gives:
% 244.05/50.49  | | 
% 244.05/50.49  | | Case 1:
% 244.05/50.49  | | | 
% 244.05/50.49  | | |   (20)  all_58_0 = e2 & op(e3, e3) = e2
% 244.05/50.49  | | | 
% 244.05/50.49  | | | ALPHA: (20) implies:
% 244.05/50.49  | | |   (21)  op(e3, e3) = e2
% 244.05/50.49  | | | 
% 244.05/50.49  | | | REF_CLOSE: (1), (13), (15), (21) are inconsistent by sub-proof #2188.
% 244.05/50.49  | | | 
% 244.05/50.49  | | Case 2:
% 244.05/50.49  | | | 
% 244.05/50.49  | | |   (22)  all_58_2 = e2 & op(e2, e3) = e2
% 244.05/50.49  | | | 
% 244.05/50.49  | | | ALPHA: (22) implies:
% 244.05/50.49  | | |   (23)  op(e2, e3) = e2
% 244.05/50.49  | | | 
% 244.05/50.49  | | | BETA: splitting (17) gives:
% 244.05/50.49  | | | 
% 244.05/50.49  | | | Case 1:
% 244.05/50.49  | | | | 
% 244.05/50.49  | | | |   (24)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 244.05/50.49  | | | |           = e1)
% 244.05/50.49  | | | | 
% 244.05/50.49  | | | | BETA: splitting (24) gives:
% 244.05/50.49  | | | | 
% 244.05/50.49  | | | | Case 1:
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | |   (25)  all_58_2 = e1 & op(e2, e3) = e1
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | | ALPHA: (25) implies:
% 244.05/50.49  | | | | |   (26)  op(e2, e3) = e1
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | | REF_CLOSE: (13), (18), (23), (26) are inconsistent by sub-proof #1633.
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | Case 2:
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | |   (27)  all_58_3 = e1 & op(e2, e2) = e1
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | | ALPHA: (27) implies:
% 244.05/50.49  | | | | |   (28)  all_58_3 = e1
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | | COMBINE_EQS: (16), (28) imply:
% 244.05/50.49  | | | | |   (29)  e1 = e0
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | | SIMP: (29) implies:
% 244.05/50.49  | | | | |   (30)  e1 = e0
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | | COMBINE_EQS: (9), (30) imply:
% 244.05/50.49  | | | | |   (31)  all_58_6 = e0
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | | REF_CLOSE: (1), (2), (4), (5), (10), (11), (13), (14), (15), (18),
% 244.05/50.49  | | | | |            (31) are inconsistent by sub-proof #1442.
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | End of split
% 244.05/50.49  | | | | 
% 244.05/50.49  | | | Case 2:
% 244.05/50.49  | | | | 
% 244.05/50.49  | | | |   (32)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 244.05/50.49  | | | |           = e1)
% 244.05/50.49  | | | | 
% 244.05/50.49  | | | | BETA: splitting (32) gives:
% 244.05/50.49  | | | | 
% 244.05/50.49  | | | | Case 1:
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | |   (33)  all_58_5 = e1 & op(e2, e1) = e1
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | | ALPHA: (33) implies:
% 244.05/50.49  | | | | |   (34)  op(e2, e1) = e1
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | | REF_CLOSE: (2), (12), (13), (34) are inconsistent by sub-proof #2255.
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | Case 2:
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | |   (35)  all_58_10 = e1 & op(e2, e0) = e1
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | | ALPHA: (35) implies:
% 244.05/50.49  | | | | |   (36)  op(e2, e0) = e1
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | | REF_CLOSE: (3), (6), (7), (13), (36) are inconsistent by sub-proof
% 244.05/50.49  | | | | |            #1427.
% 244.05/50.49  | | | | | 
% 244.05/50.49  | | | | End of split
% 244.05/50.49  | | | | 
% 244.05/50.49  | | | End of split
% 244.05/50.49  | | | 
% 244.05/50.49  | | End of split
% 244.05/50.49  | | 
% 244.05/50.49  | Case 2:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (37)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 244.05/50.49  | |           e2)
% 244.05/50.49  | | 
% 244.05/50.49  | | REF_CLOSE: (5), (8), (10), (13), (18), (37) are inconsistent by sub-proof
% 244.05/50.49  | |            #1582.
% 244.05/50.49  | | 
% 244.05/50.49  | End of split
% 244.05/50.49  | 
% 244.05/50.49  End of proof
% 244.05/50.49  
% 244.05/50.49  Sub-proof #1416 shows that the following formulas are inconsistent:
% 244.05/50.49  ----------------------------------------------------------------
% 244.05/50.49    (1)  all_58_7 = e2 & op(e1, e2) = e2
% 244.05/50.49    (2)  all_58_7 = e3
% 244.05/50.49    (3)   ~ (e3 = e2)
% 244.05/50.49  
% 244.05/50.49  Begin of proof
% 244.05/50.49  | 
% 244.05/50.49  | ALPHA: (1) implies:
% 244.05/50.49  |   (4)  all_58_7 = e2
% 244.05/50.49  | 
% 244.05/50.49  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.49  |   (5)  e3 = e2
% 244.05/50.49  | 
% 244.05/50.49  | REDUCE: (3), (5) imply:
% 244.05/50.49  |   (6)  $false
% 244.05/50.49  | 
% 244.05/50.49  | CLOSE: (6) is inconsistent.
% 244.05/50.49  | 
% 244.05/50.49  End of proof
% 244.05/50.49  
% 244.05/50.49  Sub-proof #1417 shows that the following formulas are inconsistent:
% 244.05/50.49  ----------------------------------------------------------------
% 244.05/50.49    (1)   ~ (e3 = e0)
% 244.05/50.49    (2)   ~ (e2 = e0)
% 244.05/50.49    (3)  all_58_11 = e1
% 244.05/50.49    (4)  op(e1, e0) = all_52_14
% 244.05/50.49    (5)   ~ (e3 = e1)
% 244.05/50.49    (6)  op(e1, e0) = e1
% 244.05/50.49    (7)   ~ (e3 = e2)
% 244.05/50.49    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.05/50.49         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.05/50.49    (9)   ~ (all_52_14 = e3)
% 244.05/50.49    (10)  all_58_7 = e1
% 244.05/50.49    (11)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.05/50.49          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.05/50.49    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.49    (13)   ~ (e1 = e0)
% 244.05/50.49    (14)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.05/50.49          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.49    (15)   ~ (e2 = e1)
% 244.05/50.49  
% 244.05/50.49  Begin of proof
% 244.05/50.49  | 
% 244.05/50.49  | BETA: splitting (8) gives:
% 244.05/50.49  | 
% 244.05/50.49  | Case 1:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.05/50.49  | |           e3)
% 244.05/50.49  | | 
% 244.05/50.49  | | BETA: splitting (16) gives:
% 244.05/50.49  | | 
% 244.05/50.49  | | Case 1:
% 244.05/50.49  | | | 
% 244.05/50.49  | | |   (17)  all_58_6 = e3 & op(e1, e3) = e3
% 244.05/50.49  | | | 
% 244.05/50.49  | | | ALPHA: (17) implies:
% 244.05/50.49  | | |   (18)  all_58_6 = e3
% 244.05/50.49  | | | 
% 244.05/50.49  | | | REF_CLOSE: (1), (2), (3), (6), (7), (10), (11), (12), (13), (14), (15),
% 244.05/50.49  | | |            (18) are inconsistent by sub-proof #1553.
% 244.05/50.49  | | | 
% 244.05/50.49  | | Case 2:
% 244.05/50.49  | | | 
% 244.05/50.49  | | |   (19)  all_58_7 = e3 & op(e1, e2) = e3
% 244.05/50.49  | | | 
% 244.05/50.49  | | | REF_CLOSE: (5), (10), (19) are inconsistent by sub-proof #2138.
% 244.05/50.49  | | | 
% 244.05/50.49  | | End of split
% 244.05/50.49  | | 
% 244.05/50.49  | Case 2:
% 244.05/50.49  | | 
% 244.05/50.49  | |   (20)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.05/50.49  | |           e3)
% 244.05/50.49  | | 
% 244.05/50.49  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14),
% 244.05/50.49  | |            (15), (20) are inconsistent by sub-proof #1418.
% 244.05/50.49  | | 
% 244.05/50.49  | End of split
% 244.05/50.49  | 
% 244.05/50.49  End of proof
% 244.05/50.49  
% 244.05/50.49  Sub-proof #1418 shows that the following formulas are inconsistent:
% 244.05/50.49  ----------------------------------------------------------------
% 244.05/50.49    (1)   ~ (e3 = e0)
% 244.05/50.49    (2)   ~ (e2 = e0)
% 244.05/50.49    (3)  all_58_11 = e1
% 244.05/50.49    (4)  op(e1, e0) = all_52_14
% 244.05/50.49    (5)  op(e1, e0) = e1
% 244.05/50.49    (6)   ~ (e3 = e2)
% 244.05/50.49    (7)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.05/50.49    (8)   ~ (all_52_14 = e3)
% 244.05/50.49    (9)  all_58_7 = e1
% 244.05/50.49    (10)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.05/50.49          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.05/50.49    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.49    (12)   ~ (e1 = e0)
% 244.05/50.49    (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.05/50.49          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.50    (14)   ~ (e2 = e1)
% 244.05/50.50  
% 244.05/50.50  Begin of proof
% 244.05/50.50  | 
% 244.05/50.50  | BETA: splitting (7) gives:
% 244.05/50.50  | 
% 244.05/50.50  | Case 1:
% 244.05/50.50  | | 
% 244.05/50.50  | |   (15)  all_58_8 = e3 & op(e1, e1) = e3
% 244.05/50.50  | | 
% 244.05/50.50  | | ALPHA: (15) implies:
% 244.05/50.50  | |   (16)  all_58_8 = e3
% 244.05/50.50  | |   (17)  op(e1, e1) = e3
% 244.05/50.50  | | 
% 244.05/50.50  | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (11), (12), (13), (14), (16),
% 244.05/50.50  | |            (17) are inconsistent by sub-proof #1419.
% 244.05/50.50  | | 
% 244.05/50.50  | Case 2:
% 244.05/50.50  | | 
% 244.05/50.50  | |   (18)  all_58_11 = e3 & op(e1, e0) = e3
% 244.05/50.50  | | 
% 244.05/50.50  | | ALPHA: (18) implies:
% 244.05/50.50  | |   (19)  op(e1, e0) = e3
% 244.05/50.50  | | 
% 244.05/50.50  | | REF_CLOSE: (4), (8), (11), (19) are inconsistent by sub-proof #2149.
% 244.05/50.50  | | 
% 244.05/50.50  | End of split
% 244.05/50.50  | 
% 244.05/50.50  End of proof
% 244.05/50.50  
% 244.05/50.50  Sub-proof #1419 shows that the following formulas are inconsistent:
% 244.05/50.50  ----------------------------------------------------------------
% 244.05/50.50    (1)   ~ (e3 = e0)
% 244.05/50.50    (2)   ~ (e2 = e0)
% 244.05/50.50    (3)  all_58_11 = e1
% 244.05/50.50    (4)  op(e1, e0) = e1
% 244.05/50.50    (5)   ~ (e3 = e2)
% 244.05/50.50    (6)  op(e1, e1) = e3
% 244.05/50.50    (7)  all_58_7 = e1
% 244.05/50.50    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.05/50.50         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.05/50.50    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.50    (10)  all_58_8 = e3
% 244.05/50.50    (11)   ~ (e1 = e0)
% 244.05/50.50    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.05/50.50          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.50    (13)   ~ (e2 = e1)
% 244.05/50.50  
% 244.05/50.50  Begin of proof
% 244.05/50.50  | 
% 244.05/50.50  | BETA: splitting (8) gives:
% 244.05/50.50  | 
% 244.05/50.50  | Case 1:
% 244.05/50.50  | | 
% 244.05/50.50  | |   (14)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 244.05/50.50  | |           e2)
% 244.05/50.50  | | 
% 244.05/50.50  | | BETA: splitting (14) gives:
% 244.05/50.50  | | 
% 244.05/50.50  | | Case 1:
% 244.05/50.50  | | | 
% 244.05/50.50  | | |   (15)  all_58_6 = e2 & op(e1, e3) = e2
% 244.05/50.50  | | | 
% 244.05/50.50  | | | ALPHA: (15) implies:
% 244.05/50.50  | | |   (16)  all_58_6 = e2
% 244.05/50.50  | | | 
% 244.05/50.50  | | | REF_CLOSE: (1), (2), (4), (7), (9), (10), (11), (12), (16) are
% 244.05/50.50  | | |            inconsistent by sub-proof #1420.
% 244.05/50.50  | | | 
% 244.05/50.50  | | Case 2:
% 244.05/50.50  | | | 
% 244.05/50.50  | | |   (17)  all_58_7 = e2 & op(e1, e2) = e2
% 244.05/50.50  | | | 
% 244.05/50.50  | | | REF_CLOSE: (7), (13), (17) are inconsistent by sub-proof #2218.
% 244.05/50.50  | | | 
% 244.05/50.50  | | End of split
% 244.05/50.50  | | 
% 244.05/50.50  | Case 2:
% 244.05/50.50  | | 
% 244.05/50.50  | |   (18)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 244.05/50.50  | |           e2)
% 244.05/50.50  | | 
% 244.05/50.50  | | BETA: splitting (18) gives:
% 244.05/50.50  | | 
% 244.05/50.50  | | Case 1:
% 244.05/50.50  | | | 
% 244.05/50.50  | | |   (19)  all_58_8 = e2 & op(e1, e1) = e2
% 244.05/50.50  | | | 
% 244.05/50.50  | | | ALPHA: (19) implies:
% 244.05/50.50  | | |   (20)  op(e1, e1) = e2
% 244.05/50.50  | | | 
% 244.05/50.50  | | | REF_CLOSE: (5), (6), (9), (20) are inconsistent by sub-proof #2206.
% 244.05/50.50  | | | 
% 244.05/50.50  | | Case 2:
% 244.05/50.50  | | | 
% 244.05/50.50  | | |   (21)  all_58_11 = e2 & op(e1, e0) = e2
% 244.05/50.50  | | | 
% 244.05/50.50  | | | REF_CLOSE: (3), (13), (21) are inconsistent by sub-proof #1554.
% 244.05/50.50  | | | 
% 244.05/50.50  | | End of split
% 244.05/50.50  | | 
% 244.05/50.50  | End of split
% 244.05/50.50  | 
% 244.05/50.50  End of proof
% 244.05/50.50  
% 244.05/50.50  Sub-proof #1420 shows that the following formulas are inconsistent:
% 244.05/50.50  ----------------------------------------------------------------
% 244.05/50.50    (1)   ~ (e3 = e0)
% 244.05/50.50    (2)   ~ (e2 = e0)
% 244.05/50.50    (3)  all_58_6 = e2
% 244.05/50.50    (4)  op(e1, e0) = e1
% 244.05/50.50    (5)  all_58_7 = e1
% 244.05/50.50    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.50    (7)  all_58_8 = e3
% 244.05/50.50    (8)   ~ (e1 = e0)
% 244.05/50.50    (9)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.05/50.50         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.50  
% 244.05/50.50  Begin of proof
% 244.05/50.50  | 
% 244.05/50.50  | BETA: splitting (9) gives:
% 244.05/50.50  | 
% 244.05/50.50  | Case 1:
% 244.05/50.50  | | 
% 244.05/50.50  | |   (10)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 244.05/50.50  | |           e0)
% 244.05/50.50  | | 
% 244.05/50.50  | | BETA: splitting (10) gives:
% 244.05/50.50  | | 
% 244.05/50.50  | | Case 1:
% 244.05/50.50  | | | 
% 244.05/50.50  | | |   (11)  all_58_6 = e0 & op(e1, e3) = e0
% 244.05/50.50  | | | 
% 244.05/50.50  | | | ALPHA: (11) implies:
% 244.05/50.50  | | |   (12)  all_58_6 = e0
% 244.05/50.50  | | | 
% 244.05/50.50  | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #1982.
% 244.05/50.50  | | | 
% 244.05/50.50  | | Case 2:
% 244.05/50.50  | | | 
% 244.05/50.50  | | |   (13)  all_58_7 = e0 & op(e1, e2) = e0
% 244.05/50.50  | | | 
% 244.05/50.50  | | | REF_CLOSE: (5), (8), (13) are inconsistent by sub-proof #1558.
% 244.05/50.50  | | | 
% 244.05/50.50  | | End of split
% 244.05/50.50  | | 
% 244.05/50.50  | Case 2:
% 244.05/50.50  | | 
% 244.05/50.50  | |   (14)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.05/50.50  | |           e0)
% 244.05/50.50  | | 
% 244.05/50.50  | | BETA: splitting (14) gives:
% 244.05/50.50  | | 
% 244.05/50.50  | | Case 1:
% 244.05/50.50  | | | 
% 244.05/50.50  | | |   (15)  all_58_8 = e0 & op(e1, e1) = e0
% 244.05/50.50  | | | 
% 244.05/50.50  | | | REF_CLOSE: (1), (7), (15) are inconsistent by sub-proof #1421.
% 244.05/50.50  | | | 
% 244.05/50.50  | | Case 2:
% 244.05/50.50  | | | 
% 244.05/50.50  | | |   (16)  all_58_11 = e0 & op(e1, e0) = e0
% 244.05/50.50  | | | 
% 244.05/50.50  | | | ALPHA: (16) implies:
% 244.05/50.50  | | |   (17)  op(e1, e0) = e0
% 244.05/50.50  | | | 
% 244.05/50.50  | | | REF_CLOSE: (4), (6), (8), (17) are inconsistent by sub-proof #2284.
% 244.05/50.50  | | | 
% 244.05/50.50  | | End of split
% 244.05/50.50  | | 
% 244.05/50.50  | End of split
% 244.05/50.50  | 
% 244.05/50.50  End of proof
% 244.05/50.50  
% 244.05/50.50  Sub-proof #1421 shows that the following formulas are inconsistent:
% 244.05/50.50  ----------------------------------------------------------------
% 244.05/50.50    (1)  all_58_8 = e0 & op(e1, e1) = e0
% 244.05/50.50    (2)  all_58_8 = e3
% 244.05/50.50    (3)   ~ (e3 = e0)
% 244.05/50.50  
% 244.05/50.50  Begin of proof
% 244.05/50.50  | 
% 244.05/50.50  | ALPHA: (1) implies:
% 244.05/50.50  |   (4)  all_58_8 = e0
% 244.05/50.50  | 
% 244.05/50.50  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.50  |   (5)  e3 = e0
% 244.05/50.50  | 
% 244.05/50.50  | REDUCE: (3), (5) imply:
% 244.05/50.50  |   (6)  $false
% 244.05/50.50  | 
% 244.05/50.50  | CLOSE: (6) is inconsistent.
% 244.05/50.50  | 
% 244.05/50.50  End of proof
% 244.05/50.50  
% 244.05/50.50  Sub-proof #1422 shows that the following formulas are inconsistent:
% 244.05/50.50  ----------------------------------------------------------------
% 244.05/50.50    (1)  all_58_7 = e1 & op(e1, e2) = e1
% 244.05/50.50    (2)  all_58_7 = e3
% 244.05/50.50    (3)   ~ (e3 = e1)
% 244.05/50.50  
% 244.05/50.50  Begin of proof
% 244.05/50.50  | 
% 244.05/50.50  | ALPHA: (1) implies:
% 244.05/50.50  |   (4)  all_58_7 = e1
% 244.05/50.50  | 
% 244.05/50.50  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.50  |   (5)  e3 = e1
% 244.05/50.50  | 
% 244.05/50.50  | REDUCE: (3), (5) imply:
% 244.05/50.50  |   (6)  $false
% 244.05/50.50  | 
% 244.05/50.50  | CLOSE: (6) is inconsistent.
% 244.05/50.50  | 
% 244.05/50.50  End of proof
% 244.05/50.50  
% 244.05/50.50  Sub-proof #1423 shows that the following formulas are inconsistent:
% 244.05/50.50  ----------------------------------------------------------------
% 244.05/50.50    (1)  all_58_6 = e1 & op(e1, e3) = e1
% 244.05/50.50    (2)  all_58_6 = e2
% 244.05/50.50    (3)   ~ (e2 = e1)
% 244.05/50.50  
% 244.05/50.50  Begin of proof
% 244.05/50.50  | 
% 244.05/50.50  | ALPHA: (1) implies:
% 244.05/50.50  |   (4)  all_58_6 = e1
% 244.05/50.50  | 
% 244.05/50.50  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.50  |   (5)  e2 = e1
% 244.05/50.50  | 
% 244.05/50.50  | REDUCE: (3), (5) imply:
% 244.05/50.50  |   (6)  $false
% 244.05/50.50  | 
% 244.05/50.50  | CLOSE: (6) is inconsistent.
% 244.05/50.50  | 
% 244.05/50.50  End of proof
% 244.05/50.50  
% 244.05/50.50  Sub-proof #1424 shows that the following formulas are inconsistent:
% 244.05/50.50  ----------------------------------------------------------------
% 244.05/50.50    (1)   ~ (e3 = e0)
% 244.05/50.50    (2)  op(e2, e3) = all_52_1
% 244.05/50.50    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 244.05/50.50    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.50    (5)  all_58_3 = e0
% 244.05/50.50    (6)   ~ (all_52_1 = e3)
% 244.05/50.50  
% 244.05/50.50  Begin of proof
% 244.05/50.50  | 
% 244.05/50.50  | BETA: splitting (3) gives:
% 244.05/50.50  | 
% 244.05/50.50  | Case 1:
% 244.05/50.50  | | 
% 244.05/50.50  | |   (7)  all_58_2 = e3 & op(e2, e3) = e3
% 244.05/50.50  | | 
% 244.05/50.50  | | ALPHA: (7) implies:
% 244.05/50.50  | |   (8)  op(e2, e3) = e3
% 244.05/50.50  | | 
% 244.05/50.50  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2337.
% 244.05/50.50  | | 
% 244.05/50.50  | Case 2:
% 244.05/50.50  | | 
% 244.05/50.50  | |   (9)  all_58_3 = e3 & op(e2, e2) = e3
% 244.05/50.50  | | 
% 244.05/50.50  | | ALPHA: (9) implies:
% 244.05/50.50  | |   (10)  all_58_3 = e3
% 244.05/50.50  | | 
% 244.05/50.50  | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #1460.
% 244.05/50.50  | | 
% 244.05/50.50  | End of split
% 244.05/50.50  | 
% 244.05/50.50  End of proof
% 244.05/50.50  
% 244.05/50.50  Sub-proof #1425 shows that the following formulas are inconsistent:
% 244.05/50.50  ----------------------------------------------------------------
% 244.05/50.50    (1)   ~ (all_52_3 = e0)
% 244.05/50.50    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.05/50.50             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.05/50.50           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.05/50.50         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.05/50.50           $i(all_56_7))
% 244.05/50.50    (3)  op(e0, e1) = all_52_11
% 244.05/50.50    (4)   ~ (all_52_8 = all_52_9)
% 244.05/50.50    (5)   ~ (e2 = e0)
% 244.05/50.50    (6)  op(e2, e0) = all_14_1
% 244.05/50.50    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.05/50.50           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.05/50.50             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.05/50.50           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.05/50.50             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.05/50.50           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.05/50.50           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.05/50.50           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.05/50.50           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.05/50.50           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.05/50.50           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.05/50.50             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.05/50.50           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.05/50.50           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 244.05/50.50           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.05/50.50           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.05/50.50           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.05/50.50           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.05/50.50             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.05/50.50           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.05/50.50           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.05/50.50           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.05/50.50           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.05/50.50           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.05/50.50           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.05/50.50             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.05/50.50           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.05/50.50           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.05/50.50    (8)   ~ (all_52_1 = all_52_2)
% 244.05/50.50    (9)  op(e1, e0) = all_52_14
% 244.05/50.50    (10)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.05/50.50    (11)   ~ (all_52_8 = e0)
% 244.05/50.50    (12)  op(e0, e3) = all_52_3
% 244.05/50.50    (13)   ~ (e3 = e1)
% 244.05/50.50    (14)  op(e2, e2) = e0
% 244.05/50.50    (15)  op(e1, e2) = e3
% 244.05/50.50    (16)  op(e2, e0) = e3
% 244.05/50.50    (17)   ~ (all_52_8 = all_52_12)
% 244.05/50.50    (18)  op(e3, e1) = all_52_8
% 244.05/50.50    (19)  op(e2, e1) = all_52_9
% 244.05/50.50    (20)   ~ (e3 = e2)
% 244.05/50.50    (21)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 244.05/50.50            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 244.05/50.50              e0) = all_48_1 & $i(all_48_1))
% 244.05/50.50    (22)   ~ (all_52_14 = e0)
% 244.05/50.50    (23)  all_56_31 = e0
% 244.05/50.50    (24)  op(e0, e3) = e3
% 244.05/50.50    (25)  op(e3, e0) = all_52_12
% 244.05/50.50    (26)  op(e2, e3) = all_52_1
% 244.05/50.50    (27)   ~ (all_52_2 = e3)
% 244.05/50.50    (28)   ~ (all_52_2 = e0)
% 244.05/50.50    (29)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.05/50.50          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.05/50.50    (30)   ~ (all_52_8 = all_52_11)
% 244.05/50.50    (31)  all_54_8 = all_52_2
% 244.05/50.50    (32)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.50    (33)  op(e1, e3) = all_52_2
% 244.05/50.50    (34)  op(e3, e1) = e3
% 244.05/50.50    (35)  op(e1, e1) = e0
% 244.05/50.50    (36)  all_58_4 = e3
% 244.05/50.50    (37)  all_56_1 = e0
% 244.05/50.50    (38)  op(e2, e0) = all_52_13
% 244.05/50.50    (39)   ~ (all_52_1 = e3)
% 244.05/50.50    (40)   ~ (all_52_13 = e0)
% 244.05/50.50  
% 244.05/50.50  Begin of proof
% 244.05/50.50  | 
% 244.05/50.50  | BETA: splitting (21) gives:
% 244.05/50.50  | 
% 244.05/50.50  | Case 1:
% 244.05/50.50  | | 
% 244.05/50.50  | |   (41)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 244.05/50.50  | |         all_48_1 & $i(all_48_0) & $i(all_48_1)
% 244.05/50.50  | | 
% 244.05/50.50  | | ALPHA: (41) implies:
% 244.05/50.50  | |   (42)  op(e2, e0) = all_48_1
% 244.05/50.50  | | 
% 244.05/50.50  | | GROUND_INST: instantiating (32) with all_14_1, all_48_1, e0, e2, simplifying
% 244.05/50.50  | |              with (6), (42) gives:
% 244.05/50.50  | |   (43)  all_48_1 = all_14_1
% 244.05/50.50  | | 
% 244.05/50.50  | | GROUND_INST: instantiating (32) with e3, all_48_1, e0, e2, simplifying with
% 244.05/50.50  | |              (16), (42) gives:
% 244.05/50.50  | |   (44)  all_48_1 = e3
% 244.05/50.50  | | 
% 244.05/50.50  | | GROUND_INST: instantiating (32) with all_52_8, e3, e1, e3, simplifying with
% 244.05/50.50  | |              (18), (34) gives:
% 244.05/50.50  | |   (45)  all_52_8 = e3
% 244.05/50.50  | | 
% 244.05/50.50  | | COMBINE_EQS: (43), (44) imply:
% 244.05/50.50  | |   (46)  all_14_1 = e3
% 244.05/50.50  | | 
% 244.05/50.50  | | REDUCE: (4), (45) imply:
% 244.05/50.50  | |   (47)   ~ (all_52_9 = e3)
% 244.05/50.50  | | 
% 244.05/50.50  | | SIMP: (47) implies:
% 244.05/50.50  | |   (48)   ~ (all_52_9 = e3)
% 244.05/50.50  | | 
% 244.05/50.50  | | REDUCE: (30), (45) imply:
% 244.05/50.50  | |   (49)   ~ (all_52_11 = e3)
% 244.05/50.50  | | 
% 244.05/50.50  | | SIMP: (49) implies:
% 244.05/50.50  | |   (50)   ~ (all_52_11 = e3)
% 244.05/50.50  | | 
% 244.05/50.50  | | REDUCE: (17), (45) imply:
% 244.05/50.50  | |   (51)   ~ (all_52_12 = e3)
% 244.05/50.50  | | 
% 244.05/50.50  | | SIMP: (51) implies:
% 244.05/50.50  | |   (52)   ~ (all_52_12 = e3)
% 244.05/50.50  | | 
% 244.05/50.50  | | REDUCE: (11), (45) imply:
% 244.05/50.50  | |   (53)   ~ (e3 = e0)
% 244.05/50.50  | | 
% 244.05/50.50  | | BETA: splitting (7) gives:
% 244.05/50.50  | | 
% 244.05/50.50  | | Case 1:
% 244.05/50.50  | | | 
% 244.05/50.50  | | |   (54)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.05/50.50  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.05/50.50  | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.05/50.50  | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.05/50.50  | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 244.05/50.50  | | |         | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.05/50.50  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.05/50.50  | | |           op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17
% 244.05/50.50  | | |           = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 244.05/50.50  | | |             = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.05/50.50  | | |           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.05/50.50  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.05/50.50  | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 244.05/50.50  | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 244.05/50.50  | | |             = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 244.05/50.50  | | |           e0)
% 244.05/50.50  | | | 
% 244.05/50.50  | | | BETA: splitting (54) gives:
% 244.05/50.50  | | | 
% 244.05/50.50  | | | Case 1:
% 244.05/50.50  | | | | 
% 244.05/50.50  | | | |   (55)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.05/50.50  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.05/50.50  | | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9
% 244.05/50.50  | | | |           = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.05/50.50  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.05/50.50  | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.05/50.50  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 244.05/50.50  | | | |           ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.05/50.50  | | | | 
% 244.05/50.50  | | | | BETA: splitting (55) gives:
% 244.05/50.50  | | | | 
% 244.05/50.50  | | | | Case 1:
% 244.05/50.50  | | | | | 
% 244.05/50.50  | | | | |   (56)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.05/50.50  | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.05/50.50  | | | | |         op(e3, e2) = e3 & op(e2, e3) = e3
% 244.05/50.50  | | | | | 
% 244.05/50.50  | | | | | ALPHA: (56) implies:
% 244.05/50.50  | | | | |   (57)  op(e2, e3) = e3
% 244.05/50.50  | | | | | 
% 244.05/50.50  | | | | | REF_CLOSE: (26), (32), (39), (57) are inconsistent by sub-proof #2337.
% 244.05/50.50  | | | | | 
% 244.05/50.50  | | | | Case 2:
% 244.05/50.50  | | | | | 
% 244.05/50.50  | | | | |   (58)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.05/50.50  | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 244.05/50.50  | | | | |           & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 244.05/50.50  | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 244.05/50.50  | | | | |           ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.05/50.50  | | | | |           op(e1, e3) = e3)
% 244.05/50.50  | | | | | 
% 244.05/50.50  | | | | | BETA: splitting (58) gives:
% 244.05/50.50  | | | | | 
% 244.05/50.50  | | | | | Case 1:
% 244.05/50.50  | | | | | | 
% 244.05/50.51  | | | | | |   (59)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.05/50.51  | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 244.05/50.51  | | | | | |         & op(e3, e2) = e2 & op(e2, e3) = e2
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | ALPHA: (59) implies:
% 244.05/50.51  | | | | | |   (60)  all_56_3 = e2
% 244.05/50.51  | | | | | |   (61)   ~ (all_56_31 = e3)
% 244.05/50.51  | | | | | |   (62)  op(e2, e3) = e2
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | REDUCE: (23), (61) imply:
% 244.05/50.51  | | | | | |   (63)   ~ (e3 = e0)
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | BETA: splitting (2) gives:
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | Case 1:
% 244.05/50.51  | | | | | | | 
% 244.05/50.51  | | | | | | |   (64)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 244.05/50.51  | | | | | | |           op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 244.05/50.51  | | | | | | |           $i(all_56_3))
% 244.05/50.51  | | | | | | | 
% 244.05/50.51  | | | | | | | BETA: splitting (64) gives:
% 244.05/50.51  | | | | | | | 
% 244.05/50.51  | | | | | | | Case 1:
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | |   (65)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | ALPHA: (65) implies:
% 244.05/50.51  | | | | | | | |   (66)  op(e3, all_56_1) = e3
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | REDUCE: (37), (66) imply:
% 244.05/50.51  | | | | | | | |   (67)  op(e3, e0) = e3
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | REF_CLOSE: (25), (32), (52), (67) are inconsistent by sub-proof
% 244.05/50.51  | | | | | | | |            #2179.
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | Case 2:
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | |   (68)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 244.05/50.51  | | | | | | | |         all_56_3 & $i(all_56_3)
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | ALPHA: (68) implies:
% 244.05/50.51  | | | | | | | |   (69)  op(e2, all_56_3) = e2
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | REDUCE: (60), (69) imply:
% 244.05/50.51  | | | | | | | |   (70)  op(e2, e2) = e2
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | REF_CLOSE: (5), (14), (32), (70) are inconsistent by sub-proof
% 244.05/50.51  | | | | | | | |            #2137.
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | End of split
% 244.05/50.51  | | | | | | | 
% 244.05/50.51  | | | | | | Case 2:
% 244.05/50.51  | | | | | | | 
% 244.05/50.51  | | | | | | |   (71)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 244.05/50.51  | | | | | | |           all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 244.05/50.51  | | | | | | |             all_56_7) = e0 & op(e0, e3) = all_56_7 & $i(all_56_7))
% 244.05/50.51  | | | | | | | 
% 244.05/50.51  | | | | | | | BETA: splitting (71) gives:
% 244.05/50.51  | | | | | | | 
% 244.05/50.51  | | | | | | | Case 1:
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | |   (72)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 244.05/50.51  | | | | | | | |         all_56_5 & $i(all_56_5)
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | ALPHA: (72) implies:
% 244.05/50.51  | | | | | | | |   (73)  op(e1, e3) = all_56_5
% 244.05/50.51  | | | | | | | |   (74)  op(e1, all_56_5) = e1
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | GROUND_INST: instantiating (32) with all_52_2, all_56_5, e3, e1,
% 244.05/50.51  | | | | | | | |              simplifying with (33), (73) gives:
% 244.05/50.51  | | | | | | | |   (75)  all_56_5 = all_52_2
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | GROUND_INST: instantiating (32) with all_52_1, e2, e3, e2,
% 244.05/50.51  | | | | | | | |              simplifying with (26), (62) gives:
% 244.05/50.51  | | | | | | | |   (76)  all_52_1 = e2
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | REDUCE: (8), (76) imply:
% 244.05/50.51  | | | | | | | |   (77)   ~ (all_52_2 = e2)
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | SIMP: (77) implies:
% 244.05/50.51  | | | | | | | |   (78)   ~ (all_52_2 = e2)
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | REF_CLOSE: (10), (28), (31), (32), (33), (35), (73), (74), (78)
% 244.05/50.51  | | | | | | | |            are inconsistent by sub-proof #2004.
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | Case 2:
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | |   (79)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 244.05/50.51  | | | | | | | |         all_56_7 & $i(all_56_7)
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | ALPHA: (79) implies:
% 244.05/50.51  | | | | | | | |   (80)  op(e0, e3) = all_56_7
% 244.05/50.51  | | | | | | | |   (81)  op(e0, all_56_7) = e0
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | | REF_CLOSE: (24), (32), (53), (80), (81) are inconsistent by
% 244.05/50.51  | | | | | | | |            sub-proof #2070.
% 244.05/50.51  | | | | | | | | 
% 244.05/50.51  | | | | | | | End of split
% 244.05/50.51  | | | | | | | 
% 244.05/50.51  | | | | | | End of split
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | Case 2:
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | |   (82)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.05/50.51  | | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 244.05/50.51  | | | | | |         & op(e3, e1) = e3 & op(e1, e3) = e3
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | ALPHA: (82) implies:
% 244.05/50.51  | | | | | |   (83)  op(e1, e3) = e3
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | REF_CLOSE: (27), (32), (33), (83) are inconsistent by sub-proof
% 244.05/50.51  | | | | | |            #2335.
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | End of split
% 244.05/50.51  | | | | | 
% 244.05/50.51  | | | | End of split
% 244.05/50.51  | | | | 
% 244.05/50.51  | | | Case 2:
% 244.05/50.51  | | | | 
% 244.05/50.51  | | | |   (84)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 244.05/50.51  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.05/50.51  | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 244.05/50.51  | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 244.05/50.51  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.05/50.51  | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.05/50.51  | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) & 
% 244.05/50.51  | | | |           ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.05/50.51  | | | | 
% 244.05/50.51  | | | | REF_CLOSE: (1), (12), (13), (25), (32), (34), (52), (84) are
% 244.05/50.51  | | | |            inconsistent by sub-proof #1426.
% 244.05/50.51  | | | | 
% 244.05/50.51  | | | End of split
% 244.05/50.51  | | | 
% 244.05/50.51  | | Case 2:
% 244.05/50.51  | | | 
% 244.05/50.51  | | |   (85)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 244.05/50.51  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.05/50.51  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 244.05/50.51  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 244.05/50.51  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 244.05/50.51  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.05/50.51  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.05/50.51  | | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27
% 244.05/50.51  | | |           = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 244.05/50.51  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.05/50.51  | | |           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.05/50.51  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.05/50.51  | | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29
% 244.05/50.51  | | |           = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 244.05/50.51  | | |             = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 244.05/50.51  | | |           e0)
% 244.05/50.51  | | | 
% 244.05/50.51  | | | BETA: splitting (85) gives:
% 244.05/50.51  | | | 
% 244.05/50.51  | | | Case 1:
% 244.05/50.51  | | | | 
% 244.05/50.51  | | | |   (86)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 244.05/50.51  | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.05/50.51  | | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 244.05/50.51  | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.05/50.51  | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.05/50.51  | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.05/50.51  | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) & 
% 244.05/50.51  | | | |           ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.05/50.51  | | | | 
% 244.05/50.51  | | | | BETA: splitting (86) gives:
% 244.05/50.51  | | | | 
% 244.05/50.51  | | | | Case 1:
% 244.05/50.51  | | | | | 
% 244.05/50.51  | | | | |   (87)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 244.05/50.51  | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.05/50.51  | | | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 244.05/50.51  | | | | | 
% 244.05/50.51  | | | | | ALPHA: (87) implies:
% 244.05/50.51  | | | | |   (88)  op(e1, e2) = e2
% 244.05/50.51  | | | | | 
% 244.05/50.51  | | | | | GROUND_INST: instantiating (32) with e3, e2, e2, e1, simplifying with
% 244.05/50.51  | | | | |              (15), (88) gives:
% 244.05/50.51  | | | | |   (89)  e3 = e2
% 244.05/50.51  | | | | | 
% 244.05/50.51  | | | | | COMBINE_EQS: (36), (89) imply:
% 244.05/50.51  | | | | |   (90)  all_58_4 = e2
% 244.05/50.51  | | | | | 
% 244.05/50.51  | | | | | REF_CLOSE: (3), (19), (20), (29), (32), (35), (48), (50), (53), (90)
% 244.05/50.51  | | | | |            are inconsistent by sub-proof #1493.
% 244.05/50.51  | | | | | 
% 244.05/50.51  | | | | Case 2:
% 244.05/50.51  | | | | | 
% 244.05/50.51  | | | | |   (91)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.05/50.51  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 244.05/50.51  | | | | |           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 244.05/50.51  | | | | |           all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.05/50.51  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 &
% 244.05/50.51  | | | | |           op(e0, e2) = e2)
% 244.05/50.51  | | | | | 
% 244.05/50.51  | | | | | BETA: splitting (91) gives:
% 244.05/50.51  | | | | | 
% 244.05/50.51  | | | | | Case 1:
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | |   (92)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.05/50.51  | | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 244.05/50.51  | | | | | |         & op(e2, e1) = e1 & op(e1, e2) = e1
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | ALPHA: (92) implies:
% 244.05/50.51  | | | | | |   (93)  op(e1, e2) = e1
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | GROUND_INST: instantiating (32) with e3, e1, e2, e1, simplifying
% 244.05/50.51  | | | | | |              with (15), (93) gives:
% 244.05/50.51  | | | | | |   (94)  e3 = e1
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | REDUCE: (13), (94) imply:
% 244.05/50.51  | | | | | |   (95)  $false
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | CLOSE: (95) is inconsistent.
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | Case 2:
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | |   (96)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.05/50.51  | | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.05/50.51  | | | | | |         & op(e2, e0) = e2 & op(e0, e2) = e2
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | ALPHA: (96) implies:
% 244.05/50.51  | | | | | |   (97)  op(e2, e0) = e2
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | | REF_CLOSE: (16), (20), (32), (97) are inconsistent by sub-proof
% 244.05/50.51  | | | | | |            #2152.
% 244.05/50.51  | | | | | | 
% 244.05/50.51  | | | | | End of split
% 244.05/50.51  | | | | | 
% 244.05/50.51  | | | | End of split
% 244.05/50.51  | | | | 
% 244.05/50.51  | | | Case 2:
% 244.05/50.51  | | | | 
% 244.05/50.51  | | | |   (98)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 244.05/50.51  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.05/50.51  | | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 244.05/50.51  | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 244.05/50.51  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 244.05/50.51  | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.05/50.51  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 244.05/50.51  | | | |           ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.05/50.51  | | | | 
% 244.05/50.51  | | | | REF_CLOSE: (9), (22), (23), (32), (38), (40), (98) are inconsistent by
% 244.05/50.51  | | | |            sub-proof #2321.
% 244.05/50.51  | | | | 
% 244.05/50.51  | | | End of split
% 244.05/50.51  | | | 
% 244.05/50.51  | | End of split
% 244.05/50.51  | | 
% 244.05/50.51  | Case 2:
% 244.05/50.51  | | 
% 244.05/50.51  | |   (99)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 & $i(all_48_1)
% 244.05/50.51  | | 
% 244.05/50.51  | | ALPHA: (99) implies:
% 244.05/50.51  | |   (100)   ~ (all_48_1 = e3)
% 244.05/50.51  | |   (101)  op(e2, e0) = all_48_1
% 244.05/50.51  | | 
% 244.05/50.51  | | REF_CLOSE: (6), (16), (32), (100), (101) are inconsistent by sub-proof
% 244.05/50.51  | |            #1632.
% 244.05/50.51  | | 
% 244.05/50.51  | End of split
% 244.05/50.51  | 
% 244.05/50.51  End of proof
% 244.05/50.51  
% 244.05/50.51  Sub-proof #1426 shows that the following formulas are inconsistent:
% 244.05/50.51  ----------------------------------------------------------------
% 244.05/50.51    (1)   ~ (all_52_3 = e0)
% 244.05/50.51    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.05/50.51             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.05/50.51           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 244.05/50.51           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.05/50.51           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 244.05/50.51           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.05/50.51           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.05/50.51    (3)  op(e0, e3) = all_52_3
% 244.05/50.51    (4)   ~ (e3 = e1)
% 244.05/50.51    (5)  op(e3, e0) = all_52_12
% 244.05/50.51    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.51    (7)  op(e3, e1) = e3
% 244.05/50.51    (8)   ~ (all_52_12 = e3)
% 244.05/50.51  
% 244.05/50.51  Begin of proof
% 244.05/50.51  | 
% 244.05/50.51  | BETA: splitting (2) gives:
% 244.05/50.51  | 
% 244.05/50.51  | Case 1:
% 244.05/50.51  | | 
% 244.05/50.51  | |   (9)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.05/50.51  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.05/50.51  | |        op(e1, e3) = e1
% 244.05/50.51  | | 
% 244.05/50.51  | | ALPHA: (9) implies:
% 244.05/50.51  | |   (10)  op(e3, e1) = e1
% 244.05/50.51  | | 
% 244.05/50.51  | | REF_CLOSE: (4), (6), (7), (10) are inconsistent by sub-proof #1823.
% 244.05/50.51  | | 
% 244.05/50.51  | Case 2:
% 244.05/50.51  | | 
% 244.05/50.51  | |   (11)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.05/50.51  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 244.05/50.51  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.05/50.51  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.05/50.51  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.05/50.51  | | 
% 244.05/50.51  | | REF_CLOSE: (1), (3), (5), (6), (8), (11) are inconsistent by sub-proof
% 244.05/50.51  | |            #1794.
% 244.05/50.51  | | 
% 244.05/50.51  | End of split
% 244.05/50.51  | 
% 244.05/50.51  End of proof
% 244.05/50.51  
% 244.05/50.51  Sub-proof #1427 shows that the following formulas are inconsistent:
% 244.05/50.51  ----------------------------------------------------------------
% 244.05/50.51    (1)  op(e1, e2) = e3
% 244.05/50.51    (2)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 244.05/50.51           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0) =
% 244.05/50.51           all_14_1 & $i(all_14_1))
% 244.05/50.51    (3)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) = all_48_1
% 244.05/50.51           & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0) =
% 244.05/50.51           all_48_1 & $i(all_48_1))
% 244.05/50.51    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.51    (5)  op(e2, e0) = e1
% 244.05/50.51  
% 244.05/50.51  Begin of proof
% 244.05/50.51  | 
% 244.05/50.51  | BETA: splitting (2) gives:
% 244.05/50.51  | 
% 244.05/50.51  | Case 1:
% 244.05/50.51  | | 
% 244.05/50.51  | |   (6)   ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 244.05/50.51  | |        all_14_1 & $i(all_14_0) & $i(all_14_1)
% 244.05/50.51  | | 
% 244.05/50.51  | | ALPHA: (6) implies:
% 244.05/50.51  | |   (7)   ~ (all_14_0 = e3)
% 244.05/50.51  | |   (8)  op(e2, e0) = all_14_1
% 244.05/50.51  | |   (9)  op(all_14_1, e2) = all_14_0
% 244.05/50.51  | | 
% 244.05/50.51  | | BETA: splitting (3) gives:
% 244.05/50.51  | | 
% 244.05/50.51  | | Case 1:
% 244.05/50.51  | | | 
% 244.05/50.51  | | |   (10)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 244.05/50.51  | | |         all_48_1 & $i(all_48_0) & $i(all_48_1)
% 244.05/50.51  | | | 
% 244.05/50.51  | | | ALPHA: (10) implies:
% 244.05/50.51  | | |   (11)  op(e2, e0) = all_48_1
% 244.05/50.51  | | |   (12)  op(all_48_1, e2) = all_48_0
% 244.05/50.51  | | | 
% 244.05/50.51  | | | GROUND_INST: instantiating (4) with e1, all_48_1, e0, e2, simplifying with
% 244.05/50.51  | | |              (5), (11) gives:
% 244.05/50.51  | | |   (13)  all_48_1 = e1
% 244.05/50.51  | | | 
% 244.05/50.51  | | | GROUND_INST: instantiating (4) with all_14_1, all_48_1, e0, e2,
% 244.05/50.51  | | |              simplifying with (8), (11) gives:
% 244.05/50.51  | | |   (14)  all_48_1 = all_14_1
% 244.05/50.51  | | | 
% 244.05/50.51  | | | COMBINE_EQS: (13), (14) imply:
% 244.05/50.51  | | |   (15)  all_14_1 = e1
% 244.05/50.51  | | | 
% 244.05/50.51  | | | REDUCE: (12), (13) imply:
% 244.05/50.51  | | |   (16)  op(e1, e2) = all_48_0
% 244.05/50.51  | | | 
% 244.05/50.51  | | | REDUCE: (9), (15) imply:
% 244.05/50.51  | | |   (17)  op(e1, e2) = all_14_0
% 244.05/50.51  | | | 
% 244.05/50.51  | | | GROUND_INST: instantiating (4) with e3, all_48_0, e2, e1, simplifying with
% 244.05/50.51  | | |              (1), (16) gives:
% 244.05/50.51  | | |   (18)  all_48_0 = e3
% 244.05/50.51  | | | 
% 244.05/50.51  | | | GROUND_INST: instantiating (4) with all_14_0, all_48_0, e2, e1,
% 244.05/50.51  | | |              simplifying with (16), (17) gives:
% 244.05/50.51  | | |   (19)  all_48_0 = all_14_0
% 244.05/50.51  | | | 
% 244.05/50.51  | | | COMBINE_EQS: (18), (19) imply:
% 244.05/50.51  | | |   (20)  all_14_0 = e3
% 244.05/50.51  | | | 
% 244.05/50.51  | | | REDUCE: (7), (20) imply:
% 244.05/50.51  | | |   (21)  $false
% 244.05/50.51  | | | 
% 244.05/50.51  | | | CLOSE: (21) is inconsistent.
% 244.05/50.51  | | | 
% 244.05/50.51  | | Case 2:
% 244.05/50.51  | | | 
% 244.05/50.51  | | |   (22)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 & $i(all_48_1)
% 244.05/50.51  | | | 
% 244.05/50.51  | | | ALPHA: (22) implies:
% 244.05/50.51  | | |   (23)  op(e2, e0) = all_48_1
% 244.05/50.51  | | | 
% 244.05/50.51  | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (23) are inconsistent by
% 244.05/50.51  | | |            sub-proof #1428.
% 244.05/50.51  | | | 
% 244.05/50.51  | | End of split
% 244.05/50.51  | | 
% 244.05/50.51  | Case 2:
% 244.05/50.51  | | 
% 244.05/50.51  | |   (24)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 244.05/50.51  | | 
% 244.05/50.51  | | ALPHA: (24) implies:
% 244.05/50.51  | |   (25)   ~ (all_14_1 = e1)
% 244.05/50.51  | |   (26)  op(e2, e0) = all_14_1
% 244.05/50.51  | | 
% 244.05/50.51  | | REF_CLOSE: (3), (4), (5), (25), (26) are inconsistent by sub-proof #1584.
% 244.05/50.51  | | 
% 244.05/50.51  | End of split
% 244.05/50.51  | 
% 244.05/50.51  End of proof
% 244.05/50.51  
% 244.05/50.51  Sub-proof #1428 shows that the following formulas are inconsistent:
% 244.05/50.51  ----------------------------------------------------------------
% 244.05/50.51    (1)  op(e2, e0) = all_14_1
% 244.05/50.51    (2)  op(all_14_1, e2) = all_14_0
% 244.05/50.51    (3)  op(e1, e2) = e3
% 244.05/50.51    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.51    (5)   ~ (all_14_0 = e3)
% 244.05/50.51    (6)  op(e2, e0) = e1
% 244.05/50.51    (7)  op(e2, e0) = all_48_1
% 244.05/50.51  
% 244.05/50.51  Begin of proof
% 244.05/50.51  | 
% 244.05/50.52  | GROUND_INST: instantiating (4) with e1, all_48_1, e0, e2, simplifying with
% 244.05/50.52  |              (6), (7) gives:
% 244.05/50.52  |   (8)  all_48_1 = e1
% 244.05/50.52  | 
% 244.05/50.52  | GROUND_INST: instantiating (4) with all_14_1, all_48_1, e0, e2, simplifying
% 244.05/50.52  |              with (1), (7) gives:
% 244.05/50.52  |   (9)  all_48_1 = all_14_1
% 244.05/50.52  | 
% 244.05/50.52  | COMBINE_EQS: (8), (9) imply:
% 244.05/50.52  |   (10)  all_14_1 = e1
% 244.05/50.52  | 
% 244.05/50.52  | REDUCE: (2), (10) imply:
% 244.05/50.52  |   (11)  op(e1, e2) = all_14_0
% 244.05/50.52  | 
% 244.05/50.52  | GROUND_INST: instantiating (4) with e3, all_14_0, e2, e1, simplifying with
% 244.05/50.52  |              (3), (11) gives:
% 244.05/50.52  |   (12)  all_14_0 = e3
% 244.05/50.52  | 
% 244.05/50.52  | REDUCE: (5), (12) imply:
% 244.05/50.52  |   (13)  $false
% 244.05/50.52  | 
% 244.05/50.52  | CLOSE: (13) is inconsistent.
% 244.05/50.52  | 
% 244.05/50.52  End of proof
% 244.05/50.52  
% 244.05/50.52  Sub-proof #1429 shows that the following formulas are inconsistent:
% 244.05/50.52  ----------------------------------------------------------------
% 244.05/50.52    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.05/50.52           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.05/50.52             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.05/50.52           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.05/50.52             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.05/50.52           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.05/50.52           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.05/50.52    (2)  op(e2, e3) = e3
% 244.05/50.52    (3)   ~ (e3 = e2)
% 244.05/50.52    (4)   ~ (all_52_2 = e3)
% 244.05/50.52    (5)   ~ (all_52_4 = e3)
% 244.05/50.52    (6)  op(e3, e2) = all_52_4
% 244.05/50.52    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.52    (8)  op(e1, e3) = all_52_2
% 244.05/50.52  
% 244.05/50.52  Begin of proof
% 244.05/50.52  | 
% 244.05/50.52  | BETA: splitting (1) gives:
% 244.05/50.52  | 
% 244.05/50.52  | Case 1:
% 244.05/50.52  | | 
% 244.05/50.52  | |   (9)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.05/50.52  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.05/50.52  | |        op(e2, e3) = e3
% 244.05/50.52  | | 
% 244.05/50.52  | | ALPHA: (9) implies:
% 244.05/50.52  | |   (10)  op(e3, e2) = e3
% 244.05/50.52  | | 
% 244.05/50.52  | | REF_CLOSE: (5), (6), (7), (10) are inconsistent by sub-proof #2192.
% 244.05/50.52  | | 
% 244.05/50.52  | Case 2:
% 244.05/50.52  | | 
% 244.05/50.52  | |   (11)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.05/50.52  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 244.05/50.52  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.05/50.52  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.05/50.52  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.05/50.52  | | 
% 244.05/50.52  | | REF_CLOSE: (2), (3), (4), (7), (8), (11) are inconsistent by sub-proof
% 244.05/50.52  | |            #1889.
% 244.05/50.52  | | 
% 244.05/50.52  | End of split
% 244.05/50.52  | 
% 244.05/50.52  End of proof
% 244.05/50.52  
% 244.05/50.52  Sub-proof #1430 shows that the following formulas are inconsistent:
% 244.05/50.52  ----------------------------------------------------------------
% 244.05/50.52    (1)   ~ (e3 = e0)
% 244.05/50.52    (2)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 244.05/50.52    (3)   ~ (all_52_4 = e3)
% 244.05/50.52    (4)  op(e3, e2) = all_52_4
% 244.05/50.52    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.52    (6)  all_58_3 = e0
% 244.05/50.52  
% 244.05/50.52  Begin of proof
% 244.05/50.52  | 
% 244.05/50.52  | BETA: splitting (2) gives:
% 244.05/50.52  | 
% 244.05/50.52  | Case 1:
% 244.05/50.52  | | 
% 244.05/50.52  | |   (7)  all_58_1 = e3 & op(e3, e2) = e3
% 244.05/50.52  | | 
% 244.05/50.52  | | ALPHA: (7) implies:
% 244.05/50.52  | |   (8)  op(e3, e2) = e3
% 244.05/50.52  | | 
% 244.05/50.52  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2192.
% 244.05/50.52  | | 
% 244.05/50.52  | Case 2:
% 244.05/50.52  | | 
% 244.05/50.52  | |   (9)  all_58_3 = e3 & op(e2, e2) = e3
% 244.05/50.52  | | 
% 244.05/50.52  | | ALPHA: (9) implies:
% 244.05/50.52  | |   (10)  all_58_3 = e3
% 244.05/50.52  | | 
% 244.05/50.52  | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #1460.
% 244.05/50.52  | | 
% 244.05/50.52  | End of split
% 244.05/50.52  | 
% 244.05/50.52  End of proof
% 244.05/50.52  
% 244.05/50.52  Sub-proof #1431 shows that the following formulas are inconsistent:
% 244.05/50.52  ----------------------------------------------------------------
% 244.05/50.52    (1)   ~ (e3 = e0)
% 244.05/50.52    (2)  op(e1, e0) = all_52_14
% 244.05/50.52    (3)   ~ (all_52_14 = e3)
% 244.05/50.52    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.52    (5)  op(e0, e0) = e0
% 244.05/50.52    (6)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.52  
% 244.05/50.52  Begin of proof
% 244.05/50.52  | 
% 244.05/50.52  | BETA: splitting (6) gives:
% 244.05/50.52  | 
% 244.05/50.52  | Case 1:
% 244.05/50.52  | | 
% 244.05/50.52  | |   (7)  all_58_11 = e3 & op(e1, e0) = e3
% 244.05/50.52  | | 
% 244.05/50.52  | | ALPHA: (7) implies:
% 244.05/50.52  | |   (8)  op(e1, e0) = e3
% 244.05/50.52  | | 
% 244.05/50.52  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2149.
% 244.05/50.52  | | 
% 244.05/50.52  | Case 2:
% 244.05/50.52  | | 
% 244.05/50.52  | |   (9)  all_58_15 = e3 & op(e0, e0) = e3
% 244.05/50.52  | | 
% 244.05/50.52  | | ALPHA: (9) implies:
% 244.05/50.52  | |   (10)  op(e0, e0) = e3
% 244.05/50.52  | | 
% 244.05/50.52  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2079.
% 244.05/50.52  | | 
% 244.05/50.52  | End of split
% 244.05/50.52  | 
% 244.05/50.52  End of proof
% 244.05/50.52  
% 244.05/50.52  Sub-proof #1432 shows that the following formulas are inconsistent:
% 244.05/50.52  ----------------------------------------------------------------
% 244.05/50.52    (1)   ~ (all_52_3 = e0)
% 244.05/50.52    (2)   ~ (all_52_1 = all_52_3)
% 244.05/50.52    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.52         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.52    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 244.05/50.52           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 244.05/50.52           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 244.05/50.52           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 244.05/50.52           & $i(all_56_23))
% 244.05/50.52    (5)   ~ (e3 = e0)
% 244.05/50.52    (6)  op(e3, e0) = all_16_1
% 244.05/50.52    (7)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.05/50.52           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 244.05/50.52           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 244.05/50.52         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 244.05/50.52           $i(all_56_15))
% 244.05/50.52    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.52         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.52    (9)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.05/50.52         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.05/50.52    (10)  op(e1, e0) = all_52_14
% 244.05/50.52    (11)   ~ (all_52_8 = e0)
% 244.05/50.52    (12)  op(e0, e3) = all_52_3
% 244.05/50.52    (13)   ~ (e3 = e1)
% 244.05/50.52    (14)  op(e0, e2) = e3
% 244.05/50.52    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.52          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.52    (16)  op(e3, e2) = e2
% 244.05/50.52    (17)  all_54_2 = all_52_8
% 244.05/50.52    (18)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.05/50.52    (19)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.05/50.52    (20)  all_56_21 = e0
% 244.05/50.52    (21)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.52              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 244.05/50.52                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.05/50.52                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.05/50.52    (22)  op(e3, e1) = all_52_8
% 244.05/50.52    (23)  op(e2, e3) = e2
% 244.05/50.52    (24)   ~ (all_52_14 = e0)
% 244.05/50.52    (25)  all_54_12 = all_52_3
% 244.05/50.52    (26)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.05/50.52    (27)  all_56_11 = e0
% 244.05/50.52    (28)  op(e3, e0) = e3
% 244.05/50.52    (29)  op(e2, e3) = all_52_1
% 244.05/50.52    (30)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.52          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.52    (31)  op(e3, e0) = all_50_1
% 244.05/50.52    (32)   ~ (all_52_1 = all_52_13)
% 244.05/50.52    (33)   ~ (all_52_11 = e0)
% 244.05/50.52    (34)  all_54_7 = all_52_13
% 244.05/50.52    (35)   ~ (all_52_13 = all_52_14)
% 244.05/50.52    (36)   ~ (all_52_4 = e3)
% 244.05/50.52    (37)  op(e3, e2) = all_52_4
% 244.05/50.52    (38)   ~ (all_52_8 = all_52_11)
% 244.05/50.52    (39)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.05/50.52    (40)  op(e2, e1) = e3
% 244.05/50.52    (41)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.52          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.52    (42)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.52          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.52    (43)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.52    (44)  op(e0, e0) = e0
% 244.05/50.52    (45)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.52          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.52    (46)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.52          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.05/50.52    (47)  op(e1, e1) = e0
% 244.05/50.52    (48)   ~ (e1 = e0)
% 244.05/50.52    (49)  op(e3, e3) = e0
% 244.05/50.52    (50)   ~ (all_52_13 = e3)
% 244.05/50.52    (51)  op(e2, e0) = all_52_13
% 244.05/50.52    (52)  all_58_3 = e0
% 244.05/50.52    (53)  all_56_9 = e2
% 244.05/50.52    (54)  all_54_14 = all_52_11
% 244.05/50.52    (55)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.52          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.05/50.52            e2)
% 244.05/50.52    (56)   ~ (all_52_4 = all_52_8)
% 244.05/50.52    (57)   ~ (all_52_13 = e0)
% 244.05/50.52    (58)   ~ (all_52_4 = e0)
% 244.05/50.52    (59)  all_58_13 = e3
% 244.05/50.52    (60)   ~ (e2 = e1)
% 244.05/50.52    (61)   ~ (all_52_8 = e3)
% 244.05/50.52  
% 244.05/50.52  Begin of proof
% 244.05/50.52  | 
% 244.05/50.52  | GROUND_INST: instantiating (43) with all_52_1, e2, e3, e2, simplifying with
% 244.05/50.52  |              (23), (29) gives:
% 244.05/50.52  |   (62)  all_52_1 = e2
% 244.05/50.52  | 
% 244.05/50.52  | GROUND_INST: instantiating (43) with e3, all_50_1, e0, e3, simplifying with
% 244.05/50.52  |              (28), (31) gives:
% 244.05/50.52  |   (63)  all_50_1 = e3
% 244.05/50.52  | 
% 244.05/50.52  | GROUND_INST: instantiating (43) with all_16_1, all_50_1, e0, e3, simplifying
% 244.05/50.52  |              with (6), (31) gives:
% 244.05/50.52  |   (64)  all_50_1 = all_16_1
% 244.05/50.52  | 
% 244.05/50.52  | GROUND_INST: instantiating (43) with all_52_4, e2, e2, e3, simplifying with
% 244.05/50.52  |              (16), (37) gives:
% 244.05/50.52  |   (65)  all_52_4 = e2
% 244.05/50.52  | 
% 244.05/50.52  | COMBINE_EQS: (63), (64) imply:
% 244.05/50.52  |   (66)  all_16_1 = e3
% 244.05/50.52  | 
% 244.05/50.52  | SIMP: (66) implies:
% 244.05/50.52  |   (67)  all_16_1 = e3
% 244.05/50.52  | 
% 244.05/50.52  | REDUCE: (2), (62) imply:
% 244.05/50.52  |   (68)   ~ (all_52_3 = e2)
% 244.05/50.52  | 
% 244.05/50.52  | SIMP: (68) implies:
% 244.05/50.52  |   (69)   ~ (all_52_3 = e2)
% 244.05/50.52  | 
% 244.05/50.52  | REDUCE: (32), (62) imply:
% 244.05/50.52  |   (70)   ~ (all_52_13 = e2)
% 244.05/50.52  | 
% 244.05/50.52  | SIMP: (70) implies:
% 244.05/50.52  |   (71)   ~ (all_52_13 = e2)
% 244.05/50.52  | 
% 244.05/50.52  | REDUCE: (56), (65) imply:
% 244.05/50.52  |   (72)   ~ (all_52_8 = e2)
% 244.05/50.52  | 
% 244.05/50.52  | SIMP: (72) implies:
% 244.05/50.52  |   (73)   ~ (all_52_8 = e2)
% 244.05/50.52  | 
% 244.05/50.52  | REDUCE: (36), (65) imply:
% 244.05/50.52  |   (74)   ~ (e3 = e2)
% 244.05/50.52  | 
% 244.05/50.52  | SIMP: (74) implies:
% 244.05/50.52  |   (75)   ~ (e3 = e2)
% 244.05/50.52  | 
% 244.05/50.52  | REDUCE: (58), (65) imply:
% 244.05/50.52  |   (76)   ~ (e2 = e0)
% 244.05/50.52  | 
% 244.05/50.52  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 244.05/50.52  |            (14), (15), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 244.05/50.52  |            (27), (30), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 244.05/50.52  |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 244.05/50.52  |            (53), (54), (55), (57), (59), (60), (61), (67), (69), (71), (73),
% 244.05/50.52  |            (75), (76) are inconsistent by sub-proof #1433.
% 244.05/50.52  | 
% 244.05/50.52  End of proof
% 244.05/50.52  
% 244.05/50.52  Sub-proof #1433 shows that the following formulas are inconsistent:
% 244.05/50.52  ----------------------------------------------------------------
% 244.05/50.52    (1)   ~ (all_52_3 = e0)
% 244.05/50.52    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.52         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.52    (3)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 244.05/50.52           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 244.05/50.52           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 244.05/50.52           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 244.05/50.52           & $i(all_56_23))
% 244.05/50.52    (4)   ~ (e3 = e0)
% 244.05/50.52    (5)  op(e3, e0) = all_16_1
% 244.05/50.52    (6)   ~ (e2 = e0)
% 244.05/50.52    (7)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.05/50.52           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 244.05/50.52           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 244.05/50.52         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 244.05/50.52           $i(all_56_15))
% 244.05/50.52    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.52         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.52    (9)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.05/50.52         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.05/50.52    (10)  op(e1, e0) = all_52_14
% 244.05/50.52    (11)   ~ (all_52_8 = e0)
% 244.05/50.52    (12)  op(e0, e3) = all_52_3
% 244.05/50.52    (13)   ~ (e3 = e1)
% 244.05/50.52    (14)  op(e0, e2) = e3
% 244.05/50.52    (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.52          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.52    (16)  all_54_2 = all_52_8
% 244.05/50.52    (17)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.05/50.52    (18)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.05/50.52    (19)  all_56_21 = e0
% 244.05/50.52    (20)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.52              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 244.05/50.52                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.05/50.52                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.05/50.52    (21)  op(e3, e1) = all_52_8
% 244.05/50.52    (22)   ~ (e3 = e2)
% 244.05/50.52    (23)   ~ (all_52_14 = e0)
% 244.05/50.52    (24)  all_54_12 = all_52_3
% 244.05/50.52    (25)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.05/50.52    (26)  all_16_1 = e3
% 244.05/50.52    (27)   ~ (all_52_3 = e2)
% 244.05/50.52    (28)  all_56_11 = e0
% 244.05/50.52    (29)   ~ (all_52_13 = e2)
% 244.05/50.53    (30)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.53          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.53    (31)   ~ (all_52_11 = e0)
% 244.05/50.53    (32)  all_54_7 = all_52_13
% 244.05/50.53    (33)   ~ (all_52_13 = all_52_14)
% 244.05/50.53    (34)   ~ (all_52_4 = e3)
% 244.05/50.53    (35)  op(e3, e2) = all_52_4
% 244.05/50.53    (36)   ~ (all_52_8 = all_52_11)
% 244.05/50.53    (37)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.05/50.53    (38)  op(e2, e1) = e3
% 244.05/50.53    (39)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.53          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.53    (40)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.53          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.53    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.53            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.53    (42)  op(e0, e0) = e0
% 244.05/50.53    (43)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.53          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.53    (44)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.53          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.05/50.53    (45)  op(e1, e1) = e0
% 244.05/50.53    (46)   ~ (e1 = e0)
% 244.05/50.53    (47)  op(e3, e3) = e0
% 244.05/50.53    (48)   ~ (all_52_8 = e2)
% 244.05/50.53    (49)   ~ (all_52_13 = e3)
% 244.05/50.53    (50)  op(e2, e0) = all_52_13
% 244.05/50.53    (51)  all_58_3 = e0
% 244.05/50.53    (52)  all_56_9 = e2
% 244.05/50.53    (53)  all_54_14 = all_52_11
% 244.05/50.53    (54)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.53          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.05/50.53            e2)
% 244.05/50.53    (55)   ~ (all_52_13 = e0)
% 244.05/50.53    (56)  all_58_13 = e3
% 244.05/50.53    (57)   ~ (e2 = e1)
% 244.05/50.53    (58)   ~ (all_52_8 = e3)
% 244.05/50.53  
% 244.05/50.53  Begin of proof
% 244.05/50.53  | 
% 244.05/50.53  | REDUCE: (5), (26) imply:
% 244.05/50.53  |   (59)  op(e3, e0) = e3
% 244.05/50.53  | 
% 244.05/50.53  | BETA: splitting (25) gives:
% 244.05/50.53  | 
% 244.05/50.53  | Case 1:
% 244.05/50.53  | | 
% 244.05/50.53  | |   (60)  all_54_2 = e3
% 244.05/50.53  | | 
% 244.05/50.53  | | REF_CLOSE: (16), (58), (60) are inconsistent by sub-proof #1987.
% 244.05/50.53  | | 
% 244.05/50.53  | Case 2:
% 244.05/50.53  | | 
% 244.05/50.53  | |   (61)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.05/50.53  | | 
% 244.05/50.53  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 244.05/50.53  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 244.05/50.53  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 244.05/50.53  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 244.05/50.53  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 244.05/50.53  | |            (61) are inconsistent by sub-proof #1434.
% 244.05/50.53  | | 
% 244.05/50.53  | End of split
% 244.05/50.53  | 
% 244.05/50.53  End of proof
% 244.05/50.53  
% 244.05/50.53  Sub-proof #1434 shows that the following formulas are inconsistent:
% 244.05/50.53  ----------------------------------------------------------------
% 244.05/50.53    (1)   ~ (all_52_3 = e0)
% 244.05/50.53    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.53         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.53    (3)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 244.05/50.53           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 244.05/50.53           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 244.05/50.53           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 244.05/50.53           & $i(all_56_23))
% 244.05/50.53    (4)   ~ (e3 = e0)
% 244.05/50.53    (5)   ~ (e2 = e0)
% 244.05/50.53    (6)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.05/50.53           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 244.05/50.53           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 244.05/50.53         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 244.05/50.53           $i(all_56_15))
% 244.05/50.53    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.53         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.53    (8)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.05/50.53         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.05/50.53    (9)  op(e1, e0) = all_52_14
% 244.05/50.53    (10)   ~ (all_52_8 = e0)
% 244.05/50.53    (11)  op(e0, e3) = all_52_3
% 244.05/50.53    (12)   ~ (e3 = e1)
% 244.05/50.53    (13)  op(e0, e2) = e3
% 244.05/50.53    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.53          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.53    (15)  all_54_2 = all_52_8
% 244.05/50.53    (16)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.05/50.53    (17)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.05/50.53    (18)  all_56_21 = e0
% 244.05/50.53    (19)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.53              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 244.05/50.53                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.05/50.53                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.05/50.53    (20)  op(e3, e1) = all_52_8
% 244.05/50.53    (21)   ~ (e3 = e2)
% 244.05/50.53    (22)   ~ (all_52_14 = e0)
% 244.05/50.53    (23)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.05/50.53    (24)  all_54_12 = all_52_3
% 244.05/50.53    (25)   ~ (all_52_3 = e2)
% 244.05/50.53    (26)  all_56_11 = e0
% 244.05/50.53    (27)  op(e3, e0) = e3
% 244.05/50.53    (28)   ~ (all_52_13 = e2)
% 244.05/50.53    (29)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.53          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.53    (30)   ~ (all_52_11 = e0)
% 244.05/50.53    (31)  all_54_7 = all_52_13
% 244.05/50.53    (32)   ~ (all_52_13 = all_52_14)
% 244.05/50.53    (33)   ~ (all_52_4 = e3)
% 244.05/50.53    (34)  op(e3, e2) = all_52_4
% 244.05/50.53    (35)   ~ (all_52_8 = all_52_11)
% 244.05/50.53    (36)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.05/50.53    (37)  op(e2, e1) = e3
% 244.05/50.53    (38)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.53          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.53    (39)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.53          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.53    (40)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.53            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.53    (41)  op(e0, e0) = e0
% 244.05/50.53    (42)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.53          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.53    (43)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.53          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.05/50.53    (44)  op(e1, e1) = e0
% 244.05/50.53    (45)   ~ (e1 = e0)
% 244.05/50.53    (46)  op(e3, e3) = e0
% 244.05/50.53    (47)   ~ (all_52_8 = e2)
% 244.05/50.53    (48)   ~ (all_52_13 = e3)
% 244.05/50.53    (49)  op(e2, e0) = all_52_13
% 244.05/50.53    (50)  all_58_3 = e0
% 244.05/50.53    (51)  all_56_9 = e2
% 244.05/50.53    (52)  all_54_14 = all_52_11
% 244.05/50.53    (53)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.53          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.05/50.53            e2)
% 244.05/50.53    (54)   ~ (all_52_13 = e0)
% 244.05/50.53    (55)  all_58_13 = e3
% 244.05/50.53    (56)   ~ (e2 = e1)
% 244.05/50.53    (57)   ~ (all_52_8 = e3)
% 244.05/50.53  
% 244.05/50.53  Begin of proof
% 244.05/50.53  | 
% 244.05/50.53  | BETA: splitting (6) gives:
% 244.05/50.53  | 
% 244.05/50.53  | Case 1:
% 244.05/50.53  | | 
% 244.05/50.53  | |   (58)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.05/50.53  | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 244.05/50.53  | | 
% 244.05/50.53  | | BETA: splitting (58) gives:
% 244.05/50.53  | | 
% 244.05/50.53  | | Case 1:
% 244.05/50.53  | | | 
% 244.05/50.53  | | |   (59)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.05/50.53  | | |         $i(all_56_9)
% 244.05/50.53  | | | 
% 244.05/50.53  | | | ALPHA: (59) implies:
% 244.05/50.53  | | |   (60)  op(e3, e2) = all_56_9
% 244.05/50.53  | | |   (61)  op(e3, all_56_9) = e3
% 244.05/50.53  | | | 
% 244.05/50.53  | | | REDUCE: (51), (61) imply:
% 244.05/50.53  | | |   (62)  op(e3, e2) = e3
% 244.05/50.53  | | | 
% 244.05/50.53  | | | REF_CLOSE: (1), (4), (24), (25), (36), (40), (46), (60), (61), (62) are
% 244.05/50.53  | | |            inconsistent by sub-proof #1439.
% 244.05/50.53  | | | 
% 244.05/50.53  | | Case 2:
% 244.05/50.53  | | | 
% 244.05/50.53  | | |   (63)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 244.05/50.53  | | | 
% 244.05/50.53  | | | ALPHA: (63) implies:
% 244.05/50.53  | | |   (64)  op(e2, all_56_11) = e2
% 244.05/50.53  | | | 
% 244.05/50.53  | | | REDUCE: (26), (64) imply:
% 244.05/50.53  | | |   (65)  op(e2, e0) = e2
% 244.05/50.53  | | | 
% 244.05/50.53  | | | REF_CLOSE: (28), (40), (49), (65) are inconsistent by sub-proof #2317.
% 244.05/50.53  | | | 
% 244.05/50.53  | | End of split
% 244.05/50.53  | | 
% 244.05/50.53  | Case 2:
% 244.05/50.53  | | 
% 244.05/50.53  | |   (66)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 244.05/50.53  | |           $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 244.05/50.53  | |             e2) = all_56_15 & $i(all_56_15))
% 244.05/50.53  | | 
% 244.05/50.53  | | BETA: splitting (66) gives:
% 244.05/50.53  | | 
% 244.05/50.53  | | Case 1:
% 244.05/50.53  | | | 
% 244.05/50.53  | | |   (67)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 244.05/50.53  | | |         $i(all_56_13)
% 244.05/50.53  | | | 
% 244.05/50.53  | | | ALPHA: (67) implies:
% 244.05/50.53  | | |   (68)  op(e1, e2) = all_56_13
% 244.05/50.53  | | |   (69)  op(e1, all_56_13) = e1
% 244.05/50.53  | | | 
% 244.05/50.53  | | | BETA: splitting (53) gives:
% 244.05/50.53  | | | 
% 244.05/50.53  | | | Case 1:
% 244.05/50.53  | | | | 
% 244.05/50.53  | | | |   (70)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 244.05/50.53  | | | |             e2) = e2)
% 244.05/50.53  | | | | 
% 244.05/50.53  | | | | REF_CLOSE: (11), (13), (21), (25), (40), (70) are inconsistent by
% 244.05/50.53  | | | |            sub-proof #1438.
% 244.05/50.53  | | | | 
% 244.05/50.53  | | | Case 2:
% 244.05/50.53  | | | | 
% 244.05/50.53  | | | |   (71)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 244.05/50.53  | | | |             e0) = e2)
% 244.05/50.53  | | | | 
% 244.05/50.53  | | | | BETA: splitting (71) gives:
% 244.05/50.53  | | | | 
% 244.05/50.53  | | | | Case 1:
% 244.05/50.53  | | | | | 
% 244.05/50.53  | | | | |   (72)  all_58_14 = e2 & op(e0, e1) = e2
% 244.05/50.53  | | | | | 
% 244.05/50.53  | | | | | ALPHA: (72) implies:
% 244.05/50.53  | | | | |   (73)  all_58_14 = e2
% 244.05/50.53  | | | | | 
% 244.05/50.53  | | | | | BETA: splitting (8) gives:
% 244.05/50.53  | | | | | 
% 244.05/50.53  | | | | | Case 1:
% 244.05/50.53  | | | | | | 
% 244.05/50.53  | | | | | |   (74)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 244.05/50.53  | | | | | |             e1) = e1)
% 244.05/50.53  | | | | | | 
% 244.05/50.53  | | | | | | BETA: splitting (74) gives:
% 244.05/50.53  | | | | | | 
% 244.05/50.53  | | | | | | Case 1:
% 244.05/50.53  | | | | | | | 
% 244.05/50.53  | | | | | | |   (75)  all_58_4 = e1 & op(e3, e1) = e1
% 244.05/50.53  | | | | | | | 
% 244.05/50.53  | | | | | | | ALPHA: (75) implies:
% 244.05/50.53  | | | | | | |   (76)  all_58_4 = e1
% 244.05/50.53  | | | | | | | 
% 244.05/50.53  | | | | | | | BETA: splitting (43) gives:
% 244.05/50.53  | | | | | | | 
% 244.05/50.53  | | | | | | | Case 1:
% 244.05/50.53  | | | | | | | | 
% 244.05/50.53  | | | | | | | |   (77)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 244.05/50.53  | | | | | | | |           op(e2, e2) = e1)
% 244.05/50.53  | | | | | | | | 
% 244.05/50.53  | | | | | | | | BETA: splitting (77) gives:
% 244.05/50.53  | | | | | | | | 
% 244.05/50.53  | | | | | | | | Case 1:
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | |   (78)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | ALPHA: (78) implies:
% 244.05/50.53  | | | | | | | | |   (79)  all_58_1 = e1
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | REF_CLOSE: (2), (4), (5), (12), (14), (21), (27), (29), (33),
% 244.05/50.53  | | | | | | | | |            (34), (40), (45), (56), (76), (79) are inconsistent
% 244.05/50.53  | | | | | | | | |            by sub-proof #1437.
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | Case 2:
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | |   (80)  all_58_3 = e1 & op(e2, e2) = e1
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | ALPHA: (80) implies:
% 244.05/50.53  | | | | | | | | |   (81)  all_58_3 = e1
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | COMBINE_EQS: (50), (81) imply:
% 244.05/50.53  | | | | | | | | |   (82)  e1 = e0
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | SIMP: (82) implies:
% 244.05/50.53  | | | | | | | | |   (83)  e1 = e0
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | COMBINE_EQS: (76), (83) imply:
% 244.05/50.53  | | | | | | | | |   (84)  all_58_4 = e0
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | REF_CLOSE: (2), (4), (5), (12), (14), (21), (33), (34), (39),
% 244.05/50.53  | | | | | | | | |            (40), (45), (46), (56), (84) are inconsistent by
% 244.05/50.53  | | | | | | | | |            sub-proof #1512.
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | End of split
% 244.05/50.53  | | | | | | | | 
% 244.05/50.53  | | | | | | | Case 2:
% 244.05/50.53  | | | | | | | | 
% 244.05/50.53  | | | | | | | |   (85)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 244.05/50.53  | | | | | | | |           op(e0, e2) = e1)
% 244.05/50.53  | | | | | | | | 
% 244.05/50.53  | | | | | | | | BETA: splitting (85) gives:
% 244.05/50.53  | | | | | | | | 
% 244.05/50.53  | | | | | | | | Case 1:
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | |   (86)  all_58_7 = e1 & op(e1, e2) = e1
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | ALPHA: (86) implies:
% 244.05/50.53  | | | | | | | | |   (87)  op(e1, e2) = e1
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | BETA: splitting (23) gives:
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | Case 1:
% 244.05/50.53  | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | |   (88)  all_54_2 = e2
% 244.05/50.53  | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | REF_CLOSE: (15), (47), (88) are inconsistent by sub-proof
% 244.05/50.53  | | | | | | | | | |            #1986.
% 244.05/50.53  | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | Case 2:
% 244.05/50.53  | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | |   (89)  all_54_2 = e1 | all_54_2 = e0
% 244.05/50.53  | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | BETA: splitting (89) gives:
% 244.05/50.53  | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | Case 1:
% 244.05/50.53  | | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | |   (90)  all_54_2 = e1
% 244.05/50.53  | | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | | COMBINE_EQS: (15), (90) imply:
% 244.05/50.53  | | | | | | | | | | |   (91)  all_52_8 = e1
% 244.05/50.53  | | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | | SIMP: (91) implies:
% 244.05/50.53  | | | | | | | | | | |   (92)  all_52_8 = e1
% 244.05/50.53  | | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | | REDUCE: (35), (92) imply:
% 244.05/50.53  | | | | | | | | | | |   (93)   ~ (all_52_11 = e1)
% 244.05/50.53  | | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | | SIMP: (93) implies:
% 244.05/50.53  | | | | | | | | | | |   (94)   ~ (all_52_11 = e1)
% 244.05/50.53  | | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | | REF_CLOSE: (16), (30), (40), (44), (45), (52), (68), (69),
% 244.05/50.53  | | | | | | | | | | |            (87), (94) are inconsistent by sub-proof #1934.
% 244.05/50.53  | | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | Case 2:
% 244.05/50.53  | | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | |   (95)  all_54_2 = e0
% 244.05/50.53  | | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | | REF_CLOSE: (10), (15), (95) are inconsistent by sub-proof
% 244.05/50.53  | | | | | | | | | | |            #1643.
% 244.05/50.53  | | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | | End of split
% 244.05/50.53  | | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | End of split
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | Case 2:
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | |   (96)  all_58_13 = e1 & op(e0, e2) = e1
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | ALPHA: (96) implies:
% 244.05/50.53  | | | | | | | | |   (97)  all_58_13 = e1
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | | REF_CLOSE: (12), (55), (97) are inconsistent by sub-proof
% 244.05/50.53  | | | | | | | | |            #1436.
% 244.05/50.53  | | | | | | | | | 
% 244.05/50.53  | | | | | | | | End of split
% 244.05/50.53  | | | | | | | | 
% 244.05/50.53  | | | | | | | End of split
% 244.05/50.53  | | | | | | | 
% 244.05/50.53  | | | | | | Case 2:
% 244.05/50.53  | | | | | | | 
% 244.05/50.53  | | | | | | |   (98)  all_58_5 = e1 & op(e2, e1) = e1
% 244.05/50.53  | | | | | | | 
% 244.05/50.53  | | | | | | | ALPHA: (98) implies:
% 244.05/50.53  | | | | | | |   (99)  op(e2, e1) = e1
% 244.05/50.53  | | | | | | | 
% 244.05/50.53  | | | | | | | REF_CLOSE: (12), (37), (40), (99) are inconsistent by sub-proof
% 244.05/50.53  | | | | | | |            #2255.
% 244.05/50.53  | | | | | | | 
% 244.05/50.53  | | | | | | End of split
% 244.05/50.53  | | | | | | 
% 244.05/50.53  | | | | | Case 2:
% 244.05/50.53  | | | | | | 
% 244.05/50.53  | | | | | |   (100)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 244.05/50.53  | | | | | |            op(e0, e1) = e1)
% 244.05/50.53  | | | | | | 
% 244.05/50.53  | | | | | | REF_CLOSE: (40), (44), (45), (56), (73), (100) are inconsistent by
% 244.05/50.53  | | | | | |            sub-proof #1435.
% 244.05/50.53  | | | | | | 
% 244.05/50.53  | | | | | End of split
% 244.05/50.53  | | | | | 
% 244.05/50.53  | | | | Case 2:
% 244.05/50.53  | | | | | 
% 244.05/50.53  | | | | |   (101)  all_58_15 = e2 & op(e0, e0) = e2
% 244.05/50.53  | | | | | 
% 244.05/50.53  | | | | | REF_CLOSE: (4), (5), (7), (9), (12), (19), (21), (22), (38), (40),
% 244.05/50.53  | | | | |            (41), (42), (45), (48), (49), (54), (56), (101) are
% 244.05/50.53  | | | | |            inconsistent by sub-proof #1488.
% 244.05/50.53  | | | | | 
% 244.05/50.53  | | | | End of split
% 244.05/50.53  | | | | 
% 244.05/50.53  | | | End of split
% 244.05/50.53  | | | 
% 244.05/50.53  | | Case 2:
% 244.05/50.53  | | | 
% 244.05/50.53  | | |   (102)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15
% 244.05/50.53  | | |          & $i(all_56_15)
% 244.05/50.53  | | | 
% 244.05/50.53  | | | ALPHA: (102) implies:
% 244.05/50.53  | | |   (103)  op(e0, e2) = all_56_15
% 244.05/50.53  | | |   (104)  op(e0, all_56_15) = e0
% 244.05/50.53  | | | 
% 244.05/50.53  | | | BETA: splitting (53) gives:
% 244.05/50.53  | | | 
% 244.05/50.53  | | | Case 1:
% 244.05/50.53  | | | | 
% 244.05/50.54  | | | |   (105)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 244.05/50.54  | | | |              e2) = e2)
% 244.05/50.54  | | | | 
% 244.05/50.54  | | | | REF_CLOSE: (11), (13), (21), (25), (40), (105) are inconsistent by
% 244.05/50.54  | | | |            sub-proof #1438.
% 244.05/50.54  | | | | 
% 244.05/50.54  | | | Case 2:
% 244.05/50.54  | | | | 
% 244.05/50.54  | | | |   (106)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 244.05/50.54  | | | |              e0) = e2)
% 244.05/50.54  | | | | 
% 244.05/50.54  | | | | BETA: splitting (106) gives:
% 244.05/50.54  | | | | 
% 244.05/50.54  | | | | Case 1:
% 244.05/50.54  | | | | | 
% 244.05/50.54  | | | | |   (107)  all_58_14 = e2 & op(e0, e1) = e2
% 244.05/50.54  | | | | | 
% 244.05/50.54  | | | | | ALPHA: (107) implies:
% 244.05/50.54  | | | | |   (108)  op(e0, e1) = e2
% 244.05/50.54  | | | | | 
% 244.05/50.54  | | | | | BETA: splitting (17) gives:
% 244.05/50.54  | | | | | 
% 244.05/50.54  | | | | | Case 1:
% 244.05/50.54  | | | | | | 
% 244.05/50.54  | | | | | |   (109)  all_54_7 = e2
% 244.05/50.54  | | | | | | 
% 244.05/50.54  | | | | | | REF_CLOSE: (28), (31), (109) are inconsistent by sub-proof #1997.
% 244.05/50.54  | | | | | | 
% 244.05/50.54  | | | | | Case 2:
% 244.05/50.54  | | | | | | 
% 244.05/50.54  | | | | | |   (110)  all_54_7 = e1 | all_54_7 = e0
% 244.05/50.54  | | | | | | 
% 244.05/50.54  | | | | | | BETA: splitting (110) gives:
% 244.05/50.54  | | | | | | 
% 244.05/50.54  | | | | | | Case 1:
% 244.05/50.54  | | | | | | | 
% 244.05/50.54  | | | | | | |   (111)  all_54_7 = e1
% 244.05/50.54  | | | | | | | 
% 244.05/50.54  | | | | | | | COMBINE_EQS: (31), (111) imply:
% 244.05/50.54  | | | | | | |   (112)  all_52_13 = e1
% 244.05/50.54  | | | | | | | 
% 244.05/50.54  | | | | | | | SIMP: (112) implies:
% 244.05/50.54  | | | | | | |   (113)  all_52_13 = e1
% 244.05/50.54  | | | | | | | 
% 244.05/50.54  | | | | | | | REDUCE: (32), (113) imply:
% 244.05/50.54  | | | | | | |   (114)   ~ (all_52_14 = e1)
% 244.05/50.54  | | | | | | | 
% 244.05/50.54  | | | | | | | SIMP: (114) implies:
% 244.05/50.54  | | | | | | |   (115)   ~ (all_52_14 = e1)
% 244.05/50.54  | | | | | | | 
% 244.05/50.54  | | | | | | | BETA: splitting (3) gives:
% 244.05/50.54  | | | | | | | 
% 244.05/50.54  | | | | | | | Case 1:
% 244.05/50.54  | | | | | | | | 
% 244.05/50.54  | | | | | | | |   (116)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) =
% 244.05/50.54  | | | | | | | |            all_56_17 & $i(all_56_17)) | (all_56_18 = e2 & op(e2,
% 244.05/50.54  | | | | | | | |              all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 244.05/50.54  | | | | | | | |            $i(all_56_19))
% 244.05/50.54  | | | | | | | | 
% 244.05/50.54  | | | | | | | | BETA: splitting (116) gives:
% 244.05/50.54  | | | | | | | | 
% 244.05/50.54  | | | | | | | | Case 1:
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | |   (117)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1)
% 244.05/50.54  | | | | | | | | |          = all_56_17 & $i(all_56_17)
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | ALPHA: (117) implies:
% 244.05/50.54  | | | | | | | | |   (118)  op(e3, e1) = all_56_17
% 244.05/50.54  | | | | | | | | |   (119)  op(e3, all_56_17) = e3
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | BETA: splitting (23) gives:
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | Case 1:
% 244.05/50.54  | | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | |   (120)  all_54_2 = e2
% 244.05/50.54  | | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | | REF_CLOSE: (15), (47), (120) are inconsistent by sub-proof
% 244.05/50.54  | | | | | | | | | |            #1986.
% 244.05/50.54  | | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | Case 2:
% 244.05/50.54  | | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | |   (121)  all_54_2 = e1 | all_54_2 = e0
% 244.05/50.54  | | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | | REF_CLOSE: (10), (15), (20), (40), (57), (118), (119), (121)
% 244.05/50.54  | | | | | | | | | |            are inconsistent by sub-proof #1522.
% 244.05/50.54  | | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | End of split
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | Case 2:
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | GROUND_INST: instantiating (40) with e3, all_56_15, e2, e0,
% 244.05/50.54  | | | | | | | | |              simplifying with (13), (103) gives:
% 244.05/50.54  | | | | | | | | |   (122)  all_56_15 = e3
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | REDUCE: (104), (122) imply:
% 244.05/50.54  | | | | | | | | |   (123)  op(e0, e3) = e0
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | REF_CLOSE: (1), (11), (40), (123) are inconsistent by
% 244.05/50.54  | | | | | | | | |            sub-proof #2331.
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | End of split
% 244.05/50.54  | | | | | | | | 
% 244.05/50.54  | | | | | | | Case 2:
% 244.05/50.54  | | | | | | | | 
% 244.05/50.54  | | | | | | | |   (124)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22
% 244.05/50.54  | | | | | | | |            = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 244.05/50.54  | | | | | | | |            all_56_23 & $i(all_56_23))
% 244.05/50.54  | | | | | | | | 
% 244.05/50.54  | | | | | | | | BETA: splitting (124) gives:
% 244.05/50.54  | | | | | | | | 
% 244.05/50.54  | | | | | | | | Case 1:
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | |   (125)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | ALPHA: (125) implies:
% 244.05/50.54  | | | | | | | | |   (126)  op(e1, all_56_21) = e1
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | REDUCE: (18), (126) imply:
% 244.05/50.54  | | | | | | | | |   (127)  op(e1, e0) = e1
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | REF_CLOSE: (9), (40), (115), (127) are inconsistent by
% 244.05/50.54  | | | | | | | | |            sub-proof #2304.
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | Case 2:
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | |   (128)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1)
% 244.05/50.54  | | | | | | | | |          = all_56_23 & $i(all_56_23)
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | ALPHA: (128) implies:
% 244.05/50.54  | | | | | | | | |   (129)  op(e0, e1) = all_56_23
% 244.05/50.54  | | | | | | | | |   (130)  op(e0, all_56_23) = e0
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | GROUND_INST: instantiating (40) with e2, all_56_23, e1, e0,
% 244.05/50.54  | | | | | | | | |              simplifying with (108), (129) gives:
% 244.05/50.54  | | | | | | | | |   (131)  all_56_23 = e2
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | GROUND_INST: instantiating (40) with e3, all_56_15, e2, e0,
% 244.05/50.54  | | | | | | | | |              simplifying with (13), (103) gives:
% 244.05/50.54  | | | | | | | | |   (132)  all_56_15 = e3
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | REDUCE: (130), (131) imply:
% 244.05/50.54  | | | | | | | | |   (133)  op(e0, e2) = e0
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | | REF_CLOSE: (4), (13), (40), (133) are inconsistent by
% 244.05/50.54  | | | | | | | | |            sub-proof #1961.
% 244.05/50.54  | | | | | | | | | 
% 244.05/50.54  | | | | | | | | End of split
% 244.05/50.54  | | | | | | | | 
% 244.05/50.54  | | | | | | | End of split
% 244.05/50.54  | | | | | | | 
% 244.05/50.54  | | | | | | Case 2:
% 244.05/50.54  | | | | | | | 
% 244.05/50.54  | | | | | | |   (134)  all_54_7 = e0
% 244.05/50.54  | | | | | | | 
% 244.05/50.54  | | | | | | | REF_CLOSE: (31), (54), (134) are inconsistent by sub-proof #2294.
% 244.05/50.54  | | | | | | | 
% 244.05/50.54  | | | | | | End of split
% 244.05/50.54  | | | | | | 
% 244.05/50.54  | | | | | End of split
% 244.05/50.54  | | | | | 
% 244.05/50.54  | | | | Case 2:
% 244.05/50.54  | | | | | 
% 244.05/50.54  | | | | |   (135)  all_58_15 = e2 & op(e0, e0) = e2
% 244.05/50.54  | | | | | 
% 244.05/50.54  | | | | | REF_CLOSE: (4), (5), (7), (9), (12), (19), (21), (22), (38), (40),
% 244.05/50.54  | | | | |            (41), (42), (45), (48), (49), (54), (56), (135) are
% 244.05/50.54  | | | | |            inconsistent by sub-proof #1488.
% 244.05/50.54  | | | | | 
% 244.05/50.54  | | | | End of split
% 244.05/50.54  | | | | 
% 244.05/50.54  | | | End of split
% 244.05/50.54  | | | 
% 244.05/50.54  | | End of split
% 244.05/50.54  | | 
% 244.05/50.54  | End of split
% 244.05/50.54  | 
% 244.05/50.54  End of proof
% 244.05/50.54  
% 244.05/50.54  Sub-proof #1435 shows that the following formulas are inconsistent:
% 244.05/50.54  ----------------------------------------------------------------
% 244.05/50.54    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.05/50.54    (2)  all_58_14 = e2
% 244.05/50.54    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.54    (4)  op(e1, e1) = e0
% 244.05/50.54    (5)   ~ (e1 = e0)
% 244.05/50.54    (6)   ~ (e2 = e1)
% 244.05/50.54  
% 244.05/50.54  Begin of proof
% 244.05/50.54  | 
% 244.05/50.54  | BETA: splitting (1) gives:
% 244.05/50.54  | 
% 244.05/50.54  | Case 1:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (7)  all_58_8 = e1 & op(e1, e1) = e1
% 244.05/50.54  | | 
% 244.05/50.54  | | ALPHA: (7) implies:
% 244.05/50.54  | |   (8)  op(e1, e1) = e1
% 244.05/50.54  | | 
% 244.05/50.54  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2220.
% 244.05/50.54  | | 
% 244.05/50.54  | Case 2:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (9)  all_58_14 = e1 & op(e0, e1) = e1
% 244.05/50.54  | | 
% 244.05/50.54  | | ALPHA: (9) implies:
% 244.05/50.54  | |   (10)  all_58_14 = e1
% 244.05/50.54  | | 
% 244.05/50.54  | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #2044.
% 244.05/50.54  | | 
% 244.05/50.54  | End of split
% 244.05/50.54  | 
% 244.05/50.54  End of proof
% 244.05/50.54  
% 244.05/50.54  Sub-proof #1436 shows that the following formulas are inconsistent:
% 244.05/50.54  ----------------------------------------------------------------
% 244.05/50.54    (1)  all_58_13 = e3
% 244.05/50.54    (2)  all_58_13 = e1
% 244.05/50.54    (3)   ~ (e3 = e1)
% 244.05/50.54  
% 244.05/50.54  Begin of proof
% 244.05/50.54  | 
% 244.05/50.54  | COMBINE_EQS: (1), (2) imply:
% 244.05/50.54  |   (4)  e3 = e1
% 244.05/50.54  | 
% 244.05/50.54  | SIMP: (4) implies:
% 244.05/50.54  |   (5)  e3 = e1
% 244.05/50.54  | 
% 244.05/50.54  | REDUCE: (3), (5) imply:
% 244.05/50.54  |   (6)  $false
% 244.05/50.54  | 
% 244.05/50.54  | CLOSE: (6) is inconsistent.
% 244.05/50.54  | 
% 244.05/50.54  End of proof
% 244.05/50.54  
% 244.05/50.54  Sub-proof #1437 shows that the following formulas are inconsistent:
% 244.05/50.54  ----------------------------------------------------------------
% 244.05/50.54    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.54         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.54    (2)  all_58_1 = e1
% 244.05/50.54    (3)   ~ (e3 = e0)
% 244.05/50.54    (4)   ~ (e2 = e0)
% 244.05/50.54    (5)   ~ (e3 = e1)
% 244.05/50.54    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.54         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.54    (7)   ~ (e3 = e2)
% 244.05/50.54    (8)  op(e3, e0) = e3
% 244.05/50.54    (9)  all_58_4 = e1
% 244.05/50.54    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.54          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.54    (11)   ~ (all_52_4 = e3)
% 244.05/50.54    (12)  op(e3, e2) = all_52_4
% 244.05/50.54    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.54    (14)   ~ (e1 = e0)
% 244.05/50.54    (15)   ~ (e2 = e1)
% 244.05/50.54  
% 244.05/50.54  Begin of proof
% 244.05/50.54  | 
% 244.05/50.54  | BETA: splitting (1) gives:
% 244.05/50.54  | 
% 244.05/50.54  | Case 1:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (16)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 244.05/50.54  | |           e2)
% 244.05/50.54  | | 
% 244.05/50.54  | | BETA: splitting (16) gives:
% 244.05/50.54  | | 
% 244.05/50.54  | | Case 1:
% 244.05/50.54  | | | 
% 244.05/50.54  | | |   (17)  all_58_0 = e2 & op(e3, e3) = e2
% 244.05/50.54  | | | 
% 244.05/50.54  | | | ALPHA: (17) implies:
% 244.05/50.54  | | |   (18)  op(e3, e3) = e2
% 244.05/50.54  | | | 
% 244.05/50.54  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 244.05/50.54  | | |            (14), (18) are inconsistent by sub-proof #1645.
% 244.05/50.54  | | | 
% 244.05/50.54  | | Case 2:
% 244.05/50.54  | | | 
% 244.05/50.54  | | |   (19)  all_58_1 = e2 & op(e3, e2) = e2
% 244.05/50.54  | | | 
% 244.05/50.54  | | | REF_CLOSE: (2), (15), (19) are inconsistent by sub-proof #1722.
% 244.05/50.54  | | | 
% 244.05/50.54  | | End of split
% 244.05/50.54  | | 
% 244.05/50.54  | Case 2:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (20)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 244.05/50.54  | |           e2)
% 244.05/50.54  | | 
% 244.05/50.54  | | BETA: splitting (20) gives:
% 244.05/50.54  | | 
% 244.05/50.54  | | Case 1:
% 244.05/50.54  | | | 
% 244.05/50.54  | | |   (21)  all_58_4 = e2 & op(e3, e1) = e2
% 244.05/50.54  | | | 
% 244.05/50.54  | | | REF_CLOSE: (9), (15), (21) are inconsistent by sub-proof #1471.
% 244.05/50.54  | | | 
% 244.05/50.54  | | Case 2:
% 244.05/50.54  | | | 
% 244.05/50.54  | | |   (22)  all_58_9 = e2 & op(e3, e0) = e2
% 244.05/50.54  | | | 
% 244.05/50.54  | | | ALPHA: (22) implies:
% 244.05/50.54  | | |   (23)  op(e3, e0) = e2
% 244.05/50.54  | | | 
% 244.05/50.54  | | | REF_CLOSE: (7), (8), (13), (23) are inconsistent by sub-proof #2125.
% 244.05/50.54  | | | 
% 244.05/50.54  | | End of split
% 244.05/50.54  | | 
% 244.05/50.54  | End of split
% 244.05/50.54  | 
% 244.05/50.54  End of proof
% 244.05/50.54  
% 244.05/50.54  Sub-proof #1438 shows that the following formulas are inconsistent:
% 244.05/50.54  ----------------------------------------------------------------
% 244.05/50.54    (1)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.54    (2)  op(e0, e3) = all_52_3
% 244.05/50.54    (3)  op(e0, e2) = e3
% 244.05/50.54    (4)   ~ (e3 = e2)
% 244.05/50.54    (5)   ~ (all_52_3 = e2)
% 244.05/50.54    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.54  
% 244.05/50.54  Begin of proof
% 244.05/50.54  | 
% 244.05/50.54  | BETA: splitting (1) gives:
% 244.05/50.54  | 
% 244.05/50.54  | Case 1:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (7)  all_58_12 = e2 & op(e0, e3) = e2
% 244.05/50.54  | | 
% 244.05/50.54  | | REF_CLOSE: (2), (5), (6), (7) are inconsistent by sub-proof #2315.
% 244.05/50.54  | | 
% 244.05/50.54  | Case 2:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (8)  all_58_13 = e2 & op(e0, e2) = e2
% 244.05/50.54  | | 
% 244.05/50.54  | | ALPHA: (8) implies:
% 244.05/50.54  | |   (9)  op(e0, e2) = e2
% 244.05/50.54  | | 
% 244.05/50.54  | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #2254.
% 244.05/50.54  | | 
% 244.05/50.54  | End of split
% 244.05/50.54  | 
% 244.05/50.54  End of proof
% 244.05/50.54  
% 244.05/50.54  Sub-proof #1439 shows that the following formulas are inconsistent:
% 244.05/50.54  ----------------------------------------------------------------
% 244.05/50.54    (1)   ~ (all_52_3 = e0)
% 244.05/50.54    (2)  op(e3, e2) = all_56_9
% 244.05/50.54    (3)  op(e3, all_56_9) = e3
% 244.05/50.54    (4)   ~ (e3 = e0)
% 244.05/50.54    (5)  all_54_12 = all_52_3
% 244.05/50.54    (6)   ~ (all_52_3 = e2)
% 244.05/50.54    (7)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.05/50.54    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.54    (9)  op(e3, e3) = e0
% 244.05/50.54    (10)  op(e3, e2) = e3
% 244.05/50.54  
% 244.05/50.54  Begin of proof
% 244.05/50.54  | 
% 244.05/50.54  | BETA: splitting (7) gives:
% 244.05/50.54  | 
% 244.05/50.54  | Case 1:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (11)  all_54_12 = e2
% 244.05/50.54  | | 
% 244.05/50.54  | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #2264.
% 244.05/50.54  | | 
% 244.05/50.54  | Case 2:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (12)  all_54_12 = e1 | all_54_12 = e0
% 244.05/50.54  | | 
% 244.05/50.54  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (12) are inconsistent by
% 244.05/50.54  | |            sub-proof #1440.
% 244.05/50.54  | | 
% 244.05/50.54  | End of split
% 244.05/50.54  | 
% 244.05/50.54  End of proof
% 244.05/50.54  
% 244.05/50.54  Sub-proof #1440 shows that the following formulas are inconsistent:
% 244.05/50.54  ----------------------------------------------------------------
% 244.05/50.54    (1)   ~ (all_52_3 = e0)
% 244.05/50.54    (2)  op(e3, e2) = all_56_9
% 244.05/50.54    (3)  op(e3, all_56_9) = e3
% 244.05/50.54    (4)   ~ (e3 = e0)
% 244.05/50.54    (5)  all_54_12 = e1 | all_54_12 = e0
% 244.05/50.54    (6)  all_54_12 = all_52_3
% 244.05/50.54    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.54    (8)  op(e3, e3) = e0
% 244.05/50.54    (9)  op(e3, e2) = e3
% 244.05/50.54  
% 244.05/50.54  Begin of proof
% 244.05/50.54  | 
% 244.05/50.54  | BETA: splitting (5) gives:
% 244.05/50.54  | 
% 244.05/50.54  | Case 1:
% 244.05/50.54  | | 
% 244.05/50.54  | | 
% 244.05/50.54  | | GROUND_INST: instantiating (7) with e3, all_56_9, e2, e3, simplifying with
% 244.05/50.54  | |              (2), (9) gives:
% 244.05/50.54  | |   (10)  all_56_9 = e3
% 244.05/50.54  | | 
% 244.05/50.54  | | REDUCE: (3), (10) imply:
% 244.05/50.54  | |   (11)  op(e3, e3) = e3
% 244.05/50.54  | | 
% 244.05/50.54  | | REF_CLOSE: (4), (7), (8), (11) are inconsistent by sub-proof #1940.
% 244.05/50.54  | | 
% 244.05/50.54  | Case 2:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (12)  all_54_12 = e0
% 244.05/50.54  | | 
% 244.05/50.54  | | REF_CLOSE: (1), (6), (12) are inconsistent by sub-proof #2068.
% 244.05/50.54  | | 
% 244.05/50.54  | End of split
% 244.05/50.54  | 
% 244.05/50.54  End of proof
% 244.05/50.54  
% 244.05/50.54  Sub-proof #1441 shows that the following formulas are inconsistent:
% 244.05/50.54  ----------------------------------------------------------------
% 244.05/50.54    (1)   ~ (e3 = e0)
% 244.05/50.54    (2)   ~ (e2 = e0)
% 244.05/50.54    (3)   ~ (e3 = e1)
% 244.05/50.54    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 244.05/50.54         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 244.05/50.54    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.05/50.54         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.05/50.54    (6)   ~ (e3 = e2)
% 244.05/50.54    (7)  all_58_6 = e0
% 244.05/50.54    (8)  op(e2, e3) = all_52_1
% 244.05/50.54    (9)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.05/50.54         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.05/50.54    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.54    (11)   ~ (e1 = e0)
% 244.05/50.54    (12)  op(e3, e3) = e0
% 244.05/50.54    (13)   ~ (all_52_1 = e3)
% 244.05/50.54    (14)   ~ (e2 = e1)
% 244.05/50.54  
% 244.05/50.54  Begin of proof
% 244.05/50.54  | 
% 244.05/50.54  | BETA: splitting (4) gives:
% 244.05/50.54  | 
% 244.05/50.54  | Case 1:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 244.05/50.54  | |           e3)
% 244.05/50.54  | | 
% 244.05/50.54  | | REF_CLOSE: (1), (8), (10), (12), (13), (15) are inconsistent by sub-proof
% 244.05/50.54  | |            #1445.
% 244.05/50.54  | | 
% 244.05/50.54  | Case 2:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 244.05/50.54  | |           e3)
% 244.05/50.54  | | 
% 244.05/50.54  | | BETA: splitting (16) gives:
% 244.05/50.54  | | 
% 244.05/50.54  | | Case 1:
% 244.05/50.54  | | | 
% 244.05/50.54  | | |   (17)  all_58_6 = e3 & op(e1, e3) = e3
% 244.05/50.54  | | | 
% 244.05/50.54  | | | ALPHA: (17) implies:
% 244.05/50.54  | | |   (18)  all_58_6 = e3
% 244.05/50.54  | | | 
% 244.05/50.54  | | | REF_CLOSE: (1), (7), (18) are inconsistent by sub-proof #2222.
% 244.05/50.54  | | | 
% 244.05/50.54  | | Case 2:
% 244.05/50.54  | | | 
% 244.05/50.54  | | |   (19)  all_58_12 = e3 & op(e0, e3) = e3
% 244.05/50.54  | | | 
% 244.05/50.54  | | | ALPHA: (19) implies:
% 244.05/50.54  | | |   (20)  all_58_12 = e3
% 244.05/50.54  | | | 
% 244.05/50.54  | | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (10), (11), (12), (14), (20) are
% 244.05/50.54  | | |            inconsistent by sub-proof #1442.
% 244.05/50.54  | | | 
% 244.05/50.54  | | End of split
% 244.05/50.54  | | 
% 244.05/50.54  | End of split
% 244.05/50.54  | 
% 244.05/50.54  End of proof
% 244.05/50.54  
% 244.05/50.54  Sub-proof #1442 shows that the following formulas are inconsistent:
% 244.05/50.54  ----------------------------------------------------------------
% 244.05/50.54    (1)   ~ (e2 = e0)
% 244.05/50.54    (2)   ~ (e3 = e1)
% 244.05/50.54    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.05/50.54         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.05/50.54    (4)   ~ (e3 = e2)
% 244.05/50.54    (5)  all_58_6 = e0
% 244.05/50.54    (6)  all_58_12 = e3
% 244.05/50.54    (7)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.05/50.54         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.05/50.54    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.54    (9)   ~ (e1 = e0)
% 244.05/50.54    (10)  op(e3, e3) = e0
% 244.05/50.54    (11)   ~ (e2 = e1)
% 244.05/50.54  
% 244.05/50.54  Begin of proof
% 244.05/50.54  | 
% 244.05/50.54  | BETA: splitting (7) gives:
% 244.05/50.54  | 
% 244.05/50.54  | Case 1:
% 244.05/50.54  | | 
% 244.05/50.54  | |   (12)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 244.05/50.54  | |           e1)
% 244.05/50.54  | | 
% 244.05/50.54  | | BETA: splitting (12) gives:
% 244.05/50.54  | | 
% 244.05/50.54  | | Case 1:
% 244.05/50.54  | | | 
% 244.05/50.54  | | |   (13)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.54  | | | 
% 244.05/50.54  | | | ALPHA: (13) implies:
% 244.05/50.54  | | |   (14)  op(e3, e3) = e1
% 244.05/50.55  | | | 
% 244.05/50.55  | | | REF_CLOSE: (8), (9), (10), (14) are inconsistent by sub-proof #1828.
% 244.05/50.55  | | | 
% 244.05/50.55  | | Case 2:
% 244.05/50.55  | | | 
% 244.05/50.55  | | |   (15)  all_58_2 = e1 & op(e2, e3) = e1
% 244.05/50.55  | | | 
% 244.05/50.55  | | | ALPHA: (15) implies:
% 244.05/50.55  | | |   (16)  all_58_2 = e1
% 244.05/50.55  | | | 
% 244.05/50.55  | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (11), (16) are inconsistent
% 244.05/50.55  | | |            by sub-proof #1443.
% 244.05/50.55  | | | 
% 244.05/50.55  | | End of split
% 244.05/50.55  | | 
% 244.05/50.55  | Case 2:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (17)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 244.05/50.55  | |           e1)
% 244.05/50.55  | | 
% 244.05/50.55  | | BETA: splitting (17) gives:
% 244.05/50.55  | | 
% 244.05/50.55  | | Case 1:
% 244.05/50.55  | | | 
% 244.05/50.55  | | |   (18)  all_58_6 = e1 & op(e1, e3) = e1
% 244.05/50.55  | | | 
% 244.05/50.55  | | | REF_CLOSE: (5), (9), (18) are inconsistent by sub-proof #1682.
% 244.05/50.55  | | | 
% 244.05/50.55  | | Case 2:
% 244.05/50.55  | | | 
% 244.05/50.55  | | |   (19)  all_58_12 = e1 & op(e0, e3) = e1
% 244.05/50.55  | | | 
% 244.05/50.55  | | | ALPHA: (19) implies:
% 244.05/50.55  | | |   (20)  all_58_12 = e1
% 244.05/50.55  | | | 
% 244.05/50.55  | | | REF_CLOSE: (2), (6), (20) are inconsistent by sub-proof #1542.
% 244.05/50.55  | | | 
% 244.05/50.55  | | End of split
% 244.05/50.55  | | 
% 244.05/50.55  | End of split
% 244.05/50.55  | 
% 244.05/50.55  End of proof
% 244.05/50.55  
% 244.05/50.55  Sub-proof #1443 shows that the following formulas are inconsistent:
% 244.05/50.55  ----------------------------------------------------------------
% 244.05/50.55    (1)   ~ (e2 = e0)
% 244.05/50.55    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.05/50.55         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.05/50.55    (3)   ~ (e3 = e2)
% 244.05/50.55    (4)  all_58_6 = e0
% 244.05/50.55    (5)  all_58_12 = e3
% 244.05/50.55    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.55    (7)  op(e3, e3) = e0
% 244.05/50.55    (8)  all_58_2 = e1
% 244.05/50.55    (9)   ~ (e2 = e1)
% 244.05/50.55  
% 244.05/50.55  Begin of proof
% 244.05/50.55  | 
% 244.05/50.55  | BETA: splitting (2) gives:
% 244.05/50.55  | 
% 244.05/50.55  | Case 1:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 244.05/50.55  | |           e2)
% 244.05/50.55  | | 
% 244.05/50.55  | | REF_CLOSE: (1), (6), (7), (8), (9), (10) are inconsistent by sub-proof
% 244.05/50.55  | |            #1975.
% 244.05/50.55  | | 
% 244.05/50.55  | Case 2:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (11)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 244.05/50.55  | |           e2)
% 244.05/50.55  | | 
% 244.05/50.55  | | BETA: splitting (11) gives:
% 244.05/50.55  | | 
% 244.05/50.55  | | Case 1:
% 244.05/50.55  | | | 
% 244.05/50.55  | | |   (12)  all_58_6 = e2 & op(e1, e3) = e2
% 244.05/50.55  | | | 
% 244.05/50.55  | | | REF_CLOSE: (1), (4), (12) are inconsistent by sub-proof #1444.
% 244.05/50.55  | | | 
% 244.05/50.55  | | Case 2:
% 244.05/50.55  | | | 
% 244.05/50.55  | | |   (13)  all_58_12 = e2 & op(e0, e3) = e2
% 244.05/50.55  | | | 
% 244.05/50.55  | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #1974.
% 244.05/50.55  | | | 
% 244.05/50.55  | | End of split
% 244.05/50.55  | | 
% 244.05/50.55  | End of split
% 244.05/50.55  | 
% 244.05/50.55  End of proof
% 244.05/50.55  
% 244.05/50.55  Sub-proof #1444 shows that the following formulas are inconsistent:
% 244.05/50.55  ----------------------------------------------------------------
% 244.05/50.55    (1)  all_58_6 = e2 & op(e1, e3) = e2
% 244.05/50.55    (2)  all_58_6 = e0
% 244.05/50.55    (3)   ~ (e2 = e0)
% 244.05/50.55  
% 244.05/50.55  Begin of proof
% 244.05/50.55  | 
% 244.05/50.55  | ALPHA: (1) implies:
% 244.05/50.55  |   (4)  all_58_6 = e2
% 244.05/50.55  | 
% 244.05/50.55  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.55  |   (5)  e2 = e0
% 244.05/50.55  | 
% 244.05/50.55  | REDUCE: (3), (5) imply:
% 244.05/50.55  |   (6)  $false
% 244.05/50.55  | 
% 244.05/50.55  | CLOSE: (6) is inconsistent.
% 244.05/50.55  | 
% 244.05/50.55  End of proof
% 244.05/50.55  
% 244.05/50.55  Sub-proof #1445 shows that the following formulas are inconsistent:
% 244.05/50.55  ----------------------------------------------------------------
% 244.05/50.55    (1)   ~ (e3 = e0)
% 244.05/50.55    (2)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 244.05/50.55    (3)  op(e2, e3) = all_52_1
% 244.05/50.55    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.55    (5)  op(e3, e3) = e0
% 244.05/50.55    (6)   ~ (all_52_1 = e3)
% 244.05/50.55  
% 244.05/50.55  Begin of proof
% 244.05/50.55  | 
% 244.05/50.55  | BETA: splitting (2) gives:
% 244.05/50.55  | 
% 244.05/50.55  | Case 1:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (7)  all_58_0 = e3 & op(e3, e3) = e3
% 244.05/50.55  | | 
% 244.05/50.55  | | ALPHA: (7) implies:
% 244.05/50.55  | |   (8)  op(e3, e3) = e3
% 244.05/50.55  | | 
% 244.05/50.55  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1940.
% 244.05/50.55  | | 
% 244.05/50.55  | Case 2:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (9)  all_58_2 = e3 & op(e2, e3) = e3
% 244.05/50.55  | | 
% 244.05/50.55  | | ALPHA: (9) implies:
% 244.05/50.55  | |   (10)  op(e2, e3) = e3
% 244.05/50.55  | | 
% 244.05/50.55  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #2337.
% 244.05/50.55  | | 
% 244.05/50.55  | End of split
% 244.05/50.55  | 
% 244.05/50.55  End of proof
% 244.05/50.55  
% 244.05/50.55  Sub-proof #1446 shows that the following formulas are inconsistent:
% 244.05/50.55  ----------------------------------------------------------------
% 244.05/50.55    (1)  op(e3, e2) = e1
% 244.05/50.55    (2)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.05/50.55    (3)  all_54_1 = all_48_0
% 244.05/50.55    (4)   ~ (all_48_0 = e0)
% 244.05/50.55    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.55    (6)  op(e3, e2) = all_48_0
% 244.05/50.55    (7)   ~ (all_48_0 = e1)
% 244.05/50.55  
% 244.05/50.55  Begin of proof
% 244.05/50.55  | 
% 244.05/50.55  | BETA: splitting (2) gives:
% 244.05/50.55  | 
% 244.05/50.55  | Case 1:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (8)  all_54_1 = e2
% 244.05/50.55  | | 
% 244.05/50.55  | | COMBINE_EQS: (3), (8) imply:
% 244.05/50.55  | |   (9)  all_48_0 = e2
% 244.05/50.55  | | 
% 244.05/50.55  | | SIMP: (9) implies:
% 244.05/50.55  | |   (10)  all_48_0 = e2
% 244.05/50.55  | | 
% 244.05/50.55  | | REDUCE: (7), (10) imply:
% 244.05/50.55  | |   (11)   ~ (e2 = e1)
% 244.05/50.55  | | 
% 244.05/50.55  | | REDUCE: (6), (10) imply:
% 244.05/50.55  | |   (12)  op(e3, e2) = e2
% 244.05/50.55  | | 
% 244.05/50.55  | | REF_CLOSE: (1), (5), (11), (12) are inconsistent by sub-proof #2261.
% 244.05/50.55  | | 
% 244.05/50.55  | Case 2:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (13)  all_54_1 = e1 | all_54_1 = e0
% 244.05/50.55  | | 
% 244.05/50.55  | | REF_CLOSE: (3), (4), (7), (13) are inconsistent by sub-proof #1447.
% 244.05/50.55  | | 
% 244.05/50.55  | End of split
% 244.05/50.55  | 
% 244.05/50.55  End of proof
% 244.05/50.55  
% 244.05/50.55  Sub-proof #1447 shows that the following formulas are inconsistent:
% 244.05/50.55  ----------------------------------------------------------------
% 244.05/50.55    (1)  all_54_1 = e1 | all_54_1 = e0
% 244.05/50.55    (2)  all_54_1 = all_48_0
% 244.05/50.55    (3)   ~ (all_48_0 = e1)
% 244.05/50.55    (4)   ~ (all_48_0 = e0)
% 244.05/50.55  
% 244.05/50.55  Begin of proof
% 244.05/50.55  | 
% 244.05/50.55  | BETA: splitting (1) gives:
% 244.05/50.55  | 
% 244.05/50.55  | Case 1:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (5)  all_54_1 = e1
% 244.05/50.55  | | 
% 244.05/50.55  | | COMBINE_EQS: (2), (5) imply:
% 244.05/50.55  | |   (6)  all_48_0 = e1
% 244.05/50.55  | | 
% 244.05/50.55  | | SIMP: (6) implies:
% 244.05/50.55  | |   (7)  all_48_0 = e1
% 244.05/50.55  | | 
% 244.05/50.55  | | REDUCE: (3), (7) imply:
% 244.05/50.55  | |   (8)  $false
% 244.05/50.55  | | 
% 244.05/50.55  | | CLOSE: (8) is inconsistent.
% 244.05/50.55  | | 
% 244.05/50.55  | Case 2:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (9)  all_54_1 = e0
% 244.05/50.55  | | 
% 244.05/50.55  | | COMBINE_EQS: (2), (9) imply:
% 244.05/50.55  | |   (10)  all_48_0 = e0
% 244.05/50.55  | | 
% 244.05/50.55  | | SIMP: (10) implies:
% 244.05/50.55  | |   (11)  all_48_0 = e0
% 244.05/50.55  | | 
% 244.05/50.55  | | REDUCE: (4), (11) imply:
% 244.05/50.55  | |   (12)  $false
% 244.05/50.55  | | 
% 244.05/50.55  | | CLOSE: (12) is inconsistent.
% 244.05/50.55  | | 
% 244.05/50.55  | End of split
% 244.05/50.55  | 
% 244.05/50.55  End of proof
% 244.05/50.55  
% 244.05/50.55  Sub-proof #1448 shows that the following formulas are inconsistent:
% 244.05/50.55  ----------------------------------------------------------------
% 244.05/50.55    (1)   ~ (all_52_3 = e0)
% 244.05/50.55    (2)  op(e1, e2) = e1
% 244.05/50.55    (3)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.05/50.55           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 244.05/50.55           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 244.05/50.55         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 244.05/50.55           $i(all_56_15))
% 244.05/50.55    (4)   ~ (all_52_6 = e2)
% 244.05/50.55    (5)  op(e3, e0) = e1
% 244.05/50.55    (6)  op(e0, e3) = all_52_3
% 244.05/50.55    (7)   ~ (all_52_6 = e0)
% 244.05/50.55    (8)  all_54_11 = all_52_14
% 244.05/50.55    (9)  op(e0, e2) = e3
% 244.05/50.55    (10)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 244.05/50.55    (11)  op(e2, e0) = e3
% 244.05/50.55    (12)  op(e3, e2) = e2
% 244.05/50.55    (13)  all_54_9 = all_52_6
% 244.05/50.55    (14)   ~ (e3 = e2)
% 244.05/50.55    (15)   ~ (all_52_14 = e0)
% 244.05/50.55    (16)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 244.05/50.55            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 244.05/50.55              e0) = all_16_1 & $i(all_16_1))
% 244.05/50.55    (17)  all_56_11 = e0
% 244.05/50.55    (18)   ~ (all_52_6 = all_52_14)
% 244.05/50.55    (19)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 244.05/50.55            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 244.05/50.55              e0) = all_50_1 & $i(all_50_1))
% 244.05/50.55    (20)   ~ (all_52_4 = e3)
% 244.05/50.55    (21)  op(e3, e2) = all_52_4
% 244.05/50.55    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.55    (23)  op(e1, e1) = e0
% 244.05/50.55    (24)   ~ (e1 = e0)
% 244.05/50.55    (25)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 244.05/50.55  
% 244.05/50.55  Begin of proof
% 244.05/50.55  | 
% 244.05/50.55  | BETA: splitting (3) gives:
% 244.05/50.55  | 
% 244.05/50.55  | Case 1:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (26)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.05/50.55  | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 244.05/50.55  | | 
% 244.05/50.55  | | BETA: splitting (26) gives:
% 244.05/50.55  | | 
% 244.05/50.55  | | Case 1:
% 244.05/50.55  | | | 
% 244.05/50.55  | | |   (27)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.05/50.55  | | |         $i(all_56_9)
% 244.05/50.55  | | | 
% 244.05/50.55  | | | ALPHA: (27) implies:
% 244.05/50.55  | | |   (28)  op(e3, e2) = all_56_9
% 244.05/50.55  | | |   (29)  op(e3, all_56_9) = e3
% 244.05/50.55  | | | 
% 244.05/50.55  | | | BETA: splitting (25) gives:
% 244.05/50.55  | | | 
% 244.05/50.55  | | | Case 1:
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | |   (30)  all_54_9 = e2
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | | REF_CLOSE: (4), (13), (30) are inconsistent by sub-proof #1954.
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | Case 2:
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | |   (31)  all_54_9 = e1 | all_54_9 = e0
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | | BETA: splitting (31) gives:
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | | Case 1:
% 244.05/50.55  | | | | | 
% 244.05/50.55  | | | | |   (32)  all_54_9 = e1
% 244.05/50.55  | | | | | 
% 244.05/50.55  | | | | | COMBINE_EQS: (13), (32) imply:
% 244.05/50.55  | | | | |   (33)  all_52_6 = e1
% 244.05/50.55  | | | | | 
% 244.05/50.55  | | | | | SIMP: (33) implies:
% 244.05/50.55  | | | | |   (34)  all_52_6 = e1
% 244.05/50.55  | | | | | 
% 244.05/50.55  | | | | | REDUCE: (18), (34) imply:
% 244.05/50.55  | | | | |   (35)   ~ (all_52_14 = e1)
% 244.05/50.55  | | | | | 
% 244.05/50.55  | | | | | SIMP: (35) implies:
% 244.05/50.55  | | | | |   (36)   ~ (all_52_14 = e1)
% 244.05/50.55  | | | | | 
% 244.05/50.55  | | | | | BETA: splitting (10) gives:
% 244.05/50.55  | | | | | 
% 244.05/50.55  | | | | | Case 1:
% 244.05/50.55  | | | | | | 
% 244.05/50.55  | | | | | | 
% 244.05/50.55  | | | | | | GROUND_INST: instantiating (22) with e2, all_56_9, e2, e3,
% 244.05/50.55  | | | | | |              simplifying with (12), (28) gives:
% 244.05/50.55  | | | | | |   (37)  all_56_9 = e2
% 244.05/50.55  | | | | | | 
% 244.05/50.55  | | | | | | REDUCE: (29), (37) imply:
% 244.05/50.55  | | | | | |   (38)  op(e3, e2) = e3
% 244.05/50.55  | | | | | | 
% 244.05/50.55  | | | | | | REF_CLOSE: (20), (21), (22), (38) are inconsistent by sub-proof
% 244.05/50.55  | | | | | |            #2192.
% 244.05/50.55  | | | | | | 
% 244.05/50.55  | | | | | Case 2:
% 244.05/50.55  | | | | | | 
% 244.05/50.55  | | | | | |   (39)  all_54_11 = e1 | all_54_11 = e0
% 244.05/50.55  | | | | | | 
% 244.05/50.55  | | | | | | REF_CLOSE: (8), (15), (36), (39) are inconsistent by sub-proof
% 244.05/50.55  | | | | | |            #2174.
% 244.05/50.55  | | | | | | 
% 244.05/50.55  | | | | | End of split
% 244.05/50.55  | | | | | 
% 244.05/50.55  | | | | Case 2:
% 244.05/50.55  | | | | | 
% 244.05/50.55  | | | | |   (40)  all_54_9 = e0
% 244.05/50.55  | | | | | 
% 244.05/50.55  | | | | | REF_CLOSE: (7), (13), (40) are inconsistent by sub-proof #1953.
% 244.05/50.55  | | | | | 
% 244.05/50.55  | | | | End of split
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | End of split
% 244.05/50.55  | | | 
% 244.05/50.55  | | Case 2:
% 244.05/50.55  | | | 
% 244.05/50.55  | | |   (41)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 244.05/50.55  | | | 
% 244.05/50.55  | | | ALPHA: (41) implies:
% 244.05/50.55  | | |   (42)  op(e2, all_56_11) = e2
% 244.05/50.55  | | | 
% 244.05/50.55  | | | REDUCE: (17), (42) imply:
% 244.05/50.55  | | |   (43)  op(e2, e0) = e2
% 244.05/50.55  | | | 
% 244.05/50.55  | | | REF_CLOSE: (11), (14), (22), (43) are inconsistent by sub-proof #2152.
% 244.05/50.55  | | | 
% 244.05/50.55  | | End of split
% 244.05/50.55  | | 
% 244.05/50.55  | Case 2:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (44)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 244.05/50.55  | |           $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 244.05/50.55  | |             e2) = all_56_15 & $i(all_56_15))
% 244.05/50.55  | | 
% 244.05/50.55  | | BETA: splitting (44) gives:
% 244.05/50.55  | | 
% 244.05/50.55  | | Case 1:
% 244.05/50.55  | | | 
% 244.05/50.55  | | |   (45)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 244.05/50.55  | | |         $i(all_56_13)
% 244.05/50.55  | | | 
% 244.05/50.55  | | | ALPHA: (45) implies:
% 244.05/50.55  | | |   (46)  op(e1, e2) = all_56_13
% 244.05/50.55  | | |   (47)  op(e1, all_56_13) = e1
% 244.05/50.55  | | | 
% 244.05/50.55  | | | REF_CLOSE: (2), (5), (16), (19), (22), (23), (24), (46), (47) are
% 244.05/50.55  | | |            inconsistent by sub-proof #1568.
% 244.05/50.55  | | | 
% 244.05/50.55  | | Case 2:
% 244.05/50.55  | | | 
% 244.05/50.55  | | |   (48)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 244.05/50.55  | | |         $i(all_56_15)
% 244.05/50.55  | | | 
% 244.05/50.55  | | | ALPHA: (48) implies:
% 244.05/50.55  | | |   (49)  op(e0, e2) = all_56_15
% 244.05/50.55  | | |   (50)  op(e0, all_56_15) = e0
% 244.05/50.55  | | | 
% 244.05/50.55  | | | BETA: splitting (16) gives:
% 244.05/50.55  | | | 
% 244.05/50.55  | | | Case 1:
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | | GROUND_INST: instantiating (22) with e3, all_56_15, e2, e0, simplifying
% 244.05/50.55  | | | |              with (9), (49) gives:
% 244.05/50.55  | | | |   (51)  all_56_15 = e3
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | | REDUCE: (50), (51) imply:
% 244.05/50.55  | | | |   (52)  op(e0, e3) = e0
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | | REF_CLOSE: (1), (6), (22), (52) are inconsistent by sub-proof #2331.
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | Case 2:
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | |   (53)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 & $i(all_16_1)
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | | REF_CLOSE: (5), (19), (22), (53) are inconsistent by sub-proof #1569.
% 244.05/50.55  | | | | 
% 244.05/50.55  | | | End of split
% 244.05/50.55  | | | 
% 244.05/50.55  | | End of split
% 244.05/50.55  | | 
% 244.05/50.55  | End of split
% 244.05/50.55  | 
% 244.05/50.55  End of proof
% 244.05/50.55  
% 244.05/50.55  Sub-proof #1449 shows that the following formulas are inconsistent:
% 244.05/50.55  ----------------------------------------------------------------
% 244.05/50.55    (1)  op(e3, e2) = all_14_0
% 244.05/50.55    (2)  op(e3, e2) = e1
% 244.05/50.55    (3)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.05/50.55    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.55    (5)  all_54_1 = all_14_0
% 244.05/50.55    (6)   ~ (all_14_0 = e0)
% 244.05/50.55    (7)   ~ (all_14_0 = e1)
% 244.05/50.55  
% 244.05/50.55  Begin of proof
% 244.05/50.55  | 
% 244.05/50.55  | BETA: splitting (3) gives:
% 244.05/50.55  | 
% 244.05/50.55  | Case 1:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (8)  all_54_1 = e2
% 244.05/50.55  | | 
% 244.05/50.55  | | COMBINE_EQS: (5), (8) imply:
% 244.05/50.55  | |   (9)  all_14_0 = e2
% 244.05/50.55  | | 
% 244.05/50.55  | | SIMP: (9) implies:
% 244.05/50.55  | |   (10)  all_14_0 = e2
% 244.05/50.55  | | 
% 244.05/50.55  | | REDUCE: (7), (10) imply:
% 244.05/50.55  | |   (11)   ~ (e2 = e1)
% 244.05/50.55  | | 
% 244.05/50.55  | | REDUCE: (1), (10) imply:
% 244.05/50.55  | |   (12)  op(e3, e2) = e2
% 244.05/50.55  | | 
% 244.05/50.55  | | REF_CLOSE: (2), (4), (11), (12) are inconsistent by sub-proof #2261.
% 244.05/50.55  | | 
% 244.05/50.55  | Case 2:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (13)  all_54_1 = e1 | all_54_1 = e0
% 244.05/50.55  | | 
% 244.05/50.55  | | REF_CLOSE: (5), (6), (7), (13) are inconsistent by sub-proof #1450.
% 244.05/50.55  | | 
% 244.05/50.55  | End of split
% 244.05/50.55  | 
% 244.05/50.55  End of proof
% 244.05/50.55  
% 244.05/50.55  Sub-proof #1450 shows that the following formulas are inconsistent:
% 244.05/50.55  ----------------------------------------------------------------
% 244.05/50.55    (1)  all_54_1 = e1 | all_54_1 = e0
% 244.05/50.55    (2)  all_54_1 = all_14_0
% 244.05/50.55    (3)   ~ (all_14_0 = e1)
% 244.05/50.55    (4)   ~ (all_14_0 = e0)
% 244.05/50.55  
% 244.05/50.55  Begin of proof
% 244.05/50.55  | 
% 244.05/50.55  | BETA: splitting (1) gives:
% 244.05/50.55  | 
% 244.05/50.55  | Case 1:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (5)  all_54_1 = e1
% 244.05/50.55  | | 
% 244.05/50.55  | | COMBINE_EQS: (2), (5) imply:
% 244.05/50.55  | |   (6)  all_14_0 = e1
% 244.05/50.55  | | 
% 244.05/50.55  | | SIMP: (6) implies:
% 244.05/50.55  | |   (7)  all_14_0 = e1
% 244.05/50.55  | | 
% 244.05/50.55  | | REDUCE: (3), (7) imply:
% 244.05/50.55  | |   (8)  $false
% 244.05/50.55  | | 
% 244.05/50.55  | | CLOSE: (8) is inconsistent.
% 244.05/50.55  | | 
% 244.05/50.55  | Case 2:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (9)  all_54_1 = e0
% 244.05/50.55  | | 
% 244.05/50.55  | | COMBINE_EQS: (2), (9) imply:
% 244.05/50.55  | |   (10)  all_14_0 = e0
% 244.05/50.55  | | 
% 244.05/50.55  | | SIMP: (10) implies:
% 244.05/50.55  | |   (11)  all_14_0 = e0
% 244.05/50.55  | | 
% 244.05/50.55  | | REDUCE: (4), (11) imply:
% 244.05/50.55  | |   (12)  $false
% 244.05/50.55  | | 
% 244.05/50.55  | | CLOSE: (12) is inconsistent.
% 244.05/50.55  | | 
% 244.05/50.55  | End of split
% 244.05/50.55  | 
% 244.05/50.55  End of proof
% 244.05/50.55  
% 244.05/50.55  Sub-proof #1451 shows that the following formulas are inconsistent:
% 244.05/50.55  ----------------------------------------------------------------
% 244.05/50.55    (1)  op(e0, e3) = all_52_3
% 244.05/50.55    (2)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 244.05/50.55    (3)   ~ (all_52_3 = e3)
% 244.05/50.55    (4)   ~ (all_52_2 = e3)
% 244.05/50.55    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.55    (6)  op(e1, e3) = all_52_2
% 244.05/50.55  
% 244.05/50.55  Begin of proof
% 244.05/50.55  | 
% 244.05/50.55  | BETA: splitting (2) gives:
% 244.05/50.55  | 
% 244.05/50.55  | Case 1:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (7)  all_58_6 = e3 & op(e1, e3) = e3
% 244.05/50.55  | | 
% 244.05/50.55  | | ALPHA: (7) implies:
% 244.05/50.55  | |   (8)  op(e1, e3) = e3
% 244.05/50.55  | | 
% 244.05/50.55  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2335.
% 244.05/50.55  | | 
% 244.05/50.55  | Case 2:
% 244.05/50.55  | | 
% 244.05/50.55  | |   (9)  all_58_12 = e3 & op(e0, e3) = e3
% 244.05/50.55  | | 
% 244.05/50.55  | | ALPHA: (9) implies:
% 244.05/50.55  | |   (10)  op(e0, e3) = e3
% 244.05/50.55  | | 
% 244.05/50.55  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2332.
% 244.05/50.55  | | 
% 244.05/50.55  | End of split
% 244.05/50.55  | 
% 244.05/50.55  End of proof
% 244.05/50.55  
% 244.05/50.55  Sub-proof #1452 shows that the following formulas are inconsistent:
% 244.05/50.55  ----------------------------------------------------------------
% 244.05/50.55    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.05/50.55         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.55    (2)   ~ (e3 = e0)
% 244.05/50.55    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.05/50.55         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.05/50.56    (4)   ~ (e2 = e0)
% 244.05/50.56    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.56         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.56    (6)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.56         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.56    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.56         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.56    (8)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.05/50.56         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.05/50.56    (9)  op(e1, e0) = all_52_14
% 244.05/50.56    (10)  op(e0, e3) = all_52_3
% 244.05/50.56    (11)   ~ (e3 = e1)
% 244.05/50.56    (12)  op(e0, e2) = e3
% 244.05/50.56    (13)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.05/50.56          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.05/50.56    (14)  op(e2, e2) = e0
% 244.05/50.56    (15)  op(e0, all_52_3) = e0
% 244.05/50.56    (16)  all_58_11 = e3
% 244.05/50.56    (17)  op(e2, e1) = e2
% 244.05/50.56    (18)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.56              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 244.05/50.56                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.05/50.56                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.05/50.56    (19)   ~ (e3 = e2)
% 244.05/50.56    (20)  op(e1, e0) = e3
% 244.05/50.56    (21)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 244.05/50.56          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 244.05/50.56    (22)   ~ (all_52_14 = e0)
% 244.05/50.56    (23)  op(e1, e0) = all_28_1
% 244.05/50.56    (24)  op(e3, e0) = all_52_12
% 244.05/50.56    (25)  all_58_5 = e2
% 244.05/50.56    (26)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.56          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.56    (27)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.56          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.56    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.56    (29)  op(e0, e0) = e0
% 244.05/50.56    (30)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.56          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.56    (31)  op(e3, e1) = e3
% 244.05/50.56    (32)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.56          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.05/50.56    (33)   ~ (all_52_12 = e3)
% 244.05/50.56    (34)  op(e1, e1) = e0
% 244.05/50.56    (35)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.05/50.56          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.05/50.56    (36)   ~ (e1 = e0)
% 244.05/50.56    (37)  op(e3, e3) = e0
% 244.05/50.56    (38)  all_58_4 = e3
% 244.05/50.56    (39)  all_58_2 = e3
% 244.05/50.56    (40)   ~ (all_52_13 = e3)
% 244.05/50.56    (41)  all_58_15 = e0
% 244.05/50.56    (42)  op(e2, e0) = all_52_13
% 244.05/50.56    (43)  all_58_3 = e0
% 244.05/50.56    (44)   ~ (all_28_1 = e2)
% 244.05/50.56    (45)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.56          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.05/50.56            e2)
% 244.05/50.56    (46)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.56          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.05/50.56    (47)   ~ (all_52_13 = e0)
% 244.05/50.56    (48)   ~ (e2 = e1)
% 244.05/50.56  
% 244.05/50.56  Begin of proof
% 244.05/50.56  | 
% 244.05/50.56  | BETA: splitting (46) gives:
% 244.05/50.56  | 
% 244.05/50.56  | Case 1:
% 244.05/50.56  | | 
% 244.05/50.56  | |   (49)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 244.05/50.56  | |           e1)
% 244.05/50.56  | | 
% 244.05/50.56  | | BETA: splitting (49) gives:
% 244.05/50.56  | | 
% 244.05/50.56  | | Case 1:
% 244.05/50.56  | | | 
% 244.05/50.56  | | |   (50)  all_58_2 = e1 & op(e2, e3) = e1
% 244.05/50.56  | | | 
% 244.05/50.56  | | | REF_CLOSE: (11), (39), (50) are inconsistent by sub-proof #1765.
% 244.05/50.56  | | | 
% 244.05/50.56  | | Case 2:
% 244.05/50.56  | | | 
% 244.05/50.56  | | |   (51)  all_58_3 = e1 & op(e2, e2) = e1
% 244.05/50.56  | | | 
% 244.05/50.56  | | | REF_CLOSE: (36), (43), (51) are inconsistent by sub-proof #1752.
% 244.05/50.56  | | | 
% 244.05/50.56  | | End of split
% 244.05/50.56  | | 
% 244.05/50.56  | Case 2:
% 244.05/50.56  | | 
% 244.05/50.56  | |   (52)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 244.05/50.56  | |           e1)
% 244.05/50.56  | | 
% 244.05/50.56  | | BETA: splitting (52) gives:
% 244.05/50.56  | | 
% 244.05/50.56  | | Case 1:
% 244.05/50.56  | | | 
% 244.05/50.56  | | |   (53)  all_58_5 = e1 & op(e2, e1) = e1
% 244.05/50.56  | | | 
% 244.05/50.56  | | | REF_CLOSE: (25), (48), (53) are inconsistent by sub-proof #1548.
% 244.05/50.56  | | | 
% 244.05/50.56  | | Case 2:
% 244.05/50.56  | | | 
% 244.05/50.56  | | |   (54)  all_58_10 = e1 & op(e2, e0) = e1
% 244.05/50.56  | | | 
% 244.05/50.56  | | | ALPHA: (54) implies:
% 244.05/50.56  | | |   (55)  all_58_10 = e1
% 244.05/50.56  | | |   (56)  op(e2, e0) = e1
% 244.05/50.56  | | | 
% 244.05/50.56  | | | BETA: splitting (30) gives:
% 244.05/50.56  | | | 
% 244.05/50.56  | | | Case 1:
% 244.05/50.56  | | | | 
% 244.05/50.56  | | | |   (57)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 244.05/50.56  | | | |           = e2)
% 244.05/50.56  | | | | 
% 244.05/50.56  | | | | BETA: splitting (57) gives:
% 244.05/50.56  | | | | 
% 244.05/50.56  | | | | Case 1:
% 244.05/50.56  | | | | | 
% 244.05/50.56  | | | | |   (58)  all_58_9 = e2 & op(e3, e0) = e2
% 244.05/50.56  | | | | | 
% 244.05/50.56  | | | | | ALPHA: (58) implies:
% 244.05/50.56  | | | | |   (59)  all_58_9 = e2
% 244.05/50.56  | | | | |   (60)  op(e3, e0) = e2
% 244.05/50.56  | | | | | 
% 244.05/50.56  | | | | | BETA: splitting (8) gives:
% 244.05/50.56  | | | | | 
% 244.05/50.56  | | | | | Case 1:
% 244.05/50.56  | | | | | | 
% 244.05/50.56  | | | | | |   (61)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 244.05/50.56  | | | | | |             e1) = e1)
% 244.05/50.56  | | | | | | 
% 244.05/50.56  | | | | | | REF_CLOSE: (4), (11), (16), (19), (25), (28), (30), (31), (41),
% 244.05/50.56  | | | | | |            (48), (55), (59), (61) are inconsistent by sub-proof
% 244.05/50.56  | | | | | |            #1505.
% 244.05/50.56  | | | | | | 
% 244.05/50.56  | | | | | Case 2:
% 244.05/50.56  | | | | | | 
% 244.05/50.56  | | | | | |   (62)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0,
% 244.05/50.56  | | | | | |             e1) = e1)
% 244.05/50.56  | | | | | | 
% 244.05/50.56  | | | | | | BETA: splitting (62) gives:
% 244.05/50.56  | | | | | | 
% 244.05/50.56  | | | | | | Case 1:
% 244.05/50.56  | | | | | | | 
% 244.05/50.56  | | | | | | |   (63)  all_58_8 = e1 & op(e1, e1) = e1
% 244.05/50.56  | | | | | | | 
% 244.05/50.56  | | | | | | | ALPHA: (63) implies:
% 244.05/50.56  | | | | | | |   (64)  op(e1, e1) = e1
% 244.05/50.56  | | | | | | | 
% 244.05/50.56  | | | | | | | REF_CLOSE: (28), (34), (36), (64) are inconsistent by sub-proof
% 244.05/50.56  | | | | | | |            #2220.
% 244.05/50.56  | | | | | | | 
% 244.05/50.56  | | | | | | Case 2:
% 244.05/50.56  | | | | | | | 
% 244.05/50.56  | | | | | | |   (65)  all_58_14 = e1 & op(e0, e1) = e1
% 244.05/50.56  | | | | | | | 
% 244.05/50.56  | | | | | | | ALPHA: (65) implies:
% 244.05/50.56  | | | | | | |   (66)  all_58_14 = e1
% 244.05/50.56  | | | | | | |   (67)  op(e0, e1) = e1
% 244.05/50.56  | | | | | | | 
% 244.05/50.56  | | | | | | | BETA: splitting (27) gives:
% 244.05/50.56  | | | | | | | 
% 244.05/50.56  | | | | | | | Case 1:
% 244.05/50.56  | | | | | | | | 
% 244.05/50.56  | | | | | | | |   (68)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 &
% 244.05/50.56  | | | | | | | |           op(e3, e2) = e1)
% 244.05/50.56  | | | | | | | | 
% 244.05/50.56  | | | | | | | | BETA: splitting (68) gives:
% 244.05/50.56  | | | | | | | | 
% 244.05/50.56  | | | | | | | | Case 1:
% 244.05/50.56  | | | | | | | | | 
% 244.05/50.56  | | | | | | | | |   (69)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.56  | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | ALPHA: (69) implies:
% 244.05/50.56  | | | | | | | | |   (70)  op(e3, e3) = e1
% 244.05/50.56  | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | REF_CLOSE: (28), (36), (37), (70) are inconsistent by
% 244.05/50.56  | | | | | | | | |            sub-proof #1828.
% 244.05/50.56  | | | | | | | | | 
% 244.05/50.56  | | | | | | | | Case 2:
% 244.05/50.56  | | | | | | | | | 
% 244.05/50.56  | | | | | | | | |   (71)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.56  | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | ALPHA: (71) implies:
% 244.05/50.56  | | | | | | | | |   (72)  all_58_1 = e1
% 244.05/50.56  | | | | | | | | |   (73)  op(e3, e2) = e1
% 244.05/50.56  | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | BETA: splitting (5) gives:
% 244.05/50.56  | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | Case 1:
% 244.05/50.56  | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | |   (74)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 &
% 244.05/50.56  | | | | | | | | | |           op(e2, e2) = e2)
% 244.05/50.56  | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | BETA: splitting (74) gives:
% 244.05/50.56  | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | Case 1:
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | |   (75)  all_58_1 = e2 & op(e3, e2) = e2
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | ALPHA: (75) implies:
% 244.05/50.56  | | | | | | | | | | |   (76)  op(e3, e2) = e2
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | REF_CLOSE: (28), (48), (73), (76) are inconsistent by
% 244.05/50.56  | | | | | | | | | | |            sub-proof #2261.
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | Case 2:
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | |   (77)  all_58_3 = e2 & op(e2, e2) = e2
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | ALPHA: (77) implies:
% 244.05/50.56  | | | | | | | | | | |   (78)  op(e2, e2) = e2
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | REF_CLOSE: (4), (14), (28), (78) are inconsistent by
% 244.05/50.56  | | | | | | | | | | |            sub-proof #2137.
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | End of split
% 244.05/50.56  | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | Case 2:
% 244.05/50.56  | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | |   (79)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2
% 244.05/50.56  | | | | | | | | | |           & op(e0, e2) = e2)
% 244.05/50.56  | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | BETA: splitting (79) gives:
% 244.05/50.56  | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | Case 1:
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | |   (80)  all_58_7 = e2 & op(e1, e2) = e2
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | ALPHA: (80) implies:
% 244.05/50.56  | | | | | | | | | | |   (81)  all_58_7 = e2
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | BETA: splitting (45) gives:
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | Case 1:
% 244.05/50.56  | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | |   (82)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 244.05/50.56  | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 244.05/50.56  | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | BETA: splitting (82) gives:
% 244.05/50.56  | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | Case 1:
% 244.05/50.56  | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | |   (83)  all_58_12 = e2 & op(e0, e3) = e2
% 244.05/50.56  | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | BETA: splitting (3) gives:
% 244.05/50.56  | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | Case 1:
% 244.05/50.56  | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | |   (84)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 244.05/50.56  | | | | | | | | | | | | | |           & op(e1, e2) = e1)
% 244.05/50.56  | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 244.05/50.56  | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | Case 1:
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | ALPHA: (83) implies:
% 244.05/50.56  | | | | | | | | | | | | | | |   (85)  all_58_12 = e2
% 244.05/50.56  | | | | | | | | | | | | | | |   (86)  op(e0, e3) = e2
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_52_3, e2, e3, e0,
% 244.05/50.56  | | | | | | | | | | | | | | |              simplifying with (10), (86) gives:
% 244.05/50.56  | | | | | | | | | | | | | | |   (87)  all_52_3 = e2
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_52_13, e1, e0, e2,
% 244.05/50.56  | | | | | | | | | | | | | | |              simplifying with (42), (56) gives:
% 244.05/50.56  | | | | | | | | | | | | | | |   (88)  all_52_13 = e1
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_52_12, e2, e0, e3,
% 244.05/50.56  | | | | | | | | | | | | | | |              simplifying with (24), (60) gives:
% 244.05/50.56  | | | | | | | | | | | | | | |   (89)  all_52_12 = e2
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | REDUCE: (33), (89) imply:
% 244.05/50.56  | | | | | | | | | | | | | | |   (90)   ~ (e3 = e2)
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | REDUCE: (40), (88) imply:
% 244.05/50.56  | | | | | | | | | | | | | | |   (91)   ~ (e3 = e1)
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | REDUCE: (15), (87) imply:
% 244.05/50.56  | | | | | | | | | | | | | | |   (92)  op(e0, e2) = e0
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (11), (19), (28), (29), (66), (85), (92)
% 244.05/50.56  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1772.
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | Case 2:
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | |   (93)  all_58_7 = e1 & op(e1, e2) = e1
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 244.05/50.56  | | | | | | | | | | | | | | |   (94)  all_58_7 = e1
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (12), (14), (19), (28), (48), (72), (94)
% 244.05/50.56  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1715.
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | End of split
% 244.05/50.56  | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | Case 2:
% 244.05/50.56  | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | |   (95)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 244.05/50.56  | | | | | | | | | | | | | |           e1 & op(e1, e0) = e1)
% 244.05/50.56  | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 244.05/50.56  | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | Case 1:
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | |   (96)  all_58_8 = e1 & op(e1, e1) = e1
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 244.05/50.56  | | | | | | | | | | | | | | |   (97)  op(e1, e1) = e1
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (13), (17), (28), (36), (38), (67), (97)
% 244.05/50.56  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1503.
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | Case 2:
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | |   (98)  all_58_11 = e1 & op(e1, e0) = e1
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 244.05/50.56  | | | | | | | | | | | | | | |   (99)  op(e1, e0) = e1
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | | REF_CLOSE: (11), (20), (28), (99) are inconsistent by
% 244.05/50.56  | | | | | | | | | | | | | | |            sub-proof #1894.
% 244.05/50.56  | | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | | End of split
% 244.05/50.56  | | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | End of split
% 244.05/50.56  | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | Case 2:
% 244.05/50.56  | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | |   (100)  all_58_13 = e2 & op(e0, e2) = e2
% 244.05/50.56  | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | ALPHA: (100) implies:
% 244.05/50.56  | | | | | | | | | | | | |   (101)  all_58_13 = e2
% 244.05/50.56  | | | | | | | | | | | | |   (102)  op(e0, e2) = e2
% 244.05/50.56  | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (7), (11), (19), (28), (32), (35),
% 244.05/50.56  | | | | | | | | | | | | |            (36), (48), (81), (101), (102) are inconsistent by
% 244.05/50.56  | | | | | | | | | | | | |            sub-proof #1453.
% 244.05/50.56  | | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | End of split
% 244.05/50.56  | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | Case 2:
% 244.05/50.56  | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | |   (103)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 244.05/50.56  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 244.05/50.56  | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (9), (11), (13), (18), (19), (21),
% 244.05/50.56  | | | | | | | | | | | |            (22), (25), (26), (28), (29), (30), (36), (38),
% 244.05/50.56  | | | | | | | | | | | |            (40), (42), (47), (48), (66), (103) are
% 244.05/50.56  | | | | | | | | | | | |            inconsistent by sub-proof #1479.
% 244.05/50.56  | | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | End of split
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | Case 2:
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | |   (104)  all_58_13 = e2 & op(e0, e2) = e2
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | ALPHA: (104) implies:
% 244.05/50.56  | | | | | | | | | | |   (105)  op(e0, e2) = e2
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | | REF_CLOSE: (12), (19), (28), (105) are inconsistent by
% 244.05/50.56  | | | | | | | | | | |            sub-proof #2254.
% 244.05/50.56  | | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | | End of split
% 244.05/50.56  | | | | | | | | | | 
% 244.05/50.56  | | | | | | | | | End of split
% 244.05/50.56  | | | | | | | | | 
% 244.05/50.56  | | | | | | | | End of split
% 244.05/50.56  | | | | | | | | 
% 244.05/50.56  | | | | | | | Case 2:
% 244.05/50.56  | | | | | | | | 
% 244.05/50.56  | | | | | | | |   (106)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 &
% 244.05/50.56  | | | | | | | |            op(e3, e0) = e1)
% 244.05/50.56  | | | | | | | | 
% 244.05/50.56  | | | | | | | | REF_CLOSE: (4), (11), (16), (19), (28), (30), (31), (41), (48),
% 244.05/50.56  | | | | | | | |            (55), (106) are inconsistent by sub-proof #1502.
% 244.05/50.56  | | | | | | | | 
% 244.05/50.56  | | | | | | | End of split
% 244.05/50.56  | | | | | | | 
% 244.05/50.56  | | | | | | End of split
% 244.05/50.56  | | | | | | 
% 244.05/50.56  | | | | | End of split
% 244.05/50.56  | | | | | 
% 244.05/50.56  | | | | Case 2:
% 244.05/50.56  | | | | | 
% 244.05/50.56  | | | | |   (107)  all_58_10 = e2 & op(e2, e0) = e2
% 244.05/50.56  | | | | | 
% 244.05/50.56  | | | | | ALPHA: (107) implies:
% 244.05/50.56  | | | | |   (108)  op(e2, e0) = e2
% 244.05/50.56  | | | | | 
% 244.05/50.56  | | | | | REF_CLOSE: (28), (48), (56), (108) are inconsistent by sub-proof
% 244.05/50.56  | | | | |            #1659.
% 244.05/50.56  | | | | | 
% 244.05/50.56  | | | | End of split
% 244.05/50.56  | | | | 
% 244.05/50.56  | | | Case 2:
% 244.05/50.56  | | | | 
% 244.05/50.56  | | | |   (109)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 244.05/50.56  | | | |              e0) = e2)
% 244.05/50.56  | | | | 
% 244.05/50.56  | | | | REF_CLOSE: (2), (4), (6), (9), (11), (18), (19), (22), (23), (26), (28),
% 244.05/50.56  | | | |            (29), (30), (36), (40), (42), (44), (47), (48), (109) are
% 244.05/50.56  | | | |            inconsistent by sub-proof #1487.
% 244.05/50.56  | | | | 
% 244.05/50.56  | | | End of split
% 244.05/50.56  | | | 
% 244.05/50.56  | | End of split
% 244.05/50.56  | | 
% 244.05/50.56  | End of split
% 244.05/50.56  | 
% 244.05/50.56  End of proof
% 244.05/50.56  
% 244.05/50.56  Sub-proof #1453 shows that the following formulas are inconsistent:
% 244.05/50.56  ----------------------------------------------------------------
% 244.05/50.56    (1)   ~ (e3 = e0)
% 244.05/50.56    (2)   ~ (e2 = e0)
% 244.05/50.56    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.56         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.56    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.56         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.56    (5)  op(e0, e2) = e2
% 244.05/50.56    (6)   ~ (e3 = e1)
% 244.05/50.56    (7)  all_58_7 = e2
% 244.05/50.56    (8)   ~ (e3 = e2)
% 244.05/50.56    (9)  all_58_13 = e2
% 244.05/50.56    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.56    (11)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.56          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.05/50.56    (12)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.05/50.56          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.05/50.56    (13)   ~ (e1 = e0)
% 244.05/50.56    (14)   ~ (e2 = e1)
% 244.05/50.56  
% 244.05/50.56  Begin of proof
% 244.05/50.56  | 
% 244.05/50.56  | BETA: splitting (12) gives:
% 244.05/50.56  | 
% 244.05/50.56  | Case 1:
% 244.05/50.56  | | 
% 244.05/50.57  | |   (15)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 244.05/50.57  | |           e3)
% 244.05/50.57  | | 
% 244.05/50.57  | | BETA: splitting (15) gives:
% 244.05/50.57  | | 
% 244.05/50.57  | | Case 1:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (16)  all_58_1 = e3 & op(e3, e2) = e3
% 244.05/50.57  | | | 
% 244.05/50.57  | | | ALPHA: (16) implies:
% 244.05/50.57  | | |   (17)  all_58_1 = e3
% 244.05/50.57  | | |   (18)  op(e3, e2) = e3
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 244.05/50.57  | | |            (17), (18) are inconsistent by sub-proof #1748.
% 244.05/50.57  | | | 
% 244.05/50.57  | | Case 2:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (19)  all_58_3 = e3 & op(e2, e2) = e3
% 244.05/50.57  | | | 
% 244.05/50.57  | | | ALPHA: (19) implies:
% 244.05/50.57  | | |   (20)  all_58_3 = e3
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 244.05/50.57  | | |            (14), (20) are inconsistent by sub-proof #1454.
% 244.05/50.57  | | | 
% 244.05/50.57  | | End of split
% 244.05/50.57  | | 
% 244.05/50.57  | Case 2:
% 244.05/50.57  | | 
% 244.05/50.57  | |   (21)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.05/50.57  | |           e3)
% 244.05/50.57  | | 
% 244.05/50.57  | | BETA: splitting (21) gives:
% 244.05/50.57  | | 
% 244.05/50.57  | | Case 1:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (22)  all_58_7 = e3 & op(e1, e2) = e3
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (7), (8), (22) are inconsistent by sub-proof #1675.
% 244.05/50.57  | | | 
% 244.05/50.57  | | Case 2:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (23)  all_58_13 = e3 & op(e0, e2) = e3
% 244.05/50.57  | | | 
% 244.05/50.57  | | | ALPHA: (23) implies:
% 244.05/50.57  | | |   (24)  op(e0, e2) = e3
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (5), (8), (10), (24) are inconsistent by sub-proof #2254.
% 244.05/50.57  | | | 
% 244.05/50.57  | | End of split
% 244.05/50.57  | | 
% 244.05/50.57  | End of split
% 244.05/50.57  | 
% 244.05/50.57  End of proof
% 244.05/50.57  
% 244.05/50.57  Sub-proof #1454 shows that the following formulas are inconsistent:
% 244.05/50.57  ----------------------------------------------------------------
% 244.05/50.57    (1)   ~ (e3 = e0)
% 244.05/50.57    (2)   ~ (e2 = e0)
% 244.05/50.57    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.57         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.57    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.57         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.57    (5)  op(e0, e2) = e2
% 244.05/50.57    (6)   ~ (e3 = e1)
% 244.05/50.57    (7)  all_58_7 = e2
% 244.05/50.57    (8)  all_58_3 = e3
% 244.05/50.57    (9)   ~ (e3 = e2)
% 244.05/50.57    (10)  all_58_13 = e2
% 244.05/50.57    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.57    (12)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.57          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.05/50.57    (13)   ~ (e1 = e0)
% 244.05/50.57    (14)   ~ (e2 = e1)
% 244.05/50.57  
% 244.05/50.57  Begin of proof
% 244.05/50.57  | 
% 244.05/50.57  | BETA: splitting (12) gives:
% 244.05/50.57  | 
% 244.05/50.57  | Case 1:
% 244.05/50.57  | | 
% 244.05/50.57  | |   (15)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 244.05/50.57  | |           e1)
% 244.05/50.57  | | 
% 244.05/50.57  | | BETA: splitting (15) gives:
% 244.05/50.57  | | 
% 244.05/50.57  | | Case 1:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (16)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.57  | | | 
% 244.05/50.57  | | | ALPHA: (16) implies:
% 244.05/50.57  | | |   (17)  all_58_1 = e1
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (11), (13), (17) are inconsistent
% 244.05/50.57  | | |            by sub-proof #1461.
% 244.05/50.57  | | | 
% 244.05/50.57  | | Case 2:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (18)  all_58_3 = e1 & op(e2, e2) = e1
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (6), (8), (18) are inconsistent by sub-proof #2197.
% 244.05/50.57  | | | 
% 244.05/50.57  | | End of split
% 244.05/50.57  | | 
% 244.05/50.57  | Case 2:
% 244.05/50.57  | | 
% 244.05/50.57  | |   (19)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 244.05/50.57  | |           e1)
% 244.05/50.57  | | 
% 244.05/50.57  | | BETA: splitting (19) gives:
% 244.05/50.57  | | 
% 244.05/50.57  | | Case 1:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (20)  all_58_7 = e1 & op(e1, e2) = e1
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (13), (14), (20) are
% 244.05/50.57  | | |            inconsistent by sub-proof #1456.
% 244.05/50.57  | | | 
% 244.05/50.57  | | Case 2:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (21)  all_58_13 = e1 & op(e0, e2) = e1
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (13), (14), (21) are
% 244.05/50.57  | | |            inconsistent by sub-proof #1455.
% 244.05/50.57  | | | 
% 244.05/50.57  | | End of split
% 244.05/50.57  | | 
% 244.05/50.57  | End of split
% 244.05/50.57  | 
% 244.05/50.57  End of proof
% 244.05/50.57  
% 244.05/50.57  Sub-proof #1455 shows that the following formulas are inconsistent:
% 244.05/50.57  ----------------------------------------------------------------
% 244.05/50.57    (1)   ~ (e3 = e0)
% 244.05/50.57    (2)   ~ (e2 = e0)
% 244.05/50.57    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.57         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.57    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.57         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.57    (5)  all_58_7 = e2
% 244.05/50.57    (6)  all_58_3 = e3
% 244.05/50.57    (7)   ~ (e3 = e2)
% 244.05/50.57    (8)  all_58_13 = e2
% 244.05/50.57    (9)   ~ (e1 = e0)
% 244.05/50.57    (10)  all_58_13 = e1 & op(e0, e2) = e1
% 244.05/50.57    (11)   ~ (e2 = e1)
% 244.05/50.57  
% 244.05/50.57  Begin of proof
% 244.05/50.57  | 
% 244.05/50.57  | ALPHA: (10) implies:
% 244.05/50.57  |   (12)  all_58_13 = e1
% 244.05/50.57  | 
% 244.05/50.57  | COMBINE_EQS: (8), (12) imply:
% 244.05/50.57  |   (13)  e2 = e1
% 244.05/50.57  | 
% 244.05/50.57  | SIMP: (13) implies:
% 244.05/50.57  |   (14)  e2 = e1
% 244.05/50.57  | 
% 244.05/50.57  | COMBINE_EQS: (5), (14) imply:
% 244.05/50.57  |   (15)  all_58_7 = e1
% 244.05/50.57  | 
% 244.05/50.57  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (11), (12), (15) are
% 244.05/50.57  |            inconsistent by sub-proof #1457.
% 244.05/50.57  | 
% 244.05/50.57  End of proof
% 244.05/50.57  
% 244.05/50.57  Sub-proof #1456 shows that the following formulas are inconsistent:
% 244.05/50.57  ----------------------------------------------------------------
% 244.05/50.57    (1)   ~ (e3 = e0)
% 244.05/50.57    (2)   ~ (e2 = e0)
% 244.05/50.57    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.57         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.57    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.57         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.57    (5)  all_58_7 = e2
% 244.05/50.57    (6)  all_58_3 = e3
% 244.05/50.57    (7)   ~ (e3 = e2)
% 244.05/50.57    (8)  all_58_13 = e2
% 244.05/50.57    (9)  all_58_7 = e1 & op(e1, e2) = e1
% 244.05/50.57    (10)   ~ (e1 = e0)
% 244.05/50.57    (11)   ~ (e2 = e1)
% 244.05/50.57  
% 244.05/50.57  Begin of proof
% 244.05/50.57  | 
% 244.05/50.57  | ALPHA: (9) implies:
% 244.05/50.57  |   (12)  all_58_7 = e1
% 244.05/50.57  | 
% 244.05/50.57  | COMBINE_EQS: (5), (12) imply:
% 244.05/50.57  |   (13)  e2 = e1
% 244.05/50.57  | 
% 244.05/50.57  | COMBINE_EQS: (8), (13) imply:
% 244.05/50.57  |   (14)  all_58_13 = e1
% 244.05/50.57  | 
% 244.05/50.57  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (10), (11), (12), (14) are
% 244.05/50.57  |            inconsistent by sub-proof #1457.
% 244.05/50.57  | 
% 244.05/50.57  End of proof
% 244.05/50.57  
% 244.05/50.57  Sub-proof #1457 shows that the following formulas are inconsistent:
% 244.05/50.57  ----------------------------------------------------------------
% 244.05/50.57    (1)   ~ (e3 = e0)
% 244.05/50.57    (2)   ~ (e2 = e0)
% 244.05/50.57    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.57         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.57    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.57         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.57    (5)  all_58_3 = e3
% 244.05/50.57    (6)   ~ (e3 = e2)
% 244.05/50.57    (7)  all_58_7 = e1
% 244.05/50.57    (8)   ~ (e1 = e0)
% 244.05/50.57    (9)  all_58_13 = e1
% 244.05/50.57    (10)   ~ (e2 = e1)
% 244.05/50.57  
% 244.05/50.57  Begin of proof
% 244.05/50.57  | 
% 244.05/50.57  | BETA: splitting (3) gives:
% 244.05/50.57  | 
% 244.05/50.57  | Case 1:
% 244.05/50.57  | | 
% 244.05/50.57  | |   (11)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 244.05/50.57  | |           e2)
% 244.05/50.57  | | 
% 244.05/50.57  | | BETA: splitting (11) gives:
% 244.05/50.57  | | 
% 244.05/50.57  | | Case 1:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (12)  all_58_1 = e2 & op(e3, e2) = e2
% 244.05/50.57  | | | 
% 244.05/50.57  | | | ALPHA: (12) implies:
% 244.05/50.57  | | |   (13)  all_58_1 = e2
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (13) are inconsistent by
% 244.05/50.57  | | |            sub-proof #1459.
% 244.05/50.57  | | | 
% 244.05/50.57  | | Case 2:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (14)  all_58_3 = e2 & op(e2, e2) = e2
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (5), (6), (14) are inconsistent by sub-proof #1458.
% 244.05/50.57  | | | 
% 244.05/50.57  | | End of split
% 244.05/50.57  | | 
% 244.05/50.57  | Case 2:
% 244.05/50.57  | | 
% 244.05/50.57  | |   (15)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 244.05/50.57  | |           e2)
% 244.05/50.57  | | 
% 244.05/50.57  | | BETA: splitting (15) gives:
% 244.05/50.57  | | 
% 244.05/50.57  | | Case 1:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (16)  all_58_7 = e2 & op(e1, e2) = e2
% 244.05/50.57  | | | 
% 244.05/50.57  | | | ALPHA: (16) implies:
% 244.05/50.57  | | |   (17)  all_58_7 = e2
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (7), (10), (17) are inconsistent by sub-proof #2134.
% 244.05/50.57  | | | 
% 244.05/50.57  | | Case 2:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (18)  all_58_13 = e2 & op(e0, e2) = e2
% 244.05/50.57  | | | 
% 244.05/50.57  | | | ALPHA: (18) implies:
% 244.05/50.57  | | |   (19)  all_58_13 = e2
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (9), (10), (19) are inconsistent by sub-proof #1544.
% 244.05/50.57  | | | 
% 244.05/50.57  | | End of split
% 244.05/50.57  | | 
% 244.05/50.57  | End of split
% 244.05/50.57  | 
% 244.05/50.57  End of proof
% 244.05/50.57  
% 244.05/50.57  Sub-proof #1458 shows that the following formulas are inconsistent:
% 244.05/50.57  ----------------------------------------------------------------
% 244.05/50.57    (1)  all_58_3 = e2 & op(e2, e2) = e2
% 244.05/50.57    (2)  all_58_3 = e3
% 244.05/50.57    (3)   ~ (e3 = e2)
% 244.05/50.57  
% 244.05/50.57  Begin of proof
% 244.05/50.57  | 
% 244.05/50.57  | ALPHA: (1) implies:
% 244.05/50.57  |   (4)  all_58_3 = e2
% 244.05/50.57  | 
% 244.05/50.57  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.57  |   (5)  e3 = e2
% 244.05/50.57  | 
% 244.05/50.57  | REDUCE: (3), (5) imply:
% 244.05/50.57  |   (6)  $false
% 244.05/50.57  | 
% 244.05/50.57  | CLOSE: (6) is inconsistent.
% 244.05/50.57  | 
% 244.05/50.57  End of proof
% 244.05/50.57  
% 244.05/50.57  Sub-proof #1459 shows that the following formulas are inconsistent:
% 244.05/50.57  ----------------------------------------------------------------
% 244.05/50.57    (1)   ~ (e3 = e0)
% 244.05/50.57    (2)   ~ (e2 = e0)
% 244.05/50.57    (3)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.57         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.57    (4)  all_58_3 = e3
% 244.05/50.57    (5)  all_58_7 = e1
% 244.05/50.57    (6)  all_58_1 = e2
% 244.05/50.57    (7)   ~ (e1 = e0)
% 244.05/50.57    (8)  all_58_13 = e1
% 244.05/50.57  
% 244.05/50.57  Begin of proof
% 244.05/50.57  | 
% 244.05/50.57  | BETA: splitting (3) gives:
% 244.05/50.57  | 
% 244.05/50.57  | Case 1:
% 244.05/50.57  | | 
% 244.05/50.57  | |   (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 244.05/50.57  | | 
% 244.05/50.57  | | BETA: splitting (9) gives:
% 244.05/50.57  | | 
% 244.05/50.57  | | Case 1:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (10)  all_58_1 = e0 & op(e3, e2) = e0
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #2187.
% 244.05/50.57  | | | 
% 244.05/50.57  | | Case 2:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (11)  all_58_3 = e0 & op(e2, e2) = e0
% 244.05/50.57  | | | 
% 244.05/50.57  | | | ALPHA: (11) implies:
% 244.05/50.57  | | |   (12)  all_58_3 = e0
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (1), (4), (12) are inconsistent by sub-proof #1460.
% 244.05/50.57  | | | 
% 244.05/50.57  | | End of split
% 244.05/50.57  | | 
% 244.05/50.57  | Case 2:
% 244.05/50.57  | | 
% 244.05/50.57  | |   (13)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.05/50.57  | |           e0)
% 244.05/50.57  | | 
% 244.05/50.57  | | BETA: splitting (13) gives:
% 244.05/50.57  | | 
% 244.05/50.57  | | Case 1:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (14)  all_58_7 = e0 & op(e1, e2) = e0
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (5), (7), (14) are inconsistent by sub-proof #1558.
% 244.05/50.57  | | | 
% 244.05/50.57  | | Case 2:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (15)  all_58_13 = e0 & op(e0, e2) = e0
% 244.05/50.57  | | | 
% 244.05/50.57  | | | ALPHA: (15) implies:
% 244.05/50.57  | | |   (16)  all_58_13 = e0
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (7), (8), (16) are inconsistent by sub-proof #2082.
% 244.05/50.57  | | | 
% 244.05/50.57  | | End of split
% 244.05/50.57  | | 
% 244.05/50.57  | End of split
% 244.05/50.57  | 
% 244.05/50.57  End of proof
% 244.05/50.57  
% 244.05/50.57  Sub-proof #1460 shows that the following formulas are inconsistent:
% 244.05/50.57  ----------------------------------------------------------------
% 244.05/50.57    (1)  all_58_3 = e3
% 244.05/50.57    (2)  all_58_3 = e0
% 244.05/50.57    (3)   ~ (e3 = e0)
% 244.05/50.57  
% 244.05/50.57  Begin of proof
% 244.05/50.57  | 
% 244.05/50.57  | COMBINE_EQS: (1), (2) imply:
% 244.05/50.57  |   (4)  e3 = e0
% 244.05/50.57  | 
% 244.05/50.57  | SIMP: (4) implies:
% 244.05/50.57  |   (5)  e3 = e0
% 244.05/50.57  | 
% 244.05/50.57  | REDUCE: (3), (5) imply:
% 244.05/50.57  |   (6)  $false
% 244.05/50.57  | 
% 244.05/50.57  | CLOSE: (6) is inconsistent.
% 244.05/50.57  | 
% 244.05/50.57  End of proof
% 244.05/50.57  
% 244.05/50.57  Sub-proof #1461 shows that the following formulas are inconsistent:
% 244.05/50.57  ----------------------------------------------------------------
% 244.05/50.57    (1)  all_58_1 = e1
% 244.05/50.57    (2)   ~ (e3 = e0)
% 244.05/50.57    (3)   ~ (e2 = e0)
% 244.05/50.57    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.57         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.57    (5)  op(e0, e2) = e2
% 244.05/50.57    (6)  all_58_7 = e2
% 244.05/50.57    (7)  all_58_3 = e3
% 244.05/50.57    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.57    (9)   ~ (e1 = e0)
% 244.05/50.57  
% 244.05/50.57  Begin of proof
% 244.05/50.57  | 
% 244.05/50.57  | BETA: splitting (4) gives:
% 244.05/50.57  | 
% 244.05/50.57  | Case 1:
% 244.05/50.57  | | 
% 244.05/50.57  | |   (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 244.05/50.57  | |           e0)
% 244.05/50.57  | | 
% 244.05/50.57  | | BETA: splitting (10) gives:
% 244.05/50.57  | | 
% 244.05/50.57  | | Case 1:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (11)  all_58_1 = e0 & op(e3, e2) = e0
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (1), (9), (11) are inconsistent by sub-proof #1720.
% 244.05/50.57  | | | 
% 244.05/50.57  | | Case 2:
% 244.05/50.57  | | | 
% 244.05/50.57  | | |   (12)  all_58_3 = e0 & op(e2, e2) = e0
% 244.05/50.57  | | | 
% 244.05/50.57  | | | REF_CLOSE: (2), (7), (12) are inconsistent by sub-proof #1719.
% 244.05/50.57  | | | 
% 244.05/50.57  | | End of split
% 244.05/50.57  | | 
% 244.05/50.57  | Case 2:
% 244.05/50.57  | | 
% 244.05/50.57  | |   (13)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.05/50.57  | |           e0)
% 244.05/50.57  | | 
% 244.05/50.57  | | REF_CLOSE: (3), (5), (6), (8), (13) are inconsistent by sub-proof #1749.
% 244.05/50.57  | | 
% 244.05/50.57  | End of split
% 244.05/50.57  | 
% 244.05/50.57  End of proof
% 244.05/50.57  
% 244.05/50.57  Sub-proof #1462 shows that the following formulas are inconsistent:
% 244.05/50.57  ----------------------------------------------------------------
% 244.05/50.57    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.57         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.57    (2)   ~ (e3 = e0)
% 244.05/50.57    (3)  op(e0, e1) = all_52_11
% 244.05/50.57    (4)   ~ (e2 = e0)
% 244.05/50.57    (5)  op(e1, e2) = all_52_6
% 244.05/50.57    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.57         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.57    (7)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.57         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.57    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.57         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.57    (9)  op(e1, e0) = all_52_14
% 244.05/50.57    (10)   ~ (e3 = e1)
% 244.05/50.57    (11)  op(e0, e2) = e3
% 244.05/50.57    (12)  op(e2, e2) = e0
% 244.05/50.57    (13)  all_58_11 = e3
% 244.05/50.57    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.57          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.57    (15)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.57              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 244.05/50.57                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.05/50.57                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.05/50.57    (16)   ~ (all_52_11 = e3)
% 244.05/50.57    (17)  op(e2, e1) = all_52_9
% 244.05/50.57    (18)   ~ (e3 = e2)
% 244.05/50.57    (19)  op(e0, all_52_11) = e0
% 244.05/50.57    (20)  op(e1, e0) = e3
% 244.05/50.57    (21)  all_58_10 = e2
% 244.05/50.57    (22)   ~ (all_52_14 = e0)
% 244.05/50.57    (23)  op(e1, e0) = all_28_1
% 244.05/50.57    (24)  op(e2, e0) = e2
% 244.05/50.57    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.57          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.57    (26)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.05/50.57          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.05/50.57    (27)   ~ (all_52_4 = e3)
% 244.05/50.57    (28)  op(e3, e2) = all_52_4
% 244.05/50.57    (29)   ~ (all_52_9 = e3)
% 244.05/50.57    (30)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.05/50.57          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.05/50.57    (31)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.57          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.58    (32)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.05/50.58          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.05/50.58    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.58    (34)  op(e0, e0) = e0
% 244.05/50.58    (35)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.58          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.58    (36)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.58          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.05/50.58    (37)  op(e1, e1) = e0
% 244.05/50.58    (38)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.05/50.58          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.05/50.58    (39)   ~ (e1 = e0)
% 244.05/50.58    (40)  op(e3, e3) = e0
% 244.05/50.58    (41)  all_58_4 = e3
% 244.05/50.58    (42)  all_58_2 = e3
% 244.05/50.58    (43)   ~ (all_52_13 = e3)
% 244.05/50.58    (44)  all_58_15 = e0
% 244.05/50.58    (45)  op(e2, e0) = all_52_13
% 244.05/50.58    (46)  all_58_3 = e0
% 244.05/50.58    (47)   ~ (all_28_1 = e2)
% 244.05/50.58    (48)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.58          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.05/50.58            e2)
% 244.05/50.58    (49)   ~ (all_52_13 = e0)
% 244.05/50.58    (50)  all_58_13 = e3
% 244.05/50.58    (51)   ~ (e2 = e1)
% 244.05/50.58  
% 244.05/50.58  Begin of proof
% 244.05/50.58  | 
% 244.05/50.58  | BETA: splitting (7) gives:
% 244.05/50.58  | 
% 244.05/50.58  | Case 1:
% 244.05/50.58  | | 
% 244.05/50.58  | |   (52)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 244.05/50.58  | |           e1)
% 244.05/50.58  | | 
% 244.05/50.58  | | BETA: splitting (52) gives:
% 244.05/50.58  | | 
% 244.05/50.58  | | Case 1:
% 244.05/50.58  | | | 
% 244.05/50.58  | | |   (53)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.58  | | | 
% 244.05/50.58  | | | ALPHA: (53) implies:
% 244.05/50.58  | | |   (54)  all_58_9 = e1
% 244.05/50.58  | | | 
% 244.05/50.58  | | | BETA: splitting (1) gives:
% 244.05/50.58  | | | 
% 244.05/50.58  | | | Case 1:
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | |   (55)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 244.05/50.58  | | | |           = e2)
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | | BETA: splitting (55) gives:
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | | Case 1:
% 244.05/50.58  | | | | | 
% 244.05/50.58  | | | | |   (56)  all_58_0 = e2 & op(e3, e3) = e2
% 244.05/50.58  | | | | | 
% 244.05/50.58  | | | | | ALPHA: (56) implies:
% 244.05/50.58  | | | | |   (57)  op(e3, e3) = e2
% 244.05/50.58  | | | | | 
% 244.05/50.58  | | | | | REF_CLOSE: (4), (33), (40), (57) are inconsistent by sub-proof #2188.
% 244.05/50.58  | | | | | 
% 244.05/50.58  | | | | Case 2:
% 244.05/50.58  | | | | | 
% 244.05/50.58  | | | | |   (58)  all_58_1 = e2 & op(e3, e2) = e2
% 244.05/50.58  | | | | | 
% 244.05/50.58  | | | | | ALPHA: (58) implies:
% 244.05/50.58  | | | | |   (59)  all_58_1 = e2
% 244.05/50.58  | | | | |   (60)  op(e3, e2) = e2
% 244.05/50.58  | | | | | 
% 244.05/50.58  | | | | | BETA: splitting (36) gives:
% 244.05/50.58  | | | | | 
% 244.05/50.58  | | | | | Case 1:
% 244.05/50.58  | | | | | | 
% 244.05/50.58  | | | | | |   (61)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 244.05/50.58  | | | | | |             e2) = e1)
% 244.05/50.58  | | | | | | 
% 244.05/50.58  | | | | | | REF_CLOSE: (2), (4), (7), (10), (13), (18), (31), (33), (34), (35),
% 244.05/50.58  | | | | | |            (39), (43), (45), (46), (51), (54), (60), (61) are
% 244.05/50.58  | | | | | |            inconsistent by sub-proof #1499.
% 244.05/50.58  | | | | | | 
% 244.05/50.58  | | | | | Case 2:
% 244.05/50.58  | | | | | | 
% 244.05/50.58  | | | | | |   (62)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 244.05/50.58  | | | | | |             e2) = e1)
% 244.05/50.58  | | | | | | 
% 244.05/50.58  | | | | | | BETA: splitting (62) gives:
% 244.05/50.58  | | | | | | 
% 244.05/50.58  | | | | | | Case 1:
% 244.05/50.58  | | | | | | | 
% 244.05/50.58  | | | | | | |   (63)  all_58_7 = e1 & op(e1, e2) = e1
% 244.05/50.58  | | | | | | | 
% 244.05/50.58  | | | | | | | ALPHA: (63) implies:
% 244.05/50.58  | | | | | | |   (64)  all_58_7 = e1
% 244.05/50.58  | | | | | | |   (65)  op(e1, e2) = e1
% 244.05/50.58  | | | | | | | 
% 244.05/50.58  | | | | | | | BETA: splitting (32) gives:
% 244.05/50.58  | | | | | | | 
% 244.05/50.58  | | | | | | | Case 1:
% 244.05/50.58  | | | | | | | | 
% 244.05/50.58  | | | | | | | |   (66)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 244.05/50.58  | | | | | | | |           op(e1, e2) = e2)
% 244.05/50.58  | | | | | | | | 
% 244.05/50.58  | | | | | | | | BETA: splitting (66) gives:
% 244.05/50.58  | | | | | | | | 
% 244.05/50.58  | | | | | | | | Case 1:
% 244.05/50.58  | | | | | | | | | 
% 244.05/50.58  | | | | | | | | |   (67)  all_58_6 = e2 & op(e1, e3) = e2
% 244.05/50.58  | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | ALPHA: (67) implies:
% 244.05/50.58  | | | | | | | | |   (68)  op(e1, e3) = e2
% 244.05/50.58  | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | BETA: splitting (30) gives:
% 244.05/50.58  | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | Case 1:
% 244.05/50.58  | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | |   (69)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 244.05/50.58  | | | | | | | | | |           op(e2, e3) = e1)
% 244.05/50.58  | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | BETA: splitting (69) gives:
% 244.05/50.58  | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | Case 1:
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | |   (70)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | ALPHA: (70) implies:
% 244.05/50.58  | | | | | | | | | | |   (71)  op(e3, e3) = e1
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (7), (10), (13), (14), (18), (21),
% 244.05/50.58  | | | | | | | | | | |            (25), (27), (28), (33), (34), (39), (41), (51),
% 244.05/50.58  | | | | | | | | | | |            (54), (71) are inconsistent by sub-proof #1464.
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | Case 2:
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | |   (72)  all_58_2 = e1 & op(e2, e3) = e1
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | REF_CLOSE: (10), (42), (72) are inconsistent by sub-proof
% 244.05/50.58  | | | | | | | | | | |            #1765.
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | End of split
% 244.05/50.58  | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | Case 2:
% 244.05/50.58  | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | |   (73)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 244.05/50.58  | | | | | | | | | |           & op(e0, e3) = e1)
% 244.05/50.58  | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | BETA: splitting (73) gives:
% 244.05/50.58  | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | Case 1:
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | |   (74)  all_58_6 = e1 & op(e1, e3) = e1
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | ALPHA: (74) implies:
% 244.05/50.58  | | | | | | | | | | |   (75)  op(e1, e3) = e1
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | REF_CLOSE: (33), (51), (68), (75) are inconsistent by
% 244.05/50.58  | | | | | | | | | | |            sub-proof #2226.
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | Case 2:
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | |   (76)  all_58_12 = e1 & op(e0, e3) = e1
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | ALPHA: (76) implies:
% 244.05/50.58  | | | | | | | | | | |   (77)  all_58_12 = e1
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | BETA: splitting (48) gives:
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | Case 1:
% 244.05/50.58  | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | |   (78)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 244.05/50.58  | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 244.05/50.58  | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | BETA: splitting (78) gives:
% 244.05/50.58  | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | Case 1:
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | |   (79)  all_58_12 = e2 & op(e0, e3) = e2
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | ALPHA: (79) implies:
% 244.05/50.58  | | | | | | | | | | | | |   (80)  all_58_12 = e2
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | COMBINE_EQS: (77), (80) imply:
% 244.05/50.58  | | | | | | | | | | | | |   (81)  e2 = e1
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (12), (18), (33),
% 244.05/50.58  | | | | | | | | | | | | |            (38), (39), (51), (59), (64), (65), (81) are
% 244.05/50.58  | | | | | | | | | | | | |            inconsistent by sub-proof #1497.
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | Case 2:
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | |   (82)  all_58_13 = e2 & op(e0, e2) = e2
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | ALPHA: (82) implies:
% 244.05/50.58  | | | | | | | | | | | | |   (83)  op(e0, e2) = e2
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | REF_CLOSE: (11), (18), (33), (83) are inconsistent by
% 244.05/50.58  | | | | | | | | | | | | |            sub-proof #2254.
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | End of split
% 244.05/50.58  | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | Case 2:
% 244.05/50.58  | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | |   (84)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 244.05/50.58  | | | | | | | | | | | |           e2 & op(e0, e0) = e2)
% 244.05/50.58  | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | BETA: splitting (84) gives:
% 244.05/50.58  | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | Case 1:
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | |   (85)  all_58_14 = e2 & op(e0, e1) = e2
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | BETA: splitting (35) gives:
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | Case 1:
% 244.05/50.58  | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | |   (86)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 244.05/50.58  | | | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 244.05/50.58  | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 244.05/50.58  | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | Case 1:
% 244.05/50.58  | | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | |   (87)  all_58_9 = e2 & op(e3, e0) = e2
% 244.05/50.58  | | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 244.05/50.58  | | | | | | | | | | | | | | |   (88)  all_58_9 = e2
% 244.05/50.58  | | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | | COMBINE_EQS: (54), (88) imply:
% 244.05/50.58  | | | | | | | | | | | | | | |   (89)  e2 = e1
% 244.05/50.58  | | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (12), (18), (33),
% 244.05/50.58  | | | | | | | | | | | | | | |            (38), (39), (51), (59), (64), (65), (89) are
% 244.05/50.58  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1497.
% 244.05/50.58  | | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | Case 2:
% 244.05/50.58  | | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | | ALPHA: (85) implies:
% 244.05/50.58  | | | | | | | | | | | | | | |   (90)  op(e0, e1) = e2
% 244.05/50.58  | | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_52_11, e2, e1, e0,
% 244.05/50.58  | | | | | | | | | | | | | | |              simplifying with (3), (90) gives:
% 244.05/50.58  | | | | | | | | | | | | | | |   (91)  all_52_11 = e2
% 244.05/50.58  | | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | | REDUCE: (19), (91) imply:
% 244.05/50.58  | | | | | | | | | | | | | | |   (92)  op(e0, e2) = e0
% 244.05/50.58  | | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | | REF_CLOSE: (2), (11), (33), (92) are inconsistent by
% 244.05/50.58  | | | | | | | | | | | | | | |            sub-proof #1961.
% 244.05/50.58  | | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | End of split
% 244.05/50.58  | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | Case 2:
% 244.05/50.58  | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | |   (93)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 244.05/50.58  | | | | | | | | | | | | | |           e2 & op(e0, e0) = e2)
% 244.05/50.58  | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (9), (10), (15), (18), (22), (23),
% 244.05/50.58  | | | | | | | | | | | | | |            (31), (33), (34), (35), (39), (43), (45), (47),
% 244.05/50.58  | | | | | | | | | | | | | |            (49), (51), (93) are inconsistent by sub-proof
% 244.05/50.58  | | | | | | | | | | | | | |            #1487.
% 244.05/50.58  | | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | End of split
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | Case 2:
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | |   (94)  all_58_15 = e2 & op(e0, e0) = e2
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (9), (10), (15), (18), (22), (31),
% 244.05/50.58  | | | | | | | | | | | | |            (33), (34), (35), (39), (43), (45), (49), (51),
% 244.05/50.58  | | | | | | | | | | | | |            (94) are inconsistent by sub-proof #1488.
% 244.05/50.58  | | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | | End of split
% 244.05/50.58  | | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | | End of split
% 244.05/50.58  | | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | | End of split
% 244.05/50.58  | | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | End of split
% 244.05/50.58  | | | | | | | | | 
% 244.05/50.58  | | | | | | | | Case 2:
% 244.05/50.58  | | | | | | | | | 
% 244.05/50.58  | | | | | | | | |   (95)  all_58_7 = e2 & op(e1, e2) = e2
% 244.05/50.58  | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | ALPHA: (95) implies:
% 244.05/50.58  | | | | | | | | |   (96)  all_58_7 = e2
% 244.05/50.58  | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | COMBINE_EQS: (64), (96) imply:
% 244.05/50.58  | | | | | | | | |   (97)  e2 = e1
% 244.05/50.58  | | | | | | | | | 
% 244.05/50.58  | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (12), (18), (33),
% 244.05/50.58  | | | | | | | | |            (38), (39), (51), (59), (64), (65), (97) are
% 244.05/50.58  | | | | | | | | |            inconsistent by sub-proof #1497.
% 244.05/50.58  | | | | | | | | | 
% 244.05/50.58  | | | | | | | | End of split
% 244.05/50.58  | | | | | | | | 
% 244.05/50.58  | | | | | | | Case 2:
% 244.05/50.58  | | | | | | | | 
% 244.05/50.58  | | | | | | | |   (98)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 244.05/50.58  | | | | | | | |           op(e1, e0) = e2)
% 244.05/50.58  | | | | | | | | 
% 244.05/50.58  | | | | | | | | REF_CLOSE: (4), (23), (33), (37), (47), (98) are inconsistent by
% 244.05/50.58  | | | | | | | |            sub-proof #1463.
% 244.05/50.58  | | | | | | | | 
% 244.05/50.58  | | | | | | | End of split
% 244.05/50.58  | | | | | | | 
% 244.05/50.58  | | | | | | Case 2:
% 244.05/50.58  | | | | | | | 
% 244.05/50.58  | | | | | | |   (99)  all_58_13 = e1 & op(e0, e2) = e1
% 244.05/50.58  | | | | | | | 
% 244.05/50.58  | | | | | | | REF_CLOSE: (10), (50), (99) are inconsistent by sub-proof #2013.
% 244.05/50.58  | | | | | | | 
% 244.05/50.58  | | | | | | End of split
% 244.05/50.58  | | | | | | 
% 244.05/50.58  | | | | | End of split
% 244.05/50.58  | | | | | 
% 244.05/50.58  | | | | End of split
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | Case 2:
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | |   (100)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 244.05/50.58  | | | |            = e2)
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | | REF_CLOSE: (2), (3), (4), (10), (16), (17), (18), (21), (26), (29),
% 244.05/50.58  | | | |            (31), (33), (35), (37), (44), (51), (54), (100) are
% 244.05/50.58  | | | |            inconsistent by sub-proof #1492.
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | End of split
% 244.05/50.58  | | | 
% 244.05/50.58  | | Case 2:
% 244.05/50.58  | | | 
% 244.05/50.58  | | |   (101)  all_58_10 = e1 & op(e2, e0) = e1
% 244.05/50.58  | | | 
% 244.05/50.58  | | | ALPHA: (101) implies:
% 244.05/50.58  | | |   (102)  op(e2, e0) = e1
% 244.05/50.58  | | | 
% 244.05/50.58  | | | REF_CLOSE: (24), (33), (51), (102) are inconsistent by sub-proof #1659.
% 244.05/50.58  | | | 
% 244.05/50.58  | | End of split
% 244.05/50.58  | | 
% 244.05/50.58  | Case 2:
% 244.05/50.58  | | 
% 244.05/50.58  | |   (103)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.05/50.58  | |            e1)
% 244.05/50.58  | | 
% 244.05/50.58  | | REF_CLOSE: (10), (20), (33), (34), (39), (103) are inconsistent by sub-proof
% 244.05/50.58  | |            #1583.
% 244.05/50.58  | | 
% 244.05/50.58  | End of split
% 244.05/50.58  | 
% 244.05/50.58  End of proof
% 244.05/50.58  
% 244.05/50.58  Sub-proof #1463 shows that the following formulas are inconsistent:
% 244.05/50.58  ----------------------------------------------------------------
% 244.05/50.58    (1)   ~ (e2 = e0)
% 244.05/50.58    (2)  op(e1, e0) = all_28_1
% 244.05/50.58    (3)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.05/50.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.58    (5)  op(e1, e1) = e0
% 244.05/50.58    (6)   ~ (all_28_1 = e2)
% 244.05/50.58  
% 244.05/50.58  Begin of proof
% 244.05/50.58  | 
% 244.05/50.58  | BETA: splitting (3) gives:
% 244.05/50.58  | 
% 244.05/50.58  | Case 1:
% 244.05/50.58  | | 
% 244.05/50.58  | |   (7)  all_58_8 = e2 & op(e1, e1) = e2
% 244.05/50.58  | | 
% 244.05/50.58  | | ALPHA: (7) implies:
% 244.05/50.58  | |   (8)  op(e1, e1) = e2
% 244.05/50.58  | | 
% 244.05/50.58  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2211.
% 244.05/50.58  | | 
% 244.05/50.58  | Case 2:
% 244.05/50.58  | | 
% 244.05/50.58  | |   (9)  all_58_11 = e2 & op(e1, e0) = e2
% 244.05/50.58  | | 
% 244.05/50.58  | | ALPHA: (9) implies:
% 244.05/50.58  | |   (10)  op(e1, e0) = e2
% 244.05/50.58  | | 
% 244.05/50.58  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #1944.
% 244.05/50.58  | | 
% 244.05/50.58  | End of split
% 244.05/50.58  | 
% 244.05/50.58  End of proof
% 244.05/50.58  
% 244.05/50.58  Sub-proof #1464 shows that the following formulas are inconsistent:
% 244.05/50.58  ----------------------------------------------------------------
% 244.05/50.58    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.58         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.58    (2)   ~ (e3 = e0)
% 244.05/50.58    (3)   ~ (e2 = e0)
% 244.05/50.58    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.58         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.58    (5)   ~ (e3 = e1)
% 244.05/50.58    (6)  all_58_11 = e3
% 244.05/50.58    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.58         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.58    (8)  op(e3, e3) = e1
% 244.05/50.58    (9)   ~ (e3 = e2)
% 244.05/50.58    (10)  all_58_10 = e2
% 244.05/50.58    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.58          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.58    (12)   ~ (all_52_4 = e3)
% 244.05/50.58    (13)  op(e3, e2) = all_52_4
% 244.05/50.58    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.58    (15)  op(e0, e0) = e0
% 244.05/50.58    (16)   ~ (e1 = e0)
% 244.05/50.58    (17)  all_58_4 = e3
% 244.05/50.58    (18)  all_58_9 = e1
% 244.05/50.58    (19)   ~ (e2 = e1)
% 244.05/50.58  
% 244.05/50.58  Begin of proof
% 244.05/50.58  | 
% 244.05/50.58  | BETA: splitting (11) gives:
% 244.05/50.58  | 
% 244.05/50.58  | Case 1:
% 244.05/50.58  | | 
% 244.05/50.58  | |   (20)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 244.05/50.58  | |           e0)
% 244.05/50.58  | | 
% 244.05/50.58  | | BETA: splitting (20) gives:
% 244.05/50.58  | | 
% 244.05/50.58  | | Case 1:
% 244.05/50.58  | | | 
% 244.05/50.58  | | |   (21)  all_58_0 = e0 & op(e3, e3) = e0
% 244.05/50.58  | | | 
% 244.05/50.58  | | | ALPHA: (21) implies:
% 244.05/50.58  | | |   (22)  op(e3, e3) = e0
% 244.05/50.58  | | | 
% 244.05/50.58  | | | REF_CLOSE: (8), (14), (16), (22) are inconsistent by sub-proof #1828.
% 244.05/50.58  | | | 
% 244.05/50.58  | | Case 2:
% 244.05/50.58  | | | 
% 244.05/50.58  | | |   (23)  all_58_1 = e0 & op(e3, e2) = e0
% 244.05/50.58  | | | 
% 244.05/50.58  | | | ALPHA: (23) implies:
% 244.05/50.58  | | |   (24)  all_58_1 = e0
% 244.05/50.58  | | | 
% 244.05/50.58  | | | BETA: splitting (1) gives:
% 244.05/50.58  | | | 
% 244.05/50.58  | | | Case 1:
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | |   (25)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 244.05/50.58  | | | |           = e2)
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | | REF_CLOSE: (3), (8), (14), (19), (24), (25) are inconsistent by
% 244.05/50.58  | | | |            sub-proof #1477.
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | Case 2:
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | |   (26)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 244.05/50.58  | | | |           = e2)
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | | REF_CLOSE: (9), (17), (18), (19), (26) are inconsistent by sub-proof
% 244.05/50.58  | | | |            #1475.
% 244.05/50.58  | | | | 
% 244.05/50.58  | | | End of split
% 244.05/50.58  | | | 
% 244.05/50.58  | | End of split
% 244.05/50.58  | | 
% 244.05/50.58  | Case 2:
% 244.05/50.58  | | 
% 244.05/50.58  | |   (27)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 244.05/50.58  | |           e0)
% 244.05/50.58  | | 
% 244.05/50.58  | | BETA: splitting (27) gives:
% 244.05/50.58  | | 
% 244.05/50.58  | | Case 1:
% 244.05/50.58  | | | 
% 244.05/50.58  | | |   (28)  all_58_4 = e0 & op(e3, e1) = e0
% 244.05/50.58  | | | 
% 244.05/50.58  | | | REF_CLOSE: (2), (17), (28) are inconsistent by sub-proof #1697.
% 244.05/50.58  | | | 
% 244.05/50.58  | | Case 2:
% 244.05/50.58  | | | 
% 244.05/50.58  | | |   (29)  all_58_9 = e0 & op(e3, e0) = e0
% 244.05/50.58  | | | 
% 244.05/50.58  | | | ALPHA: (29) implies:
% 244.05/50.58  | | |   (30)  all_58_9 = e0
% 244.05/50.58  | | | 
% 244.05/50.58  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 244.05/50.58  | | |            (13), (14), (15), (16), (17), (19), (30) are inconsistent by
% 244.05/50.58  | | |            sub-proof #1465.
% 244.05/50.58  | | | 
% 244.05/50.58  | | End of split
% 244.05/50.58  | | 
% 244.05/50.58  | End of split
% 244.05/50.58  | 
% 244.05/50.58  End of proof
% 244.05/50.58  
% 244.05/50.58  Sub-proof #1465 shows that the following formulas are inconsistent:
% 244.05/50.58  ----------------------------------------------------------------
% 244.05/50.59    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.59         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.59    (2)   ~ (e3 = e0)
% 244.05/50.59    (3)   ~ (e2 = e0)
% 244.05/50.59    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.59         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.59    (5)  all_58_9 = e0
% 244.05/50.59    (6)   ~ (e3 = e1)
% 244.05/50.59    (7)  all_58_11 = e3
% 244.05/50.59    (8)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.59         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.59    (9)  op(e3, e3) = e1
% 244.05/50.59    (10)   ~ (e3 = e2)
% 244.05/50.59    (11)  all_58_10 = e2
% 244.05/50.59    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.59          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.59    (13)   ~ (all_52_4 = e3)
% 244.05/50.59    (14)  op(e3, e2) = all_52_4
% 244.05/50.59    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.59    (16)  op(e0, e0) = e0
% 244.05/50.59    (17)   ~ (e1 = e0)
% 244.05/50.59    (18)  all_58_4 = e3
% 244.05/50.59    (19)   ~ (e2 = e1)
% 244.05/50.59  
% 244.05/50.59  Begin of proof
% 244.05/50.59  | 
% 244.05/50.59  | BETA: splitting (4) gives:
% 244.05/50.59  | 
% 244.05/50.59  | Case 1:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (20)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 244.05/50.59  | |           e1)
% 244.05/50.59  | | 
% 244.05/50.59  | | BETA: splitting (20) gives:
% 244.05/50.59  | | 
% 244.05/50.59  | | Case 1:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (21)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (5), (17), (21) are inconsistent by sub-proof #2183.
% 244.05/50.59  | | | 
% 244.05/50.59  | | Case 2:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (22)  all_58_10 = e1 & op(e2, e0) = e1
% 244.05/50.59  | | | 
% 244.05/50.59  | | | ALPHA: (22) implies:
% 244.05/50.59  | | |   (23)  all_58_10 = e1
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (11), (19), (23) are inconsistent by sub-proof #1598.
% 244.05/50.59  | | | 
% 244.05/50.59  | | End of split
% 244.05/50.59  | | 
% 244.05/50.59  | Case 2:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (24)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.05/50.59  | |           e1)
% 244.05/50.59  | | 
% 244.05/50.59  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (12), (13), (14), (15),
% 244.05/50.59  | |            (16), (17), (18), (19), (24) are inconsistent by sub-proof #1466.
% 244.05/50.59  | | 
% 244.05/50.59  | End of split
% 244.05/50.59  | 
% 244.05/50.59  End of proof
% 244.05/50.59  
% 244.05/50.59  Sub-proof #1466 shows that the following formulas are inconsistent:
% 244.05/50.59  ----------------------------------------------------------------
% 244.05/50.59    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.59         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.59    (2)   ~ (e3 = e0)
% 244.05/50.59    (3)   ~ (e2 = e0)
% 244.05/50.59    (4)   ~ (e3 = e1)
% 244.05/50.59    (5)  all_58_11 = e3
% 244.05/50.59    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.59         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.59    (7)  op(e3, e3) = e1
% 244.05/50.59    (8)   ~ (e3 = e2)
% 244.05/50.59    (9)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.59    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.59          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.59    (11)   ~ (all_52_4 = e3)
% 244.05/50.59    (12)  op(e3, e2) = all_52_4
% 244.05/50.59    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.59    (14)  op(e0, e0) = e0
% 244.05/50.59    (15)   ~ (e1 = e0)
% 244.05/50.59    (16)  all_58_4 = e3
% 244.05/50.59    (17)   ~ (e2 = e1)
% 244.05/50.59  
% 244.05/50.59  Begin of proof
% 244.05/50.59  | 
% 244.05/50.59  | BETA: splitting (9) gives:
% 244.05/50.59  | 
% 244.05/50.59  | Case 1:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (18)  all_58_11 = e1 & op(e1, e0) = e1
% 244.05/50.59  | | 
% 244.05/50.59  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 244.05/50.59  | |            (15), (16), (17), (18) are inconsistent by sub-proof #1467.
% 244.05/50.59  | | 
% 244.05/50.59  | Case 2:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (19)  all_58_15 = e1 & op(e0, e0) = e1
% 244.05/50.59  | | 
% 244.05/50.59  | | ALPHA: (19) implies:
% 244.05/50.59  | |   (20)  op(e0, e0) = e1
% 244.05/50.59  | | 
% 244.05/50.59  | | REF_CLOSE: (13), (14), (15), (20) are inconsistent by sub-proof #2274.
% 244.05/50.59  | | 
% 244.05/50.59  | End of split
% 244.05/50.59  | 
% 244.05/50.59  End of proof
% 244.05/50.59  
% 244.05/50.59  Sub-proof #1467 shows that the following formulas are inconsistent:
% 244.05/50.59  ----------------------------------------------------------------
% 244.05/50.59    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.59         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.59    (2)   ~ (e3 = e0)
% 244.05/50.59    (3)   ~ (e2 = e0)
% 244.05/50.59    (4)  all_58_11 = e1 & op(e1, e0) = e1
% 244.05/50.59    (5)   ~ (e3 = e1)
% 244.05/50.59    (6)  all_58_11 = e3
% 244.05/50.59    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.59         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.59    (8)  op(e3, e3) = e1
% 244.05/50.59    (9)   ~ (e3 = e2)
% 244.05/50.59    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.59          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.59    (11)   ~ (all_52_4 = e3)
% 244.05/50.59    (12)  op(e3, e2) = all_52_4
% 244.05/50.59    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.59    (14)   ~ (e1 = e0)
% 244.05/50.59    (15)  all_58_4 = e3
% 244.05/50.59    (16)   ~ (e2 = e1)
% 244.05/50.59  
% 244.05/50.59  Begin of proof
% 244.05/50.59  | 
% 244.05/50.59  | ALPHA: (4) implies:
% 244.05/50.59  |   (17)  all_58_11 = e1
% 244.05/50.59  | 
% 244.05/50.59  | COMBINE_EQS: (6), (17) imply:
% 244.05/50.59  |   (18)  e3 = e1
% 244.05/50.59  | 
% 244.05/50.59  | COMBINE_EQS: (15), (18) imply:
% 244.05/50.59  |   (19)  all_58_4 = e1
% 244.05/50.59  | 
% 244.05/50.59  | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 244.05/50.59  |            (16), (19) are inconsistent by sub-proof #1468.
% 244.05/50.59  | 
% 244.05/50.59  End of proof
% 244.05/50.59  
% 244.05/50.59  Sub-proof #1468 shows that the following formulas are inconsistent:
% 244.05/50.59  ----------------------------------------------------------------
% 244.05/50.59    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.59         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.59    (2)   ~ (e3 = e0)
% 244.05/50.59    (3)   ~ (e2 = e0)
% 244.05/50.59    (4)   ~ (e3 = e1)
% 244.05/50.59    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.59         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.59    (6)  op(e3, e3) = e1
% 244.05/50.59    (7)   ~ (e3 = e2)
% 244.05/50.59    (8)  all_58_4 = e1
% 244.05/50.59    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.59         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.59    (10)   ~ (all_52_4 = e3)
% 244.05/50.59    (11)  op(e3, e2) = all_52_4
% 244.05/50.59    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.59    (13)   ~ (e1 = e0)
% 244.05/50.59    (14)   ~ (e2 = e1)
% 244.05/50.59  
% 244.05/50.59  Begin of proof
% 244.05/50.59  | 
% 244.05/50.59  | BETA: splitting (5) gives:
% 244.05/50.59  | 
% 244.05/50.59  | Case 1:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 244.05/50.59  | |           e3)
% 244.05/50.59  | | 
% 244.05/50.59  | | BETA: splitting (15) gives:
% 244.05/50.59  | | 
% 244.05/50.59  | | Case 1:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (16)  all_58_0 = e3 & op(e3, e3) = e3
% 244.05/50.59  | | | 
% 244.05/50.59  | | | ALPHA: (16) implies:
% 244.05/50.59  | | |   (17)  op(e3, e3) = e3
% 244.05/50.59  | | | 
% 244.05/50.59  | | | GROUND_INST: instantiating (12) with e1, e3, e3, e3, simplifying with (6),
% 244.05/50.59  | | |              (17) gives:
% 244.05/50.59  | | |   (18)  e3 = e1
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REDUCE: (4), (18) imply:
% 244.05/50.59  | | |   (19)  $false
% 244.05/50.59  | | | 
% 244.05/50.59  | | | CLOSE: (19) is inconsistent.
% 244.05/50.59  | | | 
% 244.05/50.59  | | Case 2:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (20)  all_58_1 = e3 & op(e3, e2) = e3
% 244.05/50.59  | | | 
% 244.05/50.59  | | | ALPHA: (20) implies:
% 244.05/50.59  | | |   (21)  op(e3, e2) = e3
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (10), (11), (12), (21) are inconsistent by sub-proof #2192.
% 244.05/50.59  | | | 
% 244.05/50.59  | | End of split
% 244.05/50.59  | | 
% 244.05/50.59  | Case 2:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (22)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 244.05/50.59  | |           e3)
% 244.05/50.59  | | 
% 244.05/50.59  | | BETA: splitting (22) gives:
% 244.05/50.59  | | 
% 244.05/50.59  | | Case 1:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (23)  all_58_4 = e3 & op(e3, e1) = e3
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (4), (8), (23) are inconsistent by sub-proof #1474.
% 244.05/50.59  | | | 
% 244.05/50.59  | | Case 2:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (24)  all_58_9 = e3 & op(e3, e0) = e3
% 244.05/50.59  | | | 
% 244.05/50.59  | | | ALPHA: (24) implies:
% 244.05/50.59  | | |   (25)  all_58_9 = e3
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (12), (13), (14), (25) are
% 244.05/50.59  | | |            inconsistent by sub-proof #1469.
% 244.05/50.59  | | | 
% 244.05/50.59  | | End of split
% 244.05/50.59  | | 
% 244.05/50.59  | End of split
% 244.05/50.59  | 
% 244.05/50.59  End of proof
% 244.05/50.59  
% 244.05/50.59  Sub-proof #1469 shows that the following formulas are inconsistent:
% 244.05/50.59  ----------------------------------------------------------------
% 244.05/50.59    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.59         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.59    (2)   ~ (e3 = e0)
% 244.05/50.59    (3)   ~ (e2 = e0)
% 244.05/50.59    (4)  op(e3, e3) = e1
% 244.05/50.59    (5)   ~ (e3 = e2)
% 244.05/50.59    (6)  all_58_9 = e3
% 244.05/50.59    (7)  all_58_4 = e1
% 244.05/50.59    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.59         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.59    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.59    (10)   ~ (e1 = e0)
% 244.05/50.59    (11)   ~ (e2 = e1)
% 244.05/50.59  
% 244.05/50.59  Begin of proof
% 244.05/50.59  | 
% 244.05/50.59  | BETA: splitting (1) gives:
% 244.05/50.59  | 
% 244.05/50.59  | Case 1:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (12)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 244.05/50.59  | |           e2)
% 244.05/50.59  | | 
% 244.05/50.59  | | BETA: splitting (12) gives:
% 244.05/50.59  | | 
% 244.05/50.59  | | Case 1:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (13)  all_58_0 = e2 & op(e3, e3) = e2
% 244.05/50.59  | | | 
% 244.05/50.59  | | | ALPHA: (13) implies:
% 244.05/50.59  | | |   (14)  op(e3, e3) = e2
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (4), (9), (11), (14) are inconsistent by sub-proof #2267.
% 244.05/50.59  | | | 
% 244.05/50.59  | | Case 2:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (15)  all_58_1 = e2 & op(e3, e2) = e2
% 244.05/50.59  | | | 
% 244.05/50.59  | | | ALPHA: (15) implies:
% 244.05/50.59  | | |   (16)  all_58_1 = e2
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (16) are inconsistent
% 244.05/50.59  | | |            by sub-proof #1472.
% 244.05/50.59  | | | 
% 244.05/50.59  | | End of split
% 244.05/50.59  | | 
% 244.05/50.59  | Case 2:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (17)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 244.05/50.59  | |           e2)
% 244.05/50.59  | | 
% 244.05/50.59  | | BETA: splitting (17) gives:
% 244.05/50.59  | | 
% 244.05/50.59  | | Case 1:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (18)  all_58_4 = e2 & op(e3, e1) = e2
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (7), (11), (18) are inconsistent by sub-proof #1471.
% 244.05/50.59  | | | 
% 244.05/50.59  | | Case 2:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (19)  all_58_9 = e2 & op(e3, e0) = e2
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (5), (6), (19) are inconsistent by sub-proof #1470.
% 244.05/50.59  | | | 
% 244.05/50.59  | | End of split
% 244.05/50.59  | | 
% 244.05/50.59  | End of split
% 244.05/50.59  | 
% 244.05/50.59  End of proof
% 244.05/50.59  
% 244.05/50.59  Sub-proof #1470 shows that the following formulas are inconsistent:
% 244.05/50.59  ----------------------------------------------------------------
% 244.05/50.59    (1)  all_58_9 = e2 & op(e3, e0) = e2
% 244.05/50.59    (2)  all_58_9 = e3
% 244.05/50.59    (3)   ~ (e3 = e2)
% 244.05/50.59  
% 244.05/50.59  Begin of proof
% 244.05/50.59  | 
% 244.05/50.59  | ALPHA: (1) implies:
% 244.05/50.59  |   (4)  all_58_9 = e2
% 244.05/50.59  | 
% 244.05/50.59  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.59  |   (5)  e3 = e2
% 244.05/50.59  | 
% 244.05/50.59  | REDUCE: (3), (5) imply:
% 244.05/50.59  |   (6)  $false
% 244.05/50.59  | 
% 244.05/50.59  | CLOSE: (6) is inconsistent.
% 244.05/50.59  | 
% 244.05/50.59  End of proof
% 244.05/50.59  
% 244.05/50.59  Sub-proof #1471 shows that the following formulas are inconsistent:
% 244.05/50.59  ----------------------------------------------------------------
% 244.05/50.59    (1)  all_58_4 = e2 & op(e3, e1) = e2
% 244.05/50.59    (2)  all_58_4 = e1
% 244.05/50.59    (3)   ~ (e2 = e1)
% 244.05/50.59  
% 244.05/50.59  Begin of proof
% 244.05/50.59  | 
% 244.05/50.59  | ALPHA: (1) implies:
% 244.05/50.59  |   (4)  all_58_4 = e2
% 244.05/50.59  | 
% 244.05/50.59  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.59  |   (5)  e2 = e1
% 244.05/50.59  | 
% 244.05/50.59  | REDUCE: (3), (5) imply:
% 244.05/50.59  |   (6)  $false
% 244.05/50.59  | 
% 244.05/50.59  | CLOSE: (6) is inconsistent.
% 244.05/50.59  | 
% 244.05/50.59  End of proof
% 244.05/50.59  
% 244.05/50.59  Sub-proof #1472 shows that the following formulas are inconsistent:
% 244.05/50.59  ----------------------------------------------------------------
% 244.05/50.59    (1)   ~ (e3 = e0)
% 244.05/50.59    (2)   ~ (e2 = e0)
% 244.05/50.59    (3)  op(e3, e3) = e1
% 244.05/50.59    (4)  all_58_9 = e3
% 244.05/50.59    (5)  all_58_4 = e1
% 244.05/50.59    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.59         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.59    (7)  all_58_1 = e2
% 244.05/50.59    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.59    (9)   ~ (e1 = e0)
% 244.05/50.59  
% 244.05/50.59  Begin of proof
% 244.05/50.59  | 
% 244.05/50.59  | BETA: splitting (6) gives:
% 244.05/50.59  | 
% 244.05/50.59  | Case 1:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 244.05/50.59  | |           e0)
% 244.05/50.59  | | 
% 244.05/50.59  | | BETA: splitting (10) gives:
% 244.05/50.59  | | 
% 244.05/50.59  | | Case 1:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (11)  all_58_0 = e0 & op(e3, e3) = e0
% 244.05/50.59  | | | 
% 244.05/50.59  | | | ALPHA: (11) implies:
% 244.05/50.59  | | |   (12)  op(e3, e3) = e0
% 244.05/50.59  | | | 
% 244.05/50.59  | | | GROUND_INST: instantiating (8) with e0, e1, e3, e3, simplifying with (3),
% 244.05/50.59  | | |              (12) gives:
% 244.05/50.59  | | |   (13)  e1 = e0
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REDUCE: (9), (13) imply:
% 244.05/50.59  | | |   (14)  $false
% 244.05/50.59  | | | 
% 244.05/50.59  | | | CLOSE: (14) is inconsistent.
% 244.05/50.59  | | | 
% 244.05/50.59  | | Case 2:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (15)  all_58_1 = e0 & op(e3, e2) = e0
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (2), (7), (15) are inconsistent by sub-proof #2187.
% 244.05/50.59  | | | 
% 244.05/50.59  | | End of split
% 244.05/50.59  | | 
% 244.05/50.59  | Case 2:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (16)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 244.05/50.59  | |           e0)
% 244.05/50.59  | | 
% 244.05/50.59  | | BETA: splitting (16) gives:
% 244.05/50.59  | | 
% 244.05/50.59  | | Case 1:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (17)  all_58_4 = e0 & op(e3, e1) = e0
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (5), (9), (17) are inconsistent by sub-proof #1473.
% 244.05/50.59  | | | 
% 244.05/50.59  | | Case 2:
% 244.05/50.59  | | | 
% 244.05/50.59  | | |   (18)  all_58_9 = e0 & op(e3, e0) = e0
% 244.05/50.59  | | | 
% 244.05/50.59  | | | REF_CLOSE: (1), (4), (18) are inconsistent by sub-proof #2103.
% 244.05/50.59  | | | 
% 244.05/50.59  | | End of split
% 244.05/50.59  | | 
% 244.05/50.59  | End of split
% 244.05/50.59  | 
% 244.05/50.59  End of proof
% 244.05/50.59  
% 244.05/50.59  Sub-proof #1473 shows that the following formulas are inconsistent:
% 244.05/50.59  ----------------------------------------------------------------
% 244.05/50.59    (1)  all_58_4 = e0 & op(e3, e1) = e0
% 244.05/50.59    (2)  all_58_4 = e1
% 244.05/50.59    (3)   ~ (e1 = e0)
% 244.05/50.59  
% 244.05/50.59  Begin of proof
% 244.05/50.59  | 
% 244.05/50.59  | ALPHA: (1) implies:
% 244.05/50.59  |   (4)  all_58_4 = e0
% 244.05/50.59  | 
% 244.05/50.59  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.59  |   (5)  e1 = e0
% 244.05/50.59  | 
% 244.05/50.59  | REDUCE: (3), (5) imply:
% 244.05/50.59  |   (6)  $false
% 244.05/50.59  | 
% 244.05/50.59  | CLOSE: (6) is inconsistent.
% 244.05/50.59  | 
% 244.05/50.59  End of proof
% 244.05/50.59  
% 244.05/50.59  Sub-proof #1474 shows that the following formulas are inconsistent:
% 244.05/50.59  ----------------------------------------------------------------
% 244.05/50.59    (1)  all_58_4 = e3 & op(e3, e1) = e3
% 244.05/50.59    (2)  all_58_4 = e1
% 244.05/50.59    (3)   ~ (e3 = e1)
% 244.05/50.59  
% 244.05/50.59  Begin of proof
% 244.05/50.59  | 
% 244.05/50.59  | ALPHA: (1) implies:
% 244.05/50.59  |   (4)  all_58_4 = e3
% 244.05/50.59  | 
% 244.05/50.59  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.59  |   (5)  e3 = e1
% 244.05/50.59  | 
% 244.05/50.59  | REDUCE: (3), (5) imply:
% 244.05/50.59  |   (6)  $false
% 244.05/50.59  | 
% 244.05/50.59  | CLOSE: (6) is inconsistent.
% 244.05/50.59  | 
% 244.05/50.59  End of proof
% 244.05/50.59  
% 244.05/50.59  Sub-proof #1475 shows that the following formulas are inconsistent:
% 244.05/50.59  ----------------------------------------------------------------
% 244.05/50.59    (1)   ~ (e3 = e2)
% 244.05/50.59    (2)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.59    (3)  all_58_4 = e3
% 244.05/50.59    (4)  all_58_9 = e1
% 244.05/50.59    (5)   ~ (e2 = e1)
% 244.05/50.59  
% 244.05/50.59  Begin of proof
% 244.05/50.59  | 
% 244.05/50.59  | BETA: splitting (2) gives:
% 244.05/50.59  | 
% 244.05/50.59  | Case 1:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (6)  all_58_4 = e2 & op(e3, e1) = e2
% 244.05/50.59  | | 
% 244.05/50.59  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #1476.
% 244.05/50.59  | | 
% 244.05/50.59  | Case 2:
% 244.05/50.59  | | 
% 244.05/50.59  | |   (7)  all_58_9 = e2 & op(e3, e0) = e2
% 244.05/50.60  | | 
% 244.05/50.60  | | ALPHA: (7) implies:
% 244.05/50.60  | |   (8)  all_58_9 = e2
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1605.
% 244.05/50.60  | | 
% 244.05/50.60  | End of split
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1476 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)  all_58_4 = e2 & op(e3, e1) = e2
% 244.05/50.60    (2)  all_58_4 = e3
% 244.05/50.60    (3)   ~ (e3 = e2)
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | ALPHA: (1) implies:
% 244.05/50.60  |   (4)  all_58_4 = e2
% 244.05/50.60  | 
% 244.05/50.60  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.60  |   (5)  e3 = e2
% 244.05/50.60  | 
% 244.05/50.60  | REDUCE: (3), (5) imply:
% 244.05/50.60  |   (6)  $false
% 244.05/50.60  | 
% 244.05/50.60  | CLOSE: (6) is inconsistent.
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1477 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)   ~ (e2 = e0)
% 244.05/50.60    (2)  all_58_1 = e0
% 244.05/50.60    (3)  op(e3, e3) = e1
% 244.05/50.60    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.60    (5)   ~ (e2 = e1)
% 244.05/50.60    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | BETA: splitting (6) gives:
% 244.05/50.60  | 
% 244.05/50.60  | Case 1:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 244.05/50.60  | | 
% 244.05/50.60  | | ALPHA: (7) implies:
% 244.05/50.60  | |   (8)  op(e3, e3) = e2
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2267.
% 244.05/50.60  | | 
% 244.05/50.60  | Case 2:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (9)  all_58_1 = e2 & op(e3, e2) = e2
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #1478.
% 244.05/50.60  | | 
% 244.05/50.60  | End of split
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1478 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)  all_58_1 = e2 & op(e3, e2) = e2
% 244.05/50.60    (2)  all_58_1 = e0
% 244.05/50.60    (3)   ~ (e2 = e0)
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | ALPHA: (1) implies:
% 244.05/50.60  |   (4)  all_58_1 = e2
% 244.05/50.60  | 
% 244.05/50.60  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.60  |   (5)  e2 = e0
% 244.05/50.60  | 
% 244.05/50.60  | SIMP: (5) implies:
% 244.05/50.60  |   (6)  e2 = e0
% 244.05/50.60  | 
% 244.05/50.60  | REDUCE: (3), (6) imply:
% 244.05/50.60  |   (7)  $false
% 244.05/50.60  | 
% 244.05/50.60  | CLOSE: (7) is inconsistent.
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1479 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)   ~ (e3 = e0)
% 244.05/50.60    (2)   ~ (e2 = e0)
% 244.05/50.60    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.60         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.60    (4)  op(e1, e0) = all_52_14
% 244.05/50.60    (5)   ~ (e3 = e1)
% 244.05/50.60    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.05/50.60         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.05/50.60    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.60             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.05/50.60               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.05/50.60               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.05/50.60    (8)   ~ (e3 = e2)
% 244.05/50.60    (9)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 244.05/50.60         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 244.05/50.60    (10)   ~ (all_52_14 = e0)
% 244.05/50.60    (11)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.60    (12)  all_58_5 = e2
% 244.05/50.60    (13)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.60          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.60    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.60            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.60    (15)  op(e0, e0) = e0
% 244.05/50.60    (16)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.60          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.60    (17)   ~ (e1 = e0)
% 244.05/50.60    (18)  all_58_4 = e3
% 244.05/50.60    (19)   ~ (all_52_13 = e3)
% 244.05/50.60    (20)  op(e2, e0) = all_52_13
% 244.05/50.60    (21)  all_58_14 = e1
% 244.05/50.60    (22)   ~ (all_52_13 = e0)
% 244.05/50.60    (23)   ~ (e2 = e1)
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | BETA: splitting (11) gives:
% 244.05/50.60  | 
% 244.05/50.60  | Case 1:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (24)  all_58_14 = e2 & op(e0, e1) = e2
% 244.05/50.60  | | 
% 244.05/50.60  | | ALPHA: (24) implies:
% 244.05/50.60  | |   (25)  all_58_14 = e2
% 244.05/50.60  | | 
% 244.05/50.60  | | COMBINE_EQS: (21), (25) imply:
% 244.05/50.60  | |   (26)  e2 = e1
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (1), (2), (6), (8), (9), (12), (17), (18), (21), (23), (26) are
% 244.05/50.60  | |            inconsistent by sub-proof #1480.
% 244.05/50.60  | | 
% 244.05/50.60  | Case 2:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (27)  all_58_15 = e2 & op(e0, e0) = e2
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (13), (14), (15), (16),
% 244.05/50.60  | |            (17), (19), (20), (22), (23), (27) are inconsistent by sub-proof
% 244.05/50.60  | |            #1488.
% 244.05/50.60  | | 
% 244.05/50.60  | End of split
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1480 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)   ~ (e3 = e0)
% 244.05/50.60    (2)   ~ (e2 = e0)
% 244.05/50.60    (3)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.05/50.60         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.05/50.60    (4)   ~ (e3 = e2)
% 244.05/50.60    (5)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 244.05/50.60         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 244.05/50.60    (6)  all_58_5 = e2
% 244.05/50.60    (7)  e2 = e1
% 244.05/50.60    (8)   ~ (e1 = e0)
% 244.05/50.60    (9)  all_58_4 = e3
% 244.05/50.60    (10)  all_58_14 = e1
% 244.05/50.60    (11)   ~ (e2 = e1)
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | SIMP: (7) implies:
% 244.05/50.60  |   (12)  e2 = e1
% 244.05/50.60  | 
% 244.05/50.60  | COMBINE_EQS: (6), (12) imply:
% 244.05/50.60  |   (13)  all_58_5 = e1
% 244.05/50.60  | 
% 244.05/50.60  | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (13) are
% 244.05/50.60  |            inconsistent by sub-proof #1481.
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1481 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)   ~ (e3 = e0)
% 244.05/50.60    (2)   ~ (e2 = e0)
% 244.05/50.60    (3)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.05/50.60         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.05/50.60    (4)   ~ (e3 = e2)
% 244.05/50.60    (5)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 244.05/50.60         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 244.05/50.60    (6)  all_58_5 = e1
% 244.05/50.60    (7)   ~ (e1 = e0)
% 244.05/50.60    (8)  all_58_4 = e3
% 244.05/50.60    (9)  all_58_14 = e1
% 244.05/50.60    (10)   ~ (e2 = e1)
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | BETA: splitting (5) gives:
% 244.05/50.60  | 
% 244.05/50.60  | Case 1:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (11)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 244.05/50.60  | |           e2)
% 244.05/50.60  | | 
% 244.05/50.60  | | BETA: splitting (11) gives:
% 244.05/50.60  | | 
% 244.05/50.60  | | Case 1:
% 244.05/50.60  | | | 
% 244.05/50.60  | | |   (12)  all_58_4 = e2 & op(e3, e1) = e2
% 244.05/50.60  | | | 
% 244.05/50.60  | | | ALPHA: (12) implies:
% 244.05/50.60  | | |   (13)  all_58_4 = e2
% 244.05/50.60  | | | 
% 244.05/50.60  | | | REF_CLOSE: (4), (8), (13) are inconsistent by sub-proof #1902.
% 244.05/50.60  | | | 
% 244.05/50.60  | | Case 2:
% 244.05/50.60  | | | 
% 244.05/50.60  | | |   (14)  all_58_5 = e2 & op(e2, e1) = e2
% 244.05/50.60  | | | 
% 244.05/50.60  | | | ALPHA: (14) implies:
% 244.05/50.60  | | |   (15)  all_58_5 = e2
% 244.05/50.60  | | | 
% 244.05/50.60  | | | REF_CLOSE: (6), (10), (15) are inconsistent by sub-proof #1665.
% 244.05/50.60  | | | 
% 244.05/50.60  | | End of split
% 244.05/50.60  | | 
% 244.05/50.60  | Case 2:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (16)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 244.05/50.60  | |           e2)
% 244.05/50.60  | | 
% 244.05/50.60  | | BETA: splitting (16) gives:
% 244.05/50.60  | | 
% 244.05/50.60  | | Case 1:
% 244.05/50.60  | | | 
% 244.05/50.60  | | |   (17)  all_58_8 = e2 & op(e1, e1) = e2
% 244.05/50.60  | | | 
% 244.05/50.60  | | | ALPHA: (17) implies:
% 244.05/50.60  | | |   (18)  all_58_8 = e2
% 244.05/50.60  | | | 
% 244.05/50.60  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (18) are inconsistent by
% 244.05/50.60  | | |            sub-proof #1482.
% 244.05/50.60  | | | 
% 244.05/50.60  | | Case 2:
% 244.05/50.60  | | | 
% 244.05/50.60  | | |   (19)  all_58_14 = e2 & op(e0, e1) = e2
% 244.05/50.60  | | | 
% 244.05/50.60  | | | REF_CLOSE: (9), (10), (19) are inconsistent by sub-proof #1771.
% 244.05/50.60  | | | 
% 244.05/50.60  | | End of split
% 244.05/50.60  | | 
% 244.05/50.60  | End of split
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1482 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)   ~ (e3 = e0)
% 244.05/50.60    (2)   ~ (e2 = e0)
% 244.05/50.60    (3)  all_58_8 = e2
% 244.05/50.60    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.05/50.60         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.05/50.60    (5)  all_58_5 = e1
% 244.05/50.60    (6)   ~ (e1 = e0)
% 244.05/50.60    (7)  all_58_4 = e3
% 244.05/50.60    (8)  all_58_14 = e1
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | BETA: splitting (4) gives:
% 244.05/50.60  | 
% 244.05/50.60  | Case 1:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (9)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (1), (5), (6), (7), (9) are inconsistent by sub-proof #1484.
% 244.05/50.60  | | 
% 244.05/50.60  | Case 2:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (10)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 244.05/50.60  | |           e0)
% 244.05/50.60  | | 
% 244.05/50.60  | | BETA: splitting (10) gives:
% 244.05/50.60  | | 
% 244.05/50.60  | | Case 1:
% 244.05/50.60  | | | 
% 244.05/50.60  | | |   (11)  all_58_8 = e0 & op(e1, e1) = e0
% 244.05/50.60  | | | 
% 244.05/50.60  | | | ALPHA: (11) implies:
% 244.05/50.60  | | |   (12)  all_58_8 = e0
% 244.05/50.60  | | | 
% 244.05/50.60  | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #1556.
% 244.05/50.60  | | | 
% 244.05/50.60  | | Case 2:
% 244.05/50.60  | | | 
% 244.05/50.60  | | |   (13)  all_58_14 = e0 & op(e0, e1) = e0
% 244.05/50.60  | | | 
% 244.05/50.60  | | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #1483.
% 244.05/50.60  | | | 
% 244.05/50.60  | | End of split
% 244.05/50.60  | | 
% 244.05/50.60  | End of split
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1483 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)  all_58_14 = e0 & op(e0, e1) = e0
% 244.05/50.60    (2)  all_58_14 = e1
% 244.05/50.60    (3)   ~ (e1 = e0)
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | ALPHA: (1) implies:
% 244.05/50.60  |   (4)  all_58_14 = e0
% 244.05/50.60  | 
% 244.05/50.60  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.60  |   (5)  e1 = e0
% 244.05/50.60  | 
% 244.05/50.60  | REDUCE: (3), (5) imply:
% 244.05/50.60  |   (6)  $false
% 244.05/50.60  | 
% 244.05/50.60  | CLOSE: (6) is inconsistent.
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1484 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)   ~ (e3 = e0)
% 244.05/50.60    (2)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 244.05/50.60    (3)  all_58_5 = e1
% 244.05/50.60    (4)   ~ (e1 = e0)
% 244.05/50.60    (5)  all_58_4 = e3
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | BETA: splitting (2) gives:
% 244.05/50.60  | 
% 244.05/50.60  | Case 1:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (6)  all_58_4 = e0 & op(e3, e1) = e0
% 244.05/50.60  | | 
% 244.05/50.60  | | ALPHA: (6) implies:
% 244.05/50.60  | |   (7)  all_58_4 = e0
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #2186.
% 244.05/50.60  | | 
% 244.05/50.60  | Case 2:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (8)  all_58_5 = e0 & op(e2, e1) = e0
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #1485.
% 244.05/50.60  | | 
% 244.05/50.60  | End of split
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1485 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)  all_58_5 = e0 & op(e2, e1) = e0
% 244.05/50.60    (2)  all_58_5 = e1
% 244.05/50.60    (3)   ~ (e1 = e0)
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | ALPHA: (1) implies:
% 244.05/50.60  |   (4)  all_58_5 = e0
% 244.05/50.60  | 
% 244.05/50.60  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.60  |   (5)  e1 = e0
% 244.05/50.60  | 
% 244.05/50.60  | REDUCE: (3), (5) imply:
% 244.05/50.60  |   (6)  $false
% 244.05/50.60  | 
% 244.05/50.60  | CLOSE: (6) is inconsistent.
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1486 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)   ~ (e3 = e1)
% 244.05/50.60    (2)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 244.05/50.60    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.60    (4)   ~ (e1 = e0)
% 244.05/50.60    (5)  op(e3, e3) = e0
% 244.05/50.60    (6)  all_58_2 = e3
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | BETA: splitting (2) gives:
% 244.05/50.60  | 
% 244.05/50.60  | Case 1:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.60  | | 
% 244.05/50.60  | | ALPHA: (7) implies:
% 244.05/50.60  | |   (8)  op(e3, e3) = e1
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1828.
% 244.05/50.60  | | 
% 244.05/50.60  | Case 2:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (9)  all_58_2 = e1 & op(e2, e3) = e1
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #1765.
% 244.05/50.60  | | 
% 244.05/50.60  | End of split
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1487 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)   ~ (e3 = e0)
% 244.05/50.60    (2)   ~ (e2 = e0)
% 244.05/50.60    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.60         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.60    (4)  op(e1, e0) = all_52_14
% 244.05/50.60    (5)   ~ (e3 = e1)
% 244.05/50.60    (6)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.60             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.05/50.60               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.05/50.60               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.05/50.60    (7)   ~ (e3 = e2)
% 244.05/50.60    (8)   ~ (all_52_14 = e0)
% 244.05/50.60    (9)  op(e1, e0) = all_28_1
% 244.05/50.60    (10)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.60          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.60    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.60            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.60    (12)  op(e0, e0) = e0
% 244.05/50.60    (13)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.60          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.60    (14)   ~ (e1 = e0)
% 244.05/50.60    (15)   ~ (all_52_13 = e3)
% 244.05/50.60    (16)  op(e2, e0) = all_52_13
% 244.05/50.60    (17)   ~ (all_28_1 = e2)
% 244.05/50.60    (18)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.60    (19)   ~ (all_52_13 = e0)
% 244.05/50.60    (20)   ~ (e2 = e1)
% 244.05/50.60  
% 244.05/50.60  Begin of proof
% 244.05/50.60  | 
% 244.05/50.60  | BETA: splitting (18) gives:
% 244.05/50.60  | 
% 244.05/50.60  | Case 1:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (21)  all_58_11 = e2 & op(e1, e0) = e2
% 244.05/50.60  | | 
% 244.05/50.60  | | ALPHA: (21) implies:
% 244.05/50.60  | |   (22)  op(e1, e0) = e2
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (9), (11), (17), (22) are inconsistent by sub-proof #1944.
% 244.05/50.60  | | 
% 244.05/50.60  | Case 2:
% 244.05/50.60  | | 
% 244.05/50.60  | |   (23)  all_58_15 = e2 & op(e0, e0) = e2
% 244.05/50.60  | | 
% 244.05/50.60  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 244.05/50.60  | |            (14), (15), (16), (19), (20), (23) are inconsistent by sub-proof
% 244.05/50.60  | |            #1488.
% 244.05/50.60  | | 
% 244.05/50.60  | End of split
% 244.05/50.60  | 
% 244.05/50.60  End of proof
% 244.05/50.60  
% 244.05/50.60  Sub-proof #1488 shows that the following formulas are inconsistent:
% 244.05/50.60  ----------------------------------------------------------------
% 244.05/50.60    (1)   ~ (e3 = e0)
% 244.05/50.60    (2)   ~ (e2 = e0)
% 244.05/50.60    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.60         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.60    (4)  op(e1, e0) = all_52_14
% 244.05/50.60    (5)   ~ (e3 = e1)
% 244.05/50.60    (6)  all_58_15 = e2 & op(e0, e0) = e2
% 244.05/50.60    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.60             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.05/50.60               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.05/50.60               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.05/50.60    (8)   ~ (e3 = e2)
% 244.05/50.60    (9)   ~ (all_52_14 = e0)
% 244.05/50.61    (10)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.61          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.61    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.61    (12)  op(e0, e0) = e0
% 244.05/50.61    (13)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.61          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.61    (14)   ~ (e1 = e0)
% 244.05/50.61    (15)   ~ (all_52_13 = e3)
% 244.05/50.61    (16)  op(e2, e0) = all_52_13
% 244.05/50.61    (17)   ~ (all_52_13 = e0)
% 244.05/50.61    (18)   ~ (e2 = e1)
% 244.05/50.61  
% 244.05/50.61  Begin of proof
% 244.05/50.61  | 
% 244.05/50.61  | ALPHA: (6) implies:
% 244.05/50.61  |   (19)  all_58_15 = e2
% 244.05/50.61  | 
% 244.05/50.61  | BETA: splitting (7) gives:
% 244.05/50.61  | 
% 244.05/50.61  | Case 1:
% 244.05/50.61  | | 
% 244.05/50.61  | |   (20)  all_58_15 = e0 & op(e0, e0) = e0
% 244.05/50.61  | | 
% 244.05/50.61  | | ALPHA: (20) implies:
% 244.05/50.61  | |   (21)  all_58_15 = e0
% 244.05/50.61  | | 
% 244.05/50.61  | | REF_CLOSE: (2), (19), (21) are inconsistent by sub-proof #1507.
% 244.05/50.61  | | 
% 244.05/50.61  | Case 2:
% 244.05/50.61  | | 
% 244.05/50.61  | |   (22)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 244.05/50.61  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 244.05/50.61  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 244.05/50.61  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 244.05/50.61  | | 
% 244.05/50.61  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (13), (14),
% 244.05/50.61  | |            (15), (16), (17), (18), (22) are inconsistent by sub-proof #1489.
% 244.05/50.61  | | 
% 244.05/50.61  | End of split
% 244.05/50.61  | 
% 244.05/50.61  End of proof
% 244.05/50.61  
% 244.05/50.61  Sub-proof #1489 shows that the following formulas are inconsistent:
% 244.05/50.61  ----------------------------------------------------------------
% 244.05/50.61    (1)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 244.05/50.61           (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) =
% 244.05/50.61             e0) | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 244.05/50.61               e1) = e0))
% 244.05/50.61    (2)   ~ (e3 = e0)
% 244.05/50.61    (3)   ~ (e2 = e0)
% 244.05/50.61    (4)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.61         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.61    (5)  op(e1, e0) = all_52_14
% 244.05/50.61    (6)   ~ (e3 = e1)
% 244.05/50.61    (7)   ~ (e3 = e2)
% 244.05/50.61    (8)   ~ (all_52_14 = e0)
% 244.05/50.61    (9)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.61         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.61    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.61    (11)  op(e0, e0) = e0
% 244.05/50.61    (12)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.61          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.61    (13)   ~ (e1 = e0)
% 244.05/50.61    (14)   ~ (all_52_13 = e3)
% 244.05/50.61    (15)  op(e2, e0) = all_52_13
% 244.05/50.61    (16)   ~ (all_52_13 = e0)
% 244.05/50.61    (17)   ~ (e2 = e1)
% 244.05/50.61  
% 244.05/50.61  Begin of proof
% 244.05/50.61  | 
% 244.05/50.61  | ALPHA: (1) implies:
% 244.05/50.61  |   (18)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 244.05/50.61  |         | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.61  | 
% 244.05/50.61  | BETA: splitting (18) gives:
% 244.05/50.61  | 
% 244.05/50.61  | Case 1:
% 244.05/50.61  | | 
% 244.05/50.61  | |   (19)  all_58_9 = e0 & op(e3, e0) = e0
% 244.05/50.61  | | 
% 244.05/50.61  | | ALPHA: (19) implies:
% 244.05/50.61  | |   (20)  all_58_9 = e0
% 244.05/50.61  | | 
% 244.05/50.61  | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 244.05/50.61  | |            (17), (20) are inconsistent by sub-proof #1650.
% 244.05/50.61  | | 
% 244.05/50.61  | Case 2:
% 244.05/50.61  | | 
% 244.05/50.61  | |   (21)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.05/50.61  | |           e0)
% 244.05/50.61  | | 
% 244.05/50.61  | | REF_CLOSE: (5), (8), (10), (15), (16), (21) are inconsistent by sub-proof
% 244.05/50.61  | |            #1490.
% 244.05/50.61  | | 
% 244.05/50.61  | End of split
% 244.05/50.61  | 
% 244.05/50.61  End of proof
% 244.05/50.61  
% 244.05/50.61  Sub-proof #1490 shows that the following formulas are inconsistent:
% 244.05/50.61  ----------------------------------------------------------------
% 244.05/50.61    (1)  op(e1, e0) = all_52_14
% 244.05/50.61    (2)   ~ (all_52_14 = e0)
% 244.05/50.61    (3)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.61    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.61    (5)  op(e2, e0) = all_52_13
% 244.05/50.61    (6)   ~ (all_52_13 = e0)
% 244.05/50.61  
% 244.05/50.61  Begin of proof
% 244.05/50.61  | 
% 244.05/50.61  | BETA: splitting (3) gives:
% 244.05/50.61  | 
% 244.05/50.61  | Case 1:
% 244.05/50.61  | | 
% 244.05/50.61  | |   (7)  all_58_10 = e0 & op(e2, e0) = e0
% 244.05/50.61  | | 
% 244.05/50.61  | | ALPHA: (7) implies:
% 244.05/50.61  | |   (8)  op(e2, e0) = e0
% 244.05/50.61  | | 
% 244.05/50.61  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2324.
% 244.05/50.61  | | 
% 244.05/50.61  | Case 2:
% 244.05/50.61  | | 
% 244.05/50.61  | |   (9)  all_58_11 = e0 & op(e1, e0) = e0
% 244.05/50.61  | | 
% 244.05/50.61  | | ALPHA: (9) implies:
% 244.05/50.61  | |   (10)  op(e1, e0) = e0
% 244.05/50.61  | | 
% 244.05/50.61  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #2323.
% 244.05/50.61  | | 
% 244.05/50.61  | End of split
% 244.05/50.61  | 
% 244.05/50.61  End of proof
% 244.05/50.61  
% 244.05/50.61  Sub-proof #1491 shows that the following formulas are inconsistent:
% 244.05/50.61  ----------------------------------------------------------------
% 244.05/50.61    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.61         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.61    (2)   ~ (e3 = e0)
% 244.05/50.61    (3)  op(e0, e1) = all_52_11
% 244.05/50.61    (4)   ~ (e2 = e0)
% 244.05/50.61    (5)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.05/50.61         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.05/50.61    (6)  op(e1, e2) = all_52_6
% 244.05/50.61    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.61         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.61    (8)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.61         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.61    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.61         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.61    (10)   ~ (all_52_12 = e0)
% 244.05/50.61    (11)   ~ (e3 = e1)
% 244.05/50.61    (12)  op(e0, e2) = e3
% 244.05/50.61    (13)  op(e2, e2) = e0
% 244.05/50.61    (14)   ~ (all_52_12 = all_52_13)
% 244.05/50.61    (15)  all_58_11 = e3
% 244.05/50.61    (16)   ~ (all_52_11 = e3)
% 244.05/50.61    (17)  op(e2, e1) = all_52_9
% 244.05/50.61    (18)   ~ (e3 = e2)
% 244.05/50.61    (19)  op(e2, all_52_9) = e2
% 244.05/50.61    (20)  all_58_10 = e2
% 244.05/50.61    (21)  op(e2, e0) = e2
% 244.05/50.61    (22)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) =
% 244.05/50.61            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3,
% 244.05/50.61              e0) = all_16_1 & $i(all_16_1))
% 244.05/50.61    (23)  op(e3, e0) = all_52_12
% 244.05/50.61    (24)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 244.05/50.61            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 244.05/50.61              e0) = all_50_1 & $i(all_50_1))
% 244.05/50.61    (25)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.05/50.61          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.05/50.61    (26)   ~ (all_52_9 = e3)
% 244.05/50.61    (27)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.61          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.61    (28)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.61          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 244.05/50.61    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.61    (30)  op(e0, e0) = e0
% 244.05/50.61    (31)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.61          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.61    (32)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.61          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.05/50.61    (33)   ~ (all_52_12 = e3)
% 244.05/50.61    (34)  op(e1, e1) = e0
% 244.05/50.61    (35)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.05/50.61          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.05/50.61    (36)   ~ (e1 = e0)
% 244.05/50.61    (37)  op(e3, e3) = e0
% 244.05/50.61    (38)  all_58_2 = e3
% 244.05/50.61    (39)   ~ (all_52_13 = e3)
% 244.05/50.61    (40)  all_58_15 = e0
% 244.05/50.61    (41)  op(e2, e0) = all_52_13
% 244.05/50.61    (42)  all_58_3 = e0
% 244.05/50.61    (43)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.61          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.05/50.61    (44)   ~ (all_52_13 = e0)
% 244.05/50.61    (45)  all_58_13 = e3
% 244.05/50.61    (46)   ~ (e2 = e1)
% 244.05/50.61  
% 244.05/50.61  Begin of proof
% 244.05/50.61  | 
% 244.05/50.61  | BETA: splitting (8) gives:
% 244.05/50.61  | 
% 244.05/50.61  | Case 1:
% 244.05/50.61  | | 
% 244.05/50.61  | |   (47)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 244.05/50.61  | |           e1)
% 244.05/50.61  | | 
% 244.05/50.61  | | BETA: splitting (47) gives:
% 244.05/50.61  | | 
% 244.05/50.61  | | Case 1:
% 244.05/50.61  | | | 
% 244.05/50.61  | | |   (48)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.61  | | | 
% 244.05/50.61  | | | ALPHA: (48) implies:
% 244.05/50.61  | | |   (49)  all_58_9 = e1
% 244.05/50.61  | | | 
% 244.05/50.61  | | | BETA: splitting (1) gives:
% 244.05/50.61  | | | 
% 244.05/50.61  | | | Case 1:
% 244.05/50.61  | | | | 
% 244.05/50.61  | | | |   (50)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 244.05/50.61  | | | |           = e2)
% 244.05/50.61  | | | | 
% 244.05/50.61  | | | | BETA: splitting (50) gives:
% 244.05/50.61  | | | | 
% 244.05/50.61  | | | | Case 1:
% 244.05/50.61  | | | | | 
% 244.05/50.61  | | | | |   (51)  all_58_0 = e2 & op(e3, e3) = e2
% 244.05/50.61  | | | | | 
% 244.05/50.61  | | | | | ALPHA: (51) implies:
% 244.05/50.61  | | | | |   (52)  op(e3, e3) = e2
% 244.05/50.61  | | | | | 
% 244.05/50.61  | | | | | REF_CLOSE: (4), (29), (37), (52) are inconsistent by sub-proof #2188.
% 244.05/50.61  | | | | | 
% 244.05/50.61  | | | | Case 2:
% 244.05/50.61  | | | | | 
% 244.05/50.61  | | | | |   (53)  all_58_1 = e2 & op(e3, e2) = e2
% 244.05/50.61  | | | | | 
% 244.05/50.61  | | | | | ALPHA: (53) implies:
% 244.05/50.61  | | | | |   (54)  all_58_1 = e2
% 244.05/50.61  | | | | |   (55)  op(e3, e2) = e2
% 244.05/50.61  | | | | | 
% 244.05/50.61  | | | | | BETA: splitting (32) gives:
% 244.05/50.61  | | | | | 
% 244.05/50.61  | | | | | Case 1:
% 244.05/50.61  | | | | | | 
% 244.05/50.61  | | | | | |   (56)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 244.05/50.61  | | | | | |             e2) = e1)
% 244.05/50.61  | | | | | | 
% 244.05/50.61  | | | | | | REF_CLOSE: (2), (4), (8), (11), (15), (18), (27), (29), (30), (31),
% 244.05/50.61  | | | | | |            (36), (39), (41), (42), (46), (49), (55), (56) are
% 244.05/50.61  | | | | | |            inconsistent by sub-proof #1499.
% 244.05/50.61  | | | | | | 
% 244.05/50.61  | | | | | Case 2:
% 244.05/50.61  | | | | | | 
% 244.05/50.61  | | | | | |   (57)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 244.05/50.61  | | | | | |             e2) = e1)
% 244.05/50.61  | | | | | | 
% 244.05/50.61  | | | | | | BETA: splitting (57) gives:
% 244.05/50.61  | | | | | | 
% 244.05/50.61  | | | | | | Case 1:
% 244.05/50.61  | | | | | | | 
% 244.05/50.61  | | | | | | |   (58)  all_58_7 = e1 & op(e1, e2) = e1
% 244.05/50.61  | | | | | | | 
% 244.05/50.61  | | | | | | | ALPHA: (58) implies:
% 244.05/50.61  | | | | | | |   (59)  all_58_7 = e1
% 244.05/50.61  | | | | | | |   (60)  op(e1, e2) = e1
% 244.05/50.61  | | | | | | | 
% 244.05/50.61  | | | | | | | BETA: splitting (43) gives:
% 244.05/50.61  | | | | | | | 
% 244.05/50.61  | | | | | | | Case 1:
% 244.05/50.61  | | | | | | | | 
% 244.05/50.61  | | | | | | | |   (61)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 244.05/50.61  | | | | | | | |           op(e2, e2) = e1)
% 244.05/50.61  | | | | | | | | 
% 244.05/50.61  | | | | | | | | BETA: splitting (61) gives:
% 244.05/50.61  | | | | | | | | 
% 244.05/50.61  | | | | | | | | Case 1:
% 244.05/50.61  | | | | | | | | | 
% 244.05/50.61  | | | | | | | | |   (62)  all_58_2 = e1 & op(e2, e3) = e1
% 244.05/50.61  | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | REF_CLOSE: (11), (38), (62) are inconsistent by sub-proof
% 244.05/50.61  | | | | | | | | |            #1765.
% 244.05/50.61  | | | | | | | | | 
% 244.05/50.61  | | | | | | | | Case 2:
% 244.05/50.61  | | | | | | | | | 
% 244.05/50.61  | | | | | | | | |   (63)  all_58_3 = e1 & op(e2, e2) = e1
% 244.05/50.61  | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | REF_CLOSE: (2), (4), (8), (11), (15), (18), (27), (29), (30),
% 244.05/50.61  | | | | | | | | |            (31), (36), (39), (41), (42), (46), (49), (63) are
% 244.05/50.61  | | | | | | | | |            inconsistent by sub-proof #1500.
% 244.05/50.61  | | | | | | | | | 
% 244.05/50.61  | | | | | | | | End of split
% 244.05/50.61  | | | | | | | | 
% 244.05/50.61  | | | | | | | Case 2:
% 244.05/50.61  | | | | | | | | 
% 244.05/50.61  | | | | | | | |   (64)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 244.05/50.61  | | | | | | | |           op(e2, e0) = e1)
% 244.05/50.61  | | | | | | | | 
% 244.05/50.61  | | | | | | | | BETA: splitting (64) gives:
% 244.05/50.61  | | | | | | | | 
% 244.05/50.61  | | | | | | | | Case 1:
% 244.05/50.61  | | | | | | | | | 
% 244.05/50.61  | | | | | | | | |   (65)  all_58_5 = e1 & op(e2, e1) = e1
% 244.05/50.61  | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | ALPHA: (65) implies:
% 244.05/50.61  | | | | | | | | |   (66)  all_58_5 = e1
% 244.05/50.61  | | | | | | | | |   (67)  op(e2, e1) = e1
% 244.05/50.61  | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | BETA: splitting (7) gives:
% 244.05/50.61  | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | Case 1:
% 244.05/50.61  | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | |   (68)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 &
% 244.05/50.61  | | | | | | | | | |           op(e2, e2) = e2)
% 244.05/50.61  | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | BETA: splitting (68) gives:
% 244.05/50.61  | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | Case 1:
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | ALPHA: (48) implies:
% 244.05/50.61  | | | | | | | | | | |   (69)  op(e3, e0) = e1
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | GROUND_INST: instantiating (29) with all_52_6, e1, e2, e1,
% 244.05/50.61  | | | | | | | | | | |              simplifying with (6), (60) gives:
% 244.05/50.61  | | | | | | | | | | |   (70)  all_52_6 = e1
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | GROUND_INST: instantiating (29) with all_52_13, e2, e0, e2,
% 244.05/50.61  | | | | | | | | | | |              simplifying with (21), (41) gives:
% 244.05/50.61  | | | | | | | | | | |   (71)  all_52_13 = e2
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | GROUND_INST: instantiating (29) with all_52_9, e1, e1, e2,
% 244.05/50.61  | | | | | | | | | | |              simplifying with (17), (67) gives:
% 244.05/50.61  | | | | | | | | | | |   (72)  all_52_9 = e1
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | GROUND_INST: instantiating (29) with all_52_12, e1, e0, e3,
% 244.05/50.61  | | | | | | | | | | |              simplifying with (23), (69) gives:
% 244.05/50.61  | | | | | | | | | | |   (73)  all_52_12 = e1
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | REDUCE: (14), (71), (73) imply:
% 244.05/50.61  | | | | | | | | | | |   (74)   ~ (e2 = e1)
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | REDUCE: (33), (73) imply:
% 244.05/50.61  | | | | | | | | | | |   (75)   ~ (e3 = e1)
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | REDUCE: (39), (71) imply:
% 244.05/50.61  | | | | | | | | | | |   (76)   ~ (e3 = e2)
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | REDUCE: (19), (72) imply:
% 244.05/50.61  | | | | | | | | | | |   (77)  op(e2, e1) = e2
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | BETA: splitting (22) gives:
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | Case 1:
% 244.05/50.61  | | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (11), (13), (18), (29),
% 244.05/50.61  | | | | | | | | | | | |            (35), (36), (46), (54), (59), (60), (67), (77) are
% 244.05/50.61  | | | | | | | | | | | |            inconsistent by sub-proof #1498.
% 244.05/50.61  | | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | Case 2:
% 244.05/50.61  | | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | |   (78)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 &
% 244.05/50.61  | | | | | | | | | | | |         $i(all_16_1)
% 244.05/50.61  | | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | | REF_CLOSE: (24), (29), (69), (78) are inconsistent by
% 244.05/50.61  | | | | | | | | | | | |            sub-proof #1569.
% 244.05/50.61  | | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | End of split
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | Case 2:
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | |   (79)  all_58_3 = e2 & op(e2, e2) = e2
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | ALPHA: (79) implies:
% 244.05/50.61  | | | | | | | | | | |   (80)  op(e2, e2) = e2
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (11), (17), (18), (21), (28), (29),
% 244.05/50.61  | | | | | | | | | | |            (36), (66), (67), (80) are inconsistent by
% 244.05/50.61  | | | | | | | | | | |            sub-proof #2119.
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | End of split
% 244.05/50.61  | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | Case 2:
% 244.05/50.61  | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | |   (81)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2
% 244.05/50.61  | | | | | | | | | |           & op(e0, e2) = e2)
% 244.05/50.61  | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | BETA: splitting (81) gives:
% 244.05/50.61  | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | Case 1:
% 244.05/50.61  | | | | | | | | | | | 
% 244.05/50.61  | | | | | | | | | | |   (82)  all_58_7 = e2 & op(e1, e2) = e2
% 244.05/50.62  | | | | | | | | | | | 
% 244.05/50.62  | | | | | | | | | | | ALPHA: (82) implies:
% 244.05/50.62  | | | | | | | | | | |   (83)  all_58_7 = e2
% 244.05/50.62  | | | | | | | | | | | 
% 244.05/50.62  | | | | | | | | | | | COMBINE_EQS: (59), (83) imply:
% 244.05/50.62  | | | | | | | | | | |   (84)  e2 = e1
% 244.05/50.62  | | | | | | | | | | | 
% 244.05/50.62  | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (11), (13), (18), (29),
% 244.05/50.62  | | | | | | | | | | |            (35), (36), (46), (54), (59), (60), (84) are
% 244.05/50.62  | | | | | | | | | | |            inconsistent by sub-proof #1497.
% 244.05/50.62  | | | | | | | | | | | 
% 244.05/50.62  | | | | | | | | | | Case 2:
% 244.05/50.62  | | | | | | | | | | | 
% 244.05/50.62  | | | | | | | | | | |   (85)  all_58_13 = e2 & op(e0, e2) = e2
% 244.05/50.62  | | | | | | | | | | | 
% 244.05/50.62  | | | | | | | | | | | ALPHA: (85) implies:
% 244.05/50.62  | | | | | | | | | | |   (86)  op(e0, e2) = e2
% 244.05/50.62  | | | | | | | | | | | 
% 244.05/50.62  | | | | | | | | | | | REF_CLOSE: (12), (18), (29), (86) are inconsistent by
% 244.05/50.62  | | | | | | | | | | |            sub-proof #2254.
% 244.05/50.62  | | | | | | | | | | | 
% 244.05/50.62  | | | | | | | | | | End of split
% 244.05/50.62  | | | | | | | | | | 
% 244.05/50.62  | | | | | | | | | End of split
% 244.05/50.62  | | | | | | | | | 
% 244.05/50.62  | | | | | | | | Case 2:
% 244.05/50.62  | | | | | | | | | 
% 244.05/50.62  | | | | | | | | |   (87)  all_58_10 = e1 & op(e2, e0) = e1
% 244.05/50.62  | | | | | | | | | 
% 244.05/50.62  | | | | | | | | | ALPHA: (87) implies:
% 244.05/50.62  | | | | | | | | |   (88)  all_58_10 = e1
% 244.05/50.62  | | | | | | | | | 
% 244.05/50.62  | | | | | | | | | REF_CLOSE: (2), (4), (11), (18), (27), (31), (40), (46), (49),
% 244.05/50.62  | | | | | | | | |            (88) are inconsistent by sub-proof #1495.
% 244.05/50.62  | | | | | | | | | 
% 244.05/50.62  | | | | | | | | End of split
% 244.05/50.62  | | | | | | | | 
% 244.05/50.62  | | | | | | | End of split
% 244.05/50.62  | | | | | | | 
% 244.05/50.62  | | | | | | Case 2:
% 244.05/50.62  | | | | | | | 
% 244.05/50.62  | | | | | | |   (89)  all_58_13 = e1 & op(e0, e2) = e1
% 244.05/50.62  | | | | | | | 
% 244.05/50.62  | | | | | | | REF_CLOSE: (11), (45), (89) are inconsistent by sub-proof #2013.
% 244.05/50.62  | | | | | | | 
% 244.05/50.62  | | | | | | End of split
% 244.05/50.62  | | | | | | 
% 244.05/50.62  | | | | | End of split
% 244.05/50.62  | | | | | 
% 244.05/50.62  | | | | End of split
% 244.05/50.62  | | | | 
% 244.05/50.62  | | | Case 2:
% 244.05/50.62  | | | | 
% 244.05/50.62  | | | |   (90)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 244.05/50.62  | | | |           = e2)
% 244.05/50.62  | | | | 
% 244.05/50.62  | | | | REF_CLOSE: (2), (3), (4), (11), (16), (17), (18), (20), (25), (26),
% 244.05/50.62  | | | |            (27), (29), (31), (34), (40), (46), (49), (90) are
% 244.05/50.62  | | | |            inconsistent by sub-proof #1492.
% 244.05/50.62  | | | | 
% 244.05/50.62  | | | End of split
% 244.05/50.62  | | | 
% 244.05/50.62  | | Case 2:
% 244.05/50.62  | | | 
% 244.05/50.62  | | |   (91)  all_58_10 = e1 & op(e2, e0) = e1
% 244.05/50.62  | | | 
% 244.05/50.62  | | | ALPHA: (91) implies:
% 244.05/50.62  | | |   (92)  op(e2, e0) = e1
% 244.05/50.62  | | | 
% 244.05/50.62  | | | REF_CLOSE: (21), (29), (46), (92) are inconsistent by sub-proof #1659.
% 244.05/50.62  | | | 
% 244.05/50.62  | | End of split
% 244.05/50.62  | | 
% 244.05/50.62  | Case 2:
% 244.05/50.62  | | 
% 244.05/50.62  | |   (93)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.05/50.62  | |           e1)
% 244.05/50.62  | | 
% 244.05/50.62  | | BETA: splitting (93) gives:
% 244.05/50.62  | | 
% 244.05/50.62  | | Case 1:
% 244.05/50.62  | | | 
% 244.05/50.62  | | |   (94)  all_58_11 = e1 & op(e1, e0) = e1
% 244.05/50.62  | | | 
% 244.05/50.62  | | | ALPHA: (94) implies:
% 244.05/50.62  | | |   (95)  all_58_11 = e1
% 244.05/50.62  | | | 
% 244.05/50.62  | | | REF_CLOSE: (11), (15), (95) are inconsistent by sub-proof #1980.
% 244.05/50.62  | | | 
% 244.05/50.62  | | Case 2:
% 244.05/50.62  | | | 
% 244.05/50.62  | | |   (96)  all_58_15 = e1 & op(e0, e0) = e1
% 244.05/50.62  | | | 
% 244.05/50.62  | | | ALPHA: (96) implies:
% 244.05/50.62  | | |   (97)  op(e0, e0) = e1
% 244.05/50.62  | | | 
% 244.05/50.62  | | | REF_CLOSE: (29), (30), (36), (97) are inconsistent by sub-proof #2274.
% 244.05/50.62  | | | 
% 244.05/50.62  | | End of split
% 244.05/50.62  | | 
% 244.05/50.62  | End of split
% 244.05/50.62  | 
% 244.05/50.62  End of proof
% 244.05/50.62  
% 244.05/50.62  Sub-proof #1492 shows that the following formulas are inconsistent:
% 244.05/50.62  ----------------------------------------------------------------
% 244.05/50.62    (1)   ~ (e3 = e0)
% 244.05/50.62    (2)  op(e0, e1) = all_52_11
% 244.05/50.62    (3)   ~ (e2 = e0)
% 244.05/50.62    (4)   ~ (e3 = e1)
% 244.05/50.62    (5)   ~ (all_52_11 = e3)
% 244.05/50.62    (6)  op(e2, e1) = all_52_9
% 244.05/50.62    (7)   ~ (e3 = e2)
% 244.05/50.62    (8)  all_58_10 = e2
% 244.05/50.62    (9)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.62    (10)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.05/50.62          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.05/50.62    (11)   ~ (all_52_9 = e3)
% 244.05/50.62    (12)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.62          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.62    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.62    (14)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.62          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.62    (15)  op(e1, e1) = e0
% 244.05/50.62    (16)  all_58_9 = e1
% 244.05/50.62    (17)  all_58_15 = e0
% 244.05/50.62    (18)   ~ (e2 = e1)
% 244.05/50.62  
% 244.05/50.62  Begin of proof
% 244.05/50.62  | 
% 244.05/50.62  | BETA: splitting (9) gives:
% 244.05/50.62  | 
% 244.05/50.62  | Case 1:
% 244.05/50.62  | | 
% 244.05/50.62  | |   (19)  all_58_4 = e2 & op(e3, e1) = e2
% 244.05/50.62  | | 
% 244.05/50.62  | | ALPHA: (19) implies:
% 244.05/50.62  | |   (20)  all_58_4 = e2
% 244.05/50.62  | | 
% 244.05/50.62  | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (11), (13), (15), (20) are
% 244.05/50.62  | |            inconsistent by sub-proof #1493.
% 244.05/50.62  | | 
% 244.05/50.62  | Case 2:
% 244.05/50.62  | | 
% 244.05/50.62  | |   (21)  all_58_9 = e2 & op(e3, e0) = e2
% 244.05/50.62  | | 
% 244.05/50.62  | | ALPHA: (21) implies:
% 244.05/50.62  | |   (22)  all_58_9 = e2
% 244.05/50.62  | | 
% 244.05/50.62  | | COMBINE_EQS: (16), (22) imply:
% 244.05/50.62  | |   (23)  e2 = e1
% 244.05/50.62  | | 
% 244.05/50.62  | | SIMP: (23) implies:
% 244.05/50.62  | |   (24)  e2 = e1
% 244.05/50.62  | | 
% 244.05/50.62  | | COMBINE_EQS: (8), (24) imply:
% 244.05/50.62  | |   (25)  all_58_10 = e1
% 244.05/50.62  | | 
% 244.05/50.62  | | REF_CLOSE: (1), (3), (4), (7), (12), (14), (16), (17), (18), (25) are
% 244.05/50.62  | |            inconsistent by sub-proof #1495.
% 244.05/50.62  | | 
% 244.05/50.62  | End of split
% 244.05/50.62  | 
% 244.05/50.62  End of proof
% 244.05/50.62  
% 244.05/50.62  Sub-proof #1493 shows that the following formulas are inconsistent:
% 244.05/50.62  ----------------------------------------------------------------
% 244.05/50.62    (1)   ~ (e3 = e0)
% 244.05/50.62    (2)  op(e0, e1) = all_52_11
% 244.05/50.62    (3)  all_58_4 = e2
% 244.05/50.62    (4)   ~ (all_52_11 = e3)
% 244.05/50.62    (5)  op(e2, e1) = all_52_9
% 244.05/50.62    (6)   ~ (e3 = e2)
% 244.05/50.62    (7)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.05/50.62         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.05/50.62    (8)   ~ (all_52_9 = e3)
% 244.05/50.62    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.62    (10)  op(e1, e1) = e0
% 244.05/50.62  
% 244.05/50.62  Begin of proof
% 244.05/50.62  | 
% 244.05/50.62  | BETA: splitting (7) gives:
% 244.05/50.62  | 
% 244.05/50.62  | Case 1:
% 244.05/50.62  | | 
% 244.05/50.62  | |   (11)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 244.05/50.62  | |           e3)
% 244.05/50.62  | | 
% 244.05/50.62  | | REF_CLOSE: (3), (5), (6), (8), (9), (11) are inconsistent by sub-proof
% 244.05/50.62  | |            #1494.
% 244.05/50.62  | | 
% 244.05/50.62  | Case 2:
% 244.05/50.62  | | 
% 244.05/50.62  | |   (12)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 244.05/50.62  | |           e3)
% 244.05/50.62  | | 
% 244.05/50.62  | | BETA: splitting (12) gives:
% 244.05/50.62  | | 
% 244.05/50.62  | | Case 1:
% 244.05/50.62  | | | 
% 244.05/50.62  | | |   (13)  all_58_8 = e3 & op(e1, e1) = e3
% 244.05/50.62  | | | 
% 244.05/50.62  | | | REF_CLOSE: (1), (9), (10), (13) are inconsistent by sub-proof #2018.
% 244.05/50.62  | | | 
% 244.05/50.62  | | Case 2:
% 244.05/50.62  | | | 
% 244.05/50.62  | | |   (14)  all_58_14 = e3 & op(e0, e1) = e3
% 244.05/50.62  | | | 
% 244.05/50.62  | | | REF_CLOSE: (2), (4), (9), (14) are inconsistent by sub-proof #1647.
% 244.05/50.62  | | | 
% 244.05/50.62  | | End of split
% 244.05/50.62  | | 
% 244.05/50.62  | End of split
% 244.05/50.62  | 
% 244.05/50.62  End of proof
% 244.05/50.62  
% 244.05/50.62  Sub-proof #1494 shows that the following formulas are inconsistent:
% 244.05/50.62  ----------------------------------------------------------------
% 244.05/50.62    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 244.05/50.62    (2)  all_58_4 = e2
% 244.05/50.62    (3)  op(e2, e1) = all_52_9
% 244.05/50.62    (4)   ~ (e3 = e2)
% 244.05/50.62    (5)   ~ (all_52_9 = e3)
% 244.05/50.62    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.62  
% 244.05/50.62  Begin of proof
% 244.05/50.62  | 
% 244.05/50.62  | BETA: splitting (1) gives:
% 244.05/50.62  | 
% 244.05/50.62  | Case 1:
% 244.05/50.62  | | 
% 244.05/50.62  | |   (7)  all_58_4 = e3 & op(e3, e1) = e3
% 244.05/50.62  | | 
% 244.05/50.62  | | ALPHA: (7) implies:
% 244.05/50.62  | |   (8)  all_58_4 = e3
% 244.05/50.62  | | 
% 244.05/50.62  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #1902.
% 244.05/50.62  | | 
% 244.05/50.62  | Case 2:
% 244.05/50.62  | | 
% 244.05/50.62  | |   (9)  all_58_5 = e3 & op(e2, e1) = e3
% 244.05/50.62  | | 
% 244.05/50.62  | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #1822.
% 244.05/50.62  | | 
% 244.05/50.62  | End of split
% 244.05/50.62  | 
% 244.05/50.62  End of proof
% 244.05/50.62  
% 244.05/50.62  Sub-proof #1495 shows that the following formulas are inconsistent:
% 244.05/50.62  ----------------------------------------------------------------
% 244.05/50.62    (1)   ~ (e3 = e0)
% 244.05/50.62    (2)   ~ (e2 = e0)
% 244.05/50.62    (3)   ~ (e3 = e1)
% 244.05/50.62    (4)   ~ (e3 = e2)
% 244.05/50.62    (5)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.62         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.62    (6)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.62         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.62    (7)  all_58_9 = e1
% 244.05/50.62    (8)  all_58_15 = e0
% 244.05/50.62    (9)  all_58_10 = e1
% 244.05/50.62    (10)   ~ (e2 = e1)
% 244.05/50.62  
% 244.05/50.62  Begin of proof
% 244.05/50.62  | 
% 244.05/50.62  | BETA: splitting (5) gives:
% 244.05/50.62  | 
% 244.05/50.62  | Case 1:
% 244.05/50.62  | | 
% 244.05/50.62  | |   (11)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 244.05/50.62  | |           e3)
% 244.05/50.62  | | 
% 244.05/50.62  | | BETA: splitting (11) gives:
% 244.05/50.62  | | 
% 244.05/50.62  | | Case 1:
% 244.05/50.62  | | | 
% 244.05/50.62  | | |   (12)  all_58_9 = e3 & op(e3, e0) = e3
% 244.05/50.62  | | | 
% 244.05/50.62  | | | ALPHA: (12) implies:
% 244.05/50.62  | | |   (13)  all_58_9 = e3
% 244.05/50.62  | | | 
% 244.05/50.62  | | | REF_CLOSE: (3), (7), (13) are inconsistent by sub-proof #1709.
% 244.05/50.62  | | | 
% 244.05/50.62  | | Case 2:
% 244.05/50.62  | | | 
% 244.05/50.62  | | |   (14)  all_58_10 = e3 & op(e2, e0) = e3
% 244.05/50.62  | | | 
% 244.05/50.62  | | | REF_CLOSE: (3), (9), (14) are inconsistent by sub-proof #1620.
% 244.05/50.62  | | | 
% 244.05/50.62  | | End of split
% 244.05/50.62  | | 
% 244.05/50.62  | Case 2:
% 244.05/50.62  | | 
% 244.05/50.62  | |   (15)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.05/50.62  | |           e3)
% 244.05/50.62  | | 
% 244.05/50.62  | | BETA: splitting (15) gives:
% 244.05/50.62  | | 
% 244.05/50.62  | | Case 1:
% 244.05/50.62  | | | 
% 244.05/50.62  | | |   (16)  all_58_11 = e3 & op(e1, e0) = e3
% 244.05/50.62  | | | 
% 244.05/50.62  | | | ALPHA: (16) implies:
% 244.05/50.62  | | |   (17)  all_58_11 = e3
% 244.05/50.62  | | | 
% 244.05/50.62  | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (17) are inconsistent by
% 244.05/50.62  | | |            sub-proof #1506.
% 244.05/50.62  | | | 
% 244.05/50.62  | | Case 2:
% 244.05/50.62  | | | 
% 244.05/50.62  | | |   (18)  all_58_15 = e3 & op(e0, e0) = e3
% 244.05/50.62  | | | 
% 244.05/50.62  | | | REF_CLOSE: (1), (8), (18) are inconsistent by sub-proof #1496.
% 244.05/50.62  | | | 
% 244.05/50.62  | | End of split
% 244.05/50.62  | | 
% 244.05/50.62  | End of split
% 244.05/50.62  | 
% 244.05/50.62  End of proof
% 244.05/50.62  
% 244.05/50.62  Sub-proof #1496 shows that the following formulas are inconsistent:
% 244.05/50.62  ----------------------------------------------------------------
% 244.05/50.62    (1)  all_58_15 = e3 & op(e0, e0) = e3
% 244.05/50.62    (2)  all_58_15 = e0
% 244.05/50.62    (3)   ~ (e3 = e0)
% 244.05/50.62  
% 244.05/50.62  Begin of proof
% 244.05/50.62  | 
% 244.05/50.62  | ALPHA: (1) implies:
% 244.05/50.62  |   (4)  all_58_15 = e3
% 244.05/50.62  | 
% 244.05/50.62  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.62  |   (5)  e3 = e0
% 244.05/50.62  | 
% 244.05/50.62  | REDUCE: (3), (5) imply:
% 244.05/50.62  |   (6)  $false
% 244.05/50.62  | 
% 244.05/50.62  | CLOSE: (6) is inconsistent.
% 244.05/50.62  | 
% 244.05/50.62  End of proof
% 244.05/50.62  
% 244.05/50.62  Sub-proof #1497 shows that the following formulas are inconsistent:
% 244.05/50.62  ----------------------------------------------------------------
% 244.05/50.62    (1)   ~ (e3 = e0)
% 244.05/50.62    (2)  op(e1, e2) = e1
% 244.05/50.62    (3)   ~ (e2 = e0)
% 244.05/50.62    (4)  op(e1, e2) = all_52_6
% 244.05/50.62    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.62         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.62    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.62         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.62    (7)   ~ (e3 = e1)
% 244.05/50.62    (8)  op(e2, e2) = e0
% 244.05/50.62    (9)   ~ (e3 = e2)
% 244.05/50.62    (10)  all_58_7 = e1
% 244.05/50.62    (11)  all_58_1 = e2
% 244.05/50.62    (12)  e2 = e1
% 244.05/50.62    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.62    (14)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.05/50.62          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.05/50.62    (15)   ~ (e1 = e0)
% 244.05/50.62    (16)   ~ (e2 = e1)
% 244.05/50.62  
% 244.05/50.62  Begin of proof
% 244.05/50.62  | 
% 244.05/50.62  | SIMP: (12) implies:
% 244.05/50.62  |   (17)  e2 = e1
% 244.05/50.62  | 
% 244.05/50.62  | COMBINE_EQS: (11), (17) imply:
% 244.05/50.62  |   (18)  all_58_1 = e1
% 244.05/50.62  | 
% 244.05/50.62  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 244.05/50.62  |            (15), (16), (18) are inconsistent by sub-proof #1714.
% 244.05/50.62  | 
% 244.05/50.62  End of proof
% 244.05/50.62  
% 244.05/50.62  Sub-proof #1498 shows that the following formulas are inconsistent:
% 244.05/50.62  ----------------------------------------------------------------
% 244.05/50.62    (1)   ~ (e3 = e0)
% 244.05/50.62    (2)  op(e2, e1) = e1
% 244.05/50.62    (3)  op(e1, e2) = e1
% 244.05/50.62    (4)   ~ (e2 = e0)
% 244.05/50.62    (5)  op(e1, e2) = all_52_6
% 244.05/50.62    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.62         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.62    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.05/50.62         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.05/50.62    (8)   ~ (e3 = e1)
% 244.05/50.62    (9)  op(e2, e2) = e0
% 244.05/50.62    (10)  op(e2, e1) = e2
% 244.05/50.62    (11)   ~ (e3 = e2)
% 244.05/50.62    (12)  all_58_7 = e1
% 244.05/50.62    (13)  all_58_1 = e2
% 244.05/50.62    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.62    (15)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.05/50.62          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.05/50.62    (16)   ~ (e1 = e0)
% 244.05/50.62    (17)   ~ (e2 = e1)
% 244.05/50.62  
% 244.05/50.62  Begin of proof
% 244.05/50.62  | 
% 244.05/50.62  | GROUND_INST: instantiating (14) with e1, e2, e1, e2, simplifying with (2),
% 244.05/50.62  |              (10) gives:
% 244.05/50.62  |   (18)  e2 = e1
% 244.05/50.62  | 
% 244.05/50.62  | COMBINE_EQS: (13), (18) imply:
% 244.05/50.62  |   (19)  all_58_1 = e1
% 244.05/50.62  | 
% 244.05/50.62  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15),
% 244.05/50.62  |            (16), (17), (19) are inconsistent by sub-proof #1714.
% 244.05/50.62  | 
% 244.05/50.62  End of proof
% 244.05/50.62  
% 244.05/50.62  Sub-proof #1499 shows that the following formulas are inconsistent:
% 244.05/50.62  ----------------------------------------------------------------
% 244.05/50.62    (1)   ~ (e3 = e0)
% 244.05/50.62    (2)   ~ (e2 = e0)
% 244.05/50.62    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.62         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.62    (4)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 244.05/50.62    (5)   ~ (e3 = e1)
% 244.05/50.62    (6)  all_58_11 = e3
% 244.05/50.62    (7)  op(e3, e2) = e2
% 244.05/50.62    (8)   ~ (e3 = e2)
% 244.05/50.62    (9)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.62         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.62    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.62    (11)  op(e0, e0) = e0
% 244.05/50.62    (12)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.62          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.62    (13)   ~ (e1 = e0)
% 244.05/50.62    (14)  all_58_9 = e1
% 244.05/50.62    (15)   ~ (all_52_13 = e3)
% 244.05/50.62    (16)  op(e2, e0) = all_52_13
% 244.05/50.62    (17)  all_58_3 = e0
% 244.05/50.62    (18)   ~ (e2 = e1)
% 244.05/50.62  
% 244.05/50.62  Begin of proof
% 244.05/50.62  | 
% 244.05/50.62  | BETA: splitting (4) gives:
% 244.05/50.62  | 
% 244.05/50.62  | Case 1:
% 244.05/50.62  | | 
% 244.05/50.62  | |   (19)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.62  | | 
% 244.05/50.62  | | ALPHA: (19) implies:
% 244.05/50.62  | |   (20)  op(e3, e2) = e1
% 244.05/50.62  | | 
% 244.05/50.62  | | REF_CLOSE: (7), (10), (18), (20) are inconsistent by sub-proof #2261.
% 244.05/50.62  | | 
% 244.05/50.62  | Case 2:
% 244.05/50.62  | | 
% 244.05/50.62  | |   (21)  all_58_3 = e1 & op(e2, e2) = e1
% 244.05/50.62  | | 
% 244.05/50.62  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 244.05/50.62  | |            (15), (16), (17), (18), (21) are inconsistent by sub-proof #1500.
% 244.05/50.62  | | 
% 244.05/50.62  | End of split
% 244.05/50.62  | 
% 244.05/50.62  End of proof
% 244.05/50.62  
% 244.05/50.62  Sub-proof #1500 shows that the following formulas are inconsistent:
% 244.05/50.62  ----------------------------------------------------------------
% 244.05/50.62    (1)   ~ (e3 = e0)
% 244.05/50.63    (2)   ~ (e2 = e0)
% 244.05/50.63    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.05/50.63         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.63    (4)   ~ (e3 = e1)
% 244.05/50.63    (5)  all_58_11 = e3
% 244.05/50.63    (6)   ~ (e3 = e2)
% 244.05/50.63    (7)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.05/50.63         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.63    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.63    (9)  op(e0, e0) = e0
% 244.05/50.63    (10)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.63          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.63    (11)  all_58_3 = e1 & op(e2, e2) = e1
% 244.05/50.63    (12)   ~ (e1 = e0)
% 244.05/50.63    (13)  all_58_9 = e1
% 244.05/50.63    (14)   ~ (all_52_13 = e3)
% 244.05/50.63    (15)  op(e2, e0) = all_52_13
% 244.05/50.63    (16)  all_58_3 = e0
% 244.05/50.63    (17)   ~ (e2 = e1)
% 244.05/50.63  
% 244.05/50.63  Begin of proof
% 244.05/50.63  | 
% 244.05/50.63  | ALPHA: (11) implies:
% 244.05/50.63  |   (18)  all_58_3 = e1
% 244.05/50.63  | 
% 244.05/50.63  | COMBINE_EQS: (16), (18) imply:
% 244.05/50.63  |   (19)  e1 = e0
% 244.05/50.63  | 
% 244.05/50.63  | SIMP: (19) implies:
% 244.05/50.63  |   (20)  e1 = e0
% 244.05/50.63  | 
% 244.05/50.63  | COMBINE_EQS: (13), (20) imply:
% 244.05/50.63  |   (21)  all_58_9 = e0
% 244.05/50.63  | 
% 244.05/50.63  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 244.05/50.63  |            (15), (17), (21) are inconsistent by sub-proof #1651.
% 244.05/50.63  | 
% 244.05/50.63  End of proof
% 244.05/50.63  
% 244.05/50.63  Sub-proof #1501 shows that the following formulas are inconsistent:
% 244.05/50.63  ----------------------------------------------------------------
% 244.05/50.63    (1)   ~ (e3 = e0)
% 244.05/50.63    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.05/50.63         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.05/50.63    (3)   ~ (e2 = e0)
% 244.05/50.63    (4)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.63         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.63    (5)  op(e1, all_56_5) = e1
% 244.05/50.63    (6)  op(e1, e3) = all_56_5
% 244.05/50.63    (7)   ~ (e3 = e1)
% 244.05/50.63    (8)  op(e0, e2) = e3
% 244.05/50.63    (9)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.05/50.63         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.05/50.63    (10)  op(e2, e2) = e0
% 244.05/50.63    (11)  op(e0, e1) = e1
% 244.05/50.63    (12)  all_58_11 = e3
% 244.05/50.63    (13)  op(e2, e1) = e2
% 244.05/50.63    (14)   ~ (e3 = e2)
% 244.05/50.63    (15)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 244.05/50.63            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 244.05/50.63              e0) = all_14_1 & $i(all_14_1))
% 244.05/50.63    (16)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 244.05/50.63            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 244.05/50.63              e0) = all_48_1 & $i(all_48_1))
% 244.05/50.63    (17)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.63          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.63    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.63            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.63    (19)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.63          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.63    (20)  op(e3, e1) = e3
% 244.05/50.63    (21)  op(e1, e1) = e0
% 244.05/50.63    (22)   ~ (e1 = e0)
% 244.05/50.63    (23)  op(e3, e3) = e0
% 244.05/50.63    (24)  all_58_4 = e3
% 244.05/50.63    (25)  op(e2, e0) = e1
% 244.05/50.63    (26)  all_58_15 = e0
% 244.05/50.63    (27)  all_58_10 = e1
% 244.05/50.63    (28)   ~ (e2 = e1)
% 244.05/50.63  
% 244.05/50.63  Begin of proof
% 244.05/50.63  | 
% 244.05/50.63  | BETA: splitting (17) gives:
% 244.05/50.63  | 
% 244.05/50.63  | Case 1:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (29)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 244.05/50.63  | |           e1)
% 244.05/50.63  | | 
% 244.05/50.63  | | BETA: splitting (29) gives:
% 244.05/50.63  | | 
% 244.05/50.63  | | Case 1:
% 244.05/50.63  | | | 
% 244.05/50.63  | | |   (30)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.63  | | | 
% 244.05/50.63  | | | ALPHA: (30) implies:
% 244.05/50.63  | | |   (31)  op(e3, e3) = e1
% 244.05/50.63  | | | 
% 244.05/50.63  | | | REF_CLOSE: (18), (22), (23), (31) are inconsistent by sub-proof #1828.
% 244.05/50.63  | | | 
% 244.05/50.63  | | Case 2:
% 244.05/50.63  | | | 
% 244.05/50.63  | | |   (32)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.63  | | | 
% 244.05/50.63  | | | ALPHA: (32) implies:
% 244.05/50.63  | | |   (33)  all_58_1 = e1
% 244.05/50.63  | | | 
% 244.05/50.63  | | | BETA: splitting (2) gives:
% 244.05/50.63  | | | 
% 244.05/50.63  | | | Case 1:
% 244.05/50.63  | | | | 
% 244.05/50.63  | | | |   (34)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 244.05/50.63  | | | |           = e1)
% 244.05/50.63  | | | | 
% 244.05/50.63  | | | | BETA: splitting (34) gives:
% 244.05/50.63  | | | | 
% 244.05/50.63  | | | | Case 1:
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | |   (35)  all_58_6 = e1 & op(e1, e3) = e1
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | | ALPHA: (35) implies:
% 244.05/50.63  | | | | |   (36)  op(e1, e3) = e1
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | | BETA: splitting (15) gives:
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | | Case 1:
% 244.05/50.63  | | | | | | 
% 244.05/50.63  | | | | | | 
% 244.05/50.63  | | | | | | GROUND_INST: instantiating (18) with e1, all_56_5, e3, e1,
% 244.05/50.63  | | | | | |              simplifying with (6), (36) gives:
% 244.05/50.63  | | | | | |   (37)  all_56_5 = e1
% 244.05/50.63  | | | | | | 
% 244.05/50.63  | | | | | | REDUCE: (5), (37) imply:
% 244.05/50.63  | | | | | |   (38)  op(e1, e1) = e1
% 244.05/50.63  | | | | | | 
% 244.05/50.63  | | | | | | REF_CLOSE: (18), (21), (22), (38) are inconsistent by sub-proof
% 244.05/50.63  | | | | | |            #2220.
% 244.05/50.63  | | | | | | 
% 244.05/50.63  | | | | | Case 2:
% 244.05/50.63  | | | | | | 
% 244.05/50.63  | | | | | |   (39)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 244.05/50.63  | | | | | | 
% 244.05/50.63  | | | | | | ALPHA: (39) implies:
% 244.05/50.63  | | | | | |   (40)   ~ (all_14_1 = e1)
% 244.05/50.63  | | | | | |   (41)  op(e2, e0) = all_14_1
% 244.05/50.63  | | | | | | 
% 244.05/50.63  | | | | | | REF_CLOSE: (16), (18), (25), (40), (41) are inconsistent by
% 244.05/50.63  | | | | | |            sub-proof #1584.
% 244.05/50.63  | | | | | | 
% 244.05/50.63  | | | | | End of split
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | Case 2:
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | |   (42)  all_58_7 = e1 & op(e1, e2) = e1
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | | ALPHA: (42) implies:
% 244.05/50.63  | | | | |   (43)  all_58_7 = e1
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | | REF_CLOSE: (3), (4), (8), (10), (14), (18), (28), (33), (43) are
% 244.05/50.63  | | | | |            inconsistent by sub-proof #1715.
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | End of split
% 244.05/50.63  | | | | 
% 244.05/50.63  | | | Case 2:
% 244.05/50.63  | | | | 
% 244.05/50.63  | | | |   (44)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0)
% 244.05/50.63  | | | |           = e1)
% 244.05/50.63  | | | | 
% 244.05/50.63  | | | | BETA: splitting (44) gives:
% 244.05/50.63  | | | | 
% 244.05/50.63  | | | | Case 1:
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | |   (45)  all_58_8 = e1 & op(e1, e1) = e1
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | | ALPHA: (45) implies:
% 244.05/50.63  | | | | |   (46)  op(e1, e1) = e1
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | | REF_CLOSE: (1), (3), (9), (11), (13), (18), (22), (24), (46) are
% 244.05/50.63  | | | | |            inconsistent by sub-proof #1503.
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | Case 2:
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | |   (47)  all_58_11 = e1 & op(e1, e0) = e1
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | | REF_CLOSE: (7), (12), (47) are inconsistent by sub-proof #1657.
% 244.05/50.63  | | | | | 
% 244.05/50.63  | | | | End of split
% 244.05/50.63  | | | | 
% 244.05/50.63  | | | End of split
% 244.05/50.63  | | | 
% 244.05/50.63  | | End of split
% 244.05/50.63  | | 
% 244.05/50.63  | Case 2:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (48)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 244.05/50.63  | |           e1)
% 244.05/50.63  | | 
% 244.05/50.63  | | REF_CLOSE: (3), (7), (12), (14), (18), (19), (20), (26), (27), (28), (48)
% 244.05/50.63  | |            are inconsistent by sub-proof #1502.
% 244.05/50.63  | | 
% 244.05/50.63  | End of split
% 244.05/50.63  | 
% 244.05/50.63  End of proof
% 244.05/50.63  
% 244.05/50.63  Sub-proof #1502 shows that the following formulas are inconsistent:
% 244.05/50.63  ----------------------------------------------------------------
% 244.05/50.63    (1)   ~ (e2 = e0)
% 244.05/50.63    (2)   ~ (e3 = e1)
% 244.05/50.63    (3)  all_58_11 = e3
% 244.05/50.63    (4)   ~ (e3 = e2)
% 244.05/50.63    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.63    (6)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.63         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.63    (7)  op(e3, e1) = e3
% 244.05/50.63    (8)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.63    (9)  all_58_15 = e0
% 244.05/50.63    (10)  all_58_10 = e1
% 244.05/50.63    (11)   ~ (e2 = e1)
% 244.05/50.63  
% 244.05/50.63  Begin of proof
% 244.05/50.63  | 
% 244.05/50.63  | BETA: splitting (8) gives:
% 244.05/50.63  | 
% 244.05/50.63  | Case 1:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (12)  all_58_4 = e1 & op(e3, e1) = e1
% 244.05/50.63  | | 
% 244.05/50.63  | | ALPHA: (12) implies:
% 244.05/50.63  | |   (13)  op(e3, e1) = e1
% 244.05/50.63  | | 
% 244.05/50.63  | | REF_CLOSE: (2), (5), (7), (13) are inconsistent by sub-proof #1823.
% 244.05/50.63  | | 
% 244.05/50.63  | Case 2:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (14)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.63  | | 
% 244.05/50.63  | | ALPHA: (14) implies:
% 244.05/50.63  | |   (15)  all_58_9 = e1
% 244.05/50.63  | | 
% 244.05/50.63  | | REF_CLOSE: (1), (3), (4), (6), (9), (10), (11), (15) are inconsistent by
% 244.05/50.63  | |            sub-proof #1506.
% 244.05/50.63  | | 
% 244.05/50.63  | End of split
% 244.05/50.63  | 
% 244.05/50.63  End of proof
% 244.05/50.63  
% 244.05/50.63  Sub-proof #1503 shows that the following formulas are inconsistent:
% 244.05/50.63  ----------------------------------------------------------------
% 244.05/50.63    (1)   ~ (e3 = e0)
% 244.05/50.63    (2)  op(e1, e1) = e1
% 244.05/50.63    (3)   ~ (e2 = e0)
% 244.05/50.63    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.05/50.63         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.05/50.63    (5)  op(e0, e1) = e1
% 244.05/50.63    (6)  op(e2, e1) = e2
% 244.05/50.63    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.63    (8)   ~ (e1 = e0)
% 244.05/50.63    (9)  all_58_4 = e3
% 244.05/50.63  
% 244.05/50.63  Begin of proof
% 244.05/50.63  | 
% 244.05/50.63  | BETA: splitting (4) gives:
% 244.05/50.63  | 
% 244.05/50.63  | Case 1:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (10)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 244.05/50.63  | |           e0)
% 244.05/50.63  | | 
% 244.05/50.63  | | REF_CLOSE: (1), (3), (6), (7), (9), (10) are inconsistent by sub-proof
% 244.05/50.63  | |            #1504.
% 244.05/50.63  | | 
% 244.05/50.63  | Case 2:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (11)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 244.05/50.63  | |           e0)
% 244.05/50.63  | | 
% 244.05/50.63  | | BETA: splitting (11) gives:
% 244.05/50.63  | | 
% 244.05/50.63  | | Case 1:
% 244.05/50.63  | | | 
% 244.05/50.63  | | |   (12)  all_58_8 = e0 & op(e1, e1) = e0
% 244.05/50.63  | | | 
% 244.05/50.63  | | | ALPHA: (12) implies:
% 244.05/50.63  | | |   (13)  op(e1, e1) = e0
% 244.05/50.63  | | | 
% 244.05/50.63  | | | REF_CLOSE: (2), (7), (8), (13) are inconsistent by sub-proof #2220.
% 244.05/50.63  | | | 
% 244.05/50.63  | | Case 2:
% 244.05/50.63  | | | 
% 244.05/50.63  | | |   (14)  all_58_14 = e0 & op(e0, e1) = e0
% 244.05/50.63  | | | 
% 244.05/50.63  | | | ALPHA: (14) implies:
% 244.05/50.63  | | |   (15)  op(e0, e1) = e0
% 244.05/50.63  | | | 
% 244.05/50.63  | | | REF_CLOSE: (5), (7), (8), (15) are inconsistent by sub-proof #2158.
% 244.05/50.63  | | | 
% 244.05/50.63  | | End of split
% 244.05/50.63  | | 
% 244.05/50.63  | End of split
% 244.05/50.63  | 
% 244.05/50.63  End of proof
% 244.05/50.63  
% 244.05/50.63  Sub-proof #1504 shows that the following formulas are inconsistent:
% 244.05/50.63  ----------------------------------------------------------------
% 244.05/50.63    (1)   ~ (e3 = e0)
% 244.05/50.63    (2)   ~ (e2 = e0)
% 244.05/50.63    (3)  op(e2, e1) = e2
% 244.05/50.63    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 244.05/50.63    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.63    (6)  all_58_4 = e3
% 244.05/50.63  
% 244.05/50.63  Begin of proof
% 244.05/50.63  | 
% 244.05/50.63  | BETA: splitting (4) gives:
% 244.05/50.63  | 
% 244.05/50.63  | Case 1:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (7)  all_58_4 = e0 & op(e3, e1) = e0
% 244.05/50.63  | | 
% 244.05/50.63  | | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #1697.
% 244.05/50.63  | | 
% 244.05/50.63  | Case 2:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (8)  all_58_5 = e0 & op(e2, e1) = e0
% 244.05/50.63  | | 
% 244.05/50.63  | | ALPHA: (8) implies:
% 244.05/50.63  | |   (9)  op(e2, e1) = e0
% 244.05/50.63  | | 
% 244.05/50.63  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1906.
% 244.05/50.63  | | 
% 244.05/50.63  | End of split
% 244.05/50.63  | 
% 244.05/50.63  End of proof
% 244.05/50.63  
% 244.05/50.63  Sub-proof #1505 shows that the following formulas are inconsistent:
% 244.05/50.63  ----------------------------------------------------------------
% 244.05/50.63    (1)   ~ (e2 = e0)
% 244.05/50.63    (2)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 244.05/50.63    (3)   ~ (e3 = e1)
% 244.05/50.63    (4)  all_58_11 = e3
% 244.05/50.63    (5)   ~ (e3 = e2)
% 244.05/50.63    (6)  all_58_5 = e2
% 244.05/50.63    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.63    (8)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.63         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.63    (9)  op(e3, e1) = e3
% 244.05/50.63    (10)  all_58_15 = e0
% 244.05/50.63    (11)  all_58_9 = e2
% 244.05/50.63    (12)  all_58_10 = e1
% 244.05/50.63    (13)   ~ (e2 = e1)
% 244.05/50.63  
% 244.05/50.63  Begin of proof
% 244.05/50.63  | 
% 244.05/50.63  | BETA: splitting (2) gives:
% 244.05/50.63  | 
% 244.05/50.63  | Case 1:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (14)  all_58_4 = e1 & op(e3, e1) = e1
% 244.05/50.63  | | 
% 244.05/50.63  | | ALPHA: (14) implies:
% 244.05/50.63  | |   (15)  op(e3, e1) = e1
% 244.05/50.63  | | 
% 244.05/50.63  | | REF_CLOSE: (3), (7), (9), (15) are inconsistent by sub-proof #1823.
% 244.05/50.63  | | 
% 244.05/50.63  | Case 2:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (16)  all_58_5 = e1 & op(e2, e1) = e1
% 244.05/50.63  | | 
% 244.05/50.63  | | ALPHA: (16) implies:
% 244.05/50.63  | |   (17)  all_58_5 = e1
% 244.05/50.63  | | 
% 244.05/50.63  | | COMBINE_EQS: (6), (17) imply:
% 244.05/50.63  | |   (18)  e2 = e1
% 244.05/50.63  | | 
% 244.05/50.63  | | COMBINE_EQS: (11), (18) imply:
% 244.05/50.63  | |   (19)  all_58_9 = e1
% 244.05/50.63  | | 
% 244.05/50.63  | | REF_CLOSE: (1), (4), (5), (8), (10), (12), (13), (19) are inconsistent by
% 244.05/50.63  | |            sub-proof #1506.
% 244.05/50.63  | | 
% 244.05/50.63  | End of split
% 244.05/50.63  | 
% 244.05/50.63  End of proof
% 244.05/50.63  
% 244.05/50.63  Sub-proof #1506 shows that the following formulas are inconsistent:
% 244.05/50.63  ----------------------------------------------------------------
% 244.05/50.63    (1)   ~ (e2 = e0)
% 244.05/50.63    (2)  all_58_11 = e3
% 244.05/50.63    (3)   ~ (e3 = e2)
% 244.05/50.63    (4)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.63         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.63    (5)  all_58_9 = e1
% 244.05/50.63    (6)  all_58_15 = e0
% 244.05/50.63    (7)  all_58_10 = e1
% 244.05/50.63    (8)   ~ (e2 = e1)
% 244.05/50.63  
% 244.05/50.63  Begin of proof
% 244.05/50.63  | 
% 244.05/50.63  | BETA: splitting (4) gives:
% 244.05/50.63  | 
% 244.05/50.63  | Case 1:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (9)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 244.05/50.63  | |          e2)
% 244.05/50.63  | | 
% 244.05/50.63  | | REF_CLOSE: (5), (7), (8), (9) are inconsistent by sub-proof #1508.
% 244.05/50.63  | | 
% 244.05/50.63  | Case 2:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (10)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.05/50.63  | |           e2)
% 244.05/50.63  | | 
% 244.05/50.63  | | BETA: splitting (10) gives:
% 244.05/50.63  | | 
% 244.05/50.63  | | Case 1:
% 244.05/50.63  | | | 
% 244.05/50.63  | | |   (11)  all_58_11 = e2 & op(e1, e0) = e2
% 244.05/50.63  | | | 
% 244.05/50.63  | | | ALPHA: (11) implies:
% 244.05/50.63  | | |   (12)  all_58_11 = e2
% 244.05/50.63  | | | 
% 244.05/50.63  | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #2030.
% 244.05/50.63  | | | 
% 244.05/50.63  | | Case 2:
% 244.05/50.63  | | | 
% 244.05/50.63  | | |   (13)  all_58_15 = e2 & op(e0, e0) = e2
% 244.05/50.63  | | | 
% 244.05/50.63  | | | ALPHA: (13) implies:
% 244.05/50.63  | | |   (14)  all_58_15 = e2
% 244.05/50.63  | | | 
% 244.05/50.63  | | | REF_CLOSE: (1), (6), (14) are inconsistent by sub-proof #1507.
% 244.05/50.63  | | | 
% 244.05/50.63  | | End of split
% 244.05/50.63  | | 
% 244.05/50.63  | End of split
% 244.05/50.63  | 
% 244.05/50.63  End of proof
% 244.05/50.63  
% 244.05/50.63  Sub-proof #1507 shows that the following formulas are inconsistent:
% 244.05/50.63  ----------------------------------------------------------------
% 244.05/50.63    (1)  all_58_15 = e2
% 244.05/50.63    (2)  all_58_15 = e0
% 244.05/50.63    (3)   ~ (e2 = e0)
% 244.05/50.63  
% 244.05/50.63  Begin of proof
% 244.05/50.63  | 
% 244.05/50.63  | COMBINE_EQS: (1), (2) imply:
% 244.05/50.63  |   (4)  e2 = e0
% 244.05/50.63  | 
% 244.05/50.63  | SIMP: (4) implies:
% 244.05/50.63  |   (5)  e2 = e0
% 244.05/50.63  | 
% 244.05/50.63  | REDUCE: (3), (5) imply:
% 244.05/50.63  |   (6)  $false
% 244.05/50.63  | 
% 244.05/50.63  | CLOSE: (6) is inconsistent.
% 244.05/50.63  | 
% 244.05/50.63  End of proof
% 244.05/50.63  
% 244.05/50.63  Sub-proof #1508 shows that the following formulas are inconsistent:
% 244.05/50.63  ----------------------------------------------------------------
% 244.05/50.63    (1)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 244.05/50.63    (2)  all_58_9 = e1
% 244.05/50.63    (3)   ~ (e2 = e1)
% 244.05/50.63    (4)  all_58_10 = e1
% 244.05/50.63  
% 244.05/50.63  Begin of proof
% 244.05/50.63  | 
% 244.05/50.63  | BETA: splitting (1) gives:
% 244.05/50.63  | 
% 244.05/50.63  | Case 1:
% 244.05/50.63  | | 
% 244.05/50.63  | |   (5)  all_58_9 = e2 & op(e3, e0) = e2
% 244.05/50.63  | | 
% 244.05/50.63  | | ALPHA: (5) implies:
% 244.05/50.63  | |   (6)  all_58_9 = e2
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #1605.
% 244.05/50.64  | | 
% 244.05/50.64  | Case 2:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (7)  all_58_10 = e2 & op(e2, e0) = e2
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1622.
% 244.05/50.64  | | 
% 244.05/50.64  | End of split
% 244.05/50.64  | 
% 244.05/50.64  End of proof
% 244.05/50.64  
% 244.05/50.64  Sub-proof #1509 shows that the following formulas are inconsistent:
% 244.05/50.64  ----------------------------------------------------------------
% 244.05/50.64    (1)   ~ (e2 = e0)
% 244.05/50.64    (2)  op(e2, e3) = e3
% 244.05/50.64    (3)  op(e2, e2) = e0
% 244.05/50.64    (4)   ~ (e3 = e2)
% 244.05/50.64    (5)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 244.05/50.64    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.64  
% 244.05/50.64  Begin of proof
% 244.05/50.64  | 
% 244.05/50.64  | BETA: splitting (5) gives:
% 244.05/50.64  | 
% 244.05/50.64  | Case 1:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (7)  all_58_2 = e2 & op(e2, e3) = e2
% 244.05/50.64  | | 
% 244.05/50.64  | | ALPHA: (7) implies:
% 244.05/50.64  | |   (8)  op(e2, e3) = e2
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1897.
% 244.05/50.64  | | 
% 244.05/50.64  | Case 2:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (9)  all_58_3 = e2 & op(e2, e2) = e2
% 244.05/50.64  | | 
% 244.05/50.64  | | ALPHA: (9) implies:
% 244.05/50.64  | |   (10)  op(e2, e2) = e2
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #2137.
% 244.05/50.64  | | 
% 244.05/50.64  | End of split
% 244.05/50.64  | 
% 244.05/50.64  End of proof
% 244.05/50.64  
% 244.05/50.64  Sub-proof #1510 shows that the following formulas are inconsistent:
% 244.05/50.64  ----------------------------------------------------------------
% 244.05/50.64    (1)   ~ (all_52_3 = e0)
% 244.05/50.64    (2)   ~ (e3 = e0)
% 244.05/50.64    (3)  op(e0, e3) = all_52_3
% 244.05/50.64    (4)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.05/50.64         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.05/50.64    (5)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 244.05/50.64         $i(all_56_17)
% 244.05/50.64    (6)   ~ (all_52_1 = e0)
% 244.05/50.64    (7)  op(e2, e3) = all_52_1
% 244.05/50.64    (8)   ~ (all_52_2 = e0)
% 244.05/50.64    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.64    (10)  op(e1, e3) = all_52_2
% 244.05/50.64    (11)  op(e3, e1) = e3
% 244.05/50.64  
% 244.05/50.64  Begin of proof
% 244.05/50.64  | 
% 244.05/50.64  | ALPHA: (5) implies:
% 244.05/50.64  |   (12)  op(e3, e1) = all_56_17
% 244.05/50.64  |   (13)  op(e3, all_56_17) = e3
% 244.05/50.64  | 
% 244.05/50.64  | GROUND_INST: instantiating (9) with e3, all_56_17, e1, e3, simplifying with
% 244.05/50.64  |              (11), (12) gives:
% 244.05/50.64  |   (14)  all_56_17 = e3
% 244.05/50.64  | 
% 244.05/50.64  | REDUCE: (13), (14) imply:
% 244.05/50.64  |   (15)  op(e3, e3) = e3
% 244.05/50.64  | 
% 244.05/50.64  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (15) are inconsistent
% 244.05/50.64  |            by sub-proof #1938.
% 244.05/50.64  | 
% 244.05/50.64  End of proof
% 244.05/50.64  
% 244.05/50.64  Sub-proof #1511 shows that the following formulas are inconsistent:
% 244.05/50.64  ----------------------------------------------------------------
% 244.05/50.64    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.05/50.64             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 244.05/50.64    (2)  op(e2, e3) = e3
% 244.05/50.64    (3)   ~ (e3 = e2)
% 244.05/50.64    (4)  op(e3, e0) = all_52_12
% 244.05/50.64    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.64    (6)   ~ (all_52_12 = e3)
% 244.05/50.64    (7)  all_56_1 = e0
% 244.05/50.64  
% 244.05/50.64  Begin of proof
% 244.05/50.64  | 
% 244.05/50.64  | BETA: splitting (1) gives:
% 244.05/50.64  | 
% 244.05/50.64  | Case 1:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (8)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | ALPHA: (8) implies:
% 244.05/50.64  | |   (9)  op(e3, all_56_1) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | REDUCE: (7), (9) imply:
% 244.05/50.64  | |   (10)  op(e3, e0) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #2179.
% 244.05/50.64  | | 
% 244.05/50.64  | Case 2:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (11)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 244.05/50.64  | |         $i(all_56_3)
% 244.05/50.64  | | 
% 244.05/50.64  | | ALPHA: (11) implies:
% 244.05/50.64  | |   (12)  op(e2, e3) = all_56_3
% 244.05/50.64  | |   (13)  op(e2, all_56_3) = e2
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (2), (3), (5), (12), (13) are inconsistent by sub-proof #2262.
% 244.05/50.64  | | 
% 244.05/50.64  | End of split
% 244.05/50.64  | 
% 244.05/50.64  End of proof
% 244.05/50.64  
% 244.05/50.64  Sub-proof #1512 shows that the following formulas are inconsistent:
% 244.05/50.64  ----------------------------------------------------------------
% 244.05/50.64    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.05/50.64         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.05/50.64    (2)   ~ (e3 = e0)
% 244.05/50.64    (3)   ~ (e2 = e0)
% 244.05/50.64    (4)   ~ (e3 = e1)
% 244.05/50.64    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.64         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.64    (6)   ~ (e3 = e2)
% 244.05/50.64    (7)   ~ (all_52_4 = e3)
% 244.05/50.64    (8)  op(e3, e2) = all_52_4
% 244.05/50.64    (9)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.64         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.64    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.64    (11)   ~ (e1 = e0)
% 244.05/50.64    (12)  op(e3, e3) = e0
% 244.05/50.64    (13)  all_58_4 = e0
% 244.05/50.64    (14)   ~ (e2 = e1)
% 244.05/50.64  
% 244.05/50.64  Begin of proof
% 244.05/50.64  | 
% 244.05/50.64  | BETA: splitting (5) gives:
% 244.05/50.64  | 
% 244.05/50.64  | Case 1:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 244.05/50.64  | |           e3)
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (2), (7), (8), (10), (12), (15) are inconsistent by sub-proof
% 244.05/50.64  | |            #1513.
% 244.05/50.64  | | 
% 244.05/50.64  | Case 2:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (16)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 244.05/50.64  | |           e3)
% 244.05/50.64  | | 
% 244.05/50.64  | | BETA: splitting (16) gives:
% 244.05/50.64  | | 
% 244.05/50.64  | | Case 1:
% 244.05/50.64  | | | 
% 244.05/50.64  | | |   (17)  all_58_4 = e3 & op(e3, e1) = e3
% 244.05/50.64  | | | 
% 244.05/50.64  | | | ALPHA: (17) implies:
% 244.05/50.64  | | |   (18)  all_58_4 = e3
% 244.05/50.64  | | | 
% 244.05/50.64  | | | REF_CLOSE: (2), (13), (18) are inconsistent by sub-proof #2186.
% 244.05/50.64  | | | 
% 244.05/50.64  | | Case 2:
% 244.05/50.64  | | | 
% 244.05/50.64  | | |   (19)  all_58_9 = e3 & op(e3, e0) = e3
% 244.05/50.64  | | | 
% 244.05/50.64  | | | ALPHA: (19) implies:
% 244.05/50.64  | | |   (20)  all_58_9 = e3
% 244.05/50.64  | | |   (21)  op(e3, e0) = e3
% 244.05/50.64  | | | 
% 244.05/50.64  | | | REF_CLOSE: (1), (3), (4), (6), (9), (10), (11), (12), (13), (14), (20),
% 244.05/50.64  | | |            (21) are inconsistent by sub-proof #1706.
% 244.05/50.64  | | | 
% 244.05/50.64  | | End of split
% 244.05/50.64  | | 
% 244.05/50.64  | End of split
% 244.05/50.64  | 
% 244.05/50.64  End of proof
% 244.05/50.64  
% 244.05/50.64  Sub-proof #1513 shows that the following formulas are inconsistent:
% 244.05/50.64  ----------------------------------------------------------------
% 244.05/50.64    (1)   ~ (e3 = e0)
% 244.05/50.64    (2)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 244.05/50.64    (3)   ~ (all_52_4 = e3)
% 244.05/50.64    (4)  op(e3, e2) = all_52_4
% 244.05/50.64    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.64    (6)  op(e3, e3) = e0
% 244.05/50.64  
% 244.05/50.64  Begin of proof
% 244.05/50.64  | 
% 244.05/50.64  | BETA: splitting (2) gives:
% 244.05/50.64  | 
% 244.05/50.64  | Case 1:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (7)  all_58_0 = e3 & op(e3, e3) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | ALPHA: (7) implies:
% 244.05/50.64  | |   (8)  op(e3, e3) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #1940.
% 244.05/50.64  | | 
% 244.05/50.64  | Case 2:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (9)  all_58_1 = e3 & op(e3, e2) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | ALPHA: (9) implies:
% 244.05/50.64  | |   (10)  op(e3, e2) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #2192.
% 244.05/50.64  | | 
% 244.05/50.64  | End of split
% 244.05/50.64  | 
% 244.05/50.64  End of proof
% 244.05/50.64  
% 244.05/50.64  Sub-proof #1514 shows that the following formulas are inconsistent:
% 244.05/50.64  ----------------------------------------------------------------
% 244.05/50.64    (1)   ~ (all_52_3 = e0)
% 244.05/50.64    (2)   ~ (e3 = e0)
% 244.05/50.64    (3)  op(e0, e3) = all_52_3
% 244.05/50.64    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 244.05/50.64    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.05/50.64         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.05/50.64    (6)   ~ (all_52_1 = e0)
% 244.05/50.64    (7)  op(e2, e3) = all_52_1
% 244.05/50.64    (8)   ~ (all_52_2 = e0)
% 244.05/50.64    (9)   ~ (all_52_4 = e3)
% 244.05/50.64    (10)  op(e3, e2) = all_52_4
% 244.05/50.64    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.64    (12)  op(e1, e3) = all_52_2
% 244.05/50.64  
% 244.05/50.64  Begin of proof
% 244.05/50.64  | 
% 244.05/50.64  | BETA: splitting (4) gives:
% 244.05/50.64  | 
% 244.05/50.64  | Case 1:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (13)  all_58_0 = e3 & op(e3, e3) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | ALPHA: (13) implies:
% 244.05/50.64  | |   (14)  op(e3, e3) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (11), (12), (14) are
% 244.05/50.64  | |            inconsistent by sub-proof #1938.
% 244.05/50.64  | | 
% 244.05/50.64  | Case 2:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (15)  all_58_1 = e3 & op(e3, e2) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | ALPHA: (15) implies:
% 244.05/50.64  | |   (16)  op(e3, e2) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (9), (10), (11), (16) are inconsistent by sub-proof #2192.
% 244.05/50.64  | | 
% 244.05/50.64  | End of split
% 244.05/50.64  | 
% 244.05/50.64  End of proof
% 244.05/50.64  
% 244.05/50.64  Sub-proof #1515 shows that the following formulas are inconsistent:
% 244.05/50.64  ----------------------------------------------------------------
% 244.05/50.64    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.64    (2)  op(e3, e1) = all_52_8
% 244.05/50.64    (3)  op(e3, e0) = all_52_12
% 244.05/50.64    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.64    (5)   ~ (all_52_12 = e3)
% 244.05/50.64    (6)   ~ (all_52_8 = e3)
% 244.05/50.64  
% 244.05/50.64  Begin of proof
% 244.05/50.64  | 
% 244.05/50.64  | BETA: splitting (1) gives:
% 244.05/50.64  | 
% 244.05/50.64  | Case 1:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (7)  all_58_4 = e3 & op(e3, e1) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | ALPHA: (7) implies:
% 244.05/50.64  | |   (8)  op(e3, e1) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2260.
% 244.05/50.64  | | 
% 244.05/50.64  | Case 2:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (9)  all_58_9 = e3 & op(e3, e0) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | ALPHA: (9) implies:
% 244.05/50.64  | |   (10)  op(e3, e0) = e3
% 244.05/50.64  | | 
% 244.05/50.64  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #2179.
% 244.05/50.64  | | 
% 244.05/50.64  | End of split
% 244.05/50.64  | 
% 244.05/50.64  End of proof
% 244.05/50.64  
% 244.05/50.64  Sub-proof #1516 shows that the following formulas are inconsistent:
% 244.05/50.64  ----------------------------------------------------------------
% 244.05/50.64    (1)  all_58_3 = e3 & op(e2, e2) = e3
% 244.05/50.64    (2)  all_58_3 = e0
% 244.05/50.64    (3)   ~ (e3 = e0)
% 244.05/50.64  
% 244.05/50.64  Begin of proof
% 244.05/50.64  | 
% 244.05/50.64  | ALPHA: (1) implies:
% 244.05/50.64  |   (4)  all_58_3 = e3
% 244.05/50.64  | 
% 244.05/50.64  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.64  |   (5)  e3 = e0
% 244.05/50.64  | 
% 244.05/50.64  | REDUCE: (3), (5) imply:
% 244.05/50.64  |   (6)  $false
% 244.05/50.64  | 
% 244.05/50.64  | CLOSE: (6) is inconsistent.
% 244.05/50.64  | 
% 244.05/50.64  End of proof
% 244.05/50.64  
% 244.05/50.64  Sub-proof #1517 shows that the following formulas are inconsistent:
% 244.05/50.64  ----------------------------------------------------------------
% 244.05/50.64    (1)   ~ (all_52_3 = e0)
% 244.05/50.64    (2)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 244.05/50.64           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 244.05/50.64           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 244.05/50.64           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 244.05/50.64           & $i(all_56_23))
% 244.05/50.64    (3)   ~ (all_52_12 = all_18_0)
% 244.05/50.64    (4)   ~ (e3 = e0)
% 244.05/50.64    (5)  all_54_2 = all_18_0
% 244.05/50.64    (6)   ~ (e2 = e0)
% 244.05/50.64    (7)  op(e0, e1) = e3
% 244.05/50.64    (8)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.05/50.64         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.05/50.64    (9)   ~ (all_52_8 = e0)
% 244.05/50.64    (10)  op(e0, e3) = all_52_3
% 244.05/50.64    (11)   ~ (e3 = e1)
% 244.05/50.64    (12)  op(e2, e2) = e0
% 244.05/50.64    (13)  all_54_2 = all_52_8
% 244.05/50.64    (14)  all_56_21 = e0
% 244.05/50.64    (15)  op(e3, e1) = all_52_8
% 244.05/50.64    (16)   ~ (e3 = e2)
% 244.05/50.64    (17)  op(e1, e0) = e3
% 244.05/50.64    (18)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 244.05/50.64          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 244.05/50.64    (19)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 244.05/50.64            all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2,
% 244.05/50.64              e0) = all_14_1 & $i(all_14_1))
% 244.05/50.64    (20)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 244.05/50.64            all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2,
% 244.05/50.64              e0) = all_48_1 & $i(all_48_1))
% 244.05/50.64    (21)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.05/50.64    (22)   ~ (all_18_0 = e2)
% 244.05/50.64    (23)  op(e3, e0) = all_52_12
% 244.05/50.64    (24)  op(e3, e0) = e2
% 244.05/50.64    (25)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.64          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.64    (26)  op(e3, e2) = all_52_4
% 244.05/50.64    (27)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.64          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.64    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.64    (29)  all_58_14 = e3
% 244.05/50.64    (30)   ~ (all_18_0 = e0)
% 244.05/50.64    (31)  op(e1, e1) = e0
% 244.05/50.64    (32)   ~ (e1 = e0)
% 244.05/50.64    (33)  op(e3, e3) = e0
% 244.05/50.64    (34)  op(e3, e2) = e3
% 244.05/50.64    (35)  all_58_2 = e3
% 244.05/50.64    (36)  all_58_9 = e2
% 244.05/50.64    (37)  all_58_3 = e0
% 244.05/50.64    (38)   ~ (all_52_4 = all_52_8)
% 244.05/50.64    (39)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.05/50.64          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.05/50.64    (40)   ~ (e2 = e1)
% 244.05/50.64    (41)   ~ (all_52_8 = e3)
% 244.05/50.64  
% 244.05/50.64  Begin of proof
% 244.05/50.64  | 
% 244.05/50.64  | BETA: splitting (27) gives:
% 244.05/50.64  | 
% 244.05/50.64  | Case 1:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (42)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 244.05/50.64  | |           e1)
% 244.05/50.64  | | 
% 244.05/50.64  | | BETA: splitting (42) gives:
% 244.05/50.64  | | 
% 244.05/50.64  | | Case 1:
% 244.05/50.64  | | | 
% 244.05/50.64  | | |   (43)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.64  | | | 
% 244.05/50.64  | | | ALPHA: (43) implies:
% 244.05/50.64  | | |   (44)  op(e3, e3) = e1
% 244.05/50.64  | | | 
% 244.05/50.64  | | | REF_CLOSE: (4), (6), (9), (15), (24), (25), (28), (32), (34), (44) are
% 244.05/50.64  | | |            inconsistent by sub-proof #1523.
% 244.05/50.64  | | | 
% 244.05/50.64  | | Case 2:
% 244.05/50.64  | | | 
% 244.05/50.64  | | |   (45)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.64  | | | 
% 244.05/50.64  | | | ALPHA: (45) implies:
% 244.05/50.64  | | |   (46)  op(e3, e2) = e1
% 244.05/50.64  | | | 
% 244.05/50.64  | | | REF_CLOSE: (11), (28), (34), (46) are inconsistent by sub-proof #2265.
% 244.05/50.64  | | | 
% 244.05/50.64  | | End of split
% 244.05/50.64  | | 
% 244.05/50.64  | Case 2:
% 244.05/50.64  | | 
% 244.05/50.64  | |   (47)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 244.05/50.64  | |           e1)
% 244.05/50.64  | | 
% 244.05/50.64  | | BETA: splitting (47) gives:
% 244.05/50.64  | | 
% 244.05/50.64  | | Case 1:
% 244.05/50.64  | | | 
% 244.05/50.64  | | |   (48)  all_58_4 = e1 & op(e3, e1) = e1
% 244.05/50.64  | | | 
% 244.05/50.64  | | | ALPHA: (48) implies:
% 244.05/50.64  | | |   (49)  all_58_4 = e1
% 244.05/50.64  | | | 
% 244.05/50.64  | | | BETA: splitting (18) gives:
% 244.05/50.64  | | | 
% 244.05/50.64  | | | Case 1:
% 244.05/50.64  | | | | 
% 244.05/50.64  | | | |   (50)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 244.05/50.64  | | | |           = e2)
% 244.05/50.64  | | | | 
% 244.05/50.65  | | | | BETA: splitting (50) gives:
% 244.05/50.65  | | | | 
% 244.05/50.65  | | | | Case 1:
% 244.05/50.65  | | | | | 
% 244.05/50.65  | | | | |   (51)  all_58_4 = e2 & op(e3, e1) = e2
% 244.05/50.65  | | | | | 
% 244.05/50.65  | | | | | REF_CLOSE: (3), (5), (9), (13), (21), (22), (23), (26), (27), (28),
% 244.05/50.65  | | | | |            (30), (33), (38), (51) are inconsistent by sub-proof #1525.
% 244.05/50.65  | | | | | 
% 244.05/50.65  | | | | Case 2:
% 244.05/50.65  | | | | | 
% 244.05/50.65  | | | | |   (52)  all_58_5 = e2 & op(e2, e1) = e2
% 244.05/50.65  | | | | | 
% 244.05/50.65  | | | | | ALPHA: (52) implies:
% 244.05/50.65  | | | | |   (53)  all_58_5 = e2
% 244.05/50.65  | | | | |   (54)  op(e2, e1) = e2
% 244.05/50.65  | | | | | 
% 244.05/50.65  | | | | | BETA: splitting (39) gives:
% 244.05/50.65  | | | | | 
% 244.05/50.65  | | | | | Case 1:
% 244.05/50.65  | | | | | | 
% 244.05/50.65  | | | | | |   (55)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2,
% 244.05/50.65  | | | | | |             e2) = e1)
% 244.05/50.65  | | | | | | 
% 244.05/50.65  | | | | | | BETA: splitting (55) gives:
% 244.05/50.65  | | | | | | 
% 244.05/50.65  | | | | | | Case 1:
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | |   (56)  all_58_2 = e1 & op(e2, e3) = e1
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | | ALPHA: (56) implies:
% 244.05/50.65  | | | | | | |   (57)  all_58_2 = e1
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | | REF_CLOSE: (11), (35), (57) are inconsistent by sub-proof #1691.
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | Case 2:
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | |   (58)  all_58_3 = e1 & op(e2, e2) = e1
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | | ALPHA: (58) implies:
% 244.05/50.65  | | | | | | |   (59)  all_58_3 = e1
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | | COMBINE_EQS: (37), (59) imply:
% 244.05/50.65  | | | | | | |   (60)  e1 = e0
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | | REF_CLOSE: (6), (8), (11), (16), (18), (28), (29), (31), (32),
% 244.05/50.65  | | | | | | |            (40), (49), (60) are inconsistent by sub-proof #1623.
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | End of split
% 244.05/50.65  | | | | | | 
% 244.05/50.65  | | | | | Case 2:
% 244.05/50.65  | | | | | | 
% 244.05/50.65  | | | | | |   (61)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2,
% 244.05/50.65  | | | | | |             e0) = e1)
% 244.05/50.65  | | | | | | 
% 244.05/50.65  | | | | | | BETA: splitting (61) gives:
% 244.05/50.65  | | | | | | 
% 244.05/50.65  | | | | | | Case 1:
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | |   (62)  all_58_5 = e1 & op(e2, e1) = e1
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | | ALPHA: (62) implies:
% 244.05/50.65  | | | | | | |   (63)  all_58_5 = e1
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | | REF_CLOSE: (40), (53), (63) are inconsistent by sub-proof #1665.
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | Case 2:
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | |   (64)  all_58_10 = e1 & op(e2, e0) = e1
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | | ALPHA: (64) implies:
% 244.05/50.65  | | | | | | |   (65)  op(e2, e0) = e1
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | | BETA: splitting (21) gives:
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | | Case 1:
% 244.05/50.65  | | | | | | | | 
% 244.05/50.65  | | | | | | | |   (66)  all_54_2 = e2
% 244.05/50.65  | | | | | | | | 
% 244.05/50.65  | | | | | | | | REF_CLOSE: (5), (22), (66) are inconsistent by sub-proof #1527.
% 244.05/50.65  | | | | | | | | 
% 244.05/50.65  | | | | | | | Case 2:
% 244.05/50.65  | | | | | | | | 
% 244.05/50.65  | | | | | | | |   (67)  all_54_2 = e1 | all_54_2 = e0
% 244.05/50.65  | | | | | | | | 
% 244.05/50.65  | | | | | | | | BETA: splitting (2) gives:
% 244.05/50.65  | | | | | | | | 
% 244.05/50.65  | | | | | | | | Case 1:
% 244.05/50.65  | | | | | | | | | 
% 244.05/50.65  | | | | | | | | |   (68)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1)
% 244.05/50.65  | | | | | | | | |           = all_56_17 & $i(all_56_17)) | (all_56_18 = e2 &
% 244.05/50.65  | | | | | | | | |           op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 244.05/50.65  | | | | | | | | |           $i(all_56_19))
% 244.05/50.65  | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | BETA: splitting (68) gives:
% 244.05/50.65  | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | Case 1:
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | |   (69)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1)
% 244.05/50.65  | | | | | | | | | |         = all_56_17 & $i(all_56_17)
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | ALPHA: (69) implies:
% 244.05/50.65  | | | | | | | | | |   (70)  op(e3, e1) = all_56_17
% 244.05/50.65  | | | | | | | | | |   (71)  op(e3, all_56_17) = e3
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | REF_CLOSE: (9), (13), (15), (28), (41), (67), (70), (71) are
% 244.05/50.65  | | | | | | | | | |            inconsistent by sub-proof #1522.
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | Case 2:
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | |   (72)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 244.05/50.65  | | | | | | | | | |         = all_56_19 & $i(all_56_19)
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | REF_CLOSE: (6), (12), (19), (20), (28), (54), (65), (72) are
% 244.05/50.65  | | | | | | | | | |            inconsistent by sub-proof #1520.
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | End of split
% 244.05/50.65  | | | | | | | | | 
% 244.05/50.65  | | | | | | | | Case 2:
% 244.05/50.65  | | | | | | | | | 
% 244.05/50.65  | | | | | | | | |   (73)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22
% 244.05/50.65  | | | | | | | | |           = e0 & op(e0, all_56_23) = e0 & op(e0, e1) =
% 244.05/50.65  | | | | | | | | |           all_56_23 & $i(all_56_23))
% 244.05/50.65  | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | BETA: splitting (73) gives:
% 244.05/50.65  | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | Case 1:
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | |   (74)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | ALPHA: (74) implies:
% 244.05/50.65  | | | | | | | | | |   (75)  op(e1, all_56_21) = e1
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | REDUCE: (14), (75) imply:
% 244.05/50.65  | | | | | | | | | |   (76)  op(e1, e0) = e1
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | REF_CLOSE: (11), (17), (28), (76) are inconsistent by
% 244.05/50.65  | | | | | | | | | |            sub-proof #1894.
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | Case 2:
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | |   (77)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1)
% 244.05/50.65  | | | | | | | | | |         = all_56_23 & $i(all_56_23)
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | ALPHA: (77) implies:
% 244.05/50.65  | | | | | | | | | |   (78)  op(e0, e1) = all_56_23
% 244.05/50.65  | | | | | | | | | |   (79)  op(e0, all_56_23) = e0
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | BETA: splitting (20) gives:
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | Case 1:
% 244.05/50.65  | | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | |   (80)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 &
% 244.05/50.65  | | | | | | | | | | |         op(e2, e0) = all_48_1 & $i(all_48_0) &
% 244.05/50.65  | | | | | | | | | | |         $i(all_48_1)
% 244.05/50.65  | | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | | ALPHA: (80) implies:
% 244.05/50.65  | | | | | | | | | | |   (81)  op(e2, e0) = all_48_1
% 244.05/50.65  | | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | | REF_CLOSE: (1), (7), (10), (19), (28), (65), (78), (79), (81)
% 244.05/50.65  | | | | | | | | | | |            are inconsistent by sub-proof #1519.
% 244.05/50.65  | | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | Case 2:
% 244.05/50.65  | | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | |   (82)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 &
% 244.05/50.65  | | | | | | | | | | |         $i(all_48_1)
% 244.05/50.65  | | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | | ALPHA: (82) implies:
% 244.05/50.65  | | | | | | | | | | |   (83)  op(e2, e0) = all_48_1
% 244.05/50.65  | | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | | REF_CLOSE: (1), (7), (10), (19), (28), (65), (78), (79), (83)
% 244.05/50.65  | | | | | | | | | | |            are inconsistent by sub-proof #1519.
% 244.05/50.65  | | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | | End of split
% 244.05/50.65  | | | | | | | | | | 
% 244.05/50.65  | | | | | | | | | End of split
% 244.05/50.65  | | | | | | | | | 
% 244.05/50.65  | | | | | | | | End of split
% 244.05/50.65  | | | | | | | | 
% 244.05/50.65  | | | | | | | End of split
% 244.05/50.65  | | | | | | | 
% 244.05/50.65  | | | | | | End of split
% 244.05/50.65  | | | | | | 
% 244.05/50.65  | | | | | End of split
% 244.05/50.65  | | | | | 
% 244.05/50.65  | | | | End of split
% 244.05/50.65  | | | | 
% 244.05/50.65  | | | Case 2:
% 244.05/50.65  | | | | 
% 244.05/50.65  | | | |   (84)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 244.05/50.65  | | | |           = e2)
% 244.05/50.65  | | | | 
% 244.05/50.65  | | | | REF_CLOSE: (6), (16), (28), (29), (31), (84) are inconsistent by
% 244.05/50.65  | | | |            sub-proof #1664.
% 244.05/50.65  | | | | 
% 244.05/50.65  | | | End of split
% 244.05/50.65  | | | 
% 244.05/50.65  | | Case 2:
% 244.05/50.65  | | | 
% 244.05/50.65  | | |   (85)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.65  | | | 
% 244.05/50.65  | | | REF_CLOSE: (36), (40), (85) are inconsistent by sub-proof #1518.
% 244.05/50.65  | | | 
% 244.05/50.65  | | End of split
% 244.05/50.65  | | 
% 244.05/50.65  | End of split
% 244.05/50.65  | 
% 244.05/50.65  End of proof
% 244.05/50.65  
% 244.05/50.65  Sub-proof #1518 shows that the following formulas are inconsistent:
% 244.05/50.65  ----------------------------------------------------------------
% 244.05/50.65    (1)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.65    (2)  all_58_9 = e2
% 244.05/50.65    (3)   ~ (e2 = e1)
% 244.05/50.65  
% 244.05/50.65  Begin of proof
% 244.05/50.65  | 
% 244.05/50.65  | ALPHA: (1) implies:
% 244.05/50.65  |   (4)  all_58_9 = e1
% 244.05/50.65  | 
% 244.05/50.65  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.65  |   (5)  e2 = e1
% 244.05/50.65  | 
% 244.05/50.65  | REDUCE: (3), (5) imply:
% 244.05/50.65  |   (6)  $false
% 244.05/50.65  | 
% 244.05/50.65  | CLOSE: (6) is inconsistent.
% 244.05/50.65  | 
% 244.05/50.65  End of proof
% 244.05/50.65  
% 244.05/50.65  Sub-proof #1519 shows that the following formulas are inconsistent:
% 244.05/50.65  ----------------------------------------------------------------
% 244.05/50.65    (1)   ~ (all_52_3 = e0)
% 244.05/50.65    (2)  op(e0, e1) = all_56_23
% 244.05/50.65    (3)  op(e0, e1) = e3
% 244.05/50.65    (4)  op(e0, e3) = all_52_3
% 244.05/50.65    (5)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 244.05/50.65           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0) =
% 244.05/50.65           all_14_1 & $i(all_14_1))
% 244.05/50.65    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.65    (7)  op(e0, all_56_23) = e0
% 244.05/50.65    (8)  op(e2, e0) = e1
% 244.05/50.65    (9)  op(e2, e0) = all_48_1
% 244.05/50.65  
% 244.05/50.65  Begin of proof
% 244.05/50.65  | 
% 244.05/50.65  | BETA: splitting (5) gives:
% 244.05/50.65  | 
% 244.05/50.65  | Case 1:
% 244.05/50.65  | | 
% 244.05/50.65  | | 
% 244.05/50.65  | | GROUND_INST: instantiating (6) with e3, all_56_23, e1, e0, simplifying with
% 244.05/50.65  | |              (2), (3) gives:
% 244.05/50.65  | |   (10)  all_56_23 = e3
% 244.05/50.65  | | 
% 244.05/50.65  | | REDUCE: (7), (10) imply:
% 244.05/50.65  | |   (11)  op(e0, e3) = e0
% 244.05/50.65  | | 
% 244.05/50.65  | | REF_CLOSE: (1), (4), (6), (11) are inconsistent by sub-proof #2331.
% 244.05/50.65  | | 
% 244.05/50.65  | Case 2:
% 244.05/50.65  | | 
% 244.05/50.65  | |   (12)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 244.05/50.65  | | 
% 244.05/50.65  | | ALPHA: (12) implies:
% 244.05/50.65  | |   (13)   ~ (all_14_1 = e1)
% 244.05/50.65  | |   (14)  op(e2, e0) = all_14_1
% 244.05/50.65  | | 
% 244.05/50.65  | | REF_CLOSE: (6), (8), (9), (13), (14) are inconsistent by sub-proof #1585.
% 244.05/50.65  | | 
% 244.05/50.65  | End of split
% 244.05/50.65  | 
% 244.05/50.65  End of proof
% 244.05/50.65  
% 244.05/50.65  Sub-proof #1520 shows that the following formulas are inconsistent:
% 244.05/50.65  ----------------------------------------------------------------
% 244.05/50.65    (1)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 244.05/50.65         $i(all_56_19)
% 244.05/50.65    (2)   ~ (e2 = e0)
% 244.05/50.65    (3)  op(e2, e2) = e0
% 244.05/50.65    (4)  op(e2, e1) = e2
% 244.05/50.65    (5)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 244.05/50.65           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0) =
% 244.05/50.65           all_14_1 & $i(all_14_1))
% 244.05/50.65    (6)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) = all_48_1
% 244.05/50.65           & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0) =
% 244.05/50.65           all_48_1 & $i(all_48_1))
% 244.05/50.65    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.65    (8)  op(e2, e0) = e1
% 244.05/50.65  
% 244.05/50.65  Begin of proof
% 244.05/50.65  | 
% 244.05/50.65  | ALPHA: (1) implies:
% 244.05/50.65  |   (9)  op(e2, e1) = all_56_19
% 244.05/50.65  |   (10)  op(e2, all_56_19) = e2
% 244.05/50.65  | 
% 244.05/50.65  | BETA: splitting (6) gives:
% 244.05/50.65  | 
% 244.05/50.65  | Case 1:
% 244.05/50.65  | | 
% 244.05/50.65  | |   (11)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 244.05/50.65  | |         all_48_1 & $i(all_48_0) & $i(all_48_1)
% 244.05/50.65  | | 
% 244.05/50.65  | | ALPHA: (11) implies:
% 244.05/50.65  | |   (12)  op(e2, e0) = all_48_1
% 244.05/50.65  | | 
% 244.05/50.65  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12) are inconsistent by
% 244.05/50.65  | |            sub-proof #1521.
% 244.05/50.65  | | 
% 244.05/50.65  | Case 2:
% 244.05/50.65  | | 
% 244.05/50.65  | |   (13)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 & $i(all_48_1)
% 244.05/50.65  | | 
% 244.05/50.65  | | ALPHA: (13) implies:
% 244.05/50.65  | |   (14)  op(e2, e0) = all_48_1
% 244.05/50.65  | | 
% 244.05/50.65  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (14) are inconsistent by
% 244.05/50.65  | |            sub-proof #1521.
% 244.05/50.65  | | 
% 244.05/50.65  | End of split
% 244.05/50.65  | 
% 244.05/50.65  End of proof
% 244.05/50.65  
% 244.05/50.65  Sub-proof #1521 shows that the following formulas are inconsistent:
% 244.05/50.65  ----------------------------------------------------------------
% 244.05/50.65    (1)   ~ (e2 = e0)
% 244.05/50.65    (2)  op(e2, e2) = e0
% 244.05/50.65    (3)  op(e2, e1) = e2
% 244.05/50.65    (4)  ( ~ (all_14_0 = e3) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 244.05/50.65           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e2, e0) =
% 244.05/50.65           all_14_1 & $i(all_14_1))
% 244.05/50.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.65    (6)  op(e2, e1) = all_56_19
% 244.05/50.65    (7)  op(e2, e0) = e1
% 244.05/50.65    (8)  op(e2, all_56_19) = e2
% 244.05/50.65    (9)  op(e2, e0) = all_48_1
% 244.05/50.65  
% 244.05/50.65  Begin of proof
% 244.05/50.65  | 
% 244.05/50.65  | BETA: splitting (4) gives:
% 244.05/50.65  | 
% 244.05/50.65  | Case 1:
% 244.05/50.65  | | 
% 244.05/50.65  | | 
% 244.05/50.65  | | GROUND_INST: instantiating (5) with e2, all_56_19, e1, e2, simplifying with
% 244.05/50.65  | |              (3), (6) gives:
% 244.05/50.65  | |   (10)  all_56_19 = e2
% 244.05/50.65  | | 
% 244.05/50.65  | | REDUCE: (8), (10) imply:
% 244.05/50.65  | |   (11)  op(e2, e2) = e2
% 244.05/50.65  | | 
% 244.05/50.65  | | REF_CLOSE: (1), (2), (5), (11) are inconsistent by sub-proof #2137.
% 244.05/50.65  | | 
% 244.05/50.65  | Case 2:
% 244.05/50.65  | | 
% 244.05/50.65  | |   (12)   ~ (all_14_1 = e1) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 244.05/50.65  | | 
% 244.05/50.65  | | ALPHA: (12) implies:
% 244.05/50.65  | |   (13)   ~ (all_14_1 = e1)
% 244.05/50.65  | |   (14)  op(e2, e0) = all_14_1
% 244.05/50.65  | | 
% 244.05/50.65  | | REF_CLOSE: (5), (7), (9), (13), (14) are inconsistent by sub-proof #1585.
% 244.05/50.65  | | 
% 244.05/50.65  | End of split
% 244.05/50.65  | 
% 244.05/50.65  End of proof
% 244.05/50.65  
% 244.05/50.65  Sub-proof #1522 shows that the following formulas are inconsistent:
% 244.05/50.65  ----------------------------------------------------------------
% 244.05/50.65    (1)  op(e3, e1) = all_56_17
% 244.05/50.65    (2)  all_54_2 = e1 | all_54_2 = e0
% 244.05/50.65    (3)   ~ (all_52_8 = e0)
% 244.05/50.65    (4)  all_54_2 = all_52_8
% 244.05/50.65    (5)  op(e3, e1) = all_52_8
% 244.05/50.65    (6)  op(e3, all_56_17) = e3
% 244.05/50.65    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.65    (8)   ~ (all_52_8 = e3)
% 244.05/50.65  
% 244.05/50.65  Begin of proof
% 244.05/50.65  | 
% 244.05/50.65  | BETA: splitting (2) gives:
% 244.05/50.65  | 
% 244.05/50.65  | Case 1:
% 244.05/50.65  | | 
% 244.05/50.65  | |   (9)  all_54_2 = e1
% 244.05/50.65  | | 
% 244.05/50.65  | | COMBINE_EQS: (4), (9) imply:
% 244.05/50.65  | |   (10)  all_52_8 = e1
% 244.05/50.65  | | 
% 244.05/50.65  | | SIMP: (10) implies:
% 244.05/50.65  | |   (11)  all_52_8 = e1
% 244.05/50.65  | | 
% 244.05/50.65  | | REDUCE: (5), (11) imply:
% 244.05/50.65  | |   (12)  op(e3, e1) = e1
% 244.05/50.65  | | 
% 244.05/50.65  | | GROUND_INST: instantiating (7) with e1, all_56_17, e1, e3, simplifying with
% 244.05/50.65  | |              (1), (12) gives:
% 244.05/50.65  | |   (13)  all_56_17 = e1
% 244.05/50.65  | | 
% 244.05/50.65  | | REDUCE: (6), (13) imply:
% 244.05/50.65  | |   (14)  op(e3, e1) = e3
% 244.05/50.65  | | 
% 244.05/50.65  | | REF_CLOSE: (5), (7), (8), (14) are inconsistent by sub-proof #2260.
% 244.05/50.65  | | 
% 244.05/50.65  | Case 2:
% 244.05/50.65  | | 
% 244.05/50.65  | |   (15)  all_54_2 = e0
% 244.05/50.65  | | 
% 244.05/50.65  | | REF_CLOSE: (3), (4), (15) are inconsistent by sub-proof #1643.
% 244.05/50.65  | | 
% 244.05/50.65  | End of split
% 244.05/50.65  | 
% 244.05/50.65  End of proof
% 244.05/50.65  
% 244.05/50.65  Sub-proof #1523 shows that the following formulas are inconsistent:
% 244.05/50.65  ----------------------------------------------------------------
% 244.05/50.65    (1)   ~ (e3 = e0)
% 244.05/50.65    (2)   ~ (e2 = e0)
% 244.05/50.65    (3)   ~ (all_52_8 = e0)
% 244.05/50.65    (4)  op(e3, e3) = e1
% 244.05/50.65    (5)  op(e3, e1) = all_52_8
% 244.05/50.65    (6)  op(e3, e0) = e2
% 244.05/50.65    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.65         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.65    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.65    (9)   ~ (e1 = e0)
% 244.05/50.65    (10)  op(e3, e2) = e3
% 244.05/50.65  
% 244.05/50.65  Begin of proof
% 244.05/50.65  | 
% 244.05/50.65  | BETA: splitting (7) gives:
% 244.05/50.65  | 
% 244.05/50.65  | Case 1:
% 244.05/50.65  | | 
% 244.05/50.65  | |   (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 244.05/50.65  | |           e0)
% 244.05/50.65  | | 
% 244.05/50.65  | | REF_CLOSE: (1), (4), (8), (9), (10), (11) are inconsistent by sub-proof
% 244.05/50.65  | |            #1524.
% 244.05/50.65  | | 
% 244.05/50.65  | Case 2:
% 244.05/50.65  | | 
% 244.05/50.65  | |   (12)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 244.05/50.65  | |           e0)
% 244.05/50.65  | | 
% 244.05/50.65  | | BETA: splitting (12) gives:
% 244.05/50.65  | | 
% 244.05/50.65  | | Case 1:
% 244.05/50.65  | | | 
% 244.05/50.65  | | |   (13)  all_58_4 = e0 & op(e3, e1) = e0
% 244.05/50.65  | | | 
% 244.05/50.65  | | | REF_CLOSE: (3), (5), (8), (13) are inconsistent by sub-proof #1908.
% 244.05/50.65  | | | 
% 244.05/50.65  | | Case 2:
% 244.05/50.65  | | | 
% 244.05/50.65  | | |   (14)  all_58_9 = e0 & op(e3, e0) = e0
% 244.05/50.65  | | | 
% 244.05/50.65  | | | ALPHA: (14) implies:
% 244.05/50.65  | | |   (15)  op(e3, e0) = e0
% 244.05/50.65  | | | 
% 244.05/50.65  | | | REF_CLOSE: (2), (6), (8), (15) are inconsistent by sub-proof #2154.
% 244.05/50.65  | | | 
% 244.05/50.65  | | End of split
% 244.05/50.65  | | 
% 244.05/50.65  | End of split
% 244.05/50.65  | 
% 244.05/50.65  End of proof
% 244.05/50.65  
% 244.05/50.65  Sub-proof #1524 shows that the following formulas are inconsistent:
% 244.05/50.65  ----------------------------------------------------------------
% 244.05/50.65    (1)   ~ (e3 = e0)
% 244.05/50.65    (2)  op(e3, e3) = e1
% 244.05/50.65    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.65    (4)   ~ (e1 = e0)
% 244.05/50.65    (5)  op(e3, e2) = e3
% 244.05/50.65    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 244.05/50.65  
% 244.05/50.65  Begin of proof
% 244.05/50.65  | 
% 244.05/50.65  | BETA: splitting (6) gives:
% 244.05/50.65  | 
% 244.05/50.65  | Case 1:
% 244.05/50.65  | | 
% 244.05/50.65  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 244.05/50.65  | | 
% 244.05/50.65  | | ALPHA: (7) implies:
% 244.05/50.65  | |   (8)  op(e3, e3) = e0
% 244.05/50.65  | | 
% 244.05/50.65  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1828.
% 244.05/50.65  | | 
% 244.05/50.65  | Case 2:
% 244.05/50.65  | | 
% 244.05/50.65  | |   (9)  all_58_1 = e0 & op(e3, e2) = e0
% 244.05/50.65  | | 
% 244.05/50.65  | | ALPHA: (9) implies:
% 244.05/50.65  | |   (10)  op(e3, e2) = e0
% 244.05/50.65  | | 
% 244.05/50.65  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2099.
% 244.05/50.65  | | 
% 244.05/50.65  | End of split
% 244.05/50.65  | 
% 244.05/50.65  End of proof
% 244.05/50.65  
% 244.05/50.65  Sub-proof #1525 shows that the following formulas are inconsistent:
% 244.05/50.65  ----------------------------------------------------------------
% 244.05/50.65    (1)   ~ (all_52_12 = all_18_0)
% 244.05/50.65    (2)  all_54_2 = all_18_0
% 244.05/50.65    (3)   ~ (all_52_8 = e0)
% 244.05/50.65    (4)  all_54_2 = all_52_8
% 244.05/50.65    (5)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.05/50.65    (6)   ~ (all_18_0 = e2)
% 244.05/50.65    (7)  op(e3, e0) = all_52_12
% 244.05/50.65    (8)  op(e3, e2) = all_52_4
% 244.05/50.66    (9)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.66         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.66    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.66    (11)   ~ (all_18_0 = e0)
% 244.05/50.66    (12)  all_58_4 = e2 & op(e3, e1) = e2
% 244.05/50.66    (13)  op(e3, e3) = e0
% 244.05/50.66    (14)   ~ (all_52_4 = all_52_8)
% 244.05/50.66  
% 244.05/50.66  Begin of proof
% 244.05/50.66  | 
% 244.05/50.66  | ALPHA: (12) implies:
% 244.05/50.66  |   (15)  all_58_4 = e2
% 244.05/50.66  | 
% 244.05/50.66  | BETA: splitting (5) gives:
% 244.05/50.66  | 
% 244.05/50.66  | Case 1:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (16)  all_54_2 = e2
% 244.05/50.66  | | 
% 244.05/50.66  | | REF_CLOSE: (2), (6), (16) are inconsistent by sub-proof #1527.
% 244.05/50.66  | | 
% 244.05/50.66  | Case 2:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (17)   ~ (all_54_2 = e2)
% 244.05/50.66  | |   (18)  all_54_2 = e1 | all_54_2 = e0
% 244.05/50.66  | | 
% 244.05/50.66  | | BETA: splitting (18) gives:
% 244.05/50.66  | | 
% 244.05/50.66  | | Case 1:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (19)  all_54_2 = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | COMBINE_EQS: (2), (19) imply:
% 244.05/50.66  | | |   (20)  all_18_0 = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | SIMP: (20) implies:
% 244.05/50.66  | | |   (21)  all_18_0 = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REDUCE: (1), (21) imply:
% 244.05/50.66  | | |   (22)   ~ (all_52_12 = e1)
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REDUCE: (6), (21) imply:
% 244.05/50.66  | | |   (23)   ~ (e2 = e1)
% 244.05/50.66  | | | 
% 244.05/50.66  | | | SIMP: (23) implies:
% 244.05/50.66  | | |   (24)   ~ (e2 = e1)
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REDUCE: (11), (21) imply:
% 244.05/50.66  | | |   (25)   ~ (e1 = e0)
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (13), (14), (15), (18), (22),
% 244.05/50.66  | | |            (24), (25) are inconsistent by sub-proof #1526.
% 244.05/50.66  | | | 
% 244.05/50.66  | | Case 2:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (26)  all_54_2 = e0
% 244.05/50.66  | | | 
% 244.05/50.66  | | | COMBINE_EQS: (2), (26) imply:
% 244.05/50.66  | | |   (27)  all_18_0 = e0
% 244.05/50.66  | | | 
% 244.05/50.66  | | | SIMP: (27) implies:
% 244.05/50.66  | | |   (28)  all_18_0 = e0
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REDUCE: (11), (28) imply:
% 244.05/50.66  | | |   (29)  $false
% 244.05/50.66  | | | 
% 244.05/50.66  | | | CLOSE: (29) is inconsistent.
% 244.05/50.66  | | | 
% 244.05/50.66  | | End of split
% 244.05/50.66  | | 
% 244.05/50.66  | End of split
% 244.05/50.66  | 
% 244.05/50.66  End of proof
% 244.05/50.66  
% 244.05/50.66  Sub-proof #1526 shows that the following formulas are inconsistent:
% 244.05/50.66  ----------------------------------------------------------------
% 244.05/50.66    (1)  all_54_2 = e1 | all_54_2 = e0
% 244.05/50.66    (2)  all_58_4 = e2
% 244.05/50.66    (3)   ~ (all_52_8 = e0)
% 244.05/50.66    (4)   ~ (all_52_12 = e1)
% 244.05/50.66    (5)  all_54_2 = all_52_8
% 244.05/50.66    (6)  op(e3, e0) = all_52_12
% 244.05/50.66    (7)  op(e3, e2) = all_52_4
% 244.05/50.66    (8)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.66         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.66    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.66    (10)   ~ (e1 = e0)
% 244.05/50.66    (11)  op(e3, e3) = e0
% 244.05/50.66    (12)   ~ (all_52_4 = all_52_8)
% 244.05/50.66    (13)   ~ (e2 = e1)
% 244.05/50.66  
% 244.05/50.66  Begin of proof
% 244.05/50.66  | 
% 244.05/50.66  | BETA: splitting (8) gives:
% 244.05/50.66  | 
% 244.05/50.66  | Case 1:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (14)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 244.05/50.66  | |           e1)
% 244.05/50.66  | | 
% 244.05/50.66  | | BETA: splitting (14) gives:
% 244.05/50.66  | | 
% 244.05/50.66  | | Case 1:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (15)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | ALPHA: (15) implies:
% 244.05/50.66  | | |   (16)  op(e3, e3) = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REF_CLOSE: (9), (10), (11), (16) are inconsistent by sub-proof #1828.
% 244.05/50.66  | | | 
% 244.05/50.66  | | Case 2:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (17)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | ALPHA: (17) implies:
% 244.05/50.66  | | |   (18)  op(e3, e2) = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REF_CLOSE: (1), (3), (5), (7), (9), (12), (18) are inconsistent by
% 244.05/50.66  | | |            sub-proof #1642.
% 244.05/50.66  | | | 
% 244.05/50.66  | | End of split
% 244.05/50.66  | | 
% 244.05/50.66  | Case 2:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (19)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 244.05/50.66  | |           e1)
% 244.05/50.66  | | 
% 244.05/50.66  | | BETA: splitting (19) gives:
% 244.05/50.66  | | 
% 244.05/50.66  | | Case 1:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (20)  all_58_4 = e1 & op(e3, e1) = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REF_CLOSE: (2), (13), (20) are inconsistent by sub-proof #2168.
% 244.05/50.66  | | | 
% 244.05/50.66  | | Case 2:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (21)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REF_CLOSE: (4), (6), (9), (21) are inconsistent by sub-proof #2278.
% 244.05/50.66  | | | 
% 244.05/50.66  | | End of split
% 244.05/50.66  | | 
% 244.05/50.66  | End of split
% 244.05/50.66  | 
% 244.05/50.66  End of proof
% 244.05/50.66  
% 244.05/50.66  Sub-proof #1527 shows that the following formulas are inconsistent:
% 244.05/50.66  ----------------------------------------------------------------
% 244.05/50.66    (1)  all_54_2 = all_18_0
% 244.05/50.66    (2)  all_54_2 = e2
% 244.05/50.66    (3)   ~ (all_18_0 = e2)
% 244.05/50.66  
% 244.05/50.66  Begin of proof
% 244.05/50.66  | 
% 244.05/50.66  | COMBINE_EQS: (1), (2) imply:
% 244.05/50.66  |   (4)  all_18_0 = e2
% 244.05/50.66  | 
% 244.05/50.66  | SIMP: (4) implies:
% 244.05/50.66  |   (5)  all_18_0 = e2
% 244.05/50.66  | 
% 244.05/50.66  | REDUCE: (3), (5) imply:
% 244.05/50.66  |   (6)  $false
% 244.05/50.66  | 
% 244.05/50.66  | CLOSE: (6) is inconsistent.
% 244.05/50.66  | 
% 244.05/50.66  End of proof
% 244.05/50.66  
% 244.05/50.66  Sub-proof #1528 shows that the following formulas are inconsistent:
% 244.05/50.66  ----------------------------------------------------------------
% 244.05/50.66    (1)   ~ (e3 = e0)
% 244.05/50.66    (2)   ~ (e2 = e0)
% 244.05/50.66    (3)  all_58_12 = e3 & op(e0, e3) = e3
% 244.05/50.66    (4)  op(e1, e2) = all_52_6
% 244.05/50.66    (5)  op(e1, e1) = all_6_2
% 244.05/50.66    (6)  op(e1, e0) = all_52_14
% 244.05/50.66    (7)   ~ (e3 = e1)
% 244.05/50.66    (8)   ~ (all_6_2 = e3)
% 244.05/50.66    (9)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.05/50.66         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.05/50.66    (10)   ~ (e3 = e2)
% 244.05/50.66    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.05/50.66          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.05/50.66    (12)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.05/50.66          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.05/50.66    (13)   ~ (all_52_14 = e3)
% 244.05/50.66    (14)   ~ (all_52_6 = e3)
% 244.05/50.66    (15)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.05/50.66          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.05/50.66    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.66    (17)   ~ (e1 = e0)
% 244.05/50.66    (18)   ~ (e2 = e1)
% 244.05/50.66  
% 244.05/50.66  Begin of proof
% 244.05/50.66  | 
% 244.05/50.66  | ALPHA: (3) implies:
% 244.05/50.66  |   (19)  all_58_12 = e3
% 244.05/50.66  | 
% 244.05/50.66  | BETA: splitting (12) gives:
% 244.05/50.66  | 
% 244.05/50.66  | Case 1:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (20)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.05/50.66  | |           e3)
% 244.05/50.66  | | 
% 244.05/50.66  | | REF_CLOSE: (1), (2), (4), (7), (9), (10), (11), (14), (15), (16), (17),
% 244.05/50.66  | |            (18), (19), (20) are inconsistent by sub-proof #1530.
% 244.05/50.66  | | 
% 244.05/50.66  | Case 2:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (21)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.05/50.66  | |           e3)
% 244.05/50.66  | | 
% 244.05/50.66  | | REF_CLOSE: (5), (6), (8), (13), (16), (21) are inconsistent by sub-proof
% 244.05/50.66  | |            #1529.
% 244.05/50.66  | | 
% 244.05/50.66  | End of split
% 244.05/50.66  | 
% 244.05/50.66  End of proof
% 244.05/50.66  
% 244.05/50.66  Sub-proof #1529 shows that the following formulas are inconsistent:
% 244.05/50.66  ----------------------------------------------------------------
% 244.05/50.66    (1)  op(e1, e1) = all_6_2
% 244.05/50.66    (2)  op(e1, e0) = all_52_14
% 244.05/50.66    (3)   ~ (all_6_2 = e3)
% 244.05/50.66    (4)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.05/50.66    (5)   ~ (all_52_14 = e3)
% 244.05/50.66    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.66  
% 244.05/50.66  Begin of proof
% 244.05/50.66  | 
% 244.05/50.66  | BETA: splitting (4) gives:
% 244.05/50.66  | 
% 244.05/50.66  | Case 1:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 244.05/50.66  | | 
% 244.05/50.66  | | REF_CLOSE: (1), (3), (6), (7) are inconsistent by sub-proof #2092.
% 244.05/50.66  | | 
% 244.05/50.66  | Case 2:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (8)  all_58_11 = e3 & op(e1, e0) = e3
% 244.05/50.66  | | 
% 244.05/50.66  | | ALPHA: (8) implies:
% 244.05/50.66  | |   (9)  op(e1, e0) = e3
% 244.05/50.66  | | 
% 244.05/50.66  | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #2149.
% 244.05/50.66  | | 
% 244.05/50.66  | End of split
% 244.05/50.66  | 
% 244.05/50.66  End of proof
% 244.05/50.66  
% 244.05/50.66  Sub-proof #1530 shows that the following formulas are inconsistent:
% 244.05/50.66  ----------------------------------------------------------------
% 244.05/50.66    (1)   ~ (e3 = e0)
% 244.05/50.66    (2)   ~ (e2 = e0)
% 244.05/50.66    (3)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 244.05/50.66    (4)  op(e1, e2) = all_52_6
% 244.05/50.66    (5)   ~ (e3 = e1)
% 244.05/50.66    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.05/50.66         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.05/50.66    (7)   ~ (e3 = e2)
% 244.05/50.66    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.05/50.66         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.05/50.66    (9)  all_58_12 = e3
% 244.05/50.66    (10)   ~ (all_52_6 = e3)
% 244.05/50.66    (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.05/50.66          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.05/50.66    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.66    (13)   ~ (e1 = e0)
% 244.05/50.66    (14)   ~ (e2 = e1)
% 244.05/50.66  
% 244.05/50.66  Begin of proof
% 244.05/50.66  | 
% 244.05/50.66  | BETA: splitting (3) gives:
% 244.05/50.66  | 
% 244.05/50.66  | Case 1:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (15)  all_58_6 = e3 & op(e1, e3) = e3
% 244.05/50.66  | | 
% 244.05/50.66  | | ALPHA: (15) implies:
% 244.05/50.66  | |   (16)  all_58_6 = e3
% 244.05/50.66  | | 
% 244.05/50.66  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (13), (14), (16)
% 244.05/50.66  | |            are inconsistent by sub-proof #1531.
% 244.05/50.66  | | 
% 244.05/50.66  | Case 2:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (17)  all_58_7 = e3 & op(e1, e2) = e3
% 244.05/50.66  | | 
% 244.05/50.66  | | ALPHA: (17) implies:
% 244.05/50.66  | |   (18)  op(e1, e2) = e3
% 244.05/50.66  | | 
% 244.05/50.66  | | REF_CLOSE: (4), (10), (12), (18) are inconsistent by sub-proof #2191.
% 244.05/50.66  | | 
% 244.05/50.66  | End of split
% 244.05/50.66  | 
% 244.05/50.66  End of proof
% 244.05/50.66  
% 244.05/50.66  Sub-proof #1531 shows that the following formulas are inconsistent:
% 244.05/50.66  ----------------------------------------------------------------
% 244.05/50.66    (1)   ~ (e3 = e0)
% 244.05/50.66    (2)  all_58_6 = e3
% 244.05/50.66    (3)   ~ (e2 = e0)
% 244.05/50.66    (4)   ~ (e3 = e1)
% 244.05/50.66    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.05/50.66         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.05/50.66    (6)   ~ (e3 = e2)
% 244.05/50.66    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.05/50.66         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.05/50.66    (8)  all_58_12 = e3
% 244.05/50.66    (9)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.05/50.66         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.05/50.66    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.66    (11)   ~ (e1 = e0)
% 244.05/50.66    (12)   ~ (e2 = e1)
% 244.05/50.66  
% 244.05/50.66  Begin of proof
% 244.05/50.66  | 
% 244.05/50.66  | BETA: splitting (9) gives:
% 244.05/50.66  | 
% 244.05/50.66  | Case 1:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (13)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 244.05/50.66  | |           e1)
% 244.05/50.66  | | 
% 244.05/50.66  | | BETA: splitting (13) gives:
% 244.05/50.66  | | 
% 244.05/50.66  | | Case 1:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (14)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | ALPHA: (14) implies:
% 244.05/50.66  | | |   (15)  op(e3, e3) = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (15) are
% 244.05/50.66  | | |            inconsistent by sub-proof #1532.
% 244.05/50.66  | | | 
% 244.05/50.66  | | Case 2:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (16)  all_58_2 = e1 & op(e2, e3) = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | ALPHA: (16) implies:
% 244.05/50.66  | | |   (17)  all_58_2 = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (17) are
% 244.05/50.66  | | |            inconsistent by sub-proof #1970.
% 244.05/50.66  | | | 
% 244.05/50.66  | | End of split
% 244.05/50.66  | | 
% 244.05/50.66  | Case 2:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (18)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 244.05/50.66  | |           e1)
% 244.05/50.66  | | 
% 244.05/50.66  | | BETA: splitting (18) gives:
% 244.05/50.66  | | 
% 244.05/50.66  | | Case 1:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (19)  all_58_6 = e1 & op(e1, e3) = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | ALPHA: (19) implies:
% 244.05/50.66  | | |   (20)  all_58_6 = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REF_CLOSE: (2), (4), (20) are inconsistent by sub-proof #1758.
% 244.05/50.66  | | | 
% 244.05/50.66  | | Case 2:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (21)  all_58_12 = e1 & op(e0, e3) = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | ALPHA: (21) implies:
% 244.05/50.66  | | |   (22)  all_58_12 = e1
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REF_CLOSE: (4), (8), (22) are inconsistent by sub-proof #1542.
% 244.05/50.66  | | | 
% 244.05/50.66  | | End of split
% 244.05/50.66  | | 
% 244.05/50.66  | End of split
% 244.05/50.66  | 
% 244.05/50.66  End of proof
% 244.05/50.66  
% 244.05/50.66  Sub-proof #1532 shows that the following formulas are inconsistent:
% 244.05/50.66  ----------------------------------------------------------------
% 244.05/50.66    (1)   ~ (e3 = e0)
% 244.05/50.66    (2)  all_58_6 = e3
% 244.05/50.66    (3)   ~ (e2 = e0)
% 244.05/50.66    (4)  op(e3, e3) = e1
% 244.05/50.66    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.05/50.66         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.05/50.66    (6)   ~ (e3 = e2)
% 244.05/50.66    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.05/50.66         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.05/50.66    (8)  all_58_12 = e3
% 244.05/50.66    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.66    (10)   ~ (e1 = e0)
% 244.05/50.66    (11)   ~ (e2 = e1)
% 244.05/50.66  
% 244.05/50.66  Begin of proof
% 244.05/50.66  | 
% 244.05/50.66  | BETA: splitting (5) gives:
% 244.05/50.66  | 
% 244.05/50.66  | Case 1:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (12)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 244.05/50.66  | |           e2)
% 244.05/50.66  | | 
% 244.05/50.66  | | BETA: splitting (12) gives:
% 244.05/50.66  | | 
% 244.05/50.66  | | Case 1:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (13)  all_58_0 = e2 & op(e3, e3) = e2
% 244.05/50.66  | | | 
% 244.05/50.66  | | | ALPHA: (13) implies:
% 244.05/50.66  | | |   (14)  op(e3, e3) = e2
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REF_CLOSE: (4), (9), (11), (14) are inconsistent by sub-proof #2267.
% 244.05/50.66  | | | 
% 244.05/50.66  | | Case 2:
% 244.05/50.66  | | | 
% 244.05/50.66  | | |   (15)  all_58_2 = e2 & op(e2, e3) = e2
% 244.05/50.66  | | | 
% 244.05/50.66  | | | ALPHA: (15) implies:
% 244.05/50.66  | | |   (16)  all_58_2 = e2
% 244.05/50.66  | | | 
% 244.05/50.66  | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (16) are inconsistent
% 244.05/50.66  | | |            by sub-proof #1533.
% 244.05/50.66  | | | 
% 244.05/50.66  | | End of split
% 244.05/50.66  | | 
% 244.05/50.66  | Case 2:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (17)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 244.05/50.66  | |           e2)
% 244.05/50.66  | | 
% 244.05/50.66  | | REF_CLOSE: (2), (6), (8), (17) are inconsistent by sub-proof #1973.
% 244.05/50.66  | | 
% 244.05/50.66  | End of split
% 244.05/50.66  | 
% 244.05/50.66  End of proof
% 244.05/50.66  
% 244.05/50.66  Sub-proof #1533 shows that the following formulas are inconsistent:
% 244.05/50.66  ----------------------------------------------------------------
% 244.05/50.66    (1)   ~ (e3 = e0)
% 244.05/50.66    (2)  all_58_6 = e3
% 244.05/50.66    (3)   ~ (e2 = e0)
% 244.05/50.66    (4)  all_58_2 = e2
% 244.05/50.66    (5)  op(e3, e3) = e1
% 244.05/50.66    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.05/50.66         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.05/50.66    (7)  all_58_12 = e3
% 244.05/50.66    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.66    (9)   ~ (e1 = e0)
% 244.05/50.66  
% 244.05/50.66  Begin of proof
% 244.05/50.66  | 
% 244.05/50.66  | BETA: splitting (6) gives:
% 244.05/50.66  | 
% 244.05/50.66  | Case 1:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 244.05/50.66  | |           e0)
% 244.05/50.66  | | 
% 244.05/50.66  | | REF_CLOSE: (3), (4), (5), (8), (9), (10) are inconsistent by sub-proof
% 244.05/50.66  | |            #1534.
% 244.05/50.66  | | 
% 244.05/50.66  | Case 2:
% 244.05/50.66  | | 
% 244.05/50.66  | |   (11)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 244.05/50.66  | |           e0)
% 244.05/50.66  | | 
% 244.05/50.66  | | BETA: splitting (11) gives:
% 244.05/50.67  | | 
% 244.05/50.67  | | Case 1:
% 244.05/50.67  | | | 
% 244.05/50.67  | | |   (12)  all_58_6 = e0 & op(e1, e3) = e0
% 244.05/50.67  | | | 
% 244.05/50.67  | | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #2213.
% 244.05/50.67  | | | 
% 244.05/50.67  | | Case 2:
% 244.05/50.67  | | | 
% 244.05/50.67  | | |   (13)  all_58_12 = e0 & op(e0, e3) = e0
% 244.05/50.67  | | | 
% 244.05/50.67  | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #1641.
% 244.05/50.67  | | | 
% 244.05/50.67  | | End of split
% 244.05/50.67  | | 
% 244.05/50.67  | End of split
% 244.05/50.67  | 
% 244.05/50.67  End of proof
% 244.05/50.67  
% 244.05/50.67  Sub-proof #1534 shows that the following formulas are inconsistent:
% 244.05/50.67  ----------------------------------------------------------------
% 244.05/50.67    (1)   ~ (e2 = e0)
% 244.05/50.67    (2)  all_58_2 = e2
% 244.05/50.67    (3)  op(e3, e3) = e1
% 244.05/50.67    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.67    (5)   ~ (e1 = e0)
% 244.05/50.67    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 244.05/50.67  
% 244.05/50.67  Begin of proof
% 244.05/50.67  | 
% 244.05/50.67  | BETA: splitting (6) gives:
% 244.05/50.67  | 
% 244.05/50.67  | Case 1:
% 244.05/50.67  | | 
% 244.05/50.67  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 244.05/50.67  | | 
% 244.05/50.67  | | ALPHA: (7) implies:
% 244.05/50.67  | |   (8)  op(e3, e3) = e0
% 244.05/50.67  | | 
% 244.05/50.67  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1828.
% 244.05/50.67  | | 
% 244.05/50.67  | Case 2:
% 244.05/50.67  | | 
% 244.05/50.67  | |   (9)  all_58_2 = e0 & op(e2, e3) = e0
% 244.05/50.67  | | 
% 244.05/50.67  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #1535.
% 244.05/50.67  | | 
% 244.05/50.67  | End of split
% 244.05/50.67  | 
% 244.05/50.67  End of proof
% 244.05/50.67  
% 244.05/50.67  Sub-proof #1535 shows that the following formulas are inconsistent:
% 244.05/50.67  ----------------------------------------------------------------
% 244.05/50.67    (1)  all_58_2 = e0 & op(e2, e3) = e0
% 244.05/50.67    (2)  all_58_2 = e2
% 244.05/50.67    (3)   ~ (e2 = e0)
% 244.05/50.67  
% 244.05/50.67  Begin of proof
% 244.05/50.67  | 
% 244.05/50.67  | ALPHA: (1) implies:
% 244.05/50.67  |   (4)  all_58_2 = e0
% 244.05/50.67  | 
% 244.05/50.67  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.67  |   (5)  e2 = e0
% 244.05/50.67  | 
% 244.05/50.67  | REDUCE: (3), (5) imply:
% 244.05/50.67  |   (6)  $false
% 244.05/50.67  | 
% 244.05/50.67  | CLOSE: (6) is inconsistent.
% 244.05/50.67  | 
% 244.05/50.67  End of proof
% 244.05/50.67  
% 244.05/50.67  Sub-proof #1536 shows that the following formulas are inconsistent:
% 244.05/50.67  ----------------------------------------------------------------
% 244.05/50.67    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.05/50.67         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.67    (2)   ~ (e3 = e0)
% 244.05/50.67    (3)   ~ (e2 = e0)
% 244.05/50.67    (4)  all_58_14 = e2
% 244.05/50.67    (5)   ~ (all_52_7 = e3)
% 244.05/50.67    (6)  op(e0, e2) = e2
% 244.05/50.67    (7)   ~ (e3 = e1)
% 244.05/50.67    (8)  all_58_12 = e1
% 244.05/50.67    (9)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.67             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.05/50.67               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.05/50.67               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.05/50.67    (10)   ~ (e3 = e2)
% 244.05/50.67    (11)  op(e0, e2) = all_52_7
% 244.05/50.67    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.67    (13)   ~ (e1 = e0)
% 244.05/50.67  
% 244.05/50.67  Begin of proof
% 244.05/50.67  | 
% 244.05/50.67  | BETA: splitting (1) gives:
% 244.05/50.67  | 
% 244.05/50.67  | Case 1:
% 244.05/50.67  | | 
% 244.05/50.67  | |   (14)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.05/50.67  | |           e3)
% 244.05/50.67  | | 
% 244.05/50.67  | | REF_CLOSE: (5), (7), (8), (11), (12), (14) are inconsistent by sub-proof
% 244.05/50.67  | |            #1541.
% 244.05/50.67  | | 
% 244.05/50.67  | Case 2:
% 244.05/50.67  | | 
% 244.05/50.67  | |   (15)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.05/50.67  | |           e3)
% 244.05/50.67  | | 
% 244.05/50.67  | | BETA: splitting (15) gives:
% 244.05/50.67  | | 
% 244.05/50.67  | | Case 1:
% 244.05/50.67  | | | 
% 244.05/50.67  | | |   (16)  all_58_14 = e3 & op(e0, e1) = e3
% 244.05/50.67  | | | 
% 244.05/50.67  | | | ALPHA: (16) implies:
% 244.05/50.67  | | |   (17)  all_58_14 = e3
% 244.05/50.67  | | | 
% 244.05/50.67  | | | REF_CLOSE: (4), (10), (17) are inconsistent by sub-proof #2117.
% 244.05/50.67  | | | 
% 244.05/50.67  | | Case 2:
% 244.05/50.67  | | | 
% 244.05/50.67  | | |   (18)  all_58_15 = e3 & op(e0, e0) = e3
% 244.05/50.67  | | | 
% 244.05/50.67  | | | ALPHA: (18) implies:
% 244.05/50.67  | | |   (19)  all_58_15 = e3
% 244.05/50.67  | | | 
% 244.05/50.67  | | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (12), (13), (19) are inconsistent
% 244.05/50.67  | | |            by sub-proof #1537.
% 244.05/50.67  | | | 
% 244.05/50.67  | | End of split
% 244.05/50.67  | | 
% 244.05/50.67  | End of split
% 244.05/50.67  | 
% 244.05/50.67  End of proof
% 244.05/50.67  
% 244.05/50.67  Sub-proof #1537 shows that the following formulas are inconsistent:
% 244.05/50.67  ----------------------------------------------------------------
% 244.05/50.67    (1)   ~ (e3 = e0)
% 244.05/50.67    (2)   ~ (e2 = e0)
% 244.05/50.67    (3)  all_58_14 = e2
% 244.05/50.67    (4)  all_58_15 = e3
% 244.05/50.67    (5)  op(e0, e2) = e2
% 244.05/50.67    (6)  all_58_12 = e1
% 244.05/50.67    (7)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.67             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.05/50.67               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.05/50.67               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.05/50.67    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.67    (9)   ~ (e1 = e0)
% 244.05/50.67  
% 244.05/50.67  Begin of proof
% 244.05/50.67  | 
% 244.05/50.67  | BETA: splitting (7) gives:
% 244.05/50.67  | 
% 244.05/50.67  | Case 1:
% 244.05/50.67  | | 
% 244.05/50.67  | |   (10)  all_58_15 = e0 & op(e0, e0) = e0
% 244.05/50.67  | | 
% 244.05/50.67  | | ALPHA: (10) implies:
% 244.05/50.67  | |   (11)  all_58_15 = e0
% 244.05/50.67  | | 
% 244.05/50.67  | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #1540.
% 244.05/50.67  | | 
% 244.05/50.67  | Case 2:
% 244.05/50.67  | | 
% 244.05/50.67  | |   (12)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 244.05/50.67  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 244.05/50.67  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 244.05/50.67  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 244.05/50.67  | | 
% 244.05/50.67  | | ALPHA: (12) implies:
% 244.05/50.67  | |   (13)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.05/50.67  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.05/50.67  | | 
% 244.05/50.67  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (13) are inconsistent by sub-proof
% 244.05/50.67  | |            #1538.
% 244.05/50.67  | | 
% 244.05/50.67  | End of split
% 244.05/50.67  | 
% 244.05/50.67  End of proof
% 244.05/50.67  
% 244.05/50.67  Sub-proof #1538 shows that the following formulas are inconsistent:
% 244.05/50.67  ----------------------------------------------------------------
% 244.05/50.67    (1)   ~ (e2 = e0)
% 244.05/50.67    (2)  all_58_14 = e2
% 244.05/50.67    (3)  op(e0, e2) = e2
% 244.05/50.67    (4)  all_58_12 = e1
% 244.05/50.67    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.67    (6)   ~ (e1 = e0)
% 244.05/50.67    (7)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 244.05/50.67         (all_58_14 = e0 & op(e0, e1) = e0)
% 244.05/50.67  
% 244.05/50.67  Begin of proof
% 244.05/50.67  | 
% 244.05/50.67  | BETA: splitting (7) gives:
% 244.05/50.67  | 
% 244.05/50.67  | Case 1:
% 244.05/50.67  | | 
% 244.05/50.67  | |   (8)  all_58_12 = e0 & op(e0, e3) = e0
% 244.05/50.67  | | 
% 244.05/50.67  | | ALPHA: (8) implies:
% 244.05/50.67  | |   (9)  all_58_12 = e0
% 244.05/50.67  | | 
% 244.05/50.67  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #1539.
% 244.05/50.67  | | 
% 244.05/50.67  | Case 2:
% 244.05/50.67  | | 
% 244.05/50.67  | |   (10)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 244.05/50.67  | |           e0)
% 244.05/50.67  | | 
% 244.05/50.67  | | REF_CLOSE: (1), (2), (3), (5), (10) are inconsistent by sub-proof #1640.
% 244.05/50.67  | | 
% 244.05/50.67  | End of split
% 244.05/50.67  | 
% 244.05/50.67  End of proof
% 244.05/50.67  
% 244.05/50.67  Sub-proof #1539 shows that the following formulas are inconsistent:
% 244.05/50.67  ----------------------------------------------------------------
% 244.05/50.67    (1)  all_58_12 = e1
% 244.05/50.67    (2)  all_58_12 = e0
% 244.05/50.67    (3)   ~ (e1 = e0)
% 244.05/50.67  
% 244.05/50.67  Begin of proof
% 244.05/50.67  | 
% 244.05/50.67  | COMBINE_EQS: (1), (2) imply:
% 244.05/50.67  |   (4)  e1 = e0
% 244.05/50.67  | 
% 244.05/50.67  | SIMP: (4) implies:
% 244.05/50.67  |   (5)  e1 = e0
% 244.05/50.67  | 
% 244.05/50.67  | REDUCE: (3), (5) imply:
% 244.05/50.67  |   (6)  $false
% 244.05/50.67  | 
% 244.05/50.67  | CLOSE: (6) is inconsistent.
% 244.05/50.67  | 
% 244.05/50.67  End of proof
% 244.05/50.67  
% 244.05/50.67  Sub-proof #1540 shows that the following formulas are inconsistent:
% 244.05/50.67  ----------------------------------------------------------------
% 244.05/50.67    (1)  all_58_15 = e3
% 244.05/50.67    (2)  all_58_15 = e0
% 244.05/50.67    (3)   ~ (e3 = e0)
% 244.05/50.67  
% 244.05/50.67  Begin of proof
% 244.05/50.67  | 
% 244.05/50.67  | COMBINE_EQS: (1), (2) imply:
% 244.05/50.67  |   (4)  e3 = e0
% 244.05/50.67  | 
% 244.05/50.67  | SIMP: (4) implies:
% 244.05/50.67  |   (5)  e3 = e0
% 244.05/50.67  | 
% 244.05/50.67  | REDUCE: (3), (5) imply:
% 244.05/50.67  |   (6)  $false
% 244.05/50.67  | 
% 244.05/50.67  | CLOSE: (6) is inconsistent.
% 244.05/50.67  | 
% 244.05/50.67  End of proof
% 244.05/50.67  
% 244.05/50.67  Sub-proof #1541 shows that the following formulas are inconsistent:
% 244.05/50.67  ----------------------------------------------------------------
% 244.05/50.67    (1)   ~ (all_52_7 = e3)
% 244.05/50.67    (2)   ~ (e3 = e1)
% 244.05/50.67    (3)  all_58_12 = e1
% 244.05/50.67    (4)  op(e0, e2) = all_52_7
% 244.05/50.67    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.67    (6)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.05/50.67  
% 244.05/50.67  Begin of proof
% 244.05/50.67  | 
% 244.05/50.67  | BETA: splitting (6) gives:
% 244.05/50.67  | 
% 244.05/50.67  | Case 1:
% 244.05/50.67  | | 
% 244.05/50.67  | |   (7)  all_58_12 = e3 & op(e0, e3) = e3
% 244.05/50.67  | | 
% 244.05/50.67  | | ALPHA: (7) implies:
% 244.05/50.67  | |   (8)  all_58_12 = e3
% 244.05/50.67  | | 
% 244.05/50.67  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #1542.
% 244.05/50.67  | | 
% 244.05/50.67  | Case 2:
% 244.05/50.67  | | 
% 244.05/50.67  | |   (9)  all_58_13 = e3 & op(e0, e2) = e3
% 244.05/50.67  | | 
% 244.05/50.67  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1919.
% 244.05/50.67  | | 
% 244.05/50.67  | End of split
% 244.05/50.67  | 
% 244.05/50.67  End of proof
% 244.05/50.67  
% 244.05/50.67  Sub-proof #1542 shows that the following formulas are inconsistent:
% 244.05/50.67  ----------------------------------------------------------------
% 244.05/50.67    (1)  all_58_12 = e3
% 244.05/50.67    (2)  all_58_12 = e1
% 244.05/50.67    (3)   ~ (e3 = e1)
% 244.05/50.67  
% 244.05/50.67  Begin of proof
% 244.05/50.67  | 
% 244.05/50.67  | COMBINE_EQS: (1), (2) imply:
% 244.05/50.67  |   (4)  e3 = e1
% 244.05/50.67  | 
% 244.05/50.67  | SIMP: (4) implies:
% 244.05/50.67  |   (5)  e3 = e1
% 244.05/50.67  | 
% 244.05/50.67  | REDUCE: (3), (5) imply:
% 244.05/50.67  |   (6)  $false
% 244.05/50.67  | 
% 244.05/50.67  | CLOSE: (6) is inconsistent.
% 244.05/50.67  | 
% 244.05/50.67  End of proof
% 244.05/50.67  
% 244.05/50.67  Sub-proof #1543 shows that the following formulas are inconsistent:
% 244.05/50.67  ----------------------------------------------------------------
% 244.05/50.67    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.05/50.67         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.67    (2)   ~ (e3 = e0)
% 244.05/50.67    (3)  all_58_1 = e3
% 244.05/50.67    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.05/50.67         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.05/50.67    (5)  all_58_6 = e3
% 244.05/50.67    (6)   ~ (e2 = e0)
% 244.05/50.67    (7)  op(e0, e1) = e3
% 244.05/50.67    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.05/50.67         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.05/50.67    (9)  op(e1, e3) = e3
% 244.05/50.67    (10)  op(e1, e0) = all_52_14
% 244.05/50.67    (11)   ~ (all_52_7 = e3)
% 244.05/50.67    (12)   ~ (e3 = e1)
% 244.05/50.67    (13)  op(e2, e2) = e0
% 244.05/50.67    (14)   ~ (e3 = e2)
% 244.05/50.67    (15)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.05/50.67          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.05/50.67    (16)   ~ (all_52_14 = e3)
% 244.05/50.67    (17)  op(e0, e2) = all_52_7
% 244.05/50.67    (18)  all_58_12 = e2 & op(e0, e3) = e2
% 244.05/50.67    (19)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.05/50.67          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.05/50.67    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.67    (21)  op(e0, e0) = e0
% 244.05/50.67    (22)  op(e1, e1) = e0
% 244.05/50.67    (23)   ~ (e1 = e0)
% 244.05/50.67    (24)  op(e3, e2) = e3
% 244.05/50.67    (25)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.05/50.67          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.67    (26)  op(e0, all_52_7) = e0
% 244.05/50.67    (27)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.05/50.67          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.05/50.67            e1)
% 244.05/50.67    (28)   ~ (e2 = e1)
% 244.05/50.67  
% 244.05/50.67  Begin of proof
% 244.05/50.67  | 
% 244.05/50.67  | ALPHA: (18) implies:
% 244.05/50.67  |   (29)  all_58_12 = e2
% 244.05/50.67  | 
% 244.05/50.67  | BETA: splitting (27) gives:
% 244.05/50.67  | 
% 244.05/50.67  | Case 1:
% 244.05/50.67  | | 
% 244.05/50.67  | |   (30)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 244.05/50.67  | |           e1)
% 244.05/50.67  | | 
% 244.05/50.67  | | BETA: splitting (30) gives:
% 244.05/50.67  | | 
% 244.05/50.67  | | Case 1:
% 244.05/50.67  | | | 
% 244.05/50.67  | | |   (31)  all_58_12 = e1 & op(e0, e3) = e1
% 244.05/50.67  | | | 
% 244.05/50.67  | | | REF_CLOSE: (28), (29), (31) are inconsistent by sub-proof #1763.
% 244.05/50.67  | | | 
% 244.05/50.67  | | Case 2:
% 244.05/50.67  | | | 
% 244.05/50.67  | | |   (32)  all_58_13 = e1 & op(e0, e2) = e1
% 244.05/50.67  | | | 
% 244.05/50.67  | | | ALPHA: (32) implies:
% 244.05/50.67  | | |   (33)  all_58_13 = e1
% 244.05/50.67  | | |   (34)  op(e0, e2) = e1
% 244.05/50.67  | | | 
% 244.05/50.67  | | | BETA: splitting (8) gives:
% 244.05/50.67  | | | 
% 244.05/50.67  | | | Case 1:
% 244.05/50.67  | | | | 
% 244.05/50.67  | | | |   (35)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2)
% 244.05/50.67  | | | |           = e2)
% 244.05/50.67  | | | | 
% 244.05/50.67  | | | | REF_CLOSE: (6), (13), (14), (20), (24), (35) are inconsistent by
% 244.05/50.67  | | | |            sub-proof #1546.
% 244.05/50.67  | | | | 
% 244.05/50.67  | | | Case 2:
% 244.05/50.67  | | | | 
% 244.05/50.67  | | | |   (36)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2)
% 244.05/50.67  | | | |           = e2)
% 244.05/50.67  | | | | 
% 244.05/50.67  | | | | BETA: splitting (36) gives:
% 244.05/50.67  | | | | 
% 244.05/50.67  | | | | Case 1:
% 244.05/50.67  | | | | | 
% 244.05/50.67  | | | | |   (37)  all_58_7 = e2 & op(e1, e2) = e2
% 244.05/50.67  | | | | | 
% 244.05/50.67  | | | | | ALPHA: (37) implies:
% 244.05/50.67  | | | | |   (38)  all_58_7 = e2
% 244.05/50.67  | | | | | 
% 244.05/50.67  | | | | | BETA: splitting (4) gives:
% 244.05/50.67  | | | | | 
% 244.05/50.67  | | | | | Case 1:
% 244.05/50.67  | | | | | | 
% 244.05/50.67  | | | | | |   (39)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1,
% 244.05/50.67  | | | | | |             e2) = e1)
% 244.05/50.67  | | | | | | 
% 244.05/50.67  | | | | | | BETA: splitting (39) gives:
% 244.05/50.67  | | | | | | 
% 244.05/50.67  | | | | | | Case 1:
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | |   (40)  all_58_6 = e1 & op(e1, e3) = e1
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | | ALPHA: (40) implies:
% 244.05/50.67  | | | | | | |   (41)  op(e1, e3) = e1
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | | REF_CLOSE: (9), (12), (20), (41) are inconsistent by sub-proof
% 244.05/50.67  | | | | | | |            #2225.
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | Case 2:
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | |   (42)  all_58_7 = e1 & op(e1, e2) = e1
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | | ALPHA: (42) implies:
% 244.05/50.67  | | | | | | |   (43)  all_58_7 = e1
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | | REF_CLOSE: (3), (6), (8), (13), (14), (20), (28), (33), (43) are
% 244.05/50.67  | | | | | | |            inconsistent by sub-proof #1588.
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | End of split
% 244.05/50.67  | | | | | | 
% 244.05/50.67  | | | | | Case 2:
% 244.05/50.67  | | | | | | 
% 244.05/50.67  | | | | | |   (44)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1,
% 244.05/50.67  | | | | | |             e0) = e1)
% 244.05/50.67  | | | | | | 
% 244.05/50.67  | | | | | | BETA: splitting (44) gives:
% 244.05/50.67  | | | | | | 
% 244.05/50.67  | | | | | | Case 1:
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | |   (45)  all_58_8 = e1 & op(e1, e1) = e1
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | | ALPHA: (45) implies:
% 244.05/50.67  | | | | | | |   (46)  op(e1, e1) = e1
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | | REF_CLOSE: (20), (22), (23), (46) are inconsistent by sub-proof
% 244.05/50.67  | | | | | | |            #2220.
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | Case 2:
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | |   (47)  all_58_11 = e1 & op(e1, e0) = e1
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | | ALPHA: (47) implies:
% 244.05/50.67  | | | | | | |   (48)  op(e1, e0) = e1
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | | BETA: splitting (19) gives:
% 244.05/50.67  | | | | | | | 
% 244.05/50.67  | | | | | | | Case 1:
% 244.05/50.67  | | | | | | | | 
% 244.05/50.67  | | | | | | | |   (49)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 244.05/50.67  | | | | | | | |           op(e1, e2) = e2)
% 244.05/50.67  | | | | | | | | 
% 244.05/50.67  | | | | | | | | BETA: splitting (49) gives:
% 244.05/50.67  | | | | | | | | 
% 244.05/50.67  | | | | | | | | Case 1:
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | |   (50)  all_58_6 = e2 & op(e1, e3) = e2
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | | REF_CLOSE: (5), (14), (50) are inconsistent by sub-proof
% 244.05/50.67  | | | | | | | | |            #2219.
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | Case 2:
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | | GROUND_INST: instantiating (20) with all_52_7, e1, e2, e0,
% 244.05/50.67  | | | | | | | | |              simplifying with (17), (34) gives:
% 244.05/50.67  | | | | | | | | |   (51)  all_52_7 = e1
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | | REDUCE: (26), (51) imply:
% 244.05/50.67  | | | | | | | | |   (52)  op(e0, e1) = e0
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | | REF_CLOSE: (2), (7), (20), (52) are inconsistent by sub-proof
% 244.05/50.67  | | | | | | | | |            #2164.
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | End of split
% 244.05/50.67  | | | | | | | | 
% 244.05/50.67  | | | | | | | Case 2:
% 244.05/50.67  | | | | | | | | 
% 244.05/50.67  | | | | | | | |   (53)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 244.05/50.67  | | | | | | | |           op(e1, e0) = e2)
% 244.05/50.67  | | | | | | | | 
% 244.05/50.67  | | | | | | | | BETA: splitting (53) gives:
% 244.05/50.67  | | | | | | | | 
% 244.05/50.67  | | | | | | | | Case 1:
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | |   (54)  all_58_8 = e2 & op(e1, e1) = e2
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | | ALPHA: (54) implies:
% 244.05/50.67  | | | | | | | | |   (55)  all_58_8 = e2
% 244.05/50.67  | | | | | | | | |   (56)  op(e1, e1) = e2
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (12), (14), (15), (16), (20),
% 244.05/50.67  | | | | | | | | |            (23), (25), (28), (38), (55), (56) are inconsistent
% 244.05/50.67  | | | | | | | | |            by sub-proof #1545.
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.67  | | | | | | | | Case 2:
% 244.05/50.67  | | | | | | | | | 
% 244.05/50.68  | | | | | | | | |   (57)  all_58_11 = e2 & op(e1, e0) = e2
% 244.05/50.68  | | | | | | | | | 
% 244.05/50.68  | | | | | | | | | ALPHA: (57) implies:
% 244.05/50.68  | | | | | | | | |   (58)  op(e1, e0) = e2
% 244.05/50.68  | | | | | | | | | 
% 244.05/50.68  | | | | | | | | | REF_CLOSE: (20), (28), (48), (58) are inconsistent by
% 244.05/50.68  | | | | | | | | |            sub-proof #2019.
% 244.05/50.68  | | | | | | | | | 
% 244.05/50.68  | | | | | | | | End of split
% 244.05/50.68  | | | | | | | | 
% 244.05/50.68  | | | | | | | End of split
% 244.05/50.68  | | | | | | | 
% 244.05/50.68  | | | | | | End of split
% 244.05/50.68  | | | | | | 
% 244.05/50.68  | | | | | End of split
% 244.05/50.68  | | | | | 
% 244.05/50.68  | | | | Case 2:
% 244.05/50.68  | | | | | 
% 244.05/50.68  | | | | |   (59)  all_58_13 = e2 & op(e0, e2) = e2
% 244.05/50.68  | | | | | 
% 244.05/50.68  | | | | | ALPHA: (59) implies:
% 244.05/50.68  | | | | |   (60)  all_58_13 = e2
% 244.05/50.68  | | | | | 
% 244.05/50.68  | | | | | REF_CLOSE: (28), (33), (60) are inconsistent by sub-proof #1544.
% 244.05/50.68  | | | | | 
% 244.05/50.68  | | | | End of split
% 244.05/50.68  | | | | 
% 244.05/50.68  | | | End of split
% 244.05/50.68  | | | 
% 244.05/50.68  | | End of split
% 244.05/50.68  | | 
% 244.05/50.68  | Case 2:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (61)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.05/50.68  | |           e1)
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (1), (2), (11), (12), (14), (17), (20), (21), (23), (29), (61)
% 244.05/50.68  | |            are inconsistent by sub-proof #1549.
% 244.05/50.68  | | 
% 244.05/50.68  | End of split
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1544 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)  all_58_13 = e2
% 244.05/50.68    (2)  all_58_13 = e1
% 244.05/50.68    (3)   ~ (e2 = e1)
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | COMBINE_EQS: (1), (2) imply:
% 244.05/50.68  |   (4)  e2 = e1
% 244.05/50.68  | 
% 244.05/50.68  | SIMP: (4) implies:
% 244.05/50.68  |   (5)  e2 = e1
% 244.05/50.68  | 
% 244.05/50.68  | REDUCE: (3), (5) imply:
% 244.05/50.68  |   (6)  $false
% 244.05/50.68  | 
% 244.05/50.68  | CLOSE: (6) is inconsistent.
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1545 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)   ~ (e3 = e0)
% 244.05/50.68    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.05/50.68         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.05/50.68    (3)   ~ (e2 = e0)
% 244.05/50.68    (4)  op(e1, e0) = all_52_14
% 244.05/50.68    (5)   ~ (e3 = e1)
% 244.05/50.68    (6)  all_58_8 = e2
% 244.05/50.68    (7)  all_58_7 = e2
% 244.05/50.68    (8)   ~ (e3 = e2)
% 244.05/50.68    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.05/50.68         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.05/50.68    (10)   ~ (all_52_14 = e3)
% 244.05/50.68    (11)  op(e1, e1) = e2
% 244.05/50.68    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.68    (13)   ~ (e1 = e0)
% 244.05/50.68    (14)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.05/50.68          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.68    (15)   ~ (e2 = e1)
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | BETA: splitting (9) gives:
% 244.05/50.68  | 
% 244.05/50.68  | Case 1:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (16)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.05/50.68  | |           e3)
% 244.05/50.68  | | 
% 244.05/50.68  | | BETA: splitting (16) gives:
% 244.05/50.68  | | 
% 244.05/50.68  | | Case 1:
% 244.05/50.68  | | | 
% 244.05/50.68  | | |   (17)  all_58_6 = e3 & op(e1, e3) = e3
% 244.05/50.68  | | | 
% 244.05/50.68  | | | ALPHA: (17) implies:
% 244.05/50.68  | | |   (18)  all_58_6 = e3
% 244.05/50.68  | | | 
% 244.05/50.68  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (11), (12), (13), (14), (15),
% 244.05/50.68  | | |            (18) are inconsistent by sub-proof #1801.
% 244.05/50.68  | | | 
% 244.05/50.68  | | Case 2:
% 244.05/50.68  | | | 
% 244.05/50.68  | | |   (19)  all_58_7 = e3 & op(e1, e2) = e3
% 244.05/50.68  | | | 
% 244.05/50.68  | | | REF_CLOSE: (7), (8), (19) are inconsistent by sub-proof #1675.
% 244.05/50.68  | | | 
% 244.05/50.68  | | End of split
% 244.05/50.68  | | 
% 244.05/50.68  | Case 2:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (20)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.05/50.68  | |           e3)
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (4), (8), (10), (11), (12), (20) are inconsistent by sub-proof
% 244.05/50.68  | |            #2148.
% 244.05/50.68  | | 
% 244.05/50.68  | End of split
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1546 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)   ~ (e2 = e0)
% 244.05/50.68    (2)  op(e2, e2) = e0
% 244.05/50.68    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 244.05/50.68    (4)   ~ (e3 = e2)
% 244.05/50.68    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.68    (6)  op(e3, e2) = e3
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | BETA: splitting (3) gives:
% 244.05/50.68  | 
% 244.05/50.68  | Case 1:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (7)  all_58_1 = e2 & op(e3, e2) = e2
% 244.05/50.68  | | 
% 244.05/50.68  | | ALPHA: (7) implies:
% 244.05/50.68  | |   (8)  op(e3, e2) = e2
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2193.
% 244.05/50.68  | | 
% 244.05/50.68  | Case 2:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (9)  all_58_3 = e2 & op(e2, e2) = e2
% 244.05/50.68  | | 
% 244.05/50.68  | | ALPHA: (9) implies:
% 244.05/50.68  | |   (10)  op(e2, e2) = e2
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #2137.
% 244.05/50.68  | | 
% 244.05/50.68  | End of split
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1547 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 244.05/50.68    (2)   ~ (e2 = e0)
% 244.05/50.68    (3)   ~ (e3 = e2)
% 244.05/50.68    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.68    (5)  all_58_14 = e3
% 244.05/50.68    (6)  op(e1, e1) = e0
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | BETA: splitting (1) gives:
% 244.05/50.68  | 
% 244.05/50.68  | Case 1:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (7)  all_58_8 = e2 & op(e1, e1) = e2
% 244.05/50.68  | | 
% 244.05/50.68  | | ALPHA: (7) implies:
% 244.05/50.68  | |   (8)  op(e1, e1) = e2
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2211.
% 244.05/50.68  | | 
% 244.05/50.68  | Case 2:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (9)  all_58_14 = e2 & op(e0, e1) = e2
% 244.05/50.68  | | 
% 244.05/50.68  | | ALPHA: (9) implies:
% 244.05/50.68  | |   (10)  all_58_14 = e2
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #2117.
% 244.05/50.68  | | 
% 244.05/50.68  | End of split
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1548 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)  all_58_5 = e1 & op(e2, e1) = e1
% 244.05/50.68    (2)  all_58_5 = e2
% 244.05/50.68    (3)   ~ (e2 = e1)
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | ALPHA: (1) implies:
% 244.05/50.68  |   (4)  all_58_5 = e1
% 244.05/50.68  | 
% 244.05/50.68  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.68  |   (5)  e2 = e1
% 244.05/50.68  | 
% 244.05/50.68  | REDUCE: (3), (5) imply:
% 244.05/50.68  |   (6)  $false
% 244.05/50.68  | 
% 244.05/50.68  | CLOSE: (6) is inconsistent.
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1549 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.05/50.68         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.68    (2)   ~ (e3 = e0)
% 244.05/50.68    (3)  all_58_12 = e2
% 244.05/50.68    (4)   ~ (all_52_7 = e3)
% 244.05/50.68    (5)   ~ (e3 = e1)
% 244.05/50.68    (6)   ~ (e3 = e2)
% 244.05/50.68    (7)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.05/50.68    (8)  op(e0, e2) = all_52_7
% 244.05/50.68    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.68    (10)  op(e0, e0) = e0
% 244.05/50.68    (11)   ~ (e1 = e0)
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | BETA: splitting (7) gives:
% 244.05/50.68  | 
% 244.05/50.68  | Case 1:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (12)  all_58_14 = e1 & op(e0, e1) = e1
% 244.05/50.68  | | 
% 244.05/50.68  | | ALPHA: (12) implies:
% 244.05/50.68  | |   (13)  all_58_14 = e1
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (13) are
% 244.05/50.68  | |            inconsistent by sub-proof #1550.
% 244.05/50.68  | | 
% 244.05/50.68  | Case 2:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (14)  all_58_15 = e1 & op(e0, e0) = e1
% 244.05/50.68  | | 
% 244.05/50.68  | | ALPHA: (14) implies:
% 244.05/50.68  | |   (15)  op(e0, e0) = e1
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (9), (10), (11), (15) are inconsistent by sub-proof #2274.
% 244.05/50.68  | | 
% 244.05/50.68  | End of split
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1550 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.05/50.68         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.05/50.68    (2)   ~ (e3 = e0)
% 244.05/50.68    (3)  all_58_12 = e2
% 244.05/50.68    (4)   ~ (all_52_7 = e3)
% 244.05/50.68    (5)   ~ (e3 = e1)
% 244.05/50.68    (6)   ~ (e3 = e2)
% 244.05/50.68    (7)  op(e0, e2) = all_52_7
% 244.05/50.68    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.68    (9)  op(e0, e0) = e0
% 244.05/50.68    (10)  all_58_14 = e1
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | BETA: splitting (1) gives:
% 244.05/50.68  | 
% 244.05/50.68  | Case 1:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (11)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.05/50.68  | |           e3)
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (3), (4), (6), (7), (8), (11) are inconsistent by sub-proof
% 244.05/50.68  | |            #1551.
% 244.05/50.68  | | 
% 244.05/50.68  | Case 2:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (12)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.05/50.68  | |           e3)
% 244.05/50.68  | | 
% 244.05/50.68  | | BETA: splitting (12) gives:
% 244.05/50.68  | | 
% 244.05/50.68  | | Case 1:
% 244.05/50.68  | | | 
% 244.05/50.68  | | |   (13)  all_58_14 = e3 & op(e0, e1) = e3
% 244.05/50.68  | | | 
% 244.05/50.68  | | | ALPHA: (13) implies:
% 244.05/50.68  | | |   (14)  all_58_14 = e3
% 244.05/50.68  | | | 
% 244.05/50.68  | | | REF_CLOSE: (5), (10), (14) are inconsistent by sub-proof #1844.
% 244.05/50.68  | | | 
% 244.05/50.68  | | Case 2:
% 244.05/50.68  | | | 
% 244.05/50.68  | | |   (15)  all_58_15 = e3 & op(e0, e0) = e3
% 244.05/50.68  | | | 
% 244.05/50.68  | | | ALPHA: (15) implies:
% 244.05/50.68  | | |   (16)  op(e0, e0) = e3
% 244.05/50.68  | | | 
% 244.05/50.68  | | | REF_CLOSE: (2), (8), (9), (16) are inconsistent by sub-proof #2079.
% 244.05/50.68  | | | 
% 244.05/50.68  | | End of split
% 244.05/50.68  | | 
% 244.05/50.68  | End of split
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1551 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)  all_58_12 = e2
% 244.05/50.68    (2)   ~ (all_52_7 = e3)
% 244.05/50.68    (3)   ~ (e3 = e2)
% 244.05/50.68    (4)  op(e0, e2) = all_52_7
% 244.05/50.68    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.68    (6)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | BETA: splitting (6) gives:
% 244.05/50.68  | 
% 244.05/50.68  | Case 1:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (7)  all_58_12 = e3 & op(e0, e3) = e3
% 244.05/50.68  | | 
% 244.05/50.68  | | ALPHA: (7) implies:
% 244.05/50.68  | |   (8)  all_58_12 = e3
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #1552.
% 244.05/50.68  | | 
% 244.05/50.68  | Case 2:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (9)  all_58_13 = e3 & op(e0, e2) = e3
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #1919.
% 244.05/50.68  | | 
% 244.05/50.68  | End of split
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1552 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)  all_58_12 = e3
% 244.05/50.68    (2)  all_58_12 = e2
% 244.05/50.68    (3)   ~ (e3 = e2)
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | COMBINE_EQS: (1), (2) imply:
% 244.05/50.68  |   (4)  e3 = e2
% 244.05/50.68  | 
% 244.05/50.68  | SIMP: (4) implies:
% 244.05/50.68  |   (5)  e3 = e2
% 244.05/50.68  | 
% 244.05/50.68  | REDUCE: (3), (5) imply:
% 244.05/50.68  |   (6)  $false
% 244.05/50.68  | 
% 244.05/50.68  | CLOSE: (6) is inconsistent.
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1553 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)   ~ (e3 = e0)
% 244.05/50.68    (2)  all_58_6 = e3
% 244.05/50.68    (3)   ~ (e2 = e0)
% 244.05/50.68    (4)  all_58_11 = e1
% 244.05/50.68    (5)  op(e1, e0) = e1
% 244.05/50.68    (6)   ~ (e3 = e2)
% 244.05/50.68    (7)  all_58_7 = e1
% 244.05/50.68    (8)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.05/50.68         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.05/50.68    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.68    (10)   ~ (e1 = e0)
% 244.05/50.68    (11)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.05/50.68          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.68    (12)   ~ (e2 = e1)
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | BETA: splitting (8) gives:
% 244.05/50.68  | 
% 244.05/50.68  | Case 1:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (13)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 244.05/50.68  | |           e2)
% 244.05/50.68  | | 
% 244.05/50.68  | | BETA: splitting (13) gives:
% 244.05/50.68  | | 
% 244.05/50.68  | | Case 1:
% 244.05/50.68  | | | 
% 244.05/50.68  | | |   (14)  all_58_6 = e2 & op(e1, e3) = e2
% 244.05/50.68  | | | 
% 244.05/50.68  | | | ALPHA: (14) implies:
% 244.05/50.68  | | |   (15)  all_58_6 = e2
% 244.05/50.68  | | | 
% 244.05/50.68  | | | REF_CLOSE: (2), (6), (15) are inconsistent by sub-proof #2024.
% 244.05/50.68  | | | 
% 244.05/50.68  | | Case 2:
% 244.05/50.68  | | | 
% 244.05/50.68  | | |   (16)  all_58_7 = e2 & op(e1, e2) = e2
% 244.05/50.68  | | | 
% 244.05/50.68  | | | ALPHA: (16) implies:
% 244.05/50.68  | | |   (17)  all_58_7 = e2
% 244.05/50.68  | | | 
% 244.05/50.68  | | | REF_CLOSE: (7), (12), (17) are inconsistent by sub-proof #2134.
% 244.05/50.68  | | | 
% 244.05/50.68  | | End of split
% 244.05/50.68  | | 
% 244.05/50.68  | Case 2:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (18)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 244.05/50.68  | |           e2)
% 244.05/50.68  | | 
% 244.05/50.68  | | BETA: splitting (18) gives:
% 244.05/50.68  | | 
% 244.05/50.68  | | Case 1:
% 244.05/50.68  | | | 
% 244.05/50.68  | | |   (19)  all_58_8 = e2 & op(e1, e1) = e2
% 244.05/50.68  | | | 
% 244.05/50.68  | | | ALPHA: (19) implies:
% 244.05/50.68  | | |   (20)  all_58_8 = e2
% 244.05/50.68  | | | 
% 244.05/50.68  | | | REF_CLOSE: (1), (2), (3), (5), (7), (9), (10), (11), (20) are inconsistent
% 244.05/50.68  | | |            by sub-proof #1555.
% 244.05/50.68  | | | 
% 244.05/50.68  | | Case 2:
% 244.05/50.68  | | | 
% 244.05/50.68  | | |   (21)  all_58_11 = e2 & op(e1, e0) = e2
% 244.05/50.68  | | | 
% 244.05/50.68  | | | REF_CLOSE: (4), (12), (21) are inconsistent by sub-proof #1554.
% 244.05/50.68  | | | 
% 244.05/50.68  | | End of split
% 244.05/50.68  | | 
% 244.05/50.68  | End of split
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1554 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)  all_58_11 = e2 & op(e1, e0) = e2
% 244.05/50.68    (2)  all_58_11 = e1
% 244.05/50.68    (3)   ~ (e2 = e1)
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | ALPHA: (1) implies:
% 244.05/50.68  |   (4)  all_58_11 = e2
% 244.05/50.68  | 
% 244.05/50.68  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.68  |   (5)  e2 = e1
% 244.05/50.68  | 
% 244.05/50.68  | REDUCE: (3), (5) imply:
% 244.05/50.68  |   (6)  $false
% 244.05/50.68  | 
% 244.05/50.68  | CLOSE: (6) is inconsistent.
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1555 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)   ~ (e3 = e0)
% 244.05/50.68    (2)  all_58_6 = e3
% 244.05/50.68    (3)   ~ (e2 = e0)
% 244.05/50.68    (4)  all_58_8 = e2
% 244.05/50.68    (5)  op(e1, e0) = e1
% 244.05/50.68    (6)  all_58_7 = e1
% 244.05/50.68    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.68    (8)   ~ (e1 = e0)
% 244.05/50.68    (9)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.05/50.68         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | BETA: splitting (9) gives:
% 244.05/50.68  | 
% 244.05/50.68  | Case 1:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (10)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 244.05/50.68  | |           e0)
% 244.05/50.68  | | 
% 244.05/50.68  | | REF_CLOSE: (1), (2), (6), (8), (10) are inconsistent by sub-proof #1557.
% 244.05/50.68  | | 
% 244.05/50.68  | Case 2:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (11)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.05/50.68  | |           e0)
% 244.05/50.68  | | 
% 244.05/50.68  | | BETA: splitting (11) gives:
% 244.05/50.68  | | 
% 244.05/50.68  | | Case 1:
% 244.05/50.68  | | | 
% 244.05/50.68  | | |   (12)  all_58_8 = e0 & op(e1, e1) = e0
% 244.05/50.68  | | | 
% 244.05/50.68  | | | ALPHA: (12) implies:
% 244.05/50.68  | | |   (13)  all_58_8 = e0
% 244.05/50.68  | | | 
% 244.05/50.68  | | | REF_CLOSE: (3), (4), (13) are inconsistent by sub-proof #1556.
% 244.05/50.68  | | | 
% 244.05/50.68  | | Case 2:
% 244.05/50.68  | | | 
% 244.05/50.68  | | |   (14)  all_58_11 = e0 & op(e1, e0) = e0
% 244.05/50.68  | | | 
% 244.05/50.68  | | | ALPHA: (14) implies:
% 244.05/50.68  | | |   (15)  op(e1, e0) = e0
% 244.05/50.68  | | | 
% 244.05/50.68  | | | REF_CLOSE: (5), (7), (8), (15) are inconsistent by sub-proof #2284.
% 244.05/50.68  | | | 
% 244.05/50.68  | | End of split
% 244.05/50.68  | | 
% 244.05/50.68  | End of split
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1556 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)  all_58_8 = e2
% 244.05/50.68    (2)  all_58_8 = e0
% 244.05/50.68    (3)   ~ (e2 = e0)
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | COMBINE_EQS: (1), (2) imply:
% 244.05/50.68  |   (4)  e2 = e0
% 244.05/50.68  | 
% 244.05/50.68  | SIMP: (4) implies:
% 244.05/50.68  |   (5)  e2 = e0
% 244.05/50.68  | 
% 244.05/50.68  | REDUCE: (3), (5) imply:
% 244.05/50.68  |   (6)  $false
% 244.05/50.68  | 
% 244.05/50.68  | CLOSE: (6) is inconsistent.
% 244.05/50.68  | 
% 244.05/50.68  End of proof
% 244.05/50.68  
% 244.05/50.68  Sub-proof #1557 shows that the following formulas are inconsistent:
% 244.05/50.68  ----------------------------------------------------------------
% 244.05/50.68    (1)   ~ (e3 = e0)
% 244.05/50.68    (2)  all_58_6 = e3
% 244.05/50.68    (3)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 244.05/50.68    (4)  all_58_7 = e1
% 244.05/50.68    (5)   ~ (e1 = e0)
% 244.05/50.68  
% 244.05/50.68  Begin of proof
% 244.05/50.68  | 
% 244.05/50.68  | BETA: splitting (3) gives:
% 244.05/50.68  | 
% 244.05/50.68  | Case 1:
% 244.05/50.68  | | 
% 244.05/50.68  | |   (6)  all_58_6 = e0 & op(e1, e3) = e0
% 244.05/50.68  | | 
% 244.05/50.68  | | ALPHA: (6) implies:
% 244.05/50.68  | |   (7)  all_58_6 = e0
% 244.05/50.69  | | 
% 244.05/50.69  | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #2222.
% 244.05/50.69  | | 
% 244.05/50.69  | Case 2:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (8)  all_58_7 = e0 & op(e1, e2) = e0
% 244.05/50.69  | | 
% 244.05/50.69  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1558.
% 244.05/50.69  | | 
% 244.05/50.69  | End of split
% 244.05/50.69  | 
% 244.05/50.69  End of proof
% 244.05/50.69  
% 244.05/50.69  Sub-proof #1558 shows that the following formulas are inconsistent:
% 244.05/50.69  ----------------------------------------------------------------
% 244.05/50.69    (1)  all_58_7 = e0 & op(e1, e2) = e0
% 244.05/50.69    (2)  all_58_7 = e1
% 244.05/50.69    (3)   ~ (e1 = e0)
% 244.05/50.69  
% 244.05/50.69  Begin of proof
% 244.05/50.69  | 
% 244.05/50.69  | ALPHA: (1) implies:
% 244.05/50.69  |   (4)  all_58_7 = e0
% 244.05/50.69  | 
% 244.05/50.69  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.69  |   (5)  e1 = e0
% 244.05/50.69  | 
% 244.05/50.69  | REDUCE: (3), (5) imply:
% 244.05/50.69  |   (6)  $false
% 244.05/50.69  | 
% 244.05/50.69  | CLOSE: (6) is inconsistent.
% 244.05/50.69  | 
% 244.05/50.69  End of proof
% 244.05/50.69  
% 244.05/50.69  Sub-proof #1559 shows that the following formulas are inconsistent:
% 244.05/50.69  ----------------------------------------------------------------
% 244.05/50.69    (1)   ~ (e3 = e0)
% 244.05/50.69    (2)   ~ (e2 = e0)
% 244.05/50.69    (3)   ~ (e3 = e1)
% 244.05/50.69    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.69         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.69    (5)   ~ (e3 = e2)
% 244.05/50.69    (6)  op(e3, e3) = e2
% 244.05/50.69    (7)  op(e3, e0) = e2
% 244.05/50.69    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.69         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.69    (9)  op(e3, e2) = all_52_4
% 244.05/50.69    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.69          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.69    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.69    (12)   ~ (e1 = e0)
% 244.05/50.69    (13)  all_58_9 = e2
% 244.05/50.69    (14)   ~ (all_52_4 = e0)
% 244.05/50.69    (15)   ~ (e2 = e1)
% 244.05/50.69  
% 244.05/50.69  Begin of proof
% 244.05/50.69  | 
% 244.05/50.69  | BETA: splitting (8) gives:
% 244.05/50.69  | 
% 244.05/50.69  | Case 1:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (16)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 244.05/50.69  | |           e0)
% 244.05/50.69  | | 
% 244.05/50.69  | | REF_CLOSE: (2), (6), (9), (11), (14), (16) are inconsistent by sub-proof
% 244.05/50.69  | |            #1711.
% 244.05/50.69  | | 
% 244.05/50.69  | Case 2:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (17)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 244.05/50.69  | |           e0)
% 244.05/50.69  | | 
% 244.05/50.69  | | BETA: splitting (17) gives:
% 244.05/50.69  | | 
% 244.05/50.69  | | Case 1:
% 244.05/50.69  | | | 
% 244.05/50.69  | | |   (18)  all_58_4 = e0 & op(e3, e1) = e0
% 244.05/50.69  | | | 
% 244.05/50.69  | | | ALPHA: (18) implies:
% 244.05/50.69  | | |   (19)  all_58_4 = e0
% 244.05/50.69  | | | 
% 244.05/50.69  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 244.05/50.69  | | |            (15), (19) are inconsistent by sub-proof #1560.
% 244.05/50.69  | | | 
% 244.05/50.69  | | Case 2:
% 244.05/50.69  | | | 
% 244.05/50.69  | | |   (20)  all_58_9 = e0 & op(e3, e0) = e0
% 244.05/50.69  | | | 
% 244.05/50.69  | | | ALPHA: (20) implies:
% 244.05/50.69  | | |   (21)  op(e3, e0) = e0
% 244.05/50.69  | | | 
% 244.05/50.69  | | | REF_CLOSE: (2), (7), (11), (21) are inconsistent by sub-proof #2154.
% 244.05/50.69  | | | 
% 244.05/50.69  | | End of split
% 244.05/50.69  | | 
% 244.05/50.69  | End of split
% 244.05/50.69  | 
% 244.05/50.69  End of proof
% 244.05/50.69  
% 244.05/50.69  Sub-proof #1560 shows that the following formulas are inconsistent:
% 244.05/50.69  ----------------------------------------------------------------
% 244.05/50.69    (1)   ~ (e3 = e0)
% 244.05/50.69    (2)   ~ (e2 = e0)
% 244.05/50.69    (3)   ~ (e3 = e1)
% 244.05/50.69    (4)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.05/50.69         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.69    (5)   ~ (e3 = e2)
% 244.05/50.69    (6)  op(e3, e3) = e2
% 244.05/50.69    (7)  op(e3, e0) = e2
% 244.05/50.69    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.69         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.69    (9)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.69         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.69    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.69    (11)   ~ (e1 = e0)
% 244.05/50.69    (12)  all_58_9 = e2
% 244.05/50.69    (13)  all_58_4 = e0
% 244.05/50.69    (14)   ~ (e2 = e1)
% 244.05/50.69  
% 244.05/50.69  Begin of proof
% 244.05/50.69  | 
% 244.05/50.69  | BETA: splitting (4) gives:
% 244.05/50.69  | 
% 244.05/50.69  | Case 1:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (15)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 244.05/50.69  | |           e3)
% 244.05/50.69  | | 
% 244.05/50.69  | | BETA: splitting (15) gives:
% 244.05/50.69  | | 
% 244.05/50.69  | | Case 1:
% 244.05/50.69  | | | 
% 244.05/50.69  | | |   (16)  all_58_0 = e3 & op(e3, e3) = e3
% 244.05/50.69  | | | 
% 244.05/50.69  | | | ALPHA: (16) implies:
% 244.05/50.69  | | |   (17)  op(e3, e3) = e3
% 244.05/50.69  | | | 
% 244.05/50.69  | | | REF_CLOSE: (5), (6), (10), (17) are inconsistent by sub-proof #2194.
% 244.05/50.69  | | | 
% 244.05/50.69  | | Case 2:
% 244.05/50.69  | | | 
% 244.05/50.69  | | |   (18)  all_58_1 = e3 & op(e3, e2) = e3
% 244.05/50.69  | | | 
% 244.05/50.69  | | | ALPHA: (18) implies:
% 244.05/50.69  | | |   (19)  all_58_1 = e3
% 244.05/50.69  | | | 
% 244.05/50.69  | | | BETA: splitting (9) gives:
% 244.05/50.69  | | | 
% 244.05/50.69  | | | Case 1:
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | |   (20)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 244.05/50.69  | | | |           = e1)
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | | BETA: splitting (20) gives:
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | | Case 1:
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | |   (21)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | | ALPHA: (21) implies:
% 244.05/50.69  | | | | |   (22)  op(e3, e3) = e1
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | | REF_CLOSE: (6), (10), (14), (22) are inconsistent by sub-proof #2267.
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | Case 2:
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | |   (23)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | | REF_CLOSE: (3), (19), (23) are inconsistent by sub-proof #1753.
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | End of split
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | Case 2:
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | |   (24)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 244.05/50.69  | | | |           = e1)
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | | BETA: splitting (24) gives:
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | | Case 1:
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | |   (25)  all_58_4 = e1 & op(e3, e1) = e1
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | | ALPHA: (25) implies:
% 244.05/50.69  | | | | |   (26)  all_58_4 = e1
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | | REF_CLOSE: (11), (13), (26) are inconsistent by sub-proof #1710.
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | Case 2:
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | |   (27)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | | ALPHA: (27) implies:
% 244.05/50.69  | | | | |   (28)  all_58_9 = e1
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | | REF_CLOSE: (12), (14), (28) are inconsistent by sub-proof #1605.
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | End of split
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | End of split
% 244.05/50.69  | | | 
% 244.05/50.69  | | End of split
% 244.05/50.69  | | 
% 244.05/50.69  | Case 2:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (29)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 244.05/50.69  | |           e3)
% 244.05/50.69  | | 
% 244.05/50.69  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 244.05/50.69  | |            (29) are inconsistent by sub-proof #1561.
% 244.05/50.69  | | 
% 244.05/50.69  | End of split
% 244.05/50.69  | 
% 244.05/50.69  End of proof
% 244.05/50.69  
% 244.05/50.69  Sub-proof #1561 shows that the following formulas are inconsistent:
% 244.05/50.69  ----------------------------------------------------------------
% 244.05/50.69    (1)   ~ (e3 = e0)
% 244.05/50.69    (2)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.05/50.69    (3)   ~ (e2 = e0)
% 244.05/50.69    (4)   ~ (e3 = e1)
% 244.05/50.69    (5)   ~ (e3 = e2)
% 244.05/50.69    (6)  op(e3, e3) = e2
% 244.05/50.69    (7)  op(e3, e0) = e2
% 244.05/50.69    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.69         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.69    (9)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.69         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.69    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.69    (11)   ~ (e1 = e0)
% 244.05/50.69    (12)  all_58_9 = e2
% 244.05/50.69    (13)   ~ (e2 = e1)
% 244.05/50.69  
% 244.05/50.69  Begin of proof
% 244.05/50.69  | 
% 244.05/50.69  | BETA: splitting (2) gives:
% 244.05/50.69  | 
% 244.05/50.69  | Case 1:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (14)  all_58_4 = e3 & op(e3, e1) = e3
% 244.05/50.69  | | 
% 244.05/50.69  | | ALPHA: (14) implies:
% 244.05/50.69  | |   (15)  all_58_4 = e3
% 244.05/50.69  | | 
% 244.05/50.69  | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (11), (12), (13), (15) are
% 244.05/50.69  | |            inconsistent by sub-proof #1562.
% 244.05/50.69  | | 
% 244.05/50.69  | Case 2:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (16)  all_58_9 = e3 & op(e3, e0) = e3
% 244.05/50.69  | | 
% 244.05/50.69  | | ALPHA: (16) implies:
% 244.05/50.69  | |   (17)  op(e3, e0) = e3
% 244.05/50.69  | | 
% 244.05/50.69  | | REF_CLOSE: (5), (7), (10), (17) are inconsistent by sub-proof #2125.
% 244.05/50.69  | | 
% 244.05/50.69  | End of split
% 244.05/50.69  | 
% 244.05/50.69  End of proof
% 244.05/50.69  
% 244.05/50.69  Sub-proof #1562 shows that the following formulas are inconsistent:
% 244.05/50.69  ----------------------------------------------------------------
% 244.05/50.69    (1)   ~ (e3 = e0)
% 244.05/50.69    (2)   ~ (e2 = e0)
% 244.05/50.69    (3)   ~ (e3 = e1)
% 244.05/50.69    (4)  op(e3, e3) = e2
% 244.05/50.69    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.05/50.69         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.05/50.69    (6)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.69         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.69    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.69    (8)   ~ (e1 = e0)
% 244.05/50.69    (9)  all_58_4 = e3
% 244.05/50.69    (10)  all_58_9 = e2
% 244.05/50.69    (11)   ~ (e2 = e1)
% 244.05/50.69  
% 244.05/50.69  Begin of proof
% 244.05/50.69  | 
% 244.05/50.69  | BETA: splitting (5) gives:
% 244.05/50.69  | 
% 244.05/50.69  | Case 1:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 244.05/50.69  | |           e0)
% 244.05/50.69  | | 
% 244.05/50.69  | | BETA: splitting (12) gives:
% 244.05/50.69  | | 
% 244.05/50.69  | | Case 1:
% 244.05/50.69  | | | 
% 244.05/50.69  | | |   (13)  all_58_0 = e0 & op(e3, e3) = e0
% 244.05/50.69  | | | 
% 244.05/50.69  | | | ALPHA: (13) implies:
% 244.05/50.69  | | |   (14)  op(e3, e3) = e0
% 244.05/50.69  | | | 
% 244.05/50.69  | | | REF_CLOSE: (2), (4), (7), (14) are inconsistent by sub-proof #2188.
% 244.05/50.69  | | | 
% 244.05/50.69  | | Case 2:
% 244.05/50.69  | | | 
% 244.05/50.69  | | |   (15)  all_58_1 = e0 & op(e3, e2) = e0
% 244.05/50.69  | | | 
% 244.05/50.69  | | | ALPHA: (15) implies:
% 244.05/50.69  | | |   (16)  all_58_1 = e0
% 244.05/50.69  | | | 
% 244.05/50.69  | | | BETA: splitting (6) gives:
% 244.05/50.69  | | | 
% 244.05/50.69  | | | Case 1:
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | |   (17)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 244.05/50.69  | | | |           = e1)
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | | REF_CLOSE: (4), (7), (8), (11), (16), (17) are inconsistent by sub-proof
% 244.05/50.69  | | | |            #1564.
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | Case 2:
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | |   (18)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 244.05/50.69  | | | |           = e1)
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | | BETA: splitting (18) gives:
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | | Case 1:
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | |   (19)  all_58_4 = e1 & op(e3, e1) = e1
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | | ALPHA: (19) implies:
% 244.05/50.69  | | | | |   (20)  all_58_4 = e1
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | | REF_CLOSE: (3), (9), (20) are inconsistent by sub-proof #2184.
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | Case 2:
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | |   (21)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | | ALPHA: (21) implies:
% 244.05/50.69  | | | | |   (22)  all_58_9 = e1
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | | REF_CLOSE: (10), (11), (22) are inconsistent by sub-proof #1605.
% 244.05/50.69  | | | | | 
% 244.05/50.69  | | | | End of split
% 244.05/50.69  | | | | 
% 244.05/50.69  | | | End of split
% 244.05/50.69  | | | 
% 244.05/50.69  | | End of split
% 244.05/50.69  | | 
% 244.05/50.69  | Case 2:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (23)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 244.05/50.69  | |           e0)
% 244.05/50.69  | | 
% 244.05/50.69  | | BETA: splitting (23) gives:
% 244.05/50.69  | | 
% 244.05/50.69  | | Case 1:
% 244.05/50.69  | | | 
% 244.05/50.69  | | |   (24)  all_58_4 = e0 & op(e3, e1) = e0
% 244.05/50.69  | | | 
% 244.05/50.69  | | | REF_CLOSE: (1), (9), (24) are inconsistent by sub-proof #1697.
% 244.05/50.69  | | | 
% 244.05/50.69  | | Case 2:
% 244.05/50.69  | | | 
% 244.05/50.69  | | |   (25)  all_58_9 = e0 & op(e3, e0) = e0
% 244.05/50.69  | | | 
% 244.05/50.69  | | | REF_CLOSE: (2), (10), (25) are inconsistent by sub-proof #1563.
% 244.05/50.69  | | | 
% 244.05/50.69  | | End of split
% 244.05/50.69  | | 
% 244.05/50.69  | End of split
% 244.05/50.69  | 
% 244.05/50.69  End of proof
% 244.05/50.69  
% 244.05/50.69  Sub-proof #1563 shows that the following formulas are inconsistent:
% 244.05/50.69  ----------------------------------------------------------------
% 244.05/50.69    (1)  all_58_9 = e0 & op(e3, e0) = e0
% 244.05/50.69    (2)  all_58_9 = e2
% 244.05/50.69    (3)   ~ (e2 = e0)
% 244.05/50.69  
% 244.05/50.69  Begin of proof
% 244.05/50.69  | 
% 244.05/50.69  | ALPHA: (1) implies:
% 244.05/50.69  |   (4)  all_58_9 = e0
% 244.05/50.69  | 
% 244.05/50.69  | COMBINE_EQS: (2), (4) imply:
% 244.05/50.69  |   (5)  e2 = e0
% 244.05/50.69  | 
% 244.05/50.69  | REDUCE: (3), (5) imply:
% 244.05/50.69  |   (6)  $false
% 244.05/50.69  | 
% 244.05/50.69  | CLOSE: (6) is inconsistent.
% 244.05/50.69  | 
% 244.05/50.69  End of proof
% 244.05/50.69  
% 244.05/50.69  Sub-proof #1564 shows that the following formulas are inconsistent:
% 244.05/50.69  ----------------------------------------------------------------
% 244.05/50.69    (1)  all_58_1 = e0
% 244.05/50.69    (2)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 244.05/50.69    (3)  op(e3, e3) = e2
% 244.05/50.69    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.69    (5)   ~ (e1 = e0)
% 244.05/50.69    (6)   ~ (e2 = e1)
% 244.05/50.69  
% 244.05/50.69  Begin of proof
% 244.05/50.69  | 
% 244.05/50.69  | BETA: splitting (2) gives:
% 244.05/50.69  | 
% 244.05/50.69  | Case 1:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.69  | | 
% 244.05/50.69  | | ALPHA: (7) implies:
% 244.05/50.69  | |   (8)  op(e3, e3) = e1
% 244.05/50.69  | | 
% 244.05/50.69  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #2267.
% 244.05/50.69  | | 
% 244.05/50.69  | Case 2:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (9)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.69  | | 
% 244.05/50.69  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #2015.
% 244.05/50.69  | | 
% 244.05/50.69  | End of split
% 244.05/50.69  | 
% 244.05/50.69  End of proof
% 244.05/50.69  
% 244.05/50.69  Sub-proof #1565 shows that the following formulas are inconsistent:
% 244.05/50.69  ----------------------------------------------------------------
% 244.05/50.69    (1)  op(e1, e2) = all_56_13
% 244.05/50.69    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.05/50.69         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.05/50.69    (3)   ~ (e2 = e0)
% 244.05/50.69    (4)  all_58_4 = e2
% 244.05/50.69    (5)  op(e1, e3) = e3
% 244.05/50.69    (6)   ~ (e3 = e1)
% 244.05/50.69    (7)  op(e2, e0) = e3
% 244.05/50.69    (8)   ~ (e3 = e2)
% 244.05/50.69    (9)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) = all_16_1
% 244.05/50.69           & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0) =
% 244.05/50.69           all_16_1 & $i(all_16_1))
% 244.05/50.69    (10)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 244.05/50.69            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 244.05/50.69              e0) = all_50_1 & $i(all_50_1))
% 244.05/50.69    (11)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.05/50.69          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.05/50.69    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.69    (13)  op(e0, e0) = e0
% 244.05/50.69    (14)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.69          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.69    (15)  op(e1, e1) = e0
% 244.05/50.69    (16)  op(e1, all_56_13) = e1
% 244.05/50.69    (17)   ~ (e1 = e0)
% 244.05/50.69    (18)  op(e3, e3) = e0
% 244.05/50.69    (19)  op(e3, e2) = e3
% 244.05/50.69    (20)   ~ (e2 = e1)
% 244.05/50.69  
% 244.05/50.69  Begin of proof
% 244.05/50.69  | 
% 244.05/50.69  | BETA: splitting (11) gives:
% 244.05/50.69  | 
% 244.05/50.69  | Case 1:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (21)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 244.05/50.69  | |           e1)
% 244.05/50.69  | | 
% 244.05/50.69  | | REF_CLOSE: (6), (12), (17), (18), (19), (21) are inconsistent by sub-proof
% 244.05/50.69  | |            #1571.
% 244.05/50.69  | | 
% 244.05/50.69  | Case 2:
% 244.05/50.69  | | 
% 244.05/50.69  | |   (22)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 244.05/50.69  | |           e1)
% 244.05/50.69  | | 
% 244.05/50.69  | | BETA: splitting (22) gives:
% 244.05/50.69  | | 
% 244.05/50.69  | | Case 1:
% 244.05/50.69  | | | 
% 244.05/50.69  | | |   (23)  all_58_4 = e1 & op(e3, e1) = e1
% 244.05/50.69  | | | 
% 244.05/50.69  | | | REF_CLOSE: (4), (20), (23) are inconsistent by sub-proof #2168.
% 244.05/50.69  | | | 
% 244.05/50.69  | | Case 2:
% 244.05/50.69  | | | 
% 244.05/50.69  | | |   (24)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.69  | | | 
% 244.05/50.69  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 244.05/50.69  | | |            (15), (16), (17), (20), (24) are inconsistent by sub-proof
% 244.05/50.69  | | |            #1566.
% 244.05/50.69  | | | 
% 244.05/50.69  | | End of split
% 244.05/50.69  | | 
% 244.05/50.69  | End of split
% 244.05/50.69  | 
% 244.05/50.69  End of proof
% 244.05/50.69  
% 244.05/50.69  Sub-proof #1566 shows that the following formulas are inconsistent:
% 244.05/50.69  ----------------------------------------------------------------
% 244.05/50.69    (1)  op(e1, e2) = all_56_13
% 244.05/50.70    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.05/50.70         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.05/50.70    (3)   ~ (e2 = e0)
% 244.05/50.70    (4)  op(e1, e3) = e3
% 244.05/50.70    (5)   ~ (e3 = e1)
% 244.05/50.70    (6)  op(e2, e0) = e3
% 244.05/50.70    (7)  all_58_9 = e1 & op(e3, e0) = e1
% 244.05/50.70    (8)   ~ (e3 = e2)
% 244.05/50.70    (9)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) = all_16_1
% 244.05/50.70           & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0) =
% 244.05/50.70           all_16_1 & $i(all_16_1))
% 244.05/50.70    (10)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 244.05/50.70            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 244.05/50.70              e0) = all_50_1 & $i(all_50_1))
% 244.05/50.70    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.70    (12)  op(e0, e0) = e0
% 244.05/50.70    (13)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.05/50.70          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.05/50.70    (14)  op(e1, e1) = e0
% 244.05/50.70    (15)  op(e1, all_56_13) = e1
% 244.05/50.70    (16)   ~ (e1 = e0)
% 244.05/50.70    (17)   ~ (e2 = e1)
% 244.05/50.70  
% 244.05/50.70  Begin of proof
% 244.05/50.70  | 
% 244.05/50.70  | ALPHA: (7) implies:
% 244.05/50.70  |   (18)  all_58_9 = e1
% 244.05/50.70  |   (19)  op(e3, e0) = e1
% 244.05/50.70  | 
% 244.05/50.70  | BETA: splitting (13) gives:
% 244.05/50.70  | 
% 244.05/50.70  | Case 1:
% 244.05/50.70  | | 
% 244.05/50.70  | |   (20)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 244.05/50.70  | |           e2)
% 244.05/50.70  | | 
% 244.05/50.70  | | BETA: splitting (20) gives:
% 244.05/50.70  | | 
% 244.05/50.70  | | Case 1:
% 244.05/50.70  | | | 
% 244.05/50.70  | | |   (21)  all_58_9 = e2 & op(e3, e0) = e2
% 244.05/50.70  | | | 
% 244.05/50.70  | | | ALPHA: (21) implies:
% 244.05/50.70  | | |   (22)  all_58_9 = e2
% 244.05/50.70  | | | 
% 244.05/50.70  | | | REF_CLOSE: (17), (18), (22) are inconsistent by sub-proof #1605.
% 244.05/50.70  | | | 
% 244.05/50.70  | | Case 2:
% 244.05/50.70  | | | 
% 244.05/50.70  | | |   (23)  all_58_10 = e2 & op(e2, e0) = e2
% 244.05/50.70  | | | 
% 244.05/50.70  | | | ALPHA: (23) implies:
% 244.05/50.70  | | |   (24)  op(e2, e0) = e2
% 244.05/50.70  | | | 
% 244.05/50.70  | | | REF_CLOSE: (6), (8), (11), (24) are inconsistent by sub-proof #2152.
% 244.05/50.70  | | | 
% 244.05/50.70  | | End of split
% 244.05/50.70  | | 
% 244.05/50.70  | Case 2:
% 244.05/50.70  | | 
% 244.05/50.70  | |   (25)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.05/50.70  | |           e2)
% 244.05/50.70  | | 
% 244.05/50.70  | | BETA: splitting (25) gives:
% 244.05/50.70  | | 
% 244.05/50.70  | | Case 1:
% 244.05/50.70  | | | 
% 244.05/50.70  | | |   (26)  all_58_11 = e2 & op(e1, e0) = e2
% 244.05/50.70  | | | 
% 244.05/50.70  | | | ALPHA: (26) implies:
% 244.05/50.70  | | |   (27)  op(e1, e0) = e2
% 244.05/50.70  | | | 
% 244.05/50.70  | | | BETA: splitting (2) gives:
% 244.05/50.70  | | | 
% 244.05/50.70  | | | Case 1:
% 244.05/50.70  | | | | 
% 244.05/50.70  | | | |   (28)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 244.05/50.70  | | | |           = e1)
% 244.05/50.70  | | | | 
% 244.05/50.70  | | | | BETA: splitting (28) gives:
% 244.05/50.70  | | | | 
% 244.05/50.70  | | | | Case 1:
% 244.05/50.70  | | | | | 
% 244.05/50.70  | | | | |   (29)  all_58_6 = e1 & op(e1, e3) = e1
% 244.05/50.70  | | | | | 
% 244.05/50.70  | | | | | ALPHA: (29) implies:
% 244.05/50.70  | | | | |   (30)  op(e1, e3) = e1
% 244.05/50.70  | | | | | 
% 244.05/50.70  | | | | | REF_CLOSE: (4), (5), (11), (30) are inconsistent by sub-proof #2225.
% 244.05/50.70  | | | | | 
% 244.05/50.70  | | | | Case 2:
% 244.05/50.70  | | | | | 
% 244.05/50.70  | | | | |   (31)  all_58_7 = e1 & op(e1, e2) = e1
% 244.05/50.70  | | | | | 
% 244.05/50.70  | | | | | ALPHA: (31) implies:
% 244.05/50.70  | | | | |   (32)  op(e1, e2) = e1
% 244.05/50.70  | | | | | 
% 244.05/50.70  | | | | | REF_CLOSE: (1), (9), (10), (11), (14), (15), (16), (19), (32) are
% 244.05/50.70  | | | | |            inconsistent by sub-proof #1568.
% 244.05/50.70  | | | | | 
% 244.05/50.70  | | | | End of split
% 244.05/50.70  | | | | 
% 244.05/50.70  | | | Case 2:
% 244.05/50.70  | | | | 
% 244.05/50.70  | | | |   (33)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0)
% 244.05/50.70  | | | |           = e1)
% 244.05/50.70  | | | | 
% 244.05/50.70  | | | | REF_CLOSE: (11), (14), (16), (17), (27), (33) are inconsistent by
% 244.05/50.70  | | | |            sub-proof #1567.
% 244.05/50.70  | | | | 
% 244.05/50.70  | | | End of split
% 244.05/50.70  | | | 
% 244.05/50.70  | | Case 2:
% 244.05/50.70  | | | 
% 244.05/50.70  | | |   (34)  all_58_15 = e2 & op(e0, e0) = e2
% 244.05/50.70  | | | 
% 244.05/50.70  | | | ALPHA: (34) implies:
% 244.05/50.70  | | |   (35)  op(e0, e0) = e2
% 244.05/50.70  | | | 
% 244.05/50.70  | | | REF_CLOSE: (3), (11), (12), (35) are inconsistent by sub-proof #2301.
% 244.05/50.70  | | | 
% 244.05/50.70  | | End of split
% 244.05/50.70  | | 
% 244.05/50.70  | End of split
% 244.05/50.70  | 
% 244.05/50.70  End of proof
% 244.05/50.70  
% 244.05/50.70  Sub-proof #1567 shows that the following formulas are inconsistent:
% 244.05/50.70  ----------------------------------------------------------------
% 244.05/50.70    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.05/50.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.70    (3)  op(e1, e1) = e0
% 244.05/50.70    (4)  op(e1, e0) = e2
% 244.05/50.70    (5)   ~ (e1 = e0)
% 244.05/50.70    (6)   ~ (e2 = e1)
% 244.05/50.70  
% 244.05/50.70  Begin of proof
% 244.05/50.70  | 
% 244.05/50.70  | BETA: splitting (1) gives:
% 244.05/50.70  | 
% 244.05/50.70  | Case 1:
% 244.05/50.70  | | 
% 244.05/50.70  | |   (7)  all_58_8 = e1 & op(e1, e1) = e1
% 244.05/50.70  | | 
% 244.05/50.70  | | ALPHA: (7) implies:
% 244.05/50.70  | |   (8)  op(e1, e1) = e1
% 244.05/50.70  | | 
% 244.05/50.70  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #2220.
% 244.05/50.70  | | 
% 244.05/50.70  | Case 2:
% 244.05/50.70  | | 
% 244.05/50.70  | |   (9)  all_58_11 = e1 & op(e1, e0) = e1
% 244.05/50.70  | | 
% 244.05/50.70  | | ALPHA: (9) implies:
% 244.05/50.70  | |   (10)  op(e1, e0) = e1
% 244.05/50.70  | | 
% 244.05/50.70  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #2019.
% 244.05/50.70  | | 
% 244.05/50.70  | End of split
% 244.05/50.70  | 
% 244.05/50.70  End of proof
% 244.05/50.70  
% 244.05/50.70  Sub-proof #1568 shows that the following formulas are inconsistent:
% 244.05/50.70  ----------------------------------------------------------------
% 244.05/50.70    (1)  op(e1, e2) = all_56_13
% 244.05/50.70    (2)  op(e1, e2) = e1
% 244.05/50.70    (3)  op(e3, e0) = e1
% 244.05/50.70    (4)  ( ~ (all_16_0 = e2) & op(all_16_1, e3) = all_16_0 & op(e3, e0) = all_16_1
% 244.05/50.70           & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e3, e0) =
% 244.05/50.70           all_16_1 & $i(all_16_1))
% 244.05/50.70    (5)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) = all_50_1
% 244.05/50.70           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0) =
% 244.05/50.70           all_50_1 & $i(all_50_1))
% 244.05/50.70    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.70    (7)  op(e1, e1) = e0
% 244.05/50.70    (8)  op(e1, all_56_13) = e1
% 244.05/50.70    (9)   ~ (e1 = e0)
% 244.05/50.70  
% 244.05/50.70  Begin of proof
% 244.05/50.70  | 
% 244.05/50.70  | BETA: splitting (4) gives:
% 244.05/50.70  | 
% 244.05/50.70  | Case 1:
% 244.05/50.70  | | 
% 244.05/50.70  | | 
% 244.05/50.70  | | GROUND_INST: instantiating (6) with e1, all_56_13, e2, e1, simplifying with
% 244.05/50.70  | |              (1), (2) gives:
% 244.05/50.70  | |   (10)  all_56_13 = e1
% 244.05/50.70  | | 
% 244.05/50.70  | | REDUCE: (8), (10) imply:
% 244.05/50.70  | |   (11)  op(e1, e1) = e1
% 244.05/50.70  | | 
% 244.05/50.70  | | REF_CLOSE: (6), (7), (9), (11) are inconsistent by sub-proof #2220.
% 244.05/50.70  | | 
% 244.05/50.70  | Case 2:
% 244.05/50.70  | | 
% 244.05/50.70  | |   (12)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 & $i(all_16_1)
% 244.05/50.70  | | 
% 244.05/50.70  | | REF_CLOSE: (3), (5), (6), (12) are inconsistent by sub-proof #1569.
% 244.05/50.70  | | 
% 244.05/50.70  | End of split
% 244.05/50.70  | 
% 244.05/50.70  End of proof
% 244.05/50.70  
% 244.05/50.70  Sub-proof #1569 shows that the following formulas are inconsistent:
% 244.05/50.70  ----------------------------------------------------------------
% 244.05/50.70    (1)   ~ (all_16_1 = e1) & op(e3, e0) = all_16_1 & $i(all_16_1)
% 244.05/50.70    (2)  op(e3, e0) = e1
% 244.05/50.70    (3)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) = all_50_1
% 244.05/50.70           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0) =
% 244.05/50.70           all_50_1 & $i(all_50_1))
% 244.05/50.70    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.70  
% 244.05/50.70  Begin of proof
% 244.05/50.70  | 
% 244.05/50.70  | ALPHA: (1) implies:
% 244.05/50.70  |   (5)   ~ (all_16_1 = e1)
% 244.05/50.70  |   (6)  op(e3, e0) = all_16_1
% 244.05/50.70  | 
% 244.05/50.70  | BETA: splitting (3) gives:
% 244.05/50.70  | 
% 244.05/50.70  | Case 1:
% 244.05/50.70  | | 
% 244.05/50.70  | |   (7)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 244.05/50.70  | |        all_50_1 & $i(all_50_0) & $i(all_50_1)
% 244.05/50.70  | | 
% 244.05/50.70  | | ALPHA: (7) implies:
% 244.05/50.70  | |   (8)  op(e3, e0) = all_50_1
% 244.05/50.70  | | 
% 244.05/50.70  | | REF_CLOSE: (2), (4), (5), (6), (8) are inconsistent by sub-proof #1570.
% 244.05/50.70  | | 
% 244.05/50.70  | Case 2:
% 244.05/50.70  | | 
% 244.05/50.70  | |   (9)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 & $i(all_50_1)
% 244.05/50.70  | | 
% 244.05/50.70  | | ALPHA: (9) implies:
% 244.05/50.70  | |   (10)  op(e3, e0) = all_50_1
% 244.05/50.70  | | 
% 244.05/50.70  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #1570.
% 244.05/50.70  | | 
% 244.05/50.70  | End of split
% 244.05/50.70  | 
% 244.05/50.70  End of proof
% 244.05/50.70  
% 244.05/50.70  Sub-proof #1570 shows that the following formulas are inconsistent:
% 244.05/50.70  ----------------------------------------------------------------
% 244.05/50.70    (1)  op(e3, e0) = all_16_1
% 244.05/50.70    (2)  op(e3, e0) = e1
% 244.05/50.70    (3)   ~ (all_16_1 = e1)
% 244.05/50.70    (4)  op(e3, e0) = all_50_1
% 244.05/50.70    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.70  
% 244.05/50.70  Begin of proof
% 244.05/50.70  | 
% 244.05/50.70  | GROUND_INST: instantiating (5) with e1, all_50_1, e0, e3, simplifying with
% 244.05/50.70  |              (2), (4) gives:
% 244.05/50.70  |   (6)  all_50_1 = e1
% 244.05/50.70  | 
% 244.05/50.70  | GROUND_INST: instantiating (5) with all_16_1, all_50_1, e0, e3, simplifying
% 244.05/50.70  |              with (1), (4) gives:
% 244.05/50.70  |   (7)  all_50_1 = all_16_1
% 244.05/50.70  | 
% 244.05/50.70  | COMBINE_EQS: (6), (7) imply:
% 244.05/50.70  |   (8)  all_16_1 = e1
% 244.05/50.70  | 
% 244.05/50.70  | REDUCE: (3), (8) imply:
% 244.05/50.70  |   (9)  $false
% 244.05/50.70  | 
% 244.05/50.70  | CLOSE: (9) is inconsistent.
% 244.05/50.70  | 
% 244.05/50.70  End of proof
% 244.05/50.70  
% 244.05/50.70  Sub-proof #1571 shows that the following formulas are inconsistent:
% 244.05/50.70  ----------------------------------------------------------------
% 244.05/50.70    (1)   ~ (e3 = e1)
% 244.05/50.70    (2)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 244.05/50.70    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.70    (4)   ~ (e1 = e0)
% 244.05/50.70    (5)  op(e3, e3) = e0
% 244.05/50.70    (6)  op(e3, e2) = e3
% 244.05/50.70  
% 244.05/50.70  Begin of proof
% 244.05/50.70  | 
% 244.05/50.70  | BETA: splitting (2) gives:
% 244.05/50.70  | 
% 244.05/50.70  | Case 1:
% 244.05/50.70  | | 
% 244.05/50.70  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 244.05/50.70  | | 
% 244.05/50.70  | | ALPHA: (7) implies:
% 244.05/50.70  | |   (8)  op(e3, e3) = e1
% 244.05/50.70  | | 
% 244.05/50.70  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1828.
% 244.05/50.70  | | 
% 244.05/50.70  | Case 2:
% 244.05/50.70  | | 
% 244.05/50.70  | |   (9)  all_58_1 = e1 & op(e3, e2) = e1
% 244.05/50.70  | | 
% 244.05/50.70  | | ALPHA: (9) implies:
% 244.05/50.70  | |   (10)  op(e3, e2) = e1
% 244.05/50.70  | | 
% 244.05/50.70  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #2265.
% 244.05/50.70  | | 
% 244.05/50.70  | End of split
% 244.05/50.70  | 
% 244.05/50.70  End of proof
% 244.05/50.70  
% 244.05/50.70  Sub-proof #1572 shows that the following formulas are inconsistent:
% 244.05/50.70  ----------------------------------------------------------------
% 244.05/50.70    (1)   ~ (all_52_3 = e0)
% 244.05/50.70    (2)   ~ (e3 = e0)
% 244.05/50.70    (3)  all_58_6 = e3
% 244.05/50.70    (4)   ~ (e2 = e0)
% 244.05/50.70    (5)  op(e0, e3) = all_52_3
% 244.05/50.70    (6)   ~ (e3 = e1)
% 244.05/50.70    (7)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.05/50.70         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.05/50.70    (8)   ~ (e3 = e2)
% 244.05/50.70    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.05/50.70         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.05/50.70    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.05/50.70          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.05/50.70    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.05/50.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.05/50.70    (12)   ~ (e1 = e0)
% 244.05/50.70    (13)  op(e3, e3) = e3
% 244.05/50.70    (14)   ~ (e2 = e1)
% 244.05/50.70  
% 244.05/50.70  Begin of proof
% 244.05/50.70  | 
% 244.05/50.70  | BETA: splitting (9) gives:
% 244.05/50.70  | 
% 244.05/50.70  | Case 1:
% 244.05/50.70  | | 
% 244.05/50.70  | |   (15)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 244.05/50.70  | |           e0)
% 244.05/50.70  | | 
% 244.22/50.70  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 244.22/50.70  | |            (15) are inconsistent by sub-proof #1573.
% 244.22/50.70  | | 
% 244.22/50.70  | Case 2:
% 244.22/50.70  | | 
% 244.22/50.70  | |   (16)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 244.22/50.70  | |           e0)
% 244.22/50.70  | | 
% 244.22/50.70  | | BETA: splitting (16) gives:
% 244.22/50.70  | | 
% 244.22/50.70  | | Case 1:
% 244.22/50.70  | | | 
% 244.22/50.70  | | |   (17)  all_58_6 = e0 & op(e1, e3) = e0
% 244.22/50.70  | | | 
% 244.22/50.70  | | | REF_CLOSE: (2), (3), (17) are inconsistent by sub-proof #2213.
% 244.22/50.70  | | | 
% 244.22/50.70  | | Case 2:
% 244.22/50.70  | | | 
% 244.22/50.70  | | |   (18)  all_58_12 = e0 & op(e0, e3) = e0
% 244.22/50.70  | | | 
% 244.22/50.70  | | | ALPHA: (18) implies:
% 244.22/50.70  | | |   (19)  op(e0, e3) = e0
% 244.22/50.70  | | | 
% 244.22/50.70  | | | REF_CLOSE: (1), (5), (11), (19) are inconsistent by sub-proof #2331.
% 244.22/50.70  | | | 
% 244.22/50.70  | | End of split
% 244.22/50.70  | | 
% 244.22/50.70  | End of split
% 244.22/50.70  | 
% 244.22/50.70  End of proof
% 244.22/50.70  
% 244.22/50.70  Sub-proof #1573 shows that the following formulas are inconsistent:
% 244.22/50.70  ----------------------------------------------------------------
% 244.22/50.70    (1)   ~ (e3 = e0)
% 244.22/50.70    (2)  all_58_6 = e3
% 244.22/50.70    (3)   ~ (e2 = e0)
% 244.22/50.70    (4)   ~ (e3 = e1)
% 244.22/50.70    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.22/50.70         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.22/50.70    (6)   ~ (e3 = e2)
% 244.22/50.70    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.22/50.70         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.22/50.70    (8)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.22/50.70         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.22/50.70    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.70    (10)   ~ (e1 = e0)
% 244.22/50.70    (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 244.22/50.70    (12)  op(e3, e3) = e3
% 244.22/50.70    (13)   ~ (e2 = e1)
% 244.22/50.70  
% 244.22/50.70  Begin of proof
% 244.22/50.70  | 
% 244.22/50.70  | BETA: splitting (11) gives:
% 244.22/50.70  | 
% 244.22/50.70  | Case 1:
% 244.22/50.70  | | 
% 244.22/50.70  | |   (14)  all_58_0 = e0 & op(e3, e3) = e0
% 244.22/50.70  | | 
% 244.22/50.70  | | ALPHA: (14) implies:
% 244.22/50.70  | |   (15)  op(e3, e3) = e0
% 244.22/50.70  | | 
% 244.22/50.70  | | REF_CLOSE: (1), (9), (12), (15) are inconsistent by sub-proof #1940.
% 244.22/50.70  | | 
% 244.22/50.70  | Case 2:
% 244.22/50.70  | | 
% 244.22/50.70  | |   (16)  all_58_2 = e0 & op(e2, e3) = e0
% 244.22/50.70  | | 
% 244.22/50.70  | | ALPHA: (16) implies:
% 244.22/50.70  | |   (17)  all_58_2 = e0
% 244.22/50.70  | | 
% 244.22/50.70  | | BETA: splitting (8) gives:
% 244.22/50.70  | | 
% 244.22/50.70  | | Case 1:
% 244.22/50.70  | | | 
% 244.22/50.70  | | |   (18)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 244.22/50.70  | | |           e1)
% 244.22/50.70  | | | 
% 244.22/50.70  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (18)
% 244.22/50.70  | | |            are inconsistent by sub-proof #1576.
% 244.22/50.70  | | | 
% 244.22/50.70  | | Case 2:
% 244.22/50.70  | | | 
% 244.22/50.70  | | |   (19)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 244.22/50.70  | | |           e1)
% 244.22/50.70  | | | 
% 244.22/50.70  | | | BETA: splitting (19) gives:
% 244.22/50.70  | | | 
% 244.22/50.70  | | | Case 1:
% 244.22/50.70  | | | | 
% 244.22/50.70  | | | |   (20)  all_58_6 = e1 & op(e1, e3) = e1
% 244.22/50.70  | | | | 
% 244.22/50.70  | | | | ALPHA: (20) implies:
% 244.22/50.70  | | | |   (21)  all_58_6 = e1
% 244.22/50.70  | | | | 
% 244.22/50.70  | | | | REF_CLOSE: (2), (4), (21) are inconsistent by sub-proof #1758.
% 244.22/50.70  | | | | 
% 244.22/50.70  | | | Case 2:
% 244.22/50.70  | | | | 
% 244.22/50.70  | | | |   (22)  all_58_12 = e1 & op(e0, e3) = e1
% 244.22/50.70  | | | | 
% 244.22/50.70  | | | | ALPHA: (22) implies:
% 244.22/50.70  | | | |   (23)  all_58_12 = e1
% 244.22/50.70  | | | | 
% 244.22/50.70  | | | | BETA: splitting (5) gives:
% 244.22/50.70  | | | | 
% 244.22/50.70  | | | | Case 1:
% 244.22/50.70  | | | | | 
% 244.22/50.70  | | | | |   (24)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2,
% 244.22/50.70  | | | | |             e3) = e2)
% 244.22/50.70  | | | | | 
% 244.22/50.70  | | | | | BETA: splitting (24) gives:
% 244.22/50.70  | | | | | 
% 244.22/50.70  | | | | | Case 1:
% 244.22/50.70  | | | | | | 
% 244.22/50.70  | | | | | |   (25)  all_58_0 = e2 & op(e3, e3) = e2
% 244.22/50.70  | | | | | | 
% 244.22/50.70  | | | | | | ALPHA: (25) implies:
% 244.22/50.70  | | | | | |   (26)  op(e3, e3) = e2
% 244.22/50.70  | | | | | | 
% 244.22/50.70  | | | | | | REF_CLOSE: (6), (9), (12), (26) are inconsistent by sub-proof #2194.
% 244.22/50.70  | | | | | | 
% 244.22/50.70  | | | | | Case 2:
% 244.22/50.70  | | | | | | 
% 244.22/50.70  | | | | | |   (27)  all_58_2 = e2 & op(e2, e3) = e2
% 244.22/50.70  | | | | | | 
% 244.22/50.70  | | | | | | REF_CLOSE: (3), (17), (27) are inconsistent by sub-proof #1575.
% 244.22/50.70  | | | | | | 
% 244.22/50.70  | | | | | End of split
% 244.22/50.70  | | | | | 
% 244.22/50.70  | | | | Case 2:
% 244.22/50.70  | | | | | 
% 244.22/50.71  | | | | |   (28)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0,
% 244.22/50.71  | | | | |             e3) = e2)
% 244.22/50.71  | | | | | 
% 244.22/50.71  | | | | | REF_CLOSE: (2), (6), (13), (23), (28) are inconsistent by sub-proof
% 244.22/50.71  | | | | |            #1574.
% 244.22/50.71  | | | | | 
% 244.22/50.71  | | | | End of split
% 244.22/50.71  | | | | 
% 244.22/50.71  | | | End of split
% 244.22/50.71  | | | 
% 244.22/50.71  | | End of split
% 244.22/50.71  | | 
% 244.22/50.71  | End of split
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1574 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)  all_58_6 = e3
% 244.22/50.71    (2)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.22/50.71    (3)  all_58_12 = e1
% 244.22/50.71    (4)   ~ (e3 = e2)
% 244.22/50.71    (5)   ~ (e2 = e1)
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | BETA: splitting (2) gives:
% 244.22/50.71  | 
% 244.22/50.71  | Case 1:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (6)  all_58_6 = e2 & op(e1, e3) = e2
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #2219.
% 244.22/50.71  | | 
% 244.22/50.71  | Case 2:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (7)  all_58_12 = e2 & op(e0, e3) = e2
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (7) implies:
% 244.22/50.71  | |   (8)  all_58_12 = e2
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #1757.
% 244.22/50.71  | | 
% 244.22/50.71  | End of split
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1575 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)  all_58_2 = e2 & op(e2, e3) = e2
% 244.22/50.71    (2)  all_58_2 = e0
% 244.22/50.71    (3)   ~ (e2 = e0)
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | ALPHA: (1) implies:
% 244.22/50.71  |   (4)  all_58_2 = e2
% 244.22/50.71  | 
% 244.22/50.71  | COMBINE_EQS: (2), (4) imply:
% 244.22/50.71  |   (5)  e2 = e0
% 244.22/50.71  | 
% 244.22/50.71  | SIMP: (5) implies:
% 244.22/50.71  |   (6)  e2 = e0
% 244.22/50.71  | 
% 244.22/50.71  | REDUCE: (3), (6) imply:
% 244.22/50.71  |   (7)  $false
% 244.22/50.71  | 
% 244.22/50.71  | CLOSE: (7) is inconsistent.
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1576 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)   ~ (e3 = e0)
% 244.22/50.71    (2)  all_58_6 = e3
% 244.22/50.71    (3)   ~ (e2 = e0)
% 244.22/50.71    (4)   ~ (e3 = e1)
% 244.22/50.71    (5)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.22/50.71         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.22/50.71    (6)   ~ (e3 = e2)
% 244.22/50.71    (7)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 244.22/50.71    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.22/50.71         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.22/50.71    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.71    (10)   ~ (e1 = e0)
% 244.22/50.71    (11)  op(e3, e3) = e3
% 244.22/50.71    (12)   ~ (e2 = e1)
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | BETA: splitting (7) gives:
% 244.22/50.71  | 
% 244.22/50.71  | Case 1:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (13)  all_58_0 = e1 & op(e3, e3) = e1
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (13) implies:
% 244.22/50.71  | |   (14)  op(e3, e3) = e1
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (4), (9), (11), (14) are inconsistent by sub-proof #1578.
% 244.22/50.71  | | 
% 244.22/50.71  | Case 2:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (15)  all_58_2 = e1 & op(e2, e3) = e1
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (15) implies:
% 244.22/50.71  | |   (16)  all_58_2 = e1
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (12), (16) are
% 244.22/50.71  | |            inconsistent by sub-proof #1577.
% 244.22/50.71  | | 
% 244.22/50.71  | End of split
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1577 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)   ~ (e3 = e0)
% 244.22/50.71    (2)  all_58_6 = e3
% 244.22/50.71    (3)   ~ (e2 = e0)
% 244.22/50.71    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.22/50.71         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.22/50.71    (5)   ~ (e3 = e2)
% 244.22/50.71    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.22/50.71         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.22/50.71    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.71    (8)   ~ (e1 = e0)
% 244.22/50.71    (9)  op(e3, e3) = e3
% 244.22/50.71    (10)  all_58_2 = e1
% 244.22/50.71    (11)   ~ (e2 = e1)
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | BETA: splitting (6) gives:
% 244.22/50.71  | 
% 244.22/50.71  | Case 1:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 244.22/50.71  | |           e0)
% 244.22/50.71  | | 
% 244.22/50.71  | | BETA: splitting (12) gives:
% 244.22/50.71  | | 
% 244.22/50.71  | | Case 1:
% 244.22/50.71  | | | 
% 244.22/50.71  | | |   (13)  all_58_0 = e0 & op(e3, e3) = e0
% 244.22/50.71  | | | 
% 244.22/50.71  | | | ALPHA: (13) implies:
% 244.22/50.71  | | |   (14)  op(e3, e3) = e0
% 244.22/50.71  | | | 
% 244.22/50.71  | | | REF_CLOSE: (1), (7), (9), (14) are inconsistent by sub-proof #1940.
% 244.22/50.71  | | | 
% 244.22/50.71  | | Case 2:
% 244.22/50.71  | | | 
% 244.22/50.71  | | |   (15)  all_58_2 = e0 & op(e2, e3) = e0
% 244.22/50.71  | | | 
% 244.22/50.71  | | | REF_CLOSE: (8), (10), (15) are inconsistent by sub-proof #1972.
% 244.22/50.71  | | | 
% 244.22/50.71  | | End of split
% 244.22/50.71  | | 
% 244.22/50.71  | Case 2:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (16)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 244.22/50.71  | |           e0)
% 244.22/50.71  | | 
% 244.22/50.71  | | BETA: splitting (16) gives:
% 244.22/50.71  | | 
% 244.22/50.71  | | Case 1:
% 244.22/50.71  | | | 
% 244.22/50.71  | | |   (17)  all_58_6 = e0 & op(e1, e3) = e0
% 244.22/50.71  | | | 
% 244.22/50.71  | | | REF_CLOSE: (1), (2), (17) are inconsistent by sub-proof #2213.
% 244.22/50.71  | | | 
% 244.22/50.71  | | Case 2:
% 244.22/50.71  | | | 
% 244.22/50.71  | | |   (18)  all_58_12 = e0 & op(e0, e3) = e0
% 244.22/50.71  | | | 
% 244.22/50.71  | | | ALPHA: (18) implies:
% 244.22/50.71  | | |   (19)  all_58_12 = e0
% 244.22/50.71  | | | 
% 244.22/50.71  | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (19) are inconsistent
% 244.22/50.71  | | |            by sub-proof #1629.
% 244.22/50.71  | | | 
% 244.22/50.71  | | End of split
% 244.22/50.71  | | 
% 244.22/50.71  | End of split
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1578 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.71    (2)  op(e3, e3) = e3
% 244.22/50.71    (3)  op(e3, e3) = e1
% 244.22/50.71    (4)   ~ (e3 = e1)
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | GROUND_INST: instantiating (1) with e1, e3, e3, e3, simplifying with (2), (3)
% 244.22/50.71  |              gives:
% 244.22/50.71  |   (5)  e3 = e1
% 244.22/50.71  | 
% 244.22/50.71  | REDUCE: (4), (5) imply:
% 244.22/50.71  |   (6)  $false
% 244.22/50.71  | 
% 244.22/50.71  | CLOSE: (6) is inconsistent.
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1579 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)   ~ (all_52_3 = e0)
% 244.22/50.71    (2)   ~ (e3 = e0)
% 244.22/50.71    (3)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 244.22/50.71    (4)  op(e0, e3) = all_52_3
% 244.22/50.71    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.22/50.71         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.22/50.71    (6)   ~ (all_52_1 = e0)
% 244.22/50.71    (7)  op(e2, e3) = all_52_1
% 244.22/50.71    (8)   ~ (all_52_2 = e0)
% 244.22/50.71    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.71    (10)  op(e1, e3) = all_52_2
% 244.22/50.71    (11)   ~ (all_52_1 = e3)
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | BETA: splitting (3) gives:
% 244.22/50.71  | 
% 244.22/50.71  | Case 1:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (12)  all_58_0 = e3 & op(e3, e3) = e3
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (12) implies:
% 244.22/50.71  | |   (13)  op(e3, e3) = e3
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (13) are
% 244.22/50.71  | |            inconsistent by sub-proof #1938.
% 244.22/50.71  | | 
% 244.22/50.71  | Case 2:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (14)  all_58_2 = e3 & op(e2, e3) = e3
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (14) implies:
% 244.22/50.71  | |   (15)  op(e2, e3) = e3
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (7), (9), (11), (15) are inconsistent by sub-proof #2337.
% 244.22/50.71  | | 
% 244.22/50.71  | End of split
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1580 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)   ~ (e3 = e0)
% 244.22/50.71    (2)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.22/50.71    (3)  op(e0, e1) = all_52_11
% 244.22/50.71    (4)   ~ (all_52_11 = e3)
% 244.22/50.71    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.71    (6)  op(e0, e0) = e0
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | BETA: splitting (2) gives:
% 244.22/50.71  | 
% 244.22/50.71  | Case 1:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (7)  all_58_14 = e3 & op(e0, e1) = e3
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1647.
% 244.22/50.71  | | 
% 244.22/50.71  | Case 2:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (8)  all_58_15 = e3 & op(e0, e0) = e3
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (8) implies:
% 244.22/50.71  | |   (9)  op(e0, e0) = e3
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #2079.
% 244.22/50.71  | | 
% 244.22/50.71  | End of split
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1581 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)   ~ (e3 = e1)
% 244.22/50.71    (2)   ~ (e3 = e2)
% 244.22/50.71    (3)  all_56_31 = e0
% 244.22/50.71    (4)  op(e2, e1) = e3
% 244.22/50.71    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.71    (6)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.22/50.71             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.22/50.71           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.22/50.71             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 244.22/50.71           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 244.22/50.71           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.22/50.71           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | BETA: splitting (6) gives:
% 244.22/50.71  | 
% 244.22/50.71  | Case 1:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (7)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.22/50.71  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 244.22/50.71  | |        & op(e1, e2) = e2
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (7) implies:
% 244.22/50.71  | |   (8)  op(e2, e1) = e2
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2256.
% 244.22/50.71  | | 
% 244.22/50.71  | Case 2:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (9)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.22/50.71  | |            = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) =
% 244.22/50.71  | |          e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.22/50.71  | |          (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.22/50.71  | |          (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.22/50.71  | | 
% 244.22/50.71  | | BETA: splitting (9) gives:
% 244.22/50.71  | | 
% 244.22/50.71  | | Case 1:
% 244.22/50.71  | | | 
% 244.22/50.71  | | |   (10)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.22/50.71  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.22/50.71  | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 244.22/50.71  | | | 
% 244.22/50.71  | | | ALPHA: (10) implies:
% 244.22/50.71  | | |   (11)  op(e2, e1) = e1
% 244.22/50.71  | | | 
% 244.22/50.71  | | | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #2255.
% 244.22/50.71  | | | 
% 244.22/50.71  | | Case 2:
% 244.22/50.71  | | | 
% 244.22/50.71  | | |   (12)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.22/50.71  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.22/50.71  | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 244.22/50.71  | | | 
% 244.22/50.71  | | | ALPHA: (12) implies:
% 244.22/50.71  | | |   (13)   ~ (all_56_31 = e0)
% 244.22/50.71  | | | 
% 244.22/50.71  | | | REDUCE: (3), (13) imply:
% 244.22/50.71  | | |   (14)  $false
% 244.22/50.71  | | | 
% 244.22/50.71  | | | CLOSE: (14) is inconsistent.
% 244.22/50.71  | | | 
% 244.22/50.71  | | End of split
% 244.22/50.71  | | 
% 244.22/50.71  | End of split
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1582 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.22/50.71    (2)   ~ (e3 = e2)
% 244.22/50.71    (3)  op(e1, e3) = e1
% 244.22/50.71    (4)  all_58_12 = e3
% 244.22/50.71    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.71    (6)   ~ (e2 = e1)
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | BETA: splitting (1) gives:
% 244.22/50.71  | 
% 244.22/50.71  | Case 1:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (7)  all_58_6 = e2 & op(e1, e3) = e2
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (7) implies:
% 244.22/50.71  | |   (8)  op(e1, e3) = e2
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2226.
% 244.22/50.71  | | 
% 244.22/50.71  | Case 2:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (9)  all_58_12 = e2 & op(e0, e3) = e2
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #1974.
% 244.22/50.71  | | 
% 244.22/50.71  | End of split
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1583 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)   ~ (e3 = e1)
% 244.22/50.71    (2)  op(e1, e0) = e3
% 244.22/50.71    (3)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.22/50.71    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.71    (5)  op(e0, e0) = e0
% 244.22/50.71    (6)   ~ (e1 = e0)
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | BETA: splitting (3) gives:
% 244.22/50.71  | 
% 244.22/50.71  | Case 1:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (7)  all_58_11 = e1 & op(e1, e0) = e1
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (7) implies:
% 244.22/50.71  | |   (8)  op(e1, e0) = e1
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #1894.
% 244.22/50.71  | | 
% 244.22/50.71  | Case 2:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (9)  all_58_15 = e1 & op(e0, e0) = e1
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (9) implies:
% 244.22/50.71  | |   (10)  op(e0, e0) = e1
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #2274.
% 244.22/50.71  | | 
% 244.22/50.71  | End of split
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1584 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)   ~ (all_14_1 = e1)
% 244.22/50.71    (2)  op(e2, e0) = all_14_1
% 244.22/50.71    (3)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) = all_48_1
% 244.22/50.71           & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0) =
% 244.22/50.71           all_48_1 & $i(all_48_1))
% 244.22/50.71    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.71    (5)  op(e2, e0) = e1
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | BETA: splitting (3) gives:
% 244.22/50.71  | 
% 244.22/50.71  | Case 1:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (6)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 244.22/50.71  | |        all_48_1 & $i(all_48_0) & $i(all_48_1)
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (6) implies:
% 244.22/50.71  | |   (7)  op(e2, e0) = all_48_1
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (1), (2), (4), (5), (7) are inconsistent by sub-proof #1585.
% 244.22/50.71  | | 
% 244.22/50.71  | Case 2:
% 244.22/50.71  | | 
% 244.22/50.71  | |   (8)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 & $i(all_48_1)
% 244.22/50.71  | | 
% 244.22/50.71  | | ALPHA: (8) implies:
% 244.22/50.71  | |   (9)  op(e2, e0) = all_48_1
% 244.22/50.71  | | 
% 244.22/50.71  | | REF_CLOSE: (1), (2), (4), (5), (9) are inconsistent by sub-proof #1585.
% 244.22/50.71  | | 
% 244.22/50.71  | End of split
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1585 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)   ~ (all_14_1 = e1)
% 244.22/50.71    (2)  op(e2, e0) = all_14_1
% 244.22/50.71    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.71    (4)  op(e2, e0) = e1
% 244.22/50.71    (5)  op(e2, e0) = all_48_1
% 244.22/50.71  
% 244.22/50.71  Begin of proof
% 244.22/50.71  | 
% 244.22/50.71  | GROUND_INST: instantiating (3) with all_14_1, all_48_1, e0, e2, simplifying
% 244.22/50.71  |              with (2), (5) gives:
% 244.22/50.71  |   (6)  all_48_1 = all_14_1
% 244.22/50.71  | 
% 244.22/50.71  | GROUND_INST: instantiating (3) with e1, all_48_1, e0, e2, simplifying with
% 244.22/50.71  |              (4), (5) gives:
% 244.22/50.71  |   (7)  all_48_1 = e1
% 244.22/50.71  | 
% 244.22/50.71  | COMBINE_EQS: (6), (7) imply:
% 244.22/50.71  |   (8)  all_14_1 = e1
% 244.22/50.71  | 
% 244.22/50.71  | SIMP: (8) implies:
% 244.22/50.71  |   (9)  all_14_1 = e1
% 244.22/50.71  | 
% 244.22/50.71  | REDUCE: (1), (9) imply:
% 244.22/50.71  |   (10)  $false
% 244.22/50.71  | 
% 244.22/50.71  | CLOSE: (10) is inconsistent.
% 244.22/50.71  | 
% 244.22/50.71  End of proof
% 244.22/50.71  
% 244.22/50.71  Sub-proof #1586 shows that the following formulas are inconsistent:
% 244.22/50.71  ----------------------------------------------------------------
% 244.22/50.71    (1)   ~ (e2 = e0)
% 244.22/50.72    (2)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.22/50.72         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.22/50.72    (3)  all_58_7 = e2
% 244.22/50.72    (4)  op(e3, e2) = all_52_4
% 244.22/50.72    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.72    (6)   ~ (e1 = e0)
% 244.22/50.72    (7)  op(e0, e2) = e1
% 244.22/50.72    (8)  op(e2, e2) = e2
% 244.22/50.72    (9)   ~ (all_52_4 = e0)
% 244.22/50.72  
% 244.22/50.72  Begin of proof
% 244.22/50.72  | 
% 244.22/50.72  | BETA: splitting (2) gives:
% 244.22/50.72  | 
% 244.22/50.72  | Case 1:
% 244.22/50.72  | | 
% 244.22/50.72  | |   (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 244.22/50.72  | |           e0)
% 244.22/50.72  | | 
% 244.22/50.72  | | REF_CLOSE: (1), (4), (5), (8), (9), (10) are inconsistent by sub-proof
% 244.22/50.72  | |            #1967.
% 244.22/50.72  | | 
% 244.22/50.72  | Case 2:
% 244.22/50.72  | | 
% 244.22/50.72  | |   (11)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.22/50.72  | |           e0)
% 244.22/50.72  | | 
% 244.22/50.72  | | BETA: splitting (11) gives:
% 244.22/50.72  | | 
% 244.22/50.72  | | Case 1:
% 244.22/50.72  | | | 
% 244.22/50.72  | | |   (12)  all_58_7 = e0 & op(e1, e2) = e0
% 244.22/50.72  | | | 
% 244.22/50.72  | | | ALPHA: (12) implies:
% 244.22/50.72  | | |   (13)  all_58_7 = e0
% 244.22/50.72  | | | 
% 244.22/50.72  | | | REF_CLOSE: (1), (3), (13) are inconsistent by sub-proof #1587.
% 244.22/50.72  | | | 
% 244.22/50.72  | | Case 2:
% 244.22/50.72  | | | 
% 244.22/50.72  | | |   (14)  all_58_13 = e0 & op(e0, e2) = e0
% 244.22/50.72  | | | 
% 244.22/50.72  | | | ALPHA: (14) implies:
% 244.22/50.72  | | |   (15)  op(e0, e2) = e0
% 244.22/50.72  | | | 
% 244.22/50.72  | | | REF_CLOSE: (5), (6), (7), (15) are inconsistent by sub-proof #1872.
% 244.22/50.72  | | | 
% 244.22/50.72  | | End of split
% 244.22/50.72  | | 
% 244.22/50.72  | End of split
% 244.22/50.72  | 
% 244.22/50.72  End of proof
% 244.22/50.72  
% 244.22/50.72  Sub-proof #1587 shows that the following formulas are inconsistent:
% 244.22/50.72  ----------------------------------------------------------------
% 244.22/50.72    (1)  all_58_7 = e2
% 244.22/50.72    (2)  all_58_7 = e0
% 244.22/50.72    (3)   ~ (e2 = e0)
% 244.22/50.72  
% 244.22/50.72  Begin of proof
% 244.22/50.72  | 
% 244.22/50.72  | COMBINE_EQS: (1), (2) imply:
% 244.22/50.72  |   (4)  e2 = e0
% 244.22/50.72  | 
% 244.22/50.72  | SIMP: (4) implies:
% 244.22/50.72  |   (5)  e2 = e0
% 244.22/50.72  | 
% 244.22/50.72  | REDUCE: (3), (5) imply:
% 244.22/50.72  |   (6)  $false
% 244.22/50.72  | 
% 244.22/50.72  | CLOSE: (6) is inconsistent.
% 244.22/50.72  | 
% 244.22/50.72  End of proof
% 244.22/50.72  
% 244.22/50.72  Sub-proof #1588 shows that the following formulas are inconsistent:
% 244.22/50.72  ----------------------------------------------------------------
% 244.22/50.72    (1)  all_58_1 = e3
% 244.22/50.72    (2)   ~ (e2 = e0)
% 244.22/50.72    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.22/50.72         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.22/50.72    (4)  op(e2, e2) = e0
% 244.22/50.72    (5)   ~ (e3 = e2)
% 244.22/50.72    (6)  all_58_7 = e1
% 244.22/50.72    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.72    (8)  all_58_13 = e1
% 244.22/50.72    (9)   ~ (e2 = e1)
% 244.22/50.72  
% 244.22/50.72  Begin of proof
% 244.22/50.72  | 
% 244.22/50.72  | BETA: splitting (3) gives:
% 244.22/50.72  | 
% 244.22/50.72  | Case 1:
% 244.22/50.72  | | 
% 244.22/50.72  | |   (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 244.22/50.72  | |           e2)
% 244.22/50.72  | | 
% 244.22/50.72  | | REF_CLOSE: (1), (2), (4), (5), (7), (10) are inconsistent by sub-proof
% 244.22/50.72  | |            #1589.
% 244.22/50.72  | | 
% 244.22/50.72  | Case 2:
% 244.22/50.72  | | 
% 244.22/50.72  | |   (11)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 244.22/50.72  | |           e2)
% 244.22/50.72  | | 
% 244.22/50.72  | | BETA: splitting (11) gives:
% 244.22/50.72  | | 
% 244.22/50.72  | | Case 1:
% 244.22/50.72  | | | 
% 244.22/50.72  | | |   (12)  all_58_7 = e2 & op(e1, e2) = e2
% 244.22/50.72  | | | 
% 244.22/50.72  | | | ALPHA: (12) implies:
% 244.22/50.72  | | |   (13)  all_58_7 = e2
% 244.22/50.72  | | | 
% 244.22/50.72  | | | REF_CLOSE: (6), (9), (13) are inconsistent by sub-proof #2134.
% 244.22/50.72  | | | 
% 244.22/50.72  | | Case 2:
% 244.22/50.72  | | | 
% 244.22/50.72  | | |   (14)  all_58_13 = e2 & op(e0, e2) = e2
% 244.22/50.72  | | | 
% 244.22/50.72  | | | REF_CLOSE: (8), (9), (14) are inconsistent by sub-proof #2078.
% 244.22/50.72  | | | 
% 244.22/50.72  | | End of split
% 244.22/50.72  | | 
% 244.22/50.72  | End of split
% 244.22/50.72  | 
% 244.22/50.72  End of proof
% 244.22/50.72  
% 244.22/50.72  Sub-proof #1589 shows that the following formulas are inconsistent:
% 244.22/50.72  ----------------------------------------------------------------
% 244.22/50.72    (1)  all_58_1 = e3
% 244.22/50.72    (2)   ~ (e2 = e0)
% 244.22/50.72    (3)  op(e2, e2) = e0
% 244.22/50.72    (4)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 244.22/50.72    (5)   ~ (e3 = e2)
% 244.22/50.72    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.72  
% 244.22/50.72  Begin of proof
% 244.22/50.72  | 
% 244.22/50.72  | BETA: splitting (4) gives:
% 244.22/50.72  | 
% 244.22/50.72  | Case 1:
% 244.22/50.72  | | 
% 244.22/50.72  | |   (7)  all_58_1 = e2 & op(e3, e2) = e2
% 244.22/50.72  | | 
% 244.22/50.72  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #1590.
% 244.22/50.72  | | 
% 244.22/50.72  | Case 2:
% 244.22/50.72  | | 
% 244.22/50.72  | |   (8)  all_58_3 = e2 & op(e2, e2) = e2
% 244.22/50.72  | | 
% 244.22/50.72  | | ALPHA: (8) implies:
% 244.22/50.72  | |   (9)  op(e2, e2) = e2
% 244.22/50.72  | | 
% 244.22/50.72  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #2137.
% 244.22/50.72  | | 
% 244.22/50.72  | End of split
% 244.22/50.72  | 
% 244.22/50.72  End of proof
% 244.22/50.72  
% 244.22/50.72  Sub-proof #1590 shows that the following formulas are inconsistent:
% 244.22/50.72  ----------------------------------------------------------------
% 244.22/50.72    (1)  all_58_1 = e2 & op(e3, e2) = e2
% 244.22/50.72    (2)  all_58_1 = e3
% 244.22/50.72    (3)   ~ (e3 = e2)
% 244.22/50.72  
% 244.22/50.72  Begin of proof
% 244.22/50.72  | 
% 244.22/50.72  | ALPHA: (1) implies:
% 244.22/50.72  |   (4)  all_58_1 = e2
% 244.22/50.72  | 
% 244.22/50.72  | COMBINE_EQS: (2), (4) imply:
% 244.22/50.72  |   (5)  e3 = e2
% 244.22/50.72  | 
% 244.22/50.72  | REDUCE: (3), (5) imply:
% 244.22/50.72  |   (6)  $false
% 244.22/50.72  | 
% 244.22/50.72  | CLOSE: (6) is inconsistent.
% 244.22/50.72  | 
% 244.22/50.72  End of proof
% 244.22/50.72  
% 244.22/50.72  Sub-proof #1591 shows that the following formulas are inconsistent:
% 244.22/50.72  ----------------------------------------------------------------
% 244.22/50.72    (1)  all_58_3 = e1 & op(e2, e2) = e1
% 244.22/50.72    (2)  all_58_3 = e0
% 244.22/50.72    (3)   ~ (e1 = e0)
% 244.22/50.72  
% 244.22/50.72  Begin of proof
% 244.22/50.72  | 
% 244.22/50.72  | ALPHA: (1) implies:
% 244.22/50.72  |   (4)  all_58_3 = e1
% 244.22/50.72  | 
% 244.22/50.72  | COMBINE_EQS: (2), (4) imply:
% 244.22/50.72  |   (5)  e1 = e0
% 244.22/50.72  | 
% 244.22/50.72  | REDUCE: (3), (5) imply:
% 244.22/50.72  |   (6)  $false
% 244.22/50.72  | 
% 244.22/50.72  | CLOSE: (6) is inconsistent.
% 244.22/50.72  | 
% 244.22/50.72  End of proof
% 244.22/50.72  
% 244.22/50.72  Sub-proof #1592 shows that the following formulas are inconsistent:
% 244.22/50.72  ----------------------------------------------------------------
% 244.22/50.72    (1)  op(e3, e0) = all_52_12
% 244.22/50.72    (2)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.22/50.72    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.72    (4)   ~ (all_52_12 = e3)
% 244.22/50.72    (5)   ~ (all_52_13 = e3)
% 244.22/50.72    (6)  op(e2, e0) = all_52_13
% 244.22/50.72  
% 244.22/50.72  Begin of proof
% 244.22/50.72  | 
% 244.22/50.72  | BETA: splitting (2) gives:
% 244.22/50.72  | 
% 244.22/50.72  | Case 1:
% 244.22/50.72  | | 
% 244.22/50.72  | |   (7)  all_58_9 = e3 & op(e3, e0) = e3
% 244.22/50.72  | | 
% 244.22/50.72  | | ALPHA: (7) implies:
% 244.22/50.72  | |   (8)  op(e3, e0) = e3
% 244.22/50.72  | | 
% 244.22/50.72  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2179.
% 244.22/50.72  | | 
% 244.22/50.72  | Case 2:
% 244.22/50.72  | | 
% 244.22/50.72  | |   (9)  all_58_10 = e3 & op(e2, e0) = e3
% 244.22/50.72  | | 
% 244.22/50.72  | | ALPHA: (9) implies:
% 244.22/50.72  | |   (10)  op(e2, e0) = e3
% 244.22/50.72  | | 
% 244.22/50.72  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1994.
% 244.22/50.72  | | 
% 244.22/50.72  | End of split
% 244.22/50.72  | 
% 244.22/50.72  End of proof
% 244.22/50.72  
% 244.22/50.72  Sub-proof #1593 shows that the following formulas are inconsistent:
% 244.22/50.72  ----------------------------------------------------------------
% 244.22/50.72    (1)  op(e0, e0) = e1
% 244.22/50.72    (2)   ~ (all_52_3 = e0)
% 244.22/50.72    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.22/50.72         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.22/50.72    (4)   ~ (all_52_9 = all_6_2)
% 244.22/50.72    (5)   ~ (e3 = e0)
% 244.22/50.72    (6)  op(e1, e0) = e0
% 244.22/50.72    (7)   ~ (all_52_8 = all_52_9)
% 244.22/50.72    (8)   ~ (e2 = e0)
% 244.22/50.72    (9)   ~ (all_52_8 = all_6_2)
% 244.22/50.72    (10)  op(e1, e2) = all_52_6
% 244.22/50.72    (11)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.22/50.72          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.22/50.72    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.22/50.72              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.22/50.72            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 244.22/50.72            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.22/50.72            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 244.22/50.72             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.22/50.72            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.22/50.72            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.22/50.72            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 244.22/50.72            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.22/50.72            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.22/50.72              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.22/50.72            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.22/50.72            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 244.22/50.72            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.22/50.72            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 244.22/50.72            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.22/50.72            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.22/50.72              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.22/50.72            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.22/50.72            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 244.22/50.72            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.22/50.72            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 244.22/50.72            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.22/50.72            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.22/50.72              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.22/50.72            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.22/50.72            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.22/50.72    (13)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.22/50.72          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.22/50.72    (14)   ~ (all_52_12 = e0)
% 244.22/50.72    (15)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.22/50.72          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.22/50.72    (16)  op(e1, e1) = all_6_2
% 244.22/50.72    (17)   ~ (all_52_13 = e1)
% 244.22/50.72    (18)  op(e0, e3) = all_52_3
% 244.22/50.72    (19)   ~ (all_52_6 = e0)
% 244.22/50.72    (20)   ~ (all_52_12 = e1)
% 244.22/50.72    (21)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.22/50.72          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.22/50.72    (22)  op(e2, e2) = e0
% 244.22/50.72    (23)  all_54_6 = all_52_9
% 244.22/50.72    (24)   ~ (all_52_12 = all_52_13)
% 244.22/50.72    (25)  all_54_10 = all_6_2
% 244.22/50.72    (26)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 244.22/50.72          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 244.22/50.72    (27)   ~ (all_52_9 = e0)
% 244.22/50.72    (28)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.22/50.72    (29)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.22/50.72              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 244.22/50.72                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.22/50.72                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.22/50.72    (30)   ~ (all_6_2 = e3)
% 244.22/50.72    (31)   ~ (all_52_8 = all_52_12)
% 244.22/50.72    (32)  op(e3, e1) = all_52_8
% 244.22/50.72    (33)  op(e2, e1) = all_52_9
% 244.22/50.72    (34)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.22/50.72          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.22/50.72    (35)   ~ (e3 = e2)
% 244.22/50.72    (36)   ~ (all_52_7 = e1)
% 244.22/50.72    (37)   ~ (all_6_2 = e0)
% 244.22/50.72    (38)  all_56_31 = e1
% 244.22/50.72    (39)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.22/50.72    (40)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.22/50.72          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.22/50.72    (41)  all_58_15 = e1
% 244.22/50.72    (42)  op(e3, e0) = all_52_12
% 244.22/50.72    (43)  op(e0, e1) = e0
% 244.22/50.72    (44)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.22/50.72          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.22/50.72    (45)   ~ (all_52_9 = all_52_13)
% 244.22/50.72    (46)   ~ (all_52_1 = e0)
% 244.22/50.72    (47)  all_56_11 = e0
% 244.22/50.72    (48)   ~ (all_52_4 = all_52_12)
% 244.22/50.72    (49)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.22/50.72    (50)  op(e2, e3) = all_52_1
% 244.22/50.72    (51)  all_36_2 = all_6_2
% 244.22/50.72    (52)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.22/50.72    (53)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 &
% 244.22/50.72            op(e1, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 244.22/50.72              e0) & op(e1, e2) = all_36_1 & $i(all_36_1))
% 244.22/50.72    (54)   ~ (all_52_1 = all_52_13)
% 244.22/50.72    (55)   ~ (all_52_2 = e0)
% 244.22/50.72    (56)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.22/50.72          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.22/50.72    (57)  all_54_7 = all_52_13
% 244.22/50.72    (58)  op(e0, e2) = all_52_7
% 244.22/50.72    (59)  op(e3, e2) = all_52_4
% 244.22/50.72    (60)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.22/50.72          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.22/50.72    (61)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.22/50.72          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.22/50.72    (62)  all_54_3 = all_52_12
% 244.22/50.72    (63)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.72    (64)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.22/50.72          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.22/50.72    (65)  op(e1, e3) = all_52_2
% 244.22/50.72    (66)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.22/50.72          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.22/50.72    (67)  all_58_11 = e0
% 244.22/50.72    (68)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.22/50.72          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.22/50.72    (69)   ~ (e1 = e0)
% 244.22/50.72    (70)  all_56_21 = all_6_2
% 244.22/50.72    (71)  op(e3, e3) = e0
% 244.22/50.72    (72)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.22/50.72          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.22/50.72    (73)  op(e2, e0) = all_52_13
% 244.22/50.72    (74)  all_58_3 = e0
% 244.22/50.72    (75)   ~ (all_52_4 = all_52_8)
% 244.22/50.72    (76)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.22/50.72          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.22/50.72    (77)   ~ (all_52_13 = e0)
% 244.22/50.72    (78)   ~ (all_52_4 = e0)
% 244.22/50.72    (79)   ~ (e2 = e1)
% 244.22/50.72  
% 244.22/50.72  Begin of proof
% 244.22/50.72  | 
% 244.22/50.72  | BETA: splitting (53) gives:
% 244.22/50.72  | 
% 244.22/50.72  | Case 1:
% 244.22/50.72  | | 
% 244.22/50.72  | |   (80)   ~ (all_36_2 = e2)
% 244.22/50.73  | | 
% 244.22/50.73  | | REDUCE: (51), (80) imply:
% 244.22/50.73  | |   (81)   ~ (all_6_2 = e2)
% 244.22/50.73  | | 
% 244.22/50.73  | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (18), (20),
% 244.22/50.73  | |            (22), (25), (30), (32), (33), (35), (36), (37), (38), (42), (47),
% 244.22/50.73  | |            (52), (58), (59), (61), (63), (66), (68), (71), (73), (74), (75),
% 244.22/50.73  | |            (77), (78), (81) are inconsistent by sub-proof #1611.
% 244.22/50.73  | | 
% 244.22/50.73  | Case 2:
% 244.22/50.73  | | 
% 244.22/50.73  | |   (82)  all_36_2 = e2
% 244.22/50.73  | | 
% 244.22/50.73  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (10), (11), (12), (13), (14), (15),
% 244.22/50.73  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (26), (27),
% 244.22/50.73  | |            (28), (29), (30), (31), (32), (33), (34), (36), (38), (39), (40),
% 244.22/50.73  | |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 244.22/50.73  | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 244.22/50.73  | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74), (76),
% 244.22/50.73  | |            (77), (79), (82) are inconsistent by sub-proof #1594.
% 244.22/50.73  | | 
% 244.22/50.73  | End of split
% 244.22/50.73  | 
% 244.22/50.73  End of proof
% 244.22/50.73  
% 244.22/50.73  Sub-proof #1594 shows that the following formulas are inconsistent:
% 244.22/50.73  ----------------------------------------------------------------
% 244.22/50.73    (1)  op(e0, e0) = e1
% 244.22/50.73    (2)   ~ (all_52_3 = e0)
% 244.22/50.73    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.22/50.73         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.22/50.73    (4)   ~ (all_52_9 = all_6_2)
% 244.22/50.73    (5)  op(e1, e0) = e0
% 244.22/50.73    (6)   ~ (all_52_8 = all_52_9)
% 244.22/50.73    (7)  op(e1, e2) = all_52_6
% 244.22/50.73    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.22/50.73         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.22/50.73    (9)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.22/50.73           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.22/50.73             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.22/50.73           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.22/50.73             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.22/50.73           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.22/50.73           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.22/50.73           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.22/50.73           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.22/50.73           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.22/50.73           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.22/50.73             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.22/50.73           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.22/50.73           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 244.22/50.73           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.22/50.73           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.22/50.73           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.22/50.73           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.22/50.73             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.22/50.73           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.22/50.73           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.22/50.73           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.22/50.73           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.22/50.73           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.22/50.73           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.22/50.73             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.22/50.73           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.22/50.73           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.22/50.73    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.22/50.73          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.22/50.73    (11)   ~ (all_52_12 = e0)
% 244.22/50.73    (12)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.22/50.73          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.22/50.73    (13)  op(e1, e1) = all_6_2
% 244.22/50.73    (14)   ~ (all_52_13 = e1)
% 244.22/50.73    (15)  op(e0, e3) = all_52_3
% 244.22/50.73    (16)   ~ (all_52_6 = e0)
% 244.22/50.73    (17)   ~ (all_52_12 = e1)
% 244.22/50.73    (18)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.22/50.73          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.22/50.73    (19)  op(e2, e2) = e0
% 244.22/50.73    (20)  all_54_6 = all_52_9
% 244.22/50.73    (21)   ~ (all_52_12 = all_52_13)
% 244.22/50.73    (22)  all_36_2 = e2
% 244.22/50.73    (23)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 244.22/50.73          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 244.22/50.73    (24)   ~ (all_52_9 = e0)
% 244.22/50.73    (25)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.22/50.73    (26)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.22/50.73              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 244.22/50.73                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.22/50.73                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.22/50.73    (27)   ~ (all_6_2 = e3)
% 244.22/50.73    (28)   ~ (all_52_8 = all_52_12)
% 244.22/50.73    (29)  op(e3, e1) = all_52_8
% 244.22/50.73    (30)  op(e2, e1) = all_52_9
% 244.22/50.73    (31)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.22/50.73          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.22/50.73    (32)   ~ (all_52_7 = e1)
% 244.22/50.73    (33)  all_56_31 = e1
% 244.22/50.73    (34)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.22/50.73    (35)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.22/50.73          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.22/50.73    (36)  all_58_15 = e1
% 244.22/50.73    (37)  op(e3, e0) = all_52_12
% 244.22/50.73    (38)  op(e0, e1) = e0
% 244.22/50.73    (39)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.22/50.73          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.22/50.73    (40)   ~ (all_52_9 = all_52_13)
% 244.22/50.73    (41)   ~ (all_52_1 = e0)
% 244.22/50.73    (42)  all_56_11 = e0
% 244.22/50.73    (43)   ~ (all_52_4 = all_52_12)
% 244.22/50.73    (44)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.22/50.73    (45)  op(e2, e3) = all_52_1
% 244.22/50.73    (46)  all_36_2 = all_6_2
% 244.22/50.73    (47)   ~ (all_52_1 = all_52_13)
% 244.22/50.73    (48)   ~ (all_52_2 = e0)
% 244.22/50.73    (49)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.22/50.73          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.22/50.73    (50)  all_54_7 = all_52_13
% 244.22/50.73    (51)  op(e0, e2) = all_52_7
% 244.22/50.73    (52)  op(e3, e2) = all_52_4
% 244.22/50.73    (53)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.22/50.73          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.22/50.73    (54)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.22/50.73          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.22/50.73    (55)  all_54_3 = all_52_12
% 244.22/50.73    (56)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.22/50.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.22/50.73    (57)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.22/50.73          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.22/50.73    (58)  op(e1, e3) = all_52_2
% 244.22/50.73    (59)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.22/50.73          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.22/50.73    (60)  all_58_11 = e0
% 244.22/50.73    (61)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.22/50.73          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.22/50.73    (62)   ~ (e1 = e0)
% 244.22/50.73    (63)  all_56_21 = all_6_2
% 244.22/50.73    (64)  op(e3, e3) = e0
% 244.22/50.73    (65)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.22/50.73          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.22/50.73    (66)  op(e2, e0) = all_52_13
% 244.22/50.73    (67)  all_58_3 = e0
% 244.22/50.73    (68)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.22/50.73          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.22/50.73    (69)   ~ (all_52_13 = e0)
% 244.22/50.73    (70)   ~ (e2 = e1)
% 244.22/50.73  
% 244.22/50.73  Begin of proof
% 244.22/50.73  | 
% 244.22/50.73  | COMBINE_EQS: (22), (46) imply:
% 244.22/50.73  |   (71)  all_6_2 = e2
% 244.22/50.73  | 
% 244.22/50.73  | SIMP: (71) implies:
% 244.22/50.73  |   (72)  all_6_2 = e2
% 244.22/50.73  | 
% 244.22/50.73  | COMBINE_EQS: (63), (72) imply:
% 244.22/50.73  |   (73)  all_56_21 = e2
% 244.22/50.73  | 
% 244.22/50.73  | REDUCE: (4), (72) imply:
% 244.22/50.73  |   (74)   ~ (all_52_9 = e2)
% 244.22/50.73  | 
% 244.22/50.73  | REDUCE: (27), (72) imply:
% 244.22/50.73  |   (75)   ~ (e3 = e2)
% 244.22/50.73  | 
% 244.22/50.73  | SIMP: (75) implies:
% 244.22/50.73  |   (76)   ~ (e3 = e2)
% 244.22/50.73  | 
% 244.22/50.73  | REDUCE: (13), (72) imply:
% 244.22/50.73  |   (77)  op(e1, e1) = e2
% 244.22/50.73  | 
% 244.22/50.73  | BETA: splitting (34) gives:
% 244.22/50.73  | 
% 244.22/50.73  | Case 1:
% 244.22/50.73  | | 
% 244.22/50.73  | |   (78)  all_54_7 = e3
% 244.22/50.73  | | 
% 244.22/50.73  | | COMBINE_EQS: (50), (78) imply:
% 244.22/50.73  | |   (79)  all_52_13 = e3
% 244.22/50.73  | | 
% 244.22/50.73  | | SIMP: (79) implies:
% 244.22/50.73  | |   (80)  all_52_13 = e3
% 244.22/50.73  | | 
% 244.22/50.73  | | REDUCE: (47), (80) imply:
% 244.22/50.73  | |   (81)   ~ (all_52_1 = e3)
% 244.22/50.73  | | 
% 244.22/50.73  | | REDUCE: (40), (80) imply:
% 244.22/50.73  | |   (82)   ~ (all_52_9 = e3)
% 244.22/50.73  | | 
% 244.22/50.73  | | REDUCE: (21), (80) imply:
% 244.22/50.73  | |   (83)   ~ (all_52_12 = e3)
% 244.22/50.73  | | 
% 244.22/50.73  | | REDUCE: (66), (80) imply:
% 244.22/50.73  | |   (84)  op(e2, e0) = e3
% 244.22/50.73  | | 
% 244.22/50.73  | | BETA: splitting (44) gives:
% 244.22/50.73  | | 
% 244.22/50.73  | | Case 1:
% 244.22/50.73  | | | 
% 244.22/50.73  | | |   (85)  all_54_6 = e3
% 244.22/50.73  | | | 
% 244.22/50.73  | | | REF_CLOSE: (20), (82), (85) are inconsistent by sub-proof #1825.
% 244.22/50.73  | | | 
% 244.22/50.73  | | Case 2:
% 244.22/50.73  | | | 
% 244.22/50.73  | | |   (86)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.22/50.73  | | | 
% 244.22/50.73  | | | BETA: splitting (86) gives:
% 244.22/50.73  | | | 
% 244.22/50.73  | | | Case 1:
% 244.22/50.73  | | | | 
% 244.22/50.73  | | | |   (87)  all_54_6 = e2
% 244.22/50.73  | | | | 
% 244.22/50.73  | | | | REF_CLOSE: (20), (74), (87) are inconsistent by sub-proof #2247.
% 244.22/50.73  | | | | 
% 244.22/50.73  | | | Case 2:
% 244.22/50.73  | | | | 
% 244.22/50.73  | | | |   (88)   ~ (all_54_6 = e2)
% 244.22/50.73  | | | |   (89)  all_54_6 = e1 | all_54_6 = e0
% 244.22/50.73  | | | | 
% 244.22/50.73  | | | | BETA: splitting (54) gives:
% 244.22/50.73  | | | | 
% 244.22/50.73  | | | | Case 1:
% 244.22/50.73  | | | | | 
% 244.22/50.73  | | | | |   (90)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3,
% 244.22/50.73  | | | | |             e2) = e1)
% 244.22/50.73  | | | | | 
% 244.22/50.73  | | | | | BETA: splitting (90) gives:
% 244.22/50.73  | | | | | 
% 244.22/50.73  | | | | | Case 1:
% 244.22/50.73  | | | | | | 
% 244.22/50.73  | | | | | |   (91)  all_58_0 = e1 & op(e3, e3) = e1
% 244.22/50.73  | | | | | | 
% 244.22/50.73  | | | | | | ALPHA: (91) implies:
% 244.22/50.73  | | | | | |   (92)  op(e3, e3) = e1
% 244.22/50.73  | | | | | | 
% 244.22/50.73  | | | | | | REF_CLOSE: (56), (62), (64), (92) are inconsistent by sub-proof
% 244.22/50.73  | | | | | |            #1828.
% 244.22/50.73  | | | | | | 
% 244.22/50.73  | | | | | Case 2:
% 244.22/50.73  | | | | | | 
% 244.22/50.73  | | | | | |   (93)  all_58_1 = e1 & op(e3, e2) = e1
% 244.22/50.73  | | | | | | 
% 244.22/50.73  | | | | | | ALPHA: (93) implies:
% 244.22/50.73  | | | | | |   (94)  op(e3, e2) = e1
% 244.22/50.73  | | | | | | 
% 244.22/50.73  | | | | | | BETA: splitting (9) gives:
% 244.22/50.73  | | | | | | 
% 244.22/50.73  | | | | | | Case 1:
% 244.22/50.73  | | | | | | | 
% 244.22/50.73  | | | | | | |   (95)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.22/50.73  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 244.22/50.73  | | | | | | |             e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 =
% 244.22/50.73  | | | | | | |           e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.22/50.73  | | | | | | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.22/50.73  | | | | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 244.22/50.73  | | | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.22/50.73  | | | | | | |             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.22/50.73  | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1 &
% 244.22/50.73  | | | | | | |           all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.22/50.73  | | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.22/50.73  | | | | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 244.22/50.73  | | | | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.22/50.73  | | | | | | |             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.22/50.73  | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 244.22/50.73  | | | | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.22/50.73  | | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.22/50.73  | | | | | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.22/50.73  | | | | | | | 
% 244.22/50.73  | | | | | | | BETA: splitting (95) gives:
% 244.22/50.73  | | | | | | | 
% 244.22/50.73  | | | | | | | Case 1:
% 244.22/50.73  | | | | | | | | 
% 244.22/50.73  | | | | | | | |   (96)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.22/50.73  | | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 244.22/50.73  | | | | | | | |             = e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 244.22/50.73  | | | | | | | |         (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.22/50.73  | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 244.22/50.73  | | | | | | | |             = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 244.22/50.73  | | | | | | | |         (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) & 
% 244.22/50.73  | | | | | | | |           ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.22/50.73  | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.22/50.73  | | | | | | | | 
% 244.22/50.73  | | | | | | | | BETA: splitting (96) gives:
% 244.22/50.73  | | | | | | | | 
% 244.22/50.73  | | | | | | | | Case 1:
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.73  | | | | | | | | |   (97)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 244.22/50.73  | | | | | | | | |         ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.22/50.73  | | | | | | | | |         (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.73  | | | | | | | | | ALPHA: (97) implies:
% 244.22/50.73  | | | | | | | | |   (98)  op(e2, e3) = e3
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.73  | | | | | | | | | REF_CLOSE: (45), (56), (81), (98) are inconsistent by
% 244.22/50.73  | | | | | | | | |            sub-proof #2337.
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.73  | | | | | | | | Case 2:
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.73  | | | | | | | | |   (99)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) & 
% 244.22/50.73  | | | | | | | | |           ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.22/50.73  | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 244.22/50.73  | | | | | | | | |           e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1
% 244.22/50.73  | | | | | | | | |             = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 244.22/50.73  | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.22/50.73  | | | | | | | | |           = e3)
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.73  | | | | | | | | | REF_CLOSE: (33), (56), (70), (94), (99) are inconsistent by
% 244.22/50.73  | | | | | | | | |            sub-proof #1726.
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.73  | | | | | | | | End of split
% 244.22/50.73  | | | | | | | | 
% 244.22/50.73  | | | | | | | Case 2:
% 244.22/50.73  | | | | | | | | 
% 244.22/50.73  | | | | | | | |   (100)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) & 
% 244.22/50.73  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.22/50.73  | | | | | | | |            (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1)
% 244.22/50.73  | | | | | | | |          | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 244.22/50.73  | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.22/50.73  | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3)
% 244.22/50.73  | | | | | | | |          | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 244.22/50.73  | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.22/50.73  | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.22/50.73  | | | | | | | | 
% 244.22/50.73  | | | | | | | | BETA: splitting (100) gives:
% 244.22/50.73  | | | | | | | | 
% 244.22/50.73  | | | | | | | | Case 1:
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.73  | | | | | | | | |   (101)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &
% 244.22/50.73  | | | | | | | | |           ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.22/50.73  | | | | | | | | |          (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.73  | | | | | | | | | ALPHA: (101) implies:
% 244.22/50.73  | | | | | | | | |   (102)  op(e3, e1) = e1
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.73  | | | | | | | | | REF_CLOSE: (6), (20), (24), (29), (56), (89), (102) are
% 244.22/50.73  | | | | | | | | |            inconsistent by sub-proof #1945.
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.73  | | | | | | | | Case 2:
% 244.22/50.73  | | | | | | | | | 
% 244.22/50.74  | | | | | | | | |   (103)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 244.22/50.74  | | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.22/50.74  | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 244.22/50.74  | | | | | | | | |            e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.22/50.74  | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.22/50.74  | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 244.22/50.74  | | | | | | | | |            = e0 & op(e0, e3) = e0)
% 244.22/50.74  | | | | | | | | | 
% 244.22/50.74  | | | | | | | | | REF_CLOSE: (2), (15), (37), (56), (83), (103) are inconsistent
% 244.22/50.74  | | | | | | | | |            by sub-proof #1794.
% 244.22/50.74  | | | | | | | | | 
% 244.22/50.74  | | | | | | | | End of split
% 244.22/50.74  | | | | | | | | 
% 244.22/50.74  | | | | | | | End of split
% 244.22/50.74  | | | | | | | 
% 244.22/50.74  | | | | | | Case 2:
% 244.22/50.74  | | | | | | | 
% 244.22/50.74  | | | | | | |   (104)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) & 
% 244.22/50.74  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.22/50.74  | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 244.22/50.74  | | | | | | |          (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) & 
% 244.22/50.74  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.22/50.74  | | | | | | |            (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 244.22/50.74  | | | | | | |          (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) & 
% 244.22/50.74  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.22/50.74  | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 244.31/50.74  | | | | | | |          (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) & 
% 244.31/50.74  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.31/50.74  | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 244.31/50.74  | | | | | | |          (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) & 
% 244.31/50.74  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.31/50.74  | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 244.31/50.74  | | | | | | |          (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) & 
% 244.31/50.74  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.31/50.74  | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.31/50.74  | | | | | | | 
% 244.31/50.74  | | | | | | | BETA: splitting (104) gives:
% 244.31/50.74  | | | | | | | 
% 244.31/50.74  | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | 
% 244.31/50.74  | | | | | | | |   (105)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &
% 244.31/50.74  | | | | | | | |             ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.31/50.74  | | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2)
% 244.31/50.74  | | | | | | | |          | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2)
% 244.31/50.74  | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.31/50.74  | | | | | | | |            (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1)
% 244.31/50.74  | | | | | | | |          | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0)
% 244.31/50.74  | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.31/50.74  | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.31/50.74  | | | | | | | | 
% 244.31/50.74  | | | | | | | | BETA: splitting (105) gives:
% 244.31/50.74  | | | | | | | | 
% 244.31/50.74  | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | |   (106)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 244.31/50.74  | | | | | | | | |          &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.31/50.74  | | | | | | | | |          (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | ALPHA: (106) implies:
% 244.31/50.74  | | | | | | | | |   (107)  op(e2, e1) = e2
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | REF_CLOSE: (30), (56), (74), (107) are inconsistent by
% 244.31/50.74  | | | | | | | | |            sub-proof #2328.
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | Case 2:
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | |   (108)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2)
% 244.31/50.74  | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.31/50.74  | | | | | | | | |            (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 244.31/50.74  | | | | | | | | |            e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.31/50.74  | | | | | | | | |            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 244.31/50.74  | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0)
% 244.31/50.74  | | | | | | | | |            = e2 & op(e0, e2) = e2)
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | BETA: splitting (108) gives:
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | |   (109)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.31/50.74  | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &
% 244.31/50.74  | | | | | | | | | |           ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2)
% 244.31/50.74  | | | | | | | | | |          = e1
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | ALPHA: (109) implies:
% 244.31/50.74  | | | | | | | | | |   (110)   ~ (all_56_21 = e2)
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | REDUCE: (73), (110) imply:
% 244.31/50.74  | | | | | | | | | |   (111)  $false
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | CLOSE: (111) is inconsistent.
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | Case 2:
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | |   (112)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 244.31/50.74  | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &
% 244.31/50.74  | | | | | | | | | |           ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.31/50.74  | | | | | | | | | |          = e2
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | ALPHA: (112) implies:
% 244.31/50.74  | | | | | | | | | |   (113)  op(e2, e0) = e2
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | REF_CLOSE: (56), (76), (84), (113) are inconsistent by
% 244.31/50.74  | | | | | | | | | |            sub-proof #2152.
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | End of split
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | End of split
% 244.31/50.74  | | | | | | | | 
% 244.31/50.74  | | | | | | | Case 2:
% 244.31/50.74  | | | | | | | | 
% 244.31/50.74  | | | | | | | |   (114)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &
% 244.31/50.74  | | | | | | | |             ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.31/50.74  | | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0)
% 244.31/50.74  | | | | | | | |          | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0)
% 244.31/50.74  | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.31/50.74  | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1)
% 244.31/50.74  | | | | | | | |          | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1)
% 244.31/50.74  | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.31/50.74  | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.31/50.74  | | | | | | | | 
% 244.31/50.74  | | | | | | | | REF_CLOSE: (5), (33), (56), (62), (66), (69), (114) are
% 244.31/50.74  | | | | | | | |            inconsistent by sub-proof #1613.
% 244.31/50.74  | | | | | | | | 
% 244.31/50.74  | | | | | | | End of split
% 244.31/50.74  | | | | | | | 
% 244.31/50.74  | | | | | | End of split
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | End of split
% 244.31/50.74  | | | | | 
% 244.31/50.74  | | | | Case 2:
% 244.31/50.74  | | | | | 
% 244.31/50.74  | | | | |   (115)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3,
% 244.31/50.74  | | | | |              e0) = e1)
% 244.31/50.74  | | | | | 
% 244.31/50.74  | | | | | BETA: splitting (115) gives:
% 244.31/50.74  | | | | | 
% 244.31/50.74  | | | | | Case 1:
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | |   (116)  all_58_4 = e1 & op(e3, e1) = e1
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | | ALPHA: (116) implies:
% 244.31/50.74  | | | | | |   (117)  op(e3, e1) = e1
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | | REF_CLOSE: (6), (20), (24), (29), (56), (89), (117) are inconsistent
% 244.31/50.74  | | | | | |            by sub-proof #1945.
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | Case 2:
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | |   (118)  all_58_9 = e1 & op(e3, e0) = e1
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | | REF_CLOSE: (17), (37), (56), (118) are inconsistent by sub-proof
% 244.31/50.74  | | | | | |            #2278.
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | End of split
% 244.31/50.74  | | | | | 
% 244.31/50.74  | | | | End of split
% 244.31/50.74  | | | | 
% 244.31/50.74  | | | End of split
% 244.31/50.74  | | | 
% 244.31/50.74  | | End of split
% 244.31/50.74  | | 
% 244.31/50.74  | Case 2:
% 244.31/50.74  | | 
% 244.31/50.74  | |   (119)   ~ (all_54_7 = e3)
% 244.31/50.74  | |   (120)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.31/50.74  | | 
% 244.31/50.74  | | REDUCE: (50), (119) imply:
% 244.31/50.74  | |   (121)   ~ (all_52_13 = e3)
% 244.31/50.74  | | 
% 244.31/50.74  | | BETA: splitting (120) gives:
% 244.31/50.74  | | 
% 244.31/50.74  | | Case 1:
% 244.31/50.74  | | | 
% 244.31/50.74  | | |   (122)  all_54_7 = e2
% 244.31/50.74  | | | 
% 244.31/50.74  | | | COMBINE_EQS: (50), (122) imply:
% 244.31/50.74  | | |   (123)  all_52_13 = e2
% 244.31/50.74  | | | 
% 244.31/50.74  | | | SIMP: (123) implies:
% 244.31/50.74  | | |   (124)  all_52_13 = e2
% 244.31/50.74  | | | 
% 244.31/50.74  | | | REDUCE: (47), (124) imply:
% 244.31/50.74  | | |   (125)   ~ (all_52_1 = e2)
% 244.31/50.74  | | | 
% 244.31/50.74  | | | REDUCE: (21), (124) imply:
% 244.31/50.74  | | |   (126)   ~ (all_52_12 = e2)
% 244.31/50.74  | | | 
% 244.31/50.74  | | | REDUCE: (69), (124) imply:
% 244.31/50.74  | | |   (127)   ~ (e2 = e0)
% 244.31/50.74  | | | 
% 244.31/50.74  | | | REDUCE: (66), (124) imply:
% 244.31/50.74  | | |   (128)  op(e2, e0) = e2
% 244.31/50.74  | | | 
% 244.31/50.74  | | | BETA: splitting (25) gives:
% 244.31/50.74  | | | 
% 244.31/50.74  | | | Case 1:
% 244.31/50.74  | | | | 
% 244.31/50.74  | | | |   (129)  all_54_3 = e3
% 244.31/50.74  | | | | 
% 244.31/50.74  | | | | COMBINE_EQS: (55), (129) imply:
% 244.31/50.74  | | | |   (130)  all_52_12 = e3
% 244.31/50.74  | | | | 
% 244.31/50.74  | | | | SIMP: (130) implies:
% 244.31/50.74  | | | |   (131)  all_52_12 = e3
% 244.31/50.74  | | | | 
% 244.31/50.74  | | | | REDUCE: (43), (131) imply:
% 244.31/50.74  | | | |   (132)   ~ (all_52_4 = e3)
% 244.31/50.74  | | | | 
% 244.31/50.74  | | | | REDUCE: (28), (131) imply:
% 244.31/50.74  | | | |   (133)   ~ (all_52_8 = e3)
% 244.31/50.74  | | | | 
% 244.31/50.74  | | | | REDUCE: (17), (131) imply:
% 244.31/50.74  | | | |   (134)   ~ (e3 = e1)
% 244.31/50.74  | | | | 
% 244.31/50.74  | | | | REDUCE: (11), (131) imply:
% 244.31/50.74  | | | |   (135)   ~ (e3 = e0)
% 244.31/50.74  | | | | 
% 244.31/50.74  | | | | REDUCE: (37), (131) imply:
% 244.31/50.74  | | | |   (136)  op(e3, e0) = e3
% 244.31/50.74  | | | | 
% 244.31/50.74  | | | | BETA: splitting (3) gives:
% 244.31/50.74  | | | | 
% 244.31/50.74  | | | | Case 1:
% 244.31/50.74  | | | | | 
% 244.31/50.74  | | | | |   (137)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3,
% 244.31/50.74  | | | | |              e2) = e2)
% 244.31/50.74  | | | | | 
% 244.31/50.74  | | | | | BETA: splitting (137) gives:
% 244.31/50.74  | | | | | 
% 244.31/50.74  | | | | | Case 1:
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | |   (138)  all_58_0 = e2 & op(e3, e3) = e2
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | | ALPHA: (138) implies:
% 244.31/50.74  | | | | | |   (139)  op(e3, e3) = e2
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | | REF_CLOSE: (56), (64), (127), (139) are inconsistent by sub-proof
% 244.31/50.74  | | | | | |            #2188.
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | Case 2:
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | |   (140)  all_58_1 = e2 & op(e3, e2) = e2
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | | ALPHA: (140) implies:
% 244.31/50.74  | | | | | |   (141)  all_58_1 = e2
% 244.31/50.74  | | | | | |   (142)  op(e3, e2) = e2
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | | BETA: splitting (59) gives:
% 244.31/50.74  | | | | | | 
% 244.31/50.74  | | | | | | Case 1:
% 244.31/50.74  | | | | | | | 
% 244.31/50.74  | | | | | | |   (143)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 244.31/50.74  | | | | | | |            op(e2, e2) = e1)
% 244.31/50.74  | | | | | | | 
% 244.31/50.74  | | | | | | | REF_CLOSE: (56), (62), (67), (70), (142), (143) are inconsistent
% 244.31/50.74  | | | | | | |            by sub-proof #1610.
% 244.31/50.74  | | | | | | | 
% 244.31/50.74  | | | | | | Case 2:
% 244.31/50.74  | | | | | | | 
% 244.31/50.74  | | | | | | |   (144)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 244.31/50.74  | | | | | | |            op(e0, e2) = e1)
% 244.31/50.74  | | | | | | | 
% 244.31/50.74  | | | | | | | BETA: splitting (144) gives:
% 244.31/50.74  | | | | | | | 
% 244.31/50.74  | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | 
% 244.31/50.74  | | | | | | | |   (145)  all_58_7 = e1 & op(e1, e2) = e1
% 244.31/50.74  | | | | | | | | 
% 244.31/50.74  | | | | | | | | ALPHA: (145) implies:
% 244.31/50.74  | | | | | | | |   (146)  all_58_7 = e1
% 244.31/50.74  | | | | | | | |   (147)  op(e1, e2) = e1
% 244.31/50.74  | | | | | | | | 
% 244.31/50.74  | | | | | | | | BETA: splitting (54) gives:
% 244.31/50.74  | | | | | | | | 
% 244.31/50.74  | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | |   (148)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 &
% 244.31/50.74  | | | | | | | | |            op(e3, e2) = e1)
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | REF_CLOSE: (7), (8), (10), (19), (56), (61), (62), (64), (70),
% 244.31/50.74  | | | | | | | | |            (76), (127), (134), (135), (146), (147), (148) are
% 244.31/50.74  | | | | | | | | |            inconsistent by sub-proof #1609.
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | Case 2:
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | |   (149)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 &
% 244.31/50.74  | | | | | | | | |            op(e3, e0) = e1)
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | BETA: splitting (149) gives:
% 244.31/50.74  | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | |   (150)  all_58_4 = e1 & op(e3, e1) = e1
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | ALPHA: (150) implies:
% 244.31/50.74  | | | | | | | | | |   (151)  all_58_4 = e1
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | BETA: splitting (49) gives:
% 244.31/50.74  | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | |   (152)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 244.31/50.74  | | | | | | | | | | |            & op(e2, e1) = e3)
% 244.31/50.74  | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | BETA: splitting (152) gives:
% 244.31/50.74  | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | |   (153)  all_58_4 = e3 & op(e3, e1) = e3
% 244.31/50.74  | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | ALPHA: (153) implies:
% 244.31/50.74  | | | | | | | | | | | |   (154)  op(e3, e1) = e3
% 244.31/50.74  | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | REF_CLOSE: (29), (56), (133), (154) are inconsistent by
% 244.31/50.74  | | | | | | | | | | | |            sub-proof #2260.
% 244.31/50.74  | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | Case 2:
% 244.31/50.74  | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | |   (155)  all_58_5 = e3 & op(e2, e1) = e3
% 244.31/50.74  | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | ALPHA: (155) implies:
% 244.31/50.74  | | | | | | | | | | | |   (156)  op(e2, e1) = e3
% 244.31/50.74  | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | BETA: splitting (9) gives:
% 244.31/50.74  | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | |   (157)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 244.31/50.74  | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.31/50.74  | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.31/50.74  | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.31/50.74  | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.31/50.74  | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.31/50.74  | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 244.31/50.74  | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.31/50.74  | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.31/50.74  | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.31/50.74  | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 244.31/50.74  | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.31/50.74  | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.31/50.74  | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 244.31/50.74  | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.31/50.74  | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.31/50.74  | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 244.31/50.74  | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.31/50.74  | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.31/50.74  | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.31/50.74  | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 244.31/50.74  | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | BETA: splitting (157) gives:
% 244.31/50.74  | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | |   (158)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 244.31/50.74  | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.31/50.74  | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.31/50.74  | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.31/50.74  | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.31/50.74  | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.31/50.74  | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 244.31/50.74  | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.31/50.74  | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.31/50.74  | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.31/50.74  | | | | | | | | | | | | | |            = e3)
% 244.31/50.74  | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 244.31/50.74  | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | |   (159)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 244.31/50.74  | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.31/50.74  | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 244.31/50.74  | | | | | | | | | | | | | | |          e3
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 244.31/50.74  | | | | | | | | | | | | | | |   (160)  op(e3, e2) = e3
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | REF_CLOSE: (52), (56), (132), (160) are inconsistent by
% 244.31/50.74  | | | | | | | | | | | | | | |            sub-proof #2192.
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | Case 2:
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | |   (161)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 244.31/50.74  | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.31/50.74  | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.31/50.74  | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 244.31/50.74  | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 244.31/50.74  | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.31/50.74  | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | REF_CLOSE: (29), (45), (56), (125), (133), (161) are
% 244.31/50.74  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1608.
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | End of split
% 244.31/50.74  | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | Case 2:
% 244.31/50.74  | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | |   (162)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 244.31/50.74  | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.31/50.74  | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.31/50.74  | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 244.31/50.74  | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.31/50.74  | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.31/50.74  | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 244.31/50.74  | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.31/50.74  | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.31/50.74  | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 244.31/50.74  | | | | | | | | | | | | | |            = e0)
% 244.31/50.74  | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 244.31/50.74  | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | |   (163)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 244.31/50.74  | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 244.31/50.74  | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 244.31/50.74  | | | | | | | | | | | | | | |            e3) = e1
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 244.31/50.74  | | | | | | | | | | | | | | |   (164)   ~ (all_56_31 = e3)
% 244.31/50.74  | | | | | | | | | | | | | | |   (165)   ~ (all_56_21 = e3)
% 244.31/50.74  | | | | | | | | | | | | | | |   (166)   ~ (all_56_11 = e3)
% 244.31/50.74  | | | | | | | | | | | | | | |   (167)  op(e1, e3) = e1
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | REDUCE: (42), (166) imply:
% 244.31/50.74  | | | | | | | | | | | | | | |   (168)   ~ (e3 = e0)
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | REDUCE: (33), (164) imply:
% 244.31/50.74  | | | | | | | | | | | | | | |   (169)   ~ (e3 = e1)
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 244.31/50.74  | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | |   (170)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 244.31/50.74  | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 244.31/50.74  | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 244.31/50.74  | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | |   (171)  all_58_9 = e3 & op(e3, e0) = e3
% 244.31/50.74  | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 244.31/50.74  | | | | | | | | | | | | | | | | |   (172)  all_58_9 = e3
% 244.31/50.74  | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 244.31/50.74  | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | |   (173)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 244.31/50.74  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 244.31/50.74  | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | |   (174)  all_58_2 = e1 & op(e2, e3) = e1
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | |   (175)  all_58_2 = e1
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | |   (176)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (56), (64), (125), (127), (176) are
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1607.
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | Case 2:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | |   (177)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | |   (178)  all_58_6 = e2 & op(e1, e3) = e2
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | |   (179)  all_58_6 = e2
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16), (39), (56), (65), (76), (77), (127),
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | |            (134), (135), (146), (179) are inconsistent by
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1676.
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | |   (180)  all_58_12 = e2 & op(e0, e3) = e2
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | |   (181)  all_58_12 = e2
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.31/50.74  | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | |   (182)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |   (183)  all_58_0 = e3 & op(e3, e3) = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |   (184)  op(e3, e3) = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (35), (41), (45), (48), (56), (58),
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |            (135), (184) are inconsistent by sub-proof #1938.
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |   (185)  all_58_2 = e3 & op(e2, e3) = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_58_2 = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (186) imply:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |   (187)  e3 = e1
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (187) imply:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_58_9 = e1
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (26), (53), (56), (57), (62), (66), (70),
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |            (76), (121), (127), (134), (135), (188) are
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1600.
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | |   (189)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |   (190)  all_58_6 = e3 & op(e1, e3) = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |   (191)  op(e1, e3) = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (134), (167), (191) are inconsistent by
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2225.
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |   (192)  all_58_12 = e3 & op(e0, e3) = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (181), (192) are inconsistent by sub-proof
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | |            #2085.
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |   (193)  all_58_3 = e1 & op(e2, e2) = e1
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |   (194)  all_58_3 = e1
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (194) imply:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |   (195)  e1 = e0
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (195) imply:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |   (196)  all_58_4 = e0
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (56), (62), (64), (70), (134), (141), (172),
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |            (196) are inconsistent by sub-proof #1708.
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | |   (197)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 244.31/50.75  | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 244.31/50.75  | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | Case 1:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |   (198)  all_58_5 = e1 & op(e2, e1) = e1
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | ALPHA: (198) implies:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |   (199)  op(e2, e1) = e1
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (134), (156), (199) are inconsistent by
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |            sub-proof #2255.
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |   (200)  all_58_10 = e1 & op(e2, e0) = e1
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |   (201)  all_58_10 = e1
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (53), (56), (57), (60), (70), (76), (127),
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |            (134), (135), (201) are inconsistent by sub-proof
% 244.31/50.75  | | | | | | | | | | | | | | | | | | |            #1597.
% 244.31/50.75  | | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | |   (202)  all_58_10 = e3 & op(e2, e0) = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 244.31/50.75  | | | | | | | | | | | | | | | | |   (203)  op(e2, e0) = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (76), (128), (203) are inconsistent by
% 244.31/50.75  | | | | | | | | | | | | | | | | |            sub-proof #2152.
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | |   (204)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 244.31/50.75  | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 244.31/50.75  | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 244.31/50.75  | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | Case 1:
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | |   (205)  all_58_11 = e3 & op(e1, e0) = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 244.31/50.75  | | | | | | | | | | | | | | | | |   (206)  all_58_11 = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (135), (206) are inconsistent by sub-proof
% 244.31/50.75  | | | | | | | | | | | | | | | | |            #1688.
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | |   (207)  all_58_15 = e3 & op(e0, e0) = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 244.31/50.75  | | | | | | | | | | | | | | | | |   (208)  all_58_15 = e3
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (134), (208) are inconsistent by sub-proof
% 244.31/50.75  | | | | | | | | | | | | | | | | |            #2249.
% 244.31/50.75  | | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | |   (209)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 244.31/50.75  | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.31/50.75  | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.31/50.75  | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 244.31/50.75  | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.31/50.75  | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.31/50.75  | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.31/50.75  | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (42), (56), (209) are inconsistent by
% 244.31/50.75  | | | | | | | | | | | | | | |            sub-proof #1617.
% 244.31/50.75  | | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | |   (210)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.31/50.75  | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.31/50.75  | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.31/50.75  | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.31/50.75  | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 244.31/50.75  | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.31/50.75  | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 244.31/50.75  | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.31/50.75  | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.31/50.75  | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.31/50.75  | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 244.31/50.75  | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.31/50.75  | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.31/50.75  | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 244.31/50.75  | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.31/50.75  | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.31/50.75  | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 244.31/50.75  | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.31/50.75  | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.31/50.75  | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 244.31/50.75  | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 244.31/50.75  | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | BETA: splitting (210) gives:
% 244.31/50.75  | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | Case 1:
% 244.31/50.75  | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | |   (211)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.31/50.75  | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.31/50.75  | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.31/50.75  | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.31/50.75  | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 244.31/50.75  | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.31/50.75  | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 244.31/50.75  | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.31/50.75  | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.31/50.75  | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.31/50.75  | | | | | | | | | | | | | |            = e2)
% 244.31/50.75  | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | REF_CLOSE: (42), (56), (76), (134), (156), (211) are
% 244.31/50.75  | | | | | | | | | | | | | |            inconsistent by sub-proof #1683.
% 244.31/50.75  | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | |   (212)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 244.31/50.75  | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.31/50.75  | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.31/50.75  | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 244.31/50.75  | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.31/50.75  | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.31/50.75  | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 244.31/50.75  | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 244.31/50.75  | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.31/50.75  | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 244.31/50.75  | | | | | | | | | | | | | |            = e0)
% 244.31/50.75  | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | | REF_CLOSE: (5), (33), (56), (62), (127), (128), (212) are
% 244.31/50.75  | | | | | | | | | | | | | |            inconsistent by sub-proof #1596.
% 244.31/50.75  | | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | |   (213)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 244.31/50.75  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 244.31/50.75  | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | | REF_CLOSE: (38), (56), (76), (77), (135), (213) are
% 244.31/50.75  | | | | | | | | | | |            inconsistent by sub-proof #1595.
% 244.31/50.75  | | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | |   (214)  all_58_9 = e1 & op(e3, e0) = e1
% 244.31/50.75  | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | ALPHA: (214) implies:
% 244.31/50.75  | | | | | | | | | |   (215)  all_58_9 = e1
% 244.31/50.75  | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | | REF_CLOSE: (1), (26), (53), (56), (57), (62), (66), (70),
% 244.31/50.75  | | | | | | | | | |            (76), (121), (127), (134), (135), (215) are
% 244.31/50.75  | | | | | | | | | |            inconsistent by sub-proof #1600.
% 244.31/50.75  | | | | | | | | | | 
% 244.31/50.75  | | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | | 
% 244.31/50.75  | | | | | | | | End of split
% 244.31/50.75  | | | | | | | | 
% 244.31/50.75  | | | | | | | Case 2:
% 244.31/50.75  | | | | | | | | 
% 244.31/50.75  | | | | | | | |   (216)  all_58_13 = e1 & op(e0, e2) = e1
% 244.31/50.75  | | | | | | | | 
% 244.31/50.75  | | | | | | | | REF_CLOSE: (32), (51), (56), (216) are inconsistent by sub-proof
% 244.31/50.75  | | | | | | | |            #2275.
% 244.31/50.75  | | | | | | | | 
% 244.31/50.75  | | | | | | | End of split
% 244.31/50.75  | | | | | | | 
% 244.31/50.75  | | | | | | End of split
% 244.31/50.75  | | | | | | 
% 244.31/50.75  | | | | | End of split
% 244.31/50.75  | | | | | 
% 244.31/50.75  | | | | Case 2:
% 244.31/50.75  | | | | | 
% 244.31/50.75  | | | | |   (217)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3,
% 244.31/50.75  | | | | |              e0) = e2)
% 244.31/50.75  | | | | | 
% 244.31/50.75  | | | | | BETA: splitting (217) gives:
% 244.31/50.75  | | | | | 
% 244.31/50.75  | | | | | Case 1:
% 244.31/50.75  | | | | | | 
% 244.31/50.75  | | | | | |   (218)  all_58_4 = e2 & op(e3, e1) = e2
% 244.31/50.75  | | | | | | 
% 244.31/50.75  | | | | | | ALPHA: (218) implies:
% 244.31/50.75  | | | | | |   (219)  all_58_4 = e2
% 244.31/50.75  | | | | | | 
% 244.31/50.75  | | | | | | REF_CLOSE: (12), (18), (30), (38), (49), (56), (62), (70), (76),
% 244.31/50.75  | | | | | |            (77), (127), (134), (135), (219) are inconsistent by
% 244.31/50.75  | | | | | |            sub-proof #2156.
% 244.31/50.75  | | | | | | 
% 244.31/50.75  | | | | | Case 2:
% 244.31/50.75  | | | | | | 
% 244.31/50.75  | | | | | |   (220)  all_58_9 = e2 & op(e3, e0) = e2
% 244.31/50.75  | | | | | | 
% 244.31/50.75  | | | | | | ALPHA: (220) implies:
% 244.31/50.75  | | | | | |   (221)  op(e3, e0) = e2
% 244.31/50.75  | | | | | | 
% 244.31/50.75  | | | | | | REF_CLOSE: (56), (76), (136), (221) are inconsistent by sub-proof
% 244.31/50.75  | | | | | |            #2125.
% 244.31/50.75  | | | | | | 
% 244.31/50.75  | | | | | End of split
% 244.31/50.75  | | | | | 
% 244.31/50.75  | | | | End of split
% 244.31/50.75  | | | | 
% 244.31/50.75  | | | Case 2:
% 244.31/50.75  | | | | 
% 244.31/50.75  | | | |   (222)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.31/50.75  | | | | 
% 244.31/50.75  | | | | REF_CLOSE: (11), (17), (55), (126), (222) are inconsistent by sub-proof
% 244.31/50.75  | | | |            #2286.
% 244.31/50.75  | | | | 
% 244.31/50.75  | | | End of split
% 244.31/50.75  | | | 
% 244.31/50.75  | | Case 2:
% 244.31/50.75  | | | 
% 244.31/50.75  | | |   (223)  all_54_7 = e1 | all_54_7 = e0
% 244.31/50.75  | | | 
% 244.31/50.75  | | | REF_CLOSE: (14), (50), (69), (223) are inconsistent by sub-proof #2293.
% 244.31/50.75  | | | 
% 244.31/50.75  | | End of split
% 244.31/50.75  | | 
% 244.31/50.75  | End of split
% 244.31/50.75  | 
% 244.31/50.75  End of proof
% 244.31/50.75  
% 244.31/50.75  Sub-proof #1595 shows that the following formulas are inconsistent:
% 244.31/50.75  ----------------------------------------------------------------
% 244.31/50.75    (1)   ~ (e3 = e0)
% 244.31/50.75    (2)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.31/50.75    (3)   ~ (e3 = e2)
% 244.31/50.75    (4)  op(e0, e1) = e0
% 244.31/50.75    (5)  op(e1, e1) = e2
% 244.31/50.75    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.75  
% 244.31/50.75  Begin of proof
% 244.31/50.75  | 
% 244.31/50.75  | BETA: splitting (2) gives:
% 244.31/50.75  | 
% 244.31/50.75  | Case 1:
% 244.31/50.75  | | 
% 244.31/50.75  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 244.31/50.75  | | 
% 244.31/50.75  | | ALPHA: (7) implies:
% 244.31/50.75  | |   (8)  op(e1, e1) = e3
% 244.31/50.75  | | 
% 244.31/50.75  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2206.
% 244.31/50.75  | | 
% 244.31/50.75  | Case 2:
% 244.31/50.75  | | 
% 244.31/50.75  | |   (9)  all_58_14 = e3 & op(e0, e1) = e3
% 244.31/50.75  | | 
% 244.31/50.75  | | ALPHA: (9) implies:
% 244.31/50.75  | |   (10)  op(e0, e1) = e3
% 244.31/50.75  | | 
% 244.31/50.75  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #2164.
% 244.31/50.75  | | 
% 244.31/50.75  | End of split
% 244.31/50.75  | 
% 244.31/50.75  End of proof
% 244.31/50.75  
% 244.31/50.75  Sub-proof #1596 shows that the following formulas are inconsistent:
% 244.31/50.75  ----------------------------------------------------------------
% 244.31/50.75    (1)  op(e1, e0) = e0
% 244.31/50.75    (2)   ~ (e2 = e0)
% 244.31/50.75    (3)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.31/50.75             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.31/50.75           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 244.31/50.75             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.31/50.75           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 244.31/50.75           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.31/50.75           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.31/50.75    (4)  op(e2, e0) = e2
% 244.31/50.75    (5)  all_56_31 = e1
% 244.31/50.75    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.75    (7)   ~ (e1 = e0)
% 244.31/50.75  
% 244.31/50.75  Begin of proof
% 244.31/50.75  | 
% 244.31/50.75  | BETA: splitting (3) gives:
% 244.31/50.75  | 
% 244.31/50.75  | Case 1:
% 244.31/50.75  | | 
% 244.31/50.75  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.31/50.75  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 244.31/50.75  | |        & op(e0, e2) = e0
% 244.31/50.75  | | 
% 244.31/50.75  | | ALPHA: (8) implies:
% 244.31/50.75  | |   (9)  op(e2, e0) = e0
% 244.31/50.75  | | 
% 244.31/50.75  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #2121.
% 244.31/50.75  | | 
% 244.31/50.75  | Case 2:
% 244.31/50.75  | | 
% 244.31/50.75  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.31/50.75  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.31/50.75  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 244.31/50.75  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.31/50.75  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.31/50.75  | | 
% 244.31/50.75  | | REF_CLOSE: (1), (5), (6), (7), (10) are inconsistent by sub-proof #1614.
% 244.31/50.75  | | 
% 244.31/50.75  | End of split
% 244.31/50.75  | 
% 244.31/50.75  End of proof
% 244.31/50.75  
% 244.31/50.75  Sub-proof #1597 shows that the following formulas are inconsistent:
% 244.31/50.75  ----------------------------------------------------------------
% 244.31/50.75    (1)   ~ (e3 = e0)
% 244.31/50.75    (2)   ~ (e2 = e0)
% 244.31/50.75    (3)   ~ (e3 = e1)
% 244.31/50.75    (4)   ~ (e3 = e2)
% 244.31/50.75    (5)  all_58_15 = e1
% 244.31/50.75    (6)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.31/50.75         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.31/50.75    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.75    (8)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.31/50.75         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.31/50.75    (9)  all_58_11 = e0
% 244.31/50.75    (10)  all_58_10 = e1
% 244.31/50.75    (11)   ~ (e2 = e1)
% 244.31/50.75  
% 244.31/50.75  Begin of proof
% 244.31/50.75  | 
% 244.31/50.75  | BETA: splitting (8) gives:
% 244.31/50.75  | 
% 244.31/50.75  | Case 1:
% 244.31/50.75  | | 
% 244.31/50.75  | |   (12)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 244.31/50.75  | |           e2)
% 244.31/50.75  | | 
% 244.31/50.75  | | BETA: splitting (12) gives:
% 244.31/50.75  | | 
% 244.31/50.75  | | Case 1:
% 244.31/50.75  | | | 
% 244.31/50.75  | | |   (13)  all_58_9 = e2 & op(e3, e0) = e2
% 244.31/50.75  | | | 
% 244.31/50.75  | | | ALPHA: (13) implies:
% 244.31/50.75  | | |   (14)  op(e3, e0) = e2
% 244.31/50.75  | | | 
% 244.31/50.75  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (14) are inconsistent
% 244.31/50.75  | | |            by sub-proof #1599.
% 244.31/50.75  | | | 
% 244.31/50.75  | | Case 2:
% 244.31/50.75  | | | 
% 244.31/50.75  | | |   (15)  all_58_10 = e2 & op(e2, e0) = e2
% 244.31/50.75  | | | 
% 244.31/50.75  | | | ALPHA: (15) implies:
% 244.31/50.75  | | |   (16)  all_58_10 = e2
% 244.31/50.75  | | | 
% 244.31/50.75  | | | REF_CLOSE: (10), (11), (16) are inconsistent by sub-proof #1598.
% 244.31/50.75  | | | 
% 244.31/50.75  | | End of split
% 244.31/50.75  | | 
% 244.31/50.75  | Case 2:
% 244.31/50.75  | | 
% 244.31/50.75  | |   (17)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.31/50.75  | |           e2)
% 244.31/50.75  | | 
% 244.31/50.75  | | BETA: splitting (17) gives:
% 244.31/50.75  | | 
% 244.31/50.75  | | Case 1:
% 244.31/50.75  | | | 
% 244.31/50.75  | | |   (18)  all_58_11 = e2 & op(e1, e0) = e2
% 244.31/50.75  | | | 
% 244.31/50.75  | | | REF_CLOSE: (2), (9), (18) are inconsistent by sub-proof #2216.
% 244.31/50.75  | | | 
% 244.31/50.75  | | Case 2:
% 244.31/50.75  | | | 
% 244.31/50.75  | | |   (19)  all_58_15 = e2 & op(e0, e0) = e2
% 244.31/50.75  | | | 
% 244.31/50.75  | | | REF_CLOSE: (5), (11), (19) are inconsistent by sub-proof #1917.
% 244.31/50.75  | | | 
% 244.31/50.75  | | End of split
% 244.31/50.75  | | 
% 244.31/50.75  | End of split
% 244.31/50.75  | 
% 244.31/50.75  End of proof
% 244.31/50.75  
% 244.31/50.75  Sub-proof #1598 shows that the following formulas are inconsistent:
% 244.31/50.75  ----------------------------------------------------------------
% 244.31/50.75    (1)  all_58_10 = e2
% 244.31/50.75    (2)  all_58_10 = e1
% 244.31/50.75    (3)   ~ (e2 = e1)
% 244.31/50.75  
% 244.31/50.75  Begin of proof
% 244.31/50.75  | 
% 244.31/50.75  | COMBINE_EQS: (1), (2) imply:
% 244.31/50.75  |   (4)  e2 = e1
% 244.31/50.75  | 
% 244.31/50.75  | SIMP: (4) implies:
% 244.31/50.75  |   (5)  e2 = e1
% 244.31/50.75  | 
% 244.31/50.75  | REDUCE: (3), (5) imply:
% 244.31/50.75  |   (6)  $false
% 244.31/50.75  | 
% 244.31/50.75  | CLOSE: (6) is inconsistent.
% 244.31/50.75  | 
% 244.31/50.75  End of proof
% 244.31/50.75  
% 244.31/50.75  Sub-proof #1599 shows that the following formulas are inconsistent:
% 244.31/50.75  ----------------------------------------------------------------
% 244.31/50.75    (1)   ~ (e3 = e0)
% 244.31/50.75    (2)   ~ (e3 = e1)
% 244.31/50.75    (3)   ~ (e3 = e2)
% 244.31/50.75    (4)  all_58_15 = e1
% 244.31/50.75    (5)  op(e3, e0) = e2
% 244.31/50.75    (6)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.31/50.75         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.31/50.75    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.76    (8)  all_58_11 = e0
% 244.31/50.76    (9)  all_58_10 = e1
% 244.31/50.76  
% 244.31/50.76  Begin of proof
% 244.31/50.76  | 
% 244.31/50.76  | BETA: splitting (6) gives:
% 244.31/50.76  | 
% 244.31/50.76  | Case 1:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (10)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 244.31/50.76  | |           e3)
% 244.31/50.76  | | 
% 244.31/50.76  | | BETA: splitting (10) gives:
% 244.31/50.76  | | 
% 244.31/50.76  | | Case 1:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (11)  all_58_9 = e3 & op(e3, e0) = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | ALPHA: (11) implies:
% 244.31/50.76  | | |   (12)  op(e3, e0) = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (3), (5), (7), (12) are inconsistent by sub-proof #2125.
% 244.31/50.76  | | | 
% 244.31/50.76  | | Case 2:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (13)  all_58_10 = e3 & op(e2, e0) = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (2), (9), (13) are inconsistent by sub-proof #1620.
% 244.31/50.76  | | | 
% 244.31/50.76  | | End of split
% 244.31/50.76  | | 
% 244.31/50.76  | Case 2:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (14)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.31/50.76  | |           e3)
% 244.31/50.76  | | 
% 244.31/50.76  | | BETA: splitting (14) gives:
% 244.31/50.76  | | 
% 244.31/50.76  | | Case 1:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (15)  all_58_11 = e3 & op(e1, e0) = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (1), (8), (15) are inconsistent by sub-proof #2091.
% 244.31/50.76  | | | 
% 244.31/50.76  | | Case 2:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (16)  all_58_15 = e3 & op(e0, e0) = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | ALPHA: (16) implies:
% 244.31/50.76  | | |   (17)  all_58_15 = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (2), (4), (17) are inconsistent by sub-proof #2249.
% 244.31/50.76  | | | 
% 244.31/50.76  | | End of split
% 244.31/50.76  | | 
% 244.31/50.76  | End of split
% 244.31/50.76  | 
% 244.31/50.76  End of proof
% 244.31/50.76  
% 244.31/50.76  Sub-proof #1600 shows that the following formulas are inconsistent:
% 244.31/50.76  ----------------------------------------------------------------
% 244.31/50.76    (1)  op(e0, e0) = e1
% 244.31/50.76    (2)   ~ (e3 = e0)
% 244.31/50.76    (3)   ~ (e2 = e0)
% 244.31/50.76    (4)   ~ (e3 = e1)
% 244.31/50.76    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.31/50.76             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.31/50.76               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.31/50.76               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.31/50.76    (6)   ~ (e3 = e2)
% 244.31/50.76    (7)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.31/50.76         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.31/50.76    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.76    (9)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.31/50.76         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.31/50.76    (10)   ~ (e1 = e0)
% 244.31/50.76    (11)  all_58_9 = e1
% 244.31/50.76    (12)   ~ (all_52_13 = e3)
% 244.31/50.76    (13)  op(e2, e0) = all_52_13
% 244.31/50.76    (14)   ~ (e2 = e1)
% 244.31/50.76  
% 244.31/50.76  Begin of proof
% 244.31/50.76  | 
% 244.31/50.76  | BETA: splitting (7) gives:
% 244.31/50.76  | 
% 244.31/50.76  | Case 1:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (15)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 244.31/50.76  | |           e3)
% 244.31/50.76  | | 
% 244.31/50.76  | | REF_CLOSE: (4), (8), (11), (12), (13), (15) are inconsistent by sub-proof
% 244.31/50.76  | |            #1606.
% 244.31/50.76  | | 
% 244.31/50.76  | Case 2:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (16)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.31/50.76  | |           e3)
% 244.31/50.76  | | 
% 244.31/50.76  | | BETA: splitting (16) gives:
% 244.31/50.76  | | 
% 244.31/50.76  | | Case 1:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (17)  all_58_11 = e3 & op(e1, e0) = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | ALPHA: (17) implies:
% 244.31/50.76  | | |   (18)  all_58_11 = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (14), (18) are
% 244.31/50.76  | | |            inconsistent by sub-proof #1604.
% 244.31/50.76  | | | 
% 244.31/50.76  | | Case 2:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (19)  all_58_15 = e3 & op(e0, e0) = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | ALPHA: (19) implies:
% 244.31/50.76  | | |   (20)  all_58_15 = e3
% 244.31/50.76  | | |   (21)  op(e0, e0) = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | GROUND_INST: instantiating (8) with e1, e3, e0, e0, simplifying with (1),
% 244.31/50.76  | | |              (21) gives:
% 244.31/50.76  | | |   (22)  e3 = e1
% 244.31/50.76  | | | 
% 244.31/50.76  | | | COMBINE_EQS: (20), (22) imply:
% 244.31/50.76  | | |   (23)  all_58_15 = e1
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 244.31/50.76  | | |            (13), (14), (23) are inconsistent by sub-proof #1601.
% 244.31/50.76  | | | 
% 244.31/50.76  | | End of split
% 244.31/50.76  | | 
% 244.31/50.76  | End of split
% 244.31/50.76  | 
% 244.31/50.76  End of proof
% 244.31/50.76  
% 244.31/50.76  Sub-proof #1601 shows that the following formulas are inconsistent:
% 244.31/50.76  ----------------------------------------------------------------
% 244.31/50.76    (1)  op(e0, e0) = e1
% 244.31/50.76    (2)   ~ (e3 = e0)
% 244.31/50.76    (3)   ~ (e2 = e0)
% 244.31/50.76    (4)   ~ (e3 = e1)
% 244.31/50.76    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.31/50.76             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.31/50.76               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.31/50.76               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.31/50.76    (6)   ~ (e3 = e2)
% 244.31/50.76    (7)  all_58_15 = e1
% 244.31/50.76    (8)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.31/50.76         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.31/50.76    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.76    (10)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.31/50.76          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.31/50.76    (11)   ~ (e1 = e0)
% 244.31/50.76    (12)  all_58_9 = e1
% 244.31/50.76    (13)   ~ (all_52_13 = e3)
% 244.31/50.76    (14)  op(e2, e0) = all_52_13
% 244.31/50.76    (15)   ~ (e2 = e1)
% 244.31/50.76  
% 244.31/50.76  Begin of proof
% 244.31/50.76  | 
% 244.31/50.76  | BETA: splitting (8) gives:
% 244.31/50.76  | 
% 244.31/50.76  | Case 1:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (16)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 244.31/50.76  | |           e3)
% 244.31/50.76  | | 
% 244.31/50.76  | | REF_CLOSE: (4), (9), (12), (13), (14), (16) are inconsistent by sub-proof
% 244.31/50.76  | |            #1602.
% 244.31/50.76  | | 
% 244.31/50.76  | Case 2:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (17)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.31/50.76  | |           e3)
% 244.31/50.76  | | 
% 244.31/50.76  | | BETA: splitting (17) gives:
% 244.31/50.76  | | 
% 244.31/50.76  | | Case 1:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (18)  all_58_11 = e3 & op(e1, e0) = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | ALPHA: (18) implies:
% 244.31/50.76  | | |   (19)  all_58_11 = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (12), (15), (19)
% 244.31/50.76  | | |            are inconsistent by sub-proof #1740.
% 244.31/50.76  | | | 
% 244.31/50.76  | | Case 2:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (20)  all_58_15 = e3 & op(e0, e0) = e3
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (4), (7), (20) are inconsistent by sub-proof #1915.
% 244.31/50.76  | | | 
% 244.31/50.76  | | End of split
% 244.31/50.76  | | 
% 244.31/50.76  | End of split
% 244.31/50.76  | 
% 244.31/50.76  End of proof
% 244.31/50.76  
% 244.31/50.76  Sub-proof #1602 shows that the following formulas are inconsistent:
% 244.31/50.76  ----------------------------------------------------------------
% 244.31/50.76    (1)   ~ (e3 = e1)
% 244.31/50.76    (2)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.31/50.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.76    (4)  all_58_9 = e1
% 244.31/50.76    (5)   ~ (all_52_13 = e3)
% 244.31/50.76    (6)  op(e2, e0) = all_52_13
% 244.31/50.76  
% 244.31/50.76  Begin of proof
% 244.31/50.76  | 
% 244.31/50.76  | BETA: splitting (2) gives:
% 244.31/50.76  | 
% 244.31/50.76  | Case 1:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (7)  all_58_9 = e3 & op(e3, e0) = e3
% 244.31/50.76  | | 
% 244.31/50.76  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #1603.
% 244.31/50.76  | | 
% 244.31/50.76  | Case 2:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (8)  all_58_10 = e3 & op(e2, e0) = e3
% 244.31/50.76  | | 
% 244.31/50.76  | | ALPHA: (8) implies:
% 244.31/50.76  | |   (9)  op(e2, e0) = e3
% 244.31/50.76  | | 
% 244.31/50.76  | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #1994.
% 244.31/50.76  | | 
% 244.31/50.76  | End of split
% 244.31/50.76  | 
% 244.31/50.76  End of proof
% 244.31/50.76  
% 244.31/50.76  Sub-proof #1603 shows that the following formulas are inconsistent:
% 244.31/50.76  ----------------------------------------------------------------
% 244.31/50.76    (1)  all_58_9 = e3 & op(e3, e0) = e3
% 244.31/50.76    (2)  all_58_9 = e1
% 244.31/50.76    (3)   ~ (e3 = e1)
% 244.31/50.76  
% 244.31/50.76  Begin of proof
% 244.31/50.76  | 
% 244.31/50.76  | ALPHA: (1) implies:
% 244.31/50.76  |   (4)  all_58_9 = e3
% 244.31/50.76  | 
% 244.31/50.76  | COMBINE_EQS: (2), (4) imply:
% 244.31/50.76  |   (5)  e3 = e1
% 244.31/50.76  | 
% 244.31/50.76  | REDUCE: (3), (5) imply:
% 244.31/50.76  |   (6)  $false
% 244.31/50.76  | 
% 244.31/50.76  | CLOSE: (6) is inconsistent.
% 244.31/50.76  | 
% 244.31/50.76  End of proof
% 244.31/50.76  
% 244.31/50.76  Sub-proof #1604 shows that the following formulas are inconsistent:
% 244.31/50.76  ----------------------------------------------------------------
% 244.31/50.76    (1)  op(e0, e0) = e1
% 244.31/50.76    (2)   ~ (e3 = e0)
% 244.31/50.76    (3)   ~ (e2 = e0)
% 244.31/50.76    (4)  all_58_11 = e3
% 244.31/50.76    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.31/50.76             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.31/50.76               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.31/50.76               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.31/50.76    (6)   ~ (e3 = e2)
% 244.31/50.76    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.76    (8)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.31/50.76         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.31/50.76    (9)   ~ (e1 = e0)
% 244.31/50.76    (10)  all_58_9 = e1
% 244.31/50.76    (11)   ~ (e2 = e1)
% 244.31/50.76  
% 244.31/50.76  Begin of proof
% 244.31/50.76  | 
% 244.31/50.76  | BETA: splitting (8) gives:
% 244.31/50.76  | 
% 244.31/50.76  | Case 1:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (12)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 244.31/50.76  | |           e2)
% 244.31/50.76  | | 
% 244.31/50.76  | | BETA: splitting (12) gives:
% 244.31/50.76  | | 
% 244.31/50.76  | | Case 1:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (13)  all_58_9 = e2 & op(e3, e0) = e2
% 244.31/50.76  | | | 
% 244.31/50.76  | | | ALPHA: (13) implies:
% 244.31/50.76  | | |   (14)  all_58_9 = e2
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (10), (11), (14) are inconsistent by sub-proof #1605.
% 244.31/50.76  | | | 
% 244.31/50.76  | | Case 2:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (15)  all_58_10 = e2 & op(e2, e0) = e2
% 244.31/50.76  | | | 
% 244.31/50.76  | | | ALPHA: (15) implies:
% 244.31/50.76  | | |   (16)  op(e2, e0) = e2
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (16) are inconsistent
% 244.31/50.76  | | |            by sub-proof #1742.
% 244.31/50.76  | | | 
% 244.31/50.76  | | End of split
% 244.31/50.76  | | 
% 244.31/50.76  | Case 2:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (17)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.31/50.76  | |           e2)
% 244.31/50.76  | | 
% 244.31/50.76  | | BETA: splitting (17) gives:
% 244.31/50.76  | | 
% 244.31/50.76  | | Case 1:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (18)  all_58_11 = e2 & op(e1, e0) = e2
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (4), (6), (18) are inconsistent by sub-proof #1741.
% 244.31/50.76  | | | 
% 244.31/50.76  | | Case 2:
% 244.31/50.76  | | | 
% 244.31/50.76  | | |   (19)  all_58_15 = e2 & op(e0, e0) = e2
% 244.31/50.76  | | | 
% 244.31/50.76  | | | ALPHA: (19) implies:
% 244.31/50.76  | | |   (20)  all_58_15 = e2
% 244.31/50.76  | | |   (21)  op(e0, e0) = e2
% 244.31/50.76  | | | 
% 244.31/50.76  | | | GROUND_INST: instantiating (7) with e1, e2, e0, e0, simplifying with (1),
% 244.31/50.76  | | |              (21) gives:
% 244.31/50.76  | | |   (22)  e2 = e1
% 244.31/50.76  | | | 
% 244.31/50.76  | | | COMBINE_EQS: (20), (22) imply:
% 244.31/50.76  | | |   (23)  all_58_15 = e1
% 244.31/50.76  | | | 
% 244.31/50.76  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (23)
% 244.31/50.76  | | |            are inconsistent by sub-proof #1740.
% 244.31/50.76  | | | 
% 244.31/50.76  | | End of split
% 244.31/50.76  | | 
% 244.31/50.76  | End of split
% 244.31/50.76  | 
% 244.31/50.76  End of proof
% 244.31/50.76  
% 244.31/50.76  Sub-proof #1605 shows that the following formulas are inconsistent:
% 244.31/50.76  ----------------------------------------------------------------
% 244.31/50.76    (1)  all_58_9 = e2
% 244.31/50.76    (2)  all_58_9 = e1
% 244.31/50.76    (3)   ~ (e2 = e1)
% 244.31/50.76  
% 244.31/50.76  Begin of proof
% 244.31/50.76  | 
% 244.31/50.76  | COMBINE_EQS: (1), (2) imply:
% 244.31/50.76  |   (4)  e2 = e1
% 244.31/50.76  | 
% 244.31/50.76  | SIMP: (4) implies:
% 244.31/50.76  |   (5)  e2 = e1
% 244.31/50.76  | 
% 244.31/50.76  | REDUCE: (3), (5) imply:
% 244.31/50.76  |   (6)  $false
% 244.31/50.76  | 
% 244.31/50.76  | CLOSE: (6) is inconsistent.
% 244.31/50.76  | 
% 244.31/50.76  End of proof
% 244.31/50.76  
% 244.31/50.76  Sub-proof #1606 shows that the following formulas are inconsistent:
% 244.31/50.76  ----------------------------------------------------------------
% 244.31/50.76    (1)   ~ (e3 = e1)
% 244.31/50.76    (2)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.31/50.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.76    (4)  all_58_9 = e1
% 244.31/50.76    (5)   ~ (all_52_13 = e3)
% 244.31/50.76    (6)  op(e2, e0) = all_52_13
% 244.31/50.76  
% 244.31/50.76  Begin of proof
% 244.31/50.76  | 
% 244.31/50.76  | BETA: splitting (2) gives:
% 244.31/50.76  | 
% 244.31/50.76  | Case 1:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (7)  all_58_9 = e3 & op(e3, e0) = e3
% 244.31/50.76  | | 
% 244.31/50.76  | | ALPHA: (7) implies:
% 244.31/50.76  | |   (8)  all_58_9 = e3
% 244.31/50.76  | | 
% 244.31/50.76  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #1709.
% 244.31/50.76  | | 
% 244.31/50.76  | Case 2:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (9)  all_58_10 = e3 & op(e2, e0) = e3
% 244.31/50.76  | | 
% 244.31/50.76  | | ALPHA: (9) implies:
% 244.31/50.76  | |   (10)  op(e2, e0) = e3
% 244.31/50.76  | | 
% 244.31/50.76  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1994.
% 244.31/50.76  | | 
% 244.31/50.76  | End of split
% 244.31/50.76  | 
% 244.31/50.76  End of proof
% 244.31/50.76  
% 244.31/50.76  Sub-proof #1607 shows that the following formulas are inconsistent:
% 244.31/50.76  ----------------------------------------------------------------
% 244.31/50.76    (1)   ~ (e2 = e0)
% 244.31/50.76    (2)  op(e2, e3) = all_52_1
% 244.31/50.76    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 244.31/50.76    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.76    (5)  op(e3, e3) = e0
% 244.31/50.76    (6)   ~ (all_52_1 = e2)
% 244.31/50.76  
% 244.31/50.76  Begin of proof
% 244.31/50.76  | 
% 244.31/50.76  | BETA: splitting (3) gives:
% 244.31/50.76  | 
% 244.31/50.76  | Case 1:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 244.31/50.76  | | 
% 244.31/50.76  | | ALPHA: (7) implies:
% 244.31/50.76  | |   (8)  op(e3, e3) = e2
% 244.31/50.76  | | 
% 244.31/50.76  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2188.
% 244.31/50.76  | | 
% 244.31/50.76  | Case 2:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (9)  all_58_2 = e2 & op(e2, e3) = e2
% 244.31/50.76  | | 
% 244.31/50.76  | | ALPHA: (9) implies:
% 244.31/50.76  | |   (10)  op(e2, e3) = e2
% 244.31/50.76  | | 
% 244.31/50.76  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #2336.
% 244.31/50.76  | | 
% 244.31/50.76  | End of split
% 244.31/50.76  | 
% 244.31/50.76  End of proof
% 244.31/50.76  
% 244.31/50.76  Sub-proof #1608 shows that the following formulas are inconsistent:
% 244.31/50.76  ----------------------------------------------------------------
% 244.31/50.76    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 244.31/50.76           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 244.31/50.76             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.31/50.76           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 244.31/50.76             e1) = e3 & op(e1, e3) = e3)
% 244.31/50.76    (2)  op(e3, e1) = all_52_8
% 244.31/50.76    (3)  op(e2, e3) = all_52_1
% 244.31/50.76    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.76    (5)   ~ (all_52_1 = e2)
% 244.31/50.76    (6)   ~ (all_52_8 = e3)
% 244.31/50.76  
% 244.31/50.76  Begin of proof
% 244.31/50.76  | 
% 244.31/50.76  | BETA: splitting (1) gives:
% 244.31/50.76  | 
% 244.31/50.76  | Case 1:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.31/50.76  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.31/50.76  | |        op(e2, e3) = e2
% 244.31/50.76  | | 
% 244.31/50.76  | | ALPHA: (7) implies:
% 244.31/50.76  | |   (8)  op(e2, e3) = e2
% 244.31/50.76  | | 
% 244.31/50.76  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2336.
% 244.31/50.76  | | 
% 244.31/50.76  | Case 2:
% 244.31/50.76  | | 
% 244.31/50.76  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.31/50.76  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.31/50.76  | |        op(e1, e3) = e3
% 244.31/50.76  | | 
% 244.31/50.76  | | ALPHA: (9) implies:
% 244.31/50.76  | |   (10)  op(e3, e1) = e3
% 244.31/50.76  | | 
% 244.31/50.76  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #2260.
% 244.31/50.76  | | 
% 244.31/50.76  | End of split
% 244.31/50.76  | 
% 244.31/50.76  End of proof
% 244.31/50.76  
% 244.31/50.76  Sub-proof #1609 shows that the following formulas are inconsistent:
% 244.31/50.76  ----------------------------------------------------------------
% 244.31/50.76    (1)   ~ (e3 = e0)
% 244.31/50.76    (2)  op(e1, e2) = e1
% 244.31/50.76    (3)   ~ (e2 = e0)
% 244.31/50.76    (4)  op(e1, e2) = all_52_6
% 244.31/50.77    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.31/50.77         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.31/50.77    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.31/50.77         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.31/50.77    (7)   ~ (e3 = e1)
% 244.31/50.77    (8)  op(e2, e2) = e0
% 244.31/50.77    (9)   ~ (e3 = e2)
% 244.31/50.77    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 244.31/50.77    (11)  all_58_7 = e1
% 244.31/50.77    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.31/50.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.31/50.77    (13)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.31/50.77          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.31/50.77    (14)   ~ (e1 = e0)
% 244.31/50.77    (15)  op(e3, e3) = e0
% 244.31/50.77    (16)   ~ (e2 = e1)
% 244.31/50.77  
% 244.31/50.77  Begin of proof
% 244.31/50.77  | 
% 244.31/50.77  | BETA: splitting (10) gives:
% 244.31/50.77  | 
% 244.31/50.77  | Case 1:
% 244.31/50.77  | | 
% 244.31/50.77  | |   (17)  all_58_0 = e1 & op(e3, e3) = e1
% 244.31/50.77  | | 
% 244.31/50.77  | | ALPHA: (17) implies:
% 244.31/50.77  | |   (18)  op(e3, e3) = e1
% 244.31/50.77  | | 
% 244.31/50.77  | | REF_CLOSE: (12), (14), (15), (18) are inconsistent by sub-proof #1828.
% 244.31/50.77  | | 
% 244.31/50.77  | Case 2:
% 244.31/50.77  | | 
% 244.31/50.77  | |   (19)  all_58_1 = e1 & op(e3, e2) = e1
% 244.31/50.77  | | 
% 244.31/50.77  | | ALPHA: (19) implies:
% 244.31/50.77  | |   (20)  all_58_1 = e1
% 244.31/50.77  | | 
% 244.31/50.77  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 244.31/50.77  | |            (14), (16), (20) are inconsistent by sub-proof #1714.
% 244.31/50.77  | | 
% 244.31/50.77  | End of split
% 244.31/50.77  | 
% 244.31/50.77  End of proof
% 244.31/50.77  
% 244.31/50.77  Sub-proof #1610 shows that the following formulas are inconsistent:
% 244.31/50.77  ----------------------------------------------------------------
% 244.34/50.77    (1)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 244.34/50.77    (2)  op(e3, e2) = e2
% 244.34/50.77    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.77    (4)   ~ (e1 = e0)
% 244.34/50.77    (5)  all_58_3 = e0
% 244.34/50.77    (6)   ~ (e2 = e1)
% 244.34/50.77  
% 244.34/50.77  Begin of proof
% 244.34/50.77  | 
% 244.34/50.77  | BETA: splitting (1) gives:
% 244.34/50.77  | 
% 244.34/50.77  | Case 1:
% 244.34/50.77  | | 
% 244.34/50.77  | |   (7)  all_58_1 = e1 & op(e3, e2) = e1
% 244.34/50.77  | | 
% 244.34/50.77  | | ALPHA: (7) implies:
% 244.34/50.77  | |   (8)  op(e3, e2) = e1
% 244.34/50.77  | | 
% 244.34/50.77  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #2261.
% 244.34/50.77  | | 
% 244.34/50.77  | Case 2:
% 244.34/50.77  | | 
% 244.34/50.77  | |   (9)  all_58_3 = e1 & op(e2, e2) = e1
% 244.34/50.77  | | 
% 244.34/50.77  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #1752.
% 244.34/50.77  | | 
% 244.34/50.77  | End of split
% 244.34/50.77  | 
% 244.34/50.77  End of proof
% 244.34/50.77  
% 244.34/50.77  Sub-proof #1611 shows that the following formulas are inconsistent:
% 244.34/50.77  ----------------------------------------------------------------
% 244.34/50.77    (1)   ~ (all_52_3 = e0)
% 244.34/50.77    (2)   ~ (all_52_9 = all_6_2)
% 244.34/50.77    (3)   ~ (e3 = e0)
% 244.34/50.77    (4)  op(e1, e0) = e0
% 244.34/50.77    (5)   ~ (all_6_2 = e2)
% 244.34/50.77    (6)   ~ (e2 = e0)
% 244.34/50.77    (7)   ~ (all_52_8 = all_6_2)
% 244.34/50.77    (8)  op(e1, e2) = all_52_6
% 244.34/50.77    (9)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.34/50.77         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.34/50.77    (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.34/50.77              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.34/50.77            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 244.34/50.77            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.34/50.77            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 244.34/50.77             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.34/50.77            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.34/50.77            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.34/50.77            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 244.34/50.77            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.34/50.77            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.34/50.77              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.34/50.77            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.34/50.77            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 244.34/50.77            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.34/50.77            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 244.34/50.77            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.34/50.77            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.34/50.77              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.34/50.77            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.34/50.77            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 244.34/50.77            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.34/50.77            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 244.34/50.77            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.34/50.77            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.34/50.77              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.34/50.77            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.34/50.77            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.34/50.77    (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.34/50.77          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.34/50.77    (12)  op(e0, e3) = all_52_3
% 244.34/50.77    (13)   ~ (all_52_12 = e1)
% 244.34/50.77    (14)  op(e2, e2) = e0
% 244.34/50.77    (15)  all_54_10 = all_6_2
% 244.34/50.77    (16)   ~ (all_6_2 = e3)
% 244.34/50.77    (17)  op(e3, e1) = all_52_8
% 244.34/50.77    (18)  op(e2, e1) = all_52_9
% 244.34/50.77    (19)   ~ (e3 = e2)
% 244.34/50.77    (20)   ~ (all_52_7 = e1)
% 244.34/50.77    (21)   ~ (all_6_2 = e0)
% 244.34/50.77    (22)  all_56_31 = e1
% 244.34/50.77    (23)  op(e3, e0) = all_52_12
% 244.34/50.77    (24)  all_56_11 = e0
% 244.34/50.77    (25)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.34/50.77    (26)  op(e0, e2) = all_52_7
% 244.34/50.77    (27)  op(e3, e2) = all_52_4
% 244.34/50.77    (28)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.34/50.77          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.34/50.77    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.77    (30)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.34/50.77          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.34/50.77    (31)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.34/50.77          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.34/50.77    (32)  op(e3, e3) = e0
% 244.34/50.77    (33)  op(e2, e0) = all_52_13
% 244.34/50.77    (34)  all_58_3 = e0
% 244.34/50.77    (35)   ~ (all_52_4 = all_52_8)
% 244.34/50.77    (36)   ~ (all_52_13 = e0)
% 244.34/50.77    (37)   ~ (all_52_4 = e0)
% 244.34/50.77  
% 244.34/50.77  Begin of proof
% 244.34/50.77  | 
% 244.34/50.77  | BETA: splitting (25) gives:
% 244.34/50.77  | 
% 244.34/50.77  | Case 1:
% 244.34/50.77  | | 
% 244.34/50.77  | |   (38)  all_54_10 = e3
% 244.34/50.77  | | 
% 244.34/50.77  | | REF_CLOSE: (15), (16), (38) are inconsistent by sub-proof #2313.
% 244.34/50.77  | | 
% 244.34/50.77  | Case 2:
% 244.34/50.77  | | 
% 244.34/50.77  | |   (39)   ~ (all_54_10 = e3)
% 244.34/50.77  | |   (40)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.34/50.77  | | 
% 244.34/50.77  | | BETA: splitting (40) gives:
% 244.34/50.77  | | 
% 244.34/50.77  | | Case 1:
% 244.34/50.77  | | | 
% 244.34/50.77  | | |   (41)  all_54_10 = e2
% 244.34/50.77  | | | 
% 244.34/50.77  | | | REF_CLOSE: (5), (15), (41) are inconsistent by sub-proof #2312.
% 244.34/50.77  | | | 
% 244.34/50.77  | | Case 2:
% 244.34/50.77  | | | 
% 244.34/50.77  | | |   (42)   ~ (all_54_10 = e2)
% 244.34/50.77  | | |   (43)  all_54_10 = e1 | all_54_10 = e0
% 244.34/50.77  | | | 
% 244.34/50.77  | | | BETA: splitting (43) gives:
% 244.34/50.77  | | | 
% 244.34/50.77  | | | Case 1:
% 244.34/50.77  | | | | 
% 244.34/50.77  | | | |   (44)  all_54_10 = e1
% 244.34/50.77  | | | | 
% 244.34/50.77  | | | | COMBINE_EQS: (15), (44) imply:
% 244.34/50.77  | | | |   (45)  all_6_2 = e1
% 244.34/50.77  | | | | 
% 244.34/50.77  | | | | SIMP: (45) implies:
% 244.34/50.77  | | | |   (46)  all_6_2 = e1
% 244.34/50.77  | | | | 
% 244.34/50.77  | | | | REDUCE: (7), (46) imply:
% 244.34/50.77  | | | |   (47)   ~ (all_52_8 = e1)
% 244.34/50.77  | | | | 
% 244.34/50.77  | | | | REDUCE: (16), (46) imply:
% 244.34/50.77  | | | |   (48)   ~ (e3 = e1)
% 244.34/50.77  | | | | 
% 244.34/50.77  | | | | SIMP: (48) implies:
% 244.34/50.77  | | | |   (49)   ~ (e3 = e1)
% 244.34/50.77  | | | | 
% 244.34/50.77  | | | | REDUCE: (5), (46) imply:
% 244.34/50.77  | | | |   (50)   ~ (e2 = e1)
% 244.34/50.77  | | | | 
% 244.34/50.77  | | | | SIMP: (50) implies:
% 244.34/50.77  | | | |   (51)   ~ (e2 = e1)
% 244.34/50.77  | | | | 
% 244.34/50.77  | | | | REDUCE: (21), (46) imply:
% 244.34/50.77  | | | |   (52)   ~ (e1 = e0)
% 244.34/50.77  | | | | 
% 244.34/50.77  | | | | BETA: splitting (30) gives:
% 244.34/50.77  | | | | 
% 244.34/50.77  | | | | Case 1:
% 244.34/50.77  | | | | | 
% 244.34/50.77  | | | | |   (53)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 244.34/50.77  | | | | |             e2) = e1)
% 244.34/50.77  | | | | | 
% 244.34/50.77  | | | | | BETA: splitting (53) gives:
% 244.34/50.77  | | | | | 
% 244.34/50.77  | | | | | Case 1:
% 244.34/50.77  | | | | | | 
% 244.34/50.77  | | | | | |   (54)  all_58_1 = e1 & op(e3, e2) = e1
% 244.34/50.77  | | | | | | 
% 244.34/50.77  | | | | | | ALPHA: (54) implies:
% 244.34/50.77  | | | | | |   (55)  op(e3, e2) = e1
% 244.34/50.77  | | | | | | 
% 244.34/50.77  | | | | | | GROUND_INST: instantiating (29) with all_52_4, e1, e2, e3,
% 244.34/50.77  | | | | | |              simplifying with (27), (55) gives:
% 244.34/50.77  | | | | | |   (56)  all_52_4 = e1
% 244.34/50.77  | | | | | | 
% 244.34/50.77  | | | | | | REDUCE: (35), (56) imply:
% 244.34/50.77  | | | | | |   (57)   ~ (all_52_8 = e1)
% 244.34/50.77  | | | | | | 
% 244.34/50.77  | | | | | | BETA: splitting (10) gives:
% 244.34/50.77  | | | | | | 
% 244.34/50.77  | | | | | | Case 1:
% 244.34/50.77  | | | | | | | 
% 244.34/50.77  | | | | | | |   (58)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.34/50.77  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 244.34/50.77  | | | | | | |             e2) & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 =
% 244.34/50.77  | | | | | | |           e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.34/50.77  | | | | | | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.34/50.77  | | | | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 244.34/50.77  | | | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.34/50.77  | | | | | | |             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.34/50.77  | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1 &
% 244.34/50.77  | | | | | | |           all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.34/50.77  | | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.34/50.77  | | | | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 244.34/50.77  | | | | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.34/50.77  | | | | | | |             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.34/50.77  | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 244.34/50.77  | | | | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.34/50.77  | | | | | | |             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.34/50.77  | | | | | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.34/50.77  | | | | | | | 
% 244.34/50.77  | | | | | | | BETA: splitting (58) gives:
% 244.34/50.77  | | | | | | | 
% 244.34/50.77  | | | | | | | Case 1:
% 244.34/50.77  | | | | | | | | 
% 244.34/50.77  | | | | | | | |   (59)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.34/50.77  | | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 244.34/50.77  | | | | | | | |             = e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 244.34/50.77  | | | | | | | |         (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.34/50.77  | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 244.34/50.77  | | | | | | | |             = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 244.34/50.77  | | | | | | | |         (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) & 
% 244.34/50.77  | | | | | | | |           ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.34/50.77  | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.34/50.77  | | | | | | | | 
% 244.34/50.77  | | | | | | | | BETA: splitting (59) gives:
% 244.34/50.77  | | | | | | | | 
% 244.34/50.77  | | | | | | | | Case 1:
% 244.34/50.77  | | | | | | | | | 
% 244.34/50.77  | | | | | | | | |   (60)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 244.34/50.77  | | | | | | | | |         ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.34/50.77  | | | | | | | | |         (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 244.34/50.77  | | | | | | | | | 
% 244.34/50.77  | | | | | | | | | ALPHA: (60) implies:
% 244.34/50.77  | | | | | | | | |   (61)  op(e3, e2) = e3
% 244.34/50.77  | | | | | | | | | 
% 244.34/50.77  | | | | | | | | | GROUND_INST: instantiating (29) with e1, e3, e2, e3,
% 244.34/50.77  | | | | | | | | |              simplifying with (55), (61) gives:
% 244.34/50.77  | | | | | | | | |   (62)  e3 = e1
% 244.34/50.77  | | | | | | | | | 
% 244.34/50.77  | | | | | | | | | REDUCE: (49), (62) imply:
% 244.34/50.77  | | | | | | | | |   (63)  $false
% 244.34/50.77  | | | | | | | | | 
% 244.34/50.77  | | | | | | | | | CLOSE: (63) is inconsistent.
% 244.34/50.77  | | | | | | | | | 
% 244.34/50.77  | | | | | | | | Case 2:
% 244.34/50.77  | | | | | | | | | 
% 244.34/50.77  | | | | | | | | |   (64)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) & 
% 244.34/50.77  | | | | | | | | |           ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.34/50.77  | | | | | | | | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 244.34/50.77  | | | | | | | | |           e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1
% 244.34/50.77  | | | | | | | | |             = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 244.34/50.77  | | | | | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.34/50.77  | | | | | | | | |           = e3)
% 244.34/50.77  | | | | | | | | | 
% 244.34/50.77  | | | | | | | | | BETA: splitting (64) gives:
% 244.34/50.77  | | | | | | | | | 
% 244.34/50.77  | | | | | | | | | Case 1:
% 244.34/50.77  | | | | | | | | | | 
% 244.34/50.77  | | | | | | | | | |   (65)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &
% 244.34/50.77  | | | | | | | | | |          ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.34/50.77  | | | | | | | | | |         (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 244.34/50.77  | | | | | | | | | | 
% 244.34/50.77  | | | | | | | | | | ALPHA: (65) implies:
% 244.34/50.78  | | | | | | | | | |   (66)  op(e3, e2) = e2
% 244.34/50.78  | | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | | GROUND_INST: instantiating (29) with e1, e2, e2, e3,
% 244.34/50.78  | | | | | | | | | |              simplifying with (55), (66) gives:
% 244.34/50.78  | | | | | | | | | |   (67)  e2 = e1
% 244.34/50.78  | | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | | REDUCE: (51), (67) imply:
% 244.34/50.78  | | | | | | | | | |   (68)  $false
% 244.34/50.78  | | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | | CLOSE: (68) is inconsistent.
% 244.34/50.78  | | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | Case 2:
% 244.34/50.78  | | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | |   (69)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1)
% 244.34/50.78  | | | | | | | | | |         &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.34/50.78  | | | | | | | | | |         (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 244.34/50.78  | | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | | ALPHA: (69) implies:
% 244.34/50.78  | | | | | | | | | |   (70)   ~ (all_56_31 = e1)
% 244.34/50.78  | | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | | REDUCE: (22), (70) imply:
% 244.34/50.78  | | | | | | | | | |   (71)  $false
% 244.34/50.78  | | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | | CLOSE: (71) is inconsistent.
% 244.34/50.78  | | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | End of split
% 244.34/50.78  | | | | | | | | | 
% 244.34/50.78  | | | | | | | | End of split
% 244.34/50.78  | | | | | | | | 
% 244.34/50.78  | | | | | | | Case 2:
% 244.34/50.78  | | | | | | | | 
% 244.34/50.78  | | | | | | | |   (72)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) & 
% 244.34/50.78  | | | | | | | |           ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.34/50.78  | | | | | | | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1)
% 244.34/50.78  | | | | | | | |         | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &
% 244.34/50.78  | | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.34/50.78  | | | | | | | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3)
% 244.34/50.78  | | | | | | | |         | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &
% 244.34/50.78  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.34/50.78  | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.34/50.78  | | | | | | | | 
% 244.34/50.78  | | | | | | | | REF_CLOSE: (1), (12), (17), (24), (29), (47), (72) are
% 244.34/50.78  | | | | | | | |            inconsistent by sub-proof #1616.
% 244.34/50.78  | | | | | | | | 
% 244.34/50.78  | | | | | | | End of split
% 244.34/50.78  | | | | | | | 
% 244.34/50.78  | | | | | | Case 2:
% 244.34/50.78  | | | | | | | 
% 244.34/50.78  | | | | | | |   (73)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 244.34/50.78  | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 244.34/50.78  | | | | | | |             e1) & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13
% 244.34/50.78  | | | | | | |           = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.34/50.78  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 244.34/50.78  | | | | | | |             e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 244.34/50.78  | | | | | | |           = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.34/50.78  | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 244.34/50.78  | | | | | | |             e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15
% 244.34/50.78  | | | | | | |           = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 244.34/50.78  | | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 244.34/50.78  | | | | | | |             e2) & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23
% 244.34/50.78  | | | | | | |           = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.34/50.78  | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 244.34/50.78  | | | | | | |             e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 244.34/50.78  | | | | | | |           = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 244.34/50.78  | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 244.34/50.78  | | | | | | |             e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.34/50.78  | | | | | | | 
% 244.34/50.78  | | | | | | | BETA: splitting (73) gives:
% 244.34/50.78  | | | | | | | 
% 244.34/50.78  | | | | | | | Case 1:
% 244.34/50.78  | | | | | | | | 
% 244.34/50.78  | | | | | | | |   (74)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) & 
% 244.34/50.78  | | | | | | | |           ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.34/50.78  | | | | | | | |           (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2)
% 244.34/50.78  | | | | | | | |         | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2)
% 244.34/50.78  | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.34/50.78  | | | | | | | |           (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1)
% 244.34/50.78  | | | | | | | |         | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0)
% 244.34/50.78  | | | | | | | |           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.34/50.78  | | | | | | | |           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.34/50.78  | | | | | | | | 
% 244.34/50.78  | | | | | | | | BETA: splitting (74) gives:
% 244.34/50.78  | | | | | | | | 
% 244.34/50.78  | | | | | | | | Case 1:
% 244.34/50.78  | | | | | | | | | 
% 244.34/50.78  | | | | | | | | |   (75)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &
% 244.34/50.78  | | | | | | | | |          ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.34/50.78  | | | | | | | | |         (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2
% 244.34/50.78  | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | ALPHA: (75) implies:
% 244.34/50.78  | | | | | | | | |   (76)   ~ (all_56_31 = e1)
% 244.34/50.78  | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | REDUCE: (22), (76) imply:
% 244.34/50.78  | | | | | | | | |   (77)  $false
% 244.34/50.78  | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | CLOSE: (77) is inconsistent.
% 244.34/50.78  | | | | | | | | | 
% 244.34/50.78  | | | | | | | | Case 2:
% 244.34/50.78  | | | | | | | | | 
% 244.34/50.78  | | | | | | | | |   (78)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2)
% 244.34/50.78  | | | | | | | | |           &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.34/50.78  | | | | | | | | |           (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 244.34/50.78  | | | | | | | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.34/50.78  | | | | | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 244.34/50.78  | | | | | | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0)
% 244.34/50.78  | | | | | | | | |           = e2 & op(e0, e2) = e2)
% 244.34/50.78  | | | | | | | | | 
% 244.34/50.78  | | | | | | | | | REF_CLOSE: (2), (15), (18), (21), (24), (29), (43), (78) are
% 244.34/50.78  | | | | | | | | |            inconsistent by sub-proof #1615.
% 244.34/50.78  | | | | | | | | | 
% 244.34/50.78  | | | | | | | | End of split
% 244.34/50.78  | | | | | | | | 
% 244.34/50.78  | | | | | | | Case 2:
% 244.34/50.78  | | | | | | | | 
% 244.34/50.78  | | | | | | | |   (79)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) & 
% 244.34/50.78  | | | | | | | |           ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.34/50.78  | | | | | | | |           (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0)
% 244.34/50.78  | | | | | | | |         | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0)
% 244.34/50.78  | | | | | | | |           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.34/50.78  | | | | | | | |           (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1)
% 244.34/50.78  | | | | | | | |         | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1)
% 244.34/50.78  | | | | | | | |           &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.34/50.78  | | | | | | | |           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.34/50.78  | | | | | | | | 
% 244.34/50.78  | | | | | | | | REF_CLOSE: (4), (22), (29), (33), (36), (52), (79) are
% 244.34/50.78  | | | | | | | |            inconsistent by sub-proof #1613.
% 244.34/50.78  | | | | | | | | 
% 244.34/50.78  | | | | | | | End of split
% 244.34/50.78  | | | | | | | 
% 244.34/50.78  | | | | | | End of split
% 244.34/50.78  | | | | | | 
% 244.34/50.78  | | | | | Case 2:
% 244.34/50.78  | | | | | | 
% 244.34/50.78  | | | | | |   (80)  all_58_3 = e1 & op(e2, e2) = e1
% 244.34/50.78  | | | | | | 
% 244.34/50.78  | | | | | | REF_CLOSE: (34), (52), (80) are inconsistent by sub-proof #1752.
% 244.34/50.78  | | | | | | 
% 244.34/50.78  | | | | | End of split
% 244.34/50.78  | | | | | 
% 244.34/50.78  | | | | Case 2:
% 244.34/50.78  | | | | | 
% 244.34/50.78  | | | | |   (81)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0,
% 244.34/50.78  | | | | |             e2) = e1)
% 244.34/50.78  | | | | | 
% 244.34/50.78  | | | | | BETA: splitting (81) gives:
% 244.34/50.78  | | | | | 
% 244.34/50.78  | | | | | Case 1:
% 244.34/50.78  | | | | | | 
% 244.34/50.78  | | | | | |   (82)  all_58_7 = e1 & op(e1, e2) = e1
% 244.34/50.78  | | | | | | 
% 244.34/50.78  | | | | | | ALPHA: (82) implies:
% 244.34/50.78  | | | | | |   (83)  all_58_7 = e1
% 244.34/50.78  | | | | | |   (84)  op(e1, e2) = e1
% 244.34/50.78  | | | | | | 
% 244.34/50.78  | | | | | | REF_CLOSE: (3), (6), (8), (9), (11), (13), (14), (17), (19), (23),
% 244.34/50.78  | | | | | |            (28), (29), (31), (32), (47), (49), (51), (52), (83),
% 244.34/50.78  | | | | | |            (84) are inconsistent by sub-proof #1612.
% 244.34/50.78  | | | | | | 
% 244.34/50.78  | | | | | Case 2:
% 244.34/50.78  | | | | | | 
% 244.34/50.78  | | | | | |   (85)  all_58_13 = e1 & op(e0, e2) = e1
% 244.34/50.78  | | | | | | 
% 244.34/50.78  | | | | | | REF_CLOSE: (20), (26), (29), (85) are inconsistent by sub-proof
% 244.34/50.78  | | | | | |            #2275.
% 244.34/50.78  | | | | | | 
% 244.34/50.78  | | | | | End of split
% 244.34/50.78  | | | | | 
% 244.34/50.78  | | | | End of split
% 244.34/50.78  | | | | 
% 244.34/50.78  | | | Case 2:
% 244.34/50.78  | | | | 
% 244.34/50.78  | | | |   (86)  all_54_10 = e0
% 244.34/50.78  | | | | 
% 244.34/50.78  | | | | REF_CLOSE: (15), (21), (86) are inconsistent by sub-proof #2303.
% 244.34/50.78  | | | | 
% 244.34/50.78  | | | End of split
% 244.34/50.78  | | | 
% 244.34/50.78  | | End of split
% 244.34/50.78  | | 
% 244.34/50.78  | End of split
% 244.34/50.78  | 
% 244.34/50.78  End of proof
% 244.34/50.78  
% 244.34/50.78  Sub-proof #1612 shows that the following formulas are inconsistent:
% 244.34/50.78  ----------------------------------------------------------------
% 244.34/50.78    (1)   ~ (e3 = e0)
% 244.34/50.78    (2)  op(e1, e2) = e1
% 244.34/50.78    (3)   ~ (e2 = e0)
% 244.34/50.78    (4)  op(e1, e2) = all_52_6
% 244.34/50.78    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.34/50.78         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.34/50.78    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.34/50.78         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.34/50.78    (7)   ~ (e3 = e1)
% 244.34/50.78    (8)   ~ (all_52_12 = e1)
% 244.34/50.78    (9)  op(e2, e2) = e0
% 244.34/50.78    (10)   ~ (all_52_8 = e1)
% 244.34/50.78    (11)  op(e3, e1) = all_52_8
% 244.34/50.78    (12)   ~ (e3 = e2)
% 244.34/50.78    (13)  op(e3, e0) = all_52_12
% 244.34/50.78    (14)  all_58_7 = e1
% 244.34/50.79    (15)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.34/50.79          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.34/50.79    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.79    (17)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.34/50.79          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.34/50.79    (18)   ~ (e1 = e0)
% 244.34/50.79    (19)  op(e3, e3) = e0
% 244.34/50.79    (20)   ~ (e2 = e1)
% 244.34/50.79  
% 244.34/50.79  Begin of proof
% 244.34/50.79  | 
% 244.34/50.79  | BETA: splitting (15) gives:
% 244.34/50.79  | 
% 244.34/50.79  | Case 1:
% 244.34/50.79  | | 
% 244.34/50.79  | |   (21)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 244.34/50.79  | |           e1)
% 244.34/50.79  | | 
% 244.34/50.79  | | BETA: splitting (21) gives:
% 244.34/50.79  | | 
% 244.34/50.79  | | Case 1:
% 244.34/50.79  | | | 
% 244.34/50.79  | | |   (22)  all_58_0 = e1 & op(e3, e3) = e1
% 244.34/50.79  | | | 
% 244.34/50.79  | | | ALPHA: (22) implies:
% 244.34/50.79  | | |   (23)  op(e3, e3) = e1
% 244.34/50.79  | | | 
% 244.34/50.79  | | | REF_CLOSE: (16), (18), (19), (23) are inconsistent by sub-proof #1828.
% 244.34/50.79  | | | 
% 244.34/50.79  | | Case 2:
% 244.34/50.79  | | | 
% 244.34/50.79  | | |   (24)  all_58_1 = e1 & op(e3, e2) = e1
% 244.34/50.79  | | | 
% 244.34/50.79  | | | ALPHA: (24) implies:
% 244.34/50.79  | | |   (25)  all_58_1 = e1
% 244.34/50.79  | | | 
% 244.34/50.79  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (12), (14), (16), (17),
% 244.34/50.79  | | |            (18), (20), (25) are inconsistent by sub-proof #1714.
% 244.34/50.79  | | | 
% 244.34/50.79  | | End of split
% 244.34/50.79  | | 
% 244.34/50.79  | Case 2:
% 244.34/50.79  | | 
% 244.34/50.79  | |   (26)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 244.34/50.79  | |           e1)
% 244.34/50.79  | | 
% 244.34/50.79  | | REF_CLOSE: (8), (10), (11), (13), (16), (26) are inconsistent by sub-proof
% 244.34/50.79  | |            #2233.
% 244.34/50.79  | | 
% 244.34/50.79  | End of split
% 244.34/50.79  | 
% 244.34/50.79  End of proof
% 244.34/50.79  
% 244.34/50.79  Sub-proof #1613 shows that the following formulas are inconsistent:
% 244.34/50.79  ----------------------------------------------------------------
% 244.34/50.79    (1)  op(e1, e0) = e0
% 244.34/50.79    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.34/50.79             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.34/50.79           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 244.34/50.79             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.34/50.79           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 244.34/50.79           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.34/50.79           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.34/50.79    (3)  all_56_31 = e1
% 244.34/50.79    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.79    (5)   ~ (e1 = e0)
% 244.34/50.79    (6)  op(e2, e0) = all_52_13
% 244.34/50.79    (7)   ~ (all_52_13 = e0)
% 244.34/50.79  
% 244.34/50.79  Begin of proof
% 244.34/50.79  | 
% 244.34/50.79  | BETA: splitting (2) gives:
% 244.34/50.79  | 
% 244.34/50.79  | Case 1:
% 244.34/50.79  | | 
% 244.34/50.79  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.34/50.79  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 244.34/50.79  | |        & op(e0, e2) = e0
% 244.34/50.79  | | 
% 244.34/50.79  | | ALPHA: (8) implies:
% 244.34/50.79  | |   (9)  op(e2, e0) = e0
% 244.34/50.79  | | 
% 244.34/50.79  | | REF_CLOSE: (4), (6), (7), (9) are inconsistent by sub-proof #2324.
% 244.34/50.79  | | 
% 244.34/50.79  | Case 2:
% 244.34/50.79  | | 
% 244.34/50.79  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.34/50.79  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.34/50.79  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 244.34/50.79  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.34/50.79  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.34/50.79  | | 
% 244.34/50.79  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #1614.
% 244.34/50.79  | | 
% 244.34/50.79  | End of split
% 244.34/50.79  | 
% 244.34/50.79  End of proof
% 244.34/50.79  
% 244.34/50.79  Sub-proof #1614 shows that the following formulas are inconsistent:
% 244.34/50.79  ----------------------------------------------------------------
% 244.34/50.79    (1)  op(e1, e0) = e0
% 244.34/50.79    (2)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.34/50.79             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 244.34/50.79           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 244.34/50.79             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 244.34/50.79           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.34/50.79    (3)  all_56_31 = e1
% 244.34/50.79    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.79    (5)   ~ (e1 = e0)
% 244.34/50.79  
% 244.34/50.79  Begin of proof
% 244.34/50.79  | 
% 244.34/50.79  | BETA: splitting (2) gives:
% 244.34/50.79  | 
% 244.34/50.79  | Case 1:
% 244.34/50.79  | | 
% 244.34/50.79  | |   (6)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.34/50.79  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 244.34/50.79  | |        & op(e0, e1) = e1
% 244.34/50.79  | | 
% 244.34/50.79  | | ALPHA: (6) implies:
% 244.34/50.79  | |   (7)  op(e1, e0) = e1
% 244.34/50.79  | | 
% 244.34/50.79  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #2284.
% 244.34/50.79  | | 
% 244.34/50.79  | Case 2:
% 244.34/50.79  | | 
% 244.34/50.79  | |   (8)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.34/50.79  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 244.34/50.79  | |        & op(e0, e1) = e0
% 244.34/50.79  | | 
% 244.34/50.79  | | ALPHA: (8) implies:
% 244.34/50.79  | |   (9)   ~ (all_56_31 = e1)
% 244.34/50.79  | | 
% 244.34/50.79  | | REDUCE: (3), (9) imply:
% 244.34/50.79  | |   (10)  $false
% 244.34/50.79  | | 
% 244.34/50.79  | | CLOSE: (10) is inconsistent.
% 244.34/50.79  | | 
% 244.34/50.79  | End of split
% 244.34/50.79  | 
% 244.34/50.79  End of proof
% 244.34/50.79  
% 244.34/50.79  Sub-proof #1615 shows that the following formulas are inconsistent:
% 244.34/50.79  ----------------------------------------------------------------
% 244.34/50.79    (1)   ~ (all_52_9 = all_6_2)
% 244.34/50.79    (2)  all_54_10 = e1 | all_54_10 = e0
% 244.34/50.79    (3)  all_54_10 = all_6_2
% 244.34/50.79    (4)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.34/50.79             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.34/50.79           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 244.34/50.79             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.34/50.79           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.34/50.79    (5)  op(e2, e1) = all_52_9
% 244.34/50.79    (6)   ~ (all_6_2 = e0)
% 244.34/50.79    (7)  all_56_11 = e0
% 244.34/50.79    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.79  
% 244.34/50.79  Begin of proof
% 244.34/50.79  | 
% 244.34/50.79  | BETA: splitting (4) gives:
% 244.34/50.79  | 
% 244.34/50.79  | Case 1:
% 244.34/50.79  | | 
% 244.34/50.79  | |   (9)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.34/50.79  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 244.34/50.79  | |        & op(e1, e2) = e1
% 244.34/50.79  | | 
% 244.34/50.79  | | ALPHA: (9) implies:
% 244.34/50.79  | |   (10)  op(e2, e1) = e1
% 244.34/50.79  | | 
% 244.34/50.79  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10) are inconsistent by sub-proof
% 244.34/50.79  | |            #1905.
% 244.34/50.79  | | 
% 244.34/50.79  | Case 2:
% 244.34/50.79  | | 
% 244.34/50.79  | |   (11)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.34/50.79  | |           = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) =
% 244.34/50.79  | |         e2 & op(e0, e2) = e2
% 244.34/50.79  | | 
% 244.34/50.79  | | ALPHA: (11) implies:
% 244.34/50.79  | |   (12)   ~ (all_56_11 = e0)
% 244.34/50.79  | | 
% 244.34/50.79  | | REDUCE: (7), (12) imply:
% 244.34/50.79  | |   (13)  $false
% 244.34/50.79  | | 
% 244.34/50.79  | | CLOSE: (13) is inconsistent.
% 244.34/50.79  | | 
% 244.34/50.79  | End of split
% 244.34/50.79  | 
% 244.34/50.79  End of proof
% 244.34/50.79  
% 244.34/50.79  Sub-proof #1616 shows that the following formulas are inconsistent:
% 244.34/50.79  ----------------------------------------------------------------
% 244.34/50.79    (1)   ~ (all_52_3 = e0)
% 244.34/50.79    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.34/50.79             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.34/50.79           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 244.34/50.79           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.34/50.79           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 244.34/50.79           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.34/50.79           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.34/50.80    (3)  op(e0, e3) = all_52_3
% 244.34/50.80    (4)   ~ (all_52_8 = e1)
% 244.34/50.80    (5)  op(e3, e1) = all_52_8
% 244.34/50.80    (6)  all_56_11 = e0
% 244.34/50.80    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.80  
% 244.34/50.80  Begin of proof
% 244.34/50.80  | 
% 244.34/50.80  | BETA: splitting (2) gives:
% 244.34/50.80  | 
% 244.34/50.80  | Case 1:
% 244.34/50.80  | | 
% 244.34/50.80  | |   (8)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.34/50.80  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.34/50.80  | |        op(e1, e3) = e1
% 244.34/50.80  | | 
% 244.34/50.80  | | ALPHA: (8) implies:
% 244.34/50.80  | |   (9)  op(e3, e1) = e1
% 244.34/50.80  | | 
% 244.34/50.80  | | REF_CLOSE: (4), (5), (7), (9) are inconsistent by sub-proof #2309.
% 244.34/50.80  | | 
% 244.34/50.80  | Case 2:
% 244.34/50.80  | | 
% 244.34/50.80  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.34/50.80  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 244.34/50.80  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.34/50.80  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.34/50.80  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.34/50.80  | | 
% 244.34/50.80  | | REF_CLOSE: (1), (3), (6), (7), (10) are inconsistent by sub-proof #1617.
% 244.34/50.80  | | 
% 244.34/50.80  | End of split
% 244.34/50.80  | 
% 244.34/50.80  End of proof
% 244.34/50.80  
% 244.34/50.80  Sub-proof #1617 shows that the following formulas are inconsistent:
% 244.34/50.80  ----------------------------------------------------------------
% 244.34/50.80    (1)   ~ (all_52_3 = e0)
% 244.34/50.80    (2)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.34/50.80             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.34/50.80           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 244.34/50.80           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.34/50.80           op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.34/50.80    (3)  op(e0, e3) = all_52_3
% 244.34/50.80    (4)  all_56_11 = e0
% 244.34/50.80    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.80  
% 244.34/50.80  Begin of proof
% 244.34/50.80  | 
% 244.34/50.80  | BETA: splitting (2) gives:
% 244.34/50.80  | 
% 244.34/50.80  | Case 1:
% 244.34/50.80  | | 
% 244.34/50.80  | |   (6)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.34/50.80  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.34/50.80  | |        op(e0, e3) = e3
% 244.34/50.80  | | 
% 244.34/50.80  | | ALPHA: (6) implies:
% 244.34/50.80  | |   (7)   ~ (all_56_11 = e0)
% 244.34/50.80  | | 
% 244.34/50.80  | | REDUCE: (4), (7) imply:
% 244.34/50.80  | |   (8)  $false
% 244.34/50.80  | | 
% 244.34/50.80  | | CLOSE: (8) is inconsistent.
% 244.34/50.80  | | 
% 244.34/50.80  | Case 2:
% 244.34/50.80  | | 
% 244.34/50.80  | |   (9)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.34/50.80  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 244.34/50.80  | |        op(e0, e3) = e0
% 244.34/50.80  | | 
% 244.34/50.80  | | ALPHA: (9) implies:
% 244.34/50.80  | |   (10)  op(e0, e3) = e0
% 244.34/50.80  | | 
% 244.34/50.80  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2331.
% 244.34/50.80  | | 
% 244.34/50.80  | End of split
% 244.34/50.80  | 
% 244.34/50.80  End of proof
% 244.34/50.80  
% 244.34/50.80  Sub-proof #1618 shows that the following formulas are inconsistent:
% 244.34/50.80  ----------------------------------------------------------------
% 244.34/50.80    (1)   ~ (e3 = e0)
% 244.34/50.80    (2)   ~ (e2 = e0)
% 244.34/50.80    (3)  all_58_9 = e0
% 244.34/50.80    (4)   ~ (e3 = e1)
% 244.34/50.80    (5)   ~ (e3 = e2)
% 244.34/50.80    (6)  all_58_15 = e1
% 244.34/50.80    (7)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.34/50.80         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.34/50.80    (8)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.34/50.80         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.34/50.80    (9)  all_58_10 = e1
% 244.34/50.80    (10)   ~ (e2 = e1)
% 244.34/50.80  
% 244.34/50.80  Begin of proof
% 244.34/50.80  | 
% 244.34/50.80  | BETA: splitting (8) gives:
% 244.34/50.80  | 
% 244.34/50.80  | Case 1:
% 244.34/50.80  | | 
% 244.34/50.80  | |   (11)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 244.34/50.80  | |           e2)
% 244.34/50.80  | | 
% 244.34/50.80  | | BETA: splitting (11) gives:
% 244.34/50.80  | | 
% 244.34/50.80  | | Case 1:
% 244.34/50.80  | | | 
% 244.34/50.80  | | |   (12)  all_58_9 = e2 & op(e3, e0) = e2
% 244.34/50.80  | | | 
% 244.34/50.80  | | | ALPHA: (12) implies:
% 244.34/50.80  | | |   (13)  all_58_9 = e2
% 244.34/50.80  | | | 
% 244.34/50.80  | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #1660.
% 244.34/50.80  | | | 
% 244.34/50.80  | | Case 2:
% 244.34/50.80  | | | 
% 244.34/50.80  | | |   (14)  all_58_10 = e2 & op(e2, e0) = e2
% 244.34/50.80  | | | 
% 244.34/50.80  | | | REF_CLOSE: (9), (10), (14) are inconsistent by sub-proof #1622.
% 244.34/50.80  | | | 
% 244.34/50.80  | | End of split
% 244.34/50.80  | | 
% 244.34/50.80  | Case 2:
% 244.34/50.80  | | 
% 244.34/50.80  | |   (15)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.34/50.80  | |           e2)
% 244.34/50.80  | | 
% 244.34/50.80  | | BETA: splitting (15) gives:
% 244.34/50.80  | | 
% 244.34/50.80  | | Case 1:
% 244.34/50.80  | | | 
% 244.34/50.80  | | |   (16)  all_58_11 = e2 & op(e1, e0) = e2
% 244.34/50.80  | | | 
% 244.34/50.80  | | | ALPHA: (16) implies:
% 244.34/50.80  | | |   (17)  all_58_11 = e2
% 244.34/50.80  | | | 
% 244.34/50.80  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (17) are inconsistent by
% 244.34/50.80  | | |            sub-proof #1619.
% 244.34/50.80  | | | 
% 244.34/50.80  | | Case 2:
% 244.34/50.80  | | | 
% 244.34/50.80  | | |   (18)  all_58_15 = e2 & op(e0, e0) = e2
% 244.34/50.80  | | | 
% 244.34/50.80  | | | REF_CLOSE: (6), (10), (18) are inconsistent by sub-proof #1917.
% 244.34/50.80  | | | 
% 244.34/50.80  | | End of split
% 244.34/50.80  | | 
% 244.34/50.80  | End of split
% 244.34/50.80  | 
% 244.34/50.80  End of proof
% 244.34/50.80  
% 244.34/50.80  Sub-proof #1619 shows that the following formulas are inconsistent:
% 244.34/50.80  ----------------------------------------------------------------
% 244.34/50.80    (1)   ~ (e3 = e0)
% 244.34/50.80    (2)  all_58_9 = e0
% 244.34/50.80    (3)   ~ (e3 = e1)
% 244.34/50.80    (4)   ~ (e3 = e2)
% 244.34/50.80    (5)  all_58_15 = e1
% 244.34/50.80    (6)  all_58_11 = e2
% 244.34/50.80    (7)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.34/50.80         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.34/50.80    (8)  all_58_10 = e1
% 244.34/50.80  
% 244.34/50.80  Begin of proof
% 244.34/50.80  | 
% 244.34/50.80  | BETA: splitting (7) gives:
% 244.34/50.80  | 
% 244.34/50.80  | Case 1:
% 244.34/50.80  | | 
% 244.34/50.80  | |   (9)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 244.34/50.80  | |          e3)
% 244.34/50.80  | | 
% 244.34/50.80  | | BETA: splitting (9) gives:
% 244.34/50.80  | | 
% 244.34/50.80  | | Case 1:
% 244.34/50.80  | | | 
% 244.34/50.80  | | |   (10)  all_58_9 = e3 & op(e3, e0) = e3
% 244.34/50.80  | | | 
% 244.34/50.80  | | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #1621.
% 244.34/50.80  | | | 
% 244.34/50.80  | | Case 2:
% 244.34/50.80  | | | 
% 244.34/50.80  | | |   (11)  all_58_10 = e3 & op(e2, e0) = e3
% 244.34/50.80  | | | 
% 244.34/50.80  | | | REF_CLOSE: (3), (8), (11) are inconsistent by sub-proof #1620.
% 244.34/50.80  | | | 
% 244.34/50.80  | | End of split
% 244.34/50.80  | | 
% 244.34/50.80  | Case 2:
% 244.34/50.80  | | 
% 244.34/50.80  | |   (12)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.34/50.80  | |           e3)
% 244.34/50.80  | | 
% 244.34/50.80  | | BETA: splitting (12) gives:
% 244.34/50.80  | | 
% 244.34/50.80  | | Case 1:
% 244.34/50.80  | | | 
% 244.34/50.80  | | |   (13)  all_58_11 = e3 & op(e1, e0) = e3
% 244.34/50.80  | | | 
% 244.34/50.80  | | | REF_CLOSE: (4), (6), (13) are inconsistent by sub-proof #2108.
% 244.34/50.80  | | | 
% 244.34/50.80  | | Case 2:
% 244.34/50.80  | | | 
% 244.34/50.80  | | |   (14)  all_58_15 = e3 & op(e0, e0) = e3
% 244.34/50.80  | | | 
% 244.34/50.80  | | | ALPHA: (14) implies:
% 244.34/50.80  | | |   (15)  all_58_15 = e3
% 244.34/50.80  | | | 
% 244.34/50.80  | | | REF_CLOSE: (3), (5), (15) are inconsistent by sub-proof #2249.
% 244.34/50.80  | | | 
% 244.34/50.80  | | End of split
% 244.34/50.80  | | 
% 244.34/50.80  | End of split
% 244.34/50.80  | 
% 244.34/50.80  End of proof
% 244.34/50.80  
% 244.34/50.80  Sub-proof #1620 shows that the following formulas are inconsistent:
% 244.34/50.80  ----------------------------------------------------------------
% 244.34/50.80    (1)  all_58_10 = e3 & op(e2, e0) = e3
% 244.34/50.80    (2)  all_58_10 = e1
% 244.34/50.80    (3)   ~ (e3 = e1)
% 244.34/50.80  
% 244.34/50.80  Begin of proof
% 244.34/50.80  | 
% 244.34/50.80  | ALPHA: (1) implies:
% 244.34/50.80  |   (4)  all_58_10 = e3
% 244.34/50.80  | 
% 244.34/50.80  | COMBINE_EQS: (2), (4) imply:
% 244.34/50.80  |   (5)  e3 = e1
% 244.34/50.81  | 
% 244.34/50.81  | REDUCE: (3), (5) imply:
% 244.34/50.81  |   (6)  $false
% 244.34/50.81  | 
% 244.34/50.81  | CLOSE: (6) is inconsistent.
% 244.34/50.81  | 
% 244.34/50.81  End of proof
% 244.34/50.81  
% 244.34/50.81  Sub-proof #1621 shows that the following formulas are inconsistent:
% 244.34/50.81  ----------------------------------------------------------------
% 244.34/50.81    (1)  all_58_9 = e3 & op(e3, e0) = e3
% 244.34/50.81    (2)  all_58_9 = e0
% 244.34/50.81    (3)   ~ (e3 = e0)
% 244.34/50.81  
% 244.34/50.81  Begin of proof
% 244.34/50.81  | 
% 244.34/50.81  | ALPHA: (1) implies:
% 244.34/50.81  |   (4)  all_58_9 = e3
% 244.34/50.81  | 
% 244.34/50.81  | COMBINE_EQS: (2), (4) imply:
% 244.34/50.81  |   (5)  e3 = e0
% 244.34/50.81  | 
% 244.34/50.81  | REDUCE: (3), (5) imply:
% 244.34/50.81  |   (6)  $false
% 244.34/50.81  | 
% 244.34/50.81  | CLOSE: (6) is inconsistent.
% 244.34/50.81  | 
% 244.34/50.81  End of proof
% 244.34/50.81  
% 244.34/50.81  Sub-proof #1622 shows that the following formulas are inconsistent:
% 244.34/50.81  ----------------------------------------------------------------
% 244.34/50.81    (1)  all_58_10 = e2 & op(e2, e0) = e2
% 244.34/50.81    (2)  all_58_10 = e1
% 244.34/50.81    (3)   ~ (e2 = e1)
% 244.34/50.81  
% 244.34/50.81  Begin of proof
% 244.34/50.81  | 
% 244.34/50.81  | ALPHA: (1) implies:
% 244.34/50.81  |   (4)  all_58_10 = e2
% 244.34/50.81  | 
% 244.34/50.81  | COMBINE_EQS: (2), (4) imply:
% 244.34/50.81  |   (5)  e2 = e1
% 244.34/50.81  | 
% 244.34/50.81  | REDUCE: (3), (5) imply:
% 244.34/50.81  |   (6)  $false
% 244.34/50.81  | 
% 244.34/50.81  | CLOSE: (6) is inconsistent.
% 244.34/50.81  | 
% 244.34/50.81  End of proof
% 244.34/50.81  
% 244.34/50.81  Sub-proof #1623 shows that the following formulas are inconsistent:
% 244.34/50.81  ----------------------------------------------------------------
% 244.34/50.81    (1)   ~ (e2 = e0)
% 244.34/50.81    (2)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.34/50.81         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.34/50.81    (3)   ~ (e3 = e1)
% 244.34/50.81    (4)   ~ (e3 = e2)
% 244.34/50.81    (5)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 244.34/50.81         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 244.34/50.81    (6)  all_58_4 = e1
% 244.34/50.81    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.81    (8)  all_58_14 = e3
% 244.34/50.81    (9)  e1 = e0
% 244.34/50.81    (10)  op(e1, e1) = e0
% 244.34/50.81    (11)   ~ (e1 = e0)
% 244.34/50.81    (12)   ~ (e2 = e1)
% 244.34/50.81  
% 244.34/50.81  Begin of proof
% 244.34/50.81  | 
% 244.34/50.81  | SIMP: (9) implies:
% 244.34/50.81  |   (13)  e1 = e0
% 244.34/50.81  | 
% 244.34/50.81  | COMBINE_EQS: (6), (13) imply:
% 244.34/50.81  |   (14)  all_58_4 = e0
% 244.34/50.81  | 
% 244.34/50.81  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (14) are
% 244.34/50.81  |            inconsistent by sub-proof #1663.
% 244.34/50.81  | 
% 244.34/50.81  End of proof
% 244.34/50.81  
% 244.34/50.81  Sub-proof #1624 shows that the following formulas are inconsistent:
% 244.34/50.81  ----------------------------------------------------------------
% 244.34/50.81    (1)   ~ (e3 = e0)
% 244.34/50.81    (2)  e3 = e1
% 244.34/50.81    (3)  all_58_1 = e3
% 244.34/50.81    (4)  op(e1, e2) = e1
% 244.34/50.81    (5)   ~ (e2 = e0)
% 244.34/50.81    (6)  op(e1, e2) = all_52_6
% 244.34/50.81    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.34/50.81         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.34/50.81    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.34/50.81         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.34/50.81    (9)   ~ (e3 = e1)
% 244.34/50.81    (10)  op(e2, e2) = e0
% 244.34/50.81    (11)   ~ (e3 = e2)
% 244.34/50.81    (12)  all_58_7 = e1
% 244.34/50.81    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.81    (14)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.34/50.81          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.34/50.81    (15)   ~ (e1 = e0)
% 244.34/50.81    (16)   ~ (e2 = e1)
% 244.34/50.81  
% 244.34/50.81  Begin of proof
% 244.34/50.81  | 
% 244.34/50.81  | SIMP: (2) implies:
% 244.34/50.81  |   (17)  e3 = e1
% 244.34/50.81  | 
% 244.34/50.81  | COMBINE_EQS: (3), (17) imply:
% 244.34/50.81  |   (18)  all_58_1 = e1
% 244.34/50.81  | 
% 244.34/50.81  | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 244.34/50.81  |            (15), (16), (18) are inconsistent by sub-proof #1714.
% 244.34/50.81  | 
% 244.34/50.81  End of proof
% 244.34/50.81  
% 244.34/50.81  Sub-proof #1625 shows that the following formulas are inconsistent:
% 244.34/50.81  ----------------------------------------------------------------
% 244.34/50.81    (1)  all_54_13 = all_52_7
% 244.34/50.81    (2)  op(e0, e2) = e2
% 244.34/50.81    (3)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.34/50.81    (4)   ~ (all_52_7 = e1)
% 244.34/50.81    (5)  op(e0, e2) = all_56_15
% 244.34/50.81    (6)  op(e0, e2) = all_52_7
% 244.34/50.81    (7)   ~ (all_52_7 = e0)
% 244.34/50.81    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.81    (9)  op(e0, all_56_15) = e0
% 244.34/50.81  
% 244.34/50.81  Begin of proof
% 244.34/50.81  | 
% 244.34/50.81  | GROUND_INST: instantiating (8) with e2, all_56_15, e2, e0, simplifying with
% 244.34/50.81  |              (2), (5) gives:
% 244.34/50.81  |   (10)  all_56_15 = e2
% 244.34/50.81  | 
% 244.34/50.81  | REDUCE: (9), (10) imply:
% 244.34/50.81  |   (11)  op(e0, e2) = e0
% 244.34/50.81  | 
% 244.34/50.81  | REF_CLOSE: (1), (3), (4), (6), (7), (8), (11) are inconsistent by sub-proof
% 244.34/50.81  |            #1965.
% 244.34/50.81  | 
% 244.34/50.81  End of proof
% 244.34/50.81  
% 244.34/50.81  Sub-proof #1626 shows that the following formulas are inconsistent:
% 244.34/50.81  ----------------------------------------------------------------
% 244.34/50.81    (1)   ~ (e3 = e0)
% 244.34/50.81    (2)  op(e1, e1) = all_6_2
% 244.34/50.81    (3)   ~ (all_6_2 = e3)
% 244.34/50.81    (4)  op(e3, e1) = all_52_8
% 244.34/50.81    (5)  op(e2, e1) = all_52_9
% 244.34/50.81    (6)  op(e0, e1) = e0
% 244.34/50.81    (7)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.34/50.81         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.34/50.81    (8)   ~ (all_52_9 = e3)
% 244.34/50.81    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.81    (10)   ~ (all_52_8 = e3)
% 244.34/50.81  
% 244.34/50.81  Begin of proof
% 244.34/50.81  | 
% 244.34/50.81  | BETA: splitting (7) gives:
% 244.34/50.81  | 
% 244.34/50.81  | Case 1:
% 244.34/50.81  | | 
% 244.34/50.81  | |   (11)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 244.34/50.81  | |           e3)
% 244.34/50.81  | | 
% 244.34/50.81  | | REF_CLOSE: (4), (5), (8), (9), (10), (11) are inconsistent by sub-proof
% 244.34/50.81  | |            #1628.
% 244.34/50.81  | | 
% 244.34/50.81  | Case 2:
% 244.34/50.81  | | 
% 244.34/50.81  | |   (12)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 244.34/50.81  | |           e3)
% 244.34/50.81  | | 
% 244.34/50.81  | | REF_CLOSE: (1), (2), (3), (6), (9), (12) are inconsistent by sub-proof
% 244.34/50.81  | |            #1627.
% 244.34/50.81  | | 
% 244.34/50.81  | End of split
% 244.34/50.81  | 
% 244.34/50.81  End of proof
% 244.34/50.81  
% 244.34/50.81  Sub-proof #1627 shows that the following formulas are inconsistent:
% 244.34/50.81  ----------------------------------------------------------------
% 244.34/50.81    (1)   ~ (e3 = e0)
% 244.34/50.81    (2)  op(e1, e1) = all_6_2
% 244.34/50.81    (3)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.34/50.81    (4)   ~ (all_6_2 = e3)
% 244.34/50.81    (5)  op(e0, e1) = e0
% 244.34/50.81    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.81  
% 244.34/50.81  Begin of proof
% 244.34/50.81  | 
% 244.34/50.81  | BETA: splitting (3) gives:
% 244.34/50.81  | 
% 244.34/50.81  | Case 1:
% 244.34/50.81  | | 
% 244.34/50.81  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 244.34/50.81  | | 
% 244.34/50.81  | | REF_CLOSE: (2), (4), (6), (7) are inconsistent by sub-proof #2092.
% 244.34/50.81  | | 
% 244.34/50.81  | Case 2:
% 244.34/50.81  | | 
% 244.34/50.81  | |   (8)  all_58_14 = e3 & op(e0, e1) = e3
% 244.34/50.81  | | 
% 244.34/50.81  | | ALPHA: (8) implies:
% 244.34/50.81  | |   (9)  op(e0, e1) = e3
% 244.34/50.81  | | 
% 244.34/50.81  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #2164.
% 244.34/50.81  | | 
% 244.34/50.81  | End of split
% 244.34/50.81  | 
% 244.34/50.81  End of proof
% 244.34/50.81  
% 244.34/50.81  Sub-proof #1628 shows that the following formulas are inconsistent:
% 244.34/50.81  ----------------------------------------------------------------
% 244.34/50.81    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 244.34/50.81    (2)  op(e3, e1) = all_52_8
% 244.34/50.81    (3)  op(e2, e1) = all_52_9
% 244.34/50.81    (4)   ~ (all_52_9 = e3)
% 244.34/50.81    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.81    (6)   ~ (all_52_8 = e3)
% 244.34/50.81  
% 244.34/50.81  Begin of proof
% 244.34/50.81  | 
% 244.34/50.81  | BETA: splitting (1) gives:
% 244.34/50.81  | 
% 244.34/50.81  | Case 1:
% 244.34/50.81  | | 
% 244.34/50.81  | |   (7)  all_58_4 = e3 & op(e3, e1) = e3
% 244.34/50.81  | | 
% 244.34/50.81  | | ALPHA: (7) implies:
% 244.34/50.81  | |   (8)  op(e3, e1) = e3
% 244.34/50.81  | | 
% 244.34/50.81  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2260.
% 244.34/50.81  | | 
% 244.34/50.81  | Case 2:
% 244.34/50.81  | | 
% 244.34/50.81  | |   (9)  all_58_5 = e3 & op(e2, e1) = e3
% 244.34/50.81  | | 
% 244.34/50.81  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #1822.
% 244.34/50.81  | | 
% 244.34/50.81  | End of split
% 244.34/50.81  | 
% 244.34/50.81  End of proof
% 244.34/50.81  
% 244.34/50.81  Sub-proof #1629 shows that the following formulas are inconsistent:
% 244.34/50.81  ----------------------------------------------------------------
% 244.34/50.81    (1)  all_58_6 = e3
% 244.34/50.81    (2)   ~ (e2 = e0)
% 244.34/50.81    (3)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.34/50.81         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.34/50.81    (4)   ~ (e3 = e2)
% 244.34/50.81    (5)  all_58_12 = e0
% 244.34/50.81    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.81    (7)  op(e3, e3) = e3
% 244.34/50.81    (8)  all_58_2 = e1
% 244.34/50.81    (9)   ~ (e2 = e1)
% 244.34/50.81  
% 244.34/50.81  Begin of proof
% 244.34/50.81  | 
% 244.34/50.82  | BETA: splitting (3) gives:
% 244.34/50.82  | 
% 244.34/50.82  | Case 1:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (10)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 244.34/50.82  | |           e2)
% 244.34/50.82  | | 
% 244.34/50.82  | | BETA: splitting (10) gives:
% 244.34/50.82  | | 
% 244.34/50.82  | | Case 1:
% 244.34/50.82  | | | 
% 244.34/50.82  | | |   (11)  all_58_0 = e2 & op(e3, e3) = e2
% 244.34/50.82  | | | 
% 244.34/50.82  | | | ALPHA: (11) implies:
% 244.34/50.82  | | |   (12)  op(e3, e3) = e2
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REF_CLOSE: (4), (6), (7), (12) are inconsistent by sub-proof #2194.
% 244.34/50.82  | | | 
% 244.34/50.82  | | Case 2:
% 244.34/50.82  | | | 
% 244.34/50.82  | | |   (13)  all_58_2 = e2 & op(e2, e3) = e2
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REF_CLOSE: (8), (9), (13) are inconsistent by sub-proof #1630.
% 244.34/50.82  | | | 
% 244.34/50.82  | | End of split
% 244.34/50.82  | | 
% 244.34/50.82  | Case 2:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (14)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 244.34/50.82  | |           e2)
% 244.34/50.82  | | 
% 244.34/50.82  | | BETA: splitting (14) gives:
% 244.34/50.82  | | 
% 244.34/50.82  | | Case 1:
% 244.34/50.82  | | | 
% 244.34/50.82  | | |   (15)  all_58_6 = e2 & op(e1, e3) = e2
% 244.34/50.82  | | | 
% 244.34/50.82  | | | ALPHA: (15) implies:
% 244.34/50.82  | | |   (16)  all_58_6 = e2
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REF_CLOSE: (1), (4), (16) are inconsistent by sub-proof #2024.
% 244.34/50.82  | | | 
% 244.34/50.82  | | Case 2:
% 244.34/50.82  | | | 
% 244.34/50.82  | | |   (17)  all_58_12 = e2 & op(e0, e3) = e2
% 244.34/50.82  | | | 
% 244.34/50.82  | | | ALPHA: (17) implies:
% 244.34/50.82  | | |   (18)  all_58_12 = e2
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REF_CLOSE: (2), (5), (18) are inconsistent by sub-proof #2083.
% 244.34/50.82  | | | 
% 244.34/50.82  | | End of split
% 244.34/50.82  | | 
% 244.34/50.82  | End of split
% 244.34/50.82  | 
% 244.34/50.82  End of proof
% 244.34/50.82  
% 244.34/50.82  Sub-proof #1630 shows that the following formulas are inconsistent:
% 244.34/50.82  ----------------------------------------------------------------
% 244.34/50.82    (1)  all_58_2 = e2 & op(e2, e3) = e2
% 244.34/50.82    (2)  all_58_2 = e1
% 244.34/50.82    (3)   ~ (e2 = e1)
% 244.34/50.82  
% 244.34/50.82  Begin of proof
% 244.34/50.82  | 
% 244.34/50.82  | ALPHA: (1) implies:
% 244.34/50.82  |   (4)  all_58_2 = e2
% 244.34/50.82  | 
% 244.34/50.82  | COMBINE_EQS: (2), (4) imply:
% 244.34/50.82  |   (5)  e2 = e1
% 244.34/50.82  | 
% 244.34/50.82  | REDUCE: (3), (5) imply:
% 244.34/50.82  |   (6)  $false
% 244.34/50.82  | 
% 244.34/50.82  | CLOSE: (6) is inconsistent.
% 244.34/50.82  | 
% 244.34/50.82  End of proof
% 244.34/50.82  
% 244.34/50.82  Sub-proof #1631 shows that the following formulas are inconsistent:
% 244.34/50.82  ----------------------------------------------------------------
% 244.34/50.82    (1)  op(e2, e0) = all_56_27
% 244.34/50.82    (2)  op(e2, e0) = all_14_1
% 244.34/50.82    (3)  op(e2, all_56_27) = e2
% 244.34/50.82    (4)  all_54_11 = all_52_14
% 244.34/50.82    (5)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 244.34/50.82    (6)  op(e2, e0) = e3
% 244.34/50.82    (7)   ~ (all_52_14 = e1)
% 244.34/50.82    (8)  ( ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) = all_48_1
% 244.34/50.82           & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e2, e0) =
% 244.34/50.82           all_48_1 & $i(all_48_1))
% 244.34/50.82    (9)   ~ (all_52_14 = e0)
% 244.34/50.82    (10)  op(e2, e3) = e1
% 244.34/50.82    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.82  
% 244.34/50.82  Begin of proof
% 244.34/50.82  | 
% 244.34/50.82  | BETA: splitting (8) gives:
% 244.34/50.82  | 
% 244.34/50.82  | Case 1:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (12)   ~ (all_48_0 = e1) & op(all_48_1, e2) = all_48_0 & op(e2, e0) =
% 244.34/50.82  | |         all_48_1 & $i(all_48_0) & $i(all_48_1)
% 244.34/50.82  | | 
% 244.34/50.82  | | ALPHA: (12) implies:
% 244.34/50.82  | |   (13)  op(e2, e0) = all_48_1
% 244.34/50.82  | | 
% 244.34/50.82  | | BETA: splitting (5) gives:
% 244.34/50.82  | | 
% 244.34/50.82  | | Case 1:
% 244.34/50.82  | | | 
% 244.34/50.82  | | |   (14)  all_54_11 = e2
% 244.34/50.82  | | | 
% 244.34/50.82  | | | COMBINE_EQS: (4), (14) imply:
% 244.34/50.82  | | |   (15)  all_52_14 = e2
% 244.34/50.82  | | | 
% 244.34/50.82  | | | SIMP: (15) implies:
% 244.34/50.82  | | |   (16)  all_52_14 = e2
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REDUCE: (7), (16) imply:
% 244.34/50.82  | | |   (17)   ~ (e2 = e1)
% 244.34/50.82  | | | 
% 244.34/50.82  | | | GROUND_INST: instantiating (11) with all_48_1, all_56_27, e0, e2,
% 244.34/50.82  | | |              simplifying with (1), (13) gives:
% 244.34/50.82  | | |   (18)  all_56_27 = all_48_1
% 244.34/50.82  | | | 
% 244.34/50.82  | | | GROUND_INST: instantiating (11) with all_14_1, all_56_27, e0, e2,
% 244.34/50.82  | | |              simplifying with (1), (2) gives:
% 244.34/50.82  | | |   (19)  all_56_27 = all_14_1
% 244.34/50.82  | | | 
% 244.34/50.82  | | | GROUND_INST: instantiating (11) with e3, all_56_27, e0, e2, simplifying
% 244.34/50.82  | | |              with (1), (6) gives:
% 244.34/50.82  | | |   (20)  all_56_27 = e3
% 244.34/50.82  | | | 
% 244.34/50.82  | | | COMBINE_EQS: (18), (19) imply:
% 244.34/50.82  | | |   (21)  all_48_1 = all_14_1
% 244.34/50.82  | | | 
% 244.34/50.82  | | | COMBINE_EQS: (18), (20) imply:
% 244.34/50.82  | | |   (22)  all_48_1 = e3
% 244.34/50.82  | | | 
% 244.34/50.82  | | | COMBINE_EQS: (21), (22) imply:
% 244.34/50.82  | | |   (23)  all_14_1 = e3
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REDUCE: (3), (20) imply:
% 244.34/50.82  | | |   (24)  op(e2, e3) = e2
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REF_CLOSE: (10), (11), (17), (24) are inconsistent by sub-proof #1633.
% 244.34/50.82  | | | 
% 244.34/50.82  | | Case 2:
% 244.34/50.82  | | | 
% 244.34/50.82  | | |   (25)  all_54_11 = e1 | all_54_11 = e0
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REF_CLOSE: (4), (7), (9), (25) are inconsistent by sub-proof #2174.
% 244.34/50.82  | | | 
% 244.34/50.82  | | End of split
% 244.34/50.82  | | 
% 244.34/50.82  | Case 2:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (26)   ~ (all_48_1 = e3) & op(e2, e0) = all_48_1 & $i(all_48_1)
% 244.34/50.82  | | 
% 244.34/50.82  | | ALPHA: (26) implies:
% 244.34/50.82  | |   (27)   ~ (all_48_1 = e3)
% 244.34/50.82  | |   (28)  op(e2, e0) = all_48_1
% 244.34/50.82  | | 
% 244.34/50.82  | | REF_CLOSE: (2), (6), (11), (27), (28) are inconsistent by sub-proof #1632.
% 244.34/50.82  | | 
% 244.34/50.82  | End of split
% 244.34/50.82  | 
% 244.34/50.82  End of proof
% 244.34/50.82  
% 244.34/50.82  Sub-proof #1632 shows that the following formulas are inconsistent:
% 244.34/50.82  ----------------------------------------------------------------
% 244.34/50.82    (1)  op(e2, e0) = all_14_1
% 244.34/50.82    (2)   ~ (all_48_1 = e3)
% 244.34/50.82    (3)  op(e2, e0) = e3
% 244.34/50.82    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.82    (5)  op(e2, e0) = all_48_1
% 244.34/50.82  
% 244.34/50.82  Begin of proof
% 244.34/50.82  | 
% 244.34/50.82  | GROUND_INST: instantiating (4) with all_14_1, all_48_1, e0, e2, simplifying
% 244.34/50.82  |              with (1), (5) gives:
% 244.34/50.82  |   (6)  all_48_1 = all_14_1
% 244.34/50.82  | 
% 244.34/50.82  | GROUND_INST: instantiating (4) with e3, all_48_1, e0, e2, simplifying with
% 244.34/50.82  |              (3), (5) gives:
% 244.34/50.82  |   (7)  all_48_1 = e3
% 244.34/50.82  | 
% 244.34/50.82  | COMBINE_EQS: (6), (7) imply:
% 244.34/50.82  |   (8)  all_14_1 = e3
% 244.34/50.82  | 
% 244.34/50.82  | REDUCE: (2), (7) imply:
% 244.34/50.82  |   (9)  $false
% 244.34/50.82  | 
% 244.34/50.82  | CLOSE: (9) is inconsistent.
% 244.34/50.82  | 
% 244.34/50.82  End of proof
% 244.34/50.82  
% 244.34/50.82  Sub-proof #1633 shows that the following formulas are inconsistent:
% 244.34/50.82  ----------------------------------------------------------------
% 244.34/50.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.82    (2)  op(e2, e3) = e2
% 244.34/50.82    (3)  op(e2, e3) = e1
% 244.34/50.82    (4)   ~ (e2 = e1)
% 244.34/50.82  
% 244.34/50.82  Begin of proof
% 244.34/50.82  | 
% 244.34/50.82  | GROUND_INST: instantiating (1) with e1, e2, e3, e2, simplifying with (2), (3)
% 244.34/50.82  |              gives:
% 244.34/50.82  |   (5)  e2 = e1
% 244.34/50.82  | 
% 244.34/50.82  | REDUCE: (4), (5) imply:
% 244.34/50.82  |   (6)  $false
% 244.34/50.82  | 
% 244.34/50.82  | CLOSE: (6) is inconsistent.
% 244.34/50.82  | 
% 244.34/50.82  End of proof
% 244.34/50.82  
% 244.34/50.82  Sub-proof #1634 shows that the following formulas are inconsistent:
% 244.34/50.82  ----------------------------------------------------------------
% 244.34/50.82    (1)  op(e0, e0) = e1
% 244.34/50.82    (2)   ~ (e3 = e0)
% 244.34/50.82    (3)   ~ (e2 = e0)
% 244.34/50.82    (4)  op(e0, e1) = e3
% 244.34/50.82    (5)  op(e0, e2) = e2
% 244.34/50.82    (6)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.34/50.82             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.34/50.82               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.34/50.82               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.34/50.82    (7)  all_58_12 = e3
% 244.34/50.82    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.82    (9)   ~ (e1 = e0)
% 244.34/50.82  
% 244.34/50.82  Begin of proof
% 244.34/50.82  | 
% 244.34/50.82  | BETA: splitting (6) gives:
% 244.34/50.82  | 
% 244.34/50.82  | Case 1:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (10)  all_58_15 = e0 & op(e0, e0) = e0
% 244.34/50.82  | | 
% 244.34/50.82  | | ALPHA: (10) implies:
% 244.34/50.82  | |   (11)  op(e0, e0) = e0
% 244.34/50.82  | | 
% 244.34/50.82  | | REF_CLOSE: (1), (8), (9), (11) are inconsistent by sub-proof #2274.
% 244.34/50.82  | | 
% 244.34/50.82  | Case 2:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (12)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 244.34/50.82  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 244.34/50.82  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 244.34/50.82  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 244.34/50.82  | | 
% 244.34/50.82  | | ALPHA: (12) implies:
% 244.34/50.82  | |   (13)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.34/50.82  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.34/50.82  | | 
% 244.34/50.82  | | BETA: splitting (13) gives:
% 244.34/50.82  | | 
% 244.34/50.82  | | Case 1:
% 244.34/50.82  | | | 
% 244.34/50.82  | | |   (14)  all_58_12 = e0 & op(e0, e3) = e0
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #1641.
% 244.34/50.82  | | | 
% 244.34/50.82  | | Case 2:
% 244.34/50.82  | | | 
% 244.34/50.82  | | |   (15)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 244.34/50.82  | | |           = e0)
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REF_CLOSE: (2), (3), (4), (5), (8), (15) are inconsistent by sub-proof
% 244.34/50.82  | | |            #1635.
% 244.34/50.82  | | | 
% 244.34/50.82  | | End of split
% 244.34/50.82  | | 
% 244.34/50.82  | End of split
% 244.34/50.82  | 
% 244.34/50.82  End of proof
% 244.34/50.82  
% 244.34/50.82  Sub-proof #1635 shows that the following formulas are inconsistent:
% 244.34/50.82  ----------------------------------------------------------------
% 244.34/50.82    (1)   ~ (e3 = e0)
% 244.34/50.82    (2)   ~ (e2 = e0)
% 244.34/50.82    (3)  op(e0, e1) = e3
% 244.34/50.82    (4)  op(e0, e2) = e2
% 244.34/50.82    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.82    (6)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.34/50.82  
% 244.34/50.82  Begin of proof
% 244.34/50.82  | 
% 244.34/50.82  | BETA: splitting (6) gives:
% 244.34/50.82  | 
% 244.34/50.82  | Case 1:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (7)  all_58_13 = e0 & op(e0, e2) = e0
% 244.34/50.82  | | 
% 244.34/50.82  | | ALPHA: (7) implies:
% 244.34/50.82  | |   (8)  op(e0, e2) = e0
% 244.34/50.82  | | 
% 244.34/50.82  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2132.
% 244.34/50.82  | | 
% 244.34/50.82  | Case 2:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 244.34/50.82  | | 
% 244.34/50.82  | | ALPHA: (9) implies:
% 244.34/50.82  | |   (10)  op(e0, e1) = e0
% 244.34/50.82  | | 
% 244.34/50.82  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2164.
% 244.34/50.82  | | 
% 244.34/50.82  | End of split
% 244.34/50.82  | 
% 244.34/50.82  End of proof
% 244.34/50.82  
% 244.34/50.82  Sub-proof #1636 shows that the following formulas are inconsistent:
% 244.34/50.82  ----------------------------------------------------------------
% 244.34/50.82    (1)  op(e0, e0) = e1
% 244.34/50.82    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.34/50.82         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.34/50.82    (3)   ~ (e3 = e0)
% 244.34/50.82    (4)   ~ (e2 = e0)
% 244.34/50.82    (5)  all_58_14 = e2
% 244.34/50.82    (6)   ~ (all_52_7 = e3)
% 244.34/50.82    (7)  op(e0, e2) = e2
% 244.34/50.82    (8)   ~ (e3 = e1)
% 244.34/50.82    (9)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.34/50.82             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.34/50.82               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.34/50.82               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.34/50.82    (10)   ~ (e3 = e2)
% 244.34/50.82    (11)  all_58_15 = e1
% 244.34/50.82    (12)  op(e0, e2) = all_52_7
% 244.34/50.82    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.82    (14)   ~ (e1 = e0)
% 244.34/50.82  
% 244.34/50.82  Begin of proof
% 244.34/50.82  | 
% 244.34/50.82  | BETA: splitting (9) gives:
% 244.34/50.82  | 
% 244.34/50.82  | Case 1:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (15)  all_58_15 = e0 & op(e0, e0) = e0
% 244.34/50.82  | | 
% 244.34/50.82  | | ALPHA: (15) implies:
% 244.34/50.82  | |   (16)  op(e0, e0) = e0
% 244.34/50.82  | | 
% 244.34/50.82  | | REF_CLOSE: (1), (13), (14), (16) are inconsistent by sub-proof #2274.
% 244.34/50.82  | | 
% 244.34/50.82  | Case 2:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (17)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 244.34/50.82  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 244.34/50.82  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 244.34/50.82  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 244.34/50.82  | | 
% 244.34/50.82  | | ALPHA: (17) implies:
% 244.34/50.82  | |   (18)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.34/50.82  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.34/50.82  | | 
% 244.34/50.82  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (18)
% 244.34/50.82  | |            are inconsistent by sub-proof #1637.
% 244.34/50.82  | | 
% 244.34/50.82  | End of split
% 244.34/50.82  | 
% 244.34/50.82  End of proof
% 244.34/50.82  
% 244.34/50.82  Sub-proof #1637 shows that the following formulas are inconsistent:
% 244.34/50.82  ----------------------------------------------------------------
% 244.34/50.82    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.34/50.82         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.34/50.82    (2)   ~ (e3 = e0)
% 244.34/50.82    (3)   ~ (e2 = e0)
% 244.34/50.82    (4)  all_58_14 = e2
% 244.34/50.82    (5)   ~ (all_52_7 = e3)
% 244.34/50.82    (6)  op(e0, e2) = e2
% 244.34/50.82    (7)   ~ (e3 = e1)
% 244.34/50.82    (8)   ~ (e3 = e2)
% 244.34/50.82    (9)  all_58_15 = e1
% 244.34/50.82    (10)  op(e0, e2) = all_52_7
% 244.34/50.82    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.82    (12)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.34/50.82          | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.34/50.82  
% 244.34/50.82  Begin of proof
% 244.34/50.82  | 
% 244.34/50.82  | BETA: splitting (1) gives:
% 244.34/50.82  | 
% 244.34/50.82  | Case 1:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (13)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.34/50.82  | |           e3)
% 244.34/50.82  | | 
% 244.34/50.82  | | BETA: splitting (13) gives:
% 244.34/50.82  | | 
% 244.34/50.82  | | Case 1:
% 244.34/50.82  | | | 
% 244.34/50.82  | | |   (14)  all_58_12 = e3 & op(e0, e3) = e3
% 244.34/50.82  | | | 
% 244.34/50.82  | | | ALPHA: (14) implies:
% 244.34/50.82  | | |   (15)  all_58_12 = e3
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REF_CLOSE: (2), (3), (4), (6), (11), (12), (15) are inconsistent by
% 244.34/50.82  | | |            sub-proof #1639.
% 244.34/50.82  | | | 
% 244.34/50.82  | | Case 2:
% 244.34/50.82  | | | 
% 244.34/50.82  | | |   (16)  all_58_13 = e3 & op(e0, e2) = e3
% 244.34/50.82  | | | 
% 244.34/50.82  | | | REF_CLOSE: (5), (10), (11), (16) are inconsistent by sub-proof #1919.
% 244.34/50.82  | | | 
% 244.34/50.82  | | End of split
% 244.34/50.82  | | 
% 244.34/50.82  | Case 2:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (17)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.34/50.82  | |           e3)
% 244.34/50.82  | | 
% 244.34/50.82  | | REF_CLOSE: (4), (7), (8), (9), (17) are inconsistent by sub-proof #1638.
% 244.34/50.82  | | 
% 244.34/50.82  | End of split
% 244.34/50.82  | 
% 244.34/50.82  End of proof
% 244.34/50.82  
% 244.34/50.82  Sub-proof #1638 shows that the following formulas are inconsistent:
% 244.34/50.82  ----------------------------------------------------------------
% 244.34/50.82    (1)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.34/50.82    (2)  all_58_14 = e2
% 244.34/50.82    (3)   ~ (e3 = e1)
% 244.34/50.82    (4)   ~ (e3 = e2)
% 244.34/50.82    (5)  all_58_15 = e1
% 244.34/50.82  
% 244.34/50.82  Begin of proof
% 244.34/50.82  | 
% 244.34/50.82  | BETA: splitting (1) gives:
% 244.34/50.82  | 
% 244.34/50.82  | Case 1:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (6)  all_58_14 = e3 & op(e0, e1) = e3
% 244.34/50.82  | | 
% 244.34/50.82  | | ALPHA: (6) implies:
% 244.34/50.82  | |   (7)  all_58_14 = e3
% 244.34/50.82  | | 
% 244.34/50.82  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2117.
% 244.34/50.82  | | 
% 244.34/50.82  | Case 2:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (8)  all_58_15 = e3 & op(e0, e0) = e3
% 244.34/50.82  | | 
% 244.34/50.82  | | ALPHA: (8) implies:
% 244.34/50.82  | |   (9)  all_58_15 = e3
% 244.34/50.82  | | 
% 244.34/50.82  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #2249.
% 244.34/50.82  | | 
% 244.34/50.82  | End of split
% 244.34/50.82  | 
% 244.34/50.82  End of proof
% 244.34/50.82  
% 244.34/50.82  Sub-proof #1639 shows that the following formulas are inconsistent:
% 244.34/50.82  ----------------------------------------------------------------
% 244.34/50.82    (1)   ~ (e3 = e0)
% 244.34/50.82    (2)   ~ (e2 = e0)
% 244.34/50.82    (3)  all_58_14 = e2
% 244.34/50.82    (4)  op(e0, e2) = e2
% 244.34/50.82    (5)  all_58_12 = e3
% 244.34/50.82    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.82    (7)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 244.34/50.82         (all_58_14 = e0 & op(e0, e1) = e0)
% 244.34/50.82  
% 244.34/50.82  Begin of proof
% 244.34/50.82  | 
% 244.34/50.82  | BETA: splitting (7) gives:
% 244.34/50.82  | 
% 244.34/50.82  | Case 1:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (8)  all_58_12 = e0 & op(e0, e3) = e0
% 244.34/50.82  | | 
% 244.34/50.82  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #1641.
% 244.34/50.82  | | 
% 244.34/50.82  | Case 2:
% 244.34/50.82  | | 
% 244.34/50.82  | |   (9)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 244.34/50.82  | |          e0)
% 244.34/50.82  | | 
% 244.34/50.82  | | REF_CLOSE: (2), (3), (4), (6), (9) are inconsistent by sub-proof #1640.
% 244.34/50.82  | | 
% 244.34/50.82  | End of split
% 244.34/50.82  | 
% 244.34/50.82  End of proof
% 244.34/50.82  
% 244.34/50.82  Sub-proof #1640 shows that the following formulas are inconsistent:
% 244.34/50.82  ----------------------------------------------------------------
% 244.34/50.82    (1)   ~ (e2 = e0)
% 244.34/50.83    (2)  all_58_14 = e2
% 244.34/50.83    (3)  op(e0, e2) = e2
% 244.34/50.83    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.83    (5)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.34/50.83  
% 244.34/50.83  Begin of proof
% 244.34/50.83  | 
% 244.34/50.83  | BETA: splitting (5) gives:
% 244.34/50.83  | 
% 244.34/50.83  | Case 1:
% 244.34/50.83  | | 
% 244.34/50.83  | |   (6)  all_58_13 = e0 & op(e0, e2) = e0
% 244.34/50.83  | | 
% 244.34/50.83  | | ALPHA: (6) implies:
% 244.34/50.83  | |   (7)  op(e0, e2) = e0
% 244.34/50.83  | | 
% 244.34/50.83  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #2132.
% 244.34/50.83  | | 
% 244.34/50.83  | Case 2:
% 244.34/50.83  | | 
% 244.34/50.83  | |   (8)  all_58_14 = e0 & op(e0, e1) = e0
% 244.34/50.83  | | 
% 244.34/50.83  | | ALPHA: (8) implies:
% 244.34/50.83  | |   (9)  all_58_14 = e0
% 244.34/50.83  | | 
% 244.34/50.83  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #2114.
% 244.34/50.83  | | 
% 244.34/50.83  | End of split
% 244.34/50.83  | 
% 244.34/50.83  End of proof
% 244.34/50.83  
% 244.34/50.83  Sub-proof #1641 shows that the following formulas are inconsistent:
% 244.34/50.83  ----------------------------------------------------------------
% 244.34/50.83    (1)  all_58_12 = e0 & op(e0, e3) = e0
% 244.34/50.83    (2)  all_58_12 = e3
% 244.34/50.83    (3)   ~ (e3 = e0)
% 244.34/50.83  
% 244.34/50.83  Begin of proof
% 244.34/50.83  | 
% 244.34/50.83  | ALPHA: (1) implies:
% 244.34/50.83  |   (4)  all_58_12 = e0
% 244.34/50.83  | 
% 244.34/50.83  | COMBINE_EQS: (2), (4) imply:
% 244.34/50.83  |   (5)  e3 = e0
% 244.34/50.83  | 
% 244.34/50.83  | REDUCE: (3), (5) imply:
% 244.34/50.83  |   (6)  $false
% 244.34/50.83  | 
% 244.34/50.83  | CLOSE: (6) is inconsistent.
% 244.34/50.83  | 
% 244.34/50.83  End of proof
% 244.34/50.83  
% 244.34/50.83  Sub-proof #1642 shows that the following formulas are inconsistent:
% 244.34/50.83  ----------------------------------------------------------------
% 244.34/50.83    (1)  op(e3, e2) = e1
% 244.34/50.83    (2)  all_54_2 = e1 | all_54_2 = e0
% 244.34/50.83    (3)   ~ (all_52_8 = e0)
% 244.34/50.83    (4)  all_54_2 = all_52_8
% 244.34/50.83    (5)  op(e3, e2) = all_52_4
% 244.34/50.83    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.83    (7)   ~ (all_52_4 = all_52_8)
% 244.34/50.83  
% 244.34/50.83  Begin of proof
% 244.34/50.83  | 
% 244.34/50.83  | BETA: splitting (2) gives:
% 244.34/50.83  | 
% 244.34/50.83  | Case 1:
% 244.34/50.83  | | 
% 244.34/50.83  | |   (8)  all_54_2 = e1
% 244.34/50.83  | | 
% 244.34/50.83  | | COMBINE_EQS: (4), (8) imply:
% 244.34/50.83  | |   (9)  all_52_8 = e1
% 244.34/50.83  | | 
% 244.34/50.83  | | SIMP: (9) implies:
% 244.34/50.83  | |   (10)  all_52_8 = e1
% 244.34/50.83  | | 
% 244.34/50.83  | | REDUCE: (7), (10) imply:
% 244.34/50.83  | |   (11)   ~ (all_52_4 = e1)
% 244.34/50.83  | | 
% 244.34/50.83  | | REF_CLOSE: (1), (5), (6), (11) are inconsistent by sub-proof #2228.
% 244.34/50.83  | | 
% 244.34/50.83  | Case 2:
% 244.34/50.83  | | 
% 244.34/50.83  | |   (12)  all_54_2 = e0
% 244.34/50.83  | | 
% 244.34/50.83  | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #1643.
% 244.34/50.83  | | 
% 244.34/50.83  | End of split
% 244.34/50.83  | 
% 244.34/50.83  End of proof
% 244.34/50.83  
% 244.34/50.83  Sub-proof #1643 shows that the following formulas are inconsistent:
% 244.34/50.83  ----------------------------------------------------------------
% 244.34/50.83    (1)  all_54_2 = all_52_8
% 244.34/50.83    (2)  all_54_2 = e0
% 244.34/50.83    (3)   ~ (all_52_8 = e0)
% 244.34/50.83  
% 244.34/50.83  Begin of proof
% 244.34/50.83  | 
% 244.34/50.83  | COMBINE_EQS: (1), (2) imply:
% 244.34/50.83  |   (4)  all_52_8 = e0
% 244.34/50.83  | 
% 244.34/50.83  | SIMP: (4) implies:
% 244.34/50.83  |   (5)  all_52_8 = e0
% 244.34/50.83  | 
% 244.34/50.83  | REDUCE: (3), (5) imply:
% 244.34/50.83  |   (6)  $false
% 244.34/50.83  | 
% 244.34/50.83  | CLOSE: (6) is inconsistent.
% 244.34/50.83  | 
% 244.34/50.83  End of proof
% 244.34/50.83  
% 244.34/50.83  Sub-proof #1644 shows that the following formulas are inconsistent:
% 244.34/50.83  ----------------------------------------------------------------
% 244.34/50.83    (1)  all_58_1 = e1
% 244.34/50.83    (2)   ~ (e3 = e0)
% 244.34/50.83    (3)   ~ (e2 = e0)
% 244.34/50.83    (4)  all_58_15 = e3
% 244.34/50.83    (5)   ~ (e3 = e1)
% 244.34/50.83    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.34/50.83         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.34/50.83    (7)   ~ (e3 = e2)
% 244.34/50.83    (8)  all_58_15 = e1
% 244.34/50.83    (9)  op(e3, e3) = e2
% 244.34/50.83    (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.34/50.83          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.34/50.83    (11)   ~ (all_52_4 = e3)
% 244.34/50.83    (12)  op(e3, e2) = all_52_4
% 244.34/50.83    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.83    (14)   ~ (e1 = e0)
% 244.34/50.83    (15)  all_58_4 = e3
% 244.34/50.83  
% 244.34/50.83  Begin of proof
% 244.34/50.83  | 
% 244.34/50.83  | COMBINE_EQS: (4), (8) imply:
% 244.34/50.83  |   (16)  e3 = e1
% 244.34/50.83  | 
% 244.34/50.83  | SIMP: (16) implies:
% 244.34/50.83  |   (17)  e3 = e1
% 244.34/50.83  | 
% 244.34/50.83  | COMBINE_EQS: (15), (17) imply:
% 244.34/50.83  |   (18)  all_58_4 = e1
% 244.34/50.83  | 
% 244.34/50.83  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 244.34/50.83  |            (18) are inconsistent by sub-proof #1645.
% 244.34/50.83  | 
% 244.34/50.83  End of proof
% 244.34/50.83  
% 244.34/50.83  Sub-proof #1645 shows that the following formulas are inconsistent:
% 244.34/50.83  ----------------------------------------------------------------
% 244.34/50.83    (1)  all_58_1 = e1
% 244.34/50.83    (2)   ~ (e3 = e0)
% 244.34/50.83    (3)   ~ (e2 = e0)
% 244.34/50.83    (4)   ~ (e3 = e1)
% 244.34/50.83    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.34/50.83         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.34/50.83    (6)   ~ (e3 = e2)
% 244.34/50.83    (7)  all_58_4 = e1
% 244.34/50.83    (8)  op(e3, e3) = e2
% 244.34/50.83    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.34/50.83         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.34/50.83    (10)   ~ (all_52_4 = e3)
% 244.34/50.83    (11)  op(e3, e2) = all_52_4
% 244.34/50.83    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.83    (13)   ~ (e1 = e0)
% 244.34/50.83  
% 244.34/50.83  Begin of proof
% 244.34/50.83  | 
% 244.34/50.83  | BETA: splitting (5) gives:
% 244.34/50.83  | 
% 244.34/50.83  | Case 1:
% 244.34/50.83  | | 
% 244.34/50.83  | |   (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 244.34/50.83  | |           e3)
% 244.34/50.83  | | 
% 244.34/50.83  | | REF_CLOSE: (6), (8), (10), (11), (12), (14) are inconsistent by sub-proof
% 244.34/50.83  | |            #1959.
% 244.34/50.83  | | 
% 244.34/50.83  | Case 2:
% 244.34/50.83  | | 
% 244.34/50.83  | |   (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 244.34/50.83  | |           e3)
% 244.34/50.83  | | 
% 244.34/50.83  | | BETA: splitting (15) gives:
% 244.34/50.83  | | 
% 244.34/50.83  | | Case 1:
% 244.34/50.83  | | | 
% 244.34/50.83  | | |   (16)  all_58_4 = e3 & op(e3, e1) = e3
% 244.34/50.83  | | | 
% 244.34/50.83  | | | ALPHA: (16) implies:
% 244.34/50.83  | | |   (17)  all_58_4 = e3
% 244.34/50.83  | | | 
% 244.34/50.83  | | | REF_CLOSE: (4), (7), (17) are inconsistent by sub-proof #2184.
% 244.34/50.83  | | | 
% 244.34/50.83  | | Case 2:
% 244.34/50.83  | | | 
% 244.34/50.83  | | |   (18)  all_58_9 = e3 & op(e3, e0) = e3
% 244.34/50.83  | | | 
% 244.34/50.83  | | | ALPHA: (18) implies:
% 244.34/50.83  | | |   (19)  all_58_9 = e3
% 244.34/50.83  | | | 
% 244.34/50.83  | | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (12), (13), (19) are inconsistent
% 244.34/50.83  | | |            by sub-proof #1646.
% 244.34/50.83  | | | 
% 244.34/50.83  | | End of split
% 244.34/50.83  | | 
% 244.34/50.83  | End of split
% 244.34/50.83  | 
% 244.34/50.83  End of proof
% 244.34/50.83  
% 244.34/50.83  Sub-proof #1646 shows that the following formulas are inconsistent:
% 244.34/50.83  ----------------------------------------------------------------
% 244.34/50.83    (1)  all_58_1 = e1
% 244.34/50.83    (2)   ~ (e3 = e0)
% 244.34/50.83    (3)   ~ (e2 = e0)
% 244.34/50.83    (4)  all_58_9 = e3
% 244.34/50.83    (5)  all_58_4 = e1
% 244.34/50.83    (6)  op(e3, e3) = e2
% 244.34/50.83    (7)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.34/50.83         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.34/50.83    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.34/50.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.34/50.83    (9)   ~ (e1 = e0)
% 244.34/50.83  
% 244.34/50.83  Begin of proof
% 244.34/50.83  | 
% 244.34/50.83  | BETA: splitting (7) gives:
% 244.34/50.83  | 
% 244.34/50.83  | Case 1:
% 244.34/50.83  | | 
% 244.39/50.83  | |   (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 244.39/50.83  | |           e0)
% 244.39/50.83  | | 
% 244.39/50.83  | | REF_CLOSE: (1), (3), (6), (8), (9), (10) are inconsistent by sub-proof
% 244.39/50.83  | |            #1698.
% 244.39/50.83  | | 
% 244.39/50.83  | Case 2:
% 244.39/50.83  | | 
% 244.39/50.83  | |   (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 244.39/50.83  | |           e0)
% 244.39/50.83  | | 
% 244.39/50.83  | | BETA: splitting (11) gives:
% 244.39/50.83  | | 
% 244.39/50.83  | | Case 1:
% 244.39/50.83  | | | 
% 244.39/50.83  | | |   (12)  all_58_4 = e0 & op(e3, e1) = e0
% 244.39/50.83  | | | 
% 244.39/50.83  | | | ALPHA: (12) implies:
% 244.39/50.83  | | |   (13)  all_58_4 = e0
% 244.39/50.83  | | | 
% 244.39/50.83  | | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #1710.
% 244.39/50.83  | | | 
% 244.39/50.83  | | Case 2:
% 244.39/50.83  | | | 
% 244.39/50.83  | | |   (14)  all_58_9 = e0 & op(e3, e0) = e0
% 244.39/50.83  | | | 
% 244.39/50.83  | | | REF_CLOSE: (2), (4), (14) are inconsistent by sub-proof #2103.
% 244.39/50.83  | | | 
% 244.39/50.83  | | End of split
% 244.39/50.83  | | 
% 244.39/50.83  | End of split
% 244.39/50.83  | 
% 244.39/50.83  End of proof
% 244.39/50.83  
% 244.39/50.83  Sub-proof #1647 shows that the following formulas are inconsistent:
% 244.39/50.83  ----------------------------------------------------------------
% 244.39/50.83    (1)  all_58_14 = e3 & op(e0, e1) = e3
% 244.39/50.83    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.83    (3)  op(e0, e1) = all_52_11
% 244.39/50.83    (4)   ~ (all_52_11 = e3)
% 244.39/50.83  
% 244.39/50.83  Begin of proof
% 244.39/50.83  | 
% 244.39/50.83  | ALPHA: (1) implies:
% 244.39/50.83  |   (5)  op(e0, e1) = e3
% 244.39/50.83  | 
% 244.39/50.83  | GROUND_INST: instantiating (2) with all_52_11, e3, e1, e0, simplifying with
% 244.39/50.83  |              (3), (5) gives:
% 244.39/50.83  |   (6)  all_52_11 = e3
% 244.39/50.83  | 
% 244.39/50.83  | REDUCE: (4), (6) imply:
% 244.39/50.83  |   (7)  $false
% 244.39/50.83  | 
% 244.39/50.83  | CLOSE: (7) is inconsistent.
% 244.39/50.83  | 
% 244.39/50.83  End of proof
% 244.39/50.83  
% 244.39/50.83  Sub-proof #1648 shows that the following formulas are inconsistent:
% 244.39/50.83  ----------------------------------------------------------------
% 244.39/50.83    (1)   ~ (all_52_7 = e2)
% 244.39/50.83    (2)  all_54_13 = all_52_7
% 244.39/50.83    (3)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.39/50.83    (4)   ~ (all_52_7 = e1)
% 244.39/50.83    (5)   ~ (all_52_7 = e0)
% 244.39/50.83  
% 244.39/50.83  Begin of proof
% 244.39/50.83  | 
% 244.39/50.83  | BETA: splitting (3) gives:
% 244.39/50.83  | 
% 244.39/50.83  | Case 1:
% 244.39/50.83  | | 
% 244.39/50.83  | |   (6)  all_54_13 = e2
% 244.39/50.83  | | 
% 244.39/50.83  | | COMBINE_EQS: (2), (6) imply:
% 244.39/50.83  | |   (7)  all_52_7 = e2
% 244.39/50.83  | | 
% 244.39/50.83  | | REDUCE: (1), (7) imply:
% 244.39/50.83  | |   (8)  $false
% 244.39/50.83  | | 
% 244.39/50.83  | | CLOSE: (8) is inconsistent.
% 244.39/50.83  | | 
% 244.39/50.83  | Case 2:
% 244.39/50.83  | | 
% 244.39/50.83  | |   (9)  all_54_13 = e1 | all_54_13 = e0
% 244.39/50.83  | | 
% 244.39/50.83  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #1793.
% 244.39/50.83  | | 
% 244.39/50.83  | End of split
% 244.39/50.83  | 
% 244.39/50.83  End of proof
% 244.39/50.83  
% 244.39/50.83  Sub-proof #1649 shows that the following formulas are inconsistent:
% 244.39/50.83  ----------------------------------------------------------------
% 244.39/50.83    (1)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.39/50.83    (2)  op(e2, e1) = all_52_9
% 244.39/50.83    (3)   ~ (all_52_9 = e3)
% 244.39/50.83    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.83    (5)   ~ (all_52_13 = e3)
% 244.39/50.83    (6)  op(e2, e0) = all_52_13
% 244.39/50.83  
% 244.39/50.83  Begin of proof
% 244.39/50.83  | 
% 244.39/50.83  | BETA: splitting (1) gives:
% 244.39/50.83  | 
% 244.39/50.83  | Case 1:
% 244.39/50.83  | | 
% 244.39/50.83  | |   (7)  all_58_5 = e3 & op(e2, e1) = e3
% 244.39/50.83  | | 
% 244.39/50.83  | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #1822.
% 244.39/50.83  | | 
% 244.39/50.83  | Case 2:
% 244.39/50.83  | | 
% 244.39/50.83  | |   (8)  all_58_10 = e3 & op(e2, e0) = e3
% 244.39/50.83  | | 
% 244.39/50.83  | | ALPHA: (8) implies:
% 244.39/50.83  | |   (9)  op(e2, e0) = e3
% 244.39/50.83  | | 
% 244.39/50.83  | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #1994.
% 244.39/50.83  | | 
% 244.39/50.83  | End of split
% 244.39/50.83  | 
% 244.39/50.83  End of proof
% 244.39/50.83  
% 244.39/50.83  Sub-proof #1650 shows that the following formulas are inconsistent:
% 244.39/50.83  ----------------------------------------------------------------
% 244.39/50.83    (1)   ~ (e3 = e0)
% 244.39/50.83    (2)   ~ (e2 = e0)
% 244.39/50.83    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.39/50.83         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.39/50.83    (4)  all_58_9 = e0
% 244.39/50.83    (5)   ~ (e3 = e1)
% 244.39/50.83    (6)   ~ (e3 = e2)
% 244.39/50.83    (7)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.39/50.83         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.39/50.83    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.83    (9)  op(e0, e0) = e0
% 244.39/50.83    (10)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.39/50.83          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.39/50.83    (11)   ~ (e1 = e0)
% 244.39/50.83    (12)   ~ (all_52_13 = e3)
% 244.39/50.83    (13)  op(e2, e0) = all_52_13
% 244.39/50.83    (14)   ~ (e2 = e1)
% 244.39/50.83  
% 244.39/50.83  Begin of proof
% 244.39/50.83  | 
% 244.39/50.83  | BETA: splitting (7) gives:
% 244.39/50.83  | 
% 244.39/50.83  | Case 1:
% 244.39/50.83  | | 
% 244.39/50.83  | |   (15)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 244.39/50.83  | |           e3)
% 244.39/50.83  | | 
% 244.39/50.83  | | REF_CLOSE: (1), (4), (8), (12), (13), (15) are inconsistent by sub-proof
% 244.39/50.83  | |            #1661.
% 244.39/50.83  | | 
% 244.39/50.83  | Case 2:
% 244.39/50.83  | | 
% 244.39/50.83  | |   (16)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.39/50.83  | |           e3)
% 244.39/50.83  | | 
% 244.39/50.83  | | BETA: splitting (16) gives:
% 244.39/50.83  | | 
% 244.39/50.83  | | Case 1:
% 244.39/50.83  | | | 
% 244.39/50.83  | | |   (17)  all_58_11 = e3 & op(e1, e0) = e3
% 244.39/50.83  | | | 
% 244.39/50.83  | | | ALPHA: (17) implies:
% 244.39/50.83  | | |   (18)  all_58_11 = e3
% 244.39/50.83  | | | 
% 244.39/50.83  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 244.39/50.83  | | |            (13), (14), (18) are inconsistent by sub-proof #1651.
% 244.39/50.83  | | | 
% 244.39/50.83  | | Case 2:
% 244.39/50.83  | | | 
% 244.39/50.83  | | |   (19)  all_58_15 = e3 & op(e0, e0) = e3
% 244.39/50.83  | | | 
% 244.39/50.83  | | | ALPHA: (19) implies:
% 244.39/50.83  | | |   (20)  op(e0, e0) = e3
% 244.39/50.83  | | | 
% 244.39/50.83  | | | REF_CLOSE: (1), (8), (9), (20) are inconsistent by sub-proof #2079.
% 244.39/50.83  | | | 
% 244.39/50.83  | | End of split
% 244.39/50.83  | | 
% 244.39/50.83  | End of split
% 244.39/50.83  | 
% 244.39/50.83  End of proof
% 244.39/50.83  
% 244.39/50.83  Sub-proof #1651 shows that the following formulas are inconsistent:
% 244.39/50.83  ----------------------------------------------------------------
% 244.39/50.83    (1)   ~ (e3 = e0)
% 244.39/50.83    (2)   ~ (e2 = e0)
% 244.39/50.83    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.39/50.83         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.39/50.83    (4)  all_58_9 = e0
% 244.39/50.83    (5)   ~ (e3 = e1)
% 244.39/50.83    (6)  all_58_11 = e3
% 244.39/50.83    (7)   ~ (e3 = e2)
% 244.39/50.83    (8)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.39/50.83         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.39/50.83    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.83    (10)  op(e0, e0) = e0
% 244.39/50.83    (11)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.39/50.83          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.39/50.83    (12)   ~ (e1 = e0)
% 244.39/50.83    (13)   ~ (all_52_13 = e3)
% 244.39/50.83    (14)  op(e2, e0) = all_52_13
% 244.39/50.83    (15)   ~ (e2 = e1)
% 244.39/50.83  
% 244.39/50.83  Begin of proof
% 244.39/50.83  | 
% 244.39/50.83  | BETA: splitting (11) gives:
% 244.39/50.83  | 
% 244.39/50.83  | Case 1:
% 244.39/50.83  | | 
% 244.39/50.83  | |   (16)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 244.39/50.83  | |           e2)
% 244.39/50.83  | | 
% 244.39/50.83  | | BETA: splitting (16) gives:
% 244.39/50.83  | | 
% 244.39/50.83  | | Case 1:
% 244.39/50.83  | | | 
% 244.39/50.83  | | |   (17)  all_58_9 = e2 & op(e3, e0) = e2
% 244.39/50.83  | | | 
% 244.39/50.83  | | | ALPHA: (17) implies:
% 244.39/50.83  | | |   (18)  all_58_9 = e2
% 244.39/50.83  | | | 
% 244.39/50.83  | | | REF_CLOSE: (2), (4), (18) are inconsistent by sub-proof #1660.
% 244.39/50.83  | | | 
% 244.39/50.83  | | Case 2:
% 244.39/50.83  | | | 
% 244.39/50.83  | | |   (19)  all_58_10 = e2 & op(e2, e0) = e2
% 244.39/50.83  | | | 
% 244.39/50.83  | | | REF_CLOSE: (3), (4), (5), (6), (9), (10), (12), (15), (19) are
% 244.39/50.83  | | |            inconsistent by sub-proof #1656.
% 244.39/50.83  | | | 
% 244.39/50.83  | | End of split
% 244.39/50.83  | | 
% 244.39/50.83  | Case 2:
% 244.39/50.83  | | 
% 244.39/50.83  | |   (20)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.39/50.83  | |           e2)
% 244.39/50.83  | | 
% 244.39/50.83  | | BETA: splitting (20) gives:
% 244.39/50.83  | | 
% 244.39/50.83  | | Case 1:
% 244.39/50.83  | | | 
% 244.39/50.83  | | |   (21)  all_58_11 = e2 & op(e1, e0) = e2
% 244.39/50.83  | | | 
% 244.39/50.83  | | | ALPHA: (21) implies:
% 244.39/50.83  | | |   (22)  all_58_11 = e2
% 244.39/50.83  | | | 
% 244.39/50.83  | | | REF_CLOSE: (6), (7), (22) are inconsistent by sub-proof #2030.
% 244.39/50.83  | | | 
% 244.39/50.83  | | Case 2:
% 244.39/50.83  | | | 
% 244.39/50.83  | | |   (23)  all_58_15 = e2 & op(e0, e0) = e2
% 244.39/50.84  | | | 
% 244.39/50.84  | | | ALPHA: (23) implies:
% 244.39/50.84  | | |   (24)  all_58_15 = e2
% 244.39/50.84  | | |   (25)  op(e0, e0) = e2
% 244.39/50.84  | | | 
% 244.39/50.84  | | | GROUND_INST: instantiating (9) with e0, e2, e0, e0, simplifying with (10),
% 244.39/50.84  | | |              (25) gives:
% 244.39/50.84  | | |   (26)  e2 = e0
% 244.39/50.84  | | | 
% 244.39/50.84  | | | COMBINE_EQS: (24), (26) imply:
% 244.39/50.84  | | |   (27)  all_58_15 = e0
% 244.39/50.84  | | | 
% 244.39/50.84  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 244.39/50.84  | | |            (14), (15), (27) are inconsistent by sub-proof #1652.
% 244.39/50.84  | | | 
% 244.39/50.84  | | End of split
% 244.39/50.84  | | 
% 244.39/50.84  | End of split
% 244.39/50.84  | 
% 244.39/50.84  End of proof
% 244.39/50.84  
% 244.39/50.84  Sub-proof #1652 shows that the following formulas are inconsistent:
% 244.39/50.84  ----------------------------------------------------------------
% 244.39/50.84    (1)   ~ (e3 = e0)
% 244.39/50.84    (2)   ~ (e2 = e0)
% 244.39/50.84    (3)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.39/50.84         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.39/50.84    (4)  all_58_9 = e0
% 244.39/50.84    (5)   ~ (e3 = e1)
% 244.39/50.84    (6)   ~ (e3 = e2)
% 244.39/50.84    (7)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.39/50.84         (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.39/50.84    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.84    (9)  op(e0, e0) = e0
% 244.39/50.84    (10)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.39/50.84          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.39/50.84    (11)   ~ (e1 = e0)
% 244.39/50.84    (12)   ~ (all_52_13 = e3)
% 244.39/50.84    (13)  all_58_15 = e0
% 244.39/50.84    (14)  op(e2, e0) = all_52_13
% 244.39/50.84    (15)   ~ (e2 = e1)
% 244.39/50.84  
% 244.39/50.84  Begin of proof
% 244.39/50.84  | 
% 244.39/50.84  | BETA: splitting (7) gives:
% 244.39/50.84  | 
% 244.39/50.84  | Case 1:
% 244.39/50.84  | | 
% 244.39/50.84  | |   (16)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 244.39/50.84  | |           e3)
% 244.39/50.84  | | 
% 244.39/50.84  | | REF_CLOSE: (1), (4), (8), (12), (14), (16) are inconsistent by sub-proof
% 244.39/50.84  | |            #1661.
% 244.39/50.84  | | 
% 244.39/50.84  | Case 2:
% 244.39/50.84  | | 
% 244.39/50.84  | |   (17)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.39/50.84  | |           e3)
% 244.39/50.84  | | 
% 244.39/50.84  | | BETA: splitting (17) gives:
% 244.39/50.84  | | 
% 244.39/50.84  | | Case 1:
% 244.39/50.84  | | | 
% 244.39/50.84  | | |   (18)  all_58_11 = e3 & op(e1, e0) = e3
% 244.39/50.84  | | | 
% 244.39/50.84  | | | ALPHA: (18) implies:
% 244.39/50.84  | | |   (19)  all_58_11 = e3
% 244.39/50.84  | | | 
% 244.39/50.84  | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (15), (19)
% 244.39/50.84  | | |            are inconsistent by sub-proof #1653.
% 244.39/50.84  | | | 
% 244.39/50.84  | | Case 2:
% 244.39/50.84  | | | 
% 244.39/50.84  | | |   (20)  all_58_15 = e3 & op(e0, e0) = e3
% 244.39/50.84  | | | 
% 244.39/50.84  | | | ALPHA: (20) implies:
% 244.39/50.84  | | |   (21)  op(e0, e0) = e3
% 244.39/50.84  | | | 
% 244.39/50.84  | | | REF_CLOSE: (1), (8), (9), (21) are inconsistent by sub-proof #2079.
% 244.39/50.84  | | | 
% 244.39/50.84  | | End of split
% 244.39/50.84  | | 
% 244.39/50.84  | End of split
% 244.39/50.84  | 
% 244.39/50.84  End of proof
% 244.39/50.84  
% 244.39/50.84  Sub-proof #1653 shows that the following formulas are inconsistent:
% 244.39/50.84  ----------------------------------------------------------------
% 244.39/50.84    (1)   ~ (e2 = e0)
% 244.39/50.84    (2)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.39/50.84         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.39/50.84    (3)  all_58_9 = e0
% 244.39/50.84    (4)   ~ (e3 = e1)
% 244.39/50.84    (5)  all_58_11 = e3
% 244.39/50.84    (6)   ~ (e3 = e2)
% 244.39/50.84    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.84    (8)  op(e0, e0) = e0
% 244.39/50.84    (9)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.39/50.84         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.39/50.84    (10)   ~ (e1 = e0)
% 244.39/50.84    (11)  all_58_15 = e0
% 244.39/50.84    (12)   ~ (e2 = e1)
% 244.39/50.84  
% 244.39/50.84  Begin of proof
% 244.39/50.84  | 
% 244.39/50.84  | BETA: splitting (9) gives:
% 244.39/50.84  | 
% 244.39/50.84  | Case 1:
% 244.39/50.84  | | 
% 244.39/50.84  | |   (13)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 244.39/50.84  | |           e2)
% 244.39/50.84  | | 
% 244.39/50.84  | | BETA: splitting (13) gives:
% 244.39/50.84  | | 
% 244.39/50.84  | | Case 1:
% 244.39/50.84  | | | 
% 244.39/50.84  | | |   (14)  all_58_9 = e2 & op(e3, e0) = e2
% 244.39/50.84  | | | 
% 244.39/50.84  | | | REF_CLOSE: (1), (3), (14) are inconsistent by sub-proof #1655.
% 244.39/50.84  | | | 
% 244.39/50.84  | | Case 2:
% 244.39/50.84  | | | 
% 244.39/50.84  | | |   (15)  all_58_10 = e2 & op(e2, e0) = e2
% 244.39/50.84  | | | 
% 244.39/50.84  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (12), (15) are inconsistent
% 244.39/50.84  | | |            by sub-proof #1656.
% 244.39/50.84  | | | 
% 244.39/50.84  | | End of split
% 244.39/50.84  | | 
% 244.39/50.84  | Case 2:
% 244.39/50.84  | | 
% 244.39/50.84  | |   (16)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.39/50.84  | |           e2)
% 244.39/50.84  | | 
% 244.39/50.84  | | BETA: splitting (16) gives:
% 244.39/50.84  | | 
% 244.39/50.84  | | Case 1:
% 244.39/50.84  | | | 
% 244.39/50.84  | | |   (17)  all_58_11 = e2 & op(e1, e0) = e2
% 244.39/50.84  | | | 
% 244.39/50.84  | | | ALPHA: (17) implies:
% 244.39/50.84  | | |   (18)  all_58_11 = e2
% 244.39/50.84  | | | 
% 244.39/50.84  | | | REF_CLOSE: (5), (6), (18) are inconsistent by sub-proof #2030.
% 244.39/50.84  | | | 
% 244.39/50.84  | | Case 2:
% 244.39/50.84  | | | 
% 244.39/50.84  | | |   (19)  all_58_15 = e2 & op(e0, e0) = e2
% 244.39/50.84  | | | 
% 244.39/50.84  | | | REF_CLOSE: (1), (11), (19) are inconsistent by sub-proof #1654.
% 244.39/50.84  | | | 
% 244.39/50.84  | | End of split
% 244.39/50.84  | | 
% 244.39/50.84  | End of split
% 244.39/50.84  | 
% 244.39/50.84  End of proof
% 244.39/50.84  
% 244.39/50.84  Sub-proof #1654 shows that the following formulas are inconsistent:
% 244.39/50.84  ----------------------------------------------------------------
% 244.39/50.84    (1)  all_58_15 = e2 & op(e0, e0) = e2
% 244.39/50.84    (2)  all_58_15 = e0
% 244.39/50.84    (3)   ~ (e2 = e0)
% 244.39/50.84  
% 244.39/50.84  Begin of proof
% 244.39/50.84  | 
% 244.39/50.84  | ALPHA: (1) implies:
% 244.39/50.84  |   (4)  all_58_15 = e2
% 244.39/50.84  | 
% 244.39/50.84  | COMBINE_EQS: (2), (4) imply:
% 244.39/50.84  |   (5)  e2 = e0
% 244.39/50.84  | 
% 244.39/50.84  | REDUCE: (3), (5) imply:
% 244.39/50.84  |   (6)  $false
% 244.39/50.84  | 
% 244.39/50.84  | CLOSE: (6) is inconsistent.
% 244.39/50.84  | 
% 244.39/50.84  End of proof
% 244.39/50.84  
% 244.39/50.84  Sub-proof #1655 shows that the following formulas are inconsistent:
% 244.39/50.84  ----------------------------------------------------------------
% 244.39/50.84    (1)  all_58_9 = e2 & op(e3, e0) = e2
% 244.39/50.84    (2)  all_58_9 = e0
% 244.39/50.84    (3)   ~ (e2 = e0)
% 244.39/50.84  
% 244.39/50.84  Begin of proof
% 244.39/50.84  | 
% 244.39/50.84  | ALPHA: (1) implies:
% 244.39/50.84  |   (4)  all_58_9 = e2
% 244.39/50.84  | 
% 244.39/50.84  | COMBINE_EQS: (2), (4) imply:
% 244.39/50.84  |   (5)  e2 = e0
% 244.39/50.84  | 
% 244.39/50.84  | REDUCE: (3), (5) imply:
% 244.39/50.84  |   (6)  $false
% 244.39/50.84  | 
% 244.39/50.84  | CLOSE: (6) is inconsistent.
% 244.39/50.84  | 
% 244.39/50.84  End of proof
% 244.39/50.84  
% 244.39/50.84  Sub-proof #1656 shows that the following formulas are inconsistent:
% 244.39/50.84  ----------------------------------------------------------------
% 244.39/50.84    (1)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 244.39/50.84         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.39/50.84    (2)  all_58_9 = e0
% 244.39/50.84    (3)  all_58_10 = e2 & op(e2, e0) = e2
% 244.39/50.84    (4)   ~ (e3 = e1)
% 244.39/50.84    (5)  all_58_11 = e3
% 244.39/50.84    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.84    (7)  op(e0, e0) = e0
% 244.39/50.84    (8)   ~ (e1 = e0)
% 244.39/50.84    (9)   ~ (e2 = e1)
% 244.39/50.84  
% 244.39/50.84  Begin of proof
% 244.39/50.84  | 
% 244.39/50.84  | ALPHA: (3) implies:
% 244.39/50.84  |   (10)  op(e2, e0) = e2
% 244.39/50.84  | 
% 244.39/50.84  | BETA: splitting (1) gives:
% 244.39/50.84  | 
% 244.39/50.84  | Case 1:
% 244.39/50.84  | | 
% 244.39/50.84  | |   (11)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 244.39/50.84  | |           e1)
% 244.39/50.84  | | 
% 244.39/50.84  | | REF_CLOSE: (2), (6), (8), (9), (10), (11) are inconsistent by sub-proof
% 244.39/50.84  | |            #1658.
% 244.39/50.84  | | 
% 244.39/50.84  | Case 2:
% 244.39/50.84  | | 
% 244.39/50.84  | |   (12)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.39/50.84  | |           e1)
% 244.39/50.84  | | 
% 244.39/50.84  | | BETA: splitting (12) gives:
% 244.39/50.84  | | 
% 244.39/50.84  | | Case 1:
% 244.39/50.84  | | | 
% 244.39/50.84  | | |   (13)  all_58_11 = e1 & op(e1, e0) = e1
% 244.39/50.84  | | | 
% 244.39/50.84  | | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #1657.
% 244.39/50.84  | | | 
% 244.39/50.84  | | Case 2:
% 244.39/50.84  | | | 
% 244.39/50.84  | | |   (14)  all_58_15 = e1 & op(e0, e0) = e1
% 244.39/50.84  | | | 
% 244.39/50.84  | | | ALPHA: (14) implies:
% 244.39/50.84  | | |   (15)  op(e0, e0) = e1
% 244.39/50.84  | | | 
% 244.39/50.84  | | | REF_CLOSE: (6), (7), (8), (15) are inconsistent by sub-proof #2274.
% 244.39/50.84  | | | 
% 244.39/50.84  | | End of split
% 244.39/50.84  | | 
% 244.39/50.84  | End of split
% 244.39/50.84  | 
% 244.39/50.84  End of proof
% 244.39/50.84  
% 244.39/50.84  Sub-proof #1657 shows that the following formulas are inconsistent:
% 244.39/50.84  ----------------------------------------------------------------
% 244.39/50.84    (1)  all_58_11 = e1 & op(e1, e0) = e1
% 244.39/50.84    (2)  all_58_11 = e3
% 244.39/50.84    (3)   ~ (e3 = e1)
% 244.39/50.84  
% 244.39/50.84  Begin of proof
% 244.39/50.84  | 
% 244.39/50.84  | ALPHA: (1) implies:
% 244.39/50.84  |   (4)  all_58_11 = e1
% 244.39/50.84  | 
% 244.39/50.84  | COMBINE_EQS: (2), (4) imply:
% 244.39/50.84  |   (5)  e3 = e1
% 244.39/50.84  | 
% 244.39/50.84  | REDUCE: (3), (5) imply:
% 244.39/50.84  |   (6)  $false
% 244.39/50.84  | 
% 244.39/50.84  | CLOSE: (6) is inconsistent.
% 244.39/50.84  | 
% 244.39/50.84  End of proof
% 244.39/50.84  
% 244.39/50.84  Sub-proof #1658 shows that the following formulas are inconsistent:
% 244.39/50.84  ----------------------------------------------------------------
% 244.39/50.84    (1)  all_58_9 = e0
% 244.39/50.84    (2)  op(e2, e0) = e2
% 244.39/50.84    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.84    (4)   ~ (e1 = e0)
% 244.39/50.84    (5)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.39/50.84    (6)   ~ (e2 = e1)
% 244.39/50.84  
% 244.39/50.84  Begin of proof
% 244.39/50.84  | 
% 244.39/50.84  | BETA: splitting (5) gives:
% 244.39/50.84  | 
% 244.39/50.84  | Case 1:
% 244.39/50.84  | | 
% 244.39/50.84  | |   (7)  all_58_9 = e1 & op(e3, e0) = e1
% 244.39/50.84  | | 
% 244.39/50.84  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #2183.
% 244.39/50.84  | | 
% 244.39/50.84  | Case 2:
% 244.39/50.84  | | 
% 244.39/50.84  | |   (8)  all_58_10 = e1 & op(e2, e0) = e1
% 244.39/50.84  | | 
% 244.39/50.84  | | ALPHA: (8) implies:
% 244.39/50.84  | |   (9)  op(e2, e0) = e1
% 244.39/50.84  | | 
% 244.39/50.84  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #1659.
% 244.39/50.84  | | 
% 244.39/50.84  | End of split
% 244.39/50.84  | 
% 244.39/50.84  End of proof
% 244.39/50.84  
% 244.39/50.84  Sub-proof #1659 shows that the following formulas are inconsistent:
% 244.39/50.84  ----------------------------------------------------------------
% 244.39/50.84    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.85    (2)  op(e2, e0) = e2
% 244.39/50.85    (3)  op(e2, e0) = e1
% 244.39/50.85    (4)   ~ (e2 = e1)
% 244.39/50.85  
% 244.39/50.85  Begin of proof
% 244.39/50.85  | 
% 244.39/50.85  | GROUND_INST: instantiating (1) with e1, e2, e0, e2, simplifying with (2), (3)
% 244.39/50.85  |              gives:
% 244.39/50.85  |   (5)  e2 = e1
% 244.39/50.85  | 
% 244.39/50.85  | REDUCE: (4), (5) imply:
% 244.39/50.85  |   (6)  $false
% 244.39/50.85  | 
% 244.39/50.85  | CLOSE: (6) is inconsistent.
% 244.39/50.85  | 
% 244.39/50.85  End of proof
% 244.39/50.85  
% 244.39/50.85  Sub-proof #1660 shows that the following formulas are inconsistent:
% 244.39/50.85  ----------------------------------------------------------------
% 244.39/50.85    (1)  all_58_9 = e2
% 244.39/50.85    (2)  all_58_9 = e0
% 244.39/50.85    (3)   ~ (e2 = e0)
% 244.39/50.85  
% 244.39/50.85  Begin of proof
% 244.39/50.85  | 
% 244.39/50.85  | COMBINE_EQS: (1), (2) imply:
% 244.39/50.85  |   (4)  e2 = e0
% 244.39/50.85  | 
% 244.39/50.85  | SIMP: (4) implies:
% 244.39/50.85  |   (5)  e2 = e0
% 244.39/50.85  | 
% 244.39/50.85  | REDUCE: (3), (5) imply:
% 244.39/50.85  |   (6)  $false
% 244.39/50.85  | 
% 244.39/50.85  | CLOSE: (6) is inconsistent.
% 244.39/50.85  | 
% 244.39/50.85  End of proof
% 244.39/50.85  
% 244.39/50.85  Sub-proof #1661 shows that the following formulas are inconsistent:
% 244.39/50.85  ----------------------------------------------------------------
% 244.39/50.85    (1)   ~ (e3 = e0)
% 244.39/50.85    (2)  all_58_9 = e0
% 244.39/50.85    (3)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.39/50.85    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.85    (5)   ~ (all_52_13 = e3)
% 244.39/50.85    (6)  op(e2, e0) = all_52_13
% 244.39/50.85  
% 244.39/50.85  Begin of proof
% 244.39/50.85  | 
% 244.39/50.85  | BETA: splitting (3) gives:
% 244.39/50.85  | 
% 244.39/50.85  | Case 1:
% 244.39/50.85  | | 
% 244.39/50.85  | |   (7)  all_58_9 = e3 & op(e3, e0) = e3
% 244.39/50.85  | | 
% 244.39/50.85  | | ALPHA: (7) implies:
% 244.39/50.85  | |   (8)  all_58_9 = e3
% 244.39/50.85  | | 
% 244.39/50.85  | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #1958.
% 244.39/50.85  | | 
% 244.39/50.85  | Case 2:
% 244.39/50.85  | | 
% 244.39/50.85  | |   (9)  all_58_10 = e3 & op(e2, e0) = e3
% 244.39/50.85  | | 
% 244.39/50.85  | | ALPHA: (9) implies:
% 244.39/50.85  | |   (10)  op(e2, e0) = e3
% 244.39/50.85  | | 
% 244.39/50.85  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #1994.
% 244.39/50.85  | | 
% 244.39/50.85  | End of split
% 244.39/50.85  | 
% 244.39/50.85  End of proof
% 244.39/50.85  
% 244.39/50.85  Sub-proof #1662 shows that the following formulas are inconsistent:
% 244.39/50.85  ----------------------------------------------------------------
% 244.39/50.85    (1)   ~ (e3 = e0)
% 244.39/50.85    (2)   ~ (e2 = e0)
% 244.39/50.85    (3)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.39/50.85         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.39/50.85    (4)   ~ (e3 = e1)
% 244.39/50.85    (5)  op(e2, e1) = all_52_9
% 244.39/50.85    (6)   ~ (e3 = e2)
% 244.39/50.85    (7)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 244.39/50.85         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 244.39/50.85    (8)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.39/50.85         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.39/50.85    (9)   ~ (all_52_9 = e3)
% 244.39/50.85    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.85    (11)  op(e1, e1) = e0
% 244.39/50.85    (12)   ~ (e1 = e0)
% 244.39/50.85    (13)  all_58_4 = e0
% 244.39/50.85    (14)   ~ (e2 = e1)
% 244.39/50.85  
% 244.39/50.85  Begin of proof
% 244.39/50.85  | 
% 244.39/50.85  | BETA: splitting (8) gives:
% 244.39/50.85  | 
% 244.39/50.85  | Case 1:
% 244.39/50.85  | | 
% 244.39/50.85  | |   (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 244.39/50.85  | |           e3)
% 244.39/50.85  | | 
% 244.39/50.85  | | REF_CLOSE: (1), (5), (9), (10), (13), (15) are inconsistent by sub-proof
% 244.39/50.85  | |            #1667.
% 244.39/50.85  | | 
% 244.39/50.85  | Case 2:
% 244.39/50.85  | | 
% 244.39/50.85  | |   (16)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 244.39/50.85  | |           e3)
% 244.39/50.85  | | 
% 244.39/50.85  | | BETA: splitting (16) gives:
% 244.39/50.85  | | 
% 244.39/50.85  | | Case 1:
% 244.39/50.85  | | | 
% 244.39/50.85  | | |   (17)  all_58_8 = e3 & op(e1, e1) = e3
% 244.39/50.85  | | | 
% 244.39/50.85  | | | REF_CLOSE: (1), (10), (11), (17) are inconsistent by sub-proof #2018.
% 244.39/50.85  | | | 
% 244.39/50.85  | | Case 2:
% 244.39/50.85  | | | 
% 244.39/50.85  | | |   (18)  all_58_14 = e3 & op(e0, e1) = e3
% 244.39/50.85  | | | 
% 244.39/50.85  | | | ALPHA: (18) implies:
% 244.39/50.85  | | |   (19)  all_58_14 = e3
% 244.39/50.85  | | | 
% 244.39/50.85  | | | REF_CLOSE: (2), (3), (4), (6), (7), (10), (11), (12), (13), (14), (19) are
% 244.39/50.85  | | |            inconsistent by sub-proof #1663.
% 244.39/50.85  | | | 
% 244.39/50.85  | | End of split
% 244.39/50.85  | | 
% 244.39/50.85  | End of split
% 244.39/50.85  | 
% 244.39/50.85  End of proof
% 244.39/50.85  
% 244.39/50.85  Sub-proof #1663 shows that the following formulas are inconsistent:
% 244.39/50.85  ----------------------------------------------------------------
% 244.39/50.85    (1)   ~ (e2 = e0)
% 244.39/50.85    (2)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.39/50.85         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.39/50.85    (3)   ~ (e3 = e1)
% 244.39/50.85    (4)   ~ (e3 = e2)
% 244.39/50.85    (5)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 244.39/50.85         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 244.39/50.85    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.85    (7)  all_58_14 = e3
% 244.39/50.85    (8)  op(e1, e1) = e0
% 244.39/50.85    (9)   ~ (e1 = e0)
% 244.39/50.85    (10)  all_58_4 = e0
% 244.39/50.85    (11)   ~ (e2 = e1)
% 244.39/50.85  
% 244.39/50.85  Begin of proof
% 244.39/50.85  | 
% 244.39/50.85  | BETA: splitting (5) gives:
% 244.39/50.85  | 
% 244.39/50.85  | Case 1:
% 244.39/50.85  | | 
% 244.39/50.85  | |   (12)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 244.39/50.85  | |           e2)
% 244.39/50.85  | | 
% 244.39/50.85  | | BETA: splitting (12) gives:
% 244.39/50.85  | | 
% 244.39/50.85  | | Case 1:
% 244.39/50.85  | | | 
% 244.39/50.85  | | |   (13)  all_58_4 = e2 & op(e3, e1) = e2
% 244.39/50.85  | | | 
% 244.39/50.85  | | | ALPHA: (13) implies:
% 244.39/50.85  | | |   (14)  all_58_4 = e2
% 244.39/50.85  | | | 
% 244.39/50.85  | | | REF_CLOSE: (1), (10), (14) are inconsistent by sub-proof #1666.
% 244.39/50.85  | | | 
% 244.39/50.85  | | Case 2:
% 244.39/50.85  | | | 
% 244.39/50.85  | | |   (15)  all_58_5 = e2 & op(e2, e1) = e2
% 244.39/50.85  | | | 
% 244.39/50.85  | | | ALPHA: (15) implies:
% 244.39/50.85  | | |   (16)  all_58_5 = e2
% 244.39/50.85  | | | 
% 244.39/50.85  | | | BETA: splitting (2) gives:
% 244.39/50.85  | | | 
% 244.39/50.85  | | | Case 1:
% 244.39/50.85  | | | | 
% 244.39/50.85  | | | |   (17)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 244.39/50.85  | | | |           = e1)
% 244.39/50.85  | | | | 
% 244.39/50.85  | | | | BETA: splitting (17) gives:
% 244.39/50.85  | | | | 
% 244.39/50.85  | | | | Case 1:
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | |   (18)  all_58_4 = e1 & op(e3, e1) = e1
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | | ALPHA: (18) implies:
% 244.39/50.85  | | | | |   (19)  all_58_4 = e1
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | | REF_CLOSE: (9), (10), (19) are inconsistent by sub-proof #1710.
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | Case 2:
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | |   (20)  all_58_5 = e1 & op(e2, e1) = e1
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | | ALPHA: (20) implies:
% 244.39/50.85  | | | | |   (21)  all_58_5 = e1
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | | REF_CLOSE: (11), (16), (21) are inconsistent by sub-proof #1665.
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | End of split
% 244.39/50.85  | | | | 
% 244.39/50.85  | | | Case 2:
% 244.39/50.85  | | | | 
% 244.39/50.85  | | | |   (22)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 244.39/50.85  | | | |           = e1)
% 244.39/50.85  | | | | 
% 244.39/50.85  | | | | BETA: splitting (22) gives:
% 244.39/50.85  | | | | 
% 244.39/50.85  | | | | Case 1:
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | |   (23)  all_58_8 = e1 & op(e1, e1) = e1
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | | ALPHA: (23) implies:
% 244.39/50.85  | | | | |   (24)  op(e1, e1) = e1
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | | REF_CLOSE: (6), (8), (9), (24) are inconsistent by sub-proof #2220.
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | Case 2:
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | |   (25)  all_58_14 = e1 & op(e0, e1) = e1
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | | ALPHA: (25) implies:
% 244.39/50.85  | | | | |   (26)  all_58_14 = e1
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | | REF_CLOSE: (3), (7), (26) are inconsistent by sub-proof #1844.
% 244.39/50.85  | | | | | 
% 244.39/50.85  | | | | End of split
% 244.39/50.85  | | | | 
% 244.39/50.85  | | | End of split
% 244.39/50.85  | | | 
% 244.39/50.85  | | End of split
% 244.39/50.85  | | 
% 244.39/50.85  | Case 2:
% 244.39/50.85  | | 
% 244.39/50.85  | |   (27)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 244.39/50.85  | |           e2)
% 244.39/50.85  | | 
% 244.39/50.85  | | REF_CLOSE: (1), (4), (6), (7), (8), (27) are inconsistent by sub-proof
% 244.39/50.85  | |            #1664.
% 244.39/50.85  | | 
% 244.39/50.85  | End of split
% 244.39/50.85  | 
% 244.39/50.85  End of proof
% 244.39/50.85  
% 244.39/50.85  Sub-proof #1664 shows that the following formulas are inconsistent:
% 244.39/50.85  ----------------------------------------------------------------
% 244.39/50.85    (1)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 244.39/50.85    (2)   ~ (e2 = e0)
% 244.39/50.85    (3)   ~ (e3 = e2)
% 244.39/50.85    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.85    (5)  all_58_14 = e3
% 244.39/50.85    (6)  op(e1, e1) = e0
% 244.39/50.85  
% 244.39/50.85  Begin of proof
% 244.39/50.85  | 
% 244.39/50.85  | BETA: splitting (1) gives:
% 244.39/50.85  | 
% 244.39/50.85  | Case 1:
% 244.39/50.85  | | 
% 244.39/50.85  | |   (7)  all_58_8 = e2 & op(e1, e1) = e2
% 244.39/50.85  | | 
% 244.39/50.85  | | ALPHA: (7) implies:
% 244.39/50.85  | |   (8)  op(e1, e1) = e2
% 244.39/50.85  | | 
% 244.39/50.85  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2211.
% 244.39/50.85  | | 
% 244.39/50.85  | Case 2:
% 244.39/50.85  | | 
% 244.39/50.85  | |   (9)  all_58_14 = e2 & op(e0, e1) = e2
% 244.39/50.85  | | 
% 244.39/50.85  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #1864.
% 244.39/50.85  | | 
% 244.39/50.85  | End of split
% 244.39/50.85  | 
% 244.39/50.85  End of proof
% 244.39/50.85  
% 244.39/50.85  Sub-proof #1665 shows that the following formulas are inconsistent:
% 244.39/50.85  ----------------------------------------------------------------
% 244.39/50.85    (1)  all_58_5 = e2
% 244.39/50.85    (2)  all_58_5 = e1
% 244.39/50.85    (3)   ~ (e2 = e1)
% 244.39/50.85  
% 244.39/50.85  Begin of proof
% 244.39/50.85  | 
% 244.39/50.85  | COMBINE_EQS: (1), (2) imply:
% 244.39/50.85  |   (4)  e2 = e1
% 244.39/50.85  | 
% 244.39/50.85  | SIMP: (4) implies:
% 244.39/50.85  |   (5)  e2 = e1
% 244.39/50.85  | 
% 244.39/50.85  | REDUCE: (3), (5) imply:
% 244.39/50.85  |   (6)  $false
% 244.39/50.85  | 
% 244.39/50.85  | CLOSE: (6) is inconsistent.
% 244.39/50.85  | 
% 244.39/50.85  End of proof
% 244.39/50.85  
% 244.39/50.85  Sub-proof #1666 shows that the following formulas are inconsistent:
% 244.39/50.85  ----------------------------------------------------------------
% 244.39/50.85    (1)  all_58_4 = e2
% 244.39/50.85    (2)  all_58_4 = e0
% 244.39/50.85    (3)   ~ (e2 = e0)
% 244.39/50.85  
% 244.39/50.85  Begin of proof
% 244.39/50.85  | 
% 244.39/50.85  | COMBINE_EQS: (1), (2) imply:
% 244.39/50.85  |   (4)  e2 = e0
% 244.39/50.85  | 
% 244.39/50.85  | SIMP: (4) implies:
% 244.39/50.85  |   (5)  e2 = e0
% 244.39/50.85  | 
% 244.39/50.85  | REDUCE: (3), (5) imply:
% 244.39/50.85  |   (6)  $false
% 244.39/50.85  | 
% 244.39/50.85  | CLOSE: (6) is inconsistent.
% 244.39/50.85  | 
% 244.39/50.85  End of proof
% 244.39/50.85  
% 244.39/50.85  Sub-proof #1667 shows that the following formulas are inconsistent:
% 244.39/50.85  ----------------------------------------------------------------
% 244.39/50.85    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 244.39/50.85    (2)   ~ (e3 = e0)
% 244.39/50.85    (3)  op(e2, e1) = all_52_9
% 244.39/50.85    (4)   ~ (all_52_9 = e3)
% 244.39/50.85    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.85    (6)  all_58_4 = e0
% 244.39/50.85  
% 244.39/50.85  Begin of proof
% 244.39/50.85  | 
% 244.39/50.85  | BETA: splitting (1) gives:
% 244.39/50.85  | 
% 244.39/50.85  | Case 1:
% 244.39/50.85  | | 
% 244.39/50.85  | |   (7)  all_58_4 = e3 & op(e3, e1) = e3
% 244.39/50.85  | | 
% 244.39/50.85  | | ALPHA: (7) implies:
% 244.39/50.85  | |   (8)  all_58_4 = e3
% 244.39/50.85  | | 
% 244.39/50.85  | | REF_CLOSE: (2), (6), (8) are inconsistent by sub-proof #2186.
% 244.39/50.85  | | 
% 244.39/50.85  | Case 2:
% 244.39/50.85  | | 
% 244.39/50.85  | |   (9)  all_58_5 = e3 & op(e2, e1) = e3
% 244.39/50.85  | | 
% 244.39/50.85  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #1822.
% 244.39/50.85  | | 
% 244.39/50.85  | End of split
% 244.39/50.85  | 
% 244.39/50.85  End of proof
% 244.39/50.85  
% 244.39/50.85  Sub-proof #1668 shows that the following formulas are inconsistent:
% 244.39/50.85  ----------------------------------------------------------------
% 244.39/50.85    (1)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 244.39/50.85    (2)   ~ (all_10_2 = e2)
% 244.39/50.85    (3)   ~ (all_10_2 = e0)
% 244.39/50.85    (4)   ~ (all_10_2 = e1)
% 244.39/50.85    (5)  all_56_1 = e3
% 244.39/50.85    (6)   ~ (all_52_12 = all_10_2)
% 244.39/50.85    (7)  op(e3, e0) = all_52_12
% 244.39/50.86    (8)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.39/50.86           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.39/50.86             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.39/50.86           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.39/50.86             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.39/50.86           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.39/50.86           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.39/50.86           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.39/50.86           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.39/50.86           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.39/50.86           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.39/50.86             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.39/50.86           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.39/50.86           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.39/50.86    (9)  op(e2, e3) = all_52_1
% 244.39/50.86    (10)   ~ (all_52_2 = e3)
% 244.39/50.86    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.39/50.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.39/50.86    (12)  op(e1, e3) = all_52_2
% 244.39/50.86    (13)  all_54_0 = all_10_2
% 244.39/50.86    (14)   ~ (all_52_1 = e3)
% 244.39/50.86  
% 244.39/50.86  Begin of proof
% 244.39/50.86  | 
% 244.39/50.86  | BETA: splitting (8) gives:
% 244.39/50.86  | 
% 244.39/50.86  | Case 1:
% 244.39/50.86  | | 
% 244.39/50.86  | |   (15)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.39/50.86  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 244.39/50.86  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 244.39/50.86  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.39/50.86  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 244.39/50.86  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 244.39/50.86  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.39/50.86  | |           op(e1, e3) = e3)
% 244.39/50.86  | | 
% 244.39/50.86  | | REF_CLOSE: (5), (9), (10), (11), (12), (14), (15) are inconsistent by
% 244.39/50.86  | |            sub-proof #2299.
% 244.39/50.86  | | 
% 244.39/50.86  | Case 2:
% 244.39/50.86  | | 
% 244.39/50.86  | |   (16)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.39/50.86  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 244.39/50.86  | |           e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 244.39/50.86  | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.39/50.86  | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7
% 244.39/50.86  | |           = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &
% 244.39/50.86  | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 244.39/50.86  | |           op(e0, e3) = e0)
% 244.39/50.86  | | 
% 244.39/50.86  | | BETA: splitting (16) gives:
% 244.39/50.86  | | 
% 244.39/50.86  | | Case 1:
% 244.39/50.86  | | | 
% 244.39/50.86  | | |   (17)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 244.39/50.86  | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.39/50.86  | | |         op(e3, e1) = e1 & op(e1, e3) = e1
% 244.39/50.86  | | | 
% 244.39/50.86  | | | ALPHA: (17) implies:
% 244.39/50.86  | | |   (18)   ~ (all_56_1 = e3)
% 244.39/50.86  | | | 
% 244.39/50.86  | | | REDUCE: (5), (18) imply:
% 244.39/50.86  | | |   (19)  $false
% 244.39/50.86  | | | 
% 244.39/50.86  | | | CLOSE: (19) is inconsistent.
% 244.39/50.86  | | | 
% 244.39/50.86  | | Case 2:
% 244.39/50.86  | | | 
% 244.39/50.86  | | |   (20)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.39/50.86  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.39/50.86  | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 244.39/50.86  | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 244.39/50.86  | | |             = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 244.39/50.86  | | |           e0)
% 244.39/50.86  | | | 
% 244.39/50.86  | | | BETA: splitting (20) gives:
% 244.39/50.86  | | | 
% 244.39/50.86  | | | Case 1:
% 244.39/50.86  | | | | 
% 244.44/50.86  | | | |   (21)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.86  | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.44/50.86  | | | |         op(e3, e0) = e3 & op(e0, e3) = e3
% 244.44/50.86  | | | | 
% 244.44/50.86  | | | | ALPHA: (21) implies:
% 244.44/50.86  | | | |   (22)  op(e3, e0) = e3
% 244.44/50.86  | | | | 
% 244.44/50.86  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (11), (13), (22) are
% 244.44/50.86  | | | |            inconsistent by sub-proof #1669.
% 244.44/50.86  | | | | 
% 244.44/50.86  | | | Case 2:
% 244.44/50.86  | | | | 
% 244.44/50.86  | | | |   (23)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.44/50.86  | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.44/50.86  | | | |         op(e3, e0) = e0 & op(e0, e3) = e0
% 244.44/50.86  | | | | 
% 244.44/50.86  | | | | ALPHA: (23) implies:
% 244.44/50.86  | | | |   (24)   ~ (all_56_1 = e3)
% 244.44/50.86  | | | | 
% 244.44/50.86  | | | | REDUCE: (5), (24) imply:
% 244.44/50.86  | | | |   (25)  $false
% 244.44/50.86  | | | | 
% 244.44/50.86  | | | | CLOSE: (25) is inconsistent.
% 244.44/50.86  | | | | 
% 244.44/50.86  | | | End of split
% 244.44/50.86  | | | 
% 244.44/50.86  | | End of split
% 244.44/50.86  | | 
% 244.44/50.86  | End of split
% 244.44/50.86  | 
% 244.44/50.86  End of proof
% 244.44/50.86  
% 244.44/50.86  Sub-proof #1669 shows that the following formulas are inconsistent:
% 244.44/50.86  ----------------------------------------------------------------
% 244.44/50.86    (1)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 244.44/50.86    (2)   ~ (all_10_2 = e2)
% 244.44/50.86    (3)   ~ (all_10_2 = e0)
% 244.44/50.86    (4)   ~ (all_10_2 = e1)
% 244.44/50.86    (5)   ~ (all_52_12 = all_10_2)
% 244.44/50.86    (6)  op(e3, e0) = all_52_12
% 244.44/50.86    (7)  op(e3, e0) = e3
% 244.44/50.86    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.44/50.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.44/50.86    (9)  all_54_0 = all_10_2
% 244.44/50.86  
% 244.44/50.86  Begin of proof
% 244.44/50.86  | 
% 244.44/50.86  | BETA: splitting (1) gives:
% 244.44/50.86  | 
% 244.44/50.86  | Case 1:
% 244.44/50.86  | | 
% 244.44/50.86  | |   (10)  all_54_0 = e3
% 244.44/50.86  | | 
% 244.44/50.86  | | COMBINE_EQS: (9), (10) imply:
% 244.44/50.86  | |   (11)  all_10_2 = e3
% 244.44/50.86  | | 
% 244.44/50.86  | | REDUCE: (5), (11) imply:
% 244.44/50.86  | |   (12)   ~ (all_52_12 = e3)
% 244.44/50.86  | | 
% 244.44/50.86  | | REF_CLOSE: (6), (7), (8), (12) are inconsistent by sub-proof #2179.
% 244.44/50.86  | | 
% 244.44/50.86  | Case 2:
% 244.44/50.86  | | 
% 244.44/50.86  | |   (13)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 244.44/50.86  | | 
% 244.44/50.86  | | REF_CLOSE: (2), (3), (4), (9), (13) are inconsistent by sub-proof #2319.
% 244.44/50.86  | | 
% 244.44/50.86  | End of split
% 244.44/50.86  | 
% 244.44/50.86  End of proof
% 244.44/50.86  
% 244.44/50.86  Sub-proof #1670 shows that the following formulas are inconsistent:
% 244.44/50.86  ----------------------------------------------------------------
% 244.44/50.86    (1)   ~ (e3 = e0)
% 244.44/50.86    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.44/50.86         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.44/50.86    (3)   ~ (e2 = e0)
% 244.44/50.86    (4)  op(e1, e2) = all_52_6
% 244.44/50.86    (5)   ~ (all_52_6 = e0)
% 244.44/50.86    (6)   ~ (e3 = e1)
% 244.44/50.86    (7)  all_58_11 = e2 & op(e1, e0) = e2
% 244.44/50.86    (8)   ~ (e3 = e2)
% 244.44/50.86    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.44/50.86         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.44/50.86    (10)  op(e1, e1) = e2
% 244.44/50.86    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.44/50.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.44/50.86    (12)   ~ (e1 = e0)
% 244.44/50.86    (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.44/50.86          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.44/50.86    (14)   ~ (e2 = e1)
% 244.44/50.86  
% 244.44/50.86  Begin of proof
% 244.44/50.86  | 
% 244.44/50.86  | ALPHA: (7) implies:
% 244.44/50.86  |   (15)  all_58_11 = e2
% 244.44/50.86  |   (16)  op(e1, e0) = e2
% 244.44/50.86  | 
% 244.44/50.86  | BETA: splitting (9) gives:
% 244.44/50.86  | 
% 244.44/50.86  | Case 1:
% 244.44/50.86  | | 
% 244.44/50.86  | |   (17)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.44/50.86  | |           e3)
% 244.44/50.86  | | 
% 244.44/50.86  | | BETA: splitting (17) gives:
% 244.44/50.86  | | 
% 244.44/50.86  | | Case 1:
% 244.44/50.86  | | | 
% 244.44/50.86  | | |   (18)  all_58_6 = e3 & op(e1, e3) = e3
% 244.44/50.86  | | | 
% 244.44/50.86  | | | REF_CLOSE: (1), (3), (4), (5), (10), (11), (13), (15), (18) are
% 244.44/50.86  | | |            inconsistent by sub-proof #1672.
% 244.44/50.86  | | | 
% 244.44/50.86  | | Case 2:
% 244.44/50.86  | | | 
% 244.44/50.86  | | |   (19)  all_58_7 = e3 & op(e1, e2) = e3
% 244.44/50.86  | | | 
% 244.44/50.86  | | | ALPHA: (19) implies:
% 244.44/50.86  | | |   (20)  all_58_7 = e3
% 244.44/50.86  | | | 
% 244.44/50.87  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13),
% 244.44/50.87  | | |            (14), (15), (16), (20) are inconsistent by sub-proof #1671.
% 244.44/50.87  | | | 
% 244.44/50.87  | | End of split
% 244.44/50.87  | | 
% 244.44/50.87  | Case 2:
% 244.44/50.87  | | 
% 244.44/50.87  | |   (21)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.44/50.87  | |           e3)
% 244.44/50.87  | | 
% 244.44/50.87  | | REF_CLOSE: (8), (10), (11), (15), (21) are inconsistent by sub-proof #2029.
% 244.44/50.87  | | 
% 244.44/50.87  | End of split
% 244.44/50.87  | 
% 244.44/50.87  End of proof
% 244.44/50.87  
% 244.44/50.87  Sub-proof #1671 shows that the following formulas are inconsistent:
% 244.44/50.87  ----------------------------------------------------------------
% 244.44/50.87    (1)   ~ (e3 = e0)
% 244.44/50.87    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.44/50.87         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.44/50.87    (3)   ~ (e2 = e0)
% 244.44/50.87    (4)  op(e1, e2) = all_52_6
% 244.44/50.87    (5)   ~ (e3 = e1)
% 244.44/50.87    (6)   ~ (e3 = e2)
% 244.44/50.87    (7)  all_58_7 = e3
% 244.44/50.87    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.44/50.87         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.44/50.87    (9)  all_58_11 = e2
% 244.44/50.87    (10)  op(e1, e1) = e2
% 244.44/50.87    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.44/50.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.44/50.87    (12)  op(e1, e0) = e2
% 244.44/50.87    (13)   ~ (e1 = e0)
% 244.44/50.87    (14)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.44/50.87          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.44/50.87    (15)   ~ (e2 = e1)
% 244.44/50.87  
% 244.44/50.87  Begin of proof
% 244.44/50.87  | 
% 244.44/50.87  | BETA: splitting (2) gives:
% 244.44/50.87  | 
% 244.44/50.87  | Case 1:
% 244.44/50.87  | | 
% 244.44/50.87  | |   (16)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 244.44/50.87  | |           e1)
% 244.44/50.87  | | 
% 244.44/50.87  | | BETA: splitting (16) gives:
% 244.44/50.87  | | 
% 244.44/50.87  | | Case 1:
% 244.44/50.87  | | | 
% 244.44/50.87  | | |   (17)  all_58_6 = e1 & op(e1, e3) = e1
% 244.44/50.87  | | | 
% 244.44/50.87  | | | ALPHA: (17) implies:
% 244.44/50.87  | | |   (18)  all_58_6 = e1
% 244.44/50.87  | | | 
% 244.44/50.87  | | | REF_CLOSE: (1), (3), (7), (9), (10), (11), (13), (14), (18) are
% 244.44/50.87  | | |            inconsistent by sub-proof #2031.
% 244.44/50.87  | | | 
% 244.44/50.87  | | Case 2:
% 244.44/50.87  | | | 
% 244.44/50.87  | | |   (19)  all_58_7 = e1 & op(e1, e2) = e1
% 244.44/50.87  | | | 
% 244.44/50.87  | | | ALPHA: (19) implies:
% 244.44/50.87  | | |   (20)  all_58_7 = e1
% 244.44/50.87  | | |   (21)  op(e1, e2) = e1
% 244.44/50.87  | | | 
% 244.44/50.87  | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 244.44/50.87  | | |            (20), (21) are inconsistent by sub-proof #2106.
% 244.44/50.87  | | | 
% 244.44/50.87  | | End of split
% 244.44/50.87  | | 
% 244.44/50.87  | Case 2:
% 244.44/50.87  | | 
% 244.44/50.87  | |   (22)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 244.44/50.87  | |           e1)
% 244.44/50.87  | | 
% 244.44/50.87  | | REF_CLOSE: (10), (11), (12), (15), (22) are inconsistent by sub-proof #1880.
% 244.44/50.87  | | 
% 244.44/50.87  | End of split
% 244.44/50.87  | 
% 244.44/50.87  End of proof
% 244.44/50.87  
% 244.44/50.87  Sub-proof #1672 shows that the following formulas are inconsistent:
% 244.44/50.87  ----------------------------------------------------------------
% 244.44/50.87    (1)   ~ (e3 = e0)
% 244.44/50.87    (2)   ~ (e2 = e0)
% 244.44/50.87    (3)  all_58_6 = e3 & op(e1, e3) = e3
% 244.44/50.87    (4)  op(e1, e2) = all_52_6
% 244.44/50.87    (5)   ~ (all_52_6 = e0)
% 244.44/50.87    (6)  all_58_11 = e2
% 244.44/50.87    (7)  op(e1, e1) = e2
% 244.44/50.87    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.44/50.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.44/50.87    (9)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.44/50.87         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.44/50.87  
% 244.44/50.87  Begin of proof
% 244.44/50.87  | 
% 244.44/50.87  | ALPHA: (3) implies:
% 244.44/50.87  |   (10)  all_58_6 = e3
% 244.44/50.87  | 
% 244.44/50.87  | BETA: splitting (9) gives:
% 244.44/50.87  | 
% 244.44/50.87  | Case 1:
% 244.44/50.87  | | 
% 244.44/50.87  | |   (11)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 244.44/50.87  | |           e0)
% 244.44/50.87  | | 
% 244.44/50.87  | | BETA: splitting (11) gives:
% 244.44/50.87  | | 
% 244.44/50.87  | | Case 1:
% 244.44/50.87  | | | 
% 244.44/50.87  | | |   (12)  all_58_6 = e0 & op(e1, e3) = e0
% 244.44/50.87  | | | 
% 244.44/50.87  | | | REF_CLOSE: (1), (10), (12) are inconsistent by sub-proof #2213.
% 244.44/50.87  | | | 
% 244.44/50.87  | | Case 2:
% 244.44/50.87  | | | 
% 244.44/50.87  | | |   (13)  all_58_7 = e0 & op(e1, e2) = e0
% 244.44/50.87  | | | 
% 244.44/50.87  | | | REF_CLOSE: (4), (5), (8), (13) are inconsistent by sub-proof #2022.
% 244.44/50.87  | | | 
% 244.44/50.87  | | End of split
% 244.44/50.87  | | 
% 244.44/50.87  | Case 2:
% 244.44/50.87  | | 
% 244.44/50.87  | |   (14)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.44/50.87  | |           e0)
% 244.44/50.87  | | 
% 244.44/50.87  | | REF_CLOSE: (2), (6), (7), (8), (14) are inconsistent by sub-proof #2032.
% 244.44/50.87  | | 
% 244.44/50.87  | End of split
% 244.44/50.87  | 
% 244.44/50.87  End of proof
% 244.44/50.87  
% 244.44/50.87  Sub-proof #1673 shows that the following formulas are inconsistent:
% 244.44/50.87  ----------------------------------------------------------------
% 244.44/50.87    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.44/50.87    (2)   ~ (e3 = e0)
% 244.44/50.87    (3)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.44/50.87         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.44/50.87    (4)   ~ (e2 = e0)
% 244.44/50.87    (5)  op(e1, e2) = all_52_6
% 244.44/50.87    (6)   ~ (e3 = e1)
% 244.44/50.87    (7)  all_58_7 = e2
% 244.44/50.87    (8)   ~ (e3 = e2)
% 244.44/50.87    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.44/50.87         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.44/50.87    (10)  op(e1, e2) = e2
% 244.44/50.87    (11)  op(e1, e1) = e2
% 244.44/50.87    (12)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.44/50.87          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.44/50.87    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.44/50.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.44/50.87    (14)   ~ (e1 = e0)
% 244.44/50.87    (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.44/50.87          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.44/50.87    (16)   ~ (e2 = e1)
% 244.44/50.87  
% 244.44/50.87  Begin of proof
% 244.44/50.87  | 
% 244.44/50.87  | BETA: splitting (1) gives:
% 244.44/50.87  | 
% 244.44/50.87  | Case 1:
% 244.44/50.87  | | 
% 244.44/50.87  | |   (17)  all_58_8 = e0 & op(e1, e1) = e0
% 244.44/50.87  | | 
% 244.44/50.87  | | ALPHA: (17) implies:
% 244.44/50.87  | |   (18)  op(e1, e1) = e0
% 244.44/50.87  | | 
% 244.44/50.87  | | REF_CLOSE: (4), (11), (13), (18) are inconsistent by sub-proof #2211.
% 244.44/50.87  | | 
% 244.44/50.87  | Case 2:
% 244.44/50.87  | | 
% 244.44/50.87  | |   (19)  all_58_11 = e0 & op(e1, e0) = e0
% 244.44/50.87  | | 
% 244.44/50.87  | | ALPHA: (19) implies:
% 244.44/50.87  | |   (20)  all_58_11 = e0
% 244.44/50.87  | | 
% 244.44/50.87  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 244.44/50.87  | |            (14), (15), (16), (20) are inconsistent by sub-proof #1674.
% 244.44/50.87  | | 
% 244.44/50.87  | End of split
% 244.44/50.87  | 
% 244.44/50.87  End of proof
% 244.44/50.87  
% 244.44/50.87  Sub-proof #1674 shows that the following formulas are inconsistent:
% 244.44/50.87  ----------------------------------------------------------------
% 244.44/50.87    (1)   ~ (e3 = e0)
% 244.44/50.87    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.44/50.87         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.44/50.87    (3)   ~ (e2 = e0)
% 244.44/50.87    (4)  op(e1, e2) = all_52_6
% 244.44/50.87    (5)   ~ (e3 = e1)
% 244.44/50.87    (6)  all_58_7 = e2
% 244.44/50.87    (7)   ~ (e3 = e2)
% 244.44/50.87    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.44/50.87         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.44/50.87    (9)  op(e1, e2) = e2
% 244.44/50.87    (10)  op(e1, e1) = e2
% 244.44/50.87    (11)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.44/50.87          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.44/50.87    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.44/50.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.44/50.87    (13)  all_58_11 = e0
% 244.44/50.87    (14)   ~ (e1 = e0)
% 244.44/50.88    (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.44/50.88          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.44/50.88    (16)   ~ (e2 = e1)
% 244.44/50.88  
% 244.44/50.88  Begin of proof
% 244.44/50.88  | 
% 244.44/50.88  | BETA: splitting (8) gives:
% 244.44/50.88  | 
% 244.44/50.88  | Case 1:
% 244.44/50.88  | | 
% 244.44/50.88  | |   (17)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.44/50.88  | |           e3)
% 244.44/50.88  | | 
% 244.44/50.88  | | BETA: splitting (17) gives:
% 244.44/50.88  | | 
% 244.44/50.88  | | Case 1:
% 244.44/50.88  | | | 
% 244.44/50.88  | | |   (18)  all_58_6 = e3 & op(e1, e3) = e3
% 244.44/50.88  | | | 
% 244.44/50.88  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14),
% 244.44/50.88  | | |            (15), (16), (18) are inconsistent by sub-proof #2208.
% 244.44/50.88  | | | 
% 244.44/50.88  | | Case 2:
% 244.44/50.88  | | | 
% 244.44/50.88  | | |   (19)  all_58_7 = e3 & op(e1, e2) = e3
% 244.44/50.88  | | | 
% 244.44/50.88  | | | REF_CLOSE: (6), (7), (19) are inconsistent by sub-proof #1675.
% 244.44/50.88  | | | 
% 244.44/50.88  | | End of split
% 244.44/50.88  | | 
% 244.44/50.88  | Case 2:
% 244.44/50.88  | | 
% 244.44/50.88  | |   (20)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.44/50.88  | |           e3)
% 244.44/50.88  | | 
% 244.44/50.88  | | REF_CLOSE: (1), (7), (10), (12), (13), (20) are inconsistent by sub-proof
% 244.44/50.88  | |            #1687.
% 244.44/50.88  | | 
% 244.44/50.88  | End of split
% 244.44/50.88  | 
% 244.44/50.88  End of proof
% 244.44/50.88  
% 244.44/50.88  Sub-proof #1675 shows that the following formulas are inconsistent:
% 244.44/50.88  ----------------------------------------------------------------
% 244.44/50.88    (1)  all_58_7 = e3 & op(e1, e2) = e3
% 244.44/50.88    (2)  all_58_7 = e2
% 244.44/50.88    (3)   ~ (e3 = e2)
% 244.44/50.88  
% 244.44/50.88  Begin of proof
% 244.44/50.88  | 
% 244.44/50.88  | ALPHA: (1) implies:
% 244.44/50.88  |   (4)  all_58_7 = e3
% 244.44/50.88  | 
% 244.44/50.88  | COMBINE_EQS: (2), (4) imply:
% 244.44/50.88  |   (5)  e3 = e2
% 244.44/50.88  | 
% 244.44/50.88  | SIMP: (5) implies:
% 244.44/50.88  |   (6)  e3 = e2
% 244.44/50.88  | 
% 244.44/50.88  | REDUCE: (3), (6) imply:
% 244.44/50.88  |   (7)  $false
% 244.44/50.88  | 
% 244.44/50.88  | CLOSE: (7) is inconsistent.
% 244.44/50.88  | 
% 244.44/50.88  End of proof
% 244.44/50.88  
% 244.44/50.88  Sub-proof #1676 shows that the following formulas are inconsistent:
% 244.44/50.88  ----------------------------------------------------------------
% 244.44/50.88    (1)   ~ (e3 = e0)
% 244.44/50.88    (2)   ~ (e2 = e0)
% 244.44/50.88    (3)  op(e1, e2) = all_52_6
% 244.44/50.88    (4)  all_58_6 = e2
% 244.44/50.88    (5)   ~ (all_52_6 = e0)
% 244.44/50.88    (6)   ~ (e3 = e1)
% 244.44/50.88    (7)   ~ (e3 = e2)
% 244.44/50.88    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.44/50.88         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.44/50.88    (9)  op(e1, e1) = e2
% 244.44/50.88    (10)  all_58_7 = e1
% 244.44/50.88    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.44/50.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.44/50.88    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.44/50.88          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.44/50.88  
% 244.44/50.88  Begin of proof
% 244.44/50.88  | 
% 244.44/50.88  | BETA: splitting (8) gives:
% 244.44/50.88  | 
% 244.44/50.88  | Case 1:
% 244.44/50.88  | | 
% 244.44/50.88  | |   (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.44/50.88  | |           e3)
% 244.44/50.88  | | 
% 244.44/50.88  | | BETA: splitting (13) gives:
% 244.44/50.88  | | 
% 244.44/50.88  | | Case 1:
% 244.44/50.88  | | | 
% 244.44/50.88  | | |   (14)  all_58_6 = e3 & op(e1, e3) = e3
% 244.44/50.88  | | | 
% 244.44/50.88  | | | ALPHA: (14) implies:
% 244.44/50.88  | | |   (15)  all_58_6 = e3
% 244.44/50.88  | | | 
% 244.44/50.88  | | | REF_CLOSE: (4), (7), (15) are inconsistent by sub-proof #2024.
% 244.44/50.88  | | | 
% 244.44/50.88  | | Case 2:
% 244.44/50.88  | | | 
% 244.44/50.88  | | |   (16)  all_58_7 = e3 & op(e1, e2) = e3
% 244.44/50.88  | | | 
% 244.44/50.88  | | | REF_CLOSE: (6), (10), (16) are inconsistent by sub-proof #1679.
% 244.44/50.88  | | | 
% 244.44/50.88  | | End of split
% 244.44/50.88  | | 
% 244.44/50.88  | Case 2:
% 244.44/50.88  | | 
% 244.44/50.88  | |   (17)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.44/50.88  | |           e3)
% 244.44/50.88  | | 
% 244.44/50.88  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (11), (12), (17) are
% 244.44/50.88  | |            inconsistent by sub-proof #1677.
% 244.44/50.88  | | 
% 244.44/50.88  | End of split
% 244.44/50.88  | 
% 244.44/50.88  End of proof
% 244.44/50.88  
% 244.44/50.88  Sub-proof #1677 shows that the following formulas are inconsistent:
% 244.44/50.88  ----------------------------------------------------------------
% 244.44/50.88    (1)   ~ (e3 = e0)
% 244.44/50.88    (2)   ~ (e2 = e0)
% 244.44/50.88    (3)  op(e1, e2) = all_52_6
% 244.44/50.88    (4)  all_58_6 = e2
% 244.44/50.88    (5)   ~ (all_52_6 = e0)
% 244.44/50.88    (6)   ~ (e3 = e2)
% 244.44/50.88    (7)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.44/50.88    (8)  op(e1, e1) = e2
% 244.44/50.88    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.44/50.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.44/50.88    (10)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.44/50.88          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.44/50.88  
% 244.44/50.88  Begin of proof
% 244.44/50.88  | 
% 244.44/50.88  | BETA: splitting (7) gives:
% 244.44/50.88  | 
% 244.44/50.88  | Case 1:
% 244.44/50.88  | | 
% 244.44/50.88  | |   (11)  all_58_8 = e3 & op(e1, e1) = e3
% 244.44/50.88  | | 
% 244.44/50.88  | | ALPHA: (11) implies:
% 244.44/50.88  | |   (12)  op(e1, e1) = e3
% 244.44/50.88  | | 
% 244.44/50.88  | | REF_CLOSE: (6), (8), (9), (12) are inconsistent by sub-proof #2206.
% 244.44/50.88  | | 
% 244.44/50.88  | Case 2:
% 244.44/50.88  | | 
% 244.44/50.88  | |   (13)  all_58_11 = e3 & op(e1, e0) = e3
% 244.44/50.88  | | 
% 244.44/50.88  | | ALPHA: (13) implies:
% 244.44/50.88  | |   (14)  all_58_11 = e3
% 244.44/50.88  | | 
% 244.44/50.88  | | BETA: splitting (10) gives:
% 244.44/50.88  | | 
% 244.44/50.88  | | Case 1:
% 244.44/50.88  | | | 
% 244.44/50.88  | | |   (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 244.44/50.88  | | |           e0)
% 244.44/50.88  | | | 
% 244.44/50.88  | | | BETA: splitting (15) gives:
% 244.44/50.88  | | | 
% 244.44/50.88  | | | Case 1:
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | |   (16)  all_58_6 = e0 & op(e1, e3) = e0
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | | REF_CLOSE: (2), (4), (16) are inconsistent by sub-proof #1678.
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | Case 2:
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | |   (17)  all_58_7 = e0 & op(e1, e2) = e0
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | | REF_CLOSE: (3), (5), (9), (17) are inconsistent by sub-proof #2022.
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | End of split
% 244.44/50.88  | | | 
% 244.44/50.88  | | Case 2:
% 244.44/50.88  | | | 
% 244.44/50.88  | | |   (18)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.44/50.88  | | |           e0)
% 244.44/50.88  | | | 
% 244.44/50.88  | | | BETA: splitting (18) gives:
% 244.44/50.88  | | | 
% 244.44/50.88  | | | Case 1:
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | |   (19)  all_58_8 = e0 & op(e1, e1) = e0
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | | ALPHA: (19) implies:
% 244.44/50.88  | | | |   (20)  op(e1, e1) = e0
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | | REF_CLOSE: (2), (8), (9), (20) are inconsistent by sub-proof #2211.
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | Case 2:
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | |   (21)  all_58_11 = e0 & op(e1, e0) = e0
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | | ALPHA: (21) implies:
% 244.44/50.88  | | | |   (22)  all_58_11 = e0
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | | REF_CLOSE: (1), (14), (22) are inconsistent by sub-proof #1688.
% 244.44/50.88  | | | | 
% 244.44/50.88  | | | End of split
% 244.44/50.88  | | | 
% 244.44/50.88  | | End of split
% 244.44/50.88  | | 
% 244.44/50.88  | End of split
% 244.44/50.88  | 
% 244.44/50.88  End of proof
% 244.44/50.88  
% 244.44/50.88  Sub-proof #1678 shows that the following formulas are inconsistent:
% 244.44/50.88  ----------------------------------------------------------------
% 244.44/50.88    (1)  all_58_6 = e0 & op(e1, e3) = e0
% 244.44/50.88    (2)  all_58_6 = e2
% 244.44/50.88    (3)   ~ (e2 = e0)
% 244.44/50.88  
% 244.44/50.88  Begin of proof
% 244.44/50.88  | 
% 244.44/50.88  | ALPHA: (1) implies:
% 244.44/50.88  |   (4)  all_58_6 = e0
% 244.44/50.88  | 
% 244.44/50.88  | COMBINE_EQS: (2), (4) imply:
% 244.44/50.88  |   (5)  e2 = e0
% 244.44/50.88  | 
% 244.44/50.88  | REDUCE: (3), (5) imply:
% 244.44/50.88  |   (6)  $false
% 244.44/50.88  | 
% 244.44/50.88  | CLOSE: (6) is inconsistent.
% 244.44/50.88  | 
% 244.44/50.88  End of proof
% 244.44/50.88  
% 244.44/50.88  Sub-proof #1679 shows that the following formulas are inconsistent:
% 244.44/50.88  ----------------------------------------------------------------
% 244.44/50.88    (1)  all_58_7 = e3 & op(e1, e2) = e3
% 244.44/50.88    (2)  all_58_7 = e1
% 244.44/50.88    (3)   ~ (e3 = e1)
% 244.44/50.88  
% 244.44/50.88  Begin of proof
% 244.44/50.88  | 
% 244.44/50.88  | ALPHA: (1) implies:
% 244.44/50.88  |   (4)  all_58_7 = e3
% 244.44/50.88  | 
% 244.44/50.88  | COMBINE_EQS: (2), (4) imply:
% 244.44/50.88  |   (5)  e3 = e1
% 244.44/50.88  | 
% 244.44/50.88  | REDUCE: (3), (5) imply:
% 244.44/50.88  |   (6)  $false
% 244.44/50.88  | 
% 244.44/50.88  | CLOSE: (6) is inconsistent.
% 244.44/50.88  | 
% 244.44/50.88  End of proof
% 244.44/50.88  
% 244.44/50.88  Sub-proof #1680 shows that the following formulas are inconsistent:
% 244.44/50.88  ----------------------------------------------------------------
% 244.44/50.88    (1)  op(e0, e0) = e1
% 244.44/50.88    (2)   ~ (all_52_1 = all_52_3)
% 244.44/50.88    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.44/50.88             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.44/50.88           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.44/50.88         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.44/50.88           $i(all_56_7))
% 244.44/50.88    (4)  all_56_21 = e2
% 244.44/50.88    (5)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.44/50.88    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.44/50.88         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.44/50.88    (7)   ~ (all_52_3 = e1)
% 244.44/50.88    (8)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.44/50.88    (9)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.44/50.88         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.44/50.88    (10)   ~ (e3 = e0)
% 244.44/50.88    (11)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.44/50.88          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.44/50.88    (12)   ~ (e2 = e0)
% 244.44/50.88    (13)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.44/50.88          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.44/50.88    (14)  op(e1, e2) = all_52_6
% 244.44/50.88    (15)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.44/50.88          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.44/50.88    (16)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.44/50.88              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.44/50.88            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 244.44/50.88            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.44/50.88            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 244.44/50.88             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.44/50.88            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.44/50.88            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.44/50.88            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 244.44/50.88            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.88            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.44/50.88              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.44/50.88            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.44/50.88            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 244.44/50.88            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.44/50.88            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 244.44/50.88            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.44/50.88            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.44/50.88              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.44/50.88            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.44/50.88            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 244.44/50.88            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.44/50.88            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 244.44/50.88            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.88            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.44/50.88              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.44/50.88            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.44/50.88            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.44/50.88    (17)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.44/50.88          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.44/50.88    (18)   ~ (all_52_6 = e2)
% 244.44/50.88    (19)   ~ (all_52_1 = all_52_2)
% 244.44/50.88    (20)  op(e1, e0) = all_52_14
% 244.44/50.88    (21)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.44/50.88    (22)  op(e0, e3) = all_52_3
% 244.44/50.88    (23)  op(e0, e2) = e2
% 244.44/50.88    (24)   ~ (all_52_6 = e0)
% 244.44/50.88    (25)   ~ (e3 = e1)
% 244.44/50.88    (26)  all_54_11 = all_52_14
% 244.44/50.88    (27)   ~ (all_52_12 = e1)
% 244.44/50.88    (28)   ~ (all_52_2 = all_52_3)
% 244.44/50.88    (29)  op(e2, e2) = e0
% 244.44/50.88    (30)   ~ (all_52_12 = all_52_14)
% 244.44/50.88    (31)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.44/50.88          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.44/50.88    (32)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 244.44/50.88    (33)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 244.44/50.88          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 244.44/50.88    (34)   ~ (all_52_2 = all_52_14)
% 244.44/50.88    (35)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.44/50.88    (36)  all_54_4 = all_52_1
% 244.44/50.88    (37)   ~ (all_52_14 = e2)
% 244.44/50.88    (38)   ~ (all_52_8 = all_52_12)
% 244.44/50.88    (39)  op(e3, e1) = all_52_8
% 244.44/50.88    (40)  op(e2, e1) = all_52_9
% 244.44/50.88    (41)  all_54_9 = all_52_6
% 244.44/50.88    (42)   ~ (e3 = e2)
% 244.44/50.88    (43)   ~ (all_52_14 = e1)
% 244.44/50.88    (44)   ~ (all_52_7 = e1)
% 244.44/50.88    (45)  op(e2, e0) = e2
% 244.44/50.88    (46)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 244.44/50.88    (47)  all_54_12 = all_52_3
% 244.44/50.88    (48)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.44/50.88          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.44/50.88    (49)  all_58_15 = e1
% 244.44/50.88    (50)  op(e3, e0) = all_52_12
% 244.44/50.88    (51)   ~ (all_52_3 = e2)
% 244.44/50.88    (52)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.44/50.88          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.44/50.88    (53)   ~ (all_52_1 = e0)
% 244.44/50.88    (54)  all_56_11 = e0
% 244.44/50.88    (55)   ~ (all_52_4 = all_52_12)
% 244.44/50.88    (56)   ~ (all_52_6 = all_52_14)
% 244.44/50.88    (57)  op(e2, e3) = all_52_1
% 244.44/50.88    (58)  op(e3, e3) = e2
% 244.44/50.88    (59)   ~ (all_52_12 = e2)
% 244.44/50.88    (60)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.44/50.88          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.44/50.88    (61)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.44/50.88    (62)  op(e1, e1) = e2
% 244.44/50.88    (63)  op(e0, e2) = all_52_7
% 244.44/50.88    (64)  all_56_1 = e2
% 244.44/50.88    (65)  all_54_1 = all_52_4
% 244.44/50.88    (66)  op(e3, e2) = all_52_4
% 244.44/50.88    (67)   ~ (all_52_2 = e2)
% 244.44/50.88    (68)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.44/50.88          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.44/50.88    (69)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.44/50.88          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.44/50.88    (70)   ~ (all_52_4 = e2)
% 244.44/50.88    (71)  all_54_8 = all_52_2
% 244.44/50.88    (72)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.44/50.88          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.44/50.88    (73)   ~ (all_52_2 = all_52_6)
% 244.44/50.88    (74)  all_54_3 = all_52_12
% 244.44/50.88    (75)  all_40_2 = e2
% 244.44/50.88    (76)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.44/50.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.44/50.88    (77)  op(e1, e3) = all_52_2
% 244.44/50.88    (78)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.44/50.88          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.44/50.88    (79)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 244.44/50.88            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 244.44/50.88              e2) = all_36_1 & $i(all_36_1))
% 244.44/50.89    (80)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.44/50.89          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.44/50.89    (81)   ~ (e1 = e0)
% 244.44/50.89    (82)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.44/50.89          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.44/50.89    (83)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 244.44/50.89            op(e1, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 244.44/50.89              e3) & op(e1, e2) = all_40_1 & $i(all_40_1))
% 244.44/50.89    (84)  all_58_3 = e0
% 244.44/50.89    (85)   ~ (all_52_4 = all_52_8)
% 244.44/50.89    (86)   ~ (all_52_1 = e2)
% 244.44/50.89    (87)   ~ (all_52_4 = all_52_6)
% 244.44/50.89    (88)   ~ (all_52_4 = e0)
% 244.44/50.89    (89)   ~ (e2 = e1)
% 244.44/50.89    (90)   ~ (all_52_9 = e2)
% 244.44/50.89  
% 244.44/50.89  Begin of proof
% 244.44/50.89  | 
% 244.44/50.89  | BETA: splitting (83) gives:
% 244.44/50.89  | 
% 244.44/50.89  | Case 1:
% 244.44/50.89  | | 
% 244.44/50.89  | |   (91)   ~ (all_40_2 = e2)
% 244.44/50.89  | | 
% 244.44/50.89  | | REDUCE: (75), (91) imply:
% 244.44/50.89  | |   (92)  $false
% 244.44/50.89  | | 
% 244.44/50.89  | | CLOSE: (92) is inconsistent.
% 244.44/50.89  | | 
% 244.44/50.89  | Case 2:
% 244.44/50.89  | | 
% 244.44/50.89  | |   (93)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 244.44/50.89  | |           all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) &
% 244.44/50.89  | |           op(e1, e2) = all_40_1 & $i(all_40_1))
% 244.44/50.89  | | 
% 244.44/50.89  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 244.44/50.89  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 244.44/50.89  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 244.44/50.89  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 244.44/50.89  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 244.44/50.89  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 244.44/50.89  | |            (68), (69), (70), (71), (72), (73), (74), (76), (77), (78), (79),
% 244.44/50.89  | |            (80), (81), (82), (84), (85), (86), (87), (88), (89), (90), (93)
% 244.44/50.89  | |            are inconsistent by sub-proof #1681.
% 244.44/50.89  | | 
% 244.44/50.89  | End of split
% 244.44/50.89  | 
% 244.44/50.89  End of proof
% 244.44/50.89  
% 244.44/50.89  Sub-proof #1681 shows that the following formulas are inconsistent:
% 244.44/50.89  ----------------------------------------------------------------
% 244.44/50.89    (1)  op(e0, e0) = e1
% 244.44/50.89    (2)   ~ (all_52_1 = all_52_3)
% 244.44/50.89    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.44/50.89             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.44/50.89           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.44/50.89         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.44/50.89           $i(all_56_7))
% 244.44/50.89    (4)  all_56_21 = e2
% 244.44/50.89    (5)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.44/50.89    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.44/50.89         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.44/50.89    (7)   ~ (all_52_3 = e1)
% 244.44/50.89    (8)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.44/50.89    (9)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.44/50.89         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.44/50.89    (10)   ~ (e3 = e0)
% 244.44/50.89    (11)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.44/50.89          (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.44/50.89    (12)   ~ (e2 = e0)
% 244.44/50.89    (13)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.44/50.89          (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.44/50.89    (14)  op(e1, e2) = all_52_6
% 244.44/50.89    (15)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.44/50.89          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.44/50.89    (16)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.44/50.89              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.44/50.89            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 244.44/50.89            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.44/50.89            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 244.44/50.89             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.44/50.89            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.44/50.89            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.44/50.89            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 244.44/50.89            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.89            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.44/50.89              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.44/50.89            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.44/50.89            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 244.44/50.89            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.44/50.89            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 244.44/50.89            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.44/50.89            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.44/50.89              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.44/50.89            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.44/50.89            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 244.44/50.89            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.44/50.89            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 244.44/50.89            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.89            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.44/50.89              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.44/50.89            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.44/50.89            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.44/50.89    (17)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.44/50.89          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.44/50.89    (18)   ~ (all_52_6 = e2)
% 244.44/50.89    (19)   ~ (all_52_1 = all_52_2)
% 244.44/50.89    (20)  op(e1, e0) = all_52_14
% 244.44/50.89    (21)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.44/50.89    (22)  op(e0, e3) = all_52_3
% 244.44/50.89    (23)  op(e0, e2) = e2
% 244.44/50.89    (24)   ~ (all_52_6 = e0)
% 244.44/50.89    (25)   ~ (e3 = e1)
% 244.44/50.89    (26)  all_54_11 = all_52_14
% 244.44/50.89    (27)   ~ (all_52_12 = e1)
% 244.44/50.89    (28)   ~ (all_52_2 = all_52_3)
% 244.44/50.89    (29)  op(e2, e2) = e0
% 244.44/50.89    (30)   ~ (all_52_12 = all_52_14)
% 244.44/50.89    (31)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.44/50.89          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.44/50.89    (32)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 244.44/50.89    (33)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 244.44/50.89          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 244.44/50.89    (34)   ~ (all_52_2 = all_52_14)
% 244.44/50.89    (35)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.44/50.89    (36)  all_54_4 = all_52_1
% 244.44/50.89    (37)   ~ (all_52_14 = e2)
% 244.44/50.89    (38)   ~ (all_52_8 = all_52_12)
% 244.44/50.89    (39)  op(e3, e1) = all_52_8
% 244.44/50.89    (40)  op(e2, e1) = all_52_9
% 244.44/50.89    (41)  all_54_9 = all_52_6
% 244.44/50.89    (42)   ~ (e3 = e2)
% 244.44/50.89    (43)   ~ (all_52_14 = e1)
% 244.44/50.89    (44)   ~ (all_52_7 = e1)
% 244.44/50.89    (45)  op(e2, e0) = e2
% 244.44/50.89    (46)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 244.44/50.89    (47)  all_54_12 = all_52_3
% 244.44/50.89    (48)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.44/50.89          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.44/50.89    (49)  all_58_15 = e1
% 244.44/50.89    (50)  op(e3, e0) = all_52_12
% 244.44/50.89    (51)   ~ (all_52_3 = e2)
% 244.44/50.89    (52)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.44/50.89          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.44/50.89    (53)   ~ (all_52_1 = e0)
% 244.44/50.89    (54)  all_56_11 = e0
% 244.44/50.89    (55)   ~ (all_52_4 = all_52_12)
% 244.44/50.89    (56)   ~ (all_52_6 = all_52_14)
% 244.44/50.89    (57)  op(e2, e3) = all_52_1
% 244.44/50.89    (58)  op(e3, e3) = e2
% 244.44/50.89    (59)   ~ (all_52_12 = e2)
% 244.44/50.89    (60)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.44/50.89          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.44/50.89    (61)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 244.44/50.89            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 244.44/50.89              e2) = all_40_1 & $i(all_40_1))
% 244.44/50.89    (62)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.44/50.89    (63)  op(e1, e1) = e2
% 244.44/50.89    (64)  op(e0, e2) = all_52_7
% 244.44/50.89    (65)  all_56_1 = e2
% 244.44/50.89    (66)  all_54_1 = all_52_4
% 244.44/50.89    (67)  op(e3, e2) = all_52_4
% 244.44/50.89    (68)   ~ (all_52_2 = e2)
% 244.44/50.89    (69)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.44/50.89          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.44/50.89    (70)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 244.44/50.89          (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.44/50.89    (71)   ~ (all_52_4 = e2)
% 244.44/50.89    (72)  all_54_8 = all_52_2
% 244.44/50.89    (73)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.44/50.89          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.44/50.89    (74)   ~ (all_52_2 = all_52_6)
% 244.44/50.89    (75)  all_54_3 = all_52_12
% 244.44/50.89    (76)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.44/50.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.44/50.89    (77)  op(e1, e3) = all_52_2
% 244.44/50.89    (78)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.44/50.89          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.44/50.89    (79)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 244.44/50.89            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 244.44/50.89              e2) = all_36_1 & $i(all_36_1))
% 244.44/50.89    (80)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.44/50.89          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.44/50.89    (81)   ~ (e1 = e0)
% 244.44/50.89    (82)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.44/50.89          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.44/50.89    (83)  all_58_3 = e0
% 244.44/50.89    (84)   ~ (all_52_4 = all_52_8)
% 244.44/50.89    (85)   ~ (all_52_1 = e2)
% 244.44/50.89    (86)   ~ (all_52_4 = all_52_6)
% 244.44/50.89    (87)   ~ (all_52_4 = e0)
% 244.44/50.89    (88)   ~ (e2 = e1)
% 244.44/50.89    (89)   ~ (all_52_9 = e2)
% 244.44/50.89  
% 244.44/50.89  Begin of proof
% 244.44/50.89  | 
% 244.44/50.89  | BETA: splitting (35) gives:
% 244.44/50.89  | 
% 244.44/50.89  | Case 1:
% 244.44/50.89  | | 
% 244.44/50.89  | |   (90)  all_54_3 = e3
% 244.44/50.89  | | 
% 244.44/50.89  | | COMBINE_EQS: (75), (90) imply:
% 244.44/50.89  | |   (91)  all_52_12 = e3
% 244.44/50.89  | | 
% 244.44/50.89  | | SIMP: (91) implies:
% 244.44/50.89  | |   (92)  all_52_12 = e3
% 244.44/50.89  | | 
% 244.44/50.89  | | REDUCE: (55), (92) imply:
% 244.44/50.89  | |   (93)   ~ (all_52_4 = e3)
% 244.44/50.89  | | 
% 244.44/50.89  | | REDUCE: (38), (92) imply:
% 244.44/50.89  | |   (94)   ~ (all_52_8 = e3)
% 244.44/50.89  | | 
% 244.44/50.89  | | REDUCE: (30), (92) imply:
% 244.44/50.89  | |   (95)   ~ (all_52_14 = e3)
% 244.44/50.89  | | 
% 244.44/50.89  | | SIMP: (95) implies:
% 244.44/50.89  | |   (96)   ~ (all_52_14 = e3)
% 244.44/50.89  | | 
% 244.44/50.89  | | BETA: splitting (60) gives:
% 244.44/50.89  | | 
% 244.44/50.89  | | Case 1:
% 244.44/50.89  | | | 
% 244.44/50.89  | | |   (97)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 244.44/50.89  | | |           e0)
% 244.44/50.89  | | | 
% 244.44/50.89  | | | REF_CLOSE: (12), (58), (67), (76), (87), (97) are inconsistent by
% 244.44/50.89  | | |            sub-proof #1711.
% 244.44/50.89  | | | 
% 244.44/50.89  | | Case 2:
% 244.44/50.89  | | | 
% 244.44/50.89  | | |   (98)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 244.44/50.89  | | |           e0)
% 244.44/50.89  | | | 
% 244.44/50.89  | | | BETA: splitting (98) gives:
% 244.44/50.89  | | | 
% 244.44/50.89  | | | Case 1:
% 244.44/50.89  | | | | 
% 244.44/50.89  | | | |   (99)  all_58_4 = e0 & op(e3, e1) = e0
% 244.44/50.89  | | | | 
% 244.44/50.89  | | | | ALPHA: (99) implies:
% 244.44/50.89  | | | |   (100)  all_58_4 = e0
% 244.44/50.89  | | | |   (101)  op(e3, e1) = e0
% 244.44/50.89  | | | | 
% 244.44/50.89  | | | | BETA: splitting (31) gives:
% 244.44/50.89  | | | | 
% 244.44/50.89  | | | | Case 1:
% 244.44/50.89  | | | | | 
% 244.44/50.89  | | | | |   (102)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3,
% 244.44/50.89  | | | | |              e2) = e3)
% 244.44/50.89  | | | | | 
% 244.44/50.89  | | | | | REF_CLOSE: (42), (58), (67), (76), (93), (102) are inconsistent by
% 244.44/50.89  | | | | |            sub-proof #1959.
% 244.44/50.89  | | | | | 
% 244.44/50.89  | | | | Case 2:
% 244.44/50.89  | | | | | 
% 244.44/50.89  | | | | |   (103)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 244.44/50.89  | | | | |              e0) = e3)
% 244.44/50.89  | | | | | 
% 244.44/50.89  | | | | | BETA: splitting (103) gives:
% 244.44/50.89  | | | | | 
% 244.44/50.89  | | | | | Case 1:
% 244.44/50.89  | | | | | | 
% 244.44/50.89  | | | | | |   (104)  all_58_4 = e3 & op(e3, e1) = e3
% 244.44/50.89  | | | | | | 
% 244.44/50.89  | | | | | | ALPHA: (104) implies:
% 244.44/50.89  | | | | | |   (105)  op(e3, e1) = e3
% 244.44/50.89  | | | | | | 
% 244.44/50.89  | | | | | | REF_CLOSE: (10), (76), (101), (105) are inconsistent by sub-proof
% 244.44/50.89  | | | | | |            #2118.
% 244.44/50.89  | | | | | | 
% 244.44/50.89  | | | | | Case 2:
% 244.44/50.89  | | | | | | 
% 244.44/50.89  | | | | | |   (106)  all_58_9 = e3 & op(e3, e0) = e3
% 244.44/50.89  | | | | | | 
% 244.44/50.89  | | | | | | ALPHA: (106) implies:
% 244.44/50.89  | | | | | |   (107)  all_58_9 = e3
% 244.44/50.89  | | | | | |   (108)  op(e3, e0) = e3
% 244.44/50.89  | | | | | | 
% 244.44/50.89  | | | | | | BETA: splitting (80) gives:
% 244.44/50.89  | | | | | | 
% 244.44/50.89  | | | | | | Case 1:
% 244.44/50.89  | | | | | | | 
% 244.44/50.89  | | | | | | |   (109)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 &
% 244.44/50.89  | | | | | | |            op(e2, e2) = e3)
% 244.44/50.89  | | | | | | | 
% 244.44/50.89  | | | | | | | BETA: splitting (109) gives:
% 244.44/50.89  | | | | | | | 
% 244.44/50.89  | | | | | | | Case 1:
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | |   (110)  all_58_1 = e3 & op(e3, e2) = e3
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | | ALPHA: (110) implies:
% 244.44/50.89  | | | | | | | |   (111)  op(e3, e2) = e3
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | | REF_CLOSE: (67), (76), (93), (111) are inconsistent by sub-proof
% 244.44/50.89  | | | | | | | |            #2192.
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | Case 2:
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | |   (112)  all_58_3 = e3 & op(e2, e2) = e3
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | | ALPHA: (112) implies:
% 244.44/50.89  | | | | | | | |   (113)  all_58_3 = e3
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | | COMBINE_EQS: (83), (113) imply:
% 244.44/50.89  | | | | | | | |   (114)  e3 = e0
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | | SIMP: (114) implies:
% 244.44/50.89  | | | | | | | |   (115)  e3 = e0
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | | COMBINE_EQS: (107), (115) imply:
% 244.44/50.89  | | | | | | | |   (116)  all_58_9 = e0
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | | REF_CLOSE: (10), (31), (39), (42), (58), (67), (76), (93), (94),
% 244.44/50.89  | | | | | | | |            (116) are inconsistent by sub-proof #1956.
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | End of split
% 244.44/50.89  | | | | | | | 
% 244.44/50.89  | | | | | | Case 2:
% 244.44/50.89  | | | | | | | 
% 244.44/50.89  | | | | | | |   (117)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 &
% 244.44/50.89  | | | | | | |            op(e0, e2) = e3)
% 244.44/50.89  | | | | | | | 
% 244.44/50.89  | | | | | | | BETA: splitting (117) gives:
% 244.44/50.89  | | | | | | | 
% 244.44/50.89  | | | | | | | Case 1:
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | |   (118)  all_58_7 = e3 & op(e1, e2) = e3
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | | ALPHA: (118) implies:
% 244.44/50.89  | | | | | | | |   (119)  all_58_7 = e3
% 244.44/50.89  | | | | | | | |   (120)  op(e1, e2) = e3
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | | BETA: splitting (78) gives:
% 244.44/50.89  | | | | | | | | 
% 244.44/50.89  | | | | | | | | Case 1:
% 244.44/50.89  | | | | | | | | | 
% 244.44/50.90  | | | | | | | | |   (121)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 244.44/50.90  | | | | | | | | |            op(e2, e2) = e1)
% 244.44/50.90  | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | BETA: splitting (121) gives:
% 244.44/50.90  | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | |   (122)  all_58_1 = e1 & op(e3, e2) = e1
% 244.44/50.90  | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | ALPHA: (122) implies:
% 244.44/50.90  | | | | | | | | | |   (123)  all_58_1 = e1
% 244.44/50.90  | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | BETA: splitting (21) gives:
% 244.44/50.90  | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | |   (124)  all_54_1 = e3
% 244.44/50.90  | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | REF_CLOSE: (66), (93), (124) are inconsistent by sub-proof
% 244.44/50.90  | | | | | | | | | | |            #1930.
% 244.44/50.90  | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | |   (125)   ~ (all_54_1 = e3)
% 244.44/50.90  | | | | | | | | | | |   (126)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.44/50.90  | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | BETA: splitting (32) gives:
% 244.44/50.90  | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | |   (127)  all_54_11 = e3
% 244.44/50.90  | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | REF_CLOSE: (26), (96), (127) are inconsistent by sub-proof
% 244.44/50.90  | | | | | | | | | | | |            #1998.
% 244.44/50.90  | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | |   (128)   ~ (all_54_11 = e3)
% 244.44/50.90  | | | | | | | | | | | |   (129)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 244.44/50.90  | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | BETA: splitting (129) gives:
% 244.44/50.90  | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | |   (130)  all_54_11 = e2
% 244.44/50.90  | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | REF_CLOSE: (26), (37), (130) are inconsistent by sub-proof
% 244.44/50.90  | | | | | | | | | | | | |            #2177.
% 244.44/50.90  | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | |   (131)   ~ (all_54_11 = e2)
% 244.44/50.90  | | | | | | | | | | | | |   (132)  all_54_11 = e1 | all_54_11 = e0
% 244.44/50.90  | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | BETA: splitting (132) gives:
% 244.44/50.90  | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | |   (133)  all_54_11 = e1
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | REF_CLOSE: (26), (43), (133) are inconsistent by sub-proof
% 244.44/50.90  | | | | | | | | | | | | | |            #2176.
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | |   (134)  all_54_11 = e0
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | COMBINE_EQS: (26), (134) imply:
% 244.44/50.90  | | | | | | | | | | | | | |   (135)  all_52_14 = e0
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | SIMP: (135) implies:
% 244.44/50.90  | | | | | | | | | | | | | |   (136)  all_52_14 = e0
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | REDUCE: (34), (136) imply:
% 244.44/50.90  | | | | | | | | | | | | | |   (137)   ~ (all_52_2 = e0)
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | REDUCE: (96), (136) imply:
% 244.44/50.90  | | | | | | | | | | | | | |   (138)   ~ (e3 = e0)
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | REDUCE: (37), (136) imply:
% 244.44/50.90  | | | | | | | | | | | | | |   (139)   ~ (e2 = e0)
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | REDUCE: (43), (136) imply:
% 244.44/50.90  | | | | | | | | | | | | | |   (140)   ~ (e1 = e0)
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 244.44/50.90  | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | |   (141)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 244.44/50.90  | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 244.44/50.90  | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | |   (142)  all_58_0 = e0 & op(e3, e3) = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | |   (143)  op(e3, e3) = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (25), (42), (73), (76), (81), (88),
% 244.44/50.90  | | | | | | | | | | | | | | | |            (100), (107), (108), (143) are inconsistent by
% 244.44/50.90  | | | | | | | | | | | | | | | |            sub-proof #1706.
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | |   (144)  all_58_2 = e0 & op(e2, e3) = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | REF_CLOSE: (53), (57), (76), (144) are inconsistent by
% 244.44/50.90  | | | | | | | | | | | | | | | |            sub-proof #1985.
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | End of split
% 244.44/50.90  | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | |   (145)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 244.44/50.90  | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 244.44/50.90  | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | |   (146)  all_58_6 = e0 & op(e1, e3) = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | |   (147)  op(e1, e3) = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | REF_CLOSE: (76), (77), (137), (147) are inconsistent by
% 244.44/50.90  | | | | | | | | | | | | | | | |            sub-proof #2023.
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | |   (148)  all_58_12 = e0 & op(e0, e3) = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | |   (149)  all_58_12 = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | |   (150)  all_54_1 = e2
% 244.44/50.90  | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (71), (150) are inconsistent by sub-proof
% 244.44/50.90  | | | | | | | | | | | | | | | | |            #1928.
% 244.44/50.90  | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | |   (151)   ~ (all_54_1 = e2)
% 244.44/50.90  | | | | | | | | | | | | | | | | |   (152)  all_54_1 = e1 | all_54_1 = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | |   (153)  all_54_1 = e1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (153) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | |   (154)  all_52_4 = e1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | SIMP: (154) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | |   (155)  all_52_4 = e1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | REDUCE: (86), (155) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | |   (156)   ~ (all_52_6 = e1)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | SIMP: (156) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | |   (157)   ~ (all_52_6 = e1)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | REDUCE: (84), (155) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | |   (158)   ~ (all_52_8 = e1)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | SIMP: (158) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | |   (159)   ~ (all_52_8 = e1)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | REDUCE: (93), (155) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | |   (160)   ~ (e3 = e1)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | REDUCE: (71), (155) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | |   (161)   ~ (e2 = e1)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | REDUCE: (67), (155) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | |   (162)  op(e3, e2) = e1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | |   (163)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | |   (164)  all_58_6 = e1 & op(e1, e3) = e1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | |   (165)  op(e1, e3) = e1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | |   (166)  all_54_9 = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (166) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | |   (167)  all_52_6 = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | SIMP: (167) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | |   (168)  all_52_6 = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (168) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | |   (169)   ~ (all_52_2 = e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | |   (170)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | |   (171)  all_58_0 = e3 & op(e3, e3) = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | |   (172)  op(e3, e3) = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (58), (76), (172) are inconsistent by
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2194.
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | |   (173)  all_58_2 = e3 & op(e2, e3) = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | |   (174)  op(e2, e3) = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | |   (175)  all_54_8 = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (175) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | |   (176)  all_52_2 = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (176) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | |   (177)  $false
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (177) is inconsistent.
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | |   (178)   ~ (all_54_8 = e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | |   (179)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (180)  all_54_8 = e2
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (180) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (181)  all_52_2 = e2
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (181) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (182)  $false
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (182) is inconsistent.
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (183)   ~ (all_54_8 = e2)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (184)  all_54_8 = e1 | all_54_8 = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (185)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e2) = all_40_1 & $i(all_40_0) &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_40_1)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (186)  op(e1, e2) = all_40_1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (187)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_58_12 = e3 & op(e0, e3) = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (20), (25), (42), (52), (63), (76), (96),
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (149), (165), (188) are inconsistent by
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1705.
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (189)  all_58_13 = e3 & op(e0, e2) = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (190)  op(e0, e2) = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (42), (76), (190) are inconsistent by
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2254.
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (191)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (192)  all_58_14 = e3 & op(e0, e1) = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (193)  op(e0, e1) = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (194)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (197)  op(e3, e2) = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (76), (162), (197) are inconsistent by
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2265.
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (198)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (77), (88), (162), (169), (198) are
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1704.
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (199)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (201)  op(e3, e1) = e1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (76), (159), (201) are inconsistent by
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2309.
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (202)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (204)   ~ (all_56_11 = e0)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (204) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (205)  $false
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent.
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (206)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (207)  all_56_7 = e0
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (208)  all_54_8 = e1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (208) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_52_2 = e1
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (209) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (210)   ~ (all_52_1 = e1)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (209) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (211)   ~ (all_52_3 = e1)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  all_54_4 = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (212) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_52_1 = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (213) implies:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_52_1 = e3
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (214) imply:
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)   ~ (all_52_3 = e3)
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (215) implies:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)   ~ (all_52_3 = e3)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  all_54_12 = e3
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (216), (217) are inconsistent by sub-proof
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2266.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_3 & $i(all_56_3))
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (42), (65), (76), (162), (174), (219) are
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1703.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_56_7 & $i(all_56_7))
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_5 & $i(all_56_5)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (47), (51), (63), (76), (88), (165), (218),
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221) are inconsistent by sub-proof #1702.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          = all_56_7 & $i(all_56_7)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  op(e0, all_56_7) = e0
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (207), (223) imply:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  op(e0, e0) = e0
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (76), (81), (224) are inconsistent by
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (225)   ~ (all_54_4 = e3)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (225) imply:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (226)   ~ (all_52_1 = e3)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (76), (174), (226) are inconsistent by
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2337.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  all_54_8 = e0
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (227) imply:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  all_52_2 = e0
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (228) imply:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  $false
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  op(e2, e1) = e2
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (76), (89), (233) are inconsistent by
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2328.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e1
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  op(e1, e2) = e1
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (76), (79), (120), (186), (236) are
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1700.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e2
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (238)   ~ (all_56_11 = e0)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (238) imply:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (239)  $false
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (240)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e0)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (241)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (242)  op(e2, e0) = e0
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (45), (76), (242) are inconsistent by
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2121.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (243)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (20), (43), (76), (193), (243) are
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1699.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_58_15 = e3 & op(e0, e0) = e3
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  all_58_15 = e3
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (245) imply:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  e3 = e1
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (246) imply:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  all_58_9 = e1
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (25), (31), (42), (58), (60), (67),
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (76), (81), (93), (123), (247) are inconsistent by
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1694.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 &
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_40_1)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (79), (120), (248) are inconsistent by
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2144.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | |   (249)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | |   (250)  all_58_6 = e3 & op(e1, e3) = e3
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | |   (251)  op(e1, e3) = e3
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (77), (169), (251) are inconsistent by
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2335.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | |   (252)  all_58_12 = e3 & op(e0, e3) = e3
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (20), (25), (42), (52), (63), (76), (96),
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | |            (119), (149), (165), (252) are inconsistent by
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1705.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | |   (253)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (26), (32), (37), (41), (43), (56), (96),
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | |            (157), (253) are inconsistent by sub-proof #1693.
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.91  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |   (254)  all_58_7 = e1 & op(e1, e2) = e1
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |   (255)  all_58_7 = e1
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |   (256)  op(e1, e2) = e1
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (14), (15), (17), (25), (27), (29),
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            (39), (42), (50), (58), (73), (76), (80), (81),
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            (88), (159), (255), (256) are inconsistent by
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            sub-proof #1712.
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |   (257)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (43), (63), (76), (88), (257) are
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1692.
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | |   (258)  all_54_1 = e0
% 244.44/50.92  | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (87), (258) are inconsistent by sub-proof
% 244.44/50.92  | | | | | | | | | | | | | | | | | |            #2050.
% 244.44/50.92  | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | |   (259)  all_58_3 = e1 & op(e2, e2) = e1
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | REF_CLOSE: (81), (83), (259) are inconsistent by sub-proof
% 244.44/50.92  | | | | | | | | | |            #1752.
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | |   (260)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 244.44/50.92  | | | | | | | | |            op(e0, e2) = e1)
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | BETA: splitting (260) gives:
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | |   (261)  all_58_7 = e1 & op(e1, e2) = e1
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | ALPHA: (261) implies:
% 244.44/50.92  | | | | | | | | | |   (262)  op(e1, e2) = e1
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | REF_CLOSE: (25), (76), (120), (262) are inconsistent by
% 244.44/50.92  | | | | | | | | | |            sub-proof #2094.
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | |   (263)  all_58_13 = e1 & op(e0, e2) = e1
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | REF_CLOSE: (44), (64), (76), (263) are inconsistent by
% 244.44/50.92  | | | | | | | | | |            sub-proof #2275.
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | 
% 244.44/50.92  | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | 
% 244.44/50.92  | | | | | | | |   (264)  all_58_13 = e3 & op(e0, e2) = e3
% 244.44/50.92  | | | | | | | | 
% 244.44/50.92  | | | | | | | | ALPHA: (264) implies:
% 244.44/50.92  | | | | | | | |   (265)  op(e0, e2) = e3
% 244.44/50.92  | | | | | | | | 
% 244.44/50.92  | | | | | | | | REF_CLOSE: (23), (42), (76), (265) are inconsistent by sub-proof
% 244.44/50.92  | | | | | | | |            #2254.
% 244.44/50.92  | | | | | | | | 
% 244.44/50.92  | | | | | | | End of split
% 244.44/50.92  | | | | | | | 
% 244.44/50.92  | | | | | | End of split
% 244.44/50.92  | | | | | | 
% 244.44/50.92  | | | | | End of split
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | End of split
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | Case 2:
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | |   (266)  all_58_9 = e0 & op(e3, e0) = e0
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | | ALPHA: (266) implies:
% 244.44/50.92  | | | |   (267)  all_58_9 = e0
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | | BETA: splitting (31) gives:
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | | Case 1:
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | |   (268)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3,
% 244.44/50.92  | | | | |              e2) = e3)
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | | REF_CLOSE: (42), (58), (67), (76), (93), (268) are inconsistent by
% 244.44/50.92  | | | | |            sub-proof #1959.
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | Case 2:
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | |   (269)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 244.44/50.92  | | | | |              e0) = e3)
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | | REF_CLOSE: (10), (39), (76), (94), (267), (269) are inconsistent by
% 244.44/50.92  | | | | |            sub-proof #1957.
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | End of split
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | End of split
% 244.44/50.92  | | | 
% 244.44/50.92  | | End of split
% 244.44/50.92  | | 
% 244.44/50.92  | Case 2:
% 244.44/50.92  | | 
% 244.44/50.92  | |   (270)   ~ (all_54_3 = e3)
% 244.44/50.92  | |   (271)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.44/50.92  | | 
% 244.44/50.92  | | REDUCE: (75), (270) imply:
% 244.44/50.92  | |   (272)   ~ (all_52_12 = e3)
% 244.44/50.92  | | 
% 244.44/50.92  | | BETA: splitting (271) gives:
% 244.44/50.92  | | 
% 244.44/50.92  | | Case 1:
% 244.44/50.92  | | | 
% 244.44/50.92  | | |   (273)  all_54_3 = e2
% 244.44/50.92  | | | 
% 244.44/50.92  | | | REF_CLOSE: (59), (75), (273) are inconsistent by sub-proof #2290.
% 244.44/50.92  | | | 
% 244.44/50.92  | | Case 2:
% 244.44/50.92  | | | 
% 244.44/50.92  | | |   (274)   ~ (all_54_3 = e2)
% 244.44/50.92  | | |   (275)  all_54_3 = e1 | all_54_3 = e0
% 244.44/50.92  | | | 
% 244.44/50.92  | | | BETA: splitting (70) gives:
% 244.44/50.92  | | | 
% 244.44/50.92  | | | Case 1:
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | |   (276)  (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2,
% 244.44/50.92  | | | |              e0) = e3)
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | | BETA: splitting (276) gives:
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | | Case 1:
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | |   (277)  all_58_9 = e3 & op(e3, e0) = e3
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | | ALPHA: (277) implies:
% 244.44/50.92  | | | | |   (278)  op(e3, e0) = e3
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | | REF_CLOSE: (50), (76), (272), (278) are inconsistent by sub-proof
% 244.44/50.92  | | | | |            #2179.
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | Case 2:
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | |   (279)  all_58_10 = e3 & op(e2, e0) = e3
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | | ALPHA: (279) implies:
% 244.44/50.92  | | | | |   (280)  op(e2, e0) = e3
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | | REF_CLOSE: (42), (45), (76), (280) are inconsistent by sub-proof
% 244.44/50.92  | | | | |            #2152.
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | End of split
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | Case 2:
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | |   (281)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 244.44/50.92  | | | |              e0) = e3)
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | | BETA: splitting (281) gives:
% 244.44/50.92  | | | | 
% 244.44/50.92  | | | | Case 1:
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | |   (282)  all_58_11 = e3 & op(e1, e0) = e3
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | | ALPHA: (282) implies:
% 244.44/50.92  | | | | |   (283)  all_58_11 = e3
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | | BETA: splitting (82) gives:
% 244.44/50.92  | | | | | 
% 244.44/50.92  | | | | | Case 1:
% 244.44/50.92  | | | | | | 
% 244.44/50.92  | | | | | |   (284)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1,
% 244.44/50.92  | | | | | |              e2) = e0)
% 244.44/50.92  | | | | | | 
% 244.44/50.92  | | | | | | BETA: splitting (284) gives:
% 244.44/50.92  | | | | | | 
% 244.44/50.92  | | | | | | Case 1:
% 244.44/50.92  | | | | | | | 
% 244.44/50.92  | | | | | | |   (285)  all_58_6 = e0 & op(e1, e3) = e0
% 244.44/50.92  | | | | | | | 
% 244.44/50.92  | | | | | | | ALPHA: (285) implies:
% 244.44/50.92  | | | | | | |   (286)  all_58_6 = e0
% 244.44/50.92  | | | | | | | 
% 244.44/50.92  | | | | | | | BETA: splitting (69) gives:
% 244.44/50.92  | | | | | | | 
% 244.44/50.92  | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | 
% 244.44/50.92  | | | | | | | |   (287)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 244.44/50.92  | | | | | | | |            op(e2, e3) = e1)
% 244.44/50.92  | | | | | | | | 
% 244.44/50.92  | | | | | | | | BETA: splitting (287) gives:
% 244.44/50.92  | | | | | | | | 
% 244.44/50.92  | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | |   (288)  all_58_0 = e1 & op(e3, e3) = e1
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | ALPHA: (288) implies:
% 244.44/50.92  | | | | | | | | |   (289)  op(e3, e3) = e1
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | REF_CLOSE: (58), (76), (88), (289) are inconsistent by
% 244.44/50.92  | | | | | | | | |            sub-proof #2267.
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | |   (290)  all_58_2 = e1 & op(e2, e3) = e1
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | ALPHA: (290) implies:
% 244.44/50.92  | | | | | | | | |   (291)  all_58_2 = e1
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | BETA: splitting (275) gives:
% 244.44/50.92  | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | |   (292)  all_54_3 = e1
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | REF_CLOSE: (27), (75), (292) are inconsistent by sub-proof
% 244.44/50.92  | | | | | | | | | |            #2289.
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | |   (293)  all_54_3 = e0
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | COMBINE_EQS: (75), (293) imply:
% 244.44/50.92  | | | | | | | | | |   (294)  all_52_12 = e0
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | SIMP: (294) implies:
% 244.44/50.92  | | | | | | | | | |   (295)  all_52_12 = e0
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | REDUCE: (30), (295) imply:
% 244.44/50.92  | | | | | | | | | |   (296)   ~ (all_52_14 = e0)
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | SIMP: (296) implies:
% 244.44/50.92  | | | | | | | | | |   (297)   ~ (all_52_14 = e0)
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | REDUCE: (59), (295) imply:
% 244.44/50.92  | | | | | | | | | |   (298)   ~ (e2 = e0)
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | BETA: splitting (32) gives:
% 244.44/50.92  | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | |   (299)  all_54_11 = e3
% 244.44/50.92  | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | COMBINE_EQS: (26), (299) imply:
% 244.44/50.92  | | | | | | | | | | |   (300)  all_52_14 = e3
% 244.44/50.92  | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | SIMP: (300) implies:
% 244.44/50.92  | | | | | | | | | | |   (301)  all_52_14 = e3
% 244.44/50.92  | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | REDUCE: (34), (301) imply:
% 244.44/50.92  | | | | | | | | | | |   (302)   ~ (all_52_2 = e3)
% 244.44/50.92  | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | REDUCE: (56), (301) imply:
% 244.44/50.92  | | | | | | | | | | |   (303)   ~ (all_52_6 = e3)
% 244.44/50.92  | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | REDUCE: (20), (301) imply:
% 244.44/50.92  | | | | | | | | | | |   (304)  op(e1, e0) = e3
% 244.44/50.92  | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | BETA: splitting (13) gives:
% 244.44/50.92  | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | |   (305)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 244.44/50.92  | | | | | | | | | | | |            & op(e2, e2) = e3)
% 244.44/50.92  | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | BETA: splitting (305) gives:
% 244.44/50.92  | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | |   (306)  all_58_2 = e3 & op(e2, e3) = e3
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | ALPHA: (306) implies:
% 244.44/50.92  | | | | | | | | | | | | |   (307)  all_58_2 = e3
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | REF_CLOSE: (25), (291), (307) are inconsistent by sub-proof
% 244.44/50.92  | | | | | | | | | | | | |            #1691.
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | |   (308)  all_58_3 = e3 & op(e2, e2) = e3
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | ALPHA: (308) implies:
% 244.44/50.92  | | | | | | | | | | | | |   (309)  all_58_3 = e3
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | COMBINE_EQS: (83), (309) imply:
% 244.44/50.92  | | | | | | | | | | | | |   (310)  e3 = e0
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | SIMP: (310) implies:
% 244.44/50.92  | | | | | | | | | | | | |   (311)  e3 = e0
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | COMBINE_EQS: (283), (311) imply:
% 244.44/50.92  | | | | | | | | | | | | |   (312)  all_58_11 = e0
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | REF_CLOSE: (10), (14), (42), (52), (63), (76), (286), (303),
% 244.44/50.92  | | | | | | | | | | | | |            (312) are inconsistent by sub-proof #1686.
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | |   (313)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 244.44/50.92  | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 244.44/50.92  | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | BETA: splitting (313) gives:
% 244.44/50.92  | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | |   (314)  all_58_5 = e3 & op(e2, e1) = e3
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | ALPHA: (314) implies:
% 244.44/50.92  | | | | | | | | | | | | |   (315)  op(e2, e1) = e3
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | BETA: splitting (46) gives:
% 244.44/50.92  | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | |   (316)  all_54_9 = e3
% 244.44/50.92  | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | REF_CLOSE: (41), (303), (316) are inconsistent by sub-proof
% 244.44/50.92  | | | | | | | | | | | | | |            #1955.
% 244.44/50.92  | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | |   (317)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 244.44/50.92  | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 244.44/50.92  | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | |   (318)  all_54_9 = e2
% 244.44/50.92  | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | REF_CLOSE: (18), (41), (318) are inconsistent by sub-proof
% 244.44/50.92  | | | | | | | | | | | | | | |            #1954.
% 244.44/50.92  | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | |   (319)  all_54_9 = e1 | all_54_9 = e0
% 244.44/50.92  | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 244.44/50.92  | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | |   (320)  all_54_9 = e1
% 244.44/50.92  | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (320) imply:
% 244.44/50.92  | | | | | | | | | | | | | | | |   (321)  all_52_6 = e1
% 244.44/50.92  | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | SIMP: (321) implies:
% 244.44/50.92  | | | | | | | | | | | | | | | |   (322)  all_52_6 = e1
% 244.44/50.92  | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | REDUCE: (74), (322) imply:
% 244.44/50.92  | | | | | | | | | | | | | | | |   (323)   ~ (all_52_2 = e1)
% 244.44/50.92  | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | REDUCE: (86), (322) imply:
% 244.44/50.92  | | | | | | | | | | | | | | | |   (324)   ~ (all_52_4 = e1)
% 244.44/50.92  | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 244.44/50.92  | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | |   (325)  all_54_8 = e3
% 244.44/50.92  | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (302), (325) are inconsistent by sub-proof
% 244.44/50.92  | | | | | | | | | | | | | | | | |            #2011.
% 244.44/50.92  | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | |   (326)   ~ (all_54_8 = e3)
% 244.44/50.92  | | | | | | | | | | | | | | | | |   (327)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.44/50.92  | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 244.44/50.92  | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | |   (328)  all_54_1 = e3
% 244.44/50.92  | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (328) imply:
% 244.44/50.92  | | | | | | | | | | | | | | | | | |   (329)  all_52_4 = e3
% 244.44/50.92  | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | SIMP: (329) implies:
% 244.44/50.92  | | | | | | | | | | | | | | | | | |   (330)  all_52_4 = e3
% 244.44/50.92  | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | REDUCE: (67), (330) imply:
% 244.44/50.92  | | | | | | | | | | | | | | | | | |   (331)  op(e3, e2) = e3
% 244.44/50.92  | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |   (332)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.44/50.92  | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |   (333)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            = e3)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |   (334)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |          e3
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |   (335)   ~ (all_56_21 = e2)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (335) imply:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |   (336)  $false
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent.
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |   (337)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (76), (77), (302), (331), (337) are
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1685.
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |   (338)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | |            = e0)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | BETA: splitting (338) gives:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |   (339)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |   (340)  op(e1, e3) = e1
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (77), (323), (340) are inconsistent by
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1948.
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |   (341)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |   (342)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |   (343)  op(e3, e0) = e3
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (76), (272), (343) are inconsistent by
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2179.
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |   (344)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |            e3) = e0
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |   (345)  op(e0, e3) = e0
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (28), (68), (72), (76), (323), (327), (345)
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1684.
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | End of split
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.92  | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.92  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |   (346)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 244.44/50.93  | | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives:
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | 
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | Case 1:
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |   (347)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |            = e2)
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (42), (54), (76), (315), (347) are
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1683.
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | | 
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | Case 2:
% 244.44/50.93  | | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | |   (348)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | |            = e0)
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |   (349)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | | ALPHA: (349) implies:
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |   (350)  op(e2, e0) = e0
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (45), (76), (350) are inconsistent by
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2121.
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |   (351)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (25), (76), (297), (304), (351) are
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1893.
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | Case 2:
% 244.52/50.93  | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | |   (352)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.52/50.93  | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (71), (87), (324), (352) are inconsistent by
% 244.52/50.93  | | | | | | | | | | | | | | | | | |            sub-proof #2048.
% 244.52/50.93  | | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | Case 2:
% 244.52/50.93  | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | |   (353)  all_54_9 = e0
% 244.52/50.93  | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | | REF_CLOSE: (24), (41), (353) are inconsistent by sub-proof
% 244.52/50.93  | | | | | | | | | | | | | | | |            #1953.
% 244.52/50.93  | | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | Case 2:
% 244.52/50.93  | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | |   (354)  all_58_10 = e3 & op(e2, e0) = e3
% 244.52/50.93  | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | ALPHA: (354) implies:
% 244.52/50.93  | | | | | | | | | | | | |   (355)  op(e2, e0) = e3
% 244.52/50.93  | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | | REF_CLOSE: (42), (45), (76), (355) are inconsistent by
% 244.52/50.93  | | | | | | | | | | | | |            sub-proof #2152.
% 244.52/50.93  | | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | Case 2:
% 244.52/50.93  | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | |   (356)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 244.52/50.93  | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | | REF_CLOSE: (26), (37), (43), (297), (356) are inconsistent by
% 244.52/50.93  | | | | | | | | | | |            sub-proof #2173.
% 244.52/50.93  | | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | | 
% 244.52/50.93  | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | 
% 244.52/50.93  | | | | | | | Case 2:
% 244.52/50.93  | | | | | | | | 
% 244.52/50.93  | | | | | | | |   (357)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 244.52/50.93  | | | | | | | |            op(e0, e3) = e1)
% 244.52/50.93  | | | | | | | | 
% 244.52/50.93  | | | | | | | | BETA: splitting (357) gives:
% 244.52/50.93  | | | | | | | | 
% 244.52/50.93  | | | | | | | | Case 1:
% 244.52/50.93  | | | | | | | | | 
% 244.52/50.93  | | | | | | | | |   (358)  all_58_6 = e1 & op(e1, e3) = e1
% 244.52/50.93  | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | REF_CLOSE: (81), (286), (358) are inconsistent by sub-proof
% 244.52/50.93  | | | | | | | | |            #1682.
% 244.52/50.93  | | | | | | | | | 
% 244.52/50.93  | | | | | | | | Case 2:
% 244.52/50.93  | | | | | | | | | 
% 244.52/50.93  | | | | | | | | |   (359)  all_58_12 = e1 & op(e0, e3) = e1
% 244.52/50.93  | | | | | | | | | 
% 244.52/50.93  | | | | | | | | | REF_CLOSE: (7), (22), (76), (359) are inconsistent by
% 244.52/50.93  | | | | | | | | |            sub-proof #2276.
% 244.52/50.93  | | | | | | | | | 
% 244.52/50.93  | | | | | | | | End of split
% 244.52/50.93  | | | | | | | | 
% 244.52/50.93  | | | | | | | End of split
% 244.52/50.93  | | | | | | | 
% 244.52/50.93  | | | | | | Case 2:
% 244.52/50.93  | | | | | | | 
% 244.52/50.93  | | | | | | |   (360)  all_58_7 = e0 & op(e1, e2) = e0
% 244.52/50.93  | | | | | | | 
% 244.52/50.93  | | | | | | | REF_CLOSE: (14), (24), (76), (360) are inconsistent by sub-proof
% 244.52/50.93  | | | | | | |            #2022.
% 244.52/50.93  | | | | | | | 
% 244.52/50.93  | | | | | | End of split
% 244.52/50.93  | | | | | | 
% 244.52/50.93  | | | | | Case 2:
% 244.52/50.93  | | | | | | 
% 244.52/50.93  | | | | | |   (361)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 244.52/50.93  | | | | | |            op(e1, e0) = e0)
% 244.52/50.93  | | | | | | 
% 244.52/50.93  | | | | | | REF_CLOSE: (10), (12), (63), (76), (283), (361) are inconsistent by
% 244.52/50.93  | | | | | |            sub-proof #2203.
% 244.52/50.93  | | | | | | 
% 244.52/50.93  | | | | | End of split
% 244.52/50.93  | | | | | 
% 244.52/50.93  | | | | Case 2:
% 244.52/50.93  | | | | | 
% 244.52/50.93  | | | | |   (362)  all_58_15 = e3 & op(e0, e0) = e3
% 244.52/50.93  | | | | | 
% 244.52/50.93  | | | | | REF_CLOSE: (25), (49), (362) are inconsistent by sub-proof #1915.
% 244.52/50.93  | | | | | 
% 244.52/50.93  | | | | End of split
% 244.52/50.93  | | | | 
% 244.52/50.93  | | | End of split
% 244.52/50.93  | | | 
% 244.52/50.93  | | End of split
% 244.52/50.93  | | 
% 244.52/50.93  | End of split
% 244.52/50.93  | 
% 244.52/50.93  End of proof
% 244.52/50.93  
% 244.52/50.93  Sub-proof #1682 shows that the following formulas are inconsistent:
% 244.52/50.93  ----------------------------------------------------------------
% 244.52/50.93    (1)  all_58_6 = e1 & op(e1, e3) = e1
% 244.52/50.93    (2)  all_58_6 = e0
% 244.52/50.93    (3)   ~ (e1 = e0)
% 244.52/50.93  
% 244.52/50.93  Begin of proof
% 244.52/50.93  | 
% 244.52/50.93  | ALPHA: (1) implies:
% 244.52/50.93  |   (4)  all_58_6 = e1
% 244.52/50.93  | 
% 244.52/50.93  | COMBINE_EQS: (2), (4) imply:
% 244.52/50.93  |   (5)  e1 = e0
% 244.52/50.93  | 
% 244.52/50.93  | REDUCE: (3), (5) imply:
% 244.52/50.93  |   (6)  $false
% 244.52/50.93  | 
% 244.52/50.93  | CLOSE: (6) is inconsistent.
% 244.52/50.93  | 
% 244.52/50.93  End of proof
% 244.52/50.93  
% 244.52/50.93  Sub-proof #1683 shows that the following formulas are inconsistent:
% 244.52/50.93  ----------------------------------------------------------------
% 244.52/50.93    (1)   ~ (e3 = e1)
% 244.52/50.93    (2)   ~ (e3 = e2)
% 244.52/50.93    (3)  all_56_11 = e0
% 244.52/50.93    (4)  op(e2, e1) = e3
% 244.52/50.93    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.93    (6)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.52/50.93             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.52/50.93           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.52/50.93             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 244.52/50.93           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 244.52/50.93           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.52/50.93           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.52/50.93  
% 244.52/50.93  Begin of proof
% 244.52/50.93  | 
% 244.52/50.93  | BETA: splitting (6) gives:
% 244.52/50.93  | 
% 244.52/50.93  | Case 1:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (7)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.52/50.93  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 244.52/50.93  | |        & op(e1, e2) = e2
% 244.52/50.93  | | 
% 244.52/50.93  | | ALPHA: (7) implies:
% 244.52/50.93  | |   (8)  op(e2, e1) = e2
% 244.52/50.93  | | 
% 244.52/50.93  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2256.
% 244.52/50.93  | | 
% 244.52/50.93  | Case 2:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (9)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.52/50.93  | |            = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) =
% 244.52/50.93  | |          e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.52/50.93  | |          (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.52/50.93  | |          (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.52/50.93  | | 
% 244.52/50.93  | | BETA: splitting (9) gives:
% 244.52/50.93  | | 
% 244.52/50.93  | | Case 1:
% 244.52/50.93  | | | 
% 244.52/50.93  | | |   (10)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.52/50.93  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.52/50.93  | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 244.52/50.93  | | | 
% 244.52/50.93  | | | ALPHA: (10) implies:
% 244.52/50.93  | | |   (11)  op(e2, e1) = e1
% 244.52/50.93  | | | 
% 244.52/50.93  | | | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #2255.
% 244.52/50.93  | | | 
% 244.52/50.93  | | Case 2:
% 244.52/50.93  | | | 
% 244.52/50.93  | | |   (12)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.52/50.93  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.52/50.93  | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 244.52/50.93  | | | 
% 244.52/50.93  | | | ALPHA: (12) implies:
% 244.52/50.93  | | |   (13)   ~ (all_56_11 = e0)
% 244.52/50.93  | | | 
% 244.52/50.93  | | | REDUCE: (3), (13) imply:
% 244.52/50.93  | | |   (14)  $false
% 244.52/50.93  | | | 
% 244.52/50.93  | | | CLOSE: (14) is inconsistent.
% 244.52/50.93  | | | 
% 244.52/50.93  | | End of split
% 244.52/50.93  | | 
% 244.52/50.93  | End of split
% 244.52/50.93  | 
% 244.52/50.93  End of proof
% 244.52/50.93  
% 244.52/50.93  Sub-proof #1684 shows that the following formulas are inconsistent:
% 244.52/50.93  ----------------------------------------------------------------
% 244.52/50.93    (1)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.52/50.93    (2)  op(e0, e3) = all_52_3
% 244.52/50.93    (3)   ~ (all_52_2 = all_52_3)
% 244.52/50.93    (4)   ~ (all_52_2 = e1)
% 244.52/50.93    (5)  op(e0, e3) = e0
% 244.52/50.93    (6)   ~ (all_52_2 = e2)
% 244.52/50.93    (7)  all_54_8 = all_52_2
% 244.52/50.93    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.93  
% 244.52/50.93  Begin of proof
% 244.52/50.93  | 
% 244.52/50.93  | BETA: splitting (1) gives:
% 244.52/50.93  | 
% 244.52/50.93  | Case 1:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (9)  all_54_8 = e2
% 244.52/50.93  | | 
% 244.52/50.93  | | COMBINE_EQS: (7), (9) imply:
% 244.52/50.93  | |   (10)  all_52_2 = e2
% 244.52/50.93  | | 
% 244.52/50.93  | | REDUCE: (6), (10) imply:
% 244.52/50.93  | |   (11)  $false
% 244.52/50.93  | | 
% 244.52/50.93  | | CLOSE: (11) is inconsistent.
% 244.52/50.93  | | 
% 244.52/50.93  | Case 2:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (12)  all_54_8 = e1 | all_54_8 = e0
% 244.52/50.93  | | 
% 244.52/50.93  | | BETA: splitting (12) gives:
% 244.52/50.93  | | 
% 244.52/50.93  | | Case 1:
% 244.52/50.93  | | | 
% 244.52/50.93  | | |   (13)  all_54_8 = e1
% 244.52/50.93  | | | 
% 244.52/50.93  | | | COMBINE_EQS: (7), (13) imply:
% 244.52/50.93  | | |   (14)  all_52_2 = e1
% 244.52/50.93  | | | 
% 244.52/50.93  | | | REDUCE: (4), (14) imply:
% 244.52/50.93  | | |   (15)  $false
% 244.52/50.93  | | | 
% 244.52/50.93  | | | CLOSE: (15) is inconsistent.
% 244.52/50.93  | | | 
% 244.52/50.93  | | Case 2:
% 244.52/50.93  | | | 
% 244.52/50.93  | | |   (16)  all_54_8 = e0
% 244.52/50.93  | | | 
% 244.52/50.93  | | | COMBINE_EQS: (7), (16) imply:
% 244.52/50.93  | | |   (17)  all_52_2 = e0
% 244.52/50.93  | | | 
% 244.52/50.93  | | | REDUCE: (3), (17) imply:
% 244.52/50.93  | | |   (18)   ~ (all_52_3 = e0)
% 244.52/50.93  | | | 
% 244.52/50.93  | | | SIMP: (18) implies:
% 244.52/50.93  | | |   (19)   ~ (all_52_3 = e0)
% 244.52/50.93  | | | 
% 244.52/50.93  | | | REF_CLOSE: (2), (5), (8), (19) are inconsistent by sub-proof #2331.
% 244.52/50.93  | | | 
% 244.52/50.93  | | End of split
% 244.52/50.93  | | 
% 244.52/50.93  | End of split
% 244.52/50.93  | 
% 244.52/50.93  End of proof
% 244.52/50.93  
% 244.52/50.93  Sub-proof #1685 shows that the following formulas are inconsistent:
% 244.52/50.93  ----------------------------------------------------------------
% 244.52/50.93    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 244.52/50.93           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 244.52/50.93             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.52/50.93           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 244.52/50.93             e1) = e3 & op(e1, e3) = e3)
% 244.52/50.93    (2)   ~ (e3 = e2)
% 244.52/50.93    (3)   ~ (all_52_2 = e3)
% 244.52/50.93    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.93    (5)  op(e1, e3) = all_52_2
% 244.52/50.93    (6)  op(e3, e2) = e3
% 244.52/50.93  
% 244.52/50.93  Begin of proof
% 244.52/50.93  | 
% 244.52/50.93  | BETA: splitting (1) gives:
% 244.52/50.93  | 
% 244.52/50.93  | Case 1:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.52/50.93  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.52/50.93  | |        op(e2, e3) = e2
% 244.52/50.93  | | 
% 244.52/50.93  | | ALPHA: (7) implies:
% 244.52/50.93  | |   (8)  op(e3, e2) = e2
% 244.52/50.93  | | 
% 244.52/50.93  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2193.
% 244.52/50.93  | | 
% 244.52/50.93  | Case 2:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.52/50.93  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.52/50.93  | |        op(e1, e3) = e3
% 244.52/50.93  | | 
% 244.52/50.93  | | ALPHA: (9) implies:
% 244.52/50.93  | |   (10)  op(e1, e3) = e3
% 244.52/50.93  | | 
% 244.52/50.93  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #2335.
% 244.52/50.93  | | 
% 244.52/50.93  | End of split
% 244.52/50.93  | 
% 244.52/50.93  End of proof
% 244.52/50.93  
% 244.52/50.93  Sub-proof #1686 shows that the following formulas are inconsistent:
% 244.52/50.93  ----------------------------------------------------------------
% 244.52/50.93    (1)   ~ (e3 = e0)
% 244.52/50.93    (2)  op(e1, e2) = all_52_6
% 244.52/50.93    (3)   ~ (e3 = e2)
% 244.52/50.93    (4)  all_58_6 = e0
% 244.52/50.93    (5)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.52/50.93         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.52/50.93    (6)   ~ (all_52_6 = e3)
% 244.52/50.93    (7)  op(e1, e1) = e2
% 244.52/50.93    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.93    (9)  all_58_11 = e0
% 244.52/50.93  
% 244.52/50.93  Begin of proof
% 244.52/50.93  | 
% 244.52/50.93  | BETA: splitting (5) gives:
% 244.52/50.93  | 
% 244.52/50.93  | Case 1:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.52/50.93  | |           e3)
% 244.52/50.93  | | 
% 244.52/50.93  | | REF_CLOSE: (1), (2), (4), (6), (8), (10) are inconsistent by sub-proof
% 244.52/50.93  | |            #1689.
% 244.52/50.93  | | 
% 244.52/50.93  | Case 2:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (11)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.52/50.93  | |           e3)
% 244.52/50.93  | | 
% 244.52/50.93  | | REF_CLOSE: (1), (3), (7), (8), (9), (11) are inconsistent by sub-proof
% 244.52/50.93  | |            #1687.
% 244.52/50.93  | | 
% 244.52/50.93  | End of split
% 244.52/50.93  | 
% 244.52/50.93  End of proof
% 244.52/50.93  
% 244.52/50.93  Sub-proof #1687 shows that the following formulas are inconsistent:
% 244.52/50.93  ----------------------------------------------------------------
% 244.52/50.93    (1)   ~ (e3 = e0)
% 244.52/50.93    (2)   ~ (e3 = e2)
% 244.52/50.93    (3)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.52/50.93    (4)  op(e1, e1) = e2
% 244.52/50.93    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.93    (6)  all_58_11 = e0
% 244.52/50.93  
% 244.52/50.93  Begin of proof
% 244.52/50.93  | 
% 244.52/50.93  | BETA: splitting (3) gives:
% 244.52/50.93  | 
% 244.52/50.93  | Case 1:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 244.52/50.93  | | 
% 244.52/50.93  | | ALPHA: (7) implies:
% 244.52/50.93  | |   (8)  op(e1, e1) = e3
% 244.52/50.93  | | 
% 244.52/50.93  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2206.
% 244.52/50.93  | | 
% 244.52/50.93  | Case 2:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (9)  all_58_11 = e3 & op(e1, e0) = e3
% 244.52/50.93  | | 
% 244.52/50.93  | | ALPHA: (9) implies:
% 244.52/50.93  | |   (10)  all_58_11 = e3
% 244.52/50.93  | | 
% 244.52/50.93  | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #1688.
% 244.52/50.93  | | 
% 244.52/50.93  | End of split
% 244.52/50.93  | 
% 244.52/50.93  End of proof
% 244.52/50.93  
% 244.52/50.93  Sub-proof #1688 shows that the following formulas are inconsistent:
% 244.52/50.93  ----------------------------------------------------------------
% 244.52/50.93    (1)  all_58_11 = e3
% 244.52/50.93    (2)  all_58_11 = e0
% 244.52/50.93    (3)   ~ (e3 = e0)
% 244.52/50.93  
% 244.52/50.93  Begin of proof
% 244.52/50.93  | 
% 244.52/50.93  | COMBINE_EQS: (1), (2) imply:
% 244.52/50.93  |   (4)  e3 = e0
% 244.52/50.93  | 
% 244.52/50.93  | SIMP: (4) implies:
% 244.52/50.93  |   (5)  e3 = e0
% 244.52/50.93  | 
% 244.52/50.93  | REDUCE: (3), (5) imply:
% 244.52/50.93  |   (6)  $false
% 244.52/50.93  | 
% 244.52/50.93  | CLOSE: (6) is inconsistent.
% 244.52/50.93  | 
% 244.52/50.93  End of proof
% 244.52/50.93  
% 244.52/50.93  Sub-proof #1689 shows that the following formulas are inconsistent:
% 244.52/50.93  ----------------------------------------------------------------
% 244.52/50.93    (1)   ~ (e3 = e0)
% 244.52/50.93    (2)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 244.52/50.93    (3)  op(e1, e2) = all_52_6
% 244.52/50.93    (4)  all_58_6 = e0
% 244.52/50.93    (5)   ~ (all_52_6 = e3)
% 244.52/50.93    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.93  
% 244.52/50.93  Begin of proof
% 244.52/50.93  | 
% 244.52/50.93  | BETA: splitting (2) gives:
% 244.52/50.93  | 
% 244.52/50.93  | Case 1:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (7)  all_58_6 = e3 & op(e1, e3) = e3
% 244.52/50.93  | | 
% 244.52/50.93  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #1690.
% 244.52/50.93  | | 
% 244.52/50.93  | Case 2:
% 244.52/50.93  | | 
% 244.52/50.93  | |   (8)  all_58_7 = e3 & op(e1, e2) = e3
% 244.52/50.93  | | 
% 244.52/50.93  | | ALPHA: (8) implies:
% 244.52/50.93  | |   (9)  op(e1, e2) = e3
% 244.52/50.93  | | 
% 244.52/50.93  | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #2191.
% 244.52/50.93  | | 
% 244.52/50.93  | End of split
% 244.52/50.93  | 
% 244.52/50.93  End of proof
% 244.52/50.93  
% 244.52/50.93  Sub-proof #1690 shows that the following formulas are inconsistent:
% 244.52/50.93  ----------------------------------------------------------------
% 244.52/50.93    (1)  all_58_6 = e3 & op(e1, e3) = e3
% 244.52/50.93    (2)  all_58_6 = e0
% 244.52/50.93    (3)   ~ (e3 = e0)
% 244.52/50.93  
% 244.52/50.93  Begin of proof
% 244.52/50.93  | 
% 244.52/50.93  | ALPHA: (1) implies:
% 244.52/50.93  |   (4)  all_58_6 = e3
% 244.52/50.93  | 
% 244.52/50.93  | COMBINE_EQS: (2), (4) imply:
% 244.52/50.93  |   (5)  e3 = e0
% 244.52/50.93  | 
% 244.52/50.93  | REDUCE: (3), (5) imply:
% 244.52/50.93  |   (6)  $false
% 244.52/50.93  | 
% 244.52/50.93  | CLOSE: (6) is inconsistent.
% 244.52/50.93  | 
% 244.52/50.93  End of proof
% 244.52/50.93  
% 244.52/50.93  Sub-proof #1691 shows that the following formulas are inconsistent:
% 244.52/50.93  ----------------------------------------------------------------
% 244.52/50.93    (1)  all_58_2 = e3
% 244.52/50.93    (2)  all_58_2 = e1
% 244.52/50.93    (3)   ~ (e3 = e1)
% 244.52/50.93  
% 244.52/50.93  Begin of proof
% 244.52/50.93  | 
% 244.52/50.94  | COMBINE_EQS: (1), (2) imply:
% 244.52/50.94  |   (4)  e3 = e1
% 244.52/50.94  | 
% 244.52/50.94  | SIMP: (4) implies:
% 244.52/50.94  |   (5)  e3 = e1
% 244.52/50.94  | 
% 244.52/50.94  | REDUCE: (3), (5) imply:
% 244.52/50.94  |   (6)  $false
% 244.52/50.94  | 
% 244.52/50.94  | CLOSE: (6) is inconsistent.
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1692 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.52/50.94    (2)  op(e1, e0) = all_52_14
% 244.52/50.94    (3)   ~ (all_52_14 = e1)
% 244.52/50.94    (4)  op(e1, e1) = e2
% 244.52/50.94    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.94    (6)   ~ (e2 = e1)
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | BETA: splitting (1) gives:
% 244.52/50.94  | 
% 244.52/50.94  | Case 1:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (7)  all_58_8 = e1 & op(e1, e1) = e1
% 244.52/50.94  | | 
% 244.52/50.94  | | ALPHA: (7) implies:
% 244.52/50.94  | |   (8)  op(e1, e1) = e1
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2159.
% 244.52/50.94  | | 
% 244.52/50.94  | Case 2:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (9)  all_58_11 = e1 & op(e1, e0) = e1
% 244.52/50.94  | | 
% 244.52/50.94  | | ALPHA: (9) implies:
% 244.52/50.94  | |   (10)  op(e1, e0) = e1
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #2304.
% 244.52/50.94  | | 
% 244.52/50.94  | End of split
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1693 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)   ~ (all_52_6 = e1)
% 244.52/50.94    (2)   ~ (all_52_6 = e2)
% 244.52/50.94    (3)  all_54_11 = all_52_14
% 244.52/50.94    (4)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 244.52/50.94    (5)   ~ (all_52_14 = e2)
% 244.52/50.94    (6)  all_54_9 = all_52_6
% 244.52/50.94    (7)   ~ (all_52_14 = e1)
% 244.52/50.94    (8)   ~ (all_52_6 = all_52_14)
% 244.52/50.94    (9)   ~ (all_52_14 = e3)
% 244.52/50.94    (10)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | BETA: splitting (10) gives:
% 244.52/50.94  | 
% 244.52/50.94  | Case 1:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (11)  all_54_9 = e2
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (2), (6), (11) are inconsistent by sub-proof #1954.
% 244.52/50.94  | | 
% 244.52/50.94  | Case 2:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (12)  all_54_9 = e1 | all_54_9 = e0
% 244.52/50.94  | | 
% 244.52/50.94  | | BETA: splitting (12) gives:
% 244.52/50.94  | | 
% 244.52/50.94  | | Case 1:
% 244.52/50.94  | | | 
% 244.52/50.94  | | |   (13)  all_54_9 = e1
% 244.52/50.94  | | | 
% 244.52/50.94  | | | REF_CLOSE: (1), (6), (13) are inconsistent by sub-proof #2055.
% 244.52/50.94  | | | 
% 244.52/50.94  | | Case 2:
% 244.52/50.94  | | | 
% 244.52/50.94  | | |   (14)  all_54_9 = e0
% 244.52/50.94  | | | 
% 244.52/50.94  | | | COMBINE_EQS: (6), (14) imply:
% 244.52/50.94  | | |   (15)  all_52_6 = e0
% 244.52/50.94  | | | 
% 244.52/50.94  | | | SIMP: (15) implies:
% 244.52/50.94  | | |   (16)  all_52_6 = e0
% 244.52/50.94  | | | 
% 244.52/50.94  | | | REDUCE: (8), (16) imply:
% 244.52/50.94  | | |   (17)   ~ (all_52_14 = e0)
% 244.52/50.94  | | | 
% 244.52/50.94  | | | SIMP: (17) implies:
% 244.52/50.94  | | |   (18)   ~ (all_52_14 = e0)
% 244.52/50.94  | | | 
% 244.52/50.94  | | | BETA: splitting (4) gives:
% 244.52/50.94  | | | 
% 244.52/50.94  | | | Case 1:
% 244.52/50.94  | | | | 
% 244.52/50.94  | | | |   (19)  all_54_11 = e3
% 244.52/50.94  | | | | 
% 244.52/50.94  | | | | REF_CLOSE: (3), (9), (19) are inconsistent by sub-proof #1998.
% 244.52/50.94  | | | | 
% 244.52/50.94  | | | Case 2:
% 244.52/50.94  | | | | 
% 244.52/50.94  | | | |   (20)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 244.52/50.94  | | | | 
% 244.52/50.94  | | | | REF_CLOSE: (3), (5), (7), (18), (20) are inconsistent by sub-proof
% 244.52/50.94  | | | |            #2173.
% 244.52/50.94  | | | | 
% 244.52/50.94  | | | End of split
% 244.52/50.94  | | | 
% 244.52/50.94  | | End of split
% 244.52/50.94  | | 
% 244.52/50.94  | End of split
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1694 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)  all_58_1 = e1
% 244.52/50.94    (2)   ~ (e3 = e0)
% 244.52/50.94    (3)   ~ (e2 = e0)
% 244.52/50.94    (4)   ~ (e3 = e1)
% 244.52/50.94    (5)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.52/50.94         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.52/50.94    (6)   ~ (e3 = e2)
% 244.52/50.94    (7)  op(e3, e3) = e2
% 244.52/50.94    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.52/50.94         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.52/50.94    (9)   ~ (all_52_4 = e3)
% 244.52/50.94    (10)  op(e3, e2) = all_52_4
% 244.52/50.94    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.94    (12)   ~ (e1 = e0)
% 244.52/50.94    (13)  all_58_9 = e1
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | BETA: splitting (5) gives:
% 244.52/50.94  | 
% 244.52/50.94  | Case 1:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 244.52/50.94  | |           e3)
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (6), (7), (9), (10), (11), (14) are inconsistent by sub-proof
% 244.52/50.94  | |            #1959.
% 244.52/50.94  | | 
% 244.52/50.94  | Case 2:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 244.52/50.94  | |           e3)
% 244.52/50.94  | | 
% 244.52/50.94  | | BETA: splitting (15) gives:
% 244.52/50.94  | | 
% 244.52/50.94  | | Case 1:
% 244.52/50.94  | | | 
% 244.52/50.94  | | |   (16)  all_58_4 = e3 & op(e3, e1) = e3
% 244.52/50.94  | | | 
% 244.52/50.94  | | | ALPHA: (16) implies:
% 244.52/50.94  | | |   (17)  all_58_4 = e3
% 244.52/50.94  | | | 
% 244.52/50.94  | | | REF_CLOSE: (1), (2), (3), (7), (8), (11), (12), (13), (17) are
% 244.52/50.94  | | |            inconsistent by sub-proof #1695.
% 244.52/50.94  | | | 
% 244.52/50.94  | | Case 2:
% 244.52/50.94  | | | 
% 244.52/50.94  | | |   (18)  all_58_9 = e3 & op(e3, e0) = e3
% 244.52/50.94  | | | 
% 244.52/50.94  | | | ALPHA: (18) implies:
% 244.52/50.94  | | |   (19)  all_58_9 = e3
% 244.52/50.94  | | | 
% 244.52/50.94  | | | REF_CLOSE: (4), (13), (19) are inconsistent by sub-proof #1709.
% 244.52/50.94  | | | 
% 244.52/50.94  | | End of split
% 244.52/50.94  | | 
% 244.52/50.94  | End of split
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1695 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)  all_58_1 = e1
% 244.52/50.94    (2)   ~ (e3 = e0)
% 244.52/50.94    (3)   ~ (e2 = e0)
% 244.52/50.94    (4)  op(e3, e3) = e2
% 244.52/50.94    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.52/50.94         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.52/50.94    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.94    (7)   ~ (e1 = e0)
% 244.52/50.94    (8)  all_58_4 = e3
% 244.52/50.94    (9)  all_58_9 = e1
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | BETA: splitting (5) gives:
% 244.52/50.94  | 
% 244.52/50.94  | Case 1:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 244.52/50.94  | |           e0)
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (1), (3), (4), (6), (7), (10) are inconsistent by sub-proof
% 244.52/50.94  | |            #1698.
% 244.52/50.94  | | 
% 244.52/50.94  | Case 2:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 244.52/50.94  | |           e0)
% 244.52/50.94  | | 
% 244.52/50.94  | | BETA: splitting (11) gives:
% 244.52/50.94  | | 
% 244.52/50.94  | | Case 1:
% 244.52/50.94  | | | 
% 244.52/50.94  | | |   (12)  all_58_4 = e0 & op(e3, e1) = e0
% 244.52/50.94  | | | 
% 244.52/50.94  | | | REF_CLOSE: (2), (8), (12) are inconsistent by sub-proof #1697.
% 244.52/50.94  | | | 
% 244.52/50.94  | | Case 2:
% 244.52/50.94  | | | 
% 244.52/50.94  | | |   (13)  all_58_9 = e0 & op(e3, e0) = e0
% 244.52/50.94  | | | 
% 244.52/50.94  | | | REF_CLOSE: (7), (9), (13) are inconsistent by sub-proof #1696.
% 244.52/50.94  | | | 
% 244.52/50.94  | | End of split
% 244.52/50.94  | | 
% 244.52/50.94  | End of split
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1696 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)  all_58_9 = e0 & op(e3, e0) = e0
% 244.52/50.94    (2)  all_58_9 = e1
% 244.52/50.94    (3)   ~ (e1 = e0)
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | ALPHA: (1) implies:
% 244.52/50.94  |   (4)  all_58_9 = e0
% 244.52/50.94  | 
% 244.52/50.94  | COMBINE_EQS: (2), (4) imply:
% 244.52/50.94  |   (5)  e1 = e0
% 244.52/50.94  | 
% 244.52/50.94  | REDUCE: (3), (5) imply:
% 244.52/50.94  |   (6)  $false
% 244.52/50.94  | 
% 244.52/50.94  | CLOSE: (6) is inconsistent.
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1697 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)  all_58_4 = e0 & op(e3, e1) = e0
% 244.52/50.94    (2)  all_58_4 = e3
% 244.52/50.94    (3)   ~ (e3 = e0)
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | ALPHA: (1) implies:
% 244.52/50.94  |   (4)  all_58_4 = e0
% 244.52/50.94  | 
% 244.52/50.94  | COMBINE_EQS: (2), (4) imply:
% 244.52/50.94  |   (5)  e3 = e0
% 244.52/50.94  | 
% 244.52/50.94  | REDUCE: (3), (5) imply:
% 244.52/50.94  |   (6)  $false
% 244.52/50.94  | 
% 244.52/50.94  | CLOSE: (6) is inconsistent.
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1698 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)  all_58_1 = e1
% 244.52/50.94    (2)   ~ (e2 = e0)
% 244.52/50.94    (3)  op(e3, e3) = e2
% 244.52/50.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.94    (5)   ~ (e1 = e0)
% 244.52/50.94    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | BETA: splitting (6) gives:
% 244.52/50.94  | 
% 244.52/50.94  | Case 1:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 244.52/50.94  | | 
% 244.52/50.94  | | ALPHA: (7) implies:
% 244.52/50.94  | |   (8)  op(e3, e3) = e0
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2188.
% 244.52/50.94  | | 
% 244.52/50.94  | Case 2:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (9)  all_58_1 = e0 & op(e3, e2) = e0
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #1720.
% 244.52/50.94  | | 
% 244.52/50.94  | End of split
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1699 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)   ~ (e3 = e0)
% 244.52/50.94    (2)  op(e0, e1) = e3
% 244.52/50.94    (3)  op(e1, e0) = all_52_14
% 244.52/50.94    (4)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.52/50.94             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 244.52/50.94           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 244.52/50.94             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 244.52/50.94           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.52/50.94    (5)   ~ (all_52_14 = e1)
% 244.52/50.94    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | BETA: splitting (4) gives:
% 244.52/50.94  | 
% 244.52/50.94  | Case 1:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (7)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.52/50.94  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 244.52/50.94  | |        & op(e0, e1) = e1
% 244.52/50.94  | | 
% 244.52/50.94  | | ALPHA: (7) implies:
% 244.52/50.94  | |   (8)  op(e1, e0) = e1
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2304.
% 244.52/50.94  | | 
% 244.52/50.94  | Case 2:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (9)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.52/50.94  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 244.52/50.94  | |        & op(e0, e1) = e0
% 244.52/50.94  | | 
% 244.52/50.94  | | ALPHA: (9) implies:
% 244.52/50.94  | |   (10)  op(e0, e1) = e0
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #2164.
% 244.52/50.94  | | 
% 244.52/50.94  | End of split
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1700 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)  op(e1, e2) = e1
% 244.52/50.94    (2)   ~ (e3 = e1)
% 244.52/50.94    (3)  op(e1, e2) = e3
% 244.52/50.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.94    (5)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) = all_36_1
% 244.52/50.94           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2) =
% 244.52/50.94           all_36_1 & $i(all_36_1))
% 244.52/50.94    (6)  op(e1, e2) = all_40_1
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | BETA: splitting (5) gives:
% 244.52/50.94  | 
% 244.52/50.94  | Case 1:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (7)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 244.52/50.94  | |        all_36_1 & $i(all_36_0) & $i(all_36_1)
% 244.52/50.94  | | 
% 244.52/50.94  | | ALPHA: (7) implies:
% 244.52/50.94  | |   (8)  op(e1, e2) = all_36_1
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (1), (2), (3), (4), (6), (8) are inconsistent by sub-proof #1701.
% 244.52/50.94  | | 
% 244.52/50.94  | Case 2:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (9)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1)
% 244.52/50.94  | | 
% 244.52/50.94  | | ALPHA: (9) implies:
% 244.52/50.94  | |   (10)  op(e1, e2) = all_36_1
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (1), (2), (3), (4), (6), (10) are inconsistent by sub-proof
% 244.52/50.94  | |            #1701.
% 244.52/50.94  | | 
% 244.52/50.94  | End of split
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1701 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)  op(e1, e2) = e1
% 244.52/50.94    (2)   ~ (e3 = e1)
% 244.52/50.94    (3)  op(e1, e2) = e3
% 244.52/50.94    (4)  op(e1, e2) = all_36_1
% 244.52/50.94    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.94    (6)  op(e1, e2) = all_40_1
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | GROUND_INST: instantiating (5) with e1, all_36_1, e2, e1, simplifying with
% 244.52/50.94  |              (1), (4) gives:
% 244.52/50.94  |   (7)  all_36_1 = e1
% 244.52/50.94  | 
% 244.52/50.94  | GROUND_INST: instantiating (5) with all_36_1, all_40_1, e2, e1, simplifying
% 244.52/50.94  |              with (4), (6) gives:
% 244.52/50.94  |   (8)  all_40_1 = all_36_1
% 244.52/50.94  | 
% 244.52/50.94  | GROUND_INST: instantiating (5) with e3, all_40_1, e2, e1, simplifying with
% 244.52/50.94  |              (3), (6) gives:
% 244.52/50.94  |   (9)  all_40_1 = e3
% 244.52/50.94  | 
% 244.52/50.94  | COMBINE_EQS: (8), (9) imply:
% 244.52/50.94  |   (10)  all_36_1 = e3
% 244.52/50.94  | 
% 244.52/50.94  | SIMP: (10) implies:
% 244.52/50.94  |   (11)  all_36_1 = e3
% 244.52/50.94  | 
% 244.52/50.94  | COMBINE_EQS: (7), (11) imply:
% 244.52/50.94  |   (12)  e3 = e1
% 244.52/50.94  | 
% 244.52/50.94  | SIMP: (12) implies:
% 244.52/50.94  |   (13)  e3 = e1
% 244.52/50.94  | 
% 244.52/50.94  | REDUCE: (2), (13) imply:
% 244.52/50.94  |   (14)  $false
% 244.52/50.94  | 
% 244.52/50.94  | CLOSE: (14) is inconsistent.
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1702 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)   ~ (all_52_3 = e1)
% 244.52/50.94    (2)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 244.52/50.94         $i(all_56_5)
% 244.52/50.94    (3)  op(e1, e3) = e1
% 244.52/50.94    (4)  all_54_12 = all_52_3
% 244.52/50.94    (5)   ~ (all_52_3 = e2)
% 244.52/50.94    (6)  op(e1, e1) = e2
% 244.52/50.94    (7)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.52/50.94    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.94    (9)   ~ (e2 = e1)
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | ALPHA: (2) implies:
% 244.52/50.94  |   (10)  op(e1, e3) = all_56_5
% 244.52/50.94  |   (11)  op(e1, all_56_5) = e1
% 244.52/50.94  | 
% 244.52/50.94  | BETA: splitting (7) gives:
% 244.52/50.94  | 
% 244.52/50.94  | Case 1:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (12)  all_54_12 = e2
% 244.52/50.94  | | 
% 244.52/50.94  | | COMBINE_EQS: (4), (12) imply:
% 244.52/50.94  | |   (13)  all_52_3 = e2
% 244.52/50.94  | | 
% 244.52/50.94  | | REDUCE: (5), (13) imply:
% 244.52/50.94  | |   (14)  $false
% 244.52/50.94  | | 
% 244.52/50.94  | | CLOSE: (14) is inconsistent.
% 244.52/50.94  | | 
% 244.52/50.94  | Case 2:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (15)  all_54_12 = e1 | all_54_12 = e0
% 244.52/50.94  | | 
% 244.52/50.94  | | BETA: splitting (15) gives:
% 244.52/50.94  | | 
% 244.52/50.94  | | Case 1:
% 244.52/50.94  | | | 
% 244.52/50.94  | | |   (16)  all_54_12 = e1
% 244.52/50.94  | | | 
% 244.52/50.94  | | | COMBINE_EQS: (4), (16) imply:
% 244.52/50.94  | | |   (17)  all_52_3 = e1
% 244.52/50.94  | | | 
% 244.52/50.94  | | | REDUCE: (1), (17) imply:
% 244.52/50.94  | | |   (18)  $false
% 244.52/50.94  | | | 
% 244.52/50.94  | | | CLOSE: (18) is inconsistent.
% 244.52/50.94  | | | 
% 244.52/50.94  | | Case 2:
% 244.52/50.94  | | | 
% 244.52/50.94  | | | 
% 244.52/50.94  | | | GROUND_INST: instantiating (8) with e1, all_56_5, e3, e1, simplifying with
% 244.52/50.94  | | |              (3), (10) gives:
% 244.52/50.94  | | |   (19)  all_56_5 = e1
% 244.52/50.94  | | | 
% 244.52/50.94  | | | REDUCE: (11), (19) imply:
% 244.52/50.94  | | |   (20)  op(e1, e1) = e1
% 244.52/50.94  | | | 
% 244.52/50.94  | | | REF_CLOSE: (6), (8), (9), (20) are inconsistent by sub-proof #2159.
% 244.52/50.94  | | | 
% 244.52/50.94  | | End of split
% 244.52/50.94  | | 
% 244.52/50.94  | End of split
% 244.52/50.94  | 
% 244.52/50.94  End of proof
% 244.52/50.94  
% 244.52/50.94  Sub-proof #1703 shows that the following formulas are inconsistent:
% 244.52/50.94  ----------------------------------------------------------------
% 244.52/50.94    (1)  op(e3, e2) = e1
% 244.52/50.94    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.52/50.94             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 244.52/50.94    (3)  op(e2, e3) = e3
% 244.52/50.94    (4)   ~ (e3 = e1)
% 244.52/50.94    (5)   ~ (e3 = e2)
% 244.52/50.94    (6)  all_56_1 = e2
% 244.52/50.94    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.94  
% 244.52/50.94  Begin of proof
% 244.52/50.94  | 
% 244.52/50.94  | BETA: splitting (2) gives:
% 244.52/50.94  | 
% 244.52/50.94  | Case 1:
% 244.52/50.94  | | 
% 244.52/50.94  | |   (8)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 244.52/50.94  | | 
% 244.52/50.94  | | ALPHA: (8) implies:
% 244.52/50.94  | |   (9)  op(e3, all_56_1) = e3
% 244.52/50.94  | | 
% 244.52/50.94  | | REDUCE: (6), (9) imply:
% 244.52/50.94  | |   (10)  op(e3, e2) = e3
% 244.52/50.94  | | 
% 244.52/50.94  | | REF_CLOSE: (1), (4), (7), (10) are inconsistent by sub-proof #2265.
% 244.52/50.94  | | 
% 244.52/50.94  | Case 2:
% 244.52/50.94  | | 
% 244.52/50.95  | |   (11)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 244.52/50.95  | |         $i(all_56_3)
% 244.52/50.95  | | 
% 244.52/50.95  | | ALPHA: (11) implies:
% 244.52/50.95  | |   (12)  op(e2, e3) = all_56_3
% 244.52/50.95  | |   (13)  op(e2, all_56_3) = e2
% 244.52/50.95  | | 
% 244.52/50.95  | | REF_CLOSE: (3), (5), (7), (12), (13) are inconsistent by sub-proof #2262.
% 244.52/50.95  | | 
% 244.52/50.95  | End of split
% 244.52/50.95  | 
% 244.52/50.95  End of proof
% 244.52/50.95  
% 244.52/50.95  Sub-proof #1704 shows that the following formulas are inconsistent:
% 244.52/50.95  ----------------------------------------------------------------
% 244.52/50.95    (1)  op(e3, e2) = e1
% 244.52/50.95    (2)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 244.52/50.95           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 244.52/50.95             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.52/50.95           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 244.52/50.95             e1) = e3 & op(e1, e3) = e3)
% 244.52/50.95    (3)   ~ (all_52_2 = e3)
% 244.52/50.95    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.95    (5)  op(e1, e3) = all_52_2
% 244.52/50.95    (6)   ~ (e2 = e1)
% 244.52/50.95  
% 244.52/50.95  Begin of proof
% 244.52/50.95  | 
% 244.52/50.95  | BETA: splitting (2) gives:
% 244.52/50.95  | 
% 244.52/50.95  | Case 1:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.52/50.95  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.52/50.95  | |        op(e2, e3) = e2
% 244.52/50.95  | | 
% 244.52/50.95  | | ALPHA: (7) implies:
% 244.52/50.95  | |   (8)  op(e3, e2) = e2
% 244.52/50.95  | | 
% 244.52/50.95  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #2261.
% 244.52/50.95  | | 
% 244.52/50.95  | Case 2:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.52/50.95  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.52/50.95  | |        op(e1, e3) = e3
% 244.52/50.95  | | 
% 244.52/50.95  | | ALPHA: (9) implies:
% 244.52/50.95  | |   (10)  op(e1, e3) = e3
% 244.52/50.95  | | 
% 244.52/50.95  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #2335.
% 244.52/50.95  | | 
% 244.52/50.95  | End of split
% 244.52/50.95  | 
% 244.52/50.95  End of proof
% 244.52/50.95  
% 244.52/50.95  Sub-proof #1705 shows that the following formulas are inconsistent:
% 244.52/50.95  ----------------------------------------------------------------
% 244.52/50.95    (1)   ~ (e3 = e0)
% 244.52/50.95    (2)  all_58_12 = e3 & op(e0, e3) = e3
% 244.52/50.95    (3)  op(e1, e0) = all_52_14
% 244.52/50.95    (4)   ~ (e3 = e1)
% 244.52/50.95    (5)   ~ (e3 = e2)
% 244.52/50.95    (6)  op(e1, e3) = e1
% 244.52/50.95    (7)  all_58_7 = e3
% 244.52/50.95    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.52/50.95         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.52/50.95    (9)  all_58_12 = e0
% 244.52/50.95    (10)   ~ (all_52_14 = e3)
% 244.52/50.95    (11)  op(e1, e1) = e2
% 244.52/50.95    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.95  
% 244.52/50.95  Begin of proof
% 244.52/50.95  | 
% 244.52/50.95  | ALPHA: (2) implies:
% 244.52/50.95  |   (13)  all_58_12 = e3
% 244.52/50.95  | 
% 244.52/50.95  | COMBINE_EQS: (9), (13) imply:
% 244.52/50.95  |   (14)  e3 = e0
% 244.52/50.95  | 
% 244.52/50.95  | COMBINE_EQS: (7), (14) imply:
% 244.52/50.95  |   (15)  all_58_7 = e0
% 244.52/50.95  | 
% 244.52/50.95  | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (11), (12), (15) are
% 244.52/50.95  |            inconsistent by sub-proof #2147.
% 244.52/50.95  | 
% 244.52/50.95  End of proof
% 244.52/50.95  
% 244.52/50.95  Sub-proof #1706 shows that the following formulas are inconsistent:
% 244.52/50.95  ----------------------------------------------------------------
% 244.52/50.95    (1)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.52/50.95         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.52/50.95    (2)   ~ (e2 = e0)
% 244.52/50.95    (3)   ~ (e3 = e1)
% 244.52/50.95    (4)   ~ (e3 = e2)
% 244.52/50.95    (5)  all_58_9 = e3
% 244.52/50.95    (6)  op(e3, e0) = e3
% 244.52/50.95    (7)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.52/50.95         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.52/50.95    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.95    (9)   ~ (e1 = e0)
% 244.52/50.95    (10)  op(e3, e3) = e0
% 244.52/50.95    (11)  all_58_4 = e0
% 244.52/50.95    (12)   ~ (e2 = e1)
% 244.52/50.95  
% 244.52/50.95  Begin of proof
% 244.52/50.95  | 
% 244.52/50.95  | BETA: splitting (1) gives:
% 244.52/50.95  | 
% 244.52/50.95  | Case 1:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (13)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 244.52/50.95  | |           e2)
% 244.52/50.95  | | 
% 244.52/50.95  | | BETA: splitting (13) gives:
% 244.52/50.95  | | 
% 244.52/50.95  | | Case 1:
% 244.52/50.95  | | | 
% 244.52/50.95  | | |   (14)  all_58_0 = e2 & op(e3, e3) = e2
% 244.52/50.95  | | | 
% 244.52/50.95  | | | ALPHA: (14) implies:
% 244.52/50.95  | | |   (15)  op(e3, e3) = e2
% 244.52/50.95  | | | 
% 244.52/50.95  | | | REF_CLOSE: (2), (8), (10), (15) are inconsistent by sub-proof #2188.
% 244.52/50.95  | | | 
% 244.52/50.95  | | Case 2:
% 244.52/50.95  | | | 
% 244.52/50.95  | | |   (16)  all_58_1 = e2 & op(e3, e2) = e2
% 244.52/50.95  | | | 
% 244.52/50.95  | | | ALPHA: (16) implies:
% 244.52/50.95  | | |   (17)  all_58_1 = e2
% 244.52/50.95  | | | 
% 244.52/50.95  | | | REF_CLOSE: (3), (5), (7), (8), (9), (10), (11), (12), (17) are
% 244.52/50.95  | | |            inconsistent by sub-proof #1708.
% 244.52/50.95  | | | 
% 244.52/50.95  | | End of split
% 244.52/50.95  | | 
% 244.52/50.95  | Case 2:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (18)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 244.52/50.95  | |           e2)
% 244.52/50.95  | | 
% 244.52/50.95  | | BETA: splitting (18) gives:
% 244.52/50.95  | | 
% 244.52/50.95  | | Case 1:
% 244.52/50.95  | | | 
% 244.52/50.95  | | |   (19)  all_58_4 = e2 & op(e3, e1) = e2
% 244.52/50.95  | | | 
% 244.52/50.95  | | | REF_CLOSE: (2), (11), (19) are inconsistent by sub-proof #1707.
% 244.52/50.95  | | | 
% 244.52/50.95  | | Case 2:
% 244.52/50.95  | | | 
% 244.52/50.95  | | |   (20)  all_58_9 = e2 & op(e3, e0) = e2
% 244.52/50.95  | | | 
% 244.52/50.95  | | | ALPHA: (20) implies:
% 244.52/50.95  | | |   (21)  op(e3, e0) = e2
% 244.52/50.95  | | | 
% 244.52/50.95  | | | REF_CLOSE: (4), (6), (8), (21) are inconsistent by sub-proof #2125.
% 244.52/50.95  | | | 
% 244.52/50.95  | | End of split
% 244.52/50.95  | | 
% 244.52/50.95  | End of split
% 244.52/50.95  | 
% 244.52/50.95  End of proof
% 244.52/50.95  
% 244.52/50.95  Sub-proof #1707 shows that the following formulas are inconsistent:
% 244.52/50.95  ----------------------------------------------------------------
% 244.52/50.95    (1)  all_58_4 = e2 & op(e3, e1) = e2
% 244.52/50.95    (2)  all_58_4 = e0
% 244.52/50.95    (3)   ~ (e2 = e0)
% 244.52/50.95  
% 244.52/50.95  Begin of proof
% 244.52/50.95  | 
% 244.52/50.95  | ALPHA: (1) implies:
% 244.52/50.95  |   (4)  all_58_4 = e2
% 244.52/50.95  | 
% 244.52/50.95  | COMBINE_EQS: (2), (4) imply:
% 244.52/50.95  |   (5)  e2 = e0
% 244.52/50.95  | 
% 244.52/50.95  | REDUCE: (3), (5) imply:
% 244.52/50.95  |   (6)  $false
% 244.52/50.95  | 
% 244.52/50.95  | CLOSE: (6) is inconsistent.
% 244.52/50.95  | 
% 244.52/50.95  End of proof
% 244.52/50.95  
% 244.52/50.95  Sub-proof #1708 shows that the following formulas are inconsistent:
% 244.52/50.95  ----------------------------------------------------------------
% 244.52/50.95    (1)   ~ (e3 = e1)
% 244.52/50.95    (2)  all_58_9 = e3
% 244.52/50.95    (3)  all_58_1 = e2
% 244.52/50.95    (4)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.52/50.95         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.52/50.95    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.95    (6)   ~ (e1 = e0)
% 244.52/50.95    (7)  op(e3, e3) = e0
% 244.52/50.95    (8)  all_58_4 = e0
% 244.52/50.95    (9)   ~ (e2 = e1)
% 244.52/50.95  
% 244.52/50.95  Begin of proof
% 244.52/50.95  | 
% 244.52/50.95  | BETA: splitting (4) gives:
% 244.52/50.95  | 
% 244.52/50.95  | Case 1:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 244.52/50.95  | |           e1)
% 244.52/50.95  | | 
% 244.52/50.95  | | BETA: splitting (10) gives:
% 244.52/50.95  | | 
% 244.52/50.95  | | Case 1:
% 244.52/50.95  | | | 
% 244.52/50.95  | | |   (11)  all_58_0 = e1 & op(e3, e3) = e1
% 244.52/50.95  | | | 
% 244.52/50.95  | | | ALPHA: (11) implies:
% 244.52/50.95  | | |   (12)  op(e3, e3) = e1
% 244.52/50.95  | | | 
% 244.52/50.95  | | | REF_CLOSE: (5), (6), (7), (12) are inconsistent by sub-proof #1828.
% 244.52/50.95  | | | 
% 244.52/50.95  | | Case 2:
% 244.52/50.95  | | | 
% 244.52/50.95  | | |   (13)  all_58_1 = e1 & op(e3, e2) = e1
% 244.52/50.95  | | | 
% 244.52/50.95  | | | REF_CLOSE: (3), (9), (13) are inconsistent by sub-proof #2185.
% 244.52/50.95  | | | 
% 244.52/50.95  | | End of split
% 244.52/50.95  | | 
% 244.52/50.95  | Case 2:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 244.52/50.95  | |           e1)
% 244.52/50.95  | | 
% 244.52/50.95  | | BETA: splitting (14) gives:
% 244.52/50.95  | | 
% 244.52/50.95  | | Case 1:
% 244.52/50.95  | | | 
% 244.52/50.95  | | |   (15)  all_58_4 = e1 & op(e3, e1) = e1
% 244.52/50.95  | | | 
% 244.52/50.95  | | | ALPHA: (15) implies:
% 244.52/50.95  | | |   (16)  all_58_4 = e1
% 244.52/50.95  | | | 
% 244.52/50.95  | | | REF_CLOSE: (6), (8), (16) are inconsistent by sub-proof #1710.
% 244.52/50.95  | | | 
% 244.52/50.95  | | Case 2:
% 244.52/50.95  | | | 
% 244.52/50.95  | | |   (17)  all_58_9 = e1 & op(e3, e0) = e1
% 244.52/50.95  | | | 
% 244.52/50.95  | | | ALPHA: (17) implies:
% 244.52/50.95  | | |   (18)  all_58_9 = e1
% 244.52/50.95  | | | 
% 244.52/50.95  | | | REF_CLOSE: (1), (2), (18) are inconsistent by sub-proof #1709.
% 244.52/50.95  | | | 
% 244.52/50.95  | | End of split
% 244.52/50.95  | | 
% 244.52/50.95  | End of split
% 244.52/50.95  | 
% 244.52/50.95  End of proof
% 244.52/50.95  
% 244.52/50.95  Sub-proof #1709 shows that the following formulas are inconsistent:
% 244.52/50.95  ----------------------------------------------------------------
% 244.52/50.95    (1)  all_58_9 = e3
% 244.52/50.95    (2)  all_58_9 = e1
% 244.52/50.95    (3)   ~ (e3 = e1)
% 244.52/50.95  
% 244.52/50.95  Begin of proof
% 244.52/50.95  | 
% 244.52/50.95  | COMBINE_EQS: (1), (2) imply:
% 244.52/50.95  |   (4)  e3 = e1
% 244.52/50.95  | 
% 244.52/50.95  | SIMP: (4) implies:
% 244.52/50.95  |   (5)  e3 = e1
% 244.52/50.95  | 
% 244.52/50.95  | REDUCE: (3), (5) imply:
% 244.52/50.95  |   (6)  $false
% 244.52/50.95  | 
% 244.52/50.95  | CLOSE: (6) is inconsistent.
% 244.52/50.95  | 
% 244.52/50.95  End of proof
% 244.52/50.95  
% 244.52/50.95  Sub-proof #1710 shows that the following formulas are inconsistent:
% 244.52/50.95  ----------------------------------------------------------------
% 244.52/50.95    (1)  all_58_4 = e1
% 244.52/50.95    (2)  all_58_4 = e0
% 244.52/50.95    (3)   ~ (e1 = e0)
% 244.52/50.95  
% 244.52/50.95  Begin of proof
% 244.52/50.95  | 
% 244.52/50.95  | COMBINE_EQS: (1), (2) imply:
% 244.52/50.95  |   (4)  e1 = e0
% 244.52/50.95  | 
% 244.52/50.95  | SIMP: (4) implies:
% 244.52/50.95  |   (5)  e1 = e0
% 244.52/50.95  | 
% 244.52/50.95  | REDUCE: (3), (5) imply:
% 244.52/50.95  |   (6)  $false
% 244.52/50.95  | 
% 244.52/50.95  | CLOSE: (6) is inconsistent.
% 244.52/50.95  | 
% 244.52/50.95  End of proof
% 244.52/50.95  
% 244.52/50.95  Sub-proof #1711 shows that the following formulas are inconsistent:
% 244.52/50.95  ----------------------------------------------------------------
% 244.52/50.95    (1)   ~ (e2 = e0)
% 244.52/50.95    (2)  op(e3, e3) = e2
% 244.52/50.95    (3)  op(e3, e2) = all_52_4
% 244.52/50.95    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.95    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 244.52/50.95    (6)   ~ (all_52_4 = e0)
% 244.52/50.95  
% 244.52/50.95  Begin of proof
% 244.52/50.95  | 
% 244.52/50.95  | BETA: splitting (5) gives:
% 244.52/50.95  | 
% 244.52/50.95  | Case 1:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 244.52/50.95  | | 
% 244.52/50.95  | | ALPHA: (7) implies:
% 244.52/50.95  | |   (8)  op(e3, e3) = e0
% 244.52/50.95  | | 
% 244.52/50.95  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2188.
% 244.52/50.95  | | 
% 244.52/50.95  | Case 2:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (9)  all_58_1 = e0 & op(e3, e2) = e0
% 244.52/50.95  | | 
% 244.52/50.95  | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #1968.
% 244.52/50.95  | | 
% 244.52/50.95  | End of split
% 244.52/50.95  | 
% 244.52/50.95  End of proof
% 244.52/50.95  
% 244.52/50.95  Sub-proof #1712 shows that the following formulas are inconsistent:
% 244.52/50.95  ----------------------------------------------------------------
% 244.52/50.95    (1)   ~ (e3 = e0)
% 244.52/50.95    (2)  op(e1, e2) = e1
% 244.52/50.95    (3)   ~ (e2 = e0)
% 244.52/50.95    (4)  op(e1, e2) = all_52_6
% 244.52/50.95    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.52/50.95         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.52/50.95    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.52/50.95         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.52/50.95    (7)   ~ (e3 = e1)
% 244.52/50.95    (8)   ~ (all_52_12 = e1)
% 244.52/50.95    (9)  op(e2, e2) = e0
% 244.52/50.95    (10)   ~ (all_52_8 = e1)
% 244.52/50.95    (11)  op(e3, e1) = all_52_8
% 244.52/50.95    (12)   ~ (e3 = e2)
% 244.52/50.95    (13)  op(e3, e0) = all_52_12
% 244.52/50.95    (14)  op(e3, e3) = e2
% 244.52/50.95    (15)  all_58_7 = e1
% 244.52/50.95    (16)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 244.52/50.95          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 244.52/50.95    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.95    (18)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.52/50.95          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.52/50.95    (19)   ~ (e1 = e0)
% 244.52/50.95    (20)   ~ (e2 = e1)
% 244.52/50.95  
% 244.52/50.95  Begin of proof
% 244.52/50.95  | 
% 244.52/50.95  | BETA: splitting (16) gives:
% 244.52/50.95  | 
% 244.52/50.95  | Case 1:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (21)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 244.52/50.95  | |           e1)
% 244.52/50.95  | | 
% 244.52/50.95  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (12), (14), (15), (17),
% 244.52/50.95  | |            (18), (19), (20), (21) are inconsistent by sub-proof #1713.
% 244.52/50.95  | | 
% 244.52/50.95  | Case 2:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (22)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 244.52/50.95  | |           e1)
% 244.52/50.95  | | 
% 244.52/50.95  | | REF_CLOSE: (8), (10), (11), (13), (17), (22) are inconsistent by sub-proof
% 244.52/50.95  | |            #2233.
% 244.52/50.95  | | 
% 244.52/50.95  | End of split
% 244.52/50.95  | 
% 244.52/50.95  End of proof
% 244.52/50.95  
% 244.52/50.95  Sub-proof #1713 shows that the following formulas are inconsistent:
% 244.52/50.95  ----------------------------------------------------------------
% 244.52/50.95    (1)   ~ (e3 = e0)
% 244.52/50.95    (2)  op(e1, e2) = e1
% 244.52/50.95    (3)   ~ (e2 = e0)
% 244.52/50.95    (4)  op(e1, e2) = all_52_6
% 244.52/50.95    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.52/50.95         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.52/50.95    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.52/50.95         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.52/50.95    (7)   ~ (e3 = e1)
% 244.52/50.95    (8)  op(e2, e2) = e0
% 244.52/50.95    (9)   ~ (e3 = e2)
% 244.52/50.95    (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 244.52/50.95    (11)  op(e3, e3) = e2
% 244.52/50.95    (12)  all_58_7 = e1
% 244.52/50.95    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.95    (14)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.52/50.95          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.52/50.95    (15)   ~ (e1 = e0)
% 244.52/50.95    (16)   ~ (e2 = e1)
% 244.52/50.95  
% 244.52/50.95  Begin of proof
% 244.52/50.95  | 
% 244.52/50.95  | BETA: splitting (10) gives:
% 244.52/50.95  | 
% 244.52/50.95  | Case 1:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (17)  all_58_0 = e1 & op(e3, e3) = e1
% 244.52/50.95  | | 
% 244.52/50.95  | | ALPHA: (17) implies:
% 244.52/50.95  | |   (18)  op(e3, e3) = e1
% 244.52/50.95  | | 
% 244.52/50.95  | | REF_CLOSE: (11), (13), (16), (18) are inconsistent by sub-proof #2267.
% 244.52/50.95  | | 
% 244.52/50.95  | Case 2:
% 244.52/50.95  | | 
% 244.52/50.95  | |   (19)  all_58_1 = e1 & op(e3, e2) = e1
% 244.52/50.95  | | 
% 244.52/50.95  | | ALPHA: (19) implies:
% 244.52/50.95  | |   (20)  all_58_1 = e1
% 244.52/50.95  | | 
% 244.52/50.95  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 244.52/50.95  | |            (15), (16), (20) are inconsistent by sub-proof #1714.
% 244.52/50.95  | | 
% 244.52/50.95  | End of split
% 244.52/50.95  | 
% 244.52/50.95  End of proof
% 244.52/50.95  
% 244.52/50.95  Sub-proof #1714 shows that the following formulas are inconsistent:
% 244.52/50.95  ----------------------------------------------------------------
% 244.52/50.95    (1)  all_58_1 = e1
% 244.52/50.95    (2)   ~ (e3 = e0)
% 244.52/50.95    (3)  op(e1, e2) = e1
% 244.52/50.95    (4)   ~ (e2 = e0)
% 244.52/50.95    (5)  op(e1, e2) = all_52_6
% 244.52/50.95    (6)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.52/50.95         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.52/50.95    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.52/50.95         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.52/50.95    (8)   ~ (e3 = e1)
% 244.52/50.95    (9)  op(e2, e2) = e0
% 244.52/50.95    (10)   ~ (e3 = e2)
% 244.52/50.95    (11)  all_58_7 = e1
% 244.52/50.95    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.95    (13)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.52/50.95          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.52/50.95    (14)   ~ (e1 = e0)
% 244.52/50.96    (15)   ~ (e2 = e1)
% 244.52/50.96  
% 244.52/50.96  Begin of proof
% 244.52/50.96  | 
% 244.52/50.96  | BETA: splitting (13) gives:
% 244.52/50.96  | 
% 244.52/50.96  | Case 1:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (16)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 244.52/50.96  | |           e3)
% 244.52/50.96  | | 
% 244.52/50.96  | | BETA: splitting (16) gives:
% 244.52/50.96  | | 
% 244.52/50.96  | | Case 1:
% 244.52/50.96  | | | 
% 244.52/50.96  | | |   (17)  all_58_1 = e3 & op(e3, e2) = e3
% 244.52/50.96  | | | 
% 244.52/50.96  | | | REF_CLOSE: (1), (8), (17) are inconsistent by sub-proof #1723.
% 244.52/50.96  | | | 
% 244.52/50.96  | | Case 2:
% 244.52/50.96  | | | 
% 244.52/50.96  | | |   (18)  all_58_3 = e3 & op(e2, e2) = e3
% 244.52/50.96  | | | 
% 244.52/50.96  | | | ALPHA: (18) implies:
% 244.52/50.96  | | |   (19)  all_58_3 = e3
% 244.52/50.96  | | |   (20)  op(e2, e2) = e3
% 244.52/50.96  | | | 
% 244.52/50.96  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (14),
% 244.52/50.96  | | |            (15), (19), (20) are inconsistent by sub-proof #1717.
% 244.52/50.96  | | | 
% 244.52/50.96  | | End of split
% 244.52/50.96  | | 
% 244.52/50.96  | Case 2:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (21)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.52/50.96  | |           e3)
% 244.52/50.96  | | 
% 244.52/50.96  | | BETA: splitting (21) gives:
% 244.52/50.96  | | 
% 244.52/50.96  | | Case 1:
% 244.52/50.96  | | | 
% 244.52/50.96  | | |   (22)  all_58_7 = e3 & op(e1, e2) = e3
% 244.52/50.96  | | | 
% 244.52/50.96  | | | REF_CLOSE: (8), (11), (22) are inconsistent by sub-proof #2138.
% 244.52/50.96  | | | 
% 244.52/50.96  | | Case 2:
% 244.52/50.96  | | | 
% 244.52/50.96  | | |   (23)  all_58_13 = e3 & op(e0, e2) = e3
% 244.52/50.96  | | | 
% 244.52/50.96  | | | ALPHA: (23) implies:
% 244.52/50.96  | | |   (24)  op(e0, e2) = e3
% 244.52/50.96  | | | 
% 244.52/50.96  | | | REF_CLOSE: (1), (4), (6), (9), (10), (11), (12), (15), (24) are
% 244.52/50.96  | | |            inconsistent by sub-proof #1715.
% 244.52/50.96  | | | 
% 244.52/50.96  | | End of split
% 244.52/50.96  | | 
% 244.52/50.96  | End of split
% 244.52/50.96  | 
% 244.52/50.96  End of proof
% 244.52/50.96  
% 244.52/50.96  Sub-proof #1715 shows that the following formulas are inconsistent:
% 244.52/50.96  ----------------------------------------------------------------
% 244.52/50.96    (1)  all_58_1 = e1
% 244.52/50.96    (2)   ~ (e2 = e0)
% 244.52/50.96    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.52/50.96         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.52/50.96    (4)  op(e0, e2) = e3
% 244.52/50.96    (5)  op(e2, e2) = e0
% 244.52/50.96    (6)   ~ (e3 = e2)
% 244.52/50.96    (7)  all_58_7 = e1
% 244.52/50.96    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.96    (9)   ~ (e2 = e1)
% 244.52/50.96  
% 244.52/50.96  Begin of proof
% 244.52/50.96  | 
% 244.52/50.96  | BETA: splitting (3) gives:
% 244.52/50.96  | 
% 244.52/50.96  | Case 1:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 244.52/50.96  | |           e2)
% 244.52/50.96  | | 
% 244.52/50.96  | | BETA: splitting (10) gives:
% 244.52/50.96  | | 
% 244.52/50.96  | | Case 1:
% 244.52/50.96  | | | 
% 244.52/50.96  | | |   (11)  all_58_1 = e2 & op(e3, e2) = e2
% 244.52/50.96  | | | 
% 244.52/50.96  | | | REF_CLOSE: (1), (9), (11) are inconsistent by sub-proof #1722.
% 244.52/50.96  | | | 
% 244.52/50.96  | | Case 2:
% 244.52/50.96  | | | 
% 244.52/50.96  | | |   (12)  all_58_3 = e2 & op(e2, e2) = e2
% 244.52/50.96  | | | 
% 244.52/50.96  | | | ALPHA: (12) implies:
% 244.52/50.96  | | |   (13)  op(e2, e2) = e2
% 244.52/50.96  | | | 
% 244.52/50.96  | | | REF_CLOSE: (2), (5), (8), (13) are inconsistent by sub-proof #2137.
% 244.52/50.96  | | | 
% 244.52/50.96  | | End of split
% 244.52/50.96  | | 
% 244.52/50.96  | Case 2:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (14)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 244.52/50.96  | |           e2)
% 244.52/50.96  | | 
% 244.52/50.96  | | REF_CLOSE: (4), (6), (7), (8), (9), (14) are inconsistent by sub-proof
% 244.52/50.96  | |            #1716.
% 244.52/50.96  | | 
% 244.52/50.96  | End of split
% 244.52/50.96  | 
% 244.52/50.96  End of proof
% 244.52/50.96  
% 244.52/50.96  Sub-proof #1716 shows that the following formulas are inconsistent:
% 244.52/50.96  ----------------------------------------------------------------
% 244.52/50.96    (1)  op(e0, e2) = e3
% 244.52/50.96    (2)   ~ (e3 = e2)
% 244.52/50.96    (3)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.52/50.96    (4)  all_58_7 = e1
% 244.52/50.96    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.96    (6)   ~ (e2 = e1)
% 244.52/50.96  
% 244.52/50.96  Begin of proof
% 244.52/50.96  | 
% 244.52/50.96  | BETA: splitting (3) gives:
% 244.52/50.96  | 
% 244.52/50.96  | Case 1:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (7)  all_58_7 = e2 & op(e1, e2) = e2
% 244.52/50.96  | | 
% 244.52/50.96  | | ALPHA: (7) implies:
% 244.52/50.96  | |   (8)  all_58_7 = e2
% 244.52/50.96  | | 
% 244.52/50.96  | | REF_CLOSE: (4), (6), (8) are inconsistent by sub-proof #2134.
% 244.52/50.96  | | 
% 244.52/50.96  | Case 2:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (9)  all_58_13 = e2 & op(e0, e2) = e2
% 244.52/50.96  | | 
% 244.52/50.96  | | ALPHA: (9) implies:
% 244.52/50.96  | |   (10)  op(e0, e2) = e2
% 244.52/50.96  | | 
% 244.52/50.96  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #2254.
% 244.52/50.96  | | 
% 244.52/50.96  | End of split
% 244.52/50.96  | 
% 244.52/50.96  End of proof
% 244.52/50.96  
% 244.52/50.96  Sub-proof #1717 shows that the following formulas are inconsistent:
% 244.52/50.96  ----------------------------------------------------------------
% 244.52/50.96    (1)  op(e2, e2) = e3
% 244.52/50.96    (2)  all_58_1 = e1
% 244.52/50.96    (3)   ~ (e3 = e0)
% 244.52/50.96    (4)  op(e1, e2) = e1
% 244.52/50.96    (5)   ~ (e2 = e0)
% 244.52/50.96    (6)  op(e1, e2) = all_52_6
% 244.52/50.96    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.52/50.96         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.52/50.96    (8)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.52/50.96         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.52/50.96    (9)  all_58_3 = e3
% 244.52/50.96    (10)   ~ (e3 = e2)
% 244.52/50.96    (11)  all_58_7 = e1
% 244.52/50.96    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.96    (13)   ~ (e1 = e0)
% 244.52/50.96    (14)   ~ (e2 = e1)
% 244.52/50.96  
% 244.52/50.96  Begin of proof
% 244.52/50.96  | 
% 244.52/50.96  | BETA: splitting (7) gives:
% 244.52/50.96  | 
% 244.52/50.96  | Case 1:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (15)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 244.52/50.96  | |           e2)
% 244.52/50.96  | | 
% 244.52/50.96  | | REF_CLOSE: (1), (2), (10), (12), (14), (15) are inconsistent by sub-proof
% 244.52/50.96  | |            #1721.
% 244.52/50.96  | | 
% 244.52/50.96  | Case 2:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (16)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 244.52/50.96  | |           e2)
% 244.52/50.96  | | 
% 244.52/50.96  | | BETA: splitting (16) gives:
% 244.52/50.96  | | 
% 244.52/50.96  | | Case 1:
% 244.52/50.96  | | | 
% 244.52/50.96  | | |   (17)  all_58_7 = e2 & op(e1, e2) = e2
% 244.52/50.96  | | | 
% 244.52/50.96  | | | ALPHA: (17) implies:
% 244.52/50.96  | | |   (18)  all_58_7 = e2
% 244.52/50.96  | | | 
% 244.52/50.96  | | | REF_CLOSE: (11), (14), (18) are inconsistent by sub-proof #2134.
% 244.52/50.96  | | | 
% 244.52/50.96  | | Case 2:
% 244.52/50.96  | | | 
% 244.52/50.96  | | |   (19)  all_58_13 = e2 & op(e0, e2) = e2
% 244.52/50.96  | | | 
% 244.52/50.96  | | | ALPHA: (19) implies:
% 244.52/50.96  | | |   (20)  op(e0, e2) = e2
% 244.52/50.96  | | | 
% 244.52/50.96  | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (13), (20) are
% 244.52/50.96  | | |            inconsistent by sub-proof #1718.
% 244.52/50.96  | | | 
% 244.52/50.96  | | End of split
% 244.52/50.96  | | 
% 244.52/50.96  | End of split
% 244.52/50.96  | 
% 244.52/50.96  End of proof
% 244.52/50.96  
% 244.52/50.96  Sub-proof #1718 shows that the following formulas are inconsistent:
% 244.52/50.96  ----------------------------------------------------------------
% 244.52/50.96    (1)  all_58_1 = e1
% 244.52/50.96    (2)   ~ (e3 = e0)
% 244.52/50.96    (3)  op(e1, e2) = e1
% 244.52/50.96    (4)   ~ (e2 = e0)
% 244.52/50.96    (5)  op(e1, e2) = all_52_6
% 244.52/50.96    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.52/50.96         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.52/50.96    (7)  op(e0, e2) = e2
% 244.52/50.96    (8)  all_58_3 = e3
% 244.52/50.96    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.96    (10)   ~ (e1 = e0)
% 244.52/50.96  
% 244.52/50.96  Begin of proof
% 244.52/50.96  | 
% 244.52/50.96  | BETA: splitting (6) gives:
% 244.52/50.96  | 
% 244.52/50.96  | Case 1:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 244.52/50.96  | |           e0)
% 244.52/50.96  | | 
% 244.52/50.96  | | BETA: splitting (11) gives:
% 244.52/50.96  | | 
% 244.52/50.96  | | Case 1:
% 244.52/50.96  | | | 
% 244.52/50.96  | | |   (12)  all_58_1 = e0 & op(e3, e2) = e0
% 244.52/50.96  | | | 
% 244.52/50.96  | | | REF_CLOSE: (1), (10), (12) are inconsistent by sub-proof #1720.
% 244.52/50.96  | | | 
% 244.52/50.96  | | Case 2:
% 244.52/50.96  | | | 
% 244.52/50.96  | | |   (13)  all_58_3 = e0 & op(e2, e2) = e0
% 244.52/50.96  | | | 
% 244.52/50.96  | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #1719.
% 244.52/50.96  | | | 
% 244.52/50.96  | | End of split
% 244.52/50.96  | | 
% 244.52/50.96  | Case 2:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (14)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.52/50.96  | |           e0)
% 244.52/50.96  | | 
% 244.52/50.96  | | REF_CLOSE: (3), (4), (5), (7), (9), (10), (14) are inconsistent by sub-proof
% 244.52/50.96  | |            #2131.
% 244.52/50.96  | | 
% 244.52/50.96  | End of split
% 244.52/50.96  | 
% 244.52/50.96  End of proof
% 244.52/50.96  
% 244.52/50.96  Sub-proof #1719 shows that the following formulas are inconsistent:
% 244.52/50.96  ----------------------------------------------------------------
% 244.52/50.96    (1)  all_58_3 = e0 & op(e2, e2) = e0
% 244.52/50.96    (2)  all_58_3 = e3
% 244.52/50.96    (3)   ~ (e3 = e0)
% 244.52/50.96  
% 244.52/50.96  Begin of proof
% 244.52/50.96  | 
% 244.52/50.96  | ALPHA: (1) implies:
% 244.52/50.96  |   (4)  all_58_3 = e0
% 244.52/50.96  | 
% 244.52/50.96  | COMBINE_EQS: (2), (4) imply:
% 244.52/50.96  |   (5)  e3 = e0
% 244.52/50.96  | 
% 244.52/50.96  | REDUCE: (3), (5) imply:
% 244.52/50.96  |   (6)  $false
% 244.52/50.96  | 
% 244.52/50.96  | CLOSE: (6) is inconsistent.
% 244.52/50.96  | 
% 244.52/50.96  End of proof
% 244.52/50.96  
% 244.52/50.96  Sub-proof #1720 shows that the following formulas are inconsistent:
% 244.52/50.96  ----------------------------------------------------------------
% 244.52/50.96    (1)  all_58_1 = e0 & op(e3, e2) = e0
% 244.52/50.96    (2)  all_58_1 = e1
% 244.52/50.96    (3)   ~ (e1 = e0)
% 244.52/50.96  
% 244.52/50.96  Begin of proof
% 244.52/50.96  | 
% 244.52/50.96  | ALPHA: (1) implies:
% 244.52/50.96  |   (4)  all_58_1 = e0
% 244.52/50.96  | 
% 244.52/50.96  | COMBINE_EQS: (2), (4) imply:
% 244.52/50.96  |   (5)  e1 = e0
% 244.52/50.96  | 
% 244.52/50.96  | REDUCE: (3), (5) imply:
% 244.52/50.96  |   (6)  $false
% 244.52/50.96  | 
% 244.52/50.96  | CLOSE: (6) is inconsistent.
% 244.52/50.96  | 
% 244.52/50.96  End of proof
% 244.52/50.96  
% 244.52/50.96  Sub-proof #1721 shows that the following formulas are inconsistent:
% 244.52/50.96  ----------------------------------------------------------------
% 244.52/50.96    (1)  op(e2, e2) = e3
% 244.52/50.96    (2)  all_58_1 = e1
% 244.52/50.96    (3)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 244.52/50.96    (4)   ~ (e3 = e2)
% 244.52/50.96    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.96    (6)   ~ (e2 = e1)
% 244.52/50.96  
% 244.52/50.96  Begin of proof
% 244.52/50.96  | 
% 244.52/50.96  | BETA: splitting (3) gives:
% 244.52/50.96  | 
% 244.52/50.96  | Case 1:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (7)  all_58_1 = e2 & op(e3, e2) = e2
% 244.52/50.96  | | 
% 244.52/50.96  | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #1722.
% 244.52/50.96  | | 
% 244.52/50.96  | Case 2:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (8)  all_58_3 = e2 & op(e2, e2) = e2
% 244.52/50.96  | | 
% 244.52/50.96  | | ALPHA: (8) implies:
% 244.52/50.96  | |   (9)  op(e2, e2) = e2
% 244.52/50.96  | | 
% 244.52/50.96  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2140.
% 244.52/50.96  | | 
% 244.52/50.96  | End of split
% 244.52/50.96  | 
% 244.52/50.96  End of proof
% 244.52/50.96  
% 244.52/50.96  Sub-proof #1722 shows that the following formulas are inconsistent:
% 244.52/50.96  ----------------------------------------------------------------
% 244.52/50.96    (1)  all_58_1 = e2 & op(e3, e2) = e2
% 244.52/50.96    (2)  all_58_1 = e1
% 244.52/50.96    (3)   ~ (e2 = e1)
% 244.52/50.96  
% 244.52/50.96  Begin of proof
% 244.52/50.96  | 
% 244.52/50.96  | ALPHA: (1) implies:
% 244.52/50.96  |   (4)  all_58_1 = e2
% 244.52/50.96  | 
% 244.52/50.96  | COMBINE_EQS: (2), (4) imply:
% 244.52/50.96  |   (5)  e2 = e1
% 244.52/50.96  | 
% 244.52/50.96  | SIMP: (5) implies:
% 244.52/50.96  |   (6)  e2 = e1
% 244.52/50.96  | 
% 244.52/50.96  | REDUCE: (3), (6) imply:
% 244.52/50.96  |   (7)  $false
% 244.52/50.96  | 
% 244.52/50.96  | CLOSE: (7) is inconsistent.
% 244.52/50.96  | 
% 244.52/50.96  End of proof
% 244.52/50.96  
% 244.52/50.96  Sub-proof #1723 shows that the following formulas are inconsistent:
% 244.52/50.96  ----------------------------------------------------------------
% 244.52/50.96    (1)  all_58_1 = e3 & op(e3, e2) = e3
% 244.52/50.96    (2)  all_58_1 = e1
% 244.52/50.96    (3)   ~ (e3 = e1)
% 244.52/50.96  
% 244.52/50.96  Begin of proof
% 244.52/50.96  | 
% 244.52/50.96  | ALPHA: (1) implies:
% 244.52/50.96  |   (4)  all_58_1 = e3
% 244.52/50.96  | 
% 244.52/50.96  | COMBINE_EQS: (2), (4) imply:
% 244.52/50.96  |   (5)  e3 = e1
% 244.52/50.96  | 
% 244.52/50.96  | SIMP: (5) implies:
% 244.52/50.96  |   (6)  e3 = e1
% 244.52/50.96  | 
% 244.52/50.96  | REDUCE: (3), (6) imply:
% 244.52/50.96  |   (7)  $false
% 244.52/50.96  | 
% 244.52/50.96  | CLOSE: (7) is inconsistent.
% 244.52/50.96  | 
% 244.52/50.96  End of proof
% 244.52/50.96  
% 244.52/50.96  Sub-proof #1724 shows that the following formulas are inconsistent:
% 244.52/50.96  ----------------------------------------------------------------
% 244.52/50.96    (1)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.52/50.96             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.52/50.96           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 244.52/50.96             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.52/50.96           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.52/50.96    (2)  op(e2, e1) = all_52_9
% 244.52/50.96    (3)  all_56_11 = e0
% 244.52/50.96    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.52/50.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.52/50.96    (5)   ~ (all_52_9 = e1)
% 244.52/50.96  
% 244.52/50.96  Begin of proof
% 244.52/50.96  | 
% 244.52/50.96  | BETA: splitting (1) gives:
% 244.52/50.96  | 
% 244.52/50.96  | Case 1:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (6)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.52/50.96  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 244.52/50.96  | |        & op(e1, e2) = e1
% 244.52/50.96  | | 
% 244.52/50.96  | | ALPHA: (6) implies:
% 244.52/50.96  | |   (7)  op(e2, e1) = e1
% 244.52/50.96  | | 
% 244.52/50.96  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #2306.
% 244.52/50.96  | | 
% 244.52/50.96  | Case 2:
% 244.52/50.96  | | 
% 244.52/50.96  | |   (8)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.52/50.96  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 244.52/50.96  | |        & op(e0, e2) = e2
% 244.52/50.96  | | 
% 244.52/50.96  | | ALPHA: (8) implies:
% 244.52/50.96  | |   (9)   ~ (all_56_11 = e0)
% 244.52/50.96  | | 
% 244.52/50.96  | | REDUCE: (3), (9) imply:
% 244.52/50.96  | |   (10)  $false
% 244.52/50.96  | | 
% 244.52/50.96  | | CLOSE: (10) is inconsistent.
% 244.52/50.96  | | 
% 244.52/50.96  | End of split
% 244.52/50.96  | 
% 244.52/50.96  End of proof
% 244.52/50.96  
% 244.52/50.96  Sub-proof #1725 shows that the following formulas are inconsistent:
% 244.52/50.96  ----------------------------------------------------------------
% 244.52/50.96    (1)  op(e3, e2) = e1
% 244.52/50.96    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.52/50.96           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.52/50.96             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.52/50.96           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.52/50.96             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.52/50.96           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.52/50.96           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.52/50.96    (3)   ~ (e3 = e1)
% 244.52/50.96    (4)  all_56_31 = e1
% 244.56/50.96    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.96    (6)   ~ (e2 = e1)
% 244.56/50.96  
% 244.56/50.96  Begin of proof
% 244.56/50.96  | 
% 244.56/50.96  | BETA: splitting (2) gives:
% 244.56/50.96  | 
% 244.56/50.96  | Case 1:
% 244.56/50.96  | | 
% 244.56/50.96  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.56/50.96  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.56/50.96  | |        op(e2, e3) = e3
% 244.56/50.96  | | 
% 244.56/50.96  | | ALPHA: (7) implies:
% 244.56/50.96  | |   (8)  op(e3, e2) = e3
% 244.56/50.96  | | 
% 244.56/50.96  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #2265.
% 244.56/50.96  | | 
% 244.56/50.96  | Case 2:
% 244.56/50.96  | | 
% 244.56/50.96  | |   (9)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.56/50.96  | |            e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2
% 244.56/50.96  | |          & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1
% 244.56/50.96  | |            = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 244.56/50.96  | |            = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.56/50.96  | | 
% 244.56/50.96  | | REF_CLOSE: (1), (4), (5), (6), (9) are inconsistent by sub-proof #1726.
% 244.56/50.96  | | 
% 244.56/50.96  | End of split
% 244.56/50.96  | 
% 244.56/50.96  End of proof
% 244.56/50.96  
% 244.56/50.96  Sub-proof #1726 shows that the following formulas are inconsistent:
% 244.56/50.96  ----------------------------------------------------------------
% 244.56/50.96    (1)  op(e3, e2) = e1
% 244.56/50.96    (2)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 244.56/50.96           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 244.56/50.96             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.56/50.96           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 244.56/50.96             e1) = e3 & op(e1, e3) = e3)
% 244.56/50.96    (3)  all_56_31 = e1
% 244.56/50.96    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.96    (5)   ~ (e2 = e1)
% 244.56/50.96  
% 244.56/50.96  Begin of proof
% 244.56/50.96  | 
% 244.56/50.96  | BETA: splitting (2) gives:
% 244.56/50.96  | 
% 244.56/50.96  | Case 1:
% 244.56/50.96  | | 
% 244.56/50.96  | |   (6)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.56/50.96  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.56/50.96  | |        op(e2, e3) = e2
% 244.56/50.96  | | 
% 244.56/50.96  | | ALPHA: (6) implies:
% 244.56/50.96  | |   (7)  op(e3, e2) = e2
% 244.56/50.96  | | 
% 244.56/50.96  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #2261.
% 244.56/50.96  | | 
% 244.56/50.96  | Case 2:
% 244.56/50.96  | | 
% 244.56/50.96  | |   (8)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.56/50.96  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.56/50.96  | |        op(e1, e3) = e3
% 244.56/50.96  | | 
% 244.56/50.96  | | ALPHA: (8) implies:
% 244.56/50.96  | |   (9)   ~ (all_56_31 = e1)
% 244.56/50.96  | | 
% 244.56/50.96  | | REDUCE: (3), (9) imply:
% 244.56/50.96  | |   (10)  $false
% 244.56/50.96  | | 
% 244.56/50.96  | | CLOSE: (10) is inconsistent.
% 244.56/50.96  | | 
% 244.56/50.96  | End of split
% 244.56/50.96  | 
% 244.56/50.96  End of proof
% 244.56/50.96  
% 244.56/50.96  Sub-proof #1727 shows that the following formulas are inconsistent:
% 244.56/50.96  ----------------------------------------------------------------
% 244.56/50.96    (1)  op(e1, e0) = all_52_14
% 244.56/50.97    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.56/50.97             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.56/50.97           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 244.56/50.97             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.56/50.97           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 244.56/50.97           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.56/50.97           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.56/50.97    (3)   ~ (all_52_14 = e1)
% 244.56/50.97    (4)  all_56_31 = e1
% 244.56/50.97    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.97    (6)  op(e2, e0) = all_52_13
% 244.56/50.97    (7)   ~ (all_52_13 = e0)
% 244.56/50.97  
% 244.56/50.97  Begin of proof
% 244.56/50.97  | 
% 244.56/50.97  | BETA: splitting (2) gives:
% 244.56/50.97  | 
% 244.56/50.97  | Case 1:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.56/50.97  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 244.56/50.97  | |        & op(e0, e2) = e0
% 244.56/50.97  | | 
% 244.56/50.97  | | ALPHA: (8) implies:
% 244.56/50.97  | |   (9)  op(e2, e0) = e0
% 244.56/50.97  | | 
% 244.56/50.97  | | REF_CLOSE: (5), (6), (7), (9) are inconsistent by sub-proof #2324.
% 244.56/50.97  | | 
% 244.56/50.97  | Case 2:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.56/50.97  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.56/50.97  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 244.56/50.97  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.56/50.97  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.56/50.97  | | 
% 244.56/50.97  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #2269.
% 244.56/50.97  | | 
% 244.56/50.97  | End of split
% 244.56/50.97  | 
% 244.56/50.97  End of proof
% 244.56/50.97  
% 244.56/50.97  Sub-proof #1728 shows that the following formulas are inconsistent:
% 244.56/50.97  ----------------------------------------------------------------
% 244.56/50.97    (1)   ~ (all_52_9 = all_6_2)
% 244.56/50.97    (2)  all_54_10 = all_6_2
% 244.56/50.97    (3)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.56/50.97             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.56/50.97           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 244.56/50.97             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.56/50.97           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.56/50.97    (4)   ~ (all_6_2 = e3)
% 244.56/50.97    (5)  op(e2, e1) = all_52_9
% 244.56/50.97    (6)   ~ (all_6_2 = e0)
% 244.56/50.97    (7)  all_56_11 = e0
% 244.56/50.97    (8)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.56/50.97    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.97    (10)  all_56_21 = all_6_2
% 244.56/50.97  
% 244.56/50.97  Begin of proof
% 244.56/50.97  | 
% 244.56/50.97  | BETA: splitting (3) gives:
% 244.56/50.97  | 
% 244.56/50.97  | Case 1:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (11)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.56/50.97  | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) =
% 244.56/50.97  | |         e1 & op(e1, e2) = e1
% 244.56/50.97  | | 
% 244.56/50.97  | | ALPHA: (11) implies:
% 244.56/50.97  | |   (12)   ~ (all_56_21 = e2)
% 244.56/50.97  | |   (13)  op(e2, e1) = e1
% 244.56/50.97  | | 
% 244.56/50.97  | | REDUCE: (10), (12) imply:
% 244.56/50.97  | |   (14)   ~ (all_6_2 = e2)
% 244.56/50.97  | | 
% 244.56/50.97  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (13), (14) are inconsistent by
% 244.56/50.97  | |            sub-proof #1729.
% 244.56/50.97  | | 
% 244.56/50.97  | Case 2:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (15)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.56/50.97  | |           = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) =
% 244.56/50.97  | |         e2 & op(e0, e2) = e2
% 244.56/50.97  | | 
% 244.56/50.97  | | ALPHA: (15) implies:
% 244.56/50.97  | |   (16)   ~ (all_56_11 = e0)
% 244.56/50.97  | | 
% 244.56/50.97  | | REDUCE: (7), (16) imply:
% 244.56/50.97  | |   (17)  $false
% 244.56/50.97  | | 
% 244.56/50.97  | | CLOSE: (17) is inconsistent.
% 244.56/50.97  | | 
% 244.56/50.97  | End of split
% 244.56/50.97  | 
% 244.56/50.97  End of proof
% 244.56/50.97  
% 244.56/50.97  Sub-proof #1729 shows that the following formulas are inconsistent:
% 244.56/50.97  ----------------------------------------------------------------
% 244.56/50.97    (1)   ~ (all_52_9 = all_6_2)
% 244.56/50.97    (2)   ~ (all_6_2 = e2)
% 244.56/50.97    (3)  op(e2, e1) = e1
% 244.56/50.97    (4)  all_54_10 = all_6_2
% 244.56/50.97    (5)   ~ (all_6_2 = e3)
% 244.56/50.97    (6)  op(e2, e1) = all_52_9
% 244.56/50.97    (7)   ~ (all_6_2 = e0)
% 244.56/50.97    (8)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.56/50.97    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.97  
% 244.56/50.97  Begin of proof
% 244.56/50.97  | 
% 244.56/50.97  | BETA: splitting (8) gives:
% 244.56/50.97  | 
% 244.56/50.97  | Case 1:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (10)  all_54_10 = e3
% 244.56/50.97  | | 
% 244.56/50.97  | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #2313.
% 244.56/50.97  | | 
% 244.56/50.97  | Case 2:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (11)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.56/50.97  | | 
% 244.56/50.97  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (11) are inconsistent by
% 244.56/50.97  | |            sub-proof #1730.
% 244.56/50.97  | | 
% 244.56/50.97  | End of split
% 244.56/50.97  | 
% 244.56/50.97  End of proof
% 244.56/50.97  
% 244.56/50.97  Sub-proof #1730 shows that the following formulas are inconsistent:
% 244.56/50.97  ----------------------------------------------------------------
% 244.56/50.97    (1)   ~ (all_52_9 = all_6_2)
% 244.56/50.97    (2)   ~ (all_6_2 = e2)
% 244.56/50.97    (3)  op(e2, e1) = e1
% 244.56/50.97    (4)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.56/50.97    (5)  all_54_10 = all_6_2
% 244.56/50.97    (6)  op(e2, e1) = all_52_9
% 244.56/50.97    (7)   ~ (all_6_2 = e0)
% 244.56/50.97    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.97  
% 244.56/50.97  Begin of proof
% 244.56/50.97  | 
% 244.56/50.97  | BETA: splitting (4) gives:
% 244.56/50.97  | 
% 244.56/50.97  | Case 1:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (9)  all_54_10 = e2
% 244.56/50.97  | | 
% 244.56/50.97  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #2312.
% 244.56/50.97  | | 
% 244.56/50.97  | Case 2:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (10)  all_54_10 = e1 | all_54_10 = e0
% 244.56/50.97  | | 
% 244.56/50.97  | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (10) are inconsistent by sub-proof
% 244.56/50.97  | |            #1905.
% 244.56/50.97  | | 
% 244.56/50.97  | End of split
% 244.56/50.97  | 
% 244.56/50.97  End of proof
% 244.56/50.97  
% 244.56/50.97  Sub-proof #1731 shows that the following formulas are inconsistent:
% 244.56/50.97  ----------------------------------------------------------------
% 244.56/50.97    (1)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.56/50.97             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.56/50.97           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 244.56/50.97             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.56/50.97           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.56/50.97    (2)  all_56_1 = e2
% 244.56/50.97    (3)  all_56_31 = e0
% 244.56/50.97  
% 244.56/50.97  Begin of proof
% 244.56/50.97  | 
% 244.56/50.97  | BETA: splitting (1) gives:
% 244.56/50.97  | 
% 244.56/50.97  | Case 1:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (4)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.56/50.97  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 244.56/50.97  | |        & op(e1, e2) = e1
% 244.56/50.97  | | 
% 244.56/50.97  | | ALPHA: (4) implies:
% 244.56/50.97  | |   (5)   ~ (all_56_1 = e2)
% 244.56/50.97  | | 
% 244.56/50.97  | | REDUCE: (2), (5) imply:
% 244.56/50.97  | |   (6)  $false
% 244.56/50.97  | | 
% 244.56/50.97  | | CLOSE: (6) is inconsistent.
% 244.56/50.97  | | 
% 244.56/50.97  | Case 2:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (7)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.56/50.97  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 244.56/50.97  | |        & op(e0, e2) = e2
% 244.56/50.97  | | 
% 244.56/50.97  | | ALPHA: (7) implies:
% 244.56/50.97  | |   (8)   ~ (all_56_31 = e0)
% 244.56/50.97  | | 
% 244.56/50.97  | | REDUCE: (3), (8) imply:
% 244.56/50.97  | |   (9)  $false
% 244.56/50.97  | | 
% 244.56/50.97  | | CLOSE: (9) is inconsistent.
% 244.56/50.97  | | 
% 244.56/50.97  | End of split
% 244.56/50.97  | 
% 244.56/50.97  End of proof
% 244.56/50.97  
% 244.56/50.97  Sub-proof #1732 shows that the following formulas are inconsistent:
% 244.56/50.97  ----------------------------------------------------------------
% 244.56/50.97    (1)  all_56_21 = e2
% 244.56/50.97    (2)  op(e2, e1) = all_52_9
% 244.56/50.97    (3)  all_56_31 = e0
% 244.56/50.97    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.97    (5)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.56/50.97             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.56/50.97           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.56/50.97             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 244.56/50.97           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 244.56/50.97           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.56/50.97           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.56/50.97    (6)   ~ (all_52_9 = e2)
% 244.56/50.97  
% 244.56/50.97  Begin of proof
% 244.56/50.97  | 
% 244.56/50.97  | BETA: splitting (5) gives:
% 244.56/50.97  | 
% 244.56/50.97  | Case 1:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (7)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.56/50.97  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 244.56/50.97  | |        & op(e1, e2) = e2
% 244.56/50.97  | | 
% 244.56/50.97  | | ALPHA: (7) implies:
% 244.56/50.97  | |   (8)  op(e2, e1) = e2
% 244.56/50.97  | | 
% 244.56/50.97  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2328.
% 244.56/50.97  | | 
% 244.56/50.97  | Case 2:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (9)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.56/50.97  | |            = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) =
% 244.56/50.97  | |          e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.56/50.97  | |          (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.56/50.97  | |          (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.56/50.97  | | 
% 244.56/50.97  | | BETA: splitting (9) gives:
% 244.56/50.97  | | 
% 244.56/50.97  | | Case 1:
% 244.56/50.97  | | | 
% 244.56/50.97  | | |   (10)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.56/50.97  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.56/50.97  | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 244.56/50.97  | | | 
% 244.56/50.97  | | | ALPHA: (10) implies:
% 244.56/50.97  | | |   (11)   ~ (all_56_21 = e2)
% 244.56/50.97  | | | 
% 244.56/50.97  | | | REDUCE: (1), (11) imply:
% 244.56/50.97  | | |   (12)  $false
% 244.56/50.97  | | | 
% 244.56/50.97  | | | CLOSE: (12) is inconsistent.
% 244.56/50.97  | | | 
% 244.56/50.97  | | Case 2:
% 244.56/50.97  | | | 
% 244.56/50.97  | | |   (13)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.56/50.97  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.56/50.97  | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 244.56/50.97  | | | 
% 244.56/50.97  | | | ALPHA: (13) implies:
% 244.56/50.97  | | |   (14)   ~ (all_56_31 = e0)
% 244.56/50.97  | | | 
% 244.56/50.97  | | | REDUCE: (3), (14) imply:
% 244.56/50.97  | | |   (15)  $false
% 244.56/50.97  | | | 
% 244.56/50.97  | | | CLOSE: (15) is inconsistent.
% 244.56/50.97  | | | 
% 244.56/50.97  | | End of split
% 244.56/50.97  | | 
% 244.56/50.97  | End of split
% 244.56/50.97  | 
% 244.56/50.97  End of proof
% 244.56/50.97  
% 244.56/50.97  Sub-proof #1733 shows that the following formulas are inconsistent:
% 244.56/50.97  ----------------------------------------------------------------
% 244.56/50.97    (1)  op(e2, e1) = all_52_9
% 244.56/50.97    (2)  all_56_31 = e0
% 244.56/50.97    (3)  all_56_21 = e1
% 244.56/50.97    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.97    (5)   ~ (all_52_9 = e1)
% 244.56/50.97    (6)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.56/50.97             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.56/50.97           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.56/50.97             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 244.56/50.97           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 244.56/50.97           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.56/50.97           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.56/50.97  
% 244.56/50.97  Begin of proof
% 244.56/50.97  | 
% 244.56/50.97  | BETA: splitting (6) gives:
% 244.56/50.97  | 
% 244.56/50.97  | Case 1:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (7)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.56/50.97  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 244.56/50.97  | |        & op(e1, e2) = e2
% 244.56/50.97  | | 
% 244.56/50.97  | | ALPHA: (7) implies:
% 244.56/50.97  | |   (8)   ~ (all_56_21 = e1)
% 244.56/50.97  | | 
% 244.56/50.97  | | REDUCE: (3), (8) imply:
% 244.56/50.97  | |   (9)  $false
% 244.56/50.97  | | 
% 244.56/50.97  | | CLOSE: (9) is inconsistent.
% 244.56/50.97  | | 
% 244.56/50.97  | Case 2:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (10)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.56/50.97  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.56/50.97  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 244.56/50.97  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.56/50.97  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.56/50.97  | | 
% 244.56/50.97  | | REF_CLOSE: (1), (2), (4), (5), (10) are inconsistent by sub-proof #2298.
% 244.56/50.97  | | 
% 244.56/50.97  | End of split
% 244.56/50.97  | 
% 244.56/50.97  End of proof
% 244.56/50.97  
% 244.56/50.97  Sub-proof #1734 shows that the following formulas are inconsistent:
% 244.56/50.97  ----------------------------------------------------------------
% 244.56/50.97    (1)   ~ (all_52_3 = e0)
% 244.56/50.97    (2)   ~ (e3 = e0)
% 244.56/50.97    (3)  op(e0, e3) = all_52_3
% 244.56/50.97    (4)  op(e3, e1) = e0
% 244.56/50.97    (5)  all_56_1 = e3
% 244.56/50.97    (6)   ~ (all_52_3 = e3)
% 244.56/50.97    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.56/50.97           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.56/50.97             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.56/50.97           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.56/50.97             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.56/50.97           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.56/50.97           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.56/50.97           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.56/50.97           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.56/50.97           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.56/50.97           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.56/50.97             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.56/50.97           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.56/50.97           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.56/50.97    (8)  op(e2, e3) = all_52_1
% 244.56/50.97    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.97    (10)   ~ (e1 = e0)
% 244.56/50.97    (11)   ~ (all_52_1 = e3)
% 244.56/50.97  
% 244.56/50.97  Begin of proof
% 244.56/50.97  | 
% 244.56/50.97  | BETA: splitting (7) gives:
% 244.56/50.97  | 
% 244.56/50.97  | Case 1:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.56/50.97  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 244.56/50.97  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 244.56/50.97  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.56/50.97  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 244.56/50.97  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 244.56/50.97  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.56/50.97  | |           op(e1, e3) = e3)
% 244.56/50.97  | | 
% 244.56/50.97  | | BETA: splitting (12) gives:
% 244.56/50.97  | | 
% 244.56/50.97  | | Case 1:
% 244.56/50.97  | | | 
% 244.56/50.97  | | |   (13)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.56/50.97  | | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 244.56/50.97  | | |         e3 & op(e2, e3) = e3
% 244.56/50.97  | | | 
% 244.56/50.97  | | | ALPHA: (13) implies:
% 244.56/50.97  | | |   (14)  op(e2, e3) = e3
% 244.56/50.97  | | | 
% 244.56/50.97  | | | REF_CLOSE: (8), (9), (11), (14) are inconsistent by sub-proof #2337.
% 244.56/50.97  | | | 
% 244.56/50.97  | | Case 2:
% 244.56/50.97  | | | 
% 244.56/50.97  | | |   (15)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.56/50.97  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.56/50.97  | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17
% 244.56/50.97  | | |           = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 244.56/50.97  | | |             = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 244.56/50.97  | | |           e3)
% 244.56/50.97  | | | 
% 244.56/50.97  | | | BETA: splitting (15) gives:
% 244.56/50.97  | | | 
% 244.56/50.97  | | | Case 1:
% 244.56/50.97  | | | | 
% 244.56/50.97  | | | |   (16)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.56/50.97  | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.56/50.97  | | | |         op(e3, e2) = e2 & op(e2, e3) = e2
% 244.56/50.97  | | | | 
% 244.56/50.97  | | | | ALPHA: (16) implies:
% 244.56/50.97  | | | |   (17)   ~ (all_56_1 = e3)
% 244.56/50.97  | | | | 
% 244.56/50.97  | | | | REDUCE: (5), (17) imply:
% 244.56/50.97  | | | |   (18)  $false
% 244.56/50.97  | | | | 
% 244.56/50.97  | | | | CLOSE: (18) is inconsistent.
% 244.56/50.97  | | | | 
% 244.56/50.97  | | | Case 2:
% 244.56/50.97  | | | | 
% 244.56/50.97  | | | |   (19)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.56/50.97  | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.56/50.97  | | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 244.56/50.97  | | | | 
% 244.56/50.97  | | | | ALPHA: (19) implies:
% 244.56/50.97  | | | |   (20)  op(e3, e1) = e3
% 244.56/50.97  | | | | 
% 244.56/50.97  | | | | REF_CLOSE: (2), (4), (9), (20) are inconsistent by sub-proof #2118.
% 244.56/50.97  | | | | 
% 244.56/50.97  | | | End of split
% 244.56/50.97  | | | 
% 244.56/50.97  | | End of split
% 244.56/50.97  | | 
% 244.56/50.97  | Case 2:
% 244.56/50.97  | | 
% 244.56/50.97  | |   (21)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.56/50.97  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 244.56/50.97  | |           e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 244.56/50.97  | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.56/50.97  | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7
% 244.56/50.97  | |           = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &
% 244.56/50.98  | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 244.56/50.98  | |           op(e0, e3) = e0)
% 244.56/50.98  | | 
% 244.56/50.98  | | REF_CLOSE: (1), (3), (4), (6), (9), (10), (21) are inconsistent by sub-proof
% 244.56/50.98  | |            #1735.
% 244.56/50.98  | | 
% 244.56/50.98  | End of split
% 244.56/50.98  | 
% 244.56/50.98  End of proof
% 244.56/50.98  
% 244.56/50.98  Sub-proof #1735 shows that the following formulas are inconsistent:
% 244.56/50.98  ----------------------------------------------------------------
% 244.56/50.98    (1)   ~ (all_52_3 = e0)
% 244.56/50.98    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.56/50.98             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.56/50.98           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 244.56/50.98           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.56/50.98           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 244.56/50.98           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.56/50.98           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.56/50.98    (3)  op(e0, e3) = all_52_3
% 244.56/50.98    (4)  op(e3, e1) = e0
% 244.56/50.98    (5)   ~ (all_52_3 = e3)
% 244.56/50.98    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.98    (7)   ~ (e1 = e0)
% 244.56/50.98  
% 244.56/50.98  Begin of proof
% 244.56/50.98  | 
% 244.56/50.98  | BETA: splitting (2) gives:
% 244.56/50.98  | 
% 244.56/50.98  | Case 1:
% 244.56/50.98  | | 
% 244.56/50.98  | |   (8)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.56/50.98  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.56/50.98  | |        op(e1, e3) = e1
% 244.56/50.98  | | 
% 244.56/50.98  | | ALPHA: (8) implies:
% 244.56/50.98  | |   (9)  op(e3, e1) = e1
% 244.56/50.98  | | 
% 244.56/50.98  | | REF_CLOSE: (4), (6), (7), (9) are inconsistent by sub-proof #2089.
% 244.56/50.98  | | 
% 244.56/50.98  | Case 2:
% 244.56/50.98  | | 
% 244.56/50.98  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.56/50.98  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 244.56/50.98  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.56/50.98  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.56/50.98  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.56/50.98  | | 
% 244.56/50.98  | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #2330.
% 244.56/50.98  | | 
% 244.56/50.98  | End of split
% 244.56/50.98  | 
% 244.56/50.98  End of proof
% 244.56/50.98  
% 244.56/50.98  Sub-proof #1736 shows that the following formulas are inconsistent:
% 244.56/50.98  ----------------------------------------------------------------
% 244.56/50.98    (1)  all_58_0 = e0 & op(e3, e3) = e0
% 244.56/50.98    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.98    (3)  op(e3, e3) = all_10_2
% 244.56/50.98    (4)   ~ (all_10_2 = e0)
% 244.56/50.98  
% 244.56/50.98  Begin of proof
% 244.56/50.98  | 
% 244.56/50.98  | ALPHA: (1) implies:
% 244.56/50.98  |   (5)  op(e3, e3) = e0
% 244.56/50.98  | 
% 244.56/50.98  | GROUND_INST: instantiating (2) with all_10_2, e0, e3, e3, simplifying with
% 244.56/50.98  |              (3), (5) gives:
% 244.56/50.98  |   (6)  all_10_2 = e0
% 244.56/50.98  | 
% 244.56/50.98  | REDUCE: (4), (6) imply:
% 244.56/50.98  |   (7)  $false
% 244.56/50.98  | 
% 244.56/50.98  | CLOSE: (7) is inconsistent.
% 244.56/50.98  | 
% 244.56/50.98  End of proof
% 244.56/50.98  
% 244.56/50.98  Sub-proof #1737 shows that the following formulas are inconsistent:
% 244.56/50.98  ----------------------------------------------------------------
% 244.56/50.98    (1)  all_54_15 = all_4_2
% 244.56/50.98    (2)  all_54_15 = e0
% 244.56/50.98    (3)   ~ (all_4_2 = e0)
% 244.56/50.98  
% 244.56/50.98  Begin of proof
% 244.56/50.98  | 
% 244.56/50.98  | COMBINE_EQS: (1), (2) imply:
% 244.56/50.98  |   (4)  all_4_2 = e0
% 244.56/50.98  | 
% 244.56/50.98  | SIMP: (4) implies:
% 244.56/50.98  |   (5)  all_4_2 = e0
% 244.56/50.98  | 
% 244.56/50.98  | REDUCE: (3), (5) imply:
% 244.56/50.98  |   (6)  $false
% 244.56/50.98  | 
% 244.56/50.98  | CLOSE: (6) is inconsistent.
% 244.56/50.98  | 
% 244.56/50.98  End of proof
% 244.56/50.98  
% 244.56/50.98  Sub-proof #1738 shows that the following formulas are inconsistent:
% 244.56/50.98  ----------------------------------------------------------------
% 244.56/50.98    (1)  op(e0, e0) = e1
% 244.56/50.98    (2)  op(e3, e1) = all_18_0
% 244.56/50.98    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.56/50.98         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.56/50.98    (4)   ~ (e3 = e0)
% 244.56/50.98    (5)  all_58_1 = e3
% 244.56/50.98    (6)   ~ (e2 = e0)
% 244.56/50.98    (7)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.56/50.98         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.56/50.98    (8)  op(e2, e3) = e3
% 244.56/50.98    (9)  op(e0, e3) = all_52_3
% 244.56/50.98    (10)   ~ (e3 = e1)
% 244.56/50.98    (11)  all_58_7 = e2
% 244.56/50.98    (12)  all_58_11 = e3
% 244.56/50.98    (13)  op(e2, e1) = e2
% 244.56/50.98    (14)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 244.56/50.98          (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 244.56/50.98    (15)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.56/50.98              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 244.56/50.98                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.56/50.98                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.56/50.98    (16)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.56/50.98          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.56/50.98    (17)   ~ (e3 = e2)
% 244.56/50.98    (18)  op(e3, e1) = e1
% 244.56/50.98    (19)  op(e1, e3) = e1
% 244.56/50.98    (20)  op(e2, e2) = e1
% 244.56/50.98    (21)   ~ (all_18_0 = e2)
% 244.56/50.98    (22)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.56/50.98          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.56/50.98    (23)  all_58_15 = e1
% 244.56/50.98    (24)   ~ (all_52_3 = e3)
% 244.56/50.98    (25)   ~ (all_52_1 = e0)
% 244.56/50.98    (26)  op(e2, e3) = all_52_1
% 244.56/50.98    (27)  op(e0, e2) = e0
% 244.56/50.98    (28)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.56/50.98          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.56/50.98    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.98    (30)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.56/50.98          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.56/50.98    (31)  op(e2, e1) = all_56_19
% 244.56/50.98    (32)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.56/50.98          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.56/50.98    (33)   ~ (e1 = e0)
% 244.56/50.98    (34)  op(e3, e2) = e3
% 244.56/50.98    (35)  op(e2, all_56_19) = e2
% 244.56/50.98    (36)  all_58_9 = e2
% 244.56/50.98    (37)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.56/50.98          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.56/50.98            e2)
% 244.56/50.98    (38)   ~ (e2 = e1)
% 244.56/50.98  
% 244.56/50.98  Begin of proof
% 244.56/50.98  | 
% 244.56/50.98  | BETA: splitting (37) gives:
% 244.56/50.98  | 
% 244.56/50.98  | Case 1:
% 244.56/50.98  | | 
% 244.56/50.98  | |   (39)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 244.56/50.98  | |           e2)
% 244.56/50.98  | | 
% 244.56/50.98  | | BETA: splitting (39) gives:
% 244.56/50.98  | | 
% 244.56/50.98  | | Case 1:
% 244.56/50.98  | | | 
% 244.56/50.98  | | |   (40)  all_58_12 = e2 & op(e0, e3) = e2
% 244.56/50.98  | | | 
% 244.56/50.98  | | | ALPHA: (40) implies:
% 244.56/50.98  | | |   (41)  all_58_12 = e2
% 244.56/50.98  | | | 
% 244.56/50.98  | | | BETA: splitting (16) gives:
% 244.56/50.98  | | | 
% 244.56/50.98  | | | Case 1:
% 244.56/50.98  | | | | 
% 244.56/50.98  | | | |   (42)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3)
% 244.56/50.98  | | | |           = e2)
% 244.56/50.98  | | | | 
% 244.56/50.98  | | | | REF_CLOSE: (4), (6), (8), (9), (10), (14), (17), (22), (24), (25), (26),
% 244.56/50.98  | | | |            (28), (29), (33), (38), (41), (42) are inconsistent by
% 244.56/50.98  | | | |            sub-proof #1754.
% 244.56/50.98  | | | | 
% 244.56/50.98  | | | Case 2:
% 244.56/50.98  | | | | 
% 244.56/50.98  | | | |   (43)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3)
% 244.56/50.98  | | | |           = e2)
% 244.56/50.98  | | | | 
% 244.56/50.98  | | | | BETA: splitting (43) gives:
% 244.56/50.98  | | | | 
% 244.56/50.98  | | | | Case 1:
% 244.56/50.98  | | | | | 
% 244.56/50.98  | | | | |   (44)  all_58_6 = e2 & op(e1, e3) = e2
% 244.56/50.98  | | | | | 
% 244.56/50.98  | | | | | ALPHA: (44) implies:
% 244.56/50.98  | | | | |   (45)  op(e1, e3) = e2
% 244.56/50.98  | | | | | 
% 244.56/50.98  | | | | | REF_CLOSE: (19), (29), (38), (45) are inconsistent by sub-proof #2226.
% 244.56/50.98  | | | | | 
% 244.56/50.98  | | | | Case 2:
% 244.56/50.98  | | | | | 
% 244.56/50.98  | | | | | 
% 244.56/50.98  | | | | | GROUND_INST: instantiating (29) with e2, all_56_19, e1, e2,
% 244.56/50.98  | | | | |              simplifying with (13), (31) gives:
% 244.56/50.98  | | | | |   (46)  all_56_19 = e2
% 244.56/50.98  | | | | | 
% 244.56/50.98  | | | | | GROUND_INST: instantiating (29) with e1, all_18_0, e1, e3, simplifying
% 244.56/50.98  | | | | |              with (2), (18) gives:
% 244.56/50.98  | | | | |   (47)  all_18_0 = e1
% 244.56/50.98  | | | | | 
% 244.56/50.98  | | | | | REF_CLOSE: (20), (21), (29), (35), (46), (47) are inconsistent by
% 244.56/50.98  | | | | |            sub-proof #1782.
% 244.56/50.98  | | | | | 
% 244.56/50.98  | | | | End of split
% 244.56/50.98  | | | | 
% 244.56/50.98  | | | End of split
% 244.56/50.98  | | | 
% 244.56/50.98  | | Case 2:
% 244.56/50.98  | | | 
% 244.56/50.98  | | |   (48)  all_58_13 = e2 & op(e0, e2) = e2
% 244.56/50.98  | | | 
% 244.56/50.98  | | | ALPHA: (48) implies:
% 244.56/50.98  | | |   (49)  all_58_13 = e2
% 244.56/50.98  | | |   (50)  op(e0, e2) = e2
% 244.56/50.98  | | | 
% 244.56/50.98  | | | REF_CLOSE: (4), (5), (6), (7), (10), (11), (29), (32), (33), (34), (38),
% 244.56/50.98  | | |            (49), (50) are inconsistent by sub-proof #1748.
% 244.56/50.98  | | | 
% 244.56/50.98  | | End of split
% 244.56/50.98  | | 
% 244.56/50.98  | Case 2:
% 244.56/50.98  | | 
% 244.56/50.98  | |   (51)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.56/50.98  | |           e2)
% 244.56/50.98  | | 
% 244.56/50.98  | | REF_CLOSE: (1), (3), (4), (6), (9), (10), (12), (15), (17), (23), (24),
% 244.56/50.98  | |            (27), (29), (30), (33), (36), (38), (51) are inconsistent by
% 244.56/50.98  | |            sub-proof #1739.
% 244.56/50.98  | | 
% 244.56/50.98  | End of split
% 244.56/50.98  | 
% 244.56/50.98  End of proof
% 244.56/50.98  
% 244.56/50.98  Sub-proof #1739 shows that the following formulas are inconsistent:
% 244.56/50.98  ----------------------------------------------------------------
% 244.56/50.98    (1)  op(e0, e0) = e1
% 244.56/50.98    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.56/50.98         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.56/50.98    (3)   ~ (e3 = e0)
% 244.56/50.98    (4)   ~ (e2 = e0)
% 244.56/50.98    (5)  op(e0, e3) = all_52_3
% 244.56/50.98    (6)   ~ (e3 = e1)
% 244.56/50.98    (7)  all_58_11 = e3
% 244.56/50.98    (8)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.56/50.98             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.56/50.98               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.56/50.98               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.56/50.98    (9)   ~ (e3 = e2)
% 244.56/50.98    (10)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.56/50.98    (11)  all_58_15 = e1
% 244.56/50.98    (12)   ~ (all_52_3 = e3)
% 244.56/50.98    (13)  op(e0, e2) = e0
% 244.56/50.98    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.98    (15)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.56/50.98          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.56/50.98    (16)   ~ (e1 = e0)
% 244.56/50.98    (17)  all_58_9 = e2
% 244.56/50.98    (18)   ~ (e2 = e1)
% 244.56/50.98  
% 244.56/50.98  Begin of proof
% 244.56/50.98  | 
% 244.56/50.98  | BETA: splitting (10) gives:
% 244.56/50.98  | 
% 244.56/50.98  | Case 1:
% 244.56/50.98  | | 
% 244.56/50.98  | |   (19)  all_58_14 = e2 & op(e0, e1) = e2
% 244.56/50.98  | | 
% 244.56/50.98  | | ALPHA: (19) implies:
% 244.56/50.98  | |   (20)  all_58_14 = e2
% 244.56/50.98  | | 
% 244.56/50.98  | | REF_CLOSE: (2), (3), (5), (6), (9), (11), (12), (13), (14), (20) are
% 244.56/50.98  | |            inconsistent by sub-proof #1746.
% 244.56/50.98  | | 
% 244.56/50.98  | Case 2:
% 244.56/50.98  | | 
% 244.56/50.98  | |   (21)  all_58_15 = e2 & op(e0, e0) = e2
% 244.56/50.98  | | 
% 244.56/50.98  | | ALPHA: (21) implies:
% 244.56/50.98  | |   (22)  all_58_15 = e2
% 244.56/50.98  | | 
% 244.56/50.98  | | COMBINE_EQS: (11), (22) imply:
% 244.56/50.98  | |   (23)  e2 = e1
% 244.56/50.98  | | 
% 244.56/50.98  | | COMBINE_EQS: (17), (23) imply:
% 244.56/50.98  | |   (24)  all_58_9 = e1
% 244.56/50.98  | | 
% 244.56/50.98  | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (11), (14), (15), (16), (18), (24)
% 244.56/50.98  | |            are inconsistent by sub-proof #1740.
% 244.56/50.98  | | 
% 244.56/50.98  | End of split
% 244.56/50.98  | 
% 244.56/50.98  End of proof
% 244.56/50.98  
% 244.56/50.98  Sub-proof #1740 shows that the following formulas are inconsistent:
% 244.56/50.98  ----------------------------------------------------------------
% 244.56/50.98    (1)  op(e0, e0) = e1
% 244.56/50.98    (2)   ~ (e3 = e0)
% 244.56/50.98    (3)   ~ (e2 = e0)
% 244.56/50.98    (4)  all_58_11 = e3
% 244.56/50.98    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.56/50.98             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.56/50.98               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.56/50.98               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.56/50.98    (6)   ~ (e3 = e2)
% 244.56/50.98    (7)  all_58_15 = e1
% 244.56/50.98    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.98    (9)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.56/50.98         (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.56/50.98    (10)   ~ (e1 = e0)
% 244.56/50.98    (11)  all_58_9 = e1
% 244.56/50.98    (12)   ~ (e2 = e1)
% 244.56/50.98  
% 244.56/50.98  Begin of proof
% 244.56/50.98  | 
% 244.56/50.98  | BETA: splitting (9) gives:
% 244.56/50.98  | 
% 244.56/50.98  | Case 1:
% 244.56/50.98  | | 
% 244.56/50.98  | |   (13)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 244.56/50.98  | |           e2)
% 244.56/50.98  | | 
% 244.56/50.98  | | BETA: splitting (13) gives:
% 244.56/50.98  | | 
% 244.56/50.98  | | Case 1:
% 244.56/50.98  | | | 
% 244.56/50.98  | | |   (14)  all_58_9 = e2 & op(e3, e0) = e2
% 244.56/50.98  | | | 
% 244.56/50.98  | | | REF_CLOSE: (11), (12), (14) are inconsistent by sub-proof #1745.
% 244.56/50.98  | | | 
% 244.56/50.98  | | Case 2:
% 244.56/50.98  | | | 
% 244.56/50.98  | | |   (15)  all_58_10 = e2 & op(e2, e0) = e2
% 244.56/50.98  | | | 
% 244.56/50.98  | | | ALPHA: (15) implies:
% 244.56/50.98  | | |   (16)  op(e2, e0) = e2
% 244.56/50.98  | | | 
% 244.56/50.98  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (11), (16) are inconsistent
% 244.56/50.98  | | |            by sub-proof #1742.
% 244.56/50.98  | | | 
% 244.56/50.98  | | End of split
% 244.56/50.98  | | 
% 244.56/50.98  | Case 2:
% 244.56/50.98  | | 
% 244.56/50.98  | |   (17)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.56/50.98  | |           e2)
% 244.56/50.98  | | 
% 244.56/50.98  | | BETA: splitting (17) gives:
% 244.56/50.98  | | 
% 244.56/50.98  | | Case 1:
% 244.56/50.98  | | | 
% 244.56/50.98  | | |   (18)  all_58_11 = e2 & op(e1, e0) = e2
% 244.56/50.98  | | | 
% 244.56/50.98  | | | REF_CLOSE: (4), (6), (18) are inconsistent by sub-proof #1741.
% 244.56/50.98  | | | 
% 244.56/50.98  | | Case 2:
% 244.56/50.98  | | | 
% 244.56/50.98  | | |   (19)  all_58_15 = e2 & op(e0, e0) = e2
% 244.56/50.98  | | | 
% 244.56/50.98  | | | REF_CLOSE: (7), (12), (19) are inconsistent by sub-proof #1917.
% 244.56/50.98  | | | 
% 244.56/50.98  | | End of split
% 244.56/50.98  | | 
% 244.56/50.98  | End of split
% 244.56/50.98  | 
% 244.56/50.98  End of proof
% 244.56/50.98  
% 244.56/50.98  Sub-proof #1741 shows that the following formulas are inconsistent:
% 244.56/50.98  ----------------------------------------------------------------
% 244.56/50.98    (1)  all_58_11 = e2 & op(e1, e0) = e2
% 244.56/50.98    (2)  all_58_11 = e3
% 244.56/50.98    (3)   ~ (e3 = e2)
% 244.56/50.98  
% 244.56/50.98  Begin of proof
% 244.56/50.98  | 
% 244.56/50.98  | ALPHA: (1) implies:
% 244.56/50.98  |   (4)  all_58_11 = e2
% 244.56/50.98  | 
% 244.56/50.98  | COMBINE_EQS: (2), (4) imply:
% 244.56/50.98  |   (5)  e3 = e2
% 244.56/50.98  | 
% 244.56/50.98  | REDUCE: (3), (5) imply:
% 244.56/50.98  |   (6)  $false
% 244.56/50.98  | 
% 244.56/50.98  | CLOSE: (6) is inconsistent.
% 244.56/50.98  | 
% 244.56/50.98  End of proof
% 244.56/50.98  
% 244.56/50.98  Sub-proof #1742 shows that the following formulas are inconsistent:
% 244.56/50.98  ----------------------------------------------------------------
% 244.56/50.98    (1)  op(e0, e0) = e1
% 244.56/50.98    (2)   ~ (e3 = e0)
% 244.56/50.98    (3)   ~ (e2 = e0)
% 244.56/50.98    (4)  all_58_11 = e3
% 244.56/50.98    (5)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.56/50.98             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.56/50.98               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.56/50.98               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.56/50.98    (6)  op(e2, e0) = e2
% 244.56/50.98    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.99    (8)   ~ (e1 = e0)
% 244.56/50.99    (9)  all_58_9 = e1
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | BETA: splitting (5) gives:
% 244.56/50.99  | 
% 244.56/50.99  | Case 1:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (10)  all_58_15 = e0 & op(e0, e0) = e0
% 244.56/50.99  | | 
% 244.56/50.99  | | ALPHA: (10) implies:
% 244.56/50.99  | |   (11)  op(e0, e0) = e0
% 244.56/50.99  | | 
% 244.56/50.99  | | REF_CLOSE: (1), (7), (8), (11) are inconsistent by sub-proof #2274.
% 244.56/50.99  | | 
% 244.56/50.99  | Case 2:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (12)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 244.56/50.99  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 244.56/50.99  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 244.56/50.99  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 244.56/50.99  | | 
% 244.56/50.99  | | ALPHA: (12) implies:
% 244.56/50.99  | |   (13)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 244.56/50.99  | |           e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.56/50.99  | | 
% 244.56/50.99  | | BETA: splitting (13) gives:
% 244.56/50.99  | | 
% 244.56/50.99  | | Case 1:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (14)  all_58_9 = e0 & op(e3, e0) = e0
% 244.56/50.99  | | | 
% 244.56/50.99  | | | ALPHA: (14) implies:
% 244.56/50.99  | | |   (15)  all_58_9 = e0
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (8), (9), (15) are inconsistent by sub-proof #1744.
% 244.56/50.99  | | | 
% 244.56/50.99  | | Case 2:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (16)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 244.56/50.99  | | |           = e0)
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (2), (3), (4), (6), (7), (16) are inconsistent by sub-proof
% 244.56/50.99  | | |            #1743.
% 244.56/50.99  | | | 
% 244.56/50.99  | | End of split
% 244.56/50.99  | | 
% 244.56/50.99  | End of split
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1743 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)   ~ (e3 = e0)
% 244.56/50.99    (2)   ~ (e2 = e0)
% 244.56/50.99    (3)  all_58_11 = e3
% 244.56/50.99    (4)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.56/50.99    (5)  op(e2, e0) = e2
% 244.56/50.99    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | BETA: splitting (4) gives:
% 244.56/50.99  | 
% 244.56/50.99  | Case 1:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (7)  all_58_10 = e0 & op(e2, e0) = e0
% 244.56/50.99  | | 
% 244.56/50.99  | | ALPHA: (7) implies:
% 244.56/50.99  | |   (8)  op(e2, e0) = e0
% 244.56/50.99  | | 
% 244.56/50.99  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2121.
% 244.56/50.99  | | 
% 244.56/50.99  | Case 2:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (9)  all_58_11 = e0 & op(e1, e0) = e0
% 244.56/50.99  | | 
% 244.56/50.99  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #2204.
% 244.56/50.99  | | 
% 244.56/50.99  | End of split
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1744 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)  all_58_9 = e1
% 244.56/50.99    (2)  all_58_9 = e0
% 244.56/50.99    (3)   ~ (e1 = e0)
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | COMBINE_EQS: (1), (2) imply:
% 244.56/50.99  |   (4)  e1 = e0
% 244.56/50.99  | 
% 244.56/50.99  | SIMP: (4) implies:
% 244.56/50.99  |   (5)  e1 = e0
% 244.56/50.99  | 
% 244.56/50.99  | REDUCE: (3), (5) imply:
% 244.56/50.99  |   (6)  $false
% 244.56/50.99  | 
% 244.56/50.99  | CLOSE: (6) is inconsistent.
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1745 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)  all_58_9 = e2 & op(e3, e0) = e2
% 244.56/50.99    (2)  all_58_9 = e1
% 244.56/50.99    (3)   ~ (e2 = e1)
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | ALPHA: (1) implies:
% 244.56/50.99  |   (4)  all_58_9 = e2
% 244.56/50.99  | 
% 244.56/50.99  | COMBINE_EQS: (2), (4) imply:
% 244.56/50.99  |   (5)  e2 = e1
% 244.56/50.99  | 
% 244.56/50.99  | REDUCE: (3), (5) imply:
% 244.56/50.99  |   (6)  $false
% 244.56/50.99  | 
% 244.56/50.99  | CLOSE: (6) is inconsistent.
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1746 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.56/50.99         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.56/50.99    (2)   ~ (e3 = e0)
% 244.56/50.99    (3)  all_58_14 = e2
% 244.56/50.99    (4)  op(e0, e3) = all_52_3
% 244.56/50.99    (5)   ~ (e3 = e1)
% 244.56/50.99    (6)   ~ (e3 = e2)
% 244.56/50.99    (7)  all_58_15 = e1
% 244.56/50.99    (8)   ~ (all_52_3 = e3)
% 244.56/50.99    (9)  op(e0, e2) = e0
% 244.56/50.99    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | BETA: splitting (1) gives:
% 244.56/50.99  | 
% 244.56/50.99  | Case 1:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (11)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.56/50.99  | |           e3)
% 244.56/50.99  | | 
% 244.56/50.99  | | BETA: splitting (11) gives:
% 244.56/50.99  | | 
% 244.56/50.99  | | Case 1:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (12)  all_58_12 = e3 & op(e0, e3) = e3
% 244.56/50.99  | | | 
% 244.56/50.99  | | | ALPHA: (12) implies:
% 244.56/50.99  | | |   (13)  op(e0, e3) = e3
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (4), (8), (10), (13) are inconsistent by sub-proof #2332.
% 244.56/50.99  | | | 
% 244.56/50.99  | | Case 2:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (14)  all_58_13 = e3 & op(e0, e2) = e3
% 244.56/50.99  | | | 
% 244.56/50.99  | | | ALPHA: (14) implies:
% 244.56/50.99  | | |   (15)  op(e0, e2) = e3
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (2), (9), (10), (15) are inconsistent by sub-proof #1961.
% 244.56/50.99  | | | 
% 244.56/50.99  | | End of split
% 244.56/50.99  | | 
% 244.56/50.99  | Case 2:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (16)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.56/50.99  | |           e3)
% 244.56/50.99  | | 
% 244.56/50.99  | | BETA: splitting (16) gives:
% 244.56/50.99  | | 
% 244.56/50.99  | | Case 1:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (17)  all_58_14 = e3 & op(e0, e1) = e3
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (3), (6), (17) are inconsistent by sub-proof #1747.
% 244.56/50.99  | | | 
% 244.56/50.99  | | Case 2:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (18)  all_58_15 = e3 & op(e0, e0) = e3
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (5), (7), (18) are inconsistent by sub-proof #1915.
% 244.56/50.99  | | | 
% 244.56/50.99  | | End of split
% 244.56/50.99  | | 
% 244.56/50.99  | End of split
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1747 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)  all_58_14 = e3 & op(e0, e1) = e3
% 244.56/50.99    (2)  all_58_14 = e2
% 244.56/50.99    (3)   ~ (e3 = e2)
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | ALPHA: (1) implies:
% 244.56/50.99  |   (4)  all_58_14 = e3
% 244.56/50.99  | 
% 244.56/50.99  | COMBINE_EQS: (2), (4) imply:
% 244.56/50.99  |   (5)  e3 = e2
% 244.56/50.99  | 
% 244.56/50.99  | REDUCE: (3), (5) imply:
% 244.56/50.99  |   (6)  $false
% 244.56/50.99  | 
% 244.56/50.99  | CLOSE: (6) is inconsistent.
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1748 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)   ~ (e3 = e0)
% 244.56/50.99    (2)  all_58_1 = e3
% 244.56/50.99    (3)   ~ (e2 = e0)
% 244.56/50.99    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.56/50.99         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.56/50.99    (5)  op(e0, e2) = e2
% 244.56/50.99    (6)   ~ (e3 = e1)
% 244.56/50.99    (7)  all_58_7 = e2
% 244.56/50.99    (8)  all_58_13 = e2
% 244.56/50.99    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.99    (10)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.56/50.99          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.56/50.99    (11)   ~ (e1 = e0)
% 244.56/50.99    (12)  op(e3, e2) = e3
% 244.56/50.99    (13)   ~ (e2 = e1)
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | BETA: splitting (4) gives:
% 244.56/50.99  | 
% 244.56/50.99  | Case 1:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 244.56/50.99  | |           e0)
% 244.56/50.99  | | 
% 244.56/50.99  | | BETA: splitting (14) gives:
% 244.56/50.99  | | 
% 244.56/50.99  | | Case 1:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (15)  all_58_1 = e0 & op(e3, e2) = e0
% 244.56/50.99  | | | 
% 244.56/50.99  | | | ALPHA: (15) implies:
% 244.56/50.99  | | |   (16)  op(e3, e2) = e0
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (1), (9), (12), (16) are inconsistent by sub-proof #2099.
% 244.56/50.99  | | | 
% 244.56/50.99  | | Case 2:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (17)  all_58_3 = e0 & op(e2, e2) = e0
% 244.56/50.99  | | | 
% 244.56/50.99  | | | ALPHA: (17) implies:
% 244.56/50.99  | | |   (18)  all_58_3 = e0
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (2), (6), (7), (8), (10), (11), (13), (18) are inconsistent by
% 244.56/50.99  | | |            sub-proof #1750.
% 244.56/50.99  | | | 
% 244.56/50.99  | | End of split
% 244.56/50.99  | | 
% 244.56/50.99  | Case 2:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (19)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.56/50.99  | |           e0)
% 244.56/50.99  | | 
% 244.56/50.99  | | REF_CLOSE: (3), (5), (7), (9), (19) are inconsistent by sub-proof #1749.
% 244.56/50.99  | | 
% 244.56/50.99  | End of split
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1749 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)   ~ (e2 = e0)
% 244.56/50.99    (2)  op(e0, e2) = e2
% 244.56/50.99    (3)  all_58_7 = e2
% 244.56/50.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.99    (5)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | BETA: splitting (5) gives:
% 244.56/50.99  | 
% 244.56/50.99  | Case 1:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (6)  all_58_7 = e0 & op(e1, e2) = e0
% 244.56/50.99  | | 
% 244.56/50.99  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #2212.
% 244.56/50.99  | | 
% 244.56/50.99  | Case 2:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (7)  all_58_13 = e0 & op(e0, e2) = e0
% 244.56/50.99  | | 
% 244.56/50.99  | | ALPHA: (7) implies:
% 244.56/50.99  | |   (8)  op(e0, e2) = e0
% 244.56/50.99  | | 
% 244.56/50.99  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2132.
% 244.56/50.99  | | 
% 244.56/50.99  | End of split
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1750 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)  all_58_1 = e3
% 244.56/50.99    (2)   ~ (e3 = e1)
% 244.56/50.99    (3)  all_58_7 = e2
% 244.56/50.99    (4)  all_58_13 = e2
% 244.56/50.99    (5)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.56/50.99         (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.56/50.99    (6)   ~ (e1 = e0)
% 244.56/50.99    (7)  all_58_3 = e0
% 244.56/50.99    (8)   ~ (e2 = e1)
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | BETA: splitting (5) gives:
% 244.56/50.99  | 
% 244.56/50.99  | Case 1:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (9)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 244.56/50.99  | | 
% 244.56/50.99  | | BETA: splitting (9) gives:
% 244.56/50.99  | | 
% 244.56/50.99  | | Case 1:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (10)  all_58_1 = e1 & op(e3, e2) = e1
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #1753.
% 244.56/50.99  | | | 
% 244.56/50.99  | | Case 2:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (11)  all_58_3 = e1 & op(e2, e2) = e1
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (6), (7), (11) are inconsistent by sub-proof #1752.
% 244.56/50.99  | | | 
% 244.56/50.99  | | End of split
% 244.56/50.99  | | 
% 244.56/50.99  | Case 2:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (12)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 244.56/50.99  | |           e1)
% 244.56/50.99  | | 
% 244.56/50.99  | | BETA: splitting (12) gives:
% 244.56/50.99  | | 
% 244.56/50.99  | | Case 1:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (13)  all_58_7 = e1 & op(e1, e2) = e1
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #2224.
% 244.56/50.99  | | | 
% 244.56/50.99  | | Case 2:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (14)  all_58_13 = e1 & op(e0, e2) = e1
% 244.56/50.99  | | | 
% 244.56/50.99  | | | REF_CLOSE: (4), (8), (14) are inconsistent by sub-proof #1751.
% 244.56/50.99  | | | 
% 244.56/50.99  | | End of split
% 244.56/50.99  | | 
% 244.56/50.99  | End of split
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1751 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)  all_58_13 = e1 & op(e0, e2) = e1
% 244.56/50.99    (2)  all_58_13 = e2
% 244.56/50.99    (3)   ~ (e2 = e1)
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | ALPHA: (1) implies:
% 244.56/50.99  |   (4)  all_58_13 = e1
% 244.56/50.99  | 
% 244.56/50.99  | COMBINE_EQS: (2), (4) imply:
% 244.56/50.99  |   (5)  e2 = e1
% 244.56/50.99  | 
% 244.56/50.99  | REDUCE: (3), (5) imply:
% 244.56/50.99  |   (6)  $false
% 244.56/50.99  | 
% 244.56/50.99  | CLOSE: (6) is inconsistent.
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1752 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)  all_58_3 = e1 & op(e2, e2) = e1
% 244.56/50.99    (2)  all_58_3 = e0
% 244.56/50.99    (3)   ~ (e1 = e0)
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | ALPHA: (1) implies:
% 244.56/50.99  |   (4)  all_58_3 = e1
% 244.56/50.99  | 
% 244.56/50.99  | COMBINE_EQS: (2), (4) imply:
% 244.56/50.99  |   (5)  e1 = e0
% 244.56/50.99  | 
% 244.56/50.99  | SIMP: (5) implies:
% 244.56/50.99  |   (6)  e1 = e0
% 244.56/50.99  | 
% 244.56/50.99  | REDUCE: (3), (6) imply:
% 244.56/50.99  |   (7)  $false
% 244.56/50.99  | 
% 244.56/50.99  | CLOSE: (7) is inconsistent.
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1753 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)  all_58_1 = e1 & op(e3, e2) = e1
% 244.56/50.99    (2)  all_58_1 = e3
% 244.56/50.99    (3)   ~ (e3 = e1)
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | ALPHA: (1) implies:
% 244.56/50.99  |   (4)  all_58_1 = e1
% 244.56/50.99  | 
% 244.56/50.99  | COMBINE_EQS: (2), (4) imply:
% 244.56/50.99  |   (5)  e3 = e1
% 244.56/50.99  | 
% 244.56/50.99  | REDUCE: (3), (5) imply:
% 244.56/50.99  |   (6)  $false
% 244.56/50.99  | 
% 244.56/50.99  | CLOSE: (6) is inconsistent.
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1754 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)   ~ (e3 = e0)
% 244.56/50.99    (2)   ~ (e2 = e0)
% 244.56/50.99    (3)  all_58_12 = e2
% 244.56/50.99    (4)  op(e2, e3) = e3
% 244.56/50.99    (5)  op(e0, e3) = all_52_3
% 244.56/50.99    (6)   ~ (e3 = e1)
% 244.56/50.99    (7)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 244.56/50.99         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 244.56/50.99    (8)   ~ (e3 = e2)
% 244.56/50.99    (9)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.56/50.99         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.56/50.99    (10)   ~ (all_52_3 = e3)
% 244.56/50.99    (11)   ~ (all_52_1 = e0)
% 244.56/50.99    (12)  op(e2, e3) = all_52_1
% 244.56/50.99    (13)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 244.56/50.99    (14)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.56/50.99          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.56/50.99    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.99    (16)   ~ (e1 = e0)
% 244.56/50.99    (17)   ~ (e2 = e1)
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | BETA: splitting (13) gives:
% 244.56/50.99  | 
% 244.56/50.99  | Case 1:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (18)  all_58_0 = e2 & op(e3, e3) = e2
% 244.56/50.99  | | 
% 244.56/50.99  | | ALPHA: (18) implies:
% 244.56/50.99  | |   (19)  op(e3, e3) = e2
% 244.56/50.99  | | 
% 244.56/50.99  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 244.56/50.99  | |            (15), (16), (17), (19) are inconsistent by sub-proof #1755.
% 244.56/50.99  | | 
% 244.56/50.99  | Case 2:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (20)  all_58_2 = e2 & op(e2, e3) = e2
% 244.56/50.99  | | 
% 244.56/50.99  | | ALPHA: (20) implies:
% 244.56/50.99  | |   (21)  op(e2, e3) = e2
% 244.56/50.99  | | 
% 244.56/50.99  | | REF_CLOSE: (4), (8), (15), (21) are inconsistent by sub-proof #1897.
% 244.56/50.99  | | 
% 244.56/50.99  | End of split
% 244.56/50.99  | 
% 244.56/50.99  End of proof
% 244.56/50.99  
% 244.56/50.99  Sub-proof #1755 shows that the following formulas are inconsistent:
% 244.56/50.99  ----------------------------------------------------------------
% 244.56/50.99    (1)   ~ (e3 = e0)
% 244.56/50.99    (2)   ~ (e2 = e0)
% 244.56/50.99    (3)  all_58_12 = e2
% 244.56/50.99    (4)  op(e0, e3) = all_52_3
% 244.56/50.99    (5)   ~ (e3 = e1)
% 244.56/50.99    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 244.56/50.99         (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 244.56/50.99    (7)   ~ (e3 = e2)
% 244.56/50.99    (8)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.56/50.99         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.56/50.99    (9)   ~ (all_52_3 = e3)
% 244.56/50.99    (10)   ~ (all_52_1 = e0)
% 244.56/50.99    (11)  op(e2, e3) = all_52_1
% 244.56/50.99    (12)  op(e3, e3) = e2
% 244.56/50.99    (13)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.56/50.99          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.56/50.99    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/50.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/50.99    (15)   ~ (e1 = e0)
% 244.56/50.99    (16)   ~ (e2 = e1)
% 244.56/50.99  
% 244.56/50.99  Begin of proof
% 244.56/50.99  | 
% 244.56/50.99  | BETA: splitting (8) gives:
% 244.56/50.99  | 
% 244.56/50.99  | Case 1:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (17)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 244.56/50.99  | |           e0)
% 244.56/50.99  | | 
% 244.56/50.99  | | REF_CLOSE: (2), (10), (11), (12), (14), (17) are inconsistent by sub-proof
% 244.56/50.99  | |            #1984.
% 244.56/50.99  | | 
% 244.56/50.99  | Case 2:
% 244.56/50.99  | | 
% 244.56/50.99  | |   (18)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 244.56/50.99  | |           e0)
% 244.56/50.99  | | 
% 244.56/50.99  | | BETA: splitting (18) gives:
% 244.56/50.99  | | 
% 244.56/50.99  | | Case 1:
% 244.56/50.99  | | | 
% 244.56/50.99  | | |   (19)  all_58_6 = e0 & op(e1, e3) = e0
% 244.56/50.99  | | | 
% 244.56/50.99  | | | ALPHA: (19) implies:
% 244.56/50.99  | | |   (20)  all_58_6 = e0
% 244.56/50.99  | | | 
% 244.56/50.99  | | | BETA: splitting (6) gives:
% 244.56/50.99  | | | 
% 244.56/50.99  | | | Case 1:
% 244.56/50.99  | | | | 
% 244.56/51.00  | | | |   (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 244.56/51.00  | | | |           = e3)
% 244.56/51.00  | | | | 
% 244.56/51.00  | | | | BETA: splitting (21) gives:
% 244.56/51.00  | | | | 
% 244.56/51.00  | | | | Case 1:
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | |   (22)  all_58_0 = e3 & op(e3, e3) = e3
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | | ALPHA: (22) implies:
% 244.56/51.00  | | | | |   (23)  op(e3, e3) = e3
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | | REF_CLOSE: (7), (12), (14), (23) are inconsistent by sub-proof #2194.
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | Case 2:
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | |   (24)  all_58_2 = e3 & op(e2, e3) = e3
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | | ALPHA: (24) implies:
% 244.56/51.00  | | | | |   (25)  all_58_2 = e3
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | | REF_CLOSE: (3), (5), (12), (13), (14), (15), (16), (20), (25) are
% 244.56/51.00  | | | | |            inconsistent by sub-proof #1762.
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | End of split
% 244.56/51.00  | | | | 
% 244.56/51.00  | | | Case 2:
% 244.56/51.00  | | | | 
% 244.56/51.00  | | | |   (26)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 244.56/51.00  | | | |           = e3)
% 244.56/51.00  | | | | 
% 244.56/51.00  | | | | BETA: splitting (26) gives:
% 244.56/51.00  | | | | 
% 244.56/51.00  | | | | Case 1:
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | |   (27)  all_58_6 = e3 & op(e1, e3) = e3
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | | ALPHA: (27) implies:
% 244.56/51.00  | | | | |   (28)  all_58_6 = e3
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | | REF_CLOSE: (1), (2), (3), (5), (8), (12), (13), (14), (15), (16), (28)
% 244.56/51.00  | | | | |            are inconsistent by sub-proof #1756.
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | Case 2:
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | |   (29)  all_58_12 = e3 & op(e0, e3) = e3
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | | ALPHA: (29) implies:
% 244.56/51.00  | | | | |   (30)  op(e0, e3) = e3
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | | REF_CLOSE: (4), (9), (14), (30) are inconsistent by sub-proof #2332.
% 244.56/51.00  | | | | | 
% 244.56/51.00  | | | | End of split
% 244.56/51.00  | | | | 
% 244.56/51.00  | | | End of split
% 244.56/51.00  | | | 
% 244.56/51.00  | | Case 2:
% 244.56/51.00  | | | 
% 244.56/51.00  | | |   (31)  all_58_12 = e0 & op(e0, e3) = e0
% 244.56/51.00  | | | 
% 244.56/51.00  | | | REF_CLOSE: (2), (3), (31) are inconsistent by sub-proof #1760.
% 244.56/51.00  | | | 
% 244.56/51.00  | | End of split
% 244.56/51.00  | | 
% 244.56/51.00  | End of split
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1756 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)   ~ (e3 = e0)
% 244.56/51.00    (2)  all_58_6 = e3
% 244.56/51.00    (3)   ~ (e2 = e0)
% 244.56/51.00    (4)  all_58_12 = e2
% 244.56/51.00    (5)   ~ (e3 = e1)
% 244.56/51.00    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.56/51.00         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.56/51.00    (7)  op(e3, e3) = e2
% 244.56/51.00    (8)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.56/51.00         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.56/51.00    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.00    (10)   ~ (e1 = e0)
% 244.56/51.00    (11)   ~ (e2 = e1)
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | BETA: splitting (8) gives:
% 244.56/51.00  | 
% 244.56/51.00  | Case 1:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (12)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 244.56/51.00  | |           e1)
% 244.56/51.00  | | 
% 244.56/51.00  | | BETA: splitting (12) gives:
% 244.56/51.00  | | 
% 244.56/51.00  | | Case 1:
% 244.56/51.00  | | | 
% 244.56/51.00  | | |   (13)  all_58_0 = e1 & op(e3, e3) = e1
% 244.56/51.00  | | | 
% 244.56/51.00  | | | ALPHA: (13) implies:
% 244.56/51.00  | | |   (14)  op(e3, e3) = e1
% 244.56/51.00  | | | 
% 244.56/51.00  | | | REF_CLOSE: (7), (9), (11), (14) are inconsistent by sub-proof #2267.
% 244.56/51.00  | | | 
% 244.56/51.00  | | Case 2:
% 244.56/51.00  | | | 
% 244.56/51.00  | | |   (15)  all_58_2 = e1 & op(e2, e3) = e1
% 244.56/51.00  | | | 
% 244.56/51.00  | | | ALPHA: (15) implies:
% 244.56/51.00  | | |   (16)  all_58_2 = e1
% 244.56/51.00  | | | 
% 244.56/51.00  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (16) are inconsistent
% 244.56/51.00  | | |            by sub-proof #1759.
% 244.56/51.00  | | | 
% 244.56/51.00  | | End of split
% 244.56/51.00  | | 
% 244.56/51.00  | Case 2:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (17)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 244.56/51.00  | |           e1)
% 244.56/51.00  | | 
% 244.56/51.00  | | BETA: splitting (17) gives:
% 244.56/51.00  | | 
% 244.56/51.00  | | Case 1:
% 244.56/51.00  | | | 
% 244.56/51.00  | | |   (18)  all_58_6 = e1 & op(e1, e3) = e1
% 244.56/51.00  | | | 
% 244.56/51.00  | | | ALPHA: (18) implies:
% 244.56/51.00  | | |   (19)  all_58_6 = e1
% 244.56/51.00  | | | 
% 244.56/51.00  | | | REF_CLOSE: (2), (5), (19) are inconsistent by sub-proof #1758.
% 244.56/51.00  | | | 
% 244.56/51.00  | | Case 2:
% 244.56/51.00  | | | 
% 244.56/51.00  | | |   (20)  all_58_12 = e1 & op(e0, e3) = e1
% 244.56/51.00  | | | 
% 244.56/51.00  | | | ALPHA: (20) implies:
% 244.56/51.00  | | |   (21)  all_58_12 = e1
% 244.56/51.00  | | | 
% 244.56/51.00  | | | REF_CLOSE: (4), (11), (21) are inconsistent by sub-proof #1757.
% 244.56/51.00  | | | 
% 244.56/51.00  | | End of split
% 244.56/51.00  | | 
% 244.56/51.00  | End of split
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1757 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)  all_58_12 = e2
% 244.56/51.00    (2)  all_58_12 = e1
% 244.56/51.00    (3)   ~ (e2 = e1)
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | COMBINE_EQS: (1), (2) imply:
% 244.56/51.00  |   (4)  e2 = e1
% 244.56/51.00  | 
% 244.56/51.00  | SIMP: (4) implies:
% 244.56/51.00  |   (5)  e2 = e1
% 244.56/51.00  | 
% 244.56/51.00  | REDUCE: (3), (5) imply:
% 244.56/51.00  |   (6)  $false
% 244.56/51.00  | 
% 244.56/51.00  | CLOSE: (6) is inconsistent.
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1758 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)  all_58_6 = e3
% 244.56/51.00    (2)  all_58_6 = e1
% 244.56/51.00    (3)   ~ (e3 = e1)
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | COMBINE_EQS: (1), (2) imply:
% 244.56/51.00  |   (4)  e3 = e1
% 244.56/51.00  | 
% 244.56/51.00  | SIMP: (4) implies:
% 244.56/51.00  |   (5)  e3 = e1
% 244.56/51.00  | 
% 244.56/51.00  | REDUCE: (3), (5) imply:
% 244.56/51.00  |   (6)  $false
% 244.56/51.00  | 
% 244.56/51.00  | CLOSE: (6) is inconsistent.
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1759 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)   ~ (e3 = e0)
% 244.56/51.00    (2)  all_58_6 = e3
% 244.56/51.00    (3)   ~ (e2 = e0)
% 244.56/51.00    (4)  all_58_12 = e2
% 244.56/51.00    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.56/51.00         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.56/51.00    (6)  op(e3, e3) = e2
% 244.56/51.00    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.00    (8)   ~ (e1 = e0)
% 244.56/51.00    (9)  all_58_2 = e1
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | BETA: splitting (5) gives:
% 244.56/51.00  | 
% 244.56/51.00  | Case 1:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (10)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 244.56/51.00  | |           e0)
% 244.56/51.00  | | 
% 244.56/51.00  | | REF_CLOSE: (3), (6), (7), (8), (9), (10) are inconsistent by sub-proof
% 244.56/51.00  | |            #1761.
% 244.56/51.00  | | 
% 244.56/51.00  | Case 2:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (11)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 244.56/51.00  | |           e0)
% 244.56/51.00  | | 
% 244.56/51.00  | | BETA: splitting (11) gives:
% 244.56/51.00  | | 
% 244.56/51.00  | | Case 1:
% 244.56/51.00  | | | 
% 244.56/51.00  | | |   (12)  all_58_6 = e0 & op(e1, e3) = e0
% 244.56/51.00  | | | 
% 244.56/51.00  | | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #2213.
% 244.56/51.00  | | | 
% 244.56/51.00  | | Case 2:
% 244.56/51.00  | | | 
% 244.56/51.00  | | |   (13)  all_58_12 = e0 & op(e0, e3) = e0
% 244.56/51.00  | | | 
% 244.56/51.00  | | | REF_CLOSE: (3), (4), (13) are inconsistent by sub-proof #1760.
% 244.56/51.00  | | | 
% 244.56/51.00  | | End of split
% 244.56/51.00  | | 
% 244.56/51.00  | End of split
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1760 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)  all_58_12 = e0 & op(e0, e3) = e0
% 244.56/51.00    (2)  all_58_12 = e2
% 244.56/51.00    (3)   ~ (e2 = e0)
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | ALPHA: (1) implies:
% 244.56/51.00  |   (4)  all_58_12 = e0
% 244.56/51.00  | 
% 244.56/51.00  | COMBINE_EQS: (2), (4) imply:
% 244.56/51.00  |   (5)  e2 = e0
% 244.56/51.00  | 
% 244.56/51.00  | REDUCE: (3), (5) imply:
% 244.56/51.00  |   (6)  $false
% 244.56/51.00  | 
% 244.56/51.00  | CLOSE: (6) is inconsistent.
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1761 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)   ~ (e2 = e0)
% 244.56/51.00    (2)  op(e3, e3) = e2
% 244.56/51.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.00    (4)   ~ (e1 = e0)
% 244.56/51.00    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 244.56/51.00    (6)  all_58_2 = e1
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | BETA: splitting (5) gives:
% 244.56/51.00  | 
% 244.56/51.00  | Case 1:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 244.56/51.00  | | 
% 244.56/51.00  | | ALPHA: (7) implies:
% 244.56/51.00  | |   (8)  op(e3, e3) = e0
% 244.56/51.00  | | 
% 244.56/51.00  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2188.
% 244.56/51.00  | | 
% 244.56/51.00  | Case 2:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (9)  all_58_2 = e0 & op(e2, e3) = e0
% 244.56/51.00  | | 
% 244.56/51.00  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #1972.
% 244.56/51.00  | | 
% 244.56/51.00  | End of split
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1762 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)  all_58_12 = e2
% 244.56/51.00    (2)   ~ (e3 = e1)
% 244.56/51.00    (3)  all_58_6 = e0
% 244.56/51.00    (4)  op(e3, e3) = e2
% 244.56/51.00    (5)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.56/51.00         (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.56/51.00    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.00    (7)   ~ (e1 = e0)
% 244.56/51.00    (8)  all_58_2 = e3
% 244.56/51.00    (9)   ~ (e2 = e1)
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | BETA: splitting (5) gives:
% 244.56/51.00  | 
% 244.56/51.00  | Case 1:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 244.56/51.00  | |           e1)
% 244.56/51.00  | | 
% 244.56/51.00  | | REF_CLOSE: (2), (4), (6), (8), (9), (10) are inconsistent by sub-proof
% 244.56/51.00  | |            #1764.
% 244.56/51.00  | | 
% 244.56/51.00  | Case 2:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (11)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 244.56/51.00  | |           e1)
% 244.56/51.00  | | 
% 244.56/51.00  | | BETA: splitting (11) gives:
% 244.56/51.00  | | 
% 244.56/51.00  | | Case 1:
% 244.56/51.00  | | | 
% 244.56/51.00  | | |   (12)  all_58_6 = e1 & op(e1, e3) = e1
% 244.56/51.00  | | | 
% 244.56/51.00  | | | ALPHA: (12) implies:
% 244.56/51.00  | | |   (13)  all_58_6 = e1
% 244.56/51.00  | | | 
% 244.56/51.00  | | | REF_CLOSE: (3), (7), (13) are inconsistent by sub-proof #1981.
% 244.56/51.00  | | | 
% 244.56/51.00  | | Case 2:
% 244.56/51.00  | | | 
% 244.56/51.00  | | |   (14)  all_58_12 = e1 & op(e0, e3) = e1
% 244.56/51.00  | | | 
% 244.56/51.00  | | | REF_CLOSE: (1), (9), (14) are inconsistent by sub-proof #1763.
% 244.56/51.00  | | | 
% 244.56/51.00  | | End of split
% 244.56/51.00  | | 
% 244.56/51.00  | End of split
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1763 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)  all_58_12 = e1 & op(e0, e3) = e1
% 244.56/51.00    (2)  all_58_12 = e2
% 244.56/51.00    (3)   ~ (e2 = e1)
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | ALPHA: (1) implies:
% 244.56/51.00  |   (4)  all_58_12 = e1
% 244.56/51.00  | 
% 244.56/51.00  | COMBINE_EQS: (2), (4) imply:
% 244.56/51.00  |   (5)  e2 = e1
% 244.56/51.00  | 
% 244.56/51.00  | REDUCE: (3), (5) imply:
% 244.56/51.00  |   (6)  $false
% 244.56/51.00  | 
% 244.56/51.00  | CLOSE: (6) is inconsistent.
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1764 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)   ~ (e3 = e1)
% 244.56/51.00    (2)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 244.56/51.00    (3)  op(e3, e3) = e2
% 244.56/51.00    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.00    (5)  all_58_2 = e3
% 244.56/51.00    (6)   ~ (e2 = e1)
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | BETA: splitting (2) gives:
% 244.56/51.00  | 
% 244.56/51.00  | Case 1:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 244.56/51.00  | | 
% 244.56/51.00  | | ALPHA: (7) implies:
% 244.56/51.00  | |   (8)  op(e3, e3) = e1
% 244.56/51.00  | | 
% 244.56/51.00  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #2267.
% 244.56/51.00  | | 
% 244.56/51.00  | Case 2:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (9)  all_58_2 = e1 & op(e2, e3) = e1
% 244.56/51.00  | | 
% 244.56/51.00  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #1765.
% 244.56/51.00  | | 
% 244.56/51.00  | End of split
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1765 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)  all_58_2 = e1 & op(e2, e3) = e1
% 244.56/51.00    (2)  all_58_2 = e3
% 244.56/51.00    (3)   ~ (e3 = e1)
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | ALPHA: (1) implies:
% 244.56/51.00  |   (4)  all_58_2 = e1
% 244.56/51.00  | 
% 244.56/51.00  | COMBINE_EQS: (2), (4) imply:
% 244.56/51.00  |   (5)  e3 = e1
% 244.56/51.00  | 
% 244.56/51.00  | REDUCE: (3), (5) imply:
% 244.56/51.00  |   (6)  $false
% 244.56/51.00  | 
% 244.56/51.00  | CLOSE: (6) is inconsistent.
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1766 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)  all_56_17 = all_18_0
% 244.56/51.00    (2)  op(e3, e1) = all_18_0
% 244.56/51.00    (3)   ~ (all_50_0 = e1)
% 244.56/51.00    (4)  all_50_0 = e3
% 244.56/51.00    (5)  op(e3, all_56_17) = e3
% 244.56/51.00    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.00    (7)  all_18_0 = e1
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | COMBINE_EQS: (1), (7) imply:
% 244.56/51.00  |   (8)  all_56_17 = e1
% 244.56/51.00  | 
% 244.56/51.00  | REDUCE: (3), (4) imply:
% 244.56/51.00  |   (9)   ~ (e3 = e1)
% 244.56/51.00  | 
% 244.56/51.00  | REDUCE: (5), (8) imply:
% 244.56/51.00  |   (10)  op(e3, e1) = e3
% 244.56/51.00  | 
% 244.56/51.00  | REDUCE: (2), (7) imply:
% 244.56/51.00  |   (11)  op(e3, e1) = e1
% 244.56/51.00  | 
% 244.56/51.00  | REF_CLOSE: (6), (9), (10), (11) are inconsistent by sub-proof #1823.
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1767 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)   ~ (all_18_1 = e3) & op(e1, e0) = all_18_1 & $i(all_18_1)
% 244.56/51.00    (2)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 & op(e1, e0) = all_28_1
% 244.56/51.00           & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1, e0) =
% 244.56/51.00           all_28_1 & $i(all_28_1))
% 244.56/51.00    (3)  op(e1, e0) = e3
% 244.56/51.00    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | ALPHA: (1) implies:
% 244.56/51.00  |   (5)   ~ (all_18_1 = e3)
% 244.56/51.00  |   (6)  op(e1, e0) = all_18_1
% 244.56/51.00  | 
% 244.56/51.00  | BETA: splitting (2) gives:
% 244.56/51.00  | 
% 244.56/51.00  | Case 1:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (7)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 & op(e1, e0) =
% 244.56/51.00  | |        all_28_1 & $i(all_28_0) & $i(all_28_1)
% 244.56/51.00  | | 
% 244.56/51.00  | | ALPHA: (7) implies:
% 244.56/51.00  | |   (8)  op(e1, e0) = all_28_1
% 244.56/51.00  | | 
% 244.56/51.00  | | REF_CLOSE: (3), (4), (5), (6), (8) are inconsistent by sub-proof #1768.
% 244.56/51.00  | | 
% 244.56/51.00  | Case 2:
% 244.56/51.00  | | 
% 244.56/51.00  | |   (9)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 & $i(all_28_1)
% 244.56/51.00  | | 
% 244.56/51.00  | | ALPHA: (9) implies:
% 244.56/51.00  | |   (10)  op(e1, e0) = all_28_1
% 244.56/51.00  | | 
% 244.56/51.00  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #1768.
% 244.56/51.00  | | 
% 244.56/51.00  | End of split
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1768 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)   ~ (all_18_1 = e3)
% 244.56/51.00    (2)  op(e1, e0) = all_18_1
% 244.56/51.00    (3)  op(e1, e0) = e3
% 244.56/51.00    (4)  op(e1, e0) = all_28_1
% 244.56/51.00    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.00  | 
% 244.56/51.00  | GROUND_INST: instantiating (5) with all_18_1, all_28_1, e0, e1, simplifying
% 244.56/51.00  |              with (2), (4) gives:
% 244.56/51.00  |   (6)  all_28_1 = all_18_1
% 244.56/51.00  | 
% 244.56/51.00  | GROUND_INST: instantiating (5) with e3, all_28_1, e0, e1, simplifying with
% 244.56/51.00  |              (3), (4) gives:
% 244.56/51.00  |   (7)  all_28_1 = e3
% 244.56/51.00  | 
% 244.56/51.00  | COMBINE_EQS: (6), (7) imply:
% 244.56/51.00  |   (8)  all_18_1 = e3
% 244.56/51.00  | 
% 244.56/51.00  | REDUCE: (1), (8) imply:
% 244.56/51.00  |   (9)  $false
% 244.56/51.00  | 
% 244.56/51.00  | CLOSE: (9) is inconsistent.
% 244.56/51.00  | 
% 244.56/51.00  End of proof
% 244.56/51.00  
% 244.56/51.00  Sub-proof #1769 shows that the following formulas are inconsistent:
% 244.56/51.00  ----------------------------------------------------------------
% 244.56/51.00    (1)   ~ (all_52_3 = e1)
% 244.56/51.00    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.56/51.00         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.56/51.00    (3)   ~ (e3 = e0)
% 244.56/51.00    (4)   ~ (e2 = e0)
% 244.56/51.00    (5)  op(e0, e3) = all_52_3
% 244.56/51.00    (6)   ~ (e3 = e1)
% 244.56/51.00    (7)   ~ (e3 = e2)
% 244.56/51.00    (8)  all_56_15 = e0
% 244.56/51.00    (9)  op(e0, e2) = all_56_15
% 244.56/51.00    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.00    (11)  op(e0, all_56_15) = e0
% 244.56/51.00    (12)   ~ (e1 = e0)
% 244.56/51.00    (13)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.56/51.00          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.56/51.00            e1)
% 244.56/51.00    (14)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.56/51.00          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.56/51.00            e2)
% 244.56/51.00    (15)   ~ (e2 = e1)
% 244.56/51.00  
% 244.56/51.00  Begin of proof
% 244.56/51.01  | 
% 244.56/51.01  | REDUCE: (8), (11) imply:
% 244.56/51.01  |   (16)  op(e0, e0) = e0
% 244.56/51.01  | 
% 244.56/51.01  | REDUCE: (8), (9) imply:
% 244.56/51.01  |   (17)  op(e0, e2) = e0
% 244.56/51.01  | 
% 244.56/51.01  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (12), (13), (14), (15),
% 244.56/51.01  |            (16), (17) are inconsistent by sub-proof #1770.
% 244.56/51.01  | 
% 244.56/51.01  End of proof
% 244.56/51.01  
% 244.56/51.01  Sub-proof #1770 shows that the following formulas are inconsistent:
% 244.56/51.01  ----------------------------------------------------------------
% 244.56/51.01    (1)   ~ (all_52_3 = e1)
% 244.56/51.01    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.56/51.01         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.56/51.01    (3)   ~ (e3 = e0)
% 244.56/51.01    (4)   ~ (e2 = e0)
% 244.56/51.01    (5)  op(e0, e3) = all_52_3
% 244.56/51.01    (6)   ~ (e3 = e1)
% 244.56/51.01    (7)   ~ (e3 = e2)
% 244.56/51.01    (8)  op(e0, e2) = e0
% 244.56/51.01    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.01    (10)  op(e0, e0) = e0
% 244.56/51.01    (11)   ~ (e1 = e0)
% 244.56/51.01    (12)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.56/51.01          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.56/51.01            e1)
% 244.56/51.01    (13)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.56/51.01          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.56/51.01            e2)
% 244.56/51.01    (14)   ~ (e2 = e1)
% 244.56/51.01  
% 244.56/51.01  Begin of proof
% 244.56/51.01  | 
% 244.56/51.01  | BETA: splitting (12) gives:
% 244.56/51.01  | 
% 244.56/51.01  | Case 1:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (15)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 244.56/51.01  | |           e1)
% 244.56/51.01  | | 
% 244.56/51.01  | | REF_CLOSE: (1), (5), (8), (9), (11), (15) are inconsistent by sub-proof
% 244.56/51.01  | |            #1791.
% 244.56/51.01  | | 
% 244.56/51.01  | Case 2:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (16)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.56/51.01  | |           e1)
% 244.56/51.01  | | 
% 244.56/51.01  | | BETA: splitting (16) gives:
% 244.56/51.01  | | 
% 244.56/51.01  | | Case 1:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (17)  all_58_14 = e1 & op(e0, e1) = e1
% 244.56/51.01  | | | 
% 244.56/51.01  | | | ALPHA: (17) implies:
% 244.56/51.01  | | |   (18)  all_58_14 = e1
% 244.56/51.01  | | | 
% 244.56/51.01  | | | BETA: splitting (13) gives:
% 244.56/51.01  | | | 
% 244.56/51.01  | | | Case 1:
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | |   (19)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 244.56/51.01  | | | |             e2) = e2)
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | | BETA: splitting (19) gives:
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | | Case 1:
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | |   (20)  all_58_12 = e2 & op(e0, e3) = e2
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | | ALPHA: (20) implies:
% 244.56/51.01  | | | | |   (21)  all_58_12 = e2
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (18), (21) are
% 244.56/51.01  | | | | |            inconsistent by sub-proof #1772.
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | Case 2:
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | |   (22)  all_58_13 = e2 & op(e0, e2) = e2
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | | ALPHA: (22) implies:
% 244.56/51.01  | | | | |   (23)  op(e0, e2) = e2
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | | REF_CLOSE: (4), (8), (9), (23) are inconsistent by sub-proof #2132.
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | End of split
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | Case 2:
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | |   (24)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 244.56/51.01  | | | |             e0) = e2)
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | | BETA: splitting (24) gives:
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | | Case 1:
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | |   (25)  all_58_14 = e2 & op(e0, e1) = e2
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | | REF_CLOSE: (14), (18), (25) are inconsistent by sub-proof #1771.
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | Case 2:
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | |   (26)  all_58_15 = e2 & op(e0, e0) = e2
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | | ALPHA: (26) implies:
% 244.56/51.01  | | | | |   (27)  op(e0, e0) = e2
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | | REF_CLOSE: (4), (9), (10), (27) are inconsistent by sub-proof #2301.
% 244.56/51.01  | | | | | 
% 244.56/51.01  | | | | End of split
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | End of split
% 244.56/51.01  | | | 
% 244.56/51.01  | | Case 2:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (28)  all_58_15 = e1 & op(e0, e0) = e1
% 244.56/51.01  | | | 
% 244.56/51.01  | | | ALPHA: (28) implies:
% 244.56/51.01  | | |   (29)  op(e0, e0) = e1
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (9), (10), (11), (29) are inconsistent by sub-proof #2274.
% 244.56/51.01  | | | 
% 244.56/51.01  | | End of split
% 244.56/51.01  | | 
% 244.56/51.01  | End of split
% 244.56/51.01  | 
% 244.56/51.01  End of proof
% 244.56/51.01  
% 244.56/51.01  Sub-proof #1771 shows that the following formulas are inconsistent:
% 244.56/51.01  ----------------------------------------------------------------
% 244.56/51.01    (1)  all_58_14 = e2 & op(e0, e1) = e2
% 244.56/51.01    (2)  all_58_14 = e1
% 244.56/51.01    (3)   ~ (e2 = e1)
% 244.56/51.01  
% 244.56/51.01  Begin of proof
% 244.56/51.01  | 
% 244.56/51.01  | ALPHA: (1) implies:
% 244.56/51.01  |   (4)  all_58_14 = e2
% 244.56/51.01  | 
% 244.56/51.01  | COMBINE_EQS: (2), (4) imply:
% 244.56/51.01  |   (5)  e2 = e1
% 244.56/51.01  | 
% 244.56/51.01  | REDUCE: (3), (5) imply:
% 244.56/51.01  |   (6)  $false
% 244.56/51.01  | 
% 244.56/51.01  | CLOSE: (6) is inconsistent.
% 244.56/51.01  | 
% 244.56/51.01  End of proof
% 244.56/51.01  
% 244.56/51.01  Sub-proof #1772 shows that the following formulas are inconsistent:
% 244.56/51.01  ----------------------------------------------------------------
% 244.56/51.01    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.56/51.01         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.56/51.01    (2)   ~ (e3 = e0)
% 244.56/51.01    (3)  all_58_12 = e2
% 244.56/51.01    (4)   ~ (e3 = e1)
% 244.56/51.01    (5)   ~ (e3 = e2)
% 244.56/51.01    (6)  op(e0, e2) = e0
% 244.56/51.01    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.01    (8)  op(e0, e0) = e0
% 244.56/51.01    (9)  all_58_14 = e1
% 244.56/51.01  
% 244.56/51.01  Begin of proof
% 244.56/51.01  | 
% 244.56/51.01  | BETA: splitting (1) gives:
% 244.56/51.01  | 
% 244.56/51.01  | Case 1:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (10)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.56/51.01  | |           e3)
% 244.56/51.01  | | 
% 244.56/51.01  | | BETA: splitting (10) gives:
% 244.56/51.01  | | 
% 244.56/51.01  | | Case 1:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (11)  all_58_12 = e3 & op(e0, e3) = e3
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #2085.
% 244.56/51.01  | | | 
% 244.56/51.01  | | Case 2:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (12)  all_58_13 = e3 & op(e0, e2) = e3
% 244.56/51.01  | | | 
% 244.56/51.01  | | | ALPHA: (12) implies:
% 244.56/51.01  | | |   (13)  op(e0, e2) = e3
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (2), (6), (7), (13) are inconsistent by sub-proof #1961.
% 244.56/51.01  | | | 
% 244.56/51.01  | | End of split
% 244.56/51.01  | | 
% 244.56/51.01  | Case 2:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (14)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.56/51.01  | |           e3)
% 244.56/51.01  | | 
% 244.56/51.01  | | BETA: splitting (14) gives:
% 244.56/51.01  | | 
% 244.56/51.01  | | Case 1:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (15)  all_58_14 = e3 & op(e0, e1) = e3
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (4), (9), (15) are inconsistent by sub-proof #1773.
% 244.56/51.01  | | | 
% 244.56/51.01  | | Case 2:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (16)  all_58_15 = e3 & op(e0, e0) = e3
% 244.56/51.01  | | | 
% 244.56/51.01  | | | ALPHA: (16) implies:
% 244.56/51.01  | | |   (17)  op(e0, e0) = e3
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (2), (7), (8), (17) are inconsistent by sub-proof #2079.
% 244.56/51.01  | | | 
% 244.56/51.01  | | End of split
% 244.56/51.01  | | 
% 244.56/51.01  | End of split
% 244.56/51.01  | 
% 244.56/51.01  End of proof
% 244.56/51.01  
% 244.56/51.01  Sub-proof #1773 shows that the following formulas are inconsistent:
% 244.56/51.01  ----------------------------------------------------------------
% 244.56/51.01    (1)  all_58_14 = e3 & op(e0, e1) = e3
% 244.56/51.01    (2)  all_58_14 = e1
% 244.56/51.01    (3)   ~ (e3 = e1)
% 244.56/51.01  
% 244.56/51.01  Begin of proof
% 244.56/51.01  | 
% 244.56/51.01  | ALPHA: (1) implies:
% 244.56/51.01  |   (4)  all_58_14 = e3
% 244.56/51.01  | 
% 244.56/51.01  | COMBINE_EQS: (2), (4) imply:
% 244.56/51.01  |   (5)  e3 = e1
% 244.56/51.01  | 
% 244.56/51.01  | REDUCE: (3), (5) imply:
% 244.56/51.01  |   (6)  $false
% 244.56/51.01  | 
% 244.56/51.01  | CLOSE: (6) is inconsistent.
% 244.56/51.01  | 
% 244.56/51.01  End of proof
% 244.56/51.01  
% 244.56/51.01  Sub-proof #1774 shows that the following formulas are inconsistent:
% 244.56/51.01  ----------------------------------------------------------------
% 244.56/51.01    (1)  op(e1, e2) = all_56_13
% 244.56/51.01    (2)   ~ (e3 = e0)
% 244.56/51.01    (3)   ~ (e2 = e0)
% 244.56/51.01    (4)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.56/51.01         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.56/51.01    (5)   ~ (e3 = e1)
% 244.56/51.01    (6)  all_58_7 = e2
% 244.56/51.01    (7)  op(e2, e1) = all_52_9
% 244.56/51.01    (8)   ~ (e3 = e2)
% 244.56/51.01    (9)  op(e2, e2) = e1
% 244.56/51.01    (10)  op(e2, e0) = e0
% 244.56/51.01    (11)  op(e2, e3) = all_52_1
% 244.56/51.01    (12)  op(e0, e2) = e0
% 244.56/51.01    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.01    (14)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.56/51.01          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.56/51.01    (15)  op(e1, all_56_13) = e1
% 244.56/51.01    (16)   ~ (e1 = e0)
% 244.56/51.01    (17)  all_56_13 = e2
% 244.56/51.01    (18)  op(e2, e0) = all_52_13
% 244.56/51.01    (19)   ~ (all_52_9 = e1)
% 244.56/51.01    (20)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.56/51.01          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.56/51.01    (21)   ~ (e2 = e1)
% 244.56/51.01    (22)   ~ (all_52_1 = e1)
% 244.56/51.01  
% 244.56/51.01  Begin of proof
% 244.56/51.01  | 
% 244.56/51.01  | REDUCE: (15), (17) imply:
% 244.56/51.01  |   (23)  op(e1, e2) = e1
% 244.56/51.01  | 
% 244.56/51.01  | REDUCE: (1), (17) imply:
% 244.56/51.01  |   (24)  op(e1, e2) = e2
% 244.56/51.01  | 
% 244.56/51.01  | GROUND_INST: instantiating (13) with e2, e1, e2, e1, simplifying with (23),
% 244.56/51.01  |              (24) gives:
% 244.56/51.01  |   (25)  e2 = e1
% 244.56/51.01  | 
% 244.56/51.01  | COMBINE_EQS: (6), (25) imply:
% 244.56/51.01  |   (26)  all_58_7 = e1
% 244.56/51.01  | 
% 244.56/51.01  | BETA: splitting (4) gives:
% 244.56/51.01  | 
% 244.56/51.01  | Case 1:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (27)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 244.56/51.01  | |           e2)
% 244.56/51.01  | | 
% 244.56/51.01  | | BETA: splitting (27) gives:
% 244.56/51.01  | | 
% 244.56/51.01  | | Case 1:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (28)  all_58_1 = e2 & op(e3, e2) = e2
% 244.56/51.01  | | | 
% 244.56/51.01  | | | ALPHA: (28) implies:
% 244.56/51.01  | | |   (29)  op(e3, e2) = e2
% 244.56/51.01  | | | 
% 244.56/51.01  | | | BETA: splitting (14) gives:
% 244.56/51.01  | | | 
% 244.56/51.01  | | | Case 1:
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | |   (30)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2)
% 244.56/51.01  | | | |           = e3)
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | | REF_CLOSE: (5), (7), (8), (10), (11), (13), (16), (18), (19), (20),
% 244.56/51.01  | | | |            (22), (29), (30) are inconsistent by sub-proof #1776.
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | Case 2:
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | |   (31)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2)
% 244.56/51.01  | | | |           = e3)
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | | REF_CLOSE: (2), (5), (12), (13), (23), (31) are inconsistent by
% 244.56/51.01  | | | |            sub-proof #1775.
% 244.56/51.01  | | | | 
% 244.56/51.01  | | | End of split
% 244.56/51.01  | | | 
% 244.56/51.01  | | Case 2:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (32)  all_58_3 = e2 & op(e2, e2) = e2
% 244.56/51.01  | | | 
% 244.56/51.01  | | | ALPHA: (32) implies:
% 244.56/51.01  | | |   (33)  op(e2, e2) = e2
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (9), (13), (21), (33) are inconsistent by sub-proof #2235.
% 244.56/51.01  | | | 
% 244.56/51.01  | | End of split
% 244.56/51.01  | | 
% 244.56/51.01  | Case 2:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (34)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 244.56/51.01  | |           e2)
% 244.56/51.01  | | 
% 244.56/51.01  | | BETA: splitting (34) gives:
% 244.56/51.01  | | 
% 244.56/51.01  | | Case 1:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (35)  all_58_7 = e2 & op(e1, e2) = e2
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (6), (21), (26) are inconsistent by sub-proof #2134.
% 244.56/51.01  | | | 
% 244.56/51.01  | | Case 2:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (36)  all_58_13 = e2 & op(e0, e2) = e2
% 244.56/51.01  | | | 
% 244.56/51.01  | | | ALPHA: (36) implies:
% 244.56/51.01  | | |   (37)  op(e0, e2) = e2
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (3), (12), (13), (37) are inconsistent by sub-proof #2132.
% 244.56/51.01  | | | 
% 244.56/51.01  | | End of split
% 244.56/51.01  | | 
% 244.56/51.01  | End of split
% 244.56/51.01  | 
% 244.56/51.01  End of proof
% 244.56/51.01  
% 244.56/51.01  Sub-proof #1775 shows that the following formulas are inconsistent:
% 244.56/51.01  ----------------------------------------------------------------
% 244.56/51.01    (1)   ~ (e3 = e0)
% 244.56/51.01    (2)  op(e1, e2) = e1
% 244.56/51.01    (3)   ~ (e3 = e1)
% 244.56/51.01    (4)  op(e0, e2) = e0
% 244.56/51.01    (5)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.56/51.01    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.01  
% 244.56/51.01  Begin of proof
% 244.56/51.01  | 
% 244.56/51.01  | BETA: splitting (5) gives:
% 244.56/51.01  | 
% 244.56/51.01  | Case 1:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (7)  all_58_7 = e3 & op(e1, e2) = e3
% 244.56/51.01  | | 
% 244.56/51.01  | | ALPHA: (7) implies:
% 244.56/51.01  | |   (8)  op(e1, e2) = e3
% 244.56/51.01  | | 
% 244.56/51.01  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #2094.
% 244.56/51.01  | | 
% 244.56/51.01  | Case 2:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (9)  all_58_13 = e3 & op(e0, e2) = e3
% 244.56/51.01  | | 
% 244.56/51.01  | | ALPHA: (9) implies:
% 244.56/51.01  | |   (10)  op(e0, e2) = e3
% 244.56/51.01  | | 
% 244.56/51.01  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #1961.
% 244.56/51.01  | | 
% 244.56/51.01  | End of split
% 244.56/51.01  | 
% 244.56/51.01  End of proof
% 244.56/51.01  
% 244.56/51.01  Sub-proof #1776 shows that the following formulas are inconsistent:
% 244.56/51.01  ----------------------------------------------------------------
% 244.56/51.01    (1)   ~ (e3 = e1)
% 244.56/51.01    (2)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 244.56/51.01    (3)  op(e3, e2) = e2
% 244.56/51.01    (4)  op(e2, e1) = all_52_9
% 244.56/51.01    (5)   ~ (e3 = e2)
% 244.56/51.01    (6)  op(e2, e0) = e0
% 244.56/51.01    (7)  op(e2, e3) = all_52_1
% 244.56/51.01    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.01    (9)   ~ (e1 = e0)
% 244.56/51.01    (10)  op(e2, e0) = all_52_13
% 244.56/51.01    (11)   ~ (all_52_9 = e1)
% 244.56/51.01    (12)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.56/51.01          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.56/51.01    (13)   ~ (all_52_1 = e1)
% 244.56/51.01  
% 244.56/51.01  Begin of proof
% 244.56/51.01  | 
% 244.56/51.01  | BETA: splitting (2) gives:
% 244.56/51.01  | 
% 244.56/51.01  | Case 1:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (14)  all_58_1 = e3 & op(e3, e2) = e3
% 244.56/51.01  | | 
% 244.56/51.01  | | ALPHA: (14) implies:
% 244.56/51.01  | |   (15)  op(e3, e2) = e3
% 244.56/51.01  | | 
% 244.56/51.01  | | REF_CLOSE: (3), (5), (8), (15) are inconsistent by sub-proof #2193.
% 244.56/51.01  | | 
% 244.56/51.01  | Case 2:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (16)  all_58_3 = e3 & op(e2, e2) = e3
% 244.56/51.01  | | 
% 244.56/51.01  | | ALPHA: (16) implies:
% 244.56/51.01  | |   (17)  all_58_3 = e3
% 244.56/51.01  | | 
% 244.56/51.01  | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (11), (12), (13), (17) are
% 244.56/51.01  | |            inconsistent by sub-proof #1777.
% 244.56/51.01  | | 
% 244.56/51.01  | End of split
% 244.56/51.01  | 
% 244.56/51.01  End of proof
% 244.56/51.01  
% 244.56/51.01  Sub-proof #1777 shows that the following formulas are inconsistent:
% 244.56/51.01  ----------------------------------------------------------------
% 244.56/51.01    (1)   ~ (e3 = e1)
% 244.56/51.01    (2)  all_58_3 = e3
% 244.56/51.01    (3)  op(e2, e1) = all_52_9
% 244.56/51.01    (4)  op(e2, e0) = e0
% 244.56/51.01    (5)  op(e2, e3) = all_52_1
% 244.56/51.01    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.01    (7)   ~ (e1 = e0)
% 244.56/51.01    (8)  op(e2, e0) = all_52_13
% 244.56/51.01    (9)   ~ (all_52_9 = e1)
% 244.56/51.01    (10)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.56/51.01          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.56/51.01    (11)   ~ (all_52_1 = e1)
% 244.56/51.01  
% 244.56/51.01  Begin of proof
% 244.56/51.01  | 
% 244.56/51.01  | BETA: splitting (10) gives:
% 244.56/51.01  | 
% 244.56/51.01  | Case 1:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (12)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 244.56/51.01  | |           e1)
% 244.56/51.01  | | 
% 244.56/51.01  | | BETA: splitting (12) gives:
% 244.56/51.01  | | 
% 244.56/51.01  | | Case 1:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (13)  all_58_2 = e1 & op(e2, e3) = e1
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (5), (6), (11), (13) are inconsistent by sub-proof #2229.
% 244.56/51.01  | | | 
% 244.56/51.01  | | Case 2:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (14)  all_58_3 = e1 & op(e2, e2) = e1
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (1), (2), (14) are inconsistent by sub-proof #2197.
% 244.56/51.01  | | | 
% 244.56/51.01  | | End of split
% 244.56/51.01  | | 
% 244.56/51.01  | Case 2:
% 244.56/51.01  | | 
% 244.56/51.01  | |   (15)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 244.56/51.01  | |           e1)
% 244.56/51.01  | | 
% 244.56/51.01  | | BETA: splitting (15) gives:
% 244.56/51.01  | | 
% 244.56/51.01  | | Case 1:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (16)  all_58_5 = e1 & op(e2, e1) = e1
% 244.56/51.01  | | | 
% 244.56/51.01  | | | ALPHA: (16) implies:
% 244.56/51.01  | | |   (17)  op(e2, e1) = e1
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (3), (6), (9), (17) are inconsistent by sub-proof #2306.
% 244.56/51.01  | | | 
% 244.56/51.01  | | Case 2:
% 244.56/51.01  | | | 
% 244.56/51.01  | | |   (18)  all_58_10 = e1 & op(e2, e0) = e1
% 244.56/51.01  | | | 
% 244.56/51.01  | | | ALPHA: (18) implies:
% 244.56/51.01  | | |   (19)  op(e2, e0) = e1
% 244.56/51.01  | | | 
% 244.56/51.01  | | | REF_CLOSE: (4), (6), (7), (8), (19) are inconsistent by sub-proof #1778.
% 244.56/51.01  | | | 
% 244.56/51.01  | | End of split
% 244.56/51.01  | | 
% 244.56/51.01  | End of split
% 244.56/51.01  | 
% 244.56/51.01  End of proof
% 244.56/51.02  
% 244.56/51.02  Sub-proof #1778 shows that the following formulas are inconsistent:
% 244.56/51.02  ----------------------------------------------------------------
% 244.56/51.02    (1)  op(e2, e0) = e0
% 244.56/51.02    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.02    (3)   ~ (e1 = e0)
% 244.56/51.02    (4)  op(e2, e0) = e1
% 244.56/51.02    (5)  op(e2, e0) = all_52_13
% 244.56/51.02  
% 244.56/51.02  Begin of proof
% 244.56/51.02  | 
% 244.56/51.02  | GROUND_INST: instantiating (2) with all_52_13, e0, e0, e2, simplifying with
% 244.56/51.02  |              (1), (5) gives:
% 244.56/51.02  |   (6)  all_52_13 = e0
% 244.56/51.02  | 
% 244.56/51.02  | GROUND_INST: instantiating (2) with all_52_13, e1, e0, e2, simplifying with
% 244.56/51.02  |              (4), (5) gives:
% 244.56/51.02  |   (7)  all_52_13 = e1
% 244.56/51.02  | 
% 244.56/51.02  | COMBINE_EQS: (6), (7) imply:
% 244.56/51.02  |   (8)  e1 = e0
% 244.56/51.02  | 
% 244.56/51.02  | SIMP: (8) implies:
% 244.56/51.02  |   (9)  e1 = e0
% 244.56/51.02  | 
% 244.56/51.02  | REDUCE: (3), (9) imply:
% 244.56/51.02  |   (10)  $false
% 244.56/51.02  | 
% 244.56/51.02  | CLOSE: (10) is inconsistent.
% 244.56/51.02  | 
% 244.56/51.02  End of proof
% 244.56/51.02  
% 244.56/51.02  Sub-proof #1779 shows that the following formulas are inconsistent:
% 244.56/51.02  ----------------------------------------------------------------
% 244.56/51.02    (1)   ~ (all_52_3 = e0)
% 244.56/51.02    (2)   ~ (all_52_3 = e1)
% 244.56/51.02    (3)  op(e0, e1) = e3
% 244.56/51.02    (4)  (all_56_20 = e1 & op(e1, all_56_21) = e1) | (all_56_22 = e0 & op(e0,
% 244.56/51.02             all_56_23) = e0 & op(e0, e1) = all_56_23 & $i(all_56_23))
% 244.56/51.02    (5)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) = all_20_1
% 244.56/51.02           & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1) =
% 244.56/51.02           all_20_1 & $i(all_20_1))
% 244.56/51.02    (6)  op(e0, e3) = all_52_3
% 244.56/51.02    (7)   ~ (e3 = e1)
% 244.56/51.02    (8)  all_56_21 = e0
% 244.56/51.02    (9)  op(e1, e0) = e3
% 244.56/51.02    (10)  all_54_12 = all_52_3
% 244.56/51.02    (11)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.56/51.02    (12)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 244.56/51.02            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 244.56/51.02              e1) = all_34_1 & $i(all_34_1))
% 244.56/51.02    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.02  
% 244.56/51.02  Begin of proof
% 244.56/51.02  | 
% 244.56/51.02  | BETA: splitting (4) gives:
% 244.56/51.02  | 
% 244.56/51.02  | Case 1:
% 244.56/51.02  | | 
% 244.56/51.02  | |   (14)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 244.56/51.02  | | 
% 244.56/51.02  | | ALPHA: (14) implies:
% 244.56/51.02  | |   (15)  op(e1, all_56_21) = e1
% 244.56/51.02  | | 
% 244.56/51.02  | | REDUCE: (8), (15) imply:
% 244.56/51.02  | |   (16)  op(e1, e0) = e1
% 244.56/51.02  | | 
% 244.56/51.02  | | REF_CLOSE: (7), (9), (13), (16) are inconsistent by sub-proof #1894.
% 244.56/51.02  | | 
% 244.56/51.02  | Case 2:
% 244.56/51.02  | | 
% 244.56/51.02  | |   (17)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 244.56/51.02  | |         $i(all_56_23)
% 244.56/51.02  | | 
% 244.56/51.02  | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (11), (12), (13), (17) are
% 244.56/51.02  | |            inconsistent by sub-proof #1804.
% 244.56/51.02  | | 
% 244.56/51.02  | End of split
% 244.56/51.02  | 
% 244.56/51.02  End of proof
% 244.56/51.02  
% 244.56/51.02  Sub-proof #1780 shows that the following formulas are inconsistent:
% 244.56/51.02  ----------------------------------------------------------------
% 244.56/51.02    (1)   ~ (all_52_3 = e0)
% 244.56/51.02    (2)   ~ (all_52_3 = e1)
% 244.56/51.02    (3)  op(e3, e1) = all_18_0
% 244.56/51.02    (4)  op(e3, e1) = all_28_0
% 244.56/51.02    (5)  op(e2, e1) = e2
% 244.56/51.02    (6)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 244.56/51.02           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 244.56/51.02           all_30_1 & $i(all_30_1))
% 244.56/51.02    (7)  op(e3, e1) = e1
% 244.56/51.02    (8)  op(e2, e2) = e1
% 244.56/51.02    (9)  all_54_12 = all_52_3
% 244.56/51.02    (10)   ~ (all_18_0 = e2)
% 244.56/51.02    (11)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.56/51.02    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.02    (13)  op(e2, e1) = all_56_19
% 244.56/51.02    (14)  op(e2, e1) = all_22_1
% 244.56/51.02    (15)  op(e2, all_56_19) = e2
% 244.56/51.02  
% 244.56/51.02  Begin of proof
% 244.56/51.02  | 
% 244.56/51.02  | BETA: splitting (6) gives:
% 244.56/51.02  | 
% 244.56/51.02  | Case 1:
% 244.56/51.02  | | 
% 244.56/51.02  | |   (16)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) =
% 244.56/51.02  | |         all_30_1 & $i(all_30_0) & $i(all_30_1)
% 244.56/51.02  | | 
% 244.56/51.02  | | ALPHA: (16) implies:
% 244.56/51.02  | |   (17)  op(e2, e1) = all_30_1
% 244.56/51.02  | | 
% 244.56/51.02  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 244.56/51.02  | |            (14), (15), (17) are inconsistent by sub-proof #1781.
% 244.56/51.02  | | 
% 244.56/51.02  | Case 2:
% 244.56/51.02  | | 
% 244.56/51.02  | |   (18)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 & $i(all_30_1)
% 244.56/51.02  | | 
% 244.56/51.02  | | ALPHA: (18) implies:
% 244.56/51.02  | |   (19)  op(e2, e1) = all_30_1
% 244.56/51.02  | | 
% 244.56/51.02  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 244.56/51.02  | |            (14), (15), (19) are inconsistent by sub-proof #1781.
% 244.56/51.02  | | 
% 244.56/51.02  | End of split
% 244.56/51.02  | 
% 244.56/51.02  End of proof
% 244.56/51.02  
% 244.56/51.02  Sub-proof #1781 shows that the following formulas are inconsistent:
% 244.56/51.02  ----------------------------------------------------------------
% 244.56/51.02    (1)   ~ (all_52_3 = e0)
% 244.56/51.02    (2)   ~ (all_52_3 = e1)
% 244.56/51.02    (3)  op(e3, e1) = all_18_0
% 244.56/51.02    (4)  op(e3, e1) = all_28_0
% 244.56/51.02    (5)  op(e2, e1) = e2
% 244.56/51.02    (6)  op(e3, e1) = e1
% 244.56/51.02    (7)  op(e2, e2) = e1
% 244.56/51.02    (8)  all_54_12 = all_52_3
% 244.56/51.02    (9)   ~ (all_18_0 = e2)
% 244.56/51.02    (10)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.56/51.02    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.02    (12)  op(e2, e1) = all_56_19
% 244.56/51.02    (13)  op(e2, e1) = all_22_1
% 244.56/51.02    (14)  op(e2, all_56_19) = e2
% 244.56/51.02    (15)  op(e2, e1) = all_30_1
% 244.56/51.02  
% 244.56/51.02  Begin of proof
% 244.56/51.02  | 
% 244.56/51.02  | BETA: splitting (10) gives:
% 244.56/51.02  | 
% 244.56/51.02  | Case 1:
% 244.56/51.02  | | 
% 244.56/51.02  | | 
% 244.56/51.02  | | GROUND_INST: instantiating (11) with e2, all_30_1, e1, e2, simplifying with
% 244.56/51.02  | |              (5), (15) gives:
% 244.56/51.02  | |   (16)  all_30_1 = e2
% 244.56/51.02  | | 
% 244.56/51.02  | | GROUND_INST: instantiating (11) with all_30_1, all_56_19, e1, e2,
% 244.56/51.02  | |              simplifying with (12), (15) gives:
% 244.56/51.02  | |   (17)  all_56_19 = all_30_1
% 244.56/51.02  | | 
% 244.56/51.02  | | GROUND_INST: instantiating (11) with all_22_1, all_56_19, e1, e2,
% 244.56/51.02  | |              simplifying with (12), (13) gives:
% 244.56/51.02  | |   (18)  all_56_19 = all_22_1
% 244.56/51.02  | | 
% 244.56/51.02  | | GROUND_INST: instantiating (11) with e1, all_28_0, e1, e3, simplifying with
% 244.56/51.02  | |              (4), (6) gives:
% 244.56/51.02  | |   (19)  all_28_0 = e1
% 244.56/51.02  | | 
% 244.56/51.02  | | GROUND_INST: instantiating (11) with all_18_0, all_28_0, e1, e3, simplifying
% 244.56/51.02  | |              with (3), (4) gives:
% 244.56/51.02  | |   (20)  all_28_0 = all_18_0
% 244.56/51.02  | | 
% 244.56/51.02  | | COMBINE_EQS: (17), (18) imply:
% 244.56/51.02  | |   (21)  all_30_1 = all_22_1
% 244.56/51.02  | | 
% 244.56/51.02  | | SIMP: (21) implies:
% 244.56/51.02  | |   (22)  all_30_1 = all_22_1
% 244.56/51.02  | | 
% 244.56/51.02  | | COMBINE_EQS: (16), (22) imply:
% 244.56/51.02  | |   (23)  all_22_1 = e2
% 244.56/51.02  | | 
% 244.56/51.02  | | SIMP: (23) implies:
% 244.56/51.02  | |   (24)  all_22_1 = e2
% 244.56/51.02  | | 
% 244.56/51.02  | | COMBINE_EQS: (19), (20) imply:
% 244.56/51.02  | |   (25)  all_18_0 = e1
% 244.56/51.02  | | 
% 244.56/51.02  | | COMBINE_EQS: (18), (24) imply:
% 244.56/51.02  | |   (26)  all_56_19 = e2
% 244.56/51.02  | | 
% 244.56/51.02  | | REF_CLOSE: (7), (9), (11), (14), (25), (26) are inconsistent by sub-proof
% 244.56/51.02  | |            #1782.
% 244.56/51.02  | | 
% 244.56/51.02  | Case 2:
% 244.56/51.02  | | 
% 244.56/51.02  | |   (27)  all_54_12 = e1 | all_54_12 = e0
% 244.56/51.02  | | 
% 244.56/51.02  | | REF_CLOSE: (1), (2), (8), (27) are inconsistent by sub-proof #2067.
% 244.56/51.02  | | 
% 244.56/51.02  | End of split
% 244.56/51.02  | 
% 244.56/51.02  End of proof
% 244.56/51.02  
% 244.56/51.02  Sub-proof #1782 shows that the following formulas are inconsistent:
% 244.56/51.02  ----------------------------------------------------------------
% 244.56/51.02    (1)  op(e2, e2) = e1
% 244.56/51.02    (2)   ~ (all_18_0 = e2)
% 244.56/51.02    (3)  all_56_19 = e2
% 244.56/51.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.02    (5)  op(e2, all_56_19) = e2
% 244.56/51.02    (6)  all_18_0 = e1
% 244.56/51.02  
% 244.56/51.02  Begin of proof
% 244.56/51.02  | 
% 244.56/51.02  | REDUCE: (2), (6) imply:
% 244.56/51.02  |   (7)   ~ (e2 = e1)
% 244.56/51.02  | 
% 244.56/51.02  | SIMP: (7) implies:
% 244.56/51.02  |   (8)   ~ (e2 = e1)
% 244.56/51.02  | 
% 244.56/51.02  | REDUCE: (3), (5) imply:
% 244.56/51.02  |   (9)  op(e2, e2) = e2
% 244.56/51.02  | 
% 244.56/51.02  | REF_CLOSE: (1), (4), (8), (9) are inconsistent by sub-proof #2235.
% 244.56/51.02  | 
% 244.56/51.02  End of proof
% 244.56/51.02  
% 244.56/51.02  Sub-proof #1783 shows that the following formulas are inconsistent:
% 244.56/51.02  ----------------------------------------------------------------
% 244.56/51.02    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.02    (2)  op(e3, e1) = all_28_0
% 244.56/51.02    (3)  op(e3, e1) = e3
% 244.56/51.02    (4)   ~ (all_28_0 = e3)
% 244.56/51.02  
% 244.56/51.02  Begin of proof
% 244.56/51.02  | 
% 244.56/51.02  | GROUND_INST: instantiating (1) with e3, all_28_0, e1, e3, simplifying with
% 244.56/51.02  |              (2), (3) gives:
% 244.56/51.02  |   (5)  all_28_0 = e3
% 244.56/51.02  | 
% 244.56/51.02  | REDUCE: (4), (5) imply:
% 244.56/51.02  |   (6)  $false
% 244.56/51.02  | 
% 244.56/51.02  | CLOSE: (6) is inconsistent.
% 244.56/51.02  | 
% 244.56/51.02  End of proof
% 244.56/51.02  
% 244.56/51.02  Sub-proof #1784 shows that the following formulas are inconsistent:
% 244.56/51.02  ----------------------------------------------------------------
% 244.56/51.02    (1)   ~ (all_52_3 = e0)
% 244.56/51.02    (2)   ~ (e3 = e0)
% 244.56/51.02    (3)  op(e0, e3) = all_52_3
% 244.56/51.02    (4)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.56/51.02         $i(all_56_9)
% 244.56/51.02    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.56/51.02         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.56/51.02    (6)   ~ (all_52_1 = e0)
% 244.56/51.02    (7)  op(e2, e3) = all_52_1
% 244.56/51.02    (8)   ~ (all_52_2 = e0)
% 244.56/51.02    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.02    (10)  op(e1, e3) = all_52_2
% 244.56/51.02    (11)  op(e3, e2) = e3
% 244.56/51.02  
% 244.56/51.02  Begin of proof
% 244.56/51.02  | 
% 244.56/51.02  | ALPHA: (4) implies:
% 244.56/51.02  |   (12)  op(e3, e2) = all_56_9
% 244.56/51.02  |   (13)  op(e3, all_56_9) = e3
% 244.56/51.02  | 
% 244.56/51.02  | GROUND_INST: instantiating (9) with e3, all_56_9, e2, e3, simplifying with
% 244.56/51.02  |              (11), (12) gives:
% 244.56/51.02  |   (14)  all_56_9 = e3
% 244.56/51.02  | 
% 244.56/51.02  | REDUCE: (13), (14) imply:
% 244.56/51.02  |   (15)  op(e3, e3) = e3
% 244.56/51.02  | 
% 244.56/51.02  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (15) are inconsistent
% 244.56/51.02  |            by sub-proof #1938.
% 244.56/51.02  | 
% 244.56/51.02  End of proof
% 244.56/51.02  
% 244.56/51.02  Sub-proof #1785 shows that the following formulas are inconsistent:
% 244.56/51.02  ----------------------------------------------------------------
% 244.56/51.02    (1)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 244.56/51.02    (2)   ~ (e3 = e2)
% 244.56/51.02    (3)  op(e2, e2) = e1
% 244.56/51.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.02    (5)  op(e3, e2) = e3
% 244.56/51.02    (6)   ~ (e2 = e1)
% 244.56/51.02  
% 244.56/51.02  Begin of proof
% 244.56/51.02  | 
% 244.56/51.02  | BETA: splitting (1) gives:
% 244.56/51.02  | 
% 244.56/51.02  | Case 1:
% 244.56/51.02  | | 
% 244.56/51.02  | |   (7)  all_58_1 = e2 & op(e3, e2) = e2
% 244.56/51.02  | | 
% 244.56/51.02  | | ALPHA: (7) implies:
% 244.56/51.02  | |   (8)  op(e3, e2) = e2
% 244.56/51.02  | | 
% 244.56/51.02  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2193.
% 244.56/51.02  | | 
% 244.56/51.02  | Case 2:
% 244.56/51.02  | | 
% 244.56/51.02  | |   (9)  all_58_3 = e2 & op(e2, e2) = e2
% 244.56/51.02  | | 
% 244.56/51.02  | | ALPHA: (9) implies:
% 244.56/51.02  | |   (10)  op(e2, e2) = e2
% 244.56/51.02  | | 
% 244.56/51.02  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #2235.
% 244.56/51.02  | | 
% 244.56/51.02  | End of split
% 244.56/51.02  | 
% 244.56/51.02  End of proof
% 244.56/51.02  
% 244.56/51.02  Sub-proof #1786 shows that the following formulas are inconsistent:
% 244.56/51.02  ----------------------------------------------------------------
% 244.56/51.02    (1)  all_58_4 = e2
% 244.56/51.02    (2)  all_58_4 = e1
% 244.56/51.02    (3)   ~ (e2 = e1)
% 244.56/51.02  
% 244.56/51.02  Begin of proof
% 244.56/51.02  | 
% 244.56/51.02  | COMBINE_EQS: (1), (2) imply:
% 244.56/51.02  |   (4)  e2 = e1
% 244.56/51.02  | 
% 244.56/51.02  | SIMP: (4) implies:
% 244.56/51.02  |   (5)  e2 = e1
% 244.56/51.02  | 
% 244.56/51.02  | REDUCE: (3), (5) imply:
% 244.56/51.02  |   (6)  $false
% 244.56/51.02  | 
% 244.56/51.02  | CLOSE: (6) is inconsistent.
% 244.56/51.02  | 
% 244.56/51.02  End of proof
% 244.56/51.02  
% 244.56/51.02  Sub-proof #1787 shows that the following formulas are inconsistent:
% 244.56/51.02  ----------------------------------------------------------------
% 244.56/51.02    (1)   ~ (all_52_3 = e0)
% 244.56/51.02    (2)   ~ (all_52_6 = e1)
% 244.56/51.02    (3)   ~ (e3 = e0)
% 244.56/51.02    (4)  op(e0, e1) = all_52_11
% 244.56/51.02    (5)  op(e1, e2) = all_52_6
% 244.56/51.02    (6)  op(e1, e0) = all_52_14
% 244.56/51.02    (7)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.56/51.02    (8)  op(e0, e3) = all_52_3
% 244.56/51.02    (9)  all_54_11 = all_52_14
% 244.56/51.02    (10)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 244.56/51.02    (11)   ~ (all_52_14 = e1)
% 244.56/51.02    (12)   ~ (all_52_14 = e0)
% 244.56/51.02    (13)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 244.56/51.02            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 244.56/51.02            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 244.56/51.02            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 244.56/51.02            op(e0, all_56_31) = e0)
% 244.56/51.02    (14)  all_56_31 = e1
% 244.56/51.02    (15)  op(e2, e0) = e0
% 244.56/51.02    (16)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.56/51.02          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.56/51.02    (17)   ~ (all_52_1 = e0)
% 244.56/51.02    (18)  op(e3, e0) = e3
% 244.56/51.02    (19)  op(e2, e3) = all_52_1
% 244.56/51.02    (20)   ~ (all_52_14 = e3)
% 244.56/51.02    (21)  op(e3, e0) = all_50_1
% 244.56/51.02    (22)   ~ (all_52_2 = e0)
% 244.56/51.02    (23)   ~ (all_52_11 = e0)
% 244.56/51.02    (24)  all_54_1 = all_52_4
% 244.56/51.02    (25)   ~ (all_52_4 = e3)
% 244.56/51.02    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.02    (27)  op(e1, e3) = all_52_2
% 244.56/51.02    (28)   ~ (all_52_4 = e1)
% 244.56/51.02    (29)   ~ (all_52_4 = e0)
% 244.56/51.02  
% 244.56/51.02  Begin of proof
% 244.56/51.02  | 
% 244.56/51.02  | BETA: splitting (10) gives:
% 244.56/51.02  | 
% 244.56/51.02  | Case 1:
% 244.56/51.02  | | 
% 244.56/51.02  | |   (30)  all_54_11 = e3
% 244.56/51.02  | | 
% 244.56/51.02  | | COMBINE_EQS: (9), (30) imply:
% 244.56/51.02  | |   (31)  all_52_14 = e3
% 244.56/51.02  | | 
% 244.56/51.02  | | REDUCE: (20), (31) imply:
% 244.56/51.02  | |   (32)  $false
% 244.56/51.02  | | 
% 244.56/51.02  | | CLOSE: (32) is inconsistent.
% 244.56/51.02  | | 
% 244.56/51.02  | Case 2:
% 244.56/51.02  | | 
% 244.56/51.02  | |   (33)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 244.56/51.02  | | 
% 244.56/51.02  | | BETA: splitting (33) gives:
% 244.56/51.02  | | 
% 244.56/51.02  | | Case 1:
% 244.56/51.02  | | | 
% 244.56/51.02  | | |   (34)  all_54_11 = e2
% 244.56/51.02  | | | 
% 244.56/51.02  | | | COMBINE_EQS: (9), (34) imply:
% 244.56/51.02  | | |   (35)  all_52_14 = e2
% 244.56/51.02  | | | 
% 244.56/51.02  | | | REDUCE: (6), (35) imply:
% 244.56/51.02  | | |   (36)  op(e1, e0) = e2
% 244.56/51.02  | | | 
% 244.56/51.02  | | | BETA: splitting (7) gives:
% 244.56/51.02  | | | 
% 244.56/51.02  | | | Case 1:
% 244.56/51.02  | | | | 
% 244.56/51.02  | | | |   (37)  all_54_1 = e3
% 244.56/51.02  | | | | 
% 244.56/51.02  | | | | REF_CLOSE: (24), (25), (37) are inconsistent by sub-proof #1930.
% 244.56/51.02  | | | | 
% 244.56/51.02  | | | Case 2:
% 244.56/51.02  | | | | 
% 244.56/51.02  | | | |   (38)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.56/51.02  | | | | 
% 244.56/51.02  | | | | BETA: splitting (13) gives:
% 244.56/51.02  | | | | 
% 244.56/51.02  | | | | Case 1:
% 244.56/51.02  | | | | | 
% 244.56/51.02  | | | | |   (39)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 244.56/51.02  | | | | |           all_56_25 & $i(all_56_25)) | (all_56_26 = e2 & op(e2,
% 244.56/51.02  | | | | |             all_56_27) = e2 & op(e2, e0) = all_56_27 & $i(all_56_27))
% 244.56/51.02  | | | | | 
% 244.56/51.02  | | | | | BETA: splitting (39) gives:
% 244.56/51.02  | | | | | 
% 244.56/51.02  | | | | | Case 1:
% 244.56/51.02  | | | | | | 
% 244.56/51.02  | | | | | |   (40)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) =
% 244.56/51.02  | | | | | |         all_56_25 & $i(all_56_25)
% 244.56/51.02  | | | | | | 
% 244.56/51.02  | | | | | | ALPHA: (40) implies:
% 244.56/51.02  | | | | | |   (41)  op(e3, e0) = all_56_25
% 244.56/51.02  | | | | | |   (42)  op(e3, all_56_25) = e3
% 244.56/51.02  | | | | | | 
% 244.56/51.03  | | | | | | REF_CLOSE: (1), (3), (8), (16), (17), (18), (19), (21), (22), (24),
% 244.56/51.03  | | | | | |            (26), (27), (28), (29), (38), (41), (42) are inconsistent
% 244.56/51.03  | | | | | |            by sub-proof #1812.
% 244.56/51.03  | | | | | | 
% 244.56/51.03  | | | | | Case 2:
% 244.56/51.03  | | | | | | 
% 244.56/51.03  | | | | | |   (43)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) =
% 244.56/51.03  | | | | | |         all_56_27 & $i(all_56_27)
% 244.56/51.03  | | | | | | 
% 244.56/51.03  | | | | | | ALPHA: (43) implies:
% 244.56/51.03  | | | | | |   (44)  op(e2, e0) = all_56_27
% 244.56/51.03  | | | | | |   (45)  op(e2, all_56_27) = e2
% 244.56/51.03  | | | | | | 
% 244.56/51.03  | | | | | | REF_CLOSE: (9), (11), (12), (15), (26), (33), (44), (45) are
% 244.56/51.03  | | | | | |            inconsistent by sub-proof #1912.
% 244.56/51.03  | | | | | | 
% 244.56/51.03  | | | | | End of split
% 244.56/51.03  | | | | | 
% 244.56/51.03  | | | | Case 2:
% 244.56/51.03  | | | | | 
% 244.56/51.03  | | | | |   (46)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) =
% 244.56/51.03  | | | | |           all_56_29 & $i(all_56_29)) | (all_56_30 = e0 & op(e0,
% 244.56/51.03  | | | | |             all_56_31) = e0)
% 244.56/51.03  | | | | | 
% 244.56/51.03  | | | | | REF_CLOSE: (2), (4), (5), (14), (23), (26), (36), (46) are
% 244.56/51.03  | | | | |            inconsistent by sub-proof #1910.
% 244.56/51.03  | | | | | 
% 244.56/51.03  | | | | End of split
% 244.56/51.03  | | | | 
% 244.56/51.03  | | | End of split
% 244.56/51.03  | | | 
% 244.56/51.03  | | Case 2:
% 244.56/51.03  | | | 
% 244.56/51.03  | | |   (47)  all_54_11 = e1 | all_54_11 = e0
% 244.56/51.03  | | | 
% 244.56/51.03  | | | REF_CLOSE: (9), (11), (12), (47) are inconsistent by sub-proof #2174.
% 244.56/51.03  | | | 
% 244.56/51.03  | | End of split
% 244.56/51.03  | | 
% 244.56/51.03  | End of split
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.56/51.03  Sub-proof #1788 shows that the following formulas are inconsistent:
% 244.56/51.03  ----------------------------------------------------------------
% 244.56/51.03    (1)   ~ (all_52_3 = e0)
% 244.56/51.03    (2)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.56/51.03             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.56/51.03           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 244.56/51.03           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.56/51.03           op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.56/51.03    (3)  op(e0, e3) = all_52_3
% 244.56/51.03    (4)  all_56_21 = e0
% 244.56/51.03    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.03  
% 244.56/51.03  Begin of proof
% 244.56/51.03  | 
% 244.56/51.03  | BETA: splitting (2) gives:
% 244.56/51.03  | 
% 244.56/51.03  | Case 1:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (6)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.56/51.03  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.56/51.03  | |        op(e0, e3) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | ALPHA: (6) implies:
% 244.56/51.03  | |   (7)   ~ (all_56_21 = e0)
% 244.56/51.03  | | 
% 244.56/51.03  | | REDUCE: (4), (7) imply:
% 244.56/51.03  | |   (8)  $false
% 244.56/51.03  | | 
% 244.56/51.03  | | CLOSE: (8) is inconsistent.
% 244.56/51.03  | | 
% 244.56/51.03  | Case 2:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (9)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.56/51.03  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 244.56/51.03  | |        op(e0, e3) = e0
% 244.56/51.03  | | 
% 244.56/51.03  | | ALPHA: (9) implies:
% 244.56/51.03  | |   (10)  op(e0, e3) = e0
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2331.
% 244.56/51.03  | | 
% 244.56/51.03  | End of split
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.56/51.03  Sub-proof #1789 shows that the following formulas are inconsistent:
% 244.56/51.03  ----------------------------------------------------------------
% 244.56/51.03    (1)   ~ (all_52_8 = all_52_9)
% 244.56/51.03    (2)   ~ (all_52_1 = all_52_2)
% 244.56/51.03    (3)  all_54_6 = all_52_9
% 244.56/51.03    (4)   ~ (all_52_9 = e0)
% 244.56/51.03    (5)   ~ (all_52_1 = all_52_9)
% 244.56/51.03    (6)  all_54_4 = all_52_1
% 244.56/51.03    (7)  op(e3, e1) = all_52_8
% 244.56/51.03    (8)  op(e3, e1) = e1
% 244.56/51.03    (9)  op(e1, e3) = e1
% 244.56/51.03    (10)   ~ (all_52_1 = e0)
% 244.56/51.03    (11)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.56/51.03    (12)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.56/51.03    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.03    (14)  op(e1, e3) = all_52_2
% 244.56/51.03    (15)   ~ (all_52_1 = e2)
% 244.56/51.03    (16)   ~ (all_52_9 = e2)
% 244.56/51.03  
% 244.56/51.03  Begin of proof
% 244.56/51.03  | 
% 244.56/51.03  | GROUND_INST: instantiating (13) with all_52_2, e1, e3, e1, simplifying with
% 244.56/51.03  |              (9), (14) gives:
% 244.56/51.03  |   (17)  all_52_2 = e1
% 244.56/51.03  | 
% 244.56/51.03  | GROUND_INST: instantiating (13) with all_52_8, e1, e1, e3, simplifying with
% 244.56/51.03  |              (7), (8) gives:
% 244.56/51.03  |   (18)  all_52_8 = e1
% 244.56/51.03  | 
% 244.56/51.03  | REDUCE: (2), (17) imply:
% 244.56/51.03  |   (19)   ~ (all_52_1 = e1)
% 244.56/51.03  | 
% 244.56/51.03  | REDUCE: (1), (18) imply:
% 244.56/51.03  |   (20)   ~ (all_52_9 = e1)
% 244.56/51.03  | 
% 244.56/51.03  | SIMP: (20) implies:
% 244.56/51.03  |   (21)   ~ (all_52_9 = e1)
% 244.56/51.03  | 
% 244.56/51.03  | BETA: splitting (12) gives:
% 244.56/51.03  | 
% 244.56/51.03  | Case 1:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (22)  all_54_4 = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | COMBINE_EQS: (6), (22) imply:
% 244.56/51.03  | |   (23)  all_52_1 = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | SIMP: (23) implies:
% 244.56/51.03  | |   (24)  all_52_1 = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | REDUCE: (5), (24) imply:
% 244.56/51.03  | |   (25)   ~ (all_52_9 = e3)
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (3), (4), (11), (16), (21), (25) are inconsistent by sub-proof
% 244.56/51.03  | |            #1790.
% 244.56/51.03  | | 
% 244.56/51.03  | Case 2:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (26)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (6), (10), (15), (19), (26) are inconsistent by sub-proof #1921.
% 244.56/51.03  | | 
% 244.56/51.03  | End of split
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.56/51.03  Sub-proof #1790 shows that the following formulas are inconsistent:
% 244.56/51.03  ----------------------------------------------------------------
% 244.56/51.03    (1)   ~ (all_52_9 = e3)
% 244.56/51.03    (2)  all_54_6 = all_52_9
% 244.56/51.03    (3)   ~ (all_52_9 = e0)
% 244.56/51.03    (4)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.56/51.03    (5)   ~ (all_52_9 = e1)
% 244.56/51.03    (6)   ~ (all_52_9 = e2)
% 244.56/51.03  
% 244.56/51.03  Begin of proof
% 244.56/51.03  | 
% 244.56/51.03  | SIMP: (1) implies:
% 244.56/51.03  |   (7)   ~ (all_52_9 = e3)
% 244.56/51.03  | 
% 244.56/51.03  | BETA: splitting (4) gives:
% 244.56/51.03  | 
% 244.56/51.03  | Case 1:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (8)  all_54_6 = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (2), (7), (8) are inconsistent by sub-proof #1825.
% 244.56/51.03  | | 
% 244.56/51.03  | Case 2:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (9)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (2), (3), (5), (6), (9) are inconsistent by sub-proof #2244.
% 244.56/51.03  | | 
% 244.56/51.03  | End of split
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.56/51.03  Sub-proof #1791 shows that the following formulas are inconsistent:
% 244.56/51.03  ----------------------------------------------------------------
% 244.56/51.03    (1)   ~ (all_52_3 = e1)
% 244.56/51.03    (2)  op(e0, e3) = all_52_3
% 244.56/51.03    (3)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.56/51.03    (4)  op(e0, e2) = e0
% 244.56/51.03    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.03    (6)   ~ (e1 = e0)
% 244.56/51.03  
% 244.56/51.03  Begin of proof
% 244.56/51.03  | 
% 244.56/51.03  | BETA: splitting (3) gives:
% 244.56/51.03  | 
% 244.56/51.03  | Case 1:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (7)  all_58_12 = e1 & op(e0, e3) = e1
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #2276.
% 244.56/51.03  | | 
% 244.56/51.03  | Case 2:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (8)  all_58_13 = e1 & op(e0, e2) = e1
% 244.56/51.03  | | 
% 244.56/51.03  | | ALPHA: (8) implies:
% 244.56/51.03  | |   (9)  op(e0, e2) = e1
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #1872.
% 244.56/51.03  | | 
% 244.56/51.03  | End of split
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.56/51.03  Sub-proof #1792 shows that the following formulas are inconsistent:
% 244.56/51.03  ----------------------------------------------------------------
% 244.56/51.03    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.56/51.03    (2)   ~ (e3 = e1)
% 244.56/51.03    (3)   ~ (e3 = e2)
% 244.56/51.03    (4)  op(e3, e1) = e1
% 244.56/51.03    (5)  op(e3, e0) = e2
% 244.56/51.03    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.03  
% 244.56/51.03  Begin of proof
% 244.56/51.03  | 
% 244.56/51.03  | BETA: splitting (1) gives:
% 244.56/51.03  | 
% 244.56/51.03  | Case 1:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (7)  all_58_4 = e3 & op(e3, e1) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | ALPHA: (7) implies:
% 244.56/51.03  | |   (8)  op(e3, e1) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1823.
% 244.56/51.03  | | 
% 244.56/51.03  | Case 2:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (9)  all_58_9 = e3 & op(e3, e0) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | ALPHA: (9) implies:
% 244.56/51.03  | |   (10)  op(e3, e0) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #2125.
% 244.56/51.03  | | 
% 244.56/51.03  | End of split
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.56/51.03  Sub-proof #1793 shows that the following formulas are inconsistent:
% 244.56/51.03  ----------------------------------------------------------------
% 244.56/51.03    (1)  all_54_13 = e1 | all_54_13 = e0
% 244.56/51.03    (2)  all_54_13 = all_52_7
% 244.56/51.03    (3)   ~ (all_52_7 = e1)
% 244.56/51.03    (4)   ~ (all_52_7 = e0)
% 244.56/51.03  
% 244.56/51.03  Begin of proof
% 244.56/51.03  | 
% 244.56/51.03  | BETA: splitting (1) gives:
% 244.56/51.03  | 
% 244.56/51.03  | Case 1:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (5)  all_54_13 = e1
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1966.
% 244.56/51.03  | | 
% 244.56/51.03  | Case 2:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (6)  all_54_13 = e0
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2008.
% 244.56/51.03  | | 
% 244.56/51.03  | End of split
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.56/51.03  Sub-proof #1794 shows that the following formulas are inconsistent:
% 244.56/51.03  ----------------------------------------------------------------
% 244.56/51.03    (1)   ~ (all_52_3 = e0)
% 244.56/51.03    (2)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.56/51.03             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.56/51.03           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 244.56/51.03           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.56/51.03           op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.56/51.03    (3)  op(e0, e3) = all_52_3
% 244.56/51.03    (4)  op(e3, e0) = all_52_12
% 244.56/51.03    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.03    (6)   ~ (all_52_12 = e3)
% 244.56/51.03  
% 244.56/51.03  Begin of proof
% 244.56/51.03  | 
% 244.56/51.03  | BETA: splitting (2) gives:
% 244.56/51.03  | 
% 244.56/51.03  | Case 1:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (7)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.56/51.03  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.56/51.03  | |        op(e0, e3) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | ALPHA: (7) implies:
% 244.56/51.03  | |   (8)  op(e3, e0) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2179.
% 244.56/51.03  | | 
% 244.56/51.03  | Case 2:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (9)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.56/51.03  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 244.56/51.03  | |        op(e0, e3) = e0
% 244.56/51.03  | | 
% 244.56/51.03  | | ALPHA: (9) implies:
% 244.56/51.03  | |   (10)  op(e0, e3) = e0
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2331.
% 244.56/51.03  | | 
% 244.56/51.03  | End of split
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.56/51.03  Sub-proof #1795 shows that the following formulas are inconsistent:
% 244.56/51.03  ----------------------------------------------------------------
% 244.56/51.03    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.56/51.03             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 244.56/51.03    (2)   ~ (e3 = e2)
% 244.56/51.03    (3)  op(e2, e3) = e2
% 244.56/51.03    (4)  op(e2, e2) = e1
% 244.56/51.03    (5)  op(e3, e0) = e2
% 244.56/51.03    (6)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) = all_50_1
% 244.56/51.03           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3, e0) =
% 244.56/51.03           all_50_1 & $i(all_50_1))
% 244.56/51.03    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.03    (8)  all_56_1 = e0
% 244.56/51.03    (9)   ~ (e2 = e1)
% 244.56/51.03  
% 244.56/51.03  Begin of proof
% 244.56/51.03  | 
% 244.56/51.03  | BETA: splitting (1) gives:
% 244.56/51.03  | 
% 244.56/51.03  | Case 1:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (10)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | ALPHA: (10) implies:
% 244.56/51.03  | |   (11)  op(e3, all_56_1) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | REDUCE: (8), (11) imply:
% 244.56/51.03  | |   (12)  op(e3, e0) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (2), (5), (7), (12) are inconsistent by sub-proof #2125.
% 244.56/51.03  | | 
% 244.56/51.03  | Case 2:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (13)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 244.56/51.03  | |         $i(all_56_3)
% 244.56/51.03  | | 
% 244.56/51.03  | | ALPHA: (13) implies:
% 244.56/51.03  | |   (14)  op(e2, e3) = all_56_3
% 244.56/51.03  | |   (15)  op(e2, all_56_3) = e2
% 244.56/51.03  | | 
% 244.56/51.03  | | BETA: splitting (6) gives:
% 244.56/51.03  | | 
% 244.56/51.03  | | Case 1:
% 244.56/51.03  | | | 
% 244.56/51.03  | | | 
% 244.56/51.03  | | | GROUND_INST: instantiating (7) with e2, all_56_3, e3, e2, simplifying with
% 244.56/51.03  | | |              (3), (14) gives:
% 244.56/51.03  | | |   (16)  all_56_3 = e2
% 244.56/51.03  | | | 
% 244.56/51.03  | | | REDUCE: (15), (16) imply:
% 244.56/51.03  | | |   (17)  op(e2, e2) = e2
% 244.56/51.03  | | | 
% 244.56/51.03  | | | REF_CLOSE: (4), (7), (9), (17) are inconsistent by sub-proof #2235.
% 244.56/51.03  | | | 
% 244.56/51.03  | | Case 2:
% 244.56/51.03  | | | 
% 244.56/51.03  | | |   (18)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 & $i(all_50_1)
% 244.56/51.03  | | | 
% 244.56/51.03  | | | ALPHA: (18) implies:
% 244.56/51.03  | | |   (19)   ~ (all_50_1 = e2)
% 244.56/51.03  | | |   (20)  op(e3, e0) = all_50_1
% 244.56/51.03  | | | 
% 244.56/51.03  | | | REF_CLOSE: (5), (7), (19), (20) are inconsistent by sub-proof #1884.
% 244.56/51.03  | | | 
% 244.56/51.03  | | End of split
% 244.56/51.03  | | 
% 244.56/51.03  | End of split
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.56/51.03  Sub-proof #1796 shows that the following formulas are inconsistent:
% 244.56/51.03  ----------------------------------------------------------------
% 244.56/51.03    (1)  all_54_14 = all_52_11
% 244.56/51.03    (2)  all_54_14 = e3
% 244.56/51.03    (3)   ~ (all_52_11 = e3)
% 244.56/51.03  
% 244.56/51.03  Begin of proof
% 244.56/51.03  | 
% 244.56/51.03  | COMBINE_EQS: (1), (2) imply:
% 244.56/51.03  |   (4)  all_52_11 = e3
% 244.56/51.03  | 
% 244.56/51.03  | SIMP: (4) implies:
% 244.56/51.03  |   (5)  all_52_11 = e3
% 244.56/51.03  | 
% 244.56/51.03  | REDUCE: (3), (5) imply:
% 244.56/51.03  |   (6)  $false
% 244.56/51.03  | 
% 244.56/51.03  | CLOSE: (6) is inconsistent.
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.56/51.03  Sub-proof #1797 shows that the following formulas are inconsistent:
% 244.56/51.03  ----------------------------------------------------------------
% 244.56/51.03    (1)   ~ (e3 = e0)
% 244.56/51.03    (2)   ~ (e3 = e2)
% 244.56/51.03    (3)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.56/51.03    (4)  op(e1, e1) = e2
% 244.56/51.03    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.56/51.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.56/51.03    (6)  all_58_11 = e0
% 244.56/51.03  
% 244.56/51.03  Begin of proof
% 244.56/51.03  | 
% 244.56/51.03  | BETA: splitting (3) gives:
% 244.56/51.03  | 
% 244.56/51.03  | Case 1:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | ALPHA: (7) implies:
% 244.56/51.03  | |   (8)  op(e1, e1) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2206.
% 244.56/51.03  | | 
% 244.56/51.03  | Case 2:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (9)  all_58_11 = e3 & op(e1, e0) = e3
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #2091.
% 244.56/51.03  | | 
% 244.56/51.03  | End of split
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.56/51.03  Sub-proof #1798 shows that the following formulas are inconsistent:
% 244.56/51.03  ----------------------------------------------------------------
% 244.56/51.03    (1)   ~ (all_52_11 = e2)
% 244.56/51.03    (2)   ~ (all_52_11 = e1)
% 244.56/51.03    (3)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.56/51.03    (4)   ~ (all_52_11 = e0)
% 244.56/51.03    (5)  all_54_14 = all_52_11
% 244.56/51.03  
% 244.56/51.03  Begin of proof
% 244.56/51.03  | 
% 244.56/51.03  | BETA: splitting (3) gives:
% 244.56/51.03  | 
% 244.56/51.03  | Case 1:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (6)  all_54_14 = e2
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #1856.
% 244.56/51.03  | | 
% 244.56/51.03  | Case 2:
% 244.56/51.03  | | 
% 244.56/51.03  | |   (7)  all_54_14 = e1 | all_54_14 = e0
% 244.56/51.03  | | 
% 244.56/51.03  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #1935.
% 244.56/51.03  | | 
% 244.56/51.03  | End of split
% 244.56/51.03  | 
% 244.56/51.03  End of proof
% 244.56/51.03  
% 244.62/51.03  Sub-proof #1799 shows that the following formulas are inconsistent:
% 244.62/51.03  ----------------------------------------------------------------
% 244.62/51.03    (1)   ~ (e3 = e0)
% 244.62/51.03    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.62/51.03         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.62/51.03    (3)   ~ (e2 = e0)
% 244.62/51.03    (4)   ~ (e3 = e1)
% 244.62/51.03    (5)  all_58_8 = e2
% 244.62/51.03    (6)  all_58_7 = e2
% 244.62/51.03    (7)   ~ (e3 = e2)
% 244.62/51.03    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.62/51.03         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.62/51.03    (9)  all_58_6 = e1
% 244.62/51.03    (10)  op(e1, e1) = e2
% 244.62/51.03    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.03            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.03    (12)   ~ (e1 = e0)
% 244.62/51.03    (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.62/51.03          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.62/51.03    (14)   ~ (e2 = e1)
% 244.62/51.03  
% 244.62/51.03  Begin of proof
% 244.62/51.03  | 
% 244.62/51.03  | BETA: splitting (8) gives:
% 244.62/51.03  | 
% 244.62/51.03  | Case 1:
% 244.62/51.03  | | 
% 244.62/51.03  | |   (15)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.62/51.03  | |           e3)
% 244.62/51.03  | | 
% 244.62/51.03  | | BETA: splitting (15) gives:
% 244.62/51.03  | | 
% 244.62/51.03  | | Case 1:
% 244.62/51.03  | | | 
% 244.62/51.03  | | |   (16)  all_58_6 = e3 & op(e1, e3) = e3
% 244.62/51.03  | | | 
% 244.62/51.03  | | | ALPHA: (16) implies:
% 244.62/51.03  | | |   (17)  all_58_6 = e3
% 244.62/51.03  | | | 
% 244.62/51.03  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (11), (12), (13), (14),
% 244.62/51.03  | | |            (17) are inconsistent by sub-proof #1801.
% 244.62/51.03  | | | 
% 244.62/51.03  | | Case 2:
% 244.62/51.03  | | | 
% 244.62/51.04  | | |   (18)  all_58_7 = e3 & op(e1, e2) = e3
% 244.62/51.04  | | | 
% 244.62/51.04  | | | REF_CLOSE: (6), (7), (18) are inconsistent by sub-proof #1800.
% 244.62/51.04  | | | 
% 244.62/51.04  | | End of split
% 244.62/51.04  | | 
% 244.62/51.04  | Case 2:
% 244.62/51.04  | | 
% 244.62/51.04  | |   (19)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.62/51.04  | |           e3)
% 244.62/51.04  | | 
% 244.62/51.04  | | REF_CLOSE: (1), (3), (6), (7), (9), (10), (11), (12), (13), (19) are
% 244.62/51.04  | |            inconsistent by sub-proof #2201.
% 244.62/51.04  | | 
% 244.62/51.04  | End of split
% 244.62/51.04  | 
% 244.62/51.04  End of proof
% 244.62/51.04  
% 244.62/51.04  Sub-proof #1800 shows that the following formulas are inconsistent:
% 244.62/51.04  ----------------------------------------------------------------
% 244.62/51.04    (1)  all_58_7 = e3 & op(e1, e2) = e3
% 244.62/51.04    (2)  all_58_7 = e2
% 244.62/51.04    (3)   ~ (e3 = e2)
% 244.62/51.04  
% 244.62/51.04  Begin of proof
% 244.62/51.04  | 
% 244.62/51.04  | ALPHA: (1) implies:
% 244.62/51.04  |   (4)  all_58_7 = e3
% 244.62/51.04  | 
% 244.62/51.04  | COMBINE_EQS: (2), (4) imply:
% 244.62/51.04  |   (5)  e3 = e2
% 244.62/51.04  | 
% 244.62/51.04  | REDUCE: (3), (5) imply:
% 244.62/51.04  |   (6)  $false
% 244.62/51.04  | 
% 244.62/51.04  | CLOSE: (6) is inconsistent.
% 244.62/51.04  | 
% 244.62/51.04  End of proof
% 244.62/51.04  
% 244.62/51.04  Sub-proof #1801 shows that the following formulas are inconsistent:
% 244.62/51.04  ----------------------------------------------------------------
% 244.62/51.04    (1)   ~ (e3 = e0)
% 244.62/51.04    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.62/51.04         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.62/51.04    (3)  all_58_6 = e3
% 244.62/51.04    (4)   ~ (e2 = e0)
% 244.62/51.04    (5)   ~ (e3 = e1)
% 244.62/51.04    (6)  all_58_8 = e2
% 244.62/51.04    (7)  all_58_7 = e2
% 244.62/51.04    (8)  op(e1, e1) = e2
% 244.62/51.04    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.04    (10)   ~ (e1 = e0)
% 244.62/51.04    (11)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.62/51.04          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.62/51.04    (12)   ~ (e2 = e1)
% 244.62/51.04  
% 244.62/51.04  Begin of proof
% 244.62/51.04  | 
% 244.62/51.04  | BETA: splitting (2) gives:
% 244.62/51.04  | 
% 244.62/51.04  | Case 1:
% 244.62/51.04  | | 
% 244.62/51.04  | |   (13)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 244.62/51.04  | |           e1)
% 244.62/51.04  | | 
% 244.62/51.04  | | BETA: splitting (13) gives:
% 244.62/51.04  | | 
% 244.62/51.04  | | Case 1:
% 244.62/51.04  | | | 
% 244.62/51.04  | | |   (14)  all_58_6 = e1 & op(e1, e3) = e1
% 244.62/51.04  | | | 
% 244.62/51.04  | | | REF_CLOSE: (3), (5), (14) are inconsistent by sub-proof #1803.
% 244.62/51.04  | | | 
% 244.62/51.04  | | Case 2:
% 244.62/51.04  | | | 
% 244.62/51.04  | | |   (15)  all_58_7 = e1 & op(e1, e2) = e1
% 244.62/51.04  | | | 
% 244.62/51.04  | | | REF_CLOSE: (7), (12), (15) are inconsistent by sub-proof #2224.
% 244.62/51.04  | | | 
% 244.62/51.04  | | End of split
% 244.62/51.04  | | 
% 244.62/51.04  | Case 2:
% 244.62/51.04  | | 
% 244.62/51.04  | |   (16)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 244.62/51.04  | |           e1)
% 244.62/51.04  | | 
% 244.62/51.04  | | BETA: splitting (16) gives:
% 244.62/51.04  | | 
% 244.62/51.04  | | Case 1:
% 244.62/51.04  | | | 
% 244.62/51.04  | | |   (17)  all_58_8 = e1 & op(e1, e1) = e1
% 244.62/51.04  | | | 
% 244.62/51.04  | | | ALPHA: (17) implies:
% 244.62/51.04  | | |   (18)  all_58_8 = e1
% 244.62/51.04  | | | 
% 244.62/51.04  | | | REF_CLOSE: (6), (12), (18) are inconsistent by sub-proof #1802.
% 244.62/51.04  | | | 
% 244.62/51.04  | | Case 2:
% 244.62/51.04  | | | 
% 244.62/51.04  | | |   (19)  all_58_11 = e1 & op(e1, e0) = e1
% 244.62/51.04  | | | 
% 244.62/51.04  | | | ALPHA: (19) implies:
% 244.62/51.04  | | |   (20)  op(e1, e0) = e1
% 244.62/51.04  | | | 
% 244.62/51.04  | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (20) are inconsistent
% 244.62/51.04  | | |            by sub-proof #2209.
% 244.62/51.04  | | | 
% 244.62/51.04  | | End of split
% 244.62/51.04  | | 
% 244.62/51.04  | End of split
% 244.62/51.04  | 
% 244.62/51.04  End of proof
% 244.62/51.04  
% 244.62/51.04  Sub-proof #1802 shows that the following formulas are inconsistent:
% 244.62/51.04  ----------------------------------------------------------------
% 244.62/51.04    (1)  all_58_8 = e2
% 244.62/51.04    (2)  all_58_8 = e1
% 244.62/51.04    (3)   ~ (e2 = e1)
% 244.62/51.04  
% 244.62/51.04  Begin of proof
% 244.62/51.04  | 
% 244.62/51.04  | COMBINE_EQS: (1), (2) imply:
% 244.62/51.04  |   (4)  e2 = e1
% 244.62/51.04  | 
% 244.62/51.04  | SIMP: (4) implies:
% 244.62/51.04  |   (5)  e2 = e1
% 244.62/51.04  | 
% 244.62/51.04  | REDUCE: (3), (5) imply:
% 244.62/51.04  |   (6)  $false
% 244.62/51.04  | 
% 244.62/51.04  | CLOSE: (6) is inconsistent.
% 244.62/51.04  | 
% 244.62/51.04  End of proof
% 244.62/51.04  
% 244.62/51.04  Sub-proof #1803 shows that the following formulas are inconsistent:
% 244.62/51.04  ----------------------------------------------------------------
% 244.62/51.04    (1)  all_58_6 = e1 & op(e1, e3) = e1
% 244.62/51.04    (2)  all_58_6 = e3
% 244.62/51.04    (3)   ~ (e3 = e1)
% 244.62/51.04  
% 244.62/51.04  Begin of proof
% 244.62/51.04  | 
% 244.62/51.04  | ALPHA: (1) implies:
% 244.62/51.04  |   (4)  all_58_6 = e1
% 244.62/51.04  | 
% 244.62/51.04  | COMBINE_EQS: (2), (4) imply:
% 244.62/51.04  |   (5)  e3 = e1
% 244.62/51.04  | 
% 244.62/51.04  | REDUCE: (3), (5) imply:
% 244.62/51.04  |   (6)  $false
% 244.62/51.04  | 
% 244.62/51.04  | CLOSE: (6) is inconsistent.
% 244.62/51.04  | 
% 244.62/51.04  End of proof
% 244.62/51.04  
% 244.62/51.04  Sub-proof #1804 shows that the following formulas are inconsistent:
% 244.62/51.04  ----------------------------------------------------------------
% 244.62/51.04    (1)   ~ (all_52_3 = e0)
% 244.62/51.04    (2)   ~ (all_52_3 = e1)
% 244.62/51.04    (3)  op(e0, e1) = e3
% 244.62/51.04    (4)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) = all_20_1
% 244.62/51.04           & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1) =
% 244.62/51.04           all_20_1 & $i(all_20_1))
% 244.62/51.04    (5)  op(e0, e3) = all_52_3
% 244.62/51.04    (6)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23 &
% 244.62/51.04         $i(all_56_23)
% 244.62/51.04    (7)  all_54_12 = all_52_3
% 244.62/51.04    (8)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.62/51.04    (9)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) = all_34_1
% 244.62/51.04           & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1) =
% 244.62/51.04           all_34_1 & $i(all_34_1))
% 244.62/51.04    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.04            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.04  
% 244.62/51.04  Begin of proof
% 244.62/51.04  | 
% 244.62/51.04  | ALPHA: (6) implies:
% 244.62/51.04  |   (11)  op(e0, e1) = all_56_23
% 244.62/51.04  |   (12)  op(e0, all_56_23) = e0
% 244.62/51.04  | 
% 244.62/51.04  | BETA: splitting (4) gives:
% 244.62/51.04  | 
% 244.62/51.04  | Case 1:
% 244.62/51.04  | | 
% 244.62/51.04  | |   (13)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 244.62/51.04  | |         all_20_1 & $i(all_20_0) & $i(all_20_1)
% 244.62/51.04  | | 
% 244.62/51.04  | | ALPHA: (13) implies:
% 244.62/51.04  | |   (14)  op(e0, e1) = all_20_1
% 244.62/51.04  | | 
% 244.62/51.04  | | BETA: splitting (9) gives:
% 244.62/51.04  | | 
% 244.62/51.04  | | Case 1:
% 244.62/51.04  | | | 
% 244.62/51.04  | | |   (15)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 244.62/51.04  | | |         all_34_1 & $i(all_34_0) & $i(all_34_1)
% 244.62/51.04  | | | 
% 244.62/51.04  | | | ALPHA: (15) implies:
% 244.62/51.04  | | |   (16)  op(e0, e1) = all_34_1
% 244.62/51.04  | | | 
% 244.62/51.04  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (12), (14), (16) are
% 244.62/51.04  | | |            inconsistent by sub-proof #1807.
% 244.62/51.04  | | | 
% 244.62/51.04  | | Case 2:
% 244.62/51.04  | | | 
% 244.62/51.04  | | |   (17)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 244.62/51.04  | | | 
% 244.62/51.04  | | | ALPHA: (17) implies:
% 244.62/51.04  | | |   (18)  op(e0, e1) = all_34_1
% 244.62/51.04  | | | 
% 244.62/51.04  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (12), (14), (18) are
% 244.62/51.04  | | |            inconsistent by sub-proof #1807.
% 244.62/51.04  | | | 
% 244.62/51.04  | | End of split
% 244.62/51.04  | | 
% 244.62/51.04  | Case 2:
% 244.62/51.04  | | 
% 244.62/51.04  | |   (19)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 & $i(all_20_1)
% 244.62/51.04  | | 
% 244.62/51.04  | | REF_CLOSE: (3), (9), (10), (19) are inconsistent by sub-proof #1805.
% 244.62/51.04  | | 
% 244.62/51.04  | End of split
% 244.62/51.04  | 
% 244.62/51.04  End of proof
% 244.62/51.04  
% 244.62/51.04  Sub-proof #1805 shows that the following formulas are inconsistent:
% 244.62/51.04  ----------------------------------------------------------------
% 244.62/51.04    (1)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 & $i(all_20_1)
% 244.62/51.04    (2)  op(e0, e1) = e3
% 244.62/51.04    (3)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) = all_34_1
% 244.62/51.04           & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0, e1) =
% 244.62/51.04           all_34_1 & $i(all_34_1))
% 244.62/51.04    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.04  
% 244.62/51.04  Begin of proof
% 244.62/51.04  | 
% 244.62/51.04  | ALPHA: (1) implies:
% 244.62/51.04  |   (5)   ~ (all_20_1 = e3)
% 244.62/51.04  |   (6)  op(e0, e1) = all_20_1
% 244.62/51.04  | 
% 244.62/51.04  | BETA: splitting (3) gives:
% 244.62/51.04  | 
% 244.62/51.04  | Case 1:
% 244.62/51.04  | | 
% 244.62/51.04  | |   (7)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 244.62/51.04  | |        all_34_1 & $i(all_34_0) & $i(all_34_1)
% 244.62/51.04  | | 
% 244.62/51.04  | | ALPHA: (7) implies:
% 244.62/51.04  | |   (8)  op(e0, e1) = all_34_1
% 244.62/51.04  | | 
% 244.62/51.04  | | REF_CLOSE: (2), (4), (5), (6), (8) are inconsistent by sub-proof #1806.
% 244.62/51.04  | | 
% 244.62/51.04  | Case 2:
% 244.62/51.04  | | 
% 244.62/51.04  | |   (9)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 244.62/51.04  | | 
% 244.62/51.04  | | ALPHA: (9) implies:
% 244.62/51.04  | |   (10)  op(e0, e1) = all_34_1
% 244.62/51.04  | | 
% 244.62/51.04  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #1806.
% 244.62/51.04  | | 
% 244.62/51.04  | End of split
% 244.62/51.04  | 
% 244.62/51.04  End of proof
% 244.62/51.04  
% 244.62/51.04  Sub-proof #1806 shows that the following formulas are inconsistent:
% 244.62/51.04  ----------------------------------------------------------------
% 244.62/51.04    (1)  op(e0, e1) = e3
% 244.62/51.04    (2)  op(e0, e1) = all_34_1
% 244.62/51.04    (3)  op(e0, e1) = all_20_1
% 244.62/51.04    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.04    (5)   ~ (all_20_1 = e3)
% 244.62/51.04  
% 244.62/51.04  Begin of proof
% 244.62/51.04  | 
% 244.62/51.04  | GROUND_INST: instantiating (4) with e3, all_34_1, e1, e0, simplifying with
% 244.62/51.04  |              (1), (2) gives:
% 244.62/51.04  |   (6)  all_34_1 = e3
% 244.62/51.04  | 
% 244.62/51.04  | GROUND_INST: instantiating (4) with all_20_1, all_34_1, e1, e0, simplifying
% 244.62/51.04  |              with (2), (3) gives:
% 244.62/51.04  |   (7)  all_34_1 = all_20_1
% 244.62/51.04  | 
% 244.62/51.04  | COMBINE_EQS: (6), (7) imply:
% 244.62/51.04  |   (8)  all_20_1 = e3
% 244.62/51.04  | 
% 244.62/51.04  | SIMP: (8) implies:
% 244.62/51.04  |   (9)  all_20_1 = e3
% 244.62/51.04  | 
% 244.62/51.04  | REDUCE: (5), (9) imply:
% 244.62/51.04  |   (10)  $false
% 244.62/51.04  | 
% 244.62/51.04  | CLOSE: (10) is inconsistent.
% 244.62/51.04  | 
% 244.62/51.04  End of proof
% 244.62/51.04  
% 244.62/51.04  Sub-proof #1807 shows that the following formulas are inconsistent:
% 244.62/51.04  ----------------------------------------------------------------
% 244.62/51.04    (1)   ~ (all_52_3 = e0)
% 244.62/51.04    (2)   ~ (all_52_3 = e1)
% 244.62/51.04    (3)  op(e0, e1) = all_56_23
% 244.62/51.04    (4)  op(e0, e1) = e3
% 244.62/51.04    (5)  op(e0, e1) = all_34_1
% 244.62/51.04    (6)  op(e0, e3) = all_52_3
% 244.62/51.04    (7)  all_54_12 = all_52_3
% 244.62/51.04    (8)  op(e0, e1) = all_20_1
% 244.62/51.04    (9)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.62/51.04    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.04            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.04    (11)  op(e0, all_56_23) = e0
% 244.62/51.04  
% 244.62/51.04  Begin of proof
% 244.62/51.04  | 
% 244.62/51.04  | BETA: splitting (9) gives:
% 244.62/51.04  | 
% 244.62/51.04  | Case 1:
% 244.62/51.04  | | 
% 244.62/51.04  | |   (12)  all_54_12 = e2
% 244.62/51.04  | | 
% 244.62/51.04  | | COMBINE_EQS: (7), (12) imply:
% 244.62/51.04  | |   (13)  all_52_3 = e2
% 244.62/51.04  | | 
% 244.62/51.04  | | SIMP: (13) implies:
% 244.62/51.04  | |   (14)  all_52_3 = e2
% 244.62/51.04  | | 
% 244.62/51.04  | | REDUCE: (1), (14) imply:
% 244.62/51.04  | |   (15)   ~ (e2 = e0)
% 244.62/51.04  | | 
% 244.62/51.04  | | REDUCE: (6), (14) imply:
% 244.62/51.04  | |   (16)  op(e0, e3) = e2
% 244.62/51.04  | | 
% 244.62/51.04  | | GROUND_INST: instantiating (10) with e3, all_34_1, e1, e0, simplifying with
% 244.62/51.04  | |              (4), (5) gives:
% 244.62/51.04  | |   (17)  all_34_1 = e3
% 244.62/51.04  | | 
% 244.62/51.04  | | GROUND_INST: instantiating (10) with all_34_1, all_56_23, e1, e0,
% 244.62/51.04  | |              simplifying with (3), (5) gives:
% 244.62/51.04  | |   (18)  all_56_23 = all_34_1
% 244.62/51.04  | | 
% 244.62/51.04  | | GROUND_INST: instantiating (10) with all_20_1, all_56_23, e1, e0,
% 244.62/51.04  | |              simplifying with (3), (8) gives:
% 244.62/51.04  | |   (19)  all_56_23 = all_20_1
% 244.62/51.04  | | 
% 244.62/51.04  | | COMBINE_EQS: (18), (19) imply:
% 244.62/51.04  | |   (20)  all_34_1 = all_20_1
% 244.62/51.04  | | 
% 244.62/51.04  | | SIMP: (20) implies:
% 244.62/51.04  | |   (21)  all_34_1 = all_20_1
% 244.62/51.04  | | 
% 244.62/51.04  | | COMBINE_EQS: (17), (21) imply:
% 244.62/51.04  | |   (22)  all_20_1 = e3
% 244.62/51.04  | | 
% 244.62/51.04  | | COMBINE_EQS: (19), (22) imply:
% 244.62/51.04  | |   (23)  all_56_23 = e3
% 244.62/51.04  | | 
% 244.62/51.04  | | REDUCE: (11), (23) imply:
% 244.62/51.04  | |   (24)  op(e0, e3) = e0
% 244.62/51.04  | | 
% 244.62/51.04  | | REF_CLOSE: (10), (15), (16), (24) are inconsistent by sub-proof #1896.
% 244.62/51.04  | | 
% 244.62/51.04  | Case 2:
% 244.62/51.04  | | 
% 244.62/51.04  | |   (25)  all_54_12 = e1 | all_54_12 = e0
% 244.62/51.04  | | 
% 244.62/51.04  | | REF_CLOSE: (1), (2), (7), (25) are inconsistent by sub-proof #2067.
% 244.62/51.04  | | 
% 244.62/51.04  | End of split
% 244.62/51.04  | 
% 244.62/51.04  End of proof
% 244.62/51.04  
% 244.62/51.04  Sub-proof #1808 shows that the following formulas are inconsistent:
% 244.62/51.04  ----------------------------------------------------------------
% 244.62/51.04    (1)   ~ (all_52_3 = e0)
% 244.62/51.04    (2)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.62/51.04    (3)   ~ (e3 = e0)
% 244.62/51.04    (4)  op(e1, e0) = e0
% 244.62/51.04    (5)  op(e0, e1) = all_52_11
% 244.62/51.04    (6)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 244.62/51.04         (all_58_11 = e0 & op(e1, e0) = e0)
% 244.62/51.04    (7)  op(e0, e1) = e3
% 244.62/51.04    (8)  op(e1, e2) = all_52_6
% 244.62/51.04    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.62/51.04         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.62/51.04    (10)   ~ (all_52_7 = e3)
% 244.62/51.04    (11)  op(e0, e3) = all_52_3
% 244.62/51.04    (12)   ~ (e3 = e1)
% 244.62/51.04    (13)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 244.62/51.04            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 244.62/51.04            = all_56_27 & $i(all_56_27)) | (all_56_28 = e1 & op(e1, all_56_29) =
% 244.62/51.04            e1 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 = e0 &
% 244.62/51.04            op(e0, all_56_31) = e0)
% 244.62/51.04    (14)  op(e2, e0) = e2
% 244.62/51.04    (15)  all_56_31 = e1
% 244.62/51.04    (16)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.62/51.04          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.62/51.04    (17)   ~ (all_52_1 = e0)
% 244.62/51.04    (18)  all_58_9 = e3
% 244.62/51.04    (19)  op(e3, e0) = e3
% 244.62/51.04    (20)  op(e2, e3) = all_52_1
% 244.62/51.04    (21)  ( ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 244.62/51.04            all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e3,
% 244.62/51.04              e0) = all_50_1 & $i(all_50_1))
% 244.62/51.04    (22)   ~ (all_52_2 = e0)
% 244.62/51.04    (23)   ~ (all_52_11 = e0)
% 244.62/51.04    (24)  op(e0, e2) = all_52_7
% 244.62/51.04    (25)  op(e0, e1) = all_20_1
% 244.62/51.04    (26)  op(e2, e1) = e0
% 244.62/51.04    (27)  all_54_1 = all_52_4
% 244.62/51.04    (28)  op(e3, e2) = all_52_4
% 244.62/51.04    (29)  all_58_1 = e2
% 244.62/51.04    (30)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 244.62/51.04            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 244.62/51.04              e1) = all_34_1 & $i(all_34_1))
% 244.62/51.04    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.04            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.04    (32)  op(e1, e3) = all_52_2
% 244.62/51.04    (33)  op(e2, e1) = all_56_19
% 244.62/51.04    (34)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.62/51.04          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.62/51.04    (35)   ~ (all_52_4 = e1)
% 244.62/51.04    (36)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.62/51.04          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.62/51.04    (37)   ~ (e1 = e0)
% 244.62/51.04    (38)  op(e2, all_56_19) = e2
% 244.62/51.04    (39)   ~ (all_52_4 = e0)
% 244.62/51.04    (40)  op(e2, e1) = all_30_1
% 244.62/51.04  
% 244.62/51.04  Begin of proof
% 244.62/51.04  | 
% 244.62/51.04  | BETA: splitting (13) gives:
% 244.62/51.04  | 
% 244.62/51.04  | Case 1:
% 244.62/51.04  | | 
% 244.62/51.04  | |   (41)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 244.62/51.04  | |           $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2,
% 244.62/51.04  | |             e0) = all_56_27 & $i(all_56_27))
% 244.62/51.04  | | 
% 244.62/51.04  | | BETA: splitting (41) gives:
% 244.62/51.04  | | 
% 244.62/51.04  | | Case 1:
% 244.62/51.04  | | | 
% 244.62/51.04  | | |   (42)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 244.62/51.04  | | |         $i(all_56_25)
% 244.62/51.04  | | | 
% 244.62/51.04  | | | ALPHA: (42) implies:
% 244.62/51.04  | | |   (43)  op(e3, e0) = all_56_25
% 244.62/51.04  | | |   (44)  op(e3, all_56_25) = e3
% 244.62/51.04  | | | 
% 244.62/51.04  | | | BETA: splitting (21) gives:
% 244.62/51.04  | | | 
% 244.62/51.04  | | | Case 1:
% 244.62/51.04  | | | | 
% 244.62/51.05  | | | |   (45)   ~ (all_50_0 = e1) & op(all_50_1, e3) = all_50_0 & op(e3, e0) =
% 244.62/51.05  | | | |         all_50_1 & $i(all_50_0) & $i(all_50_1)
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | ALPHA: (45) implies:
% 244.62/51.05  | | | |   (46)  op(e3, e0) = all_50_1
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | REF_CLOSE: (1), (2), (3), (11), (16), (17), (19), (20), (22), (27),
% 244.62/51.05  | | | |            (31), (32), (35), (39), (43), (44), (46) are inconsistent by
% 244.62/51.05  | | | |            sub-proof #1812.
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | Case 2:
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | |   (47)   ~ (all_50_1 = e2) & op(e3, e0) = all_50_1 & $i(all_50_1)
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | ALPHA: (47) implies:
% 244.62/51.05  | | | |   (48)  op(e3, e0) = all_50_1
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | REF_CLOSE: (1), (2), (3), (11), (16), (17), (19), (20), (22), (27),
% 244.62/51.05  | | | |            (31), (32), (35), (39), (43), (44), (48) are inconsistent by
% 244.62/51.05  | | | |            sub-proof #1812.
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | End of split
% 244.62/51.05  | | | 
% 244.62/51.05  | | Case 2:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (49)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 244.62/51.05  | | |         $i(all_56_27)
% 244.62/51.05  | | | 
% 244.62/51.05  | | | ALPHA: (49) implies:
% 244.62/51.05  | | |   (50)  op(e2, e0) = all_56_27
% 244.62/51.05  | | |   (51)  op(e2, all_56_27) = e2
% 244.62/51.05  | | | 
% 244.62/51.05  | | | BETA: splitting (30) gives:
% 244.62/51.05  | | | 
% 244.62/51.05  | | | Case 1:
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | |   (52)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 244.62/51.05  | | | |         all_34_1 & $i(all_34_0) & $i(all_34_1)
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | ALPHA: (52) implies:
% 244.62/51.05  | | | |   (53)   ~ (all_34_0 = e3)
% 244.62/51.05  | | | |   (54)  op(e0, e1) = all_34_1
% 244.62/51.05  | | | |   (55)  op(all_34_1, e0) = all_34_0
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | REF_CLOSE: (7), (19), (25), (31), (53), (54), (55) are inconsistent by
% 244.62/51.05  | | | |            sub-proof #2250.
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | Case 2:
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | |   (56)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | ALPHA: (56) implies:
% 244.62/51.05  | | | |   (57)   ~ (all_34_1 = e2)
% 244.62/51.05  | | | |   (58)  op(e0, e1) = all_34_1
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | BETA: splitting (2) gives:
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | Case 1:
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | |   (59)  all_54_1 = e2
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | | COMBINE_EQS: (27), (59) imply:
% 244.62/51.05  | | | | |   (60)  all_52_4 = e2
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | | SIMP: (60) implies:
% 244.62/51.05  | | | | |   (61)  all_52_4 = e2
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | | REDUCE: (35), (61) imply:
% 244.62/51.05  | | | | |   (62)   ~ (e2 = e1)
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | | REDUCE: (39), (61) imply:
% 244.62/51.05  | | | | |   (63)   ~ (e2 = e0)
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | | REDUCE: (28), (61) imply:
% 244.62/51.05  | | | | |   (64)  op(e3, e2) = e2
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | | GROUND_INST: instantiating (31) with e3, all_34_1, e1, e0, simplifying
% 244.62/51.05  | | | | |              with (7), (58) gives:
% 244.62/51.05  | | | | |   (65)  all_34_1 = e3
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | | GROUND_INST: instantiating (31) with e2, all_56_27, e0, e2,
% 244.62/51.05  | | | | |              simplifying with (14), (50) gives:
% 244.62/51.05  | | | | |   (66)  all_56_27 = e2
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | | REDUCE: (57), (65) imply:
% 244.62/51.05  | | | | |   (67)   ~ (e3 = e2)
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | | REDUCE: (51), (66) imply:
% 244.62/51.05  | | | | |   (68)  op(e2, e2) = e2
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | | REF_CLOSE: (3), (8), (9), (10), (12), (24), (29), (31), (34), (36),
% 244.62/51.05  | | | | |            (37), (62), (63), (64), (67), (68) are inconsistent by
% 244.62/51.05  | | | | |            sub-proof #1809.
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | Case 2:
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | |   (69)  all_54_1 = e1 | all_54_1 = e0
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | | REF_CLOSE: (27), (35), (39), (69) are inconsistent by sub-proof #2049.
% 244.62/51.05  | | | | | 
% 244.62/51.05  | | | | End of split
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | End of split
% 244.62/51.05  | | | 
% 244.62/51.05  | | End of split
% 244.62/51.05  | | 
% 244.62/51.05  | Case 2:
% 244.62/51.05  | | 
% 244.62/51.05  | |   (70)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 244.62/51.05  | |           $i(all_56_29)) | (all_56_30 = e0 & op(e0, all_56_31) = e0)
% 244.62/51.05  | | 
% 244.62/51.05  | | BETA: splitting (70) gives:
% 244.62/51.05  | | 
% 244.62/51.05  | | Case 1:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (71)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 244.62/51.05  | | |         $i(all_56_29)
% 244.62/51.05  | | | 
% 244.62/51.05  | | | ALPHA: (71) implies:
% 244.62/51.05  | | |   (72)  op(e1, e0) = all_56_29
% 244.62/51.05  | | |   (73)  op(e1, all_56_29) = e1
% 244.62/51.05  | | | 
% 244.62/51.05  | | | BETA: splitting (2) gives:
% 244.62/51.05  | | | 
% 244.62/51.05  | | | Case 1:
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | |   (74)  all_54_1 = e2
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | COMBINE_EQS: (27), (74) imply:
% 244.62/51.05  | | | |   (75)  all_52_4 = e2
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | SIMP: (75) implies:
% 244.62/51.05  | | | |   (76)  all_52_4 = e2
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | REDUCE: (39), (76) imply:
% 244.62/51.05  | | | |   (77)   ~ (e2 = e0)
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | GROUND_INST: instantiating (31) with e0, all_56_29, e0, e1, simplifying
% 244.62/51.05  | | | |              with (4), (72) gives:
% 244.62/51.05  | | | |   (78)  all_56_29 = e0
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | GROUND_INST: instantiating (31) with all_30_1, all_56_19, e1, e2,
% 244.62/51.05  | | | |              simplifying with (33), (40) gives:
% 244.62/51.05  | | | |   (79)  all_56_19 = all_30_1
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | GROUND_INST: instantiating (31) with e0, all_56_19, e1, e2, simplifying
% 244.62/51.05  | | | |              with (26), (33) gives:
% 244.62/51.05  | | | |   (80)  all_56_19 = e0
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | COMBINE_EQS: (79), (80) imply:
% 244.62/51.05  | | | |   (81)  all_30_1 = e0
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | REDUCE: (73), (78) imply:
% 244.62/51.05  | | | |   (82)  op(e1, e0) = e1
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | REF_CLOSE: (3), (6), (14), (18), (31), (37), (77), (82) are inconsistent
% 244.62/51.05  | | | |            by sub-proof #2101.
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | Case 2:
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | |   (83)  all_54_1 = e1 | all_54_1 = e0
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | | REF_CLOSE: (27), (35), (39), (83) are inconsistent by sub-proof #2049.
% 244.62/51.05  | | | | 
% 244.62/51.05  | | | End of split
% 244.62/51.05  | | | 
% 244.62/51.05  | | Case 2:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (84)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 244.62/51.05  | | | 
% 244.62/51.05  | | | ALPHA: (84) implies:
% 244.62/51.05  | | |   (85)  op(e0, all_56_31) = e0
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REDUCE: (15), (85) imply:
% 244.62/51.05  | | |   (86)  op(e0, e1) = e0
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REF_CLOSE: (5), (23), (31), (86) are inconsistent by sub-proof #1911.
% 244.62/51.05  | | | 
% 244.62/51.05  | | End of split
% 244.62/51.05  | | 
% 244.62/51.05  | End of split
% 244.62/51.05  | 
% 244.62/51.05  End of proof
% 244.62/51.05  
% 244.62/51.05  Sub-proof #1809 shows that the following formulas are inconsistent:
% 244.62/51.05  ----------------------------------------------------------------
% 244.62/51.05    (1)   ~ (e3 = e0)
% 244.62/51.05    (2)   ~ (e2 = e0)
% 244.62/51.05    (3)  op(e1, e2) = all_52_6
% 244.62/51.05    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.62/51.05         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.62/51.05    (5)   ~ (all_52_7 = e3)
% 244.62/51.05    (6)   ~ (e3 = e1)
% 244.62/51.05    (7)  op(e3, e2) = e2
% 244.62/51.05    (8)   ~ (e3 = e2)
% 244.62/51.05    (9)  op(e0, e2) = all_52_7
% 244.62/51.05    (10)  all_58_1 = e2
% 244.62/51.05    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.05    (12)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.62/51.05          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.62/51.05    (13)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.62/51.05          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.62/51.05    (14)   ~ (e1 = e0)
% 244.62/51.05    (15)  op(e2, e2) = e2
% 244.62/51.05    (16)   ~ (e2 = e1)
% 244.62/51.05  
% 244.62/51.05  Begin of proof
% 244.62/51.05  | 
% 244.62/51.05  | BETA: splitting (13) gives:
% 244.62/51.05  | 
% 244.62/51.05  | Case 1:
% 244.62/51.05  | | 
% 244.62/51.05  | |   (17)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 244.62/51.05  | |           e3)
% 244.62/51.05  | | 
% 244.62/51.05  | | REF_CLOSE: (8), (10), (11), (15), (17) are inconsistent by sub-proof #2139.
% 244.62/51.05  | | 
% 244.62/51.05  | Case 2:
% 244.62/51.05  | | 
% 244.62/51.05  | |   (18)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.62/51.05  | |           e3)
% 244.62/51.05  | | 
% 244.62/51.05  | | BETA: splitting (18) gives:
% 244.62/51.05  | | 
% 244.62/51.05  | | Case 1:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (19)  all_58_7 = e3 & op(e1, e2) = e3
% 244.62/51.05  | | | 
% 244.62/51.05  | | | ALPHA: (19) implies:
% 244.62/51.05  | | |   (20)  all_58_7 = e3
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (13),
% 244.62/51.05  | | |            (14), (15), (16), (20) are inconsistent by sub-proof #1810.
% 244.62/51.05  | | | 
% 244.62/51.05  | | Case 2:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (21)  all_58_13 = e3 & op(e0, e2) = e3
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REF_CLOSE: (5), (9), (11), (21) are inconsistent by sub-proof #1919.
% 244.62/51.05  | | | 
% 244.62/51.05  | | End of split
% 244.62/51.05  | | 
% 244.62/51.05  | End of split
% 244.62/51.05  | 
% 244.62/51.05  End of proof
% 244.62/51.05  
% 244.62/51.05  Sub-proof #1810 shows that the following formulas are inconsistent:
% 244.62/51.05  ----------------------------------------------------------------
% 244.62/51.05    (1)   ~ (e3 = e0)
% 244.62/51.05    (2)   ~ (e2 = e0)
% 244.62/51.05    (3)  op(e1, e2) = all_52_6
% 244.62/51.05    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.62/51.05         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.62/51.05    (5)   ~ (e3 = e1)
% 244.62/51.05    (6)  op(e3, e2) = e2
% 244.62/51.05    (7)   ~ (e3 = e2)
% 244.62/51.05    (8)  all_58_7 = e3
% 244.62/51.05    (9)  all_58_1 = e2
% 244.62/51.05    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.05    (11)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.62/51.05          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.62/51.05    (12)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.62/51.05          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.62/51.05    (13)   ~ (e1 = e0)
% 244.62/51.05    (14)  op(e2, e2) = e2
% 244.62/51.05    (15)   ~ (e2 = e1)
% 244.62/51.05  
% 244.62/51.05  Begin of proof
% 244.62/51.05  | 
% 244.62/51.05  | BETA: splitting (4) gives:
% 244.62/51.05  | 
% 244.62/51.05  | Case 1:
% 244.62/51.05  | | 
% 244.62/51.05  | |   (16)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 244.62/51.05  | |           e0)
% 244.62/51.05  | | 
% 244.62/51.05  | | BETA: splitting (16) gives:
% 244.62/51.05  | | 
% 244.62/51.05  | | Case 1:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (17)  all_58_1 = e0 & op(e3, e2) = e0
% 244.62/51.05  | | | 
% 244.62/51.05  | | | ALPHA: (17) implies:
% 244.62/51.05  | | |   (18)  op(e3, e2) = e0
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REF_CLOSE: (2), (6), (10), (18) are inconsistent by sub-proof #2026.
% 244.62/51.05  | | | 
% 244.62/51.05  | | Case 2:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (19)  all_58_3 = e0 & op(e2, e2) = e0
% 244.62/51.05  | | | 
% 244.62/51.05  | | | ALPHA: (19) implies:
% 244.62/51.05  | | |   (20)  op(e2, e2) = e0
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REF_CLOSE: (2), (10), (14), (20) are inconsistent by sub-proof #2137.
% 244.62/51.05  | | | 
% 244.62/51.05  | | End of split
% 244.62/51.05  | | 
% 244.62/51.05  | Case 2:
% 244.62/51.05  | | 
% 244.62/51.05  | |   (21)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.62/51.05  | |           e0)
% 244.62/51.05  | | 
% 244.62/51.05  | | BETA: splitting (21) gives:
% 244.62/51.05  | | 
% 244.62/51.05  | | Case 1:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (22)  all_58_7 = e0 & op(e1, e2) = e0
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REF_CLOSE: (1), (8), (22) are inconsistent by sub-proof #1837.
% 244.62/51.05  | | | 
% 244.62/51.05  | | Case 2:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (23)  all_58_13 = e0 & op(e0, e2) = e0
% 244.62/51.05  | | | 
% 244.62/51.05  | | | ALPHA: (23) implies:
% 244.62/51.05  | | |   (24)  op(e0, e2) = e0
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13),
% 244.62/51.05  | | |            (14), (15), (24) are inconsistent by sub-proof #1811.
% 244.62/51.05  | | | 
% 244.62/51.05  | | End of split
% 244.62/51.05  | | 
% 244.62/51.05  | End of split
% 244.62/51.05  | 
% 244.62/51.05  End of proof
% 244.62/51.05  
% 244.62/51.05  Sub-proof #1811 shows that the following formulas are inconsistent:
% 244.62/51.05  ----------------------------------------------------------------
% 244.62/51.05    (1)   ~ (e3 = e0)
% 244.62/51.05    (2)   ~ (e2 = e0)
% 244.62/51.05    (3)  op(e1, e2) = all_52_6
% 244.62/51.05    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.62/51.05         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.62/51.05    (5)   ~ (e3 = e1)
% 244.62/51.05    (6)   ~ (e3 = e2)
% 244.62/51.05    (7)  op(e0, e2) = e0
% 244.62/51.05    (8)  all_58_1 = e2
% 244.62/51.05    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.05    (10)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.62/51.05          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.62/51.05    (11)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.62/51.05          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.62/51.05    (12)   ~ (e1 = e0)
% 244.62/51.05    (13)  op(e2, e2) = e2
% 244.62/51.05    (14)   ~ (e2 = e1)
% 244.62/51.05  
% 244.62/51.05  Begin of proof
% 244.62/51.05  | 
% 244.62/51.05  | BETA: splitting (10) gives:
% 244.62/51.05  | 
% 244.62/51.05  | Case 1:
% 244.62/51.05  | | 
% 244.62/51.05  | |   (15)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 244.62/51.05  | |           e1)
% 244.62/51.05  | | 
% 244.62/51.05  | | BETA: splitting (15) gives:
% 244.62/51.05  | | 
% 244.62/51.05  | | Case 1:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (16)  all_58_1 = e1 & op(e3, e2) = e1
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REF_CLOSE: (8), (14), (16) are inconsistent by sub-proof #2185.
% 244.62/51.05  | | | 
% 244.62/51.05  | | Case 2:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (17)  all_58_3 = e1 & op(e2, e2) = e1
% 244.62/51.05  | | | 
% 244.62/51.05  | | | ALPHA: (17) implies:
% 244.62/51.05  | | |   (18)  op(e2, e2) = e1
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REF_CLOSE: (9), (13), (14), (18) are inconsistent by sub-proof #2235.
% 244.62/51.05  | | | 
% 244.62/51.05  | | End of split
% 244.62/51.05  | | 
% 244.62/51.05  | Case 2:
% 244.62/51.05  | | 
% 244.62/51.05  | |   (19)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 244.62/51.05  | |           e1)
% 244.62/51.05  | | 
% 244.62/51.05  | | BETA: splitting (19) gives:
% 244.62/51.05  | | 
% 244.62/51.05  | | Case 1:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (20)  all_58_7 = e1 & op(e1, e2) = e1
% 244.62/51.05  | | | 
% 244.62/51.05  | | | ALPHA: (20) implies:
% 244.62/51.05  | | |   (21)  all_58_7 = e1
% 244.62/51.05  | | |   (22)  op(e1, e2) = e1
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), (21),
% 244.62/51.05  | | |            (22) are inconsistent by sub-proof #2135.
% 244.62/51.05  | | | 
% 244.62/51.05  | | Case 2:
% 244.62/51.05  | | | 
% 244.62/51.05  | | |   (23)  all_58_13 = e1 & op(e0, e2) = e1
% 244.62/51.05  | | | 
% 244.62/51.05  | | | ALPHA: (23) implies:
% 244.62/51.05  | | |   (24)  op(e0, e2) = e1
% 244.62/51.05  | | | 
% 244.62/51.05  | | | REF_CLOSE: (7), (9), (12), (24) are inconsistent by sub-proof #1872.
% 244.62/51.05  | | | 
% 244.62/51.05  | | End of split
% 244.62/51.05  | | 
% 244.62/51.05  | End of split
% 244.62/51.05  | 
% 244.62/51.05  End of proof
% 244.62/51.05  
% 244.62/51.05  Sub-proof #1812 shows that the following formulas are inconsistent:
% 244.62/51.05  ----------------------------------------------------------------
% 244.62/51.05    (1)   ~ (all_52_3 = e0)
% 244.62/51.05    (2)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.62/51.05    (3)   ~ (e3 = e0)
% 244.62/51.05    (4)  op(e0, e3) = all_52_3
% 244.62/51.05    (5)  op(e3, all_56_25) = e3
% 244.62/51.05    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.62/51.05         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.62/51.05    (7)   ~ (all_52_1 = e0)
% 244.62/51.05    (8)  op(e3, e0) = e3
% 244.62/51.05    (9)  op(e2, e3) = all_52_1
% 244.62/51.05    (10)  op(e3, e0) = all_50_1
% 244.62/51.05    (11)  op(e3, e0) = all_56_25
% 244.62/51.05    (12)   ~ (all_52_2 = e0)
% 244.62/51.05    (13)  all_54_1 = all_52_4
% 244.62/51.05    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.05    (15)  op(e1, e3) = all_52_2
% 244.62/51.05    (16)   ~ (all_52_4 = e1)
% 244.62/51.05    (17)   ~ (all_52_4 = e0)
% 244.62/51.05  
% 244.62/51.05  Begin of proof
% 244.62/51.05  | 
% 244.62/51.05  | BETA: splitting (2) gives:
% 244.62/51.05  | 
% 244.62/51.05  | Case 1:
% 244.62/51.05  | | 
% 244.62/51.05  | | 
% 244.62/51.05  | | GROUND_INST: instantiating (14) with all_50_1, all_56_25, e0, e3,
% 244.62/51.05  | |              simplifying with (10), (11) gives:
% 244.62/51.05  | |   (18)  all_56_25 = all_50_1
% 244.62/51.05  | | 
% 244.62/51.05  | | GROUND_INST: instantiating (14) with e3, all_56_25, e0, e3, simplifying with
% 244.62/51.05  | |              (8), (11) gives:
% 244.62/51.05  | |   (19)  all_56_25 = e3
% 244.62/51.05  | | 
% 244.62/51.05  | | COMBINE_EQS: (18), (19) imply:
% 244.62/51.05  | |   (20)  all_50_1 = e3
% 244.62/51.05  | | 
% 244.62/51.05  | | REDUCE: (5), (19) imply:
% 244.62/51.05  | |   (21)  op(e3, e3) = e3
% 244.62/51.05  | | 
% 244.62/51.05  | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (12), (14), (15), (21) are
% 244.62/51.05  | |            inconsistent by sub-proof #1938.
% 244.62/51.05  | | 
% 244.62/51.05  | Case 2:
% 244.62/51.05  | | 
% 244.62/51.06  | |   (22)  all_54_1 = e1 | all_54_1 = e0
% 244.62/51.06  | | 
% 244.62/51.06  | | REF_CLOSE: (13), (16), (17), (22) are inconsistent by sub-proof #2049.
% 244.62/51.06  | | 
% 244.62/51.06  | End of split
% 244.62/51.06  | 
% 244.62/51.06  End of proof
% 244.62/51.06  
% 244.62/51.06  Sub-proof #1813 shows that the following formulas are inconsistent:
% 244.62/51.06  ----------------------------------------------------------------
% 244.62/51.06    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.62/51.06         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.62/51.06    (2)  all_58_12 = e2
% 244.62/51.06    (3)   ~ (all_52_7 = e3)
% 244.62/51.06    (4)   ~ (e3 = e1)
% 244.62/51.06    (5)  all_58_15 = e3 & op(e0, e0) = e3
% 244.62/51.06    (6)   ~ (e3 = e2)
% 244.62/51.06    (7)  all_58_15 = e1
% 244.62/51.06    (8)  op(e0, e2) = all_52_7
% 244.62/51.06    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.06    (10)  all_58_14 = e3
% 244.62/51.06  
% 244.62/51.06  Begin of proof
% 244.62/51.06  | 
% 244.62/51.06  | ALPHA: (5) implies:
% 244.62/51.06  |   (11)  all_58_15 = e3
% 244.62/51.06  | 
% 244.62/51.06  | COMBINE_EQS: (7), (11) imply:
% 244.62/51.06  |   (12)  e3 = e1
% 244.62/51.06  | 
% 244.62/51.06  | COMBINE_EQS: (10), (12) imply:
% 244.62/51.06  |   (13)  all_58_14 = e1
% 244.62/51.06  | 
% 244.62/51.06  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (13) are inconsistent by
% 244.62/51.06  |            sub-proof #1814.
% 244.62/51.06  | 
% 244.62/51.06  End of proof
% 244.62/51.06  
% 244.62/51.06  Sub-proof #1814 shows that the following formulas are inconsistent:
% 244.62/51.06  ----------------------------------------------------------------
% 244.62/51.06    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.62/51.06         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.62/51.06    (2)  all_58_12 = e2
% 244.62/51.06    (3)   ~ (all_52_7 = e3)
% 244.62/51.06    (4)   ~ (e3 = e1)
% 244.62/51.06    (5)   ~ (e3 = e2)
% 244.62/51.06    (6)  all_58_15 = e1
% 244.62/51.06    (7)  op(e0, e2) = all_52_7
% 244.62/51.06    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.06    (9)  all_58_14 = e1
% 244.62/51.06  
% 244.62/51.06  Begin of proof
% 244.62/51.06  | 
% 244.62/51.06  | BETA: splitting (1) gives:
% 244.62/51.06  | 
% 244.62/51.06  | Case 1:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (10)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.62/51.06  | |           e3)
% 244.62/51.06  | | 
% 244.62/51.06  | | BETA: splitting (10) gives:
% 244.62/51.06  | | 
% 244.62/51.06  | | Case 1:
% 244.62/51.06  | | | 
% 244.62/51.06  | | |   (11)  all_58_12 = e3 & op(e0, e3) = e3
% 244.62/51.06  | | | 
% 244.62/51.06  | | | REF_CLOSE: (2), (5), (11) are inconsistent by sub-proof #2085.
% 244.62/51.06  | | | 
% 244.62/51.06  | | Case 2:
% 244.62/51.06  | | | 
% 244.62/51.06  | | |   (12)  all_58_13 = e3 & op(e0, e2) = e3
% 244.62/51.06  | | | 
% 244.62/51.06  | | | REF_CLOSE: (3), (7), (8), (12) are inconsistent by sub-proof #1919.
% 244.62/51.06  | | | 
% 244.62/51.06  | | End of split
% 244.62/51.06  | | 
% 244.62/51.06  | Case 2:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (13)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.62/51.06  | |           e3)
% 244.62/51.06  | | 
% 244.62/51.06  | | BETA: splitting (13) gives:
% 244.62/51.06  | | 
% 244.62/51.06  | | Case 1:
% 244.62/51.06  | | | 
% 244.62/51.06  | | |   (14)  all_58_14 = e3 & op(e0, e1) = e3
% 244.62/51.06  | | | 
% 244.62/51.06  | | | ALPHA: (14) implies:
% 244.62/51.06  | | |   (15)  all_58_14 = e3
% 244.62/51.06  | | | 
% 244.62/51.06  | | | REF_CLOSE: (4), (9), (15) are inconsistent by sub-proof #1844.
% 244.62/51.06  | | | 
% 244.62/51.06  | | Case 2:
% 244.62/51.06  | | | 
% 244.62/51.06  | | |   (16)  all_58_15 = e3 & op(e0, e0) = e3
% 244.62/51.06  | | | 
% 244.62/51.06  | | | ALPHA: (16) implies:
% 244.62/51.06  | | |   (17)  all_58_15 = e3
% 244.62/51.06  | | | 
% 244.62/51.06  | | | REF_CLOSE: (4), (6), (17) are inconsistent by sub-proof #2249.
% 244.62/51.06  | | | 
% 244.62/51.06  | | End of split
% 244.62/51.06  | | 
% 244.62/51.06  | End of split
% 244.62/51.06  | 
% 244.62/51.06  End of proof
% 244.62/51.06  
% 244.62/51.06  Sub-proof #1815 shows that the following formulas are inconsistent:
% 244.62/51.06  ----------------------------------------------------------------
% 244.62/51.06    (1)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.62/51.06    (2)  all_54_13 = all_52_7
% 244.62/51.06    (3)   ~ (all_52_7 = e3)
% 244.62/51.06    (4)  op(e0, e2) = e2
% 244.62/51.06    (5)   ~ (all_52_7 = e1)
% 244.62/51.06    (6)  op(e0, e2) = all_52_7
% 244.62/51.06    (7)  all_54_1 = all_52_4
% 244.62/51.06    (8)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.62/51.06    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.06    (10)   ~ (all_52_4 = e1)
% 244.62/51.06    (11)   ~ (all_52_4 = e0)
% 244.62/51.06    (12)   ~ (all_52_4 = all_52_7)
% 244.62/51.06  
% 244.62/51.06  Begin of proof
% 244.62/51.06  | 
% 244.62/51.06  | BETA: splitting (1) gives:
% 244.62/51.06  | 
% 244.62/51.06  | Case 1:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (13)  all_54_1 = e2
% 244.62/51.06  | | 
% 244.62/51.06  | | COMBINE_EQS: (7), (13) imply:
% 244.62/51.06  | |   (14)  all_52_4 = e2
% 244.62/51.06  | | 
% 244.62/51.06  | | SIMP: (14) implies:
% 244.62/51.06  | |   (15)  all_52_4 = e2
% 244.62/51.06  | | 
% 244.62/51.06  | | REDUCE: (12), (15) imply:
% 244.62/51.06  | |   (16)   ~ (all_52_7 = e2)
% 244.62/51.06  | | 
% 244.62/51.06  | | SIMP: (16) implies:
% 244.62/51.06  | |   (17)   ~ (all_52_7 = e2)
% 244.62/51.06  | | 
% 244.62/51.06  | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (17) are inconsistent by
% 244.62/51.06  | |            sub-proof #1816.
% 244.62/51.06  | | 
% 244.62/51.06  | Case 2:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (18)  all_54_1 = e1 | all_54_1 = e0
% 244.62/51.06  | | 
% 244.62/51.06  | | REF_CLOSE: (7), (10), (11), (18) are inconsistent by sub-proof #2049.
% 244.62/51.06  | | 
% 244.62/51.06  | End of split
% 244.62/51.06  | 
% 244.62/51.06  End of proof
% 244.62/51.06  
% 244.62/51.06  Sub-proof #1816 shows that the following formulas are inconsistent:
% 244.62/51.06  ----------------------------------------------------------------
% 244.62/51.06    (1)   ~ (all_52_7 = e2)
% 244.62/51.06    (2)  all_54_13 = all_52_7
% 244.62/51.06    (3)   ~ (all_52_7 = e3)
% 244.62/51.06    (4)  op(e0, e2) = e2
% 244.62/51.06    (5)   ~ (all_52_7 = e1)
% 244.62/51.06    (6)  op(e0, e2) = all_52_7
% 244.62/51.06    (7)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.62/51.06    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.06  
% 244.62/51.06  Begin of proof
% 244.62/51.06  | 
% 244.62/51.06  | BETA: splitting (7) gives:
% 244.62/51.06  | 
% 244.62/51.06  | Case 1:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (9)  all_54_13 = e3
% 244.62/51.06  | | 
% 244.62/51.06  | | COMBINE_EQS: (2), (9) imply:
% 244.62/51.06  | |   (10)  all_52_7 = e3
% 244.62/51.06  | | 
% 244.62/51.06  | | REDUCE: (3), (10) imply:
% 244.62/51.06  | |   (11)  $false
% 244.62/51.06  | | 
% 244.62/51.06  | | CLOSE: (11) is inconsistent.
% 244.62/51.06  | | 
% 244.62/51.06  | Case 2:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (12)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.62/51.06  | | 
% 244.62/51.06  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (12) are inconsistent by sub-proof
% 244.62/51.06  | |            #1817.
% 244.62/51.06  | | 
% 244.62/51.06  | End of split
% 244.62/51.06  | 
% 244.62/51.06  End of proof
% 244.62/51.06  
% 244.62/51.06  Sub-proof #1817 shows that the following formulas are inconsistent:
% 244.62/51.06  ----------------------------------------------------------------
% 244.62/51.06    (1)   ~ (all_52_7 = e2)
% 244.62/51.06    (2)  all_54_13 = all_52_7
% 244.62/51.06    (3)  op(e0, e2) = e2
% 244.62/51.06    (4)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.62/51.06    (5)   ~ (all_52_7 = e1)
% 244.62/51.06    (6)  op(e0, e2) = all_52_7
% 244.62/51.06    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.06  
% 244.62/51.06  Begin of proof
% 244.62/51.06  | 
% 244.62/51.06  | BETA: splitting (4) gives:
% 244.62/51.06  | 
% 244.62/51.06  | Case 1:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (8)  all_54_13 = e2
% 244.62/51.06  | | 
% 244.62/51.06  | | COMBINE_EQS: (2), (8) imply:
% 244.62/51.06  | |   (9)  all_52_7 = e2
% 244.62/51.06  | | 
% 244.62/51.06  | | REDUCE: (1), (9) imply:
% 244.62/51.06  | |   (10)  $false
% 244.62/51.06  | | 
% 244.62/51.06  | | CLOSE: (10) is inconsistent.
% 244.62/51.06  | | 
% 244.62/51.06  | Case 2:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (11)   ~ (all_54_13 = e2)
% 244.62/51.06  | |   (12)  all_54_13 = e1 | all_54_13 = e0
% 244.62/51.06  | | 
% 244.62/51.06  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (12) are inconsistent by sub-proof
% 244.62/51.06  | |            #1818.
% 244.62/51.06  | | 
% 244.62/51.06  | End of split
% 244.62/51.06  | 
% 244.62/51.06  End of proof
% 244.62/51.06  
% 244.62/51.06  Sub-proof #1818 shows that the following formulas are inconsistent:
% 244.62/51.06  ----------------------------------------------------------------
% 244.62/51.06    (1)   ~ (all_52_7 = e2)
% 244.62/51.06    (2)  all_54_13 = all_52_7
% 244.62/51.06    (3)  all_54_13 = e1 | all_54_13 = e0
% 244.62/51.06    (4)  op(e0, e2) = e2
% 244.62/51.06    (5)   ~ (all_52_7 = e1)
% 244.62/51.06    (6)  op(e0, e2) = all_52_7
% 244.62/51.06    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.06  
% 244.62/51.06  Begin of proof
% 244.62/51.06  | 
% 244.62/51.06  | BETA: splitting (3) gives:
% 244.62/51.06  | 
% 244.62/51.06  | Case 1:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (8)  all_54_13 = e1
% 244.62/51.06  | | 
% 244.62/51.06  | | COMBINE_EQS: (2), (8) imply:
% 244.62/51.06  | |   (9)  all_52_7 = e1
% 244.62/51.06  | | 
% 244.62/51.06  | | REDUCE: (5), (9) imply:
% 244.62/51.06  | |   (10)  $false
% 244.62/51.06  | | 
% 244.62/51.06  | | CLOSE: (10) is inconsistent.
% 244.62/51.06  | | 
% 244.62/51.06  | Case 2:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (11)  all_54_13 = e0
% 244.62/51.06  | | 
% 244.62/51.06  | | COMBINE_EQS: (2), (11) imply:
% 244.62/51.06  | |   (12)  all_52_7 = e0
% 244.62/51.06  | | 
% 244.62/51.06  | | REDUCE: (1), (12) imply:
% 244.62/51.06  | |   (13)   ~ (e2 = e0)
% 244.62/51.06  | | 
% 244.62/51.06  | | SIMP: (13) implies:
% 244.62/51.06  | |   (14)   ~ (e2 = e0)
% 244.62/51.06  | | 
% 244.62/51.06  | | REDUCE: (6), (12) imply:
% 244.62/51.06  | |   (15)  op(e0, e2) = e0
% 244.62/51.06  | | 
% 244.62/51.06  | | REF_CLOSE: (4), (7), (14), (15) are inconsistent by sub-proof #2132.
% 244.62/51.06  | | 
% 244.62/51.06  | End of split
% 244.62/51.06  | 
% 244.62/51.06  End of proof
% 244.62/51.06  
% 244.62/51.06  Sub-proof #1819 shows that the following formulas are inconsistent:
% 244.62/51.06  ----------------------------------------------------------------
% 244.62/51.06    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.62/51.06             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.62/51.06           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 244.62/51.06           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.62/51.06           op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.62/51.06    (2)   ~ (e2 = e0)
% 244.62/51.06    (3)  op(e0, e3) = all_52_3
% 244.62/51.06    (4)   ~ (all_52_3 = e3)
% 244.62/51.06    (5)  op(e0, e3) = e2
% 244.62/51.06    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.06  
% 244.62/51.06  Begin of proof
% 244.62/51.06  | 
% 244.62/51.06  | BETA: splitting (1) gives:
% 244.62/51.06  | 
% 244.62/51.06  | Case 1:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (7)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.62/51.06  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.62/51.06  | |        op(e0, e3) = e3
% 244.62/51.06  | | 
% 244.62/51.06  | | ALPHA: (7) implies:
% 244.62/51.06  | |   (8)  op(e0, e3) = e3
% 244.62/51.06  | | 
% 244.62/51.06  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #2332.
% 244.62/51.06  | | 
% 244.62/51.06  | Case 2:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (9)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.62/51.06  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 244.62/51.06  | |        op(e0, e3) = e0
% 244.62/51.06  | | 
% 244.62/51.06  | | ALPHA: (9) implies:
% 244.62/51.06  | |   (10)  op(e0, e3) = e0
% 244.62/51.06  | | 
% 244.62/51.06  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1896.
% 244.62/51.06  | | 
% 244.62/51.06  | End of split
% 244.62/51.06  | 
% 244.62/51.06  End of proof
% 244.62/51.06  
% 244.62/51.06  Sub-proof #1820 shows that the following formulas are inconsistent:
% 244.62/51.06  ----------------------------------------------------------------
% 244.62/51.06    (1)  op(e3, e1) = all_56_17
% 244.62/51.06    (2)   ~ (e3 = e0)
% 244.62/51.06    (3)   ~ (all_52_7 = e2)
% 244.62/51.06    (4)  all_54_13 = all_52_7
% 244.62/51.06    (5)   ~ (all_52_7 = e3)
% 244.62/51.06    (6)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.62/51.06    (7)  op(e3, all_56_17) = e3
% 244.62/51.06    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.06    (9)  op(e3, e1) = e3
% 244.62/51.06    (10)  op(e3, e3) = e0
% 244.62/51.06  
% 244.62/51.06  Begin of proof
% 244.62/51.06  | 
% 244.62/51.06  | BETA: splitting (6) gives:
% 244.62/51.06  | 
% 244.62/51.06  | Case 1:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (11)  all_54_13 = e3
% 244.62/51.06  | | 
% 244.62/51.06  | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #2010.
% 244.62/51.06  | | 
% 244.62/51.06  | Case 2:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (12)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.62/51.06  | | 
% 244.62/51.06  | | BETA: splitting (12) gives:
% 244.62/51.06  | | 
% 244.62/51.06  | | Case 1:
% 244.62/51.06  | | | 
% 244.62/51.06  | | |   (13)  all_54_13 = e2
% 244.62/51.06  | | | 
% 244.62/51.06  | | | COMBINE_EQS: (4), (13) imply:
% 244.62/51.06  | | |   (14)  all_52_7 = e2
% 244.62/51.06  | | | 
% 244.62/51.06  | | | REDUCE: (3), (14) imply:
% 244.62/51.06  | | |   (15)  $false
% 244.62/51.06  | | | 
% 244.62/51.06  | | | CLOSE: (15) is inconsistent.
% 244.62/51.06  | | | 
% 244.62/51.06  | | Case 2:
% 244.62/51.06  | | | 
% 244.62/51.06  | | | 
% 244.62/51.06  | | | GROUND_INST: instantiating (8) with e3, all_56_17, e1, e3, simplifying
% 244.62/51.06  | | |              with (1), (9) gives:
% 244.62/51.06  | | |   (16)  all_56_17 = e3
% 244.62/51.06  | | | 
% 244.62/51.06  | | | REDUCE: (7), (16) imply:
% 244.62/51.06  | | |   (17)  op(e3, e3) = e3
% 244.62/51.06  | | | 
% 244.62/51.06  | | | REF_CLOSE: (2), (8), (10), (17) are inconsistent by sub-proof #1940.
% 244.62/51.06  | | | 
% 244.62/51.06  | | End of split
% 244.62/51.06  | | 
% 244.62/51.06  | End of split
% 244.62/51.06  | 
% 244.62/51.06  End of proof
% 244.62/51.06  
% 244.62/51.06  Sub-proof #1821 shows that the following formulas are inconsistent:
% 244.62/51.06  ----------------------------------------------------------------
% 244.62/51.06    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 244.62/51.06    (2)   ~ (e3 = e1)
% 244.62/51.06    (3)  op(e2, e1) = all_52_9
% 244.62/51.06    (4)  op(e3, e1) = e1
% 244.62/51.06    (5)   ~ (all_52_9 = e3)
% 244.62/51.06    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.06  
% 244.62/51.06  Begin of proof
% 244.62/51.06  | 
% 244.62/51.06  | BETA: splitting (1) gives:
% 244.62/51.06  | 
% 244.62/51.06  | Case 1:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (7)  all_58_4 = e3 & op(e3, e1) = e3
% 244.62/51.06  | | 
% 244.62/51.06  | | ALPHA: (7) implies:
% 244.62/51.06  | |   (8)  op(e3, e1) = e3
% 244.62/51.06  | | 
% 244.62/51.06  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1823.
% 244.62/51.06  | | 
% 244.62/51.06  | Case 2:
% 244.62/51.06  | | 
% 244.62/51.06  | |   (9)  all_58_5 = e3 & op(e2, e1) = e3
% 244.62/51.06  | | 
% 244.62/51.06  | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #1822.
% 244.62/51.06  | | 
% 244.62/51.06  | End of split
% 244.62/51.06  | 
% 244.62/51.06  End of proof
% 244.62/51.06  
% 244.62/51.06  Sub-proof #1822 shows that the following formulas are inconsistent:
% 244.62/51.07  ----------------------------------------------------------------
% 244.62/51.07    (1)  all_58_5 = e3 & op(e2, e1) = e3
% 244.62/51.07    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.07    (3)  op(e2, e1) = all_52_9
% 244.62/51.07    (4)   ~ (all_52_9 = e3)
% 244.62/51.07  
% 244.62/51.07  Begin of proof
% 244.62/51.07  | 
% 244.62/51.07  | ALPHA: (1) implies:
% 244.62/51.07  |   (5)  op(e2, e1) = e3
% 244.62/51.07  | 
% 244.62/51.07  | GROUND_INST: instantiating (2) with all_52_9, e3, e1, e2, simplifying with
% 244.62/51.07  |              (3), (5) gives:
% 244.62/51.07  |   (6)  all_52_9 = e3
% 244.62/51.07  | 
% 244.62/51.07  | REDUCE: (4), (6) imply:
% 244.62/51.07  |   (7)  $false
% 244.62/51.07  | 
% 244.62/51.07  | CLOSE: (7) is inconsistent.
% 244.62/51.07  | 
% 244.62/51.07  End of proof
% 244.62/51.07  
% 244.62/51.07  Sub-proof #1823 shows that the following formulas are inconsistent:
% 244.62/51.07  ----------------------------------------------------------------
% 244.62/51.07    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.07    (2)  op(e3, e1) = e3
% 244.62/51.07    (3)  op(e3, e1) = e1
% 244.62/51.07    (4)   ~ (e3 = e1)
% 244.62/51.07  
% 244.62/51.07  Begin of proof
% 244.62/51.07  | 
% 244.62/51.07  | GROUND_INST: instantiating (1) with e3, e1, e1, e3, simplifying with (2), (3)
% 244.62/51.07  |              gives:
% 244.62/51.07  |   (5)  e3 = e1
% 244.62/51.07  | 
% 244.62/51.07  | REDUCE: (4), (5) imply:
% 244.62/51.07  |   (6)  $false
% 244.62/51.07  | 
% 244.62/51.07  | CLOSE: (6) is inconsistent.
% 244.62/51.07  | 
% 244.62/51.07  End of proof
% 244.62/51.07  
% 244.62/51.07  Sub-proof #1824 shows that the following formulas are inconsistent:
% 244.62/51.07  ----------------------------------------------------------------
% 244.62/51.07    (1)   ~ (e2 = e0)
% 244.62/51.07    (2)  op(e2, e3) = e3
% 244.62/51.07    (3)   ~ (e3 = e2)
% 244.62/51.07    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 244.62/51.07    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.07    (6)  op(e3, e3) = e0
% 244.62/51.07  
% 244.62/51.07  Begin of proof
% 244.62/51.07  | 
% 244.62/51.07  | BETA: splitting (4) gives:
% 244.62/51.07  | 
% 244.62/51.07  | Case 1:
% 244.62/51.07  | | 
% 244.62/51.07  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 244.62/51.07  | | 
% 244.62/51.07  | | ALPHA: (7) implies:
% 244.62/51.07  | |   (8)  op(e3, e3) = e2
% 244.62/51.07  | | 
% 244.62/51.07  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2188.
% 244.62/51.07  | | 
% 244.62/51.07  | Case 2:
% 244.62/51.07  | | 
% 244.62/51.07  | |   (9)  all_58_2 = e2 & op(e2, e3) = e2
% 244.62/51.07  | | 
% 244.62/51.07  | | ALPHA: (9) implies:
% 244.62/51.07  | |   (10)  op(e2, e3) = e2
% 244.62/51.07  | | 
% 244.62/51.07  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #1897.
% 244.62/51.07  | | 
% 244.62/51.07  | End of split
% 244.62/51.07  | 
% 244.62/51.07  End of proof
% 244.62/51.07  
% 244.62/51.07  Sub-proof #1825 shows that the following formulas are inconsistent:
% 244.62/51.07  ----------------------------------------------------------------
% 244.62/51.07    (1)  all_54_6 = all_52_9
% 244.62/51.07    (2)  all_54_6 = e3
% 244.62/51.07    (3)   ~ (all_52_9 = e3)
% 244.62/51.07  
% 244.62/51.07  Begin of proof
% 244.62/51.07  | 
% 244.62/51.07  | COMBINE_EQS: (1), (2) imply:
% 244.62/51.07  |   (4)  all_52_9 = e3
% 244.62/51.07  | 
% 244.62/51.07  | SIMP: (4) implies:
% 244.62/51.07  |   (5)  all_52_9 = e3
% 244.62/51.07  | 
% 244.62/51.07  | REDUCE: (3), (5) imply:
% 244.62/51.07  |   (6)  $false
% 244.62/51.07  | 
% 244.62/51.07  | CLOSE: (6) is inconsistent.
% 244.62/51.07  | 
% 244.62/51.07  End of proof
% 244.62/51.07  
% 244.62/51.07  Sub-proof #1826 shows that the following formulas are inconsistent:
% 244.62/51.07  ----------------------------------------------------------------
% 244.62/51.07    (1)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 244.62/51.07    (2)  op(e3, e2) = all_52_4
% 244.62/51.07    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.62/51.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.62/51.07    (4)   ~ (all_52_4 = e1)
% 244.62/51.07    (5)   ~ (e1 = e0)
% 244.62/51.07    (6)  op(e3, e3) = e0
% 244.62/51.07  
% 244.62/51.07  Begin of proof
% 244.62/51.07  | 
% 244.62/51.07  | BETA: splitting (1) gives:
% 244.62/51.07  | 
% 244.62/51.07  | Case 1:
% 244.62/51.07  | | 
% 244.62/51.07  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 244.66/51.07  | | 
% 244.66/51.07  | | ALPHA: (7) implies:
% 244.66/51.07  | |   (8)  op(e3, e3) = e1
% 244.66/51.07  | | 
% 244.66/51.07  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #1828.
% 244.66/51.07  | | 
% 244.66/51.07  | Case 2:
% 244.66/51.07  | | 
% 244.66/51.07  | |   (9)  all_58_1 = e1 & op(e3, e2) = e1
% 244.66/51.07  | | 
% 244.66/51.07  | | ALPHA: (9) implies:
% 244.66/51.07  | |   (10)  op(e3, e2) = e1
% 244.66/51.07  | | 
% 244.66/51.07  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #2228.
% 244.66/51.07  | | 
% 244.66/51.07  | End of split
% 244.66/51.07  | 
% 244.66/51.07  End of proof
% 244.66/51.07  
% 244.66/51.07  Sub-proof #1827 shows that the following formulas are inconsistent:
% 244.66/51.07  ----------------------------------------------------------------
% 244.66/51.07    (1)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 244.66/51.07    (2)  op(e2, e3) = all_52_1
% 244.66/51.07    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.07    (4)   ~ (e1 = e0)
% 244.66/51.07    (5)  op(e3, e3) = e0
% 244.66/51.07    (6)   ~ (all_52_1 = e1)
% 244.66/51.07  
% 244.66/51.07  Begin of proof
% 244.66/51.07  | 
% 244.66/51.07  | BETA: splitting (1) gives:
% 244.66/51.07  | 
% 244.66/51.07  | Case 1:
% 244.66/51.07  | | 
% 244.66/51.07  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 244.66/51.07  | | 
% 244.66/51.07  | | ALPHA: (7) implies:
% 244.66/51.07  | |   (8)  op(e3, e3) = e1
% 244.66/51.07  | | 
% 244.66/51.07  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1828.
% 244.66/51.07  | | 
% 244.66/51.07  | Case 2:
% 244.66/51.07  | | 
% 244.66/51.07  | |   (9)  all_58_2 = e1 & op(e2, e3) = e1
% 244.66/51.07  | | 
% 244.66/51.07  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #2229.
% 244.66/51.07  | | 
% 244.66/51.07  | End of split
% 244.66/51.07  | 
% 244.66/51.07  End of proof
% 244.66/51.07  
% 244.66/51.07  Sub-proof #1828 shows that the following formulas are inconsistent:
% 244.66/51.07  ----------------------------------------------------------------
% 244.66/51.07    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.07    (2)  op(e3, e3) = e1
% 244.66/51.07    (3)  op(e3, e3) = e0
% 244.66/51.07    (4)   ~ (e1 = e0)
% 244.66/51.07  
% 244.66/51.07  Begin of proof
% 244.66/51.07  | 
% 244.66/51.07  | GROUND_INST: instantiating (1) with e0, e1, e3, e3, simplifying with (2), (3)
% 244.66/51.07  |              gives:
% 244.66/51.07  |   (5)  e1 = e0
% 244.66/51.07  | 
% 244.66/51.07  | REDUCE: (4), (5) imply:
% 244.66/51.07  |   (6)  $false
% 244.66/51.07  | 
% 244.66/51.07  | CLOSE: (6) is inconsistent.
% 244.66/51.07  | 
% 244.66/51.07  End of proof
% 244.66/51.07  
% 244.66/51.07  Sub-proof #1829 shows that the following formulas are inconsistent:
% 244.66/51.07  ----------------------------------------------------------------
% 244.66/51.07    (1)   ~ (all_52_3 = e0)
% 244.66/51.07    (2)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.66/51.07             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.66/51.07           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 244.66/51.07           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.66/51.07           op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.66/51.07    (3)  op(e0, e3) = all_52_3
% 244.66/51.07    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.07    (5)  all_56_1 = e0
% 244.66/51.07  
% 244.66/51.07  Begin of proof
% 244.66/51.07  | 
% 244.66/51.07  | BETA: splitting (2) gives:
% 244.66/51.07  | 
% 244.66/51.07  | Case 1:
% 244.66/51.07  | | 
% 244.66/51.07  | |   (6)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.66/51.07  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.66/51.07  | |        op(e0, e3) = e3
% 244.66/51.07  | | 
% 244.66/51.07  | | ALPHA: (6) implies:
% 244.66/51.07  | |   (7)   ~ (all_56_1 = e0)
% 244.66/51.07  | | 
% 244.66/51.07  | | REDUCE: (5), (7) imply:
% 244.66/51.07  | |   (8)  $false
% 244.66/51.07  | | 
% 244.66/51.07  | | CLOSE: (8) is inconsistent.
% 244.66/51.07  | | 
% 244.66/51.07  | Case 2:
% 244.66/51.07  | | 
% 244.66/51.07  | |   (9)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.66/51.07  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 244.66/51.07  | |        op(e0, e3) = e0
% 244.66/51.07  | | 
% 244.66/51.07  | | ALPHA: (9) implies:
% 244.66/51.07  | |   (10)  op(e0, e3) = e0
% 244.66/51.07  | | 
% 244.66/51.07  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #2331.
% 244.66/51.07  | | 
% 244.66/51.07  | End of split
% 244.66/51.07  | 
% 244.66/51.07  End of proof
% 244.66/51.07  
% 244.66/51.07  Sub-proof #1830 shows that the following formulas are inconsistent:
% 244.66/51.07  ----------------------------------------------------------------
% 244.66/51.07    (1)   ~ (all_8_2 = e1)
% 244.66/51.07    (2)   ~ (all_52_1 = all_52_3)
% 244.66/51.07    (3)   ~ (all_52_9 = all_8_2)
% 244.66/51.07    (4)   ~ (all_8_2 = e0)
% 244.66/51.07    (5)   ~ (all_52_9 = all_6_2)
% 244.66/51.07    (6)   ~ (e3 = e0)
% 244.66/51.07    (7)   ~ (all_52_8 = all_52_9)
% 244.66/51.07    (8)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.66/51.07         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.66/51.07    (9)  op(e1, e2) = all_52_6
% 244.66/51.07    (10)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.66/51.07          (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.66/51.07    (11)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.66/51.07              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.66/51.07            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 244.66/51.07            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.66/51.07            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 244.66/51.07             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.07            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.66/51.07            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.66/51.07            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 244.66/51.07            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.07            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.66/51.07              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.66/51.07            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.07            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 244.66/51.07            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.66/51.07            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 244.66/51.07            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.66/51.07            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.66/51.07              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.66/51.07            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.07            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 244.66/51.07            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.66/51.07            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 244.66/51.07            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.07            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.66/51.07              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.66/51.07            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.07            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.66/51.07    (12)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.66/51.07          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.66/51.07    (13)  op(e1, e1) = all_6_2
% 244.66/51.07    (14)  op(e1, e0) = all_52_14
% 244.66/51.07    (15)   ~ (all_52_13 = e1)
% 244.66/51.07    (16)  op(e0, e3) = all_52_3
% 244.66/51.07    (17)   ~ (e3 = e1)
% 244.66/51.07    (18)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.66/51.07          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.66/51.07    (19)  all_54_10 = all_6_2
% 244.66/51.07    (20)   ~ (all_6_2 = e3)
% 244.66/51.07    (21)  op(e3, e1) = all_52_8
% 244.66/51.07    (22)  op(e2, e1) = all_52_9
% 244.66/51.07    (23)   ~ (all_52_7 = e1)
% 244.66/51.07    (24)   ~ (all_6_2 = e0)
% 244.66/51.07    (25)  all_56_31 = e1
% 244.66/51.07    (26)  all_58_15 = e1
% 244.66/51.07    (27)  op(e3, e0) = all_52_12
% 244.66/51.07    (28)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.66/51.07          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.66/51.07    (29)   ~ (all_52_6 = all_52_14)
% 244.66/51.07    (30)  op(e2, e2) = all_8_2
% 244.66/51.07    (31)  all_54_5 = all_8_2
% 244.66/51.07    (32)  op(e2, e3) = all_52_1
% 244.66/51.07    (33)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.66/51.07    (34)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 244.66/51.07    (35)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.66/51.07          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.66/51.07    (36)  op(e0, e2) = all_52_7
% 244.66/51.07    (37)  op(e3, e2) = all_52_4
% 244.66/51.07    (38)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.66/51.07          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 244.66/51.07    (39)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.07            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.07    (40)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.66/51.07          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.66/51.07    (41)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.66/51.07          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.66/51.07    (42)   ~ (all_52_4 = e1)
% 244.66/51.07    (43)   ~ (all_8_2 = e3)
% 244.66/51.07    (44)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.66/51.07          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.66/51.07    (45)   ~ (e1 = e0)
% 244.66/51.07    (46)  all_56_21 = all_6_2
% 244.66/51.07    (47)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.66/51.07          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.66/51.07    (48)  op(e2, e0) = all_52_13
% 244.66/51.07    (49)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.66/51.07          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.66/51.07            e2)
% 244.66/51.07    (50)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.66/51.07          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.66/51.07    (51)   ~ (all_52_1 = e1)
% 244.66/51.07  
% 244.66/51.07  Begin of proof
% 244.66/51.07  | 
% 244.66/51.07  | BETA: splitting (34) gives:
% 244.66/51.07  | 
% 244.66/51.07  | Case 1:
% 244.66/51.07  | | 
% 244.66/51.07  | |   (52)  all_54_5 = e3
% 244.66/51.07  | | 
% 244.66/51.07  | | COMBINE_EQS: (31), (52) imply:
% 244.66/51.07  | |   (53)  all_8_2 = e3
% 244.66/51.07  | | 
% 244.66/51.07  | | REDUCE: (43), (53) imply:
% 244.66/51.07  | |   (54)  $false
% 244.66/51.07  | | 
% 244.66/51.07  | | CLOSE: (54) is inconsistent.
% 244.66/51.07  | | 
% 244.66/51.07  | Case 2:
% 244.66/51.07  | | 
% 244.66/51.07  | |   (55)   ~ (all_54_5 = e3)
% 244.66/51.07  | |   (56)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 244.66/51.07  | | 
% 244.66/51.07  | | BETA: splitting (56) gives:
% 244.66/51.07  | | 
% 244.66/51.07  | | Case 1:
% 244.66/51.07  | | | 
% 244.66/51.07  | | |   (57)  all_54_5 = e2
% 244.66/51.07  | | | 
% 244.66/51.07  | | | COMBINE_EQS: (31), (57) imply:
% 244.66/51.07  | | |   (58)  all_8_2 = e2
% 244.66/51.07  | | | 
% 244.66/51.07  | | | REDUCE: (3), (58) imply:
% 244.66/51.07  | | |   (59)   ~ (all_52_9 = e2)
% 244.66/51.07  | | | 
% 244.66/51.07  | | | REDUCE: (43), (58) imply:
% 244.66/51.07  | | |   (60)   ~ (e3 = e2)
% 244.66/51.07  | | | 
% 244.66/51.07  | | | SIMP: (60) implies:
% 244.66/51.07  | | |   (61)   ~ (e3 = e2)
% 244.66/51.07  | | | 
% 244.66/51.07  | | | REDUCE: (1), (58) imply:
% 244.66/51.07  | | |   (62)   ~ (e2 = e1)
% 244.66/51.07  | | | 
% 244.66/51.07  | | | REDUCE: (4), (58) imply:
% 244.66/51.07  | | |   (63)   ~ (e2 = e0)
% 244.66/51.07  | | | 
% 244.66/51.07  | | | REDUCE: (30), (58) imply:
% 244.66/51.07  | | |   (64)  op(e2, e2) = e2
% 244.66/51.07  | | | 
% 244.66/51.07  | | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 244.66/51.07  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 244.66/51.07  | | |            (25), (26), (27), (28), (29), (32), (33), (35), (36), (37),
% 244.66/51.07  | | |            (38), (39), (40), (41), (42), (44), (45), (46), (47), (48),
% 244.66/51.07  | | |            (49), (50), (51), (59), (61), (62), (63), (64) are inconsistent
% 244.66/51.07  | | |            by sub-proof #2105.
% 244.66/51.07  | | | 
% 244.66/51.07  | | Case 2:
% 244.66/51.07  | | | 
% 244.66/51.07  | | |   (65)  all_54_5 = e1 | all_54_5 = e0
% 244.66/51.07  | | | 
% 244.66/51.07  | | | REF_CLOSE: (1), (4), (31), (65) are inconsistent by sub-proof #2300.
% 244.66/51.07  | | | 
% 244.66/51.07  | | End of split
% 244.66/51.07  | | 
% 244.66/51.07  | End of split
% 244.66/51.07  | 
% 244.66/51.07  End of proof
% 244.66/51.07  
% 244.66/51.07  Sub-proof #1831 shows that the following formulas are inconsistent:
% 244.66/51.07  ----------------------------------------------------------------
% 244.66/51.07    (1)  all_56_11 = e2
% 244.66/51.07    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.66/51.07           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.66/51.07             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.66/51.07           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.66/51.07             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.66/51.07           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.07           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.66/51.07    (3)  all_56_31 = e1
% 244.66/51.07    (4)  op(e2, e3) = all_52_1
% 244.66/51.07    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.07    (6)   ~ (all_52_1 = e2)
% 244.66/51.07  
% 244.66/51.07  Begin of proof
% 244.66/51.07  | 
% 244.66/51.07  | BETA: splitting (2) gives:
% 244.66/51.07  | 
% 244.66/51.07  | Case 1:
% 244.66/51.07  | | 
% 244.66/51.07  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.66/51.07  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.66/51.07  | |        op(e2, e3) = e3
% 244.66/51.07  | | 
% 244.66/51.07  | | ALPHA: (7) implies:
% 244.66/51.07  | |   (8)   ~ (all_56_11 = e2)
% 244.66/51.07  | | 
% 244.66/51.07  | | REDUCE: (1), (8) imply:
% 244.66/51.07  | |   (9)  $false
% 244.66/51.07  | | 
% 244.66/51.07  | | CLOSE: (9) is inconsistent.
% 244.66/51.07  | | 
% 244.66/51.07  | Case 2:
% 244.66/51.07  | | 
% 244.66/51.07  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.66/51.07  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 244.66/51.07  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.66/51.07  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.07  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.66/51.07  | | 
% 244.66/51.07  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #2126.
% 244.66/51.07  | | 
% 244.66/51.07  | End of split
% 244.66/51.07  | 
% 244.66/51.07  End of proof
% 244.66/51.07  
% 244.66/51.07  Sub-proof #1832 shows that the following formulas are inconsistent:
% 244.66/51.07  ----------------------------------------------------------------
% 244.66/51.07    (1)  op(e0, e1) = all_52_11
% 244.66/51.07    (2)  op(e1, e1) = all_6_2
% 244.66/51.07    (3)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.66/51.07    (4)   ~ (all_6_2 = e0)
% 244.66/51.07    (5)   ~ (all_52_11 = e0)
% 244.66/51.07    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.07  
% 244.66/51.07  Begin of proof
% 244.66/51.07  | 
% 244.66/51.07  | BETA: splitting (3) gives:
% 244.66/51.07  | 
% 244.66/51.07  | Case 1:
% 244.66/51.07  | | 
% 244.66/51.07  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 244.66/51.07  | | 
% 244.66/51.07  | | REF_CLOSE: (2), (4), (6), (7) are inconsistent by sub-proof #1833.
% 244.66/51.07  | | 
% 244.66/51.07  | Case 2:
% 244.66/51.07  | | 
% 244.66/51.07  | |   (8)  all_58_14 = e0 & op(e0, e1) = e0
% 244.66/51.07  | | 
% 244.66/51.07  | | ALPHA: (8) implies:
% 244.66/51.07  | |   (9)  op(e0, e1) = e0
% 244.66/51.07  | | 
% 244.66/51.07  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #1911.
% 244.66/51.07  | | 
% 244.66/51.07  | End of split
% 244.66/51.07  | 
% 244.66/51.07  End of proof
% 244.66/51.07  
% 244.66/51.07  Sub-proof #1833 shows that the following formulas are inconsistent:
% 244.66/51.07  ----------------------------------------------------------------
% 244.66/51.07    (1)  all_58_8 = e0 & op(e1, e1) = e0
% 244.66/51.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.08    (3)  op(e1, e1) = all_6_2
% 244.66/51.08    (4)   ~ (all_6_2 = e0)
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | ALPHA: (1) implies:
% 244.66/51.08  |   (5)  op(e1, e1) = e0
% 244.66/51.08  | 
% 244.66/51.08  | GROUND_INST: instantiating (2) with all_6_2, e0, e1, e1, simplifying with (3),
% 244.66/51.08  |              (5) gives:
% 244.66/51.08  |   (6)  all_6_2 = e0
% 244.66/51.08  | 
% 244.66/51.08  | REDUCE: (4), (6) imply:
% 244.66/51.08  |   (7)  $false
% 244.66/51.08  | 
% 244.66/51.08  | CLOSE: (7) is inconsistent.
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1834 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)   ~ (e3 = e0)
% 244.66/51.08    (2)   ~ (e2 = e0)
% 244.66/51.08    (3)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.66/51.08    (4)  op(e0, e3) = all_52_3
% 244.66/51.08    (5)   ~ (e3 = e1)
% 244.66/51.08    (6)  op(e1, e0) = e1
% 244.66/51.08    (7)   ~ (e3 = e2)
% 244.66/51.08    (8)   ~ (all_52_3 = e2)
% 244.66/51.08    (9)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.66/51.08         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.66/51.08    (10)  op(e1, e1) = e2
% 244.66/51.08    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.08            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.08    (12)   ~ (e1 = e0)
% 244.66/51.08    (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.66/51.08          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | BETA: splitting (3) gives:
% 244.66/51.08  | 
% 244.66/51.08  | Case 1:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (14)  all_58_6 = e2 & op(e1, e3) = e2
% 244.66/51.08  | | 
% 244.66/51.08  | | ALPHA: (14) implies:
% 244.66/51.08  | |   (15)  all_58_6 = e2
% 244.66/51.08  | | 
% 244.66/51.08  | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (13), (15) are
% 244.66/51.08  | |            inconsistent by sub-proof #1835.
% 244.66/51.08  | | 
% 244.66/51.08  | Case 2:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (16)  all_58_12 = e2 & op(e0, e3) = e2
% 244.66/51.08  | | 
% 244.66/51.08  | | REF_CLOSE: (4), (8), (11), (16) are inconsistent by sub-proof #2315.
% 244.66/51.08  | | 
% 244.66/51.08  | End of split
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1835 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)   ~ (e3 = e0)
% 244.66/51.08    (2)   ~ (e2 = e0)
% 244.66/51.08    (3)  all_58_6 = e2
% 244.66/51.08    (4)   ~ (e3 = e1)
% 244.66/51.08    (5)  op(e1, e0) = e1
% 244.66/51.08    (6)   ~ (e3 = e2)
% 244.66/51.08    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.66/51.08         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.66/51.08    (8)  op(e1, e1) = e2
% 244.66/51.08    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.08    (10)   ~ (e1 = e0)
% 244.66/51.08    (11)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.66/51.08          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | BETA: splitting (7) gives:
% 244.66/51.08  | 
% 244.66/51.08  | Case 1:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (12)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.66/51.08  | |           e3)
% 244.66/51.08  | | 
% 244.66/51.08  | | BETA: splitting (12) gives:
% 244.66/51.08  | | 
% 244.66/51.08  | | Case 1:
% 244.66/51.08  | | | 
% 244.66/51.08  | | |   (13)  all_58_6 = e3 & op(e1, e3) = e3
% 244.66/51.08  | | | 
% 244.66/51.08  | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #1838.
% 244.66/51.08  | | | 
% 244.66/51.08  | | Case 2:
% 244.66/51.08  | | | 
% 244.66/51.08  | | |   (14)  all_58_7 = e3 & op(e1, e2) = e3
% 244.66/51.08  | | | 
% 244.66/51.08  | | | ALPHA: (14) implies:
% 244.66/51.08  | | |   (15)  all_58_7 = e3
% 244.66/51.08  | | | 
% 244.66/51.08  | | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (10), (11), (15) are inconsistent
% 244.66/51.08  | | |            by sub-proof #1836.
% 244.66/51.08  | | | 
% 244.66/51.08  | | End of split
% 244.66/51.08  | | 
% 244.66/51.08  | Case 2:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (16)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.66/51.08  | |           e3)
% 244.66/51.08  | | 
% 244.66/51.08  | | BETA: splitting (16) gives:
% 244.66/51.08  | | 
% 244.66/51.08  | | Case 1:
% 244.66/51.08  | | | 
% 244.66/51.08  | | |   (17)  all_58_8 = e3 & op(e1, e1) = e3
% 244.66/51.08  | | | 
% 244.66/51.08  | | | ALPHA: (17) implies:
% 244.66/51.08  | | |   (18)  op(e1, e1) = e3
% 244.66/51.08  | | | 
% 244.66/51.08  | | | REF_CLOSE: (6), (8), (9), (18) are inconsistent by sub-proof #2206.
% 244.66/51.08  | | | 
% 244.66/51.08  | | Case 2:
% 244.66/51.08  | | | 
% 244.66/51.08  | | |   (19)  all_58_11 = e3 & op(e1, e0) = e3
% 244.66/51.08  | | | 
% 244.66/51.08  | | | ALPHA: (19) implies:
% 244.66/51.08  | | |   (20)  op(e1, e0) = e3
% 244.66/51.08  | | | 
% 244.66/51.08  | | | REF_CLOSE: (4), (5), (9), (20) are inconsistent by sub-proof #1894.
% 244.66/51.08  | | | 
% 244.66/51.08  | | End of split
% 244.66/51.08  | | 
% 244.66/51.08  | End of split
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1836 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)   ~ (e3 = e0)
% 244.66/51.08    (2)   ~ (e2 = e0)
% 244.66/51.08    (3)  all_58_6 = e2
% 244.66/51.08    (4)  op(e1, e0) = e1
% 244.66/51.08    (5)  all_58_7 = e3
% 244.66/51.08    (6)  op(e1, e1) = e2
% 244.66/51.08    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.08    (8)   ~ (e1 = e0)
% 244.66/51.08    (9)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.66/51.08         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | BETA: splitting (9) gives:
% 244.66/51.08  | 
% 244.66/51.08  | Case 1:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (10)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 244.66/51.08  | |           e0)
% 244.66/51.08  | | 
% 244.66/51.08  | | BETA: splitting (10) gives:
% 244.66/51.08  | | 
% 244.66/51.08  | | Case 1:
% 244.66/51.08  | | | 
% 244.66/51.08  | | |   (11)  all_58_6 = e0 & op(e1, e3) = e0
% 244.66/51.08  | | | 
% 244.66/51.08  | | | ALPHA: (11) implies:
% 244.66/51.08  | | |   (12)  all_58_6 = e0
% 244.66/51.08  | | | 
% 244.66/51.08  | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #1982.
% 244.66/51.08  | | | 
% 244.66/51.08  | | Case 2:
% 244.66/51.08  | | | 
% 244.66/51.08  | | |   (13)  all_58_7 = e0 & op(e1, e2) = e0
% 244.66/51.08  | | | 
% 244.66/51.08  | | | REF_CLOSE: (1), (5), (13) are inconsistent by sub-proof #1837.
% 244.66/51.08  | | | 
% 244.66/51.08  | | End of split
% 244.66/51.08  | | 
% 244.66/51.08  | Case 2:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (14)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.66/51.08  | |           e0)
% 244.66/51.08  | | 
% 244.66/51.08  | | REF_CLOSE: (2), (4), (6), (7), (8), (14) are inconsistent by sub-proof
% 244.66/51.08  | |            #2210.
% 244.66/51.08  | | 
% 244.66/51.08  | End of split
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1837 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)  all_58_7 = e0 & op(e1, e2) = e0
% 244.66/51.08    (2)  all_58_7 = e3
% 244.66/51.08    (3)   ~ (e3 = e0)
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | ALPHA: (1) implies:
% 244.66/51.08  |   (4)  all_58_7 = e0
% 244.66/51.08  | 
% 244.66/51.08  | COMBINE_EQS: (2), (4) imply:
% 244.66/51.08  |   (5)  e3 = e0
% 244.66/51.08  | 
% 244.66/51.08  | SIMP: (5) implies:
% 244.66/51.08  |   (6)  e3 = e0
% 244.66/51.08  | 
% 244.66/51.08  | REDUCE: (3), (6) imply:
% 244.66/51.08  |   (7)  $false
% 244.66/51.08  | 
% 244.66/51.08  | CLOSE: (7) is inconsistent.
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1838 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)  all_58_6 = e3 & op(e1, e3) = e3
% 244.66/51.08    (2)  all_58_6 = e2
% 244.66/51.08    (3)   ~ (e3 = e2)
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | ALPHA: (1) implies:
% 244.66/51.08  |   (4)  all_58_6 = e3
% 244.66/51.08  | 
% 244.66/51.08  | COMBINE_EQS: (2), (4) imply:
% 244.66/51.08  |   (5)  e3 = e2
% 244.66/51.08  | 
% 244.66/51.08  | REDUCE: (3), (5) imply:
% 244.66/51.08  |   (6)  $false
% 244.66/51.08  | 
% 244.66/51.08  | CLOSE: (6) is inconsistent.
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1839 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.08    (2)  op(e2, e1) = all_30_1
% 244.66/51.08    (3)  op(e2, e1) = e3
% 244.66/51.08    (4)   ~ (all_30_1 = e3)
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | GROUND_INST: instantiating (1) with e3, all_30_1, e1, e2, simplifying with
% 244.66/51.08  |              (2), (3) gives:
% 244.66/51.08  |   (5)  all_30_1 = e3
% 244.66/51.08  | 
% 244.66/51.08  | REDUCE: (4), (5) imply:
% 244.66/51.08  |   (6)  $false
% 244.66/51.08  | 
% 244.66/51.08  | CLOSE: (6) is inconsistent.
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1840 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)  op(e1, e2) = all_52_6
% 244.66/51.08    (2)  op(e1, e2) = e0
% 244.66/51.08    (3)   ~ (all_52_7 = e1)
% 244.66/51.08    (4)  op(e0, e2) = all_52_7
% 244.66/51.08    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.08    (6)   ~ (e1 = e0)
% 244.66/51.08    (7)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | BETA: splitting (7) gives:
% 244.66/51.08  | 
% 244.66/51.08  | Case 1:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (8)  all_58_7 = e1 & op(e1, e2) = e1
% 244.66/51.08  | | 
% 244.66/51.08  | | ALPHA: (8) implies:
% 244.66/51.08  | |   (9)  op(e1, e2) = e1
% 244.66/51.08  | | 
% 244.66/51.08  | | REF_CLOSE: (1), (2), (5), (6), (9) are inconsistent by sub-proof #2136.
% 244.66/51.08  | | 
% 244.66/51.08  | Case 2:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (10)  all_58_13 = e1 & op(e0, e2) = e1
% 244.66/51.08  | | 
% 244.66/51.08  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #2275.
% 244.66/51.08  | | 
% 244.66/51.08  | End of split
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1841 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)   ~ (all_22_1 = e0)
% 244.66/51.08    (2)  op(e2, e1) = e0
% 244.66/51.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.08    (4)  op(e2, e1) = all_22_1
% 244.66/51.08    (5)  op(e2, e1) = all_30_1
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | GROUND_INST: instantiating (3) with e0, all_30_1, e1, e2, simplifying with
% 244.66/51.08  |              (2), (5) gives:
% 244.66/51.08  |   (6)  all_30_1 = e0
% 244.66/51.08  | 
% 244.66/51.08  | GROUND_INST: instantiating (3) with all_22_1, all_30_1, e1, e2, simplifying
% 244.66/51.08  |              with (4), (5) gives:
% 244.66/51.08  |   (7)  all_30_1 = all_22_1
% 244.66/51.08  | 
% 244.66/51.08  | COMBINE_EQS: (6), (7) imply:
% 244.66/51.08  |   (8)  all_22_1 = e0
% 244.66/51.08  | 
% 244.66/51.08  | REDUCE: (1), (8) imply:
% 244.66/51.08  |   (9)  $false
% 244.66/51.08  | 
% 244.66/51.08  | CLOSE: (9) is inconsistent.
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1842 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)  all_54_13 = e1 | all_54_13 = e0
% 244.66/51.08    (2)  all_54_13 = all_22_0
% 244.66/51.08    (3)   ~ (all_22_0 = e1)
% 244.66/51.08    (4)   ~ (all_22_0 = e0)
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | BETA: splitting (1) gives:
% 244.66/51.08  | 
% 244.66/51.08  | Case 1:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (5)  all_54_13 = e1
% 244.66/51.08  | | 
% 244.66/51.08  | | COMBINE_EQS: (2), (5) imply:
% 244.66/51.08  | |   (6)  all_22_0 = e1
% 244.66/51.08  | | 
% 244.66/51.08  | | SIMP: (6) implies:
% 244.66/51.08  | |   (7)  all_22_0 = e1
% 244.66/51.08  | | 
% 244.66/51.08  | | REDUCE: (3), (7) imply:
% 244.66/51.08  | |   (8)  $false
% 244.66/51.08  | | 
% 244.66/51.08  | | CLOSE: (8) is inconsistent.
% 244.66/51.08  | | 
% 244.66/51.08  | Case 2:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (9)  all_54_13 = e0
% 244.66/51.08  | | 
% 244.66/51.08  | | COMBINE_EQS: (2), (9) imply:
% 244.66/51.08  | |   (10)  all_22_0 = e0
% 244.66/51.08  | | 
% 244.66/51.08  | | SIMP: (10) implies:
% 244.66/51.08  | |   (11)  all_22_0 = e0
% 244.66/51.08  | | 
% 244.66/51.08  | | REDUCE: (4), (11) imply:
% 244.66/51.08  | |   (12)  $false
% 244.66/51.08  | | 
% 244.66/51.08  | | CLOSE: (12) is inconsistent.
% 244.66/51.08  | | 
% 244.66/51.08  | End of split
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1843 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)   ~ (e3 = e1)
% 244.66/51.08    (2)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.66/51.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.08    (4)  op(e0, e0) = e0
% 244.66/51.08    (5)  all_58_14 = e3
% 244.66/51.08    (6)   ~ (e1 = e0)
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | BETA: splitting (2) gives:
% 244.66/51.08  | 
% 244.66/51.08  | Case 1:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (7)  all_58_14 = e1 & op(e0, e1) = e1
% 244.66/51.08  | | 
% 244.66/51.08  | | ALPHA: (7) implies:
% 244.66/51.08  | |   (8)  all_58_14 = e1
% 244.66/51.08  | | 
% 244.66/51.08  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #1844.
% 244.66/51.08  | | 
% 244.66/51.08  | Case 2:
% 244.66/51.08  | | 
% 244.66/51.08  | |   (9)  all_58_15 = e1 & op(e0, e0) = e1
% 244.66/51.08  | | 
% 244.66/51.08  | | ALPHA: (9) implies:
% 244.66/51.08  | |   (10)  op(e0, e0) = e1
% 244.66/51.08  | | 
% 244.66/51.08  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #2274.
% 244.66/51.08  | | 
% 244.66/51.08  | End of split
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1844 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)  all_58_14 = e3
% 244.66/51.08    (2)  all_58_14 = e1
% 244.66/51.08    (3)   ~ (e3 = e1)
% 244.66/51.08  
% 244.66/51.08  Begin of proof
% 244.66/51.08  | 
% 244.66/51.08  | COMBINE_EQS: (1), (2) imply:
% 244.66/51.08  |   (4)  e3 = e1
% 244.66/51.08  | 
% 244.66/51.08  | SIMP: (4) implies:
% 244.66/51.08  |   (5)  e3 = e1
% 244.66/51.08  | 
% 244.66/51.08  | REDUCE: (3), (5) imply:
% 244.66/51.08  |   (6)  $false
% 244.66/51.08  | 
% 244.66/51.08  | CLOSE: (6) is inconsistent.
% 244.66/51.08  | 
% 244.66/51.08  End of proof
% 244.66/51.08  
% 244.66/51.08  Sub-proof #1845 shows that the following formulas are inconsistent:
% 244.66/51.08  ----------------------------------------------------------------
% 244.66/51.08    (1)   ~ (all_52_3 = e0)
% 244.66/51.08    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.66/51.08             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.66/51.08           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.66/51.08         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.66/51.08           $i(all_56_7))
% 244.66/51.08    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.66/51.08    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 244.66/51.08         (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 244.66/51.08    (5)   ~ (all_52_9 = all_6_2)
% 244.66/51.08    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.66/51.08    (7)  all_56_11 = e1
% 244.66/51.08    (8)  op(e0, e1) = all_52_11
% 244.66/51.08    (9)   ~ (e2 = e0)
% 244.66/51.08    (10)  op(e0, e1) = e3
% 244.66/51.08    (11)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.66/51.08              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.66/51.08            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 244.66/51.08            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.66/51.08            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 244.66/51.08             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.08            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.66/51.08            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.66/51.08            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 244.66/51.08            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.08            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.66/51.08              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.66/51.08            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.08            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 244.66/51.08            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.66/51.08            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 244.66/51.08            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.66/51.08            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.66/51.08              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.66/51.08            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.08            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 244.66/51.08            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.66/51.08            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 244.66/51.08            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.08            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.66/51.08              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.66/51.08            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.08            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.66/51.08    (12)   ~ (all_52_7 = all_52_11)
% 244.66/51.08    (13)   ~ (all_52_12 = e0)
% 244.66/51.08    (14)   ~ (all_52_1 = all_52_2)
% 244.66/51.08    (15)  op(e1, e0) = all_52_14
% 244.66/51.08    (16)  op(e0, e3) = all_52_3
% 244.66/51.08    (17)  op(e0, e2) = e2
% 244.66/51.08    (18)  op(e1, e0) = e1
% 244.66/51.08    (19)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.66/51.08          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.66/51.08    (20)   ~ (all_52_2 = all_52_3)
% 244.66/51.09    (21)   ~ (all_52_12 = all_52_14)
% 244.66/51.09    (22)   ~ (all_52_12 = all_52_13)
% 244.66/51.09    (23)   ~ (all_52_2 = e1)
% 244.66/51.09    (24)  all_54_10 = all_6_2
% 244.66/51.09    (25)  all_58_10 = e3 & op(e2, e0) = e3
% 244.66/51.09    (26)   ~ (all_52_2 = all_52_14)
% 244.66/51.09    (27)   ~ (all_52_3 = all_52_7)
% 244.66/51.09    (28)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.66/51.09    (29)  all_54_4 = all_52_1
% 244.66/51.09    (30)   ~ (all_6_2 = e3)
% 244.66/51.09    (31)  op(e3, e1) = all_52_8
% 244.66/51.09    (32)  op(e2, e1) = all_52_9
% 244.66/51.09    (33)   ~ (e3 = e2)
% 244.66/51.09    (34)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.66/51.09    (35)   ~ (all_52_3 = all_52_11)
% 244.66/51.09    (36)   ~ (all_52_14 = all_6_2)
% 244.66/51.09    (37)   ~ (all_6_2 = e0)
% 244.66/51.09    (38)   ~ (all_52_14 = e0)
% 244.66/51.09    (39)  all_56_31 = e0
% 244.66/51.09    (40)  all_54_12 = all_52_3
% 244.66/51.09    (41)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.66/51.09    (42)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.66/51.09          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.66/51.09    (43)   ~ (all_52_1 = e0)
% 244.66/51.09    (44)   ~ (all_52_4 = all_52_12)
% 244.66/51.09    (45)  op(e2, e3) = all_52_1
% 244.66/51.09    (46)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.66/51.09    (47)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.66/51.09    (48)  op(e1, e1) = e2
% 244.66/51.09    (49)   ~ (all_52_1 = all_52_13)
% 244.66/51.09    (50)   ~ (all_52_2 = e0)
% 244.66/51.09    (51)   ~ (all_52_11 = e0)
% 244.66/51.09    (52)  all_54_7 = all_52_13
% 244.66/51.09    (53)  op(e0, e2) = all_52_7
% 244.66/51.09    (54)   ~ (all_52_13 = all_52_14)
% 244.66/51.09    (55)  op(e2, e1) = e0
% 244.66/51.09    (56)  op(e3, e2) = all_52_4
% 244.66/51.09    (57)   ~ (all_52_8 = all_52_11)
% 244.66/51.09    (58)   ~ (all_52_2 = e2)
% 244.66/51.09    (59)  all_54_8 = all_52_2
% 244.66/51.09    (60)  all_54_3 = all_52_12
% 244.66/51.09    (61)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.09            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.09    (62)  op(e0, e0) = e0
% 244.66/51.09    (63)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.66/51.09          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.66/51.09    (64)  op(e1, e3) = all_52_2
% 244.66/51.09    (65)   ~ (e1 = e0)
% 244.66/51.09    (66)  all_56_21 = all_6_2
% 244.66/51.09    (67)  op(e3, e3) = e0
% 244.66/51.09    (68)  op(e3, e2) = e3
% 244.66/51.09    (69)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.66/51.09          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.66/51.09    (70)  all_56_1 = e0
% 244.66/51.09    (71)  op(e2, e0) = all_52_13
% 244.66/51.09    (72)  all_54_14 = all_52_11
% 244.66/51.09    (73)   ~ (all_52_9 = all_52_11)
% 244.66/51.09    (74)   ~ (all_52_13 = e0)
% 244.66/51.09    (75)   ~ (e2 = e1)
% 244.66/51.09    (76)   ~ (all_52_1 = e1)
% 244.66/51.09  
% 244.66/51.09  Begin of proof
% 244.66/51.09  | 
% 244.66/51.09  | ALPHA: (25) implies:
% 244.66/51.09  |   (77)  op(e2, e0) = e3
% 244.66/51.09  | 
% 244.66/51.09  | BETA: splitting (4) gives:
% 244.66/51.09  | 
% 244.66/51.09  | Case 1:
% 244.66/51.09  | | 
% 244.66/51.09  | |   (78)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 244.66/51.09  | |           e2)
% 244.66/51.09  | | 
% 244.66/51.09  | | REF_CLOSE: (9), (33), (61), (67), (68), (78) are inconsistent by sub-proof
% 244.66/51.09  | |            #1857.
% 244.66/51.09  | | 
% 244.66/51.09  | Case 2:
% 244.66/51.09  | | 
% 244.66/51.09  | |   (79)  (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 244.66/51.09  | |           e2)
% 244.66/51.09  | | 
% 244.66/51.09  | | BETA: splitting (79) gives:
% 244.66/51.09  | | 
% 244.66/51.09  | | Case 1:
% 244.66/51.09  | | | 
% 244.66/51.09  | | |   (80)  all_58_4 = e2 & op(e3, e1) = e2
% 244.66/51.09  | | | 
% 244.66/51.09  | | | ALPHA: (80) implies:
% 244.66/51.09  | | |   (81)  all_58_4 = e2
% 244.66/51.09  | | | 
% 244.66/51.09  | | | BETA: splitting (63) gives:
% 244.66/51.09  | | | 
% 244.66/51.09  | | | Case 1:
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | |   (82)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 244.66/51.09  | | | |           = e2)
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | BETA: splitting (82) gives:
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | Case 1:
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | |   (83)  all_58_9 = e2 & op(e3, e0) = e2
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | | ALPHA: (83) implies:
% 244.66/51.09  | | | | |   (84)  op(e3, e0) = e2
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | | BETA: splitting (6) gives:
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | | Case 1:
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | |   (85)  all_54_8 = e3
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | | COMBINE_EQS: (59), (85) imply:
% 244.66/51.09  | | | | | |   (86)  all_52_2 = e3
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | | SIMP: (86) implies:
% 244.66/51.09  | | | | | |   (87)  all_52_2 = e3
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | | REDUCE: (14), (87) imply:
% 244.66/51.09  | | | | | |   (88)   ~ (all_52_1 = e3)
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | | REDUCE: (26), (87) imply:
% 244.66/51.09  | | | | | |   (89)   ~ (all_52_14 = e3)
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | | SIMP: (89) implies:
% 244.66/51.09  | | | | | |   (90)   ~ (all_52_14 = e3)
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | | REDUCE: (23), (87) imply:
% 244.66/51.09  | | | | | |   (91)   ~ (e3 = e1)
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | | REDUCE: (50), (87) imply:
% 244.66/51.09  | | | | | |   (92)   ~ (e3 = e0)
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | | BETA: splitting (47) gives:
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | | Case 1:
% 244.66/51.09  | | | | | | | 
% 244.66/51.09  | | | | | | |   (93)  all_54_4 = e3
% 244.66/51.09  | | | | | | | 
% 244.66/51.09  | | | | | | | REF_CLOSE: (29), (88), (93) are inconsistent by sub-proof #2100.
% 244.66/51.09  | | | | | | | 
% 244.66/51.09  | | | | | | Case 2:
% 244.66/51.09  | | | | | | | 
% 244.66/51.09  | | | | | | |   (94)   ~ (all_54_4 = e3)
% 244.66/51.09  | | | | | | |   (95)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.66/51.09  | | | | | | | 
% 244.66/51.09  | | | | | | | BETA: splitting (95) gives:
% 244.66/51.09  | | | | | | | 
% 244.66/51.09  | | | | | | | Case 1:
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | |   (96)  all_54_4 = e2
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | | COMBINE_EQS: (29), (96) imply:
% 244.66/51.09  | | | | | | | |   (97)  all_52_1 = e2
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | | SIMP: (97) implies:
% 244.66/51.09  | | | | | | | |   (98)  all_52_1 = e2
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | | REDUCE: (49), (98) imply:
% 244.66/51.09  | | | | | | | |   (99)   ~ (all_52_13 = e2)
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | | SIMP: (99) implies:
% 244.66/51.09  | | | | | | | |   (100)   ~ (all_52_13 = e2)
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | | REDUCE: (88), (98) imply:
% 244.66/51.09  | | | | | | | |   (101)   ~ (e3 = e2)
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | | BETA: splitting (11) gives:
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | | Case 1:
% 244.66/51.09  | | | | | | | | | 
% 244.66/51.09  | | | | | | | | |   (102)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &
% 244.66/51.09  | | | | | | | | |             ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 244.66/51.09  | | | | | | | | |            e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1
% 244.66/51.09  | | | | | | | | |              = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 244.66/51.09  | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 244.66/51.09  | | | | | | | | |              e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 244.66/51.09  | | | | | | | | |            = e3 & op(e1, e3) = e3) | (all_56_5 = e1 &
% 244.66/51.09  | | | | | | | | |            all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.66/51.09  | | | | | | | | |              = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 244.66/51.09  | | | | | | | | |            & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 =
% 244.66/51.09  | | | | | | | | |            e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 244.66/51.09  | | | | | | | | |            e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 244.66/51.09  | | | | | | | | |            = e0 & op(e0, e3) = e0)
% 244.66/51.09  | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | BETA: splitting (102) gives:
% 244.66/51.09  | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | Case 1:
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | |   (103)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 244.66/51.09  | | | | | | | | | |            &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 244.66/51.09  | | | | | | | | | |            e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.66/51.09  | | | | | | | | | |              e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 244.66/51.09  | | | | | | | | | |            all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 244.66/51.09  | | | | | | | | | |            e3)
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | REF_CLOSE: (1), (3), (12), (17), (20), (27), (31), (33),
% 244.66/51.09  | | | | | | | | | |            (34), (35), (40), (45), (51), (53), (57), (61),
% 244.66/51.09  | | | | | | | | | |            (64), (68), (72), (88), (103) are inconsistent by
% 244.66/51.09  | | | | | | | | | |            sub-proof #1852.
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | Case 2:
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | |   (104)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 244.66/51.09  | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 244.66/51.09  | | | | | | | | | |            &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 244.66/51.09  | | | | | | | | | |              e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 & 
% 244.66/51.09  | | | | | | | | | |            ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.66/51.09  | | | | | | | | | |              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 244.66/51.09  | | | | | | | | | |            all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 244.66/51.09  | | | | | | | | | |            e0)
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | REF_CLOSE: (1), (9), (15), (16), (33), (38), (42), (48),
% 244.66/51.09  | | | | | | | | | |            (50), (61), (64), (69), (84), (90), (91), (92),
% 244.66/51.09  | | | | | | | | | |            (104) are inconsistent by sub-proof #1848.
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | End of split
% 244.66/51.09  | | | | | | | | | 
% 244.66/51.09  | | | | | | | | Case 2:
% 244.66/51.09  | | | | | | | | | 
% 244.66/51.09  | | | | | | | | |   (105)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1)
% 244.66/51.09  | | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.66/51.09  | | | | | | | | |            e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1)
% 244.66/51.09  | | | | | | | | |            = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 244.66/51.09  | | | | | | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.66/51.09  | | | | | | | | |              = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.66/51.09  | | | | | | | | |            & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 244.66/51.09  | | | | | | | | |            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.66/51.09  | | | | | | | | |            e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 244.66/51.09  | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0)
% 244.66/51.09  | | | | | | | | |            = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 244.66/51.09  | | | | | | | | |            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.66/51.09  | | | | | | | | |              = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 244.66/51.09  | | | | | | | | |            & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.66/51.09  | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | BETA: splitting (105) gives:
% 244.66/51.09  | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | Case 1:
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | |   (106)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.66/51.09  | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 244.66/51.09  | | | | | | | | | |            &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 244.66/51.09  | | | | | | | | | |              e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 & 
% 244.66/51.09  | | | | | | | | | |            ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.66/51.09  | | | | | | | | | |              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 244.66/51.09  | | | | | | | | | |            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 244.66/51.09  | | | | | | | | | |            e2)
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | BETA: splitting (106) gives:
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | Case 1:
% 244.66/51.09  | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | |   (107)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.66/51.09  | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 244.66/51.09  | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 244.66/51.09  | | | | | | | | | | |            e2) = e2
% 244.66/51.09  | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | ALPHA: (107) implies:
% 244.66/51.09  | | | | | | | | | | |   (108)  op(e2, e1) = e2
% 244.66/51.09  | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | REF_CLOSE: (9), (55), (61), (108) are inconsistent by
% 244.66/51.09  | | | | | | | | | | |            sub-proof #1906.
% 244.66/51.09  | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | Case 2:
% 244.66/51.09  | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | |   (109)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.66/51.09  | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.66/51.09  | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.66/51.09  | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 244.66/51.09  | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.66/51.09  | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.66/51.09  | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.66/51.09  | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | BETA: splitting (109) gives:
% 244.66/51.09  | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | Case 1:
% 244.66/51.09  | | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | |   (110)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.66/51.09  | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 244.66/51.09  | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 244.66/51.09  | | | | | | | | | | | |            e2) = e1
% 244.66/51.09  | | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | | ALPHA: (110) implies:
% 244.66/51.09  | | | | | | | | | | | |   (111)  op(e2, e1) = e1
% 244.66/51.09  | | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | | REF_CLOSE: (9), (10), (19), (32), (48), (61), (65), (81),
% 244.66/51.09  | | | | | | | | | | | |            (92), (111) are inconsistent by sub-proof #2162.
% 244.66/51.09  | | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | Case 2:
% 244.66/51.09  | | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | |   (112)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 244.66/51.09  | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 244.66/51.09  | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 244.66/51.09  | | | | | | | | | | | |            e2) = e2
% 244.66/51.09  | | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | | ALPHA: (112) implies:
% 244.66/51.09  | | | | | | | | | | | |   (113)  op(e2, e0) = e2
% 244.66/51.09  | | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | | REF_CLOSE: (61), (71), (100), (113) are inconsistent by
% 244.66/51.09  | | | | | | | | | | | |            sub-proof #2317.
% 244.66/51.09  | | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | | End of split
% 244.66/51.09  | | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | End of split
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | Case 2:
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | |   (114)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 244.66/51.09  | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 244.66/51.09  | | | | | | | | | |            &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 244.66/51.09  | | | | | | | | | |              e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 & 
% 244.66/51.09  | | | | | | | | | |            ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.66/51.09  | | | | | | | | | |              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 244.66/51.09  | | | | | | | | | |            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.09  | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 244.66/51.09  | | | | | | | | | |            e0)
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | | REF_CLOSE: (1), (5), (7), (8), (11), (13), (15), (16), (18),
% 244.66/51.09  | | | | | | | | | |            (21), (22), (24), (28), (30), (31), (32), (36),
% 244.66/51.09  | | | | | | | | | |            (37), (38), (39), (41), (44), (45), (46), (49),
% 244.66/51.09  | | | | | | | | | |            (52), (54), (56), (57), (60), (61), (65), (66),
% 244.66/51.09  | | | | | | | | | |            (71), (73), (74), (114) are inconsistent by
% 244.66/51.09  | | | | | | | | | |            sub-proof #1847.
% 244.66/51.09  | | | | | | | | | | 
% 244.66/51.09  | | | | | | | | | End of split
% 244.66/51.09  | | | | | | | | | 
% 244.66/51.09  | | | | | | | | End of split
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | Case 2:
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | |   (115)  all_54_4 = e1 | all_54_4 = e0
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | | REF_CLOSE: (29), (43), (76), (115) are inconsistent by sub-proof
% 244.66/51.09  | | | | | | | |            #1922.
% 244.66/51.09  | | | | | | | | 
% 244.66/51.09  | | | | | | | End of split
% 244.66/51.09  | | | | | | | 
% 244.66/51.09  | | | | | | End of split
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | Case 2:
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | |   (116)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | | REF_CLOSE: (23), (50), (58), (59), (116) are inconsistent by
% 244.66/51.09  | | | | | |            sub-proof #1949.
% 244.66/51.09  | | | | | | 
% 244.66/51.09  | | | | | End of split
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | Case 2:
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | |   (117)  all_58_10 = e2 & op(e2, e0) = e2
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | | ALPHA: (117) implies:
% 244.66/51.09  | | | | |   (118)  op(e2, e0) = e2
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | | REF_CLOSE: (33), (61), (77), (118) are inconsistent by sub-proof
% 244.66/51.09  | | | | |            #2152.
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | End of split
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | Case 2:
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | |   (119)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 244.66/51.09  | | | |              e0) = e2)
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | BETA: splitting (119) gives:
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | Case 1:
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | |   (120)  all_58_11 = e2 & op(e1, e0) = e2
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | | ALPHA: (120) implies:
% 244.66/51.09  | | | | |   (121)  op(e1, e0) = e2
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | | REF_CLOSE: (18), (61), (75), (121) are inconsistent by sub-proof
% 244.66/51.09  | | | | |            #2019.
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | Case 2:
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | |   (122)  all_58_15 = e2 & op(e0, e0) = e2
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | | ALPHA: (122) implies:
% 244.66/51.09  | | | | |   (123)  op(e0, e0) = e2
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | | REF_CLOSE: (9), (61), (62), (123) are inconsistent by sub-proof #2301.
% 244.66/51.09  | | | | | 
% 244.66/51.09  | | | | End of split
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | End of split
% 244.66/51.09  | | | 
% 244.66/51.09  | | Case 2:
% 244.66/51.09  | | | 
% 244.66/51.09  | | |   (124)  all_58_9 = e2 & op(e3, e0) = e2
% 244.66/51.09  | | | 
% 244.66/51.09  | | | ALPHA: (124) implies:
% 244.66/51.09  | | |   (125)  op(e3, e0) = e2
% 244.66/51.09  | | | 
% 244.66/51.09  | | | BETA: splitting (6) gives:
% 244.66/51.09  | | | 
% 244.66/51.09  | | | Case 1:
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | |   (126)  all_54_8 = e3
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | COMBINE_EQS: (59), (126) imply:
% 244.66/51.09  | | | |   (127)  all_52_2 = e3
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | SIMP: (127) implies:
% 244.66/51.09  | | | |   (128)  all_52_2 = e3
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | REDUCE: (14), (128) imply:
% 244.66/51.09  | | | |   (129)   ~ (all_52_1 = e3)
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | REDUCE: (26), (128) imply:
% 244.66/51.09  | | | |   (130)   ~ (all_52_14 = e3)
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | SIMP: (130) implies:
% 244.66/51.09  | | | |   (131)   ~ (all_52_14 = e3)
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | REDUCE: (23), (128) imply:
% 244.66/51.09  | | | |   (132)   ~ (e3 = e1)
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | REDUCE: (50), (128) imply:
% 244.66/51.09  | | | |   (133)   ~ (e3 = e0)
% 244.66/51.09  | | | | 
% 244.66/51.09  | | | | REDUCE: (64), (128) imply:
% 244.66/51.10  | | | |   (134)  op(e1, e3) = e3
% 244.66/51.10  | | | | 
% 244.66/51.10  | | | | BETA: splitting (2) gives:
% 244.66/51.10  | | | | 
% 244.66/51.10  | | | | Case 1:
% 244.66/51.10  | | | | | 
% 244.66/51.10  | | | | |   (135)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 244.66/51.10  | | | | |            op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 244.66/51.10  | | | | |            $i(all_56_3))
% 244.66/51.10  | | | | | 
% 244.66/51.10  | | | | | BETA: splitting (135) gives:
% 244.66/51.10  | | | | | 
% 244.66/51.10  | | | | | Case 1:
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | |   (136)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | | ALPHA: (136) implies:
% 244.66/51.10  | | | | | |   (137)  op(e3, all_56_1) = e3
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | | REDUCE: (70), (137) imply:
% 244.66/51.10  | | | | | |   (138)  op(e3, e0) = e3
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | | REF_CLOSE: (33), (61), (125), (138) are inconsistent by sub-proof
% 244.66/51.10  | | | | | |            #2125.
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | Case 2:
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | |   (139)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 244.66/51.10  | | | | | |          all_56_3 & $i(all_56_3)
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | | ALPHA: (139) implies:
% 244.66/51.10  | | | | | |   (140)  op(e2, e3) = all_56_3
% 244.66/51.10  | | | | | |   (141)  op(e2, all_56_3) = e2
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | | BETA: splitting (11) gives:
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | | Case 1:
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | |   (142)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 244.66/51.10  | | | | | | |          (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 244.66/51.10  | | | | | | |          (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 244.66/51.10  | | | | | | |          (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 244.66/51.10  | | | | | | |          (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 244.66/51.10  | | | | | | |          (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | | BETA: splitting (142) gives:
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | | Case 1:
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | |   (143)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 244.66/51.10  | | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) = e3)
% 244.66/51.10  | | | | | | | |          | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &
% 244.66/51.10  | | | | | | | |             ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 244.66/51.10  | | | | | | | |          | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1)
% 244.66/51.10  | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | | BETA: splitting (143) gives:
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | | Case 1:
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | |   (144)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 244.66/51.10  | | | | | | | | |          ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.66/51.10  | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) = e3
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | ALPHA: (144) implies:
% 244.66/51.10  | | | | | | | | |   (145)  op(e2, e3) = e3
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | REF_CLOSE: (33), (61), (140), (141), (145) are inconsistent by
% 244.66/51.10  | | | | | | | | |            sub-proof #2262.
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | Case 2:
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | |   (146)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &
% 244.66/51.10  | | | | | | | | |             ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.10  | | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 244.66/51.10  | | | | | | | | |            e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.66/51.10  | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.66/51.10  | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1)
% 244.66/51.10  | | | | | | | | |            = e3 & op(e1, e3) = e3)
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | REF_CLOSE: (1), (3), (12), (17), (20), (27), (31), (33), (34),
% 244.66/51.10  | | | | | | | | |            (35), (40), (51), (53), (57), (61), (64), (68),
% 244.66/51.10  | | | | | | | | |            (72), (146) are inconsistent by sub-proof #1853.
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | End of split
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | Case 2:
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | |   (147)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) & 
% 244.66/51.10  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1)
% 244.66/51.10  | | | | | | | |          | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 244.66/51.10  | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3)
% 244.66/51.10  | | | | | | | |          | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 244.66/51.10  | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | | REF_CLOSE: (1), (9), (15), (16), (33), (38), (42), (48), (50),
% 244.66/51.10  | | | | | | | |            (61), (64), (69), (125), (131), (132), (133), (147)
% 244.66/51.10  | | | | | | | |            are inconsistent by sub-proof #1848.
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | End of split
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | Case 2:
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | |   (148)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 244.66/51.10  | | | | | | |          (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 244.66/51.10  | | | | | | |          (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 244.66/51.10  | | | | | | |          (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 244.66/51.10  | | | | | | |          (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 244.66/51.10  | | | | | | |          (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | | REF_CLOSE: (1), (5), (7), (8), (9), (11), (13), (15), (16), (18),
% 244.66/51.10  | | | | | | |            (21), (22), (24), (28), (30), (31), (32), (33), (36),
% 244.66/51.10  | | | | | | |            (37), (38), (39), (41), (44), (45), (46), (49), (52),
% 244.66/51.10  | | | | | | |            (54), (55), (56), (57), (60), (61), (65), (66), (71),
% 244.66/51.10  | | | | | | |            (73), (74), (77), (148) are inconsistent by sub-proof
% 244.66/51.10  | | | | | | |            #1846.
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | End of split
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | End of split
% 244.66/51.10  | | | | | 
% 244.66/51.10  | | | | Case 2:
% 244.66/51.10  | | | | | 
% 244.66/51.10  | | | | |   (149)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 244.66/51.10  | | | | |            all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 244.66/51.10  | | | | |              all_56_7) = e0 & op(e0, e3) = all_56_7 & $i(all_56_7))
% 244.66/51.10  | | | | | 
% 244.66/51.10  | | | | | BETA: splitting (149) gives:
% 244.66/51.10  | | | | | 
% 244.66/51.10  | | | | | Case 1:
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | |   (150)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 244.66/51.10  | | | | | |          all_56_5 & $i(all_56_5)
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | | ALPHA: (150) implies:
% 244.66/51.10  | | | | | |   (151)  op(e1, e3) = all_56_5
% 244.66/51.10  | | | | | |   (152)  op(e1, all_56_5) = e1
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | | REF_CLOSE: (61), (132), (134), (151), (152) are inconsistent by
% 244.66/51.10  | | | | | |            sub-proof #2243.
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | Case 2:
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | |   (153)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 244.66/51.10  | | | | | |          all_56_7 & $i(all_56_7)
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | | ALPHA: (153) implies:
% 244.66/51.10  | | | | | |   (154)  op(e0, e3) = all_56_7
% 244.66/51.10  | | | | | |   (155)  op(e0, all_56_7) = e0
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | | BETA: splitting (11) gives:
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | | Case 1:
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | |   (156)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e2) & op(e3, e2) = e3 & op(e2, e3) = e3) |
% 244.66/51.10  | | | | | | |          (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) |
% 244.66/51.10  | | | | | | |          (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 244.66/51.10  | | | | | | |          (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) |
% 244.66/51.10  | | | | | | |          (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) |
% 244.66/51.10  | | | | | | |          (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.66/51.10  | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31
% 244.66/51.10  | | | | | | |              = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | | BETA: splitting (156) gives:
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | | Case 1:
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | |   (157)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) & 
% 244.66/51.10  | | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) = e3)
% 244.66/51.10  | | | | | | | |          | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &
% 244.66/51.10  | | | | | | | |             ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 244.66/51.10  | | | | | | | |          | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1)
% 244.66/51.10  | | | | | | | |            &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | | REF_CLOSE: (1), (3), (12), (17), (20), (27), (31), (33), (34),
% 244.66/51.10  | | | | | | | |            (35), (40), (45), (51), (53), (57), (61), (64), (68),
% 244.66/51.10  | | | | | | | |            (72), (129), (157) are inconsistent by sub-proof
% 244.66/51.10  | | | | | | | |            #1852.
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | Case 2:
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | |   (158)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) & 
% 244.66/51.10  | | | | | | | |            ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1)
% 244.66/51.10  | | | | | | | |          | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 244.66/51.10  | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3)
% 244.66/51.10  | | | | | | | |          | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 244.66/51.10  | | | | | | | |            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.10  | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | | BETA: splitting (158) gives:
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | | Case 1:
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | |   (159)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &
% 244.66/51.10  | | | | | | | | |           ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.10  | | | | | | | | |          (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | ALPHA: (159) implies:
% 244.66/51.10  | | | | | | | | |   (160)  op(e1, e3) = e1
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | REF_CLOSE: (9), (15), (33), (38), (42), (48), (50), (61),
% 244.66/51.10  | | | | | | | | |            (64), (69), (131), (132), (133), (160) are
% 244.66/51.10  | | | | | | | | |            inconsistent by sub-proof #1850.
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | Case 2:
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | |   (161)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 244.66/51.10  | | | | | | | | |            &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.10  | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 244.66/51.10  | | | | | | | | |            e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.66/51.10  | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.66/51.10  | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0)
% 244.66/51.10  | | | | | | | | |            = e0 & op(e0, e3) = e0)
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | BETA: splitting (161) gives:
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | Case 1:
% 244.66/51.10  | | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | |   (162)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 244.66/51.10  | | | | | | | | | |          &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.10  | | | | | | | | | |          (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 244.66/51.10  | | | | | | | | | |          e3
% 244.66/51.10  | | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | | ALPHA: (162) implies:
% 244.66/51.10  | | | | | | | | | |   (163)  op(e0, e3) = e3
% 244.66/51.10  | | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | | REF_CLOSE: (61), (133), (154), (155), (163) are inconsistent
% 244.66/51.10  | | | | | | | | | |            by sub-proof #2070.
% 244.66/51.10  | | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | Case 2:
% 244.66/51.10  | | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | |   (164)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 244.66/51.10  | | | | | | | | | |          &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.10  | | | | | | | | | |          (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 244.66/51.10  | | | | | | | | | |          e0
% 244.66/51.10  | | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | | ALPHA: (164) implies:
% 244.66/51.10  | | | | | | | | | |   (165)  op(e0, e3) = e0
% 244.66/51.10  | | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | | REF_CLOSE: (1), (16), (61), (165) are inconsistent by
% 244.66/51.10  | | | | | | | | | |            sub-proof #2331.
% 244.66/51.10  | | | | | | | | | | 
% 244.66/51.10  | | | | | | | | | End of split
% 244.66/51.10  | | | | | | | | | 
% 244.66/51.10  | | | | | | | | End of split
% 244.66/51.10  | | | | | | | | 
% 244.66/51.10  | | | | | | | End of split
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | Case 2:
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | |   (166)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) = e2) |
% 244.66/51.10  | | | | | | |          (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 244.66/51.10  | | | | | | |          (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 244.66/51.10  | | | | | | |          (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 244.66/51.10  | | | | | | |          (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 244.66/51.10  | | | | | | |          (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) & 
% 244.66/51.10  | | | | | | |            ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.10  | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | | REF_CLOSE: (1), (5), (7), (8), (9), (11), (13), (15), (16), (18),
% 244.66/51.10  | | | | | | |            (21), (22), (24), (28), (30), (31), (32), (33), (36),
% 244.66/51.10  | | | | | | |            (37), (38), (39), (41), (44), (45), (46), (49), (52),
% 244.66/51.10  | | | | | | |            (54), (55), (56), (57), (60), (61), (65), (66), (71),
% 244.66/51.10  | | | | | | |            (73), (74), (77), (166) are inconsistent by sub-proof
% 244.66/51.10  | | | | | | |            #1846.
% 244.66/51.10  | | | | | | | 
% 244.66/51.10  | | | | | | End of split
% 244.66/51.10  | | | | | | 
% 244.66/51.10  | | | | | End of split
% 244.66/51.10  | | | | | 
% 244.66/51.10  | | | | End of split
% 244.66/51.10  | | | | 
% 244.66/51.10  | | | Case 2:
% 244.66/51.10  | | | | 
% 244.66/51.10  | | | |   (167)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.66/51.10  | | | | 
% 244.66/51.10  | | | | REF_CLOSE: (23), (50), (58), (59), (167) are inconsistent by sub-proof
% 244.66/51.10  | | | |            #1949.
% 244.66/51.10  | | | | 
% 244.66/51.10  | | | End of split
% 244.66/51.10  | | | 
% 244.66/51.10  | | End of split
% 244.66/51.10  | | 
% 244.66/51.10  | End of split
% 244.66/51.10  | 
% 244.66/51.10  End of proof
% 244.66/51.10  
% 244.66/51.10  Sub-proof #1846 shows that the following formulas are inconsistent:
% 244.66/51.10  ----------------------------------------------------------------
% 244.66/51.10    (1)   ~ (all_52_3 = e0)
% 244.66/51.10    (2)   ~ (all_52_9 = all_6_2)
% 244.66/51.10    (3)  all_56_11 = e1
% 244.66/51.10    (4)  op(e0, e1) = all_52_11
% 244.66/51.10    (5)   ~ (e2 = e0)
% 244.66/51.10    (6)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.66/51.10           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.66/51.10             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.66/51.10           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.66/51.10             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.66/51.10           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.10           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.66/51.10           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.66/51.10           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.66/51.10           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.10           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.66/51.10             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.66/51.10           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.10           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 244.66/51.10           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.66/51.10           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.66/51.10           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.66/51.10           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.66/51.10             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.66/51.10           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.10           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.66/51.10           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.66/51.10           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.66/51.10           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.10           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.66/51.10             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.66/51.10           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.10           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.66/51.11    (7)   ~ (all_52_12 = e0)
% 244.66/51.11    (8)  op(e1, e0) = all_52_14
% 244.66/51.11    (9)  op(e0, e3) = all_52_3
% 244.66/51.11    (10)  op(e1, e0) = e1
% 244.66/51.11    (11)   ~ (all_52_12 = all_52_14)
% 244.66/51.11    (12)   ~ (all_52_12 = all_52_13)
% 244.66/51.11    (13)  op(e2, e0) = e3
% 244.66/51.11    (14)  all_54_10 = all_6_2
% 244.66/51.11    (15)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.66/51.11    (16)   ~ (all_6_2 = e3)
% 244.66/51.11    (17)  op(e3, e1) = all_52_8
% 244.66/51.11    (18)  op(e2, e1) = all_52_9
% 244.66/51.11    (19)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.66/51.11              e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.66/51.11            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.66/51.11              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 244.66/51.11              e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 244.66/51.11            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 244.66/51.11            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.66/51.11            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 244.66/51.11            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.66/51.11              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 244.66/51.11            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.11            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 =
% 244.66/51.11            e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.66/51.11            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 244.66/51.11            = e0)
% 244.66/51.11    (20)   ~ (e3 = e2)
% 244.66/51.11    (21)   ~ (all_52_14 = all_6_2)
% 244.66/51.11    (22)   ~ (all_6_2 = e0)
% 244.66/51.11    (23)   ~ (all_52_14 = e0)
% 244.66/51.11    (24)  all_56_31 = e0
% 244.66/51.11    (25)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.66/51.11    (26)   ~ (all_52_4 = all_52_12)
% 244.66/51.11    (27)  op(e2, e3) = all_52_1
% 244.66/51.11    (28)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.66/51.11    (29)   ~ (all_52_1 = all_52_13)
% 244.66/51.11    (30)  all_54_7 = all_52_13
% 244.66/51.11    (31)   ~ (all_52_13 = all_52_14)
% 244.66/51.11    (32)  op(e2, e1) = e0
% 244.66/51.11    (33)  op(e3, e2) = all_52_4
% 244.66/51.11    (34)   ~ (all_52_8 = all_52_11)
% 244.66/51.11    (35)  all_54_3 = all_52_12
% 244.66/51.11    (36)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.11    (37)   ~ (e1 = e0)
% 244.66/51.11    (38)  all_56_21 = all_6_2
% 244.66/51.11    (39)  op(e2, e0) = all_52_13
% 244.66/51.11    (40)   ~ (all_52_9 = all_52_11)
% 244.66/51.11    (41)   ~ (all_52_13 = e0)
% 244.66/51.11  
% 244.66/51.11  Begin of proof
% 244.66/51.11  | 
% 244.66/51.11  | BETA: splitting (19) gives:
% 244.66/51.11  | 
% 244.66/51.11  | Case 1:
% 244.66/51.11  | | 
% 244.66/51.11  | |   (42)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 244.66/51.11  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.66/51.11  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.66/51.11  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.66/51.11  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 244.66/51.11  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.11  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.66/51.11  | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.66/51.11  | | 
% 244.66/51.11  | | BETA: splitting (42) gives:
% 244.66/51.11  | | 
% 244.66/51.11  | | Case 1:
% 244.66/51.11  | | | 
% 244.66/51.11  | | |   (43)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 244.66/51.11  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.66/51.11  | | |         op(e2, e1) = e2 & op(e1, e2) = e2
% 244.66/51.11  | | | 
% 244.66/51.11  | | | ALPHA: (43) implies:
% 244.66/51.11  | | |   (44)  op(e2, e1) = e2
% 244.66/51.11  | | | 
% 244.66/51.11  | | | REF_CLOSE: (5), (32), (36), (44) are inconsistent by sub-proof #1906.
% 244.66/51.11  | | | 
% 244.66/51.11  | | Case 2:
% 244.66/51.11  | | | 
% 244.66/51.11  | | |   (45)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.66/51.11  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.66/51.11  | | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27
% 244.66/51.11  | | |           = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 244.66/51.11  | | |             = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) =
% 244.66/51.11  | | |           e2)
% 244.66/51.11  | | | 
% 244.66/51.11  | | | BETA: splitting (45) gives:
% 244.66/51.11  | | | 
% 244.66/51.11  | | | Case 1:
% 244.66/51.11  | | | | 
% 244.66/51.11  | | | |   (46)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.66/51.11  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.66/51.11  | | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 244.66/51.11  | | | | 
% 244.66/51.11  | | | | ALPHA: (46) implies:
% 244.66/51.11  | | | |   (47)  op(e2, e1) = e1
% 244.66/51.11  | | | | 
% 244.66/51.11  | | | | REF_CLOSE: (18), (32), (36), (37), (47) are inconsistent by sub-proof
% 244.66/51.11  | | | |            #2165.
% 244.66/51.11  | | | | 
% 244.66/51.11  | | | Case 2:
% 244.66/51.11  | | | | 
% 244.66/51.11  | | | |   (48)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.11  | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.66/51.11  | | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 244.66/51.11  | | | | 
% 244.66/51.11  | | | | ALPHA: (48) implies:
% 244.66/51.11  | | | |   (49)  op(e2, e0) = e2
% 244.66/51.11  | | | | 
% 244.66/51.11  | | | | REF_CLOSE: (13), (20), (36), (49) are inconsistent by sub-proof #2152.
% 244.66/51.11  | | | | 
% 244.66/51.11  | | | End of split
% 244.66/51.11  | | | 
% 244.66/51.11  | | End of split
% 244.66/51.11  | | 
% 244.66/51.11  | Case 2:
% 244.66/51.11  | | 
% 244.66/51.11  | |   (50)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 244.66/51.11  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.66/51.11  | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 244.66/51.11  | |           e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.66/51.11  | |             e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 244.66/51.11  | |         (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 244.66/51.11  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.66/51.11  | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.66/51.11  | | 
% 244.66/51.11  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 244.66/51.11  | |            (15), (16), (17), (18), (21), (22), (23), (24), (25), (26), (27),
% 244.66/51.11  | |            (28), (29), (30), (31), (33), (34), (35), (36), (37), (38), (39),
% 244.66/51.11  | |            (40), (41), (50) are inconsistent by sub-proof #1847.
% 244.66/51.11  | | 
% 244.66/51.11  | End of split
% 244.66/51.11  | 
% 244.66/51.11  End of proof
% 244.66/51.11  
% 244.66/51.11  Sub-proof #1847 shows that the following formulas are inconsistent:
% 244.66/51.11  ----------------------------------------------------------------
% 244.66/51.11    (1)   ~ (all_52_3 = e0)
% 244.66/51.11    (2)   ~ (all_52_9 = all_6_2)
% 244.66/51.11    (3)  all_56_11 = e1
% 244.66/51.11    (4)  op(e0, e1) = all_52_11
% 244.66/51.11    (5)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.66/51.11           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.66/51.11             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.66/51.11           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.66/51.11             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.66/51.11           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.11           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.66/51.11           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.66/51.11           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.66/51.11           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.11           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.66/51.11             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.66/51.11           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.11           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 244.66/51.11           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.66/51.11           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.66/51.11           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.66/51.11           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.66/51.11             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.66/51.11           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.66/51.11           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.66/51.11           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.66/51.11           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.66/51.11           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.11           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.66/51.11             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.66/51.11           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.11           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.66/51.11    (6)   ~ (all_52_12 = e0)
% 244.66/51.11    (7)  op(e1, e0) = all_52_14
% 244.66/51.11    (8)  op(e0, e3) = all_52_3
% 244.66/51.11    (9)  op(e1, e0) = e1
% 244.66/51.11    (10)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.66/51.11              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.66/51.11            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 244.66/51.11              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 244.66/51.11              e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 &
% 244.66/51.11            all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.66/51.11            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 244.66/51.11            = e0)
% 244.66/51.11    (11)   ~ (all_52_12 = all_52_14)
% 244.66/51.11    (12)   ~ (all_52_12 = all_52_13)
% 244.66/51.11    (13)  all_54_10 = all_6_2
% 244.66/51.11    (14)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.66/51.11    (15)   ~ (all_6_2 = e3)
% 244.66/51.11    (16)  op(e3, e1) = all_52_8
% 244.66/51.11    (17)  op(e2, e1) = all_52_9
% 244.66/51.11    (18)   ~ (all_52_14 = all_6_2)
% 244.66/51.11    (19)   ~ (all_6_2 = e0)
% 244.66/51.11    (20)   ~ (all_52_14 = e0)
% 244.66/51.11    (21)  all_56_31 = e0
% 244.66/51.11    (22)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.66/51.11    (23)   ~ (all_52_4 = all_52_12)
% 244.66/51.11    (24)  op(e2, e3) = all_52_1
% 244.66/51.11    (25)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.66/51.11    (26)   ~ (all_52_1 = all_52_13)
% 244.66/51.11    (27)  all_54_7 = all_52_13
% 244.66/51.11    (28)   ~ (all_52_13 = all_52_14)
% 244.66/51.11    (29)  op(e3, e2) = all_52_4
% 244.66/51.11    (30)   ~ (all_52_8 = all_52_11)
% 244.66/51.11    (31)  all_54_3 = all_52_12
% 244.66/51.11    (32)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.11    (33)   ~ (e1 = e0)
% 244.66/51.11    (34)  all_56_21 = all_6_2
% 244.66/51.11    (35)  op(e2, e0) = all_52_13
% 244.66/51.11    (36)   ~ (all_52_9 = all_52_11)
% 244.66/51.11    (37)   ~ (all_52_13 = e0)
% 244.66/51.11  
% 244.66/51.11  Begin of proof
% 244.66/51.11  | 
% 244.66/51.11  | BETA: splitting (10) gives:
% 244.66/51.11  | 
% 244.66/51.11  | Case 1:
% 244.66/51.11  | | 
% 244.66/51.11  | |   (38)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.66/51.11  | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) =
% 244.66/51.11  | |         e0 & op(e0, e2) = e0
% 244.66/51.11  | | 
% 244.66/51.11  | | ALPHA: (38) implies:
% 244.66/51.11  | |   (39)  op(e2, e0) = e0
% 244.66/51.11  | | 
% 244.66/51.11  | | REF_CLOSE: (32), (35), (37), (39) are inconsistent by sub-proof #2324.
% 244.66/51.11  | | 
% 244.66/51.11  | Case 2:
% 244.66/51.11  | | 
% 244.66/51.11  | |   (40)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.11  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.66/51.11  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 244.66/51.11  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.66/51.11  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.66/51.11  | | 
% 244.66/51.11  | | BETA: splitting (40) gives:
% 244.66/51.11  | | 
% 244.66/51.11  | | Case 1:
% 244.66/51.11  | | | 
% 244.66/51.11  | | |   (41)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.66/51.11  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.66/51.11  | | |         op(e1, e0) = e1 & op(e0, e1) = e1
% 244.66/51.11  | | | 
% 244.66/51.11  | | | ALPHA: (41) implies:
% 244.66/51.11  | | |   (42)  op(e0, e1) = e1
% 244.66/51.11  | | | 
% 244.66/51.11  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 244.66/51.11  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 244.66/51.11  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (34),
% 244.66/51.11  | | |            (35), (36), (37), (42) are inconsistent by sub-proof #2281.
% 244.66/51.11  | | | 
% 244.66/51.11  | | Case 2:
% 244.66/51.11  | | | 
% 244.66/51.11  | | |   (43)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 244.66/51.11  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.66/51.11  | | |         op(e1, e0) = e0 & op(e0, e1) = e0
% 244.66/51.11  | | | 
% 244.66/51.11  | | | ALPHA: (43) implies:
% 244.66/51.11  | | |   (44)  op(e1, e0) = e0
% 244.66/51.11  | | | 
% 244.66/51.11  | | | REF_CLOSE: (9), (32), (33), (44) are inconsistent by sub-proof #2284.
% 244.66/51.11  | | | 
% 244.66/51.11  | | End of split
% 244.66/51.11  | | 
% 244.66/51.11  | End of split
% 244.66/51.11  | 
% 244.66/51.11  End of proof
% 244.66/51.11  
% 244.66/51.11  Sub-proof #1848 shows that the following formulas are inconsistent:
% 244.66/51.11  ----------------------------------------------------------------
% 244.66/51.11    (1)   ~ (all_52_3 = e0)
% 244.66/51.11    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.66/51.11             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.66/51.11           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 244.66/51.11           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.66/51.11           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 244.66/51.11           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.11           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.66/51.11    (3)   ~ (e3 = e0)
% 244.66/51.11    (4)   ~ (e2 = e0)
% 244.66/51.11    (5)  op(e1, e0) = all_52_14
% 244.66/51.11    (6)  op(e0, e3) = all_52_3
% 244.66/51.11    (7)   ~ (e3 = e1)
% 244.66/51.11    (8)   ~ (e3 = e2)
% 244.66/51.11    (9)   ~ (all_52_14 = e0)
% 244.66/51.11    (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.66/51.11          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.66/51.11    (11)   ~ (all_52_14 = e3)
% 244.66/51.11    (12)  op(e3, e0) = e2
% 244.66/51.11    (13)  op(e1, e1) = e2
% 244.66/51.11    (14)   ~ (all_52_2 = e0)
% 244.66/51.11    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.11    (16)  op(e1, e3) = all_52_2
% 244.66/51.11    (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.66/51.11          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.66/51.11  
% 244.66/51.11  Begin of proof
% 244.66/51.11  | 
% 244.66/51.11  | BETA: splitting (2) gives:
% 244.66/51.11  | 
% 244.66/51.11  | Case 1:
% 244.66/51.11  | | 
% 244.66/51.11  | |   (18)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.66/51.11  | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 244.66/51.11  | |         e1 & op(e1, e3) = e1
% 244.66/51.11  | | 
% 244.66/51.11  | | ALPHA: (18) implies:
% 244.66/51.11  | |   (19)  op(e1, e3) = e1
% 244.66/51.11  | | 
% 244.66/51.11  | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (11), (13), (14), (15), (16),
% 244.66/51.11  | |            (17), (19) are inconsistent by sub-proof #1850.
% 244.66/51.11  | | 
% 244.66/51.11  | Case 2:
% 244.66/51.11  | | 
% 244.66/51.11  | |   (20)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.66/51.11  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 244.66/51.11  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.66/51.11  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.66/51.11  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.66/51.11  | | 
% 244.66/51.11  | | REF_CLOSE: (1), (6), (8), (12), (15), (20) are inconsistent by sub-proof
% 244.66/51.11  | |            #1849.
% 244.66/51.11  | | 
% 244.66/51.11  | End of split
% 244.66/51.11  | 
% 244.66/51.11  End of proof
% 244.66/51.11  
% 244.66/51.11  Sub-proof #1849 shows that the following formulas are inconsistent:
% 244.66/51.11  ----------------------------------------------------------------
% 244.66/51.11    (1)   ~ (all_52_3 = e0)
% 244.66/51.11    (2)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.66/51.11             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.66/51.11           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 244.66/51.11           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.66/51.11           op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.66/51.11    (3)  op(e0, e3) = all_52_3
% 244.66/51.11    (4)   ~ (e3 = e2)
% 244.66/51.11    (5)  op(e3, e0) = e2
% 244.66/51.11    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.11  
% 244.66/51.11  Begin of proof
% 244.66/51.11  | 
% 244.66/51.11  | BETA: splitting (2) gives:
% 244.66/51.11  | 
% 244.66/51.11  | Case 1:
% 244.66/51.11  | | 
% 244.66/51.12  | |   (7)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.66/51.12  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.66/51.12  | |        op(e0, e3) = e3
% 244.66/51.12  | | 
% 244.66/51.12  | | ALPHA: (7) implies:
% 244.66/51.12  | |   (8)  op(e3, e0) = e3
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2125.
% 244.66/51.12  | | 
% 244.66/51.12  | Case 2:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (9)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.66/51.12  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 244.66/51.12  | |        op(e0, e3) = e0
% 244.66/51.12  | | 
% 244.66/51.12  | | ALPHA: (9) implies:
% 244.66/51.12  | |   (10)  op(e0, e3) = e0
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #2331.
% 244.66/51.12  | | 
% 244.66/51.12  | End of split
% 244.66/51.12  | 
% 244.66/51.12  End of proof
% 244.66/51.12  
% 244.66/51.12  Sub-proof #1850 shows that the following formulas are inconsistent:
% 244.66/51.12  ----------------------------------------------------------------
% 244.66/51.12    (1)   ~ (e3 = e0)
% 244.66/51.12    (2)   ~ (e2 = e0)
% 244.66/51.12    (3)  op(e1, e0) = all_52_14
% 244.66/51.12    (4)   ~ (e3 = e1)
% 244.66/51.12    (5)   ~ (e3 = e2)
% 244.66/51.12    (6)   ~ (all_52_14 = e0)
% 244.66/51.12    (7)  op(e1, e3) = e1
% 244.66/51.12    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.66/51.12         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.66/51.12    (9)   ~ (all_52_14 = e3)
% 244.66/51.12    (10)  op(e1, e1) = e2
% 244.66/51.12    (11)   ~ (all_52_2 = e0)
% 244.66/51.12    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.12    (13)  op(e1, e3) = all_52_2
% 244.66/51.12    (14)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.66/51.12          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.66/51.12  
% 244.66/51.12  Begin of proof
% 244.66/51.12  | 
% 244.66/51.12  | BETA: splitting (14) gives:
% 244.66/51.12  | 
% 244.66/51.12  | Case 1:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 244.66/51.12  | |           e0)
% 244.66/51.12  | | 
% 244.66/51.12  | | BETA: splitting (15) gives:
% 244.66/51.12  | | 
% 244.66/51.12  | | Case 1:
% 244.66/51.12  | | | 
% 244.66/51.12  | | |   (16)  all_58_6 = e0 & op(e1, e3) = e0
% 244.66/51.12  | | | 
% 244.66/51.12  | | | ALPHA: (16) implies:
% 244.66/51.12  | | |   (17)  op(e1, e3) = e0
% 244.66/51.12  | | | 
% 244.66/51.12  | | | REF_CLOSE: (11), (12), (13), (17) are inconsistent by sub-proof #2023.
% 244.66/51.12  | | | 
% 244.66/51.12  | | Case 2:
% 244.66/51.12  | | | 
% 244.66/51.12  | | |   (18)  all_58_7 = e0 & op(e1, e2) = e0
% 244.66/51.12  | | | 
% 244.66/51.12  | | | ALPHA: (18) implies:
% 244.66/51.12  | | |   (19)  all_58_7 = e0
% 244.66/51.12  | | | 
% 244.66/51.12  | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (19) are
% 244.66/51.12  | | |            inconsistent by sub-proof #2147.
% 244.66/51.12  | | | 
% 244.66/51.12  | | End of split
% 244.66/51.12  | | 
% 244.66/51.12  | Case 2:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (20)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.66/51.12  | |           e0)
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (2), (3), (6), (10), (12), (20) are inconsistent by sub-proof
% 244.66/51.12  | |            #1851.
% 244.66/51.12  | | 
% 244.66/51.12  | End of split
% 244.66/51.12  | 
% 244.66/51.12  End of proof
% 244.66/51.12  
% 244.66/51.12  Sub-proof #1851 shows that the following formulas are inconsistent:
% 244.66/51.12  ----------------------------------------------------------------
% 244.66/51.12    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.66/51.12    (2)   ~ (e2 = e0)
% 244.66/51.12    (3)  op(e1, e0) = all_52_14
% 244.66/51.12    (4)   ~ (all_52_14 = e0)
% 244.66/51.12    (5)  op(e1, e1) = e2
% 244.66/51.12    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.12  
% 244.66/51.12  Begin of proof
% 244.66/51.12  | 
% 244.66/51.12  | BETA: splitting (1) gives:
% 244.66/51.12  | 
% 244.66/51.12  | Case 1:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 244.66/51.12  | | 
% 244.66/51.12  | | ALPHA: (7) implies:
% 244.66/51.12  | |   (8)  op(e1, e1) = e0
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2211.
% 244.66/51.12  | | 
% 244.66/51.12  | Case 2:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (9)  all_58_11 = e0 & op(e1, e0) = e0
% 244.66/51.12  | | 
% 244.66/51.12  | | ALPHA: (9) implies:
% 244.66/51.12  | |   (10)  op(e1, e0) = e0
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #2323.
% 244.66/51.12  | | 
% 244.66/51.12  | End of split
% 244.66/51.12  | 
% 244.66/51.12  End of proof
% 244.66/51.12  
% 244.66/51.12  Sub-proof #1852 shows that the following formulas are inconsistent:
% 244.66/51.12  ----------------------------------------------------------------
% 244.66/51.12    (1)   ~ (all_52_3 = e0)
% 244.66/51.12    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.66/51.12    (3)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.66/51.12           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.66/51.12             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.66/51.12           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.66/51.12             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.66/51.12           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.12           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.66/51.12    (4)   ~ (all_52_7 = all_52_11)
% 244.66/51.12    (5)  op(e0, e2) = e2
% 244.66/51.12    (6)   ~ (all_52_2 = all_52_3)
% 244.66/51.12    (7)   ~ (all_52_3 = all_52_7)
% 244.66/51.12    (8)  op(e3, e1) = all_52_8
% 244.66/51.12    (9)   ~ (e3 = e2)
% 244.66/51.12    (10)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.66/51.12    (11)   ~ (all_52_3 = all_52_11)
% 244.66/51.12    (12)  all_54_12 = all_52_3
% 244.66/51.12    (13)  op(e2, e3) = all_52_1
% 244.66/51.12    (14)   ~ (all_52_11 = e0)
% 244.66/51.12    (15)  op(e0, e2) = all_52_7
% 244.66/51.12    (16)   ~ (all_52_8 = all_52_11)
% 244.66/51.12    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.12    (18)  op(e1, e3) = all_52_2
% 244.66/51.12    (19)  op(e3, e2) = e3
% 244.66/51.12    (20)   ~ (all_52_1 = e3)
% 244.66/51.12    (21)  all_54_14 = all_52_11
% 244.66/51.12  
% 244.66/51.12  Begin of proof
% 244.66/51.12  | 
% 244.66/51.12  | BETA: splitting (3) gives:
% 244.66/51.12  | 
% 244.66/51.12  | Case 1:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (22)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.66/51.12  | |           e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3
% 244.66/51.12  | |         & op(e2, e3) = e3
% 244.66/51.12  | | 
% 244.66/51.12  | | ALPHA: (22) implies:
% 244.66/51.12  | |   (23)  op(e2, e3) = e3
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (13), (17), (20), (23) are inconsistent by sub-proof #2337.
% 244.66/51.12  | | 
% 244.66/51.12  | Case 2:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (24)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.66/51.12  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 244.66/51.12  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.66/51.12  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.66/51.12  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 244.66/51.12  | |            (15), (16), (17), (18), (19), (21), (24) are inconsistent by
% 244.66/51.12  | |            sub-proof #1853.
% 244.66/51.12  | | 
% 244.66/51.12  | End of split
% 244.66/51.12  | 
% 244.66/51.12  End of proof
% 244.66/51.12  
% 244.66/51.12  Sub-proof #1853 shows that the following formulas are inconsistent:
% 244.66/51.12  ----------------------------------------------------------------
% 244.66/51.12    (1)   ~ (all_52_3 = e0)
% 244.66/51.12    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.66/51.12    (3)   ~ (all_52_7 = all_52_11)
% 244.66/51.12    (4)  op(e0, e2) = e2
% 244.66/51.12    (5)   ~ (all_52_2 = all_52_3)
% 244.66/51.12    (6)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 244.66/51.12           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 244.66/51.12             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.66/51.12           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 244.66/51.12             e1) = e3 & op(e1, e3) = e3)
% 244.66/51.12    (7)   ~ (all_52_3 = all_52_7)
% 244.66/51.12    (8)  op(e3, e1) = all_52_8
% 244.66/51.12    (9)   ~ (e3 = e2)
% 244.66/51.12    (10)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.66/51.12    (11)   ~ (all_52_3 = all_52_11)
% 244.66/51.12    (12)  all_54_12 = all_52_3
% 244.66/51.12    (13)   ~ (all_52_11 = e0)
% 244.66/51.12    (14)  op(e0, e2) = all_52_7
% 244.66/51.12    (15)   ~ (all_52_8 = all_52_11)
% 244.66/51.12    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.12    (17)  op(e1, e3) = all_52_2
% 244.66/51.12    (18)  op(e3, e2) = e3
% 244.66/51.12    (19)  all_54_14 = all_52_11
% 244.66/51.12  
% 244.66/51.12  Begin of proof
% 244.66/51.12  | 
% 244.66/51.12  | BETA: splitting (6) gives:
% 244.66/51.12  | 
% 244.66/51.12  | Case 1:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (20)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.66/51.12  | |           e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2
% 244.66/51.12  | |         & op(e2, e3) = e2
% 244.66/51.12  | | 
% 244.66/51.12  | | ALPHA: (20) implies:
% 244.66/51.12  | |   (21)  op(e3, e2) = e2
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (9), (16), (18), (21) are inconsistent by sub-proof #2193.
% 244.66/51.12  | | 
% 244.66/51.12  | Case 2:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (22)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.66/51.12  | |           = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) =
% 244.66/51.12  | |         e3 & op(e1, e3) = e3
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 244.66/51.12  | |            (15), (16), (17), (19), (22) are inconsistent by sub-proof #1854.
% 244.66/51.12  | | 
% 244.66/51.12  | End of split
% 244.66/51.12  | 
% 244.66/51.12  End of proof
% 244.66/51.12  
% 244.66/51.12  Sub-proof #1854 shows that the following formulas are inconsistent:
% 244.66/51.12  ----------------------------------------------------------------
% 244.66/51.12    (1)   ~ (all_52_3 = e0)
% 244.66/51.12    (2)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.66/51.12    (3)   ~ (all_52_7 = all_52_11)
% 244.66/51.12    (4)  op(e0, e2) = e2
% 244.66/51.12    (5)   ~ (all_52_2 = all_52_3)
% 244.66/51.12    (6)   ~ (all_52_3 = all_52_7)
% 244.66/51.12    (7)  op(e3, e1) = all_52_8
% 244.66/51.12    (8)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.66/51.12    (9)   ~ (all_52_3 = all_52_11)
% 244.66/51.12    (10)  all_54_12 = all_52_3
% 244.66/51.12    (11)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.66/51.12            e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.66/51.12          op(e1, e3) = e3
% 244.66/51.12    (12)   ~ (all_52_11 = e0)
% 244.66/51.12    (13)  op(e0, e2) = all_52_7
% 244.66/51.12    (14)   ~ (all_52_8 = all_52_11)
% 244.66/51.12    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.12    (16)  op(e1, e3) = all_52_2
% 244.66/51.12    (17)  all_54_14 = all_52_11
% 244.66/51.12  
% 244.66/51.12  Begin of proof
% 244.66/51.12  | 
% 244.66/51.12  | ALPHA: (11) implies:
% 244.66/51.12  |   (18)  op(e1, e3) = e3
% 244.66/51.12  |   (19)  op(e3, e1) = e3
% 244.66/51.12  | 
% 244.66/51.12  | GROUND_INST: instantiating (15) with all_52_7, e2, e2, e0, simplifying with
% 244.66/51.12  |              (4), (13) gives:
% 244.66/51.12  |   (20)  all_52_7 = e2
% 244.66/51.12  | 
% 244.66/51.12  | GROUND_INST: instantiating (15) with all_52_2, e3, e3, e1, simplifying with
% 244.66/51.12  |              (16), (18) gives:
% 244.66/51.12  |   (21)  all_52_2 = e3
% 244.66/51.12  | 
% 244.66/51.12  | GROUND_INST: instantiating (15) with all_52_8, e3, e1, e3, simplifying with
% 244.66/51.12  |              (7), (19) gives:
% 244.66/51.12  |   (22)  all_52_8 = e3
% 244.66/51.12  | 
% 244.66/51.12  | REDUCE: (5), (21) imply:
% 244.66/51.12  |   (23)   ~ (all_52_3 = e3)
% 244.66/51.12  | 
% 244.66/51.12  | SIMP: (23) implies:
% 244.66/51.12  |   (24)   ~ (all_52_3 = e3)
% 244.66/51.12  | 
% 244.66/51.12  | REDUCE: (6), (20) imply:
% 244.66/51.12  |   (25)   ~ (all_52_3 = e2)
% 244.66/51.12  | 
% 244.66/51.12  | REDUCE: (3), (20) imply:
% 244.66/51.12  |   (26)   ~ (all_52_11 = e2)
% 244.66/51.12  | 
% 244.66/51.12  | SIMP: (26) implies:
% 244.66/51.12  |   (27)   ~ (all_52_11 = e2)
% 244.66/51.12  | 
% 244.66/51.12  | REDUCE: (14), (22) imply:
% 244.66/51.12  |   (28)   ~ (all_52_11 = e3)
% 244.66/51.12  | 
% 244.66/51.12  | SIMP: (28) implies:
% 244.66/51.12  |   (29)   ~ (all_52_11 = e3)
% 244.66/51.12  | 
% 244.66/51.12  | BETA: splitting (8) gives:
% 244.66/51.12  | 
% 244.66/51.12  | Case 1:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (30)  all_54_14 = e3
% 244.66/51.12  | | 
% 244.66/51.12  | | COMBINE_EQS: (17), (30) imply:
% 244.66/51.12  | |   (31)  all_52_11 = e3
% 244.66/51.12  | | 
% 244.66/51.12  | | REDUCE: (29), (31) imply:
% 244.66/51.12  | |   (32)  $false
% 244.66/51.12  | | 
% 244.66/51.12  | | CLOSE: (32) is inconsistent.
% 244.66/51.12  | | 
% 244.66/51.12  | Case 2:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (33)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.66/51.12  | | 
% 244.66/51.12  | | BETA: splitting (2) gives:
% 244.66/51.12  | | 
% 244.66/51.12  | | Case 1:
% 244.66/51.12  | | | 
% 244.66/51.12  | | |   (34)  all_54_12 = e3
% 244.66/51.12  | | | 
% 244.66/51.12  | | | REF_CLOSE: (10), (24), (34) are inconsistent by sub-proof #2266.
% 244.66/51.12  | | | 
% 244.66/51.12  | | Case 2:
% 244.66/51.12  | | | 
% 244.66/51.12  | | |   (35)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.66/51.12  | | | 
% 244.66/51.12  | | | REF_CLOSE: (1), (9), (10), (12), (17), (25), (27), (33), (35) are
% 244.66/51.12  | | |            inconsistent by sub-proof #1855.
% 244.66/51.12  | | | 
% 244.66/51.12  | | End of split
% 244.66/51.12  | | 
% 244.66/51.12  | End of split
% 244.66/51.12  | 
% 244.66/51.12  End of proof
% 244.66/51.12  
% 244.66/51.12  Sub-proof #1855 shows that the following formulas are inconsistent:
% 244.66/51.12  ----------------------------------------------------------------
% 244.66/51.12    (1)   ~ (all_52_3 = e0)
% 244.66/51.12    (2)   ~ (all_52_11 = e2)
% 244.66/51.12    (3)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.66/51.12    (4)   ~ (all_52_3 = all_52_11)
% 244.66/51.12    (5)  all_54_12 = all_52_3
% 244.66/51.12    (6)   ~ (all_52_3 = e2)
% 244.66/51.12    (7)   ~ (all_52_11 = e0)
% 244.66/51.12    (8)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.66/51.12    (9)  all_54_14 = all_52_11
% 244.66/51.12  
% 244.66/51.12  Begin of proof
% 244.66/51.12  | 
% 244.66/51.12  | BETA: splitting (8) gives:
% 244.66/51.12  | 
% 244.66/51.12  | Case 1:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (10)  all_54_12 = e2
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #2264.
% 244.66/51.12  | | 
% 244.66/51.12  | Case 2:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (11)  all_54_12 = e1 | all_54_12 = e0
% 244.66/51.12  | | 
% 244.66/51.12  | | BETA: splitting (11) gives:
% 244.66/51.12  | | 
% 244.66/51.12  | | Case 1:
% 244.66/51.12  | | | 
% 244.66/51.12  | | |   (12)  all_54_12 = e1
% 244.66/51.12  | | | 
% 244.66/51.12  | | | COMBINE_EQS: (5), (12) imply:
% 244.66/51.12  | | |   (13)  all_52_3 = e1
% 244.66/51.12  | | | 
% 244.66/51.12  | | | SIMP: (13) implies:
% 244.66/51.12  | | |   (14)  all_52_3 = e1
% 244.66/51.12  | | | 
% 244.66/51.12  | | | REDUCE: (4), (14) imply:
% 244.66/51.12  | | |   (15)   ~ (all_52_11 = e1)
% 244.66/51.12  | | | 
% 244.66/51.12  | | | SIMP: (15) implies:
% 244.66/51.12  | | |   (16)   ~ (all_52_11 = e1)
% 244.66/51.12  | | | 
% 244.66/51.12  | | | BETA: splitting (3) gives:
% 244.66/51.12  | | | 
% 244.66/51.12  | | | Case 1:
% 244.66/51.12  | | | | 
% 244.66/51.12  | | | |   (17)  all_54_14 = e2
% 244.66/51.12  | | | | 
% 244.66/51.12  | | | | REF_CLOSE: (2), (9), (17) are inconsistent by sub-proof #1856.
% 244.66/51.12  | | | | 
% 244.66/51.12  | | | Case 2:
% 244.66/51.12  | | | | 
% 244.66/51.12  | | | |   (18)  all_54_14 = e1 | all_54_14 = e0
% 244.66/51.12  | | | | 
% 244.66/51.12  | | | | REF_CLOSE: (7), (9), (16), (18) are inconsistent by sub-proof #1935.
% 244.66/51.12  | | | | 
% 244.66/51.12  | | | End of split
% 244.66/51.12  | | | 
% 244.66/51.12  | | Case 2:
% 244.66/51.12  | | | 
% 244.66/51.12  | | |   (19)  all_54_12 = e0
% 244.66/51.12  | | | 
% 244.66/51.12  | | | REF_CLOSE: (1), (5), (19) are inconsistent by sub-proof #2068.
% 244.66/51.12  | | | 
% 244.66/51.12  | | End of split
% 244.66/51.12  | | 
% 244.66/51.12  | End of split
% 244.66/51.12  | 
% 244.66/51.12  End of proof
% 244.66/51.12  
% 244.66/51.12  Sub-proof #1856 shows that the following formulas are inconsistent:
% 244.66/51.12  ----------------------------------------------------------------
% 244.66/51.12    (1)  all_54_14 = all_52_11
% 244.66/51.12    (2)  all_54_14 = e2
% 244.66/51.12    (3)   ~ (all_52_11 = e2)
% 244.66/51.12  
% 244.66/51.12  Begin of proof
% 244.66/51.12  | 
% 244.66/51.12  | COMBINE_EQS: (1), (2) imply:
% 244.66/51.12  |   (4)  all_52_11 = e2
% 244.66/51.12  | 
% 244.66/51.12  | SIMP: (4) implies:
% 244.66/51.12  |   (5)  all_52_11 = e2
% 244.66/51.12  | 
% 244.66/51.12  | REDUCE: (3), (5) imply:
% 244.66/51.12  |   (6)  $false
% 244.66/51.12  | 
% 244.66/51.12  | CLOSE: (6) is inconsistent.
% 244.66/51.12  | 
% 244.66/51.12  End of proof
% 244.66/51.12  
% 244.66/51.12  Sub-proof #1857 shows that the following formulas are inconsistent:
% 244.66/51.12  ----------------------------------------------------------------
% 244.66/51.12    (1)   ~ (e2 = e0)
% 244.66/51.12    (2)   ~ (e3 = e2)
% 244.66/51.12    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.12    (4)  op(e3, e3) = e0
% 244.66/51.12    (5)  op(e3, e2) = e3
% 244.66/51.12    (6)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 244.66/51.12  
% 244.66/51.12  Begin of proof
% 244.66/51.12  | 
% 244.66/51.12  | BETA: splitting (6) gives:
% 244.66/51.12  | 
% 244.66/51.12  | Case 1:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 244.66/51.12  | | 
% 244.66/51.12  | | ALPHA: (7) implies:
% 244.66/51.12  | |   (8)  op(e3, e3) = e2
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2188.
% 244.66/51.12  | | 
% 244.66/51.12  | Case 2:
% 244.66/51.12  | | 
% 244.66/51.12  | |   (9)  all_58_1 = e2 & op(e3, e2) = e2
% 244.66/51.12  | | 
% 244.66/51.12  | | ALPHA: (9) implies:
% 244.66/51.12  | |   (10)  op(e3, e2) = e2
% 244.66/51.12  | | 
% 244.66/51.12  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #2193.
% 244.66/51.12  | | 
% 244.66/51.12  | End of split
% 244.66/51.12  | 
% 244.66/51.12  End of proof
% 244.66/51.12  
% 244.66/51.12  Sub-proof #1858 shows that the following formulas are inconsistent:
% 244.66/51.12  ----------------------------------------------------------------
% 244.66/51.12    (1)   ~ (all_6_2 = e2)
% 244.66/51.12    (2)  op(e1, e0) = all_52_14
% 244.66/51.12    (3)  op(e1, e0) = e1
% 244.66/51.12    (4)  all_54_10 = all_6_2
% 244.66/51.12    (5)   ~ (all_6_2 = e3)
% 244.66/51.12    (6)   ~ (all_52_14 = all_6_2)
% 244.66/51.12    (7)   ~ (all_6_2 = e0)
% 244.66/51.12    (8)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.66/51.12    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.13  
% 244.66/51.13  Begin of proof
% 244.66/51.13  | 
% 244.66/51.13  | BETA: splitting (8) gives:
% 244.66/51.13  | 
% 244.66/51.13  | Case 1:
% 244.66/51.13  | | 
% 244.66/51.13  | |   (10)  all_54_10 = e3
% 244.66/51.13  | | 
% 244.66/51.13  | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #2313.
% 244.66/51.13  | | 
% 244.66/51.13  | Case 2:
% 244.66/51.13  | | 
% 244.66/51.13  | |   (11)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.66/51.13  | | 
% 244.66/51.13  | | BETA: splitting (11) gives:
% 244.66/51.13  | | 
% 244.66/51.13  | | Case 1:
% 244.66/51.13  | | | 
% 244.66/51.13  | | |   (12)  all_54_10 = e2
% 244.66/51.13  | | | 
% 244.66/51.13  | | | REF_CLOSE: (1), (4), (12) are inconsistent by sub-proof #2312.
% 244.66/51.13  | | | 
% 244.66/51.13  | | Case 2:
% 244.66/51.13  | | | 
% 244.66/51.13  | | |   (13)  all_54_10 = e1 | all_54_10 = e0
% 244.66/51.13  | | | 
% 244.66/51.13  | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (13) are inconsistent by
% 244.66/51.13  | | |            sub-proof #2302.
% 244.66/51.13  | | | 
% 244.66/51.13  | | End of split
% 244.66/51.13  | | 
% 244.66/51.13  | End of split
% 244.66/51.13  | 
% 244.66/51.13  End of proof
% 244.66/51.13  
% 244.66/51.13  Sub-proof #1859 shows that the following formulas are inconsistent:
% 244.66/51.13  ----------------------------------------------------------------
% 244.66/51.13    (1)   ~ (all_52_3 = e0)
% 244.66/51.13    (2)  op(e3, e2) = all_56_9
% 244.66/51.13    (3)  op(e3, all_56_9) = e3
% 244.66/51.13    (4)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.66/51.13         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.66/51.13    (5)   ~ (e3 = e0)
% 244.66/51.13    (6)  op(e0, e1) = all_52_11
% 244.66/51.13    (7)   ~ (e2 = e0)
% 244.66/51.13    (8)  op(e0, e3) = all_52_3
% 244.66/51.13    (9)   ~ (e3 = e1)
% 244.66/51.13    (10)   ~ (all_22_0 = e3)
% 244.66/51.13    (11)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.66/51.13              | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 244.66/51.13                = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.66/51.13                op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.66/51.13    (12)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) =
% 244.66/51.13            all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2,
% 244.66/51.13              e1) = all_30_1 & $i(all_30_1))
% 244.66/51.13    (13)   ~ (e3 = e2)
% 244.66/51.13    (14)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.66/51.13          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.66/51.13    (15)   ~ (all_52_1 = e0)
% 244.66/51.13    (16)  op(e2, e3) = all_52_1
% 244.66/51.13    (17)  op(all_22_1, e2) = all_22_0
% 244.66/51.13    (18)   ~ (all_52_2 = e0)
% 244.66/51.13    (19)   ~ (all_52_11 = e0)
% 244.66/51.13    (20)  op(e2, e1) = e0
% 244.66/51.13    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.66/51.13    (22)  op(e0, e0) = e0
% 244.66/51.13    (23)  all_58_14 = e3
% 244.66/51.13    (24)  op(e1, e3) = all_52_2
% 244.66/51.13    (25)   ~ (e1 = e0)
% 244.66/51.13    (26)  op(e2, e1) = all_22_1
% 244.66/51.13    (27)  op(e3, e2) = e3
% 244.66/51.13    (28)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.66/51.13          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.66/51.13            e1)
% 244.66/51.13    (29)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.66/51.13          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.66/51.13            e2)
% 244.66/51.13    (30)   ~ (e2 = e1)
% 244.66/51.13  
% 244.66/51.13  Begin of proof
% 244.66/51.13  | 
% 244.66/51.13  | BETA: splitting (4) gives:
% 244.66/51.13  | 
% 244.66/51.13  | Case 1:
% 244.66/51.13  | | 
% 244.66/51.13  | |   (31)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.66/51.13  | |           e3)
% 244.66/51.13  | | 
% 244.66/51.13  | | BETA: splitting (31) gives:
% 244.66/51.13  | | 
% 244.66/51.13  | | Case 1:
% 244.66/51.13  | | | 
% 244.66/51.13  | | |   (32)  all_58_12 = e3 & op(e0, e3) = e3
% 244.66/51.13  | | | 
% 244.66/51.13  | | | ALPHA: (32) implies:
% 244.66/51.13  | | |   (33)  all_58_12 = e3
% 244.66/51.13  | | | 
% 244.66/51.13  | | | REF_CLOSE: (5), (7), (9), (11), (13), (21), (23), (25), (28), (29), (30),
% 244.66/51.13  | | |            (33) are inconsistent by sub-proof #1862.
% 244.66/51.13  | | | 
% 244.66/51.13  | | Case 2:
% 244.66/51.13  | | | 
% 244.66/51.13  | | |   (34)  all_58_13 = e3 & op(e0, e2) = e3
% 244.66/51.13  | | | 
% 244.66/51.13  | | | ALPHA: (34) implies:
% 244.66/51.13  | | |   (35)  op(e0, e2) = e3
% 244.66/51.13  | | | 
% 244.66/51.13  | | | REF_CLOSE: (10), (12), (17), (20), (21), (26), (35) are inconsistent by
% 244.66/51.13  | | |            sub-proof #1860.
% 244.66/51.13  | | | 
% 244.66/51.13  | | End of split
% 244.66/51.13  | | 
% 244.66/51.13  | Case 2:
% 244.66/51.13  | | 
% 244.66/51.13  | |   (36)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.66/51.13  | |           e3)
% 244.66/51.13  | | 
% 244.66/51.13  | | BETA: splitting (36) gives:
% 244.66/51.13  | | 
% 244.66/51.13  | | Case 1:
% 244.66/51.13  | | | 
% 244.66/51.13  | | |   (37)  all_58_14 = e3 & op(e0, e1) = e3
% 244.66/51.13  | | | 
% 244.66/51.13  | | | ALPHA: (37) implies:
% 244.66/51.13  | | |   (38)  op(e0, e1) = e3
% 244.66/51.13  | | | 
% 244.66/51.13  | | | GROUND_INST: instantiating (21) with all_52_11, e3, e1, e0, simplifying
% 244.66/51.13  | | |              with (6), (38) gives:
% 244.66/51.13  | | |   (39)  all_52_11 = e3
% 244.66/51.13  | | | 
% 244.66/51.13  | | | GROUND_INST: instantiating (21) with e3, all_56_9, e2, e3, simplifying
% 244.66/51.13  | | |              with (2), (27) gives:
% 244.66/51.13  | | |   (40)  all_56_9 = e3
% 244.66/51.13  | | | 
% 244.66/51.13  | | | REDUCE: (3), (40) imply:
% 244.66/51.13  | | |   (41)  op(e3, e3) = e3
% 244.66/51.13  | | | 
% 244.66/51.13  | | | REF_CLOSE: (1), (5), (8), (14), (15), (16), (18), (21), (24), (41) are
% 244.66/51.13  | | |            inconsistent by sub-proof #1938.
% 244.66/51.13  | | | 
% 244.66/51.13  | | Case 2:
% 244.66/51.13  | | | 
% 244.66/51.13  | | |   (42)  all_58_15 = e3 & op(e0, e0) = e3
% 244.66/51.13  | | | 
% 244.66/51.13  | | | ALPHA: (42) implies:
% 244.66/51.13  | | |   (43)  op(e0, e0) = e3
% 244.66/51.13  | | | 
% 244.66/51.13  | | | REF_CLOSE: (5), (21), (22), (43) are inconsistent by sub-proof #2079.
% 244.66/51.13  | | | 
% 244.66/51.13  | | End of split
% 244.66/51.13  | | 
% 244.66/51.13  | End of split
% 244.66/51.13  | 
% 244.66/51.13  End of proof
% 244.66/51.13  
% 244.66/51.13  Sub-proof #1860 shows that the following formulas are inconsistent:
% 244.66/51.13  ----------------------------------------------------------------
% 244.66/51.13    (1)  op(e0, e2) = e3
% 244.66/51.13    (2)   ~ (all_22_0 = e3)
% 244.66/51.13    (3)  ( ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) = all_30_1
% 244.66/51.13           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e2, e1) =
% 244.66/51.13           all_30_1 & $i(all_30_1))
% 244.66/51.13    (4)  op(all_22_1, e2) = all_22_0
% 244.66/51.13    (5)  op(e2, e1) = e0
% 244.66/51.13    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.66/51.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.13    (7)  op(e2, e1) = all_22_1
% 244.72/51.13  
% 244.72/51.13  Begin of proof
% 244.72/51.13  | 
% 244.72/51.13  | BETA: splitting (3) gives:
% 244.72/51.13  | 
% 244.72/51.13  | Case 1:
% 244.72/51.13  | | 
% 244.72/51.13  | |   (8)   ~ (all_30_0 = e0) & op(all_30_1, e2) = all_30_0 & op(e2, e1) =
% 244.72/51.13  | |        all_30_1 & $i(all_30_0) & $i(all_30_1)
% 244.72/51.13  | | 
% 244.72/51.13  | | ALPHA: (8) implies:
% 244.72/51.13  | |   (9)  op(e2, e1) = all_30_1
% 244.72/51.13  | |   (10)  op(all_30_1, e2) = all_30_0
% 244.72/51.13  | | 
% 244.72/51.13  | | GROUND_INST: instantiating (6) with e0, all_30_1, e1, e2, simplifying with
% 244.72/51.13  | |              (5), (9) gives:
% 244.72/51.13  | |   (11)  all_30_1 = e0
% 244.72/51.13  | | 
% 244.72/51.13  | | GROUND_INST: instantiating (6) with all_22_1, all_30_1, e1, e2, simplifying
% 244.72/51.13  | |              with (7), (9) gives:
% 244.72/51.13  | |   (12)  all_30_1 = all_22_1
% 244.72/51.13  | | 
% 244.72/51.13  | | COMBINE_EQS: (11), (12) imply:
% 244.72/51.13  | |   (13)  all_22_1 = e0
% 244.72/51.13  | | 
% 244.72/51.13  | | REDUCE: (10), (11) imply:
% 244.72/51.13  | |   (14)  op(e0, e2) = all_30_0
% 244.72/51.13  | | 
% 244.72/51.13  | | REDUCE: (4), (13) imply:
% 244.72/51.13  | |   (15)  op(e0, e2) = all_22_0
% 244.72/51.13  | | 
% 244.72/51.13  | | GROUND_INST: instantiating (6) with e3, all_30_0, e2, e0, simplifying with
% 244.72/51.13  | |              (1), (14) gives:
% 244.72/51.13  | |   (16)  all_30_0 = e3
% 244.72/51.13  | | 
% 244.72/51.13  | | GROUND_INST: instantiating (6) with all_22_0, all_30_0, e2, e0, simplifying
% 244.72/51.13  | |              with (14), (15) gives:
% 244.72/51.13  | |   (17)  all_30_0 = all_22_0
% 244.72/51.13  | | 
% 244.72/51.13  | | REF_CLOSE: (2), (16), (17) are inconsistent by sub-proof #1876.
% 244.72/51.13  | | 
% 244.72/51.13  | Case 2:
% 244.72/51.13  | | 
% 244.72/51.13  | |   (18)   ~ (all_30_1 = e3) & op(e2, e1) = all_30_1 & $i(all_30_1)
% 244.72/51.13  | | 
% 244.72/51.13  | | ALPHA: (18) implies:
% 244.72/51.13  | |   (19)  op(e2, e1) = all_30_1
% 244.72/51.13  | | 
% 244.72/51.13  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (19) are inconsistent by sub-proof
% 244.72/51.13  | |            #1861.
% 244.72/51.13  | | 
% 244.72/51.13  | End of split
% 244.72/51.13  | 
% 244.72/51.13  End of proof
% 244.72/51.13  
% 244.72/51.13  Sub-proof #1861 shows that the following formulas are inconsistent:
% 244.72/51.13  ----------------------------------------------------------------
% 244.72/51.13    (1)  op(e0, e2) = e3
% 244.72/51.13    (2)   ~ (all_22_0 = e3)
% 244.72/51.13    (3)  op(all_22_1, e2) = all_22_0
% 244.72/51.13    (4)  op(e2, e1) = e0
% 244.72/51.13    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.13    (6)  op(e2, e1) = all_22_1
% 244.72/51.13    (7)  op(e2, e1) = all_30_1
% 244.72/51.13  
% 244.72/51.13  Begin of proof
% 244.72/51.13  | 
% 244.72/51.13  | GROUND_INST: instantiating (5) with e0, all_30_1, e1, e2, simplifying with
% 244.72/51.13  |              (4), (7) gives:
% 244.72/51.13  |   (8)  all_30_1 = e0
% 244.72/51.13  | 
% 244.72/51.13  | GROUND_INST: instantiating (5) with all_22_1, all_30_1, e1, e2, simplifying
% 244.72/51.13  |              with (6), (7) gives:
% 244.72/51.13  |   (9)  all_30_1 = all_22_1
% 244.72/51.13  | 
% 244.72/51.13  | COMBINE_EQS: (8), (9) imply:
% 244.72/51.13  |   (10)  all_22_1 = e0
% 244.72/51.13  | 
% 244.72/51.13  | REDUCE: (3), (10) imply:
% 244.72/51.13  |   (11)  op(e0, e2) = all_22_0
% 244.72/51.13  | 
% 244.72/51.13  | GROUND_INST: instantiating (5) with e3, all_22_0, e2, e0, simplifying with
% 244.72/51.13  |              (1), (11) gives:
% 244.72/51.13  |   (12)  all_22_0 = e3
% 244.72/51.13  | 
% 244.72/51.13  | REDUCE: (2), (12) imply:
% 244.72/51.13  |   (13)  $false
% 244.72/51.13  | 
% 244.72/51.13  | CLOSE: (13) is inconsistent.
% 244.72/51.13  | 
% 244.72/51.13  End of proof
% 244.72/51.13  
% 244.72/51.13  Sub-proof #1862 shows that the following formulas are inconsistent:
% 244.72/51.13  ----------------------------------------------------------------
% 244.72/51.13    (1)   ~ (e3 = e0)
% 244.72/51.13    (2)   ~ (e2 = e0)
% 244.72/51.13    (3)   ~ (e3 = e1)
% 244.72/51.13    (4)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.72/51.13             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.72/51.13               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.72/51.13               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.72/51.13    (5)   ~ (e3 = e2)
% 244.72/51.13    (6)  all_58_12 = e3
% 244.72/51.13    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.13    (8)  all_58_14 = e3
% 244.72/51.13    (9)   ~ (e1 = e0)
% 244.72/51.13    (10)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.72/51.13          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.72/51.13            e1)
% 244.72/51.13    (11)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.72/51.13          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.72/51.13            e2)
% 244.72/51.13    (12)   ~ (e2 = e1)
% 244.72/51.13  
% 244.72/51.13  Begin of proof
% 244.72/51.13  | 
% 244.72/51.13  | BETA: splitting (10) gives:
% 244.72/51.13  | 
% 244.72/51.13  | Case 1:
% 244.72/51.13  | | 
% 244.72/51.13  | |   (13)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 244.72/51.13  | |           e1)
% 244.72/51.13  | | 
% 244.72/51.13  | | BETA: splitting (13) gives:
% 244.72/51.13  | | 
% 244.72/51.13  | | Case 1:
% 244.72/51.13  | | | 
% 244.72/51.13  | | |   (14)  all_58_12 = e1 & op(e0, e3) = e1
% 244.72/51.13  | | | 
% 244.72/51.13  | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #1874.
% 244.72/51.13  | | | 
% 244.72/51.13  | | Case 2:
% 244.72/51.13  | | | 
% 244.72/51.13  | | |   (15)  all_58_13 = e1 & op(e0, e2) = e1
% 244.72/51.13  | | | 
% 244.72/51.13  | | | ALPHA: (15) implies:
% 244.72/51.13  | | |   (16)  all_58_13 = e1
% 244.72/51.13  | | |   (17)  op(e0, e2) = e1
% 244.72/51.13  | | | 
% 244.72/51.13  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (16), (17)
% 244.72/51.13  | | |            are inconsistent by sub-proof #1868.
% 244.72/51.13  | | | 
% 244.72/51.13  | | End of split
% 244.72/51.13  | | 
% 244.72/51.13  | Case 2:
% 244.72/51.13  | | 
% 244.72/51.13  | |   (18)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.72/51.13  | |           e1)
% 244.72/51.13  | | 
% 244.72/51.13  | | BETA: splitting (18) gives:
% 244.72/51.13  | | 
% 244.72/51.13  | | Case 1:
% 244.72/51.13  | | | 
% 244.72/51.13  | | |   (19)  all_58_14 = e1 & op(e0, e1) = e1
% 244.72/51.13  | | | 
% 244.72/51.13  | | | REF_CLOSE: (3), (8), (19) are inconsistent by sub-proof #1900.
% 244.72/51.13  | | | 
% 244.72/51.13  | | Case 2:
% 244.72/51.13  | | | 
% 244.72/51.13  | | |   (20)  all_58_15 = e1 & op(e0, e0) = e1
% 244.72/51.13  | | | 
% 244.72/51.13  | | | ALPHA: (20) implies:
% 244.72/51.13  | | |   (21)  all_58_15 = e1
% 244.72/51.13  | | | 
% 244.72/51.13  | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (12), (21) are
% 244.72/51.13  | | |            inconsistent by sub-proof #1863.
% 244.72/51.13  | | | 
% 244.72/51.13  | | End of split
% 244.72/51.13  | | 
% 244.72/51.13  | End of split
% 244.72/51.13  | 
% 244.72/51.13  End of proof
% 244.72/51.13  
% 244.72/51.13  Sub-proof #1863 shows that the following formulas are inconsistent:
% 244.72/51.13  ----------------------------------------------------------------
% 244.72/51.13    (1)   ~ (e3 = e0)
% 244.72/51.13    (2)   ~ (e2 = e0)
% 244.72/51.13    (3)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.72/51.13             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.72/51.13               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.72/51.13               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.72/51.13    (4)   ~ (e3 = e2)
% 244.72/51.13    (5)  all_58_15 = e1
% 244.72/51.13    (6)  all_58_12 = e3
% 244.72/51.13    (7)  all_58_14 = e3
% 244.72/51.13    (8)   ~ (e1 = e0)
% 244.72/51.13    (9)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 244.72/51.13         (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.72/51.13    (10)   ~ (e2 = e1)
% 244.72/51.13  
% 244.72/51.13  Begin of proof
% 244.72/51.13  | 
% 244.72/51.13  | BETA: splitting (9) gives:
% 244.72/51.13  | 
% 244.72/51.13  | Case 1:
% 244.72/51.13  | | 
% 244.72/51.13  | |   (11)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 244.72/51.13  | |           e2)
% 244.72/51.13  | | 
% 244.72/51.13  | | BETA: splitting (11) gives:
% 244.72/51.13  | | 
% 244.72/51.13  | | Case 1:
% 244.72/51.13  | | | 
% 244.72/51.13  | | |   (12)  all_58_12 = e2 & op(e0, e3) = e2
% 244.72/51.13  | | | 
% 244.72/51.13  | | | REF_CLOSE: (4), (6), (12) are inconsistent by sub-proof #1974.
% 244.72/51.13  | | | 
% 244.72/51.13  | | Case 2:
% 244.72/51.13  | | | 
% 244.72/51.13  | | |   (13)  all_58_13 = e2 & op(e0, e2) = e2
% 244.72/51.13  | | | 
% 244.72/51.13  | | | ALPHA: (13) implies:
% 244.72/51.13  | | |   (14)  all_58_13 = e2
% 244.72/51.13  | | | 
% 244.72/51.13  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (14) are inconsistent by
% 244.72/51.13  | | |            sub-proof #1865.
% 244.72/51.13  | | | 
% 244.72/51.13  | | End of split
% 244.72/51.13  | | 
% 244.72/51.13  | Case 2:
% 244.72/51.13  | | 
% 244.72/51.13  | |   (15)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.72/51.13  | |           e2)
% 244.72/51.13  | | 
% 244.72/51.13  | | BETA: splitting (15) gives:
% 244.72/51.13  | | 
% 244.72/51.13  | | Case 1:
% 244.72/51.13  | | | 
% 244.72/51.13  | | |   (16)  all_58_14 = e2 & op(e0, e1) = e2
% 244.72/51.13  | | | 
% 244.72/51.13  | | | REF_CLOSE: (4), (7), (16) are inconsistent by sub-proof #1864.
% 244.72/51.13  | | | 
% 244.72/51.13  | | Case 2:
% 244.72/51.13  | | | 
% 244.72/51.13  | | |   (17)  all_58_15 = e2 & op(e0, e0) = e2
% 244.72/51.13  | | | 
% 244.72/51.13  | | | REF_CLOSE: (5), (10), (17) are inconsistent by sub-proof #1917.
% 244.72/51.13  | | | 
% 244.72/51.13  | | End of split
% 244.72/51.13  | | 
% 244.72/51.13  | End of split
% 244.72/51.13  | 
% 244.72/51.13  End of proof
% 244.72/51.13  
% 244.72/51.13  Sub-proof #1864 shows that the following formulas are inconsistent:
% 244.72/51.13  ----------------------------------------------------------------
% 244.72/51.13    (1)  all_58_14 = e2 & op(e0, e1) = e2
% 244.72/51.13    (2)  all_58_14 = e3
% 244.72/51.13    (3)   ~ (e3 = e2)
% 244.72/51.13  
% 244.72/51.13  Begin of proof
% 244.72/51.13  | 
% 244.72/51.13  | ALPHA: (1) implies:
% 244.72/51.13  |   (4)  all_58_14 = e2
% 244.72/51.13  | 
% 244.72/51.13  | COMBINE_EQS: (2), (4) imply:
% 244.72/51.13  |   (5)  e3 = e2
% 244.72/51.13  | 
% 244.72/51.13  | REDUCE: (3), (5) imply:
% 244.72/51.13  |   (6)  $false
% 244.72/51.13  | 
% 244.72/51.13  | CLOSE: (6) is inconsistent.
% 244.72/51.13  | 
% 244.72/51.13  End of proof
% 244.72/51.13  
% 244.72/51.13  Sub-proof #1865 shows that the following formulas are inconsistent:
% 244.72/51.13  ----------------------------------------------------------------
% 244.72/51.13    (1)   ~ (e3 = e0)
% 244.72/51.13    (2)   ~ (e2 = e0)
% 244.72/51.13    (3)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.72/51.13             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.72/51.13               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.72/51.13               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.72/51.13    (4)  all_58_15 = e1
% 244.72/51.13    (5)  all_58_13 = e2
% 244.72/51.13    (6)  all_58_12 = e3
% 244.72/51.13    (7)  all_58_14 = e3
% 244.72/51.13    (8)   ~ (e1 = e0)
% 244.72/51.13  
% 244.72/51.13  Begin of proof
% 244.72/51.13  | 
% 244.72/51.13  | BETA: splitting (3) gives:
% 244.72/51.13  | 
% 244.72/51.13  | Case 1:
% 244.72/51.13  | | 
% 244.72/51.13  | |   (9)  all_58_15 = e0 & op(e0, e0) = e0
% 244.72/51.13  | | 
% 244.72/51.13  | | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #1867.
% 244.72/51.13  | | 
% 244.72/51.13  | Case 2:
% 244.72/51.13  | | 
% 244.72/51.13  | |   (10)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 244.72/51.14  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 244.72/51.14  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 244.72/51.14  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 244.72/51.14  | | 
% 244.72/51.14  | | ALPHA: (10) implies:
% 244.72/51.14  | |   (11)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.72/51.14  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.72/51.14  | | 
% 244.72/51.14  | | BETA: splitting (11) gives:
% 244.72/51.14  | | 
% 244.72/51.14  | | Case 1:
% 244.72/51.14  | | | 
% 244.72/51.14  | | |   (12)  all_58_12 = e0 & op(e0, e3) = e0
% 244.72/51.14  | | | 
% 244.72/51.14  | | | ALPHA: (12) implies:
% 244.72/51.14  | | |   (13)  all_58_12 = e0
% 244.72/51.14  | | | 
% 244.72/51.14  | | | REF_CLOSE: (1), (6), (13) are inconsistent by sub-proof #1971.
% 244.72/51.14  | | | 
% 244.72/51.14  | | Case 2:
% 244.72/51.14  | | | 
% 244.72/51.14  | | |   (14)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 244.72/51.14  | | |           = e0)
% 244.72/51.14  | | | 
% 244.72/51.14  | | | BETA: splitting (14) gives:
% 244.72/51.14  | | | 
% 244.72/51.14  | | | Case 1:
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | |   (15)  all_58_13 = e0 & op(e0, e2) = e0
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | | REF_CLOSE: (2), (5), (15) are inconsistent by sub-proof #1866.
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | Case 2:
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | |   (16)  all_58_14 = e0 & op(e0, e1) = e0
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | | ALPHA: (16) implies:
% 244.72/51.14  | | | |   (17)  all_58_14 = e0
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | | REF_CLOSE: (1), (7), (17) are inconsistent by sub-proof #1871.
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | End of split
% 244.72/51.14  | | | 
% 244.72/51.14  | | End of split
% 244.72/51.14  | | 
% 244.72/51.14  | End of split
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1866 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)  all_58_13 = e0 & op(e0, e2) = e0
% 244.72/51.14    (2)  all_58_13 = e2
% 244.72/51.14    (3)   ~ (e2 = e0)
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | ALPHA: (1) implies:
% 244.72/51.14  |   (4)  all_58_13 = e0
% 244.72/51.14  | 
% 244.72/51.14  | COMBINE_EQS: (2), (4) imply:
% 244.72/51.14  |   (5)  e2 = e0
% 244.72/51.14  | 
% 244.72/51.14  | SIMP: (5) implies:
% 244.72/51.14  |   (6)  e2 = e0
% 244.72/51.14  | 
% 244.72/51.14  | REDUCE: (3), (6) imply:
% 244.72/51.14  |   (7)  $false
% 244.72/51.14  | 
% 244.72/51.14  | CLOSE: (7) is inconsistent.
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1867 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)  all_58_15 = e0 & op(e0, e0) = e0
% 244.72/51.14    (2)  all_58_15 = e1
% 244.72/51.14    (3)   ~ (e1 = e0)
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | ALPHA: (1) implies:
% 244.72/51.14  |   (4)  all_58_15 = e0
% 244.72/51.14  | 
% 244.72/51.14  | COMBINE_EQS: (2), (4) imply:
% 244.72/51.14  |   (5)  e1 = e0
% 244.72/51.14  | 
% 244.72/51.14  | SIMP: (5) implies:
% 244.72/51.14  |   (6)  e1 = e0
% 244.72/51.14  | 
% 244.72/51.14  | REDUCE: (3), (6) imply:
% 244.72/51.14  |   (7)  $false
% 244.72/51.14  | 
% 244.72/51.14  | CLOSE: (7) is inconsistent.
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1868 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)   ~ (e3 = e0)
% 244.72/51.14    (2)   ~ (e2 = e0)
% 244.72/51.14    (3)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.72/51.14             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.72/51.14               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.72/51.14               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.72/51.14    (4)   ~ (e3 = e2)
% 244.72/51.14    (5)  all_58_12 = e3
% 244.72/51.14    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.14    (7)  all_58_14 = e3
% 244.72/51.14    (8)   ~ (e1 = e0)
% 244.72/51.14    (9)  all_58_13 = e1
% 244.72/51.14    (10)  op(e0, e2) = e1
% 244.72/51.14    (11)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.72/51.14          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.72/51.14            e2)
% 244.72/51.14    (12)   ~ (e2 = e1)
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | BETA: splitting (11) gives:
% 244.72/51.14  | 
% 244.72/51.14  | Case 1:
% 244.72/51.14  | | 
% 244.72/51.14  | |   (13)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 244.72/51.14  | |           e2)
% 244.72/51.14  | | 
% 244.72/51.14  | | BETA: splitting (13) gives:
% 244.72/51.14  | | 
% 244.72/51.14  | | Case 1:
% 244.72/51.14  | | | 
% 244.72/51.14  | | |   (14)  all_58_12 = e2 & op(e0, e3) = e2
% 244.72/51.14  | | | 
% 244.72/51.14  | | | REF_CLOSE: (4), (5), (14) are inconsistent by sub-proof #1974.
% 244.72/51.14  | | | 
% 244.72/51.14  | | Case 2:
% 244.72/51.14  | | | 
% 244.72/51.14  | | |   (15)  all_58_13 = e2 & op(e0, e2) = e2
% 244.72/51.14  | | | 
% 244.72/51.14  | | | REF_CLOSE: (9), (12), (15) are inconsistent by sub-proof #2078.
% 244.72/51.14  | | | 
% 244.72/51.14  | | End of split
% 244.72/51.14  | | 
% 244.72/51.14  | Case 2:
% 244.72/51.14  | | 
% 244.72/51.14  | |   (16)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.72/51.14  | |           e2)
% 244.72/51.14  | | 
% 244.72/51.14  | | BETA: splitting (16) gives:
% 244.72/51.14  | | 
% 244.72/51.14  | | Case 1:
% 244.72/51.14  | | | 
% 244.72/51.14  | | |   (17)  all_58_14 = e2 & op(e0, e1) = e2
% 244.72/51.14  | | | 
% 244.72/51.14  | | | ALPHA: (17) implies:
% 244.72/51.14  | | |   (18)  all_58_14 = e2
% 244.72/51.14  | | | 
% 244.72/51.14  | | | REF_CLOSE: (4), (7), (18) are inconsistent by sub-proof #2117.
% 244.72/51.14  | | | 
% 244.72/51.14  | | Case 2:
% 244.72/51.14  | | | 
% 244.72/51.14  | | |   (19)  all_58_15 = e2 & op(e0, e0) = e2
% 244.72/51.14  | | | 
% 244.72/51.14  | | | ALPHA: (19) implies:
% 244.72/51.14  | | |   (20)  all_58_15 = e2
% 244.72/51.14  | | | 
% 244.72/51.14  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (20) are inconsistent
% 244.72/51.14  | | |            by sub-proof #1869.
% 244.72/51.14  | | | 
% 244.72/51.14  | | End of split
% 244.72/51.14  | | 
% 244.72/51.14  | End of split
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1869 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)   ~ (e3 = e0)
% 244.72/51.14    (2)   ~ (e2 = e0)
% 244.72/51.14    (3)  all_58_15 = e2
% 244.72/51.14    (4)  (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 244.72/51.14             | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.72/51.14               e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 244.72/51.14               op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 244.72/51.14    (5)  all_58_12 = e3
% 244.72/51.14    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.14    (7)  all_58_14 = e3
% 244.72/51.14    (8)   ~ (e1 = e0)
% 244.72/51.14    (9)  op(e0, e2) = e1
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | BETA: splitting (4) gives:
% 244.72/51.14  | 
% 244.72/51.14  | Case 1:
% 244.72/51.14  | | 
% 244.72/51.14  | |   (10)  all_58_15 = e0 & op(e0, e0) = e0
% 244.72/51.14  | | 
% 244.72/51.14  | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #1873.
% 244.72/51.14  | | 
% 244.72/51.14  | Case 2:
% 244.72/51.14  | | 
% 244.72/51.14  | |   (11)  ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 244.72/51.14  | |             e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 244.72/51.14  | |             op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 244.72/51.14  | |           (all_58_14 = e0 & op(e0, e1) = e0))
% 244.72/51.14  | | 
% 244.72/51.14  | | ALPHA: (11) implies:
% 244.72/51.14  | |   (12)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.72/51.14  | |           e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.72/51.14  | | 
% 244.72/51.14  | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (12) are inconsistent by sub-proof
% 244.72/51.14  | |            #1870.
% 244.72/51.14  | | 
% 244.72/51.14  | End of split
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1870 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)   ~ (e3 = e0)
% 244.72/51.14    (2)  all_58_12 = e3
% 244.72/51.14    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.14    (4)  all_58_14 = e3
% 244.72/51.14    (5)   ~ (e1 = e0)
% 244.72/51.14    (6)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 244.72/51.14         (all_58_14 = e0 & op(e0, e1) = e0)
% 244.72/51.14    (7)  op(e0, e2) = e1
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | BETA: splitting (6) gives:
% 244.72/51.14  | 
% 244.72/51.14  | Case 1:
% 244.72/51.14  | | 
% 244.72/51.14  | |   (8)  all_58_12 = e0 & op(e0, e3) = e0
% 244.72/51.14  | | 
% 244.72/51.14  | | ALPHA: (8) implies:
% 244.72/51.14  | |   (9)  all_58_12 = e0
% 244.72/51.14  | | 
% 244.72/51.14  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #1971.
% 244.72/51.14  | | 
% 244.72/51.14  | Case 2:
% 244.72/51.14  | | 
% 244.72/51.14  | |   (10)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 244.72/51.14  | |           e0)
% 244.72/51.14  | | 
% 244.72/51.14  | | BETA: splitting (10) gives:
% 244.72/51.14  | | 
% 244.72/51.14  | | Case 1:
% 244.72/51.14  | | | 
% 244.72/51.14  | | |   (11)  all_58_13 = e0 & op(e0, e2) = e0
% 244.72/51.14  | | | 
% 244.72/51.14  | | | ALPHA: (11) implies:
% 244.72/51.14  | | |   (12)  op(e0, e2) = e0
% 244.72/51.14  | | | 
% 244.72/51.14  | | | REF_CLOSE: (3), (5), (7), (12) are inconsistent by sub-proof #1872.
% 244.72/51.14  | | | 
% 244.72/51.14  | | Case 2:
% 244.72/51.14  | | | 
% 244.72/51.14  | | |   (13)  all_58_14 = e0 & op(e0, e1) = e0
% 244.72/51.14  | | | 
% 244.72/51.14  | | | ALPHA: (13) implies:
% 244.72/51.14  | | |   (14)  all_58_14 = e0
% 244.72/51.14  | | | 
% 244.72/51.14  | | | REF_CLOSE: (1), (4), (14) are inconsistent by sub-proof #1871.
% 244.72/51.14  | | | 
% 244.72/51.14  | | End of split
% 244.72/51.14  | | 
% 244.72/51.14  | End of split
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1871 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)  all_58_14 = e3
% 244.72/51.14    (2)  all_58_14 = e0
% 244.72/51.14    (3)   ~ (e3 = e0)
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | COMBINE_EQS: (1), (2) imply:
% 244.72/51.14  |   (4)  e3 = e0
% 244.72/51.14  | 
% 244.72/51.14  | SIMP: (4) implies:
% 244.72/51.14  |   (5)  e3 = e0
% 244.72/51.14  | 
% 244.72/51.14  | REDUCE: (3), (5) imply:
% 244.72/51.14  |   (6)  $false
% 244.72/51.14  | 
% 244.72/51.14  | CLOSE: (6) is inconsistent.
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1872 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.14    (2)  op(e0, e2) = e1
% 244.72/51.14    (3)  op(e0, e2) = e0
% 244.72/51.14    (4)   ~ (e1 = e0)
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | GROUND_INST: instantiating (1) with e1, e0, e2, e0, simplifying with (2), (3)
% 244.72/51.14  |              gives:
% 244.72/51.14  |   (5)  e1 = e0
% 244.72/51.14  | 
% 244.72/51.14  | REDUCE: (4), (5) imply:
% 244.72/51.14  |   (6)  $false
% 244.72/51.14  | 
% 244.72/51.14  | CLOSE: (6) is inconsistent.
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1873 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)  all_58_15 = e0 & op(e0, e0) = e0
% 244.72/51.14    (2)  all_58_15 = e2
% 244.72/51.14    (3)   ~ (e2 = e0)
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | ALPHA: (1) implies:
% 244.72/51.14  |   (4)  all_58_15 = e0
% 244.72/51.14  | 
% 244.72/51.14  | COMBINE_EQS: (2), (4) imply:
% 244.72/51.14  |   (5)  e2 = e0
% 244.72/51.14  | 
% 244.72/51.14  | REDUCE: (3), (5) imply:
% 244.72/51.14  |   (6)  $false
% 244.72/51.14  | 
% 244.72/51.14  | CLOSE: (6) is inconsistent.
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1874 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)  all_58_12 = e1 & op(e0, e3) = e1
% 244.72/51.14    (2)  all_58_12 = e3
% 244.72/51.14    (3)   ~ (e3 = e1)
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | ALPHA: (1) implies:
% 244.72/51.14  |   (4)  all_58_12 = e1
% 244.72/51.14  | 
% 244.72/51.14  | COMBINE_EQS: (2), (4) imply:
% 244.72/51.14  |   (5)  e3 = e1
% 244.72/51.14  | 
% 244.72/51.14  | REDUCE: (3), (5) imply:
% 244.72/51.14  |   (6)  $false
% 244.72/51.14  | 
% 244.72/51.14  | CLOSE: (6) is inconsistent.
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1875 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)   ~ (all_22_0 = e3)
% 244.72/51.14    (2)  op(all_22_1, e2) = all_22_0
% 244.72/51.14    (3)  op(e2, e1) = e3
% 244.72/51.14    (4)  op(all_30_1, e2) = all_30_0
% 244.72/51.14    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.14    (6)  op(e2, e1) = all_22_1
% 244.72/51.14    (7)  op(e3, e2) = e3
% 244.72/51.14    (8)  op(e2, e1) = all_30_1
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | GROUND_INST: instantiating (5) with e3, all_30_1, e1, e2, simplifying with
% 244.72/51.14  |              (3), (8) gives:
% 244.72/51.14  |   (9)  all_30_1 = e3
% 244.72/51.14  | 
% 244.72/51.14  | GROUND_INST: instantiating (5) with all_22_1, all_30_1, e1, e2, simplifying
% 244.72/51.14  |              with (6), (8) gives:
% 244.72/51.14  |   (10)  all_30_1 = all_22_1
% 244.72/51.14  | 
% 244.72/51.14  | COMBINE_EQS: (9), (10) imply:
% 244.72/51.14  |   (11)  all_22_1 = e3
% 244.72/51.14  | 
% 244.72/51.14  | REDUCE: (4), (9) imply:
% 244.72/51.14  |   (12)  op(e3, e2) = all_30_0
% 244.72/51.14  | 
% 244.72/51.14  | REDUCE: (2), (11) imply:
% 244.72/51.14  |   (13)  op(e3, e2) = all_22_0
% 244.72/51.14  | 
% 244.72/51.14  | GROUND_INST: instantiating (5) with e3, all_30_0, e2, e3, simplifying with
% 244.72/51.14  |              (7), (12) gives:
% 244.72/51.14  |   (14)  all_30_0 = e3
% 244.72/51.14  | 
% 244.72/51.14  | GROUND_INST: instantiating (5) with all_22_0, all_30_0, e2, e3, simplifying
% 244.72/51.14  |              with (12), (13) gives:
% 244.72/51.14  |   (15)  all_30_0 = all_22_0
% 244.72/51.14  | 
% 244.72/51.14  | REF_CLOSE: (1), (14), (15) are inconsistent by sub-proof #1876.
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1876 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)  all_30_0 = all_22_0
% 244.72/51.14    (2)  all_30_0 = e3
% 244.72/51.14    (3)   ~ (all_22_0 = e3)
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | COMBINE_EQS: (1), (2) imply:
% 244.72/51.14  |   (4)  all_22_0 = e3
% 244.72/51.14  | 
% 244.72/51.14  | SIMP: (4) implies:
% 244.72/51.14  |   (5)  all_22_0 = e3
% 244.72/51.14  | 
% 244.72/51.14  | REDUCE: (3), (5) imply:
% 244.72/51.14  |   (6)  $false
% 244.72/51.14  | 
% 244.72/51.14  | CLOSE: (6) is inconsistent.
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1877 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)  all_54_13 = all_22_0
% 244.72/51.14    (2)  all_54_13 = e3
% 244.72/51.14    (3)   ~ (all_22_0 = e3)
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | COMBINE_EQS: (1), (2) imply:
% 244.72/51.14  |   (4)  all_22_0 = e3
% 244.72/51.14  | 
% 244.72/51.14  | SIMP: (4) implies:
% 244.72/51.14  |   (5)  all_22_0 = e3
% 244.72/51.14  | 
% 244.72/51.14  | REDUCE: (3), (5) imply:
% 244.72/51.14  |   (6)  $false
% 244.72/51.14  | 
% 244.72/51.14  | CLOSE: (6) is inconsistent.
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1878 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 244.72/51.14    (2)  all_58_5 = e0
% 244.72/51.14    (3)   ~ (e3 = e0)
% 244.72/51.14    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.72/51.14         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.72/51.14    (5)  all_58_14 = e2
% 244.72/51.14    (6)   ~ (e3 = e1)
% 244.72/51.14    (7)  op(e2, e1) = all_52_9
% 244.72/51.14    (8)  op(e1, e1) = e2
% 244.72/51.14    (9)  op(e2, e1) = e0
% 244.72/51.14    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.14    (11)   ~ (e1 = e0)
% 244.72/51.14    (12)   ~ (e2 = e1)
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | BETA: splitting (1) gives:
% 244.72/51.14  | 
% 244.72/51.14  | Case 1:
% 244.72/51.14  | | 
% 244.72/51.14  | |   (13)  all_58_4 = e3 & op(e3, e1) = e3
% 244.72/51.14  | | 
% 244.72/51.14  | | ALPHA: (13) implies:
% 244.72/51.14  | |   (14)  all_58_4 = e3
% 244.72/51.14  | | 
% 244.72/51.14  | | BETA: splitting (4) gives:
% 244.72/51.14  | | 
% 244.72/51.14  | | Case 1:
% 244.72/51.14  | | | 
% 244.72/51.14  | | |   (15)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 244.72/51.14  | | |           e1)
% 244.72/51.14  | | | 
% 244.72/51.14  | | | REF_CLOSE: (6), (7), (9), (10), (11), (14), (15) are inconsistent by
% 244.72/51.14  | | |            sub-proof #1879.
% 244.72/51.14  | | | 
% 244.72/51.14  | | Case 2:
% 244.72/51.14  | | | 
% 244.72/51.14  | | |   (16)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 244.72/51.14  | | |           e1)
% 244.72/51.14  | | | 
% 244.72/51.14  | | | BETA: splitting (16) gives:
% 244.72/51.14  | | | 
% 244.72/51.14  | | | Case 1:
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | |   (17)  all_58_8 = e1 & op(e1, e1) = e1
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | | ALPHA: (17) implies:
% 244.72/51.14  | | | |   (18)  op(e1, e1) = e1
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | | REF_CLOSE: (8), (10), (12), (18) are inconsistent by sub-proof #2159.
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | Case 2:
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | |   (19)  all_58_14 = e1 & op(e0, e1) = e1
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | | ALPHA: (19) implies:
% 244.72/51.14  | | | |   (20)  all_58_14 = e1
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | | REF_CLOSE: (5), (12), (20) are inconsistent by sub-proof #2044.
% 244.72/51.14  | | | | 
% 244.72/51.14  | | | End of split
% 244.72/51.14  | | | 
% 244.72/51.14  | | End of split
% 244.72/51.14  | | 
% 244.72/51.14  | Case 2:
% 244.72/51.14  | | 
% 244.72/51.14  | |   (21)  all_58_5 = e3 & op(e2, e1) = e3
% 244.72/51.14  | | 
% 244.72/51.14  | | ALPHA: (21) implies:
% 244.72/51.14  | |   (22)  all_58_5 = e3
% 244.72/51.14  | | 
% 244.72/51.14  | | REF_CLOSE: (2), (3), (22) are inconsistent by sub-proof #2038.
% 244.72/51.14  | | 
% 244.72/51.14  | End of split
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1879 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 244.72/51.14    (2)   ~ (e3 = e1)
% 244.72/51.14    (3)  op(e2, e1) = all_52_9
% 244.72/51.14    (4)  op(e2, e1) = e0
% 244.72/51.14    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.14    (6)   ~ (e1 = e0)
% 244.72/51.14    (7)  all_58_4 = e3
% 244.72/51.14  
% 244.72/51.14  Begin of proof
% 244.72/51.14  | 
% 244.72/51.14  | BETA: splitting (1) gives:
% 244.72/51.14  | 
% 244.72/51.14  | Case 1:
% 244.72/51.14  | | 
% 244.72/51.14  | |   (8)  all_58_4 = e1 & op(e3, e1) = e1
% 244.72/51.14  | | 
% 244.72/51.14  | | ALPHA: (8) implies:
% 244.72/51.14  | |   (9)  all_58_4 = e1
% 244.72/51.14  | | 
% 244.72/51.14  | | REF_CLOSE: (2), (7), (9) are inconsistent by sub-proof #2184.
% 244.72/51.14  | | 
% 244.72/51.14  | Case 2:
% 244.72/51.14  | | 
% 244.72/51.14  | |   (10)  all_58_5 = e1 & op(e2, e1) = e1
% 244.72/51.14  | | 
% 244.72/51.14  | | ALPHA: (10) implies:
% 244.72/51.14  | |   (11)  op(e2, e1) = e1
% 244.72/51.14  | | 
% 244.72/51.14  | | REF_CLOSE: (3), (4), (5), (6), (11) are inconsistent by sub-proof #2165.
% 244.72/51.14  | | 
% 244.72/51.14  | End of split
% 244.72/51.14  | 
% 244.72/51.14  End of proof
% 244.72/51.14  
% 244.72/51.14  Sub-proof #1880 shows that the following formulas are inconsistent:
% 244.72/51.14  ----------------------------------------------------------------
% 244.72/51.14    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.72/51.15    (2)  op(e1, e1) = e2
% 244.72/51.15    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.15    (4)  op(e1, e0) = e2
% 244.72/51.15    (5)   ~ (e2 = e1)
% 244.72/51.15  
% 244.72/51.15  Begin of proof
% 244.72/51.15  | 
% 244.72/51.15  | BETA: splitting (1) gives:
% 244.72/51.15  | 
% 244.72/51.15  | Case 1:
% 244.72/51.15  | | 
% 244.72/51.15  | |   (6)  all_58_8 = e1 & op(e1, e1) = e1
% 244.72/51.15  | | 
% 244.72/51.15  | | ALPHA: (6) implies:
% 244.72/51.15  | |   (7)  op(e1, e1) = e1
% 244.72/51.15  | | 
% 244.72/51.15  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #2159.
% 244.72/51.15  | | 
% 244.72/51.15  | Case 2:
% 244.72/51.15  | | 
% 244.72/51.15  | |   (8)  all_58_11 = e1 & op(e1, e0) = e1
% 244.72/51.15  | | 
% 244.72/51.15  | | ALPHA: (8) implies:
% 244.72/51.15  | |   (9)  op(e1, e0) = e1
% 244.72/51.15  | | 
% 244.72/51.15  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #2019.
% 244.72/51.15  | | 
% 244.72/51.15  | End of split
% 244.72/51.15  | 
% 244.72/51.15  End of proof
% 244.72/51.15  
% 244.72/51.15  Sub-proof #1881 shows that the following formulas are inconsistent:
% 244.72/51.15  ----------------------------------------------------------------
% 244.72/51.15    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.72/51.15             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.72/51.15           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.72/51.15         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.72/51.15           $i(all_56_7))
% 244.72/51.15    (2)  all_56_21 = e2
% 244.72/51.15    (3)   ~ (e3 = e0)
% 244.72/51.15    (4)   ~ (all_52_7 = e2)
% 244.72/51.15    (5)   ~ (e2 = e0)
% 244.72/51.15    (6)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.72/51.15           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.72/51.15             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.72/51.15           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.72/51.15             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.72/51.15           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.72/51.15           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.72/51.15           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.72/51.15           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.72/51.15           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.72/51.15           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.72/51.15             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.72/51.15           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.72/51.15           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 244.72/51.15           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.72/51.15           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.72/51.15           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.72/51.15           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.72/51.15             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.72/51.15           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.72/51.15           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.72/51.15           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.72/51.15           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.72/51.15           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.72/51.15           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.72/51.15             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.72/51.15           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.72/51.15           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.72/51.15    (7)  op(e1, e0) = all_52_14
% 244.72/51.15    (8)  op(e2, e3) = e3
% 244.72/51.15    (9)   ~ (e3 = e1)
% 244.72/51.15    (10)   ~ (all_40_1 = e3)
% 244.72/51.15    (11)   ~ (all_36_0 = e0)
% 244.72/51.15    (12)   ~ (all_36_0 = e2)
% 244.72/51.15    (13)  op(e3, e1) = all_52_8
% 244.72/51.15    (14)  op(e2, e1) = all_52_9
% 244.72/51.15    (15)   ~ (e3 = e2)
% 244.72/51.15    (16)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.72/51.15    (17)   ~ (all_52_14 = e0)
% 244.72/51.15    (18)  all_54_14 = all_36_0
% 244.72/51.15    (19)   ~ (all_52_8 = all_36_0)
% 244.72/51.15    (20)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.72/51.15          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.72/51.15    (21)  op(e0, e3) = e2
% 244.72/51.15    (22)  op(e3, e0) = e2
% 244.72/51.15    (23)  op(e1, e2) = all_36_1
% 244.72/51.15    (24)   ~ (all_52_2 = e3)
% 244.72/51.15    (25)  op(e1, e1) = e2
% 244.72/51.15    (26)  op(e0, e2) = all_52_7
% 244.72/51.15    (27)  op(e2, e1) = e0
% 244.72/51.15    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.15    (29)  op(e1, e3) = all_52_2
% 244.72/51.15    (30)  op(e1, e2) = all_40_1
% 244.72/51.15    (31)   ~ (e1 = e0)
% 244.72/51.15    (32)   ~ (all_36_0 = e3)
% 244.72/51.15    (33)  all_56_1 = e0
% 244.72/51.15    (34)  op(e2, e0) = all_52_13
% 244.72/51.15    (35)   ~ (all_52_13 = e0)
% 244.72/51.15    (36)   ~ (e2 = e1)
% 244.72/51.15  
% 244.72/51.15  Begin of proof
% 244.72/51.15  | 
% 244.72/51.15  | BETA: splitting (1) gives:
% 244.72/51.15  | 
% 244.72/51.15  | Case 1:
% 244.72/51.15  | | 
% 244.72/51.15  | |   (37)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.72/51.15  | |             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 244.72/51.15  | | 
% 244.72/51.15  | | REF_CLOSE: (8), (15), (22), (28), (33), (37) are inconsistent by sub-proof
% 244.72/51.15  | |            #1898.
% 244.72/51.15  | | 
% 244.72/51.15  | Case 2:
% 244.72/51.15  | | 
% 244.72/51.15  | |   (38)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 244.72/51.15  | |           $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0,
% 244.72/51.15  | |             e3) = all_56_7 & $i(all_56_7))
% 244.72/51.15  | | 
% 244.72/51.15  | | BETA: splitting (38) gives:
% 244.72/51.15  | | 
% 244.72/51.15  | | Case 1:
% 244.72/51.15  | | | 
% 244.72/51.15  | | |   (39)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 244.72/51.15  | | |         $i(all_56_5)
% 244.72/51.15  | | | 
% 244.72/51.15  | | | ALPHA: (39) implies:
% 244.72/51.15  | | |   (40)  op(e1, e3) = all_56_5
% 244.72/51.15  | | |   (41)  op(e1, all_56_5) = e1
% 244.72/51.15  | | | 
% 244.72/51.15  | | | BETA: splitting (20) gives:
% 244.72/51.15  | | | 
% 244.72/51.15  | | | Case 1:
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | |   (42)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 244.72/51.15  | | | |           = e3)
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | | BETA: splitting (42) gives:
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | | Case 1:
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | |   (43)  all_58_6 = e3 & op(e1, e3) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | ALPHA: (43) implies:
% 244.72/51.15  | | | | |   (44)  op(e1, e3) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | REF_CLOSE: (9), (28), (40), (41), (44) are inconsistent by sub-proof
% 244.72/51.15  | | | | |            #2243.
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | Case 2:
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | |   (45)  all_58_7 = e3 & op(e1, e2) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | ALPHA: (45) implies:
% 244.72/51.15  | | | | |   (46)  op(e1, e2) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | REF_CLOSE: (10), (23), (28), (30), (46) are inconsistent by sub-proof
% 244.72/51.15  | | | | |            #2145.
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | End of split
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | Case 2:
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | |   (47)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 244.72/51.15  | | | |           = e3)
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (14), (15), (17), (21),
% 244.72/51.15  | | | |            (22), (25), (26), (27), (28), (31), (34), (35), (36), (40),
% 244.72/51.15  | | | |            (41), (47) are inconsistent by sub-proof #1891.
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | End of split
% 244.72/51.15  | | | 
% 244.72/51.15  | | Case 2:
% 244.72/51.15  | | | 
% 244.72/51.15  | | |   (48)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.72/51.15  | | |         $i(all_56_7)
% 244.72/51.15  | | | 
% 244.72/51.15  | | | ALPHA: (48) implies:
% 244.72/51.15  | | |   (49)  op(e0, e3) = all_56_7
% 244.72/51.15  | | |   (50)  op(e0, all_56_7) = e0
% 244.72/51.15  | | | 
% 244.72/51.15  | | | BETA: splitting (20) gives:
% 244.72/51.15  | | | 
% 244.72/51.15  | | | Case 1:
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | |   (51)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 244.72/51.15  | | | |           = e3)
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | | BETA: splitting (51) gives:
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | | Case 1:
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | |   (52)  all_58_6 = e3 & op(e1, e3) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | ALPHA: (52) implies:
% 244.72/51.15  | | | | |   (53)  op(e1, e3) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | REF_CLOSE: (24), (28), (29), (53) are inconsistent by sub-proof #2335.
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | Case 2:
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | |   (54)  all_58_7 = e3 & op(e1, e2) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | ALPHA: (54) implies:
% 244.72/51.15  | | | | |   (55)  op(e1, e2) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | REF_CLOSE: (10), (23), (28), (30), (55) are inconsistent by sub-proof
% 244.72/51.15  | | | | |            #2145.
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | End of split
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | Case 2:
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | |   (56)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 244.72/51.15  | | | |           = e3)
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | | BETA: splitting (56) gives:
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | | Case 1:
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | |   (57)  all_58_8 = e3 & op(e1, e1) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | ALPHA: (57) implies:
% 244.72/51.15  | | | | |   (58)  op(e1, e1) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | REF_CLOSE: (15), (25), (28), (58) are inconsistent by sub-proof #2206.
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | Case 2:
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | |   (59)  all_58_11 = e3 & op(e1, e0) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | ALPHA: (59) implies:
% 244.72/51.15  | | | | |   (60)  op(e1, e0) = e3
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | BETA: splitting (16) gives:
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | | Case 1:
% 244.72/51.15  | | | | | | 
% 244.72/51.15  | | | | | |   (61)  all_54_14 = e3
% 244.72/51.15  | | | | | | 
% 244.72/51.15  | | | | | | REF_CLOSE: (18), (32), (61) are inconsistent by sub-proof #1890.
% 244.72/51.15  | | | | | | 
% 244.72/51.15  | | | | | Case 2:
% 244.72/51.15  | | | | | | 
% 244.72/51.15  | | | | | |   (62)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.72/51.15  | | | | | | 
% 244.72/51.15  | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 244.72/51.15  | | | | | |            (14), (15), (17), (18), (19), (21), (24), (26), (27),
% 244.72/51.15  | | | | | |            (28), (29), (31), (34), (35), (49), (50), (60), (62) are
% 244.72/51.15  | | | | | |            inconsistent by sub-proof #1888.
% 244.72/51.15  | | | | | | 
% 244.72/51.15  | | | | | End of split
% 244.72/51.15  | | | | | 
% 244.72/51.15  | | | | End of split
% 244.72/51.15  | | | | 
% 244.72/51.15  | | | End of split
% 244.72/51.15  | | | 
% 244.72/51.15  | | End of split
% 244.72/51.15  | | 
% 244.72/51.15  | End of split
% 244.72/51.15  | 
% 244.72/51.15  End of proof
% 244.72/51.15  
% 244.72/51.15  Sub-proof #1882 shows that the following formulas are inconsistent:
% 244.72/51.15  ----------------------------------------------------------------
% 244.72/51.15    (1)  all_58_5 = e0
% 244.72/51.15    (2)   ~ (e3 = e0)
% 244.72/51.15    (3)   ~ (e2 = e0)
% 244.72/51.15    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.72/51.15         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.72/51.15    (5)   ~ (e3 = e1)
% 244.72/51.15    (6)  all_58_8 = e2
% 244.72/51.15    (7)  op(e2, e1) = all_52_9
% 244.72/51.15    (8)   ~ (e3 = e2)
% 244.72/51.15    (9)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.72/51.15    (10)  op(e1, e1) = e2
% 244.72/51.15    (11)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.72/51.15          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.72/51.15    (12)  op(e2, e1) = e0
% 244.72/51.15    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.15    (14)  op(e0, e0) = e0
% 244.72/51.15    (15)   ~ (e1 = e0)
% 244.72/51.15    (16)   ~ (e2 = e1)
% 244.72/51.15  
% 244.72/51.15  Begin of proof
% 244.72/51.15  | 
% 244.72/51.15  | BETA: splitting (9) gives:
% 244.72/51.15  | 
% 244.72/51.15  | Case 1:
% 244.72/51.15  | | 
% 244.72/51.15  | |   (17)  all_58_14 = e2 & op(e0, e1) = e2
% 244.72/51.15  | | 
% 244.72/51.15  | | ALPHA: (17) implies:
% 244.72/51.15  | |   (18)  all_58_14 = e2
% 244.72/51.15  | | 
% 244.72/51.15  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (12), (13), (15),
% 244.72/51.15  | |            (16), (18) are inconsistent by sub-proof #2037.
% 244.72/51.15  | | 
% 244.72/51.15  | Case 2:
% 244.72/51.15  | | 
% 244.72/51.15  | |   (19)  all_58_15 = e2 & op(e0, e0) = e2
% 244.72/51.15  | | 
% 244.72/51.15  | | ALPHA: (19) implies:
% 244.72/51.15  | |   (20)  op(e0, e0) = e2
% 244.72/51.15  | | 
% 244.72/51.15  | | REF_CLOSE: (3), (13), (14), (20) are inconsistent by sub-proof #2301.
% 244.72/51.15  | | 
% 244.72/51.15  | End of split
% 244.72/51.15  | 
% 244.72/51.15  End of proof
% 244.72/51.15  
% 244.72/51.15  Sub-proof #1883 shows that the following formulas are inconsistent:
% 244.72/51.15  ----------------------------------------------------------------
% 244.72/51.15    (1)  op(e1, e2) = e0
% 244.72/51.15    (2)  op(e1, e2) = all_36_1
% 244.72/51.15    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.15    (4)   ~ (all_36_1 = e0)
% 244.72/51.15    (5)  op(e1, e2) = all_40_1
% 244.72/51.15  
% 244.72/51.15  Begin of proof
% 244.72/51.15  | 
% 244.72/51.15  | GROUND_INST: instantiating (3) with e0, all_40_1, e2, e1, simplifying with
% 244.72/51.15  |              (1), (5) gives:
% 244.72/51.15  |   (6)  all_40_1 = e0
% 244.72/51.15  | 
% 244.72/51.15  | GROUND_INST: instantiating (3) with all_36_1, all_40_1, e2, e1, simplifying
% 244.72/51.15  |              with (2), (5) gives:
% 244.72/51.15  |   (7)  all_40_1 = all_36_1
% 244.72/51.15  | 
% 244.72/51.15  | COMBINE_EQS: (6), (7) imply:
% 244.72/51.15  |   (8)  all_36_1 = e0
% 244.72/51.15  | 
% 244.72/51.15  | SIMP: (8) implies:
% 244.72/51.15  |   (9)  all_36_1 = e0
% 244.72/51.15  | 
% 244.72/51.15  | REDUCE: (4), (9) imply:
% 244.72/51.15  |   (10)  $false
% 244.72/51.15  | 
% 244.72/51.15  | CLOSE: (10) is inconsistent.
% 244.72/51.15  | 
% 244.72/51.15  End of proof
% 244.72/51.15  
% 244.72/51.15  Sub-proof #1884 shows that the following formulas are inconsistent:
% 244.72/51.15  ----------------------------------------------------------------
% 244.72/51.15    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.15    (2)  op(e3, e0) = all_50_1
% 244.72/51.15    (3)  op(e3, e0) = e2
% 244.72/51.15    (4)   ~ (all_50_1 = e2)
% 244.72/51.15  
% 244.72/51.15  Begin of proof
% 244.72/51.15  | 
% 244.72/51.15  | GROUND_INST: instantiating (1) with e2, all_50_1, e0, e3, simplifying with
% 244.72/51.15  |              (2), (3) gives:
% 244.72/51.15  |   (5)  all_50_1 = e2
% 244.72/51.15  | 
% 244.72/51.15  | REDUCE: (4), (5) imply:
% 244.72/51.15  |   (6)  $false
% 244.72/51.15  | 
% 244.72/51.15  | CLOSE: (6) is inconsistent.
% 244.72/51.15  | 
% 244.72/51.15  End of proof
% 244.72/51.15  
% 244.72/51.15  Sub-proof #1885 shows that the following formulas are inconsistent:
% 244.72/51.15  ----------------------------------------------------------------
% 244.72/51.15    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.72/51.15    (2)   ~ (all_50_0 = e2)
% 244.72/51.15    (3)   ~ (all_50_0 = e1)
% 244.72/51.15    (4)   ~ (all_50_0 = e0)
% 244.72/51.15    (5)  all_54_4 = all_50_0
% 244.72/51.15  
% 244.72/51.15  Begin of proof
% 244.72/51.15  | 
% 244.72/51.15  | BETA: splitting (1) gives:
% 244.72/51.15  | 
% 244.72/51.15  | Case 1:
% 244.72/51.15  | | 
% 244.72/51.15  | |   (6)  all_54_4 = e2
% 244.72/51.15  | | 
% 244.72/51.15  | | COMBINE_EQS: (5), (6) imply:
% 244.72/51.15  | |   (7)  all_50_0 = e2
% 244.72/51.15  | | 
% 244.72/51.15  | | SIMP: (7) implies:
% 244.72/51.15  | |   (8)  all_50_0 = e2
% 244.72/51.15  | | 
% 244.72/51.15  | | REDUCE: (2), (8) imply:
% 244.72/51.15  | |   (9)  $false
% 244.72/51.15  | | 
% 244.72/51.15  | | CLOSE: (9) is inconsistent.
% 244.72/51.15  | | 
% 244.72/51.15  | Case 2:
% 244.72/51.15  | | 
% 244.72/51.15  | |   (10)  all_54_4 = e1 | all_54_4 = e0
% 244.72/51.15  | | 
% 244.72/51.15  | | BETA: splitting (10) gives:
% 244.72/51.15  | | 
% 244.72/51.15  | | Case 1:
% 244.72/51.15  | | | 
% 244.72/51.15  | | |   (11)  all_54_4 = e1
% 244.72/51.15  | | | 
% 244.72/51.15  | | | COMBINE_EQS: (5), (11) imply:
% 244.72/51.15  | | |   (12)  all_50_0 = e1
% 244.72/51.15  | | | 
% 244.72/51.15  | | | REDUCE: (3), (12) imply:
% 244.72/51.15  | | |   (13)  $false
% 244.72/51.15  | | | 
% 244.72/51.15  | | | CLOSE: (13) is inconsistent.
% 244.72/51.15  | | | 
% 244.72/51.15  | | Case 2:
% 244.72/51.15  | | | 
% 244.72/51.15  | | |   (14)  all_54_4 = e0
% 244.72/51.15  | | | 
% 244.72/51.15  | | | COMBINE_EQS: (5), (14) imply:
% 244.72/51.15  | | |   (15)  all_50_0 = e0
% 244.72/51.15  | | | 
% 244.72/51.15  | | | REDUCE: (4), (15) imply:
% 244.72/51.15  | | |   (16)  $false
% 244.72/51.15  | | | 
% 244.72/51.15  | | | CLOSE: (16) is inconsistent.
% 244.72/51.15  | | | 
% 244.72/51.15  | | End of split
% 244.72/51.15  | | 
% 244.72/51.15  | End of split
% 244.72/51.15  | 
% 244.72/51.15  End of proof
% 244.72/51.15  
% 244.72/51.15  Sub-proof #1886 shows that the following formulas are inconsistent:
% 244.72/51.15  ----------------------------------------------------------------
% 244.72/51.15    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.72/51.15    (2)  all_54_4 = all_16_0
% 244.72/51.15    (3)   ~ (all_16_0 = e0)
% 244.72/51.15    (4)   ~ (all_16_0 = e2)
% 244.72/51.15    (5)   ~ (all_16_0 = e1)
% 244.72/51.15  
% 244.72/51.15  Begin of proof
% 244.72/51.15  | 
% 244.72/51.15  | BETA: splitting (1) gives:
% 244.72/51.15  | 
% 244.72/51.15  | Case 1:
% 244.72/51.15  | | 
% 244.72/51.15  | |   (6)  all_54_4 = e2
% 244.72/51.15  | | 
% 244.72/51.15  | | COMBINE_EQS: (2), (6) imply:
% 244.72/51.15  | |   (7)  all_16_0 = e2
% 244.72/51.15  | | 
% 244.72/51.15  | | SIMP: (7) implies:
% 244.72/51.15  | |   (8)  all_16_0 = e2
% 244.72/51.15  | | 
% 244.72/51.15  | | REDUCE: (4), (8) imply:
% 244.72/51.15  | |   (9)  $false
% 244.72/51.15  | | 
% 244.72/51.15  | | CLOSE: (9) is inconsistent.
% 244.72/51.15  | | 
% 244.72/51.15  | Case 2:
% 244.72/51.15  | | 
% 244.72/51.15  | |   (10)  all_54_4 = e1 | all_54_4 = e0
% 244.72/51.15  | | 
% 244.72/51.15  | | BETA: splitting (10) gives:
% 244.72/51.15  | | 
% 244.72/51.15  | | Case 1:
% 244.72/51.15  | | | 
% 244.72/51.15  | | |   (11)  all_54_4 = e1
% 244.72/51.15  | | | 
% 244.72/51.15  | | | COMBINE_EQS: (2), (11) imply:
% 244.72/51.15  | | |   (12)  all_16_0 = e1
% 244.72/51.15  | | | 
% 244.72/51.15  | | | REDUCE: (5), (12) imply:
% 244.72/51.15  | | |   (13)  $false
% 244.72/51.15  | | | 
% 244.72/51.15  | | | CLOSE: (13) is inconsistent.
% 244.72/51.15  | | | 
% 244.72/51.15  | | Case 2:
% 244.72/51.15  | | | 
% 244.72/51.16  | | |   (14)  all_54_4 = e0
% 244.72/51.16  | | | 
% 244.72/51.16  | | | COMBINE_EQS: (2), (14) imply:
% 244.72/51.16  | | |   (15)  all_16_0 = e0
% 244.72/51.16  | | | 
% 244.72/51.16  | | | REDUCE: (3), (15) imply:
% 244.72/51.16  | | |   (16)  $false
% 244.72/51.16  | | | 
% 244.72/51.16  | | | CLOSE: (16) is inconsistent.
% 244.72/51.16  | | | 
% 244.72/51.16  | | End of split
% 244.72/51.16  | | 
% 244.72/51.16  | End of split
% 244.72/51.16  | 
% 244.72/51.16  End of proof
% 244.72/51.16  
% 244.72/51.16  Sub-proof #1887 shows that the following formulas are inconsistent:
% 244.72/51.16  ----------------------------------------------------------------
% 244.72/51.16    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.72/51.16             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.72/51.16           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.72/51.16         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.72/51.16           $i(all_56_7))
% 244.72/51.16    (2)  all_56_21 = e2
% 244.72/51.16    (3)   ~ (e3 = e0)
% 244.72/51.16    (4)   ~ (all_52_7 = e2)
% 244.72/51.16    (5)   ~ (e2 = e0)
% 244.72/51.16    (6)  all_58_7 = e0
% 244.72/51.16    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.72/51.16           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.72/51.16             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.72/51.16           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.72/51.16             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.72/51.16           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.72/51.16           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.72/51.16           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.72/51.16           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.72/51.16           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.72/51.16           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.72/51.16             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.72/51.16           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.72/51.16           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 244.72/51.16           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.72/51.16           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.72/51.16           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.72/51.16           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.72/51.16             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.72/51.16           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.72/51.16           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.72/51.16           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.72/51.16           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.72/51.16           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.72/51.16           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.72/51.16             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.72/51.16           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.72/51.16           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.72/51.16    (8)  op(e1, e0) = all_52_14
% 244.72/51.16    (9)  op(e2, e3) = e3
% 244.72/51.16    (10)   ~ (e3 = e1)
% 244.72/51.16    (11)   ~ (all_36_0 = e0)
% 244.72/51.16    (12)   ~ (all_36_0 = e2)
% 244.72/51.16    (13)  op(e3, e1) = all_52_8
% 244.72/51.16    (14)  op(e2, e1) = all_52_9
% 244.72/51.16    (15)   ~ (e3 = e2)
% 244.72/51.16    (16)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.72/51.16    (17)   ~ (all_52_14 = e0)
% 244.72/51.16    (18)  all_54_14 = all_36_0
% 244.72/51.16    (19)   ~ (all_52_8 = all_36_0)
% 244.72/51.16    (20)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.72/51.16          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.72/51.16    (21)  op(e0, e3) = e2
% 244.72/51.16    (22)  op(e3, e0) = e2
% 244.72/51.16    (23)   ~ (all_52_2 = e3)
% 244.72/51.16    (24)  op(e1, e1) = e2
% 244.72/51.16    (25)  op(e0, e2) = all_52_7
% 244.72/51.16    (26)  op(e2, e1) = e0
% 244.72/51.16    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.72/51.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.72/51.16    (28)  op(e1, e3) = all_52_2
% 244.72/51.16    (29)   ~ (e1 = e0)
% 244.72/51.16    (30)   ~ (all_36_0 = e3)
% 244.72/51.16    (31)  all_56_1 = e0
% 244.72/51.16    (32)  op(e2, e0) = all_52_13
% 244.72/51.16    (33)   ~ (all_52_13 = e0)
% 244.72/51.16    (34)   ~ (e2 = e1)
% 244.72/51.16  
% 244.72/51.16  Begin of proof
% 244.72/51.16  | 
% 244.72/51.16  | BETA: splitting (1) gives:
% 244.72/51.16  | 
% 244.72/51.16  | Case 1:
% 244.72/51.16  | | 
% 244.72/51.16  | |   (35)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.72/51.16  | |             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 244.72/51.16  | | 
% 244.72/51.16  | | REF_CLOSE: (9), (15), (22), (27), (31), (35) are inconsistent by sub-proof
% 244.72/51.16  | |            #1898.
% 244.72/51.16  | | 
% 244.72/51.16  | Case 2:
% 244.72/51.16  | | 
% 244.72/51.16  | |   (36)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 244.72/51.16  | |           $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0,
% 244.72/51.16  | |             e3) = all_56_7 & $i(all_56_7))
% 244.72/51.16  | | 
% 244.72/51.16  | | BETA: splitting (36) gives:
% 244.72/51.16  | | 
% 244.72/51.16  | | Case 1:
% 244.72/51.16  | | | 
% 244.72/51.16  | | |   (37)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 244.72/51.16  | | |         $i(all_56_5)
% 244.72/51.16  | | | 
% 244.72/51.16  | | | ALPHA: (37) implies:
% 244.72/51.16  | | |   (38)  op(e1, e3) = all_56_5
% 244.72/51.16  | | |   (39)  op(e1, all_56_5) = e1
% 244.72/51.16  | | | 
% 244.72/51.16  | | | BETA: splitting (20) gives:
% 244.72/51.16  | | | 
% 244.72/51.16  | | | Case 1:
% 244.72/51.16  | | | | 
% 244.72/51.16  | | | |   (40)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 244.72/51.16  | | | |           = e3)
% 244.72/51.16  | | | | 
% 244.72/51.16  | | | | BETA: splitting (40) gives:
% 244.72/51.16  | | | | 
% 244.72/51.16  | | | | Case 1:
% 244.72/51.16  | | | | | 
% 244.72/51.16  | | | | |   (41)  all_58_6 = e3 & op(e1, e3) = e3
% 244.72/51.16  | | | | | 
% 244.72/51.16  | | | | | ALPHA: (41) implies:
% 244.72/51.16  | | | | |   (42)  op(e1, e3) = e3
% 244.72/51.16  | | | | | 
% 244.72/51.16  | | | | | REF_CLOSE: (10), (27), (38), (39), (42) are inconsistent by sub-proof
% 244.72/51.16  | | | | |            #2243.
% 244.72/51.16  | | | | | 
% 244.72/51.16  | | | | Case 2:
% 244.72/51.16  | | | | | 
% 244.72/51.16  | | | | |   (43)  all_58_7 = e3 & op(e1, e2) = e3
% 244.72/51.16  | | | | | 
% 244.72/51.16  | | | | | REF_CLOSE: (3), (6), (43) are inconsistent by sub-proof #2150.
% 244.72/51.16  | | | | | 
% 244.72/51.16  | | | | End of split
% 244.72/51.16  | | | | 
% 244.72/51.16  | | | Case 2:
% 244.72/51.16  | | | | 
% 244.72/51.16  | | | |   (44)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 244.72/51.16  | | | |           = e3)
% 244.72/51.16  | | | | 
% 244.76/51.16  | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (14), (15), (17), (21),
% 244.76/51.16  | | | |            (22), (24), (25), (26), (27), (29), (32), (33), (34), (38),
% 244.76/51.16  | | | |            (39), (44) are inconsistent by sub-proof #1891.
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | End of split
% 244.76/51.16  | | | 
% 244.76/51.16  | | Case 2:
% 244.76/51.16  | | | 
% 244.76/51.16  | | |   (45)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.76/51.16  | | |         $i(all_56_7)
% 244.76/51.16  | | | 
% 244.76/51.16  | | | ALPHA: (45) implies:
% 244.76/51.16  | | |   (46)  op(e0, e3) = all_56_7
% 244.76/51.16  | | |   (47)  op(e0, all_56_7) = e0
% 244.76/51.16  | | | 
% 244.76/51.16  | | | BETA: splitting (16) gives:
% 244.76/51.16  | | | 
% 244.76/51.16  | | | Case 1:
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | |   (48)  all_54_14 = e3
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | | REF_CLOSE: (18), (30), (48) are inconsistent by sub-proof #1890.
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | Case 2:
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | |   (49)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | | BETA: splitting (20) gives:
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | | Case 1:
% 244.76/51.16  | | | | | 
% 244.76/51.16  | | | | |   (50)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 244.76/51.16  | | | | |             e2) = e3)
% 244.76/51.16  | | | | | 
% 244.76/51.16  | | | | | BETA: splitting (50) gives:
% 244.76/51.16  | | | | | 
% 244.76/51.16  | | | | | Case 1:
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | |   (51)  all_58_6 = e3 & op(e1, e3) = e3
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | | ALPHA: (51) implies:
% 244.76/51.16  | | | | | |   (52)  op(e1, e3) = e3
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | | REF_CLOSE: (23), (27), (28), (52) are inconsistent by sub-proof
% 244.76/51.16  | | | | | |            #2335.
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | Case 2:
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | |   (53)  all_58_7 = e3 & op(e1, e2) = e3
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | | REF_CLOSE: (3), (6), (53) are inconsistent by sub-proof #2150.
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | End of split
% 244.76/51.16  | | | | | 
% 244.76/51.16  | | | | Case 2:
% 244.76/51.16  | | | | | 
% 244.76/51.16  | | | | |   (54)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 244.76/51.16  | | | | |             e0) = e3)
% 244.76/51.16  | | | | | 
% 244.76/51.16  | | | | | BETA: splitting (54) gives:
% 244.76/51.16  | | | | | 
% 244.76/51.16  | | | | | Case 1:
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | |   (55)  all_58_8 = e3 & op(e1, e1) = e3
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | | ALPHA: (55) implies:
% 244.76/51.16  | | | | | |   (56)  op(e1, e1) = e3
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | | REF_CLOSE: (15), (24), (27), (56) are inconsistent by sub-proof
% 244.76/51.16  | | | | | |            #2206.
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | Case 2:
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | |   (57)  all_58_11 = e3 & op(e1, e0) = e3
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | | ALPHA: (57) implies:
% 244.76/51.16  | | | | | |   (58)  op(e1, e0) = e3
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 244.76/51.16  | | | | | |            (13), (14), (15), (17), (18), (19), (21), (23), (25),
% 244.76/51.16  | | | | | |            (26), (27), (28), (29), (32), (33), (46), (47), (49),
% 244.76/51.16  | | | | | |            (58) are inconsistent by sub-proof #1888.
% 244.76/51.16  | | | | | | 
% 244.76/51.16  | | | | | End of split
% 244.76/51.16  | | | | | 
% 244.76/51.16  | | | | End of split
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | End of split
% 244.76/51.16  | | | 
% 244.76/51.16  | | End of split
% 244.76/51.16  | | 
% 244.76/51.16  | End of split
% 244.76/51.16  | 
% 244.76/51.16  End of proof
% 244.76/51.16  
% 244.76/51.16  Sub-proof #1888 shows that the following formulas are inconsistent:
% 244.76/51.16  ----------------------------------------------------------------
% 244.76/51.16    (1)  all_56_21 = e2
% 244.76/51.16    (2)   ~ (e3 = e0)
% 244.76/51.16    (3)   ~ (all_52_7 = e2)
% 244.76/51.16    (4)   ~ (e2 = e0)
% 244.76/51.16    (5)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.76/51.16           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.76/51.16             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.16           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.76/51.16             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.76/51.16           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.16           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.76/51.16           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.76/51.16           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.76/51.16           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.16           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.76/51.16             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.76/51.16           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.76/51.16           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 244.76/51.16           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.76/51.16           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.76/51.16           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.16           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.76/51.16             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.76/51.16           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.76/51.16           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.76/51.16           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.76/51.16           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.76/51.16           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.16           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.76/51.16             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.76/51.16           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.16           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.16    (6)  op(e1, e0) = all_52_14
% 244.76/51.16    (7)  op(e2, e3) = e3
% 244.76/51.16    (8)   ~ (e3 = e1)
% 244.76/51.16    (9)  op(e0, e3) = all_56_7
% 244.76/51.16    (10)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.76/51.16    (11)   ~ (all_36_0 = e0)
% 244.76/51.16    (12)   ~ (all_36_0 = e2)
% 244.76/51.16    (13)  op(e3, e1) = all_52_8
% 244.76/51.16    (14)  op(e2, e1) = all_52_9
% 244.76/51.16    (15)   ~ (e3 = e2)
% 244.76/51.16    (16)  op(e1, e0) = e3
% 244.76/51.16    (17)   ~ (all_52_14 = e0)
% 244.76/51.16    (18)  all_54_14 = all_36_0
% 244.76/51.16    (19)   ~ (all_52_8 = all_36_0)
% 244.76/51.16    (20)  op(e0, e3) = e2
% 244.76/51.16    (21)   ~ (all_52_2 = e3)
% 244.76/51.16    (22)  op(e0, e2) = all_52_7
% 244.76/51.16    (23)  op(e2, e1) = e0
% 244.76/51.16    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.16    (25)  op(e1, e3) = all_52_2
% 244.76/51.16    (26)  op(e0, all_56_7) = e0
% 244.76/51.16    (27)   ~ (e1 = e0)
% 244.76/51.16    (28)  op(e2, e0) = all_52_13
% 244.76/51.16    (29)   ~ (all_52_13 = e0)
% 244.76/51.16  
% 244.76/51.16  Begin of proof
% 244.76/51.16  | 
% 244.76/51.16  | BETA: splitting (5) gives:
% 244.76/51.16  | 
% 244.76/51.16  | Case 1:
% 244.76/51.16  | | 
% 244.76/51.16  | |   (30)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.76/51.16  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 244.76/51.16  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 244.76/51.16  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.76/51.16  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 244.76/51.16  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 244.76/51.16  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.76/51.16  | |           op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1
% 244.76/51.16  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.76/51.16  | |           (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7
% 244.76/51.16  | |           = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &
% 244.76/51.16  | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.76/51.16  | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1
% 244.76/51.16  | |             = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.76/51.16  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.76/51.16  | | 
% 244.76/51.16  | | BETA: splitting (30) gives:
% 244.76/51.16  | | 
% 244.76/51.16  | | Case 1:
% 244.76/51.16  | | | 
% 244.76/51.16  | | |   (31)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.16  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.76/51.16  | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.76/51.16  | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.76/51.16  | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 244.76/51.16  | | |         | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.16  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.76/51.16  | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.76/51.16  | | | 
% 244.76/51.16  | | | BETA: splitting (31) gives:
% 244.76/51.16  | | | 
% 244.76/51.16  | | | Case 1:
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | |   (32)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.16  | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.76/51.16  | | | |         op(e3, e2) = e3 & op(e2, e3) = e3
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | | ALPHA: (32) implies:
% 244.76/51.16  | | | |   (33)   ~ (all_56_21 = e2)
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | | REDUCE: (1), (33) imply:
% 244.76/51.16  | | | |   (34)  $false
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | | CLOSE: (34) is inconsistent.
% 244.76/51.16  | | | | 
% 244.76/51.16  | | | Case 2:
% 244.76/51.16  | | | | 
% 244.76/51.17  | | | |   (35)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.17  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.17  | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 244.76/51.17  | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.76/51.17  | | | |           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.76/51.17  | | | |           op(e1, e3) = e3)
% 244.76/51.17  | | | | 
% 244.76/51.17  | | | | REF_CLOSE: (7), (15), (21), (24), (25), (35) are inconsistent by
% 244.76/51.17  | | | |            sub-proof #1889.
% 244.76/51.17  | | | | 
% 244.76/51.17  | | | End of split
% 244.76/51.17  | | | 
% 244.76/51.17  | | Case 2:
% 244.76/51.17  | | | 
% 244.76/51.17  | | |   (36)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.17  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.17  | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25
% 244.76/51.17  | | |           = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 244.76/51.17  | | |             = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) =
% 244.76/51.17  | | |           e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.17  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.17  | | |           op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.76/51.17  | | | 
% 244.76/51.17  | | | BETA: splitting (36) gives:
% 244.76/51.17  | | | 
% 244.76/51.17  | | | Case 1:
% 244.76/51.17  | | | | 
% 244.76/51.17  | | | |   (37)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.17  | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.17  | | | |         op(e3, e1) = e1 & op(e1, e3) = e1
% 244.76/51.17  | | | | 
% 244.76/51.17  | | | | ALPHA: (37) implies:
% 244.76/51.17  | | | |   (38)  op(e3, e1) = e1
% 244.76/51.17  | | | | 
% 244.76/51.17  | | | | BETA: splitting (10) gives:
% 244.76/51.17  | | | | 
% 244.76/51.17  | | | | Case 1:
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | |   (39)  all_54_14 = e2
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | | COMBINE_EQS: (18), (39) imply:
% 244.76/51.17  | | | | |   (40)  all_36_0 = e2
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | | SIMP: (40) implies:
% 244.76/51.17  | | | | |   (41)  all_36_0 = e2
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | | REDUCE: (12), (41) imply:
% 244.76/51.17  | | | | |   (42)  $false
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | | CLOSE: (42) is inconsistent.
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | Case 2:
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | |   (43)  all_54_14 = e1 | all_54_14 = e0
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | | BETA: splitting (43) gives:
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | | Case 1:
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | |   (44)  all_54_14 = e1
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | | COMBINE_EQS: (18), (44) imply:
% 244.76/51.17  | | | | | |   (45)  all_36_0 = e1
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | | SIMP: (45) implies:
% 244.76/51.17  | | | | | |   (46)  all_36_0 = e1
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | | REDUCE: (19), (46) imply:
% 244.76/51.17  | | | | | |   (47)   ~ (all_52_8 = e1)
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | | REF_CLOSE: (13), (24), (38), (47) are inconsistent by sub-proof
% 244.76/51.17  | | | | | |            #2309.
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | Case 2:
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | |   (48)  all_54_14 = e0
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | | COMBINE_EQS: (18), (48) imply:
% 244.76/51.17  | | | | | |   (49)  all_36_0 = e0
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | | SIMP: (49) implies:
% 244.76/51.17  | | | | | |   (50)  all_36_0 = e0
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | | REDUCE: (11), (50) imply:
% 244.76/51.17  | | | | | |   (51)  $false
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | | CLOSE: (51) is inconsistent.
% 244.76/51.17  | | | | | | 
% 244.76/51.17  | | | | | End of split
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | End of split
% 244.76/51.17  | | | | 
% 244.76/51.17  | | | Case 2:
% 244.76/51.17  | | | | 
% 244.76/51.17  | | | |   (52)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.17  | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.17  | | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 244.76/51.17  | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.76/51.17  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 244.76/51.17  | | | |           op(e0, e3) = e0)
% 244.76/51.17  | | | | 
% 244.76/51.17  | | | | BETA: splitting (52) gives:
% 244.76/51.17  | | | | 
% 244.76/51.17  | | | | Case 1:
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | |   (53)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.17  | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.17  | | | | |         op(e3, e0) = e3 & op(e0, e3) = e3
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | | ALPHA: (53) implies:
% 244.76/51.17  | | | | |   (54)  op(e0, e3) = e3
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | | REF_CLOSE: (2), (9), (24), (26), (54) are inconsistent by sub-proof
% 244.76/51.17  | | | | |            #2070.
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | Case 2:
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | |   (55)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.17  | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.17  | | | | |         op(e3, e0) = e0 & op(e0, e3) = e0
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | | ALPHA: (55) implies:
% 244.76/51.17  | | | | |   (56)  op(e0, e3) = e0
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | | REF_CLOSE: (4), (20), (24), (56) are inconsistent by sub-proof #1896.
% 244.76/51.17  | | | | | 
% 244.76/51.17  | | | | End of split
% 244.76/51.17  | | | | 
% 244.76/51.17  | | | End of split
% 244.76/51.17  | | | 
% 244.76/51.17  | | End of split
% 244.76/51.17  | | 
% 244.76/51.17  | Case 2:
% 244.76/51.17  | | 
% 244.76/51.17  | |   (57)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.17  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.76/51.17  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.76/51.17  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.76/51.17  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 244.76/51.17  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.17  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.17  | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27 =
% 244.76/51.17  | |           e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.76/51.17  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) = e0) |
% 244.76/51.17  | |         (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.17  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.17  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 244.76/51.17  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.76/51.17  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.17  | | 
% 244.76/51.17  | | BETA: splitting (57) gives:
% 244.76/51.17  | | 
% 244.76/51.17  | | Case 1:
% 244.76/51.17  | | | 
% 244.76/51.17  | | |   (58)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.17  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.76/51.17  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 244.76/51.17  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 244.76/51.17  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 244.76/51.17  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.17  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.17  | | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.76/51.17  | | | 
% 244.76/51.17  | | | REF_CLOSE: (3), (4), (14), (22), (23), (24), (27), (58) are inconsistent
% 244.76/51.17  | | |            by sub-proof #1895.
% 244.76/51.17  | | | 
% 244.76/51.17  | | Case 2:
% 244.76/51.17  | | | 
% 244.76/51.17  | | |   (59)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.17  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.76/51.17  | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29
% 244.76/51.17  | | |           = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21
% 244.76/51.17  | | |             = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) =
% 244.76/51.17  | | |           e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.17  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.76/51.17  | | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.17  | | | 
% 244.76/51.17  | | | REF_CLOSE: (6), (8), (16), (17), (24), (28), (29), (59) are inconsistent
% 244.76/51.17  | | |            by sub-proof #1892.
% 244.76/51.17  | | | 
% 244.76/51.17  | | End of split
% 244.76/51.17  | | 
% 244.76/51.17  | End of split
% 244.76/51.17  | 
% 244.76/51.17  End of proof
% 244.76/51.17  
% 244.76/51.17  Sub-proof #1889 shows that the following formulas are inconsistent:
% 244.76/51.17  ----------------------------------------------------------------
% 244.76/51.17    (1)  op(e2, e3) = e3
% 244.76/51.17    (2)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 244.76/51.17           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 244.76/51.17             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.17           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 244.76/51.17             e1) = e3 & op(e1, e3) = e3)
% 244.76/51.17    (3)   ~ (e3 = e2)
% 244.76/51.17    (4)   ~ (all_52_2 = e3)
% 244.76/51.17    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.17    (6)  op(e1, e3) = all_52_2
% 244.76/51.17  
% 244.76/51.17  Begin of proof
% 244.76/51.17  | 
% 244.76/51.17  | BETA: splitting (2) gives:
% 244.76/51.17  | 
% 244.76/51.17  | Case 1:
% 244.76/51.17  | | 
% 244.76/51.17  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.76/51.17  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.76/51.17  | |        op(e2, e3) = e2
% 244.76/51.17  | | 
% 244.76/51.17  | | ALPHA: (7) implies:
% 244.76/51.17  | |   (8)  op(e2, e3) = e2
% 244.76/51.17  | | 
% 244.76/51.17  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1897.
% 244.76/51.17  | | 
% 244.76/51.17  | Case 2:
% 244.76/51.17  | | 
% 244.76/51.17  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.76/51.17  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.76/51.17  | |        op(e1, e3) = e3
% 244.76/51.17  | | 
% 244.76/51.17  | | ALPHA: (9) implies:
% 244.76/51.17  | |   (10)  op(e1, e3) = e3
% 244.76/51.17  | | 
% 244.76/51.17  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #2335.
% 244.76/51.17  | | 
% 244.76/51.17  | End of split
% 244.76/51.17  | 
% 244.76/51.17  End of proof
% 244.76/51.17  
% 244.76/51.17  Sub-proof #1890 shows that the following formulas are inconsistent:
% 244.76/51.17  ----------------------------------------------------------------
% 244.76/51.17    (1)  all_54_14 = all_36_0
% 244.76/51.17    (2)  all_54_14 = e3
% 244.76/51.17    (3)   ~ (all_36_0 = e3)
% 244.76/51.17  
% 244.76/51.17  Begin of proof
% 244.76/51.17  | 
% 244.76/51.17  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.17  |   (4)  all_36_0 = e3
% 244.76/51.17  | 
% 244.76/51.17  | SIMP: (4) implies:
% 244.76/51.17  |   (5)  all_36_0 = e3
% 244.76/51.17  | 
% 244.76/51.17  | REDUCE: (3), (5) imply:
% 244.76/51.17  |   (6)  $false
% 244.76/51.17  | 
% 244.76/51.17  | CLOSE: (6) is inconsistent.
% 244.76/51.17  | 
% 244.76/51.17  End of proof
% 244.76/51.17  
% 244.76/51.17  Sub-proof #1891 shows that the following formulas are inconsistent:
% 244.76/51.17  ----------------------------------------------------------------
% 244.76/51.17    (1)  all_56_21 = e2
% 244.76/51.17    (2)   ~ (all_52_7 = e2)
% 244.76/51.17    (3)   ~ (e2 = e0)
% 244.76/51.17    (4)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.76/51.17           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.76/51.17             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.17           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.76/51.17             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.76/51.17           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.17           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.76/51.17           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.76/51.17           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.76/51.17           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.17           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.76/51.17             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.76/51.17           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.76/51.17           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 244.76/51.17           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.76/51.17           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.76/51.17           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.17           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.76/51.17             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.76/51.17           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.76/51.17           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.76/51.17           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.76/51.17           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.76/51.17           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.17           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.76/51.17             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.76/51.17           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.17           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.17    (5)  op(e1, all_56_5) = e1
% 244.76/51.17    (6)  op(e1, e3) = all_56_5
% 244.76/51.17    (7)  op(e1, e0) = all_52_14
% 244.76/51.17    (8)  op(e2, e3) = e3
% 244.76/51.17    (9)   ~ (e3 = e1)
% 244.76/51.17    (10)  op(e2, e1) = all_52_9
% 244.76/51.17    (11)   ~ (e3 = e2)
% 244.76/51.17    (12)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.76/51.17    (13)   ~ (all_52_14 = e0)
% 244.76/51.17    (14)  op(e0, e3) = e2
% 244.76/51.17    (15)  op(e3, e0) = e2
% 244.76/51.17    (16)  op(e1, e1) = e2
% 244.76/51.18    (17)  op(e0, e2) = all_52_7
% 244.76/51.18    (18)  op(e2, e1) = e0
% 244.76/51.18    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.18    (20)   ~ (e1 = e0)
% 244.76/51.18    (21)  op(e2, e0) = all_52_13
% 244.76/51.18    (22)   ~ (all_52_13 = e0)
% 244.76/51.18    (23)   ~ (e2 = e1)
% 244.76/51.18  
% 244.76/51.18  Begin of proof
% 244.76/51.18  | 
% 244.76/51.18  | BETA: splitting (12) gives:
% 244.76/51.18  | 
% 244.76/51.18  | Case 1:
% 244.76/51.18  | | 
% 244.76/51.18  | |   (24)  all_58_8 = e3 & op(e1, e1) = e3
% 244.76/51.18  | | 
% 244.76/51.18  | | ALPHA: (24) implies:
% 244.76/51.18  | |   (25)  op(e1, e1) = e3
% 244.76/51.18  | | 
% 244.76/51.18  | | REF_CLOSE: (11), (16), (19), (25) are inconsistent by sub-proof #2206.
% 244.76/51.18  | | 
% 244.76/51.18  | Case 2:
% 244.76/51.18  | | 
% 244.76/51.18  | |   (26)  all_58_11 = e3 & op(e1, e0) = e3
% 244.76/51.18  | | 
% 244.76/51.18  | | ALPHA: (26) implies:
% 244.76/51.18  | |   (27)  op(e1, e0) = e3
% 244.76/51.18  | | 
% 244.76/51.18  | | BETA: splitting (4) gives:
% 244.76/51.18  | | 
% 244.76/51.18  | | Case 1:
% 244.76/51.18  | | | 
% 244.76/51.18  | | |   (28)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.18  | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.76/51.18  | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.76/51.18  | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.76/51.18  | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2)
% 244.76/51.18  | | |         | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.18  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.76/51.18  | | |           op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1 & all_56_17
% 244.76/51.18  | | |           = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 244.76/51.18  | | |             = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.76/51.18  | | |           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.18  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.18  | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25
% 244.76/51.18  | | |           = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21
% 244.76/51.18  | | |             = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) =
% 244.76/51.18  | | |           e0)
% 244.76/51.18  | | | 
% 244.76/51.18  | | | BETA: splitting (28) gives:
% 244.76/51.18  | | | 
% 244.76/51.18  | | | Case 1:
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | |   (29)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.18  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.76/51.18  | | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9
% 244.76/51.18  | | | |           = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.76/51.18  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.76/51.18  | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.76/51.18  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 244.76/51.18  | | | |           ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | | BETA: splitting (29) gives:
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | | Case 1:
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | |   (30)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.18  | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.76/51.18  | | | | |         op(e3, e2) = e3 & op(e2, e3) = e3
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | | ALPHA: (30) implies:
% 244.76/51.18  | | | | |   (31)   ~ (all_56_21 = e2)
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | | REDUCE: (1), (31) imply:
% 244.76/51.18  | | | | |   (32)  $false
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | | CLOSE: (32) is inconsistent.
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | Case 2:
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | |   (33)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.18  | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 244.76/51.18  | | | | |           & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 &
% 244.76/51.18  | | | | |           all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 244.76/51.18  | | | | |           ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.76/51.18  | | | | |           op(e1, e3) = e3)
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | | BETA: splitting (33) gives:
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | | Case 1:
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | |   (34)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.18  | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 244.76/51.18  | | | | | |         & op(e3, e2) = e2 & op(e2, e3) = e2
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | | ALPHA: (34) implies:
% 244.76/51.18  | | | | | |   (35)  op(e2, e3) = e2
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | | REF_CLOSE: (8), (11), (19), (35) are inconsistent by sub-proof
% 244.76/51.18  | | | | | |            #1897.
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | Case 2:
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | |   (36)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.18  | | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 244.76/51.18  | | | | | |         & op(e3, e1) = e3 & op(e1, e3) = e3
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | | ALPHA: (36) implies:
% 244.76/51.18  | | | | | |   (37)  op(e1, e3) = e3
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | | REF_CLOSE: (5), (6), (9), (19), (37) are inconsistent by sub-proof
% 244.76/51.18  | | | | | |            #2243.
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | End of split
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | End of split
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | Case 2:
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | |   (38)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.18  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.18  | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 244.76/51.18  | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 244.76/51.18  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.76/51.18  | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.76/51.18  | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) & 
% 244.76/51.18  | | | |           ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | | BETA: splitting (38) gives:
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | | Case 1:
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | |   (39)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.18  | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.18  | | | | |         op(e3, e1) = e1 & op(e1, e3) = e1
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | | ALPHA: (39) implies:
% 244.76/51.18  | | | | |   (40)  all_56_5 = e1
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | | REDUCE: (5), (40) imply:
% 244.76/51.18  | | | | |   (41)  op(e1, e1) = e1
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | | REF_CLOSE: (16), (19), (23), (41) are inconsistent by sub-proof #2159.
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | Case 2:
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | |   (42)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.18  | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.76/51.18  | | | | |           & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 &
% 244.76/51.18  | | | | |           all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.76/51.18  | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 244.76/51.18  | | | | |           op(e0, e3) = e0)
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | | BETA: splitting (42) gives:
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | | Case 1:
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | |   (43)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.18  | | | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.76/51.18  | | | | | |         & op(e3, e0) = e3 & op(e0, e3) = e3
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | | ALPHA: (43) implies:
% 244.76/51.18  | | | | | |   (44)  op(e3, e0) = e3
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | | REF_CLOSE: (11), (15), (19), (44) are inconsistent by sub-proof
% 244.76/51.18  | | | | | |            #2125.
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | Case 2:
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | |   (45)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.18  | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 244.76/51.18  | | | | | |         & op(e3, e0) = e0 & op(e0, e3) = e0
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | | ALPHA: (45) implies:
% 244.76/51.18  | | | | | |   (46)  op(e0, e3) = e0
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | | REF_CLOSE: (3), (14), (19), (46) are inconsistent by sub-proof
% 244.76/51.18  | | | | | |            #1896.
% 244.76/51.18  | | | | | | 
% 244.76/51.18  | | | | | End of split
% 244.76/51.18  | | | | | 
% 244.76/51.18  | | | | End of split
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | End of split
% 244.76/51.18  | | | 
% 244.76/51.18  | | Case 2:
% 244.76/51.18  | | | 
% 244.76/51.18  | | |   (47)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.18  | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.76/51.18  | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19
% 244.76/51.18  | | |           = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 244.76/51.18  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) =
% 244.76/51.18  | | |           e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.18  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.18  | | |           op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0 & all_56_27
% 244.76/51.18  | | |           = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21
% 244.76/51.18  | | |             = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.76/51.18  | | |           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.18  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.18  | | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29
% 244.76/51.18  | | |           = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 244.76/51.18  | | |             = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 244.76/51.18  | | |           e0)
% 244.76/51.18  | | | 
% 244.76/51.18  | | | BETA: splitting (47) gives:
% 244.76/51.18  | | | 
% 244.76/51.18  | | | Case 1:
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | |   (48)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.18  | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.76/51.18  | | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 244.76/51.18  | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.76/51.18  | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.76/51.18  | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.76/51.18  | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) & 
% 244.76/51.18  | | | |           ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | | REF_CLOSE: (2), (3), (10), (17), (18), (19), (20), (48) are inconsistent
% 244.76/51.18  | | | |            by sub-proof #1895.
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | Case 2:
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | |   (49)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.18  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.76/51.18  | | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 244.76/51.18  | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 244.76/51.18  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 244.76/51.18  | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.76/51.18  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 244.76/51.18  | | | |           ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | | REF_CLOSE: (7), (9), (13), (19), (21), (22), (27), (49) are inconsistent
% 244.76/51.18  | | | |            by sub-proof #1892.
% 244.76/51.18  | | | | 
% 244.76/51.18  | | | End of split
% 244.76/51.18  | | | 
% 244.76/51.18  | | End of split
% 244.76/51.18  | | 
% 244.76/51.18  | End of split
% 244.76/51.18  | 
% 244.76/51.18  End of proof
% 244.76/51.18  
% 244.76/51.18  Sub-proof #1892 shows that the following formulas are inconsistent:
% 244.76/51.18  ----------------------------------------------------------------
% 244.76/51.18    (1)  op(e1, e0) = all_52_14
% 244.76/51.18    (2)   ~ (e3 = e1)
% 244.76/51.18    (3)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.76/51.18             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.76/51.18           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 244.76/51.18             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.76/51.18           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 244.76/51.18           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.18           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.18    (4)  op(e1, e0) = e3
% 244.76/51.18    (5)   ~ (all_52_14 = e0)
% 244.76/51.18    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.18    (7)  op(e2, e0) = all_52_13
% 244.76/51.18    (8)   ~ (all_52_13 = e0)
% 244.76/51.18  
% 244.76/51.18  Begin of proof
% 244.76/51.18  | 
% 244.76/51.18  | BETA: splitting (3) gives:
% 244.76/51.18  | 
% 244.76/51.18  | Case 1:
% 244.76/51.18  | | 
% 244.76/51.18  | |   (9)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.76/51.18  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 244.76/51.18  | |        & op(e0, e2) = e0
% 244.76/51.18  | | 
% 244.76/51.18  | | ALPHA: (9) implies:
% 244.76/51.18  | |   (10)  op(e2, e0) = e0
% 244.76/51.18  | | 
% 244.76/51.18  | | REF_CLOSE: (6), (7), (8), (10) are inconsistent by sub-proof #2324.
% 244.76/51.18  | | 
% 244.76/51.18  | Case 2:
% 244.76/51.18  | | 
% 244.76/51.18  | |   (11)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.18  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.18  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 244.76/51.18  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.76/51.18  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.18  | | 
% 244.76/51.18  | | REF_CLOSE: (1), (2), (4), (5), (6), (11) are inconsistent by sub-proof
% 244.76/51.18  | |            #1893.
% 244.76/51.18  | | 
% 244.76/51.18  | End of split
% 244.76/51.18  | 
% 244.76/51.18  End of proof
% 244.76/51.18  
% 244.76/51.18  Sub-proof #1893 shows that the following formulas are inconsistent:
% 244.76/51.18  ----------------------------------------------------------------
% 244.76/51.18    (1)  op(e1, e0) = all_52_14
% 244.76/51.18    (2)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.76/51.18             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 244.76/51.18           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 244.76/51.18             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 244.76/51.18           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.18    (3)   ~ (e3 = e1)
% 244.76/51.18    (4)  op(e1, e0) = e3
% 244.76/51.18    (5)   ~ (all_52_14 = e0)
% 244.76/51.18    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.18  
% 244.76/51.18  Begin of proof
% 244.76/51.18  | 
% 244.76/51.18  | BETA: splitting (2) gives:
% 244.76/51.18  | 
% 244.76/51.18  | Case 1:
% 244.76/51.18  | | 
% 244.76/51.18  | |   (7)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.76/51.18  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 244.76/51.18  | |        & op(e0, e1) = e1
% 244.76/51.18  | | 
% 244.76/51.18  | | ALPHA: (7) implies:
% 244.76/51.18  | |   (8)  op(e1, e0) = e1
% 244.76/51.18  | | 
% 244.76/51.18  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #1894.
% 244.76/51.18  | | 
% 244.76/51.18  | Case 2:
% 244.76/51.18  | | 
% 244.76/51.18  | |   (9)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.76/51.18  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 244.76/51.18  | |        & op(e0, e1) = e0
% 244.76/51.18  | | 
% 244.76/51.18  | | ALPHA: (9) implies:
% 244.76/51.18  | |   (10)  op(e1, e0) = e0
% 244.76/51.18  | | 
% 244.76/51.18  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #2323.
% 244.76/51.18  | | 
% 244.76/51.18  | End of split
% 244.76/51.18  | 
% 244.76/51.18  End of proof
% 244.76/51.18  
% 244.76/51.18  Sub-proof #1894 shows that the following formulas are inconsistent:
% 244.76/51.18  ----------------------------------------------------------------
% 244.76/51.18    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.18    (2)  op(e1, e0) = e3
% 244.76/51.18    (3)  op(e1, e0) = e1
% 244.76/51.18    (4)   ~ (e3 = e1)
% 244.76/51.18  
% 244.76/51.18  Begin of proof
% 244.76/51.18  | 
% 244.76/51.18  | GROUND_INST: instantiating (1) with e3, e1, e0, e1, simplifying with (2), (3)
% 244.76/51.18  |              gives:
% 244.76/51.18  |   (5)  e3 = e1
% 244.76/51.18  | 
% 244.76/51.18  | REDUCE: (4), (5) imply:
% 244.76/51.18  |   (6)  $false
% 244.76/51.18  | 
% 244.76/51.18  | CLOSE: (6) is inconsistent.
% 244.76/51.18  | 
% 244.76/51.18  End of proof
% 244.76/51.18  
% 244.76/51.18  Sub-proof #1895 shows that the following formulas are inconsistent:
% 244.76/51.18  ----------------------------------------------------------------
% 244.76/51.18    (1)   ~ (all_52_7 = e2)
% 244.76/51.18    (2)   ~ (e2 = e0)
% 244.76/51.18    (3)  op(e2, e1) = all_52_9
% 244.76/51.18    (4)  op(e0, e2) = all_52_7
% 244.76/51.18    (5)  op(e2, e1) = e0
% 244.76/51.18    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.18    (7)   ~ (e1 = e0)
% 244.76/51.18    (8)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.76/51.18             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.76/51.18           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.76/51.18             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 244.76/51.18           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 244.76/51.18           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.76/51.18           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.76/51.18  
% 244.76/51.18  Begin of proof
% 244.76/51.18  | 
% 244.76/51.18  | BETA: splitting (8) gives:
% 244.76/51.18  | 
% 244.76/51.18  | Case 1:
% 244.76/51.18  | | 
% 244.76/51.18  | |   (9)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.76/51.18  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 244.76/51.18  | |        & op(e1, e2) = e2
% 244.76/51.18  | | 
% 244.76/51.18  | | ALPHA: (9) implies:
% 244.76/51.18  | |   (10)  op(e2, e1) = e2
% 244.76/51.18  | | 
% 244.76/51.18  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1906.
% 244.76/51.18  | | 
% 244.76/51.18  | Case 2:
% 244.76/51.18  | | 
% 244.76/51.18  | |   (11)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.18  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.76/51.18  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 244.76/51.18  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.76/51.18  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.76/51.18  | | 
% 244.76/51.18  | | BETA: splitting (11) gives:
% 244.76/51.18  | | 
% 244.76/51.18  | | Case 1:
% 244.76/51.18  | | | 
% 244.76/51.18  | | |   (12)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.18  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.76/51.18  | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 244.76/51.18  | | | 
% 244.76/51.18  | | | ALPHA: (12) implies:
% 244.76/51.18  | | |   (13)  op(e2, e1) = e1
% 244.76/51.18  | | | 
% 244.76/51.18  | | | REF_CLOSE: (3), (5), (6), (7), (13) are inconsistent by sub-proof #2165.
% 244.76/51.18  | | | 
% 244.76/51.18  | | Case 2:
% 244.76/51.18  | | | 
% 244.76/51.18  | | |   (14)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.18  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.18  | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 244.76/51.19  | | | 
% 244.76/51.19  | | | ALPHA: (14) implies:
% 244.76/51.19  | | |   (15)  op(e0, e2) = e2
% 244.76/51.19  | | | 
% 244.76/51.19  | | | REF_CLOSE: (1), (4), (6), (15) are inconsistent by sub-proof #2327.
% 244.76/51.19  | | | 
% 244.76/51.19  | | End of split
% 244.76/51.19  | | 
% 244.76/51.19  | End of split
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1896 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.19    (2)  op(e0, e3) = e2
% 244.76/51.19    (3)  op(e0, e3) = e0
% 244.76/51.19    (4)   ~ (e2 = e0)
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | GROUND_INST: instantiating (1) with e2, e0, e3, e0, simplifying with (2), (3)
% 244.76/51.19  |              gives:
% 244.76/51.19  |   (5)  e2 = e0
% 244.76/51.19  | 
% 244.76/51.19  | REDUCE: (4), (5) imply:
% 244.76/51.19  |   (6)  $false
% 244.76/51.19  | 
% 244.76/51.19  | CLOSE: (6) is inconsistent.
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1897 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.19    (2)  op(e2, e3) = e3
% 244.76/51.19    (3)  op(e2, e3) = e2
% 244.76/51.19    (4)   ~ (e3 = e2)
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | GROUND_INST: instantiating (1) with e3, e2, e3, e2, simplifying with (2), (3)
% 244.76/51.19  |              gives:
% 244.76/51.19  |   (5)  e3 = e2
% 244.76/51.19  | 
% 244.76/51.19  | REDUCE: (4), (5) imply:
% 244.76/51.19  |   (6)  $false
% 244.76/51.19  | 
% 244.76/51.19  | CLOSE: (6) is inconsistent.
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1898 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.76/51.19             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 244.76/51.19    (2)  op(e2, e3) = e3
% 244.76/51.19    (3)   ~ (e3 = e2)
% 244.76/51.19    (4)  op(e3, e0) = e2
% 244.76/51.19    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.19    (6)  all_56_1 = e0
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | BETA: splitting (1) gives:
% 244.76/51.19  | 
% 244.76/51.19  | Case 1:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (7)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 244.76/51.19  | | 
% 244.76/51.19  | | ALPHA: (7) implies:
% 244.76/51.19  | |   (8)  op(e3, all_56_1) = e3
% 244.76/51.19  | | 
% 244.76/51.19  | | REDUCE: (6), (8) imply:
% 244.76/51.19  | |   (9)  op(e3, e0) = e3
% 244.76/51.19  | | 
% 244.76/51.19  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #2125.
% 244.76/51.19  | | 
% 244.76/51.19  | Case 2:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (10)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 244.76/51.19  | |         $i(all_56_3)
% 244.76/51.19  | | 
% 244.76/51.19  | | ALPHA: (10) implies:
% 244.76/51.19  | |   (11)  op(e2, e3) = all_56_3
% 244.76/51.19  | |   (12)  op(e2, all_56_3) = e2
% 244.76/51.19  | | 
% 244.76/51.19  | | REF_CLOSE: (2), (3), (5), (11), (12) are inconsistent by sub-proof #2262.
% 244.76/51.19  | | 
% 244.76/51.19  | End of split
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1899 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)   ~ (e3 = e0)
% 244.76/51.19    (2)   ~ (e2 = e0)
% 244.76/51.19    (3)  all_58_4 = e2
% 244.76/51.19    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.76/51.19         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.76/51.19    (5)   ~ (e3 = e1)
% 244.76/51.19    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.76/51.19         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.76/51.19    (7)  op(e2, e1) = all_52_9
% 244.76/51.19    (8)   ~ (e3 = e2)
% 244.76/51.19    (9)  op(e1, e1) = e2
% 244.76/51.19    (10)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.76/51.19          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.76/51.19    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.19    (12)   ~ (e1 = e0)
% 244.76/51.19    (13)   ~ (e2 = e1)
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | BETA: splitting (10) gives:
% 244.76/51.19  | 
% 244.76/51.19  | Case 1:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (14)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 244.76/51.19  | |           e3)
% 244.76/51.19  | | 
% 244.76/51.19  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 244.76/51.19  | |            (13), (14) are inconsistent by sub-proof #1901.
% 244.76/51.19  | | 
% 244.76/51.19  | Case 2:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (15)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 244.76/51.19  | |           e3)
% 244.76/51.19  | | 
% 244.76/51.19  | | BETA: splitting (15) gives:
% 244.76/51.19  | | 
% 244.76/51.19  | | Case 1:
% 244.76/51.19  | | | 
% 244.76/51.19  | | |   (16)  all_58_8 = e3 & op(e1, e1) = e3
% 244.76/51.19  | | | 
% 244.76/51.19  | | | ALPHA: (16) implies:
% 244.76/51.19  | | |   (17)  op(e1, e1) = e3
% 244.76/51.19  | | | 
% 244.76/51.19  | | | REF_CLOSE: (8), (9), (11), (17) are inconsistent by sub-proof #2206.
% 244.76/51.19  | | | 
% 244.76/51.19  | | Case 2:
% 244.76/51.19  | | | 
% 244.76/51.19  | | |   (18)  all_58_14 = e3 & op(e0, e1) = e3
% 244.76/51.19  | | | 
% 244.76/51.19  | | | ALPHA: (18) implies:
% 244.76/51.19  | | |   (19)  all_58_14 = e3
% 244.76/51.19  | | | 
% 244.76/51.19  | | | BETA: splitting (4) gives:
% 244.76/51.19  | | | 
% 244.76/51.19  | | | Case 1:
% 244.76/51.19  | | | | 
% 244.76/51.19  | | | |   (20)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 244.76/51.19  | | | |           = e1)
% 244.76/51.19  | | | | 
% 244.76/51.19  | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 244.76/51.19  | | | |            (13), (20) are inconsistent by sub-proof #2160.
% 244.76/51.19  | | | | 
% 244.76/51.19  | | | Case 2:
% 244.76/51.19  | | | | 
% 244.76/51.19  | | | |   (21)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 244.76/51.19  | | | |           = e1)
% 244.76/51.19  | | | | 
% 244.76/51.19  | | | | BETA: splitting (21) gives:
% 244.76/51.19  | | | | 
% 244.76/51.19  | | | | Case 1:
% 244.76/51.19  | | | | | 
% 244.76/51.19  | | | | |   (22)  all_58_8 = e1 & op(e1, e1) = e1
% 244.76/51.19  | | | | | 
% 244.76/51.19  | | | | | ALPHA: (22) implies:
% 244.76/51.19  | | | | |   (23)  op(e1, e1) = e1
% 244.76/51.19  | | | | | 
% 244.76/51.19  | | | | | REF_CLOSE: (9), (11), (13), (23) are inconsistent by sub-proof #2159.
% 244.76/51.19  | | | | | 
% 244.76/51.19  | | | | Case 2:
% 244.76/51.19  | | | | | 
% 244.76/51.19  | | | | |   (24)  all_58_14 = e1 & op(e0, e1) = e1
% 244.76/51.19  | | | | | 
% 244.76/51.19  | | | | | REF_CLOSE: (5), (19), (24) are inconsistent by sub-proof #1900.
% 244.76/51.19  | | | | | 
% 244.76/51.19  | | | | End of split
% 244.76/51.19  | | | | 
% 244.76/51.19  | | | End of split
% 244.76/51.19  | | | 
% 244.76/51.19  | | End of split
% 244.76/51.19  | | 
% 244.76/51.19  | End of split
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1900 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)  all_58_14 = e1 & op(e0, e1) = e1
% 244.76/51.19    (2)  all_58_14 = e3
% 244.76/51.19    (3)   ~ (e3 = e1)
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | ALPHA: (1) implies:
% 244.76/51.19  |   (4)  all_58_14 = e1
% 244.76/51.19  | 
% 244.76/51.19  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.19  |   (5)  e3 = e1
% 244.76/51.19  | 
% 244.76/51.19  | REDUCE: (3), (5) imply:
% 244.76/51.19  |   (6)  $false
% 244.76/51.19  | 
% 244.76/51.19  | CLOSE: (6) is inconsistent.
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1901 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 244.76/51.19    (2)   ~ (e3 = e0)
% 244.76/51.19    (3)   ~ (e2 = e0)
% 244.76/51.19    (4)  all_58_4 = e2
% 244.76/51.19    (5)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.76/51.19         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.76/51.19    (6)   ~ (e3 = e1)
% 244.76/51.19    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.76/51.19         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.76/51.19    (8)  op(e2, e1) = all_52_9
% 244.76/51.19    (9)   ~ (e3 = e2)
% 244.76/51.19    (10)  op(e1, e1) = e2
% 244.76/51.19    (11)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.76/51.19          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.76/51.19    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.19    (13)   ~ (e1 = e0)
% 244.76/51.19    (14)   ~ (e2 = e1)
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | BETA: splitting (1) gives:
% 244.76/51.19  | 
% 244.76/51.19  | Case 1:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (15)  all_58_4 = e3 & op(e3, e1) = e3
% 244.76/51.19  | | 
% 244.76/51.19  | | ALPHA: (15) implies:
% 244.76/51.19  | |   (16)  all_58_4 = e3
% 244.76/51.19  | | 
% 244.76/51.19  | | REF_CLOSE: (4), (9), (16) are inconsistent by sub-proof #1902.
% 244.76/51.19  | | 
% 244.76/51.19  | Case 2:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (17)  all_58_5 = e3 & op(e2, e1) = e3
% 244.76/51.19  | | 
% 244.76/51.19  | | ALPHA: (17) implies:
% 244.76/51.19  | |   (18)  all_58_5 = e3
% 244.76/51.19  | | 
% 244.76/51.19  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 244.76/51.19  | |            (14), (18) are inconsistent by sub-proof #2155.
% 244.76/51.19  | | 
% 244.76/51.19  | End of split
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1902 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)  all_58_4 = e3
% 244.76/51.19    (2)  all_58_4 = e2
% 244.76/51.19    (3)   ~ (e3 = e2)
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.19  |   (4)  e3 = e2
% 244.76/51.19  | 
% 244.76/51.19  | SIMP: (4) implies:
% 244.76/51.19  |   (5)  e3 = e2
% 244.76/51.19  | 
% 244.76/51.19  | REDUCE: (3), (5) imply:
% 244.76/51.19  |   (6)  $false
% 244.76/51.19  | 
% 244.76/51.19  | CLOSE: (6) is inconsistent.
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1903 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)  op(e1, e0) = all_52_14
% 244.76/51.19    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.76/51.19             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.76/51.19           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 244.76/51.19             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.76/51.19           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 244.76/51.19           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.19           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.19    (3)   ~ (all_52_14 = e1)
% 244.76/51.19    (4)   ~ (all_52_14 = e0)
% 244.76/51.19    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.19    (6)  op(e2, e0) = all_52_13
% 244.76/51.19    (7)   ~ (all_52_13 = e0)
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | BETA: splitting (2) gives:
% 244.76/51.19  | 
% 244.76/51.19  | Case 1:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.76/51.19  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 244.76/51.19  | |        & op(e0, e2) = e0
% 244.76/51.19  | | 
% 244.76/51.19  | | ALPHA: (8) implies:
% 244.76/51.19  | |   (9)  op(e2, e0) = e0
% 244.76/51.19  | | 
% 244.76/51.19  | | REF_CLOSE: (5), (6), (7), (9) are inconsistent by sub-proof #2324.
% 244.76/51.19  | | 
% 244.76/51.19  | Case 2:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.19  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.19  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 244.76/51.19  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.76/51.19  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.19  | | 
% 244.76/51.19  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #1989.
% 244.76/51.19  | | 
% 244.76/51.19  | End of split
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1904 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)   ~ (all_52_9 = all_6_2)
% 244.76/51.19    (2)   ~ (all_52_7 = e2)
% 244.76/51.19    (3)  all_54_10 = e1 | all_54_10 = e0
% 244.76/51.19    (4)  all_54_10 = all_6_2
% 244.76/51.19    (5)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.76/51.19             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.76/51.19           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 244.76/51.19             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.76/51.19           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.76/51.19    (6)  op(e2, e1) = all_52_9
% 244.76/51.19    (7)   ~ (all_6_2 = e0)
% 244.76/51.19    (8)  op(e0, e2) = all_52_7
% 244.76/51.19    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | BETA: splitting (5) gives:
% 244.76/51.19  | 
% 244.76/51.19  | Case 1:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (10)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.76/51.19  | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) =
% 244.76/51.19  | |         e1 & op(e1, e2) = e1
% 244.76/51.19  | | 
% 244.76/51.19  | | ALPHA: (10) implies:
% 244.76/51.19  | |   (11)  op(e2, e1) = e1
% 244.76/51.19  | | 
% 244.76/51.19  | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (11) are inconsistent by sub-proof
% 244.76/51.19  | |            #1905.
% 244.76/51.19  | | 
% 244.76/51.19  | Case 2:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (12)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.76/51.19  | |           = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) =
% 244.76/51.19  | |         e2 & op(e0, e2) = e2
% 244.76/51.19  | | 
% 244.76/51.19  | | ALPHA: (12) implies:
% 244.76/51.19  | |   (13)  op(e0, e2) = e2
% 244.76/51.19  | | 
% 244.76/51.19  | | REF_CLOSE: (2), (8), (9), (13) are inconsistent by sub-proof #2327.
% 244.76/51.19  | | 
% 244.76/51.19  | End of split
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1905 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)   ~ (all_52_9 = all_6_2)
% 244.76/51.19    (2)  all_54_10 = e1 | all_54_10 = e0
% 244.76/51.19    (3)  op(e2, e1) = e1
% 244.76/51.19    (4)  all_54_10 = all_6_2
% 244.76/51.19    (5)  op(e2, e1) = all_52_9
% 244.76/51.19    (6)   ~ (all_6_2 = e0)
% 244.76/51.19    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | BETA: splitting (2) gives:
% 244.76/51.19  | 
% 244.76/51.19  | Case 1:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (8)  all_54_10 = e1
% 244.76/51.19  | | 
% 244.76/51.19  | | COMBINE_EQS: (4), (8) imply:
% 244.76/51.19  | |   (9)  all_6_2 = e1
% 244.76/51.19  | | 
% 244.76/51.19  | | SIMP: (9) implies:
% 244.76/51.19  | |   (10)  all_6_2 = e1
% 244.76/51.19  | | 
% 244.76/51.19  | | REDUCE: (1), (10) imply:
% 244.76/51.19  | |   (11)   ~ (all_52_9 = e1)
% 244.76/51.19  | | 
% 244.76/51.19  | | REF_CLOSE: (3), (5), (7), (11) are inconsistent by sub-proof #2306.
% 244.76/51.19  | | 
% 244.76/51.19  | Case 2:
% 244.76/51.19  | | 
% 244.76/51.19  | |   (12)  all_54_10 = e0
% 244.76/51.19  | | 
% 244.76/51.19  | | REF_CLOSE: (4), (6), (12) are inconsistent by sub-proof #2303.
% 244.76/51.19  | | 
% 244.76/51.19  | End of split
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1906 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.19    (2)  op(e2, e1) = e2
% 244.76/51.19    (3)  op(e2, e1) = e0
% 244.76/51.19    (4)   ~ (e2 = e0)
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | GROUND_INST: instantiating (1) with e0, e2, e1, e2, simplifying with (2), (3)
% 244.76/51.19  |              gives:
% 244.76/51.19  |   (5)  e2 = e0
% 244.76/51.19  | 
% 244.76/51.19  | REDUCE: (4), (5) imply:
% 244.76/51.19  |   (6)  $false
% 244.76/51.19  | 
% 244.76/51.19  | CLOSE: (6) is inconsistent.
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1907 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)  all_54_5 = all_8_2
% 244.76/51.19    (2)  all_54_5 = e3
% 244.76/51.19    (3)   ~ (all_8_2 = e3)
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.19  |   (4)  all_8_2 = e3
% 244.76/51.19  | 
% 244.76/51.19  | SIMP: (4) implies:
% 244.76/51.19  |   (5)  all_8_2 = e3
% 244.76/51.19  | 
% 244.76/51.19  | REDUCE: (3), (5) imply:
% 244.76/51.19  |   (6)  $false
% 244.76/51.19  | 
% 244.76/51.19  | CLOSE: (6) is inconsistent.
% 244.76/51.19  | 
% 244.76/51.19  End of proof
% 244.76/51.19  
% 244.76/51.19  Sub-proof #1908 shows that the following formulas are inconsistent:
% 244.76/51.19  ----------------------------------------------------------------
% 244.76/51.19    (1)  all_58_4 = e0 & op(e3, e1) = e0
% 244.76/51.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.19    (3)  op(e3, e1) = all_52_8
% 244.76/51.19    (4)   ~ (all_52_8 = e0)
% 244.76/51.19  
% 244.76/51.19  Begin of proof
% 244.76/51.19  | 
% 244.76/51.19  | ALPHA: (1) implies:
% 244.76/51.19  |   (5)  op(e3, e1) = e0
% 244.76/51.19  | 
% 244.76/51.19  | GROUND_INST: instantiating (2) with all_52_8, e0, e1, e3, simplifying with
% 244.76/51.19  |              (3), (5) gives:
% 244.76/51.19  |   (6)  all_52_8 = e0
% 244.76/51.19  | 
% 244.76/51.19  | REDUCE: (4), (6) imply:
% 244.76/51.19  |   (7)  $false
% 244.76/51.19  | 
% 244.76/51.19  | CLOSE: (7) is inconsistent.
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1909 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)   ~ (e3 = e0)
% 244.76/51.20    (2)  op(e1, e0) = all_52_14
% 244.76/51.20    (3)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.76/51.20    (4)   ~ (all_52_14 = e3)
% 244.76/51.20    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.20    (6)  op(e1, e1) = e0
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | BETA: splitting (3) gives:
% 244.76/51.20  | 
% 244.76/51.20  | Case 1:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (1), (5), (6), (7) are inconsistent by sub-proof #2018.
% 244.76/51.20  | | 
% 244.76/51.20  | Case 2:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (8)  all_58_11 = e3 & op(e1, e0) = e3
% 244.76/51.20  | | 
% 244.76/51.20  | | ALPHA: (8) implies:
% 244.76/51.20  | |   (9)  op(e1, e0) = e3
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2149.
% 244.76/51.20  | | 
% 244.76/51.20  | End of split
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1910 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)   ~ (all_52_6 = e1)
% 244.76/51.20    (2)  op(e0, e1) = all_52_11
% 244.76/51.20    (3)  op(e1, e2) = all_52_6
% 244.76/51.20    (4)  (all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 244.76/51.20           $i(all_56_29)) | (all_56_30 = e0 & op(e0, all_56_31) = e0)
% 244.76/51.20    (5)  all_56_31 = e1
% 244.76/51.20    (6)   ~ (all_52_11 = e0)
% 244.76/51.20    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.20    (8)  op(e1, e0) = e2
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | BETA: splitting (4) gives:
% 244.76/51.20  | 
% 244.76/51.20  | Case 1:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (9)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 244.76/51.20  | |        $i(all_56_29)
% 244.76/51.20  | | 
% 244.76/51.20  | | ALPHA: (9) implies:
% 244.76/51.20  | |   (10)  op(e1, e0) = all_56_29
% 244.76/51.20  | |   (11)  op(e1, all_56_29) = e1
% 244.76/51.20  | | 
% 244.76/51.20  | | GROUND_INST: instantiating (7) with e2, all_56_29, e0, e1, simplifying with
% 244.76/51.20  | |              (8), (10) gives:
% 244.76/51.20  | |   (12)  all_56_29 = e2
% 244.76/51.20  | | 
% 244.76/51.20  | | REDUCE: (11), (12) imply:
% 244.76/51.20  | |   (13)  op(e1, e2) = e1
% 244.76/51.20  | | 
% 244.76/51.20  | | GROUND_INST: instantiating (7) with all_52_6, e1, e2, e1, simplifying with
% 244.76/51.20  | |              (3), (13) gives:
% 244.76/51.20  | |   (14)  all_52_6 = e1
% 244.76/51.20  | | 
% 244.76/51.20  | | REDUCE: (1), (14) imply:
% 244.76/51.20  | |   (15)  $false
% 244.76/51.20  | | 
% 244.76/51.20  | | CLOSE: (15) is inconsistent.
% 244.76/51.20  | | 
% 244.76/51.20  | Case 2:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (16)  all_56_30 = e0 & op(e0, all_56_31) = e0
% 244.76/51.20  | | 
% 244.76/51.20  | | ALPHA: (16) implies:
% 244.76/51.20  | |   (17)  op(e0, all_56_31) = e0
% 244.76/51.20  | | 
% 244.76/51.20  | | REDUCE: (5), (17) imply:
% 244.76/51.20  | |   (18)  op(e0, e1) = e0
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (2), (6), (7), (18) are inconsistent by sub-proof #1911.
% 244.76/51.20  | | 
% 244.76/51.20  | End of split
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1911 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.20    (2)  op(e0, e1) = all_52_11
% 244.76/51.20    (3)  op(e0, e1) = e0
% 244.76/51.20    (4)   ~ (all_52_11 = e0)
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | GROUND_INST: instantiating (1) with all_52_11, e0, e1, e0, simplifying with
% 244.76/51.20  |              (2), (3) gives:
% 244.76/51.20  |   (5)  all_52_11 = e0
% 244.76/51.20  | 
% 244.76/51.20  | REDUCE: (4), (5) imply:
% 244.76/51.20  |   (6)  $false
% 244.76/51.20  | 
% 244.76/51.20  | CLOSE: (6) is inconsistent.
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1912 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)  op(e2, e0) = all_56_27
% 244.76/51.20    (2)  op(e2, all_56_27) = e2
% 244.76/51.20    (3)  all_54_11 = all_52_14
% 244.76/51.20    (4)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 244.76/51.20    (5)   ~ (all_52_14 = e1)
% 244.76/51.20    (6)   ~ (all_52_14 = e0)
% 244.76/51.20    (7)  op(e2, e0) = e0
% 244.76/51.20    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | BETA: splitting (4) gives:
% 244.76/51.20  | 
% 244.76/51.20  | Case 1:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (9)  all_54_11 = e2
% 244.76/51.20  | | 
% 244.76/51.20  | | COMBINE_EQS: (3), (9) imply:
% 244.76/51.20  | |   (10)  all_52_14 = e2
% 244.76/51.20  | | 
% 244.76/51.20  | | SIMP: (10) implies:
% 244.76/51.20  | |   (11)  all_52_14 = e2
% 244.76/51.20  | | 
% 244.76/51.20  | | REDUCE: (6), (11) imply:
% 244.76/51.20  | |   (12)   ~ (e2 = e0)
% 244.76/51.20  | | 
% 244.76/51.20  | | GROUND_INST: instantiating (8) with e0, all_56_27, e0, e2, simplifying with
% 244.76/51.20  | |              (1), (7) gives:
% 244.76/51.20  | |   (13)  all_56_27 = e0
% 244.76/51.20  | | 
% 244.76/51.20  | | REDUCE: (2), (13) imply:
% 244.76/51.20  | |   (14)  op(e2, e0) = e2
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (7), (8), (12), (14) are inconsistent by sub-proof #2121.
% 244.76/51.20  | | 
% 244.76/51.20  | Case 2:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (15)  all_54_11 = e1 | all_54_11 = e0
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (3), (5), (6), (15) are inconsistent by sub-proof #2174.
% 244.76/51.20  | | 
% 244.76/51.20  | End of split
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1913 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.76/51.20    (2)  op(e2, e1) = e2
% 244.76/51.20    (3)   ~ (e3 = e2)
% 244.76/51.20    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.20    (5)   ~ (all_52_13 = e3)
% 244.76/51.20    (6)  op(e2, e0) = all_52_13
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | BETA: splitting (1) gives:
% 244.76/51.20  | 
% 244.76/51.20  | Case 1:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (7)  all_58_5 = e3 & op(e2, e1) = e3
% 244.76/51.20  | | 
% 244.76/51.20  | | ALPHA: (7) implies:
% 244.76/51.20  | |   (8)  op(e2, e1) = e3
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2256.
% 244.76/51.20  | | 
% 244.76/51.20  | Case 2:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (9)  all_58_10 = e3 & op(e2, e0) = e3
% 244.76/51.20  | | 
% 244.76/51.20  | | ALPHA: (9) implies:
% 244.76/51.20  | |   (10)  op(e2, e0) = e3
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #1994.
% 244.76/51.20  | | 
% 244.76/51.20  | End of split
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1914 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.76/51.20         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.76/51.20    (2)   ~ (e3 = e0)
% 244.76/51.20    (3)   ~ (e2 = e0)
% 244.76/51.20    (4)   ~ (all_52_7 = e3)
% 244.76/51.20    (5)   ~ (e3 = e1)
% 244.76/51.20    (6)   ~ (e3 = e2)
% 244.76/51.20    (7)  all_58_15 = e1
% 244.76/51.20    (8)  all_58_12 = e0
% 244.76/51.20    (9)  op(e0, e2) = e0
% 244.76/51.20    (10)  op(e0, e2) = all_52_7
% 244.76/51.20    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.20    (12)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.76/51.20          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.76/51.20            e2)
% 244.76/51.20    (13)   ~ (e2 = e1)
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | BETA: splitting (1) gives:
% 244.76/51.20  | 
% 244.76/51.20  | Case 1:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (14)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.76/51.20  | |           e3)
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (2), (4), (8), (10), (11), (14) are inconsistent by sub-proof
% 244.76/51.20  | |            #1918.
% 244.76/51.20  | | 
% 244.76/51.20  | Case 2:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (15)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 244.76/51.20  | |           e3)
% 244.76/51.20  | | 
% 244.76/51.20  | | BETA: splitting (15) gives:
% 244.76/51.20  | | 
% 244.76/51.20  | | Case 1:
% 244.76/51.20  | | | 
% 244.76/51.20  | | |   (16)  all_58_14 = e3 & op(e0, e1) = e3
% 244.76/51.20  | | | 
% 244.76/51.20  | | | ALPHA: (16) implies:
% 244.76/51.20  | | |   (17)  all_58_14 = e3
% 244.76/51.20  | | | 
% 244.76/51.20  | | | REF_CLOSE: (3), (6), (7), (8), (9), (11), (12), (13), (17) are
% 244.76/51.20  | | |            inconsistent by sub-proof #1916.
% 244.76/51.20  | | | 
% 244.76/51.20  | | Case 2:
% 244.76/51.20  | | | 
% 244.76/51.20  | | |   (18)  all_58_15 = e3 & op(e0, e0) = e3
% 244.76/51.20  | | | 
% 244.76/51.20  | | | REF_CLOSE: (5), (7), (18) are inconsistent by sub-proof #1915.
% 244.76/51.20  | | | 
% 244.76/51.20  | | End of split
% 244.76/51.20  | | 
% 244.76/51.20  | End of split
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1915 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)  all_58_15 = e3 & op(e0, e0) = e3
% 244.76/51.20    (2)  all_58_15 = e1
% 244.76/51.20    (3)   ~ (e3 = e1)
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | ALPHA: (1) implies:
% 244.76/51.20  |   (4)  all_58_15 = e3
% 244.76/51.20  | 
% 244.76/51.20  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.20  |   (5)  e3 = e1
% 244.76/51.20  | 
% 244.76/51.20  | REDUCE: (3), (5) imply:
% 244.76/51.20  |   (6)  $false
% 244.76/51.20  | 
% 244.76/51.20  | CLOSE: (6) is inconsistent.
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1916 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)   ~ (e2 = e0)
% 244.76/51.20    (2)   ~ (e3 = e2)
% 244.76/51.20    (3)  all_58_15 = e1
% 244.76/51.20    (4)  all_58_12 = e0
% 244.76/51.20    (5)  op(e0, e2) = e0
% 244.76/51.20    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.20    (7)  all_58_14 = e3
% 244.76/51.20    (8)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 244.76/51.20         (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.76/51.20    (9)   ~ (e2 = e1)
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | BETA: splitting (8) gives:
% 244.76/51.20  | 
% 244.76/51.20  | Case 1:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (10)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 244.76/51.20  | |           e2)
% 244.76/51.20  | | 
% 244.76/51.20  | | BETA: splitting (10) gives:
% 244.76/51.20  | | 
% 244.76/51.20  | | Case 1:
% 244.76/51.20  | | | 
% 244.76/51.20  | | |   (11)  all_58_12 = e2 & op(e0, e3) = e2
% 244.76/51.20  | | | 
% 244.76/51.20  | | | ALPHA: (11) implies:
% 244.76/51.20  | | |   (12)  all_58_12 = e2
% 244.76/51.20  | | | 
% 244.76/51.20  | | | REF_CLOSE: (1), (4), (12) are inconsistent by sub-proof #2083.
% 244.76/51.20  | | | 
% 244.76/51.20  | | Case 2:
% 244.76/51.20  | | | 
% 244.76/51.20  | | |   (13)  all_58_13 = e2 & op(e0, e2) = e2
% 244.76/51.20  | | | 
% 244.76/51.20  | | | ALPHA: (13) implies:
% 244.76/51.20  | | |   (14)  op(e0, e2) = e2
% 244.76/51.20  | | | 
% 244.76/51.20  | | | REF_CLOSE: (1), (5), (6), (14) are inconsistent by sub-proof #2132.
% 244.76/51.20  | | | 
% 244.76/51.20  | | End of split
% 244.76/51.20  | | 
% 244.76/51.20  | Case 2:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (15)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.76/51.20  | |           e2)
% 244.76/51.20  | | 
% 244.76/51.20  | | BETA: splitting (15) gives:
% 244.76/51.20  | | 
% 244.76/51.20  | | Case 1:
% 244.76/51.20  | | | 
% 244.76/51.20  | | |   (16)  all_58_14 = e2 & op(e0, e1) = e2
% 244.76/51.20  | | | 
% 244.76/51.20  | | | ALPHA: (16) implies:
% 244.76/51.20  | | |   (17)  all_58_14 = e2
% 244.76/51.20  | | | 
% 244.76/51.20  | | | REF_CLOSE: (2), (7), (17) are inconsistent by sub-proof #2117.
% 244.76/51.20  | | | 
% 244.76/51.20  | | Case 2:
% 244.76/51.20  | | | 
% 244.76/51.20  | | |   (18)  all_58_15 = e2 & op(e0, e0) = e2
% 244.76/51.20  | | | 
% 244.76/51.20  | | | REF_CLOSE: (3), (9), (18) are inconsistent by sub-proof #1917.
% 244.76/51.20  | | | 
% 244.76/51.20  | | End of split
% 244.76/51.20  | | 
% 244.76/51.20  | End of split
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1917 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)  all_58_15 = e2 & op(e0, e0) = e2
% 244.76/51.20    (2)  all_58_15 = e1
% 244.76/51.20    (3)   ~ (e2 = e1)
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | ALPHA: (1) implies:
% 244.76/51.20  |   (4)  all_58_15 = e2
% 244.76/51.20  | 
% 244.76/51.20  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.20  |   (5)  e2 = e1
% 244.76/51.20  | 
% 244.76/51.20  | REDUCE: (3), (5) imply:
% 244.76/51.20  |   (6)  $false
% 244.76/51.20  | 
% 244.76/51.20  | CLOSE: (6) is inconsistent.
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1918 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)   ~ (e3 = e0)
% 244.76/51.20    (2)   ~ (all_52_7 = e3)
% 244.76/51.20    (3)  all_58_12 = e0
% 244.76/51.20    (4)  op(e0, e2) = all_52_7
% 244.76/51.20    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.20    (6)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | BETA: splitting (6) gives:
% 244.76/51.20  | 
% 244.76/51.20  | Case 1:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (7)  all_58_12 = e3 & op(e0, e3) = e3
% 244.76/51.20  | | 
% 244.76/51.20  | | ALPHA: (7) implies:
% 244.76/51.20  | |   (8)  all_58_12 = e3
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #1971.
% 244.76/51.20  | | 
% 244.76/51.20  | Case 2:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (9)  all_58_13 = e3 & op(e0, e2) = e3
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #1919.
% 244.76/51.20  | | 
% 244.76/51.20  | End of split
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1919 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)  all_58_13 = e3 & op(e0, e2) = e3
% 244.76/51.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.20    (3)  op(e0, e2) = all_52_7
% 244.76/51.20    (4)   ~ (all_52_7 = e3)
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | ALPHA: (1) implies:
% 244.76/51.20  |   (5)  op(e0, e2) = e3
% 244.76/51.20  | 
% 244.76/51.20  | GROUND_INST: instantiating (2) with all_52_7, e3, e2, e0, simplifying with
% 244.76/51.20  |              (3), (5) gives:
% 244.76/51.20  |   (6)  all_52_7 = e3
% 244.76/51.20  | 
% 244.76/51.20  | REDUCE: (4), (6) imply:
% 244.76/51.20  |   (7)  $false
% 244.76/51.20  | 
% 244.76/51.20  | CLOSE: (7) is inconsistent.
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1920 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)   ~ (e2 = e0)
% 244.76/51.20    (2)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.76/51.20             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.76/51.20           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 244.76/51.20             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.76/51.20           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.76/51.20    (3)  op(e2, e1) = all_52_9
% 244.76/51.20    (4)  op(e2, e0) = e0
% 244.76/51.20    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.20    (6)   ~ (all_52_9 = e1)
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | BETA: splitting (2) gives:
% 244.76/51.20  | 
% 244.76/51.20  | Case 1:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (7)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.76/51.20  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 244.76/51.20  | |        & op(e1, e2) = e1
% 244.76/51.20  | | 
% 244.76/51.20  | | ALPHA: (7) implies:
% 244.76/51.20  | |   (8)  op(e2, e1) = e1
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2306.
% 244.76/51.20  | | 
% 244.76/51.20  | Case 2:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (9)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.76/51.20  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 244.76/51.20  | |        & op(e0, e2) = e2
% 244.76/51.20  | | 
% 244.76/51.20  | | ALPHA: (9) implies:
% 244.76/51.20  | |   (10)  op(e2, e0) = e2
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2121.
% 244.76/51.20  | | 
% 244.76/51.20  | End of split
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1921 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.76/51.20    (2)  all_54_4 = all_52_1
% 244.76/51.20    (3)   ~ (all_52_1 = e0)
% 244.76/51.20    (4)   ~ (all_52_1 = e2)
% 244.76/51.20    (5)   ~ (all_52_1 = e1)
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | BETA: splitting (1) gives:
% 244.76/51.20  | 
% 244.76/51.20  | Case 1:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (6)  all_54_4 = e2
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2096.
% 244.76/51.20  | | 
% 244.76/51.20  | Case 2:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (7)  all_54_4 = e1 | all_54_4 = e0
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #1922.
% 244.76/51.20  | | 
% 244.76/51.20  | End of split
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1922 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)  all_54_4 = e1 | all_54_4 = e0
% 244.76/51.20    (2)  all_54_4 = all_52_1
% 244.76/51.20    (3)   ~ (all_52_1 = e1)
% 244.76/51.20    (4)   ~ (all_52_1 = e0)
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | BETA: splitting (1) gives:
% 244.76/51.20  | 
% 244.76/51.20  | Case 1:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (5)  all_54_4 = e1
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2086.
% 244.76/51.20  | | 
% 244.76/51.20  | Case 2:
% 244.76/51.20  | | 
% 244.76/51.20  | |   (6)  all_54_4 = e0
% 244.76/51.20  | | 
% 244.76/51.20  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1923.
% 244.76/51.20  | | 
% 244.76/51.20  | End of split
% 244.76/51.20  | 
% 244.76/51.20  End of proof
% 244.76/51.20  
% 244.76/51.20  Sub-proof #1923 shows that the following formulas are inconsistent:
% 244.76/51.20  ----------------------------------------------------------------
% 244.76/51.20    (1)  all_54_4 = all_52_1
% 244.76/51.20    (2)  all_54_4 = e0
% 244.76/51.20    (3)   ~ (all_52_1 = e0)
% 244.76/51.20  
% 244.76/51.20  Begin of proof
% 244.76/51.20  | 
% 244.76/51.20  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.20  |   (4)  all_52_1 = e0
% 244.76/51.20  | 
% 244.76/51.20  | SIMP: (4) implies:
% 244.76/51.20  |   (5)  all_52_1 = e0
% 244.76/51.20  | 
% 244.76/51.21  | REDUCE: (3), (5) imply:
% 244.76/51.21  |   (6)  $false
% 244.76/51.21  | 
% 244.76/51.21  | CLOSE: (6) is inconsistent.
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1924 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)   ~ (e3 = e0)
% 244.76/51.21    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.76/51.21             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3))
% 244.76/51.21    (3)  op(e2, e3) = e3
% 244.76/51.21    (4)   ~ (e3 = e2)
% 244.76/51.21    (5)  op(e3, e2) = e0
% 244.76/51.21    (6)  all_56_1 = e2
% 244.76/51.21    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | BETA: splitting (2) gives:
% 244.76/51.21  | 
% 244.76/51.21  | Case 1:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (8)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 244.76/51.21  | | 
% 244.76/51.21  | | ALPHA: (8) implies:
% 244.76/51.21  | |   (9)  op(e3, all_56_1) = e3
% 244.76/51.21  | | 
% 244.76/51.21  | | REDUCE: (6), (9) imply:
% 244.76/51.21  | |   (10)  op(e3, e2) = e3
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (1), (5), (7), (10) are inconsistent by sub-proof #2099.
% 244.76/51.21  | | 
% 244.76/51.21  | Case 2:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (11)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 244.76/51.21  | |         $i(all_56_3)
% 244.76/51.21  | | 
% 244.76/51.21  | | ALPHA: (11) implies:
% 244.76/51.21  | |   (12)  op(e2, e3) = all_56_3
% 244.76/51.21  | |   (13)  op(e2, all_56_3) = e2
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (3), (4), (7), (12), (13) are inconsistent by sub-proof #2262.
% 244.76/51.21  | | 
% 244.76/51.21  | End of split
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1925 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)   ~ (e3 = e0)
% 244.76/51.21    (2)   ~ (e2 = e0)
% 244.76/51.21    (3)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.76/51.21           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.76/51.21             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.21           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.76/51.21             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.76/51.21           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.21           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.76/51.21    (4)   ~ (e3 = e1)
% 244.76/51.21    (5)  op(e1, e3) = e1
% 244.76/51.21    (6)  op(e3, e2) = e0
% 244.76/51.21    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | BETA: splitting (3) gives:
% 244.76/51.21  | 
% 244.76/51.21  | Case 1:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.76/51.21  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.76/51.21  | |        op(e2, e3) = e3
% 244.76/51.21  | | 
% 244.76/51.21  | | ALPHA: (8) implies:
% 244.76/51.21  | |   (9)  op(e3, e2) = e3
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (1), (6), (7), (9) are inconsistent by sub-proof #2099.
% 244.76/51.21  | | 
% 244.76/51.21  | Case 2:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.76/51.21  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 244.76/51.21  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.76/51.21  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.21  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.76/51.21  | | 
% 244.76/51.21  | | BETA: splitting (10) gives:
% 244.76/51.21  | | 
% 244.76/51.21  | | Case 1:
% 244.76/51.21  | | | 
% 244.76/51.21  | | |   (11)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.76/51.21  | | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 244.76/51.21  | | |         e2 & op(e2, e3) = e2
% 244.76/51.21  | | | 
% 244.76/51.21  | | | ALPHA: (11) implies:
% 244.76/51.21  | | |   (12)  op(e3, e2) = e2
% 244.76/51.21  | | | 
% 244.76/51.21  | | | REF_CLOSE: (2), (6), (7), (12) are inconsistent by sub-proof #2026.
% 244.76/51.21  | | | 
% 244.76/51.21  | | Case 2:
% 244.76/51.21  | | | 
% 244.76/51.21  | | |   (13)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.21  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.76/51.21  | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 244.76/51.21  | | | 
% 244.76/51.21  | | | ALPHA: (13) implies:
% 244.76/51.21  | | |   (14)  op(e1, e3) = e3
% 244.76/51.21  | | | 
% 244.76/51.21  | | | REF_CLOSE: (4), (5), (7), (14) are inconsistent by sub-proof #2225.
% 244.76/51.21  | | | 
% 244.76/51.21  | | End of split
% 244.76/51.21  | | 
% 244.76/51.21  | End of split
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1926 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)   ~ (e3 = e0)
% 244.76/51.21    (2)  op(e3, all_56_25) = e3
% 244.76/51.21    (3)  op(e3, e0) = all_56_25
% 244.76/51.21    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.21    (5)  op(e3, e0) = e0
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | GROUND_INST: instantiating (4) with e0, all_56_25, e0, e3, simplifying with
% 244.76/51.21  |              (3), (5) gives:
% 244.76/51.21  |   (6)  all_56_25 = e0
% 244.76/51.21  | 
% 244.76/51.21  | REDUCE: (2), (6) imply:
% 244.76/51.21  |   (7)  op(e3, e0) = e3
% 244.76/51.21  | 
% 244.76/51.21  | GROUND_INST: instantiating (4) with e0, e3, e0, e3, simplifying with (5), (7)
% 244.76/51.21  |              gives:
% 244.76/51.21  |   (8)  e3 = e0
% 244.76/51.21  | 
% 244.76/51.21  | REDUCE: (1), (8) imply:
% 244.76/51.21  |   (9)  $false
% 244.76/51.21  | 
% 244.76/51.21  | CLOSE: (9) is inconsistent.
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1927 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)   ~ (e3 = e0)
% 244.76/51.21    (2)   ~ (e2 = e0)
% 244.76/51.21    (3)  op(e3, e3) = e2
% 244.76/51.21    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.21    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 244.76/51.21    (6)  all_58_2 = e3
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | BETA: splitting (5) gives:
% 244.76/51.21  | 
% 244.76/51.21  | Case 1:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | ALPHA: (7) implies:
% 244.76/51.21  | |   (8)  op(e3, e3) = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2188.
% 244.76/51.21  | | 
% 244.76/51.21  | Case 2:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (9)  all_58_2 = e0 & op(e2, e3) = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | ALPHA: (9) implies:
% 244.76/51.21  | |   (10)  all_58_2 = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #2124.
% 244.76/51.21  | | 
% 244.76/51.21  | End of split
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1928 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)  all_54_1 = all_52_4
% 244.76/51.21    (2)  all_54_1 = e2
% 244.76/51.21    (3)   ~ (all_52_4 = e2)
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.21  |   (4)  all_52_4 = e2
% 244.76/51.21  | 
% 244.76/51.21  | SIMP: (4) implies:
% 244.76/51.21  |   (5)  all_52_4 = e2
% 244.76/51.21  | 
% 244.76/51.21  | REDUCE: (3), (5) imply:
% 244.76/51.21  |   (6)  $false
% 244.76/51.21  | 
% 244.76/51.21  | CLOSE: (6) is inconsistent.
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1929 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)  op(e2, e2) = e1
% 244.76/51.21    (2)  op(e2, e3) = all_52_1
% 244.76/51.21    (3)  (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 244.76/51.21    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.21    (5)   ~ (all_52_1 = e2)
% 244.76/51.21    (6)   ~ (e2 = e1)
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | BETA: splitting (3) gives:
% 244.76/51.21  | 
% 244.76/51.21  | Case 1:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (7)  all_58_2 = e2 & op(e2, e3) = e2
% 244.76/51.21  | | 
% 244.76/51.21  | | ALPHA: (7) implies:
% 244.76/51.21  | |   (8)  op(e2, e3) = e2
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2336.
% 244.76/51.21  | | 
% 244.76/51.21  | Case 2:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (9)  all_58_3 = e2 & op(e2, e2) = e2
% 244.76/51.21  | | 
% 244.76/51.21  | | ALPHA: (9) implies:
% 244.76/51.21  | |   (10)  op(e2, e2) = e2
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #2235.
% 244.76/51.21  | | 
% 244.76/51.21  | End of split
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1930 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)  all_54_1 = all_52_4
% 244.76/51.21    (2)  all_54_1 = e3
% 244.76/51.21    (3)   ~ (all_52_4 = e3)
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.21  |   (4)  all_52_4 = e3
% 244.76/51.21  | 
% 244.76/51.21  | SIMP: (4) implies:
% 244.76/51.21  |   (5)  all_52_4 = e3
% 244.76/51.21  | 
% 244.76/51.21  | REDUCE: (3), (5) imply:
% 244.76/51.21  |   (6)  $false
% 244.76/51.21  | 
% 244.76/51.21  | CLOSE: (6) is inconsistent.
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1931 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)   ~ (all_52_6 = e0)
% 244.76/51.21    (2)  all_54_9 = all_52_6
% 244.76/51.21    (3)  op(e1, e3) = e1
% 244.76/51.21    (4)   ~ (all_52_2 = all_52_6)
% 244.76/51.21    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.21    (6)  op(e1, e3) = all_52_2
% 244.76/51.21    (7)  all_54_9 = e1 | all_54_9 = e0
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | BETA: splitting (7) gives:
% 244.76/51.21  | 
% 244.76/51.21  | Case 1:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (8)  all_54_9 = e1
% 244.76/51.21  | | 
% 244.76/51.21  | | COMBINE_EQS: (2), (8) imply:
% 244.76/51.21  | |   (9)  all_52_6 = e1
% 244.76/51.21  | | 
% 244.76/51.21  | | SIMP: (9) implies:
% 244.76/51.21  | |   (10)  all_52_6 = e1
% 244.76/51.21  | | 
% 244.76/51.21  | | REDUCE: (4), (10) imply:
% 244.76/51.21  | |   (11)   ~ (all_52_2 = e1)
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (3), (5), (6), (11) are inconsistent by sub-proof #1948.
% 244.76/51.21  | | 
% 244.76/51.21  | Case 2:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (12)  all_54_9 = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #1953.
% 244.76/51.21  | | 
% 244.76/51.21  | End of split
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1932 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)  op(e0, e0) = e1
% 244.76/51.21    (2)   ~ (all_52_7 = e2)
% 244.76/51.21    (3)  all_54_13 = all_52_7
% 244.76/51.21    (4)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 244.76/51.21         $i(all_56_15)
% 244.76/51.21    (5)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.76/51.21    (6)   ~ (all_52_7 = e1)
% 244.76/51.21    (7)  op(e0, e2) = all_52_7
% 244.76/51.21    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | ALPHA: (4) implies:
% 244.76/51.21  |   (9)  op(e0, e2) = all_56_15
% 244.76/51.21  |   (10)  op(e0, all_56_15) = e0
% 244.76/51.21  | 
% 244.76/51.21  | BETA: splitting (5) gives:
% 244.76/51.21  | 
% 244.76/51.21  | Case 1:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (11)  all_54_13 = e2
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (2), (3), (11) are inconsistent by sub-proof #2009.
% 244.76/51.21  | | 
% 244.76/51.21  | Case 2:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (12)  all_54_13 = e1 | all_54_13 = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (12) are inconsistent by
% 244.76/51.21  | |            sub-proof #1933.
% 244.76/51.21  | | 
% 244.76/51.21  | End of split
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1933 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)  op(e0, e0) = e1
% 244.76/51.21    (2)  all_54_13 = all_52_7
% 244.76/51.21    (3)  all_54_13 = e1 | all_54_13 = e0
% 244.76/51.21    (4)   ~ (all_52_7 = e1)
% 244.76/51.21    (5)  op(e0, e2) = all_56_15
% 244.76/51.21    (6)  op(e0, e2) = all_52_7
% 244.76/51.21    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.21    (8)  op(e0, all_56_15) = e0
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | BETA: splitting (3) gives:
% 244.76/51.21  | 
% 244.76/51.21  | Case 1:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (9)  all_54_13 = e1
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #1966.
% 244.76/51.21  | | 
% 244.76/51.21  | Case 2:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (10)  all_54_13 = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | COMBINE_EQS: (2), (10) imply:
% 244.76/51.21  | |   (11)  all_52_7 = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | SIMP: (11) implies:
% 244.76/51.21  | |   (12)  all_52_7 = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | REDUCE: (4), (12) imply:
% 244.76/51.21  | |   (13)   ~ (e1 = e0)
% 244.76/51.21  | | 
% 244.76/51.21  | | SIMP: (13) implies:
% 244.76/51.21  | |   (14)   ~ (e1 = e0)
% 244.76/51.21  | | 
% 244.76/51.21  | | REDUCE: (6), (12) imply:
% 244.76/51.21  | |   (15)  op(e0, e2) = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | GROUND_INST: instantiating (7) with e0, all_56_15, e2, e0, simplifying with
% 244.76/51.21  | |              (5), (15) gives:
% 244.76/51.21  | |   (16)  all_56_15 = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | REDUCE: (8), (16) imply:
% 244.76/51.21  | |   (17)  op(e0, e0) = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (1), (7), (14), (17) are inconsistent by sub-proof #2274.
% 244.76/51.21  | | 
% 244.76/51.21  | End of split
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1934 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)  op(e1, e2) = all_56_13
% 244.76/51.21    (2)  op(e1, e2) = e1
% 244.76/51.21    (3)   ~ (all_52_11 = e1)
% 244.76/51.21    (4)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 244.76/51.21    (5)   ~ (all_52_11 = e0)
% 244.76/51.21    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.21    (7)  op(e1, e1) = e0
% 244.76/51.21    (8)  op(e1, all_56_13) = e1
% 244.76/51.21    (9)   ~ (e1 = e0)
% 244.76/51.21    (10)  all_54_14 = all_52_11
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | BETA: splitting (4) gives:
% 244.76/51.21  | 
% 244.76/51.21  | Case 1:
% 244.76/51.21  | | 
% 244.76/51.21  | | 
% 244.76/51.21  | | GROUND_INST: instantiating (6) with e1, all_56_13, e2, e1, simplifying with
% 244.76/51.21  | |              (1), (2) gives:
% 244.76/51.21  | |   (11)  all_56_13 = e1
% 244.76/51.21  | | 
% 244.76/51.21  | | REDUCE: (8), (11) imply:
% 244.76/51.21  | |   (12)  op(e1, e1) = e1
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (6), (7), (9), (12) are inconsistent by sub-proof #2220.
% 244.76/51.21  | | 
% 244.76/51.21  | Case 2:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (13)  all_54_14 = e1 | all_54_14 = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (3), (5), (10), (13) are inconsistent by sub-proof #1935.
% 244.76/51.21  | | 
% 244.76/51.21  | End of split
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1935 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)  all_54_14 = e1 | all_54_14 = e0
% 244.76/51.21    (2)  all_54_14 = all_52_11
% 244.76/51.21    (3)   ~ (all_52_11 = e1)
% 244.76/51.21    (4)   ~ (all_52_11 = e0)
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | BETA: splitting (1) gives:
% 244.76/51.21  | 
% 244.76/51.21  | Case 1:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (5)  all_54_14 = e1
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1937.
% 244.76/51.21  | | 
% 244.76/51.21  | Case 2:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (6)  all_54_14 = e0
% 244.76/51.21  | | 
% 244.76/51.21  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1936.
% 244.76/51.21  | | 
% 244.76/51.21  | End of split
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1936 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)  all_54_14 = all_52_11
% 244.76/51.21    (2)  all_54_14 = e0
% 244.76/51.21    (3)   ~ (all_52_11 = e0)
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.21  |   (4)  all_52_11 = e0
% 244.76/51.21  | 
% 244.76/51.21  | SIMP: (4) implies:
% 244.76/51.21  |   (5)  all_52_11 = e0
% 244.76/51.21  | 
% 244.76/51.21  | REDUCE: (3), (5) imply:
% 244.76/51.21  |   (6)  $false
% 244.76/51.21  | 
% 244.76/51.21  | CLOSE: (6) is inconsistent.
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1937 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)  all_54_14 = all_52_11
% 244.76/51.21    (2)  all_54_14 = e1
% 244.76/51.21    (3)   ~ (all_52_11 = e1)
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.21  |   (4)  all_52_11 = e1
% 244.76/51.21  | 
% 244.76/51.21  | SIMP: (4) implies:
% 244.76/51.21  |   (5)  all_52_11 = e1
% 244.76/51.21  | 
% 244.76/51.21  | REDUCE: (3), (5) imply:
% 244.76/51.21  |   (6)  $false
% 244.76/51.21  | 
% 244.76/51.21  | CLOSE: (6) is inconsistent.
% 244.76/51.21  | 
% 244.76/51.21  End of proof
% 244.76/51.21  
% 244.76/51.21  Sub-proof #1938 shows that the following formulas are inconsistent:
% 244.76/51.21  ----------------------------------------------------------------
% 244.76/51.21    (1)   ~ (all_52_3 = e0)
% 244.76/51.21    (2)   ~ (e3 = e0)
% 244.76/51.21    (3)  op(e0, e3) = all_52_3
% 244.76/51.21    (4)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.76/51.21         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.76/51.21    (5)   ~ (all_52_1 = e0)
% 244.76/51.21    (6)  op(e2, e3) = all_52_1
% 244.76/51.21    (7)   ~ (all_52_2 = e0)
% 244.76/51.21    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.21    (9)  op(e1, e3) = all_52_2
% 244.76/51.21    (10)  op(e3, e3) = e3
% 244.76/51.21  
% 244.76/51.21  Begin of proof
% 244.76/51.21  | 
% 244.76/51.21  | BETA: splitting (4) gives:
% 244.76/51.21  | 
% 244.76/51.21  | Case 1:
% 244.76/51.21  | | 
% 244.76/51.21  | |   (11)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 244.76/51.21  | |           e0)
% 244.76/51.21  | | 
% 244.76/51.21  | | BETA: splitting (11) gives:
% 244.76/51.21  | | 
% 244.76/51.21  | | Case 1:
% 244.76/51.21  | | | 
% 244.76/51.21  | | |   (12)  all_58_0 = e0 & op(e3, e3) = e0
% 244.76/51.21  | | | 
% 244.76/51.21  | | | ALPHA: (12) implies:
% 244.76/51.22  | | |   (13)  op(e3, e3) = e0
% 244.76/51.22  | | | 
% 244.76/51.22  | | | REF_CLOSE: (2), (8), (10), (13) are inconsistent by sub-proof #1940.
% 244.76/51.22  | | | 
% 244.76/51.22  | | Case 2:
% 244.76/51.22  | | | 
% 244.76/51.22  | | |   (14)  all_58_2 = e0 & op(e2, e3) = e0
% 244.76/51.22  | | | 
% 244.76/51.22  | | | REF_CLOSE: (5), (6), (8), (14) are inconsistent by sub-proof #1985.
% 244.76/51.22  | | | 
% 244.76/51.22  | | End of split
% 244.76/51.22  | | 
% 244.76/51.22  | Case 2:
% 244.76/51.22  | | 
% 244.76/51.22  | |   (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 244.76/51.22  | |           e0)
% 244.76/51.22  | | 
% 244.76/51.22  | | REF_CLOSE: (1), (3), (7), (8), (9), (15) are inconsistent by sub-proof
% 244.76/51.22  | |            #1939.
% 244.76/51.22  | | 
% 244.76/51.22  | End of split
% 244.76/51.22  | 
% 244.76/51.22  End of proof
% 244.76/51.22  
% 244.76/51.22  Sub-proof #1939 shows that the following formulas are inconsistent:
% 244.76/51.22  ----------------------------------------------------------------
% 244.76/51.22    (1)   ~ (all_52_3 = e0)
% 244.76/51.22    (2)  op(e0, e3) = all_52_3
% 244.76/51.22    (3)   ~ (all_52_2 = e0)
% 244.76/51.22    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.22    (5)  op(e1, e3) = all_52_2
% 244.76/51.22    (6)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.76/51.22  
% 244.76/51.22  Begin of proof
% 244.76/51.22  | 
% 244.76/51.22  | BETA: splitting (6) gives:
% 244.76/51.22  | 
% 244.76/51.22  | Case 1:
% 244.76/51.22  | | 
% 244.76/51.22  | |   (7)  all_58_6 = e0 & op(e1, e3) = e0
% 244.76/51.22  | | 
% 244.76/51.22  | | ALPHA: (7) implies:
% 244.76/51.22  | |   (8)  op(e1, e3) = e0
% 244.76/51.22  | | 
% 244.76/51.22  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2023.
% 244.76/51.22  | | 
% 244.76/51.22  | Case 2:
% 244.76/51.22  | | 
% 244.76/51.22  | |   (9)  all_58_12 = e0 & op(e0, e3) = e0
% 244.76/51.22  | | 
% 244.76/51.22  | | ALPHA: (9) implies:
% 244.76/51.22  | |   (10)  op(e0, e3) = e0
% 244.76/51.22  | | 
% 244.76/51.22  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #2331.
% 244.76/51.22  | | 
% 244.76/51.22  | End of split
% 244.76/51.22  | 
% 244.76/51.22  End of proof
% 244.76/51.22  
% 244.76/51.22  Sub-proof #1940 shows that the following formulas are inconsistent:
% 244.76/51.22  ----------------------------------------------------------------
% 244.76/51.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.22    (2)  op(e3, e3) = e3
% 244.76/51.22    (3)  op(e3, e3) = e0
% 244.76/51.22    (4)   ~ (e3 = e0)
% 244.76/51.22  
% 244.76/51.22  Begin of proof
% 244.76/51.22  | 
% 244.76/51.22  | GROUND_INST: instantiating (1) with e0, e3, e3, e3, simplifying with (2), (3)
% 244.76/51.22  |              gives:
% 244.76/51.22  |   (5)  e3 = e0
% 244.76/51.22  | 
% 244.76/51.22  | REDUCE: (4), (5) imply:
% 244.76/51.22  |   (6)  $false
% 244.76/51.22  | 
% 244.76/51.22  | CLOSE: (6) is inconsistent.
% 244.76/51.22  | 
% 244.76/51.22  End of proof
% 244.76/51.22  
% 244.76/51.22  Sub-proof #1941 shows that the following formulas are inconsistent:
% 244.76/51.22  ----------------------------------------------------------------
% 244.76/51.22    (1)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.76/51.22             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.76/51.22           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 244.76/51.22             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.76/51.22           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.76/51.22    (2)  all_56_21 = e0
% 244.76/51.22    (3)  op(e2, e1) = all_52_9
% 244.76/51.22    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.22    (5)   ~ (all_52_9 = e1)
% 244.76/51.22  
% 244.76/51.22  Begin of proof
% 244.76/51.22  | 
% 244.76/51.22  | BETA: splitting (1) gives:
% 244.76/51.22  | 
% 244.76/51.22  | Case 1:
% 244.76/51.22  | | 
% 244.76/51.22  | |   (6)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.76/51.22  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 244.76/51.22  | |        & op(e1, e2) = e1
% 244.76/51.22  | | 
% 244.76/51.22  | | ALPHA: (6) implies:
% 244.76/51.22  | |   (7)  op(e2, e1) = e1
% 244.76/51.22  | | 
% 244.76/51.22  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #2306.
% 244.76/51.22  | | 
% 244.76/51.22  | Case 2:
% 244.76/51.22  | | 
% 244.76/51.22  | |   (8)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.76/51.22  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 244.76/51.22  | |        & op(e0, e2) = e2
% 244.76/51.22  | | 
% 244.76/51.22  | | ALPHA: (8) implies:
% 244.76/51.22  | |   (9)   ~ (all_56_21 = e0)
% 244.76/51.22  | | 
% 244.76/51.22  | | REDUCE: (2), (9) imply:
% 244.76/51.22  | |   (10)  $false
% 244.76/51.22  | | 
% 244.76/51.22  | | CLOSE: (10) is inconsistent.
% 244.76/51.22  | | 
% 244.76/51.22  | End of split
% 244.76/51.22  | 
% 244.76/51.22  End of proof
% 244.76/51.22  
% 244.76/51.22  Sub-proof #1942 shows that the following formulas are inconsistent:
% 244.76/51.22  ----------------------------------------------------------------
% 244.76/51.22    (1)  op(e0, e0) = e1
% 244.76/51.22    (2)   ~ (all_52_1 = all_52_3)
% 244.76/51.22    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.76/51.22             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.76/51.22           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.76/51.22         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.76/51.22           $i(all_56_7))
% 244.76/51.22    (4)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.76/51.22    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.76/51.22         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.76/51.22    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.76/51.22         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.76/51.22    (7)   ~ (all_52_8 = all_52_9)
% 244.76/51.22    (8)  op(e0, e1) = e2
% 244.76/51.22    (9)  all_54_13 = all_52_7
% 244.76/51.22    (10)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 & op(e1, e0) =
% 244.76/51.22            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1,
% 244.76/51.22              e0) = all_28_1 & $i(all_28_1))
% 244.76/51.22    (11)  op(e1, e2) = all_52_6
% 244.76/51.22    (12)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.76/51.22              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.76/51.22            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 244.76/51.22            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.22            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 244.76/51.22             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.22            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.76/51.22            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.76/51.22            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 244.76/51.22            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.22            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.76/51.22              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.76/51.22            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.76/51.22            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 244.76/51.22            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.76/51.22            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 244.76/51.22            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.22            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.76/51.22              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.76/51.22            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.76/51.22            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 244.76/51.22            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.76/51.22            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 244.76/51.22            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.22            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.76/51.22              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.76/51.22            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.22            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.22    (13)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.76/51.22          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.76/51.22    (14)   ~ (all_52_6 = e2)
% 244.76/51.22    (15)   ~ (all_52_1 = all_52_2)
% 244.76/51.22    (16)  op(e0, e1) = all_34_1
% 244.76/51.22    (17)  op(e1, e0) = all_52_14
% 244.76/51.22    (18)   ~ (all_52_13 = e1)
% 244.76/51.22    (19)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.76/51.22    (20)   ~ (all_52_8 = e0)
% 244.76/51.22    (21)  op(e0, e3) = all_52_3
% 244.76/51.22    (22)   ~ (all_52_6 = e0)
% 244.76/51.22    (23)   ~ (all_52_12 = e1)
% 244.76/51.22    (24)   ~ (all_52_2 = all_52_3)
% 244.76/51.22    (25)  all_54_6 = all_52_9
% 244.76/51.22    (26)  op(all_34_1, e0) = all_34_0
% 244.76/51.22    (27)   ~ (all_52_12 = all_52_13)
% 244.76/51.22    (28)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.76/51.22          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.76/51.22    (29)  all_54_2 = all_52_8
% 244.76/51.22    (30)   ~ (all_52_1 = all_52_9)
% 244.76/51.22    (31)   ~ (all_52_3 = all_52_7)
% 244.76/51.22    (32)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.76/51.22    (33)  op(e1, e0) = all_18_1
% 244.76/51.22    (34)  all_54_4 = all_52_1
% 244.76/51.22    (35)   ~ (all_52_8 = all_52_12)
% 244.76/51.22    (36)  op(e3, e1) = all_52_8
% 244.76/51.22    (37)  op(e2, e1) = all_52_9
% 244.76/51.22    (38)  all_54_9 = all_52_6
% 244.76/51.22    (39)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.76/51.22          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.76/51.22    (40)   ~ (all_52_7 = e1)
% 244.76/51.22    (41)   ~ (all_52_14 = e0)
% 244.76/51.22    (42)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 244.76/51.22    (43)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.76/51.22    (44)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.76/51.22    (45)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.76/51.22          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.76/51.22    (46)  all_58_15 = e1
% 244.76/51.22    (47)  op(e3, e0) = all_52_12
% 244.76/51.22    (48)   ~ (all_34_0 = e3)
% 244.76/51.22    (49)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.76/51.22          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.76/51.22    (50)   ~ (all_52_9 = all_52_13)
% 244.76/51.22    (51)   ~ (all_52_4 = all_52_12)
% 244.76/51.22    (52)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.76/51.22    (53)  all_58_11 = e2
% 244.76/51.22    (54)  op(e2, e3) = all_52_1
% 244.76/51.22    (55)  op(e3, e3) = e2
% 244.76/51.22    (56)   ~ (all_52_12 = e2)
% 244.76/51.22    (57)   ~ (all_52_13 = e2)
% 244.76/51.22    (58)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.76/51.22          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.76/51.22    (59)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.76/51.22    (60)   ~ (all_52_1 = all_52_13)
% 244.76/51.22    (61)   ~ (all_52_2 = e0)
% 244.76/51.22    (62)  all_54_7 = all_52_13
% 244.76/51.22    (63)  op(e0, e2) = all_52_7
% 244.76/51.22    (64)  op(e0, e1) = all_20_1
% 244.76/51.22    (65)  all_56_1 = e2
% 244.76/51.22    (66)  all_54_1 = all_52_4
% 244.76/51.22    (67)  op(e3, e2) = all_52_4
% 244.76/51.22    (68)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.76/51.22    (69)   ~ (all_52_2 = e2)
% 244.76/51.22    (70)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.76/51.22          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.76/51.22    (71)   ~ (all_52_4 = e2)
% 244.76/51.22    (72)  all_54_8 = all_52_2
% 244.76/51.22    (73)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.76/51.22          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.76/51.22    (74)   ~ (all_52_2 = all_52_6)
% 244.76/51.22    (75)  all_54_3 = all_52_12
% 244.76/51.22    (76)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.22    (77)  op(e1, e3) = all_52_2
% 244.76/51.22    (78)  op(e1, e1) = e0
% 244.76/51.22    (79)  op(e1, e0) = e2
% 244.76/51.22    (80)   ~ (all_52_8 = e2)
% 244.76/51.22    (81)  op(e2, e0) = all_52_13
% 244.76/51.22    (82)  op(e2, e2) = e2
% 244.76/51.22    (83)   ~ (all_52_4 = all_52_8)
% 244.76/51.22    (84)   ~ (all_52_1 = e2)
% 244.76/51.22    (85)   ~ (all_52_4 = all_52_7)
% 244.76/51.22    (86)   ~ (all_52_9 = e2)
% 244.76/51.22  
% 244.76/51.22  Begin of proof
% 244.76/51.22  | 
% 244.76/51.22  | GROUND_INST: instantiating (76) with e2, all_34_1, e1, e0, simplifying with
% 244.76/51.22  |              (8), (16) gives:
% 244.76/51.22  |   (87)  all_34_1 = e2
% 244.76/51.22  | 
% 244.76/51.22  | GROUND_INST: instantiating (76) with all_20_1, all_34_1, e1, e0, simplifying
% 244.76/51.22  |              with (16), (64) gives:
% 244.76/51.22  |   (88)  all_34_1 = all_20_1
% 244.76/51.22  | 
% 244.76/51.22  | GROUND_INST: instantiating (76) with e2, all_18_1, e0, e1, simplifying with
% 244.76/51.22  |              (33), (79) gives:
% 244.76/51.22  |   (89)  all_18_1 = e2
% 244.76/51.22  | 
% 244.76/51.22  | COMBINE_EQS: (87), (88) imply:
% 244.76/51.22  |   (90)  all_20_1 = e2
% 244.76/51.22  | 
% 244.76/51.22  | REDUCE: (26), (87) imply:
% 244.76/51.22  |   (91)  op(e2, e0) = all_34_0
% 244.76/51.22  | 
% 244.76/51.22  | BETA: splitting (10) gives:
% 244.76/51.22  | 
% 244.76/51.22  | Case 1:
% 244.76/51.22  | | 
% 244.76/51.22  | |   (92)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 & op(e1, e0) =
% 244.76/51.22  | |         all_28_1 & $i(all_28_0) & $i(all_28_1)
% 244.76/51.22  | | 
% 244.76/51.22  | | ALPHA: (92) implies:
% 244.76/51.22  | |   (93)  op(e1, e0) = all_28_1
% 244.76/51.22  | | 
% 244.76/51.22  | | GROUND_INST: instantiating (76) with e2, all_28_1, e0, e1, simplifying with
% 244.76/51.22  | |              (79), (93) gives:
% 244.76/51.22  | |   (94)  all_28_1 = e2
% 244.76/51.22  | | 
% 244.76/51.22  | | GROUND_INST: instantiating (76) with all_52_13, all_34_0, e0, e2,
% 244.76/51.22  | |              simplifying with (81), (91) gives:
% 244.76/51.22  | |   (95)  all_52_13 = all_34_0
% 244.76/51.22  | | 
% 244.76/51.22  | | COMBINE_EQS: (62), (95) imply:
% 244.76/51.22  | |   (96)  all_54_7 = all_34_0
% 244.76/51.22  | | 
% 244.76/51.22  | | REDUCE: (60), (95) imply:
% 244.76/51.22  | |   (97)   ~ (all_52_1 = all_34_0)
% 244.76/51.22  | | 
% 244.76/51.22  | | REDUCE: (50), (95) imply:
% 244.76/51.22  | |   (98)   ~ (all_52_9 = all_34_0)
% 244.76/51.22  | | 
% 244.76/51.22  | | REDUCE: (27), (95) imply:
% 244.76/51.22  | |   (99)   ~ (all_52_12 = all_34_0)
% 244.76/51.22  | | 
% 244.76/51.22  | | REDUCE: (57), (95) imply:
% 244.76/51.22  | |   (100)   ~ (all_34_0 = e2)
% 244.76/51.22  | | 
% 244.76/51.22  | | REDUCE: (18), (95) imply:
% 244.76/51.22  | |   (101)   ~ (all_34_0 = e1)
% 244.76/51.22  | | 
% 244.76/51.22  | | BETA: splitting (43) gives:
% 244.76/51.22  | | 
% 244.76/51.22  | | Case 1:
% 244.76/51.22  | | | 
% 244.76/51.22  | | |   (102)  all_54_7 = e3
% 244.76/51.22  | | | 
% 244.76/51.22  | | | COMBINE_EQS: (96), (102) imply:
% 244.76/51.22  | | |   (103)  all_34_0 = e3
% 244.76/51.22  | | | 
% 244.76/51.22  | | | REDUCE: (48), (103) imply:
% 244.76/51.22  | | |   (104)  $false
% 244.76/51.22  | | | 
% 244.76/51.22  | | | CLOSE: (104) is inconsistent.
% 244.76/51.22  | | | 
% 244.76/51.22  | | Case 2:
% 244.76/51.22  | | | 
% 244.76/51.22  | | |   (105)   ~ (all_54_7 = e3)
% 244.76/51.22  | | |   (106)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.76/51.22  | | | 
% 244.76/51.22  | | | BETA: splitting (106) gives:
% 244.76/51.22  | | | 
% 244.76/51.22  | | | Case 1:
% 244.76/51.22  | | | | 
% 244.76/51.22  | | | |   (107)  all_54_7 = e2
% 244.76/51.22  | | | | 
% 244.76/51.22  | | | | COMBINE_EQS: (96), (107) imply:
% 244.76/51.22  | | | |   (108)  all_34_0 = e2
% 244.76/51.22  | | | | 
% 244.76/51.22  | | | | REDUCE: (100), (108) imply:
% 244.76/51.22  | | | |   (109)  $false
% 244.76/51.22  | | | | 
% 244.76/51.22  | | | | CLOSE: (109) is inconsistent.
% 244.76/51.22  | | | | 
% 244.76/51.22  | | | Case 2:
% 244.76/51.22  | | | | 
% 244.76/51.22  | | | |   (110)   ~ (all_54_7 = e2)
% 244.76/51.22  | | | |   (111)  all_54_7 = e1 | all_54_7 = e0
% 244.76/51.22  | | | | 
% 244.76/51.22  | | | | BETA: splitting (111) gives:
% 244.76/51.22  | | | | 
% 244.76/51.22  | | | | Case 1:
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | |   (112)  all_54_7 = e1
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | | COMBINE_EQS: (96), (112) imply:
% 244.76/51.22  | | | | |   (113)  all_34_0 = e1
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | | SIMP: (113) implies:
% 244.76/51.22  | | | | |   (114)  all_34_0 = e1
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | | REDUCE: (101), (114) imply:
% 244.76/51.22  | | | | |   (115)  $false
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | | CLOSE: (115) is inconsistent.
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | Case 2:
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | |   (116)  all_54_7 = e0
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | | COMBINE_EQS: (96), (116) imply:
% 244.76/51.22  | | | | |   (117)  all_34_0 = e0
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | | SIMP: (117) implies:
% 244.76/51.22  | | | | |   (118)  all_34_0 = e0
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | | REDUCE: (97), (118) imply:
% 244.76/51.22  | | | | |   (119)   ~ (all_52_1 = e0)
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | | REDUCE: (98), (118) imply:
% 244.76/51.22  | | | | |   (120)   ~ (all_52_9 = e0)
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | | REDUCE: (99), (118) imply:
% 244.76/51.22  | | | | |   (121)   ~ (all_52_12 = e0)
% 244.76/51.22  | | | | | 
% 244.76/51.22  | | | | | REDUCE: (100), (118) imply:
% 244.76/51.23  | | | | |   (122)   ~ (e2 = e0)
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | SIMP: (122) implies:
% 244.76/51.23  | | | | |   (123)   ~ (e2 = e0)
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | BETA: splitting (32) gives:
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | Case 1:
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | |   (124)  all_54_3 = e3
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | COMBINE_EQS: (75), (124) imply:
% 244.76/51.23  | | | | | |   (125)  all_52_12 = e3
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | SIMP: (125) implies:
% 244.76/51.23  | | | | | |   (126)  all_52_12 = e3
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | REDUCE: (51), (126) imply:
% 244.76/51.23  | | | | | |   (127)   ~ (all_52_4 = e3)
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | REDUCE: (35), (126) imply:
% 244.76/51.23  | | | | | |   (128)   ~ (all_52_8 = e3)
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | REDUCE: (47), (126) imply:
% 244.76/51.23  | | | | | |   (129)  op(e3, e0) = e3
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | BETA: splitting (44) gives:
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | Case 1:
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | |   (130)  all_54_2 = e3
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | | REF_CLOSE: (29), (128), (130) are inconsistent by sub-proof #1987.
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | Case 2:
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | |   (131)   ~ (all_54_2 = e3)
% 244.76/51.23  | | | | | | |   (132)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | | BETA: splitting (132) gives:
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | | Case 1:
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | |   (133)  all_54_2 = e2
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | | REF_CLOSE: (29), (80), (133) are inconsistent by sub-proof
% 244.76/51.23  | | | | | | | |            #1986.
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | Case 2:
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | |   (134)  all_54_2 = e1 | all_54_2 = e0
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | | BETA: splitting (134) gives:
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | | Case 1:
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | |   (135)  all_54_2 = e1
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | COMBINE_EQS: (29), (135) imply:
% 244.76/51.23  | | | | | | | | |   (136)  all_52_8 = e1
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | REDUCE: (83), (136) imply:
% 244.76/51.23  | | | | | | | | |   (137)   ~ (all_52_4 = e1)
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | REDUCE: (7), (136) imply:
% 244.76/51.23  | | | | | | | | |   (138)   ~ (all_52_9 = e1)
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | SIMP: (138) implies:
% 244.76/51.23  | | | | | | | | |   (139)   ~ (all_52_9 = e1)
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | REDUCE: (36), (136) imply:
% 244.76/51.23  | | | | | | | | |   (140)  op(e3, e1) = e1
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | BETA: splitting (52) gives:
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | Case 1:
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | |   (141)  all_54_6 = e3
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | COMBINE_EQS: (25), (141) imply:
% 244.76/51.23  | | | | | | | | | |   (142)  all_52_9 = e3
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | REDUCE: (30), (142) imply:
% 244.76/51.23  | | | | | | | | | |   (143)   ~ (all_52_1 = e3)
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | REDUCE: (37), (142) imply:
% 244.76/51.23  | | | | | | | | | |   (144)  op(e2, e1) = e3
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (11), (12),
% 244.76/51.23  | | | | | | | | | |            (13), (14), (15), (16), (17), (19), (21), (22),
% 244.76/51.23  | | | | | | | | | |            (24), (26), (28), (31), (34), (36), (38), (39),
% 244.76/51.23  | | | | | | | | | |            (40), (41), (42), (45), (46), (47), (48), (49),
% 244.76/51.23  | | | | | | | | | |            (51), (53), (54), (55), (58), (59), (61), (63),
% 244.76/51.23  | | | | | | | | | |            (64), (65), (66), (67), (68), (69), (70), (71),
% 244.76/51.23  | | | | | | | | | |            (72), (73), (74), (76), (77), (78), (79), (82),
% 244.76/51.23  | | | | | | | | | |            (84), (85), (119), (123), (127), (128), (129),
% 244.76/51.23  | | | | | | | | | |            (137), (140), (143), (144) are inconsistent by
% 244.76/51.23  | | | | | | | | | |            sub-proof #1946.
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | Case 2:
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | |   (145)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | REF_CLOSE: (25), (86), (120), (139), (145) are inconsistent
% 244.76/51.23  | | | | | | | | | |            by sub-proof #2244.
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | End of split
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | Case 2:
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | |   (146)  all_54_2 = e0
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | COMBINE_EQS: (29), (146) imply:
% 244.76/51.23  | | | | | | | | |   (147)  all_52_8 = e0
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | REDUCE: (20), (147) imply:
% 244.76/51.23  | | | | | | | | |   (148)  $false
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | CLOSE: (148) is inconsistent.
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | End of split
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | End of split
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | End of split
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | Case 2:
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | |   (149)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | REF_CLOSE: (23), (56), (75), (121), (149) are inconsistent by
% 244.76/51.23  | | | | | |            sub-proof #2286.
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | End of split
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | End of split
% 244.76/51.23  | | | | 
% 244.76/51.23  | | | End of split
% 244.76/51.23  | | | 
% 244.76/51.23  | | End of split
% 244.76/51.23  | | 
% 244.76/51.23  | Case 2:
% 244.76/51.23  | | 
% 244.76/51.23  | |   (150)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 & $i(all_28_1)
% 244.76/51.23  | | 
% 244.76/51.23  | | ALPHA: (150) implies:
% 244.76/51.23  | |   (151)   ~ (all_28_1 = e2)
% 244.76/51.23  | |   (152)  op(e1, e0) = all_28_1
% 244.76/51.23  | | 
% 244.76/51.23  | | REF_CLOSE: (76), (79), (151), (152) are inconsistent by sub-proof #1944.
% 244.76/51.23  | | 
% 244.76/51.23  | End of split
% 244.76/51.23  | 
% 244.76/51.23  End of proof
% 244.76/51.23  
% 244.76/51.23  Sub-proof #1943 shows that the following formulas are inconsistent:
% 244.76/51.23  ----------------------------------------------------------------
% 244.76/51.23    (1)  op(e0, e0) = e1
% 244.76/51.23    (2)   ~ (all_52_1 = all_52_3)
% 244.76/51.23    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.76/51.23             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.76/51.23           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.76/51.23         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.76/51.23           $i(all_56_7))
% 244.76/51.23    (4)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.76/51.23    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.76/51.23         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.76/51.23    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.76/51.23         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.76/51.23    (7)   ~ (all_52_8 = all_52_9)
% 244.76/51.23    (8)  op(e0, e1) = e2
% 244.76/51.23    (9)  op(all_18_1, e1) = all_18_0
% 244.76/51.23    (10)  all_54_13 = all_52_7
% 244.76/51.23    (11)  ( ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 & op(e1, e0) =
% 244.76/51.23            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e1,
% 244.76/51.23              e0) = all_28_1 & $i(all_28_1))
% 244.76/51.23    (12)  op(e1, e2) = all_52_6
% 244.76/51.23    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.76/51.23              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.76/51.23            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 244.76/51.23            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.23            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 244.76/51.23             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.23            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.76/51.23            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.76/51.23            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 244.76/51.23            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.23            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.76/51.23              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.76/51.23            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.76/51.23            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 244.76/51.23            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.76/51.23            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 244.76/51.23            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.23            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.76/51.23              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.76/51.23            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.76/51.23            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 244.76/51.23            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.76/51.23            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 244.76/51.23            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.23            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.76/51.23              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.76/51.23            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.23            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.23    (14)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.76/51.23          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.76/51.23    (15)   ~ (all_52_6 = e2)
% 244.76/51.23    (16)   ~ (all_52_1 = all_52_2)
% 244.76/51.23    (17)  op(e0, e1) = all_34_1
% 244.76/51.23    (18)  op(e1, e0) = all_52_14
% 244.76/51.23    (19)   ~ (all_52_13 = e1)
% 244.76/51.23    (20)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.76/51.23    (21)   ~ (all_52_8 = e0)
% 244.76/51.23    (22)  op(e0, e3) = all_52_3
% 244.76/51.23    (23)   ~ (all_52_6 = e0)
% 244.76/51.23    (24)   ~ (all_52_12 = e1)
% 244.76/51.23    (25)   ~ (all_52_2 = all_52_3)
% 244.76/51.23    (26)  all_54_6 = all_52_9
% 244.76/51.23    (27)  op(all_34_1, e0) = all_34_0
% 244.76/51.23    (28)   ~ (all_52_12 = all_52_13)
% 244.76/51.23    (29)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.76/51.23          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.76/51.23    (30)  all_54_2 = all_52_8
% 244.76/51.23    (31)   ~ (all_52_9 = e0)
% 244.76/51.23    (32)   ~ (all_52_1 = all_52_9)
% 244.76/51.23    (33)   ~ (all_52_3 = all_52_7)
% 244.76/51.23    (34)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.76/51.23    (35)  op(e1, e0) = all_18_1
% 244.76/51.23    (36)  all_54_4 = all_52_1
% 244.76/51.23    (37)   ~ (all_52_8 = all_52_12)
% 244.76/51.23    (38)  op(e3, e1) = all_52_8
% 244.76/51.23    (39)  op(e2, e1) = all_52_9
% 244.76/51.23    (40)  all_54_9 = all_52_6
% 244.76/51.23    (41)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.76/51.23          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.76/51.23    (42)   ~ (all_52_7 = e1)
% 244.76/51.23    (43)   ~ (all_52_14 = e0)
% 244.76/51.23    (44)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 244.76/51.23    (45)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.76/51.23    (46)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.76/51.23    (47)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.76/51.23          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.76/51.23    (48)  all_58_15 = e1
% 244.76/51.23    (49)  op(e3, e0) = all_52_12
% 244.76/51.23    (50)   ~ (all_34_0 = e3)
% 244.76/51.23    (51)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.76/51.23          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.76/51.23    (52)   ~ (all_52_4 = all_52_12)
% 244.76/51.23    (53)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.76/51.23    (54)  all_58_11 = e2
% 244.76/51.23    (55)  op(e2, e3) = all_52_1
% 244.76/51.23    (56)  op(e3, e3) = e2
% 244.76/51.23    (57)   ~ (all_52_12 = e2)
% 244.76/51.23    (58)   ~ (all_52_13 = e2)
% 244.76/51.23    (59)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.76/51.23          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.76/51.23    (60)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.76/51.23    (61)   ~ (all_52_1 = all_52_13)
% 244.76/51.23    (62)   ~ (all_52_2 = e0)
% 244.76/51.23    (63)  all_54_7 = all_52_13
% 244.76/51.23    (64)  op(e0, e2) = all_52_7
% 244.76/51.23    (65)  op(e0, e1) = all_20_1
% 244.76/51.23    (66)  all_56_1 = e2
% 244.76/51.23    (67)  all_54_1 = all_52_4
% 244.76/51.23    (68)  op(e3, e2) = all_52_4
% 244.76/51.23    (69)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.76/51.23    (70)   ~ (all_52_2 = e2)
% 244.76/51.23    (71)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.76/51.23          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.76/51.23    (72)   ~ (all_52_4 = e2)
% 244.76/51.23    (73)  all_54_8 = all_52_2
% 244.76/51.23    (74)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.76/51.23          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.76/51.23    (75)   ~ (all_52_2 = all_52_6)
% 244.76/51.23    (76)  all_54_3 = all_52_12
% 244.76/51.23    (77)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.23    (78)  op(e1, e3) = all_52_2
% 244.76/51.23    (79)  op(e1, e1) = e0
% 244.76/51.23    (80)  op(e1, e0) = e2
% 244.76/51.23    (81)   ~ (all_52_8 = e2)
% 244.76/51.23    (82)  op(e2, e0) = all_52_13
% 244.76/51.23    (83)  op(e2, e2) = e2
% 244.76/51.23    (84)   ~ (all_52_4 = all_52_8)
% 244.76/51.23    (85)   ~ (all_52_1 = e2)
% 244.76/51.23    (86)   ~ (all_52_4 = all_52_7)
% 244.76/51.23    (87)   ~ (all_52_9 = e2)
% 244.76/51.23  
% 244.76/51.23  Begin of proof
% 244.76/51.23  | 
% 244.76/51.23  | GROUND_INST: instantiating (77) with e2, all_34_1, e1, e0, simplifying with
% 244.76/51.23  |              (8), (17) gives:
% 244.76/51.23  |   (88)  all_34_1 = e2
% 244.76/51.23  | 
% 244.76/51.23  | GROUND_INST: instantiating (77) with all_20_1, all_34_1, e1, e0, simplifying
% 244.76/51.23  |              with (17), (65) gives:
% 244.76/51.23  |   (89)  all_34_1 = all_20_1
% 244.76/51.23  | 
% 244.76/51.23  | GROUND_INST: instantiating (77) with e2, all_18_1, e0, e1, simplifying with
% 244.76/51.23  |              (35), (80) gives:
% 244.76/51.23  |   (90)  all_18_1 = e2
% 244.76/51.23  | 
% 244.76/51.23  | COMBINE_EQS: (88), (89) imply:
% 244.76/51.23  |   (91)  all_20_1 = e2
% 244.76/51.23  | 
% 244.76/51.23  | REDUCE: (27), (88) imply:
% 244.76/51.23  |   (92)  op(e2, e0) = all_34_0
% 244.76/51.23  | 
% 244.76/51.23  | REDUCE: (9), (90) imply:
% 244.76/51.23  |   (93)  op(e2, e1) = all_18_0
% 244.76/51.23  | 
% 244.76/51.23  | BETA: splitting (11) gives:
% 244.76/51.23  | 
% 244.76/51.23  | Case 1:
% 244.76/51.23  | | 
% 244.76/51.23  | |   (94)   ~ (all_28_0 = e3) & op(all_28_1, e1) = all_28_0 & op(e1, e0) =
% 244.76/51.23  | |         all_28_1 & $i(all_28_0) & $i(all_28_1)
% 244.76/51.23  | | 
% 244.76/51.23  | | ALPHA: (94) implies:
% 244.76/51.23  | |   (95)  op(e1, e0) = all_28_1
% 244.76/51.23  | | 
% 244.76/51.23  | | GROUND_INST: instantiating (77) with e2, all_28_1, e0, e1, simplifying with
% 244.76/51.23  | |              (80), (95) gives:
% 244.76/51.23  | |   (96)  all_28_1 = e2
% 244.76/51.23  | | 
% 244.76/51.23  | | GROUND_INST: instantiating (77) with all_52_13, all_34_0, e0, e2,
% 244.76/51.23  | |              simplifying with (82), (92) gives:
% 244.76/51.23  | |   (97)  all_52_13 = all_34_0
% 244.76/51.23  | | 
% 244.76/51.23  | | GROUND_INST: instantiating (77) with all_52_9, all_18_0, e1, e2, simplifying
% 244.76/51.23  | |              with (39), (93) gives:
% 244.76/51.23  | |   (98)  all_52_9 = all_18_0
% 244.76/51.23  | | 
% 244.76/51.23  | | COMBINE_EQS: (63), (97) imply:
% 244.76/51.23  | |   (99)  all_54_7 = all_34_0
% 244.76/51.23  | | 
% 244.76/51.23  | | COMBINE_EQS: (26), (98) imply:
% 244.76/51.23  | |   (100)  all_54_6 = all_18_0
% 244.76/51.23  | | 
% 244.76/51.23  | | REDUCE: (32), (98) imply:
% 244.76/51.23  | |   (101)   ~ (all_52_1 = all_18_0)
% 244.76/51.23  | | 
% 244.76/51.23  | | REDUCE: (61), (97) imply:
% 244.76/51.23  | |   (102)   ~ (all_52_1 = all_34_0)
% 244.76/51.23  | | 
% 244.76/51.23  | | REDUCE: (87), (98) imply:
% 244.76/51.23  | |   (103)   ~ (all_18_0 = e2)
% 244.76/51.23  | | 
% 244.76/51.23  | | REDUCE: (28), (97) imply:
% 244.76/51.23  | |   (104)   ~ (all_52_12 = all_34_0)
% 244.76/51.23  | | 
% 244.76/51.23  | | REDUCE: (58), (97) imply:
% 244.76/51.23  | |   (105)   ~ (all_34_0 = e2)
% 244.76/51.23  | | 
% 244.76/51.23  | | REDUCE: (19), (97) imply:
% 244.76/51.23  | |   (106)   ~ (all_34_0 = e1)
% 244.76/51.23  | | 
% 244.76/51.23  | | BETA: splitting (45) gives:
% 244.76/51.23  | | 
% 244.76/51.23  | | Case 1:
% 244.76/51.23  | | | 
% 244.76/51.23  | | |   (107)  all_54_7 = e3
% 244.76/51.23  | | | 
% 244.76/51.23  | | | COMBINE_EQS: (99), (107) imply:
% 244.76/51.23  | | |   (108)  all_34_0 = e3
% 244.76/51.23  | | | 
% 244.76/51.23  | | | REDUCE: (50), (108) imply:
% 244.76/51.23  | | |   (109)  $false
% 244.76/51.23  | | | 
% 244.76/51.23  | | | CLOSE: (109) is inconsistent.
% 244.76/51.23  | | | 
% 244.76/51.23  | | Case 2:
% 244.76/51.23  | | | 
% 244.76/51.23  | | |   (110)   ~ (all_54_7 = e3)
% 244.76/51.23  | | |   (111)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.76/51.23  | | | 
% 244.76/51.23  | | | BETA: splitting (111) gives:
% 244.76/51.23  | | | 
% 244.76/51.23  | | | Case 1:
% 244.76/51.23  | | | | 
% 244.76/51.23  | | | |   (112)  all_54_7 = e2
% 244.76/51.23  | | | | 
% 244.76/51.23  | | | | COMBINE_EQS: (99), (112) imply:
% 244.76/51.23  | | | |   (113)  all_34_0 = e2
% 244.76/51.23  | | | | 
% 244.76/51.23  | | | | REDUCE: (105), (113) imply:
% 244.76/51.23  | | | |   (114)  $false
% 244.76/51.23  | | | | 
% 244.76/51.23  | | | | CLOSE: (114) is inconsistent.
% 244.76/51.23  | | | | 
% 244.76/51.23  | | | Case 2:
% 244.76/51.23  | | | | 
% 244.76/51.23  | | | |   (115)   ~ (all_54_7 = e2)
% 244.76/51.23  | | | |   (116)  all_54_7 = e1 | all_54_7 = e0
% 244.76/51.23  | | | | 
% 244.76/51.23  | | | | BETA: splitting (116) gives:
% 244.76/51.23  | | | | 
% 244.76/51.23  | | | | Case 1:
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | |   (117)  all_54_7 = e1
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | COMBINE_EQS: (99), (117) imply:
% 244.76/51.23  | | | | |   (118)  all_34_0 = e1
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | REDUCE: (106), (118) imply:
% 244.76/51.23  | | | | |   (119)  $false
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | CLOSE: (119) is inconsistent.
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | Case 2:
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | |   (120)  all_54_7 = e0
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | COMBINE_EQS: (99), (120) imply:
% 244.76/51.23  | | | | |   (121)  all_34_0 = e0
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | REDUCE: (102), (121) imply:
% 244.76/51.23  | | | | |   (122)   ~ (all_52_1 = e0)
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | REDUCE: (104), (121) imply:
% 244.76/51.23  | | | | |   (123)   ~ (all_52_12 = e0)
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | REDUCE: (105), (121) imply:
% 244.76/51.23  | | | | |   (124)   ~ (e2 = e0)
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | SIMP: (124) implies:
% 244.76/51.23  | | | | |   (125)   ~ (e2 = e0)
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | BETA: splitting (34) gives:
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | | Case 1:
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | |   (126)  all_54_3 = e3
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | COMBINE_EQS: (76), (126) imply:
% 244.76/51.23  | | | | | |   (127)  all_52_12 = e3
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | SIMP: (127) implies:
% 244.76/51.23  | | | | | |   (128)  all_52_12 = e3
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | REDUCE: (52), (128) imply:
% 244.76/51.23  | | | | | |   (129)   ~ (all_52_4 = e3)
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | REDUCE: (37), (128) imply:
% 244.76/51.23  | | | | | |   (130)   ~ (all_52_8 = e3)
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | REDUCE: (49), (128) imply:
% 244.76/51.23  | | | | | |   (131)  op(e3, e0) = e3
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | BETA: splitting (46) gives:
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | Case 1:
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | |   (132)  all_54_2 = e3
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | | REF_CLOSE: (30), (130), (132) are inconsistent by sub-proof #1987.
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | Case 2:
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | |   (133)   ~ (all_54_2 = e3)
% 244.76/51.23  | | | | | | |   (134)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | | BETA: splitting (134) gives:
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | | Case 1:
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | |   (135)  all_54_2 = e2
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | | REF_CLOSE: (30), (81), (135) are inconsistent by sub-proof
% 244.76/51.23  | | | | | | | |            #1986.
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | Case 2:
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | |   (136)  all_54_2 = e1 | all_54_2 = e0
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | | BETA: splitting (136) gives:
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | | Case 1:
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | |   (137)  all_54_2 = e1
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | COMBINE_EQS: (30), (137) imply:
% 244.76/51.23  | | | | | | | | |   (138)  all_52_8 = e1
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | REDUCE: (84), (138) imply:
% 244.76/51.23  | | | | | | | | |   (139)   ~ (all_52_4 = e1)
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | REDUCE: (38), (138) imply:
% 244.76/51.23  | | | | | | | | |   (140)  op(e3, e1) = e1
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | BETA: splitting (53) gives:
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | Case 1:
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | |   (141)  all_54_6 = e3
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | COMBINE_EQS: (100), (141) imply:
% 244.76/51.23  | | | | | | | | | |   (142)  all_18_0 = e3
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | REDUCE: (101), (142) imply:
% 244.76/51.23  | | | | | | | | | |   (143)   ~ (all_52_1 = e3)
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | REDUCE: (93), (142) imply:
% 244.76/51.23  | | | | | | | | | |   (144)  op(e2, e1) = e3
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (12), (13),
% 244.76/51.23  | | | | | | | | | |            (14), (15), (16), (17), (18), (20), (22), (23),
% 244.76/51.23  | | | | | | | | | |            (25), (27), (29), (33), (36), (38), (40), (41),
% 244.76/51.23  | | | | | | | | | |            (42), (43), (44), (47), (48), (49), (50), (51),
% 244.76/51.23  | | | | | | | | | |            (52), (54), (55), (56), (59), (60), (62), (64),
% 244.76/51.23  | | | | | | | | | |            (65), (66), (67), (68), (69), (70), (71), (72),
% 244.76/51.23  | | | | | | | | | |            (73), (74), (75), (77), (78), (79), (80), (83),
% 244.76/51.23  | | | | | | | | | |            (85), (86), (122), (125), (129), (130), (131),
% 244.76/51.23  | | | | | | | | | |            (139), (140), (143), (144) are inconsistent by
% 244.76/51.23  | | | | | | | | | |            sub-proof #1946.
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | Case 2:
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | |   (145)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | BETA: splitting (145) gives:
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | Case 1:
% 244.76/51.23  | | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | |   (146)  all_54_6 = e2
% 244.76/51.23  | | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | | COMBINE_EQS: (100), (146) imply:
% 244.76/51.23  | | | | | | | | | | |   (147)  all_18_0 = e2
% 244.76/51.23  | | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | | REDUCE: (103), (147) imply:
% 244.76/51.23  | | | | | | | | | | |   (148)  $false
% 244.76/51.23  | | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | | CLOSE: (148) is inconsistent.
% 244.76/51.23  | | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | Case 2:
% 244.76/51.23  | | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | |   (149)  all_54_6 = e1 | all_54_6 = e0
% 244.76/51.23  | | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | | REF_CLOSE: (7), (26), (31), (38), (77), (140), (149) are
% 244.76/51.23  | | | | | | | | | | |            inconsistent by sub-proof #1945.
% 244.76/51.23  | | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | | End of split
% 244.76/51.23  | | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | End of split
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | Case 2:
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | |   (150)  all_54_2 = e0
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | COMBINE_EQS: (30), (150) imply:
% 244.76/51.23  | | | | | | | | |   (151)  all_52_8 = e0
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | REDUCE: (21), (151) imply:
% 244.76/51.23  | | | | | | | | |   (152)  $false
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | | CLOSE: (152) is inconsistent.
% 244.76/51.23  | | | | | | | | | 
% 244.76/51.23  | | | | | | | | End of split
% 244.76/51.23  | | | | | | | | 
% 244.76/51.23  | | | | | | | End of split
% 244.76/51.23  | | | | | | | 
% 244.76/51.23  | | | | | | End of split
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | Case 2:
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | |   (153)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | | REF_CLOSE: (24), (57), (76), (123), (153) are inconsistent by
% 244.76/51.23  | | | | | |            sub-proof #2286.
% 244.76/51.23  | | | | | | 
% 244.76/51.23  | | | | | End of split
% 244.76/51.23  | | | | | 
% 244.76/51.23  | | | | End of split
% 244.76/51.23  | | | | 
% 244.76/51.23  | | | End of split
% 244.76/51.23  | | | 
% 244.76/51.23  | | End of split
% 244.76/51.23  | | 
% 244.76/51.23  | Case 2:
% 244.76/51.23  | | 
% 244.76/51.23  | |   (154)   ~ (all_28_1 = e2) & op(e1, e0) = all_28_1 & $i(all_28_1)
% 244.76/51.23  | | 
% 244.76/51.23  | | ALPHA: (154) implies:
% 244.76/51.23  | |   (155)   ~ (all_28_1 = e2)
% 244.76/51.23  | |   (156)  op(e1, e0) = all_28_1
% 244.76/51.23  | | 
% 244.76/51.23  | | REF_CLOSE: (77), (80), (155), (156) are inconsistent by sub-proof #1944.
% 244.76/51.23  | | 
% 244.76/51.23  | End of split
% 244.76/51.23  | 
% 244.76/51.23  End of proof
% 244.76/51.23  
% 244.76/51.23  Sub-proof #1944 shows that the following formulas are inconsistent:
% 244.76/51.23  ----------------------------------------------------------------
% 244.76/51.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.23    (2)  op(e1, e0) = all_28_1
% 244.76/51.23    (3)  op(e1, e0) = e2
% 244.76/51.23    (4)   ~ (all_28_1 = e2)
% 244.76/51.23  
% 244.76/51.23  Begin of proof
% 244.76/51.23  | 
% 244.76/51.23  | GROUND_INST: instantiating (1) with e2, all_28_1, e0, e1, simplifying with
% 244.76/51.23  |              (2), (3) gives:
% 244.76/51.23  |   (5)  all_28_1 = e2
% 244.76/51.23  | 
% 244.76/51.23  | REDUCE: (4), (5) imply:
% 244.76/51.23  |   (6)  $false
% 244.76/51.23  | 
% 244.76/51.23  | CLOSE: (6) is inconsistent.
% 244.76/51.23  | 
% 244.76/51.23  End of proof
% 244.76/51.23  
% 244.76/51.23  Sub-proof #1945 shows that the following formulas are inconsistent:
% 244.76/51.23  ----------------------------------------------------------------
% 244.76/51.23    (1)   ~ (all_52_8 = all_52_9)
% 244.76/51.23    (2)  all_54_6 = all_52_9
% 244.76/51.23    (3)   ~ (all_52_9 = e0)
% 244.76/51.23    (4)  op(e3, e1) = all_52_8
% 244.76/51.23    (5)  op(e3, e1) = e1
% 244.76/51.23    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.23    (7)  all_54_6 = e1 | all_54_6 = e0
% 244.76/51.23  
% 244.76/51.23  Begin of proof
% 244.76/51.23  | 
% 244.76/51.23  | BETA: splitting (7) gives:
% 244.76/51.23  | 
% 244.76/51.23  | Case 1:
% 244.76/51.23  | | 
% 244.76/51.23  | |   (8)  all_54_6 = e1
% 244.76/51.23  | | 
% 244.76/51.23  | | COMBINE_EQS: (2), (8) imply:
% 244.76/51.23  | |   (9)  all_52_9 = e1
% 244.76/51.23  | | 
% 244.76/51.23  | | SIMP: (9) implies:
% 244.76/51.23  | |   (10)  all_52_9 = e1
% 244.76/51.23  | | 
% 244.76/51.23  | | REDUCE: (1), (10) imply:
% 244.76/51.23  | |   (11)   ~ (all_52_8 = e1)
% 244.76/51.23  | | 
% 244.76/51.23  | | REF_CLOSE: (4), (5), (6), (11) are inconsistent by sub-proof #2309.
% 244.76/51.23  | | 
% 244.76/51.23  | Case 2:
% 244.76/51.23  | | 
% 244.76/51.23  | |   (12)  all_54_6 = e0
% 244.76/51.23  | | 
% 244.76/51.23  | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #2245.
% 244.76/51.23  | | 
% 244.76/51.23  | End of split
% 244.76/51.23  | 
% 244.76/51.23  End of proof
% 244.76/51.23  
% 244.76/51.23  Sub-proof #1946 shows that the following formulas are inconsistent:
% 244.76/51.23  ----------------------------------------------------------------
% 244.76/51.23    (1)  op(e0, e0) = e1
% 244.76/51.23    (2)   ~ (all_52_1 = all_52_3)
% 244.76/51.23    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.76/51.23             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.76/51.23           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.76/51.23         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.76/51.23           $i(all_56_7))
% 244.76/51.23    (4)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.76/51.23    (5)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.76/51.23         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.76/51.23    (6)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.76/51.23         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.76/51.23    (7)   ~ (e2 = e0)
% 244.76/51.23    (8)  all_54_13 = all_52_7
% 244.76/51.23    (9)  op(e1, e2) = all_52_6
% 244.76/51.24    (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.76/51.24              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.76/51.24            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 244.76/51.24            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.24            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 244.76/51.24             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.24            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.76/51.24            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.76/51.24            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 244.76/51.24            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.24            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.76/51.24              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.76/51.24            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.76/51.24            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 244.76/51.24            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.76/51.24            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 244.76/51.24            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.76/51.24            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.76/51.24              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.76/51.24            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.76/51.24            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 244.76/51.24            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.76/51.24            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 244.76/51.24            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.24            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.76/51.24              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.76/51.24            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.24            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.24    (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.76/51.24          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.76/51.24    (12)   ~ (all_52_6 = e2)
% 244.76/51.24    (13)   ~ (all_52_1 = all_52_2)
% 244.76/51.24    (14)  op(e0, e1) = all_34_1
% 244.76/51.24    (15)  op(e1, e0) = all_52_14
% 244.76/51.24    (16)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.76/51.24    (17)  op(e0, e3) = all_52_3
% 244.76/51.24    (18)   ~ (all_52_6 = e0)
% 244.76/51.24    (19)   ~ (all_52_2 = all_52_3)
% 244.76/51.24    (20)  op(all_34_1, e0) = all_34_0
% 244.76/51.24    (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.76/51.24          (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.76/51.24    (22)   ~ (all_52_3 = all_52_7)
% 244.76/51.24    (23)  all_54_4 = all_52_1
% 244.76/51.24    (24)  op(e3, e1) = all_52_8
% 244.76/51.24    (25)  all_54_9 = all_52_6
% 244.76/51.24    (26)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.76/51.24          (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.76/51.24    (27)   ~ (all_52_7 = e1)
% 244.76/51.24    (28)  op(e3, e1) = e1
% 244.76/51.24    (29)   ~ (all_52_14 = e0)
% 244.76/51.24    (30)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 244.76/51.24    (31)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.76/51.24          (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.76/51.24    (32)  all_58_15 = e1
% 244.76/51.24    (33)  op(e3, e0) = all_52_12
% 244.76/51.24    (34)   ~ (all_34_0 = e3)
% 244.76/51.24    (35)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.76/51.24          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.76/51.24    (36)   ~ (all_52_1 = e0)
% 244.76/51.24    (37)   ~ (all_52_4 = all_52_12)
% 244.76/51.24    (38)  op(e3, e0) = e3
% 244.76/51.24    (39)  all_58_11 = e2
% 244.76/51.24    (40)  op(e2, e3) = all_52_1
% 244.76/51.24    (41)  op(e3, e3) = e2
% 244.76/51.24    (42)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 244.76/51.24          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 244.76/51.24    (43)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.76/51.24    (44)   ~ (all_52_2 = e0)
% 244.76/51.24    (45)  op(e0, e2) = all_52_7
% 244.76/51.24    (46)  op(e0, e1) = all_20_1
% 244.76/51.24    (47)  all_56_1 = e2
% 244.76/51.24    (48)  all_54_1 = all_52_4
% 244.76/51.24    (49)   ~ (all_52_4 = e3)
% 244.76/51.24    (50)  op(e3, e2) = all_52_4
% 244.76/51.24    (51)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.76/51.24    (52)   ~ (all_52_2 = e2)
% 244.76/51.24    (53)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 244.76/51.24          (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.76/51.24    (54)  op(e2, e1) = e3
% 244.76/51.24    (55)   ~ (all_52_4 = e2)
% 244.76/51.24    (56)  all_54_8 = all_52_2
% 244.76/51.24    (57)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.76/51.24          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.76/51.24    (58)   ~ (all_52_2 = all_52_6)
% 244.76/51.24    (59)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.24    (60)  op(e1, e3) = all_52_2
% 244.76/51.24    (61)  op(e1, e1) = e0
% 244.76/51.24    (62)   ~ (all_52_4 = e1)
% 244.76/51.24    (63)  op(e1, e0) = e2
% 244.76/51.24    (64)   ~ (all_52_1 = e3)
% 244.76/51.24    (65)  op(e2, e2) = e2
% 244.76/51.24    (66)   ~ (all_52_1 = e2)
% 244.76/51.24    (67)   ~ (all_52_4 = all_52_7)
% 244.76/51.24    (68)   ~ (all_52_8 = e3)
% 244.76/51.24  
% 244.76/51.24  Begin of proof
% 244.76/51.24  | 
% 244.76/51.24  | BETA: splitting (43) gives:
% 244.76/51.24  | 
% 244.76/51.24  | Case 1:
% 244.76/51.24  | | 
% 244.76/51.24  | |   (69)  all_54_4 = e3
% 244.76/51.24  | | 
% 244.76/51.24  | | COMBINE_EQS: (23), (69) imply:
% 244.76/51.24  | |   (70)  all_52_1 = e3
% 244.76/51.24  | | 
% 244.76/51.24  | | REDUCE: (64), (70) imply:
% 244.76/51.24  | |   (71)  $false
% 244.76/51.24  | | 
% 244.76/51.24  | | CLOSE: (71) is inconsistent.
% 244.76/51.24  | | 
% 244.76/51.24  | Case 2:
% 244.76/51.24  | | 
% 244.76/51.24  | |   (72)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.76/51.24  | | 
% 244.76/51.24  | | BETA: splitting (72) gives:
% 244.76/51.24  | | 
% 244.76/51.24  | | Case 1:
% 244.76/51.24  | | | 
% 244.76/51.24  | | |   (73)  all_54_4 = e2
% 244.76/51.24  | | | 
% 244.76/51.24  | | | COMBINE_EQS: (23), (73) imply:
% 244.76/51.24  | | |   (74)  all_52_1 = e2
% 244.76/51.24  | | | 
% 244.76/51.24  | | | REDUCE: (66), (74) imply:
% 244.76/51.24  | | |   (75)  $false
% 244.76/51.24  | | | 
% 244.76/51.24  | | | CLOSE: (75) is inconsistent.
% 244.76/51.24  | | | 
% 244.76/51.24  | | Case 2:
% 244.76/51.24  | | | 
% 244.76/51.24  | | |   (76)   ~ (all_54_4 = e2)
% 244.76/51.24  | | |   (77)  all_54_4 = e1 | all_54_4 = e0
% 244.76/51.24  | | | 
% 244.76/51.24  | | | BETA: splitting (77) gives:
% 244.76/51.24  | | | 
% 244.76/51.24  | | | Case 1:
% 244.76/51.24  | | | | 
% 244.76/51.24  | | | |   (78)  all_54_4 = e1
% 244.76/51.24  | | | | 
% 244.76/51.24  | | | | COMBINE_EQS: (23), (78) imply:
% 244.76/51.24  | | | |   (79)  all_52_1 = e1
% 244.76/51.24  | | | | 
% 244.76/51.24  | | | | REDUCE: (13), (79) imply:
% 244.76/51.24  | | | |   (80)   ~ (all_52_2 = e1)
% 244.76/51.24  | | | | 
% 244.76/51.24  | | | | SIMP: (80) implies:
% 244.76/51.24  | | | |   (81)   ~ (all_52_2 = e1)
% 244.76/51.24  | | | | 
% 244.76/51.24  | | | | REDUCE: (2), (79) imply:
% 244.76/51.24  | | | |   (82)   ~ (all_52_3 = e1)
% 244.76/51.24  | | | | 
% 244.76/51.24  | | | | SIMP: (82) implies:
% 244.76/51.24  | | | |   (83)   ~ (all_52_3 = e1)
% 244.76/51.24  | | | | 
% 244.76/51.24  | | | | REDUCE: (66), (79) imply:
% 244.76/51.24  | | | |   (84)   ~ (e2 = e1)
% 244.76/51.24  | | | | 
% 244.76/51.24  | | | | SIMP: (84) implies:
% 244.76/51.24  | | | |   (85)   ~ (e2 = e1)
% 244.76/51.24  | | | | 
% 244.76/51.24  | | | | REDUCE: (36), (79) imply:
% 244.76/51.24  | | | |   (86)   ~ (e1 = e0)
% 244.76/51.24  | | | | 
% 244.76/51.24  | | | | BETA: splitting (53) gives:
% 244.76/51.24  | | | | 
% 244.76/51.24  | | | | Case 1:
% 244.76/51.24  | | | | | 
% 244.76/51.24  | | | | |   (87)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 244.76/51.24  | | | | |             e3) = e1)
% 244.76/51.24  | | | | | 
% 244.76/51.24  | | | | | BETA: splitting (87) gives:
% 244.76/51.24  | | | | | 
% 244.76/51.24  | | | | | Case 1:
% 244.76/51.24  | | | | | | 
% 244.76/51.24  | | | | | |   (88)  all_58_0 = e1 & op(e3, e3) = e1
% 244.76/51.24  | | | | | | 
% 244.76/51.24  | | | | | | ALPHA: (88) implies:
% 244.76/51.24  | | | | | |   (89)  op(e3, e3) = e1
% 244.76/51.24  | | | | | | 
% 244.76/51.24  | | | | | | REF_CLOSE: (41), (59), (85), (89) are inconsistent by sub-proof
% 244.76/51.24  | | | | | |            #2267.
% 244.76/51.24  | | | | | | 
% 244.76/51.24  | | | | | Case 2:
% 244.76/51.24  | | | | | | 
% 244.76/51.24  | | | | | |   (90)  all_58_2 = e1 & op(e2, e3) = e1
% 244.76/51.24  | | | | | | 
% 244.76/51.24  | | | | | | ALPHA: (90) implies:
% 244.76/51.24  | | | | | |   (91)  all_58_2 = e1
% 244.76/51.24  | | | | | | 
% 244.76/51.24  | | | | | | BETA: splitting (4) gives:
% 244.76/51.24  | | | | | | 
% 244.76/51.24  | | | | | | Case 1:
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | |   (92)  all_54_8 = e3
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | | COMBINE_EQS: (56), (92) imply:
% 244.76/51.24  | | | | | | |   (93)  all_52_2 = e3
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | | SIMP: (93) implies:
% 244.76/51.24  | | | | | | |   (94)  all_52_2 = e3
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | | REDUCE: (19), (94) imply:
% 244.76/51.24  | | | | | | |   (95)   ~ (all_52_3 = e3)
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | | SIMP: (95) implies:
% 244.76/51.24  | | | | | | |   (96)   ~ (all_52_3 = e3)
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | | REDUCE: (58), (94) imply:
% 244.76/51.24  | | | | | | |   (97)   ~ (all_52_6 = e3)
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | | SIMP: (97) implies:
% 244.76/51.24  | | | | | | |   (98)   ~ (all_52_6 = e3)
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | | REDUCE: (52), (94) imply:
% 244.76/51.24  | | | | | | |   (99)   ~ (e3 = e2)
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | | REDUCE: (81), (94) imply:
% 244.76/51.24  | | | | | | |   (100)   ~ (e3 = e1)
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | | REDUCE: (44), (94) imply:
% 244.76/51.24  | | | | | | |   (101)   ~ (e3 = e0)
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | | BETA: splitting (35) gives:
% 244.76/51.24  | | | | | | | 
% 244.76/51.24  | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | 
% 244.76/51.24  | | | | | | | |   (102)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 &
% 244.76/51.24  | | | | | | | |            op(e1, e2) = e3)
% 244.76/51.24  | | | | | | | | 
% 244.76/51.24  | | | | | | | | BETA: splitting (102) gives:
% 244.76/51.24  | | | | | | | | 
% 244.76/51.24  | | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | | 
% 244.76/51.24  | | | | | | | | |   (103)  all_58_6 = e3 & op(e1, e3) = e3
% 244.76/51.24  | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | ALPHA: (103) implies:
% 244.76/51.24  | | | | | | | | |   (104)  all_58_6 = e3
% 244.76/51.24  | | | | | | | | |   (105)  op(e1, e3) = e3
% 244.76/51.24  | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | BETA: splitting (31) gives:
% 244.76/51.24  | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | |   (106)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 244.76/51.24  | | | | | | | | | |            & op(e2, e3) = e0)
% 244.76/51.24  | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | REF_CLOSE: (7), (36), (40), (41), (59), (106) are
% 244.76/51.24  | | | | | | | | | |            inconsistent by sub-proof #1984.
% 244.76/51.24  | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | Case 2:
% 244.76/51.24  | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | |   (107)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0
% 244.76/51.24  | | | | | | | | | |            & op(e0, e3) = e0)
% 244.76/51.24  | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | BETA: splitting (107) gives:
% 244.76/51.24  | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | |   (108)  all_58_6 = e0 & op(e1, e3) = e0
% 244.76/51.24  | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | ALPHA: (108) implies:
% 244.76/51.24  | | | | | | | | | | |   (109)  all_58_6 = e0
% 244.76/51.24  | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (35), (57), (59), (61), (85), (86),
% 244.76/51.24  | | | | | | | | | | |            (98), (99), (100), (101), (109) are inconsistent
% 244.76/51.24  | | | | | | | | | | |            by sub-proof #1977.
% 244.76/51.24  | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | Case 2:
% 244.76/51.24  | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | |   (110)  all_58_12 = e0 & op(e0, e3) = e0
% 244.76/51.24  | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | ALPHA: (110) implies:
% 244.76/51.24  | | | | | | | | | | |   (111)  op(e0, e3) = e0
% 244.76/51.24  | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | BETA: splitting (3) gives:
% 244.76/51.24  | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | |   (112)  (all_56_0 = e3 & op(e3, all_56_1) = e3) |
% 244.76/51.24  | | | | | | | | | | | |          (all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2,
% 244.76/51.24  | | | | | | | | | | | |              e3) = all_56_3 & $i(all_56_3))
% 244.76/51.24  | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | BETA: splitting (112) gives:
% 244.76/51.24  | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | |   (113)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 244.76/51.24  | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | ALPHA: (113) implies:
% 244.76/51.24  | | | | | | | | | | | | |   (114)  op(e3, all_56_1) = e3
% 244.76/51.24  | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | REDUCE: (47), (114) imply:
% 244.76/51.24  | | | | | | | | | | | | |   (115)  op(e3, e2) = e3
% 244.76/51.24  | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | REF_CLOSE: (49), (50), (59), (115) are inconsistent by
% 244.76/51.24  | | | | | | | | | | | | |            sub-proof #2192.
% 244.76/51.24  | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | Case 2:
% 244.76/51.24  | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | |   (116)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3)
% 244.76/51.24  | | | | | | | | | | | | |          = all_56_3 & $i(all_56_3)
% 244.76/51.24  | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | ALPHA: (116) implies:
% 244.76/51.24  | | | | | | | | | | | | |   (117)  op(e2, e3) = all_56_3
% 244.76/51.24  | | | | | | | | | | | | |   (118)  op(e2, all_56_3) = e2
% 244.76/51.24  | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | BETA: splitting (5) gives:
% 244.76/51.24  | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | |   (119)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 244.76/51.24  | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 244.76/51.24  | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 244.76/51.24  | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | |   (120)  all_58_12 = e3 & op(e0, e3) = e3
% 244.76/51.24  | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 244.76/51.24  | | | | | | | | | | | | | | |   (121)  all_58_12 = e3
% 244.76/51.24  | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | REF_CLOSE: (7), (26), (31), (59), (85), (86), (91), (99),
% 244.76/51.24  | | | | | | | | | | | | | | |            (101), (104), (121) are inconsistent by sub-proof
% 244.76/51.24  | | | | | | | | | | | | | | |            #1970.
% 244.76/51.24  | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | Case 2:
% 244.76/51.24  | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | |   (122)  all_58_13 = e3 & op(e0, e2) = e3
% 244.76/51.24  | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 244.76/51.24  | | | | | | | | | | | | | | |   (123)  op(e0, e2) = e3
% 244.76/51.24  | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 244.76/51.24  | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | |   (124)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 244.76/51.24  | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 244.76/51.24  | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 244.76/51.24  | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | |   (125)  all_58_0 = e0 & op(e3, e3) = e0
% 244.76/51.24  | | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 244.76/51.24  | | | | | | | | | | | | | | | | |   (126)  op(e3, e3) = e0
% 244.76/51.24  | | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (59), (126) are inconsistent by
% 244.76/51.24  | | | | | | | | | | | | | | | | |            sub-proof #2188.
% 244.76/51.24  | | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | Case 2:
% 244.76/51.24  | | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | |   (127)  all_58_1 = e0 & op(e3, e2) = e0
% 244.76/51.24  | | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 244.76/51.24  | | | | | | | | | | | | | | | | |   (128)  op(e3, e2) = e0
% 244.76/51.24  | | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 244.76/51.24  | | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | | |   (129)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 244.76/51.24  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.76/51.24  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.76/51.24  | | | | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.76/51.24  | | | | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.76/51.24  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 244.76/51.24  | | | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 244.76/51.24  | | | | | | | | | | | | | | | | | | 
% 244.76/51.24  | | | | | | | | | | | | | | | | | | Case 1:
% 244.76/51.24  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |   (130)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            = e3)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |   (131)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |          e3
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |   (132)  op(e2, e3) = e3
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (99), (117), (118), (132) are inconsistent
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            by sub-proof #2262.
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |   (133)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |   (134)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |          (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |          e2
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |   (135)  op(e3, e2) = e2
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (59), (128), (135) are inconsistent by
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2026.
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |   (136)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1,
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |   (137)  op(e3, e1) = e3
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (59), (68), (137) are inconsistent by
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2260.
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |   (138)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            = e0)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |   (139)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            e3) = e1
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |   (140)  op(e1, e3) = e1
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (59), (98), (100), (102), (140) are
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1969.
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |   (141)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (59), (61), (99), (101), (141) are
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2017.
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |   (142)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |   (143)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            e3) = e3
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |   (144)  op(e0, e3) = e3
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (59), (96), (144) are inconsistent by
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2332.
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |   (145)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            e3) = e0
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |   (146)  op(e3, e0) = e0
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (11), (16), (17), (18), (22), (27),
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            (33), (37), (45), (48), (50), (51), (55), (59),
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            (62), (65), (67), (111), (146) are inconsistent by
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1962.
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | |   (147)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.76/51.25  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 244.76/51.25  | | | | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | Case 1:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |   (148)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            = e2)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (59), (99), (100), (123), (148) are
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2253.
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |   (149)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | |            = e0)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |   (150)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0,
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            e2) = e0
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |   (151)  op(e0, e2) = e0
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (101), (123), (151) are inconsistent by
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            sub-proof #1961.
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |   (152)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (29), (59), (63), (85), (152) are
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1960.
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | |   (153)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 244.76/51.25  | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 244.76/51.25  | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 244.76/51.25  | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | Case 1:
% 244.76/51.25  | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | |   (154)  all_58_4 = e0 & op(e3, e1) = e0
% 244.76/51.25  | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 244.76/51.25  | | | | | | | | | | | | | | | | |   (155)  op(e3, e1) = e0
% 244.76/51.25  | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (59), (86), (155) are inconsistent by
% 244.76/51.25  | | | | | | | | | | | | | | | | |            sub-proof #2089.
% 244.76/51.25  | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | |   (156)  all_58_9 = e0 & op(e3, e0) = e0
% 244.76/51.25  | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 244.76/51.25  | | | | | | | | | | | | | | | | |   (157)  all_58_9 = e0
% 244.76/51.25  | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (24), (41), (49), (50), (59), (68), (99),
% 244.76/51.25  | | | | | | | | | | | | | | | | |            (101), (157) are inconsistent by sub-proof #1956.
% 244.76/51.25  | | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | |   (158)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 244.76/51.25  | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 244.76/51.25  | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | | REF_CLOSE: (14), (20), (32), (34), (38), (46), (59), (100),
% 244.76/51.25  | | | | | | | | | | | | | |            (158) are inconsistent by sub-proof #2248.
% 244.76/51.25  | | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | |   (159)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1,
% 244.76/51.25  | | | | | | | | | | | |              e3) = all_56_5 & $i(all_56_5)) | (all_56_6 =
% 244.76/51.25  | | | | | | | | | | | |            e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 244.76/51.25  | | | | | | | | | | | |            all_56_7 & $i(all_56_7))
% 244.76/51.25  | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | BETA: splitting (159) gives:
% 244.76/51.25  | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | Case 1:
% 244.76/51.25  | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | |   (160)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3)
% 244.76/51.25  | | | | | | | | | | | | |          = all_56_5 & $i(all_56_5)
% 244.76/51.25  | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | ALPHA: (160) implies:
% 244.76/51.25  | | | | | | | | | | | | |   (161)  op(e1, e3) = all_56_5
% 244.76/51.25  | | | | | | | | | | | | |   (162)  op(e1, all_56_5) = e1
% 244.76/51.25  | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | REF_CLOSE: (59), (100), (105), (161), (162) are inconsistent
% 244.76/51.25  | | | | | | | | | | | | |            by sub-proof #2243.
% 244.76/51.25  | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | Case 2:
% 244.76/51.25  | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | |   (163)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3)
% 244.76/51.25  | | | | | | | | | | | | |          = all_56_7 & $i(all_56_7)
% 244.76/51.25  | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | ALPHA: (163) implies:
% 244.76/51.25  | | | | | | | | | | | | |   (164)  op(e0, e3) = all_56_7
% 244.76/51.25  | | | | | | | | | | | | |   (165)  op(e0, all_56_7) = e0
% 244.76/51.25  | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | | REF_CLOSE: (1), (12), (18), (25), (30), (59), (98), (111),
% 244.76/51.25  | | | | | | | | | | | | |            (164), (165) are inconsistent by sub-proof #1952.
% 244.76/51.25  | | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | | 
% 244.76/51.25  | | | | | | | | | | | End of split
% 244.76/51.25  | | | | | | | | | | | 
% 244.76/51.26  | | | | | | | | | | End of split
% 244.76/51.26  | | | | | | | | | | 
% 244.76/51.26  | | | | | | | | | End of split
% 244.76/51.26  | | | | | | | | | 
% 244.76/51.26  | | | | | | | | Case 2:
% 244.76/51.26  | | | | | | | | | 
% 244.76/51.26  | | | | | | | | |   (166)  all_58_7 = e3 & op(e1, e2) = e3
% 244.76/51.26  | | | | | | | | | 
% 244.76/51.26  | | | | | | | | | ALPHA: (166) implies:
% 244.76/51.26  | | | | | | | | |   (167)  op(e1, e2) = e3
% 244.76/51.26  | | | | | | | | | 
% 244.76/51.26  | | | | | | | | | REF_CLOSE: (9), (59), (98), (167) are inconsistent by
% 244.76/51.26  | | | | | | | | |            sub-proof #2191.
% 244.76/51.26  | | | | | | | | | 
% 244.76/51.26  | | | | | | | | End of split
% 244.76/51.26  | | | | | | | | 
% 244.76/51.26  | | | | | | | Case 2:
% 244.76/51.26  | | | | | | | | 
% 244.76/51.26  | | | | | | | |   (168)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 &
% 244.76/51.26  | | | | | | | |            op(e1, e0) = e3)
% 244.76/51.26  | | | | | | | | 
% 244.76/51.26  | | | | | | | | REF_CLOSE: (39), (59), (61), (99), (101), (168) are inconsistent
% 244.76/51.26  | | | | | | | |            by sub-proof #2017.
% 244.76/51.26  | | | | | | | | 
% 244.76/51.26  | | | | | | | End of split
% 244.76/51.26  | | | | | | | 
% 244.76/51.26  | | | | | | Case 2:
% 244.76/51.26  | | | | | | | 
% 244.76/51.26  | | | | | | |   (169)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.76/51.26  | | | | | | | 
% 244.76/51.26  | | | | | | | REF_CLOSE: (44), (52), (56), (81), (169) are inconsistent by
% 244.76/51.26  | | | | | | |            sub-proof #1949.
% 244.76/51.26  | | | | | | | 
% 244.76/51.26  | | | | | | End of split
% 244.76/51.26  | | | | | | 
% 244.76/51.26  | | | | | End of split
% 244.76/51.26  | | | | | 
% 244.76/51.26  | | | | Case 2:
% 244.76/51.26  | | | | | 
% 244.76/51.26  | | | | |   (170)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 244.76/51.26  | | | | |              e3) = e1)
% 244.76/51.26  | | | | | 
% 244.76/51.26  | | | | | REF_CLOSE: (17), (59), (60), (81), (83), (170) are inconsistent by
% 244.76/51.26  | | | | |            sub-proof #1947.
% 244.76/51.26  | | | | | 
% 244.76/51.26  | | | | End of split
% 244.76/51.26  | | | | 
% 244.76/51.26  | | | Case 2:
% 244.76/51.26  | | | | 
% 244.76/51.26  | | | |   (171)  all_54_4 = e0
% 244.76/51.26  | | | | 
% 244.76/51.26  | | | | COMBINE_EQS: (23), (171) imply:
% 244.76/51.26  | | | |   (172)  all_52_1 = e0
% 244.76/51.26  | | | | 
% 244.76/51.26  | | | | REDUCE: (36), (172) imply:
% 244.76/51.26  | | | |   (173)  $false
% 244.76/51.26  | | | | 
% 244.76/51.26  | | | | CLOSE: (173) is inconsistent.
% 244.76/51.26  | | | | 
% 244.76/51.26  | | | End of split
% 244.76/51.26  | | | 
% 244.76/51.26  | | End of split
% 244.76/51.26  | | 
% 244.76/51.26  | End of split
% 244.76/51.26  | 
% 244.76/51.26  End of proof
% 244.76/51.26  
% 244.76/51.26  Sub-proof #1947 shows that the following formulas are inconsistent:
% 244.76/51.26  ----------------------------------------------------------------
% 244.76/51.26    (1)   ~ (all_52_3 = e1)
% 244.76/51.26    (2)  op(e0, e3) = all_52_3
% 244.76/51.26    (3)   ~ (all_52_2 = e1)
% 244.76/51.26    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 244.76/51.26    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.26    (6)  op(e1, e3) = all_52_2
% 244.76/51.26  
% 244.76/51.26  Begin of proof
% 244.76/51.26  | 
% 244.76/51.26  | BETA: splitting (4) gives:
% 244.76/51.26  | 
% 244.76/51.26  | Case 1:
% 244.76/51.26  | | 
% 244.76/51.26  | |   (7)  all_58_6 = e1 & op(e1, e3) = e1
% 244.76/51.26  | | 
% 244.76/51.26  | | ALPHA: (7) implies:
% 244.76/51.26  | |   (8)  op(e1, e3) = e1
% 244.76/51.26  | | 
% 244.76/51.26  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #1948.
% 244.76/51.26  | | 
% 244.76/51.26  | Case 2:
% 244.76/51.26  | | 
% 244.76/51.26  | |   (9)  all_58_12 = e1 & op(e0, e3) = e1
% 244.76/51.26  | | 
% 244.76/51.26  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2276.
% 244.76/51.26  | | 
% 244.76/51.26  | End of split
% 244.76/51.26  | 
% 244.76/51.26  End of proof
% 244.76/51.26  
% 244.76/51.26  Sub-proof #1948 shows that the following formulas are inconsistent:
% 244.76/51.26  ----------------------------------------------------------------
% 244.76/51.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.26    (2)  op(e1, e3) = all_52_2
% 244.76/51.26    (3)  op(e1, e3) = e1
% 244.76/51.26    (4)   ~ (all_52_2 = e1)
% 244.76/51.26  
% 244.76/51.26  Begin of proof
% 244.76/51.26  | 
% 244.76/51.26  | GROUND_INST: instantiating (1) with all_52_2, e1, e3, e1, simplifying with
% 244.76/51.26  |              (2), (3) gives:
% 244.76/51.26  |   (5)  all_52_2 = e1
% 244.76/51.26  | 
% 244.76/51.26  | REDUCE: (4), (5) imply:
% 244.76/51.26  |   (6)  $false
% 244.76/51.26  | 
% 244.76/51.26  | CLOSE: (6) is inconsistent.
% 244.76/51.26  | 
% 244.76/51.26  End of proof
% 244.76/51.26  
% 244.76/51.26  Sub-proof #1949 shows that the following formulas are inconsistent:
% 244.76/51.26  ----------------------------------------------------------------
% 244.76/51.26    (1)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.76/51.26    (2)   ~ (all_52_2 = e1)
% 244.76/51.26    (3)   ~ (all_52_2 = e0)
% 244.76/51.26    (4)   ~ (all_52_2 = e2)
% 244.76/51.26    (5)  all_54_8 = all_52_2
% 244.76/51.26  
% 244.76/51.26  Begin of proof
% 244.76/51.26  | 
% 244.76/51.26  | BETA: splitting (1) gives:
% 244.76/51.26  | 
% 244.76/51.26  | Case 1:
% 244.76/51.26  | | 
% 244.76/51.26  | |   (6)  all_54_8 = e2
% 244.76/51.26  | | 
% 244.76/51.26  | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #2007.
% 244.76/51.26  | | 
% 244.76/51.26  | Case 2:
% 244.76/51.26  | | 
% 244.76/51.26  | |   (7)  all_54_8 = e1 | all_54_8 = e0
% 244.76/51.26  | | 
% 244.76/51.26  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #1950.
% 244.76/51.26  | | 
% 244.76/51.26  | End of split
% 244.76/51.26  | 
% 244.76/51.26  End of proof
% 244.76/51.26  
% 244.76/51.26  Sub-proof #1950 shows that the following formulas are inconsistent:
% 244.76/51.26  ----------------------------------------------------------------
% 244.76/51.26    (1)  all_54_8 = e1 | all_54_8 = e0
% 244.76/51.26    (2)  all_54_8 = all_52_2
% 244.76/51.26    (3)   ~ (all_52_2 = e1)
% 244.76/51.26    (4)   ~ (all_52_2 = e0)
% 244.76/51.26  
% 244.76/51.26  Begin of proof
% 244.76/51.26  | 
% 244.76/51.26  | BETA: splitting (1) gives:
% 244.76/51.26  | 
% 244.76/51.26  | Case 1:
% 244.76/51.26  | | 
% 244.76/51.26  | |   (5)  all_54_8 = e1
% 244.76/51.26  | | 
% 244.76/51.26  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1951.
% 244.76/51.26  | | 
% 244.76/51.26  | Case 2:
% 244.76/51.26  | | 
% 244.76/51.26  | |   (6)  all_54_8 = e0
% 244.76/51.26  | | 
% 244.76/51.26  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2006.
% 244.76/51.26  | | 
% 244.76/51.26  | End of split
% 244.76/51.26  | 
% 244.76/51.26  End of proof
% 244.76/51.26  
% 244.76/51.26  Sub-proof #1951 shows that the following formulas are inconsistent:
% 244.76/51.26  ----------------------------------------------------------------
% 244.76/51.26    (1)  all_54_8 = all_52_2
% 244.76/51.26    (2)  all_54_8 = e1
% 244.76/51.26    (3)   ~ (all_52_2 = e1)
% 244.76/51.26  
% 244.76/51.26  Begin of proof
% 244.76/51.26  | 
% 244.76/51.26  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.26  |   (4)  all_52_2 = e1
% 244.76/51.26  | 
% 244.76/51.26  | SIMP: (4) implies:
% 244.76/51.26  |   (5)  all_52_2 = e1
% 244.76/51.26  | 
% 244.76/51.26  | REDUCE: (3), (5) imply:
% 244.76/51.26  |   (6)  $false
% 244.76/51.26  | 
% 244.76/51.26  | CLOSE: (6) is inconsistent.
% 244.76/51.26  | 
% 244.76/51.26  End of proof
% 244.76/51.26  
% 244.76/51.26  Sub-proof #1952 shows that the following formulas are inconsistent:
% 244.76/51.26  ----------------------------------------------------------------
% 244.76/51.26    (1)  op(e0, e0) = e1
% 244.76/51.26    (2)   ~ (all_52_6 = e2)
% 244.76/51.26    (3)   ~ (all_52_6 = e0)
% 244.76/51.26    (4)  op(e0, e3) = all_56_7
% 244.76/51.26    (5)  all_54_9 = all_52_6
% 244.76/51.26    (6)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 244.76/51.26    (7)  op(e0, e3) = e0
% 244.76/51.26    (8)   ~ (all_52_6 = e3)
% 244.76/51.26    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.26    (10)  op(e0, all_56_7) = e0
% 244.76/51.26  
% 244.76/51.26  Begin of proof
% 244.76/51.26  | 
% 244.76/51.26  | BETA: splitting (6) gives:
% 244.76/51.26  | 
% 244.76/51.26  | Case 1:
% 244.76/51.26  | | 
% 244.76/51.26  | |   (11)  all_54_9 = e3
% 244.76/51.26  | | 
% 244.76/51.26  | | REF_CLOSE: (5), (8), (11) are inconsistent by sub-proof #1955.
% 244.76/51.26  | | 
% 244.76/51.26  | Case 2:
% 244.76/51.26  | | 
% 244.76/51.26  | |   (12)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 244.76/51.26  | | 
% 244.76/51.26  | | BETA: splitting (12) gives:
% 244.76/51.26  | | 
% 244.76/51.26  | | Case 1:
% 244.76/51.26  | | | 
% 244.76/51.26  | | |   (13)  all_54_9 = e2
% 244.76/51.26  | | | 
% 244.76/51.26  | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #1954.
% 244.76/51.26  | | | 
% 244.76/51.26  | | Case 2:
% 244.76/51.26  | | | 
% 244.76/51.26  | | |   (14)  all_54_9 = e1 | all_54_9 = e0
% 244.76/51.27  | | | 
% 244.76/51.27  | | | BETA: splitting (14) gives:
% 244.76/51.27  | | | 
% 244.76/51.27  | | | Case 1:
% 244.76/51.27  | | | | 
% 244.76/51.27  | | | |   (15)  all_54_9 = e1
% 244.76/51.27  | | | | 
% 244.76/51.27  | | | | COMBINE_EQS: (5), (15) imply:
% 244.76/51.27  | | | |   (16)  all_52_6 = e1
% 244.76/51.27  | | | | 
% 244.76/51.27  | | | | SIMP: (16) implies:
% 244.76/51.27  | | | |   (17)  all_52_6 = e1
% 244.76/51.27  | | | | 
% 244.76/51.27  | | | | REDUCE: (3), (17) imply:
% 244.76/51.27  | | | |   (18)   ~ (e1 = e0)
% 244.76/51.27  | | | | 
% 244.76/51.27  | | | | GROUND_INST: instantiating (9) with e0, all_56_7, e3, e0, simplifying
% 244.76/51.27  | | | |              with (4), (7) gives:
% 244.76/51.27  | | | |   (19)  all_56_7 = e0
% 244.76/51.27  | | | | 
% 244.76/51.27  | | | | REDUCE: (10), (19) imply:
% 244.76/51.27  | | | |   (20)  op(e0, e0) = e0
% 244.76/51.27  | | | | 
% 244.76/51.27  | | | | REF_CLOSE: (1), (9), (18), (20) are inconsistent by sub-proof #2274.
% 244.76/51.27  | | | | 
% 244.76/51.27  | | | Case 2:
% 244.76/51.27  | | | | 
% 244.76/51.27  | | | |   (21)  all_54_9 = e0
% 244.76/51.27  | | | | 
% 244.76/51.27  | | | | REF_CLOSE: (3), (5), (21) are inconsistent by sub-proof #1953.
% 244.76/51.27  | | | | 
% 244.76/51.27  | | | End of split
% 244.76/51.27  | | | 
% 244.76/51.27  | | End of split
% 244.76/51.27  | | 
% 244.76/51.27  | End of split
% 244.76/51.27  | 
% 244.76/51.27  End of proof
% 244.76/51.27  
% 244.76/51.27  Sub-proof #1953 shows that the following formulas are inconsistent:
% 244.76/51.27  ----------------------------------------------------------------
% 244.76/51.27    (1)  all_54_9 = all_52_6
% 244.76/51.27    (2)  all_54_9 = e0
% 244.76/51.27    (3)   ~ (all_52_6 = e0)
% 244.76/51.27  
% 244.76/51.27  Begin of proof
% 244.76/51.27  | 
% 244.76/51.27  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.27  |   (4)  all_52_6 = e0
% 244.76/51.27  | 
% 244.76/51.27  | SIMP: (4) implies:
% 244.76/51.27  |   (5)  all_52_6 = e0
% 244.76/51.27  | 
% 244.76/51.27  | REDUCE: (3), (5) imply:
% 244.76/51.27  |   (6)  $false
% 244.76/51.27  | 
% 244.76/51.27  | CLOSE: (6) is inconsistent.
% 244.76/51.27  | 
% 244.76/51.27  End of proof
% 244.76/51.27  
% 244.76/51.27  Sub-proof #1954 shows that the following formulas are inconsistent:
% 244.76/51.27  ----------------------------------------------------------------
% 244.76/51.27    (1)  all_54_9 = all_52_6
% 244.76/51.27    (2)  all_54_9 = e2
% 244.76/51.27    (3)   ~ (all_52_6 = e2)
% 244.76/51.27  
% 244.76/51.27  Begin of proof
% 244.76/51.27  | 
% 244.76/51.27  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.27  |   (4)  all_52_6 = e2
% 244.76/51.27  | 
% 244.76/51.27  | SIMP: (4) implies:
% 244.76/51.27  |   (5)  all_52_6 = e2
% 244.76/51.27  | 
% 244.76/51.27  | REDUCE: (3), (5) imply:
% 244.76/51.27  |   (6)  $false
% 244.76/51.27  | 
% 244.76/51.27  | CLOSE: (6) is inconsistent.
% 244.76/51.27  | 
% 244.76/51.27  End of proof
% 244.76/51.27  
% 244.76/51.27  Sub-proof #1955 shows that the following formulas are inconsistent:
% 244.76/51.27  ----------------------------------------------------------------
% 244.76/51.27    (1)  all_54_9 = all_52_6
% 244.76/51.27    (2)  all_54_9 = e3
% 244.76/51.27    (3)   ~ (all_52_6 = e3)
% 244.76/51.27  
% 244.76/51.27  Begin of proof
% 244.76/51.27  | 
% 244.76/51.27  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.27  |   (4)  all_52_6 = e3
% 244.76/51.27  | 
% 244.76/51.27  | SIMP: (4) implies:
% 244.76/51.27  |   (5)  all_52_6 = e3
% 244.76/51.27  | 
% 244.76/51.27  | REDUCE: (3), (5) imply:
% 244.76/51.27  |   (6)  $false
% 244.76/51.27  | 
% 244.76/51.27  | CLOSE: (6) is inconsistent.
% 244.76/51.27  | 
% 244.76/51.27  End of proof
% 244.76/51.27  
% 244.76/51.27  Sub-proof #1956 shows that the following formulas are inconsistent:
% 244.76/51.27  ----------------------------------------------------------------
% 244.76/51.27    (1)   ~ (e3 = e0)
% 244.76/51.27    (2)  all_58_9 = e0
% 244.76/51.27    (3)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 244.76/51.27         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.76/51.27    (4)  op(e3, e1) = all_52_8
% 244.76/51.27    (5)   ~ (e3 = e2)
% 244.76/51.27    (6)  op(e3, e3) = e2
% 244.76/51.27    (7)   ~ (all_52_4 = e3)
% 244.76/51.27    (8)  op(e3, e2) = all_52_4
% 244.76/51.27    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.27    (10)   ~ (all_52_8 = e3)
% 244.76/51.27  
% 244.76/51.27  Begin of proof
% 244.76/51.27  | 
% 244.76/51.27  | BETA: splitting (3) gives:
% 244.76/51.27  | 
% 244.76/51.27  | Case 1:
% 244.76/51.27  | | 
% 244.76/51.27  | |   (11)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 244.76/51.27  | |           e3)
% 244.76/51.27  | | 
% 244.76/51.27  | | REF_CLOSE: (5), (6), (7), (8), (9), (11) are inconsistent by sub-proof
% 244.76/51.27  | |            #1959.
% 244.76/51.27  | | 
% 244.76/51.27  | Case 2:
% 244.76/51.27  | | 
% 244.76/51.27  | |   (12)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 244.76/51.27  | |           e3)
% 244.76/51.27  | | 
% 244.76/51.27  | | REF_CLOSE: (1), (2), (4), (9), (10), (12) are inconsistent by sub-proof
% 244.76/51.27  | |            #1957.
% 244.76/51.27  | | 
% 244.76/51.27  | End of split
% 244.76/51.27  | 
% 244.76/51.27  End of proof
% 244.76/51.27  
% 244.76/51.27  Sub-proof #1957 shows that the following formulas are inconsistent:
% 244.76/51.27  ----------------------------------------------------------------
% 244.76/51.27    (1)   ~ (e3 = e0)
% 244.76/51.27    (2)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 244.76/51.27    (3)  all_58_9 = e0
% 244.76/51.27    (4)  op(e3, e1) = all_52_8
% 244.76/51.27    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.27    (6)   ~ (all_52_8 = e3)
% 244.76/51.27  
% 244.76/51.27  Begin of proof
% 244.76/51.27  | 
% 244.76/51.27  | BETA: splitting (2) gives:
% 244.76/51.27  | 
% 244.76/51.27  | Case 1:
% 244.76/51.27  | | 
% 244.76/51.27  | |   (7)  all_58_4 = e3 & op(e3, e1) = e3
% 244.76/51.27  | | 
% 244.76/51.27  | | ALPHA: (7) implies:
% 244.76/51.27  | |   (8)  op(e3, e1) = e3
% 244.76/51.27  | | 
% 244.76/51.27  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2260.
% 244.76/51.27  | | 
% 244.76/51.27  | Case 2:
% 244.76/51.27  | | 
% 244.76/51.27  | |   (9)  all_58_9 = e3 & op(e3, e0) = e3
% 244.76/51.27  | | 
% 244.76/51.27  | | ALPHA: (9) implies:
% 244.76/51.27  | |   (10)  all_58_9 = e3
% 244.76/51.27  | | 
% 244.76/51.27  | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #1958.
% 244.76/51.27  | | 
% 244.76/51.27  | End of split
% 244.76/51.27  | 
% 244.76/51.27  End of proof
% 244.76/51.27  
% 244.76/51.27  Sub-proof #1958 shows that the following formulas are inconsistent:
% 244.76/51.27  ----------------------------------------------------------------
% 244.76/51.27    (1)  all_58_9 = e3
% 244.76/51.27    (2)  all_58_9 = e0
% 244.76/51.27    (3)   ~ (e3 = e0)
% 244.76/51.27  
% 244.76/51.27  Begin of proof
% 244.76/51.27  | 
% 244.76/51.27  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.27  |   (4)  e3 = e0
% 244.76/51.27  | 
% 244.76/51.27  | SIMP: (4) implies:
% 244.76/51.27  |   (5)  e3 = e0
% 244.76/51.27  | 
% 244.76/51.27  | REDUCE: (3), (5) imply:
% 244.76/51.27  |   (6)  $false
% 244.76/51.27  | 
% 244.76/51.27  | CLOSE: (6) is inconsistent.
% 244.76/51.27  | 
% 244.76/51.27  End of proof
% 244.76/51.27  
% 244.76/51.27  Sub-proof #1959 shows that the following formulas are inconsistent:
% 244.76/51.27  ----------------------------------------------------------------
% 244.76/51.27    (1)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 244.76/51.27    (2)   ~ (e3 = e2)
% 244.76/51.27    (3)  op(e3, e3) = e2
% 244.76/51.27    (4)   ~ (all_52_4 = e3)
% 244.76/51.27    (5)  op(e3, e2) = all_52_4
% 244.76/51.27    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.27  
% 244.76/51.27  Begin of proof
% 244.76/51.27  | 
% 244.76/51.27  | BETA: splitting (1) gives:
% 244.76/51.27  | 
% 244.76/51.27  | Case 1:
% 244.76/51.27  | | 
% 244.76/51.27  | |   (7)  all_58_0 = e3 & op(e3, e3) = e3
% 244.76/51.27  | | 
% 244.76/51.27  | | ALPHA: (7) implies:
% 244.76/51.27  | |   (8)  op(e3, e3) = e3
% 244.76/51.27  | | 
% 244.76/51.27  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #2194.
% 244.76/51.27  | | 
% 244.76/51.27  | Case 2:
% 244.76/51.27  | | 
% 244.76/51.27  | |   (9)  all_58_1 = e3 & op(e3, e2) = e3
% 244.76/51.27  | | 
% 244.76/51.27  | | ALPHA: (9) implies:
% 244.76/51.28  | |   (10)  op(e3, e2) = e3
% 244.76/51.28  | | 
% 244.76/51.28  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #2192.
% 244.76/51.28  | | 
% 244.76/51.28  | End of split
% 244.76/51.28  | 
% 244.76/51.28  End of proof
% 244.76/51.28  
% 244.76/51.28  Sub-proof #1960 shows that the following formulas are inconsistent:
% 244.76/51.28  ----------------------------------------------------------------
% 244.76/51.28    (1)  op(e1, e0) = all_52_14
% 244.76/51.28    (2)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.76/51.28             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 244.76/51.28           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 244.76/51.28             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 244.76/51.28           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.28    (3)   ~ (all_52_14 = e0)
% 244.76/51.28    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.28    (5)  op(e1, e0) = e2
% 244.76/51.28    (6)   ~ (e2 = e1)
% 244.76/51.28  
% 244.76/51.28  Begin of proof
% 244.76/51.28  | 
% 244.76/51.28  | BETA: splitting (2) gives:
% 244.76/51.28  | 
% 244.76/51.28  | Case 1:
% 244.76/51.28  | | 
% 244.76/51.28  | |   (7)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.76/51.28  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 244.76/51.28  | |        & op(e0, e1) = e1
% 244.76/51.28  | | 
% 244.76/51.28  | | ALPHA: (7) implies:
% 244.76/51.28  | |   (8)  op(e1, e0) = e1
% 244.76/51.28  | | 
% 244.76/51.28  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2019.
% 244.76/51.28  | | 
% 244.76/51.28  | Case 2:
% 244.76/51.28  | | 
% 244.76/51.28  | |   (9)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.76/51.28  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 244.76/51.28  | |        & op(e0, e1) = e0
% 244.76/51.28  | | 
% 244.76/51.28  | | ALPHA: (9) implies:
% 244.76/51.28  | |   (10)  op(e1, e0) = e0
% 244.76/51.28  | | 
% 244.76/51.28  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #2323.
% 244.76/51.28  | | 
% 244.76/51.28  | End of split
% 244.76/51.28  | 
% 244.76/51.28  End of proof
% 244.76/51.28  
% 244.76/51.28  Sub-proof #1961 shows that the following formulas are inconsistent:
% 244.76/51.28  ----------------------------------------------------------------
% 244.76/51.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.28    (2)  op(e0, e2) = e3
% 244.76/51.28    (3)  op(e0, e2) = e0
% 244.76/51.28    (4)   ~ (e3 = e0)
% 244.76/51.28  
% 244.76/51.28  Begin of proof
% 244.76/51.28  | 
% 244.76/51.28  | GROUND_INST: instantiating (1) with e3, e0, e2, e0, simplifying with (2), (3)
% 244.76/51.28  |              gives:
% 244.76/51.28  |   (5)  e3 = e0
% 244.76/51.28  | 
% 244.76/51.28  | REDUCE: (4), (5) imply:
% 244.76/51.28  |   (6)  $false
% 244.76/51.28  | 
% 244.76/51.28  | CLOSE: (6) is inconsistent.
% 244.76/51.28  | 
% 244.76/51.28  End of proof
% 244.76/51.28  
% 244.76/51.28  Sub-proof #1962 shows that the following formulas are inconsistent:
% 244.76/51.28  ----------------------------------------------------------------
% 244.76/51.28    (1)   ~ (e2 = e0)
% 244.76/51.28    (2)  all_54_13 = all_52_7
% 244.76/51.28    (3)  op(e1, e2) = all_52_6
% 244.76/51.28    (4)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.76/51.28         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.76/51.28    (5)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.76/51.28    (6)  op(e0, e3) = all_52_3
% 244.76/51.28    (7)   ~ (all_52_6 = e0)
% 244.76/51.28    (8)   ~ (all_52_3 = all_52_7)
% 244.76/51.28    (9)   ~ (all_52_7 = e1)
% 244.76/51.28    (10)  op(e0, e3) = e0
% 244.76/51.28    (11)  op(e3, e0) = all_52_12
% 244.76/51.28    (12)   ~ (all_52_4 = all_52_12)
% 244.76/51.28    (13)  op(e0, e2) = all_52_7
% 244.76/51.28    (14)  all_54_1 = all_52_4
% 244.76/51.28    (15)  op(e3, e2) = all_52_4
% 244.76/51.28    (16)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.76/51.28    (17)   ~ (all_52_4 = e2)
% 244.76/51.28    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.28    (19)  op(e3, e0) = e0
% 244.76/51.28    (20)   ~ (all_52_4 = e1)
% 244.76/51.28    (21)  op(e2, e2) = e2
% 244.76/51.28    (22)   ~ (all_52_4 = all_52_7)
% 244.76/51.28  
% 244.76/51.28  Begin of proof
% 244.76/51.28  | 
% 244.76/51.28  | GROUND_INST: instantiating (18) with all_52_3, e0, e3, e0, simplifying with
% 244.76/51.28  |              (6), (10) gives:
% 244.76/51.28  |   (23)  all_52_3 = e0
% 244.76/51.28  | 
% 244.76/51.28  | GROUND_INST: instantiating (18) with all_52_12, e0, e0, e3, simplifying with
% 244.76/51.28  |              (11), (19) gives:
% 244.76/51.28  |   (24)  all_52_12 = e0
% 244.76/51.28  | 
% 244.76/51.28  | REDUCE: (8), (23) imply:
% 244.76/51.28  |   (25)   ~ (all_52_7 = e0)
% 244.76/51.28  | 
% 244.76/51.28  | SIMP: (25) implies:
% 244.76/51.28  |   (26)   ~ (all_52_7 = e0)
% 244.76/51.28  | 
% 244.76/51.28  | REDUCE: (12), (24) imply:
% 244.76/51.28  |   (27)   ~ (all_52_4 = e0)
% 244.76/51.28  | 
% 244.76/51.28  | BETA: splitting (4) gives:
% 244.76/51.28  | 
% 244.76/51.28  | Case 1:
% 244.76/51.28  | | 
% 244.76/51.28  | |   (28)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 244.76/51.28  | |           e0)
% 244.76/51.28  | | 
% 244.76/51.28  | | REF_CLOSE: (1), (15), (18), (21), (27), (28) are inconsistent by sub-proof
% 244.76/51.28  | |            #1967.
% 244.76/51.28  | | 
% 244.76/51.28  | Case 2:
% 244.76/51.28  | | 
% 244.76/51.28  | |   (29)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 244.76/51.28  | |           e0)
% 244.76/51.28  | | 
% 244.76/51.28  | | BETA: splitting (29) gives:
% 244.76/51.28  | | 
% 244.76/51.28  | | Case 1:
% 244.76/51.28  | | | 
% 244.76/51.28  | | |   (30)  all_58_7 = e0 & op(e1, e2) = e0
% 244.76/51.28  | | | 
% 244.76/51.28  | | | REF_CLOSE: (3), (7), (18), (30) are inconsistent by sub-proof #2022.
% 244.76/51.28  | | | 
% 244.76/51.28  | | Case 2:
% 244.76/51.28  | | | 
% 244.76/51.28  | | |   (31)  all_58_13 = e0 & op(e0, e2) = e0
% 244.76/51.28  | | | 
% 244.76/51.28  | | | ALPHA: (31) implies:
% 244.76/51.28  | | |   (32)  op(e0, e2) = e0
% 244.76/51.28  | | | 
% 244.76/51.28  | | | REF_CLOSE: (2), (5), (9), (13), (14), (16), (17), (18), (20), (22), (26),
% 244.76/51.28  | | |            (27), (32) are inconsistent by sub-proof #1963.
% 244.76/51.28  | | | 
% 244.76/51.28  | | End of split
% 244.76/51.28  | | 
% 244.76/51.28  | End of split
% 244.76/51.28  | 
% 244.76/51.28  End of proof
% 244.76/51.28  
% 244.76/51.28  Sub-proof #1963 shows that the following formulas are inconsistent:
% 244.76/51.28  ----------------------------------------------------------------
% 244.76/51.28    (1)  all_54_13 = all_52_7
% 244.76/51.28    (2)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.76/51.28    (3)   ~ (all_52_7 = e1)
% 244.76/51.28    (4)  op(e0, e2) = e0
% 244.76/51.28    (5)  op(e0, e2) = all_52_7
% 244.76/51.28    (6)  all_54_1 = all_52_4
% 244.76/51.28    (7)   ~ (all_52_7 = e0)
% 244.76/51.28    (8)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.76/51.28    (9)   ~ (all_52_4 = e2)
% 244.76/51.28    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.28    (11)   ~ (all_52_4 = e1)
% 244.76/51.28    (12)   ~ (all_52_4 = e0)
% 244.76/51.28    (13)   ~ (all_52_4 = all_52_7)
% 244.76/51.28  
% 244.76/51.28  Begin of proof
% 244.76/51.28  | 
% 244.76/51.28  | BETA: splitting (2) gives:
% 244.76/51.28  | 
% 244.76/51.28  | Case 1:
% 244.76/51.28  | | 
% 244.76/51.28  | |   (14)  all_54_1 = e3
% 244.76/51.28  | | 
% 244.76/51.28  | | COMBINE_EQS: (6), (14) imply:
% 244.76/51.28  | |   (15)  all_52_4 = e3
% 244.76/51.28  | | 
% 244.76/51.28  | | REDUCE: (13), (15) imply:
% 244.76/51.28  | |   (16)   ~ (all_52_7 = e3)
% 244.76/51.28  | | 
% 244.76/51.28  | | SIMP: (16) implies:
% 244.76/51.28  | |   (17)   ~ (all_52_7 = e3)
% 244.76/51.28  | | 
% 244.76/51.28  | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (17) are inconsistent by
% 244.76/51.28  | |            sub-proof #1964.
% 244.76/51.28  | | 
% 244.76/51.28  | Case 2:
% 244.76/51.29  | | 
% 244.76/51.29  | |   (18)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.76/51.29  | | 
% 244.76/51.29  | | REF_CLOSE: (6), (9), (11), (12), (18) are inconsistent by sub-proof #2048.
% 244.76/51.29  | | 
% 244.76/51.29  | End of split
% 244.76/51.29  | 
% 244.76/51.29  End of proof
% 244.76/51.29  
% 244.76/51.29  Sub-proof #1964 shows that the following formulas are inconsistent:
% 244.76/51.29  ----------------------------------------------------------------
% 244.76/51.29    (1)  all_54_13 = all_52_7
% 244.76/51.29    (2)   ~ (all_52_7 = e3)
% 244.76/51.29    (3)   ~ (all_52_7 = e1)
% 244.76/51.29    (4)  op(e0, e2) = e0
% 244.76/51.29    (5)  op(e0, e2) = all_52_7
% 244.76/51.29    (6)   ~ (all_52_7 = e0)
% 244.76/51.29    (7)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.76/51.29    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.29  
% 244.76/51.29  Begin of proof
% 244.76/51.29  | 
% 244.76/51.29  | BETA: splitting (7) gives:
% 244.76/51.29  | 
% 244.76/51.29  | Case 1:
% 244.76/51.29  | | 
% 244.76/51.29  | |   (9)  all_54_13 = e3
% 244.76/51.29  | | 
% 244.76/51.29  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #2010.
% 244.76/51.29  | | 
% 244.76/51.29  | Case 2:
% 244.76/51.29  | | 
% 244.76/51.29  | |   (10)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.76/51.29  | | 
% 244.76/51.29  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10) are inconsistent by sub-proof
% 244.76/51.29  | |            #1965.
% 244.76/51.29  | | 
% 244.76/51.29  | End of split
% 244.76/51.29  | 
% 244.76/51.29  End of proof
% 244.76/51.29  
% 244.76/51.29  Sub-proof #1965 shows that the following formulas are inconsistent:
% 244.76/51.29  ----------------------------------------------------------------
% 244.76/51.29    (1)  all_54_13 = all_52_7
% 244.76/51.29    (2)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.76/51.29    (3)   ~ (all_52_7 = e1)
% 244.76/51.29    (4)  op(e0, e2) = e0
% 244.76/51.29    (5)  op(e0, e2) = all_52_7
% 244.76/51.29    (6)   ~ (all_52_7 = e0)
% 244.76/51.29    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.29  
% 244.76/51.29  Begin of proof
% 244.76/51.29  | 
% 244.76/51.29  | BETA: splitting (2) gives:
% 244.76/51.29  | 
% 244.76/51.29  | Case 1:
% 244.76/51.29  | | 
% 244.76/51.29  | |   (8)  all_54_13 = e2
% 244.76/51.29  | | 
% 244.76/51.29  | | COMBINE_EQS: (1), (8) imply:
% 244.76/51.29  | |   (9)  all_52_7 = e2
% 244.76/51.29  | | 
% 244.76/51.29  | | SIMP: (9) implies:
% 244.76/51.29  | |   (10)  all_52_7 = e2
% 244.76/51.29  | | 
% 244.76/51.29  | | REDUCE: (6), (10) imply:
% 244.76/51.29  | |   (11)   ~ (e2 = e0)
% 244.76/51.29  | | 
% 244.76/51.29  | | REDUCE: (5), (10) imply:
% 244.76/51.29  | |   (12)  op(e0, e2) = e2
% 244.76/51.29  | | 
% 244.76/51.29  | | REF_CLOSE: (4), (7), (11), (12) are inconsistent by sub-proof #2132.
% 244.76/51.29  | | 
% 244.76/51.29  | Case 2:
% 244.76/51.29  | | 
% 244.76/51.29  | |   (13)  all_54_13 = e1 | all_54_13 = e0
% 244.76/51.29  | | 
% 244.76/51.29  | | BETA: splitting (13) gives:
% 244.76/51.29  | | 
% 244.76/51.29  | | Case 1:
% 244.76/51.29  | | | 
% 244.76/51.29  | | |   (14)  all_54_13 = e1
% 244.76/51.29  | | | 
% 244.76/51.29  | | | REF_CLOSE: (1), (3), (14) are inconsistent by sub-proof #1966.
% 244.76/51.29  | | | 
% 244.76/51.29  | | Case 2:
% 244.76/51.29  | | | 
% 244.76/51.29  | | |   (15)  all_54_13 = e0
% 244.76/51.29  | | | 
% 244.76/51.29  | | | REF_CLOSE: (1), (6), (15) are inconsistent by sub-proof #2008.
% 244.76/51.29  | | | 
% 244.76/51.29  | | End of split
% 244.76/51.29  | | 
% 244.76/51.29  | End of split
% 244.76/51.29  | 
% 244.76/51.29  End of proof
% 244.76/51.29  
% 244.76/51.29  Sub-proof #1966 shows that the following formulas are inconsistent:
% 244.76/51.29  ----------------------------------------------------------------
% 244.76/51.29    (1)  all_54_13 = all_52_7
% 244.76/51.29    (2)  all_54_13 = e1
% 244.76/51.29    (3)   ~ (all_52_7 = e1)
% 244.76/51.29  
% 244.76/51.29  Begin of proof
% 244.76/51.29  | 
% 244.76/51.29  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.29  |   (4)  all_52_7 = e1
% 244.76/51.29  | 
% 244.76/51.29  | SIMP: (4) implies:
% 244.76/51.29  |   (5)  all_52_7 = e1
% 244.76/51.29  | 
% 244.76/51.29  | REDUCE: (3), (5) imply:
% 244.76/51.29  |   (6)  $false
% 244.76/51.29  | 
% 244.76/51.29  | CLOSE: (6) is inconsistent.
% 244.76/51.29  | 
% 244.76/51.29  End of proof
% 244.76/51.29  
% 244.76/51.29  Sub-proof #1967 shows that the following formulas are inconsistent:
% 244.76/51.29  ----------------------------------------------------------------
% 244.76/51.29    (1)   ~ (e2 = e0)
% 244.76/51.29    (2)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 244.76/51.29    (3)  op(e3, e2) = all_52_4
% 244.76/51.29    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.29    (5)  op(e2, e2) = e2
% 244.76/51.29    (6)   ~ (all_52_4 = e0)
% 244.76/51.29  
% 244.76/51.29  Begin of proof
% 244.76/51.29  | 
% 244.76/51.29  | BETA: splitting (2) gives:
% 244.76/51.29  | 
% 244.76/51.29  | Case 1:
% 244.76/51.29  | | 
% 244.76/51.29  | |   (7)  all_58_1 = e0 & op(e3, e2) = e0
% 244.76/51.29  | | 
% 244.76/51.29  | | REF_CLOSE: (3), (4), (6), (7) are inconsistent by sub-proof #1968.
% 244.76/51.29  | | 
% 244.76/51.29  | Case 2:
% 244.76/51.29  | | 
% 244.76/51.29  | |   (8)  all_58_3 = e0 & op(e2, e2) = e0
% 244.76/51.29  | | 
% 244.76/51.29  | | ALPHA: (8) implies:
% 244.76/51.29  | |   (9)  op(e2, e2) = e0
% 244.76/51.29  | | 
% 244.76/51.29  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2137.
% 244.76/51.29  | | 
% 244.76/51.29  | End of split
% 244.76/51.29  | 
% 244.76/51.29  End of proof
% 244.76/51.29  
% 244.76/51.29  Sub-proof #1968 shows that the following formulas are inconsistent:
% 244.76/51.29  ----------------------------------------------------------------
% 244.76/51.29    (1)  all_58_1 = e0 & op(e3, e2) = e0
% 244.76/51.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.29    (3)  op(e3, e2) = all_52_4
% 244.76/51.29    (4)   ~ (all_52_4 = e0)
% 244.76/51.29  
% 244.76/51.29  Begin of proof
% 244.76/51.29  | 
% 244.76/51.29  | ALPHA: (1) implies:
% 244.76/51.29  |   (5)  op(e3, e2) = e0
% 244.76/51.29  | 
% 244.76/51.29  | GROUND_INST: instantiating (2) with all_52_4, e0, e2, e3, simplifying with
% 244.76/51.29  |              (3), (5) gives:
% 244.76/51.29  |   (6)  all_52_4 = e0
% 244.76/51.29  | 
% 244.76/51.29  | REDUCE: (4), (6) imply:
% 244.76/51.29  |   (7)  $false
% 244.76/51.29  | 
% 244.76/51.29  | CLOSE: (7) is inconsistent.
% 244.76/51.29  | 
% 244.76/51.29  End of proof
% 244.76/51.29  
% 244.76/51.29  Sub-proof #1969 shows that the following formulas are inconsistent:
% 244.76/51.29  ----------------------------------------------------------------
% 244.76/51.29    (1)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 244.76/51.29    (2)  op(e1, e2) = all_52_6
% 244.76/51.29    (3)   ~ (e3 = e1)
% 244.76/51.29    (4)  op(e1, e3) = e1
% 244.76/51.29    (5)   ~ (all_52_6 = e3)
% 244.76/51.29    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.29  
% 244.76/51.29  Begin of proof
% 244.76/51.29  | 
% 244.76/51.29  | BETA: splitting (1) gives:
% 244.76/51.29  | 
% 244.76/51.29  | Case 1:
% 244.76/51.29  | | 
% 244.76/51.29  | |   (7)  all_58_6 = e3 & op(e1, e3) = e3
% 244.76/51.29  | | 
% 244.76/51.29  | | ALPHA: (7) implies:
% 244.76/51.29  | |   (8)  op(e1, e3) = e3
% 244.76/51.29  | | 
% 244.76/51.29  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #2225.
% 244.76/51.29  | | 
% 244.76/51.29  | Case 2:
% 244.76/51.29  | | 
% 244.76/51.29  | |   (9)  all_58_7 = e3 & op(e1, e2) = e3
% 244.76/51.29  | | 
% 244.76/51.29  | | ALPHA: (9) implies:
% 244.76/51.29  | |   (10)  op(e1, e2) = e3
% 244.76/51.29  | | 
% 244.76/51.29  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #2191.
% 244.76/51.29  | | 
% 244.76/51.29  | End of split
% 244.76/51.29  | 
% 244.76/51.29  End of proof
% 244.76/51.29  
% 244.76/51.29  Sub-proof #1970 shows that the following formulas are inconsistent:
% 244.76/51.29  ----------------------------------------------------------------
% 244.76/51.29    (1)   ~ (e3 = e0)
% 244.76/51.29    (2)  all_58_6 = e3
% 244.76/51.29    (3)   ~ (e2 = e0)
% 244.76/51.29    (4)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 244.76/51.29         (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.76/51.29    (5)   ~ (e3 = e2)
% 244.76/51.29    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 244.76/51.29         (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 244.76/51.29    (7)  all_58_12 = e3
% 244.76/51.29    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.29    (9)   ~ (e1 = e0)
% 244.76/51.29    (10)  all_58_2 = e1
% 244.76/51.29    (11)   ~ (e2 = e1)
% 244.76/51.29  
% 244.76/51.29  Begin of proof
% 244.76/51.29  | 
% 244.76/51.29  | BETA: splitting (6) gives:
% 244.76/51.29  | 
% 244.76/51.29  | Case 1:
% 244.76/51.29  | | 
% 244.76/51.29  | |   (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 244.76/51.29  | |           e0)
% 244.76/51.29  | | 
% 244.76/51.30  | | BETA: splitting (12) gives:
% 244.76/51.30  | | 
% 244.76/51.30  | | Case 1:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (13)  all_58_0 = e0 & op(e3, e3) = e0
% 244.76/51.30  | | | 
% 244.76/51.30  | | | ALPHA: (13) implies:
% 244.76/51.30  | | |   (14)  op(e3, e3) = e0
% 244.76/51.30  | | | 
% 244.76/51.30  | | | BETA: splitting (4) gives:
% 244.76/51.30  | | | 
% 244.76/51.30  | | | Case 1:
% 244.76/51.30  | | | | 
% 244.76/51.30  | | | |   (15)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3)
% 244.76/51.30  | | | |           = e2)
% 244.76/51.30  | | | | 
% 244.76/51.30  | | | | REF_CLOSE: (3), (8), (10), (11), (14), (15) are inconsistent by
% 244.76/51.30  | | | |            sub-proof #1975.
% 244.76/51.30  | | | | 
% 244.76/51.30  | | | Case 2:
% 244.76/51.30  | | | | 
% 244.76/51.30  | | | |   (16)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3)
% 244.76/51.30  | | | |           = e2)
% 244.76/51.30  | | | | 
% 244.76/51.30  | | | | REF_CLOSE: (2), (5), (7), (16) are inconsistent by sub-proof #1973.
% 244.76/51.30  | | | | 
% 244.76/51.30  | | | End of split
% 244.76/51.30  | | | 
% 244.76/51.30  | | Case 2:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (17)  all_58_2 = e0 & op(e2, e3) = e0
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (9), (10), (17) are inconsistent by sub-proof #1972.
% 244.76/51.30  | | | 
% 244.76/51.30  | | End of split
% 244.76/51.30  | | 
% 244.76/51.30  | Case 2:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (18)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 244.76/51.30  | |           e0)
% 244.76/51.30  | | 
% 244.76/51.30  | | BETA: splitting (18) gives:
% 244.76/51.30  | | 
% 244.76/51.30  | | Case 1:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (19)  all_58_6 = e0 & op(e1, e3) = e0
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (1), (2), (19) are inconsistent by sub-proof #2213.
% 244.76/51.30  | | | 
% 244.76/51.30  | | Case 2:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (20)  all_58_12 = e0 & op(e0, e3) = e0
% 244.76/51.30  | | | 
% 244.76/51.30  | | | ALPHA: (20) implies:
% 244.76/51.30  | | |   (21)  all_58_12 = e0
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (1), (7), (21) are inconsistent by sub-proof #1971.
% 244.76/51.30  | | | 
% 244.76/51.30  | | End of split
% 244.76/51.30  | | 
% 244.76/51.30  | End of split
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1971 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)  all_58_12 = e3
% 244.76/51.30    (2)  all_58_12 = e0
% 244.76/51.30    (3)   ~ (e3 = e0)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.30  |   (4)  e3 = e0
% 244.76/51.30  | 
% 244.76/51.30  | SIMP: (4) implies:
% 244.76/51.30  |   (5)  e3 = e0
% 244.76/51.30  | 
% 244.76/51.30  | REDUCE: (3), (5) imply:
% 244.76/51.30  |   (6)  $false
% 244.76/51.30  | 
% 244.76/51.30  | CLOSE: (6) is inconsistent.
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1972 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)  all_58_2 = e0 & op(e2, e3) = e0
% 244.76/51.30    (2)  all_58_2 = e1
% 244.76/51.30    (3)   ~ (e1 = e0)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | ALPHA: (1) implies:
% 244.76/51.30  |   (4)  all_58_2 = e0
% 244.76/51.30  | 
% 244.76/51.30  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.30  |   (5)  e1 = e0
% 244.76/51.30  | 
% 244.76/51.30  | REDUCE: (3), (5) imply:
% 244.76/51.30  |   (6)  $false
% 244.76/51.30  | 
% 244.76/51.30  | CLOSE: (6) is inconsistent.
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1973 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 244.76/51.30    (2)  all_58_6 = e3
% 244.76/51.30    (3)   ~ (e3 = e2)
% 244.76/51.30    (4)  all_58_12 = e3
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | BETA: splitting (1) gives:
% 244.76/51.30  | 
% 244.76/51.30  | Case 1:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (5)  all_58_6 = e2 & op(e1, e3) = e2
% 244.76/51.30  | | 
% 244.76/51.30  | | ALPHA: (5) implies:
% 244.76/51.30  | |   (6)  all_58_6 = e2
% 244.76/51.30  | | 
% 244.76/51.30  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #2024.
% 244.76/51.30  | | 
% 244.76/51.30  | Case 2:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (7)  all_58_12 = e2 & op(e0, e3) = e2
% 244.76/51.30  | | 
% 244.76/51.30  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1974.
% 244.76/51.30  | | 
% 244.76/51.30  | End of split
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1974 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)  all_58_12 = e2 & op(e0, e3) = e2
% 244.76/51.30    (2)  all_58_12 = e3
% 244.76/51.30    (3)   ~ (e3 = e2)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | ALPHA: (1) implies:
% 244.76/51.30  |   (4)  all_58_12 = e2
% 244.76/51.30  | 
% 244.76/51.30  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.30  |   (5)  e3 = e2
% 244.76/51.30  | 
% 244.76/51.30  | REDUCE: (3), (5) imply:
% 244.76/51.30  |   (6)  $false
% 244.76/51.30  | 
% 244.76/51.30  | CLOSE: (6) is inconsistent.
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1975 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)   ~ (e2 = e0)
% 244.76/51.30    (2)  (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 244.76/51.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.30    (4)  op(e3, e3) = e0
% 244.76/51.30    (5)  all_58_2 = e1
% 244.76/51.30    (6)   ~ (e2 = e1)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | BETA: splitting (2) gives:
% 244.76/51.30  | 
% 244.76/51.30  | Case 1:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (7)  all_58_0 = e2 & op(e3, e3) = e2
% 244.76/51.30  | | 
% 244.76/51.30  | | ALPHA: (7) implies:
% 244.76/51.30  | |   (8)  op(e3, e3) = e2
% 244.76/51.30  | | 
% 244.76/51.30  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2188.
% 244.76/51.30  | | 
% 244.76/51.30  | Case 2:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (9)  all_58_2 = e2 & op(e2, e3) = e2
% 244.76/51.30  | | 
% 244.76/51.30  | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #1976.
% 244.76/51.30  | | 
% 244.76/51.30  | End of split
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1976 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)  all_58_2 = e2 & op(e2, e3) = e2
% 244.76/51.30    (2)  all_58_2 = e1
% 244.76/51.30    (3)   ~ (e2 = e1)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | ALPHA: (1) implies:
% 244.76/51.30  |   (4)  all_58_2 = e2
% 244.76/51.30  | 
% 244.76/51.30  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.30  |   (5)  e2 = e1
% 244.76/51.30  | 
% 244.76/51.30  | SIMP: (5) implies:
% 244.76/51.30  |   (6)  e2 = e1
% 244.76/51.30  | 
% 244.76/51.30  | REDUCE: (3), (6) imply:
% 244.76/51.30  |   (7)  $false
% 244.76/51.30  | 
% 244.76/51.30  | CLOSE: (7) is inconsistent.
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1977 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)   ~ (e3 = e0)
% 244.76/51.30    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.76/51.30         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.76/51.30    (3)   ~ (e2 = e0)
% 244.76/51.30    (4)  op(e1, e2) = all_52_6
% 244.76/51.30    (5)   ~ (e3 = e1)
% 244.76/51.30    (6)   ~ (e3 = e2)
% 244.76/51.30    (7)  all_58_6 = e0
% 244.76/51.30    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.76/51.30         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.76/51.30    (9)   ~ (all_52_6 = e3)
% 244.76/51.30    (10)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.76/51.30          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.76/51.30    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.30            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.30    (12)  op(e1, e1) = e0
% 244.76/51.30    (13)   ~ (e1 = e0)
% 244.76/51.30    (14)   ~ (e2 = e1)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | BETA: splitting (8) gives:
% 244.76/51.30  | 
% 244.76/51.30  | Case 1:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (15)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.76/51.30  | |           e3)
% 244.76/51.30  | | 
% 244.76/51.30  | | REF_CLOSE: (1), (4), (7), (9), (11), (15) are inconsistent by sub-proof
% 244.76/51.30  | |            #1983.
% 244.76/51.30  | | 
% 244.76/51.30  | Case 2:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (16)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.76/51.30  | |           e3)
% 244.76/51.30  | | 
% 244.76/51.30  | | BETA: splitting (16) gives:
% 244.76/51.30  | | 
% 244.76/51.30  | | Case 1:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (17)  all_58_8 = e3 & op(e1, e1) = e3
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (1), (11), (12), (17) are inconsistent by sub-proof #2018.
% 244.76/51.30  | | | 
% 244.76/51.30  | | Case 2:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (18)  all_58_11 = e3 & op(e1, e0) = e3
% 244.76/51.30  | | | 
% 244.76/51.30  | | | ALPHA: (18) implies:
% 244.76/51.30  | | |   (19)  all_58_11 = e3
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (2), (3), (5), (6), (7), (10), (11), (12), (13), (14), (19) are
% 244.76/51.30  | | |            inconsistent by sub-proof #1978.
% 244.76/51.30  | | | 
% 244.76/51.30  | | End of split
% 244.76/51.30  | | 
% 244.76/51.30  | End of split
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1978 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.76/51.30         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.76/51.30    (2)   ~ (e2 = e0)
% 244.76/51.30    (3)   ~ (e3 = e1)
% 244.76/51.30    (4)  all_58_11 = e3
% 244.76/51.30    (5)   ~ (e3 = e2)
% 244.76/51.30    (6)  all_58_6 = e0
% 244.76/51.30    (7)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.76/51.30         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.76/51.30    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.30    (9)  op(e1, e1) = e0
% 244.76/51.30    (10)   ~ (e1 = e0)
% 244.76/51.30    (11)   ~ (e2 = e1)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | BETA: splitting (7) gives:
% 244.76/51.30  | 
% 244.76/51.30  | Case 1:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (12)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 244.76/51.30  | |           e2)
% 244.76/51.30  | | 
% 244.76/51.30  | | BETA: splitting (12) gives:
% 244.76/51.30  | | 
% 244.76/51.30  | | Case 1:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (13)  all_58_6 = e2 & op(e1, e3) = e2
% 244.76/51.30  | | | 
% 244.76/51.30  | | | ALPHA: (13) implies:
% 244.76/51.30  | | |   (14)  all_58_6 = e2
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (2), (6), (14) are inconsistent by sub-proof #1982.
% 244.76/51.30  | | | 
% 244.76/51.30  | | Case 2:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (15)  all_58_7 = e2 & op(e1, e2) = e2
% 244.76/51.30  | | | 
% 244.76/51.30  | | | ALPHA: (15) implies:
% 244.76/51.30  | | |   (16)  all_58_7 = e2
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (11), (16) are inconsistent
% 244.76/51.30  | | |            by sub-proof #1979.
% 244.76/51.30  | | | 
% 244.76/51.30  | | End of split
% 244.76/51.30  | | 
% 244.76/51.30  | Case 2:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (17)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 244.76/51.30  | |           e2)
% 244.76/51.30  | | 
% 244.76/51.30  | | BETA: splitting (17) gives:
% 244.76/51.30  | | 
% 244.76/51.30  | | Case 1:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (18)  all_58_8 = e2 & op(e1, e1) = e2
% 244.76/51.30  | | | 
% 244.76/51.30  | | | ALPHA: (18) implies:
% 244.76/51.30  | | |   (19)  op(e1, e1) = e2
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (2), (8), (9), (19) are inconsistent by sub-proof #2211.
% 244.76/51.30  | | | 
% 244.76/51.30  | | Case 2:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (20)  all_58_11 = e2 & op(e1, e0) = e2
% 244.76/51.30  | | | 
% 244.76/51.30  | | | ALPHA: (20) implies:
% 244.76/51.30  | | |   (21)  all_58_11 = e2
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (4), (5), (21) are inconsistent by sub-proof #2030.
% 244.76/51.30  | | | 
% 244.76/51.30  | | End of split
% 244.76/51.30  | | 
% 244.76/51.30  | End of split
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1979 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 244.76/51.30         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 244.76/51.30    (2)   ~ (e3 = e1)
% 244.76/51.30    (3)  all_58_7 = e2
% 244.76/51.30    (4)  all_58_11 = e3
% 244.76/51.30    (5)  all_58_6 = e0
% 244.76/51.30    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.30    (7)  op(e1, e1) = e0
% 244.76/51.30    (8)   ~ (e1 = e0)
% 244.76/51.30    (9)   ~ (e2 = e1)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | BETA: splitting (1) gives:
% 244.76/51.30  | 
% 244.76/51.30  | Case 1:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (10)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 244.76/51.30  | |           e1)
% 244.76/51.30  | | 
% 244.76/51.30  | | BETA: splitting (10) gives:
% 244.76/51.30  | | 
% 244.76/51.30  | | Case 1:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (11)  all_58_6 = e1 & op(e1, e3) = e1
% 244.76/51.30  | | | 
% 244.76/51.30  | | | ALPHA: (11) implies:
% 244.76/51.30  | | |   (12)  all_58_6 = e1
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (5), (8), (12) are inconsistent by sub-proof #1981.
% 244.76/51.30  | | | 
% 244.76/51.30  | | Case 2:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (13)  all_58_7 = e1 & op(e1, e2) = e1
% 244.76/51.30  | | | 
% 244.76/51.30  | | | ALPHA: (13) implies:
% 244.76/51.30  | | |   (14)  all_58_7 = e1
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (3), (9), (14) are inconsistent by sub-proof #2134.
% 244.76/51.30  | | | 
% 244.76/51.30  | | End of split
% 244.76/51.30  | | 
% 244.76/51.30  | Case 2:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (15)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 244.76/51.30  | |           e1)
% 244.76/51.30  | | 
% 244.76/51.30  | | BETA: splitting (15) gives:
% 244.76/51.30  | | 
% 244.76/51.30  | | Case 1:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (16)  all_58_8 = e1 & op(e1, e1) = e1
% 244.76/51.30  | | | 
% 244.76/51.30  | | | ALPHA: (16) implies:
% 244.76/51.30  | | |   (17)  op(e1, e1) = e1
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (6), (7), (8), (17) are inconsistent by sub-proof #2220.
% 244.76/51.30  | | | 
% 244.76/51.30  | | Case 2:
% 244.76/51.30  | | | 
% 244.76/51.30  | | |   (18)  all_58_11 = e1 & op(e1, e0) = e1
% 244.76/51.30  | | | 
% 244.76/51.30  | | | ALPHA: (18) implies:
% 244.76/51.30  | | |   (19)  all_58_11 = e1
% 244.76/51.30  | | | 
% 244.76/51.30  | | | REF_CLOSE: (2), (4), (19) are inconsistent by sub-proof #1980.
% 244.76/51.30  | | | 
% 244.76/51.30  | | End of split
% 244.76/51.30  | | 
% 244.76/51.30  | End of split
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1980 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)  all_58_11 = e3
% 244.76/51.30    (2)  all_58_11 = e1
% 244.76/51.30    (3)   ~ (e3 = e1)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.30  |   (4)  e3 = e1
% 244.76/51.30  | 
% 244.76/51.30  | SIMP: (4) implies:
% 244.76/51.30  |   (5)  e3 = e1
% 244.76/51.30  | 
% 244.76/51.30  | REDUCE: (3), (5) imply:
% 244.76/51.30  |   (6)  $false
% 244.76/51.30  | 
% 244.76/51.30  | CLOSE: (6) is inconsistent.
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1981 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)  all_58_6 = e1
% 244.76/51.30    (2)  all_58_6 = e0
% 244.76/51.30    (3)   ~ (e1 = e0)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.30  |   (4)  e1 = e0
% 244.76/51.30  | 
% 244.76/51.30  | SIMP: (4) implies:
% 244.76/51.30  |   (5)  e1 = e0
% 244.76/51.30  | 
% 244.76/51.30  | REDUCE: (3), (5) imply:
% 244.76/51.30  |   (6)  $false
% 244.76/51.30  | 
% 244.76/51.30  | CLOSE: (6) is inconsistent.
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1982 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)  all_58_6 = e2
% 244.76/51.30    (2)  all_58_6 = e0
% 244.76/51.30    (3)   ~ (e2 = e0)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.30  |   (4)  e2 = e0
% 244.76/51.30  | 
% 244.76/51.30  | SIMP: (4) implies:
% 244.76/51.30  |   (5)  e2 = e0
% 244.76/51.30  | 
% 244.76/51.30  | REDUCE: (3), (5) imply:
% 244.76/51.30  |   (6)  $false
% 244.76/51.30  | 
% 244.76/51.30  | CLOSE: (6) is inconsistent.
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1983 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)   ~ (e3 = e0)
% 244.76/51.30    (2)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 244.76/51.30    (3)  op(e1, e2) = all_52_6
% 244.76/51.30    (4)  all_58_6 = e0
% 244.76/51.30    (5)   ~ (all_52_6 = e3)
% 244.76/51.30    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | BETA: splitting (2) gives:
% 244.76/51.30  | 
% 244.76/51.30  | Case 1:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (7)  all_58_6 = e3 & op(e1, e3) = e3
% 244.76/51.30  | | 
% 244.76/51.30  | | ALPHA: (7) implies:
% 244.76/51.30  | |   (8)  all_58_6 = e3
% 244.76/51.30  | | 
% 244.76/51.30  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #2222.
% 244.76/51.30  | | 
% 244.76/51.30  | Case 2:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (9)  all_58_7 = e3 & op(e1, e2) = e3
% 244.76/51.30  | | 
% 244.76/51.30  | | ALPHA: (9) implies:
% 244.76/51.30  | |   (10)  op(e1, e2) = e3
% 244.76/51.30  | | 
% 244.76/51.30  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #2191.
% 244.76/51.30  | | 
% 244.76/51.30  | End of split
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1984 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)   ~ (e2 = e0)
% 244.76/51.30    (2)   ~ (all_52_1 = e0)
% 244.76/51.30    (3)  op(e2, e3) = all_52_1
% 244.76/51.30    (4)  op(e3, e3) = e2
% 244.76/51.30    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.30    (6)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | BETA: splitting (6) gives:
% 244.76/51.30  | 
% 244.76/51.30  | Case 1:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (7)  all_58_0 = e0 & op(e3, e3) = e0
% 244.76/51.30  | | 
% 244.76/51.30  | | ALPHA: (7) implies:
% 244.76/51.30  | |   (8)  op(e3, e3) = e0
% 244.76/51.30  | | 
% 244.76/51.30  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2188.
% 244.76/51.30  | | 
% 244.76/51.30  | Case 2:
% 244.76/51.30  | | 
% 244.76/51.30  | |   (9)  all_58_2 = e0 & op(e2, e3) = e0
% 244.76/51.30  | | 
% 244.76/51.30  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1985.
% 244.76/51.30  | | 
% 244.76/51.30  | End of split
% 244.76/51.30  | 
% 244.76/51.30  End of proof
% 244.76/51.30  
% 244.76/51.30  Sub-proof #1985 shows that the following formulas are inconsistent:
% 244.76/51.30  ----------------------------------------------------------------
% 244.76/51.30    (1)  all_58_2 = e0 & op(e2, e3) = e0
% 244.76/51.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.30    (3)  op(e2, e3) = all_52_1
% 244.76/51.30    (4)   ~ (all_52_1 = e0)
% 244.76/51.30  
% 244.76/51.30  Begin of proof
% 244.76/51.30  | 
% 244.76/51.30  | ALPHA: (1) implies:
% 244.76/51.30  |   (5)  op(e2, e3) = e0
% 244.76/51.30  | 
% 244.76/51.30  | GROUND_INST: instantiating (2) with all_52_1, e0, e3, e2, simplifying with
% 244.76/51.30  |              (3), (5) gives:
% 244.76/51.31  |   (6)  all_52_1 = e0
% 244.76/51.31  | 
% 244.76/51.31  | REDUCE: (4), (6) imply:
% 244.76/51.31  |   (7)  $false
% 244.76/51.31  | 
% 244.76/51.31  | CLOSE: (7) is inconsistent.
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1986 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)  all_54_2 = all_52_8
% 244.76/51.31    (2)  all_54_2 = e2
% 244.76/51.31    (3)   ~ (all_52_8 = e2)
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.31  |   (4)  all_52_8 = e2
% 244.76/51.31  | 
% 244.76/51.31  | SIMP: (4) implies:
% 244.76/51.31  |   (5)  all_52_8 = e2
% 244.76/51.31  | 
% 244.76/51.31  | REDUCE: (3), (5) imply:
% 244.76/51.31  |   (6)  $false
% 244.76/51.31  | 
% 244.76/51.31  | CLOSE: (6) is inconsistent.
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1987 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)  all_54_2 = all_52_8
% 244.76/51.31    (2)  all_54_2 = e3
% 244.76/51.31    (3)   ~ (all_52_8 = e3)
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.31  |   (4)  all_52_8 = e3
% 244.76/51.31  | 
% 244.76/51.31  | SIMP: (4) implies:
% 244.76/51.31  |   (5)  all_52_8 = e3
% 244.76/51.31  | 
% 244.76/51.31  | REDUCE: (3), (5) imply:
% 244.76/51.31  |   (6)  $false
% 244.76/51.31  | 
% 244.76/51.31  | CLOSE: (6) is inconsistent.
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1988 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)  all_56_11 = e2
% 244.76/51.31    (2)  op(e1, e0) = all_52_14
% 244.76/51.31    (3)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.76/51.31             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.76/51.31           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 244.76/51.31             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 244.76/51.31           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 244.76/51.31           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.31           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.31    (4)   ~ (all_52_14 = e1)
% 244.76/51.31    (5)   ~ (all_52_14 = e0)
% 244.76/51.31    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | BETA: splitting (3) gives:
% 244.76/51.31  | 
% 244.76/51.31  | Case 1:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (7)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 244.76/51.31  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 244.76/51.31  | |        & op(e0, e2) = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | ALPHA: (7) implies:
% 244.76/51.31  | |   (8)   ~ (all_56_11 = e2)
% 244.76/51.31  | | 
% 244.76/51.31  | | REDUCE: (1), (8) imply:
% 244.76/51.31  | |   (9)  $false
% 244.76/51.31  | | 
% 244.76/51.31  | | CLOSE: (9) is inconsistent.
% 244.76/51.31  | | 
% 244.76/51.31  | Case 2:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.76/51.31  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.76/51.31  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 244.76/51.31  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.76/51.31  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.31  | | 
% 244.76/51.31  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #1989.
% 244.76/51.31  | | 
% 244.76/51.31  | End of split
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1989 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)  op(e1, e0) = all_52_14
% 244.76/51.31    (2)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 244.76/51.31             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 244.76/51.31           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 244.76/51.31             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 244.76/51.31           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.76/51.31    (3)   ~ (all_52_14 = e1)
% 244.76/51.31    (4)   ~ (all_52_14 = e0)
% 244.76/51.31    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | BETA: splitting (2) gives:
% 244.76/51.31  | 
% 244.76/51.31  | Case 1:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (6)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 244.76/51.31  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 244.76/51.31  | |        & op(e0, e1) = e1
% 244.76/51.31  | | 
% 244.76/51.31  | | ALPHA: (6) implies:
% 244.76/51.31  | |   (7)  op(e1, e0) = e1
% 244.76/51.31  | | 
% 244.76/51.31  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #2304.
% 244.76/51.31  | | 
% 244.76/51.31  | Case 2:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (8)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 244.76/51.31  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 244.76/51.31  | |        & op(e0, e1) = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | ALPHA: (8) implies:
% 244.76/51.31  | |   (9)  op(e1, e0) = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2323.
% 244.76/51.31  | | 
% 244.76/51.31  | End of split
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1990 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)  op(e1, e2) = all_52_6
% 244.76/51.31    (2)   ~ (all_52_6 = e0)
% 244.76/51.31    (3)  op(e0, e2) = all_52_7
% 244.76/51.31    (4)   ~ (all_52_7 = e0)
% 244.76/51.31    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.31    (6)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | BETA: splitting (6) gives:
% 244.76/51.31  | 
% 244.76/51.31  | Case 1:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (7)  all_58_7 = e0 & op(e1, e2) = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #2022.
% 244.76/51.31  | | 
% 244.76/51.31  | Case 2:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (8)  all_58_13 = e0 & op(e0, e2) = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | ALPHA: (8) implies:
% 244.76/51.31  | |   (9)  op(e0, e2) = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #2252.
% 244.76/51.31  | | 
% 244.76/51.31  | End of split
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1991 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 244.76/51.31    (2)   ~ (all_52_9 = e0)
% 244.76/51.31    (3)  op(e2, e1) = all_52_9
% 244.76/51.31    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.31    (5)  op(e2, e0) = all_52_13
% 244.76/51.31    (6)   ~ (all_52_13 = e0)
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | BETA: splitting (1) gives:
% 244.76/51.31  | 
% 244.76/51.31  | Case 1:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (7)  all_58_5 = e0 & op(e2, e1) = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #2088.
% 244.76/51.31  | | 
% 244.76/51.31  | Case 2:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (8)  all_58_10 = e0 & op(e2, e0) = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | ALPHA: (8) implies:
% 244.76/51.31  | |   (9)  op(e2, e0) = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #2324.
% 244.76/51.31  | | 
% 244.76/51.31  | End of split
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1992 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)  all_58_3 = e0 & op(e2, e2) = e0
% 244.76/51.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.31    (3)  op(e2, e2) = all_8_2
% 244.76/51.31    (4)   ~ (all_8_2 = e0)
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | ALPHA: (1) implies:
% 244.76/51.31  |   (5)  op(e2, e2) = e0
% 244.76/51.31  | 
% 244.76/51.31  | GROUND_INST: instantiating (2) with all_8_2, e0, e2, e2, simplifying with (3),
% 244.76/51.31  |              (5) gives:
% 244.76/51.31  |   (6)  all_8_2 = e0
% 244.76/51.31  | 
% 244.76/51.31  | REDUCE: (4), (6) imply:
% 244.76/51.31  |   (7)  $false
% 244.76/51.31  | 
% 244.76/51.31  | CLOSE: (7) is inconsistent.
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1993 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)   ~ (e3 = e0)
% 244.76/51.31    (2)  op(e1, e2) = e1
% 244.76/51.31    (3)   ~ (e2 = e0)
% 244.76/51.31    (4)   ~ (e3 = e1)
% 244.76/51.31    (5)   ~ (e3 = e2)
% 244.76/51.31    (6)  op(e1, e3) = e1
% 244.76/51.31    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.76/51.31         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.76/51.31    (8)  all_58_7 = e1
% 244.76/51.31    (9)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 244.76/51.31         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 244.76/51.31    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.31    (11)  op(e1, e1) = e0
% 244.76/51.31    (12)   ~ (e2 = e1)
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | BETA: splitting (9) gives:
% 244.76/51.31  | 
% 244.76/51.31  | Case 1:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (13)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 244.76/51.31  | |           e2)
% 244.76/51.31  | | 
% 244.76/51.31  | | BETA: splitting (13) gives:
% 244.76/51.31  | | 
% 244.76/51.31  | | Case 1:
% 244.76/51.31  | | | 
% 244.76/51.31  | | |   (14)  all_58_6 = e2 & op(e1, e3) = e2
% 244.76/51.31  | | | 
% 244.76/51.31  | | | ALPHA: (14) implies:
% 244.76/51.31  | | |   (15)  op(e1, e3) = e2
% 244.76/51.31  | | | 
% 244.76/51.31  | | | REF_CLOSE: (6), (10), (12), (15) are inconsistent by sub-proof #2226.
% 244.76/51.31  | | | 
% 244.76/51.31  | | Case 2:
% 244.76/51.31  | | | 
% 244.76/51.31  | | |   (16)  all_58_7 = e2 & op(e1, e2) = e2
% 244.76/51.31  | | | 
% 244.76/51.31  | | | ALPHA: (16) implies:
% 244.76/51.31  | | |   (17)  all_58_7 = e2
% 244.76/51.31  | | | 
% 244.76/51.31  | | | REF_CLOSE: (8), (12), (17) are inconsistent by sub-proof #2134.
% 244.76/51.31  | | | 
% 244.76/51.31  | | End of split
% 244.76/51.31  | | 
% 244.76/51.31  | Case 2:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (18)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 244.76/51.31  | |           e2)
% 244.76/51.31  | | 
% 244.76/51.31  | | BETA: splitting (18) gives:
% 244.76/51.31  | | 
% 244.76/51.31  | | Case 1:
% 244.76/51.31  | | | 
% 244.76/51.31  | | |   (19)  all_58_8 = e2 & op(e1, e1) = e2
% 244.76/51.31  | | | 
% 244.76/51.31  | | | ALPHA: (19) implies:
% 244.76/51.31  | | |   (20)  op(e1, e1) = e2
% 244.76/51.31  | | | 
% 244.76/51.31  | | | REF_CLOSE: (3), (10), (11), (20) are inconsistent by sub-proof #2211.
% 244.76/51.31  | | | 
% 244.76/51.31  | | Case 2:
% 244.76/51.31  | | | 
% 244.76/51.31  | | |   (21)  all_58_11 = e2 & op(e1, e0) = e2
% 244.76/51.31  | | | 
% 244.76/51.31  | | | ALPHA: (21) implies:
% 244.76/51.31  | | |   (22)  all_58_11 = e2
% 244.76/51.31  | | | 
% 244.76/51.31  | | | BETA: splitting (7) gives:
% 244.76/51.31  | | | 
% 244.76/51.31  | | | Case 1:
% 244.76/51.31  | | | | 
% 244.76/51.31  | | | |   (23)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 244.76/51.31  | | | |           = e3)
% 244.76/51.31  | | | | 
% 244.76/51.31  | | | | REF_CLOSE: (2), (4), (6), (10), (23) are inconsistent by sub-proof
% 244.76/51.31  | | | |            #2093.
% 244.76/51.31  | | | | 
% 244.76/51.31  | | | Case 2:
% 244.76/51.31  | | | | 
% 244.76/51.31  | | | |   (24)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 244.76/51.31  | | | |           = e3)
% 244.76/51.31  | | | | 
% 244.76/51.31  | | | | BETA: splitting (24) gives:
% 244.76/51.31  | | | | 
% 244.76/51.31  | | | | Case 1:
% 244.76/51.31  | | | | | 
% 244.76/51.31  | | | | |   (25)  all_58_8 = e3 & op(e1, e1) = e3
% 244.76/51.31  | | | | | 
% 244.76/51.31  | | | | | REF_CLOSE: (1), (10), (11), (25) are inconsistent by sub-proof #2018.
% 244.76/51.31  | | | | | 
% 244.76/51.31  | | | | Case 2:
% 244.76/51.31  | | | | | 
% 244.76/51.31  | | | | |   (26)  all_58_11 = e3 & op(e1, e0) = e3
% 244.76/51.31  | | | | | 
% 244.76/51.31  | | | | | REF_CLOSE: (5), (22), (26) are inconsistent by sub-proof #2108.
% 244.76/51.31  | | | | | 
% 244.76/51.31  | | | | End of split
% 244.76/51.31  | | | | 
% 244.76/51.31  | | | End of split
% 244.76/51.31  | | | 
% 244.76/51.31  | | End of split
% 244.76/51.31  | | 
% 244.76/51.31  | End of split
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1994 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.31    (2)  op(e2, e0) = all_52_13
% 244.76/51.31    (3)  op(e2, e0) = e3
% 244.76/51.31    (4)   ~ (all_52_13 = e3)
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | GROUND_INST: instantiating (1) with all_52_13, e3, e0, e2, simplifying with
% 244.76/51.31  |              (2), (3) gives:
% 244.76/51.31  |   (5)  all_52_13 = e3
% 244.76/51.31  | 
% 244.76/51.31  | REDUCE: (4), (5) imply:
% 244.76/51.31  |   (6)  $false
% 244.76/51.31  | 
% 244.76/51.31  | CLOSE: (6) is inconsistent.
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1995 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)   ~ (all_52_13 = e1)
% 244.76/51.31    (2)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 244.76/51.31    (3)  op(e2, e0) = e2
% 244.76/51.31    (4)   ~ (all_52_13 = e2)
% 244.76/51.31    (5)  all_54_7 = all_52_13
% 244.76/51.31    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.31    (7)  op(e2, e0) = all_52_13
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | BETA: splitting (2) gives:
% 244.76/51.31  | 
% 244.76/51.31  | Case 1:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (8)  all_54_7 = e2
% 244.76/51.31  | | 
% 244.76/51.31  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1997.
% 244.76/51.31  | | 
% 244.76/51.31  | Case 2:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (9)   ~ (all_54_7 = e2)
% 244.76/51.31  | |   (10)  all_54_7 = e1 | all_54_7 = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10) are inconsistent by sub-proof
% 244.76/51.31  | |            #1996.
% 244.76/51.31  | | 
% 244.76/51.31  | End of split
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1996 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)   ~ (all_52_13 = e1)
% 244.76/51.31    (2)  all_54_7 = e1 | all_54_7 = e0
% 244.76/51.31    (3)  op(e2, e0) = e2
% 244.76/51.31    (4)   ~ (all_52_13 = e2)
% 244.76/51.31    (5)  all_54_7 = all_52_13
% 244.76/51.31    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.31    (7)  op(e2, e0) = all_52_13
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | BETA: splitting (2) gives:
% 244.76/51.31  | 
% 244.76/51.31  | Case 1:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (8)  all_54_7 = e1
% 244.76/51.31  | | 
% 244.76/51.31  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #2295.
% 244.76/51.31  | | 
% 244.76/51.31  | Case 2:
% 244.76/51.31  | | 
% 244.76/51.31  | |   (9)  all_54_7 = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | COMBINE_EQS: (5), (9) imply:
% 244.76/51.31  | |   (10)  all_52_13 = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | SIMP: (10) implies:
% 244.76/51.31  | |   (11)  all_52_13 = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | REDUCE: (4), (11) imply:
% 244.76/51.31  | |   (12)   ~ (e2 = e0)
% 244.76/51.31  | | 
% 244.76/51.31  | | SIMP: (12) implies:
% 244.76/51.31  | |   (13)   ~ (e2 = e0)
% 244.76/51.31  | | 
% 244.76/51.31  | | REDUCE: (7), (11) imply:
% 244.76/51.31  | |   (14)  op(e2, e0) = e0
% 244.76/51.31  | | 
% 244.76/51.31  | | REF_CLOSE: (3), (6), (13), (14) are inconsistent by sub-proof #2121.
% 244.76/51.31  | | 
% 244.76/51.31  | End of split
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1997 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)  all_54_7 = all_52_13
% 244.76/51.31    (2)  all_54_7 = e2
% 244.76/51.31    (3)   ~ (all_52_13 = e2)
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.31  |   (4)  all_52_13 = e2
% 244.76/51.31  | 
% 244.76/51.31  | SIMP: (4) implies:
% 244.76/51.31  |   (5)  all_52_13 = e2
% 244.76/51.31  | 
% 244.76/51.31  | REDUCE: (3), (5) imply:
% 244.76/51.31  |   (6)  $false
% 244.76/51.31  | 
% 244.76/51.31  | CLOSE: (6) is inconsistent.
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1998 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)  all_54_11 = all_52_14
% 244.76/51.31    (2)  all_54_11 = e3
% 244.76/51.31    (3)   ~ (all_52_14 = e3)
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.31  |   (4)  all_52_14 = e3
% 244.76/51.31  | 
% 244.76/51.31  | SIMP: (4) implies:
% 244.76/51.31  |   (5)  all_52_14 = e3
% 244.76/51.31  | 
% 244.76/51.31  | REDUCE: (3), (5) imply:
% 244.76/51.31  |   (6)  $false
% 244.76/51.31  | 
% 244.76/51.31  | CLOSE: (6) is inconsistent.
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #1999 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)  all_58_3 = e3
% 244.76/51.31    (2)  all_58_3 = e1
% 244.76/51.31    (3)   ~ (e3 = e1)
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.31  |   (4)  e3 = e1
% 244.76/51.31  | 
% 244.76/51.31  | SIMP: (4) implies:
% 244.76/51.31  |   (5)  e3 = e1
% 244.76/51.31  | 
% 244.76/51.31  | REDUCE: (3), (5) imply:
% 244.76/51.31  |   (6)  $false
% 244.76/51.31  | 
% 244.76/51.31  | CLOSE: (6) is inconsistent.
% 244.76/51.31  | 
% 244.76/51.31  End of proof
% 244.76/51.31  
% 244.76/51.31  Sub-proof #2000 shows that the following formulas are inconsistent:
% 244.76/51.31  ----------------------------------------------------------------
% 244.76/51.31    (1)   ~ (e3 = e0)
% 244.76/51.31    (2)  all_56_11 = e1
% 244.76/51.31    (3)   ~ (e2 = e0)
% 244.76/51.31    (4)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.76/51.31           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.76/51.31             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.76/51.31           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.76/51.31             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.76/51.31           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.76/51.31           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.76/51.31    (5)  op(e3, e2) = e0
% 244.76/51.31    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.31  
% 244.76/51.31  Begin of proof
% 244.76/51.31  | 
% 244.76/51.31  | BETA: splitting (4) gives:
% 244.76/51.31  | 
% 244.76/51.31  | Case 1:
% 244.76/51.31  | | 
% 244.76/51.32  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 244.76/51.32  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.76/51.32  | |        op(e2, e3) = e3
% 244.76/51.32  | | 
% 244.76/51.32  | | ALPHA: (7) implies:
% 244.76/51.32  | |   (8)  op(e3, e2) = e3
% 244.76/51.32  | | 
% 244.76/51.32  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2099.
% 244.76/51.32  | | 
% 244.76/51.32  | Case 2:
% 244.76/51.32  | | 
% 244.76/51.32  | |   (9)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.76/51.32  | |            e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2
% 244.76/51.32  | |          & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1
% 244.76/51.32  | |            = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31
% 244.76/51.32  | |            = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.76/51.32  | | 
% 244.76/51.32  | | BETA: splitting (9) gives:
% 244.76/51.32  | | 
% 244.76/51.32  | | Case 1:
% 244.76/51.32  | | | 
% 244.76/51.32  | | |   (10)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 244.76/51.32  | | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 244.76/51.32  | | |         e2 & op(e2, e3) = e2
% 244.76/51.32  | | | 
% 244.76/51.32  | | | ALPHA: (10) implies:
% 244.76/51.32  | | |   (11)  op(e3, e2) = e2
% 244.76/51.32  | | | 
% 244.76/51.32  | | | REF_CLOSE: (3), (5), (6), (11) are inconsistent by sub-proof #2026.
% 244.76/51.32  | | | 
% 244.76/51.32  | | Case 2:
% 244.76/51.32  | | | 
% 244.76/51.32  | | |   (12)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.32  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.76/51.32  | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 244.76/51.32  | | | 
% 244.76/51.32  | | | ALPHA: (12) implies:
% 244.76/51.32  | | |   (13)   ~ (all_56_11 = e1)
% 244.76/51.32  | | | 
% 244.76/51.32  | | | REDUCE: (2), (13) imply:
% 244.76/51.32  | | |   (14)  $false
% 244.76/51.32  | | | 
% 244.76/51.32  | | | CLOSE: (14) is inconsistent.
% 244.76/51.32  | | | 
% 244.76/51.32  | | End of split
% 244.76/51.32  | | 
% 244.76/51.32  | End of split
% 244.76/51.32  | 
% 244.76/51.32  End of proof
% 244.76/51.32  
% 244.76/51.32  Sub-proof #2001 shows that the following formulas are inconsistent:
% 244.76/51.32  ----------------------------------------------------------------
% 244.76/51.32    (1)   ~ (e3 = e0)
% 244.76/51.32    (2)  all_58_1 = e0
% 244.76/51.32    (3)   ~ (e3 = e1)
% 244.76/51.32    (4)  all_58_7 = e2
% 244.76/51.32    (5)   ~ (e3 = e2)
% 244.76/51.32    (6)  op(e3, e2) = e0
% 244.76/51.32    (7)  op(e1, e2) = e2
% 244.76/51.32    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.32    (9)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.76/51.32         (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.76/51.32    (10)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.76/51.32          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.76/51.32    (11)   ~ (e1 = e0)
% 244.76/51.32    (12)  op(e2, e2) = e2
% 244.76/51.32    (13)   ~ (e2 = e1)
% 244.76/51.32  
% 244.76/51.32  Begin of proof
% 244.76/51.32  | 
% 244.76/51.32  | BETA: splitting (10) gives:
% 244.76/51.32  | 
% 244.76/51.32  | Case 1:
% 244.76/51.32  | | 
% 244.76/51.32  | |   (14)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 244.76/51.32  | |           e3)
% 244.76/51.32  | | 
% 244.76/51.32  | | REF_CLOSE: (1), (5), (6), (8), (12), (14) are inconsistent by sub-proof
% 244.76/51.32  | |            #2016.
% 244.76/51.32  | | 
% 244.76/51.32  | Case 2:
% 244.76/51.32  | | 
% 244.76/51.32  | |   (15)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.76/51.32  | |           e3)
% 244.76/51.32  | | 
% 244.76/51.32  | | BETA: splitting (15) gives:
% 244.76/51.32  | | 
% 244.76/51.32  | | Case 1:
% 244.76/51.32  | | | 
% 244.76/51.32  | | |   (16)  all_58_7 = e3 & op(e1, e2) = e3
% 244.76/51.32  | | | 
% 244.76/51.32  | | | ALPHA: (16) implies:
% 244.76/51.32  | | |   (17)  op(e1, e2) = e3
% 244.76/51.32  | | | 
% 244.76/51.32  | | | REF_CLOSE: (5), (7), (8), (17) are inconsistent by sub-proof #2207.
% 244.76/51.32  | | | 
% 244.76/51.32  | | Case 2:
% 244.76/51.32  | | | 
% 244.76/51.32  | | |   (18)  all_58_13 = e3 & op(e0, e2) = e3
% 244.76/51.32  | | | 
% 244.76/51.32  | | | ALPHA: (18) implies:
% 244.76/51.32  | | |   (19)  all_58_13 = e3
% 244.76/51.32  | | | 
% 244.76/51.32  | | | BETA: splitting (9) gives:
% 244.76/51.32  | | | 
% 244.76/51.32  | | | Case 1:
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | |   (20)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2)
% 244.76/51.32  | | | |           = e1)
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | | REF_CLOSE: (2), (8), (11), (12), (13), (20) are inconsistent by
% 244.76/51.32  | | | |            sub-proof #2014.
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | Case 2:
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | |   (21)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 244.76/51.32  | | | |           = e1)
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | | BETA: splitting (21) gives:
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | | Case 1:
% 244.76/51.32  | | | | | 
% 244.76/51.32  | | | | |   (22)  all_58_7 = e1 & op(e1, e2) = e1
% 244.76/51.32  | | | | | 
% 244.76/51.32  | | | | | REF_CLOSE: (4), (13), (22) are inconsistent by sub-proof #2224.
% 244.76/51.32  | | | | | 
% 244.76/51.32  | | | | Case 2:
% 244.76/51.32  | | | | | 
% 244.76/51.32  | | | | |   (23)  all_58_13 = e1 & op(e0, e2) = e1
% 244.76/51.32  | | | | | 
% 244.76/51.32  | | | | | REF_CLOSE: (3), (19), (23) are inconsistent by sub-proof #2013.
% 244.76/51.32  | | | | | 
% 244.76/51.32  | | | | End of split
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | End of split
% 244.76/51.32  | | | 
% 244.76/51.32  | | End of split
% 244.76/51.32  | | 
% 244.76/51.32  | End of split
% 244.76/51.32  | 
% 244.76/51.32  End of proof
% 244.76/51.32  
% 244.76/51.32  Sub-proof #2002 shows that the following formulas are inconsistent:
% 244.76/51.32  ----------------------------------------------------------------
% 244.76/51.32    (1)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 & $i(all_32_1)
% 244.76/51.32    (2)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 244.76/51.32           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 244.76/51.32           all_24_1 & $i(all_24_1))
% 244.76/51.32    (3)  op(e3, e2) = e0
% 244.76/51.32    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.32  
% 244.76/51.32  Begin of proof
% 244.76/51.32  | 
% 244.76/51.32  | ALPHA: (1) implies:
% 244.76/51.32  |   (5)   ~ (all_32_1 = e0)
% 244.76/51.32  |   (6)  op(e3, e2) = all_32_1
% 244.76/51.32  | 
% 244.76/51.32  | BETA: splitting (2) gives:
% 244.76/51.32  | 
% 244.76/51.32  | Case 1:
% 244.76/51.32  | | 
% 244.76/51.32  | |   (7)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) =
% 244.76/51.32  | |        all_24_1 & $i(all_24_0) & $i(all_24_1)
% 244.76/51.32  | | 
% 244.76/51.32  | | ALPHA: (7) implies:
% 244.76/51.32  | |   (8)  op(e3, e2) = all_24_1
% 244.76/51.32  | | 
% 244.76/51.32  | | REF_CLOSE: (3), (4), (5), (6), (8) are inconsistent by sub-proof #2065.
% 244.76/51.32  | | 
% 244.76/51.32  | Case 2:
% 244.76/51.32  | | 
% 244.76/51.32  | |   (9)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 & $i(all_24_1)
% 244.76/51.32  | | 
% 244.76/51.32  | | ALPHA: (9) implies:
% 244.76/51.32  | |   (10)  op(e3, e2) = all_24_1
% 244.76/51.32  | | 
% 244.76/51.32  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #2065.
% 244.76/51.32  | | 
% 244.76/51.32  | End of split
% 244.76/51.32  | 
% 244.76/51.32  End of proof
% 244.76/51.32  
% 244.76/51.32  Sub-proof #2003 shows that the following formulas are inconsistent:
% 244.76/51.32  ----------------------------------------------------------------
% 244.76/51.32    (1)   ~ (all_52_3 = e0)
% 244.76/51.32    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.76/51.32             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.76/51.32           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.76/51.32         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.76/51.32           $i(all_56_7))
% 244.76/51.32    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.76/51.32    (4)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.76/51.32    (5)   ~ (all_52_7 = e2)
% 244.76/51.32    (6)  op(e2, e3) = e0
% 244.76/51.32    (7)  all_54_13 = all_52_7
% 244.76/51.32    (8)  op(e0, e3) = all_52_3
% 244.76/51.32    (9)   ~ (all_52_2 = all_52_3)
% 244.76/51.32    (10)   ~ (all_52_3 = all_52_7)
% 244.76/51.32    (11)  op(e3, e2) = all_24_1
% 244.76/51.32    (12)  all_54_12 = all_52_3
% 244.76/51.32    (13)   ~ (all_52_3 = e2)
% 244.76/51.32    (14)  op(e3, e2) = e0
% 244.76/51.32    (15)   ~ (all_52_13 = e2)
% 244.76/51.32    (16)   ~ (all_52_2 = e0)
% 244.76/51.32    (17)  all_56_1 = e2
% 244.76/51.32    (18)  op(e0, e3) = all_32_0
% 244.76/51.32    (19)   ~ (all_52_7 = e0)
% 244.76/51.32    (20)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.76/51.32    (21)   ~ (all_52_2 = e2)
% 244.76/51.32    (22)  all_54_8 = all_52_2
% 244.76/51.32    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.32    (24)  op(e1, e3) = all_52_2
% 244.76/51.32    (25)  op(e1, e1) = e0
% 244.76/51.32    (26)  op(e2, e0) = all_52_13
% 244.76/51.32    (27)   ~ (all_32_0 = e1)
% 244.76/51.32  
% 244.76/51.32  Begin of proof
% 244.76/51.32  | 
% 244.76/51.32  | GROUND_INST: instantiating (23) with all_52_3, all_32_0, e3, e0, simplifying
% 244.76/51.32  |              with (8), (18) gives:
% 244.76/51.32  |   (28)  all_52_3 = all_32_0
% 244.76/51.32  | 
% 244.76/51.32  | GROUND_INST: instantiating (23) with e0, all_24_1, e2, e3, simplifying with
% 244.76/51.32  |              (11), (14) gives:
% 244.76/51.32  |   (29)  all_24_1 = e0
% 244.76/51.32  | 
% 244.76/51.32  | COMBINE_EQS: (12), (28) imply:
% 244.76/51.32  |   (30)  all_54_12 = all_32_0
% 244.76/51.32  | 
% 244.76/51.32  | REDUCE: (9), (28) imply:
% 244.76/51.32  |   (31)   ~ (all_52_2 = all_32_0)
% 244.76/51.32  | 
% 244.76/51.32  | REDUCE: (10), (28) imply:
% 244.76/51.32  |   (32)   ~ (all_52_7 = all_32_0)
% 244.76/51.32  | 
% 244.76/51.32  | SIMP: (32) implies:
% 244.76/51.32  |   (33)   ~ (all_52_7 = all_32_0)
% 244.76/51.32  | 
% 244.76/51.32  | REDUCE: (13), (28) imply:
% 244.76/51.32  |   (34)   ~ (all_32_0 = e2)
% 244.76/51.32  | 
% 244.76/51.32  | REDUCE: (1), (28) imply:
% 244.76/51.32  |   (35)   ~ (all_32_0 = e0)
% 244.76/51.32  | 
% 244.76/51.32  | BETA: splitting (3) gives:
% 244.76/51.32  | 
% 244.76/51.32  | Case 1:
% 244.76/51.32  | | 
% 244.76/51.32  | |   (36)  all_54_12 = e3
% 244.76/51.32  | | 
% 244.76/51.32  | | COMBINE_EQS: (30), (36) imply:
% 244.76/51.32  | |   (37)  all_32_0 = e3
% 244.76/51.32  | | 
% 244.76/51.32  | | SIMP: (37) implies:
% 244.76/51.32  | |   (38)  all_32_0 = e3
% 244.76/51.32  | | 
% 244.76/51.32  | | REDUCE: (31), (38) imply:
% 244.76/51.32  | |   (39)   ~ (all_52_2 = e3)
% 244.76/51.32  | | 
% 244.76/51.32  | | REDUCE: (33), (38) imply:
% 244.76/51.32  | |   (40)   ~ (all_52_7 = e3)
% 244.76/51.32  | | 
% 244.76/51.32  | | REDUCE: (35), (38) imply:
% 244.76/51.32  | |   (41)   ~ (e3 = e0)
% 244.76/51.32  | | 
% 244.76/51.32  | | REDUCE: (18), (38) imply:
% 244.76/51.32  | |   (42)  op(e0, e3) = e3
% 244.76/51.32  | | 
% 244.76/51.32  | | BETA: splitting (4) gives:
% 244.76/51.32  | | 
% 244.76/51.32  | | Case 1:
% 244.76/51.32  | | | 
% 244.76/51.32  | | |   (43)  all_54_8 = e3
% 244.76/51.32  | | | 
% 244.76/51.32  | | | REF_CLOSE: (22), (39), (43) are inconsistent by sub-proof #2011.
% 244.76/51.32  | | | 
% 244.76/51.32  | | Case 2:
% 244.76/51.32  | | | 
% 244.76/51.32  | | |   (44)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.76/51.32  | | | 
% 244.76/51.32  | | | BETA: splitting (20) gives:
% 244.76/51.32  | | | 
% 244.76/51.32  | | | Case 1:
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | |   (45)  all_54_13 = e3
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | | REF_CLOSE: (7), (40), (45) are inconsistent by sub-proof #2010.
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | Case 2:
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | |   (46)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | | BETA: splitting (2) gives:
% 244.76/51.32  | | | | 
% 244.76/51.32  | | | | Case 1:
% 244.76/51.32  | | | | | 
% 244.76/51.32  | | | | |   (47)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 244.76/51.32  | | | | |           op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 244.76/51.32  | | | | |           $i(all_56_3))
% 244.76/51.32  | | | | | 
% 244.76/51.32  | | | | | BETA: splitting (47) gives:
% 244.76/51.32  | | | | | 
% 244.76/51.32  | | | | | Case 1:
% 244.76/51.32  | | | | | | 
% 244.76/51.32  | | | | | |   (48)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 244.76/51.32  | | | | | | 
% 244.76/51.32  | | | | | | ALPHA: (48) implies:
% 244.76/51.32  | | | | | |   (49)  op(e3, all_56_1) = e3
% 244.76/51.32  | | | | | | 
% 244.76/51.32  | | | | | | REDUCE: (17), (49) imply:
% 244.76/51.32  | | | | | |   (50)  op(e3, e2) = e3
% 244.76/51.32  | | | | | | 
% 244.76/51.32  | | | | | | REF_CLOSE: (14), (23), (41), (50) are inconsistent by sub-proof
% 244.76/51.32  | | | | | |            #2099.
% 244.76/51.32  | | | | | | 
% 244.76/51.32  | | | | | Case 2:
% 244.76/51.32  | | | | | | 
% 244.76/51.32  | | | | | |   (51)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 244.76/51.32  | | | | | |         all_56_3 & $i(all_56_3)
% 244.76/51.32  | | | | | | 
% 244.76/51.32  | | | | | | ALPHA: (51) implies:
% 244.76/51.32  | | | | | |   (52)  op(e2, e3) = all_56_3
% 244.76/51.32  | | | | | |   (53)  op(e2, all_56_3) = e2
% 244.76/51.32  | | | | | | 
% 244.76/51.32  | | | | | | BETA: splitting (46) gives:
% 244.76/51.32  | | | | | | 
% 244.76/51.32  | | | | | | Case 1:
% 244.76/51.32  | | | | | | | 
% 244.76/51.32  | | | | | | |   (54)  all_54_13 = e2
% 244.76/51.32  | | | | | | | 
% 244.76/51.32  | | | | | | | REF_CLOSE: (5), (7), (54) are inconsistent by sub-proof #2009.
% 244.76/51.32  | | | | | | | 
% 244.76/51.32  | | | | | | Case 2:
% 244.76/51.32  | | | | | | | 
% 244.76/51.32  | | | | | | |   (55)  all_54_13 = e1 | all_54_13 = e0
% 244.76/51.32  | | | | | | | 
% 244.76/51.32  | | | | | | | BETA: splitting (55) gives:
% 244.76/51.32  | | | | | | | 
% 244.76/51.32  | | | | | | | Case 1:
% 244.76/51.32  | | | | | | | | 
% 244.76/51.32  | | | | | | | | 
% 244.76/51.32  | | | | | | | | GROUND_INST: instantiating (23) with e0, all_56_3, e3, e2,
% 244.76/51.32  | | | | | | | |              simplifying with (6), (52) gives:
% 244.76/51.32  | | | | | | | |   (56)  all_56_3 = e0
% 244.76/51.32  | | | | | | | | 
% 244.76/51.32  | | | | | | | | REDUCE: (53), (56) imply:
% 244.76/51.32  | | | | | | | |   (57)  op(e2, e0) = e2
% 244.76/51.32  | | | | | | | | 
% 244.76/51.32  | | | | | | | | REF_CLOSE: (15), (23), (26), (57) are inconsistent by sub-proof
% 244.76/51.32  | | | | | | | |            #2317.
% 244.76/51.32  | | | | | | | | 
% 244.76/51.32  | | | | | | | Case 2:
% 244.76/51.32  | | | | | | | | 
% 244.76/51.32  | | | | | | | |   (58)  all_54_13 = e0
% 244.76/51.32  | | | | | | | | 
% 244.76/51.32  | | | | | | | | REF_CLOSE: (7), (19), (58) are inconsistent by sub-proof #2008.
% 244.76/51.32  | | | | | | | | 
% 244.76/51.32  | | | | | | | End of split
% 244.76/51.32  | | | | | | | 
% 244.76/51.32  | | | | | | End of split
% 244.76/51.33  | | | | | | 
% 244.76/51.33  | | | | | End of split
% 244.76/51.33  | | | | | 
% 244.76/51.33  | | | | Case 2:
% 244.76/51.33  | | | | | 
% 244.76/51.33  | | | | |   (59)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5
% 244.76/51.33  | | | | |           & $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 &
% 244.76/51.33  | | | | |           op(e0, e3) = all_56_7 & $i(all_56_7))
% 244.76/51.33  | | | | | 
% 244.76/51.33  | | | | | BETA: splitting (59) gives:
% 244.76/51.33  | | | | | 
% 244.76/51.33  | | | | | Case 1:
% 244.76/51.33  | | | | | | 
% 244.76/51.33  | | | | | |   (60)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 244.76/51.33  | | | | | |         all_56_5 & $i(all_56_5)
% 244.76/51.33  | | | | | | 
% 244.76/51.33  | | | | | | ALPHA: (60) implies:
% 244.76/51.33  | | | | | |   (61)  op(e1, e3) = all_56_5
% 244.76/51.33  | | | | | |   (62)  op(e1, all_56_5) = e1
% 244.76/51.33  | | | | | | 
% 244.76/51.33  | | | | | | REF_CLOSE: (16), (21), (22), (23), (24), (25), (44), (61), (62) are
% 244.76/51.33  | | | | | |            inconsistent by sub-proof #2004.
% 244.76/51.33  | | | | | | 
% 244.76/51.33  | | | | | Case 2:
% 244.76/51.33  | | | | | | 
% 244.76/51.33  | | | | | |   (63)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 244.76/51.33  | | | | | |         all_56_7 & $i(all_56_7)
% 244.76/51.33  | | | | | | 
% 244.76/51.33  | | | | | | ALPHA: (63) implies:
% 244.76/51.33  | | | | | |   (64)  op(e0, e3) = all_56_7
% 244.76/51.33  | | | | | |   (65)  op(e0, all_56_7) = e0
% 244.76/51.33  | | | | | | 
% 244.76/51.33  | | | | | | REF_CLOSE: (23), (41), (42), (64), (65) are inconsistent by
% 244.76/51.33  | | | | | |            sub-proof #2070.
% 244.76/51.33  | | | | | | 
% 244.76/51.33  | | | | | End of split
% 244.76/51.33  | | | | | 
% 244.76/51.33  | | | | End of split
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | End of split
% 244.76/51.33  | | | 
% 244.76/51.33  | | End of split
% 244.76/51.33  | | 
% 244.76/51.33  | Case 2:
% 244.76/51.33  | | 
% 244.76/51.33  | |   (66)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.76/51.33  | | 
% 244.76/51.33  | | BETA: splitting (66) gives:
% 244.76/51.33  | | 
% 244.76/51.33  | | Case 1:
% 244.76/51.33  | | | 
% 244.76/51.33  | | |   (67)  all_54_12 = e2
% 244.76/51.33  | | | 
% 244.76/51.33  | | | COMBINE_EQS: (30), (67) imply:
% 244.76/51.33  | | |   (68)  all_32_0 = e2
% 244.76/51.33  | | | 
% 244.76/51.33  | | | SIMP: (68) implies:
% 244.76/51.33  | | |   (69)  all_32_0 = e2
% 244.76/51.33  | | | 
% 244.76/51.33  | | | REDUCE: (34), (69) imply:
% 244.76/51.33  | | |   (70)  $false
% 244.76/51.33  | | | 
% 244.76/51.33  | | | CLOSE: (70) is inconsistent.
% 244.76/51.33  | | | 
% 244.76/51.33  | | Case 2:
% 244.76/51.33  | | | 
% 244.76/51.33  | | |   (71)  all_54_12 = e1 | all_54_12 = e0
% 244.76/51.33  | | | 
% 244.76/51.33  | | | BETA: splitting (71) gives:
% 244.76/51.33  | | | 
% 244.76/51.33  | | | Case 1:
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | |   (72)  all_54_12 = e1
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | | COMBINE_EQS: (30), (72) imply:
% 244.76/51.33  | | | |   (73)  all_32_0 = e1
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | | SIMP: (73) implies:
% 244.76/51.33  | | | |   (74)  all_32_0 = e1
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | | REDUCE: (27), (74) imply:
% 244.76/51.33  | | | |   (75)  $false
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | | CLOSE: (75) is inconsistent.
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | Case 2:
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | |   (76)  all_54_12 = e0
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | | COMBINE_EQS: (30), (76) imply:
% 244.76/51.33  | | | |   (77)  all_32_0 = e0
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | | SIMP: (77) implies:
% 244.76/51.33  | | | |   (78)  all_32_0 = e0
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | | REDUCE: (35), (78) imply:
% 244.76/51.33  | | | |   (79)  $false
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | | CLOSE: (79) is inconsistent.
% 244.76/51.33  | | | | 
% 244.76/51.33  | | | End of split
% 244.76/51.33  | | | 
% 244.76/51.33  | | End of split
% 244.76/51.33  | | 
% 244.76/51.33  | End of split
% 244.76/51.33  | 
% 244.76/51.33  End of proof
% 244.76/51.33  
% 244.76/51.33  Sub-proof #2004 shows that the following formulas are inconsistent:
% 244.76/51.33  ----------------------------------------------------------------
% 244.76/51.33    (1)  op(e1, all_56_5) = e1
% 244.76/51.33    (2)  op(e1, e3) = all_56_5
% 244.76/51.33    (3)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 244.76/51.33    (4)   ~ (all_52_2 = e0)
% 244.76/51.33    (5)   ~ (all_52_2 = e2)
% 244.76/51.33    (6)  all_54_8 = all_52_2
% 244.76/51.33    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.33    (8)  op(e1, e3) = all_52_2
% 244.76/51.33    (9)  op(e1, e1) = e0
% 244.76/51.33  
% 244.76/51.33  Begin of proof
% 244.76/51.33  | 
% 244.76/51.33  | BETA: splitting (3) gives:
% 244.76/51.33  | 
% 244.76/51.33  | Case 1:
% 244.76/51.33  | | 
% 244.76/51.33  | |   (10)  all_54_8 = e2
% 244.76/51.33  | | 
% 244.76/51.33  | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #2007.
% 244.76/51.33  | | 
% 244.76/51.33  | Case 2:
% 244.76/51.33  | | 
% 244.76/51.33  | |   (11)  all_54_8 = e1 | all_54_8 = e0
% 244.76/51.33  | | 
% 244.76/51.33  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (11) are inconsistent by
% 244.76/51.33  | |            sub-proof #2005.
% 244.76/51.33  | | 
% 244.76/51.33  | End of split
% 244.76/51.33  | 
% 244.76/51.33  End of proof
% 244.76/51.33  
% 244.76/51.33  Sub-proof #2005 shows that the following formulas are inconsistent:
% 244.76/51.33  ----------------------------------------------------------------
% 244.76/51.33    (1)  op(e1, all_56_5) = e1
% 244.76/51.33    (2)  op(e1, e3) = all_56_5
% 244.76/51.33    (3)  all_54_8 = e1 | all_54_8 = e0
% 244.76/51.33    (4)   ~ (all_52_2 = e0)
% 244.76/51.33    (5)  all_54_8 = all_52_2
% 244.76/51.33    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.33    (7)  op(e1, e3) = all_52_2
% 244.76/51.33    (8)  op(e1, e1) = e0
% 244.76/51.33  
% 244.76/51.33  Begin of proof
% 244.76/51.33  | 
% 244.76/51.33  | BETA: splitting (3) gives:
% 244.76/51.33  | 
% 244.76/51.33  | Case 1:
% 244.76/51.33  | | 
% 244.76/51.33  | |   (9)  all_54_8 = e1
% 244.76/51.33  | | 
% 244.76/51.33  | | COMBINE_EQS: (5), (9) imply:
% 244.76/51.33  | |   (10)  all_52_2 = e1
% 244.76/51.33  | | 
% 244.76/51.33  | | SIMP: (10) implies:
% 244.76/51.33  | |   (11)  all_52_2 = e1
% 244.76/51.33  | | 
% 244.76/51.33  | | REDUCE: (4), (11) imply:
% 244.76/51.33  | |   (12)   ~ (e1 = e0)
% 244.76/51.33  | | 
% 244.76/51.33  | | REDUCE: (7), (11) imply:
% 244.76/51.33  | |   (13)  op(e1, e3) = e1
% 244.76/51.33  | | 
% 244.76/51.33  | | GROUND_INST: instantiating (6) with e1, all_56_5, e3, e1, simplifying with
% 244.76/51.33  | |              (2), (13) gives:
% 244.76/51.33  | |   (14)  all_56_5 = e1
% 244.76/51.33  | | 
% 244.76/51.33  | | REDUCE: (1), (14) imply:
% 244.76/51.33  | |   (15)  op(e1, e1) = e1
% 244.76/51.33  | | 
% 244.76/51.33  | | REF_CLOSE: (6), (8), (12), (15) are inconsistent by sub-proof #2220.
% 244.76/51.33  | | 
% 244.76/51.33  | Case 2:
% 244.76/51.33  | | 
% 244.76/51.33  | |   (16)  all_54_8 = e0
% 244.76/51.33  | | 
% 244.76/51.33  | | REF_CLOSE: (4), (5), (16) are inconsistent by sub-proof #2006.
% 244.76/51.33  | | 
% 244.76/51.33  | End of split
% 244.76/51.33  | 
% 244.76/51.33  End of proof
% 244.76/51.33  
% 244.76/51.33  Sub-proof #2006 shows that the following formulas are inconsistent:
% 244.76/51.33  ----------------------------------------------------------------
% 244.76/51.33    (1)  all_54_8 = all_52_2
% 244.76/51.33    (2)  all_54_8 = e0
% 244.76/51.33    (3)   ~ (all_52_2 = e0)
% 244.76/51.33  
% 244.76/51.33  Begin of proof
% 244.76/51.33  | 
% 244.76/51.33  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.33  |   (4)  all_52_2 = e0
% 244.76/51.33  | 
% 244.76/51.33  | SIMP: (4) implies:
% 244.76/51.33  |   (5)  all_52_2 = e0
% 244.76/51.33  | 
% 244.76/51.33  | REDUCE: (3), (5) imply:
% 244.76/51.33  |   (6)  $false
% 244.76/51.33  | 
% 244.76/51.33  | CLOSE: (6) is inconsistent.
% 244.76/51.33  | 
% 244.76/51.33  End of proof
% 244.76/51.33  
% 244.76/51.33  Sub-proof #2007 shows that the following formulas are inconsistent:
% 244.76/51.33  ----------------------------------------------------------------
% 244.76/51.33    (1)  all_54_8 = all_52_2
% 244.76/51.33    (2)  all_54_8 = e2
% 244.76/51.33    (3)   ~ (all_52_2 = e2)
% 244.76/51.33  
% 244.76/51.33  Begin of proof
% 244.76/51.33  | 
% 244.76/51.33  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.33  |   (4)  all_52_2 = e2
% 244.76/51.33  | 
% 244.76/51.33  | SIMP: (4) implies:
% 244.76/51.33  |   (5)  all_52_2 = e2
% 244.76/51.33  | 
% 244.76/51.33  | REDUCE: (3), (5) imply:
% 244.76/51.33  |   (6)  $false
% 244.76/51.33  | 
% 244.76/51.33  | CLOSE: (6) is inconsistent.
% 244.76/51.33  | 
% 244.76/51.33  End of proof
% 244.76/51.33  
% 244.76/51.33  Sub-proof #2008 shows that the following formulas are inconsistent:
% 244.76/51.33  ----------------------------------------------------------------
% 244.76/51.33    (1)  all_54_13 = all_52_7
% 244.76/51.33    (2)  all_54_13 = e0
% 244.76/51.33    (3)   ~ (all_52_7 = e0)
% 244.76/51.33  
% 244.76/51.33  Begin of proof
% 244.76/51.33  | 
% 244.76/51.33  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.33  |   (4)  all_52_7 = e0
% 244.76/51.33  | 
% 244.76/51.33  | SIMP: (4) implies:
% 244.76/51.33  |   (5)  all_52_7 = e0
% 244.76/51.33  | 
% 244.76/51.33  | REDUCE: (3), (5) imply:
% 244.76/51.33  |   (6)  $false
% 244.76/51.33  | 
% 244.76/51.33  | CLOSE: (6) is inconsistent.
% 244.76/51.33  | 
% 244.76/51.33  End of proof
% 244.76/51.33  
% 244.76/51.33  Sub-proof #2009 shows that the following formulas are inconsistent:
% 244.76/51.33  ----------------------------------------------------------------
% 244.76/51.33    (1)  all_54_13 = all_52_7
% 244.76/51.33    (2)  all_54_13 = e2
% 244.76/51.33    (3)   ~ (all_52_7 = e2)
% 244.76/51.33  
% 244.76/51.33  Begin of proof
% 244.76/51.33  | 
% 244.76/51.33  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.33  |   (4)  all_52_7 = e2
% 244.76/51.33  | 
% 244.76/51.33  | SIMP: (4) implies:
% 244.76/51.33  |   (5)  all_52_7 = e2
% 244.76/51.33  | 
% 244.76/51.33  | REDUCE: (3), (5) imply:
% 244.76/51.33  |   (6)  $false
% 244.76/51.33  | 
% 244.76/51.33  | CLOSE: (6) is inconsistent.
% 244.76/51.33  | 
% 244.76/51.33  End of proof
% 244.76/51.33  
% 244.76/51.33  Sub-proof #2010 shows that the following formulas are inconsistent:
% 244.76/51.33  ----------------------------------------------------------------
% 244.76/51.33    (1)  all_54_13 = all_52_7
% 244.76/51.33    (2)  all_54_13 = e3
% 244.76/51.33    (3)   ~ (all_52_7 = e3)
% 244.76/51.33  
% 244.76/51.33  Begin of proof
% 244.76/51.33  | 
% 244.76/51.33  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.33  |   (4)  all_52_7 = e3
% 244.76/51.33  | 
% 244.76/51.33  | SIMP: (4) implies:
% 244.76/51.33  |   (5)  all_52_7 = e3
% 244.76/51.33  | 
% 244.76/51.33  | REDUCE: (3), (5) imply:
% 244.76/51.33  |   (6)  $false
% 244.76/51.33  | 
% 244.76/51.33  | CLOSE: (6) is inconsistent.
% 244.76/51.33  | 
% 244.76/51.33  End of proof
% 244.76/51.33  
% 244.76/51.33  Sub-proof #2011 shows that the following formulas are inconsistent:
% 244.76/51.33  ----------------------------------------------------------------
% 244.76/51.33    (1)  all_54_8 = all_52_2
% 244.76/51.33    (2)  all_54_8 = e3
% 244.76/51.33    (3)   ~ (all_52_2 = e3)
% 244.76/51.33  
% 244.76/51.33  Begin of proof
% 244.76/51.33  | 
% 244.76/51.33  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.33  |   (4)  all_52_2 = e3
% 244.76/51.33  | 
% 244.76/51.33  | SIMP: (4) implies:
% 244.76/51.33  |   (5)  all_52_2 = e3
% 244.76/51.33  | 
% 244.76/51.33  | REDUCE: (3), (5) imply:
% 244.76/51.33  |   (6)  $false
% 244.76/51.33  | 
% 244.76/51.33  | CLOSE: (6) is inconsistent.
% 244.76/51.33  | 
% 244.76/51.33  End of proof
% 244.76/51.33  
% 244.76/51.33  Sub-proof #2012 shows that the following formulas are inconsistent:
% 244.76/51.33  ----------------------------------------------------------------
% 244.76/51.33    (1)   ~ (e3 = e0)
% 244.76/51.33    (2)   ~ (e2 = e0)
% 244.76/51.33    (3)  op(e1, e2) = all_52_6
% 244.76/51.33    (4)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.76/51.33         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.76/51.33    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.76/51.33         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.76/51.33    (6)  all_58_1 = e0
% 244.76/51.33    (7)   ~ (e3 = e1)
% 244.76/51.33    (8)  all_58_7 = e2
% 244.76/51.33    (9)   ~ (e3 = e2)
% 244.76/51.33    (10)  op(e3, e2) = e0
% 244.76/51.33    (11)  op(e1, e2) = e2
% 244.76/51.33    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.33    (13)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.76/51.33          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.76/51.33    (14)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.76/51.33          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.76/51.34    (15)   ~ (e1 = e0)
% 244.76/51.34    (16)  all_58_3 = e2
% 244.76/51.34    (17)  op(e2, e2) = e2
% 244.76/51.34    (18)   ~ (e2 = e1)
% 244.76/51.34  
% 244.76/51.34  Begin of proof
% 244.76/51.34  | 
% 244.76/51.34  | BETA: splitting (14) gives:
% 244.76/51.34  | 
% 244.76/51.34  | Case 1:
% 244.76/51.34  | | 
% 244.76/51.34  | |   (19)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 244.76/51.34  | |           e3)
% 244.76/51.34  | | 
% 244.76/51.34  | | REF_CLOSE: (1), (9), (10), (12), (17), (19) are inconsistent by sub-proof
% 244.76/51.34  | |            #2016.
% 244.76/51.34  | | 
% 244.76/51.34  | Case 2:
% 244.76/51.34  | | 
% 244.76/51.34  | |   (20)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 244.76/51.34  | |           e3)
% 244.76/51.34  | | 
% 244.76/51.34  | | BETA: splitting (20) gives:
% 244.76/51.34  | | 
% 244.76/51.34  | | Case 1:
% 244.76/51.34  | | | 
% 244.76/51.34  | | |   (21)  all_58_7 = e3 & op(e1, e2) = e3
% 244.76/51.34  | | | 
% 244.76/51.34  | | | ALPHA: (21) implies:
% 244.76/51.34  | | |   (22)  op(e1, e2) = e3
% 244.76/51.34  | | | 
% 244.76/51.34  | | | REF_CLOSE: (9), (11), (12), (22) are inconsistent by sub-proof #2207.
% 244.76/51.34  | | | 
% 244.76/51.34  | | Case 2:
% 244.76/51.34  | | | 
% 244.76/51.34  | | |   (23)  all_58_13 = e3 & op(e0, e2) = e3
% 244.76/51.34  | | | 
% 244.76/51.34  | | | ALPHA: (23) implies:
% 244.76/51.34  | | |   (24)  all_58_13 = e3
% 244.76/51.34  | | | 
% 244.76/51.34  | | | BETA: splitting (13) gives:
% 244.76/51.34  | | | 
% 244.76/51.34  | | | Case 1:
% 244.76/51.34  | | | | 
% 244.76/51.34  | | | |   (25)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2)
% 244.76/51.34  | | | |           = e1)
% 244.76/51.34  | | | | 
% 244.76/51.34  | | | | REF_CLOSE: (6), (12), (15), (17), (18), (25) are inconsistent by
% 244.76/51.34  | | | |            sub-proof #2014.
% 244.76/51.34  | | | | 
% 244.76/51.34  | | | Case 2:
% 244.76/51.34  | | | | 
% 244.76/51.34  | | | |   (26)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 244.76/51.34  | | | |           = e1)
% 244.76/51.34  | | | | 
% 244.76/51.34  | | | | BETA: splitting (26) gives:
% 244.76/51.34  | | | | 
% 244.76/51.34  | | | | Case 1:
% 244.76/51.34  | | | | | 
% 244.76/51.34  | | | | |   (27)  all_58_7 = e1 & op(e1, e2) = e1
% 244.76/51.34  | | | | | 
% 244.76/51.34  | | | | | ALPHA: (27) implies:
% 244.76/51.34  | | | | |   (28)  all_58_7 = e1
% 244.76/51.34  | | | | |   (29)  op(e1, e2) = e1
% 244.76/51.34  | | | | | 
% 244.76/51.34  | | | | | COMBINE_EQS: (8), (28) imply:
% 244.76/51.34  | | | | |   (30)  e2 = e1
% 244.76/51.34  | | | | | 
% 244.76/51.34  | | | | | COMBINE_EQS: (16), (30) imply:
% 244.76/51.34  | | | | |   (31)  all_58_3 = e1
% 244.76/51.34  | | | | | 
% 244.76/51.34  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (12), (14), (15), (17),
% 244.76/51.34  | | | | |            (18), (28), (29), (31) are inconsistent by sub-proof #2127.
% 244.76/51.34  | | | | | 
% 244.76/51.34  | | | | Case 2:
% 244.76/51.34  | | | | | 
% 244.76/51.34  | | | | |   (32)  all_58_13 = e1 & op(e0, e2) = e1
% 244.76/51.34  | | | | | 
% 244.76/51.34  | | | | | REF_CLOSE: (7), (24), (32) are inconsistent by sub-proof #2013.
% 244.76/51.34  | | | | | 
% 244.76/51.34  | | | | End of split
% 244.76/51.34  | | | | 
% 244.76/51.34  | | | End of split
% 244.76/51.34  | | | 
% 244.76/51.34  | | End of split
% 244.76/51.34  | | 
% 244.76/51.34  | End of split
% 244.76/51.34  | 
% 244.76/51.34  End of proof
% 244.76/51.34  
% 244.76/51.34  Sub-proof #2013 shows that the following formulas are inconsistent:
% 244.76/51.34  ----------------------------------------------------------------
% 244.76/51.34    (1)  all_58_13 = e1 & op(e0, e2) = e1
% 244.76/51.34    (2)  all_58_13 = e3
% 244.76/51.34    (3)   ~ (e3 = e1)
% 244.76/51.34  
% 244.76/51.34  Begin of proof
% 244.76/51.34  | 
% 244.76/51.34  | ALPHA: (1) implies:
% 244.76/51.34  |   (4)  all_58_13 = e1
% 244.76/51.34  | 
% 244.76/51.34  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.34  |   (5)  e3 = e1
% 244.76/51.34  | 
% 244.76/51.34  | REDUCE: (3), (5) imply:
% 244.76/51.34  |   (6)  $false
% 244.76/51.34  | 
% 244.76/51.34  | CLOSE: (6) is inconsistent.
% 244.76/51.34  | 
% 244.76/51.34  End of proof
% 244.76/51.34  
% 244.76/51.34  Sub-proof #2014 shows that the following formulas are inconsistent:
% 244.76/51.34  ----------------------------------------------------------------
% 244.76/51.34    (1)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 244.76/51.34    (2)  all_58_1 = e0
% 244.76/51.34    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.34    (4)   ~ (e1 = e0)
% 244.76/51.34    (5)  op(e2, e2) = e2
% 244.76/51.34    (6)   ~ (e2 = e1)
% 244.76/51.34  
% 244.76/51.34  Begin of proof
% 244.76/51.34  | 
% 244.76/51.34  | BETA: splitting (1) gives:
% 244.76/51.34  | 
% 244.76/51.34  | Case 1:
% 244.76/51.34  | | 
% 244.76/51.34  | |   (7)  all_58_1 = e1 & op(e3, e2) = e1
% 244.76/51.34  | | 
% 244.76/51.34  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2015.
% 244.76/51.34  | | 
% 244.76/51.34  | Case 2:
% 244.76/51.34  | | 
% 244.76/51.34  | |   (8)  all_58_3 = e1 & op(e2, e2) = e1
% 244.76/51.34  | | 
% 244.76/51.34  | | ALPHA: (8) implies:
% 244.76/51.34  | |   (9)  op(e2, e2) = e1
% 244.76/51.34  | | 
% 244.76/51.34  | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #2235.
% 244.76/51.34  | | 
% 244.76/51.34  | End of split
% 244.76/51.34  | 
% 244.76/51.34  End of proof
% 244.76/51.34  
% 244.76/51.34  Sub-proof #2015 shows that the following formulas are inconsistent:
% 244.76/51.34  ----------------------------------------------------------------
% 244.76/51.34    (1)  all_58_1 = e1 & op(e3, e2) = e1
% 244.76/51.34    (2)  all_58_1 = e0
% 244.76/51.34    (3)   ~ (e1 = e0)
% 244.76/51.34  
% 244.76/51.34  Begin of proof
% 244.76/51.34  | 
% 244.76/51.34  | ALPHA: (1) implies:
% 244.76/51.34  |   (4)  all_58_1 = e1
% 244.76/51.34  | 
% 244.76/51.34  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.34  |   (5)  e1 = e0
% 244.76/51.34  | 
% 244.76/51.34  | SIMP: (5) implies:
% 244.76/51.34  |   (6)  e1 = e0
% 244.76/51.34  | 
% 244.76/51.34  | REDUCE: (3), (6) imply:
% 244.76/51.34  |   (7)  $false
% 244.76/51.34  | 
% 244.76/51.34  | CLOSE: (7) is inconsistent.
% 244.76/51.34  | 
% 244.76/51.34  End of proof
% 244.76/51.34  
% 244.76/51.34  Sub-proof #2016 shows that the following formulas are inconsistent:
% 244.76/51.34  ----------------------------------------------------------------
% 244.76/51.34    (1)   ~ (e3 = e0)
% 244.76/51.34    (2)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 244.76/51.34    (3)   ~ (e3 = e2)
% 244.76/51.34    (4)  op(e3, e2) = e0
% 244.76/51.34    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.34    (6)  op(e2, e2) = e2
% 244.76/51.34  
% 244.76/51.34  Begin of proof
% 244.76/51.34  | 
% 244.76/51.34  | BETA: splitting (2) gives:
% 244.76/51.34  | 
% 244.76/51.34  | Case 1:
% 244.76/51.34  | | 
% 244.76/51.34  | |   (7)  all_58_1 = e3 & op(e3, e2) = e3
% 244.76/51.34  | | 
% 244.76/51.34  | | ALPHA: (7) implies:
% 244.76/51.34  | |   (8)  op(e3, e2) = e3
% 244.76/51.34  | | 
% 244.76/51.34  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2099.
% 244.76/51.34  | | 
% 244.76/51.34  | Case 2:
% 244.76/51.34  | | 
% 244.76/51.34  | |   (9)  all_58_3 = e3 & op(e2, e2) = e3
% 244.76/51.34  | | 
% 244.76/51.34  | | ALPHA: (9) implies:
% 244.76/51.34  | |   (10)  op(e2, e2) = e3
% 244.76/51.34  | | 
% 244.76/51.34  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #2140.
% 244.76/51.34  | | 
% 244.76/51.34  | End of split
% 244.76/51.34  | 
% 244.76/51.34  End of proof
% 244.76/51.34  
% 244.76/51.34  Sub-proof #2017 shows that the following formulas are inconsistent:
% 244.76/51.34  ----------------------------------------------------------------
% 244.76/51.34    (1)   ~ (e3 = e0)
% 244.76/51.34    (2)   ~ (e3 = e2)
% 244.76/51.34    (3)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.76/51.34    (4)  all_58_11 = e2
% 244.76/51.34    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.34    (6)  op(e1, e1) = e0
% 244.76/51.34  
% 244.76/51.34  Begin of proof
% 244.76/51.34  | 
% 244.76/51.34  | BETA: splitting (3) gives:
% 244.76/51.34  | 
% 244.76/51.34  | Case 1:
% 244.76/51.34  | | 
% 244.76/51.35  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 244.76/51.35  | | 
% 244.76/51.35  | | REF_CLOSE: (1), (5), (6), (7) are inconsistent by sub-proof #2018.
% 244.76/51.35  | | 
% 244.76/51.35  | Case 2:
% 244.76/51.35  | | 
% 244.76/51.35  | |   (8)  all_58_11 = e3 & op(e1, e0) = e3
% 244.76/51.35  | | 
% 244.76/51.35  | | ALPHA: (8) implies:
% 244.76/51.35  | |   (9)  all_58_11 = e3
% 244.76/51.35  | | 
% 244.76/51.35  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #2030.
% 244.76/51.35  | | 
% 244.76/51.35  | End of split
% 244.76/51.35  | 
% 244.76/51.35  End of proof
% 244.76/51.35  
% 244.76/51.35  Sub-proof #2018 shows that the following formulas are inconsistent:
% 244.76/51.35  ----------------------------------------------------------------
% 244.76/51.35    (1)  all_58_8 = e3 & op(e1, e1) = e3
% 244.76/51.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.35    (3)  op(e1, e1) = e0
% 244.76/51.35    (4)   ~ (e3 = e0)
% 244.76/51.35  
% 244.76/51.35  Begin of proof
% 244.76/51.35  | 
% 244.76/51.35  | ALPHA: (1) implies:
% 244.76/51.35  |   (5)  op(e1, e1) = e3
% 244.76/51.35  | 
% 244.76/51.35  | GROUND_INST: instantiating (2) with e0, e3, e1, e1, simplifying with (3), (5)
% 244.76/51.35  |              gives:
% 244.76/51.35  |   (6)  e3 = e0
% 244.76/51.35  | 
% 244.76/51.35  | REDUCE: (4), (6) imply:
% 244.76/51.35  |   (7)  $false
% 244.76/51.35  | 
% 244.76/51.35  | CLOSE: (7) is inconsistent.
% 244.76/51.35  | 
% 244.76/51.35  End of proof
% 244.76/51.35  
% 244.76/51.35  Sub-proof #2019 shows that the following formulas are inconsistent:
% 244.76/51.35  ----------------------------------------------------------------
% 244.76/51.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.35    (2)  op(e1, e0) = e2
% 244.76/51.35    (3)  op(e1, e0) = e1
% 244.76/51.35    (4)   ~ (e2 = e1)
% 244.76/51.35  
% 244.76/51.35  Begin of proof
% 244.76/51.35  | 
% 244.76/51.35  | GROUND_INST: instantiating (1) with e2, e1, e0, e1, simplifying with (2), (3)
% 244.76/51.35  |              gives:
% 244.76/51.35  |   (5)  e2 = e1
% 244.76/51.35  | 
% 244.76/51.35  | REDUCE: (4), (5) imply:
% 244.76/51.35  |   (6)  $false
% 244.76/51.35  | 
% 244.76/51.35  | CLOSE: (6) is inconsistent.
% 244.76/51.35  | 
% 244.76/51.35  End of proof
% 244.76/51.35  
% 244.76/51.35  Sub-proof #2020 shows that the following formulas are inconsistent:
% 244.76/51.35  ----------------------------------------------------------------
% 244.76/51.35    (1)  op(e1, e1) = e1
% 244.76/51.35    (2)  op(e1, e2) = all_52_6
% 244.76/51.35    (3)  op(e1, e0) = all_52_14
% 244.76/51.35    (4)   ~ (all_52_6 = e0)
% 244.76/51.35    (5)   ~ (all_52_14 = e0)
% 244.76/51.35    (6)   ~ (all_52_2 = e0)
% 244.76/51.35    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.35    (8)  op(e1, e3) = all_52_2
% 244.76/51.35    (9)   ~ (e1 = e0)
% 244.76/51.35    (10)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.76/51.35          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.76/51.35  
% 244.76/51.35  Begin of proof
% 244.76/51.35  | 
% 244.76/51.35  | BETA: splitting (10) gives:
% 244.76/51.35  | 
% 244.76/51.35  | Case 1:
% 244.76/51.35  | | 
% 244.76/51.35  | |   (11)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 244.76/51.35  | |           e0)
% 244.76/51.35  | | 
% 244.76/51.35  | | REF_CLOSE: (2), (4), (6), (7), (8), (11) are inconsistent by sub-proof
% 244.76/51.35  | |            #2021.
% 244.76/51.35  | | 
% 244.76/51.35  | Case 2:
% 244.76/51.35  | | 
% 244.76/51.35  | |   (12)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.76/51.35  | |           e0)
% 244.76/51.35  | | 
% 244.76/51.35  | | BETA: splitting (12) gives:
% 244.76/51.35  | | 
% 244.76/51.35  | | Case 1:
% 244.76/51.35  | | | 
% 244.76/51.35  | | |   (13)  all_58_8 = e0 & op(e1, e1) = e0
% 244.76/51.35  | | | 
% 244.76/51.35  | | | ALPHA: (13) implies:
% 244.76/51.35  | | |   (14)  op(e1, e1) = e0
% 244.76/51.35  | | | 
% 244.76/51.35  | | | REF_CLOSE: (1), (7), (9), (14) are inconsistent by sub-proof #2220.
% 244.76/51.35  | | | 
% 244.76/51.35  | | Case 2:
% 244.76/51.35  | | | 
% 244.76/51.35  | | |   (15)  all_58_11 = e0 & op(e1, e0) = e0
% 244.76/51.35  | | | 
% 244.76/51.35  | | | ALPHA: (15) implies:
% 244.76/51.35  | | |   (16)  op(e1, e0) = e0
% 244.76/51.35  | | | 
% 244.76/51.35  | | | REF_CLOSE: (3), (5), (7), (16) are inconsistent by sub-proof #2323.
% 244.76/51.35  | | | 
% 244.76/51.35  | | End of split
% 244.76/51.35  | | 
% 244.76/51.35  | End of split
% 244.76/51.35  | 
% 244.76/51.35  End of proof
% 244.76/51.35  
% 244.76/51.35  Sub-proof #2021 shows that the following formulas are inconsistent:
% 244.76/51.35  ----------------------------------------------------------------
% 244.76/51.35    (1)  op(e1, e2) = all_52_6
% 244.76/51.35    (2)   ~ (all_52_6 = e0)
% 244.76/51.35    (3)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 244.76/51.35    (4)   ~ (all_52_2 = e0)
% 244.76/51.35    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.35    (6)  op(e1, e3) = all_52_2
% 244.76/51.35  
% 244.76/51.35  Begin of proof
% 244.76/51.35  | 
% 244.76/51.35  | BETA: splitting (3) gives:
% 244.76/51.35  | 
% 244.76/51.35  | Case 1:
% 244.76/51.35  | | 
% 244.76/51.35  | |   (7)  all_58_6 = e0 & op(e1, e3) = e0
% 244.76/51.35  | | 
% 244.76/51.35  | | ALPHA: (7) implies:
% 244.76/51.35  | |   (8)  op(e1, e3) = e0
% 244.76/51.35  | | 
% 244.76/51.35  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #2023.
% 244.76/51.35  | | 
% 244.76/51.35  | Case 2:
% 244.76/51.35  | | 
% 244.76/51.35  | |   (9)  all_58_7 = e0 & op(e1, e2) = e0
% 244.76/51.35  | | 
% 244.76/51.35  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2022.
% 244.76/51.35  | | 
% 244.76/51.35  | End of split
% 244.76/51.35  | 
% 244.76/51.35  End of proof
% 244.76/51.35  
% 244.76/51.35  Sub-proof #2022 shows that the following formulas are inconsistent:
% 244.76/51.35  ----------------------------------------------------------------
% 244.76/51.35    (1)  all_58_7 = e0 & op(e1, e2) = e0
% 244.76/51.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.35    (3)  op(e1, e2) = all_52_6
% 244.76/51.35    (4)   ~ (all_52_6 = e0)
% 244.76/51.35  
% 244.76/51.35  Begin of proof
% 244.76/51.35  | 
% 244.76/51.35  | ALPHA: (1) implies:
% 244.76/51.35  |   (5)  op(e1, e2) = e0
% 244.76/51.35  | 
% 244.76/51.35  | GROUND_INST: instantiating (2) with all_52_6, e0, e2, e1, simplifying with
% 244.76/51.35  |              (3), (5) gives:
% 244.76/51.35  |   (6)  all_52_6 = e0
% 244.76/51.35  | 
% 244.76/51.35  | REDUCE: (4), (6) imply:
% 244.76/51.35  |   (7)  $false
% 244.76/51.35  | 
% 244.76/51.35  | CLOSE: (7) is inconsistent.
% 244.76/51.35  | 
% 244.76/51.35  End of proof
% 244.76/51.35  
% 244.76/51.35  Sub-proof #2023 shows that the following formulas are inconsistent:
% 244.76/51.35  ----------------------------------------------------------------
% 244.76/51.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.35    (2)  op(e1, e3) = all_52_2
% 244.76/51.35    (3)  op(e1, e3) = e0
% 244.76/51.35    (4)   ~ (all_52_2 = e0)
% 244.76/51.35  
% 244.76/51.35  Begin of proof
% 244.76/51.35  | 
% 244.76/51.35  | GROUND_INST: instantiating (1) with all_52_2, e0, e3, e1, simplifying with
% 244.76/51.35  |              (2), (3) gives:
% 244.76/51.35  |   (5)  all_52_2 = e0
% 244.76/51.35  | 
% 244.76/51.35  | REDUCE: (4), (5) imply:
% 244.76/51.35  |   (6)  $false
% 244.76/51.35  | 
% 244.76/51.35  | CLOSE: (6) is inconsistent.
% 244.76/51.35  | 
% 244.76/51.35  End of proof
% 244.76/51.35  
% 244.76/51.35  Sub-proof #2024 shows that the following formulas are inconsistent:
% 244.76/51.35  ----------------------------------------------------------------
% 244.76/51.35    (1)  all_58_6 = e3
% 244.76/51.35    (2)  all_58_6 = e2
% 244.76/51.35    (3)   ~ (e3 = e2)
% 244.76/51.35  
% 244.76/51.35  Begin of proof
% 244.76/51.35  | 
% 244.76/51.35  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.35  |   (4)  e3 = e2
% 244.76/51.35  | 
% 244.76/51.35  | SIMP: (4) implies:
% 244.76/51.35  |   (5)  e3 = e2
% 244.76/51.35  | 
% 244.76/51.35  | REDUCE: (3), (5) imply:
% 244.76/51.36  |   (6)  $false
% 244.76/51.36  | 
% 244.76/51.36  | CLOSE: (6) is inconsistent.
% 244.76/51.36  | 
% 244.76/51.36  End of proof
% 244.76/51.36  
% 244.76/51.36  Sub-proof #2025 shows that the following formulas are inconsistent:
% 244.76/51.36  ----------------------------------------------------------------
% 244.76/51.36    (1)   ~ (e2 = e0)
% 244.76/51.36    (2)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 244.76/51.36           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 244.76/51.36             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.76/51.36           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 244.76/51.36             e1) = e3 & op(e1, e3) = e3)
% 244.76/51.36    (3)  op(e3, e2) = e0
% 244.76/51.36    (4)   ~ (all_52_2 = e3)
% 244.76/51.36    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.36    (6)  op(e1, e3) = all_52_2
% 244.76/51.36  
% 244.76/51.36  Begin of proof
% 244.76/51.36  | 
% 244.76/51.36  | BETA: splitting (2) gives:
% 244.76/51.36  | 
% 244.76/51.36  | Case 1:
% 244.76/51.36  | | 
% 244.76/51.36  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.76/51.36  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.76/51.36  | |        op(e2, e3) = e2
% 244.76/51.36  | | 
% 244.76/51.36  | | ALPHA: (7) implies:
% 244.76/51.36  | |   (8)  op(e3, e2) = e2
% 244.76/51.36  | | 
% 244.76/51.36  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #2026.
% 244.76/51.36  | | 
% 244.76/51.36  | Case 2:
% 244.76/51.36  | | 
% 244.76/51.36  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.76/51.36  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.76/51.36  | |        op(e1, e3) = e3
% 244.76/51.36  | | 
% 244.76/51.36  | | ALPHA: (9) implies:
% 244.76/51.36  | |   (10)  op(e1, e3) = e3
% 244.76/51.36  | | 
% 244.76/51.36  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #2335.
% 244.76/51.36  | | 
% 244.76/51.36  | End of split
% 244.76/51.36  | 
% 244.76/51.36  End of proof
% 244.76/51.36  
% 244.76/51.36  Sub-proof #2026 shows that the following formulas are inconsistent:
% 244.76/51.36  ----------------------------------------------------------------
% 244.76/51.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.36    (2)  op(e3, e2) = e2
% 244.76/51.36    (3)  op(e3, e2) = e0
% 244.76/51.36    (4)   ~ (e2 = e0)
% 244.76/51.36  
% 244.76/51.36  Begin of proof
% 244.76/51.36  | 
% 244.76/51.36  | GROUND_INST: instantiating (1) with e0, e2, e2, e3, simplifying with (2), (3)
% 244.76/51.36  |              gives:
% 244.76/51.36  |   (5)  e2 = e0
% 244.76/51.36  | 
% 244.76/51.36  | REDUCE: (4), (5) imply:
% 244.76/51.36  |   (6)  $false
% 244.76/51.36  | 
% 244.76/51.36  | CLOSE: (6) is inconsistent.
% 244.76/51.36  | 
% 244.76/51.36  End of proof
% 244.76/51.36  
% 244.76/51.36  Sub-proof #2027 shows that the following formulas are inconsistent:
% 244.76/51.36  ----------------------------------------------------------------
% 244.76/51.36    (1)   ~ (e3 = e0)
% 244.76/51.36    (2)   ~ (e2 = e0)
% 244.76/51.36    (3)   ~ (e3 = e1)
% 244.76/51.36    (4)   ~ (e3 = e2)
% 244.76/51.36    (5)  op(e1, e3) = e1
% 244.76/51.36    (6)  all_58_15 = e1
% 244.76/51.36    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.76/51.36         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.76/51.36    (8)  all_58_6 = e1
% 244.76/51.36    (9)  op(e1, e1) = e2
% 244.76/51.36    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.36    (11)   ~ (e1 = e0)
% 244.76/51.36    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.76/51.36          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.76/51.36    (13)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.76/51.36    (14)   ~ (e2 = e1)
% 244.76/51.36  
% 244.76/51.36  Begin of proof
% 244.76/51.36  | 
% 244.76/51.36  | BETA: splitting (13) gives:
% 244.76/51.36  | 
% 244.76/51.36  | Case 1:
% 244.76/51.36  | | 
% 244.76/51.36  | |   (15)  all_58_11 = e2 & op(e1, e0) = e2
% 244.76/51.36  | | 
% 244.76/51.36  | | ALPHA: (15) implies:
% 244.76/51.36  | |   (16)  all_58_11 = e2
% 244.76/51.36  | | 
% 244.76/51.36  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (16)
% 244.76/51.36  | |            are inconsistent by sub-proof #2028.
% 244.76/51.36  | | 
% 244.76/51.36  | Case 2:
% 244.76/51.36  | | 
% 244.76/51.36  | |   (17)  all_58_15 = e2 & op(e0, e0) = e2
% 244.76/51.36  | | 
% 244.76/51.36  | | ALPHA: (17) implies:
% 244.76/51.36  | |   (18)  all_58_15 = e2
% 244.76/51.36  | | 
% 244.76/51.36  | | REF_CLOSE: (6), (14), (18) are inconsistent by sub-proof #2231.
% 244.76/51.36  | | 
% 244.76/51.36  | End of split
% 244.76/51.36  | 
% 244.76/51.36  End of proof
% 244.76/51.36  
% 244.76/51.36  Sub-proof #2028 shows that the following formulas are inconsistent:
% 244.76/51.36  ----------------------------------------------------------------
% 244.76/51.36    (1)   ~ (e3 = e0)
% 244.76/51.36    (2)   ~ (e2 = e0)
% 244.76/51.36    (3)   ~ (e3 = e1)
% 244.76/51.36    (4)   ~ (e3 = e2)
% 244.76/51.36    (5)  op(e1, e3) = e1
% 244.76/51.36    (6)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.76/51.36         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.76/51.36    (7)  all_58_6 = e1
% 244.76/51.36    (8)  all_58_11 = e2
% 244.76/51.36    (9)  op(e1, e1) = e2
% 244.76/51.36    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.36    (11)   ~ (e1 = e0)
% 244.76/51.36    (12)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.76/51.36          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.76/51.36  
% 244.76/51.36  Begin of proof
% 244.76/51.36  | 
% 244.76/51.36  | BETA: splitting (6) gives:
% 244.76/51.36  | 
% 244.76/51.36  | Case 1:
% 244.76/51.36  | | 
% 244.76/51.36  | |   (13)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.76/51.36  | |           e3)
% 244.76/51.36  | | 
% 244.76/51.36  | | BETA: splitting (13) gives:
% 244.76/51.36  | | 
% 244.76/51.36  | | Case 1:
% 244.76/51.36  | | | 
% 244.76/51.36  | | |   (14)  all_58_6 = e3 & op(e1, e3) = e3
% 244.76/51.36  | | | 
% 244.76/51.36  | | | ALPHA: (14) implies:
% 244.76/51.36  | | |   (15)  op(e1, e3) = e3
% 244.76/51.36  | | | 
% 244.76/51.36  | | | REF_CLOSE: (3), (5), (10), (15) are inconsistent by sub-proof #2225.
% 244.76/51.36  | | | 
% 244.76/51.36  | | Case 2:
% 244.76/51.36  | | | 
% 244.76/51.36  | | |   (16)  all_58_7 = e3 & op(e1, e2) = e3
% 244.76/51.36  | | | 
% 244.76/51.36  | | | ALPHA: (16) implies:
% 244.76/51.36  | | |   (17)  all_58_7 = e3
% 244.76/51.36  | | | 
% 244.76/51.36  | | | REF_CLOSE: (1), (2), (7), (8), (9), (10), (11), (12), (17) are
% 244.76/51.36  | | |            inconsistent by sub-proof #2031.
% 244.76/51.36  | | | 
% 244.76/51.36  | | End of split
% 244.76/51.36  | | 
% 244.76/51.36  | Case 2:
% 244.76/51.36  | | 
% 244.76/51.36  | |   (18)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.76/51.36  | |           e3)
% 244.76/51.36  | | 
% 244.76/51.36  | | REF_CLOSE: (4), (8), (9), (10), (18) are inconsistent by sub-proof #2029.
% 244.76/51.36  | | 
% 244.76/51.36  | End of split
% 244.76/51.36  | 
% 244.76/51.36  End of proof
% 244.76/51.36  
% 244.76/51.36  Sub-proof #2029 shows that the following formulas are inconsistent:
% 244.76/51.36  ----------------------------------------------------------------
% 244.76/51.36    (1)   ~ (e3 = e2)
% 244.76/51.36    (2)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.76/51.36    (3)  all_58_11 = e2
% 244.76/51.36    (4)  op(e1, e1) = e2
% 244.76/51.37    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | BETA: splitting (2) gives:
% 244.76/51.37  | 
% 244.76/51.37  | Case 1:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (6)  all_58_8 = e3 & op(e1, e1) = e3
% 244.76/51.37  | | 
% 244.76/51.37  | | ALPHA: (6) implies:
% 244.76/51.37  | |   (7)  op(e1, e1) = e3
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #2206.
% 244.76/51.37  | | 
% 244.76/51.37  | Case 2:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (8)  all_58_11 = e3 & op(e1, e0) = e3
% 244.76/51.37  | | 
% 244.76/51.37  | | ALPHA: (8) implies:
% 244.76/51.37  | |   (9)  all_58_11 = e3
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #2030.
% 244.76/51.37  | | 
% 244.76/51.37  | End of split
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2030 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  all_58_11 = e3
% 244.76/51.37    (2)  all_58_11 = e2
% 244.76/51.37    (3)   ~ (e3 = e2)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.37  |   (4)  e3 = e2
% 244.76/51.37  | 
% 244.76/51.37  | SIMP: (4) implies:
% 244.76/51.37  |   (5)  e3 = e2
% 244.76/51.37  | 
% 244.76/51.37  | REDUCE: (3), (5) imply:
% 244.76/51.37  |   (6)  $false
% 244.76/51.37  | 
% 244.76/51.37  | CLOSE: (6) is inconsistent.
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2031 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)   ~ (e3 = e0)
% 244.76/51.37    (2)   ~ (e2 = e0)
% 244.76/51.37    (3)  all_58_7 = e3
% 244.76/51.37    (4)  all_58_6 = e1
% 244.76/51.37    (5)  all_58_11 = e2
% 244.76/51.37    (6)  op(e1, e1) = e2
% 244.76/51.37    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.37    (8)   ~ (e1 = e0)
% 244.76/51.37    (9)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.76/51.37         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | BETA: splitting (9) gives:
% 244.76/51.37  | 
% 244.76/51.37  | Case 1:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (10)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 244.76/51.37  | |           e0)
% 244.76/51.37  | | 
% 244.76/51.37  | | BETA: splitting (10) gives:
% 244.76/51.37  | | 
% 244.76/51.37  | | Case 1:
% 244.76/51.37  | | | 
% 244.76/51.37  | | |   (11)  all_58_6 = e0 & op(e1, e3) = e0
% 244.76/51.37  | | | 
% 244.76/51.37  | | | REF_CLOSE: (4), (8), (11) are inconsistent by sub-proof #2205.
% 244.76/51.37  | | | 
% 244.76/51.37  | | Case 2:
% 244.76/51.37  | | | 
% 244.76/51.37  | | |   (12)  all_58_7 = e0 & op(e1, e2) = e0
% 244.76/51.37  | | | 
% 244.76/51.37  | | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #2034.
% 244.76/51.37  | | | 
% 244.76/51.37  | | End of split
% 244.76/51.37  | | 
% 244.76/51.37  | Case 2:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (13)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.76/51.37  | |           e0)
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (2), (5), (6), (7), (13) are inconsistent by sub-proof #2032.
% 244.76/51.37  | | 
% 244.76/51.37  | End of split
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2032 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.76/51.37    (2)   ~ (e2 = e0)
% 244.76/51.37    (3)  all_58_11 = e2
% 244.76/51.37    (4)  op(e1, e1) = e2
% 244.76/51.37    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | BETA: splitting (1) gives:
% 244.76/51.37  | 
% 244.76/51.37  | Case 1:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (6)  all_58_8 = e0 & op(e1, e1) = e0
% 244.76/51.37  | | 
% 244.76/51.37  | | ALPHA: (6) implies:
% 244.76/51.37  | |   (7)  op(e1, e1) = e0
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #2211.
% 244.76/51.37  | | 
% 244.76/51.37  | Case 2:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (8)  all_58_11 = e0 & op(e1, e0) = e0
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2033.
% 244.76/51.37  | | 
% 244.76/51.37  | End of split
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2033 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  all_58_11 = e0 & op(e1, e0) = e0
% 244.76/51.37    (2)  all_58_11 = e2
% 244.76/51.37    (3)   ~ (e2 = e0)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | ALPHA: (1) implies:
% 244.76/51.37  |   (4)  all_58_11 = e0
% 244.76/51.37  | 
% 244.76/51.37  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.37  |   (5)  e2 = e0
% 244.76/51.37  | 
% 244.76/51.37  | REDUCE: (3), (5) imply:
% 244.76/51.37  |   (6)  $false
% 244.76/51.37  | 
% 244.76/51.37  | CLOSE: (6) is inconsistent.
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2034 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  all_58_7 = e0 & op(e1, e2) = e0
% 244.76/51.37    (2)  all_58_7 = e3
% 244.76/51.37    (3)   ~ (e3 = e0)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | ALPHA: (1) implies:
% 244.76/51.37  |   (4)  all_58_7 = e0
% 244.76/51.37  | 
% 244.76/51.37  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.37  |   (5)  e3 = e0
% 244.76/51.37  | 
% 244.76/51.37  | REDUCE: (3), (5) imply:
% 244.76/51.37  |   (6)  $false
% 244.76/51.37  | 
% 244.76/51.37  | CLOSE: (6) is inconsistent.
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2035 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)   ~ (e2 = e0)
% 244.76/51.37    (2)  all_58_14 = e2
% 244.76/51.37    (3)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.76/51.37    (4)  op(e1, e1) = e2
% 244.76/51.37    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | BETA: splitting (3) gives:
% 244.76/51.37  | 
% 244.76/51.37  | Case 1:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (6)  all_58_8 = e0 & op(e1, e1) = e0
% 244.76/51.37  | | 
% 244.76/51.37  | | ALPHA: (6) implies:
% 244.76/51.37  | |   (7)  op(e1, e1) = e0
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #2211.
% 244.76/51.37  | | 
% 244.76/51.37  | Case 2:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (8)  all_58_14 = e0 & op(e0, e1) = e0
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #2036.
% 244.76/51.37  | | 
% 244.76/51.37  | End of split
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2036 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  all_58_14 = e0 & op(e0, e1) = e0
% 244.76/51.37    (2)  all_58_14 = e2
% 244.76/51.37    (3)   ~ (e2 = e0)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | ALPHA: (1) implies:
% 244.76/51.37  |   (4)  all_58_14 = e0
% 244.76/51.37  | 
% 244.76/51.37  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.37  |   (5)  e2 = e0
% 244.76/51.37  | 
% 244.76/51.37  | REDUCE: (3), (5) imply:
% 244.76/51.37  |   (6)  $false
% 244.76/51.37  | 
% 244.76/51.37  | CLOSE: (6) is inconsistent.
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2037 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  all_58_5 = e0
% 244.76/51.37    (2)   ~ (e3 = e0)
% 244.76/51.37    (3)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.76/51.37         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.76/51.37    (4)  all_58_14 = e2
% 244.76/51.37    (5)   ~ (e3 = e1)
% 244.76/51.37    (6)  all_58_8 = e2
% 244.76/51.37    (7)  op(e2, e1) = all_52_9
% 244.76/51.37    (8)   ~ (e3 = e2)
% 244.76/51.37    (9)  op(e1, e1) = e2
% 244.76/51.37    (10)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.76/51.37          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.76/51.37    (11)  op(e2, e1) = e0
% 244.76/51.37    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.37    (13)   ~ (e1 = e0)
% 244.76/51.37    (14)   ~ (e2 = e1)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | BETA: splitting (10) gives:
% 244.76/51.37  | 
% 244.76/51.37  | Case 1:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (15)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 244.76/51.37  | |           e3)
% 244.76/51.37  | | 
% 244.76/51.37  | | BETA: splitting (15) gives:
% 244.76/51.37  | | 
% 244.76/51.37  | | Case 1:
% 244.76/51.37  | | | 
% 244.76/51.37  | | |   (16)  all_58_4 = e3 & op(e3, e1) = e3
% 244.76/51.37  | | | 
% 244.76/51.37  | | | ALPHA: (16) implies:
% 244.76/51.37  | | |   (17)  all_58_4 = e3
% 244.76/51.37  | | | 
% 244.76/51.37  | | | REF_CLOSE: (3), (4), (5), (6), (7), (11), (12), (13), (14), (17) are
% 244.76/51.37  | | |            inconsistent by sub-proof #2039.
% 244.76/51.37  | | | 
% 244.76/51.37  | | Case 2:
% 244.76/51.37  | | | 
% 244.76/51.37  | | |   (18)  all_58_5 = e3 & op(e2, e1) = e3
% 244.76/51.37  | | | 
% 244.76/51.37  | | | ALPHA: (18) implies:
% 244.76/51.37  | | |   (19)  all_58_5 = e3
% 244.76/51.37  | | | 
% 244.76/51.37  | | | REF_CLOSE: (1), (2), (19) are inconsistent by sub-proof #2038.
% 244.76/51.37  | | | 
% 244.76/51.37  | | End of split
% 244.76/51.37  | | 
% 244.76/51.37  | Case 2:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (20)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 244.76/51.37  | |           e3)
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (4), (8), (9), (12), (20) are inconsistent by sub-proof #2116.
% 244.76/51.37  | | 
% 244.76/51.37  | End of split
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2038 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  all_58_5 = e3
% 244.76/51.37    (2)  all_58_5 = e0
% 244.76/51.37    (3)   ~ (e3 = e0)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.37  |   (4)  e3 = e0
% 244.76/51.37  | 
% 244.76/51.37  | SIMP: (4) implies:
% 244.76/51.37  |   (5)  e3 = e0
% 244.76/51.37  | 
% 244.76/51.37  | REDUCE: (3), (5) imply:
% 244.76/51.37  |   (6)  $false
% 244.76/51.37  | 
% 244.76/51.37  | CLOSE: (6) is inconsistent.
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2039 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.76/51.37         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.76/51.37    (2)  all_58_14 = e2
% 244.76/51.37    (3)   ~ (e3 = e1)
% 244.76/51.37    (4)  all_58_8 = e2
% 244.76/51.37    (5)  op(e2, e1) = all_52_9
% 244.76/51.37    (6)  op(e2, e1) = e0
% 244.76/51.37    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.37    (8)   ~ (e1 = e0)
% 244.76/51.37    (9)  all_58_4 = e3
% 244.76/51.37    (10)   ~ (e2 = e1)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | BETA: splitting (1) gives:
% 244.76/51.37  | 
% 244.76/51.37  | Case 1:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (11)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 244.76/51.37  | |           e1)
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (11) are inconsistent by sub-proof
% 244.76/51.37  | |            #2041.
% 244.76/51.37  | | 
% 244.76/51.37  | Case 2:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (12)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 244.76/51.37  | |           e1)
% 244.76/51.37  | | 
% 244.76/51.37  | | BETA: splitting (12) gives:
% 244.76/51.37  | | 
% 244.76/51.37  | | Case 1:
% 244.76/51.37  | | | 
% 244.76/51.37  | | |   (13)  all_58_8 = e1 & op(e1, e1) = e1
% 244.76/51.37  | | | 
% 244.76/51.37  | | | REF_CLOSE: (4), (10), (13) are inconsistent by sub-proof #2045.
% 244.76/51.37  | | | 
% 244.76/51.37  | | Case 2:
% 244.76/51.37  | | | 
% 244.76/51.37  | | |   (14)  all_58_14 = e1 & op(e0, e1) = e1
% 244.76/51.37  | | | 
% 244.76/51.37  | | | REF_CLOSE: (2), (10), (14) are inconsistent by sub-proof #2040.
% 244.76/51.37  | | | 
% 244.76/51.37  | | End of split
% 244.76/51.37  | | 
% 244.76/51.37  | End of split
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2040 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  all_58_14 = e1 & op(e0, e1) = e1
% 244.76/51.37    (2)  all_58_14 = e2
% 244.76/51.37    (3)   ~ (e2 = e1)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | ALPHA: (1) implies:
% 244.76/51.37  |   (4)  all_58_14 = e1
% 244.76/51.37  | 
% 244.76/51.37  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.37  |   (5)  e2 = e1
% 244.76/51.37  | 
% 244.76/51.37  | REDUCE: (3), (5) imply:
% 244.76/51.37  |   (6)  $false
% 244.76/51.37  | 
% 244.76/51.37  | CLOSE: (6) is inconsistent.
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2041 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 244.76/51.37    (2)   ~ (e3 = e1)
% 244.76/51.37    (3)  op(e2, e1) = all_52_9
% 244.76/51.37    (4)  op(e2, e1) = e0
% 244.76/51.37    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.37    (6)   ~ (e1 = e0)
% 244.76/51.37    (7)  all_58_4 = e3
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | BETA: splitting (1) gives:
% 244.76/51.37  | 
% 244.76/51.37  | Case 1:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (8)  all_58_4 = e1 & op(e3, e1) = e1
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (2), (7), (8) are inconsistent by sub-proof #2042.
% 244.76/51.37  | | 
% 244.76/51.37  | Case 2:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (9)  all_58_5 = e1 & op(e2, e1) = e1
% 244.76/51.37  | | 
% 244.76/51.37  | | ALPHA: (9) implies:
% 244.76/51.37  | |   (10)  op(e2, e1) = e1
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #2165.
% 244.76/51.37  | | 
% 244.76/51.37  | End of split
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2042 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  all_58_4 = e1 & op(e3, e1) = e1
% 244.76/51.37    (2)  all_58_4 = e3
% 244.76/51.37    (3)   ~ (e3 = e1)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | ALPHA: (1) implies:
% 244.76/51.37  |   (4)  all_58_4 = e1
% 244.76/51.37  | 
% 244.76/51.37  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.37  |   (5)  e3 = e1
% 244.76/51.37  | 
% 244.76/51.37  | REDUCE: (3), (5) imply:
% 244.76/51.37  |   (6)  $false
% 244.76/51.37  | 
% 244.76/51.37  | CLOSE: (6) is inconsistent.
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2043 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)   ~ (e3 = e0)
% 244.76/51.37    (2)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 244.76/51.37         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 244.76/51.37    (3)  all_58_14 = e2
% 244.76/51.37    (4)   ~ (e3 = e1)
% 244.76/51.37    (5)  all_58_8 = e2
% 244.76/51.37    (6)  op(e3, e1) = e0
% 244.76/51.37    (7)   ~ (e3 = e2)
% 244.76/51.37    (8)  op(e1, e1) = e2
% 244.76/51.37    (9)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.76/51.37         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.76/51.37    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.37    (11)   ~ (e1 = e0)
% 244.76/51.37    (12)  all_58_4 = e0
% 244.76/51.37    (13)   ~ (e2 = e1)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | BETA: splitting (2) gives:
% 244.76/51.37  | 
% 244.76/51.37  | Case 1:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 244.76/51.37  | |           e1)
% 244.76/51.37  | | 
% 244.76/51.37  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14) are
% 244.76/51.37  | |            inconsistent by sub-proof #2046.
% 244.76/51.37  | | 
% 244.76/51.37  | Case 2:
% 244.76/51.37  | | 
% 244.76/51.37  | |   (15)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 244.76/51.37  | |           e1)
% 244.76/51.37  | | 
% 244.76/51.37  | | BETA: splitting (15) gives:
% 244.76/51.37  | | 
% 244.76/51.37  | | Case 1:
% 244.76/51.37  | | | 
% 244.76/51.37  | | |   (16)  all_58_8 = e1 & op(e1, e1) = e1
% 244.76/51.37  | | | 
% 244.76/51.37  | | | REF_CLOSE: (5), (13), (16) are inconsistent by sub-proof #2045.
% 244.76/51.37  | | | 
% 244.76/51.37  | | Case 2:
% 244.76/51.37  | | | 
% 244.76/51.37  | | |   (17)  all_58_14 = e1 & op(e0, e1) = e1
% 244.76/51.37  | | | 
% 244.76/51.37  | | | ALPHA: (17) implies:
% 244.76/51.37  | | |   (18)  all_58_14 = e1
% 244.76/51.37  | | | 
% 244.76/51.37  | | | REF_CLOSE: (3), (13), (18) are inconsistent by sub-proof #2044.
% 244.76/51.37  | | | 
% 244.76/51.37  | | End of split
% 244.76/51.37  | | 
% 244.76/51.37  | End of split
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2044 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  all_58_14 = e2
% 244.76/51.37    (2)  all_58_14 = e1
% 244.76/51.37    (3)   ~ (e2 = e1)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.37  |   (4)  e2 = e1
% 244.76/51.37  | 
% 244.76/51.37  | SIMP: (4) implies:
% 244.76/51.37  |   (5)  e2 = e1
% 244.76/51.37  | 
% 244.76/51.37  | REDUCE: (3), (5) imply:
% 244.76/51.37  |   (6)  $false
% 244.76/51.37  | 
% 244.76/51.37  | CLOSE: (6) is inconsistent.
% 244.76/51.37  | 
% 244.76/51.37  End of proof
% 244.76/51.37  
% 244.76/51.37  Sub-proof #2045 shows that the following formulas are inconsistent:
% 244.76/51.37  ----------------------------------------------------------------
% 244.76/51.37    (1)  all_58_8 = e1 & op(e1, e1) = e1
% 244.76/51.37    (2)  all_58_8 = e2
% 244.76/51.37    (3)   ~ (e2 = e1)
% 244.76/51.37  
% 244.76/51.37  Begin of proof
% 244.76/51.37  | 
% 244.76/51.37  | ALPHA: (1) implies:
% 244.76/51.37  |   (4)  all_58_8 = e1
% 244.76/51.38  | 
% 244.76/51.38  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.38  |   (5)  e2 = e1
% 244.76/51.38  | 
% 244.76/51.38  | REDUCE: (3), (5) imply:
% 244.76/51.38  |   (6)  $false
% 244.76/51.38  | 
% 244.76/51.38  | CLOSE: (6) is inconsistent.
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2046 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)   ~ (e3 = e0)
% 244.76/51.38    (2)  all_58_14 = e2
% 244.76/51.38    (3)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 244.76/51.38    (4)   ~ (e3 = e1)
% 244.76/51.38    (5)  op(e3, e1) = e0
% 244.76/51.38    (6)   ~ (e3 = e2)
% 244.76/51.38    (7)  op(e1, e1) = e2
% 244.76/51.38    (8)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.76/51.38         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.76/51.38    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.38    (10)   ~ (e1 = e0)
% 244.76/51.38    (11)  all_58_4 = e0
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | BETA: splitting (3) gives:
% 244.76/51.38  | 
% 244.76/51.38  | Case 1:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (12)  all_58_4 = e1 & op(e3, e1) = e1
% 244.76/51.38  | | 
% 244.76/51.38  | | REF_CLOSE: (10), (11), (12) are inconsistent by sub-proof #2047.
% 244.76/51.38  | | 
% 244.76/51.38  | Case 2:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (13)  all_58_5 = e1 & op(e2, e1) = e1
% 244.76/51.38  | | 
% 244.76/51.38  | | ALPHA: (13) implies:
% 244.76/51.38  | |   (14)  all_58_5 = e1
% 244.76/51.38  | | 
% 244.76/51.38  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (14) are inconsistent by
% 244.76/51.38  | |            sub-proof #2115.
% 244.76/51.38  | | 
% 244.76/51.38  | End of split
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2047 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)  all_58_4 = e1 & op(e3, e1) = e1
% 244.76/51.38    (2)  all_58_4 = e0
% 244.76/51.38    (3)   ~ (e1 = e0)
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | ALPHA: (1) implies:
% 244.76/51.38  |   (4)  all_58_4 = e1
% 244.76/51.38  | 
% 244.76/51.38  | COMBINE_EQS: (2), (4) imply:
% 244.76/51.38  |   (5)  e1 = e0
% 244.76/51.38  | 
% 244.76/51.38  | REDUCE: (3), (5) imply:
% 244.76/51.38  |   (6)  $false
% 244.76/51.38  | 
% 244.76/51.38  | CLOSE: (6) is inconsistent.
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2048 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 244.76/51.38    (2)  all_54_1 = all_52_4
% 244.76/51.38    (3)   ~ (all_52_4 = e2)
% 244.76/51.38    (4)   ~ (all_52_4 = e1)
% 244.76/51.38    (5)   ~ (all_52_4 = e0)
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | BETA: splitting (1) gives:
% 244.76/51.38  | 
% 244.76/51.38  | Case 1:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (6)  all_54_1 = e2
% 244.76/51.38  | | 
% 244.76/51.38  | | COMBINE_EQS: (2), (6) imply:
% 244.76/51.38  | |   (7)  all_52_4 = e2
% 244.76/51.38  | | 
% 244.76/51.38  | | REDUCE: (3), (7) imply:
% 244.76/51.38  | |   (8)  $false
% 244.76/51.38  | | 
% 244.76/51.38  | | CLOSE: (8) is inconsistent.
% 244.76/51.38  | | 
% 244.76/51.38  | Case 2:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (9)  all_54_1 = e1 | all_54_1 = e0
% 244.76/51.38  | | 
% 244.76/51.38  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2049.
% 244.76/51.38  | | 
% 244.76/51.38  | End of split
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2049 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)  all_54_1 = e1 | all_54_1 = e0
% 244.76/51.38    (2)  all_54_1 = all_52_4
% 244.76/51.38    (3)   ~ (all_52_4 = e1)
% 244.76/51.38    (4)   ~ (all_52_4 = e0)
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | BETA: splitting (1) gives:
% 244.76/51.38  | 
% 244.76/51.38  | Case 1:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (5)  all_54_1 = e1
% 244.76/51.38  | | 
% 244.76/51.38  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2051.
% 244.76/51.38  | | 
% 244.76/51.38  | Case 2:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (6)  all_54_1 = e0
% 244.76/51.38  | | 
% 244.76/51.38  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2050.
% 244.76/51.38  | | 
% 244.76/51.38  | End of split
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2050 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)  all_54_1 = all_52_4
% 244.76/51.38    (2)  all_54_1 = e0
% 244.76/51.38    (3)   ~ (all_52_4 = e0)
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.38  |   (4)  all_52_4 = e0
% 244.76/51.38  | 
% 244.76/51.38  | SIMP: (4) implies:
% 244.76/51.38  |   (5)  all_52_4 = e0
% 244.76/51.38  | 
% 244.76/51.38  | REDUCE: (3), (5) imply:
% 244.76/51.38  |   (6)  $false
% 244.76/51.38  | 
% 244.76/51.38  | CLOSE: (6) is inconsistent.
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2051 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)  all_54_1 = all_52_4
% 244.76/51.38    (2)  all_54_1 = e1
% 244.76/51.38    (3)   ~ (all_52_4 = e1)
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.38  |   (4)  all_52_4 = e1
% 244.76/51.38  | 
% 244.76/51.38  | SIMP: (4) implies:
% 244.76/51.38  |   (5)  all_52_4 = e1
% 244.76/51.38  | 
% 244.76/51.38  | REDUCE: (3), (5) imply:
% 244.76/51.38  |   (6)  $false
% 244.76/51.38  | 
% 244.76/51.38  | CLOSE: (6) is inconsistent.
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2052 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)  all_54_3 = e1 | all_54_3 = e0
% 244.76/51.38    (2)   ~ (all_52_6 = e1)
% 244.76/51.38    (3)   ~ (all_52_9 = all_6_2)
% 244.76/51.38    (4)  all_56_11 = e1
% 244.76/51.38    (5)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.76/51.38           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2) | (all_56_12
% 244.76/51.38           = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 & $i(all_56_13))
% 244.76/51.38         | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 244.76/51.38           $i(all_56_15))
% 244.76/51.38    (6)  op(e3, e2) = all_32_1
% 244.76/51.38    (7)  op(e1, e2) = all_52_6
% 244.76/51.38    (8)  op(e1, e0) = all_52_14
% 244.76/51.38    (9)  op(e0, e2) = e2
% 244.76/51.38    (10)   ~ (all_52_12 = e1)
% 244.76/51.38    (11)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.76/51.38    (12)  all_54_10 = all_6_2
% 244.76/51.38    (13)  op(e2, e1) = all_52_9
% 244.76/51.38    (14)  all_54_9 = all_52_6
% 244.76/51.38    (15)   ~ (e3 = e2)
% 244.76/51.38    (16)   ~ (all_52_14 = e1)
% 244.76/51.38    (17)   ~ (all_6_2 = e0)
% 244.76/51.38    (18)   ~ (all_6_2 = e1)
% 244.76/51.38    (19)  op(e3, e3) = e2
% 244.76/51.38    (20)   ~ (all_52_12 = e2)
% 244.76/51.38    (21)  all_54_3 = all_52_12
% 244.76/51.38    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.38    (23)  all_54_9 = e1 | all_54_9 = e0
% 244.76/51.38    (24)  op(e3, e2) = e3
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | BETA: splitting (5) gives:
% 244.76/51.38  | 
% 244.76/51.38  | Case 1:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (25)  (all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.76/51.38  | |           $i(all_56_9)) | (all_56_10 = e2 & op(e2, all_56_11) = e2)
% 244.76/51.38  | | 
% 244.76/51.38  | | BETA: splitting (25) gives:
% 244.76/51.38  | | 
% 244.76/51.38  | | Case 1:
% 244.76/51.38  | | | 
% 244.76/51.38  | | |   (26)  all_56_8 = e3 & op(e3, all_56_9) = e3 & op(e3, e2) = all_56_9 &
% 244.76/51.38  | | |         $i(all_56_9)
% 244.76/51.38  | | | 
% 244.76/51.38  | | | ALPHA: (26) implies:
% 244.76/51.38  | | |   (27)  op(e3, e2) = all_56_9
% 244.76/51.38  | | |   (28)  op(e3, all_56_9) = e3
% 244.76/51.38  | | | 
% 244.76/51.38  | | | BETA: splitting (1) gives:
% 244.76/51.38  | | | 
% 244.76/51.38  | | | Case 1:
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | |   (29)  all_54_3 = e1
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | REF_CLOSE: (10), (21), (29) are inconsistent by sub-proof #2289.
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | Case 2:
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | GROUND_INST: instantiating (22) with all_32_1, all_56_9, e2, e3,
% 244.76/51.38  | | | |              simplifying with (6), (27) gives:
% 244.76/51.38  | | | |   (30)  all_56_9 = all_32_1
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | GROUND_INST: instantiating (22) with e3, all_56_9, e2, e3, simplifying
% 244.76/51.38  | | | |              with (24), (27) gives:
% 244.76/51.38  | | | |   (31)  all_56_9 = e3
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | COMBINE_EQS: (30), (31) imply:
% 244.76/51.38  | | | |   (32)  all_32_1 = e3
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | REDUCE: (28), (31) imply:
% 244.76/51.38  | | | |   (33)  op(e3, e3) = e3
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | REF_CLOSE: (15), (19), (22), (33) are inconsistent by sub-proof #2194.
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | End of split
% 244.76/51.38  | | | 
% 244.76/51.38  | | Case 2:
% 244.76/51.38  | | | 
% 244.76/51.38  | | |   (34)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 244.76/51.38  | | | 
% 244.76/51.38  | | | REF_CLOSE: (3), (4), (11), (12), (13), (17), (18), (22), (34) are
% 244.76/51.38  | | |            inconsistent by sub-proof #2056.
% 244.76/51.38  | | | 
% 244.76/51.38  | | End of split
% 244.76/51.38  | | 
% 244.76/51.38  | Case 2:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (35)  (all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 244.76/51.38  | |           $i(all_56_13)) | (all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0,
% 244.76/51.38  | |             e2) = all_56_15 & $i(all_56_15))
% 244.76/51.38  | | 
% 244.76/51.38  | | BETA: splitting (35) gives:
% 244.76/51.38  | | 
% 244.76/51.38  | | Case 1:
% 244.76/51.38  | | | 
% 244.76/51.38  | | |   (36)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 244.76/51.38  | | |         $i(all_56_13)
% 244.76/51.38  | | | 
% 244.76/51.38  | | | REF_CLOSE: (2), (7), (8), (14), (16), (22), (23), (36) are inconsistent by
% 244.76/51.38  | | |            sub-proof #2054.
% 244.76/51.38  | | | 
% 244.76/51.38  | | Case 2:
% 244.76/51.38  | | | 
% 244.76/51.38  | | |   (37)  all_56_14 = e0 & op(e0, all_56_15) = e0 & op(e0, e2) = all_56_15 &
% 244.76/51.38  | | |         $i(all_56_15)
% 244.76/51.38  | | | 
% 244.76/51.38  | | | ALPHA: (37) implies:
% 244.76/51.38  | | |   (38)  op(e0, e2) = all_56_15
% 244.76/51.38  | | |   (39)  op(e0, all_56_15) = e0
% 244.76/51.38  | | | 
% 244.76/51.38  | | | BETA: splitting (1) gives:
% 244.76/51.38  | | | 
% 244.76/51.38  | | | Case 1:
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | |   (40)  all_54_3 = e1
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | REF_CLOSE: (10), (21), (40) are inconsistent by sub-proof #2289.
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | Case 2:
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | |   (41)  all_54_3 = e0
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | COMBINE_EQS: (21), (41) imply:
% 244.76/51.38  | | | |   (42)  all_52_12 = e0
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | SIMP: (42) implies:
% 244.76/51.38  | | | |   (43)  all_52_12 = e0
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | REDUCE: (20), (43) imply:
% 244.76/51.38  | | | |   (44)   ~ (e2 = e0)
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | SIMP: (44) implies:
% 244.76/51.38  | | | |   (45)   ~ (e2 = e0)
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | | REF_CLOSE: (9), (22), (38), (39), (45) are inconsistent by sub-proof
% 244.76/51.38  | | | |            #2053.
% 244.76/51.38  | | | | 
% 244.76/51.38  | | | End of split
% 244.76/51.38  | | | 
% 244.76/51.38  | | End of split
% 244.76/51.38  | | 
% 244.76/51.38  | End of split
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2053 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)   ~ (e2 = e0)
% 244.76/51.38    (2)  op(e0, e2) = e2
% 244.76/51.38    (3)  op(e0, e2) = all_56_15
% 244.76/51.38    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.38    (5)  op(e0, all_56_15) = e0
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | GROUND_INST: instantiating (4) with e2, all_56_15, e2, e0, simplifying with
% 244.76/51.38  |              (2), (3) gives:
% 244.76/51.38  |   (6)  all_56_15 = e2
% 244.76/51.38  | 
% 244.76/51.38  | REDUCE: (5), (6) imply:
% 244.76/51.38  |   (7)  op(e0, e2) = e0
% 244.76/51.38  | 
% 244.76/51.38  | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #2132.
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2054 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)   ~ (all_52_6 = e1)
% 244.76/51.38    (2)  op(e1, e2) = all_52_6
% 244.76/51.38    (3)  op(e1, e0) = all_52_14
% 244.76/51.38    (4)  all_54_9 = all_52_6
% 244.76/51.38    (5)   ~ (all_52_14 = e1)
% 244.76/51.38    (6)  all_56_12 = e1 & op(e1, all_56_13) = e1 & op(e1, e2) = all_56_13 &
% 244.76/51.38         $i(all_56_13)
% 244.76/51.38    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.38    (8)  all_54_9 = e1 | all_54_9 = e0
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | ALPHA: (6) implies:
% 244.76/51.38  |   (9)  op(e1, e2) = all_56_13
% 244.76/51.38  |   (10)  op(e1, all_56_13) = e1
% 244.76/51.38  | 
% 244.76/51.38  | BETA: splitting (8) gives:
% 244.76/51.38  | 
% 244.76/51.38  | Case 1:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (11)  all_54_9 = e1
% 244.76/51.38  | | 
% 244.76/51.38  | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #2055.
% 244.76/51.38  | | 
% 244.76/51.38  | Case 2:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (12)  all_54_9 = e0
% 244.76/51.38  | | 
% 244.76/51.38  | | COMBINE_EQS: (4), (12) imply:
% 244.76/51.38  | |   (13)  all_52_6 = e0
% 244.76/51.38  | | 
% 244.76/51.38  | | SIMP: (13) implies:
% 244.76/51.38  | |   (14)  all_52_6 = e0
% 244.76/51.38  | | 
% 244.76/51.38  | | REDUCE: (2), (14) imply:
% 244.76/51.38  | |   (15)  op(e1, e2) = e0
% 244.76/51.38  | | 
% 244.76/51.38  | | GROUND_INST: instantiating (7) with e0, all_56_13, e2, e1, simplifying with
% 244.76/51.38  | |              (9), (15) gives:
% 244.76/51.38  | |   (16)  all_56_13 = e0
% 244.76/51.38  | | 
% 244.76/51.38  | | REDUCE: (10), (16) imply:
% 244.76/51.38  | |   (17)  op(e1, e0) = e1
% 244.76/51.38  | | 
% 244.76/51.38  | | REF_CLOSE: (3), (5), (7), (17) are inconsistent by sub-proof #2304.
% 244.76/51.38  | | 
% 244.76/51.38  | End of split
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2055 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)  all_54_9 = all_52_6
% 244.76/51.38    (2)  all_54_9 = e1
% 244.76/51.38    (3)   ~ (all_52_6 = e1)
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.38  |   (4)  all_52_6 = e1
% 244.76/51.38  | 
% 244.76/51.38  | SIMP: (4) implies:
% 244.76/51.38  |   (5)  all_52_6 = e1
% 244.76/51.38  | 
% 244.76/51.38  | REDUCE: (3), (5) imply:
% 244.76/51.38  |   (6)  $false
% 244.76/51.38  | 
% 244.76/51.38  | CLOSE: (6) is inconsistent.
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2056 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)   ~ (all_52_9 = all_6_2)
% 244.76/51.38    (2)  all_56_11 = e1
% 244.76/51.38    (3)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.76/51.38    (4)  all_54_10 = all_6_2
% 244.76/51.38    (5)  op(e2, e1) = all_52_9
% 244.76/51.38    (6)   ~ (all_6_2 = e0)
% 244.76/51.38    (7)   ~ (all_6_2 = e1)
% 244.76/51.38    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.38    (9)  all_56_10 = e2 & op(e2, all_56_11) = e2
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | ALPHA: (9) implies:
% 244.76/51.38  |   (10)  op(e2, all_56_11) = e2
% 244.76/51.38  | 
% 244.76/51.38  | REDUCE: (2), (10) imply:
% 244.76/51.38  |   (11)  op(e2, e1) = e2
% 244.76/51.38  | 
% 244.76/51.38  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (11) are inconsistent by
% 244.76/51.38  |            sub-proof #2198.
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2057 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)  all_54_3 = all_52_12
% 244.76/51.38    (2)  all_54_3 = e3
% 244.76/51.38    (3)   ~ (all_52_12 = e3)
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | COMBINE_EQS: (1), (2) imply:
% 244.76/51.38  |   (4)  all_52_12 = e3
% 244.76/51.38  | 
% 244.76/51.38  | SIMP: (4) implies:
% 244.76/51.38  |   (5)  all_52_12 = e3
% 244.76/51.38  | 
% 244.76/51.38  | REDUCE: (3), (5) imply:
% 244.76/51.38  |   (6)  $false
% 244.76/51.38  | 
% 244.76/51.38  | CLOSE: (6) is inconsistent.
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2058 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)  op(e1, e0) = all_52_14
% 244.76/51.38    (2)   ~ (e3 = e1)
% 244.76/51.38    (3)  all_58_15 = e1
% 244.76/51.38    (4)   ~ (all_52_14 = e3)
% 244.76/51.38    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.76/51.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.76/51.38    (6)  (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.76/51.38  
% 244.76/51.38  Begin of proof
% 244.76/51.38  | 
% 244.76/51.38  | BETA: splitting (6) gives:
% 244.76/51.38  | 
% 244.76/51.38  | Case 1:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (7)  all_58_11 = e3 & op(e1, e0) = e3
% 244.76/51.38  | | 
% 244.76/51.38  | | ALPHA: (7) implies:
% 244.76/51.38  | |   (8)  op(e1, e0) = e3
% 244.76/51.38  | | 
% 244.76/51.38  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2149.
% 244.76/51.38  | | 
% 244.76/51.38  | Case 2:
% 244.76/51.38  | | 
% 244.76/51.38  | |   (9)  all_58_15 = e3 & op(e0, e0) = e3
% 244.76/51.38  | | 
% 244.76/51.38  | | ALPHA: (9) implies:
% 244.76/51.38  | |   (10)  all_58_15 = e3
% 244.76/51.38  | | 
% 244.76/51.38  | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #2249.
% 244.76/51.38  | | 
% 244.76/51.38  | End of split
% 244.76/51.38  | 
% 244.76/51.38  End of proof
% 244.76/51.38  
% 244.76/51.38  Sub-proof #2059 shows that the following formulas are inconsistent:
% 244.76/51.38  ----------------------------------------------------------------
% 244.76/51.38    (1)  op(e1, e0) = e0
% 244.76/51.38    (2)   ~ (e2 = e0)
% 244.76/51.38    (3)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 244.76/51.38         (all_58_11 = e0 & op(e1, e0) = e0)
% 244.76/51.38    (4)  op(e1, e2) = e3
% 244.76/51.38    (5)  op(e2, e0) = e2
% 244.76/51.38    (6)  all_56_28 = e1 & op(e1, all_56_29) = e1 & op(e1, e0) = all_56_29 &
% 244.76/51.38         $i(all_56_29)
% 244.76/51.38    (7)  all_58_9 = e3
% 244.88/51.38    (8)  op(e1, e2) = all_36_1
% 244.88/51.38    (9)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) = all_40_1
% 244.88/51.38           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2) =
% 244.88/51.38           all_40_1 & $i(all_40_1))
% 244.88/51.38    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.88/51.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.88/51.38    (11)   ~ (all_36_1 = e0)
% 244.88/51.39    (12)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 244.88/51.39            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 244.88/51.39              e2) = all_36_1 & $i(all_36_1))
% 244.88/51.39    (13)   ~ (e1 = e0)
% 244.88/51.39  
% 244.88/51.39  Begin of proof
% 244.88/51.39  | 
% 244.88/51.39  | ALPHA: (6) implies:
% 244.88/51.39  |   (14)  op(e1, e0) = all_56_29
% 244.88/51.39  |   (15)  op(e1, all_56_29) = e1
% 244.88/51.39  | 
% 244.88/51.39  | BETA: splitting (9) gives:
% 244.88/51.39  | 
% 244.88/51.39  | Case 1:
% 244.88/51.39  | | 
% 244.88/51.39  | |   (16)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 244.88/51.39  | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 244.88/51.39  | | 
% 244.88/51.39  | | ALPHA: (16) implies:
% 244.88/51.39  | |   (17)  op(e1, e2) = all_40_1
% 244.88/51.39  | | 
% 244.88/51.39  | | GROUND_INST: instantiating (10) with e0, all_56_29, e0, e1, simplifying with
% 244.88/51.39  | |              (1), (14) gives:
% 244.88/51.39  | |   (18)  all_56_29 = e0
% 244.88/51.39  | | 
% 244.88/51.39  | | GROUND_INST: instantiating (10) with all_36_1, all_40_1, e2, e1, simplifying
% 244.88/51.39  | |              with (8), (17) gives:
% 244.88/51.39  | |   (19)  all_40_1 = all_36_1
% 244.88/51.39  | | 
% 244.88/51.39  | | GROUND_INST: instantiating (10) with e3, all_40_1, e2, e1, simplifying with
% 244.88/51.39  | |              (4), (17) gives:
% 244.88/51.39  | |   (20)  all_40_1 = e3
% 244.88/51.39  | | 
% 244.88/51.39  | | COMBINE_EQS: (19), (20) imply:
% 244.88/51.39  | |   (21)  all_36_1 = e3
% 244.88/51.39  | | 
% 244.88/51.39  | | REDUCE: (11), (21) imply:
% 244.88/51.39  | |   (22)   ~ (e3 = e0)
% 244.88/51.39  | | 
% 244.88/51.39  | | REDUCE: (15), (18) imply:
% 244.88/51.39  | |   (23)  op(e1, e0) = e1
% 244.88/51.39  | | 
% 244.88/51.39  | | REF_CLOSE: (2), (3), (5), (7), (10), (13), (22), (23) are inconsistent by
% 244.88/51.39  | |            sub-proof #2101.
% 244.88/51.39  | | 
% 244.88/51.39  | Case 2:
% 244.88/51.39  | | 
% 244.88/51.39  | |   (24)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 244.88/51.39  | | 
% 244.88/51.39  | | REF_CLOSE: (4), (10), (12), (24) are inconsistent by sub-proof #2144.
% 244.88/51.39  | | 
% 244.88/51.39  | End of split
% 244.88/51.39  | 
% 244.88/51.39  End of proof
% 244.88/51.39  
% 244.88/51.39  Sub-proof #2060 shows that the following formulas are inconsistent:
% 244.88/51.39  ----------------------------------------------------------------
% 244.88/51.39    (1)   ~ (all_52_1 = all_52_3)
% 244.88/51.39    (2)   ~ (all_52_9 = all_6_2)
% 244.88/51.39    (3)   ~ (all_52_8 = all_52_9)
% 244.88/51.39    (4)   ~ (e2 = e0)
% 244.88/51.39    (5)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.88/51.39         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.88/51.39    (6)  op(e1, e2) = all_52_6
% 244.88/51.39    (7)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.88/51.39         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.88/51.39    (8)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.88/51.39           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.88/51.39             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.88/51.39           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.88/51.39             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.88/51.39           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.88/51.39           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.88/51.39           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.88/51.39           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.88/51.39           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.88/51.39           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.88/51.39             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.88/51.39           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.88/51.39           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 244.88/51.39           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.88/51.39           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.88/51.39           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.88/51.39           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.88/51.39             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.88/51.39           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.88/51.39           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.88/51.39           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.88/51.39           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.88/51.39           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.88/51.39           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.88/51.39             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.88/51.39           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.88/51.39           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.88/51.39    (9)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.88/51.39         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.88/51.39    (10)  op(e1, e1) = all_6_2
% 244.88/51.39    (11)  op(e1, e0) = all_52_14
% 244.88/51.39    (12)   ~ (all_52_13 = e1)
% 244.88/51.39    (13)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 244.88/51.39            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 244.88/51.39            = all_56_27 & $i(all_56_27))
% 244.88/51.39    (14)  op(e0, e3) = all_52_3
% 244.88/51.39    (15)   ~ (e3 = e1)
% 244.88/51.39    (16)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.88/51.39          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.88/51.39    (17)  op(e1, e2) = e3
% 244.88/51.39    (18)  all_54_10 = all_6_2
% 244.88/51.39    (19)   ~ (all_6_2 = e3)
% 244.88/51.39    (20)  op(e3, e1) = all_52_8
% 244.88/51.39    (21)  op(e2, e1) = all_52_9
% 244.88/51.39    (22)   ~ (e3 = e2)
% 244.88/51.39    (23)   ~ (all_52_7 = e1)
% 244.88/51.39    (24)   ~ (all_6_2 = e0)
% 244.88/51.39    (25)  op(e2, e0) = e2
% 244.88/51.39    (26)  all_56_31 = e1
% 244.88/51.39    (27)  all_58_15 = e1
% 244.88/51.39    (28)  op(e3, e0) = all_52_12
% 244.88/51.39    (29)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.88/51.39          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.88/51.39    (30)   ~ (all_52_6 = all_52_14)
% 244.88/51.39    (31)  op(e3, e0) = e3
% 244.88/51.39    (32)  op(e2, e3) = all_52_1
% 244.88/51.39    (33)  op(e3, e3) = e2
% 244.88/51.39    (34)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.88/51.39    (35)  op(e1, e2) = all_36_1
% 244.88/51.39    (36)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 244.88/51.39            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 244.88/51.39              e2) = all_40_1 & $i(all_40_1))
% 244.88/51.39    (37)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.88/51.39          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.88/51.39    (38)  op(e0, e2) = all_52_7
% 244.88/51.39    (39)  op(e3, e2) = all_52_4
% 244.88/51.39    (40)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.88/51.39          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 244.88/51.39    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.88/51.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.88/51.39    (42)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.88/51.39          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.88/51.39    (43)   ~ (all_36_1 = e0)
% 244.88/51.39    (44)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.88/51.39          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.88/51.39    (45)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 244.88/51.39            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 244.88/51.39              e2) = all_36_1 & $i(all_36_1))
% 244.88/51.39    (46)   ~ (all_52_4 = e1)
% 244.88/51.39    (47)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.88/51.39          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.88/51.39    (48)   ~ (e1 = e0)
% 244.88/51.39    (49)  all_56_21 = all_6_2
% 244.88/51.39    (50)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.88/51.39          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.88/51.39    (51)  op(e2, e0) = all_52_13
% 244.88/51.39    (52)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.88/51.39          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.88/51.39            e2)
% 244.88/51.39    (53)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.88/51.39          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.88/51.39    (54)   ~ (e2 = e1)
% 244.88/51.39    (55)   ~ (all_52_1 = e1)
% 244.88/51.39    (56)   ~ (all_52_9 = e2)
% 244.88/51.39  
% 244.88/51.39  Begin of proof
% 244.88/51.39  | 
% 244.88/51.39  | BETA: splitting (13) gives:
% 244.88/51.39  | 
% 244.88/51.39  | Case 1:
% 244.88/51.39  | | 
% 244.88/51.39  | |   (57)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 244.88/51.39  | |         $i(all_56_25)
% 244.88/51.39  | | 
% 244.88/51.39  | | REF_CLOSE: (17), (22), (31), (33), (36), (41), (45), (57) are inconsistent
% 244.88/51.39  | |            by sub-proof #2143.
% 244.88/51.39  | | 
% 244.88/51.39  | Case 2:
% 244.88/51.39  | | 
% 244.88/51.39  | |   (58)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 244.88/51.39  | |         $i(all_56_27)
% 244.88/51.39  | | 
% 244.88/51.39  | | ALPHA: (58) implies:
% 244.88/51.39  | |   (59)  op(e2, e0) = all_56_27
% 244.88/51.39  | |   (60)  op(e2, all_56_27) = e2
% 244.88/51.39  | | 
% 244.88/51.39  | | BETA: splitting (36) gives:
% 244.88/51.39  | | 
% 244.88/51.39  | | Case 1:
% 244.88/51.39  | | | 
% 244.88/51.39  | | |   (61)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 244.88/51.39  | | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 244.88/51.39  | | | 
% 244.88/51.39  | | | ALPHA: (61) implies:
% 244.88/51.39  | | |   (62)  op(e1, e2) = all_40_1
% 244.88/51.39  | | | 
% 244.88/51.39  | | | GROUND_INST: instantiating (41) with all_36_1, all_40_1, e2, e1,
% 244.88/51.39  | | |              simplifying with (35), (62) gives:
% 244.88/51.39  | | |   (63)  all_40_1 = all_36_1
% 244.88/51.39  | | | 
% 244.88/51.39  | | | GROUND_INST: instantiating (41) with e3, all_40_1, e2, e1, simplifying
% 244.88/51.39  | | |              with (17), (62) gives:
% 244.88/51.39  | | |   (64)  all_40_1 = e3
% 244.88/51.39  | | | 
% 244.88/51.39  | | | GROUND_INST: instantiating (41) with e2, all_56_27, e0, e2, simplifying
% 244.88/51.39  | | |              with (25), (59) gives:
% 244.88/51.39  | | |   (65)  all_56_27 = e2
% 244.88/51.39  | | | 
% 244.88/51.39  | | | COMBINE_EQS: (63), (64) imply:
% 244.88/51.39  | | |   (66)  all_36_1 = e3
% 244.88/51.39  | | | 
% 244.88/51.39  | | | SIMP: (66) implies:
% 244.88/51.39  | | |   (67)  all_36_1 = e3
% 244.88/51.39  | | | 
% 244.88/51.39  | | | REDUCE: (43), (67) imply:
% 244.88/51.39  | | |   (68)   ~ (e3 = e0)
% 244.88/51.39  | | | 
% 244.88/51.39  | | | REDUCE: (60), (65) imply:
% 244.88/51.39  | | |   (69)  op(e2, e2) = e2
% 244.88/51.39  | | | 
% 244.88/51.39  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 244.88/51.39  | | |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 244.88/51.39  | | |            (26), (27), (28), (29), (30), (32), (34), (37), (38), (39),
% 244.88/51.39  | | |            (40), (41), (42), (44), (46), (47), (48), (49), (50), (51),
% 244.88/51.39  | | |            (52), (53), (54), (55), (56), (68), (69) are inconsistent by
% 244.88/51.39  | | |            sub-proof #2105.
% 244.88/51.39  | | | 
% 244.88/51.39  | | Case 2:
% 244.88/51.39  | | | 
% 244.88/51.39  | | |   (70)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 244.88/51.39  | | | 
% 244.88/51.39  | | | REF_CLOSE: (17), (41), (45), (70) are inconsistent by sub-proof #2144.
% 244.88/51.39  | | | 
% 244.88/51.39  | | End of split
% 244.88/51.39  | | 
% 244.88/51.39  | End of split
% 244.88/51.39  | 
% 244.88/51.39  End of proof
% 244.88/51.39  
% 244.88/51.39  Sub-proof #2061 shows that the following formulas are inconsistent:
% 244.88/51.39  ----------------------------------------------------------------
% 244.88/51.39    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.88/51.39             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.88/51.39           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.88/51.39         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.88/51.39           $i(all_56_7))
% 244.88/51.39    (2)  all_56_21 = e2
% 244.88/51.39    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.88/51.39    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 244.88/51.39           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 244.88/51.39           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 244.88/51.39           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 244.88/51.39           & $i(all_56_23))
% 244.88/51.39    (5)   ~ (all_52_3 = e1)
% 244.88/51.39    (6)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.88/51.39         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.88/51.39    (7)  op(e0, e1) = all_52_11
% 244.88/51.39    (8)   ~ (all_52_11 = e2)
% 244.88/51.39    (9)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.88/51.39         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.88/51.39    (10)  op(e1, e1) = all_6_2
% 244.88/51.39    (11)   ~ (all_52_13 = e1)
% 244.88/51.39    (12)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 244.88/51.39            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 244.88/51.39              e1) = all_20_1 & $i(all_20_1))
% 244.88/51.39    (13)  op(e0, e3) = all_52_3
% 244.88/51.39    (14)   ~ (all_24_1 = e1)
% 244.88/51.39    (15)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.88/51.39          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.88/51.39    (16)  all_54_6 = all_52_9
% 244.88/51.39    (17)  op(e1, e2) = e3
% 244.88/51.39    (18)   ~ (all_52_1 = all_52_9)
% 244.88/51.39    (19)  all_54_4 = all_52_1
% 244.88/51.39    (20)   ~ (all_6_2 = e3)
% 244.88/51.39    (21)  op(e2, e1) = all_52_9
% 244.88/51.39    (22)  op(e3, e2) = all_24_1
% 244.88/51.39    (23)  op(e3, e1) = e1
% 244.88/51.39    (24)   ~ (all_52_3 = all_52_11)
% 244.88/51.39    (25)  op(e1, e3) = e1
% 244.88/51.39    (26)  op(e2, e0) = e2
% 244.88/51.39    (27)  all_54_12 = all_52_3
% 244.88/51.39    (28)  op(e0, e1) = e0
% 244.88/51.39    (29)   ~ (all_52_3 = e2)
% 244.88/51.39    (30)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.88/51.39          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.88/51.39    (31)  op(e3, e2) = e0
% 244.88/51.39    (32)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.88/51.39    (33)  op(e2, e3) = all_52_1
% 244.88/51.39    (34)  op(e3, e3) = e2
% 244.88/51.39    (35)  op(e1, e2) = all_36_1
% 244.88/51.39    (36)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 244.88/51.39            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 244.88/51.39              e2) = all_40_1 & $i(all_40_1))
% 244.88/51.39    (37)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.88/51.40    (38)  op(e1, e1) = e2
% 244.88/51.40    (39)  all_56_1 = e2
% 244.88/51.40    (40)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 244.88/51.40            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 244.88/51.40              e1) = all_34_1 & $i(all_34_1))
% 244.88/51.40    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.88/51.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.88/51.40    (42)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 244.88/51.40            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 244.88/51.40              e2) = all_36_1 & $i(all_36_1))
% 244.88/51.40    (43)  all_58_11 = e0
% 244.88/51.40    (44)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 244.88/51.40            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3,
% 244.88/51.40              e2) = all_32_1 & $i(all_32_1))
% 244.88/51.40    (45)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.88/51.40          | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.88/51.40    (46)  op(e2, e0) = all_52_13
% 244.88/51.40    (47)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.88/51.40          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.88/51.40            e1)
% 244.88/51.40    (48)   ~ (all_52_9 = e1)
% 244.88/51.40    (49)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.88/51.40          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.88/51.40            e2)
% 244.88/51.40    (50)   ~ (all_52_9 = all_52_11)
% 244.88/51.40    (51)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.88/51.40          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.88/51.40    (52)   ~ (all_52_1 = e2)
% 244.88/51.40    (53)   ~ (e2 = e1)
% 244.88/51.40    (54)   ~ (all_52_1 = e1)
% 244.88/51.40    (55)   ~ (all_52_9 = e2)
% 244.88/51.40  
% 244.88/51.40  Begin of proof
% 244.88/51.40  | 
% 244.88/51.40  | BETA: splitting (44) gives:
% 244.88/51.40  | 
% 244.88/51.40  | Case 1:
% 244.88/51.40  | | 
% 244.88/51.40  | |   (56)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 244.88/51.40  | |         all_32_1 & $i(all_32_0) & $i(all_32_1)
% 244.88/51.40  | | 
% 244.88/51.40  | | ALPHA: (56) implies:
% 244.88/51.40  | |   (57)   ~ (all_32_0 = e1)
% 244.88/51.40  | |   (58)  op(e3, e2) = all_32_1
% 244.88/51.40  | |   (59)  op(all_32_1, e3) = all_32_0
% 244.88/51.40  | | 
% 244.88/51.40  | | BETA: splitting (36) gives:
% 244.88/51.40  | | 
% 244.88/51.40  | | Case 1:
% 244.88/51.40  | | | 
% 244.88/51.40  | | |   (60)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 244.88/51.40  | | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 244.88/51.40  | | | 
% 244.88/51.40  | | | ALPHA: (60) implies:
% 244.88/51.40  | | |   (61)   ~ (all_40_0 = e0)
% 244.88/51.40  | | |   (62)  op(e1, e2) = all_40_1
% 244.88/51.40  | | |   (63)  op(all_40_1, e1) = all_40_0
% 244.88/51.40  | | | 
% 244.88/51.40  | | | GROUND_INST: instantiating (41) with all_52_11, e0, e1, e0, simplifying
% 244.88/51.40  | | |              with (7), (28) gives:
% 244.88/51.40  | | |   (64)  all_52_11 = e0
% 244.88/51.40  | | | 
% 244.88/51.40  | | | GROUND_INST: instantiating (41) with all_36_1, all_40_1, e2, e1,
% 244.88/51.40  | | |              simplifying with (35), (62) gives:
% 244.88/51.40  | | |   (65)  all_40_1 = all_36_1
% 244.88/51.40  | | | 
% 244.88/51.40  | | | GROUND_INST: instantiating (41) with e3, all_40_1, e2, e1, simplifying
% 244.88/51.40  | | |              with (17), (62) gives:
% 244.88/51.40  | | |   (66)  all_40_1 = e3
% 244.88/51.40  | | | 
% 244.88/51.40  | | | GROUND_INST: instantiating (41) with all_24_1, all_32_1, e2, e3,
% 244.88/51.40  | | |              simplifying with (22), (58) gives:
% 244.88/51.40  | | |   (67)  all_32_1 = all_24_1
% 244.88/51.40  | | | 
% 244.88/51.40  | | | GROUND_INST: instantiating (41) with e0, all_32_1, e2, e3, simplifying
% 244.88/51.40  | | |              with (31), (58) gives:
% 244.88/51.40  | | |   (68)  all_32_1 = e0
% 244.88/51.40  | | | 
% 244.88/51.40  | | | COMBINE_EQS: (65), (66) imply:
% 244.88/51.40  | | |   (69)  all_36_1 = e3
% 244.88/51.40  | | | 
% 244.88/51.40  | | | COMBINE_EQS: (67), (68) imply:
% 244.88/51.40  | | |   (70)  all_24_1 = e0
% 244.88/51.40  | | | 
% 244.88/51.40  | | | SIMP: (70) implies:
% 244.88/51.40  | | |   (71)  all_24_1 = e0
% 244.88/51.40  | | | 
% 244.88/51.40  | | | REDUCE: (24), (64) imply:
% 244.88/51.40  | | |   (72)   ~ (all_52_3 = e0)
% 244.88/51.40  | | | 
% 244.88/51.40  | | | REDUCE: (50), (64) imply:
% 244.88/51.40  | | |   (73)   ~ (all_52_9 = e0)
% 244.88/51.40  | | | 
% 244.88/51.40  | | | REDUCE: (8), (64) imply:
% 244.88/51.40  | | |   (74)   ~ (e2 = e0)
% 244.88/51.40  | | | 
% 244.88/51.40  | | | SIMP: (74) implies:
% 244.88/51.40  | | |   (75)   ~ (e2 = e0)
% 244.88/51.40  | | | 
% 244.88/51.40  | | | REDUCE: (14), (71) imply:
% 244.88/51.40  | | |   (76)   ~ (e1 = e0)
% 244.88/51.40  | | | 
% 244.88/51.40  | | | SIMP: (76) implies:
% 244.88/51.40  | | |   (77)   ~ (e1 = e0)
% 244.88/51.40  | | | 
% 244.88/51.40  | | | REDUCE: (63), (66) imply:
% 244.88/51.40  | | |   (78)  op(e3, e1) = all_40_0
% 244.88/51.40  | | | 
% 244.88/51.40  | | | REDUCE: (59), (68) imply:
% 244.88/51.40  | | |   (79)  op(e0, e3) = all_32_0
% 244.88/51.40  | | | 
% 244.88/51.40  | | | BETA: splitting (3) gives:
% 244.88/51.40  | | | 
% 244.88/51.40  | | | Case 1:
% 244.88/51.40  | | | | 
% 244.88/51.40  | | | |   (80)  all_54_12 = e3
% 244.88/51.40  | | | | 
% 244.88/51.40  | | | | COMBINE_EQS: (27), (80) imply:
% 244.88/51.40  | | | |   (81)  all_52_3 = e3
% 244.88/51.40  | | | | 
% 244.88/51.40  | | | | SIMP: (81) implies:
% 244.88/51.40  | | | |   (82)  all_52_3 = e3
% 244.88/51.40  | | | | 
% 244.88/51.40  | | | | REDUCE: (13), (82) imply:
% 244.88/51.40  | | | |   (83)  op(e0, e3) = e3
% 244.88/51.40  | | | | 
% 244.88/51.40  | | | | BETA: splitting (32) gives:
% 244.88/51.40  | | | | 
% 244.88/51.40  | | | | Case 1:
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | |   (84)  all_54_6 = e3
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | | COMBINE_EQS: (16), (84) imply:
% 244.88/51.40  | | | | |   (85)  all_52_9 = e3
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | | SIMP: (85) implies:
% 244.88/51.40  | | | | |   (86)  all_52_9 = e3
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | | REDUCE: (18), (86) imply:
% 244.88/51.40  | | | | |   (87)   ~ (all_52_1 = e3)
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | | REDUCE: (55), (86) imply:
% 244.88/51.40  | | | | |   (88)   ~ (e3 = e2)
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | | REDUCE: (48), (86) imply:
% 244.88/51.40  | | | | |   (89)   ~ (e3 = e1)
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | | REDUCE: (73), (86) imply:
% 244.88/51.40  | | | | |   (90)   ~ (e3 = e0)
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | | REDUCE: (21), (86) imply:
% 244.88/51.40  | | | | |   (91)  op(e2, e1) = e3
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | | BETA: splitting (37) gives:
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | | Case 1:
% 244.88/51.40  | | | | | | 
% 244.88/51.40  | | | | | |   (92)  all_54_4 = e3
% 244.88/51.40  | | | | | | 
% 244.88/51.40  | | | | | | REF_CLOSE: (19), (87), (92) are inconsistent by sub-proof #2100.
% 244.88/51.40  | | | | | | 
% 244.88/51.40  | | | | | Case 2:
% 244.88/51.40  | | | | | | 
% 244.88/51.40  | | | | | |   (93)   ~ (all_54_4 = e3)
% 244.88/51.40  | | | | | |   (94)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.88/51.40  | | | | | | 
% 244.88/51.40  | | | | | | BETA: splitting (1) gives:
% 244.88/51.40  | | | | | | 
% 244.88/51.40  | | | | | | Case 1:
% 244.88/51.40  | | | | | | | 
% 244.88/51.40  | | | | | | |   (95)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 244.88/51.40  | | | | | | |           op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 244.88/51.40  | | | | | | |           $i(all_56_3))
% 244.88/51.40  | | | | | | | 
% 244.88/51.40  | | | | | | | BETA: splitting (95) gives:
% 244.88/51.40  | | | | | | | 
% 244.88/51.40  | | | | | | | Case 1:
% 244.88/51.40  | | | | | | | | 
% 244.88/51.40  | | | | | | | |   (96)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 244.88/51.40  | | | | | | | | 
% 244.88/51.40  | | | | | | | | ALPHA: (96) implies:
% 244.88/51.40  | | | | | | | |   (97)  op(e3, all_56_1) = e3
% 244.88/51.40  | | | | | | | | 
% 244.88/51.40  | | | | | | | | REDUCE: (39), (97) imply:
% 244.88/51.40  | | | | | | | |   (98)  op(e3, e2) = e3
% 244.88/51.40  | | | | | | | | 
% 244.88/51.40  | | | | | | | | REF_CLOSE: (31), (41), (90), (98) are inconsistent by sub-proof
% 244.88/51.40  | | | | | | | |            #2099.
% 244.88/51.40  | | | | | | | | 
% 244.88/51.40  | | | | | | | Case 2:
% 244.88/51.40  | | | | | | | | 
% 244.88/51.40  | | | | | | | |   (99)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 244.88/51.40  | | | | | | | |         all_56_3 & $i(all_56_3)
% 244.88/51.40  | | | | | | | | 
% 244.88/51.40  | | | | | | | | ALPHA: (99) implies:
% 244.88/51.40  | | | | | | | |   (100)  op(e2, e3) = all_56_3
% 244.88/51.40  | | | | | | | |   (101)  op(e2, all_56_3) = e2
% 244.88/51.40  | | | | | | | | 
% 244.88/51.40  | | | | | | | | BETA: splitting (4) gives:
% 244.88/51.40  | | | | | | | | 
% 244.88/51.40  | | | | | | | | Case 1:
% 244.88/51.40  | | | | | | | | | 
% 244.88/51.40  | | | | | | | | |   (102)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1)
% 244.88/51.40  | | | | | | | | |            = all_56_17 & $i(all_56_17)) | (all_56_18 = e2 &
% 244.88/51.40  | | | | | | | | |            op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 244.88/51.40  | | | | | | | | |            $i(all_56_19))
% 244.88/51.40  | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | BETA: splitting (102) gives:
% 244.88/51.40  | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | Case 1:
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | |   (103)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 244.88/51.40  | | | | | | | | | |            e1) = all_56_17 & $i(all_56_17)
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | ALPHA: (103) implies:
% 244.88/51.40  | | | | | | | | | |   (104)  op(e3, e1) = all_56_17
% 244.88/51.40  | | | | | | | | | |   (105)  op(e3, all_56_17) = e3
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | REF_CLOSE: (9), (11), (21), (23), (26), (33), (34), (41),
% 244.88/51.40  | | | | | | | | | |            (46), (48), (51), (54), (78), (88), (89), (100),
% 244.88/51.40  | | | | | | | | | |            (101), (104), (105) are inconsistent by sub-proof
% 244.88/51.40  | | | | | | | | | |            #2097.
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | Case 2:
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | |   (106)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 244.88/51.40  | | | | | | | | | |            e1) = all_56_19 & $i(all_56_19)
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | REF_CLOSE: (19), (33), (41), (52), (91), (94), (106) are
% 244.88/51.40  | | | | | | | | | |            inconsistent by sub-proof #2095.
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | End of split
% 244.88/51.40  | | | | | | | | | 
% 244.88/51.40  | | | | | | | | Case 2:
% 244.88/51.40  | | | | | | | | | 
% 244.88/51.40  | | | | | | | | |   (107)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 244.88/51.40  | | | | | | | | |          (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1)
% 244.88/51.40  | | | | | | | | |            = all_56_23 & $i(all_56_23))
% 244.88/51.40  | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | BETA: splitting (107) gives:
% 244.88/51.40  | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | Case 1:
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | |   (108)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | ALPHA: (108) implies:
% 244.88/51.40  | | | | | | | | | |   (109)  op(e1, all_56_21) = e1
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | REDUCE: (2), (109) imply:
% 244.88/51.40  | | | | | | | | | |   (110)  op(e1, e2) = e1
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | REF_CLOSE: (10), (20), (25), (30), (41), (43), (89), (90),
% 244.88/51.40  | | | | | | | | | |            (110) are inconsistent by sub-proof #2090.
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | Case 2:
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | |   (111)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 244.88/51.40  | | | | | | | | | |            e1) = all_56_23 & $i(all_56_23)
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | ALPHA: (111) implies:
% 244.88/51.40  | | | | | | | | | |   (112)  op(e0, e1) = all_56_23
% 244.88/51.40  | | | | | | | | | |   (113)  op(e0, all_56_23) = e0
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | BETA: splitting (15) gives:
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | Case 1:
% 244.88/51.40  | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | |   (114)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 244.88/51.40  | | | | | | | | | | |            & op(e2, e1) = e0)
% 244.88/51.40  | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | REF_CLOSE: (21), (23), (41), (73), (77), (114) are
% 244.88/51.40  | | | | | | | | | | |            inconsistent by sub-proof #2087.
% 244.88/51.40  | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | Case 2:
% 244.88/51.40  | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | |   (115)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 244.88/51.40  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 244.88/51.40  | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | BETA: splitting (115) gives:
% 244.88/51.40  | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | Case 1:
% 244.88/51.40  | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | |   (116)  all_58_8 = e0 & op(e1, e1) = e0
% 244.88/51.40  | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | ALPHA: (116) implies:
% 244.88/51.40  | | | | | | | | | | | |   (117)  op(e1, e1) = e0
% 244.88/51.40  | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | REF_CLOSE: (38), (41), (75), (117) are inconsistent by
% 244.88/51.40  | | | | | | | | | | | |            sub-proof #2211.
% 244.88/51.40  | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | Case 2:
% 244.88/51.40  | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | |   (118)  all_58_14 = e0 & op(e0, e1) = e0
% 244.88/51.40  | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | ALPHA: (118) implies:
% 244.88/51.40  | | | | | | | | | | | |   (119)  all_58_14 = e0
% 244.88/51.40  | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | BETA: splitting (12) gives:
% 244.88/51.40  | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | Case 1:
% 244.88/51.40  | | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | |   (120)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 244.88/51.40  | | | | | | | | | | | | |          op(e0, e1) = all_20_1 & $i(all_20_0) &
% 244.88/51.40  | | | | | | | | | | | | |          $i(all_20_1)
% 244.88/51.40  | | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | | ALPHA: (120) implies:
% 244.88/51.40  | | | | | | | | | | | | |   (121)  op(e0, e1) = all_20_1
% 244.88/51.40  | | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (13), (19), (23), (28), (40), (41),
% 244.88/51.40  | | | | | | | | | | | | |            (45), (47), (49), (52), (53), (54), (57), (61),
% 244.88/51.40  | | | | | | | | | | | | |            (78), (79), (83), (87), (88), (94), (112), (113),
% 244.88/51.40  | | | | | | | | | | | | |            (119), (121) are inconsistent by sub-proof #2062.
% 244.88/51.40  | | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | Case 2:
% 244.88/51.40  | | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | |   (122)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 244.88/51.40  | | | | | | | | | | | | |          $i(all_20_1)
% 244.88/51.40  | | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | | ALPHA: (122) implies:
% 244.88/51.40  | | | | | | | | | | | | |   (123)  op(e0, e1) = all_20_1
% 244.88/51.40  | | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (13), (19), (23), (28), (40), (41),
% 244.88/51.40  | | | | | | | | | | | | |            (45), (47), (49), (52), (53), (54), (57), (61),
% 244.88/51.40  | | | | | | | | | | | | |            (78), (79), (83), (87), (88), (94), (112), (113),
% 244.88/51.40  | | | | | | | | | | | | |            (119), (123) are inconsistent by sub-proof #2062.
% 244.88/51.40  | | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | | End of split
% 244.88/51.40  | | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | | End of split
% 244.88/51.40  | | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | | End of split
% 244.88/51.40  | | | | | | | | | | 
% 244.88/51.40  | | | | | | | | | End of split
% 244.88/51.40  | | | | | | | | | 
% 244.88/51.40  | | | | | | | | End of split
% 244.88/51.40  | | | | | | | | 
% 244.88/51.40  | | | | | | | End of split
% 244.88/51.40  | | | | | | | 
% 244.88/51.40  | | | | | | Case 2:
% 244.88/51.40  | | | | | | | 
% 244.88/51.40  | | | | | | |   (124)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 244.88/51.40  | | | | | | |            all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 244.88/51.40  | | | | | | |              all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.88/51.40  | | | | | | |            $i(all_56_7))
% 244.88/51.40  | | | | | | | 
% 244.88/51.40  | | | | | | | REF_CLOSE: (19), (25), (38), (41), (52), (53), (54), (83), (90),
% 244.88/51.40  | | | | | | |            (94), (124) are inconsistent by sub-proof #2069.
% 244.88/51.40  | | | | | | | 
% 244.88/51.40  | | | | | | End of split
% 244.88/51.40  | | | | | | 
% 244.88/51.40  | | | | | End of split
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | Case 2:
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | |   (125)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | | REF_CLOSE: (16), (48), (55), (73), (125) are inconsistent by sub-proof
% 244.88/51.40  | | | | |            #2244.
% 244.88/51.40  | | | | | 
% 244.88/51.40  | | | | End of split
% 244.88/51.40  | | | | 
% 244.88/51.40  | | | Case 2:
% 244.88/51.40  | | | | 
% 244.88/51.40  | | | |   (126)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.88/51.40  | | | | 
% 244.88/51.40  | | | | REF_CLOSE: (5), (27), (29), (72), (126) are inconsistent by sub-proof
% 244.88/51.40  | | | |            #2066.
% 244.88/51.40  | | | | 
% 244.88/51.40  | | | End of split
% 244.88/51.40  | | | 
% 244.88/51.40  | | Case 2:
% 244.88/51.40  | | | 
% 244.88/51.40  | | |   (127)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 244.88/51.40  | | | 
% 244.88/51.40  | | | REF_CLOSE: (17), (41), (42), (127) are inconsistent by sub-proof #2144.
% 244.88/51.40  | | | 
% 244.88/51.40  | | End of split
% 244.88/51.40  | | 
% 244.88/51.40  | Case 2:
% 244.88/51.40  | | 
% 244.88/51.40  | |   (128)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 & $i(all_32_1)
% 244.88/51.40  | | 
% 244.88/51.40  | | ALPHA: (128) implies:
% 244.88/51.40  | |   (129)   ~ (all_32_1 = e0)
% 244.88/51.40  | |   (130)  op(e3, e2) = all_32_1
% 244.88/51.40  | | 
% 244.88/51.40  | | REF_CLOSE: (22), (31), (41), (129), (130) are inconsistent by sub-proof
% 244.88/51.40  | |            #2065.
% 244.88/51.40  | | 
% 244.88/51.40  | End of split
% 244.88/51.40  | 
% 244.88/51.40  End of proof
% 244.88/51.40  
% 244.88/51.40  Sub-proof #2062 shows that the following formulas are inconsistent:
% 244.88/51.40  ----------------------------------------------------------------
% 244.88/51.40    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.88/51.40    (2)   ~ (all_52_3 = e1)
% 244.88/51.40    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.88/51.40         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.88/51.40    (4)  op(e0, e1) = all_56_23
% 244.88/51.40    (5)  op(e0, e3) = all_52_3
% 244.88/51.40    (6)  all_54_4 = all_52_1
% 244.88/51.40    (7)   ~ (e3 = e2)
% 244.88/51.40    (8)  op(e3, e1) = e1
% 244.88/51.40    (9)  op(e3, e1) = all_40_0
% 244.88/51.40    (10)  op(e0, e3) = e3
% 244.88/51.40    (11)  op(e0, e1) = e0
% 244.88/51.40    (12)  op(e0, e1) = all_20_1
% 244.88/51.40    (13)  op(e0, e3) = all_32_0
% 244.88/51.40    (14)  all_58_14 = e0
% 244.88/51.40    (15)   ~ (all_40_0 = e0)
% 244.88/51.40    (16)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 244.88/51.40            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 244.88/51.40              e1) = all_34_1 & $i(all_34_1))
% 244.88/51.40    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.88/51.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.88/51.40    (18)  op(e0, all_56_23) = e0
% 244.88/51.40    (19)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.88/51.40          | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.88/51.40    (20)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.88/51.40          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.88/51.40            e1)
% 244.88/51.41    (21)   ~ (all_52_1 = e3)
% 244.88/51.41    (22)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.88/51.41          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.88/51.41            e2)
% 244.88/51.41    (23)   ~ (all_32_0 = e1)
% 244.88/51.41    (24)   ~ (all_52_1 = e2)
% 244.88/51.41    (25)   ~ (e2 = e1)
% 244.88/51.41    (26)   ~ (all_52_1 = e1)
% 244.88/51.41  
% 244.88/51.41  Begin of proof
% 244.88/51.41  | 
% 244.88/51.41  | BETA: splitting (16) gives:
% 244.88/51.41  | 
% 244.88/51.41  | Case 1:
% 244.88/51.41  | | 
% 244.88/51.41  | |   (27)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 244.88/51.41  | |         all_34_1 & $i(all_34_0) & $i(all_34_1)
% 244.88/51.41  | | 
% 244.88/51.41  | | ALPHA: (27) implies:
% 244.88/51.41  | |   (28)  op(e0, e1) = all_34_1
% 244.88/51.41  | | 
% 244.88/51.41  | | BETA: splitting (1) gives:
% 244.88/51.41  | | 
% 244.88/51.41  | | Case 1:
% 244.88/51.41  | | | 
% 244.88/51.41  | | |   (29)  all_54_4 = e2
% 244.88/51.41  | | | 
% 244.88/51.41  | | | REF_CLOSE: (6), (24), (29) are inconsistent by sub-proof #2096.
% 244.88/51.41  | | | 
% 244.88/51.41  | | Case 2:
% 244.88/51.41  | | | 
% 244.88/51.41  | | |   (30)   ~ (all_54_4 = e2)
% 244.88/51.41  | | |   (31)  all_54_4 = e1 | all_54_4 = e0
% 244.88/51.41  | | | 
% 244.88/51.41  | | | BETA: splitting (31) gives:
% 244.88/51.41  | | | 
% 244.88/51.41  | | | Case 1:
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | |   (32)  all_54_4 = e1
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | REF_CLOSE: (6), (26), (32) are inconsistent by sub-proof #2086.
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | Case 2:
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | |   (33)  all_54_4 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | COMBINE_EQS: (6), (33) imply:
% 244.88/51.41  | | | |   (34)  all_52_1 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | SIMP: (34) implies:
% 244.88/51.41  | | | |   (35)  all_52_1 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | REDUCE: (21), (35) imply:
% 244.88/51.41  | | | |   (36)   ~ (e3 = e0)
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | SIMP: (36) implies:
% 244.88/51.41  | | | |   (37)   ~ (e3 = e0)
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | REDUCE: (24), (35) imply:
% 244.88/51.41  | | | |   (38)   ~ (e2 = e0)
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | SIMP: (38) implies:
% 244.88/51.41  | | | |   (39)   ~ (e2 = e0)
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | GROUND_INST: instantiating (17) with e0, all_56_23, e1, e0, simplifying
% 244.88/51.41  | | | |              with (4), (11) gives:
% 244.88/51.41  | | | |   (40)  all_56_23 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | GROUND_INST: instantiating (17) with all_34_1, all_56_23, e1, e0,
% 244.88/51.41  | | | |              simplifying with (4), (28) gives:
% 244.88/51.41  | | | |   (41)  all_56_23 = all_34_1
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | GROUND_INST: instantiating (17) with all_20_1, all_56_23, e1, e0,
% 244.88/51.41  | | | |              simplifying with (4), (12) gives:
% 244.88/51.41  | | | |   (42)  all_56_23 = all_20_1
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | GROUND_INST: instantiating (17) with e3, all_32_0, e3, e0, simplifying
% 244.88/51.41  | | | |              with (10), (13) gives:
% 244.88/51.41  | | | |   (43)  all_32_0 = e3
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | GROUND_INST: instantiating (17) with e1, all_40_0, e1, e3, simplifying
% 244.88/51.41  | | | |              with (8), (9) gives:
% 244.88/51.41  | | | |   (44)  all_40_0 = e1
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | COMBINE_EQS: (40), (41) imply:
% 244.88/51.41  | | | |   (45)  all_34_1 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | COMBINE_EQS: (41), (42) imply:
% 244.88/51.41  | | | |   (46)  all_34_1 = all_20_1
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | COMBINE_EQS: (45), (46) imply:
% 244.88/51.41  | | | |   (47)  all_20_1 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | SIMP: (47) implies:
% 244.88/51.41  | | | |   (48)  all_20_1 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | REDUCE: (15), (44) imply:
% 244.88/51.41  | | | |   (49)   ~ (e1 = e0)
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | REF_CLOSE: (2), (3), (5), (7), (12), (14), (17), (18), (19), (20), (22),
% 244.88/51.41  | | | |            (23), (25), (37), (39), (40), (43), (48), (49) are
% 244.88/51.41  | | | |            inconsistent by sub-proof #2063.
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | End of split
% 244.88/51.41  | | | 
% 244.88/51.41  | | End of split
% 244.88/51.41  | | 
% 244.88/51.41  | Case 2:
% 244.88/51.41  | | 
% 244.88/51.41  | |   (50)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 244.88/51.41  | | 
% 244.88/51.41  | | ALPHA: (50) implies:
% 244.88/51.41  | |   (51)   ~ (all_34_1 = e2)
% 244.88/51.41  | |   (52)  op(e0, e1) = all_34_1
% 244.88/51.41  | | 
% 244.88/51.41  | | BETA: splitting (1) gives:
% 244.88/51.41  | | 
% 244.88/51.41  | | Case 1:
% 244.88/51.41  | | | 
% 244.88/51.41  | | |   (53)  all_54_4 = e2
% 244.88/51.41  | | | 
% 244.88/51.41  | | | REF_CLOSE: (6), (24), (53) are inconsistent by sub-proof #2096.
% 244.88/51.41  | | | 
% 244.88/51.41  | | Case 2:
% 244.88/51.41  | | | 
% 244.88/51.41  | | |   (54)  all_54_4 = e1 | all_54_4 = e0
% 244.88/51.41  | | | 
% 244.88/51.41  | | | BETA: splitting (54) gives:
% 244.88/51.41  | | | 
% 244.88/51.41  | | | Case 1:
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | |   (55)  all_54_4 = e1
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | REF_CLOSE: (6), (26), (55) are inconsistent by sub-proof #2086.
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | Case 2:
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | |   (56)  all_54_4 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | COMBINE_EQS: (6), (56) imply:
% 244.88/51.41  | | | |   (57)  all_52_1 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | SIMP: (57) implies:
% 244.88/51.41  | | | |   (58)  all_52_1 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | REDUCE: (21), (58) imply:
% 244.88/51.41  | | | |   (59)   ~ (e3 = e0)
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | SIMP: (59) implies:
% 244.88/51.41  | | | |   (60)   ~ (e3 = e0)
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | GROUND_INST: instantiating (17) with e0, all_56_23, e1, e0, simplifying
% 244.88/51.41  | | | |              with (4), (11) gives:
% 244.88/51.41  | | | |   (61)  all_56_23 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | GROUND_INST: instantiating (17) with all_34_1, all_56_23, e1, e0,
% 244.88/51.41  | | | |              simplifying with (4), (52) gives:
% 244.88/51.41  | | | |   (62)  all_56_23 = all_34_1
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | GROUND_INST: instantiating (17) with all_20_1, all_56_23, e1, e0,
% 244.88/51.41  | | | |              simplifying with (4), (12) gives:
% 244.88/51.41  | | | |   (63)  all_56_23 = all_20_1
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | GROUND_INST: instantiating (17) with e3, all_32_0, e3, e0, simplifying
% 244.88/51.41  | | | |              with (10), (13) gives:
% 244.88/51.41  | | | |   (64)  all_32_0 = e3
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | GROUND_INST: instantiating (17) with e1, all_40_0, e1, e3, simplifying
% 244.88/51.41  | | | |              with (8), (9) gives:
% 244.88/51.41  | | | |   (65)  all_40_0 = e1
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | COMBINE_EQS: (61), (62) imply:
% 244.88/51.41  | | | |   (66)  all_34_1 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | COMBINE_EQS: (62), (63) imply:
% 244.88/51.41  | | | |   (67)  all_34_1 = all_20_1
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | COMBINE_EQS: (66), (67) imply:
% 244.88/51.41  | | | |   (68)  all_20_1 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | SIMP: (68) implies:
% 244.88/51.41  | | | |   (69)  all_20_1 = e0
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | REDUCE: (15), (65) imply:
% 244.88/51.41  | | | |   (70)   ~ (e1 = e0)
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | REDUCE: (51), (66) imply:
% 244.88/51.41  | | | |   (71)   ~ (e2 = e0)
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | SIMP: (71) implies:
% 244.88/51.41  | | | |   (72)   ~ (e2 = e0)
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | | REF_CLOSE: (2), (3), (5), (7), (12), (14), (17), (18), (19), (20), (22),
% 244.88/51.41  | | | |            (23), (25), (60), (61), (64), (69), (70), (72) are
% 244.88/51.41  | | | |            inconsistent by sub-proof #2063.
% 244.88/51.41  | | | | 
% 244.88/51.41  | | | End of split
% 244.88/51.41  | | | 
% 244.88/51.41  | | End of split
% 244.88/51.41  | | 
% 244.88/51.41  | End of split
% 244.88/51.41  | 
% 244.88/51.41  End of proof
% 244.88/51.41  
% 244.88/51.41  Sub-proof #2063 shows that the following formulas are inconsistent:
% 244.88/51.41  ----------------------------------------------------------------
% 244.88/51.41    (1)  all_56_23 = e0
% 244.88/51.41    (2)   ~ (all_52_3 = e1)
% 244.88/51.41    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.88/51.41         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.88/51.41    (4)   ~ (e3 = e0)
% 244.88/51.41    (5)   ~ (e2 = e0)
% 244.88/51.41    (6)  op(e0, e3) = all_52_3
% 244.88/51.41    (7)   ~ (e3 = e2)
% 244.88/51.41    (8)  all_20_1 = e0
% 244.88/51.41    (9)  op(e0, e1) = all_20_1
% 244.88/51.41    (10)  all_32_0 = e3
% 244.88/51.41    (11)  all_58_14 = e0
% 244.88/51.41    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.88/51.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.88/51.41    (13)  op(e0, all_56_23) = e0
% 244.88/51.41    (14)   ~ (e1 = e0)
% 244.88/51.41    (15)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.88/51.41          | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.88/51.41    (16)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.88/51.41          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.88/51.41            e1)
% 244.88/51.41    (17)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.88/51.41          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.88/51.41            e2)
% 244.88/51.41    (18)   ~ (all_32_0 = e1)
% 244.88/51.41    (19)   ~ (e2 = e1)
% 244.88/51.41  
% 244.88/51.41  Begin of proof
% 244.88/51.41  | 
% 244.88/51.41  | REDUCE: (10), (18) imply:
% 244.88/51.41  |   (20)   ~ (e3 = e1)
% 244.88/51.41  | 
% 244.88/51.41  | REDUCE: (1), (13) imply:
% 244.88/51.41  |   (21)  op(e0, e0) = e0
% 244.88/51.41  | 
% 244.88/51.41  | REDUCE: (8), (9) imply:
% 244.88/51.41  |   (22)  op(e0, e1) = e0
% 244.88/51.41  | 
% 244.88/51.41  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (11), (12), (14), (15), (16), (17),
% 244.88/51.41  |            (19), (20), (21), (22) are inconsistent by sub-proof #2073.
% 244.88/51.41  | 
% 244.88/51.41  End of proof
% 244.88/51.41  
% 244.88/51.41  Sub-proof #2064 shows that the following formulas are inconsistent:
% 244.88/51.41  ----------------------------------------------------------------
% 244.88/51.41    (1)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 244.88/51.41             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 244.88/51.41           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 244.88/51.41         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.88/51.41           $i(all_56_7))
% 244.88/51.41    (2)  all_56_21 = e2
% 244.88/51.41    (3)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.88/51.41    (4)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1) = all_56_17 &
% 244.88/51.41           $i(all_56_17)) | (all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1)
% 244.88/51.41           = all_56_19 & $i(all_56_19)) | (all_56_20 = e1 & op(e1, all_56_21) =
% 244.88/51.41           e1) | (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1) = all_56_23
% 244.88/51.41           & $i(all_56_23))
% 244.88/51.41    (5)   ~ (all_52_3 = e1)
% 244.88/51.41    (6)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.88/51.41         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.88/51.41    (7)  op(e0, e1) = all_52_11
% 244.88/51.41    (8)   ~ (all_52_11 = e2)
% 244.88/51.41    (9)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.88/51.41         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.88/51.41    (10)   ~ (all_52_11 = e1)
% 244.88/51.41    (11)  op(e1, e1) = all_6_2
% 244.88/51.41    (12)   ~ (all_52_13 = e1)
% 244.88/51.41    (13)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 244.88/51.41            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 244.88/51.41              e1) = all_20_1 & $i(all_20_1))
% 244.88/51.41    (14)  op(e0, e3) = all_52_3
% 244.88/51.41    (15)  op(all_24_1, e3) = all_24_0
% 244.88/51.41    (16)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.88/51.41          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.88/51.41    (17)  all_54_6 = all_52_9
% 244.88/51.41    (18)  op(e1, e2) = e3
% 244.88/51.41    (19)   ~ (all_24_0 = e0)
% 244.88/51.41    (20)   ~ (all_52_1 = all_52_9)
% 244.88/51.41    (21)  all_54_4 = all_52_1
% 244.88/51.41    (22)   ~ (all_6_2 = e3)
% 244.88/51.41    (23)  op(e2, e1) = all_52_9
% 244.88/51.41    (24)  op(e3, e2) = all_24_1
% 244.88/51.41    (25)  op(e3, e1) = e1
% 244.88/51.41    (26)   ~ (all_52_3 = all_52_11)
% 244.88/51.41    (27)  op(e1, e3) = e1
% 244.88/51.41    (28)  op(e2, e0) = e2
% 244.88/51.41    (29)  all_54_12 = all_52_3
% 244.88/51.41    (30)  op(e0, e1) = e0
% 244.88/51.41    (31)   ~ (all_52_3 = e2)
% 244.88/51.41    (32)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.88/51.41          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.88/51.41    (33)  op(e3, e2) = e0
% 244.88/51.41    (34)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.88/51.41    (35)  op(e2, e3) = all_52_1
% 244.88/51.41    (36)  op(e3, e3) = e2
% 244.88/51.41    (37)  op(e1, e2) = all_36_1
% 244.88/51.41    (38)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 244.88/51.41            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 244.88/51.41              e2) = all_40_1 & $i(all_40_1))
% 244.88/51.41    (39)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.88/51.41    (40)  op(e1, e1) = e2
% 244.88/51.41    (41)  all_56_1 = e2
% 244.88/51.41    (42)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 244.88/51.41            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 244.88/51.41              e1) = all_34_1 & $i(all_34_1))
% 244.88/51.41    (43)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.88/51.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.88/51.41    (44)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 244.88/51.41            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 244.88/51.41              e2) = all_36_1 & $i(all_36_1))
% 244.88/51.41    (45)  all_58_11 = e0
% 244.88/51.41    (46)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 244.88/51.41            all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3,
% 244.88/51.41              e2) = all_32_1 & $i(all_32_1))
% 244.88/51.41    (47)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.88/51.41          | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.88/51.41    (48)  op(e2, e0) = all_52_13
% 244.88/51.41    (49)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.88/51.41          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.88/51.41            e1)
% 244.88/51.41    (50)   ~ (all_52_9 = e1)
% 244.88/51.41    (51)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.88/51.41          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.88/51.41            e2)
% 244.88/51.41    (52)   ~ (all_52_9 = all_52_11)
% 244.88/51.41    (53)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.88/51.41          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.88/51.41    (54)   ~ (all_52_1 = e2)
% 244.88/51.41    (55)   ~ (e2 = e1)
% 244.88/51.41    (56)   ~ (all_52_1 = e1)
% 244.88/51.41    (57)   ~ (all_52_9 = e2)
% 244.88/51.41  
% 244.88/51.41  Begin of proof
% 244.88/51.41  | 
% 244.88/51.41  | BETA: splitting (46) gives:
% 244.88/51.41  | 
% 244.88/51.41  | Case 1:
% 244.88/51.41  | | 
% 244.88/51.41  | |   (58)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 244.88/51.41  | |         all_32_1 & $i(all_32_0) & $i(all_32_1)
% 244.88/51.41  | | 
% 244.88/51.41  | | ALPHA: (58) implies:
% 244.88/51.41  | |   (59)   ~ (all_32_0 = e1)
% 244.88/51.41  | |   (60)  op(e3, e2) = all_32_1
% 244.88/51.41  | |   (61)  op(all_32_1, e3) = all_32_0
% 244.88/51.41  | | 
% 244.88/51.41  | | BETA: splitting (38) gives:
% 244.88/51.41  | | 
% 244.88/51.41  | | Case 1:
% 244.88/51.41  | | | 
% 244.88/51.41  | | |   (62)   ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 244.88/51.41  | | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 244.88/51.41  | | | 
% 244.88/51.41  | | | ALPHA: (62) implies:
% 244.88/51.41  | | |   (63)   ~ (all_40_0 = e0)
% 244.88/51.41  | | |   (64)  op(e1, e2) = all_40_1
% 244.88/51.41  | | |   (65)  op(all_40_1, e1) = all_40_0
% 244.88/51.41  | | | 
% 244.88/51.41  | | | GROUND_INST: instantiating (43) with all_52_11, e0, e1, e0, simplifying
% 244.88/51.41  | | |              with (7), (30) gives:
% 244.88/51.41  | | |   (66)  all_52_11 = e0
% 244.88/51.41  | | | 
% 244.88/51.41  | | | GROUND_INST: instantiating (43) with all_36_1, all_40_1, e2, e1,
% 244.88/51.41  | | |              simplifying with (37), (64) gives:
% 244.88/51.41  | | |   (67)  all_40_1 = all_36_1
% 244.88/51.41  | | | 
% 244.88/51.42  | | | GROUND_INST: instantiating (43) with e3, all_40_1, e2, e1, simplifying
% 244.88/51.42  | | |              with (18), (64) gives:
% 244.88/51.42  | | |   (68)  all_40_1 = e3
% 244.88/51.42  | | | 
% 244.88/51.42  | | | GROUND_INST: instantiating (43) with all_24_1, all_32_1, e2, e3,
% 244.88/51.42  | | |              simplifying with (24), (60) gives:
% 244.88/51.42  | | |   (69)  all_32_1 = all_24_1
% 244.88/51.42  | | | 
% 244.88/51.42  | | | GROUND_INST: instantiating (43) with e0, all_32_1, e2, e3, simplifying
% 244.88/51.42  | | |              with (33), (60) gives:
% 244.88/51.42  | | |   (70)  all_32_1 = e0
% 244.88/51.42  | | | 
% 244.88/51.42  | | | COMBINE_EQS: (67), (68) imply:
% 244.88/51.42  | | |   (71)  all_36_1 = e3
% 244.88/51.42  | | | 
% 244.88/51.42  | | | COMBINE_EQS: (69), (70) imply:
% 244.88/51.42  | | |   (72)  all_24_1 = e0
% 244.88/51.42  | | | 
% 244.88/51.42  | | | SIMP: (72) implies:
% 244.88/51.42  | | |   (73)  all_24_1 = e0
% 244.88/51.42  | | | 
% 244.88/51.42  | | | REDUCE: (26), (66) imply:
% 244.88/51.42  | | |   (74)   ~ (all_52_3 = e0)
% 244.88/51.42  | | | 
% 244.88/51.42  | | | REDUCE: (52), (66) imply:
% 244.88/51.42  | | |   (75)   ~ (all_52_9 = e0)
% 244.88/51.42  | | | 
% 244.88/51.42  | | | REDUCE: (8), (66) imply:
% 244.88/51.42  | | |   (76)   ~ (e2 = e0)
% 244.88/51.42  | | | 
% 244.88/51.42  | | | SIMP: (76) implies:
% 244.88/51.42  | | |   (77)   ~ (e2 = e0)
% 244.88/51.42  | | | 
% 244.88/51.42  | | | REDUCE: (10), (66) imply:
% 244.88/51.42  | | |   (78)   ~ (e1 = e0)
% 244.88/51.42  | | | 
% 244.88/51.42  | | | SIMP: (78) implies:
% 244.88/51.42  | | |   (79)   ~ (e1 = e0)
% 244.88/51.42  | | | 
% 244.88/51.42  | | | REDUCE: (65), (68) imply:
% 244.88/51.42  | | |   (80)  op(e3, e1) = all_40_0
% 244.88/51.42  | | | 
% 244.88/51.42  | | | REDUCE: (61), (70) imply:
% 244.88/51.42  | | |   (81)  op(e0, e3) = all_32_0
% 244.88/51.42  | | | 
% 244.88/51.42  | | | REDUCE: (15), (73) imply:
% 244.88/51.42  | | |   (82)  op(e0, e3) = all_24_0
% 244.88/51.42  | | | 
% 244.88/51.42  | | | BETA: splitting (3) gives:
% 244.88/51.42  | | | 
% 244.88/51.42  | | | Case 1:
% 244.88/51.42  | | | | 
% 244.88/51.42  | | | |   (83)  all_54_12 = e3
% 244.88/51.42  | | | | 
% 244.88/51.42  | | | | COMBINE_EQS: (29), (83) imply:
% 244.88/51.42  | | | |   (84)  all_52_3 = e3
% 244.88/51.42  | | | | 
% 244.88/51.42  | | | | SIMP: (84) implies:
% 244.88/51.42  | | | |   (85)  all_52_3 = e3
% 244.88/51.42  | | | | 
% 244.88/51.42  | | | | REDUCE: (14), (85) imply:
% 244.88/51.42  | | | |   (86)  op(e0, e3) = e3
% 244.88/51.42  | | | | 
% 244.88/51.42  | | | | BETA: splitting (34) gives:
% 244.88/51.42  | | | | 
% 244.88/51.42  | | | | Case 1:
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | |   (87)  all_54_6 = e3
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | | COMBINE_EQS: (17), (87) imply:
% 244.88/51.42  | | | | |   (88)  all_52_9 = e3
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | | SIMP: (88) implies:
% 244.88/51.42  | | | | |   (89)  all_52_9 = e3
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | | REDUCE: (20), (89) imply:
% 244.88/51.42  | | | | |   (90)   ~ (all_52_1 = e3)
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | | REDUCE: (57), (89) imply:
% 244.88/51.42  | | | | |   (91)   ~ (e3 = e2)
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | | REDUCE: (50), (89) imply:
% 244.88/51.42  | | | | |   (92)   ~ (e3 = e1)
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | | REDUCE: (75), (89) imply:
% 244.88/51.42  | | | | |   (93)   ~ (e3 = e0)
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | | REDUCE: (23), (89) imply:
% 244.88/51.42  | | | | |   (94)  op(e2, e1) = e3
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | | BETA: splitting (39) gives:
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | | Case 1:
% 244.88/51.42  | | | | | | 
% 244.88/51.42  | | | | | |   (95)  all_54_4 = e3
% 244.88/51.42  | | | | | | 
% 244.88/51.42  | | | | | | REF_CLOSE: (21), (90), (95) are inconsistent by sub-proof #2100.
% 244.88/51.42  | | | | | | 
% 244.88/51.42  | | | | | Case 2:
% 244.88/51.42  | | | | | | 
% 244.88/51.42  | | | | | |   (96)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.88/51.42  | | | | | | 
% 244.88/51.42  | | | | | | BETA: splitting (1) gives:
% 244.88/51.42  | | | | | | 
% 244.88/51.42  | | | | | | Case 1:
% 244.88/51.42  | | | | | | | 
% 244.88/51.42  | | | | | | |   (97)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 244.88/51.42  | | | | | | |           op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 244.88/51.42  | | | | | | |           $i(all_56_3))
% 244.88/51.42  | | | | | | | 
% 244.88/51.42  | | | | | | | BETA: splitting (97) gives:
% 244.88/51.42  | | | | | | | 
% 244.88/51.42  | | | | | | | Case 1:
% 244.88/51.42  | | | | | | | | 
% 244.88/51.42  | | | | | | | |   (98)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 244.88/51.42  | | | | | | | | 
% 244.88/51.42  | | | | | | | | ALPHA: (98) implies:
% 244.88/51.42  | | | | | | | |   (99)  op(e3, all_56_1) = e3
% 244.88/51.42  | | | | | | | | 
% 244.88/51.42  | | | | | | | | REDUCE: (41), (99) imply:
% 244.88/51.42  | | | | | | | |   (100)  op(e3, e2) = e3
% 244.88/51.42  | | | | | | | | 
% 244.88/51.42  | | | | | | | | REF_CLOSE: (33), (43), (93), (100) are inconsistent by sub-proof
% 244.88/51.42  | | | | | | | |            #2099.
% 244.88/51.42  | | | | | | | | 
% 244.88/51.42  | | | | | | | Case 2:
% 244.88/51.42  | | | | | | | | 
% 244.88/51.42  | | | | | | | |   (101)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 244.88/51.42  | | | | | | | |          all_56_3 & $i(all_56_3)
% 244.88/51.42  | | | | | | | | 
% 244.88/51.42  | | | | | | | | ALPHA: (101) implies:
% 244.88/51.42  | | | | | | | |   (102)  op(e2, e3) = all_56_3
% 244.88/51.42  | | | | | | | |   (103)  op(e2, all_56_3) = e2
% 244.88/51.42  | | | | | | | | 
% 244.88/51.42  | | | | | | | | BETA: splitting (4) gives:
% 244.88/51.42  | | | | | | | | 
% 244.88/51.42  | | | | | | | | Case 1:
% 244.88/51.42  | | | | | | | | | 
% 244.88/51.42  | | | | | | | | |   (104)  (all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3, e1)
% 244.88/51.42  | | | | | | | | |            = all_56_17 & $i(all_56_17)) | (all_56_18 = e2 &
% 244.88/51.42  | | | | | | | | |            op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 244.88/51.42  | | | | | | | | |            $i(all_56_19))
% 244.88/51.42  | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | BETA: splitting (104) gives:
% 244.88/51.42  | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | Case 1:
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | |   (105)  all_56_16 = e3 & op(e3, all_56_17) = e3 & op(e3,
% 244.88/51.42  | | | | | | | | | |            e1) = all_56_17 & $i(all_56_17)
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | ALPHA: (105) implies:
% 244.88/51.42  | | | | | | | | | |   (106)  op(e3, e1) = all_56_17
% 244.88/51.42  | | | | | | | | | |   (107)  op(e3, all_56_17) = e3
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | REF_CLOSE: (9), (12), (23), (25), (28), (35), (36), (43),
% 244.88/51.42  | | | | | | | | | |            (48), (50), (53), (56), (80), (91), (92), (102),
% 244.88/51.42  | | | | | | | | | |            (103), (106), (107) are inconsistent by sub-proof
% 244.88/51.42  | | | | | | | | | |            #2097.
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | Case 2:
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | |   (108)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2,
% 244.88/51.42  | | | | | | | | | |            e1) = all_56_19 & $i(all_56_19)
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | REF_CLOSE: (21), (35), (43), (54), (94), (96), (108) are
% 244.88/51.42  | | | | | | | | | |            inconsistent by sub-proof #2095.
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | End of split
% 244.88/51.42  | | | | | | | | | 
% 244.88/51.42  | | | | | | | | Case 2:
% 244.88/51.42  | | | | | | | | | 
% 244.88/51.42  | | | | | | | | |   (109)  (all_56_20 = e1 & op(e1, all_56_21) = e1) |
% 244.88/51.42  | | | | | | | | |          (all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0, e1)
% 244.88/51.42  | | | | | | | | |            = all_56_23 & $i(all_56_23))
% 244.88/51.42  | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | BETA: splitting (109) gives:
% 244.88/51.42  | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | Case 1:
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | |   (110)  all_56_20 = e1 & op(e1, all_56_21) = e1
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | ALPHA: (110) implies:
% 244.88/51.42  | | | | | | | | | |   (111)  op(e1, all_56_21) = e1
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | REDUCE: (2), (111) imply:
% 244.88/51.42  | | | | | | | | | |   (112)  op(e1, e2) = e1
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | REF_CLOSE: (11), (22), (27), (32), (43), (45), (92), (93),
% 244.88/51.42  | | | | | | | | | |            (112) are inconsistent by sub-proof #2090.
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | Case 2:
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | |   (113)  all_56_22 = e0 & op(e0, all_56_23) = e0 & op(e0,
% 244.88/51.42  | | | | | | | | | |            e1) = all_56_23 & $i(all_56_23)
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | ALPHA: (113) implies:
% 244.88/51.42  | | | | | | | | | |   (114)  op(e0, e1) = all_56_23
% 244.88/51.42  | | | | | | | | | |   (115)  op(e0, all_56_23) = e0
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | BETA: splitting (16) gives:
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | Case 1:
% 244.88/51.42  | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | |   (116)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 244.88/51.42  | | | | | | | | | | |            & op(e2, e1) = e0)
% 244.88/51.42  | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | REF_CLOSE: (23), (25), (43), (75), (79), (116) are
% 244.88/51.42  | | | | | | | | | | |            inconsistent by sub-proof #2087.
% 244.88/51.42  | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | Case 2:
% 244.88/51.42  | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | |   (117)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 244.88/51.42  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 244.88/51.42  | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | BETA: splitting (117) gives:
% 244.88/51.42  | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | Case 1:
% 244.88/51.42  | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | |   (118)  all_58_8 = e0 & op(e1, e1) = e0
% 244.88/51.42  | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | ALPHA: (118) implies:
% 244.88/51.42  | | | | | | | | | | | |   (119)  op(e1, e1) = e0
% 244.88/51.42  | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | REF_CLOSE: (40), (43), (77), (119) are inconsistent by
% 244.88/51.42  | | | | | | | | | | | |            sub-proof #2211.
% 244.88/51.42  | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | Case 2:
% 244.88/51.42  | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | |   (120)  all_58_14 = e0 & op(e0, e1) = e0
% 244.88/51.42  | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | ALPHA: (120) implies:
% 244.88/51.42  | | | | | | | | | | | |   (121)  all_58_14 = e0
% 244.88/51.42  | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | BETA: splitting (13) gives:
% 244.88/51.42  | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | Case 1:
% 244.88/51.42  | | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | |   (122)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 &
% 244.88/51.42  | | | | | | | | | | | | |          op(e0, e1) = all_20_1 & $i(all_20_0) &
% 244.88/51.42  | | | | | | | | | | | | |          $i(all_20_1)
% 244.88/51.42  | | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | | ALPHA: (122) implies:
% 244.88/51.42  | | | | | | | | | | | | |   (123)  op(e0, e1) = all_20_1
% 244.88/51.42  | | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14), (19), (21), (25), (30), (42),
% 244.88/51.42  | | | | | | | | | | | | |            (43), (47), (49), (51), (54), (55), (56), (59),
% 244.88/51.42  | | | | | | | | | | | | |            (63), (80), (81), (82), (86), (91), (96), (114),
% 244.88/51.42  | | | | | | | | | | | | |            (115), (121), (123) are inconsistent by sub-proof
% 244.88/51.42  | | | | | | | | | | | | |            #2071.
% 244.88/51.42  | | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | Case 2:
% 244.88/51.42  | | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | |   (124)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 &
% 244.88/51.42  | | | | | | | | | | | | |          $i(all_20_1)
% 244.88/51.42  | | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | | ALPHA: (124) implies:
% 244.88/51.42  | | | | | | | | | | | | |   (125)  op(e0, e1) = all_20_1
% 244.88/51.42  | | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14), (19), (21), (25), (30), (42),
% 244.88/51.42  | | | | | | | | | | | | |            (43), (47), (49), (51), (54), (55), (56), (59),
% 244.88/51.42  | | | | | | | | | | | | |            (63), (80), (81), (82), (86), (91), (96), (114),
% 244.88/51.42  | | | | | | | | | | | | |            (115), (121), (125) are inconsistent by sub-proof
% 244.88/51.42  | | | | | | | | | | | | |            #2071.
% 244.88/51.42  | | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | | End of split
% 244.88/51.42  | | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | | End of split
% 244.88/51.42  | | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | | End of split
% 244.88/51.42  | | | | | | | | | | 
% 244.88/51.42  | | | | | | | | | End of split
% 244.88/51.42  | | | | | | | | | 
% 244.88/51.42  | | | | | | | | End of split
% 244.88/51.42  | | | | | | | | 
% 244.88/51.42  | | | | | | | End of split
% 244.88/51.42  | | | | | | | 
% 244.88/51.42  | | | | | | Case 2:
% 244.88/51.42  | | | | | | | 
% 244.88/51.42  | | | | | | |   (126)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 244.88/51.42  | | | | | | |            all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 244.88/51.42  | | | | | | |              all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.88/51.42  | | | | | | |            $i(all_56_7))
% 244.88/51.42  | | | | | | | 
% 244.88/51.42  | | | | | | | REF_CLOSE: (21), (27), (40), (43), (54), (55), (56), (86), (93),
% 244.88/51.42  | | | | | | |            (96), (126) are inconsistent by sub-proof #2069.
% 244.88/51.42  | | | | | | | 
% 244.88/51.42  | | | | | | End of split
% 244.88/51.42  | | | | | | 
% 244.88/51.42  | | | | | End of split
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | Case 2:
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | |   (127)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | | REF_CLOSE: (17), (50), (57), (75), (127) are inconsistent by sub-proof
% 244.88/51.42  | | | | |            #2244.
% 244.88/51.42  | | | | | 
% 244.88/51.42  | | | | End of split
% 244.88/51.42  | | | | 
% 244.88/51.42  | | | Case 2:
% 244.88/51.42  | | | | 
% 244.88/51.42  | | | |   (128)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.88/51.42  | | | | 
% 244.88/51.42  | | | | REF_CLOSE: (5), (29), (31), (74), (128) are inconsistent by sub-proof
% 244.88/51.42  | | | |            #2066.
% 244.88/51.42  | | | | 
% 244.88/51.42  | | | End of split
% 244.88/51.42  | | | 
% 244.88/51.42  | | Case 2:
% 244.88/51.42  | | | 
% 244.88/51.42  | | |   (129)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 244.88/51.42  | | | 
% 244.88/51.42  | | | REF_CLOSE: (18), (43), (44), (129) are inconsistent by sub-proof #2144.
% 244.88/51.42  | | | 
% 244.88/51.42  | | End of split
% 244.88/51.42  | | 
% 244.88/51.42  | Case 2:
% 244.88/51.42  | | 
% 244.88/51.42  | |   (130)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 & $i(all_32_1)
% 244.88/51.42  | | 
% 244.88/51.42  | | ALPHA: (130) implies:
% 244.88/51.42  | |   (131)   ~ (all_32_1 = e0)
% 244.88/51.42  | |   (132)  op(e3, e2) = all_32_1
% 244.88/51.42  | | 
% 244.88/51.42  | | REF_CLOSE: (24), (33), (43), (131), (132) are inconsistent by sub-proof
% 244.88/51.42  | |            #2065.
% 244.88/51.42  | | 
% 244.88/51.42  | End of split
% 244.88/51.42  | 
% 244.88/51.42  End of proof
% 244.88/51.42  
% 244.88/51.42  Sub-proof #2065 shows that the following formulas are inconsistent:
% 244.88/51.42  ----------------------------------------------------------------
% 244.88/51.42    (1)  op(e3, e2) = all_32_1
% 244.88/51.42    (2)  op(e3, e2) = all_24_1
% 244.88/51.42    (3)  op(e3, e2) = e0
% 244.88/51.42    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.88/51.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.88/51.42    (5)   ~ (all_32_1 = e0)
% 244.88/51.42  
% 244.88/51.42  Begin of proof
% 244.88/51.42  | 
% 244.88/51.42  | GROUND_INST: instantiating (4) with e0, all_32_1, e2, e3, simplifying with
% 244.88/51.42  |              (1), (3) gives:
% 244.88/51.42  |   (6)  all_32_1 = e0
% 244.88/51.42  | 
% 244.88/51.42  | GROUND_INST: instantiating (4) with all_24_1, all_32_1, e2, e3, simplifying
% 244.88/51.42  |              with (1), (2) gives:
% 244.88/51.42  |   (7)  all_32_1 = all_24_1
% 244.88/51.42  | 
% 244.88/51.42  | COMBINE_EQS: (6), (7) imply:
% 244.88/51.42  |   (8)  all_24_1 = e0
% 244.88/51.42  | 
% 244.88/51.42  | REDUCE: (5), (6) imply:
% 244.88/51.42  |   (9)  $false
% 244.88/51.42  | 
% 244.88/51.42  | CLOSE: (9) is inconsistent.
% 244.88/51.42  | 
% 244.88/51.42  End of proof
% 244.88/51.42  
% 244.88/51.42  Sub-proof #2066 shows that the following formulas are inconsistent:
% 244.88/51.42  ----------------------------------------------------------------
% 244.88/51.42    (1)   ~ (all_52_3 = e0)
% 244.88/51.42    (2)   ~ (all_52_3 = e1)
% 244.88/51.42    (3)  all_54_12 = all_52_3
% 244.99/51.42    (4)   ~ (all_52_3 = e2)
% 244.99/51.42    (5)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 244.99/51.42  
% 244.99/51.42  Begin of proof
% 244.99/51.42  | 
% 244.99/51.42  | BETA: splitting (5) gives:
% 244.99/51.42  | 
% 244.99/51.42  | Case 1:
% 244.99/51.42  | | 
% 244.99/51.42  | |   (6)  all_54_12 = e2
% 244.99/51.42  | | 
% 244.99/51.42  | | COMBINE_EQS: (3), (6) imply:
% 244.99/51.42  | |   (7)  all_52_3 = e2
% 244.99/51.42  | | 
% 244.99/51.42  | | REDUCE: (4), (7) imply:
% 244.99/51.42  | |   (8)  $false
% 244.99/51.42  | | 
% 244.99/51.42  | | CLOSE: (8) is inconsistent.
% 244.99/51.42  | | 
% 244.99/51.42  | Case 2:
% 244.99/51.42  | | 
% 244.99/51.42  | |   (9)  all_54_12 = e1 | all_54_12 = e0
% 244.99/51.42  | | 
% 244.99/51.42  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #2067.
% 244.99/51.42  | | 
% 244.99/51.42  | End of split
% 244.99/51.42  | 
% 244.99/51.42  End of proof
% 244.99/51.42  
% 244.99/51.42  Sub-proof #2067 shows that the following formulas are inconsistent:
% 244.99/51.42  ----------------------------------------------------------------
% 244.99/51.42    (1)  all_54_12 = e1 | all_54_12 = e0
% 244.99/51.42    (2)  all_54_12 = all_52_3
% 244.99/51.42    (3)   ~ (all_52_3 = e1)
% 244.99/51.42    (4)   ~ (all_52_3 = e0)
% 244.99/51.42  
% 244.99/51.42  Begin of proof
% 244.99/51.42  | 
% 244.99/51.42  | BETA: splitting (1) gives:
% 244.99/51.42  | 
% 244.99/51.42  | Case 1:
% 244.99/51.42  | | 
% 244.99/51.42  | |   (5)  all_54_12 = e1
% 244.99/51.42  | | 
% 244.99/51.42  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2263.
% 244.99/51.42  | | 
% 244.99/51.42  | Case 2:
% 244.99/51.42  | | 
% 244.99/51.42  | |   (6)  all_54_12 = e0
% 244.99/51.42  | | 
% 244.99/51.42  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2068.
% 244.99/51.42  | | 
% 244.99/51.42  | End of split
% 244.99/51.42  | 
% 244.99/51.42  End of proof
% 244.99/51.42  
% 244.99/51.42  Sub-proof #2068 shows that the following formulas are inconsistent:
% 244.99/51.42  ----------------------------------------------------------------
% 244.99/51.42    (1)  all_54_12 = all_52_3
% 244.99/51.42    (2)  all_54_12 = e0
% 244.99/51.42    (3)   ~ (all_52_3 = e0)
% 244.99/51.42  
% 244.99/51.42  Begin of proof
% 244.99/51.42  | 
% 244.99/51.42  | COMBINE_EQS: (1), (2) imply:
% 244.99/51.42  |   (4)  all_52_3 = e0
% 244.99/51.42  | 
% 244.99/51.42  | SIMP: (4) implies:
% 244.99/51.42  |   (5)  all_52_3 = e0
% 244.99/51.42  | 
% 244.99/51.42  | REDUCE: (3), (5) imply:
% 244.99/51.42  |   (6)  $false
% 244.99/51.42  | 
% 244.99/51.42  | CLOSE: (6) is inconsistent.
% 244.99/51.42  | 
% 244.99/51.42  End of proof
% 244.99/51.42  
% 244.99/51.42  Sub-proof #2069 shows that the following formulas are inconsistent:
% 244.99/51.42  ----------------------------------------------------------------
% 244.99/51.42    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.99/51.42    (2)   ~ (e3 = e0)
% 244.99/51.42    (3)  all_54_4 = all_52_1
% 244.99/51.42    (4)  op(e1, e3) = e1
% 244.99/51.42    (5)  op(e0, e3) = e3
% 244.99/51.42    (6)  op(e1, e1) = e2
% 244.99/51.42    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.42    (8)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 244.99/51.42           $i(all_56_5)) | (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 244.99/51.42           all_56_7 & $i(all_56_7))
% 244.99/51.42    (9)   ~ (all_52_1 = e2)
% 244.99/51.42    (10)   ~ (e2 = e1)
% 244.99/51.42    (11)   ~ (all_52_1 = e1)
% 244.99/51.42  
% 244.99/51.42  Begin of proof
% 244.99/51.42  | 
% 244.99/51.42  | BETA: splitting (8) gives:
% 244.99/51.42  | 
% 244.99/51.42  | Case 1:
% 244.99/51.42  | | 
% 244.99/51.42  | |   (12)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 &
% 244.99/51.42  | |         $i(all_56_5)
% 244.99/51.42  | | 
% 244.99/51.42  | | ALPHA: (12) implies:
% 244.99/51.42  | |   (13)  op(e1, e3) = all_56_5
% 244.99/51.42  | |   (14)  op(e1, all_56_5) = e1
% 244.99/51.42  | | 
% 244.99/51.42  | | BETA: splitting (1) gives:
% 244.99/51.42  | | 
% 244.99/51.42  | | Case 1:
% 244.99/51.42  | | | 
% 244.99/51.42  | | |   (15)  all_54_4 = e2
% 244.99/51.42  | | | 
% 244.99/51.42  | | | REF_CLOSE: (3), (9), (15) are inconsistent by sub-proof #2096.
% 244.99/51.42  | | | 
% 244.99/51.42  | | Case 2:
% 244.99/51.42  | | | 
% 244.99/51.42  | | |   (16)  all_54_4 = e1 | all_54_4 = e0
% 244.99/51.42  | | | 
% 244.99/51.42  | | | BETA: splitting (16) gives:
% 244.99/51.42  | | | 
% 244.99/51.42  | | | Case 1:
% 244.99/51.42  | | | | 
% 244.99/51.42  | | | |   (17)  all_54_4 = e1
% 244.99/51.42  | | | | 
% 244.99/51.42  | | | | REF_CLOSE: (3), (11), (17) are inconsistent by sub-proof #2086.
% 244.99/51.42  | | | | 
% 244.99/51.42  | | | Case 2:
% 244.99/51.42  | | | | 
% 244.99/51.42  | | | | 
% 244.99/51.42  | | | | GROUND_INST: instantiating (7) with e1, all_56_5, e3, e1, simplifying
% 244.99/51.42  | | | |              with (4), (13) gives:
% 244.99/51.42  | | | |   (18)  all_56_5 = e1
% 244.99/51.42  | | | | 
% 244.99/51.42  | | | | REDUCE: (14), (18) imply:
% 244.99/51.42  | | | |   (19)  op(e1, e1) = e1
% 244.99/51.42  | | | | 
% 244.99/51.42  | | | | REF_CLOSE: (6), (7), (10), (19) are inconsistent by sub-proof #2159.
% 244.99/51.42  | | | | 
% 244.99/51.42  | | | End of split
% 244.99/51.42  | | | 
% 244.99/51.42  | | End of split
% 244.99/51.42  | | 
% 244.99/51.42  | Case 2:
% 244.99/51.42  | | 
% 244.99/51.42  | |   (20)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 244.99/51.42  | |         $i(all_56_7)
% 244.99/51.42  | | 
% 244.99/51.42  | | ALPHA: (20) implies:
% 244.99/51.42  | |   (21)  op(e0, e3) = all_56_7
% 244.99/51.42  | |   (22)  op(e0, all_56_7) = e0
% 244.99/51.42  | | 
% 244.99/51.42  | | REF_CLOSE: (2), (5), (7), (21), (22) are inconsistent by sub-proof #2070.
% 244.99/51.42  | | 
% 244.99/51.42  | End of split
% 244.99/51.42  | 
% 244.99/51.42  End of proof
% 244.99/51.42  
% 244.99/51.42  Sub-proof #2070 shows that the following formulas are inconsistent:
% 244.99/51.42  ----------------------------------------------------------------
% 244.99/51.42    (1)   ~ (e3 = e0)
% 244.99/51.42    (2)  op(e0, e3) = all_56_7
% 244.99/51.43    (3)  op(e0, e3) = e3
% 244.99/51.43    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.43    (5)  op(e0, all_56_7) = e0
% 244.99/51.43  
% 244.99/51.43  Begin of proof
% 244.99/51.43  | 
% 244.99/51.43  | GROUND_INST: instantiating (4) with e3, all_56_7, e3, e0, simplifying with
% 244.99/51.43  |              (2), (3) gives:
% 244.99/51.43  |   (6)  all_56_7 = e3
% 244.99/51.43  | 
% 244.99/51.43  | REDUCE: (5), (6) imply:
% 244.99/51.43  |   (7)  op(e0, e3) = e0
% 244.99/51.43  | 
% 244.99/51.43  | GROUND_INST: instantiating (4) with e3, e0, e3, e0, simplifying with (3), (7)
% 244.99/51.43  |              gives:
% 244.99/51.43  |   (8)  e3 = e0
% 244.99/51.43  | 
% 244.99/51.43  | REDUCE: (1), (8) imply:
% 244.99/51.43  |   (9)  $false
% 244.99/51.43  | 
% 244.99/51.43  | CLOSE: (9) is inconsistent.
% 244.99/51.43  | 
% 244.99/51.43  End of proof
% 244.99/51.43  
% 244.99/51.43  Sub-proof #2071 shows that the following formulas are inconsistent:
% 244.99/51.43  ----------------------------------------------------------------
% 244.99/51.43    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.99/51.43    (2)   ~ (all_52_3 = e1)
% 244.99/51.43    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.99/51.43         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.99/51.43    (4)  op(e0, e1) = all_56_23
% 244.99/51.43    (5)  op(e0, e3) = all_52_3
% 244.99/51.43    (6)   ~ (all_24_0 = e0)
% 244.99/51.43    (7)  all_54_4 = all_52_1
% 244.99/51.43    (8)   ~ (e3 = e2)
% 244.99/51.43    (9)  op(e3, e1) = e1
% 244.99/51.43    (10)  op(e3, e1) = all_40_0
% 244.99/51.43    (11)  op(e0, e3) = e3
% 244.99/51.43    (12)  op(e0, e1) = e0
% 244.99/51.43    (13)  op(e0, e1) = all_20_1
% 244.99/51.43    (14)  op(e0, e3) = all_32_0
% 244.99/51.43    (15)  all_58_14 = e0
% 244.99/51.43    (16)   ~ (all_40_0 = e0)
% 244.99/51.43    (17)  op(e0, e3) = all_24_0
% 244.99/51.43    (18)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 244.99/51.43            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 244.99/51.43              e1) = all_34_1 & $i(all_34_1))
% 244.99/51.43    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.43    (20)  op(e0, all_56_23) = e0
% 244.99/51.43    (21)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.99/51.43          | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.99/51.43    (22)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.99/51.43          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.99/51.43            e1)
% 244.99/51.43    (23)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.99/51.43          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.99/51.43            e2)
% 244.99/51.43    (24)   ~ (all_32_0 = e1)
% 244.99/51.43    (25)   ~ (all_52_1 = e2)
% 244.99/51.43    (26)   ~ (e2 = e1)
% 244.99/51.43    (27)   ~ (all_52_1 = e1)
% 244.99/51.43  
% 244.99/51.43  Begin of proof
% 244.99/51.43  | 
% 244.99/51.43  | BETA: splitting (18) gives:
% 244.99/51.43  | 
% 244.99/51.43  | Case 1:
% 244.99/51.43  | | 
% 244.99/51.43  | |   (28)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 244.99/51.43  | |         all_34_1 & $i(all_34_0) & $i(all_34_1)
% 244.99/51.43  | | 
% 244.99/51.43  | | ALPHA: (28) implies:
% 244.99/51.43  | |   (29)  op(e0, e1) = all_34_1
% 244.99/51.43  | | 
% 244.99/51.43  | | BETA: splitting (1) gives:
% 244.99/51.43  | | 
% 244.99/51.43  | | Case 1:
% 244.99/51.43  | | | 
% 244.99/51.43  | | |   (30)  all_54_4 = e2
% 244.99/51.43  | | | 
% 244.99/51.43  | | | REF_CLOSE: (7), (25), (30) are inconsistent by sub-proof #2096.
% 244.99/51.43  | | | 
% 244.99/51.43  | | Case 2:
% 244.99/51.43  | | | 
% 244.99/51.43  | | |   (31)   ~ (all_54_4 = e2)
% 244.99/51.43  | | |   (32)  all_54_4 = e1 | all_54_4 = e0
% 244.99/51.43  | | | 
% 244.99/51.43  | | | BETA: splitting (32) gives:
% 244.99/51.43  | | | 
% 244.99/51.43  | | | Case 1:
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | |   (33)  all_54_4 = e1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | REF_CLOSE: (7), (27), (33) are inconsistent by sub-proof #2086.
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | Case 2:
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | |   (34)  all_54_4 = e0
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | COMBINE_EQS: (7), (34) imply:
% 244.99/51.43  | | | |   (35)  all_52_1 = e0
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | SIMP: (35) implies:
% 244.99/51.43  | | | |   (36)  all_52_1 = e0
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | REDUCE: (25), (36) imply:
% 244.99/51.43  | | | |   (37)   ~ (e2 = e0)
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | SIMP: (37) implies:
% 244.99/51.43  | | | |   (38)   ~ (e2 = e0)
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with e0, all_34_1, e1, e0, simplifying
% 244.99/51.43  | | | |              with (12), (29) gives:
% 244.99/51.43  | | | |   (39)  all_34_1 = e0
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with all_34_1, all_56_23, e1, e0,
% 244.99/51.43  | | | |              simplifying with (4), (29) gives:
% 244.99/51.43  | | | |   (40)  all_56_23 = all_34_1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with all_20_1, all_56_23, e1, e0,
% 244.99/51.43  | | | |              simplifying with (4), (13) gives:
% 244.99/51.43  | | | |   (41)  all_56_23 = all_20_1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with all_24_0, all_32_0, e3, e0,
% 244.99/51.43  | | | |              simplifying with (14), (17) gives:
% 244.99/51.43  | | | |   (42)  all_32_0 = all_24_0
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with e3, all_32_0, e3, e0, simplifying
% 244.99/51.43  | | | |              with (11), (14) gives:
% 244.99/51.43  | | | |   (43)  all_32_0 = e3
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with e1, all_40_0, e1, e3, simplifying
% 244.99/51.43  | | | |              with (9), (10) gives:
% 244.99/51.43  | | | |   (44)  all_40_0 = e1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | COMBINE_EQS: (40), (41) imply:
% 244.99/51.43  | | | |   (45)  all_34_1 = all_20_1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | SIMP: (45) implies:
% 244.99/51.43  | | | |   (46)  all_34_1 = all_20_1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | COMBINE_EQS: (39), (46) imply:
% 244.99/51.43  | | | |   (47)  all_20_1 = e0
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | COMBINE_EQS: (42), (43) imply:
% 244.99/51.43  | | | |   (48)  all_24_0 = e3
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | COMBINE_EQS: (41), (47) imply:
% 244.99/51.43  | | | |   (49)  all_56_23 = e0
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | REDUCE: (16), (44) imply:
% 244.99/51.43  | | | |   (50)   ~ (e1 = e0)
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | REF_CLOSE: (2), (3), (5), (6), (8), (13), (15), (19), (20), (21), (22),
% 244.99/51.43  | | | |            (23), (24), (26), (38), (43), (47), (48), (49), (50) are
% 244.99/51.43  | | | |            inconsistent by sub-proof #2072.
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | End of split
% 244.99/51.43  | | | 
% 244.99/51.43  | | End of split
% 244.99/51.43  | | 
% 244.99/51.43  | Case 2:
% 244.99/51.43  | | 
% 244.99/51.43  | |   (51)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 & $i(all_34_1)
% 244.99/51.43  | | 
% 244.99/51.43  | | ALPHA: (51) implies:
% 244.99/51.43  | |   (52)   ~ (all_34_1 = e2)
% 244.99/51.43  | |   (53)  op(e0, e1) = all_34_1
% 244.99/51.43  | | 
% 244.99/51.43  | | BETA: splitting (1) gives:
% 244.99/51.43  | | 
% 244.99/51.43  | | Case 1:
% 244.99/51.43  | | | 
% 244.99/51.43  | | |   (54)  all_54_4 = e2
% 244.99/51.43  | | | 
% 244.99/51.43  | | | REF_CLOSE: (7), (25), (54) are inconsistent by sub-proof #2096.
% 244.99/51.43  | | | 
% 244.99/51.43  | | Case 2:
% 244.99/51.43  | | | 
% 244.99/51.43  | | |   (55)  all_54_4 = e1 | all_54_4 = e0
% 244.99/51.43  | | | 
% 244.99/51.43  | | | BETA: splitting (55) gives:
% 244.99/51.43  | | | 
% 244.99/51.43  | | | Case 1:
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | |   (56)  all_54_4 = e1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | REF_CLOSE: (7), (27), (56) are inconsistent by sub-proof #2086.
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | Case 2:
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with e0, all_34_1, e1, e0, simplifying
% 244.99/51.43  | | | |              with (12), (53) gives:
% 244.99/51.43  | | | |   (57)  all_34_1 = e0
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with all_34_1, all_56_23, e1, e0,
% 244.99/51.43  | | | |              simplifying with (4), (53) gives:
% 244.99/51.43  | | | |   (58)  all_56_23 = all_34_1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with all_20_1, all_56_23, e1, e0,
% 244.99/51.43  | | | |              simplifying with (4), (13) gives:
% 244.99/51.43  | | | |   (59)  all_56_23 = all_20_1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with all_24_0, all_32_0, e3, e0,
% 244.99/51.43  | | | |              simplifying with (14), (17) gives:
% 244.99/51.43  | | | |   (60)  all_32_0 = all_24_0
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with e3, all_32_0, e3, e0, simplifying
% 244.99/51.43  | | | |              with (11), (14) gives:
% 244.99/51.43  | | | |   (61)  all_32_0 = e3
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | GROUND_INST: instantiating (19) with e1, all_40_0, e1, e3, simplifying
% 244.99/51.43  | | | |              with (9), (10) gives:
% 244.99/51.43  | | | |   (62)  all_40_0 = e1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | COMBINE_EQS: (58), (59) imply:
% 244.99/51.43  | | | |   (63)  all_34_1 = all_20_1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | SIMP: (63) implies:
% 244.99/51.43  | | | |   (64)  all_34_1 = all_20_1
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | COMBINE_EQS: (57), (64) imply:
% 244.99/51.43  | | | |   (65)  all_20_1 = e0
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | COMBINE_EQS: (60), (61) imply:
% 244.99/51.43  | | | |   (66)  all_24_0 = e3
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | COMBINE_EQS: (59), (65) imply:
% 244.99/51.43  | | | |   (67)  all_56_23 = e0
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | REDUCE: (16), (62) imply:
% 244.99/51.43  | | | |   (68)   ~ (e1 = e0)
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | REDUCE: (52), (57) imply:
% 244.99/51.43  | | | |   (69)   ~ (e2 = e0)
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | SIMP: (69) implies:
% 244.99/51.43  | | | |   (70)   ~ (e2 = e0)
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | | REF_CLOSE: (2), (3), (5), (6), (8), (13), (15), (19), (20), (21), (22),
% 244.99/51.43  | | | |            (23), (24), (26), (61), (65), (66), (67), (68), (70) are
% 244.99/51.43  | | | |            inconsistent by sub-proof #2072.
% 244.99/51.43  | | | | 
% 244.99/51.43  | | | End of split
% 244.99/51.43  | | | 
% 244.99/51.43  | | End of split
% 244.99/51.43  | | 
% 244.99/51.43  | End of split
% 244.99/51.43  | 
% 244.99/51.43  End of proof
% 244.99/51.43  
% 244.99/51.43  Sub-proof #2072 shows that the following formulas are inconsistent:
% 244.99/51.43  ----------------------------------------------------------------
% 244.99/51.43    (1)  all_56_23 = e0
% 244.99/51.43    (2)   ~ (all_52_3 = e1)
% 244.99/51.43    (3)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.99/51.43         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.99/51.43    (4)   ~ (e2 = e0)
% 244.99/51.43    (5)  op(e0, e3) = all_52_3
% 244.99/51.43    (6)   ~ (all_24_0 = e0)
% 244.99/51.43    (7)   ~ (e3 = e2)
% 244.99/51.43    (8)  all_20_1 = e0
% 244.99/51.43    (9)  op(e0, e1) = all_20_1
% 244.99/51.43    (10)  all_32_0 = e3
% 244.99/51.43    (11)  all_58_14 = e0
% 244.99/51.43    (12)  all_24_0 = e3
% 244.99/51.43    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.43    (14)  op(e0, all_56_23) = e0
% 244.99/51.43    (15)   ~ (e1 = e0)
% 244.99/51.43    (16)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.99/51.43          | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.99/51.43    (17)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.99/51.43          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.99/51.43            e1)
% 244.99/51.43    (18)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.99/51.43          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.99/51.43            e2)
% 244.99/51.43    (19)   ~ (all_32_0 = e1)
% 244.99/51.43    (20)   ~ (e2 = e1)
% 244.99/51.43  
% 244.99/51.43  Begin of proof
% 244.99/51.43  | 
% 244.99/51.43  | REDUCE: (10), (19) imply:
% 244.99/51.43  |   (21)   ~ (e3 = e1)
% 244.99/51.43  | 
% 244.99/51.43  | REDUCE: (6), (12) imply:
% 244.99/51.43  |   (22)   ~ (e3 = e0)
% 244.99/51.43  | 
% 244.99/51.43  | REDUCE: (1), (14) imply:
% 244.99/51.43  |   (23)  op(e0, e0) = e0
% 244.99/51.43  | 
% 244.99/51.43  | REDUCE: (8), (9) imply:
% 244.99/51.43  |   (24)  op(e0, e1) = e0
% 244.99/51.43  | 
% 244.99/51.43  | REF_CLOSE: (2), (3), (4), (5), (7), (11), (13), (15), (16), (17), (18), (20),
% 244.99/51.43  |            (21), (22), (23), (24) are inconsistent by sub-proof #2073.
% 244.99/51.43  | 
% 244.99/51.43  End of proof
% 244.99/51.43  
% 244.99/51.43  Sub-proof #2073 shows that the following formulas are inconsistent:
% 244.99/51.43  ----------------------------------------------------------------
% 244.99/51.43    (1)   ~ (all_52_3 = e1)
% 244.99/51.43    (2)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.99/51.43         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.99/51.43    (3)   ~ (e3 = e0)
% 244.99/51.43    (4)   ~ (e2 = e0)
% 244.99/51.43    (5)  op(e0, e3) = all_52_3
% 244.99/51.43    (6)   ~ (e3 = e1)
% 244.99/51.43    (7)   ~ (e3 = e2)
% 244.99/51.43    (8)  op(e0, e1) = e0
% 244.99/51.43    (9)  all_58_14 = e0
% 244.99/51.43    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.43    (11)  op(e0, e0) = e0
% 244.99/51.43    (12)   ~ (e1 = e0)
% 244.99/51.43    (13)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.99/51.43          | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.99/51.43    (14)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.99/51.43          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.99/51.43            e1)
% 244.99/51.43    (15)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.99/51.43          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.99/51.43            e2)
% 244.99/51.43    (16)   ~ (e2 = e1)
% 244.99/51.43  
% 244.99/51.43  Begin of proof
% 244.99/51.43  | 
% 244.99/51.43  | BETA: splitting (14) gives:
% 244.99/51.43  | 
% 244.99/51.43  | Case 1:
% 244.99/51.43  | | 
% 244.99/51.43  | |   (17)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 244.99/51.43  | |           e1)
% 244.99/51.43  | | 
% 244.99/51.43  | | BETA: splitting (17) gives:
% 244.99/51.43  | | 
% 244.99/51.43  | | Case 1:
% 244.99/51.43  | | | 
% 244.99/51.43  | | |   (18)  all_58_12 = e1 & op(e0, e3) = e1
% 244.99/51.43  | | | 
% 244.99/51.43  | | | REF_CLOSE: (1), (5), (10), (18) are inconsistent by sub-proof #2276.
% 244.99/51.43  | | | 
% 244.99/51.43  | | Case 2:
% 244.99/51.43  | | | 
% 244.99/51.43  | | |   (19)  all_58_13 = e1 & op(e0, e2) = e1
% 244.99/51.43  | | | 
% 244.99/51.43  | | | ALPHA: (19) implies:
% 244.99/51.43  | | |   (20)  all_58_13 = e1
% 244.99/51.43  | | | 
% 244.99/51.43  | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (15),
% 244.99/51.43  | | |            (16), (20) are inconsistent by sub-proof #2075.
% 244.99/51.43  | | | 
% 244.99/51.43  | | End of split
% 244.99/51.43  | | 
% 244.99/51.43  | Case 2:
% 244.99/51.43  | | 
% 244.99/51.43  | |   (21)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 244.99/51.43  | |           e1)
% 244.99/51.43  | | 
% 244.99/51.43  | | REF_CLOSE: (8), (10), (11), (12), (21) are inconsistent by sub-proof #2074.
% 244.99/51.43  | | 
% 244.99/51.43  | End of split
% 244.99/51.43  | 
% 244.99/51.43  End of proof
% 244.99/51.43  
% 244.99/51.43  Sub-proof #2074 shows that the following formulas are inconsistent:
% 244.99/51.43  ----------------------------------------------------------------
% 244.99/51.43    (1)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 244.99/51.43    (2)  op(e0, e1) = e0
% 244.99/51.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.43    (4)  op(e0, e0) = e0
% 244.99/51.43    (5)   ~ (e1 = e0)
% 244.99/51.43  
% 244.99/51.43  Begin of proof
% 244.99/51.43  | 
% 244.99/51.43  | BETA: splitting (1) gives:
% 244.99/51.43  | 
% 244.99/51.43  | Case 1:
% 244.99/51.43  | | 
% 244.99/51.43  | |   (6)  all_58_14 = e1 & op(e0, e1) = e1
% 244.99/51.43  | | 
% 244.99/51.43  | | ALPHA: (6) implies:
% 244.99/51.43  | |   (7)  op(e0, e1) = e1
% 244.99/51.43  | | 
% 244.99/51.43  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #2158.
% 244.99/51.43  | | 
% 244.99/51.43  | Case 2:
% 244.99/51.43  | | 
% 244.99/51.43  | |   (8)  all_58_15 = e1 & op(e0, e0) = e1
% 244.99/51.43  | | 
% 244.99/51.43  | | ALPHA: (8) implies:
% 244.99/51.43  | |   (9)  op(e0, e0) = e1
% 244.99/51.43  | | 
% 244.99/51.43  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #2274.
% 244.99/51.43  | | 
% 244.99/51.43  | End of split
% 244.99/51.43  | 
% 244.99/51.43  End of proof
% 244.99/51.43  
% 244.99/51.43  Sub-proof #2075 shows that the following formulas are inconsistent:
% 244.99/51.43  ----------------------------------------------------------------
% 244.99/51.43    (1)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 244.99/51.43         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 244.99/51.43    (2)   ~ (e3 = e0)
% 244.99/51.43    (3)   ~ (e2 = e0)
% 244.99/51.43    (4)   ~ (e3 = e1)
% 244.99/51.43    (5)   ~ (e3 = e2)
% 244.99/51.43    (6)  all_58_14 = e0
% 244.99/51.43    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.43    (8)  op(e0, e0) = e0
% 244.99/51.43    (9)   ~ (e1 = e0)
% 244.99/51.43    (10)  all_58_13 = e1
% 244.99/51.44    (11)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.99/51.44          | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.99/51.44    (12)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.99/51.44          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.99/51.44            e2)
% 244.99/51.44    (13)   ~ (e2 = e1)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | BETA: splitting (12) gives:
% 244.99/51.44  | 
% 244.99/51.44  | Case 1:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (14)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 244.99/51.44  | |           e2)
% 244.99/51.44  | | 
% 244.99/51.44  | | BETA: splitting (14) gives:
% 244.99/51.44  | | 
% 244.99/51.44  | | Case 1:
% 244.99/51.44  | | | 
% 244.99/51.44  | | |   (15)  all_58_12 = e2 & op(e0, e3) = e2
% 244.99/51.44  | | | 
% 244.99/51.44  | | | ALPHA: (15) implies:
% 244.99/51.44  | | |   (16)  all_58_12 = e2
% 244.99/51.44  | | | 
% 244.99/51.44  | | | BETA: splitting (1) gives:
% 244.99/51.44  | | | 
% 244.99/51.44  | | | Case 1:
% 244.99/51.44  | | | | 
% 244.99/51.44  | | | |   (17)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 244.99/51.44  | | | |             e2) = e3)
% 244.99/51.44  | | | | 
% 244.99/51.44  | | | | BETA: splitting (17) gives:
% 244.99/51.44  | | | | 
% 244.99/51.44  | | | | Case 1:
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | |   (18)  all_58_12 = e3 & op(e0, e3) = e3
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | | REF_CLOSE: (5), (16), (18) are inconsistent by sub-proof #2085.
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | Case 2:
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | |   (19)  all_58_13 = e3 & op(e0, e2) = e3
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | | REF_CLOSE: (4), (10), (19) are inconsistent by sub-proof #2084.
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | End of split
% 244.99/51.44  | | | | 
% 244.99/51.44  | | | Case 2:
% 244.99/51.44  | | | | 
% 244.99/51.44  | | | |   (20)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 244.99/51.44  | | | |             e0) = e3)
% 244.99/51.44  | | | | 
% 244.99/51.44  | | | | BETA: splitting (20) gives:
% 244.99/51.44  | | | | 
% 244.99/51.44  | | | | Case 1:
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | |   (21)  all_58_14 = e3 & op(e0, e1) = e3
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | | ALPHA: (21) implies:
% 244.99/51.44  | | | | |   (22)  all_58_14 = e3
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | | REF_CLOSE: (2), (3), (9), (10), (11), (16), (22) are inconsistent by
% 244.99/51.44  | | | | |            sub-proof #2080.
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | Case 2:
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | |   (23)  all_58_15 = e3 & op(e0, e0) = e3
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | | ALPHA: (23) implies:
% 244.99/51.44  | | | | |   (24)  op(e0, e0) = e3
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | | REF_CLOSE: (2), (7), (8), (24) are inconsistent by sub-proof #2079.
% 244.99/51.44  | | | | | 
% 244.99/51.44  | | | | End of split
% 244.99/51.44  | | | | 
% 244.99/51.44  | | | End of split
% 244.99/51.44  | | | 
% 244.99/51.44  | | Case 2:
% 244.99/51.44  | | | 
% 244.99/51.44  | | |   (25)  all_58_13 = e2 & op(e0, e2) = e2
% 244.99/51.44  | | | 
% 244.99/51.44  | | | REF_CLOSE: (10), (13), (25) are inconsistent by sub-proof #2078.
% 244.99/51.44  | | | 
% 244.99/51.44  | | End of split
% 244.99/51.44  | | 
% 244.99/51.44  | Case 2:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (26)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.99/51.44  | |           e2)
% 244.99/51.44  | | 
% 244.99/51.44  | | REF_CLOSE: (3), (6), (7), (8), (26) are inconsistent by sub-proof #2076.
% 244.99/51.44  | | 
% 244.99/51.44  | End of split
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2076 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)   ~ (e2 = e0)
% 244.99/51.44    (2)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.99/51.44    (3)  all_58_14 = e0
% 244.99/51.44    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.44    (5)  op(e0, e0) = e0
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | BETA: splitting (2) gives:
% 244.99/51.44  | 
% 244.99/51.44  | Case 1:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (6)  all_58_14 = e2 & op(e0, e1) = e2
% 244.99/51.44  | | 
% 244.99/51.44  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #2077.
% 244.99/51.44  | | 
% 244.99/51.44  | Case 2:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (7)  all_58_15 = e2 & op(e0, e0) = e2
% 244.99/51.44  | | 
% 244.99/51.44  | | ALPHA: (7) implies:
% 244.99/51.44  | |   (8)  op(e0, e0) = e2
% 244.99/51.44  | | 
% 244.99/51.44  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2301.
% 244.99/51.44  | | 
% 244.99/51.44  | End of split
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2077 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  all_58_14 = e2 & op(e0, e1) = e2
% 244.99/51.44    (2)  all_58_14 = e0
% 244.99/51.44    (3)   ~ (e2 = e0)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | ALPHA: (1) implies:
% 244.99/51.44  |   (4)  all_58_14 = e2
% 244.99/51.44  | 
% 244.99/51.44  | COMBINE_EQS: (2), (4) imply:
% 244.99/51.44  |   (5)  e2 = e0
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (3), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2078 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  all_58_13 = e2 & op(e0, e2) = e2
% 244.99/51.44    (2)  all_58_13 = e1
% 244.99/51.44    (3)   ~ (e2 = e1)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | ALPHA: (1) implies:
% 244.99/51.44  |   (4)  all_58_13 = e2
% 244.99/51.44  | 
% 244.99/51.44  | COMBINE_EQS: (2), (4) imply:
% 244.99/51.44  |   (5)  e2 = e1
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (3), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2079 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.44    (2)  op(e0, e0) = e3
% 244.99/51.44    (3)  op(e0, e0) = e0
% 244.99/51.44    (4)   ~ (e3 = e0)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | GROUND_INST: instantiating (1) with e3, e0, e0, e0, simplifying with (2), (3)
% 244.99/51.44  |              gives:
% 244.99/51.44  |   (5)  e3 = e0
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (4), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2080 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)   ~ (e3 = e0)
% 244.99/51.44    (2)   ~ (e2 = e0)
% 244.99/51.44    (3)  all_58_12 = e2
% 244.99/51.44    (4)  all_58_14 = e3
% 244.99/51.44    (5)   ~ (e1 = e0)
% 244.99/51.44    (6)  all_58_13 = e1
% 244.99/51.44    (7)  (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 244.99/51.44         (all_58_14 = e0 & op(e0, e1) = e0)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | BETA: splitting (7) gives:
% 244.99/51.44  | 
% 244.99/51.44  | Case 1:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (8)  all_58_12 = e0 & op(e0, e3) = e0
% 244.99/51.44  | | 
% 244.99/51.44  | | ALPHA: (8) implies:
% 244.99/51.44  | |   (9)  all_58_12 = e0
% 244.99/51.44  | | 
% 244.99/51.44  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #2083.
% 244.99/51.44  | | 
% 244.99/51.44  | Case 2:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (10)  (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 244.99/51.44  | |           e0)
% 244.99/51.44  | | 
% 244.99/51.44  | | BETA: splitting (10) gives:
% 244.99/51.44  | | 
% 244.99/51.44  | | Case 1:
% 244.99/51.44  | | | 
% 244.99/51.44  | | |   (11)  all_58_13 = e0 & op(e0, e2) = e0
% 244.99/51.44  | | | 
% 244.99/51.44  | | | ALPHA: (11) implies:
% 244.99/51.44  | | |   (12)  all_58_13 = e0
% 244.99/51.44  | | | 
% 244.99/51.44  | | | REF_CLOSE: (5), (6), (12) are inconsistent by sub-proof #2082.
% 244.99/51.44  | | | 
% 244.99/51.44  | | Case 2:
% 244.99/51.44  | | | 
% 244.99/51.44  | | |   (13)  all_58_14 = e0 & op(e0, e1) = e0
% 244.99/51.44  | | | 
% 244.99/51.44  | | | REF_CLOSE: (1), (4), (13) are inconsistent by sub-proof #2081.
% 244.99/51.44  | | | 
% 244.99/51.44  | | End of split
% 244.99/51.44  | | 
% 244.99/51.44  | End of split
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2081 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  all_58_14 = e0 & op(e0, e1) = e0
% 244.99/51.44    (2)  all_58_14 = e3
% 244.99/51.44    (3)   ~ (e3 = e0)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | ALPHA: (1) implies:
% 244.99/51.44  |   (4)  all_58_14 = e0
% 244.99/51.44  | 
% 244.99/51.44  | COMBINE_EQS: (2), (4) imply:
% 244.99/51.44  |   (5)  e3 = e0
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (3), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2082 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  all_58_13 = e1
% 244.99/51.44    (2)  all_58_13 = e0
% 244.99/51.44    (3)   ~ (e1 = e0)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | COMBINE_EQS: (1), (2) imply:
% 244.99/51.44  |   (4)  e1 = e0
% 244.99/51.44  | 
% 244.99/51.44  | SIMP: (4) implies:
% 244.99/51.44  |   (5)  e1 = e0
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (3), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2083 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  all_58_12 = e2
% 244.99/51.44    (2)  all_58_12 = e0
% 244.99/51.44    (3)   ~ (e2 = e0)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | COMBINE_EQS: (1), (2) imply:
% 244.99/51.44  |   (4)  e2 = e0
% 244.99/51.44  | 
% 244.99/51.44  | SIMP: (4) implies:
% 244.99/51.44  |   (5)  e2 = e0
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (3), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2084 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  all_58_13 = e3 & op(e0, e2) = e3
% 244.99/51.44    (2)  all_58_13 = e1
% 244.99/51.44    (3)   ~ (e3 = e1)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | ALPHA: (1) implies:
% 244.99/51.44  |   (4)  all_58_13 = e3
% 244.99/51.44  | 
% 244.99/51.44  | COMBINE_EQS: (2), (4) imply:
% 244.99/51.44  |   (5)  e3 = e1
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (3), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2085 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  all_58_12 = e3 & op(e0, e3) = e3
% 244.99/51.44    (2)  all_58_12 = e2
% 244.99/51.44    (3)   ~ (e3 = e2)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | ALPHA: (1) implies:
% 244.99/51.44  |   (4)  all_58_12 = e3
% 244.99/51.44  | 
% 244.99/51.44  | COMBINE_EQS: (2), (4) imply:
% 244.99/51.44  |   (5)  e3 = e2
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (3), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2086 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  all_54_4 = all_52_1
% 244.99/51.44    (2)  all_54_4 = e1
% 244.99/51.44    (3)   ~ (all_52_1 = e1)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | COMBINE_EQS: (1), (2) imply:
% 244.99/51.44  |   (4)  all_52_1 = e1
% 244.99/51.44  | 
% 244.99/51.44  | SIMP: (4) implies:
% 244.99/51.44  |   (5)  all_52_1 = e1
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (3), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2087 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)   ~ (all_52_9 = e0)
% 244.99/51.44    (2)  op(e2, e1) = all_52_9
% 244.99/51.44    (3)  op(e3, e1) = e1
% 244.99/51.44    (4)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 244.99/51.44    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.44    (6)   ~ (e1 = e0)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | BETA: splitting (4) gives:
% 244.99/51.44  | 
% 244.99/51.44  | Case 1:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (7)  all_58_4 = e0 & op(e3, e1) = e0
% 244.99/51.44  | | 
% 244.99/51.44  | | ALPHA: (7) implies:
% 244.99/51.44  | |   (8)  op(e3, e1) = e0
% 244.99/51.44  | | 
% 244.99/51.44  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2089.
% 244.99/51.44  | | 
% 244.99/51.44  | Case 2:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (9)  all_58_5 = e0 & op(e2, e1) = e0
% 244.99/51.44  | | 
% 244.99/51.44  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2088.
% 244.99/51.44  | | 
% 244.99/51.44  | End of split
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2088 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  all_58_5 = e0 & op(e2, e1) = e0
% 244.99/51.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.44    (3)  op(e2, e1) = all_52_9
% 244.99/51.44    (4)   ~ (all_52_9 = e0)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | ALPHA: (1) implies:
% 244.99/51.44  |   (5)  op(e2, e1) = e0
% 244.99/51.44  | 
% 244.99/51.44  | GROUND_INST: instantiating (2) with all_52_9, e0, e1, e2, simplifying with
% 244.99/51.44  |              (3), (5) gives:
% 244.99/51.44  |   (6)  all_52_9 = e0
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (4), (6) imply:
% 244.99/51.44  |   (7)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (7) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2089 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.44    (2)  op(e3, e1) = e1
% 244.99/51.44    (3)  op(e3, e1) = e0
% 244.99/51.44    (4)   ~ (e1 = e0)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | GROUND_INST: instantiating (1) with e0, e1, e1, e3, simplifying with (2), (3)
% 244.99/51.44  |              gives:
% 244.99/51.44  |   (5)  e1 = e0
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (4), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2090 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)   ~ (e3 = e0)
% 244.99/51.44    (2)  op(e1, e2) = e1
% 244.99/51.44    (3)  op(e1, e1) = all_6_2
% 244.99/51.44    (4)   ~ (e3 = e1)
% 244.99/51.44    (5)   ~ (all_6_2 = e3)
% 244.99/51.44    (6)  op(e1, e3) = e1
% 244.99/51.44    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.99/51.44         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.99/51.44    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.44    (9)  all_58_11 = e0
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | BETA: splitting (7) gives:
% 244.99/51.44  | 
% 244.99/51.44  | Case 1:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (10)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.99/51.44  | |           e3)
% 244.99/51.44  | | 
% 244.99/51.44  | | REF_CLOSE: (2), (4), (6), (8), (10) are inconsistent by sub-proof #2093.
% 244.99/51.44  | | 
% 244.99/51.44  | Case 2:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (11)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.99/51.44  | |           e3)
% 244.99/51.44  | | 
% 244.99/51.44  | | BETA: splitting (11) gives:
% 244.99/51.44  | | 
% 244.99/51.44  | | Case 1:
% 244.99/51.44  | | | 
% 244.99/51.44  | | |   (12)  all_58_8 = e3 & op(e1, e1) = e3
% 244.99/51.44  | | | 
% 244.99/51.44  | | | REF_CLOSE: (3), (5), (8), (12) are inconsistent by sub-proof #2092.
% 244.99/51.44  | | | 
% 244.99/51.44  | | Case 2:
% 244.99/51.44  | | | 
% 244.99/51.44  | | |   (13)  all_58_11 = e3 & op(e1, e0) = e3
% 244.99/51.44  | | | 
% 244.99/51.44  | | | REF_CLOSE: (1), (9), (13) are inconsistent by sub-proof #2091.
% 244.99/51.44  | | | 
% 244.99/51.44  | | End of split
% 244.99/51.44  | | 
% 244.99/51.44  | End of split
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2091 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  all_58_11 = e3 & op(e1, e0) = e3
% 244.99/51.44    (2)  all_58_11 = e0
% 244.99/51.44    (3)   ~ (e3 = e0)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | ALPHA: (1) implies:
% 244.99/51.44  |   (4)  all_58_11 = e3
% 244.99/51.44  | 
% 244.99/51.44  | COMBINE_EQS: (2), (4) imply:
% 244.99/51.44  |   (5)  e3 = e0
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (3), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2092 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  all_58_8 = e3 & op(e1, e1) = e3
% 244.99/51.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.44    (3)  op(e1, e1) = all_6_2
% 244.99/51.44    (4)   ~ (all_6_2 = e3)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | ALPHA: (1) implies:
% 244.99/51.44  |   (5)  op(e1, e1) = e3
% 244.99/51.44  | 
% 244.99/51.44  | GROUND_INST: instantiating (2) with all_6_2, e3, e1, e1, simplifying with (3),
% 244.99/51.44  |              (5) gives:
% 244.99/51.44  |   (6)  all_6_2 = e3
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (4), (6) imply:
% 244.99/51.44  |   (7)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (7) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2093 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)  op(e1, e2) = e1
% 244.99/51.44    (2)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 244.99/51.44    (3)   ~ (e3 = e1)
% 244.99/51.44    (4)  op(e1, e3) = e1
% 244.99/51.44    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | BETA: splitting (2) gives:
% 244.99/51.44  | 
% 244.99/51.44  | Case 1:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (6)  all_58_6 = e3 & op(e1, e3) = e3
% 244.99/51.44  | | 
% 244.99/51.44  | | ALPHA: (6) implies:
% 244.99/51.44  | |   (7)  op(e1, e3) = e3
% 244.99/51.44  | | 
% 244.99/51.44  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #2225.
% 244.99/51.44  | | 
% 244.99/51.44  | Case 2:
% 244.99/51.44  | | 
% 244.99/51.44  | |   (8)  all_58_7 = e3 & op(e1, e2) = e3
% 244.99/51.44  | | 
% 244.99/51.44  | | ALPHA: (8) implies:
% 244.99/51.44  | |   (9)  op(e1, e2) = e3
% 244.99/51.44  | | 
% 244.99/51.44  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #2094.
% 244.99/51.44  | | 
% 244.99/51.44  | End of split
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2094 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.44    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.44    (2)  op(e1, e2) = e3
% 244.99/51.44    (3)  op(e1, e2) = e1
% 244.99/51.44    (4)   ~ (e3 = e1)
% 244.99/51.44  
% 244.99/51.44  Begin of proof
% 244.99/51.44  | 
% 244.99/51.44  | GROUND_INST: instantiating (1) with e3, e1, e2, e1, simplifying with (2), (3)
% 244.99/51.44  |              gives:
% 244.99/51.44  |   (5)  e3 = e1
% 244.99/51.44  | 
% 244.99/51.44  | REDUCE: (4), (5) imply:
% 244.99/51.44  |   (6)  $false
% 244.99/51.44  | 
% 244.99/51.44  | CLOSE: (6) is inconsistent.
% 244.99/51.44  | 
% 244.99/51.44  End of proof
% 244.99/51.44  
% 244.99/51.44  Sub-proof #2095 shows that the following formulas are inconsistent:
% 244.99/51.44  ----------------------------------------------------------------
% 244.99/51.45    (1)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 244.99/51.45    (2)  all_56_18 = e2 & op(e2, all_56_19) = e2 & op(e2, e1) = all_56_19 &
% 244.99/51.45         $i(all_56_19)
% 244.99/51.45    (3)  all_54_4 = all_52_1
% 244.99/51.45    (4)  op(e2, e3) = all_52_1
% 244.99/51.45    (5)  op(e2, e1) = e3
% 244.99/51.45    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.45    (7)   ~ (all_52_1 = e2)
% 244.99/51.45  
% 244.99/51.45  Begin of proof
% 244.99/51.45  | 
% 244.99/51.45  | ALPHA: (2) implies:
% 244.99/51.45  |   (8)  op(e2, e1) = all_56_19
% 244.99/51.45  |   (9)  op(e2, all_56_19) = e2
% 244.99/51.45  | 
% 244.99/51.45  | BETA: splitting (1) gives:
% 244.99/51.45  | 
% 244.99/51.45  | Case 1:
% 244.99/51.45  | | 
% 244.99/51.45  | |   (10)  all_54_4 = e2
% 244.99/51.45  | | 
% 244.99/51.45  | | REF_CLOSE: (3), (7), (10) are inconsistent by sub-proof #2096.
% 244.99/51.45  | | 
% 244.99/51.45  | Case 2:
% 244.99/51.45  | | 
% 244.99/51.45  | |   (11)   ~ (all_54_4 = e2)
% 244.99/51.45  | | 
% 244.99/51.45  | | GROUND_INST: instantiating (6) with e3, all_56_19, e1, e2, simplifying with
% 244.99/51.45  | |              (5), (8) gives:
% 244.99/51.45  | |   (12)  all_56_19 = e3
% 244.99/51.45  | | 
% 244.99/51.45  | | REDUCE: (9), (12) imply:
% 244.99/51.45  | |   (13)  op(e2, e3) = e2
% 244.99/51.45  | | 
% 244.99/51.45  | | REF_CLOSE: (4), (6), (7), (13) are inconsistent by sub-proof #2336.
% 244.99/51.45  | | 
% 244.99/51.45  | End of split
% 244.99/51.45  | 
% 244.99/51.45  End of proof
% 244.99/51.45  
% 244.99/51.45  Sub-proof #2096 shows that the following formulas are inconsistent:
% 244.99/51.45  ----------------------------------------------------------------
% 244.99/51.45    (1)  all_54_4 = all_52_1
% 244.99/51.45    (2)  all_54_4 = e2
% 244.99/51.45    (3)   ~ (all_52_1 = e2)
% 244.99/51.45  
% 244.99/51.45  Begin of proof
% 244.99/51.45  | 
% 244.99/51.45  | COMBINE_EQS: (1), (2) imply:
% 244.99/51.45  |   (4)  all_52_1 = e2
% 244.99/51.45  | 
% 244.99/51.45  | SIMP: (4) implies:
% 244.99/51.45  |   (5)  all_52_1 = e2
% 244.99/51.45  | 
% 244.99/51.45  | REDUCE: (3), (5) imply:
% 244.99/51.45  |   (6)  $false
% 244.99/51.45  | 
% 244.99/51.45  | CLOSE: (6) is inconsistent.
% 244.99/51.45  | 
% 244.99/51.45  End of proof
% 244.99/51.45  
% 244.99/51.45  Sub-proof #2097 shows that the following formulas are inconsistent:
% 244.99/51.45  ----------------------------------------------------------------
% 244.99/51.45    (1)  op(e2, e3) = all_56_3
% 244.99/51.45    (2)  op(e3, e1) = all_56_17
% 244.99/51.45    (3)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.99/51.45         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.99/51.45    (4)   ~ (all_52_13 = e1)
% 244.99/51.45    (5)   ~ (e3 = e1)
% 244.99/51.45    (6)  op(e2, e1) = all_52_9
% 244.99/51.45    (7)   ~ (e3 = e2)
% 244.99/51.45    (8)  op(e3, e1) = e1
% 244.99/51.45    (9)  op(e3, e1) = all_40_0
% 244.99/51.45    (10)  op(e2, e0) = e2
% 244.99/51.45    (11)  op(e2, e3) = all_52_1
% 244.99/51.45    (12)  op(e3, e3) = e2
% 244.99/51.45    (13)  op(e2, all_56_3) = e2
% 244.99/51.45    (14)  op(e3, all_56_17) = e3
% 244.99/51.45    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.45    (16)  op(e2, e0) = all_52_13
% 244.99/51.45    (17)   ~ (all_52_9 = e1)
% 244.99/51.45    (18)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.99/51.45          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.99/51.45    (19)   ~ (all_52_1 = e1)
% 244.99/51.45  
% 244.99/51.45  Begin of proof
% 244.99/51.45  | 
% 244.99/51.45  | BETA: splitting (3) gives:
% 244.99/51.45  | 
% 244.99/51.45  | Case 1:
% 244.99/51.45  | | 
% 244.99/51.45  | |   (20)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 244.99/51.45  | |           e3)
% 244.99/51.45  | | 
% 244.99/51.45  | | BETA: splitting (20) gives:
% 244.99/51.45  | | 
% 244.99/51.45  | | Case 1:
% 244.99/51.45  | | | 
% 244.99/51.45  | | |   (21)  all_58_2 = e3 & op(e2, e3) = e3
% 244.99/51.45  | | | 
% 244.99/51.45  | | | ALPHA: (21) implies:
% 244.99/51.45  | | |   (22)  op(e2, e3) = e3
% 244.99/51.45  | | | 
% 244.99/51.45  | | | REF_CLOSE: (1), (7), (13), (15), (22) are inconsistent by sub-proof #2262.
% 244.99/51.45  | | | 
% 244.99/51.45  | | Case 2:
% 244.99/51.45  | | | 
% 244.99/51.45  | | |   (23)  all_58_3 = e3 & op(e2, e2) = e3
% 244.99/51.45  | | | 
% 244.99/51.45  | | | REF_CLOSE: (4), (5), (6), (11), (15), (16), (17), (18), (19), (23) are
% 244.99/51.45  | | |            inconsistent by sub-proof #2196.
% 244.99/51.45  | | | 
% 244.99/51.45  | | End of split
% 244.99/51.45  | | 
% 244.99/51.45  | Case 2:
% 244.99/51.45  | | 
% 244.99/51.45  | |   (24)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 244.99/51.45  | |           e3)
% 244.99/51.45  | | 
% 244.99/51.45  | | BETA: splitting (24) gives:
% 244.99/51.45  | | 
% 244.99/51.45  | | Case 1:
% 244.99/51.45  | | | 
% 244.99/51.45  | | | 
% 244.99/51.45  | | | GROUND_INST: instantiating (15) with e1, all_56_17, e1, e3, simplifying
% 244.99/51.45  | | |              with (2), (8) gives:
% 244.99/51.45  | | |   (25)  all_56_17 = e1
% 244.99/51.45  | | | 
% 244.99/51.45  | | | GROUND_INST: instantiating (15) with all_40_0, all_56_17, e1, e3,
% 244.99/51.45  | | |              simplifying with (2), (9) gives:
% 244.99/51.45  | | |   (26)  all_56_17 = all_40_0
% 244.99/51.45  | | | 
% 244.99/51.45  | | | COMBINE_EQS: (25), (26) imply:
% 244.99/51.45  | | |   (27)  all_40_0 = e1
% 244.99/51.45  | | | 
% 244.99/51.45  | | | REDUCE: (14), (25) imply:
% 244.99/51.45  | | |   (28)  op(e3, e1) = e3
% 244.99/51.45  | | | 
% 244.99/51.45  | | | REF_CLOSE: (2), (7), (12), (14), (15), (28) are inconsistent by sub-proof
% 244.99/51.45  | | |            #2098.
% 244.99/51.45  | | | 
% 244.99/51.45  | | Case 2:
% 244.99/51.45  | | | 
% 244.99/51.45  | | |   (29)  all_58_10 = e3 & op(e2, e0) = e3
% 244.99/51.45  | | | 
% 244.99/51.45  | | | ALPHA: (29) implies:
% 244.99/51.45  | | |   (30)  op(e2, e0) = e3
% 244.99/51.45  | | | 
% 244.99/51.45  | | | REF_CLOSE: (7), (10), (15), (30) are inconsistent by sub-proof #2152.
% 244.99/51.45  | | | 
% 244.99/51.45  | | End of split
% 244.99/51.45  | | 
% 244.99/51.45  | End of split
% 244.99/51.45  | 
% 244.99/51.45  End of proof
% 244.99/51.45  
% 244.99/51.45  Sub-proof #2098 shows that the following formulas are inconsistent:
% 244.99/51.45  ----------------------------------------------------------------
% 244.99/51.45    (1)  op(e3, e1) = all_56_17
% 244.99/51.45    (2)   ~ (e3 = e2)
% 244.99/51.45    (3)  op(e3, e3) = e2
% 244.99/51.45    (4)  op(e3, all_56_17) = e3
% 244.99/51.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.45    (6)  op(e3, e1) = e3
% 244.99/51.45  
% 244.99/51.45  Begin of proof
% 244.99/51.45  | 
% 244.99/51.45  | GROUND_INST: instantiating (5) with e3, all_56_17, e1, e3, simplifying with
% 244.99/51.45  |              (1), (6) gives:
% 244.99/51.45  |   (7)  all_56_17 = e3
% 244.99/51.45  | 
% 244.99/51.45  | REDUCE: (4), (7) imply:
% 244.99/51.45  |   (8)  op(e3, e3) = e3
% 244.99/51.45  | 
% 244.99/51.45  | GROUND_INST: instantiating (5) with e2, e3, e3, e3, simplifying with (3), (8)
% 244.99/51.45  |              gives:
% 244.99/51.45  |   (9)  e3 = e2
% 244.99/51.45  | 
% 244.99/51.45  | REDUCE: (2), (9) imply:
% 244.99/51.45  |   (10)  $false
% 244.99/51.45  | 
% 244.99/51.45  | CLOSE: (10) is inconsistent.
% 244.99/51.45  | 
% 244.99/51.45  End of proof
% 244.99/51.45  
% 244.99/51.45  Sub-proof #2099 shows that the following formulas are inconsistent:
% 244.99/51.45  ----------------------------------------------------------------
% 244.99/51.45    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.45    (2)  op(e3, e2) = e3
% 244.99/51.45    (3)  op(e3, e2) = e0
% 244.99/51.45    (4)   ~ (e3 = e0)
% 244.99/51.45  
% 244.99/51.45  Begin of proof
% 244.99/51.45  | 
% 244.99/51.45  | GROUND_INST: instantiating (1) with e0, e3, e2, e3, simplifying with (2), (3)
% 244.99/51.45  |              gives:
% 244.99/51.45  |   (5)  e3 = e0
% 244.99/51.45  | 
% 244.99/51.45  | REDUCE: (4), (5) imply:
% 244.99/51.45  |   (6)  $false
% 244.99/51.45  | 
% 244.99/51.45  | CLOSE: (6) is inconsistent.
% 244.99/51.45  | 
% 244.99/51.45  End of proof
% 244.99/51.45  
% 244.99/51.45  Sub-proof #2100 shows that the following formulas are inconsistent:
% 244.99/51.45  ----------------------------------------------------------------
% 244.99/51.45    (1)  all_54_4 = all_52_1
% 244.99/51.45    (2)  all_54_4 = e3
% 244.99/51.45    (3)   ~ (all_52_1 = e3)
% 244.99/51.45  
% 244.99/51.45  Begin of proof
% 244.99/51.45  | 
% 244.99/51.45  | COMBINE_EQS: (1), (2) imply:
% 244.99/51.45  |   (4)  all_52_1 = e3
% 244.99/51.45  | 
% 244.99/51.45  | SIMP: (4) implies:
% 244.99/51.45  |   (5)  all_52_1 = e3
% 244.99/51.45  | 
% 244.99/51.45  | REDUCE: (3), (5) imply:
% 244.99/51.45  |   (6)  $false
% 244.99/51.45  | 
% 244.99/51.45  | CLOSE: (6) is inconsistent.
% 244.99/51.45  | 
% 244.99/51.45  End of proof
% 244.99/51.45  
% 244.99/51.45  Sub-proof #2101 shows that the following formulas are inconsistent:
% 244.99/51.45  ----------------------------------------------------------------
% 244.99/51.45    (1)   ~ (e3 = e0)
% 244.99/51.45    (2)   ~ (e2 = e0)
% 244.99/51.45    (3)  (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 244.99/51.45         (all_58_11 = e0 & op(e1, e0) = e0)
% 244.99/51.45    (4)  op(e1, e0) = e1
% 244.99/51.45    (5)  op(e2, e0) = e2
% 244.99/51.45    (6)  all_58_9 = e3
% 244.99/51.45    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.45    (8)   ~ (e1 = e0)
% 244.99/51.45  
% 244.99/51.45  Begin of proof
% 244.99/51.45  | 
% 244.99/51.45  | BETA: splitting (3) gives:
% 244.99/51.45  | 
% 244.99/51.45  | Case 1:
% 244.99/51.45  | | 
% 244.99/51.45  | |   (9)  all_58_9 = e0 & op(e3, e0) = e0
% 244.99/51.45  | | 
% 244.99/51.45  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #2103.
% 244.99/51.45  | | 
% 244.99/51.45  | Case 2:
% 244.99/51.45  | | 
% 244.99/51.45  | |   (10)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 244.99/51.45  | |           e0)
% 244.99/51.45  | | 
% 244.99/51.45  | | REF_CLOSE: (2), (4), (5), (7), (8), (10) are inconsistent by sub-proof
% 244.99/51.45  | |            #2102.
% 244.99/51.45  | | 
% 244.99/51.45  | End of split
% 244.99/51.45  | 
% 244.99/51.45  End of proof
% 244.99/51.45  
% 244.99/51.45  Sub-proof #2102 shows that the following formulas are inconsistent:
% 244.99/51.45  ----------------------------------------------------------------
% 244.99/51.45    (1)   ~ (e2 = e0)
% 244.99/51.45    (2)  op(e1, e0) = e1
% 244.99/51.45    (3)  (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.99/51.45    (4)  op(e2, e0) = e2
% 244.99/51.45    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.45    (6)   ~ (e1 = e0)
% 244.99/51.45  
% 244.99/51.45  Begin of proof
% 244.99/51.45  | 
% 244.99/51.45  | BETA: splitting (3) gives:
% 244.99/51.45  | 
% 244.99/51.45  | Case 1:
% 244.99/51.45  | | 
% 244.99/51.45  | |   (7)  all_58_10 = e0 & op(e2, e0) = e0
% 244.99/51.45  | | 
% 244.99/51.45  | | ALPHA: (7) implies:
% 244.99/51.45  | |   (8)  op(e2, e0) = e0
% 244.99/51.45  | | 
% 244.99/51.45  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2121.
% 244.99/51.45  | | 
% 244.99/51.45  | Case 2:
% 244.99/51.45  | | 
% 244.99/51.45  | |   (9)  all_58_11 = e0 & op(e1, e0) = e0
% 244.99/51.45  | | 
% 244.99/51.45  | | ALPHA: (9) implies:
% 244.99/51.45  | |   (10)  op(e1, e0) = e0
% 244.99/51.45  | | 
% 244.99/51.45  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #2284.
% 244.99/51.45  | | 
% 244.99/51.45  | End of split
% 244.99/51.45  | 
% 244.99/51.45  End of proof
% 244.99/51.45  
% 244.99/51.45  Sub-proof #2103 shows that the following formulas are inconsistent:
% 244.99/51.45  ----------------------------------------------------------------
% 244.99/51.45    (1)  all_58_9 = e0 & op(e3, e0) = e0
% 244.99/51.45    (2)  all_58_9 = e3
% 244.99/51.45    (3)   ~ (e3 = e0)
% 244.99/51.45  
% 244.99/51.45  Begin of proof
% 244.99/51.45  | 
% 244.99/51.45  | ALPHA: (1) implies:
% 244.99/51.45  |   (4)  all_58_9 = e0
% 244.99/51.45  | 
% 244.99/51.45  | COMBINE_EQS: (2), (4) imply:
% 244.99/51.45  |   (5)  e3 = e0
% 244.99/51.45  | 
% 244.99/51.45  | REDUCE: (3), (5) imply:
% 244.99/51.45  |   (6)  $false
% 244.99/51.45  | 
% 244.99/51.45  | CLOSE: (6) is inconsistent.
% 244.99/51.45  | 
% 244.99/51.45  End of proof
% 244.99/51.45  
% 244.99/51.45  Sub-proof #2104 shows that the following formulas are inconsistent:
% 244.99/51.45  ----------------------------------------------------------------
% 244.99/51.45    (1)   ~ (all_52_1 = all_52_3)
% 244.99/51.45    (2)   ~ (all_52_9 = all_6_2)
% 244.99/51.45    (3)   ~ (e3 = e0)
% 244.99/51.45    (4)   ~ (all_52_8 = all_52_9)
% 244.99/51.45    (5)   ~ (e2 = e0)
% 244.99/51.45    (6)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.99/51.45         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.99/51.45    (7)  op(e1, e2) = all_52_6
% 244.99/51.45    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.99/51.45         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.99/51.45    (9)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.99/51.45           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.99/51.45             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.99/51.45           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.99/51.45             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.99/51.45           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.99/51.45           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.99/51.45           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.99/51.45           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.99/51.45           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.99/51.45           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.99/51.45             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.99/51.45           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.99/51.45           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 244.99/51.45           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.99/51.45           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.99/51.45           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.99/51.45           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.99/51.45             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.99/51.45           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.99/51.45           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.99/51.45           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.99/51.45           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.99/51.45           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.99/51.45           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.99/51.45             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.99/51.45           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.99/51.45           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.99/51.45    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.99/51.45          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.99/51.45    (11)  op(e1, e1) = all_6_2
% 244.99/51.45    (12)  op(e1, e0) = all_52_14
% 244.99/51.45    (13)   ~ (all_52_13 = e1)
% 244.99/51.45    (14)  (all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 244.99/51.45            $i(all_56_25)) | (all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0)
% 244.99/51.45            = all_56_27 & $i(all_56_27))
% 244.99/51.45    (15)  op(e0, e3) = all_52_3
% 244.99/51.45    (16)   ~ (e3 = e1)
% 244.99/51.45    (17)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.99/51.45          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.99/51.45    (18)  op(e1, e2) = e3
% 244.99/51.45    (19)  all_54_10 = all_6_2
% 244.99/51.45    (20)   ~ (all_6_2 = e3)
% 244.99/51.45    (21)  op(e3, e1) = all_52_8
% 244.99/51.45    (22)  op(e2, e1) = all_52_9
% 244.99/51.45    (23)   ~ (e3 = e2)
% 244.99/51.45    (24)   ~ (all_52_7 = e1)
% 244.99/51.45    (25)   ~ (all_6_2 = e0)
% 244.99/51.45    (26)  op(e2, e0) = e2
% 244.99/51.45    (27)  all_56_31 = e1
% 244.99/51.45    (28)  all_58_15 = e1
% 244.99/51.45    (29)  op(e3, e0) = all_52_12
% 244.99/51.45    (30)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.99/51.45          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.99/51.45    (31)   ~ (all_52_6 = all_52_14)
% 244.99/51.45    (32)  op(e3, e0) = e3
% 244.99/51.45    (33)  op(e2, e3) = all_52_1
% 244.99/51.45    (34)  op(e3, e3) = e2
% 244.99/51.45    (35)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.99/51.45    (36)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) =
% 244.99/51.45            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1,
% 244.99/51.45              e2) = all_40_1 & $i(all_40_1))
% 244.99/51.45    (37)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.99/51.45          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.99/51.45    (38)  op(e0, e2) = all_52_7
% 244.99/51.45    (39)  op(e3, e2) = all_52_4
% 244.99/51.45    (40)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.99/51.45          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 244.99/51.46    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.46    (42)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.99/51.46          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.99/51.46    (43)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.99/51.46          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.99/51.46    (44)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 244.99/51.46            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1,
% 244.99/51.46              e2) = all_36_1 & $i(all_36_1))
% 244.99/51.46    (45)   ~ (all_52_4 = e1)
% 244.99/51.46    (46)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.99/51.46          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.99/51.46    (47)   ~ (e1 = e0)
% 244.99/51.46    (48)  all_56_21 = all_6_2
% 244.99/51.46    (49)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.99/51.46          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.99/51.46    (50)  op(e2, e0) = all_52_13
% 244.99/51.46    (51)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.99/51.46          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.99/51.46            e2)
% 244.99/51.46    (52)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.99/51.46          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.99/51.46    (53)   ~ (e2 = e1)
% 244.99/51.46    (54)   ~ (all_52_1 = e1)
% 244.99/51.46    (55)   ~ (all_52_9 = e2)
% 244.99/51.46  
% 244.99/51.46  Begin of proof
% 244.99/51.46  | 
% 244.99/51.46  | BETA: splitting (14) gives:
% 244.99/51.46  | 
% 244.99/51.46  | Case 1:
% 244.99/51.46  | | 
% 244.99/51.46  | |   (56)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 244.99/51.46  | |         $i(all_56_25)
% 244.99/51.46  | | 
% 244.99/51.46  | | REF_CLOSE: (18), (23), (32), (34), (36), (41), (44), (56) are inconsistent
% 244.99/51.46  | |            by sub-proof #2143.
% 244.99/51.46  | | 
% 244.99/51.46  | Case 2:
% 244.99/51.46  | | 
% 244.99/51.46  | |   (57)  all_56_26 = e2 & op(e2, all_56_27) = e2 & op(e2, e0) = all_56_27 &
% 244.99/51.46  | |         $i(all_56_27)
% 244.99/51.46  | | 
% 244.99/51.46  | | ALPHA: (57) implies:
% 244.99/51.46  | |   (58)  op(e2, e0) = all_56_27
% 244.99/51.46  | |   (59)  op(e2, all_56_27) = e2
% 244.99/51.46  | | 
% 244.99/51.46  | | BETA: splitting (36) gives:
% 244.99/51.46  | | 
% 244.99/51.46  | | Case 1:
% 244.99/51.46  | | | 
% 244.99/51.46  | | | 
% 244.99/51.46  | | | GROUND_INST: instantiating (41) with e2, all_56_27, e0, e2, simplifying
% 244.99/51.46  | | |              with (26), (58) gives:
% 244.99/51.46  | | |   (60)  all_56_27 = e2
% 244.99/51.46  | | | 
% 244.99/51.46  | | | REDUCE: (59), (60) imply:
% 244.99/51.46  | | |   (61)  op(e2, e2) = e2
% 244.99/51.46  | | | 
% 244.99/51.46  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 244.99/51.46  | | |            (13), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 244.99/51.46  | | |            (25), (27), (28), (29), (30), (31), (33), (35), (37), (38),
% 244.99/51.46  | | |            (39), (40), (41), (42), (43), (45), (46), (47), (48), (49),
% 244.99/51.46  | | |            (50), (51), (52), (53), (54), (55), (61) are inconsistent by
% 244.99/51.46  | | |            sub-proof #2105.
% 244.99/51.46  | | | 
% 244.99/51.46  | | Case 2:
% 244.99/51.46  | | | 
% 244.99/51.46  | | |   (62)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 244.99/51.46  | | | 
% 244.99/51.46  | | | REF_CLOSE: (18), (41), (44), (62) are inconsistent by sub-proof #2144.
% 244.99/51.46  | | | 
% 244.99/51.46  | | End of split
% 244.99/51.46  | | 
% 244.99/51.46  | End of split
% 244.99/51.46  | 
% 244.99/51.46  End of proof
% 244.99/51.46  
% 244.99/51.46  Sub-proof #2105 shows that the following formulas are inconsistent:
% 244.99/51.46  ----------------------------------------------------------------
% 244.99/51.46    (1)   ~ (all_52_1 = all_52_3)
% 244.99/51.46    (2)   ~ (all_52_9 = all_6_2)
% 244.99/51.46    (3)   ~ (e3 = e0)
% 244.99/51.46    (4)   ~ (all_52_8 = all_52_9)
% 244.99/51.46    (5)   ~ (e2 = e0)
% 244.99/51.46    (6)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.99/51.46         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.99/51.46    (7)  op(e1, e2) = all_52_6
% 244.99/51.46    (8)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.99/51.46         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.99/51.46    (9)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 244.99/51.46           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 244.99/51.46             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 244.99/51.46           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.99/51.46             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 244.99/51.46           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.99/51.46           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 244.99/51.46           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.99/51.46           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 244.99/51.46           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.99/51.46           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 244.99/51.46             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.99/51.46           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.99/51.46           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 244.99/51.46           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.99/51.46           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 244.99/51.46           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 244.99/51.46           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.99/51.46             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 244.99/51.46           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.99/51.46           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 244.99/51.46           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.99/51.46           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 244.99/51.46           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.99/51.46           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 244.99/51.46             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.99/51.46           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.99/51.46           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 244.99/51.46    (10)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.99/51.46          (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.99/51.46    (11)  op(e1, e1) = all_6_2
% 244.99/51.46    (12)  op(e1, e0) = all_52_14
% 244.99/51.46    (13)   ~ (all_52_13 = e1)
% 244.99/51.46    (14)  op(e0, e3) = all_52_3
% 244.99/51.46    (15)   ~ (e3 = e1)
% 244.99/51.46    (16)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 244.99/51.46          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.99/51.46    (17)  all_54_10 = all_6_2
% 244.99/51.46    (18)   ~ (all_6_2 = e3)
% 244.99/51.46    (19)  op(e3, e1) = all_52_8
% 244.99/51.46    (20)  op(e2, e1) = all_52_9
% 244.99/51.46    (21)   ~ (e3 = e2)
% 244.99/51.46    (22)   ~ (all_52_7 = e1)
% 244.99/51.46    (23)   ~ (all_6_2 = e0)
% 244.99/51.46    (24)  all_56_31 = e1
% 244.99/51.46    (25)  all_58_15 = e1
% 244.99/51.46    (26)  op(e3, e0) = all_52_12
% 244.99/51.46    (27)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.99/51.46          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.99/51.46    (28)   ~ (all_52_6 = all_52_14)
% 244.99/51.46    (29)  op(e2, e3) = all_52_1
% 244.99/51.46    (30)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.99/51.46    (31)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.99/51.46          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.99/51.46    (32)  op(e0, e2) = all_52_7
% 244.99/51.46    (33)  op(e3, e2) = all_52_4
% 244.99/51.46    (34)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.99/51.46          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 244.99/51.46    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.46    (36)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 244.99/51.46          (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 244.99/51.46    (37)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.99/51.46          (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 244.99/51.46    (38)   ~ (all_52_4 = e1)
% 244.99/51.46    (39)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.99/51.46          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.99/51.46    (40)   ~ (e1 = e0)
% 244.99/51.46    (41)  all_56_21 = all_6_2
% 244.99/51.46    (42)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.99/51.46          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.99/51.46    (43)  op(e2, e0) = all_52_13
% 244.99/51.46    (44)  op(e2, e2) = e2
% 244.99/51.46    (45)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.99/51.46          | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 244.99/51.46            e2)
% 244.99/51.46    (46)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 244.99/51.46          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 244.99/51.46    (47)   ~ (e2 = e1)
% 244.99/51.46    (48)   ~ (all_52_1 = e1)
% 244.99/51.46    (49)   ~ (all_52_9 = e2)
% 244.99/51.46  
% 244.99/51.46  Begin of proof
% 244.99/51.46  | 
% 244.99/51.46  | BETA: splitting (37) gives:
% 244.99/51.46  | 
% 244.99/51.46  | Case 1:
% 244.99/51.46  | | 
% 244.99/51.46  | |   (50)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 244.99/51.46  | |           e1)
% 244.99/51.46  | | 
% 244.99/51.46  | | REF_CLOSE: (33), (35), (38), (44), (47), (50) are inconsistent by sub-proof
% 244.99/51.46  | |            #2142.
% 244.99/51.46  | | 
% 244.99/51.46  | Case 2:
% 244.99/51.46  | | 
% 244.99/51.46  | |   (51)  (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 244.99/51.46  | |           e1)
% 244.99/51.46  | | 
% 244.99/51.46  | | BETA: splitting (51) gives:
% 244.99/51.46  | | 
% 244.99/51.46  | | Case 1:
% 244.99/51.46  | | | 
% 244.99/51.46  | | |   (52)  all_58_7 = e1 & op(e1, e2) = e1
% 244.99/51.46  | | | 
% 244.99/51.46  | | | ALPHA: (52) implies:
% 244.99/51.46  | | |   (53)  all_58_7 = e1
% 244.99/51.46  | | |   (54)  op(e1, e2) = e1
% 244.99/51.46  | | | 
% 244.99/51.46  | | | BETA: splitting (46) gives:
% 244.99/51.46  | | | 
% 244.99/51.46  | | | Case 1:
% 244.99/51.46  | | | | 
% 244.99/51.46  | | | |   (55)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 244.99/51.46  | | | |           = e1)
% 244.99/51.46  | | | | 
% 244.99/51.46  | | | | BETA: splitting (55) gives:
% 244.99/51.46  | | | | 
% 244.99/51.46  | | | | Case 1:
% 244.99/51.46  | | | | | 
% 244.99/51.46  | | | | |   (56)  all_58_2 = e1 & op(e2, e3) = e1
% 244.99/51.46  | | | | | 
% 244.99/51.46  | | | | | REF_CLOSE: (29), (35), (48), (56) are inconsistent by sub-proof #2229.
% 244.99/51.46  | | | | | 
% 244.99/51.46  | | | | Case 2:
% 244.99/51.46  | | | | | 
% 244.99/51.46  | | | | |   (57)  all_58_3 = e1 & op(e2, e2) = e1
% 244.99/51.46  | | | | | 
% 244.99/51.46  | | | | | ALPHA: (57) implies:
% 244.99/51.46  | | | | |   (58)  all_58_3 = e1
% 244.99/51.46  | | | | | 
% 244.99/51.46  | | | | | REF_CLOSE: (3), (5), (7), (8), (10), (15), (21), (35), (39), (40),
% 244.99/51.46  | | | | |            (44), (47), (53), (54), (58) are inconsistent by sub-proof
% 244.99/51.46  | | | | |            #2127.
% 244.99/51.46  | | | | | 
% 244.99/51.46  | | | | End of split
% 244.99/51.46  | | | | 
% 244.99/51.46  | | | Case 2:
% 244.99/51.46  | | | | 
% 244.99/51.46  | | | |   (59)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 244.99/51.46  | | | |           = e1)
% 244.99/51.46  | | | | 
% 244.99/51.46  | | | | BETA: splitting (59) gives:
% 244.99/51.46  | | | | 
% 244.99/51.46  | | | | Case 1:
% 244.99/51.46  | | | | | 
% 244.99/51.46  | | | | |   (60)  all_58_5 = e1 & op(e2, e1) = e1
% 244.99/51.46  | | | | | 
% 244.99/51.46  | | | | | ALPHA: (60) implies:
% 244.99/51.46  | | | | |   (61)  all_58_5 = e1
% 244.99/51.46  | | | | |   (62)  op(e2, e1) = e1
% 244.99/51.46  | | | | | 
% 244.99/51.46  | | | | | BETA: splitting (8) gives:
% 244.99/51.46  | | | | | 
% 244.99/51.46  | | | | | Case 1:
% 244.99/51.46  | | | | | | 
% 244.99/51.46  | | | | | |   (63)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2,
% 244.99/51.46  | | | | | |             e2) = e2)
% 244.99/51.46  | | | | | | 
% 244.99/51.46  | | | | | | BETA: splitting (63) gives:
% 244.99/51.46  | | | | | | 
% 244.99/51.46  | | | | | | Case 1:
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | |   (64)  all_58_1 = e2 & op(e3, e2) = e2
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | ALPHA: (64) implies:
% 244.99/51.46  | | | | | | |   (65)  all_58_1 = e2
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | REF_CLOSE: (3), (5), (7), (10), (15), (21), (35), (39), (40),
% 244.99/51.46  | | | | | | |            (44), (53), (54), (65) are inconsistent by sub-proof
% 244.99/51.46  | | | | | | |            #2135.
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | Case 2:
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | |   (66)  all_58_3 = e2 & op(e2, e2) = e2
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | ALPHA: (66) implies:
% 244.99/51.46  | | | | | | |   (67)  all_58_3 = e2
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | GROUND_INST: instantiating (35) with all_52_6, e1, e2, e1,
% 244.99/51.46  | | | | | | |              simplifying with (7), (54) gives:
% 244.99/51.46  | | | | | | |   (68)  all_52_6 = e1
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | GROUND_INST: instantiating (35) with all_52_9, e1, e1, e2,
% 244.99/51.46  | | | | | | |              simplifying with (20), (62) gives:
% 244.99/51.46  | | | | | | |   (69)  all_52_9 = e1
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | REDUCE: (28), (68) imply:
% 244.99/51.46  | | | | | | |   (70)   ~ (all_52_14 = e1)
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | SIMP: (70) implies:
% 244.99/51.46  | | | | | | |   (71)   ~ (all_52_14 = e1)
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | REDUCE: (4), (69) imply:
% 244.99/51.46  | | | | | | |   (72)   ~ (all_52_8 = e1)
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | REDUCE: (2), (69) imply:
% 244.99/51.46  | | | | | | |   (73)   ~ (all_6_2 = e1)
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | SIMP: (73) implies:
% 244.99/51.46  | | | | | | |   (74)   ~ (all_6_2 = e1)
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | BETA: splitting (30) gives:
% 244.99/51.46  | | | | | | | 
% 244.99/51.46  | | | | | | | Case 1:
% 244.99/51.46  | | | | | | | | 
% 244.99/51.46  | | | | | | | |   (75)  all_54_10 = e3
% 244.99/51.46  | | | | | | | | 
% 244.99/51.46  | | | | | | | | REF_CLOSE: (17), (18), (75) are inconsistent by sub-proof #2313.
% 244.99/51.46  | | | | | | | | 
% 244.99/51.46  | | | | | | | Case 2:
% 244.99/51.46  | | | | | | | | 
% 244.99/51.46  | | | | | | | |   (76)   ~ (all_54_10 = e3)
% 244.99/51.46  | | | | | | | |   (77)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 244.99/51.46  | | | | | | | | 
% 244.99/51.46  | | | | | | | | BETA: splitting (77) gives:
% 244.99/51.46  | | | | | | | | 
% 244.99/51.46  | | | | | | | | Case 1:
% 244.99/51.46  | | | | | | | | | 
% 244.99/51.46  | | | | | | | | |   (78)  all_54_10 = e2
% 244.99/51.46  | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | COMBINE_EQS: (17), (78) imply:
% 244.99/51.46  | | | | | | | | |   (79)  all_6_2 = e2
% 244.99/51.46  | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | SIMP: (79) implies:
% 244.99/51.46  | | | | | | | | |   (80)  all_6_2 = e2
% 244.99/51.46  | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | COMBINE_EQS: (41), (80) imply:
% 244.99/51.46  | | | | | | | | |   (81)  all_56_21 = e2
% 244.99/51.46  | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | REDUCE: (18), (80) imply:
% 244.99/51.46  | | | | | | | | |   (82)   ~ (e3 = e2)
% 244.99/51.46  | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | REDUCE: (11), (80) imply:
% 244.99/51.46  | | | | | | | | |   (83)  op(e1, e1) = e2
% 244.99/51.46  | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | BETA: splitting (36) gives:
% 244.99/51.46  | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | Case 1:
% 244.99/51.46  | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | |   (84)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2
% 244.99/51.46  | | | | | | | | | |           & op(e2, e0) = e2)
% 244.99/51.46  | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | | BETA: splitting (84) gives:
% 244.99/51.46  | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | | Case 1:
% 244.99/51.46  | | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | | |   (85)  all_58_9 = e2 & op(e3, e0) = e2
% 244.99/51.46  | | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | | | ALPHA: (85) implies:
% 244.99/51.46  | | | | | | | | | | |   (86)  op(e3, e0) = e2
% 244.99/51.46  | | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | | | BETA: splitting (45) gives:
% 244.99/51.46  | | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | | | Case 1:
% 244.99/51.46  | | | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | | | |   (87)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 244.99/51.46  | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 244.99/51.46  | | | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | | | | BETA: splitting (87) gives:
% 244.99/51.46  | | | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | | | | Case 1:
% 244.99/51.46  | | | | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | | | | |   (88)  all_58_12 = e2 & op(e0, e3) = e2
% 244.99/51.46  | | | | | | | | | | | | | 
% 244.99/51.46  | | | | | | | | | | | | | ALPHA: (88) implies:
% 244.99/51.47  | | | | | | | | | | | | |   (89)  op(e0, e3) = e2
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_52_3, e2, e3, e0,
% 244.99/51.47  | | | | | | | | | | | | |              simplifying with (14), (89) gives:
% 244.99/51.47  | | | | | | | | | | | | |   (90)  all_52_3 = e2
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_52_12, e2, e0, e3,
% 244.99/51.47  | | | | | | | | | | | | |              simplifying with (26), (86) gives:
% 244.99/51.47  | | | | | | | | | | | | |   (91)  all_52_12 = e2
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | REDUCE: (1), (90) imply:
% 244.99/51.47  | | | | | | | | | | | | |   (92)   ~ (all_52_1 = e2)
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | BETA: splitting (9) gives:
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | |   (93)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.99/51.47  | | | | | | | | | | | | | |             e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.99/51.47  | | | | | | | | | | | | | |           op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.99/51.47  | | | | | | | | | | | | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.99/51.47  | | | | | | | | | | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.99/51.47  | | | | | | | | | | | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 244.99/51.47  | | | | | | | | | | | | | |           e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.99/51.47  | | | | | | | | | | | | | |           = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 244.99/51.47  | | | | | | | | | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.99/51.47  | | | | | | | | | | | | | |             e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 244.99/51.47  | | | | | | | | | | | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 244.99/51.47  | | | | | | | | | | | | | |           = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 244.99/51.47  | | | | | | | | | | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 244.99/51.47  | | | | | | | | | | | | | |             e0) = e0 & op(e0, e3) = e0)
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | |   (94)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | |             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.99/51.47  | | | | | | | | | | | | | | |             e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 244.99/51.47  | | | | | | | | | | | | | | |           op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 244.99/51.47  | | | | | | | | | | | | | | |           e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.99/51.47  | | | | | | | | | | | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.99/51.47  | | | | | | | | | | | | | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 244.99/51.47  | | | | | | | | | | | | | | |           e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.99/51.47  | | | | | | | | | | | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.99/51.47  | | | | | | | | | | | | | | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 244.99/51.47  | | | | | | | | | | | | | | |           = e3)
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | |   (95)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 244.99/51.47  | | | | | | | | | | | | | | | |         &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 244.99/51.47  | | | | | | | | | | | | | | | |         (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 244.99/51.47  | | | | | | | | | | | | | | | |         e3
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 244.99/51.47  | | | | | | | | | | | | | | | |   (96)   ~ (all_56_21 = e2)
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | REDUCE: (81), (96) imply:
% 244.99/51.47  | | | | | | | | | | | | | | | |   (97)  $false
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | CLOSE: (97) is inconsistent.
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | |   (98)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.99/51.47  | | | | | | | | | | | | | | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.99/51.47  | | | | | | | | | | | | | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 244.99/51.47  | | | | | | | | | | | | | | | |           e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 244.99/51.47  | | | | | | | | | | | | | | | |           ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 244.99/51.47  | | | | | | | | | | | | | | | |           op(e3, e1) = e3 & op(e1, e3) = e3)
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | REF_CLOSE: (24), (29), (35), (92), (98) are inconsistent by
% 244.99/51.47  | | | | | | | | | | | | | | | |            sub-proof #2126.
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | |   (99)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | |             e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 244.99/51.47  | | | | | | | | | | | | | | |             e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 244.99/51.47  | | | | | | | | | | | | | | |           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 244.99/51.47  | | | | | | | | | | | | | | |           e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.99/51.47  | | | | | | | | | | | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.99/51.47  | | | | | | | | | | | | | | |           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 244.99/51.47  | | | | | | | | | | | | | | |           e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 244.99/51.47  | | | | | | | | | | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 244.99/51.47  | | | | | | | | | | | | | | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 244.99/51.47  | | | | | | | | | | | | | | |           = e0)
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | |   (100)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 244.99/51.47  | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 244.99/51.47  | | | | | | | | | | | | | | | |            e3) = e1
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 244.99/51.47  | | | | | | | | | | | | | | | |   (101)  op(e3, e1) = e1
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | REF_CLOSE: (19), (35), (72), (101) are inconsistent by
% 244.99/51.47  | | | | | | | | | | | | | | | |            sub-proof #2309.
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | |   (102)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 244.99/51.47  | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 244.99/51.47  | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 244.99/51.47  | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 244.99/51.47  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 244.99/51.47  | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | |   (103)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 244.99/51.47  | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e3, e0) = e3 & op(e0,
% 244.99/51.47  | | | | | | | | | | | | | | | | |            e3) = e3
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 244.99/51.47  | | | | | | | | | | | | | | | | |   (104)  op(e3, e0) = e3
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (35), (86), (104) are inconsistent by
% 244.99/51.47  | | | | | | | | | | | | | | | | |            sub-proof #2125.
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | |   (105)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 244.99/51.47  | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0,
% 244.99/51.47  | | | | | | | | | | | | | | | | |            e3) = e0
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 244.99/51.47  | | | | | | | | | | | | | | | | |   (106)  op(e3, e0) = e0
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (35), (86), (106) are inconsistent by
% 244.99/51.47  | | | | | | | | | | | | | | | | |            sub-proof #2154.
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | |   (107)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.99/51.47  | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.99/51.47  | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.99/51.47  | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 244.99/51.47  | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.99/51.47  | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 244.99/51.47  | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.99/51.47  | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 244.99/51.47  | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 244.99/51.47  | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 244.99/51.47  | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 244.99/51.47  | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 244.99/51.47  | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 244.99/51.47  | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 244.99/51.47  | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | |   (108)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 244.99/51.47  | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 244.99/51.47  | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 244.99/51.47  | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 244.99/51.47  | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 244.99/51.47  | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 244.99/51.47  | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 244.99/51.47  | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 244.99/51.47  | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 244.99/51.47  | | | | | | | | | | | | | | |            = e2)
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | |   (109)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | | |            e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 244.99/51.47  | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1,
% 244.99/51.47  | | | | | | | | | | | | | | | |            e2) = e2
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 244.99/51.47  | | | | | | | | | | | | | | | |   (110)  op(e2, e1) = e2
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | REF_CLOSE: (20), (35), (49), (110) are inconsistent by
% 244.99/51.47  | | | | | | | | | | | | | | | |            sub-proof #2328.
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | |   (111)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.99/51.47  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 244.99/51.47  | | | | | | | | | | | | | | | |            op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 244.99/51.47  | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.99/51.47  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.99/51.47  | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & op(e0, e2) = e2)
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | |   (112)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | | | |            e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2)
% 244.99/51.47  | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1,
% 244.99/51.47  | | | | | | | | | | | | | | | | |            e2) = e1
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 244.99/51.47  | | | | | | | | | | | | | | | | |   (113)   ~ (all_56_21 = e2)
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | | REDUCE: (81), (113) imply:
% 244.99/51.47  | | | | | | | | | | | | | | | | |   (114)  $false
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | | CLOSE: (114) is inconsistent.
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | |   (115)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | | | |            e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 244.99/51.47  | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0,
% 244.99/51.47  | | | | | | | | | | | | | | | | |            e2) = e2
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 244.99/51.47  | | | | | | | | | | | | | | | | |   (116)  op(e2, e0) = e2
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (15), (20), (21), (34), (35), (40),
% 244.99/51.47  | | | | | | | | | | | | | | | | |            (44), (61), (62), (116) are inconsistent by
% 244.99/51.47  | | | | | | | | | | | | | | | | |            sub-proof #2119.
% 244.99/51.47  | | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | |   (117)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 244.99/51.47  | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 244.99/51.47  | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 244.99/51.47  | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 244.99/51.47  | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 244.99/51.47  | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 244.99/51.47  | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 244.99/51.47  | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 244.99/51.47  | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 244.99/51.47  | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 244.99/51.47  | | | | | | | | | | | | | | |            = e0)
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | REF_CLOSE: (12), (24), (35), (71), (81), (117) are
% 244.99/51.47  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2151.
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | |   (118)  all_58_13 = e2 & op(e0, e2) = e2
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | ALPHA: (118) implies:
% 244.99/51.47  | | | | | | | | | | | | |   (119)  all_58_13 = e2
% 244.99/51.47  | | | | | | | | | | | | |   (120)  op(e0, e2) = e2
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (10), (15), (21), (35), (39), (40),
% 244.99/51.47  | | | | | | | | | | | | |            (44), (53), (54), (119), (120) are inconsistent by
% 244.99/51.47  | | | | | | | | | | | | |            sub-proof #2128.
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | |   (121)  (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 244.99/51.47  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 244.99/51.47  | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | BETA: splitting (121) gives:
% 244.99/51.47  | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | |   (122)  all_58_14 = e2 & op(e0, e1) = e2
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | ALPHA: (122) implies:
% 244.99/51.47  | | | | | | | | | | | | |   (123)  all_58_14 = e2
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | BETA: splitting (16) gives:
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | |   (124)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 244.99/51.47  | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | |   (125)  all_58_4 = e0 & op(e3, e1) = e0
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 244.99/51.47  | | | | | | | | | | | | | | |   (126)  op(e3, e1) = e0
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | REF_CLOSE: (3), (15), (21), (31), (35), (61), (83), (123),
% 244.99/51.47  | | | | | | | | | | | | | | |            (126) are inconsistent by sub-proof #2115.
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | |   (127)  all_58_5 = e0 & op(e2, e1) = e0
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 244.99/51.47  | | | | | | | | | | | | | | |   (128)  op(e2, e1) = e0
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | | REF_CLOSE: (20), (35), (40), (62), (128) are inconsistent by
% 244.99/51.47  | | | | | | | | | | | | | | |            sub-proof #2165.
% 244.99/51.47  | | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | |   (129)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 244.99/51.47  | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | | REF_CLOSE: (5), (35), (83), (123), (129) are inconsistent by
% 244.99/51.47  | | | | | | | | | | | | | |            sub-proof #2113.
% 244.99/51.47  | | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | |   (130)  all_58_15 = e2 & op(e0, e0) = e2
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | ALPHA: (130) implies:
% 244.99/51.47  | | | | | | | | | | | | |   (131)  all_58_15 = e2
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (10), (15), (21), (25), (35),
% 244.99/51.47  | | | | | | | | | | | | |            (39), (40), (44), (47), (53), (54), (67), (131)
% 244.99/51.47  | | | | | | | | | | | | |            are inconsistent by sub-proof #2112.
% 244.99/51.47  | | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | |   (132)  all_58_10 = e2 & op(e2, e0) = e2
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | ALPHA: (132) implies:
% 244.99/51.47  | | | | | | | | | | |   (133)  op(e2, e0) = e2
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (15), (20), (21), (34), (35), (40),
% 244.99/51.47  | | | | | | | | | | |            (44), (61), (62), (133) are inconsistent by
% 244.99/51.47  | | | | | | | | | | |            sub-proof #2119.
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | |   (134)  (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 244.99/51.47  | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 244.99/51.47  | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | BETA: splitting (134) gives:
% 244.99/51.47  | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | Case 1:
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | |   (135)  all_58_11 = e2 & op(e1, e0) = e2
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | ALPHA: (135) implies:
% 244.99/51.47  | | | | | | | | | | |   (136)  all_58_11 = e2
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (15), (21), (27), (35), (40), (42),
% 244.99/51.47  | | | | | | | | | | |            (53), (54), (83), (136) are inconsistent by
% 244.99/51.47  | | | | | | | | | | |            sub-proof #2106.
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | |   (137)  all_58_15 = e2 & op(e0, e0) = e2
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | ALPHA: (137) implies:
% 244.99/51.47  | | | | | | | | | | |   (138)  all_58_15 = e2
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (10), (15), (21), (25), (35),
% 244.99/51.47  | | | | | | | | | | |            (39), (40), (44), (47), (53), (54), (67), (138)
% 244.99/51.47  | | | | | | | | | | |            are inconsistent by sub-proof #2112.
% 244.99/51.47  | | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | | 
% 244.99/51.47  | | | | | | | | Case 2:
% 244.99/51.47  | | | | | | | | | 
% 244.99/51.47  | | | | | | | | |   (139)  all_54_10 = e1 | all_54_10 = e0
% 244.99/51.47  | | | | | | | | | 
% 244.99/51.47  | | | | | | | | | REF_CLOSE: (17), (23), (74), (139) are inconsistent by
% 244.99/51.47  | | | | | | | | |            sub-proof #2282.
% 244.99/51.47  | | | | | | | | | 
% 244.99/51.47  | | | | | | | | End of split
% 244.99/51.47  | | | | | | | | 
% 244.99/51.47  | | | | | | | End of split
% 244.99/51.47  | | | | | | | 
% 244.99/51.47  | | | | | | End of split
% 244.99/51.47  | | | | | | 
% 244.99/51.47  | | | | | Case 2:
% 244.99/51.47  | | | | | | 
% 244.99/51.47  | | | | | |   (140)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 &
% 244.99/51.47  | | | | | |            op(e0, e2) = e2)
% 244.99/51.47  | | | | | | 
% 244.99/51.47  | | | | | | BETA: splitting (140) gives:
% 244.99/51.47  | | | | | | 
% 244.99/51.47  | | | | | | Case 1:
% 244.99/51.47  | | | | | | | 
% 244.99/51.47  | | | | | | |   (141)  all_58_7 = e2 & op(e1, e2) = e2
% 244.99/51.47  | | | | | | | 
% 244.99/51.47  | | | | | | | ALPHA: (141) implies:
% 244.99/51.47  | | | | | | |   (142)  all_58_7 = e2
% 244.99/51.47  | | | | | | | 
% 244.99/51.47  | | | | | | | REF_CLOSE: (47), (53), (142) are inconsistent by sub-proof #2134.
% 244.99/51.47  | | | | | | | 
% 244.99/51.47  | | | | | | Case 2:
% 244.99/51.47  | | | | | | | 
% 244.99/51.47  | | | | | | |   (143)  all_58_13 = e2 & op(e0, e2) = e2
% 244.99/51.47  | | | | | | | 
% 244.99/51.47  | | | | | | | ALPHA: (143) implies:
% 244.99/51.47  | | | | | | |   (144)  all_58_13 = e2
% 244.99/51.47  | | | | | | |   (145)  op(e0, e2) = e2
% 244.99/51.47  | | | | | | | 
% 244.99/51.47  | | | | | | | REF_CLOSE: (3), (5), (7), (10), (15), (21), (35), (39), (40),
% 244.99/51.47  | | | | | | |            (44), (53), (54), (144), (145) are inconsistent by
% 244.99/51.47  | | | | | | |            sub-proof #2128.
% 244.99/51.47  | | | | | | | 
% 244.99/51.47  | | | | | | End of split
% 244.99/51.47  | | | | | | 
% 244.99/51.47  | | | | | End of split
% 244.99/51.47  | | | | | 
% 244.99/51.47  | | | | Case 2:
% 244.99/51.47  | | | | | 
% 244.99/51.47  | | | | |   (146)  all_58_10 = e1 & op(e2, e0) = e1
% 244.99/51.47  | | | | | 
% 244.99/51.47  | | | | | REF_CLOSE: (13), (35), (43), (146) are inconsistent by sub-proof
% 244.99/51.47  | | | | |            #2277.
% 244.99/51.47  | | | | | 
% 244.99/51.47  | | | | End of split
% 244.99/51.47  | | | | 
% 244.99/51.47  | | | End of split
% 244.99/51.47  | | | 
% 244.99/51.47  | | Case 2:
% 244.99/51.47  | | | 
% 244.99/51.47  | | |   (147)  all_58_13 = e1 & op(e0, e2) = e1
% 244.99/51.47  | | | 
% 244.99/51.47  | | | REF_CLOSE: (22), (32), (35), (147) are inconsistent by sub-proof #2275.
% 244.99/51.47  | | | 
% 244.99/51.47  | | End of split
% 244.99/51.47  | | 
% 244.99/51.47  | End of split
% 244.99/51.47  | 
% 244.99/51.47  End of proof
% 244.99/51.47  
% 244.99/51.47  Sub-proof #2106 shows that the following formulas are inconsistent:
% 244.99/51.47  ----------------------------------------------------------------
% 244.99/51.47    (1)   ~ (e3 = e0)
% 244.99/51.47    (2)  op(e1, e2) = e1
% 244.99/51.48    (3)   ~ (e2 = e0)
% 244.99/51.48    (4)  op(e1, e2) = all_52_6
% 244.99/51.48    (5)   ~ (e3 = e1)
% 244.99/51.48    (6)   ~ (e3 = e2)
% 244.99/51.48    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 244.99/51.48         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.99/51.48    (8)  all_58_11 = e2
% 244.99/51.48    (9)  op(e1, e1) = e2
% 244.99/51.48    (10)  all_58_7 = e1
% 244.99/51.48    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.48    (12)   ~ (e1 = e0)
% 244.99/51.48    (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 244.99/51.48          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | BETA: splitting (7) gives:
% 244.99/51.48  | 
% 244.99/51.48  | Case 1:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (14)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 244.99/51.48  | |           e3)
% 244.99/51.48  | | 
% 244.99/51.48  | | BETA: splitting (14) gives:
% 244.99/51.48  | | 
% 244.99/51.48  | | Case 1:
% 244.99/51.48  | | | 
% 244.99/51.48  | | |   (15)  all_58_6 = e3 & op(e1, e3) = e3
% 244.99/51.48  | | | 
% 244.99/51.48  | | | ALPHA: (15) implies:
% 244.99/51.48  | | |   (16)  all_58_6 = e3
% 244.99/51.48  | | | 
% 244.99/51.48  | | | BETA: splitting (13) gives:
% 244.99/51.48  | | | 
% 244.99/51.48  | | | Case 1:
% 244.99/51.48  | | | | 
% 244.99/51.48  | | | |   (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2)
% 244.99/51.48  | | | |           = e0)
% 244.99/51.48  | | | | 
% 244.99/51.48  | | | | REF_CLOSE: (1), (2), (4), (11), (12), (16), (17) are inconsistent by
% 244.99/51.48  | | | |            sub-proof #2111.
% 244.99/51.48  | | | | 
% 244.99/51.48  | | | Case 2:
% 244.99/51.48  | | | | 
% 244.99/51.48  | | | |   (18)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0)
% 244.99/51.48  | | | |           = e0)
% 244.99/51.48  | | | | 
% 244.99/51.48  | | | | REF_CLOSE: (3), (8), (9), (11), (18) are inconsistent by sub-proof
% 244.99/51.48  | | | |            #2109.
% 244.99/51.48  | | | | 
% 244.99/51.48  | | | End of split
% 244.99/51.48  | | | 
% 244.99/51.48  | | Case 2:
% 244.99/51.48  | | | 
% 244.99/51.48  | | |   (19)  all_58_7 = e3 & op(e1, e2) = e3
% 244.99/51.48  | | | 
% 244.99/51.48  | | | REF_CLOSE: (5), (10), (19) are inconsistent by sub-proof #2138.
% 244.99/51.48  | | | 
% 244.99/51.48  | | End of split
% 244.99/51.48  | | 
% 244.99/51.48  | Case 2:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (20)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 244.99/51.48  | |           e3)
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (6), (8), (9), (11), (20) are inconsistent by sub-proof #2107.
% 244.99/51.48  | | 
% 244.99/51.48  | End of split
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2107 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)   ~ (e3 = e2)
% 244.99/51.48    (2)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 244.99/51.48    (3)  all_58_11 = e2
% 244.99/51.48    (4)  op(e1, e1) = e2
% 244.99/51.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | BETA: splitting (2) gives:
% 244.99/51.48  | 
% 244.99/51.48  | Case 1:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (6)  all_58_8 = e3 & op(e1, e1) = e3
% 244.99/51.48  | | 
% 244.99/51.48  | | ALPHA: (6) implies:
% 244.99/51.48  | |   (7)  op(e1, e1) = e3
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #2206.
% 244.99/51.48  | | 
% 244.99/51.48  | Case 2:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (8)  all_58_11 = e3 & op(e1, e0) = e3
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #2108.
% 244.99/51.48  | | 
% 244.99/51.48  | End of split
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2108 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)  all_58_11 = e3 & op(e1, e0) = e3
% 244.99/51.48    (2)  all_58_11 = e2
% 244.99/51.48    (3)   ~ (e3 = e2)
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | ALPHA: (1) implies:
% 244.99/51.48  |   (4)  all_58_11 = e3
% 244.99/51.48  | 
% 244.99/51.48  | COMBINE_EQS: (2), (4) imply:
% 244.99/51.48  |   (5)  e3 = e2
% 244.99/51.48  | 
% 244.99/51.48  | REDUCE: (3), (5) imply:
% 244.99/51.48  |   (6)  $false
% 244.99/51.48  | 
% 244.99/51.48  | CLOSE: (6) is inconsistent.
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2109 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 244.99/51.48    (2)   ~ (e2 = e0)
% 244.99/51.48    (3)  all_58_11 = e2
% 244.99/51.48    (4)  op(e1, e1) = e2
% 244.99/51.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | BETA: splitting (1) gives:
% 244.99/51.48  | 
% 244.99/51.48  | Case 1:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (6)  all_58_8 = e0 & op(e1, e1) = e0
% 244.99/51.48  | | 
% 244.99/51.48  | | ALPHA: (6) implies:
% 244.99/51.48  | |   (7)  op(e1, e1) = e0
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #2211.
% 244.99/51.48  | | 
% 244.99/51.48  | Case 2:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (8)  all_58_11 = e0 & op(e1, e0) = e0
% 244.99/51.48  | | 
% 244.99/51.48  | | ALPHA: (8) implies:
% 244.99/51.48  | |   (9)  all_58_11 = e0
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #2110.
% 244.99/51.48  | | 
% 244.99/51.48  | End of split
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2110 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)  all_58_11 = e2
% 244.99/51.48    (2)  all_58_11 = e0
% 244.99/51.48    (3)   ~ (e2 = e0)
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | COMBINE_EQS: (1), (2) imply:
% 244.99/51.48  |   (4)  e2 = e0
% 244.99/51.48  | 
% 244.99/51.48  | SIMP: (4) implies:
% 244.99/51.48  |   (5)  e2 = e0
% 244.99/51.48  | 
% 244.99/51.48  | REDUCE: (3), (5) imply:
% 244.99/51.48  |   (6)  $false
% 244.99/51.48  | 
% 244.99/51.48  | CLOSE: (6) is inconsistent.
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2111 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)   ~ (e3 = e0)
% 244.99/51.48    (2)  all_58_6 = e3
% 244.99/51.48    (3)  op(e1, e2) = e1
% 244.99/51.48    (4)  op(e1, e2) = all_52_6
% 244.99/51.48    (5)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 244.99/51.48    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.48    (7)   ~ (e1 = e0)
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | BETA: splitting (5) gives:
% 244.99/51.48  | 
% 244.99/51.48  | Case 1:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (8)  all_58_6 = e0 & op(e1, e3) = e0
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #2213.
% 244.99/51.48  | | 
% 244.99/51.48  | Case 2:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (9)  all_58_7 = e0 & op(e1, e2) = e0
% 244.99/51.48  | | 
% 244.99/51.48  | | ALPHA: (9) implies:
% 244.99/51.48  | |   (10)  op(e1, e2) = e0
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (3), (4), (6), (7), (10) are inconsistent by sub-proof #2136.
% 244.99/51.48  | | 
% 244.99/51.48  | End of split
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2112 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)   ~ (e3 = e0)
% 244.99/51.48    (2)  op(e1, e2) = e1
% 244.99/51.48    (3)   ~ (e2 = e0)
% 244.99/51.48    (4)  op(e1, e2) = all_52_6
% 244.99/51.48    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.99/51.48         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.99/51.48    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.99/51.48         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.99/51.48    (7)   ~ (e3 = e1)
% 244.99/51.48    (8)  all_58_15 = e2
% 244.99/51.48    (9)   ~ (e3 = e2)
% 244.99/51.48    (10)  all_58_15 = e1
% 244.99/51.48    (11)  all_58_7 = e1
% 244.99/51.48    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.48    (13)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.99/51.48          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.99/51.48    (14)   ~ (e1 = e0)
% 244.99/51.48    (15)  all_58_3 = e2
% 244.99/51.48    (16)  op(e2, e2) = e2
% 244.99/51.48    (17)   ~ (e2 = e1)
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | COMBINE_EQS: (8), (10) imply:
% 244.99/51.48  |   (18)  e2 = e1
% 244.99/51.48  | 
% 244.99/51.48  | COMBINE_EQS: (15), (18) imply:
% 244.99/51.48  |   (19)  all_58_3 = e1
% 244.99/51.48  | 
% 244.99/51.48  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (13), (14),
% 244.99/51.48  |            (16), (17), (19) are inconsistent by sub-proof #2127.
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2113 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)   ~ (e2 = e0)
% 244.99/51.48    (2)  all_58_14 = e2
% 244.99/51.48    (3)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 244.99/51.48    (4)  op(e1, e1) = e2
% 244.99/51.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | BETA: splitting (3) gives:
% 244.99/51.48  | 
% 244.99/51.48  | Case 1:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (6)  all_58_8 = e0 & op(e1, e1) = e0
% 244.99/51.48  | | 
% 244.99/51.48  | | ALPHA: (6) implies:
% 244.99/51.48  | |   (7)  op(e1, e1) = e0
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #2211.
% 244.99/51.48  | | 
% 244.99/51.48  | Case 2:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (8)  all_58_14 = e0 & op(e0, e1) = e0
% 244.99/51.48  | | 
% 244.99/51.48  | | ALPHA: (8) implies:
% 244.99/51.48  | |   (9)  all_58_14 = e0
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #2114.
% 244.99/51.48  | | 
% 244.99/51.48  | End of split
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2114 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)  all_58_14 = e2
% 244.99/51.48    (2)  all_58_14 = e0
% 244.99/51.48    (3)   ~ (e2 = e0)
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | COMBINE_EQS: (1), (2) imply:
% 244.99/51.48  |   (4)  e2 = e0
% 244.99/51.48  | 
% 244.99/51.48  | SIMP: (4) implies:
% 244.99/51.48  |   (5)  e2 = e0
% 244.99/51.48  | 
% 244.99/51.48  | REDUCE: (3), (5) imply:
% 244.99/51.48  |   (6)  $false
% 244.99/51.48  | 
% 244.99/51.48  | CLOSE: (6) is inconsistent.
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2115 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)   ~ (e3 = e0)
% 244.99/51.48    (2)  all_58_14 = e2
% 244.99/51.48    (3)   ~ (e3 = e1)
% 244.99/51.48    (4)  op(e3, e1) = e0
% 244.99/51.48    (5)   ~ (e3 = e2)
% 244.99/51.48    (6)  op(e1, e1) = e2
% 244.99/51.48    (7)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 244.99/51.48         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.99/51.48    (8)  all_58_5 = e1
% 244.99/51.48    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | BETA: splitting (7) gives:
% 244.99/51.48  | 
% 244.99/51.48  | Case 1:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (10)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 244.99/51.48  | |           e3)
% 244.99/51.48  | | 
% 244.99/51.48  | | BETA: splitting (10) gives:
% 244.99/51.48  | | 
% 244.99/51.48  | | Case 1:
% 244.99/51.48  | | | 
% 244.99/51.48  | | |   (11)  all_58_4 = e3 & op(e3, e1) = e3
% 244.99/51.48  | | | 
% 244.99/51.48  | | | ALPHA: (11) implies:
% 244.99/51.48  | | |   (12)  op(e3, e1) = e3
% 244.99/51.48  | | | 
% 244.99/51.48  | | | REF_CLOSE: (1), (4), (9), (12) are inconsistent by sub-proof #2118.
% 244.99/51.48  | | | 
% 244.99/51.48  | | Case 2:
% 244.99/51.48  | | | 
% 244.99/51.48  | | |   (13)  all_58_5 = e3 & op(e2, e1) = e3
% 244.99/51.48  | | | 
% 244.99/51.48  | | | ALPHA: (13) implies:
% 244.99/51.48  | | |   (14)  all_58_5 = e3
% 244.99/51.48  | | | 
% 244.99/51.48  | | | REF_CLOSE: (3), (8), (14) are inconsistent by sub-proof #2123.
% 244.99/51.48  | | | 
% 244.99/51.48  | | End of split
% 244.99/51.48  | | 
% 244.99/51.48  | Case 2:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (15)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 244.99/51.48  | |           e3)
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (2), (5), (6), (9), (15) are inconsistent by sub-proof #2116.
% 244.99/51.48  | | 
% 244.99/51.48  | End of split
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2116 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)  all_58_14 = e2
% 244.99/51.48    (2)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 244.99/51.48    (3)   ~ (e3 = e2)
% 244.99/51.48    (4)  op(e1, e1) = e2
% 244.99/51.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | BETA: splitting (2) gives:
% 244.99/51.48  | 
% 244.99/51.48  | Case 1:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (6)  all_58_8 = e3 & op(e1, e1) = e3
% 244.99/51.48  | | 
% 244.99/51.48  | | ALPHA: (6) implies:
% 244.99/51.48  | |   (7)  op(e1, e1) = e3
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #2206.
% 244.99/51.48  | | 
% 244.99/51.48  | Case 2:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (8)  all_58_14 = e3 & op(e0, e1) = e3
% 244.99/51.48  | | 
% 244.99/51.48  | | ALPHA: (8) implies:
% 244.99/51.48  | |   (9)  all_58_14 = e3
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #2117.
% 244.99/51.48  | | 
% 244.99/51.48  | End of split
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2117 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)  all_58_14 = e3
% 244.99/51.48    (2)  all_58_14 = e2
% 244.99/51.48    (3)   ~ (e3 = e2)
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | COMBINE_EQS: (1), (2) imply:
% 244.99/51.48  |   (4)  e3 = e2
% 244.99/51.48  | 
% 244.99/51.48  | SIMP: (4) implies:
% 244.99/51.48  |   (5)  e3 = e2
% 244.99/51.48  | 
% 244.99/51.48  | REDUCE: (3), (5) imply:
% 244.99/51.48  |   (6)  $false
% 244.99/51.48  | 
% 244.99/51.48  | CLOSE: (6) is inconsistent.
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2118 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.48    (2)  op(e3, e1) = e3
% 244.99/51.48    (3)  op(e3, e1) = e0
% 244.99/51.48    (4)   ~ (e3 = e0)
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | GROUND_INST: instantiating (1) with e0, e3, e1, e3, simplifying with (2), (3)
% 244.99/51.48  |              gives:
% 244.99/51.48  |   (5)  e3 = e0
% 244.99/51.48  | 
% 244.99/51.48  | REDUCE: (4), (5) imply:
% 244.99/51.48  |   (6)  $false
% 244.99/51.48  | 
% 244.99/51.48  | CLOSE: (6) is inconsistent.
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2119 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)   ~ (e3 = e0)
% 244.99/51.48    (2)  op(e2, e1) = e1
% 244.99/51.48    (3)   ~ (e2 = e0)
% 244.99/51.48    (4)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.99/51.48         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.99/51.48    (5)   ~ (e3 = e1)
% 244.99/51.48    (6)  op(e2, e1) = all_52_9
% 244.99/51.48    (7)   ~ (e3 = e2)
% 244.99/51.48    (8)  op(e2, e0) = e2
% 244.99/51.48    (9)  all_58_5 = e1
% 244.99/51.48    (10)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.99/51.48          (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 244.99/51.48    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.48    (12)   ~ (e1 = e0)
% 244.99/51.48    (13)  op(e2, e2) = e2
% 244.99/51.48  
% 244.99/51.48  Begin of proof
% 244.99/51.48  | 
% 244.99/51.48  | BETA: splitting (10) gives:
% 244.99/51.48  | 
% 244.99/51.48  | Case 1:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (14)  (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 244.99/51.48  | |           e0)
% 244.99/51.48  | | 
% 244.99/51.48  | | BETA: splitting (14) gives:
% 244.99/51.48  | | 
% 244.99/51.48  | | Case 1:
% 244.99/51.48  | | | 
% 244.99/51.48  | | |   (15)  all_58_2 = e0 & op(e2, e3) = e0
% 244.99/51.48  | | | 
% 244.99/51.48  | | | ALPHA: (15) implies:
% 244.99/51.48  | | |   (16)  all_58_2 = e0
% 244.99/51.48  | | | 
% 244.99/51.48  | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (11), (13), (16) are inconsistent
% 244.99/51.48  | | |            by sub-proof #2122.
% 244.99/51.48  | | | 
% 244.99/51.48  | | Case 2:
% 244.99/51.48  | | | 
% 244.99/51.48  | | |   (17)  all_58_3 = e0 & op(e2, e2) = e0
% 244.99/51.48  | | | 
% 244.99/51.48  | | | ALPHA: (17) implies:
% 244.99/51.48  | | |   (18)  op(e2, e2) = e0
% 244.99/51.48  | | | 
% 244.99/51.48  | | | REF_CLOSE: (3), (11), (13), (18) are inconsistent by sub-proof #2137.
% 244.99/51.48  | | | 
% 244.99/51.48  | | End of split
% 244.99/51.48  | | 
% 244.99/51.48  | Case 2:
% 244.99/51.48  | | 
% 244.99/51.48  | |   (19)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 244.99/51.48  | |           e0)
% 244.99/51.48  | | 
% 244.99/51.48  | | REF_CLOSE: (2), (3), (6), (8), (11), (12), (19) are inconsistent by
% 244.99/51.48  | |            sub-proof #2120.
% 244.99/51.48  | | 
% 244.99/51.48  | End of split
% 244.99/51.48  | 
% 244.99/51.48  End of proof
% 244.99/51.48  
% 244.99/51.48  Sub-proof #2120 shows that the following formulas are inconsistent:
% 244.99/51.48  ----------------------------------------------------------------
% 244.99/51.48    (1)  (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 244.99/51.48    (2)  op(e2, e1) = e1
% 244.99/51.48    (3)   ~ (e2 = e0)
% 244.99/51.49    (4)  op(e2, e1) = all_52_9
% 244.99/51.49    (5)  op(e2, e0) = e2
% 244.99/51.49    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.49    (7)   ~ (e1 = e0)
% 244.99/51.49  
% 244.99/51.49  Begin of proof
% 244.99/51.49  | 
% 244.99/51.49  | BETA: splitting (1) gives:
% 244.99/51.49  | 
% 244.99/51.49  | Case 1:
% 244.99/51.49  | | 
% 244.99/51.49  | |   (8)  all_58_5 = e0 & op(e2, e1) = e0
% 244.99/51.49  | | 
% 244.99/51.49  | | ALPHA: (8) implies:
% 244.99/51.49  | |   (9)  op(e2, e1) = e0
% 244.99/51.49  | | 
% 244.99/51.49  | | REF_CLOSE: (2), (4), (6), (7), (9) are inconsistent by sub-proof #2165.
% 244.99/51.49  | | 
% 244.99/51.49  | Case 2:
% 244.99/51.49  | | 
% 244.99/51.49  | |   (10)  all_58_10 = e0 & op(e2, e0) = e0
% 244.99/51.49  | | 
% 244.99/51.49  | | ALPHA: (10) implies:
% 244.99/51.49  | |   (11)  op(e2, e0) = e0
% 244.99/51.49  | | 
% 244.99/51.49  | | REF_CLOSE: (3), (5), (6), (11) are inconsistent by sub-proof #2121.
% 244.99/51.49  | | 
% 244.99/51.49  | End of split
% 244.99/51.49  | 
% 244.99/51.49  End of proof
% 244.99/51.49  
% 244.99/51.49  Sub-proof #2121 shows that the following formulas are inconsistent:
% 244.99/51.49  ----------------------------------------------------------------
% 244.99/51.49    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.49    (2)  op(e2, e0) = e2
% 244.99/51.49    (3)  op(e2, e0) = e0
% 244.99/51.49    (4)   ~ (e2 = e0)
% 244.99/51.49  
% 244.99/51.49  Begin of proof
% 244.99/51.49  | 
% 244.99/51.49  | GROUND_INST: instantiating (1) with e0, e2, e0, e2, simplifying with (2), (3)
% 244.99/51.49  |              gives:
% 244.99/51.49  |   (5)  e2 = e0
% 244.99/51.49  | 
% 244.99/51.49  | REDUCE: (4), (5) imply:
% 244.99/51.49  |   (6)  $false
% 244.99/51.49  | 
% 244.99/51.49  | CLOSE: (6) is inconsistent.
% 244.99/51.49  | 
% 244.99/51.49  End of proof
% 244.99/51.49  
% 244.99/51.49  Sub-proof #2122 shows that the following formulas are inconsistent:
% 244.99/51.49  ----------------------------------------------------------------
% 244.99/51.49    (1)   ~ (e3 = e0)
% 244.99/51.49    (2)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.99/51.49         (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 244.99/51.49    (3)   ~ (e3 = e1)
% 244.99/51.49    (4)   ~ (e3 = e2)
% 244.99/51.49    (5)  op(e2, e0) = e2
% 244.99/51.49    (6)  all_58_2 = e0
% 244.99/51.49    (7)  all_58_5 = e1
% 244.99/51.49    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.49    (9)  op(e2, e2) = e2
% 244.99/51.49  
% 244.99/51.49  Begin of proof
% 244.99/51.49  | 
% 244.99/51.49  | BETA: splitting (2) gives:
% 244.99/51.49  | 
% 244.99/51.49  | Case 1:
% 244.99/51.49  | | 
% 244.99/51.49  | |   (10)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 244.99/51.49  | |           e3)
% 244.99/51.49  | | 
% 244.99/51.49  | | BETA: splitting (10) gives:
% 244.99/51.49  | | 
% 244.99/51.49  | | Case 1:
% 244.99/51.49  | | | 
% 244.99/51.49  | | |   (11)  all_58_2 = e3 & op(e2, e3) = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | ALPHA: (11) implies:
% 244.99/51.49  | | |   (12)  all_58_2 = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | REF_CLOSE: (1), (6), (12) are inconsistent by sub-proof #2124.
% 244.99/51.49  | | | 
% 244.99/51.49  | | Case 2:
% 244.99/51.49  | | | 
% 244.99/51.49  | | |   (13)  all_58_3 = e3 & op(e2, e2) = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | ALPHA: (13) implies:
% 244.99/51.49  | | |   (14)  op(e2, e2) = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | REF_CLOSE: (4), (8), (9), (14) are inconsistent by sub-proof #2140.
% 244.99/51.49  | | | 
% 244.99/51.49  | | End of split
% 244.99/51.49  | | 
% 244.99/51.49  | Case 2:
% 244.99/51.49  | | 
% 244.99/51.49  | |   (15)  (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 244.99/51.49  | |           e3)
% 244.99/51.49  | | 
% 244.99/51.49  | | BETA: splitting (15) gives:
% 244.99/51.49  | | 
% 244.99/51.49  | | Case 1:
% 244.99/51.49  | | | 
% 244.99/51.49  | | |   (16)  all_58_5 = e3 & op(e2, e1) = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | ALPHA: (16) implies:
% 244.99/51.49  | | |   (17)  all_58_5 = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | REF_CLOSE: (3), (7), (17) are inconsistent by sub-proof #2123.
% 244.99/51.49  | | | 
% 244.99/51.49  | | Case 2:
% 244.99/51.49  | | | 
% 244.99/51.49  | | |   (18)  all_58_10 = e3 & op(e2, e0) = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | ALPHA: (18) implies:
% 244.99/51.49  | | |   (19)  op(e2, e0) = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | REF_CLOSE: (4), (5), (8), (19) are inconsistent by sub-proof #2152.
% 244.99/51.49  | | | 
% 244.99/51.49  | | End of split
% 244.99/51.49  | | 
% 244.99/51.49  | End of split
% 244.99/51.49  | 
% 244.99/51.49  End of proof
% 244.99/51.49  
% 244.99/51.49  Sub-proof #2123 shows that the following formulas are inconsistent:
% 244.99/51.49  ----------------------------------------------------------------
% 244.99/51.49    (1)  all_58_5 = e3
% 244.99/51.49    (2)  all_58_5 = e1
% 244.99/51.49    (3)   ~ (e3 = e1)
% 244.99/51.49  
% 244.99/51.49  Begin of proof
% 244.99/51.49  | 
% 244.99/51.49  | COMBINE_EQS: (1), (2) imply:
% 244.99/51.49  |   (4)  e3 = e1
% 244.99/51.49  | 
% 244.99/51.49  | SIMP: (4) implies:
% 244.99/51.49  |   (5)  e3 = e1
% 244.99/51.49  | 
% 244.99/51.49  | REDUCE: (3), (5) imply:
% 244.99/51.49  |   (6)  $false
% 244.99/51.49  | 
% 244.99/51.49  | CLOSE: (6) is inconsistent.
% 244.99/51.49  | 
% 244.99/51.49  End of proof
% 244.99/51.49  
% 244.99/51.49  Sub-proof #2124 shows that the following formulas are inconsistent:
% 244.99/51.49  ----------------------------------------------------------------
% 244.99/51.49    (1)  all_58_2 = e3
% 244.99/51.49    (2)  all_58_2 = e0
% 244.99/51.49    (3)   ~ (e3 = e0)
% 244.99/51.49  
% 244.99/51.49  Begin of proof
% 244.99/51.49  | 
% 244.99/51.49  | COMBINE_EQS: (1), (2) imply:
% 244.99/51.49  |   (4)  e3 = e0
% 244.99/51.49  | 
% 244.99/51.49  | SIMP: (4) implies:
% 244.99/51.49  |   (5)  e3 = e0
% 244.99/51.49  | 
% 244.99/51.49  | REDUCE: (3), (5) imply:
% 244.99/51.49  |   (6)  $false
% 244.99/51.49  | 
% 244.99/51.49  | CLOSE: (6) is inconsistent.
% 244.99/51.49  | 
% 244.99/51.49  End of proof
% 244.99/51.49  
% 244.99/51.49  Sub-proof #2125 shows that the following formulas are inconsistent:
% 244.99/51.49  ----------------------------------------------------------------
% 244.99/51.49    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.49    (2)  op(e3, e0) = e3
% 244.99/51.49    (3)  op(e3, e0) = e2
% 244.99/51.49    (4)   ~ (e3 = e2)
% 244.99/51.49  
% 244.99/51.49  Begin of proof
% 244.99/51.49  | 
% 244.99/51.49  | GROUND_INST: instantiating (1) with e2, e3, e0, e3, simplifying with (2), (3)
% 244.99/51.49  |              gives:
% 244.99/51.49  |   (5)  e3 = e2
% 244.99/51.49  | 
% 244.99/51.49  | REDUCE: (4), (5) imply:
% 244.99/51.49  |   (6)  $false
% 244.99/51.49  | 
% 244.99/51.49  | CLOSE: (6) is inconsistent.
% 244.99/51.49  | 
% 244.99/51.49  End of proof
% 244.99/51.49  
% 244.99/51.49  Sub-proof #2126 shows that the following formulas are inconsistent:
% 244.99/51.49  ----------------------------------------------------------------
% 244.99/51.49    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 244.99/51.49           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 244.99/51.49             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 244.99/51.49           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 244.99/51.49             e1) = e3 & op(e1, e3) = e3)
% 244.99/51.49    (2)  all_56_31 = e1
% 244.99/51.49    (3)  op(e2, e3) = all_52_1
% 244.99/51.49    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.49    (5)   ~ (all_52_1 = e2)
% 244.99/51.49  
% 244.99/51.49  Begin of proof
% 244.99/51.49  | 
% 244.99/51.49  | BETA: splitting (1) gives:
% 244.99/51.49  | 
% 244.99/51.49  | Case 1:
% 244.99/51.49  | | 
% 244.99/51.49  | |   (6)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 244.99/51.49  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 244.99/51.49  | |        op(e2, e3) = e2
% 244.99/51.49  | | 
% 244.99/51.49  | | ALPHA: (6) implies:
% 244.99/51.49  | |   (7)  op(e2, e3) = e2
% 244.99/51.49  | | 
% 244.99/51.49  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #2336.
% 244.99/51.49  | | 
% 244.99/51.49  | Case 2:
% 244.99/51.49  | | 
% 244.99/51.49  | |   (8)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 244.99/51.49  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 244.99/51.49  | |        op(e1, e3) = e3
% 244.99/51.49  | | 
% 244.99/51.49  | | ALPHA: (8) implies:
% 244.99/51.49  | |   (9)   ~ (all_56_31 = e1)
% 244.99/51.49  | | 
% 244.99/51.49  | | REDUCE: (2), (9) imply:
% 244.99/51.49  | |   (10)  $false
% 244.99/51.49  | | 
% 244.99/51.49  | | CLOSE: (10) is inconsistent.
% 244.99/51.49  | | 
% 244.99/51.49  | End of split
% 244.99/51.49  | 
% 244.99/51.49  End of proof
% 244.99/51.49  
% 244.99/51.49  Sub-proof #2127 shows that the following formulas are inconsistent:
% 244.99/51.49  ----------------------------------------------------------------
% 244.99/51.49    (1)   ~ (e3 = e0)
% 244.99/51.49    (2)  op(e1, e2) = e1
% 244.99/51.49    (3)   ~ (e2 = e0)
% 244.99/51.49    (4)  op(e1, e2) = all_52_6
% 244.99/51.49    (5)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 244.99/51.49         (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 244.99/51.49    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.99/51.49         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.99/51.49    (7)   ~ (e3 = e1)
% 244.99/51.49    (8)  all_58_3 = e1
% 244.99/51.49    (9)   ~ (e3 = e2)
% 244.99/51.49    (10)  all_58_7 = e1
% 244.99/51.49    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.49    (12)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.99/51.49          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.99/51.49    (13)   ~ (e1 = e0)
% 244.99/51.49    (14)  op(e2, e2) = e2
% 244.99/51.49    (15)   ~ (e2 = e1)
% 244.99/51.49  
% 244.99/51.49  Begin of proof
% 244.99/51.49  | 
% 244.99/51.49  | BETA: splitting (5) gives:
% 244.99/51.49  | 
% 244.99/51.49  | Case 1:
% 244.99/51.49  | | 
% 244.99/51.49  | |   (16)  (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 244.99/51.49  | |           e2)
% 244.99/51.49  | | 
% 244.99/51.49  | | BETA: splitting (16) gives:
% 244.99/51.49  | | 
% 244.99/51.49  | | Case 1:
% 244.99/51.49  | | | 
% 244.99/51.49  | | |   (17)  all_58_1 = e2 & op(e3, e2) = e2
% 244.99/51.49  | | | 
% 244.99/51.49  | | | ALPHA: (17) implies:
% 244.99/51.49  | | |   (18)  all_58_1 = e2
% 244.99/51.49  | | | 
% 244.99/51.49  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13),
% 244.99/51.49  | | |            (14), (18) are inconsistent by sub-proof #2135.
% 244.99/51.49  | | | 
% 244.99/51.49  | | Case 2:
% 244.99/51.49  | | | 
% 244.99/51.49  | | |   (19)  all_58_3 = e2 & op(e2, e2) = e2
% 244.99/51.49  | | | 
% 244.99/51.49  | | | ALPHA: (19) implies:
% 244.99/51.49  | | |   (20)  all_58_3 = e2
% 244.99/51.49  | | | 
% 244.99/51.49  | | | COMBINE_EQS: (8), (20) imply:
% 244.99/51.49  | | |   (21)  e2 = e1
% 244.99/51.49  | | | 
% 244.99/51.49  | | | SIMP: (21) implies:
% 244.99/51.49  | | |   (22)  e2 = e1
% 244.99/51.49  | | | 
% 244.99/51.49  | | | REDUCE: (15), (22) imply:
% 244.99/51.49  | | |   (23)  $false
% 244.99/51.49  | | | 
% 244.99/51.49  | | | CLOSE: (23) is inconsistent.
% 244.99/51.49  | | | 
% 244.99/51.49  | | End of split
% 244.99/51.49  | | 
% 244.99/51.49  | Case 2:
% 244.99/51.49  | | 
% 244.99/51.49  | |   (24)  (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 244.99/51.49  | |           e2)
% 244.99/51.49  | | 
% 244.99/51.49  | | BETA: splitting (24) gives:
% 244.99/51.49  | | 
% 244.99/51.49  | | Case 1:
% 244.99/51.49  | | | 
% 244.99/51.49  | | |   (25)  all_58_7 = e2 & op(e1, e2) = e2
% 244.99/51.49  | | | 
% 244.99/51.49  | | | ALPHA: (25) implies:
% 244.99/51.49  | | |   (26)  all_58_7 = e2
% 244.99/51.49  | | | 
% 244.99/51.49  | | | REF_CLOSE: (10), (15), (26) are inconsistent by sub-proof #2134.
% 244.99/51.49  | | | 
% 244.99/51.49  | | Case 2:
% 244.99/51.49  | | | 
% 244.99/51.49  | | |   (27)  all_58_13 = e2 & op(e0, e2) = e2
% 244.99/51.49  | | | 
% 244.99/51.49  | | | ALPHA: (27) implies:
% 244.99/51.49  | | |   (28)  all_58_13 = e2
% 244.99/51.49  | | |   (29)  op(e0, e2) = e2
% 244.99/51.49  | | | 
% 244.99/51.49  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13),
% 244.99/51.49  | | |            (14), (28), (29) are inconsistent by sub-proof #2128.
% 244.99/51.49  | | | 
% 244.99/51.49  | | End of split
% 244.99/51.49  | | 
% 244.99/51.49  | End of split
% 244.99/51.49  | 
% 244.99/51.49  End of proof
% 244.99/51.49  
% 244.99/51.49  Sub-proof #2128 shows that the following formulas are inconsistent:
% 244.99/51.49  ----------------------------------------------------------------
% 244.99/51.49    (1)   ~ (e3 = e0)
% 244.99/51.49    (2)  op(e1, e2) = e1
% 244.99/51.49    (3)   ~ (e2 = e0)
% 244.99/51.49    (4)  op(e1, e2) = all_52_6
% 244.99/51.49    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 244.99/51.49         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 244.99/51.49    (6)  op(e0, e2) = e2
% 244.99/51.49    (7)   ~ (e3 = e1)
% 244.99/51.49    (8)   ~ (e3 = e2)
% 244.99/51.49    (9)  all_58_13 = e2
% 244.99/51.49    (10)  all_58_7 = e1
% 244.99/51.49    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 244.99/51.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 244.99/51.49    (12)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 244.99/51.49          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 244.99/51.49    (13)   ~ (e1 = e0)
% 244.99/51.49    (14)  op(e2, e2) = e2
% 244.99/51.49  
% 244.99/51.49  Begin of proof
% 244.99/51.49  | 
% 244.99/51.49  | BETA: splitting (12) gives:
% 244.99/51.49  | 
% 244.99/51.49  | Case 1:
% 244.99/51.49  | | 
% 244.99/51.49  | |   (15)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 244.99/51.49  | |           e3)
% 244.99/51.49  | | 
% 244.99/51.49  | | BETA: splitting (15) gives:
% 244.99/51.49  | | 
% 244.99/51.49  | | Case 1:
% 244.99/51.49  | | | 
% 244.99/51.49  | | |   (16)  all_58_1 = e3 & op(e3, e2) = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | ALPHA: (16) implies:
% 244.99/51.49  | | |   (17)  all_58_1 = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (11), (13), (14), (17) are
% 244.99/51.49  | | |            inconsistent by sub-proof #2130.
% 244.99/51.49  | | | 
% 244.99/51.49  | | Case 2:
% 244.99/51.49  | | | 
% 244.99/51.49  | | |   (18)  all_58_3 = e3 & op(e2, e2) = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | ALPHA: (18) implies:
% 244.99/51.49  | | |   (19)  op(e2, e2) = e3
% 244.99/51.49  | | | 
% 244.99/51.49  | | | REF_CLOSE: (8), (11), (14), (19) are inconsistent by sub-proof #2140.
% 244.99/51.49  | | | 
% 244.99/51.49  | | End of split
% 244.99/51.49  | | 
% 244.99/51.49  | Case 2:
% 244.99/51.49  | | 
% 245.06/51.49  | |   (20)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 245.06/51.49  | |           e3)
% 245.06/51.49  | | 
% 245.06/51.49  | | BETA: splitting (20) gives:
% 245.06/51.49  | | 
% 245.06/51.49  | | Case 1:
% 245.06/51.49  | | | 
% 245.06/51.49  | | |   (21)  all_58_7 = e3 & op(e1, e2) = e3
% 245.06/51.49  | | | 
% 245.06/51.49  | | | REF_CLOSE: (7), (10), (21) are inconsistent by sub-proof #2138.
% 245.06/51.49  | | | 
% 245.06/51.49  | | Case 2:
% 245.06/51.49  | | | 
% 245.06/51.49  | | |   (22)  all_58_13 = e3 & op(e0, e2) = e3
% 245.06/51.49  | | | 
% 245.06/51.49  | | | ALPHA: (22) implies:
% 245.06/51.49  | | |   (23)  all_58_13 = e3
% 245.06/51.49  | | | 
% 245.06/51.49  | | | REF_CLOSE: (8), (9), (23) are inconsistent by sub-proof #2129.
% 245.06/51.49  | | | 
% 245.06/51.49  | | End of split
% 245.06/51.49  | | 
% 245.06/51.49  | End of split
% 245.06/51.49  | 
% 245.06/51.49  End of proof
% 245.06/51.49  
% 245.06/51.49  Sub-proof #2129 shows that the following formulas are inconsistent:
% 245.06/51.49  ----------------------------------------------------------------
% 245.06/51.49    (1)  all_58_13 = e3
% 245.06/51.49    (2)  all_58_13 = e2
% 245.06/51.49    (3)   ~ (e3 = e2)
% 245.06/51.49  
% 245.06/51.49  Begin of proof
% 245.06/51.49  | 
% 245.06/51.49  | COMBINE_EQS: (1), (2) imply:
% 245.06/51.49  |   (4)  e3 = e2
% 245.06/51.49  | 
% 245.06/51.49  | SIMP: (4) implies:
% 245.06/51.49  |   (5)  e3 = e2
% 245.06/51.49  | 
% 245.06/51.49  | REDUCE: (3), (5) imply:
% 245.06/51.49  |   (6)  $false
% 245.06/51.49  | 
% 245.06/51.49  | CLOSE: (6) is inconsistent.
% 245.06/51.49  | 
% 245.06/51.49  End of proof
% 245.06/51.49  
% 245.06/51.49  Sub-proof #2130 shows that the following formulas are inconsistent:
% 245.06/51.49  ----------------------------------------------------------------
% 245.06/51.49    (1)   ~ (e3 = e0)
% 245.06/51.49    (2)  all_58_1 = e3
% 245.06/51.49    (3)  op(e1, e2) = e1
% 245.06/51.49    (4)   ~ (e2 = e0)
% 245.06/51.49    (5)  op(e1, e2) = all_52_6
% 245.06/51.49    (6)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 245.06/51.49         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 245.06/51.49    (7)  op(e0, e2) = e2
% 245.06/51.49    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.49    (9)   ~ (e1 = e0)
% 245.06/51.49    (10)  op(e2, e2) = e2
% 245.06/51.49  
% 245.06/51.49  Begin of proof
% 245.06/51.49  | 
% 245.06/51.49  | BETA: splitting (6) gives:
% 245.06/51.49  | 
% 245.06/51.49  | Case 1:
% 245.06/51.49  | | 
% 245.06/51.49  | |   (11)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 245.06/51.49  | |           e0)
% 245.06/51.49  | | 
% 245.06/51.49  | | BETA: splitting (11) gives:
% 245.06/51.49  | | 
% 245.06/51.49  | | Case 1:
% 245.06/51.49  | | | 
% 245.06/51.49  | | |   (12)  all_58_1 = e0 & op(e3, e2) = e0
% 245.06/51.49  | | | 
% 245.06/51.49  | | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #2133.
% 245.06/51.49  | | | 
% 245.06/51.49  | | Case 2:
% 245.06/51.49  | | | 
% 245.06/51.49  | | |   (13)  all_58_3 = e0 & op(e2, e2) = e0
% 245.06/51.49  | | | 
% 245.06/51.49  | | | ALPHA: (13) implies:
% 245.06/51.49  | | |   (14)  op(e2, e2) = e0
% 245.06/51.49  | | | 
% 245.06/51.49  | | | REF_CLOSE: (4), (8), (10), (14) are inconsistent by sub-proof #2137.
% 245.06/51.49  | | | 
% 245.06/51.49  | | End of split
% 245.06/51.49  | | 
% 245.06/51.49  | Case 2:
% 245.06/51.49  | | 
% 245.06/51.49  | |   (15)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 245.06/51.49  | |           e0)
% 245.06/51.49  | | 
% 245.06/51.49  | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (15) are inconsistent by sub-proof
% 245.06/51.49  | |            #2131.
% 245.06/51.49  | | 
% 245.06/51.49  | End of split
% 245.06/51.49  | 
% 245.06/51.49  End of proof
% 245.06/51.49  
% 245.06/51.49  Sub-proof #2131 shows that the following formulas are inconsistent:
% 245.06/51.49  ----------------------------------------------------------------
% 245.06/51.49    (1)  op(e1, e2) = e1
% 245.06/51.49    (2)   ~ (e2 = e0)
% 245.06/51.49    (3)  op(e1, e2) = all_52_6
% 245.06/51.49    (4)  op(e0, e2) = e2
% 245.06/51.49    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.49    (6)   ~ (e1 = e0)
% 245.06/51.49    (7)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 245.06/51.49  
% 245.06/51.49  Begin of proof
% 245.06/51.49  | 
% 245.06/51.49  | BETA: splitting (7) gives:
% 245.06/51.49  | 
% 245.06/51.49  | Case 1:
% 245.06/51.49  | | 
% 245.06/51.49  | |   (8)  all_58_7 = e0 & op(e1, e2) = e0
% 245.06/51.49  | | 
% 245.06/51.49  | | ALPHA: (8) implies:
% 245.06/51.49  | |   (9)  op(e1, e2) = e0
% 245.06/51.49  | | 
% 245.06/51.49  | | REF_CLOSE: (1), (3), (5), (6), (9) are inconsistent by sub-proof #2136.
% 245.06/51.49  | | 
% 245.06/51.49  | Case 2:
% 245.06/51.49  | | 
% 245.06/51.50  | |   (10)  all_58_13 = e0 & op(e0, e2) = e0
% 245.06/51.50  | | 
% 245.06/51.50  | | ALPHA: (10) implies:
% 245.06/51.50  | |   (11)  op(e0, e2) = e0
% 245.06/51.50  | | 
% 245.06/51.50  | | REF_CLOSE: (2), (4), (5), (11) are inconsistent by sub-proof #2132.
% 245.06/51.50  | | 
% 245.06/51.50  | End of split
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2132 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.50    (2)  op(e0, e2) = e2
% 245.06/51.50    (3)  op(e0, e2) = e0
% 245.06/51.50    (4)   ~ (e2 = e0)
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | GROUND_INST: instantiating (1) with e0, e2, e2, e0, simplifying with (2), (3)
% 245.06/51.50  |              gives:
% 245.06/51.50  |   (5)  e2 = e0
% 245.06/51.50  | 
% 245.06/51.50  | REDUCE: (4), (5) imply:
% 245.06/51.50  |   (6)  $false
% 245.06/51.50  | 
% 245.06/51.50  | CLOSE: (6) is inconsistent.
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2133 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)  all_58_1 = e0 & op(e3, e2) = e0
% 245.06/51.50    (2)  all_58_1 = e3
% 245.06/51.50    (3)   ~ (e3 = e0)
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | ALPHA: (1) implies:
% 245.06/51.50  |   (4)  all_58_1 = e0
% 245.06/51.50  | 
% 245.06/51.50  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.50  |   (5)  e3 = e0
% 245.06/51.50  | 
% 245.06/51.50  | REDUCE: (3), (5) imply:
% 245.06/51.50  |   (6)  $false
% 245.06/51.50  | 
% 245.06/51.50  | CLOSE: (6) is inconsistent.
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2134 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)  all_58_7 = e2
% 245.06/51.50    (2)  all_58_7 = e1
% 245.06/51.50    (3)   ~ (e2 = e1)
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | COMBINE_EQS: (1), (2) imply:
% 245.06/51.50  |   (4)  e2 = e1
% 245.06/51.50  | 
% 245.06/51.50  | SIMP: (4) implies:
% 245.06/51.50  |   (5)  e2 = e1
% 245.06/51.50  | 
% 245.06/51.50  | REDUCE: (3), (5) imply:
% 245.06/51.50  |   (6)  $false
% 245.06/51.50  | 
% 245.06/51.50  | CLOSE: (6) is inconsistent.
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2135 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)   ~ (e3 = e0)
% 245.06/51.50    (2)  op(e1, e2) = e1
% 245.06/51.50    (3)   ~ (e2 = e0)
% 245.06/51.50    (4)  op(e1, e2) = all_52_6
% 245.06/51.50    (5)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 245.06/51.50         (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 245.06/51.50    (6)   ~ (e3 = e1)
% 245.06/51.50    (7)   ~ (e3 = e2)
% 245.06/51.50    (8)  all_58_7 = e1
% 245.06/51.50    (9)  all_58_1 = e2
% 245.06/51.50    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.50    (11)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 245.06/51.50          (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 245.06/51.50    (12)   ~ (e1 = e0)
% 245.06/51.50    (13)  op(e2, e2) = e2
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | BETA: splitting (11) gives:
% 245.06/51.50  | 
% 245.06/51.50  | Case 1:
% 245.06/51.50  | | 
% 245.06/51.50  | |   (14)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 245.06/51.50  | |           e3)
% 245.06/51.50  | | 
% 245.06/51.50  | | REF_CLOSE: (7), (9), (10), (13), (14) are inconsistent by sub-proof #2139.
% 245.06/51.50  | | 
% 245.06/51.50  | Case 2:
% 245.06/51.50  | | 
% 245.06/51.50  | |   (15)  (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 245.06/51.50  | |           e3)
% 245.06/51.50  | | 
% 245.06/51.50  | | BETA: splitting (15) gives:
% 245.06/51.50  | | 
% 245.06/51.50  | | Case 1:
% 245.06/51.50  | | | 
% 245.06/51.50  | | |   (16)  all_58_7 = e3 & op(e1, e2) = e3
% 245.06/51.50  | | | 
% 245.06/51.50  | | | REF_CLOSE: (6), (8), (16) are inconsistent by sub-proof #2138.
% 245.06/51.50  | | | 
% 245.06/51.50  | | Case 2:
% 245.06/51.50  | | | 
% 245.06/51.50  | | |   (17)  all_58_13 = e3 & op(e0, e2) = e3
% 245.06/51.50  | | | 
% 245.06/51.50  | | | ALPHA: (17) implies:
% 245.06/51.50  | | |   (18)  all_58_13 = e3
% 245.06/51.50  | | | 
% 245.06/51.50  | | | BETA: splitting (5) gives:
% 245.06/51.50  | | | 
% 245.06/51.50  | | | Case 1:
% 245.06/51.50  | | | | 
% 245.06/51.50  | | | |   (19)  (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2)
% 245.06/51.50  | | | |           = e0)
% 245.06/51.50  | | | | 
% 245.06/51.50  | | | | BETA: splitting (19) gives:
% 245.06/51.50  | | | | 
% 245.06/51.50  | | | | Case 1:
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | |   (20)  all_58_1 = e0 & op(e3, e2) = e0
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | | REF_CLOSE: (3), (9), (20) are inconsistent by sub-proof #2187.
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | Case 2:
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | |   (21)  all_58_3 = e0 & op(e2, e2) = e0
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | | ALPHA: (21) implies:
% 245.06/51.50  | | | | |   (22)  op(e2, e2) = e0
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | | REF_CLOSE: (3), (10), (13), (22) are inconsistent by sub-proof #2137.
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | End of split
% 245.06/51.50  | | | | 
% 245.06/51.50  | | | Case 2:
% 245.06/51.50  | | | | 
% 245.06/51.50  | | | |   (23)  (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2)
% 245.06/51.50  | | | |           = e0)
% 245.06/51.50  | | | | 
% 245.06/51.50  | | | | BETA: splitting (23) gives:
% 245.06/51.50  | | | | 
% 245.06/51.50  | | | | Case 1:
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | |   (24)  all_58_7 = e0 & op(e1, e2) = e0
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | | ALPHA: (24) implies:
% 245.06/51.50  | | | | |   (25)  op(e1, e2) = e0
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | | REF_CLOSE: (2), (4), (10), (12), (25) are inconsistent by sub-proof
% 245.06/51.50  | | | | |            #2136.
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | Case 2:
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | |   (26)  all_58_13 = e0 & op(e0, e2) = e0
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | | ALPHA: (26) implies:
% 245.06/51.50  | | | | |   (27)  all_58_13 = e0
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | | COMBINE_EQS: (18), (27) imply:
% 245.06/51.50  | | | | |   (28)  e3 = e0
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | | SIMP: (28) implies:
% 245.06/51.50  | | | | |   (29)  e3 = e0
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | | REDUCE: (1), (29) imply:
% 245.06/51.50  | | | | |   (30)  $false
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | | CLOSE: (30) is inconsistent.
% 245.06/51.50  | | | | | 
% 245.06/51.50  | | | | End of split
% 245.06/51.50  | | | | 
% 245.06/51.50  | | | End of split
% 245.06/51.50  | | | 
% 245.06/51.50  | | End of split
% 245.06/51.50  | | 
% 245.06/51.50  | End of split
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2136 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)  op(e1, e2) = e1
% 245.06/51.50    (2)  op(e1, e2) = all_52_6
% 245.06/51.50    (3)  op(e1, e2) = e0
% 245.06/51.50    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.50    (5)   ~ (e1 = e0)
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | GROUND_INST: instantiating (4) with all_52_6, e0, e2, e1, simplifying with
% 245.06/51.50  |              (2), (3) gives:
% 245.06/51.50  |   (6)  all_52_6 = e0
% 245.06/51.50  | 
% 245.06/51.50  | GROUND_INST: instantiating (4) with all_52_6, e1, e2, e1, simplifying with
% 245.06/51.50  |              (1), (2) gives:
% 245.06/51.50  |   (7)  all_52_6 = e1
% 245.06/51.50  | 
% 245.06/51.50  | COMBINE_EQS: (6), (7) imply:
% 245.06/51.50  |   (8)  e1 = e0
% 245.06/51.50  | 
% 245.06/51.50  | SIMP: (8) implies:
% 245.06/51.50  |   (9)  e1 = e0
% 245.06/51.50  | 
% 245.06/51.50  | REDUCE: (5), (9) imply:
% 245.06/51.50  |   (10)  $false
% 245.06/51.50  | 
% 245.06/51.50  | CLOSE: (10) is inconsistent.
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2137 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.50    (2)  op(e2, e2) = e2
% 245.06/51.50    (3)  op(e2, e2) = e0
% 245.06/51.50    (4)   ~ (e2 = e0)
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | GROUND_INST: instantiating (1) with e0, e2, e2, e2, simplifying with (2), (3)
% 245.06/51.50  |              gives:
% 245.06/51.50  |   (5)  e2 = e0
% 245.06/51.50  | 
% 245.06/51.50  | REDUCE: (4), (5) imply:
% 245.06/51.50  |   (6)  $false
% 245.06/51.50  | 
% 245.06/51.50  | CLOSE: (6) is inconsistent.
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2138 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)  all_58_7 = e3 & op(e1, e2) = e3
% 245.06/51.50    (2)  all_58_7 = e1
% 245.06/51.50    (3)   ~ (e3 = e1)
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | ALPHA: (1) implies:
% 245.06/51.50  |   (4)  all_58_7 = e3
% 245.06/51.50  | 
% 245.06/51.50  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.50  |   (5)  e3 = e1
% 245.06/51.50  | 
% 245.06/51.50  | SIMP: (5) implies:
% 245.06/51.50  |   (6)  e3 = e1
% 245.06/51.50  | 
% 245.06/51.50  | REDUCE: (3), (6) imply:
% 245.06/51.50  |   (7)  $false
% 245.06/51.50  | 
% 245.06/51.50  | CLOSE: (7) is inconsistent.
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2139 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)  (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 245.06/51.50    (2)   ~ (e3 = e2)
% 245.06/51.50    (3)  all_58_1 = e2
% 245.06/51.50    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.50    (5)  op(e2, e2) = e2
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | BETA: splitting (1) gives:
% 245.06/51.50  | 
% 245.06/51.50  | Case 1:
% 245.06/51.50  | | 
% 245.06/51.50  | |   (6)  all_58_1 = e3 & op(e3, e2) = e3
% 245.06/51.50  | | 
% 245.06/51.50  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #2141.
% 245.06/51.50  | | 
% 245.06/51.50  | Case 2:
% 245.06/51.50  | | 
% 245.06/51.50  | |   (7)  all_58_3 = e3 & op(e2, e2) = e3
% 245.06/51.50  | | 
% 245.06/51.50  | | ALPHA: (7) implies:
% 245.06/51.50  | |   (8)  op(e2, e2) = e3
% 245.06/51.50  | | 
% 245.06/51.50  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2140.
% 245.06/51.50  | | 
% 245.06/51.50  | End of split
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2140 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.50    (2)  op(e2, e2) = e3
% 245.06/51.50    (3)  op(e2, e2) = e2
% 245.06/51.50    (4)   ~ (e3 = e2)
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | GROUND_INST: instantiating (1) with e3, e2, e2, e2, simplifying with (2), (3)
% 245.06/51.50  |              gives:
% 245.06/51.50  |   (5)  e3 = e2
% 245.06/51.50  | 
% 245.06/51.50  | REDUCE: (4), (5) imply:
% 245.06/51.50  |   (6)  $false
% 245.06/51.50  | 
% 245.06/51.50  | CLOSE: (6) is inconsistent.
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2141 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)  all_58_1 = e3 & op(e3, e2) = e3
% 245.06/51.50    (2)  all_58_1 = e2
% 245.06/51.50    (3)   ~ (e3 = e2)
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | ALPHA: (1) implies:
% 245.06/51.50  |   (4)  all_58_1 = e3
% 245.06/51.50  | 
% 245.06/51.50  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.50  |   (5)  e3 = e2
% 245.06/51.50  | 
% 245.06/51.50  | SIMP: (5) implies:
% 245.06/51.50  |   (6)  e3 = e2
% 245.06/51.50  | 
% 245.06/51.50  | REDUCE: (3), (6) imply:
% 245.06/51.50  |   (7)  $false
% 245.06/51.50  | 
% 245.06/51.50  | CLOSE: (7) is inconsistent.
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2142 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)  (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 245.06/51.50    (2)  op(e3, e2) = all_52_4
% 245.06/51.50    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.50    (4)   ~ (all_52_4 = e1)
% 245.06/51.50    (5)  op(e2, e2) = e2
% 245.06/51.50    (6)   ~ (e2 = e1)
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | BETA: splitting (1) gives:
% 245.06/51.50  | 
% 245.06/51.50  | Case 1:
% 245.06/51.50  | | 
% 245.06/51.50  | |   (7)  all_58_1 = e1 & op(e3, e2) = e1
% 245.06/51.50  | | 
% 245.06/51.50  | | ALPHA: (7) implies:
% 245.06/51.50  | |   (8)  op(e3, e2) = e1
% 245.06/51.50  | | 
% 245.06/51.50  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2228.
% 245.06/51.50  | | 
% 245.06/51.50  | Case 2:
% 245.06/51.50  | | 
% 245.06/51.50  | |   (9)  all_58_3 = e1 & op(e2, e2) = e1
% 245.06/51.50  | | 
% 245.06/51.50  | | ALPHA: (9) implies:
% 245.06/51.50  | |   (10)  op(e2, e2) = e1
% 245.06/51.50  | | 
% 245.06/51.50  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #2235.
% 245.06/51.50  | | 
% 245.06/51.50  | End of split
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2143 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)  all_56_24 = e3 & op(e3, all_56_25) = e3 & op(e3, e0) = all_56_25 &
% 245.06/51.50         $i(all_56_25)
% 245.06/51.50    (2)  op(e1, e2) = e3
% 245.06/51.50    (3)   ~ (e3 = e2)
% 245.06/51.50    (4)  op(e3, e0) = e3
% 245.06/51.50    (5)  op(e3, e3) = e2
% 245.06/51.50    (6)  ( ~ (all_40_0 = e0) & op(all_40_1, e1) = all_40_0 & op(e1, e2) = all_40_1
% 245.06/51.50           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e1, e2) =
% 245.06/51.50           all_40_1 & $i(all_40_1))
% 245.06/51.50    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.50    (8)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) = all_36_1
% 245.06/51.50           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2) =
% 245.06/51.50           all_36_1 & $i(all_36_1))
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | ALPHA: (1) implies:
% 245.06/51.50  |   (9)  op(e3, e0) = all_56_25
% 245.06/51.50  |   (10)  op(e3, all_56_25) = e3
% 245.06/51.50  | 
% 245.06/51.50  | BETA: splitting (6) gives:
% 245.06/51.50  | 
% 245.06/51.50  | Case 1:
% 245.06/51.50  | | 
% 245.06/51.50  | | 
% 245.06/51.50  | | GROUND_INST: instantiating (7) with e3, all_56_25, e0, e3, simplifying with
% 245.06/51.50  | |              (4), (9) gives:
% 245.06/51.50  | |   (11)  all_56_25 = e3
% 245.06/51.50  | | 
% 245.06/51.50  | | REDUCE: (10), (11) imply:
% 245.06/51.50  | |   (12)  op(e3, e3) = e3
% 245.06/51.50  | | 
% 245.06/51.50  | | REF_CLOSE: (3), (5), (7), (12) are inconsistent by sub-proof #2194.
% 245.06/51.50  | | 
% 245.06/51.50  | Case 2:
% 245.06/51.50  | | 
% 245.06/51.50  | |   (13)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 245.06/51.50  | | 
% 245.06/51.50  | | REF_CLOSE: (2), (7), (8), (13) are inconsistent by sub-proof #2144.
% 245.06/51.50  | | 
% 245.06/51.50  | End of split
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2144 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)   ~ (all_40_1 = e3) & op(e1, e2) = all_40_1 & $i(all_40_1)
% 245.06/51.50    (2)  op(e1, e2) = e3
% 245.06/51.50    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.50    (4)  ( ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) = all_36_1
% 245.06/51.50           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e1, e2) =
% 245.06/51.50           all_36_1 & $i(all_36_1))
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | ALPHA: (1) implies:
% 245.06/51.50  |   (5)   ~ (all_40_1 = e3)
% 245.06/51.50  |   (6)  op(e1, e2) = all_40_1
% 245.06/51.50  | 
% 245.06/51.50  | BETA: splitting (4) gives:
% 245.06/51.50  | 
% 245.06/51.50  | Case 1:
% 245.06/51.50  | | 
% 245.06/51.50  | |   (7)   ~ (all_36_0 = e3) & op(all_36_1, e1) = all_36_0 & op(e1, e2) =
% 245.06/51.50  | |        all_36_1 & $i(all_36_0) & $i(all_36_1)
% 245.06/51.50  | | 
% 245.06/51.50  | | ALPHA: (7) implies:
% 245.06/51.50  | |   (8)  op(e1, e2) = all_36_1
% 245.06/51.50  | | 
% 245.06/51.50  | | REF_CLOSE: (2), (3), (5), (6), (8) are inconsistent by sub-proof #2145.
% 245.06/51.50  | | 
% 245.06/51.50  | Case 2:
% 245.06/51.50  | | 
% 245.06/51.50  | |   (9)   ~ (all_36_1 = e0) & op(e1, e2) = all_36_1 & $i(all_36_1)
% 245.06/51.50  | | 
% 245.06/51.50  | | ALPHA: (9) implies:
% 245.06/51.50  | |   (10)  op(e1, e2) = all_36_1
% 245.06/51.50  | | 
% 245.06/51.50  | | REF_CLOSE: (2), (3), (5), (6), (10) are inconsistent by sub-proof #2145.
% 245.06/51.50  | | 
% 245.06/51.50  | End of split
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2145 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)   ~ (all_40_1 = e3)
% 245.06/51.50    (2)  op(e1, e2) = e3
% 245.06/51.50    (3)  op(e1, e2) = all_36_1
% 245.06/51.50    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.50    (5)  op(e1, e2) = all_40_1
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | GROUND_INST: instantiating (4) with all_36_1, all_40_1, e2, e1, simplifying
% 245.06/51.50  |              with (3), (5) gives:
% 245.06/51.50  |   (6)  all_40_1 = all_36_1
% 245.06/51.50  | 
% 245.06/51.50  | GROUND_INST: instantiating (4) with e3, all_40_1, e2, e1, simplifying with
% 245.06/51.50  |              (2), (5) gives:
% 245.06/51.50  |   (7)  all_40_1 = e3
% 245.06/51.50  | 
% 245.06/51.50  | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #2146.
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2146 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)  all_40_1 = e3
% 245.06/51.50    (2)  all_40_1 = all_36_1
% 245.06/51.50    (3)   ~ (all_40_1 = e3)
% 245.06/51.50  
% 245.06/51.50  Begin of proof
% 245.06/51.50  | 
% 245.06/51.50  | COMBINE_EQS: (1), (2) imply:
% 245.06/51.50  |   (4)  all_36_1 = e3
% 245.06/51.50  | 
% 245.06/51.50  | REDUCE: (1), (3) imply:
% 245.06/51.50  |   (5)  $false
% 245.06/51.50  | 
% 245.06/51.50  | CLOSE: (5) is inconsistent.
% 245.06/51.50  | 
% 245.06/51.50  End of proof
% 245.06/51.50  
% 245.06/51.50  Sub-proof #2147 shows that the following formulas are inconsistent:
% 245.06/51.50  ----------------------------------------------------------------
% 245.06/51.50    (1)   ~ (e3 = e0)
% 245.06/51.50    (2)  all_58_7 = e0
% 245.06/51.50    (3)  op(e1, e0) = all_52_14
% 245.06/51.50    (4)   ~ (e3 = e1)
% 245.06/51.50    (5)   ~ (e3 = e2)
% 245.06/51.50    (6)  op(e1, e3) = e1
% 245.06/51.51    (7)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 245.06/51.51         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 245.06/51.51    (8)   ~ (all_52_14 = e3)
% 245.06/51.51    (9)  op(e1, e1) = e2
% 245.06/51.51    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | BETA: splitting (7) gives:
% 245.06/51.51  | 
% 245.06/51.51  | Case 1:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (11)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 245.06/51.51  | |           e3)
% 245.06/51.51  | | 
% 245.06/51.51  | | BETA: splitting (11) gives:
% 245.06/51.51  | | 
% 245.06/51.51  | | Case 1:
% 245.06/51.51  | | | 
% 245.06/51.51  | | |   (12)  all_58_6 = e3 & op(e1, e3) = e3
% 245.06/51.51  | | | 
% 245.06/51.51  | | | ALPHA: (12) implies:
% 245.06/51.51  | | |   (13)  op(e1, e3) = e3
% 245.06/51.51  | | | 
% 245.06/51.51  | | | REF_CLOSE: (4), (6), (10), (13) are inconsistent by sub-proof #2225.
% 245.06/51.51  | | | 
% 245.06/51.51  | | Case 2:
% 245.06/51.51  | | | 
% 245.06/51.51  | | |   (14)  all_58_7 = e3 & op(e1, e2) = e3
% 245.06/51.51  | | | 
% 245.06/51.51  | | | REF_CLOSE: (1), (2), (14) are inconsistent by sub-proof #2150.
% 245.06/51.51  | | | 
% 245.06/51.51  | | End of split
% 245.06/51.51  | | 
% 245.06/51.51  | Case 2:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (15)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 245.06/51.51  | |           e3)
% 245.06/51.51  | | 
% 245.06/51.51  | | REF_CLOSE: (3), (5), (8), (9), (10), (15) are inconsistent by sub-proof
% 245.06/51.51  | |            #2148.
% 245.06/51.51  | | 
% 245.06/51.51  | End of split
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2148 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)  op(e1, e0) = all_52_14
% 245.06/51.51    (2)   ~ (e3 = e2)
% 245.06/51.51    (3)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 245.06/51.51    (4)   ~ (all_52_14 = e3)
% 245.06/51.51    (5)  op(e1, e1) = e2
% 245.06/51.51    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | BETA: splitting (3) gives:
% 245.06/51.51  | 
% 245.06/51.51  | Case 1:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (7)  all_58_8 = e3 & op(e1, e1) = e3
% 245.06/51.51  | | 
% 245.06/51.51  | | ALPHA: (7) implies:
% 245.06/51.51  | |   (8)  op(e1, e1) = e3
% 245.06/51.51  | | 
% 245.06/51.51  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2206.
% 245.06/51.51  | | 
% 245.06/51.51  | Case 2:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (9)  all_58_11 = e3 & op(e1, e0) = e3
% 245.06/51.51  | | 
% 245.06/51.51  | | ALPHA: (9) implies:
% 245.06/51.51  | |   (10)  op(e1, e0) = e3
% 245.06/51.51  | | 
% 245.06/51.51  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #2149.
% 245.06/51.51  | | 
% 245.06/51.51  | End of split
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2149 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51    (2)  op(e1, e0) = all_52_14
% 245.06/51.51    (3)  op(e1, e0) = e3
% 245.06/51.51    (4)   ~ (all_52_14 = e3)
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | GROUND_INST: instantiating (1) with all_52_14, e3, e0, e1, simplifying with
% 245.06/51.51  |              (2), (3) gives:
% 245.06/51.51  |   (5)  all_52_14 = e3
% 245.06/51.51  | 
% 245.06/51.51  | REDUCE: (4), (5) imply:
% 245.06/51.51  |   (6)  $false
% 245.06/51.51  | 
% 245.06/51.51  | CLOSE: (6) is inconsistent.
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2150 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)  all_58_7 = e3 & op(e1, e2) = e3
% 245.06/51.51    (2)  all_58_7 = e0
% 245.06/51.51    (3)   ~ (e3 = e0)
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | ALPHA: (1) implies:
% 245.06/51.51  |   (4)  all_58_7 = e3
% 245.06/51.51  | 
% 245.06/51.51  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.51  |   (5)  e3 = e0
% 245.06/51.51  | 
% 245.06/51.51  | REDUCE: (3), (5) imply:
% 245.06/51.51  |   (6)  $false
% 245.06/51.51  | 
% 245.06/51.51  | CLOSE: (6) is inconsistent.
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2151 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)  all_56_21 = e2
% 245.06/51.51    (2)  op(e1, e0) = all_52_14
% 245.06/51.51    (3)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.06/51.51             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 245.06/51.51           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 245.06/51.51             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 245.06/51.51           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 245.06/51.51           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.06/51.51           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.06/51.51    (4)   ~ (all_52_14 = e1)
% 245.06/51.51    (5)  all_56_31 = e1
% 245.06/51.51    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | BETA: splitting (3) gives:
% 245.06/51.51  | 
% 245.06/51.51  | Case 1:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (7)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 245.06/51.51  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 245.06/51.51  | |        & op(e0, e2) = e0
% 245.06/51.51  | | 
% 245.06/51.51  | | ALPHA: (7) implies:
% 245.06/51.51  | |   (8)   ~ (all_56_21 = e2)
% 245.06/51.51  | | 
% 245.06/51.51  | | REDUCE: (1), (8) imply:
% 245.06/51.51  | |   (9)  $false
% 245.06/51.51  | | 
% 245.06/51.51  | | CLOSE: (9) is inconsistent.
% 245.06/51.51  | | 
% 245.06/51.51  | Case 2:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.06/51.51  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.06/51.51  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 245.06/51.51  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 245.06/51.51  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.06/51.51  | | 
% 245.06/51.51  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #2269.
% 245.06/51.51  | | 
% 245.06/51.51  | End of split
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2152 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51    (2)  op(e2, e0) = e3
% 245.06/51.51    (3)  op(e2, e0) = e2
% 245.06/51.51    (4)   ~ (e3 = e2)
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | GROUND_INST: instantiating (1) with e3, e2, e0, e2, simplifying with (2), (3)
% 245.06/51.51  |              gives:
% 245.06/51.51  |   (5)  e3 = e2
% 245.06/51.51  | 
% 245.06/51.51  | REDUCE: (4), (5) imply:
% 245.06/51.51  |   (6)  $false
% 245.06/51.51  | 
% 245.06/51.51  | CLOSE: (6) is inconsistent.
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2153 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)  all_54_3 = e1 | all_54_3 = e0
% 245.06/51.51    (2)   ~ (all_52_12 = e1)
% 245.06/51.51    (3)  op(e3, e0) = all_52_12
% 245.06/51.51    (4)  op(e3, e0) = e2
% 245.06/51.51    (5)   ~ (all_52_12 = e2)
% 245.06/51.51    (6)  all_54_3 = all_52_12
% 245.06/51.51    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | BETA: splitting (1) gives:
% 245.06/51.51  | 
% 245.06/51.51  | Case 1:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (8)  all_54_3 = e1
% 245.06/51.51  | | 
% 245.06/51.51  | | REF_CLOSE: (2), (6), (8) are inconsistent by sub-proof #2289.
% 245.06/51.51  | | 
% 245.06/51.51  | Case 2:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (9)  all_54_3 = e0
% 245.06/51.51  | | 
% 245.06/51.51  | | COMBINE_EQS: (6), (9) imply:
% 245.06/51.51  | |   (10)  all_52_12 = e0
% 245.06/51.51  | | 
% 245.06/51.51  | | SIMP: (10) implies:
% 245.06/51.51  | |   (11)  all_52_12 = e0
% 245.06/51.51  | | 
% 245.06/51.51  | | REDUCE: (5), (11) imply:
% 245.06/51.51  | |   (12)   ~ (e2 = e0)
% 245.06/51.51  | | 
% 245.06/51.51  | | SIMP: (12) implies:
% 245.06/51.51  | |   (13)   ~ (e2 = e0)
% 245.06/51.51  | | 
% 245.06/51.51  | | REDUCE: (3), (11) imply:
% 245.06/51.51  | |   (14)  op(e3, e0) = e0
% 245.06/51.51  | | 
% 245.06/51.51  | | REF_CLOSE: (4), (7), (13), (14) are inconsistent by sub-proof #2154.
% 245.06/51.51  | | 
% 245.06/51.51  | End of split
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2154 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51    (2)  op(e3, e0) = e2
% 245.06/51.51    (3)  op(e3, e0) = e0
% 245.06/51.51    (4)   ~ (e2 = e0)
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | GROUND_INST: instantiating (1) with e2, e0, e0, e3, simplifying with (2), (3)
% 245.06/51.51  |              gives:
% 245.06/51.51  |   (5)  e2 = e0
% 245.06/51.51  | 
% 245.06/51.51  | REDUCE: (4), (5) imply:
% 245.06/51.51  |   (6)  $false
% 245.06/51.51  | 
% 245.06/51.51  | CLOSE: (6) is inconsistent.
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2155 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)   ~ (e3 = e0)
% 245.06/51.51    (2)   ~ (e2 = e0)
% 245.06/51.51    (3)  all_58_5 = e3
% 245.06/51.51    (4)  all_58_4 = e2
% 245.06/51.51    (5)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 245.06/51.51         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 245.06/51.51    (6)   ~ (e3 = e1)
% 245.06/51.51    (7)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 245.06/51.51         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 245.06/51.51    (8)  op(e2, e1) = all_52_9
% 245.06/51.51    (9)   ~ (e3 = e2)
% 245.06/51.51    (10)  op(e1, e1) = e2
% 245.06/51.51    (11)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 245.06/51.51          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 245.06/51.51    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51    (13)   ~ (e1 = e0)
% 245.06/51.51    (14)   ~ (e2 = e1)
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | BETA: splitting (7) gives:
% 245.06/51.51  | 
% 245.06/51.51  | Case 1:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (15)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 245.06/51.51  | |           e0)
% 245.06/51.51  | | 
% 245.06/51.51  | | BETA: splitting (15) gives:
% 245.06/51.51  | | 
% 245.06/51.51  | | Case 1:
% 245.06/51.51  | | | 
% 245.06/51.51  | | |   (16)  all_58_4 = e0 & op(e3, e1) = e0
% 245.06/51.51  | | | 
% 245.06/51.51  | | | REF_CLOSE: (2), (4), (16) are inconsistent by sub-proof #2170.
% 245.06/51.51  | | | 
% 245.06/51.51  | | Case 2:
% 245.06/51.51  | | | 
% 245.06/51.51  | | |   (17)  all_58_5 = e0 & op(e2, e1) = e0
% 245.06/51.51  | | | 
% 245.06/51.51  | | | REF_CLOSE: (1), (3), (17) are inconsistent by sub-proof #2169.
% 245.06/51.51  | | | 
% 245.06/51.51  | | End of split
% 245.06/51.51  | | 
% 245.06/51.51  | Case 2:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (18)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 245.06/51.51  | |           e0)
% 245.06/51.51  | | 
% 245.06/51.51  | | BETA: splitting (18) gives:
% 245.06/51.51  | | 
% 245.06/51.51  | | Case 1:
% 245.06/51.51  | | | 
% 245.06/51.51  | | |   (19)  all_58_8 = e0 & op(e1, e1) = e0
% 245.06/51.51  | | | 
% 245.06/51.51  | | | ALPHA: (19) implies:
% 245.06/51.51  | | |   (20)  op(e1, e1) = e0
% 245.06/51.51  | | | 
% 245.06/51.51  | | | REF_CLOSE: (2), (10), (12), (20) are inconsistent by sub-proof #2211.
% 245.06/51.51  | | | 
% 245.06/51.51  | | Case 2:
% 245.06/51.51  | | | 
% 245.06/51.51  | | |   (21)  all_58_14 = e0 & op(e0, e1) = e0
% 245.06/51.51  | | | 
% 245.06/51.51  | | | ALPHA: (21) implies:
% 245.06/51.51  | | |   (22)  op(e0, e1) = e0
% 245.06/51.51  | | | 
% 245.06/51.51  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 245.06/51.51  | | |            (14), (22) are inconsistent by sub-proof #2156.
% 245.06/51.51  | | | 
% 245.06/51.51  | | End of split
% 245.06/51.51  | | 
% 245.06/51.51  | End of split
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2156 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)   ~ (e3 = e0)
% 245.06/51.51    (2)   ~ (e2 = e0)
% 245.06/51.51    (3)  all_58_4 = e2
% 245.06/51.51    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 245.06/51.51         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 245.06/51.51    (5)   ~ (e3 = e1)
% 245.06/51.51    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 245.06/51.51         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 245.06/51.51    (7)  op(e2, e1) = all_52_9
% 245.06/51.51    (8)   ~ (e3 = e2)
% 245.06/51.51    (9)  op(e0, e1) = e0
% 245.06/51.51    (10)  op(e1, e1) = e2
% 245.06/51.51    (11)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 245.06/51.51          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 245.06/51.51    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51    (13)   ~ (e1 = e0)
% 245.06/51.51    (14)   ~ (e2 = e1)
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | BETA: splitting (4) gives:
% 245.06/51.51  | 
% 245.06/51.51  | Case 1:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (15)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 245.06/51.51  | |           e1)
% 245.06/51.51  | | 
% 245.06/51.51  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 245.06/51.51  | |            (15) are inconsistent by sub-proof #2160.
% 245.06/51.51  | | 
% 245.06/51.51  | Case 2:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (16)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 245.06/51.51  | |           e1)
% 245.06/51.51  | | 
% 245.06/51.51  | | REF_CLOSE: (9), (10), (12), (13), (14), (16) are inconsistent by sub-proof
% 245.06/51.51  | |            #2157.
% 245.06/51.51  | | 
% 245.06/51.51  | End of split
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2157 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 245.06/51.51    (2)  op(e0, e1) = e0
% 245.06/51.51    (3)  op(e1, e1) = e2
% 245.06/51.51    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51    (5)   ~ (e1 = e0)
% 245.06/51.51    (6)   ~ (e2 = e1)
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | BETA: splitting (1) gives:
% 245.06/51.51  | 
% 245.06/51.51  | Case 1:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (7)  all_58_8 = e1 & op(e1, e1) = e1
% 245.06/51.51  | | 
% 245.06/51.51  | | ALPHA: (7) implies:
% 245.06/51.51  | |   (8)  op(e1, e1) = e1
% 245.06/51.51  | | 
% 245.06/51.51  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #2159.
% 245.06/51.51  | | 
% 245.06/51.51  | Case 2:
% 245.06/51.51  | | 
% 245.06/51.51  | |   (9)  all_58_14 = e1 & op(e0, e1) = e1
% 245.06/51.51  | | 
% 245.06/51.51  | | ALPHA: (9) implies:
% 245.06/51.51  | |   (10)  op(e0, e1) = e1
% 245.06/51.51  | | 
% 245.06/51.51  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #2158.
% 245.06/51.51  | | 
% 245.06/51.51  | End of split
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2158 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51    (2)  op(e0, e1) = e1
% 245.06/51.51    (3)  op(e0, e1) = e0
% 245.06/51.51    (4)   ~ (e1 = e0)
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | GROUND_INST: instantiating (1) with e0, e1, e1, e0, simplifying with (2), (3)
% 245.06/51.51  |              gives:
% 245.06/51.51  |   (5)  e1 = e0
% 245.06/51.51  | 
% 245.06/51.51  | REDUCE: (4), (5) imply:
% 245.06/51.51  |   (6)  $false
% 245.06/51.51  | 
% 245.06/51.51  | CLOSE: (6) is inconsistent.
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2159 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.51    (2)  op(e1, e1) = e2
% 245.06/51.51    (3)  op(e1, e1) = e1
% 245.06/51.51    (4)   ~ (e2 = e1)
% 245.06/51.51  
% 245.06/51.51  Begin of proof
% 245.06/51.51  | 
% 245.06/51.51  | GROUND_INST: instantiating (1) with e1, e2, e1, e1, simplifying with (2), (3)
% 245.06/51.51  |              gives:
% 245.06/51.51  |   (5)  e2 = e1
% 245.06/51.51  | 
% 245.06/51.51  | REDUCE: (4), (5) imply:
% 245.06/51.51  |   (6)  $false
% 245.06/51.51  | 
% 245.06/51.51  | CLOSE: (6) is inconsistent.
% 245.06/51.51  | 
% 245.06/51.51  End of proof
% 245.06/51.51  
% 245.06/51.51  Sub-proof #2160 shows that the following formulas are inconsistent:
% 245.06/51.51  ----------------------------------------------------------------
% 245.06/51.51    (1)   ~ (e3 = e0)
% 245.06/51.51    (2)   ~ (e2 = e0)
% 245.06/51.51    (3)  all_58_4 = e2
% 245.06/51.51    (4)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 245.06/51.51    (5)   ~ (e3 = e1)
% 245.06/51.51    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 245.06/51.51         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 245.06/51.51    (7)  op(e2, e1) = all_52_9
% 245.06/51.51    (8)   ~ (e3 = e2)
% 245.06/51.51    (9)  op(e1, e1) = e2
% 245.06/51.52    (10)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 245.06/51.52          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 245.06/51.52    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.52    (12)   ~ (e1 = e0)
% 245.06/51.52    (13)   ~ (e2 = e1)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | BETA: splitting (4) gives:
% 245.06/51.52  | 
% 245.06/51.52  | Case 1:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (14)  all_58_4 = e1 & op(e3, e1) = e1
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (3), (13), (14) are inconsistent by sub-proof #2168.
% 245.06/51.52  | | 
% 245.06/51.52  | Case 2:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (15)  all_58_5 = e1 & op(e2, e1) = e1
% 245.06/51.52  | | 
% 245.06/51.52  | | ALPHA: (15) implies:
% 245.06/51.52  | |   (16)  all_58_5 = e1
% 245.06/51.52  | |   (17)  op(e2, e1) = e1
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (16),
% 245.06/51.52  | |            (17) are inconsistent by sub-proof #2161.
% 245.06/51.52  | | 
% 245.06/51.52  | End of split
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2161 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)   ~ (e3 = e0)
% 245.06/51.52    (2)  op(e2, e1) = e1
% 245.06/51.52    (3)   ~ (e2 = e0)
% 245.06/51.52    (4)  all_58_4 = e2
% 245.06/51.52    (5)   ~ (e3 = e1)
% 245.06/51.52    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 245.06/51.52         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 245.06/51.52    (7)  op(e2, e1) = all_52_9
% 245.06/51.52    (8)   ~ (e3 = e2)
% 245.06/51.52    (9)  op(e1, e1) = e2
% 245.06/51.52    (10)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 245.06/51.52          (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 245.06/51.52    (11)  all_58_5 = e1
% 245.06/51.52    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.52    (13)   ~ (e1 = e0)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | BETA: splitting (10) gives:
% 245.06/51.52  | 
% 245.06/51.52  | Case 1:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (14)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 245.06/51.52  | |           e3)
% 245.06/51.52  | | 
% 245.06/51.52  | | BETA: splitting (14) gives:
% 245.06/51.52  | | 
% 245.06/51.52  | | Case 1:
% 245.06/51.52  | | | 
% 245.06/51.52  | | |   (15)  all_58_4 = e3 & op(e3, e1) = e3
% 245.06/51.52  | | | 
% 245.06/51.52  | | | REF_CLOSE: (4), (8), (15) are inconsistent by sub-proof #2167.
% 245.06/51.52  | | | 
% 245.06/51.52  | | Case 2:
% 245.06/51.52  | | | 
% 245.06/51.52  | | |   (16)  all_58_5 = e3 & op(e2, e1) = e3
% 245.06/51.52  | | | 
% 245.06/51.52  | | | REF_CLOSE: (5), (11), (16) are inconsistent by sub-proof #2166.
% 245.06/51.52  | | | 
% 245.06/51.52  | | End of split
% 245.06/51.52  | | 
% 245.06/51.52  | Case 2:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (17)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 245.06/51.52  | |           e3)
% 245.06/51.52  | | 
% 245.06/51.52  | | BETA: splitting (17) gives:
% 245.06/51.52  | | 
% 245.06/51.52  | | Case 1:
% 245.06/51.52  | | | 
% 245.06/51.52  | | |   (18)  all_58_8 = e3 & op(e1, e1) = e3
% 245.06/51.52  | | | 
% 245.06/51.52  | | | ALPHA: (18) implies:
% 245.06/51.52  | | |   (19)  op(e1, e1) = e3
% 245.06/51.52  | | | 
% 245.06/51.52  | | | REF_CLOSE: (8), (9), (12), (19) are inconsistent by sub-proof #2206.
% 245.06/51.52  | | | 
% 245.06/51.52  | | Case 2:
% 245.06/51.52  | | | 
% 245.06/51.52  | | |   (20)  all_58_14 = e3 & op(e0, e1) = e3
% 245.06/51.52  | | | 
% 245.06/51.52  | | | ALPHA: (20) implies:
% 245.06/51.52  | | |   (21)  op(e0, e1) = e3
% 245.06/51.52  | | | 
% 245.06/51.52  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (12), (13), (21) are
% 245.06/51.52  | | |            inconsistent by sub-proof #2162.
% 245.06/51.52  | | | 
% 245.06/51.52  | | End of split
% 245.06/51.52  | | 
% 245.06/51.52  | End of split
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2162 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)   ~ (e3 = e0)
% 245.06/51.52    (2)  op(e2, e1) = e1
% 245.06/51.52    (3)   ~ (e2 = e0)
% 245.06/51.52    (4)  op(e0, e1) = e3
% 245.06/51.52    (5)  all_58_4 = e2
% 245.06/51.52    (6)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 245.06/51.52         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 245.06/51.52    (7)  op(e2, e1) = all_52_9
% 245.06/51.52    (8)  op(e1, e1) = e2
% 245.06/51.52    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.52    (10)   ~ (e1 = e0)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | BETA: splitting (6) gives:
% 245.06/51.52  | 
% 245.06/51.52  | Case 1:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (11)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 245.06/51.52  | |           e0)
% 245.06/51.52  | | 
% 245.06/51.52  | | BETA: splitting (11) gives:
% 245.06/51.52  | | 
% 245.06/51.52  | | Case 1:
% 245.06/51.52  | | | 
% 245.06/51.52  | | |   (12)  all_58_4 = e0 & op(e3, e1) = e0
% 245.06/51.52  | | | 
% 245.06/51.52  | | | REF_CLOSE: (3), (5), (12) are inconsistent by sub-proof #2170.
% 245.06/51.52  | | | 
% 245.06/51.52  | | Case 2:
% 245.06/51.52  | | | 
% 245.06/51.52  | | |   (13)  all_58_5 = e0 & op(e2, e1) = e0
% 245.06/51.52  | | | 
% 245.06/51.52  | | | ALPHA: (13) implies:
% 245.06/51.52  | | |   (14)  op(e2, e1) = e0
% 245.06/51.52  | | | 
% 245.06/51.52  | | | REF_CLOSE: (2), (7), (9), (10), (14) are inconsistent by sub-proof #2165.
% 245.06/51.52  | | | 
% 245.06/51.52  | | End of split
% 245.06/51.52  | | 
% 245.06/51.52  | Case 2:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (15)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 245.06/51.52  | |           e0)
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (1), (3), (4), (8), (9), (15) are inconsistent by sub-proof
% 245.06/51.52  | |            #2163.
% 245.06/51.52  | | 
% 245.06/51.52  | End of split
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2163 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)   ~ (e3 = e0)
% 245.06/51.52    (2)   ~ (e2 = e0)
% 245.06/51.52    (3)  op(e0, e1) = e3
% 245.06/51.52    (4)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 245.06/51.52    (5)  op(e1, e1) = e2
% 245.06/51.52    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | BETA: splitting (4) gives:
% 245.06/51.52  | 
% 245.06/51.52  | Case 1:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 245.06/51.52  | | 
% 245.06/51.52  | | ALPHA: (7) implies:
% 245.06/51.52  | |   (8)  op(e1, e1) = e0
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2211.
% 245.06/51.52  | | 
% 245.06/51.52  | Case 2:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (9)  all_58_14 = e0 & op(e0, e1) = e0
% 245.06/51.52  | | 
% 245.06/51.52  | | ALPHA: (9) implies:
% 245.06/51.52  | |   (10)  op(e0, e1) = e0
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #2164.
% 245.06/51.52  | | 
% 245.06/51.52  | End of split
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2164 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.52    (2)  op(e0, e1) = e3
% 245.06/51.52    (3)  op(e0, e1) = e0
% 245.06/51.52    (4)   ~ (e3 = e0)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | GROUND_INST: instantiating (1) with e3, e0, e1, e0, simplifying with (2), (3)
% 245.06/51.52  |              gives:
% 245.06/51.52  |   (5)  e3 = e0
% 245.06/51.52  | 
% 245.06/51.52  | REDUCE: (4), (5) imply:
% 245.06/51.52  |   (6)  $false
% 245.06/51.52  | 
% 245.06/51.52  | CLOSE: (6) is inconsistent.
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2165 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  op(e2, e1) = e1
% 245.06/51.52    (2)  op(e2, e1) = all_52_9
% 245.06/51.52    (3)  op(e2, e1) = e0
% 245.06/51.52    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.52    (5)   ~ (e1 = e0)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | GROUND_INST: instantiating (4) with all_52_9, e0, e1, e2, simplifying with
% 245.06/51.52  |              (2), (3) gives:
% 245.06/51.52  |   (6)  all_52_9 = e0
% 245.06/51.52  | 
% 245.06/51.52  | GROUND_INST: instantiating (4) with all_52_9, e1, e1, e2, simplifying with
% 245.06/51.52  |              (1), (2) gives:
% 245.06/51.52  |   (7)  all_52_9 = e1
% 245.06/51.52  | 
% 245.06/51.52  | COMBINE_EQS: (6), (7) imply:
% 245.06/51.52  |   (8)  e1 = e0
% 245.06/51.52  | 
% 245.06/51.52  | REDUCE: (5), (8) imply:
% 245.06/51.52  |   (9)  $false
% 245.06/51.52  | 
% 245.06/51.52  | CLOSE: (9) is inconsistent.
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2166 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  all_58_5 = e3 & op(e2, e1) = e3
% 245.06/51.52    (2)  all_58_5 = e1
% 245.06/51.52    (3)   ~ (e3 = e1)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | ALPHA: (1) implies:
% 245.06/51.52  |   (4)  all_58_5 = e3
% 245.06/51.52  | 
% 245.06/51.52  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.52  |   (5)  e3 = e1
% 245.06/51.52  | 
% 245.06/51.52  | REDUCE: (3), (5) imply:
% 245.06/51.52  |   (6)  $false
% 245.06/51.52  | 
% 245.06/51.52  | CLOSE: (6) is inconsistent.
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2167 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  all_58_4 = e3 & op(e3, e1) = e3
% 245.06/51.52    (2)  all_58_4 = e2
% 245.06/51.52    (3)   ~ (e3 = e2)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | ALPHA: (1) implies:
% 245.06/51.52  |   (4)  all_58_4 = e3
% 245.06/51.52  | 
% 245.06/51.52  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.52  |   (5)  e3 = e2
% 245.06/51.52  | 
% 245.06/51.52  | REDUCE: (3), (5) imply:
% 245.06/51.52  |   (6)  $false
% 245.06/51.52  | 
% 245.06/51.52  | CLOSE: (6) is inconsistent.
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2168 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  all_58_4 = e1 & op(e3, e1) = e1
% 245.06/51.52    (2)  all_58_4 = e2
% 245.06/51.52    (3)   ~ (e2 = e1)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | ALPHA: (1) implies:
% 245.06/51.52  |   (4)  all_58_4 = e1
% 245.06/51.52  | 
% 245.06/51.52  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.52  |   (5)  e2 = e1
% 245.06/51.52  | 
% 245.06/51.52  | REDUCE: (3), (5) imply:
% 245.06/51.52  |   (6)  $false
% 245.06/51.52  | 
% 245.06/51.52  | CLOSE: (6) is inconsistent.
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2169 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  all_58_5 = e0 & op(e2, e1) = e0
% 245.06/51.52    (2)  all_58_5 = e3
% 245.06/51.52    (3)   ~ (e3 = e0)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | ALPHA: (1) implies:
% 245.06/51.52  |   (4)  all_58_5 = e0
% 245.06/51.52  | 
% 245.06/51.52  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.52  |   (5)  e3 = e0
% 245.06/51.52  | 
% 245.06/51.52  | REDUCE: (3), (5) imply:
% 245.06/51.52  |   (6)  $false
% 245.06/51.52  | 
% 245.06/51.52  | CLOSE: (6) is inconsistent.
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2170 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  all_58_4 = e0 & op(e3, e1) = e0
% 245.06/51.52    (2)  all_58_4 = e2
% 245.06/51.52    (3)   ~ (e2 = e0)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | ALPHA: (1) implies:
% 245.06/51.52  |   (4)  all_58_4 = e0
% 245.06/51.52  | 
% 245.06/51.52  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.52  |   (5)  e2 = e0
% 245.06/51.52  | 
% 245.06/51.52  | REDUCE: (3), (5) imply:
% 245.06/51.52  |   (6)  $false
% 245.06/51.52  | 
% 245.06/51.52  | CLOSE: (6) is inconsistent.
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2171 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 245.06/51.52    (2)  op(e0, e3) = all_52_3
% 245.06/51.52    (3)  op(e1, e3) = e1
% 245.06/51.52    (4)   ~ (all_52_3 = e2)
% 245.06/51.52    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.52    (6)   ~ (e2 = e1)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | BETA: splitting (1) gives:
% 245.06/51.52  | 
% 245.06/51.52  | Case 1:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (7)  all_58_6 = e2 & op(e1, e3) = e2
% 245.06/51.52  | | 
% 245.06/51.52  | | ALPHA: (7) implies:
% 245.06/51.52  | |   (8)  op(e1, e3) = e2
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2226.
% 245.06/51.52  | | 
% 245.06/51.52  | Case 2:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (9)  all_58_12 = e2 & op(e0, e3) = e2
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2315.
% 245.06/51.52  | | 
% 245.06/51.52  | End of split
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2172 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  all_54_3 = e1 | all_54_3 = e0
% 245.06/51.52    (2)   ~ (all_52_13 = e1)
% 245.06/51.52    (3)  all_54_11 = all_52_14
% 245.06/51.52    (4)   ~ (all_52_12 = e1)
% 245.06/51.52    (5)   ~ (all_52_12 = all_52_14)
% 245.06/51.52    (6)   ~ (all_52_12 = all_52_13)
% 245.06/51.52    (7)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 245.06/51.52    (8)   ~ (all_52_14 = e2)
% 245.06/51.52    (9)   ~ (all_52_14 = e1)
% 245.06/51.52    (10)  op(e2, e3) = e2
% 245.06/51.52    (11)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.06/51.52    (12)  op(e2, e3) = all_52_1
% 245.06/51.52    (13)   ~ (all_52_1 = all_52_13)
% 245.06/51.52    (14)  all_54_7 = all_52_13
% 245.06/51.52    (15)   ~ (all_52_13 = all_52_14)
% 245.06/51.52    (16)  all_54_3 = all_52_12
% 245.06/51.52    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | BETA: splitting (1) gives:
% 245.06/51.52  | 
% 245.06/51.52  | Case 1:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (18)  all_54_3 = e1
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (4), (16), (18) are inconsistent by sub-proof #2289.
% 245.06/51.52  | | 
% 245.06/51.52  | Case 2:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (19)  all_54_3 = e0
% 245.06/51.52  | | 
% 245.06/51.52  | | COMBINE_EQS: (16), (19) imply:
% 245.06/51.52  | |   (20)  all_52_12 = e0
% 245.06/51.52  | | 
% 245.06/51.52  | | SIMP: (20) implies:
% 245.06/51.52  | |   (21)  all_52_12 = e0
% 245.06/51.52  | | 
% 245.06/51.52  | | REDUCE: (6), (21) imply:
% 245.06/51.52  | |   (22)   ~ (all_52_13 = e0)
% 245.06/51.52  | | 
% 245.06/51.52  | | SIMP: (22) implies:
% 245.06/51.52  | |   (23)   ~ (all_52_13 = e0)
% 245.06/51.52  | | 
% 245.06/51.52  | | REDUCE: (5), (21) imply:
% 245.06/51.52  | |   (24)   ~ (all_52_14 = e0)
% 245.06/51.52  | | 
% 245.06/51.52  | | SIMP: (24) implies:
% 245.06/51.52  | |   (25)   ~ (all_52_14 = e0)
% 245.06/51.52  | | 
% 245.06/51.52  | | BETA: splitting (7) gives:
% 245.06/51.52  | | 
% 245.06/51.52  | | Case 1:
% 245.06/51.52  | | | 
% 245.06/51.52  | | |   (26)  all_54_11 = e3
% 245.06/51.52  | | | 
% 245.06/51.52  | | | COMBINE_EQS: (3), (26) imply:
% 245.06/51.52  | | |   (27)  all_52_14 = e3
% 245.06/51.52  | | | 
% 245.06/51.52  | | | REDUCE: (15), (27) imply:
% 245.06/51.52  | | |   (28)   ~ (all_52_13 = e3)
% 245.06/51.52  | | | 
% 245.06/51.52  | | | BETA: splitting (11) gives:
% 245.06/51.52  | | | 
% 245.06/51.52  | | | Case 1:
% 245.06/51.52  | | | | 
% 245.06/51.52  | | | |   (29)  all_54_7 = e3
% 245.06/51.52  | | | | 
% 245.06/51.52  | | | | REF_CLOSE: (14), (28), (29) are inconsistent by sub-proof #2296.
% 245.06/51.52  | | | | 
% 245.06/51.52  | | | Case 2:
% 245.06/51.52  | | | | 
% 245.06/51.52  | | | |   (30)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.06/51.52  | | | | 
% 245.06/51.52  | | | | REF_CLOSE: (2), (10), (12), (13), (14), (17), (23), (30) are
% 245.06/51.52  | | | |            inconsistent by sub-proof #2292.
% 245.06/51.52  | | | | 
% 245.06/51.52  | | | End of split
% 245.06/51.52  | | | 
% 245.06/51.52  | | Case 2:
% 245.06/51.52  | | | 
% 245.06/51.52  | | |   (31)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 245.06/51.52  | | | 
% 245.06/51.52  | | | REF_CLOSE: (3), (8), (9), (25), (31) are inconsistent by sub-proof #2173.
% 245.06/51.52  | | | 
% 245.06/51.52  | | End of split
% 245.06/51.52  | | 
% 245.06/51.52  | End of split
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2173 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  all_54_11 = all_52_14
% 245.06/51.52    (2)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 245.06/51.52    (3)   ~ (all_52_14 = e2)
% 245.06/51.52    (4)   ~ (all_52_14 = e1)
% 245.06/51.52    (5)   ~ (all_52_14 = e0)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | BETA: splitting (2) gives:
% 245.06/51.52  | 
% 245.06/51.52  | Case 1:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (6)  all_54_11 = e2
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #2177.
% 245.06/51.52  | | 
% 245.06/51.52  | Case 2:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (7)  all_54_11 = e1 | all_54_11 = e0
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #2174.
% 245.06/51.52  | | 
% 245.06/51.52  | End of split
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2174 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  all_54_11 = e1 | all_54_11 = e0
% 245.06/51.52    (2)  all_54_11 = all_52_14
% 245.06/51.52    (3)   ~ (all_52_14 = e1)
% 245.06/51.52    (4)   ~ (all_52_14 = e0)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | BETA: splitting (1) gives:
% 245.06/51.52  | 
% 245.06/51.52  | Case 1:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (5)  all_54_11 = e1
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2176.
% 245.06/51.52  | | 
% 245.06/51.52  | Case 2:
% 245.06/51.52  | | 
% 245.06/51.52  | |   (6)  all_54_11 = e0
% 245.06/51.52  | | 
% 245.06/51.52  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2175.
% 245.06/51.52  | | 
% 245.06/51.52  | End of split
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2175 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  all_54_11 = all_52_14
% 245.06/51.52    (2)  all_54_11 = e0
% 245.06/51.52    (3)   ~ (all_52_14 = e0)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | COMBINE_EQS: (1), (2) imply:
% 245.06/51.52  |   (4)  all_52_14 = e0
% 245.06/51.52  | 
% 245.06/51.52  | SIMP: (4) implies:
% 245.06/51.52  |   (5)  all_52_14 = e0
% 245.06/51.52  | 
% 245.06/51.52  | REDUCE: (3), (5) imply:
% 245.06/51.52  |   (6)  $false
% 245.06/51.52  | 
% 245.06/51.52  | CLOSE: (6) is inconsistent.
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2176 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  all_54_11 = all_52_14
% 245.06/51.52    (2)  all_54_11 = e1
% 245.06/51.52    (3)   ~ (all_52_14 = e1)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | COMBINE_EQS: (1), (2) imply:
% 245.06/51.52  |   (4)  all_52_14 = e1
% 245.06/51.52  | 
% 245.06/51.52  | SIMP: (4) implies:
% 245.06/51.52  |   (5)  all_52_14 = e1
% 245.06/51.52  | 
% 245.06/51.52  | REDUCE: (3), (5) imply:
% 245.06/51.52  |   (6)  $false
% 245.06/51.52  | 
% 245.06/51.52  | CLOSE: (6) is inconsistent.
% 245.06/51.52  | 
% 245.06/51.52  End of proof
% 245.06/51.52  
% 245.06/51.52  Sub-proof #2177 shows that the following formulas are inconsistent:
% 245.06/51.52  ----------------------------------------------------------------
% 245.06/51.52    (1)  all_54_11 = all_52_14
% 245.06/51.52    (2)  all_54_11 = e2
% 245.06/51.52    (3)   ~ (all_52_14 = e2)
% 245.06/51.52  
% 245.06/51.52  Begin of proof
% 245.06/51.52  | 
% 245.06/51.52  | COMBINE_EQS: (1), (2) imply:
% 245.06/51.52  |   (4)  all_52_14 = e2
% 245.06/51.52  | 
% 245.06/51.53  | SIMP: (4) implies:
% 245.06/51.53  |   (5)  all_52_14 = e2
% 245.06/51.53  | 
% 245.06/51.53  | REDUCE: (3), (5) imply:
% 245.06/51.53  |   (6)  $false
% 245.06/51.53  | 
% 245.06/51.53  | CLOSE: (6) is inconsistent.
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2178 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)   ~ (e3 = e0)
% 245.06/51.53    (2)   ~ (e2 = e0)
% 245.06/51.53    (3)  op(e1, e2) = all_52_6
% 245.06/51.53    (4)   ~ (e3 = e1)
% 245.06/51.53    (5)  op(e1, e2) = e3
% 245.06/51.53    (6)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 245.06/51.53         (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 245.06/51.53    (7)  all_54_9 = all_52_6
% 245.06/51.53    (8)   ~ (e3 = e2)
% 245.06/51.53    (9)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 245.06/51.53    (10)  op(e3, e0) = all_52_12
% 245.06/51.53    (11)  op(e3, e3) = e2
% 245.06/51.53    (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 245.06/51.53          (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 245.06/51.53    (13)  op(e3, e2) = all_52_4
% 245.06/51.53    (14)  all_58_1 = e2
% 245.06/51.53    (15)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 245.06/51.53          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 245.06/51.53    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.53            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.53    (17)   ~ (all_52_12 = e3)
% 245.06/51.53    (18)   ~ (e1 = e0)
% 245.06/51.53    (19)   ~ (all_52_4 = all_52_6)
% 245.06/51.53    (20)   ~ (e2 = e1)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | BETA: splitting (6) gives:
% 245.06/51.53  | 
% 245.06/51.53  | Case 1:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (21)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 245.06/51.53  | |           e3)
% 245.06/51.53  | | 
% 245.06/51.53  | | REF_CLOSE: (3), (5), (7), (8), (9), (11), (13), (16), (19), (21) are
% 245.06/51.53  | |            inconsistent by sub-proof #2189.
% 245.06/51.53  | | 
% 245.06/51.53  | Case 2:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (22)  (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 245.06/51.53  | |           e3)
% 245.06/51.53  | | 
% 245.06/51.53  | | BETA: splitting (22) gives:
% 245.06/51.53  | | 
% 245.06/51.53  | | Case 1:
% 245.06/51.53  | | | 
% 245.06/51.53  | | |   (23)  all_58_4 = e3 & op(e3, e1) = e3
% 245.06/51.53  | | | 
% 245.06/51.53  | | | ALPHA: (23) implies:
% 245.06/51.53  | | |   (24)  all_58_4 = e3
% 245.06/51.53  | | | 
% 245.06/51.53  | | | REF_CLOSE: (1), (2), (4), (11), (12), (14), (15), (16), (18), (20), (24)
% 245.06/51.53  | | |            are inconsistent by sub-proof #2180.
% 245.06/51.53  | | | 
% 245.06/51.53  | | Case 2:
% 245.06/51.53  | | | 
% 245.06/51.53  | | |   (25)  all_58_9 = e3 & op(e3, e0) = e3
% 245.06/51.53  | | | 
% 245.06/51.53  | | | ALPHA: (25) implies:
% 245.06/51.53  | | |   (26)  op(e3, e0) = e3
% 245.06/51.53  | | | 
% 245.06/51.53  | | | REF_CLOSE: (10), (16), (17), (26) are inconsistent by sub-proof #2179.
% 245.06/51.53  | | | 
% 245.06/51.53  | | End of split
% 245.06/51.53  | | 
% 245.06/51.53  | End of split
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2179 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.53    (2)  op(e3, e0) = all_52_12
% 245.06/51.53    (3)  op(e3, e0) = e3
% 245.06/51.53    (4)   ~ (all_52_12 = e3)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | GROUND_INST: instantiating (1) with all_52_12, e3, e0, e3, simplifying with
% 245.06/51.53  |              (2), (3) gives:
% 245.06/51.53  |   (5)  all_52_12 = e3
% 245.06/51.53  | 
% 245.06/51.53  | REDUCE: (4), (5) imply:
% 245.06/51.53  |   (6)  $false
% 245.06/51.53  | 
% 245.06/51.53  | CLOSE: (6) is inconsistent.
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2180 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)   ~ (e3 = e0)
% 245.06/51.53    (2)   ~ (e2 = e0)
% 245.06/51.53    (3)   ~ (e3 = e1)
% 245.06/51.53    (4)  op(e3, e3) = e2
% 245.06/51.53    (5)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 245.06/51.53         (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 245.06/51.53    (6)  all_58_1 = e2
% 245.06/51.53    (7)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 245.06/51.53         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 245.06/51.53    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.53    (9)   ~ (e1 = e0)
% 245.06/51.53    (10)  all_58_4 = e3
% 245.06/51.53    (11)   ~ (e2 = e1)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | BETA: splitting (5) gives:
% 245.06/51.53  | 
% 245.06/51.53  | Case 1:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (12)  (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 245.06/51.53  | |           e0)
% 245.06/51.53  | | 
% 245.06/51.53  | | BETA: splitting (12) gives:
% 245.06/51.53  | | 
% 245.06/51.53  | | Case 1:
% 245.06/51.53  | | | 
% 245.06/51.53  | | |   (13)  all_58_0 = e0 & op(e3, e3) = e0
% 245.06/51.53  | | | 
% 245.06/51.53  | | | ALPHA: (13) implies:
% 245.06/51.53  | | |   (14)  op(e3, e3) = e0
% 245.06/51.53  | | | 
% 245.06/51.53  | | | REF_CLOSE: (2), (4), (8), (14) are inconsistent by sub-proof #2188.
% 245.06/51.53  | | | 
% 245.06/51.53  | | Case 2:
% 245.06/51.53  | | | 
% 245.06/51.53  | | |   (15)  all_58_1 = e0 & op(e3, e2) = e0
% 245.06/51.53  | | | 
% 245.06/51.53  | | | REF_CLOSE: (2), (6), (15) are inconsistent by sub-proof #2187.
% 245.06/51.53  | | | 
% 245.06/51.53  | | End of split
% 245.06/51.53  | | 
% 245.06/51.53  | Case 2:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (16)  (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 245.06/51.53  | |           e0)
% 245.06/51.53  | | 
% 245.06/51.53  | | BETA: splitting (16) gives:
% 245.06/51.53  | | 
% 245.06/51.53  | | Case 1:
% 245.06/51.53  | | | 
% 245.06/51.53  | | |   (17)  all_58_4 = e0 & op(e3, e1) = e0
% 245.06/51.53  | | | 
% 245.06/51.53  | | | ALPHA: (17) implies:
% 245.06/51.53  | | |   (18)  all_58_4 = e0
% 245.06/51.53  | | | 
% 245.06/51.53  | | | REF_CLOSE: (1), (10), (18) are inconsistent by sub-proof #2186.
% 245.06/51.53  | | | 
% 245.06/51.53  | | Case 2:
% 245.06/51.53  | | | 
% 245.06/51.53  | | |   (19)  all_58_9 = e0 & op(e3, e0) = e0
% 245.06/51.53  | | | 
% 245.06/51.53  | | | ALPHA: (19) implies:
% 245.06/51.53  | | |   (20)  all_58_9 = e0
% 245.06/51.53  | | | 
% 245.06/51.53  | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (20) are inconsistent
% 245.06/51.53  | | |            by sub-proof #2181.
% 245.06/51.53  | | | 
% 245.06/51.53  | | End of split
% 245.06/51.53  | | 
% 245.06/51.53  | End of split
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2181 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)  all_58_9 = e0
% 245.06/51.53    (2)   ~ (e3 = e1)
% 245.06/51.53    (3)  op(e3, e3) = e2
% 245.06/51.53    (4)  all_58_1 = e2
% 245.06/51.53    (5)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 245.06/51.53         (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 245.06/51.53    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.53    (7)   ~ (e1 = e0)
% 245.06/51.53    (8)  all_58_4 = e3
% 245.06/51.53    (9)   ~ (e2 = e1)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | BETA: splitting (5) gives:
% 245.06/51.53  | 
% 245.06/51.53  | Case 1:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (10)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 245.06/51.53  | |           e1)
% 245.06/51.53  | | 
% 245.06/51.53  | | BETA: splitting (10) gives:
% 245.06/51.53  | | 
% 245.06/51.53  | | Case 1:
% 245.06/51.53  | | | 
% 245.06/51.53  | | |   (11)  all_58_0 = e1 & op(e3, e3) = e1
% 245.06/51.53  | | | 
% 245.06/51.53  | | | ALPHA: (11) implies:
% 245.06/51.53  | | |   (12)  op(e3, e3) = e1
% 245.06/51.53  | | | 
% 245.06/51.53  | | | REF_CLOSE: (3), (6), (9), (12) are inconsistent by sub-proof #2267.
% 245.06/51.53  | | | 
% 245.06/51.53  | | Case 2:
% 245.06/51.53  | | | 
% 245.06/51.53  | | |   (13)  all_58_1 = e1 & op(e3, e2) = e1
% 245.06/51.53  | | | 
% 245.06/51.53  | | | REF_CLOSE: (4), (9), (13) are inconsistent by sub-proof #2185.
% 245.06/51.53  | | | 
% 245.06/51.53  | | End of split
% 245.06/51.53  | | 
% 245.06/51.53  | Case 2:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (14)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 245.06/51.53  | |           e1)
% 245.06/51.53  | | 
% 245.06/51.53  | | REF_CLOSE: (1), (2), (7), (8), (14) are inconsistent by sub-proof #2182.
% 245.06/51.53  | | 
% 245.06/51.53  | End of split
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2182 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)  all_58_9 = e0
% 245.06/51.53    (2)   ~ (e3 = e1)
% 245.06/51.53    (3)   ~ (e1 = e0)
% 245.06/51.53    (4)  all_58_4 = e3
% 245.06/51.53    (5)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | BETA: splitting (5) gives:
% 245.06/51.53  | 
% 245.06/51.53  | Case 1:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (6)  all_58_4 = e1 & op(e3, e1) = e1
% 245.06/51.53  | | 
% 245.06/51.53  | | ALPHA: (6) implies:
% 245.06/51.53  | |   (7)  all_58_4 = e1
% 245.06/51.53  | | 
% 245.06/51.53  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2184.
% 245.06/51.53  | | 
% 245.06/51.53  | Case 2:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (8)  all_58_9 = e1 & op(e3, e0) = e1
% 245.06/51.53  | | 
% 245.06/51.53  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #2183.
% 245.06/51.53  | | 
% 245.06/51.53  | End of split
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2183 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)  all_58_9 = e1 & op(e3, e0) = e1
% 245.06/51.53    (2)  all_58_9 = e0
% 245.06/51.53    (3)   ~ (e1 = e0)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | ALPHA: (1) implies:
% 245.06/51.53  |   (4)  all_58_9 = e1
% 245.06/51.53  | 
% 245.06/51.53  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.53  |   (5)  e1 = e0
% 245.06/51.53  | 
% 245.06/51.53  | REDUCE: (3), (5) imply:
% 245.06/51.53  |   (6)  $false
% 245.06/51.53  | 
% 245.06/51.53  | CLOSE: (6) is inconsistent.
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2184 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)  all_58_4 = e3
% 245.06/51.53    (2)  all_58_4 = e1
% 245.06/51.53    (3)   ~ (e3 = e1)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | COMBINE_EQS: (1), (2) imply:
% 245.06/51.53  |   (4)  e3 = e1
% 245.06/51.53  | 
% 245.06/51.53  | SIMP: (4) implies:
% 245.06/51.53  |   (5)  e3 = e1
% 245.06/51.53  | 
% 245.06/51.53  | REDUCE: (3), (5) imply:
% 245.06/51.53  |   (6)  $false
% 245.06/51.53  | 
% 245.06/51.53  | CLOSE: (6) is inconsistent.
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2185 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)  all_58_1 = e1 & op(e3, e2) = e1
% 245.06/51.53    (2)  all_58_1 = e2
% 245.06/51.53    (3)   ~ (e2 = e1)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | ALPHA: (1) implies:
% 245.06/51.53  |   (4)  all_58_1 = e1
% 245.06/51.53  | 
% 245.06/51.53  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.53  |   (5)  e2 = e1
% 245.06/51.53  | 
% 245.06/51.53  | REDUCE: (3), (5) imply:
% 245.06/51.53  |   (6)  $false
% 245.06/51.53  | 
% 245.06/51.53  | CLOSE: (6) is inconsistent.
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2186 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)  all_58_4 = e3
% 245.06/51.53    (2)  all_58_4 = e0
% 245.06/51.53    (3)   ~ (e3 = e0)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | COMBINE_EQS: (1), (2) imply:
% 245.06/51.53  |   (4)  e3 = e0
% 245.06/51.53  | 
% 245.06/51.53  | SIMP: (4) implies:
% 245.06/51.53  |   (5)  e3 = e0
% 245.06/51.53  | 
% 245.06/51.53  | REDUCE: (3), (5) imply:
% 245.06/51.53  |   (6)  $false
% 245.06/51.53  | 
% 245.06/51.53  | CLOSE: (6) is inconsistent.
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2187 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)  all_58_1 = e0 & op(e3, e2) = e0
% 245.06/51.53    (2)  all_58_1 = e2
% 245.06/51.53    (3)   ~ (e2 = e0)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | ALPHA: (1) implies:
% 245.06/51.53  |   (4)  all_58_1 = e0
% 245.06/51.53  | 
% 245.06/51.53  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.53  |   (5)  e2 = e0
% 245.06/51.53  | 
% 245.06/51.53  | REDUCE: (3), (5) imply:
% 245.06/51.53  |   (6)  $false
% 245.06/51.53  | 
% 245.06/51.53  | CLOSE: (6) is inconsistent.
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2188 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.53    (2)  op(e3, e3) = e2
% 245.06/51.53    (3)  op(e3, e3) = e0
% 245.06/51.53    (4)   ~ (e2 = e0)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | GROUND_INST: instantiating (1) with e0, e2, e3, e3, simplifying with (2), (3)
% 245.06/51.53  |              gives:
% 245.06/51.53  |   (5)  e2 = e0
% 245.06/51.53  | 
% 245.06/51.53  | REDUCE: (4), (5) imply:
% 245.06/51.53  |   (6)  $false
% 245.06/51.53  | 
% 245.06/51.53  | CLOSE: (6) is inconsistent.
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2189 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)  op(e1, e2) = all_52_6
% 245.06/51.53    (2)  (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 245.06/51.53    (3)  op(e1, e2) = e3
% 245.06/51.53    (4)  all_54_9 = all_52_6
% 245.06/51.53    (5)   ~ (e3 = e2)
% 245.06/51.53    (6)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 245.06/51.53    (7)  op(e3, e3) = e2
% 245.06/51.53    (8)  op(e3, e2) = all_52_4
% 245.06/51.53    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.53    (10)   ~ (all_52_4 = all_52_6)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | BETA: splitting (2) gives:
% 245.06/51.53  | 
% 245.06/51.53  | Case 1:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (11)  all_58_0 = e3 & op(e3, e3) = e3
% 245.06/51.53  | | 
% 245.06/51.53  | | ALPHA: (11) implies:
% 245.06/51.53  | |   (12)  op(e3, e3) = e3
% 245.06/51.53  | | 
% 245.06/51.53  | | REF_CLOSE: (5), (7), (9), (12) are inconsistent by sub-proof #2194.
% 245.06/51.53  | | 
% 245.06/51.53  | Case 2:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (13)  all_58_1 = e3 & op(e3, e2) = e3
% 245.06/51.53  | | 
% 245.06/51.53  | | ALPHA: (13) implies:
% 245.06/51.53  | |   (14)  op(e3, e2) = e3
% 245.06/51.53  | | 
% 245.06/51.53  | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (14) are inconsistent by
% 245.06/51.53  | |            sub-proof #2190.
% 245.06/51.53  | | 
% 245.06/51.53  | End of split
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2190 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)  op(e1, e2) = all_52_6
% 245.06/51.53    (2)  op(e1, e2) = e3
% 245.06/51.53    (3)  all_54_9 = all_52_6
% 245.06/51.53    (4)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 245.06/51.53    (5)  op(e3, e2) = all_52_4
% 245.06/51.53    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.53    (7)  op(e3, e2) = e3
% 245.06/51.53    (8)   ~ (all_52_4 = all_52_6)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | BETA: splitting (4) gives:
% 245.06/51.53  | 
% 245.06/51.53  | Case 1:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (9)  all_54_9 = e3
% 245.06/51.53  | | 
% 245.06/51.53  | | COMBINE_EQS: (3), (9) imply:
% 245.06/51.53  | |   (10)  all_52_6 = e3
% 245.06/51.53  | | 
% 245.06/51.53  | | SIMP: (10) implies:
% 245.06/51.53  | |   (11)  all_52_6 = e3
% 245.06/51.53  | | 
% 245.06/51.53  | | REDUCE: (8), (11) imply:
% 245.06/51.53  | |   (12)   ~ (all_52_4 = e3)
% 245.06/51.53  | | 
% 245.06/51.53  | | REF_CLOSE: (5), (6), (7), (12) are inconsistent by sub-proof #2192.
% 245.06/51.53  | | 
% 245.06/51.53  | Case 2:
% 245.06/51.53  | | 
% 245.06/51.53  | |   (13)   ~ (all_54_9 = e3)
% 245.06/51.53  | | 
% 245.06/51.53  | | REDUCE: (3), (13) imply:
% 245.06/51.53  | |   (14)   ~ (all_52_6 = e3)
% 245.06/51.53  | | 
% 245.06/51.53  | | REF_CLOSE: (1), (2), (6), (14) are inconsistent by sub-proof #2191.
% 245.06/51.53  | | 
% 245.06/51.53  | End of split
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2191 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.53    (2)  op(e1, e2) = all_52_6
% 245.06/51.53    (3)  op(e1, e2) = e3
% 245.06/51.53    (4)   ~ (all_52_6 = e3)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | GROUND_INST: instantiating (1) with all_52_6, e3, e2, e1, simplifying with
% 245.06/51.53  |              (2), (3) gives:
% 245.06/51.53  |   (5)  all_52_6 = e3
% 245.06/51.53  | 
% 245.06/51.53  | REDUCE: (4), (5) imply:
% 245.06/51.53  |   (6)  $false
% 245.06/51.53  | 
% 245.06/51.53  | CLOSE: (6) is inconsistent.
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2192 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.53    (2)  op(e3, e2) = all_52_4
% 245.06/51.53    (3)  op(e3, e2) = e3
% 245.06/51.53    (4)   ~ (all_52_4 = e3)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | GROUND_INST: instantiating (1) with all_52_4, e3, e2, e3, simplifying with
% 245.06/51.53  |              (2), (3) gives:
% 245.06/51.53  |   (5)  all_52_4 = e3
% 245.06/51.53  | 
% 245.06/51.53  | REDUCE: (4), (5) imply:
% 245.06/51.53  |   (6)  $false
% 245.06/51.53  | 
% 245.06/51.53  | CLOSE: (6) is inconsistent.
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2193 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.53    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.53    (2)  op(e3, e2) = e3
% 245.06/51.53    (3)  op(e3, e2) = e2
% 245.06/51.53    (4)   ~ (e3 = e2)
% 245.06/51.53  
% 245.06/51.53  Begin of proof
% 245.06/51.53  | 
% 245.06/51.53  | GROUND_INST: instantiating (1) with e3, e2, e2, e3, simplifying with (2), (3)
% 245.06/51.53  |              gives:
% 245.06/51.53  |   (5)  e3 = e2
% 245.06/51.53  | 
% 245.06/51.53  | REDUCE: (4), (5) imply:
% 245.06/51.53  |   (6)  $false
% 245.06/51.53  | 
% 245.06/51.53  | CLOSE: (6) is inconsistent.
% 245.06/51.53  | 
% 245.06/51.53  End of proof
% 245.06/51.53  
% 245.06/51.53  Sub-proof #2194 shows that the following formulas are inconsistent:
% 245.06/51.53  ----------------------------------------------------------------
% 245.06/51.54    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.54    (2)  op(e3, e3) = e3
% 245.06/51.54    (3)  op(e3, e3) = e2
% 245.06/51.54    (4)   ~ (e3 = e2)
% 245.06/51.54  
% 245.06/51.54  Begin of proof
% 245.06/51.54  | 
% 245.06/51.54  | GROUND_INST: instantiating (1) with e2, e3, e3, e3, simplifying with (2), (3)
% 245.06/51.54  |              gives:
% 245.06/51.54  |   (5)  e3 = e2
% 245.06/51.54  | 
% 245.06/51.54  | REDUCE: (4), (5) imply:
% 245.06/51.54  |   (6)  $false
% 245.06/51.54  | 
% 245.06/51.54  | CLOSE: (6) is inconsistent.
% 245.06/51.54  | 
% 245.06/51.54  End of proof
% 245.06/51.54  
% 245.06/51.54  Sub-proof #2195 shows that the following formulas are inconsistent:
% 245.06/51.54  ----------------------------------------------------------------
% 245.06/51.54    (1)   ~ (all_52_13 = e1)
% 245.06/51.54    (2)   ~ (e3 = e1)
% 245.06/51.54    (3)  op(e2, e1) = all_52_9
% 245.06/51.54    (4)  op(e2, e3) = all_52_1
% 245.06/51.54    (5)  (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 245.06/51.54    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.54    (7)  op(e2, e0) = all_52_13
% 245.06/51.54    (8)   ~ (all_52_1 = e3)
% 245.06/51.54    (9)   ~ (all_52_9 = e1)
% 245.06/51.54    (10)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 245.06/51.54          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 245.06/51.54    (11)   ~ (all_52_1 = e1)
% 245.06/51.54  
% 245.06/51.54  Begin of proof
% 245.06/51.54  | 
% 245.06/51.54  | BETA: splitting (5) gives:
% 245.06/51.54  | 
% 245.06/51.54  | Case 1:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (12)  all_58_2 = e3 & op(e2, e3) = e3
% 245.06/51.54  | | 
% 245.06/51.54  | | ALPHA: (12) implies:
% 245.06/51.54  | |   (13)  op(e2, e3) = e3
% 245.06/51.54  | | 
% 245.06/51.54  | | REF_CLOSE: (4), (6), (8), (13) are inconsistent by sub-proof #2337.
% 245.06/51.54  | | 
% 245.06/51.54  | Case 2:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (14)  all_58_3 = e3 & op(e2, e2) = e3
% 245.06/51.54  | | 
% 245.06/51.54  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (14) are
% 245.06/51.54  | |            inconsistent by sub-proof #2196.
% 245.06/51.54  | | 
% 245.06/51.54  | End of split
% 245.06/51.54  | 
% 245.06/51.54  End of proof
% 245.06/51.54  
% 245.06/51.54  Sub-proof #2196 shows that the following formulas are inconsistent:
% 245.06/51.54  ----------------------------------------------------------------
% 245.06/51.54    (1)  all_58_3 = e3 & op(e2, e2) = e3
% 245.06/51.54    (2)   ~ (all_52_13 = e1)
% 245.06/51.54    (3)   ~ (e3 = e1)
% 245.06/51.54    (4)  op(e2, e1) = all_52_9
% 245.06/51.54    (5)  op(e2, e3) = all_52_1
% 245.06/51.54    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.54    (7)  op(e2, e0) = all_52_13
% 245.06/51.54    (8)   ~ (all_52_9 = e1)
% 245.06/51.54    (9)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 245.06/51.54         (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 245.06/51.54    (10)   ~ (all_52_1 = e1)
% 245.06/51.54  
% 245.06/51.54  Begin of proof
% 245.06/51.54  | 
% 245.06/51.54  | ALPHA: (1) implies:
% 245.06/51.54  |   (11)  all_58_3 = e3
% 245.06/51.54  | 
% 245.06/51.54  | BETA: splitting (9) gives:
% 245.06/51.54  | 
% 245.06/51.54  | Case 1:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (12)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 245.06/51.54  | |           e1)
% 245.06/51.54  | | 
% 245.06/51.54  | | BETA: splitting (12) gives:
% 245.06/51.54  | | 
% 245.06/51.54  | | Case 1:
% 245.06/51.54  | | | 
% 245.06/51.54  | | |   (13)  all_58_2 = e1 & op(e2, e3) = e1
% 245.06/51.54  | | | 
% 245.06/51.54  | | | REF_CLOSE: (5), (6), (10), (13) are inconsistent by sub-proof #2229.
% 245.06/51.54  | | | 
% 245.06/51.54  | | Case 2:
% 245.06/51.54  | | | 
% 245.06/51.54  | | |   (14)  all_58_3 = e1 & op(e2, e2) = e1
% 245.06/51.54  | | | 
% 245.06/51.54  | | | REF_CLOSE: (3), (11), (14) are inconsistent by sub-proof #2197.
% 245.06/51.54  | | | 
% 245.06/51.54  | | End of split
% 245.06/51.54  | | 
% 245.06/51.54  | Case 2:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (15)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 245.06/51.54  | |           e1)
% 245.06/51.54  | | 
% 245.06/51.54  | | REF_CLOSE: (2), (4), (6), (7), (8), (15) are inconsistent by sub-proof
% 245.06/51.54  | |            #2234.
% 245.06/51.54  | | 
% 245.06/51.54  | End of split
% 245.06/51.54  | 
% 245.06/51.54  End of proof
% 245.06/51.54  
% 245.06/51.54  Sub-proof #2197 shows that the following formulas are inconsistent:
% 245.06/51.54  ----------------------------------------------------------------
% 245.06/51.54    (1)  all_58_3 = e1 & op(e2, e2) = e1
% 245.06/51.54    (2)  all_58_3 = e3
% 245.06/51.54    (3)   ~ (e3 = e1)
% 245.06/51.54  
% 245.06/51.54  Begin of proof
% 245.06/51.54  | 
% 245.06/51.54  | ALPHA: (1) implies:
% 245.06/51.54  |   (4)  all_58_3 = e1
% 245.06/51.54  | 
% 245.06/51.54  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.54  |   (5)  e3 = e1
% 245.06/51.54  | 
% 245.06/51.54  | REDUCE: (3), (5) imply:
% 245.06/51.54  |   (6)  $false
% 245.06/51.54  | 
% 245.06/51.54  | CLOSE: (6) is inconsistent.
% 245.06/51.54  | 
% 245.06/51.54  End of proof
% 245.06/51.54  
% 245.06/51.54  Sub-proof #2198 shows that the following formulas are inconsistent:
% 245.06/51.54  ----------------------------------------------------------------
% 245.06/51.54    (1)   ~ (all_52_9 = all_6_2)
% 245.06/51.54    (2)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 245.06/51.54    (3)  all_54_10 = all_6_2
% 245.06/51.54    (4)  op(e2, e1) = e2
% 245.06/51.54    (5)  op(e2, e1) = all_52_9
% 245.06/51.54    (6)   ~ (all_6_2 = e0)
% 245.06/51.54    (7)   ~ (all_6_2 = e1)
% 245.06/51.54    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.54  
% 245.06/51.54  Begin of proof
% 245.06/51.54  | 
% 245.06/51.54  | BETA: splitting (2) gives:
% 245.06/51.54  | 
% 245.06/51.54  | Case 1:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (9)  all_54_10 = e2
% 245.06/51.54  | | 
% 245.06/51.54  | | COMBINE_EQS: (3), (9) imply:
% 245.06/51.54  | |   (10)  all_6_2 = e2
% 245.06/51.54  | | 
% 245.06/51.54  | | SIMP: (10) implies:
% 245.06/51.54  | |   (11)  all_6_2 = e2
% 245.06/51.54  | | 
% 245.06/51.54  | | REDUCE: (1), (11) imply:
% 245.06/51.54  | |   (12)   ~ (all_52_9 = e2)
% 245.06/51.54  | | 
% 245.06/51.54  | | REF_CLOSE: (4), (5), (8), (12) are inconsistent by sub-proof #2328.
% 245.06/51.54  | | 
% 245.06/51.54  | Case 2:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (13)  all_54_10 = e1 | all_54_10 = e0
% 245.06/51.54  | | 
% 245.06/51.54  | | REF_CLOSE: (3), (6), (7), (13) are inconsistent by sub-proof #2282.
% 245.06/51.54  | | 
% 245.06/51.54  | End of split
% 245.06/51.54  | 
% 245.06/51.54  End of proof
% 245.06/51.54  
% 245.06/51.54  Sub-proof #2199 shows that the following formulas are inconsistent:
% 245.06/51.54  ----------------------------------------------------------------
% 245.06/51.54    (1)  op(e0, e3) = all_52_3
% 245.06/51.54    (2)   ~ (e3 = e1)
% 245.06/51.54    (3)  all_56_1 = e3
% 245.06/51.54    (4)  op(e1, e3) = e1
% 245.06/51.54    (5)   ~ (all_52_3 = e3)
% 245.06/51.54    (6)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 245.06/51.54           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 245.06/51.54             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.06/51.54           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 245.06/51.54             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.06/51.54           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.06/51.54           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 245.06/51.54           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 245.06/51.54           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 245.06/51.54           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 245.06/51.54           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 245.06/51.54             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.06/51.54           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.06/51.54           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.06/51.54    (7)  op(e2, e3) = all_52_1
% 245.06/51.54    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.54    (9)   ~ (all_52_1 = e3)
% 245.06/51.54  
% 245.06/51.54  Begin of proof
% 245.06/51.54  | 
% 245.06/51.54  | BETA: splitting (6) gives:
% 245.06/51.54  | 
% 245.06/51.54  | Case 1:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 245.06/51.54  | |             = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 245.06/51.54  | |           e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~
% 245.06/51.54  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.06/51.54  | |           (all_56_31 = e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5
% 245.06/51.54  | |           = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &
% 245.06/51.54  | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 245.06/51.54  | |           op(e1, e3) = e3)
% 245.06/51.54  | | 
% 245.06/51.54  | | BETA: splitting (10) gives:
% 245.06/51.54  | | 
% 245.06/51.54  | | Case 1:
% 245.06/51.54  | | | 
% 245.06/51.54  | | |   (11)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 245.06/51.54  | | |           = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) =
% 245.06/51.54  | | |         e3 & op(e2, e3) = e3
% 245.06/51.54  | | | 
% 245.06/51.54  | | | ALPHA: (11) implies:
% 245.06/51.54  | | |   (12)  op(e2, e3) = e3
% 245.06/51.54  | | | 
% 245.06/51.54  | | | REF_CLOSE: (7), (8), (9), (12) are inconsistent by sub-proof #2337.
% 245.06/51.54  | | | 
% 245.06/51.54  | | Case 2:
% 245.06/51.54  | | | 
% 245.06/51.54  | | |   (13)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.06/51.54  | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.06/51.54  | | |           op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17
% 245.06/51.54  | | |           = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 245.06/51.54  | | |             = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) =
% 245.06/51.54  | | |           e3)
% 245.06/51.54  | | | 
% 245.06/51.54  | | | BETA: splitting (13) gives:
% 245.06/51.54  | | | 
% 245.06/51.54  | | | Case 1:
% 245.06/51.54  | | | | 
% 245.06/51.54  | | | |   (14)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.06/51.54  | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.06/51.54  | | | |         op(e3, e2) = e2 & op(e2, e3) = e2
% 245.06/51.54  | | | | 
% 245.06/51.54  | | | | ALPHA: (14) implies:
% 245.06/51.54  | | | |   (15)   ~ (all_56_1 = e3)
% 245.06/51.54  | | | | 
% 245.06/51.54  | | | | REDUCE: (3), (15) imply:
% 245.06/51.54  | | | |   (16)  $false
% 245.06/51.54  | | | | 
% 245.06/51.54  | | | | CLOSE: (16) is inconsistent.
% 245.06/51.54  | | | | 
% 245.06/51.54  | | | Case 2:
% 245.06/51.54  | | | | 
% 245.06/51.54  | | | |   (17)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 245.06/51.54  | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 245.06/51.54  | | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 245.06/51.54  | | | | 
% 245.06/51.54  | | | | ALPHA: (17) implies:
% 245.06/51.54  | | | |   (18)  op(e1, e3) = e3
% 245.06/51.54  | | | | 
% 245.06/51.54  | | | | REF_CLOSE: (2), (4), (8), (18) are inconsistent by sub-proof #2225.
% 245.06/51.54  | | | | 
% 245.06/51.54  | | | End of split
% 245.06/51.54  | | | 
% 245.06/51.54  | | End of split
% 245.06/51.54  | | 
% 245.06/51.54  | Case 2:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (19)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 245.06/51.54  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) =
% 245.06/51.54  | |           e1 & op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~
% 245.06/51.54  | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.06/51.54  | |           (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7
% 245.06/51.54  | |           = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &
% 245.06/51.54  | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 245.06/51.54  | |           op(e0, e3) = e0)
% 245.06/51.54  | | 
% 245.06/51.54  | | REF_CLOSE: (1), (3), (5), (8), (19) are inconsistent by sub-proof #2270.
% 245.06/51.54  | | 
% 245.06/51.54  | End of split
% 245.06/51.54  | 
% 245.06/51.54  End of proof
% 245.06/51.54  
% 245.06/51.54  Sub-proof #2200 shows that the following formulas are inconsistent:
% 245.06/51.54  ----------------------------------------------------------------
% 245.06/51.54    (1)   ~ (e3 = e0)
% 245.06/51.54    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 245.06/51.54         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 245.06/51.54    (3)   ~ (e2 = e0)
% 245.06/51.54    (4)  op(e1, e2) = all_52_6
% 245.06/51.54    (5)   ~ (e3 = e1)
% 245.06/51.54    (6)  all_58_7 = e2
% 245.06/51.54    (7)   ~ (e3 = e2)
% 245.06/51.54    (8)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 245.06/51.54         (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 245.06/51.54    (9)  all_58_6 = e1
% 245.06/51.54    (10)  op(e1, e2) = e2
% 245.06/51.54    (11)  op(e1, e1) = e2
% 245.06/51.54    (12)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 245.06/51.54          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 245.06/51.54    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.54    (14)   ~ (e1 = e0)
% 245.06/51.54    (15)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 245.06/51.54          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 245.06/51.54    (16)   ~ (e2 = e1)
% 245.06/51.54  
% 245.06/51.54  Begin of proof
% 245.06/51.54  | 
% 245.06/51.54  | BETA: splitting (8) gives:
% 245.06/51.54  | 
% 245.06/51.54  | Case 1:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (17)  (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 245.06/51.54  | |           e3)
% 245.06/51.54  | | 
% 245.06/51.54  | | BETA: splitting (17) gives:
% 245.06/51.54  | | 
% 245.06/51.54  | | Case 1:
% 245.06/51.54  | | | 
% 245.06/51.54  | | |   (18)  all_58_6 = e3 & op(e1, e3) = e3
% 245.06/51.54  | | | 
% 245.06/51.54  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13),
% 245.06/51.54  | | |            (14), (15), (16), (18) are inconsistent by sub-proof #2208.
% 245.06/51.54  | | | 
% 245.06/51.54  | | Case 2:
% 245.06/51.54  | | | 
% 245.06/51.54  | | |   (19)  all_58_7 = e3 & op(e1, e2) = e3
% 245.06/51.54  | | | 
% 245.06/51.54  | | | ALPHA: (19) implies:
% 245.06/51.54  | | |   (20)  op(e1, e2) = e3
% 245.06/51.54  | | | 
% 245.06/51.54  | | | REF_CLOSE: (7), (10), (13), (20) are inconsistent by sub-proof #2207.
% 245.06/51.54  | | | 
% 245.06/51.54  | | End of split
% 245.06/51.54  | | 
% 245.06/51.54  | Case 2:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (21)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 245.06/51.54  | |           e3)
% 245.06/51.54  | | 
% 245.06/51.54  | | REF_CLOSE: (1), (3), (6), (7), (9), (11), (13), (14), (15), (21) are
% 245.06/51.54  | |            inconsistent by sub-proof #2201.
% 245.06/51.54  | | 
% 245.06/51.54  | End of split
% 245.06/51.54  | 
% 245.06/51.54  End of proof
% 245.06/51.54  
% 245.06/51.54  Sub-proof #2201 shows that the following formulas are inconsistent:
% 245.06/51.54  ----------------------------------------------------------------
% 245.06/51.54    (1)   ~ (e3 = e0)
% 245.06/51.54    (2)   ~ (e2 = e0)
% 245.06/51.54    (3)  all_58_7 = e2
% 245.06/51.54    (4)   ~ (e3 = e2)
% 245.06/51.54    (5)  (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 245.06/51.54    (6)  all_58_6 = e1
% 245.06/51.54    (7)  op(e1, e1) = e2
% 245.06/51.54    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.54    (9)   ~ (e1 = e0)
% 245.06/51.54    (10)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 245.06/51.54          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 245.06/51.54  
% 245.06/51.54  Begin of proof
% 245.06/51.54  | 
% 245.06/51.54  | BETA: splitting (5) gives:
% 245.06/51.54  | 
% 245.06/51.54  | Case 1:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (11)  all_58_8 = e3 & op(e1, e1) = e3
% 245.06/51.54  | | 
% 245.06/51.54  | | ALPHA: (11) implies:
% 245.06/51.54  | |   (12)  op(e1, e1) = e3
% 245.06/51.54  | | 
% 245.06/51.54  | | REF_CLOSE: (4), (7), (8), (12) are inconsistent by sub-proof #2206.
% 245.06/51.54  | | 
% 245.06/51.54  | Case 2:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (13)  all_58_11 = e3 & op(e1, e0) = e3
% 245.06/51.54  | | 
% 245.06/51.54  | | ALPHA: (13) implies:
% 245.06/51.54  | |   (14)  all_58_11 = e3
% 245.06/51.54  | | 
% 245.06/51.54  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (14) are inconsistent by
% 245.06/51.54  | |            sub-proof #2202.
% 245.06/51.54  | | 
% 245.06/51.54  | End of split
% 245.06/51.54  | 
% 245.06/51.54  End of proof
% 245.06/51.54  
% 245.06/51.54  Sub-proof #2202 shows that the following formulas are inconsistent:
% 245.06/51.54  ----------------------------------------------------------------
% 245.06/51.54    (1)   ~ (e3 = e0)
% 245.06/51.54    (2)   ~ (e2 = e0)
% 245.06/51.54    (3)  all_58_7 = e2
% 245.06/51.54    (4)  all_58_11 = e3
% 245.06/51.54    (5)  all_58_6 = e1
% 245.06/51.54    (6)  op(e1, e1) = e2
% 245.06/51.54    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.54    (8)   ~ (e1 = e0)
% 245.06/51.54    (9)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 245.06/51.54         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 245.06/51.54  
% 245.06/51.54  Begin of proof
% 245.06/51.54  | 
% 245.06/51.54  | BETA: splitting (9) gives:
% 245.06/51.54  | 
% 245.06/51.54  | Case 1:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (10)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 245.06/51.54  | |           e0)
% 245.06/51.54  | | 
% 245.06/51.54  | | BETA: splitting (10) gives:
% 245.06/51.54  | | 
% 245.06/51.54  | | Case 1:
% 245.06/51.54  | | | 
% 245.06/51.54  | | |   (11)  all_58_6 = e0 & op(e1, e3) = e0
% 245.06/51.54  | | | 
% 245.06/51.54  | | | REF_CLOSE: (5), (8), (11) are inconsistent by sub-proof #2205.
% 245.06/51.54  | | | 
% 245.06/51.54  | | Case 2:
% 245.06/51.54  | | | 
% 245.06/51.54  | | |   (12)  all_58_7 = e0 & op(e1, e2) = e0
% 245.06/51.54  | | | 
% 245.06/51.54  | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #2212.
% 245.06/51.54  | | | 
% 245.06/51.54  | | End of split
% 245.06/51.54  | | 
% 245.06/51.54  | Case 2:
% 245.06/51.54  | | 
% 245.06/51.54  | |   (13)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 245.06/51.54  | |           e0)
% 245.06/51.54  | | 
% 245.06/51.54  | | REF_CLOSE: (1), (2), (4), (6), (7), (13) are inconsistent by sub-proof
% 245.06/51.54  | |            #2203.
% 245.06/51.54  | | 
% 245.06/51.54  | End of split
% 245.06/51.54  | 
% 245.06/51.54  End of proof
% 245.06/51.54  
% 245.06/51.54  Sub-proof #2203 shows that the following formulas are inconsistent:
% 245.06/51.54  ----------------------------------------------------------------
% 245.06/51.54    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 245.06/51.55    (2)   ~ (e3 = e0)
% 245.06/51.55    (3)   ~ (e2 = e0)
% 245.06/51.55    (4)  all_58_11 = e3
% 245.06/51.55    (5)  op(e1, e1) = e2
% 245.06/51.55    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | BETA: splitting (1) gives:
% 245.06/51.55  | 
% 245.06/51.55  | Case 1:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 245.06/51.55  | | 
% 245.06/51.55  | | ALPHA: (7) implies:
% 245.06/51.55  | |   (8)  op(e1, e1) = e0
% 245.06/51.55  | | 
% 245.06/51.55  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2211.
% 245.06/51.55  | | 
% 245.06/51.55  | Case 2:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (9)  all_58_11 = e0 & op(e1, e0) = e0
% 245.06/51.55  | | 
% 245.06/51.55  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #2204.
% 245.06/51.55  | | 
% 245.06/51.55  | End of split
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2204 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)  all_58_11 = e0 & op(e1, e0) = e0
% 245.06/51.55    (2)  all_58_11 = e3
% 245.06/51.55    (3)   ~ (e3 = e0)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | ALPHA: (1) implies:
% 245.06/51.55  |   (4)  all_58_11 = e0
% 245.06/51.55  | 
% 245.06/51.55  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.55  |   (5)  e3 = e0
% 245.06/51.55  | 
% 245.06/51.55  | REDUCE: (3), (5) imply:
% 245.06/51.55  |   (6)  $false
% 245.06/51.55  | 
% 245.06/51.55  | CLOSE: (6) is inconsistent.
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2205 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)  all_58_6 = e0 & op(e1, e3) = e0
% 245.06/51.55    (2)  all_58_6 = e1
% 245.06/51.55    (3)   ~ (e1 = e0)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | ALPHA: (1) implies:
% 245.06/51.55  |   (4)  all_58_6 = e0
% 245.06/51.55  | 
% 245.06/51.55  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.55  |   (5)  e1 = e0
% 245.06/51.55  | 
% 245.06/51.55  | REDUCE: (3), (5) imply:
% 245.06/51.55  |   (6)  $false
% 245.06/51.55  | 
% 245.06/51.55  | CLOSE: (6) is inconsistent.
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2206 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.55    (2)  op(e1, e1) = e3
% 245.06/51.55    (3)  op(e1, e1) = e2
% 245.06/51.55    (4)   ~ (e3 = e2)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | GROUND_INST: instantiating (1) with e2, e3, e1, e1, simplifying with (2), (3)
% 245.06/51.55  |              gives:
% 245.06/51.55  |   (5)  e3 = e2
% 245.06/51.55  | 
% 245.06/51.55  | REDUCE: (4), (5) imply:
% 245.06/51.55  |   (6)  $false
% 245.06/51.55  | 
% 245.06/51.55  | CLOSE: (6) is inconsistent.
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2207 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.55    (2)  op(e1, e2) = e3
% 245.06/51.55    (3)  op(e1, e2) = e2
% 245.06/51.55    (4)   ~ (e3 = e2)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | GROUND_INST: instantiating (1) with e3, e2, e2, e1, simplifying with (2), (3)
% 245.06/51.55  |              gives:
% 245.06/51.55  |   (5)  e3 = e2
% 245.06/51.55  | 
% 245.06/51.55  | REDUCE: (4), (5) imply:
% 245.06/51.55  |   (6)  $false
% 245.06/51.55  | 
% 245.06/51.55  | CLOSE: (6) is inconsistent.
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2208 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)   ~ (e3 = e0)
% 245.06/51.55    (2)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 245.06/51.55         (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 245.06/51.55    (3)   ~ (e2 = e0)
% 245.06/51.55    (4)  all_58_6 = e3 & op(e1, e3) = e3
% 245.06/51.55    (5)  op(e1, e2) = all_52_6
% 245.06/51.55    (6)   ~ (e3 = e1)
% 245.06/51.55    (7)  all_58_7 = e2
% 245.06/51.55    (8)   ~ (e3 = e2)
% 245.06/51.55    (9)  op(e1, e2) = e2
% 245.06/51.55    (10)  op(e1, e1) = e2
% 245.06/51.55    (11)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 245.06/51.55          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 245.06/51.55    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.55    (13)   ~ (e1 = e0)
% 245.06/51.55    (14)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 245.06/51.55          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 245.06/51.55    (15)   ~ (e2 = e1)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | ALPHA: (4) implies:
% 245.06/51.55  |   (16)  all_58_6 = e3
% 245.06/51.55  |   (17)  op(e1, e3) = e3
% 245.06/51.55  | 
% 245.06/51.55  | BETA: splitting (2) gives:
% 245.06/51.55  | 
% 245.06/51.55  | Case 1:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (18)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 245.06/51.55  | |           e1)
% 245.06/51.55  | | 
% 245.06/51.55  | | REF_CLOSE: (6), (7), (12), (15), (17), (18) are inconsistent by sub-proof
% 245.06/51.55  | |            #2223.
% 245.06/51.55  | | 
% 245.06/51.55  | Case 2:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (19)  (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 245.06/51.55  | |           e1)
% 245.06/51.55  | | 
% 245.06/51.55  | | BETA: splitting (19) gives:
% 245.06/51.55  | | 
% 245.06/51.55  | | Case 1:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (20)  all_58_8 = e1 & op(e1, e1) = e1
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 245.06/51.55  | | |            (15), (16), (20) are inconsistent by sub-proof #2214.
% 245.06/51.55  | | | 
% 245.06/51.55  | | Case 2:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (21)  all_58_11 = e1 & op(e1, e0) = e1
% 245.06/51.55  | | | 
% 245.06/51.55  | | | ALPHA: (21) implies:
% 245.06/51.55  | | |   (22)  op(e1, e0) = e1
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (1), (3), (7), (10), (12), (13), (14), (16), (22) are
% 245.06/51.55  | | |            inconsistent by sub-proof #2209.
% 245.06/51.55  | | | 
% 245.06/51.55  | | End of split
% 245.06/51.55  | | 
% 245.06/51.55  | End of split
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2209 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)   ~ (e3 = e0)
% 245.06/51.55    (2)  all_58_6 = e3
% 245.06/51.55    (3)   ~ (e2 = e0)
% 245.06/51.55    (4)  all_58_7 = e2
% 245.06/51.55    (5)  op(e1, e0) = e1
% 245.06/51.55    (6)  op(e1, e1) = e2
% 245.06/51.55    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.55    (8)   ~ (e1 = e0)
% 245.06/51.55    (9)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 245.06/51.55         (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | BETA: splitting (9) gives:
% 245.06/51.55  | 
% 245.06/51.55  | Case 1:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (10)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 245.06/51.55  | |           e0)
% 245.06/51.55  | | 
% 245.06/51.55  | | BETA: splitting (10) gives:
% 245.06/51.55  | | 
% 245.06/51.55  | | Case 1:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (11)  all_58_6 = e0 & op(e1, e3) = e0
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (1), (2), (11) are inconsistent by sub-proof #2213.
% 245.06/51.55  | | | 
% 245.06/51.55  | | Case 2:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (12)  all_58_7 = e0 & op(e1, e2) = e0
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #2212.
% 245.06/51.55  | | | 
% 245.06/51.55  | | End of split
% 245.06/51.55  | | 
% 245.06/51.55  | Case 2:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (13)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 245.06/51.55  | |           e0)
% 245.06/51.55  | | 
% 245.06/51.55  | | REF_CLOSE: (3), (5), (6), (7), (8), (13) are inconsistent by sub-proof
% 245.06/51.55  | |            #2210.
% 245.06/51.55  | | 
% 245.06/51.55  | End of split
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2210 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 245.06/51.55    (2)   ~ (e2 = e0)
% 245.06/51.55    (3)  op(e1, e0) = e1
% 245.06/51.55    (4)  op(e1, e1) = e2
% 245.06/51.55    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.55    (6)   ~ (e1 = e0)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | BETA: splitting (1) gives:
% 245.06/51.55  | 
% 245.06/51.55  | Case 1:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (7)  all_58_8 = e0 & op(e1, e1) = e0
% 245.06/51.55  | | 
% 245.06/51.55  | | ALPHA: (7) implies:
% 245.06/51.55  | |   (8)  op(e1, e1) = e0
% 245.06/51.55  | | 
% 245.06/51.55  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2211.
% 245.06/51.55  | | 
% 245.06/51.55  | Case 2:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (9)  all_58_11 = e0 & op(e1, e0) = e0
% 245.06/51.55  | | 
% 245.06/51.55  | | ALPHA: (9) implies:
% 245.06/51.55  | |   (10)  op(e1, e0) = e0
% 245.06/51.55  | | 
% 245.06/51.55  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #2284.
% 245.06/51.55  | | 
% 245.06/51.55  | End of split
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2211 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.55    (2)  op(e1, e1) = e2
% 245.06/51.55    (3)  op(e1, e1) = e0
% 245.06/51.55    (4)   ~ (e2 = e0)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | GROUND_INST: instantiating (1) with e0, e2, e1, e1, simplifying with (2), (3)
% 245.06/51.55  |              gives:
% 245.06/51.55  |   (5)  e2 = e0
% 245.06/51.55  | 
% 245.06/51.55  | REDUCE: (4), (5) imply:
% 245.06/51.55  |   (6)  $false
% 245.06/51.55  | 
% 245.06/51.55  | CLOSE: (6) is inconsistent.
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2212 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)  all_58_7 = e0 & op(e1, e2) = e0
% 245.06/51.55    (2)  all_58_7 = e2
% 245.06/51.55    (3)   ~ (e2 = e0)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | ALPHA: (1) implies:
% 245.06/51.55  |   (4)  all_58_7 = e0
% 245.06/51.55  | 
% 245.06/51.55  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.55  |   (5)  e2 = e0
% 245.06/51.55  | 
% 245.06/51.55  | REDUCE: (3), (5) imply:
% 245.06/51.55  |   (6)  $false
% 245.06/51.55  | 
% 245.06/51.55  | CLOSE: (6) is inconsistent.
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2213 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)  all_58_6 = e0 & op(e1, e3) = e0
% 245.06/51.55    (2)  all_58_6 = e3
% 245.06/51.55    (3)   ~ (e3 = e0)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | ALPHA: (1) implies:
% 245.06/51.55  |   (4)  all_58_6 = e0
% 245.06/51.55  | 
% 245.06/51.55  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.55  |   (5)  e3 = e0
% 245.06/51.55  | 
% 245.06/51.55  | REDUCE: (3), (5) imply:
% 245.06/51.55  |   (6)  $false
% 245.06/51.55  | 
% 245.06/51.55  | CLOSE: (6) is inconsistent.
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2214 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)   ~ (e3 = e0)
% 245.06/51.55    (2)  all_58_6 = e3
% 245.06/51.55    (3)   ~ (e2 = e0)
% 245.06/51.55    (4)  op(e1, e2) = all_52_6
% 245.06/51.55    (5)  all_58_7 = e2
% 245.06/51.55    (6)   ~ (e3 = e2)
% 245.06/51.55    (7)  all_58_8 = e1 & op(e1, e1) = e1
% 245.06/51.55    (8)  op(e1, e2) = e2
% 245.06/51.55    (9)  op(e1, e1) = e2
% 245.06/51.55    (10)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 245.06/51.55          (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 245.06/51.55    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.55    (12)   ~ (e1 = e0)
% 245.06/51.55    (13)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 245.06/51.55          (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 245.06/51.55    (14)   ~ (e2 = e1)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | ALPHA: (7) implies:
% 245.06/51.55  |   (15)  all_58_8 = e1
% 245.06/51.55  |   (16)  op(e1, e1) = e1
% 245.06/51.55  | 
% 245.06/51.55  | BETA: splitting (13) gives:
% 245.06/51.55  | 
% 245.06/51.55  | Case 1:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (17)  (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 245.06/51.55  | |           e0)
% 245.06/51.55  | | 
% 245.06/51.55  | | BETA: splitting (17) gives:
% 245.06/51.55  | | 
% 245.06/51.55  | | Case 1:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (18)  all_58_6 = e0 & op(e1, e3) = e0
% 245.06/51.55  | | | 
% 245.06/51.55  | | | ALPHA: (18) implies:
% 245.06/51.55  | | |   (19)  all_58_6 = e0
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (1), (2), (19) are inconsistent by sub-proof #2222.
% 245.06/51.55  | | | 
% 245.06/51.55  | | Case 2:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (20)  all_58_7 = e0 & op(e1, e2) = e0
% 245.06/51.55  | | | 
% 245.06/51.55  | | | ALPHA: (20) implies:
% 245.06/51.55  | | |   (21)  op(e1, e2) = e0
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (4), (8), (9), (11), (12), (16), (21) are inconsistent by
% 245.06/51.55  | | |            sub-proof #2221.
% 245.06/51.55  | | | 
% 245.06/51.55  | | End of split
% 245.06/51.55  | | 
% 245.06/51.55  | Case 2:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (22)  (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 245.06/51.55  | |           e0)
% 245.06/51.55  | | 
% 245.06/51.55  | | BETA: splitting (22) gives:
% 245.06/51.55  | | 
% 245.06/51.55  | | Case 1:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (23)  all_58_8 = e0 & op(e1, e1) = e0
% 245.06/51.55  | | | 
% 245.06/51.55  | | | ALPHA: (23) implies:
% 245.06/51.55  | | |   (24)  op(e1, e1) = e0
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (11), (12), (16), (24) are inconsistent by sub-proof #2220.
% 245.06/51.55  | | | 
% 245.06/51.55  | | Case 2:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (25)  all_58_11 = e0 & op(e1, e0) = e0
% 245.06/51.55  | | | 
% 245.06/51.55  | | | ALPHA: (25) implies:
% 245.06/51.55  | | |   (26)  all_58_11 = e0
% 245.06/51.55  | | | 
% 245.06/51.55  | | | GROUND_INST: instantiating (11) with e1, e2, e1, e1, simplifying with (9),
% 245.06/51.55  | | |              (16) gives:
% 245.06/51.55  | | |   (27)  e2 = e1
% 245.06/51.55  | | | 
% 245.06/51.55  | | | COMBINE_EQS: (5), (27) imply:
% 245.06/51.55  | | |   (28)  all_58_7 = e1
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (2), (3), (6), (10), (14), (15), (26), (28) are inconsistent by
% 245.06/51.55  | | |            sub-proof #2215.
% 245.06/51.55  | | | 
% 245.06/51.55  | | End of split
% 245.06/51.55  | | 
% 245.06/51.55  | End of split
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2215 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)  all_58_6 = e3
% 245.06/51.55    (2)   ~ (e2 = e0)
% 245.06/51.55    (3)  all_58_8 = e1
% 245.06/51.55    (4)   ~ (e3 = e2)
% 245.06/51.55    (5)  all_58_7 = e1
% 245.06/51.55    (6)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 245.06/51.55         (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 245.06/51.55    (7)  all_58_11 = e0
% 245.06/51.55    (8)   ~ (e2 = e1)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | BETA: splitting (6) gives:
% 245.06/51.55  | 
% 245.06/51.55  | Case 1:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (9)  (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 245.06/51.55  | | 
% 245.06/51.55  | | BETA: splitting (9) gives:
% 245.06/51.55  | | 
% 245.06/51.55  | | Case 1:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (10)  all_58_6 = e2 & op(e1, e3) = e2
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (1), (4), (10) are inconsistent by sub-proof #2219.
% 245.06/51.55  | | | 
% 245.06/51.55  | | Case 2:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (11)  all_58_7 = e2 & op(e1, e2) = e2
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (5), (8), (11) are inconsistent by sub-proof #2218.
% 245.06/51.55  | | | 
% 245.06/51.55  | | End of split
% 245.06/51.55  | | 
% 245.06/51.55  | Case 2:
% 245.06/51.55  | | 
% 245.06/51.55  | |   (12)  (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 245.06/51.55  | |           e2)
% 245.06/51.55  | | 
% 245.06/51.55  | | BETA: splitting (12) gives:
% 245.06/51.55  | | 
% 245.06/51.55  | | Case 1:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (13)  all_58_8 = e2 & op(e1, e1) = e2
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #2217.
% 245.06/51.55  | | | 
% 245.06/51.55  | | Case 2:
% 245.06/51.55  | | | 
% 245.06/51.55  | | |   (14)  all_58_11 = e2 & op(e1, e0) = e2
% 245.06/51.55  | | | 
% 245.06/51.55  | | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #2216.
% 245.06/51.55  | | | 
% 245.06/51.55  | | End of split
% 245.06/51.55  | | 
% 245.06/51.55  | End of split
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2216 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)  all_58_11 = e2 & op(e1, e0) = e2
% 245.06/51.55    (2)  all_58_11 = e0
% 245.06/51.55    (3)   ~ (e2 = e0)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | ALPHA: (1) implies:
% 245.06/51.55  |   (4)  all_58_11 = e2
% 245.06/51.55  | 
% 245.06/51.55  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.55  |   (5)  e2 = e0
% 245.06/51.55  | 
% 245.06/51.55  | REDUCE: (3), (5) imply:
% 245.06/51.55  |   (6)  $false
% 245.06/51.55  | 
% 245.06/51.55  | CLOSE: (6) is inconsistent.
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2217 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)  all_58_8 = e2 & op(e1, e1) = e2
% 245.06/51.55    (2)  all_58_8 = e1
% 245.06/51.55    (3)   ~ (e2 = e1)
% 245.06/51.55  
% 245.06/51.55  Begin of proof
% 245.06/51.55  | 
% 245.06/51.55  | ALPHA: (1) implies:
% 245.06/51.55  |   (4)  all_58_8 = e2
% 245.06/51.55  | 
% 245.06/51.55  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.55  |   (5)  e2 = e1
% 245.06/51.55  | 
% 245.06/51.55  | REDUCE: (3), (5) imply:
% 245.06/51.55  |   (6)  $false
% 245.06/51.55  | 
% 245.06/51.55  | CLOSE: (6) is inconsistent.
% 245.06/51.55  | 
% 245.06/51.55  End of proof
% 245.06/51.55  
% 245.06/51.55  Sub-proof #2218 shows that the following formulas are inconsistent:
% 245.06/51.55  ----------------------------------------------------------------
% 245.06/51.55    (1)  all_58_7 = e2 & op(e1, e2) = e2
% 245.06/51.55    (2)  all_58_7 = e1
% 245.06/51.56    (3)   ~ (e2 = e1)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | ALPHA: (1) implies:
% 245.06/51.56  |   (4)  all_58_7 = e2
% 245.06/51.56  | 
% 245.06/51.56  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.56  |   (5)  e2 = e1
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (3), (5) imply:
% 245.06/51.56  |   (6)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (6) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2219 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)  all_58_6 = e2 & op(e1, e3) = e2
% 245.06/51.56    (2)  all_58_6 = e3
% 245.06/51.56    (3)   ~ (e3 = e2)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | ALPHA: (1) implies:
% 245.06/51.56  |   (4)  all_58_6 = e2
% 245.06/51.56  | 
% 245.06/51.56  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.56  |   (5)  e3 = e2
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (3), (5) imply:
% 245.06/51.56  |   (6)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (6) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2220 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.56    (2)  op(e1, e1) = e1
% 245.06/51.56    (3)  op(e1, e1) = e0
% 245.06/51.56    (4)   ~ (e1 = e0)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | GROUND_INST: instantiating (1) with e0, e1, e1, e1, simplifying with (2), (3)
% 245.06/51.56  |              gives:
% 245.06/51.56  |   (5)  e1 = e0
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (4), (5) imply:
% 245.06/51.56  |   (6)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (6) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2221 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)  op(e1, e1) = e1
% 245.06/51.56    (2)  op(e1, e2) = all_52_6
% 245.06/51.56    (3)  op(e1, e2) = e0
% 245.06/51.56    (4)  op(e1, e2) = e2
% 245.06/51.56    (5)  op(e1, e1) = e2
% 245.06/51.56    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.56    (7)   ~ (e1 = e0)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | GROUND_INST: instantiating (6) with e1, e2, e1, e1, simplifying with (1), (5)
% 245.06/51.56  |              gives:
% 245.06/51.56  |   (8)  e2 = e1
% 245.06/51.56  | 
% 245.06/51.56  | GROUND_INST: instantiating (6) with all_52_6, e0, e2, e1, simplifying with
% 245.06/51.56  |              (2), (3) gives:
% 245.06/51.56  |   (9)  all_52_6 = e0
% 245.06/51.56  | 
% 245.06/51.56  | GROUND_INST: instantiating (6) with all_52_6, e2, e2, e1, simplifying with
% 245.06/51.56  |              (2), (4) gives:
% 245.06/51.56  |   (10)  all_52_6 = e2
% 245.06/51.56  | 
% 245.06/51.56  | COMBINE_EQS: (9), (10) imply:
% 245.06/51.56  |   (11)  e2 = e0
% 245.06/51.56  | 
% 245.06/51.56  | SIMP: (11) implies:
% 245.06/51.56  |   (12)  e2 = e0
% 245.06/51.56  | 
% 245.06/51.56  | COMBINE_EQS: (8), (12) imply:
% 245.06/51.56  |   (13)  e1 = e0
% 245.06/51.56  | 
% 245.06/51.56  | SIMP: (13) implies:
% 245.06/51.56  |   (14)  e1 = e0
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (7), (14) imply:
% 245.06/51.56  |   (15)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (15) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2222 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)  all_58_6 = e3
% 245.06/51.56    (2)  all_58_6 = e0
% 245.06/51.56    (3)   ~ (e3 = e0)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | COMBINE_EQS: (1), (2) imply:
% 245.06/51.56  |   (4)  e3 = e0
% 245.06/51.56  | 
% 245.06/51.56  | SIMP: (4) implies:
% 245.06/51.56  |   (5)  e3 = e0
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (3), (5) imply:
% 245.06/51.56  |   (6)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (6) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2223 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)  op(e1, e3) = e3
% 245.06/51.56    (2)   ~ (e3 = e1)
% 245.06/51.56    (3)  all_58_7 = e2
% 245.06/51.56    (4)  (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 245.06/51.56    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.56    (6)   ~ (e2 = e1)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | BETA: splitting (4) gives:
% 245.06/51.56  | 
% 245.06/51.56  | Case 1:
% 245.06/51.56  | | 
% 245.06/51.56  | |   (7)  all_58_6 = e1 & op(e1, e3) = e1
% 245.06/51.56  | | 
% 245.06/51.56  | | ALPHA: (7) implies:
% 245.06/51.56  | |   (8)  op(e1, e3) = e1
% 245.06/51.56  | | 
% 245.06/51.56  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #2225.
% 245.06/51.56  | | 
% 245.06/51.56  | Case 2:
% 245.06/51.56  | | 
% 245.06/51.56  | |   (9)  all_58_7 = e1 & op(e1, e2) = e1
% 245.06/51.56  | | 
% 245.06/51.56  | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #2224.
% 245.06/51.56  | | 
% 245.06/51.56  | End of split
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2224 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)  all_58_7 = e1 & op(e1, e2) = e1
% 245.06/51.56    (2)  all_58_7 = e2
% 245.06/51.56    (3)   ~ (e2 = e1)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | ALPHA: (1) implies:
% 245.06/51.56  |   (4)  all_58_7 = e1
% 245.06/51.56  | 
% 245.06/51.56  | COMBINE_EQS: (2), (4) imply:
% 245.06/51.56  |   (5)  e2 = e1
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (3), (5) imply:
% 245.06/51.56  |   (6)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (6) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2225 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.56    (2)  op(e1, e3) = e3
% 245.06/51.56    (3)  op(e1, e3) = e1
% 245.06/51.56    (4)   ~ (e3 = e1)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | GROUND_INST: instantiating (1) with e1, e3, e3, e1, simplifying with (2), (3)
% 245.06/51.56  |              gives:
% 245.06/51.56  |   (5)  e3 = e1
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (4), (5) imply:
% 245.06/51.56  |   (6)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (6) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2226 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.56    (2)  op(e1, e3) = e2
% 245.06/51.56    (3)  op(e1, e3) = e1
% 245.06/51.56    (4)   ~ (e2 = e1)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | GROUND_INST: instantiating (1) with e2, e1, e3, e1, simplifying with (2), (3)
% 245.06/51.56  |              gives:
% 245.06/51.56  |   (5)  e2 = e1
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (4), (5) imply:
% 245.06/51.56  |   (6)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (6) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2227 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)   ~ (all_10_2 = e1)
% 245.06/51.56    (2)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 245.06/51.56    (3)  op(e3, e2) = all_52_4
% 245.06/51.56    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.56    (5)  op(e3, e3) = all_10_2
% 245.06/51.56    (6)   ~ (all_52_4 = e1)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | BETA: splitting (2) gives:
% 245.06/51.56  | 
% 245.06/51.56  | Case 1:
% 245.06/51.56  | | 
% 245.06/51.56  | |   (7)  all_58_0 = e1 & op(e3, e3) = e1
% 245.06/51.56  | | 
% 245.06/51.56  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #2230.
% 245.06/51.56  | | 
% 245.06/51.56  | Case 2:
% 245.06/51.56  | | 
% 245.06/51.56  | |   (8)  all_58_1 = e1 & op(e3, e2) = e1
% 245.06/51.56  | | 
% 245.06/51.56  | | ALPHA: (8) implies:
% 245.06/51.56  | |   (9)  op(e3, e2) = e1
% 245.06/51.56  | | 
% 245.06/51.56  | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #2228.
% 245.06/51.56  | | 
% 245.06/51.56  | End of split
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2228 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.56    (2)  op(e3, e2) = all_52_4
% 245.06/51.56    (3)  op(e3, e2) = e1
% 245.06/51.56    (4)   ~ (all_52_4 = e1)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | GROUND_INST: instantiating (1) with all_52_4, e1, e2, e3, simplifying with
% 245.06/51.56  |              (2), (3) gives:
% 245.06/51.56  |   (5)  all_52_4 = e1
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (4), (5) imply:
% 245.06/51.56  |   (6)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (6) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2229 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)  all_58_2 = e1 & op(e2, e3) = e1
% 245.06/51.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.56    (3)  op(e2, e3) = all_52_1
% 245.06/51.56    (4)   ~ (all_52_1 = e1)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | ALPHA: (1) implies:
% 245.06/51.56  |   (5)  op(e2, e3) = e1
% 245.06/51.56  | 
% 245.06/51.56  | GROUND_INST: instantiating (2) with all_52_1, e1, e3, e2, simplifying with
% 245.06/51.56  |              (3), (5) gives:
% 245.06/51.56  |   (6)  all_52_1 = e1
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (4), (6) imply:
% 245.06/51.56  |   (7)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (7) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2230 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)  all_58_0 = e1 & op(e3, e3) = e1
% 245.06/51.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.56    (3)  op(e3, e3) = all_10_2
% 245.06/51.56    (4)   ~ (all_10_2 = e1)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | ALPHA: (1) implies:
% 245.06/51.56  |   (5)  op(e3, e3) = e1
% 245.06/51.56  | 
% 245.06/51.56  | GROUND_INST: instantiating (2) with all_10_2, e1, e3, e3, simplifying with
% 245.06/51.56  |              (3), (5) gives:
% 245.06/51.56  |   (6)  all_10_2 = e1
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (4), (6) imply:
% 245.06/51.56  |   (7)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (7) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2231 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)  all_58_15 = e2
% 245.06/51.56    (2)  all_58_15 = e1
% 245.06/51.56    (3)   ~ (e2 = e1)
% 245.06/51.56  
% 245.06/51.56  Begin of proof
% 245.06/51.56  | 
% 245.06/51.56  | COMBINE_EQS: (1), (2) imply:
% 245.06/51.56  |   (4)  e2 = e1
% 245.06/51.56  | 
% 245.06/51.56  | SIMP: (4) implies:
% 245.06/51.56  |   (5)  e2 = e1
% 245.06/51.56  | 
% 245.06/51.56  | REDUCE: (3), (5) imply:
% 245.06/51.56  |   (6)  $false
% 245.06/51.56  | 
% 245.06/51.56  | CLOSE: (6) is inconsistent.
% 245.06/51.56  | 
% 245.06/51.56  End of proof
% 245.06/51.56  
% 245.06/51.56  Sub-proof #2232 shows that the following formulas are inconsistent:
% 245.06/51.56  ----------------------------------------------------------------
% 245.06/51.56    (1)  op(e0, e0) = e1
% 245.06/51.56    (2)   ~ (all_52_1 = all_52_3)
% 245.06/51.56    (3)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 245.06/51.56             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 245.06/51.56           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 245.06/51.56         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 245.06/51.56           $i(all_56_7))
% 245.06/51.56    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 245.06/51.56    (5)   ~ (all_52_9 = all_6_2)
% 245.06/51.56    (6)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 245.06/51.56    (7)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 245.06/51.56         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 245.06/51.56    (8)  ( ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 & op(e3, e2) = all_24_1
% 245.06/51.56           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e3, e2) =
% 245.06/51.56           all_24_1 & $i(all_24_1))
% 245.06/51.56    (9)   ~ (all_32_2 = e2) | ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 245.06/51.56           op(e3, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 245.06/51.56             e0) & op(e3, e2) = all_32_1 & $i(all_32_1))
% 245.06/51.56    (10)  op(e0, e1) = e2
% 245.06/51.56    (11)   ~ (all_6_2 = e2)
% 245.06/51.56    (12)   ~ (all_52_8 = all_6_2)
% 245.06/51.56    (13)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.06/51.56              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 245.06/51.56            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 245.06/51.56            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.06/51.56            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 245.06/51.56             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.06/51.56            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 245.06/51.56            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 245.06/51.56            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 245.06/51.56            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 245.06/51.56            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 245.06/51.56              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.06/51.56            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.06/51.56            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 245.06/51.56            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 245.06/51.56            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 245.06/51.56            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 245.06/51.56            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 245.06/51.56              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 245.06/51.56            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.06/51.56            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 245.06/51.56            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 245.06/51.56            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 245.06/51.56            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.06/51.56            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 245.06/51.56              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 245.06/51.56            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.06/51.56            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.06/51.56    (14)   ~ (all_52_1 = all_52_2)
% 245.06/51.56    (15)  op(e1, e0) = all_52_14
% 245.06/51.56    (16)   ~ (all_52_13 = e1)
% 245.06/51.56    (17)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 245.06/51.56            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0,
% 245.06/51.56              e1) = all_20_1 & $i(all_20_1))
% 245.06/51.56    (18)  op(e0, e3) = all_52_3
% 245.06/51.56    (19)   ~ (all_52_12 = e1)
% 245.06/51.56    (20)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 245.06/51.56    (21)   ~ (all_52_2 = all_52_3)
% 245.06/51.56    (22)  all_54_6 = all_52_9
% 245.06/51.56    (23)   ~ (all_52_12 = all_52_13)
% 245.06/51.56    (24)  all_54_10 = all_6_2
% 245.06/51.56    (25)   ~ (all_52_1 = all_52_9)
% 245.06/51.56    (26)   ~ (all_52_3 = all_52_7)
% 245.06/51.56    (27)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 245.06/51.56    (28)   ~ (all_52_8 = all_52_12)
% 245.06/51.56    (29)  op(e3, e1) = all_52_8
% 245.06/51.56    (30)  op(e2, e1) = all_52_9
% 245.06/51.56    (31)   ~ (all_52_14 = e1)
% 245.06/51.56    (32)   ~ (all_6_2 = e0)
% 245.06/51.56    (33)  all_56_31 = e1
% 245.06/51.56    (34)  all_54_12 = all_52_3
% 245.06/51.56    (35)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.06/51.56    (36)  all_58_15 = e1
% 245.06/51.56    (37)  op(e3, e0) = all_52_12
% 245.06/51.56    (38)   ~ (all_52_3 = e2)
% 245.06/51.56    (39)   ~ (all_52_9 = all_52_13)
% 245.06/51.56    (40)   ~ (all_52_4 = all_52_12)
% 245.06/51.56    (41)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 245.06/51.56    (42)  op(e2, e3) = all_52_1
% 245.06/51.56    (43)  op(e3, e3) = e2
% 245.06/51.56    (44)   ~ (all_52_12 = e2)
% 245.06/51.56    (45)   ~ (all_52_13 = e2)
% 245.06/51.56    (46)   ~ (all_52_1 = all_52_13)
% 245.06/51.56    (47)  all_54_7 = all_52_13
% 245.06/51.56    (48)  op(e0, e2) = all_52_7
% 245.06/51.56    (49)  op(e0, e1) = all_20_1
% 245.06/51.56    (50)  all_56_1 = e2
% 245.06/51.56    (51)  op(e3, e2) = all_52_4
% 245.06/51.56    (52)  all_32_2 = e2
% 245.06/51.56    (53)   ~ (all_52_2 = e2)
% 245.06/51.56    (54)  ( ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 & op(e0, e1) =
% 245.06/51.56            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e0,
% 245.06/51.56              e1) = all_34_1 & $i(all_34_1))
% 245.06/51.56    (55)   ~ (all_52_4 = e2)
% 245.06/51.56    (56)  all_54_8 = all_52_2
% 245.06/51.56    (57)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 245.06/51.56          (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 245.06/51.57    (58)  all_54_3 = all_52_12
% 245.06/51.57    (59)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.06/51.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.06/51.57    (60)  op(e1, e3) = all_52_2
% 245.06/51.57    (61)  op(e2, e0) = all_52_13
% 245.06/51.57    (62)  op(e2, e2) = e2
% 245.06/51.57    (63)   ~ (all_52_4 = all_52_8)
% 245.06/51.57    (64)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 245.06/51.57          (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 245.06/51.57    (65)   ~ (all_52_9 = e2)
% 245.06/51.57  
% 245.06/51.57  Begin of proof
% 245.06/51.57  | 
% 245.06/51.57  | BETA: splitting (20) gives:
% 245.06/51.57  | 
% 245.06/51.57  | Case 1:
% 245.06/51.57  | | 
% 245.06/51.57  | |   (66)  all_54_10 = e2
% 245.06/51.57  | | 
% 245.06/51.57  | | REF_CLOSE: (11), (24), (66) are inconsistent by sub-proof #2312.
% 245.06/51.57  | | 
% 245.06/51.57  | Case 2:
% 245.06/51.57  | | 
% 245.06/51.57  | |   (67)   ~ (all_54_10 = e2)
% 245.06/51.57  | |   (68)  all_54_10 = e1 | all_54_10 = e0
% 245.06/51.57  | | 
% 245.06/51.57  | | BETA: splitting (68) gives:
% 245.06/51.57  | | 
% 245.06/51.57  | | Case 1:
% 245.06/51.57  | | | 
% 245.06/51.57  | | |   (69)  all_54_10 = e1
% 245.06/51.57  | | | 
% 245.06/51.57  | | | COMBINE_EQS: (24), (69) imply:
% 245.06/51.57  | | |   (70)  all_6_2 = e1
% 245.06/51.57  | | | 
% 245.06/51.57  | | | SIMP: (70) implies:
% 245.06/51.57  | | |   (71)  all_6_2 = e1
% 245.06/51.57  | | | 
% 245.06/51.57  | | | REDUCE: (12), (71) imply:
% 245.06/51.57  | | |   (72)   ~ (all_52_8 = e1)
% 245.06/51.57  | | | 
% 245.06/51.57  | | | REDUCE: (5), (71) imply:
% 245.06/51.57  | | |   (73)   ~ (all_52_9 = e1)
% 245.06/51.57  | | | 
% 245.06/51.57  | | | REDUCE: (11), (71) imply:
% 245.06/51.57  | | |   (74)   ~ (e2 = e1)
% 245.06/51.57  | | | 
% 245.06/51.57  | | | SIMP: (74) implies:
% 245.06/51.57  | | |   (75)   ~ (e2 = e1)
% 245.06/51.57  | | | 
% 245.06/51.57  | | | BETA: splitting (57) gives:
% 245.06/51.57  | | | 
% 245.06/51.57  | | | Case 1:
% 245.06/51.57  | | | | 
% 245.06/51.57  | | | |   (76)  (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 245.06/51.57  | | | |           = e1)
% 245.06/51.57  | | | | 
% 245.06/51.57  | | | | BETA: splitting (76) gives:
% 245.06/51.57  | | | | 
% 245.06/51.57  | | | | Case 1:
% 245.06/51.57  | | | | | 
% 245.06/51.57  | | | | |   (77)  all_58_0 = e1 & op(e3, e3) = e1
% 245.06/51.57  | | | | | 
% 245.06/51.57  | | | | | ALPHA: (77) implies:
% 245.06/51.57  | | | | |   (78)  op(e3, e3) = e1
% 245.06/51.57  | | | | | 
% 245.06/51.57  | | | | | REF_CLOSE: (43), (59), (75), (78) are inconsistent by sub-proof #2267.
% 245.06/51.57  | | | | | 
% 245.06/51.57  | | | | Case 2:
% 245.06/51.57  | | | | | 
% 245.06/51.57  | | | | |   (79)  all_58_1 = e1 & op(e3, e2) = e1
% 245.06/51.57  | | | | | 
% 245.06/51.57  | | | | | ALPHA: (79) implies:
% 245.06/51.57  | | | | |   (80)  op(e3, e2) = e1
% 245.06/51.57  | | | | | 
% 245.06/51.57  | | | | | BETA: splitting (64) gives:
% 245.06/51.57  | | | | | 
% 245.06/51.57  | | | | | Case 1:
% 245.06/51.57  | | | | | | 
% 245.06/51.57  | | | | | |   (81)  (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2,
% 245.06/51.57  | | | | | |             e2) = e1)
% 245.06/51.57  | | | | | | 
% 245.06/51.57  | | | | | | BETA: splitting (81) gives:
% 245.06/51.57  | | | | | | 
% 245.06/51.57  | | | | | | Case 1:
% 245.06/51.57  | | | | | | | 
% 245.06/51.57  | | | | | | |   (82)  all_58_2 = e1 & op(e2, e3) = e1
% 245.06/51.57  | | | | | | | 
% 245.06/51.57  | | | | | | | ALPHA: (82) implies:
% 245.06/51.57  | | | | | | |   (83)  op(e2, e3) = e1
% 245.06/51.57  | | | | | | | 
% 245.06/51.57  | | | | | | | GROUND_INST: instantiating (59) with e2, all_20_1, e1, e0,
% 245.06/51.57  | | | | | | |              simplifying with (10), (49) gives:
% 245.06/51.57  | | | | | | |   (84)  all_20_1 = e2
% 245.06/51.57  | | | | | | | 
% 245.06/51.57  | | | | | | | GROUND_INST: instantiating (59) with all_52_1, e1, e3, e2,
% 245.06/51.57  | | | | | | |              simplifying with (42), (83) gives:
% 245.06/51.57  | | | | | | |   (85)  all_52_1 = e1
% 245.06/51.57  | | | | | | | 
% 245.06/51.57  | | | | | | | GROUND_INST: instantiating (59) with all_52_4, e1, e2, e3,
% 245.06/51.57  | | | | | | |              simplifying with (51), (80) gives:
% 245.06/51.57  | | | | | | |   (86)  all_52_4 = e1
% 245.06/51.57  | | | | | | | 
% 245.06/51.57  | | | | | | | REDUCE: (14), (85) imply:
% 245.06/51.57  | | | | | | |   (87)   ~ (all_52_2 = e1)
% 245.06/51.57  | | | | | | | 
% 245.06/51.57  | | | | | | | SIMP: (87) implies:
% 245.06/51.57  | | | | | | |   (88)   ~ (all_52_2 = e1)
% 245.06/51.57  | | | | | | | 
% 245.06/51.57  | | | | | | | REDUCE: (2), (85) imply:
% 245.06/51.57  | | | | | | |   (89)   ~ (all_52_3 = e1)
% 245.06/51.57  | | | | | | | 
% 245.06/51.57  | | | | | | | SIMP: (89) implies:
% 245.06/51.57  | | | | | | |   (90)   ~ (all_52_3 = e1)
% 245.06/51.57  | | | | | | | 
% 245.06/51.57  | | | | | | | REDUCE: (25), (85) imply:
% 245.06/51.57  | | | | | | |   (91)   ~ (all_52_9 = e1)
% 245.06/51.57  | | | | | | | 
% 245.06/51.57  | | | | | | | REDUCE: (46), (85) imply:
% 245.06/51.57  | | | | | | |   (92)   ~ (all_52_13 = e1)
% 245.14/51.57  | | | | | | | 
% 245.14/51.57  | | | | | | | REDUCE: (63), (86) imply:
% 245.14/51.57  | | | | | | |   (93)   ~ (all_52_8 = e1)
% 245.14/51.57  | | | | | | | 
% 245.14/51.57  | | | | | | | REDUCE: (40), (86) imply:
% 245.14/51.57  | | | | | | |   (94)   ~ (all_52_12 = e1)
% 245.14/51.57  | | | | | | | 
% 245.14/51.57  | | | | | | | BETA: splitting (9) gives:
% 245.14/51.57  | | | | | | | 
% 245.14/51.57  | | | | | | | Case 1:
% 245.14/51.57  | | | | | | | | 
% 245.14/51.57  | | | | | | | |   (95)   ~ (all_32_2 = e2)
% 245.14/51.57  | | | | | | | | 
% 245.14/51.57  | | | | | | | | REDUCE: (52), (95) imply:
% 245.14/51.57  | | | | | | | |   (96)  $false
% 245.14/51.57  | | | | | | | | 
% 245.14/51.57  | | | | | | | | CLOSE: (96) is inconsistent.
% 245.14/51.57  | | | | | | | | 
% 245.14/51.57  | | | | | | | Case 2:
% 245.14/51.57  | | | | | | | | 
% 245.14/51.57  | | | | | | | |   (97)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 245.14/51.57  | | | | | | | |           op(e3, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) |
% 245.14/51.57  | | | | | | | |         ( ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 245.14/51.57  | | | | | | | |           $i(all_32_1))
% 245.14/51.57  | | | | | | | | 
% 245.14/51.57  | | | | | | | | BETA: splitting (54) gives:
% 245.14/51.57  | | | | | | | | 
% 245.14/51.57  | | | | | | | | Case 1:
% 245.14/51.57  | | | | | | | | | 
% 245.14/51.57  | | | | | | | | |   (98)   ~ (all_34_0 = e3) & op(all_34_1, e0) = all_34_0 &
% 245.14/51.57  | | | | | | | | |         op(e0, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)
% 245.14/51.57  | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | ALPHA: (98) implies:
% 245.14/51.57  | | | | | | | | |   (99)   ~ (all_34_0 = e3)
% 245.14/51.57  | | | | | | | | |   (100)  op(e0, e1) = all_34_1
% 245.14/51.57  | | | | | | | | |   (101)  op(all_34_1, e0) = all_34_0
% 245.14/51.57  | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | BETA: splitting (8) gives:
% 245.14/51.57  | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | Case 1:
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | |   (102)   ~ (all_24_0 = e0) & op(all_24_1, e3) = all_24_0 &
% 245.14/51.57  | | | | | | | | | |          op(e3, e2) = all_24_1 & $i(all_24_0) & $i(all_24_1)
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | ALPHA: (102) implies:
% 245.14/51.57  | | | | | | | | | |   (103)   ~ (all_24_0 = e0)
% 245.14/51.57  | | | | | | | | | |   (104)  op(e3, e2) = all_24_1
% 245.14/51.57  | | | | | | | | | |   (105)  op(all_24_1, e3) = all_24_0
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | GROUND_INST: instantiating (59) with e2, all_34_1, e1, e0,
% 245.14/51.57  | | | | | | | | | |              simplifying with (10), (100) gives:
% 245.14/51.57  | | | | | | | | | |   (106)  all_34_1 = e2
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | GROUND_INST: instantiating (59) with e1, all_24_1, e2, e3,
% 245.14/51.57  | | | | | | | | | |              simplifying with (80), (104) gives:
% 245.14/51.57  | | | | | | | | | |   (107)  all_24_1 = e1
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | REDUCE: (101), (106) imply:
% 245.14/51.57  | | | | | | | | | |   (108)  op(e2, e0) = all_34_0
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | REDUCE: (105), (107) imply:
% 245.14/51.57  | | | | | | | | | |   (109)  op(e1, e3) = all_24_0
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | BETA: splitting (97) gives:
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | Case 1:
% 245.14/51.57  | | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | |   (110)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 &
% 245.14/51.57  | | | | | | | | | | |          op(e3, e2) = all_32_1 & $i(all_32_0) &
% 245.14/51.57  | | | | | | | | | | |          $i(all_32_1)
% 245.14/51.57  | | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | | ALPHA: (110) implies:
% 245.14/51.57  | | | | | | | | | | |   (111)  op(e3, e2) = all_32_1
% 245.14/51.57  | | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (13), (15), (16), (18),
% 245.14/51.57  | | | | | | | | | | |            (19), (21), (22), (23), (26), (27), (28), (29),
% 245.14/51.57  | | | | | | | | | | |            (30), (31), (33), (34), (35), (36), (37), (38),
% 245.14/51.57  | | | | | | | | | | |            (39), (41), (44), (45), (47), (48), (49), (50),
% 245.14/51.57  | | | | | | | | | | |            (53), (56), (58), (59), (60), (61), (65), (72),
% 245.14/51.57  | | | | | | | | | | |            (73), (75), (80), (88), (90), (99), (100), (101),
% 245.14/51.57  | | | | | | | | | | |            (103), (108), (109), (111) are inconsistent by
% 245.14/51.57  | | | | | | | | | | |            sub-proof #2240.
% 245.14/51.57  | | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | Case 2:
% 245.14/51.57  | | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | |   (112)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 &
% 245.14/51.57  | | | | | | | | | | |          $i(all_32_1)
% 245.14/51.57  | | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | | ALPHA: (112) implies:
% 245.14/51.57  | | | | | | | | | | |   (113)  op(e3, e2) = all_32_1
% 245.14/51.57  | | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (13), (15), (16), (18),
% 245.14/51.57  | | | | | | | | | | |            (19), (21), (22), (23), (26), (27), (28), (29),
% 245.14/51.57  | | | | | | | | | | |            (30), (31), (33), (34), (35), (36), (37), (38),
% 245.14/51.57  | | | | | | | | | | |            (39), (41), (44), (45), (47), (48), (49), (50),
% 245.14/51.57  | | | | | | | | | | |            (53), (56), (58), (59), (60), (61), (65), (72),
% 245.14/51.57  | | | | | | | | | | |            (73), (75), (80), (88), (90), (99), (100), (101),
% 245.14/51.57  | | | | | | | | | | |            (103), (108), (109), (113) are inconsistent by
% 245.14/51.57  | | | | | | | | | | |            sub-proof #2240.
% 245.14/51.57  | | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | End of split
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | Case 2:
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | |   (114)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 &
% 245.14/51.57  | | | | | | | | | |          $i(all_24_1)
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | | REF_CLOSE: (59), (80), (97), (114) are inconsistent by
% 245.14/51.57  | | | | | | | | | |            sub-proof #2238.
% 245.14/51.57  | | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | End of split
% 245.14/51.57  | | | | | | | | | 
% 245.14/51.57  | | | | | | | | Case 2:
% 245.14/51.57  | | | | | | | | | 
% 245.14/51.57  | | | | | | | | |   (115)   ~ (all_34_1 = e2) & op(e0, e1) = all_34_1 &
% 245.14/51.57  | | | | | | | | |          $i(all_34_1)
% 245.14/51.57  | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | ALPHA: (115) implies:
% 245.14/51.57  | | | | | | | | |   (116)   ~ (all_34_1 = e2)
% 245.14/51.57  | | | | | | | | |   (117)  op(e0, e1) = all_34_1
% 245.14/51.57  | | | | | | | | | 
% 245.14/51.57  | | | | | | | | | REF_CLOSE: (10), (17), (59), (116), (117) are inconsistent by
% 245.14/51.57  | | | | | | | | |            sub-proof #2236.
% 245.14/51.57  | | | | | | | | | 
% 245.14/51.57  | | | | | | | | End of split
% 245.14/51.57  | | | | | | | | 
% 245.14/51.57  | | | | | | | End of split
% 245.14/51.57  | | | | | | | 
% 245.14/51.57  | | | | | | Case 2:
% 245.14/51.57  | | | | | | | 
% 245.14/51.57  | | | | | | |   (118)  all_58_3 = e1 & op(e2, e2) = e1
% 245.14/51.57  | | | | | | | 
% 245.14/51.57  | | | | | | | ALPHA: (118) implies:
% 245.14/51.57  | | | | | | |   (119)  op(e2, e2) = e1
% 245.14/51.57  | | | | | | | 
% 245.14/51.57  | | | | | | | REF_CLOSE: (59), (62), (75), (119) are inconsistent by sub-proof
% 245.14/51.57  | | | | | | |            #2235.
% 245.14/51.57  | | | | | | | 
% 245.14/51.57  | | | | | | End of split
% 245.14/51.57  | | | | | | 
% 245.14/51.57  | | | | | Case 2:
% 245.14/51.57  | | | | | | 
% 245.14/51.57  | | | | | |   (120)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 245.14/51.57  | | | | | |            op(e2, e0) = e1)
% 245.14/51.57  | | | | | | 
% 245.14/51.57  | | | | | | REF_CLOSE: (16), (30), (59), (61), (73), (120) are inconsistent by
% 245.14/51.57  | | | | | |            sub-proof #2234.
% 245.14/51.57  | | | | | | 
% 245.14/51.57  | | | | | End of split
% 245.14/51.57  | | | | | 
% 245.14/51.57  | | | | End of split
% 245.14/51.57  | | | | 
% 245.14/51.57  | | | Case 2:
% 245.14/51.57  | | | | 
% 245.14/51.57  | | | |   (121)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 245.14/51.57  | | | |            = e1)
% 245.14/51.57  | | | | 
% 245.14/51.57  | | | | REF_CLOSE: (19), (29), (37), (59), (72), (121) are inconsistent by
% 245.14/51.57  | | | |            sub-proof #2233.
% 245.14/51.57  | | | | 
% 245.14/51.57  | | | End of split
% 245.14/51.57  | | | 
% 245.14/51.57  | | Case 2:
% 245.14/51.57  | | | 
% 245.14/51.57  | | |   (122)  all_54_10 = e0
% 245.14/51.57  | | | 
% 245.14/51.57  | | | REF_CLOSE: (24), (32), (122) are inconsistent by sub-proof #2303.
% 245.14/51.57  | | | 
% 245.14/51.57  | | End of split
% 245.14/51.57  | | 
% 245.14/51.57  | End of split
% 245.14/51.57  | 
% 245.14/51.57  End of proof
% 245.14/51.57  
% 245.14/51.57  Sub-proof #2233 shows that the following formulas are inconsistent:
% 245.14/51.57  ----------------------------------------------------------------
% 245.14/51.57    (1)   ~ (all_52_12 = e1)
% 245.14/51.57    (2)   ~ (all_52_8 = e1)
% 245.14/51.57    (3)  op(e3, e1) = all_52_8
% 245.14/51.57    (4)  op(e3, e0) = all_52_12
% 245.14/51.57    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.57    (6)  (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 245.14/51.57  
% 245.14/51.57  Begin of proof
% 245.14/51.57  | 
% 245.14/51.57  | BETA: splitting (6) gives:
% 245.14/51.57  | 
% 245.14/51.57  | Case 1:
% 245.14/51.57  | | 
% 245.14/51.57  | |   (7)  all_58_4 = e1 & op(e3, e1) = e1
% 245.14/51.57  | | 
% 245.14/51.57  | | ALPHA: (7) implies:
% 245.14/51.57  | |   (8)  op(e3, e1) = e1
% 245.14/51.57  | | 
% 245.14/51.57  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #2309.
% 245.14/51.57  | | 
% 245.14/51.57  | Case 2:
% 245.14/51.57  | | 
% 245.14/51.57  | |   (9)  all_58_9 = e1 & op(e3, e0) = e1
% 245.14/51.57  | | 
% 245.14/51.57  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2278.
% 245.14/51.57  | | 
% 245.14/51.57  | End of split
% 245.14/51.57  | 
% 245.14/51.57  End of proof
% 245.14/51.57  
% 245.14/51.57  Sub-proof #2234 shows that the following formulas are inconsistent:
% 245.14/51.57  ----------------------------------------------------------------
% 245.14/51.57    (1)   ~ (all_52_13 = e1)
% 245.14/51.57    (2)  op(e2, e1) = all_52_9
% 245.14/51.57    (3)  (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 245.14/51.57    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.57    (5)  op(e2, e0) = all_52_13
% 245.14/51.57    (6)   ~ (all_52_9 = e1)
% 245.14/51.57  
% 245.14/51.57  Begin of proof
% 245.14/51.57  | 
% 245.14/51.57  | BETA: splitting (3) gives:
% 245.14/51.57  | 
% 245.14/51.57  | Case 1:
% 245.14/51.57  | | 
% 245.14/51.57  | |   (7)  all_58_5 = e1 & op(e2, e1) = e1
% 245.14/51.57  | | 
% 245.14/51.57  | | ALPHA: (7) implies:
% 245.14/51.57  | |   (8)  op(e2, e1) = e1
% 245.14/51.57  | | 
% 245.14/51.57  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2306.
% 245.14/51.57  | | 
% 245.14/51.57  | Case 2:
% 245.14/51.57  | | 
% 245.14/51.57  | |   (9)  all_58_10 = e1 & op(e2, e0) = e1
% 245.14/51.57  | | 
% 245.14/51.57  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2277.
% 245.14/51.57  | | 
% 245.14/51.57  | End of split
% 245.14/51.57  | 
% 245.14/51.57  End of proof
% 245.14/51.57  
% 245.14/51.57  Sub-proof #2235 shows that the following formulas are inconsistent:
% 245.14/51.57  ----------------------------------------------------------------
% 245.14/51.57    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.57    (2)  op(e2, e2) = e2
% 245.14/51.57    (3)  op(e2, e2) = e1
% 245.14/51.57    (4)   ~ (e2 = e1)
% 245.14/51.57  
% 245.14/51.57  Begin of proof
% 245.14/51.57  | 
% 245.14/51.57  | GROUND_INST: instantiating (1) with e1, e2, e2, e2, simplifying with (2), (3)
% 245.14/51.57  |              gives:
% 245.14/51.57  |   (5)  e2 = e1
% 245.14/51.57  | 
% 245.14/51.57  | REDUCE: (4), (5) imply:
% 245.14/51.57  |   (6)  $false
% 245.14/51.57  | 
% 245.14/51.57  | CLOSE: (6) is inconsistent.
% 245.14/51.57  | 
% 245.14/51.57  End of proof
% 245.14/51.57  
% 245.14/51.57  Sub-proof #2236 shows that the following formulas are inconsistent:
% 245.14/51.57  ----------------------------------------------------------------
% 245.14/51.57    (1)   ~ (all_34_1 = e2)
% 245.14/51.57    (2)  op(e0, e1) = e2
% 245.14/51.57    (3)  op(e0, e1) = all_34_1
% 245.14/51.57    (4)  ( ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) = all_20_1
% 245.14/51.57           & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e0, e1) =
% 245.14/51.57           all_20_1 & $i(all_20_1))
% 245.14/51.57    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.57  
% 245.14/51.57  Begin of proof
% 245.14/51.57  | 
% 245.14/51.57  | BETA: splitting (4) gives:
% 245.14/51.57  | 
% 245.14/51.57  | Case 1:
% 245.14/51.57  | | 
% 245.14/51.57  | |   (6)   ~ (all_20_0 = e2) & op(all_20_1, e0) = all_20_0 & op(e0, e1) =
% 245.14/51.57  | |        all_20_1 & $i(all_20_0) & $i(all_20_1)
% 245.14/51.57  | | 
% 245.14/51.57  | | ALPHA: (6) implies:
% 245.14/51.57  | |   (7)  op(e0, e1) = all_20_1
% 245.14/51.57  | | 
% 245.14/51.57  | | REF_CLOSE: (1), (2), (3), (5), (7) are inconsistent by sub-proof #2237.
% 245.14/51.57  | | 
% 245.14/51.57  | Case 2:
% 245.14/51.57  | | 
% 245.14/51.57  | |   (8)   ~ (all_20_1 = e3) & op(e0, e1) = all_20_1 & $i(all_20_1)
% 245.14/51.57  | | 
% 245.14/51.57  | | ALPHA: (8) implies:
% 245.14/51.57  | |   (9)  op(e0, e1) = all_20_1
% 245.14/51.57  | | 
% 245.14/51.57  | | REF_CLOSE: (1), (2), (3), (5), (9) are inconsistent by sub-proof #2237.
% 245.14/51.57  | | 
% 245.14/51.57  | End of split
% 245.14/51.57  | 
% 245.14/51.57  End of proof
% 245.14/51.57  
% 245.14/51.57  Sub-proof #2237 shows that the following formulas are inconsistent:
% 245.14/51.57  ----------------------------------------------------------------
% 245.14/51.57    (1)   ~ (all_34_1 = e2)
% 245.14/51.57    (2)  op(e0, e1) = e2
% 245.14/51.57    (3)  op(e0, e1) = all_34_1
% 245.14/51.57    (4)  op(e0, e1) = all_20_1
% 245.14/51.57    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.57  
% 245.14/51.57  Begin of proof
% 245.14/51.57  | 
% 245.14/51.57  | GROUND_INST: instantiating (5) with all_20_1, all_34_1, e1, e0, simplifying
% 245.14/51.57  |              with (3), (4) gives:
% 245.14/51.57  |   (6)  all_34_1 = all_20_1
% 245.14/51.57  | 
% 245.14/51.57  | GROUND_INST: instantiating (5) with e2, all_34_1, e1, e0, simplifying with
% 245.14/51.57  |              (2), (3) gives:
% 245.14/51.57  |   (7)  all_34_1 = e2
% 245.14/51.57  | 
% 245.14/51.57  | COMBINE_EQS: (6), (7) imply:
% 245.14/51.57  |   (8)  all_20_1 = e2
% 245.14/51.57  | 
% 245.14/51.57  | REDUCE: (1), (7) imply:
% 245.14/51.57  |   (9)  $false
% 245.14/51.57  | 
% 245.14/51.57  | CLOSE: (9) is inconsistent.
% 245.14/51.57  | 
% 245.14/51.57  End of proof
% 245.14/51.57  
% 245.14/51.57  Sub-proof #2238 shows that the following formulas are inconsistent:
% 245.14/51.57  ----------------------------------------------------------------
% 245.14/51.57    (1)   ~ (all_24_1 = e1) & op(e3, e2) = all_24_1 & $i(all_24_1)
% 245.14/51.57    (2)  op(e3, e2) = e1
% 245.14/51.57    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.58    (4)  ( ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) = all_32_1
% 245.14/51.58           & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) & op(e3, e2) =
% 245.14/51.58           all_32_1 & $i(all_32_1))
% 245.14/51.58  
% 245.14/51.58  Begin of proof
% 245.14/51.58  | 
% 245.14/51.58  | ALPHA: (1) implies:
% 245.14/51.58  |   (5)   ~ (all_24_1 = e1)
% 245.14/51.58  |   (6)  op(e3, e2) = all_24_1
% 245.14/51.58  | 
% 245.14/51.58  | BETA: splitting (4) gives:
% 245.14/51.58  | 
% 245.14/51.58  | Case 1:
% 245.14/51.58  | | 
% 245.14/51.58  | |   (7)   ~ (all_32_0 = e1) & op(all_32_1, e3) = all_32_0 & op(e3, e2) =
% 245.14/51.58  | |        all_32_1 & $i(all_32_0) & $i(all_32_1)
% 245.14/51.58  | | 
% 245.14/51.58  | | ALPHA: (7) implies:
% 245.14/51.58  | |   (8)  op(e3, e2) = all_32_1
% 245.14/51.58  | | 
% 245.14/51.58  | | REF_CLOSE: (2), (3), (5), (6), (8) are inconsistent by sub-proof #2239.
% 245.14/51.58  | | 
% 245.14/51.58  | Case 2:
% 245.14/51.58  | | 
% 245.14/51.58  | |   (9)   ~ (all_32_1 = e0) & op(e3, e2) = all_32_1 & $i(all_32_1)
% 245.14/51.58  | | 
% 245.14/51.58  | | ALPHA: (9) implies:
% 245.14/51.58  | |   (10)  op(e3, e2) = all_32_1
% 245.14/51.58  | | 
% 245.14/51.58  | | REF_CLOSE: (2), (3), (5), (6), (10) are inconsistent by sub-proof #2239.
% 245.14/51.58  | | 
% 245.14/51.58  | End of split
% 245.14/51.58  | 
% 245.14/51.58  End of proof
% 245.14/51.58  
% 245.14/51.58  Sub-proof #2239 shows that the following formulas are inconsistent:
% 245.14/51.58  ----------------------------------------------------------------
% 245.14/51.58    (1)  op(e3, e2) = e1
% 245.14/51.58    (2)  op(e3, e2) = all_32_1
% 245.14/51.58    (3)   ~ (all_24_1 = e1)
% 245.14/51.58    (4)  op(e3, e2) = all_24_1
% 245.14/51.58    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.58  
% 245.14/51.58  Begin of proof
% 245.14/51.58  | 
% 245.14/51.58  | GROUND_INST: instantiating (5) with all_24_1, all_32_1, e2, e3, simplifying
% 245.14/51.58  |              with (2), (4) gives:
% 245.14/51.58  |   (6)  all_32_1 = all_24_1
% 245.14/51.58  | 
% 245.14/51.58  | GROUND_INST: instantiating (5) with e1, all_32_1, e2, e3, simplifying with
% 245.14/51.58  |              (1), (2) gives:
% 245.14/51.58  |   (7)  all_32_1 = e1
% 245.14/51.58  | 
% 245.14/51.58  | COMBINE_EQS: (6), (7) imply:
% 245.14/51.58  |   (8)  all_24_1 = e1
% 245.14/51.58  | 
% 245.14/51.58  | SIMP: (8) implies:
% 245.14/51.58  |   (9)  all_24_1 = e1
% 245.14/51.58  | 
% 245.14/51.58  | REDUCE: (3), (9) imply:
% 245.14/51.58  |   (10)  $false
% 245.14/51.58  | 
% 245.14/51.58  | CLOSE: (10) is inconsistent.
% 245.14/51.58  | 
% 245.14/51.58  End of proof
% 245.14/51.58  
% 245.14/51.58  Sub-proof #2240 shows that the following formulas are inconsistent:
% 245.14/51.58  ----------------------------------------------------------------
% 245.14/51.58    (1)  op(e0, e0) = e1
% 245.14/51.58    (2)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 & op(e2,
% 245.14/51.58             all_56_3) = e2 & op(e2, e3) = all_56_3 & $i(all_56_3)) | (all_56_4 =
% 245.14/51.58           e1 & op(e1, all_56_5) = e1 & op(e1, e3) = all_56_5 & $i(all_56_5)) |
% 245.14/51.58         (all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 245.14/51.58           $i(all_56_7))
% 245.14/51.58    (3)  op(e3, e2) = e1
% 245.14/51.58    (4)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 245.14/51.58    (5)  op(e1, e3) = all_24_0
% 245.14/51.58    (6)   ~ (all_52_3 = e1)
% 245.14/51.58    (7)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 245.14/51.58    (8)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 245.14/51.58         (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 245.14/51.58    (9)  op(e3, e2) = all_32_1
% 245.14/51.58    (10)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.14/51.58              e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 245.14/51.58            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3)
% 245.14/51.58            &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.14/51.58            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &
% 245.14/51.58             ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.14/51.58            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 245.14/51.58            & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 245.14/51.58            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3)
% 245.14/51.58            = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 245.14/51.58            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 245.14/51.58              e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.14/51.58            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.14/51.58            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 =
% 245.14/51.58            e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 245.14/51.58            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2)
% 245.14/51.58            = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 245.14/51.58            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 245.14/51.58              e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 245.14/51.58            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.14/51.58            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 =
% 245.14/51.58            e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 245.14/51.58            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2)
% 245.14/51.58            = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.14/51.58            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 245.14/51.58              e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 245.14/51.58            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.14/51.58            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.14/51.58    (11)  op(e0, e1) = all_34_1
% 245.14/51.58    (12)  op(e1, e0) = all_52_14
% 245.14/51.58    (13)   ~ (all_52_13 = e1)
% 245.14/51.58    (14)  op(e0, e3) = all_52_3
% 245.14/51.58    (15)   ~ (all_52_12 = e1)
% 245.14/51.58    (16)   ~ (all_52_2 = all_52_3)
% 245.14/51.58    (17)  all_54_6 = all_52_9
% 245.14/51.58    (18)   ~ (all_52_8 = e1)
% 245.14/51.58    (19)  op(all_34_1, e0) = all_34_0
% 245.14/51.58    (20)   ~ (all_52_12 = all_52_13)
% 245.14/51.58    (21)   ~ (all_52_2 = e1)
% 245.14/51.58    (22)   ~ (all_24_0 = e0)
% 245.14/51.58    (23)  op(e2, e0) = all_34_0
% 245.14/51.58    (24)   ~ (all_52_3 = all_52_7)
% 245.14/51.58    (25)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 245.14/51.58    (26)   ~ (all_52_8 = all_52_12)
% 245.14/51.58    (27)  op(e3, e1) = all_52_8
% 245.14/51.58    (28)  op(e2, e1) = all_52_9
% 245.14/51.58    (29)   ~ (all_52_14 = e1)
% 245.14/51.58    (30)  all_56_31 = e1
% 245.14/51.58    (31)  all_54_12 = all_52_3
% 245.14/51.58    (32)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.14/51.58    (33)  all_58_15 = e1
% 245.14/51.58    (34)  op(e3, e0) = all_52_12
% 245.14/51.58    (35)   ~ (all_52_3 = e2)
% 245.14/51.58    (36)   ~ (all_34_0 = e3)
% 245.14/51.58    (37)   ~ (all_52_9 = all_52_13)
% 245.14/51.58    (38)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 245.14/51.58    (39)   ~ (all_52_12 = e2)
% 245.14/51.58    (40)   ~ (all_52_13 = e2)
% 245.14/51.58    (41)  all_54_7 = all_52_13
% 245.14/51.58    (42)  op(e0, e2) = all_52_7
% 245.14/51.58    (43)  op(e0, e1) = all_20_1
% 245.14/51.58    (44)  all_56_1 = e2
% 245.14/51.58    (45)   ~ (all_52_2 = e2)
% 245.14/51.58    (46)  all_54_8 = all_52_2
% 245.14/51.58    (47)  all_54_3 = all_52_12
% 245.14/51.58    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.58    (49)  op(e1, e3) = all_52_2
% 245.14/51.58    (50)  op(e2, e0) = all_52_13
% 245.14/51.58    (51)   ~ (all_52_9 = e1)
% 245.14/51.58    (52)   ~ (e2 = e1)
% 245.14/51.58    (53)   ~ (all_52_9 = e2)
% 245.14/51.58  
% 245.14/51.58  Begin of proof
% 245.14/51.58  | 
% 245.14/51.58  | GROUND_INST: instantiating (48) with all_52_2, all_24_0, e3, e1, simplifying
% 245.14/51.58  |              with (5), (49) gives:
% 245.14/51.58  |   (54)  all_52_2 = all_24_0
% 245.14/51.58  | 
% 245.14/51.58  | GROUND_INST: instantiating (48) with all_52_13, all_34_0, e0, e2, simplifying
% 245.14/51.58  |              with (23), (50) gives:
% 245.14/51.58  |   (55)  all_52_13 = all_34_0
% 245.14/51.58  | 
% 245.14/51.58  | GROUND_INST: instantiating (48) with e1, all_32_1, e2, e3, simplifying with
% 245.14/51.58  |              (3), (9) gives:
% 245.14/51.58  |   (56)  all_32_1 = e1
% 245.14/51.58  | 
% 245.14/51.58  | COMBINE_EQS: (46), (54) imply:
% 245.14/51.58  |   (57)  all_54_8 = all_24_0
% 245.14/51.58  | 
% 245.14/51.58  | COMBINE_EQS: (41), (55) imply:
% 245.14/51.58  |   (58)  all_54_7 = all_34_0
% 245.14/51.58  | 
% 245.14/51.58  | REDUCE: (16), (54) imply:
% 245.14/51.58  |   (59)   ~ (all_52_3 = all_24_0)
% 245.14/51.58  | 
% 245.14/51.58  | SIMP: (59) implies:
% 245.14/51.58  |   (60)   ~ (all_52_3 = all_24_0)
% 245.14/51.58  | 
% 245.14/51.58  | REDUCE: (45), (54) imply:
% 245.14/51.58  |   (61)   ~ (all_24_0 = e2)
% 245.14/51.58  | 
% 245.14/51.58  | REDUCE: (21), (54) imply:
% 245.14/51.58  |   (62)   ~ (all_24_0 = e1)
% 245.14/51.58  | 
% 245.14/51.58  | REDUCE: (37), (55) imply:
% 245.14/51.58  |   (63)   ~ (all_52_9 = all_34_0)
% 245.14/51.58  | 
% 245.14/51.58  | REDUCE: (20), (55) imply:
% 245.14/51.58  |   (64)   ~ (all_52_12 = all_34_0)
% 245.14/51.58  | 
% 245.14/51.58  | REDUCE: (40), (55) imply:
% 245.14/51.58  |   (65)   ~ (all_34_0 = e2)
% 245.14/51.58  | 
% 245.14/51.58  | REDUCE: (13), (55) imply:
% 245.14/51.58  |   (66)   ~ (all_34_0 = e1)
% 245.14/51.58  | 
% 245.14/51.58  | BETA: splitting (7) gives:
% 245.14/51.58  | 
% 245.14/51.58  | Case 1:
% 245.14/51.58  | | 
% 245.14/51.58  | |   (67)  all_54_8 = e3
% 245.14/51.58  | | 
% 245.14/51.58  | | COMBINE_EQS: (57), (67) imply:
% 245.14/51.58  | |   (68)  all_24_0 = e3
% 245.14/51.58  | | 
% 245.14/51.58  | | REDUCE: (60), (68) imply:
% 245.14/51.58  | |   (69)   ~ (all_52_3 = e3)
% 245.14/51.58  | | 
% 245.14/51.58  | | REDUCE: (62), (68) imply:
% 245.14/51.58  | |   (70)   ~ (e3 = e1)
% 245.14/51.58  | | 
% 245.14/51.58  | | REDUCE: (5), (68) imply:
% 245.14/51.58  | |   (71)  op(e1, e3) = e3
% 245.14/51.58  | | 
% 245.14/51.58  | | BETA: splitting (32) gives:
% 245.14/51.58  | | 
% 245.14/51.58  | | Case 1:
% 245.14/51.58  | | | 
% 245.14/51.58  | | |   (72)  all_54_7 = e3
% 245.14/51.58  | | | 
% 245.14/51.58  | | | COMBINE_EQS: (58), (72) imply:
% 245.14/51.58  | | |   (73)  all_34_0 = e3
% 245.14/51.58  | | | 
% 245.14/51.58  | | | REDUCE: (36), (73) imply:
% 245.14/51.58  | | |   (74)  $false
% 245.14/51.58  | | | 
% 245.14/51.58  | | | CLOSE: (74) is inconsistent.
% 245.14/51.58  | | | 
% 245.14/51.58  | | Case 2:
% 245.14/51.58  | | | 
% 245.14/51.58  | | |   (75)   ~ (all_54_7 = e3)
% 245.14/51.58  | | |   (76)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.14/51.58  | | | 
% 245.14/51.58  | | | BETA: splitting (76) gives:
% 245.14/51.58  | | | 
% 245.14/51.58  | | | Case 1:
% 245.14/51.58  | | | | 
% 245.14/51.58  | | | |   (77)  all_54_7 = e2
% 245.14/51.58  | | | | 
% 245.14/51.58  | | | | COMBINE_EQS: (58), (77) imply:
% 245.14/51.58  | | | |   (78)  all_34_0 = e2
% 245.14/51.58  | | | | 
% 245.14/51.58  | | | | REDUCE: (65), (78) imply:
% 245.14/51.58  | | | |   (79)  $false
% 245.14/51.58  | | | | 
% 245.14/51.58  | | | | CLOSE: (79) is inconsistent.
% 245.14/51.58  | | | | 
% 245.14/51.58  | | | Case 2:
% 245.14/51.58  | | | | 
% 245.14/51.58  | | | |   (80)  all_54_7 = e1 | all_54_7 = e0
% 245.14/51.58  | | | | 
% 245.14/51.58  | | | | BETA: splitting (4) gives:
% 245.14/51.58  | | | | 
% 245.14/51.58  | | | | Case 1:
% 245.14/51.58  | | | | | 
% 245.14/51.58  | | | | |   (81)  all_54_12 = e3
% 245.14/51.58  | | | | | 
% 245.14/51.58  | | | | | REF_CLOSE: (31), (69), (81) are inconsistent by sub-proof #2266.
% 245.14/51.58  | | | | | 
% 245.14/51.58  | | | | Case 2:
% 245.14/51.58  | | | | | 
% 245.14/51.58  | | | | |   (82)   ~ (all_54_12 = e3)
% 245.14/51.58  | | | | |   (83)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 245.14/51.58  | | | | | 
% 245.14/51.58  | | | | | BETA: splitting (2) gives:
% 245.14/51.58  | | | | | 
% 245.14/51.58  | | | | | Case 1:
% 245.14/51.58  | | | | | | 
% 245.14/51.58  | | | | | |   (84)  (all_56_0 = e3 & op(e3, all_56_1) = e3) | (all_56_2 = e2 &
% 245.14/51.58  | | | | | |           op(e2, all_56_3) = e2 & op(e2, e3) = all_56_3 &
% 245.14/51.58  | | | | | |           $i(all_56_3))
% 245.14/51.58  | | | | | | 
% 245.14/51.58  | | | | | | BETA: splitting (84) gives:
% 245.14/51.58  | | | | | | 
% 245.14/51.58  | | | | | | Case 1:
% 245.14/51.58  | | | | | | | 
% 245.14/51.58  | | | | | | |   (85)  all_56_0 = e3 & op(e3, all_56_1) = e3
% 245.14/51.58  | | | | | | | 
% 245.14/51.58  | | | | | | | ALPHA: (85) implies:
% 245.14/51.58  | | | | | | |   (86)  op(e3, all_56_1) = e3
% 245.14/51.58  | | | | | | | 
% 245.14/51.58  | | | | | | | REDUCE: (44), (86) imply:
% 245.14/51.58  | | | | | | |   (87)  op(e3, e2) = e3
% 245.14/51.58  | | | | | | | 
% 245.14/51.58  | | | | | | | REF_CLOSE: (3), (48), (70), (87) are inconsistent by sub-proof
% 245.14/51.58  | | | | | | |            #2265.
% 245.14/51.58  | | | | | | | 
% 245.14/51.58  | | | | | | Case 2:
% 245.14/51.58  | | | | | | | 
% 245.14/51.58  | | | | | | |   (88)  all_56_2 = e2 & op(e2, all_56_3) = e2 & op(e2, e3) =
% 245.14/51.58  | | | | | | |         all_56_3 & $i(all_56_3)
% 245.14/51.58  | | | | | | | 
% 245.14/51.58  | | | | | | | ALPHA: (88) implies:
% 245.14/51.58  | | | | | | |   (89)  op(e2, e3) = all_56_3
% 245.14/51.58  | | | | | | |   (90)  op(e2, all_56_3) = e2
% 245.14/51.58  | | | | | | | 
% 245.14/51.58  | | | | | | | BETA: splitting (80) gives:
% 245.14/51.58  | | | | | | | 
% 245.14/51.58  | | | | | | | Case 1:
% 245.14/51.58  | | | | | | | | 
% 245.14/51.58  | | | | | | | |   (91)  all_54_7 = e1
% 245.14/51.58  | | | | | | | | 
% 245.14/51.58  | | | | | | | | COMBINE_EQS: (58), (91) imply:
% 245.14/51.58  | | | | | | | |   (92)  all_34_0 = e1
% 245.14/51.58  | | | | | | | | 
% 245.14/51.58  | | | | | | | | REDUCE: (66), (92) imply:
% 245.14/51.58  | | | | | | | |   (93)  $false
% 245.14/51.58  | | | | | | | | 
% 245.14/51.58  | | | | | | | | CLOSE: (93) is inconsistent.
% 245.14/51.58  | | | | | | | | 
% 245.14/51.58  | | | | | | | Case 2:
% 245.14/51.58  | | | | | | | | 
% 245.14/51.58  | | | | | | | |   (94)  all_54_7 = e0
% 245.14/51.58  | | | | | | | | 
% 245.14/51.58  | | | | | | | | COMBINE_EQS: (58), (94) imply:
% 245.14/51.58  | | | | | | | |   (95)  all_34_0 = e0
% 245.14/51.58  | | | | | | | | 
% 245.14/51.58  | | | | | | | | REDUCE: (63), (95) imply:
% 245.14/51.58  | | | | | | | |   (96)   ~ (all_52_9 = e0)
% 245.14/51.58  | | | | | | | | 
% 245.14/51.58  | | | | | | | | REDUCE: (64), (95) imply:
% 245.14/51.58  | | | | | | | |   (97)   ~ (all_52_12 = e0)
% 245.14/51.58  | | | | | | | | 
% 245.14/51.58  | | | | | | | | BETA: splitting (38) gives:
% 245.14/51.58  | | | | | | | | 
% 245.14/51.58  | | | | | | | | Case 1:
% 245.14/51.58  | | | | | | | | | 
% 245.14/51.58  | | | | | | | | |   (98)  all_54_6 = e3
% 245.14/51.58  | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | COMBINE_EQS: (17), (98) imply:
% 245.14/51.58  | | | | | | | | |   (99)  all_52_9 = e3
% 245.14/51.58  | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | REDUCE: (28), (99) imply:
% 245.14/51.58  | | | | | | | | |   (100)  op(e2, e1) = e3
% 245.14/51.58  | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | BETA: splitting (25) gives:
% 245.14/51.58  | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | Case 1:
% 245.14/51.58  | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | |   (101)  all_54_3 = e3
% 245.14/51.58  | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | COMBINE_EQS: (47), (101) imply:
% 245.14/51.58  | | | | | | | | | |   (102)  all_52_12 = e3
% 245.14/51.58  | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | REDUCE: (26), (102) imply:
% 245.14/51.58  | | | | | | | | | |   (103)   ~ (all_52_8 = e3)
% 245.14/51.58  | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | REDUCE: (39), (102) imply:
% 245.14/51.58  | | | | | | | | | |   (104)   ~ (e3 = e2)
% 245.14/51.58  | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | REDUCE: (34), (102) imply:
% 245.14/51.58  | | | | | | | | | |   (105)  op(e3, e0) = e3
% 245.14/51.58  | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | BETA: splitting (8) gives:
% 245.14/51.58  | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | Case 1:
% 245.14/51.58  | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | |   (106)  (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 245.14/51.58  | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 245.14/51.58  | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | BETA: splitting (106) gives:
% 245.14/51.58  | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | Case 1:
% 245.14/51.58  | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | |   (107)  all_58_12 = e3 & op(e0, e3) = e3
% 245.14/51.58  | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | ALPHA: (107) implies:
% 245.14/51.58  | | | | | | | | | | | |   (108)  op(e0, e3) = e3
% 245.14/51.58  | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | REF_CLOSE: (14), (48), (69), (108) are inconsistent by
% 245.14/51.58  | | | | | | | | | | | |            sub-proof #2332.
% 245.14/51.58  | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | Case 2:
% 245.14/51.58  | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | |   (109)  all_58_13 = e3 & op(e0, e2) = e3
% 245.14/51.58  | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | ALPHA: (109) implies:
% 245.14/51.58  | | | | | | | | | | | |   (110)  op(e0, e2) = e3
% 245.14/51.58  | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | BETA: splitting (83) gives:
% 245.14/51.58  | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | Case 1:
% 245.14/51.58  | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | |   (111)  all_54_12 = e2
% 245.14/51.58  | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | REF_CLOSE: (31), (35), (111) are inconsistent by sub-proof
% 245.14/51.58  | | | | | | | | | | | | |            #2264.
% 245.14/51.58  | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | Case 2:
% 245.14/51.58  | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | |   (112)  all_54_12 = e1 | all_54_12 = e0
% 245.14/51.58  | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | BETA: splitting (112) gives:
% 245.14/51.58  | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | Case 1:
% 245.14/51.58  | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | |   (113)  all_54_12 = e1
% 245.14/51.58  | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | | REF_CLOSE: (6), (31), (113) are inconsistent by sub-proof
% 245.14/51.58  | | | | | | | | | | | | | |            #2263.
% 245.14/51.58  | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | Case 2:
% 245.14/51.58  | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | |   (114)  all_54_12 = e0
% 245.14/51.58  | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | | COMBINE_EQS: (31), (114) imply:
% 245.14/51.58  | | | | | | | | | | | | | |   (115)  all_52_3 = e0
% 245.14/51.58  | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | | SIMP: (115) implies:
% 245.14/51.58  | | | | | | | | | | | | | |   (116)  all_52_3 = e0
% 245.14/51.58  | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | | REDUCE: (24), (116) imply:
% 245.14/51.58  | | | | | | | | | | | | | |   (117)   ~ (all_52_7 = e0)
% 245.14/51.58  | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | | SIMP: (117) implies:
% 245.14/51.58  | | | | | | | | | | | | | |   (118)   ~ (all_52_7 = e0)
% 245.14/51.58  | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 245.14/51.58  | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | | Case 1:
% 245.14/51.58  | | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | | |   (119)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 245.14/51.58  | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 245.14/51.58  | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 245.14/51.58  | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 245.14/51.58  | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 245.14/51.58  | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.14/51.58  | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 245.14/51.58  | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 245.14/51.58  | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.14/51.58  | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 245.14/51.58  | | | | | | | | | | | | | | |            = e3) | (all_56_5 = e1 & all_56_17 = e1 &  ~
% 245.14/51.58  | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 245.14/51.58  | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 245.14/51.58  | | | | | | | | | | | | | | |              e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 245.14/51.58  | | | | | | | | | | | | | | |            all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 245.14/51.58  | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.14/51.58  | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e3, e0) = e3 & op(e0, e3)
% 245.14/51.58  | | | | | | | | | | | | | | |            = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.14/51.58  | | | | | | | | | | | | | | |            (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 245.14/51.58  | | | | | | | | | | | | | | |            (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 245.14/51.58  | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e3) = e0)
% 245.14/51.58  | | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 245.14/51.58  | | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | | | Case 1:
% 245.14/51.58  | | | | | | | | | | | | | | | | 
% 245.14/51.58  | | | | | | | | | | | | | | | |   (120)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 =
% 245.14/51.58  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 245.14/51.58  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 245.14/51.58  | | | | | | | | | | | | | | | |            op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9 =
% 245.14/51.58  | | | | | | | | | | | | | | | |            e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 245.14/51.58  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.14/51.58  | | | | | | | | | | | | | | | |            op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 245.14/51.58  | | | | | | | | | | | | | | | |            e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 245.14/51.58  | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3)
% 245.14/51.59  | | | | | | | | | | | | | | | |            = e3)
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | Case 1:
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | |   (121)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2)
% 245.14/51.59  | | | | | | | | | | | | | | | | |          &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | | | |          (all_56_31 = e2) & op(e3, e2) = e3 & op(e2, e3) =
% 245.14/51.59  | | | | | | | | | | | | | | | | |          e3
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 245.14/51.59  | | | | | | | | | | | | | | | | |   (122)  op(e2, e3) = e3
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (89), (90), (104), (122) are inconsistent by
% 245.14/51.59  | | | | | | | | | | | | | | | | |            sub-proof #2262.
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | Case 2:
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | |   (123)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 =
% 245.14/51.59  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 245.14/51.59  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 245.14/51.59  | | | | | | | | | | | | | | | | |            op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 =
% 245.14/51.59  | | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) & 
% 245.14/51.59  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 245.14/51.59  | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e1, e3) = e3)
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (27), (48), (52), (103), (123) are
% 245.14/51.59  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2259.
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | End of split
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | Case 2:
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | |   (124)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 245.14/51.59  | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 =
% 245.14/51.59  | | | | | | | | | | | | | | | |              e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 245.14/51.59  | | | | | | | | | | | | | | | |            op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 =
% 245.14/51.59  | | | | | | | | | | | | | | | |            e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 245.14/51.59  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.14/51.59  | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 =
% 245.14/51.59  | | | | | | | | | | | | | | | |            e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | | |            (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | | |            (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3)
% 245.14/51.59  | | | | | | | | | | | | | | | |            = e0)
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | Case 1:
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | |   (125)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 =
% 245.14/51.59  | | | | | | | | | | | | | | | | |            e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 245.14/51.59  | | | | | | | | | | | | | | | | |          &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1,
% 245.14/51.59  | | | | | | | | | | | | | | | | |            e3) = e1
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 245.14/51.59  | | | | | | | | | | | | | | | | |   (126)  op(e3, e1) = e1
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (27), (48), (126) are inconsistent by
% 245.14/51.59  | | | | | | | | | | | | | | | | |            sub-proof #2309.
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | Case 2:
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | |   (127)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 =
% 245.14/51.59  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 245.14/51.59  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 245.14/51.59  | | | | | | | | | | | | | | | | |            op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 =
% 245.14/51.59  | | | | | | | | | | | | | | | | |            e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 245.14/51.59  | | | | | | | | | | | | | | | | |            ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.14/51.59  | | | | | | | | | | | | | | | | |            op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (34), (48), (69), (97), (127) are
% 245.14/51.59  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2257.
% 245.14/51.59  | | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | End of split
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | End of split
% 245.14/51.59  | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | Case 2:
% 245.14/51.59  | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | |   (128)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 245.14/51.59  | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 245.14/51.59  | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 245.14/51.59  | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 245.14/51.59  | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 245.14/51.59  | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 245.14/51.59  | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 245.14/51.59  | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 245.14/51.59  | | | | | | | | | | | | | | |            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~
% 245.14/51.59  | | | | | | | | | | | | | | |            (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | |            (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 245.14/51.59  | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1
% 245.14/51.59  | | | | | | | | | | | | | | |            & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1)
% 245.14/51.59  | | | | | | | | | | | | | | |            = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 245.14/51.59  | | | | | | | | | | | | | | |            (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | |            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 245.14/51.59  | | | | | | | | | | | | | | |              e0) = e0 & op(e0, e1) = e0)
% 245.14/51.59  | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 245.14/51.59  | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | Case 1:
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | |   (129)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 =
% 245.14/51.59  | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 245.14/51.59  | | | | | | | | | | | | | | | |              e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 245.14/51.59  | | | | | | | | | | | | | | | |            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 245.14/51.59  | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 245.14/51.59  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 245.14/51.59  | | | | | | | | | | | | | | | |            op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15
% 245.14/51.59  | | | | | | | | | | | | | | | |            = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | | |            (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | | |            (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 245.14/51.59  | | | | | | | | | | | | | | | |            = e2)
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | REF_CLOSE: (48), (70), (100), (104), (110), (129) are
% 245.14/51.59  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2253.
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | Case 2:
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | |   (130)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 =
% 245.14/51.59  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 245.14/51.59  | | | | | | | | | | | | | | | |              e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 245.14/51.59  | | | | | | | | | | | | | | | |            op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 245.14/51.59  | | | | | | | | | | | | | | | |            e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 245.14/51.59  | | | | | | | | | | | | | | | |            ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.14/51.59  | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23
% 245.14/51.59  | | | | | | | | | | | | | | | |            = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | | |            (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.14/51.59  | | | | | | | | | | | | | | | |            (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 245.14/51.59  | | | | | | | | | | | | | | | |            = e0)
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | | REF_CLOSE: (12), (29), (30), (42), (48), (118), (130) are
% 245.14/51.59  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2251.
% 245.14/51.59  | | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | | End of split
% 245.14/51.59  | | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | | End of split
% 245.14/51.59  | | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | | End of split
% 245.14/51.59  | | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | | End of split
% 245.14/51.59  | | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | End of split
% 245.14/51.59  | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | Case 2:
% 245.14/51.59  | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | |   (131)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 245.14/51.59  | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 245.14/51.59  | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | | REF_CLOSE: (11), (19), (33), (36), (43), (48), (70), (105),
% 245.14/51.59  | | | | | | | | | | |            (131) are inconsistent by sub-proof #2248.
% 245.14/51.59  | | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | End of split
% 245.14/51.59  | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | Case 2:
% 245.14/51.59  | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | |   (132)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 245.14/51.59  | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | | REF_CLOSE: (15), (39), (47), (97), (132) are inconsistent by
% 245.14/51.59  | | | | | | | | | |            sub-proof #2286.
% 245.14/51.59  | | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | End of split
% 245.14/51.59  | | | | | | | | | 
% 245.14/51.59  | | | | | | | | Case 2:
% 245.14/51.59  | | | | | | | | | 
% 245.14/51.59  | | | | | | | | |   (133)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 245.14/51.59  | | | | | | | | | 
% 245.14/51.59  | | | | | | | | | REF_CLOSE: (17), (51), (53), (96), (133) are inconsistent by
% 245.14/51.59  | | | | | | | | |            sub-proof #2244.
% 245.14/51.59  | | | | | | | | | 
% 245.14/51.59  | | | | | | | | End of split
% 245.14/51.59  | | | | | | | | 
% 245.14/51.59  | | | | | | | End of split
% 245.14/51.59  | | | | | | | 
% 245.14/51.59  | | | | | | End of split
% 245.14/51.59  | | | | | | 
% 245.14/51.59  | | | | | Case 2:
% 245.14/51.59  | | | | | | 
% 245.14/51.59  | | | | | |   (134)  (all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 245.14/51.59  | | | | | |            all_56_5 & $i(all_56_5)) | (all_56_6 = e0 & op(e0,
% 245.14/51.59  | | | | | |              all_56_7) = e0 & op(e0, e3) = all_56_7 & $i(all_56_7))
% 245.14/51.59  | | | | | | 
% 245.14/51.59  | | | | | | BETA: splitting (134) gives:
% 245.14/51.59  | | | | | | 
% 245.14/51.59  | | | | | | Case 1:
% 245.14/51.59  | | | | | | | 
% 245.14/51.59  | | | | | | |   (135)  all_56_4 = e1 & op(e1, all_56_5) = e1 & op(e1, e3) =
% 245.14/51.59  | | | | | | |          all_56_5 & $i(all_56_5)
% 245.14/51.59  | | | | | | | 
% 245.14/51.59  | | | | | | | ALPHA: (135) implies:
% 245.14/51.59  | | | | | | |   (136)  op(e1, e3) = all_56_5
% 245.14/51.59  | | | | | | |   (137)  op(e1, all_56_5) = e1
% 245.14/51.59  | | | | | | | 
% 245.14/51.59  | | | | | | | REF_CLOSE: (48), (70), (71), (136), (137) are inconsistent by
% 245.14/51.59  | | | | | | |            sub-proof #2243.
% 245.14/51.59  | | | | | | | 
% 245.14/51.59  | | | | | | Case 2:
% 245.14/51.59  | | | | | | | 
% 245.14/51.59  | | | | | | |   (138)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) =
% 245.14/51.59  | | | | | | |          all_56_7 & $i(all_56_7)
% 245.14/51.59  | | | | | | | 
% 245.14/51.59  | | | | | | | REF_CLOSE: (1), (6), (14), (31), (35), (48), (83), (138) are
% 245.14/51.59  | | | | | | |            inconsistent by sub-proof #2242.
% 245.14/51.59  | | | | | | | 
% 245.14/51.59  | | | | | | End of split
% 245.14/51.59  | | | | | | 
% 245.14/51.59  | | | | | End of split
% 245.14/51.59  | | | | | 
% 245.14/51.59  | | | | End of split
% 245.14/51.59  | | | | 
% 245.14/51.59  | | | End of split
% 245.14/51.59  | | | 
% 245.14/51.59  | | End of split
% 245.14/51.59  | | 
% 245.14/51.59  | Case 2:
% 245.14/51.59  | | 
% 245.14/51.59  | |   (139)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 245.14/51.59  | | 
% 245.14/51.59  | | REF_CLOSE: (22), (57), (61), (62), (139) are inconsistent by sub-proof
% 245.14/51.59  | |            #2241.
% 245.14/51.59  | | 
% 245.14/51.59  | End of split
% 245.14/51.59  | 
% 245.14/51.59  End of proof
% 245.14/51.59  
% 245.14/51.59  Sub-proof #2241 shows that the following formulas are inconsistent:
% 245.14/51.59  ----------------------------------------------------------------
% 245.14/51.59    (1)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 245.14/51.59    (2)   ~ (all_24_0 = e0)
% 245.14/51.59    (3)   ~ (all_24_0 = e1)
% 245.14/51.59    (4)  all_54_8 = all_24_0
% 245.14/51.59    (5)   ~ (all_24_0 = e2)
% 245.14/51.59  
% 245.14/51.59  Begin of proof
% 245.14/51.59  | 
% 245.14/51.59  | BETA: splitting (1) gives:
% 245.14/51.59  | 
% 245.14/51.59  | Case 1:
% 245.14/51.59  | | 
% 245.14/51.59  | |   (6)  all_54_8 = e2
% 245.14/51.59  | | 
% 245.14/51.59  | | COMBINE_EQS: (4), (6) imply:
% 245.14/51.59  | |   (7)  all_24_0 = e2
% 245.14/51.59  | | 
% 245.14/51.59  | | SIMP: (7) implies:
% 245.14/51.59  | |   (8)  all_24_0 = e2
% 245.14/51.59  | | 
% 245.14/51.59  | | REDUCE: (5), (8) imply:
% 245.14/51.59  | |   (9)  $false
% 245.14/51.59  | | 
% 245.14/51.59  | | CLOSE: (9) is inconsistent.
% 245.14/51.59  | | 
% 245.14/51.59  | Case 2:
% 245.14/51.59  | | 
% 245.14/51.59  | |   (10)  all_54_8 = e1 | all_54_8 = e0
% 245.14/51.59  | | 
% 245.14/51.59  | | BETA: splitting (10) gives:
% 245.14/51.59  | | 
% 245.14/51.59  | | Case 1:
% 245.14/51.59  | | | 
% 245.14/51.59  | | |   (11)  all_54_8 = e1
% 245.14/51.59  | | | 
% 245.14/51.59  | | | COMBINE_EQS: (4), (11) imply:
% 245.14/51.59  | | |   (12)  all_24_0 = e1
% 245.14/51.59  | | | 
% 245.14/51.59  | | | SIMP: (12) implies:
% 245.14/51.59  | | |   (13)  all_24_0 = e1
% 245.14/51.59  | | | 
% 245.14/51.59  | | | REDUCE: (3), (13) imply:
% 245.14/51.59  | | |   (14)  $false
% 245.14/51.59  | | | 
% 245.14/51.59  | | | CLOSE: (14) is inconsistent.
% 245.14/51.59  | | | 
% 245.14/51.59  | | Case 2:
% 245.14/51.59  | | | 
% 245.14/51.59  | | |   (15)  all_54_8 = e0
% 245.14/51.59  | | | 
% 245.14/51.59  | | | COMBINE_EQS: (4), (15) imply:
% 245.14/51.59  | | |   (16)  all_24_0 = e0
% 245.14/51.59  | | | 
% 245.14/51.59  | | | SIMP: (16) implies:
% 245.14/51.59  | | |   (17)  all_24_0 = e0
% 245.14/51.59  | | | 
% 245.14/51.59  | | | REDUCE: (2), (17) imply:
% 245.14/51.59  | | |   (18)  $false
% 245.14/51.59  | | | 
% 245.14/51.59  | | | CLOSE: (18) is inconsistent.
% 245.14/51.59  | | | 
% 245.14/51.59  | | End of split
% 245.14/51.59  | | 
% 245.14/51.59  | End of split
% 245.14/51.59  | 
% 245.14/51.59  End of proof
% 245.14/51.59  
% 245.14/51.59  Sub-proof #2242 shows that the following formulas are inconsistent:
% 245.14/51.59  ----------------------------------------------------------------
% 245.14/51.59    (1)  op(e0, e0) = e1
% 245.14/51.59    (2)   ~ (all_52_3 = e1)
% 245.14/51.59    (3)  all_56_6 = e0 & op(e0, all_56_7) = e0 & op(e0, e3) = all_56_7 &
% 245.14/51.59         $i(all_56_7)
% 245.14/51.59    (4)  op(e0, e3) = all_52_3
% 245.14/51.59    (5)  all_54_12 = all_52_3
% 245.14/51.59    (6)   ~ (all_52_3 = e2)
% 245.14/51.59    (7)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 245.14/51.59    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.59  
% 245.14/51.59  Begin of proof
% 245.14/51.59  | 
% 245.14/51.59  | ALPHA: (3) implies:
% 245.14/51.59  |   (9)  op(e0, e3) = all_56_7
% 245.14/51.59  |   (10)  op(e0, all_56_7) = e0
% 245.14/51.59  | 
% 245.14/51.59  | BETA: splitting (7) gives:
% 245.14/51.59  | 
% 245.14/51.59  | Case 1:
% 245.14/51.59  | | 
% 245.14/51.59  | |   (11)  all_54_12 = e2
% 245.14/51.59  | | 
% 245.14/51.59  | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #2264.
% 245.14/51.59  | | 
% 245.14/51.59  | Case 2:
% 245.14/51.59  | | 
% 245.14/51.59  | |   (12)  all_54_12 = e1 | all_54_12 = e0
% 245.14/51.59  | | 
% 245.14/51.59  | | BETA: splitting (12) gives:
% 245.14/51.59  | | 
% 245.14/51.59  | | Case 1:
% 245.14/51.59  | | | 
% 245.14/51.59  | | |   (13)  all_54_12 = e1
% 245.14/51.59  | | | 
% 245.14/51.59  | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #2263.
% 245.14/51.59  | | | 
% 245.14/51.59  | | Case 2:
% 245.14/51.59  | | | 
% 245.14/51.59  | | |   (14)  all_54_12 = e0
% 245.14/51.59  | | | 
% 245.14/51.59  | | | COMBINE_EQS: (5), (14) imply:
% 245.14/51.59  | | |   (15)  all_52_3 = e0
% 245.14/51.59  | | | 
% 245.14/51.59  | | | SIMP: (15) implies:
% 245.14/51.59  | | |   (16)  all_52_3 = e0
% 245.14/51.59  | | | 
% 245.14/51.59  | | | REDUCE: (2), (16) imply:
% 245.14/51.59  | | |   (17)   ~ (e1 = e0)
% 245.14/51.59  | | | 
% 245.14/51.59  | | | SIMP: (17) implies:
% 245.14/51.59  | | |   (18)   ~ (e1 = e0)
% 245.14/51.59  | | | 
% 245.14/51.59  | | | REDUCE: (4), (16) imply:
% 245.14/51.59  | | |   (19)  op(e0, e3) = e0
% 245.14/51.59  | | | 
% 245.14/51.59  | | | GROUND_INST: instantiating (8) with e0, all_56_7, e3, e0, simplifying with
% 245.14/51.59  | | |              (9), (19) gives:
% 245.14/51.59  | | |   (20)  all_56_7 = e0
% 245.14/51.59  | | | 
% 245.14/51.59  | | | REDUCE: (10), (20) imply:
% 245.14/51.59  | | |   (21)  op(e0, e0) = e0
% 245.14/51.59  | | | 
% 245.14/51.59  | | | REF_CLOSE: (1), (8), (18), (21) are inconsistent by sub-proof #2274.
% 245.14/51.59  | | | 
% 245.14/51.59  | | End of split
% 245.14/51.59  | | 
% 245.14/51.59  | End of split
% 245.14/51.59  | 
% 245.14/51.59  End of proof
% 245.14/51.59  
% 245.14/51.59  Sub-proof #2243 shows that the following formulas are inconsistent:
% 245.14/51.59  ----------------------------------------------------------------
% 245.14/51.59    (1)  op(e1, all_56_5) = e1
% 245.14/51.59    (2)  op(e1, e3) = all_56_5
% 245.14/51.59    (3)  op(e1, e3) = e3
% 245.14/51.59    (4)   ~ (e3 = e1)
% 245.14/51.59    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.59  
% 245.14/51.59  Begin of proof
% 245.14/51.59  | 
% 245.14/51.59  | GROUND_INST: instantiating (5) with e3, all_56_5, e3, e1, simplifying with
% 245.14/51.59  |              (2), (3) gives:
% 245.14/51.59  |   (6)  all_56_5 = e3
% 245.14/51.59  | 
% 245.14/51.59  | REDUCE: (1), (6) imply:
% 245.14/51.59  |   (7)  op(e1, e3) = e1
% 245.14/51.59  | 
% 245.14/51.59  | GROUND_INST: instantiating (5) with e3, e1, e3, e1, simplifying with (3), (7)
% 245.14/51.59  |              gives:
% 245.14/51.59  |   (8)  e3 = e1
% 245.14/51.59  | 
% 245.14/51.59  | REDUCE: (4), (8) imply:
% 245.14/51.59  |   (9)  $false
% 245.14/51.59  | 
% 245.14/51.59  | CLOSE: (9) is inconsistent.
% 245.14/51.59  | 
% 245.14/51.59  End of proof
% 245.14/51.59  
% 245.14/51.59  Sub-proof #2244 shows that the following formulas are inconsistent:
% 245.14/51.59  ----------------------------------------------------------------
% 245.14/51.59    (1)  all_54_6 = all_52_9
% 245.14/51.59    (2)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 245.14/51.59    (3)   ~ (all_52_9 = e0)
% 245.14/51.59    (4)   ~ (all_52_9 = e1)
% 245.14/51.59    (5)   ~ (all_52_9 = e2)
% 245.14/51.59  
% 245.14/51.59  Begin of proof
% 245.14/51.59  | 
% 245.14/51.59  | BETA: splitting (2) gives:
% 245.14/51.59  | 
% 245.14/51.59  | Case 1:
% 245.14/51.59  | | 
% 245.14/51.59  | |   (6)  all_54_6 = e2
% 245.14/51.59  | | 
% 245.14/51.59  | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #2247.
% 245.14/51.59  | | 
% 245.14/51.59  | Case 2:
% 245.14/51.59  | | 
% 245.14/51.59  | |   (7)  all_54_6 = e1 | all_54_6 = e0
% 245.14/51.59  | | 
% 245.14/51.59  | | BETA: splitting (7) gives:
% 245.14/51.59  | | 
% 245.14/51.59  | | Case 1:
% 245.14/51.59  | | | 
% 245.14/51.59  | | |   (8)  all_54_6 = e1
% 245.14/51.59  | | | 
% 245.14/51.59  | | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #2246.
% 245.14/51.59  | | | 
% 245.14/51.59  | | Case 2:
% 245.14/51.59  | | | 
% 245.14/51.59  | | |   (9)  all_54_6 = e0
% 245.14/51.59  | | | 
% 245.14/51.59  | | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #2245.
% 245.14/51.59  | | | 
% 245.14/51.59  | | End of split
% 245.14/51.59  | | 
% 245.14/51.59  | End of split
% 245.14/51.59  | 
% 245.14/51.59  End of proof
% 245.14/51.59  
% 245.14/51.59  Sub-proof #2245 shows that the following formulas are inconsistent:
% 245.14/51.59  ----------------------------------------------------------------
% 245.14/51.59    (1)  all_54_6 = all_52_9
% 245.14/51.59    (2)  all_54_6 = e0
% 245.14/51.59    (3)   ~ (all_52_9 = e0)
% 245.14/51.59  
% 245.14/51.59  Begin of proof
% 245.14/51.59  | 
% 245.14/51.59  | COMBINE_EQS: (1), (2) imply:
% 245.14/51.59  |   (4)  all_52_9 = e0
% 245.14/51.59  | 
% 245.14/51.59  | SIMP: (4) implies:
% 245.14/51.59  |   (5)  all_52_9 = e0
% 245.14/51.59  | 
% 245.14/51.59  | REDUCE: (3), (5) imply:
% 245.14/51.59  |   (6)  $false
% 245.14/51.59  | 
% 245.14/51.59  | CLOSE: (6) is inconsistent.
% 245.14/51.59  | 
% 245.14/51.59  End of proof
% 245.14/51.59  
% 245.14/51.59  Sub-proof #2246 shows that the following formulas are inconsistent:
% 245.14/51.59  ----------------------------------------------------------------
% 245.14/51.59    (1)  all_54_6 = all_52_9
% 245.14/51.59    (2)  all_54_6 = e1
% 245.14/51.59    (3)   ~ (all_52_9 = e1)
% 245.14/51.59  
% 245.14/51.59  Begin of proof
% 245.14/51.59  | 
% 245.14/51.59  | COMBINE_EQS: (1), (2) imply:
% 245.14/51.59  |   (4)  all_52_9 = e1
% 245.14/51.59  | 
% 245.14/51.59  | SIMP: (4) implies:
% 245.14/51.59  |   (5)  all_52_9 = e1
% 245.14/51.59  | 
% 245.14/51.59  | REDUCE: (3), (5) imply:
% 245.14/51.59  |   (6)  $false
% 245.14/51.59  | 
% 245.14/51.59  | CLOSE: (6) is inconsistent.
% 245.14/51.59  | 
% 245.14/51.59  End of proof
% 245.14/51.59  
% 245.14/51.59  Sub-proof #2247 shows that the following formulas are inconsistent:
% 245.14/51.59  ----------------------------------------------------------------
% 245.14/51.59    (1)  all_54_6 = all_52_9
% 245.14/51.59    (2)  all_54_6 = e2
% 245.14/51.59    (3)   ~ (all_52_9 = e2)
% 245.14/51.59  
% 245.14/51.59  Begin of proof
% 245.14/51.59  | 
% 245.14/51.59  | COMBINE_EQS: (1), (2) imply:
% 245.14/51.59  |   (4)  all_52_9 = e2
% 245.14/51.59  | 
% 245.14/51.59  | SIMP: (4) implies:
% 245.14/51.59  |   (5)  all_52_9 = e2
% 245.14/51.59  | 
% 245.14/51.59  | REDUCE: (3), (5) imply:
% 245.14/51.59  |   (6)  $false
% 245.14/51.59  | 
% 245.14/51.59  | CLOSE: (6) is inconsistent.
% 245.14/51.59  | 
% 245.14/51.59  End of proof
% 245.14/51.59  
% 245.14/51.59  Sub-proof #2248 shows that the following formulas are inconsistent:
% 245.14/51.59  ----------------------------------------------------------------
% 245.14/51.59    (1)  (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 245.14/51.59    (2)  op(e0, e1) = all_34_1
% 245.14/51.59    (3)   ~ (e3 = e1)
% 245.14/51.59    (4)  op(all_34_1, e0) = all_34_0
% 245.14/51.59    (5)  all_58_15 = e1
% 245.14/51.59    (6)   ~ (all_34_0 = e3)
% 245.14/51.59    (7)  op(e3, e0) = e3
% 245.14/51.59    (8)  op(e0, e1) = all_20_1
% 245.14/51.59    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.59  
% 245.14/51.59  Begin of proof
% 245.14/51.59  | 
% 245.14/51.59  | BETA: splitting (1) gives:
% 245.14/51.59  | 
% 245.14/51.59  | Case 1:
% 245.14/51.59  | | 
% 245.14/51.59  | |   (10)  all_58_14 = e3 & op(e0, e1) = e3
% 245.14/51.59  | | 
% 245.14/51.59  | | ALPHA: (10) implies:
% 245.14/51.59  | |   (11)  op(e0, e1) = e3
% 245.14/51.59  | | 
% 245.14/51.59  | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (11) are inconsistent by sub-proof
% 245.14/51.59  | |            #2250.
% 245.14/51.59  | | 
% 245.14/51.59  | Case 2:
% 245.14/51.59  | | 
% 245.14/51.59  | |   (12)  all_58_15 = e3 & op(e0, e0) = e3
% 245.14/51.59  | | 
% 245.14/51.59  | | ALPHA: (12) implies:
% 245.14/51.59  | |   (13)  all_58_15 = e3
% 245.14/51.59  | | 
% 245.14/51.59  | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #2249.
% 245.14/51.59  | | 
% 245.14/51.59  | End of split
% 245.14/51.59  | 
% 245.14/51.59  End of proof
% 245.14/51.59  
% 245.14/51.59  Sub-proof #2249 shows that the following formulas are inconsistent:
% 245.14/51.59  ----------------------------------------------------------------
% 245.14/51.59    (1)  all_58_15 = e3
% 245.14/51.59    (2)  all_58_15 = e1
% 245.14/51.59    (3)   ~ (e3 = e1)
% 245.14/51.59  
% 245.14/51.59  Begin of proof
% 245.14/51.59  | 
% 245.14/51.59  | COMBINE_EQS: (1), (2) imply:
% 245.14/51.59  |   (4)  e3 = e1
% 245.14/51.59  | 
% 245.14/51.59  | SIMP: (4) implies:
% 245.14/51.59  |   (5)  e3 = e1
% 245.14/51.59  | 
% 245.14/51.59  | REDUCE: (3), (5) imply:
% 245.14/51.59  |   (6)  $false
% 245.14/51.59  | 
% 245.14/51.59  | CLOSE: (6) is inconsistent.
% 245.14/51.59  | 
% 245.14/51.59  End of proof
% 245.14/51.59  
% 245.14/51.59  Sub-proof #2250 shows that the following formulas are inconsistent:
% 245.14/51.59  ----------------------------------------------------------------
% 245.14/51.59    (1)  op(e0, e1) = e3
% 245.14/51.59    (2)  op(e0, e1) = all_34_1
% 245.14/51.59    (3)  op(all_34_1, e0) = all_34_0
% 245.14/51.59    (4)   ~ (all_34_0 = e3)
% 245.14/51.59    (5)  op(e3, e0) = e3
% 245.14/51.59    (6)  op(e0, e1) = all_20_1
% 245.14/51.59    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.59  
% 245.14/51.59  Begin of proof
% 245.14/51.59  | 
% 245.14/51.59  | GROUND_INST: instantiating (7) with e3, all_34_1, e1, e0, simplifying with
% 245.14/51.59  |              (1), (2) gives:
% 245.14/51.59  |   (8)  all_34_1 = e3
% 245.14/51.59  | 
% 245.14/51.59  | GROUND_INST: instantiating (7) with all_20_1, all_34_1, e1, e0, simplifying
% 245.14/51.59  |              with (2), (6) gives:
% 245.14/51.59  |   (9)  all_34_1 = all_20_1
% 245.14/51.59  | 
% 245.14/51.59  | COMBINE_EQS: (8), (9) imply:
% 245.14/51.59  |   (10)  all_20_1 = e3
% 245.14/51.59  | 
% 245.14/51.59  | REDUCE: (3), (8) imply:
% 245.14/51.59  |   (11)  op(e3, e0) = all_34_0
% 245.14/51.59  | 
% 245.14/51.59  | GROUND_INST: instantiating (7) with e3, all_34_0, e0, e3, simplifying with
% 245.14/51.59  |              (5), (11) gives:
% 245.14/51.59  |   (12)  all_34_0 = e3
% 245.14/51.59  | 
% 245.14/51.59  | REDUCE: (4), (12) imply:
% 245.14/51.60  |   (13)  $false
% 245.14/51.60  | 
% 245.14/51.60  | CLOSE: (13) is inconsistent.
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2251 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)  op(e1, e0) = all_52_14
% 245.14/51.60    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.14/51.60             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 245.14/51.60           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 245.14/51.60             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 245.14/51.60           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 245.14/51.60           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.14/51.60           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.14/51.60    (3)   ~ (all_52_14 = e1)
% 245.14/51.60    (4)  all_56_31 = e1
% 245.14/51.60    (5)  op(e0, e2) = all_52_7
% 245.14/51.60    (6)   ~ (all_52_7 = e0)
% 245.14/51.60    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.60  
% 245.14/51.60  Begin of proof
% 245.14/51.60  | 
% 245.14/51.60  | BETA: splitting (2) gives:
% 245.14/51.60  | 
% 245.14/51.60  | Case 1:
% 245.14/51.60  | | 
% 245.14/51.60  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 245.14/51.60  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 245.14/51.60  | |        & op(e0, e2) = e0
% 245.14/51.60  | | 
% 245.14/51.60  | | ALPHA: (8) implies:
% 245.14/51.60  | |   (9)  op(e0, e2) = e0
% 245.14/51.60  | | 
% 245.14/51.60  | | REF_CLOSE: (5), (6), (7), (9) are inconsistent by sub-proof #2252.
% 245.14/51.60  | | 
% 245.14/51.60  | Case 2:
% 245.14/51.60  | | 
% 245.14/51.60  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.14/51.60  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.14/51.60  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 245.14/51.60  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 245.14/51.60  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.14/51.60  | | 
% 245.14/51.60  | | REF_CLOSE: (1), (3), (4), (7), (10) are inconsistent by sub-proof #2269.
% 245.14/51.60  | | 
% 245.14/51.60  | End of split
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2252 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.60    (2)  op(e0, e2) = all_52_7
% 245.14/51.60    (3)  op(e0, e2) = e0
% 245.14/51.60    (4)   ~ (all_52_7 = e0)
% 245.14/51.60  
% 245.14/51.60  Begin of proof
% 245.14/51.60  | 
% 245.14/51.60  | GROUND_INST: instantiating (1) with all_52_7, e0, e2, e0, simplifying with
% 245.14/51.60  |              (2), (3) gives:
% 245.14/51.60  |   (5)  all_52_7 = e0
% 245.14/51.60  | 
% 245.14/51.60  | REDUCE: (4), (5) imply:
% 245.14/51.60  |   (6)  $false
% 245.14/51.60  | 
% 245.14/51.60  | CLOSE: (6) is inconsistent.
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2253 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)   ~ (e3 = e1)
% 245.14/51.60    (2)  op(e0, e2) = e3
% 245.14/51.60    (3)   ~ (e3 = e2)
% 245.14/51.60    (4)  op(e2, e1) = e3
% 245.14/51.60    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.60    (6)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 245.14/51.60             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 245.14/51.60           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 245.14/51.60             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 245.14/51.60           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 245.14/51.60           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.14/51.60           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 245.14/51.60  
% 245.14/51.60  Begin of proof
% 245.14/51.60  | 
% 245.14/51.60  | BETA: splitting (6) gives:
% 245.14/51.60  | 
% 245.14/51.60  | Case 1:
% 245.14/51.60  | | 
% 245.14/51.60  | |   (7)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 245.14/51.60  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 245.14/51.60  | |        & op(e1, e2) = e2
% 245.14/51.60  | | 
% 245.14/51.60  | | ALPHA: (7) implies:
% 245.14/51.60  | |   (8)  op(e2, e1) = e2
% 245.14/51.60  | | 
% 245.14/51.60  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2256.
% 245.14/51.60  | | 
% 245.14/51.60  | Case 2:
% 245.14/51.60  | | 
% 245.14/51.60  | |   (9)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 245.14/51.60  | |            = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) =
% 245.14/51.60  | |          e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 245.14/51.60  | |          (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.14/51.60  | |          (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 245.14/51.60  | | 
% 245.14/51.60  | | BETA: splitting (9) gives:
% 245.14/51.60  | | 
% 245.14/51.60  | | Case 1:
% 245.14/51.60  | | | 
% 245.14/51.60  | | |   (10)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 245.14/51.60  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 245.14/51.60  | | |         op(e2, e1) = e1 & op(e1, e2) = e1
% 245.14/51.60  | | | 
% 245.14/51.60  | | | ALPHA: (10) implies:
% 245.14/51.60  | | |   (11)  op(e2, e1) = e1
% 245.14/51.60  | | | 
% 245.14/51.60  | | | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #2255.
% 245.14/51.60  | | | 
% 245.14/51.60  | | Case 2:
% 245.14/51.60  | | | 
% 245.14/51.60  | | |   (12)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 245.14/51.60  | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.14/51.60  | | |         op(e2, e0) = e2 & op(e0, e2) = e2
% 245.14/51.60  | | | 
% 245.14/51.60  | | | ALPHA: (12) implies:
% 245.14/51.60  | | |   (13)  op(e0, e2) = e2
% 245.14/51.60  | | | 
% 245.14/51.60  | | | REF_CLOSE: (2), (3), (5), (13) are inconsistent by sub-proof #2254.
% 245.14/51.60  | | | 
% 245.14/51.60  | | End of split
% 245.14/51.60  | | 
% 245.14/51.60  | End of split
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2254 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.60    (2)  op(e0, e2) = e3
% 245.14/51.60    (3)  op(e0, e2) = e2
% 245.14/51.60    (4)   ~ (e3 = e2)
% 245.14/51.60  
% 245.14/51.60  Begin of proof
% 245.14/51.60  | 
% 245.14/51.60  | GROUND_INST: instantiating (1) with e3, e2, e2, e0, simplifying with (2), (3)
% 245.14/51.60  |              gives:
% 245.14/51.60  |   (5)  e3 = e2
% 245.14/51.60  | 
% 245.14/51.60  | REDUCE: (4), (5) imply:
% 245.14/51.60  |   (6)  $false
% 245.14/51.60  | 
% 245.14/51.60  | CLOSE: (6) is inconsistent.
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2255 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.60    (2)  op(e2, e1) = e3
% 245.14/51.60    (3)  op(e2, e1) = e1
% 245.14/51.60    (4)   ~ (e3 = e1)
% 245.14/51.60  
% 245.14/51.60  Begin of proof
% 245.14/51.60  | 
% 245.14/51.60  | GROUND_INST: instantiating (1) with e3, e1, e1, e2, simplifying with (2), (3)
% 245.14/51.60  |              gives:
% 245.14/51.60  |   (5)  e3 = e1
% 245.14/51.60  | 
% 245.14/51.60  | REDUCE: (4), (5) imply:
% 245.14/51.60  |   (6)  $false
% 245.14/51.60  | 
% 245.14/51.60  | CLOSE: (6) is inconsistent.
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2256 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.60    (2)  op(e2, e1) = e3
% 245.14/51.60    (3)  op(e2, e1) = e2
% 245.14/51.60    (4)   ~ (e3 = e2)
% 245.14/51.60  
% 245.14/51.60  Begin of proof
% 245.14/51.60  | 
% 245.14/51.60  | GROUND_INST: instantiating (1) with e3, e2, e1, e2, simplifying with (2), (3)
% 245.14/51.60  |              gives:
% 245.14/51.60  |   (5)  e3 = e2
% 245.14/51.60  | 
% 245.14/51.60  | REDUCE: (4), (5) imply:
% 245.14/51.60  |   (6)  $false
% 245.14/51.60  | 
% 245.14/51.60  | CLOSE: (6) is inconsistent.
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2257 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.14/51.60             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 245.14/51.60           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 245.14/51.60           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.14/51.60           op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.14/51.60    (2)   ~ (all_52_12 = e0)
% 245.14/51.60    (3)  op(e0, e3) = all_52_3
% 245.14/51.60    (4)  op(e3, e0) = all_52_12
% 245.14/51.60    (5)   ~ (all_52_3 = e3)
% 245.14/51.60    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.60  
% 245.14/51.60  Begin of proof
% 245.14/51.60  | 
% 245.14/51.60  | BETA: splitting (1) gives:
% 245.14/51.60  | 
% 245.14/51.60  | Case 1:
% 245.14/51.60  | | 
% 245.14/51.60  | |   (7)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.14/51.60  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 245.14/51.60  | |        op(e0, e3) = e3
% 245.14/51.60  | | 
% 245.14/51.60  | | ALPHA: (7) implies:
% 245.14/51.60  | |   (8)  op(e0, e3) = e3
% 245.14/51.60  | | 
% 245.14/51.60  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2332.
% 245.14/51.60  | | 
% 245.14/51.60  | Case 2:
% 245.14/51.60  | | 
% 245.14/51.60  | |   (9)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.14/51.60  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 245.14/51.60  | |        op(e0, e3) = e0
% 245.14/51.60  | | 
% 245.14/51.60  | | ALPHA: (9) implies:
% 245.14/51.60  | |   (10)  op(e3, e0) = e0
% 245.14/51.60  | | 
% 245.14/51.60  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #2258.
% 245.14/51.60  | | 
% 245.14/51.60  | End of split
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2258 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.60    (2)  op(e3, e0) = all_52_12
% 245.14/51.60    (3)  op(e3, e0) = e0
% 245.14/51.60    (4)   ~ (all_52_12 = e0)
% 245.14/51.60  
% 245.14/51.60  Begin of proof
% 245.14/51.60  | 
% 245.14/51.60  | GROUND_INST: instantiating (1) with all_52_12, e0, e0, e3, simplifying with
% 245.14/51.60  |              (2), (3) gives:
% 245.14/51.60  |   (5)  all_52_12 = e0
% 245.14/51.60  | 
% 245.14/51.60  | REDUCE: (4), (5) imply:
% 245.14/51.60  |   (6)  $false
% 245.14/51.60  | 
% 245.14/51.60  | CLOSE: (6) is inconsistent.
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2259 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)  op(e3, e2) = e1
% 245.14/51.60    (2)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 245.14/51.60           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 245.14/51.60             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 245.14/51.60           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 245.14/51.60             e1) = e3 & op(e1, e3) = e3)
% 245.14/51.60    (3)  op(e3, e1) = all_52_8
% 245.14/51.60    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.60    (5)   ~ (e2 = e1)
% 245.14/51.60    (6)   ~ (all_52_8 = e3)
% 245.14/51.60  
% 245.14/51.60  Begin of proof
% 245.14/51.60  | 
% 245.14/51.60  | BETA: splitting (2) gives:
% 245.14/51.60  | 
% 245.14/51.60  | Case 1:
% 245.14/51.60  | | 
% 245.14/51.60  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.14/51.60  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 245.14/51.60  | |        op(e2, e3) = e2
% 245.14/51.60  | | 
% 245.14/51.60  | | ALPHA: (7) implies:
% 245.14/51.60  | |   (8)  op(e3, e2) = e2
% 245.14/51.60  | | 
% 245.14/51.60  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2261.
% 245.14/51.60  | | 
% 245.14/51.60  | Case 2:
% 245.14/51.60  | | 
% 245.14/51.60  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 245.14/51.60  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 245.14/51.60  | |        op(e1, e3) = e3
% 245.14/51.60  | | 
% 245.14/51.60  | | ALPHA: (9) implies:
% 245.14/51.60  | |   (10)  op(e3, e1) = e3
% 245.14/51.60  | | 
% 245.14/51.60  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #2260.
% 245.14/51.60  | | 
% 245.14/51.60  | End of split
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2260 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.60    (2)  op(e3, e1) = all_52_8
% 245.14/51.60    (3)  op(e3, e1) = e3
% 245.14/51.60    (4)   ~ (all_52_8 = e3)
% 245.14/51.60  
% 245.14/51.60  Begin of proof
% 245.14/51.60  | 
% 245.14/51.60  | GROUND_INST: instantiating (1) with all_52_8, e3, e1, e3, simplifying with
% 245.14/51.60  |              (2), (3) gives:
% 245.14/51.60  |   (5)  all_52_8 = e3
% 245.14/51.60  | 
% 245.14/51.60  | REDUCE: (4), (5) imply:
% 245.14/51.60  |   (6)  $false
% 245.14/51.60  | 
% 245.14/51.60  | CLOSE: (6) is inconsistent.
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2261 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.14/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.14/51.60    (2)  op(e3, e2) = e2
% 245.14/51.60    (3)  op(e3, e2) = e1
% 245.14/51.60    (4)   ~ (e2 = e1)
% 245.14/51.60  
% 245.14/51.60  Begin of proof
% 245.14/51.60  | 
% 245.14/51.60  | GROUND_INST: instantiating (1) with e1, e2, e2, e3, simplifying with (2), (3)
% 245.14/51.60  |              gives:
% 245.14/51.60  |   (5)  e2 = e1
% 245.14/51.60  | 
% 245.14/51.60  | REDUCE: (4), (5) imply:
% 245.14/51.60  |   (6)  $false
% 245.14/51.60  | 
% 245.14/51.60  | CLOSE: (6) is inconsistent.
% 245.14/51.60  | 
% 245.14/51.60  End of proof
% 245.14/51.60  
% 245.14/51.60  Sub-proof #2262 shows that the following formulas are inconsistent:
% 245.14/51.60  ----------------------------------------------------------------
% 245.14/51.60    (1)  op(e2, e3) = all_56_3
% 245.14/51.60    (2)  op(e2, e3) = e3
% 245.14/51.60    (3)   ~ (e3 = e2)
% 245.17/51.60    (4)  op(e2, all_56_3) = e2
% 245.17/51.60    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.60  
% 245.17/51.60  Begin of proof
% 245.17/51.60  | 
% 245.17/51.60  | GROUND_INST: instantiating (5) with e3, all_56_3, e3, e2, simplifying with
% 245.17/51.60  |              (1), (2) gives:
% 245.17/51.60  |   (6)  all_56_3 = e3
% 245.17/51.60  | 
% 245.17/51.60  | REDUCE: (4), (6) imply:
% 245.17/51.60  |   (7)  op(e2, e3) = e2
% 245.17/51.60  | 
% 245.17/51.60  | GROUND_INST: instantiating (5) with e3, e2, e3, e2, simplifying with (2), (7)
% 245.17/51.60  |              gives:
% 245.17/51.60  |   (8)  e3 = e2
% 245.17/51.60  | 
% 245.17/51.60  | REDUCE: (3), (8) imply:
% 245.17/51.60  |   (9)  $false
% 245.17/51.60  | 
% 245.17/51.60  | CLOSE: (9) is inconsistent.
% 245.17/51.60  | 
% 245.17/51.60  End of proof
% 245.17/51.60  
% 245.17/51.60  Sub-proof #2263 shows that the following formulas are inconsistent:
% 245.17/51.60  ----------------------------------------------------------------
% 245.17/51.60    (1)  all_54_12 = all_52_3
% 245.17/51.60    (2)  all_54_12 = e1
% 245.17/51.60    (3)   ~ (all_52_3 = e1)
% 245.17/51.60  
% 245.17/51.60  Begin of proof
% 245.17/51.60  | 
% 245.17/51.60  | COMBINE_EQS: (1), (2) imply:
% 245.17/51.60  |   (4)  all_52_3 = e1
% 245.17/51.60  | 
% 245.17/51.60  | SIMP: (4) implies:
% 245.17/51.60  |   (5)  all_52_3 = e1
% 245.17/51.60  | 
% 245.17/51.60  | REDUCE: (3), (5) imply:
% 245.17/51.60  |   (6)  $false
% 245.17/51.60  | 
% 245.17/51.60  | CLOSE: (6) is inconsistent.
% 245.17/51.60  | 
% 245.17/51.60  End of proof
% 245.17/51.60  
% 245.17/51.60  Sub-proof #2264 shows that the following formulas are inconsistent:
% 245.17/51.60  ----------------------------------------------------------------
% 245.17/51.60    (1)  all_54_12 = all_52_3
% 245.17/51.60    (2)  all_54_12 = e2
% 245.17/51.60    (3)   ~ (all_52_3 = e2)
% 245.17/51.60  
% 245.17/51.60  Begin of proof
% 245.17/51.60  | 
% 245.17/51.60  | COMBINE_EQS: (1), (2) imply:
% 245.17/51.60  |   (4)  all_52_3 = e2
% 245.17/51.60  | 
% 245.17/51.60  | SIMP: (4) implies:
% 245.17/51.60  |   (5)  all_52_3 = e2
% 245.17/51.60  | 
% 245.17/51.60  | REDUCE: (3), (5) imply:
% 245.17/51.60  |   (6)  $false
% 245.17/51.60  | 
% 245.17/51.60  | CLOSE: (6) is inconsistent.
% 245.17/51.60  | 
% 245.17/51.60  End of proof
% 245.17/51.60  
% 245.17/51.60  Sub-proof #2265 shows that the following formulas are inconsistent:
% 245.17/51.60  ----------------------------------------------------------------
% 245.17/51.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.60    (2)  op(e3, e2) = e3
% 245.17/51.60    (3)  op(e3, e2) = e1
% 245.17/51.60    (4)   ~ (e3 = e1)
% 245.17/51.60  
% 245.17/51.60  Begin of proof
% 245.17/51.60  | 
% 245.17/51.60  | GROUND_INST: instantiating (1) with e1, e3, e2, e3, simplifying with (2), (3)
% 245.17/51.60  |              gives:
% 245.17/51.60  |   (5)  e3 = e1
% 245.17/51.60  | 
% 245.17/51.60  | REDUCE: (4), (5) imply:
% 245.17/51.60  |   (6)  $false
% 245.17/51.60  | 
% 245.17/51.60  | CLOSE: (6) is inconsistent.
% 245.17/51.60  | 
% 245.17/51.60  End of proof
% 245.17/51.60  
% 245.17/51.60  Sub-proof #2266 shows that the following formulas are inconsistent:
% 245.17/51.60  ----------------------------------------------------------------
% 245.17/51.60    (1)  all_54_12 = all_52_3
% 245.17/51.60    (2)  all_54_12 = e3
% 245.17/51.60    (3)   ~ (all_52_3 = e3)
% 245.17/51.60  
% 245.17/51.60  Begin of proof
% 245.17/51.60  | 
% 245.17/51.60  | COMBINE_EQS: (1), (2) imply:
% 245.17/51.60  |   (4)  all_52_3 = e3
% 245.17/51.60  | 
% 245.17/51.60  | SIMP: (4) implies:
% 245.17/51.60  |   (5)  all_52_3 = e3
% 245.17/51.60  | 
% 245.17/51.60  | REDUCE: (3), (5) imply:
% 245.17/51.60  |   (6)  $false
% 245.17/51.60  | 
% 245.17/51.60  | CLOSE: (6) is inconsistent.
% 245.17/51.60  | 
% 245.17/51.60  End of proof
% 245.17/51.60  
% 245.17/51.60  Sub-proof #2267 shows that the following formulas are inconsistent:
% 245.17/51.60  ----------------------------------------------------------------
% 245.17/51.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.60    (2)  op(e3, e3) = e2
% 245.17/51.60    (3)  op(e3, e3) = e1
% 245.17/51.60    (4)   ~ (e2 = e1)
% 245.17/51.60  
% 245.17/51.60  Begin of proof
% 245.17/51.60  | 
% 245.17/51.60  | GROUND_INST: instantiating (1) with e1, e2, e3, e3, simplifying with (2), (3)
% 245.17/51.60  |              gives:
% 245.17/51.60  |   (5)  e2 = e1
% 245.17/51.60  | 
% 245.17/51.60  | REDUCE: (4), (5) imply:
% 245.17/51.60  |   (6)  $false
% 245.17/51.60  | 
% 245.17/51.60  | CLOSE: (6) is inconsistent.
% 245.17/51.60  | 
% 245.17/51.60  End of proof
% 245.17/51.60  
% 245.17/51.60  Sub-proof #2268 shows that the following formulas are inconsistent:
% 245.17/51.60  ----------------------------------------------------------------
% 245.17/51.60    (1)  all_56_11 = e2
% 245.17/51.60    (2)  op(e1, e0) = all_52_14
% 245.17/51.60    (3)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.17/51.60             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 245.17/51.60           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 245.17/51.60             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 245.17/51.60           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 245.17/51.60           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.17/51.60           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.17/51.60    (4)   ~ (all_52_14 = e1)
% 245.17/51.60    (5)  all_56_31 = e1
% 245.17/51.60    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.60  
% 245.17/51.60  Begin of proof
% 245.17/51.60  | 
% 245.17/51.60  | BETA: splitting (3) gives:
% 245.17/51.60  | 
% 245.17/51.60  | Case 1:
% 245.17/51.60  | | 
% 245.17/51.61  | |   (7)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 245.17/51.61  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 245.17/51.61  | |        & op(e0, e2) = e0
% 245.17/51.61  | | 
% 245.17/51.61  | | ALPHA: (7) implies:
% 245.17/51.61  | |   (8)   ~ (all_56_11 = e2)
% 245.17/51.61  | | 
% 245.17/51.61  | | REDUCE: (1), (8) imply:
% 245.17/51.61  | |   (9)  $false
% 245.17/51.61  | | 
% 245.17/51.61  | | CLOSE: (9) is inconsistent.
% 245.17/51.61  | | 
% 245.17/51.61  | Case 2:
% 245.17/51.61  | | 
% 245.17/51.61  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.17/51.61  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.17/51.61  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 245.17/51.61  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 245.17/51.61  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.17/51.61  | | 
% 245.17/51.61  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #2269.
% 245.17/51.61  | | 
% 245.17/51.61  | End of split
% 245.17/51.61  | 
% 245.17/51.61  End of proof
% 245.17/51.61  
% 245.17/51.61  Sub-proof #2269 shows that the following formulas are inconsistent:
% 245.17/51.61  ----------------------------------------------------------------
% 245.17/51.61    (1)  op(e1, e0) = all_52_14
% 245.17/51.61    (2)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.17/51.61             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 245.17/51.61           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 245.17/51.61             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 245.17/51.61           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.17/51.61    (3)   ~ (all_52_14 = e1)
% 245.17/51.61    (4)  all_56_31 = e1
% 245.17/51.61    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.61  
% 245.17/51.61  Begin of proof
% 245.17/51.61  | 
% 245.17/51.61  | BETA: splitting (2) gives:
% 245.17/51.61  | 
% 245.17/51.61  | Case 1:
% 245.17/51.61  | | 
% 245.17/51.61  | |   (6)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 245.17/51.61  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 245.17/51.61  | |        & op(e0, e1) = e1
% 245.17/51.61  | | 
% 245.17/51.61  | | ALPHA: (6) implies:
% 245.17/51.61  | |   (7)  op(e1, e0) = e1
% 245.17/51.61  | | 
% 245.17/51.61  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #2304.
% 245.17/51.61  | | 
% 245.17/51.61  | Case 2:
% 245.17/51.61  | | 
% 245.17/51.61  | |   (8)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 245.17/51.61  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 245.17/51.61  | |        & op(e0, e1) = e0
% 245.17/51.61  | | 
% 245.17/51.61  | | ALPHA: (8) implies:
% 245.17/51.61  | |   (9)   ~ (all_56_31 = e1)
% 245.17/51.61  | | 
% 245.17/51.61  | | REDUCE: (4), (9) imply:
% 245.17/51.61  | |   (10)  $false
% 245.17/51.61  | | 
% 245.17/51.61  | | CLOSE: (10) is inconsistent.
% 245.17/51.61  | | 
% 245.17/51.61  | End of split
% 245.17/51.61  | 
% 245.17/51.61  End of proof
% 245.17/51.61  
% 245.17/51.61  Sub-proof #2270 shows that the following formulas are inconsistent:
% 245.17/51.61  ----------------------------------------------------------------
% 245.17/51.61    (1)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.17/51.61             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 245.17/51.61           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 245.17/51.61           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.17/51.61           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 245.17/51.61           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.17/51.61           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.17/51.61    (2)  op(e0, e3) = all_52_3
% 245.17/51.61    (3)  all_56_1 = e3
% 245.17/51.61    (4)   ~ (all_52_3 = e3)
% 245.17/51.61    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.61  
% 245.17/51.61  Begin of proof
% 245.17/51.61  | 
% 245.17/51.61  | BETA: splitting (1) gives:
% 245.17/51.61  | 
% 245.17/51.61  | Case 1:
% 245.17/51.61  | | 
% 245.17/51.61  | |   (6)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.17/51.61  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 245.17/51.61  | |        op(e1, e3) = e1
% 245.17/51.61  | | 
% 245.17/51.61  | | ALPHA: (6) implies:
% 245.17/51.61  | |   (7)   ~ (all_56_1 = e3)
% 245.17/51.61  | | 
% 245.17/51.61  | | REDUCE: (3), (7) imply:
% 245.17/51.61  | |   (8)  $false
% 245.17/51.61  | | 
% 245.17/51.61  | | CLOSE: (8) is inconsistent.
% 245.17/51.61  | | 
% 245.17/51.61  | Case 2:
% 245.17/51.61  | | 
% 245.17/51.61  | |   (9)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 245.17/51.61  | |            = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 245.17/51.61  | |          e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.17/51.61  | |          (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.17/51.61  | |          (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.17/51.61  | | 
% 245.17/51.61  | | REF_CLOSE: (2), (3), (4), (5), (9) are inconsistent by sub-proof #2271.
% 245.17/51.61  | | 
% 245.17/51.61  | End of split
% 245.17/51.61  | 
% 245.17/51.61  End of proof
% 245.17/51.61  
% 245.17/51.61  Sub-proof #2271 shows that the following formulas are inconsistent:
% 245.17/51.61  ----------------------------------------------------------------
% 245.17/51.61    (1)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.17/51.61             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 245.17/51.61           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 245.17/51.61           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.17/51.61           op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.17/51.61    (2)  op(e0, e3) = all_52_3
% 245.17/51.61    (3)  all_56_1 = e3
% 245.17/51.61    (4)   ~ (all_52_3 = e3)
% 245.17/51.61    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.61  
% 245.17/51.61  Begin of proof
% 245.17/51.61  | 
% 245.17/51.61  | BETA: splitting (1) gives:
% 245.17/51.61  | 
% 245.17/51.61  | Case 1:
% 245.17/51.61  | | 
% 245.17/51.61  | |   (6)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.17/51.61  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 245.17/51.61  | |        op(e0, e3) = e3
% 245.17/51.61  | | 
% 245.17/51.61  | | ALPHA: (6) implies:
% 245.17/51.61  | |   (7)  op(e0, e3) = e3
% 245.17/51.61  | | 
% 245.17/51.61  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #2332.
% 245.17/51.61  | | 
% 245.17/51.61  | Case 2:
% 245.17/51.61  | | 
% 245.17/51.61  | |   (8)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.17/51.61  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 245.17/51.61  | |        op(e0, e3) = e0
% 245.17/51.61  | | 
% 245.17/51.61  | | ALPHA: (8) implies:
% 245.17/51.61  | |   (9)   ~ (all_56_1 = e3)
% 245.17/51.61  | | 
% 245.17/51.61  | | REDUCE: (3), (9) imply:
% 245.17/51.61  | |   (10)  $false
% 245.17/51.61  | | 
% 245.17/51.61  | | CLOSE: (10) is inconsistent.
% 245.17/51.61  | | 
% 245.17/51.61  | End of split
% 245.17/51.61  | 
% 245.17/51.61  End of proof
% 245.17/51.61  
% 245.17/51.61  Sub-proof #2272 shows that the following formulas are inconsistent:
% 245.17/51.61  ----------------------------------------------------------------
% 245.17/51.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.61    (2)  op(e0, e1) = all_52_11
% 245.17/51.61    (3)  op(e0, e1) = e1
% 245.17/51.61    (4)   ~ (all_52_11 = e1)
% 245.17/51.61  
% 245.17/51.61  Begin of proof
% 245.17/51.61  | 
% 245.17/51.61  | GROUND_INST: instantiating (1) with all_52_11, e1, e1, e0, simplifying with
% 245.17/51.61  |              (2), (3) gives:
% 245.17/51.61  |   (5)  all_52_11 = e1
% 245.17/51.61  | 
% 245.17/51.61  | REDUCE: (4), (5) imply:
% 245.17/51.61  |   (6)  $false
% 245.17/51.61  | 
% 245.17/51.61  | CLOSE: (6) is inconsistent.
% 245.17/51.61  | 
% 245.17/51.61  End of proof
% 245.17/51.61  
% 245.17/51.61  Sub-proof #2273 shows that the following formulas are inconsistent:
% 245.17/51.61  ----------------------------------------------------------------
% 245.17/51.61    (1)   ~ (all_52_3 = e0)
% 245.17/51.61    (2)   ~ (all_52_3 = e1)
% 245.17/51.61    (3)   ~ (all_52_9 = all_6_2)
% 245.17/51.61    (4)  all_56_11 = e1
% 245.17/51.61    (5)  op(e0, e1) = all_52_11
% 245.17/51.61    (6)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 245.17/51.61         (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 245.17/51.61    (7)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 245.17/51.61           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 245.17/51.61             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.17/51.61           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 245.17/51.61             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.17/51.61           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.17/51.61           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 245.17/51.61           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 245.17/51.61           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 245.17/51.61           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 245.17/51.61           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 245.17/51.61             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.17/51.61           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.17/51.61           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 245.17/51.61           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 245.17/51.61           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 245.17/51.61           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 245.17/51.61           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 245.17/51.61             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 245.17/51.61           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.17/51.61           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 245.17/51.61           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 245.17/51.61           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 245.17/51.61           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.17/51.61           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 245.17/51.61             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 245.17/51.61           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.17/51.61           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.17/51.61    (8)   ~ (all_52_12 = e0)
% 245.17/51.61    (9)  op(e1, e0) = all_52_14
% 245.17/51.61    (10)   ~ (all_52_13 = e1)
% 245.17/51.61    (11)  op(e0, e3) = all_52_3
% 245.17/51.61    (12)   ~ (all_52_12 = e1)
% 245.17/51.61    (13)   ~ (all_52_12 = all_52_14)
% 245.17/51.61    (14)   ~ (all_52_12 = all_52_13)
% 245.17/51.61    (15)  all_54_10 = all_6_2
% 245.17/51.61    (16)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 245.17/51.61    (17)   ~ (all_6_2 = e3)
% 245.17/51.61    (18)  op(e3, e1) = all_52_8
% 245.17/51.61    (19)  op(e2, e1) = all_52_9
% 245.17/51.61    (20)   ~ (all_52_7 = e1)
% 245.17/51.61    (21)   ~ (all_52_14 = all_6_2)
% 245.17/51.61    (22)   ~ (all_6_2 = e0)
% 245.17/51.61    (23)   ~ (all_52_14 = e0)
% 245.17/51.61    (24)  all_56_31 = e0
% 245.17/51.61    (25)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.17/51.61    (26)  op(e3, e0) = all_52_12
% 245.17/51.61    (27)   ~ (all_52_4 = all_52_12)
% 245.17/51.61    (28)  op(e2, e3) = all_52_1
% 245.17/51.61    (29)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 245.17/51.61    (30)   ~ (all_52_1 = all_52_13)
% 245.17/51.61    (31)  all_54_7 = all_52_13
% 245.17/51.61    (32)  op(e0, e2) = all_52_7
% 245.17/51.61    (33)   ~ (all_52_13 = all_52_14)
% 245.17/51.61    (34)  op(e3, e2) = all_52_4
% 245.17/51.61    (35)   ~ (all_52_8 = all_52_11)
% 245.17/51.61    (36)  all_54_3 = all_52_12
% 245.17/51.61    (37)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.61    (38)  op(e0, e0) = e0
% 245.17/51.61    (39)   ~ (e1 = e0)
% 245.17/51.61    (40)  all_56_21 = all_6_2
% 245.17/51.61    (41)  op(e2, e0) = all_52_13
% 245.17/51.61    (42)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 245.17/51.61          | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 245.17/51.61            e1)
% 245.17/51.61    (43)   ~ (all_52_9 = all_52_11)
% 245.17/51.61    (44)   ~ (all_52_13 = e0)
% 245.17/51.61  
% 245.17/51.61  Begin of proof
% 245.17/51.61  | 
% 245.17/51.61  | BETA: splitting (6) gives:
% 245.17/51.61  | 
% 245.17/51.61  | Case 1:
% 245.17/51.61  | | 
% 245.17/51.61  | |   (45)  (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 245.17/51.61  | |           e1)
% 245.17/51.61  | | 
% 245.17/51.61  | | BETA: splitting (45) gives:
% 245.17/51.61  | | 
% 245.17/51.61  | | Case 1:
% 245.17/51.61  | | | 
% 245.17/51.61  | | |   (46)  all_58_9 = e1 & op(e3, e0) = e1
% 245.17/51.61  | | | 
% 245.17/51.61  | | | REF_CLOSE: (12), (26), (37), (46) are inconsistent by sub-proof #2278.
% 245.17/51.61  | | | 
% 245.17/51.61  | | Case 2:
% 245.17/51.61  | | | 
% 245.17/51.61  | | |   (47)  all_58_10 = e1 & op(e2, e0) = e1
% 245.17/51.61  | | | 
% 245.17/51.61  | | | REF_CLOSE: (10), (37), (41), (47) are inconsistent by sub-proof #2277.
% 245.17/51.61  | | | 
% 245.17/51.61  | | End of split
% 245.17/51.61  | | 
% 245.17/51.61  | Case 2:
% 245.17/51.61  | | 
% 245.17/51.61  | |   (48)  (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 245.17/51.61  | |           e1)
% 245.17/51.61  | | 
% 245.17/51.61  | | BETA: splitting (48) gives:
% 245.17/51.61  | | 
% 245.17/51.61  | | Case 1:
% 245.17/51.61  | | | 
% 245.17/51.61  | | |   (49)  all_58_11 = e1 & op(e1, e0) = e1
% 245.17/51.61  | | | 
% 245.17/51.61  | | | ALPHA: (49) implies:
% 245.17/51.61  | | |   (50)  op(e1, e0) = e1
% 245.17/51.61  | | | 
% 245.17/51.61  | | | BETA: splitting (42) gives:
% 245.17/51.61  | | | 
% 245.17/51.61  | | | Case 1:
% 245.17/51.61  | | | | 
% 245.17/51.61  | | | |   (51)  (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0,
% 245.17/51.61  | | | |             e2) = e1)
% 245.17/51.61  | | | | 
% 245.17/51.61  | | | | BETA: splitting (51) gives:
% 245.17/51.61  | | | | 
% 245.17/51.61  | | | | Case 1:
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | |   (52)  all_58_12 = e1 & op(e0, e3) = e1
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | | REF_CLOSE: (2), (11), (37), (52) are inconsistent by sub-proof #2276.
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | Case 2:
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | |   (53)  all_58_13 = e1 & op(e0, e2) = e1
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | | REF_CLOSE: (20), (32), (37), (53) are inconsistent by sub-proof #2275.
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | End of split
% 245.17/51.61  | | | | 
% 245.17/51.61  | | | Case 2:
% 245.17/51.61  | | | | 
% 245.17/51.61  | | | |   (54)  (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 245.17/51.61  | | | |             e0) = e1)
% 245.17/51.61  | | | | 
% 245.17/51.61  | | | | BETA: splitting (54) gives:
% 245.17/51.61  | | | | 
% 245.17/51.61  | | | | Case 1:
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | |   (55)  all_58_14 = e1 & op(e0, e1) = e1
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | | ALPHA: (55) implies:
% 245.17/51.61  | | | | |   (56)  op(e0, e1) = e1
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (11), (13), (14), (15),
% 245.17/51.61  | | | | |            (16), (17), (18), (19), (21), (22), (23), (24), (25), (27),
% 245.17/51.61  | | | | |            (28), (29), (30), (31), (33), (34), (35), (36), (37), (40),
% 245.17/51.61  | | | | |            (41), (43), (44), (50), (56) are inconsistent by sub-proof
% 245.17/51.61  | | | | |            #2281.
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | Case 2:
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | |   (57)  all_58_15 = e1 & op(e0, e0) = e1
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | | ALPHA: (57) implies:
% 245.17/51.61  | | | | |   (58)  op(e0, e0) = e1
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | | REF_CLOSE: (37), (38), (39), (58) are inconsistent by sub-proof #2274.
% 245.17/51.61  | | | | | 
% 245.17/51.61  | | | | End of split
% 245.17/51.61  | | | | 
% 245.17/51.61  | | | End of split
% 245.17/51.61  | | | 
% 245.17/51.61  | | Case 2:
% 245.17/51.61  | | | 
% 245.17/51.61  | | |   (59)  all_58_15 = e1 & op(e0, e0) = e1
% 245.17/51.61  | | | 
% 245.17/51.61  | | | ALPHA: (59) implies:
% 245.17/51.61  | | |   (60)  op(e0, e0) = e1
% 245.17/51.61  | | | 
% 245.17/51.61  | | | REF_CLOSE: (37), (38), (39), (60) are inconsistent by sub-proof #2274.
% 245.17/51.61  | | | 
% 245.17/51.61  | | End of split
% 245.17/51.61  | | 
% 245.17/51.61  | End of split
% 245.17/51.61  | 
% 245.17/51.61  End of proof
% 245.17/51.61  
% 245.17/51.61  Sub-proof #2274 shows that the following formulas are inconsistent:
% 245.17/51.61  ----------------------------------------------------------------
% 245.17/51.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.61    (2)  op(e0, e0) = e1
% 245.17/51.61    (3)  op(e0, e0) = e0
% 245.17/51.61    (4)   ~ (e1 = e0)
% 245.17/51.61  
% 245.17/51.61  Begin of proof
% 245.17/51.61  | 
% 245.17/51.61  | GROUND_INST: instantiating (1) with e0, e1, e0, e0, simplifying with (2), (3)
% 245.17/51.61  |              gives:
% 245.17/51.61  |   (5)  e1 = e0
% 245.17/51.61  | 
% 245.17/51.61  | REDUCE: (4), (5) imply:
% 245.17/51.61  |   (6)  $false
% 245.17/51.61  | 
% 245.17/51.61  | CLOSE: (6) is inconsistent.
% 245.17/51.61  | 
% 245.17/51.61  End of proof
% 245.17/51.61  
% 245.17/51.61  Sub-proof #2275 shows that the following formulas are inconsistent:
% 245.17/51.61  ----------------------------------------------------------------
% 245.17/51.61    (1)  all_58_13 = e1 & op(e0, e2) = e1
% 245.17/51.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.61    (3)  op(e0, e2) = all_52_7
% 245.17/51.61    (4)   ~ (all_52_7 = e1)
% 245.17/51.61  
% 245.17/51.61  Begin of proof
% 245.17/51.61  | 
% 245.17/51.61  | ALPHA: (1) implies:
% 245.17/51.61  |   (5)  op(e0, e2) = e1
% 245.17/51.61  | 
% 245.17/51.61  | GROUND_INST: instantiating (2) with all_52_7, e1, e2, e0, simplifying with
% 245.17/51.61  |              (3), (5) gives:
% 245.17/51.61  |   (6)  all_52_7 = e1
% 245.17/51.61  | 
% 245.17/51.61  | REDUCE: (4), (6) imply:
% 245.17/51.61  |   (7)  $false
% 245.17/51.61  | 
% 245.17/51.61  | CLOSE: (7) is inconsistent.
% 245.17/51.61  | 
% 245.17/51.61  End of proof
% 245.17/51.61  
% 245.17/51.61  Sub-proof #2276 shows that the following formulas are inconsistent:
% 245.17/51.61  ----------------------------------------------------------------
% 245.17/51.61    (1)  all_58_12 = e1 & op(e0, e3) = e1
% 245.17/51.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.61    (3)  op(e0, e3) = all_52_3
% 245.17/51.61    (4)   ~ (all_52_3 = e1)
% 245.17/51.61  
% 245.17/51.61  Begin of proof
% 245.17/51.61  | 
% 245.17/51.61  | ALPHA: (1) implies:
% 245.17/51.61  |   (5)  op(e0, e3) = e1
% 245.17/51.61  | 
% 245.17/51.61  | GROUND_INST: instantiating (2) with all_52_3, e1, e3, e0, simplifying with
% 245.17/51.61  |              (3), (5) gives:
% 245.17/51.61  |   (6)  all_52_3 = e1
% 245.17/51.61  | 
% 245.17/51.61  | REDUCE: (4), (6) imply:
% 245.17/51.61  |   (7)  $false
% 245.17/51.61  | 
% 245.17/51.61  | CLOSE: (7) is inconsistent.
% 245.17/51.61  | 
% 245.17/51.61  End of proof
% 245.17/51.61  
% 245.17/51.61  Sub-proof #2277 shows that the following formulas are inconsistent:
% 245.17/51.61  ----------------------------------------------------------------
% 245.17/51.61    (1)  all_58_10 = e1 & op(e2, e0) = e1
% 245.17/51.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.61    (3)  op(e2, e0) = all_52_13
% 245.17/51.61    (4)   ~ (all_52_13 = e1)
% 245.17/51.61  
% 245.17/51.61  Begin of proof
% 245.17/51.61  | 
% 245.17/51.61  | ALPHA: (1) implies:
% 245.17/51.61  |   (5)  op(e2, e0) = e1
% 245.17/51.61  | 
% 245.17/51.61  | GROUND_INST: instantiating (2) with all_52_13, e1, e0, e2, simplifying with
% 245.17/51.61  |              (3), (5) gives:
% 245.17/51.61  |   (6)  all_52_13 = e1
% 245.17/51.61  | 
% 245.17/51.61  | REDUCE: (4), (6) imply:
% 245.17/51.61  |   (7)  $false
% 245.17/51.61  | 
% 245.17/51.61  | CLOSE: (7) is inconsistent.
% 245.17/51.61  | 
% 245.17/51.61  End of proof
% 245.17/51.61  
% 245.17/51.61  Sub-proof #2278 shows that the following formulas are inconsistent:
% 245.17/51.61  ----------------------------------------------------------------
% 245.17/51.61    (1)  all_58_9 = e1 & op(e3, e0) = e1
% 245.17/51.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.62    (3)  op(e3, e0) = all_52_12
% 245.17/51.62    (4)   ~ (all_52_12 = e1)
% 245.17/51.62  
% 245.17/51.62  Begin of proof
% 245.17/51.62  | 
% 245.17/51.62  | ALPHA: (1) implies:
% 245.17/51.62  |   (5)  op(e3, e0) = e1
% 245.17/51.62  | 
% 245.17/51.62  | GROUND_INST: instantiating (2) with all_52_12, e1, e0, e3, simplifying with
% 245.17/51.62  |              (3), (5) gives:
% 245.17/51.62  |   (6)  all_52_12 = e1
% 245.17/51.62  | 
% 245.17/51.62  | REDUCE: (4), (6) imply:
% 245.17/51.62  |   (7)  $false
% 245.17/51.62  | 
% 245.17/51.62  | CLOSE: (7) is inconsistent.
% 245.17/51.62  | 
% 245.17/51.62  End of proof
% 245.17/51.62  
% 245.17/51.62  Sub-proof #2279 shows that the following formulas are inconsistent:
% 245.17/51.62  ----------------------------------------------------------------
% 245.17/51.62    (1)  all_56_11 = e1
% 245.17/51.62    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 245.17/51.62           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 245.17/51.62             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.17/51.62           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 245.17/51.62             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.17/51.62           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.17/51.62           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 245.17/51.62    (3)  op(e2, e3) = all_52_1
% 245.17/51.62    (4)  all_56_1 = e2
% 245.17/51.62    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.62    (6)   ~ (all_52_1 = e2)
% 245.17/51.62  
% 245.17/51.62  Begin of proof
% 245.17/51.62  | 
% 245.17/51.62  | BETA: splitting (2) gives:
% 245.17/51.62  | 
% 245.17/51.62  | Case 1:
% 245.17/51.62  | | 
% 245.17/51.62  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.17/51.62  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 245.17/51.62  | |        op(e2, e3) = e3
% 245.17/51.62  | | 
% 245.17/51.62  | | ALPHA: (7) implies:
% 245.17/51.62  | |   (8)   ~ (all_56_1 = e2)
% 245.17/51.62  | | 
% 245.17/51.62  | | REDUCE: (4), (8) imply:
% 245.17/51.62  | |   (9)  $false
% 245.17/51.62  | | 
% 245.17/51.62  | | CLOSE: (9) is inconsistent.
% 245.17/51.62  | | 
% 245.17/51.62  | Case 2:
% 245.17/51.62  | | 
% 245.17/51.62  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 245.17/51.62  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 245.17/51.62  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.17/51.62  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.17/51.62  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 245.17/51.62  | | 
% 245.17/51.62  | | BETA: splitting (10) gives:
% 245.17/51.62  | | 
% 245.17/51.62  | | Case 1:
% 245.17/51.62  | | | 
% 245.17/51.62  | | |   (11)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 245.17/51.62  | | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 245.17/51.62  | | |         e2 & op(e2, e3) = e2
% 245.17/51.62  | | | 
% 245.17/51.62  | | | ALPHA: (11) implies:
% 245.17/51.62  | | |   (12)  op(e2, e3) = e2
% 245.17/51.62  | | | 
% 245.17/51.62  | | | REF_CLOSE: (3), (5), (6), (12) are inconsistent by sub-proof #2336.
% 245.17/51.62  | | | 
% 245.17/51.62  | | Case 2:
% 245.17/51.62  | | | 
% 245.17/51.62  | | |   (13)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 245.17/51.62  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 245.17/51.62  | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 245.17/51.62  | | | 
% 245.17/51.62  | | | ALPHA: (13) implies:
% 245.17/51.62  | | |   (14)   ~ (all_56_11 = e1)
% 245.17/51.62  | | | 
% 245.17/51.62  | | | REDUCE: (1), (14) imply:
% 245.17/51.62  | | |   (15)  $false
% 245.17/51.62  | | | 
% 245.17/51.62  | | | CLOSE: (15) is inconsistent.
% 245.17/51.62  | | | 
% 245.17/51.62  | | End of split
% 245.17/51.62  | | 
% 245.17/51.62  | End of split
% 245.17/51.62  | 
% 245.17/51.62  End of proof
% 245.17/51.62  
% 245.17/51.62  Sub-proof #2280 shows that the following formulas are inconsistent:
% 245.17/51.62  ----------------------------------------------------------------
% 245.17/51.62    (1)   ~ (all_52_3 = e0)
% 245.17/51.62    (2)   ~ (all_52_9 = all_6_2)
% 245.17/51.62    (3)  all_56_11 = e1
% 245.17/51.62    (4)  op(e0, e1) = all_52_11
% 245.17/51.62    (5)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 245.17/51.62           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 245.17/51.62             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.17/51.62           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 245.17/51.62             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.17/51.62           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.17/51.62           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 245.17/51.62           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 245.17/51.62           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 245.17/51.62           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 245.17/51.62           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 245.17/51.62             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.17/51.62           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.17/51.62           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 245.17/51.62           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 245.17/51.62           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 245.17/51.62           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 245.17/51.62           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 245.17/51.62             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 245.17/51.62           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.17/51.62           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 245.17/51.62           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 245.17/51.62           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 245.17/51.62           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.17/51.62           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 245.17/51.62             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 245.17/51.62           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.17/51.62           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.17/51.62    (6)   ~ (all_52_12 = e0)
% 245.17/51.62    (7)  op(e1, e0) = all_52_14
% 245.17/51.62    (8)  op(e0, e3) = all_52_3
% 245.17/51.62    (9)   ~ (all_52_12 = all_52_14)
% 245.17/51.62    (10)   ~ (all_52_12 = all_52_13)
% 245.17/51.62    (11)  all_54_10 = all_6_2
% 245.17/51.62    (12)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 245.17/51.62    (13)   ~ (all_6_2 = e3)
% 245.17/51.62    (14)  op(e3, e1) = all_52_8
% 245.17/51.62    (15)  op(e2, e1) = all_52_9
% 245.17/51.62    (16)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 245.17/51.62              e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 245.17/51.62            op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 245.17/51.62              e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 245.17/51.62              e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 &
% 245.17/51.62            all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 245.17/51.62            (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2)
% 245.17/51.62            = e2) | (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 245.17/51.62            (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 245.17/51.62              e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~
% 245.17/51.62            (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.17/51.62            (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 =
% 245.17/51.62            e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 245.17/51.62            (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1)
% 245.17/51.62            = e0)
% 245.17/51.62    (17)   ~ (all_52_14 = all_6_2)
% 245.17/51.62    (18)   ~ (all_6_2 = e0)
% 245.17/51.62    (19)   ~ (all_52_14 = e0)
% 245.17/51.62    (20)  all_56_31 = e0
% 245.17/51.62    (21)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.17/51.62    (22)   ~ (all_52_4 = all_52_12)
% 245.17/51.62    (23)  op(e2, e3) = all_52_1
% 245.17/51.62    (24)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 245.17/51.62    (25)   ~ (all_52_1 = all_52_13)
% 245.17/51.62    (26)  all_54_7 = all_52_13
% 245.17/51.62    (27)   ~ (all_52_13 = all_52_14)
% 245.17/51.62    (28)  op(e3, e2) = all_52_4
% 245.17/51.62    (29)   ~ (all_52_8 = all_52_11)
% 245.17/51.62    (30)  all_54_3 = all_52_12
% 245.17/51.62    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.62    (32)  all_56_21 = all_6_2
% 245.17/51.62    (33)  op(e2, e0) = all_52_13
% 245.17/51.62    (34)   ~ (all_52_9 = e1)
% 245.17/51.62    (35)   ~ (all_52_9 = all_52_11)
% 245.17/51.62    (36)   ~ (all_52_13 = e0)
% 245.17/51.62  
% 245.17/51.62  Begin of proof
% 245.17/51.62  | 
% 245.17/51.62  | BETA: splitting (16) gives:
% 245.17/51.62  | 
% 245.17/51.62  | Case 1:
% 245.17/51.62  | | 
% 245.17/51.62  | |   (37)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 245.17/51.62  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 245.17/51.62  | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 =
% 245.17/51.62  | |           e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 =
% 245.17/51.62  | |             e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 & op(e1, e2) = e1) |
% 245.17/51.62  | |         (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~
% 245.17/51.62  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.17/51.62  | |           op(e2, e0) = e2 & op(e0, e2) = e2)
% 245.17/51.62  | | 
% 245.17/51.62  | | REF_CLOSE: (3), (15), (20), (31), (34), (37) are inconsistent by sub-proof
% 245.17/51.62  | |            #2297.
% 245.17/51.62  | | 
% 245.17/51.62  | Case 2:
% 245.17/51.62  | | 
% 245.17/51.62  | |   (38)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 245.17/51.62  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 245.17/51.62  | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 =
% 245.17/51.62  | |           e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 245.17/51.62  | |             e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 & op(e0, e1) = e1) |
% 245.17/51.62  | |         (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 245.17/51.62  | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 245.17/51.62  | |           op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.17/51.62  | | 
% 245.17/51.62  | | BETA: splitting (38) gives:
% 245.17/51.62  | | 
% 245.17/51.62  | | Case 1:
% 245.17/51.62  | | | 
% 245.17/51.62  | | |   (39)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 245.17/51.62  | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 245.17/51.62  | | |         op(e2, e0) = e0 & op(e0, e2) = e0
% 245.17/51.62  | | | 
% 245.17/51.62  | | | ALPHA: (39) implies:
% 245.17/51.62  | | |   (40)  op(e2, e0) = e0
% 245.17/51.62  | | | 
% 245.17/51.62  | | | REF_CLOSE: (31), (33), (36), (40) are inconsistent by sub-proof #2324.
% 245.17/51.62  | | | 
% 245.17/51.62  | | Case 2:
% 245.17/51.62  | | | 
% 245.17/51.62  | | |   (41)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.17/51.62  | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.17/51.62  | | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29
% 245.17/51.62  | | |           = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21
% 245.17/51.62  | | |             = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) =
% 245.17/51.62  | | |           e0)
% 245.17/51.62  | | | 
% 245.17/51.62  | | | BETA: splitting (41) gives:
% 245.17/51.62  | | | 
% 245.17/51.62  | | | Case 1:
% 245.17/51.62  | | | | 
% 245.17/51.62  | | | |   (42)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.17/51.62  | | | |         (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.17/51.62  | | | |         op(e1, e0) = e1 & op(e0, e1) = e1
% 245.17/51.62  | | | | 
% 245.17/51.62  | | | | ALPHA: (42) implies:
% 245.17/51.62  | | | |   (43)  op(e0, e1) = e1
% 245.17/51.62  | | | |   (44)  op(e1, e0) = e1
% 245.17/51.62  | | | | 
% 245.17/51.62  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 245.17/51.62  | | | |            (12), (13), (14), (15), (17), (18), (19), (20), (21), (22),
% 245.17/51.62  | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 245.17/51.62  | | | |            (33), (35), (36), (43), (44) are inconsistent by sub-proof
% 245.17/51.62  | | | |            #2281.
% 245.17/51.62  | | | | 
% 245.17/51.62  | | | Case 2:
% 245.17/51.62  | | | | 
% 245.17/51.62  | | | |   (45)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~
% 245.17/51.62  | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 245.17/51.62  | | | |         op(e1, e0) = e0 & op(e0, e1) = e0
% 245.17/51.62  | | | | 
% 245.17/51.62  | | | | ALPHA: (45) implies:
% 245.17/51.62  | | | |   (46)  op(e1, e0) = e0
% 245.17/51.62  | | | | 
% 245.17/51.62  | | | | REF_CLOSE: (7), (19), (31), (46) are inconsistent by sub-proof #2323.
% 245.17/51.62  | | | | 
% 245.17/51.62  | | | End of split
% 245.17/51.62  | | | 
% 245.17/51.62  | | End of split
% 245.17/51.62  | | 
% 245.17/51.62  | End of split
% 245.17/51.62  | 
% 245.17/51.62  End of proof
% 245.17/51.62  
% 245.17/51.62  Sub-proof #2281 shows that the following formulas are inconsistent:
% 245.17/51.62  ----------------------------------------------------------------
% 245.17/51.62    (1)   ~ (all_52_3 = e0)
% 245.17/51.62    (2)   ~ (all_52_9 = all_6_2)
% 245.17/51.62    (3)  all_56_11 = e1
% 245.17/51.62    (4)  op(e0, e1) = all_52_11
% 245.17/51.62    (5)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 245.17/51.62           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 245.17/51.62             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.17/51.62           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 245.17/51.62             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.17/51.62           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.17/51.62           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) | (all_56_5 = e1
% 245.17/51.62           & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 245.17/51.62           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 & op(e1, e3) =
% 245.17/51.62           e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~
% 245.17/51.62           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3,
% 245.17/51.62             e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.17/51.62           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.17/51.62           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0) | (all_56_13 = e2
% 245.17/51.62           & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~
% 245.17/51.62           (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 & op(e1, e2) =
% 245.17/51.62           e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 245.17/51.62           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2,
% 245.17/51.62             e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 245.17/51.62           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.17/51.62           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) | (all_56_15 = e0
% 245.17/51.62           & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 245.17/51.62           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 & op(e0, e2) =
% 245.17/51.62           e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.17/51.62           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1,
% 245.17/51.62             e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 245.17/51.62           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.17/51.62           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.17/51.62    (6)   ~ (all_52_12 = e0)
% 245.17/51.62    (7)  op(e1, e0) = all_52_14
% 245.17/51.62    (8)  op(e0, e3) = all_52_3
% 245.17/51.62    (9)  op(e1, e0) = e1
% 245.17/51.62    (10)   ~ (all_52_12 = all_52_14)
% 245.17/51.62    (11)   ~ (all_52_12 = all_52_13)
% 245.17/51.62    (12)  op(e0, e1) = e1
% 245.17/51.62    (13)  all_54_10 = all_6_2
% 245.17/51.62    (14)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 245.17/51.62    (15)   ~ (all_6_2 = e3)
% 245.17/51.62    (16)  op(e3, e1) = all_52_8
% 245.17/51.62    (17)  op(e2, e1) = all_52_9
% 245.17/51.62    (18)   ~ (all_52_14 = all_6_2)
% 245.17/51.62    (19)   ~ (all_6_2 = e0)
% 245.17/51.62    (20)   ~ (all_52_14 = e0)
% 245.17/51.62    (21)  all_56_31 = e0
% 245.17/51.62    (22)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.17/51.62    (23)   ~ (all_52_4 = all_52_12)
% 245.17/51.62    (24)  op(e2, e3) = all_52_1
% 245.17/51.62    (25)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 245.17/51.62    (26)   ~ (all_52_1 = all_52_13)
% 245.17/51.62    (27)  all_54_7 = all_52_13
% 245.17/51.62    (28)   ~ (all_52_13 = all_52_14)
% 245.17/51.62    (29)  op(e3, e2) = all_52_4
% 245.17/51.62    (30)   ~ (all_52_8 = all_52_11)
% 245.17/51.62    (31)  all_54_3 = all_52_12
% 245.17/51.62    (32)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.17/51.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.17/51.62    (33)  all_56_21 = all_6_2
% 245.17/51.62    (34)  op(e2, e0) = all_52_13
% 245.17/51.62    (35)   ~ (all_52_9 = all_52_11)
% 245.17/51.62    (36)   ~ (all_52_13 = e0)
% 245.17/51.62  
% 245.17/51.62  Begin of proof
% 245.17/51.62  | 
% 245.17/51.62  | GROUND_INST: instantiating (32) with all_52_11, e1, e1, e0, simplifying with
% 245.17/51.62  |              (4), (12) gives:
% 245.17/51.62  |   (37)  all_52_11 = e1
% 245.17/51.62  | 
% 245.17/51.62  | GROUND_INST: instantiating (32) with all_52_14, e1, e0, e1, simplifying with
% 245.17/51.62  |              (7), (9) gives:
% 245.17/51.62  |   (38)  all_52_14 = e1
% 245.17/51.62  | 
% 245.17/51.62  | REDUCE: (30), (37) imply:
% 245.17/51.62  |   (39)   ~ (all_52_8 = e1)
% 245.17/51.62  | 
% 245.17/51.62  | REDUCE: (35), (37) imply:
% 245.17/51.62  |   (40)   ~ (all_52_9 = e1)
% 245.17/51.62  | 
% 245.17/51.62  | REDUCE: (10), (38) imply:
% 245.17/51.62  |   (41)   ~ (all_52_12 = e1)
% 245.17/51.62  | 
% 245.17/51.62  | REDUCE: (28), (38) imply:
% 245.17/51.62  |   (42)   ~ (all_52_13 = e1)
% 245.17/51.62  | 
% 245.17/51.62  | REDUCE: (18), (38) imply:
% 245.17/51.62  |   (43)   ~ (all_6_2 = e1)
% 245.17/51.62  | 
% 245.17/51.62  | SIMP: (43) implies:
% 245.17/51.62  |   (44)   ~ (all_6_2 = e1)
% 245.17/51.62  | 
% 245.17/51.62  | REDUCE: (20), (38) imply:
% 245.17/51.62  |   (45)   ~ (e1 = e0)
% 245.17/51.62  | 
% 245.17/51.62  | BETA: splitting (25) gives:
% 245.17/51.62  | 
% 245.17/51.62  | Case 1:
% 245.17/51.62  | | 
% 245.17/51.62  | |   (46)  all_54_10 = e3
% 245.17/51.62  | | 
% 245.17/51.62  | | REF_CLOSE: (13), (15), (46) are inconsistent by sub-proof #2313.
% 245.17/51.62  | | 
% 245.17/51.62  | Case 2:
% 245.17/51.62  | | 
% 245.17/51.62  | |   (47)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 245.17/51.62  | | 
% 245.17/51.62  | | BETA: splitting (47) gives:
% 245.17/51.62  | | 
% 245.17/51.62  | | Case 1:
% 245.17/51.62  | | | 
% 245.17/51.62  | | |   (48)  all_54_10 = e2
% 245.17/51.62  | | | 
% 245.17/51.62  | | | COMBINE_EQS: (13), (48) imply:
% 245.17/51.62  | | |   (49)  all_6_2 = e2
% 245.17/51.62  | | | 
% 245.17/51.62  | | | SIMP: (49) implies:
% 245.17/51.62  | | |   (50)  all_6_2 = e2
% 245.17/51.62  | | | 
% 245.17/51.62  | | | COMBINE_EQS: (33), (50) imply:
% 245.17/51.62  | | |   (51)  all_56_21 = e2
% 245.17/51.62  | | | 
% 245.17/51.62  | | | REDUCE: (2), (50) imply:
% 245.17/51.62  | | |   (52)   ~ (all_52_9 = e2)
% 245.17/51.62  | | | 
% 245.17/51.62  | | | BETA: splitting (5) gives:
% 245.17/51.62  | | | 
% 245.17/51.62  | | | Case 1:
% 245.17/51.62  | | | | 
% 245.17/51.63  | | | |   (53)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 245.17/51.63  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 245.17/51.63  | | | |           op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 & all_56_9
% 245.17/51.63  | | | |           = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~
% 245.17/51.63  | | | |           (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 245.17/51.63  | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.17/51.63  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 245.17/51.63  | | | |           ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3) |
% 245.17/51.63  | | | |         (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 245.17/51.63  | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.17/51.63  | | | |           op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 245.17/51.63  | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 245.17/51.63  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 245.17/51.63  | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.17/51.63  | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) & 
% 245.17/51.63  | | | |           ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.17/51.63  | | | | 
% 245.17/51.63  | | | | BETA: splitting (53) gives:
% 245.17/51.63  | | | | 
% 245.17/51.63  | | | | Case 1:
% 245.17/51.63  | | | | | 
% 245.17/51.63  | | | | |   (54)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 245.17/51.63  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 245.17/51.63  | | | | |           & op(e3, e2) = e3 & op(e2, e3) = e3) | (all_56_3 = e2 &
% 245.17/51.63  | | | | |           all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) & 
% 245.17/51.63  | | | | |           ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 245.17/51.63  | | | | |           op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.17/51.63  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 245.17/51.63  | | | | |           &  ~ (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 245.17/51.63  | | | | | 
% 245.17/51.63  | | | | | BETA: splitting (54) gives:
% 245.17/51.63  | | | | | 
% 245.17/51.63  | | | | | Case 1:
% 245.17/51.63  | | | | | | 
% 245.17/51.63  | | | | | |   (55)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~
% 245.17/51.63  | | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 245.17/51.63  | | | | | |         & op(e3, e2) = e3 & op(e2, e3) = e3
% 245.17/51.63  | | | | | | 
% 245.17/51.63  | | | | | | ALPHA: (55) implies:
% 245.17/51.63  | | | | | |   (56)   ~ (all_56_21 = e2)
% 245.17/51.63  | | | | | | 
% 245.17/51.63  | | | | | | REDUCE: (51), (56) imply:
% 245.17/51.63  | | | | | |   (57)  $false
% 245.17/51.63  | | | | | | 
% 245.17/51.63  | | | | | | CLOSE: (57) is inconsistent.
% 245.17/51.63  | | | | | | 
% 245.17/51.63  | | | | | Case 2:
% 245.17/51.63  | | | | | | 
% 245.17/51.63  | | | | | |   (58)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.17/51.63  | | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 245.17/51.63  | | | | | |             e3) & op(e3, e2) = e2 & op(e2, e3) = e2) | (all_56_5 =
% 245.17/51.63  | | | | | |           e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 245.17/51.63  | | | | | |             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 245.17/51.63  | | | | | |             e1) = e3 & op(e1, e3) = e3)
% 245.17/51.63  | | | | | | 
% 245.17/51.63  | | | | | | BETA: splitting (58) gives:
% 245.17/51.63  | | | | | | 
% 245.17/51.63  | | | | | | Case 1:
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | |   (59)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.17/51.63  | | | | | | |         (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 =
% 245.17/51.63  | | | | | | |           e3) & op(e3, e2) = e2 & op(e2, e3) = e2
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | | ALPHA: (59) implies:
% 245.17/51.63  | | | | | | |   (60)  op(e2, e3) = e2
% 245.17/51.63  | | | | | | |   (61)  op(e3, e2) = e2
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | | GROUND_INST: instantiating (32) with all_52_1, e2, e3, e2,
% 245.17/51.63  | | | | | | |              simplifying with (24), (60) gives:
% 245.17/51.63  | | | | | | |   (62)  all_52_1 = e2
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | | GROUND_INST: instantiating (32) with all_52_4, e2, e2, e3,
% 245.17/51.63  | | | | | | |              simplifying with (29), (61) gives:
% 245.17/51.63  | | | | | | |   (63)  all_52_4 = e2
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | | REDUCE: (23), (63) imply:
% 245.17/51.63  | | | | | | |   (64)   ~ (all_52_12 = e2)
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | | SIMP: (64) implies:
% 245.17/51.63  | | | | | | |   (65)   ~ (all_52_12 = e2)
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | | REF_CLOSE: (6), (11), (14), (22), (24), (26), (27), (31), (32),
% 245.17/51.63  | | | | | | |            (36), (41), (42), (60), (65) are inconsistent by
% 245.17/51.63  | | | | | | |            sub-proof #2285.
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | Case 2:
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | |   (66)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 245.17/51.63  | | | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 =
% 245.17/51.63  | | | | | | |           e1) & op(e3, e1) = e3 & op(e1, e3) = e3
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | | ALPHA: (66) implies:
% 245.17/51.63  | | | | | | |   (67)   ~ (all_56_11 = e1)
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | | REDUCE: (3), (67) imply:
% 245.17/51.63  | | | | | | |   (68)  $false
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | | CLOSE: (68) is inconsistent.
% 245.17/51.63  | | | | | | | 
% 245.17/51.63  | | | | | | End of split
% 245.17/51.63  | | | | | | 
% 245.17/51.63  | | | | | End of split
% 245.17/51.63  | | | | | 
% 245.17/51.63  | | | | Case 2:
% 245.17/51.63  | | | | | 
% 245.17/51.63  | | | | |   (69)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~
% 245.17/51.63  | | | | |           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3)
% 245.17/51.63  | | | | |           & op(e3, e1) = e1 & op(e1, e3) = e1) | (all_56_7 = e3 &
% 245.17/51.63  | | | | |           all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 245.17/51.63  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 245.17/51.63  | | | | |           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.17/51.63  | | | | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3)
% 245.17/51.63  | | | | |           &  ~ (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.17/51.63  | | | | | 
% 245.17/51.63  | | | | | REF_CLOSE: (1), (8), (16), (21), (32), (39), (69) are inconsistent by
% 245.17/51.63  | | | | |            sub-proof #2307.
% 245.17/51.63  | | | | | 
% 245.17/51.63  | | | | End of split
% 245.17/51.63  | | | | 
% 245.17/51.63  | | | Case 2:
% 245.17/51.63  | | | | 
% 245.19/51.63  | | | |   (70)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 245.19/51.63  | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 245.19/51.63  | | | |           op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 245.19/51.63  | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) &  ~
% 245.19/51.63  | | | |           (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 245.19/51.63  | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 245.19/51.63  | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) & 
% 245.19/51.63  | | | |           ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2) |
% 245.19/51.63  | | | |         (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 245.19/51.63  | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 245.19/51.63  | | | |           op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 245.19/51.63  | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~
% 245.19/51.63  | | | |           (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 245.19/51.63  | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 245.19/51.63  | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) & 
% 245.19/51.63  | | | |           ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.19/51.63  | | | | 
% 245.19/51.63  | | | | BETA: splitting (70) gives:
% 245.19/51.63  | | | | 
% 245.19/51.63  | | | | Case 1:
% 245.19/51.63  | | | | | 
% 245.19/51.63  | | | | |   (71)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 245.19/51.63  | | | | |           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 245.19/51.63  | | | | |           & op(e2, e1) = e2 & op(e1, e2) = e2) | (all_56_13 = e1 &
% 245.19/51.63  | | | | |           all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2) & 
% 245.19/51.63  | | | | |           ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 245.19/51.63  | | | | |           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~
% 245.19/51.63  | | | | |           (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0)
% 245.19/51.63  | | | | |           &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 245.19/51.63  | | | | | 
% 245.19/51.63  | | | | | BETA: splitting (71) gives:
% 245.19/51.63  | | | | | 
% 245.19/51.63  | | | | | Case 1:
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | |   (72)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~
% 245.19/51.63  | | | | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 245.19/51.63  | | | | | |         & op(e2, e1) = e2 & op(e1, e2) = e2
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | | ALPHA: (72) implies:
% 245.19/51.63  | | | | | |   (73)  op(e2, e1) = e2
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | | REF_CLOSE: (17), (32), (52), (73) are inconsistent by sub-proof
% 245.19/51.63  | | | | | |            #2328.
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | Case 2:
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | |   (74)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 245.19/51.63  | | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 =
% 245.19/51.63  | | | | | |             e2) & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 =
% 245.19/51.63  | | | | | |           e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.19/51.63  | | | | | |             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2,
% 245.19/51.63  | | | | | |             e0) = e2 & op(e0, e2) = e2)
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | | REF_CLOSE: (17), (21), (32), (40), (74) are inconsistent by
% 245.19/51.63  | | | | | |            sub-proof #2298.
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | End of split
% 245.19/51.63  | | | | | 
% 245.19/51.63  | | | | Case 2:
% 245.19/51.63  | | | | | 
% 245.19/51.63  | | | | |   (75)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 245.19/51.63  | | | | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 245.19/51.63  | | | | |           & op(e2, e0) = e0 & op(e0, e2) = e0) | (all_56_23 = e1 &
% 245.19/51.63  | | | | |           all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) & 
% 245.19/51.63  | | | | |           ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 245.19/51.63  | | | | |           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~
% 245.19/51.63  | | | | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1)
% 245.19/51.63  | | | | |           &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.19/51.63  | | | | | 
% 245.19/51.63  | | | | | BETA: splitting (75) gives:
% 245.19/51.63  | | | | | 
% 245.19/51.63  | | | | | Case 1:
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | |   (76)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~
% 245.19/51.63  | | | | | |         (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 245.19/51.63  | | | | | |         & op(e2, e0) = e0 & op(e0, e2) = e0
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | | ALPHA: (76) implies:
% 245.19/51.63  | | | | | |   (77)  op(e2, e0) = e0
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | | REF_CLOSE: (32), (34), (36), (77) are inconsistent by sub-proof
% 245.19/51.63  | | | | | |            #2324.
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | Case 2:
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | |   (78)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.19/51.63  | | | | | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 =
% 245.19/51.63  | | | | | |             e0) & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 =
% 245.19/51.63  | | | | | |           e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 245.19/51.63  | | | | | |             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1,
% 245.19/51.63  | | | | | |             e0) = e0 & op(e0, e1) = e0)
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | | REF_CLOSE: (9), (21), (32), (45), (78) are inconsistent by sub-proof
% 245.19/51.63  | | | | | |            #2283.
% 245.19/51.63  | | | | | | 
% 245.19/51.63  | | | | | End of split
% 245.19/51.63  | | | | | 
% 245.19/51.63  | | | | End of split
% 245.19/51.63  | | | | 
% 245.19/51.63  | | | End of split
% 245.19/51.63  | | | 
% 245.19/51.63  | | Case 2:
% 245.19/51.63  | | | 
% 245.19/51.63  | | |   (79)  all_54_10 = e1 | all_54_10 = e0
% 245.19/51.63  | | | 
% 245.19/51.63  | | | REF_CLOSE: (13), (19), (44), (79) are inconsistent by sub-proof #2282.
% 245.19/51.63  | | | 
% 245.19/51.63  | | End of split
% 245.19/51.63  | | 
% 245.19/51.63  | End of split
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2282 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)  all_54_10 = e1 | all_54_10 = e0
% 245.19/51.63    (2)  all_54_10 = all_6_2
% 245.19/51.63    (3)   ~ (all_6_2 = e1)
% 245.19/51.63    (4)   ~ (all_6_2 = e0)
% 245.19/51.63  
% 245.19/51.63  Begin of proof
% 245.19/51.63  | 
% 245.19/51.63  | BETA: splitting (1) gives:
% 245.19/51.63  | 
% 245.19/51.63  | Case 1:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (5)  all_54_10 = e1
% 245.19/51.63  | | 
% 245.19/51.63  | | COMBINE_EQS: (2), (5) imply:
% 245.19/51.63  | |   (6)  all_6_2 = e1
% 245.19/51.63  | | 
% 245.19/51.63  | | SIMP: (6) implies:
% 245.19/51.63  | |   (7)  all_6_2 = e1
% 245.19/51.63  | | 
% 245.19/51.63  | | REDUCE: (3), (7) imply:
% 245.19/51.63  | |   (8)  $false
% 245.19/51.63  | | 
% 245.19/51.63  | | CLOSE: (8) is inconsistent.
% 245.19/51.63  | | 
% 245.19/51.63  | Case 2:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (9)  all_54_10 = e0
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #2303.
% 245.19/51.63  | | 
% 245.19/51.63  | End of split
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2283 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.19/51.63             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 245.19/51.63           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 245.19/51.63             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 245.19/51.63           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.19/51.63    (2)  op(e1, e0) = e1
% 245.19/51.63    (3)  all_56_31 = e0
% 245.19/51.63    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.63    (5)   ~ (e1 = e0)
% 245.19/51.63  
% 245.19/51.63  Begin of proof
% 245.19/51.63  | 
% 245.19/51.63  | BETA: splitting (1) gives:
% 245.19/51.63  | 
% 245.19/51.63  | Case 1:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (6)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 245.19/51.63  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 245.19/51.63  | |        & op(e0, e1) = e1
% 245.19/51.63  | | 
% 245.19/51.63  | | ALPHA: (6) implies:
% 245.19/51.63  | |   (7)   ~ (all_56_31 = e0)
% 245.19/51.63  | | 
% 245.19/51.63  | | REDUCE: (3), (7) imply:
% 245.19/51.63  | |   (8)  $false
% 245.19/51.63  | | 
% 245.19/51.63  | | CLOSE: (8) is inconsistent.
% 245.19/51.63  | | 
% 245.19/51.63  | Case 2:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (9)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 245.19/51.63  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 245.19/51.63  | |        & op(e0, e1) = e0
% 245.19/51.63  | | 
% 245.19/51.63  | | ALPHA: (9) implies:
% 245.19/51.63  | |   (10)  op(e1, e0) = e0
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #2284.
% 245.19/51.63  | | 
% 245.19/51.63  | End of split
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2284 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.63    (2)  op(e1, e0) = e1
% 245.19/51.63    (3)  op(e1, e0) = e0
% 245.19/51.63    (4)   ~ (e1 = e0)
% 245.19/51.63  
% 245.19/51.63  Begin of proof
% 245.19/51.63  | 
% 245.19/51.63  | GROUND_INST: instantiating (1) with e0, e1, e0, e1, simplifying with (2), (3)
% 245.19/51.63  |              gives:
% 245.19/51.63  |   (5)  e1 = e0
% 245.19/51.63  | 
% 245.19/51.63  | REDUCE: (4), (5) imply:
% 245.19/51.63  |   (6)  $false
% 245.19/51.63  | 
% 245.19/51.63  | CLOSE: (6) is inconsistent.
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2285 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)   ~ (all_52_12 = e0)
% 245.19/51.63    (2)   ~ (all_52_13 = e1)
% 245.19/51.63    (3)   ~ (all_52_12 = e1)
% 245.19/51.63    (4)   ~ (all_52_12 = all_52_13)
% 245.19/51.63    (5)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 245.19/51.63    (6)  op(e2, e3) = e2
% 245.19/51.63    (7)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.19/51.63    (8)  op(e2, e3) = all_52_1
% 245.19/51.63    (9)   ~ (all_52_12 = e2)
% 245.19/51.63    (10)   ~ (all_52_1 = all_52_13)
% 245.19/51.63    (11)  all_54_7 = all_52_13
% 245.19/51.63    (12)  all_54_3 = all_52_12
% 245.19/51.63    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.63            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.63    (14)   ~ (all_52_13 = e0)
% 245.19/51.63  
% 245.19/51.63  Begin of proof
% 245.19/51.63  | 
% 245.19/51.63  | BETA: splitting (5) gives:
% 245.19/51.63  | 
% 245.19/51.63  | Case 1:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (15)  all_54_3 = e3
% 245.19/51.63  | | 
% 245.19/51.63  | | COMBINE_EQS: (12), (15) imply:
% 245.19/51.63  | |   (16)  all_52_12 = e3
% 245.19/51.63  | | 
% 245.19/51.63  | | REDUCE: (4), (16) imply:
% 245.19/51.63  | |   (17)   ~ (all_52_13 = e3)
% 245.19/51.63  | | 
% 245.19/51.63  | | SIMP: (17) implies:
% 245.19/51.63  | |   (18)   ~ (all_52_13 = e3)
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (2), (6), (7), (8), (10), (11), (13), (14), (18) are inconsistent
% 245.19/51.63  | |            by sub-proof #2291.
% 245.19/51.63  | | 
% 245.19/51.63  | Case 2:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (19)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (1), (3), (9), (12), (19) are inconsistent by sub-proof #2286.
% 245.19/51.63  | | 
% 245.19/51.63  | End of split
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2286 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)   ~ (all_52_12 = e0)
% 245.19/51.63    (2)   ~ (all_52_12 = e1)
% 245.19/51.63    (3)   ~ (all_52_12 = e2)
% 245.19/51.63    (4)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 245.19/51.63    (5)  all_54_3 = all_52_12
% 245.19/51.63  
% 245.19/51.63  Begin of proof
% 245.19/51.63  | 
% 245.19/51.63  | BETA: splitting (4) gives:
% 245.19/51.63  | 
% 245.19/51.63  | Case 1:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (6)  all_54_3 = e2
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #2290.
% 245.19/51.63  | | 
% 245.19/51.63  | Case 2:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (7)  all_54_3 = e1 | all_54_3 = e0
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #2287.
% 245.19/51.63  | | 
% 245.19/51.63  | End of split
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2287 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)  all_54_3 = e1 | all_54_3 = e0
% 245.19/51.63    (2)  all_54_3 = all_52_12
% 245.19/51.63    (3)   ~ (all_52_12 = e1)
% 245.19/51.63    (4)   ~ (all_52_12 = e0)
% 245.19/51.63  
% 245.19/51.63  Begin of proof
% 245.19/51.63  | 
% 245.19/51.63  | BETA: splitting (1) gives:
% 245.19/51.63  | 
% 245.19/51.63  | Case 1:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (5)  all_54_3 = e1
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2289.
% 245.19/51.63  | | 
% 245.19/51.63  | Case 2:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (6)  all_54_3 = e0
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2288.
% 245.19/51.63  | | 
% 245.19/51.63  | End of split
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2288 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)  all_54_3 = all_52_12
% 245.19/51.63    (2)  all_54_3 = e0
% 245.19/51.63    (3)   ~ (all_52_12 = e0)
% 245.19/51.63  
% 245.19/51.63  Begin of proof
% 245.19/51.63  | 
% 245.19/51.63  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.63  |   (4)  all_52_12 = e0
% 245.19/51.63  | 
% 245.19/51.63  | SIMP: (4) implies:
% 245.19/51.63  |   (5)  all_52_12 = e0
% 245.19/51.63  | 
% 245.19/51.63  | REDUCE: (3), (5) imply:
% 245.19/51.63  |   (6)  $false
% 245.19/51.63  | 
% 245.19/51.63  | CLOSE: (6) is inconsistent.
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2289 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)  all_54_3 = all_52_12
% 245.19/51.63    (2)  all_54_3 = e1
% 245.19/51.63    (3)   ~ (all_52_12 = e1)
% 245.19/51.63  
% 245.19/51.63  Begin of proof
% 245.19/51.63  | 
% 245.19/51.63  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.63  |   (4)  all_52_12 = e1
% 245.19/51.63  | 
% 245.19/51.63  | SIMP: (4) implies:
% 245.19/51.63  |   (5)  all_52_12 = e1
% 245.19/51.63  | 
% 245.19/51.63  | REDUCE: (3), (5) imply:
% 245.19/51.63  |   (6)  $false
% 245.19/51.63  | 
% 245.19/51.63  | CLOSE: (6) is inconsistent.
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2290 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)  all_54_3 = all_52_12
% 245.19/51.63    (2)  all_54_3 = e2
% 245.19/51.63    (3)   ~ (all_52_12 = e2)
% 245.19/51.63  
% 245.19/51.63  Begin of proof
% 245.19/51.63  | 
% 245.19/51.63  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.63  |   (4)  all_52_12 = e2
% 245.19/51.63  | 
% 245.19/51.63  | SIMP: (4) implies:
% 245.19/51.63  |   (5)  all_52_12 = e2
% 245.19/51.63  | 
% 245.19/51.63  | REDUCE: (3), (5) imply:
% 245.19/51.63  |   (6)  $false
% 245.19/51.63  | 
% 245.19/51.63  | CLOSE: (6) is inconsistent.
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2291 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)   ~ (all_52_13 = e1)
% 245.19/51.63    (2)  op(e2, e3) = e2
% 245.19/51.63    (3)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.19/51.63    (4)  op(e2, e3) = all_52_1
% 245.19/51.63    (5)   ~ (all_52_1 = all_52_13)
% 245.19/51.63    (6)  all_54_7 = all_52_13
% 245.19/51.63    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.63    (8)   ~ (all_52_13 = e3)
% 245.19/51.63    (9)   ~ (all_52_13 = e0)
% 245.19/51.63  
% 245.19/51.63  Begin of proof
% 245.19/51.63  | 
% 245.19/51.63  | BETA: splitting (3) gives:
% 245.19/51.63  | 
% 245.19/51.63  | Case 1:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (10)  all_54_7 = e3
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (6), (8), (10) are inconsistent by sub-proof #2296.
% 245.19/51.63  | | 
% 245.19/51.63  | Case 2:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (11)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11) are inconsistent by
% 245.19/51.63  | |            sub-proof #2292.
% 245.19/51.63  | | 
% 245.19/51.63  | End of split
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2292 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)   ~ (all_52_13 = e1)
% 245.19/51.63    (2)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 245.19/51.63    (3)  op(e2, e3) = e2
% 245.19/51.63    (4)  op(e2, e3) = all_52_1
% 245.19/51.63    (5)   ~ (all_52_1 = all_52_13)
% 245.19/51.63    (6)  all_54_7 = all_52_13
% 245.19/51.63    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.63    (8)   ~ (all_52_13 = e0)
% 245.19/51.63  
% 245.19/51.63  Begin of proof
% 245.19/51.63  | 
% 245.19/51.63  | BETA: splitting (2) gives:
% 245.19/51.63  | 
% 245.19/51.63  | Case 1:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (9)  all_54_7 = e2
% 245.19/51.63  | | 
% 245.19/51.63  | | COMBINE_EQS: (6), (9) imply:
% 245.19/51.63  | |   (10)  all_52_13 = e2
% 245.19/51.63  | | 
% 245.19/51.63  | | SIMP: (10) implies:
% 245.19/51.63  | |   (11)  all_52_13 = e2
% 245.19/51.63  | | 
% 245.19/51.63  | | REDUCE: (5), (11) imply:
% 245.19/51.63  | |   (12)   ~ (all_52_1 = e2)
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (3), (4), (7), (12) are inconsistent by sub-proof #2336.
% 245.19/51.63  | | 
% 245.19/51.63  | Case 2:
% 245.19/51.63  | | 
% 245.19/51.63  | |   (13)  all_54_7 = e1 | all_54_7 = e0
% 245.19/51.63  | | 
% 245.19/51.63  | | REF_CLOSE: (1), (6), (8), (13) are inconsistent by sub-proof #2293.
% 245.19/51.63  | | 
% 245.19/51.63  | End of split
% 245.19/51.63  | 
% 245.19/51.63  End of proof
% 245.19/51.63  
% 245.19/51.63  Sub-proof #2293 shows that the following formulas are inconsistent:
% 245.19/51.63  ----------------------------------------------------------------
% 245.19/51.63    (1)  all_54_7 = e1 | all_54_7 = e0
% 245.19/51.63    (2)  all_54_7 = all_52_13
% 245.19/51.63    (3)   ~ (all_52_13 = e1)
% 245.19/51.64    (4)   ~ (all_52_13 = e0)
% 245.19/51.64  
% 245.19/51.64  Begin of proof
% 245.19/51.64  | 
% 245.19/51.64  | BETA: splitting (1) gives:
% 245.19/51.64  | 
% 245.19/51.64  | Case 1:
% 245.19/51.64  | | 
% 245.19/51.64  | |   (5)  all_54_7 = e1
% 245.19/51.64  | | 
% 245.19/51.64  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2295.
% 245.19/51.64  | | 
% 245.19/51.64  | Case 2:
% 245.19/51.64  | | 
% 245.19/51.64  | |   (6)  all_54_7 = e0
% 245.19/51.64  | | 
% 245.19/51.64  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2294.
% 245.19/51.64  | | 
% 245.19/51.64  | End of split
% 245.19/51.64  | 
% 245.19/51.64  End of proof
% 245.19/51.64  
% 245.19/51.64  Sub-proof #2294 shows that the following formulas are inconsistent:
% 245.19/51.64  ----------------------------------------------------------------
% 245.19/51.64    (1)  all_54_7 = all_52_13
% 245.19/51.64    (2)  all_54_7 = e0
% 245.19/51.64    (3)   ~ (all_52_13 = e0)
% 245.19/51.64  
% 245.19/51.64  Begin of proof
% 245.19/51.64  | 
% 245.19/51.64  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.64  |   (4)  all_52_13 = e0
% 245.19/51.64  | 
% 245.19/51.64  | SIMP: (4) implies:
% 245.19/51.64  |   (5)  all_52_13 = e0
% 245.19/51.64  | 
% 245.19/51.64  | REDUCE: (3), (5) imply:
% 245.19/51.64  |   (6)  $false
% 245.19/51.64  | 
% 245.19/51.64  | CLOSE: (6) is inconsistent.
% 245.19/51.64  | 
% 245.19/51.64  End of proof
% 245.19/51.64  
% 245.19/51.64  Sub-proof #2295 shows that the following formulas are inconsistent:
% 245.19/51.64  ----------------------------------------------------------------
% 245.19/51.64    (1)  all_54_7 = all_52_13
% 245.19/51.64    (2)  all_54_7 = e1
% 245.19/51.64    (3)   ~ (all_52_13 = e1)
% 245.19/51.64  
% 245.19/51.64  Begin of proof
% 245.19/51.64  | 
% 245.19/51.64  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.64  |   (4)  all_52_13 = e1
% 245.19/51.64  | 
% 245.19/51.64  | SIMP: (4) implies:
% 245.19/51.64  |   (5)  all_52_13 = e1
% 245.19/51.64  | 
% 245.19/51.64  | REDUCE: (3), (5) imply:
% 245.19/51.64  |   (6)  $false
% 245.19/51.64  | 
% 245.19/51.64  | CLOSE: (6) is inconsistent.
% 245.19/51.64  | 
% 245.19/51.64  End of proof
% 245.19/51.64  
% 245.19/51.64  Sub-proof #2296 shows that the following formulas are inconsistent:
% 245.19/51.64  ----------------------------------------------------------------
% 245.19/51.64    (1)  all_54_7 = all_52_13
% 245.19/51.64    (2)  all_54_7 = e3
% 245.19/51.64    (3)   ~ (all_52_13 = e3)
% 245.19/51.64  
% 245.19/51.64  Begin of proof
% 245.19/51.64  | 
% 245.19/51.64  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.64  |   (4)  all_52_13 = e3
% 245.19/51.64  | 
% 245.19/51.64  | SIMP: (4) implies:
% 245.19/51.64  |   (5)  all_52_13 = e3
% 245.19/51.64  | 
% 245.19/51.64  | REDUCE: (3), (5) imply:
% 245.19/51.64  |   (6)  $false
% 245.19/51.64  | 
% 245.19/51.64  | CLOSE: (6) is inconsistent.
% 245.19/51.64  | 
% 245.19/51.64  End of proof
% 245.19/51.64  
% 245.19/51.64  Sub-proof #2297 shows that the following formulas are inconsistent:
% 245.19/51.64  ----------------------------------------------------------------
% 245.19/51.64    (1)  all_56_11 = e1
% 245.19/51.64    (2)  op(e2, e1) = all_52_9
% 245.19/51.64    (3)  all_56_31 = e0
% 245.19/51.64    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.64    (5)   ~ (all_52_9 = e1)
% 245.19/51.64    (6)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 245.19/51.64             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 245.19/51.64           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 245.19/51.64             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 245.19/51.64           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 245.19/51.64           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.19/51.64           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 245.19/51.64  
% 245.19/51.64  Begin of proof
% 245.19/51.64  | 
% 245.19/51.64  | BETA: splitting (6) gives:
% 245.19/51.64  | 
% 245.19/51.64  | Case 1:
% 245.19/51.64  | | 
% 245.19/51.64  | |   (7)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 245.19/51.64  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 245.19/51.64  | |        & op(e1, e2) = e2
% 245.19/51.64  | | 
% 245.19/51.64  | | ALPHA: (7) implies:
% 245.19/51.64  | |   (8)   ~ (all_56_11 = e1)
% 245.19/51.64  | | 
% 245.19/51.64  | | REDUCE: (1), (8) imply:
% 245.19/51.64  | |   (9)  $false
% 245.19/51.64  | | 
% 245.19/51.64  | | CLOSE: (9) is inconsistent.
% 245.19/51.64  | | 
% 245.19/51.64  | Case 2:
% 245.19/51.64  | | 
% 245.19/51.64  | |   (10)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 245.19/51.64  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 245.19/51.64  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 245.19/51.64  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 245.19/51.64  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 245.19/51.64  | | 
% 245.19/51.64  | | REF_CLOSE: (2), (3), (4), (5), (10) are inconsistent by sub-proof #2298.
% 245.19/51.64  | | 
% 245.19/51.64  | End of split
% 245.19/51.64  | 
% 245.19/51.64  End of proof
% 245.19/51.64  
% 245.19/51.64  Sub-proof #2298 shows that the following formulas are inconsistent:
% 245.19/51.64  ----------------------------------------------------------------
% 245.19/51.64    (1)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.19/51.64             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 245.19/51.64           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 245.19/51.64             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 245.19/51.64           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 245.19/51.64    (2)  op(e2, e1) = all_52_9
% 245.19/51.64    (3)  all_56_31 = e0
% 245.19/51.64    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.64    (5)   ~ (all_52_9 = e1)
% 245.19/51.64  
% 245.19/51.64  Begin of proof
% 245.19/51.64  | 
% 245.19/51.64  | BETA: splitting (1) gives:
% 245.19/51.64  | 
% 245.19/51.64  | Case 1:
% 245.19/51.64  | | 
% 245.19/51.64  | |   (6)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 245.19/51.64  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 245.19/51.64  | |        & op(e1, e2) = e1
% 245.19/51.64  | | 
% 245.19/51.64  | | ALPHA: (6) implies:
% 245.19/51.64  | |   (7)  op(e2, e1) = e1
% 245.19/51.64  | | 
% 245.19/51.64  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #2306.
% 245.19/51.64  | | 
% 245.19/51.64  | Case 2:
% 245.19/51.64  | | 
% 245.19/51.64  | |   (8)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 245.19/51.64  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 245.19/51.64  | |        & op(e0, e2) = e2
% 245.19/51.64  | | 
% 245.19/51.64  | | ALPHA: (8) implies:
% 245.19/51.64  | |   (9)   ~ (all_56_31 = e0)
% 245.19/51.64  | | 
% 245.19/51.64  | | REDUCE: (3), (9) imply:
% 245.19/51.64  | |   (10)  $false
% 245.19/51.64  | | 
% 245.19/51.64  | | CLOSE: (10) is inconsistent.
% 245.19/51.64  | | 
% 245.19/51.64  | End of split
% 245.19/51.64  | 
% 245.19/51.64  End of proof
% 245.19/51.64  
% 245.19/51.64  Sub-proof #2299 shows that the following formulas are inconsistent:
% 245.19/51.64  ----------------------------------------------------------------
% 245.19/51.64    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 245.19/51.64           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 245.19/51.64             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.19/51.64           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 245.19/51.64             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.19/51.64           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.19/51.64           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 245.19/51.64    (2)  all_56_1 = e3
% 245.19/51.64    (3)  op(e2, e3) = all_52_1
% 245.19/51.64    (4)   ~ (all_52_2 = e3)
% 245.19/51.64    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.64    (6)  op(e1, e3) = all_52_2
% 245.19/51.64    (7)   ~ (all_52_1 = e3)
% 245.19/51.64  
% 245.19/51.64  Begin of proof
% 245.19/51.64  | 
% 245.19/51.64  | BETA: splitting (1) gives:
% 245.19/51.64  | 
% 245.19/51.64  | Case 1:
% 245.19/51.64  | | 
% 245.19/51.64  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.19/51.64  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 245.19/51.64  | |        op(e2, e3) = e3
% 245.19/51.64  | | 
% 245.19/51.64  | | ALPHA: (8) implies:
% 245.19/51.64  | |   (9)  op(e2, e3) = e3
% 245.19/51.64  | | 
% 245.19/51.64  | | REF_CLOSE: (3), (5), (7), (9) are inconsistent by sub-proof #2337.
% 245.19/51.64  | | 
% 245.19/51.64  | Case 2:
% 245.19/51.64  | | 
% 245.19/51.64  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 245.19/51.64  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 245.19/51.64  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.19/51.64  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.19/51.64  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 245.19/51.64  | | 
% 245.19/51.64  | | BETA: splitting (10) gives:
% 245.19/51.64  | | 
% 245.19/51.64  | | Case 1:
% 245.19/51.64  | | | 
% 245.19/51.64  | | |   (11)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 245.19/51.64  | | |           = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 245.19/51.64  | | |         e2 & op(e2, e3) = e2
% 245.19/51.64  | | | 
% 245.19/51.64  | | | ALPHA: (11) implies:
% 245.19/51.64  | | |   (12)   ~ (all_56_1 = e3)
% 245.19/51.64  | | | 
% 245.19/51.64  | | | REDUCE: (2), (12) imply:
% 245.19/51.64  | | |   (13)  $false
% 245.19/51.64  | | | 
% 245.19/51.64  | | | CLOSE: (13) is inconsistent.
% 245.19/51.64  | | | 
% 245.19/51.64  | | Case 2:
% 245.19/51.64  | | | 
% 245.19/51.64  | | |   (14)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 245.19/51.64  | | |         (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) &
% 245.19/51.64  | | |         op(e3, e1) = e3 & op(e1, e3) = e3
% 245.19/51.64  | | | 
% 245.19/51.64  | | | ALPHA: (14) implies:
% 245.19/51.64  | | |   (15)  op(e1, e3) = e3
% 245.19/51.64  | | | 
% 245.19/51.64  | | | REF_CLOSE: (4), (5), (6), (15) are inconsistent by sub-proof #2335.
% 245.19/51.64  | | | 
% 245.19/51.64  | | End of split
% 245.19/51.64  | | 
% 245.19/51.64  | End of split
% 245.19/51.64  | 
% 245.19/51.64  End of proof
% 245.19/51.64  
% 245.19/51.64  Sub-proof #2300 shows that the following formulas are inconsistent:
% 245.19/51.64  ----------------------------------------------------------------
% 245.19/51.64    (1)  all_54_5 = e1 | all_54_5 = e0
% 245.19/51.64    (2)  all_54_5 = all_8_2
% 245.19/51.64    (3)   ~ (all_8_2 = e1)
% 245.19/51.64    (4)   ~ (all_8_2 = e0)
% 245.19/51.64  
% 245.19/51.64  Begin of proof
% 245.19/51.64  | 
% 245.19/51.64  | BETA: splitting (1) gives:
% 245.19/51.64  | 
% 245.19/51.64  | Case 1:
% 245.19/51.64  | | 
% 245.19/51.64  | |   (5)  all_54_5 = e1
% 245.19/51.64  | | 
% 245.19/51.64  | | COMBINE_EQS: (2), (5) imply:
% 245.19/51.64  | |   (6)  all_8_2 = e1
% 245.19/51.64  | | 
% 245.19/51.64  | | REDUCE: (3), (6) imply:
% 245.19/51.64  | |   (7)  $false
% 245.19/51.64  | | 
% 245.19/51.64  | | CLOSE: (7) is inconsistent.
% 245.19/51.64  | | 
% 245.19/51.64  | Case 2:
% 245.19/51.64  | | 
% 245.19/51.64  | |   (8)  all_54_5 = e0
% 245.19/51.64  | | 
% 245.19/51.64  | | COMBINE_EQS: (2), (8) imply:
% 245.19/51.64  | |   (9)  all_8_2 = e0
% 245.19/51.64  | | 
% 245.19/51.64  | | REDUCE: (4), (9) imply:
% 245.19/51.64  | |   (10)  $false
% 245.19/51.64  | | 
% 245.19/51.64  | | CLOSE: (10) is inconsistent.
% 245.19/51.64  | | 
% 245.19/51.64  | End of split
% 245.19/51.64  | 
% 245.19/51.64  End of proof
% 245.19/51.64  
% 245.19/51.64  Sub-proof #2301 shows that the following formulas are inconsistent:
% 245.19/51.64  ----------------------------------------------------------------
% 245.19/51.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.64    (2)  op(e0, e0) = e2
% 245.19/51.64    (3)  op(e0, e0) = e0
% 245.19/51.64    (4)   ~ (e2 = e0)
% 245.19/51.64  
% 245.19/51.64  Begin of proof
% 245.19/51.64  | 
% 245.19/51.64  | GROUND_INST: instantiating (1) with e0, e2, e0, e0, simplifying with (2), (3)
% 245.19/51.64  |              gives:
% 245.19/51.64  |   (5)  e2 = e0
% 245.19/51.64  | 
% 245.19/51.64  | REDUCE: (4), (5) imply:
% 245.19/51.64  |   (6)  $false
% 245.19/51.64  | 
% 245.19/51.64  | CLOSE: (6) is inconsistent.
% 245.19/51.64  | 
% 245.19/51.64  End of proof
% 245.19/51.64  
% 245.19/51.64  Sub-proof #2302 shows that the following formulas are inconsistent:
% 245.19/51.64  ----------------------------------------------------------------
% 245.19/51.64    (1)  all_54_10 = e1 | all_54_10 = e0
% 245.19/51.64    (2)  op(e1, e0) = all_52_14
% 245.19/51.65    (3)  op(e1, e0) = e1
% 245.19/51.65    (4)  all_54_10 = all_6_2
% 245.19/51.65    (5)   ~ (all_52_14 = all_6_2)
% 245.19/51.65    (6)   ~ (all_6_2 = e0)
% 245.19/51.65    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (1) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (8)  all_54_10 = e1
% 245.19/51.65  | | 
% 245.19/51.65  | | COMBINE_EQS: (4), (8) imply:
% 245.19/51.65  | |   (9)  all_6_2 = e1
% 245.19/51.65  | | 
% 245.19/51.65  | | SIMP: (9) implies:
% 245.19/51.65  | |   (10)  all_6_2 = e1
% 245.19/51.65  | | 
% 245.19/51.65  | | REDUCE: (5), (10) imply:
% 245.19/51.65  | |   (11)   ~ (all_52_14 = e1)
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (2), (3), (7), (11) are inconsistent by sub-proof #2304.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (12)  all_54_10 = e0
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (4), (6), (12) are inconsistent by sub-proof #2303.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2303 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)  all_54_10 = all_6_2
% 245.19/51.65    (2)  all_54_10 = e0
% 245.19/51.65    (3)   ~ (all_6_2 = e0)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.65  |   (4)  all_6_2 = e0
% 245.19/51.65  | 
% 245.19/51.65  | SIMP: (4) implies:
% 245.19/51.65  |   (5)  all_6_2 = e0
% 245.19/51.65  | 
% 245.19/51.65  | REDUCE: (3), (5) imply:
% 245.19/51.65  |   (6)  $false
% 245.19/51.65  | 
% 245.19/51.65  | CLOSE: (6) is inconsistent.
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2304 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (2)  op(e1, e0) = all_52_14
% 245.19/51.65    (3)  op(e1, e0) = e1
% 245.19/51.65    (4)   ~ (all_52_14 = e1)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | GROUND_INST: instantiating (1) with all_52_14, e1, e0, e1, simplifying with
% 245.19/51.65  |              (2), (3) gives:
% 245.19/51.65  |   (5)  all_52_14 = e1
% 245.19/51.65  | 
% 245.19/51.65  | REDUCE: (4), (5) imply:
% 245.19/51.65  |   (6)  $false
% 245.19/51.65  | 
% 245.19/51.65  | CLOSE: (6) is inconsistent.
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2305 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)   ~ (all_52_7 = e2)
% 245.19/51.65    (2)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.19/51.65             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 245.19/51.65           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 245.19/51.65             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 245.19/51.65           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 245.19/51.65    (3)  op(e2, e1) = all_52_9
% 245.19/51.65    (4)  op(e0, e2) = all_52_7
% 245.19/51.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (6)   ~ (all_52_9 = e1)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (2) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (7)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 245.19/51.65  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 245.19/51.65  | |        & op(e1, e2) = e1
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (7) implies:
% 245.19/51.65  | |   (8)  op(e2, e1) = e1
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #2306.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (9)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 245.19/51.65  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 245.19/51.65  | |        & op(e0, e2) = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (9) implies:
% 245.19/51.65  | |   (10)  op(e0, e2) = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2327.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2306 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (2)  op(e2, e1) = all_52_9
% 245.19/51.65    (3)  op(e2, e1) = e1
% 245.19/51.65    (4)   ~ (all_52_9 = e1)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | GROUND_INST: instantiating (1) with all_52_9, e1, e1, e2, simplifying with
% 245.19/51.65  |              (2), (3) gives:
% 245.19/51.65  |   (5)  all_52_9 = e1
% 245.19/51.65  | 
% 245.19/51.65  | REDUCE: (4), (5) imply:
% 245.19/51.65  |   (6)  $false
% 245.19/51.65  | 
% 245.19/51.65  | CLOSE: (6) is inconsistent.
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2307 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)   ~ (all_52_3 = e0)
% 245.19/51.65    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.19/51.65             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 245.19/51.65           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 245.19/51.65           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.19/51.65           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 245.19/51.65           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.19/51.65           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.19/51.65    (3)  op(e0, e3) = all_52_3
% 245.19/51.65    (4)   ~ (all_52_8 = e1)
% 245.19/51.65    (5)  op(e3, e1) = all_52_8
% 245.19/51.65    (6)  all_56_31 = e0
% 245.19/51.65    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (2) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (8)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.19/51.65  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 245.19/51.65  | |        op(e1, e3) = e1
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (8) implies:
% 245.19/51.65  | |   (9)  op(e3, e1) = e1
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (4), (5), (7), (9) are inconsistent by sub-proof #2309.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 245.19/51.65  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 245.19/51.65  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.19/51.65  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.19/51.65  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (1), (3), (6), (7), (10) are inconsistent by sub-proof #2308.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2308 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)   ~ (all_52_3 = e0)
% 245.19/51.65    (2)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.19/51.65             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 245.19/51.65           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 245.19/51.65           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.19/51.65           op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.19/51.65    (3)  op(e0, e3) = all_52_3
% 245.19/51.65    (4)  all_56_31 = e0
% 245.19/51.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (2) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (6)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.19/51.65  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 245.19/51.65  | |        op(e0, e3) = e3
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (6) implies:
% 245.19/51.65  | |   (7)   ~ (all_56_31 = e0)
% 245.19/51.65  | | 
% 245.19/51.65  | | REDUCE: (4), (7) imply:
% 245.19/51.65  | |   (8)  $false
% 245.19/51.65  | | 
% 245.19/51.65  | | CLOSE: (8) is inconsistent.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (9)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.19/51.65  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 245.19/51.65  | |        op(e0, e3) = e0
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (9) implies:
% 245.19/51.65  | |   (10)  op(e0, e3) = e0
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2331.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2309 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (2)  op(e3, e1) = all_52_8
% 245.19/51.65    (3)  op(e3, e1) = e1
% 245.19/51.65    (4)   ~ (all_52_8 = e1)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | GROUND_INST: instantiating (1) with all_52_8, e1, e1, e3, simplifying with
% 245.19/51.65  |              (2), (3) gives:
% 245.19/51.65  |   (5)  all_52_8 = e1
% 245.19/51.65  | 
% 245.19/51.65  | REDUCE: (4), (5) imply:
% 245.19/51.65  |   (6)  $false
% 245.19/51.65  | 
% 245.19/51.65  | CLOSE: (6) is inconsistent.
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2310 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)  all_56_11 = e2
% 245.19/51.65    (2)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 245.19/51.65           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 245.19/51.65             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.19/51.65           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 245.19/51.65             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.19/51.65           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.19/51.65           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 245.19/51.65    (3)  op(e2, e3) = all_52_1
% 245.19/51.65    (4)  all_56_21 = e1
% 245.19/51.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (6)   ~ (all_52_1 = e2)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (2) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (7)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.19/51.65  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 245.19/51.65  | |        op(e2, e3) = e3
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (7) implies:
% 245.19/51.65  | |   (8)   ~ (all_56_11 = e2)
% 245.19/51.65  | | 
% 245.19/51.65  | | REDUCE: (1), (8) imply:
% 245.19/51.65  | |   (9)  $false
% 245.19/51.65  | | 
% 245.19/51.65  | | CLOSE: (9) is inconsistent.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 245.19/51.65  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 245.19/51.65  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.19/51.65  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.19/51.65  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #2311.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2311 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 245.19/51.65           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 245.19/51.65             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 245.19/51.65           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 245.19/51.65             e1) = e3 & op(e1, e3) = e3)
% 245.19/51.65    (2)  op(e2, e3) = all_52_1
% 245.19/51.65    (3)  all_56_21 = e1
% 245.19/51.65    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (5)   ~ (all_52_1 = e2)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (1) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (6)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.19/51.65  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 245.19/51.65  | |        op(e2, e3) = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (6) implies:
% 245.19/51.65  | |   (7)  op(e2, e3) = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #2336.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (8)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 245.19/51.65  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 245.19/51.65  | |        op(e1, e3) = e3
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (8) implies:
% 245.19/51.65  | |   (9)   ~ (all_56_21 = e1)
% 245.19/51.65  | | 
% 245.19/51.65  | | REDUCE: (3), (9) imply:
% 245.19/51.65  | |   (10)  $false
% 245.19/51.65  | | 
% 245.19/51.65  | | CLOSE: (10) is inconsistent.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2312 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)  all_54_10 = all_6_2
% 245.19/51.65    (2)  all_54_10 = e2
% 245.19/51.65    (3)   ~ (all_6_2 = e2)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.65  |   (4)  all_6_2 = e2
% 245.19/51.65  | 
% 245.19/51.65  | SIMP: (4) implies:
% 245.19/51.65  |   (5)  all_6_2 = e2
% 245.19/51.65  | 
% 245.19/51.65  | REDUCE: (3), (5) imply:
% 245.19/51.65  |   (6)  $false
% 245.19/51.65  | 
% 245.19/51.65  | CLOSE: (6) is inconsistent.
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2313 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)  all_54_10 = all_6_2
% 245.19/51.65    (2)  all_54_10 = e3
% 245.19/51.65    (3)   ~ (all_6_2 = e3)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.65  |   (4)  all_6_2 = e3
% 245.19/51.65  | 
% 245.19/51.65  | SIMP: (4) implies:
% 245.19/51.65  |   (5)  all_6_2 = e3
% 245.19/51.65  | 
% 245.19/51.65  | REDUCE: (3), (5) imply:
% 245.19/51.65  |   (6)  $false
% 245.19/51.65  | 
% 245.19/51.65  | CLOSE: (6) is inconsistent.
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2314 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)   ~ (all_52_7 = e2)
% 245.19/51.65    (2)  (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 245.19/51.65    (3)  op(e0, e3) = all_52_3
% 245.19/51.65    (4)   ~ (all_52_3 = e2)
% 245.19/51.65    (5)  op(e0, e2) = all_52_7
% 245.19/51.65    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (2) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (7)  all_58_12 = e2 & op(e0, e3) = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (3), (4), (6), (7) are inconsistent by sub-proof #2315.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (8)  all_58_13 = e2 & op(e0, e2) = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (8) implies:
% 245.19/51.65  | |   (9)  op(e0, e2) = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #2327.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2315 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)  all_58_12 = e2 & op(e0, e3) = e2
% 245.19/51.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (3)  op(e0, e3) = all_52_3
% 245.19/51.65    (4)   ~ (all_52_3 = e2)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | ALPHA: (1) implies:
% 245.19/51.65  |   (5)  op(e0, e3) = e2
% 245.19/51.65  | 
% 245.19/51.65  | GROUND_INST: instantiating (2) with all_52_3, e2, e3, e0, simplifying with
% 245.19/51.65  |              (3), (5) gives:
% 245.19/51.65  |   (6)  all_52_3 = e2
% 245.19/51.65  | 
% 245.19/51.65  | REDUCE: (4), (6) imply:
% 245.19/51.65  |   (7)  $false
% 245.19/51.65  | 
% 245.19/51.65  | CLOSE: (7) is inconsistent.
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2316 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)  op(e3, e0) = all_52_12
% 245.19/51.65    (2)   ~ (all_52_12 = e2)
% 245.19/51.65    (3)   ~ (all_52_13 = e2)
% 245.19/51.65    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (5)  (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 245.19/51.65    (6)  op(e2, e0) = all_52_13
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (5) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (7)  all_58_9 = e2 & op(e3, e0) = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #2318.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (8)  all_58_10 = e2 & op(e2, e0) = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (8) implies:
% 245.19/51.65  | |   (9)  op(e2, e0) = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #2317.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2317 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (2)  op(e2, e0) = all_52_13
% 245.19/51.65    (3)  op(e2, e0) = e2
% 245.19/51.65    (4)   ~ (all_52_13 = e2)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | GROUND_INST: instantiating (1) with all_52_13, e2, e0, e2, simplifying with
% 245.19/51.65  |              (2), (3) gives:
% 245.19/51.65  |   (5)  all_52_13 = e2
% 245.19/51.65  | 
% 245.19/51.65  | REDUCE: (4), (5) imply:
% 245.19/51.65  |   (6)  $false
% 245.19/51.65  | 
% 245.19/51.65  | CLOSE: (6) is inconsistent.
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2318 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)  all_58_9 = e2 & op(e3, e0) = e2
% 245.19/51.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (3)  op(e3, e0) = all_52_12
% 245.19/51.65    (4)   ~ (all_52_12 = e2)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | ALPHA: (1) implies:
% 245.19/51.65  |   (5)  op(e3, e0) = e2
% 245.19/51.65  | 
% 245.19/51.65  | GROUND_INST: instantiating (2) with all_52_12, e2, e0, e3, simplifying with
% 245.19/51.65  |              (3), (5) gives:
% 245.19/51.65  |   (6)  all_52_12 = e2
% 245.19/51.65  | 
% 245.19/51.65  | REDUCE: (4), (6) imply:
% 245.19/51.65  |   (7)  $false
% 245.19/51.65  | 
% 245.19/51.65  | CLOSE: (7) is inconsistent.
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2319 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)   ~ (all_10_2 = e2)
% 245.19/51.65    (2)   ~ (all_10_2 = e0)
% 245.19/51.65    (3)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 245.19/51.65    (4)   ~ (all_10_2 = e1)
% 245.19/51.65    (5)  all_54_0 = all_10_2
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (3) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (6)  all_54_0 = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | COMBINE_EQS: (5), (6) imply:
% 245.19/51.65  | |   (7)  all_10_2 = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | SIMP: (7) implies:
% 245.19/51.65  | |   (8)  all_10_2 = e2
% 245.19/51.65  | | 
% 245.19/51.65  | | REDUCE: (1), (8) imply:
% 245.19/51.65  | |   (9)  $false
% 245.19/51.65  | | 
% 245.19/51.65  | | CLOSE: (9) is inconsistent.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (10)  all_54_0 = e1 | all_54_0 = e0
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #2320.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2320 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)  all_54_0 = e1 | all_54_0 = e0
% 245.19/51.65    (2)  all_54_0 = all_10_2
% 245.19/51.65    (3)   ~ (all_10_2 = e1)
% 245.19/51.65    (4)   ~ (all_10_2 = e0)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (1) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (5)  all_54_0 = e1
% 245.19/51.65  | | 
% 245.19/51.65  | | COMBINE_EQS: (2), (5) imply:
% 245.19/51.65  | |   (6)  all_10_2 = e1
% 245.19/51.65  | | 
% 245.19/51.65  | | REDUCE: (3), (6) imply:
% 245.19/51.65  | |   (7)  $false
% 245.19/51.65  | | 
% 245.19/51.65  | | CLOSE: (7) is inconsistent.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (8)  all_54_0 = e0
% 245.19/51.65  | | 
% 245.19/51.65  | | COMBINE_EQS: (2), (8) imply:
% 245.19/51.65  | |   (9)  all_10_2 = e0
% 245.19/51.65  | | 
% 245.19/51.65  | | REDUCE: (4), (9) imply:
% 245.19/51.65  | |   (10)  $false
% 245.19/51.65  | | 
% 245.19/51.65  | | CLOSE: (10) is inconsistent.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2321 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)  op(e1, e0) = all_52_14
% 245.19/51.65    (2)  (all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.19/51.65             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0 &
% 245.19/51.65           op(e0, e2) = e0) | (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 =
% 245.19/51.65             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 245.19/51.65           & op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0
% 245.19/51.65           &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.19/51.65           (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.19/51.65    (3)   ~ (all_52_14 = e0)
% 245.19/51.65    (4)  all_56_31 = e0
% 245.19/51.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (6)  op(e2, e0) = all_52_13
% 245.19/51.65    (7)   ~ (all_52_13 = e0)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (2) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (8)  all_56_15 = e0 & all_56_27 = e0 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 245.19/51.65  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e0) = e0
% 245.19/51.65  | |        & op(e0, e2) = e0
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (8) implies:
% 245.19/51.65  | |   (9)  op(e2, e0) = e0
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (5), (6), (7), (9) are inconsistent by sub-proof #2324.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (10)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~
% 245.19/51.65  | |           (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.19/51.65  | |           op(e1, e0) = e1 & op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 =
% 245.19/51.65  | |           e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 =
% 245.19/51.65  | |             e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #2322.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2322 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)  op(e1, e0) = all_52_14
% 245.19/51.65    (2)  (all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.19/51.65             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1 &
% 245.19/51.65           op(e0, e1) = e1) | (all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 =
% 245.19/51.65             e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1)
% 245.19/51.65           & op(e1, e0) = e0 & op(e0, e1) = e0)
% 245.19/51.65    (3)   ~ (all_52_14 = e0)
% 245.19/51.65    (4)  all_56_31 = e0
% 245.19/51.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | BETA: splitting (2) gives:
% 245.19/51.65  | 
% 245.19/51.65  | Case 1:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (6)  all_56_23 = e1 & all_56_29 = e1 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 245.19/51.65  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e1, e0) = e1
% 245.19/51.65  | |        & op(e0, e1) = e1
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (6) implies:
% 245.19/51.65  | |   (7)   ~ (all_56_31 = e0)
% 245.19/51.65  | | 
% 245.19/51.65  | | REDUCE: (4), (7) imply:
% 245.19/51.65  | |   (8)  $false
% 245.19/51.65  | | 
% 245.19/51.65  | | CLOSE: (8) is inconsistent.
% 245.19/51.65  | | 
% 245.19/51.65  | Case 2:
% 245.19/51.65  | | 
% 245.19/51.65  | |   (9)  all_56_23 = e0 & all_56_29 = e0 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 245.19/51.65  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e1, e0) = e0
% 245.19/51.65  | |        & op(e0, e1) = e0
% 245.19/51.65  | | 
% 245.19/51.65  | | ALPHA: (9) implies:
% 245.19/51.65  | |   (10)  op(e1, e0) = e0
% 245.19/51.65  | | 
% 245.19/51.65  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2323.
% 245.19/51.65  | | 
% 245.19/51.65  | End of split
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2323 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (2)  op(e1, e0) = all_52_14
% 245.19/51.65    (3)  op(e1, e0) = e0
% 245.19/51.65    (4)   ~ (all_52_14 = e0)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | GROUND_INST: instantiating (1) with all_52_14, e0, e0, e1, simplifying with
% 245.19/51.65  |              (2), (3) gives:
% 245.19/51.65  |   (5)  all_52_14 = e0
% 245.19/51.65  | 
% 245.19/51.65  | REDUCE: (4), (5) imply:
% 245.19/51.65  |   (6)  $false
% 245.19/51.65  | 
% 245.19/51.65  | CLOSE: (6) is inconsistent.
% 245.19/51.65  | 
% 245.19/51.65  End of proof
% 245.19/51.65  
% 245.19/51.65  Sub-proof #2324 shows that the following formulas are inconsistent:
% 245.19/51.65  ----------------------------------------------------------------
% 245.19/51.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.65    (2)  op(e2, e0) = all_52_13
% 245.19/51.65    (3)  op(e2, e0) = e0
% 245.19/51.65    (4)   ~ (all_52_13 = e0)
% 245.19/51.65  
% 245.19/51.65  Begin of proof
% 245.19/51.65  | 
% 245.19/51.65  | GROUND_INST: instantiating (1) with all_52_13, e0, e0, e2, simplifying with
% 245.19/51.65  |              (2), (3) gives:
% 245.19/51.65  |   (5)  all_52_13 = e0
% 245.19/51.65  | 
% 245.19/51.66  | REDUCE: (4), (5) imply:
% 245.19/51.66  |   (6)  $false
% 245.19/51.66  | 
% 245.19/51.66  | CLOSE: (6) is inconsistent.
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2325 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)  all_56_11 = e2
% 245.19/51.66    (2)   ~ (all_52_7 = e2)
% 245.19/51.66    (3)  op(e2, e1) = all_52_9
% 245.19/51.66    (4)  op(e0, e2) = all_52_7
% 245.19/51.66    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66    (6)  (all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 245.19/51.66             e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2 &
% 245.19/51.66           op(e1, e2) = e2) | (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 =
% 245.19/51.66             e2) &  ~ (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2)
% 245.19/51.66           & op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2
% 245.19/51.66           &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~
% 245.19/51.66           (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 245.19/51.66    (7)   ~ (all_52_9 = e2)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | BETA: splitting (6) gives:
% 245.19/51.66  | 
% 245.19/51.66  | Case 1:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (8)  all_56_13 = e2 & all_56_19 = e2 &  ~ (all_56_1 = e1) &  ~ (all_56_11
% 245.19/51.66  | |          = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e2, e1) = e2
% 245.19/51.66  | |        & op(e1, e2) = e2
% 245.19/51.66  | | 
% 245.19/51.66  | | ALPHA: (8) implies:
% 245.19/51.66  | |   (9)  op(e2, e1) = e2
% 245.19/51.66  | | 
% 245.19/51.66  | | REF_CLOSE: (3), (5), (7), (9) are inconsistent by sub-proof #2328.
% 245.19/51.66  | | 
% 245.19/51.66  | Case 2:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (10)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~
% 245.19/51.66  | |           (all_56_11 = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) &
% 245.19/51.66  | |           op(e2, e1) = e1 & op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 =
% 245.19/51.66  | |           e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 =
% 245.19/51.66  | |             e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2 & op(e0, e2) = e2)
% 245.19/51.66  | | 
% 245.19/51.66  | | REF_CLOSE: (1), (2), (4), (5), (10) are inconsistent by sub-proof #2326.
% 245.19/51.66  | | 
% 245.19/51.66  | End of split
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2326 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)  all_56_11 = e2
% 245.19/51.66    (2)   ~ (all_52_7 = e2)
% 245.19/51.66    (3)  (all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.19/51.66             e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1 &
% 245.19/51.66           op(e1, e2) = e1) | (all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 =
% 245.19/51.66             e0) &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0)
% 245.19/51.66           & op(e2, e0) = e2 & op(e0, e2) = e2)
% 245.19/51.66    (4)  op(e0, e2) = all_52_7
% 245.19/51.66    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | BETA: splitting (3) gives:
% 245.19/51.66  | 
% 245.19/51.66  | Case 1:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (6)  all_56_13 = e1 & all_56_19 = e1 &  ~ (all_56_1 = e2) &  ~ (all_56_11
% 245.19/51.66  | |          = e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e2, e1) = e1
% 245.19/51.66  | |        & op(e1, e2) = e1
% 245.19/51.66  | | 
% 245.19/51.66  | | ALPHA: (6) implies:
% 245.19/51.66  | |   (7)   ~ (all_56_11 = e2)
% 245.19/51.66  | | 
% 245.19/51.66  | | REDUCE: (1), (7) imply:
% 245.19/51.66  | |   (8)  $false
% 245.19/51.66  | | 
% 245.19/51.66  | | CLOSE: (8) is inconsistent.
% 245.19/51.66  | | 
% 245.19/51.66  | Case 2:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (9)  all_56_15 = e2 & all_56_27 = e2 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 245.19/51.66  | |          = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e2, e0) = e2
% 245.19/51.66  | |        & op(e0, e2) = e2
% 245.19/51.66  | | 
% 245.19/51.66  | | ALPHA: (9) implies:
% 245.19/51.66  | |   (10)  op(e0, e2) = e2
% 245.19/51.66  | | 
% 245.19/51.66  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #2327.
% 245.19/51.66  | | 
% 245.19/51.66  | End of split
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2327 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66    (2)  op(e0, e2) = all_52_7
% 245.19/51.66    (3)  op(e0, e2) = e2
% 245.19/51.66    (4)   ~ (all_52_7 = e2)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | GROUND_INST: instantiating (1) with all_52_7, e2, e2, e0, simplifying with
% 245.19/51.66  |              (2), (3) gives:
% 245.19/51.66  |   (5)  all_52_7 = e2
% 245.19/51.66  | 
% 245.19/51.66  | REDUCE: (4), (5) imply:
% 245.19/51.66  |   (6)  $false
% 245.19/51.66  | 
% 245.19/51.66  | CLOSE: (6) is inconsistent.
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2328 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66    (2)  op(e2, e1) = all_52_9
% 245.19/51.66    (3)  op(e2, e1) = e2
% 245.19/51.66    (4)   ~ (all_52_9 = e2)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | GROUND_INST: instantiating (1) with all_52_9, e2, e1, e2, simplifying with
% 245.19/51.66  |              (2), (3) gives:
% 245.19/51.66  |   (5)  all_52_9 = e2
% 245.19/51.66  | 
% 245.19/51.66  | REDUCE: (4), (5) imply:
% 245.19/51.66  |   (6)  $false
% 245.19/51.66  | 
% 245.19/51.66  | CLOSE: (6) is inconsistent.
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2329 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)   ~ (all_52_3 = e0)
% 245.19/51.66    (2)  (all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.19/51.66             e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 245.19/51.66           op(e1, e3) = e1) | (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0)
% 245.19/51.66           &  ~ (all_56_11 = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) &
% 245.19/51.66           op(e3, e0) = e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 & 
% 245.19/51.66           ~ (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.19/51.66           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.19/51.66    (3)  op(e0, e3) = all_52_3
% 245.19/51.66    (4)  all_56_1 = e3
% 245.19/51.66    (5)   ~ (all_52_3 = e3)
% 245.19/51.66    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | BETA: splitting (2) gives:
% 245.19/51.66  | 
% 245.19/51.66  | Case 1:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (7)  all_56_5 = e1 & all_56_17 = e1 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.19/51.66  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e1) = e1 &
% 245.19/51.66  | |        op(e1, e3) = e1
% 245.19/51.66  | | 
% 245.19/51.66  | | ALPHA: (7) implies:
% 245.19/51.66  | |   (8)   ~ (all_56_1 = e3)
% 245.19/51.66  | | 
% 245.19/51.66  | | REDUCE: (4), (8) imply:
% 245.19/51.66  | |   (9)  $false
% 245.19/51.66  | | 
% 245.19/51.66  | | CLOSE: (9) is inconsistent.
% 245.19/51.66  | | 
% 245.19/51.66  | Case 2:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (10)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11
% 245.19/51.66  | |             = e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) =
% 245.19/51.66  | |           e3 & op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~
% 245.19/51.66  | |           (all_56_1 = e3) &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~
% 245.19/51.66  | |           (all_56_31 = e3) & op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.19/51.66  | | 
% 245.19/51.66  | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #2330.
% 245.19/51.66  | | 
% 245.19/51.66  | End of split
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2330 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)   ~ (all_52_3 = e0)
% 245.19/51.66    (2)  (all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.19/51.66             e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 245.19/51.66           op(e0, e3) = e3) | (all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3)
% 245.19/51.66           &  ~ (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) &
% 245.19/51.66           op(e3, e0) = e0 & op(e0, e3) = e0)
% 245.19/51.66    (3)  op(e0, e3) = all_52_3
% 245.19/51.66    (4)   ~ (all_52_3 = e3)
% 245.19/51.66    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | BETA: splitting (2) gives:
% 245.19/51.66  | 
% 245.19/51.66  | Case 1:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (6)  all_56_7 = e3 & all_56_25 = e3 &  ~ (all_56_1 = e0) &  ~ (all_56_11 =
% 245.19/51.66  | |          e0) &  ~ (all_56_21 = e0) &  ~ (all_56_31 = e0) & op(e3, e0) = e3 &
% 245.19/51.66  | |        op(e0, e3) = e3
% 245.19/51.66  | | 
% 245.19/51.66  | | ALPHA: (6) implies:
% 245.19/51.66  | |   (7)  op(e0, e3) = e3
% 245.19/51.66  | | 
% 245.19/51.66  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #2332.
% 245.19/51.66  | | 
% 245.19/51.66  | Case 2:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (8)  all_56_7 = e0 & all_56_25 = e0 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.19/51.66  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e0) = e0 &
% 245.19/51.66  | |        op(e0, e3) = e0
% 245.19/51.66  | | 
% 245.19/51.66  | | ALPHA: (8) implies:
% 245.19/51.66  | |   (9)  op(e0, e3) = e0
% 245.19/51.66  | | 
% 245.19/51.66  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #2331.
% 245.19/51.66  | | 
% 245.19/51.66  | End of split
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2331 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66    (2)  op(e0, e3) = all_52_3
% 245.19/51.66    (3)  op(e0, e3) = e0
% 245.19/51.66    (4)   ~ (all_52_3 = e0)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | GROUND_INST: instantiating (1) with all_52_3, e0, e3, e0, simplifying with
% 245.19/51.66  |              (2), (3) gives:
% 245.19/51.66  |   (5)  all_52_3 = e0
% 245.19/51.66  | 
% 245.19/51.66  | REDUCE: (4), (5) imply:
% 245.19/51.66  |   (6)  $false
% 245.19/51.66  | 
% 245.19/51.66  | CLOSE: (6) is inconsistent.
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2332 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66    (2)  op(e0, e3) = all_52_3
% 245.19/51.66    (3)  op(e0, e3) = e3
% 245.19/51.66    (4)   ~ (all_52_3 = e3)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | GROUND_INST: instantiating (1) with all_52_3, e3, e3, e0, simplifying with
% 245.19/51.66  |              (2), (3) gives:
% 245.19/51.66  |   (5)  all_52_3 = e3
% 245.19/51.66  | 
% 245.19/51.66  | REDUCE: (4), (5) imply:
% 245.19/51.66  |   (6)  $false
% 245.19/51.66  | 
% 245.19/51.66  | CLOSE: (6) is inconsistent.
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2333 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)  (all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 = e2)
% 245.19/51.66           &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 & op(e2,
% 245.19/51.66             e3) = e3) | (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~
% 245.19/51.66           (all_56_11 = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3,
% 245.19/51.66             e2) = e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.19/51.66           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.19/51.66           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 245.19/51.66    (2)  op(e2, e3) = all_52_1
% 245.19/51.66    (3)   ~ (all_52_2 = e3)
% 245.19/51.66    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66    (5)  op(e1, e3) = all_52_2
% 245.19/51.66    (6)   ~ (all_52_1 = e3)
% 245.19/51.66    (7)   ~ (all_52_1 = e2)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | BETA: splitting (1) gives:
% 245.19/51.66  | 
% 245.19/51.66  | Case 1:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (8)  all_56_3 = e3 & all_56_9 = e3 &  ~ (all_56_1 = e2) &  ~ (all_56_11 =
% 245.19/51.66  | |          e2) &  ~ (all_56_21 = e2) &  ~ (all_56_31 = e2) & op(e3, e2) = e3 &
% 245.19/51.66  | |        op(e2, e3) = e3
% 245.19/51.66  | | 
% 245.19/51.66  | | ALPHA: (8) implies:
% 245.19/51.66  | |   (9)  op(e2, e3) = e3
% 245.19/51.66  | | 
% 245.19/51.66  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #2337.
% 245.19/51.66  | | 
% 245.19/51.66  | Case 2:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (10)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11
% 245.19/51.66  | |             = e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) =
% 245.19/51.66  | |           e2 & op(e2, e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~
% 245.19/51.66  | |           (all_56_1 = e1) &  ~ (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~
% 245.19/51.66  | |           (all_56_31 = e1) & op(e3, e1) = e3 & op(e1, e3) = e3)
% 245.19/51.66  | | 
% 245.19/51.66  | | REF_CLOSE: (2), (3), (4), (5), (7), (10) are inconsistent by sub-proof
% 245.19/51.66  | |            #2334.
% 245.19/51.66  | | 
% 245.19/51.66  | End of split
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2334 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)  (all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 = e3)
% 245.19/51.66           &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 & op(e2,
% 245.19/51.66             e3) = e2) | (all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~
% 245.19/51.66           (all_56_11 = e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3,
% 245.19/51.66             e1) = e3 & op(e1, e3) = e3)
% 245.19/51.66    (2)  op(e2, e3) = all_52_1
% 245.19/51.66    (3)   ~ (all_52_2 = e3)
% 245.19/51.66    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66    (5)  op(e1, e3) = all_52_2
% 245.19/51.66    (6)   ~ (all_52_1 = e2)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | BETA: splitting (1) gives:
% 245.19/51.66  | 
% 245.19/51.66  | Case 1:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (7)  all_56_3 = e2 & all_56_9 = e2 &  ~ (all_56_1 = e3) &  ~ (all_56_11 =
% 245.19/51.66  | |          e3) &  ~ (all_56_21 = e3) &  ~ (all_56_31 = e3) & op(e3, e2) = e2 &
% 245.19/51.66  | |        op(e2, e3) = e2
% 245.19/51.66  | | 
% 245.19/51.66  | | ALPHA: (7) implies:
% 245.19/51.66  | |   (8)  op(e2, e3) = e2
% 245.19/51.66  | | 
% 245.19/51.66  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2336.
% 245.19/51.66  | | 
% 245.19/51.66  | Case 2:
% 245.19/51.66  | | 
% 245.19/51.66  | |   (9)  all_56_5 = e3 & all_56_17 = e3 &  ~ (all_56_1 = e1) &  ~ (all_56_11 =
% 245.19/51.66  | |          e1) &  ~ (all_56_21 = e1) &  ~ (all_56_31 = e1) & op(e3, e1) = e3 &
% 245.19/51.66  | |        op(e1, e3) = e3
% 245.19/51.66  | | 
% 245.19/51.66  | | ALPHA: (9) implies:
% 245.19/51.66  | |   (10)  op(e1, e3) = e3
% 245.19/51.66  | | 
% 245.19/51.66  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #2335.
% 245.19/51.66  | | 
% 245.19/51.66  | End of split
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2335 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66    (2)  op(e1, e3) = all_52_2
% 245.19/51.66    (3)  op(e1, e3) = e3
% 245.19/51.66    (4)   ~ (all_52_2 = e3)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | GROUND_INST: instantiating (1) with all_52_2, e3, e3, e1, simplifying with
% 245.19/51.66  |              (2), (3) gives:
% 245.19/51.66  |   (5)  all_52_2 = e3
% 245.19/51.66  | 
% 245.19/51.66  | REDUCE: (4), (5) imply:
% 245.19/51.66  |   (6)  $false
% 245.19/51.66  | 
% 245.19/51.66  | CLOSE: (6) is inconsistent.
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2336 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66    (2)  op(e2, e3) = all_52_1
% 245.19/51.66    (3)  op(e2, e3) = e2
% 245.19/51.66    (4)   ~ (all_52_1 = e2)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | GROUND_INST: instantiating (1) with all_52_1, e2, e3, e2, simplifying with
% 245.19/51.66  |              (2), (3) gives:
% 245.19/51.66  |   (5)  all_52_1 = e2
% 245.19/51.66  | 
% 245.19/51.66  | REDUCE: (4), (5) imply:
% 245.19/51.66  |   (6)  $false
% 245.19/51.66  | 
% 245.19/51.66  | CLOSE: (6) is inconsistent.
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2337 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 245.19/51.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 245.19/51.66    (2)  op(e2, e3) = all_52_1
% 245.19/51.66    (3)  op(e2, e3) = e3
% 245.19/51.66    (4)   ~ (all_52_1 = e3)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | GROUND_INST: instantiating (1) with all_52_1, e3, e3, e2, simplifying with
% 245.19/51.66  |              (2), (3) gives:
% 245.19/51.66  |   (5)  all_52_1 = e3
% 245.19/51.66  | 
% 245.19/51.66  | REDUCE: (4), (5) imply:
% 245.19/51.66  |   (6)  $false
% 245.19/51.66  | 
% 245.19/51.66  | CLOSE: (6) is inconsistent.
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2338 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)  all_54_15 = all_4_2
% 245.19/51.66    (2)  all_54_15 = e1
% 245.19/51.66    (3)   ~ (all_4_2 = e1)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.66  |   (4)  all_4_2 = e1
% 245.19/51.66  | 
% 245.19/51.66  | SIMP: (4) implies:
% 245.19/51.66  |   (5)  all_4_2 = e1
% 245.19/51.66  | 
% 245.19/51.66  | REDUCE: (3), (5) imply:
% 245.19/51.66  |   (6)  $false
% 245.19/51.66  | 
% 245.19/51.66  | CLOSE: (6) is inconsistent.
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2339 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)  all_54_15 = all_4_2
% 245.19/51.66    (2)  all_54_15 = e2
% 245.19/51.66    (3)   ~ (all_4_2 = e2)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.66  |   (4)  all_4_2 = e2
% 245.19/51.66  | 
% 245.19/51.66  | SIMP: (4) implies:
% 245.19/51.66  |   (5)  all_4_2 = e2
% 245.19/51.66  | 
% 245.19/51.66  | REDUCE: (3), (5) imply:
% 245.19/51.66  |   (6)  $false
% 245.19/51.66  | 
% 245.19/51.66  | CLOSE: (6) is inconsistent.
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  
% 245.19/51.66  Sub-proof #2340 shows that the following formulas are inconsistent:
% 245.19/51.66  ----------------------------------------------------------------
% 245.19/51.66    (1)  all_54_15 = all_4_2
% 245.19/51.66    (2)  all_54_15 = e3
% 245.19/51.66    (3)   ~ (all_4_2 = e3)
% 245.19/51.66  
% 245.19/51.66  Begin of proof
% 245.19/51.66  | 
% 245.19/51.66  | COMBINE_EQS: (1), (2) imply:
% 245.19/51.66  |   (4)  all_4_2 = e3
% 245.19/51.66  | 
% 245.19/51.66  | SIMP: (4) implies:
% 245.19/51.66  |   (5)  all_4_2 = e3
% 245.19/51.66  | 
% 245.19/51.66  | REDUCE: (3), (5) imply:
% 245.19/51.66  |   (6)  $false
% 245.19/51.66  | 
% 245.19/51.66  | CLOSE: (6) is inconsistent.
% 245.19/51.66  | 
% 245.19/51.66  End of proof
% 245.19/51.66  % SZS output end Proof for theBenchmark
% 245.19/51.66  
% 245.19/51.66  51140ms
%------------------------------------------------------------------------------